diff options
Diffstat (limited to 'REORG.TODO/sysdeps/ieee754/dbl-64')
163 files changed, 54591 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/Makefile b/REORG.TODO/sysdeps/ieee754/dbl-64/Makefile new file mode 100644 index 0000000000..5557c75b45 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/Makefile @@ -0,0 +1,6 @@ +ifeq ($(subdir),math) +# branred depends on precise IEEE double rounding +CFLAGS-branred.c = $(config-cflags-nofma) +CFLAGS-e_sqrt.c = $(config-cflags-nofma) +CFLAGS-e_pow.c = $(config-cflags-nofma) +endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/MathLib.h b/REORG.TODO/sysdeps/ieee754/dbl-64/MathLib.h new file mode 100644 index 0000000000..ffda70a413 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/MathLib.h @@ -0,0 +1,100 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/********************************************************************/ +/* Ultimate math functions. Each function computes the exact */ +/* theoretical value of its argument rounded to nearest or even. */ +/* */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round nearest mode of IEEE 754 standard. */ +/********************************************************************/ + +#ifndef UMATH_LIB +#define UMATH_LIB +/********************************************************************/ +/* Function changes the precision mode to IEEE 754 double precision */ +/* and the rounding mode to nearest or even. */ +/* It returns the original status of these modes. */ +/* See further explanations of usage in DPChange.h */ +/********************************************************************/ +unsigned short Init_Lib (void); + +/********************************************************************/ +/* Function that changes the precision and rounding modes to the */ +/* specified by the argument received. See further explanations in */ +/* DPChange.h */ +/********************************************************************/ +void Exit_Lib (unsigned short); + + +/* The asin() function calculates the arc sine of its argument. */ +/* The function returns the arc sine in radians */ +/* (between -PI/2 and PI/2). */ +/* If the argument is greater than 1 or less than -1 it returns */ +/* a NaN. */ +double uasin (double); + + +/* The acos() function calculates the arc cosine of its argument. */ +/* The function returns the arc cosine in radians */ +/* (between -PI/2 and PI/2). */ +/* If the argument is greater than 1 or less than -1 it returns */ +/* a NaN. */ +double uacos (double); + +/* The atan() function calculates the arctanget of its argument. */ +/* The function returns the arc tangent in radians */ +/* (between -PI/2 and PI/2). */ +double uatan (double); + + +/* The uatan2() function calculates the arc tangent of the two arguments x */ +/* and y (x is the right argument and y is the left one).The signs of both */ +/* arguments are used to determine the quadrant of the result. */ +/* The function returns the result in radians, which is between -PI and PI */ +double uatan2 (double, double); + +/* Compute log(x). The base of log is e (natural logarithm) */ +double ulog (double); + +/* Compute e raised to the power of argument x. */ +double uexp (double); + +/* Compute sin(x). The argument x is assumed to be given in radians.*/ +double usin (double); + +/* Compute cos(x). The argument x is assumed to be given in radians.*/ +double ucos (double); + +/* Compute tan(x). The argument x is assumed to be given in radians.*/ +double utan (double); + +/* Compute the square root of non-negative argument x. */ +/* If x is negative the returned value is NaN. */ +double usqrt (double); + +/* Compute x raised to the power of y, where x is the left argument */ +/* and y is the right argument. The function returns a NaN if x<0. */ +/* If x equals zero it returns -inf */ +double upow (double, double); + +/* Computing x mod y, where x is the left argument and y is the */ +/* right one. */ +double uremainder (double, double); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/asincos.tbl b/REORG.TODO/sysdeps/ieee754/dbl-64/asincos.tbl new file mode 100644 index 0000000000..5e7670c3b1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/asincos.tbl @@ -0,0 +1,5168 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/***************************************************************************/ +/* Table for arcsin() and arccos() FUNCTIONS */ +/***************************************************************************/ + +#ifdef BIG_ENDI +static const union {int4 i[5136];double x[2568];} asncs = { .i = { +/**/ 0x3FC04000, 0x00000000, +/**/ 0x3FF02169, 0x88994424, +/**/ 0x3FB0A6A2, 0xB799B115, +/**/ 0x3FC6EF15, 0xD57409A0, +/**/ 0x3FAA141E, 0xAF52EAA0, +/**/ 0x3FB75591, 0xABBBE261, +/**/ 0x3FA72B51, 0xD206D88F, +/**/ 0x3C96B595, 0x5BB33E7D, +/**/ 0x3FC04B41, 0xA03E2700, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF7E9677, 0x66BBDC7C, +/**/ 0x3FC0C000, 0x00000000, +/**/ 0x3FF02386, 0xF9E23A56, +/**/ 0x3FB1308C, 0x60FD0235, +/**/ 0x3FC7099F, 0x14D16B02, +/**/ 0x3FAAFED6, 0x27C01EE1, +/**/ 0x3FB79C6F, 0xDBCD5F98, +/**/ 0x3FA8144A, 0x4084DAAC, +/**/ 0xBC87C092, 0x38D8505E, +/**/ 0x3FC0CC55, 0x56C9F380, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF7C7906, 0x1DC5AA24, +/**/ 0x3FC14000, 0x00000000, +/**/ 0x3FF025B5, 0xB27141F6, +/**/ 0x3FB1BB18, 0x04CE7400, +/**/ 0x3FC72514, 0x72907342, +/**/ 0x3FABEC60, 0x0BF4222C, +/**/ 0x3FB7E610, 0x75B3736C, +/**/ 0x3FA9024C, 0x5199C343, +/**/ 0xBC8AE84C, 0x06B56F60, +/**/ 0x3FC14D7A, 0x3DEFA070, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF7A4A4D, 0x8EBE0A5C, +/**/ 0x3FC1C000, 0x00000000, +/**/ 0x3FF027F5, 0xC6DE8F57, +/**/ 0x3FB2464B, 0x345751E1, +/**/ 0x3FC74178, 0xCF026805, +/**/ 0x3FACDCD8, 0x40A9E0D6, +/**/ 0x3FB83282, 0xEB1D9C38, +/**/ 0x3FA9F590, 0xD7BE707B, +/**/ 0xBCAB9768, 0x03A2A6D6, +/**/ 0x3FC1CEB0, 0xE03B4870, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF780A39, 0x2170A943, +/**/ 0x3FC24000, 0x00000000, +/**/ 0x3FF02A47, 0x4C759796, +/**/ 0x3FB2D22B, 0x92771935, +/**/ 0x3FC75ECF, 0x26ABA06D, +/**/ 0x3FADD05B, 0x486A1932, +/**/ 0x3FB881D7, 0x5AF971D5, +/**/ 0x3FAAEE52, 0x831AEE0C, +/**/ 0x3CA13F57, 0xAD1B1BEF, +/**/ 0x3FC24FF9, 0xC8E09330, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF75B8B3, 0x8A68699B, +/**/ 0x3FC2C000, 0x00000000, +/**/ 0x3FF02CAA, 0x59374E09, +/**/ 0x3FB35EBE, 0xD44E8BEA, +/**/ 0x3FC77D1A, 0x92E4BE8A, +/**/ 0x3FAEC706, 0x4A6C34FD, +/**/ 0x3FB8D41E, 0x972F6E07, +/**/ 0x3FABECCD, 0xF9845F69, +/**/ 0x3C8BA1FA, 0x945C4185, +/**/ 0x3FC2D155, 0x83C058B0, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF7355A6, 0xC8B1F774, +/**/ 0x3FC34000, 0x00000000, +/**/ 0x3FF02F1F, 0x03DC7745, +/**/ 0x3FB3EC0A, 0xC1EE9F61, +/**/ 0x3FC79C5E, 0x4A82E6D2, +/**/ 0x3FAFC0F7, 0x19B1EF72, +/**/ 0x3FB9296A, 0x2AA943E5, +/**/ 0x3FACF141, 0xEF8B9DE7, +/**/ 0xBC834081, 0x083C8716, +/**/ 0x3FC352C4, 0x9D6E5610, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF70E0FC, 0x2388BB30, +/**/ 0x3FC3C000, 0x00000000, +/**/ 0x3FF031A5, 0x63D81251, +/**/ 0x3FB47A15, 0x370B721F, +/**/ 0x3FC7BC9D, 0xA28731E5, +/**/ 0x3FB05F26, 0x1E305BE9, +/**/ 0x3FB981CC, 0x5FA50FBD, +/**/ 0x3FADFBEF, 0x42AC4083, +/**/ 0x3CA20ACB, 0xA8E107C7, +/**/ 0x3FC3D447, 0xA336F5E0, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF6CB538, 0x4FDB5D5C, +/**/ 0x3FC44000, 0x00000000, +/**/ 0x3FF0343D, 0x9159D86F, +/**/ 0x3FB508E4, 0x23B3747C, +/**/ 0x3FC7DDDC, 0x0ED597CB, +/**/ 0x3FB0DF92, 0x79ADF104, +/**/ 0x3FB9DD58, 0x4658D945, +/**/ 0x3FAF0D19, 0x14ACA06B, +/**/ 0xBCA4E10D, 0xDF636EFE, +/**/ 0x3FC455DF, 0x23252C00, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF6784DD, 0x4C4F221A, +/**/ 0x3FC4C000, 0x00000000, +/**/ 0x3FF036E7, 0xA550D410, +/**/ 0x3FB5987D, 0x8D0AF1E7, +/**/ 0x3FC8001D, 0x22F39726, +/**/ 0x3FB161D0, 0xA1116D73, +/**/ 0x3FBA3C21, 0xBBEA1528, +/**/ 0x3FB01282, 0x74202FF6, +/**/ 0x3CAA0611, 0xD10866E2, +/**/ 0x3FC4D78B, 0xAC086560, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF6230B5, 0x5E57DF8A, +/**/ 0x3FC54000, 0x00000000, +/**/ 0x3FF039A3, 0xB96E0F8A, +/**/ 0x3FB628E7, 0x8E0C29F6, +/**/ 0x3FC82364, 0x92CEDE01, +/**/ 0x3FB1E5F0, 0xFB7B5D84, +/**/ 0x3FBA9E3D, 0x71BD08EE, +/**/ 0x3FB0A1FD, 0x5F7FFAB4, +/**/ 0xBC90F980, 0xEF04F6E7, +/**/ 0x3FC5594D, 0xCD7A8DC0, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF59711A, 0x47C1D879, +/**/ 0x3FC5C000, 0x00000000, +/**/ 0x3FF03C71, 0xE8275C12, +/**/ 0x3FB6BA28, 0x584C2A23, +/**/ 0x3FC847B6, 0x338C3D4B, +/**/ 0x3FB26C04, 0x59A55DD8, +/**/ 0x3FBB03C0, 0xF5202D6A, +/**/ 0x3FB13522, 0x9C6466A4, +/**/ 0x3C983C9A, 0x2A268973, +/**/ 0x3FC5DB26, 0x17E62A20, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF4C70BE, 0xC51F7008, +/**/ 0x3FC64000, 0x00000000, +/**/ 0x3FF03F52, 0x4CBA31A9, +/**/ 0x3FB74C46, 0x34C49ADE, +/**/ 0x3FC86D15, 0xFC5F33CC, +/**/ 0x3FB2F41B, 0xFA419D7C, +/**/ 0x3FBB6CC2, 0xB757E82A, +/**/ 0x3FB1CC18, 0xDA4D5C39, +/**/ 0xBCA862D4, 0x2DFB224D, +/**/ 0x3FC65D15, 0x1C8C8AF0, +/**/ 0x3FF04000, 0x00000000, +/**/ 0xBF25B668, 0xB9CADBBF, +/**/ 0x3FC6C000, 0x00000000, +/**/ 0x3FF04245, 0x032EA88F, +/**/ 0x3FB7DF47, 0x84A2B473, +/**/ 0x3FC89388, 0x076A60F5, +/**/ 0x3FB37E49, 0x8E8394C1, +/**/ 0x3FBBD95A, 0x160F3472, +/**/ 0x3FB26708, 0x39844810, +/**/ 0x3C994228, 0x698BC8EA, +/**/ 0x3FC6DF1B, 0x6D8C14A0, +/**/ 0x3FF04000, 0x00000000, +/**/ 0x3F422819, 0x754477AC, +/**/ 0x3FC74000, 0x00000000, +/**/ 0x3FF0454A, 0x285A8CEB, +/**/ 0x3FB87332, 0xC21B9224, +/**/ 0x3FC8BB10, 0x92A93402, +/**/ 0x3FB40A9F, 0x3ED3F586, +/**/ 0x3FBC499F, 0x643217C8, +/**/ 0x3FB3061A, 0x5D29A16B, +/**/ 0xBCA3B2DF, 0x3DF9F2D7, +/**/ 0x3FC76139, 0x9DE6A160, +/**/ 0x3FF04000, 0x00000000, +/**/ 0x3F5528A1, 0x6A33AB4B, +/**/ 0x3FC7C000, 0x00000000, +/**/ 0x3FF04861, 0xD9E48D58, +/**/ 0x3FB9080E, 0x81461BF6, +/**/ 0x3FC8E3B4, 0x00E32FFA, +/**/ 0x3FB4992F, 0xAFB1F2A5, +/**/ 0x3FBCBDAB, 0xF33705D5, +/**/ 0x3FB3A97A, 0x7E23EE89, +/**/ 0x3C7AAD12, 0xCCE44C41, +/**/ 0x3FC7E370, 0x4187FAE0, +/**/ 0x3FF04000, 0x00000000, +/**/ 0x3F60C3B3, 0xC91AAF11, +/**/ 0x3FC84000, 0x00000000, +/**/ 0x3FF04B8C, 0x36478509, +/**/ 0x3FB99DE1, 0x70FAC1B4, +/**/ 0x3FC90D76, 0xDAA92166, +/**/ 0x3FB52A0E, 0x06C416A6, +/**/ 0x3FBD359A, 0x1CDCA344, +/**/ 0x3FB45155, 0x7EFD4CA0, +/**/ 0x3C396CA5, 0x35A8895D, +/**/ 0x3FC865BF, 0xED4C6EF0, +/**/ 0x3FF04000, 0x00000000, +/**/ 0x3F67186C, 0x8F0A11A4, +/**/ 0x3FC8C000, 0x00000000, +/**/ 0x3FF04EC9, 0x5CD5E248, +/**/ 0x3FBA34B2, 0x5BB94403, +/**/ 0x3FC9385D, 0xCF5CA73A, +/**/ 0x3FB5BD4D, 0xF01AFDBE, +/**/ 0x3FBDB185, 0x4D61A7A9, +/**/ 0x3FB4FDDA, 0x00BD47CF, +/**/ 0xBC9D1119, 0x727E8B64, +/**/ 0x3FC8E829, 0x37077E20, +/**/ 0x3FF04000, 0x00000000, +/**/ 0x3F6D92B9, 0xABC490CB, +/**/ 0x3FC94000, 0x00000000, +/**/ 0x3FF05219, 0x6DBD2A10, +/**/ 0x3FBACC88, 0x2894CAA1, +/**/ 0x3FC9646D, 0xB6427516, +/**/ 0x3FB65303, 0xA3A864D7, +/**/ 0x3FBE318A, 0x0E3CF3D4, +/**/ 0x3FB5AF38, 0x78CDA678, +/**/ 0x3CA3841D, 0xDA9D51DF, +/**/ 0x3FC96AAC, 0xB58AA660, +/**/ 0x3FF04000, 0x00000000, +/**/ 0x3F72196D, 0xBD2A1052, +/**/ 0x3FC9C000, 0x00000000, +/**/ 0x3FF0557C, 0x8A099990, +/**/ 0x3FBB6569, 0xDC268965, +/**/ 0x3FC991AB, 0x8F9FBA21, +/**/ 0x3FB6EB43, 0xEAED1E85, +/**/ 0x3FBEB5C6, 0x115C4C63, +/**/ 0x3FB665A3, 0x47F9AEFA, +/**/ 0xBCA1F8FD, 0x03AB3673, +/**/ 0x3FC9ED4B, 0x00AC4A60, +/**/ 0x3FF04000, 0x00000000, +/**/ 0x3F757C8A, 0x0999905B, +/**/ 0x3FCA4000, 0x00000000, +/**/ 0x3FF058F2, 0xD3A9E674, +/**/ 0x3FBBFF5E, 0x99873832, +/**/ 0x3FC9C01C, 0x85E31CE9, +/**/ 0x3FB78624, 0x26E09FF2, +/**/ 0x3FBF3E58, 0x3CF0885C, +/**/ 0x3FB7214E, 0xD2986239, +/**/ 0x3C97E3E5, 0x3E594694, +/**/ 0x3FCA7004, 0xB14EB5D0, +/**/ 0x3FF04000, 0x00000000, +/**/ 0x3F78F2D3, 0xA9E6746B, +/**/ 0x3FCAC000, 0x00000000, +/**/ 0x3FF05C7C, 0x6D731ECB, +/**/ 0x3FBC9A6D, 0xA34FA4B3, +/**/ 0x3FC9EFC5, 0xEED9C253, +/**/ 0x3FB823BA, 0x5614FAEB, +/**/ 0x3FBFCB60, 0xB7CE698F, +/**/ 0x3FB7E271, 0x99F3292F, +/**/ 0xBC9842C6, 0x068D709C, +/**/ 0x3FCAF2DA, 0x61674110, +/**/ 0x3FF04000, 0x00000000, +/**/ 0x3F7C7C6D, 0x731ECAE2, +/**/ 0x3FCB4000, 0x00000000, +/**/ 0x3FF06019, 0x7B24A973, +/**/ 0x3FBD369E, 0x5CA0A798, +/**/ 0x3FCA20AD, 0x4CF0DB64, +/**/ 0x3FB8C41D, 0x1B1A3F31, +/**/ 0x3FC02E80, 0x7B35E049, +/**/ 0x3FB8A944, 0x56FB8A97, +/**/ 0xBCACBF9C, 0xD337B37C, +/**/ 0x3FCB75CC, 0xAC059370, +/**/ 0x3FF08000, 0x00000000, +/**/ 0xBF7FE684, 0xDB568D78, +/**/ 0x3FCBC000, 0x00000000, +/**/ 0x3FF063CA, 0x216C6801, +/**/ 0x3FBDD3F8, 0x4A32C9FD, +/**/ 0x3FCA52D8, 0x50843BC9, +/**/ 0x3FB96763, 0xC324648A, +/**/ 0x3FC079AD, 0xE4407899, +/**/ 0x3FB97602, 0x1663A5DC, +/**/ 0xBCA3ADC3, 0xC637289D, +/**/ 0x3FCBF8DC, 0x2D5B06A0, +/**/ 0x3FF08000, 0x00000000, +/**/ 0xBF7C35DE, 0x9397FEA6, +/**/ 0x3FCC4000, 0x00000000, +/**/ 0x3FF0678E, 0x85EAFB1F, +/**/ 0x3FBE7283, 0x136DEAC6, +/**/ 0x3FCA864C, 0xD93A817D, +/**/ 0x3FBA0DA6, 0x4CF7089B, +/**/ 0x3FC0C74A, 0xB3ABB322, +/**/ 0x3FBA48E8, 0x562E6E1E, +/**/ 0xBC951E3E, 0x7EB8FFF8, +/**/ 0x3FCC7C09, 0x82C22B80, +/**/ 0x3FF08000, 0x00000000, +/**/ 0xBF78717A, 0x1504E0D3, +/**/ 0x3FCCC000, 0x00000000, +/**/ 0x3FF06B66, 0xCF382A59, +/**/ 0x3FBF1246, 0x838936FB, +/**/ 0x3FCABB10, 0xF76F5C94, +/**/ 0x3FBAB6FD, 0x701A77AE, +/**/ 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0x4101A722, 0x718322C8, +/**/ 0x413CA4C6, 0x9533D806, +/**/ 0x417812B7, 0xE9899583, +/**/ 0x41B4B875, 0x85EE8B86, +/**/ 0xBC99DEFB, 0xD1AEEED1, +/**/ 0x3FF38957, 0xB510476E, +/**/ 0x40076000, 0x00000000, +/**/ 0xBF6E22F8, 0xB8901BF9, +/**/ 0x3FEE3000, 0x00000000, +/**/ 0x40081CE6, 0xE1C37E57, +/**/ 0x4029D4F3, 0xD3DC9910, +/**/ 0x405CD074, 0xE3095065, +/**/ 0x4093E764, 0xC5C38224, +/**/ 0x40CEC5AE, 0x3CAE1F31, +/**/ 0x41097A50, 0xC0645F38, +/**/ 0x41461866, 0xD8A7F25E, +/**/ 0x4183DAF5, 0x8C2F04A3, +/**/ 0x41C2450E, 0xA9143C1F, +/**/ 0x3C7D25BE, 0x9FD995BC, +/**/ 0x3FF3B8C9, 0xC35D33E6, +/**/ 0x40082000, 0x00000000, +/**/ 0xBF58C8F1, 0xE40D49E0, +/**/ 0x3FEE5000, 0x00000000, +/**/ 0x4008F706, 0x285640BB, +/**/ 0x402CC96B, 0x3B2B7CD1, +/**/ 0x40613ADF, 0xC5341328, +/**/ 0x4099908D, 0x16E928A9, +/**/ 0x40D53986, 0x7CC08A3C, +/**/ 0x4112DFC5, 0x31DD3E45, +/**/ 0x41519499, 0xE2A13787, +/**/ 0x4190F943, 0xF94424AD, +/**/ 0x41D0C6BC, 0xCDCD49BE, +/**/ 0xBC9E2458, 0x6D41701D, +/**/ 0x3FF3E9D9, 0xC088BD28, +/**/ 0x40090000, 0x00000000, +/**/ 0xBF71F3AF, 0x537E8A00, +/**/ 0x3FEE7000, 0x00000000, +/**/ 0x4009EB18, 0x6562D1E0, +/**/ 0x40302C31, 0x75651223, +/**/ 0x4064E431, 0x336E41C7, +/**/ 0x40A0BCA6, 0xA065DA69, +/**/ 0x40DE034D, 0x917AF357, +/**/ 0x411CD2C1, 0x4168FB0F, +/**/ 0x415CFEB6, 0x15BB794D, +/**/ 0x419E3EE1, 0x6EFFD5E5, +/**/ 0x41E024E7, 0x1ACB4D9C, +/**/ 0xBC9C29C8, 0xD93F153F, +/**/ 0x3FF41CB7, 0x2183E810, +/**/ 0x4009E000, 0x00000000, +/**/ 0x3F7630CA, 0xC5A3C038, +/**/ 0x3FEE9000, 0x00000000, +/**/ 0x400AFEA6, 0xA364196F, +/**/ 0x403258F3, 0x0B19A2EB, +/**/ 0x4069BDA5, 0x2520AC75, +/**/ 0x40A669BC, 0x8F67EDEA, +/**/ 0x40E5D78C, 0xC026C9F8, +/**/ 0x4126CCB4, 0x1E3B36C2, +/**/ 0x4168EDE4, 0xBF45C805, +/**/ 0x41AC2F6A, 0x8AC89E76, +/**/ 0x41F0675E, 0x4CA9EB55, +/**/ 0x42336AC1, 0x0D13E3DF, +/**/ 0x3C9B1D74, 0xF2DE93A6, +/**/ 0x3FF4519B, 0x155FB22E, +/**/ 0x400B0000, 0x00000000, +/**/ 0xBF4595C9, 0xBE690E67, +/**/ 0x3FEEB000, 0x00000000, +/**/ 0x400C3908, 0x4BD1C065, +/**/ 0x40350D88, 0x26C39FFD, +/**/ 0x4070296B, 0x69D3E79E, +/**/ 0x40AED279, 0xD7FEEA5D, +/**/ 0x40F072A8, 0xFD5BD547, +/**/ 0x4132CDB9, 0x4A08BB38, +/**/ 0x41768482, 0x536BED06, +/**/ 0x41BBE1FF, 0x2F10E88D, +/**/ 0x4201C966, 0xABDBBDAC, +/**/ 0x42471011, 0x02E62DDA, +/**/ 0xBCA0855D, 0x3E907E71, +/**/ 0x3FF488CB, 0x8FA73920, +/**/ 0x400C4000, 0x00000000, +/**/ 0xBF6BDED0, 0xB8FE6DDF, +/**/ 0x3FEED000, 0x00000000, +/**/ 0x400DA439, 0x12AAF9A9, +/**/ 0x40387D46, 0x62F25109, +/**/ 0x4074C339, 0x3F133A3F, +/**/ 0x40B5E143, 0x662036F9, +/**/ 0x40F9CF04, 0x74467831, +/**/ 0x41404E10, 0x576C6FA8, +/**/ 0x41859489, 0xFF4F8E88, +/**/ 0x41CD88D2, 0xB44962A9, +/**/ 0x4214D838, 0x97A288F3, +/**/ 0x425DE10B, 0x6CF738B3, +/**/ 0xBC8E9EA7, 0x5F7263CC, +/**/ 0x3FF4C29F, 0xAA786F36, +/**/ 0x400DA000, 0x00000000, +/**/ 0x3F60E44A, 0xABE6A2AD, +/**/ 0x3FEEF000, 0x00000000, +/**/ 0x400F4E35, 0xC169B52F, +/**/ 0x403CF773, 0x29E8699C, +/**/ 0x407B6D37, 0xFC1818D6, +/**/ 0x40C02655, 0x1386790A, +/**/ 0x41054A1F, 0x4FF79D1E, +/**/ 0x414E104A, 0x7DB0265A, +/**/ 0x41963C39, 0xE5C8114B, +/**/ 0x41E10156, 0xF52A87DB, +/**/ 0x422ADD76, 0x2E9E7ABE, +/**/ 0x427586AB, 0x6EC81361, +/**/ 0x3C935690, 0xE395EEA6, +/**/ 0x3FF4FF86, 0x2E5965A2, +/**/ 0x400F4000, 0x00000000, +/**/ 0x3F7C6B82, 0xD36A5E70 } }; + +#else +#ifdef LITTLE_ENDI +static const union {int4 i[5136];double x[2568];} asncs = { .i = { +/**/ 0x00000000, 0x3FC04000, +/**/ 0x88994424, 0x3FF02169, +/**/ 0xB799B115, 0x3FB0A6A2, +/**/ 0xD57409A0, 0x3FC6EF15, +/**/ 0xAF52EAA0, 0x3FAA141E, +/**/ 0xABBBE261, 0x3FB75591, +/**/ 0xD206D88F, 0x3FA72B51, +/**/ 0x5BB33E7D, 0x3C96B595, +/**/ 0xA03E2700, 0x3FC04B41, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x66BBDC7C, 0xBF7E9677, +/**/ 0x00000000, 0x3FC0C000, +/**/ 0xF9E23A56, 0x3FF02386, +/**/ 0x60FD0235, 0x3FB1308C, +/**/ 0x14D16B02, 0x3FC7099F, +/**/ 0x27C01EE1, 0x3FAAFED6, +/**/ 0xDBCD5F98, 0x3FB79C6F, +/**/ 0x4084DAAC, 0x3FA8144A, +/**/ 0x38D8505E, 0xBC87C092, +/**/ 0x56C9F380, 0x3FC0CC55, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x1DC5AA24, 0xBF7C7906, +/**/ 0x00000000, 0x3FC14000, +/**/ 0xB27141F6, 0x3FF025B5, +/**/ 0x04CE7400, 0x3FB1BB18, +/**/ 0x72907342, 0x3FC72514, +/**/ 0x0BF4222C, 0x3FABEC60, +/**/ 0x75B3736C, 0x3FB7E610, +/**/ 0x5199C343, 0x3FA9024C, +/**/ 0x06B56F60, 0xBC8AE84C, +/**/ 0x3DEFA070, 0x3FC14D7A, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x8EBE0A5C, 0xBF7A4A4D, +/**/ 0x00000000, 0x3FC1C000, +/**/ 0xC6DE8F57, 0x3FF027F5, +/**/ 0x345751E1, 0x3FB2464B, +/**/ 0xCF026805, 0x3FC74178, +/**/ 0x40A9E0D6, 0x3FACDCD8, +/**/ 0xEB1D9C38, 0x3FB83282, +/**/ 0xD7BE707B, 0x3FA9F590, +/**/ 0x03A2A6D6, 0xBCAB9768, +/**/ 0xE03B4870, 0x3FC1CEB0, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x2170A943, 0xBF780A39, +/**/ 0x00000000, 0x3FC24000, +/**/ 0x4C759796, 0x3FF02A47, +/**/ 0x92771935, 0x3FB2D22B, +/**/ 0x26ABA06D, 0x3FC75ECF, +/**/ 0x486A1932, 0x3FADD05B, +/**/ 0x5AF971D5, 0x3FB881D7, +/**/ 0x831AEE0C, 0x3FAAEE52, +/**/ 0xAD1B1BEF, 0x3CA13F57, +/**/ 0xC8E09330, 0x3FC24FF9, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x8A68699B, 0xBF75B8B3, +/**/ 0x00000000, 0x3FC2C000, +/**/ 0x59374E09, 0x3FF02CAA, +/**/ 0xD44E8BEA, 0x3FB35EBE, +/**/ 0x92E4BE8A, 0x3FC77D1A, +/**/ 0x4A6C34FD, 0x3FAEC706, +/**/ 0x972F6E07, 0x3FB8D41E, +/**/ 0xF9845F69, 0x3FABECCD, +/**/ 0x945C4185, 0x3C8BA1FA, +/**/ 0x83C058B0, 0x3FC2D155, +/**/ 0x00000000, 0x3FF04000, +/**/ 0xC8B1F774, 0xBF7355A6, +/**/ 0x00000000, 0x3FC34000, +/**/ 0x03DC7745, 0x3FF02F1F, +/**/ 0xC1EE9F61, 0x3FB3EC0A, +/**/ 0x4A82E6D2, 0x3FC79C5E, +/**/ 0x19B1EF72, 0x3FAFC0F7, +/**/ 0x2AA943E5, 0x3FB9296A, +/**/ 0xEF8B9DE7, 0x3FACF141, +/**/ 0x083C8716, 0xBC834081, +/**/ 0x9D6E5610, 0x3FC352C4, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x2388BB30, 0xBF70E0FC, +/**/ 0x00000000, 0x3FC3C000, +/**/ 0x63D81251, 0x3FF031A5, +/**/ 0x370B721F, 0x3FB47A15, +/**/ 0xA28731E5, 0x3FC7BC9D, +/**/ 0x1E305BE9, 0x3FB05F26, +/**/ 0x5FA50FBD, 0x3FB981CC, +/**/ 0x42AC4083, 0x3FADFBEF, +/**/ 0xA8E107C7, 0x3CA20ACB, +/**/ 0xA336F5E0, 0x3FC3D447, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x4FDB5D5C, 0xBF6CB538, +/**/ 0x00000000, 0x3FC44000, +/**/ 0x9159D86F, 0x3FF0343D, +/**/ 0x23B3747C, 0x3FB508E4, +/**/ 0x0ED597CB, 0x3FC7DDDC, +/**/ 0x79ADF104, 0x3FB0DF92, +/**/ 0x4658D945, 0x3FB9DD58, +/**/ 0x14ACA06B, 0x3FAF0D19, +/**/ 0xDF636EFE, 0xBCA4E10D, +/**/ 0x23252C00, 0x3FC455DF, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x4C4F221A, 0xBF6784DD, +/**/ 0x00000000, 0x3FC4C000, +/**/ 0xA550D410, 0x3FF036E7, +/**/ 0x8D0AF1E7, 0x3FB5987D, +/**/ 0x22F39726, 0x3FC8001D, +/**/ 0xA1116D73, 0x3FB161D0, +/**/ 0xBBEA1528, 0x3FBA3C21, +/**/ 0x74202FF6, 0x3FB01282, +/**/ 0xD10866E2, 0x3CAA0611, +/**/ 0xAC086560, 0x3FC4D78B, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x5E57DF8A, 0xBF6230B5, +/**/ 0x00000000, 0x3FC54000, +/**/ 0xB96E0F8A, 0x3FF039A3, +/**/ 0x8E0C29F6, 0x3FB628E7, +/**/ 0x92CEDE01, 0x3FC82364, +/**/ 0xFB7B5D84, 0x3FB1E5F0, +/**/ 0x71BD08EE, 0x3FBA9E3D, +/**/ 0x5F7FFAB4, 0x3FB0A1FD, +/**/ 0xEF04F6E7, 0xBC90F980, +/**/ 0xCD7A8DC0, 0x3FC5594D, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x47C1D879, 0xBF59711A, +/**/ 0x00000000, 0x3FC5C000, +/**/ 0xE8275C12, 0x3FF03C71, +/**/ 0x584C2A23, 0x3FB6BA28, +/**/ 0x338C3D4B, 0x3FC847B6, +/**/ 0x59A55DD8, 0x3FB26C04, +/**/ 0xF5202D6A, 0x3FBB03C0, +/**/ 0x9C6466A4, 0x3FB13522, +/**/ 0x2A268973, 0x3C983C9A, +/**/ 0x17E62A20, 0x3FC5DB26, +/**/ 0x00000000, 0x3FF04000, +/**/ 0xC51F7008, 0xBF4C70BE, +/**/ 0x00000000, 0x3FC64000, +/**/ 0x4CBA31A9, 0x3FF03F52, +/**/ 0x34C49ADE, 0x3FB74C46, +/**/ 0xFC5F33CC, 0x3FC86D15, +/**/ 0xFA419D7C, 0x3FB2F41B, +/**/ 0xB757E82A, 0x3FBB6CC2, +/**/ 0xDA4D5C39, 0x3FB1CC18, +/**/ 0x2DFB224D, 0xBCA862D4, +/**/ 0x1C8C8AF0, 0x3FC65D15, +/**/ 0x00000000, 0x3FF04000, +/**/ 0xB9CADBBF, 0xBF25B668, +/**/ 0x00000000, 0x3FC6C000, +/**/ 0x032EA88F, 0x3FF04245, +/**/ 0x84A2B473, 0x3FB7DF47, +/**/ 0x076A60F5, 0x3FC89388, +/**/ 0x8E8394C1, 0x3FB37E49, +/**/ 0x160F3472, 0x3FBBD95A, +/**/ 0x39844810, 0x3FB26708, +/**/ 0x698BC8EA, 0x3C994228, +/**/ 0x6D8C14A0, 0x3FC6DF1B, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x754477AC, 0x3F422819, +/**/ 0x00000000, 0x3FC74000, +/**/ 0x285A8CEB, 0x3FF0454A, +/**/ 0xC21B9224, 0x3FB87332, +/**/ 0x92A93402, 0x3FC8BB10, +/**/ 0x3ED3F586, 0x3FB40A9F, +/**/ 0x643217C8, 0x3FBC499F, +/**/ 0x5D29A16B, 0x3FB3061A, +/**/ 0x3DF9F2D7, 0xBCA3B2DF, +/**/ 0x9DE6A160, 0x3FC76139, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x6A33AB4B, 0x3F5528A1, +/**/ 0x00000000, 0x3FC7C000, +/**/ 0xD9E48D58, 0x3FF04861, +/**/ 0x81461BF6, 0x3FB9080E, +/**/ 0x00E32FFA, 0x3FC8E3B4, +/**/ 0xAFB1F2A5, 0x3FB4992F, +/**/ 0xF33705D5, 0x3FBCBDAB, +/**/ 0x7E23EE89, 0x3FB3A97A, +/**/ 0xCCE44C41, 0x3C7AAD12, +/**/ 0x4187FAE0, 0x3FC7E370, +/**/ 0x00000000, 0x3FF04000, +/**/ 0xC91AAF11, 0x3F60C3B3, +/**/ 0x00000000, 0x3FC84000, +/**/ 0x36478509, 0x3FF04B8C, +/**/ 0x70FAC1B4, 0x3FB99DE1, +/**/ 0xDAA92166, 0x3FC90D76, +/**/ 0x06C416A6, 0x3FB52A0E, +/**/ 0x1CDCA344, 0x3FBD359A, +/**/ 0x7EFD4CA0, 0x3FB45155, +/**/ 0x35A8895D, 0x3C396CA5, +/**/ 0xED4C6EF0, 0x3FC865BF, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x8F0A11A4, 0x3F67186C, +/**/ 0x00000000, 0x3FC8C000, +/**/ 0x5CD5E248, 0x3FF04EC9, +/**/ 0x5BB94403, 0x3FBA34B2, +/**/ 0xCF5CA73A, 0x3FC9385D, +/**/ 0xF01AFDBE, 0x3FB5BD4D, +/**/ 0x4D61A7A9, 0x3FBDB185, +/**/ 0x00BD47CF, 0x3FB4FDDA, +/**/ 0x727E8B64, 0xBC9D1119, +/**/ 0x37077E20, 0x3FC8E829, +/**/ 0x00000000, 0x3FF04000, +/**/ 0xABC490CB, 0x3F6D92B9, +/**/ 0x00000000, 0x3FC94000, +/**/ 0x6DBD2A10, 0x3FF05219, +/**/ 0x2894CAA1, 0x3FBACC88, +/**/ 0xB6427516, 0x3FC9646D, +/**/ 0xA3A864D7, 0x3FB65303, +/**/ 0x0E3CF3D4, 0x3FBE318A, +/**/ 0x78CDA678, 0x3FB5AF38, +/**/ 0xDA9D51DF, 0x3CA3841D, +/**/ 0xB58AA660, 0x3FC96AAC, +/**/ 0x00000000, 0x3FF04000, +/**/ 0xBD2A1052, 0x3F72196D, +/**/ 0x00000000, 0x3FC9C000, +/**/ 0x8A099990, 0x3FF0557C, +/**/ 0xDC268965, 0x3FBB6569, +/**/ 0x8F9FBA21, 0x3FC991AB, +/**/ 0xEAED1E85, 0x3FB6EB43, +/**/ 0x115C4C63, 0x3FBEB5C6, +/**/ 0x47F9AEFA, 0x3FB665A3, +/**/ 0x03AB3673, 0xBCA1F8FD, +/**/ 0x00AC4A60, 0x3FC9ED4B, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x0999905B, 0x3F757C8A, +/**/ 0x00000000, 0x3FCA4000, +/**/ 0xD3A9E674, 0x3FF058F2, +/**/ 0x99873832, 0x3FBBFF5E, +/**/ 0x85E31CE9, 0x3FC9C01C, +/**/ 0x26E09FF2, 0x3FB78624, +/**/ 0x3CF0885C, 0x3FBF3E58, +/**/ 0xD2986239, 0x3FB7214E, +/**/ 0x3E594694, 0x3C97E3E5, +/**/ 0xB14EB5D0, 0x3FCA7004, +/**/ 0x00000000, 0x3FF04000, +/**/ 0xA9E6746B, 0x3F78F2D3, +/**/ 0x00000000, 0x3FCAC000, +/**/ 0x6D731ECB, 0x3FF05C7C, +/**/ 0xA34FA4B3, 0x3FBC9A6D, +/**/ 0xEED9C253, 0x3FC9EFC5, +/**/ 0x5614FAEB, 0x3FB823BA, +/**/ 0xB7CE698F, 0x3FBFCB60, +/**/ 0x99F3292F, 0x3FB7E271, +/**/ 0x068D709C, 0xBC9842C6, +/**/ 0x61674110, 0x3FCAF2DA, +/**/ 0x00000000, 0x3FF04000, +/**/ 0x731ECAE2, 0x3F7C7C6D, +/**/ 0x00000000, 0x3FCB4000, +/**/ 0x7B24A973, 0x3FF06019, +/**/ 0x5CA0A798, 0x3FBD369E, +/**/ 0x4CF0DB64, 0x3FCA20AD, +/**/ 0x1B1A3F31, 0x3FB8C41D, +/**/ 0x7B35E049, 0x3FC02E80, +/**/ 0x56FB8A97, 0x3FB8A944, +/**/ 0xD337B37C, 0xBCACBF9C, +/**/ 0xAC059370, 0x3FCB75CC, +/**/ 0x00000000, 0x3FF08000, +/**/ 0xDB568D78, 0xBF7FE684, +/**/ 0x00000000, 0x3FCBC000, +/**/ 0x216C6801, 0x3FF063CA, +/**/ 0x4A32C9FD, 0x3FBDD3F8, +/**/ 0x50843BC9, 0x3FCA52D8, +/**/ 0xC324648A, 0x3FB96763, +/**/ 0xE4407899, 0x3FC079AD, +/**/ 0x1663A5DC, 0x3FB97602, +/**/ 0xC637289D, 0xBCA3ADC3, +/**/ 0x2D5B06A0, 0x3FCBF8DC, +/**/ 0x00000000, 0x3FF08000, +/**/ 0x9397FEA6, 0xBF7C35DE, +/**/ 0x00000000, 0x3FCC4000, +/**/ 0x85EAFB1F, 0x3FF0678E, +/**/ 0x136DEAC6, 0x3FBE7283, +/**/ 0xD93A817D, 0x3FCA864C, +/**/ 0x4CF7089B, 0x3FBA0DA6, +/**/ 0xB3ABB322, 0x3FC0C74A, +/**/ 0x562E6E1E, 0x3FBA48E8, +/**/ 0x7EB8FFF8, 0xBC951E3E, +/**/ 0x82C22B80, 0x3FCC7C09, +/**/ 0x00000000, 0x3FF08000, +/**/ 0x1504E0D3, 0xBF78717A, +/**/ 0x00000000, 0x3FCCC000, +/**/ 0xCF382A59, 0x3FF06B66, +/**/ 0x838936FB, 0x3FBF1246, +/**/ 0xF76F5C94, 0x3FCABB10, +/**/ 0x701A77AE, 0x3FBAB6FD, +/**/ 0xC26702C6, 0x3FC11769, +/**/ 0x24CDF38E, 0x3FBB2237, +/**/ 0xE28307A9, 0xBC8DB69A, +/**/ 0x4AC67190, 0x3FCCFF55, +/**/ 0x00000000, 0x3FF08000, +/**/ 0xC7D5A6B9, 0xBF749930, +/**/ 0x00000000, 0x3FCD4000, +/**/ 0x24E7707F, 0x3FF06F53, +/**/ 0x8AB3CBB2, 0x3FBFB34A, +/**/ 0xEDAC8D74, 0x3FCAF12A, +/**/ 0xA45DA614, 0x3FBB6382, +/**/ 0xAD8E9F44, 0x3FC16A1E, +/**/ 0x41E7749D, 0x3FBC0231, +/**/ 0x22DC16A2, 0x3C76CA27, +/**/ 0x252BF240, 0x3FCD82C0, +/**/ 0x00000000, 0x3FF08000, +/**/ 0x188F814B, 0xBF70ACDB, +/**/ 0x00000000, 0x3FCDC000, +/**/ 0xAF8CADA0, 0x3FF07353, +/**/ 0x9FA32DC9, 0x3FC02ACB, +/**/ 0x32323718, 0x3FCB28A1, +/**/ 0x29A8F15E, 0x3FBC1350, +/**/ 0xDEB270E1, 0x3FC1BF7D, +/**/ 0x40D67463, 0x3FBCE91C, +/**/ 0x104BAA08, 0x3CA6E976, +/**/ 0xB2F76140, 0x3FCE064A, +/**/ 0x00000000, 0x3FF08000, +/**/ 0xE6A4BFC9, 0xBF6958A0, +/**/ 0x00000000, 0x3FCE4000, +/**/ 0x98C0FFD9, 0x3FF07768, +/**/ 0x6F7F1AF0, 0x3FC07C9A, +/**/ 0x708F2AFB, 0x3FCB617A, +/**/ 0x1025B50C, 0x3FBCC681, +/**/ 0x9487453A, 0x3FC2179C, +/**/ 0xAD09B3AB, 0x3FBDD740, +/**/ 0x189038C0, 0xBC8D32DB, +/**/ 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0xD944F636, 0x408499B5, +/**/ 0x37F73BAC, 0x40BA64B8, +/**/ 0x259B27FC, 0x40F21B9F, +/**/ 0x265D5B9F, 0x412A0669, +/**/ 0x3DC806E2, 0x41635D8E, +/**/ 0x36AD8B00, 0x419D8657, +/**/ 0x3FFCDCA3, 0x3CA4CEEB, +/**/ 0xC69D2D10, 0x3FF32EB3, +/**/ 0x00000000, 0x40060000, +/**/ 0x6C678625, 0x3F5FA9E9, +/**/ 0x00000000, 0x3FEDF000, +/**/ 0x5FCDF915, 0x4006A65F, +/**/ 0x68321BDA, 0x40253B6E, +/**/ 0x706E8DA9, 0x4054D949, +/**/ 0x4A70D2D7, 0x408950EF, +/**/ 0x1F15E14E, 0x40C13319, +/**/ 0x846A9BD5, 0x40F907B1, +/**/ 0x17C39016, 0x4133139C, +/**/ 0xBC86F11B, 0x416E1DA3, +/**/ 0xD9F86F3B, 0x41A8597F, +/**/ 0x7D0D5190, 0x3C32D4F8, +/**/ 0xAFA88354, 0x3FF35B5B, +/**/ 0x00000000, 0x4006A000, +/**/ 0x37E455FD, 0x3F697D7F, +/**/ 0x00000000, 0x3FEE1000, +/**/ 0x41D1DBF9, 0x40075877, +/**/ 0xF5852184, 0x402758A8, +/**/ 0x65C0F467, 0x405861EE, +/**/ 0xD2D91276, 0x408F83C0, +/**/ 0x43EC3B0E, 0x40C6CA7C, +/**/ 0x718322C8, 0x4101A722, +/**/ 0x9533D806, 0x413CA4C6, +/**/ 0xE9899583, 0x417812B7, +/**/ 0x85EE8B86, 0x41B4B875, +/**/ 0xD1AEEED1, 0xBC99DEFB, +/**/ 0xB510476E, 0x3FF38957, +/**/ 0x00000000, 0x40076000, +/**/ 0xB8901BF9, 0xBF6E22F8, +/**/ 0x00000000, 0x3FEE3000, +/**/ 0xE1C37E57, 0x40081CE6, +/**/ 0xD3DC9910, 0x4029D4F3, +/**/ 0xE3095065, 0x405CD074, +/**/ 0xC5C38224, 0x4093E764, +/**/ 0x3CAE1F31, 0x40CEC5AE, +/**/ 0xC0645F38, 0x41097A50, +/**/ 0xD8A7F25E, 0x41461866, +/**/ 0x8C2F04A3, 0x4183DAF5, +/**/ 0xA9143C1F, 0x41C2450E, +/**/ 0x9FD995BC, 0x3C7D25BE, +/**/ 0xC35D33E6, 0x3FF3B8C9, +/**/ 0x00000000, 0x40082000, +/**/ 0xE40D49E0, 0xBF58C8F1, +/**/ 0x00000000, 0x3FEE5000, +/**/ 0x285640BB, 0x4008F706, +/**/ 0x3B2B7CD1, 0x402CC96B, +/**/ 0xC5341328, 0x40613ADF, +/**/ 0x16E928A9, 0x4099908D, +/**/ 0x7CC08A3C, 0x40D53986, +/**/ 0x31DD3E45, 0x4112DFC5, +/**/ 0xE2A13787, 0x41519499, +/**/ 0xF94424AD, 0x4190F943, +/**/ 0xCDCD49BE, 0x41D0C6BC, +/**/ 0x6D41701D, 0xBC9E2458, +/**/ 0xC088BD28, 0x3FF3E9D9, +/**/ 0x00000000, 0x40090000, +/**/ 0x537E8A00, 0xBF71F3AF, +/**/ 0x00000000, 0x3FEE7000, +/**/ 0x6562D1E0, 0x4009EB18, +/**/ 0x75651223, 0x40302C31, +/**/ 0x336E41C7, 0x4064E431, +/**/ 0xA065DA69, 0x40A0BCA6, +/**/ 0x917AF357, 0x40DE034D, +/**/ 0x4168FB0F, 0x411CD2C1, +/**/ 0x15BB794D, 0x415CFEB6, +/**/ 0x6EFFD5E5, 0x419E3EE1, +/**/ 0x1ACB4D9C, 0x41E024E7, +/**/ 0xD93F153F, 0xBC9C29C8, +/**/ 0x2183E810, 0x3FF41CB7, +/**/ 0x00000000, 0x4009E000, +/**/ 0xC5A3C038, 0x3F7630CA, +/**/ 0x00000000, 0x3FEE9000, +/**/ 0xA364196F, 0x400AFEA6, +/**/ 0x0B19A2EB, 0x403258F3, +/**/ 0x2520AC75, 0x4069BDA5, +/**/ 0x8F67EDEA, 0x40A669BC, +/**/ 0xC026C9F8, 0x40E5D78C, +/**/ 0x1E3B36C2, 0x4126CCB4, +/**/ 0xBF45C805, 0x4168EDE4, +/**/ 0x8AC89E76, 0x41AC2F6A, +/**/ 0x4CA9EB55, 0x41F0675E, +/**/ 0x0D13E3DF, 0x42336AC1, +/**/ 0xF2DE93A6, 0x3C9B1D74, +/**/ 0x155FB22E, 0x3FF4519B, +/**/ 0x00000000, 0x400B0000, +/**/ 0xBE690E67, 0xBF4595C9, +/**/ 0x00000000, 0x3FEEB000, +/**/ 0x4BD1C065, 0x400C3908, +/**/ 0x26C39FFD, 0x40350D88, +/**/ 0x69D3E79E, 0x4070296B, +/**/ 0xD7FEEA5D, 0x40AED279, +/**/ 0xFD5BD547, 0x40F072A8, +/**/ 0x4A08BB38, 0x4132CDB9, +/**/ 0x536BED06, 0x41768482, +/**/ 0x2F10E88D, 0x41BBE1FF, +/**/ 0xABDBBDAC, 0x4201C966, +/**/ 0x02E62DDA, 0x42471011, +/**/ 0x3E907E71, 0xBCA0855D, +/**/ 0x8FA73920, 0x3FF488CB, +/**/ 0x00000000, 0x400C4000, +/**/ 0xB8FE6DDF, 0xBF6BDED0, +/**/ 0x00000000, 0x3FEED000, +/**/ 0x12AAF9A9, 0x400DA439, +/**/ 0x62F25109, 0x40387D46, +/**/ 0x3F133A3F, 0x4074C339, +/**/ 0x662036F9, 0x40B5E143, +/**/ 0x74467831, 0x40F9CF04, +/**/ 0x576C6FA8, 0x41404E10, +/**/ 0xFF4F8E88, 0x41859489, +/**/ 0xB44962A9, 0x41CD88D2, +/**/ 0x97A288F3, 0x4214D838, +/**/ 0x6CF738B3, 0x425DE10B, +/**/ 0x5F7263CC, 0xBC8E9EA7, +/**/ 0xAA786F36, 0x3FF4C29F, +/**/ 0x00000000, 0x400DA000, +/**/ 0xABE6A2AD, 0x3F60E44A, +/**/ 0x00000000, 0x3FEEF000, +/**/ 0xC169B52F, 0x400F4E35, +/**/ 0x29E8699C, 0x403CF773, +/**/ 0xFC1818D6, 0x407B6D37, +/**/ 0x1386790A, 0x40C02655, +/**/ 0x4FF79D1E, 0x41054A1F, +/**/ 0x7DB0265A, 0x414E104A, +/**/ 0xE5C8114B, 0x41963C39, +/**/ 0xF52A87DB, 0x41E10156, +/**/ 0x2E9E7ABE, 0x422ADD76, +/**/ 0x6EC81361, 0x427586AB, +/**/ 0xE395EEA6, 0x3C935690, +/**/ 0x2E5965A2, 0x3FF4FF86, +/**/ 0x00000000, 0x400F4000, +/**/ 0xD36A5E70, 0x3F7C6B82 } }; + +#endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/atnat.h b/REORG.TODO/sysdeps/ieee754/dbl-64/atnat.h new file mode 100644 index 0000000000..3ba064ae59 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/atnat.h @@ -0,0 +1,154 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/************************************************************************/ +/* MODULE_NAME: atnat.h */ +/* */ +/* */ +/* common data and variables definition for BIG or LITTLE ENDIAN */ +/************************************************************************/ +#ifndef ATNAT_H +#define ATNAT_H + +#define M 4 + +#ifdef BIG_ENDI + static const number + /* polynomial I */ +/**/ d3 = {{0xbfd55555, 0x55555555} }, /* -0.333... */ +/**/ d5 = {{0x3fc99999, 0x999997fd} }, /* 0.199... */ +/**/ d7 = {{0xbfc24924, 0x923f7603} }, /* -0.142... */ +/**/ d9 = {{0x3fbc71c6, 0xe5129a3b} }, /* 0.111... */ +/**/ d11 = {{0xbfb74580, 0x22b13c25} }, /* -0.090... */ +/**/ d13 = {{0x3fb375f0, 0x8b31cbce} }, /* 0.076... */ + /* polynomial II */ +/**/ f3 = {{0xbfd55555, 0x55555555} }, /* -1/3 */ +/**/ ff3 = {{0xbc755555, 0x55555555} }, /* -1/3-f3 */ +/**/ f5 = {{0x3fc99999, 0x9999999a} }, /* 1/5 */ +/**/ ff5 = {{0xbc699999, 0x9999999a} }, /* 1/5-f5 */ +/**/ f7 = {{0xbfc24924, 0x92492492} }, /* -1/7 */ +/**/ ff7 = {{0xbc624924, 0x92492492} }, /* -1/7-f7 */ +/**/ f9 = {{0x3fbc71c7, 0x1c71c71c} }, /* 1/9 */ +/**/ ff9 = {{0x3c5c71c7, 0x1c71c71c} }, /* 1/9-f9 */ +/**/ f11 = {{0xbfb745d1, 0x745d1746} }, /* -1/11 */ +/**/ f13 = {{0x3fb3b13b, 0x13b13b14} }, /* 1/13 */ +/**/ f15 = {{0xbfb11111, 0x11111111} }, /* -1/15 */ +/**/ f17 = {{0x3fae1e1e, 0x1e1e1e1e} }, /* 1/17 */ +/**/ f19 = {{0xbfaaf286, 0xbca1af28} }, /* -1/19 */ + /* constants */ +/**/ a = {{0x3e4bb67a, 0x00000000} }, /* 1.290e-8 */ +/**/ b = {{0x3fb00000, 0x00000000} }, /* 1/16 */ +/**/ c = {{0x3ff00000, 0x00000000} }, /* 1 */ +/**/ d = {{0x40300000, 0x00000000} }, /* 16 */ +/**/ e = {{0x43349ff2, 0x00000000} }, /* 5.805e15 */ +/**/ hpi = {{0x3ff921fb, 0x54442d18} }, /* pi/2 */ +/**/ mhpi = {{0xbff921fb, 0x54442d18} }, /* -pi/2 */ +/**/ hpi1 = {{0x3c91a626, 0x33145c07} }, /* pi/2-hpi */ +/**/ u1 = {{0x3c2d3382, 0x00000000} }, /* 7.915e-19 */ +/**/ u21 = {{0x3c6dffc0, 0x00000000} }, /* 1.301e-17 */ +/**/ u22 = {{0x3c527bd0, 0x00000000} }, /* 4.008e-18 */ +/**/ u23 = {{0x3c3cd057, 0x00000000} }, /* 1.562e-18 */ +/**/ u24 = {{0x3c329cdf, 0x00000000} }, /* 1.009e-18 */ +/**/ u31 = {{0x3c3a1edf, 0x00000000} }, /* 1.416e-18 */ +/**/ u32 = {{0x3c33f0e1, 0x00000000} }, /* 1.081e-18 */ +/**/ u4 = {{0x3bf955e4, 0x00000000} }, /* 8.584e-20 */ +/**/ u5 = {{0x3aaef2d1, 0x00000000} }, /* 5e-26 */ +/**/ u6 = {{0x3a98c56d, 0x00000000} }, /* 2.001e-26 */ +/**/ u7 = {{0x3a9375de, 0x00000000} }, /* 1.572e-26 */ +/**/ u8 = {{0x3a6eeb36, 0x00000000} }, /* 3.122e-27 */ +/**/ u9[M] ={{{0x38c1aa5b, 0x00000000} }, /* 2.658e-35 */ +/**/ {{0x35c1aa4d, 0x00000000} }, /* 9.443e-50 */ +/**/ {{0x32c1aa88, 0x00000000} }, /* 3.355e-64 */ +/**/ {{0x11c1aa56, 0x00000000} }};/* 3.818e-223 */ + +#else +#ifdef LITTLE_ENDI + static const number + /* polynomial I */ +/**/ d3 = {{0x55555555, 0xbfd55555} }, /* -0.333... */ +/**/ d5 = {{0x999997fd, 0x3fc99999} }, /* 0.199... */ +/**/ d7 = {{0x923f7603, 0xbfc24924} }, /* -0.142... */ +/**/ d9 = {{0xe5129a3b, 0x3fbc71c6} }, /* 0.111... */ +/**/ d11 = {{0x22b13c25, 0xbfb74580} }, /* -0.090... */ +/**/ d13 = {{0x8b31cbce, 0x3fb375f0} }, /* 0.076... */ + /* polynomial II */ +/**/ f3 = {{0x55555555, 0xbfd55555} }, /* -1/3 */ +/**/ ff3 = {{0x55555555, 0xbc755555} }, /* -1/3-f3 */ +/**/ f5 = {{0x9999999a, 0x3fc99999} }, /* 1/5 */ +/**/ ff5 = {{0x9999999a, 0xbc699999} }, /* 1/5-f5 */ +/**/ f7 = {{0x92492492, 0xbfc24924} }, /* -1/7 */ +/**/ ff7 = {{0x92492492, 0xbc624924} }, /* -1/7-f7 */ +/**/ f9 = {{0x1c71c71c, 0x3fbc71c7} }, /* 1/9 */ +/**/ ff9 = {{0x1c71c71c, 0x3c5c71c7} }, /* 1/9-f9 */ +/**/ f11 = {{0x745d1746, 0xbfb745d1} }, /* -1/11 */ +/**/ f13 = {{0x13b13b14, 0x3fb3b13b} }, /* 1/13 */ +/**/ f15 = {{0x11111111, 0xbfb11111} }, /* -1/15 */ +/**/ f17 = {{0x1e1e1e1e, 0x3fae1e1e} }, /* 1/17 */ +/**/ f19 = {{0xbca1af28, 0xbfaaf286} }, /* -1/19 */ + /* constants */ +/**/ a = {{0x00000000, 0x3e4bb67a} }, /* 1.290e-8 */ +/**/ b = {{0x00000000, 0x3fb00000} }, /* 1/16 */ +/**/ c = {{0x00000000, 0x3ff00000} }, /* 1 */ +/**/ d = {{0x00000000, 0x40300000} }, /* 16 */ +/**/ e = {{0x00000000, 0x43349ff2} }, /* 5.805e15 */ +/**/ hpi = {{0x54442d18, 0x3ff921fb} }, /* pi/2 */ +/**/ mhpi = {{0x54442d18, 0xbff921fb} }, /* -pi/2 */ +/**/ hpi1 = {{0x33145c07, 0x3c91a626} }, /* pi/2-hpi */ +/**/ u1 = {{0x00000000, 0x3c2d3382} }, /* 7.915e-19 */ +/**/ u21 = {{0x00000000, 0x3c6dffc0} }, /* 1.301e-17 */ +/**/ u22 = {{0x00000000, 0x3c527bd0} }, /* 4.008e-18 */ +/**/ u23 = {{0x00000000, 0x3c3cd057} }, /* 1.562e-18 */ +/**/ u24 = {{0x00000000, 0x3c329cdf} }, /* 1.009e-18 */ +/**/ u31 = {{0x00000000, 0x3c3a1edf} }, /* 1.416e-18 */ +/**/ u32 = {{0x00000000, 0x3c33f0e1} }, /* 1.081e-18 */ +/**/ u4 = {{0x00000000, 0x3bf955e4} }, /* 8.584e-20 */ +/**/ u5 = {{0x00000000, 0x3aaef2d1} }, /* 5e-26 */ +/**/ u6 = {{0x00000000, 0x3a98c56d} }, /* 2.001e-26 */ +/**/ u7 = {{0x00000000, 0x3a9375de} }, /* 1.572e-26 */ +/**/ u8 = {{0x00000000, 0x3a6eeb36} }, /* 3.122e-27 */ +/**/ u9[M] ={{{0x00000000, 0x38c1aa5b} }, /* 2.658e-35 */ +/**/ {{0x00000000, 0x35c1aa4d} }, /* 9.443e-50 */ +/**/ {{0x00000000, 0x32c1aa88} }, /* 3.355e-64 */ +/**/ {{0x00000000, 0x11c1aa56} }};/* 3.818e-223 */ + +#endif +#endif + +#define A a.d +#define B b.d +#define C c.d +#define D d.d +#define E e.d +#define HPI hpi.d +#define MHPI mhpi.d +#define HPI1 hpi1.d +#define U1 u1.d +#define U21 u21.d +#define U22 u22.d +#define U23 u23.d +#define U24 u24.d +#define U31 u31.d +#define U32 u32.d +#define U4 u4.d +#define U5 u5.d +#define U6 u6.d +#define U7 u7.d +#define U8 u8.d + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/atnat2.h b/REORG.TODO/sysdeps/ieee754/dbl-64/atnat2.h new file mode 100644 index 0000000000..27033b6ceb --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/atnat2.h @@ -0,0 +1,161 @@ + +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/************************************************************************/ +/* MODULE_NAME: atnat2.h */ +/* */ +/* */ +/* common data and variables definition for BIG or LITTLE ENDIAN */ +/************************************************************************/ + + + +#ifndef ATNAT2_H +#define ATNAT2_H + + +#define MM 5 +#ifdef BIG_ENDI + + static const number + /* polynomial I */ +/**/ d3 = {{0xbfd55555, 0x55555555} }, /* -0.333... */ +/**/ d5 = {{0x3fc99999, 0x999997fd} }, /* 0.199... */ +/**/ d7 = {{0xbfc24924, 0x923f7603} }, /* -0.142... */ +/**/ d9 = {{0x3fbc71c6, 0xe5129a3b} }, /* 0.111... */ +/**/ d11 = {{0xbfb74580, 0x22b13c25} }, /* -0.090... */ +/**/ d13 = {{0x3fb375f0, 0x8b31cbce} }, /* 0.076... */ + /* polynomial II */ +/**/ f3 = {{0xbfd55555, 0x55555555} }, /* -1/3 */ +/**/ ff3 = {{0xbc755555, 0x55555555} }, /* -1/3-f3 */ +/**/ f5 = {{0x3fc99999, 0x9999999a} }, /* 1/5 */ +/**/ ff5 = {{0xbc699999, 0x9999999a} }, /* 1/5-f5 */ +/**/ f7 = {{0xbfc24924, 0x92492492} }, /* -1/7 */ +/**/ ff7 = {{0xbc624924, 0x92492492} }, /* -1/7-f7 */ +/**/ f9 = {{0x3fbc71c7, 0x1c71c71c} }, /* 1/9 */ +/**/ ff9 = {{0x3c5c71c7, 0x1c71c71c} }, /* 1/9-f9 */ +/**/ f11 = {{0xbfb745d1, 0x745d1746} }, /* -1/11 */ +/**/ f13 = {{0x3fb3b13b, 0x13b13b14} }, /* 1/13 */ +/**/ f15 = {{0xbfb11111, 0x11111111} }, /* -1/15 */ +/**/ f17 = {{0x3fae1e1e, 0x1e1e1e1e} }, /* 1/17 */ +/**/ f19 = {{0xbfaaf286, 0xbca1af28} }, /* -1/19 */ + /* constants */ +/**/ inv16 = {{0x3fb00000, 0x00000000} }, /* 1/16 */ +/**/ opi = {{0x400921fb, 0x54442d18} }, /* pi */ +/**/ opi1 = {{0x3ca1a626, 0x33145c07} }, /* pi-opi */ +/**/ mopi = {{0xc00921fb, 0x54442d18} }, /* -pi */ +/**/ hpi = {{0x3ff921fb, 0x54442d18} }, /* pi/2 */ +/**/ hpi1 = {{0x3c91a626, 0x33145c07} }, /* pi/2-hpi */ +/**/ mhpi = {{0xbff921fb, 0x54442d18} }, /* -pi/2 */ +/**/ qpi = {{0x3fe921fb, 0x54442d18} }, /* pi/4 */ +/**/ mqpi = {{0xbfe921fb, 0x54442d18} }, /* -pi/4 */ +/**/ tqpi = {{0x4002d97c, 0x7f3321d2} }, /* 3pi/4 */ +/**/ mtqpi = {{0xc002d97c, 0x7f3321d2} }, /* -3pi/4 */ +/**/ u1 = {{0x3c314c2a, 0x00000000} }, /* 9.377e-19 */ +/**/ u2 = {{0x3bf955e4, 0x00000000} }, /* 8.584e-20 */ +/**/ u3 = {{0x3bf955e4, 0x00000000} }, /* 8.584e-20 */ +/**/ u4 = {{0x3bf955e4, 0x00000000} }, /* 8.584e-20 */ +/**/ u5 = {{0x3aaef2d1, 0x00000000} }, /* 5e-26 */ +/**/ u6 = {{0x3a6eeb36, 0x00000000} }, /* 3.122e-27 */ +/**/ u7 = {{0x3a6eeb36, 0x00000000} }, /* 3.122e-27 */ +/**/ u8 = {{0x3a6eeb36, 0x00000000} }, /* 3.122e-27 */ +/**/ u91 = {{0x3c6dffc0, 0x00000000} }, /* 1.301e-17 */ +/**/ u92 = {{0x3c527bd0, 0x00000000} }, /* 4.008e-18 */ +/**/ u93 = {{0x3c3cd057, 0x00000000} }, /* 1.562e-18 */ +/**/ u94 = {{0x3c329cdf, 0x00000000} }, /* 1.009e-18 */ +/**/ ua1 = {{0x3c3a1edf, 0x00000000} }, /* 1.416e-18 */ +/**/ ua2 = {{0x3c33f0e1, 0x00000000} }, /* 1.081e-18 */ +/**/ ub = {{0x3a98c56d, 0x00000000} }, /* 2.001e-26 */ +/**/ uc = {{0x3a9375de, 0x00000000} }, /* 1.572e-26 */ +/**/ ud[MM] ={{{0x38c6eddf, 0x00000000} }, /* 3.450e-35 */ +/**/ {{0x35c6ef60, 0x00000000} }, /* 1.226e-49 */ +/**/ {{0x32c6ed2f, 0x00000000} }, /* 4.354e-64 */ +/**/ {{0x23c6eee8, 0x00000000} }, /* 2.465e-136 */ +/**/ {{0x11c6ed16, 0x00000000} }},/* 4.955e-223 */ +/**/ ue = {{0x38900e9d, 0x00000000} }, /* 3.02e-36 */ +/**/ two500 = {{0x5f300000, 0x00000000} }, /* 2**500 */ +/**/ twom500 = {{0x20b00000, 0x00000000} }; /* 2**(-500) */ + +#else +#ifdef LITTLE_ENDI + + static const number + /* polynomial I */ +/**/ d3 = {{0x55555555, 0xbfd55555} }, /* -0.333... */ +/**/ d5 = {{0x999997fd, 0x3fc99999} }, /* 0.199... */ +/**/ d7 = {{0x923f7603, 0xbfc24924} }, /* -0.142... */ +/**/ d9 = {{0xe5129a3b, 0x3fbc71c6} }, /* 0.111... */ +/**/ d11 = {{0x22b13c25, 0xbfb74580} }, /* -0.090... */ +/**/ d13 = {{0x8b31cbce, 0x3fb375f0} }, /* 0.076... */ + /* polynomial II */ +/**/ f3 = {{0x55555555, 0xbfd55555} }, /* -1/3 */ +/**/ ff3 = {{0x55555555, 0xbc755555} }, /* -1/3-f3 */ +/**/ f5 = {{0x9999999a, 0x3fc99999} }, /* 1/5 */ +/**/ ff5 = {{0x9999999a, 0xbc699999} }, /* 1/5-f5 */ +/**/ f7 = {{0x92492492, 0xbfc24924} }, /* -1/7 */ +/**/ ff7 = {{0x92492492, 0xbc624924} }, /* -1/7-f7 */ +/**/ f9 = {{0x1c71c71c, 0x3fbc71c7} }, /* 1/9 */ +/**/ ff9 = {{0x1c71c71c, 0x3c5c71c7} }, /* 1/9-f9 */ +/**/ f11 = {{0x745d1746, 0xbfb745d1} }, /* -1/11 */ +/**/ f13 = {{0x13b13b14, 0x3fb3b13b} }, /* 1/13 */ +/**/ f15 = {{0x11111111, 0xbfb11111} }, /* -1/15 */ +/**/ f17 = {{0x1e1e1e1e, 0x3fae1e1e} }, /* 1/17 */ +/**/ f19 = {{0xbca1af28, 0xbfaaf286} }, /* -1/19 */ + /* constants */ +/**/ inv16 = {{0x00000000, 0x3fb00000} }, /* 1/16 */ +/**/ opi = {{0x54442d18, 0x400921fb} }, /* pi */ +/**/ opi1 = {{0x33145c07, 0x3ca1a626} }, /* pi-opi */ +/**/ mopi = {{0x54442d18, 0xc00921fb} }, /* -pi */ +/**/ hpi = {{0x54442d18, 0x3ff921fb} }, /* pi/2 */ +/**/ hpi1 = {{0x33145c07, 0x3c91a626} }, /* pi/2-hpi */ +/**/ mhpi = {{0x54442d18, 0xbff921fb} }, /* -pi/2 */ +/**/ qpi = {{0x54442d18, 0x3fe921fb} }, /* pi/4 */ +/**/ mqpi = {{0x54442d18, 0xbfe921fb} }, /* -pi/4 */ +/**/ tqpi = {{0x7f3321d2, 0x4002d97c} }, /* 3pi/4 */ +/**/ mtqpi = {{0x7f3321d2, 0xc002d97c} }, /* -3pi/4 */ +/**/ u1 = {{0x00000000, 0x3c314c2a} }, /* 9.377e-19 */ +/**/ u2 = {{0x00000000, 0x3bf955e4} }, /* 8.584e-20 */ +/**/ u3 = {{0x00000000, 0x3bf955e4} }, /* 8.584e-20 */ +/**/ u4 = {{0x00000000, 0x3bf955e4} }, /* 8.584e-20 */ +/**/ u5 = {{0x00000000, 0x3aaef2d1} }, /* 5e-26 */ +/**/ u6 = {{0x00000000, 0x3a6eeb36} }, /* 3.122e-27 */ +/**/ u7 = {{0x00000000, 0x3a6eeb36} }, /* 3.122e-27 */ +/**/ u8 = {{0x00000000, 0x3a6eeb36} }, /* 3.122e-27 */ +/**/ u91 = {{0x00000000, 0x3c6dffc0} }, /* 1.301e-17 */ +/**/ u92 = {{0x00000000, 0x3c527bd0} }, /* 4.008e-18 */ +/**/ u93 = {{0x00000000, 0x3c3cd057} }, /* 1.562e-18 */ +/**/ u94 = {{0x00000000, 0x3c329cdf} }, /* 1.009e-18 */ +/**/ ua1 = {{0x00000000, 0x3c3a1edf} }, /* 1.416e-18 */ +/**/ ua2 = {{0x00000000, 0x3c33f0e1} }, /* 1.081e-18 */ +/**/ ub = {{0x00000000, 0x3a98c56d} }, /* 2.001e-26 */ +/**/ uc = {{0x00000000, 0x3a9375de} }, /* 1.572e-26 */ +/**/ ud[MM] ={{{0x00000000, 0x38c6eddf} }, /* 3.450e-35 */ +/**/ {{0x00000000, 0x35c6ef60} }, /* 1.226e-49 */ +/**/ {{0x00000000, 0x32c6ed2f} }, /* 4.354e-64 */ +/**/ {{0x00000000, 0x23c6eee8} }, /* 2.465e-136 */ +/**/ {{0x00000000, 0x11c6ed16} }},/* 4.955e-223 */ +/**/ ue = {{0x00000000, 0x38900e9d} }, /* 3.02e-36 */ +/**/ two500 = {{0x00000000, 0x5f300000} }, /* 2**500 */ +/**/ twom500 = {{0x00000000, 0x20b00000} }; /* 2**(-500) */ + +#endif +#endif + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/branred.c b/REORG.TODO/sysdeps/ieee754/dbl-64/branred.c new file mode 100644 index 0000000000..30ae9c79e2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/branred.c @@ -0,0 +1,144 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/*******************************************************************/ +/* */ +/* MODULE_NAME: branred.c */ +/* */ +/* FUNCTIONS: branred */ +/* */ +/* FILES NEEDED: branred.h mydefs.h endian.h mpa.h */ +/* mha.c */ +/* */ +/* Routine branred() performs range reduction of a double number */ +/* x into Double length number a+aa,such that */ +/* x=n*pi/2+(a+aa), abs(a+aa)<pi/4, n=0,+-1,+-2,.... */ +/* Routine returns the integer (n mod 4) of the above description */ +/* of x. */ +/*******************************************************************/ + +#include "endian.h" +#include "mydefs.h" +#include "branred.h" +#include <math.h> +#include <math_private.h> + +#ifndef SECTION +# define SECTION +#endif + + +/*******************************************************************/ +/* Routine branred() performs range reduction of a double number */ +/* x into Double length number a+aa,such that */ +/* x=n*pi/2+(a+aa), abs(a+aa)<pi/4, n=0,+-1,+-2,.... */ +/* Routine return integer (n mod 4) */ +/*******************************************************************/ +int +SECTION +__branred(double x, double *a, double *aa) +{ + int i,k; + mynumber u,gor; + double r[6],s,t,sum,b,bb,sum1,sum2,b1,bb1,b2,bb2,x1,x2,t1,t2; + + x*=tm600.x; + t=x*split; /* split x to two numbers */ + x1=t-(t-x); + x2=x-x1; + sum=0; + u.x = x1; + k = (u.i[HIGH_HALF]>>20)&2047; + k = (k-450)/24; + if (k<0) + k=0; + gor.x = t576.x; + gor.i[HIGH_HALF] -= ((k*24)<<20); + for (i=0;i<6;i++) + { r[i] = x1*toverp[k+i]*gor.x; gor.x *= tm24.x; } + for (i=0;i<3;i++) { + s=(r[i]+big.x)-big.x; + sum+=s; + r[i]-=s; + } + t=0; + for (i=0;i<6;i++) + t+=r[5-i]; + bb=(((((r[0]-t)+r[1])+r[2])+r[3])+r[4])+r[5]; + s=(t+big.x)-big.x; + sum+=s; + t-=s; + b=t+bb; + bb=(t-b)+bb; + s=(sum+big1.x)-big1.x; + sum-=s; + b1=b; + bb1=bb; + sum1=sum; + sum=0; + + u.x = x2; + k = (u.i[HIGH_HALF]>>20)&2047; + k = (k-450)/24; + if (k<0) + k=0; + gor.x = t576.x; + gor.i[HIGH_HALF] -= ((k*24)<<20); + for (i=0;i<6;i++) + { r[i] = x2*toverp[k+i]*gor.x; gor.x *= tm24.x; } + for (i=0;i<3;i++) { + s=(r[i]+big.x)-big.x; + sum+=s; + r[i]-=s; + } + t=0; + for (i=0;i<6;i++) + t+=r[5-i]; + bb=(((((r[0]-t)+r[1])+r[2])+r[3])+r[4])+r[5]; + s=(t+big.x)-big.x; + sum+=s; + t-=s; + b=t+bb; + bb=(t-b)+bb; + s=(sum+big1.x)-big1.x; + sum-=s; + + b2=b; + bb2=bb; + sum2=sum; + + sum=sum1+sum2; + b=b1+b2; + bb = (fabs(b1)>fabs(b2))? (b1-b)+b2 : (b2-b)+b1; + if (b > 0.5) + {b-=1.0; sum+=1.0;} + else if (b < -0.5) + {b+=1.0; sum-=1.0;} + s=b+(bb+bb1+bb2); + t=((b-s)+bb)+(bb1+bb2); + b=s*split; + t1=b-(b-s); + t2=s-t1; + b=s*hp0.x; + bb=(((t1*mp1.x-b)+t1*mp2.x)+t2*mp1.x)+(t2*mp2.x+s*hp1.x+t*hp0.x); + s=b+bb; + t=(b-s)+bb; + *a=s; + *aa=t; + return ((int) sum)&3; /* return quater of unit circle */ +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/branred.h b/REORG.TODO/sysdeps/ieee754/dbl-64/branred.h new file mode 100644 index 0000000000..c3fd7dd27b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/branred.h @@ -0,0 +1,80 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/************************************************************************/ +/* MODULE_NAME: branred.h */ +/* */ +/* */ +/* common data and variables definition for BIG or LITTLE ENDIAN */ +/************************************************************************/ + +#ifndef BRANRED_H +#define BRANRED_H + +#include <dla.h> + +#ifdef BIG_ENDI +static const mynumber + +/**/ t576 = {{0x63f00000, 0x00000000}}, /* 2 ^ 576 */ +/**/ tm600 = {{0x1a700000, 0x00000000}}, /* 2 ^- 600 */ +/**/ tm24 = {{0x3e700000, 0x00000000}}, /* 2 ^- 24 */ +/**/ big = {{0x43380000, 0x00000000}}, /* 6755399441055744 */ +/**/ big1 = {{0x43580000, 0x00000000}}, /* 27021597764222976 */ +/**/ hp0 = {{0x3FF921FB, 0x54442D18}} ,/* 1.5707963267948966 */ +/**/ hp1 = {{0x3C91A626, 0x33145C07}} ,/* 6.123233995736766e-17 */ +/**/ mp1 = {{0x3FF921FB, 0x58000000}}, /* 1.5707963407039642 */ +/**/ mp2 = {{0xBE4DDE97, 0x40000000}}; /*-1.3909067675399456e-08 */ + +#else +#ifdef LITTLE_ENDI +static const mynumber + +/**/ t576 = {{0x00000000, 0x63f00000}}, /* 2 ^ 576 */ +/**/ tm600 = {{0x00000000, 0x1a700000}}, /* 2 ^- 600 */ +/**/ tm24 = {{0x00000000, 0x3e700000}}, /* 2 ^- 24 */ +/**/ big = {{0x00000000, 0x43380000}}, /* 6755399441055744 */ +/**/ big1 = {{0x00000000, 0x43580000}}, /* 27021597764222976 */ +/**/ hp0 = {{0x54442D18, 0x3FF921FB}}, /* 1.5707963267948966 */ +/**/ hp1 = {{0x33145C07, 0x3C91A626}}, /* 6.123233995736766e-17 */ +/**/ mp1 = {{0x58000000, 0x3FF921FB}}, /* 1.5707963407039642 */ +/**/ mp2 = {{0x40000000, 0xBE4DDE97}}; /*-1.3909067675399456e-08 */ + +#endif +#endif + +static const double toverp[75] = { /* 2/ PI base 24*/ + 10680707.0, 7228996.0, 1387004.0, 2578385.0, 16069853.0, + 12639074.0, 9804092.0, 4427841.0, 16666979.0, 11263675.0, + 12935607.0, 2387514.0, 4345298.0, 14681673.0, 3074569.0, + 13734428.0, 16653803.0, 1880361.0, 10960616.0, 8533493.0, + 3062596.0, 8710556.0, 7349940.0, 6258241.0, 3772886.0, + 3769171.0, 3798172.0, 8675211.0, 12450088.0, 3874808.0, + 9961438.0, 366607.0, 15675153.0, 9132554.0, 7151469.0, + 3571407.0, 2607881.0, 12013382.0, 4155038.0, 6285869.0, + 7677882.0, 13102053.0, 15825725.0, 473591.0, 9065106.0, + 15363067.0, 6271263.0, 9264392.0, 5636912.0, 4652155.0, + 7056368.0, 13614112.0, 10155062.0, 1944035.0, 9527646.0, + 15080200.0, 6658437.0, 6231200.0, 6832269.0, 16767104.0, + 5075751.0, 3212806.0, 1398474.0, 7579849.0, 6349435.0, + 12618859.0, 4703257.0, 12806093.0, 14477321.0, 2786137.0, + 12875403.0, 9837734.0, 14528324.0, 13719321.0, 343717.0 }; + +static const double split = CN; /* 2^27 + 1 */ + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/dbl2mpn.c b/REORG.TODO/sysdeps/ieee754/dbl-64/dbl2mpn.c new file mode 100644 index 0000000000..8294dc26ed --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/dbl2mpn.c @@ -0,0 +1,107 @@ +/* Copyright (C) 1993-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "gmp.h" +#include "gmp-impl.h" +#include "longlong.h" +#include <ieee754.h> +#include <float.h> +#include <stdlib.h> + +/* Convert a `double' in IEEE754 standard double-precision format to a + multi-precision integer representing the significand scaled up by its + number of bits (52 for double) and an integral power of two (MPN frexp). */ + +mp_size_t +__mpn_extract_double (mp_ptr res_ptr, mp_size_t size, + int *expt, int *is_neg, + double value) +{ + union ieee754_double u; + u.d = value; + + *is_neg = u.ieee.negative; + *expt = (int) u.ieee.exponent - IEEE754_DOUBLE_BIAS; + +#if BITS_PER_MP_LIMB == 32 + res_ptr[0] = u.ieee.mantissa1; /* Low-order 32 bits of fraction. */ + res_ptr[1] = u.ieee.mantissa0; /* High-order 20 bits. */ + # define N 2 +#elif BITS_PER_MP_LIMB == 64 + /* Hopefully the compiler will combine the two bitfield extracts + and this composition into just the original quadword extract. */ + res_ptr[0] = ((mp_limb_t) u.ieee.mantissa0 << 32) | u.ieee.mantissa1; + # define N 1 +#else + # error "mp_limb size " BITS_PER_MP_LIMB "not accounted for" +#endif +/* The format does not fill the last limb. There are some zeros. */ +#define NUM_LEADING_ZEROS (BITS_PER_MP_LIMB \ + - (DBL_MANT_DIG - ((N - 1) * BITS_PER_MP_LIMB))) + + if (u.ieee.exponent == 0) + { + /* A biased exponent of zero is a special case. + Either it is a zero or it is a denormal number. */ + if (res_ptr[0] == 0 && res_ptr[N - 1] == 0) /* Assumes N<=2. */ + /* It's zero. */ + *expt = 0; + else + { + /* It is a denormal number, meaning it has no implicit leading + one bit, and its exponent is in fact the format minimum. */ + int cnt; + + if (res_ptr[N - 1] != 0) + { + count_leading_zeros (cnt, res_ptr[N - 1]); + cnt -= NUM_LEADING_ZEROS; +#if N == 2 + res_ptr[N - 1] = res_ptr[1] << cnt + | (N - 1) + * (res_ptr[0] >> (BITS_PER_MP_LIMB - cnt)); + res_ptr[0] <<= cnt; +#else + res_ptr[N - 1] <<= cnt; +#endif + *expt = DBL_MIN_EXP - 1 - cnt; + } + else + { + count_leading_zeros (cnt, res_ptr[0]); + if (cnt >= NUM_LEADING_ZEROS) + { + res_ptr[N - 1] = res_ptr[0] << (cnt - NUM_LEADING_ZEROS); + res_ptr[0] = 0; + } + else + { + res_ptr[N - 1] = res_ptr[0] >> (NUM_LEADING_ZEROS - cnt); + res_ptr[0] <<= BITS_PER_MP_LIMB - (NUM_LEADING_ZEROS - cnt); + } + *expt = DBL_MIN_EXP - 1 + - (BITS_PER_MP_LIMB - NUM_LEADING_ZEROS) - cnt; + } + } + } + else + /* Add the implicit leading one bit for a normalized number. */ + res_ptr[N - 1] |= (mp_limb_t) 1 << (DBL_MANT_DIG - 1 + - ((N - 1) * BITS_PER_MP_LIMB)); + + return N; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/dla.h b/REORG.TODO/sysdeps/ieee754/dbl-64/dla.h new file mode 100644 index 0000000000..88e8ffb1ca --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/dla.h @@ -0,0 +1,183 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +#include <math.h> + +/***********************************************************************/ +/*MODULE_NAME: dla.h */ +/* */ +/* This file holds C language macros for 'Double Length Floating Point */ +/* Arithmetic'. The macros are based on the paper: */ +/* T.J.Dekker, "A floating-point Technique for extending the */ +/* Available Precision", Number. Math. 18, 224-242 (1971). */ +/* A Double-Length number is defined by a pair (r,s), of IEEE double */ +/* precision floating point numbers that satisfy, */ +/* */ +/* abs(s) <= abs(r+s)*2**(-53)/(1+2**(-53)). */ +/* */ +/* The computer arithmetic assumed is IEEE double precision in */ +/* round to nearest mode. All variables in the macros must be of type */ +/* IEEE double. */ +/***********************************************************************/ + +/* CN = 1+2**27 = '41a0000002000000' IEEE double format. Use it to split a + double for better accuracy. */ +#define CN 134217729.0 + + +/* Exact addition of two single-length floating point numbers, Dekker. */ +/* The macro produces a double-length number (z,zz) that satisfies */ +/* z+zz = x+y exactly. */ + +#define EADD(x,y,z,zz) \ + z=(x)+(y); zz=(fabs(x)>fabs(y)) ? (((x)-(z))+(y)) : (((y)-(z))+(x)); + + +/* Exact subtraction of two single-length floating point numbers, Dekker. */ +/* The macro produces a double-length number (z,zz) that satisfies */ +/* z+zz = x-y exactly. */ + +#define ESUB(x,y,z,zz) \ + z=(x)-(y); zz=(fabs(x)>fabs(y)) ? (((x)-(z))-(y)) : ((x)-((y)+(z))); + + +#ifdef __FP_FAST_FMA +# define DLA_FMS(x, y, z) __builtin_fma (x, y, -(z)) +#endif + +/* Exact multiplication of two single-length floating point numbers, */ +/* Veltkamp. The macro produces a double-length number (z,zz) that */ +/* satisfies z+zz = x*y exactly. p,hx,tx,hy,ty are temporary */ +/* storage variables of type double. */ + +#ifdef DLA_FMS +# define EMULV(x, y, z, zz, p, hx, tx, hy, ty) \ + z = x * y; zz = DLA_FMS (x, y, z); +#else +# define EMULV(x, y, z, zz, p, hx, tx, hy, ty) \ + p = CN * (x); hx = ((x) - p) + p; tx = (x) - hx; \ + p = CN * (y); hy = ((y) - p) + p; ty = (y) - hy; \ + z = (x) * (y); zz = (((hx * hy - z) + hx * ty) + tx * hy) + tx * ty; +#endif + + +/* Exact multiplication of two single-length floating point numbers, Dekker. */ +/* The macro produces a nearly double-length number (z,zz) (see Dekker) */ +/* that satisfies z+zz = x*y exactly. p,hx,tx,hy,ty,q are temporary */ +/* storage variables of type double. */ + +#ifdef DLA_FMS +# define MUL12(x,y,z,zz,p,hx,tx,hy,ty,q) \ + EMULV(x,y,z,zz,p,hx,tx,hy,ty) +#else +# define MUL12(x,y,z,zz,p,hx,tx,hy,ty,q) \ + p=CN*(x); hx=((x)-p)+p; tx=(x)-hx; \ + p=CN*(y); hy=((y)-p)+p; ty=(y)-hy; \ + p=hx*hy; q=hx*ty+tx*hy; z=p+q; zz=((p-z)+q)+tx*ty; +#endif + + +/* Double-length addition, Dekker. The macro produces a double-length */ +/* number (z,zz) which satisfies approximately z+zz = x+xx + y+yy. */ +/* An error bound: (abs(x+xx)+abs(y+yy))*4.94e-32. (x,xx), (y,yy) */ +/* are assumed to be double-length numbers. r,s are temporary */ +/* storage variables of type double. */ + +#define ADD2(x, xx, y, yy, z, zz, r, s) \ + r = (x) + (y); s = (fabs (x) > fabs (y)) ? \ + (((((x) - r) + (y)) + (yy)) + (xx)) : \ + (((((y) - r) + (x)) + (xx)) + (yy)); \ + z = r + s; zz = (r - z) + s; + + +/* Double-length subtraction, Dekker. The macro produces a double-length */ +/* number (z,zz) which satisfies approximately z+zz = x+xx - (y+yy). */ +/* An error bound: (abs(x+xx)+abs(y+yy))*4.94e-32. (x,xx), (y,yy) */ +/* are assumed to be double-length numbers. r,s are temporary */ +/* storage variables of type double. */ + +#define SUB2(x, xx, y, yy, z, zz, r, s) \ + r = (x) - (y); s = (fabs (x) > fabs (y)) ? \ + (((((x) - r) - (y)) - (yy)) + (xx)) : \ + ((((x) - ((y) + r)) + (xx)) - (yy)); \ + z = r + s; zz = (r - z) + s; + + +/* Double-length multiplication, Dekker. The macro produces a double-length */ +/* number (z,zz) which satisfies approximately z+zz = (x+xx)*(y+yy). */ +/* An error bound: abs((x+xx)*(y+yy))*1.24e-31. (x,xx), (y,yy) */ +/* are assumed to be double-length numbers. p,hx,tx,hy,ty,q,c,cc are */ +/* temporary storage variables of type double. */ + +#define MUL2(x, xx, y, yy, z, zz, p, hx, tx, hy, ty, q, c, cc) \ + MUL12 (x, y, c, cc, p, hx, tx, hy, ty, q) \ + cc = ((x) * (yy) + (xx) * (y)) + cc; z = c + cc; zz = (c - z) + cc; + + +/* Double-length division, Dekker. The macro produces a double-length */ +/* number (z,zz) which satisfies approximately z+zz = (x+xx)/(y+yy). */ +/* An error bound: abs((x+xx)/(y+yy))*1.50e-31. (x,xx), (y,yy) */ +/* are assumed to be double-length numbers. p,hx,tx,hy,ty,q,c,cc,u,uu */ +/* are temporary storage variables of type double. */ + +#define DIV2(x,xx,y,yy,z,zz,p,hx,tx,hy,ty,q,c,cc,u,uu) \ + c=(x)/(y); MUL12(c,y,u,uu,p,hx,tx,hy,ty,q) \ + cc=(((((x)-u)-uu)+(xx))-c*(yy))/(y); z=c+cc; zz=(c-z)+cc; + + +/* Double-length addition, slower but more accurate than ADD2. */ +/* The macro produces a double-length */ +/* number (z,zz) which satisfies approximately z+zz = (x+xx)+(y+yy). */ +/* An error bound: abs(x+xx + y+yy)*1.50e-31. (x,xx), (y,yy) */ +/* are assumed to be double-length numbers. r,rr,s,ss,u,uu,w */ +/* are temporary storage variables of type double. */ + +#define ADD2A(x, xx, y, yy, z, zz, r, rr, s, ss, u, uu, w) \ + r = (x) + (y); \ + if (fabs (x) > fabs (y)) { rr = ((x) - r) + (y); s = (rr + (yy)) + (xx); } \ + else { rr = ((y) - r) + (x); s = (rr + (xx)) + (yy); } \ + if (rr != 0.0) { \ + z = r + s; zz = (r - z) + s; } \ + else { \ + ss = (fabs (xx) > fabs (yy)) ? (((xx) - s) + (yy)) : (((yy) - s) + (xx));\ + u = r + s; \ + uu = (fabs (r) > fabs (s)) ? ((r - u) + s) : ((s - u) + r); \ + w = uu + ss; z = u + w; \ + zz = (fabs (u) > fabs (w)) ? ((u - z) + w) : ((w - z) + u); } + + +/* Double-length subtraction, slower but more accurate than SUB2. */ +/* The macro produces a double-length */ +/* number (z,zz) which satisfies approximately z+zz = (x+xx)-(y+yy). */ +/* An error bound: abs(x+xx - (y+yy))*1.50e-31. (x,xx), (y,yy) */ +/* are assumed to be double-length numbers. r,rr,s,ss,u,uu,w */ +/* are temporary storage variables of type double. */ + +#define SUB2A(x, xx, y, yy, z, zz, r, rr, s, ss, u, uu, w) \ + r = (x) - (y); \ + if (fabs (x) > fabs (y)) { rr = ((x) - r) - (y); s = (rr - (yy)) + (xx); } \ + else { rr = (x) - ((y) + r); s = (rr + (xx)) - (yy); } \ + if (rr != 0.0) { \ + z = r + s; zz = (r - z) + s; } \ + else { \ + ss = (fabs (xx) > fabs (yy)) ? (((xx) - s) - (yy)) : ((xx) - ((yy) + s)); \ + u = r + s; \ + uu = (fabs (r) > fabs (s)) ? ((r - u) + s) : ((s - u) + r); \ + w = uu + ss; z = u + w; \ + zz = (fabs (u) > fabs (w)) ? ((u - z) + w) : ((w - z) + u); } diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/doasin.c b/REORG.TODO/sysdeps/ieee754/dbl-64/doasin.c new file mode 100644 index 0000000000..7c2f3c3dc2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/doasin.c @@ -0,0 +1,84 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/**********************************************************************/ +/* MODULE_NAME: doasin.c */ +/* */ +/* FUNCTION: doasin */ +/* */ +/* FILES NEEDED:endian.h mydefs.h dla.h doasin.h */ +/* mpa.c */ +/* */ +/* Compute arcsin(x,dx,v) of double-length number (x+dx) the result */ +/* stored in v where v= v[0]+v[1] =arcsin(x+dx) */ +/**********************************************************************/ + +#include "endian.h" +#include "mydefs.h" +#include <dla.h> +#include <math_private.h> + +#ifndef SECTION +# define SECTION +#endif + +/********************************************************************/ +/* Compute arcsin(x,dx,v) of double-length number (x+dx) the result */ +/* stored in v where v= v[0]+v[1] =arcsin(x+dx) */ +/********************************************************************/ +void +SECTION +__doasin(double x, double dx, double v[]) { + +#include "doasin.h" + + static const double + d5 = 0.22372159090911789889975459505194491E-01, + d6 = 0.17352764422456822913014975683014622E-01, + d7 = 0.13964843843786693521653681033981614E-01, + d8 = 0.11551791438485242609036067259086589E-01, + d9 = 0.97622386568166960207425666787248914E-02, + d10 = 0.83638737193775788576092749009744976E-02, + d11 = 0.79470250400727425881446981833568758E-02; + + double xx,p,pp,u,uu,r,s; + double tc,tcc; +#ifndef DLA_FMS + double hx,tx,hy,ty,tp,tq; +#endif + + +/* Taylor series for arcsin for Double-Length numbers */ + xx = x*x+2.0*x*dx; + p = ((((((d11*xx+d10)*xx+d9)*xx+d8)*xx+d7)*xx+d6)*xx+d5)*xx; + pp = 0; + + MUL2(x,dx,x,dx,u,uu,tp,hx,tx,hy,ty,tq,tc,tcc); + ADD2(p,pp,c4.x,cc4.x,p,pp,r,s); + MUL2(p,pp,u,uu,p,pp,tp,hx,tx,hy,ty,tq,tc,tcc); + ADD2(p,pp,c3.x,cc3.x,p,pp,r,s); + MUL2(p,pp,u,uu,p,pp,tp,hx,tx,hy,ty,tq,tc,tcc); + ADD2(p,pp,c2.x,cc2.x,p,pp,r,s); + MUL2(p,pp,u,uu,p,pp,tp,hx,tx,hy,ty,tq,tc,tcc); + ADD2(p,pp,c1.x,cc1.x,p,pp,r,s); + MUL2(p,pp,u,uu,p,pp,tp,hx,tx,hy,ty,tq,tc,tcc); + MUL2(p,pp,x,dx,p,pp,tp,hx,tx,hy,ty,tq,tc,tcc); + ADD2(p,pp,x,dx,p,pp,r,s); + v[0]=p; + v[1]=pp; /* arcsin(x+dx)=v[0]+v[1] */ +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/doasin.h b/REORG.TODO/sysdeps/ieee754/dbl-64/doasin.h new file mode 100644 index 0000000000..c6b64597fb --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/doasin.h @@ -0,0 +1,63 @@ + +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/************************************************************************/ +/* MODULE_NAME: doasin.h */ +/* */ +/* */ +/* common data and variables definition for BIG or LITTLE ENDIAN */ +/************************************************************************/ + + + +#ifndef DOASIN_H +#define DOASIN_H + +#ifdef BIG_ENDI + + static const mynumber +/**/ c1 = {{0x3FC55555, 0x55555555}}, /* 0.16666666666666666 */ +/**/ cc1 = {{0x3C655555, 0x55775389}}, /* 9.2518585419753846e-18 */ +/**/ c2 = {{0x3FB33333, 0x33333333}}, /* 0.074999999999999997 */ +/**/ cc2 = {{0x3C499993, 0x63F1A115}}, /* 2.7755472886508899e-18 */ +/**/ c3 = {{0x3FA6DB6D, 0xB6DB6DB7}}, /* 0.044642857142857144 */ +/**/ cc3 = {{0xBC320FC0, 0x3D5CF0C5}}, /* -9.7911734574147224e-19 */ +/**/ c4 = {{0x3F9F1C71, 0xC71C71C5}}, /* 0.030381944444444437 */ +/**/ cc4 = {{0xBC02B240, 0xFF23ED1E}}; /* -1.2669108566898312e-19 */ + +#else +#ifdef LITTLE_ENDI + + static const mynumber +/**/ c1 = {{0x55555555, 0x3FC55555}}, /* 0.16666666666666666 */ +/**/ cc1 = {{0x55775389, 0x3C655555}}, /* 9.2518585419753846e-18 */ +/**/ c2 = {{0x33333333, 0x3FB33333}}, /* 0.074999999999999997 */ +/**/ cc2 = {{0x63F1A115, 0x3C499993}}, /* 2.7755472886508899e-18 */ +/**/ c3 = {{0xB6DB6DB7, 0x3FA6DB6D}}, /* 0.044642857142857144 */ +/**/ cc3 = {{0x3D5CF0C5, 0xBC320FC0}}, /* -9.7911734574147224e-19 */ +/**/ c4 = {{0xC71C71C5, 0x3F9F1C71}}, /* 0.030381944444444437 */ +/**/ cc4 = {{0xFF23ED1E, 0xBC02B240}}; /* -1.2669108566898312e-19 */ + + +#endif +#endif + + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/dosincos.c b/REORG.TODO/sysdeps/ieee754/dbl-64/dosincos.c new file mode 100644 index 0000000000..372872b42b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/dosincos.c @@ -0,0 +1,223 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/********************************************************************/ +/* */ +/* MODULE_NAME: dosincos.c */ +/* */ +/* */ +/* FUNCTIONS: dubsin */ +/* dubcos */ +/* docos */ +/* FILES NEEDED: endian.h mydefs.h dla.h dosincos.h */ +/* sincos.tbl */ +/* */ +/* Routines compute sin() and cos() as Double-Length numbers */ +/********************************************************************/ + + + +#include "endian.h" +#include "mydefs.h" +#include <dla.h> +#include "dosincos.h" +#include <math_private.h> + +#ifndef SECTION +# define SECTION +#endif + +extern const union +{ + int4 i[880]; + double x[440]; +} __sincostab attribute_hidden; + +/***********************************************************************/ +/* Routine receive Double-Length number (x+dx) and computing sin(x+dx) */ +/* as Double-Length number and store it at array v .It computes it by */ +/* arithmetic action on Double-Length numbers */ +/*(x+dx) between 0 and PI/4 */ +/***********************************************************************/ + +void +SECTION +__dubsin (double x, double dx, double v[]) +{ + double r, s, c, cc, d, dd, d2, dd2, e, ee, + sn, ssn, cs, ccs, ds, dss, dc, dcc; +#ifndef DLA_FMS + double p, hx, tx, hy, ty, q; +#endif + mynumber u; + int4 k; + + u.x = x + big.x; + k = u.i[LOW_HALF] << 2; + x = x - (u.x - big.x); + d = x + dx; + dd = (x - d) + dx; + /* sin(x+dx)=sin(Xi+t)=sin(Xi)*cos(t) + cos(Xi)sin(t) where t ->0 */ + MUL2 (d, dd, d, dd, d2, dd2, p, hx, tx, hy, ty, q, c, cc); + sn = __sincostab.x[k]; /* */ + ssn = __sincostab.x[k + 1]; /* sin(Xi) and cos(Xi) */ + cs = __sincostab.x[k + 2]; /* */ + ccs = __sincostab.x[k + 3]; /* */ + /* Taylor series for sin ds=sin(t) */ + MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, s5.x, ss5.x, ds, dss, r, s); + MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, s3.x, ss3.x, ds, dss, r, s); + MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + MUL2 (d, dd, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, d, dd, ds, dss, r, s); + + /* Taylor series for cos dc=cos(t) */ + MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c6.x, cc6.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c4.x, cc4.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c2.x, cc2.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + + MUL2 (cs, ccs, ds, dss, e, ee, p, hx, tx, hy, ty, q, c, cc); + MUL2 (dc, dcc, sn, ssn, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + SUB2 (e, ee, dc, dcc, e, ee, r, s); + ADD2 (e, ee, sn, ssn, e, ee, r, s); /* e+ee=sin(x+dx) */ + + v[0] = e; + v[1] = ee; +} +/**********************************************************************/ +/* Routine receive Double-Length number (x+dx) and computes cos(x+dx) */ +/* as Double-Length number and store it in array v .It computes it by */ +/* arithmetic action on Double-Length numbers */ +/*(x+dx) between 0 and PI/4 */ +/**********************************************************************/ + +void +SECTION +__dubcos (double x, double dx, double v[]) +{ + double r, s, c, cc, d, dd, d2, dd2, e, ee, + sn, ssn, cs, ccs, ds, dss, dc, dcc; +#ifndef DLA_FMS + double p, hx, tx, hy, ty, q; +#endif + mynumber u; + int4 k; + u.x = x + big.x; + k = u.i[LOW_HALF] << 2; + x = x - (u.x - big.x); + d = x + dx; + dd = (x - d) + dx; /* cos(x+dx)=cos(Xi+t)=cos(Xi)cos(t) - sin(Xi)sin(t) */ + MUL2 (d, dd, d, dd, d2, dd2, p, hx, tx, hy, ty, q, c, cc); + sn = __sincostab.x[k]; /* */ + ssn = __sincostab.x[k + 1]; /* sin(Xi) and cos(Xi) */ + cs = __sincostab.x[k + 2]; /* */ + ccs = __sincostab.x[k + 3]; /* */ + MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, s5.x, ss5.x, ds, dss, r, s); + MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, s3.x, ss3.x, ds, dss, r, s); + MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + MUL2 (d, dd, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, d, dd, ds, dss, r, s); + + MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c6.x, cc6.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c4.x, cc4.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c2.x, cc2.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + + MUL2 (cs, ccs, ds, dss, e, ee, p, hx, tx, hy, ty, q, c, cc); + MUL2 (dc, dcc, sn, ssn, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + + MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, s5.x, ss5.x, ds, dss, r, s); + MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, s3.x, ss3.x, ds, dss, r, s); + MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + MUL2 (d, dd, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, d, dd, ds, dss, r, s); + MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c6.x, cc6.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c4.x, cc4.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c2.x, cc2.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + MUL2 (sn, ssn, ds, dss, e, ee, p, hx, tx, hy, ty, q, c, cc); + MUL2 (dc, dcc, cs, ccs, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (e, ee, dc, dcc, e, ee, r, s); + SUB2 (cs, ccs, e, ee, e, ee, r, s); + + v[0] = e; + v[1] = ee; +} +/**********************************************************************/ +/* Routine receive Double-Length number (x+dx) and computes cos(x+dx) */ +/* as Double-Length number and store it in array v */ +/**********************************************************************/ +void +SECTION +__docos (double x, double dx, double v[]) +{ + double y, yy, p, w[2]; + if (x > 0) + { + y = x; yy = dx; + } + else + { + y = -x; yy = -dx; + } + if (y < 0.5 * hp0.x) /* y< PI/4 */ + { + __dubcos (y, yy, w); v[0] = w[0]; v[1] = w[1]; + } + else if (y < 1.5 * hp0.x) /* y< 3/4 * PI */ + { + p = hp0.x - y; /* p = PI/2 - y */ + yy = hp1.x - yy; + y = p + yy; + yy = (p - y) + yy; + if (y > 0) + { + __dubsin (y, yy, w); v[0] = w[0]; v[1] = w[1]; + } + /* cos(x) = sin ( 90 - x ) */ + else + { + __dubsin (-y, -yy, w); v[0] = -w[0]; v[1] = -w[1]; + } + } + else /* y>= 3/4 * PI */ + { + p = 2.0 * hp0.x - y; /* p = PI- y */ + yy = 2.0 * hp1.x - yy; + y = p + yy; + yy = (p - y) + yy; + __dubcos (y, yy, w); + v[0] = -w[0]; + v[1] = -w[1]; + } +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/dosincos.h b/REORG.TODO/sysdeps/ieee754/dbl-64/dosincos.h new file mode 100644 index 0000000000..9fda3d77cc --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/dosincos.h @@ -0,0 +1,80 @@ + +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/************************************************************************/ +/* MODULE_NAME: dosincos.h */ +/* */ +/* */ +/* common data and variables definition for BIG or LITTLE ENDIAN */ +/************************************************************************/ + + + +#ifndef DOSINCOS_H +#define DOSINCOS_H + + +#ifdef BIG_ENDI +static const mynumber +/**/ s3 = {{0xBFC55555, 0x55555555}},/* -0.16666666666666666 */ +/**/ ss3 = {{0xBC6553AA, 0xE77EE482}},/* -9.2490366677784492e-18 */ +/**/ s5 = {{0x3F811111, 0x11110F15}},/* 0.008333333333332452 */ +/**/ ss5 = {{0xBC21AC06, 0xDA488820}},/* -4.7899996586987931e-19 */ +/**/ s7 = {{0xBF2A019F, 0x5816C78D}},/* -0.00019841261022928957 */ +/**/ ss7 = {{0x3BCDCEC9, 0x6A18BF2A}},/* 1.2624077757871259e-20 */ +/**/ c2 = {{0x3FE00000, 0x00000000}},/* 0.5 */ +/**/ cc2 = {{0xBA282FD8, 0x00000000}},/* -1.5264073330037701e-28 */ +/**/ c4 = {{0xBFA55555, 0x55555555}},/* -0.041666666666666664 */ +/**/ cc4 = {{0xBC4554BC, 0x2FFF257E}},/* -2.312711276085743e-18 */ +/**/ c6 = {{0x3F56C16C, 0x16C16A96}},/* 0.0013888888888888055 */ +/**/ cc6 = {{0xBBD2E846, 0xE6346F14}},/* -1.6015133010194884e-20 */ +/**/ c8 = {{0xBEFA019F, 0x821D5987}},/* -2.480157866754367e-05 */ +/**/ cc8 = {{0x3B7AB71E, 0x72FFE5CC}},/* 3.5357416224857556e-22 */ + +/**/ big = {{0x42c80000, 0x00000000}}, /* 52776558133248 */ + +/**/ hp0 = {{0x3FF921FB, 0x54442D18}}, /* PI / 2 */ +/**/ hp1 = {{0x3C91A626, 0x33145C07}}; /* 6.123233995736766e-17 */ +#else +#ifdef LITTLE_ENDI +static const mynumber +/**/ s3 = {{0x55555555, 0xBFC55555}},/* -0.16666666666666666 */ +/**/ ss3 = {{0xE77EE482, 0xBC6553AA}},/* -9.2490366677784492e-18 */ +/**/ s5 = {{0x11110F15, 0x3F811111}},/* 0.008333333333332452 */ +/**/ ss5 = {{0xDA488820, 0xBC21AC06}},/* -4.7899996586987931e-19 */ +/**/ s7 = {{0x5816C78D, 0xBF2A019F}},/* -0.00019841261022928957 */ +/**/ ss7 = {{0x6A18BF2A, 0x3BCDCEC9}},/* 1.2624077757871259e-20 */ +/**/ c2 = {{0x00000000, 0x3FE00000}},/* 0.5 */ +/**/ cc2 = {{0x00000000, 0xBA282FD8}},/* -1.5264073330037701e-28 */ +/**/ c4 = {{0x55555555, 0xBFA55555}},/* -0.041666666666666664 */ +/**/ cc4 = {{0x2FFF257E, 0xBC4554BC}},/* -2.312711276085743e-18 */ +/**/ c6 = {{0x16C16A96, 0x3F56C16C}},/* 0.0013888888888888055 */ +/**/ cc6 = {{0xE6346F14, 0xBBD2E846}},/* -1.6015133010194884e-20 */ +/**/ c8 = {{0x821D5987, 0xBEFA019F}},/* -2.480157866754367e-05 */ +/**/ cc8 = {{0x72FFE5CC, 0x3B7AB71E}},/* 3.5357416224857556e-22 */ + +/**/ big = {{0x00000000, 0x42c80000}}, /* 52776558133248 */ + +/**/ hp0 = {{0x54442D18, 0x3FF921FB}}, /* PI / 2 */ +/**/ hp1 = {{0x33145C07, 0x3C91A626}}; /* 6.123233995736766e-17 */ +#endif +#endif + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_acos.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_acos.c new file mode 100644 index 0000000000..8f7cd89249 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_acos.c @@ -0,0 +1 @@ +/* In e_asin.c */ diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_acosh.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_acosh.c new file mode 100644 index 0000000000..c1f3590f75 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_acosh.c @@ -0,0 +1,69 @@ +/* @(#)e_acosh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_acosh(x) + * Method : + * Based on + * acosh(x) = log [ x + sqrt(x*x-1) ] + * we have + * acosh(x) := log(x)+ln2, if x is large; else + * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else + * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. + * + * Special cases: + * acosh(x) is NaN with signal if x<1. + * acosh(NaN) is NaN without signal. + */ + +#include <math.h> +#include <math_private.h> + +static const double + one = 1.0, + ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ + +double +__ieee754_acosh (double x) +{ + double t; + int32_t hx; + u_int32_t lx; + EXTRACT_WORDS (hx, lx, x); + if (hx < 0x3ff00000) /* x < 1 */ + { + return (x - x) / (x - x); + } + else if (hx >= 0x41b00000) /* x > 2**28 */ + { + if (hx >= 0x7ff00000) /* x is inf of NaN */ + { + return x + x; + } + else + return __ieee754_log (x) + ln2; /* acosh(huge)=log(2x) */ + } + else if (((hx - 0x3ff00000) | lx) == 0) + { + return 0.0; /* acosh(1) = 0 */ + } + else if (hx > 0x40000000) /* 2**28 > x > 2 */ + { + t = x * x; + return __ieee754_log (2.0 * x - one / (x + __ieee754_sqrt (t - one))); + } + else /* 1<x<2 */ + { + t = x - one; + return __log1p (t + __ieee754_sqrt (2.0 * t + t * t)); + } +} +strong_alias (__ieee754_acosh, __acosh_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_asin.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_asin.c new file mode 100644 index 0000000000..9808f3981c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_asin.c @@ -0,0 +1,647 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/******************************************************************/ +/* MODULE_NAME:uasncs.c */ +/* */ +/* FUNCTIONS: uasin */ +/* uacos */ +/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h usncs.h */ +/* doasin.c sincos32.c dosincos.c mpa.c */ +/* sincos.tbl asincos.tbl powtwo.tbl root.tbl */ +/* */ +/* Ultimate asin/acos routines. Given an IEEE double machine */ +/* number x, compute the correctly rounded value of */ +/* arcsin(x)or arccos(x) according to the function called. */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round to nearest mode of IEEE 754 standard. */ +/* */ +/******************************************************************/ +#include "endian.h" +#include "mydefs.h" +#include "asincos.tbl" +#include "root.tbl" +#include "powtwo.tbl" +#include "MathLib.h" +#include "uasncs.h" +#include <float.h> +#include <math.h> +#include <math_private.h> + +#ifndef SECTION +# define SECTION +#endif + +void __doasin(double x, double dx, double w[]); +void __dubsin(double x, double dx, double v[]); +void __dubcos(double x, double dx, double v[]); +void __docos(double x, double dx, double v[]); +double __sin32(double x, double res, double res1); +double __cos32(double x, double res, double res1); + +/***************************************************************************/ +/* An ultimate asin routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of arcsin(x) */ +/***************************************************************************/ +double +SECTION +__ieee754_asin(double x){ + double x1,x2,xx,s1,s2,res1,p,t,res,r,cor,cc,y,c,z,w[2]; + mynumber u,v; + int4 k,m,n; + + u.x = x; + m = u.i[HIGH_HALF]; + k = 0x7fffffff&m; /* no sign */ + + if (k < 0x3e500000) + { + math_check_force_underflow (x); + return x; /* for x->0 => sin(x)=x */ + } + /*----------------------2^-26 <= |x| < 2^ -3 -----------------*/ + else + if (k < 0x3fc00000) { + x2 = x*x; + t = (((((f6*x2 + f5)*x2 + f4)*x2 + f3)*x2 + f2)*x2 + f1)*(x2*x); + res = x+t; /* res=arcsin(x) according to Taylor series */ + cor = (x-res)+t; + if (res == res+1.025*cor) return res; + else { + x1 = x+big; + xx = x*x; + x1 -= big; + x2 = x - x1; + p = x1*x1*x1; + s1 = a1.x*p; + s2 = ((((((c7*xx + c6)*xx + c5)*xx + c4)*xx + c3)*xx + c2)*xx*xx*x + + ((a1.x+a2.x)*x2*x2+ 0.5*x1*x)*x2) + a2.x*p; + res1 = x+s1; + s2 = ((x-res1)+s1)+s2; + res = res1+s2; + cor = (res1-res)+s2; + if (res == res+1.00014*cor) return res; + else { + __doasin(x,0,w); + if (w[0]==(w[0]+1.00000001*w[1])) return w[0]; + else { + y=fabs(x); + res=fabs(w[0]); + res1=fabs(w[0]+1.1*w[1]); + return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1); + } + } + } + } + /*---------------------0.125 <= |x| < 0.5 -----------------------------*/ + else if (k < 0x3fe00000) { + if (k<0x3fd00000) n = 11*((k&0x000fffff)>>15); + else n = 11*((k&0x000fffff)>>14)+352; + if (m>0) xx = x - asncs.x[n]; + else xx = -x - asncs.x[n]; + t = asncs.x[n+1]*xx; + p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+xx*(asncs.x[n+5] + +xx*asncs.x[n+6]))))+asncs.x[n+7]; + t+=p; + res =asncs.x[n+8] +t; + cor = (asncs.x[n+8]-res)+t; + if (res == res+1.05*cor) return (m>0)?res:-res; + else { + r=asncs.x[n+8]+xx*asncs.x[n+9]; + t=((asncs.x[n+8]-r)+xx*asncs.x[n+9])+(p+xx*asncs.x[n+10]); + res = r+t; + cor = (r-res)+t; + if (res == res+1.0005*cor) return (m>0)?res:-res; + else { + res1=res+1.1*cor; + z=0.5*(res1-res); + __dubsin(res,z,w); + z=(w[0]-fabs(x))+w[1]; + if (z>1.0e-27) return (m>0)?min(res,res1):-min(res,res1); + else if (z<-1.0e-27) return (m>0)?max(res,res1):-max(res,res1); + else { + y=fabs(x); + return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1); + } + } + } + } /* else if (k < 0x3fe00000) */ + /*-------------------- 0.5 <= |x| < 0.75 -----------------------------*/ + else + if (k < 0x3fe80000) { + n = 1056+((k&0x000fe000)>>11)*3; + if (m>0) xx = x - asncs.x[n]; + else xx = -x - asncs.x[n]; + t = asncs.x[n+1]*xx; + p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+xx*(asncs.x[n+5] + +xx*(asncs.x[n+6]+xx*asncs.x[n+7])))))+asncs.x[n+8]; + t+=p; + res =asncs.x[n+9] +t; + cor = (asncs.x[n+9]-res)+t; + if (res == res+1.01*cor) return (m>0)?res:-res; + else { + r=asncs.x[n+9]+xx*asncs.x[n+10]; + t=((asncs.x[n+9]-r)+xx*asncs.x[n+10])+(p+xx*asncs.x[n+11]); + res = r+t; + cor = (r-res)+t; + if (res == res+1.0005*cor) return (m>0)?res:-res; + else { + res1=res+1.1*cor; + z=0.5*(res1-res); + __dubsin(res,z,w); + z=(w[0]-fabs(x))+w[1]; + if (z>1.0e-27) return (m>0)?min(res,res1):-min(res,res1); + else if (z<-1.0e-27) return (m>0)?max(res,res1):-max(res,res1); + else { + y=fabs(x); + return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1); + } + } + } + } /* else if (k < 0x3fe80000) */ + /*--------------------- 0.75 <= |x|< 0.921875 ----------------------*/ + else + if (k < 0x3fed8000) { + n = 992+((k&0x000fe000)>>13)*13; + if (m>0) xx = x - asncs.x[n]; + else xx = -x - asncs.x[n]; + t = asncs.x[n+1]*xx; + p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+xx*(asncs.x[n+5] + +xx*(asncs.x[n+6]+xx*(asncs.x[n+7]+xx*asncs.x[n+8]))))))+asncs.x[n+9]; + t+=p; + res =asncs.x[n+10] +t; + cor = (asncs.x[n+10]-res)+t; + if (res == res+1.01*cor) return (m>0)?res:-res; + else { + r=asncs.x[n+10]+xx*asncs.x[n+11]; + t=((asncs.x[n+10]-r)+xx*asncs.x[n+11])+(p+xx*asncs.x[n+12]); + res = r+t; + cor = (r-res)+t; + if (res == res+1.0008*cor) return (m>0)?res:-res; + else { + res1=res+1.1*cor; + z=0.5*(res1-res); + y=hp0.x-res; + z=((hp0.x-y)-res)+(hp1.x-z); + __dubcos(y,z,w); + z=(w[0]-fabs(x))+w[1]; + if (z>1.0e-27) return (m>0)?min(res,res1):-min(res,res1); + else if (z<-1.0e-27) return (m>0)?max(res,res1):-max(res,res1); + else { + y=fabs(x); + return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1); + } + } + } + } /* else if (k < 0x3fed8000) */ + /*-------------------0.921875 <= |x| < 0.953125 ------------------------*/ + else + if (k < 0x3fee8000) { + n = 884+((k&0x000fe000)>>13)*14; + if (m>0) xx = x - asncs.x[n]; + else xx = -x - asncs.x[n]; + t = asncs.x[n+1]*xx; + p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+ + xx*(asncs.x[n+5]+xx*(asncs.x[n+6] + +xx*(asncs.x[n+7]+xx*(asncs.x[n+8]+ + xx*asncs.x[n+9])))))))+asncs.x[n+10]; + t+=p; + res =asncs.x[n+11] +t; + cor = (asncs.x[n+11]-res)+t; + if (res == res+1.01*cor) return (m>0)?res:-res; + else { + r=asncs.x[n+11]+xx*asncs.x[n+12]; + t=((asncs.x[n+11]-r)+xx*asncs.x[n+12])+(p+xx*asncs.x[n+13]); + res = r+t; + cor = (r-res)+t; + if (res == res+1.0007*cor) return (m>0)?res:-res; + else { + res1=res+1.1*cor; + z=0.5*(res1-res); + y=(hp0.x-res)-z; + z=y+hp1.x; + y=(y-z)+hp1.x; + __dubcos(z,y,w); + z=(w[0]-fabs(x))+w[1]; + if (z>1.0e-27) return (m>0)?min(res,res1):-min(res,res1); + else if (z<-1.0e-27) return (m>0)?max(res,res1):-max(res,res1); + else { + y=fabs(x); + return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1); + } + } + } + } /* else if (k < 0x3fee8000) */ + + /*--------------------0.953125 <= |x| < 0.96875 ------------------------*/ + else + if (k < 0x3fef0000) { + n = 768+((k&0x000fe000)>>13)*15; + if (m>0) xx = x - asncs.x[n]; + else xx = -x - asncs.x[n]; + t = asncs.x[n+1]*xx; + p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+ + xx*(asncs.x[n+5]+xx*(asncs.x[n+6] + +xx*(asncs.x[n+7]+xx*(asncs.x[n+8]+ + xx*(asncs.x[n+9]+xx*asncs.x[n+10]))))))))+asncs.x[n+11]; + t+=p; + res =asncs.x[n+12] +t; + cor = (asncs.x[n+12]-res)+t; + if (res == res+1.01*cor) return (m>0)?res:-res; + else { + r=asncs.x[n+12]+xx*asncs.x[n+13]; + t=((asncs.x[n+12]-r)+xx*asncs.x[n+13])+(p+xx*asncs.x[n+14]); + res = r+t; + cor = (r-res)+t; + if (res == res+1.0007*cor) return (m>0)?res:-res; + else { + res1=res+1.1*cor; + z=0.5*(res1-res); + y=(hp0.x-res)-z; + z=y+hp1.x; + y=(y-z)+hp1.x; + __dubcos(z,y,w); + z=(w[0]-fabs(x))+w[1]; + if (z>1.0e-27) return (m>0)?min(res,res1):-min(res,res1); + else if (z<-1.0e-27) return (m>0)?max(res,res1):-max(res,res1); + else { + y=fabs(x); + return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1); + } + } + } + } /* else if (k < 0x3fef0000) */ + /*--------------------0.96875 <= |x| < 1 --------------------------------*/ + else + if (k<0x3ff00000) { + z = 0.5*((m>0)?(1.0-x):(1.0+x)); + v.x=z; + k=v.i[HIGH_HALF]; + t=inroot[(k&0x001fffff)>>14]*powtwo[511-(k>>21)]; + r=1.0-t*t*z; + t = t*(rt0+r*(rt1+r*(rt2+r*rt3))); + c=t*z; + t=c*(1.5-0.5*t*c); + y=(c+t24)-t24; + cc = (z-y*y)/(t+y); + p=(((((f6*z+f5)*z+f4)*z+f3)*z+f2)*z+f1)*z; + cor = (hp1.x - 2.0*cc)-2.0*(y+cc)*p; + res1 = hp0.x - 2.0*y; + res =res1 + cor; + if (res == res+1.003*((res1-res)+cor)) return (m>0)?res:-res; + else { + c=y+cc; + cc=(y-c)+cc; + __doasin(c,cc,w); + res1=hp0.x-2.0*w[0]; + cor=((hp0.x-res1)-2.0*w[0])+(hp1.x-2.0*w[1]); + res = res1+cor; + cor = (res1-res)+cor; + if (res==(res+1.0000001*cor)) return (m>0)?res:-res; + else { + y=fabs(x); + res1=res+1.1*cor; + return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1); + } + } + } /* else if (k < 0x3ff00000) */ + /*---------------------------- |x|>=1 -------------------------------*/ + else if (k==0x3ff00000 && u.i[LOW_HALF]==0) return (m>0)?hp0.x:-hp0.x; + else + if (k>0x7ff00000 || (k == 0x7ff00000 && u.i[LOW_HALF] != 0)) return x + x; + else { + u.i[HIGH_HALF]=0x7ff00000; + v.i[HIGH_HALF]=0x7ff00000; + u.i[LOW_HALF]=0; + v.i[LOW_HALF]=0; + return u.x/v.x; /* NaN */ + } +} +#ifndef __ieee754_asin +strong_alias (__ieee754_asin, __asin_finite) +#endif + +/*******************************************************************/ +/* */ +/* End of arcsine, below is arccosine */ +/* */ +/*******************************************************************/ + +double +SECTION +__ieee754_acos(double x) +{ + double x1,x2,xx,s1,s2,res1,p,t,res,r,cor,cc,y,c,z,w[2],eps; + mynumber u,v; + int4 k,m,n; + u.x = x; + m = u.i[HIGH_HALF]; + k = 0x7fffffff&m; + /*------------------- |x|<2.77556*10^-17 ----------------------*/ + if (k < 0x3c880000) return hp0.x; + + /*----------------- 2.77556*10^-17 <= |x| < 2^-3 --------------*/ + else + if (k < 0x3fc00000) { + x2 = x*x; + t = (((((f6*x2 + f5)*x2 + f4)*x2 + f3)*x2 + f2)*x2 + f1)*(x2*x); + r=hp0.x-x; + cor=(((hp0.x-r)-x)+hp1.x)-t; + res = r+cor; + cor = (r-res)+cor; + if (res == res+1.004*cor) return res; + else { + x1 = x+big; + xx = x*x; + x1 -= big; + x2 = x - x1; + p = x1*x1*x1; + s1 = a1.x*p; + s2 = ((((((c7*xx + c6)*xx + c5)*xx + c4)*xx + c3)*xx + c2)*xx*xx*x + + ((a1.x+a2.x)*x2*x2+ 0.5*x1*x)*x2) + a2.x*p; + res1 = x+s1; + s2 = ((x-res1)+s1)+s2; + r=hp0.x-res1; + cor=(((hp0.x-r)-res1)+hp1.x)-s2; + res = r+cor; + cor = (r-res)+cor; + if (res == res+1.00004*cor) return res; + else { + __doasin(x,0,w); + r=hp0.x-w[0]; + cor=((hp0.x-r)-w[0])+(hp1.x-w[1]); + res=r+cor; + cor=(r-res)+cor; + if (res ==(res +1.00000001*cor)) return res; + else { + res1=res+1.1*cor; + return __cos32(x,res,res1); + } + } + } + } /* else if (k < 0x3fc00000) */ + /*---------------------- 0.125 <= |x| < 0.5 --------------------*/ + else + if (k < 0x3fe00000) { + if (k<0x3fd00000) n = 11*((k&0x000fffff)>>15); + else n = 11*((k&0x000fffff)>>14)+352; + if (m>0) xx = x - asncs.x[n]; + else xx = -x - asncs.x[n]; + t = asncs.x[n+1]*xx; + p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+ + xx*(asncs.x[n+5]+xx*asncs.x[n+6]))))+asncs.x[n+7]; + t+=p; + y = (m>0)?(hp0.x-asncs.x[n+8]):(hp0.x+asncs.x[n+8]); + t = (m>0)?(hp1.x-t):(hp1.x+t); + res = y+t; + if (res == res+1.02*((y-res)+t)) return res; + else { + r=asncs.x[n+8]+xx*asncs.x[n+9]; + t=((asncs.x[n+8]-r)+xx*asncs.x[n+9])+(p+xx*asncs.x[n+10]); + if (m>0) + {p = hp0.x-r; t = (((hp0.x-p)-r)-t)+hp1.x; } + else + {p = hp0.x+r; t = ((hp0.x-p)+r)+(hp1.x+t); } + res = p+t; + cor = (p-res)+t; + if (res == (res+1.0002*cor)) return res; + else { + res1=res+1.1*cor; + z=0.5*(res1-res); + __docos(res,z,w); + z=(w[0]-x)+w[1]; + if (z>1.0e-27) return max(res,res1); + else if (z<-1.0e-27) return min(res,res1); + else return __cos32(x,res,res1); + } + } + } /* else if (k < 0x3fe00000) */ + + /*--------------------------- 0.5 <= |x| < 0.75 ---------------------*/ + else + if (k < 0x3fe80000) { + n = 1056+((k&0x000fe000)>>11)*3; + if (m>0) {xx = x - asncs.x[n]; eps=1.04; } + else {xx = -x - asncs.x[n]; eps=1.02; } + t = asncs.x[n+1]*xx; + p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+ + xx*(asncs.x[n+5]+xx*(asncs.x[n+6]+ + xx*asncs.x[n+7])))))+asncs.x[n+8]; + t+=p; + y = (m>0)?(hp0.x-asncs.x[n+9]):(hp0.x+asncs.x[n+9]); + t = (m>0)?(hp1.x-t):(hp1.x+t); + res = y+t; + if (res == res+eps*((y-res)+t)) return res; + else { + r=asncs.x[n+9]+xx*asncs.x[n+10]; + t=((asncs.x[n+9]-r)+xx*asncs.x[n+10])+(p+xx*asncs.x[n+11]); + if (m>0) {p = hp0.x-r; t = (((hp0.x-p)-r)-t)+hp1.x; eps=1.0004; } + else {p = hp0.x+r; t = ((hp0.x-p)+r)+(hp1.x+t); eps=1.0002; } + res = p+t; + cor = (p-res)+t; + if (res == (res+eps*cor)) return res; + else { + res1=res+1.1*cor; + z=0.5*(res1-res); + __docos(res,z,w); + z=(w[0]-x)+w[1]; + if (z>1.0e-27) return max(res,res1); + else if (z<-1.0e-27) return min(res,res1); + else return __cos32(x,res,res1); + } + } + } /* else if (k < 0x3fe80000) */ + +/*------------------------- 0.75 <= |x| < 0.921875 -------------*/ + else + if (k < 0x3fed8000) { + n = 992+((k&0x000fe000)>>13)*13; + if (m>0) {xx = x - asncs.x[n]; eps = 1.04; } + else {xx = -x - asncs.x[n]; eps = 1.01; } + t = asncs.x[n+1]*xx; + p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+ + xx*(asncs.x[n+5]+xx*(asncs.x[n+6]+xx*(asncs.x[n+7]+ + xx*asncs.x[n+8]))))))+asncs.x[n+9]; + t+=p; + y = (m>0)?(hp0.x-asncs.x[n+10]):(hp0.x+asncs.x[n+10]); + t = (m>0)?(hp1.x-t):(hp1.x+t); + res = y+t; + if (res == res+eps*((y-res)+t)) return res; + else { + r=asncs.x[n+10]+xx*asncs.x[n+11]; + t=((asncs.x[n+10]-r)+xx*asncs.x[n+11])+(p+xx*asncs.x[n+12]); + if (m>0) {p = hp0.x-r; t = (((hp0.x-p)-r)-t)+hp1.x; eps=1.0032; } + else {p = hp0.x+r; t = ((hp0.x-p)+r)+(hp1.x+t); eps=1.0008; } + res = p+t; + cor = (p-res)+t; + if (res == (res+eps*cor)) return res; + else { + res1=res+1.1*cor; + z=0.5*(res1-res); + __docos(res,z,w); + z=(w[0]-x)+w[1]; + if (z>1.0e-27) return max(res,res1); + else if (z<-1.0e-27) return min(res,res1); + else return __cos32(x,res,res1); + } + } + } /* else if (k < 0x3fed8000) */ + +/*-------------------0.921875 <= |x| < 0.953125 ------------------*/ + else + if (k < 0x3fee8000) { + n = 884+((k&0x000fe000)>>13)*14; + if (m>0) {xx = x - asncs.x[n]; eps=1.04; } + else {xx = -x - asncs.x[n]; eps =1.005; } + t = asncs.x[n+1]*xx; + p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+ + xx*(asncs.x[n+5]+xx*(asncs.x[n+6] + +xx*(asncs.x[n+7]+xx*(asncs.x[n+8]+ + xx*asncs.x[n+9])))))))+asncs.x[n+10]; + t+=p; + y = (m>0)?(hp0.x-asncs.x[n+11]):(hp0.x+asncs.x[n+11]); + t = (m>0)?(hp1.x-t):(hp1.x+t); + res = y+t; + if (res == res+eps*((y-res)+t)) return res; + else { + r=asncs.x[n+11]+xx*asncs.x[n+12]; + t=((asncs.x[n+11]-r)+xx*asncs.x[n+12])+(p+xx*asncs.x[n+13]); + if (m>0) {p = hp0.x-r; t = (((hp0.x-p)-r)-t)+hp1.x; eps=1.0030; } + else {p = hp0.x+r; t = ((hp0.x-p)+r)+(hp1.x+t); eps=1.0005; } + res = p+t; + cor = (p-res)+t; + if (res == (res+eps*cor)) return res; + else { + res1=res+1.1*cor; + z=0.5*(res1-res); + __docos(res,z,w); + z=(w[0]-x)+w[1]; + if (z>1.0e-27) return max(res,res1); + else if (z<-1.0e-27) return min(res,res1); + else return __cos32(x,res,res1); + } + } + } /* else if (k < 0x3fee8000) */ + + /*--------------------0.953125 <= |x| < 0.96875 ----------------*/ + else + if (k < 0x3fef0000) { + n = 768+((k&0x000fe000)>>13)*15; + if (m>0) {xx = x - asncs.x[n]; eps=1.04; } + else {xx = -x - asncs.x[n]; eps=1.005;} + t = asncs.x[n+1]*xx; + p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+ + xx*(asncs.x[n+5]+xx*(asncs.x[n+6] + +xx*(asncs.x[n+7]+xx*(asncs.x[n+8]+xx*(asncs.x[n+9]+ + xx*asncs.x[n+10]))))))))+asncs.x[n+11]; + t+=p; + y = (m>0)?(hp0.x-asncs.x[n+12]):(hp0.x+asncs.x[n+12]); + t = (m>0)?(hp1.x-t):(hp1.x+t); + res = y+t; + if (res == res+eps*((y-res)+t)) return res; + else { + r=asncs.x[n+12]+xx*asncs.x[n+13]; + t=((asncs.x[n+12]-r)+xx*asncs.x[n+13])+(p+xx*asncs.x[n+14]); + if (m>0) {p = hp0.x-r; t = (((hp0.x-p)-r)-t)+hp1.x; eps=1.0030; } + else {p = hp0.x+r; t = ((hp0.x-p)+r)+(hp1.x+t); eps=1.0005; } + res = p+t; + cor = (p-res)+t; + if (res == (res+eps*cor)) return res; + else { + res1=res+1.1*cor; + z=0.5*(res1-res); + __docos(res,z,w); + z=(w[0]-x)+w[1]; + if (z>1.0e-27) return max(res,res1); + else if (z<-1.0e-27) return min(res,res1); + else return __cos32(x,res,res1); + } + } + } /* else if (k < 0x3fef0000) */ + /*-----------------0.96875 <= |x| < 1 ---------------------------*/ + + else + if (k<0x3ff00000) { + z = 0.5*((m>0)?(1.0-x):(1.0+x)); + v.x=z; + k=v.i[HIGH_HALF]; + t=inroot[(k&0x001fffff)>>14]*powtwo[511-(k>>21)]; + r=1.0-t*t*z; + t = t*(rt0+r*(rt1+r*(rt2+r*rt3))); + c=t*z; + t=c*(1.5-0.5*t*c); + y = (t27*c+c)-t27*c; + cc = (z-y*y)/(t+y); + p=(((((f6*z+f5)*z+f4)*z+f3)*z+f2)*z+f1)*z; + if (m<0) { + cor = (hp1.x - cc)-(y+cc)*p; + res1 = hp0.x - y; + res =res1 + cor; + if (res == res+1.002*((res1-res)+cor)) return (res+res); + else { + c=y+cc; + cc=(y-c)+cc; + __doasin(c,cc,w); + res1=hp0.x-w[0]; + cor=((hp0.x-res1)-w[0])+(hp1.x-w[1]); + res = res1+cor; + cor = (res1-res)+cor; + if (res==(res+1.000001*cor)) return (res+res); + else { + res=res+res; + res1=res+1.2*cor; + return __cos32(x,res,res1); + } + } + } + else { + cor = cc+p*(y+cc); + res = y + cor; + if (res == res+1.03*((y-res)+cor)) return (res+res); + else { + c=y+cc; + cc=(y-c)+cc; + __doasin(c,cc,w); + res = w[0]; + cor=w[1]; + if (res==(res+1.000001*cor)) return (res+res); + else { + res=res+res; + res1=res+1.2*cor; + return __cos32(x,res,res1); + } + } + } + } /* else if (k < 0x3ff00000) */ + + /*---------------------------- |x|>=1 -----------------------*/ + else + if (k==0x3ff00000 && u.i[LOW_HALF]==0) return (m>0)?0:2.0*hp0.x; + else + if (k>0x7ff00000 || (k == 0x7ff00000 && u.i[LOW_HALF] != 0)) return x + x; + else { + u.i[HIGH_HALF]=0x7ff00000; + v.i[HIGH_HALF]=0x7ff00000; + u.i[LOW_HALF]=0; + v.i[LOW_HALF]=0; + return u.x/v.x; + } +} +#ifndef __ieee754_acos +strong_alias (__ieee754_acos, __acos_finite) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_atan2.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_atan2.c new file mode 100644 index 0000000000..3c9d964b9b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_atan2.c @@ -0,0 +1,620 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/************************************************************************/ +/* MODULE_NAME: atnat2.c */ +/* */ +/* FUNCTIONS: uatan2 */ +/* atan2Mp */ +/* signArctan2 */ +/* normalized */ +/* */ +/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h atnat2.h */ +/* mpatan.c mpatan2.c mpsqrt.c */ +/* uatan.tbl */ +/* */ +/* An ultimate atan2() routine. Given two IEEE double machine numbers y,*/ +/* x it computes the correctly rounded (to nearest) value of atan2(y,x).*/ +/* */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round to nearest mode of IEEE 754 standard. */ +/* */ +/************************************************************************/ + +#include <dla.h> +#include "mpa.h" +#include "MathLib.h" +#include "uatan.tbl" +#include "atnat2.h" +#include <fenv.h> +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <stap-probe.h> + +#ifndef SECTION +# define SECTION +#endif + +/************************************************************************/ +/* An ultimate atan2 routine. Given two IEEE double machine numbers y,x */ +/* it computes the correctly rounded (to nearest) value of atan2(y,x). */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round to nearest mode of IEEE 754 standard. */ +/************************************************************************/ +static double atan2Mp (double, double, const int[]); + /* Fix the sign and return after stage 1 or stage 2 */ +static double +signArctan2 (double y, double z) +{ + return __copysign (z, y); +} + +static double normalized (double, double, double, double); +void __mpatan2 (mp_no *, mp_no *, mp_no *, int); + +double +SECTION +__ieee754_atan2 (double y, double x) +{ + int i, de, ux, dx, uy, dy; + static const int pr[MM] = { 6, 8, 10, 20, 32 }; + double ax, ay, u, du, u9, ua, v, vv, dv, t1, t2, t3, t7, t8, + z, zz, cor, s1, ss1, s2, ss2; +#ifndef DLA_FMS + double t4, t5, t6; +#endif + number num; + + static const int ep = 59768832, /* 57*16**5 */ + em = -59768832; /* -57*16**5 */ + + /* x=NaN or y=NaN */ + num.d = x; + ux = num.i[HIGH_HALF]; + dx = num.i[LOW_HALF]; + if ((ux & 0x7ff00000) == 0x7ff00000) + { + if (((ux & 0x000fffff) | dx) != 0x00000000) + return x + y; + } + num.d = y; + uy = num.i[HIGH_HALF]; + dy = num.i[LOW_HALF]; + if ((uy & 0x7ff00000) == 0x7ff00000) + { + if (((uy & 0x000fffff) | dy) != 0x00000000) + return y + y; + } + + /* y=+-0 */ + if (uy == 0x00000000) + { + if (dy == 0x00000000) + { + if ((ux & 0x80000000) == 0x00000000) + return 0; + else + return opi.d; + } + } + else if (uy == 0x80000000) + { + if (dy == 0x00000000) + { + if ((ux & 0x80000000) == 0x00000000) + return -0.0; + else + return mopi.d; + } + } + + /* x=+-0 */ + if (x == 0) + { + if ((uy & 0x80000000) == 0x00000000) + return hpi.d; + else + return mhpi.d; + } + + /* x=+-INF */ + if (ux == 0x7ff00000) + { + if (dx == 0x00000000) + { + if (uy == 0x7ff00000) + { + if (dy == 0x00000000) + return qpi.d; + } + else if (uy == 0xfff00000) + { + if (dy == 0x00000000) + return mqpi.d; + } + else + { + if ((uy & 0x80000000) == 0x00000000) + return 0; + else + return -0.0; + } + } + } + else if (ux == 0xfff00000) + { + if (dx == 0x00000000) + { + if (uy == 0x7ff00000) + { + if (dy == 0x00000000) + return tqpi.d; + } + else if (uy == 0xfff00000) + { + if (dy == 0x00000000) + return mtqpi.d; + } + else + { + if ((uy & 0x80000000) == 0x00000000) + return opi.d; + else + return mopi.d; + } + } + } + + /* y=+-INF */ + if (uy == 0x7ff00000) + { + if (dy == 0x00000000) + return hpi.d; + } + else if (uy == 0xfff00000) + { + if (dy == 0x00000000) + return mhpi.d; + } + + SET_RESTORE_ROUND (FE_TONEAREST); + /* either x/y or y/x is very close to zero */ + ax = (x < 0) ? -x : x; + ay = (y < 0) ? -y : y; + de = (uy & 0x7ff00000) - (ux & 0x7ff00000); + if (de >= ep) + { + return ((y > 0) ? hpi.d : mhpi.d); + } + else if (de <= em) + { + if (x > 0) + { + double ret; + if ((z = ay / ax) < TWOM1022) + ret = normalized (ax, ay, y, z); + else + ret = signArctan2 (y, z); + if (fabs (ret) < DBL_MIN) + { + double vret = ret ? ret : DBL_MIN; + double force_underflow = vret * vret; + math_force_eval (force_underflow); + } + return ret; + } + else + { + return ((y > 0) ? opi.d : mopi.d); + } + } + + /* if either x or y is extremely close to zero, scale abs(x), abs(y). */ + if (ax < twom500.d || ay < twom500.d) + { + ax *= two500.d; + ay *= two500.d; + } + + /* Likewise for large x and y. */ + if (ax > two500.d || ay > two500.d) + { + ax *= twom500.d; + ay *= twom500.d; + } + + /* x,y which are neither special nor extreme */ + if (ay < ax) + { + u = ay / ax; + EMULV (ax, u, v, vv, t1, t2, t3, t4, t5); + du = ((ay - v) - vv) / ax; + } + else + { + u = ax / ay; + EMULV (ay, u, v, vv, t1, t2, t3, t4, t5); + du = ((ax - v) - vv) / ay; + } + + if (x > 0) + { + /* (i) x>0, abs(y)< abs(x): atan(ay/ax) */ + if (ay < ax) + { + if (u < inv16.d) + { + v = u * u; + + zz = du + u * v * (d3.d + + v * (d5.d + + v * (d7.d + + v * (d9.d + + v * (d11.d + + v * d13.d))))); + + if ((z = u + (zz - u1.d * u)) == u + (zz + u1.d * u)) + return signArctan2 (y, z); + + MUL2 (u, du, u, du, v, vv, t1, t2, t3, t4, t5, t6, t7, t8); + s1 = v * (f11.d + v * (f13.d + + v * (f15.d + v * (f17.d + v * f19.d)))); + ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (u, du, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (u, du, s2, ss2, s1, ss1, t1, t2); + + if ((z = s1 + (ss1 - u5.d * s1)) == s1 + (ss1 + u5.d * s1)) + return signArctan2 (y, z); + + return atan2Mp (x, y, pr); + } + + i = (TWO52 + TWO8 * u) - TWO52; + i -= 16; + t3 = u - cij[i][0].d; + EADD (t3, du, v, dv); + t1 = cij[i][1].d; + t2 = cij[i][2].d; + zz = v * t2 + (dv * t2 + + v * v * (cij[i][3].d + + v * (cij[i][4].d + + v * (cij[i][5].d + + v * cij[i][6].d)))); + if (i < 112) + { + if (i < 48) + u9 = u91.d; /* u < 1/4 */ + else + u9 = u92.d; + } /* 1/4 <= u < 1/2 */ + else + { + if (i < 176) + u9 = u93.d; /* 1/2 <= u < 3/4 */ + else + u9 = u94.d; + } /* 3/4 <= u <= 1 */ + if ((z = t1 + (zz - u9 * t1)) == t1 + (zz + u9 * t1)) + return signArctan2 (y, z); + + t1 = u - hij[i][0].d; + EADD (t1, du, v, vv); + s1 = v * (hij[i][11].d + + v * (hij[i][12].d + + v * (hij[i][13].d + + v * (hij[i][14].d + + v * hij[i][15].d)))); + ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2); + + if ((z = s2 + (ss2 - ub.d * s2)) == s2 + (ss2 + ub.d * s2)) + return signArctan2 (y, z); + return atan2Mp (x, y, pr); + } + + /* (ii) x>0, abs(x)<=abs(y): pi/2-atan(ax/ay) */ + if (u < inv16.d) + { + v = u * u; + zz = u * v * (d3.d + + v * (d5.d + + v * (d7.d + + v * (d9.d + + v * (d11.d + + v * d13.d))))); + ESUB (hpi.d, u, t2, cor); + t3 = ((hpi1.d + cor) - du) - zz; + if ((z = t2 + (t3 - u2.d)) == t2 + (t3 + u2.d)) + return signArctan2 (y, z); + + MUL2 (u, du, u, du, v, vv, t1, t2, t3, t4, t5, t6, t7, t8); + s1 = v * (f11.d + + v * (f13.d + + v * (f15.d + v * (f17.d + v * f19.d)))); + ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (u, du, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (u, du, s2, ss2, s1, ss1, t1, t2); + SUB2 (hpi.d, hpi1.d, s1, ss1, s2, ss2, t1, t2); + + if ((z = s2 + (ss2 - u6.d)) == s2 + (ss2 + u6.d)) + return signArctan2 (y, z); + return atan2Mp (x, y, pr); + } + + i = (TWO52 + TWO8 * u) - TWO52; + i -= 16; + v = (u - cij[i][0].d) + du; + + zz = hpi1.d - v * (cij[i][2].d + + v * (cij[i][3].d + + v * (cij[i][4].d + + v * (cij[i][5].d + + v * cij[i][6].d)))); + t1 = hpi.d - cij[i][1].d; + if (i < 112) + ua = ua1.d; /* w < 1/2 */ + else + ua = ua2.d; /* w >= 1/2 */ + if ((z = t1 + (zz - ua)) == t1 + (zz + ua)) + return signArctan2 (y, z); + + t1 = u - hij[i][0].d; + EADD (t1, du, v, vv); + + s1 = v * (hij[i][11].d + + v * (hij[i][12].d + + v * (hij[i][13].d + + v * (hij[i][14].d + + v * hij[i][15].d)))); + + ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2); + SUB2 (hpi.d, hpi1.d, s2, ss2, s1, ss1, t1, t2); + + if ((z = s1 + (ss1 - uc.d)) == s1 + (ss1 + uc.d)) + return signArctan2 (y, z); + return atan2Mp (x, y, pr); + } + + /* (iii) x<0, abs(x)< abs(y): pi/2+atan(ax/ay) */ + if (ax < ay) + { + if (u < inv16.d) + { + v = u * u; + zz = u * v * (d3.d + + v * (d5.d + + v * (d7.d + + v * (d9.d + + v * (d11.d + v * d13.d))))); + EADD (hpi.d, u, t2, cor); + t3 = ((hpi1.d + cor) + du) + zz; + if ((z = t2 + (t3 - u3.d)) == t2 + (t3 + u3.d)) + return signArctan2 (y, z); + + MUL2 (u, du, u, du, v, vv, t1, t2, t3, t4, t5, t6, t7, t8); + s1 = v * (f11.d + + v * (f13.d + v * (f15.d + v * (f17.d + v * f19.d)))); + ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (u, du, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (u, du, s2, ss2, s1, ss1, t1, t2); + ADD2 (hpi.d, hpi1.d, s1, ss1, s2, ss2, t1, t2); + + if ((z = s2 + (ss2 - u7.d)) == s2 + (ss2 + u7.d)) + return signArctan2 (y, z); + return atan2Mp (x, y, pr); + } + + i = (TWO52 + TWO8 * u) - TWO52; + i -= 16; + v = (u - cij[i][0].d) + du; + zz = hpi1.d + v * (cij[i][2].d + + v * (cij[i][3].d + + v * (cij[i][4].d + + v * (cij[i][5].d + + v * cij[i][6].d)))); + t1 = hpi.d + cij[i][1].d; + if (i < 112) + ua = ua1.d; /* w < 1/2 */ + else + ua = ua2.d; /* w >= 1/2 */ + if ((z = t1 + (zz - ua)) == t1 + (zz + ua)) + return signArctan2 (y, z); + + t1 = u - hij[i][0].d; + EADD (t1, du, v, vv); + s1 = v * (hij[i][11].d + + v * (hij[i][12].d + + v * (hij[i][13].d + + v * (hij[i][14].d + + v * hij[i][15].d)))); + ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2); + ADD2 (hpi.d, hpi1.d, s2, ss2, s1, ss1, t1, t2); + + if ((z = s1 + (ss1 - uc.d)) == s1 + (ss1 + uc.d)) + return signArctan2 (y, z); + return atan2Mp (x, y, pr); + } + + /* (iv) x<0, abs(y)<=abs(x): pi-atan(ax/ay) */ + if (u < inv16.d) + { + v = u * u; + zz = u * v * (d3.d + + v * (d5.d + + v * (d7.d + + v * (d9.d + v * (d11.d + v * d13.d))))); + ESUB (opi.d, u, t2, cor); + t3 = ((opi1.d + cor) - du) - zz; + if ((z = t2 + (t3 - u4.d)) == t2 + (t3 + u4.d)) + return signArctan2 (y, z); + + MUL2 (u, du, u, du, v, vv, t1, t2, t3, t4, t5, t6, t7, t8); + s1 = v * (f11.d + v * (f13.d + v * (f15.d + v * (f17.d + v * f19.d)))); + ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (u, du, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (u, du, s2, ss2, s1, ss1, t1, t2); + SUB2 (opi.d, opi1.d, s1, ss1, s2, ss2, t1, t2); + + if ((z = s2 + (ss2 - u8.d)) == s2 + (ss2 + u8.d)) + return signArctan2 (y, z); + return atan2Mp (x, y, pr); + } + + i = (TWO52 + TWO8 * u) - TWO52; + i -= 16; + v = (u - cij[i][0].d) + du; + zz = opi1.d - v * (cij[i][2].d + + v * (cij[i][3].d + + v * (cij[i][4].d + + v * (cij[i][5].d + v * cij[i][6].d)))); + t1 = opi.d - cij[i][1].d; + if (i < 112) + ua = ua1.d; /* w < 1/2 */ + else + ua = ua2.d; /* w >= 1/2 */ + if ((z = t1 + (zz - ua)) == t1 + (zz + ua)) + return signArctan2 (y, z); + + t1 = u - hij[i][0].d; + + EADD (t1, du, v, vv); + + s1 = v * (hij[i][11].d + + v * (hij[i][12].d + + v * (hij[i][13].d + + v * (hij[i][14].d + v * hij[i][15].d)))); + + ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2); + SUB2 (opi.d, opi1.d, s2, ss2, s1, ss1, t1, t2); + + if ((z = s1 + (ss1 - uc.d)) == s1 + (ss1 + uc.d)) + return signArctan2 (y, z); + return atan2Mp (x, y, pr); +} + +#ifndef __ieee754_atan2 +strong_alias (__ieee754_atan2, __atan2_finite) +#endif + +/* Treat the Denormalized case */ +static double +SECTION +normalized (double ax, double ay, double y, double z) +{ + int p; + mp_no mpx, mpy, mpz, mperr, mpz2, mpt1; + p = 6; + __dbl_mp (ax, &mpx, p); + __dbl_mp (ay, &mpy, p); + __dvd (&mpy, &mpx, &mpz, p); + __dbl_mp (ue.d, &mpt1, p); + __mul (&mpz, &mpt1, &mperr, p); + __sub (&mpz, &mperr, &mpz2, p); + __mp_dbl (&mpz2, &z, p); + return signArctan2 (y, z); +} + +/* Stage 3: Perform a multi-Precision computation */ +static double +SECTION +atan2Mp (double x, double y, const int pr[]) +{ + double z1, z2; + int i, p; + mp_no mpx, mpy, mpz, mpz1, mpz2, mperr, mpt1; + for (i = 0; i < MM; i++) + { + p = pr[i]; + __dbl_mp (x, &mpx, p); + __dbl_mp (y, &mpy, p); + __mpatan2 (&mpy, &mpx, &mpz, p); + __dbl_mp (ud[i].d, &mpt1, p); + __mul (&mpz, &mpt1, &mperr, p); + __add (&mpz, &mperr, &mpz1, p); + __sub (&mpz, &mperr, &mpz2, p); + __mp_dbl (&mpz1, &z1, p); + __mp_dbl (&mpz2, &z2, p); + if (z1 == z2) + { + LIBC_PROBE (slowatan2, 4, &p, &x, &y, &z1); + return z1; + } + } + LIBC_PROBE (slowatan2_inexact, 4, &p, &x, &y, &z1); + return z1; /*if impossible to do exact computing */ +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_atanh.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_atanh.c new file mode 100644 index 0000000000..a9d19a0472 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_atanh.c @@ -0,0 +1,74 @@ +/* Copyright (C) 2011-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@gmail.com>, 2011. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + + +/* __ieee754_atanh(x) + Method : + 1.Reduced x to positive by atanh(-x) = -atanh(x) + 2.For x>=0.5 + 1 2x x + atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) + 2 1 - x 1 - x + + For x<0.5 + atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) + + Special cases: + atanh(x) is NaN if |x| > 1 with signal; + atanh(NaN) is that NaN with no signal; + atanh(+-1) is +-INF with signal. + + */ + +#include <float.h> +#include <inttypes.h> +#include <math.h> +#include <math_private.h> + +static const double huge = 1e300; + +double +__ieee754_atanh (double x) +{ + double xa = fabs (x); + double t; + if (isless (xa, 0.5)) + { + if (__glibc_unlikely (xa < 0x1.0p-28)) + { + math_force_eval (huge + x); + math_check_force_underflow (x); + return x; + } + + t = xa + xa; + t = 0.5 * __log1p (t + t * xa / (1.0 - xa)); + } + else if (__glibc_likely (isless (xa, 1.0))) + t = 0.5 * __log1p ((xa + xa) / (1.0 - xa)); + else + { + if (isgreater (xa, 1.0)) + return (x - x) / (x - x); + + return x / 0.0; + } + + return __copysign (t, x); +} +strong_alias (__ieee754_atanh, __atanh_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_cosh.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_cosh.c new file mode 100644 index 0000000000..52a5d5007d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_cosh.c @@ -0,0 +1,88 @@ +/* Optimized by Ulrich Drepper <drepper@gmail.com>, 2011 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_cosh(x) + * Method : + * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 + * 1. Replace x by |x| (cosh(x) = cosh(-x)). + * 2. + * [ exp(x) - 1 ]^2 + * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- + * 2*exp(x) + * + * exp(x) + 1/exp(x) + * ln2/2 <= x <= 22 : cosh(x) := ------------------- + * 2 + * 22 <= x <= lnovft : cosh(x) := exp(x)/2 + * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) + * ln2ovft < x : cosh(x) := huge*huge (overflow) + * + * Special cases: + * cosh(x) is |x| if x is +INF, -INF, or NaN. + * only cosh(0)=1 is exact for finite x. + */ + +#include <math.h> +#include <math_private.h> + +static const double one = 1.0, half = 0.5, huge = 1.0e300; + +double +__ieee754_cosh (double x) +{ + double t, w; + int32_t ix; + u_int32_t lx; + + /* High word of |x|. */ + GET_HIGH_WORD (ix, x); + ix &= 0x7fffffff; + + /* |x| in [0,22] */ + if (ix < 0x40360000) + { + /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ + if (ix < 0x3fd62e43) + { + if (ix < 0x3c800000) + return one; /* cosh(tiny) = 1 */ + t = __expm1 (fabs (x)); + w = one + t; + return one + (t * t) / (w + w); + } + + /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ + t = __ieee754_exp (fabs (x)); + return half * t + half / t; + } + + /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ + if (ix < 0x40862e42) + return half * __ieee754_exp (fabs (x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + GET_LOW_WORD (lx, x); + if (ix < 0x408633ce || ((ix == 0x408633ce) && (lx <= (u_int32_t) 0x8fb9f87d))) + { + w = __ieee754_exp (half * fabs (x)); + t = half * w; + return t * w; + } + + /* x is INF or NaN */ + if (ix >= 0x7ff00000) + return x * x; + + /* |x| > overflowthresold, cosh(x) overflow */ + return math_narrow_eval (huge * huge); +} +strong_alias (__ieee754_cosh, __cosh_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_exp.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_exp.c new file mode 100644 index 0000000000..6757a14ce1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_exp.c @@ -0,0 +1,361 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/***************************************************************************/ +/* MODULE_NAME:uexp.c */ +/* */ +/* FUNCTION:uexp */ +/* exp1 */ +/* */ +/* FILES NEEDED:dla.h endian.h mpa.h mydefs.h uexp.h */ +/* mpa.c mpexp.x slowexp.c */ +/* */ +/* An ultimate exp routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of e^x */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round to nearest mode of IEEE 754 standard. */ +/* */ +/***************************************************************************/ + +#include <math.h> +#include "endian.h" +#include "uexp.h" +#include "mydefs.h" +#include "MathLib.h" +#include "uexp.tbl" +#include <math_private.h> +#include <fenv.h> +#include <float.h> + +#ifndef SECTION +# define SECTION +#endif + +double __slowexp (double); + +/* An ultimate exp routine. Given an IEEE double machine number x it computes + the correctly rounded (to nearest) value of e^x. */ +double +SECTION +__ieee754_exp (double x) +{ + double bexp, t, eps, del, base, y, al, bet, res, rem, cor; + mynumber junk1, junk2, binexp = {{0, 0}}; + int4 i, j, m, n, ex; + double retval; + + { + SET_RESTORE_ROUND (FE_TONEAREST); + + junk1.x = x; + m = junk1.i[HIGH_HALF]; + n = m & hugeint; + + if (n > smallint && n < bigint) + { + y = x * log2e.x + three51.x; + bexp = y - three51.x; /* multiply the result by 2**bexp */ + + junk1.x = y; + + eps = bexp * ln_two2.x; /* x = bexp*ln(2) + t - eps */ + t = x - bexp * ln_two1.x; + + y = t + three33.x; + base = y - three33.x; /* t rounded to a multiple of 2**-18 */ + junk2.x = y; + del = (t - base) - eps; /* x = bexp*ln(2) + base + del */ + eps = del + del * del * (p3.x * del + p2.x); + + binexp.i[HIGH_HALF] = (junk1.i[LOW_HALF] + 1023) << 20; + + i = ((junk2.i[LOW_HALF] >> 8) & 0xfffffffe) + 356; + j = (junk2.i[LOW_HALF] & 511) << 1; + + al = coar.x[i] * fine.x[j]; + bet = ((coar.x[i] * fine.x[j + 1] + coar.x[i + 1] * fine.x[j]) + + coar.x[i + 1] * fine.x[j + 1]); + + rem = (bet + bet * eps) + al * eps; + res = al + rem; + cor = (al - res) + rem; + if (res == (res + cor * err_0)) + { + retval = res * binexp.x; + goto ret; + } + else + { + retval = __slowexp (x); + goto ret; + } /*if error is over bound */ + } + + if (n <= smallint) + { + retval = 1.0; + goto ret; + } + + if (n >= badint) + { + if (n > infint) + { + retval = x + x; + goto ret; + } /* x is NaN */ + if (n < infint) + { + if (x > 0) + goto ret_huge; + else + goto ret_tiny; + } + /* x is finite, cause either overflow or underflow */ + if (junk1.i[LOW_HALF] != 0) + { + retval = x + x; + goto ret; + } /* x is NaN */ + retval = (x > 0) ? inf.x : zero; /* |x| = inf; return either inf or 0 */ + goto ret; + } + + y = x * log2e.x + three51.x; + bexp = y - three51.x; + junk1.x = y; + eps = bexp * ln_two2.x; + t = x - bexp * ln_two1.x; + y = t + three33.x; + base = y - three33.x; + junk2.x = y; + del = (t - base) - eps; + eps = del + del * del * (p3.x * del + p2.x); + i = ((junk2.i[LOW_HALF] >> 8) & 0xfffffffe) + 356; + j = (junk2.i[LOW_HALF] & 511) << 1; + al = coar.x[i] * fine.x[j]; + bet = ((coar.x[i] * fine.x[j + 1] + coar.x[i + 1] * fine.x[j]) + + coar.x[i + 1] * fine.x[j + 1]); + rem = (bet + bet * eps) + al * eps; + res = al + rem; + cor = (al - res) + rem; + if (m >> 31) + { + ex = junk1.i[LOW_HALF]; + if (res < 1.0) + { + res += res; + cor += cor; + ex -= 1; + } + if (ex >= -1022) + { + binexp.i[HIGH_HALF] = (1023 + ex) << 20; + if (res == (res + cor * err_0)) + { + retval = res * binexp.x; + goto ret; + } + else + { + retval = __slowexp (x); + goto check_uflow_ret; + } /*if error is over bound */ + } + ex = -(1022 + ex); + binexp.i[HIGH_HALF] = (1023 - ex) << 20; + res *= binexp.x; + cor *= binexp.x; + eps = 1.0000000001 + err_0 * binexp.x; + t = 1.0 + res; + y = ((1.0 - t) + res) + cor; + res = t + y; + cor = (t - res) + y; + if (res == (res + eps * cor)) + { + binexp.i[HIGH_HALF] = 0x00100000; + retval = (res - 1.0) * binexp.x; + goto check_uflow_ret; + } + else + { + retval = __slowexp (x); + goto check_uflow_ret; + } /* if error is over bound */ + check_uflow_ret: + if (retval < DBL_MIN) + { + double force_underflow = tiny * tiny; + math_force_eval (force_underflow); + } + if (retval == 0) + goto ret_tiny; + goto ret; + } + else + { + binexp.i[HIGH_HALF] = (junk1.i[LOW_HALF] + 767) << 20; + if (res == (res + cor * err_0)) + retval = res * binexp.x * t256.x; + else + retval = __slowexp (x); + if (isinf (retval)) + goto ret_huge; + else + goto ret; + } + } +ret: + return retval; + + ret_huge: + return hhuge * hhuge; + + ret_tiny: + return tiny * tiny; +} +#ifndef __ieee754_exp +strong_alias (__ieee754_exp, __exp_finite) +#endif + +/* Compute e^(x+xx). The routine also receives bound of error of previous + calculation. If after computing exp the error exceeds the allowed bounds, + the routine returns a non-positive number. Otherwise it returns the + computed result, which is always positive. */ +double +SECTION +__exp1 (double x, double xx, double error) +{ + double bexp, t, eps, del, base, y, al, bet, res, rem, cor; + mynumber junk1, junk2, binexp = {{0, 0}}; + int4 i, j, m, n, ex; + + junk1.x = x; + m = junk1.i[HIGH_HALF]; + n = m & hugeint; /* no sign */ + + if (n > smallint && n < bigint) + { + y = x * log2e.x + three51.x; + bexp = y - three51.x; /* multiply the result by 2**bexp */ + + junk1.x = y; + + eps = bexp * ln_two2.x; /* x = bexp*ln(2) + t - eps */ + t = x - bexp * ln_two1.x; + + y = t + three33.x; + base = y - three33.x; /* t rounded to a multiple of 2**-18 */ + junk2.x = y; + del = (t - base) + (xx - eps); /* x = bexp*ln(2) + base + del */ + eps = del + del * del * (p3.x * del + p2.x); + + binexp.i[HIGH_HALF] = (junk1.i[LOW_HALF] + 1023) << 20; + + i = ((junk2.i[LOW_HALF] >> 8) & 0xfffffffe) + 356; + j = (junk2.i[LOW_HALF] & 511) << 1; + + al = coar.x[i] * fine.x[j]; + bet = ((coar.x[i] * fine.x[j + 1] + coar.x[i + 1] * fine.x[j]) + + coar.x[i + 1] * fine.x[j + 1]); + + rem = (bet + bet * eps) + al * eps; + res = al + rem; + cor = (al - res) + rem; + if (res == (res + cor * (1.0 + error + err_1))) + return res * binexp.x; + else + return -10.0; + } + + if (n <= smallint) + return 1.0; /* if x->0 e^x=1 */ + + if (n >= badint) + { + if (n > infint) + return (zero / zero); /* x is NaN, return invalid */ + if (n < infint) + return ((x > 0) ? (hhuge * hhuge) : (tiny * tiny)); + /* x is finite, cause either overflow or underflow */ + if (junk1.i[LOW_HALF] != 0) + return (zero / zero); /* x is NaN */ + return ((x > 0) ? inf.x : zero); /* |x| = inf; return either inf or 0 */ + } + + y = x * log2e.x + three51.x; + bexp = y - three51.x; + junk1.x = y; + eps = bexp * ln_two2.x; + t = x - bexp * ln_two1.x; + y = t + three33.x; + base = y - three33.x; + junk2.x = y; + del = (t - base) + (xx - eps); + eps = del + del * del * (p3.x * del + p2.x); + i = ((junk2.i[LOW_HALF] >> 8) & 0xfffffffe) + 356; + j = (junk2.i[LOW_HALF] & 511) << 1; + al = coar.x[i] * fine.x[j]; + bet = ((coar.x[i] * fine.x[j + 1] + coar.x[i + 1] * fine.x[j]) + + coar.x[i + 1] * fine.x[j + 1]); + rem = (bet + bet * eps) + al * eps; + res = al + rem; + cor = (al - res) + rem; + if (m >> 31) + { + ex = junk1.i[LOW_HALF]; + if (res < 1.0) + { + res += res; + cor += cor; + ex -= 1; + } + if (ex >= -1022) + { + binexp.i[HIGH_HALF] = (1023 + ex) << 20; + if (res == (res + cor * (1.0 + error + err_1))) + return res * binexp.x; + else + return -10.0; + } + ex = -(1022 + ex); + binexp.i[HIGH_HALF] = (1023 - ex) << 20; + res *= binexp.x; + cor *= binexp.x; + eps = 1.00000000001 + (error + err_1) * binexp.x; + t = 1.0 + res; + y = ((1.0 - t) + res) + cor; + res = t + y; + cor = (t - res) + y; + if (res == (res + eps * cor)) + { + binexp.i[HIGH_HALF] = 0x00100000; + return (res - 1.0) * binexp.x; + } + else + return -10.0; + } + else + { + binexp.i[HIGH_HALF] = (junk1.i[LOW_HALF] + 767) << 20; + if (res == (res + cor * (1.0 + error + err_1))) + return res * binexp.x * t256.x; + else + return -10.0; + } +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_exp10.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_exp10.c new file mode 100644 index 0000000000..6c8783e405 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_exp10.c @@ -0,0 +1,50 @@ +/* Copyright (C) 2012-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +static const double log10_high = 0x2.4d7637p0; +static const double log10_low = 0x7.6aaa2b05ba95cp-28; + +double +__ieee754_exp10 (double arg) +{ + int32_t lx; + double arg_high, arg_low; + double exp_high, exp_low; + + if (!isfinite (arg)) + return __ieee754_exp (arg); + if (arg < DBL_MIN_10_EXP - DBL_DIG - 10) + return DBL_MIN * DBL_MIN; + else if (arg > DBL_MAX_10_EXP + 1) + return DBL_MAX * DBL_MAX; + else if (fabs (arg) < 0x1p-56) + return 1.0; + + GET_LOW_WORD (lx, arg); + lx &= 0xf8000000; + arg_high = arg; + SET_LOW_WORD (arg_high, lx); + arg_low = arg - arg_high; + exp_high = arg_high * log10_high; + exp_low = arg_high * log10_low + arg_low * M_LN10; + return __ieee754_exp (exp_high) * __ieee754_exp (exp_low); +} +strong_alias (__ieee754_exp10, __exp10_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_exp2.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_exp2.c new file mode 100644 index 0000000000..9efda23f06 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_exp2.c @@ -0,0 +1,133 @@ +/* Double-precision floating point 2^x. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Geoffrey Keating <geoffk@ozemail.com.au> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* The basic design here is from + Shmuel Gal and Boris Bachelis, "An Accurate Elementary Mathematical + Library for the IEEE Floating Point Standard", ACM Trans. Math. Soft., + 17 (1), March 1991, pp. 26-45. + It has been slightly modified to compute 2^x instead of e^x. + */ +#include <stdlib.h> +#include <float.h> +#include <ieee754.h> +#include <math.h> +#include <fenv.h> +#include <inttypes.h> +#include <math_private.h> + +#include "t_exp2.h" + +static const double TWO1023 = 8.988465674311579539e+307; +static const double TWOM1000 = 9.3326361850321887899e-302; + +double +__ieee754_exp2 (double x) +{ + static const double himark = (double) DBL_MAX_EXP; + static const double lomark = (double) (DBL_MIN_EXP - DBL_MANT_DIG - 1); + + /* Check for usual case. */ + if (__glibc_likely (isless (x, himark))) + { + /* Exceptional cases: */ + if (__glibc_unlikely (!isgreaterequal (x, lomark))) + { + if (isinf (x)) + /* e^-inf == 0, with no error. */ + return 0; + else + /* Underflow */ + return TWOM1000 * TWOM1000; + } + + static const double THREEp42 = 13194139533312.0; + int tval, unsafe; + double rx, x22, result; + union ieee754_double ex2_u, scale_u; + + if (fabs (x) < DBL_EPSILON / 4.0) + return 1.0 + x; + + { + SET_RESTORE_ROUND_NOEX (FE_TONEAREST); + + /* 1. Argument reduction. + Choose integers ex, -256 <= t < 256, and some real + -1/1024 <= x1 <= 1024 so that + x = ex + t/512 + x1. + + First, calculate rx = ex + t/512. */ + rx = x + THREEp42; + rx -= THREEp42; + x -= rx; /* Compute x=x1. */ + /* Compute tval = (ex*512 + t)+256. + Now, t = (tval mod 512)-256 and ex=tval/512 [that's mod, NOT %; + and /-round-to-nearest not the usual c integer /]. */ + tval = (int) (rx * 512.0 + 256.0); + + /* 2. Adjust for accurate table entry. + Find e so that + x = ex + t/512 + e + x2 + where -1e6 < e < 1e6, and + (double)(2^(t/512+e)) + is accurate to one part in 2^-64. */ + + /* 'tval & 511' is the same as 'tval%512' except that it's always + positive. + Compute x = x2. */ + x -= exp2_deltatable[tval & 511]; + + /* 3. Compute ex2 = 2^(t/512+e+ex). */ + ex2_u.d = exp2_accuratetable[tval & 511]; + tval >>= 9; + /* x2 is an integer multiple of 2^-54; avoid intermediate + underflow from the calculation of x22 * x. */ + unsafe = abs (tval) >= -DBL_MIN_EXP - 56; + ex2_u.ieee.exponent += tval >> unsafe; + scale_u.d = 1.0; + scale_u.ieee.exponent += tval - (tval >> unsafe); + + /* 4. Approximate 2^x2 - 1, using a fourth-degree polynomial, + with maximum error in [-2^-10-2^-30,2^-10+2^-30] + less than 10^-19. */ + + x22 = (((.0096181293647031180 + * x + .055504110254308625) + * x + .240226506959100583) + * x + .69314718055994495) * ex2_u.d; + math_opt_barrier (x22); + } + + /* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex). */ + result = x22 * x + ex2_u.d; + + if (!unsafe) + return result; + else + { + result *= scale_u.d; + math_check_force_underflow_nonneg (result); + return result; + } + } + else + /* Return x, if x is a NaN or Inf; or overflow, otherwise. */ + return TWO1023 * x; +} +strong_alias (__ieee754_exp2, __exp2_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_fmod.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_fmod.c new file mode 100644 index 0000000000..e82b302200 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_fmod.c @@ -0,0 +1,173 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * __ieee754_fmod(x,y) + * Return x mod y in exact arithmetic + * Method: shift and subtract + */ + +#include <math.h> +#include <math_private.h> + +static const double one = 1.0, Zero[] = { 0.0, -0.0, }; + +double +__ieee754_fmod (double x, double y) +{ + int32_t n, hx, hy, hz, ix, iy, sx, i; + u_int32_t lx, ly, lz; + + EXTRACT_WORDS (hx, lx, x); + EXTRACT_WORDS (hy, ly, y); + sx = hx & 0x80000000; /* sign of x */ + hx ^= sx; /* |x| */ + hy &= 0x7fffffff; /* |y| */ + + /* purge off exception values */ + if ((hy | ly) == 0 || (hx >= 0x7ff00000) || /* y=0,or x not finite */ + ((hy | ((ly | -ly) >> 31)) > 0x7ff00000)) /* or y is NaN */ + return (x * y) / (x * y); + if (hx <= hy) + { + if ((hx < hy) || (lx < ly)) + return x; /* |x|<|y| return x */ + if (lx == ly) + return Zero[(u_int32_t) sx >> 31]; /* |x|=|y| return x*0*/ + } + + /* determine ix = ilogb(x) */ + if (__glibc_unlikely (hx < 0x00100000)) /* subnormal x */ + { + if (hx == 0) + { + for (ix = -1043, i = lx; i > 0; i <<= 1) + ix -= 1; + } + else + { + for (ix = -1022, i = (hx << 11); i > 0; i <<= 1) + ix -= 1; + } + } + else + ix = (hx >> 20) - 1023; + + /* determine iy = ilogb(y) */ + if (__glibc_unlikely (hy < 0x00100000)) /* subnormal y */ + { + if (hy == 0) + { + for (iy = -1043, i = ly; i > 0; i <<= 1) + iy -= 1; + } + else + { + for (iy = -1022, i = (hy << 11); i > 0; i <<= 1) + iy -= 1; + } + } + else + iy = (hy >> 20) - 1023; + + /* set up {hx,lx}, {hy,ly} and align y to x */ + if (__glibc_likely (ix >= -1022)) + hx = 0x00100000 | (0x000fffff & hx); + else /* subnormal x, shift x to normal */ + { + n = -1022 - ix; + if (n <= 31) + { + hx = (hx << n) | (lx >> (32 - n)); + lx <<= n; + } + else + { + hx = lx << (n - 32); + lx = 0; + } + } + if (__glibc_likely (iy >= -1022)) + hy = 0x00100000 | (0x000fffff & hy); + else /* subnormal y, shift y to normal */ + { + n = -1022 - iy; + if (n <= 31) + { + hy = (hy << n) | (ly >> (32 - n)); + ly <<= n; + } + else + { + hy = ly << (n - 32); + ly = 0; + } + } + + /* fix point fmod */ + n = ix - iy; + while (n--) + { + hz = hx - hy; lz = lx - ly; if (lx < ly) + hz -= 1; + if (hz < 0) + { + hx = hx + hx + (lx >> 31); lx = lx + lx; + } + else + { + if ((hz | lz) == 0) /* return sign(x)*0 */ + return Zero[(u_int32_t) sx >> 31]; + hx = hz + hz + (lz >> 31); lx = lz + lz; + } + } + hz = hx - hy; lz = lx - ly; if (lx < ly) + hz -= 1; + if (hz >= 0) + { + hx = hz; lx = lz; + } + + /* convert back to floating value and restore the sign */ + if ((hx | lx) == 0) /* return sign(x)*0 */ + return Zero[(u_int32_t) sx >> 31]; + while (hx < 0x00100000) /* normalize x */ + { + hx = hx + hx + (lx >> 31); lx = lx + lx; + iy -= 1; + } + if (__glibc_likely (iy >= -1022)) /* normalize output */ + { + hx = ((hx - 0x00100000) | ((iy + 1023) << 20)); + INSERT_WORDS (x, hx | sx, lx); + } + else /* subnormal output */ + { + n = -1022 - iy; + if (n <= 20) + { + lx = (lx >> n) | ((u_int32_t) hx << (32 - n)); + hx >>= n; + } + else if (n <= 31) + { + lx = (hx << (32 - n)) | (lx >> n); hx = sx; + } + else + { + lx = hx >> (n - 32); hx = sx; + } + INSERT_WORDS (x, hx | sx, lx); + x *= one; /* create necessary signal */ + } + return x; /* exact output */ +} +strong_alias (__ieee754_fmod, __fmod_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_gamma_r.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_gamma_r.c new file mode 100644 index 0000000000..818fa94766 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_gamma_r.c @@ -0,0 +1,220 @@ +/* Implementation of gamma function according to ISO C. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's + approximation to gamma function. */ + +static const double gamma_coeff[] = + { + 0x1.5555555555555p-4, + -0xb.60b60b60b60b8p-12, + 0x3.4034034034034p-12, + -0x2.7027027027028p-12, + 0x3.72a3c5631fe46p-12, + -0x7.daac36664f1f4p-12, + }; + +#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0])) + +/* Return gamma (X), for positive X less than 184, in the form R * + 2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to + avoid overflow or underflow in intermediate calculations. */ + +static double +gamma_positive (double x, int *exp2_adj) +{ + int local_signgam; + if (x < 0.5) + { + *exp2_adj = 0; + return __ieee754_exp (__ieee754_lgamma_r (x + 1, &local_signgam)) / x; + } + else if (x <= 1.5) + { + *exp2_adj = 0; + return __ieee754_exp (__ieee754_lgamma_r (x, &local_signgam)); + } + else if (x < 6.5) + { + /* Adjust into the range for using exp (lgamma). */ + *exp2_adj = 0; + double n = __ceil (x - 1.5); + double x_adj = x - n; + double eps; + double prod = __gamma_product (x_adj, 0, n, &eps); + return (__ieee754_exp (__ieee754_lgamma_r (x_adj, &local_signgam)) + * prod * (1.0 + eps)); + } + else + { + double eps = 0; + double x_eps = 0; + double x_adj = x; + double prod = 1; + if (x < 12.0) + { + /* Adjust into the range for applying Stirling's + approximation. */ + double n = __ceil (12.0 - x); + x_adj = math_narrow_eval (x + n); + x_eps = (x - (x_adj - n)); + prod = __gamma_product (x_adj - n, x_eps, n, &eps); + } + /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)). + Compute gamma (X_ADJ + X_EPS) using Stirling's approximation, + starting by computing pow (X_ADJ, X_ADJ) with a power of 2 + factored out. */ + double exp_adj = -eps; + double x_adj_int = __round (x_adj); + double x_adj_frac = x_adj - x_adj_int; + int x_adj_log2; + double x_adj_mant = __frexp (x_adj, &x_adj_log2); + if (x_adj_mant < M_SQRT1_2) + { + x_adj_log2--; + x_adj_mant *= 2.0; + } + *exp2_adj = x_adj_log2 * (int) x_adj_int; + double ret = (__ieee754_pow (x_adj_mant, x_adj) + * __ieee754_exp2 (x_adj_log2 * x_adj_frac) + * __ieee754_exp (-x_adj) + * __ieee754_sqrt (2 * M_PI / x_adj) + / prod); + exp_adj += x_eps * __ieee754_log (x_adj); + double bsum = gamma_coeff[NCOEFF - 1]; + double x_adj2 = x_adj * x_adj; + for (size_t i = 1; i <= NCOEFF - 1; i++) + bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i]; + exp_adj += bsum / x_adj; + return ret + ret * __expm1 (exp_adj); + } +} + +double +__ieee754_gamma_r (double x, int *signgamp) +{ + int32_t hx; + u_int32_t lx; + double ret; + + EXTRACT_WORDS (hx, lx, x); + + if (__glibc_unlikely (((hx & 0x7fffffff) | lx) == 0)) + { + /* Return value for x == 0 is Inf with divide by zero exception. */ + *signgamp = 0; + return 1.0 / x; + } + if (__builtin_expect (hx < 0, 0) + && (u_int32_t) hx < 0xfff00000 && __rint (x) == x) + { + /* Return value for integer x < 0 is NaN with invalid exception. */ + *signgamp = 0; + return (x - x) / (x - x); + } + if (__glibc_unlikely ((unsigned int) hx == 0xfff00000 && lx == 0)) + { + /* x == -Inf. According to ISO this is NaN. */ + *signgamp = 0; + return x - x; + } + if (__glibc_unlikely ((hx & 0x7ff00000) == 0x7ff00000)) + { + /* Positive infinity (return positive infinity) or NaN (return + NaN). */ + *signgamp = 0; + return x + x; + } + + if (x >= 172.0) + { + /* Overflow. */ + *signgamp = 0; + ret = math_narrow_eval (DBL_MAX * DBL_MAX); + return ret; + } + else + { + SET_RESTORE_ROUND (FE_TONEAREST); + if (x > 0.0) + { + *signgamp = 0; + int exp2_adj; + double tret = gamma_positive (x, &exp2_adj); + ret = __scalbn (tret, exp2_adj); + } + else if (x >= -DBL_EPSILON / 4.0) + { + *signgamp = 0; + ret = 1.0 / x; + } + else + { + double tx = __trunc (x); + *signgamp = (tx == 2.0 * __trunc (tx / 2.0)) ? -1 : 1; + if (x <= -184.0) + /* Underflow. */ + ret = DBL_MIN * DBL_MIN; + else + { + double frac = tx - x; + if (frac > 0.5) + frac = 1.0 - frac; + double sinpix = (frac <= 0.25 + ? __sin (M_PI * frac) + : __cos (M_PI * (0.5 - frac))); + int exp2_adj; + double tret = M_PI / (-x * sinpix + * gamma_positive (-x, &exp2_adj)); + ret = __scalbn (tret, -exp2_adj); + math_check_force_underflow_nonneg (ret); + } + } + ret = math_narrow_eval (ret); + } + if (isinf (ret) && x != 0) + { + if (*signgamp < 0) + { + ret = math_narrow_eval (-__copysign (DBL_MAX, ret) * DBL_MAX); + ret = -ret; + } + else + ret = math_narrow_eval (__copysign (DBL_MAX, ret) * DBL_MAX); + return ret; + } + else if (ret == 0) + { + if (*signgamp < 0) + { + ret = math_narrow_eval (-__copysign (DBL_MIN, ret) * DBL_MIN); + ret = -ret; + } + else + ret = math_narrow_eval (__copysign (DBL_MIN, ret) * DBL_MIN); + return ret; + } + else + return ret; +} +strong_alias (__ieee754_gamma_r, __gamma_r_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_hypot.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_hypot.c new file mode 100644 index 0000000000..76eb408348 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_hypot.c @@ -0,0 +1,161 @@ +/* @(#)e_hypot.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_hypot(x,y) + * + * Method : + * If (assume round-to-nearest) z=x*x+y*y + * has error less than sqrt(2)/2 ulp, than + * sqrt(z) has error less than 1 ulp (exercise). + * + * So, compute sqrt(x*x+y*y) with some care as + * follows to get the error below 1 ulp: + * + * Assume x>y>0; + * (if possible, set rounding to round-to-nearest) + * 1. if x > 2y use + * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y + * where x1 = x with lower 32 bits cleared, x2 = x-x1; else + * 2. if x <= 2y use + * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) + * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, + * y1= y with lower 32 bits chopped, y2 = y-y1. + * + * NOTE: scaling may be necessary if some argument is too + * large or too tiny + * + * Special cases: + * hypot(x,y) is INF if x or y is +INF or -INF; else + * hypot(x,y) is NAN if x or y is NAN. + * + * Accuracy: + * hypot(x,y) returns sqrt(x^2+y^2) with error less + * than 1 ulps (units in the last place) + */ + +#include <math.h> +#include <math_private.h> + +double +__ieee754_hypot (double x, double y) +{ + double a, b, t1, t2, y1, y2, w; + int32_t j, k, ha, hb; + + GET_HIGH_WORD (ha, x); + ha &= 0x7fffffff; + GET_HIGH_WORD (hb, y); + hb &= 0x7fffffff; + if (hb > ha) + { + a = y; b = x; j = ha; ha = hb; hb = j; + } + else + { + a = x; b = y; + } + SET_HIGH_WORD (a, ha); /* a <- |a| */ + SET_HIGH_WORD (b, hb); /* b <- |b| */ + if ((ha - hb) > 0x3c00000) + { + return a + b; + } /* x/y > 2**60 */ + k = 0; + if (__glibc_unlikely (ha > 0x5f300000)) /* a>2**500 */ + { + if (ha >= 0x7ff00000) /* Inf or NaN */ + { + u_int32_t low; + w = a + b; /* for sNaN */ + if (issignaling (a) || issignaling (b)) + return w; + GET_LOW_WORD (low, a); + if (((ha & 0xfffff) | low) == 0) + w = a; + GET_LOW_WORD (low, b); + if (((hb ^ 0x7ff00000) | low) == 0) + w = b; + return w; + } + /* scale a and b by 2**-600 */ + ha -= 0x25800000; hb -= 0x25800000; k += 600; + SET_HIGH_WORD (a, ha); + SET_HIGH_WORD (b, hb); + } + if (__builtin_expect (hb < 0x23d00000, 0)) /* b < 2**-450 */ + { + if (hb <= 0x000fffff) /* subnormal b or 0 */ + { + u_int32_t low; + GET_LOW_WORD (low, b); + if ((hb | low) == 0) + return a; + t1 = 0; + SET_HIGH_WORD (t1, 0x7fd00000); /* t1=2^1022 */ + b *= t1; + a *= t1; + k -= 1022; + GET_HIGH_WORD (ha, a); + GET_HIGH_WORD (hb, b); + if (hb > ha) + { + t1 = a; + a = b; + b = t1; + j = ha; + ha = hb; + hb = j; + } + } + else /* scale a and b by 2^600 */ + { + ha += 0x25800000; /* a *= 2^600 */ + hb += 0x25800000; /* b *= 2^600 */ + k -= 600; + SET_HIGH_WORD (a, ha); + SET_HIGH_WORD (b, hb); + } + } + /* medium size a and b */ + w = a - b; + if (w > b) + { + t1 = 0; + SET_HIGH_WORD (t1, ha); + t2 = a - t1; + w = __ieee754_sqrt (t1 * t1 - (b * (-b) - t2 * (a + t1))); + } + else + { + a = a + a; + y1 = 0; + SET_HIGH_WORD (y1, hb); + y2 = b - y1; + t1 = 0; + SET_HIGH_WORD (t1, ha + 0x00100000); + t2 = a - t1; + w = __ieee754_sqrt (t1 * y1 - (w * (-w) - (t1 * y2 + t2 * b))); + } + if (k != 0) + { + u_int32_t high; + t1 = 1.0; + GET_HIGH_WORD (high, t1); + SET_HIGH_WORD (t1, high + (k << 20)); + w *= t1; + math_check_force_underflow_nonneg (w); + return w; + } + else + return w; +} +strong_alias (__ieee754_hypot, __hypot_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_ilogb.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_ilogb.c new file mode 100644 index 0000000000..1e338a59c1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_ilogb.c @@ -0,0 +1,63 @@ +/* @(#)s_ilogb.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_ilogb.c,v 1.9 1995/05/10 20:47:28 jtc Exp $"; +#endif + +/* ilogb(double x) + * return the binary exponent of non-zero x + * ilogb(0) = FP_ILOGB0 + * ilogb(NaN) = FP_ILOGBNAN (no signal is raised) + * ilogb(+-Inf) = INT_MAX (no signal is raised) + */ + +#include <limits.h> +#include <math.h> +#include <math_private.h> + +int +__ieee754_ilogb (double x) +{ + int32_t hx, lx, ix; + + GET_HIGH_WORD (hx, x); + hx &= 0x7fffffff; + if (hx < 0x00100000) + { + GET_LOW_WORD (lx, x); + if ((hx | lx) == 0) + return FP_ILOGB0; /* ilogb(0) = FP_ILOGB0 */ + else /* subnormal x */ + if (hx == 0) + { + for (ix = -1043; lx > 0; lx <<= 1) + ix -= 1; + } + else + { + for (ix = -1022, hx <<= 11; hx > 0; hx <<= 1) + ix -= 1; + } + return ix; + } + else if (hx < 0x7ff00000) + return (hx >> 20) - 1023; + else if (FP_ILOGBNAN != INT_MAX) + { + /* ISO C99 requires ilogb(+-Inf) == INT_MAX. */ + GET_LOW_WORD (lx, x); + if (((hx ^ 0x7ff00000) | lx) == 0) + return INT_MAX; + } + return FP_ILOGBNAN; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_j0.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_j0.c new file mode 100644 index 0000000000..4b440cf0d0 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_j0.c @@ -0,0 +1,458 @@ +/* @(#)e_j0.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/26, + for performance improvement on pipelined processors. + */ + +/* __ieee754_j0(x), __ieee754_y0(x) + * Bessel function of the first and second kinds of order zero. + * Method -- j0(x): + * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ... + * 2. Reduce x to |x| since j0(x)=j0(-x), and + * for x in (0,2) + * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x; + * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 ) + * for x in (2,inf) + * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0)) + * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) + * as follow: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (cos(x) + sin(x)) + * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * (To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one.) + * + * 3 Special cases + * j0(nan)= nan + * j0(0) = 1 + * j0(inf) = 0 + * + * Method -- y0(x): + * 1. For x<2. + * Since + * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) + * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function. + * We use the following function to approximate y0, + * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2 + * where + * U(z) = u00 + u01*z + ... + u06*z^6 + * V(z) = 1 + v01*z + ... + v04*z^4 + * with absolute approximation error bounded by 2**-72. + * Note: For tiny x, U/V = u0 and j0(x)~1, hence + * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) + * 2. For x>=2. + * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0)) + * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) + * by the method mentioned above. + * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0. + */ + +#include <math.h> +#include <math_private.h> + +static double pzero (double), qzero (double); + +static const double + huge = 1e300, + one = 1.0, + invsqrtpi = 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ + tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ +/* R0/S0 on [0, 2.00] */ + R[] = { 0.0, 0.0, 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */ + -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */ + 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */ + -4.61832688532103189199e-09 }, /* 0xBE33D5E7, 0x73D63FCE */ + S[] = { 0.0, 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */ + 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */ + 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */ + 1.16614003333790000205e-09 }; /* 0x3E1408BC, 0xF4745D8F */ + +static const double zero = 0.0; + +double +__ieee754_j0 (double x) +{ + double z, s, c, ss, cc, r, u, v, r1, r2, s1, s2, z2, z4; + int32_t hx, ix; + + GET_HIGH_WORD (hx, x); + ix = hx & 0x7fffffff; + if (ix >= 0x7ff00000) + return one / (x * x); + x = fabs (x); + if (ix >= 0x40000000) /* |x| >= 2.0 */ + { + __sincos (x, &s, &c); + ss = s - c; + cc = s + c; + if (ix < 0x7fe00000) /* make sure x+x not overflow */ + { + z = -__cos (x + x); + if ((s * c) < zero) + cc = z / ss; + else + ss = z / cc; + } + /* + * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) + * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) + */ + if (ix > 0x48000000) + z = (invsqrtpi * cc) / __ieee754_sqrt (x); + else + { + u = pzero (x); v = qzero (x); + z = invsqrtpi * (u * cc - v * ss) / __ieee754_sqrt (x); + } + return z; + } + if (ix < 0x3f200000) /* |x| < 2**-13 */ + { + math_force_eval (huge + x); /* raise inexact if x != 0 */ + if (ix < 0x3e400000) + return one; /* |x|<2**-27 */ + else + return one - 0.25 * x * x; + } + z = x * x; + r1 = z * R[2]; z2 = z * z; + r2 = R[3] + z * R[4]; z4 = z2 * z2; + r = r1 + z2 * r2 + z4 * R[5]; + s1 = one + z * S[1]; + s2 = S[2] + z * S[3]; + s = s1 + z2 * s2 + z4 * S[4]; + if (ix < 0x3FF00000) /* |x| < 1.00 */ + { + return one + z * (-0.25 + (r / s)); + } + else + { + u = 0.5 * x; + return ((one + u) * (one - u) + z * (r / s)); + } +} +strong_alias (__ieee754_j0, __j0_finite) + +static const double +U[] = { -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */ + 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */ + -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */ + 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */ + -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */ + 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */ + -3.98205194132103398453e-11 }, /* 0xBDC5E43D, 0x693FB3C8 */ +V[] = { 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ + 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */ + 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ + 4.41110311332675467403e-10 }; /* 0x3DFE5018, 0x3BD6D9EF */ + +double +__ieee754_y0 (double x) +{ + double z, s, c, ss, cc, u, v, z2, z4, z6, u1, u2, u3, v1, v2; + int32_t hx, ix, lx; + + EXTRACT_WORDS (hx, lx, x); + ix = 0x7fffffff & hx; + /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0, y0(0) is -inf. */ + if (ix >= 0x7ff00000) + return one / (x + x * x); + if ((ix | lx) == 0) + return -1 / zero; /* -inf and divide by zero exception. */ + if (hx < 0) + return zero / (zero * x); + if (ix >= 0x40000000) /* |x| >= 2.0 */ + { /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) + * where x0 = x-pi/4 + * Better formula: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (sin(x) + cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + __sincos (x, &s, &c); + ss = s - c; + cc = s + c; + /* + * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) + * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) + */ + if (ix < 0x7fe00000) /* make sure x+x not overflow */ + { + z = -__cos (x + x); + if ((s * c) < zero) + cc = z / ss; + else + ss = z / cc; + } + if (ix > 0x48000000) + z = (invsqrtpi * ss) / __ieee754_sqrt (x); + else + { + u = pzero (x); v = qzero (x); + z = invsqrtpi * (u * ss + v * cc) / __ieee754_sqrt (x); + } + return z; + } + if (ix <= 0x3e400000) /* x < 2**-27 */ + { + return (U[0] + tpi * __ieee754_log (x)); + } + z = x * x; + u1 = U[0] + z * U[1]; z2 = z * z; + u2 = U[2] + z * U[3]; z4 = z2 * z2; + u3 = U[4] + z * U[5]; z6 = z4 * z2; + u = u1 + z2 * u2 + z4 * u3 + z6 * U[6]; + v1 = one + z * V[0]; + v2 = V[1] + z * V[2]; + v = v1 + z2 * v2 + z4 * V[3]; + return (u / v + tpi * (__ieee754_j0 (x) * __ieee754_log (x))); +} +strong_alias (__ieee754_y0, __y0_finite) + +/* The asymptotic expansions of pzero is + * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. + * For x >= 2, We approximate pzero by + * pzero(x) = 1 + (R/S) + * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 + * S = 1 + pS0*s^2 + ... + pS4*s^10 + * and + * | pzero(x)-1-R/S | <= 2 ** ( -60.26) + */ +static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */ + -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */ + -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */ + -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */ + -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */ +}; +static const double pS8[5] = { + 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */ + 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */ + 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */ + 1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */ + 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */ +}; + +static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */ + -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */ + -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */ + -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */ + -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */ + -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */ +}; +static const double pS5[5] = { + 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */ + 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */ + 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */ + 9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */ + 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */ +}; + +static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ + -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */ + -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */ + -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */ + -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */ + -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */ + -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */ +}; +static const double pS3[5] = { + 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */ + 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */ + 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */ + 1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */ + 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */ +}; + +static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */ + -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */ + -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */ + -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */ + -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */ + -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */ +}; +static const double pS2[5] = { + 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */ + 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */ + 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */ + 1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */ + 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */ +}; + +static double +pzero (double x) +{ + const double *p, *q; + double z, r, s, z2, z4, r1, r2, r3, s1, s2, s3; + int32_t ix; + GET_HIGH_WORD (ix, x); + ix &= 0x7fffffff; + /* ix >= 0x40000000 for all calls to this function. */ + if (ix >= 0x41b00000) + { + return one; + } + else if (ix >= 0x40200000) + { + p = pR8; q = pS8; + } + else if (ix >= 0x40122E8B) + { + p = pR5; q = pS5; + } + else if (ix >= 0x4006DB6D) + { + p = pR3; q = pS3; + } + else + { + p = pR2; q = pS2; + } + z = one / (x * x); + r1 = p[0] + z * p[1]; z2 = z * z; + r2 = p[2] + z * p[3]; z4 = z2 * z2; + r3 = p[4] + z * p[5]; + r = r1 + z2 * r2 + z4 * r3; + s1 = one + z * q[0]; + s2 = q[1] + z * q[2]; + s3 = q[3] + z * q[4]; + s = s1 + z2 * s2 + z4 * s3; + return one + r / s; +} + + +/* For x >= 8, the asymptotic expansions of qzero is + * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. + * We approximate pzero by + * qzero(x) = s*(-1.25 + (R/S)) + * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 + * S = 1 + qS0*s^2 + ... + qS5*s^12 + * and + * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) + */ +static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */ + 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */ + 5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */ + 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */ + 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */ +}; +static const double qS8[6] = { + 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */ + 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */ + 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */ + 8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */ + 8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */ + -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */ +}; + +static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */ + 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */ + 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */ + 1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */ + 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */ + 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */ +}; +static const double qS5[6] = { + 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */ + 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */ + 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */ + 5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */ + 3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */ + -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */ +}; + +static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ + 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */ + 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */ + 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */ + 4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */ + 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */ + 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */ +}; +static const double qS3[6] = { + 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */ + 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */ + 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */ + 6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */ + 2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */ + -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */ +}; + +static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */ + 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */ + 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */ + 1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */ + 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */ + 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */ +}; +static const double qS2[6] = { + 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */ + 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */ + 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */ + 8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */ + 2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */ + -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */ +}; + +static double +qzero (double x) +{ + const double *p, *q; + double s, r, z, z2, z4, z6, r1, r2, r3, s1, s2, s3; + int32_t ix; + GET_HIGH_WORD (ix, x); + ix &= 0x7fffffff; + /* ix >= 0x40000000 for all calls to this function. */ + if (ix >= 0x41b00000) + { + return -.125 / x; + } + else if (ix >= 0x40200000) + { + p = qR8; q = qS8; + } + else if (ix >= 0x40122E8B) + { + p = qR5; q = qS5; + } + else if (ix >= 0x4006DB6D) + { + p = qR3; q = qS3; + } + else + { + p = qR2; q = qS2; + } + z = one / (x * x); + r1 = p[0] + z * p[1]; z2 = z * z; + r2 = p[2] + z * p[3]; z4 = z2 * z2; + r3 = p[4] + z * p[5]; z6 = z4 * z2; + r = r1 + z2 * r2 + z4 * r3; + s1 = one + z * q[0]; + s2 = q[1] + z * q[2]; + s3 = q[3] + z * q[4]; + s = s1 + z2 * s2 + z4 * s3 + z6 * q[5]; + return (-.125 + r / s) / x; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_j1.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_j1.c new file mode 100644 index 0000000000..eb446fd102 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_j1.c @@ -0,0 +1,466 @@ +/* @(#)e_j1.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/26, + for performance improvement on pipelined processors. + */ + +/* __ieee754_j1(x), __ieee754_y1(x) + * Bessel function of the first and second kinds of order zero. + * Method -- j1(x): + * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ... + * 2. Reduce x to |x| since j1(x)=-j1(-x), and + * for x in (0,2) + * j1(x) = x/2 + x*z*R0/S0, where z = x*x; + * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 ) + * for x in (2,inf) + * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1)) + * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) + * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) + * as follow: + * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = -1/sqrt(2) * (sin(x) + cos(x)) + * (To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one.) + * + * 3 Special cases + * j1(nan)= nan + * j1(0) = 0 + * j1(inf) = 0 + * + * Method -- y1(x): + * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN + * 2. For x<2. + * Since + * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) + * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function. + * We use the following function to approximate y1, + * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2 + * where for x in [0,2] (abs err less than 2**-65.89) + * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4 + * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5 + * Note: For tiny x, 1/x dominate y1 and hence + * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54) + * 3. For x>=2. + * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) + * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) + * by method mentioned above. + */ + +#include <errno.h> +#include <float.h> +#include <math.h> +#include <math_private.h> + +static double pone (double), qone (double); + +static const double + huge = 1e300, + one = 1.0, + invsqrtpi = 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ + tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ +/* R0/S0 on [0,2] */ + R[] = { -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */ + 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */ + -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */ + 4.96727999609584448412e-08 }, /* 0x3E6AAAFA, 0x46CA0BD9 */ + S[] = { 0.0, 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */ + 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */ + 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */ + 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */ + 1.23542274426137913908e-11 }; /* 0x3DAB2ACF, 0xCFB97ED8 */ + +static const double zero = 0.0; + +double +__ieee754_j1 (double x) +{ + double z, s, c, ss, cc, r, u, v, y, r1, r2, s1, s2, s3, z2, z4; + int32_t hx, ix; + + GET_HIGH_WORD (hx, x); + ix = hx & 0x7fffffff; + if (__glibc_unlikely (ix >= 0x7ff00000)) + return one / x; + y = fabs (x); + if (ix >= 0x40000000) /* |x| >= 2.0 */ + { + __sincos (y, &s, &c); + ss = -s - c; + cc = s - c; + if (ix < 0x7fe00000) /* make sure y+y not overflow */ + { + z = __cos (y + y); + if ((s * c) > zero) + cc = z / ss; + else + ss = z / cc; + } + /* + * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) + * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) + */ + if (ix > 0x48000000) + z = (invsqrtpi * cc) / __ieee754_sqrt (y); + else + { + u = pone (y); v = qone (y); + z = invsqrtpi * (u * cc - v * ss) / __ieee754_sqrt (y); + } + if (hx < 0) + return -z; + else + return z; + } + if (__glibc_unlikely (ix < 0x3e400000)) /* |x|<2**-27 */ + { + if (huge + x > one) /* inexact if x!=0 necessary */ + { + double ret = math_narrow_eval (0.5 * x); + math_check_force_underflow (ret); + if (ret == 0 && x != 0) + __set_errno (ERANGE); + return ret; + } + } + z = x * x; + r1 = z * R[0]; z2 = z * z; + r2 = R[1] + z * R[2]; z4 = z2 * z2; + r = r1 + z2 * r2 + z4 * R[3]; + r *= x; + s1 = one + z * S[1]; + s2 = S[2] + z * S[3]; + s3 = S[4] + z * S[5]; + s = s1 + z2 * s2 + z4 * s3; + return (x * 0.5 + r / s); +} +strong_alias (__ieee754_j1, __j1_finite) + +static const double U0[5] = { + -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */ + 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */ + -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */ + 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */ + -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */ +}; +static const double V0[5] = { + 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */ + 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */ + 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */ + 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */ + 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */ +}; + +double +__ieee754_y1 (double x) +{ + double z, s, c, ss, cc, u, v, u1, u2, v1, v2, v3, z2, z4; + int32_t hx, ix, lx; + + EXTRACT_WORDS (hx, lx, x); + ix = 0x7fffffff & hx; + /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ + if (__glibc_unlikely (ix >= 0x7ff00000)) + return one / (x + x * x); + if (__glibc_unlikely ((ix | lx) == 0)) + return -1 / zero; /* -inf and divide by zero exception. */ + /* -inf and overflow exception. */; + if (__glibc_unlikely (hx < 0)) + return zero / (zero * x); + if (ix >= 0x40000000) /* |x| >= 2.0 */ + { + __sincos (x, &s, &c); + ss = -s - c; + cc = s - c; + if (ix < 0x7fe00000) /* make sure x+x not overflow */ + { + z = __cos (x + x); + if ((s * c) > zero) + cc = z / ss; + else + ss = z / cc; + } + /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) + * where x0 = x-3pi/4 + * Better formula: + * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = -1/sqrt(2) * (cos(x) + sin(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + if (ix > 0x48000000) + z = (invsqrtpi * ss) / __ieee754_sqrt (x); + else + { + u = pone (x); v = qone (x); + z = invsqrtpi * (u * ss + v * cc) / __ieee754_sqrt (x); + } + return z; + } + if (__glibc_unlikely (ix <= 0x3c900000)) /* x < 2**-54 */ + { + z = -tpi / x; + if (isinf (z)) + __set_errno (ERANGE); + return z; + } + z = x * x; + u1 = U0[0] + z * U0[1]; z2 = z * z; + u2 = U0[2] + z * U0[3]; z4 = z2 * z2; + u = u1 + z2 * u2 + z4 * U0[4]; + v1 = one + z * V0[0]; + v2 = V0[1] + z * V0[2]; + v3 = V0[3] + z * V0[4]; + v = v1 + z2 * v2 + z4 * v3; + return (x * (u / v) + tpi * (__ieee754_j1 (x) * __ieee754_log (x) - one / x)); +} +strong_alias (__ieee754_y1, __y1_finite) + +/* For x >= 8, the asymptotic expansions of pone is + * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. + * We approximate pone by + * pone(x) = 1 + (R/S) + * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 + * S = 1 + ps0*s^2 + ... + ps4*s^10 + * and + * | pone(x)-1-R/S | <= 2 ** ( -60.06) + */ + +static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */ + 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */ + 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */ + 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */ + 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */ +}; +static const double ps8[5] = { + 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */ + 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */ + 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */ + 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */ + 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */ +}; + +static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */ + 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */ + 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */ + 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */ + 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */ + 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */ +}; +static const double ps5[5] = { + 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */ + 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */ + 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */ + 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */ + 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */ +}; + +static const double pr3[6] = { + 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */ + 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */ + 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */ + 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */ + 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */ + 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */ +}; +static const double ps3[5] = { + 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */ + 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */ + 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */ + 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */ + 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */ +}; + +static const double pr2[6] = { /* for x in [2.8570,2]=1/[0.3499,0.5] */ + 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */ + 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */ + 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */ + 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */ + 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */ + 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */ +}; +static const double ps2[5] = { + 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */ + 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */ + 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */ + 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */ + 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */ +}; + +static double +pone (double x) +{ + const double *p, *q; + double z, r, s, r1, r2, r3, s1, s2, s3, z2, z4; + int32_t ix; + GET_HIGH_WORD (ix, x); + ix &= 0x7fffffff; + /* ix >= 0x40000000 for all calls to this function. */ + if (ix >= 0x41b00000) + { + return one; + } + else if (ix >= 0x40200000) + { + p = pr8; q = ps8; + } + else if (ix >= 0x40122E8B) + { + p = pr5; q = ps5; + } + else if (ix >= 0x4006DB6D) + { + p = pr3; q = ps3; + } + else + { + p = pr2; q = ps2; + } + z = one / (x * x); + r1 = p[0] + z * p[1]; z2 = z * z; + r2 = p[2] + z * p[3]; z4 = z2 * z2; + r3 = p[4] + z * p[5]; + r = r1 + z2 * r2 + z4 * r3; + s1 = one + z * q[0]; + s2 = q[1] + z * q[2]; + s3 = q[3] + z * q[4]; + s = s1 + z2 * s2 + z4 * s3; + return one + r / s; +} + + +/* For x >= 8, the asymptotic expansions of qone is + * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. + * We approximate pone by + * qone(x) = s*(0.375 + (R/S)) + * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 + * S = 1 + qs1*s^2 + ... + qs6*s^12 + * and + * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) + */ + +static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */ + -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */ + -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */ + -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */ + -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */ +}; +static const double qs8[6] = { + 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */ + 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */ + 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */ + 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */ + 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */ + -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */ +}; + +static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */ + -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */ + -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */ + -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */ + -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */ + -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */ +}; +static const double qs5[6] = { + 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */ + 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */ + 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */ + 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */ + 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */ + -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */ +}; + +static const double qr3[6] = { + -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */ + -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */ + -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */ + -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */ + -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */ + -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */ +}; +static const double qs3[6] = { + 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */ + 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */ + 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */ + 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */ + 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */ + -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */ +}; + +static const double qr2[6] = { /* for x in [2.8570,2]=1/[0.3499,0.5] */ + -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */ + -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */ + -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */ + -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */ + -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */ + -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */ +}; +static const double qs2[6] = { + 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */ + 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */ + 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */ + 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */ + 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */ + -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */ +}; + +static double +qone (double x) +{ + const double *p, *q; + double s, r, z, r1, r2, r3, s1, s2, s3, z2, z4, z6; + int32_t ix; + GET_HIGH_WORD (ix, x); + ix &= 0x7fffffff; + /* ix >= 0x40000000 for all calls to this function. */ + if (ix >= 0x41b00000) + { + return .375 / x; + } + else if (ix >= 0x40200000) + { + p = qr8; q = qs8; + } + else if (ix >= 0x40122E8B) + { + p = qr5; q = qs5; + } + else if (ix >= 0x4006DB6D) + { + p = qr3; q = qs3; + } + else + { + p = qr2; q = qs2; + } + z = one / (x * x); + r1 = p[0] + z * p[1]; z2 = z * z; + r2 = p[2] + z * p[3]; z4 = z2 * z2; + r3 = p[4] + z * p[5]; z6 = z4 * z2; + r = r1 + z2 * r2 + z4 * r3; + s1 = one + z * q[0]; + s2 = q[1] + z * q[2]; + s3 = q[3] + z * q[4]; + s = s1 + z2 * s2 + z4 * s3 + z6 * q[5]; + return (.375 + r / s) / x; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_jn.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_jn.c new file mode 100644 index 0000000000..3fecf82f10 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_jn.c @@ -0,0 +1,347 @@ +/* @(#)e_jn.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * __ieee754_jn(n, x), __ieee754_yn(n, x) + * floating point Bessel's function of the 1st and 2nd kind + * of order n + * + * Special cases: + * y0(0)=y1(0)=yn(n,0) = -inf with overflow signal; + * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. + * Note 2. About jn(n,x), yn(n,x) + * For n=0, j0(x) is called, + * for n=1, j1(x) is called, + * for n<x, forward recursion us used starting + * from values of j0(x) and j1(x). + * for n>x, a continued fraction approximation to + * j(n,x)/j(n-1,x) is evaluated and then backward + * recursion is used starting from a supposed value + * for j(n,x). The resulting value of j(0,x) is + * compared with the actual value to correct the + * supposed value of j(n,x). + * + * yn(n,x) is similar in all respects, except + * that forward recursion is used for all + * values of n>1. + * + */ + +#include <errno.h> +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const double + invsqrtpi = 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ + two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ + one = 1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */ + +static const double zero = 0.00000000000000000000e+00; + +double +__ieee754_jn (int n, double x) +{ + int32_t i, hx, ix, lx, sgn; + double a, b, temp, di, ret; + double z, w; + + /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) + * Thus, J(-n,x) = J(n,-x) + */ + EXTRACT_WORDS (hx, lx, x); + ix = 0x7fffffff & hx; + /* if J(n,NaN) is NaN */ + if (__glibc_unlikely ((ix | ((u_int32_t) (lx | -lx)) >> 31) > 0x7ff00000)) + return x + x; + if (n < 0) + { + n = -n; + x = -x; + hx ^= 0x80000000; + } + if (n == 0) + return (__ieee754_j0 (x)); + if (n == 1) + return (__ieee754_j1 (x)); + sgn = (n & 1) & (hx >> 31); /* even n -- 0, odd n -- sign(x) */ + x = fabs (x); + { + SET_RESTORE_ROUND (FE_TONEAREST); + if (__glibc_unlikely ((ix | lx) == 0 || ix >= 0x7ff00000)) + /* if x is 0 or inf */ + return sgn == 1 ? -zero : zero; + else if ((double) n <= x) + { + /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ + if (ix >= 0x52D00000) /* x > 2**302 */ + { /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + double s; + double c; + __sincos (x, &s, &c); + switch (n & 3) + { + case 0: temp = c + s; break; + case 1: temp = -c + s; break; + case 2: temp = -c - s; break; + case 3: temp = c - s; break; + } + b = invsqrtpi * temp / __ieee754_sqrt (x); + } + else + { + a = __ieee754_j0 (x); + b = __ieee754_j1 (x); + for (i = 1; i < n; i++) + { + temp = b; + b = b * ((double) (i + i) / x) - a; /* avoid underflow */ + a = temp; + } + } + } + else + { + if (ix < 0x3e100000) /* x < 2**-29 */ + { /* x is tiny, return the first Taylor expansion of J(n,x) + * J(n,x) = 1/n!*(x/2)^n - ... + */ + if (n > 33) /* underflow */ + b = zero; + else + { + temp = x * 0.5; b = temp; + for (a = one, i = 2; i <= n; i++) + { + a *= (double) i; /* a = n! */ + b *= temp; /* b = (x/2)^n */ + } + b = b / a; + } + } + else + { + /* use backward recurrence */ + /* x x^2 x^2 + * J(n,x)/J(n-1,x) = ---- ------ ------ ..... + * 2n - 2(n+1) - 2(n+2) + * + * 1 1 1 + * (for large x) = ---- ------ ------ ..... + * 2n 2(n+1) 2(n+2) + * -- - ------ - ------ - + * x x x + * + * Let w = 2n/x and h=2/x, then the above quotient + * is equal to the continued fraction: + * 1 + * = ----------------------- + * 1 + * w - ----------------- + * 1 + * w+h - --------- + * w+2h - ... + * + * To determine how many terms needed, let + * Q(0) = w, Q(1) = w(w+h) - 1, + * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), + * When Q(k) > 1e4 good for single + * When Q(k) > 1e9 good for double + * When Q(k) > 1e17 good for quadruple + */ + /* determine k */ + double t, v; + double q0, q1, h, tmp; int32_t k, m; + w = (n + n) / (double) x; h = 2.0 / (double) x; + q0 = w; z = w + h; q1 = w * z - 1.0; k = 1; + while (q1 < 1.0e9) + { + k += 1; z += h; + tmp = z * q1 - q0; + q0 = q1; + q1 = tmp; + } + m = n + n; + for (t = zero, i = 2 * (n + k); i >= m; i -= 2) + t = one / (i / x - t); + a = t; + b = one; + /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n) + * Hence, if n*(log(2n/x)) > ... + * single 8.8722839355e+01 + * double 7.09782712893383973096e+02 + * long double 1.1356523406294143949491931077970765006170e+04 + * then recurrent value may overflow and the result is + * likely underflow to zero + */ + tmp = n; + v = two / x; + tmp = tmp * __ieee754_log (fabs (v * tmp)); + if (tmp < 7.09782712893383973096e+02) + { + for (i = n - 1, di = (double) (i + i); i > 0; i--) + { + temp = b; + b *= di; + b = b / x - a; + a = temp; + di -= two; + } + } + else + { + for (i = n - 1, di = (double) (i + i); i > 0; i--) + { + temp = b; + b *= di; + b = b / x - a; + a = temp; + di -= two; + /* scale b to avoid spurious overflow */ + if (b > 1e100) + { + a /= b; + t /= b; + b = one; + } + } + } + /* j0() and j1() suffer enormous loss of precision at and + * near zero; however, we know that their zero points never + * coincide, so just choose the one further away from zero. + */ + z = __ieee754_j0 (x); + w = __ieee754_j1 (x); + if (fabs (z) >= fabs (w)) + b = (t * z / b); + else + b = (t * w / a); + } + } + if (sgn == 1) + ret = -b; + else + ret = b; + ret = math_narrow_eval (ret); + } + if (ret == 0) + { + ret = math_narrow_eval (__copysign (DBL_MIN, ret) * DBL_MIN); + __set_errno (ERANGE); + } + else + math_check_force_underflow (ret); + return ret; +} +strong_alias (__ieee754_jn, __jn_finite) + +double +__ieee754_yn (int n, double x) +{ + int32_t i, hx, ix, lx; + int32_t sign; + double a, b, temp, ret; + + EXTRACT_WORDS (hx, lx, x); + ix = 0x7fffffff & hx; + /* if Y(n,NaN) is NaN */ + if (__glibc_unlikely ((ix | ((u_int32_t) (lx | -lx)) >> 31) > 0x7ff00000)) + return x + x; + if (__glibc_unlikely ((ix | lx) == 0)) + return -HUGE_VAL + x; + /* -inf and overflow exception. */; + if (__glibc_unlikely (hx < 0)) + return zero / (zero * x); + sign = 1; + if (n < 0) + { + n = -n; + sign = 1 - ((n & 1) << 1); + } + if (n == 0) + return (__ieee754_y0 (x)); + { + SET_RESTORE_ROUND (FE_TONEAREST); + if (n == 1) + { + ret = sign * __ieee754_y1 (x); + goto out; + } + if (__glibc_unlikely (ix == 0x7ff00000)) + return zero; + if (ix >= 0x52D00000) /* x > 2**302 */ + { /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + double c; + double s; + __sincos (x, &s, &c); + switch (n & 3) + { + case 0: temp = s - c; break; + case 1: temp = -s - c; break; + case 2: temp = -s + c; break; + case 3: temp = s + c; break; + } + b = invsqrtpi * temp / __ieee754_sqrt (x); + } + else + { + u_int32_t high; + a = __ieee754_y0 (x); + b = __ieee754_y1 (x); + /* quit if b is -inf */ + GET_HIGH_WORD (high, b); + for (i = 1; i < n && high != 0xfff00000; i++) + { + temp = b; + b = ((double) (i + i) / x) * b - a; + GET_HIGH_WORD (high, b); + a = temp; + } + /* If B is +-Inf, set up errno accordingly. */ + if (!isfinite (b)) + __set_errno (ERANGE); + } + if (sign > 0) + ret = b; + else + ret = -b; + } + out: + if (isinf (ret)) + ret = __copysign (DBL_MAX, ret) * DBL_MAX; + return ret; +} +strong_alias (__ieee754_yn, __yn_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_lgamma_r.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_lgamma_r.c new file mode 100644 index 0000000000..b5860d8a24 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_lgamma_r.c @@ -0,0 +1,310 @@ +/* @(#)er_lgamma.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_lgamma_r(x, signgamp) + * Reentrant version of the logarithm of the Gamma function + * with user provide pointer for the sign of Gamma(x). + * + * Method: + * 1. Argument Reduction for 0 < x <= 8 + * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may + * reduce x to a number in [1.5,2.5] by + * lgamma(1+s) = log(s) + lgamma(s) + * for example, + * lgamma(7.3) = log(6.3) + lgamma(6.3) + * = log(6.3*5.3) + lgamma(5.3) + * = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3) + * 2. Polynomial approximation of lgamma around its + * minimun ymin=1.461632144968362245 to maintain monotonicity. + * On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use + * Let z = x-ymin; + * lgamma(x) = -1.214862905358496078218 + z^2*poly(z) + * where + * poly(z) is a 14 degree polynomial. + * 2. Rational approximation in the primary interval [2,3] + * We use the following approximation: + * s = x-2.0; + * lgamma(x) = 0.5*s + s*P(s)/Q(s) + * with accuracy + * |P/Q - (lgamma(x)-0.5s)| < 2**-61.71 + * Our algorithms are based on the following observation + * + * zeta(2)-1 2 zeta(3)-1 3 + * lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ... + * 2 3 + * + * where Euler = 0.5771... is the Euler constant, which is very + * close to 0.5. + * + * 3. For x>=8, we have + * lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+.... + * (better formula: + * lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...) + * Let z = 1/x, then we approximation + * f(z) = lgamma(x) - (x-0.5)(log(x)-1) + * by + * 3 5 11 + * w = w0 + w1*z + w2*z + w3*z + ... + w6*z + * where + * |w - f(z)| < 2**-58.74 + * + * 4. For negative x, since (G is gamma function) + * -x*G(-x)*G(x) = pi/sin(pi*x), + * we have + * G(x) = pi/(sin(pi*x)*(-x)*G(-x)) + * since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0 + * Hence, for x<0, signgam = sign(sin(pi*x)) and + * lgamma(x) = log(|Gamma(x)|) + * = log(pi/(|x*sin(pi*x)|)) - lgamma(-x); + * Note: one should avoid compute pi*(-x) directly in the + * computation of sin(pi*(-x)). + * + * 5. Special Cases + * lgamma(2+s) ~ s*(1-Euler) for tiny s + * lgamma(1)=lgamma(2)=0 + * lgamma(x) ~ -log(x) for tiny x + * lgamma(0) = lgamma(inf) = inf + * lgamma(-integer) = +-inf + * + */ + +#include <math.h> +#include <math_private.h> +#include <libc-diag.h> + +static const double +two52= 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ +half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ +a0 = 7.72156649015328655494e-02, /* 0x3FB3C467, 0xE37DB0C8 */ +a1 = 3.22467033424113591611e-01, /* 0x3FD4A34C, 0xC4A60FAD */ +a2 = 6.73523010531292681824e-02, /* 0x3FB13E00, 0x1A5562A7 */ +a3 = 2.05808084325167332806e-02, /* 0x3F951322, 0xAC92547B */ +a4 = 7.38555086081402883957e-03, /* 0x3F7E404F, 0xB68FEFE8 */ +a5 = 2.89051383673415629091e-03, /* 0x3F67ADD8, 0xCCB7926B */ +a6 = 1.19270763183362067845e-03, /* 0x3F538A94, 0x116F3F5D */ +a7 = 5.10069792153511336608e-04, /* 0x3F40B6C6, 0x89B99C00 */ +a8 = 2.20862790713908385557e-04, /* 0x3F2CF2EC, 0xED10E54D */ +a9 = 1.08011567247583939954e-04, /* 0x3F1C5088, 0x987DFB07 */ +a10 = 2.52144565451257326939e-05, /* 0x3EFA7074, 0x428CFA52 */ +a11 = 4.48640949618915160150e-05, /* 0x3F07858E, 0x90A45837 */ +tc = 1.46163214496836224576e+00, /* 0x3FF762D8, 0x6356BE3F */ +tf = -1.21486290535849611461e-01, /* 0xBFBF19B9, 0xBCC38A42 */ +/* tt = -(tail of tf) */ +tt = -3.63867699703950536541e-18, /* 0xBC50C7CA, 0xA48A971F */ +t0 = 4.83836122723810047042e-01, /* 0x3FDEF72B, 0xC8EE38A2 */ +t1 = -1.47587722994593911752e-01, /* 0xBFC2E427, 0x8DC6C509 */ +t2 = 6.46249402391333854778e-02, /* 0x3FB08B42, 0x94D5419B */ +t3 = -3.27885410759859649565e-02, /* 0xBFA0C9A8, 0xDF35B713 */ +t4 = 1.79706750811820387126e-02, /* 0x3F9266E7, 0x970AF9EC */ +t5 = -1.03142241298341437450e-02, /* 0xBF851F9F, 0xBA91EC6A */ +t6 = 6.10053870246291332635e-03, /* 0x3F78FCE0, 0xE370E344 */ +t7 = -3.68452016781138256760e-03, /* 0xBF6E2EFF, 0xB3E914D7 */ +t8 = 2.25964780900612472250e-03, /* 0x3F6282D3, 0x2E15C915 */ +t9 = -1.40346469989232843813e-03, /* 0xBF56FE8E, 0xBF2D1AF1 */ +t10 = 8.81081882437654011382e-04, /* 0x3F4CDF0C, 0xEF61A8E9 */ +t11 = -5.38595305356740546715e-04, /* 0xBF41A610, 0x9C73E0EC */ +t12 = 3.15632070903625950361e-04, /* 0x3F34AF6D, 0x6C0EBBF7 */ +t13 = -3.12754168375120860518e-04, /* 0xBF347F24, 0xECC38C38 */ +t14 = 3.35529192635519073543e-04, /* 0x3F35FD3E, 0xE8C2D3F4 */ +u0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ +u1 = 6.32827064025093366517e-01, /* 0x3FE4401E, 0x8B005DFF */ +u2 = 1.45492250137234768737e+00, /* 0x3FF7475C, 0xD119BD6F */ +u3 = 9.77717527963372745603e-01, /* 0x3FEF4976, 0x44EA8450 */ +u4 = 2.28963728064692451092e-01, /* 0x3FCD4EAE, 0xF6010924 */ +u5 = 1.33810918536787660377e-02, /* 0x3F8B678B, 0xBF2BAB09 */ +v1 = 2.45597793713041134822e+00, /* 0x4003A5D7, 0xC2BD619C */ +v2 = 2.12848976379893395361e+00, /* 0x40010725, 0xA42B18F5 */ +v3 = 7.69285150456672783825e-01, /* 0x3FE89DFB, 0xE45050AF */ +v4 = 1.04222645593369134254e-01, /* 0x3FBAAE55, 0xD6537C88 */ +v5 = 3.21709242282423911810e-03, /* 0x3F6A5ABB, 0x57D0CF61 */ +s0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ +s1 = 2.14982415960608852501e-01, /* 0x3FCB848B, 0x36E20878 */ +s2 = 3.25778796408930981787e-01, /* 0x3FD4D98F, 0x4F139F59 */ +s3 = 1.46350472652464452805e-01, /* 0x3FC2BB9C, 0xBEE5F2F7 */ +s4 = 2.66422703033638609560e-02, /* 0x3F9B481C, 0x7E939961 */ +s5 = 1.84028451407337715652e-03, /* 0x3F5E26B6, 0x7368F239 */ +s6 = 3.19475326584100867617e-05, /* 0x3F00BFEC, 0xDD17E945 */ +r1 = 1.39200533467621045958e+00, /* 0x3FF645A7, 0x62C4AB74 */ +r2 = 7.21935547567138069525e-01, /* 0x3FE71A18, 0x93D3DCDC */ +r3 = 1.71933865632803078993e-01, /* 0x3FC601ED, 0xCCFBDF27 */ +r4 = 1.86459191715652901344e-02, /* 0x3F9317EA, 0x742ED475 */ +r5 = 7.77942496381893596434e-04, /* 0x3F497DDA, 0xCA41A95B */ +r6 = 7.32668430744625636189e-06, /* 0x3EDEBAF7, 0xA5B38140 */ +w0 = 4.18938533204672725052e-01, /* 0x3FDACFE3, 0x90C97D69 */ +w1 = 8.33333333333329678849e-02, /* 0x3FB55555, 0x5555553B */ +w2 = -2.77777777728775536470e-03, /* 0xBF66C16C, 0x16B02E5C */ +w3 = 7.93650558643019558500e-04, /* 0x3F4A019F, 0x98CF38B6 */ +w4 = -5.95187557450339963135e-04, /* 0xBF4380CB, 0x8C0FE741 */ +w5 = 8.36339918996282139126e-04, /* 0x3F4B67BA, 0x4CDAD5D1 */ +w6 = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */ + +static const double zero= 0.00000000000000000000e+00; + +static double +sin_pi(double x) +{ + double y,z; + int n,ix; + + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + + if(ix<0x3fd00000) return __sin(pi*x); + y = -x; /* x is assume negative */ + + /* + * argument reduction, make sure inexact flag not raised if input + * is an integer + */ + z = __floor(y); + if(z!=y) { /* inexact anyway */ + y *= 0.5; + y = 2.0*(y - __floor(y)); /* y = |x| mod 2.0 */ + n = (int) (y*4.0); + } else { + if(ix>=0x43400000) { + y = zero; n = 0; /* y must be even */ + } else { + if(ix<0x43300000) z = y+two52; /* exact */ + GET_LOW_WORD(n,z); + n &= 1; + y = n; + n<<= 2; + } + } + switch (n) { + case 0: y = __sin(pi*y); break; + case 1: + case 2: y = __cos(pi*(0.5-y)); break; + case 3: + case 4: y = __sin(pi*(one-y)); break; + case 5: + case 6: y = -__cos(pi*(y-1.5)); break; + default: y = __sin(pi*(y-2.0)); break; + } + return -y; +} + + +double +__ieee754_lgamma_r(double x, int *signgamp) +{ + double t,y,z,nadj,p,p1,p2,p3,q,r,w; + int i,hx,lx,ix; + + EXTRACT_WORDS(hx,lx,x); + + /* purge off +-inf, NaN, +-0, and negative arguments */ + *signgamp = 1; + ix = hx&0x7fffffff; + if(__builtin_expect(ix>=0x7ff00000, 0)) return x*x; + if(__builtin_expect((ix|lx)==0, 0)) + { + if (hx < 0) + *signgamp = -1; + return one/fabs(x); + } + if(__builtin_expect(ix<0x3b900000, 0)) { + /* |x|<2**-70, return -log(|x|) */ + if(hx<0) { + *signgamp = -1; + return -__ieee754_log(-x); + } else return -__ieee754_log(x); + } + if(hx<0) { + if(__builtin_expect(ix>=0x43300000, 0)) + /* |x|>=2**52, must be -integer */ + return __fabs (x)/zero; + if (x < -2.0 && x > -28.0) + return __lgamma_neg (x, signgamp); + t = sin_pi(x); + if(t==zero) return one/fabsf(t); /* -integer */ + nadj = __ieee754_log(pi/fabs(t*x)); + if(t<zero) *signgamp = -1; + x = -x; + } + + /* purge off 1 and 2 */ + if((((ix-0x3ff00000)|lx)==0)||(((ix-0x40000000)|lx)==0)) r = 0; + /* for x < 2.0 */ + else if(ix<0x40000000) { + if(ix<=0x3feccccc) { /* lgamma(x) = lgamma(x+1)-log(x) */ + r = -__ieee754_log(x); + if(ix>=0x3FE76944) {y = one-x; i= 0;} + else if(ix>=0x3FCDA661) {y= x-(tc-one); i=1;} + else {y = x; i=2;} + } else { + r = zero; + if(ix>=0x3FFBB4C3) {y=2.0-x;i=0;} /* [1.7316,2] */ + else if(ix>=0x3FF3B4C4) {y=x-tc;i=1;} /* [1.23,1.73] */ + else {y=x-one;i=2;} + } + switch(i) { + case 0: + z = y*y; + p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); + p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); + p = y*p1+p2; + r += (p-0.5*y); break; + case 1: + z = y*y; + w = z*y; + p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ + p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); + p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); + p = z*p1-(tt-w*(p2+y*p3)); + r += (tf + p); break; + case 2: + p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); + p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); + r += (-0.5*y + p1/p2); + } + } + else if(ix<0x40200000) { /* x < 8.0 */ + i = (int)x; + t = zero; + y = x-(double)i; + p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); + q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); + r = half*y+p/q; + z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ + switch(i) { + case 7: z *= (y+6.0); /* FALLTHRU */ + case 6: z *= (y+5.0); /* FALLTHRU */ + case 5: z *= (y+4.0); /* FALLTHRU */ + case 4: z *= (y+3.0); /* FALLTHRU */ + case 3: z *= (y+2.0); /* FALLTHRU */ + r += __ieee754_log(z); break; + } + /* 8.0 <= x < 2**58 */ + } else if (ix < 0x43900000) { + t = __ieee754_log(x); + z = one/x; + y = z*z; + w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); + r = (x-half)*(t-one)+w; + } else + /* 2**58 <= x <= inf */ + r = math_narrow_eval (x*(__ieee754_log(x)-one)); + /* NADJ is set for negative arguments but not otherwise, + resulting in warnings that it may be used uninitialized + although in the cases where it is used it has always been + set. */ + DIAG_PUSH_NEEDS_COMMENT; + DIAG_IGNORE_NEEDS_COMMENT (4.9, "-Wmaybe-uninitialized"); + if(hx<0) r = nadj - r; + DIAG_POP_NEEDS_COMMENT; + return r; +} +strong_alias (__ieee754_lgamma_r, __lgamma_r_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_log.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_log.c new file mode 100644 index 0000000000..e7cddc29c8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_log.c @@ -0,0 +1,262 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/*********************************************************************/ +/* */ +/* MODULE_NAME:ulog.c */ +/* */ +/* FUNCTION:ulog */ +/* */ +/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h ulog.h */ +/* mpexp.c mplog.c mpa.c */ +/* ulog.tbl */ +/* */ +/* An ultimate log routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of log(x). */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round to nearest mode of IEEE 754 standard. */ +/* */ +/*********************************************************************/ + + +#include "endian.h" +#include <dla.h> +#include "mpa.h" +#include "MathLib.h" +#include <math.h> +#include <math_private.h> +#include <stap-probe.h> + +#ifndef SECTION +# define SECTION +#endif + +void __mplog (mp_no *, mp_no *, int); + +/*********************************************************************/ +/* An ultimate log routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of log(x). */ +/*********************************************************************/ +double +SECTION +__ieee754_log (double x) +{ +#define M 4 + static const int pr[M] = { 8, 10, 18, 32 }; + int i, j, n, ux, dx, p; + double dbl_n, u, p0, q, r0, w, nln2a, luai, lubi, lvaj, lvbj, + sij, ssij, ttij, A, B, B0, y, y1, y2, polI, polII, sa, sb, + t1, t2, t7, t8, t, ra, rb, ww, + a0, aa0, s1, s2, ss2, s3, ss3, a1, aa1, a, aa, b, bb, c; +#ifndef DLA_FMS + double t3, t4, t5, t6; +#endif + number num; + mp_no mpx, mpy, mpy1, mpy2, mperr; + +#include "ulog.tbl" +#include "ulog.h" + + /* Treating special values of x ( x<=0, x=INF, x=NaN etc.). */ + + num.d = x; + ux = num.i[HIGH_HALF]; + dx = num.i[LOW_HALF]; + n = 0; + if (__glibc_unlikely (ux < 0x00100000)) + { + if (__glibc_unlikely (((ux & 0x7fffffff) | dx) == 0)) + return MHALF / 0.0; /* return -INF */ + if (__glibc_unlikely (ux < 0)) + return (x - x) / 0.0; /* return NaN */ + n -= 54; + x *= two54.d; /* scale x */ + num.d = x; + } + if (__glibc_unlikely (ux >= 0x7ff00000)) + return x + x; /* INF or NaN */ + + /* Regular values of x */ + + w = x - 1; + if (__glibc_likely (fabs (w) > U03)) + goto case_03; + + /* log (1) is +0 in all rounding modes. */ + if (w == 0.0) + return 0.0; + + /*--- Stage I, the case abs(x-1) < 0.03 */ + + t8 = MHALF * w; + EMULV (t8, w, a, aa, t1, t2, t3, t4, t5); + EADD (w, a, b, bb); + /* Evaluate polynomial II */ + polII = b7.d + w * b8.d; + polII = b6.d + w * polII; + polII = b5.d + w * polII; + polII = b4.d + w * polII; + polII = b3.d + w * polII; + polII = b2.d + w * polII; + polII = b1.d + w * polII; + polII = b0.d + w * polII; + polII *= w * w * w; + c = (aa + bb) + polII; + + /* End stage I, case abs(x-1) < 0.03 */ + if ((y = b + (c + b * E2)) == b + (c - b * E2)) + return y; + + /*--- Stage II, the case abs(x-1) < 0.03 */ + + a = d19.d + w * d20.d; + a = d18.d + w * a; + a = d17.d + w * a; + a = d16.d + w * a; + a = d15.d + w * a; + a = d14.d + w * a; + a = d13.d + w * a; + a = d12.d + w * a; + a = d11.d + w * a; + + EMULV (w, a, s2, ss2, t1, t2, t3, t4, t5); + ADD2 (d10.d, dd10.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (d9.d, dd9.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (d8.d, dd8.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (d7.d, dd7.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (d6.d, dd6.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (d5.d, dd5.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (d4.d, dd4.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (d3.d, dd3.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (d2.d, dd2.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (w, 0, s2, ss2, s3, ss3, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (w, 0, s3, ss3, b, bb, t1, t2); + + /* End stage II, case abs(x-1) < 0.03 */ + if ((y = b + (bb + b * E4)) == b + (bb - b * E4)) + return y; + goto stage_n; + + /*--- Stage I, the case abs(x-1) > 0.03 */ +case_03: + + /* Find n,u such that x = u*2**n, 1/sqrt(2) < u < sqrt(2) */ + n += (num.i[HIGH_HALF] >> 20) - 1023; + num.i[HIGH_HALF] = (num.i[HIGH_HALF] & 0x000fffff) | 0x3ff00000; + if (num.d > SQRT_2) + { + num.d *= HALF; + n++; + } + u = num.d; + dbl_n = (double) n; + + /* Find i such that ui=1+(i-75)/2**8 is closest to u (i= 0,1,2,...,181) */ + num.d += h1.d; + i = (num.i[HIGH_HALF] & 0x000fffff) >> 12; + + /* Find j such that vj=1+(j-180)/2**16 is closest to v=u/ui (j= 0,...,361) */ + num.d = u * Iu[i].d + h2.d; + j = (num.i[HIGH_HALF] & 0x000fffff) >> 4; + + /* Compute w=(u-ui*vj)/(ui*vj) */ + p0 = (1 + (i - 75) * DEL_U) * (1 + (j - 180) * DEL_V); + q = u - p0; + r0 = Iu[i].d * Iv[j].d; + w = q * r0; + + /* Evaluate polynomial I */ + polI = w + (a2.d + a3.d * w) * w * w; + + /* Add up everything */ + nln2a = dbl_n * LN2A; + luai = Lu[i][0].d; + lubi = Lu[i][1].d; + lvaj = Lv[j][0].d; + lvbj = Lv[j][1].d; + EADD (luai, lvaj, sij, ssij); + EADD (nln2a, sij, A, ttij); + B0 = (((lubi + lvbj) + ssij) + ttij) + dbl_n * LN2B; + B = polI + B0; + + /* End stage I, case abs(x-1) >= 0.03 */ + if ((y = A + (B + E1)) == A + (B - E1)) + return y; + + + /*--- Stage II, the case abs(x-1) > 0.03 */ + + /* Improve the accuracy of r0 */ + EMULV (p0, r0, sa, sb, t1, t2, t3, t4, t5); + t = r0 * ((1 - sa) - sb); + EADD (r0, t, ra, rb); + + /* Compute w */ + MUL2 (q, 0, ra, rb, w, ww, t1, t2, t3, t4, t5, t6, t7, t8); + + EADD (A, B0, a0, aa0); + + /* Evaluate polynomial III */ + s1 = (c3.d + (c4.d + c5.d * w) * w) * w; + EADD (c2.d, s1, s2, ss2); + MUL2 (s2, ss2, w, ww, s3, ss3, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (s3, ss3, w, ww, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (s2, ss2, w, ww, s3, ss3, t1, t2); + ADD2 (s3, ss3, a0, aa0, a1, aa1, t1, t2); + + /* End stage II, case abs(x-1) >= 0.03 */ + if ((y = a1 + (aa1 + E3)) == a1 + (aa1 - E3)) + return y; + + + /* Final stages. Use multi-precision arithmetic. */ +stage_n: + + for (i = 0; i < M; i++) + { + p = pr[i]; + __dbl_mp (x, &mpx, p); + __dbl_mp (y, &mpy, p); + __mplog (&mpx, &mpy, p); + __dbl_mp (e[i].d, &mperr, p); + __add (&mpy, &mperr, &mpy1, p); + __sub (&mpy, &mperr, &mpy2, p); + __mp_dbl (&mpy1, &y1, p); + __mp_dbl (&mpy2, &y2, p); + if (y1 == y2) + { + LIBC_PROBE (slowlog, 3, &p, &x, &y1); + return y1; + } + } + LIBC_PROBE (slowlog_inexact, 3, &p, &x, &y1); + return y1; +} + +#ifndef __ieee754_log +strong_alias (__ieee754_log, __log_finite) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_log10.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_log10.c new file mode 100644 index 0000000000..bf40bca874 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_log10.c @@ -0,0 +1,88 @@ +/* @(#)e_log10.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_log10(x) + * Return the base 10 logarithm of x + * + * Method : + * Let log10_2hi = leading 40 bits of log10(2) and + * log10_2lo = log10(2) - log10_2hi, + * ivln10 = 1/log(10) rounded. + * Then + * n = ilogb(x), + * if(n<0) n = n+1; + * x = scalbn(x,-n); + * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) + * + * Note 1: + * To guarantee log10(10**n)=n, where 10**n is normal, the rounding + * mode must set to Round-to-Nearest. + * Note 2: + * [1/log(10)] rounded to 53 bits has error .198 ulps; + * log10 is monotonic at all binary break points. + * + * Special cases: + * log10(x) is NaN with signal if x < 0; + * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; + * log10(NaN) is that NaN with no signal; + * log10(10**N) = N for N=0,1,...,22. + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +#include <math.h> +#include <math_private.h> +#include <fix-int-fp-convert-zero.h> + +static const double two54 = 1.80143985094819840000e+16; /* 0x43500000, 0x00000000 */ +static const double ivln10 = 4.34294481903251816668e-01; /* 0x3FDBCB7B, 0x1526E50E */ +static const double log10_2hi = 3.01029995663611771306e-01; /* 0x3FD34413, 0x509F6000 */ +static const double log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ + +double +__ieee754_log10 (double x) +{ + double y, z; + int32_t i, k, hx; + u_int32_t lx; + + EXTRACT_WORDS (hx, lx, x); + + k = 0; + if (hx < 0x00100000) + { /* x < 2**-1022 */ + if (__glibc_unlikely (((hx & 0x7fffffff) | lx) == 0)) + return -two54 / __fabs (x); /* log(+-0)=-inf */ + if (__glibc_unlikely (hx < 0)) + return (x - x) / (x - x); /* log(-#) = NaN */ + k -= 54; + x *= two54; /* subnormal number, scale up x */ + GET_HIGH_WORD (hx, x); + } + if (__glibc_unlikely (hx >= 0x7ff00000)) + return x + x; + k += (hx >> 20) - 1023; + i = ((u_int32_t) k & 0x80000000) >> 31; + hx = (hx & 0x000fffff) | ((0x3ff - i) << 20); + y = (double) (k + i); + if (FIX_INT_FP_CONVERT_ZERO && y == 0.0) + y = 0.0; + SET_HIGH_WORD (x, hx); + z = y * log10_2lo + ivln10 * __ieee754_log (x); + return z + y * log10_2hi; +} + +strong_alias (__ieee754_log10, __log10_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_log2.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_log2.c new file mode 100644 index 0000000000..5af68d8ecc --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_log2.c @@ -0,0 +1,133 @@ +/* Adapted for log2 by Ulrich Drepper <drepper@cygnus.com>. */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_log2(x) + * Return the logarithm to base 2 of x + * + * Method : + * 1. Argument Reduction: find k and f such that + * x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * 2. Approximation of log(1+f). + * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * = 2s + s*R + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error + * of this polynomial approximation is bounded by 2**-58.45. In + * other words, + * 2 4 6 8 10 12 14 + * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s + * (the values of Lg1 to Lg7 are listed in the program) + * and + * | 2 14 | -58.45 + * | Lg1*s +...+Lg7*s - R(z) | <= 2 + * | | + * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. + * In order to guarantee error in log below 1ulp, we compute log + * by + * log(1+f) = f - s*(f - R) (if f is not too large) + * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) + * + * 3. Finally, log(x) = k + log(1+f). + * = k+(f-(hfsq-(s*(hfsq+R)))) + * + * Special cases: + * log2(x) is NaN with signal if x < 0 (including -INF) ; + * log2(+INF) is +INF; log(0) is -INF with signal; + * log2(NaN) is that NaN with no signal. + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include <math.h> +#include <math_private.h> +#include <fix-int-fp-convert-zero.h> + +static const double ln2 = 0.69314718055994530942; +static const double two54 = 1.80143985094819840000e+16; /* 43500000 00000000 */ +static const double Lg1 = 6.666666666666735130e-01; /* 3FE55555 55555593 */ +static const double Lg2 = 3.999999999940941908e-01; /* 3FD99999 9997FA04 */ +static const double Lg3 = 2.857142874366239149e-01; /* 3FD24924 94229359 */ +static const double Lg4 = 2.222219843214978396e-01; /* 3FCC71C5 1D8E78AF */ +static const double Lg5 = 1.818357216161805012e-01; /* 3FC74664 96CB03DE */ +static const double Lg6 = 1.531383769920937332e-01; /* 3FC39A09 D078C69F */ +static const double Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ + +static const double zero = 0.0; + +double +__ieee754_log2 (double x) +{ + double hfsq, f, s, z, R, w, t1, t2, dk; + int32_t k, hx, i, j; + u_int32_t lx; + + EXTRACT_WORDS (hx, lx, x); + + k = 0; + if (hx < 0x00100000) + { /* x < 2**-1022 */ + if (__glibc_unlikely (((hx & 0x7fffffff) | lx) == 0)) + return -two54 / __fabs (x); /* log(+-0)=-inf */ + if (__glibc_unlikely (hx < 0)) + return (x - x) / (x - x); /* log(-#) = NaN */ + k -= 54; + x *= two54; /* subnormal number, scale up x */ + GET_HIGH_WORD (hx, x); + } + if (__glibc_unlikely (hx >= 0x7ff00000)) + return x + x; + k += (hx >> 20) - 1023; + hx &= 0x000fffff; + i = (hx + 0x95f64) & 0x100000; + SET_HIGH_WORD (x, hx | (i ^ 0x3ff00000)); /* normalize x or x/2 */ + k += (i >> 20); + dk = (double) k; + f = x - 1.0; + if ((0x000fffff & (2 + hx)) < 3) + { /* |f| < 2**-20 */ + if (f == zero) + { + if (FIX_INT_FP_CONVERT_ZERO && dk == 0.0) + dk = 0.0; + return dk; + } + R = f * f * (0.5 - 0.33333333333333333 * f); + return dk - (R - f) / ln2; + } + s = f / (2.0 + f); + z = s * s; + i = hx - 0x6147a; + w = z * z; + j = 0x6b851 - hx; + t1 = w * (Lg2 + w * (Lg4 + w * Lg6)); + t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7))); + i |= j; + R = t2 + t1; + if (i > 0) + { + hfsq = 0.5 * f * f; + return dk - ((hfsq - (s * (hfsq + R))) - f) / ln2; + } + else + { + return dk - ((s * (f - R)) - f) / ln2; + } +} + +strong_alias (__ieee754_log2, __log2_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_pow.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_pow.c new file mode 100644 index 0000000000..9f6439ee42 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_pow.c @@ -0,0 +1,481 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/***************************************************************************/ +/* MODULE_NAME: upow.c */ +/* */ +/* FUNCTIONS: upow */ +/* power1 */ +/* my_log2 */ +/* log1 */ +/* checkint */ +/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h */ +/* halfulp.c mpexp.c mplog.c slowexp.c slowpow.c mpa.c */ +/* uexp.c upow.c */ +/* root.tbl uexp.tbl upow.tbl */ +/* An ultimate power routine. Given two IEEE double machine numbers y,x */ +/* it computes the correctly rounded (to nearest) value of x^y. */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round to nearest mode of IEEE 754 standard. */ +/* */ +/***************************************************************************/ +#include <math.h> +#include "endian.h" +#include "upow.h" +#include <dla.h> +#include "mydefs.h" +#include "MathLib.h" +#include "upow.tbl" +#include <math_private.h> +#include <fenv.h> + +#ifndef SECTION +# define SECTION +#endif + +static const double huge = 1.0e300, tiny = 1.0e-300; + +double __exp1 (double x, double xx, double error); +static double log1 (double x, double *delta, double *error); +static double my_log2 (double x, double *delta, double *error); +double __slowpow (double x, double y, double z); +static double power1 (double x, double y); +static int checkint (double x); + +/* An ultimate power routine. Given two IEEE double machine numbers y, x it + computes the correctly rounded (to nearest) value of X^y. */ +double +SECTION +__ieee754_pow (double x, double y) +{ + double z, a, aa, error, t, a1, a2, y1, y2; + mynumber u, v; + int k; + int4 qx, qy; + v.x = y; + u.x = x; + if (v.i[LOW_HALF] == 0) + { /* of y */ + qx = u.i[HIGH_HALF] & 0x7fffffff; + /* Is x a NaN? */ + if ((((qx == 0x7ff00000) && (u.i[LOW_HALF] != 0)) || (qx > 0x7ff00000)) + && (y != 0 || issignaling (x))) + return x + x; + if (y == 1.0) + return x; + if (y == 2.0) + return x * x; + if (y == -1.0) + return 1.0 / x; + if (y == 0) + return 1.0; + } + /* else */ + if (((u.i[HIGH_HALF] > 0 && u.i[HIGH_HALF] < 0x7ff00000) || /* x>0 and not x->0 */ + (u.i[HIGH_HALF] == 0 && u.i[LOW_HALF] != 0)) && + /* 2^-1023< x<= 2^-1023 * 0x1.0000ffffffff */ + (v.i[HIGH_HALF] & 0x7fffffff) < 0x4ff00000) + { /* if y<-1 or y>1 */ + double retval; + + { + SET_RESTORE_ROUND (FE_TONEAREST); + + /* Avoid internal underflow for tiny y. The exact value of y does + not matter if |y| <= 2**-64. */ + if (fabs (y) < 0x1p-64) + y = y < 0 ? -0x1p-64 : 0x1p-64; + z = log1 (x, &aa, &error); /* x^y =e^(y log (X)) */ + t = y * CN; + y1 = t - (t - y); + y2 = y - y1; + t = z * CN; + a1 = t - (t - z); + a2 = (z - a1) + aa; + a = y1 * a1; + aa = y2 * a1 + y * a2; + a1 = a + aa; + a2 = (a - a1) + aa; + error = error * fabs (y); + t = __exp1 (a1, a2, 1.9e16 * error); /* return -10 or 0 if wasn't computed exactly */ + retval = (t > 0) ? t : power1 (x, y); + } + + if (isinf (retval)) + retval = huge * huge; + else if (retval == 0) + retval = tiny * tiny; + else + math_check_force_underflow_nonneg (retval); + return retval; + } + + if (x == 0) + { + if (((v.i[HIGH_HALF] & 0x7fffffff) == 0x7ff00000 && v.i[LOW_HALF] != 0) + || (v.i[HIGH_HALF] & 0x7fffffff) > 0x7ff00000) /* NaN */ + return y + y; + if (fabs (y) > 1.0e20) + return (y > 0) ? 0 : 1.0 / 0.0; + k = checkint (y); + if (k == -1) + return y < 0 ? 1.0 / x : x; + else + return y < 0 ? 1.0 / 0.0 : 0.0; /* return 0 */ + } + + qx = u.i[HIGH_HALF] & 0x7fffffff; /* no sign */ + qy = v.i[HIGH_HALF] & 0x7fffffff; /* no sign */ + + if (qx >= 0x7ff00000 && (qx > 0x7ff00000 || u.i[LOW_HALF] != 0)) /* NaN */ + return x + y; + if (qy >= 0x7ff00000 && (qy > 0x7ff00000 || v.i[LOW_HALF] != 0)) /* NaN */ + return x == 1.0 && !issignaling (y) ? 1.0 : y + y; + + /* if x<0 */ + if (u.i[HIGH_HALF] < 0) + { + k = checkint (y); + if (k == 0) + { + if (qy == 0x7ff00000) + { + if (x == -1.0) + return 1.0; + else if (x > -1.0) + return v.i[HIGH_HALF] < 0 ? INF.x : 0.0; + else + return v.i[HIGH_HALF] < 0 ? 0.0 : INF.x; + } + else if (qx == 0x7ff00000) + return y < 0 ? 0.0 : INF.x; + return (x - x) / (x - x); /* y not integer and x<0 */ + } + else if (qx == 0x7ff00000) + { + if (k < 0) + return y < 0 ? nZERO.x : nINF.x; + else + return y < 0 ? 0.0 : INF.x; + } + /* if y even or odd */ + if (k == 1) + return __ieee754_pow (-x, y); + else + { + double retval; + { + SET_RESTORE_ROUND (FE_TONEAREST); + retval = -__ieee754_pow (-x, y); + } + if (isinf (retval)) + retval = -huge * huge; + else if (retval == 0) + retval = -tiny * tiny; + return retval; + } + } + /* x>0 */ + + if (qx == 0x7ff00000) /* x= 2^-0x3ff */ + return y > 0 ? x : 0; + + if (qy > 0x45f00000 && qy < 0x7ff00000) + { + if (x == 1.0) + return 1.0; + if (y > 0) + return (x > 1.0) ? huge * huge : tiny * tiny; + if (y < 0) + return (x < 1.0) ? huge * huge : tiny * tiny; + } + + if (x == 1.0) + return 1.0; + if (y > 0) + return (x > 1.0) ? INF.x : 0; + if (y < 0) + return (x < 1.0) ? INF.x : 0; + return 0; /* unreachable, to make the compiler happy */ +} + +#ifndef __ieee754_pow +strong_alias (__ieee754_pow, __pow_finite) +#endif + +/* Compute x^y using more accurate but more slow log routine. */ +static double +SECTION +power1 (double x, double y) +{ + double z, a, aa, error, t, a1, a2, y1, y2; + z = my_log2 (x, &aa, &error); + t = y * CN; + y1 = t - (t - y); + y2 = y - y1; + t = z * CN; + a1 = t - (t - z); + a2 = z - a1; + a = y * z; + aa = ((y1 * a1 - a) + y1 * a2 + y2 * a1) + y2 * a2 + aa * y; + a1 = a + aa; + a2 = (a - a1) + aa; + error = error * fabs (y); + t = __exp1 (a1, a2, 1.9e16 * error); + return (t >= 0) ? t : __slowpow (x, y, z); +} + +/* Compute log(x) (x is left argument). The result is the returned double + the + parameter DELTA. The result is bounded by ERROR. */ +static double +SECTION +log1 (double x, double *delta, double *error) +{ + unsigned int i, j; + int m; + double uu, vv, eps, nx, e, e1, e2, t, t1, t2, res, add = 0; + mynumber u, v; +#ifdef BIG_ENDI + mynumber /**/ two52 = {{0x43300000, 0x00000000}}; /* 2**52 */ +#else +# ifdef LITTLE_ENDI + mynumber /**/ two52 = {{0x00000000, 0x43300000}}; /* 2**52 */ +# endif +#endif + + u.x = x; + m = u.i[HIGH_HALF]; + *error = 0; + *delta = 0; + if (m < 0x00100000) /* 1<x<2^-1007 */ + { + x = x * t52.x; + add = -52.0; + u.x = x; + m = u.i[HIGH_HALF]; + } + + if ((m & 0x000fffff) < 0x0006a09e) + { + u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3ff00000; + two52.i[LOW_HALF] = (m >> 20); + } + else + { + u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3fe00000; + two52.i[LOW_HALF] = (m >> 20) + 1; + } + + v.x = u.x + bigu.x; + uu = v.x - bigu.x; + i = (v.i[LOW_HALF] & 0x000003ff) << 2; + if (two52.i[LOW_HALF] == 1023) /* nx = 0 */ + { + if (i > 1192 && i < 1208) /* |x-1| < 1.5*2**-10 */ + { + t = x - 1.0; + t1 = (t + 5.0e6) - 5.0e6; + t2 = t - t1; + e1 = t - 0.5 * t1 * t1; + e2 = (t * t * t * (r3 + t * (r4 + t * (r5 + t * (r6 + t + * (r7 + t * r8))))) + - 0.5 * t2 * (t + t1)); + res = e1 + e2; + *error = 1.0e-21 * fabs (t); + *delta = (e1 - res) + e2; + return res; + } /* |x-1| < 1.5*2**-10 */ + else + { + v.x = u.x * (ui.x[i] + ui.x[i + 1]) + bigv.x; + vv = v.x - bigv.x; + j = v.i[LOW_HALF] & 0x0007ffff; + j = j + j + j; + eps = u.x - uu * vv; + e1 = eps * ui.x[i]; + e2 = eps * (ui.x[i + 1] + vj.x[j] * (ui.x[i] + ui.x[i + 1])); + e = e1 + e2; + e2 = ((e1 - e) + e2); + t = ui.x[i + 2] + vj.x[j + 1]; + t1 = t + e; + t2 = ((((t - t1) + e) + (ui.x[i + 3] + vj.x[j + 2])) + e2 + e * e + * (p2 + e * (p3 + e * p4))); + res = t1 + t2; + *error = 1.0e-24; + *delta = (t1 - res) + t2; + return res; + } + } /* nx = 0 */ + else /* nx != 0 */ + { + eps = u.x - uu; + nx = (two52.x - two52e.x) + add; + e1 = eps * ui.x[i]; + e2 = eps * ui.x[i + 1]; + e = e1 + e2; + e2 = (e1 - e) + e2; + t = nx * ln2a.x + ui.x[i + 2]; + t1 = t + e; + t2 = ((((t - t1) + e) + nx * ln2b.x + ui.x[i + 3] + e2) + e * e + * (q2 + e * (q3 + e * (q4 + e * (q5 + e * q6))))); + res = t1 + t2; + *error = 1.0e-21; + *delta = (t1 - res) + t2; + return res; + } /* nx != 0 */ +} + +/* Slower but more accurate routine of log. The returned result is double + + DELTA. The result is bounded by ERROR. */ +static double +SECTION +my_log2 (double x, double *delta, double *error) +{ + unsigned int i, j; + int m; + double uu, vv, eps, nx, e, e1, e2, t, t1, t2, res, add = 0; + double ou1, ou2, lu1, lu2, ov, lv1, lv2, a, a1, a2; + double y, yy, z, zz, j1, j2, j7, j8; +#ifndef DLA_FMS + double j3, j4, j5, j6; +#endif + mynumber u, v; +#ifdef BIG_ENDI + mynumber /**/ two52 = {{0x43300000, 0x00000000}}; /* 2**52 */ +#else +# ifdef LITTLE_ENDI + mynumber /**/ two52 = {{0x00000000, 0x43300000}}; /* 2**52 */ +# endif +#endif + + u.x = x; + m = u.i[HIGH_HALF]; + *error = 0; + *delta = 0; + add = 0; + if (m < 0x00100000) + { /* x < 2^-1022 */ + x = x * t52.x; + add = -52.0; + u.x = x; + m = u.i[HIGH_HALF]; + } + + if ((m & 0x000fffff) < 0x0006a09e) + { + u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3ff00000; + two52.i[LOW_HALF] = (m >> 20); + } + else + { + u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3fe00000; + two52.i[LOW_HALF] = (m >> 20) + 1; + } + + v.x = u.x + bigu.x; + uu = v.x - bigu.x; + i = (v.i[LOW_HALF] & 0x000003ff) << 2; + /*------------------------------------- |x-1| < 2**-11------------------------------- */ + if ((two52.i[LOW_HALF] == 1023) && (i == 1200)) + { + t = x - 1.0; + EMULV (t, s3, y, yy, j1, j2, j3, j4, j5); + ADD2 (-0.5, 0, y, yy, z, zz, j1, j2); + MUL2 (t, 0, z, zz, y, yy, j1, j2, j3, j4, j5, j6, j7, j8); + MUL2 (t, 0, y, yy, z, zz, j1, j2, j3, j4, j5, j6, j7, j8); + + e1 = t + z; + e2 = ((((t - e1) + z) + zz) + t * t * t + * (ss3 + t * (s4 + t * (s5 + t * (s6 + t * (s7 + t * s8)))))); + res = e1 + e2; + *error = 1.0e-25 * fabs (t); + *delta = (e1 - res) + e2; + return res; + } + /*----------------------------- |x-1| > 2**-11 -------------------------- */ + else + { /*Computing log(x) according to log table */ + nx = (two52.x - two52e.x) + add; + ou1 = ui.x[i]; + ou2 = ui.x[i + 1]; + lu1 = ui.x[i + 2]; + lu2 = ui.x[i + 3]; + v.x = u.x * (ou1 + ou2) + bigv.x; + vv = v.x - bigv.x; + j = v.i[LOW_HALF] & 0x0007ffff; + j = j + j + j; + eps = u.x - uu * vv; + ov = vj.x[j]; + lv1 = vj.x[j + 1]; + lv2 = vj.x[j + 2]; + a = (ou1 + ou2) * (1.0 + ov); + a1 = (a + 1.0e10) - 1.0e10; + a2 = a * (1.0 - a1 * uu * vv); + e1 = eps * a1; + e2 = eps * a2; + e = e1 + e2; + e2 = (e1 - e) + e2; + t = nx * ln2a.x + lu1 + lv1; + t1 = t + e; + t2 = ((((t - t1) + e) + (lu2 + lv2 + nx * ln2b.x + e2)) + e * e + * (p2 + e * (p3 + e * p4))); + res = t1 + t2; + *error = 1.0e-27; + *delta = (t1 - res) + t2; + return res; + } +} + +/* This function receives a double x and checks if it is an integer. If not, + it returns 0, else it returns 1 if even or -1 if odd. */ +static int +SECTION +checkint (double x) +{ + union + { + int4 i[2]; + double x; + } u; + int k, m, n; + u.x = x; + m = u.i[HIGH_HALF] & 0x7fffffff; /* no sign */ + if (m >= 0x7ff00000) + return 0; /* x is +/-inf or NaN */ + if (m >= 0x43400000) + return 1; /* |x| >= 2**53 */ + if (m < 0x40000000) + return 0; /* |x| < 2, can not be 0 or 1 */ + n = u.i[LOW_HALF]; + k = (m >> 20) - 1023; /* 1 <= k <= 52 */ + if (k == 52) + return (n & 1) ? -1 : 1; /* odd or even */ + if (k > 20) + { + if (n << (k - 20) != 0) + return 0; /* if not integer */ + return (n << (k - 21) != 0) ? -1 : 1; + } + if (n) + return 0; /*if not integer */ + if (k == 20) + return (m & 1) ? -1 : 1; + if (m << (k + 12) != 0) + return 0; + return (m << (k + 11) != 0) ? -1 : 1; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_rem_pio2.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_rem_pio2.c new file mode 100644 index 0000000000..2f55ca294b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_rem_pio2.c @@ -0,0 +1,193 @@ +#ifdef NOT_NEEDED_ANYMORE + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_rem_pio2(x,y) + * + * return the remainder of x rem pi/2 in y[0]+y[1] + * use __kernel_rem_pio2() + */ + +#include <math.h> +#include <math_private.h> + +/* + * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi + */ +static const int32_t two_over_pi[] = { +0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, +0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, +0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, +0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, +0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, +0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, +0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, +0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, +0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, +0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, +0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, +}; + +static const int32_t npio2_hw[] = { +0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, +0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, +0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, +0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, +0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, +0x404858EB, 0x404921FB, +}; + +/* + * invpio2: 53 bits of 2/pi + * pio2_1: first 33 bit of pi/2 + * pio2_1t: pi/2 - pio2_1 + * pio2_2: second 33 bit of pi/2 + * pio2_2t: pi/2 - (pio2_1+pio2_2) + * pio2_3: third 33 bit of pi/2 + * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) + */ + +static const double + zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ + two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ + invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ + pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ + pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ + pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ + pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ + pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ + pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ + +int32_t +__ieee754_rem_pio2 (double x, double *y) +{ + double z, w, t, r, fn; + double tx[3]; + int32_t e0, i, j, nx, n, ix, hx; + u_int32_t low; + + GET_HIGH_WORD (hx, x); /* high word of x */ + ix = hx & 0x7fffffff; + if (ix <= 0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ + { + y[0] = x; y[1] = 0; return 0; + } + if (ix < 0x4002d97c) /* |x| < 3pi/4, special case with n=+-1 */ + { + if (hx > 0) + { + z = x - pio2_1; + if (ix != 0x3ff921fb) /* 33+53 bit pi is good enough */ + { + y[0] = z - pio2_1t; + y[1] = (z - y[0]) - pio2_1t; + } + else /* near pi/2, use 33+33+53 bit pi */ + { + z -= pio2_2; + y[0] = z - pio2_2t; + y[1] = (z - y[0]) - pio2_2t; + } + return 1; + } + else /* negative x */ + { + z = x + pio2_1; + if (ix != 0x3ff921fb) /* 33+53 bit pi is good enough */ + { + y[0] = z + pio2_1t; + y[1] = (z - y[0]) + pio2_1t; + } + else /* near pi/2, use 33+33+53 bit pi */ + { + z += pio2_2; + y[0] = z + pio2_2t; + y[1] = (z - y[0]) + pio2_2t; + } + return -1; + } + } + if (ix <= 0x413921fb) /* |x| ~<= 2^19*(pi/2), medium size */ + { + t = fabs (x); + n = (int32_t) (t * invpio2 + half); + fn = (double) n; + r = t - fn * pio2_1; + w = fn * pio2_1t; /* 1st round good to 85 bit */ + if (n < 32 && ix != npio2_hw[n - 1]) + { + y[0] = r - w; /* quick check no cancellation */ + } + else + { + u_int32_t high; + j = ix >> 20; + y[0] = r - w; + GET_HIGH_WORD (high, y[0]); + i = j - ((high >> 20) & 0x7ff); + if (i > 16) /* 2nd iteration needed, good to 118 */ + { + t = r; + w = fn * pio2_2; + r = t - w; + w = fn * pio2_2t - ((t - r) - w); + y[0] = r - w; + GET_HIGH_WORD (high, y[0]); + i = j - ((high >> 20) & 0x7ff); + if (i > 49) /* 3rd iteration need, 151 bits acc */ + { + t = r; /* will cover all possible cases */ + w = fn * pio2_3; + r = t - w; + w = fn * pio2_3t - ((t - r) - w); + y[0] = r - w; + } + } + } + y[1] = (r - y[0]) - w; + if (hx < 0) + { + y[0] = -y[0]; y[1] = -y[1]; return -n; + } + else + return n; + } + /* + * all other (large) arguments + */ + if (ix >= 0x7ff00000) /* x is inf or NaN */ + { + y[0] = y[1] = x - x; return 0; + } + /* set z = scalbn(|x|,ilogb(x)-23) */ + GET_LOW_WORD (low, x); + SET_LOW_WORD (z, low); + e0 = (ix >> 20) - 1046; /* e0 = ilogb(z)-23; */ + SET_HIGH_WORD (z, ix - ((int32_t) (e0 << 20))); + for (i = 0; i < 2; i++) + { + tx[i] = (double) ((int32_t) (z)); + z = (z - tx[i]) * two24; + } + tx[2] = z; + nx = 3; + while (tx[nx - 1] == zero) + nx--; /* skip zero term */ + n = __kernel_rem_pio2 (tx, y, e0, nx, 2, two_over_pi); + if (hx < 0) + { + y[0] = -y[0]; y[1] = -y[1]; return -n; + } + return n; +} +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_remainder.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_remainder.c new file mode 100644 index 0000000000..1a2eeed2e1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_remainder.c @@ -0,0 +1,152 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/**************************************************************************/ +/* MODULE_NAME urem.c */ +/* */ +/* FUNCTION: uremainder */ +/* */ +/* An ultimate remainder routine. Given two IEEE double machine numbers x */ +/* ,y it computes the correctly rounded (to nearest) value of remainder */ +/* of dividing x by y. */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round to nearest mode of IEEE 754 standard. */ +/* */ +/* ************************************************************************/ + +#include "endian.h" +#include "mydefs.h" +#include "urem.h" +#include "MathLib.h" +#include <math.h> +#include <math_private.h> + +/**************************************************************************/ +/* An ultimate remainder routine. Given two IEEE double machine numbers x */ +/* ,y it computes the correctly rounded (to nearest) value of remainder */ +/**************************************************************************/ +double +__ieee754_remainder (double x, double y) +{ + double z, d, xx; + int4 kx, ky, n, nn, n1, m1, l; + mynumber u, t, w = { { 0, 0 } }, v = { { 0, 0 } }, ww = { { 0, 0 } }, r; + u.x = x; + t.x = y; + kx = u.i[HIGH_HALF] & 0x7fffffff; /* no sign for x*/ + t.i[HIGH_HALF] &= 0x7fffffff; /*no sign for y */ + ky = t.i[HIGH_HALF]; + /*------ |x| < 2^1023 and 2^-970 < |y| < 2^1024 ------------------*/ + if (kx < 0x7fe00000 && ky < 0x7ff00000 && ky >= 0x03500000) + { + SET_RESTORE_ROUND_NOEX (FE_TONEAREST); + if (kx + 0x00100000 < ky) + return x; + if ((kx - 0x01500000) < ky) + { + z = x / t.x; + v.i[HIGH_HALF] = t.i[HIGH_HALF]; + d = (z + big.x) - big.x; + xx = (x - d * v.x) - d * (t.x - v.x); + if (d - z != 0.5 && d - z != -0.5) + return (xx != 0) ? xx : ((x > 0) ? ZERO.x : nZERO.x); + else + { + if (fabs (xx) > 0.5 * t.x) + return (z > d) ? xx - t.x : xx + t.x; + else + return xx; + } + } /* (kx<(ky+0x01500000)) */ + else + { + r.x = 1.0 / t.x; + n = t.i[HIGH_HALF]; + nn = (n & 0x7ff00000) + 0x01400000; + w.i[HIGH_HALF] = n; + ww.x = t.x - w.x; + l = (kx - nn) & 0xfff00000; + n1 = ww.i[HIGH_HALF]; + m1 = r.i[HIGH_HALF]; + while (l > 0) + { + r.i[HIGH_HALF] = m1 - l; + z = u.x * r.x; + w.i[HIGH_HALF] = n + l; + ww.i[HIGH_HALF] = (n1) ? n1 + l : n1; + d = (z + big.x) - big.x; + u.x = (u.x - d * w.x) - d * ww.x; + l = (u.i[HIGH_HALF] & 0x7ff00000) - nn; + } + r.i[HIGH_HALF] = m1; + w.i[HIGH_HALF] = n; + ww.i[HIGH_HALF] = n1; + z = u.x * r.x; + d = (z + big.x) - big.x; + u.x = (u.x - d * w.x) - d * ww.x; + if (fabs (u.x) < 0.5 * t.x) + return (u.x != 0) ? u.x : ((x > 0) ? ZERO.x : nZERO.x); + else + if (fabs (u.x) > 0.5 * t.x) + return (d > z) ? u.x + t.x : u.x - t.x; + else + { + z = u.x / t.x; d = (z + big.x) - big.x; + return ((u.x - d * w.x) - d * ww.x); + } + } + } /* (kx<0x7fe00000&&ky<0x7ff00000&&ky>=0x03500000) */ + else + { + if (kx < 0x7fe00000 && ky < 0x7ff00000 && (ky > 0 || t.i[LOW_HALF] != 0)) + { + y = fabs (y) * t128.x; + z = __ieee754_remainder (x, y) * t128.x; + z = __ieee754_remainder (z, y) * tm128.x; + return z; + } + else + { + if ((kx & 0x7ff00000) == 0x7fe00000 && ky < 0x7ff00000 && + (ky > 0 || t.i[LOW_HALF] != 0)) + { + y = fabs (y); + z = 2.0 * __ieee754_remainder (0.5 * x, y); + d = fabs (z); + if (d <= fabs (d - y)) + return z; + else if (d == y) + return 0.0 * x; + else + return (z > 0) ? z - y : z + y; + } + else /* if x is too big */ + { + if (ky == 0 && t.i[LOW_HALF] == 0) /* y = 0 */ + return (x * y) / (x * y); + else if (kx >= 0x7ff00000 /* x not finite */ + || (ky > 0x7ff00000 /* y is NaN */ + || (ky == 0x7ff00000 && t.i[LOW_HALF] != 0))) + return (x * y) / (x * y); + else + return x; + } + } + } +} +strong_alias (__ieee754_remainder, __remainder_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_sinh.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_sinh.c new file mode 100644 index 0000000000..8479bdd9b8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_sinh.c @@ -0,0 +1,90 @@ +/* @(#)e_sinh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_sinh.c,v 1.7 1995/05/10 20:46:13 jtc Exp $"; +#endif + +/* __ieee754_sinh(x) + * Method : + * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 + * 1. Replace x by |x| (sinh(-x) = -sinh(x)). + * 2. + * E + E/(E+1) + * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x) + * 2 + * + * 22 <= x <= lnovft : sinh(x) := exp(x)/2 + * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2) + * ln2ovft < x : sinh(x) := x*shuge (overflow) + * + * Special cases: + * sinh(x) is |x| if x is +INF, -INF, or NaN. + * only sinh(0)=0 is exact for finite x. + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const double one = 1.0, shuge = 1.0e307; + +double +__ieee754_sinh (double x) +{ + double t, w, h; + int32_t ix, jx; + u_int32_t lx; + + /* High word of |x|. */ + GET_HIGH_WORD (jx, x); + ix = jx & 0x7fffffff; + + /* x is INF or NaN */ + if (__glibc_unlikely (ix >= 0x7ff00000)) + return x + x; + + h = 0.5; + if (jx < 0) + h = -h; + /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ + if (ix < 0x40360000) /* |x|<22 */ + { + if (__glibc_unlikely (ix < 0x3e300000)) { /* |x|<2**-28 */ + math_check_force_underflow (x); + if (shuge + x > one) + return x; + /* sinh(tiny) = tiny with inexact */ + } + t = __expm1 (fabs (x)); + if (ix < 0x3ff00000) + return h * (2.0 * t - t * t / (t + one)); + return h * (t + t / (t + one)); + } + + /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ + if (ix < 0x40862e42) + return h * __ieee754_exp (fabs (x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + GET_LOW_WORD (lx, x); + if (ix < 0x408633ce || ((ix == 0x408633ce) && (lx <= (u_int32_t) 0x8fb9f87d))) + { + w = __ieee754_exp (0.5 * fabs (x)); + t = h * w; + return t * w; + } + + /* |x| > overflowthresold, sinh(x) overflow */ + return math_narrow_eval (x * shuge); +} +strong_alias (__ieee754_sinh, __sinh_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_sqrt.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_sqrt.c new file mode 100644 index 0000000000..017d30416c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_sqrt.c @@ -0,0 +1,139 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/*********************************************************************/ +/* MODULE_NAME: uroot.c */ +/* */ +/* FUNCTION: usqrt */ +/* */ +/* FILES NEEDED: dla.h endian.h mydefs.h */ +/* uroot.tbl */ +/* */ +/* An ultimate sqrt routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of square */ +/* root of x. */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round to nearest mode of IEEE 754 standard. */ +/* */ +/*********************************************************************/ + +#include "endian.h" +#include "mydefs.h" +#include <dla.h> +#include "MathLib.h" +#include "root.tbl" +#include <math_private.h> + +/*********************************************************************/ +/* An ultimate sqrt routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of square */ +/* root of x. */ +/*********************************************************************/ +double +__ieee754_sqrt (double x) +{ + static const double + rt0 = 9.99999999859990725855365213134618E-01, + rt1 = 4.99999999495955425917856814202739E-01, + rt2 = 3.75017500867345182581453026130850E-01, + rt3 = 3.12523626554518656309172508769531E-01; + static const double big = 134217728.0; + double y, t, del, res, res1, hy, z, zz, p, hx, tx, ty, s; + mynumber a, c = { { 0, 0 } }; + int4 k; + + a.x = x; + k = a.i[HIGH_HALF]; + a.i[HIGH_HALF] = (k & 0x001fffff) | 0x3fe00000; + t = inroot[(k & 0x001fffff) >> 14]; + s = a.x; + /*----------------- 2^-1022 <= | x |< 2^1024 -----------------*/ + if (k > 0x000fffff && k < 0x7ff00000) + { + int rm = __fegetround (); + fenv_t env; + libc_feholdexcept_setround (&env, FE_TONEAREST); + double ret; + y = 1.0 - t * (t * s); + t = t * (rt0 + y * (rt1 + y * (rt2 + y * rt3))); + c.i[HIGH_HALF] = 0x20000000 + ((k & 0x7fe00000) >> 1); + y = t * s; + hy = (y + big) - big; + del = 0.5 * t * ((s - hy * hy) - (y - hy) * (y + hy)); + res = y + del; + if (res == (res + 1.002 * ((y - res) + del))) + ret = res * c.x; + else + { + res1 = res + 1.5 * ((y - res) + del); + EMULV (res, res1, z, zz, p, hx, tx, hy, ty); /* (z+zz)=res*res1 */ + res = ((((z - s) + zz) < 0) ? max (res, res1) : + min (res, res1)); + ret = res * c.x; + } + math_force_eval (ret); + libc_fesetenv (&env); + double dret = x / ret; + if (dret != ret) + { + double force_inexact = 1.0 / 3.0; + math_force_eval (force_inexact); + /* The square root is inexact, ret is the round-to-nearest + value which may need adjusting for other rounding + modes. */ + switch (rm) + { +#ifdef FE_UPWARD + case FE_UPWARD: + if (dret > ret) + ret = (res + 0x1p-1022) * c.x; + break; +#endif + +#ifdef FE_DOWNWARD + case FE_DOWNWARD: +#endif +#ifdef FE_TOWARDZERO + case FE_TOWARDZERO: +#endif +#if defined FE_DOWNWARD || defined FE_TOWARDZERO + if (dret < ret) + ret = (res - 0x1p-1022) * c.x; + break; +#endif + + default: + break; + } + } + /* Otherwise (x / ret == ret), either the square root was exact or + the division was inexact. */ + return ret; + } + else + { + if ((k & 0x7ff00000) == 0x7ff00000) + return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */ + if (x == 0) + return x; /* sqrt(+0)=+0, sqrt(-0)=-0 */ + if (k < 0) + return (x - x) / (x - x); /* sqrt(-ve)=sNaN */ + return 0x1p-256 * __ieee754_sqrt (x * 0x1p512); + } +} +strong_alias (__ieee754_sqrt, __sqrt_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/gamma_product.c b/REORG.TODO/sysdeps/ieee754/dbl-64/gamma_product.c new file mode 100644 index 0000000000..d946b3c845 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/gamma_product.c @@ -0,0 +1,45 @@ +/* Compute a product of X, X+1, ..., with an error estimate. + Copyright (C) 2013-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <mul_split.h> + +/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N + - 1, in the form R * (1 + *EPS) where the return value R is an + approximation to the product and *EPS is set to indicate the + approximate error in the return value. X is such that all the + values X + 1, ..., X + N - 1 are exactly representable, and X_EPS / + X is small enough that factors quadratic in it can be + neglected. */ + +double +__gamma_product (double x, double x_eps, int n, double *eps) +{ + SET_RESTORE_ROUND (FE_TONEAREST); + double ret = x; + *eps = x_eps / x; + for (int i = 1; i < n; i++) + { + *eps += x_eps / (x + i); + double lo; + mul_split (&ret, &lo, ret, x + i); + *eps += lo / ret; + } + return ret; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/gamma_productf.c b/REORG.TODO/sysdeps/ieee754/dbl-64/gamma_productf.c new file mode 100644 index 0000000000..49c15b14b4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/gamma_productf.c @@ -0,0 +1,43 @@ +/* Compute a product of X, X+1, ..., with an error estimate. + Copyright (C) 2013-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N + - 1, in the form R * (1 + *EPS) where the return value R is an + approximation to the product and *EPS is set to indicate the + approximate error in the return value. X is such that all the + values X + 1, ..., X + N - 1 are exactly representable, and X_EPS / + X is small enough that factors quadratic in it can be + neglected. */ + +float +__gamma_productf (float x, float x_eps, int n, float *eps) +{ + double x_full = (double) x + (double) x_eps; + double ret = x_full; + for (int i = 1; i < n; i++) + ret *= x_full + i; + + float fret = math_narrow_eval ((float) ret); + *eps = (ret - fret) / fret; + + return fret; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/halfulp.c b/REORG.TODO/sysdeps/ieee754/dbl-64/halfulp.c new file mode 100644 index 0000000000..d5f8a010e2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/halfulp.c @@ -0,0 +1,152 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/************************************************************************/ +/* */ +/* MODULE_NAME:halfulp.c */ +/* */ +/* FUNCTIONS:halfulp */ +/* FILES NEEDED: mydefs.h dla.h endian.h */ +/* uroot.c */ +/* */ +/*Routine halfulp(double x, double y) computes x^y where result does */ +/*not need rounding. If the result is closer to 0 than can be */ +/*represented it returns 0. */ +/* In the following cases the function does not compute anything */ +/*and returns a negative number: */ +/*1. if the result needs rounding, */ +/*2. if y is outside the interval [0, 2^20-1], */ +/*3. if x can be represented by x=2**n for some integer n. */ +/************************************************************************/ + +#include "endian.h" +#include "mydefs.h" +#include <dla.h> +#include <math_private.h> + +#ifndef SECTION +# define SECTION +#endif + +static const int4 tab54[32] = { + 262143, 11585, 1782, 511, 210, 107, 63, 42, + 30, 22, 17, 14, 12, 10, 9, 7, + 7, 6, 5, 5, 5, 4, 4, 4, + 3, 3, 3, 3, 3, 3, 3, 3 +}; + + +double +SECTION +__halfulp (double x, double y) +{ + mynumber v; + double z, u, uu; +#ifndef DLA_FMS + double j1, j2, j3, j4, j5; +#endif + int4 k, l, m, n; + if (y <= 0) /*if power is negative or zero */ + { + v.x = y; + if (v.i[LOW_HALF] != 0) + return -10.0; + v.x = x; + if (v.i[LOW_HALF] != 0) + return -10.0; + if ((v.i[HIGH_HALF] & 0x000fffff) != 0) + return -10; /* if x =2 ^ n */ + k = ((v.i[HIGH_HALF] & 0x7fffffff) >> 20) - 1023; /* find this n */ + z = (double) k; + return (z * y == -1075.0) ? 0 : -10.0; + } + /* if y > 0 */ + v.x = y; + if (v.i[LOW_HALF] != 0) + return -10.0; + + v.x = x; + /* case where x = 2**n for some integer n */ + if (((v.i[HIGH_HALF] & 0x000fffff) | v.i[LOW_HALF]) == 0) + { + k = (v.i[HIGH_HALF] >> 20) - 1023; + return (((double) k) * y == -1075.0) ? 0 : -10.0; + } + + v.x = y; + k = v.i[HIGH_HALF]; + m = k << 12; + l = 0; + while (m) + { + m = m << 1; l++; + } + n = (k & 0x000fffff) | 0x00100000; + n = n >> (20 - l); /* n is the odd integer of y */ + k = ((k >> 20) - 1023) - l; /* y = n*2**k */ + if (k > 5) + return -10.0; + if (k > 0) + for (; k > 0; k--) + n *= 2; + if (n > 34) + return -10.0; + k = -k; + if (k > 5) + return -10.0; + + /* now treat x */ + while (k > 0) + { + z = __ieee754_sqrt (x); + EMULV (z, z, u, uu, j1, j2, j3, j4, j5); + if (((u - x) + uu) != 0) + break; + x = z; + k--; + } + if (k) + return -10.0; + + /* it is impossible that n == 2, so the mantissa of x must be short */ + + v.x = x; + if (v.i[LOW_HALF]) + return -10.0; + k = v.i[HIGH_HALF]; + m = k << 12; + l = 0; + while (m) + { + m = m << 1; l++; + } + m = (k & 0x000fffff) | 0x00100000; + m = m >> (20 - l); /* m is the odd integer of x */ + + /* now check whether the length of m**n is at most 54 bits */ + + if (m > tab54[n - 3]) + return -10.0; + + /* yes, it is - now compute x**n by simple multiplications */ + + u = x; + for (k = 1; k < n; k++) + u = u * x; + return u; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/k_cos.c b/REORG.TODO/sysdeps/ieee754/dbl-64/k_cos.c new file mode 100644 index 0000000000..cc5c205a5f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/k_cos.c @@ -0,0 +1 @@ +/* Not needed anymore. */ diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/k_rem_pio2.c b/REORG.TODO/sysdeps/ieee754/dbl-64/k_rem_pio2.c new file mode 100644 index 0000000000..2b5add6976 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/k_rem_pio2.c @@ -0,0 +1,362 @@ +/* @(#)k_rem_pio2.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: k_rem_pio2.c,v 1.7 1995/05/10 20:46:25 jtc Exp $"; +#endif + +/* + * __kernel_rem_pio2(x,y,e0,nx,prec,ipio2) + * double x[],y[]; int e0,nx,prec; int ipio2[]; + * + * __kernel_rem_pio2 return the last three digits of N with + * y = x - N*pi/2 + * so that |y| < pi/2. + * + * The method is to compute the integer (mod 8) and fraction parts of + * (2/pi)*x without doing the full multiplication. In general we + * skip the part of the product that are known to be a huge integer ( + * more accurately, = 0 mod 8 ). Thus the number of operations are + * independent of the exponent of the input. + * + * (2/pi) is represented by an array of 24-bit integers in ipio2[]. + * + * Input parameters: + * x[] The input value (must be positive) is broken into nx + * pieces of 24-bit integers in double precision format. + * x[i] will be the i-th 24 bit of x. The scaled exponent + * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0 + * match x's up to 24 bits. + * + * Example of breaking a double positive z into x[0]+x[1]+x[2]: + * e0 = ilogb(z)-23 + * z = scalbn(z,-e0) + * for i = 0,1,2 + * x[i] = floor(z) + * z = (z-x[i])*2**24 + * + * + * y[] ouput result in an array of double precision numbers. + * The dimension of y[] is: + * 24-bit precision 1 + * 53-bit precision 2 + * 64-bit precision 2 + * 113-bit precision 3 + * The actual value is the sum of them. Thus for 113-bit + * precision, one may have to do something like: + * + * long double t,w,r_head, r_tail; + * t = (long double)y[2] + (long double)y[1]; + * w = (long double)y[0]; + * r_head = t+w; + * r_tail = w - (r_head - t); + * + * e0 The exponent of x[0] + * + * nx dimension of x[] + * + * prec an integer indicating the precision: + * 0 24 bits (single) + * 1 53 bits (double) + * 2 64 bits (extended) + * 3 113 bits (quad) + * + * ipio2[] + * integer array, contains the (24*i)-th to (24*i+23)-th + * bit of 2/pi after binary point. The corresponding + * floating value is + * + * ipio2[i] * 2^(-24(i+1)). + * + * External function: + * double scalbn(), floor(); + * + * + * Here is the description of some local variables: + * + * jk jk+1 is the initial number of terms of ipio2[] needed + * in the computation. The recommended value is 2,3,4, + * 6 for single, double, extended,and quad. + * + * jz local integer variable indicating the number of + * terms of ipio2[] used. + * + * jx nx - 1 + * + * jv index for pointing to the suitable ipio2[] for the + * computation. In general, we want + * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8 + * is an integer. Thus + * e0-3-24*jv >= 0 or (e0-3)/24 >= jv + * Hence jv = max(0,(e0-3)/24). + * + * jp jp+1 is the number of terms in PIo2[] needed, jp = jk. + * + * q[] double array with integral value, representing the + * 24-bits chunk of the product of x and 2/pi. + * + * q0 the corresponding exponent of q[0]. Note that the + * exponent for q[i] would be q0-24*i. + * + * PIo2[] double precision array, obtained by cutting pi/2 + * into 24 bits chunks. + * + * f[] ipio2[] in floating point + * + * iq[] integer array by breaking up q[] in 24-bits chunk. + * + * fq[] final product of x*(2/pi) in fq[0],..,fq[jk] + * + * ih integer. If >0 it indicates q[] is >= 0.5, hence + * it also indicates the *sign* of the result. + * + */ + + +/* + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include <math.h> +#include <math_private.h> +#include <libc-diag.h> + +static const int init_jk[] = {2,3,4,6}; /* initial value for jk */ + +static const double PIo2[] = { + 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */ + 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */ + 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */ + 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */ + 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */ + 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */ + 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */ + 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */ +}; + +static const double + zero = 0.0, + one = 1.0, + two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ + twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */ + +int +__kernel_rem_pio2 (double *x, double *y, int e0, int nx, int prec, + const int32_t *ipio2) +{ + int32_t jz, jx, jv, jp, jk, carry, n, iq[20], i, j, k, m, q0, ih; + double z, fw, f[20], fq[20], q[20]; + + /* initialize jk*/ + jk = init_jk[prec]; + jp = jk; + + /* determine jx,jv,q0, note that 3>q0 */ + jx = nx - 1; + jv = (e0 - 3) / 24; if (jv < 0) + jv = 0; + q0 = e0 - 24 * (jv + 1); + + /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ + j = jv - jx; m = jx + jk; + for (i = 0; i <= m; i++, j++) + f[i] = (j < 0) ? zero : (double) ipio2[j]; + + /* compute q[0],q[1],...q[jk] */ + for (i = 0; i <= jk; i++) + { + for (j = 0, fw = 0.0; j <= jx; j++) + fw += x[j] * f[jx + i - j]; + q[i] = fw; + } + + jz = jk; +recompute: + /* distill q[] into iq[] reversingly */ + for (i = 0, j = jz, z = q[jz]; j > 0; i++, j--) + { + fw = (double) ((int32_t) (twon24 * z)); + iq[i] = (int32_t) (z - two24 * fw); + z = q[j - 1] + fw; + } + + /* compute n */ + z = __scalbn (z, q0); /* actual value of z */ + z -= 8.0 * __floor (z * 0.125); /* trim off integer >= 8 */ + n = (int32_t) z; + z -= (double) n; + ih = 0; + if (q0 > 0) /* need iq[jz-1] to determine n */ + { + i = (iq[jz - 1] >> (24 - q0)); n += i; + iq[jz - 1] -= i << (24 - q0); + ih = iq[jz - 1] >> (23 - q0); + } + else if (q0 == 0) + ih = iq[jz - 1] >> 23; + else if (z >= 0.5) + ih = 2; + + if (ih > 0) /* q > 0.5 */ + { + n += 1; carry = 0; + for (i = 0; i < jz; i++) /* compute 1-q */ + { + j = iq[i]; + if (carry == 0) + { + if (j != 0) + { + carry = 1; iq[i] = 0x1000000 - j; + } + } + else + iq[i] = 0xffffff - j; + } + if (q0 > 0) /* rare case: chance is 1 in 12 */ + { + switch (q0) + { + case 1: + iq[jz - 1] &= 0x7fffff; break; + case 2: + iq[jz - 1] &= 0x3fffff; break; + } + } + if (ih == 2) + { + z = one - z; + if (carry != 0) + z -= __scalbn (one, q0); + } + } + + /* check if recomputation is needed */ + if (z == zero) + { + j = 0; + for (i = jz - 1; i >= jk; i--) + j |= iq[i]; + if (j == 0) /* need recomputation */ + { + /* On s390x gcc 6.1 -O3 produces the warning "array subscript is below + array bounds [-Werror=array-bounds]". Only __ieee754_rem_pio2l + calls __kernel_rem_pio2 for normal numbers and |x| > pi/4 in case + of ldbl-96 and |x| > 3pi/4 in case of ldbl-128[ibm]. + Thus x can't be zero and ipio2 is not zero, too. Thus not all iq[] + values can't be zero. */ + DIAG_PUSH_NEEDS_COMMENT; + DIAG_IGNORE_NEEDS_COMMENT (6.1, "-Warray-bounds"); + for (k = 1; iq[jk - k] == 0; k++) + ; /* k = no. of terms needed */ + DIAG_POP_NEEDS_COMMENT; + + for (i = jz + 1; i <= jz + k; i++) /* add q[jz+1] to q[jz+k] */ + { + f[jx + i] = (double) ipio2[jv + i]; + for (j = 0, fw = 0.0; j <= jx; j++) + fw += x[j] * f[jx + i - j]; + q[i] = fw; + } + jz += k; + goto recompute; + } + } + + /* chop off zero terms */ + if (z == 0.0) + { + jz -= 1; q0 -= 24; + while (iq[jz] == 0) + { + jz--; q0 -= 24; + } + } + else /* break z into 24-bit if necessary */ + { + z = __scalbn (z, -q0); + if (z >= two24) + { + fw = (double) ((int32_t) (twon24 * z)); + iq[jz] = (int32_t) (z - two24 * fw); + jz += 1; q0 += 24; + iq[jz] = (int32_t) fw; + } + else + iq[jz] = (int32_t) z; + } + + /* convert integer "bit" chunk to floating-point value */ + fw = __scalbn (one, q0); + for (i = jz; i >= 0; i--) + { + q[i] = fw * (double) iq[i]; fw *= twon24; + } + + /* compute PIo2[0,...,jp]*q[jz,...,0] */ + for (i = jz; i >= 0; i--) + { + for (fw = 0.0, k = 0; k <= jp && k <= jz - i; k++) + fw += PIo2[k] * q[i + k]; + fq[jz - i] = fw; + } + + /* compress fq[] into y[] */ + switch (prec) + { + case 0: + fw = 0.0; + for (i = jz; i >= 0; i--) + fw += fq[i]; + y[0] = (ih == 0) ? fw : -fw; + break; + case 1: + case 2:; + double fv = 0.0; + for (i = jz; i >= 0; i--) + fv = math_narrow_eval (fv + fq[i]); + y[0] = (ih == 0) ? fv : -fv; + fv = math_narrow_eval (fq[0] - fv); + for (i = 1; i <= jz; i++) + fv = math_narrow_eval (fv + fq[i]); + y[1] = (ih == 0) ? fv : -fv; + break; + case 3: /* painful */ + for (i = jz; i > 0; i--) + { + double fv = math_narrow_eval (fq[i - 1] + fq[i]); + fq[i] += fq[i - 1] - fv; + fq[i - 1] = fv; + } + for (i = jz; i > 1; i--) + { + double fv = math_narrow_eval (fq[i - 1] + fq[i]); + fq[i] += fq[i - 1] - fv; + fq[i - 1] = fv; + } + for (fw = 0.0, i = jz; i >= 2; i--) + fw += fq[i]; + if (ih == 0) + { + y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; + } + else + { + y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; + } + } + return n & 7; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/k_sin.c b/REORG.TODO/sysdeps/ieee754/dbl-64/k_sin.c new file mode 100644 index 0000000000..cc5c205a5f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/k_sin.c @@ -0,0 +1 @@ +/* Not needed anymore. */ diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/k_tan.c b/REORG.TODO/sysdeps/ieee754/dbl-64/k_tan.c new file mode 100644 index 0000000000..cc5c205a5f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/k_tan.c @@ -0,0 +1 @@ +/* Not needed anymore. */ diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/lgamma_neg.c b/REORG.TODO/sysdeps/ieee754/dbl-64/lgamma_neg.c new file mode 100644 index 0000000000..ccde9a1fe5 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/lgamma_neg.c @@ -0,0 +1,383 @@ +/* lgamma expanding around zeros. + Copyright (C) 2015-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const double lgamma_zeros[][2] = + { + { -0x2.74ff92c01f0d8p+0, -0x2.abec9f315f1ap-56 }, + { -0x2.bf6821437b202p+0, 0x6.866a5b4b9be14p-56 }, + { -0x3.24c1b793cb35ep+0, -0xf.b8be699ad3d98p-56 }, + { -0x3.f48e2a8f85fcap+0, -0x1.70d4561291237p-56 }, + { -0x4.0a139e1665604p+0, 0xf.3c60f4f21e7fp-56 }, + { -0x4.fdd5de9bbabf4p+0, 0xa.ef2f55bf89678p-56 }, + { -0x5.021a95fc2db64p+0, -0x3.2a4c56e595394p-56 }, + { -0x5.ffa4bd647d034p+0, -0x1.7dd4ed62cbd32p-52 }, + { -0x6.005ac9625f234p+0, 0x4.9f83d2692e9c8p-56 }, + { -0x6.fff2fddae1bcp+0, 0xc.29d949a3dc03p-60 }, + { -0x7.000cff7b7f87cp+0, 0x1.20bb7d2324678p-52 }, + { -0x7.fffe5fe05673cp+0, -0x3.ca9e82b522b0cp-56 }, + { -0x8.0001a01459fc8p+0, -0x1.f60cb3cec1cedp-52 }, + { -0x8.ffffd1c425e8p+0, -0xf.fc864e9574928p-56 }, + { -0x9.00002e3bb47d8p+0, -0x6.d6d843fedc35p-56 }, + { -0x9.fffffb606bep+0, 0x2.32f9d51885afap-52 }, + { -0xa.0000049f93bb8p+0, -0x1.927b45d95e154p-52 }, + { -0xa.ffffff9466eap+0, 0xe.4c92532d5243p-56 }, + { -0xb.0000006b9915p+0, -0x3.15d965a6ffea4p-52 }, + { -0xb.fffffff708938p+0, -0x7.387de41acc3d4p-56 }, + { -0xc.00000008f76c8p+0, 0x8.cea983f0fdafp-56 }, + { -0xc.ffffffff4f6ep+0, 0x3.09e80685a0038p-52 }, + { -0xd.00000000b092p+0, -0x3.09c06683dd1bap-52 }, + { -0xd.fffffffff3638p+0, 0x3.a5461e7b5c1f6p-52 }, + { -0xe.000000000c9c8p+0, -0x3.a545e94e75ec6p-52 }, + { -0xe.ffffffffff29p+0, 0x3.f9f399fb10cfcp-52 }, + { -0xf.0000000000d7p+0, -0x3.f9f399bd0e42p-52 }, + { -0xf.fffffffffff28p+0, -0xc.060c6621f513p-56 }, + { -0x1.000000000000dp+4, -0x7.3f9f399da1424p-52 }, + { -0x1.0ffffffffffffp+4, -0x3.569c47e7a93e2p-52 }, + { -0x1.1000000000001p+4, 0x3.569c47e7a9778p-52 }, + { -0x1.2p+4, 0xb.413c31dcbecdp-56 }, + { -0x1.2p+4, -0xb.413c31dcbeca8p-56 }, + { -0x1.3p+4, 0x9.7a4da340a0ab8p-60 }, + { -0x1.3p+4, -0x9.7a4da340a0ab8p-60 }, + { -0x1.4p+4, 0x7.950ae90080894p-64 }, + { -0x1.4p+4, -0x7.950ae90080894p-64 }, + { -0x1.5p+4, 0x5.c6e3bdb73d5c8p-68 }, + { -0x1.5p+4, -0x5.c6e3bdb73d5c8p-68 }, + { -0x1.6p+4, 0x4.338e5b6dfe14cp-72 }, + { -0x1.6p+4, -0x4.338e5b6dfe14cp-72 }, + { -0x1.7p+4, 0x2.ec368262c7034p-76 }, + { -0x1.7p+4, -0x2.ec368262c7034p-76 }, + { -0x1.8p+4, 0x1.f2cf01972f578p-80 }, + { -0x1.8p+4, -0x1.f2cf01972f578p-80 }, + { -0x1.9p+4, 0x1.3f3ccdd165fa9p-84 }, + { -0x1.9p+4, -0x1.3f3ccdd165fa9p-84 }, + { -0x1.ap+4, 0xc.4742fe35272dp-92 }, + { -0x1.ap+4, -0xc.4742fe35272dp-92 }, + { -0x1.bp+4, 0x7.46ac70b733a8cp-96 }, + { -0x1.bp+4, -0x7.46ac70b733a8cp-96 }, + { -0x1.cp+4, 0x4.2862898d42174p-100 }, + }; + +static const double e_hi = 0x2.b7e151628aed2p+0, e_lo = 0xa.6abf7158809dp-56; + +/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) in Stirling's + approximation to lgamma function. */ + +static const double lgamma_coeff[] = + { + 0x1.5555555555555p-4, + -0xb.60b60b60b60b8p-12, + 0x3.4034034034034p-12, + -0x2.7027027027028p-12, + 0x3.72a3c5631fe46p-12, + -0x7.daac36664f1f4p-12, + 0x1.a41a41a41a41ap-8, + -0x7.90a1b2c3d4e6p-8, + 0x2.dfd2c703c0dp-4, + -0x1.6476701181f3ap+0, + 0xd.672219167003p+0, + -0x9.cd9292e6660d8p+4, + }; + +#define NCOEFF (sizeof (lgamma_coeff) / sizeof (lgamma_coeff[0])) + +/* Polynomial approximations to (|gamma(x)|-1)(x-n)/(x-x0), where n is + the integer end-point of the half-integer interval containing x and + x0 is the zero of lgamma in that half-integer interval. Each + polynomial is expressed in terms of x-xm, where xm is the midpoint + of the interval for which the polynomial applies. */ + +static const double poly_coeff[] = + { + /* Interval [-2.125, -2] (polynomial degree 10). */ + -0x1.0b71c5c54d42fp+0, + -0xc.73a1dc05f3758p-4, + -0x1.ec84140851911p-4, + -0xe.37c9da23847e8p-4, + -0x1.03cd87cdc0ac6p-4, + -0xe.ae9aedce12eep-4, + 0x9.b11a1780cfd48p-8, + -0xe.f25fc460bdebp-4, + 0x2.6e984c61ca912p-4, + -0xf.83fea1c6d35p-4, + 0x4.760c8c8909758p-4, + /* Interval [-2.25, -2.125] (polynomial degree 11). */ + -0xf.2930890d7d678p-4, + -0xc.a5cfde054eaa8p-4, + 0x3.9c9e0fdebd99cp-4, + -0x1.02a5ad35619d9p+0, + 0x9.6e9b1167c164p-4, + -0x1.4d8332eba090ap+0, + 0x1.1c0c94b1b2b6p+0, + -0x1.c9a70d138c74ep+0, + 0x1.d7d9cf1d4c196p+0, + -0x2.91fbf4cd6abacp+0, + 0x2.f6751f74b8ff8p+0, + -0x3.e1bb7b09e3e76p+0, + /* Interval [-2.375, -2.25] (polynomial degree 12). */ + -0xd.7d28d505d618p-4, + -0xe.69649a3040958p-4, + 0xb.0d74a2827cd6p-4, + -0x1.924b09228a86ep+0, + 0x1.d49b12bcf6175p+0, + -0x3.0898bb530d314p+0, + 0x4.207a6be8fda4cp+0, + -0x6.39eef56d4e9p+0, + 0x8.e2e42acbccec8p+0, + -0xd.0d91c1e596a68p+0, + 0x1.2e20d7099c585p+4, + -0x1.c4eb6691b4ca9p+4, + 0x2.96a1a11fd85fep+4, + /* Interval [-2.5, -2.375] (polynomial degree 13). */ + -0xb.74ea1bcfff948p-4, + -0x1.2a82bd590c376p+0, + 0x1.88020f828b81p+0, + -0x3.32279f040d7aep+0, + 0x5.57ac8252ce868p+0, + -0x9.c2aedd093125p+0, + 0x1.12c132716e94cp+4, + -0x1.ea94dfa5c0a6dp+4, + 0x3.66b61abfe858cp+4, + -0x6.0cfceb62a26e4p+4, + 0xa.beeba09403bd8p+4, + -0x1.3188d9b1b288cp+8, + 0x2.37f774dd14c44p+8, + -0x3.fdf0a64cd7136p+8, + /* Interval [-2.625, -2.5] (polynomial degree 13). */ + -0x3.d10108c27ebbp-4, + 0x1.cd557caff7d2fp+0, + 0x3.819b4856d36cep+0, + 0x6.8505cbacfc42p+0, + 0xb.c1b2e6567a4dp+0, + 0x1.50a53a3ce6c73p+4, + 0x2.57adffbb1ec0cp+4, + 0x4.2b15549cf400cp+4, + 0x7.698cfd82b3e18p+4, + 0xd.2decde217755p+4, + 0x1.7699a624d07b9p+8, + 0x2.98ecf617abbfcp+8, + 0x4.d5244d44d60b4p+8, + 0x8.e962bf7395988p+8, + /* Interval [-2.75, -2.625] (polynomial degree 12). */ + -0x6.b5d252a56e8a8p-4, + 0x1.28d60383da3a6p+0, + 0x1.db6513ada89bep+0, + 0x2.e217118fa8c02p+0, + 0x4.450112c651348p+0, + 0x6.4af990f589b8cp+0, + 0x9.2db5963d7a238p+0, + 0xd.62c03647da19p+0, + 0x1.379f81f6416afp+4, + 0x1.c5618b4fdb96p+4, + 0x2.9342d0af2ac4ep+4, + 0x3.d9cdf56d2b186p+4, + 0x5.ab9f91d5a27a4p+4, + /* Interval [-2.875, -2.75] (polynomial degree 11). */ + -0x8.a41b1e4f36ff8p-4, + 0xc.da87d3b69dbe8p-4, + 0x1.1474ad5c36709p+0, + 0x1.761ecb90c8c5cp+0, + 0x1.d279bff588826p+0, + 0x2.4e5d003fb36a8p+0, + 0x2.d575575566842p+0, + 0x3.85152b0d17756p+0, + 0x4.5213d921ca13p+0, + 0x5.55da7dfcf69c4p+0, + 0x6.acef729b9404p+0, + 0x8.483cc21dd0668p+0, + /* Interval [-3, -2.875] (polynomial degree 11). */ + -0xa.046d667e468f8p-4, + 0x9.70b88dcc006cp-4, + 0xa.a8a39421c94dp-4, + 0xd.2f4d1363f98ep-4, + 0xd.ca9aa19975b7p-4, + 0xf.cf09c2f54404p-4, + 0x1.04b1365a9adfcp+0, + 0x1.22b54ef213798p+0, + 0x1.2c52c25206bf5p+0, + 0x1.4aa3d798aace4p+0, + 0x1.5c3f278b504e3p+0, + 0x1.7e08292cc347bp+0, + }; + +static const size_t poly_deg[] = + { + 10, + 11, + 12, + 13, + 13, + 12, + 11, + 11, + }; + +static const size_t poly_end[] = + { + 10, + 22, + 35, + 49, + 63, + 76, + 88, + 100, + }; + +/* Compute sin (pi * X) for -0.25 <= X <= 0.5. */ + +static double +lg_sinpi (double x) +{ + if (x <= 0.25) + return __sin (M_PI * x); + else + return __cos (M_PI * (0.5 - x)); +} + +/* Compute cos (pi * X) for -0.25 <= X <= 0.5. */ + +static double +lg_cospi (double x) +{ + if (x <= 0.25) + return __cos (M_PI * x); + else + return __sin (M_PI * (0.5 - x)); +} + +/* Compute cot (pi * X) for -0.25 <= X <= 0.5. */ + +static double +lg_cotpi (double x) +{ + return lg_cospi (x) / lg_sinpi (x); +} + +/* Compute lgamma of a negative argument -28 < X < -2, setting + *SIGNGAMP accordingly. */ + +double +__lgamma_neg (double x, int *signgamp) +{ + /* Determine the half-integer region X lies in, handle exact + integers and determine the sign of the result. */ + int i = __floor (-2 * x); + if ((i & 1) == 0 && i == -2 * x) + return 1.0 / 0.0; + double xn = ((i & 1) == 0 ? -i / 2 : (-i - 1) / 2); + i -= 4; + *signgamp = ((i & 2) == 0 ? -1 : 1); + + SET_RESTORE_ROUND (FE_TONEAREST); + + /* Expand around the zero X0 = X0_HI + X0_LO. */ + double x0_hi = lgamma_zeros[i][0], x0_lo = lgamma_zeros[i][1]; + double xdiff = x - x0_hi - x0_lo; + + /* For arguments in the range -3 to -2, use polynomial + approximations to an adjusted version of the gamma function. */ + if (i < 2) + { + int j = __floor (-8 * x) - 16; + double xm = (-33 - 2 * j) * 0.0625; + double x_adj = x - xm; + size_t deg = poly_deg[j]; + size_t end = poly_end[j]; + double g = poly_coeff[end]; + for (size_t j = 1; j <= deg; j++) + g = g * x_adj + poly_coeff[end - j]; + return __log1p (g * xdiff / (x - xn)); + } + + /* The result we want is log (sinpi (X0) / sinpi (X)) + + log (gamma (1 - X0) / gamma (1 - X)). */ + double x_idiff = fabs (xn - x), x0_idiff = fabs (xn - x0_hi - x0_lo); + double log_sinpi_ratio; + if (x0_idiff < x_idiff * 0.5) + /* Use log not log1p to avoid inaccuracy from log1p of arguments + close to -1. */ + log_sinpi_ratio = __ieee754_log (lg_sinpi (x0_idiff) + / lg_sinpi (x_idiff)); + else + { + /* Use log1p not log to avoid inaccuracy from log of arguments + close to 1. X0DIFF2 has positive sign if X0 is further from + XN than X is from XN, negative sign otherwise. */ + double x0diff2 = ((i & 1) == 0 ? xdiff : -xdiff) * 0.5; + double sx0d2 = lg_sinpi (x0diff2); + double cx0d2 = lg_cospi (x0diff2); + log_sinpi_ratio = __log1p (2 * sx0d2 + * (-sx0d2 + cx0d2 * lg_cotpi (x_idiff))); + } + + double log_gamma_ratio; + double y0 = math_narrow_eval (1 - x0_hi); + double y0_eps = -x0_hi + (1 - y0) - x0_lo; + double y = math_narrow_eval (1 - x); + double y_eps = -x + (1 - y); + /* We now wish to compute LOG_GAMMA_RATIO + = log (gamma (Y0 + Y0_EPS) / gamma (Y + Y_EPS)). XDIFF + accurately approximates the difference Y0 + Y0_EPS - Y - + Y_EPS. Use Stirling's approximation. First, we may need to + adjust into the range where Stirling's approximation is + sufficiently accurate. */ + double log_gamma_adj = 0; + if (i < 6) + { + int n_up = (7 - i) / 2; + double ny0, ny0_eps, ny, ny_eps; + ny0 = math_narrow_eval (y0 + n_up); + ny0_eps = y0 - (ny0 - n_up) + y0_eps; + y0 = ny0; + y0_eps = ny0_eps; + ny = math_narrow_eval (y + n_up); + ny_eps = y - (ny - n_up) + y_eps; + y = ny; + y_eps = ny_eps; + double prodm1 = __lgamma_product (xdiff, y - n_up, y_eps, n_up); + log_gamma_adj = -__log1p (prodm1); + } + double log_gamma_high + = (xdiff * __log1p ((y0 - e_hi - e_lo + y0_eps) / e_hi) + + (y - 0.5 + y_eps) * __log1p (xdiff / y) + log_gamma_adj); + /* Compute the sum of (B_2k / 2k(2k-1))(Y0^-(2k-1) - Y^-(2k-1)). */ + double y0r = 1 / y0, yr = 1 / y; + double y0r2 = y0r * y0r, yr2 = yr * yr; + double rdiff = -xdiff / (y * y0); + double bterm[NCOEFF]; + double dlast = rdiff, elast = rdiff * yr * (yr + y0r); + bterm[0] = dlast * lgamma_coeff[0]; + for (size_t j = 1; j < NCOEFF; j++) + { + double dnext = dlast * y0r2 + elast; + double enext = elast * yr2; + bterm[j] = dnext * lgamma_coeff[j]; + dlast = dnext; + elast = enext; + } + double log_gamma_low = 0; + for (size_t j = 0; j < NCOEFF; j++) + log_gamma_low += bterm[NCOEFF - 1 - j]; + log_gamma_ratio = log_gamma_high + log_gamma_low; + + return log_sinpi_ratio + log_gamma_ratio; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/lgamma_product.c b/REORG.TODO/sysdeps/ieee754/dbl-64/lgamma_product.c new file mode 100644 index 0000000000..a894f488b0 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/lgamma_product.c @@ -0,0 +1,52 @@ +/* Compute a product of 1 + (T/X), 1 + (T/(X+1)), .... + Copyright (C) 2015-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <mul_split.h> + +/* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS + + 1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1. X is such that + all the values X + 1, ..., X + N - 1 are exactly representable, and + X_EPS / X is small enough that factors quadratic in it can be + neglected. */ + +double +__lgamma_product (double t, double x, double x_eps, int n) +{ + double ret = 0, ret_eps = 0; + for (int i = 0; i < n; i++) + { + double xi = x + i; + double quot = t / xi; + double mhi, mlo; + mul_split (&mhi, &mlo, quot, xi); + double quot_lo = (t - mhi - mlo) / xi - t * x_eps / (xi * xi); + /* We want (1 + RET + RET_EPS) * (1 + QUOT + QUOT_LO) - 1. */ + double rhi, rlo; + mul_split (&rhi, &rlo, ret, quot); + double rpq = ret + quot; + double rpq_eps = (ret - rpq) + quot; + double nret = rpq + rhi; + double nret_eps = (rpq - nret) + rhi; + ret_eps += (rpq_eps + nret_eps + rlo + ret_eps * quot + + quot_lo + quot_lo * (ret + ret_eps)); + ret = nret; + } + return ret + ret_eps; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mpa-arch.h b/REORG.TODO/sysdeps/ieee754/dbl-64/mpa-arch.h new file mode 100644 index 0000000000..4428ac1301 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mpa-arch.h @@ -0,0 +1,47 @@ +/* Overridable constants and operations. + Copyright (C) 2013-2017 Free Software Foundation, Inc. + + This program is free software; you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation; either version 2.1 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program; if not, see <http://www.gnu.org/licenses/>. */ + +#include <stdint.h> + +typedef long mantissa_t; +typedef int64_t mantissa_store_t; + +#define TWOPOW(i) (1L << i) + +#define RADIX_EXP 24 +#define RADIX TWOPOW (RADIX_EXP) /* 2^24 */ + +/* Divide D by RADIX and put the remainder in R. D must be a non-negative + integral value. */ +#define DIV_RADIX(d, r) \ + ({ \ + r = d & (RADIX - 1); \ + d >>= RADIX_EXP; \ + }) + +/* Put the integer component of a double X in R and retain the fraction in + X. This is used in extracting mantissa digits for MP_NO by using the + integer portion of the current value of the number as the current mantissa + digit and then scaling by RADIX to get the next mantissa digit in the same + manner. */ +#define INTEGER_OF(x, i) \ + ({ \ + i = (mantissa_t) x; \ + x -= i; \ + }) + +/* Align IN down to F. The code assumes that F is a power of two. */ +#define ALIGN_DOWN_TO(in, f) ((in) & - (f)) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mpa.c b/REORG.TODO/sysdeps/ieee754/dbl-64/mpa.c new file mode 100644 index 0000000000..3820335172 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mpa.c @@ -0,0 +1,906 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/************************************************************************/ +/* MODULE_NAME: mpa.c */ +/* */ +/* FUNCTIONS: */ +/* mcr */ +/* acr */ +/* cpy */ +/* norm */ +/* denorm */ +/* mp_dbl */ +/* dbl_mp */ +/* add_magnitudes */ +/* sub_magnitudes */ +/* add */ +/* sub */ +/* mul */ +/* inv */ +/* dvd */ +/* */ +/* Arithmetic functions for multiple precision numbers. */ +/* Relative errors are bounded */ +/************************************************************************/ + + +#include "endian.h" +#include "mpa.h" +#include <sys/param.h> +#include <alloca.h> + +#ifndef SECTION +# define SECTION +#endif + +#ifndef NO__CONST +const mp_no __mpone = { 1, { 1.0, 1.0 } }; +const mp_no __mptwo = { 1, { 1.0, 2.0 } }; +#endif + +#ifndef NO___ACR +/* Compare mantissa of two multiple precision numbers regardless of the sign + and exponent of the numbers. */ +static int +mcr (const mp_no *x, const mp_no *y, int p) +{ + long i; + long p2 = p; + for (i = 1; i <= p2; i++) + { + if (X[i] == Y[i]) + continue; + else if (X[i] > Y[i]) + return 1; + else + return -1; + } + return 0; +} + +/* Compare the absolute values of two multiple precision numbers. */ +int +__acr (const mp_no *x, const mp_no *y, int p) +{ + long i; + + if (X[0] == 0) + { + if (Y[0] == 0) + i = 0; + else + i = -1; + } + else if (Y[0] == 0) + i = 1; + else + { + if (EX > EY) + i = 1; + else if (EX < EY) + i = -1; + else + i = mcr (x, y, p); + } + + return i; +} +#endif + +#ifndef NO___CPY +/* Copy multiple precision number X into Y. They could be the same + number. */ +void +__cpy (const mp_no *x, mp_no *y, int p) +{ + long i; + + EY = EX; + for (i = 0; i <= p; i++) + Y[i] = X[i]; +} +#endif + +#ifndef NO___MP_DBL +/* Convert a multiple precision number *X into a double precision + number *Y, normalized case (|x| >= 2**(-1022))). X has precision + P, which is positive. */ +static void +norm (const mp_no *x, double *y, int p) +{ +# define R RADIXI + long i; + double c; + mantissa_t a, u, v, z[5]; + if (p < 5) + { + if (p == 1) + c = X[1]; + else if (p == 2) + c = X[1] + R * X[2]; + else if (p == 3) + c = X[1] + R * (X[2] + R * X[3]); + else /* p == 4. */ + c = (X[1] + R * X[2]) + R * R * (X[3] + R * X[4]); + } + else + { + for (a = 1, z[1] = X[1]; z[1] < TWO23; ) + { + a *= 2; + z[1] *= 2; + } + + for (i = 2; i < 5; i++) + { + mantissa_store_t d, r; + d = X[i] * (mantissa_store_t) a; + DIV_RADIX (d, r); + z[i] = r; + z[i - 1] += d; + } + + u = ALIGN_DOWN_TO (z[3], TWO19); + v = z[3] - u; + + if (v == TWO18) + { + if (z[4] == 0) + { + for (i = 5; i <= p; i++) + { + if (X[i] == 0) + continue; + else + { + z[3] += 1; + break; + } + } + } + else + z[3] += 1; + } + + c = (z[1] + R * (z[2] + R * z[3])) / a; + } + + c *= X[0]; + + for (i = 1; i < EX; i++) + c *= RADIX; + for (i = 1; i > EX; i--) + c *= RADIXI; + + *y = c; +# undef R +} + +/* Convert a multiple precision number *X into a double precision + number *Y, Denormal case (|x| < 2**(-1022))). */ +static void +denorm (const mp_no *x, double *y, int p) +{ + long i, k; + long p2 = p; + double c; + mantissa_t u, z[5]; + +# define R RADIXI + if (EX < -44 || (EX == -44 && X[1] < TWO5)) + { + *y = 0; + return; + } + + if (p2 == 1) + { + if (EX == -42) + { + z[1] = X[1] + TWO10; + z[2] = 0; + z[3] = 0; + k = 3; + } + else if (EX == -43) + { + z[1] = TWO10; + z[2] = X[1]; + z[3] = 0; + k = 2; + } + else + { + z[1] = TWO10; + z[2] = 0; + z[3] = X[1]; + k = 1; + } + } + else if (p2 == 2) + { + if (EX == -42) + { + z[1] = X[1] + TWO10; + z[2] = X[2]; + z[3] = 0; + k = 3; + } + else if (EX == -43) + { + z[1] = TWO10; + z[2] = X[1]; + z[3] = X[2]; + k = 2; + } + else + { + z[1] = TWO10; + z[2] = 0; + z[3] = X[1]; + k = 1; + } + } + else + { + if (EX == -42) + { + z[1] = X[1] + TWO10; + z[2] = X[2]; + k = 3; + } + else if (EX == -43) + { + z[1] = TWO10; + z[2] = X[1]; + k = 2; + } + else + { + z[1] = TWO10; + z[2] = 0; + k = 1; + } + z[3] = X[k]; + } + + u = ALIGN_DOWN_TO (z[3], TWO5); + + if (u == z[3]) + { + for (i = k + 1; i <= p2; i++) + { + if (X[i] == 0) + continue; + else + { + z[3] += 1; + break; + } + } + } + + c = X[0] * ((z[1] + R * (z[2] + R * z[3])) - TWO10); + + *y = c * TWOM1032; +# undef R +} + +/* Convert multiple precision number *X into double precision number *Y. The + result is correctly rounded to the nearest/even. */ +void +__mp_dbl (const mp_no *x, double *y, int p) +{ + if (X[0] == 0) + { + *y = 0; + return; + } + + if (__glibc_likely (EX > -42 || (EX == -42 && X[1] >= TWO10))) + norm (x, y, p); + else + denorm (x, y, p); +} +#endif + +/* Get the multiple precision equivalent of X into *Y. If the precision is too + small, the result is truncated. */ +void +SECTION +__dbl_mp (double x, mp_no *y, int p) +{ + long i, n; + long p2 = p; + + /* Sign. */ + if (x == 0) + { + Y[0] = 0; + return; + } + else if (x > 0) + Y[0] = 1; + else + { + Y[0] = -1; + x = -x; + } + + /* Exponent. */ + for (EY = 1; x >= RADIX; EY += 1) + x *= RADIXI; + for (; x < 1; EY -= 1) + x *= RADIX; + + /* Digits. */ + n = MIN (p2, 4); + for (i = 1; i <= n; i++) + { + INTEGER_OF (x, Y[i]); + x *= RADIX; + } + for (; i <= p2; i++) + Y[i] = 0; +} + +/* Add magnitudes of *X and *Y assuming that abs (*X) >= abs (*Y) > 0. The + sign of the sum *Z is not changed. X and Y may overlap but not X and Z or + Y and Z. No guard digit is used. The result equals the exact sum, + truncated. */ +static void +SECTION +add_magnitudes (const mp_no *x, const mp_no *y, mp_no *z, int p) +{ + long i, j, k; + long p2 = p; + mantissa_t zk; + + EZ = EX; + + i = p2; + j = p2 + EY - EX; + k = p2 + 1; + + if (__glibc_unlikely (j < 1)) + { + __cpy (x, z, p); + return; + } + + zk = 0; + + for (; j > 0; i--, j--) + { + zk += X[i] + Y[j]; + if (zk >= RADIX) + { + Z[k--] = zk - RADIX; + zk = 1; + } + else + { + Z[k--] = zk; + zk = 0; + } + } + + for (; i > 0; i--) + { + zk += X[i]; + if (zk >= RADIX) + { + Z[k--] = zk - RADIX; + zk = 1; + } + else + { + Z[k--] = zk; + zk = 0; + } + } + + if (zk == 0) + { + for (i = 1; i <= p2; i++) + Z[i] = Z[i + 1]; + } + else + { + Z[1] = zk; + EZ += 1; + } +} + +/* Subtract the magnitudes of *X and *Y assuming that abs (*x) > abs (*y) > 0. + The sign of the difference *Z is not changed. X and Y may overlap but not X + and Z or Y and Z. One guard digit is used. The error is less than one + ULP. */ +static void +SECTION +sub_magnitudes (const mp_no *x, const mp_no *y, mp_no *z, int p) +{ + long i, j, k; + long p2 = p; + mantissa_t zk; + + EZ = EX; + i = p2; + j = p2 + EY - EX; + k = p2; + + /* Y is too small compared to X, copy X over to the result. */ + if (__glibc_unlikely (j < 1)) + { + __cpy (x, z, p); + return; + } + + /* The relevant least significant digit in Y is non-zero, so we factor it in + to enhance accuracy. */ + if (j < p2 && Y[j + 1] > 0) + { + Z[k + 1] = RADIX - Y[j + 1]; + zk = -1; + } + else + zk = Z[k + 1] = 0; + + /* Subtract and borrow. */ + for (; j > 0; i--, j--) + { + zk += (X[i] - Y[j]); + if (zk < 0) + { + Z[k--] = zk + RADIX; + zk = -1; + } + else + { + Z[k--] = zk; + zk = 0; + } + } + + /* We're done with digits from Y, so it's just digits in X. */ + for (; i > 0; i--) + { + zk += X[i]; + if (zk < 0) + { + Z[k--] = zk + RADIX; + zk = -1; + } + else + { + Z[k--] = zk; + zk = 0; + } + } + + /* Normalize. */ + for (i = 1; Z[i] == 0; i++) + ; + EZ = EZ - i + 1; + for (k = 1; i <= p2 + 1; ) + Z[k++] = Z[i++]; + for (; k <= p2; ) + Z[k++] = 0; +} + +/* Add *X and *Y and store the result in *Z. X and Y may overlap, but not X + and Z or Y and Z. One guard digit is used. The error is less than one + ULP. */ +void +SECTION +__add (const mp_no *x, const mp_no *y, mp_no *z, int p) +{ + int n; + + if (X[0] == 0) + { + __cpy (y, z, p); + return; + } + else if (Y[0] == 0) + { + __cpy (x, z, p); + return; + } + + if (X[0] == Y[0]) + { + if (__acr (x, y, p) > 0) + { + add_magnitudes (x, y, z, p); + Z[0] = X[0]; + } + else + { + add_magnitudes (y, x, z, p); + Z[0] = Y[0]; + } + } + else + { + if ((n = __acr (x, y, p)) == 1) + { + sub_magnitudes (x, y, z, p); + Z[0] = X[0]; + } + else if (n == -1) + { + sub_magnitudes (y, x, z, p); + Z[0] = Y[0]; + } + else + Z[0] = 0; + } +} + +/* Subtract *Y from *X and return the result in *Z. X and Y may overlap but + not X and Z or Y and Z. One guard digit is used. The error is less than + one ULP. */ +void +SECTION +__sub (const mp_no *x, const mp_no *y, mp_no *z, int p) +{ + int n; + + if (X[0] == 0) + { + __cpy (y, z, p); + Z[0] = -Z[0]; + return; + } + else if (Y[0] == 0) + { + __cpy (x, z, p); + return; + } + + if (X[0] != Y[0]) + { + if (__acr (x, y, p) > 0) + { + add_magnitudes (x, y, z, p); + Z[0] = X[0]; + } + else + { + add_magnitudes (y, x, z, p); + Z[0] = -Y[0]; + } + } + else + { + if ((n = __acr (x, y, p)) == 1) + { + sub_magnitudes (x, y, z, p); + Z[0] = X[0]; + } + else if (n == -1) + { + sub_magnitudes (y, x, z, p); + Z[0] = -Y[0]; + } + else + Z[0] = 0; + } +} + +#ifndef NO__MUL +/* Multiply *X and *Y and store result in *Z. X and Y may overlap but not X + and Z or Y and Z. For P in [1, 2, 3], the exact result is truncated to P + digits. In case P > 3 the error is bounded by 1.001 ULP. */ +void +SECTION +__mul (const mp_no *x, const mp_no *y, mp_no *z, int p) +{ + long i, j, k, ip, ip2; + long p2 = p; + mantissa_store_t zk; + const mp_no *a; + mantissa_store_t *diag; + + /* Is z=0? */ + if (__glibc_unlikely (X[0] * Y[0] == 0)) + { + Z[0] = 0; + return; + } + + /* We need not iterate through all X's and Y's since it's pointless to + multiply zeroes. Here, both are zero... */ + for (ip2 = p2; ip2 > 0; ip2--) + if (X[ip2] != 0 || Y[ip2] != 0) + break; + + a = X[ip2] != 0 ? y : x; + + /* ... and here, at least one of them is still zero. */ + for (ip = ip2; ip > 0; ip--) + if (a->d[ip] != 0) + break; + + /* The product looks like this for p = 3 (as an example): + + + a1 a2 a3 + x b1 b2 b3 + ----------------------------- + a1*b3 a2*b3 a3*b3 + a1*b2 a2*b2 a3*b2 + a1*b1 a2*b1 a3*b1 + + So our K needs to ideally be P*2, but we're limiting ourselves to P + 3 + for P >= 3. We compute the above digits in two parts; the last P-1 + digits and then the first P digits. The last P-1 digits are a sum of + products of the input digits from P to P-k where K is 0 for the least + significant digit and increases as we go towards the left. The product + term is of the form X[k]*X[P-k] as can be seen in the above example. + + The first P digits are also a sum of products with the same product term, + except that the sum is from 1 to k. This is also evident from the above + example. + + Another thing that becomes evident is that only the most significant + ip+ip2 digits of the result are non-zero, where ip and ip2 are the + 'internal precision' of the input numbers, i.e. digits after ip and ip2 + are all 0. */ + + k = (__glibc_unlikely (p2 < 3)) ? p2 + p2 : p2 + 3; + + while (k > ip + ip2 + 1) + Z[k--] = 0; + + zk = 0; + + /* Precompute sums of diagonal elements so that we can directly use them + later. See the next comment to know we why need them. */ + diag = alloca (k * sizeof (mantissa_store_t)); + mantissa_store_t d = 0; + for (i = 1; i <= ip; i++) + { + d += X[i] * (mantissa_store_t) Y[i]; + diag[i] = d; + } + while (i < k) + diag[i++] = d; + + while (k > p2) + { + long lim = k / 2; + + if (k % 2 == 0) + /* We want to add this only once, but since we subtract it in the sum + of products above, we add twice. */ + zk += 2 * X[lim] * (mantissa_store_t) Y[lim]; + + for (i = k - p2, j = p2; i < j; i++, j--) + zk += (X[i] + X[j]) * (mantissa_store_t) (Y[i] + Y[j]); + + zk -= diag[k - 1]; + + DIV_RADIX (zk, Z[k]); + k--; + } + + /* The real deal. Mantissa digit Z[k] is the sum of all X[i] * Y[j] where i + goes from 1 -> k - 1 and j goes the same range in reverse. To reduce the + number of multiplications, we halve the range and if k is an even number, + add the diagonal element X[k/2]Y[k/2]. Through the half range, we compute + X[i] * Y[j] as (X[i] + X[j]) * (Y[i] + Y[j]) - X[i] * Y[i] - X[j] * Y[j]. + + This reduction tells us that we're summing two things, the first term + through the half range and the negative of the sum of the product of all + terms of X and Y in the full range. i.e. + + SUM(X[i] * Y[i]) for k terms. This is precalculated above for each k in + a single loop so that it completes in O(n) time and can hence be directly + used in the loop below. */ + while (k > 1) + { + long lim = k / 2; + + if (k % 2 == 0) + /* We want to add this only once, but since we subtract it in the sum + of products above, we add twice. */ + zk += 2 * X[lim] * (mantissa_store_t) Y[lim]; + + for (i = 1, j = k - 1; i < j; i++, j--) + zk += (X[i] + X[j]) * (mantissa_store_t) (Y[i] + Y[j]); + + zk -= diag[k - 1]; + + DIV_RADIX (zk, Z[k]); + k--; + } + Z[k] = zk; + + /* Get the exponent sum into an intermediate variable. This is a subtle + optimization, where given enough registers, all operations on the exponent + happen in registers and the result is written out only once into EZ. */ + int e = EX + EY; + + /* Is there a carry beyond the most significant digit? */ + if (__glibc_unlikely (Z[1] == 0)) + { + for (i = 1; i <= p2; i++) + Z[i] = Z[i + 1]; + e--; + } + + EZ = e; + Z[0] = X[0] * Y[0]; +} +#endif + +#ifndef NO__SQR +/* Square *X and store result in *Y. X and Y may not overlap. For P in + [1, 2, 3], the exact result is truncated to P digits. In case P > 3 the + error is bounded by 1.001 ULP. This is a faster special case of + multiplication. */ +void +SECTION +__sqr (const mp_no *x, mp_no *y, int p) +{ + long i, j, k, ip; + mantissa_store_t yk; + + /* Is z=0? */ + if (__glibc_unlikely (X[0] == 0)) + { + Y[0] = 0; + return; + } + + /* We need not iterate through all X's since it's pointless to + multiply zeroes. */ + for (ip = p; ip > 0; ip--) + if (X[ip] != 0) + break; + + k = (__glibc_unlikely (p < 3)) ? p + p : p + 3; + + while (k > 2 * ip + 1) + Y[k--] = 0; + + yk = 0; + + while (k > p) + { + mantissa_store_t yk2 = 0; + long lim = k / 2; + + if (k % 2 == 0) + yk += X[lim] * (mantissa_store_t) X[lim]; + + /* In __mul, this loop (and the one within the next while loop) run + between a range to calculate the mantissa as follows: + + Z[k] = X[k] * Y[n] + X[k+1] * Y[n-1] ... + X[n-1] * Y[k+1] + + X[n] * Y[k] + + For X == Y, we can get away with summing halfway and doubling the + result. For cases where the range size is even, the mid-point needs + to be added separately (above). */ + for (i = k - p, j = p; i < j; i++, j--) + yk2 += X[i] * (mantissa_store_t) X[j]; + + yk += 2 * yk2; + + DIV_RADIX (yk, Y[k]); + k--; + } + + while (k > 1) + { + mantissa_store_t yk2 = 0; + long lim = k / 2; + + if (k % 2 == 0) + yk += X[lim] * (mantissa_store_t) X[lim]; + + /* Likewise for this loop. */ + for (i = 1, j = k - 1; i < j; i++, j--) + yk2 += X[i] * (mantissa_store_t) X[j]; + + yk += 2 * yk2; + + DIV_RADIX (yk, Y[k]); + k--; + } + Y[k] = yk; + + /* Squares are always positive. */ + Y[0] = 1; + + /* Get the exponent sum into an intermediate variable. This is a subtle + optimization, where given enough registers, all operations on the exponent + happen in registers and the result is written out only once into EZ. */ + int e = EX * 2; + + /* Is there a carry beyond the most significant digit? */ + if (__glibc_unlikely (Y[1] == 0)) + { + for (i = 1; i <= p; i++) + Y[i] = Y[i + 1]; + e--; + } + + EY = e; +} +#endif + +/* Invert *X and store in *Y. Relative error bound: + - For P = 2: 1.001 * R ^ (1 - P) + - For P = 3: 1.063 * R ^ (1 - P) + - For P > 3: 2.001 * R ^ (1 - P) + + *X = 0 is not permissible. */ +static void +SECTION +__inv (const mp_no *x, mp_no *y, int p) +{ + long i; + double t; + mp_no z, w; + static const int np1[] = + { 0, 0, 0, 0, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, + 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 + }; + + __cpy (x, &z, p); + z.e = 0; + __mp_dbl (&z, &t, p); + t = 1 / t; + __dbl_mp (t, y, p); + EY -= EX; + + for (i = 0; i < np1[p]; i++) + { + __cpy (y, &w, p); + __mul (x, &w, y, p); + __sub (&__mptwo, y, &z, p); + __mul (&w, &z, y, p); + } +} + +/* Divide *X by *Y and store result in *Z. X and Y may overlap but not X and Z + or Y and Z. Relative error bound: + - For P = 2: 2.001 * R ^ (1 - P) + - For P = 3: 2.063 * R ^ (1 - P) + - For P > 3: 3.001 * R ^ (1 - P) + + *X = 0 is not permissible. */ +void +SECTION +__dvd (const mp_no *x, const mp_no *y, mp_no *z, int p) +{ + mp_no w; + + if (X[0] == 0) + Z[0] = 0; + else + { + __inv (y, &w, p); + __mul (x, &w, z, p); + } +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mpa.h b/REORG.TODO/sysdeps/ieee754/dbl-64/mpa.h new file mode 100644 index 0000000000..a665e6b8f7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mpa.h @@ -0,0 +1,154 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/************************************************************************/ +/* MODULE_NAME: mpa.h */ +/* */ +/* FUNCTIONS: */ +/* mcr */ +/* acr */ +/* cpy */ +/* mp_dbl */ +/* dbl_mp */ +/* add */ +/* sub */ +/* mul */ +/* dvd */ +/* */ +/* Arithmetic functions for multiple precision numbers. */ +/* Common types and definition */ +/************************************************************************/ + +#include <mpa-arch.h> + +/* The mp_no structure holds the details of a multi-precision floating point + number. + + - The radix of the number (R) is 2 ^ 24. + + - E: The exponent of the number. + + - D[0]: The sign (-1, 1) or 0 if the value is 0. In the latter case, the + values of the remaining members of the structure are ignored. + + - D[1] - D[p]: The mantissa of the number where: + + 0 <= D[i] < R and + P is the precision of the number and 1 <= p <= 32 + + D[p+1] ... D[39] have no significance. + + - The value of the number is: + + D[1] * R ^ (E - 1) + D[2] * R ^ (E - 2) ... D[p] * R ^ (E - p) + + */ +typedef struct +{ + int e; + mantissa_t d[40]; +} mp_no; + +typedef union +{ + int i[2]; + double d; +} number; + +extern const mp_no __mpone; +extern const mp_no __mptwo; + +#define X x->d +#define Y y->d +#define Z z->d +#define EX x->e +#define EY y->e +#define EZ z->e + +#ifndef RADIXI +# define RADIXI 0x1.0p-24 /* 2^-24 */ +#endif + +#ifndef TWO52 +# define TWO52 0x1.0p52 /* 2^52 */ +#endif + +#define TWO5 TWOPOW (5) /* 2^5 */ +#define TWO8 TWOPOW (8) /* 2^52 */ +#define TWO10 TWOPOW (10) /* 2^10 */ +#define TWO18 TWOPOW (18) /* 2^18 */ +#define TWO19 TWOPOW (19) /* 2^19 */ +#define TWO23 TWOPOW (23) /* 2^23 */ + +#define HALFRAD TWO23 + +#define TWO57 0x1.0p57 /* 2^57 */ +#define TWO71 0x1.0p71 /* 2^71 */ +#define TWOM1032 0x1.0p-1032 /* 2^-1032 */ +#define TWOM1022 0x1.0p-1022 /* 2^-1022 */ + +#define HALF 0x1.0p-1 /* 1/2 */ +#define MHALF -0x1.0p-1 /* -1/2 */ + +int __acr (const mp_no *, const mp_no *, int); +void __cpy (const mp_no *, mp_no *, int); +void __mp_dbl (const mp_no *, double *, int); +void __dbl_mp (double, mp_no *, int); +void __add (const mp_no *, const mp_no *, mp_no *, int); +void __sub (const mp_no *, const mp_no *, mp_no *, int); +void __mul (const mp_no *, const mp_no *, mp_no *, int); +void __sqr (const mp_no *, mp_no *, int); +void __dvd (const mp_no *, const mp_no *, mp_no *, int); + +extern void __mpatan (mp_no *, mp_no *, int); +extern void __mpatan2 (mp_no *, mp_no *, mp_no *, int); +extern void __mpsqrt (mp_no *, mp_no *, int); +extern void __mpexp (mp_no *, mp_no *, int); +extern void __c32 (mp_no *, mp_no *, mp_no *, int); +extern int __mpranred (double, mp_no *, int); + +/* Given a power POW, build a multiprecision number 2^POW. */ +static inline void +__pow_mp (int pow, mp_no *y, int p) +{ + int i, rem; + + /* The exponent is E such that E is a factor of 2^24. The remainder (of the + form 2^x) goes entirely into the first digit of the mantissa as it is + always less than 2^24. */ + EY = pow / 24; + rem = pow - EY * 24; + EY++; + + /* If the remainder is negative, it means that POW was negative since + |EY * 24| <= |pow|. Adjust so that REM is positive and still less than + 24 because of which, the mantissa digit is less than 2^24. */ + if (rem < 0) + { + EY--; + rem += 24; + } + /* The sign of any 2^x is always positive. */ + Y[0] = 1; + Y[1] = 1 << rem; + + /* Everything else is 0. */ + for (i = 2; i <= p; i++) + Y[i] = 0; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mpatan.c b/REORG.TODO/sysdeps/ieee754/dbl-64/mpatan.c new file mode 100644 index 0000000000..b84fbc5e41 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mpatan.c @@ -0,0 +1,116 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/******************************************************************/ +/* */ +/* MODULE_NAME:mpatan.c */ +/* */ +/* FUNCTIONS:mpatan */ +/* */ +/* FILES NEEDED: mpa.h endian.h mpatan.h */ +/* mpa.c */ +/* */ +/* Multi-Precision Atan function subroutine, for precision p >= 4.*/ +/* The relative error of the result is bounded by 34.32*r**(1-p), */ +/* where r=2**24. */ +/******************************************************************/ + +#include "endian.h" +#include "mpa.h" +#include <math.h> + +#ifndef SECTION +# define SECTION +#endif + +#include "mpatan.h" + +void +SECTION +__mpatan (mp_no *x, mp_no *y, int p) +{ + int i, m, n; + double dx; + mp_no mptwoim1 = + { + 0, + { + 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 + } + }; + + mp_no mps, mpsm, mpt, mpt1, mpt2, mpt3; + + /* Choose m and initiate mptwoim1. */ + if (EX > 0) + m = 7; + else if (EX < 0) + m = 0; + else + { + __mp_dbl (x, &dx, p); + dx = fabs (dx); + for (m = 6; m > 0; m--) + { + if (dx > __atan_xm[m].d) + break; + } + } + mptwoim1.e = 1; + mptwoim1.d[0] = 1; + + /* Reduce x m times. */ + __sqr (x, &mpsm, p); + if (m == 0) + __cpy (x, &mps, p); + else + { + for (i = 0; i < m; i++) + { + __add (&__mpone, &mpsm, &mpt1, p); + __mpsqrt (&mpt1, &mpt2, p); + __add (&mpt2, &mpt2, &mpt1, p); + __add (&__mptwo, &mpsm, &mpt2, p); + __add (&mpt1, &mpt2, &mpt3, p); + __dvd (&mpsm, &mpt3, &mpt1, p); + __cpy (&mpt1, &mpsm, p); + } + __mpsqrt (&mpsm, &mps, p); + mps.d[0] = X[0]; + } + + /* Evaluate a truncated power series for Atan(s). */ + n = __atan_np[p]; + mptwoim1.d[1] = __atan_twonm1[p].d; + __dvd (&mpsm, &mptwoim1, &mpt, p); + for (i = n - 1; i > 1; i--) + { + mptwoim1.d[1] -= 2; + __dvd (&mpsm, &mptwoim1, &mpt1, p); + __mul (&mpsm, &mpt, &mpt2, p); + __sub (&mpt1, &mpt2, &mpt, p); + } + __mul (&mps, &mpt, &mpt1, p); + __sub (&mps, &mpt1, &mpt, p); + + /* Compute Atan(x). */ + mptwoim1.d[1] = 1 << m; + __mul (&mptwoim1, &mpt, y, p); +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mpatan.h b/REORG.TODO/sysdeps/ieee754/dbl-64/mpatan.h new file mode 100644 index 0000000000..65c856be17 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mpatan.h @@ -0,0 +1,145 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/******************************************************************/ +/* */ +/* MODULE_NAME:mpatan.h */ +/* */ +/* common data and variables prototype and definition */ +/******************************************************************/ + +#ifndef MPATAN_H +#define MPATAN_H + +extern const number __atan_xm[8] attribute_hidden; +extern const number __atan_twonm1[33] attribute_hidden; +extern const number __atan_twom[8] attribute_hidden; +extern const int __atan_np[33] attribute_hidden; + + +#ifndef AVOID_MPATAN_H +#ifdef BIG_ENDI + const number + __atan_xm[8] = { /* x[m] */ +/**/ {{0x00000000, 0x00000000} }, /* 0.0 */ +/**/ {{0x3f8930be, 0x00000000} }, /* 0.0123 */ +/**/ {{0x3f991687, 0x00000000} }, /* 0.0245 */ +/**/ {{0x3fa923a2, 0x00000000} }, /* 0.0491 */ +/**/ {{0x3fb930be, 0x00000000} }, /* 0.0984 */ +/**/ {{0x3fc95810, 0x00000000} }, /* 0.198 */ +/**/ {{0x3fda7ef9, 0x00000000} }, /* 0.414 */ +/**/ {{0x3ff00000, 0x00000000} }, /* 1.0 */ + }; + const number + __atan_twonm1[33] = { /* 2n-1 */ +/**/ {{0x00000000, 0x00000000} }, /* 0 */ +/**/ {{0x00000000, 0x00000000} }, /* 0 */ +/**/ {{0x00000000, 0x00000000} }, /* 0 */ +/**/ {{0x00000000, 0x00000000} }, /* 0 */ +/**/ {{0x40260000, 0x00000000} }, /* 11 */ +/**/ {{0x402e0000, 0x00000000} }, /* 15 */ +/**/ {{0x40330000, 0x00000000} }, /* 19 */ +/**/ {{0x40350000, 0x00000000} }, /* 21 */ +/**/ {{0x40390000, 0x00000000} }, /* 25 */ +/**/ {{0x403d0000, 0x00000000} }, /* 29 */ +/**/ {{0x40408000, 0x00000000} }, /* 33 */ +/**/ {{0x40428000, 0x00000000} }, /* 37 */ +/**/ {{0x40448000, 0x00000000} }, /* 41 */ +/**/ {{0x40468000, 0x00000000} }, /* 45 */ +/**/ {{0x40488000, 0x00000000} }, /* 49 */ +/**/ {{0x404a8000, 0x00000000} }, /* 53 */ +/**/ {{0x404b8000, 0x00000000} }, /* 55 */ +/**/ {{0x404d8000, 0x00000000} }, /* 59 */ +/**/ {{0x404f8000, 0x00000000} }, /* 63 */ +/**/ {{0x4050c000, 0x00000000} }, /* 67 */ +/**/ {{0x4051c000, 0x00000000} }, /* 71 */ +/**/ {{0x4052c000, 0x00000000} }, /* 75 */ +/**/ {{0x4053c000, 0x00000000} }, /* 79 */ +/**/ {{0x4054c000, 0x00000000} }, /* 83 */ +/**/ {{0x40554000, 0x00000000} }, /* 85 */ +/**/ {{0x40564000, 0x00000000} }, /* 89 */ +/**/ {{0x40574000, 0x00000000} }, /* 93 */ +/**/ {{0x40584000, 0x00000000} }, /* 97 */ +/**/ {{0x40594000, 0x00000000} }, /* 101 */ +/**/ {{0x405a4000, 0x00000000} }, /* 105 */ +/**/ {{0x405b4000, 0x00000000} }, /* 109 */ +/**/ {{0x405c4000, 0x00000000} }, /* 113 */ +/**/ {{0x405d4000, 0x00000000} }, /* 117 */ + }; + +#else +#ifdef LITTLE_ENDI + + const number + __atan_xm[8] = { /* x[m] */ +/**/ {{0x00000000, 0x00000000} }, /* 0.0 */ +/**/ {{0x00000000, 0x3f8930be} }, /* 0.0123 */ +/**/ {{0x00000000, 0x3f991687} }, /* 0.0245 */ +/**/ {{0x00000000, 0x3fa923a2} }, /* 0.0491 */ +/**/ {{0x00000000, 0x3fb930be} }, /* 0.0984 */ +/**/ {{0x00000000, 0x3fc95810} }, /* 0.198 */ +/**/ {{0x00000000, 0x3fda7ef9} }, /* 0.414 */ +/**/ {{0x00000000, 0x3ff00000} }, /* 1.0 */ + }; + const number +__atan_twonm1[33] = { /* 2n-1 */ +/**/ {{0x00000000, 0x00000000} }, /* 0 */ +/**/ {{0x00000000, 0x00000000} }, /* 0 */ +/**/ {{0x00000000, 0x00000000} }, /* 0 */ +/**/ {{0x00000000, 0x00000000} }, /* 0 */ +/**/ {{0x00000000, 0x40260000} }, /* 11 */ +/**/ {{0x00000000, 0x402e0000} }, /* 15 */ +/**/ {{0x00000000, 0x40330000} }, /* 19 */ +/**/ {{0x00000000, 0x40350000} }, /* 21 */ +/**/ {{0x00000000, 0x40390000} }, /* 25 */ +/**/ {{0x00000000, 0x403d0000} }, /* 29 */ +/**/ {{0x00000000, 0x40408000} }, /* 33 */ +/**/ {{0x00000000, 0x40428000} }, /* 37 */ +/**/ {{0x00000000, 0x40448000} }, /* 41 */ +/**/ {{0x00000000, 0x40468000} }, /* 45 */ +/**/ {{0x00000000, 0x40488000} }, /* 49 */ +/**/ {{0x00000000, 0x404a8000} }, /* 53 */ +/**/ {{0x00000000, 0x404b8000} }, /* 55 */ +/**/ {{0x00000000, 0x404d8000} }, /* 59 */ +/**/ {{0x00000000, 0x404f8000} }, /* 63 */ +/**/ {{0x00000000, 0x4050c000} }, /* 67 */ +/**/ {{0x00000000, 0x4051c000} }, /* 71 */ +/**/ {{0x00000000, 0x4052c000} }, /* 75 */ +/**/ {{0x00000000, 0x4053c000} }, /* 79 */ +/**/ {{0x00000000, 0x4054c000} }, /* 83 */ +/**/ {{0x00000000, 0x40554000} }, /* 85 */ +/**/ {{0x00000000, 0x40564000} }, /* 89 */ +/**/ {{0x00000000, 0x40574000} }, /* 93 */ +/**/ {{0x00000000, 0x40584000} }, /* 97 */ +/**/ {{0x00000000, 0x40594000} }, /* 101 */ +/**/ {{0x00000000, 0x405a4000} }, /* 105 */ +/**/ {{0x00000000, 0x405b4000} }, /* 109 */ +/**/ {{0x00000000, 0x405c4000} }, /* 113 */ +/**/ {{0x00000000, 0x405d4000} }, /* 117 */ + }; + +#endif +#endif + + const int + __atan_np[33] = { 0, 0, 0, 0, 6, 8,10,11,13,15,17,19,21,23,25,27,28, + 30,32,34,36,38,40,42,43,45,47,49,51,53,55,57,59}; + +#endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mpatan2.c b/REORG.TODO/sysdeps/ieee754/dbl-64/mpatan2.c new file mode 100644 index 0000000000..94e4a66148 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mpatan2.c @@ -0,0 +1,67 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/******************************************************************/ +/* MODULE_NAME: mpatan2.c */ +/* */ +/* FUNCTIONS:mpatan2 */ +/* */ +/* FILES NEEDED: mpa.h */ +/* mpa.c mpatan.c mpsqrt.c */ +/* */ +/* Multi-Precision Atan2(y,x) function subroutine, */ +/* for precision p >= 4. */ +/* y=0 is not permitted if x<=0. No error messages are given. */ +/* The relative error of the result is bounded by 44.84*r**(1-p) */ +/* if x <= 0, y != 0 and by 37.33*r**(1-p) if x>0. here r=2**24. */ +/* */ +/******************************************************************/ + +#include "mpa.h" + +#ifndef SECTION +# define SECTION +#endif + +/* Multi-Precision Atan2 (y, x) function subroutine, for p >= 4. + y = 0 is not permitted if x <= 0. No error messages are given. */ +void +SECTION +__mpatan2 (mp_no *y, mp_no *x, mp_no *z, int p) +{ + mp_no mpt1, mpt2, mpt3; + + if (X[0] <= 0) + { + __dvd (x, y, &mpt1, p); + __mul (&mpt1, &mpt1, &mpt2, p); + if (mpt1.d[0] != 0) + mpt1.d[0] = 1; + __add (&mpt2, &__mpone, &mpt3, p); + __mpsqrt (&mpt3, &mpt2, p); + __add (&mpt1, &mpt2, &mpt3, p); + mpt3.d[0] = Y[0]; + __mpatan (&mpt3, &mpt1, p); + __add (&mpt1, &mpt1, z, p); + } + else + { + __dvd (y, x, &mpt1, p); + __mpatan (&mpt1, z, p); + } +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mpexp.c b/REORG.TODO/sysdeps/ieee754/dbl-64/mpexp.c new file mode 100644 index 0000000000..e08f424133 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mpexp.c @@ -0,0 +1,163 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/*************************************************************************/ +/* MODULE_NAME:mpexp.c */ +/* */ +/* FUNCTIONS: mpexp */ +/* */ +/* FILES NEEDED: mpa.h endian.h mpexp.h */ +/* mpa.c */ +/* */ +/* Multi-Precision exponential function subroutine */ +/* ( for p >= 4, 2**(-55) <= abs(x) <= 1024 ). */ +/*************************************************************************/ + +#include "endian.h" +#include "mpa.h" +#include <assert.h> + +#ifndef SECTION +# define SECTION +#endif + +/* Multi-Precision exponential function subroutine (for p >= 4, + 2**(-55) <= abs(x) <= 1024). */ +void +SECTION +__mpexp (mp_no *x, mp_no *y, int p) +{ + int i, j, k, m, m1, m2, n; + mantissa_t b; + static const int np[33] = + { + 0, 0, 0, 0, 3, 3, 4, 4, 5, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 6, + 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8 + }; + + static const int m1p[33] = + { + 0, 0, 0, 0, + 17, 23, 23, 28, + 27, 38, 42, 39, + 43, 47, 43, 47, + 50, 54, 57, 60, + 64, 67, 71, 74, + 68, 71, 74, 77, + 70, 73, 76, 78, + 81 + }; + static const int m1np[7][18] = + { + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 36, 48, 60, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 24, 32, 40, 48, 56, 64, 72, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 17, 23, 29, 35, 41, 47, 53, 59, 65, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 23, 28, 33, 38, 42, 47, 52, 57, 62, 66, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 27, 0, 0, 39, 43, 47, 51, 55, 59, 63}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43, 47, 50, 54} + }; + mp_no mps, mpk, mpt1, mpt2; + + /* Choose m,n and compute a=2**(-m). */ + n = np[p]; + m1 = m1p[p]; + b = X[1]; + m2 = 24 * EX; + for (; b < HALFRAD; m2--) + b *= 2; + if (b == HALFRAD) + { + for (i = 2; i <= p; i++) + { + if (X[i] != 0) + break; + } + if (i == p + 1) + m2--; + } + + m = m1 + m2; + if (__glibc_unlikely (m <= 0)) + { + /* The m1np array which is used to determine if we can reduce the + polynomial expansion iterations, has only 18 elements. Besides, + numbers smaller than those required by p >= 18 should not come here + at all since the fast phase of exp returns 1.0 for anything less + than 2^-55. */ + assert (p < 18); + m = 0; + for (i = n - 1; i > 0; i--, n--) + if (m1np[i][p] + m2 > 0) + break; + } + + /* Compute s=x*2**(-m). Put result in mps. This is the range-reduced input + that we will use to compute e^s. For the final result, simply raise it + to 2^m. */ + __pow_mp (-m, &mpt1, p); + __mul (x, &mpt1, &mps, p); + + /* Compute the Taylor series for e^s: + + 1 + x/1! + x^2/2! + x^3/3! ... + + for N iterations. We compute this as: + + e^x = 1 + (x * n!/1! + x^2 * n!/2! + x^3 * n!/3!) / n! + = 1 + (x * (n!/1! + x * (n!/2! + x * (n!/3! + x ...)))) / n! + + k! is computed on the fly as KF and at the end of the polynomial loop, KF + is n!, which can be used directly. */ + __cpy (&mps, &mpt2, p); + + double kf = 1.0; + + /* Evaluate the rest. The result will be in mpt2. */ + for (k = n - 1; k > 0; k--) + { + /* n! / k! = n * (n - 1) ... * (n - k + 1) */ + kf *= k + 1; + + __dbl_mp (kf, &mpk, p); + __add (&mpt2, &mpk, &mpt1, p); + __mul (&mps, &mpt1, &mpt2, p); + } + __dbl_mp (kf, &mpk, p); + __dvd (&mpt2, &mpk, &mpt1, p); + __add (&__mpone, &mpt1, &mpt2, p); + + /* Raise polynomial value to the power of 2**m. Put result in y. */ + for (k = 0, j = 0; k < m;) + { + __sqr (&mpt2, &mpt1, p); + k++; + if (k == m) + { + j = 1; + break; + } + __sqr (&mpt1, &mpt2, p); + k++; + } + if (j) + __cpy (&mpt1, y, p); + else + __cpy (&mpt2, y, p); + return; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mplog.c b/REORG.TODO/sysdeps/ieee754/dbl-64/mplog.c new file mode 100644 index 0000000000..5b03117d07 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mplog.c @@ -0,0 +1,65 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/************************************************************************/ +/* */ +/* MODULE_NAME:mplog.c */ +/* */ +/* FUNCTIONS: mplog */ +/* */ +/* FILES NEEDED: endian.h mpa.h mplog.h */ +/* mpexp.c */ +/* */ +/* Multi-Precision logarithm function subroutine (for precision p >= 4, */ +/* 2**(-1024) < x < 2**1024) and x is outside of the interval */ +/* [1-2**(-54),1+2**(-54)]. Upon entry, x should be set to the */ +/* multi-precision value of the input and y should be set into a multi- */ +/* precision value of an approximation of log(x) with relative error */ +/* bound of at most 2**(-52). The routine improves the accuracy of y. */ +/* */ +/************************************************************************/ +#include "endian.h" +#include "mpa.h" + +void +__mplog (mp_no *x, mp_no *y, int p) +{ + int i, m; + static const int mp[33] = + { + 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, + 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 + }; + mp_no mpt1, mpt2; + + /* Choose m. */ + m = mp[p]; + + /* Perform m newton iterations to solve for y: exp(y) - x = 0. The + iterations formula is: y(n + 1) = y(n) + (x * exp(-y(n)) - 1). */ + __cpy (y, &mpt1, p); + for (i = 0; i < m; i++) + { + mpt1.d[0] = -mpt1.d[0]; + __mpexp (&mpt1, &mpt2, p); + __mul (x, &mpt2, &mpt1, p); + __sub (&mpt1, &__mpone, &mpt2, p); + __add (y, &mpt2, &mpt1, p); + __cpy (&mpt1, y, p); + } +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mpn2dbl.c b/REORG.TODO/sysdeps/ieee754/dbl-64/mpn2dbl.c new file mode 100644 index 0000000000..1fec0ce920 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mpn2dbl.c @@ -0,0 +1,47 @@ +/* Copyright (C) 1995-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "gmp.h" +#include "gmp-impl.h" +#include <ieee754.h> +#include <float.h> + +/* Convert a multi-precision integer of the needed number of bits (53 for + double) and an integral power of two to a `double' in IEEE754 double- + precision format. */ + +double +__mpn_construct_double (mp_srcptr frac_ptr, int expt, int negative) +{ + union ieee754_double u; + + u.ieee.negative = negative; + u.ieee.exponent = expt + IEEE754_DOUBLE_BIAS; +#if BITS_PER_MP_LIMB == 32 + u.ieee.mantissa1 = frac_ptr[0]; + u.ieee.mantissa0 = frac_ptr[1] & (((mp_limb_t) 1 + << (DBL_MANT_DIG - 32)) - 1); +#elif BITS_PER_MP_LIMB == 64 + u.ieee.mantissa1 = frac_ptr[0] & (((mp_limb_t) 1 << 32) - 1); + u.ieee.mantissa0 = (frac_ptr[0] >> 32) & (((mp_limb_t) 1 + << (DBL_MANT_DIG - 32)) - 1); +#else + # error "mp_limb size " BITS_PER_MP_LIMB "not accounted for" +#endif + + return u.d; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mpsqrt.c b/REORG.TODO/sysdeps/ieee754/dbl-64/mpsqrt.c new file mode 100644 index 0000000000..be6d01eeef --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mpsqrt.c @@ -0,0 +1,111 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/****************************************************************************/ +/* MODULE_NAME:mpsqrt.c */ +/* */ +/* FUNCTION:mpsqrt */ +/* fastiroot */ +/* */ +/* FILES NEEDED:endian.h mpa.h mpsqrt.h */ +/* mpa.c */ +/* Multi-Precision square root function subroutine for precision p >= 4. */ +/* The relative error is bounded by 3.501*r**(1-p), where r=2**24. */ +/* */ +/****************************************************************************/ +#include "endian.h" +#include "mpa.h" + +#ifndef SECTION +# define SECTION +#endif + +#include "mpsqrt.h" + +/****************************************************************************/ +/* Multi-Precision square root function subroutine for precision p >= 4. */ +/* The relative error is bounded by 3.501*r**(1-p), where r=2**24. */ +/* Routine receives two pointers to Multi Precision numbers: */ +/* x (left argument) and y (next argument). Routine also receives precision */ +/* p as integer. Routine computes sqrt(*x) and stores result in *y */ +/****************************************************************************/ + +static double fastiroot (double); + +void +SECTION +__mpsqrt (mp_no *x, mp_no *y, int p) +{ + int i, m, ey; + double dx, dy; + static const mp_no mphalf = {0, {1.0, HALFRAD}}; + static const mp_no mp3halfs = {1, {1.0, 1.0, HALFRAD}}; + mp_no mpxn, mpz, mpu, mpt1, mpt2; + + ey = EX / 2; + __cpy (x, &mpxn, p); + mpxn.e -= (ey + ey); + __mp_dbl (&mpxn, &dx, p); + dy = fastiroot (dx); + __dbl_mp (dy, &mpu, p); + __mul (&mpxn, &mphalf, &mpz, p); + + m = __mpsqrt_mp[p]; + for (i = 0; i < m; i++) + { + __sqr (&mpu, &mpt1, p); + __mul (&mpt1, &mpz, &mpt2, p); + __sub (&mp3halfs, &mpt2, &mpt1, p); + __mul (&mpu, &mpt1, &mpt2, p); + __cpy (&mpt2, &mpu, p); + } + __mul (&mpxn, &mpu, y, p); + EY += ey; +} + +/***********************************************************/ +/* Compute a double precision approximation for 1/sqrt(x) */ +/* with the relative error bounded by 2**-51. */ +/***********************************************************/ +static double +SECTION +fastiroot (double x) +{ + union + { + int i[2]; + double d; + } p, q; + double y, z, t; + int n; + static const double c0 = 0.99674, c1 = -0.53380; + static const double c2 = 0.45472, c3 = -0.21553; + + p.d = x; + p.i[HIGH_HALF] = (p.i[HIGH_HALF] & 0x3FFFFFFF) | 0x3FE00000; + q.d = x; + y = p.d; + z = y - 1.0; + n = (q.i[HIGH_HALF] - p.i[HIGH_HALF]) >> 1; + z = ((c3 * z + c2) * z + c1) * z + c0; /* 2**-7 */ + z = z * (1.5 - 0.5 * y * z * z); /* 2**-14 */ + p.d = z * (1.5 - 0.5 * y * z * z); /* 2**-28 */ + p.i[HIGH_HALF] -= n; + t = x * p.d; + return p.d * (1.5 - 0.5 * p.d * t); +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mpsqrt.h b/REORG.TODO/sysdeps/ieee754/dbl-64/mpsqrt.h new file mode 100644 index 0000000000..66c3dc684f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mpsqrt.h @@ -0,0 +1,38 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/******************************************************************/ +/* */ +/* MODULE_NAME:mpatan.h */ +/* */ +/* common data and variables prototype and definition */ +/******************************************************************/ + +#ifndef MPSQRT_H +#define MPSQRT_H + +extern const int __mpsqrt_mp[33] attribute_hidden; + + +#ifndef AVOID_MPSQRT_H + const int __mpsqrt_mp[33] = {0,0,0,0,1,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4, + 4,4,4,4,4,4,4,4,4}; +#endif + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mptan.c b/REORG.TODO/sysdeps/ieee754/dbl-64/mptan.c new file mode 100644 index 0000000000..6976028f8f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mptan.c @@ -0,0 +1,63 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/**********************************************************************/ +/* MODULE_NAME:mptan.c */ +/* */ +/* FUNCTION: mptan */ +/* */ +/* FILES NEEDED: endian.h mpa.h */ +/* mpa.c sincos32.c branred.c */ +/* */ +/* Multi-Precision tan() function subroutine, for p=32. It is based */ +/* on the routines mpranred() and c32(). mpranred() performs range */ +/* reduction of a double number x into a multiple precision number */ +/* y, such that y=x-n*pi/2, abs(y)<pi/4, n=0,+-1,+-2,.... c32() */ +/* computes both sin(y), cos(y). tan(x) is either sin(y)/cos(y) */ +/* or -cos(y)/sin(y). The precision of the result is of about 559 */ +/* significant bits. */ +/* */ +/**********************************************************************/ +#include "endian.h" +#include "mpa.h" + +#ifndef SECTION +# define SECTION +#endif + +void +SECTION +__mptan (double x, mp_no *mpy, int p) +{ + int n; + mp_no mpw, mpc, mps; + + /* Negative or positive result. */ + n = __mpranred (x, &mpw, p) & 0x00000001; + /* Computing sin(x) and cos(x). */ + __c32 (&mpw, &mpc, &mps, p); + /* Second or fourth quarter of unit circle. */ + if (n) + { + __dvd (&mpc, &mps, mpy, p); + mpy->d[0] *= -1; + } + /* tan is negative in this area. */ + else + __dvd (&mps, &mpc, mpy, p); +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/mydefs.h b/REORG.TODO/sysdeps/ieee754/dbl-64/mydefs.h new file mode 100644 index 0000000000..027398e861 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/mydefs.h @@ -0,0 +1,35 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/******************************************************************/ +/* */ +/* MODULE_NAME:mydefs.h */ +/* */ +/* common data and definition */ +/******************************************************************/ + +#ifndef MY_H +#define MY_H + +typedef int int4; +typedef union { int4 i[2]; double x; } mynumber; + +#define max(x, y) (((y) > (x)) ? (y) : (x)) +#define min(x, y) (((y) < (x)) ? (y) : (x)) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/powtwo.tbl b/REORG.TODO/sysdeps/ieee754/dbl-64/powtwo.tbl new file mode 100644 index 0000000000..7d5ae52174 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/powtwo.tbl @@ -0,0 +1,31 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/****************************************************************/ +/* TABLES FOR THE upow() FUNCTION */ +/****************************************************************/ + + + +static const double powtwo[] = { 1.0, 2.0, 4.0, + 8.0, 16.0, 32.0, 64.0, 128.0, + 256.0, 512.0, 1024.0, 2048.0, 4096.0, + 8192.0, 16384.0, 32768.0, 65536.0, 131072.0, + 262144.0, 524288.0, 1048576.0, 2097152.0, 4194304.0, + 8388608.0, 16777216.0, 33554432.0, 67108864.0, 134217728.0 }; diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/root.tbl b/REORG.TODO/sysdeps/ieee754/dbl-64/root.tbl new file mode 100644 index 0000000000..6d2760aa1f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/root.tbl @@ -0,0 +1,57 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/****************************************************************/ +/* TABLES FOR THE usqrt() FUNCTION */ +/****************************************************************/ + + +static const double inroot[128] = { + 1.40872145012100, 1.39792649065766, 1.38737595123859, 1.37706074531819, + 1.36697225234682, 1.35710228748795, 1.34744307370643, 1.33798721601135, + 1.32872767765984, 1.31965775814772, 1.31077107283046, 1.30206153403386, + 1.29352333352711, 1.28515092624400, 1.27693901514820, 1.26888253714903, + 1.26097664998256, 1.25321671998073, 1.24559831065844, 1.23811717205462, + 1.23076923076923, 1.22355058064300, 1.21645747403153, 1.20948631362953, + 1.20263364480453, 1.19589614840310, 1.18927063399547, 1.18275403352732, + 1.17634339535009, 1.17003587860341, 1.16382874792529, 1.15771936846787, + 1.15170520119791, 1.14578379846309, 1.13995279980655, 1.13420992801334, + 1.12855298537376, 1.12297985014975, 1.11748847323133, 1.11207687497107, + 1.10674314218572, 1.10148542531442, 1.09630193572405, 1.09119094315276, + 1.08615077328341, 1.08117980543918, 1.07627647039410, 1.07143924829188, + 1.06666666666667, 1.06195729855996, 1.05730976072814, 1.05272271193563, + 1.04819485132867, 1.04372491688551, 1.03931168393861, 1.03495396376504, + 1.03065060224133, 1.02640047855933, 1.02220250399990, 1.01805562076124, + 1.01395880083916, 1.00991104495649, 1.00591138153909, 1.00195886573624, + 0.99611649018350, 0.98848330114434, 0.98102294317595, 0.97372899112030, + 0.96659534932828, 0.95961623024651, 0.95278613468066, 0.94609983358253, + 0.93955235122353, 0.93313894963169, 0.92685511418159, 0.92069654023750, + 0.91465912076005, 0.90873893479530, 0.90293223677296, 0.89723544654727, + 0.89164514012056, 0.88615804099474, 0.88077101210109, 0.87548104826333, + 0.87028526915267, 0.86518091269740, 0.86016532891275, 0.85523597411976, + 0.85039040552437, 0.84562627613070, 0.84094132996422, 0.83633339758291, + 0.83180039185606, 0.82734030399203, 0.82295119979782, 0.81863121615464, + 0.81437855769486, 0.81019149366693, 0.80606835497581, 0.80200753138734, + 0.79800746888611, 0.79406666717674, 0.79018367731967, 0.78635709949278, + 0.78258558087123, 0.77886781361798, 0.77520253297841, 0.77158851547266, + 0.76802457717971, 0.76450957210799, 0.76104239064719, 0.75762195809661, + 0.75424723326565, 0.75091720714229, 0.74763090162560, 0.74438736831878, + 0.74118568737933, 0.73802496642311, 0.73490433947940, 0.73182296599416, + 0.72878002987884, 0.72577473860242, 0.72280632232420, 0.71987403306536, + 0.71697714391715, 0.71411494828392, 0.71128675915902, 0.70849190843208 }; diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_asinh.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_asinh.c new file mode 100644 index 0000000000..9193301b5e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_asinh.c @@ -0,0 +1,72 @@ +/* @(#)s_asinh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* asinh(x) + * Method : + * Based on + * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] + * we have + * asinh(x) := x if 1+x*x=1, + * := sign(x)*(log(x)+ln2)) for large |x|, else + * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else + * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const double + one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ + ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ + huge = 1.00000000000000000000e+300; + +double +__asinh (double x) +{ + double w; + int32_t hx, ix; + GET_HIGH_WORD (hx, x); + ix = hx & 0x7fffffff; + if (__glibc_unlikely (ix < 0x3e300000)) /* |x|<2**-28 */ + { + math_check_force_underflow (x); + if (huge + x > one) + return x; /* return x inexact except 0 */ + } + if (__glibc_unlikely (ix > 0x41b00000)) /* |x| > 2**28 */ + { + if (ix >= 0x7ff00000) + return x + x; /* x is inf or NaN */ + w = __ieee754_log (fabs (x)) + ln2; + } + else + { + double xa = fabs (x); + if (ix > 0x40000000) /* 2**28 > |x| > 2.0 */ + { + w = __ieee754_log (2.0 * xa + one / (__ieee754_sqrt (xa * xa + one) + + xa)); + } + else /* 2.0 > |x| > 2**-28 */ + { + double t = xa * xa; + w = __log1p (xa + t / (one + __ieee754_sqrt (one + t))); + } + } + return __copysign (w, x); +} +weak_alias (__asinh, asinh) +#ifdef NO_LONG_DOUBLE +strong_alias (__asinh, __asinhl) +weak_alias (__asinh, asinhl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_atan.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_atan.c new file mode 100644 index 0000000000..3641a35ce1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_atan.c @@ -0,0 +1,328 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/************************************************************************/ +/* MODULE_NAME: atnat.c */ +/* */ +/* FUNCTIONS: uatan */ +/* atanMp */ +/* signArctan */ +/* */ +/* */ +/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h atnat.h */ +/* mpatan.c mpatan2.c mpsqrt.c */ +/* uatan.tbl */ +/* */ +/* An ultimate atan() routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of atan(x). */ +/* */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round to nearest mode of IEEE 754 standard. */ +/* */ +/************************************************************************/ + +#include <dla.h> +#include "mpa.h" +#include "MathLib.h" +#include "uatan.tbl" +#include "atnat.h" +#include <fenv.h> +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <stap-probe.h> + +void __mpatan (mp_no *, mp_no *, int); /* see definition in mpatan.c */ +static double atanMp (double, const int[]); + + /* Fix the sign of y and return */ +static double +__signArctan (double x, double y) +{ + return __copysign (y, x); +} + + +/* An ultimate atan() routine. Given an IEEE double machine number x, */ +/* routine computes the correctly rounded (to nearest) value of atan(x). */ +double +atan (double x) +{ + double cor, s1, ss1, s2, ss2, t1, t2, t3, t7, t8, t9, t10, u, u2, u3, + v, vv, w, ww, y, yy, z, zz; +#ifndef DLA_FMS + double t4, t5, t6; +#endif + int i, ux, dx; + static const int pr[M] = { 6, 8, 10, 32 }; + number num; + + num.d = x; + ux = num.i[HIGH_HALF]; + dx = num.i[LOW_HALF]; + + /* x=NaN */ + if (((ux & 0x7ff00000) == 0x7ff00000) + && (((ux & 0x000fffff) | dx) != 0x00000000)) + return x + x; + + /* Regular values of x, including denormals +-0 and +-INF */ + SET_RESTORE_ROUND (FE_TONEAREST); + u = (x < 0) ? -x : x; + if (u < C) + { + if (u < B) + { + if (u < A) + { + math_check_force_underflow_nonneg (u); + return x; + } + else + { /* A <= u < B */ + v = x * x; + yy = d11.d + v * d13.d; + yy = d9.d + v * yy; + yy = d7.d + v * yy; + yy = d5.d + v * yy; + yy = d3.d + v * yy; + yy *= x * v; + + if ((y = x + (yy - U1 * x)) == x + (yy + U1 * x)) + return y; + + EMULV (x, x, v, vv, t1, t2, t3, t4, t5); /* v+vv=x^2 */ + + s1 = f17.d + v * f19.d; + s1 = f15.d + v * s1; + s1 = f13.d + v * s1; + s1 = f11.d + v * s1; + s1 *= v; + + ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (x, 0, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, + t8); + ADD2 (x, 0, s2, ss2, s1, ss1, t1, t2); + if ((y = s1 + (ss1 - U5 * s1)) == s1 + (ss1 + U5 * s1)) + return y; + + return atanMp (x, pr); + } + } + else + { /* B <= u < C */ + i = (TWO52 + TWO8 * u) - TWO52; + i -= 16; + z = u - cij[i][0].d; + yy = cij[i][5].d + z * cij[i][6].d; + yy = cij[i][4].d + z * yy; + yy = cij[i][3].d + z * yy; + yy = cij[i][2].d + z * yy; + yy *= z; + + t1 = cij[i][1].d; + if (i < 112) + { + if (i < 48) + u2 = U21; /* u < 1/4 */ + else + u2 = U22; + } /* 1/4 <= u < 1/2 */ + else + { + if (i < 176) + u2 = U23; /* 1/2 <= u < 3/4 */ + else + u2 = U24; + } /* 3/4 <= u <= 1 */ + if ((y = t1 + (yy - u2 * t1)) == t1 + (yy + u2 * t1)) + return __signArctan (x, y); + + z = u - hij[i][0].d; + + s1 = hij[i][14].d + z * hij[i][15].d; + s1 = hij[i][13].d + z * s1; + s1 = hij[i][12].d + z * s1; + s1 = hij[i][11].d + z * s1; + s1 *= z; + + ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2); + MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2); + if ((y = s2 + (ss2 - U6 * s2)) == s2 + (ss2 + U6 * s2)) + return __signArctan (x, y); + + return atanMp (x, pr); + } + } + else + { + if (u < D) + { /* C <= u < D */ + w = 1 / u; + EMULV (w, u, t1, t2, t3, t4, t5, t6, t7); + ww = w * ((1 - t1) - t2); + i = (TWO52 + TWO8 * w) - TWO52; + i -= 16; + z = (w - cij[i][0].d) + ww; + + yy = cij[i][5].d + z * cij[i][6].d; + yy = cij[i][4].d + z * yy; + yy = cij[i][3].d + z * yy; + yy = cij[i][2].d + z * yy; + yy = HPI1 - z * yy; + + t1 = HPI - cij[i][1].d; + if (i < 112) + u3 = U31; /* w < 1/2 */ + else + u3 = U32; /* w >= 1/2 */ + if ((y = t1 + (yy - u3)) == t1 + (yy + u3)) + return __signArctan (x, y); + + DIV2 (1, 0, u, 0, w, ww, t1, t2, t3, t4, t5, t6, t7, t8, t9, + t10); + t1 = w - hij[i][0].d; + EADD (t1, ww, z, zz); + + s1 = hij[i][14].d + z * hij[i][15].d; + s1 = hij[i][13].d + z * s1; + s1 = hij[i][12].d + z * s1; + s1 = hij[i][11].d + z * s1; + s1 *= z; + + ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2); + MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2); + SUB2 (HPI, HPI1, s2, ss2, s1, ss1, t1, t2); + if ((y = s1 + (ss1 - U7)) == s1 + (ss1 + U7)) + return __signArctan (x, y); + + return atanMp (x, pr); + } + else + { + if (u < E) + { /* D <= u < E */ + w = 1 / u; + v = w * w; + EMULV (w, u, t1, t2, t3, t4, t5, t6, t7); + + yy = d11.d + v * d13.d; + yy = d9.d + v * yy; + yy = d7.d + v * yy; + yy = d5.d + v * yy; + yy = d3.d + v * yy; + yy *= w * v; + + ww = w * ((1 - t1) - t2); + ESUB (HPI, w, t3, cor); + yy = ((HPI1 + cor) - ww) - yy; + if ((y = t3 + (yy - U4)) == t3 + (yy + U4)) + return __signArctan (x, y); + + DIV2 (1, 0, u, 0, w, ww, t1, t2, t3, t4, t5, t6, t7, t8, + t9, t10); + MUL2 (w, ww, w, ww, v, vv, t1, t2, t3, t4, t5, t6, t7, t8); + + s1 = f17.d + v * f19.d; + s1 = f15.d + v * s1; + s1 = f13.d + v * s1; + s1 = f11.d + v * s1; + s1 *= v; + + ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (w, ww, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (w, ww, s2, ss2, s1, ss1, t1, t2); + SUB2 (HPI, HPI1, s1, ss1, s2, ss2, t1, t2); + + if ((y = s2 + (ss2 - U8)) == s2 + (ss2 + U8)) + return __signArctan (x, y); + + return atanMp (x, pr); + } + else + { + /* u >= E */ + if (x > 0) + return HPI; + else + return MHPI; + } + } + } +} + + /* Final stages. Compute atan(x) by multiple precision arithmetic */ +static double +atanMp (double x, const int pr[]) +{ + mp_no mpx, mpy, mpy2, mperr, mpt1, mpy1; + double y1, y2; + int i, p; + + for (i = 0; i < M; i++) + { + p = pr[i]; + __dbl_mp (x, &mpx, p); + __mpatan (&mpx, &mpy, p); + __dbl_mp (u9[i].d, &mpt1, p); + __mul (&mpy, &mpt1, &mperr, p); + __add (&mpy, &mperr, &mpy1, p); + __sub (&mpy, &mperr, &mpy2, p); + __mp_dbl (&mpy1, &y1, p); + __mp_dbl (&mpy2, &y2, p); + if (y1 == y2) + { + LIBC_PROBE (slowatan, 3, &p, &x, &y1); + return y1; + } + } + LIBC_PROBE (slowatan_inexact, 3, &p, &x, &y1); + return y1; /*if impossible to do exact computing */ +} + +#ifdef NO_LONG_DOUBLE +weak_alias (atan, atanl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_cbrt.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_cbrt.c new file mode 100644 index 0000000000..689abc89ec --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_cbrt.c @@ -0,0 +1,76 @@ +/* Compute cubic root of double value. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Dirk Alboth <dirka@uni-paderborn.de> and + Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + + +#define CBRT2 1.2599210498948731648 /* 2^(1/3) */ +#define SQR_CBRT2 1.5874010519681994748 /* 2^(2/3) */ + +static const double factor[5] = +{ + 1.0 / SQR_CBRT2, + 1.0 / CBRT2, + 1.0, + CBRT2, + SQR_CBRT2 +}; + + +double +__cbrt (double x) +{ + double xm, ym, u, t2; + int xe; + + /* Reduce X. XM now is an range 1.0 to 0.5. */ + xm = __frexp (fabs (x), &xe); + + /* If X is not finite or is null return it (with raising exceptions + if necessary. + Note: *Our* version of `frexp' sets XE to zero if the argument is + Inf or NaN. This is not portable but faster. */ + if (xe == 0 && fpclassify (x) <= FP_ZERO) + return x + x; + + u = (0.354895765043919860 + + ((1.50819193781584896 + + ((-2.11499494167371287 + + ((2.44693122563534430 + + ((-1.83469277483613086 + + (0.784932344976639262 - 0.145263899385486377 * xm) + * xm) + * xm)) + * xm)) + * xm)) + * xm)); + + t2 = u * u * u; + + ym = u * (t2 + 2.0 * xm) / (2.0 * t2 + xm) * factor[2 + xe % 3]; + + return __ldexp (x > 0.0 ? ym : -ym, xe / 3); +} +weak_alias (__cbrt, cbrt) +#ifdef NO_LONG_DOUBLE +strong_alias (__cbrt, __cbrtl) +weak_alias (__cbrt, cbrtl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_ceil.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_ceil.c new file mode 100644 index 0000000000..c291c26f57 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_ceil.c @@ -0,0 +1,89 @@ +/* @(#)s_ceil.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * ceil(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + */ + +#include <math.h> +#include <math_private.h> + +double +__ceil (double x) +{ + int32_t i0, i1, j0; + u_int32_t i, j; + EXTRACT_WORDS (i0, i1, x); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + if (j0 < 20) + { + if (j0 < 0) + { + /* return 0*sign(x) if |x|<1 */ + if (i0 < 0) + { + i0 = 0x80000000; i1 = 0; + } + else if ((i0 | i1) != 0) + { + i0 = 0x3ff00000; i1 = 0; + } + } + else + { + i = (0x000fffff) >> j0; + if (((i0 & i) | i1) == 0) + return x; /* x is integral */ + if (i0 > 0) + i0 += (0x00100000) >> j0; + i0 &= (~i); i1 = 0; + } + } + else if (j0 > 51) + { + if (j0 == 0x400) + return x + x; /* inf or NaN */ + else + return x; /* x is integral */ + } + else + { + i = ((u_int32_t) (0xffffffff)) >> (j0 - 20); + if ((i1 & i) == 0) + return x; /* x is integral */ + if (i0 > 0) + { + if (j0 == 20) + i0 += 1; + else + { + j = i1 + (1 << (52 - j0)); + if (j < i1) + i0 += 1; /* got a carry */ + i1 = j; + } + } + i1 &= (~i); + } + INSERT_WORDS (x, i0, i1); + return x; +} +#ifndef __ceil +weak_alias (__ceil, ceil) +# ifdef NO_LONG_DOUBLE +strong_alias (__ceil, __ceill) +weak_alias (__ceil, ceill) +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_copysign.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_copysign.c new file mode 100644 index 0000000000..9caf24e8f2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_copysign.c @@ -0,0 +1,39 @@ +/* @(#)s_copysign.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_copysign.c,v 1.8 1995/05/10 20:46:57 jtc Exp $"; +#endif + +/* + * copysign(double x, double y) + * copysign(x,y) returns a value with the magnitude of x and + * with the sign bit of y. + */ + +#include <math.h> +#include <math_private.h> + +double +__copysign (double x, double y) +{ + u_int32_t hx, hy; + GET_HIGH_WORD (hx, x); + GET_HIGH_WORD (hy, y); + SET_HIGH_WORD (x, (hx & 0x7fffffff) | (hy & 0x80000000)); + return x; +} +weak_alias (__copysign, copysign) +#ifdef NO_LONG_DOUBLE +strong_alias (__copysign, __copysignl) +weak_alias (__copysign, copysignl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_cos.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_cos.c new file mode 100644 index 0000000000..4be1276ccb --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_cos.c @@ -0,0 +1 @@ +/* In s_sin.c. */ diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_erf.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_erf.c new file mode 100644 index 0000000000..b4975a8af8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_erf.c @@ -0,0 +1,428 @@ +/* @(#)s_erf.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25, + for performance improvement on pipelined processors. +*/ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_erf.c,v 1.8 1995/05/10 20:47:05 jtc Exp $"; +#endif + +/* double erf(double x) + * double erfc(double x) + * x + * 2 |\ + * erf(x) = --------- | exp(-t*t)dt + * sqrt(pi) \| + * 0 + * + * erfc(x) = 1-erf(x) + * Note that + * erf(-x) = -erf(x) + * erfc(-x) = 2 - erfc(x) + * + * Method: + * 1. For |x| in [0, 0.84375] + * erf(x) = x + x*R(x^2) + * erfc(x) = 1 - erf(x) if x in [-.84375,0.25] + * = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375] + * where R = P/Q where P is an odd poly of degree 8 and + * Q is an odd poly of degree 10. + * -57.90 + * | R - (erf(x)-x)/x | <= 2 + * + * + * Remark. The formula is derived by noting + * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....) + * and that + * 2/sqrt(pi) = 1.128379167095512573896158903121545171688 + * is close to one. The interval is chosen because the fix + * point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is + * near 0.6174), and by some experiment, 0.84375 is chosen to + * guarantee the error is less than one ulp for erf. + * + * 2. For |x| in [0.84375,1.25], let s = |x| - 1, and + * c = 0.84506291151 rounded to single (24 bits) + * erf(x) = sign(x) * (c + P1(s)/Q1(s)) + * erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0 + * 1+(c+P1(s)/Q1(s)) if x < 0 + * |P1/Q1 - (erf(|x|)-c)| <= 2**-59.06 + * Remark: here we use the taylor series expansion at x=1. + * erf(1+s) = erf(1) + s*Poly(s) + * = 0.845.. + P1(s)/Q1(s) + * That is, we use rational approximation to approximate + * erf(1+s) - (c = (single)0.84506291151) + * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25] + * where + * P1(s) = degree 6 poly in s + * Q1(s) = degree 6 poly in s + * + * 3. For x in [1.25,1/0.35(~2.857143)], + * erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1) + * erf(x) = 1 - erfc(x) + * where + * R1(z) = degree 7 poly in z, (z=1/x^2) + * S1(z) = degree 8 poly in z + * + * 4. For x in [1/0.35,28] + * erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0 + * = 2.0 - (1/x)*exp(-x*x-0.5625+R2/S2) if -6<x<0 + * = 2.0 - tiny (if x <= -6) + * erf(x) = sign(x)*(1.0 - erfc(x)) if x < 6, else + * erf(x) = sign(x)*(1.0 - tiny) + * where + * R2(z) = degree 6 poly in z, (z=1/x^2) + * S2(z) = degree 7 poly in z + * + * Note1: + * To compute exp(-x*x-0.5625+R/S), let s be a single + * precision number and s := x; then + * -x*x = -s*s + (s-x)*(s+x) + * exp(-x*x-0.5626+R/S) = + * exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S); + * Note2: + * Here 4 and 5 make use of the asymptotic series + * exp(-x*x) + * erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) ) + * x*sqrt(pi) + * We use rational approximation to approximate + * g(s)=f(1/x^2) = log(erfc(x)*x) - x*x + 0.5625 + * Here is the error bound for R1/S1 and R2/S2 + * |R1/S1 - f(x)| < 2**(-62.57) + * |R2/S2 - f(x)| < 2**(-61.52) + * + * 5. For inf > x >= 28 + * erf(x) = sign(x) *(1 - tiny) (raise inexact) + * erfc(x) = tiny*tiny (raise underflow) if x > 0 + * = 2 - tiny if x<0 + * + * 7. Special case: + * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, + * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, + * erfc/erf(NaN) is NaN + */ + + +#include <errno.h> +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <fix-int-fp-convert-zero.h> + +static const double + tiny = 1e-300, + half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ + one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ + two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ +/* c = (float)0.84506291151 */ + erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */ +/* + * Coefficients for approximation to erf on [0,0.84375] + */ + efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */ + pp[] = { 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */ + -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */ + -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */ + -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */ + -2.37630166566501626084e-05 }, /* 0xBEF8EAD6, 0x120016AC */ + qq[] = { 0.0, 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */ + 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */ + 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */ + 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */ + -3.96022827877536812320e-06 }, /* 0xBED09C43, 0x42A26120 */ +/* + * Coefficients for approximation to erf in [0.84375,1.25] + */ + pa[] = { -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */ + 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */ + -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */ + 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */ + -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */ + 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */ + -2.16637559486879084300e-03 }, /* 0xBF61BF38, 0x0A96073F */ + qa[] = { 0.0, 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */ + 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */ + 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */ + 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */ + 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */ + 1.19844998467991074170e-02 }, /* 0x3F888B54, 0x5735151D */ +/* + * Coefficients for approximation to erfc in [1.25,1/0.35] + */ + ra[] = { -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */ + -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */ + -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */ + -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */ + -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */ + -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */ + -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */ + -9.81432934416914548592e+00 }, /* 0xC023A0EF, 0xC69AC25C */ + sa[] = { 0.0, 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */ + 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */ + 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */ + 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */ + 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */ + 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */ + 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */ + -6.04244152148580987438e-02 }, /* 0xBFAEEFF2, 0xEE749A62 */ +/* + * Coefficients for approximation to erfc in [1/.35,28] + */ + rb[] = { -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */ + -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */ + -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */ + -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */ + -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */ + -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */ + -4.83519191608651397019e+02 }, /* 0xC07E384E, 0x9BDC383F */ + sb[] = { 0.0, 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */ + 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */ + 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */ + 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */ + 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */ + 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */ + -2.24409524465858183362e+01 }; /* 0xC03670E2, 0x42712D62 */ + +double +__erf (double x) +{ + int32_t hx, ix, i; + double R, S, P, Q, s, y, z, r; + GET_HIGH_WORD (hx, x); + ix = hx & 0x7fffffff; + if (ix >= 0x7ff00000) /* erf(nan)=nan */ + { + i = ((u_int32_t) hx >> 31) << 1; + return (double) (1 - i) + one / x; /* erf(+-inf)=+-1 */ + } + + if (ix < 0x3feb0000) /* |x|<0.84375 */ + { + double r1, r2, s1, s2, s3, z2, z4; + if (ix < 0x3e300000) /* |x|<2**-28 */ + { + if (ix < 0x00800000) + { + /* Avoid spurious underflow. */ + double ret = 0.0625 * (16.0 * x + (16.0 * efx) * x); + math_check_force_underflow (ret); + return ret; + } + return x + efx * x; + } + z = x * x; + r1 = pp[0] + z * pp[1]; z2 = z * z; + r2 = pp[2] + z * pp[3]; z4 = z2 * z2; + s1 = one + z * qq[1]; + s2 = qq[2] + z * qq[3]; + s3 = qq[4] + z * qq[5]; + r = r1 + z2 * r2 + z4 * pp[4]; + s = s1 + z2 * s2 + z4 * s3; + y = r / s; + return x + x * y; + } + if (ix < 0x3ff40000) /* 0.84375 <= |x| < 1.25 */ + { + double s2, s4, s6, P1, P2, P3, P4, Q1, Q2, Q3, Q4; + s = fabs (x) - one; + P1 = pa[0] + s * pa[1]; s2 = s * s; + Q1 = one + s * qa[1]; s4 = s2 * s2; + P2 = pa[2] + s * pa[3]; s6 = s4 * s2; + Q2 = qa[2] + s * qa[3]; + P3 = pa[4] + s * pa[5]; + Q3 = qa[4] + s * qa[5]; + P4 = pa[6]; + Q4 = qa[6]; + P = P1 + s2 * P2 + s4 * P3 + s6 * P4; + Q = Q1 + s2 * Q2 + s4 * Q3 + s6 * Q4; + if (hx >= 0) + return erx + P / Q; + else + return -erx - P / Q; + } + if (ix >= 0x40180000) /* inf>|x|>=6 */ + { + if (hx >= 0) + return one - tiny; + else + return tiny - one; + } + x = fabs (x); + s = one / (x * x); + if (ix < 0x4006DB6E) /* |x| < 1/0.35 */ + { + double R1, R2, R3, R4, S1, S2, S3, S4, s2, s4, s6, s8; + R1 = ra[0] + s * ra[1]; s2 = s * s; + S1 = one + s * sa[1]; s4 = s2 * s2; + R2 = ra[2] + s * ra[3]; s6 = s4 * s2; + S2 = sa[2] + s * sa[3]; s8 = s4 * s4; + R3 = ra[4] + s * ra[5]; + S3 = sa[4] + s * sa[5]; + R4 = ra[6] + s * ra[7]; + S4 = sa[6] + s * sa[7]; + R = R1 + s2 * R2 + s4 * R3 + s6 * R4; + S = S1 + s2 * S2 + s4 * S3 + s6 * S4 + s8 * sa[8]; + } + else /* |x| >= 1/0.35 */ + { + double R1, R2, R3, S1, S2, S3, S4, s2, s4, s6; + R1 = rb[0] + s * rb[1]; s2 = s * s; + S1 = one + s * sb[1]; s4 = s2 * s2; + R2 = rb[2] + s * rb[3]; s6 = s4 * s2; + S2 = sb[2] + s * sb[3]; + R3 = rb[4] + s * rb[5]; + S3 = sb[4] + s * sb[5]; + S4 = sb[6] + s * sb[7]; + R = R1 + s2 * R2 + s4 * R3 + s6 * rb[6]; + S = S1 + s2 * S2 + s4 * S3 + s6 * S4; + } + z = x; + SET_LOW_WORD (z, 0); + r = __ieee754_exp (-z * z - 0.5625) * + __ieee754_exp ((z - x) * (z + x) + R / S); + if (hx >= 0) + return one - r / x; + else + return r / x - one; +} +weak_alias (__erf, erf) +#ifdef NO_LONG_DOUBLE +strong_alias (__erf, __erfl) +weak_alias (__erf, erfl) +#endif + +double +__erfc (double x) +{ + int32_t hx, ix; + double R, S, P, Q, s, y, z, r; + GET_HIGH_WORD (hx, x); + ix = hx & 0x7fffffff; + if (ix >= 0x7ff00000) /* erfc(nan)=nan */ + { /* erfc(+-inf)=0,2 */ + double ret = (double) (((u_int32_t) hx >> 31) << 1) + one / x; + if (FIX_INT_FP_CONVERT_ZERO && ret == 0.0) + return 0.0; + return ret; + } + + if (ix < 0x3feb0000) /* |x|<0.84375 */ + { + double r1, r2, s1, s2, s3, z2, z4; + if (ix < 0x3c700000) /* |x|<2**-56 */ + return one - x; + z = x * x; + r1 = pp[0] + z * pp[1]; z2 = z * z; + r2 = pp[2] + z * pp[3]; z4 = z2 * z2; + s1 = one + z * qq[1]; + s2 = qq[2] + z * qq[3]; + s3 = qq[4] + z * qq[5]; + r = r1 + z2 * r2 + z4 * pp[4]; + s = s1 + z2 * s2 + z4 * s3; + y = r / s; + if (hx < 0x3fd00000) /* x<1/4 */ + { + return one - (x + x * y); + } + else + { + r = x * y; + r += (x - half); + return half - r; + } + } + if (ix < 0x3ff40000) /* 0.84375 <= |x| < 1.25 */ + { + double s2, s4, s6, P1, P2, P3, P4, Q1, Q2, Q3, Q4; + s = fabs (x) - one; + P1 = pa[0] + s * pa[1]; s2 = s * s; + Q1 = one + s * qa[1]; s4 = s2 * s2; + P2 = pa[2] + s * pa[3]; s6 = s4 * s2; + Q2 = qa[2] + s * qa[3]; + P3 = pa[4] + s * pa[5]; + Q3 = qa[4] + s * qa[5]; + P4 = pa[6]; + Q4 = qa[6]; + P = P1 + s2 * P2 + s4 * P3 + s6 * P4; + Q = Q1 + s2 * Q2 + s4 * Q3 + s6 * Q4; + if (hx >= 0) + { + z = one - erx; return z - P / Q; + } + else + { + z = erx + P / Q; return one + z; + } + } + if (ix < 0x403c0000) /* |x|<28 */ + { + x = fabs (x); + s = one / (x * x); + if (ix < 0x4006DB6D) /* |x| < 1/.35 ~ 2.857143*/ + { + double R1, R2, R3, R4, S1, S2, S3, S4, s2, s4, s6, s8; + R1 = ra[0] + s * ra[1]; s2 = s * s; + S1 = one + s * sa[1]; s4 = s2 * s2; + R2 = ra[2] + s * ra[3]; s6 = s4 * s2; + S2 = sa[2] + s * sa[3]; s8 = s4 * s4; + R3 = ra[4] + s * ra[5]; + S3 = sa[4] + s * sa[5]; + R4 = ra[6] + s * ra[7]; + S4 = sa[6] + s * sa[7]; + R = R1 + s2 * R2 + s4 * R3 + s6 * R4; + S = S1 + s2 * S2 + s4 * S3 + s6 * S4 + s8 * sa[8]; + } + else /* |x| >= 1/.35 ~ 2.857143 */ + { + double R1, R2, R3, S1, S2, S3, S4, s2, s4, s6; + if (hx < 0 && ix >= 0x40180000) + return two - tiny; /* x < -6 */ + R1 = rb[0] + s * rb[1]; s2 = s * s; + S1 = one + s * sb[1]; s4 = s2 * s2; + R2 = rb[2] + s * rb[3]; s6 = s4 * s2; + S2 = sb[2] + s * sb[3]; + R3 = rb[4] + s * rb[5]; + S3 = sb[4] + s * sb[5]; + S4 = sb[6] + s * sb[7]; + R = R1 + s2 * R2 + s4 * R3 + s6 * rb[6]; + S = S1 + s2 * S2 + s4 * S3 + s6 * S4; + } + z = x; + SET_LOW_WORD (z, 0); + r = __ieee754_exp (-z * z - 0.5625) * + __ieee754_exp ((z - x) * (z + x) + R / S); + if (hx > 0) + { + double ret = math_narrow_eval (r / x); + if (ret == 0) + __set_errno (ERANGE); + return ret; + } + else + return two - r / x; + } + else + { + if (hx > 0) + { + __set_errno (ERANGE); + return tiny * tiny; + } + else + return two - tiny; + } +} +weak_alias (__erfc, erfc) +#ifdef NO_LONG_DOUBLE +strong_alias (__erfc, __erfcl) +weak_alias (__erfc, erfcl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_expm1.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_expm1.c new file mode 100644 index 0000000000..54d771007a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_expm1.c @@ -0,0 +1,262 @@ +/* @(#)s_expm1.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25, + for performance improvement on pipelined processors. + */ + +/* expm1(x) + * Returns exp(x)-1, the exponential of x minus 1. + * + * Method + * 1. Argument reduction: + * Given x, find r and integer k such that + * + * x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658 + * + * Here a correction term c will be computed to compensate + * the error in r when rounded to a floating-point number. + * + * 2. Approximating expm1(r) by a special rational function on + * the interval [0,0.34658]: + * Since + * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ... + * we define R1(r*r) by + * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r) + * That is, + * R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r) + * = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r)) + * = 1 - r^2/60 + r^4/2520 - r^6/100800 + ... + * We use a special Reme algorithm on [0,0.347] to generate + * a polynomial of degree 5 in r*r to approximate R1. The + * maximum error of this polynomial approximation is bounded + * by 2**-61. In other words, + * R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5 + * where Q1 = -1.6666666666666567384E-2, + * Q2 = 3.9682539681370365873E-4, + * Q3 = -9.9206344733435987357E-6, + * Q4 = 2.5051361420808517002E-7, + * Q5 = -6.2843505682382617102E-9; + * (where z=r*r, and the values of Q1 to Q5 are listed below) + * with error bounded by + * | 5 | -61 + * | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2 + * | | + * + * expm1(r) = exp(r)-1 is then computed by the following + * specific way which minimize the accumulation rounding error: + * 2 3 + * r r [ 3 - (R1 + R1*r/2) ] + * expm1(r) = r + --- + --- * [--------------------] + * 2 2 [ 6 - r*(3 - R1*r/2) ] + * + * To compensate the error in the argument reduction, we use + * expm1(r+c) = expm1(r) + c + expm1(r)*c + * ~ expm1(r) + c + r*c + * Thus c+r*c will be added in as the correction terms for + * expm1(r+c). Now rearrange the term to avoid optimization + * screw up: + * ( 2 2 ) + * ({ ( r [ R1 - (3 - R1*r/2) ] ) } r ) + * expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- ) + * ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 ) + * ( ) + * + * = r - E + * 3. Scale back to obtain expm1(x): + * From step 1, we have + * expm1(x) = either 2^k*[expm1(r)+1] - 1 + * = or 2^k*[expm1(r) + (1-2^-k)] + * 4. Implementation notes: + * (A). To save one multiplication, we scale the coefficient Qi + * to Qi*2^i, and replace z by (x^2)/2. + * (B). To achieve maximum accuracy, we compute expm1(x) by + * (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf) + * (ii) if k=0, return r-E + * (iii) if k=-1, return 0.5*(r-E)-0.5 + * (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E) + * else return 1.0+2.0*(r-E); + * (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1) + * (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else + * (vii) return 2^k(1-((E+2^-k)-r)) + * + * Special cases: + * expm1(INF) is INF, expm1(NaN) is NaN; + * expm1(-INF) is -1, and + * for finite argument, only expm1(0)=0 is exact. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Misc. info. + * For IEEE double + * if x > 7.09782712893383973096e+02 then expm1(x) overflow + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include <errno.h> +#include <float.h> +#include <math.h> +#include <math_private.h> +#define one Q[0] +static const double + huge = 1.0e+300, + tiny = 1.0e-300, + o_threshold = 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ + ln2_hi = 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */ + ln2_lo = 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */ + invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */ +/* scaled coefficients related to expm1 */ + Q[] = { 1.0, -3.33333333333331316428e-02, /* BFA11111 111110F4 */ + 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */ + -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */ + 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */ + -2.01099218183624371326e-07 }; /* BE8AFDB7 6E09C32D */ + +double +__expm1 (double x) +{ + double y, hi, lo, c, t, e, hxs, hfx, r1, h2, h4, R1, R2, R3; + int32_t k, xsb; + u_int32_t hx; + + GET_HIGH_WORD (hx, x); + xsb = hx & 0x80000000; /* sign bit of x */ + if (xsb == 0) + y = x; + else + y = -x; /* y = |x| */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out huge and non-finite argument */ + if (hx >= 0x4043687A) /* if |x|>=56*ln2 */ + { + if (hx >= 0x40862E42) /* if |x|>=709.78... */ + { + if (hx >= 0x7ff00000) + { + u_int32_t low; + GET_LOW_WORD (low, x); + if (((hx & 0xfffff) | low) != 0) + return x + x; /* NaN */ + else + return (xsb == 0) ? x : -1.0; /* exp(+-inf)={inf,-1} */ + } + if (x > o_threshold) + { + __set_errno (ERANGE); + return huge * huge; /* overflow */ + } + } + if (xsb != 0) /* x < -56*ln2, return -1.0 with inexact */ + { + math_force_eval (x + tiny); /* raise inexact */ + return tiny - one; /* return -1 */ + } + } + + /* argument reduction */ + if (hx > 0x3fd62e42) /* if |x| > 0.5 ln2 */ + { + if (hx < 0x3FF0A2B2) /* and |x| < 1.5 ln2 */ + { + if (xsb == 0) + { + hi = x - ln2_hi; lo = ln2_lo; k = 1; + } + else + { + hi = x + ln2_hi; lo = -ln2_lo; k = -1; + } + } + else + { + k = invln2 * x + ((xsb == 0) ? 0.5 : -0.5); + t = k; + hi = x - t * ln2_hi; /* t*ln2_hi is exact here */ + lo = t * ln2_lo; + } + x = hi - lo; + c = (hi - x) - lo; + } + else if (hx < 0x3c900000) /* when |x|<2**-54, return x */ + { + math_check_force_underflow (x); + t = huge + x; /* return x with inexact flags when x!=0 */ + return x - (t - (huge + x)); + } + else + k = 0; + + /* x is now in primary range */ + hfx = 0.5 * x; + hxs = x * hfx; + R1 = one + hxs * Q[1]; h2 = hxs * hxs; + R2 = Q[2] + hxs * Q[3]; h4 = h2 * h2; + R3 = Q[4] + hxs * Q[5]; + r1 = R1 + h2 * R2 + h4 * R3; + t = 3.0 - r1 * hfx; + e = hxs * ((r1 - t) / (6.0 - x * t)); + if (k == 0) + return x - (x * e - hxs); /* c is 0 */ + else + { + e = (x * (e - c) - c); + e -= hxs; + if (k == -1) + return 0.5 * (x - e) - 0.5; + if (k == 1) + { + if (x < -0.25) + return -2.0 * (e - (x + 0.5)); + else + return one + 2.0 * (x - e); + } + if (k <= -2 || k > 56) /* suffice to return exp(x)-1 */ + { + u_int32_t high; + y = one - (e - x); + GET_HIGH_WORD (high, y); + SET_HIGH_WORD (y, high + (k << 20)); /* add k to y's exponent */ + return y - one; + } + t = one; + if (k < 20) + { + u_int32_t high; + SET_HIGH_WORD (t, 0x3ff00000 - (0x200000 >> k)); /* t=1-2^-k */ + y = t - (e - x); + GET_HIGH_WORD (high, y); + SET_HIGH_WORD (y, high + (k << 20)); /* add k to y's exponent */ + } + else + { + u_int32_t high; + SET_HIGH_WORD (t, ((0x3ff - k) << 20)); /* 2^-k */ + y = x - (e + t); + y += one; + GET_HIGH_WORD (high, y); + SET_HIGH_WORD (y, high + (k << 20)); /* add k to y's exponent */ + } + } + return y; +} +weak_alias (__expm1, expm1) +#ifdef NO_LONG_DOUBLE +strong_alias (__expm1, __expm1l) +weak_alias (__expm1, expm1l) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_fabs.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fabs.c new file mode 100644 index 0000000000..73c09a269e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fabs.c @@ -0,0 +1,32 @@ +/* @(#)s_fabs.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_fabs.c,v 1.7 1995/05/10 20:47:13 jtc Exp $"; +#endif + +/* + * fabs(x) returns the absolute value of x. + */ + +#include <math.h> + +double +__fabs (double x) +{ + return __builtin_fabs (x); +} +weak_alias (__fabs, fabs) +#ifdef NO_LONG_DOUBLE +strong_alias (__fabs, __fabsl) +weak_alias (__fabs, fabsl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_finite.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_finite.c new file mode 100644 index 0000000000..69141db75d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_finite.c @@ -0,0 +1,50 @@ +/* @(#)s_finite.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_finite.c,v 1.8 1995/05/10 20:47:17 jtc Exp $"; +#endif + +/* + * finite(x) returns 1 is x is finite, else 0; + * no branching! + */ + +#include <math.h> +#include <math_private.h> +#include <shlib-compat.h> + +#undef __finite + +#ifndef FINITE +# define FINITE __finite +#endif + +int FINITE(double x) +{ + int32_t hx; + GET_HIGH_WORD (hx, x); + return (int) ((u_int32_t) ((hx & 0x7ff00000) - 0x7ff00000) >> 31); +} +hidden_def (__finite) +weak_alias (__finite, finite) +#ifdef NO_LONG_DOUBLE +# ifdef LDBL_CLASSIFY_COMPAT +# if SHLIB_COMPAT (libc, GLIBC_2_0, GLIBC_2_23) +compat_symbol (libc, __finite, __finitel, GLIBC_2_0); +# endif +# if SHLIB_COMPAT (libm, GLIBC_2_1, GLIBC_2_23) +compat_symbol (libm, __finite, __finitel, GLIBC_2_1); +# endif +# endif +weak_alias (__finite, finitel) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_floor.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_floor.c new file mode 100644 index 0000000000..8f86aa31ee --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_floor.c @@ -0,0 +1,89 @@ +/* @(#)s_floor.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * floor(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + */ + +#include <math.h> +#include <math_private.h> + +double +__floor (double x) +{ + int32_t i0, i1, j0; + u_int32_t i, j; + EXTRACT_WORDS (i0, i1, x); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + if (j0 < 20) + { + if (j0 < 0) + { + /* return 0*sign(x) if |x|<1 */ + if (i0 >= 0) + { + i0 = i1 = 0; + } + else if (((i0 & 0x7fffffff) | i1) != 0) + { + i0 = 0xbff00000; i1 = 0; + } + } + else + { + i = (0x000fffff) >> j0; + if (((i0 & i) | i1) == 0) + return x; /* x is integral */ + if (i0 < 0) + i0 += (0x00100000) >> j0; + i0 &= (~i); i1 = 0; + } + } + else if (j0 > 51) + { + if (j0 == 0x400) + return x + x; /* inf or NaN */ + else + return x; /* x is integral */ + } + else + { + i = ((u_int32_t) (0xffffffff)) >> (j0 - 20); + if ((i1 & i) == 0) + return x; /* x is integral */ + if (i0 < 0) + { + if (j0 == 20) + i0 += 1; + else + { + j = i1 + (1 << (52 - j0)); + if (j < i1) + i0 += 1; /* got a carry */ + i1 = j; + } + } + i1 &= (~i); + } + INSERT_WORDS (x, i0, i1); + return x; +} +#ifndef __floor +weak_alias (__floor, floor) +# ifdef NO_LONG_DOUBLE +strong_alias (__floor, __floorl) +weak_alias (__floor, floorl) +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_fma.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fma.c new file mode 100644 index 0000000000..68c8515fb1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fma.c @@ -0,0 +1,301 @@ +/* Compute x * y + z as ternary operation. + Copyright (C) 2010-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jakub@redhat.com>, 2010. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <fenv.h> +#include <ieee754.h> +#include <math_private.h> +#include <tininess.h> + +/* This implementation uses rounding to odd to avoid problems with + double rounding. See a paper by Boldo and Melquiond: + http://www.lri.fr/~melquion/doc/08-tc.pdf */ + +double +__fma (double x, double y, double z) +{ + union ieee754_double u, v, w; + int adjust = 0; + u.d = x; + v.d = y; + w.d = z; + if (__builtin_expect (u.ieee.exponent + v.ieee.exponent + >= 0x7ff + IEEE754_DOUBLE_BIAS - DBL_MANT_DIG, 0) + || __builtin_expect (u.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0) + || __builtin_expect (v.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0) + || __builtin_expect (w.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0) + || __builtin_expect (u.ieee.exponent + v.ieee.exponent + <= IEEE754_DOUBLE_BIAS + DBL_MANT_DIG, 0)) + { + /* If z is Inf, but x and y are finite, the result should be + z rather than NaN. */ + if (w.ieee.exponent == 0x7ff + && u.ieee.exponent != 0x7ff + && v.ieee.exponent != 0x7ff) + return (z + x) + y; + /* If z is zero and x are y are nonzero, compute the result + as x * y to avoid the wrong sign of a zero result if x * y + underflows to 0. */ + if (z == 0 && x != 0 && y != 0) + return x * y; + /* If x or y or z is Inf/NaN, or if x * y is zero, compute as + x * y + z. */ + if (u.ieee.exponent == 0x7ff + || v.ieee.exponent == 0x7ff + || w.ieee.exponent == 0x7ff + || x == 0 + || y == 0) + return x * y + z; + /* If fma will certainly overflow, compute as x * y. */ + if (u.ieee.exponent + v.ieee.exponent > 0x7ff + IEEE754_DOUBLE_BIAS) + return x * y; + /* If x * y is less than 1/4 of DBL_TRUE_MIN, neither the + result nor whether there is underflow depends on its exact + value, only on its sign. */ + if (u.ieee.exponent + v.ieee.exponent + < IEEE754_DOUBLE_BIAS - DBL_MANT_DIG - 2) + { + int neg = u.ieee.negative ^ v.ieee.negative; + double tiny = neg ? -0x1p-1074 : 0x1p-1074; + if (w.ieee.exponent >= 3) + return tiny + z; + /* Scaling up, adding TINY and scaling down produces the + correct result, because in round-to-nearest mode adding + TINY has no effect and in other modes double rounding is + harmless. But it may not produce required underflow + exceptions. */ + v.d = z * 0x1p54 + tiny; + if (TININESS_AFTER_ROUNDING + ? v.ieee.exponent < 55 + : (w.ieee.exponent == 0 + || (w.ieee.exponent == 1 + && w.ieee.negative != neg + && w.ieee.mantissa1 == 0 + && w.ieee.mantissa0 == 0))) + { + double force_underflow = x * y; + math_force_eval (force_underflow); + } + return v.d * 0x1p-54; + } + if (u.ieee.exponent + v.ieee.exponent + >= 0x7ff + IEEE754_DOUBLE_BIAS - DBL_MANT_DIG) + { + /* Compute 1p-53 times smaller result and multiply + at the end. */ + if (u.ieee.exponent > v.ieee.exponent) + u.ieee.exponent -= DBL_MANT_DIG; + else + v.ieee.exponent -= DBL_MANT_DIG; + /* If x + y exponent is very large and z exponent is very small, + it doesn't matter if we don't adjust it. */ + if (w.ieee.exponent > DBL_MANT_DIG) + w.ieee.exponent -= DBL_MANT_DIG; + adjust = 1; + } + else if (w.ieee.exponent >= 0x7ff - DBL_MANT_DIG) + { + /* Similarly. + If z exponent is very large and x and y exponents are + very small, adjust them up to avoid spurious underflows, + rather than down. */ + if (u.ieee.exponent + v.ieee.exponent + <= IEEE754_DOUBLE_BIAS + 2 * DBL_MANT_DIG) + { + if (u.ieee.exponent > v.ieee.exponent) + u.ieee.exponent += 2 * DBL_MANT_DIG + 2; + else + v.ieee.exponent += 2 * DBL_MANT_DIG + 2; + } + else if (u.ieee.exponent > v.ieee.exponent) + { + if (u.ieee.exponent > DBL_MANT_DIG) + u.ieee.exponent -= DBL_MANT_DIG; + } + else if (v.ieee.exponent > DBL_MANT_DIG) + v.ieee.exponent -= DBL_MANT_DIG; + w.ieee.exponent -= DBL_MANT_DIG; + adjust = 1; + } + else if (u.ieee.exponent >= 0x7ff - DBL_MANT_DIG) + { + u.ieee.exponent -= DBL_MANT_DIG; + if (v.ieee.exponent) + v.ieee.exponent += DBL_MANT_DIG; + else + v.d *= 0x1p53; + } + else if (v.ieee.exponent >= 0x7ff - DBL_MANT_DIG) + { + v.ieee.exponent -= DBL_MANT_DIG; + if (u.ieee.exponent) + u.ieee.exponent += DBL_MANT_DIG; + else + u.d *= 0x1p53; + } + else /* if (u.ieee.exponent + v.ieee.exponent + <= IEEE754_DOUBLE_BIAS + DBL_MANT_DIG) */ + { + if (u.ieee.exponent > v.ieee.exponent) + u.ieee.exponent += 2 * DBL_MANT_DIG + 2; + else + v.ieee.exponent += 2 * DBL_MANT_DIG + 2; + if (w.ieee.exponent <= 4 * DBL_MANT_DIG + 6) + { + if (w.ieee.exponent) + w.ieee.exponent += 2 * DBL_MANT_DIG + 2; + else + w.d *= 0x1p108; + adjust = -1; + } + /* Otherwise x * y should just affect inexact + and nothing else. */ + } + x = u.d; + y = v.d; + z = w.d; + } + + /* Ensure correct sign of exact 0 + 0. */ + if (__glibc_unlikely ((x == 0 || y == 0) && z == 0)) + { + x = math_opt_barrier (x); + return x * y + z; + } + + fenv_t env; + libc_feholdexcept_setround (&env, FE_TONEAREST); + + /* Multiplication m1 + m2 = x * y using Dekker's algorithm. */ +#define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1) + double x1 = x * C; + double y1 = y * C; + double m1 = x * y; + x1 = (x - x1) + x1; + y1 = (y - y1) + y1; + double x2 = x - x1; + double y2 = y - y1; + double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2; + + /* Addition a1 + a2 = z + m1 using Knuth's algorithm. */ + double a1 = z + m1; + double t1 = a1 - z; + double t2 = a1 - t1; + t1 = m1 - t1; + t2 = z - t2; + double a2 = t1 + t2; + /* Ensure the arithmetic is not scheduled after feclearexcept call. */ + math_force_eval (m2); + math_force_eval (a2); + feclearexcept (FE_INEXACT); + + /* If the result is an exact zero, ensure it has the correct sign. */ + if (a1 == 0 && m2 == 0) + { + libc_feupdateenv (&env); + /* Ensure that round-to-nearest value of z + m1 is not reused. */ + z = math_opt_barrier (z); + return z + m1; + } + + libc_fesetround (FE_TOWARDZERO); + + /* Perform m2 + a2 addition with round to odd. */ + u.d = a2 + m2; + + if (__glibc_unlikely (adjust < 0)) + { + if ((u.ieee.mantissa1 & 1) == 0) + u.ieee.mantissa1 |= libc_fetestexcept (FE_INEXACT) != 0; + v.d = a1 + u.d; + /* Ensure the addition is not scheduled after fetestexcept call. */ + math_force_eval (v.d); + } + + /* Reset rounding mode and test for inexact simultaneously. */ + int j = libc_feupdateenv_test (&env, FE_INEXACT) != 0; + + if (__glibc_likely (adjust == 0)) + { + if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7ff) + u.ieee.mantissa1 |= j; + /* Result is a1 + u.d. */ + return a1 + u.d; + } + else if (__glibc_likely (adjust > 0)) + { + if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7ff) + u.ieee.mantissa1 |= j; + /* Result is a1 + u.d, scaled up. */ + return (a1 + u.d) * 0x1p53; + } + else + { + /* If a1 + u.d is exact, the only rounding happens during + scaling down. */ + if (j == 0) + return v.d * 0x1p-108; + /* If result rounded to zero is not subnormal, no double + rounding will occur. */ + if (v.ieee.exponent > 108) + return (a1 + u.d) * 0x1p-108; + /* If v.d * 0x1p-108 with round to zero is a subnormal above + or equal to DBL_MIN / 2, then v.d * 0x1p-108 shifts mantissa + down just by 1 bit, which means v.ieee.mantissa1 |= j would + change the round bit, not sticky or guard bit. + v.d * 0x1p-108 never normalizes by shifting up, + so round bit plus sticky bit should be already enough + for proper rounding. */ + if (v.ieee.exponent == 108) + { + /* If the exponent would be in the normal range when + rounding to normal precision with unbounded exponent + range, the exact result is known and spurious underflows + must be avoided on systems detecting tininess after + rounding. */ + if (TININESS_AFTER_ROUNDING) + { + w.d = a1 + u.d; + if (w.ieee.exponent == 109) + return w.d * 0x1p-108; + } + /* v.ieee.mantissa1 & 2 is LSB bit of the result before rounding, + v.ieee.mantissa1 & 1 is the round bit and j is our sticky + bit. */ + w.d = 0.0; + w.ieee.mantissa1 = ((v.ieee.mantissa1 & 3) << 1) | j; + w.ieee.negative = v.ieee.negative; + v.ieee.mantissa1 &= ~3U; + v.d *= 0x1p-108; + w.d *= 0x1p-2; + return v.d + w.d; + } + v.ieee.mantissa1 |= j; + return v.d * 0x1p-108; + } +} +#ifndef __fma +weak_alias (__fma, fma) +#endif + +#ifdef NO_LONG_DOUBLE +strong_alias (__fma, __fmal) +weak_alias (__fmal, fmal) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_fmaf.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fmaf.c new file mode 100644 index 0000000000..e6c0fed64d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fmaf.c @@ -0,0 +1,64 @@ +/* Compute x * y + z as ternary operation. + Copyright (C) 2010-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jakub@redhat.com>, 2010. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <fenv.h> +#include <ieee754.h> +#include <math_private.h> + +/* This implementation relies on double being more than twice as + precise as float and uses rounding to odd in order to avoid problems + with double rounding. + See a paper by Boldo and Melquiond: + http://www.lri.fr/~melquion/doc/08-tc.pdf */ + +float +__fmaf (float x, float y, float z) +{ + fenv_t env; + + /* Multiplication is always exact. */ + double temp = (double) x * (double) y; + + /* Ensure correct sign of an exact zero result by performing the + addition in the original rounding mode in that case. */ + if (temp == -z) + return (float) temp + z; + + union ieee754_double u; + + libc_feholdexcept_setround (&env, FE_TOWARDZERO); + + /* Perform addition with round to odd. */ + u.d = temp + (double) z; + /* Ensure the addition is not scheduled after fetestexcept call. */ + math_force_eval (u.d); + + /* Reset rounding mode and test for inexact simultaneously. */ + int j = libc_feupdateenv_test (&env, FE_INEXACT) != 0; + + if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7ff) + u.ieee.mantissa1 |= j; + + /* And finally truncation with round to nearest. */ + return (float) u.d; +} +#ifndef __fmaf +weak_alias (__fmaf, fmaf) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_fpclassify.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fpclassify.c new file mode 100644 index 0000000000..3fa9117ff0 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fpclassify.c @@ -0,0 +1,43 @@ +/* Return classification value corresponding to argument. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> + + +int +__fpclassify (double x) +{ + u_int32_t hx, lx; + int retval = FP_NORMAL; + + EXTRACT_WORDS (hx, lx, x); + lx |= hx & 0xfffff; + hx &= 0x7ff00000; + if ((hx | lx) == 0) + retval = FP_ZERO; + else if (hx == 0) + retval = FP_SUBNORMAL; + else if (hx == 0x7ff00000) + retval = lx != 0 ? FP_NAN : FP_INFINITE; + + return retval; +} +libm_hidden_def (__fpclassify) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_frexp.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_frexp.c new file mode 100644 index 0000000000..874214ec7c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_frexp.c @@ -0,0 +1,58 @@ +/* @(#)s_frexp.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_frexp.c,v 1.9 1995/05/10 20:47:24 jtc Exp $"; +#endif + +/* + * for non-zero x + * x = frexp(arg,&exp); + * return a double fp quantity x such that 0.5 <= |x| <1.0 + * and the corresponding binary exponent "exp". That is + * arg = x*2^exp. + * If arg is inf, 0.0, or NaN, then frexp(arg,&exp) returns arg + * with *exp=0. + */ + +#include <math.h> +#include <math_private.h> + +static const double + two54 = 1.80143985094819840000e+16; /* 0x43500000, 0x00000000 */ + +double +__frexp (double x, int *eptr) +{ + int32_t hx, ix, lx; + EXTRACT_WORDS (hx, lx, x); + ix = 0x7fffffff & hx; + *eptr = 0; + if (ix >= 0x7ff00000 || ((ix | lx) == 0)) + return x + x; /* 0,inf,nan */ + if (ix < 0x00100000) /* subnormal */ + { + x *= two54; + GET_HIGH_WORD (hx, x); + ix = hx & 0x7fffffff; + *eptr = -54; + } + *eptr += (ix >> 20) - 1022; + hx = (hx & 0x800fffff) | 0x3fe00000; + SET_HIGH_WORD (x, hx); + return x; +} +weak_alias (__frexp, frexp) +#ifdef NO_LONG_DOUBLE +strong_alias (__frexp, __frexpl) +weak_alias (__frexp, frexpl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_fromfp.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fromfp.c new file mode 100644 index 0000000000..92fbe0c162 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fromfp.c @@ -0,0 +1,7 @@ +#define UNSIGNED 0 +#define INEXACT 0 +#define FUNC fromfp +#include <s_fromfp_main.c> +#ifdef NO_LONG_DOUBLE +weak_alias (fromfp, fromfpl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_fromfp_main.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fromfp_main.c new file mode 100644 index 0000000000..ca0aa82092 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fromfp_main.c @@ -0,0 +1,82 @@ +/* Round to integer type. dbl-64 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <errno.h> +#include <fenv.h> +#include <math.h> +#include <math_private.h> +#include <stdbool.h> +#include <stdint.h> + +#define BIAS 0x3ff +#define MANT_DIG 53 + +#if UNSIGNED +# define RET_TYPE uintmax_t +#else +# define RET_TYPE intmax_t +#endif + +#include <fromfp.h> + +RET_TYPE +FUNC (double x, int round, unsigned int width) +{ + if (width > INTMAX_WIDTH) + width = INTMAX_WIDTH; + uint64_t ix; + EXTRACT_WORDS64 (ix, x); + bool negative = (ix & 0x8000000000000000ULL) != 0; + if (width == 0) + return fromfp_domain_error (negative, width); + ix &= 0x7fffffffffffffffULL; + if (ix == 0) + return 0; + int exponent = ix >> (MANT_DIG - 1); + exponent -= BIAS; + int max_exponent = fromfp_max_exponent (negative, width); + if (exponent > max_exponent) + return fromfp_domain_error (negative, width); + + ix &= ((1ULL << (MANT_DIG - 1)) - 1); + ix |= 1ULL << (MANT_DIG - 1); + uintmax_t uret; + bool half_bit, more_bits; + if (exponent >= MANT_DIG - 1) + { + uret = ix; + uret <<= exponent - (MANT_DIG - 1); + half_bit = false; + more_bits = false; + } + else if (exponent >= -1) + { + uint64_t h = 1ULL << (MANT_DIG - 2 - exponent); + half_bit = (ix & h) != 0; + more_bits = (ix & (h - 1)) != 0; + uret = ix >> (MANT_DIG - 1 - exponent); + } + else + { + uret = 0; + half_bit = false; + more_bits = true; + } + return fromfp_round_and_return (negative, uret, half_bit, more_bits, round, + exponent, max_exponent, width); +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_fromfpx.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fromfpx.c new file mode 100644 index 0000000000..bbfb969813 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_fromfpx.c @@ -0,0 +1,7 @@ +#define UNSIGNED 0 +#define INEXACT 1 +#define FUNC fromfpx +#include <s_fromfp_main.c> +#ifdef NO_LONG_DOUBLE +weak_alias (fromfpx, fromfpxl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_getpayload.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_getpayload.c new file mode 100644 index 0000000000..63288e0f45 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_getpayload.c @@ -0,0 +1,37 @@ +/* Get NaN payload. dbl-64 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fix-int-fp-convert-zero.h> +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +double +getpayload (const double *x) +{ + uint32_t hx, lx; + EXTRACT_WORDS (hx, lx, *x); + hx &= 0x7ffff; + uint64_t ix = ((uint64_t) hx << 32) | lx; + if (FIX_INT_FP_CONVERT_ZERO && ix == 0) + return 0.0f; + return (double) ix; +} +#ifdef NO_LONG_DOUBLE +weak_alias (getpayload, getpayloadl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_isinf.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_isinf.c new file mode 100644 index 0000000000..c0ad54538a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_isinf.c @@ -0,0 +1,36 @@ +/* + * Written by J.T. Conklin <jtc@netbsd.org>. + * Changed to return -1 for -Inf by Ulrich Drepper <drepper@cygnus.com>. + * Public domain. + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_isinf.c,v 1.3 1995/05/11 23:20:14 jtc Exp $"; +#endif + +/* + * isinf(x) returns 1 is x is inf, -1 if x is -inf, else 0; + * no branching! + */ + +#include <math.h> +#include <math_private.h> +#include <shlib-compat.h> + +int +__isinf (double x) +{ + int32_t hx, lx; + EXTRACT_WORDS (hx, lx, x); + lx |= (hx & 0x7fffffff) ^ 0x7ff00000; + lx |= -lx; + return ~(lx >> 31) & (hx >> 30); +} +hidden_def (__isinf) +weak_alias (__isinf, isinf) +#ifdef NO_LONG_DOUBLE +# if defined LDBL_CLASSIFY_COMPAT && SHLIB_COMPAT (libc, GLIBC_2_0, GLIBC_2_23) +compat_symbol (libc, __isinf, __isinfl, GLIBC_2_0); +# endif +weak_alias (__isinf, isinfl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_isnan.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_isnan.c new file mode 100644 index 0000000000..2174d988d8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_isnan.c @@ -0,0 +1,44 @@ +/* @(#)s_isnan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_isnan.c,v 1.8 1995/05/10 20:47:36 jtc Exp $"; +#endif + +/* + * isnan(x) returns 1 is x is nan, else 0; + * no branching! + */ + +#include <math.h> +#include <math_private.h> +#include <shlib-compat.h> + +#undef __isnan +int +__isnan (double x) +{ + int32_t hx, lx; + EXTRACT_WORDS (hx, lx, x); + hx &= 0x7fffffff; + hx |= (u_int32_t) (lx | (-lx)) >> 31; + hx = 0x7ff00000 - hx; + return (int) (((u_int32_t) hx) >> 31); +} +hidden_def (__isnan) +weak_alias (__isnan, isnan) +#ifdef NO_LONG_DOUBLE +# if defined LDBL_CLASSIFY_COMPAT && SHLIB_COMPAT (libc, GLIBC_2_0, GLIBC_2_23) +compat_symbol (libc, __isnan, __isnanl, GLIBC_2_0); +# endif +weak_alias (__isnan, isnanl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_issignaling.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_issignaling.c new file mode 100644 index 0000000000..09e12f9a6a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_issignaling.c @@ -0,0 +1,47 @@ +/* Test for signaling NaN. + Copyright (C) 2013-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> + +int +__issignaling (double x) +{ +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN + u_int32_t hxi; + GET_HIGH_WORD (hxi, x); + /* We only have to care about the high-order bit of x's significand, because + having it set (sNaN) already makes the significand different from that + used to designate infinity. */ + return (hxi & 0x7ff80000) == 0x7ff80000; +#else + u_int32_t hxi, lxi; + EXTRACT_WORDS (hxi, lxi, x); + /* To keep the following comparison simple, toggle the quiet/signaling bit, + so that it is set for sNaNs. This is inverse to IEEE 754-2008 (as well as + common practice for IEEE 754-1985). */ + hxi ^= 0x00080000; + /* If lxi != 0, then set any suitable bit of the significand in hxi. */ + hxi |= (lxi | -lxi) >> 31; + /* We have to compare for greater (instead of greater or equal), because x's + significand being all-zero designates infinity not NaN. */ + return (hxi & 0x7fffffff) > 0x7ff80000; +#endif +} +libm_hidden_def (__issignaling) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_llrint.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_llrint.c new file mode 100644 index 0000000000..08781c3acd --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_llrint.c @@ -0,0 +1,103 @@ +/* Round argument to nearest integral value according to current rounding + direction. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <limits.h> +#include <math.h> + +#include <math_private.h> +#include <fix-fp-int-convert-overflow.h> + +static const double two52[2] = +{ + 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ + -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ +}; + + +long long int +__llrint (double x) +{ + int32_t j0; + u_int32_t i1, i0; + long long int result; + double w; + double t; + int sx; + + EXTRACT_WORDS (i0, i1, x); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + sx = i0 >> 31; + i0 &= 0xfffff; + i0 |= 0x100000; + + if (j0 < 20) + { + w = math_narrow_eval (two52[sx] + x); + t = w - two52[sx]; + EXTRACT_WORDS (i0, i1, t); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + i0 &= 0xfffff; + i0 |= 0x100000; + + result = (j0 < 0 ? 0 : i0 >> (20 - j0)); + } + else if (j0 < (int32_t) (8 * sizeof (long long int)) - 1) + { + if (j0 >= 52) + result = (((long long int) i0 << 32) | i1) << (j0 - 52); + else + { + w = math_narrow_eval (two52[sx] + x); + t = w - two52[sx]; + EXTRACT_WORDS (i0, i1, t); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + i0 &= 0xfffff; + i0 |= 0x100000; + + if (j0 == 20) + result = (long long int) i0; + else + result = ((long long int) i0 << (j0 - 20)) | (i1 >> (52 - j0)); + } + } + else + { +#ifdef FE_INVALID + /* The number is too large. Unless it rounds to LLONG_MIN, + FE_INVALID must be raised and the return value is + unspecified. */ + if (FIX_DBL_LLONG_CONVERT_OVERFLOW && x != (double) LLONG_MIN) + { + feraiseexcept (FE_INVALID); + return sx == 0 ? LLONG_MAX : LLONG_MIN; + } +#endif + return (long long int) x; + } + + return sx ? -result : result; +} + +weak_alias (__llrint, llrint) +#ifdef NO_LONG_DOUBLE +strong_alias (__llrint, __llrintl) +weak_alias (__llrint, llrintl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_llround.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_llround.c new file mode 100644 index 0000000000..8790e9df57 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_llround.c @@ -0,0 +1,91 @@ +/* Round double value to long long int. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <limits.h> +#include <math.h> + +#include <math_private.h> +#include <fix-fp-int-convert-overflow.h> + + +long long int +__llround (double x) +{ + int32_t j0; + u_int32_t i1, i0; + long long int result; + int sign; + + EXTRACT_WORDS (i0, i1, x); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + sign = (i0 & 0x80000000) != 0 ? -1 : 1; + i0 &= 0xfffff; + i0 |= 0x100000; + + if (j0 < 20) + { + if (j0 < 0) + return j0 < -1 ? 0 : sign; + else + { + i0 += 0x80000 >> j0; + + result = i0 >> (20 - j0); + } + } + else if (j0 < (int32_t) (8 * sizeof (long long int)) - 1) + { + if (j0 >= 52) + result = (((long long int) i0 << 32) | i1) << (j0 - 52); + else + { + u_int32_t j = i1 + (0x80000000 >> (j0 - 20)); + if (j < i1) + ++i0; + + if (j0 == 20) + result = (long long int) i0; + else + result = ((long long int) i0 << (j0 - 20)) | (j >> (52 - j0)); + } + } + else + { +#ifdef FE_INVALID + /* The number is too large. Unless it rounds to LLONG_MIN, + FE_INVALID must be raised and the return value is + unspecified. */ + if (FIX_DBL_LLONG_CONVERT_OVERFLOW && x != (double) LLONG_MIN) + { + feraiseexcept (FE_INVALID); + return sign == 1 ? LLONG_MAX : LLONG_MIN; + } +#endif + return (long long int) x; + } + + return sign * result; +} + +weak_alias (__llround, llround) +#ifdef NO_LONG_DOUBLE +strong_alias (__llround, __llroundl) +weak_alias (__llround, llroundl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_log1p.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_log1p.c new file mode 100644 index 0000000000..340f6377f7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_log1p.c @@ -0,0 +1,195 @@ +/* @(#)s_log1p.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25, + for performance improvement on pipelined processors. + */ + +/* double log1p(double x) + * + * Method : + * 1. Argument Reduction: find k and f such that + * 1+x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * Note. If k=0, then f=x is exact. However, if k!=0, then f + * may not be representable exactly. In that case, a correction + * term is need. Let u=1+x rounded. Let c = (1+x)-u, then + * log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u), + * and add back the correction term c/u. + * (Note: when x > 2**53, one can simply return log(x)) + * + * 2. Approximation of log1p(f). + * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * = 2s + s*R + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error + * of this polynomial approximation is bounded by 2**-58.45. In + * other words, + * 2 4 6 8 10 12 14 + * R(z) ~ Lp1*s +Lp2*s +Lp3*s +Lp4*s +Lp5*s +Lp6*s +Lp7*s + * (the values of Lp1 to Lp7 are listed in the program) + * and + * | 2 14 | -58.45 + * | Lp1*s +...+Lp7*s - R(z) | <= 2 + * | | + * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. + * In order to guarantee error in log below 1ulp, we compute log + * by + * log1p(f) = f - (hfsq - s*(hfsq+R)). + * + * 3. Finally, log1p(x) = k*ln2 + log1p(f). + * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) + * Here ln2 is split into two floating point number: + * ln2_hi + ln2_lo, + * where n*ln2_hi is always exact for |n| < 2000. + * + * Special cases: + * log1p(x) is NaN with signal if x < -1 (including -INF) ; + * log1p(+INF) is +INF; log1p(-1) is -INF with signal; + * log1p(NaN) is that NaN with no signal. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + * + * Note: Assuming log() return accurate answer, the following + * algorithm can be used to compute log1p(x) to within a few ULP: + * + * u = 1+x; + * if(u==1.0) return x ; else + * return log(u)*(x/(u-1.0)); + * + * See HP-15C Advanced Functions Handbook, p.193. + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const double + ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ + ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ + two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ + Lp[] = { 0.0, 6.666666666666735130e-01, /* 3FE55555 55555593 */ + 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ + 2.857142874366239149e-01, /* 3FD24924 94229359 */ + 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ + 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ + 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ + 1.479819860511658591e-01 }; /* 3FC2F112 DF3E5244 */ + +static const double zero = 0.0; + +double +__log1p (double x) +{ + double hfsq, f, c, s, z, R, u, z2, z4, z6, R1, R2, R3, R4; + int32_t k, hx, hu, ax; + + GET_HIGH_WORD (hx, x); + ax = hx & 0x7fffffff; + + k = 1; + if (hx < 0x3FDA827A) /* x < 0.41422 */ + { + if (__glibc_unlikely (ax >= 0x3ff00000)) /* x <= -1.0 */ + { + if (x == -1.0) + return -two54 / zero; /* log1p(-1)=-inf */ + else + return (x - x) / (x - x); /* log1p(x<-1)=NaN */ + } + if (__glibc_unlikely (ax < 0x3e200000)) /* |x| < 2**-29 */ + { + math_force_eval (two54 + x); /* raise inexact */ + if (ax < 0x3c900000) /* |x| < 2**-54 */ + { + math_check_force_underflow (x); + return x; + } + else + return x - x * x * 0.5; + } + if (hx > 0 || hx <= ((int32_t) 0xbfd2bec3)) + { + k = 0; f = x; hu = 1; + } /* -0.2929<x<0.41422 */ + } + else if (__glibc_unlikely (hx >= 0x7ff00000)) + return x + x; + if (k != 0) + { + if (hx < 0x43400000) + { + u = 1.0 + x; + GET_HIGH_WORD (hu, u); + k = (hu >> 20) - 1023; + c = (k > 0) ? 1.0 - (u - x) : x - (u - 1.0); /* correction term */ + c /= u; + } + else + { + u = x; + GET_HIGH_WORD (hu, u); + k = (hu >> 20) - 1023; + c = 0; + } + hu &= 0x000fffff; + if (hu < 0x6a09e) + { + SET_HIGH_WORD (u, hu | 0x3ff00000); /* normalize u */ + } + else + { + k += 1; + SET_HIGH_WORD (u, hu | 0x3fe00000); /* normalize u/2 */ + hu = (0x00100000 - hu) >> 2; + } + f = u - 1.0; + } + hfsq = 0.5 * f * f; + if (hu == 0) /* |f| < 2**-20 */ + { + if (f == zero) + { + if (k == 0) + return zero; + else + { + c += k * ln2_lo; return k * ln2_hi + c; + } + } + R = hfsq * (1.0 - 0.66666666666666666 * f); + if (k == 0) + return f - R; + else + return k * ln2_hi - ((R - (k * ln2_lo + c)) - f); + } + s = f / (2.0 + f); + z = s * s; + R1 = z * Lp[1]; z2 = z * z; + R2 = Lp[2] + z * Lp[3]; z4 = z2 * z2; + R3 = Lp[4] + z * Lp[5]; z6 = z4 * z2; + R4 = Lp[6] + z * Lp[7]; + R = R1 + z2 * R2 + z4 * R3 + z6 * R4; + if (k == 0) + return f - (hfsq - s * (hfsq + R)); + else + return k * ln2_hi - ((hfsq - (s * (hfsq + R) + (k * ln2_lo + c))) - f); +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_logb.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_logb.c new file mode 100644 index 0000000000..3a26b18f78 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_logb.c @@ -0,0 +1,52 @@ +/* @(#)s_logb.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * double logb(x) + * IEEE 754 logb. Included to pass IEEE test suite. Not recommend. + * Use ilogb instead. + */ + +#include <math.h> +#include <math_private.h> +#include <fix-int-fp-convert-zero.h> + +double +__logb (double x) +{ + int32_t lx, ix, rix; + + EXTRACT_WORDS (ix, lx, x); + ix &= 0x7fffffff; /* high |x| */ + if ((ix | lx) == 0) + return -1.0 / fabs (x); + if (ix >= 0x7ff00000) + return x * x; + if (__glibc_unlikely ((rix = ix >> 20) == 0)) + { + /* POSIX specifies that denormal number is treated as + though it were normalized. */ + int ma; + if (ix == 0) + ma = __builtin_clz (lx) + 32; + else + ma = __builtin_clz (ix); + rix -= ma - 12; + } + if (FIX_INT_FP_CONVERT_ZERO && rix == 1023) + return 0.0; + return (double) (rix - 1023); +} +weak_alias (__logb, logb) +#ifdef NO_LONG_DOUBLE +strong_alias (__logb, __logbl) weak_alias (__logb, logbl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_lrint.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_lrint.c new file mode 100644 index 0000000000..ac610bfbd0 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_lrint.c @@ -0,0 +1,127 @@ +/* Round argument to nearest integral value according to current rounding + direction. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <limits.h> +#include <math.h> + +#include <math_private.h> +#include <fix-fp-int-convert-overflow.h> + +static const double two52[2] = +{ + 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ + -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ +}; + + +long int +__lrint (double x) +{ + int32_t j0; + u_int32_t i0, i1; + double w; + double t; + long int result; + int sx; + + EXTRACT_WORDS (i0, i1, x); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + sx = i0 >> 31; + i0 &= 0xfffff; + i0 |= 0x100000; + + if (j0 < 20) + { + w = math_narrow_eval (two52[sx] + x); + t = w - two52[sx]; + EXTRACT_WORDS (i0, i1, t); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + i0 &= 0xfffff; + i0 |= 0x100000; + + result = (j0 < 0 ? 0 : i0 >> (20 - j0)); + } + else if (j0 < (int32_t) (8 * sizeof (long int)) - 1) + { + if (j0 >= 52) + result = ((long int) i0 << (j0 - 20)) | ((long int) i1 << (j0 - 52)); + else + { +#if defined FE_INVALID || defined FE_INEXACT + /* X < LONG_MAX + 1 implied by J0 < 31. */ + if (sizeof (long int) == 4 + && x > (double) LONG_MAX) + { + /* In the event of overflow we must raise the "invalid" + exception, but not "inexact". */ + t = __nearbyint (x); + feraiseexcept (t == LONG_MAX ? FE_INEXACT : FE_INVALID); + } + else +#endif + { + w = math_narrow_eval (two52[sx] + x); + t = w - two52[sx]; + } + EXTRACT_WORDS (i0, i1, t); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + i0 &= 0xfffff; + i0 |= 0x100000; + + if (j0 == 20) + result = (long int) i0; + else + result = ((long int) i0 << (j0 - 20)) | (i1 >> (52 - j0)); + } + } + else + { + /* The number is too large. Unless it rounds to LONG_MIN, + FE_INVALID must be raised and the return value is + unspecified. */ +#if defined FE_INVALID || defined FE_INEXACT + if (sizeof (long int) == 4 + && x < (double) LONG_MIN + && x > (double) LONG_MIN - 1.0) + { + /* If truncation produces LONG_MIN, the cast will not raise + the exception, but may raise "inexact". */ + t = __nearbyint (x); + feraiseexcept (t == LONG_MIN ? FE_INEXACT : FE_INVALID); + return LONG_MIN; + } + else if (FIX_DBL_LONG_CONVERT_OVERFLOW && x != (double) LONG_MIN) + { + feraiseexcept (FE_INVALID); + return sx == 0 ? LONG_MAX : LONG_MIN; + } +#endif + return (long int) x; + } + + return sx ? -result : result; +} + +weak_alias (__lrint, lrint) +#ifdef NO_LONG_DOUBLE +strong_alias (__lrint, __lrintl) +weak_alias (__lrint, lrintl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_lround.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_lround.c new file mode 100644 index 0000000000..df4775e344 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_lround.c @@ -0,0 +1,113 @@ +/* Round double value to long int. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <limits.h> +#include <math.h> + +#include <math_private.h> +#include <fix-fp-int-convert-overflow.h> + + +long int +__lround (double x) +{ + int32_t j0; + u_int32_t i1, i0; + long int result; + int sign; + + EXTRACT_WORDS (i0, i1, x); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + sign = (i0 & 0x80000000) != 0 ? -1 : 1; + i0 &= 0xfffff; + i0 |= 0x100000; + + if (j0 < 20) + { + if (j0 < 0) + return j0 < -1 ? 0 : sign; + else + { + i0 += 0x80000 >> j0; + + result = i0 >> (20 - j0); + } + } + else if (j0 < (int32_t) (8 * sizeof (long int)) - 1) + { + if (j0 >= 52) + result = ((long int) i0 << (j0 - 20)) | ((long int) i1 << (j0 - 52)); + else + { + u_int32_t j = i1 + (0x80000000 >> (j0 - 20)); + if (j < i1) + ++i0; + + if (j0 == 20) + result = (long int) i0; + else + { + result = ((long int) i0 << (j0 - 20)) | (j >> (52 - j0)); +#ifdef FE_INVALID + if (sizeof (long int) == 4 + && sign == 1 + && result == LONG_MIN) + /* Rounding brought the value out of range. */ + feraiseexcept (FE_INVALID); +#endif + } + } + } + else + { + /* The number is too large. Unless it rounds to LONG_MIN, + FE_INVALID must be raised and the return value is + unspecified. */ +#ifdef FE_INVALID + if (FIX_DBL_LONG_CONVERT_OVERFLOW + && !(sign == -1 + && (sizeof (long int) == 4 + ? x > (double) LONG_MIN - 0.5 + : x >= (double) LONG_MIN))) + { + feraiseexcept (FE_INVALID); + return sign == 1 ? LONG_MAX : LONG_MIN; + } + else if (!FIX_DBL_LONG_CONVERT_OVERFLOW + && sizeof (long int) == 4 + && x <= (double) LONG_MIN - 0.5) + { + /* If truncation produces LONG_MIN, the cast will not raise + the exception, but may raise "inexact". */ + feraiseexcept (FE_INVALID); + return LONG_MIN; + } +#endif + return (long int) x; + } + + return sign * result; +} + +weak_alias (__lround, lround) +#ifdef NO_LONG_DOUBLE +strong_alias (__lround, __lroundl) +weak_alias (__lround, lroundl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_modf.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_modf.c new file mode 100644 index 0000000000..0a1e13008f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_modf.c @@ -0,0 +1,86 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * modf(double x, double *iptr) + * return fraction part of x, and return x's integral part in *iptr. + * Method: + * Bit twiddling. + * + * Exception: + * No exception. + */ + +#include <math.h> +#include <math_private.h> + +static const double one = 1.0; + +double +__modf (double x, double *iptr) +{ + int32_t i0, i1, j0; + u_int32_t i; + EXTRACT_WORDS (i0, i1, x); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; /* exponent of x */ + if (j0 < 20) /* integer part in high x */ + { + if (j0 < 0) /* |x|<1 */ + { + INSERT_WORDS (*iptr, i0 & 0x80000000, 0); /* *iptr = +-0 */ + return x; + } + else + { + i = (0x000fffff) >> j0; + if (((i0 & i) | i1) == 0) /* x is integral */ + { + *iptr = x; + INSERT_WORDS (x, i0 & 0x80000000, 0); /* return +-0 */ + return x; + } + else + { + INSERT_WORDS (*iptr, i0 & (~i), 0); + return x - *iptr; + } + } + } + else if (__glibc_unlikely (j0 > 51)) /* no fraction part */ + { + *iptr = x * one; + /* We must handle NaNs separately. */ + if (j0 == 0x400 && ((i0 & 0xfffff) | i1)) + return x * one; + INSERT_WORDS (x, i0 & 0x80000000, 0); /* return +-0 */ + return x; + } + else /* fraction part in low x */ + { + i = ((u_int32_t) (0xffffffff)) >> (j0 - 20); + if ((i1 & i) == 0) /* x is integral */ + { + *iptr = x; + INSERT_WORDS (x, i0 & 0x80000000, 0); /* return +-0 */ + return x; + } + else + { + INSERT_WORDS (*iptr, i0, i1 & (~i)); + return x - *iptr; + } + } +} +weak_alias (__modf, modf) +#ifdef NO_LONG_DOUBLE +strong_alias (__modf, __modfl) +weak_alias (__modf, modfl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_nearbyint.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_nearbyint.c new file mode 100644 index 0000000000..dec0c5d6ee --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_nearbyint.c @@ -0,0 +1,78 @@ +/* Adapted for use as nearbyint by Ulrich Drepper <drepper@cygnus.com>. */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_rint.c,v 1.8 1995/05/10 20:48:04 jtc Exp $"; +#endif + +/* + * rint(x) + * Return x rounded to integral value according to the prevailing + * rounding mode. + * Method: + * Using floating addition. + * Exception: + * Inexact flag raised if x not equal to rint(x). + */ + +#include <fenv.h> +#include <math.h> +#include <math_private.h> + +static const double + TWO52[2] = { + 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ + -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ +}; + +double +__nearbyint (double x) +{ + fenv_t env; + int32_t i0, j0, sx; + double w, t; + GET_HIGH_WORD (i0, x); + sx = (i0 >> 31) & 1; + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + if (j0 < 52) + { + if (j0 < 0) + { + libc_feholdexcept (&env); + w = TWO52[sx] + x; + t = w - TWO52[sx]; + math_force_eval (t); + libc_fesetenv (&env); + GET_HIGH_WORD (i0, t); + SET_HIGH_WORD (t, (i0 & 0x7fffffff) | (sx << 31)); + return t; + } + } + else + { + if (j0 == 0x400) + return x + x; /* inf or NaN */ + else + return x; /* x is integral */ + } + libc_feholdexcept (&env); + w = TWO52[sx] + x; + t = w - TWO52[sx]; + math_force_eval (t); + libc_fesetenv (&env); + return t; +} +weak_alias (__nearbyint, nearbyint) +#ifdef NO_LONG_DOUBLE +strong_alias (__nearbyint, __nearbyintl) +weak_alias (__nearbyint, nearbyintl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_nexttoward.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_nexttoward.c new file mode 100644 index 0000000000..c68ba98cb3 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_nexttoward.c @@ -0,0 +1 @@ +/* This function is the same as nextafter so we use an alias there. */ diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_nextup.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_nextup.c new file mode 100644 index 0000000000..983bd662b7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_nextup.c @@ -0,0 +1,58 @@ +/* Return the least floating-point number greater than X. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + +/* Return the least floating-point number greater than X. */ +double +__nextup (double x) +{ + int32_t hx, ix; + u_int32_t lx; + + EXTRACT_WORDS (hx, lx, x); + ix = hx & 0x7fffffff; + + if (((ix >= 0x7ff00000) && ((ix - 0x7ff00000) | lx) != 0)) /* x is nan. */ + return x + x; + if ((ix | lx) == 0) + return DBL_TRUE_MIN; + if (hx >= 0) + { /* x > 0. */ + if (isinf (x)) + return x; + lx += 1; + if (lx == 0) + hx += 1; + } + else + { /* x < 0. */ + if (lx == 0) + hx -= 1; + lx -= 1; + } + INSERT_WORDS (x, hx, lx); + return x; +} + +weak_alias (__nextup, nextup) +#ifdef NO_LONG_DOUBLE +strong_alias (__nextup, __nextupl) +weak_alias (__nextup, nextupl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_remquo.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_remquo.c new file mode 100644 index 0000000000..2693c0e62c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_remquo.c @@ -0,0 +1,115 @@ +/* Compute remainder and a congruent to the quotient. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> + + +static const double zero = 0.0; + + +double +__remquo (double x, double y, int *quo) +{ + int32_t hx, hy; + u_int32_t sx, lx, ly; + int cquo, qs; + + EXTRACT_WORDS (hx, lx, x); + EXTRACT_WORDS (hy, ly, y); + sx = hx & 0x80000000; + qs = sx ^ (hy & 0x80000000); + hy &= 0x7fffffff; + hx &= 0x7fffffff; + + /* Purge off exception values. */ + if ((hy | ly) == 0) + return (x * y) / (x * y); /* y = 0 */ + if ((hx >= 0x7ff00000) /* x not finite */ + || ((hy >= 0x7ff00000) /* p is NaN */ + && (((hy - 0x7ff00000) | ly) != 0))) + return (x * y) / (x * y); + + if (hy <= 0x7fbfffff) + x = __ieee754_fmod (x, 8 * y); /* now x < 8y */ + + if (((hx - hy) | (lx - ly)) == 0) + { + *quo = qs ? -1 : 1; + return zero * x; + } + + x = fabs (x); + y = fabs (y); + cquo = 0; + + if (hy <= 0x7fcfffff && x >= 4 * y) + { + x -= 4 * y; + cquo += 4; + } + if (hy <= 0x7fdfffff && x >= 2 * y) + { + x -= 2 * y; + cquo += 2; + } + + if (hy < 0x00200000) + { + if (x + x > y) + { + x -= y; + ++cquo; + if (x + x >= y) + { + x -= y; + ++cquo; + } + } + } + else + { + double y_half = 0.5 * y; + if (x > y_half) + { + x -= y; + ++cquo; + if (x >= y_half) + { + x -= y; + ++cquo; + } + } + } + + *quo = qs ? -cquo : cquo; + + /* Ensure correct sign of zero result in round-downward mode. */ + if (x == 0.0) + x = 0.0; + if (sx) + x = -x; + return x; +} +weak_alias (__remquo, remquo) +#ifdef NO_LONG_DOUBLE +strong_alias (__remquo, __remquol) +weak_alias (__remquo, remquol) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_rint.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_rint.c new file mode 100644 index 0000000000..a9c0d27842 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_rint.c @@ -0,0 +1,67 @@ +/* @(#)s_rint.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * rint(x) + * Return x rounded to integral value according to the prevailing + * rounding mode. + * Method: + * Using floating addition. + * Exception: + * Inexact flag raised if x not equal to rint(x). + */ + +#include <math.h> +#include <math_private.h> + +static const double + TWO52[2] = { + 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ + -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ +}; + +double +__rint (double x) +{ + int32_t i0, j0, sx; + double w, t; + GET_HIGH_WORD (i0, x); + sx = (i0 >> 31) & 1; + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + if (j0 < 52) + { + if (j0 < 0) + { + w = TWO52[sx] + x; + t = w - TWO52[sx]; + GET_HIGH_WORD (i0, t); + SET_HIGH_WORD (t, (i0 & 0x7fffffff) | (sx << 31)); + return t; + } + } + else + { + if (j0 == 0x400) + return x + x; /* inf or NaN */ + else + return x; /* x is integral */ + } + w = TWO52[sx] + x; + return w - TWO52[sx]; +} +#ifndef __rint +weak_alias (__rint, rint) +# ifdef NO_LONG_DOUBLE +strong_alias (__rint, __rintl) +weak_alias (__rint, rintl) +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_round.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_round.c new file mode 100644 index 0000000000..390e3f7180 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_round.c @@ -0,0 +1,83 @@ +/* Round double to integer away from zero. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> + + +double +__round (double x) +{ + int32_t i0, j0; + u_int32_t i1; + + EXTRACT_WORDS (i0, i1, x); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + if (j0 < 20) + { + if (j0 < 0) + { + i0 &= 0x80000000; + if (j0 == -1) + i0 |= 0x3ff00000; + i1 = 0; + } + else + { + u_int32_t i = 0x000fffff >> j0; + if (((i0 & i) | i1) == 0) + /* X is integral. */ + return x; + + i0 += 0x00080000 >> j0; + i0 &= ~i; + i1 = 0; + } + } + else if (j0 > 51) + { + if (j0 == 0x400) + /* Inf or NaN. */ + return x + x; + else + return x; + } + else + { + u_int32_t i = 0xffffffff >> (j0 - 20); + if ((i1 & i) == 0) + /* X is integral. */ + return x; + + u_int32_t j = i1 + (1 << (51 - j0)); + if (j < i1) + i0 += 1; + i1 = j; + i1 &= ~i; + } + + INSERT_WORDS (x, i0, i1); + return x; +} +weak_alias (__round, round) +#ifdef NO_LONG_DOUBLE +strong_alias (__round, __roundl) +weak_alias (__round, roundl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_roundeven.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_roundeven.c new file mode 100644 index 0000000000..78d81a070c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_roundeven.c @@ -0,0 +1,106 @@ +/* Round to nearest integer value, rounding halfway cases to even. + dbl-64 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +#define BIAS 0x3ff +#define MANT_DIG 53 +#define MAX_EXP (2 * BIAS + 1) + +double +roundeven (double x) +{ + uint32_t hx, lx, uhx; + EXTRACT_WORDS (hx, lx, x); + uhx = hx & 0x7fffffff; + int exponent = uhx >> (MANT_DIG - 1 - 32); + if (exponent >= BIAS + MANT_DIG - 1) + { + /* Integer, infinity or NaN. */ + if (exponent == MAX_EXP) + /* Infinity or NaN; quiet signaling NaNs. */ + return x + x; + else + return x; + } + else if (exponent >= BIAS + MANT_DIG - 32) + { + /* Not necessarily an integer; integer bit is in low word. + Locate the bits with exponents 0 and -1. */ + int int_pos = (BIAS + MANT_DIG - 1) - exponent; + int half_pos = int_pos - 1; + uint32_t half_bit = 1U << half_pos; + uint32_t int_bit = 1U << int_pos; + if ((lx & (int_bit | (half_bit - 1))) != 0) + { + /* Carry into the exponent works correctly. No need to test + whether HALF_BIT is set. */ + lx += half_bit; + hx += lx < half_bit; + } + lx &= ~(int_bit - 1); + } + else if (exponent == BIAS + MANT_DIG - 33) + { + /* Not necessarily an integer; integer bit is bottom of high + word, half bit is top of low word. */ + if (((hx & 1) | (lx & 0x7fffffff)) != 0) + { + lx += 0x80000000; + hx += lx < 0x80000000; + } + lx = 0; + } + else if (exponent >= BIAS) + { + /* At least 1; not necessarily an integer, integer bit and half + bit are in the high word. Locate the bits with exponents 0 + and -1 (when the unbiased exponent is 0, the bit with + exponent 0 is implicit, but as the bias is odd it is OK to + take it from the low bit of the exponent). */ + int int_pos = (BIAS + MANT_DIG - 33) - exponent; + int half_pos = int_pos - 1; + uint32_t half_bit = 1U << half_pos; + uint32_t int_bit = 1U << int_pos; + if (((hx & (int_bit | (half_bit - 1))) | lx) != 0) + hx += half_bit; + hx &= ~(int_bit - 1); + lx = 0; + } + else if (exponent == BIAS - 1 && (uhx > 0x3fe00000 || lx != 0)) + { + /* Interval (0.5, 1). */ + hx = (hx & 0x80000000) | 0x3ff00000; + lx = 0; + } + else + { + /* Rounds to 0. */ + hx &= 0x80000000; + lx = 0; + } + INSERT_WORDS (x, hx, lx); + return x; +} +hidden_def (roundeven) +#ifdef NO_LONG_DOUBLE +weak_alias (roundeven, roundevenl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_scalbln.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_scalbln.c new file mode 100644 index 0000000000..32cd12e3b0 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_scalbln.c @@ -0,0 +1,63 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * scalbn (double x, int n) + * scalbn(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include <math.h> +#include <math_private.h> + +static const double + two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ + twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ + huge = 1.0e+300, + tiny = 1.0e-300; + +double +__scalbln (double x, long int n) +{ + int32_t k, hx, lx; + EXTRACT_WORDS (hx, lx, x); + k = (hx & 0x7ff00000) >> 20; /* extract exponent */ + if (__glibc_unlikely (k == 0)) /* 0 or subnormal x */ + { + if ((lx | (hx & 0x7fffffff)) == 0) + return x; /* +-0 */ + x *= two54; + GET_HIGH_WORD (hx, x); + k = ((hx & 0x7ff00000) >> 20) - 54; + } + if (__glibc_unlikely (k == 0x7ff)) + return x + x; /* NaN or Inf */ + if (__glibc_unlikely (n < -50000)) + return tiny * __copysign (tiny, x); /*underflow*/ + if (__glibc_unlikely (n > 50000 || k + n > 0x7fe)) + return huge * __copysign (huge, x); /* overflow */ + /* Now k and n are bounded we know that k = k+n does not + overflow. */ + k = k + n; + if (__glibc_likely (k > 0)) /* normal result */ + { + SET_HIGH_WORD (x, (hx & 0x800fffff) | (k << 20)); return x; + } + if (k <= -54) + return tiny * __copysign (tiny, x); /*underflow*/ + k += 54; /* subnormal result */ + SET_HIGH_WORD (x, (hx & 0x800fffff) | (k << 20)); + return x * twom54; +} +#ifdef NO_LONG_DOUBLE +strong_alias (__scalbln, __scalblnl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_scalbn.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_scalbn.c new file mode 100644 index 0000000000..58c7e1b33a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_scalbn.c @@ -0,0 +1,63 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * scalbn (double x, int n) + * scalbn(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include <math.h> +#include <math_private.h> + +static const double + two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ + twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ + huge = 1.0e+300, + tiny = 1.0e-300; + +double +__scalbn (double x, int n) +{ + int32_t k, hx, lx; + EXTRACT_WORDS (hx, lx, x); + k = (hx & 0x7ff00000) >> 20; /* extract exponent */ + if (__glibc_unlikely (k == 0)) /* 0 or subnormal x */ + { + if ((lx | (hx & 0x7fffffff)) == 0) + return x; /* +-0 */ + x *= two54; + GET_HIGH_WORD (hx, x); + k = ((hx & 0x7ff00000) >> 20) - 54; + } + if (__glibc_unlikely (k == 0x7ff)) + return x + x; /* NaN or Inf */ + if (__glibc_unlikely (n < -50000)) + return tiny * __copysign (tiny, x); /*underflow*/ + if (__glibc_unlikely (n > 50000 || k + n > 0x7fe)) + return huge * __copysign (huge, x); /* overflow */ + /* Now k and n are bounded we know that k = k+n does not + overflow. */ + k = k + n; + if (__glibc_likely (k > 0)) /* normal result */ + { + SET_HIGH_WORD (x, (hx & 0x800fffff) | (k << 20)); return x; + } + if (k <= -54) + return tiny * __copysign (tiny, x); /*underflow*/ + k += 54; /* subnormal result */ + SET_HIGH_WORD (x, (hx & 0x800fffff) | (k << 20)); + return x * twom54; +} +#ifdef NO_LONG_DOUBLE +strong_alias (__scalbn, __scalbnl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_setpayload.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_setpayload.c new file mode 100644 index 0000000000..5ab70dee73 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_setpayload.c @@ -0,0 +1,6 @@ +#define SIG 0 +#define FUNC setpayload +#include <s_setpayload_main.c> +#ifdef NO_LONG_DOUBLE +weak_alias (setpayload, setpayloadl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_setpayload_main.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_setpayload_main.c new file mode 100644 index 0000000000..c6128c7fe4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_setpayload_main.c @@ -0,0 +1,69 @@ +/* Set NaN payload. dbl-64 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +#define SET_HIGH_BIT (HIGH_ORDER_BIT_IS_SET_FOR_SNAN ? SIG : !SIG) +#define BIAS 0x3ff +#define PAYLOAD_DIG 51 +#define EXPLICIT_MANT_DIG 52 + +int +FUNC (double *x, double payload) +{ + uint32_t hx, lx; + EXTRACT_WORDS (hx, lx, payload); + int exponent = hx >> (EXPLICIT_MANT_DIG - 32); + /* Test if argument is (a) negative or too large; (b) too small, + except for 0 when allowed; (c) not an integer. */ + if (exponent >= BIAS + PAYLOAD_DIG + || (exponent < BIAS && !(SET_HIGH_BIT && hx == 0 && lx == 0))) + { + INSERT_WORDS (*x, 0, 0); + return 1; + } + int shift = BIAS + EXPLICIT_MANT_DIG - exponent; + if (shift < 32 + ? (lx & ((1U << shift) - 1)) != 0 + : (lx != 0 || (hx & ((1U << (shift - 32)) - 1)) != 0)) + { + INSERT_WORDS (*x, 0, 0); + return 1; + } + if (exponent != 0) + { + hx &= (1U << (EXPLICIT_MANT_DIG - 32)) - 1; + hx |= 1U << (EXPLICIT_MANT_DIG - 32); + if (shift >= 32) + { + lx = hx >> (shift - 32); + hx = 0; + } + else if (shift != 0) + { + lx = (lx >> shift) | (hx << (32 - shift)); + hx >>= shift; + } + } + hx |= 0x7ff00000 | (SET_HIGH_BIT ? 0x80000 : 0); + INSERT_WORDS (*x, hx, lx); + return 0; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_setpayloadsig.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_setpayloadsig.c new file mode 100644 index 0000000000..c3d1ba1e6e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_setpayloadsig.c @@ -0,0 +1,6 @@ +#define SIG 1 +#define FUNC setpayloadsig +#include <s_setpayload_main.c> +#ifdef NO_LONG_DOUBLE +weak_alias (setpayloadsig, setpayloadsigl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_signbit.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_signbit.c new file mode 100644 index 0000000000..1beab1025c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_signbit.c @@ -0,0 +1,26 @@ +/* Return nonzero value if number is negative. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +int +__signbit (double x) +{ + return __builtin_signbit (x); +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_sin.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_sin.c new file mode 100644 index 0000000000..c258d39e49 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_sin.c @@ -0,0 +1,927 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/****************************************************************************/ +/* */ +/* MODULE_NAME:usncs.c */ +/* */ +/* FUNCTIONS: usin */ +/* ucos */ +/* slow */ +/* slow1 */ +/* slow2 */ +/* sloww */ +/* sloww1 */ +/* sloww2 */ +/* bsloww */ +/* bsloww1 */ +/* bsloww2 */ +/* cslow2 */ +/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h usncs.h */ +/* branred.c sincos32.c dosincos.c mpa.c */ +/* sincos.tbl */ +/* */ +/* An ultimate sin and routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of sin(x) or cos(x) */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round to nearest mode of IEEE 754 standard. */ +/* */ +/****************************************************************************/ + + +#include <errno.h> +#include <float.h> +#include "endian.h" +#include "mydefs.h" +#include "usncs.h" +#include "MathLib.h" +#include <math.h> +#include <math_private.h> +#include <fenv.h> + +/* Helper macros to compute sin of the input values. */ +#define POLYNOMIAL2(xx) ((((s5 * (xx) + s4) * (xx) + s3) * (xx) + s2) * (xx)) + +#define POLYNOMIAL(xx) (POLYNOMIAL2 (xx) + s1) + +/* The computed polynomial is a variation of the Taylor series expansion for + sin(a): + + a - a^3/3! + a^5/5! - a^7/7! + a^9/9! + (1 - a^2) * da / 2 + + The constants s1, s2, s3, etc. are pre-computed values of 1/3!, 1/5! and so + on. The result is returned to LHS and correction in COR. */ +#define TAYLOR_SIN(xx, a, da, cor) \ +({ \ + double t = ((POLYNOMIAL (xx) * (a) - 0.5 * (da)) * (xx) + (da)); \ + double res = (a) + t; \ + (cor) = ((a) - res) + t; \ + res; \ +}) + +/* This is again a variation of the Taylor series expansion with the term + x^3/3! expanded into the following for better accuracy: + + bb * x ^ 3 + 3 * aa * x * x1 * x2 + aa * x1 ^ 3 + aa * x2 ^ 3 + + The correction term is dx and bb + aa = -1/3! + */ +#define TAYLOR_SLOW(x0, dx, cor) \ +({ \ + static const double th2_36 = 206158430208.0; /* 1.5*2**37 */ \ + double xx = (x0) * (x0); \ + double x1 = ((x0) + th2_36) - th2_36; \ + double y = aa * x1 * x1 * x1; \ + double r = (x0) + y; \ + double x2 = ((x0) - x1) + (dx); \ + double t = (((POLYNOMIAL2 (xx) + bb) * xx + 3.0 * aa * x1 * x2) \ + * (x0) + aa * x2 * x2 * x2 + (dx)); \ + t = (((x0) - r) + y) + t; \ + double res = r + t; \ + (cor) = (r - res) + t; \ + res; \ +}) + +#define SINCOS_TABLE_LOOKUP(u, sn, ssn, cs, ccs) \ +({ \ + int4 k = u.i[LOW_HALF] << 2; \ + sn = __sincostab.x[k]; \ + ssn = __sincostab.x[k + 1]; \ + cs = __sincostab.x[k + 2]; \ + ccs = __sincostab.x[k + 3]; \ +}) + +#ifndef SECTION +# define SECTION +#endif + +extern const union +{ + int4 i[880]; + double x[440]; +} __sincostab attribute_hidden; + +static const double + sn3 = -1.66666666666664880952546298448555E-01, + sn5 = 8.33333214285722277379541354343671E-03, + cs2 = 4.99999999999999999999950396842453E-01, + cs4 = -4.16666666666664434524222570944589E-02, + cs6 = 1.38888874007937613028114285595617E-03; + +static const double t22 = 0x1.8p22; + +void __dubsin (double x, double dx, double w[]); +void __docos (double x, double dx, double w[]); +double __mpsin (double x, double dx, bool reduce_range); +double __mpcos (double x, double dx, bool reduce_range); +static double slow (double x); +static double slow1 (double x); +static double slow2 (double x); +static double sloww (double x, double dx, double orig, bool shift_quadrant); +static double sloww1 (double x, double dx, double orig, bool shift_quadrant); +static double sloww2 (double x, double dx, double orig, int n); +static double bsloww (double x, double dx, double orig, int n); +static double bsloww1 (double x, double dx, double orig, int n); +static double bsloww2 (double x, double dx, double orig, int n); +int __branred (double x, double *a, double *aa); +static double cslow2 (double x); + +/* Given a number partitioned into X and DX, this function computes the cosine + of the number by combining the sin and cos of X (as computed by a variation + of the Taylor series) with the values looked up from the sin/cos table to + get the result in RES and a correction value in COR. */ +static inline double +__always_inline +do_cos (double x, double dx, double *corp) +{ + mynumber u; + + if (x < 0) + dx = -dx; + + u.x = big + fabs (x); + x = fabs (x) - (u.x - big) + dx; + + double xx, s, sn, ssn, c, cs, ccs, res, cor; + xx = x * x; + s = x + x * xx * (sn3 + xx * sn5); + c = xx * (cs2 + xx * (cs4 + xx * cs6)); + SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs); + cor = (ccs - s * ssn - cs * c) - sn * s; + res = cs + cor; + cor = (cs - res) + cor; + *corp = cor; + return res; +} + +/* A more precise variant of DO_COS. EPS is the adjustment to the correction + COR. */ +static inline double +__always_inline +do_cos_slow (double x, double dx, double eps, double *corp) +{ + mynumber u; + + if (x <= 0) + dx = -dx; + + u.x = big + fabs (x); + x = fabs (x) - (u.x - big); + + double xx, y, x1, x2, e1, e2, res, cor; + double s, sn, ssn, c, cs, ccs; + xx = x * x; + s = x * xx * (sn3 + xx * sn5); + c = x * dx + xx * (cs2 + xx * (cs4 + xx * cs6)); + SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs); + x1 = (x + t22) - t22; + x2 = (x - x1) + dx; + e1 = (sn + t22) - t22; + e2 = (sn - e1) + ssn; + cor = (ccs - cs * c - e1 * x2 - e2 * x) - sn * s; + y = cs - e1 * x1; + cor = cor + ((cs - y) - e1 * x1); + res = y + cor; + cor = (y - res) + cor; + cor = 1.0005 * cor + __copysign (eps, cor); + *corp = cor; + return res; +} + +/* Given a number partitioned into X and DX, this function computes the sine of + the number by combining the sin and cos of X (as computed by a variation of + the Taylor series) with the values looked up from the sin/cos table to get + the result in RES and a correction value in COR. */ +static inline double +__always_inline +do_sin (double x, double dx, double *corp) +{ + mynumber u; + + if (x <= 0) + dx = -dx; + u.x = big + fabs (x); + x = fabs (x) - (u.x - big); + + double xx, s, sn, ssn, c, cs, ccs, cor, res; + xx = x * x; + s = x + (dx + x * xx * (sn3 + xx * sn5)); + c = x * dx + xx * (cs2 + xx * (cs4 + xx * cs6)); + SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs); + cor = (ssn + s * ccs - sn * c) + cs * s; + res = sn + cor; + cor = (sn - res) + cor; + *corp = cor; + return res; +} + +/* A more precise variant of DO_SIN. EPS is the adjustment to the correction + COR. */ +static inline double +__always_inline +do_sin_slow (double x, double dx, double eps, double *corp) +{ + mynumber u; + + if (x <= 0) + dx = -dx; + u.x = big + fabs (x); + x = fabs (x) - (u.x - big); + + double xx, y, x1, x2, c1, c2, res, cor; + double s, sn, ssn, c, cs, ccs; + xx = x * x; + s = x * xx * (sn3 + xx * sn5); + c = xx * (cs2 + xx * (cs4 + xx * cs6)); + SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs); + x1 = (x + t22) - t22; + x2 = (x - x1) + dx; + c1 = (cs + t22) - t22; + c2 = (cs - c1) + ccs; + cor = (ssn + s * ccs + cs * s + c2 * x + c1 * x2 - sn * x * dx) - sn * c; + y = sn + c1 * x1; + cor = cor + ((sn - y) + c1 * x1); + res = y + cor; + cor = (y - res) + cor; + cor = 1.0005 * cor + __copysign (eps, cor); + *corp = cor; + return res; +} + +/* Reduce range of X and compute sin of a + da. When SHIFT_QUADRANT is true, + the routine returns the cosine of a + da by rotating the quadrant once and + computing the sine of the result. */ +static inline double +__always_inline +reduce_and_compute (double x, bool shift_quadrant) +{ + double retval = 0, a, da; + unsigned int n = __branred (x, &a, &da); + int4 k = (n + shift_quadrant) % 4; + switch (k) + { + case 2: + a = -a; + da = -da; + /* Fall through. */ + case 0: + if (a * a < 0.01588) + retval = bsloww (a, da, x, n); + else + retval = bsloww1 (a, da, x, n); + break; + + case 1: + case 3: + retval = bsloww2 (a, da, x, n); + break; + } + return retval; +} + +static inline int4 +__always_inline +reduce_sincos_1 (double x, double *a, double *da) +{ + mynumber v; + + double t = (x * hpinv + toint); + double xn = t - toint; + v.x = t; + double y = (x - xn * mp1) - xn * mp2; + int4 n = v.i[LOW_HALF] & 3; + double db = xn * mp3; + double b = y - db; + db = (y - b) - db; + + *a = b; + *da = db; + + return n; +} + +/* Compute sin (A + DA). cos can be computed by passing SHIFT_QUADRANT as + true, which results in shifting the quadrant N clockwise. */ +static double +__always_inline +do_sincos_1 (double a, double da, double x, int4 n, bool shift_quadrant) +{ + double xx, retval, res, cor; + double eps = fabs (x) * 1.2e-30; + + int k1 = (n + shift_quadrant) & 3; + switch (k1) + { /* quarter of unit circle */ + case 2: + a = -a; + da = -da; + /* Fall through. */ + case 0: + xx = a * a; + if (xx < 0.01588) + { + /* Taylor series. */ + res = TAYLOR_SIN (xx, a, da, cor); + cor = 1.02 * cor + __copysign (eps, cor); + retval = (res == res + cor) ? res : sloww (a, da, x, shift_quadrant); + } + else + { + res = do_sin (a, da, &cor); + cor = 1.035 * cor + __copysign (eps, cor); + retval = ((res == res + cor) ? __copysign (res, a) + : sloww1 (a, da, x, shift_quadrant)); + } + break; + + case 1: + case 3: + res = do_cos (a, da, &cor); + cor = 1.025 * cor + __copysign (eps, cor); + retval = ((res == res + cor) ? ((n & 2) ? -res : res) + : sloww2 (a, da, x, n)); + break; + } + + return retval; +} + +static inline int4 +__always_inline +reduce_sincos_2 (double x, double *a, double *da) +{ + mynumber v; + + double t = (x * hpinv + toint); + double xn = t - toint; + v.x = t; + double xn1 = (xn + 8.0e22) - 8.0e22; + double xn2 = xn - xn1; + double y = ((((x - xn1 * mp1) - xn1 * mp2) - xn2 * mp1) - xn2 * mp2); + int4 n = v.i[LOW_HALF] & 3; + double db = xn1 * pp3; + t = y - db; + db = (y - t) - db; + db = (db - xn2 * pp3) - xn * pp4; + double b = t + db; + db = (t - b) + db; + + *a = b; + *da = db; + + return n; +} + +/* Compute sin (A + DA). cos can be computed by passing SHIFT_QUADRANT as + true, which results in shifting the quadrant N clockwise. */ +static double +__always_inline +do_sincos_2 (double a, double da, double x, int4 n, bool shift_quadrant) +{ + double res, retval, cor, xx; + + double eps = 1.0e-24; + + int4 k = (n + shift_quadrant) & 3; + + switch (k) + { + case 2: + a = -a; + da = -da; + /* Fall through. */ + case 0: + xx = a * a; + if (xx < 0.01588) + { + /* Taylor series. */ + res = TAYLOR_SIN (xx, a, da, cor); + cor = 1.02 * cor + __copysign (eps, cor); + retval = (res == res + cor) ? res : bsloww (a, da, x, n); + } + else + { + res = do_sin (a, da, &cor); + cor = 1.035 * cor + __copysign (eps, cor); + retval = ((res == res + cor) ? __copysign (res, a) + : bsloww1 (a, da, x, n)); + } + break; + + case 1: + case 3: + res = do_cos (a, da, &cor); + cor = 1.025 * cor + __copysign (eps, cor); + retval = ((res == res + cor) ? ((n & 2) ? -res : res) + : bsloww2 (a, da, x, n)); + break; + } + + return retval; +} + +/*******************************************************************/ +/* An ultimate sin routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of sin(x) */ +/*******************************************************************/ +#ifdef IN_SINCOS +static double +#else +double +SECTION +#endif +__sin (double x) +{ + double xx, res, t, cor; + mynumber u; + int4 k, m; + double retval = 0; + +#ifndef IN_SINCOS + SET_RESTORE_ROUND_53BIT (FE_TONEAREST); +#endif + + u.x = x; + m = u.i[HIGH_HALF]; + k = 0x7fffffff & m; /* no sign */ + if (k < 0x3e500000) /* if x->0 =>sin(x)=x */ + { + math_check_force_underflow (x); + retval = x; + } + /*---------------------------- 2^-26 < |x|< 0.25 ----------------------*/ + else if (k < 0x3fd00000) + { + xx = x * x; + /* Taylor series. */ + t = POLYNOMIAL (xx) * (xx * x); + res = x + t; + cor = (x - res) + t; + retval = (res == res + 1.07 * cor) ? res : slow (x); + } /* else if (k < 0x3fd00000) */ +/*---------------------------- 0.25<|x|< 0.855469---------------------- */ + else if (k < 0x3feb6000) + { + res = do_sin (x, 0, &cor); + retval = (res == res + 1.096 * cor) ? res : slow1 (x); + retval = __copysign (retval, x); + } /* else if (k < 0x3feb6000) */ + +/*----------------------- 0.855469 <|x|<2.426265 ----------------------*/ + else if (k < 0x400368fd) + { + + t = hp0 - fabs (x); + res = do_cos (t, hp1, &cor); + retval = (res == res + 1.020 * cor) ? res : slow2 (x); + retval = __copysign (retval, x); + } /* else if (k < 0x400368fd) */ + +#ifndef IN_SINCOS +/*-------------------------- 2.426265<|x|< 105414350 ----------------------*/ + else if (k < 0x419921FB) + { + double a, da; + int4 n = reduce_sincos_1 (x, &a, &da); + retval = do_sincos_1 (a, da, x, n, false); + } /* else if (k < 0x419921FB ) */ + +/*---------------------105414350 <|x|< 281474976710656 --------------------*/ + else if (k < 0x42F00000) + { + double a, da; + + int4 n = reduce_sincos_2 (x, &a, &da); + retval = do_sincos_2 (a, da, x, n, false); + } /* else if (k < 0x42F00000 ) */ + +/* -----------------281474976710656 <|x| <2^1024----------------------------*/ + else if (k < 0x7ff00000) + retval = reduce_and_compute (x, false); + +/*--------------------- |x| > 2^1024 ----------------------------------*/ + else + { + if (k == 0x7ff00000 && u.i[LOW_HALF] == 0) + __set_errno (EDOM); + retval = x / x; + } +#endif + + return retval; +} + + +/*******************************************************************/ +/* An ultimate cos routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of cos(x) */ +/*******************************************************************/ + +#ifdef IN_SINCOS +static double +#else +double +SECTION +#endif +__cos (double x) +{ + double y, xx, res, cor, a, da; + mynumber u; + int4 k, m; + + double retval = 0; + +#ifndef IN_SINCOS + SET_RESTORE_ROUND_53BIT (FE_TONEAREST); +#endif + + u.x = x; + m = u.i[HIGH_HALF]; + k = 0x7fffffff & m; + + /* |x|<2^-27 => cos(x)=1 */ + if (k < 0x3e400000) + retval = 1.0; + + else if (k < 0x3feb6000) + { /* 2^-27 < |x| < 0.855469 */ + res = do_cos (x, 0, &cor); + retval = (res == res + 1.020 * cor) ? res : cslow2 (x); + } /* else if (k < 0x3feb6000) */ + + else if (k < 0x400368fd) + { /* 0.855469 <|x|<2.426265 */ ; + y = hp0 - fabs (x); + a = y + hp1; + da = (y - a) + hp1; + xx = a * a; + if (xx < 0.01588) + { + res = TAYLOR_SIN (xx, a, da, cor); + cor = 1.02 * cor + __copysign (1.0e-31, cor); + retval = (res == res + cor) ? res : sloww (a, da, x, true); + } + else + { + res = do_sin (a, da, &cor); + cor = 1.035 * cor + __copysign (1.0e-31, cor); + retval = ((res == res + cor) ? __copysign (res, a) + : sloww1 (a, da, x, true)); + } + + } /* else if (k < 0x400368fd) */ + + +#ifndef IN_SINCOS + else if (k < 0x419921FB) + { /* 2.426265<|x|< 105414350 */ + double a, da; + int4 n = reduce_sincos_1 (x, &a, &da); + retval = do_sincos_1 (a, da, x, n, true); + } /* else if (k < 0x419921FB ) */ + + else if (k < 0x42F00000) + { + double a, da; + + int4 n = reduce_sincos_2 (x, &a, &da); + retval = do_sincos_2 (a, da, x, n, true); + } /* else if (k < 0x42F00000 ) */ + + /* 281474976710656 <|x| <2^1024 */ + else if (k < 0x7ff00000) + retval = reduce_and_compute (x, true); + + else + { + if (k == 0x7ff00000 && u.i[LOW_HALF] == 0) + __set_errno (EDOM); + retval = x / x; /* |x| > 2^1024 */ + } +#endif + + return retval; +} + +/************************************************************************/ +/* Routine compute sin(x) for 2^-26 < |x|< 0.25 by Taylor with more */ +/* precision and if still doesn't accurate enough by mpsin or dubsin */ +/************************************************************************/ + +static inline double +__always_inline +slow (double x) +{ + double res, cor, w[2]; + res = TAYLOR_SLOW (x, 0, cor); + if (res == res + 1.0007 * cor) + return res; + + __dubsin (fabs (x), 0, w); + if (w[0] == w[0] + 1.000000001 * w[1]) + return __copysign (w[0], x); + + return __copysign (__mpsin (fabs (x), 0, false), x); +} + +/*******************************************************************************/ +/* Routine compute sin(x) for 0.25<|x|< 0.855469 by __sincostab.tbl and Taylor */ +/* and if result still doesn't accurate enough by mpsin or dubsin */ +/*******************************************************************************/ + +static inline double +__always_inline +slow1 (double x) +{ + double w[2], cor, res; + + res = do_sin_slow (x, 0, 0, &cor); + if (res == res + cor) + return res; + + __dubsin (fabs (x), 0, w); + if (w[0] == w[0] + 1.000000005 * w[1]) + return w[0]; + + return __mpsin (fabs (x), 0, false); +} + +/**************************************************************************/ +/* Routine compute sin(x) for 0.855469 <|x|<2.426265 by __sincostab.tbl */ +/* and if result still doesn't accurate enough by mpsin or dubsin */ +/**************************************************************************/ +static inline double +__always_inline +slow2 (double x) +{ + double w[2], y, y1, y2, cor, res; + + double t = hp0 - fabs (x); + res = do_cos_slow (t, hp1, 0, &cor); + if (res == res + cor) + return res; + + y = fabs (x) - hp0; + y1 = y - hp1; + y2 = (y - y1) - hp1; + __docos (y1, y2, w); + if (w[0] == w[0] + 1.000000005 * w[1]) + return w[0]; + + return __mpsin (fabs (x), 0, false); +} + +/* Compute sin(x + dx) where X is small enough to use Taylor series around zero + and (x + dx) in the first or third quarter of the unit circle. ORIG is the + original value of X for computing error of the result. If the result is not + accurate enough, the routine calls mpsin or dubsin. SHIFT_QUADRANT rotates + the unit circle by 1 to compute the cosine instead of sine. */ +static inline double +__always_inline +sloww (double x, double dx, double orig, bool shift_quadrant) +{ + double y, t, res, cor, w[2], a, da, xn; + mynumber v; + int4 n; + res = TAYLOR_SLOW (x, dx, cor); + + double eps = fabs (orig) * 3.1e-30; + + cor = 1.0005 * cor + __copysign (eps, cor); + + if (res == res + cor) + return res; + + a = fabs (x); + da = (x > 0) ? dx : -dx; + __dubsin (a, da, w); + eps = fabs (orig) * 1.1e-30; + cor = 1.000000001 * w[1] + __copysign (eps, w[1]); + + if (w[0] == w[0] + cor) + return __copysign (w[0], x); + + t = (orig * hpinv + toint); + xn = t - toint; + v.x = t; + y = (orig - xn * mp1) - xn * mp2; + n = (v.i[LOW_HALF] + shift_quadrant) & 3; + da = xn * pp3; + t = y - da; + da = (y - t) - da; + y = xn * pp4; + a = t - y; + da = ((t - a) - y) + da; + + if (n & 2) + { + a = -a; + da = -da; + } + x = fabs (a); + dx = (a > 0) ? da : -da; + __dubsin (x, dx, w); + eps = fabs (orig) * 1.1e-40; + cor = 1.000000001 * w[1] + __copysign (eps, w[1]); + + if (w[0] == w[0] + cor) + return __copysign (w[0], a); + + return shift_quadrant ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true); +} + +/* Compute sin(x + dx) where X is in the first or third quarter of the unit + circle. ORIG is the original value of X for computing error of the result. + If the result is not accurate enough, the routine calls mpsin or dubsin. + SHIFT_QUADRANT rotates the unit circle by 1 to compute the cosine instead of + sine. */ +static inline double +__always_inline +sloww1 (double x, double dx, double orig, bool shift_quadrant) +{ + double w[2], cor, res; + + res = do_sin_slow (x, dx, 3.1e-30 * fabs (orig), &cor); + + if (res == res + cor) + return __copysign (res, x); + + dx = (x > 0 ? dx : -dx); + __dubsin (fabs (x), dx, w); + + double eps = 1.1e-30 * fabs (orig); + cor = 1.000000005 * w[1] + __copysign (eps, w[1]); + + if (w[0] == w[0] + cor) + return __copysign (w[0], x); + + return shift_quadrant ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true); +} + +/***************************************************************************/ +/* Routine compute sin(x+dx) (Double-Length number) where x in second or */ +/* fourth quarter of unit circle.Routine receive also the original value */ +/* and quarter(n= 1or 3)of x for computing error of result.And if result not*/ +/* accurate enough routine calls mpsin1 or dubsin */ +/***************************************************************************/ + +static inline double +__always_inline +sloww2 (double x, double dx, double orig, int n) +{ + double w[2], cor, res; + + res = do_cos_slow (x, dx, 3.1e-30 * fabs (orig), &cor); + + if (res == res + cor) + return (n & 2) ? -res : res; + + dx = x > 0 ? dx : -dx; + __docos (fabs (x), dx, w); + + double eps = 1.1e-30 * fabs (orig); + cor = 1.000000005 * w[1] + __copysign (eps, w[1]); + + if (w[0] == w[0] + cor) + return (n & 2) ? -w[0] : w[0]; + + return (n & 1) ? __mpsin (orig, 0, true) : __mpcos (orig, 0, true); +} + +/***************************************************************************/ +/* Routine compute sin(x+dx) or cos(x+dx) (Double-Length number) where x */ +/* is small enough to use Taylor series around zero and (x+dx) */ +/* in first or third quarter of unit circle.Routine receive also */ +/* (right argument) the original value of x for computing error of */ +/* result.And if result not accurate enough routine calls other routines */ +/***************************************************************************/ + +static inline double +__always_inline +bsloww (double x, double dx, double orig, int n) +{ + double res, cor, w[2], a, da; + + res = TAYLOR_SLOW (x, dx, cor); + cor = 1.0005 * cor + __copysign (1.1e-24, cor); + if (res == res + cor) + return res; + + a = fabs (x); + da = (x > 0) ? dx : -dx; + __dubsin (a, da, w); + cor = 1.000000001 * w[1] + __copysign (1.1e-24, w[1]); + + if (w[0] == w[0] + cor) + return __copysign (w[0], x); + + return (n & 1) ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true); +} + +/***************************************************************************/ +/* Routine compute sin(x+dx) or cos(x+dx) (Double-Length number) where x */ +/* in first or third quarter of unit circle.Routine receive also */ +/* (right argument) the original value of x for computing error of result.*/ +/* And if result not accurate enough routine calls other routines */ +/***************************************************************************/ + +static inline double +__always_inline +bsloww1 (double x, double dx, double orig, int n) +{ + double w[2], cor, res; + + res = do_sin_slow (x, dx, 1.1e-24, &cor); + if (res == res + cor) + return (x > 0) ? res : -res; + + dx = (x > 0) ? dx : -dx; + __dubsin (fabs (x), dx, w); + + cor = 1.000000005 * w[1] + __copysign (1.1e-24, w[1]); + + if (w[0] == w[0] + cor) + return __copysign (w[0], x); + + return (n & 1) ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true); +} + +/***************************************************************************/ +/* Routine compute sin(x+dx) or cos(x+dx) (Double-Length number) where x */ +/* in second or fourth quarter of unit circle.Routine receive also the */ +/* original value and quarter(n= 1or 3)of x for computing error of result. */ +/* And if result not accurate enough routine calls other routines */ +/***************************************************************************/ + +static inline double +__always_inline +bsloww2 (double x, double dx, double orig, int n) +{ + double w[2], cor, res; + + res = do_cos_slow (x, dx, 1.1e-24, &cor); + if (res == res + cor) + return (n & 2) ? -res : res; + + dx = (x > 0) ? dx : -dx; + __docos (fabs (x), dx, w); + + cor = 1.000000005 * w[1] + __copysign (1.1e-24, w[1]); + + if (w[0] == w[0] + cor) + return (n & 2) ? -w[0] : w[0]; + + return (n & 1) ? __mpsin (orig, 0, true) : __mpcos (orig, 0, true); +} + +/************************************************************************/ +/* Routine compute cos(x) for 2^-27 < |x|< 0.25 by Taylor with more */ +/* precision and if still doesn't accurate enough by mpcos or docos */ +/************************************************************************/ + +static inline double +__always_inline +cslow2 (double x) +{ + double w[2], cor, res; + + res = do_cos_slow (x, 0, 0, &cor); + if (res == res + cor) + return res; + + __docos (fabs (x), 0, w); + if (w[0] == w[0] + 1.000000005 * w[1]) + return w[0]; + + return __mpcos (x, 0, false); +} + +#ifndef __cos +weak_alias (__cos, cos) +# ifdef NO_LONG_DOUBLE +strong_alias (__cos, __cosl) +weak_alias (__cos, cosl) +# endif +#endif +#ifndef __sin +weak_alias (__sin, sin) +# ifdef NO_LONG_DOUBLE +strong_alias (__sin, __sinl) +weak_alias (__sin, sinl) +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_sincos.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_sincos.c new file mode 100644 index 0000000000..05cff50ce8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_sincos.c @@ -0,0 +1,113 @@ +/* Compute sine and cosine of argument. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <errno.h> +#include <math.h> + +#include <math_private.h> + +#define __sin __sin_local +#define __cos __cos_local +#define IN_SINCOS 1 +#include "s_sin.c" + +/* Consolidated version of reduce_and_compute in s_sin.c that does range + reduction only once and computes sin and cos together. */ +static inline void +__always_inline +reduce_and_compute_sincos (double x, double *sinx, double *cosx) +{ + double a, da; + unsigned int n = __branred (x, &a, &da); + + n = n & 3; + + if (n == 1 || n == 2) + { + a = -a; + da = -da; + } + + if (n & 1) + { + double *temp = cosx; + cosx = sinx; + sinx = temp; + } + + if (a * a < 0.01588) + *sinx = bsloww (a, da, x, n); + else + *sinx = bsloww1 (a, da, x, n); + *cosx = bsloww2 (a, da, x, n); +} + +void +__sincos (double x, double *sinx, double *cosx) +{ + mynumber u; + int k; + + SET_RESTORE_ROUND_53BIT (FE_TONEAREST); + + u.x = x; + k = 0x7fffffff & u.i[HIGH_HALF]; + + if (k < 0x400368fd) + { + *sinx = __sin_local (x); + *cosx = __cos_local (x); + return; + } + if (k < 0x419921FB) + { + double a, da; + int4 n = reduce_sincos_1 (x, &a, &da); + + *sinx = do_sincos_1 (a, da, x, n, false); + *cosx = do_sincos_1 (a, da, x, n, true); + + return; + } + if (k < 0x42F00000) + { + double a, da; + int4 n = reduce_sincos_2 (x, &a, &da); + + *sinx = do_sincos_2 (a, da, x, n, false); + *cosx = do_sincos_2 (a, da, x, n, true); + + return; + } + if (k < 0x7ff00000) + { + reduce_and_compute_sincos (x, sinx, cosx); + return; + } + + if (isinf (x)) + __set_errno (EDOM); + + *sinx = *cosx = x / x; +} +weak_alias (__sincos, sincos) +#ifdef NO_LONG_DOUBLE +strong_alias (__sincos, __sincosl) +weak_alias (__sincos, sincosl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_tan.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_tan.c new file mode 100644 index 0000000000..b2a8681a6d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_tan.c @@ -0,0 +1,848 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/*********************************************************************/ +/* MODULE_NAME: utan.c */ +/* */ +/* FUNCTIONS: utan */ +/* tanMp */ +/* */ +/* FILES NEEDED:dla.h endian.h mpa.h mydefs.h utan.h */ +/* branred.c sincos32.c mptan.c */ +/* utan.tbl */ +/* */ +/* An ultimate tan routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of tan(x). */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round to nearest mode of IEEE 754 standard. */ +/* */ +/*********************************************************************/ + +#include <errno.h> +#include <float.h> +#include "endian.h" +#include <dla.h> +#include "mpa.h" +#include "MathLib.h" +#include <math.h> +#include <math_private.h> +#include <fenv.h> +#include <stap-probe.h> + +#ifndef SECTION +# define SECTION +#endif + +static double tanMp (double); +void __mptan (double, mp_no *, int); + +double +SECTION +tan (double x) +{ +#include "utan.h" +#include "utan.tbl" + + int ux, i, n; + double a, da, a2, b, db, c, dc, c1, cc1, c2, cc2, c3, cc3, fi, ffi, gi, pz, + s, sy, t, t1, t2, t3, t4, t7, t8, t9, t10, w, x2, xn, xx2, y, ya, + yya, z0, z, zz, z2, zz2; +#ifndef DLA_FMS + double t5, t6; +#endif + int p; + number num, v; + mp_no mpa, mpt1, mpt2; + + double retval; + + int __branred (double, double *, double *); + int __mpranred (double, mp_no *, int); + + SET_RESTORE_ROUND_53BIT (FE_TONEAREST); + + /* x=+-INF, x=NaN */ + num.d = x; + ux = num.i[HIGH_HALF]; + if ((ux & 0x7ff00000) == 0x7ff00000) + { + if ((ux & 0x7fffffff) == 0x7ff00000) + __set_errno (EDOM); + retval = x - x; + goto ret; + } + + w = (x < 0.0) ? -x : x; + + /* (I) The case abs(x) <= 1.259e-8 */ + if (w <= g1.d) + { + math_check_force_underflow_nonneg (w); + retval = x; + goto ret; + } + + /* (II) The case 1.259e-8 < abs(x) <= 0.0608 */ + if (w <= g2.d) + { + /* First stage */ + x2 = x * x; + + t2 = d9.d + x2 * d11.d; + t2 = d7.d + x2 * t2; + t2 = d5.d + x2 * t2; + t2 = d3.d + x2 * t2; + t2 *= x * x2; + + if ((y = x + (t2 - u1.d * t2)) == x + (t2 + u1.d * t2)) + { + retval = y; + goto ret; + } + + /* Second stage */ + c1 = a25.d + x2 * a27.d; + c1 = a23.d + x2 * c1; + c1 = a21.d + x2 * c1; + c1 = a19.d + x2 * c1; + c1 = a17.d + x2 * c1; + c1 = a15.d + x2 * c1; + c1 *= x2; + + EMULV (x, x, x2, xx2, t1, t2, t3, t4, t5); + ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (x, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (x, 0.0, c2, cc2, c1, cc1, t1, t2); + if ((y = c1 + (cc1 - u2.d * c1)) == c1 + (cc1 + u2.d * c1)) + { + retval = y; + goto ret; + } + retval = tanMp (x); + goto ret; + } + + /* (III) The case 0.0608 < abs(x) <= 0.787 */ + if (w <= g3.d) + { + /* First stage */ + i = ((int) (mfftnhf.d + TWO8 * w)); + z = w - xfg[i][0].d; + z2 = z * z; + s = (x < 0.0) ? -1 : 1; + pz = z + z * z2 * (e0.d + z2 * e1.d); + fi = xfg[i][1].d; + gi = xfg[i][2].d; + t2 = pz * (gi + fi) / (gi - pz); + if ((y = fi + (t2 - fi * u3.d)) == fi + (t2 + fi * u3.d)) + { + retval = (s * y); + goto ret; + } + t3 = (t2 < 0.0) ? -t2 : t2; + t4 = fi * ua3.d + t3 * ub3.d; + if ((y = fi + (t2 - t4)) == fi + (t2 + t4)) + { + retval = (s * y); + goto ret; + } + + /* Second stage */ + ffi = xfg[i][3].d; + c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d)); + EMULV (z, z, z2, zz2, t1, t2, t3, t4, t5); + ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2); + MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (z, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (z, 0.0, c2, cc2, c1, cc1, t1, t2); + + ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2); + MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8); + SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2); + DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, + t10); + + if ((y = c3 + (cc3 - u4.d * c3)) == c3 + (cc3 + u4.d * c3)) + { + retval = (s * y); + goto ret; + } + retval = tanMp (x); + goto ret; + } + + /* (---) The case 0.787 < abs(x) <= 25 */ + if (w <= g4.d) + { + /* Range reduction by algorithm i */ + t = (x * hpinv.d + toint.d); + xn = t - toint.d; + v.d = t; + t1 = (x - xn * mp1.d) - xn * mp2.d; + n = v.i[LOW_HALF] & 0x00000001; + da = xn * mp3.d; + a = t1 - da; + da = (t1 - a) - da; + if (a < 0.0) + { + ya = -a; + yya = -da; + sy = -1; + } + else + { + ya = a; + yya = da; + sy = 1; + } + + /* (IV),(V) The case 0.787 < abs(x) <= 25, abs(y) <= 1e-7 */ + if (ya <= gy1.d) + { + retval = tanMp (x); + goto ret; + } + + /* (VI) The case 0.787 < abs(x) <= 25, 1e-7 < abs(y) <= 0.0608 */ + if (ya <= gy2.d) + { + a2 = a * a; + t2 = d9.d + a2 * d11.d; + t2 = d7.d + a2 * t2; + t2 = d5.d + a2 * t2; + t2 = d3.d + a2 * t2; + t2 = da + a * a2 * t2; + + if (n) + { + /* First stage -cot */ + EADD (a, t2, b, db); + DIV2 (1.0, 0.0, b, db, c, dc, t1, t2, t3, t4, t5, t6, t7, t8, + t9, t10); + if ((y = c + (dc - u6.d * c)) == c + (dc + u6.d * c)) + { + retval = (-y); + goto ret; + } + } + else + { + /* First stage tan */ + if ((y = a + (t2 - u5.d * a)) == a + (t2 + u5.d * a)) + { + retval = y; + goto ret; + } + } + /* Second stage */ + /* Range reduction by algorithm ii */ + t = (x * hpinv.d + toint.d); + xn = t - toint.d; + v.d = t; + t1 = (x - xn * mp1.d) - xn * mp2.d; + n = v.i[LOW_HALF] & 0x00000001; + da = xn * pp3.d; + t = t1 - da; + da = (t1 - t) - da; + t1 = xn * pp4.d; + a = t - t1; + da = ((t - a) - t1) + da; + + /* Second stage */ + EADD (a, da, t1, t2); + a = t1; + da = t2; + MUL2 (a, da, a, da, x2, xx2, t1, t2, t3, t4, t5, t6, t7, t8); + + c1 = a25.d + x2 * a27.d; + c1 = a23.d + x2 * c1; + c1 = a21.d + x2 * c1; + c1 = a19.d + x2 * c1; + c1 = a17.d + x2 * c1; + c1 = a15.d + x2 * c1; + c1 *= x2; + + ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (a, da, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a, da, c2, cc2, c1, cc1, t1, t2); + + if (n) + { + /* Second stage -cot */ + DIV2 (1.0, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, + t8, t9, t10); + if ((y = c2 + (cc2 - u8.d * c2)) == c2 + (cc2 + u8.d * c2)) + { + retval = (-y); + goto ret; + } + } + else + { + /* Second stage tan */ + if ((y = c1 + (cc1 - u7.d * c1)) == c1 + (cc1 + u7.d * c1)) + { + retval = y; + goto ret; + } + } + retval = tanMp (x); + goto ret; + } + + /* (VII) The case 0.787 < abs(x) <= 25, 0.0608 < abs(y) <= 0.787 */ + + /* First stage */ + i = ((int) (mfftnhf.d + TWO8 * ya)); + z = (z0 = (ya - xfg[i][0].d)) + yya; + z2 = z * z; + pz = z + z * z2 * (e0.d + z2 * e1.d); + fi = xfg[i][1].d; + gi = xfg[i][2].d; + + if (n) + { + /* -cot */ + t2 = pz * (fi + gi) / (fi + pz); + if ((y = gi - (t2 - gi * u10.d)) == gi - (t2 + gi * u10.d)) + { + retval = (-sy * y); + goto ret; + } + t3 = (t2 < 0.0) ? -t2 : t2; + t4 = gi * ua10.d + t3 * ub10.d; + if ((y = gi - (t2 - t4)) == gi - (t2 + t4)) + { + retval = (-sy * y); + goto ret; + } + } + else + { + /* tan */ + t2 = pz * (gi + fi) / (gi - pz); + if ((y = fi + (t2 - fi * u9.d)) == fi + (t2 + fi * u9.d)) + { + retval = (sy * y); + goto ret; + } + t3 = (t2 < 0.0) ? -t2 : t2; + t4 = fi * ua9.d + t3 * ub9.d; + if ((y = fi + (t2 - t4)) == fi + (t2 + t4)) + { + retval = (sy * y); + goto ret; + } + } + + /* Second stage */ + ffi = xfg[i][3].d; + EADD (z0, yya, z, zz) + MUL2 (z, zz, z, zz, z2, zz2, t1, t2, t3, t4, t5, t6, t7, t8); + c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d)); + ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2); + MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (z, zz, c2, cc2, c1, cc1, t1, t2); + + ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2); + MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8); + SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2); + + if (n) + { + /* -cot */ + DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, + t10); + if ((y = c3 + (cc3 - u12.d * c3)) == c3 + (cc3 + u12.d * c3)) + { + retval = (-sy * y); + goto ret; + } + } + else + { + /* tan */ + DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, + t10); + if ((y = c3 + (cc3 - u11.d * c3)) == c3 + (cc3 + u11.d * c3)) + { + retval = (sy * y); + goto ret; + } + } + + retval = tanMp (x); + goto ret; + } + + /* (---) The case 25 < abs(x) <= 1e8 */ + if (w <= g5.d) + { + /* Range reduction by algorithm ii */ + t = (x * hpinv.d + toint.d); + xn = t - toint.d; + v.d = t; + t1 = (x - xn * mp1.d) - xn * mp2.d; + n = v.i[LOW_HALF] & 0x00000001; + da = xn * pp3.d; + t = t1 - da; + da = (t1 - t) - da; + t1 = xn * pp4.d; + a = t - t1; + da = ((t - a) - t1) + da; + EADD (a, da, t1, t2); + a = t1; + da = t2; + if (a < 0.0) + { + ya = -a; + yya = -da; + sy = -1; + } + else + { + ya = a; + yya = da; + sy = 1; + } + + /* (+++) The case 25 < abs(x) <= 1e8, abs(y) <= 1e-7 */ + if (ya <= gy1.d) + { + retval = tanMp (x); + goto ret; + } + + /* (VIII) The case 25 < abs(x) <= 1e8, 1e-7 < abs(y) <= 0.0608 */ + if (ya <= gy2.d) + { + a2 = a * a; + t2 = d9.d + a2 * d11.d; + t2 = d7.d + a2 * t2; + t2 = d5.d + a2 * t2; + t2 = d3.d + a2 * t2; + t2 = da + a * a2 * t2; + + if (n) + { + /* First stage -cot */ + EADD (a, t2, b, db); + DIV2 (1.0, 0.0, b, db, c, dc, t1, t2, t3, t4, t5, t6, t7, t8, + t9, t10); + if ((y = c + (dc - u14.d * c)) == c + (dc + u14.d * c)) + { + retval = (-y); + goto ret; + } + } + else + { + /* First stage tan */ + if ((y = a + (t2 - u13.d * a)) == a + (t2 + u13.d * a)) + { + retval = y; + goto ret; + } + } + + /* Second stage */ + MUL2 (a, da, a, da, x2, xx2, t1, t2, t3, t4, t5, t6, t7, t8); + c1 = a25.d + x2 * a27.d; + c1 = a23.d + x2 * c1; + c1 = a21.d + x2 * c1; + c1 = a19.d + x2 * c1; + c1 = a17.d + x2 * c1; + c1 = a15.d + x2 * c1; + c1 *= x2; + + ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (a, da, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a, da, c2, cc2, c1, cc1, t1, t2); + + if (n) + { + /* Second stage -cot */ + DIV2 (1.0, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, + t8, t9, t10); + if ((y = c2 + (cc2 - u16.d * c2)) == c2 + (cc2 + u16.d * c2)) + { + retval = (-y); + goto ret; + } + } + else + { + /* Second stage tan */ + if ((y = c1 + (cc1 - u15.d * c1)) == c1 + (cc1 + u15.d * c1)) + { + retval = (y); + goto ret; + } + } + retval = tanMp (x); + goto ret; + } + + /* (IX) The case 25 < abs(x) <= 1e8, 0.0608 < abs(y) <= 0.787 */ + /* First stage */ + i = ((int) (mfftnhf.d + TWO8 * ya)); + z = (z0 = (ya - xfg[i][0].d)) + yya; + z2 = z * z; + pz = z + z * z2 * (e0.d + z2 * e1.d); + fi = xfg[i][1].d; + gi = xfg[i][2].d; + + if (n) + { + /* -cot */ + t2 = pz * (fi + gi) / (fi + pz); + if ((y = gi - (t2 - gi * u18.d)) == gi - (t2 + gi * u18.d)) + { + retval = (-sy * y); + goto ret; + } + t3 = (t2 < 0.0) ? -t2 : t2; + t4 = gi * ua18.d + t3 * ub18.d; + if ((y = gi - (t2 - t4)) == gi - (t2 + t4)) + { + retval = (-sy * y); + goto ret; + } + } + else + { + /* tan */ + t2 = pz * (gi + fi) / (gi - pz); + if ((y = fi + (t2 - fi * u17.d)) == fi + (t2 + fi * u17.d)) + { + retval = (sy * y); + goto ret; + } + t3 = (t2 < 0.0) ? -t2 : t2; + t4 = fi * ua17.d + t3 * ub17.d; + if ((y = fi + (t2 - t4)) == fi + (t2 + t4)) + { + retval = (sy * y); + goto ret; + } + } + + /* Second stage */ + ffi = xfg[i][3].d; + EADD (z0, yya, z, zz); + MUL2 (z, zz, z, zz, z2, zz2, t1, t2, t3, t4, t5, t6, t7, t8); + c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d)); + ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2); + MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (z, zz, c2, cc2, c1, cc1, t1, t2); + + ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2); + MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8); + SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2); + + if (n) + { + /* -cot */ + DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, + t10); + if ((y = c3 + (cc3 - u20.d * c3)) == c3 + (cc3 + u20.d * c3)) + { + retval = (-sy * y); + goto ret; + } + } + else + { + /* tan */ + DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, + t10); + if ((y = c3 + (cc3 - u19.d * c3)) == c3 + (cc3 + u19.d * c3)) + { + retval = (sy * y); + goto ret; + } + } + retval = tanMp (x); + goto ret; + } + + /* (---) The case 1e8 < abs(x) < 2**1024 */ + /* Range reduction by algorithm iii */ + n = (__branred (x, &a, &da)) & 0x00000001; + EADD (a, da, t1, t2); + a = t1; + da = t2; + if (a < 0.0) + { + ya = -a; + yya = -da; + sy = -1; + } + else + { + ya = a; + yya = da; + sy = 1; + } + + /* (+++) The case 1e8 < abs(x) < 2**1024, abs(y) <= 1e-7 */ + if (ya <= gy1.d) + { + retval = tanMp (x); + goto ret; + } + + /* (X) The case 1e8 < abs(x) < 2**1024, 1e-7 < abs(y) <= 0.0608 */ + if (ya <= gy2.d) + { + a2 = a * a; + t2 = d9.d + a2 * d11.d; + t2 = d7.d + a2 * t2; + t2 = d5.d + a2 * t2; + t2 = d3.d + a2 * t2; + t2 = da + a * a2 * t2; + if (n) + { + /* First stage -cot */ + EADD (a, t2, b, db); + DIV2 (1.0, 0.0, b, db, c, dc, t1, t2, t3, t4, t5, t6, t7, t8, t9, + t10); + if ((y = c + (dc - u22.d * c)) == c + (dc + u22.d * c)) + { + retval = (-y); + goto ret; + } + } + else + { + /* First stage tan */ + if ((y = a + (t2 - u21.d * a)) == a + (t2 + u21.d * a)) + { + retval = y; + goto ret; + } + } + + /* Second stage */ + /* Reduction by algorithm iv */ + p = 10; + n = (__mpranred (x, &mpa, p)) & 0x00000001; + __mp_dbl (&mpa, &a, p); + __dbl_mp (a, &mpt1, p); + __sub (&mpa, &mpt1, &mpt2, p); + __mp_dbl (&mpt2, &da, p); + + MUL2 (a, da, a, da, x2, xx2, t1, t2, t3, t4, t5, t6, t7, t8); + + c1 = a25.d + x2 * a27.d; + c1 = a23.d + x2 * c1; + c1 = a21.d + x2 * c1; + c1 = a19.d + x2 * c1; + c1 = a17.d + x2 * c1; + c1 = a15.d + x2 * c1; + c1 *= x2; + + ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (a, da, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a, da, c2, cc2, c1, cc1, t1, t2); + + if (n) + { + /* Second stage -cot */ + DIV2 (1.0, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8, + t9, t10); + if ((y = c2 + (cc2 - u24.d * c2)) == c2 + (cc2 + u24.d * c2)) + { + retval = (-y); + goto ret; + } + } + else + { + /* Second stage tan */ + if ((y = c1 + (cc1 - u23.d * c1)) == c1 + (cc1 + u23.d * c1)) + { + retval = y; + goto ret; + } + } + retval = tanMp (x); + goto ret; + } + + /* (XI) The case 1e8 < abs(x) < 2**1024, 0.0608 < abs(y) <= 0.787 */ + /* First stage */ + i = ((int) (mfftnhf.d + TWO8 * ya)); + z = (z0 = (ya - xfg[i][0].d)) + yya; + z2 = z * z; + pz = z + z * z2 * (e0.d + z2 * e1.d); + fi = xfg[i][1].d; + gi = xfg[i][2].d; + + if (n) + { + /* -cot */ + t2 = pz * (fi + gi) / (fi + pz); + if ((y = gi - (t2 - gi * u26.d)) == gi - (t2 + gi * u26.d)) + { + retval = (-sy * y); + goto ret; + } + t3 = (t2 < 0.0) ? -t2 : t2; + t4 = gi * ua26.d + t3 * ub26.d; + if ((y = gi - (t2 - t4)) == gi - (t2 + t4)) + { + retval = (-sy * y); + goto ret; + } + } + else + { + /* tan */ + t2 = pz * (gi + fi) / (gi - pz); + if ((y = fi + (t2 - fi * u25.d)) == fi + (t2 + fi * u25.d)) + { + retval = (sy * y); + goto ret; + } + t3 = (t2 < 0.0) ? -t2 : t2; + t4 = fi * ua25.d + t3 * ub25.d; + if ((y = fi + (t2 - t4)) == fi + (t2 + t4)) + { + retval = (sy * y); + goto ret; + } + } + + /* Second stage */ + ffi = xfg[i][3].d; + EADD (z0, yya, z, zz); + MUL2 (z, zz, z, zz, z2, zz2, t1, t2, t3, t4, t5, t6, t7, t8); + c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d)); + ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2); + MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); + MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (z, zz, c2, cc2, c1, cc1, t1, t2); + + ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2); + MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8); + SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2); + + if (n) + { + /* -cot */ + DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, + t10); + if ((y = c3 + (cc3 - u28.d * c3)) == c3 + (cc3 + u28.d * c3)) + { + retval = (-sy * y); + goto ret; + } + } + else + { + /* tan */ + DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, + t10); + if ((y = c3 + (cc3 - u27.d * c3)) == c3 + (cc3 + u27.d * c3)) + { + retval = (sy * y); + goto ret; + } + } + retval = tanMp (x); + goto ret; + +ret: + return retval; +} + +/* multiple precision stage */ +/* Convert x to multi precision number,compute tan(x) by mptan() routine */ +/* and converts result back to double */ +static double +SECTION +tanMp (double x) +{ + int p; + double y; + mp_no mpy; + p = 32; + __mptan (x, &mpy, p); + __mp_dbl (&mpy, &y, p); + LIBC_PROBE (slowtan, 2, &x, &y); + return y; +} + +#ifdef NO_LONG_DOUBLE +weak_alias (tan, tanl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_tanh.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_tanh.c new file mode 100644 index 0000000000..344a2f0330 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_tanh.c @@ -0,0 +1,98 @@ +/* @(#)s_tanh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_tanh.c,v 1.7 1995/05/10 20:48:22 jtc Exp $"; +#endif + +/* Tanh(x) + * Return the Hyperbolic Tangent of x + * + * Method : + * x -x + * e - e + * 0. tanh(x) is defined to be ----------- + * x -x + * e + e + * 1. reduce x to non-negative by tanh(-x) = -tanh(x). + * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x) + * -t + * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x) + * t + 2 + * 2 + * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x) + * t + 2 + * 22.0 < x <= INF : tanh(x) := 1. + * + * Special cases: + * tanh(NaN) is NaN; + * only tanh(0)=0 is exact for finite argument. + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const double one = 1.0, two = 2.0, tiny = 1.0e-300; + +double +__tanh (double x) +{ + double t, z; + int32_t jx, ix, lx; + + /* High word of |x|. */ + EXTRACT_WORDS (jx, lx, x); + ix = jx & 0x7fffffff; + + /* x is INF or NaN */ + if (ix >= 0x7ff00000) + { + if (jx >= 0) + return one / x + one; /* tanh(+-inf)=+-1 */ + else + return one / x - one; /* tanh(NaN) = NaN */ + } + + /* |x| < 22 */ + if (ix < 0x40360000) /* |x|<22 */ + { + if ((ix | lx) == 0) + return x; /* x == +-0 */ + if (ix < 0x3c800000) /* |x|<2**-55 */ + { + math_check_force_underflow (x); + return x * (one + x); /* tanh(small) = small */ + } + if (ix >= 0x3ff00000) /* |x|>=1 */ + { + t = __expm1 (two * fabs (x)); + z = one - two / (t + two); + } + else + { + t = __expm1 (-two * fabs (x)); + z = -t / (t + two); + } + /* |x| > 22, return +-1 */ + } + else + { + z = one - tiny; /* raised inexact flag */ + } + return (jx >= 0) ? z : -z; +} +weak_alias (__tanh, tanh) +#ifdef NO_LONG_DOUBLE +strong_alias (__tanh, __tanhl) +weak_alias (__tanh, tanhl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_totalorder.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_totalorder.c new file mode 100644 index 0000000000..f229119c27 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_totalorder.c @@ -0,0 +1,54 @@ +/* Total order operation. dbl-64 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +int +totalorder (double x, double y) +{ + int32_t hx, hy; + uint32_t lx, ly; + EXTRACT_WORDS (hx, lx, x); + EXTRACT_WORDS (hy, ly, y); +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN + uint32_t uhx = hx & 0x7fffffff, uhy = hy & 0x7fffffff; + /* For the preferred quiet NaN convention, this operation is a + comparison of the representations of the arguments interpreted as + sign-magnitude integers. If both arguments are NaNs, invert the + quiet/signaling bit so comparing that way works. */ + if ((uhx > 0x7ff00000 || (uhx == 0x7ff00000 && lx != 0)) + && (uhy > 0x7ff00000 || (uhy == 0x7ff00000 && ly != 0))) + { + hx ^= 0x00080000; + hy ^= 0x00080000; + } +#endif + uint32_t hx_sign = hx >> 31; + uint32_t hy_sign = hy >> 31; + hx ^= hx_sign >> 1; + lx ^= hx_sign; + hy ^= hy_sign >> 1; + ly ^= hy_sign; + return hx < hy || (hx == hy && lx <= ly); +} +#ifdef NO_LONG_DOUBLE +weak_alias (totalorder, totalorderl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_totalordermag.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_totalordermag.c new file mode 100644 index 0000000000..b1bdd833db --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_totalordermag.c @@ -0,0 +1,49 @@ +/* Total order operation on absolute values. dbl-64 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +int +totalordermag (double x, double y) +{ + uint32_t hx, hy; + uint32_t lx, ly; + EXTRACT_WORDS (hx, lx, x); + EXTRACT_WORDS (hy, ly, y); + hx &= 0x7fffffff; + hy &= 0x7fffffff; +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN + /* For the preferred quiet NaN convention, this operation is a + comparison of the representations of the absolute values of the + arguments. If both arguments are NaNs, invert the + quiet/signaling bit so comparing that way works. */ + if ((hx > 0x7ff00000 || (hx == 0x7ff00000 && lx != 0)) + && (hy > 0x7ff00000 || (hy == 0x7ff00000 && ly != 0))) + { + hx ^= 0x00080000; + hy ^= 0x00080000; + } +#endif + return hx < hy || (hx == hy && lx <= ly); +} +#ifdef NO_LONG_DOUBLE +weak_alias (totalordermag, totalordermagl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_trunc.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_trunc.c new file mode 100644 index 0000000000..730c1b377c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_trunc.c @@ -0,0 +1,62 @@ +/* Truncate argument to nearest integral value not larger than the argument. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> + + +double +__trunc (double x) +{ + int32_t i0, j0; + u_int32_t i1; + int sx; + + EXTRACT_WORDS (i0, i1, x); + sx = i0 & 0x80000000; + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + if (j0 < 20) + { + if (j0 < 0) + /* The magnitude of the number is < 1 so the result is +-0. */ + INSERT_WORDS (x, sx, 0); + else + INSERT_WORDS (x, sx | (i0 & ~(0x000fffff >> j0)), 0); + } + else if (j0 > 51) + { + if (j0 == 0x400) + /* x is inf or NaN. */ + return x + x; + } + else + { + INSERT_WORDS (x, i0, i1 & ~(0xffffffffu >> (j0 - 20))); + } + + return x; +} +#ifndef __trunc +weak_alias (__trunc, trunc) +# ifdef NO_LONG_DOUBLE +strong_alias (__trunc, __truncl) +weak_alias (__trunc, truncl) +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_ufromfp.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_ufromfp.c new file mode 100644 index 0000000000..c3d9047930 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_ufromfp.c @@ -0,0 +1,7 @@ +#define UNSIGNED 1 +#define INEXACT 0 +#define FUNC ufromfp +#include <s_fromfp_main.c> +#ifdef NO_LONG_DOUBLE +weak_alias (ufromfp, ufromfpl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_ufromfpx.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_ufromfpx.c new file mode 100644 index 0000000000..dee607f8c0 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_ufromfpx.c @@ -0,0 +1,7 @@ +#define UNSIGNED 1 +#define INEXACT 1 +#define FUNC ufromfpx +#include <s_fromfp_main.c> +#ifdef NO_LONG_DOUBLE +weak_alias (ufromfpx, ufromfpxl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/sincos32.c b/REORG.TODO/sysdeps/ieee754/dbl-64/sincos32.c new file mode 100644 index 0000000000..9cd8e2f97f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/sincos32.c @@ -0,0 +1,369 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/****************************************************************/ +/* MODULE_NAME: sincos32.c */ +/* */ +/* FUNCTIONS: ss32 */ +/* cc32 */ +/* c32 */ +/* sin32 */ +/* cos32 */ +/* mpsin */ +/* mpcos */ +/* mpranred */ +/* mpsin1 */ +/* mpcos1 */ +/* */ +/* FILES NEEDED: endian.h mpa.h sincos32.h */ +/* mpa.c */ +/* */ +/* Multi Precision sin() and cos() function with p=32 for sin()*/ +/* cos() arcsin() and arccos() routines */ +/* In addition mpranred() routine performs range reduction of */ +/* a double number x into multi precision number y, */ +/* such that y=x-n*pi/2, abs(y)<pi/4, n=0,+-1,+-2,.... */ +/****************************************************************/ +#include "endian.h" +#include "mpa.h" +#include "sincos32.h" +#include <math.h> +#include <math_private.h> +#include <stap-probe.h> + +#ifndef SECTION +# define SECTION +#endif + +/* Compute Multi-Precision sin() function for given p. Receive Multi Precision + number x and result stored at y. */ +static void +SECTION +ss32 (mp_no *x, mp_no *y, int p) +{ + int i; + double a; + mp_no mpt1, x2, gor, sum, mpk = {1, {1.0}}; + for (i = 1; i <= p; i++) + mpk.d[i] = 0; + + __sqr (x, &x2, p); + __cpy (&oofac27, &gor, p); + __cpy (&gor, &sum, p); + for (a = 27.0; a > 1.0; a -= 2.0) + { + mpk.d[1] = a * (a - 1.0); + __mul (&gor, &mpk, &mpt1, p); + __cpy (&mpt1, &gor, p); + __mul (&x2, &sum, &mpt1, p); + __sub (&gor, &mpt1, &sum, p); + } + __mul (x, &sum, y, p); +} + +/* Compute Multi-Precision cos() function for given p. Receive Multi Precision + number x and result stored at y. */ +static void +SECTION +cc32 (mp_no *x, mp_no *y, int p) +{ + int i; + double a; + mp_no mpt1, x2, gor, sum, mpk = {1, {1.0}}; + for (i = 1; i <= p; i++) + mpk.d[i] = 0; + + __sqr (x, &x2, p); + mpk.d[1] = 27.0; + __mul (&oofac27, &mpk, &gor, p); + __cpy (&gor, &sum, p); + for (a = 26.0; a > 2.0; a -= 2.0) + { + mpk.d[1] = a * (a - 1.0); + __mul (&gor, &mpk, &mpt1, p); + __cpy (&mpt1, &gor, p); + __mul (&x2, &sum, &mpt1, p); + __sub (&gor, &mpt1, &sum, p); + } + __mul (&x2, &sum, y, p); +} + +/* Compute both sin(x), cos(x) as Multi precision numbers. */ +void +SECTION +__c32 (mp_no *x, mp_no *y, mp_no *z, int p) +{ + mp_no u, t, t1, t2, c, s; + int i; + __cpy (x, &u, p); + u.e = u.e - 1; + cc32 (&u, &c, p); + ss32 (&u, &s, p); + for (i = 0; i < 24; i++) + { + __mul (&c, &s, &t, p); + __sub (&s, &t, &t1, p); + __add (&t1, &t1, &s, p); + __sub (&__mptwo, &c, &t1, p); + __mul (&t1, &c, &t2, p); + __add (&t2, &t2, &c, p); + } + __sub (&__mpone, &c, y, p); + __cpy (&s, z, p); +} + +/* Receive double x and two double results of sin(x) and return result which is + more accurate, computing sin(x) with multi precision routine c32. */ +double +SECTION +__sin32 (double x, double res, double res1) +{ + int p; + mp_no a, b, c; + p = 32; + __dbl_mp (res, &a, p); + __dbl_mp (0.5 * (res1 - res), &b, p); + __add (&a, &b, &c, p); + if (x > 0.8) + { + __sub (&hp, &c, &a, p); + __c32 (&a, &b, &c, p); + } + else + __c32 (&c, &a, &b, p); /* b=sin(0.5*(res+res1)) */ + __dbl_mp (x, &c, p); /* c = x */ + __sub (&b, &c, &a, p); + /* if a > 0 return min (res, res1), otherwise return max (res, res1). */ + if ((a.d[0] > 0 && res >= res1) || (a.d[0] <= 0 && res <= res1)) + res = res1; + LIBC_PROBE (slowasin, 2, &res, &x); + return res; +} + +/* Receive double x and two double results of cos(x) and return result which is + more accurate, computing cos(x) with multi precision routine c32. */ +double +SECTION +__cos32 (double x, double res, double res1) +{ + int p; + mp_no a, b, c; + p = 32; + __dbl_mp (res, &a, p); + __dbl_mp (0.5 * (res1 - res), &b, p); + __add (&a, &b, &c, p); + if (x > 2.4) + { + __sub (&pi, &c, &a, p); + __c32 (&a, &b, &c, p); + b.d[0] = -b.d[0]; + } + else if (x > 0.8) + { + __sub (&hp, &c, &a, p); + __c32 (&a, &c, &b, p); + } + else + __c32 (&c, &b, &a, p); /* b=cos(0.5*(res+res1)) */ + __dbl_mp (x, &c, p); /* c = x */ + __sub (&b, &c, &a, p); + /* if a > 0 return max (res, res1), otherwise return min (res, res1). */ + if ((a.d[0] > 0 && res <= res1) || (a.d[0] <= 0 && res >= res1)) + res = res1; + LIBC_PROBE (slowacos, 2, &res, &x); + return res; +} + +/* Compute sin() of double-length number (X + DX) as Multi Precision number and + return result as double. If REDUCE_RANGE is true, X is assumed to be the + original input and DX is ignored. */ +double +SECTION +__mpsin (double x, double dx, bool reduce_range) +{ + double y; + mp_no a, b, c, s; + int n; + int p = 32; + + if (reduce_range) + { + n = __mpranred (x, &a, p); /* n is 0, 1, 2 or 3. */ + __c32 (&a, &c, &s, p); + } + else + { + n = -1; + __dbl_mp (x, &b, p); + __dbl_mp (dx, &c, p); + __add (&b, &c, &a, p); + if (x > 0.8) + { + __sub (&hp, &a, &b, p); + __c32 (&b, &s, &c, p); + } + else + __c32 (&a, &c, &s, p); /* b = sin(x+dx) */ + } + + /* Convert result based on which quarter of unit circle y is in. */ + switch (n) + { + case 1: + __mp_dbl (&c, &y, p); + break; + + case 3: + __mp_dbl (&c, &y, p); + y = -y; + break; + + case 2: + __mp_dbl (&s, &y, p); + y = -y; + break; + + /* Quadrant not set, so the result must be sin (X + DX), which is also in + S. */ + case 0: + default: + __mp_dbl (&s, &y, p); + } + LIBC_PROBE (slowsin, 3, &x, &dx, &y); + return y; +} + +/* Compute cos() of double-length number (X + DX) as Multi Precision number and + return result as double. If REDUCE_RANGE is true, X is assumed to be the + original input and DX is ignored. */ +double +SECTION +__mpcos (double x, double dx, bool reduce_range) +{ + double y; + mp_no a, b, c, s; + int n; + int p = 32; + + if (reduce_range) + { + n = __mpranred (x, &a, p); /* n is 0, 1, 2 or 3. */ + __c32 (&a, &c, &s, p); + } + else + { + n = -1; + __dbl_mp (x, &b, p); + __dbl_mp (dx, &c, p); + __add (&b, &c, &a, p); + if (x > 0.8) + { + __sub (&hp, &a, &b, p); + __c32 (&b, &s, &c, p); + } + else + __c32 (&a, &c, &s, p); /* a = cos(x+dx) */ + } + + /* Convert result based on which quarter of unit circle y is in. */ + switch (n) + { + case 1: + __mp_dbl (&s, &y, p); + y = -y; + break; + + case 3: + __mp_dbl (&s, &y, p); + break; + + case 2: + __mp_dbl (&c, &y, p); + y = -y; + break; + + /* Quadrant not set, so the result must be cos (X + DX), which is also + stored in C. */ + case 0: + default: + __mp_dbl (&c, &y, p); + } + LIBC_PROBE (slowcos, 3, &x, &dx, &y); + return y; +} + +/* Perform range reduction of a double number x into multi precision number y, + such that y = x - n * pi / 2, abs (y) < pi / 4, n = 0, +-1, +-2, ... + Return int which indicates in which quarter of circle x is. */ +int +SECTION +__mpranred (double x, mp_no *y, int p) +{ + number v; + double t, xn; + int i, k, n; + mp_no a, b, c; + + if (fabs (x) < 2.8e14) + { + t = (x * hpinv.d + toint.d); + xn = t - toint.d; + v.d = t; + n = v.i[LOW_HALF] & 3; + __dbl_mp (xn, &a, p); + __mul (&a, &hp, &b, p); + __dbl_mp (x, &c, p); + __sub (&c, &b, y, p); + return n; + } + else + { + /* If x is very big more precision required. */ + __dbl_mp (x, &a, p); + a.d[0] = 1.0; + k = a.e - 5; + if (k < 0) + k = 0; + b.e = -k; + b.d[0] = 1.0; + for (i = 0; i < p; i++) + b.d[i + 1] = toverp[i + k]; + __mul (&a, &b, &c, p); + t = c.d[c.e]; + for (i = 1; i <= p - c.e; i++) + c.d[i] = c.d[i + c.e]; + for (i = p + 1 - c.e; i <= p; i++) + c.d[i] = 0; + c.e = 0; + if (c.d[1] >= HALFRAD) + { + t += 1.0; + __sub (&c, &__mpone, &b, p); + __mul (&b, &hp, y, p); + } + else + __mul (&c, &hp, y, p); + n = (int) t; + if (x < 0) + { + y->d[0] = -y->d[0]; + n = -n; + } + return (n & 3); + } +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/sincos32.h b/REORG.TODO/sysdeps/ieee754/dbl-64/sincos32.h new file mode 100644 index 0000000000..8265a23e77 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/sincos32.h @@ -0,0 +1,81 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/******************************************************************/ +/* */ +/* MODULE_NAME:sincos32.h */ +/* */ +/* common data and variables prototype and definition */ +/******************************************************************/ + +#ifndef SINCOS32_H +#define SINCCOS32_H + +#ifdef BIG_ENDI +static const number +/**/ hpinv = {{0x3FE45F30, 0x6DC9C883}}, /* 0.63661977236758138 */ +/**/ toint = {{0x43380000, 0x00000000}}; /* 6755399441055744 */ + +#else +#ifdef LITTLE_ENDI +static const number +/**/ hpinv = {{0x6DC9C883, 0x3FE45F30}}, /* 0.63661977236758138 */ +/**/ toint = {{0x00000000, 0x43380000}}; /* 6755399441055744 */ + +#endif +#endif + +static const mp_no + oofac27 = {-3,{1.0,7.0,4631664.0,12006312.0,13118056.0,6538613.0,646354.0, + 8508025.0,9131256.0,7548776.0,2529842.0,8864927.0,660489.0,15595125.0,12777885.0, + 11618489.0,13348664.0,5486686.0,514518.0,11275535.0,4727621.0,3575562.0, + 13579710.0,5829745.0,7531862.0,9507898.0,6915060.0,4079264.0,1907586.0, + 6078398.0,13789314.0,5504104.0,14136.0}}, + pi = {1,{1.0,3.0, + 2375530.0,8947107.0,578323.0,1673774.0,225395.0,4498441.0,3678761.0, + 10432976.0,536314.0,10021966.0,7113029.0,2630118.0,3723283.0,7847508.0, + 6737716.0,15273068.0,12626985.0,12044668.0,5299519.0,8705461.0,11880201.0, + 1544726.0,14014857.0,7994139.0,13709579.0,10918111.0,11906095.0,16610011.0, + 13638367.0,12040417.0,11529578.0,2522774.0}}, + hp = {1,{1.0, 1.0, + 9576373.0,4473553.0,8677769.0,9225495.0,112697.0,10637828.0, + 10227988.0,13605096.0,268157.0,5010983.0,3556514.0,9703667.0, + 1861641.0,12312362.0,3368858.0,7636534.0,6313492.0,14410942.0, + 2649759.0,12741338.0,14328708.0,9160971.0,7007428.0,12385677.0, + 15243397.0,13847663.0,14341655.0,16693613.0,15207791.0,14408816.0, + 14153397.0,1261387.0,6110792.0,2291862.0,4181138.0,5295267.0}}; + +static const double toverp[75] = { + 10680707.0, 7228996.0, 1387004.0, 2578385.0, 16069853.0, + 12639074.0, 9804092.0, 4427841.0, 16666979.0, 11263675.0, + 12935607.0, 2387514.0, 4345298.0, 14681673.0, 3074569.0, + 13734428.0, 16653803.0, 1880361.0, 10960616.0, 8533493.0, + 3062596.0, 8710556.0, 7349940.0, 6258241.0, 3772886.0, + 3769171.0, 3798172.0, 8675211.0, 12450088.0, 3874808.0, + 9961438.0, 366607.0, 15675153.0, 9132554.0, 7151469.0, + 3571407.0, 2607881.0, 12013382.0, 4155038.0, 6285869.0, + 7677882.0, 13102053.0, 15825725.0, 473591.0, 9065106.0, + 15363067.0, 6271263.0, 9264392.0, 5636912.0, 4652155.0, + 7056368.0, 13614112.0, 10155062.0, 1944035.0, 9527646.0, + 15080200.0, 6658437.0, 6231200.0, 6832269.0, 16767104.0, + 5075751.0, 3212806.0, 1398474.0, 7579849.0, 6349435.0, + 12618859.0, 4703257.0, 12806093.0, 14477321.0, 2786137.0, + 12875403.0, 9837734.0, 14528324.0, 13719321.0, 343717.0 }; + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/sincostab.c b/REORG.TODO/sysdeps/ieee754/dbl-64/sincostab.c new file mode 100644 index 0000000000..b3e06bfebd --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/sincostab.c @@ -0,0 +1,914 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +#include <mydefs.h> +#include <endian.h> + +/****************************************************************/ +/* TABLES FOR THE usin() and ucos() FUNCTION */ +/****************************************************************/ + + +#ifdef BIG_ENDI +const union {int4 i[880]; double x[440];}__sincostab = { .i = { +/**/ 0x00000000, 0x00000000, +/**/ 0x00000000, 0x00000000, +/**/ 0x3FF00000, 0x00000000, +/**/ 0x00000000, 0x00000000, +/**/ 0x3F7FFFEA, 0xAAAEEEEF, +/**/ 0xBC1E45E2, 0xEC67B77C, +/**/ 0x3FEFFFC0, 0x00155552, +/**/ 0x3C8F4A01, 0xA0196DAE, +/**/ 0x3F8FFFAA, 0xAAEEEED5, +/**/ 0xBC02AB63, 0x9A9F0777, +/**/ 0x3FEFFF00, 0x0155549F, +/**/ 0x3C828A28, 0xA03A5EF3, +/**/ 0x3F97FF70, 0x01033255, +/**/ 0x3BFEFE2B, 0x51527336, +/**/ 0x3FEFFDC0, 0x06BFF7E6, +/**/ 0x3C8AE6DA, 0xE86977BD, +/**/ 0x3F9FFEAA, 0xAEEEE86F, +/**/ 0xBC3CD406, 0xFB224AE2, +/**/ 0x3FEFFC00, 0x155527D3, +/**/ 0xBC83B544, 0x92D89B5B, +/**/ 0x3FA3FEB2, 0xB12D45D5, +/**/ 0x3C34EC54, 0x203D1C11, +/**/ 0x3FEFF9C0, 0x3414A7BA, +/**/ 0x3C6991F4, 0xBE6C59BF, +/**/ 0x3FA7FDC0, 0x1032FBA9, +/**/ 0xBC4599BD, 0xF46E997A, +/**/ 0x3FEFF700, 0x6BFDF99F, +/**/ 0xBC78B3B5, 0x60648D5F, +/**/ 0x3FABFC6D, 0x78586DAC, +/**/ 0x3C18E4FD, 0x03DBF236, +/**/ 0x3FEFF3C0, 0xC8103A31, +/**/ 0x3C74856D, 0xBDDC0E66, +/**/ 0x3FAFFAAA, 0xEEED4EDB, +/**/ 0xBC42D16D, 0x32684B69, +/**/ 0x3FEFF001, 0x5549F4D3, +/**/ 0x3C832838, 0x7B99426F, +/**/ 0x3FB1FC34, 0x3D808BEF, +/**/ 0xBC5F3D32, 0xE6F3BE4F, +/**/ 0x3FEFEBC2, 0x22A8EF9F, +/**/ 0x3C579349, 0x34F54C77, +/**/ 0x3FB3FACB, 0x12D1755B, +/**/ 0xBC592191, 0x5299468C, +/**/ 0x3FEFE703, 0x4129EF6F, +/**/ 0xBC6CBF43, 0x37C96F97, +/**/ 0x3FB5F911, 0xFD10B737, +/**/ 0xBC50184F, 0x02BE9102, +/**/ 0x3FEFE1C4, 0xC3C873EB, +/**/ 0xBC35A9C9, 0x057C4A02, +/**/ 0x3FB7F701, 0x032550E4, +/**/ 0x3C3AFC2D, 0x1800501A, +/**/ 0x3FEFDC06, 0xBF7E6B9B, +/**/ 0x3C831902, 0xB535F8DB, +/**/ 0x3FB9F490, 0x2D55D1F9, +/**/ 0x3C52696D, 0x7EAC1DC1, +/**/ 0x3FEFD5C9, 0x4B43E000, +/**/ 0xBC62E768, 0xCB4F92F9, +/**/ 0x3FBBF1B7, 0x8568391D, +/**/ 0x3C5E9184, 0x1DEA4CC8, +/**/ 0x3FEFCF0C, 0x800E99B1, +/**/ 0x3C6EA3D7, 0x86D186AC, +/**/ 0x3FBDEE6F, 0x16C1CCE6, +/**/ 0xBC450F8E, 0x2FB71673, +/**/ 0x3FEFC7D0, 0x78D1BC88, +/**/ 0x3C8075D2, 0x447DB685, +/**/ 0x3FBFEAAE, 0xEE86EE36, +/**/ 0xBC4AFCB2, 0xBCC6F03B, +/**/ 0x3FEFC015, 0x527D5BD3, +/**/ 0x3C8B68F3, 0x5094EFB8, +/**/ 0x3FC0F337, 0x8DDD71D1, +/**/ 0x3C6D8468, 0x724F0F9E, +/**/ 0x3FEFB7DB, 0x2BFE0695, +/**/ 0x3C821DAD, 0xF4F65AB1, +/**/ 0x3FC1F0D3, 0xD7AFCEAF, +/**/ 0xBC66EF95, 0x099769A5, +/**/ 0x3FEFAF22, 0x263C4BD3, +/**/ 0xBC552ACE, 0x133A2769, +/**/ 0x3FC2EE28, 0x5E4AB88F, +/**/ 0xBC6E4D0F, 0x05DEE058, +/**/ 0x3FEFA5EA, 0x641C36F2, +/**/ 0x3C404DA6, 0xED17CC7C, +/**/ 0x3FC3EB31, 0x2C5D66CB, +/**/ 0x3C647D66, 0x6B66CB91, +/**/ 0x3FEF9C34, 0x0A7CC428, +/**/ 0x3C8C5B6B, 0x063B7462, +/**/ 0x3FC4E7EA, 0x4DC5F27B, +/**/ 0x3C5949DB, 0x2AC072FC, +/**/ 0x3FEF91FF, 0x40374D01, +/**/ 0xBC67D03F, 0x4D3A9E4C, +/**/ 0x3FC5E44F, 0xCFA126F3, +/**/ 0xBC66F443, 0x063F89B6, +/**/ 0x3FEF874C, 0x2E1EECF6, +/**/ 0xBC8C6514, 0xE1332B16, +/**/ 0x3FC6E05D, 0xC05A4D4C, +/**/ 0xBBD32C5C, 0x8B81C940, +/**/ 0x3FEF7C1A, 0xFEFFDE24, +/**/ 0xBC78F55B, 0xC47540B1, +/**/ 0x3FC7DC10, 0x2FBAF2B5, +/**/ 0x3C45AB50, 0xE23C97C3, +/**/ 0x3FEF706B, 0xDF9ECE1C, +/**/ 0xBC8698C8, 0x0C36DCB4, +/**/ 0x3FC8D763, 0x2EFAA944, +/**/ 0xBC620FA2, 0x62CBB953, +/**/ 0x3FEF643E, 0xFEB82ACD, +/**/ 0x3C76B00A, 0xC1FE28AC, +/**/ 0x3FC9D252, 0xD0CEC312, +/**/ 0x3C59C43D, 0x80B1137D, +/**/ 0x3FEF5794, 0x8CFF6797, +/**/ 0x3C6E3A0D, 0x3E03B1D5, +/**/ 0x3FCACCDB, 0x297A0765, +/**/ 0xBC59883B, 0x57D6CDEB, +/**/ 0x3FEF4A6C, 0xBD1E3A79, +/**/ 0x3C813DF0, 0xEDAEBB57, +/**/ 0x3FCBC6F8, 0x4EDC6199, +/**/ 0x3C69C1A5, 0x6A7B0CAB, +/**/ 0x3FEF3CC7, 0xC3B3D16E, +/**/ 0xBC621A3A, 0xD28A3494, +/**/ 0x3FCCC0A6, 0x588289A3, +/**/ 0xBC6868D0, 0x9BC87C6B, +/**/ 0x3FEF2EA5, 0xD753FFED, +/**/ 0x3C8CC421, 0x5F56D583, +/**/ 0x3FCDB9E1, 0x5FB5A5D0, +/**/ 0xBC632E20, 0xD6CC6FC2, +/**/ 0x3FEF2007, 0x3086649F, +/**/ 0x3C7B9404, 0x16C1984B, +/**/ 0x3FCEB2A5, 0x7F8AE5A3, +/**/ 0xBC60BE06, 0xAF572CEB, +/**/ 0x3FEF10EC, 0x09C5873B, +/**/ 0x3C8D9072, 0x762C1283, +/**/ 0x3FCFAAEE, 0xD4F31577, +/**/ 0xBC615D88, 0x508E32B8, +/**/ 0x3FEF0154, 0x9F7DEEA1, +/**/ 0x3C8D3C1E, 0x99E5CAFD, +/**/ 0x3FD0515C, 0xBF65155C, +/**/ 0xBC79B8C2, 0x9DFD8EC8, +/**/ 0x3FEEF141, 0x300D2F26, +/**/ 0xBC82AA1B, 0x08DED372, +/**/ 0x3FD0CD00, 0xCEF36436, +/**/ 0xBC79FB0A, 0x0C93E2B5, +/**/ 0x3FEEE0B1, 0xFBC0F11C, +/**/ 0xBC4BFD23, 0x80BBC3B1, +/**/ 0x3FD14861, 0xAA94DDEB, +/**/ 0xBC6BE881, 0xB5B615A4, +/**/ 0x3FEECFA7, 0x44D5EFA1, +/**/ 0xBC556D0A, 0x4AF541D0, +/**/ 0x3FD1C37D, 0x64C6B876, +/**/ 0x3C746076, 0xFE0DCFF5, +/**/ 0x3FEEBE21, 0x4F76EFA8, +/**/ 0xBC802F9F, 0x12BA543E, +/**/ 0x3FD23E52, 0x111AAF36, +/**/ 0xBC74F080, 0x334EFF18, +/**/ 0x3FEEAC20, 0x61BBAF4F, +/**/ 0x3C62C1D5, 0x3E94658D, +/**/ 0x3FD2B8DD, 0xC43EB49F, +/**/ 0x3C615538, 0x99F2D807, +/**/ 0x3FEE99A4, 0xC3A7CD83, +/**/ 0xBC82264B, 0x1BC53CE8, +/**/ 0x3FD3331E, 0x94049F87, +/**/ 0x3C7E0CB6, 0xB40C302C, +/**/ 0x3FEE86AE, 0xBF29A9ED, +/**/ 0x3C89397A, 0xFDBB58A7, +/**/ 0x3FD3AD12, 0x9769D3D8, +/**/ 0x3C003D55, 0x04878398, +/**/ 0x3FEE733E, 0xA0193D40, +/**/ 0xBC86428B, 0x3546CE13, +/**/ 0x3FD426B7, 0xE69EE697, +/**/ 0xBC7F09C7, 0x5705C59F, +/**/ 0x3FEE5F54, 0xB436E9D0, +/**/ 0x3C87EB0F, 0xD02FC8BC, +/**/ 0x3FD4A00C, 0x9B0F3D20, +/**/ 0x3C7823BA, 0x6BB08EAD, +/**/ 0x3FEE4AF1, 0x4B2A449C, +/**/ 0xBC868CA0, 0x2E8A6833, +/**/ 0x3FD5190E, 0xCF68A77A, +/**/ 0x3C7B3571, 0x55EEF0F3, +/**/ 0x3FEE3614, 0xB680D6A5, +/**/ 0xBC727793, 0xAA015237, +/**/ 0x3FD591BC, 0x9FA2F597, +/**/ 0x3C67C74B, 0xAC3FE0CB, +/**/ 0x3FEE20BF, 0x49ACD6C1, +/**/ 0xBC5660AE, 0xC7EF636C, +/**/ 0x3FD60A14, 0x29078775, +/**/ 0x3C5B1FD8, 0x0BA89133, +/**/ 0x3FEE0AF1, 0x5A03DBCE, +/**/ 0x3C5FE8E7, 0x02771AE6, +/**/ 0x3FD68213, 0x8A38D7F7, +/**/ 0xBC7D8892, 0x02444AAD, +/**/ 0x3FEDF4AB, 0x3EBD875E, +/**/ 0xBC8E2D8A, 0x7E6736C4, +/**/ 0x3FD6F9B8, 0xE33A0255, +/**/ 0x3C742BC1, 0x4EE9DA0D, +/**/ 0x3FEDDDED, 0x50F228D6, +/**/ 0xBC6E80C8, 0xD42BA2BF, +/**/ 0x3FD77102, 0x55764214, +/**/ 0xBC66EAD7, 0x314BB6CE, +/**/ 0x3FEDC6B7, 0xEB995912, +/**/ 0x3C54B364, 0x776DCD35, +/**/ 0x3FD7E7EE, 0x03C86D4E, +/**/ 0xBC7B63BC, 0xDABF5AF2, +/**/ 0x3FEDAF0B, 0x6B888E83, +/**/ 0x3C8A249E, 0x2B5E5CEA, +/**/ 0x3FD85E7A, 0x12826949, +/**/ 0x3C78A40E, 0x9B5FACE0, +/**/ 0x3FED96E8, 0x2F71A9DC, +/**/ 0x3C8FF61B, 0xD5D2039D, +/**/ 0x3FD8D4A4, 0xA774992F, +/**/ 0x3C744A02, 0xEA766326, +/**/ 0x3FED7E4E, 0x97E17B4A, +/**/ 0xBC63B770, 0x352BED94, +/**/ 0x3FD94A6B, 0xE9F546C5, +/**/ 0xBC769CE1, 0x3E683F58, +/**/ 0x3FED653F, 0x073E4040, +/**/ 0xBC876236, 0x434BEC37, +/**/ 0x3FD9BFCE, 0x02E80510, +/**/ 0x3C709E39, 0xA320B0A4, +/**/ 0x3FED4BB9, 0xE1C619E0, +/**/ 0x3C8F34BB, 0x77858F61, +/**/ 0x3FDA34C9, 0x1CC50CCA, +/**/ 0xBC5A310E, 0x3B50CECD, +/**/ 0x3FED31BF, 0x8D8D7C06, +/**/ 0x3C7E60DD, 0x3089CBDD, +/**/ 0x3FDAA95B, 0x63A09277, +/**/ 0xBC66293E, 0xB13C0381, +/**/ 0x3FED1750, 0x727D94F0, +/**/ 0x3C80D52B, 0x1EC1A48E, +/**/ 0x3FDB1D83, 0x05321617, +/**/ 0xBC7AE242, 0xCB99F519, +/**/ 0x3FECFC6C, 0xFA52AD9F, +/**/ 0x3C88B5B5, 0x508F2A0D, +/**/ 0x3FDB913E, 0x30DBAC43, +/**/ 0xBC7E38AD, 0x2F6C3FF1, +/**/ 0x3FECE115, 0x909A82E5, +/**/ 0x3C81F139, 0xBB31109A, +/**/ 0x3FDC048B, 0x17B140A3, +/**/ 0x3C619FE6, 0x757E9FA7, +/**/ 0x3FECC54A, 0xA2B2972E, +/**/ 0x3C64EE16, 0x2BA83A98, +/**/ 0x3FDC7767, 0xEC7FD19E, +/**/ 0xBC5EB14D, 0x1A3D5826, +/**/ 0x3FECA90C, 0x9FC67D0B, +/**/ 0xBC646A81, 0x485E3462, +/**/ 0x3FDCE9D2, 0xE3D4A51F, +/**/ 0xBC62FC8A, 0x12DAE298, +/**/ 0x3FEC8C5B, 0xF8CE1A84, +/**/ 0x3C7AB3D1, 0xA1590123, +/**/ 0x3FDD5BCA, 0x34047661, +/**/ 0x3C728A44, 0xA75FC29C, +/**/ 0x3FEC6F39, 0x208BE53B, +/**/ 0xBC8741DB, 0xFBAADB42, +/**/ 0x3FDDCD4C, 0x15329C9A, +/**/ 0x3C70D4C6, 0xE171FD9A, +/**/ 0x3FEC51A4, 0x8B8B175E, +/**/ 0xBC61BBB4, 0x3B9AA880, +/**/ 0x3FDE3E56, 0xC1582A69, +/**/ 0xBC50A482, 0x1099F88F, +/**/ 0x3FEC339E, 0xB01DDD81, +/**/ 0xBC8CAAF5, 0xEE82C5C0, +/**/ 0x3FDEAEE8, 0x744B05F0, +/**/ 0xBC5789B4, 0x3C9B027D, +/**/ 0x3FEC1528, 0x065B7D50, +/**/ 0xBC889211, 0x1312E828, +/**/ 0x3FDF1EFF, 0x6BC4F97B, +/**/ 0x3C717212, 0xF8A7525C, +/**/ 0x3FEBF641, 0x081E7536, +/**/ 0x3C8B7BD7, 0x1628A9A1, +/**/ 0x3FDF8E99, 0xE76ABC97, +/**/ 0x3C59D950, 0xAF2D00A3, +/**/ 0x3FEBD6EA, 0x310294F5, +/**/ 0x3C731BBC, 0xC88C109D, +/**/ 0x3FDFFDB6, 0x28D2F57A, +/**/ 0x3C6F4A99, 0x2E905B6A, +/**/ 0x3FEBB723, 0xFE630F32, +/**/ 0x3C772BD2, 0x452D0A39, +/**/ 0x3FE03629, 0x39C69955, +/**/ 0xBC82D8CD, 0x78397B01, +/**/ 0x3FEB96EE, 0xEF58840E, +/**/ 0x3C545A3C, 0xC78FADE0, +/**/ 0x3FE06D36, 0x86946E5B, +/**/ 0x3C83F5AE, 0x4538FF1B, +/**/ 0x3FEB764B, 0x84B704C2, +/**/ 0xBC8F5848, 0xC21B389B, +/**/ 0x3FE0A402, 0x1E9E1001, +/**/ 0xBC86F643, 0xA13914F6, +/**/ 0x3FEB553A, 0x410C104E, +/**/ 0x3C58FF79, 0x47027A16, +/**/ 0x3FE0DA8B, 0x26B5672E, +/**/ 0xBC8A58DE, 0xF0BEE909, +/**/ 0x3FEB33BB, 0xA89C8948, +/**/ 0x3C8EA6A5, 0x1D1F6CA9, +/**/ 0x3FE110D0, 0xC4B69C3B, +/**/ 0x3C8D9189, 0x98809981, +/**/ 0x3FEB11D0, 0x4162A4C6, +/**/ 0x3C71DD56, 0x1EFBC0C2, +/**/ 0x3FE146D2, 0x1F8B7F82, +/**/ 0x3C7BF953, 0x5E2739A8, +/**/ 0x3FEAEF78, 0x930BD275, +/**/ 0xBC7F8362, 0x79746F94, +/**/ 0x3FE17C8E, 0x5F2EEDB0, +/**/ 0x3C635E57, 0x102E2488, +/**/ 0x3FEACCB5, 0x26F69DE5, +/**/ 0x3C88FB6A, 0x8DD6B6CC, +/**/ 0x3FE1B204, 0xACB02FDD, +/**/ 0xBC5F190C, 0x70CBB5FF, +/**/ 0x3FEAA986, 0x88308913, +/**/ 0xBC0B83D6, 0x07CD5070, +/**/ 0x3FE1E734, 0x3236574C, +/**/ 0x3C722A3F, 0xA4F41D5A, +/**/ 0x3FEA85ED, 0x4373E02D, +/**/ 0x3C69BE06, 0x385EC792, +/**/ 0x3FE21C1C, 0x1B0394CF, +/**/ 0x3C5E5B32, 0x4B23AA31, +/**/ 0x3FEA61E9, 0xE72586AF, +/**/ 0x3C858330, 0xE2FD453F, +/**/ 0x3FE250BB, 0x93788BBB, +/**/ 0x3C7EA3D0, 0x2457BCCE, +/**/ 0x3FEA3D7D, 0x0352BDCF, +/**/ 0xBC868DBA, 0xECA19669, +/**/ 0x3FE28511, 0xC917A067, +/**/ 0xBC801DF1, 0xD9A16B70, +/**/ 0x3FEA18A7, 0x29AEE445, +/**/ 0x3C395E25, 0x736C0358, +/**/ 0x3FE2B91D, 0xEA88421E, +/**/ 0xBC8FA371, 0xDB216AB0, +/**/ 0x3FE9F368, 0xED912F85, +/**/ 0xBC81D200, 0xC5791606, +/**/ 0x3FE2ECDF, 0x279A3082, +/**/ 0x3C8D3557, 0xE0E7E37E, +/**/ 0x3FE9CDC2, 0xE3F25E5C, +/**/ 0x3C83F991, 0x12993F62, +/**/ 0x3FE32054, 0xB148BC4F, +/**/ 0x3C8F6B42, 0x095A135B, +/**/ 0x3FE9A7B5, 0xA36A6514, +/**/ 0x3C8722CF, 0xCC9FA7A9, +/**/ 0x3FE3537D, 0xB9BE0367, +/**/ 0x3C6B327E, 0x7AF040F0, +/**/ 0x3FE98141, 0xC42E1310, +/**/ 0x3C8D1FF8, 0x0488F08D, +/**/ 0x3FE38659, 0x7456282B, +/**/ 0xBC710FAD, 0xA93B07A8, +/**/ 0x3FE95A67, 0xE00CB1FD, +/**/ 0xBC80BEFD, 0xA21F862D, +/**/ 0x3FE3B8E7, 0x15A2840A, +/**/ 0xBC797653, 0xA7D2F07B, +/**/ 0x3FE93328, 0x926D9E92, +/**/ 0xBC8BB770, 0x03600CDA, +/**/ 0x3FE3EB25, 0xD36CD53A, +/**/ 0xBC5BE570, 0xE1570FC0, +/**/ 0x3FE90B84, 0x784DDAF7, +/**/ 0xBC70FEB1, 0x0AB93B87, +/**/ 0x3FE41D14, 0xE4BA6790, +/**/ 0x3C84608F, 0xD287ECF5, +/**/ 0x3FE8E37C, 0x303D9AD1, +/**/ 0xBC6463A4, 0xB53D4BF8, +/**/ 0x3FE44EB3, 0x81CF386B, +/**/ 0xBC83ED6C, 0x1E6A5505, +/**/ 0x3FE8BB10, 0x5A5DC900, +/**/ 0x3C8863E0, 0x3E9474C1, +/**/ 0x3FE48000, 0xE431159F, +/**/ 0xBC8B194A, 0x7463ED10, +/**/ 0x3FE89241, 0x985D871F, +/**/ 0x3C8C48D9, 0xC413ED84, +/**/ 0x3FE4B0FC, 0x46AAB761, +/**/ 0x3C20DA05, 0x738CC59A, +/**/ 0x3FE86910, 0x8D77A6C6, +/**/ 0x3C7338FF, 0xE2BFE9DD, +/**/ 0x3FE4E1A4, 0xE54ED51B, +/**/ 0xBC8A492F, 0x89B7C76A, +/**/ 0x3FE83F7D, 0xDE701CA0, +/**/ 0xBC4152CF, 0x609BC6E8, +/**/ 0x3FE511F9, 0xFD7B351C, +/**/ 0xBC85C0E8, 0x61C48831, +/**/ 0x3FE8158A, 0x31916D5D, +/**/ 0xBC6DE8B9, 0x0B8228DE, +/**/ 0x3FE541FA, 0xCDDBB724, +/**/ 0x3C7232C2, 0x8520D391, +/**/ 0x3FE7EB36, 0x2EAA1488, +/**/ 0x3C5A1D65, 0xA4A5959F, +/**/ 0x3FE571A6, 0x966D59B3, +/**/ 0x3C5C843B, 0x4D0FB198, +/**/ 0x3FE7C082, 0x7F09E54F, +/**/ 0xBC6C73D6, 0xD72AEE68, +/**/ 0x3FE5A0FC, 0x98813A12, +/**/ 0xBC8D82E2, 0xB7D4227B, +/**/ 0x3FE7956F, 0xCD7F6543, +/**/ 0xBC8AB276, 0xE9D45AE4, +/**/ 0x3FE5CFFC, 0x16BF8F0D, +/**/ 0x3C896CB3, 0x70EB578A, +/**/ 0x3FE769FE, 0xC655211F, +/**/ 0xBC6827D5, 0xCF8C68C5, +/**/ 0x3FE5FEA4, 0x552A9E57, +/**/ 0x3C80B6CE, 0xF7EE20B7, +/**/ 0x3FE73E30, 0x174EFBA1, +/**/ 0xBC65D3AE, 0x3D94AD5F, +/**/ 0x3FE62CF4, 0x9921AC79, +/**/ 0xBC8EDD98, 0x55B6241A, +/**/ 0x3FE71204, 0x6FA77678, +/**/ 0x3C8425B0, 0xA5029C81, +/**/ 0x3FE65AEC, 0x2963E755, +/**/ 0x3C8126F9, 0x6B71053C, +/**/ 0x3FE6E57C, 0x800CF55E, +/**/ 0x3C860286, 0xDEDBD0A6, +/**/ 0x3FE6888A, 0x4E134B2F, +/**/ 0xBC86B7D3, 0x7644D5E6, +/**/ 0x3FE6B898, 0xFA9EFB5D, +/**/ 0x3C715AC7, 0x86CCF4B2, +/**/ 0x3FE6B5CE, 0x50B7821A, +/**/ 0xBC65D515, 0x8F702E0F, +/**/ 0x3FE68B5A, 0x92EB6253, +/**/ 0xBC89A91A, 0xD985F89C, +/**/ 0x3FE6E2B7, 0x7C40BDE1, +/**/ 0xBC70E729, 0x857FAD53, +/**/ 0x3FE65DC1, 0xFDEB8CBA, +/**/ 0xBC597C1B, 0x47337C77, +/**/ 0x3FE70F45, 0x1D0A8C40, +/**/ 0x3C697EDE, 0x3885770D, +/**/ 0x3FE62FCF, 0xF20191C7, +/**/ 0x3C6D9143, 0x895756EF, +/**/ 0x3FE73B76, 0x80DEA578, +/**/ 0xBC722483, 0x06DC12A2, +/**/ 0x3FE60185, 0x26F563DF, +/**/ 0x3C846CA5, 0xE0E432D0, +/**/ 0x3FE7674A, 0xF6F7B524, +/**/ 0x3C7E9D3F, 0x94AC84A8, +/**/ 0x3FE5D2E2, 0x55F1F17A, +/**/ 0x3C803141, 0x04C8892B, +/**/ 0x3FE792C1, 0xD0041D52, +/**/ 0xBC8ABF05, 0xEEB354EB, +/**/ 0x3FE5A3E8, 0x39824077, +/**/ 0x3C8428AA, 0x2759BE62, +/**/ 0x3FE7BDDA, 0x5E28B3C2, +/**/ 0x3C4AD119, 0x7CCD0393, +/**/ 0x3FE57497, 0x8D8E83F2, +/**/ 0x3C8F4714, 0xAF282D23, +/**/ 0x3FE7E893, 0xF5037959, +/**/ 0x3C80EEFB, 0xAA650C4C, +/**/ 0x3FE544F1, 0x0F592CA5, +/**/ 0xBC8E7AE8, 0xE6C7A62F, +/**/ 0x3FE812ED, 0xE9AE4BA4, +/**/ 0xBC87830A, 0xDF402DDA, +/**/ 0x3FE514F5, 0x7D7BF3DA, +/**/ 0x3C747A10, 0x8073C259 } }; +#else +#ifdef LITTLE_ENDI +const union {int4 i[880]; double x[440];} __sincostab = { .i = { +/**/ 0x00000000, 0x00000000, +/**/ 0x00000000, 0x00000000, +/**/ 0x00000000, 0x3FF00000, +/**/ 0x00000000, 0x00000000, +/**/ 0xAAAEEEEF, 0x3F7FFFEA, +/**/ 0xEC67B77C, 0xBC1E45E2, +/**/ 0x00155552, 0x3FEFFFC0, +/**/ 0xA0196DAE, 0x3C8F4A01, +/**/ 0xAAEEEED5, 0x3F8FFFAA, +/**/ 0x9A9F0777, 0xBC02AB63, +/**/ 0x0155549F, 0x3FEFFF00, +/**/ 0xA03A5EF3, 0x3C828A28, +/**/ 0x01033255, 0x3F97FF70, +/**/ 0x51527336, 0x3BFEFE2B, +/**/ 0x06BFF7E6, 0x3FEFFDC0, +/**/ 0xE86977BD, 0x3C8AE6DA, +/**/ 0xAEEEE86F, 0x3F9FFEAA, +/**/ 0xFB224AE2, 0xBC3CD406, +/**/ 0x155527D3, 0x3FEFFC00, +/**/ 0x92D89B5B, 0xBC83B544, +/**/ 0xB12D45D5, 0x3FA3FEB2, +/**/ 0x203D1C11, 0x3C34EC54, +/**/ 0x3414A7BA, 0x3FEFF9C0, +/**/ 0xBE6C59BF, 0x3C6991F4, +/**/ 0x1032FBA9, 0x3FA7FDC0, +/**/ 0xF46E997A, 0xBC4599BD, +/**/ 0x6BFDF99F, 0x3FEFF700, +/**/ 0x60648D5F, 0xBC78B3B5, +/**/ 0x78586DAC, 0x3FABFC6D, +/**/ 0x03DBF236, 0x3C18E4FD, +/**/ 0xC8103A31, 0x3FEFF3C0, +/**/ 0xBDDC0E66, 0x3C74856D, +/**/ 0xEEED4EDB, 0x3FAFFAAA, +/**/ 0x32684B69, 0xBC42D16D, +/**/ 0x5549F4D3, 0x3FEFF001, +/**/ 0x7B99426F, 0x3C832838, +/**/ 0x3D808BEF, 0x3FB1FC34, +/**/ 0xE6F3BE4F, 0xBC5F3D32, +/**/ 0x22A8EF9F, 0x3FEFEBC2, +/**/ 0x34F54C77, 0x3C579349, +/**/ 0x12D1755B, 0x3FB3FACB, +/**/ 0x5299468C, 0xBC592191, +/**/ 0x4129EF6F, 0x3FEFE703, +/**/ 0x37C96F97, 0xBC6CBF43, +/**/ 0xFD10B737, 0x3FB5F911, +/**/ 0x02BE9102, 0xBC50184F, +/**/ 0xC3C873EB, 0x3FEFE1C4, +/**/ 0x057C4A02, 0xBC35A9C9, +/**/ 0x032550E4, 0x3FB7F701, +/**/ 0x1800501A, 0x3C3AFC2D, +/**/ 0xBF7E6B9B, 0x3FEFDC06, +/**/ 0xB535F8DB, 0x3C831902, +/**/ 0x2D55D1F9, 0x3FB9F490, +/**/ 0x7EAC1DC1, 0x3C52696D, +/**/ 0x4B43E000, 0x3FEFD5C9, +/**/ 0xCB4F92F9, 0xBC62E768, +/**/ 0x8568391D, 0x3FBBF1B7, +/**/ 0x1DEA4CC8, 0x3C5E9184, +/**/ 0x800E99B1, 0x3FEFCF0C, +/**/ 0x86D186AC, 0x3C6EA3D7, +/**/ 0x16C1CCE6, 0x3FBDEE6F, +/**/ 0x2FB71673, 0xBC450F8E, +/**/ 0x78D1BC88, 0x3FEFC7D0, +/**/ 0x447DB685, 0x3C8075D2, +/**/ 0xEE86EE36, 0x3FBFEAAE, +/**/ 0xBCC6F03B, 0xBC4AFCB2, +/**/ 0x527D5BD3, 0x3FEFC015, +/**/ 0x5094EFB8, 0x3C8B68F3, +/**/ 0x8DDD71D1, 0x3FC0F337, +/**/ 0x724F0F9E, 0x3C6D8468, +/**/ 0x2BFE0695, 0x3FEFB7DB, +/**/ 0xF4F65AB1, 0x3C821DAD, +/**/ 0xD7AFCEAF, 0x3FC1F0D3, +/**/ 0x099769A5, 0xBC66EF95, +/**/ 0x263C4BD3, 0x3FEFAF22, +/**/ 0x133A2769, 0xBC552ACE, +/**/ 0x5E4AB88F, 0x3FC2EE28, +/**/ 0x05DEE058, 0xBC6E4D0F, +/**/ 0x641C36F2, 0x3FEFA5EA, +/**/ 0xED17CC7C, 0x3C404DA6, +/**/ 0x2C5D66CB, 0x3FC3EB31, +/**/ 0x6B66CB91, 0x3C647D66, +/**/ 0x0A7CC428, 0x3FEF9C34, +/**/ 0x063B7462, 0x3C8C5B6B, +/**/ 0x4DC5F27B, 0x3FC4E7EA, +/**/ 0x2AC072FC, 0x3C5949DB, +/**/ 0x40374D01, 0x3FEF91FF, +/**/ 0x4D3A9E4C, 0xBC67D03F, +/**/ 0xCFA126F3, 0x3FC5E44F, +/**/ 0x063F89B6, 0xBC66F443, +/**/ 0x2E1EECF6, 0x3FEF874C, +/**/ 0xE1332B16, 0xBC8C6514, +/**/ 0xC05A4D4C, 0x3FC6E05D, +/**/ 0x8B81C940, 0xBBD32C5C, +/**/ 0xFEFFDE24, 0x3FEF7C1A, +/**/ 0xC47540B1, 0xBC78F55B, +/**/ 0x2FBAF2B5, 0x3FC7DC10, +/**/ 0xE23C97C3, 0x3C45AB50, +/**/ 0xDF9ECE1C, 0x3FEF706B, +/**/ 0x0C36DCB4, 0xBC8698C8, +/**/ 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0x8D8E83F2, 0x3FE57497, +/**/ 0xAF282D23, 0x3C8F4714, +/**/ 0xF5037959, 0x3FE7E893, +/**/ 0xAA650C4C, 0x3C80EEFB, +/**/ 0x0F592CA5, 0x3FE544F1, +/**/ 0xE6C7A62F, 0xBC8E7AE8, +/**/ 0xE9AE4BA4, 0x3FE812ED, +/**/ 0xDF402DDA, 0xBC87830A, +/**/ 0x7D7BF3DA, 0x3FE514F5, +/**/ 0x8073C259, 0x3C747A10 } }; +#endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/slowexp.c b/REORG.TODO/sysdeps/ieee754/dbl-64/slowexp.c new file mode 100644 index 0000000000..e8fa2e263b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/slowexp.c @@ -0,0 +1,86 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/**************************************************************************/ +/* MODULE_NAME:slowexp.c */ +/* */ +/* FUNCTION:slowexp */ +/* */ +/* FILES NEEDED:mpa.h */ +/* mpa.c mpexp.c */ +/* */ +/*Converting from double precision to Multi-precision and calculating */ +/* e^x */ +/**************************************************************************/ +#include <math_private.h> + +#include <stap-probe.h> + +#ifndef USE_LONG_DOUBLE_FOR_MP +# include "mpa.h" +void __mpexp (mp_no *x, mp_no *y, int p); +#endif + +#ifndef SECTION +# define SECTION +#endif + +/*Converting from double precision to Multi-precision and calculating e^x */ +double +SECTION +__slowexp (double x) +{ +#ifndef USE_LONG_DOUBLE_FOR_MP + double w, z, res, eps = 3.0e-26; + int p; + mp_no mpx, mpy, mpz, mpw, mpeps, mpcor; + + /* Use the multiple precision __MPEXP function to compute the exponential + First at 144 bits and if it is not accurate enough, at 768 bits. */ + p = 6; + __dbl_mp (x, &mpx, p); + __mpexp (&mpx, &mpy, p); + __dbl_mp (eps, &mpeps, p); + __mul (&mpeps, &mpy, &mpcor, p); + __add (&mpy, &mpcor, &mpw, p); + __sub (&mpy, &mpcor, &mpz, p); + __mp_dbl (&mpw, &w, p); + __mp_dbl (&mpz, &z, p); + if (w == z) + { + /* Track how often we get to the slow exp code plus + its input/output values. */ + LIBC_PROBE (slowexp_p6, 2, &x, &w); + return w; + } + else + { + p = 32; + __dbl_mp (x, &mpx, p); + __mpexp (&mpx, &mpy, p); + __mp_dbl (&mpy, &res, p); + + /* Track how often we get to the uber-slow exp code plus + its input/output values. */ + LIBC_PROBE (slowexp_p32, 2, &x, &res); + return res; + } +#else + return (double) __ieee754_expl((long double)x); +#endif +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/slowpow.c b/REORG.TODO/sysdeps/ieee754/dbl-64/slowpow.c new file mode 100644 index 0000000000..1176b2689c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/slowpow.c @@ -0,0 +1,125 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/*************************************************************************/ +/* MODULE_NAME:slowpow.c */ +/* */ +/* FUNCTION:slowpow */ +/* */ +/*FILES NEEDED:mpa.h */ +/* mpa.c mpexp.c mplog.c halfulp.c */ +/* */ +/* Given two IEEE double machine numbers y,x , routine computes the */ +/* correctly rounded (to nearest) value of x^y. Result calculated by */ +/* multiplication (in halfulp.c) or if result isn't accurate enough */ +/* then routine converts x and y into multi-precision doubles and */ +/* calls to mpexp routine */ +/*************************************************************************/ + +#include "mpa.h" +#include <math_private.h> + +#include <stap-probe.h> + +#ifndef SECTION +# define SECTION +#endif + +void __mpexp (mp_no *x, mp_no *y, int p); +void __mplog (mp_no *x, mp_no *y, int p); +double ulog (double); +double __halfulp (double x, double y); + +double +SECTION +__slowpow (double x, double y, double z) +{ + double res, res1; + mp_no mpx, mpy, mpz, mpw, mpp, mpr, mpr1; + static const mp_no eps = {-3, {1.0, 4.0}}; + int p; + + /* __HALFULP returns -10 or X^Y. */ + res = __halfulp (x, y); + + /* Return if the result was computed by __HALFULP. */ + if (res >= 0) + return res; + + /* Compute pow as long double. This is currently only used by powerpc, where + one may get 106 bits of accuracy. */ +#ifdef USE_LONG_DOUBLE_FOR_MP + long double ldw, ldz, ldpp; + static const long double ldeps = 0x4.0p-96; + + ldz = __ieee754_logl ((long double) x); + ldw = (long double) y *ldz; + ldpp = __ieee754_expl (ldw); + res = (double) (ldpp + ldeps); + res1 = (double) (ldpp - ldeps); + + /* Return the result if it is accurate enough. */ + if (res == res1) + return res; +#endif + + /* Or else, calculate using multiple precision. P = 10 implies accuracy of + 240 bits accuracy, since MP_NO has a radix of 2^24. */ + p = 10; + __dbl_mp (x, &mpx, p); + __dbl_mp (y, &mpy, p); + __dbl_mp (z, &mpz, p); + + /* z = x ^ y + log (z) = y * log (x) + z = exp (y * log (x)) */ + __mplog (&mpx, &mpz, p); + __mul (&mpy, &mpz, &mpw, p); + __mpexp (&mpw, &mpp, p); + + /* Add and subtract EPS to ensure that the result remains unchanged, i.e. we + have last bit accuracy. */ + __add (&mpp, &eps, &mpr, p); + __mp_dbl (&mpr, &res, p); + __sub (&mpp, &eps, &mpr1, p); + __mp_dbl (&mpr1, &res1, p); + if (res == res1) + { + /* Track how often we get to the slow pow code plus + its input/output values. */ + LIBC_PROBE (slowpow_p10, 4, &x, &y, &z, &res); + return res; + } + + /* If we don't, then we repeat using a higher precision. 768 bits of + precision ought to be enough for anybody. */ + p = 32; + __dbl_mp (x, &mpx, p); + __dbl_mp (y, &mpy, p); + __dbl_mp (z, &mpz, p); + __mplog (&mpx, &mpz, p); + __mul (&mpy, &mpz, &mpw, p); + __mpexp (&mpw, &mpp, p); + __mp_dbl (&mpp, &res, p); + + /* Track how often we get to the uber-slow pow code plus + its input/output values. */ + LIBC_PROBE (slowpow_p32, 4, &x, &y, &z, &res); + + return res; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/t_exp.c b/REORG.TODO/sysdeps/ieee754/dbl-64/t_exp.c new file mode 100644 index 0000000000..58866e7794 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/t_exp.c @@ -0,0 +1,435 @@ +/* Accurate tables for exp(). + Copyright (C) 1998-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Geoffrey Keating <geoffk@ozemail.com.au> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* This table has the property that, for all integers -177 <= i <= 177, + exp(i/512.0 + __exp_deltatable[abs(i)]) == __exp_atable[i+177] + r + for some -2^-64 < r < 2^-64 (abs(r) < 2^-65 if i <= 0); and that + __exp_deltatable[abs(i)] == t * 2^-60 + for integer t so that abs(t) <= 8847927 * 2^8. */ + +#define W52 (2.22044605e-16) +#define W55 (2.77555756e-17) +#define W58 (3.46944695e-18) +#define W59 (1.73472348e-18) +#define W60 (8.67361738e-19) +const float __exp_deltatable[178] = { + 0*W60, 16558714*W60, -10672149*W59, 1441652*W60, + -15787963*W55, 462888*W60, 7291806*W60, 1698880*W60, + -14375103*W58, -2021016*W60, 728829*W60, -3759654*W60, + 3202123*W60, -10916019*W58, -251570*W60, -1043086*W60, + 8207536*W60, -409964*W60, -5993931*W60, -475500*W60, + 2237522*W60, 324170*W60, -244117*W60, 32077*W60, + 123907*W60, -1019734*W60, -143*W60, 813077*W60, + 743345*W60, 462461*W60, 629794*W60, 2125066*W60, + -2339121*W60, -337951*W60, 9922067*W60, -648704*W60, + 149407*W60, -2687209*W60, -631608*W60, 2128280*W60, + -4882082*W60, 2001360*W60, 175074*W60, 2923216*W60, + -538947*W60, -1212193*W60, -1920926*W60, -1080577*W60, + 3690196*W60, 2643367*W60, 2911937*W60, 671455*W60, + -1128674*W60, 593282*W60, -5219347*W60, -1941490*W60, + 11007953*W60, 239609*W60, -2969658*W60, -1183650*W60, + 942998*W60, 699063*W60, 450569*W60, -329250*W60, + -7257875*W60, -312436*W60, 51626*W60, 555877*W60, + -641761*W60, 1565666*W60, 884327*W60, -10960035*W60, + -2004679*W60, -995793*W60, -2229051*W60, -146179*W60, + -510327*W60, 1453482*W60, -3778852*W60, -2238056*W60, + -4895983*W60, 3398883*W60, -252738*W60, 1230155*W60, + 346918*W60, 1109352*W60, 268941*W60, -2930483*W60, + -1036263*W60, -1159280*W60, 1328176*W60, 2937642*W60, + -9371420*W60, -6902650*W60, -1419134*W60, 1442904*W60, + -1319056*W60, -16369*W60, 696555*W60, -279987*W60, + -7919763*W60, 252741*W60, 459711*W60, -1709645*W60, + 354913*W60, 6025867*W60, -421460*W60, -853103*W60, + -338649*W60, 962151*W60, 955965*W60, 784419*W60, + -3633653*W60, 2277133*W60, -8847927*W52, 1223028*W60, + 5907079*W60, 623167*W60, 5142888*W60, 2599099*W60, + 1214280*W60, 4870359*W60, 593349*W60, -57705*W60, + 7761209*W60, -5564097*W60, 2051261*W60, 6216869*W60, + 4692163*W60, 601691*W60, -5264906*W60, 1077872*W60, + -3205949*W60, 1833082*W60, 2081746*W60, -987363*W60, + -1049535*W60, 2015244*W60, 874230*W60, 2168259*W60, + -1740124*W60, -10068269*W60, -18242*W60, -3013583*W60, + 580601*W60, -2547161*W60, -535689*W60, 2220815*W60, + 1285067*W60, 2806933*W60, -983086*W60, -1729097*W60, + -1162985*W60, -2561904*W60, 801988*W60, 244351*W60, + 1441893*W60, -7517981*W60, 271781*W60, -15021588*W60, + -2341588*W60, -919198*W60, 1642232*W60, 4771771*W60, + -1220099*W60, -3062372*W60, 628624*W60, 1278114*W60, + 13083513*W60, -10521925*W60, 3180310*W60, -1659307*W60, + 3543773*W60, 2501203*W60, 4151*W60, -340748*W60, + -2285625*W60, 2495202*W60 +}; + +const double __exp_atable[355] /* __attribute__((mode(DF))) */ = { + 0.707722561055888932371, /* 0x0.b52d4e46605c27ffd */ + 0.709106182438804188967, /* 0x0.b587fb96f75097ffb */ + 0.710492508843861281234, /* 0x0.b5e2d649899167ffd */ + 0.711881545564593931623, /* 0x0.b63dde74d36bdfffe */ + 0.713273297897442870573, /* 0x0.b699142f945f87ffc */ + 0.714667771153751463236, /* 0x0.b6f477909c4ea0001 */ + 0.716064970655995725059, /* 0x0.b75008aec758f8004 */ + 0.717464901723956938193, /* 0x0.b7abc7a0eea7e0002 */ + 0.718867569715736398602, /* 0x0.b807b47e1586c7ff8 */ + 0.720272979947266023271, /* 0x0.b863cf5d10e380003 */ + 0.721681137825144314297, /* 0x0.b8c01855195c37ffb */ + 0.723092048691992950199, /* 0x0.b91c8f7d213740004 */ + 0.724505717938892290800, /* 0x0.b97934ec5002d0007 */ + 0.725922150953176470431, /* 0x0.b9d608b9c92ea7ffc */ + 0.727341353138962865022, /* 0x0.ba330afcc29e98003 */ + 0.728763329918453162104, /* 0x0.ba903bcc8618b7ffc */ + 0.730188086709957051568, /* 0x0.baed9b40591ba0000 */ + 0.731615628948127705309, /* 0x0.bb4b296f931e30002 */ + 0.733045962086486091436, /* 0x0.bba8e671a05617ff9 */ + 0.734479091556371366251, /* 0x0.bc06d25dd49568001 */ + 0.735915022857225542529, /* 0x0.bc64ed4bce8f6fff9 */ + 0.737353761441304711410, /* 0x0.bcc33752f915d7ff9 */ + 0.738795312814142124419, /* 0x0.bd21b08af98e78005 */ + 0.740239682467211168593, /* 0x0.bd80590b65e9a8000 */ + 0.741686875913991849885, /* 0x0.bddf30ebec4a10000 */ + 0.743136898669507939299, /* 0x0.be3e38443c84e0007 */ + 0.744589756269486091620, /* 0x0.be9d6f2c1d32a0002 */ + 0.746045454254026796384, /* 0x0.befcd5bb59baf8004 */ + 0.747503998175051087583, /* 0x0.bf5c6c09ca84c0003 */ + 0.748965393601880857739, /* 0x0.bfbc322f5b18b7ff8 */ + 0.750429646104262104698, /* 0x0.c01c2843f776fffff */ + 0.751896761271877989160, /* 0x0.c07c4e5fa18b88002 */ + 0.753366744698445112140, /* 0x0.c0dca49a5fb18fffd */ + 0.754839601988627206827, /* 0x0.c13d2b0c444db0005 */ + 0.756315338768691947122, /* 0x0.c19de1cd798578006 */ + 0.757793960659406629066, /* 0x0.c1fec8f623723fffd */ + 0.759275473314173443536, /* 0x0.c25fe09e8a0f47ff8 */ + 0.760759882363831851927, /* 0x0.c2c128dedc88f8000 */ + 0.762247193485956486805, /* 0x0.c322a1cf7d6e7fffa */ + 0.763737412354726363781, /* 0x0.c3844b88cb9347ffc */ + 0.765230544649828092739, /* 0x0.c3e626232bd8f7ffc */ + 0.766726596071518051729, /* 0x0.c44831b719bf18002 */ + 0.768225572321911687194, /* 0x0.c4aa6e5d12d078001 */ + 0.769727479119219348810, /* 0x0.c50cdc2da64a37ffb */ + 0.771232322196981678892, /* 0x0.c56f7b41744490001 */ + 0.772740107296721268087, /* 0x0.c5d24bb1259e70004 */ + 0.774250840160724651565, /* 0x0.c6354d95640dd0007 */ + 0.775764526565368872643, /* 0x0.c6988106fec447fff */ + 0.777281172269557396602, /* 0x0.c6fbe61eb1bd0ffff */ + 0.778800783068235302750, /* 0x0.c75f7cf560942fffc */ + 0.780323364758801041312, /* 0x0.c7c345a3f1983fffe */ + 0.781848923151573727006, /* 0x0.c8274043594cb0002 */ + 0.783377464064598849602, /* 0x0.c88b6cec94b3b7ff9 */ + 0.784908993312207869935, /* 0x0.c8efcbb89cba27ffe */ + 0.786443516765346961618, /* 0x0.c9545cc0a88c70003 */ + 0.787981040257604625744, /* 0x0.c9b9201dc643bfffa */ + 0.789521569657452682047, /* 0x0.ca1e15e92a5410007 */ + 0.791065110849462849192, /* 0x0.ca833e3c1ae510005 */ + 0.792611669712891875319, /* 0x0.cae8992fd84667ffd */ + 0.794161252150049179450, /* 0x0.cb4e26ddbc207fff8 */ + 0.795713864077794763584, /* 0x0.cbb3e75f301b60003 */ + 0.797269511407239561694, /* 0x0.cc19dacd978cd8002 */ + 0.798828200086368567220, /* 0x0.cc8001427e55d7ffb */ + 0.800389937624300440456, /* 0x0.cce65ade24d360006 */ + 0.801954725261124767840, /* 0x0.cd4ce7a5de839fffb */ + 0.803522573691593189330, /* 0x0.cdb3a7c79a678fffd */ + 0.805093487311204114563, /* 0x0.ce1a9b563965ffffc */ + 0.806667472122675088819, /* 0x0.ce81c26b838db8000 */ + 0.808244534127439906441, /* 0x0.cee91d213f8428002 */ + 0.809824679342317166307, /* 0x0.cf50ab9144d92fff9 */ + 0.811407913793616542005, /* 0x0.cfb86dd5758c2ffff */ + 0.812994243520784198882, /* 0x0.d0206407c20e20005 */ + 0.814583674571603966162, /* 0x0.d0888e4223facfff9 */ + 0.816176213022088536960, /* 0x0.d0f0ec9eb3f7c8002 */ + 0.817771864936188586101, /* 0x0.d1597f377d6768002 */ + 0.819370636400374108252, /* 0x0.d1c24626a46eafff8 */ + 0.820972533518165570298, /* 0x0.d22b41865ff1e7ff9 */ + 0.822577562404315121269, /* 0x0.d2947170f32ec7ff9 */ + 0.824185729164559344159, /* 0x0.d2fdd60097795fff8 */ + 0.825797039949601741075, /* 0x0.d3676f4fb796d0001 */ + 0.827411500902565544264, /* 0x0.d3d13d78b5f68fffb */ + 0.829029118181348834154, /* 0x0.d43b40960546d8001 */ + 0.830649897953322891022, /* 0x0.d4a578c222a058000 */ + 0.832273846408250750368, /* 0x0.d50fe617a3ba78005 */ + 0.833900969738858188772, /* 0x0.d57a88b1218e90002 */ + 0.835531274148056613016, /* 0x0.d5e560a94048f8006 */ + 0.837164765846411529371, /* 0x0.d6506e1aac8078003 */ + 0.838801451086016225394, /* 0x0.d6bbb1204074e0001 */ + 0.840441336100884561780, /* 0x0.d72729d4c28518004 */ + 0.842084427144139224814, /* 0x0.d792d8530e12b0001 */ + 0.843730730487052604790, /* 0x0.d7febcb61273e7fff */ + 0.845380252404570153833, /* 0x0.d86ad718c308dfff9 */ + 0.847032999194574087728, /* 0x0.d8d727962c69d7fff */ + 0.848688977161248581090, /* 0x0.d943ae49621ce7ffb */ + 0.850348192619261200615, /* 0x0.d9b06b4d832ef8005 */ + 0.852010651900976245816, /* 0x0.da1d5ebdc22220005 */ + 0.853676361342631029337, /* 0x0.da8a88b555baa0006 */ + 0.855345327311054837175, /* 0x0.daf7e94f965f98004 */ + 0.857017556155879489641, /* 0x0.db6580a7c98f7fff8 */ + 0.858693054267390953857, /* 0x0.dbd34ed9617befff8 */ + 0.860371828028939855647, /* 0x0.dc4153ffc8b65fff9 */ + 0.862053883854957292436, /* 0x0.dcaf90368bfca8004 */ + 0.863739228154875360306, /* 0x0.dd1e0399328d87ffe */ + 0.865427867361348468455, /* 0x0.dd8cae435d303fff9 */ + 0.867119807911702289458, /* 0x0.ddfb9050b1cee8006 */ + 0.868815056264353846599, /* 0x0.de6aa9dced8448001 */ + 0.870513618890481399881, /* 0x0.ded9fb03db7320006 */ + 0.872215502247877139094, /* 0x0.df4983e1380657ff8 */ + 0.873920712852848668986, /* 0x0.dfb94490ffff77ffd */ + 0.875629257204025623884, /* 0x0.e0293d2f1cb01fff9 */ + 0.877341141814212965880, /* 0x0.e0996dd786fff0007 */ + 0.879056373217612985183, /* 0x0.e109d6a64f5d57ffc */ + 0.880774957955916648615, /* 0x0.e17a77b78e72a7ffe */ + 0.882496902590150900078, /* 0x0.e1eb5127722cc7ff8 */ + 0.884222213673356738383, /* 0x0.e25c63121fb0c8006 */ + 0.885950897802399772740, /* 0x0.e2cdad93ec5340003 */ + 0.887682961567391237685, /* 0x0.e33f30c925fb97ffb */ + 0.889418411575228162725, /* 0x0.e3b0ecce2d05ffff9 */ + 0.891157254447957902797, /* 0x0.e422e1bf727718006 */ + 0.892899496816652704641, /* 0x0.e4950fb9713fc7ffe */ + 0.894645145323828439008, /* 0x0.e50776d8b0e60fff8 */ + 0.896394206626591749641, /* 0x0.e57a1739c8fadfffc */ + 0.898146687421414902124, /* 0x0.e5ecf0f97c5798007 */ + 0.899902594367530173098, /* 0x0.e660043464e378005 */ + 0.901661934163603406867, /* 0x0.e6d3510747e150006 */ + 0.903424713533971135418, /* 0x0.e746d78f06cd97ffd */ + 0.905190939194458810123, /* 0x0.e7ba97e879c91fffc */ + 0.906960617885092856864, /* 0x0.e82e92309390b0007 */ + 0.908733756358986566306, /* 0x0.e8a2c6845544afffa */ + 0.910510361377119825629, /* 0x0.e9173500c8abc7ff8 */ + 0.912290439722343249336, /* 0x0.e98bddc30f98b0002 */ + 0.914073998177417412765, /* 0x0.ea00c0e84bc4c7fff */ + 0.915861043547953501680, /* 0x0.ea75de8db8094fffe */ + 0.917651582652244779397, /* 0x0.eaeb36d09d3137ffe */ + 0.919445622318405764159, /* 0x0.eb60c9ce4ed3dffff */ + 0.921243169397334638073, /* 0x0.ebd697a43995b0007 */ + 0.923044230737526172328, /* 0x0.ec4ca06fc7768fffa */ + 0.924848813220121135342, /* 0x0.ecc2e44e865b6fffb */ + 0.926656923710931002014, /* 0x0.ed39635df34e70006 */ + 0.928468569126343790092, /* 0x0.edb01dbbc2f5b7ffa */ + 0.930283756368834757725, /* 0x0.ee2713859aab57ffa */ + 0.932102492359406786818, /* 0x0.ee9e44d9342870004 */ + 0.933924784042873379360, /* 0x0.ef15b1d4635438005 */ + 0.935750638358567643520, /* 0x0.ef8d5a94f60f50007 */ + 0.937580062297704630580, /* 0x0.f0053f38f345cffff */ + 0.939413062815381727516, /* 0x0.f07d5fde3a2d98001 */ + 0.941249646905368053689, /* 0x0.f0f5bca2d481a8004 */ + 0.943089821583810716806, /* 0x0.f16e55a4e497d7ffe */ + 0.944933593864477061592, /* 0x0.f1e72b028a2827ffb */ + 0.946780970781518460559, /* 0x0.f2603cd9fb5430001 */ + 0.948631959382661205081, /* 0x0.f2d98b497d2a87ff9 */ + 0.950486566729423554277, /* 0x0.f353166f63e3dffff */ + 0.952344799896018723290, /* 0x0.f3ccde6a11ae37ffe */ + 0.954206665969085765512, /* 0x0.f446e357f66120000 */ + 0.956072172053890279009, /* 0x0.f4c12557964f0fff9 */ + 0.957941325265908139014, /* 0x0.f53ba48781046fffb */ + 0.959814132734539637840, /* 0x0.f5b66106555d07ffa */ + 0.961690601603558903308, /* 0x0.f6315af2c2027fffc */ + 0.963570739036113010927, /* 0x0.f6ac926b8aeb80004 */ + 0.965454552202857141381, /* 0x0.f728078f7c5008002 */ + 0.967342048278315158608, /* 0x0.f7a3ba7d66a908001 */ + 0.969233234469444204768, /* 0x0.f81fab543e1897ffb */ + 0.971128118008140250896, /* 0x0.f89bda33122c78007 */ + 0.973026706099345495256, /* 0x0.f9184738d4cf97ff8 */ + 0.974929006031422851235, /* 0x0.f994f284d3a5c0008 */ + 0.976835024947348973265, /* 0x0.fa11dc35bc7820002 */ + 0.978744770239899142285, /* 0x0.fa8f046b4fb7f8007 */ + 0.980658249138918636210, /* 0x0.fb0c6b449ab1cfff9 */ + 0.982575468959622777535, /* 0x0.fb8a10e1088fb7ffa */ + 0.984496437054508843888, /* 0x0.fc07f5602d79afffc */ + 0.986421160608523028820, /* 0x0.fc8618e0e55e47ffb */ + 0.988349647107594098099, /* 0x0.fd047b83571b1fffa */ + 0.990281903873210800357, /* 0x0.fd831d66f4c018002 */ + 0.992217938695037382475, /* 0x0.fe01fead3320bfff8 */ + 0.994157757657894713987, /* 0x0.fe811f703491e8006 */ + 0.996101369488558541238, /* 0x0.ff007fd5744490005 */ + 0.998048781093141101932, /* 0x0.ff801ffa9b9280007 */ + 1.000000000000000000000, /* 0x1.00000000000000000 */ + 1.001955033605393285965, /* 0x1.0080200565d29ffff */ + 1.003913889319761887310, /* 0x1.0100802aa0e80fff0 */ + 1.005876574715736104818, /* 0x1.01812090377240007 */ + 1.007843096764807100351, /* 0x1.020201541aad7fff6 */ + 1.009813464316352327214, /* 0x1.0283229c4c9820007 */ + 1.011787683565730677817, /* 0x1.030484836910a000e */ + 1.013765762469146736174, /* 0x1.0386272b9c077fffe */ + 1.015747708536026694351, /* 0x1.04080ab526304fff0 */ + 1.017733529475172815584, /* 0x1.048a2f412375ffff0 */ + 1.019723232714418781378, /* 0x1.050c94ef7ad5e000a */ + 1.021716825883923762690, /* 0x1.058f3be0f1c2d0004 */ + 1.023714316605201180057, /* 0x1.06122436442e2000e */ + 1.025715712440059545995, /* 0x1.06954e0fec63afff2 */ + 1.027721021151397406936, /* 0x1.0718b98f41c92fff6 */ + 1.029730250269221158939, /* 0x1.079c66d49bb2ffff1 */ + 1.031743407506447551857, /* 0x1.082056011a9230009 */ + 1.033760500517691527387, /* 0x1.08a487359ebd50002 */ + 1.035781537016238873464, /* 0x1.0928fa93490d4fff3 */ + 1.037806524719013578963, /* 0x1.09adb03b3e5b3000d */ + 1.039835471338248051878, /* 0x1.0a32a84e9e5760004 */ + 1.041868384612101516848, /* 0x1.0ab7e2eea5340ffff */ + 1.043905272300907460835, /* 0x1.0b3d603ca784f0009 */ + 1.045946142174331239262, /* 0x1.0bc3205a042060000 */ + 1.047991002016745332165, /* 0x1.0c4923682a086fffe */ + 1.050039859627715177527, /* 0x1.0ccf698898f3a000d */ + 1.052092722826109660856, /* 0x1.0d55f2dce5d1dfffb */ + 1.054149599440827866881, /* 0x1.0ddcbf86b09a5fff6 */ + 1.056210497317612961855, /* 0x1.0e63cfa7abc97fffd */ + 1.058275424318780855142, /* 0x1.0eeb23619c146fffb */ + 1.060344388322010722446, /* 0x1.0f72bad65714bffff */ + 1.062417397220589476718, /* 0x1.0ffa9627c38d30004 */ + 1.064494458915699715017, /* 0x1.1082b577d0eef0003 */ + 1.066575581342167566880, /* 0x1.110b18e893a90000a */ + 1.068660772440545025953, /* 0x1.1193c09c267610006 */ + 1.070750040138235936705, /* 0x1.121cacb4959befff6 */ + 1.072843392435016474095, /* 0x1.12a5dd543cf36ffff */ + 1.074940837302467588937, /* 0x1.132f529d59552000b */ + 1.077042382749654914030, /* 0x1.13b90cb250d08fff5 */ + 1.079148036789447484528, /* 0x1.14430bb58da3dfff9 */ + 1.081257807444460983297, /* 0x1.14cd4fc984c4a000e */ + 1.083371702785017154417, /* 0x1.1557d910df9c7000e */ + 1.085489730853784307038, /* 0x1.15e2a7ae292d30002 */ + 1.087611899742884524772, /* 0x1.166dbbc422d8c0004 */ + 1.089738217537583819804, /* 0x1.16f9157586772ffff */ + 1.091868692357631731528, /* 0x1.1784b4e533cacfff0 */ + 1.094003332327482702577, /* 0x1.18109a360fc23fff2 */ + 1.096142145591650907149, /* 0x1.189cc58b155a70008 */ + 1.098285140311341168136, /* 0x1.1929370751ea50002 */ + 1.100432324652149906842, /* 0x1.19b5eecdd79cefff0 */ + 1.102583706811727015711, /* 0x1.1a42ed01dbdba000e */ + 1.104739294993289488947, /* 0x1.1ad031c69a2eafff0 */ + 1.106899097422573863281, /* 0x1.1b5dbd3f66e120003 */ + 1.109063122341542140286, /* 0x1.1beb8f8fa8150000b */ + 1.111231377994659874592, /* 0x1.1c79a8dac6ad0fff4 */ + 1.113403872669181282605, /* 0x1.1d0809445a97ffffc */ + 1.115580614653132185460, /* 0x1.1d96b0effc9db000e */ + 1.117761612217810673898, /* 0x1.1e25a001332190000 */ + 1.119946873713312474002, /* 0x1.1eb4d69bdb2a9fff1 */ + 1.122136407473298902480, /* 0x1.1f4454e3bfae00006 */ + 1.124330221845670330058, /* 0x1.1fd41afcbb48bfff8 */ + 1.126528325196519908506, /* 0x1.2064290abc98c0001 */ + 1.128730725913251964394, /* 0x1.20f47f31c9aa7000f */ + 1.130937432396844410880, /* 0x1.21851d95f776dfff0 */ + 1.133148453059692917203, /* 0x1.2216045b6784efffa */ + 1.135363796355857157764, /* 0x1.22a733a6692ae0004 */ + 1.137583470716100553249, /* 0x1.2338ab9b3221a0004 */ + 1.139807484614418608939, /* 0x1.23ca6c5e27aadfff7 */ + 1.142035846532929888057, /* 0x1.245c7613b7f6c0004 */ + 1.144268564977221958089, /* 0x1.24eec8e06b035000c */ + 1.146505648458203463465, /* 0x1.258164e8cea85fff8 */ + 1.148747105501412235671, /* 0x1.26144a5180d380009 */ + 1.150992944689175123667, /* 0x1.26a7793f5de2efffa */ + 1.153243174560058870217, /* 0x1.273af1d712179000d */ + 1.155497803703682491111, /* 0x1.27ceb43d81d42fff1 */ + 1.157756840726344771440, /* 0x1.2862c097a3d29000c */ + 1.160020294239811677834, /* 0x1.28f7170a74cf4fff1 */ + 1.162288172883275239058, /* 0x1.298bb7bb0faed0004 */ + 1.164560485298402170388, /* 0x1.2a20a2ce920dffff4 */ + 1.166837240167474476460, /* 0x1.2ab5d86a4631ffff6 */ + 1.169118446164539637555, /* 0x1.2b4b58b36d5220009 */ + 1.171404112007080167155, /* 0x1.2be123cf786790002 */ + 1.173694246390975415341, /* 0x1.2c7739e3c0aac000d */ + 1.175988858069749065617, /* 0x1.2d0d9b15deb58fff6 */ + 1.178287955789017793514, /* 0x1.2da4478b627040002 */ + 1.180591548323240091978, /* 0x1.2e3b3f69fb794fffc */ + 1.182899644456603782686, /* 0x1.2ed282d76421d0004 */ + 1.185212252993012693694, /* 0x1.2f6a11f96c685fff3 */ + 1.187529382762033236513, /* 0x1.3001ecf60082ffffa */ + 1.189851042595508889847, /* 0x1.309a13f30f28a0004 */ + 1.192177241354644978669, /* 0x1.31328716a758cfff7 */ + 1.194507987909589896687, /* 0x1.31cb4686e1e85fffb */ + 1.196843291137896336843, /* 0x1.32645269dfd04000a */ + 1.199183159977805113226, /* 0x1.32fdaae604c39000f */ + 1.201527603343041317132, /* 0x1.339750219980dfff3 */ + 1.203876630171082595692, /* 0x1.3431424300e480007 */ + 1.206230249419600664189, /* 0x1.34cb8170b3fee000e */ + 1.208588470077065268869, /* 0x1.35660dd14dbd4fffc */ + 1.210951301134513435915, /* 0x1.3600e78b6bdfc0005 */ + 1.213318751604272271958, /* 0x1.369c0ec5c38ebfff2 */ + 1.215690830512196507537, /* 0x1.373783a718d29000f */ + 1.218067546930756250870, /* 0x1.37d3465662f480007 */ + 1.220448909901335365929, /* 0x1.386f56fa770fe0008 */ + 1.222834928513994334780, /* 0x1.390bb5ba5fc540004 */ + 1.225225611877684750397, /* 0x1.39a862bd3c7a8fff3 */ + 1.227620969111500981433, /* 0x1.3a455e2a37bcafffd */ + 1.230021009336254911271, /* 0x1.3ae2a8287dfbefff6 */ + 1.232425741726685064472, /* 0x1.3b8040df76f39fffa */ + 1.234835175450728295084, /* 0x1.3c1e287682e48fff1 */ + 1.237249319699482263931, /* 0x1.3cbc5f151b86bfff8 */ + 1.239668183679933477545, /* 0x1.3d5ae4e2cc0a8000f */ + 1.242091776620540377629, /* 0x1.3df9ba07373bf0006 */ + 1.244520107762172811399, /* 0x1.3e98deaa0d8cafffe */ + 1.246953186383919165383, /* 0x1.3f3852f32973efff0 */ + 1.249391019292643401078, /* 0x1.3fd816ffc72b90001 */ + 1.251833623164381181797, /* 0x1.40782b17863250005 */ + 1.254280999953110153911, /* 0x1.41188f42caf400000 */ + 1.256733161434815393410, /* 0x1.41b943b42945bfffd */ + 1.259190116985283935980, /* 0x1.425a4893e5f10000a */ + 1.261651875958665236542, /* 0x1.42fb9e0a2df4c0009 */ + 1.264118447754797758244, /* 0x1.439d443f608c4fff9 */ + 1.266589841787181258708, /* 0x1.443f3b5bebf850008 */ + 1.269066067469190262045, /* 0x1.44e183883e561fff7 */ + 1.271547134259576328224, /* 0x1.45841cecf7a7a0001 */ + 1.274033051628237434048, /* 0x1.462707b2c43020009 */ + 1.276523829025464573684, /* 0x1.46ca44023aa410007 */ + 1.279019475999373156531, /* 0x1.476dd2045d46ffff0 */ + 1.281520002043128991825, /* 0x1.4811b1e1f1f19000b */ + 1.284025416692967214122, /* 0x1.48b5e3c3edd74fff4 */ + 1.286535729509738823464, /* 0x1.495a67d3613c8fff7 */ + 1.289050950070396384145, /* 0x1.49ff3e396e19d000b */ + 1.291571087985403654081, /* 0x1.4aa4671f5b401fff1 */ + 1.294096152842774794011, /* 0x1.4b49e2ae56d19000d */ + 1.296626154297237043484, /* 0x1.4befb10fd84a3fff4 */ + 1.299161101984141142272, /* 0x1.4c95d26d41d84fff8 */ + 1.301701005575179204100, /* 0x1.4d3c46f01d9f0fff3 */ + 1.304245874766450485904, /* 0x1.4de30ec21097d0003 */ + 1.306795719266019562007, /* 0x1.4e8a2a0ccce3d0002 */ + 1.309350548792467483458, /* 0x1.4f3198fa10346fff5 */ + 1.311910373099227200545, /* 0x1.4fd95bb3be8cffffd */ + 1.314475201942565174546, /* 0x1.50817263bf0e5fffb */ + 1.317045045107389400535, /* 0x1.5129dd3418575000e */ + 1.319619912422941299109, /* 0x1.51d29c4f01c54ffff */ + 1.322199813675649204855, /* 0x1.527bafde83a310009 */ + 1.324784758729532718739, /* 0x1.5325180cfb8b3fffd */ + 1.327374757430096474625, /* 0x1.53ced504b2bd0fff4 */ + 1.329969819671041886272, /* 0x1.5478e6f02775e0001 */ + 1.332569955346704748651, /* 0x1.55234df9d8a59fff8 */ + 1.335175174370685002822, /* 0x1.55ce0a4c5a6a9fff6 */ + 1.337785486688218616860, /* 0x1.56791c1263abefff7 */ + 1.340400902247843806217, /* 0x1.57248376aef21fffa */ + 1.343021431036279800211, /* 0x1.57d040a420c0bfff3 */ + 1.345647083048053138662, /* 0x1.587c53c5a630f0002 */ + 1.348277868295411074918, /* 0x1.5928bd063fd7bfff9 */ + 1.350913796821875845231, /* 0x1.59d57c9110ad60006 */ + 1.353554878672557082439, /* 0x1.5a8292913d68cfffc */ + 1.356201123929036356254, /* 0x1.5b2fff3212db00007 */ + 1.358852542671913132777, /* 0x1.5bddc29edcc06fff3 */ + 1.361509145047255398051, /* 0x1.5c8bdd032ed16000f */ + 1.364170941142184734180, /* 0x1.5d3a4e8a5bf61fff4 */ + 1.366837941171020309735, /* 0x1.5de9176042f1effff */ + 1.369510155261156381121, /* 0x1.5e9837b062f4e0005 */ + 1.372187593620959988833, /* 0x1.5f47afa69436cfff1 */ + 1.374870266463378287715, /* 0x1.5ff77f6eb3f8cfffd */ + 1.377558184010425845733, /* 0x1.60a7a734a9742fff9 */ + 1.380251356531521533853, /* 0x1.6158272490016000c */ + 1.382949794301995272203, /* 0x1.6208ff6a8978a000f */ + 1.385653507605306700170, /* 0x1.62ba3032c0a280004 */ + 1.388362506772382154503, /* 0x1.636bb9a994784000f */ + 1.391076802081129493127, /* 0x1.641d9bfb29a7bfff6 */ + 1.393796403973427855412, /* 0x1.64cfd7545928b0002 */ + 1.396521322756352656542, /* 0x1.65826be167badfff8 */ + 1.399251568859207761660, /* 0x1.663559cf20826000c */ + 1.401987152677323100733, /* 0x1.66e8a14a29486fffc */ + 1.404728084651919228815, /* 0x1.679c427f5a4b6000b */ + 1.407474375243217723560, /* 0x1.68503d9ba0add000f */ + 1.410226034922914983815, /* 0x1.690492cbf6303fff9 */ + 1.412983074197955213304, /* 0x1.69b9423d7b548fff6 */ +}; diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/t_exp2.h b/REORG.TODO/sysdeps/ieee754/dbl-64/t_exp2.h new file mode 100644 index 0000000000..1fd73338cf --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/t_exp2.h @@ -0,0 +1,585 @@ +/* These values are accurate to 52+12 bits when represented as + a double. */ +static const double exp2_accuratetable[512] = { +0.707106781187802013759 /* 0x0.b504f333fb3f80007 */, +0.708064712808760599040 /* 0x0.b543baa0f71b38000 */, +0.709023942160304065938 /* 0x0.b58297d3a8d518002 */, +0.709984470998547667624 /* 0x0.b5c18ad39b4ba0001 */, +0.710946301084324217006 /* 0x0.b60093a85e8d30001 */, +0.711909434180505784637 /* 0x0.b63fb25984e628005 */, +0.712873872052760648733 /* 0x0.b67ee6eea3b5f8003 */, +0.713839616467838999908 /* 0x0.b6be316f518c98001 */, +0.714806669195984345523 /* 0x0.b6fd91e328d148007 */, +0.715775032009894562898 /* 0x0.b73d0851c69e20002 */, +0.716744706683768884058 /* 0x0.b77c94c2c9b3d0003 */, +0.717715694995770148178 /* 0x0.b7bc373dd52eb0003 */, +0.718687998724665488852 /* 0x0.b7fbefca8cd530004 */, +0.719661619652575468291 /* 0x0.b83bbe70981da8001 */, +0.720636559564428180758 /* 0x0.b87ba337a194b0006 */, +0.721612820246623098989 /* 0x0.b8bb9e27556508004 */, +0.722590403488338473025 /* 0x0.b8fbaf4762c798006 */, +0.723569311081411870036 /* 0x0.b93bd69f7be1d0000 */, +0.724549544820974333906 /* 0x0.b97c1437567828007 */, +0.725531106502312561633 /* 0x0.b9bc6816a87ae8002 */, +0.726513997924421062181 /* 0x0.b9fcd2452bee00000 */, +0.727498220889519875430 /* 0x0.ba3d52ca9e6148002 */, +0.728483777200401694265 /* 0x0.ba7de9aebe05c8003 */, +0.729470668664712662563 /* 0x0.babe96f94e62a8002 */, +0.730458897090379144517 /* 0x0.baff5ab2134df0004 */, +0.731448464287988597833 /* 0x0.bb4034e0d38ab0000 */, +0.732439372072965166897 /* 0x0.bb81258d5b2d60001 */, +0.733431622260458326859 /* 0x0.bbc22cbf75fd28001 */, +0.734425216668725511232 /* 0x0.bc034a7ef32c00001 */, +0.735420157118880535324 /* 0x0.bc447ed3a50fe0005 */, +0.736416445434497690674 /* 0x0.bc85c9c560b350001 */, +0.737414083433310718618 /* 0x0.bcc72b5bf4b4e0000 */, +0.738413072966152328496 /* 0x0.bd08a39f5417a8007 */, +0.739413415848264365956 /* 0x0.bd4a32974abcd0002 */, +0.740415113911250699637 /* 0x0.bd8bd84bb68300002 */, +0.741418168994518067562 /* 0x0.bdcd94c47ddd30003 */, +0.742422582936659858376 /* 0x0.be0f6809865968006 */, +0.743428357577745613238 /* 0x0.be515222b72530003 */, +0.744435494762383687126 /* 0x0.be935317fc6ba0002 */, +0.745443996335090397492 /* 0x0.bed56af1423de8001 */, +0.746453864145572798553 /* 0x0.bf1799b67a6248007 */, +0.747465100043933849969 /* 0x0.bf59df6f970e70002 */, +0.748477705883256683178 /* 0x0.bf9c3c248dbee8001 */, +0.749491683518965001732 /* 0x0.bfdeafdd568308000 */, +0.750507034813367890373 /* 0x0.c0213aa1f0fc38004 */, +0.751523761622240105153 /* 0x0.c063dc7a559ca0003 */, +0.752541865811731880422 /* 0x0.c0a6956e883ed8000 */, +0.753561349247157341600 /* 0x0.c0e965868bd220006 */, +0.754582213796583967110 /* 0x0.c12c4cca664cb8002 */, +0.755604461332336940791 /* 0x0.c16f4b42225350006 */, +0.756628093726406381068 /* 0x0.c1b260f5ca2c48002 */, +0.757653112855631305506 /* 0x0.c1f58ded6d72d8001 */, +0.758679520599333412360 /* 0x0.c238d2311e7d08001 */, +0.759707318837184453227 /* 0x0.c27c2dc8f00368005 */, +0.760736509456435783249 /* 0x0.c2bfa0bcfd1400000 */, +0.761767094336480043995 /* 0x0.c3032b155818d0000 */, +0.762799075372231349951 /* 0x0.c346ccda248cc0001 */, +0.763832454453522768941 /* 0x0.c38a8613805488005 */, +0.764867233473625618441 /* 0x0.c3ce56c98d1ca8005 */, +0.765903414329434539816 /* 0x0.c4123f04708d80002 */, +0.766940998920452976510 /* 0x0.c4563ecc532dc0001 */, +0.767979989148100838946 /* 0x0.c49a56295f9f88006 */, +0.769020386915772125040 /* 0x0.c4de8523c2b0a0001 */, +0.770062194131770905170 /* 0x0.c522cbc3ae94e0003 */, +0.771105412703856241146 /* 0x0.c5672a1154e6b8004 */, +0.772150044545352520777 /* 0x0.c5aba014ed5f18003 */, +0.773196091570364285606 /* 0x0.c5f02dd6b09288003 */, +0.774243555696622731700 /* 0x0.c634d35edb1260003 */, +0.775292438842697939641 /* 0x0.c67990b5aa5c18004 */, +0.776342742931542928455 /* 0x0.c6be65e360bed8000 */, +0.777394469888802008854 /* 0x0.c70352f0437f50004 */, +0.778447621641124243320 /* 0x0.c74857e498fd00006 */, +0.779502200118583399303 /* 0x0.c78d74c8ab5b60000 */, +0.780558207255445668515 /* 0x0.c7d2a9a4c959f8000 */, +0.781615644985491186966 /* 0x0.c817f681412f80002 */, +0.782674515247667956808 /* 0x0.c85d5b6666c150006 */, +0.783734819983036512536 /* 0x0.c8a2d85c904760003 */, +0.784796561133562109454 /* 0x0.c8e86d6c14f850002 */, +0.785859740645942328471 /* 0x0.c92e1a9d513ec8002 */, +0.786924360469767103536 /* 0x0.c973dff8a4b390007 */, +0.787990422552312885808 /* 0x0.c9b9bd866c6440007 */, +0.789057928854407064640 /* 0x0.c9ffb34f1444b0001 */, +0.790126881326406182996 /* 0x0.ca45c15afcc570001 */, +0.791197281930050233534 /* 0x0.ca8be7b292db38000 */, +0.792269132620954885659 /* 0x0.cad2265e3cbee8000 */, +0.793342435380726906957 /* 0x0.cb187d667d3d38006 */, +0.794417192158282659010 /* 0x0.cb5eecd3b33158006 */, +0.795493404931386649540 /* 0x0.cba574ae5d2e80001 */, +0.796571075671306805268 /* 0x0.cbec14fef2a348004 */, +0.797650206352955137846 /* 0x0.cc32cdcdef0000000 */, +0.798730798954342069432 /* 0x0.cc799f23d11d18000 */, +0.799812855456121796232 /* 0x0.ccc089091abb28004 */, +0.800896377841454287795 /* 0x0.cd078b86505c18003 */, +0.801981368096190028208 /* 0x0.cd4ea6a3f97720007 */, +0.803067828208752554378 /* 0x0.cd95da6aa057b8007 */, +0.804155760170129796375 /* 0x0.cddd26e2d21b28001 */, +0.805245165974338261710 /* 0x0.ce248c151f3330001 */, +0.806336047619038653883 /* 0x0.ce6c0a0a1c1350001 */, +0.807428407102107836855 /* 0x0.ceb3a0ca5d6be0006 */, +0.808522246427078927792 /* 0x0.cefb505e7e2550007 */, +0.809617567597010201484 /* 0x0.cf4318cf18a268002 */, +0.810714372621179513182 /* 0x0.cf8afa24ce1c98004 */, +0.811812663508675536069 /* 0x0.cfd2f4683f9810005 */, +0.812912442272482604912 /* 0x0.d01b07a2126188003 */, +0.814013710929394895825 /* 0x0.d06333daeff618001 */, +0.815116471495287542325 /* 0x0.d0ab791b80d028006 */, +0.816220725993571205593 /* 0x0.d0f3d76c75b330000 */, +0.817326476447408967199 /* 0x0.d13c4ed67f1cf8000 */, +0.818433724883006474832 /* 0x0.d184df6250e3b0001 */, +0.819542473330909460055 /* 0x0.d1cd8918a3a328004 */, +0.820652723822034690935 /* 0x0.d2164c02305fa0002 */, +0.821764478391968422618 /* 0x0.d25f2827b53fb0005 */, +0.822877739077315761840 /* 0x0.d2a81d91f188b8000 */, +0.823992507918612782109 /* 0x0.d2f12c49a8d290005 */, +0.825108786960634610365 /* 0x0.d33a5457a35e40003 */, +0.826226578247117093869 /* 0x0.d38395c4a84848007 */, +0.827345883828319528258 /* 0x0.d3ccf09985d958004 */, +0.828466705754248966560 /* 0x0.d41664df0a1320005 */, +0.829589046080638992111 /* 0x0.d45ff29e094330000 */, +0.830712906863802391671 /* 0x0.d4a999df585a20005 */, +0.831838290163696481037 /* 0x0.d4f35aabd04a60006 */, +0.832965198041969556729 /* 0x0.d53d350c4be258002 */, +0.834093632565442222342 /* 0x0.d5872909aba050007 */, +0.835223595802037643865 /* 0x0.d5d136acd138e8006 */, +0.836355089820669306292 /* 0x0.d61b5dfe9f7780004 */, +0.837488116698010487424 /* 0x0.d6659f0801afa8005 */, +0.838622678508982644113 /* 0x0.d6aff9d1e147d8004 */, +0.839758777333464490056 /* 0x0.d6fa6e652d19e0000 */, +0.840896415254110962690 /* 0x0.d744fccad70d00003 */, +0.842035594355151628676 /* 0x0.d78fa50bd2c3b0000 */, +0.843176316724478125433 /* 0x0.d7da673117e730007 */, +0.844318584453106590905 /* 0x0.d8254343a19038003 */, +0.845462399634695271912 /* 0x0.d870394c6dbf30003 */, +0.846607764365415071965 /* 0x0.d8bb49547d37c0004 */, +0.847754680744707056494 /* 0x0.d9067364d45608003 */, +0.848903150873708822763 /* 0x0.d951b7867953b0006 */, +0.850053176859071113491 /* 0x0.d99d15c2787a30006 */, +0.851204760807439786431 /* 0x0.d9e88e21de11a0003 */, +0.852357904828824897169 /* 0x0.da3420adba1508003 */, +0.853512611037803181642 /* 0x0.da7fcd6f2184d8005 */, +0.854668881550406100980 /* 0x0.dacb946f2afaf8000 */, +0.855826718478671755185 /* 0x0.db1775b6e8ad48000 */, +0.856986123964844970247 /* 0x0.db63714f8e0818006 */, +0.858147100114499461478 /* 0x0.dbaf87422625b8000 */, +0.859309649060962410524 /* 0x0.dbfbb797daa460002 */, +0.860473772936213743282 /* 0x0.dc480259d3a710001 */, +0.861639473872910177676 /* 0x0.dc9467913a0f48006 */, +0.862806754008130227807 /* 0x0.dce0e7473b9b28003 */, +0.863975615481124226159 /* 0x0.dd2d8185086c20006 */, +0.865146060433749419813 /* 0x0.dd7a3653d38168005 */, +0.866318091005120138881 /* 0x0.ddc705bcccd628000 */, +0.867491709362415264210 /* 0x0.de13efc9434100004 */, +0.868666917636779056818 /* 0x0.de60f4825df9b8005 */, +0.869843717989716047624 /* 0x0.deae13f16599c0003 */, +0.871022112578215268471 /* 0x0.defb4e1f9dc388002 */, +0.872202103559697183859 /* 0x0.df48a3164a92f0001 */, +0.873383693097737778847 /* 0x0.df9612deb6e878007 */, +0.874566883362160263365 /* 0x0.dfe39d82348310001 */, +0.875751676517234511901 /* 0x0.e031430a0f0688000 */, +0.876938074732511840819 /* 0x0.e07f037f97e548001 */, +0.878126080186539592654 /* 0x0.e0ccdeec2a75e0006 */, +0.879315695055312818168 /* 0x0.e11ad5591f4078001 */, +0.880506921518618312932 /* 0x0.e168e6cfd2f880004 */, +0.881699761760385225541 /* 0x0.e1b71359a6df60003 */, +0.882894217964411143207 /* 0x0.e2055afffc1178000 */, +0.884090292325693805080 /* 0x0.e253bdcc3ffbb8001 */, +0.885287987031581180559 /* 0x0.e2a23bc7d7a1d8002 */, +0.886487304278189114386 /* 0x0.e2f0d4fc31ab80004 */, +0.887688246263368285778 /* 0x0.e33f8972bea8a8005 */, +0.888890815189881999840 /* 0x0.e38e5934f49010007 */, +0.890095013257492739835 /* 0x0.e3dd444c460bd0007 */, +0.891300842677948068626 /* 0x0.e42c4ac232f380000 */, +0.892508305659222567226 /* 0x0.e47b6ca036f8b8005 */, +0.893717404414979710310 /* 0x0.e4caa9efd40e58002 */, +0.894928141160697743242 /* 0x0.e51a02ba8e2610007 */, +0.896140518115016826430 /* 0x0.e5697709ecab90000 */, +0.897354537501434679237 /* 0x0.e5b906e77c61d0006 */, +0.898570201543732793877 /* 0x0.e608b25cca5ba8005 */, +0.899787512470129891014 /* 0x0.e6587973688ce8002 */, 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0x0.ec58f3f16a3910002 */, +0.924483034755387955725 /* 0x0.ecaaeb8ffb3168005 */, +0.925735450311948926408 /* 0x0.ecfcff9bd67078000 */, +0.926989562542820610982 /* 0x0.ed4f301edad1a0007 */, +0.928245373740515189457 /* 0x0.eda17d22e0f9b0001 */, +0.929502886213858126045 /* 0x0.edf3e6b1d37d40001 */, +0.930762102264245716494 /* 0x0.ee466cd594c5c8005 */, +0.932023024199046146183 /* 0x0.ee990f980dcdb0005 */, +0.933285654329454095216 /* 0x0.eeebcf032bc470007 */, +0.934549994971191289044 /* 0x0.ef3eab20e0d3c0001 */, +0.935816048439005676599 /* 0x0.ef91a3fb1e1340004 */, +0.937083817055075818404 /* 0x0.efe4b99bdcc618006 */, +0.938353303143720007819 /* 0x0.f037ec0d1889b8000 */, +0.939624509028518128972 /* 0x0.f08b3b58cc2bb8006 */, +0.940897437041863904384 /* 0x0.f0dea788fc2a90000 */, +0.942172089516254085427 /* 0x0.f13230a7ad21b8003 */, +0.943448468787511540534 /* 0x0.f185d6bee754e0006 */, +0.944726577195256100890 /* 0x0.f1d999d8b73478005 */, +0.946006417082291717338 /* 0x0.f22d79ff2cb130000 */, 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0x1.60d84fd155d15000e */, +1.380167867259843417228 /* 0x1.6152ae6cdf0030003 */, +1.382037608124419003675 /* 0x1.61cd3778bc879000d */, +1.383909881963391264069 /* 0x1.6247eb03a4dc40009 */, +1.385784692209972801544 /* 0x1.62c2c91c56d9b0002 */, +1.387662042298923203992 /* 0x1.633dd1d1930ec0001 */, +1.389541935670444372533 /* 0x1.63b90532200630004 */, +1.391424375772021271329 /* 0x1.6434634ccc4cc0007 */, +1.393309366052102982208 /* 0x1.64afec30677e90008 */, +1.395196909966106124701 /* 0x1.652b9febc8e0f000d */, +1.397087010973788290271 /* 0x1.65a77e8dcc7f10004 */, +1.398979672539331309267 /* 0x1.66238825534170000 */, +1.400874898129892187656 /* 0x1.669fbcc1415600008 */, +1.402772691220124823310 /* 0x1.671c1c708328e000a */, +1.404673055288671035301 /* 0x1.6798a7420988b000d */, +1.406575993818903302975 /* 0x1.68155d44ca77a000f */, +1.408481510297352468121 /* 0x1.68923e87bf70e000a */, +1.410389608216942924956 /* 0x1.690f4b19e8f74000c */, +1.412300291075172076232 /* 0x1.698c830a4c94c0008 */ +}; +#define S (1.0/4503599627370496.0) /* 2^-52 */ +static const float exp2_deltatable[512] = { + 11527*S, -963*S, 884*S, -781*S, -2363*S, -3441*S, 123*S, 526*S, + -6*S, 1254*S, -1138*S, 1519*S, 1576*S, -65*S, 1040*S, 793*S, + -1662*S, -5063*S, -387*S, 968*S, -941*S, 984*S, -2856*S, -545*S, + 495*S, -5246*S, -2109*S, 1281*S, 2075*S, 909*S, -1642*S,-78233*S, +-31653*S, -265*S, 130*S, 430*S, 2482*S, -742*S, 1616*S, -2213*S, + -519*S, 20*S, -3134*S,-13981*S, 1343*S, -1740*S, 247*S, 1679*S, + -1097*S, 3131*S, 871*S, -1480*S, 1936*S, -1827*S, 17325*S, 528*S, + -322*S, 1404*S, -152*S, -1845*S, -212*S, 2639*S, -476*S, 2960*S, + -962*S, -1012*S, -1231*S, 3030*S, 1659*S, -486*S, 2154*S, 1728*S, + -2793*S, 699*S, -1560*S, -2125*S, 2156*S, 142*S, -1888*S, 4426*S, +-13443*S, 1970*S, -50*S, 1771*S,-43399*S, 4979*S, -2448*S, -370*S, + 1414*S, 1075*S, 232*S, 206*S, 873*S, 2141*S, 2970*S, 1279*S, + -2331*S, 336*S, -2595*S, 753*S, -3384*S, -616*S, 89*S, -818*S, + 5755*S, -241*S, -528*S, -661*S, -3777*S, -354*S, 250*S, 3881*S, + 2632*S, -2131*S, 2565*S, -316*S, 1746*S, -2541*S, -1324*S, -50*S, + 2564*S, -782*S, 1176*S, 6452*S, -1002*S, 1288*S, 336*S, -185*S, + 3063*S, 3784*S, 2169*S, 686*S, 328*S, -400*S, 312*S, -4517*S, + -1457*S, 1046*S, -1530*S, -685*S, 1328*S,-49815*S, -895*S, 1063*S, + -2091*S, -672*S, -1710*S, -665*S, 1545*S, 1819*S,-45265*S, 3548*S, + -554*S, -568*S, 4752*S, -1907*S,-13738*S, 675*S, 9611*S, -1115*S, + -815*S, 408*S, -1281*S, -937*S,-16376*S, -4772*S, -1440*S, 992*S, + 788*S, 10364*S, -1602*S, -661*S, -1783*S, -265*S, -20*S, -3781*S, + -861*S, -345*S, -994*S, 1364*S, -5339*S, 1620*S, 9390*S, -1066*S, + -305*S, -170*S, 175*S, 2461*S, -490*S, -769*S, -1450*S, 3315*S, + 2418*S, -45*S, -852*S, -1295*S, -488*S, -96*S, 1142*S, -2639*S, + 7905*S, -9306*S, -3859*S, 760*S, 1057*S, -1570*S, 3977*S, 209*S, + -514*S, 7151*S, 1646*S, 627*S, 599*S, -774*S, -1468*S, 633*S, + -473*S, 851*S, 2406*S, 143*S, 74*S, 4260*S, 1177*S, -913*S, + 2670*S, -3298*S, -1662*S, -120*S, -3264*S, -2148*S, 410*S, 2078*S, + -2098*S, -926*S, 3580*S, -1289*S, 2450*S, -1158*S, 907*S, -590*S, + 986*S, 1801*S, 1145*S, -1677*S, 3455*S, 956*S, 710*S, 144*S, + 153*S, -255*S, -1898*S, 28102*S, 2748*S, 1194*S, -3009*S, 7076*S, + 0*S, -2720*S, 711*S, 1225*S, -3034*S, -473*S, 378*S, -1046*S, + 962*S, -2006*S, 4647*S, 3206*S, 1769*S, -2665*S, 1254*S, 2025*S, + -2430*S, 6193*S, 1224*S, -856*S, -1592*S, -325*S, -1521*S, 1827*S, + -264*S, 2403*S, -1065*S, 967*S, -681*S, -2106*S, -474*S, 1333*S, + -893*S, 2296*S, 592*S, -1220*S, -326*S, 990*S, 139*S, 206*S, + -779*S, -1683*S, 1238*S, 6098*S, 136*S, 1197*S, 790*S, -107*S, + -1004*S, -2449*S, 939*S, 5568*S, 156*S, 1812*S, 2792*S, -1094*S, + -2677*S, -251*S, 2297*S, 943*S, -1329*S, 2883*S, -853*S, -2626*S, +-105929*S, -6552*S, 1095*S, -1508*S, 1003*S, 5039*S, -2600*S, -749*S, + 1790*S, 890*S, 2016*S, -1073*S, 624*S, -2084*S, -1536*S, -1330*S, + 358*S, 2444*S, -179*S,-25759*S, -243*S, -552*S, -124*S, 3766*S, + 1192*S, -1614*S, 6*S, -1227*S, 345*S, -981*S, -295*S, -1006*S, + -995*S, -1195*S, 706*S, 2512*S, -1758*S, -734*S, -6286*S, -922*S, + 1530*S, 1542*S, 1223*S, 61*S, -83*S, 522*S,116937*S, -914*S, + -418*S, -7339*S, 249*S, -520*S, -762*S, 426*S, -505*S, 2664*S, + -1093*S, -1035*S, 2130*S, 4878*S, 1982*S, 1551*S, 2304*S, 193*S, + 1532*S, -7268*S, 24357*S, 531*S, 2676*S, -1170*S, 1465*S, -1917*S, + 2143*S, 1466*S, -7*S, -7300*S, 3297*S, -1197*S, -289*S, -1548*S, + 26226*S, 4401*S, 4123*S, -1588*S, 4243*S, 4069*S, -1276*S, -2010*S, + 1407*S, 1478*S, 488*S, -2366*S, -2909*S, -2534*S, -1285*S, 7095*S, + -645*S, -2089*S, -944*S, -40*S, -1363*S, -833*S, 917*S, 1609*S, + 1286*S, 1677*S, 1613*S, -2295*S, -1248*S, 40*S, 26*S, 2038*S, + 698*S, 2675*S, -1755*S, -3522*S, -1614*S, -6111*S, 270*S, 1822*S, + -234*S, -2844*S, -1201*S, -830*S, 1193*S, 2354*S, 47*S, 1522*S, + -78*S, -640*S, 2425*S, -1596*S, 1563*S, 1169*S, -1006*S, -83*S, + 2362*S, -3521*S, -314*S, 1814*S, -1751*S, 305*S, 1715*S, -3741*S, + 7847*S, 1291*S, 1206*S, 36*S, 1397*S, -1419*S, -1194*S, -2014*S, + 1742*S, -578*S, -207*S, 875*S, 1539*S, 2826*S, -1165*S, -909*S, + 1849*S, 927*S, 2018*S, -981*S, 1637*S, -463*S, 905*S, 6618*S, + 400*S, 630*S, 2614*S, 900*S, 2323*S, -1094*S, -1858*S, -212*S, + -2069*S, 747*S, 1845*S, -1450*S, 444*S, -213*S, -438*S, 1158*S, + 4738*S, 2497*S, -370*S, -2016*S, -518*S, -1160*S, -1510*S, 123*S +}; +/* Maximum magnitude in above table: 116937 */ +#undef S diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/uasncs.h b/REORG.TODO/sysdeps/ieee754/dbl-64/uasncs.h new file mode 100644 index 0000000000..d754932558 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/uasncs.h @@ -0,0 +1,69 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/******************************************************************/ +/* */ +/* MODULE_NAME:uasncs.h */ +/* */ +/* common data and variables prototype and definition */ +/******************************************************************/ + +#ifndef UANSNCS_H +#define UANSNCS_H + +#ifdef BIG_ENDI + static const mynumber +/**/ a1 = {{0x3FC55580, 0x00000000 }}, /* 0.1666717529296875 */ +/**/ a2 = {{0xBED55555, 0x55552330 }}, /* -5.0862630208224597e-06 */ +/**/ hp0 = {{0x3FF921FB, 0x54442D18 }}, /* 1.5707963267948966 */ +/**/ hp1 = {{0x3C91A626, 0x33145C07 }}; /* 6.123233995736766e-17 */ + +#else +#ifdef LITTLE_ENDI + static const mynumber +/**/ a1 = {{0x00000000, 0x3FC55580 }}, /* 0.1666717529296875 */ +/**/ a2 = {{0x55552330, 0xBED55555 }}, /* -5.0862630208224597e-06 */ +/**/ hp0 = {{0x54442D18, 0x3FF921FB }}, /* 1.5707963267948966 */ +/**/ hp1 = {{0x33145C07, 0x3C91A626 }}; /* 6.123233995736766e-17 */ + +#endif +#endif + +static const double + f1 = 1.66666666666664110590506577996662E-01, + f2 = 7.50000000026122686814431784722623E-02, + f3 = 4.46428561421059750978517350006940E-02, + f4 = 3.03821268582119319911193410625235E-02, + f5 = 2.23551211026525610742786300334557E-02, + f6 = 1.81382903404565056280372531963613E-02; +static const double + c2 = 0.74999999999985410757087492918602258E-01, + c3 = 0.44642857150311968932423372477866076E-01, + c4 = 0.30381942574778615766200591683810471E-01, + c5 = 0.22372413472984868331447708777000650E-01, + c6 = 0.17333630246451830686009693735025490E-01, + c7 = 0.14710362893628210269950864741085777E-01; + +static const double big = 103079215104.0, t24 = 16777216.0, t27 = 134217728.0; +static const double + rt0 = 9.99999999859990725855365213134618E-01, + rt1 = 4.99999999495955425917856814202739E-01, + rt2 = 3.75017500867345182581453026130850E-01, + rt3 = 3.12523626554518656309172508769531E-01; +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/uatan.tbl b/REORG.TODO/sysdeps/ieee754/dbl-64/uatan.tbl new file mode 100644 index 0000000000..06608a3edb --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/uatan.tbl @@ -0,0 +1,11134 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/****************************************************************/ +/* TABLES FOR THE uatan() FUNCTION */ +/****************************************************************/ + +#include "endian.h" + +#ifdef BIG_ENDI + + static const number + cij[241][7] = { /* x0,cij for (1/16,1) */ +/**/ {{{0X3FB04006, 0X65E0244E} }, +/**/ {{0X3FB03A73, 0X7B53DD20} }, +/**/ {{0X3FEFDF1F, 0XCF5CFB72} }, +/**/ {{0XBFB01EB3, 0XCE2AE4C2} }, +/**/ {{0XBFD4D29E, 0XDD58A40D} }, +/**/ {{0X3FAFDA4A, 0XD907A18A} }, +/**/ {{0X3FC814DF, 0X4DF65B18} } }, +/**/ {{{0X3FB0FFFD, 0XB9B88CD8} }, +/**/ {{0X3FB0F99C, 0X63645300} }, +/**/ {{0X3FEFDC08, 0XA3DED30F} }, +/**/ {{0XBFB0D9DC, 0X669C1AED} }, +/**/ {{0XBFD4C669, 0XF7138DE2} }, +/**/ {{0X3FB0A12F, 0X29D085A7} }, +/**/ {{0X3FC7F0EE, 0XCFD48D20} } }, +/**/ {{{0X3FB1FFF1, 0X5A73D4F1} }, +/**/ {{0X3FB1F85F, 0X2BEE2040} }, +/**/ {{0X3FEFD7B3, 0X42B56D31} }, +/**/ {{0XBFB1D2B7, 0XB69DEA40} }, +/**/ {{0XBFD4B552, 0X3922ECC9} }, +/**/ {{0X3FB18F93, 0X522B1A04} }, +/**/ {{0X3FC7BEAD, 0X5660F061} } }, +/**/ {{{0X3FB2FFFD, 0XB2524AA2} }, +/**/ {{0X3FB2F716, 0XE71790A0} }, +/**/ {{0X3FEFD31F, 0X53B496A4} }, +/**/ {{0XBFB2CAD8, 0X4AAB7374} }, +/**/ {{0XBFD4A34B, 0X58DD2FB2} }, +/**/ {{0X3FB27C0A, 0XD0CECC18} }, +/**/ {{0X3FC789D2, 0X5D2743D7} } }, +/**/ {{{0X3FB3FFFE, 0X0573F3AC} }, +/**/ {{0X3FB3F59D, 0X1702F6A0} }, +/**/ {{0X3FEFCE4D, 0XB071ACC2} }, +/**/ {{0XBFB3C20F, 0X64DB3686} }, +/**/ {{0XBFD49059, 0XEB3BFE93} }, +/**/ {{0X3FB36659, 0XCAF74FED} }, +/**/ {{0X3FC75269, 0X1C011FB0} } }, +/**/ {{{0X3FB4FFEF, 0X894384D6} }, +/**/ {{0X3FB4F3ED, 0X0CE204C0} }, +/**/ {{0X3FEFC93E, 0XA8EA5A01} }, +/**/ {{0XBFB4B84F, 0X7B5457C9} }, +/**/ {{0XBFD47C80, 0X7401F2F9} }, +/**/ {{0X3FB44E64, 0XB4F67209} }, +/**/ {{0X3FC7187D, 0X4C540B77} } }, +/**/ {{{0X3FB5FFF8, 0XDF406528} }, +/**/ {{0X3FB5F22B, 0X3C73D820} }, +/**/ {{0X3FEFC3F1, 0XB1F60F13} }, +/**/ {{0XBFB5ADB2, 0XCB7FA73B} }, +/**/ {{0XBFD467BE, 0X2B1EB555} }, +/**/ {{0X3FB53435, 0X99EDC463} }, +/**/ {{0X3FC6DC1B, 0X238F5059} } }, +/**/ {{{0X3FB7000F, 0X8C4F0D56} }, +/**/ {{0X3FB6F04B, 0X495A2FA0} }, +/**/ {{0X3FEFBE67, 0X340DCE97} }, +/**/ {{0XBFB6A224, 0X4D98E1AD} }, +/**/ {{0XBFD45216, 0X14064DF1} }, +/**/ {{0X3FB617AA, 0X2BA78A66} }, +/**/ {{0X3FC69D4F, 0X50A3D7AC} } }, +/**/ {{{0X3FB8000F, 0XBB4057CF} }, +/**/ {{0X3FB7EE27, 0XBE2CD3A0} }, +/**/ {{0X3FEFB8A0, 0X39EC9246} }, +/**/ {{0XBFB79577, 0X31D9C773} }, +/**/ {{0XBFD43B8D, 0XB6DC7D72} }, +/**/ {{0X3FB6F88A, 0XD69547DF} }, +/**/ {{0X3FC65C26, 0XF633CE8C} } }, +/**/ {{{0X3FB8FFF2, 0X39CF2B7F} }, +/**/ {{0X3FB8EBB7, 0X9F979E80} }, +/**/ {{0X3FEFB29D, 0X435506E1} }, +/**/ {{0XBFB8879A, 0X69B9CDB5} }, +/**/ {{0XBFD42428, 0X85FEAFA9} }, +/**/ {{0X3FB7D6BA, 0XB6191A0E} }, +/**/ {{0X3FC618AF, 0XA7CB8BB5} } }, +/**/ {{{0X3FB9FFF9, 0X6E2F0772} }, +/**/ {{0X3FB9E93A, 0XD32A9480} }, +/**/ {{0X3FEFAC5D, 0X04A3EC40} }, +/**/ {{0XBFB978C2, 0X53F6EA97} }, +/**/ {{0XBFD40BE3, 0X089C36F6} }, +/**/ {{0X3FB8B25C, 0X885AEB77} }, +/**/ {{0X3FC5D2F7, 0X63CADCE1} } }, +/**/ {{{0X3FBB0002, 0X6316B097} }, +/**/ {{0X3FBAE68C, 0XCE24CC00} }, +/**/ {{0X3FEFA5E0, 0X938C5C66} }, +/**/ {{0XBFBA68C3, 0X76F14E4B} }, +/**/ {{0XBFD3F2C3, 0X1696CD7C} }, +/**/ {{0X3FB98B3B, 0X722A2CB4} }, +/**/ {{0X3FC58B0C, 0X9067AD62} } }, +/**/ {{{0X3FBC0008, 0X604F58B1} }, +/**/ {{0X3FBBE3A7, 0X05650780} }, +/**/ {{0X3FEF9F28, 0X5A7A2773} }, +/**/ {{0XBFBB578F, 0X3D5AC0A4} }, +/**/ {{0XBFD3D8CB, 0XF767119F} }, +/**/ {{0X3FBA613D, 0XC7E31B88} }, +/**/ {{0X3FC540FD, 0XF5594565} } }, +/**/ {{{0X3FBD0002, 0X6CCA4EBA} }, +/**/ {{0X3FBCE07E, 0XC1298A80} }, +/**/ {{0X3FEF9834, 0XE8D36C4A} }, +/**/ {{0XBFBC4513, 0X5BCAC5FE} }, +/**/ {{0XBFD3BE01, 0X8B5236F1} }, +/**/ {{0X3FBB3447, 0X2E991970} }, +/**/ {{0X3FC4F4DA, 0XB8ADB373} } }, +/**/ {{{0X3FBDFFF4, 0XB2B47FCA} }, +/**/ {{0X3FBDDD16, 0X4A051D80} }, +/**/ {{0X3FEF9106, 0X78DCC895} }, +/**/ {{0XBFBD3149, 0XF0966844} }, +/**/ {{0XBFD3A266, 0X744F9A5F} }, +/**/ {{0X3FBC0446, 0XEDB7F27A} }, +/**/ {{0X3FC4A6B2, 0X583F9ECA} } }, +/**/ {{{0X3FBF000A, 0XA9A05BE0} }, +/**/ {{0X3FBED996, 0XA3BDA540} }, +/**/ {{0X3FEF899C, 0X1B8BA97F} }, +/**/ {{0XBFBE1C51, 0X2287A677} }, +/**/ {{0XBFD385F8, 0XEDC130BB} }, +/**/ {{0X3FBCD14B, 0XF306FF50} }, +/**/ {{0X3FC45694, 0XA667A72B} } }, +/**/ {{{0X3FBFFFFA, 0XBA8F63DE} }, +/**/ {{0X3FBFD5B5, 0X69FE4780} }, +/**/ {{0X3FEF81F8, 0X4863DC7D} }, +/**/ {{0XBFBF05DB, 0XD1518706} }, +/**/ {{0XBFD368C4, 0X4687A69C} }, +/**/ {{0X3FBD9B08, 0X1B3868DA} }, +/**/ {{0X3FC40491, 0XC345ADFC} } }, +/**/ {{{0X3FC07FFA, 0X6ECCADA8} }, +/**/ {{0X3FC068D0, 0X0A396400} }, +/**/ {{0X3FEF7A19, 0XF1FCFC6B} }, +/**/ {{0XBFBFEE0C, 0X861DF0DF} }, +/**/ {{0XBFD34AC6, 0X5A586C0C} }, +/**/ {{0X3FBE618F, 0X189D637A} }, +/**/ {{0X3FC3B0BA, 0X195779D4} } }, +/**/ 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{{{0X3FEEC000, 0X5A13BA60} }, +/**/ {{0X3FE87ED1, 0X19B163E0} }, +/**/ {{0X3FE0A31F, 0X2EBB7AD7} }, +/**/ {{0XBFD09FBE, 0X33A3FCE1} }, +/**/ {{0X3FB53AA8, 0X89D9AF5D} }, +/**/ {{0X3F760799, 0XF7F7040B} }, +/**/ {{0XBF9EE456, 0XD3F0B3FB} } }, +/**/ {{{0X3FEEDFFF, 0X58F8DD18} }, +/**/ {{0X3FE88F6B, 0X6681CA80} }, +/**/ {{0X3FE09287, 0XEC4360B3} }, +/**/ {{0XBFD08FD0, 0XB7CE07E5} }, +/**/ {{0X3FB53FDD, 0X7BDEDD3F} }, +/**/ {{0X3F73A366, 0X70C52E66} }, +/**/ {{0XBF9E5630, 0X5DCA7315} } }, +/**/ {{{0X3FEEFFFF, 0XBE033400} }, +/**/ {{0X3FE89FF5, 0XDD4D7960} }, +/**/ {{0X3FE081FF, 0XDFFE15BD} }, +/**/ {{0XBFD07FDE, 0XDAE56C0F} }, +/**/ {{0X3FB5447A, 0XF84D6F5D} }, +/**/ {{0X3F714A24, 0X7982941E} }, +/**/ {{0XBF9DC982, 0X81E68835} } }, +/**/ {{{0X3FEF2001, 0XE6B5125D} }, +/**/ {{0X3FE8B070, 0XBBE88160} }, +/**/ {{0X3FE07186, 0XDF7122E2} }, +/**/ {{0XBFD06FE8, 0XDE905325} }, +/**/ {{0X3FB54883, 0XB5DEEC7A} }, +/**/ {{0X3F6DF762, 0XB4A186D5} }, +/**/ {{0XBF9D3E4E, 0XDE20F495} } }, +/**/ {{{0X3FEF3FFD, 0XF770E0DB} }, +/**/ {{0X3FE8C0D8, 0X09E96380} }, +/**/ {{0X3FE06120, 0XF5A576A9} }, +/**/ {{0XBFD05FF3, 0X1D2912FF} }, +/**/ {{0X3FB54BF9, 0X8CD1001F} }, +/**/ {{0X3F6970FC, 0X6E90DC16} }, +/**/ {{0XBF9CB496, 0XD8EB587E} } }, +/**/ {{{0X3FEF5FFE, 0X4E16DA33} }, +/**/ {{0X3FE8D131, 0X29BCCDC0} }, +/**/ {{0X3FE050C8, 0XD33BA4E9} }, +/**/ {{0XBFD04FF8, 0XD74C83D2} }, +/**/ {{0X3FB54EE0, 0X592BB252} }, +/**/ {{0X3F64FF61, 0X7193EEB5} }, +/**/ {{0XBF9C2C5B, 0XA459AC86} } }, +/**/ {{{0X3FEF8000, 0X4576FF2E} }, +/**/ {{0X3FE8E17A, 0XCCE443A0} }, +/**/ {{0X3FE0407F, 0XD8A97B6C} }, +/**/ {{0XBFD03FFB, 0XC91B3E55} }, +/**/ {{0X3FB5513A, 0X5F3357F7} }, +/**/ {{0X3F60A2BA, 0X14C92B53} }, +/**/ {{0XBF9BA59E, 0X3E70DF71} } }, +/**/ {{{0X3FEF9FFF, 0X39B6A330} }, +/**/ {{0X3FE8F1B2, 0XA7F515A0} }, +/**/ {{0X3FE03048, 0X63064158} }, +/**/ {{0XBFD02FFE, 0XACBAADA8} }, +/**/ {{0X3FB55309, 0XF27448C0} }, +/**/ {{0X3F58B6D6, 0X4850006B} }, +/**/ {{0XBF9B205F, 0X742323DF} } }, +/**/ {{{0X3FEFC001, 0XAA76C0B9} }, +/**/ {{0X3FE901DC, 0X15D66D80} }, +/**/ {{0X3FE0201F, 0X28D9B4AA} }, +/**/ {{0XBFD01FFE, 0XA98D4C38} }, +/**/ {{0X3FB55452, 0X089780F8} }, +/**/ {{0X3F5050B5, 0X7F35C5BB} }, +/**/ {{0XBF9A9C9F, 0XE19247AF} } }, +/**/ {{{0X3FEFDFFE, 0X39A592CA} }, +/**/ {{0X3FE911F2, 0X6D88A780} }, +/**/ {{0X3FE01008, 0XE40C6538} }, +/**/ {{0XBFD01000, 0XD31688DE} }, +/**/ {{0X3FB55514, 0XE32F1816} }, +/**/ {{0X3F402A15, 0X4E1628D2} }, +/**/ {{0XBF9A1A5F, 0XF4FAF5A0} } }, +/**/ {{{0X3FEFF801, 0X8E92D1B0} }, +/**/ {{0X3FE91DFB, 0X9BB4BF00} }, +/**/ {{0X3FE003FF, 0XB884C5A9} }, +/**/ {{0XBFD003FF, 0X3876A954} }, +/**/ {{0X3FB55551, 0X5539DDFB} }, +/**/ {{0X3F2007E7, 0X7B95E6C2} }, +/**/ {{0XBF99B9A7, 0X18A3BA58} } }, + }; + + static const number + hij[241][16] = { /* x0,hij for (1/16,1) */ +/**/ {{{0x3fb04000, 0x00000000} }, +/**/ {{0x3fb03a6d, 0x1c06693d} }, +/**/ {{0xbc428a02, 0xd4e7f128} }, +/**/ {{0x3fefdf1f, 0xe92592ae} }, +/**/ {{0x3c88bfc0, 0xb5490162} }, +/**/ {{0xbfb01ead, 0x8f7e4151} }, +/**/ {{0xbc5395e8, 0x0b64d205} }, +/**/ {{0xbfd4d29f, 0x433dd49b} }, +/**/ {{0xbc75b19d, 0x4aa42633} }, +/**/ {{0x3fafda41, 0xce35961d} }, +/**/ {{0x3c4e6a5f, 0x425d7696} }, +/**/ {{0x3fc814dd, 0x6c1bb5e2} }, +/**/ {{0xbfaf4cb7, 0x2b33739f} }, +/**/ {{0xbfc048b2, 0xc267d8ec} }, +/**/ {{0x3fae9649, 0xe8ababc6} }, +/**/ {{0x3fb78293, 0xfe802692} } }, +/**/ {{{0x3fb10000, 0x00000000} }, +/**/ {{0x3fb0f99e, 0xa71d52a7} }, +/**/ {{0xbc22069f, 0xeec3624f} }, +/**/ {{0x3fefdc08, 0x9a49d2a9} }, +/**/ {{0x3c7780f7, 0x68b2ce25} }, +/**/ {{0xbfb0d9de, 0x9da73e1d} }, +/**/ {{0x3c4ebf46, 0xa1a487bf} }, +/**/ {{0xbfd4c669, 0xd13ea108} }, +/**/ {{0x3c7354bc, 0xebb4528c} }, +/**/ {{0x3fb0a137, 0x789374c1} }, +/**/ {{0xbc56c223, 0xc3f2c5c2} }, +/**/ {{0x3fc7f0e7, 0x79c60cda} }, +/**/ {{0xbfb05062, 0xcdcc7b81} }, +/**/ {{0xbfc019e4, 0xc5266783} }, +/**/ {{0x3fafd0b2, 0xf2540289} }, +/**/ {{0x3fb71107, 0xf6d3cd8a} } }, +/**/ {{{0x3fb20000, 0x00000000} }, +/**/ {{0x3fb1f86d, 0xbf082d59} }, +/**/ {{0xbc4095dc, 0x7732ef81} }, +/**/ {{0x3fefd7b3, 0x01722b81} }, +/**/ {{0xbc5e618c, 0x8a212e02} }, +/**/ {{0xbfb1d2c5, 0xee4e9cfa} }, +/**/ {{0x3c426273, 0x29abece0} }, +/**/ {{0xbfd4b551, 0x37eb7f46} }, +/**/ {{0x3c73b360, 0x01d8bf12} }, +/**/ {{0x3fb18fa7, 0x6adb6a7c} }, +/**/ {{0xbc5c00d8, 0x398999ad} }, +/**/ {{0x3fc7bea5, 0xf4a7cff3} }, +/**/ {{0xbfb13008, 0x61f84829} }, +/**/ {{0xbfbfb14f, 0xa8e135a1} }, +/**/ {{0x3fb0b532, 0x4324f177} }, +/**/ {{0x3fb6734a, 0x3498dd9d} } }, +/**/ {{{0x3fb30000, 0x00000000} }, +/**/ {{0x3fb2f719, 0x318a4a9a} }, +/**/ {{0x3c03fd17, 0x79b9801f} }, +/**/ {{0x3fefd31f, 0x48e238fe} }, +/**/ {{0xbc876a7a, 0xd8c45327} }, +/**/ {{0xbfb2cada, 0x852096e2} }, +/**/ {{0x3c460860, 0x11efd787} }, +/**/ {{0xbfd4a34b, 0x2e476a39} }, +/**/ {{0x3c7254f2, 0xeb11ee51} }, +/**/ {{0x3fb27c13, 0xc54ae225} }, +/**/ {{0x3c513096, 0x4ae66f0c} }, +/**/ {{0x3fc789ca, 0xef0d59d0} }, +/**/ {{0xbfb20c06, 0x6d9aaa8c} }, +/**/ {{0xbfbf2885, 0x846ba912} }, +/**/ {{0x3fb17c5f, 0xc697ef5e} }, +/**/ {{0x3fb5ce93, 0xcad31e6e} } }, +/**/ {{{0x3fb40000, 0x00000000} }, +/**/ {{0x3fb3f59f, 0x0e7c559d} }, +/**/ {{0x3c5ac4ce, 0x285df847} }, +/**/ {{0x3fefce4d, 0xa6ab93e9} }, +/**/ {{0xbc6be46b, 0x18a97736} }, +/**/ {{0xbfb3c211, 0x4d22b635} }, +/**/ {{0x3c42033c, 0x6950679f} }, +/**/ {{0xbfd49059, 0xc4d74033} }, +/**/ {{0x3c57dd7c, 0xd7e376aa} }, +/**/ {{0x3fb36662, 0xc0896a7c} }, +/**/ {{0xbc36cf6a, 0xd79232cf} }, +/**/ {{0x3fc75261, 0xa13a97a2} }, +/**/ {{0xbfb2e431, 0x5fdd1509} }, +/**/ {{0xbfbe9999, 0x6e52db32} }, +/**/ {{0x3fb23da4, 0xb0a71e9f} }, +/**/ {{0x3fb52335, 0xe3bc8178} } }, +/**/ {{{0x3fb50000, 0x00000000} }, +/**/ {{0x3fb4f3fd, 0x677292fb} }, +/**/ {{0x3c4008d3, 0x6264979e} }, +/**/ {{0x3fefc93e, 0x53a1ee0d} }, +/**/ {{0xbc64421a, 0x20fd2bdf} }, +/**/ {{0xbfb4b85f, 0x4aba88e3} }, +/**/ {{0x3c54f184, 0x3c9d1e89} }, +/**/ {{0xbfd47c7f, 0x25ae4668} }, +/**/ {{0xbc7d7581, 0x816630d1} }, +/**/ {{0x3fb44e7b, 0x07f85056} }, +/**/ {{0x3c56d63c, 0x910bdf4f} }, +/**/ {{0x3fc71875, 0xc439029c} }, +/**/ {{0xbfb3b85e, 0xf2bcfa10} }, +/**/ {{0xbfbe04bb, 0x9707b205} }, +/**/ {{0x3fb2f8c6, 0x95e3e0cc} }, +/**/ {{0x3fb47184, 0x8093431b} } }, +/**/ {{{0x3fb60000, 0x00000000} }, +/**/ {{0x3fb5f232, 0x4fd2d7b2} }, +/**/ {{0x3c58a8da, 0x4401318e} }, +/**/ {{0x3fefc3f1, 0x8b549418} }, +/**/ {{0x3c34d896, 0x836f8130} }, +/**/ {{0xbfb5adb9, 0x9cdd92e7} }, +/**/ {{0x3c4d4161, 0xeb397cc3} }, +/**/ {{0xbfd467bd, 0x93f8f1dc} }, +/**/ {{0xbc609d7b, 0xffc760ad} }, +/**/ {{0x3fb53443, 0xbea6b2fe} }, +/**/ {{0x3c5eb03c, 0x4b24f5db} }, +/**/ {{0x3fc6dc13, 0x8de3d005} }, +/**/ {{0xbfb48866, 0x37d2d99d} }, +/**/ {{0xbfbd6a1d, 0xf6663fcb} }, +/**/ {{0x3fb3ad8e, 0x0adff464} }, +/**/ {{0x3fb3b9d6, 0x4159c223} } }, +/**/ {{{0x3fb70000, 0x00000000} }, +/**/ {{0x3fb6f03b, 0xdcea4b0d} }, +/**/ {{0xbc33f00e, 0x512fa17d} }, +/**/ {{0x3fefbe67, 0x8c07a436} }, +/**/ {{0xbc84baaa, 0x46250d6f} }, +/**/ {{0xbfb6a215, 0x7e3ba4c7} }, +/**/ {{0xbc3504e7, 0x54503f8d} }, +/**/ {{0xbfd45217, 0x6b82d03a} }, +/**/ {{0x3c7d1f0d, 0xbebdd1db} }, +/**/ {{0x3fb617a4, 0x841d5604} }, +/**/ {{0xbc47168b, 0x6681c436} }, +/**/ {{0x3fc69d47, 0xaccec6ce} }, +/**/ {{0xbfb5541f, 0xa4715800} }, +/**/ {{0xbfbcc9f4, 0x335a1c1b} }, +/**/ {{0x3fb45bc6, 0xbac0061f} }, +/**/ {{0x3fb2fc84, 0x2b3853b6} } }, +/**/ {{{0x3fb80000, 0x00000000} }, +/**/ {{0x3fb7ee18, 0x2602f10f} }, +/**/ {{0xbc5cfb65, 0x4c0c3d98} }, +/**/ {{0x3fefb8a0, 0x96acfacc} }, +/**/ {{0xbc82962e, 0x18495af3} }, +/**/ {{0xbfb79568, 0x46635c89} }, +/**/ {{0x3c5ac468, 0xa6bfd498} }, +/**/ {{0xbfd43b8f, 0x2037b997} }, +/**/ {{0xbc72ad53, 0xe2f12373} }, +/**/ {{0x3fb6f885, 0x7900c4ee} }, +/**/ {{0x3c53145d, 0x0aef1f9d} }, +/**/ {{0x3fc65c1f, 0x4409ba0e} }, +/**/ {{0xbfb61b65, 0x1d176e0c} }, +/**/ {{0xbfbc2473, 0x8ad65152} }, +/**/ {{0x3fb5033f, 0x7bc246c1} }, +/**/ {{0x3fb239e9, 0x6db30b46} } }, +/**/ {{{0x3fb90000, 0x00000000} }, +/**/ {{0x3fb8ebc5, 0x4478fb28} }, +/**/ {{0x3c473288, 0x0cad24cc} }, +/**/ {{0x3fefb29c, 0xeedcd6d7} }, +/**/ {{0x3c8efa9e, 0x23ea50f0} }, +/**/ {{0xbfb887a7, 0x6ae09982} }, +/**/ {{0x3c5b2275, 0x53801511} }, +/**/ {{0xbfd42427, 0x3da0757c} }, +/**/ {{0xbc7199e5, 0x311c7ac8} }, +/**/ {{0x3fb7d6cf, 0x4388717b} }, +/**/ {{0xbc5c4eb2, 0x3dd070b4} }, +/**/ {{0x3fc618a7, 0xe6c2b5f3} }, +/**/ {{0xbfb6de12, 0x00313569} }, +/**/ {{0xbfbb79d2, 0xb6316619} }, +/**/ {{0x3fb5a3ca, 0x61af5c21} }, +/**/ {{0x3fb17263, 0x26e60289} } }, +/**/ {{{0x3fba0000, 0x00000000} }, +/**/ {{0x3fb9e941, 0x53cfdcf1} }, +/**/ {{0x3c5a332e, 0x1d69c47e} }, +/**/ {{0x3fefac5c, 0xdace3776} }, +/**/ {{0xbc8c9a78, 0x1ad91ab5} }, +/**/ {{0xbfb978c8, 0x8054ad75} }, +/**/ {{0xbc5e35b8, 0x8ed66c17} }, +/**/ {{0xbfd40be2, 0x665afed1} }, +/**/ {{0x3c62eeef, 0x08ef10fb} }, +/**/ {{0x3fb8b26b, 0x13c989d2} }, +/**/ {{0x3c329f11, 0xbfeab3ba} }, +/**/ {{0x3fc5d2ef, 0x93c8f97c} }, +/**/ {{0xbfb79c03, 0x30234881} }, +/**/ {{0xbfbaca49, 0xd0f650c8} }, +/**/ {{0x3fb63d3c, 0xce2dcccc} }, +/**/ {{0x3fb0a650, 0x26fb0af2} } }, +/**/ {{{0x3fbb0000, 0x00000000} }, +/**/ {{0x3fbae68a, 0x71c722b8} }, +/**/ {{0x3c4c014e, 0x6910b9db} }, +/**/ {{0x3fefa5e0, 0xa34ef42b} }, +/**/ {{0xbc836583, 0xeb56d5b9} }, +/**/ {{0xbfba68c1, 0x3b881779} }, +/**/ {{0xbc473a0d, 0x13a09314} }, +/**/ {{0xbfd3f2c3, 0x538e939c} }, +/**/ {{0xbc68ed49, 0xee53e648} }, +/**/ {{0x3fb98b42, 0xa7d45973} }, +/**/ {{0xbc523943, 0x461ca7c4} }, +/**/ {{0x3fc58b04, 0xb0f2e2bb} }, +/**/ {{0xbfb85517, 0x1c9d23dc} }, +/**/ {{0xbfba1612, 0x3e3b5a66} }, +/**/ {{0x3fb6cf6f, 0x7ef1d0b9} }, +/**/ {{0x3fafac21, 0x6617b315} } }, +/**/ {{{0x3fbc0000, 0x00000000} }, +/**/ {{0x3fbbe39e, 0xbe6f07c3} }, +/**/ {{0x3c5f7b8f, 0x29a05987} }, +/**/ {{0x3fef9f28, 0x93bb9192} }, +/**/ {{0x3c78260b, 0x7cd1bdab} }, +/**/ {{0xbfbb5787, 0x72759741} }, +/**/ {{0x3c52f93f, 0xa6767247} }, +/**/ {{0xbfd3d8cc, 0xd45bbe91} }, +/**/ {{0x3c664839, 0x2edc0762} }, +/**/ {{0x3fba6140, 0x4fa31d26} }, +/**/ {{0x3c400647, 0x97891510} }, +/**/ {{0x3fc540f6, 0x0668fd66} }, +/**/ {{0xbfb9092d, 0xcb2f6e8f} }, +/**/ {{0xbfb95d66, 0x8d902073} }, +/**/ {{0x3fb75a3e, 0x99c53d16} }, +/**/ {{0x3fae040c, 0x8f475e61} } }, +/**/ {{{0x3fbd0000, 0x00000000} }, +/**/ {{0x3fbce07c, 0x5c3cca32} }, +/**/ {{0x3c4138e6, 0x425918a7} }, +/**/ {{0x3fef9834, 0xf9f6d421} }, +/**/ {{0x3c6f3089, 0x8c22a239} }, +/**/ {{0xbfbc4511, 0x1d4e69a5} }, +/**/ {{0x3c254c0f, 0xd2083ce8} }, +/**/ {{0xbfd3be01, 0xcd488978} }, +/**/ {{0x3c5612db, 0x6362ec0f} }, +/**/ {{0x3fbb344e, 0xf0d94873} }, +/**/ {{0xbc182beb, 0xfdf7db72} }, +/**/ {{0x3fc4f4d2, 0xb9d86c04} }, +/**/ {{0xbfb9b828, 0xdf238807} }, +/**/ {{0xbfb8a082, 0x5f93ffd6} }, +/**/ {{0x3fb7dd89, 0xb6650b0c} }, +/**/ {{0x3fac5526, 0xb62676ef} } }, +/**/ {{{0x3fbe0000, 0x00000000} }, +/**/ {{0x3fbddd21, 0x701eba6e} }, +/**/ {{0x3c594eff, 0xcd76fe58} }, +/**/ {{0x3fef9106, 0x266112ba} }, +/**/ {{0x3c74c302, 0x6b7e18b1} }, +/**/ {{0xbfbd3154, 0x5777816c} }, +/**/ {{0x3c5dc7e4, 0x1f9dbddd} }, +/**/ {{0xbfd3a265, 0x37a90881} }, +/**/ {{0xbc75bd61, 0xeb7ba840} }, +/**/ {{0x3fbc045a, 0x0a52514b} }, +/**/ {{0xbc35ca88, 0xcff49a99} }, +/**/ {{0x3fc4a6aa, 0x498eeb56} }, +/**/ {{0xbfba61eb, 0xa09232cf} }, +/**/ {{0xbfb7dfa2, 0x4a464027} }, +/**/ {{0x3fb85933, 0xe633c053} }, +/**/ {{0x3faaa036, 0x3f920107} } }, +/**/ {{{0x3fbf0000, 0x00000000} }, +/**/ {{0x3fbed98c, 0x2190043b} }, +/**/ {{0xbc23a598, 0x592c7b13} }, +/**/ {{0x3fef899c, 0x6bcf4ad8} }, +/**/ {{0x3c55fd73, 0x912c09b0} }, +/**/ {{0xbfbe1c47, 0x607f91a0} }, +/**/ {{0x3c576677, 0x5b5db022} }, +/**/ {{0xbfd385fa, 0x21046f5f} }, +/**/ {{0x3c7f01c3, 0x4487f4b8} }, +/**/ {{0x3fbcd14d, 0xb77f2d51} }, +/**/ {{0x3c57a86d, 0x30a2ccfe} }, +/**/ {{0x3fc4568c, 0x8782b530} }, +/**/ {{0xbfbb065b, 0x02b7ad2d} }, +/**/ {{0xbfb71b03, 0xbd215555} }, +/**/ {{0x3fb8cd23, 0xb9c1c1de} }, +/**/ {{0x3fa8e602, 0x8dbfa69b} } }, +/**/ {{{0x3fc00000, 0x00000000} }, +/**/ {{0x3fbfd5ba, 0x9aac2f6e} }, +/**/ {{0xbc4cd376, 0x86760c17} }, +/**/ {{0x3fef81f8, 0x1f81f820} }, +/**/ {{0xbc8f81f8, 0x1f81f820} }, +/**/ {{0xbfbf05e0, 0x9d0dc11b} }, +/**/ {{0xbc35a199, 0x1d821725} }, +/**/ {{0xbfd368c3, 0xaa76e1d7} }, +/**/ {{0xbc672d4c, 0xc796f8cd} }, +/**/ {{0x3fbd9b16, 0xb391c2e3} }, +/**/ {{0x3c58051b, 0x8086c51d} }, +/**/ {{0x3fc40489, 0x94488c86} }, +/**/ {{0xbfbba55d, 0xa98401c8} }, +/**/ {{0xbfb652e4, 0xe5127e64} }, +/**/ {{0x3fb93943, 0x442e53ae} }, +/**/ {{0x3fa72753, 0x86286f75} } }, +/**/ {{{0x3fc08000, 0x00000000} }, +/**/ {{0x3fc068d5, 0x84212b3e} }, +/**/ {{0xbc69e2d2, 0x83019bfd} }, +/**/ {{0x3fef7a19, 0x991bb133} }, +/**/ {{0x3c7a956a, 0x66627723} }, +/**/ {{0xbfbfee16, 0x97c8e137} }, +/**/ {{0x3c4d9399, 0x66dbe7af} }, +/**/ {{0xbfd34ac5, 0x0810323a} }, +/**/ {{0x3c6a1a57, 0x6bc6c512} }, +/**/ {{0x3fbe61a2, 0x5c75a6f9} }, +/**/ {{0xbc492b99, 0xd75c8f85} }, +/**/ {{0x3fc3b0b1, 0xd9fa3f20} }, +/**/ {{0xbfbc3edb, 0xee66d309} }, +/**/ {{0xbfb58784, 0x905eeb33} }, +/**/ {{0x3fb99d80, 0x1c65bb14} }, +/**/ {{0x3fa564f1, 0x18a09884} } }, +/**/ {{{0x3fc10000, 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{{0x3fc0ad06, 0xf5c213ab} }, +/**/ {{0x3c625bf2, 0xabea9e66} }, +/**/ {{0x3fc25054, 0x5f93bbb2} }, +/**/ {{0xbfbe6c0c, 0xc80a32c8} }, +/**/ {{0xbfb23e6c, 0x678d0d1e} }, +/**/ {{0x3fbadea2, 0xebf8ae4b} }, +/**/ {{0x3f9c8bd7, 0x527f133b} } }, +/**/ {{{0x3fc30000, 0x00000000} }, +/**/ {{0x3fc2dcbd, 0xb2fba1ff} }, +/**/ {{0x3c58f287, 0x05561534} }, +/**/ {{0x3fef4f64, 0x2ee76e94} }, +/**/ {{0x3c80ec89, 0xc6da5865} }, +/**/ {{0xbfc23089, 0xb322f867} }, +/**/ {{0x3c4c2b54, 0x5fcd0d6f} }, +/**/ {{0xbfd2a986, 0x45802261} }, +/**/ {{0xbc79a132, 0x5ae78b8a} }, +/**/ {{0x3fc107b3, 0x35a9d974} }, +/**/ {{0x3c5ef22d, 0xb725e335} }, +/**/ {{0x3fc1f453, 0x9bd98832} }, +/**/ {{0xbfbee8cf, 0x2057aad4} }, +/**/ {{0xbfb16681, 0x1e1bc3a1} }, +/**/ {{0x3fbb1ad8, 0x759c8f58} }, +/**/ {{0x3f98f941, 0x0b15b4aa} } }, +/**/ {{{0x3fc38000, 0x00000000} }, +/**/ {{0x3fc359e8, 0xedeb99a4} }, +/**/ {{0xbc6a5fd7, 0x4e4604c6} }, +/**/ {{0x3fef462f, 0xfce28238} }, +/**/ {{0x3c83dc01, 0xd90595d1} }, +/**/ {{0xbfc2a01b, 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{{{0x3fd80000, 0x00000000} }, +/**/ {{0x3fd6f619, 0x41e4def1} }, +/**/ {{0xbc7c63aa, 0xe6f6e918} }, +/**/ {{0x3fec0e07, 0x0381c0e0} }, +/**/ {{0x3c8c0e07, 0x0381c0e0} }, +/**/ {{0xbfd2726d, 0xd135c174} }, +/**/ {{0xbc2d352d, 0xe0951cf8} }, +/**/ {{0xbfc09f37, 0xb38cc8cf} }, +/**/ {{0xbc69db81, 0xae75327f} }, +/**/ {{0x3fc85eac, 0xd7da413c} }, +/**/ {{0x3c5b1a89, 0x6ebae2bc} }, +/**/ {{0xbfa04d69, 0x80fcc815} }, +/**/ {{0xbfb8054c, 0x1df326f9} }, +/**/ {{0x3fb2a47e, 0x082bda60} }, +/**/ {{0x3f944639, 0x7091d5a4} }, +/**/ {{0xbfaf5961, 0xe072e48c} } }, +/**/ {{{0x3fd84000, 0x00000000} }, +/**/ {{0x3fd72e22, 0xd53aa2aa} }, +/**/ {{0xbc7d9c93, 0x4e79f27c} }, +/**/ {{0x3febfb88, 0x36a04729} }, +/**/ {{0xbc872745, 0x9ac2ea21} }, +/**/ {{0xbfd28b13, 0x9d7702cf} }, +/**/ {{0x3c7819b9, 0x4be8bff6} }, +/**/ {{0xbfc03de6, 0xb0a35176} }, +/**/ {{0x3c5dbfb0, 0xc83347af} }, +/**/ {{0x3fc84999, 0x332a4f86} }, +/**/ {{0x3c5d304e, 0x0a22d12d} }, +/**/ {{0xbfa16a97, 0xed6b2d30} }, +/**/ {{0xbfb78243, 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{{0xbc8ce80d, 0xf30411fb} }, +/**/ {{0x3fe16f10, 0x6bbc577a} }, +/**/ {{0xbc7d0db6, 0xbd8abf47} }, +/**/ {{0xbfd15d1b, 0x58355b5f} }, +/**/ {{0xbc5b5457, 0xbcc70038} }, +/**/ {{0x3fb4c9e4, 0xe8fdd51d} }, +/**/ {{0x3c462959, 0x28ac9383} }, +/**/ {{0x3f8b20c3, 0x2029f143} }, +/**/ {{0xbc2f8a44, 0x2b420400} }, +/**/ {{0xbfa2fea7, 0x7b921c49} }, +/**/ {{0x3f9a9aa0, 0xf468e79e} }, +/**/ {{0xbf7fb66c, 0xcccbcb4f} }, +/**/ {{0xbf6fb0d0, 0x9bd39a5f} }, +/**/ {{0x3f7b7748, 0x8813998f} } }, +/**/ {{{0x3fed6000, 0x00000000} }, +/**/ {{0x3fe7c3d3, 0x11a6092b} }, +/**/ {{0x3c8bb3cb, 0x2d303288} }, +/**/ {{0x3fe15dbb, 0x1dc61b17} }, +/**/ {{0xbc8f0487, 0xbb77dc56} }, +/**/ {{0xbfd14d7e, 0xee0771ca} }, +/**/ {{0x3c72d38b, 0xdc2fcbd0} }, +/**/ {{0x3fb4d716, 0xd6080f0e} }, +/**/ {{0xbc5cb5bc, 0xa9fbc2c3} }, +/**/ {{0x3f89a7f9, 0xfc42e02f} }, +/**/ {{0xbc201eec, 0x857be8a4} }, +/**/ {{0xbfa2af2b, 0x44ceebb3} }, +/**/ {{0x3f9a62b5, 0x08511639} }, +/**/ {{0xbf8018ad, 0xc8de23de} }, +/**/ {{0xbf6dc8a2, 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+/**/ {{0xbfa21230, 0x34b94b56} }, +/**/ {{0x3f99f078, 0xa827f95a} }, +/**/ {{0xbf808869, 0x19caa997} }, +/**/ {{0xbf6a1d29, 0xf8c46d26} }, +/**/ {{0x3f796b9a, 0xae59da17} } }, +/**/ {{{0x3fedc000, 0x00000000} }, +/**/ {{0x3fe7f79e, 0xacb97898} }, +/**/ {{0x3c8fd5ca, 0x80ead221} }, +/**/ {{0x3fe12a19, 0x20604825} }, +/**/ {{0xbc5cc7d6, 0xa18970f8} }, +/**/ {{0xbfd11e72, 0x1dfe6ba4} }, +/**/ {{0x3c706717, 0x9d653d1c} }, +/**/ {{0x3fb4fa57, 0xd5fcbb3b} }, +/**/ {{0x3c1922c8, 0x5f50bc06} }, +/**/ {{0x3f856283, 0xe93a179f} }, +/**/ {{0xbc01c2ec, 0x5ea7135a} }, +/**/ {{0xbfa1c4b5, 0xf0c06b4f} }, +/**/ {{0x3f99b641, 0xe48a3b04} }, +/**/ {{0xbf80badd, 0xe1280a21} }, +/**/ {{0xbf68599e, 0x1be3c5dd} }, +/**/ {{0x3f78c0b3, 0x3a72c8e6} } }, +/**/ {{{0x3fede000, 0x00000000} }, +/**/ {{0x3fe808c0, 0x3940694b} }, +/**/ {{0xbc800f32, 0x7715f6a5} }, +/**/ {{0x3fe11902, 0x8d73d98e} }, +/**/ {{0x3c71d158, 0x30f8e290} }, +/**/ {{0xbfd10eb2, 0x6fc305eb} }, +/**/ {{0xbc7fd2e3, 0x3858c4b7} }, +/**/ 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+/**/ {{{0x3fee6000, 0x00000000} }, +/**/ {{0x3fe84c9c, 0x7653f7eb} }, +/**/ {{0xbc383611, 0xfe0a3e8f} }, +/**/ {{0x3fe0d546, 0x2a7f71b5} }, +/**/ {{0x3c757061, 0x596848c6} }, +/**/ {{0xbfd0cf6d, 0xb4cf51a6} }, +/**/ {{0x3c4c99ab, 0x5b18bb8c} }, +/**/ {{0x3fb5275f, 0x24486227} }, +/**/ {{0x3c5b4a59, 0xbb1f4f56} }, +/**/ {{0x3f7d77be, 0x36238bb2} }, +/**/ {{0x3c1ddbd1, 0xcaec6ba2} }, +/**/ {{0xbfa04bc1, 0xe1406cd0} }, +/**/ {{0x3f988a1e, 0x7f96d6ca} }, +/**/ {{0xbf8184c5, 0xcdffc380} }, +/**/ {{0xbf603841, 0x12561f8b} }, +/**/ {{0x3f7588b9, 0x4d81a668} } }, +/**/ {{{0x3fee8000, 0x00000000} }, +/**/ {{0x3fe85d69, 0x576cc2c5} }, +/**/ {{0x3c66b66e, 0x7fc8b8c3} }, +/**/ {{0x3fe0c47e, 0xac74fadc} }, +/**/ {{0xbc8035f8, 0x77bb1887} }, +/**/ {{0xbfd0bf8d, 0x7e8202a9} }, +/**/ {{0x3c798048, 0x1f4d2357} }, +/**/ {{0x3fb52e6c, 0x13725c73} }, +/**/ {{0xbc34c3af, 0xf5b19ded} }, +/**/ {{0x3f7af1a3, 0x7d9c2711} }, +/**/ {{0x3bea7ec7, 0x1af1098d} }, +/**/ {{0xbfa0027f, 0xb643d11f} }, +/**/ 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0x0844ff86} }, +/**/ {{0x3f76077c, 0xacf1a65c} }, +/**/ {{0xbc19a3b2, 0xb13331a9} }, +/**/ {{0xbf9ee450, 0x472733eb} }, +/**/ {{0x3f97d05c, 0x21e541d7} }, +/**/ {{0xbf81d8da, 0x9d9d4dfc} }, +/**/ {{0xbf57be45, 0xd3ce1b4a} }, +/**/ {{0x3f73b4ba, 0x7cb60047} } }, +/**/ {{{0x3feee000, 0x00000000} }, +/**/ {{0x3fe88f6b, 0xbd023119} }, +/**/ {{0xbc532d1d, 0x25aba660} }, +/**/ {{0x3fe09287, 0x95d126c6} }, +/**/ {{0x3c85aad3, 0xeccc37a6} }, +/**/ {{0xbfd08fd0, 0x649e7367} }, +/**/ {{0x3c71e96c, 0xed21a127} }, +/**/ {{0x3fb53fdd, 0x957ec910} }, +/**/ {{0xbc339c23, 0xaf97a601} }, +/**/ {{0x3f73a336, 0x5a18e5a2} }, +/**/ {{0xbc1f7225, 0x477571de} }, +/**/ {{0xbf9e5629, 0xd4044135} }, +/**/ {{0x3f9791bd, 0x32786dc4} }, +/**/ {{0xbf81ef39, 0xbdf030c4} }, +/**/ {{0xbf550386, 0xe21b8bcb} }, +/**/ {{0x3f731d62, 0x97aa7fb2} } }, +/**/ {{{0x3fef0000, 0x00000000} }, +/**/ {{0x3fe89ff5, 0xff57f1f8} }, +/**/ {{0xbc855b9a, 0x5e177a1b} }, +/**/ {{0x3fe081ff, 0xbdf80108} }, +/**/ {{0x3c6ffbdf, 0x80108200} }, +/**/ {{0xbfd07fde, 0xba010928} }, +/**/ {{0x3c38d37f, 0x7bae0295} }, +/**/ {{0x3fb5447b, 0x0136e69f} }, +/**/ {{0x3c50316a, 0x0dda278d} }, +/**/ {{0x3f7149fc, 0x55103947} }, +/**/ {{0x3c176e96, 0x849e505f} }, +/**/ {{0xbf9dc97b, 0xfbe9a2ee} }, +/**/ {{0x3f9752d4, 0xb08adda9} }, +/**/ {{0xbf8202e8, 0xb540d106} }, +/**/ {{0xbf525de5, 0x859de3e9} }, +/**/ {{0x3f72886c, 0x4afd9f21} } }, +/**/ {{{0x3fef2000, 0x00000000} }, +/**/ {{0x3fe8b06f, 0xc1cf3dff} }, +/**/ {{0xbc80fb31, 0x2656db6d} }, +/**/ {{0x3fe07187, 0xd971cd38} }, +/**/ {{0x3c89baa4, 0x202c20ac} }, +/**/ {{0xbfd06fe9, 0xd15893ab} }, +/**/ {{0xbc7a864b, 0xdc0cb586} }, +/**/ {{0x3fb54883, 0x7ce57fed} }, +/**/ {{0xbc49498e, 0x294f4b18} }, +/**/ {{0x3f6df762, 0x426ebecc} }, +/**/ {{0xbc022f08, 0xf28644c0} }, +/**/ {{0xbf9d3e48, 0x5c564b44} }, +/**/ {{0x3f9713ab, 0xdfea7acf} }, +/**/ {{0xbf8213fc, 0x761db35c} }, +/**/ {{0xbf4f9a17, 0x10d60f49} }, +/**/ {{0x3f71f5de, 0x58700e9b} } }, +/**/ {{{0x3fef4000, 0x00000000} }, +/**/ {{0x3fe8c0d9, 0x145cf49d} }, +/**/ {{0x3c8bea40, 0x76dc4333} }, +/**/ {{0x3fe0611f, 0xeb45139a} }, +/**/ {{0x3c7e4998, 0x65aadb1f} }, +/**/ {{0xbfd05ff2, 0x1953a316} }, +/**/ {{0x3c759922, 0xa1b67b0f} }, +/**/ {{0x3fb54bf9, 0xc08c1d66} }, +/**/ {{0x3c5b9353, 0xd220330c} }, +/**/ {{0x3f69706e, 0x478cb604} }, +/**/ {{0xbbfdb6d3, 0xa22fd45a} }, +/**/ {{0xbf9cb490, 0x5c0d1d38} }, +/**/ {{0x3f96d44b, 0xbbaba2f2} }, +/**/ {{0xbf822289, 0x9c6b7de1} }, +/**/ {{0xbf4aa143, 0xa49803b6} }, +/**/ {{0x3f7165be, 0x9270e49e} } }, +/**/ {{{0x3fef6000, 0x00000000} }, +/**/ {{0x3fe8d132, 0x06f8c4cb} }, +/**/ {{0xbc7b018c, 0xbaa89a8b} }, +/**/ {{0x3fe050c7, 0xf60ab1f4} }, +/**/ {{0x3c63f8e2, 0xc6cf5796} }, +/**/ {{0xbfd04ff7, 0xfe998dc0} }, +/**/ {{0x3c77873c, 0x7dc56419} }, +/**/ {{0x3fb54ee0, 0x7cc24121} }, +/**/ {{0x3c313117, 0x8e5c84c5} }, +/**/ {{0x3f64fee1, 0x50066301} }, +/**/ {{0x3c043698, 0x017261a1} }, +/**/ {{0xbf9c2c55, 0x2cc5b4f1} }, +/**/ {{0x3f9694bc, 0xf759f369} }, +/**/ {{0xbf822ea4, 0x6c93426a} }, +/**/ {{0xbf45d0a1, 0x135d6c51} }, +/**/ {{0x3f70d811, 0xe62dc18f} } }, +/**/ {{{0x3fef8000, 0x00000000} }, +/**/ {{0x3fe8e17a, 0xa99cc05e} }, +/**/ {{0xbc7ec182, 0xab042f61} }, +/**/ {{0x3fe0407f, 0xfbefe001} }, +/**/ {{0x3c401ffe, 0xfbf80041} }, +/**/ {{0xbfd03ffb, 0xebd00209} }, +/**/ {{0xbc53ff3c, 0xb9004112} }, +/**/ {{0x3fb5513a, 0x5aaf6d91} }, +/**/ {{0x3c54a20d, 0xc0516ddb} }, +/**/ {{0x3f60a27f, 0xc6ac4038} }, +/**/ {{0x3bf06bee, 0x2a340912} }, +/**/ {{0xbf9ba597, 0xccd6032a} }, +/**/ {{0x3f965508, 0x002bb974} }, +/**/ {{0xbf823860, 0xd2d1068b} }, +/**/ {{0xbf41277e, 0x666265bc} }, +/**/ {{0x3f704cdc, 0x656b66ea} } }, +/**/ {{{0x3fefa000, 0x00000000} }, +/**/ {{0x3fe8f1b3, 0x0c44f167} }, +/**/ {{0x3c6dd1ca, 0xb93933fd} }, +/**/ {{0x3fe03047, 0xfeb82e4e} }, +/**/ {{0x3c69ee56, 0x5272e5ac} }, +/**/ {{0xbfd02ffe, 0x49a09c45} }, +/**/ {{0xbc700a59, 0xb26267bb} }, +/**/ {{0x3fb55309, 0xfc062d2f} }, +/**/ {{0x3c5dba48, 0xb11938e0} }, +/**/ {{0x3f58b61b, 0xe4f365be} }, +/**/ {{0x3bf8b585, 0xa79ad31a} }, +/**/ {{0xbf9b2059, 0x08d4ad17} }, +/**/ {{0x3f961534, 0xfe379940} }, +/**/ {{0xbf823fd2, 0x62a1270e} }, +/**/ {{0xbf394a53, 0x3f3a0aec} }, +/**/ {{0x3f6f8842, 0xa04bcae2} } }, +/**/ {{{0x3fefc000, 0x00000000} }, +/**/ {{0x3fe901db, 0x3eeef187} }, +/**/ {{0x3c868665, 0xe5603c8f} }, +/**/ {{0x3fe0201f, 0xffbf7f80} }, +/**/ {{0x3c20201f, 0xffbf7f80} }, +/**/ {{0xbfd01fff, 0x7ebe8004} }, +/**/ {{0xbc4213ff, 0xcf979001} }, +/**/ {{0x3fb55451, 0xfb0012db} }, +/**/ {{0xbc395606, 0xf73aa59f} }, +/**/ {{0x3f50509f, 0xfc757100} }, +/**/ {{0x3bebc7da, 0xfee554d0} }, +/**/ {{0xbf9a9c99, 0x7d3424d0} }, +/**/ {{0x3f95d54b, 0xd5ac0217} }, +/**/ {{0xbf82450c, 0x564b3c49} }, +/**/ {{0xbf3091df, 0xe6d3e986} }, +/**/ {{0x3f6e7bc6, 0x3bef5a22} } }, +/**/ {{{0x3fefe000, 0x00000000} }, +/**/ {{0x3fe911f3, 0x5199833b} }, +/**/ {{0x3c63ae8a, 0x0edbf522} }, +/**/ {{0x3fe01007, 0xfffbfbfe} }, +/**/ {{0x3ba01007, 0xfffbfbfe} }, +/**/ {{0xbfd00fff, 0xefebf400} }, +/**/ {{0xbc401209, 0xfff9f97d} }, +/**/ {{0x3fb55514, 0xea5aaaf6} }, +/**/ {{0xbc529baa, 0xb5b7b240} }, +/**/ {{0x3f402827, 0xffc7abc4} }, +/**/ {{0x3b5ba3d6, 0xbfee6ab3} }, +/**/ {{0xbf9a1a59, 0x97d67093} }, +/**/ {{0x3f959554, 0x28080aaf} }, +/**/ {{0xbf824821, 0x8e892ce2} }, +/**/ {{0xbf204877, 0xfe70a2a6} }, +/**/ {{0x3f6d7447, 0x0e8ddd67} } }, +/**/ {{{0x3feff800, 0x00000000} }, +/**/ {{0x3fe91dfa, 0xd439826e} }, +/**/ {{0xbc786a19, 0x6df48d55} }, +/**/ {{0x3fe00400, 0x7ffffbff} }, +/**/ {{0xbbeffffe, 0xffbff800} }, +/**/ {{0xbfd003ff, 0xffbfebfd} }, +/**/ {{0xbb600480, 0x9ffff9fe} }, +/**/ {{0x3fb55551, 0x53aa5aab} }, +/**/ {{0xbc542a4a, 0x9baaab5b} }, +/**/ {{0x3f200a02, 0x7fffc7eb} }, +/**/ {{0xbb7dfffe, 0x4770e940} }, +/**/ {{0xbf99b9a5, 0x9997d8d0} }, +/**/ {{0x3f956555, 0x50a80a03} }, +/**/ {{0xbf824914, 0x86456493} }, +/**/ {{0xbf001207, 0x7ffe7329} }, +/**/ {{0x3f6cb1ef, 0x1c63fe2a} } }, + }; + +#else +#ifdef LITTLE_ENDI + + static const number + cij[241][7] = { /* x0,cij for (1/16,1) */ +/**/ {{{0X65E0244E, 0X3FB04006} }, +/**/ {{0X7B53DD20, 0X3FB03A73} }, +/**/ {{0XCF5CFB72, 0X3FEFDF1F} }, +/**/ {{0XCE2AE4C2, 0XBFB01EB3} }, +/**/ {{0XDD58A40D, 0XBFD4D29E} }, +/**/ {{0XD907A18A, 0X3FAFDA4A} }, +/**/ {{0X4DF65B18, 0X3FC814DF} } }, +/**/ {{{0XB9B88CD8, 0X3FB0FFFD} }, +/**/ {{0X63645300, 0X3FB0F99C} }, +/**/ {{0XA3DED30F, 0X3FEFDC08} }, +/**/ {{0X669C1AED, 0XBFB0D9DC} }, +/**/ {{0XF7138DE2, 0XBFD4C669} }, +/**/ {{0X29D085A7, 0X3FB0A12F} }, +/**/ {{0XCFD48D20, 0X3FC7F0EE} } }, +/**/ {{{0X5A73D4F1, 0X3FB1FFF1} }, +/**/ {{0X2BEE2040, 0X3FB1F85F} }, +/**/ {{0X42B56D31, 0X3FEFD7B3} }, +/**/ {{0XB69DEA40, 0XBFB1D2B7} }, +/**/ {{0X3922ECC9, 0XBFD4B552} }, +/**/ {{0X522B1A04, 0X3FB18F93} }, +/**/ {{0X5660F061, 0X3FC7BEAD} } }, +/**/ {{{0XB2524AA2, 0X3FB2FFFD} }, +/**/ {{0XE71790A0, 0X3FB2F716} }, +/**/ {{0X53B496A4, 0X3FEFD31F} }, +/**/ {{0X4AAB7374, 0XBFB2CAD8} }, +/**/ {{0X58DD2FB2, 0XBFD4A34B} }, +/**/ {{0XD0CECC18, 0X3FB27C0A} }, +/**/ {{0X5D2743D7, 0X3FC789D2} } }, +/**/ {{{0X0573F3AC, 0X3FB3FFFE} }, +/**/ {{0X1702F6A0, 0X3FB3F59D} }, +/**/ {{0XB071ACC2, 0X3FEFCE4D} }, +/**/ {{0X64DB3686, 0XBFB3C20F} }, +/**/ {{0XEB3BFE93, 0XBFD49059} }, +/**/ {{0XCAF74FED, 0X3FB36659} }, +/**/ {{0X1C011FB0, 0X3FC75269} } }, +/**/ {{{0X894384D6, 0X3FB4FFEF} }, +/**/ {{0X0CE204C0, 0X3FB4F3ED} }, +/**/ {{0XA8EA5A01, 0X3FEFC93E} }, +/**/ {{0X7B5457C9, 0XBFB4B84F} }, +/**/ {{0X7401F2F9, 0XBFD47C80} }, +/**/ {{0XB4F67209, 0X3FB44E64} }, +/**/ {{0X4C540B77, 0X3FC7187D} } }, +/**/ {{{0XDF406528, 0X3FB5FFF8} }, +/**/ {{0X3C73D820, 0X3FB5F22B} }, +/**/ {{0XB1F60F13, 0X3FEFC3F1} }, +/**/ {{0XCB7FA73B, 0XBFB5ADB2} }, +/**/ {{0X2B1EB555, 0XBFD467BE} }, +/**/ {{0X99EDC463, 0X3FB53435} }, +/**/ {{0X238F5059, 0X3FC6DC1B} } }, +/**/ {{{0X8C4F0D56, 0X3FB7000F} }, +/**/ {{0X495A2FA0, 0X3FB6F04B} }, +/**/ {{0X340DCE97, 0X3FEFBE67} }, +/**/ {{0X4D98E1AD, 0XBFB6A224} }, +/**/ {{0X14064DF1, 0XBFD45216} }, +/**/ {{0X2BA78A66, 0X3FB617AA} }, +/**/ {{0X50A3D7AC, 0X3FC69D4F} } }, +/**/ {{{0XBB4057CF, 0X3FB8000F} }, +/**/ {{0XBE2CD3A0, 0X3FB7EE27} }, +/**/ {{0X39EC9246, 0X3FEFB8A0} }, +/**/ {{0X31D9C773, 0XBFB79577} }, +/**/ {{0XB6DC7D72, 0XBFD43B8D} }, +/**/ {{0XD69547DF, 0X3FB6F88A} }, +/**/ {{0XF633CE8C, 0X3FC65C26} } }, +/**/ {{{0X39CF2B7F, 0X3FB8FFF2} }, +/**/ {{0X9F979E80, 0X3FB8EBB7} }, +/**/ {{0X435506E1, 0X3FEFB29D} }, +/**/ {{0X69B9CDB5, 0XBFB8879A} }, +/**/ {{0X85FEAFA9, 0XBFD42428} }, +/**/ {{0XB6191A0E, 0X3FB7D6BA} }, +/**/ {{0XA7CB8BB5, 0X3FC618AF} } }, +/**/ {{{0X6E2F0772, 0X3FB9FFF9} }, +/**/ {{0XD32A9480, 0X3FB9E93A} }, +/**/ {{0X04A3EC40, 0X3FEFAC5D} }, +/**/ {{0X53F6EA97, 0XBFB978C2} }, +/**/ {{0X089C36F6, 0XBFD40BE3} }, +/**/ {{0X885AEB77, 0X3FB8B25C} }, +/**/ {{0X63CADCE1, 0X3FC5D2F7} } }, +/**/ {{{0X6316B097, 0X3FBB0002} }, +/**/ {{0XCE24CC00, 0X3FBAE68C} }, +/**/ {{0X938C5C66, 0X3FEFA5E0} }, +/**/ {{0X76F14E4B, 0XBFBA68C3} }, +/**/ {{0X1696CD7C, 0XBFD3F2C3} }, +/**/ {{0X722A2CB4, 0X3FB98B3B} }, +/**/ {{0X9067AD62, 0X3FC58B0C} } }, +/**/ {{{0X604F58B1, 0X3FBC0008} }, +/**/ {{0X05650780, 0X3FBBE3A7} }, +/**/ {{0X5A7A2773, 0X3FEF9F28} }, +/**/ {{0X3D5AC0A4, 0XBFBB578F} }, +/**/ {{0XF767119F, 0XBFD3D8CB} }, +/**/ {{0XC7E31B88, 0X3FBA613D} }, +/**/ {{0XF5594565, 0X3FC540FD} } }, +/**/ {{{0X6CCA4EBA, 0X3FBD0002} }, +/**/ {{0XC1298A80, 0X3FBCE07E} }, +/**/ {{0XE8D36C4A, 0X3FEF9834} }, +/**/ {{0X5BCAC5FE, 0XBFBC4513} }, +/**/ {{0X8B5236F1, 0XBFD3BE01} }, +/**/ {{0X2E991970, 0X3FBB3447} }, +/**/ {{0XB8ADB373, 0X3FC4F4DA} } }, +/**/ {{{0XB2B47FCA, 0X3FBDFFF4} }, +/**/ {{0X4A051D80, 0X3FBDDD16} }, +/**/ {{0X78DCC895, 0X3FEF9106} }, +/**/ {{0XF0966844, 0XBFBD3149} }, +/**/ {{0X744F9A5F, 0XBFD3A266} }, +/**/ {{0XEDB7F27A, 0X3FBC0446} }, +/**/ {{0X583F9ECA, 0X3FC4A6B2} } }, +/**/ {{{0XA9A05BE0, 0X3FBF000A} }, +/**/ {{0XA3BDA540, 0X3FBED996} }, +/**/ {{0X1B8BA97F, 0X3FEF899C} }, +/**/ {{0X2287A677, 0XBFBE1C51} }, +/**/ {{0XEDC130BB, 0XBFD385F8} }, +/**/ {{0XF306FF50, 0X3FBCD14B} }, +/**/ {{0XA667A72B, 0X3FC45694} } }, +/**/ {{{0XBA8F63DE, 0X3FBFFFFA} }, +/**/ {{0X69FE4780, 0X3FBFD5B5} }, +/**/ {{0X4863DC7D, 0X3FEF81F8} }, +/**/ {{0XD1518706, 0XBFBF05DB} }, +/**/ {{0X4687A69C, 0XBFD368C4} }, +/**/ {{0X1B3868DA, 0X3FBD9B08} }, +/**/ {{0XC345ADFC, 0X3FC40491} } }, +/**/ {{{0X6ECCADA8, 0X3FC07FFA} }, +/**/ {{0X0A396400, 0X3FC068D0} }, +/**/ {{0XF1FCFC6B, 0X3FEF7A19} }, +/**/ {{0X861DF0DF, 0XBFBFEE0C} }, +/**/ {{0X5A586C0C, 0XBFD34AC6} }, +/**/ {{0X189D637A, 0X3FBE618F} }, +/**/ {{0X195779D4, 0X3FC3B0BA} } }, +/**/ {{{0X33432713, 0X3FC10003} }, +/**/ {{0XF203D1A0, 0X3FC0E6B0} }, +/**/ {{0XFE0EB463, 0X3FEF7200} }, +/**/ {{0XE15CB19A, 0XBFC06A72} }, +/**/ {{0XB8DB761E, 0XBFD32C00} }, +/**/ {{0XA11F5E3E, 0X3FBF24D8} }, +/**/ {{0X569E85DD, 0X3FC35B1E} } }, +/**/ {{{0XDA1C4811, 0X3FC17FFC} }, +/**/ {{0X29EBDA00, 0X3FC16462} }, +/**/ {{0X7D558737, 0X3FEF69AF} }, +/**/ {{0X0B33969B, 0XBFC0DD17} }, +/**/ {{0X33AC50D1, 0XBFD30C7D} }, +/**/ {{0X9BE43F0F, 0X3FBFE4AA} }, +/**/ {{0X692539CB, 0X3FC303CF} } }, +/**/ {{{0X3CCA418D, 0X3FC1FFFF} }, +/**/ {{0X3B978EA0, 0X3FC1E1FA} }, +/**/ {{0X45D421A9, 0X3FEF6124} }, +/**/ {{0XACAC8AA8, 0XBFC14F03} }, +/**/ {{0X62E675A3, 0XBFD2EC39} }, +/**/ {{0X2FA6B426, 0X3FC0508C} }, +/**/ {{0X780A6467, 0X3FC2AADE} } }, +/**/ {{{0XD9C78922, 0X3FC27FF7} }, +/**/ {{0X1B91E640, 0X3FC25F66} }, +/**/ {{0XF52E192C, 0X3FEF5860} }, +/**/ {{0XE5DE2394, 0XBFC1C023} }, +/**/ {{0X6BEE0ABD, 0XBFD2CB3D} }, +/**/ {{0X5E075C1A, 0X3FC0ACFB} }, +/**/ {{0XDFFE453A, 0X3FC2505C} } }, +/**/ {{{0XA1FC1AAA, 0X3FC2FFF7} }, +/**/ {{0X83257C40, 0X3FC2DCB5} }, +/**/ {{0XC719B6FB, 0X3FEF4F64} }, +/**/ {{0X61514083, 0XBFC23082} }, +/**/ {{0X7F7B72D5, 0XBFD2A988} }, +/**/ {{0X7C887402, 0X3FC107A7} }, +/**/ {{0X2C3CD6D1, 0X3FC1F45C} } }, +/**/ {{{0X9D78E15E, 0X3FC38005} }, +/**/ {{0X6AC98EE0, 0X3FC359EE} }, +/**/ {{0X944CEC16, 0X3FEF462F} }, +/**/ {{0XD85B87A9, 0XBFC2A020} }, +/**/ {{0X2E4AB369, 0XBFD2871C} }, +/**/ {{0XC31A65D9, 0X3FC1608D} }, +/**/ {{0X130BBE50, 0X3FC196EE} } }, +/**/ {{{0X9F431B1A, 0X3FC40004} }, +/**/ {{0X6BD65360, 0X3FC3D6F3} }, +/**/ {{0XDD99B68A, 0X3FEF3CC3} }, +/**/ {{0XB3DD00ED, 0XBFC30EE1} }, +/**/ {{0XF8482664, 0XBFD26403} }, +/**/ {{0XFE136626, 0X3FC1B792} }, +/**/ {{0X6EAC7440, 0X3FC13824} } }, +/**/ {{{0XE01D95A1, 0X3FC48004} }, +/**/ {{0X86F00CC0, 0X3FC453D3} }, +/**/ {{0XE3970539, 0X3FEF3320} }, +/**/ {{0X0A5279AA, 0XBFC37CCF} }, +/**/ {{0X3B151D5D, 0XBFD2403F} }, +/**/ {{0XE331C9E6, 0X3FC20CBB} }, +/**/ {{0X39E3F097, 0X3FC0D811} } }, +/**/ {{{0XAA9382DD, 0X3FC4FFF7} }, +/**/ {{0X8C590A80, 0X3FC4D07F} }, +/**/ {{0X34DF28E0, 0X3FEF2948} }, +/**/ {{0X5B43915C, 0XBFC3E9D8} }, +/**/ {{0XEB8845A2, 0XBFD21BD5} }, +/**/ {{0XAC6AC8AD, 0X3FC25FF8} }, +/**/ {{0X88ED96CA, 0X3FC076C6} } }, +/**/ {{{0X352408BE, 0X3FC58006} }, +/**/ {{0XC39A73E0, 0X3FC54D1E} }, +/**/ {{0X09AE009C, 0X3FEF1F37} }, +/**/ {{0XB9BE8550, 0XBFC4561C} }, +/**/ {{0X0053F52E, 0XBFD1F6C0} }, +/**/ {{0XEF783BE9, 0X3FC2B15D} }, +/**/ {{0X8615239B, 0X3FC01456} } }, +/**/ 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{{{0X57F250B8, 0X3FEA8001} }, +/**/ {{0XDD6453A0, 0X3FE6220D} }, +/**/ {{0XCFFFCC1E, 0X3FE2FB6F} }, +/**/ {{0X6F8D8291, 0XBFD2A648} }, +/**/ {{0X03654CC3, 0X3FB2D56F} }, +/**/ {{0X4BB6E7A6, 0X3FA07EE3} }, +/**/ {{0X87992F03, 0XBFAA5F2A} } }, +/**/ {{{0XDD839D49, 0X3FEAA000} }, +/**/ {{0XB412C9A0, 0X3FE634FF} }, +/**/ {{0XE2D59E01, 0X3FE2E8D0} }, +/**/ {{0X5467CFDD, 0XBFD2981C} }, +/**/ {{0XFF1FADB5, 0X3FB2F5E8} }, +/**/ {{0XA3BA803C, 0X3F9FF7D6} }, +/**/ {{0X46AF8DB7, 0XBFAA04E3} } }, +/**/ {{{0X770DF220, 0X3FEAC000} }, +/**/ {{0XFEF70020, 0X3FE647DE} }, +/**/ {{0X220AFF7F, 0X3FE2D640} }, +/**/ {{0X36F9E74F, 0XBFD289D8} }, +/**/ {{0XE509140A, 0X3FB3155E} }, +/**/ {{0X61AB0B7F, 0X3F9EF56B} }, +/**/ {{0X98CE391F, 0XBFA9AAE2} } }, +/**/ {{{0X125BBE48, 0X3FEAE001} }, +/**/ {{0X57A24D20, 0X3FE65AAC} }, +/**/ {{0X1BFB3559, 0X3FE2C3BD} }, +/**/ {{0X6DDE55DD, 0XBFD27B7C} }, +/**/ {{0X15C4C270, 0X3FB333D5} }, +/**/ {{0X9BAC4ECF, 0X3F9DF67A} }, +/**/ {{0X363A972B, 0XBFA9512F} } }, +/**/ {{{0X7C321839, 0X3FEAFFFE} }, +/**/ {{0X569B83C0, 0X3FE66D65} }, +/**/ {{0X53FBF8D9, 0X3FE2B14A} }, +/**/ {{0X9CFA03CE, 0XBFD26D0B} }, +/**/ {{0X2CAA2E0C, 0X3FB3514B} }, +/**/ {{0X4597BE9A, 0X3F9CFB22} }, +/**/ {{0X99110022, 0XBFA8F7CF} } }, +/**/ {{{0X75486924, 0X3FEB1FFE} }, +/**/ {{0X68CEFB40, 0X3FE6800D} }, +/**/ {{0X8E6AA814, 0X3FE29EE4} }, +/**/ {{0XE8AFA7EB, 0XBFD25E83} }, +/**/ {{0XFB0E8AC8, 0X3FB36DC9} }, +/**/ {{0XAD5D66CA, 0X3F9C0331} }, +/**/ {{0XFEDB1E8B, 0XBFA89EC9} } }, +/**/ {{{0X5FB8DEB8, 0X3FEB4001} }, +/**/ {{0XD137C500, 0X3FE692A4} }, +/**/ {{0XABFF668E, 0X3FE28C8B} }, +/**/ {{0XD8E71E0A, 0XBFD24FE5} }, +/**/ {{0X1297317A, 0X3FB38955} }, +/**/ {{0X1D844655, 0X3F9B0EA3} }, +/**/ {{0X6914067D, 0XBFA84624} } }, +/**/ {{{0X386C27B9, 0X3FEB6000} }, +/**/ {{0X8CDF6FC0, 0X3FE6A527} }, +/**/ {{0XC5758DB8, 0X3FE27A43} }, +/**/ {{0X59CADCE0, 0XBFD24135} }, +/**/ {{0XEE34AE91, 0X3FB3A3E9} }, +/**/ {{0X1C5FFF05, 0X3F9A1DA8} }, +/**/ {{0X9EC8AAC6, 0XBFA7EDE4} } }, +/**/ {{{0XD1EFDDB3, 0X3FEB8000} }, +/**/ {{0X0ACCB660, 0X3FE6B799} }, +/**/ {{0X9983AAB2, 0X3FE26809} }, +/**/ {{0X76047E08, 0XBFD23270} }, +/**/ {{0XF132139B, 0X3FB3BD90} }, +/**/ {{0X58DEB3E1, 0X3F993010} }, +/**/ {{0X2D194CE9, 0XBFA79610} } }, +/**/ {{{0X42CC4047, 0X3FEB9FFE} }, +/**/ {{0X86445E60, 0X3FE6C9F6} }, +/**/ {{0X069F871F, 0X3FE255E0} }, +/**/ {{0X25461639, 0XBFD2239A} }, +/**/ {{0XA926C127, 0X3FB3D649} }, +/**/ {{0XC5A21F70, 0X3F9845FB} }, +/**/ {{0X68E20BE6, 0XBFA73EAC} } }, +/**/ {{{0X951AEAAD, 0X3FEBC001} }, +/**/ {{0X3C4E45A0, 0X3FE6DC45} }, +/**/ {{0XFF6573B0, 0X3FE243C1} }, +/**/ {{0XE38FA7E7, 0XBFD214AE} }, +/**/ {{0X5EA1330F, 0X3FB3EE1E} }, +/**/ {{0X2BCCE6DF, 0X3F975F24} }, +/**/ {{0X6F3902C5, 0XBFA6E7BE} } }, +/**/ {{{0X6616FE11, 0X3FEBDFFE} }, +/**/ {{0X27106FE0, 0X3FE6EE7E} }, +/**/ {{0X97B587F0, 0X3FE231B6} }, +/**/ {{0X240FEF32, 0XBFD205B5} }, +/**/ {{0X44EB818C, 0X3FB40509} }, +/**/ {{0X108160F9, 0X3F967BDE} }, +/**/ {{0X271D18AD, 0XBFA6914B} } }, +/**/ {{{0X54511C72, 0X3FEBFFFF} }, +/**/ {{0X643BBB40, 0X3FE700A7} }, +/**/ {{0XE1823C8B, 0X3FE21FB7} }, +/**/ {{0X9A854F7A, 0XBFD1F6A8} }, +/**/ {{0X71F04837, 0X3FB41B15} }, +/**/ {{0XBBD10F7C, 0X3F959BD8} }, +/**/ {{0X41F03711, 0XBFA63B57} } }, +/**/ {{{0XC537593E, 0X3FEC2000} }, +/**/ {{0XF36D6400, 0X3FE712BE} }, +/**/ {{0XF754B2D5, 0X3FE20DC7} }, +/**/ {{0X9D24DBED, 0XBFD1E78B} }, +/**/ {{0X94F485E0, 0X3FB43043} }, +/**/ {{0X122A6884, 0X3F94BF29} }, +/**/ {{0X3D2AA4E9, 0XBFA5E5E7} } }, +/**/ {{{0XDDD35719, 0X3FEC4000} }, +/**/ {{0XD7FA3000, 0X3FE724C3} }, +/**/ {{0XF2A8B1BF, 0X3FE1FBE7} }, +/**/ {{0XB25DDDF6, 0XBFD1D85F} }, +/**/ {{0XD2E3B20F, 0X3FB44495} }, +/**/ {{0X7FCC1B30, 0X3F93E5D6} }, +/**/ {{0X62D0D00F, 0XBFA590FF} } }, +/**/ {{{0X402375B6, 0X3FEC6000} }, +/**/ {{0X7DFF3720, 0X3FE736B6} }, +/**/ {{0X86C92387, 0X3FE1EA17} }, +/**/ {{0X31DDFC58, 0XBFD1C925} }, +/**/ {{0XF8B6CBC2, 0X3FB4580F} }, +/**/ {{0X00CE998E, 0X3F930FD7} }, +/**/ {{0XCB299E5F, 0XBFA53CA3} } }, +/**/ {{{0X19904FE4, 0X3FEC7FFF} }, +/**/ {{0X0F395860, 0X3FE74897} }, +/**/ {{0XA825BA33, 0X3FE1D856} }, +/**/ {{0XA75E0FC5, 0XBFD1B9DC} }, +/**/ {{0X79F8FD7D, 0X3FB46AB5} }, +/**/ {{0XA5A90AFE, 0X3F923D23} }, +/**/ {{0X5D2F574B, 0XBFA4E8D8} } }, +/**/ {{{0XF9E2409D, 0X3FEC9FFE} }, +/**/ {{0X79E7F1C0, 0X3FE75A66} }, +/**/ {{0X8740D2E9, 0X3FE1C6A4} }, +/**/ {{0XF198392C, 0XBFD1AA85} }, +/**/ {{0X808C583A, 0X3FB47C8A} }, +/**/ {{0X857F2526, 0X3F916DAC} }, +/**/ {{0XD0477576, 0XBFA495A0} } }, +/**/ {{{0XE038EF72, 0X3FECC001} }, +/**/ {{0XE6815140, 0X3FE76C25} }, +/**/ {{0X19BDADF8, 0X3FE1B500} }, +/**/ {{0XB4A469AE, 0XBFD19B20} }, +/**/ {{0X42387EA2, 0X3FB48D93} }, +/**/ {{0X7305BAF5, 0X3F90A15F} }, +/**/ {{0XACAE4E17, 0XBFA44300} } }, +/**/ {{{0XEB72037F, 0X3FECDFFE} }, +/**/ {{0X7A7A4AA0, 0X3FE77DD0} }, +/**/ {{0X4F1F6702, 0X3FE1A36E} }, +/**/ {{0XD0992CF8, 0XBFD18BB1} }, +/**/ {{0X5AA4990D, 0X3FB49DCE} }, +/**/ {{0X63759665, 0X3F8FB0DD} }, +/**/ {{0X4D2F0C0F, 0XBFA3F0FB} } }, +/**/ {{{0XEA4839ED, 0X3FECFFFF} }, +/**/ {{0XB17088C0, 0X3FE78F6B} }, +/**/ {{0XCF32122F, 0X3FE191E9} }, +/**/ {{0X220400AC, 0XBFD17C35} }, +/**/ {{0X0A159641, 0X3FB4AD44} }, +/**/ {{0X80894CA9, 0X3F8E252C} }, +/**/ {{0XDF89C265, 0XBFA39F93} } }, +/**/ {{{0XEC3EC8B2, 0X3FED1FFD} }, +/**/ {{0XC8C6C880, 0X3FE7A0F3} }, +/**/ {{0X729F01D6, 0X3FE18076} }, +/**/ {{0X98515540, 0XBFD16CAE} }, +/**/ {{0X1B0933FF, 0X3FB4BBF4} }, +/**/ {{0XE09A60CD, 0X3F8C9FF5} }, +/**/ {{0X662A5704, 0XBFA34ECD} } }, +/**/ {{{0X7084EDD4, 0X3FED3FFF} }, +/**/ {{0X5F02F220, 0X3FE7B26C} }, +/**/ {{0XB9973206, 0X3FE16F10} }, +/**/ {{0X9E1E0A54, 0XBFD15D1B} }, +/**/ {{0XAC2C9A30, 0X3FB4C9E4} }, +/**/ {{0XEFCE76CC, 0X3F8B20DD} }, +/**/ {{0XB888BC37, 0XBFA2FEAA} } }, +/**/ {{{0X8D728E7C, 0X3FED5FFE} }, +/**/ {{0X488D7E80, 0X3FE7C3D2} }, +/**/ {{0XE622A5A7, 0X3FE15DBB} }, +/**/ {{0XA305CEB2, 0XBFD14D7F} }, +/**/ {{0X417BF1C7, 0X3FB4D716} }, +/**/ {{0XE19FE239, 0X3F89A81E} }, +/**/ {{0X84DDAD07, 0XBFA2AF2E} } }, +/**/ {{{0X70AA3B03, 0X3FED7FFF} }, +/**/ {{0XDB239580, 0X3FE7D527} }, +/**/ {{0XBE4FEA01, 0X3FE14C75} }, +/**/ {{0X2AD706AA, 0XBFD13DD9} }, +/**/ {{0XB49D32AA, 0X3FB4E38D} }, +/**/ {{0X37DF2B6D, 0X3F88357A} }, +/**/ {{0X507CD77B, 0XBFA2605B} } }, +/**/ {{{0X1434FBA3, 0X3FED9FFF} }, +/**/ {{0X82C8A720, 0X3FE7E66B} }, +/**/ {{0XED9B7FED, 0X3FE13B3F} }, +/**/ {{0X3AC9D646, 0XBFD12E2A} }, +/**/ {{0XE7B01CF5, 0X3FB4EF4C} }, +/**/ {{0XD25FD52D, 0X3F86C905} }, +/**/ {{0X798666EF, 0XBFA21233} } }, +/**/ {{{0XA8C8DE8C, 0X3FEDBFFE} }, +/**/ {{0XF4A0A520, 0X3FE7F79D} }, +/**/ {{0XD7FC2119, 0X3FE12A19} }, +/**/ {{0XC6BE19DF, 0XBFD11E72} }, +/**/ {{0X634E1B91, 0X3FB4FA57} }, +/**/ {{0X47F96DF5, 0X3F8562A6} }, +/**/ {{0X373AF599, 0XBFA1C4B9} } }, +/**/ {{{0X26573DF5, 0X3FEDE000} }, +/**/ {{0X4DBCB960, 0X3FE808C0} }, +/**/ {{0X7903E4B9, 0X3FE11902} }, +/**/ {{0X5CDFED06, 0XBFD10EB2} }, +/**/ {{0XCCA681FA, 0X3FB504B0} }, +/**/ {{0X6F3CDE09, 0X3F840238} }, +/**/ {{0X9BA8FA6A, 0XBFA177EE} } }, +/**/ {{{0X35009B66, 0X3FEDFFFE} }, +/**/ {{0XC2CB5340, 0X3FE819CF} }, +/**/ {{0XB1C942B5, 0X3FE107FC} }, +/**/ {{0X230D7D92, 0XBFD0FEEC} }, +/**/ {{0X75C5B4F1, 0X3FB50E5A} }, +/**/ {{0XE3C139D8, 0X3F82A7E8} }, +/**/ {{0X93FA642B, 0XBFA12BD5} } }, +/**/ {{{0X492D4C68, 0X3FEE2000} }, +/**/ {{0X5CCB8680, 0X3FE82AD0} }, +/**/ {{0X928E55DF, 0X3FE0F704} }, +/**/ {{0XEE0B0721, 0XBFD0EF1C} }, +/**/ {{0X937BFB74, 0X3FB51759} }, +/**/ {{0X2BC9FDDB, 0X3F815359} }, +/**/ {{0XEA1D1824, 0XBFA0E06F} } }, +/**/ {{{0X9412BB65, 0X3FEE4000} }, +/**/ {{0X14001A60, 0X3FE83BBF} }, +/**/ {{0X37F485DA, 0X3FE0E61D} }, +/**/ {{0X1B2BD37D, 0XBFD0DF48} }, +/**/ {{0X64024D14, 0X3FB51FAF} }, +/**/ {{0X9B849698, 0X3F8004B9} }, +/**/ {{0X450A2434, 0XBFA095BF} } }, +/**/ {{{0X4758EF2F, 0X3FEE5FFF} }, +/**/ {{0X1531C180, 0X3FE84C9C} }, +/**/ {{0X8B7FECE7, 0X3FE0D546} }, +/**/ {{0X105BFE1E, 0XBFD0CF6E} }, +/**/ {{0XF9C5E03A, 0X3FB5275E} }, +/**/ {{0X17AA1137, 0X3F7D77F2} }, +/**/ {{0X2A6891E1, 0XBFA04BC5} } }, +/**/ {{{0X380F819F, 0X3FEE8000} }, +/**/ {{0X74CCC060, 0X3FE85D69} }, +/**/ {{0X8F1DA5B5, 0X3FE0C47E} }, +/**/ {{0X62AD700F, 0XBFD0BF8D} }, +/**/ {{0X1F3FBC2B, 0X3FB52E6C} }, +/**/ {{0XEE24AD7D, 0X3F7AF1C3} }, +/**/ {{0XFECE26C9, 0XBFA00282} } }, +/**/ {{{0XA6D8CB7B, 0X3FEEA000} }, +/**/ {{0XD00E3A60, 0X3FE86E25} }, +/**/ {{0XBA314D62, 0X3FE0B3C6} }, +/**/ {{0XE7CB2D84, 0XBFD0AFA7} }, +/**/ {{0X08E9071F, 0X3FB534D9} }, +/**/ {{0X4CE5E5C9, 0X3F787704} }, +/**/ {{0X0EB7C9D5, 0XBF9F73F4} } }, +/**/ {{{0X5A13BA60, 0X3FEEC000} }, +/**/ {{0X19B163E0, 0X3FE87ED1} }, +/**/ {{0X2EBB7AD7, 0X3FE0A31F} }, +/**/ {{0X33A3FCE1, 0XBFD09FBE} }, +/**/ {{0X89D9AF5D, 0X3FB53AA8} }, +/**/ {{0XF7F7040B, 0X3F760799} }, +/**/ {{0XD3F0B3FB, 0XBF9EE456} } }, +/**/ {{{0X58F8DD18, 0X3FEEDFFF} }, +/**/ {{0X6681CA80, 0X3FE88F6B} }, +/**/ {{0XEC4360B3, 0X3FE09287} }, +/**/ {{0XB7CE07E5, 0XBFD08FD0} }, +/**/ {{0X7BDEDD3F, 0X3FB53FDD} }, +/**/ {{0X70C52E66, 0X3F73A366} }, +/**/ {{0X5DCA7315, 0XBF9E5630} } }, +/**/ {{{0XBE033400, 0X3FEEFFFF} }, +/**/ {{0XDD4D7960, 0X3FE89FF5} }, +/**/ {{0XDFFE15BD, 0X3FE081FF} }, +/**/ {{0XDAE56C0F, 0XBFD07FDE} }, +/**/ {{0XF84D6F5D, 0X3FB5447A} }, +/**/ {{0X7982941E, 0X3F714A24} }, +/**/ {{0X81E68835, 0XBF9DC982} } }, +/**/ {{{0XE6B5125D, 0X3FEF2001} }, +/**/ {{0XBBE88160, 0X3FE8B070} }, +/**/ {{0XDF7122E2, 0X3FE07186} }, +/**/ {{0XDE905325, 0XBFD06FE8} }, +/**/ {{0XB5DEEC7A, 0X3FB54883} }, +/**/ {{0XB4A186D5, 0X3F6DF762} }, +/**/ {{0XDE20F495, 0XBF9D3E4E} } }, +/**/ {{{0XF770E0DB, 0X3FEF3FFD} }, +/**/ {{0X09E96380, 0X3FE8C0D8} }, +/**/ {{0XF5A576A9, 0X3FE06120} }, +/**/ {{0X1D2912FF, 0XBFD05FF3} }, +/**/ {{0X8CD1001F, 0X3FB54BF9} }, +/**/ {{0X6E90DC16, 0X3F6970FC} }, +/**/ {{0XD8EB587E, 0XBF9CB496} } }, +/**/ {{{0X4E16DA33, 0X3FEF5FFE} }, +/**/ {{0X29BCCDC0, 0X3FE8D131} }, +/**/ {{0XD33BA4E9, 0X3FE050C8} }, +/**/ {{0XD74C83D2, 0XBFD04FF8} }, +/**/ {{0X592BB252, 0X3FB54EE0} }, +/**/ {{0X7193EEB5, 0X3F64FF61} }, +/**/ {{0XA459AC86, 0XBF9C2C5B} } }, +/**/ {{{0X4576FF2E, 0X3FEF8000} }, +/**/ {{0XCCE443A0, 0X3FE8E17A} }, +/**/ {{0XD8A97B6C, 0X3FE0407F} }, +/**/ {{0XC91B3E55, 0XBFD03FFB} }, +/**/ {{0X5F3357F7, 0X3FB5513A} }, +/**/ {{0X14C92B53, 0X3F60A2BA} }, +/**/ {{0X3E70DF71, 0XBF9BA59E} } }, +/**/ {{{0X39B6A330, 0X3FEF9FFF} }, +/**/ {{0XA7F515A0, 0X3FE8F1B2} }, +/**/ {{0X63064158, 0X3FE03048} }, +/**/ {{0XACBAADA8, 0XBFD02FFE} }, +/**/ {{0XF27448C0, 0X3FB55309} }, +/**/ {{0X4850006B, 0X3F58B6D6} }, +/**/ {{0X742323DF, 0XBF9B205F} } }, +/**/ {{{0XAA76C0B9, 0X3FEFC001} }, +/**/ {{0X15D66D80, 0X3FE901DC} }, +/**/ {{0X28D9B4AA, 0X3FE0201F} }, +/**/ {{0XA98D4C38, 0XBFD01FFE} }, +/**/ {{0X089780F8, 0X3FB55452} }, +/**/ {{0X7F35C5BB, 0X3F5050B5} }, +/**/ {{0XE19247AF, 0XBF9A9C9F} } }, +/**/ {{{0X39A592CA, 0X3FEFDFFE} }, +/**/ {{0X6D88A780, 0X3FE911F2} }, +/**/ {{0XE40C6538, 0X3FE01008} }, +/**/ {{0XD31688DE, 0XBFD01000} }, +/**/ {{0XE32F1816, 0X3FB55514} }, +/**/ {{0X4E1628D2, 0X3F402A15} }, +/**/ {{0XF4FAF5A0, 0XBF9A1A5F} } }, +/**/ {{{0X8E92D1B0, 0X3FEFF801} }, +/**/ {{0X9BB4BF00, 0X3FE91DFB} }, +/**/ {{0XB884C5A9, 0X3FE003FF} }, +/**/ {{0X3876A954, 0XBFD003FF} }, +/**/ {{0X5539DDFB, 0X3FB55551} }, +/**/ {{0X7B95E6C2, 0X3F2007E7} }, +/**/ {{0X18A3BA58, 0XBF99B9A7} } }, + }; + + static const number + hij[241][16] = { /* x0,hij for (1/16,1) */ +/**/ {{{0x00000000, 0x3fb04000} }, +/**/ {{0x1c06693d, 0x3fb03a6d} }, +/**/ {{0xd4e7f128, 0xbc428a02} }, +/**/ {{0xe92592ae, 0x3fefdf1f} }, +/**/ {{0xb5490162, 0x3c88bfc0} }, +/**/ {{0x8f7e4151, 0xbfb01ead} }, +/**/ {{0x0b64d205, 0xbc5395e8} }, +/**/ {{0x433dd49b, 0xbfd4d29f} }, +/**/ {{0x4aa42633, 0xbc75b19d} }, +/**/ {{0xce35961d, 0x3fafda41} }, +/**/ {{0x425d7696, 0x3c4e6a5f} }, +/**/ {{0x6c1bb5e2, 0x3fc814dd} }, +/**/ {{0x2b33739f, 0xbfaf4cb7} }, +/**/ {{0xc267d8ec, 0xbfc048b2} }, +/**/ {{0xe8ababc6, 0x3fae9649} }, +/**/ {{0xfe802692, 0x3fb78293} } }, +/**/ {{{0x00000000, 0x3fb10000} }, +/**/ {{0xa71d52a7, 0x3fb0f99e} }, +/**/ {{0xeec3624f, 0xbc22069f} }, +/**/ {{0x9a49d2a9, 0x3fefdc08} }, +/**/ {{0x68b2ce25, 0x3c7780f7} }, +/**/ {{0x9da73e1d, 0xbfb0d9de} }, +/**/ {{0xa1a487bf, 0x3c4ebf46} }, +/**/ {{0xd13ea108, 0xbfd4c669} }, +/**/ {{0xebb4528c, 0x3c7354bc} }, +/**/ {{0x789374c1, 0x3fb0a137} }, +/**/ {{0xc3f2c5c2, 0xbc56c223} }, +/**/ {{0x79c60cda, 0x3fc7f0e7} }, +/**/ {{0xcdcc7b81, 0xbfb05062} }, +/**/ {{0xc5266783, 0xbfc019e4} }, +/**/ {{0xf2540289, 0x3fafd0b2} }, +/**/ {{0xf6d3cd8a, 0x3fb71107} } }, +/**/ {{{0x00000000, 0x3fb20000} }, +/**/ {{0xbf082d59, 0x3fb1f86d} }, +/**/ {{0x7732ef81, 0xbc4095dc} }, +/**/ {{0x01722b81, 0x3fefd7b3} }, +/**/ {{0x8a212e02, 0xbc5e618c} }, +/**/ {{0xee4e9cfa, 0xbfb1d2c5} }, +/**/ {{0x29abece0, 0x3c426273} }, +/**/ {{0x37eb7f46, 0xbfd4b551} }, +/**/ {{0x01d8bf12, 0x3c73b360} }, +/**/ {{0x6adb6a7c, 0x3fb18fa7} }, +/**/ {{0x398999ad, 0xbc5c00d8} }, +/**/ {{0xf4a7cff3, 0x3fc7bea5} }, +/**/ {{0x61f84829, 0xbfb13008} }, +/**/ {{0xa8e135a1, 0xbfbfb14f} }, +/**/ {{0x4324f177, 0x3fb0b532} }, +/**/ {{0x3498dd9d, 0x3fb6734a} } }, +/**/ {{{0x00000000, 0x3fb30000} }, +/**/ {{0x318a4a9a, 0x3fb2f719} }, +/**/ {{0x79b9801f, 0x3c03fd17} }, +/**/ {{0x48e238fe, 0x3fefd31f} }, +/**/ {{0xd8c45327, 0xbc876a7a} }, +/**/ {{0x852096e2, 0xbfb2cada} }, +/**/ {{0x11efd787, 0x3c460860} }, +/**/ {{0x2e476a39, 0xbfd4a34b} }, +/**/ {{0xeb11ee51, 0x3c7254f2} }, +/**/ {{0xc54ae225, 0x3fb27c13} }, +/**/ {{0x4ae66f0c, 0x3c513096} }, +/**/ {{0xef0d59d0, 0x3fc789ca} }, +/**/ {{0x6d9aaa8c, 0xbfb20c06} }, +/**/ {{0x846ba912, 0xbfbf2885} }, +/**/ {{0xc697ef5e, 0x3fb17c5f} }, +/**/ {{0xcad31e6e, 0x3fb5ce93} } }, +/**/ {{{0x00000000, 0x3fb40000} }, +/**/ {{0x0e7c559d, 0x3fb3f59f} }, +/**/ {{0x285df847, 0x3c5ac4ce} }, +/**/ {{0xa6ab93e9, 0x3fefce4d} }, +/**/ {{0x18a97736, 0xbc6be46b} }, +/**/ {{0x4d22b635, 0xbfb3c211} }, +/**/ {{0x6950679f, 0x3c42033c} }, +/**/ {{0xc4d74033, 0xbfd49059} }, +/**/ {{0xd7e376aa, 0x3c57dd7c} }, +/**/ {{0xc0896a7c, 0x3fb36662} }, +/**/ {{0xd79232cf, 0xbc36cf6a} }, +/**/ {{0xa13a97a2, 0x3fc75261} }, +/**/ {{0x5fdd1509, 0xbfb2e431} }, +/**/ {{0x6e52db32, 0xbfbe9999} }, +/**/ {{0xb0a71e9f, 0x3fb23da4} }, +/**/ {{0xe3bc8178, 0x3fb52335} } }, +/**/ {{{0x00000000, 0x3fb50000} }, +/**/ {{0x677292fb, 0x3fb4f3fd} }, +/**/ {{0x6264979e, 0x3c4008d3} }, +/**/ {{0x53a1ee0d, 0x3fefc93e} }, +/**/ {{0x20fd2bdf, 0xbc64421a} }, +/**/ {{0x4aba88e3, 0xbfb4b85f} }, +/**/ {{0x3c9d1e89, 0x3c54f184} }, +/**/ {{0x25ae4668, 0xbfd47c7f} }, +/**/ {{0x816630d1, 0xbc7d7581} }, +/**/ {{0x07f85056, 0x3fb44e7b} }, +/**/ {{0x910bdf4f, 0x3c56d63c} }, +/**/ {{0xc439029c, 0x3fc71875} }, +/**/ {{0xf2bcfa10, 0xbfb3b85e} }, +/**/ {{0x9707b205, 0xbfbe04bb} }, +/**/ {{0x95e3e0cc, 0x3fb2f8c6} }, +/**/ {{0x8093431b, 0x3fb47184} } }, +/**/ {{{0x00000000, 0x3fb60000} }, +/**/ {{0x4fd2d7b2, 0x3fb5f232} }, +/**/ {{0x4401318e, 0x3c58a8da} }, +/**/ {{0x8b549418, 0x3fefc3f1} }, +/**/ {{0x836f8130, 0x3c34d896} }, +/**/ {{0x9cdd92e7, 0xbfb5adb9} }, +/**/ {{0xeb397cc3, 0x3c4d4161} }, +/**/ {{0x93f8f1dc, 0xbfd467bd} }, +/**/ {{0xffc760ad, 0xbc609d7b} }, +/**/ {{0xbea6b2fe, 0x3fb53443} }, +/**/ {{0x4b24f5db, 0x3c5eb03c} }, +/**/ {{0x8de3d005, 0x3fc6dc13} }, +/**/ {{0x37d2d99d, 0xbfb48866} }, +/**/ {{0xf6663fcb, 0xbfbd6a1d} }, +/**/ {{0x0adff464, 0x3fb3ad8e} }, +/**/ {{0x4159c223, 0x3fb3b9d6} } }, +/**/ {{{0x00000000, 0x3fb70000} }, +/**/ {{0xdcea4b0d, 0x3fb6f03b} }, +/**/ {{0x512fa17d, 0xbc33f00e} }, +/**/ {{0x8c07a436, 0x3fefbe67} }, +/**/ {{0x46250d6f, 0xbc84baaa} }, +/**/ {{0x7e3ba4c7, 0xbfb6a215} }, +/**/ {{0x54503f8d, 0xbc3504e7} }, +/**/ {{0x6b82d03a, 0xbfd45217} }, +/**/ {{0xbebdd1db, 0x3c7d1f0d} }, +/**/ {{0x841d5604, 0x3fb617a4} }, +/**/ {{0x6681c436, 0xbc47168b} }, +/**/ {{0xaccec6ce, 0x3fc69d47} }, +/**/ {{0xa4715800, 0xbfb5541f} }, +/**/ {{0x335a1c1b, 0xbfbcc9f4} }, +/**/ {{0xbac0061f, 0x3fb45bc6} }, +/**/ {{0x2b3853b6, 0x3fb2fc84} } }, +/**/ {{{0x00000000, 0x3fb80000} }, +/**/ {{0x2602f10f, 0x3fb7ee18} }, +/**/ {{0x4c0c3d98, 0xbc5cfb65} }, +/**/ {{0x96acfacc, 0x3fefb8a0} }, +/**/ {{0x18495af3, 0xbc82962e} }, +/**/ {{0x46635c89, 0xbfb79568} }, +/**/ {{0xa6bfd498, 0x3c5ac468} }, +/**/ {{0x2037b997, 0xbfd43b8f} }, +/**/ {{0xe2f12373, 0xbc72ad53} }, +/**/ {{0x7900c4ee, 0x3fb6f885} }, +/**/ {{0x0aef1f9d, 0x3c53145d} }, +/**/ {{0x4409ba0e, 0x3fc65c1f} }, +/**/ {{0x1d176e0c, 0xbfb61b65} }, +/**/ {{0x8ad65152, 0xbfbc2473} }, +/**/ {{0x7bc246c1, 0x3fb5033f} }, +/**/ {{0x6db30b46, 0x3fb239e9} } }, +/**/ {{{0x00000000, 0x3fb90000} }, +/**/ {{0x4478fb28, 0x3fb8ebc5} }, +/**/ {{0x0cad24cc, 0x3c473288} }, +/**/ {{0xeedcd6d7, 0x3fefb29c} }, +/**/ {{0x23ea50f0, 0x3c8efa9e} }, +/**/ {{0x6ae09982, 0xbfb887a7} }, +/**/ {{0x53801511, 0x3c5b2275} }, +/**/ {{0x3da0757c, 0xbfd42427} }, +/**/ {{0x311c7ac8, 0xbc7199e5} }, +/**/ {{0x4388717b, 0x3fb7d6cf} }, +/**/ {{0x3dd070b4, 0xbc5c4eb2} }, +/**/ {{0xe6c2b5f3, 0x3fc618a7} }, +/**/ {{0x00313569, 0xbfb6de12} }, +/**/ {{0xb6316619, 0xbfbb79d2} }, +/**/ {{0x61af5c21, 0x3fb5a3ca} }, +/**/ {{0x26e60289, 0x3fb17263} } }, +/**/ {{{0x00000000, 0x3fba0000} }, +/**/ {{0x53cfdcf1, 0x3fb9e941} }, +/**/ {{0x1d69c47e, 0x3c5a332e} }, +/**/ {{0xdace3776, 0x3fefac5c} }, +/**/ {{0x1ad91ab5, 0xbc8c9a78} }, +/**/ {{0x8054ad75, 0xbfb978c8} }, +/**/ {{0x8ed66c17, 0xbc5e35b8} }, +/**/ {{0x665afed1, 0xbfd40be2} }, +/**/ {{0x08ef10fb, 0x3c62eeef} }, +/**/ {{0x13c989d2, 0x3fb8b26b} }, +/**/ {{0xbfeab3ba, 0x3c329f11} }, +/**/ {{0x93c8f97c, 0x3fc5d2ef} }, +/**/ {{0x30234881, 0xbfb79c03} }, +/**/ {{0xd0f650c8, 0xbfbaca49} }, +/**/ {{0xce2dcccc, 0x3fb63d3c} }, +/**/ {{0x26fb0af2, 0x3fb0a650} } }, +/**/ {{{0x00000000, 0x3fbb0000} }, +/**/ {{0x71c722b8, 0x3fbae68a} }, +/**/ {{0x6910b9db, 0x3c4c014e} }, +/**/ {{0xa34ef42b, 0x3fefa5e0} }, +/**/ {{0xeb56d5b9, 0xbc836583} }, +/**/ {{0x3b881779, 0xbfba68c1} }, +/**/ {{0x13a09314, 0xbc473a0d} }, +/**/ {{0x538e939c, 0xbfd3f2c3} }, +/**/ {{0xee53e648, 0xbc68ed49} }, +/**/ {{0xa7d45973, 0x3fb98b42} }, +/**/ {{0x461ca7c4, 0xbc523943} }, +/**/ {{0xb0f2e2bb, 0x3fc58b04} }, +/**/ {{0x1c9d23dc, 0xbfb85517} }, +/**/ {{0x3e3b5a66, 0xbfba1612} }, +/**/ {{0x7ef1d0b9, 0x3fb6cf6f} }, +/**/ {{0x6617b315, 0x3fafac21} } }, +/**/ {{{0x00000000, 0x3fbc0000} }, +/**/ {{0xbe6f07c3, 0x3fbbe39e} }, +/**/ {{0x29a05987, 0x3c5f7b8f} }, +/**/ {{0x93bb9192, 0x3fef9f28} }, +/**/ {{0x7cd1bdab, 0x3c78260b} }, +/**/ {{0x72759741, 0xbfbb5787} }, +/**/ {{0xa6767247, 0x3c52f93f} }, +/**/ {{0xd45bbe91, 0xbfd3d8cc} }, +/**/ {{0x2edc0762, 0x3c664839} }, +/**/ {{0x4fa31d26, 0x3fba6140} }, +/**/ {{0x97891510, 0x3c400647} }, +/**/ {{0x0668fd66, 0x3fc540f6} }, +/**/ {{0xcb2f6e8f, 0xbfb9092d} }, +/**/ {{0x8d902073, 0xbfb95d66} }, +/**/ {{0x99c53d16, 0x3fb75a3e} }, +/**/ {{0x8f475e61, 0x3fae040c} } }, +/**/ {{{0x00000000, 0x3fbd0000} }, +/**/ {{0x5c3cca32, 0x3fbce07c} }, +/**/ {{0x425918a7, 0x3c4138e6} }, +/**/ {{0xf9f6d421, 0x3fef9834} }, +/**/ {{0x8c22a239, 0x3c6f3089} }, +/**/ {{0x1d4e69a5, 0xbfbc4511} }, +/**/ {{0xd2083ce8, 0x3c254c0f} }, +/**/ {{0xcd488978, 0xbfd3be01} }, +/**/ {{0x6362ec0f, 0x3c5612db} }, +/**/ {{0xf0d94873, 0x3fbb344e} }, +/**/ {{0xfdf7db72, 0xbc182beb} }, +/**/ {{0xb9d86c04, 0x3fc4f4d2} }, +/**/ {{0xdf238807, 0xbfb9b828} }, +/**/ {{0x5f93ffd6, 0xbfb8a082} }, +/**/ {{0xb6650b0c, 0x3fb7dd89} }, +/**/ {{0xb62676ef, 0x3fac5526} } }, +/**/ {{{0x00000000, 0x3fbe0000} }, +/**/ {{0x701eba6e, 0x3fbddd21} }, +/**/ {{0xcd76fe58, 0x3c594eff} }, +/**/ {{0x266112ba, 0x3fef9106} }, +/**/ {{0x6b7e18b1, 0x3c74c302} }, +/**/ {{0x5777816c, 0xbfbd3154} }, +/**/ {{0x1f9dbddd, 0x3c5dc7e4} }, +/**/ {{0x37a90881, 0xbfd3a265} }, +/**/ {{0xeb7ba840, 0xbc75bd61} }, +/**/ {{0x0a52514b, 0x3fbc045a} }, +/**/ {{0xcff49a99, 0xbc35ca88} }, +/**/ {{0x498eeb56, 0x3fc4a6aa} }, +/**/ {{0xa09232cf, 0xbfba61eb} }, +/**/ {{0x4a464027, 0xbfb7dfa2} }, +/**/ {{0xe633c053, 0x3fb85933} }, +/**/ {{0x3f920107, 0x3faaa036} } }, +/**/ {{{0x00000000, 0x3fbf0000} }, +/**/ {{0x2190043b, 0x3fbed98c} }, +/**/ {{0x592c7b13, 0xbc23a598} }, +/**/ {{0x6bcf4ad8, 0x3fef899c} }, +/**/ {{0x912c09b0, 0x3c55fd73} }, +/**/ {{0x607f91a0, 0xbfbe1c47} }, +/**/ {{0x5b5db022, 0x3c576677} }, +/**/ {{0x21046f5f, 0xbfd385fa} }, +/**/ {{0x4487f4b8, 0x3c7f01c3} }, +/**/ {{0xb77f2d51, 0x3fbcd14d} }, +/**/ {{0x30a2ccfe, 0x3c57a86d} }, +/**/ {{0x8782b530, 0x3fc4568c} }, +/**/ {{0x02b7ad2d, 0xbfbb065b} }, +/**/ {{0xbd215555, 0xbfb71b03} }, +/**/ {{0xb9c1c1de, 0x3fb8cd23} }, +/**/ {{0x8dbfa69b, 0x3fa8e602} } }, +/**/ {{{0x00000000, 0x3fc00000} }, +/**/ {{0x9aac2f6e, 0x3fbfd5ba} }, +/**/ {{0x86760c17, 0xbc4cd376} }, +/**/ {{0x1f81f820, 0x3fef81f8} }, +/**/ {{0x1f81f820, 0xbc8f81f8} }, +/**/ {{0x9d0dc11b, 0xbfbf05e0} }, +/**/ {{0x1d821725, 0xbc35a199} }, +/**/ {{0xaa76e1d7, 0xbfd368c3} }, +/**/ {{0xc796f8cd, 0xbc672d4c} }, +/**/ {{0xb391c2e3, 0x3fbd9b16} }, +/**/ {{0x8086c51d, 0x3c58051b} }, +/**/ {{0x94488c86, 0x3fc40489} }, +/**/ {{0xa98401c8, 0xbfbba55d} }, +/**/ {{0xe5127e64, 0xbfb652e4} }, +/**/ {{0x442e53ae, 0x3fb93943} }, +/**/ {{0x86286f75, 0x3fa72753} } }, +/**/ {{{0x00000000, 0x3fc08000} }, +/**/ {{0x84212b3e, 0x3fc068d5} }, +/**/ {{0x83019bfd, 0xbc69e2d2} }, +/**/ {{0x991bb133, 0x3fef7a19} }, +/**/ {{0x66627723, 0x3c7a956a} }, +/**/ {{0x97c8e137, 0xbfbfee16} }, +/**/ {{0x66dbe7af, 0x3c4d9399} }, +/**/ {{0x0810323a, 0xbfd34ac5} }, +/**/ {{0x6bc6c512, 0x3c6a1a57} }, +/**/ {{0x5c75a6f9, 0x3fbe61a2} }, +/**/ {{0xd75c8f85, 0xbc492b99} }, +/**/ {{0xd9fa3f20, 0x3fc3b0b1} }, +/**/ {{0xee66d309, 0xbfbc3edb} }, +/**/ {{0x905eeb33, 0xbfb58784} }, +/**/ {{0x1c65bb14, 0x3fb99d80} }, +/**/ {{0x18a09884, 0x3fa564f1} } }, +/**/ {{{0x00000000, 0x3fc10000} }, +/**/ {{0xccf40882, 0x3fc0e6ad} }, +/**/ {{0x1bb98d0d, 0xbc6d71a3} }, +/**/ {{0x32978bad, 0x3fef7201} }, +/**/ {{0x599381e9, 0x3c816476} }, +/**/ {{0x011b81fd, 0xbfc06a70} }, +/**/ {{0x9ba697ca, 0xbc422f5d} }, +/**/ {{0x802fc0a5, 0xbfd32c01} }, +/**/ {{0x08a20868, 0x3c7d8e47} }, +/**/ {{0xb59597fe, 0x3fbf24de} }, +/**/ {{0x410d31eb, 0xbc43288f} }, +/**/ {{0x070feb24, 0x3fc35b16} }, +/**/ {{0xe4565b78, 0xbfbcd2bf} }, +/**/ {{0x128768c6, 0xbfb4b922} }, +/**/ {{0x5c42a097, 0x3fb9f9cb} }, +/**/ {{0xc7f97f2e, 0x3fa39fa2} } }, +/**/ {{{0x00000000, 0x3fc18000} }, +/**/ {{0x41060850, 0x3fc16465} }, +/**/ {{0x8ae7ea92, 0x3c66bcee} }, +/**/ {{0x483f492b, 0x3fef69af} }, +/**/ {{0x57db963e, 0xbc6e3280} }, +/**/ {{0xdacaa844, 0xbfc0dd19} }, +/**/ {{0xad7fc21e, 0xbc6133c7} }, +/**/ {{0x6addaea8, 0xbfd30c7c} }, +/**/ {{0x89161c76, 0xbc71443d} }, +/**/ {{0x6a6d3cd2, 0x3fbfe4ba} }, +/**/ {{0x423ee67a, 0x3c50d4b8} }, +/**/ {{0x092e569a, 0x3fc303c7} }, +/**/ {{0x5b11d3b6, 0xbfbd60f5} }, +/**/ {{0x283b5c55, 0xbfb3e7fd} }, +/**/ {{0x9d9a6ab7, 0x3fba4e19} }, +/**/ {{0x3487cc29, 0x3fa1d82f} } }, +/**/ {{{0x00000000, 0x3fc20000} }, +/**/ {{0xfb043727, 0x3fc1e1fa} }, +/**/ {{0x14dacf8c, 0xbc4b4859} }, +/**/ {{0x38a14f5e, 0x3fef6124} }, +/**/ {{0x001f6124, 0x3c798e9e} }, +/**/ {{0x59d3fb7c, 0xbfc14f04} }, +/**/ {{0x4cc99cb2, 0x3c531efa} }, +/**/ {{0x31219b34, 0xbfd2ec39} }, +/**/ {{0x6e004611, 0xbc618697} }, +/**/ {{0x68736312, 0x3fc05092} }, +/**/ {{0x8a06e4b5, 0x3c67aad4} }, +/**/ {{0x07eca5ec, 0x3fc2aad6} }, +/**/ {{0xe19fe31c, 0xbfbde969} }, +/**/ {{0xdb6b9127, 0xbfb31455} }, +/**/ {{0xf53dd9ee, 0x3fba9a62} }, +/**/ {{0xa8e4ede0, 0x3fa00f5b} } }, +/**/ {{{0x00000000, 0x3fc28000} }, +/**/ {{0x171a535c, 0x3fc25f6e} }, +/**/ {{0xbde1a310, 0x3c67c6d7} }, +/**/ {{0x64866d22, 0x3fef5860} }, +/**/ {{0xd1f6326c, 0x3c88c6ff} }, +/**/ {{0x13c11396, 0xbfc1c02b} }, +/**/ {{0xffeb1a0f, 0xbc51b469} }, +/**/ {{0x4c571b0f, 0xbfd2cb3b} }, +/**/ {{0x2fb0b163, 0x3c6e4f76} }, +/**/ {{0xf5c213ab, 0x3fc0ad06} }, +/**/ {{0xabea9e66, 0x3c625bf2} }, +/**/ {{0x5f93bbb2, 0x3fc25054} }, +/**/ {{0xc80a32c8, 0xbfbe6c0c} }, +/**/ {{0x678d0d1e, 0xbfb23e6c} }, +/**/ {{0xebf8ae4b, 0x3fbadea2} }, +/**/ {{0x527f133b, 0x3f9c8bd7} } }, +/**/ {{{0x00000000, 0x3fc30000} }, +/**/ {{0xb2fba1ff, 0x3fc2dcbd} }, +/**/ {{0x05561534, 0x3c58f287} }, +/**/ {{0x2ee76e94, 0x3fef4f64} }, +/**/ {{0xc6da5865, 0x3c80ec89} }, +/**/ {{0xb322f867, 0xbfc23089} }, +/**/ {{0x5fcd0d6f, 0x3c4c2b54} }, +/**/ 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{{0x280318fd, 0xbfb11c35} } }, +/**/ {{{0x00000000, 0x3fd44000} }, +/**/ {{0xeb76157c, 0x3fd39cb4} }, +/**/ {{0x5a214713, 0xbc72f4da} }, +/**/ {{0x22c31625, 0x3fed1682} }, +/**/ {{0xd5e51b41, 0x3c8ac111} }, +/**/ {{0x07e9a89a, 0xbfd0bb6b} }, +/**/ {{0x7faa1dda, 0x3c76fb53} }, +/**/ {{0xb75f0772, 0xbfc66be7} }, +/**/ {{0xee6d618b, 0xbc69a77d} }, +/**/ {{0x6e943d69, 0x3fc8e1eb} }, +/**/ {{0xc5ec9ebe, 0xbc6982c4} }, +/**/ {{0x9c2d3c0c, 0x3f78e73c} }, +/**/ {{0x7059f387, 0xbfbee752} }, +/**/ {{0x16982f58, 0x3fac73f0} }, +/**/ {{0xc146b407, 0x3fabd0e4} }, +/**/ {{0x82f43254, 0xbfb12b5c} } }, +/**/ {{{0x00000000, 0x3fd48000} }, +/**/ {{0x29271134, 0x3fd3d6d1} }, +/**/ {{0x41cc958a, 0x3c7137ca} }, +/**/ {{0xffb0304c, 0x3fed05b5} }, +/**/ {{0x33e896e5, 0xbc8fc921} }, +/**/ {{0x3a49e254, 0xbfd0dcc2} }, +/**/ {{0x925cb599, 0x3c704578} }, +/**/ {{0x75708502, 0xbfc60859} }, +/**/ {{0x9feebe6c, 0xbc5f88bc} }, +/**/ {{0xc3fb5c1c, 0x3fc8e4e8} }, +/**/ {{0xd6b77a05, 0x3c6de114} }, +/**/ {{0xdbc6c857, 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{{0x5e282403, 0x3fc8b25b} }, +/**/ {{0x707e09fa, 0xbbef7d58} }, +/**/ {{0xb65add31, 0xbf94c1e0} }, +/**/ {{0xafa52f1b, 0xbfba815f} }, +/**/ {{0x63712acc, 0x3fb1a16f} }, +/**/ {{0x95a8d3ad, 0x3f9fa5b5} }, +/**/ {{0x72814750, 0xbfb09d01} } }, +/**/ {{{0x00000000, 0x3fd70000} }, +/**/ {{0x0309cfe2, 0x3fd61484} }, +/**/ {{0x15711f00, 0xbc7a7257} }, +/**/ {{0x27afd9eb, 0x3fec5703} }, +/**/ {{0xb32c1d72, 0x3c63c2ab} }, +/**/ {{0x06000419, 0xbfd20a1c} }, +/**/ {{0xf51a3a28, 0xbc7b5fe7} }, +/**/ {{0x486ad2c8, 0xbfc22771} }, +/**/ {{0xf84a7eae, 0xbc499ab5} }, +/**/ {{0x9d027817, 0x3fc8a49c} }, +/**/ {{0x2e376ecc, 0xbc53fcab} }, +/**/ {{0xeaabcb23, 0xbf973831} }, +/**/ {{0x8c46fbce, 0xbfba051d} }, +/**/ {{0x9132e9cc, 0x3fb1de66} }, +/**/ {{0xd48d5d65, 0x3f9d5269} }, +/**/ {{0x712354a4, 0xbfb074bb} } }, +/**/ {{{0x00000000, 0x3fd74000} }, +/**/ {{0xf635c1c6, 0x3fd64d1f} }, +/**/ {{0xe7c0fdbe, 0xbc7fa403} }, +/**/ {{0x86b5cbf8, 0x3fec44eb} }, +/**/ {{0xbc5b562d, 0xbc6a4101} }, +/**/ {{0x50fb21ad, 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{{0x0ef9b688, 0x3c50e395} }, +/**/ {{0xc8a9b4c0, 0xbf922b65} }, +/**/ {{0xd319146f, 0x3c2835ee} }, +/**/ {{0x00b681bd, 0x3fc16fb8} }, +/**/ {{0x279133b0, 0x3c1df633} }, +/**/ {{0x0a3b410c, 0xbfb54af9} }, +/**/ {{0xebe14682, 0xbf889682} }, +/**/ {{0xdf89e086, 0x3fabe94c} }, +/**/ {{0x0e55a6f8, 0xbfa0ec0e} }, +/**/ {{0x08af68f3, 0xbf809a3e} } }, +/**/ {{{0x00000000, 0x3fe18000} }, +/**/ {{0x73c1a40c, 0x3fe0039c} }, +/**/ {{0x49c9d593, 0xbc8b32c9} }, +/**/ {{0xe931fcd3, 0x3fe8a209} }, +/**/ {{0x8e68c94c, 0x3c6cb8f0} }, +/**/ {{0xb35ad2d8, 0xbfd4bd59} }, +/**/ {{0xcaa606b4, 0xbc61ac1a} }, +/**/ {{0x6dc339ef, 0xbf9000c3} }, +/**/ {{0xaeaeaa73, 0x3c2c62e2} }, +/**/ {{0x7812ee2d, 0x3fc13a66} }, +/**/ {{0x948ffe5b, 0x3c6a8cc2} }, +/**/ {{0xb5955c9c, 0xbfb55c46} }, +/**/ {{0x0fd2b503, 0xbf85906b} }, +/**/ {{0x577de2da, 0x3fab615d} }, +/**/ {{0xa34d31ec, 0xbfa10f0a} }, +/**/ {{0xefe48ad0, 0xbf7d02cb} } }, +/**/ {{{0x00000000, 0x3fe1a000} }, +/**/ {{0x1e82422d, 0x3fe01c34} }, +/**/ {{0xfcca90ee, 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{{{0x00000000, 0x3fe2c000} }, +/**/ {{0x8b67e295, 0x3fe0f5e2} }, +/**/ {{0x7ec990d0, 0x3be311b1} }, +/**/ {{0xa145af59, 0x3fe7d24f} }, +/**/ {{0xabdb623b, 0xbc83c6d1} }, +/**/ {{0x6b9bdb30, 0xbfd4c7fc} }, +/**/ {{0xd3bbb84b, 0x3c7c2fae} }, +/**/ {{0xc729b366, 0x3f70e125} }, +/**/ {{0x7a19993c, 0x3c1291fb} }, +/**/ {{0x66cf0dd8, 0x3fbe3fef} }, +/**/ {{0xcd5e7640, 0xbc5428b7} }, +/**/ {{0xa3273c21, 0xbfb59517} }, +/**/ {{0x36891acb, 0x3f65adcf} }, +/**/ {{0xe121c017, 0x3fa5f05a} }, +/**/ {{0x384bad65, 0xbfa180c2} }, +/**/ {{0xd31e02a7, 0x3f5bd6f1} } }, +/**/ {{{0x00000000, 0x3fe2e000} }, +/**/ {{0x77307a0d, 0x3fe10daa} }, +/**/ {{0xd44c7b05, 0x3c869c33} }, +/**/ {{0x19337139, 0x3fe7bd88} }, +/**/ {{0x00e777ef, 0xbc7fd248} }, +/**/ {{0xb3e16264, 0xbfd4c704} }, +/**/ {{0xd46ed4e3, 0xbc7ed720} }, +/**/ {{0x62c1daf7, 0x3f7863a5} }, +/**/ {{0x30cc82d1, 0x3c155e73} }, +/**/ {{0x97a241da, 0x3fbdd411} }, +/**/ {{0x9ac44edd, 0x3c27a15a} }, +/**/ {{0x9a6c71a6, 0xbfb59022} }, +/**/ {{0xb5534ebe, 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{{0xf45873a6, 0x3c3cd061} }, +/**/ {{0x88dfb80c, 0x3fac2f8b} }, +/**/ {{0x53add20b, 0xbc14fcbc} }, +/**/ {{0x08c71945, 0xbfb0ba99} }, +/**/ {{0x3d79f13f, 0x3f9d7b0c} }, +/**/ {{0x357dfc67, 0x3f795393} }, +/**/ {{0x3aa97829, 0xbf937822} }, +/**/ {{0xa8b90db0, 0x3f8aec90} } }, +/**/ {{{0x00000000, 0x3fe82000} }, +/**/ {{0xb1c71762, 0x3fe4ac00} }, +/**/ {{0x2382b900, 0x3c8b20e7} }, +/**/ {{0xe8e45252, 0x3fe4673d} }, +/**/ {{0x67458f9c, 0x3c57d208} }, +/**/ {{0x6c24e1b3, 0xbfd39d8c} }, +/**/ {{0x973c6d15, 0xbc7830c5} }, +/**/ {{0x12b78147, 0x3faf318c} }, +/**/ {{0xd318184c, 0xbc4fa440} }, +/**/ {{0x158b44e7, 0x3fab891f} }, +/**/ {{0x45d7f1f3, 0x3c4d5f9f} }, +/**/ {{0x47a3e8ba, 0xbfb08e40} }, +/**/ {{0xc4c1a21a, 0x3f9da541} }, +/**/ {{0x3c0d1d71, 0x3f76ec1e} }, +/**/ {{0x152e0bfc, 0xbf92ff48} }, +/**/ {{0x9955298f, 0x3f8ac8f0} } }, +/**/ {{{0x00000000, 0x3fe84000} }, +/**/ {{0x22de94e5, 0x3fe4c05e} }, +/**/ {{0xf09f2edf, 0xbc8c0ac1} }, +/**/ {{0x3c9a6560, 0x3fe453a6} }, +/**/ {{0x828bba02, 0x3c77a95f} }, +/**/ {{0x5a0e5b1c, 0xbfd391c5} }, +/**/ {{0xcd3f76d2, 0x3c7d553d} }, +/**/ {{0x9adede86, 0x3faf9e66} }, +/**/ {{0xd6d2bac0, 0xbc225e54} }, +/**/ {{0x4bdf89d7, 0x3faae46f} }, +/**/ {{0x2b25b8d9, 0x3c39c98c} }, +/**/ {{0x5765a5c1, 0xbfb061ab} }, +/**/ {{0x7127d649, 0x3f9dcb4f} }, +/**/ {{0x13002646, 0x3f7493ba} }, +/**/ {{0xa397d1a6, 0xbf928718} }, +/**/ {{0x494648b5, 0x3f8aa0bc} } }, +/**/ {{{0x00000000, 0x3fe86000} }, +/**/ {{0x023414e8, 0x3fe4d4a8} }, +/**/ {{0x1daa88b0, 0x3c6e3a89} }, +/**/ {{0x6ba2786e, 0x3fe4401a} }, +/**/ {{0xe3b5f317, 0xbc4b8213} }, +/**/ {{0xf11905c0, 0xbfd385d5} }, +/**/ {{0xa2f42dd1, 0xbc72a1e9} }, +/**/ {{0xf07a526f, 0x3fb00458} }, +/**/ {{0xac5fd817, 0xbc14f965} }, +/**/ {{0x66ca7da2, 0x3faa417e} }, +/**/ {{0xa050b433, 0x3c4b1e1a} }, +/**/ {{0x60182e4f, 0xbfb034e0} }, +/**/ {{0x8cafa41b, 0x3f9ded4f} }, +/**/ {{0x1fa4f037, 0x3f724a50} }, +/**/ {{0xfd90e915, 0xbf920fa7} }, +/**/ {{0xf59e7acf, 0x3f8a742d} } }, +/**/ {{{0x00000000, 0x3fe88000} }, +/**/ {{0x5bb6ec04, 0x3fe4e8de} }, +/**/ {{0xbeb3796c, 0x3c84a33d} }, +/**/ {{0x9dd8fdc1, 0x3fe42c9a} }, +/**/ {{0xaf80050b, 0x3c5192da} }, +/**/ {{0x25adf97f, 0xbfd379bf} }, +/**/ {{0x20cd3651, 0xbc774019} }, +/**/ {{0x724dbb01, 0x3fb0383a} }, +/**/ {{0xeb93e538, 0x3c5c4e67} }, +/**/ {{0x646e65df, 0x3fa9a04e} }, +/**/ {{0x894a6b77, 0x3c21a7cb} }, +/**/ {{0x62771c79, 0xbfb007e5} }, +/**/ {{0x37a45544, 0x3f9e0b5c} }, +/**/ {{0x54993092, 0x3f700fc7} }, +/**/ {{0x37534c25, 0xbf919909} }, +/**/ {{0xae51732a, 0x3f8a437e} } }, +/**/ {{{0x00000000, 0x3fe8a000} }, +/**/ {{0x3b7dd17e, 0x3fe4fd01} }, +/**/ {{0x3e7c24b5, 0x3c7d513f} }, +/**/ {{0xfa274ef1, 0x3fe41926} }, +/**/ {{0x4d72ecb3, 0x3c8ad830} }, +/**/ {{0xe995018a, 0xbfd36d81} }, +/**/ {{0x6fd6094d, 0x3c7e7ec5} }, +/**/ {{0x567bb975, 0x3fb06adb} }, +/**/ {{0xf0d7364f, 0x3c5212c1} }, +/**/ {{0x07a9b624, 0x3fa900e1} }, +/**/ {{0xc16bcc85, 0xbc4e5b5b} }, +/**/ {{0x705f052b, 0xbfafb580} }, +/**/ {{0x646ce12e, 0x3f9e258f} }, +/**/ {{0xa3c63841, 0x3f6bc808} }, +/**/ {{0x67043d41, 0xbf91234e} }, +/**/ {{0x4f11b221, 0x3f8a0ee6} } }, +/**/ {{{0x00000000, 0x3fe8c000} }, +/**/ {{0xadc5ed81, 0x3fe51110} }, +/**/ {{0x6832a63e, 0x3c723dcd} }, +/**/ {{0xa6864f90, 0x3fe405bf} }, +/**/ {{0x662cd5df, 0xbc7419c5} }, +/**/ {{0x2bf1f7e4, 0xbfd3611f} }, +/**/ {{0x65483b78, 0xbc6e94dd} }, +/**/ {{0x23e21be9, 0x3fb09c3f} }, +/**/ {{0xcaca858d, 0x3c22db63} }, +/**/ {{0xd99c3f1d, 0x3fa86337} }, +/**/ {{0xdc0a6dfc, 0x3c034382} }, +/**/ {{0x284f8093, 0xbfaf5aed} }, +/**/ {{0xd396fb43, 0x3f9e3c02} }, +/**/ {{0x08b96150, 0x3f678dd3} }, +/**/ {{0xaa2dcc3a, 0xbf90ae88} }, +/**/ {{0x79128ee7, 0x3f89d69b} } }, +/**/ {{{0x00000000, 0x3fe8e000} }, +/**/ {{0xbef1e9fb, 0x3fe5250c} }, +/**/ {{0xa3228870, 0xbc5539b7} }, +/**/ {{0xc8011245, 0x3fe3f264} }, +/**/ {{0x44cc720b, 0xbc6641f1} }, +/**/ {{0xd942778a, 0xbfd35497} }, +/**/ {{0x9bd7dbd6, 0x3c750a5a} }, +/**/ {{0x6438739e, 0x3fb0cc69} }, +/**/ {{0x435f798d, 0x3bf5d933} }, +/**/ {{0x2b29722f, 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+/**/ {{0x5f3d8fd8, 0x3c6ef16e} }, +/**/ {{0x703d3bf6, 0x3fb1291f} }, +/**/ {{0xb04e0672, 0xbc566e82} }, +/**/ {{0x806b26f2, 0x3fa694e1} }, +/**/ {{0xafcee740, 0x3c302819} }, +/**/ {{0x16dcee96, 0xbfae49eb} }, +/**/ {{0xfbfdb35f, 0x3f9e69dc} }, +/**/ {{0x70c48510, 0x3f571910} }, +/**/ {{0xe90198c8, 0xbf8ead25} }, +/**/ {{0xa1c723cb, 0x3f89199b} } }, +/**/ {{{0x00000000, 0x3fe94000} }, +/**/ {{0x29c70c34, 0x3fe5608d} }, +/**/ {{0xf0de8088, 0x3c89939c} }, +/**/ {{0x4fcf28c3, 0x3fe3b8a0} }, +/**/ {{0xcb80013c, 0xbc469c2b} }, +/**/ {{0x77ec4ef9, 0xbfd32e2f} }, +/**/ {{0xc61f7341, 0x3c7f9d06} }, +/**/ {{0x59c3bcdf, 0x3fb155b2} }, +/**/ {{0x3583c01b, 0xbc2d692e} }, +/**/ {{0x1a1fe15d, 0x3fa5fe54} }, +/**/ {{0x5d9bad81, 0x3c430dc5} }, +/**/ {{0x01d944a8, 0xbfadeea0} }, +/**/ {{0x9683b244, 0x3f9e724e} }, +/**/ {{0x491379ef, 0x3f4f13d4} }, +/**/ {{0x0b7cf74b, 0xbf8dcc74} }, +/**/ {{0xff5f0625, 0x3f88d48f} } }, +/**/ {{{0x00000000, 0x3fe96000} }, +/**/ {{0x352b33ba, 0x3fe5743c} }, +/**/ {{0x34c87ea6, 0xbc8ea00d} }, +/**/ {{0xa5f05e48, 0x3fe3a578} }, +/**/ {{0x00e4639b, 0xbc8ba1ec} }, +/**/ {{0xd8b7a43f, 0xbfd3211e} }, +/**/ {{0x676e23a8, 0xbc6d4b54} }, +/**/ {{0xf11b2c2d, 0x3fb18119} }, +/**/ {{0x3a3bf5fa, 0x3c34855b} }, +/**/ {{0x625c76bf, 0x3fa5698f} }, +/**/ {{0xbedb0264, 0xbc2f758a} }, +/**/ {{0x81b60103, 0xbfad9340} }, +/**/ {{0xce91900f, 0x3f9e777d} }, +/**/ {{0x34fddb2f, 0x3f406543} }, +/**/ {{0xe6077f81, 0xbf8cee3b} }, +/**/ {{0xfe42afde, 0x3f888ccf} } }, +/**/ {{{0x00000000, 0x3fe98000} }, +/**/ {{0x1f732fbb, 0x3fe587d8} }, +/**/ {{0xd8c5a950, 0xbc75e5c9} }, +/**/ {{0x1cd28c98, 0x3fe3925e} }, +/**/ {{0x1ffec6da, 0x3c8c8443} }, +/**/ {{0x1af2c622, 0xbfd313ee} }, +/**/ {{0xbc3f7ac8, 0x3c0a0e9b} }, +/**/ {{0xc7f683c3, 0x3fb1ab59} }, +/**/ {{0x12c04500, 0x3c5eaf17} }, +/**/ {{0xa7039179, 0x3fa4d693} }, +/**/ {{0xa4ce58a2, 0xbc4c8d74} }, +/**/ {{0x391400b3, 0xbfad37d6} }, +/**/ {{0xf2148a36, 0x3f9e7982} }, +/**/ {{0xb6df63ca, 0x3f112956} }, +/**/ {{0xfbd0f7ee, 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+/**/ {{0x6f398221, 0xbfac8106} }, +/**/ {{0xc97073c7, 0x3f9e746e} }, +/**/ {{0xecfc2d6a, 0xbf4914de} }, +/**/ {{0xcfa74bd5, 0xbf8a6350} }, +/**/ {{0x6f38ad9e, 0x3f87a724} } }, +/**/ {{{0x00000000, 0x3fe9e000} }, +/**/ {{0x9c244261, 0x3fe5c239} }, +/**/ {{0xe9e56b35, 0xbc831bd4} }, +/**/ {{0x7e9af2dc, 0x3fe3595e} }, +/**/ {{0x9dc90e6a, 0x3c81ef2d} }, +/**/ {{0xb99eb689, 0xbfd2eba3} }, +/**/ {{0x6a2f2701, 0xbc7b12ef} }, +/**/ {{0x7ec46b9b, 0x3fb2234e} }, +/**/ {{0x8d415d66, 0x3c59f30c} }, +/**/ {{0xaabf0d26, 0x3fa32856} }, +/**/ {{0x3f33d7ea, 0xbc122571} }, +/**/ {{0xcc3da9ce, 0xbfac25b2} }, +/**/ {{0xa8630cad, 0x3f9e6d84} }, +/**/ {{0xbeba707a, 0xbf5308c5} }, +/**/ {{0xa1585fd1, 0xbf898fda} }, +/**/ {{0x0dc54356, 0x3f87565b} } }, +/**/ {{{0x00000000, 0x3fea0000} }, +/**/ {{0x87169b18, 0x3fe5d589} }, +/**/ {{0x4bc5e7ca, 0x3c60028e} }, +/**/ {{0xace01346, 0x3fe34679} }, +/**/ {{0x04d19e6b, 0x3c8e6b38} }, +/**/ {{0x03913da2, 0xbfd2ddfb} }, +/**/ {{0x9a19adbd, 0xbc763ec8} }, +/**/ {{0x07b46905, 0x3fb24913} }, +/**/ {{0xd6f0307f, 0xbc4e7be8} }, +/**/ {{0x4b96b773, 0x3fa29c7e} }, +/**/ {{0x9182d783, 0xbc24c2cd} }, +/**/ {{0x1f071f44, 0xbfabca78} }, +/**/ {{0xc4b7b7c4, 0x3f9e63ce} }, +/**/ {{0x125f35b0, 0xbf59529a} }, +/**/ {{0xed369b2b, 0xbf88bf43} }, +/**/ {{0xc97185cd, 0x3f8703ba} } }, +/**/ {{{0x00000000, 0x3fea2000} }, +/**/ {{0x941043d0, 0x3fe5e8c6} }, +/**/ {{0xbe451e70, 0xbc70bf75} }, +/**/ {{0x91e21aec, 0x3fe333a2} }, +/**/ {{0x7acfc84f, 0x3c7ae035} }, +/**/ {{0x628d5861, 0xbfd2d036} }, +/**/ {{0xe463d006, 0x3c67c5fb} }, +/**/ {{0xa7d77fb2, 0x3fb26dc1} }, +/**/ {{0xc47ba861, 0xbc5432bd} }, +/**/ {{0xc229bece, 0x3fa2126d} }, +/**/ {{0x1da8ed9e, 0xbc4be1bf} }, +/**/ {{0xa890e568, 0xbfab6f5e} }, +/**/ {{0xeec5339a, 0x3f9e5763} }, +/**/ {{0x5274aa52, 0xbf5f68a6} }, +/**/ {{0x8a9df558, 0xbf87f19c} }, +/**/ {{0xff809dc5, 0x3f86af6b} } }, +/**/ {{{0x00000000, 0x3fea4000} }, +/**/ {{0xd0d5cc4a, 0x3fe5fbf0} }, +/**/ {{0x000b7158, 0xbc5b4cfd} }, +/**/ {{0x49243ad8, 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{{{0x00000000, 0x3fed6000} }, +/**/ {{0x11a6092b, 0x3fe7c3d3} }, +/**/ {{0x2d303288, 0x3c8bb3cb} }, +/**/ {{0x1dc61b17, 0x3fe15dbb} }, +/**/ {{0xbb77dc56, 0xbc8f0487} }, +/**/ {{0xee0771ca, 0xbfd14d7e} }, +/**/ {{0xdc2fcbd0, 0x3c72d38b} }, +/**/ {{0xd6080f0e, 0x3fb4d716} }, +/**/ {{0xa9fbc2c3, 0xbc5cb5bc} }, +/**/ {{0xfc42e02f, 0x3f89a7f9} }, +/**/ {{0x857be8a4, 0xbc201eec} }, +/**/ {{0x44ceebb3, 0xbfa2af2b} }, +/**/ {{0x08511639, 0x3f9a62b5} }, +/**/ {{0xc8de23de, 0xbf8018ad} }, +/**/ {{0xc964501a, 0xbf6dc8a2} }, +/**/ {{0xeb913697, 0x3f7ac6f9} } }, +/**/ {{{0x00000000, 0x3fed8000} }, +/**/ {{0x289fa093, 0x3fe7d528} }, +/**/ {{0x1e2f3aa9, 0x3c856082} }, +/**/ {{0x711551bb, 0x3fe14c75} }, +/**/ {{0x71970f2c, 0xbc80c88e} }, +/**/ {{0xe4aa5095, 0xbfd13dd8} }, +/**/ {{0xb4b7ae12, 0x3c66dd31} }, +/**/ {{0xead4c211, 0x3fb4e38d} }, +/**/ {{0xe392a31e, 0x3c513fb0} }, +/**/ {{0xf6b74576, 0x3f88355f} }, +/**/ {{0xf3561ab7, 0x3ba8cb44} }, +/**/ {{0x0de0faaa, 0xbfa26058} }, +/**/ {{0x989371f0, 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+/**/ {{0xd971cd38, 0x3fe07187} }, +/**/ {{0x202c20ac, 0x3c89baa4} }, +/**/ {{0xd15893ab, 0xbfd06fe9} }, +/**/ {{0xdc0cb586, 0xbc7a864b} }, +/**/ {{0x7ce57fed, 0x3fb54883} }, +/**/ {{0x294f4b18, 0xbc49498e} }, +/**/ {{0x426ebecc, 0x3f6df762} }, +/**/ {{0xf28644c0, 0xbc022f08} }, +/**/ {{0x5c564b44, 0xbf9d3e48} }, +/**/ {{0xdfea7acf, 0x3f9713ab} }, +/**/ {{0x761db35c, 0xbf8213fc} }, +/**/ {{0x10d60f49, 0xbf4f9a17} }, +/**/ {{0x58700e9b, 0x3f71f5de} } }, +/**/ {{{0x00000000, 0x3fef4000} }, +/**/ {{0x145cf49d, 0x3fe8c0d9} }, +/**/ {{0x76dc4333, 0x3c8bea40} }, +/**/ {{0xeb45139a, 0x3fe0611f} }, +/**/ {{0x65aadb1f, 0x3c7e4998} }, +/**/ {{0x1953a316, 0xbfd05ff2} }, +/**/ {{0xa1b67b0f, 0x3c759922} }, +/**/ {{0xc08c1d66, 0x3fb54bf9} }, +/**/ {{0xd220330c, 0x3c5b9353} }, +/**/ {{0x478cb604, 0x3f69706e} }, +/**/ {{0xa22fd45a, 0xbbfdb6d3} }, +/**/ {{0x5c0d1d38, 0xbf9cb490} }, +/**/ {{0xbbaba2f2, 0x3f96d44b} }, +/**/ {{0x9c6b7de1, 0xbf822289} }, +/**/ {{0xa49803b6, 0xbf4aa143} }, +/**/ {{0x9270e49e, 0x3f7165be} } }, +/**/ {{{0x00000000, 0x3fef6000} }, +/**/ {{0x06f8c4cb, 0x3fe8d132} }, +/**/ {{0xbaa89a8b, 0xbc7b018c} }, +/**/ {{0xf60ab1f4, 0x3fe050c7} }, +/**/ {{0xc6cf5796, 0x3c63f8e2} }, +/**/ {{0xfe998dc0, 0xbfd04ff7} }, +/**/ {{0x7dc56419, 0x3c77873c} }, +/**/ {{0x7cc24121, 0x3fb54ee0} }, +/**/ {{0x8e5c84c5, 0x3c313117} }, +/**/ {{0x50066301, 0x3f64fee1} }, +/**/ {{0x017261a1, 0x3c043698} }, +/**/ {{0x2cc5b4f1, 0xbf9c2c55} }, +/**/ {{0xf759f369, 0x3f9694bc} }, +/**/ {{0x6c93426a, 0xbf822ea4} }, +/**/ {{0x135d6c51, 0xbf45d0a1} }, +/**/ {{0xe62dc18f, 0x3f70d811} } }, +/**/ {{{0x00000000, 0x3fef8000} }, +/**/ {{0xa99cc05e, 0x3fe8e17a} }, +/**/ {{0xab042f61, 0xbc7ec182} }, +/**/ {{0xfbefe001, 0x3fe0407f} }, +/**/ {{0xfbf80041, 0x3c401ffe} }, +/**/ {{0xebd00209, 0xbfd03ffb} }, +/**/ {{0xb9004112, 0xbc53ff3c} }, +/**/ {{0x5aaf6d91, 0x3fb5513a} }, +/**/ {{0xc0516ddb, 0x3c54a20d} }, +/**/ {{0xc6ac4038, 0x3f60a27f} }, +/**/ {{0x2a340912, 0x3bf06bee} }, +/**/ {{0xccd6032a, 0xbf9ba597} }, +/**/ {{0x002bb974, 0x3f965508} }, +/**/ {{0xd2d1068b, 0xbf823860} }, +/**/ {{0x666265bc, 0xbf41277e} }, +/**/ {{0x656b66ea, 0x3f704cdc} } }, +/**/ {{{0x00000000, 0x3fefa000} }, +/**/ {{0x0c44f167, 0x3fe8f1b3} }, +/**/ {{0xb93933fd, 0x3c6dd1ca} }, +/**/ {{0xfeb82e4e, 0x3fe03047} }, +/**/ {{0x5272e5ac, 0x3c69ee56} }, +/**/ {{0x49a09c45, 0xbfd02ffe} }, +/**/ {{0xb26267bb, 0xbc700a59} }, +/**/ {{0xfc062d2f, 0x3fb55309} }, +/**/ {{0xb11938e0, 0x3c5dba48} }, +/**/ {{0xe4f365be, 0x3f58b61b} }, +/**/ {{0xa79ad31a, 0x3bf8b585} }, +/**/ {{0x08d4ad17, 0xbf9b2059} }, +/**/ {{0xfe379940, 0x3f961534} }, +/**/ {{0x62a1270e, 0xbf823fd2} }, +/**/ {{0x3f3a0aec, 0xbf394a53} }, +/**/ {{0xa04bcae2, 0x3f6f8842} } }, +/**/ {{{0x00000000, 0x3fefc000} }, +/**/ {{0x3eeef187, 0x3fe901db} }, +/**/ {{0xe5603c8f, 0x3c868665} }, +/**/ {{0xffbf7f80, 0x3fe0201f} }, +/**/ {{0xffbf7f80, 0x3c20201f} }, +/**/ {{0x7ebe8004, 0xbfd01fff} }, +/**/ {{0xcf979001, 0xbc4213ff} }, +/**/ {{0xfb0012db, 0x3fb55451} }, +/**/ {{0xf73aa59f, 0xbc395606} }, +/**/ {{0xfc757100, 0x3f50509f} }, +/**/ {{0xfee554d0, 0x3bebc7da} }, +/**/ {{0x7d3424d0, 0xbf9a9c99} }, +/**/ {{0xd5ac0217, 0x3f95d54b} }, +/**/ {{0x564b3c49, 0xbf82450c} }, +/**/ {{0xe6d3e986, 0xbf3091df} }, +/**/ {{0x3bef5a22, 0x3f6e7bc6} } }, +/**/ {{{0x00000000, 0x3fefe000} }, +/**/ {{0x5199833b, 0x3fe911f3} }, +/**/ {{0x0edbf522, 0x3c63ae8a} }, +/**/ {{0xfffbfbfe, 0x3fe01007} }, +/**/ {{0xfffbfbfe, 0x3ba01007} }, +/**/ {{0xefebf400, 0xbfd00fff} }, +/**/ {{0xfff9f97d, 0xbc401209} }, +/**/ {{0xea5aaaf6, 0x3fb55514} }, +/**/ {{0xb5b7b240, 0xbc529baa} }, +/**/ {{0xffc7abc4, 0x3f402827} }, +/**/ {{0xbfee6ab3, 0x3b5ba3d6} }, +/**/ {{0x97d67093, 0xbf9a1a59} }, +/**/ {{0x28080aaf, 0x3f959554} }, +/**/ {{0x8e892ce2, 0xbf824821} }, +/**/ {{0xfe70a2a6, 0xbf204877} }, +/**/ {{0x0e8ddd67, 0x3f6d7447} } }, +/**/ {{{0x00000000, 0x3feff800} }, +/**/ {{0xd439826e, 0x3fe91dfa} }, +/**/ {{0x6df48d55, 0xbc786a19} }, +/**/ {{0x7ffffbff, 0x3fe00400} }, +/**/ {{0xffbff800, 0xbbeffffe} }, +/**/ {{0xffbfebfd, 0xbfd003ff} }, +/**/ {{0x9ffff9fe, 0xbb600480} }, +/**/ {{0x53aa5aab, 0x3fb55551} }, +/**/ {{0x9baaab5b, 0xbc542a4a} }, +/**/ {{0x7fffc7eb, 0x3f200a02} }, +/**/ {{0x4770e940, 0xbb7dfffe} }, +/**/ {{0x9997d8d0, 0xbf99b9a5} }, +/**/ {{0x50a80a03, 0x3f956555} }, +/**/ {{0x86456493, 0xbf824914} }, +/**/ {{0x7ffe7329, 0xbf001207} }, +/**/ {{0x1c63fe2a, 0x3f6cb1ef} } }, + }; + +#endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/uexp.h b/REORG.TODO/sysdeps/ieee754/dbl-64/uexp.h new file mode 100644 index 0000000000..83f9b618f6 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/uexp.h @@ -0,0 +1,69 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/******************************************************************/ +/* */ +/* MODULE_NAME:uexp.h */ +/* */ +/* common data and variables prototype and definition */ +/******************************************************************/ + +#ifndef UEXP_H +#define UEXP_H + +#include "mydefs.h" + +const static double zero = 0.0, hhuge = 1.0e300, tiny = 1.0e-300, +err_0 = 1.000014, err_1 = 0.000016; +const static int4 bigint = 0x40862002, + badint = 0x40876000,smallint = 0x3C8fffff; +const static int4 hugeint = 0x7FFFFFFF, infint = 0x7ff00000; + +#ifdef BIG_ENDI +const static mynumber inf = {{0x7FF00000, 0}}; /* inf */ +const static mynumber t256 = {{0x4ff00000, 0}}; /* 2^256 */ + +const static mynumber ln_two1 = {{0x3FE62E42, 0xFEFA3800}};/*0.69314718055989033 */ +const static mynumber ln_two2 = {{0x3D2EF357, 0x93C76730}};/*5.4979230187083712e-14*/ +const static mynumber log2e = {{0x3FF71547, 0x652B82FE}};/* 1.4426950408889634 */ + +const static mynumber p2 = {{0x3FE00000, 0x000004DC}};/* 0.50000000000013811 */ +const static mynumber p3 = {{0x3FC55555, 0x55555A0F}};/* 0.16666666666670024 */ + +const static mynumber three33 = {{0x42180000, 0}}; /* 25769803776 */ +const static mynumber three51 = {{0x43380000, 0}}; /* 6755399441055744 */ + +#else +#ifdef LITTLE_ENDI + const static mynumber inf = {{0, 0x7FF00000}}; /* inf */ + const static mynumber t256 = {{0, 0x4ff00000}}; /* 2^256 */ + + const static mynumber ln_two1 = {{0xFEFA3800, 0x3FE62E42}};/*0.69314718055989033 */ + const static mynumber ln_two2 = {{0x93C76730, 0x3D2EF357}};/*5.4979230187083712e-14*/ + const static mynumber log2e = {{0x652B82FE, 0x3FF71547}};/* 1.4426950408889634 */ + + const static mynumber p2 = {{0x000004DC, 0x3FE00000}};/* 0.50000000000013811 */ + const static mynumber p3 = {{0x55555A0F, 0x3FC55555}};/* 0.16666666666670024 */ + + const static mynumber three33 = {{0, 0x42180000}}; /* 25769803776 */ + const static mynumber three51 = {{0, 0x43380000}}; /* 6755399441055744 */ + +#endif +#endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/uexp.tbl b/REORG.TODO/sysdeps/ieee754/dbl-64/uexp.tbl new file mode 100644 index 0000000000..3e5fdc5783 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/uexp.tbl @@ -0,0 +1,1786 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/****************************************************************/ +/* TABLES FOR THE ulog() FUNCTION */ +/****************************************************************/ + +#ifdef BIG_ENDI + +static const union { + int i[1424]; + double x[712]; +} coar = { .i = { + 0x3FE69A59, 0xC8000000, 0x3DF22D4D, 0x6079C9F7, + 0x3FE6A5A9, 0xC8000000, 0x3E19882D, 0x25AF6823, + 0x3FE6B0FF, 0x74000000, 0xBE221476, 0x31DABF59, + 0x3FE6BC5A, 0xC8000000, 0x3E2312AC, 0x99A2DC0A, + 0x3FE6C7BB, 0xD0000000, 0xBE265926, 0xCE9F9355, + 0x3FE6D322, 0x84000000, 0x3E2F2C26, 0x2D298DED, + 0x3FE6DE8E, 0xF4000000, 0xBE2EC28E, 0x1E748D2F, + 0x3FE6EA01, 0x14000000, 0x3E2D8C6D, 0xC68CB7E5, + 0x3FE6F578, 0xF4000000, 0x3DEE1A9E, 0x419FE2F0, + 0x3FE700F6, 0x90000000, 0xBDFF1AFD, 0xDEAEAE34, + 0x3FE70C79, 0xEC000000, 0xBE0730FE, 0x558B7122, + 0x3FE71803, 0x0C000000, 0xBE25CB85, 0x2D280C3B, + 0x3FE72391, 0xF0000000, 0xBE06F2CE, 0x337B7B54, + 0x3FE72F26, 0x9C000000, 0x3E289BCA, 0x45C02B72, + 0x3FE73AC1, 0x18000000, 0xBE18DEA6, 0x5039F1CA, + 0x3FE74661, 0x60000000, 0xBE09D090, 0x86CE0538, + 0x3FE75207, 0x78000000, 0x3E290E79, 0xCFCE5DDB, + 0x3FE75DB3, 0x68000000, 0x3DD61DF0, 0xB249A17C, + 0x3FE76965, 0x2C000000, 0x3E2F22F7, 0xE13445F7, + 0x3FE7751C, 0xD0000000, 0xBE2CD454, 0x874E75CE, + 0x3FE780DA, 0x4C000000, 0xBE0159CE, 0xDF43E3BC, + 0x3FE78C9D, 0xA8000000, 0x3E279291, 0x699A1332, + 0x3FE79866, 0xEC000000, 0xBE2A0BCD, 0x2DD98C6C, + 0x3FE7A436, 0x10000000, 0x3E25F375, 0x15AC979E, + 0x3FE7B00B, 0x20000000, 0x3E26CCF5, 0x2FEAFCF6, + 0x3FE7BBE6, 0x1C000000, 0x3E27D4F4, 0x53ADAD67, + 0x3FE7C7C7, 0x08000000, 0x3E10EEC7, 0x7FBD9566, + 0x3FE7D3AD, 0xE4000000, 0x3E2837F0, 0x9A831D86, + 0x3FE7DF9A, 0xB8000000, 0xBE129BE0, 0x5CB4C35B, + 0x3FE7EB8D, 0x80000000, 0x3E23990A, 0x0234F04D, + 0x3FE7F786, 0x44000000, 0x3E2EB807, 0x64D5C842, + 0x3FE80385, 0x08000000, 0x3E0FC86F, 0x02B4E9E8, + 0x3FE80F89, 0xCC000000, 0xBDD7B5B3, 0x7B4274BF, + 0x3FE81B94, 0x94000000, 0xBE16888B, 0xB899B00F, + 0x3FE827A5, 0x60000000, 0x3E288971, 0x5E94D155, + 0x3FE833BC, 0x38000000, 0x3E2AEEB2, 0x099F3E5E, + 0x3FE83FD9, 0x20000000, 0xBE23B922, 0x3FF60B7C, + 0x3FE84BFC, 0x14000000, 0xBDF7D3B1, 0x2DBD8012, + 0x3FE85825, 0x1C000000, 0xBDF24BA3, 0xA8872BEB, + 0x3FE86454, 0x38000000, 0x3E2EFE04, 0x01AA18A7, + 0x3FE87089, 0x70000000, 0x3E21986C, 0x944496A2, + 0x3FE87CC4, 0xC4000000, 0x3E096A8B, 0xB71FFAFF, + 0x3FE88906, 0x38000000, 0xBE21CE0A, 0xBC4C7AC5, + 0x3FE8954D, 0xCC000000, 0xBE076F45, 0xBAC02491, + 0x3FE8A19B, 0x84000000, 0x3E2B4FA2, 0xD922B925, + 0x3FE8ADEF, 0x68000000, 0x3DF759DB, 0x641863AF, + 0x3FE8BA49, 0x78000000, 0xBE2DB97C, 0xC6AB5E04, + 0x3FE8C6A9, 0xB4000000, 0xBE25364C, 0xE2156713, + 0x3FE8D310, 0x20000000, 0x3E1BEB7C, 0x862BEFF7, + 0x3FE8DF7C, 0xC4000000, 0xBDF4DD0C, 0x1CEA33A5, + 0x3FE8EBEF, 0xA0000000, 0xBE2537DF, 0x51797D47, + 0x3FE8F868, 0xB4000000, 0x3E0FB1C4, 0xF0107B28, + 0x3FE904E8, 0x08000000, 0x3E0AD6A1, 0xE01B68BD, + 0x3FE9116D, 0x9C000000, 0x3E292117, 0x1F78D9D9, + 0x3FE91DF9, 0x78000000, 0xBE1D75DA, 0x4F50E5CF, + 0x3FE92A8B, 0x98000000, 0x3DE5102B, 0x74959E58, + 0x3FE93724, 0x04000000, 0xBE01CA50, 0xD2216C35, + 0x3FE943C2, 0xBC000000, 0x3E225BFD, 0xB0B05884, + 0x3FE95067, 0xC8000000, 0xBE0F2183, 0x60B7C5C1, + 0x3FE95D13, 0x24000000, 0x3E2FB47A, 0xB5860441, + 0x3FE969C4, 0xDC000000, 0xBE01FFD2, 0xE2D4059E, + 0x3FE9767C, 0xEC000000, 0xBDE9ED72, 0x12BB6A8D, + 0x3FE9833B, 0x58000000, 0x3E2B3815, 0x43BFFB24, + 0x3FE99000, 0x28000000, 0x3E03FA22, 0xEE9EAD1E, + 0x3FE99CCB, 0x5C000000, 0xBE213841, 0x377138F7, + 0x3FE9A99C, 0xF4000000, 0x3E178105, 0xDB636C94, + 0x3FE9B674, 0xF8000000, 0x3E1E5E7A, 0xF5720122, + 0x3FE9C353, 0x6C000000, 0xBE238BFF, 0xA2AC5AAE, + 0x3FE9D038, 0x4C000000, 0x3E270893, 0xF93BDBD8, + 0x3FE9DD23, 0xA4000000, 0x3DF40420, 0x354B86CF, + 0x3FE9EA15, 0x74000000, 0xBE2D76D3, 0x88CB06B7, + 0x3FE9F70D, 0xBC000000, 0xBE251639, 0x9ED0EC60, + 0x3FEA040C, 0x80000000, 0x3E1F06E9, 0xE2DDE506, + 0x3FEA1111, 0xC8000000, 0x3E014549, 0x8E6DB477, + 0x3FEA1E1D, 0x94000000, 0xBDF4BC17, 0xF8716509, + 0x3FEA2B2F, 0xE8000000, 0xBE2107DB, 0xDA723A49, + 0x3FEA3848, 0xC4000000, 0x3E1A932A, 0x986AA369, + 0x3FEA4568, 0x30000000, 0x3E198092, 0x41592CDB, + 0x3FEA528E, 0x30000000, 0xBE2E260F, 0x676BCAB8, + 0x3FEA5FBA, 0xC0000000, 0x3DE2E821, 0x2D5D5610, + 0x3FEA6CED, 0xE8000000, 0x3E2F7046, 0x7DA20167, + 0x3FEA7A27, 0xB0000000, 0xBE1D2832, 0xF9FAAD30, + 0x3FEA8768, 0x14000000, 0xBE23F788, 0x43FA6C45, + 0x3FEA94AF, 0x18000000, 0x3E011E27, 0xAA082732, + 0x3FEAA1FC, 0xC4000000, 0xBE20BACB, 0xC682F0BF, + 0x3FEAAF51, 0x18000000, 0xBE2DC7DD, 0x7BD08C78, + 0x3FEABCAC, 0x14000000, 0x3E2271A2, 0xA3B10F9A, + 0x3FEACA0D, 0xC4000000, 0xBE15449C, 0x7966F94C, + 0x3FEAD776, 0x24000000, 0x3DD06137, 0x6FD8F3EE, + 0x3FEAE4E5, 0x3C000000, 0xBE267CD1, 0x8C5A144A, + 0x3FEAF25B, 0x0C000000, 0xBE29E584, 0xB59DA94B, + 0x3FEAFFD7, 0x98000000, 0xBE23DFCF, 0x7B52192F, + 0x3FEB0D5A, 0xE4000000, 0xBE1CF2FE, 0x78A76B45, + 0x3FEB1AE4, 0xF4000000, 0xBE23A561, 0x7EC80FF6, + 0x3FEB2875, 0xC8000000, 0x3E22C4C9, 0x932EED68, + 0x3FEB360D, 0x68000000, 0x3E2B085C, 0xB5833C97, + 0x3FEB43AB, 0xD8000000, 0xBE01F093, 0x93B9319A, + 0x3FEB5151, 0x18000000, 0xBE254F01, 0xFABCE670, + 0x3FEB5EFD, 0x28000000, 0x3E2F24C2, 0x627ABFB0, + 0x3FEB6CB0, 0x14000000, 0x3E1F1EEC, 0xE6AC0B48, + 0x3FEB7A69, 0xDC000000, 0xBE1A8671, 0x127F9ABC, + 0x3FEB882A, 0x80000000, 0xBDCB0C28, 0xC87C73B3, + 0x3FEB95F2, 0x08000000, 0xBE22E8DD, 0x7F2B5A97, + 0x3FEBA3C0, 0x74000000, 0xBE1B3645, 0x2D22A9D5, + 0x3FEBB195, 0xC8000000, 0x3E0ADACA, 0x428F8B88, + 0x3FEBBF72, 0x0C000000, 0xBE2E9E07, 0xCDF9F681, + 0x3FEBCD55, 0x3C000000, 0xBE08A127, 0x7FA54ACF, + 0x3FEBDB3F, 0x60000000, 0x3E0E92CE, 0x8225B385, + 0x3FEBE930, 0x7C000000, 0x3DF38C2A, 0x7BB09485, + 0x3FEBF728, 0x94000000, 0xBE2DFD64, 0xF681FA5F, + 0x3FEC0527, 0xA4000000, 0x3E2E384D, 0xDCE88BD2, + 0x3FEC132D, 0xBC000000, 0xBE20F111, 0xFE46A893, + 0x3FEC213A, 0xD4000000, 0x3E193DA1, 0xB189BFDA, + 0x3FEC2F4E, 0xF8000000, 0xBE20E3A1, 0x0E39FB00, + 0x3FEC3D6A, 0x24000000, 0x3E1DB044, 0x30F0FAC5, + 0x3FEC4B8C, 0x64000000, 0xBE2BC12C, 0x97446B17, + 0x3FEC59B5, 0xB4000000, 0xBE282696, 0x963F4150, + 0x3FEC67E6, 0x18000000, 0x3E224D26, 0x3049824B, + 0x3FEC761D, 0x98000000, 0x3E2C5BA5, 0x87F84C7D, + 0x3FEC845C, 0x38000000, 0xBDE1D14D, 0xC4852339, + 0x3FEC92A1, 0xF8000000, 0xBE1A451E, 0x5588D9E1, + 0x3FECA0EE, 0xDC000000, 0xBE1D3B96, 0x68BFF457, + 0x3FECAF42, 0xE8000000, 0xBE18B670, 0x4DADF774, + 0x3FECBD9E, 0x20000000, 0xBE1A1548, 0x7FB1FC01, + 0x3FECCC00, 0x88000000, 0xBE273F2E, 0x78FC5AF0, + 0x3FECDA6A, 0x20000000, 0x3E1D218F, 0xA6F4A841, + 0x3FECE8DA, 0xF0000000, 0x3E2E0BA9, 0x4D002CA0, + 0x3FECF752, 0xFC000000, 0x3E20F4BB, 0x065EF979, + 0x3FED05D2, 0x48000000, 0xBE2ED3D5, 0x11793B33, + 0x3FED1458, 0xD0000000, 0x3E115E3C, 0x913341B3, + 0x3FED22E6, 0xA0000000, 0x3DE97C02, 0xB3546109, + 0x3FED317B, 0xB8000000, 0x3E087540, 0x1BF898EF, + 0x3FED4018, 0x1C000000, 0x3E209430, 0x346F9641, + 0x3FED4EBB, 0xD0000000, 0x3E2B6DF4, 0x88F4B20B, + 0x3FED5D66, 0xDC000000, 0xBE2EC68F, 0x0CB26035, + 0x3FED6C19, 0x38000000, 0x3E2CA2C8, 0x1F44D9C3, + 0x3FED7AD2, 0xF4000000, 0x3E10E6F4, 0x41704EE0, + 0x3FED8994, 0x0C000000, 0x3E2F9273, 0x25F8F0E2, + 0x3FED985C, 0x88000000, 0x3E2D041A, 0x318798DE, + 0x3FEDA72C, 0x6C000000, 0xBE005680, 0x9349CF58, + 0x3FEDB603, 0xB8000000, 0xBE10F665, 0xCF0C934D, + 0x3FEDC4E2, 0x70000000, 0x3E166124, 0x19461C64, + 0x3FEDD3C8, 0x9C000000, 0xBE1B2ED6, 0x405624C8, + 0x3FEDE2B6, 0x3C000000, 0xBE273A7F, 0x62171501, + 0x3FEDF1AB, 0x54000000, 0xBE26022B, 0xE36E1450, + 0x3FEE00A7, 0xE8000000, 0xBE1C341E, 0x2E07AE15, + 0x3FEE0FAB, 0xFC000000, 0xBDFC7EAE, 0x18D0E701, + 0x3FEE1EB7, 0x94000000, 0x3E06B34F, 0xECD1FF8B, + 0x3FEE2DCA, 0xB4000000, 0x3E1394A3, 0x6813A649, + 0x3FEE3CE5, 0x60000000, 0x3E045496, 0xC1754D14, + 0x3FEE4C07, 0x9C000000, 0xBE180FFF, 0xF5C6087C, + 0x3FEE5B31, 0x68000000, 0x3E22FBCD, 0xADD9A300, + 0x3FEE6A62, 0xCC000000, 0x3E2EC7C7, 0xAF0289E5, + 0x3FEE799B, 0xCC000000, 0x3E242182, 0x3FB3EDD4, + 0x3FEE88DC, 0x6C000000, 0xBE201304, 0x04E39885, + 0x3FEE9824, 0xAC000000, 0xBE20D352, 0xE6831D31, + 0x3FEEA774, 0x90000000, 0x3E1E032D, 0x618DFCEB, + 0x3FEEB6CC, 0x20000000, 0x3E1956A3, 0xF9BB457E, + 0x3FEEC62B, 0x60000000, 0xBE2A77E0, 0x50845DB2, + 0x3FEED592, 0x4C000000, 0x3E2714F7, 0x47C43858, + 0x3FEEE500, 0xF0000000, 0x3E2EED96, 0x71813A66, + 0x3FEEF477, 0x50000000, 0xBE04CDBE, 0x4FB4AA34, + 0x3FEF03F5, 0x6C000000, 0xBE2774A2, 0x86EB4FF5, + 0x3FEF137B, 0x48000000, 0xBE29DD95, 0xAD43B2D2, + 0x3FEF2308, 0xE8000000, 0xBE1CADB0, 0xAC16E506, + 0x3FEF329E, 0x50000000, 0x3E12AC33, 0x58745C7B, + 0x3FEF423B, 0x88000000, 0xBE248118, 0x6EC2D854, + 0x3FEF51E0, 0x8C000000, 0x3E26986B, 0x304ACE08, + 0x3FEF618D, 0x68000000, 0x3E126D81, 0x3B09354E, + 0x3FEF7142, 0x1C000000, 0x3DF06AAE, 0x773C23B3, + 0x3FEF80FE, 0xAC000000, 0xBDA105B6, 0xD82EF423, + 0x3FEF90C3, 0x1C000000, 0x3DECDEED, 0x465499B8, + 0x3FEFA08F, 0x70000000, 0x3E0AEFD4, 0xE2EF03AE, + 0x3FEFB063, 0xAC000000, 0x3E1BD4C0, 0x0567B2E7, + 0x3FEFC03F, 0xD4000000, 0x3E26AA22, 0x4F97FCBF, + 0x3FEFD023, 0xF0000000, 0xBE2F9420, 0x5E4E88D1, + 0x3FEFE00F, 0xFC000000, 0xBE254004, 0x438E52E2, + 0x3FEFF004, 0x00000000, 0xBE1552AA, 0xEEE93EFC, + 0x3FF00000, 0x00000000, 0x00000000, 0x00000000, + 0x3FF00802, 0x00000000, 0x3E155800, 0x4449F507, + 0x3FF01008, 0x04000000, 0xBE354AA8, 0x882D75D6, + 0x3FF01812, 0x08000000, 0x3E303610, 0x3740DE56, + 0x3FF02020, 0x14000000, 0x3E360044, 0x5B0C3264, + 0x3FF02832, 0x28000000, 0x3E3C4C26, 0x0197EDC3, + 0x3FF03048, 0x48000000, 0x3E0B103B, 0x5046CA09, + 0x3FF03862, 0x74000000, 0xBE34659C, 0xF9A62624, + 0x3FF04080, 0xAC000000, 0xBE254438, 0xDD0A8F37, + 0x3FF048A2, 0xF4000000, 0x3DF256C2, 0x97AFB6E2, + 0x3FF050C9, 0x50000000, 0xBE3085DF, 0x923D25E1, + 0x3FF058F3, 0xC0000000, 0xBE3F0A93, 0x5EA3B091, + 0x3FF06122, 0x44000000, 0xBE237DE4, 0x5D63534C, + 0x3FF06954, 0xE0000000, 0x3E301719, 0xFF0C58B7, + 0x3FF0718B, 0x98000000, 0x3E2E8410, 0x9DF7B665, + 0x3FF079C6, 0x6C000000, 0x3E349CB9, 0x3B127222, + 0x3FF08205, 0x60000000, 0x3DF127EC, 0x98E0BD08, + 0x3FF08A48, 0x74000000, 0xBE24C1B6, 0x706CC41F, + 0x3FF0928F, 0xA8000000, 0x3E334EF9, 0x093044EF, + 0x3FF09ADB, 0x04000000, 0xBE1304B1, 0x56BC6C83, + 0x3FF0A32A, 0x84000000, 0x3E2D383E, 0xB028B984, + 0x3FF0AB7E, 0x30000000, 0xBE315B1E, 0x64E7A202, + 0x3FF0B3D6, 0x04000000, 0xBE0AC1E6, 0xC678291E, + 0x3FF0BC32, 0x04000000, 0x3E3A0418, 0x2F12FFE2, + 0x3FF0C492, 0x38000000, 0xBE37D617, 0x43D6D302, + 0x3FF0CCF6, 0x98000000, 0x3E2133F2, 0x152CC8FA, + 0x3FF0D55F, 0x2C000000, 0x3E3CE5D1, 0xE966E6B7, + 0x3FF0DDCB, 0xF8000000, 0x3E1ABF24, 0x7BCACA64, + 0x3FF0E63C, 0xFC000000, 0xBE3854F6, 0x2E8CDBED, + 0x3FF0EEB2, 0x38000000, 0xBE3E6463, 0x0C32156B, + 0x3FF0F72B, 0xAC000000, 0x3E365671, 0xB69772CC, + 0x3FF0FFA9, 0x64000000, 0xBE383E9A, 0x02B1201A, + 0x3FF1082B, 0x58000000, 0xBE205962, 0x50549CC0, + 0x3FF110B1, 0x90000000, 0xBE376BFE, 0xFFDACA72, + 0x3FF1193C, 0x08000000, 0x3E3C1C59, 0x5C43E2F3, + 0x3FF121CA, 0xCC000000, 0xBE26D374, 0xF7067C8B, + 0x3FF12A5D, 0xD4000000, 0x3E343CCC, 0x4DDAFE1D, + 0x3FF132F5, 0x28000000, 0x3E3D5C16, 0x58EBCB7F, + 0x3FF13B90, 0xCC000000, 0xBE2B5D12, 0xB66E8B53, + 0x3FF14430, 0xBC000000, 0xBE24E919, 0xB326B482, + 0x3FF14CD4, 0xFC000000, 0x3E23139A, 0xC8AABD43, + 0x3FF1557D, 0x90000000, 0x3E30DD8B, 0x16743B55, + 0x3FF15E2A, 0x7C000000, 0xBE31D701, 0x35904C50, + 0x3FF166DB, 0xBC000000, 0x3E107F42, 0x30E0CA83, + 0x3FF16F91, 0x58000000, 0xBE24F1F2, 0xDA1B7123, + 0x3FF1784B, 0x50000000, 0xBE3ACAF2, 0x0DC79E23, + 0x3FF18109, 0xA4000000, 0xBE23DC79, 0x609374EE, + 0x3FF189CC, 0x58000000, 0x3E262CF7, 0x3A40C3B7, + 0x3FF19293, 0x70000000, 0x3E1D3833, 0x5A24F463, + 0x3FF19B5E, 0xEC000000, 0x3E2BA9AD, 0x8A2E4440, + 0x3FF1A42E, 0xD0000000, 0x3DFD8CBC, 0x61C41828, + 0x3FF1AD03, 0x1C000000, 0x3E1A65E6, 0x5A4DDF0D, + 0x3FF1B5DB, 0xD4000000, 0xBDE2FDBB, 0x9F828DB5, + 0x3FF1BEB8, 0xF8000000, 0x3E2F4EE8, 0xB79B700F, + 0x3FF1C79A, 0x8C000000, 0x3E3ACC35, 0x0DE1D7E8, + 0x3FF1D080, 0x94000000, 0x3E11729E, 0xFF9E20A0, + 0x3FF1D96B, 0x10000000, 0xBE300F18, 0x6C2EA70B, + 0x3FF1E25A, 0x00000000, 0x3DF32E02, 0xCE425A35, + 0x3FF1EB4D, 0x68000000, 0x3E3BDE56, 0x9A322D12, + 0x3FF1F445, 0x50000000, 0xBE3C3F0D, 0xBA737AEF, + 0x3FF1FD41, 0xB0000000, 0xBE0A2DD0, 0xC896DB7A, + 0x3FF20642, 0x90000000, 0x3E2577B0, 0xF8B782F6, + 0x3FF20F47, 0xF4000000, 0xBE2C6DA3, 0x73607FC8, + 0x3FF21851, 0xD8000000, 0x3E35F7D1, 0xC8917348, + 0x3FF22160, 0x44000000, 0x3E3B6F5C, 0xCF9CED69, + 0x3FF22A73, 0x3C000000, 0xBE39967E, 0x85775C2E, + 0x3FF2338A, 0xB8000000, 0x3E3B3213, 0x497226D4, + 0x3FF23CA6, 0xC4000000, 0x3E3E2710, 0x30733227, + 0x3FF245C7, 0x60000000, 0x3E33B8A9, 0xAF215A72, + 0x3FF24EEC, 0x90000000, 0xBE3F96B2, 0x1365623F, + 0x3FF25816, 0x50000000, 0xBE37324F, 0x27DEE202, + 0x3FF26144, 0xA4000000, 0x3E318CD5, 0x4E484D87, + 0x3FF26A77, 0x94000000, 0xBDE3FD37, 0xA94519E8, + 0x3FF273AF, 0x1C000000, 0x3E37132F, 0xEE788C29, + 0x3FF27CEB, 0x44000000, 0xBE03DDB7, 0xE842E5C0, + 0x3FF2862C, 0x08000000, 0x3E37A3FB, 0xE17C9693, + 0x3FF28F71, 0x70000000, 0x3E24EABF, 0xAEB3D9A0, + 0x3FF298BB, 0x7C000000, 0xBE13C7B6, 0x853B0733, + 0x3FF2A20A, 0x2C000000, 0x3E2D2C80, 0xC7B588B5, + 0x3FF2AB5D, 0x88000000, 0xBE35B750, 0x708F3912, + 0x3FF2B4B5, 0x8C000000, 0xBE291A70, 0xD5FD9130, + 0x3FF2BE12, 0x3C000000, 0x3E2EE937, 0x0CCF9F73, + 0x3FF2C773, 0xA0000000, 0xBE3C3F0C, 0xD42CF76C, + 0x3FF2D0D9, 0xB0000000, 0x3E35DD54, 0x60763D61, + 0x3FF2DA44, 0x78000000, 0x3E26C418, 0xE7D6AA3B, + 0x3FF2E3B3, 0xF8000000, 0xBE3605C6, 0x6FB9B7A8, + 0x3FF2ED28, 0x2C000000, 0x3E3763D4, 0x24DCDDF5, + 0x3FF2F6A1, 0x20000000, 0xBE1A411E, 0xA8EC1AA8, + 0x3FF3001E, 0xD0000000, 0xBE23FCA1, 0x1FE8546F, + 0x3FF309A1, 0x40000000, 0xBE29DF0D, 0x3AAEE75E, + 0x3FF31328, 0x70000000, 0x3E36A5D6, 0x3C2C4206, + 0x3FF31CB4, 0x68000000, 0x3E1B7A3E, 0xB4C979B0, + 0x3FF32645, 0x28000000, 0xBE36157D, 0x706CD593, + 0x3FF32FDA, 0xB0000000, 0xBE39F357, 0x8DA4C646, + 0x3FF33975, 0x04000000, 0xBE3E64DE, 0xD575FE6F, + 0x3FF34314, 0x24000000, 0x3E07F9E3, 0x44D008E0, + 0x3FF34CB8, 0x18000000, 0xBE2E94F9, 0x5A563E77, + 0x3FF35660, 0xDC000000, 0x3E314DC2, 0x2475EF19, + 0x3FF3600E, 0x78000000, 0x3E26D623, 0xA33AC606, + 0x3FF369C0, 0xEC000000, 0x3E170F86, 0xC05B3160, + 0x3FF37378, 0x3C000000, 0xBE38DDFE, 0xDB0AE31A, + 0x3FF37D34, 0x64000000, 0x3E3662A9, 0x5706B570, + 0x3FF386F5, 0x70000000, 0xBE1625E4, 0x6770731E, + 0x3FF390BB, 0x5C000000, 0xBE1678F1, 0x62971091, + 0x3FF39A86, 0x2C000000, 0xBE061F7C, 0xD045CB0C, + 0x3FF3A455, 0xE4000000, 0xBE35CF51, 0x568B1CA2, + 0x3FF3AE2A, 0x84000000, 0xBE378185, 0x7FB61F58, + 0x3FF3B804, 0x0C000000, 0x3E3F77F4, 0x4FA133AF, + 0x3FF3C1E2, 0x88000000, 0xBE22F96A, 0xB00B73FE, + 0x3FF3CBC5, 0xF0000000, 0x3E351A64, 0x1EB4CE2F, + 0x3FF3D5AE, 0x50000000, 0xBE3D3516, 0xD3755639, + 0x3FF3DF9B, 0xA0000000, 0x3E1CD938, 0x43E8C10E, + 0x3FF3E98D, 0xEC000000, 0xBE35EE23, 0x455C8842, + 0x3FF3F385, 0x30000000, 0xBE29B282, 0x96C9F4ED, + 0x3FF3FD81, 0x70000000, 0x3E24A40E, 0x3168CC0B, + 0x3FF40782, 0xB0000000, 0x3E3784BC, 0x86C72839, + 0x3FF41188, 0xF4000000, 0x3E061F19, 0x0785D847, + 0x3FF41B94, 0x3C000000, 0xBE27AEF2, 0xE654A9C9, + 0x3FF425A4, 0x88000000, 0x3E33DFC3, 0xF9E4C1BA, + 0x3FF42FB9, 0xE0000000, 0x3E2455A8, 0x593D0C75, + 0x3FF439D4, 0x44000000, 0xBDE41D4E, 0x238B65D1, + 0x3FF443F3, 0xB4000000, 0x3E3BE616, 0x454CBECB, + 0x3FF44E18, 0x38000000, 0x3E207B3C, 0x931C5332, + 0x3FF45841, 0xD0000000, 0xBE330846, 0x7615DCC9, + 0x3FF46270, 0x7C000000, 0xBE2A8A7B, 0xE497F84E, + 0x3FF46CA4, 0x40000000, 0x3E020B50, 0xF737AF78, + 0x3FF476DD, 0x20000000, 0x3E116B19, 0xE34AFBD3, + 0x3FF4811B, 0x20000000, 0xBE3E15A7, 0x841EDB52, + 0x3FF48B5E, 0x3C000000, 0x3E0F40C3, 0x33B3DE1E, + 0x3FF495A6, 0x7C000000, 0x3E33607F, 0x92EFEE02, + 0x3FF49FF3, 0xE4000000, 0xBE1A2DB5, 0x14F7E168, + 0x3FF4AA46, 0x70000000, 0x3E3F59EC, 0x3EBA1C94, + 0x3FF4B49E, 0x2C000000, 0xBE31A539, 0x8B9AE885, + 0x3FF4BEFB, 0x10000000, 0x3E2FAC0B, 0xF13C8C95, + 0x3FF4C95D, 0x28000000, 0xBE32C0BB, 0xF8B74775, + 0x3FF4D3C4, 0x70000000, 0xBE2FC24E, 0x4F9474BB, + 0x3FF4DE30, 0xEC000000, 0x3E008F30, 0x09DA911F, + 0x3FF4E8A2, 0xA0000000, 0x3E2994C1, 0xBAF8D98B, + 0x3FF4F319, 0x90000000, 0xBE17C38C, 0x18648D0A, + 0x3FF4FD95, 0xBC000000, 0xBE288852, 0xF22F8698, + 0x3FF50817, 0x28000000, 0xBE3C3EC3, 0x30A2C153, + 0x3FF5129D, 0xD4000000, 0xBE27B606, 0x968492AA, + 0x3FF51D29, 0xC4000000, 0x3E2E0396, 0x61101629, + 0x3FF527BA, 0xFC000000, 0x3E3E876F, 0xDAEEAB38, + 0x3FF53251, 0x80000000, 0x3E29F59E, 0xED945B30, + 0x3FF53CED, 0x50000000, 0x3E12D7DA, 0x0B4AE3F1, + 0x3FF5478E, 0x70000000, 0xBE2FAFB8, 0x5FB946D0, + 0x3FF55234, 0xE0000000, 0xBE18A8B3, 0x87D80C66, + 0x3FF55CE0, 0xA4000000, 0x3E28B18F, 0x764CF85C, + 0x3FF56791, 0xC0000000, 0x3E326017, 0x2BDBC6F4, + 0x3FF57248, 0x38000000, 0xBE229F98, 0x53D523FE, + 0x3FF57D04, 0x0C000000, 0xBE3BDD08, 0x4D9B8720, + 0x3FF587C5, 0x3C000000, 0x3E169EBC, 0x09D8749E, + 0x3FF5928B, 0xD0000000, 0x3E190C8C, 0x339C2080, + 0x3FF59D57, 0xC8000000, 0x3E310FA4, 0xDE75E9CA, + 0x3FF5A829, 0x28000000, 0x3E313D18, 0x1097F186, + 0x3FF5B2FF, 0xF4000000, 0xBE2BDE04, 0xD51C23F6, + 0x3FF5BDDC, 0x28000000, 0x3E3EE67E, 0x8938C386, + 0x3FF5C8BD, 0xD0000000, 0x3E0973B8, 0x47DF6575, + 0x3FF5D3A4, 0xE8000000, 0x3E24DF02, 0x1DB97781, + 0x3FF5DE91, 0x78000000, 0xBE3FBA00, 0xAC4AECDC, + 0x3FF5E983, 0x7C000000, 0xBE2F37AF, 0x939F646A, + 0x3FF5F47A, 0xFC000000, 0xBE396DEF, 0x58A6EEE9, + 0x3FF5FF77, 0xF8000000, 0xBE315248, 0xE3613C7B, + 0x3FF60A7A, 0x74000000, 0xBE26A9E2, 0xF1553706, + 0x3FF61582, 0x74000000, 0xBE3B6BF6, 0xAE4D7CB6, + 0x3FF6208F, 0xF8000000, 0xBE35775B, 0x9EB5EBA5, + 0x3FF62BA3, 0x04000000, 0xBE2A821B, 0xC1E43506, + 0x3FF636BB, 0x9C000000, 0xBE367CDA, 0x7B2D8CF4, + 0x3FF641D9, 0xC0000000, 0xBE13218B, 0x3E907A1D, + 0x3FF64CFD, 0x74000000, 0x3E3454EE, 0x7BF5DFE4, + 0x3FF65826, 0xC0000000, 0xBE3E960F, 0x6366C5FD, + 0x3FF66355, 0x9C000000, 0x3E2E378F, 0x8B43C17E, + 0x3FF66E8A, 0x14000000, 0x3E244BE0, 0xA4306535, + 0x3FF679C4, 0x28000000, 0xBDE4B6C1, 0x8DF63D6E, + 0x3FF68503, 0xD8000000, 0x3E3BA122, 0xE6A239CF, + 0x3FF69049, 0x2C000000, 0x3E27F286, 0x59FB5F30, + 0x3FF69B94, 0x24000000, 0xBE044041, 0x971D3970 } }; + +static const union { + int4 i[2048]; + double x[1024]; +} fine = { .i = { + 0x3FF00000, 0x00000000, 0x00000000, 0x00000000, + 0x3FF00004, 0x00000000, 0x3DA00001, 0x55556AAB, + 0x3FF00008, 0x00000000, 0x3DC00002, 0xAAAB0000, + 0x3FF0000C, 0x00000000, 0x3DD20004, 0x8000D800, + 0x3FF00010, 0x00000000, 0x3DE00005, 0x5556AAAB, + 0x3FF00014, 0x00000000, 0x3DE9000A, 0x6AADEC01, + 0x3FF00018, 0x00000000, 0x3DF20009, 0x00036001, + 0x3FF0001C, 0x00000000, 0x3DF8800E, 0x4AB0EB58, + 0x3FF00020, 0x00000000, 0x3E00000A, 0xAAB00002, + 0x3FF00024, 0x00000000, 0x3E04400F, 0x30088B04, + 0x3FF00028, 0x00000000, 0x3E090014, 0xD5625AB1, + 0x3FF0002C, 0x00000000, 0x3E0E401B, 0xBABDBB0A, + 0x3FF00030, 0x00000000, 0x3E120012, 0x000D8008, + 0x3FF00034, 0x00000000, 0x3E152016, 0xE2BD42E1, + 0x3FF00038, 0x00000000, 0x3E18801C, 0x956E5812, + 0x3FF0003C, 0x00000000, 0x3E1C2023, 0x2820F599, + 0x3FF00040, 0x00000000, 0x3E200015, 0x556AAABC, + 0x3FF00044, 0x00000000, 0x3E221019, 0x96C5DAD7, + 0x3FF00048, 0x00000000, 0x3E24401E, 0x60222C1F, + 0x3FF0004C, 0x00000000, 0x3E269023, 0xB97FC193, + 0x3FF00050, 0x00000000, 0x3E290029, 0xAADEC034, + 0x3FF00054, 0x00000000, 0x3E2B9030, 0x3C3F4F02, + 0x3FF00058, 0x00000000, 0x3E2E4037, 0x75A196FF, + 0x3FF0005C, 0x00000000, 0x3E30881F, 0xAF82E194, + 0x3FF00060, 0x00000000, 0x3E320024, 0x00360041, + 0x3FF00064, 0x00000000, 0x3E338828, 0xB0EA3F05, + 0x3FF00068, 0x00000000, 0x3E35202D, 0xC59FB661, + 0x3FF0006C, 0x00000000, 0x3E36C833, 0x42567FD5, + 0x3FF00070, 0x00000000, 0x3E388039, 0x2B0EB5E1, + 0x3FF00074, 0x00000000, 0x3E3A483F, 0x83C87407, + 0x3FF00078, 0x00000000, 0x3E3C2046, 0x5083D6C6, + 0x3FF0007C, 0x00000000, 0x3E3E084D, 0x9540FB9E, + 0x3FF00080, 0x04000000, 0xBE3FFFAA, 0xA9FFFEEF, + 0x3FF00084, 0x04000000, 0xBE3DF7A2, 0x693EF962, + 0x3FF00088, 0x04000000, 0xBE3BDF99, 0xA47BD339, + 0x3FF0008C, 0x04000000, 0xBE39B790, 0x57B66AF5, + 0x3FF00090, 0x04000000, 0xBE377F86, 0x7EEE9E14, + 0x3FF00094, 0x04000000, 0xBE35377C, 0x16244916, + 0x3FF00098, 0x04000000, 0xBE32DF71, 0x1957477B, + 0x3FF0009C, 0x04000000, 0xBE307765, 0x848773C2, + 0x3FF000A0, 0x04000000, 0xBE2BFEB2, 0xA7694ED3, + 0x3FF000A4, 0x04000000, 0xBE26EE99, 0x05BD75E2, + 0x3FF000A8, 0x04000000, 0xBE21BE7E, 0x1C0B0BB1, + 0x3FF000AC, 0x04000000, 0xBE18DCC3, 0xC4A37A79, + 0x3FF000B0, 0x04000000, 0xBE0BF911, 0x4244D60F, + 0x3FF000B4, 0x04000000, 0xBDE6E255, 0xEC91D848, + 0x3FF000B8, 0x04000000, 0x3E0107EB, 0xEC1B8F0C, + 0x3FF000BC, 0x04000000, 0x3E142439, 0x89BE52AA, + 0x3FF000C0, 0x04000000, 0x3E200240, 0x06C01033, + 0x3FF000C4, 0x04000000, 0x3E261264, 0xC8A9F760, + 0x3FF000C8, 0x04000000, 0x3E2C428B, 0x129D3FDE, + 0x3FF000CC, 0x04000000, 0x3E314959, 0x764D2658, + 0x3FF000D0, 0x04000000, 0x3E34816E, 0x2F50C16C, + 0x3FF000D4, 0x04000000, 0x3E37C983, 0xB859A4AB, + 0x3FF000D8, 0x04000000, 0x3E3B219A, 0x15680499, + 0x3FF000DC, 0x04000000, 0x3E3E89B1, 0x4A7C16B5, + 0x3FF000E0, 0x08000000, 0xBE3DFE36, 0xA469EE7E, + 0x3FF000E4, 0x08000000, 0xBE3A761D, 0xB349D37F, + 0x3FF000E8, 0x08000000, 0xBE36DE03, 0xDE235FCD, + 0x3FF000EC, 0x08000000, 0xBE3335E9, 0x20F659E6, + 0x3FF000F0, 0x08000000, 0xBE2EFB9A, 0xEF850E8F, + 0x3FF000F4, 0x08000000, 0xBE276B61, 0xBD0F58E2, + 0x3FF000F8, 0x08000000, 0xBE1F764D, 0x45163381, + 0x3FF000FC, 0x08000000, 0xBE0FABA6, 0x5FDF589A, + 0x3FF00100, 0x08000000, 0x3D8555AA, 0xABBBBE94, + 0x3FF00104, 0x08000000, 0x3E102B2C, 0xDABB690B, + 0x3FF00108, 0x08000000, 0x3E2045D9, 0x7820FBA0, + 0x3FF0010C, 0x08000000, 0x3E28961E, 0x92F54742, + 0x3FF00110, 0x08000000, 0x3E308332, 0xE2ED8E39, + 0x3FF00114, 0x08000000, 0x3E34CB57, 0x8C698119, + 0x3FF00118, 0x08000000, 0x3E39237D, 0x49EEC0C4, + 0x3FF0011C, 0x08000000, 0x3E3D8BA4, 0x1F7D92BC, + 0x3FF00120, 0x0C000000, 0xBE3DFC33, 0xEEE9C27D, + 0x3FF00124, 0x0C000000, 0xBE39740A, 0xDD46F763, + 0x3FF00128, 0x0C000000, 0xBE34DBE0, 0xA799C375, + 0x3FF0012C, 0x0C000000, 0xBE3033B5, 0x49E1DD2F, + 0x3FF00130, 0x0C000000, 0xBE26F711, 0x803DF41F, + 0x3FF00134, 0x0C000000, 0xBE1ACD6C, 0x19433A4C, + 0x3FF00138, 0x0C000000, 0xBDFDB2C1, 0x8770E36F, + 0x3FF0013C, 0x0C000000, 0x3E086820, 0x6B74A43E, + 0x3FF00140, 0x0C000000, 0x3E200A6A, 0xDEC0D058, + 0x3FF00144, 0x0C000000, 0x3E2A1AD0, 0x22BD7872, + 0x3FF00148, 0x0C000000, 0x3E32259B, 0xF769E132, + 0x3FF0014C, 0x0C000000, 0x3E374DD1, 0x2582289A, + 0x3FF00150, 0x0C000000, 0x3E3C8607, 0x9FA7E4F4, + 0x3FF00154, 0x10000000, 0xBE3E31C0, 0x9624963C, + 0x3FF00158, 0x10000000, 0xBE38D987, 0x77E2F472, + 0x3FF0015C, 0x10000000, 0xBE33714D, 0x0192E02C, + 0x3FF00160, 0x10000000, 0xBE2BF222, 0x5E6805CB, + 0x3FF00164, 0x10000000, 0xBE20E1A7, 0xF98C0A34, + 0x3FF00168, 0x10000000, 0xBE06C4AB, 0x32447238, + 0x3FF0016C, 0x10000000, 0x3E067D54, 0xC225D8C1, + 0x3FF00170, 0x10000000, 0x3E210FD8, 0x05C4630F, + 0x3FF00174, 0x10000000, 0x3E2CA05D, 0xBB206115, + 0x3FF00178, 0x10000000, 0x3E342873, 0x2C4F14A6, + 0x3FF0017C, 0x10000000, 0x3E3A10B8, 0xF31F3B5E, + 0x3FF00180, 0x14000000, 0xBE3FF6FF, 0xC9FEFCC9, + 0x3FF00184, 0x14000000, 0xBE39EEB7, 0x070B344A, + 0x3FF00188, 0x14000000, 0xBE33D66C, 0xC0050AA2, + 0x3FF0018C, 0x14000000, 0xBE2B5C41, 0xE1D83C97, + 0x3FF00190, 0x14000000, 0xBE1DD74E, 0x57003305, + 0x3FF00194, 0x14000000, 0xBDF2D84A, 0xA80727F1, + 0x3FF00198, 0x14000000, 0x3E14AB2F, 0x534C5401, + 0x3FF0019C, 0x14000000, 0x3E27263B, 0xD875DE83, + 0x3FF001A0, 0x14000000, 0x3E320B71, 0x9FB782CA, + 0x3FF001A4, 0x14000000, 0x3E3893C6, 0xF349371F, + 0x3FF001A8, 0x14000000, 0x3E3F2C1D, 0xEAF074C6, + 0x3FF001AC, 0x18000000, 0xBE3A2B89, 0x75525ABC, + 0x3FF001B0, 0x18000000, 0xBE33732F, 0x297ECCE2, + 0x3FF001B4, 0x18000000, 0xBE2955A6, 0x5B28EC49, + 0x3FF001B8, 0x18000000, 0xBE1749D5, 0xF64BA7FD, + 0x3FF001BC, 0x18000000, 0x3DF15E9E, 0xA8645141, + 0x3FF001C0, 0x18000000, 0x3E201C96, 0x1D6F0B37, + 0x3FF001C4, 0x18000000, 0x3E2E2D5B, 0xE6028E39, + 0x3FF001C8, 0x18000000, 0x3E362F12, 0x9B63FA1E, + 0x3FF001CC, 0x18000000, 0x3E3D5779, 0x0BE01026, + 0x3FF001D0, 0x1C000000, 0xBE3B701E, 0xB78A0445, + 0x3FF001D4, 0x1C000000, 0xBE3427B4, 0xAAD9CF9D, + 0x3FF001D8, 0x1C000000, 0xBE299E91, 0x941DBAB5, + 0x3FF001DC, 0x1C000000, 0xBE159B6C, 0x44A2DFDD, + 0x3FF001E0, 0x1C000000, 0x3E008CA4, 0x1EC8B89C, + 0x3FF001E4, 0x1C000000, 0x3E23340B, 0xF1EE0E9A, + 0x3FF001E8, 0x1C000000, 0x3E313279, 0x5231913C, + 0x3FF001EC, 0x1C000000, 0x3E38DAEE, 0x93892E68, + 0x3FF001F0, 0x20000000, 0xBE3F6C9A, 0x3F01A6A8, + 0x3FF001F4, 0x20000000, 0xBE37A421, 0x216E726C, + 0x3FF001F8, 0x20000000, 0xBE2F974C, 0x1F7970B9, + 0x3FF001FC, 0x20000000, 0xBE1F8CA4, 0x17AFEBC8, + 0x3FF00200, 0x20000000, 0x3DB55600, 0x04445B06, + 0x3FF00204, 0x20000000, 0x3E203BAE, 0x0C290A26, + 0x3FF00208, 0x20000000, 0x3E30365A, 0x104547BD, + 0x3FF0020C, 0x20000000, 0x3E385EDF, 0x22970DE3, + 0x3FF00210, 0x24000000, 0xBE3F6899, 0xBEF5A5F4, + 0x3FF00214, 0x24000000, 0xBE372010, 0x90605040, + 0x3FF00218, 0x24000000, 0xBE2D8F0A, 0x9B50D8EE, + 0x3FF0021C, 0x24000000, 0xBE197BDF, 0xCB35D444, + 0x3FF00220, 0x24000000, 0x3E00CCBC, 0x2188E3D5, + 0x3FF00224, 0x24000000, 0x3E254452, 0x36A79F6A, + 0x3FF00228, 0x24000000, 0x3E333ABC, 0xD69B2D28, + 0x3FF0022C, 0x24000000, 0x3E3BE352, 0xBA07BE5B, + 0x3FF00230, 0x28000000, 0xBE3B6415, 0x3665F227, + 0x3FF00234, 0x28000000, 0xBE329B7A, 0xF6AD58D5, + 0x3FF00238, 0x28000000, 0xBE2385BD, 0x059BD24A, + 0x3FF0023C, 0x28000000, 0xBDEB47FA, 0xD8E2B1B4, + 0x3FF00240, 0x28000000, 0x3E203CC2, 0x22CF60F6, + 0x3FF00244, 0x28000000, 0x3E312704, 0x39BEF87F, + 0x3FF00248, 0x28000000, 0x3E3A3FA9, 0xA63F5309, + 0x3FF0024C, 0x2C000000, 0xBE3C97AE, 0xA516AE5E, + 0x3FF00250, 0x2C000000, 0xBE335F04, 0xA442792A, + 0x3FF00254, 0x2C000000, 0xBE242CB0, 0xA686F3A2, + 0x3FF00258, 0x2C000000, 0xBDE7B535, 0xC3237903, + 0x3FF0025C, 0x2C000000, 0x3E21560E, 0x9E7A6CF7, + 0x3FF00260, 0x2C000000, 0x3E3223BA, 0xA8C01385, + 0x3FF00264, 0x2C000000, 0x3E3BAC70, 0x627012DF, + 0x3FF00268, 0x30000000, 0xBE3ABAD7, 0x7FB232EA, + 0x3FF0026C, 0x30000000, 0xBE31121C, 0xF9A6244B, + 0x3FF00270, 0x30000000, 0xBE1D6580, 0x1DAC9AE4, + 0x3FF00274, 0x30000000, 0x3E037AFA, 0xD7FB0AC3, + 0x3FF00278, 0x30000000, 0x3E289042, 0x633420EB, + 0x3FF0027C, 0x30000000, 0x3E3630E5, 0x8065842A, + 0x3FF00280, 0x34000000, 0xBE3FD653, 0xB49DA4FF, + 0x3FF00284, 0x34000000, 0xBE35CD8A, 0x696ECB76, + 0x3FF00288, 0x34000000, 0xBE27697D, 0x341A9D63, + 0x3FF0028C, 0x34000000, 0xBDF8BF04, 0x2788D238, + 0x3FF00290, 0x34000000, 0x3E2159C1, 0x42A03782, + 0x3FF00294, 0x34000000, 0x3E32F5B4, 0x154D4F89, + 0x3FF00298, 0x34000000, 0x3E3D4E8A, 0x1D7FB2C1, + 0x3FF0029C, 0x38000000, 0xBE38489D, 0x42181508, + 0x3FF002A0, 0x38000000, 0xBE2B9F84, 0x0AF2C28C, + 0x3FF002A4, 0x38000000, 0xBE0A3721, 0x451C5357, + 0x3FF002A8, 0x38000000, 0x3E1D47F1, 0x61A8605E, + 0x3FF002AC, 0x38000000, 0x3E31FADF, 0x81B02FCF, + 0x3FF002B0, 0x38000000, 0x3E3CB3C5, 0x572F674A, + 0x3FF002B4, 0x3C000000, 0xBE388352, 0x231795EA, + 0x3FF002B8, 0x3C000000, 0xBE2B54CD, 0xD248367A, + 0x3FF002BC, 0x3C000000, 0xBE060BC7, 0xB7ABD90D, + 0x3FF002C0, 0x3C000000, 0x3E206EEF, 0x6EE9F1EF, + 0x3FF002C4, 0x3C000000, 0x3E33406B, 0x261BF09E, + 0x3FF002C8, 0x3C000000, 0x3E3E5961, 0x59001C60, + 0x3FF002CC, 0x40000000, 0xBE367DA5, 0xABDDD232, + 0x3FF002D0, 0x40000000, 0xBE268953, 0xC8FA5113, + 0x3FF002D4, 0x40000000, 0x3D9152CC, 0x8B33A701, + 0x3FF002D8, 0x40000000, 0x3E26BAAC, 0x3E058570, + 0x3FF002DC, 0x40000000, 0x3E36C65A, 0x63236E71, + 0x3FF002E0, 0x44000000, 0xBE3DC09E, 0x7C7A795C, + 0x3FF002E4, 0x44000000, 0xBE323794, 0x7BD63D1D, + 0x3FF002E8, 0x44000000, 0xBE1A7A1E, 0x5BBC9105, + 0x3FF002EC, 0x44000000, 0x3E142A20, 0xD8EE2B1B, + 0x3FF002F0, 0x44000000, 0x3E30C39A, 0xEFAA8A8D, + 0x3FF002F4, 0x44000000, 0x3E3C8CB0, 0x995E96A2, + 0x3FF002F8, 0x48000000, 0xBE379A36, 0xC8A79469, + 0x3FF002FC, 0x48000000, 0xBE276236, 0x64CE7203, + 0x3FF00300, 0x48000000, 0x3DD200D8, 0x0819DA68, + 0x3FF00304, 0x48000000, 0x3E28A249, 0xE5E018D4, + 0x3FF00308, 0x48000000, 0x3E386A49, 0x8A087692, + 0x3FF0030C, 0x4C000000, 0xBE3B6C8E, 0xD695988B, + 0x3FF00310, 0x4C000000, 0xBE2E66C8, 0x55D2BCBA, + 0x3FF00314, 0x4C000000, 0xBE0751B3, 0x7790BA7A, + 0x3FF00318, 0x4C000000, 0x3E22DDF4, 0xC2A20261, + 0x3FF0031C, 0x4C000000, 0x3E35D82E, 0x49E0B0B5, + 0x3FF00320, 0x50000000, 0xBE3DAE9A, 0xB142422E, + 0x3FF00324, 0x50000000, 0xBE312560, 0x8C170FE6, + 0x3FF00328, 0x50000000, 0xBE12308D, 0x0A73BF77, + 0x3FF0032C, 0x50000000, 0x3E203A3A, 0x5E59CEFA, + 0x3FF00330, 0x50000000, 0x3E34D660, 0xCD4740BF, + 0x3FF00334, 0x54000000, 0xBE3E6058, 0x644D1883, + 0x3FF00338, 0x54000000, 0xBE31870E, 0x618F57B6, + 0x3FF0033C, 0x54000000, 0xBE127704, 0x99FABD0F, + 0x3FF00340, 0x54000000, 0x3E20B71E, 0xA1CB5ECF, + 0x3FF00344, 0x54000000, 0x3E3564E3, 0x089E93E1, + 0x3FF00348, 0x58000000, 0xBE3D81C5, 0xFB533142, + 0x3FF0034C, 0x58000000, 0xBE30586B, 0xB6EECE6C, + 0x3FF00350, 0x58000000, 0xBE08F871, 0x319B883E, + 0x3FF00354, 0x58000000, 0x3E2454A5, 0x75BF7503, + 0x3FF00358, 0x58000000, 0x3E3783B6, 0xF04B88C5, + 0x3FF0035C, 0x5C000000, 0xBE3B12E1, 0x81EF30A7, + 0x3FF00360, 0x5C000000, 0xBE2B32ED, 0x2F9F3657, + 0x3FF00364, 0x5C000000, 0xBDB0084D, 0x54DF31BC, + 0x3FF00368, 0x5C000000, 0x3E2B12D2, 0xC303B7B9, + 0x3FF0036C, 0x5C000000, 0x3E3B32DE, 0x78B56F97, + 0x3FF00370, 0x60000000, 0xBE3713A9, 0x03B9496C, + 0x3FF00374, 0x60000000, 0xBE22945A, 0x1F92E726, + 0x3FF00378, 0x60000000, 0x3E123D49, 0x621736DF, + 0x3FF0037C, 0x60000000, 0x3E3278D5, 0x3935580D, + 0x3FF00380, 0x64000000, 0xBE3F8DA4, 0x69B9F5FB, + 0x3FF00384, 0x64000000, 0xBE31841A, 0x8C473CC8, + 0x3FF00388, 0x64000000, 0xBE0B5469, 0x538CDE07, + 0x3FF0038C, 0x64000000, 0x3E257E07, 0x7F8F9D65, + 0x3FF00390, 0x64000000, 0x3E38F898, 0x3665E52B, + 0x3FF00394, 0x68000000, 0xBE38BDCF, 0xC29674BD, + 0x3FF00398, 0x68000000, 0xBE24C868, 0x4E58B4D9, + 0x3FF0039C, 0x68000000, 0x3E1015AC, 0x329466D7, + 0x3FF003A0, 0x68000000, 0x3E327F0D, 0xDCDECE44, + 0x3FF003A4, 0x6C000000, 0xBE3EF74B, 0xB27E5528, + 0x3FF003A8, 0x6C000000, 0xBE305DA1, 0x9D7167F2, + 0x3FF003AC, 0x6C000000, 0xBDFB3F3D, 0xFF980820, + 0x3FF003B0, 0x6C000000, 0x3E2A0B7B, 0x13D49789, + 0x3FF003B4, 0x6C000000, 0x3E3BCF72, 0xA43AE87C, + 0x3FF003B8, 0x70000000, 0xBE3556D4, 0x8D06BDC0, + 0x3FF003BC, 0x70000000, 0xBE19B460, 0x1766E54D, + 0x3FF003C0, 0x70000000, 0x3E211950, 0x7B85C8BA, + 0x3FF003C4, 0x70000000, 0x3E37966C, 0x41D00AED, + 0x3FF003C8, 0x74000000, 0xBE394FCB, 0xF5B15507, + 0x3FF003CC, 0x74000000, 0xBE244C00, 0xC98093C4, + 0x3FF003D0, 0x74000000, 0x3E144F3B, 0xE2907BDF, + 0x3FF003D4, 0x74000000, 0x3E345DA2, 0x267CD924, + 0x3FF003D8, 0x78000000, 0xBE3C4886, 0xD73526C0, + 0x3FF003DC, 0x78000000, 0xBE29BD57, 0xF8E1D62E, + 0x3FF003E0, 0x78000000, 0x3E04D995, 0xD65415E1, + 0x3FF003E4, 0x78000000, 0x3E322515, 0x527E1A58, + 0x3FF003E8, 0x7C000000, 0xBE3E4104, 0x31552BA5, + 0x3FF003EC, 0x7C000000, 0xBE2D2E33, 0x995CAB3B, + 0x3FF003F0, 0x7C000000, 0x3DF22D48, 0x473970DC, + 0x3FF003F4, 0x7C000000, 0x3E30ECC6, 0xC61195FC, + 0x3FF003F8, 0x80000000, 0xBE3F3943, 0x03D35C34, + 0x3FF003FC, 0x80000000, 0xBE2E9E91, 0xAA7483C7, + 0x3FF00400, 0x80000000, 0x3DE556AA, 0xBBBC71CE, + 0x3FF00404, 0x80000000, 0x3E30B4B7, 0x817613C1, + 0x3FF00408, 0x84000000, 0xBE3F3142, 0x4E70B0AC, + 0x3FF0040C, 0x84000000, 0xBE2E0E70, 0x2BAAD02F, + 0x3FF00410, 0x84000000, 0x3DF32D62, 0xF48F01F2, + 0x3FF00414, 0x84000000, 0x3E317CE8, 0x84EB5B98, + 0x3FF00418, 0x88000000, 0xBE3E2901, 0x10ED210B, + 0x3FF0041C, 0x88000000, 0xBE2B7DCD, 0x1C7F0051, + 0x3FF00420, 0x88000000, 0x3E05D9C0, 0x87AA2706, + 0x3FF00424, 0x88000000, 0x3E33455A, 0xD0B235B3, + 0x3FF00428, 0x8C000000, 0xBE3C207E, 0x4B07A510, + 0x3FF0042C, 0x8C000000, 0xBE26ECA6, 0x7C6E838B, + 0x3FF00430, 0x8C000000, 0x3E150F6F, 0xEC91A8D5, + 0x3FF00434, 0x8C000000, 0x3E360E0F, 0x650C6A83, + 0x3FF00438, 0x90000000, 0xBE3917B8, 0xFC7E3439, + 0x3FF0043C, 0x90000000, 0xBE205AFA, 0x4AF4C8B6, + 0x3FF00440, 0x90000000, 0x3E219985, 0xDC31D181, + 0x3FF00444, 0x90000000, 0x3E39D707, 0x423CC2BE, + 0x3FF00448, 0x94000000, 0xBE350EB0, 0x250DC5BF, + 0x3FF0044C, 0x94000000, 0xBE0F231A, 0x1E2CF893, + 0x3FF00450, 0x94000000, 0x3E2AABDB, 0xD42C92D4, + 0x3FF00454, 0x94000000, 0x3E3EA043, 0x6887075B, + 0x3FF00458, 0x98000000, 0xBE300562, 0xC472509B, + 0x3FF0045C, 0x98000000, 0x3DF64FB6, 0x72B572E0, + 0x3FF00460, 0x98000000, 0x3E32DF5D, 0xEF61155C, + 0x3FF00464, 0x9C000000, 0xBE3B963B, 0x27CFFE6A, + 0x3FF00468, 0x9C000000, 0xBE23F79F, 0xB4CD96FE, + 0x3FF0046C, 0x9C000000, 0x3E1EBA7F, 0x6E771F13, + 0x3FF00470, 0x9C000000, 0x3E396913, 0xFE3ED608, + 0x3FF00474, 0xA0000000, 0xBE34CC73, 0x6E82850F, + 0x3FF00478, 0xA0000000, 0xBE078FB3, 0x352966B7, + 0x3FF0047C, 0xA0000000, 0x3E2DF116, 0x33AFF8AE, + 0x3FF00480, 0xA4000000, 0xBE3F0CEE, 0xE909EADD, + 0x3FF00484, 0xA4000000, 0xBE2A04C8, 0xD6938597, + 0x3FF00488, 0xA4000000, 0x3E1460AA, 0x5C6654D8, + 0x3FF0048C, 0xA4000000, 0x3E3742BE, 0x22213ECF, + 0x3FF00490, 0xA8000000, 0xBE3682A9, 0xC631A356, + 0x3FF00494, 0xA8000000, 0xBE10E034, 0x7777B644, + 0x3FF00498, 0xA8000000, 0x3E2C4528, 0x3E3B0991, + 0x3FF0049C, 0xAC000000, 0xBE3F72C6, 0x0B3E269F, + 0x3FF004A0, 0xAC000000, 0xBE29F037, 0x31DF923B, + 0x3FF004A4, 0xAC000000, 0x3E164A4D, 0xE82713DE, + 0x3FF004A8, 0xAC000000, 0x3E382D47, 0x31AFAC4B, + 0x3FF004AC, 0xB0000000, 0xBE352800, 0x6DFCE978, + 0x3FF004B0, 0xB0000000, 0xBE036A1B, 0x07D68D27, + 0x3FF004B4, 0xB0000000, 0x3E305D7E, 0x5CB71F6F, + 0x3FF004B8, 0xB4000000, 0xBE3CC7BB, 0x30E5E990, + 0x3FF004BC, 0xB4000000, 0xBE23B9E0, 0x0BA17DEA, + 0x3FF004C0, 0xB4000000, 0x3E223BBF, 0xC3EF9BD8, + 0x3FF004C4, 0xB4000000, 0x3E3C28B4, 0x8A74ECC0, + 0x3FF004C8, 0xB8000000, 0xBE30BC72, 0x085831CA, + 0x3FF004CC, 0xB8000000, 0x3E037361, 0x6C8D1FC8, + 0x3FF004D0, 0xB8000000, 0x3E35A94F, 0x3033A0B8, + 0x3FF004D4, 0xBC000000, 0xBE370BC8, 0xFC7107DE, + 0x3FF004D8, 0xBC000000, 0xBE0D86E2, 0xA2D908DA, + 0x3FF004DC, 0xBC000000, 0x3E2F742A, 0x58ED155E, + 0x3FF004E0, 0xC0000000, 0xBE3CCAF4, 0x75FACDD0, + 0x3FF004E4, 0xC0000000, 0xBE227FF2, 0x6F5BE5D3, + 0x3FF004E8, 0xC0000000, 0x3E24B60D, 0xD6BCA827, + 0x3FF004EC, 0xC0000000, 0x3E3E060B, 0xF72B40D6, + 0x3FF004F0, 0xC4000000, 0xBE2C7DD4, 0x208BE3E3, + 0x3FF004F4, 0xC4000000, 0x3E163093, 0x642FDDB8, + 0x3FF004F8, 0xC4000000, 0x3E396738, 0xB72239A5, + 0x3FF004FC, 0xC8000000, 0xBE32ADAE, 0x7201ED9B, + 0x3FF00500, 0xC8000000, 0x3DF4D6F6, 0x1A0C05F3, + 0x3FF00504, 0xC8000000, 0x3E355892, 0x360B8346, + 0x3FF00508, 0xCC000000, 0xBE368C45, 0xF0C06435, + 0x3FF0050C, 0xCC000000, 0xBE0308C8, 0x760DA2F6, + 0x3FF00510, 0xCC000000, 0x3E31DA18, 0xE008D57B, + 0x3FF00514, 0xD0000000, 0xBE39DAB0, 0x205F82F4, + 0x3FF00518, 0xD0000000, 0xBE15FDD0, 0x2FE5E3E3, + 0x3FF0051C, 0xD0000000, 0x3E2DD79A, 0x42787241, + 0x3FF00520, 0xD4000000, 0xBE3C98EC, 0x94BD25F4, + 0x3FF00524, 0xD4000000, 0xBE201B42, 0x53C89D03, + 0x3FF00528, 0xD4000000, 0x3E291B5E, 0xCB901057, + 0x3FF0052C, 0xD8000000, 0xBE3EC6FA, 0xE1B6D837, + 0x3FF00530, 0xD8000000, 0xBE24173F, 0xF8BF49E7, + 0x3FF00534, 0xD8000000, 0x3E257F80, 0x339DDB57, + 0x3FF00538, 0xD8000000, 0x3E3F9B25, 0x64D62C5C, + 0x3FF0053C, 0xDC000000, 0xBE26F2E0, 0x2E913659, + 0x3FF00540, 0xDC000000, 0x3E2303FF, 0x52E7CB93, + 0x3FF00544, 0xDC000000, 0x3E3E8D74, 0xAB0CFEF5, + 0x3FF00548, 0xE0000000, 0xBE28AE22, 0x1CF7FDE6, + 0x3FF0054C, 0xE0000000, 0x3E21A8DD, 0x01B47B93, + 0x3FF00550, 0xE0000000, 0x3E3E0FF3, 0x5D1107E2, + 0x3FF00554, 0xE4000000, 0xBE294904, 0xEBAC99E1, + 0x3FF00558, 0xE4000000, 0x3E216E1A, 0x184B2814, + 0x3FF0055C, 0xE4000000, 0x3E3E22A1, 0xE706008B, + 0x3FF00560, 0xE8000000, 0xBE28C387, 0xC267616A, + 0x3FF00564, 0xE8000000, 0x3E2253B7, 0x6EF3B008, + 0x3FF00568, 0xE8000000, 0x3E3EC580, 0xB50FF371, + 0x3FF0056C, 0xEC000000, 0xBE271DA9, 0xC8E0096B, + 0x3FF00570, 0xEC000000, 0x3E2459B5, 0xDDF69498, + 0x3FF00574, 0xEC000000, 0x3E3FF890, 0x33533C31, + 0x3FF00578, 0xF0000000, 0xBE24576A, 0x26CDA497, + 0x3FF0057C, 0xF0000000, 0x3E278016, 0x3D9CF923, + 0x3FF00580, 0xF4000000, 0xBE3E442F, 0x320B787B, + 0x3FF00584, 0xF4000000, 0xBE2070C8, 0x03E6A36B, + 0x3FF00588, 0xF4000000, 0x3E2BC6D9, 0x6630A33F, + 0x3FF0058C, 0xF8000000, 0xBE3BF0BD, 0x0EE72CBF, + 0x3FF00590, 0xF8000000, 0xBE16D385, 0x0FC1A853, + 0x3FF00594, 0xF8000000, 0x3E309700, 0x17FDFD5D, + 0x3FF00598, 0xFC000000, 0xBE390D18, 0xF71A91AC, + 0x3FF0059C, 0xFC000000, 0xBE050963, 0x69C58B86, + 0x3FF005A0, 0xFC000000, 0x3E33DAC5, 0xB9A504CD, + 0x3FF005A5, 0x00000000, 0xBE359942, 0x7E800734, + 0x3FF005A9, 0x00000000, 0x3DF02BAE, 0xE59934CD, + 0x3FF005AD, 0x00000000, 0x3E37AEBE, 0x04333E0E, + 0x3FF005B1, 0x04000000, 0xBE319539, 0x38F19C2F, + 0x3FF005B5, 0x04000000, 0x3E14DB54, 0xEBB1C157, + 0x3FF005B9, 0x04000000, 0x3E3C12E9, 0x63CED05D, + 0x3FF005BD, 0x08000000, 0xBE2A01F9, 0x74921CAF, + 0x3FF005C1, 0x08000000, 0x3E23F645, 0xC94C85F2, + 0x3FF005C5, 0x0C000000, 0xBE3EF8B7, 0xBB61CBEE, + 0x3FF005C9, 0x0C000000, 0xBE1F7232, 0x597F2931, + 0x3FF005CD, 0x0C000000, 0x3E2E9F48, 0xAF5B7345, + 0x3FF005D1, 0x10000000, 0xBE397424, 0xED37CD5F, + 0x3FF005D5, 0x10000000, 0xBE013F43, 0x08775C6B, + 0x3FF005D9, 0x10000000, 0x3E35345A, 0x0029D3DB, + 0x3FF005DD, 0x14000000, 0xBE335F5D, 0xC58C1962, + 0x3FF005E1, 0x14000000, 0x3E1073C1, 0x47430E04, + 0x3FF005E5, 0x14000000, 0x3E3BA944, 0x4A41E248, + 0x3FF005E9, 0x18000000, 0xBE2974C3, 0xB06E888E, + 0x3FF005ED, 0x18000000, 0x3E25E3FB, 0xDCCD9333, + 0x3FF005F1, 0x1C000000, 0xBE3D519C, 0x5DE27951, + 0x3FF005F5, 0x1C000000, 0xBE1614C2, 0xE4464502, + 0x3FF005F9, 0x1C000000, 0x3E325740, 0xE0DAFE93, + 0x3FF005FD, 0x20000000, 0xBE35BC47, 0x8C1B4C10, + 0x3FF00601, 0x20000000, 0x3E0201B0, 0x20686CE9, + 0x3FF00605, 0x20000000, 0x3E3A4CB9, 0x95558B63, + 0x3FF00609, 0x24000000, 0xBE2B2D79, 0xA880A3EB, + 0x3FF0060D, 0x24000000, 0x3E252BA5, 0x9699EEB7, + 0x3FF00611, 0x28000000, 0xBE3D2D97, 0x880115E1, + 0x3FF00615, 0x28000000, 0xBE1383EF, 0x28A3D788, + 0x3FF00619, 0x28000000, 0x3E337BA6, 0x08D6DC23, + 0x3FF0061D, 0x2C000000, 0xBE3417B2, 0x0B001A08, + 0x3FF00621, 0x2C000000, 0x3E1193EF, 0xF94EB99A, + 0x3FF00625, 0x2C000000, 0x3E3CF1B0, 0x28D3BD3B, + 0x3FF00629, 0x30000000, 0xBE24E32B, 0x0EFCC982, + 0x3FF0062D, 0x30000000, 0x3E2C7655, 0xE2BDA47F, + 0x3FF00631, 0x34000000, 0xBE39080E, 0x689312F8, + 0x3FF00635, 0x34000000, 0xBDCDA0C8, 0xA9444DB4, + 0x3FF00639, 0x34000000, 0x3E38A191, 0x7B21FE23, + 0x3FF0063D, 0x38000000, 0xBE2CE32A, 0x7E67E1E1, + 0x3FF00641, 0x38000000, 0x3E251694, 0x875A71F0, + 0x3FF00645, 0x3C000000, 0xBE3C67CF, 0xF838F455, + 0x3FF00649, 0x3C000000, 0xBE0A571F, 0x77274052, + 0x3FF0064D, 0x3C000000, 0x3E35E20E, 0x63AAEFA8, + 0x3FF00651, 0x40000000, 0xBE30E0F8, 0xFC87DA70, + 0x3FF00655, 0x40000000, 0x3E20D80B, 0xE9089AFD, + 0x3FF00659, 0x44000000, 0xBE3E36F4, 0xC52F03BD, + 0x3FF0065D, 0x44000000, 0xBE1327A4, 0x9680E14E, + 0x3FF00661, 0x44000000, 0x3E34B328, 0xD732468D, + 0x3FF00665, 0x48000000, 0xBE31BFBE, 0xCAB5EF4A, + 0x3FF00669, 0x48000000, 0x3E1F757F, 0xE2A2FBE1, + 0x3FF0066D, 0x4C000000, 0xBE3E757A, 0xDAB014DA, + 0x3FF00671, 0x4C000000, 0xBE12E13D, 0x02FB3FBB, + 0x3FF00675, 0x4C000000, 0x3E3514E2, 0xCA7E298D, + 0x3FF00679, 0x50000000, 0xBE310DE4, 0xB4F78B94, + 0x3FF0067D, 0x50000000, 0x3E21BEB4, 0x89C35D05, + 0x3FF00681, 0x54000000, 0xBE3D2360, 0x43F4895C, + 0x3FF00685, 0x54000000, 0xBE08B0A2, 0x5BC49ADF, + 0x3FF00689, 0x54000000, 0x3E37073E, 0x32573159, + 0x3FF0068D, 0x58000000, 0xBE2D96D1, 0x8D0732D2, + 0x3FF00691, 0x58000000, 0x3E26E3ED, 0x9BF15E67, + 0x3FF00695, 0x5C000000, 0xBE3A40A3, 0x0C3250FB, + 0x3FF00699, 0x5C000000, 0x3DBCC9AE, 0xFD0AE214, + 0x3FF0069D, 0x5C000000, 0x3E3A8A3D, 0x038868A1, + 0x3FF006A1, 0x60000000, 0xBE25F092, 0x151D21CE, + 0x3FF006A5, 0x60000000, 0x3E2F2A6F, 0x11738C43, + 0x3FF006A9, 0x64000000, 0xBE35CD41, 0x3E9CE96D, + 0x3FF006AD, 0x64000000, 0x3E138132, 0x8DBC2918, + 0x3FF006B1, 0x64000000, 0x3E3F9DE1, 0x32DF4C13, + 0x3FF006B5, 0x68000000, 0xBE16520E, 0x3129E0B2, + 0x3FF006B9, 0x68000000, 0x3E35491E, 0x69F36A61, + 0x3FF006BD, 0x6C000000, 0xBE2F9271, 0xCCCABCD4, + 0x3FF006C1, 0x6C000000, 0x3E2668ED, 0x0D59B899, + 0x3FF006C5, 0x70000000, 0xBE39BDD3, 0x4AD435A0, + 0x3FF006C9, 0x70000000, 0x3DF5FE9A, 0x9191CABB, + 0x3FF006CD, 0x70000000, 0x3E3C8DAD, 0x6676850B, + 0x3FF006D1, 0x74000000, 0xBE206910, 0x1D74934A, + 0x3FF006D5, 0x74000000, 0x3E331949, 0x4D886478, + 0x3FF006D9, 0x78000000, 0xBE3188DE, 0x80BFBBC2, + 0x3FF006DD, 0x78000000, 0x3E23CA01, 0x14DE1719, + 0x3FF006E1, 0x7C000000, 0xBE3A9D19, 0x8CE98EC0, + 0x3FF006E5, 0x7C000000, 0x3DEE1A67, 0xA705A6E7, + 0x3FF006E9, 0x7C000000, 0x3E3C8EC6, 0xECD5F851, + 0x3FF006ED, 0x80000000, 0xBE1F0CF9, 0xE839CE4D, + 0x3FF006F1, 0x80000000, 0x3E33FAC3, 0x0C8CA46A, + 0x3FF006F5, 0x84000000, 0xBE303734, 0x7B5703D8, + 0x3FF006F9, 0x84000000, 0x3E274DB5, 0xE490A112, + 0x3FF006FD, 0x88000000, 0xBE386B0E, 0xA693A093, + 0x3FF00701, 0x88000000, 0x3E0C9875, 0xF0B73DAA, + 0x3FF00705, 0x88000000, 0x3E3FA133, 0x2449A944, + 0x3FF00709, 0x8C000000, 0xBE110285, 0xBFE66C14, + 0x3FF0070D, 0x8C000000, 0x3E37ED91, 0x054EDCBD, + 0x3FF00711, 0x90000000, 0xBE27A86A, 0xEFB65924, + 0x3FF00715, 0x90000000, 0x3E307A0B, 0x1C8A0CF1, + 0x3FF00719, 0x94000000, 0xBE3327AD, 0x397FB1D6, + 0x3FF0071D, 0x94000000, 0x3E228D43, 0x1412B9FB, + 0x3FF00721, 0x98000000, 0xBE3A3B08, 0x94D8FFB0, + 0x3FF00725, 0x98000000, 0x3E029AA3, 0x6ED80040, + 0x3FF00729, 0x98000000, 0x3E3EF1B8, 0x9627250A, + 0x3FF0072D, 0x9C000000, 0xBE117F70, 0x5FCB1B09, + 0x3FF00731, 0x9C000000, 0x3E385E96, 0x678F0789, + 0x3FF00735, 0xA0000000, 0xBE25A5DF, 0xCEA3485B, + 0x3FF00739, 0xA0000000, 0x3E320B90, 0xFF6D0303, + 0x3FF0073D, 0xA4000000, 0xBE3105E6, 0xE03334FF, + 0x3FF00741, 0xA4000000, 0x3E27F150, 0xFB9F056D, + 0x3FF00745, 0xA8000000, 0xBE36F8C0, 0xE28905F4, + 0x3FF00749, 0xA8000000, 0x3E189774, 0x0B1407AA, + 0x3FF0074D, 0xAC000000, 0xBE3CAB7D, 0xCE4493C4, + 0x3FF00751, 0xAC000000, 0x3DE265D5, 0xCB817D78, + 0x3FF00755, 0xAC000000, 0x3E3DE1E2, 0x7CA8B4E3, + 0x3FF00759, 0xB0000000, 0xBE12FD89, 0x7D730FC6, + 0x3FF0075D, 0xB0000000, 0x3E38AF60, 0x1E4D7759, + 0x3FF00761, 0xB4000000, 0xBE23A3AC, 0x0CAD84A2, + 0x3FF00765, 0xB4000000, 0x3E33BCFB, 0x36B866FD, + 0x3FF00769, 0xB8000000, 0xBE2D4858, 0x4D0667A1, + 0x3FF0076D, 0xB8000000, 0x3E2E1567, 0xCBF08E6A, + 0x3FF00771, 0xBC000000, 0xBE333664, 0x9FD34D05, + 0x3FF00775, 0xBC000000, 0x3E253114, 0x9837D6E0, + 0x3FF00779, 0xC0000000, 0xBE37887F, 0x5238327D, + 0x3FF0077D, 0xC0000000, 0x3E1999FA, 0x24C8DC90, + 0x3FF00781, 0xC4000000, 0xBE3B9A7C, 0x1DA2F8BE, + 0x3FF00785, 0xC4000000, 0x3E03A485, 0xEA50EE6A, + 0x3FF00789, 0xC8000000, 0xBE3F6C5A, 0xE204A449, + 0x3FF0078D, 0xC8000000, 0xBDF3D3EF, 0x78D5D0F3, + 0x3FF00791, 0xC8000000, 0x3E3D01E4, 0x80B1D66C, + 0x3FF00795, 0xCC000000, 0xBE12BBC1, 0xD5149796, + 0x3FF00799, 0xCC000000, 0x3E39B042, 0x2A8F92F0, + 0x3FF0079D, 0xD0000000, 0xBE1F820E, 0x6F386487, + 0x3FF007A1, 0xD0000000, 0x3E369EBE, 0x3BA3BCDA, + 0x3FF007A5, 0xD4000000, 0xBE25A3F0, 0x96320652, + 0x3FF007A9, 0xD4000000, 0x3E33CD58, 0xD3FD8FCA, + 0x3FF007AD, 0xD8000000, 0xBE2B069C, 0xC62D40B1, + 0x3FF007B1, 0xD8000000, 0x3E313C12, 0x13AC5766, + 0x3FF007B5, 0xDC000000, 0xBE2FE90B, 0x876F3A0B, + 0x3FF007B9, 0xDC000000, 0x3E2DD5D4, 0x357EDEB8, + 0x3FF007BD, 0xE0000000, 0xBE32259E, 0x4CEC957E, + 0x3FF007C1, 0xE0000000, 0x3E29B3C2, 0x128C86C6, + 0x3FF007C5, 0xE4000000, 0xBE341697, 0xDEA61608, + 0x3FF007C9, 0xE4000000, 0x3E2611ED, 0xFEA09E70, + 0x3FF007CD, 0xE8000000, 0xBE35C772, 0x58D49AE3, + 0x3FF007D1, 0xE8000000, 0x3E22F058, 0x39DA3D42, + 0x3FF007D5, 0xEC000000, 0xBE37382D, 0x9B689043, + 0x3FF007D9, 0xEC000000, 0x3E204F01, 0x04589AD6, + 0x3FF007DD, 0xF0000000, 0xBE3868C9, 0x86525259, + 0x3FF007E1, 0xF0000000, 0x3E1C5BD1, 0x3C761DAC, + 0x3FF007E5, 0xF4000000, 0xBE395945, 0xF9822D4C, + 0x3FF007E9, 0xF4000000, 0x3E191A1E, 0x8F4221F9, + 0x3FF007ED, 0xF8000000, 0xBE3A09A2, 0xD4E85D3A, + 0x3FF007F1, 0xF8000000, 0x3E16D8EA, 0x81547225, + 0x3FF007F5, 0xFC000000, 0xBE3A79DF, 0xF8750E3B, + 0x3FF007F9, 0xFC000000, 0x3E159835, 0x92EC7DE3, + 0x3FF007FE, 0x00000000, 0xBE3AA9FD, 0x44185C5D } }; + +#else +#ifdef LITTLE_ENDI + +static const union { + int i[1424]; + double x[712]; +} coar = { .i = { + 0xC8000000, 0x3FE69A59, 0x6079C9F7, 0x3DF22D4D, + 0xC8000000, 0x3FE6A5A9, 0x25AF6823, 0x3E19882D, + 0x74000000, 0x3FE6B0FF, 0x31DABF59, 0xBE221476, + 0xC8000000, 0x3FE6BC5A, 0x99A2DC0A, 0x3E2312AC, + 0xD0000000, 0x3FE6C7BB, 0xCE9F9355, 0xBE265926, + 0x84000000, 0x3FE6D322, 0x2D298DED, 0x3E2F2C26, + 0xF4000000, 0x3FE6DE8E, 0x1E748D2F, 0xBE2EC28E, + 0x14000000, 0x3FE6EA01, 0xC68CB7E5, 0x3E2D8C6D, + 0xF4000000, 0x3FE6F578, 0x419FE2F0, 0x3DEE1A9E, + 0x90000000, 0x3FE700F6, 0xDEAEAE34, 0xBDFF1AFD, + 0xEC000000, 0x3FE70C79, 0x558B7122, 0xBE0730FE, + 0x0C000000, 0x3FE71803, 0x2D280C3B, 0xBE25CB85, + 0xF0000000, 0x3FE72391, 0x337B7B54, 0xBE06F2CE, + 0x9C000000, 0x3FE72F26, 0x45C02B72, 0x3E289BCA, + 0x18000000, 0x3FE73AC1, 0x5039F1CA, 0xBE18DEA6, + 0x60000000, 0x3FE74661, 0x86CE0538, 0xBE09D090, + 0x78000000, 0x3FE75207, 0xCFCE5DDB, 0x3E290E79, + 0x68000000, 0x3FE75DB3, 0xB249A17C, 0x3DD61DF0, + 0x2C000000, 0x3FE76965, 0xE13445F7, 0x3E2F22F7, + 0xD0000000, 0x3FE7751C, 0x874E75CE, 0xBE2CD454, + 0x4C000000, 0x3FE780DA, 0xDF43E3BC, 0xBE0159CE, + 0xA8000000, 0x3FE78C9D, 0x699A1332, 0x3E279291, + 0xEC000000, 0x3FE79866, 0x2DD98C6C, 0xBE2A0BCD, + 0x10000000, 0x3FE7A436, 0x15AC979E, 0x3E25F375, + 0x20000000, 0x3FE7B00B, 0x2FEAFCF6, 0x3E26CCF5, + 0x1C000000, 0x3FE7BBE6, 0x53ADAD67, 0x3E27D4F4, + 0x08000000, 0x3FE7C7C7, 0x7FBD9566, 0x3E10EEC7, + 0xE4000000, 0x3FE7D3AD, 0x9A831D86, 0x3E2837F0, + 0xB8000000, 0x3FE7DF9A, 0x5CB4C35B, 0xBE129BE0, + 0x80000000, 0x3FE7EB8D, 0x0234F04D, 0x3E23990A, + 0x44000000, 0x3FE7F786, 0x64D5C842, 0x3E2EB807, + 0x08000000, 0x3FE80385, 0x02B4E9E8, 0x3E0FC86F, + 0xCC000000, 0x3FE80F89, 0x7B4274BF, 0xBDD7B5B3, + 0x94000000, 0x3FE81B94, 0xB899B00F, 0xBE16888B, + 0x60000000, 0x3FE827A5, 0x5E94D155, 0x3E288971, + 0x38000000, 0x3FE833BC, 0x099F3E5E, 0x3E2AEEB2, + 0x20000000, 0x3FE83FD9, 0x3FF60B7C, 0xBE23B922, + 0x14000000, 0x3FE84BFC, 0x2DBD8012, 0xBDF7D3B1, + 0x1C000000, 0x3FE85825, 0xA8872BEB, 0xBDF24BA3, + 0x38000000, 0x3FE86454, 0x01AA18A7, 0x3E2EFE04, + 0x70000000, 0x3FE87089, 0x944496A2, 0x3E21986C, + 0xC4000000, 0x3FE87CC4, 0xB71FFAFF, 0x3E096A8B, + 0x38000000, 0x3FE88906, 0xBC4C7AC5, 0xBE21CE0A, + 0xCC000000, 0x3FE8954D, 0xBAC02491, 0xBE076F45, + 0x84000000, 0x3FE8A19B, 0xD922B925, 0x3E2B4FA2, + 0x68000000, 0x3FE8ADEF, 0x641863AF, 0x3DF759DB, + 0x78000000, 0x3FE8BA49, 0xC6AB5E04, 0xBE2DB97C, + 0xB4000000, 0x3FE8C6A9, 0xE2156713, 0xBE25364C, + 0x20000000, 0x3FE8D310, 0x862BEFF7, 0x3E1BEB7C, + 0xC4000000, 0x3FE8DF7C, 0x1CEA33A5, 0xBDF4DD0C, + 0xA0000000, 0x3FE8EBEF, 0x51797D47, 0xBE2537DF, + 0xB4000000, 0x3FE8F868, 0xF0107B28, 0x3E0FB1C4, + 0x08000000, 0x3FE904E8, 0xE01B68BD, 0x3E0AD6A1, + 0x9C000000, 0x3FE9116D, 0x1F78D9D9, 0x3E292117, + 0x78000000, 0x3FE91DF9, 0x4F50E5CF, 0xBE1D75DA, + 0x98000000, 0x3FE92A8B, 0x74959E58, 0x3DE5102B, + 0x04000000, 0x3FE93724, 0xD2216C35, 0xBE01CA50, + 0xBC000000, 0x3FE943C2, 0xB0B05884, 0x3E225BFD, + 0xC8000000, 0x3FE95067, 0x60B7C5C1, 0xBE0F2183, + 0x24000000, 0x3FE95D13, 0xB5860441, 0x3E2FB47A, + 0xDC000000, 0x3FE969C4, 0xE2D4059E, 0xBE01FFD2, + 0xEC000000, 0x3FE9767C, 0x12BB6A8D, 0xBDE9ED72, + 0x58000000, 0x3FE9833B, 0x43BFFB24, 0x3E2B3815, + 0x28000000, 0x3FE99000, 0xEE9EAD1E, 0x3E03FA22, + 0x5C000000, 0x3FE99CCB, 0x377138F7, 0xBE213841, + 0xF4000000, 0x3FE9A99C, 0xDB636C94, 0x3E178105, + 0xF8000000, 0x3FE9B674, 0xF5720122, 0x3E1E5E7A, + 0x6C000000, 0x3FE9C353, 0xA2AC5AAE, 0xBE238BFF, + 0x4C000000, 0x3FE9D038, 0xF93BDBD8, 0x3E270893, + 0xA4000000, 0x3FE9DD23, 0x354B86CF, 0x3DF40420, + 0x74000000, 0x3FE9EA15, 0x88CB06B7, 0xBE2D76D3, + 0xBC000000, 0x3FE9F70D, 0x9ED0EC60, 0xBE251639, + 0x80000000, 0x3FEA040C, 0xE2DDE506, 0x3E1F06E9, + 0xC8000000, 0x3FEA1111, 0x8E6DB477, 0x3E014549, + 0x94000000, 0x3FEA1E1D, 0xF8716509, 0xBDF4BC17, + 0xE8000000, 0x3FEA2B2F, 0xDA723A49, 0xBE2107DB, + 0xC4000000, 0x3FEA3848, 0x986AA369, 0x3E1A932A, + 0x30000000, 0x3FEA4568, 0x41592CDB, 0x3E198092, + 0x30000000, 0x3FEA528E, 0x676BCAB8, 0xBE2E260F, + 0xC0000000, 0x3FEA5FBA, 0x2D5D5610, 0x3DE2E821, + 0xE8000000, 0x3FEA6CED, 0x7DA20167, 0x3E2F7046, + 0xB0000000, 0x3FEA7A27, 0xF9FAAD30, 0xBE1D2832, + 0x14000000, 0x3FEA8768, 0x43FA6C45, 0xBE23F788, + 0x18000000, 0x3FEA94AF, 0xAA082732, 0x3E011E27, + 0xC4000000, 0x3FEAA1FC, 0xC682F0BF, 0xBE20BACB, + 0x18000000, 0x3FEAAF51, 0x7BD08C78, 0xBE2DC7DD, + 0x14000000, 0x3FEABCAC, 0xA3B10F9A, 0x3E2271A2, + 0xC4000000, 0x3FEACA0D, 0x7966F94C, 0xBE15449C, + 0x24000000, 0x3FEAD776, 0x6FD8F3EE, 0x3DD06137, + 0x3C000000, 0x3FEAE4E5, 0x8C5A144A, 0xBE267CD1, + 0x0C000000, 0x3FEAF25B, 0xB59DA94B, 0xBE29E584, + 0x98000000, 0x3FEAFFD7, 0x7B52192F, 0xBE23DFCF, + 0xE4000000, 0x3FEB0D5A, 0x78A76B45, 0xBE1CF2FE, + 0xF4000000, 0x3FEB1AE4, 0x7EC80FF6, 0xBE23A561, + 0xC8000000, 0x3FEB2875, 0x932EED68, 0x3E22C4C9, + 0x68000000, 0x3FEB360D, 0xB5833C97, 0x3E2B085C, + 0xD8000000, 0x3FEB43AB, 0x93B9319A, 0xBE01F093, + 0x18000000, 0x3FEB5151, 0xFABCE670, 0xBE254F01, + 0x28000000, 0x3FEB5EFD, 0x627ABFB0, 0x3E2F24C2, + 0x14000000, 0x3FEB6CB0, 0xE6AC0B48, 0x3E1F1EEC, + 0xDC000000, 0x3FEB7A69, 0x127F9ABC, 0xBE1A8671, + 0x80000000, 0x3FEB882A, 0xC87C73B3, 0xBDCB0C28, + 0x08000000, 0x3FEB95F2, 0x7F2B5A97, 0xBE22E8DD, + 0x74000000, 0x3FEBA3C0, 0x2D22A9D5, 0xBE1B3645, + 0xC8000000, 0x3FEBB195, 0x428F8B88, 0x3E0ADACA, + 0x0C000000, 0x3FEBBF72, 0xCDF9F681, 0xBE2E9E07, + 0x3C000000, 0x3FEBCD55, 0x7FA54ACF, 0xBE08A127, + 0x60000000, 0x3FEBDB3F, 0x8225B385, 0x3E0E92CE, + 0x7C000000, 0x3FEBE930, 0x7BB09485, 0x3DF38C2A, + 0x94000000, 0x3FEBF728, 0xF681FA5F, 0xBE2DFD64, + 0xA4000000, 0x3FEC0527, 0xDCE88BD2, 0x3E2E384D, + 0xBC000000, 0x3FEC132D, 0xFE46A893, 0xBE20F111, + 0xD4000000, 0x3FEC213A, 0xB189BFDA, 0x3E193DA1, + 0xF8000000, 0x3FEC2F4E, 0x0E39FB00, 0xBE20E3A1, + 0x24000000, 0x3FEC3D6A, 0x30F0FAC5, 0x3E1DB044, + 0x64000000, 0x3FEC4B8C, 0x97446B17, 0xBE2BC12C, + 0xB4000000, 0x3FEC59B5, 0x963F4150, 0xBE282696, + 0x18000000, 0x3FEC67E6, 0x3049824B, 0x3E224D26, + 0x98000000, 0x3FEC761D, 0x87F84C7D, 0x3E2C5BA5, + 0x38000000, 0x3FEC845C, 0xC4852339, 0xBDE1D14D, + 0xF8000000, 0x3FEC92A1, 0x5588D9E1, 0xBE1A451E, + 0xDC000000, 0x3FECA0EE, 0x68BFF457, 0xBE1D3B96, + 0xE8000000, 0x3FECAF42, 0x4DADF774, 0xBE18B670, + 0x20000000, 0x3FECBD9E, 0x7FB1FC01, 0xBE1A1548, + 0x88000000, 0x3FECCC00, 0x78FC5AF0, 0xBE273F2E, + 0x20000000, 0x3FECDA6A, 0xA6F4A841, 0x3E1D218F, + 0xF0000000, 0x3FECE8DA, 0x4D002CA0, 0x3E2E0BA9, + 0xFC000000, 0x3FECF752, 0x065EF979, 0x3E20F4BB, + 0x48000000, 0x3FED05D2, 0x11793B33, 0xBE2ED3D5, + 0xD0000000, 0x3FED1458, 0x913341B3, 0x3E115E3C, + 0xA0000000, 0x3FED22E6, 0xB3546109, 0x3DE97C02, + 0xB8000000, 0x3FED317B, 0x1BF898EF, 0x3E087540, + 0x1C000000, 0x3FED4018, 0x346F9641, 0x3E209430, + 0xD0000000, 0x3FED4EBB, 0x88F4B20B, 0x3E2B6DF4, + 0xDC000000, 0x3FED5D66, 0x0CB26035, 0xBE2EC68F, + 0x38000000, 0x3FED6C19, 0x1F44D9C3, 0x3E2CA2C8, + 0xF4000000, 0x3FED7AD2, 0x41704EE0, 0x3E10E6F4, + 0x0C000000, 0x3FED8994, 0x25F8F0E2, 0x3E2F9273, + 0x88000000, 0x3FED985C, 0x318798DE, 0x3E2D041A, + 0x6C000000, 0x3FEDA72C, 0x9349CF58, 0xBE005680, + 0xB8000000, 0x3FEDB603, 0xCF0C934D, 0xBE10F665, + 0x70000000, 0x3FEDC4E2, 0x19461C64, 0x3E166124, + 0x9C000000, 0x3FEDD3C8, 0x405624C8, 0xBE1B2ED6, + 0x3C000000, 0x3FEDE2B6, 0x62171501, 0xBE273A7F, + 0x54000000, 0x3FEDF1AB, 0xE36E1450, 0xBE26022B, + 0xE8000000, 0x3FEE00A7, 0x2E07AE15, 0xBE1C341E, + 0xFC000000, 0x3FEE0FAB, 0x18D0E701, 0xBDFC7EAE, + 0x94000000, 0x3FEE1EB7, 0xECD1FF8B, 0x3E06B34F, + 0xB4000000, 0x3FEE2DCA, 0x6813A649, 0x3E1394A3, + 0x60000000, 0x3FEE3CE5, 0xC1754D14, 0x3E045496, + 0x9C000000, 0x3FEE4C07, 0xF5C6087C, 0xBE180FFF, + 0x68000000, 0x3FEE5B31, 0xADD9A300, 0x3E22FBCD, + 0xCC000000, 0x3FEE6A62, 0xAF0289E5, 0x3E2EC7C7, + 0xCC000000, 0x3FEE799B, 0x3FB3EDD4, 0x3E242182, + 0x6C000000, 0x3FEE88DC, 0x04E39885, 0xBE201304, + 0xAC000000, 0x3FEE9824, 0xE6831D31, 0xBE20D352, + 0x90000000, 0x3FEEA774, 0x618DFCEB, 0x3E1E032D, + 0x20000000, 0x3FEEB6CC, 0xF9BB457E, 0x3E1956A3, + 0x60000000, 0x3FEEC62B, 0x50845DB2, 0xBE2A77E0, + 0x4C000000, 0x3FEED592, 0x47C43858, 0x3E2714F7, + 0xF0000000, 0x3FEEE500, 0x71813A66, 0x3E2EED96, + 0x50000000, 0x3FEEF477, 0x4FB4AA34, 0xBE04CDBE, + 0x6C000000, 0x3FEF03F5, 0x86EB4FF5, 0xBE2774A2, + 0x48000000, 0x3FEF137B, 0xAD43B2D2, 0xBE29DD95, + 0xE8000000, 0x3FEF2308, 0xAC16E506, 0xBE1CADB0, + 0x50000000, 0x3FEF329E, 0x58745C7B, 0x3E12AC33, + 0x88000000, 0x3FEF423B, 0x6EC2D854, 0xBE248118, + 0x8C000000, 0x3FEF51E0, 0x304ACE08, 0x3E26986B, + 0x68000000, 0x3FEF618D, 0x3B09354E, 0x3E126D81, + 0x1C000000, 0x3FEF7142, 0x773C23B3, 0x3DF06AAE, + 0xAC000000, 0x3FEF80FE, 0xD82EF423, 0xBDA105B6, + 0x1C000000, 0x3FEF90C3, 0x465499B8, 0x3DECDEED, + 0x70000000, 0x3FEFA08F, 0xE2EF03AE, 0x3E0AEFD4, + 0xAC000000, 0x3FEFB063, 0x0567B2E7, 0x3E1BD4C0, + 0xD4000000, 0x3FEFC03F, 0x4F97FCBF, 0x3E26AA22, + 0xF0000000, 0x3FEFD023, 0x5E4E88D1, 0xBE2F9420, + 0xFC000000, 0x3FEFE00F, 0x438E52E2, 0xBE254004, + 0x00000000, 0x3FEFF004, 0xEEE93EFC, 0xBE1552AA, + 0x00000000, 0x3FF00000, 0x00000000, 0x00000000, + 0x00000000, 0x3FF00802, 0x4449F507, 0x3E155800, + 0x04000000, 0x3FF01008, 0x882D75D6, 0xBE354AA8, + 0x08000000, 0x3FF01812, 0x3740DE56, 0x3E303610, + 0x14000000, 0x3FF02020, 0x5B0C3264, 0x3E360044, + 0x28000000, 0x3FF02832, 0x0197EDC3, 0x3E3C4C26, + 0x48000000, 0x3FF03048, 0x5046CA09, 0x3E0B103B, + 0x74000000, 0x3FF03862, 0xF9A62624, 0xBE34659C, + 0xAC000000, 0x3FF04080, 0xDD0A8F37, 0xBE254438, + 0xF4000000, 0x3FF048A2, 0x97AFB6E2, 0x3DF256C2, + 0x50000000, 0x3FF050C9, 0x923D25E1, 0xBE3085DF, + 0xC0000000, 0x3FF058F3, 0x5EA3B091, 0xBE3F0A93, + 0x44000000, 0x3FF06122, 0x5D63534C, 0xBE237DE4, + 0xE0000000, 0x3FF06954, 0xFF0C58B7, 0x3E301719, + 0x98000000, 0x3FF0718B, 0x9DF7B665, 0x3E2E8410, + 0x6C000000, 0x3FF079C6, 0x3B127222, 0x3E349CB9, + 0x60000000, 0x3FF08205, 0x98E0BD08, 0x3DF127EC, + 0x74000000, 0x3FF08A48, 0x706CC41F, 0xBE24C1B6, + 0xA8000000, 0x3FF0928F, 0x093044EF, 0x3E334EF9, + 0x04000000, 0x3FF09ADB, 0x56BC6C83, 0xBE1304B1, + 0x84000000, 0x3FF0A32A, 0xB028B984, 0x3E2D383E, + 0x30000000, 0x3FF0AB7E, 0x64E7A202, 0xBE315B1E, + 0x04000000, 0x3FF0B3D6, 0xC678291E, 0xBE0AC1E6, + 0x04000000, 0x3FF0BC32, 0x2F12FFE2, 0x3E3A0418, + 0x38000000, 0x3FF0C492, 0x43D6D302, 0xBE37D617, + 0x98000000, 0x3FF0CCF6, 0x152CC8FA, 0x3E2133F2, + 0x2C000000, 0x3FF0D55F, 0xE966E6B7, 0x3E3CE5D1, + 0xF8000000, 0x3FF0DDCB, 0x7BCACA64, 0x3E1ABF24, + 0xFC000000, 0x3FF0E63C, 0x2E8CDBED, 0xBE3854F6, + 0x38000000, 0x3FF0EEB2, 0x0C32156B, 0xBE3E6463, + 0xAC000000, 0x3FF0F72B, 0xB69772CC, 0x3E365671, + 0x64000000, 0x3FF0FFA9, 0x02B1201A, 0xBE383E9A, + 0x58000000, 0x3FF1082B, 0x50549CC0, 0xBE205962, + 0x90000000, 0x3FF110B1, 0xFFDACA72, 0xBE376BFE, + 0x08000000, 0x3FF1193C, 0x5C43E2F3, 0x3E3C1C59, + 0xCC000000, 0x3FF121CA, 0xF7067C8B, 0xBE26D374, + 0xD4000000, 0x3FF12A5D, 0x4DDAFE1D, 0x3E343CCC, + 0x28000000, 0x3FF132F5, 0x58EBCB7F, 0x3E3D5C16, + 0xCC000000, 0x3FF13B90, 0xB66E8B53, 0xBE2B5D12, + 0xBC000000, 0x3FF14430, 0xB326B482, 0xBE24E919, + 0xFC000000, 0x3FF14CD4, 0xC8AABD43, 0x3E23139A, + 0x90000000, 0x3FF1557D, 0x16743B55, 0x3E30DD8B, + 0x7C000000, 0x3FF15E2A, 0x35904C50, 0xBE31D701, + 0xBC000000, 0x3FF166DB, 0x30E0CA83, 0x3E107F42, + 0x58000000, 0x3FF16F91, 0xDA1B7123, 0xBE24F1F2, + 0x50000000, 0x3FF1784B, 0x0DC79E23, 0xBE3ACAF2, + 0xA4000000, 0x3FF18109, 0x609374EE, 0xBE23DC79, + 0x58000000, 0x3FF189CC, 0x3A40C3B7, 0x3E262CF7, + 0x70000000, 0x3FF19293, 0x5A24F463, 0x3E1D3833, + 0xEC000000, 0x3FF19B5E, 0x8A2E4440, 0x3E2BA9AD, + 0xD0000000, 0x3FF1A42E, 0x61C41828, 0x3DFD8CBC, + 0x1C000000, 0x3FF1AD03, 0x5A4DDF0D, 0x3E1A65E6, + 0xD4000000, 0x3FF1B5DB, 0x9F828DB5, 0xBDE2FDBB, + 0xF8000000, 0x3FF1BEB8, 0xB79B700F, 0x3E2F4EE8, + 0x8C000000, 0x3FF1C79A, 0x0DE1D7E8, 0x3E3ACC35, + 0x94000000, 0x3FF1D080, 0xFF9E20A0, 0x3E11729E, + 0x10000000, 0x3FF1D96B, 0x6C2EA70B, 0xBE300F18, + 0x00000000, 0x3FF1E25A, 0xCE425A35, 0x3DF32E02, + 0x68000000, 0x3FF1EB4D, 0x9A322D12, 0x3E3BDE56, + 0x50000000, 0x3FF1F445, 0xBA737AEF, 0xBE3C3F0D, + 0xB0000000, 0x3FF1FD41, 0xC896DB7A, 0xBE0A2DD0, + 0x90000000, 0x3FF20642, 0xF8B782F6, 0x3E2577B0, + 0xF4000000, 0x3FF20F47, 0x73607FC8, 0xBE2C6DA3, + 0xD8000000, 0x3FF21851, 0xC8917348, 0x3E35F7D1, + 0x44000000, 0x3FF22160, 0xCF9CED69, 0x3E3B6F5C, + 0x3C000000, 0x3FF22A73, 0x85775C2E, 0xBE39967E, + 0xB8000000, 0x3FF2338A, 0x497226D4, 0x3E3B3213, + 0xC4000000, 0x3FF23CA6, 0x30733227, 0x3E3E2710, + 0x60000000, 0x3FF245C7, 0xAF215A72, 0x3E33B8A9, + 0x90000000, 0x3FF24EEC, 0x1365623F, 0xBE3F96B2, + 0x50000000, 0x3FF25816, 0x27DEE202, 0xBE37324F, + 0xA4000000, 0x3FF26144, 0x4E484D87, 0x3E318CD5, + 0x94000000, 0x3FF26A77, 0xA94519E8, 0xBDE3FD37, + 0x1C000000, 0x3FF273AF, 0xEE788C29, 0x3E37132F, + 0x44000000, 0x3FF27CEB, 0xE842E5C0, 0xBE03DDB7, + 0x08000000, 0x3FF2862C, 0xE17C9693, 0x3E37A3FB, + 0x70000000, 0x3FF28F71, 0xAEB3D9A0, 0x3E24EABF, + 0x7C000000, 0x3FF298BB, 0x853B0733, 0xBE13C7B6, + 0x2C000000, 0x3FF2A20A, 0xC7B588B5, 0x3E2D2C80, + 0x88000000, 0x3FF2AB5D, 0x708F3912, 0xBE35B750, + 0x8C000000, 0x3FF2B4B5, 0xD5FD9130, 0xBE291A70, + 0x3C000000, 0x3FF2BE12, 0x0CCF9F73, 0x3E2EE937, + 0xA0000000, 0x3FF2C773, 0xD42CF76C, 0xBE3C3F0C, + 0xB0000000, 0x3FF2D0D9, 0x60763D61, 0x3E35DD54, + 0x78000000, 0x3FF2DA44, 0xE7D6AA3B, 0x3E26C418, + 0xF8000000, 0x3FF2E3B3, 0x6FB9B7A8, 0xBE3605C6, + 0x2C000000, 0x3FF2ED28, 0x24DCDDF5, 0x3E3763D4, + 0x20000000, 0x3FF2F6A1, 0xA8EC1AA8, 0xBE1A411E, + 0xD0000000, 0x3FF3001E, 0x1FE8546F, 0xBE23FCA1, + 0x40000000, 0x3FF309A1, 0x3AAEE75E, 0xBE29DF0D, + 0x70000000, 0x3FF31328, 0x3C2C4206, 0x3E36A5D6, + 0x68000000, 0x3FF31CB4, 0xB4C979B0, 0x3E1B7A3E, + 0x28000000, 0x3FF32645, 0x706CD593, 0xBE36157D, + 0xB0000000, 0x3FF32FDA, 0x8DA4C646, 0xBE39F357, + 0x04000000, 0x3FF33975, 0xD575FE6F, 0xBE3E64DE, + 0x24000000, 0x3FF34314, 0x44D008E0, 0x3E07F9E3, + 0x18000000, 0x3FF34CB8, 0x5A563E77, 0xBE2E94F9, + 0xDC000000, 0x3FF35660, 0x2475EF19, 0x3E314DC2, + 0x78000000, 0x3FF3600E, 0xA33AC606, 0x3E26D623, + 0xEC000000, 0x3FF369C0, 0xC05B3160, 0x3E170F86, + 0x3C000000, 0x3FF37378, 0xDB0AE31A, 0xBE38DDFE, + 0x64000000, 0x3FF37D34, 0x5706B570, 0x3E3662A9, + 0x70000000, 0x3FF386F5, 0x6770731E, 0xBE1625E4, + 0x5C000000, 0x3FF390BB, 0x62971091, 0xBE1678F1, + 0x2C000000, 0x3FF39A86, 0xD045CB0C, 0xBE061F7C, + 0xE4000000, 0x3FF3A455, 0x568B1CA2, 0xBE35CF51, + 0x84000000, 0x3FF3AE2A, 0x7FB61F58, 0xBE378185, + 0x0C000000, 0x3FF3B804, 0x4FA133AF, 0x3E3F77F4, + 0x88000000, 0x3FF3C1E2, 0xB00B73FE, 0xBE22F96A, + 0xF0000000, 0x3FF3CBC5, 0x1EB4CE2F, 0x3E351A64, + 0x50000000, 0x3FF3D5AE, 0xD3755639, 0xBE3D3516, + 0xA0000000, 0x3FF3DF9B, 0x43E8C10E, 0x3E1CD938, + 0xEC000000, 0x3FF3E98D, 0x455C8842, 0xBE35EE23, + 0x30000000, 0x3FF3F385, 0x96C9F4ED, 0xBE29B282, + 0x70000000, 0x3FF3FD81, 0x3168CC0B, 0x3E24A40E, + 0xB0000000, 0x3FF40782, 0x86C72839, 0x3E3784BC, + 0xF4000000, 0x3FF41188, 0x0785D847, 0x3E061F19, + 0x3C000000, 0x3FF41B94, 0xE654A9C9, 0xBE27AEF2, + 0x88000000, 0x3FF425A4, 0xF9E4C1BA, 0x3E33DFC3, + 0xE0000000, 0x3FF42FB9, 0x593D0C75, 0x3E2455A8, + 0x44000000, 0x3FF439D4, 0x238B65D1, 0xBDE41D4E, + 0xB4000000, 0x3FF443F3, 0x454CBECB, 0x3E3BE616, + 0x38000000, 0x3FF44E18, 0x931C5332, 0x3E207B3C, + 0xD0000000, 0x3FF45841, 0x7615DCC9, 0xBE330846, + 0x7C000000, 0x3FF46270, 0xE497F84E, 0xBE2A8A7B, + 0x40000000, 0x3FF46CA4, 0xF737AF78, 0x3E020B50, + 0x20000000, 0x3FF476DD, 0xE34AFBD3, 0x3E116B19, + 0x20000000, 0x3FF4811B, 0x841EDB52, 0xBE3E15A7, + 0x3C000000, 0x3FF48B5E, 0x33B3DE1E, 0x3E0F40C3, + 0x7C000000, 0x3FF495A6, 0x92EFEE02, 0x3E33607F, + 0xE4000000, 0x3FF49FF3, 0x14F7E168, 0xBE1A2DB5, + 0x70000000, 0x3FF4AA46, 0x3EBA1C94, 0x3E3F59EC, + 0x2C000000, 0x3FF4B49E, 0x8B9AE885, 0xBE31A539, + 0x10000000, 0x3FF4BEFB, 0xF13C8C95, 0x3E2FAC0B, + 0x28000000, 0x3FF4C95D, 0xF8B74775, 0xBE32C0BB, + 0x70000000, 0x3FF4D3C4, 0x4F9474BB, 0xBE2FC24E, + 0xEC000000, 0x3FF4DE30, 0x09DA911F, 0x3E008F30, + 0xA0000000, 0x3FF4E8A2, 0xBAF8D98B, 0x3E2994C1, + 0x90000000, 0x3FF4F319, 0x18648D0A, 0xBE17C38C, + 0xBC000000, 0x3FF4FD95, 0xF22F8698, 0xBE288852, + 0x28000000, 0x3FF50817, 0x30A2C153, 0xBE3C3EC3, + 0xD4000000, 0x3FF5129D, 0x968492AA, 0xBE27B606, + 0xC4000000, 0x3FF51D29, 0x61101629, 0x3E2E0396, + 0xFC000000, 0x3FF527BA, 0xDAEEAB38, 0x3E3E876F, + 0x80000000, 0x3FF53251, 0xED945B30, 0x3E29F59E, + 0x50000000, 0x3FF53CED, 0x0B4AE3F1, 0x3E12D7DA, + 0x70000000, 0x3FF5478E, 0x5FB946D0, 0xBE2FAFB8, + 0xE0000000, 0x3FF55234, 0x87D80C66, 0xBE18A8B3, + 0xA4000000, 0x3FF55CE0, 0x764CF85C, 0x3E28B18F, + 0xC0000000, 0x3FF56791, 0x2BDBC6F4, 0x3E326017, + 0x38000000, 0x3FF57248, 0x53D523FE, 0xBE229F98, + 0x0C000000, 0x3FF57D04, 0x4D9B8720, 0xBE3BDD08, + 0x3C000000, 0x3FF587C5, 0x09D8749E, 0x3E169EBC, + 0xD0000000, 0x3FF5928B, 0x339C2080, 0x3E190C8C, + 0xC8000000, 0x3FF59D57, 0xDE75E9CA, 0x3E310FA4, + 0x28000000, 0x3FF5A829, 0x1097F186, 0x3E313D18, + 0xF4000000, 0x3FF5B2FF, 0xD51C23F6, 0xBE2BDE04, + 0x28000000, 0x3FF5BDDC, 0x8938C386, 0x3E3EE67E, + 0xD0000000, 0x3FF5C8BD, 0x47DF6575, 0x3E0973B8, + 0xE8000000, 0x3FF5D3A4, 0x1DB97781, 0x3E24DF02, + 0x78000000, 0x3FF5DE91, 0xAC4AECDC, 0xBE3FBA00, + 0x7C000000, 0x3FF5E983, 0x939F646A, 0xBE2F37AF, + 0xFC000000, 0x3FF5F47A, 0x58A6EEE9, 0xBE396DEF, + 0xF8000000, 0x3FF5FF77, 0xE3613C7B, 0xBE315248, + 0x74000000, 0x3FF60A7A, 0xF1553706, 0xBE26A9E2, + 0x74000000, 0x3FF61582, 0xAE4D7CB6, 0xBE3B6BF6, + 0xF8000000, 0x3FF6208F, 0x9EB5EBA5, 0xBE35775B, + 0x04000000, 0x3FF62BA3, 0xC1E43506, 0xBE2A821B, + 0x9C000000, 0x3FF636BB, 0x7B2D8CF4, 0xBE367CDA, + 0xC0000000, 0x3FF641D9, 0x3E907A1D, 0xBE13218B, + 0x74000000, 0x3FF64CFD, 0x7BF5DFE4, 0x3E3454EE, + 0xC0000000, 0x3FF65826, 0x6366C5FD, 0xBE3E960F, + 0x9C000000, 0x3FF66355, 0x8B43C17E, 0x3E2E378F, + 0x14000000, 0x3FF66E8A, 0xA4306535, 0x3E244BE0, + 0x28000000, 0x3FF679C4, 0x8DF63D6E, 0xBDE4B6C1, + 0xD8000000, 0x3FF68503, 0xE6A239CF, 0x3E3BA122, + 0x2C000000, 0x3FF69049, 0x59FB5F30, 0x3E27F286, + 0x24000000, 0x3FF69B94, 0x971D3970, 0xBE044041 } }; + +static const union { + int4 i[2048]; + double x[1024]; +} fine = { .i = { + 0x00000000, 0x3FF00000, 0x00000000, 0x00000000, + 0x00000000, 0x3FF00004, 0x55556AAB, 0x3DA00001, + 0x00000000, 0x3FF00008, 0xAAAB0000, 0x3DC00002, + 0x00000000, 0x3FF0000C, 0x8000D800, 0x3DD20004, + 0x00000000, 0x3FF00010, 0x5556AAAB, 0x3DE00005, + 0x00000000, 0x3FF00014, 0x6AADEC01, 0x3DE9000A, + 0x00000000, 0x3FF00018, 0x00036001, 0x3DF20009, + 0x00000000, 0x3FF0001C, 0x4AB0EB58, 0x3DF8800E, + 0x00000000, 0x3FF00020, 0xAAB00002, 0x3E00000A, + 0x00000000, 0x3FF00024, 0x30088B04, 0x3E04400F, + 0x00000000, 0x3FF00028, 0xD5625AB1, 0x3E090014, + 0x00000000, 0x3FF0002C, 0xBABDBB0A, 0x3E0E401B, + 0x00000000, 0x3FF00030, 0x000D8008, 0x3E120012, + 0x00000000, 0x3FF00034, 0xE2BD42E1, 0x3E152016, + 0x00000000, 0x3FF00038, 0x956E5812, 0x3E18801C, + 0x00000000, 0x3FF0003C, 0x2820F599, 0x3E1C2023, + 0x00000000, 0x3FF00040, 0x556AAABC, 0x3E200015, + 0x00000000, 0x3FF00044, 0x96C5DAD7, 0x3E221019, + 0x00000000, 0x3FF00048, 0x60222C1F, 0x3E24401E, + 0x00000000, 0x3FF0004C, 0xB97FC193, 0x3E269023, + 0x00000000, 0x3FF00050, 0xAADEC034, 0x3E290029, + 0x00000000, 0x3FF00054, 0x3C3F4F02, 0x3E2B9030, + 0x00000000, 0x3FF00058, 0x75A196FF, 0x3E2E4037, + 0x00000000, 0x3FF0005C, 0xAF82E194, 0x3E30881F, + 0x00000000, 0x3FF00060, 0x00360041, 0x3E320024, + 0x00000000, 0x3FF00064, 0xB0EA3F05, 0x3E338828, + 0x00000000, 0x3FF00068, 0xC59FB661, 0x3E35202D, + 0x00000000, 0x3FF0006C, 0x42567FD5, 0x3E36C833, + 0x00000000, 0x3FF00070, 0x2B0EB5E1, 0x3E388039, + 0x00000000, 0x3FF00074, 0x83C87407, 0x3E3A483F, + 0x00000000, 0x3FF00078, 0x5083D6C6, 0x3E3C2046, + 0x00000000, 0x3FF0007C, 0x9540FB9E, 0x3E3E084D, + 0x04000000, 0x3FF00080, 0xA9FFFEEF, 0xBE3FFFAA, + 0x04000000, 0x3FF00084, 0x693EF962, 0xBE3DF7A2, + 0x04000000, 0x3FF00088, 0xA47BD339, 0xBE3BDF99, + 0x04000000, 0x3FF0008C, 0x57B66AF5, 0xBE39B790, + 0x04000000, 0x3FF00090, 0x7EEE9E14, 0xBE377F86, + 0x04000000, 0x3FF00094, 0x16244916, 0xBE35377C, + 0x04000000, 0x3FF00098, 0x1957477B, 0xBE32DF71, + 0x04000000, 0x3FF0009C, 0x848773C2, 0xBE307765, + 0x04000000, 0x3FF000A0, 0xA7694ED3, 0xBE2BFEB2, + 0x04000000, 0x3FF000A4, 0x05BD75E2, 0xBE26EE99, + 0x04000000, 0x3FF000A8, 0x1C0B0BB1, 0xBE21BE7E, + 0x04000000, 0x3FF000AC, 0xC4A37A79, 0xBE18DCC3, + 0x04000000, 0x3FF000B0, 0x4244D60F, 0xBE0BF911, + 0x04000000, 0x3FF000B4, 0xEC91D848, 0xBDE6E255, + 0x04000000, 0x3FF000B8, 0xEC1B8F0C, 0x3E0107EB, + 0x04000000, 0x3FF000BC, 0x89BE52AA, 0x3E142439, + 0x04000000, 0x3FF000C0, 0x06C01033, 0x3E200240, + 0x04000000, 0x3FF000C4, 0xC8A9F760, 0x3E261264, + 0x04000000, 0x3FF000C8, 0x129D3FDE, 0x3E2C428B, + 0x04000000, 0x3FF000CC, 0x764D2658, 0x3E314959, + 0x04000000, 0x3FF000D0, 0x2F50C16C, 0x3E34816E, + 0x04000000, 0x3FF000D4, 0xB859A4AB, 0x3E37C983, + 0x04000000, 0x3FF000D8, 0x15680499, 0x3E3B219A, + 0x04000000, 0x3FF000DC, 0x4A7C16B5, 0x3E3E89B1, + 0x08000000, 0x3FF000E0, 0xA469EE7E, 0xBE3DFE36, + 0x08000000, 0x3FF000E4, 0xB349D37F, 0xBE3A761D, + 0x08000000, 0x3FF000E8, 0xDE235FCD, 0xBE36DE03, + 0x08000000, 0x3FF000EC, 0x20F659E6, 0xBE3335E9, + 0x08000000, 0x3FF000F0, 0xEF850E8F, 0xBE2EFB9A, + 0x08000000, 0x3FF000F4, 0xBD0F58E2, 0xBE276B61, + 0x08000000, 0x3FF000F8, 0x45163381, 0xBE1F764D, + 0x08000000, 0x3FF000FC, 0x5FDF589A, 0xBE0FABA6, + 0x08000000, 0x3FF00100, 0xABBBBE94, 0x3D8555AA, + 0x08000000, 0x3FF00104, 0xDABB690B, 0x3E102B2C, + 0x08000000, 0x3FF00108, 0x7820FBA0, 0x3E2045D9, + 0x08000000, 0x3FF0010C, 0x92F54742, 0x3E28961E, + 0x08000000, 0x3FF00110, 0xE2ED8E39, 0x3E308332, + 0x08000000, 0x3FF00114, 0x8C698119, 0x3E34CB57, + 0x08000000, 0x3FF00118, 0x49EEC0C4, 0x3E39237D, + 0x08000000, 0x3FF0011C, 0x1F7D92BC, 0x3E3D8BA4, + 0x0C000000, 0x3FF00120, 0xEEE9C27D, 0xBE3DFC33, + 0x0C000000, 0x3FF00124, 0xDD46F763, 0xBE39740A, + 0x0C000000, 0x3FF00128, 0xA799C375, 0xBE34DBE0, + 0x0C000000, 0x3FF0012C, 0x49E1DD2F, 0xBE3033B5, + 0x0C000000, 0x3FF00130, 0x803DF41F, 0xBE26F711, + 0x0C000000, 0x3FF00134, 0x19433A4C, 0xBE1ACD6C, + 0x0C000000, 0x3FF00138, 0x8770E36F, 0xBDFDB2C1, + 0x0C000000, 0x3FF0013C, 0x6B74A43E, 0x3E086820, + 0x0C000000, 0x3FF00140, 0xDEC0D058, 0x3E200A6A, + 0x0C000000, 0x3FF00144, 0x22BD7872, 0x3E2A1AD0, + 0x0C000000, 0x3FF00148, 0xF769E132, 0x3E32259B, + 0x0C000000, 0x3FF0014C, 0x2582289A, 0x3E374DD1, + 0x0C000000, 0x3FF00150, 0x9FA7E4F4, 0x3E3C8607, + 0x10000000, 0x3FF00154, 0x9624963C, 0xBE3E31C0, + 0x10000000, 0x3FF00158, 0x77E2F472, 0xBE38D987, + 0x10000000, 0x3FF0015C, 0x0192E02C, 0xBE33714D, + 0x10000000, 0x3FF00160, 0x5E6805CB, 0xBE2BF222, + 0x10000000, 0x3FF00164, 0xF98C0A34, 0xBE20E1A7, + 0x10000000, 0x3FF00168, 0x32447238, 0xBE06C4AB, + 0x10000000, 0x3FF0016C, 0xC225D8C1, 0x3E067D54, + 0x10000000, 0x3FF00170, 0x05C4630F, 0x3E210FD8, + 0x10000000, 0x3FF00174, 0xBB206115, 0x3E2CA05D, + 0x10000000, 0x3FF00178, 0x2C4F14A6, 0x3E342873, + 0x10000000, 0x3FF0017C, 0xF31F3B5E, 0x3E3A10B8, + 0x14000000, 0x3FF00180, 0xC9FEFCC9, 0xBE3FF6FF, + 0x14000000, 0x3FF00184, 0x070B344A, 0xBE39EEB7, + 0x14000000, 0x3FF00188, 0xC0050AA2, 0xBE33D66C, + 0x14000000, 0x3FF0018C, 0xE1D83C97, 0xBE2B5C41, + 0x14000000, 0x3FF00190, 0x57003305, 0xBE1DD74E, + 0x14000000, 0x3FF00194, 0xA80727F1, 0xBDF2D84A, + 0x14000000, 0x3FF00198, 0x534C5401, 0x3E14AB2F, + 0x14000000, 0x3FF0019C, 0xD875DE83, 0x3E27263B, + 0x14000000, 0x3FF001A0, 0x9FB782CA, 0x3E320B71, + 0x14000000, 0x3FF001A4, 0xF349371F, 0x3E3893C6, + 0x14000000, 0x3FF001A8, 0xEAF074C6, 0x3E3F2C1D, + 0x18000000, 0x3FF001AC, 0x75525ABC, 0xBE3A2B89, + 0x18000000, 0x3FF001B0, 0x297ECCE2, 0xBE33732F, + 0x18000000, 0x3FF001B4, 0x5B28EC49, 0xBE2955A6, + 0x18000000, 0x3FF001B8, 0xF64BA7FD, 0xBE1749D5, + 0x18000000, 0x3FF001BC, 0xA8645141, 0x3DF15E9E, + 0x18000000, 0x3FF001C0, 0x1D6F0B37, 0x3E201C96, + 0x18000000, 0x3FF001C4, 0xE6028E39, 0x3E2E2D5B, + 0x18000000, 0x3FF001C8, 0x9B63FA1E, 0x3E362F12, + 0x18000000, 0x3FF001CC, 0x0BE01026, 0x3E3D5779, + 0x1C000000, 0x3FF001D0, 0xB78A0445, 0xBE3B701E, + 0x1C000000, 0x3FF001D4, 0xAAD9CF9D, 0xBE3427B4, + 0x1C000000, 0x3FF001D8, 0x941DBAB5, 0xBE299E91, + 0x1C000000, 0x3FF001DC, 0x44A2DFDD, 0xBE159B6C, + 0x1C000000, 0x3FF001E0, 0x1EC8B89C, 0x3E008CA4, + 0x1C000000, 0x3FF001E4, 0xF1EE0E9A, 0x3E23340B, + 0x1C000000, 0x3FF001E8, 0x5231913C, 0x3E313279, + 0x1C000000, 0x3FF001EC, 0x93892E68, 0x3E38DAEE, + 0x20000000, 0x3FF001F0, 0x3F01A6A8, 0xBE3F6C9A, + 0x20000000, 0x3FF001F4, 0x216E726C, 0xBE37A421, + 0x20000000, 0x3FF001F8, 0x1F7970B9, 0xBE2F974C, + 0x20000000, 0x3FF001FC, 0x17AFEBC8, 0xBE1F8CA4, + 0x20000000, 0x3FF00200, 0x04445B06, 0x3DB55600, + 0x20000000, 0x3FF00204, 0x0C290A26, 0x3E203BAE, + 0x20000000, 0x3FF00208, 0x104547BD, 0x3E30365A, + 0x20000000, 0x3FF0020C, 0x22970DE3, 0x3E385EDF, + 0x24000000, 0x3FF00210, 0xBEF5A5F4, 0xBE3F6899, + 0x24000000, 0x3FF00214, 0x90605040, 0xBE372010, + 0x24000000, 0x3FF00218, 0x9B50D8EE, 0xBE2D8F0A, + 0x24000000, 0x3FF0021C, 0xCB35D444, 0xBE197BDF, + 0x24000000, 0x3FF00220, 0x2188E3D5, 0x3E00CCBC, + 0x24000000, 0x3FF00224, 0x36A79F6A, 0x3E254452, + 0x24000000, 0x3FF00228, 0xD69B2D28, 0x3E333ABC, + 0x24000000, 0x3FF0022C, 0xBA07BE5B, 0x3E3BE352, + 0x28000000, 0x3FF00230, 0x3665F227, 0xBE3B6415, + 0x28000000, 0x3FF00234, 0xF6AD58D5, 0xBE329B7A, + 0x28000000, 0x3FF00238, 0x059BD24A, 0xBE2385BD, + 0x28000000, 0x3FF0023C, 0xD8E2B1B4, 0xBDEB47FA, + 0x28000000, 0x3FF00240, 0x22CF60F6, 0x3E203CC2, + 0x28000000, 0x3FF00244, 0x39BEF87F, 0x3E312704, + 0x28000000, 0x3FF00248, 0xA63F5309, 0x3E3A3FA9, + 0x2C000000, 0x3FF0024C, 0xA516AE5E, 0xBE3C97AE, + 0x2C000000, 0x3FF00250, 0xA442792A, 0xBE335F04, + 0x2C000000, 0x3FF00254, 0xA686F3A2, 0xBE242CB0, + 0x2C000000, 0x3FF00258, 0xC3237903, 0xBDE7B535, + 0x2C000000, 0x3FF0025C, 0x9E7A6CF7, 0x3E21560E, + 0x2C000000, 0x3FF00260, 0xA8C01385, 0x3E3223BA, + 0x2C000000, 0x3FF00264, 0x627012DF, 0x3E3BAC70, + 0x30000000, 0x3FF00268, 0x7FB232EA, 0xBE3ABAD7, + 0x30000000, 0x3FF0026C, 0xF9A6244B, 0xBE31121C, + 0x30000000, 0x3FF00270, 0x1DAC9AE4, 0xBE1D6580, + 0x30000000, 0x3FF00274, 0xD7FB0AC3, 0x3E037AFA, + 0x30000000, 0x3FF00278, 0x633420EB, 0x3E289042, + 0x30000000, 0x3FF0027C, 0x8065842A, 0x3E3630E5, + 0x34000000, 0x3FF00280, 0xB49DA4FF, 0xBE3FD653, + 0x34000000, 0x3FF00284, 0x696ECB76, 0xBE35CD8A, + 0x34000000, 0x3FF00288, 0x341A9D63, 0xBE27697D, + 0x34000000, 0x3FF0028C, 0x2788D238, 0xBDF8BF04, + 0x34000000, 0x3FF00290, 0x42A03782, 0x3E2159C1, + 0x34000000, 0x3FF00294, 0x154D4F89, 0x3E32F5B4, + 0x34000000, 0x3FF00298, 0x1D7FB2C1, 0x3E3D4E8A, + 0x38000000, 0x3FF0029C, 0x42181508, 0xBE38489D, + 0x38000000, 0x3FF002A0, 0x0AF2C28C, 0xBE2B9F84, + 0x38000000, 0x3FF002A4, 0x451C5357, 0xBE0A3721, + 0x38000000, 0x3FF002A8, 0x61A8605E, 0x3E1D47F1, + 0x38000000, 0x3FF002AC, 0x81B02FCF, 0x3E31FADF, + 0x38000000, 0x3FF002B0, 0x572F674A, 0x3E3CB3C5, + 0x3C000000, 0x3FF002B4, 0x231795EA, 0xBE388352, + 0x3C000000, 0x3FF002B8, 0xD248367A, 0xBE2B54CD, + 0x3C000000, 0x3FF002BC, 0xB7ABD90D, 0xBE060BC7, + 0x3C000000, 0x3FF002C0, 0x6EE9F1EF, 0x3E206EEF, + 0x3C000000, 0x3FF002C4, 0x261BF09E, 0x3E33406B, + 0x3C000000, 0x3FF002C8, 0x59001C60, 0x3E3E5961, + 0x40000000, 0x3FF002CC, 0xABDDD232, 0xBE367DA5, + 0x40000000, 0x3FF002D0, 0xC8FA5113, 0xBE268953, + 0x40000000, 0x3FF002D4, 0x8B33A701, 0x3D9152CC, + 0x40000000, 0x3FF002D8, 0x3E058570, 0x3E26BAAC, + 0x40000000, 0x3FF002DC, 0x63236E71, 0x3E36C65A, + 0x44000000, 0x3FF002E0, 0x7C7A795C, 0xBE3DC09E, + 0x44000000, 0x3FF002E4, 0x7BD63D1D, 0xBE323794, + 0x44000000, 0x3FF002E8, 0x5BBC9105, 0xBE1A7A1E, + 0x44000000, 0x3FF002EC, 0xD8EE2B1B, 0x3E142A20, + 0x44000000, 0x3FF002F0, 0xEFAA8A8D, 0x3E30C39A, + 0x44000000, 0x3FF002F4, 0x995E96A2, 0x3E3C8CB0, + 0x48000000, 0x3FF002F8, 0xC8A79469, 0xBE379A36, + 0x48000000, 0x3FF002FC, 0x64CE7203, 0xBE276236, + 0x48000000, 0x3FF00300, 0x0819DA68, 0x3DD200D8, + 0x48000000, 0x3FF00304, 0xE5E018D4, 0x3E28A249, + 0x48000000, 0x3FF00308, 0x8A087692, 0x3E386A49, + 0x4C000000, 0x3FF0030C, 0xD695988B, 0xBE3B6C8E, + 0x4C000000, 0x3FF00310, 0x55D2BCBA, 0xBE2E66C8, + 0x4C000000, 0x3FF00314, 0x7790BA7A, 0xBE0751B3, + 0x4C000000, 0x3FF00318, 0xC2A20261, 0x3E22DDF4, + 0x4C000000, 0x3FF0031C, 0x49E0B0B5, 0x3E35D82E, + 0x50000000, 0x3FF00320, 0xB142422E, 0xBE3DAE9A, + 0x50000000, 0x3FF00324, 0x8C170FE6, 0xBE312560, + 0x50000000, 0x3FF00328, 0x0A73BF77, 0xBE12308D, + 0x50000000, 0x3FF0032C, 0x5E59CEFA, 0x3E203A3A, + 0x50000000, 0x3FF00330, 0xCD4740BF, 0x3E34D660, + 0x54000000, 0x3FF00334, 0x644D1883, 0xBE3E6058, + 0x54000000, 0x3FF00338, 0x618F57B6, 0xBE31870E, + 0x54000000, 0x3FF0033C, 0x99FABD0F, 0xBE127704, + 0x54000000, 0x3FF00340, 0xA1CB5ECF, 0x3E20B71E, + 0x54000000, 0x3FF00344, 0x089E93E1, 0x3E3564E3, + 0x58000000, 0x3FF00348, 0xFB533142, 0xBE3D81C5, + 0x58000000, 0x3FF0034C, 0xB6EECE6C, 0xBE30586B, + 0x58000000, 0x3FF00350, 0x319B883E, 0xBE08F871, + 0x58000000, 0x3FF00354, 0x75BF7503, 0x3E2454A5, + 0x58000000, 0x3FF00358, 0xF04B88C5, 0x3E3783B6, + 0x5C000000, 0x3FF0035C, 0x81EF30A7, 0xBE3B12E1, + 0x5C000000, 0x3FF00360, 0x2F9F3657, 0xBE2B32ED, + 0x5C000000, 0x3FF00364, 0x54DF31BC, 0xBDB0084D, + 0x5C000000, 0x3FF00368, 0xC303B7B9, 0x3E2B12D2, + 0x5C000000, 0x3FF0036C, 0x78B56F97, 0x3E3B32DE, + 0x60000000, 0x3FF00370, 0x03B9496C, 0xBE3713A9, + 0x60000000, 0x3FF00374, 0x1F92E726, 0xBE22945A, + 0x60000000, 0x3FF00378, 0x621736DF, 0x3E123D49, + 0x60000000, 0x3FF0037C, 0x3935580D, 0x3E3278D5, + 0x64000000, 0x3FF00380, 0x69B9F5FB, 0xBE3F8DA4, + 0x64000000, 0x3FF00384, 0x8C473CC8, 0xBE31841A, + 0x64000000, 0x3FF00388, 0x538CDE07, 0xBE0B5469, + 0x64000000, 0x3FF0038C, 0x7F8F9D65, 0x3E257E07, + 0x64000000, 0x3FF00390, 0x3665E52B, 0x3E38F898, + 0x68000000, 0x3FF00394, 0xC29674BD, 0xBE38BDCF, + 0x68000000, 0x3FF00398, 0x4E58B4D9, 0xBE24C868, + 0x68000000, 0x3FF0039C, 0x329466D7, 0x3E1015AC, + 0x68000000, 0x3FF003A0, 0xDCDECE44, 0x3E327F0D, + 0x6C000000, 0x3FF003A4, 0xB27E5528, 0xBE3EF74B, + 0x6C000000, 0x3FF003A8, 0x9D7167F2, 0xBE305DA1, + 0x6C000000, 0x3FF003AC, 0xFF980820, 0xBDFB3F3D, + 0x6C000000, 0x3FF003B0, 0x13D49789, 0x3E2A0B7B, + 0x6C000000, 0x3FF003B4, 0xA43AE87C, 0x3E3BCF72, + 0x70000000, 0x3FF003B8, 0x8D06BDC0, 0xBE3556D4, + 0x70000000, 0x3FF003BC, 0x1766E54D, 0xBE19B460, + 0x70000000, 0x3FF003C0, 0x7B85C8BA, 0x3E211950, + 0x70000000, 0x3FF003C4, 0x41D00AED, 0x3E37966C, + 0x74000000, 0x3FF003C8, 0xF5B15507, 0xBE394FCB, + 0x74000000, 0x3FF003CC, 0xC98093C4, 0xBE244C00, + 0x74000000, 0x3FF003D0, 0xE2907BDF, 0x3E144F3B, + 0x74000000, 0x3FF003D4, 0x267CD924, 0x3E345DA2, + 0x78000000, 0x3FF003D8, 0xD73526C0, 0xBE3C4886, + 0x78000000, 0x3FF003DC, 0xF8E1D62E, 0xBE29BD57, + 0x78000000, 0x3FF003E0, 0xD65415E1, 0x3E04D995, + 0x78000000, 0x3FF003E4, 0x527E1A58, 0x3E322515, + 0x7C000000, 0x3FF003E8, 0x31552BA5, 0xBE3E4104, + 0x7C000000, 0x3FF003EC, 0x995CAB3B, 0xBE2D2E33, + 0x7C000000, 0x3FF003F0, 0x473970DC, 0x3DF22D48, + 0x7C000000, 0x3FF003F4, 0xC61195FC, 0x3E30ECC6, + 0x80000000, 0x3FF003F8, 0x03D35C34, 0xBE3F3943, + 0x80000000, 0x3FF003FC, 0xAA7483C7, 0xBE2E9E91, + 0x80000000, 0x3FF00400, 0xBBBC71CE, 0x3DE556AA, + 0x80000000, 0x3FF00404, 0x817613C1, 0x3E30B4B7, + 0x84000000, 0x3FF00408, 0x4E70B0AC, 0xBE3F3142, + 0x84000000, 0x3FF0040C, 0x2BAAD02F, 0xBE2E0E70, + 0x84000000, 0x3FF00410, 0xF48F01F2, 0x3DF32D62, + 0x84000000, 0x3FF00414, 0x84EB5B98, 0x3E317CE8, + 0x88000000, 0x3FF00418, 0x10ED210B, 0xBE3E2901, + 0x88000000, 0x3FF0041C, 0x1C7F0051, 0xBE2B7DCD, + 0x88000000, 0x3FF00420, 0x87AA2706, 0x3E05D9C0, + 0x88000000, 0x3FF00424, 0xD0B235B3, 0x3E33455A, + 0x8C000000, 0x3FF00428, 0x4B07A510, 0xBE3C207E, + 0x8C000000, 0x3FF0042C, 0x7C6E838B, 0xBE26ECA6, + 0x8C000000, 0x3FF00430, 0xEC91A8D5, 0x3E150F6F, + 0x8C000000, 0x3FF00434, 0x650C6A83, 0x3E360E0F, + 0x90000000, 0x3FF00438, 0xFC7E3439, 0xBE3917B8, + 0x90000000, 0x3FF0043C, 0x4AF4C8B6, 0xBE205AFA, + 0x90000000, 0x3FF00440, 0xDC31D181, 0x3E219985, + 0x90000000, 0x3FF00444, 0x423CC2BE, 0x3E39D707, + 0x94000000, 0x3FF00448, 0x250DC5BF, 0xBE350EB0, + 0x94000000, 0x3FF0044C, 0x1E2CF893, 0xBE0F231A, + 0x94000000, 0x3FF00450, 0xD42C92D4, 0x3E2AABDB, + 0x94000000, 0x3FF00454, 0x6887075B, 0x3E3EA043, + 0x98000000, 0x3FF00458, 0xC472509B, 0xBE300562, + 0x98000000, 0x3FF0045C, 0x72B572E0, 0x3DF64FB6, + 0x98000000, 0x3FF00460, 0xEF61155C, 0x3E32DF5D, + 0x9C000000, 0x3FF00464, 0x27CFFE6A, 0xBE3B963B, + 0x9C000000, 0x3FF00468, 0xB4CD96FE, 0xBE23F79F, + 0x9C000000, 0x3FF0046C, 0x6E771F13, 0x3E1EBA7F, + 0x9C000000, 0x3FF00470, 0xFE3ED608, 0x3E396913, + 0xA0000000, 0x3FF00474, 0x6E82850F, 0xBE34CC73, + 0xA0000000, 0x3FF00478, 0x352966B7, 0xBE078FB3, + 0xA0000000, 0x3FF0047C, 0x33AFF8AE, 0x3E2DF116, + 0xA4000000, 0x3FF00480, 0xE909EADD, 0xBE3F0CEE, + 0xA4000000, 0x3FF00484, 0xD6938597, 0xBE2A04C8, + 0xA4000000, 0x3FF00488, 0x5C6654D8, 0x3E1460AA, + 0xA4000000, 0x3FF0048C, 0x22213ECF, 0x3E3742BE, + 0xA8000000, 0x3FF00490, 0xC631A356, 0xBE3682A9, + 0xA8000000, 0x3FF00494, 0x7777B644, 0xBE10E034, + 0xA8000000, 0x3FF00498, 0x3E3B0991, 0x3E2C4528, + 0xAC000000, 0x3FF0049C, 0x0B3E269F, 0xBE3F72C6, + 0xAC000000, 0x3FF004A0, 0x31DF923B, 0xBE29F037, + 0xAC000000, 0x3FF004A4, 0xE82713DE, 0x3E164A4D, + 0xAC000000, 0x3FF004A8, 0x31AFAC4B, 0x3E382D47, + 0xB0000000, 0x3FF004AC, 0x6DFCE978, 0xBE352800, + 0xB0000000, 0x3FF004B0, 0x07D68D27, 0xBE036A1B, + 0xB0000000, 0x3FF004B4, 0x5CB71F6F, 0x3E305D7E, + 0xB4000000, 0x3FF004B8, 0x30E5E990, 0xBE3CC7BB, + 0xB4000000, 0x3FF004BC, 0x0BA17DEA, 0xBE23B9E0, + 0xB4000000, 0x3FF004C0, 0xC3EF9BD8, 0x3E223BBF, + 0xB4000000, 0x3FF004C4, 0x8A74ECC0, 0x3E3C28B4, + 0xB8000000, 0x3FF004C8, 0x085831CA, 0xBE30BC72, + 0xB8000000, 0x3FF004CC, 0x6C8D1FC8, 0x3E037361, + 0xB8000000, 0x3FF004D0, 0x3033A0B8, 0x3E35A94F, + 0xBC000000, 0x3FF004D4, 0xFC7107DE, 0xBE370BC8, + 0xBC000000, 0x3FF004D8, 0xA2D908DA, 0xBE0D86E2, + 0xBC000000, 0x3FF004DC, 0x58ED155E, 0x3E2F742A, + 0xC0000000, 0x3FF004E0, 0x75FACDD0, 0xBE3CCAF4, + 0xC0000000, 0x3FF004E4, 0x6F5BE5D3, 0xBE227FF2, + 0xC0000000, 0x3FF004E8, 0xD6BCA827, 0x3E24B60D, + 0xC0000000, 0x3FF004EC, 0xF72B40D6, 0x3E3E060B, + 0xC4000000, 0x3FF004F0, 0x208BE3E3, 0xBE2C7DD4, + 0xC4000000, 0x3FF004F4, 0x642FDDB8, 0x3E163093, + 0xC4000000, 0x3FF004F8, 0xB72239A5, 0x3E396738, + 0xC8000000, 0x3FF004FC, 0x7201ED9B, 0xBE32ADAE, + 0xC8000000, 0x3FF00500, 0x1A0C05F3, 0x3DF4D6F6, + 0xC8000000, 0x3FF00504, 0x360B8346, 0x3E355892, + 0xCC000000, 0x3FF00508, 0xF0C06435, 0xBE368C45, + 0xCC000000, 0x3FF0050C, 0x760DA2F6, 0xBE0308C8, + 0xCC000000, 0x3FF00510, 0xE008D57B, 0x3E31DA18, + 0xD0000000, 0x3FF00514, 0x205F82F4, 0xBE39DAB0, + 0xD0000000, 0x3FF00518, 0x2FE5E3E3, 0xBE15FDD0, + 0xD0000000, 0x3FF0051C, 0x42787241, 0x3E2DD79A, + 0xD4000000, 0x3FF00520, 0x94BD25F4, 0xBE3C98EC, + 0xD4000000, 0x3FF00524, 0x53C89D03, 0xBE201B42, + 0xD4000000, 0x3FF00528, 0xCB901057, 0x3E291B5E, + 0xD8000000, 0x3FF0052C, 0xE1B6D837, 0xBE3EC6FA, + 0xD8000000, 0x3FF00530, 0xF8BF49E7, 0xBE24173F, + 0xD8000000, 0x3FF00534, 0x339DDB57, 0x3E257F80, + 0xD8000000, 0x3FF00538, 0x64D62C5C, 0x3E3F9B25, + 0xDC000000, 0x3FF0053C, 0x2E913659, 0xBE26F2E0, + 0xDC000000, 0x3FF00540, 0x52E7CB93, 0x3E2303FF, + 0xDC000000, 0x3FF00544, 0xAB0CFEF5, 0x3E3E8D74, + 0xE0000000, 0x3FF00548, 0x1CF7FDE6, 0xBE28AE22, + 0xE0000000, 0x3FF0054C, 0x01B47B93, 0x3E21A8DD, + 0xE0000000, 0x3FF00550, 0x5D1107E2, 0x3E3E0FF3, + 0xE4000000, 0x3FF00554, 0xEBAC99E1, 0xBE294904, + 0xE4000000, 0x3FF00558, 0x184B2814, 0x3E216E1A, + 0xE4000000, 0x3FF0055C, 0xE706008B, 0x3E3E22A1, + 0xE8000000, 0x3FF00560, 0xC267616A, 0xBE28C387, + 0xE8000000, 0x3FF00564, 0x6EF3B008, 0x3E2253B7, + 0xE8000000, 0x3FF00568, 0xB50FF371, 0x3E3EC580, + 0xEC000000, 0x3FF0056C, 0xC8E0096B, 0xBE271DA9, + 0xEC000000, 0x3FF00570, 0xDDF69498, 0x3E2459B5, + 0xEC000000, 0x3FF00574, 0x33533C31, 0x3E3FF890, + 0xF0000000, 0x3FF00578, 0x26CDA497, 0xBE24576A, + 0xF0000000, 0x3FF0057C, 0x3D9CF923, 0x3E278016, + 0xF4000000, 0x3FF00580, 0x320B787B, 0xBE3E442F, + 0xF4000000, 0x3FF00584, 0x03E6A36B, 0xBE2070C8, + 0xF4000000, 0x3FF00588, 0x6630A33F, 0x3E2BC6D9, + 0xF8000000, 0x3FF0058C, 0x0EE72CBF, 0xBE3BF0BD, + 0xF8000000, 0x3FF00590, 0x0FC1A853, 0xBE16D385, + 0xF8000000, 0x3FF00594, 0x17FDFD5D, 0x3E309700, + 0xFC000000, 0x3FF00598, 0xF71A91AC, 0xBE390D18, + 0xFC000000, 0x3FF0059C, 0x69C58B86, 0xBE050963, + 0xFC000000, 0x3FF005A0, 0xB9A504CD, 0x3E33DAC5, + 0x00000000, 0x3FF005A5, 0x7E800734, 0xBE359942, + 0x00000000, 0x3FF005A9, 0xE59934CD, 0x3DF02BAE, + 0x00000000, 0x3FF005AD, 0x04333E0E, 0x3E37AEBE, + 0x04000000, 0x3FF005B1, 0x38F19C2F, 0xBE319539, + 0x04000000, 0x3FF005B5, 0xEBB1C157, 0x3E14DB54, + 0x04000000, 0x3FF005B9, 0x63CED05D, 0x3E3C12E9, + 0x08000000, 0x3FF005BD, 0x74921CAF, 0xBE2A01F9, + 0x08000000, 0x3FF005C1, 0xC94C85F2, 0x3E23F645, + 0x0C000000, 0x3FF005C5, 0xBB61CBEE, 0xBE3EF8B7, + 0x0C000000, 0x3FF005C9, 0x597F2931, 0xBE1F7232, + 0x0C000000, 0x3FF005CD, 0xAF5B7345, 0x3E2E9F48, + 0x10000000, 0x3FF005D1, 0xED37CD5F, 0xBE397424, + 0x10000000, 0x3FF005D5, 0x08775C6B, 0xBE013F43, + 0x10000000, 0x3FF005D9, 0x0029D3DB, 0x3E35345A, + 0x14000000, 0x3FF005DD, 0xC58C1962, 0xBE335F5D, + 0x14000000, 0x3FF005E1, 0x47430E04, 0x3E1073C1, + 0x14000000, 0x3FF005E5, 0x4A41E248, 0x3E3BA944, + 0x18000000, 0x3FF005E9, 0xB06E888E, 0xBE2974C3, + 0x18000000, 0x3FF005ED, 0xDCCD9333, 0x3E25E3FB, + 0x1C000000, 0x3FF005F1, 0x5DE27951, 0xBE3D519C, + 0x1C000000, 0x3FF005F5, 0xE4464502, 0xBE1614C2, + 0x1C000000, 0x3FF005F9, 0xE0DAFE93, 0x3E325740, + 0x20000000, 0x3FF005FD, 0x8C1B4C10, 0xBE35BC47, + 0x20000000, 0x3FF00601, 0x20686CE9, 0x3E0201B0, + 0x20000000, 0x3FF00605, 0x95558B63, 0x3E3A4CB9, + 0x24000000, 0x3FF00609, 0xA880A3EB, 0xBE2B2D79, + 0x24000000, 0x3FF0060D, 0x9699EEB7, 0x3E252BA5, + 0x28000000, 0x3FF00611, 0x880115E1, 0xBE3D2D97, + 0x28000000, 0x3FF00615, 0x28A3D788, 0xBE1383EF, + 0x28000000, 0x3FF00619, 0x08D6DC23, 0x3E337BA6, + 0x2C000000, 0x3FF0061D, 0x0B001A08, 0xBE3417B2, + 0x2C000000, 0x3FF00621, 0xF94EB99A, 0x3E1193EF, + 0x2C000000, 0x3FF00625, 0x28D3BD3B, 0x3E3CF1B0, + 0x30000000, 0x3FF00629, 0x0EFCC982, 0xBE24E32B, + 0x30000000, 0x3FF0062D, 0xE2BDA47F, 0x3E2C7655, + 0x34000000, 0x3FF00631, 0x689312F8, 0xBE39080E, + 0x34000000, 0x3FF00635, 0xA9444DB4, 0xBDCDA0C8, + 0x34000000, 0x3FF00639, 0x7B21FE23, 0x3E38A191, + 0x38000000, 0x3FF0063D, 0x7E67E1E1, 0xBE2CE32A, + 0x38000000, 0x3FF00641, 0x875A71F0, 0x3E251694, + 0x3C000000, 0x3FF00645, 0xF838F455, 0xBE3C67CF, + 0x3C000000, 0x3FF00649, 0x77274052, 0xBE0A571F, + 0x3C000000, 0x3FF0064D, 0x63AAEFA8, 0x3E35E20E, + 0x40000000, 0x3FF00651, 0xFC87DA70, 0xBE30E0F8, + 0x40000000, 0x3FF00655, 0xE9089AFD, 0x3E20D80B, + 0x44000000, 0x3FF00659, 0xC52F03BD, 0xBE3E36F4, + 0x44000000, 0x3FF0065D, 0x9680E14E, 0xBE1327A4, + 0x44000000, 0x3FF00661, 0xD732468D, 0x3E34B328, + 0x48000000, 0x3FF00665, 0xCAB5EF4A, 0xBE31BFBE, + 0x48000000, 0x3FF00669, 0xE2A2FBE1, 0x3E1F757F, + 0x4C000000, 0x3FF0066D, 0xDAB014DA, 0xBE3E757A, + 0x4C000000, 0x3FF00671, 0x02FB3FBB, 0xBE12E13D, + 0x4C000000, 0x3FF00675, 0xCA7E298D, 0x3E3514E2, + 0x50000000, 0x3FF00679, 0xB4F78B94, 0xBE310DE4, + 0x50000000, 0x3FF0067D, 0x89C35D05, 0x3E21BEB4, + 0x54000000, 0x3FF00681, 0x43F4895C, 0xBE3D2360, + 0x54000000, 0x3FF00685, 0x5BC49ADF, 0xBE08B0A2, + 0x54000000, 0x3FF00689, 0x32573159, 0x3E37073E, + 0x58000000, 0x3FF0068D, 0x8D0732D2, 0xBE2D96D1, + 0x58000000, 0x3FF00691, 0x9BF15E67, 0x3E26E3ED, + 0x5C000000, 0x3FF00695, 0x0C3250FB, 0xBE3A40A3, + 0x5C000000, 0x3FF00699, 0xFD0AE214, 0x3DBCC9AE, + 0x5C000000, 0x3FF0069D, 0x038868A1, 0x3E3A8A3D, + 0x60000000, 0x3FF006A1, 0x151D21CE, 0xBE25F092, + 0x60000000, 0x3FF006A5, 0x11738C43, 0x3E2F2A6F, + 0x64000000, 0x3FF006A9, 0x3E9CE96D, 0xBE35CD41, + 0x64000000, 0x3FF006AD, 0x8DBC2918, 0x3E138132, + 0x64000000, 0x3FF006B1, 0x32DF4C13, 0x3E3F9DE1, + 0x68000000, 0x3FF006B5, 0x3129E0B2, 0xBE16520E, + 0x68000000, 0x3FF006B9, 0x69F36A61, 0x3E35491E, + 0x6C000000, 0x3FF006BD, 0xCCCABCD4, 0xBE2F9271, + 0x6C000000, 0x3FF006C1, 0x0D59B899, 0x3E2668ED, + 0x70000000, 0x3FF006C5, 0x4AD435A0, 0xBE39BDD3, + 0x70000000, 0x3FF006C9, 0x9191CABB, 0x3DF5FE9A, + 0x70000000, 0x3FF006CD, 0x6676850B, 0x3E3C8DAD, + 0x74000000, 0x3FF006D1, 0x1D74934A, 0xBE206910, + 0x74000000, 0x3FF006D5, 0x4D886478, 0x3E331949, + 0x78000000, 0x3FF006D9, 0x80BFBBC2, 0xBE3188DE, + 0x78000000, 0x3FF006DD, 0x14DE1719, 0x3E23CA01, + 0x7C000000, 0x3FF006E1, 0x8CE98EC0, 0xBE3A9D19, + 0x7C000000, 0x3FF006E5, 0xA705A6E7, 0x3DEE1A67, + 0x7C000000, 0x3FF006E9, 0xECD5F851, 0x3E3C8EC6, + 0x80000000, 0x3FF006ED, 0xE839CE4D, 0xBE1F0CF9, + 0x80000000, 0x3FF006F1, 0x0C8CA46A, 0x3E33FAC3, + 0x84000000, 0x3FF006F5, 0x7B5703D8, 0xBE303734, + 0x84000000, 0x3FF006F9, 0xE490A112, 0x3E274DB5, + 0x88000000, 0x3FF006FD, 0xA693A093, 0xBE386B0E, + 0x88000000, 0x3FF00701, 0xF0B73DAA, 0x3E0C9875, + 0x88000000, 0x3FF00705, 0x2449A944, 0x3E3FA133, + 0x8C000000, 0x3FF00709, 0xBFE66C14, 0xBE110285, + 0x8C000000, 0x3FF0070D, 0x054EDCBD, 0x3E37ED91, + 0x90000000, 0x3FF00711, 0xEFB65924, 0xBE27A86A, + 0x90000000, 0x3FF00715, 0x1C8A0CF1, 0x3E307A0B, + 0x94000000, 0x3FF00719, 0x397FB1D6, 0xBE3327AD, + 0x94000000, 0x3FF0071D, 0x1412B9FB, 0x3E228D43, + 0x98000000, 0x3FF00721, 0x94D8FFB0, 0xBE3A3B08, + 0x98000000, 0x3FF00725, 0x6ED80040, 0x3E029AA3, + 0x98000000, 0x3FF00729, 0x9627250A, 0x3E3EF1B8, + 0x9C000000, 0x3FF0072D, 0x5FCB1B09, 0xBE117F70, + 0x9C000000, 0x3FF00731, 0x678F0789, 0x3E385E96, + 0xA0000000, 0x3FF00735, 0xCEA3485B, 0xBE25A5DF, + 0xA0000000, 0x3FF00739, 0xFF6D0303, 0x3E320B90, + 0xA4000000, 0x3FF0073D, 0xE03334FF, 0xBE3105E6, + 0xA4000000, 0x3FF00741, 0xFB9F056D, 0x3E27F150, + 0xA8000000, 0x3FF00745, 0xE28905F4, 0xBE36F8C0, + 0xA8000000, 0x3FF00749, 0x0B1407AA, 0x3E189774, + 0xAC000000, 0x3FF0074D, 0xCE4493C4, 0xBE3CAB7D, + 0xAC000000, 0x3FF00751, 0xCB817D78, 0x3DE265D5, + 0xAC000000, 0x3FF00755, 0x7CA8B4E3, 0x3E3DE1E2, + 0xB0000000, 0x3FF00759, 0x7D730FC6, 0xBE12FD89, + 0xB0000000, 0x3FF0075D, 0x1E4D7759, 0x3E38AF60, + 0xB4000000, 0x3FF00761, 0x0CAD84A2, 0xBE23A3AC, + 0xB4000000, 0x3FF00765, 0x36B866FD, 0x3E33BCFB, + 0xB8000000, 0x3FF00769, 0x4D0667A1, 0xBE2D4858, + 0xB8000000, 0x3FF0076D, 0xCBF08E6A, 0x3E2E1567, + 0xBC000000, 0x3FF00771, 0x9FD34D05, 0xBE333664, + 0xBC000000, 0x3FF00775, 0x9837D6E0, 0x3E253114, + 0xC0000000, 0x3FF00779, 0x5238327D, 0xBE37887F, + 0xC0000000, 0x3FF0077D, 0x24C8DC90, 0x3E1999FA, + 0xC4000000, 0x3FF00781, 0x1DA2F8BE, 0xBE3B9A7C, + 0xC4000000, 0x3FF00785, 0xEA50EE6A, 0x3E03A485, + 0xC8000000, 0x3FF00789, 0xE204A449, 0xBE3F6C5A, + 0xC8000000, 0x3FF0078D, 0x78D5D0F3, 0xBDF3D3EF, + 0xC8000000, 0x3FF00791, 0x80B1D66C, 0x3E3D01E4, + 0xCC000000, 0x3FF00795, 0xD5149796, 0xBE12BBC1, + 0xCC000000, 0x3FF00799, 0x2A8F92F0, 0x3E39B042, + 0xD0000000, 0x3FF0079D, 0x6F386487, 0xBE1F820E, + 0xD0000000, 0x3FF007A1, 0x3BA3BCDA, 0x3E369EBE, + 0xD4000000, 0x3FF007A5, 0x96320652, 0xBE25A3F0, + 0xD4000000, 0x3FF007A9, 0xD3FD8FCA, 0x3E33CD58, + 0xD8000000, 0x3FF007AD, 0xC62D40B1, 0xBE2B069C, + 0xD8000000, 0x3FF007B1, 0x13AC5766, 0x3E313C12, + 0xDC000000, 0x3FF007B5, 0x876F3A0B, 0xBE2FE90B, + 0xDC000000, 0x3FF007B9, 0x357EDEB8, 0x3E2DD5D4, + 0xE0000000, 0x3FF007BD, 0x4CEC957E, 0xBE32259E, + 0xE0000000, 0x3FF007C1, 0x128C86C6, 0x3E29B3C2, + 0xE4000000, 0x3FF007C5, 0xDEA61608, 0xBE341697, + 0xE4000000, 0x3FF007C9, 0xFEA09E70, 0x3E2611ED, + 0xE8000000, 0x3FF007CD, 0x58D49AE3, 0xBE35C772, + 0xE8000000, 0x3FF007D1, 0x39DA3D42, 0x3E22F058, + 0xEC000000, 0x3FF007D5, 0x9B689043, 0xBE37382D, + 0xEC000000, 0x3FF007D9, 0x04589AD6, 0x3E204F01, + 0xF0000000, 0x3FF007DD, 0x86525259, 0xBE3868C9, + 0xF0000000, 0x3FF007E1, 0x3C761DAC, 0x3E1C5BD1, + 0xF4000000, 0x3FF007E5, 0xF9822D4C, 0xBE395945, + 0xF4000000, 0x3FF007E9, 0x8F4221F9, 0x3E191A1E, + 0xF8000000, 0x3FF007ED, 0xD4E85D3A, 0xBE3A09A2, + 0xF8000000, 0x3FF007F1, 0x81547225, 0x3E16D8EA, + 0xFC000000, 0x3FF007F5, 0xF8750E3B, 0xBE3A79DF, + 0xFC000000, 0x3FF007F9, 0x92EC7DE3, 0x3E159835, + 0x00000000, 0x3FF007FE, 0x44185C5D, 0xBE3AA9FD } }; + +#endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/ulog.h b/REORG.TODO/sysdeps/ieee754/dbl-64/ulog.h new file mode 100644 index 0000000000..e5fbad044e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/ulog.h @@ -0,0 +1,187 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/******************************************************************/ +/* */ +/* MODULE_NAME:ulog.h */ +/* */ +/* common data and variables prototype and definition */ +/******************************************************************/ + +#ifndef ULOG_H +#define ULOG_H + +#ifdef BIG_ENDI + static const number + /* polynomial I */ +/**/ a2 = {{0xbfe00000, 0x0001aa8f} }, /* -0.500... */ +/**/ a3 = {{0x3fd55555, 0x55588d2e} }, /* 0.333... */ + /* polynomial II */ +/**/ b0 = {{0x3fd55555, 0x55555555} }, /* 0.333... */ +/**/ b1 = {{0xbfcfffff, 0xffffffbb} }, /* -0.249... */ +/**/ b2 = {{0x3fc99999, 0x9999992f} }, /* 0.199... */ +/**/ b3 = {{0xbfc55555, 0x556503fd} }, /* -0.166... */ +/**/ b4 = {{0x3fc24924, 0x925b3d62} }, /* 0.142... */ +/**/ b5 = {{0xbfbffffe, 0x160472fc} }, /* -0.124... */ +/**/ b6 = {{0x3fbc71c5, 0x25db58ac} }, /* 0.111... */ +/**/ b7 = {{0xbfb9a4ac, 0x11a2a61c} }, /* -0.100... */ +/**/ b8 = {{0x3fb75077, 0x0df2b591} }, /* 0.091... */ + /* polynomial III */ +#if 0 +/**/ c1 = {{0x3ff00000, 0x00000000} }, /* 1 */ +#endif +/**/ c2 = {{0xbfe00000, 0x00000000} }, /* -1/2 */ +/**/ c3 = {{0x3fd55555, 0x55555555} }, /* 1/3 */ +/**/ c4 = {{0xbfd00000, 0x00000000} }, /* -1/4 */ +/**/ c5 = {{0x3fc99999, 0x9999999a} }, /* 1/5 */ + /* polynomial IV */ +/**/ d2 = {{0xbfe00000, 0x00000000} }, /* -1/2 */ +/**/ dd2 = {{0x00000000, 0x00000000} }, /* -1/2-d2 */ +/**/ d3 = {{0x3fd55555, 0x55555555} }, /* 1/3 */ +/**/ dd3 = {{0x3c755555, 0x55555555} }, /* 1/3-d3 */ +/**/ d4 = {{0xbfd00000, 0x00000000} }, /* -1/4 */ +/**/ dd4 = {{0x00000000, 0x00000000} }, /* -1/4-d4 */ +/**/ d5 = {{0x3fc99999, 0x9999999a} }, /* 1/5 */ +/**/ dd5 = {{0xbc699999, 0x9999999a} }, /* 1/5-d5 */ +/**/ d6 = {{0xbfc55555, 0x55555555} }, /* -1/6 */ +/**/ dd6 = {{0xbc655555, 0x55555555} }, /* -1/6-d6 */ +/**/ d7 = {{0x3fc24924, 0x92492492} }, /* 1/7 */ +/**/ dd7 = {{0x3c624924, 0x92492492} }, /* 1/7-d7 */ +/**/ d8 = {{0xbfc00000, 0x00000000} }, /* -1/8 */ +/**/ dd8 = {{0x00000000, 0x00000000} }, /* -1/8-d8 */ +/**/ d9 = {{0x3fbc71c7, 0x1c71c71c} }, /* 1/9 */ +/**/ dd9 = {{0x3c5c71c7, 0x1c71c71c} }, /* 1/9-d9 */ +/**/ d10 = {{0xbfb99999, 0x9999999a} }, /* -1/10 */ +/**/ dd10 = {{0x3c599999, 0x9999999a} }, /* -1/10-d10 */ +/**/ d11 = {{0x3fb745d1, 0x745d1746} }, /* 1/11 */ +/**/ d12 = {{0xbfb55555, 0x55555555} }, /* -1/12 */ +/**/ d13 = {{0x3fb3b13b, 0x13b13b14} }, /* 1/13 */ +/**/ d14 = {{0xbfb24924, 0x92492492} }, /* -1/14 */ +/**/ d15 = {{0x3fb11111, 0x11111111} }, /* 1/15 */ +/**/ d16 = {{0xbfb00000, 0x00000000} }, /* -1/16 */ +/**/ d17 = {{0x3fae1e1e, 0x1e1e1e1e} }, /* 1/17 */ +/**/ d18 = {{0xbfac71c7, 0x1c71c71c} }, /* -1/18 */ +/**/ d19 = {{0x3faaf286, 0xbca1af28} }, /* 1/19 */ +/**/ d20 = {{0xbfa99999, 0x9999999a} }, /* -1/20 */ + /* constants */ +/**/ sqrt_2 = {{0x3ff6a09e, 0x667f3bcc} }, /* sqrt(2) */ +/**/ h1 = {{0x3fd2e000, 0x00000000} }, /* 151/2**9 */ +/**/ h2 = {{0x3f669000, 0x00000000} }, /* 361/2**17 */ +/**/ delu = {{0x3f700000, 0x00000000} }, /* 1/2**8 */ +/**/ delv = {{0x3ef00000, 0x00000000} }, /* 1/2**16 */ +/**/ ln2a = {{0x3fe62e42, 0xfefa3800} }, /* ln(2) 43 bits */ +/**/ ln2b = {{0x3d2ef357, 0x93c76730} }, /* ln(2)-ln2a */ +/**/ e1 = {{0x3bbcc868, 0x00000000} }, /* 6.095e-21 */ +/**/ e2 = {{0x3c1138ce, 0x00000000} }, /* 2.334e-19 */ +/**/ e3 = {{0x3aa1565d, 0x00000000} }, /* 2.801e-26 */ +/**/ e4 = {{0x39809d88, 0x00000000} }, /* 1.024e-31 */ +/**/ e[M] ={{{0x37da223a, 0x00000000} }, /* 1.2e-39 */ +/**/ {{0x35c851c4, 0x00000000} }, /* 1.3e-49 */ +/**/ {{0x2ab85e51, 0x00000000} }, /* 6.8e-103 */ +/**/ {{0x17383827, 0x00000000} }},/* 8.1e-197 */ +/**/ two54 = {{0x43500000, 0x00000000} }, /* 2**54 */ +/**/ u03 = {{0x3f9eb851, 0xeb851eb8} }; /* 0.03 */ + +#else +#ifdef LITTLE_ENDI + static const number + /* polynomial I */ +/**/ a2 = {{0x0001aa8f, 0xbfe00000} }, /* -0.500... */ +/**/ a3 = {{0x55588d2e, 0x3fd55555} }, /* 0.333... */ + /* polynomial II */ +/**/ b0 = {{0x55555555, 0x3fd55555} }, /* 0.333... */ +/**/ b1 = {{0xffffffbb, 0xbfcfffff} }, /* -0.249... */ +/**/ b2 = {{0x9999992f, 0x3fc99999} }, /* 0.199... */ +/**/ b3 = {{0x556503fd, 0xbfc55555} }, /* -0.166... */ +/**/ b4 = {{0x925b3d62, 0x3fc24924} }, /* 0.142... */ +/**/ b5 = {{0x160472fc, 0xbfbffffe} }, /* -0.124... */ +/**/ b6 = {{0x25db58ac, 0x3fbc71c5} }, /* 0.111... */ +/**/ b7 = {{0x11a2a61c, 0xbfb9a4ac} }, /* -0.100... */ +/**/ b8 = {{0x0df2b591, 0x3fb75077} }, /* 0.091... */ + /* polynomial III */ +#if 0 +/**/ c1 = {{0x00000000, 0x3ff00000} }, /* 1 */ +#endif +/**/ c2 = {{0x00000000, 0xbfe00000} }, /* -1/2 */ +/**/ c3 = {{0x55555555, 0x3fd55555} }, /* 1/3 */ +/**/ c4 = {{0x00000000, 0xbfd00000} }, /* -1/4 */ +/**/ c5 = {{0x9999999a, 0x3fc99999} }, /* 1/5 */ + /* polynomial IV */ +/**/ d2 = {{0x00000000, 0xbfe00000} }, /* -1/2 */ +/**/ dd2 = {{0x00000000, 0x00000000} }, /* -1/2-d2 */ +/**/ d3 = {{0x55555555, 0x3fd55555} }, /* 1/3 */ +/**/ dd3 = {{0x55555555, 0x3c755555} }, /* 1/3-d3 */ +/**/ d4 = {{0x00000000, 0xbfd00000} }, /* -1/4 */ +/**/ dd4 = {{0x00000000, 0x00000000} }, /* -1/4-d4 */ +/**/ d5 = {{0x9999999a, 0x3fc99999} }, /* 1/5 */ +/**/ dd5 = {{0x9999999a, 0xbc699999} }, /* 1/5-d5 */ +/**/ d6 = {{0x55555555, 0xbfc55555} }, /* -1/6 */ +/**/ dd6 = {{0x55555555, 0xbc655555} }, /* -1/6-d6 */ +/**/ d7 = {{0x92492492, 0x3fc24924} }, /* 1/7 */ +/**/ dd7 = {{0x92492492, 0x3c624924} }, /* 1/7-d7 */ +/**/ d8 = {{0x00000000, 0xbfc00000} }, /* -1/8 */ +/**/ dd8 = {{0x00000000, 0x00000000} }, /* -1/8-d8 */ +/**/ d9 = {{0x1c71c71c, 0x3fbc71c7} }, /* 1/9 */ +/**/ dd9 = {{0x1c71c71c, 0x3c5c71c7} }, /* 1/9-d9 */ +/**/ d10 = {{0x9999999a, 0xbfb99999} }, /* -1/10 */ +/**/ dd10 = {{0x9999999a, 0x3c599999} }, /* -1/10-d10 */ +/**/ d11 = {{0x745d1746, 0x3fb745d1} }, /* 1/11 */ +/**/ d12 = {{0x55555555, 0xbfb55555} }, /* -1/12 */ +/**/ d13 = {{0x13b13b14, 0x3fb3b13b} }, /* 1/13 */ +/**/ d14 = {{0x92492492, 0xbfb24924} }, /* -1/14 */ +/**/ d15 = {{0x11111111, 0x3fb11111} }, /* 1/15 */ +/**/ d16 = {{0x00000000, 0xbfb00000} }, /* -1/16 */ +/**/ d17 = {{0x1e1e1e1e, 0x3fae1e1e} }, /* 1/17 */ +/**/ d18 = {{0x1c71c71c, 0xbfac71c7} }, /* -1/18 */ +/**/ d19 = {{0xbca1af28, 0x3faaf286} }, /* 1/19 */ +/**/ d20 = {{0x9999999a, 0xbfa99999} }, /* -1/20 */ + /* constants */ +/**/ sqrt_2 = {{0x667f3bcc, 0x3ff6a09e} }, /* sqrt(2) */ +/**/ h1 = {{0x00000000, 0x3fd2e000} }, /* 151/2**9 */ +/**/ h2 = {{0x00000000, 0x3f669000} }, /* 361/2**17 */ +/**/ delu = {{0x00000000, 0x3f700000} }, /* 1/2**8 */ +/**/ delv = {{0x00000000, 0x3ef00000} }, /* 1/2**16 */ +/**/ ln2a = {{0xfefa3800, 0x3fe62e42} }, /* ln(2) 43 bits */ +/**/ ln2b = {{0x93c76730, 0x3d2ef357} }, /* ln(2)-ln2a */ +/**/ e1 = {{0x00000000, 0x3bbcc868} }, /* 6.095e-21 */ +/**/ e2 = {{0x00000000, 0x3c1138ce} }, /* 2.334e-19 */ +/**/ e3 = {{0x00000000, 0x3aa1565d} }, /* 2.801e-26 */ +/**/ e4 = {{0x00000000, 0x39809d88} }, /* 1.024e-31 */ +/**/ e[M] ={{{0x00000000, 0x37da223a} }, /* 1.2e-39 */ +/**/ {{0x00000000, 0x35c851c4} }, /* 1.3e-49 */ +/**/ {{0x00000000, 0x2ab85e51} }, /* 6.8e-103 */ +/**/ {{0x00000000, 0x17383827} }},/* 8.1e-197 */ +/**/ two54 = {{0x00000000, 0x43500000} }, /* 2**54 */ +/**/ u03 = {{0xeb851eb8, 0x3f9eb851} }; /* 0.03 */ + +#endif +#endif + +#define SQRT_2 sqrt_2.d +#define DEL_U delu.d +#define DEL_V delv.d +#define LN2A ln2a.d +#define LN2B ln2b.d +#define E1 e1.d +#define E2 e2.d +#define E3 e3.d +#define E4 e4.d +#define U03 u03.d + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/ulog.tbl b/REORG.TODO/sysdeps/ieee754/dbl-64/ulog.tbl new file mode 100644 index 0000000000..8714ea3a6a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/ulog.tbl @@ -0,0 +1,3326 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/****************************************************************/ +/* TABLES FOR THE ulog() FUNCTION */ +/****************************************************************/ + +#ifdef BIG_ENDI + static const number + Iu[182] = { /* 1/ui */ +/**/ {{0x3ff6a13c, 0xd1537290} }, +/**/ {{0x3ff68168, 0x16816817} }, +/**/ {{0x3ff661ec, 0x6a5122f9} }, +/**/ {{0x3ff642c8, 0x590b2164} }, +/**/ {{0x3ff623fa, 0x77016240} }, +/**/ {{0x3ff60581, 0x60581606} }, +/**/ {{0x3ff5e75b, 0xb8d015e7} }, +/**/ {{0x3ff5c988, 0x2b931057} }, +/**/ {{0x3ff5ac05, 0x6b015ac0} }, +/**/ {{0x3ff58ed2, 0x308158ed} }, +/**/ {{0x3ff571ed, 0x3c506b3a} }, +/**/ {{0x3ff55555, 0x55555555} }, +/**/ {{0x3ff53909, 0x48f40feb} }, +/**/ {{0x3ff51d07, 0xeae2f815} }, +/**/ {{0x3ff50150, 0x15015015} }, +/**/ {{0x3ff4e5e0, 0xa72f0539} }, +/**/ {{0x3ff4cab8, 0x8725af6e} }, +/**/ {{0x3ff4afd6, 0xa052bf5b} }, +/**/ {{0x3ff49539, 0xe3b2d067} }, +/**/ {{0x3ff47ae1, 0x47ae147b} }, +/**/ {{0x3ff460cb, 0xc7f5cf9a} }, +/**/ {{0x3ff446f8, 0x6562d9fb} }, +/**/ {{0x3ff42d66, 0x25d51f87} }, +/**/ {{0x3ff41414, 0x14141414} }, +/**/ {{0x3ff3fb01, 0x3fb013fb} }, +/**/ {{0x3ff3e22c, 0xbce4a902} }, +/**/ {{0x3ff3c995, 0xa47babe7} }, +/**/ {{0x3ff3b13b, 0x13b13b14} }, +/**/ {{0x3ff3991c, 0x2c187f63} }, +/**/ {{0x3ff38138, 0x13813814} }, +/**/ {{0x3ff3698d, 0xf3de0748} }, +/**/ {{0x3ff3521c, 0xfb2b78c1} }, +/**/ {{0x3ff33ae4, 0x5b57bcb2} }, +/**/ {{0x3ff323e3, 0x4a2b10bf} }, +/**/ {{0x3ff30d19, 0x0130d190} }, +/**/ {{0x3ff2f684, 0xbda12f68} }, +/**/ {{0x3ff2e025, 0xc04b8097} }, +/**/ {{0x3ff2c9fb, 0x4d812ca0} }, +/**/ {{0x3ff2b404, 0xad012b40} }, +/**/ {{0x3ff29e41, 0x29e4129e} }, +/**/ {{0x3ff288b0, 0x1288b013} }, +/**/ {{0x3ff27350, 0xb8812735} }, +/**/ {{0x3ff25e22, 0x708092f1} }, +/**/ {{0x3ff24924, 0x92492492} }, +/**/ {{0x3ff23456, 0x789abcdf} }, +/**/ {{0x3ff21fb7, 0x8121fb78} }, +/**/ {{0x3ff20b47, 0x0c67c0d9} }, +/**/ {{0x3ff1f704, 0x7dc11f70} }, +/**/ {{0x3ff1e2ef, 0x3b3fb874} }, +/**/ {{0x3ff1cf06, 0xada2811d} }, +/**/ {{0x3ff1bb4a, 0x4046ed29} }, +/**/ {{0x3ff1a7b9, 0x611a7b96} }, +/**/ {{0x3ff19453, 0x808ca29c} }, +/**/ {{0x3ff18118, 0x11811812} }, +/**/ {{0x3ff16e06, 0x89427379} }, +/**/ {{0x3ff15b1e, 0x5f75270d} }, +/**/ {{0x3ff1485f, 0x0e0acd3b} }, +/**/ {{0x3ff135c8, 0x1135c811} }, +/**/ {{0x3ff12358, 0xe75d3033} }, +/**/ {{0x3ff11111, 0x11111111} }, +/**/ {{0x3ff0fef0, 0x10fef011} }, +/**/ {{0x3ff0ecf5, 0x6be69c90} }, +/**/ {{0x3ff0db20, 0xa88f4696} }, +/**/ {{0x3ff0c971, 0x4fbcda3b} }, +/**/ {{0x3ff0b7e6, 0xec259dc8} }, +/**/ {{0x3ff0a681, 0x0a6810a7} }, +/**/ {{0x3ff0953f, 0x39010954} }, +/**/ {{0x3ff08421, 0x08421084} }, +/**/ {{0x3ff07326, 0x0a47f7c6} }, +/**/ {{0x3ff0624d, 0xd2f1a9fc} }, +/**/ {{0x3ff05197, 0xf7d73404} }, +/**/ {{0x3ff04104, 0x10410410} }, +/**/ {{0x3ff03091, 0xb51f5e1a} }, +/**/ {{0x3ff02040, 0x81020408} }, +/**/ {{0x3ff01010, 0x10101010} }, +/**/ {{0x3ff00000, 0x00000000} }, +/**/ {{0x3fefe01f, 0xe01fe020} }, +/**/ {{0x3fefc07f, 0x01fc07f0} }, +/**/ {{0x3fefa11c, 0xaa01fa12} }, +/**/ {{0x3fef81f8, 0x1f81f820} }, +/**/ {{0x3fef6310, 0xaca0dbb5} }, +/**/ {{0x3fef4465, 0x9e4a4271} }, +/**/ {{0x3fef25f6, 0x44230ab5} }, +/**/ {{0x3fef07c1, 0xf07c1f08} }, +/**/ {{0x3feee9c7, 0xf8458e02} }, +/**/ {{0x3feecc07, 0xb301ecc0} }, +/**/ {{0x3feeae80, 0x7aba01eb} }, +/**/ {{0x3fee9131, 0xabf0b767} }, +/**/ {{0x3fee741a, 0xa59750e4} }, +/**/ {{0x3fee573a, 0xc901e574} }, +/**/ {{0x3fee3a91, 0x79dc1a73} }, +/**/ {{0x3fee1e1e, 0x1e1e1e1e} }, +/**/ {{0x3fee01e0, 0x1e01e01e} }, +/**/ {{0x3fede5d6, 0xe3f8868a} }, +/**/ {{0x3fedca01, 0xdca01dca} }, +/**/ {{0x3fedae60, 0x76b981db} }, +/**/ {{0x3fed92f2, 0x231e7f8a} }, +/**/ {{0x3fed77b6, 0x54b82c34} }, +/**/ {{0x3fed5cac, 0x807572b2} }, +/**/ {{0x3fed41d4, 0x1d41d41d} }, +/**/ {{0x3fed272c, 0xa3fc5b1a} }, +/**/ {{0x3fed0cb5, 0x8f6ec074} }, +/**/ {{0x3fecf26e, 0x5c44bfc6} }, +/**/ {{0x3fecd856, 0x89039b0b} }, +/**/ {{0x3fecbe6d, 0x9601cbe7} }, +/**/ {{0x3feca4b3, 0x055ee191} }, +/**/ {{0x3fec8b26, 0x5afb8a42} }, +/**/ {{0x3fec71c7, 0x1c71c71c} }, +/**/ {{0x3fec5894, 0xd10d4986} }, +/**/ {{0x3fec3f8f, 0x01c3f8f0} }, +/**/ {{0x3fec26b5, 0x392ea01c} }, +/**/ {{0x3fec0e07, 0x0381c0e0} }, +/**/ {{0x3febf583, 0xee868d8b} }, +/**/ {{0x3febdd2b, 0x899406f7} }, +/**/ {{0x3febc4fd, 0x65883e7b} }, +/**/ {{0x3febacf9, 0x14c1bad0} }, +/**/ {{0x3feb951e, 0x2b18ff23} }, +/**/ {{0x3feb7d6c, 0x3dda338b} }, +/**/ {{0x3feb65e2, 0xe3beee05} }, +/**/ {{0x3feb4e81, 0xb4e81b4f} }, +/**/ {{0x3feb3748, 0x4ad806ce} }, +/**/ {{0x3feb2036, 0x406c80d9} }, +/**/ {{0x3feb094b, 0x31d922a4} }, +/**/ {{0x3feaf286, 0xbca1af28} }, +/**/ {{0x3feadbe8, 0x7f94905e} }, +/**/ {{0x3feac570, 0x1ac5701b} }, +/**/ {{0x3feaaf1d, 0x2f87ebfd} }, +/**/ {{0x3fea98ef, 0x606a63be} }, +/**/ {{0x3fea82e6, 0x5130e159} }, +/**/ {{0x3fea6d01, 0xa6d01a6d} }, +/**/ {{0x3fea5741, 0x07688a4a} }, +/**/ {{0x3fea41a4, 0x1a41a41a} }, +/**/ {{0x3fea2c2a, 0x87c51ca0} }, +/**/ {{0x3fea16d3, 0xf97a4b02} }, +/**/ {{0x3fea01a0, 0x1a01a01a} }, +/**/ {{0x3fe9ec8e, 0x951033d9} }, +/**/ {{0x3fe9d79f, 0x176b682d} }, +/**/ {{0x3fe9c2d1, 0x4ee4a102} }, +/**/ {{0x3fe9ae24, 0xea5510da} }, +/**/ {{0x3fe99999, 0x9999999a} }, +/**/ {{0x3fe9852f, 0x0d8ec0ff} }, +/**/ {{0x3fe970e4, 0xf80cb872} }, +/**/ {{0x3fe95cbb, 0x0be377ae} }, +/**/ {{0x3fe948b0, 0xfcd6e9e0} }, +/**/ {{0x3fe934c6, 0x7f9b2ce6} }, +/**/ {{0x3fe920fb, 0x49d0e229} }, +/**/ {{0x3fe90d4f, 0x120190d5} }, +/**/ {{0x3fe8f9c1, 0x8f9c18fa} }, +/**/ {{0x3fe8e652, 0x7af1373f} }, +/**/ {{0x3fe8d301, 0x8d3018d3} }, +/**/ {{0x3fe8bfce, 0x8062ff3a} }, +/**/ {{0x3fe8acb9, 0x0f6bf3aa} }, +/**/ {{0x3fe899c0, 0xf601899c} }, +/**/ {{0x3fe886e5, 0xf0abb04a} }, +/**/ {{0x3fe87427, 0xbcc092b9} }, +/**/ {{0x3fe86186, 0x18618618} }, +/**/ {{0x3fe84f00, 0xc2780614} }, +/**/ {{0x3fe83c97, 0x7ab2bedd} }, +/**/ {{0x3fe82a4a, 0x0182a4a0} }, +/**/ {{0x3fe81818, 0x18181818} }, +/**/ {{0x3fe80601, 0x80601806} }, +/**/ {{0x3fe7f405, 0xfd017f40} }, +/**/ {{0x3fe7e225, 0x515a4f1d} }, +/**/ {{0x3fe7d05f, 0x417d05f4} }, +/**/ {{0x3fe7beb3, 0x922e017c} }, +/**/ {{0x3fe7ad22, 0x08e0ecc3} }, +/**/ {{0x3fe79baa, 0x6bb6398b} }, +/**/ {{0x3fe78a4c, 0x8178a4c8} }, +/**/ {{0x3fe77908, 0x119ac60d} }, +/**/ {{0x3fe767dc, 0xe434a9b1} }, +/**/ {{0x3fe756ca, 0xc201756d} }, +/**/ {{0x3fe745d1, 0x745d1746} }, +/**/ {{0x3fe734f0, 0xc541fe8d} }, +/**/ {{0x3fe72428, 0x7f46debc} }, +/**/ {{0x3fe71378, 0x6d9c7c09} }, +/**/ {{0x3fe702e0, 0x5c0b8170} }, +/**/ {{0x3fe6f260, 0x16f26017} }, +/**/ {{0x3fe6e1f7, 0x6b4337c7} }, +/**/ {{0x3fe6d1a6, 0x2681c861} }, +/**/ {{0x3fe6c16c, 0x16c16c17} }, +/**/ {{0x3fe6b149, 0x0aa31a3d} }, +/**/ {{0x3fe6a13c, 0xd1537290} }, + }; + + static const number + Iv[362] = { /* 1/vj */ +/**/ {{0x3ff00b47, 0xee93bfe3} }, +/**/ {{0x3ff00b37, 0xd80c106f} }, +/**/ {{0x3ff00b27, 0xc1a4a47a} }, +/**/ {{0x3ff00b17, 0xab5d7ba2} }, +/**/ {{0x3ff00b07, 0x95369587} }, +/**/ {{0x3ff00af7, 0x7f2ff1c6} }, +/**/ {{0x3ff00ae7, 0x69499000} }, +/**/ {{0x3ff00ad7, 0x53836fd3} }, +/**/ {{0x3ff00ac7, 0x3ddd90dd} }, +/**/ {{0x3ff00ab7, 0x2857f2bf} }, +/**/ {{0x3ff00aa7, 0x12f29517} }, +/**/ {{0x3ff00a96, 0xfdad7784} }, +/**/ {{0x3ff00a86, 0xe88899a5} }, +/**/ {{0x3ff00a76, 0xd383fb19} }, +/**/ {{0x3ff00a66, 0xbe9f9b7f} }, +/**/ {{0x3ff00a56, 0xa9db7a76} }, +/**/ {{0x3ff00a46, 0x9537979d} }, +/**/ {{0x3ff00a36, 0x80b3f293} }, +/**/ {{0x3ff00a26, 0x6c508af8} }, +/**/ {{0x3ff00a16, 0x580d606a} }, +/**/ {{0x3ff00a06, 0x43ea7288} }, +/**/ {{0x3ff009f6, 0x2fe7c0f1} }, +/**/ {{0x3ff009e6, 0x1c054b44} }, +/**/ {{0x3ff009d6, 0x08431122} }, +/**/ {{0x3ff009c5, 0xf4a11227} }, +/**/ {{0x3ff009b5, 0xe11f4df4} }, +/**/ {{0x3ff009a5, 0xcdbdc428} }, +/**/ {{0x3ff00995, 0xba7c7462} }, +/**/ {{0x3ff00985, 0xa75b5e40} }, +/**/ {{0x3ff00975, 0x945a8162} }, +/**/ {{0x3ff00965, 0x8179dd68} }, +/**/ {{0x3ff00955, 0x6eb971ef} }, +/**/ {{0x3ff00945, 0x5c193e98} }, +/**/ {{0x3ff00935, 0x49994301} }, +/**/ {{0x3ff00925, 0x37397eca} }, +/**/ {{0x3ff00915, 0x24f9f192} }, +/**/ {{0x3ff00905, 0x12da9af7} }, +/**/ {{0x3ff008f5, 0x00db7a99} }, +/**/ {{0x3ff008e4, 0xeefc9018} }, +/**/ {{0x3ff008d4, 0xdd3ddb12} }, +/**/ {{0x3ff008c4, 0xcb9f5b26} }, +/**/ {{0x3ff008b4, 0xba210ff4} }, +/**/ {{0x3ff008a4, 0xa8c2f91a} }, +/**/ {{0x3ff00894, 0x97851639} }, +/**/ {{0x3ff00884, 0x866766ef} }, +/**/ {{0x3ff00874, 0x7569eadb} }, +/**/ {{0x3ff00864, 0x648ca19d} }, +/**/ {{0x3ff00854, 0x53cf8ad3} }, +/**/ {{0x3ff00844, 0x4332a61e} }, +/**/ {{0x3ff00834, 0x32b5f31b} }, +/**/ {{0x3ff00824, 0x2259716c} }, +/**/ {{0x3ff00814, 0x121d20ad} }, +/**/ {{0x3ff00804, 0x02010080} }, +/**/ {{0x3ff007f3, 0xf2051083} }, +/**/ {{0x3ff007e3, 0xe2295056} }, +/**/ {{0x3ff007d3, 0xd26dbf97} }, +/**/ {{0x3ff007c3, 0xc2d25de5} }, +/**/ {{0x3ff007b3, 0xb3572ae2} }, +/**/ {{0x3ff007a3, 0xa3fc262a} }, +/**/ {{0x3ff00793, 0x94c14f5f} }, +/**/ {{0x3ff00783, 0x85a6a61e} }, +/**/ {{0x3ff00773, 0x76ac2a08} }, +/**/ {{0x3ff00763, 0x67d1dabb} }, +/**/ {{0x3ff00753, 0x5917b7d7} }, +/**/ {{0x3ff00743, 0x4a7dc0fb} }, +/**/ {{0x3ff00733, 0x3c03f5c7} }, +/**/ {{0x3ff00723, 0x2daa55da} }, +/**/ {{0x3ff00713, 0x1f70e0d3} }, +/**/ {{0x3ff00703, 0x11579652} }, +/**/ {{0x3ff006f3, 0x035e75f5} }, +/**/ {{0x3ff006e2, 0xf5857f5d} }, +/**/ {{0x3ff006d2, 0xe7ccb228} }, +/**/ {{0x3ff006c2, 0xda340df6} }, +/**/ {{0x3ff006b2, 0xccbb9266} }, +/**/ {{0x3ff006a2, 0xbf633f18} }, +/**/ {{0x3ff00692, 0xb22b13ab} }, +/**/ {{0x3ff00682, 0xa5130fbe} }, +/**/ {{0x3ff00672, 0x981b32f1} }, +/**/ {{0x3ff00662, 0x8b437ce4} }, +/**/ {{0x3ff00652, 0x7e8bed35} }, +/**/ {{0x3ff00642, 0x71f48383} }, +/**/ {{0x3ff00632, 0x657d3f70} }, +/**/ {{0x3ff00622, 0x59262098} }, +/**/ {{0x3ff00612, 0x4cef269e} }, +/**/ {{0x3ff00602, 0x40d8511e} }, +/**/ {{0x3ff005f2, 0x34e19fba} }, +/**/ {{0x3ff005e2, 0x290b1211} }, +/**/ {{0x3ff005d2, 0x1d54a7c1} }, +/**/ {{0x3ff005c2, 0x11be606b} }, +/**/ {{0x3ff005b2, 0x06483bad} }, +/**/ {{0x3ff005a1, 0xfaf23928} }, +/**/ {{0x3ff00591, 0xefbc587b} }, +/**/ {{0x3ff00581, 0xe4a69945} }, +/**/ {{0x3ff00571, 0xd9b0fb25} }, +/**/ {{0x3ff00561, 0xcedb7dbc} }, +/**/ {{0x3ff00551, 0xc42620a9} }, +/**/ {{0x3ff00541, 0xb990e38b} }, +/**/ {{0x3ff00531, 0xaf1bc601} }, +/**/ {{0x3ff00521, 0xa4c6c7ac} }, +/**/ {{0x3ff00511, 0x9a91e82a} }, +/**/ {{0x3ff00501, 0x907d271c} }, +/**/ {{0x3ff004f1, 0x86888421} }, +/**/ {{0x3ff004e1, 0x7cb3fed8} }, +/**/ {{0x3ff004d1, 0x72ff96e0} }, +/**/ {{0x3ff004c1, 0x696b4bdb} }, +/**/ {{0x3ff004b1, 0x5ff71d66} }, +/**/ {{0x3ff004a1, 0x56a30b21} }, +/**/ {{0x3ff00491, 0x4d6f14ad} }, +/**/ {{0x3ff00481, 0x445b39a8} }, +/**/ {{0x3ff00471, 0x3b6779b3} }, +/**/ {{0x3ff00461, 0x3293d46c} }, +/**/ {{0x3ff00451, 0x29e04974} }, +/**/ {{0x3ff00441, 0x214cd869} }, +/**/ {{0x3ff00431, 0x18d980ed} }, +/**/ {{0x3ff00421, 0x1086429d} }, +/**/ {{0x3ff00411, 0x08531d1a} }, +/**/ {{0x3ff00401, 0x00401004} }, +/**/ {{0x3ff003f0, 0xf84d1afa} }, +/**/ {{0x3ff003e0, 0xf07a3d9b} }, +/**/ {{0x3ff003d0, 0xe8c77787} }, +/**/ {{0x3ff003c0, 0xe134c85f} }, +/**/ {{0x3ff003b0, 0xd9c22fc1} }, +/**/ {{0x3ff003a0, 0xd26fad4d} }, +/**/ {{0x3ff00390, 0xcb3d40a3} }, +/**/ {{0x3ff00380, 0xc42ae963} }, +/**/ {{0x3ff00370, 0xbd38a72c} }, +/**/ {{0x3ff00360, 0xb666799e} }, +/**/ {{0x3ff00350, 0xafb46058} }, +/**/ {{0x3ff00340, 0xa9225afa} }, +/**/ {{0x3ff00330, 0xa2b06925} }, +/**/ {{0x3ff00320, 0x9c5e8a77} }, +/**/ {{0x3ff00310, 0x962cbe90} }, +/**/ {{0x3ff00300, 0x901b0511} }, +/**/ {{0x3ff002f0, 0x8a295d98} }, +/**/ {{0x3ff002e0, 0x8457c7c6} }, +/**/ {{0x3ff002d0, 0x7ea6433a} }, +/**/ {{0x3ff002c0, 0x7914cf94} }, +/**/ {{0x3ff002b0, 0x73a36c73} }, +/**/ {{0x3ff002a0, 0x6e521978} }, +/**/ {{0x3ff00290, 0x6920d642} }, +/**/ {{0x3ff00280, 0x640fa271} }, +/**/ {{0x3ff00270, 0x5f1e7da5} }, +/**/ {{0x3ff00260, 0x5a4d677d} }, +/**/ {{0x3ff00250, 0x559c5f9a} }, +/**/ {{0x3ff00240, 0x510b659a} }, +/**/ {{0x3ff00230, 0x4c9a791f} }, +/**/ {{0x3ff00220, 0x484999c6} }, +/**/ {{0x3ff00210, 0x4418c732} }, +/**/ {{0x3ff00200, 0x40080100} }, +/**/ {{0x3ff001f0, 0x3c1746d2} }, +/**/ {{0x3ff001e0, 0x38469846} }, +/**/ {{0x3ff001d0, 0x3495f4fd} }, +/**/ {{0x3ff001c0, 0x31055c96} }, +/**/ {{0x3ff001b0, 0x2d94ceb2} }, +/**/ {{0x3ff001a0, 0x2a444af0} }, +/**/ {{0x3ff00190, 0x2713d0ef} }, +/**/ {{0x3ff00180, 0x24036051} }, +/**/ {{0x3ff00170, 0x2112f8b4} }, +/**/ {{0x3ff00160, 0x1e4299b9} }, +/**/ {{0x3ff00150, 0x1b9242ff} }, +/**/ {{0x3ff00140, 0x1901f427} }, +/**/ {{0x3ff00130, 0x1691acd0} }, +/**/ {{0x3ff00120, 0x14416c9a} }, +/**/ {{0x3ff00110, 0x12113324} }, +/**/ {{0x3ff00100, 0x10010010} }, +/**/ {{0x3ff000f0, 0x0e10d2fc} }, +/**/ {{0x3ff000e0, 0x0c40ab89} }, +/**/ {{0x3ff000d0, 0x0a908957} }, +/**/ {{0x3ff000c0, 0x09006c05} }, +/**/ {{0x3ff000b0, 0x07905334} }, +/**/ {{0x3ff000a0, 0x06403e82} }, +/**/ {{0x3ff00090, 0x05102d92} }, +/**/ {{0x3ff00080, 0x04002001} }, +/**/ {{0x3ff00070, 0x03101571} }, +/**/ {{0x3ff00060, 0x02400d80} }, +/**/ {{0x3ff00050, 0x019007d0} }, +/**/ {{0x3ff00040, 0x01000400} }, +/**/ {{0x3ff00030, 0x009001b0} }, +/**/ {{0x3ff00020, 0x00400080} }, +/**/ {{0x3ff00010, 0x00100010} }, +/**/ {{0x3ff00000, 0x00000000} }, +/**/ {{0x3fefffe0, 0x001fffe0} }, +/**/ {{0x3fefffc0, 0x007fff00} }, +/**/ {{0x3fefffa0, 0x011ffca0} }, +/**/ {{0x3fefff80, 0x01fff800} }, +/**/ {{0x3fefff60, 0x031ff060} }, +/**/ {{0x3fefff40, 0x047fe501} }, +/**/ {{0x3fefff20, 0x061fd521} }, +/**/ {{0x3fefff00, 0x07ffc002} }, +/**/ {{0x3feffee0, 0x0a1fa4e3} }, +/**/ {{0x3feffec0, 0x0c7f8305} }, +/**/ {{0x3feffea0, 0x0f1f59a7} }, +/**/ {{0x3feffe80, 0x11ff280a} }, +/**/ {{0x3feffe60, 0x151eed6e} }, +/**/ {{0x3feffe40, 0x187ea913} }, +/**/ {{0x3feffe20, 0x1c1e5a39} }, +/**/ {{0x3feffe00, 0x1ffe0020} }, +/**/ {{0x3feffde0, 0x241d9a09} }, +/**/ {{0x3feffdc0, 0x287d2733} }, +/**/ {{0x3feffda0, 0x2d1ca6e0} }, +/**/ {{0x3feffd80, 0x31fc184e} }, +/**/ {{0x3feffd60, 0x371b7abf} }, +/**/ {{0x3feffd40, 0x3c7acd72} }, +/**/ {{0x3feffd20, 0x421a0fa9} }, +/**/ {{0x3feffd00, 0x47f940a2} }, +/**/ {{0x3feffce0, 0x4e185f9f} }, +/**/ {{0x3feffcc0, 0x54776bdf} }, +/**/ {{0x3feffca0, 0x5b1664a3} }, +/**/ {{0x3feffc80, 0x61f5492c} }, +/**/ {{0x3feffc60, 0x691418b9} }, +/**/ {{0x3feffc40, 0x7072d28b} }, +/**/ {{0x3feffc20, 0x781175e3} }, +/**/ {{0x3feffc00, 0x7ff00200} }, +/**/ {{0x3feffbe0, 0x880e7623} }, +/**/ {{0x3feffbc0, 0x906cd18c} }, +/**/ {{0x3feffba0, 0x990b137c} }, +/**/ {{0x3feffb80, 0xa1e93b34} }, +/**/ {{0x3feffb60, 0xab0747f3} }, +/**/ {{0x3feffb40, 0xb46538fa} }, +/**/ {{0x3feffb20, 0xbe030d89} }, +/**/ {{0x3feffb00, 0xc7e0c4e1} }, +/**/ {{0x3feffae0, 0xd1fe5e43} }, +/**/ {{0x3feffac0, 0xdc5bd8ee} }, +/**/ {{0x3feffaa0, 0xe6f93424} }, +/**/ {{0x3feffa80, 0xf1d66f25} }, +/**/ {{0x3feffa60, 0xfcf38931} }, +/**/ {{0x3feffa41, 0x08508189} }, +/**/ {{0x3feffa21, 0x13ed576d} }, +/**/ {{0x3feffa01, 0x1fca0a1e} }, +/**/ {{0x3feff9e1, 0x2be698dd} }, +/**/ {{0x3feff9c1, 0x384302e9} }, +/**/ {{0x3feff9a1, 0x44df4785} }, +/**/ {{0x3feff981, 0x51bb65ef} }, +/**/ {{0x3feff961, 0x5ed75d6a} }, +/**/ {{0x3feff941, 0x6c332d34} }, +/**/ {{0x3feff921, 0x79ced490} }, +/**/ {{0x3feff901, 0x87aa52be} }, +/**/ {{0x3feff8e1, 0x95c5a6fe} }, +/**/ {{0x3feff8c1, 0xa420d091} }, +/**/ {{0x3feff8a1, 0xb2bbceb7} }, +/**/ {{0x3feff881, 0xc196a0b2} }, +/**/ {{0x3feff861, 0xd0b145c2} }, +/**/ {{0x3feff841, 0xe00bbd28} }, +/**/ {{0x3feff821, 0xefa60624} }, +/**/ {{0x3feff801, 0xff801ff8} }, +/**/ {{0x3feff7e2, 0x0f9a09e3} }, +/**/ {{0x3feff7c2, 0x1ff3c328} }, +/**/ {{0x3feff7a2, 0x308d4b05} }, +/**/ {{0x3feff782, 0x4166a0bd} }, +/**/ {{0x3feff762, 0x527fc390} }, +/**/ {{0x3feff742, 0x63d8b2bf} }, +/**/ {{0x3feff722, 0x75716d8b} }, +/**/ {{0x3feff702, 0x8749f334} }, +/**/ {{0x3feff6e2, 0x996242fb} }, +/**/ {{0x3feff6c2, 0xabba5c21} }, +/**/ {{0x3feff6a2, 0xbe523de8} }, +/**/ {{0x3feff682, 0xd129e78f} }, +/**/ {{0x3feff662, 0xe4415858} }, +/**/ {{0x3feff642, 0xf7988f84} }, +/**/ {{0x3feff623, 0x0b2f8c54} }, +/**/ {{0x3feff603, 0x1f064e08} }, +/**/ {{0x3feff5e3, 0x331cd3e1} }, +/**/ {{0x3feff5c3, 0x47731d21} }, +/**/ {{0x3feff5a3, 0x5c092908} }, +/**/ {{0x3feff583, 0x70def6d7} }, +/**/ {{0x3feff563, 0x85f485d0} }, +/**/ {{0x3feff543, 0x9b49d532} }, +/**/ {{0x3feff523, 0xb0dee440} }, +/**/ {{0x3feff503, 0xc6b3b23b} }, +/**/ {{0x3feff4e3, 0xdcc83e62} }, +/**/ {{0x3feff4c3, 0xf31c87f8} }, +/**/ {{0x3feff4a4, 0x09b08e3d} }, +/**/ {{0x3feff484, 0x20845073} }, +/**/ {{0x3feff464, 0x3797cdda} }, +/**/ {{0x3feff444, 0x4eeb05b4} }, +/**/ {{0x3feff424, 0x667df741} }, +/**/ {{0x3feff404, 0x7e50a1c3} }, +/**/ {{0x3feff3e4, 0x9663047b} }, +/**/ {{0x3feff3c4, 0xaeb51eaa} }, +/**/ {{0x3feff3a4, 0xc746ef91} }, +/**/ {{0x3feff384, 0xe0187672} }, +/**/ {{0x3feff364, 0xf929b28d} }, +/**/ {{0x3feff345, 0x127aa323} }, +/**/ {{0x3feff325, 0x2c0b4776} }, +/**/ {{0x3feff305, 0x45db9ec7} }, +/**/ {{0x3feff2e5, 0x5feba858} }, +/**/ {{0x3feff2c5, 0x7a3b6369} }, +/**/ {{0x3feff2a5, 0x94cacf3b} }, +/**/ {{0x3feff285, 0xaf99eb11} }, +/**/ {{0x3feff265, 0xcaa8b62a} }, +/**/ {{0x3feff245, 0xe5f72fc9} }, +/**/ {{0x3feff226, 0x0185572f} }, +/**/ {{0x3feff206, 0x1d532b9d} }, +/**/ {{0x3feff1e6, 0x3960ac54} }, +/**/ {{0x3feff1c6, 0x55add896} }, +/**/ {{0x3feff1a6, 0x723aafa3} }, +/**/ {{0x3feff186, 0x8f0730be} }, +/**/ {{0x3feff166, 0xac135b27} }, +/**/ {{0x3feff146, 0xc95f2e21} }, +/**/ {{0x3feff126, 0xe6eaa8eb} }, +/**/ {{0x3feff107, 0x04b5cac9} }, +/**/ {{0x3feff0e7, 0x22c092fb} }, +/**/ {{0x3feff0c7, 0x410b00c2} }, +/**/ {{0x3feff0a7, 0x5f951360} }, +/**/ {{0x3feff087, 0x7e5eca16} }, +/**/ {{0x3feff067, 0x9d682426} }, +/**/ {{0x3feff047, 0xbcb120d2} }, +/**/ {{0x3feff027, 0xdc39bf5a} }, +/**/ {{0x3feff007, 0xfc01ff00} }, +/**/ {{0x3fefefe8, 0x1c09df07} }, +/**/ {{0x3fefefc8, 0x3c515eae} }, +/**/ {{0x3fefefa8, 0x5cd87d38} }, +/**/ {{0x3fefef88, 0x7d9f39e6} }, +/**/ {{0x3fefef68, 0x9ea593fa} }, +/**/ {{0x3fefef48, 0xbfeb8ab5} }, +/**/ {{0x3fefef28, 0xe1711d5a} }, +/**/ {{0x3fefef09, 0x03364b28} }, +/**/ {{0x3fefeee9, 0x253b1363} }, +/**/ {{0x3fefeec9, 0x477f754b} }, +/**/ {{0x3fefeea9, 0x6a037022} }, +/**/ {{0x3fefee89, 0x8cc7032a} }, +/**/ {{0x3fefee69, 0xafca2da5} }, +/**/ {{0x3fefee49, 0xd30ceed4} }, +/**/ {{0x3fefee29, 0xf68f45f8} }, +/**/ {{0x3fefee0a, 0x1a513254} }, +/**/ {{0x3fefedea, 0x3e52b329} }, +/**/ {{0x3fefedca, 0x6293c7b8} }, +/**/ {{0x3fefedaa, 0x87146f44} }, +/**/ {{0x3fefed8a, 0xabd4a90e} }, +/**/ {{0x3fefed6a, 0xd0d47458} }, +/**/ {{0x3fefed4a, 0xf613d064} }, +/**/ {{0x3fefed2b, 0x1b92bc73} }, +/**/ {{0x3fefed0b, 0x415137c7} }, +/**/ {{0x3fefeceb, 0x674f41a2} }, +/**/ {{0x3fefeccb, 0x8d8cd945} }, +/**/ {{0x3fefecab, 0xb409fdf3} }, +/**/ {{0x3fefec8b, 0xdac6aeed} }, +/**/ {{0x3fefec6c, 0x01c2eb76} }, +/**/ {{0x3fefec4c, 0x28feb2ce} }, +/**/ {{0x3fefec2c, 0x507a0437} }, +/**/ {{0x3fefec0c, 0x7834def5} }, +/**/ {{0x3fefebec, 0xa02f4247} }, +/**/ {{0x3fefebcc, 0xc8692d71} }, +/**/ {{0x3fefebac, 0xf0e29fb4} }, +/**/ {{0x3fefeb8d, 0x199b9852} }, +/**/ {{0x3fefeb6d, 0x4294168d} }, +/**/ {{0x3fefeb4d, 0x6bcc19a7} }, +/**/ {{0x3fefeb2d, 0x9543a0e2} }, +/**/ {{0x3fefeb0d, 0xbefaab7f} }, +/**/ {{0x3fefeaed, 0xe8f138c2} }, +/**/ {{0x3fefeace, 0x132747ea} }, +/**/ {{0x3fefeaae, 0x3d9cd83c} }, +/**/ {{0x3fefea8e, 0x6851e8f7} }, +/**/ {{0x3fefea6e, 0x93467960} }, +/**/ {{0x3fefea4e, 0xbe7a88b7} }, +/**/ {{0x3fefea2e, 0xe9ee163f} }, +/**/ {{0x3fefea0f, 0x15a12139} }, +/**/ {{0x3fefe9ef, 0x4193a8e8} }, +/**/ {{0x3fefe9cf, 0x6dc5ac8e} }, +/**/ {{0x3fefe9af, 0x9a372b6d} }, +/**/ {{0x3fefe98f, 0xc6e824c6} }, +/**/ {{0x3fefe96f, 0xf3d897dd} }, + }; + + static const number + Lu[182][2] = { /* log(ui) */ +/**/ {{{0xbfd63003, 0x0b3aac49} }, +/**/ {{0xbc6dc18c, 0xe51fff99} },}, +/**/ {{{0xbfd5d5bd, 0xdf595f30} }, +/**/ {{0x3c765411, 0x48cbb8a2} },}, +/**/ {{{0xbfd57bf7, 0x53c8d1fb} }, +/**/ {{0x3c60908d, 0x15f88b63} },}, +/**/ {{{0xbfd522ae, 0x0738a3d8} }, +/**/ {{0x3c68f7e9, 0xb38a6979} },}, +/**/ {{{0xbfd4c9e0, 0x9e172c3c} }, +/**/ {{0x3c512361, 0x5b147a5d} },}, +/**/ {{{0xbfd4718d, 0xc271c41b} }, +/**/ {{0xbc38fb4c, 0x14c56eef} },}, +/**/ {{{0xbfd419b4, 0x23d5e8c7} }, +/**/ {{0xbc60dbb2, 0x43827392} },}, +/**/ {{{0xbfd3c252, 0x77333184} }, +/**/ {{0x3c72ad27, 0xe50a8ec6} },}, +/**/ {{{0xbfd36b67, 0x76be1117} }, +/**/ {{0x3c5324f0, 0xe883858e} },}, +/**/ {{{0xbfd314f1, 0xe1d35ce4} }, +/**/ {{0x3c73d699, 0x09e5c3dc} },}, +/**/ {{{0xbfd2bef0, 0x7cdc9354} }, +/**/ {{0x3c782dad, 0x7fd86088} },}, +/**/ {{{0xbfd26962, 0x1134db92} }, +/**/ {{0xbc7e0efa, 0xdd9db02b} },}, +/**/ {{{0xbfd21445, 0x6d0eb8d4} }, +/**/ {{0xbc6f7ae9, 0x1aeba60a} },}, +/**/ {{{0xbfd1bf99, 0x635a6b95} }, +/**/ {{0x3c612aeb, 0x84249223} },}, +/**/ {{{0xbfd16b5c, 0xcbacfb73} }, +/**/ {{0xbc766fbd, 0x28b40935} },}, +/**/ {{{0xbfd1178e, 0x8227e47c} }, +/**/ {{0x3c60e63a, 0x5f01c691} },}, +/**/ {{{0xbfd0c42d, 0x676162e3} }, +/**/ {{0xbc5162c7, 0x9d5d11ee} },}, +/**/ {{{0xbfd07138, 0x604d5862} }, +/**/ {{0xbc7cdb16, 0xed4e9138} },}, +/**/ {{{0xbfd01eae, 0x5626c691} }, +/**/ {{0x3c418290, 0xbd2932e2} },}, +/**/ {{{0xbfcf991c, 0x6cb3b379} }, +/**/ {{0xbc6f6650, 0x66f980a2} },}, +/**/ {{{0xbfcef5ad, 0xe4dcffe6} }, +/**/ {{0x3c508ab2, 0xddc708a0} },}, +/**/ {{{0xbfce530e, 0xffe71012} }, +/**/ {{0xbc422760, 0x41f43042} },}, +/**/ {{{0xbfcdb13d, 0xb0d48940} }, +/**/ {{0xbc5aa11d, 0x49f96cb9} },}, +/**/ {{{0xbfcd1037, 0xf2655e7b} }, +/**/ {{0xbc660629, 0x242471a2} },}, +/**/ {{{0xbfcc6ffb, 0xc6f00f71} }, +/**/ {{0x3c68e58b, 0x2c57a4a5} },}, +/**/ {{{0xbfcbd087, 0x383bd8ad} }, +/**/ {{0xbc3dd355, 0xf6a516d7} },}, +/**/ {{{0xbfcb31d8, 0x575bce3d} }, +/**/ {{0x3c66353a, 0xb386a94d} },}, +/**/ {{{0xbfca93ed, 0x3c8ad9e3} }, +/**/ {{0xbc6bcafa, 0x9de97203} },}, +/**/ {{{0xbfc9f6c4, 0x07089664} }, +/**/ {{0xbc435a19, 0x605e67ef} },}, +/**/ {{{0xbfc95a5a, 0xdcf7017f} }, +/**/ {{0xbc5142c5, 0x07fb7a3d} },}, +/**/ {{{0xbfc8beaf, 0xeb38fe8c} }, +/**/ {{0xbc555aa8, 0xb6997a40} },}, +/**/ {{{0xbfc823c1, 0x6551a3c2} }, +/**/ {{0x3c61232c, 0xe70be781} },}, +/**/ {{{0xbfc7898d, 0x85444c73} }, +/**/ {{0xbc5ef8f6, 0xebcfb201} },}, +/**/ {{{0xbfc6f012, 0x8b756abc} }, +/**/ {{0x3c68de59, 0xc21e166c} },}, +/**/ {{{0xbfc6574e, 0xbe8c133a} }, +/**/ {{0x3c3d34f0, 0xf4621bed} },}, +/**/ {{{0xbfc5bf40, 0x6b543db2} }, +/**/ {{0x3c21f5b4, 0x4c0df7e7} },}, +/**/ {{{0xbfc527e5, 0xe4a1b58d} }, +/**/ {{0x3c271a96, 0x82395bfd} },}, +/**/ {{{0xbfc4913d, 0x8333b561} }, +/**/ {{0x3c50d560, 0x4930f135} },}, +/**/ {{{0xbfc3fb45, 0xa59928cc} }, +/**/ {{0x3c6d87e6, 0xa354d056} },}, +/**/ {{{0xbfc365fc, 0xb0159016} }, +/**/ {{0xbc57d411, 0xa5b944ad} },}, +/**/ {{{0xbfc2d161, 0x0c86813a} }, +/**/ {{0x3c5499a3, 0xf25af95f} },}, +/**/ {{{0xbfc23d71, 0x2a49c202} }, +/**/ {{0x3c66e381, 0x61051d69} },}, +/**/ {{{0xbfc1aa2b, 0x7e23f72a} }, +/**/ {{0x3c4c6ef1, 0xd9b2ef7e} },}, +/**/ {{{0xbfc1178e, 0x8227e47c} }, +/**/ {{0x3c50e63a, 0x5f01c691} },}, +/**/ {{{0xbfc08598, 0xb59e3a07} }, +/**/ {{0x3c6dd700, 0x9902bf32} },}, +/**/ {{{0xbfbfe891, 0x39dbd566} }, +/**/ {{0x3c5ac9f4, 0x215f9393} },}, +/**/ {{{0xbfbec739, 0x830a1120} }, +/**/ {{0x3c4a2bf9, 0x91780d3f} },}, +/**/ {{{0xbfbda727, 0x638446a2} }, +/**/ {{0xbc5401fa, 0x71733019} },}, +/**/ {{{0xbfbc8858, 0x01bc4b23} }, +/**/ {{0xbc5a38cb, 0x559a6706} },}, +/**/ {{{0xbfbb6ac8, 0x8dad5b1c} }, +/**/ {{0x3c40057e, 0xed1ca59f} },}, +/**/ {{{0xbfba4e76, 0x40b1bc38} }, +/**/ {{0x3c55b5ca, 0x203e4259} },}, +/**/ {{{0xbfb9335e, 0x5d594989} }, +/**/ {{0x3c5478a8, 0x5704ccb7} },}, +/**/ {{{0xbfb8197e, 0x2f40e3f0} }, +/**/ {{0xbc3b9f2d, 0xffbeed43} },}, +/**/ {{{0xbfb700d3, 0x0aeac0e1} }, +/**/ {{0x3c272566, 0x212cdd05} },}, +/**/ {{{0xbfb5e95a, 0x4d9791cb} }, +/**/ {{0xbc5f3874, 0x5c5c450a} },}, +/**/ {{{0xbfb4d311, 0x5d207eac} }, +/**/ {{0xbc5769f4, 0x2c7842cc} },}, +/**/ {{{0xbfb3bdf5, 0xa7d1ee64} }, +/**/ {{0xbc47a976, 0xd3b5b45f} },}, +/**/ {{{0xbfb2aa04, 0xa44717a5} }, +/**/ {{0x3c5d15d3, 0x8d2fa3f7} },}, +/**/ {{{0xbfb1973b, 0xd1465567} }, +/**/ {{0x3c475583, 0x67a6acf6} },}, +/**/ {{{0xbfb08598, 0xb59e3a07} }, +/**/ {{0x3c5dd700, 0x9902bf32} },}, +/**/ {{{0xbfaeea31, 0xc006b87c} }, +/**/ {{0x3c43e4fc, 0x93b7b66c} },}, +/**/ {{{0xbfaccb73, 0xcdddb2cc} }, +/**/ {{0x3c4e48fb, 0x0500efd4} },}, +/**/ {{{0xbfaaaef2, 0xd0fb10fc} }, +/**/ {{0xbc2a353b, 0xb42e0add} },}, +/**/ {{{0xbfa894aa, 0x149fb343} }, +/**/ {{0xbc3a8be9, 0x7660a23d} },}, +/**/ {{{0xbfa67c94, 0xf2d4bb58} }, +/**/ {{0xbc40413e, 0x6505e603} },}, +/**/ {{{0xbfa466ae, 0xd42de3ea} }, +/**/ {{0x3c4cdd6f, 0x7f4a137e} },}, +/**/ {{{0xbfa252f3, 0x2f8d183f} }, +/**/ {{0x3c4947f7, 0x92615916} },}, +/**/ {{{0xbfa0415d, 0x89e74444} }, +/**/ {{0xbc4c05cf, 0x1d753622} },}, +/**/ {{{0xbf9c63d2, 0xec14aaf2} }, +/**/ {{0x3c3ce030, 0xa686bd86} },}, +/**/ {{{0xbf984925, 0x28c8cabf} }, +/**/ {{0x3c3d192d, 0x0619fa67} },}, +/**/ {{{0xbf9432a9, 0x25980cc1} }, +/**/ {{0x3c38cdaf, 0x39004192} },}, +/**/ {{{0xbf902056, 0x58935847} }, +/**/ {{0xbc327c8e, 0x8416e71f} },}, +/**/ {{{0xbf882448, 0xa388a2aa} }, +/**/ {{0xbc104b16, 0x137f09a0} },}, +/**/ {{{0xbf801015, 0x7588de71} }, +/**/ {{0xbc146662, 0xd417ced0} },}, +/**/ {{{0xbf700805, 0x59588b35} }, +/**/ {{0xbc1f9663, 0x8cf63677} },}, +/**/ {{{0x00000000, 0x00000000} }, +/**/ {{0x00000000, 0x00000000} },}, +/**/ {{{0x3f6ff00a, 0xa2b10bc0} }, +/**/ {{0x3c02821a, 0xd5a6d353} },}, +/**/ {{{0x3f7fe02a, 0x6b106789} }, +/**/ {{0xbbce44b7, 0xe3711ebf} },}, +/**/ {{{0x3f87dc47, 0x5f810a77} }, +/**/ {{0xbc116d76, 0x87d3df21} },}, +/**/ {{{0x3f8fc0a8, 0xb0fc03e4} }, +/**/ {{0xbc183092, 0xc59642a1} },}, +/**/ {{{0x3f93cea4, 0x4346a575} }, +/**/ {{0xbc10cb5a, 0x902b3a1c} },}, +/**/ {{{0x3f97b91b, 0x07d5b11b} }, +/**/ {{0xbc35b602, 0xace3a510} },}, +/**/ {{{0x3f9b9fc0, 0x27af9198} }, +/**/ {{0xbbf0ae69, 0x229dc868} },}, +/**/ {{{0x3f9f829b, 0x0e783300} }, +/**/ {{0x3c333e3f, 0x04f1ef23} },}, +/**/ {{{0x3fa1b0d9, 0x8923d980} }, +/**/ {{0xbc3e9ae8, 0x89bac481} },}, +/**/ {{{0x3fa39e87, 0xb9febd60} }, +/**/ {{0xbc45bfa9, 0x37f551bb} },}, +/**/ {{{0x3fa58a5b, 0xafc8e4d5} }, +/**/ {{0xbc4ce55c, 0x2b4e2b72} },}, +/**/ {{{0x3fa77458, 0xf632dcfc} }, +/**/ {{0x3c418d3c, 0xa87b9296} },}, +/**/ {{{0x3fa95c83, 0x0ec8e3eb} }, +/**/ {{0x3c4f5a0e, 0x80520bf2} },}, +/**/ {{{0x3fab42dd, 0x711971bf} }, +/**/ {{0xbc3eb975, 0x9c130499} },}, +/**/ {{{0x3fad276b, 0x8adb0b52} }, +/**/ {{0x3c21e3c5, 0x3257fd47} },}, +/**/ {{{0x3faf0a30, 0xc01162a6} }, +/**/ {{0x3c485f32, 0x5c5bbacd} },}, +/**/ {{{0x3fb07598, 0x3598e471} }, +/**/ {{0x3c480da5, 0x333c45b8} },}, +/**/ {{{0x3fb16536, 0xeea37ae1} }, +/**/ {{0xbc379da3, 0xe8c22cda} },}, +/**/ {{{0x3fb253f6, 0x2f0a1417} }, +/**/ {{0xbc1c1259, 0x63fc4cfd} },}, +/**/ {{{0x3fb341d7, 0x961bd1d1} }, +/**/ {{0xbc5b599f, 0x227becbb} },}, +/**/ {{{0x3fb42edc, 0xbea646f0} }, +/**/ {{0x3c4ddd4f, 0x935996c9} },}, +/**/ {{{0x3fb51b07, 0x3f06183f} }, +/**/ {{0x3c5a49e3, 0x9a1a8be4} },}, +/**/ {{{0x3fb60658, 0xa93750c4} }, +/**/ {{0xbc538845, 0x8ec21b6a} },}, +/**/ {{{0x3fb6f0d2, 0x8ae56b4c} }, +/**/ {{0xbc5906d9, 0x9184b992} },}, +/**/ {{{0x3fb7da76, 0x6d7b12cd} }, +/**/ {{0xbc5eeedf, 0xcdd94131} },}, +/**/ {{{0x3fb8c345, 0xd6319b21} }, +/**/ {{0xbc24a697, 0xab3424a9} },}, +/**/ {{{0x3fb9ab42, 0x462033ad} }, +/**/ {{0xbc42099e, 0x1c184e8e} },}, +/**/ {{{0x3fba926d, 0x3a4ad563} }, +/**/ {{0x3c5942f4, 0x8aa70ea9} },}, +/**/ {{{0x3fbb78c8, 0x2bb0eda1} }, +/**/ {{0x3c20878c, 0xf0327e21} },}, +/**/ {{{0x3fbc5e54, 0x8f5bc743} }, +/**/ {{0x3c35d617, 0xef8161b1} },}, +/**/ {{{0x3fbd4313, 0xd66cb35d} }, +/**/ {{0x3c5790dd, 0x951d90fa} },}, +/**/ {{{0x3fbe2707, 0x6e2af2e6} }, +/**/ {{0xbc361578, 0x001e0162} },}, +/**/ {{{0x3fbf0a30, 0xc01162a6} }, +/**/ {{0x3c585f32, 0x5c5bbacd} },}, +/**/ {{{0x3fbfec91, 0x31dbeabb} }, +/**/ {{0xbc55746b, 0x9981b36c} },}, +/**/ {{{0x3fc06715, 0x12ca596e} }, +/**/ {{0x3c550c64, 0x7eb86499} },}, +/**/ {{{0x3fc0d77e, 0x7cd08e59} }, +/**/ {{0x3c69a5dc, 0x5e9030ac} },}, +/**/ {{{0x3fc14785, 0x846742ac} }, +/**/ {{0x3c6a2881, 0x3e3a7f07} },}, +/**/ {{{0x3fc1b72a, 0xd52f67a0} }, +/**/ {{0x3c548302, 0x3472cd74} },}, +/**/ {{{0x3fc2266f, 0x190a5acb} }, +/**/ {{0x3c6f547b, 0xf1809e88} },}, +/**/ {{{0x3fc29552, 0xf81ff523} }, +/**/ {{0x3c630177, 0x1c407dbf} },}, +/**/ {{{0x3fc303d7, 0x18e47fd3} }, +/**/ {{0xbc06b9c7, 0xd96091fa} },}, +/**/ {{{0x3fc371fc, 0x201e8f74} }, +/**/ {{0x3c5de6cb, 0x62af18a0} },}, +/**/ {{{0x3fc3dfc2, 0xb0ecc62a} }, +/**/ {{0xbc5ab3a8, 0xe7d81017} },}, +/**/ {{{0x3fc44d2b, 0x6ccb7d1e} }, +/**/ {{0x3c69f4f6, 0x543e1f88} },}, +/**/ {{{0x3fc4ba36, 0xf39a55e5} }, +/**/ {{0x3c668981, 0xbcc36756} },}, +/**/ {{{0x3fc526e5, 0xe3a1b438} }, +/**/ {{0xbc6746ff, 0x8a470d3a} },}, +/**/ {{{0x3fc59338, 0xd9982086} }, +/**/ {{0xbc565d22, 0xaa8ad7cf} },}, +/**/ {{{0x3fc5ff30, 0x70a793d4} }, +/**/ {{0xbc5bc60e, 0xfafc6f6e} },}, +/**/ {{{0x3fc66acd, 0x4272ad51} }, +/**/ {{0xbc50900e, 0x4e1ea8b2} },}, +/**/ {{{0x3fc6d60f, 0xe719d21d} }, +/**/ {{0xbc6caae2, 0x68ecd179} },}, +/**/ {{{0x3fc740f8, 0xf54037a5} }, +/**/ {{0xbc5b2640, 0x62a84cdb} },}, +/**/ {{{0x3fc7ab89, 0x0210d909} }, +/**/ {{0x3c4be36b, 0x2d6a0608} },}, +/**/ {{{0x3fc815c0, 0xa14357eb} }, +/**/ {{0xbc54be48, 0x073a0564} },}, +/**/ {{{0x3fc87fa0, 0x6520c911} }, +/**/ {{0xbc6bf7fd, 0xbfa08d9a} },}, +/**/ {{{0x3fc8e928, 0xde886d41} }, +/**/ {{0xbc6569d8, 0x51a56770} },}, +/**/ {{{0x3fc9525a, 0x9cf456b4} }, +/**/ {{0x3c6d904c, 0x1d4e2e26} },}, +/**/ {{{0x3fc9bb36, 0x2e7dfb83} }, +/**/ {{0x3c6575e3, 0x1f003e0c} },}, +/**/ {{{0x3fca23bc, 0x1fe2b563} }, +/**/ {{0x3c493711, 0xb07a998c} },}, +/**/ {{{0x3fca8bec, 0xfc882f19} }, +/**/ {{0xbc5e8c37, 0x918c39eb} },}, +/**/ {{{0x3fcaf3c9, 0x4e80bff3} }, +/**/ {{0xbc5398cf, 0xf3641985} },}, +/**/ {{{0x3fcb5b51, 0x9e8fb5a4} }, +/**/ {{0x3c6ba27f, 0xdc19e1a0} },}, +/**/ {{{0x3fcbc286, 0x742d8cd6} }, +/**/ {{0x3c54fce7, 0x44870f55} },}, +/**/ {{{0x3fcc2968, 0x558c18c1} }, +/**/ {{0xbc673dee, 0x38a3fb6b} },}, +/**/ {{{0x3fcc8ff7, 0xc79a9a22} }, +/**/ {{0xbc64f689, 0xf8434012} },}, +/**/ {{{0x3fccf635, 0x4e09c5dc} }, +/**/ {{0x3c6239a0, 0x7d55b695} },}, +/**/ {{{0x3fcd5c21, 0x6b4fbb91} }, +/**/ {{0x3c66e443, 0x597e4d40} },}, +/**/ {{{0x3fcdc1bc, 0xa0abec7d} }, +/**/ {{0x3c6834c5, 0x1998b6fc} },}, +/**/ {{{0x3fce2707, 0x6e2af2e6} }, +/**/ {{0xbc461578, 0x001e0162} },}, +/**/ {{{0x3fce8c02, 0x52aa5a60} }, +/**/ {{0xbc46e03a, 0x39bfc89b} },}, +/**/ {{{0x3fcef0ad, 0xcbdc5936} }, +/**/ {{0x3c648637, 0x950dc20d} },}, +/**/ {{{0x3fcf550a, 0x564b7b37} }, +/**/ {{0x3c2c5f6d, 0xfd018c37} },}, +/**/ {{{0x3fcfb918, 0x6d5e3e2b} }, +/**/ {{0xbc6caaae, 0x64f21acb} },}, +/**/ {{{0x3fd00e6c, 0x45ad501d} }, +/**/ {{0xbc6cb956, 0x8ff6fead} },}, +/**/ {{{0x3fd04025, 0x94b4d041} }, +/**/ {{0xbc628ec2, 0x17a5022d} },}, +/**/ {{{0x3fd071b8, 0x5fcd590d} }, +/**/ {{0x3c5d1707, 0xf97bde80} },}, +/**/ {{{0x3fd0a324, 0xe27390e3} }, +/**/ {{0x3c77dcfd, 0xe8061c03} },}, +/**/ {{{0x3fd0d46b, 0x579ab74b} }, +/**/ {{0x3c603ec8, 0x1c3cbd92} },}, +/**/ {{{0x3fd1058b, 0xf9ae4ad5} }, +/**/ {{0x3c589fa0, 0xab4cb31d} },}, +/**/ {{{0x3fd13687, 0x0293a8b0} }, +/**/ {{0x3c77b662, 0x98edd24a} },}, +/**/ {{{0x3fd1675c, 0xababa60e} }, +/**/ {{0x3c2ce63e, 0xab883717} },}, +/**/ {{{0x3fd1980d, 0x2dd4236f} }, +/**/ {{0x3c79d3d1, 0xb0e4d147} },}, +/**/ {{{0x3fd1c898, 0xc16999fb} }, +/**/ {{0xbc30e5c6, 0x2aff1c44} },}, +/**/ {{{0x3fd1f8ff, 0x9e48a2f3} }, +/**/ {{0xbc7c9fdf, 0x9a0c4b07} },}, +/**/ {{{0x3fd22941, 0xfbcf7966} }, +/**/ {{0xbc776f5e, 0xb09628af} },}, +/**/ {{{0x3fd25960, 0x10df763a} }, +/**/ {{0xbc50f76c, 0x57075e9e} },}, +/**/ {{{0x3fd2895a, 0x13de86a3} }, +/**/ {{0x3c77ad24, 0xc13f040e} },}, +/**/ {{{0x3fd2b930, 0x3ab89d25} }, +/**/ {{0xbc7896b5, 0xfd852ad4} },}, +/**/ {{{0x3fd2e8e2, 0xbae11d31} }, +/**/ {{0xbc78f4cd, 0xb95ebdf9} },}, +/**/ {{{0x3fd31871, 0xc9544185} }, +/**/ {{0xbc351acc, 0x4c09b379} },}, +/**/ {{{0x3fd347dd, 0x9a987d55} }, +/**/ {{0xbc64dd4c, 0x580919f8} },}, +/**/ {{{0x3fd37726, 0x62bfd85b} }, +/**/ {{0xbc4b5629, 0xd8117de7} },}, +/**/ {{{0x3fd3a64c, 0x556945ea} }, +/**/ {{0xbc6c6865, 0x1945f97c} },}, +/**/ {{{0x3fd3d54f, 0xa5c1f710} }, +/**/ {{0xbc7e3265, 0xc6a1c98d} },}, +/**/ {{{0x3fd40430, 0x8686a7e4} }, +/**/ {{0xbc70bcfb, 0x6082ce6d} },}, +/**/ {{{0x3fd432ef, 0x2a04e814} }, +/**/ {{0xbc729931, 0x715ac903} },}, +/**/ {{{0x3fd4618b, 0xc21c5ec2} }, +/**/ {{0x3c7f42de, 0xcdeccf1d} },}, +/**/ {{{0x3fd49006, 0x804009d1} }, +/**/ {{0xbc69ffc3, 0x41f177dc} },}, +/**/ {{{0x3fd4be5f, 0x957778a1} }, +/**/ {{0xbc6259b3, 0x5b04813d} },}, +/**/ {{{0x3fd4ec97, 0x3260026a} }, +/**/ {{0xbc742a87, 0xd977dc5e} },}, +/**/ {{{0x3fd51aad, 0x872df82d} }, +/**/ {{0x3c43927a, 0xc19f55e3} },}, +/**/ {{{0x3fd548a2, 0xc3add263} }, +/**/ {{0xbc6819cf, 0x7e308ddb} },}, +/**/ {{{0x3fd57677, 0x17455a6c} }, +/**/ {{0x3c7526ad, 0xb283660c} },}, +/**/ {{{0x3fd5a42a, 0xb0f4cfe2} }, +/**/ {{0xbc78ebcb, 0x7dee9a3d} },}, +/**/ {{{0x3fd5d1bd, 0xbf5809ca} }, +/**/ {{0x3c742363, 0x83dc7fe1} },}, +/**/ {{{0x3fd5ff30, 0x70a793d4} }, +/**/ {{0xbc6bc60e, 0xfafc6f6e} },}, +/**/ {{{0x3fd62c82, 0xf2b9c795} }, +/**/ {{0x3c67b7af, 0x915300e5} },}, + }; + + static const number + Lv[362][2] = { /* log(vj) */ + +/**/ {{{0xbf6687ec, 0xb72daabf} }, +/**/ {{0x3c052c69, 0x0f13318f} },}, +/**/ {{{0xbf6667d6, 0x3767104f} }, +/**/ {{0x3bd3efa3, 0xd27a7bac} },}, +/**/ {{{0xbf6647bf, 0xd7cd64fb} }, +/**/ {{0x3c09b725, 0x55a89c36} },}, +/**/ {{{0xbf6627a9, 0x9860683b} }, +/**/ {{0x3bcbae22, 0xfebc844a} },}, +/**/ {{{0xbf660793, 0x791fd98a} }, +/**/ {{0xbbfe34af, 0x78fa1cb5} },}, +/**/ {{{0xbf65e77d, 0x7a0b7863} }, +/**/ {{0xbc02f1b1, 0xea78fdd0} },}, +/**/ {{{0xbf65c767, 0x9b230442} }, +/**/ {{0x3bf70d8c, 0x2202b2ca} },}, +/**/ {{{0xbf65a751, 0xdc663ca2} }, +/**/ {{0xbbfdc63d, 0xc3444e64} },}, +/**/ {{{0xbf65873c, 0x3dd4e102} }, +/**/ {{0x3c021b11, 0x370d69c3} },}, +/**/ {{{0xbf656726, 0xbf6eb0de} }, +/**/ {{0xbbfb6da8, 0x154dd8d8} },}, +/**/ {{{0xbf654711, 0x61336bb6} }, +/**/ {{0xbc0b12d2, 0xdf9a4709} },}, +/**/ {{{0xbf6526fc, 0x2322d10a} }, +/**/ {{0x3bf997f2, 0x68d1274f} },}, +/**/ {{{0xbf6506e7, 0x053ca059} }, +/**/ {{0x3c0c2a1f, 0xe70c852a} },}, +/**/ {{{0xbf64e6d2, 0x07809924} }, +/**/ {{0x3c04cc9e, 0xa808538f} },}, +/**/ {{{0xbf64c6bd, 0x29ee7aed} }, +/**/ {{0x3befe68c, 0x7797a4bd} },}, +/**/ {{{0xbf64a6a8, 0x6c860537} }, +/**/ {{0x3c06794d, 0x9efaae3d} },}, +/**/ {{{0xbf648693, 0xcf46f784} }, +/**/ {{0xbbfed318, 0xb2ddd9d1} },}, +/**/ {{{0xbf64667f, 0x5231115a} }, +/**/ {{0x3c061f62, 0x4643624b} },}, +/**/ {{{0xbf64466a, 0xf544123c} }, +/**/ {{0x3c0666a0, 0x9387f11e} },}, +/**/ {{{0xbf642656, 0xb87fb9b0} }, +/**/ {{0x3c0043b2, 0x116ec598} },}, +/**/ {{{0xbf640642, 0x9be3c73c} }, +/**/ {{0xbbfbd84d, 0xd2de6e3e} },}, +/**/ {{{0xbf63e62e, 0x9f6ffa68} }, +/**/ {{0xbbe9149b, 0x433d8c65} },}, +/**/ {{{0xbf63c61a, 0xc32412bb} }, +/**/ {{0xbbf6b88d, 0x08e5a7bb} },}, +/**/ {{{0xbf63a607, 0x06ffcfbe} }, +/**/ {{0xbb9f3c7a, 0xccfac9e2} },}, +/**/ {{{0xbf6385f3, 0x6b02f0fa} }, +/**/ {{0x3bee405c, 0xbec6f6e4} },}, +/**/ {{{0xbf6365df, 0xef2d35f9} }, +/**/ {{0x3bf02993, 0xaf0c0b4c} },}, +/**/ {{{0xbf6345cc, 0x937e5e46} }, +/**/ {{0x3bf9be97, 0xaa64716f} },}, +/**/ {{{0xbf6325b9, 0x57f6296c} }, +/**/ {{0xbbfdeb4d, 0xa2e863ae} },}, +/**/ {{{0xbf6305a6, 0x3c9456f9} }, +/**/ {{0x3c0f3c7f, 0x636d2b2c} },}, +/**/ {{{0xbf62e593, 0x4158a678} }, +/**/ {{0x3c01a8df, 0xb166ca7f} },}, +/**/ {{{0xbf62c580, 0x6642d778} }, +/**/ {{0x3c020ff1, 0x53a2d534} },}, +/**/ {{{0xbf62a56d, 0xab52a987} }, +/**/ {{0xbbe8fef1, 0x0412f1e7} },}, +/**/ {{{0xbf62855b, 0x1087dc35} }, +/**/ {{0xbbfcd17e, 0x4b7ac6c6} },}, +/**/ {{{0xbf626548, 0x95e22f12} }, +/**/ {{0xbbfbfc21, 0x9a8127bf} },}, +/**/ {{{0xbf624536, 0x3b6161af} }, +/**/ {{0x3bd7eda1, 0x66d42390} },}, +/**/ {{{0xbf622524, 0x0105339d} }, +/**/ {{0xbbdf374e, 0x77fedcad} },}, +/**/ {{{0xbf620511, 0xe6cd646f} }, +/**/ {{0x3be1d1fb, 0x52d05dea} },}, +/**/ {{{0xbf61e4ff, 0xecb9b3b8} }, +/**/ {{0x3c02c2fc, 0xffd8e706} },}, +/**/ {{{0xbf61c4ee, 0x12c9e10b} }, +/**/ {{0xbc02b4f8, 0xf1d5cc2c} },}, +/**/ {{{0xbf61a4dc, 0x58fdabfe} }, +/**/ {{0xbc0618c3, 0x1315b191} },}, +/**/ {{{0xbf6184ca, 0xbf54d426} }, +/**/ {{0xbc01f8d5, 0xcb3cdab0} },}, +/**/ {{{0xbf6164b9, 0x45cf1919} }, +/**/ {{0xbc014ff7, 0xc025605a} },}, +/**/ {{{0xbf6144a7, 0xec6c3a6e} }, +/**/ {{0xbbff04ff, 0x87cb08cd} },}, +/**/ {{{0xbf612496, 0xb32bf7bd} }, +/**/ {{0x3bee89b4, 0xe6af1b84} },}, +/**/ {{{0xbf610485, 0x9a0e109e} }, +/**/ {{0x3c07e99e, 0x35a60879} },}, +/**/ {{{0xbf60e474, 0xa11244aa} }, +/**/ {{0x3c04b698, 0x20f2325a} },}, +/**/ {{{0xbf60c463, 0xc838537b} }, +/**/ {{0x3bc0657e, 0x3617200d} },}, +/**/ {{{0xbf60a453, 0x0f7ffcac} }, +/**/ {{0xbc008feb, 0xa5080961} },}, +/**/ {{{0xbf608442, 0x76e8ffd9} }, +/**/ {{0x3bd13002, 0xbb5e1df7} },}, +/**/ {{{0xbf606431, 0xfe731c9d} }, +/**/ {{0xbc0509f3, 0x6e2858c0} },}, +/**/ {{{0xbf604421, 0xa61e1296} }, +/**/ {{0xbc04b556, 0x5f5d9695} },}, +/**/ {{{0xbf602411, 0x6de9a162} }, +/**/ {{0x3c042b89, 0xe79a4e00} },}, +/**/ {{{0xbf600401, 0x55d5889e} }, +/**/ {{0x3be8f98e, 0x1113f403} },}, +/**/ {{{0xbf5fc7e2, 0xbbc30fd4} }, +/**/ {{0xbbfc709b, 0x93382bc9} },}, 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{{0x3bf838ca, 0xe3a09391} },}, +/**/ {{{0xbf5c0621, 0xc9eb99ee} }, +/**/ {{0xbbdc2a9e, 0x61b7de71} },}, +/**/ {{{0xbf5bc605, 0xddc2388e} }, +/**/ {{0xbbea9808, 0x4accb195} },}, +/**/ {{{0xbf5b85ea, 0x31d07b5c} }, +/**/ {{0xbbd811a2, 0x032e030b} },}, +/**/ {{{0xbf5b45ce, 0xc615e1b1} }, +/**/ {{0xbbfd5427, 0x821e0b81} },}, +/**/ {{{0xbf5b05b3, 0x9a91eaea} }, +/**/ {{0x3bfffeba, 0x2619306b} },}, +/**/ {{{0xbf5ac598, 0xaf441661} }, +/**/ {{0x3bd22824, 0x9eac7d15} },}, +/**/ {{{0xbf5a857e, 0x042be376} }, +/**/ {{0x3bc20736, 0x24893f0e} },}, +/**/ {{{0xbf5a4563, 0x9948d188} }, +/**/ {{0xbbf58ab4, 0x04d734cd} },}, +/**/ {{{0xbf5a0549, 0x6e9a5ff9} }, +/**/ {{0xbbf22673, 0x5723a6c3} },}, +/**/ {{{0xbf59c52f, 0x84200e2c} }, +/**/ {{0x3bfc81da, 0xa538e8e1} },}, +/**/ {{{0xbf598515, 0xd9d95b83} }, +/**/ {{0xbbfa1a37, 0x2a8e3feb} },}, +/**/ {{{0xbf5944fc, 0x6fc5c767} }, +/**/ {{0x3bf8e1ce, 0x385159f9} },}, +/**/ {{{0xbf5904e3, 0x45e4d13c} }, +/**/ {{0xbbfc4737, 0x1567c7a7} },}, +/**/ {{{0xbf58c4ca, 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{{0x3bfb055a, 0x54100f9e} },}, +/**/ {{{0xbf51c276, 0x949a2c12} }, +/**/ {{0xbbff6978, 0xa2e9f1b4} },}, +/**/ {{{0xbf518264, 0xefbe402a} }, +/**/ {{0x3bf01fb9, 0xbc188323} },}, +/**/ {{{0xbf514253, 0x8b0562a1} }, +/**/ {{0xbbf7c87c, 0x957bf23a} },}, +/**/ {{{0xbf510242, 0x666f1311} }, +/**/ {{0x3bdc2cb9, 0xc8be6880} },}, +/**/ {{{0xbf50c231, 0x81fad111} }, +/**/ {{0xbbf59fc1, 0x07ba000d} },}, +/**/ {{{0xbf508220, 0xdda81c3d} }, +/**/ {{0xbbf06a0a, 0xbf5c8a0b} },}, +/**/ {{{0xbf504210, 0x79767431} }, +/**/ {{0x3bf3a6cf, 0xa9a705bc} },}, +/**/ {{{0xbf500200, 0x55655889} }, +/**/ {{0xbbe9abe6, 0xbf0fa436} },}, +/**/ {{{0xbf4f83e0, 0xe2e891cc} }, +/**/ {{0x3be4aa59, 0x1b81bf62} },}, +/**/ {{{0xbf4f03c1, 0x9b4589ce} }, +/**/ {{0xbbe60518, 0x8a47f50a} },}, +/**/ {{{0xbf4e83a2, 0xd3e0985f} }, +/**/ {{0x3bed32d8, 0x5ef17e96} },}, +/**/ {{{0xbf4e0384, 0x8cb8bcc3} }, +/**/ {{0xbbeb7b30, 0xf09afa4d} },}, +/**/ {{{0xbf4d8366, 0xc5ccf647} }, +/**/ {{0xbbd527fc, 0xf586cec2} },}, +/**/ {{{0xbf4d0349, 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+/**/ {{{0xbf080024, 0x004800a2} }, +/**/ {{0xbb484d09, 0x8d690542} },}, +/**/ {{{0xbf000010, 0x00155575} }, +/**/ {{0xbba56222, 0x37779c0a} },}, +/**/ {{{0xbef00008, 0x00055559} }, +/**/ {{0xbb955622, 0x22cccd5f} },}, +/**/ {{{0x00000000, 0x00000000} }, +/**/ {{0x00000000, 0x00000000} },}, +/**/ {{{0x3eeffff0, 0x000aaaa3} }, +/**/ {{0xbb8553bb, 0xbd110fec} },}, +/**/ {{{0x3effffe0, 0x002aaa6b} }, +/**/ {{0xbb953bbb, 0xe6661d42} },}, +/**/ {{{0x3f07ffdc, 0x0047ff5e} }, +/**/ {{0x3b484c90, 0x0d69020e} },}, +/**/ {{{0x3f0fffc0, 0x00aaa8ab} }, +/**/ {{0xbba3bbc1, 0x10fec82c} },}, +/**/ {{{0x3f13ffce, 0x00a6a83a} }, +/**/ {{0xbbb2e45f, 0x81546808} },}, +/**/ {{{0x3f17ffb8, 0x011ffaf0} }, +/**/ {{0x3b984c53, 0x4f3d9b6a} },}, +/**/ {{{0x3f1bff9e, 0x01c94bf5} }, +/**/ {{0xbbbd8990, 0xdaa368ee} },}, +/**/ {{{0x3f1fff80, 0x02aa9aab} }, +/**/ {{0x3b910e66, 0x78af0afc} },}, +/**/ {{{0x3f21ffaf, 0x01e5f330} }, +/**/ {{0xbbb1df8d, 0x26467402} },}, +/**/ {{{0x3f23ff9c, 0x029a9723} }, +/**/ {{0x3bc1b965, 0x303b23b1} },}, +/**/ {{{0x3f25ff87, 0x037738be} }, +/**/ {{0xbbb787a3, 0x53d3dc06} },}, +/**/ {{{0x3f27ff70, 0x047fd782} }, +/**/ {{0xbbced098, 0xa5c0aff0} },}, +/**/ {{{0x3f29ff57, 0x05b872e4} }, +/**/ {{0x3bcbadd4, 0x81c30d42} },}, +/**/ {{{0x3f2bff3c, 0x07250a51} }, +/**/ {{0xbbc89dd6, 0xd6bad8c1} },}, +/**/ {{{0x3f2dff1f, 0x08c99d24} }, +/**/ {{0x3bb12609, 0xaede8ad0} },}, +/**/ {{{0x3f2fff00, 0x0aaa2ab1} }, +/**/ {{0x3ba0bbc0, 0x4dc4e3dc} },}, +/**/ {{{0x3f30ff6f, 0x8665591f} }, +/**/ {{0xbbd013d3, 0x80357b54} },}, +/**/ {{{0x3f31ff5e, 0x07979982} }, +/**/ {{0xbbce0e70, 0x4817ebcd} },}, +/**/ {{{0x3f32ff4b, 0x88edd619} }, +/**/ {{0xbbd72b9e, 0xc582abc3} },}, +/**/ {{{0x3f33ff38, 0x0a6a0e74} }, +/**/ {{0x3bdb81fc, 0xb95bc1fe} },}, +/**/ {{{0x3f34ff23, 0x8c0e4220} }, +/**/ {{0x3bcaed12, 0x9b549aae} },}, +/**/ {{{0x3f35ff0e, 0x0ddc70a1} }, +/**/ {{0x3bacf6f3, 0xd97a3c05} },}, +/**/ {{{0x3f36fef7, 0x8fd69976} }, +/**/ {{0x3bab2dcf, 0x6f810a3c} },}, +/**/ {{{0x3f37fee0, 0x11febc18} }, +/**/ {{0x3bd2b9bc, 0xf5d3f323} },}, +/**/ {{{0x3f38fec7, 0x9456d7fb} }, +/**/ {{0xbbbfb258, 0x6eaa1d6a} },}, +/**/ {{{0x3f39feae, 0x16e0ec8b} }, +/**/ {{0xbbb6137a, 0xceeb34b1} },}, +/**/ {{{0x3f3afe93, 0x999ef930} }, +/**/ {{0xbbde70e0, 0xdc639b08} },}, +/**/ {{{0x3f3bfe78, 0x1c92fd4a} }, +/**/ {{0xbbc4ed10, 0x713cc126} },}, +/**/ {{{0x3f3cfe5b, 0x9fbef835} }, +/**/ {{0xbb873d63, 0xcc0e81bd} },}, +/**/ {{{0x3f3dfe3e, 0x2324e946} }, +/**/ {{0x3bc09164, 0x62dd5deb} },}, +/**/ {{{0x3f3efe1f, 0xa6c6cfcc} }, +/**/ {{0x3bdac2da, 0x3512d15c} },}, +/**/ {{{0x3f3ffe00, 0x2aa6ab11} }, +/**/ {{0x3b999e2b, 0x62cc632d} },}, +/**/ {{{0x3f407eef, 0xd7633d2c} }, +/**/ {{0xbbebc98b, 0x63ff6024} },}, +/**/ {{{0x3f40fedf, 0x19941e6e} }, +/**/ {{0xbbb194c2, 0xe0aa6338} },}, +/**/ {{{0x3f417ecd, 0xdbe6f8eb} }, +/**/ {{0x3be4241b, 0x57b0f571} },}, +/**/ {{{0x3f41febc, 0x1e5ccc3c} }, +/**/ {{0x3bdc657d, 0x895d3592} },}, +/**/ {{{0x3f427ea9, 0xe0f697f6} }, +/**/ {{0x3be35a5d, 0x1c0ec17c} },}, +/**/ {{{0x3f42fe97, 0x23b55bac} }, +/**/ {{0x3bd6cfb7, 0x3e538464} },}, +/**/ {{{0x3f437e83, 0xe69a16ed} }, +/**/ {{0x3bee96f7, 0x7cef2478} },}, +/**/ {{{0x3f43fe70, 0x29a5c947} }, +/**/ {{0xbbd4d578, 0xbf46e36a} },}, +/**/ {{{0x3f447e5b, 0xecd97242} }, +/**/ {{0xbbc9eb66, 0x3ff7dd44} },}, +/**/ {{{0x3f44fe47, 0x30361165} }, +/**/ {{0x3be400d7, 0x7e93f2fd} },}, +/**/ {{{0x3f457e31, 0xf3bca635} }, +/**/ {{0xbbe0e2a2, 0xd375017f} },}, +/**/ {{{0x3f45fe1c, 0x376e3031} }, +/**/ {{0xbbd524eb, 0x8a5ae7f6} },}, +/**/ {{{0x3f467e05, 0xfb4baed7} }, +/**/ {{0x3be204fb, 0x4e85c4e9} },}, +/**/ {{{0x3f46fdef, 0x3f5621a3} }, +/**/ {{0xbbdf09d7, 0x34886d52} },}, +/**/ {{{0x3f477dd8, 0x038e880b} }, +/**/ {{0xbbb8900e, 0x14e596a3} },}, +/**/ {{{0x3f47fdc0, 0x47f5e185} }, +/**/ {{0xbbebfa5c, 0x57d202d3} },}, +/**/ {{{0x3f487da8, 0x0c8d2d81} }, +/**/ {{0x3be2f6ae, 0xd68c0614} },}, +/**/ {{{0x3f48fd8f, 0x51556b70} }, +/**/ {{0xbbd0f4f2, 0xe08fd201} },}, +/**/ {{{0x3f497d76, 0x164f9abc} }, +/**/ {{0x3b5296b7, 0xa871af60} },}, +/**/ {{{0x3f49fd5c, 0x5b7cbace} }, +/**/ {{0x3beb6ed4, 0x9f17d42d} },}, +/**/ {{{0x3f4a7d42, 0x20ddcb0d} }, +/**/ {{0xbbcb1149, 0x67c30397} },}, +/**/ {{{0x3f4afd27, 0x6673cada} }, +/**/ {{0x3bd32225, 0x45da594f} },}, +/**/ {{{0x3f4b7d0c, 0x2c3fb996} }, +/**/ {{0xbbb68893, 0x208d4630} },}, +/**/ {{{0x3f4bfcf0, 0x7242969d} }, +/**/ {{0x3bc5db4d, 0x2b3efe1c} },}, +/**/ {{{0x3f4c7cd4, 0x387d6149} }, +/**/ {{0x3be46eff, 0xed57d98a} },}, +/**/ {{{0x3f4cfcb7, 0x7ef118f1} }, +/**/ {{0x3becc554, 0x06f300fb} },}, +/**/ {{{0x3f4d7c9a, 0x459ebce9} }, +/**/ {{0x3be1d251, 0x13638eb6} },}, +/**/ {{{0x3f4dfc7c, 0x8c874c82} }, +/**/ {{0xbbe863e9, 0xd57a176f} },}, +/**/ {{{0x3f4e7c5e, 0x53abc708} }, +/**/ {{0x3be2d95c, 0x9528e50d} },}, +/**/ {{{0x3f4efc3f, 0x9b0d2bc8} }, +/**/ {{0x3bd1e8e8, 0xa5f5b8b7} },}, +/**/ {{{0x3f4f7c20, 0x62ac7a09} }, +/**/ {{0x3b5c8123, 0x17802a46} },}, +/**/ {{{0x3f4ffc00, 0xaa8ab110} }, +/**/ {{0xbbe0fecb, 0xeb9b6cdb} },}, +/**/ {{{0x3f503df0, 0x3954680f} }, +/**/ {{0x3bdac89b, 0x1c693678} },}, +/**/ {{{0x3f507ddf, 0xdd83eb3a} }, +/**/ {{0xbbf638f6, 0x0a75ad5f} },}, +/**/ {{{0x3f50bdcf, 0x41d461a5} }, +/**/ {{0x3bfd4bc9, 0x45f05b10} },}, +/**/ {{{0x3f50fdbe, 0x66464aef} }, +/**/ {{0xbbbd0554, 0x6abbf59c} },}, +/**/ {{{0x3f513dad, 0x4ada26b1} }, +/**/ {{0x3be38c65, 0x6036fe6f} },}, +/**/ {{{0x3f517d9b, 0xef907485} }, +/**/ {{0x3bfdc8a1, 0xf158bbc3} },}, +/**/ {{{0x3f51bd8a, 0x5469b404} }, +/**/ {{0xbbdea231, 0x55632e3f} },}, +/**/ {{{0x3f51fd78, 0x796664c3} }, +/**/ {{0xbbe00849, 0x2edb73c2} },}, +/**/ {{{0x3f523d66, 0x5e870657} }, +/**/ {{0x3bfba943, 0x0789343e} },}, +/**/ {{{0x3f527d54, 0x03cc1855} }, +/**/ {{0x3bc5f644, 0xeafafc52} },}, +/**/ {{{0x3f52bd41, 0x69361a4e} }, +/**/ {{0xbbf2f743, 0xa4a6e79f} },}, +/**/ {{{0x3f52fd2e, 0x8ec58bd2} }, +/**/ {{0xbbd4f786, 0x5ceb1abf} },}, +/**/ {{{0x3f533d1b, 0x747aec71} }, +/**/ {{0xbbf369e3, 0x49dc497d} },}, +/**/ {{{0x3f537d08, 0x1a56bbb8} }, +/**/ {{0xbbfc5e6f, 0x3726b14a} },}, +/**/ {{{0x3f53bcf4, 0x80597933} }, +/**/ {{0xbbfe8b82, 0x808f75a7} },}, +/**/ {{{0x3f53fce0, 0xa683a46c} }, +/**/ {{0x3be02719, 0x9cd06ae6} },}, +/**/ {{{0x3f543ccc, 0x8cd5bced} }, +/**/ {{0x3bf9f98d, 0x758f80f8} },}, +/**/ {{{0x3f547cb8, 0x3350423e} }, +/**/ {{0xbbd79c3d, 0x48401f45} },}, +/**/ {{{0x3f54bca3, 0x99f3b3e4} }, +/**/ {{0xbbf422b8, 0x2fba8948} },}, +/**/ {{{0x3f54fc8e, 0xc0c09163} }, +/**/ {{0x3bf32cc1, 0xf4044be8} },}, +/**/ {{{0x3f553c79, 0xa7b75a40} }, +/**/ {{0xbbe72cac, 0xf2249008} },}, +/**/ {{{0x3f557c64, 0x4ed88dfb} }, +/**/ {{0xbbe7183c, 0x459a204f} },}, +/**/ {{{0x3f55bc4e, 0xb624ac14} }, +/**/ {{0x3bf8aa64, 0xba26d3d7} },}, +/**/ {{{0x3f55fc38, 0xdd9c340b} }, +/**/ {{0x3bdbb2ff, 0x45fa193c} },}, +/**/ {{{0x3f563c22, 0xc53fa55c} }, +/**/ {{0x3bd67249, 0x0484397b} },}, +/**/ {{{0x3f567c0c, 0x6d0f7f83} }, +/**/ {{0xbbd183d7, 0xf1e73188} },}, +/**/ {{{0x3f56bbf5, 0xd50c41fa} }, +/**/ {{0xbbef433d, 0x4ab68187} },}, +/**/ {{{0x3f56fbde, 0xfd366c39} }, +/**/ {{0x3be796b8, 0x66e09e58} },}, +/**/ {{{0x3f573bc7, 0xe58e7db8} }, +/**/ {{0x3bf65ec5, 0x81e6e7e6} },}, +/**/ {{{0x3f577bb0, 0x8e14f5ed} }, +/**/ {{0xbbdb944d, 0xa9463a9c} },}, +/**/ {{{0x3f57bb98, 0xf6ca544b} }, +/**/ {{0xbbc396ec, 0xc5eda344} },}, +/**/ {{{0x3f57fb81, 0x1faf1845} }, +/**/ {{0x3beb9e6d, 0xbb624f97} },}, +/**/ {{{0x3f583b69, 0x08c3c14d} }, +/**/ {{0xbbe6ee13, 0xe6295bf2} },}, +/**/ {{{0x3f587b50, 0xb208ced1} }, +/**/ {{0x3bfcf1a5, 0x6ca19875} },}, +/**/ {{{0x3f58bb38, 0x1b7ec041} }, +/**/ {{0x3bf2d181, 0x07b4fc7e} },}, +/**/ {{{0x3f58fb1f, 0x45261509} }, +/**/ {{0x3bc419c5, 0x21bad336} },}, +/**/ {{{0x3f593b06, 0x2eff4c94} }, +/**/ {{0xbbdc2a4c, 0x700b305b} },}, +/**/ {{{0x3f597aec, 0xd90ae64c} }, +/**/ {{0xbbfc53d3, 0xa23f359c} },}, +/**/ {{{0x3f59bad3, 0x43496198} }, +/**/ {{0x3bf0c270, 0xaed6b50f} },}, +/**/ {{{0x3f59fab9, 0x6dbb3de1} }, +/**/ {{0xbbf11464, 0x7a8be031} },}, +/**/ {{{0x3f5a3a9f, 0x5860fa8a} }, +/**/ {{0x3beae9e7, 0x470dbe32} },}, +/**/ {{{0x3f5a7a85, 0x033b16f8} }, +/**/ {{0x3bfc4721, 0xda1f8579} },}, +/**/ {{{0x3f5aba6a, 0x6e4a128e} }, +/**/ {{0xbbf41852, 0x029258ce} },}, +/**/ {{{0x3f5afa4f, 0x998e6cab} }, +/**/ {{0xbbf28584, 0x2eb18782} },}, +/**/ {{{0x3f5b3a34, 0x8508a4af} }, +/**/ {{0xbbea7970, 0x23241a2c} },}, +/**/ {{{0x3f5b7a19, 0x30b939f8} }, +/**/ {{0xbbf1d8db, 0x600551b6} },}, +/**/ {{{0x3f5bb9fd, 0x9ca0abe2} }, +/**/ {{0xbbeaa412, 0x8c26cc71} },}, +/**/ {{{0x3f5bf9e1, 0xc8bf79c8} }, +/**/ {{0xbbe7f81b, 0x30427cfc} },}, +/**/ {{{0x3f5c39c5, 0xb5162303} }, +/**/ {{0x3bd9ec5f, 0xd1f134e1} },}, +/**/ {{{0x3f5c79a9, 0x61a526eb} }, +/**/ {{0x3bff0cb0, 0x8980e47d} },}, +/**/ {{{0x3f5cb98c, 0xce6d04d7} }, +/**/ {{0x3bf35aca, 0xe84ca4e2} },}, +/**/ {{{0x3f5cf96f, 0xfb6e3c1b} }, +/**/ {{0x3bf9b1b8, 0x1b0bd69f} },}, +/**/ {{{0x3f5d3952, 0xe8a94c0b} }, +/**/ {{0x3be21310, 0x3ce51832} },}, +/**/ {{{0x3f5d7935, 0x961eb3f8} }, +/**/ {{0x3bf90786, 0x840c58ce} },}, +/**/ {{{0x3f5db918, 0x03cef334} }, +/**/ {{0xbbfe0048, 0xf2dfb3f4} },}, +/**/ {{{0x3f5df8fa, 0x31ba890b} }, +/**/ {{0x3bfcf652, 0x3e295bec} },}, +/**/ {{{0x3f5e38dc, 0x1fe1f4ce} }, +/**/ {{0xbbfc5ebe, 0x151c9300} },}, +/**/ {{{0x3f5e78bd, 0xce45b5c6} }, +/**/ {{0xbbef2cc4, 0x8a25b9c7} },}, +/**/ {{{0x3f5eb89f, 0x3ce64b3e} }, +/**/ {{0x3bfe6d27, 0xa6fea7bd} },}, +/**/ {{{0x3f5ef880, 0x6bc43481} }, +/**/ {{0xbbf68037, 0x914a6dab} },}, +/**/ {{{0x3f5f3861, 0x5adff0d4} }, +/**/ {{0xbbf1d2f3, 0xf909e0e6} },}, +/**/ {{{0x3f5f7842, 0x0a39ff7e} }, +/**/ {{0xbbf64661, 0xff1e1f71} },}, +/**/ {{{0x3f5fb822, 0x79d2dfc3} }, +/**/ {{0xbbd76ce8, 0x5a6f9e9a} },}, +/**/ {{{0x3f5ff802, 0xa9ab10e6} }, +/**/ {{0x3bfe29e3, 0xa153e3b2} },}, +/**/ {{{0x3f601bf1, 0x4ce18915} }, +/**/ {{0xbbe57c28, 0xa3a73044} },}, +/**/ {{{0x3f603be1, 0x250db166} }, +/**/ {{0x3c0fd271, 0xc1ad9590} },}, +/**/ {{{0x3f605bd0, 0xdd5a4107} }, +/**/ {{0x3bfe4b5d, 0xc424c676} },}, +/**/ {{{0x3f607bc0, 0x75c77796} }, +/**/ {{0xbc068804, 0xc0eff1ba} },}, +/**/ {{{0x3f609baf, 0xee5594b0} }, +/**/ {{0xbc0ff798, 0x51dbded5} },}, +/**/ {{{0x3f60bb9f, 0x4704d7f2} }, +/**/ {{0xbbf70ef4, 0x2d5aba70} },}, +/**/ {{{0x3f60db8e, 0x7fd580f9} }, +/**/ {{0xbbeccb65, 0x7ae804b5} },}, +/**/ {{{0x3f60fb7d, 0x98c7cf60} }, +/**/ {{0x3bfede2f, 0x1775134d} },}, +/**/ {{{0x3f611b6c, 0x91dc02c3} }, +/**/ {{0xbc04d41e, 0x91ca4a67} },}, +/**/ {{{0x3f613b5b, 0x6b125aba} }, +/**/ {{0x3bfe6d0c, 0x4a12201d} },}, +/**/ {{{0x3f615b4a, 0x246b16e0} }, +/**/ {{0x3bfe507d, 0x4d4238d3} },}, +/**/ {{{0x3f617b38, 0xbde676cd} }, +/**/ {{0x3bfe0272, 0x0640462a} },}, +/**/ {{{0x3f619b27, 0x3784ba19} }, +/**/ {{0x3bd94ab3, 0x02285659} },}, +/**/ {{{0x3f61bb15, 0x9146205b} }, +/**/ {{0xbbff1e2e, 0x1cc35b7b} },}, +/**/ {{{0x3f61db03, 0xcb2ae929} }, +/**/ {{0xbc03ee8e, 0x12f6bf8d} },}, +/**/ {{{0x3f61faf1, 0xe5335418} }, +/**/ {{0x3c0bae5f, 0x7b7d619b} },}, +/**/ {{{0x3f621adf, 0xdf5fa0bf} }, +/**/ {{0xbbf5546a, 0xb3b731b0} },}, +/**/ {{{0x3f623acd, 0xb9b00eb0} }, +/**/ {{0xbbafb2b0, 0x105fd253} },}, +/**/ {{{0x3f625abb, 0x7424dd7f} }, +/**/ {{0x3c011647, 0xca53444b} },}, +/**/ {{{0x3f627aa9, 0x0ebe4cbf} }, +/**/ {{0x3c01678f, 0x592f3be8} },}, +/**/ {{{0x3f629a96, 0x897c9c02} }, +/**/ {{0xbbef2b12, 0x4347451d} },}, +/**/ {{{0x3f62ba83, 0xe4600ad8} }, +/**/ {{0x3bfb5bb7, 0xb2a477bc} },}, +/**/ {{{0x3f62da71, 0x1f68d8d3} }, +/**/ {{0xbc0590e1, 0x7a5822e4} },}, +/**/ {{{0x3f62fa5e, 0x3a974581} }, +/**/ {{0xbbf0f2e5, 0x53123101} },}, +/**/ {{{0x3f631a4b, 0x35eb9072} }, +/**/ {{0xbc018db4, 0x0e3f5fde} },}, +/**/ {{{0x3f633a38, 0x1165f933} }, +/**/ {{0x3c0921d5, 0x8d0afb38} },}, +/**/ {{{0x3f635a24, 0xcd06bf53} }, +/**/ {{0x3c01f6ba, 0xb5791b80} },}, +/**/ {{{0x3f637a11, 0x68ce225e} }, +/**/ {{0x3bde2af8, 0xa1894236} },}, +/**/ {{{0x3f6399fd, 0xe4bc61e0} }, +/**/ {{0xbc062a48, 0xd0f06ff3} },}, +/**/ {{{0x3f63b9ea, 0x40d1bd63} }, +/**/ {{0x3bffc80c, 0x4b4f9c11} },}, +/**/ {{{0x3f63d9d6, 0x7d0e7473} }, +/**/ {{0x3c02219b, 0x6a92c891} },}, +/**/ {{{0x3f63f9c2, 0x9972c699} }, +/**/ {{0x3c0d3590, 0x790ade9e} },}, +/**/ {{{0x3f6419ae, 0x95fef35f} }, +/**/ {{0xbc01c279, 0x792a458c} },}, +/**/ {{{0x3f64399a, 0x72b33a4b} }, +/**/ {{0x3c02ce64, 0x327bffae} },}, +/**/ {{{0x3f645986, 0x2f8fdae7} }, +/**/ {{0xbc070aec, 0xd231155c} },}, +/**/ {{{0x3f647971, 0xcc9514b7} }, +/**/ {{0x3c0f373d, 0xe4bbf776} },}, +/**/ {{{0x3f64995d, 0x49c32744} }, +/**/ {{0xbbf6d7e5, 0xbf22b2a7} },}, +/**/ {{{0x3f64b948, 0xa71a5211} }, +/**/ {{0xbbedec69, 0x64fe2936} },}, +/**/ {{{0x3f64d933, 0xe49ad4a3} }, +/**/ {{0x3bf5fc4b, 0xabee4257} },}, +/**/ {{{0x3f64f91f, 0x0244ee7e} }, +/**/ {{0x3c0c6fe3, 0x3cd1474f} },}, +/**/ {{{0x3f65190a, 0x0018df26} }, +/**/ {{0xbc023957, 0xd11e7fa5} },}, +/**/ {{{0x3f6538f4, 0xde16e61b} }, +/**/ {{0x3c006c31, 0x55380346} },}, +/**/ {{{0x3f6558df, 0x9c3f42e1} }, +/**/ {{0xbc09b7d4, 0xc4a5134c} },}, +/**/ {{{0x3f6578ca, 0x3a9234f7} }, +/**/ {{0xbc0e3f10, 0x2772c19c} },}, +/**/ {{{0x3f6598b4, 0xb90ffbdd} }, +/**/ {{0x3be6f110, 0x5592b468} },}, +/**/ {{{0x3f65b89f, 0x17b8d714} }, +/**/ {{0xbc0a5fea, 0xb251ace2} },}, +/**/ {{{0x3f65d889, 0x568d0619} }, +/**/ {{0xbc0aacc9, 0x315da285} },}, +/**/ {{{0x3f65f873, 0x758cc86a} }, +/**/ {{0xbbeb0782, 0xba64d81a} },}, +/**/ {{{0x3f66185d, 0x74b85d85} }, +/**/ {{0xbc09b459, 0x8e1eb3fa} },}, +/**/ {{{0x3f663847, 0x541004e5} }, +/**/ {{0x3bce9c22, 0x1d86e863} },}, +/**/ {{{0x3f665831, 0x1393fe07} }, +/**/ {{0xbbfbeb77, 0xcf37ee90} },}, +/**/ {{{0x3f66781a, 0xb3448865} }, +/**/ {{0xbc02dc68, 0xc252e3c9} },}, +/**/ {{{0x3f669804, 0x3321e379} }, +/**/ {{0xbbe73a0b, 0xb40b3741} },}, + }; + +#else +#ifdef LITTLE_ENDI + static const number + Iu[182] = { /* 1/ui */ +/**/ {{0xd1537290, 0x3ff6a13c} }, +/**/ {{0x16816817, 0x3ff68168} }, +/**/ {{0x6a5122f9, 0x3ff661ec} }, +/**/ {{0x590b2164, 0x3ff642c8} }, +/**/ {{0x77016240, 0x3ff623fa} }, +/**/ {{0x60581606, 0x3ff60581} }, +/**/ {{0xb8d015e7, 0x3ff5e75b} }, +/**/ {{0x2b931057, 0x3ff5c988} }, +/**/ {{0x6b015ac0, 0x3ff5ac05} }, +/**/ {{0x308158ed, 0x3ff58ed2} }, +/**/ {{0x3c506b3a, 0x3ff571ed} }, +/**/ {{0x55555555, 0x3ff55555} }, +/**/ {{0x48f40feb, 0x3ff53909} }, +/**/ {{0xeae2f815, 0x3ff51d07} }, +/**/ {{0x15015015, 0x3ff50150} }, +/**/ {{0xa72f0539, 0x3ff4e5e0} }, +/**/ {{0x8725af6e, 0x3ff4cab8} }, +/**/ {{0xa052bf5b, 0x3ff4afd6} }, +/**/ {{0xe3b2d067, 0x3ff49539} }, +/**/ {{0x47ae147b, 0x3ff47ae1} }, +/**/ {{0xc7f5cf9a, 0x3ff460cb} }, +/**/ {{0x6562d9fb, 0x3ff446f8} }, +/**/ {{0x25d51f87, 0x3ff42d66} }, +/**/ {{0x14141414, 0x3ff41414} }, +/**/ {{0x3fb013fb, 0x3ff3fb01} }, +/**/ {{0xbce4a902, 0x3ff3e22c} }, +/**/ {{0xa47babe7, 0x3ff3c995} }, +/**/ {{0x13b13b14, 0x3ff3b13b} }, +/**/ {{0x2c187f63, 0x3ff3991c} }, +/**/ {{0x13813814, 0x3ff38138} }, +/**/ {{0xf3de0748, 0x3ff3698d} }, +/**/ {{0xfb2b78c1, 0x3ff3521c} }, +/**/ {{0x5b57bcb2, 0x3ff33ae4} }, +/**/ {{0x4a2b10bf, 0x3ff323e3} }, +/**/ {{0x0130d190, 0x3ff30d19} }, +/**/ {{0xbda12f68, 0x3ff2f684} }, +/**/ {{0xc04b8097, 0x3ff2e025} }, +/**/ {{0x4d812ca0, 0x3ff2c9fb} }, +/**/ {{0xad012b40, 0x3ff2b404} }, +/**/ {{0x29e4129e, 0x3ff29e41} }, +/**/ {{0x1288b013, 0x3ff288b0} }, +/**/ {{0xb8812735, 0x3ff27350} }, +/**/ {{0x708092f1, 0x3ff25e22} }, +/**/ {{0x92492492, 0x3ff24924} }, +/**/ {{0x789abcdf, 0x3ff23456} }, +/**/ {{0x8121fb78, 0x3ff21fb7} }, +/**/ {{0x0c67c0d9, 0x3ff20b47} }, +/**/ {{0x7dc11f70, 0x3ff1f704} }, +/**/ {{0x3b3fb874, 0x3ff1e2ef} }, +/**/ {{0xada2811d, 0x3ff1cf06} }, +/**/ {{0x4046ed29, 0x3ff1bb4a} }, +/**/ {{0x611a7b96, 0x3ff1a7b9} }, +/**/ {{0x808ca29c, 0x3ff19453} }, +/**/ {{0x11811812, 0x3ff18118} }, +/**/ {{0x89427379, 0x3ff16e06} }, +/**/ {{0x5f75270d, 0x3ff15b1e} }, +/**/ {{0x0e0acd3b, 0x3ff1485f} }, +/**/ {{0x1135c811, 0x3ff135c8} }, +/**/ {{0xe75d3033, 0x3ff12358} }, +/**/ {{0x11111111, 0x3ff11111} }, +/**/ {{0x10fef011, 0x3ff0fef0} }, +/**/ {{0x6be69c90, 0x3ff0ecf5} }, +/**/ {{0xa88f4696, 0x3ff0db20} }, +/**/ {{0x4fbcda3b, 0x3ff0c971} }, +/**/ {{0xec259dc8, 0x3ff0b7e6} }, +/**/ {{0x0a6810a7, 0x3ff0a681} }, +/**/ {{0x39010954, 0x3ff0953f} }, +/**/ {{0x08421084, 0x3ff08421} }, +/**/ {{0x0a47f7c6, 0x3ff07326} }, +/**/ {{0xd2f1a9fc, 0x3ff0624d} }, +/**/ {{0xf7d73404, 0x3ff05197} }, +/**/ {{0x10410410, 0x3ff04104} }, +/**/ {{0xb51f5e1a, 0x3ff03091} }, +/**/ {{0x81020408, 0x3ff02040} }, +/**/ {{0x10101010, 0x3ff01010} }, +/**/ {{0x00000000, 0x3ff00000} }, +/**/ {{0xe01fe020, 0x3fefe01f} }, +/**/ {{0x01fc07f0, 0x3fefc07f} }, +/**/ {{0xaa01fa12, 0x3fefa11c} }, +/**/ {{0x1f81f820, 0x3fef81f8} }, +/**/ {{0xaca0dbb5, 0x3fef6310} }, +/**/ {{0x9e4a4271, 0x3fef4465} }, +/**/ {{0x44230ab5, 0x3fef25f6} }, +/**/ {{0xf07c1f08, 0x3fef07c1} }, +/**/ {{0xf8458e02, 0x3feee9c7} }, +/**/ {{0xb301ecc0, 0x3feecc07} }, +/**/ {{0x7aba01eb, 0x3feeae80} }, +/**/ {{0xabf0b767, 0x3fee9131} }, +/**/ {{0xa59750e4, 0x3fee741a} }, +/**/ {{0xc901e574, 0x3fee573a} }, +/**/ {{0x79dc1a73, 0x3fee3a91} }, +/**/ {{0x1e1e1e1e, 0x3fee1e1e} }, +/**/ {{0x1e01e01e, 0x3fee01e0} }, +/**/ {{0xe3f8868a, 0x3fede5d6} }, +/**/ {{0xdca01dca, 0x3fedca01} }, +/**/ {{0x76b981db, 0x3fedae60} }, +/**/ {{0x231e7f8a, 0x3fed92f2} }, +/**/ {{0x54b82c34, 0x3fed77b6} }, +/**/ {{0x807572b2, 0x3fed5cac} }, +/**/ {{0x1d41d41d, 0x3fed41d4} }, +/**/ {{0xa3fc5b1a, 0x3fed272c} }, +/**/ {{0x8f6ec074, 0x3fed0cb5} }, +/**/ {{0x5c44bfc6, 0x3fecf26e} }, +/**/ {{0x89039b0b, 0x3fecd856} }, +/**/ {{0x9601cbe7, 0x3fecbe6d} }, +/**/ {{0x055ee191, 0x3feca4b3} }, +/**/ {{0x5afb8a42, 0x3fec8b26} }, +/**/ {{0x1c71c71c, 0x3fec71c7} }, +/**/ {{0xd10d4986, 0x3fec5894} }, +/**/ {{0x01c3f8f0, 0x3fec3f8f} }, +/**/ {{0x392ea01c, 0x3fec26b5} }, +/**/ {{0x0381c0e0, 0x3fec0e07} }, +/**/ {{0xee868d8b, 0x3febf583} }, +/**/ {{0x899406f7, 0x3febdd2b} }, +/**/ {{0x65883e7b, 0x3febc4fd} }, +/**/ {{0x14c1bad0, 0x3febacf9} }, +/**/ {{0x2b18ff23, 0x3feb951e} }, +/**/ {{0x3dda338b, 0x3feb7d6c} }, +/**/ {{0xe3beee05, 0x3feb65e2} }, +/**/ {{0xb4e81b4f, 0x3feb4e81} }, +/**/ {{0x4ad806ce, 0x3feb3748} }, +/**/ {{0x406c80d9, 0x3feb2036} }, +/**/ {{0x31d922a4, 0x3feb094b} }, +/**/ {{0xbca1af28, 0x3feaf286} }, +/**/ {{0x7f94905e, 0x3feadbe8} }, +/**/ {{0x1ac5701b, 0x3feac570} }, +/**/ {{0x2f87ebfd, 0x3feaaf1d} }, +/**/ {{0x606a63be, 0x3fea98ef} }, +/**/ {{0x5130e159, 0x3fea82e6} }, +/**/ {{0xa6d01a6d, 0x3fea6d01} }, +/**/ {{0x07688a4a, 0x3fea5741} }, +/**/ {{0x1a41a41a, 0x3fea41a4} }, +/**/ {{0x87c51ca0, 0x3fea2c2a} }, +/**/ {{0xf97a4b02, 0x3fea16d3} }, +/**/ {{0x1a01a01a, 0x3fea01a0} }, +/**/ {{0x951033d9, 0x3fe9ec8e} }, +/**/ {{0x176b682d, 0x3fe9d79f} }, +/**/ {{0x4ee4a102, 0x3fe9c2d1} }, +/**/ {{0xea5510da, 0x3fe9ae24} }, +/**/ {{0x9999999a, 0x3fe99999} }, +/**/ {{0x0d8ec0ff, 0x3fe9852f} }, +/**/ {{0xf80cb872, 0x3fe970e4} }, +/**/ {{0x0be377ae, 0x3fe95cbb} }, +/**/ {{0xfcd6e9e0, 0x3fe948b0} }, +/**/ {{0x7f9b2ce6, 0x3fe934c6} }, +/**/ {{0x49d0e229, 0x3fe920fb} }, +/**/ {{0x120190d5, 0x3fe90d4f} }, +/**/ {{0x8f9c18fa, 0x3fe8f9c1} }, +/**/ {{0x7af1373f, 0x3fe8e652} }, +/**/ {{0x8d3018d3, 0x3fe8d301} }, +/**/ {{0x8062ff3a, 0x3fe8bfce} }, +/**/ {{0x0f6bf3aa, 0x3fe8acb9} }, +/**/ {{0xf601899c, 0x3fe899c0} }, +/**/ {{0xf0abb04a, 0x3fe886e5} }, +/**/ {{0xbcc092b9, 0x3fe87427} }, +/**/ {{0x18618618, 0x3fe86186} }, +/**/ {{0xc2780614, 0x3fe84f00} }, +/**/ {{0x7ab2bedd, 0x3fe83c97} }, +/**/ {{0x0182a4a0, 0x3fe82a4a} }, +/**/ {{0x18181818, 0x3fe81818} }, +/**/ {{0x80601806, 0x3fe80601} }, +/**/ {{0xfd017f40, 0x3fe7f405} }, +/**/ {{0x515a4f1d, 0x3fe7e225} }, +/**/ {{0x417d05f4, 0x3fe7d05f} }, +/**/ {{0x922e017c, 0x3fe7beb3} }, +/**/ {{0x08e0ecc3, 0x3fe7ad22} }, +/**/ {{0x6bb6398b, 0x3fe79baa} }, +/**/ {{0x8178a4c8, 0x3fe78a4c} }, +/**/ {{0x119ac60d, 0x3fe77908} }, +/**/ {{0xe434a9b1, 0x3fe767dc} }, +/**/ {{0xc201756d, 0x3fe756ca} }, +/**/ {{0x745d1746, 0x3fe745d1} }, +/**/ {{0xc541fe8d, 0x3fe734f0} }, +/**/ {{0x7f46debc, 0x3fe72428} }, +/**/ {{0x6d9c7c09, 0x3fe71378} }, +/**/ {{0x5c0b8170, 0x3fe702e0} }, +/**/ {{0x16f26017, 0x3fe6f260} }, +/**/ {{0x6b4337c7, 0x3fe6e1f7} }, +/**/ {{0x2681c861, 0x3fe6d1a6} }, +/**/ {{0x16c16c17, 0x3fe6c16c} }, +/**/ {{0x0aa31a3d, 0x3fe6b149} }, +/**/ {{0xd1537290, 0x3fe6a13c} }, + }; + + static const number + Iv[362] = { /* 1/vj */ +/**/ {{0xee93bfe3, 0x3ff00b47} }, +/**/ {{0xd80c106f, 0x3ff00b37} }, +/**/ {{0xc1a4a47a, 0x3ff00b27} }, +/**/ {{0xab5d7ba2, 0x3ff00b17} }, +/**/ {{0x95369587, 0x3ff00b07} }, +/**/ {{0x7f2ff1c6, 0x3ff00af7} }, +/**/ {{0x69499000, 0x3ff00ae7} }, +/**/ {{0x53836fd3, 0x3ff00ad7} }, +/**/ {{0x3ddd90dd, 0x3ff00ac7} }, +/**/ {{0x2857f2bf, 0x3ff00ab7} }, +/**/ {{0x12f29517, 0x3ff00aa7} }, +/**/ {{0xfdad7784, 0x3ff00a96} }, +/**/ {{0xe88899a5, 0x3ff00a86} }, +/**/ {{0xd383fb19, 0x3ff00a76} }, +/**/ {{0xbe9f9b7f, 0x3ff00a66} }, +/**/ {{0xa9db7a76, 0x3ff00a56} }, +/**/ {{0x9537979d, 0x3ff00a46} }, +/**/ {{0x80b3f293, 0x3ff00a36} }, +/**/ {{0x6c508af8, 0x3ff00a26} }, +/**/ {{0x580d606a, 0x3ff00a16} }, +/**/ {{0x43ea7288, 0x3ff00a06} }, +/**/ {{0x2fe7c0f1, 0x3ff009f6} }, +/**/ {{0x1c054b44, 0x3ff009e6} }, +/**/ {{0x08431122, 0x3ff009d6} }, +/**/ {{0xf4a11227, 0x3ff009c5} }, +/**/ {{0xe11f4df4, 0x3ff009b5} }, +/**/ {{0xcdbdc428, 0x3ff009a5} }, +/**/ {{0xba7c7462, 0x3ff00995} }, +/**/ {{0xa75b5e40, 0x3ff00985} }, +/**/ {{0x945a8162, 0x3ff00975} }, +/**/ {{0x8179dd68, 0x3ff00965} }, +/**/ {{0x6eb971ef, 0x3ff00955} }, +/**/ {{0x5c193e98, 0x3ff00945} }, +/**/ {{0x49994301, 0x3ff00935} }, +/**/ {{0x37397eca, 0x3ff00925} }, +/**/ {{0x24f9f192, 0x3ff00915} }, +/**/ {{0x12da9af7, 0x3ff00905} }, +/**/ {{0x00db7a99, 0x3ff008f5} }, +/**/ {{0xeefc9018, 0x3ff008e4} }, +/**/ {{0xdd3ddb12, 0x3ff008d4} }, +/**/ {{0xcb9f5b26, 0x3ff008c4} }, +/**/ {{0xba210ff4, 0x3ff008b4} }, +/**/ {{0xa8c2f91a, 0x3ff008a4} }, +/**/ {{0x97851639, 0x3ff00894} }, +/**/ {{0x866766ef, 0x3ff00884} }, +/**/ {{0x7569eadb, 0x3ff00874} }, +/**/ {{0x648ca19d, 0x3ff00864} }, +/**/ {{0x53cf8ad3, 0x3ff00854} }, +/**/ {{0x4332a61e, 0x3ff00844} }, +/**/ {{0x32b5f31b, 0x3ff00834} }, +/**/ {{0x2259716c, 0x3ff00824} }, +/**/ {{0x121d20ad, 0x3ff00814} }, +/**/ {{0x02010080, 0x3ff00804} }, +/**/ {{0xf2051083, 0x3ff007f3} }, +/**/ {{0xe2295056, 0x3ff007e3} }, +/**/ {{0xd26dbf97, 0x3ff007d3} }, +/**/ {{0xc2d25de5, 0x3ff007c3} }, +/**/ {{0xb3572ae2, 0x3ff007b3} }, +/**/ {{0xa3fc262a, 0x3ff007a3} }, +/**/ {{0x94c14f5f, 0x3ff00793} }, +/**/ {{0x85a6a61e, 0x3ff00783} }, +/**/ {{0x76ac2a08, 0x3ff00773} }, +/**/ {{0x67d1dabb, 0x3ff00763} }, +/**/ {{0x5917b7d7, 0x3ff00753} }, +/**/ {{0x4a7dc0fb, 0x3ff00743} }, +/**/ {{0x3c03f5c7, 0x3ff00733} }, +/**/ {{0x2daa55da, 0x3ff00723} }, +/**/ {{0x1f70e0d3, 0x3ff00713} }, +/**/ {{0x11579652, 0x3ff00703} }, +/**/ {{0x035e75f5, 0x3ff006f3} }, +/**/ {{0xf5857f5d, 0x3ff006e2} }, +/**/ {{0xe7ccb228, 0x3ff006d2} }, +/**/ {{0xda340df6, 0x3ff006c2} }, +/**/ {{0xccbb9266, 0x3ff006b2} }, +/**/ {{0xbf633f18, 0x3ff006a2} }, +/**/ {{0xb22b13ab, 0x3ff00692} }, +/**/ {{0xa5130fbe, 0x3ff00682} }, +/**/ {{0x981b32f1, 0x3ff00672} }, +/**/ {{0x8b437ce4, 0x3ff00662} }, +/**/ {{0x7e8bed35, 0x3ff00652} }, +/**/ {{0x71f48383, 0x3ff00642} }, +/**/ {{0x657d3f70, 0x3ff00632} }, +/**/ {{0x59262098, 0x3ff00622} }, +/**/ {{0x4cef269e, 0x3ff00612} }, +/**/ {{0x40d8511e, 0x3ff00602} }, +/**/ {{0x34e19fba, 0x3ff005f2} }, +/**/ {{0x290b1211, 0x3ff005e2} }, +/**/ {{0x1d54a7c1, 0x3ff005d2} }, +/**/ {{0x11be606b, 0x3ff005c2} }, +/**/ {{0x06483bad, 0x3ff005b2} }, +/**/ {{0xfaf23928, 0x3ff005a1} }, +/**/ {{0xefbc587b, 0x3ff00591} }, +/**/ {{0xe4a69945, 0x3ff00581} }, +/**/ {{0xd9b0fb25, 0x3ff00571} }, +/**/ {{0xcedb7dbc, 0x3ff00561} }, +/**/ {{0xc42620a9, 0x3ff00551} }, +/**/ {{0xb990e38b, 0x3ff00541} }, +/**/ {{0xaf1bc601, 0x3ff00531} }, +/**/ {{0xa4c6c7ac, 0x3ff00521} }, +/**/ {{0x9a91e82a, 0x3ff00511} }, +/**/ {{0x907d271c, 0x3ff00501} }, +/**/ {{0x86888421, 0x3ff004f1} }, +/**/ {{0x7cb3fed8, 0x3ff004e1} }, +/**/ {{0x72ff96e0, 0x3ff004d1} }, +/**/ {{0x696b4bdb, 0x3ff004c1} }, +/**/ {{0x5ff71d66, 0x3ff004b1} }, +/**/ {{0x56a30b21, 0x3ff004a1} }, +/**/ {{0x4d6f14ad, 0x3ff00491} }, +/**/ {{0x445b39a8, 0x3ff00481} }, +/**/ {{0x3b6779b3, 0x3ff00471} }, +/**/ {{0x3293d46c, 0x3ff00461} }, +/**/ {{0x29e04974, 0x3ff00451} }, +/**/ {{0x214cd869, 0x3ff00441} }, +/**/ {{0x18d980ed, 0x3ff00431} }, +/**/ {{0x1086429d, 0x3ff00421} }, +/**/ {{0x08531d1a, 0x3ff00411} }, +/**/ {{0x00401004, 0x3ff00401} }, +/**/ {{0xf84d1afa, 0x3ff003f0} }, +/**/ {{0xf07a3d9b, 0x3ff003e0} }, +/**/ {{0xe8c77787, 0x3ff003d0} }, +/**/ {{0xe134c85f, 0x3ff003c0} }, +/**/ {{0xd9c22fc1, 0x3ff003b0} }, +/**/ {{0xd26fad4d, 0x3ff003a0} }, +/**/ {{0xcb3d40a3, 0x3ff00390} }, +/**/ {{0xc42ae963, 0x3ff00380} }, +/**/ {{0xbd38a72c, 0x3ff00370} }, +/**/ {{0xb666799e, 0x3ff00360} }, +/**/ {{0xafb46058, 0x3ff00350} }, +/**/ {{0xa9225afa, 0x3ff00340} }, +/**/ {{0xa2b06925, 0x3ff00330} }, +/**/ {{0x9c5e8a77, 0x3ff00320} }, +/**/ {{0x962cbe90, 0x3ff00310} }, +/**/ {{0x901b0511, 0x3ff00300} }, +/**/ {{0x8a295d98, 0x3ff002f0} }, +/**/ {{0x8457c7c6, 0x3ff002e0} }, +/**/ {{0x7ea6433a, 0x3ff002d0} }, +/**/ {{0x7914cf94, 0x3ff002c0} }, +/**/ {{0x73a36c73, 0x3ff002b0} }, +/**/ {{0x6e521978, 0x3ff002a0} }, +/**/ {{0x6920d642, 0x3ff00290} }, +/**/ {{0x640fa271, 0x3ff00280} }, +/**/ {{0x5f1e7da5, 0x3ff00270} }, +/**/ {{0x5a4d677d, 0x3ff00260} }, +/**/ {{0x559c5f9a, 0x3ff00250} }, +/**/ {{0x510b659a, 0x3ff00240} }, +/**/ {{0x4c9a791f, 0x3ff00230} }, +/**/ {{0x484999c6, 0x3ff00220} }, +/**/ {{0x4418c732, 0x3ff00210} }, +/**/ {{0x40080100, 0x3ff00200} }, +/**/ {{0x3c1746d2, 0x3ff001f0} }, +/**/ {{0x38469846, 0x3ff001e0} }, +/**/ {{0x3495f4fd, 0x3ff001d0} }, +/**/ {{0x31055c96, 0x3ff001c0} }, +/**/ {{0x2d94ceb2, 0x3ff001b0} }, +/**/ {{0x2a444af0, 0x3ff001a0} }, +/**/ {{0x2713d0ef, 0x3ff00190} }, +/**/ {{0x24036051, 0x3ff00180} }, +/**/ {{0x2112f8b4, 0x3ff00170} }, +/**/ {{0x1e4299b9, 0x3ff00160} }, +/**/ {{0x1b9242ff, 0x3ff00150} }, +/**/ {{0x1901f427, 0x3ff00140} }, +/**/ {{0x1691acd0, 0x3ff00130} }, +/**/ {{0x14416c9a, 0x3ff00120} }, +/**/ {{0x12113324, 0x3ff00110} }, +/**/ {{0x10010010, 0x3ff00100} }, +/**/ {{0x0e10d2fc, 0x3ff000f0} }, +/**/ {{0x0c40ab89, 0x3ff000e0} }, +/**/ {{0x0a908957, 0x3ff000d0} }, +/**/ {{0x09006c05, 0x3ff000c0} }, +/**/ {{0x07905334, 0x3ff000b0} }, +/**/ {{0x06403e82, 0x3ff000a0} }, +/**/ {{0x05102d92, 0x3ff00090} }, +/**/ {{0x04002001, 0x3ff00080} }, +/**/ {{0x03101571, 0x3ff00070} }, +/**/ {{0x02400d80, 0x3ff00060} }, +/**/ {{0x019007d0, 0x3ff00050} }, +/**/ {{0x01000400, 0x3ff00040} }, +/**/ {{0x009001b0, 0x3ff00030} }, +/**/ {{0x00400080, 0x3ff00020} }, +/**/ {{0x00100010, 0x3ff00010} }, +/**/ {{0x00000000, 0x3ff00000} }, +/**/ {{0x001fffe0, 0x3fefffe0} }, +/**/ {{0x007fff00, 0x3fefffc0} }, +/**/ {{0x011ffca0, 0x3fefffa0} }, +/**/ {{0x01fff800, 0x3fefff80} }, +/**/ {{0x031ff060, 0x3fefff60} }, +/**/ {{0x047fe501, 0x3fefff40} }, +/**/ {{0x061fd521, 0x3fefff20} }, +/**/ {{0x07ffc002, 0x3fefff00} }, +/**/ {{0x0a1fa4e3, 0x3feffee0} }, +/**/ {{0x0c7f8305, 0x3feffec0} }, +/**/ {{0x0f1f59a7, 0x3feffea0} }, +/**/ {{0x11ff280a, 0x3feffe80} }, +/**/ {{0x151eed6e, 0x3feffe60} }, +/**/ {{0x187ea913, 0x3feffe40} }, +/**/ {{0x1c1e5a39, 0x3feffe20} }, +/**/ {{0x1ffe0020, 0x3feffe00} }, +/**/ {{0x241d9a09, 0x3feffde0} }, +/**/ {{0x287d2733, 0x3feffdc0} }, +/**/ {{0x2d1ca6e0, 0x3feffda0} }, +/**/ {{0x31fc184e, 0x3feffd80} }, +/**/ {{0x371b7abf, 0x3feffd60} }, +/**/ {{0x3c7acd72, 0x3feffd40} }, +/**/ {{0x421a0fa9, 0x3feffd20} }, +/**/ {{0x47f940a2, 0x3feffd00} }, +/**/ {{0x4e185f9f, 0x3feffce0} }, +/**/ {{0x54776bdf, 0x3feffcc0} }, +/**/ {{0x5b1664a3, 0x3feffca0} }, +/**/ {{0x61f5492c, 0x3feffc80} }, +/**/ {{0x691418b9, 0x3feffc60} }, +/**/ {{0x7072d28b, 0x3feffc40} }, +/**/ {{0x781175e3, 0x3feffc20} }, +/**/ {{0x7ff00200, 0x3feffc00} }, +/**/ {{0x880e7623, 0x3feffbe0} }, +/**/ {{0x906cd18c, 0x3feffbc0} }, +/**/ {{0x990b137c, 0x3feffba0} }, +/**/ {{0xa1e93b34, 0x3feffb80} }, +/**/ {{0xab0747f3, 0x3feffb60} }, +/**/ {{0xb46538fa, 0x3feffb40} }, +/**/ {{0xbe030d89, 0x3feffb20} }, +/**/ {{0xc7e0c4e1, 0x3feffb00} }, +/**/ {{0xd1fe5e43, 0x3feffae0} }, +/**/ {{0xdc5bd8ee, 0x3feffac0} }, +/**/ {{0xe6f93424, 0x3feffaa0} }, +/**/ {{0xf1d66f25, 0x3feffa80} }, +/**/ {{0xfcf38931, 0x3feffa60} }, +/**/ {{0x08508189, 0x3feffa41} }, +/**/ {{0x13ed576d, 0x3feffa21} }, +/**/ {{0x1fca0a1e, 0x3feffa01} }, +/**/ {{0x2be698dd, 0x3feff9e1} }, +/**/ {{0x384302e9, 0x3feff9c1} }, +/**/ {{0x44df4785, 0x3feff9a1} }, +/**/ {{0x51bb65ef, 0x3feff981} }, +/**/ {{0x5ed75d6a, 0x3feff961} }, +/**/ {{0x6c332d34, 0x3feff941} }, +/**/ {{0x79ced490, 0x3feff921} }, +/**/ {{0x87aa52be, 0x3feff901} }, +/**/ {{0x95c5a6fe, 0x3feff8e1} }, +/**/ {{0xa420d091, 0x3feff8c1} }, +/**/ {{0xb2bbceb7, 0x3feff8a1} }, +/**/ {{0xc196a0b2, 0x3feff881} }, +/**/ {{0xd0b145c2, 0x3feff861} }, +/**/ {{0xe00bbd28, 0x3feff841} }, +/**/ {{0xefa60624, 0x3feff821} }, +/**/ {{0xff801ff8, 0x3feff801} }, +/**/ {{0x0f9a09e3, 0x3feff7e2} }, +/**/ {{0x1ff3c328, 0x3feff7c2} }, +/**/ {{0x308d4b05, 0x3feff7a2} }, +/**/ {{0x4166a0bd, 0x3feff782} }, +/**/ {{0x527fc390, 0x3feff762} }, +/**/ {{0x63d8b2bf, 0x3feff742} }, +/**/ {{0x75716d8b, 0x3feff722} }, +/**/ {{0x8749f334, 0x3feff702} }, +/**/ {{0x996242fb, 0x3feff6e2} }, +/**/ {{0xabba5c21, 0x3feff6c2} }, +/**/ {{0xbe523de8, 0x3feff6a2} }, +/**/ {{0xd129e78f, 0x3feff682} }, +/**/ {{0xe4415858, 0x3feff662} }, +/**/ {{0xf7988f84, 0x3feff642} }, +/**/ {{0x0b2f8c54, 0x3feff623} }, +/**/ {{0x1f064e08, 0x3feff603} }, +/**/ {{0x331cd3e1, 0x3feff5e3} }, +/**/ {{0x47731d21, 0x3feff5c3} }, +/**/ {{0x5c092908, 0x3feff5a3} }, +/**/ {{0x70def6d7, 0x3feff583} }, +/**/ {{0x85f485d0, 0x3feff563} }, +/**/ {{0x9b49d532, 0x3feff543} }, +/**/ {{0xb0dee440, 0x3feff523} }, +/**/ {{0xc6b3b23b, 0x3feff503} }, +/**/ {{0xdcc83e62, 0x3feff4e3} }, +/**/ {{0xf31c87f8, 0x3feff4c3} }, +/**/ {{0x09b08e3d, 0x3feff4a4} }, +/**/ {{0x20845073, 0x3feff484} }, +/**/ {{0x3797cdda, 0x3feff464} }, +/**/ {{0x4eeb05b4, 0x3feff444} }, +/**/ {{0x667df741, 0x3feff424} }, +/**/ {{0x7e50a1c3, 0x3feff404} }, +/**/ {{0x9663047b, 0x3feff3e4} }, +/**/ {{0xaeb51eaa, 0x3feff3c4} }, +/**/ {{0xc746ef91, 0x3feff3a4} }, +/**/ {{0xe0187672, 0x3feff384} }, +/**/ {{0xf929b28d, 0x3feff364} }, +/**/ {{0x127aa323, 0x3feff345} }, +/**/ {{0x2c0b4776, 0x3feff325} }, +/**/ {{0x45db9ec7, 0x3feff305} }, +/**/ {{0x5feba858, 0x3feff2e5} }, +/**/ {{0x7a3b6369, 0x3feff2c5} }, +/**/ {{0x94cacf3b, 0x3feff2a5} }, +/**/ {{0xaf99eb11, 0x3feff285} }, +/**/ {{0xcaa8b62a, 0x3feff265} }, +/**/ {{0xe5f72fc9, 0x3feff245} }, +/**/ {{0x0185572f, 0x3feff226} }, +/**/ {{0x1d532b9d, 0x3feff206} }, +/**/ {{0x3960ac54, 0x3feff1e6} }, +/**/ {{0x55add896, 0x3feff1c6} }, +/**/ {{0x723aafa3, 0x3feff1a6} }, +/**/ {{0x8f0730be, 0x3feff186} }, +/**/ {{0xac135b27, 0x3feff166} }, +/**/ {{0xc95f2e21, 0x3feff146} }, +/**/ {{0xe6eaa8eb, 0x3feff126} }, +/**/ {{0x04b5cac9, 0x3feff107} }, +/**/ {{0x22c092fb, 0x3feff0e7} }, +/**/ {{0x410b00c2, 0x3feff0c7} }, +/**/ {{0x5f951360, 0x3feff0a7} }, +/**/ {{0x7e5eca16, 0x3feff087} }, +/**/ {{0x9d682426, 0x3feff067} }, +/**/ {{0xbcb120d2, 0x3feff047} }, +/**/ {{0xdc39bf5a, 0x3feff027} }, +/**/ {{0xfc01ff00, 0x3feff007} }, +/**/ {{0x1c09df07, 0x3fefefe8} }, +/**/ {{0x3c515eae, 0x3fefefc8} }, +/**/ {{0x5cd87d38, 0x3fefefa8} }, +/**/ {{0x7d9f39e6, 0x3fefef88} }, +/**/ {{0x9ea593fa, 0x3fefef68} }, +/**/ {{0xbfeb8ab5, 0x3fefef48} }, +/**/ {{0xe1711d5a, 0x3fefef28} }, +/**/ {{0x03364b28, 0x3fefef09} }, +/**/ {{0x253b1363, 0x3fefeee9} }, +/**/ {{0x477f754b, 0x3fefeec9} }, +/**/ {{0x6a037022, 0x3fefeea9} }, +/**/ {{0x8cc7032a, 0x3fefee89} }, +/**/ {{0xafca2da5, 0x3fefee69} }, +/**/ {{0xd30ceed4, 0x3fefee49} }, +/**/ {{0xf68f45f8, 0x3fefee29} }, +/**/ {{0x1a513254, 0x3fefee0a} }, +/**/ {{0x3e52b329, 0x3fefedea} }, +/**/ {{0x6293c7b8, 0x3fefedca} }, +/**/ {{0x87146f44, 0x3fefedaa} }, +/**/ {{0xabd4a90e, 0x3fefed8a} }, +/**/ {{0xd0d47458, 0x3fefed6a} }, +/**/ {{0xf613d064, 0x3fefed4a} }, +/**/ {{0x1b92bc73, 0x3fefed2b} }, +/**/ {{0x415137c7, 0x3fefed0b} }, +/**/ {{0x674f41a2, 0x3fefeceb} }, +/**/ {{0x8d8cd945, 0x3fefeccb} }, +/**/ {{0xb409fdf3, 0x3fefecab} }, +/**/ {{0xdac6aeed, 0x3fefec8b} }, +/**/ {{0x01c2eb76, 0x3fefec6c} }, +/**/ {{0x28feb2ce, 0x3fefec4c} }, +/**/ {{0x507a0437, 0x3fefec2c} }, +/**/ {{0x7834def5, 0x3fefec0c} }, +/**/ {{0xa02f4247, 0x3fefebec} }, +/**/ {{0xc8692d71, 0x3fefebcc} }, +/**/ {{0xf0e29fb4, 0x3fefebac} }, +/**/ {{0x199b9852, 0x3fefeb8d} }, +/**/ {{0x4294168d, 0x3fefeb6d} }, +/**/ {{0x6bcc19a7, 0x3fefeb4d} }, +/**/ {{0x9543a0e2, 0x3fefeb2d} }, +/**/ {{0xbefaab7f, 0x3fefeb0d} }, +/**/ {{0xe8f138c2, 0x3fefeaed} }, +/**/ {{0x132747ea, 0x3fefeace} }, +/**/ {{0x3d9cd83c, 0x3fefeaae} }, +/**/ {{0x6851e8f7, 0x3fefea8e} }, +/**/ {{0x93467960, 0x3fefea6e} }, +/**/ {{0xbe7a88b7, 0x3fefea4e} }, +/**/ {{0xe9ee163f, 0x3fefea2e} }, +/**/ {{0x15a12139, 0x3fefea0f} }, +/**/ {{0x4193a8e8, 0x3fefe9ef} }, +/**/ {{0x6dc5ac8e, 0x3fefe9cf} }, +/**/ {{0x9a372b6d, 0x3fefe9af} }, +/**/ {{0xc6e824c6, 0x3fefe98f} }, +/**/ {{0xf3d897dd, 0x3fefe96f} }, + }; + + static const number + Lu[182][2] = { /* log(ui) */ +/**/ {{{0x0b3aac49, 0xbfd63003} }, +/**/ {{0xe51fff99, 0xbc6dc18c} },}, +/**/ {{{0xdf595f30, 0xbfd5d5bd} }, +/**/ {{0x48cbb8a2, 0x3c765411} },}, +/**/ {{{0x53c8d1fb, 0xbfd57bf7} }, +/**/ {{0x15f88b63, 0x3c60908d} },}, +/**/ {{{0x0738a3d8, 0xbfd522ae} }, +/**/ {{0xb38a6979, 0x3c68f7e9} },}, +/**/ {{{0x9e172c3c, 0xbfd4c9e0} }, +/**/ {{0x5b147a5d, 0x3c512361} },}, +/**/ {{{0xc271c41b, 0xbfd4718d} }, +/**/ {{0x14c56eef, 0xbc38fb4c} },}, +/**/ {{{0x23d5e8c7, 0xbfd419b4} }, +/**/ {{0x43827392, 0xbc60dbb2} },}, +/**/ {{{0x77333184, 0xbfd3c252} }, +/**/ {{0xe50a8ec6, 0x3c72ad27} },}, +/**/ {{{0x76be1117, 0xbfd36b67} }, +/**/ {{0xe883858e, 0x3c5324f0} },}, +/**/ {{{0xe1d35ce4, 0xbfd314f1} }, +/**/ {{0x09e5c3dc, 0x3c73d699} },}, +/**/ {{{0x7cdc9354, 0xbfd2bef0} }, +/**/ {{0x7fd86088, 0x3c782dad} },}, +/**/ {{{0x1134db92, 0xbfd26962} }, +/**/ {{0xdd9db02b, 0xbc7e0efa} },}, +/**/ {{{0x6d0eb8d4, 0xbfd21445} }, +/**/ {{0x1aeba60a, 0xbc6f7ae9} },}, +/**/ {{{0x635a6b95, 0xbfd1bf99} }, +/**/ {{0x84249223, 0x3c612aeb} },}, +/**/ {{{0xcbacfb73, 0xbfd16b5c} }, +/**/ {{0x28b40935, 0xbc766fbd} },}, +/**/ {{{0x8227e47c, 0xbfd1178e} }, +/**/ {{0x5f01c691, 0x3c60e63a} },}, +/**/ {{{0x676162e3, 0xbfd0c42d} }, +/**/ {{0x9d5d11ee, 0xbc5162c7} },}, +/**/ {{{0x604d5862, 0xbfd07138} }, +/**/ {{0xed4e9138, 0xbc7cdb16} },}, +/**/ {{{0x5626c691, 0xbfd01eae} }, +/**/ {{0xbd2932e2, 0x3c418290} },}, +/**/ {{{0x6cb3b379, 0xbfcf991c} }, +/**/ {{0x66f980a2, 0xbc6f6650} },}, +/**/ {{{0xe4dcffe6, 0xbfcef5ad} }, +/**/ {{0xddc708a0, 0x3c508ab2} },}, +/**/ {{{0xffe71012, 0xbfce530e} }, +/**/ {{0x41f43042, 0xbc422760} },}, +/**/ {{{0xb0d48940, 0xbfcdb13d} }, +/**/ {{0x49f96cb9, 0xbc5aa11d} },}, +/**/ {{{0xf2655e7b, 0xbfcd1037} }, +/**/ {{0x242471a2, 0xbc660629} },}, +/**/ {{{0xc6f00f71, 0xbfcc6ffb} }, +/**/ {{0x2c57a4a5, 0x3c68e58b} },}, +/**/ {{{0x383bd8ad, 0xbfcbd087} }, +/**/ {{0xf6a516d7, 0xbc3dd355} },}, +/**/ {{{0x575bce3d, 0xbfcb31d8} }, +/**/ {{0xb386a94d, 0x3c66353a} },}, +/**/ {{{0x3c8ad9e3, 0xbfca93ed} }, +/**/ {{0x9de97203, 0xbc6bcafa} },}, +/**/ {{{0x07089664, 0xbfc9f6c4} }, +/**/ {{0x605e67ef, 0xbc435a19} },}, +/**/ {{{0xdcf7017f, 0xbfc95a5a} }, +/**/ {{0x07fb7a3d, 0xbc5142c5} },}, +/**/ {{{0xeb38fe8c, 0xbfc8beaf} }, +/**/ {{0xb6997a40, 0xbc555aa8} },}, +/**/ {{{0x6551a3c2, 0xbfc823c1} }, +/**/ {{0xe70be781, 0x3c61232c} },}, +/**/ {{{0x85444c73, 0xbfc7898d} }, +/**/ {{0xebcfb201, 0xbc5ef8f6} },}, +/**/ {{{0x8b756abc, 0xbfc6f012} }, +/**/ {{0xc21e166c, 0x3c68de59} },}, +/**/ {{{0xbe8c133a, 0xbfc6574e} }, +/**/ {{0xf4621bed, 0x3c3d34f0} },}, +/**/ {{{0x6b543db2, 0xbfc5bf40} }, +/**/ {{0x4c0df7e7, 0x3c21f5b4} },}, +/**/ {{{0xe4a1b58d, 0xbfc527e5} }, +/**/ {{0x82395bfd, 0x3c271a96} },}, +/**/ {{{0x8333b561, 0xbfc4913d} }, +/**/ {{0x4930f135, 0x3c50d560} },}, +/**/ {{{0xa59928cc, 0xbfc3fb45} }, +/**/ {{0xa354d056, 0x3c6d87e6} },}, +/**/ {{{0xb0159016, 0xbfc365fc} }, +/**/ {{0xa5b944ad, 0xbc57d411} },}, +/**/ {{{0x0c86813a, 0xbfc2d161} }, +/**/ {{0xf25af95f, 0x3c5499a3} },}, +/**/ {{{0x2a49c202, 0xbfc23d71} }, +/**/ {{0x61051d69, 0x3c66e381} },}, +/**/ {{{0x7e23f72a, 0xbfc1aa2b} }, +/**/ {{0xd9b2ef7e, 0x3c4c6ef1} },}, +/**/ {{{0x8227e47c, 0xbfc1178e} }, +/**/ {{0x5f01c691, 0x3c50e63a} },}, +/**/ {{{0xb59e3a07, 0xbfc08598} }, +/**/ {{0x9902bf32, 0x3c6dd700} },}, +/**/ {{{0x39dbd566, 0xbfbfe891} }, +/**/ {{0x215f9393, 0x3c5ac9f4} },}, +/**/ {{{0x830a1120, 0xbfbec739} }, +/**/ {{0x91780d3f, 0x3c4a2bf9} },}, +/**/ {{{0x638446a2, 0xbfbda727} }, +/**/ {{0x71733019, 0xbc5401fa} },}, +/**/ {{{0x01bc4b23, 0xbfbc8858} }, +/**/ {{0x559a6706, 0xbc5a38cb} },}, +/**/ {{{0x8dad5b1c, 0xbfbb6ac8} }, +/**/ {{0xed1ca59f, 0x3c40057e} },}, +/**/ {{{0x40b1bc38, 0xbfba4e76} }, +/**/ {{0x203e4259, 0x3c55b5ca} },}, +/**/ {{{0x5d594989, 0xbfb9335e} }, +/**/ {{0x5704ccb7, 0x3c5478a8} },}, +/**/ {{{0x2f40e3f0, 0xbfb8197e} }, +/**/ {{0xffbeed43, 0xbc3b9f2d} },}, +/**/ {{{0x0aeac0e1, 0xbfb700d3} }, +/**/ {{0x212cdd05, 0x3c272566} },}, +/**/ {{{0x4d9791cb, 0xbfb5e95a} }, +/**/ {{0x5c5c450a, 0xbc5f3874} },}, +/**/ {{{0x5d207eac, 0xbfb4d311} }, +/**/ {{0x2c7842cc, 0xbc5769f4} },}, +/**/ {{{0xa7d1ee64, 0xbfb3bdf5} }, +/**/ {{0xd3b5b45f, 0xbc47a976} },}, +/**/ {{{0xa44717a5, 0xbfb2aa04} }, +/**/ {{0x8d2fa3f7, 0x3c5d15d3} },}, +/**/ {{{0xd1465567, 0xbfb1973b} }, +/**/ {{0x67a6acf6, 0x3c475583} },}, +/**/ {{{0xb59e3a07, 0xbfb08598} }, +/**/ {{0x9902bf32, 0x3c5dd700} },}, +/**/ {{{0xc006b87c, 0xbfaeea31} }, +/**/ {{0x93b7b66c, 0x3c43e4fc} },}, +/**/ {{{0xcdddb2cc, 0xbfaccb73} }, +/**/ {{0x0500efd4, 0x3c4e48fb} },}, +/**/ {{{0xd0fb10fc, 0xbfaaaef2} }, +/**/ {{0xb42e0add, 0xbc2a353b} },}, +/**/ {{{0x149fb343, 0xbfa894aa} }, +/**/ {{0x7660a23d, 0xbc3a8be9} },}, +/**/ {{{0xf2d4bb58, 0xbfa67c94} }, +/**/ {{0x6505e603, 0xbc40413e} },}, +/**/ {{{0xd42de3ea, 0xbfa466ae} }, +/**/ {{0x7f4a137e, 0x3c4cdd6f} },}, +/**/ {{{0x2f8d183f, 0xbfa252f3} }, +/**/ {{0x92615916, 0x3c4947f7} },}, +/**/ {{{0x89e74444, 0xbfa0415d} }, +/**/ {{0x1d753622, 0xbc4c05cf} },}, +/**/ {{{0xec14aaf2, 0xbf9c63d2} }, +/**/ {{0xa686bd86, 0x3c3ce030} },}, +/**/ {{{0x28c8cabf, 0xbf984925} }, +/**/ {{0x0619fa67, 0x3c3d192d} },}, +/**/ {{{0x25980cc1, 0xbf9432a9} }, +/**/ {{0x39004192, 0x3c38cdaf} },}, +/**/ {{{0x58935847, 0xbf902056} }, +/**/ {{0x8416e71f, 0xbc327c8e} },}, +/**/ {{{0xa388a2aa, 0xbf882448} }, +/**/ {{0x137f09a0, 0xbc104b16} },}, +/**/ {{{0x7588de71, 0xbf801015} }, +/**/ {{0xd417ced0, 0xbc146662} },}, +/**/ {{{0x59588b35, 0xbf700805} }, +/**/ {{0x8cf63677, 0xbc1f9663} },}, +/**/ {{{0x00000000, 0x00000000} }, +/**/ {{0x00000000, 0x00000000} },}, +/**/ {{{0xa2b10bc0, 0x3f6ff00a} }, +/**/ {{0xd5a6d353, 0x3c02821a} },}, +/**/ {{{0x6b106789, 0x3f7fe02a} }, +/**/ {{0xe3711ebf, 0xbbce44b7} },}, +/**/ {{{0x5f810a77, 0x3f87dc47} }, +/**/ {{0x87d3df21, 0xbc116d76} },}, +/**/ {{{0xb0fc03e4, 0x3f8fc0a8} }, +/**/ {{0xc59642a1, 0xbc183092} },}, +/**/ {{{0x4346a575, 0x3f93cea4} }, +/**/ {{0x902b3a1c, 0xbc10cb5a} },}, +/**/ {{{0x07d5b11b, 0x3f97b91b} }, +/**/ {{0xace3a510, 0xbc35b602} },}, +/**/ {{{0x27af9198, 0x3f9b9fc0} }, +/**/ {{0x229dc868, 0xbbf0ae69} },}, +/**/ {{{0x0e783300, 0x3f9f829b} }, +/**/ {{0x04f1ef23, 0x3c333e3f} },}, +/**/ {{{0x8923d980, 0x3fa1b0d9} }, +/**/ {{0x89bac481, 0xbc3e9ae8} },}, +/**/ {{{0xb9febd60, 0x3fa39e87} }, +/**/ {{0x37f551bb, 0xbc45bfa9} },}, +/**/ {{{0xafc8e4d5, 0x3fa58a5b} }, +/**/ {{0x2b4e2b72, 0xbc4ce55c} },}, +/**/ {{{0xf632dcfc, 0x3fa77458} }, +/**/ {{0xa87b9296, 0x3c418d3c} },}, +/**/ {{{0x0ec8e3eb, 0x3fa95c83} }, +/**/ {{0x80520bf2, 0x3c4f5a0e} },}, +/**/ {{{0x711971bf, 0x3fab42dd} }, +/**/ {{0x9c130499, 0xbc3eb975} },}, +/**/ {{{0x8adb0b52, 0x3fad276b} }, +/**/ {{0x3257fd47, 0x3c21e3c5} },}, +/**/ {{{0xc01162a6, 0x3faf0a30} }, +/**/ {{0x5c5bbacd, 0x3c485f32} },}, +/**/ {{{0x3598e471, 0x3fb07598} }, +/**/ {{0x333c45b8, 0x3c480da5} },}, +/**/ {{{0xeea37ae1, 0x3fb16536} }, +/**/ {{0xe8c22cda, 0xbc379da3} },}, +/**/ {{{0x2f0a1417, 0x3fb253f6} }, +/**/ {{0x63fc4cfd, 0xbc1c1259} },}, +/**/ {{{0x961bd1d1, 0x3fb341d7} }, +/**/ {{0x227becbb, 0xbc5b599f} },}, +/**/ {{{0xbea646f0, 0x3fb42edc} }, +/**/ {{0x935996c9, 0x3c4ddd4f} },}, +/**/ {{{0x3f06183f, 0x3fb51b07} }, +/**/ {{0x9a1a8be4, 0x3c5a49e3} },}, +/**/ {{{0xa93750c4, 0x3fb60658} }, +/**/ {{0x8ec21b6a, 0xbc538845} },}, +/**/ {{{0x8ae56b4c, 0x3fb6f0d2} }, +/**/ {{0x9184b992, 0xbc5906d9} },}, +/**/ {{{0x6d7b12cd, 0x3fb7da76} }, +/**/ {{0xcdd94131, 0xbc5eeedf} },}, +/**/ {{{0xd6319b21, 0x3fb8c345} }, +/**/ {{0xab3424a9, 0xbc24a697} },}, +/**/ {{{0x462033ad, 0x3fb9ab42} }, +/**/ {{0x1c184e8e, 0xbc42099e} },}, +/**/ {{{0x3a4ad563, 0x3fba926d} }, +/**/ {{0x8aa70ea9, 0x3c5942f4} },}, +/**/ {{{0x2bb0eda1, 0x3fbb78c8} }, +/**/ {{0xf0327e21, 0x3c20878c} },}, +/**/ {{{0x8f5bc743, 0x3fbc5e54} }, +/**/ {{0xef8161b1, 0x3c35d617} },}, +/**/ {{{0xd66cb35d, 0x3fbd4313} }, +/**/ {{0x951d90fa, 0x3c5790dd} },}, +/**/ {{{0x6e2af2e6, 0x3fbe2707} }, +/**/ {{0x001e0162, 0xbc361578} },}, +/**/ {{{0xc01162a6, 0x3fbf0a30} }, +/**/ {{0x5c5bbacd, 0x3c585f32} },}, +/**/ {{{0x31dbeabb, 0x3fbfec91} }, +/**/ {{0x9981b36c, 0xbc55746b} },}, +/**/ {{{0x12ca596e, 0x3fc06715} }, +/**/ {{0x7eb86499, 0x3c550c64} },}, +/**/ {{{0x7cd08e59, 0x3fc0d77e} }, +/**/ {{0x5e9030ac, 0x3c69a5dc} },}, +/**/ {{{0x846742ac, 0x3fc14785} }, +/**/ {{0x3e3a7f07, 0x3c6a2881} },}, +/**/ {{{0xd52f67a0, 0x3fc1b72a} }, +/**/ {{0x3472cd74, 0x3c548302} },}, +/**/ {{{0x190a5acb, 0x3fc2266f} }, +/**/ {{0xf1809e88, 0x3c6f547b} },}, +/**/ {{{0xf81ff523, 0x3fc29552} }, +/**/ {{0x1c407dbf, 0x3c630177} },}, +/**/ {{{0x18e47fd3, 0x3fc303d7} }, +/**/ {{0xd96091fa, 0xbc06b9c7} },}, +/**/ {{{0x201e8f74, 0x3fc371fc} }, +/**/ {{0x62af18a0, 0x3c5de6cb} },}, +/**/ {{{0xb0ecc62a, 0x3fc3dfc2} }, +/**/ {{0xe7d81017, 0xbc5ab3a8} },}, +/**/ {{{0x6ccb7d1e, 0x3fc44d2b} }, +/**/ {{0x543e1f88, 0x3c69f4f6} },}, +/**/ {{{0xf39a55e5, 0x3fc4ba36} }, +/**/ {{0xbcc36756, 0x3c668981} },}, +/**/ {{{0xe3a1b438, 0x3fc526e5} }, +/**/ {{0x8a470d3a, 0xbc6746ff} },}, +/**/ {{{0xd9982086, 0x3fc59338} }, +/**/ {{0xaa8ad7cf, 0xbc565d22} },}, +/**/ {{{0x70a793d4, 0x3fc5ff30} }, +/**/ {{0xfafc6f6e, 0xbc5bc60e} },}, +/**/ {{{0x4272ad51, 0x3fc66acd} }, +/**/ {{0x4e1ea8b2, 0xbc50900e} },}, +/**/ {{{0xe719d21d, 0x3fc6d60f} }, +/**/ {{0x68ecd179, 0xbc6caae2} },}, +/**/ {{{0xf54037a5, 0x3fc740f8} }, +/**/ {{0x62a84cdb, 0xbc5b2640} },}, +/**/ {{{0x0210d909, 0x3fc7ab89} }, +/**/ {{0x2d6a0608, 0x3c4be36b} },}, +/**/ {{{0xa14357eb, 0x3fc815c0} }, +/**/ {{0x073a0564, 0xbc54be48} },}, +/**/ {{{0x6520c911, 0x3fc87fa0} }, +/**/ {{0xbfa08d9a, 0xbc6bf7fd} },}, +/**/ {{{0xde886d41, 0x3fc8e928} }, +/**/ {{0x51a56770, 0xbc6569d8} },}, +/**/ {{{0x9cf456b4, 0x3fc9525a} }, +/**/ {{0x1d4e2e26, 0x3c6d904c} },}, +/**/ {{{0x2e7dfb83, 0x3fc9bb36} }, +/**/ {{0x1f003e0c, 0x3c6575e3} },}, +/**/ {{{0x1fe2b563, 0x3fca23bc} }, +/**/ {{0xb07a998c, 0x3c493711} },}, +/**/ {{{0xfc882f19, 0x3fca8bec} }, +/**/ {{0x918c39eb, 0xbc5e8c37} },}, +/**/ {{{0x4e80bff3, 0x3fcaf3c9} }, +/**/ {{0xf3641985, 0xbc5398cf} },}, +/**/ {{{0x9e8fb5a4, 0x3fcb5b51} }, +/**/ {{0xdc19e1a0, 0x3c6ba27f} },}, +/**/ {{{0x742d8cd6, 0x3fcbc286} }, +/**/ {{0x44870f55, 0x3c54fce7} },}, +/**/ {{{0x558c18c1, 0x3fcc2968} }, +/**/ {{0x38a3fb6b, 0xbc673dee} },}, +/**/ {{{0xc79a9a22, 0x3fcc8ff7} }, +/**/ {{0xf8434012, 0xbc64f689} },}, +/**/ {{{0x4e09c5dc, 0x3fccf635} }, +/**/ {{0x7d55b695, 0x3c6239a0} },}, +/**/ {{{0x6b4fbb91, 0x3fcd5c21} }, +/**/ {{0x597e4d40, 0x3c66e443} },}, +/**/ {{{0xa0abec7d, 0x3fcdc1bc} }, +/**/ {{0x1998b6fc, 0x3c6834c5} },}, +/**/ {{{0x6e2af2e6, 0x3fce2707} }, +/**/ {{0x001e0162, 0xbc461578} },}, +/**/ {{{0x52aa5a60, 0x3fce8c02} }, +/**/ {{0x39bfc89b, 0xbc46e03a} },}, +/**/ {{{0xcbdc5936, 0x3fcef0ad} }, +/**/ {{0x950dc20d, 0x3c648637} },}, +/**/ {{{0x564b7b37, 0x3fcf550a} }, +/**/ {{0xfd018c37, 0x3c2c5f6d} },}, +/**/ {{{0x6d5e3e2b, 0x3fcfb918} }, +/**/ {{0x64f21acb, 0xbc6caaae} },}, +/**/ {{{0x45ad501d, 0x3fd00e6c} }, +/**/ {{0x8ff6fead, 0xbc6cb956} },}, +/**/ {{{0x94b4d041, 0x3fd04025} }, +/**/ {{0x17a5022d, 0xbc628ec2} },}, +/**/ {{{0x5fcd590d, 0x3fd071b8} }, +/**/ {{0xf97bde80, 0x3c5d1707} },}, +/**/ {{{0xe27390e3, 0x3fd0a324} }, +/**/ {{0xe8061c03, 0x3c77dcfd} },}, +/**/ {{{0x579ab74b, 0x3fd0d46b} }, +/**/ {{0x1c3cbd92, 0x3c603ec8} },}, +/**/ {{{0xf9ae4ad5, 0x3fd1058b} }, +/**/ {{0xab4cb31d, 0x3c589fa0} },}, +/**/ {{{0x0293a8b0, 0x3fd13687} }, +/**/ {{0x98edd24a, 0x3c77b662} },}, +/**/ {{{0xababa60e, 0x3fd1675c} }, +/**/ {{0xab883717, 0x3c2ce63e} },}, +/**/ {{{0x2dd4236f, 0x3fd1980d} }, +/**/ {{0xb0e4d147, 0x3c79d3d1} },}, +/**/ {{{0xc16999fb, 0x3fd1c898} }, +/**/ {{0x2aff1c44, 0xbc30e5c6} },}, +/**/ {{{0x9e48a2f3, 0x3fd1f8ff} }, +/**/ {{0x9a0c4b07, 0xbc7c9fdf} },}, +/**/ {{{0xfbcf7966, 0x3fd22941} }, +/**/ {{0xb09628af, 0xbc776f5e} },}, +/**/ {{{0x10df763a, 0x3fd25960} }, +/**/ {{0x57075e9e, 0xbc50f76c} },}, +/**/ {{{0x13de86a3, 0x3fd2895a} }, +/**/ {{0xc13f040e, 0x3c77ad24} },}, +/**/ {{{0x3ab89d25, 0x3fd2b930} }, +/**/ {{0xfd852ad4, 0xbc7896b5} },}, +/**/ {{{0xbae11d31, 0x3fd2e8e2} }, +/**/ {{0xb95ebdf9, 0xbc78f4cd} },}, +/**/ {{{0xc9544185, 0x3fd31871} }, +/**/ {{0x4c09b379, 0xbc351acc} },}, +/**/ {{{0x9a987d55, 0x3fd347dd} }, +/**/ {{0x580919f8, 0xbc64dd4c} },}, +/**/ {{{0x62bfd85b, 0x3fd37726} }, +/**/ {{0xd8117de7, 0xbc4b5629} },}, +/**/ {{{0x556945ea, 0x3fd3a64c} }, +/**/ {{0x1945f97c, 0xbc6c6865} },}, +/**/ {{{0xa5c1f710, 0x3fd3d54f} }, +/**/ {{0xc6a1c98d, 0xbc7e3265} },}, +/**/ {{{0x8686a7e4, 0x3fd40430} }, +/**/ {{0x6082ce6d, 0xbc70bcfb} },}, +/**/ {{{0x2a04e814, 0x3fd432ef} }, +/**/ {{0x715ac903, 0xbc729931} },}, +/**/ {{{0xc21c5ec2, 0x3fd4618b} }, +/**/ {{0xcdeccf1d, 0x3c7f42de} },}, +/**/ {{{0x804009d1, 0x3fd49006} }, +/**/ {{0x41f177dc, 0xbc69ffc3} },}, +/**/ {{{0x957778a1, 0x3fd4be5f} }, +/**/ {{0x5b04813d, 0xbc6259b3} },}, +/**/ {{{0x3260026a, 0x3fd4ec97} }, +/**/ {{0xd977dc5e, 0xbc742a87} },}, +/**/ {{{0x872df82d, 0x3fd51aad} }, +/**/ {{0xc19f55e3, 0x3c43927a} },}, +/**/ {{{0xc3add263, 0x3fd548a2} }, +/**/ {{0x7e308ddb, 0xbc6819cf} },}, +/**/ {{{0x17455a6c, 0x3fd57677} }, +/**/ {{0xb283660c, 0x3c7526ad} },}, +/**/ {{{0xb0f4cfe2, 0x3fd5a42a} }, +/**/ {{0x7dee9a3d, 0xbc78ebcb} },}, +/**/ {{{0xbf5809ca, 0x3fd5d1bd} }, +/**/ {{0x83dc7fe1, 0x3c742363} },}, +/**/ {{{0x70a793d4, 0x3fd5ff30} }, +/**/ {{0xfafc6f6e, 0xbc6bc60e} },}, +/**/ {{{0xf2b9c795, 0x3fd62c82} }, +/**/ {{0x915300e5, 0x3c67b7af} },}, + }; + + static const number + Lv[362][2] = { /* log(vj) */ + +/**/ {{{0xb72daabf, 0xbf6687ec} }, +/**/ {{0x0f13318f, 0x3c052c69} },}, +/**/ {{{0x3767104f, 0xbf6667d6} }, +/**/ {{0xd27a7bac, 0x3bd3efa3} },}, +/**/ {{{0xd7cd64fb, 0xbf6647bf} }, +/**/ {{0x55a89c36, 0x3c09b725} },}, +/**/ {{{0x9860683b, 0xbf6627a9} }, +/**/ {{0xfebc844a, 0x3bcbae22} },}, +/**/ {{{0x791fd98a, 0xbf660793} }, +/**/ {{0x78fa1cb5, 0xbbfe34af} },}, +/**/ {{{0x7a0b7863, 0xbf65e77d} }, +/**/ {{0xea78fdd0, 0xbc02f1b1} },}, +/**/ {{{0x9b230442, 0xbf65c767} }, +/**/ {{0x2202b2ca, 0x3bf70d8c} },}, +/**/ {{{0xdc663ca2, 0xbf65a751} }, +/**/ {{0xc3444e64, 0xbbfdc63d} },}, +/**/ {{{0x3dd4e102, 0xbf65873c} }, +/**/ {{0x370d69c3, 0x3c021b11} },}, +/**/ {{{0xbf6eb0de, 0xbf656726} }, +/**/ {{0x154dd8d8, 0xbbfb6da8} },}, +/**/ {{{0x61336bb6, 0xbf654711} }, +/**/ {{0xdf9a4709, 0xbc0b12d2} },}, +/**/ {{{0x2322d10a, 0xbf6526fc} }, +/**/ {{0x68d1274f, 0x3bf997f2} },}, +/**/ {{{0x053ca059, 0xbf6506e7} }, +/**/ {{0xe70c852a, 0x3c0c2a1f} },}, +/**/ {{{0x07809924, 0xbf64e6d2} }, +/**/ {{0xa808538f, 0x3c04cc9e} },}, +/**/ {{{0x29ee7aed, 0xbf64c6bd} }, +/**/ {{0x7797a4bd, 0x3befe68c} },}, +/**/ {{{0x6c860537, 0xbf64a6a8} }, +/**/ {{0x9efaae3d, 0x3c06794d} },}, +/**/ {{{0xcf46f784, 0xbf648693} }, +/**/ {{0xb2ddd9d1, 0xbbfed318} },}, +/**/ {{{0x5231115a, 0xbf64667f} }, +/**/ {{0x4643624b, 0x3c061f62} },}, +/**/ {{{0xf544123c, 0xbf64466a} }, +/**/ {{0x9387f11e, 0x3c0666a0} },}, +/**/ {{{0xb87fb9b0, 0xbf642656} }, +/**/ {{0x116ec598, 0x3c0043b2} },}, +/**/ {{{0x9be3c73c, 0xbf640642} }, +/**/ {{0xd2de6e3e, 0xbbfbd84d} },}, +/**/ {{{0x9f6ffa68, 0xbf63e62e} }, +/**/ {{0x433d8c65, 0xbbe9149b} },}, +/**/ {{{0xc32412bb, 0xbf63c61a} }, +/**/ {{0x08e5a7bb, 0xbbf6b88d} },}, +/**/ {{{0x06ffcfbe, 0xbf63a607} }, +/**/ {{0xccfac9e2, 0xbb9f3c7a} },}, +/**/ {{{0x6b02f0fa, 0xbf6385f3} }, +/**/ {{0xbec6f6e4, 0x3bee405c} },}, +/**/ {{{0xef2d35f9, 0xbf6365df} }, +/**/ {{0xaf0c0b4c, 0x3bf02993} },}, +/**/ {{{0x937e5e46, 0xbf6345cc} }, +/**/ {{0xaa64716f, 0x3bf9be97} },}, +/**/ {{{0x57f6296c, 0xbf6325b9} }, +/**/ {{0xa2e863ae, 0xbbfdeb4d} },}, +/**/ {{{0x3c9456f9, 0xbf6305a6} }, +/**/ {{0x636d2b2c, 0x3c0f3c7f} },}, +/**/ {{{0x4158a678, 0xbf62e593} }, +/**/ {{0xb166ca7f, 0x3c01a8df} },}, +/**/ {{{0x6642d778, 0xbf62c580} }, +/**/ {{0x53a2d534, 0x3c020ff1} },}, +/**/ {{{0xab52a987, 0xbf62a56d} }, +/**/ {{0x0412f1e7, 0xbbe8fef1} },}, +/**/ {{{0x1087dc35, 0xbf62855b} }, +/**/ {{0x4b7ac6c6, 0xbbfcd17e} },}, +/**/ {{{0x95e22f12, 0xbf626548} }, +/**/ {{0x9a8127bf, 0xbbfbfc21} },}, +/**/ {{{0x3b6161af, 0xbf624536} }, +/**/ {{0x66d42390, 0x3bd7eda1} },}, +/**/ {{{0x0105339d, 0xbf622524} }, +/**/ {{0x77fedcad, 0xbbdf374e} },}, +/**/ {{{0xe6cd646f, 0xbf620511} }, +/**/ {{0x52d05dea, 0x3be1d1fb} },}, +/**/ {{{0xecb9b3b8, 0xbf61e4ff} }, +/**/ {{0xffd8e706, 0x3c02c2fc} },}, +/**/ {{{0x12c9e10b, 0xbf61c4ee} }, +/**/ {{0xf1d5cc2c, 0xbc02b4f8} },}, +/**/ {{{0x58fdabfe, 0xbf61a4dc} }, +/**/ {{0x1315b191, 0xbc0618c3} },}, +/**/ {{{0xbf54d426, 0xbf6184ca} }, +/**/ {{0xcb3cdab0, 0xbc01f8d5} },}, +/**/ {{{0x45cf1919, 0xbf6164b9} }, +/**/ {{0xc025605a, 0xbc014ff7} },}, +/**/ {{{0xec6c3a6e, 0xbf6144a7} }, +/**/ {{0x87cb08cd, 0xbbff04ff} },}, +/**/ {{{0xb32bf7bd, 0xbf612496} }, +/**/ {{0xe6af1b84, 0x3bee89b4} },}, +/**/ {{{0x9a0e109e, 0xbf610485} }, +/**/ {{0x35a60879, 0x3c07e99e} },}, +/**/ {{{0xa11244aa, 0xbf60e474} }, +/**/ {{0x20f2325a, 0x3c04b698} },}, +/**/ {{{0xc838537b, 0xbf60c463} }, +/**/ {{0x3617200d, 0x3bc0657e} },}, +/**/ {{{0x0f7ffcac, 0xbf60a453} }, +/**/ {{0xa5080961, 0xbc008feb} },}, +/**/ {{{0x76e8ffd9, 0xbf608442} }, +/**/ {{0xbb5e1df7, 0x3bd13002} },}, +/**/ {{{0xfe731c9d, 0xbf606431} }, +/**/ {{0x6e2858c0, 0xbc0509f3} },}, +/**/ {{{0xa61e1296, 0xbf604421} }, +/**/ {{0x5f5d9695, 0xbc04b556} },}, +/**/ {{{0x6de9a162, 0xbf602411} }, +/**/ {{0xe79a4e00, 0x3c042b89} },}, +/**/ {{{0x55d5889e, 0xbf600401} }, +/**/ {{0x1113f403, 0x3be8f98e} },}, +/**/ {{{0xbbc30fd4, 0xbf5fc7e2} }, +/**/ {{0x93382bc9, 0xbbfc709b} },}, +/**/ {{{0x0c1abdcd, 0xbf5f87c3} }, +/**/ {{0x76a55d1c, 0xbbf2a90d} },}, +/**/ {{{0x9cb19a68, 0xbf5f47a3} }, +/**/ {{0x76e7826b, 0x3be1b815} },}, +/**/ {{{0x6d8724e7, 0xbf5f0784} }, +/**/ {{0x2b63756d, 0xbbe72d46} },}, +/**/ {{{0x7e9adc90, 0xbf5ec765} }, +/**/ {{0x73bb17c5, 0x3beb1a66} },}, +/**/ {{{0xcfec40a8, 0xbf5e8746} }, +/**/ {{0xb5e5a553, 0x3bf11af5} },}, +/**/ {{{0x617ad077, 0xbf5e4728} }, +/**/ {{0xf57dd14f, 0x3bfb2cad} },}, +/**/ {{{0x33460b45, 0xbf5e070a} }, +/**/ {{0x4902c8d5, 0xbbf8db75} },}, +/**/ {{{0x454d705f, 0xbf5dc6ec} }, +/**/ {{0xe8a41057, 0x3bef5cc6} },}, +/**/ {{{0x97907f0f, 0xbf5d86ce} }, +/**/ {{0xdf8672ef, 0x3bed8277} },}, +/**/ {{{0x2a0eb6a3, 0xbf5d46b1} }, +/**/ {{0x3717e5ee, 0xbbc2f9c2} },}, +/**/ {{{0xfcc7966b, 0xbf5d0693} }, +/**/ {{0xab4852c6, 0x3bf4deed} },}, +/**/ {{{0x0fba9db6, 0xbf5cc677} }, +/**/ {{0x9db2a368, 0xbbf3a2b4} },}, +/**/ {{{0x62e74bd8, 0xbf5c865a} }, +/**/ {{0x58fa0c24, 0xbbd2c51d} },}, +/**/ {{{0xf64d2024, 0xbf5c463d} }, +/**/ {{0xe3a09391, 0x3bf838ca} },}, +/**/ {{{0xc9eb99ee, 0xbf5c0621} }, +/**/ {{0x61b7de71, 0xbbdc2a9e} },}, +/**/ {{{0xddc2388e, 0xbf5bc605} }, +/**/ {{0x4accb195, 0xbbea9808} },}, +/**/ {{{0x31d07b5c, 0xbf5b85ea} }, +/**/ {{0x032e030b, 0xbbd811a2} },}, +/**/ {{{0xc615e1b1, 0xbf5b45ce} }, +/**/ {{0x821e0b81, 0xbbfd5427} },}, +/**/ {{{0x9a91eaea, 0xbf5b05b3} }, +/**/ {{0x2619306b, 0x3bfffeba} },}, +/**/ {{{0xaf441661, 0xbf5ac598} }, +/**/ {{0x9eac7d15, 0x3bd22824} },}, +/**/ {{{0x042be376, 0xbf5a857e} }, +/**/ {{0x24893f0e, 0x3bc20736} },}, +/**/ {{{0x9948d188, 0xbf5a4563} }, +/**/ {{0x04d734cd, 0xbbf58ab4} },}, +/**/ {{{0x6e9a5ff9, 0xbf5a0549} }, +/**/ {{0x5723a6c3, 0xbbf22673} },}, +/**/ {{{0x84200e2c, 0xbf59c52f} }, +/**/ {{0xa538e8e1, 0x3bfc81da} },}, +/**/ {{{0xd9d95b83, 0xbf598515} }, +/**/ {{0x2a8e3feb, 0xbbfa1a37} },}, +/**/ {{{0x6fc5c767, 0xbf5944fc} }, +/**/ {{0x385159f9, 0x3bf8e1ce} },}, +/**/ {{{0x45e4d13c, 0xbf5904e3} }, +/**/ {{0x1567c7a7, 0xbbfc4737} },}, +/**/ {{{0x5c35f86e, 0xbf58c4ca} }, +/**/ {{0x23c9ae0c, 0x3bf41581} },}, +/**/ {{{0xb2b8bc65, 0xbf5884b1} }, +/**/ {{0x2b66cfb6, 0x3bf70c2c} },}, +/**/ {{{0x496c9c8d, 0xbf584499} }, +/**/ {{0xe5a11e3e, 0xbbdb9042} },}, +/**/ {{{0x20511854, 0xbf580481} }, +/**/ {{0x61bcb040, 0xbbf9cf9d} },}, +/**/ {{{0x3765af29, 0xbf57c469} }, +/**/ {{0xe26a419b, 0xbbf65ceb} },}, +/**/ {{{0x8ea9e07c, 0xbf578451} }, +/**/ {{0xb70a4088, 0xbbf1c2f5} },}, +/**/ {{{0x261d2bbf, 0xbf57443a} }, +/**/ {{0x29704ba7, 0xbbbc7b8f} },}, +/**/ {{{0xfdbf1065, 0xbf570422} }, +/**/ {{0x433ccb3b, 0x3bca0a54} },}, +/**/ {{{0x158f0de3, 0xbf56c40c} }, +/**/ {{0x207cde2d, 0x3bd9e257} },}, +/**/ {{{0x6d8ca3af, 0xbf5683f5} }, +/**/ {{0xf7b51b49, 0xbbef17a4} },}, +/**/ {{{0x05b75142, 0xbf5643df} }, +/**/ {{0x9d345bf8, 0x3be28239} },}, +/**/ {{{0xde0e9614, 0xbf5603c8} }, +/**/ {{0x0918d1bf, 0xbbde6c21} },}, +/**/ {{{0xf691f1a1, 0xbf55c3b2} }, +/**/ {{0x377de4c8, 0x3bd37d78} },}, +/**/ {{{0x4f40e365, 0xbf55839d} }, +/**/ {{0xbbf7c9d1, 0x3bf52b7d} },}, +/**/ {{{0xe81aeadd, 0xbf554387} }, +/**/ {{0x679c3d9a, 0xbbf0be6a} },}, +/**/ {{{0xc11f878a, 0xbf550372} }, +/**/ {{0xb6cdd88e, 0xbbdd9e20} },}, +/**/ {{{0xda4e38ec, 0xbf54c35d} }, +/**/ {{0x09302da0, 0xbbe3b1e7} },}, +/**/ {{{0x33a67e86, 0xbf548349} }, +/**/ {{0x085b922d, 0x3be8cba8} },}, +/**/ {{{0xcd27d7db, 0xbf544334} }, +/**/ {{0xf024ab43, 0xbba5f2c9} },}, +/**/ {{{0xa6d1c471, 0xbf540320} }, +/**/ {{0xf686cf3d, 0xbbeb31f3} },}, +/**/ {{{0xc0a3c3cf, 0xbf53c30c} }, +/**/ {{0xd4ad32f6, 0xbbf74ffe} },}, +/**/ {{{0x1a9d557e, 0xbf5382f9} }, +/**/ {{0x4acb368f, 0x3bd2e555} },}, +/**/ {{{0xb4bdf907, 0xbf5342e5} }, +/**/ {{0x07812806, 0x3be13442} },}, +/**/ {{{0x8f052df6, 0xbf5302d2} }, +/**/ {{0x70b1e756, 0x3bf5f429} },}, +/**/ {{{0xa97273d7, 0xbf52c2bf} }, +/**/ {{0x43a03fff, 0xbbf20aa3} },}, +/**/ {{{0x04054a3a, 0xbf5282ad} }, +/**/ {{0x8bebd7ad, 0xbbed4d57} },}, +/**/ {{{0x9ebd30ae, 0xbf52429a} }, +/**/ {{0x5a71c5a4, 0xbbff9529} },}, +/**/ {{{0x7999a6c6, 0xbf520288} }, +/**/ {{0x54100f9e, 0x3bfb055a} },}, +/**/ {{{0x949a2c12, 0xbf51c276} }, +/**/ {{0xa2e9f1b4, 0xbbff6978} },}, +/**/ {{{0xefbe402a, 0xbf518264} }, +/**/ {{0xbc188323, 0x3bf01fb9} },}, +/**/ {{{0x8b0562a1, 0xbf514253} }, +/**/ {{0x957bf23a, 0xbbf7c87c} },}, +/**/ {{{0x666f1311, 0xbf510242} }, +/**/ {{0xc8be6880, 0x3bdc2cb9} },}, +/**/ {{{0x81fad111, 0xbf50c231} }, +/**/ {{0x07ba000d, 0xbbf59fc1} },}, +/**/ {{{0xdda81c3d, 0xbf508220} }, +/**/ {{0xbf5c8a0b, 0xbbf06a0a} },}, +/**/ {{{0x79767431, 0xbf504210} }, +/**/ {{0xa9a705bc, 0x3bf3a6cf} },}, +/**/ {{{0x55655889, 0xbf500200} }, +/**/ {{0xbf0fa436, 0xbbe9abe6} },}, +/**/ {{{0xe2e891cc, 0xbf4f83e0} }, +/**/ {{0x1b81bf62, 0x3be4aa59} },}, +/**/ {{{0x9b4589ce, 0xbf4f03c1} }, +/**/ {{0x8a47f50a, 0xbbe60518} },}, +/**/ {{{0xd3e0985f, 0xbf4e83a2} }, +/**/ {{0x5ef17e96, 0x3bed32d8} },}, +/**/ {{{0x8cb8bcc3, 0xbf4e0384} }, +/**/ {{0xf09afa4d, 0xbbeb7b30} },}, +/**/ {{{0xc5ccf647, 0xbf4d8366} }, +/**/ {{0xf586cec2, 0xbbd527fc} },}, +/**/ {{{0x7f1c4437, 0xbf4d0349} }, +/**/ {{0x4a686886, 0x3bc2bcf0} },}, +/**/ {{{0xb8a5a5e3, 0xbf4c832c} }, +/**/ {{0x721c2ebe, 0x3bc98f93} },}, +/**/ {{{0x72681a9e, 0xbf4c0310} }, +/**/ {{0xb5308d22, 0xbbe20f00} },}, +/**/ {{{0xac62a1bf, 0xbf4b82f4} }, +/**/ {{0x9737b561, 0xbbe1edd0} },}, +/**/ {{{0x66943a9f, 0xbf4b02d9} }, +/**/ {{0x23f894a1, 0xbbcc950b} },}, +/**/ {{{0xa0fbe49a, 0xbf4a82be} }, +/**/ {{0x866bc982, 0xbb81da04} },}, +/**/ {{{0x5b989f0f, 0xbf4a02a4} }, +/**/ {{0x9d76196e, 0xbbd9114d} },}, +/**/ {{{0x96696961, 0xbf49828a} }, +/**/ {{0xd3292fd6, 0x3bc10d20} },}, +/**/ {{{0x516d42f4, 0xbf490271} }, +/**/ {{0x2e9a5dd5, 0xbbee53a3} },}, +/**/ {{{0x8ca32b32, 0xbf488258} }, +/**/ {{0xd18f8004, 0xbbc55af5} },}, +/**/ {{{0x480a2185, 0xbf480240} }, +/**/ {{0xa9b0178a, 0xbbb32d23} },}, +/**/ {{{0x83a1255c, 0xbf478228} }, +/**/ {{0x8152093a, 0x3be84cc3} },}, +/**/ {{{0x3f673627, 0xbf470211} }, +/**/ {{0xf4881c71, 0xbbd0055a} },}, +/**/ {{{0x7b5b535c, 0xbf4681fa} }, +/**/ {{0xb98336ea, 0x3bd2b73f} },}, +/**/ {{{0x377c7c71, 0xbf4601e4} }, +/**/ {{0x2ed05089, 0xbbcdcbed} },}, +/**/ {{{0x73c9b0e1, 0xbf4581ce} }, +/**/ {{0x61414697, 0xbbdda0c2} },}, +/**/ {{{0x3041f02a, 0xbf4501b9} }, +/**/ {{0x22f8b33c, 0x3bee5d53} },}, +/**/ {{{0x6ce439ca, 0xbf4481a4} }, +/**/ {{0x9c25c999, 0xbbe5512f} },}, +/**/ {{{0x29af8d47, 0xbf440190} }, +/**/ {{0xa4df0dfd, 0x3b7f48c2} },}, +/**/ {{{0x66a2ea26, 0xbf43817c} }, +/**/ {{0x517febd8, 0x3bd157c0} },}, +/**/ {{{0x23bd4ff0, 0xbf430169} }, +/**/ {{0x0176d244, 0xbbe2e229} },}, +/**/ {{{0x60fdbe33, 0xbf428156} }, +/**/ {{0x175812b3, 0x3be64664} },}, +/**/ {{{0x1e63347c, 0xbf420144} }, +/**/ {{0xd9355524, 0xbbe39ab4} },}, +/**/ {{{0x5becb260, 0xbf418132} }, +/**/ {{0xb6e1edc9, 0x3be74b27} },}, +/**/ {{{0x19993772, 0xbf410121} }, +/**/ {{0x393ab56a, 0xbbaa390b} },}, +/**/ {{{0x5767c34c, 0xbf408110} }, +/**/ {{0xf8c7783b, 0x3bd128e6} },}, +/**/ {{{0x15575589, 0xbf400100} }, +/**/ {{0xf23ef222, 0x3bec8863} },}, +/**/ {{{0xa6cddb8d, 0xbf3f01e0} }, +/**/ {{0xcdd29c3f, 0x3b8a9419} },}, +/**/ {{{0x232b174e, 0xbf3e01c2} }, +/**/ {{0xd5f5b191, 0xbbc7cf55} },}, +/**/ {{{0x9fc45d9e, 0xbf3d01a4} }, +/**/ {{0xb5038e7e, 0x3bddc58f} },}, +/**/ {{{0x1c97adca, 0xbf3c0188} }, +/**/ {{0xbb933e41, 0x3bc0238d} },}, +/**/ {{{0x99a30728, 0xbf3b016c} }, +/**/ {{0xc3c43664, 0xbbabde04} },}, +/**/ {{{0x16e46913, 0xbf3a0152} }, +/**/ {{0x5adc3673, 0x3bafe081} },}, +/**/ {{{0x9459d2eb, 0xbf390138} }, +/**/ {{0xc2a33d26, 0xbbd949da} },}, +/**/ {{{0x12014418, 0xbf380120} }, +/**/ {{0xf76e0326, 0xbbd3acbc} },}, +/**/ {{{0x8fd8bc07, 0xbf370108} }, +/**/ {{0x4cd6ce34, 0x3bdbde09} },}, +/**/ {{{0x0dde3a29, 0xbf3600f2} }, +/**/ {{0x05442a35, 0xbbb0bc28} },}, +/**/ {{{0x8c0fbdf9, 0xbf3500dc} }, +/**/ {{0x0908cbf7, 0x3bd21c68} },}, +/**/ {{{0x0a6b46f4, 0xbf3400c8} }, +/**/ {{0x0f107564, 0xbbdbd35e} },}, +/**/ {{{0x88eed4a1, 0xbf3300b4} }, +/**/ {{0x49a3dcb8, 0xbbc22067} },}, +/**/ {{{0x0798668a, 0xbf3200a2} }, +/**/ {{0xe7c5d0e5, 0x3bcdb7f0} },}, +/**/ {{{0x8665fc3f, 0xbf310090} }, +/**/ {{0xc7f9d69c, 0xbbd00add} },}, +/**/ {{{0x05559559, 0xbf300080} }, +/**/ {{0xa0e20e2f, 0x3bddd332} },}, +/**/ {{{0x08ca62e5, 0xbf2e00e1} }, +/**/ {{0x3a04bb77, 0xbbb15ff9} },}, +/**/ {{{0x0725a061, 0xbf2c00c4} }, +/**/ {{0xcc052f3e, 0x3bc88ab0} },}, +/**/ {{{0x05b8e275, 0xbf2a00a9} }, +/**/ {{0xf5f3cbcf, 0xbbcbba1a} },}, +/**/ {{{0x04802882, 0xbf280090} }, +/**/ {{0xa5bd7bd0, 0x3bcec900} },}, +/**/ {{{0x037771ef, 0xbf260079} }, +/**/ {{0x9b7b54fa, 0x3bb77ea0} },}, +/**/ {{{0x029abe33, 0xbf240064} }, +/**/ {{0x3ae68d18, 0xbbc1bbf0} },}, +/**/ {{{0x01e60cd1, 0xbf220051} }, +/**/ {{0x2b45cfcd, 0x3bb1dcd9} },}, +/**/ {{{0x01555d56, 0xbf200040} }, +/**/ {{0x863f53f6, 0x3bcddd88} },}, +/**/ {{{0x01c95eb7, 0xbf1c0062} }, +/**/ {{0xaa4dfd9a, 0x3bbd88f7} },}, +/**/ {{{0x01200510, 0xbf180048} }, +/**/ {{0x4f3db50b, 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{{{0x0ddc70a1, 0x3f35ff0e} }, +/**/ {{0xd97a3c05, 0x3bacf6f3} },}, +/**/ {{{0x8fd69976, 0x3f36fef7} }, +/**/ {{0x6f810a3c, 0x3bab2dcf} },}, +/**/ {{{0x11febc18, 0x3f37fee0} }, +/**/ {{0xf5d3f323, 0x3bd2b9bc} },}, +/**/ {{{0x9456d7fb, 0x3f38fec7} }, +/**/ {{0x6eaa1d6a, 0xbbbfb258} },}, +/**/ {{{0x16e0ec8b, 0x3f39feae} }, +/**/ {{0xceeb34b1, 0xbbb6137a} },}, +/**/ {{{0x999ef930, 0x3f3afe93} }, +/**/ {{0xdc639b08, 0xbbde70e0} },}, +/**/ {{{0x1c92fd4a, 0x3f3bfe78} }, +/**/ {{0x713cc126, 0xbbc4ed10} },}, +/**/ {{{0x9fbef835, 0x3f3cfe5b} }, +/**/ {{0xcc0e81bd, 0xbb873d63} },}, +/**/ {{{0x2324e946, 0x3f3dfe3e} }, +/**/ {{0x62dd5deb, 0x3bc09164} },}, +/**/ {{{0xa6c6cfcc, 0x3f3efe1f} }, +/**/ {{0x3512d15c, 0x3bdac2da} },}, +/**/ {{{0x2aa6ab11, 0x3f3ffe00} }, +/**/ {{0x62cc632d, 0x3b999e2b} },}, +/**/ {{{0xd7633d2c, 0x3f407eef} }, +/**/ {{0x63ff6024, 0xbbebc98b} },}, +/**/ {{{0x19941e6e, 0x3f40fedf} }, +/**/ {{0xe0aa6338, 0xbbb194c2} },}, +/**/ {{{0xdbe6f8eb, 0x3f417ecd} }, +/**/ {{0x57b0f571, 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{{{0x62ac7a09, 0x3f4f7c20} }, +/**/ {{0x17802a46, 0x3b5c8123} },}, +/**/ {{{0xaa8ab110, 0x3f4ffc00} }, +/**/ {{0xeb9b6cdb, 0xbbe0fecb} },}, +/**/ {{{0x3954680f, 0x3f503df0} }, +/**/ {{0x1c693678, 0x3bdac89b} },}, +/**/ {{{0xdd83eb3a, 0x3f507ddf} }, +/**/ {{0x0a75ad5f, 0xbbf638f6} },}, +/**/ {{{0x41d461a5, 0x3f50bdcf} }, +/**/ {{0x45f05b10, 0x3bfd4bc9} },}, +/**/ {{{0x66464aef, 0x3f50fdbe} }, +/**/ {{0x6abbf59c, 0xbbbd0554} },}, +/**/ {{{0x4ada26b1, 0x3f513dad} }, +/**/ {{0x6036fe6f, 0x3be38c65} },}, +/**/ {{{0xef907485, 0x3f517d9b} }, +/**/ {{0xf158bbc3, 0x3bfdc8a1} },}, +/**/ {{{0x5469b404, 0x3f51bd8a} }, +/**/ {{0x55632e3f, 0xbbdea231} },}, +/**/ {{{0x796664c3, 0x3f51fd78} }, +/**/ {{0x2edb73c2, 0xbbe00849} },}, +/**/ {{{0x5e870657, 0x3f523d66} }, +/**/ {{0x0789343e, 0x3bfba943} },}, +/**/ {{{0x03cc1855, 0x3f527d54} }, +/**/ {{0xeafafc52, 0x3bc5f644} },}, +/**/ {{{0x69361a4e, 0x3f52bd41} }, +/**/ {{0xa4a6e79f, 0xbbf2f743} },}, +/**/ {{{0x8ec58bd2, 0x3f52fd2e} }, +/**/ {{0x5ceb1abf, 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{{{0x6dbb3de1, 0x3f59fab9} }, +/**/ {{0x7a8be031, 0xbbf11464} },}, +/**/ {{{0x5860fa8a, 0x3f5a3a9f} }, +/**/ {{0x470dbe32, 0x3beae9e7} },}, +/**/ {{{0x033b16f8, 0x3f5a7a85} }, +/**/ {{0xda1f8579, 0x3bfc4721} },}, +/**/ {{{0x6e4a128e, 0x3f5aba6a} }, +/**/ {{0x029258ce, 0xbbf41852} },}, +/**/ {{{0x998e6cab, 0x3f5afa4f} }, +/**/ {{0x2eb18782, 0xbbf28584} },}, +/**/ {{{0x8508a4af, 0x3f5b3a34} }, +/**/ {{0x23241a2c, 0xbbea7970} },}, +/**/ {{{0x30b939f8, 0x3f5b7a19} }, +/**/ {{0x600551b6, 0xbbf1d8db} },}, +/**/ {{{0x9ca0abe2, 0x3f5bb9fd} }, +/**/ {{0x8c26cc71, 0xbbeaa412} },}, +/**/ {{{0xc8bf79c8, 0x3f5bf9e1} }, +/**/ {{0x30427cfc, 0xbbe7f81b} },}, +/**/ {{{0xb5162303, 0x3f5c39c5} }, +/**/ {{0xd1f134e1, 0x3bd9ec5f} },}, +/**/ {{{0x61a526eb, 0x3f5c79a9} }, +/**/ {{0x8980e47d, 0x3bff0cb0} },}, +/**/ {{{0xce6d04d7, 0x3f5cb98c} }, +/**/ {{0xe84ca4e2, 0x3bf35aca} },}, +/**/ {{{0xfb6e3c1b, 0x3f5cf96f} }, +/**/ {{0x1b0bd69f, 0x3bf9b1b8} },}, +/**/ {{{0xe8a94c0b, 0x3f5d3952} }, +/**/ {{0x3ce51832, 0x3be21310} },}, +/**/ {{{0x961eb3f8, 0x3f5d7935} }, +/**/ {{0x840c58ce, 0x3bf90786} },}, +/**/ {{{0x03cef334, 0x3f5db918} }, +/**/ {{0xf2dfb3f4, 0xbbfe0048} },}, +/**/ {{{0x31ba890b, 0x3f5df8fa} }, +/**/ {{0x3e295bec, 0x3bfcf652} },}, +/**/ {{{0x1fe1f4ce, 0x3f5e38dc} }, +/**/ {{0x151c9300, 0xbbfc5ebe} },}, +/**/ {{{0xce45b5c6, 0x3f5e78bd} }, +/**/ {{0x8a25b9c7, 0xbbef2cc4} },}, +/**/ {{{0x3ce64b3e, 0x3f5eb89f} }, +/**/ {{0xa6fea7bd, 0x3bfe6d27} },}, +/**/ {{{0x6bc43481, 0x3f5ef880} }, +/**/ {{0x914a6dab, 0xbbf68037} },}, +/**/ {{{0x5adff0d4, 0x3f5f3861} }, +/**/ {{0xf909e0e6, 0xbbf1d2f3} },}, +/**/ {{{0x0a39ff7e, 0x3f5f7842} }, +/**/ {{0xff1e1f71, 0xbbf64661} },}, +/**/ {{{0x79d2dfc3, 0x3f5fb822} }, +/**/ {{0x5a6f9e9a, 0xbbd76ce8} },}, +/**/ {{{0xa9ab10e6, 0x3f5ff802} }, +/**/ {{0xa153e3b2, 0x3bfe29e3} },}, +/**/ {{{0x4ce18915, 0x3f601bf1} }, +/**/ {{0xa3a73044, 0xbbe57c28} },}, +/**/ {{{0x250db166, 0x3f603be1} }, +/**/ {{0xc1ad9590, 0x3c0fd271} },}, +/**/ {{{0xdd5a4107, 0x3f605bd0} }, +/**/ {{0xc424c676, 0x3bfe4b5d} },}, +/**/ {{{0x75c77796, 0x3f607bc0} }, +/**/ {{0xc0eff1ba, 0xbc068804} },}, +/**/ {{{0xee5594b0, 0x3f609baf} }, +/**/ {{0x51dbded5, 0xbc0ff798} },}, +/**/ {{{0x4704d7f2, 0x3f60bb9f} }, +/**/ {{0x2d5aba70, 0xbbf70ef4} },}, +/**/ {{{0x7fd580f9, 0x3f60db8e} }, +/**/ {{0x7ae804b5, 0xbbeccb65} },}, +/**/ {{{0x98c7cf60, 0x3f60fb7d} }, +/**/ {{0x1775134d, 0x3bfede2f} },}, +/**/ {{{0x91dc02c3, 0x3f611b6c} }, +/**/ {{0x91ca4a67, 0xbc04d41e} },}, +/**/ {{{0x6b125aba, 0x3f613b5b} }, +/**/ {{0x4a12201d, 0x3bfe6d0c} },}, +/**/ {{{0x246b16e0, 0x3f615b4a} }, +/**/ {{0x4d4238d3, 0x3bfe507d} },}, +/**/ {{{0xbde676cd, 0x3f617b38} }, +/**/ {{0x0640462a, 0x3bfe0272} },}, +/**/ {{{0x3784ba19, 0x3f619b27} }, +/**/ {{0x02285659, 0x3bd94ab3} },}, +/**/ {{{0x9146205b, 0x3f61bb15} }, +/**/ {{0x1cc35b7b, 0xbbff1e2e} },}, +/**/ {{{0xcb2ae929, 0x3f61db03} }, +/**/ {{0x12f6bf8d, 0xbc03ee8e} },}, +/**/ {{{0xe5335418, 0x3f61faf1} }, +/**/ {{0x7b7d619b, 0x3c0bae5f} },}, +/**/ {{{0xdf5fa0bf, 0x3f621adf} }, +/**/ {{0xb3b731b0, 0xbbf5546a} },}, +/**/ {{{0xb9b00eb0, 0x3f623acd} }, +/**/ {{0x105fd253, 0xbbafb2b0} },}, +/**/ {{{0x7424dd7f, 0x3f625abb} }, +/**/ {{0xca53444b, 0x3c011647} },}, +/**/ {{{0x0ebe4cbf, 0x3f627aa9} }, +/**/ {{0x592f3be8, 0x3c01678f} },}, +/**/ {{{0x897c9c02, 0x3f629a96} }, +/**/ {{0x4347451d, 0xbbef2b12} },}, +/**/ {{{0xe4600ad8, 0x3f62ba83} }, +/**/ {{0xb2a477bc, 0x3bfb5bb7} },}, +/**/ {{{0x1f68d8d3, 0x3f62da71} }, +/**/ {{0x7a5822e4, 0xbc0590e1} },}, +/**/ {{{0x3a974581, 0x3f62fa5e} }, +/**/ {{0x53123101, 0xbbf0f2e5} },}, +/**/ {{{0x35eb9072, 0x3f631a4b} }, +/**/ {{0x0e3f5fde, 0xbc018db4} },}, +/**/ {{{0x1165f933, 0x3f633a38} }, +/**/ {{0x8d0afb38, 0x3c0921d5} },}, +/**/ {{{0xcd06bf53, 0x3f635a24} }, +/**/ {{0xb5791b80, 0x3c01f6ba} },}, +/**/ {{{0x68ce225e, 0x3f637a11} }, +/**/ {{0xa1894236, 0x3bde2af8} },}, +/**/ {{{0xe4bc61e0, 0x3f6399fd} }, +/**/ {{0xd0f06ff3, 0xbc062a48} },}, +/**/ {{{0x40d1bd63, 0x3f63b9ea} }, +/**/ {{0x4b4f9c11, 0x3bffc80c} },}, +/**/ {{{0x7d0e7473, 0x3f63d9d6} }, +/**/ {{0x6a92c891, 0x3c02219b} },}, +/**/ {{{0x9972c699, 0x3f63f9c2} }, +/**/ {{0x790ade9e, 0x3c0d3590} },}, +/**/ {{{0x95fef35f, 0x3f6419ae} }, +/**/ {{0x792a458c, 0xbc01c279} },}, +/**/ {{{0x72b33a4b, 0x3f64399a} }, +/**/ {{0x327bffae, 0x3c02ce64} },}, +/**/ {{{0x2f8fdae7, 0x3f645986} }, +/**/ {{0xd231155c, 0xbc070aec} },}, +/**/ {{{0xcc9514b7, 0x3f647971} }, +/**/ {{0xe4bbf776, 0x3c0f373d} },}, +/**/ {{{0x49c32744, 0x3f64995d} }, +/**/ {{0xbf22b2a7, 0xbbf6d7e5} },}, +/**/ {{{0xa71a5211, 0x3f64b948} }, +/**/ {{0x64fe2936, 0xbbedec69} },}, +/**/ {{{0xe49ad4a3, 0x3f64d933} }, +/**/ {{0xabee4257, 0x3bf5fc4b} },}, +/**/ {{{0x0244ee7e, 0x3f64f91f} }, +/**/ {{0x3cd1474f, 0x3c0c6fe3} },}, +/**/ {{{0x0018df26, 0x3f65190a} }, +/**/ {{0xd11e7fa5, 0xbc023957} },}, +/**/ {{{0xde16e61b, 0x3f6538f4} }, +/**/ {{0x55380346, 0x3c006c31} },}, +/**/ {{{0x9c3f42e1, 0x3f6558df} }, +/**/ {{0xc4a5134c, 0xbc09b7d4} },}, +/**/ {{{0x3a9234f7, 0x3f6578ca} }, +/**/ {{0x2772c19c, 0xbc0e3f10} },}, +/**/ {{{0xb90ffbdd, 0x3f6598b4} }, +/**/ {{0x5592b468, 0x3be6f110} },}, +/**/ {{{0x17b8d714, 0x3f65b89f} }, +/**/ {{0xb251ace2, 0xbc0a5fea} },}, +/**/ {{{0x568d0619, 0x3f65d889} }, +/**/ {{0x315da285, 0xbc0aacc9} },}, +/**/ {{{0x758cc86a, 0x3f65f873} }, +/**/ {{0xba64d81a, 0xbbeb0782} },}, +/**/ {{{0x74b85d85, 0x3f66185d} }, +/**/ {{0x8e1eb3fa, 0xbc09b459} },}, +/**/ {{{0x541004e5, 0x3f663847} }, +/**/ {{0x1d86e863, 0x3bce9c22} },}, +/**/ {{{0x1393fe07, 0x3f665831} }, +/**/ {{0xcf37ee90, 0xbbfbeb77} },}, +/**/ {{{0xb3448865, 0x3f66781a} }, +/**/ {{0xc252e3c9, 0xbc02dc68} },}, +/**/ {{{0x3321e379, 0x3f669804} }, +/**/ {{0xb40b3741, 0xbbe73a0b} },}, + }; + +#endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/upow.h b/REORG.TODO/sysdeps/ieee754/dbl-64/upow.h new file mode 100644 index 0000000000..9dcbd3eb2b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/upow.h @@ -0,0 +1,76 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/******************************************************************/ +/* */ +/* MODULE_NAME:upow.h */ +/* */ +/* common data and variables prototype and definition */ +/******************************************************************/ + +#ifndef UPOW_H +#define UPOW_H + +#include "mydefs.h" + +#ifdef BIG_ENDI + const static mynumber +/**/ nZERO = {{0x80000000, 0}}, /* -0.0 */ +/**/ INF = {{0x7ff00000, 0x00000000}}, /* INF */ +/**/ nINF = {{0xfff00000, 0x00000000}}, /* -INF */ +/**/ ln2a = {{0x3fe62e42, 0xfefa3800}}, /* ln(2) 43 bits */ +/**/ ln2b = {{0x3d2ef357, 0x93c76730}}, /* ln(2)-ln2a */ +/**/ bigu = {{0x4297ffff, 0xfffffd2c}}, /* 1.5*2**42 -724*2**-10 */ +/**/ bigv = {{0x4207ffff, 0xfff8016a}}, /* 1.5*2**33-1+362*2**-19 */ +/**/ t52 = {{0x43300000, 0x00000000}}, /* 2**52 */ +/**/ two52e = {{0x43300000, 0x000003ff}}; /* 2**52' */ + +#else +#ifdef LITTLE_ENDI + const static mynumber +/**/ nZERO = {{0, 0x80000000}}, /* -0.0 */ +/**/ INF = {{0x00000000, 0x7ff00000}}, /* INF */ +/**/ nINF = {{0x00000000, 0xfff00000}}, /* -INF */ +/**/ ln2a = {{0xfefa3800, 0x3fe62e42}}, /* ln(2) 43 bits */ +/**/ ln2b = {{0x93c76730, 0x3d2ef357}}, /* ln(2)-ln2a */ +/**/ bigu = {{0xfffffd2c, 0x4297ffff}}, /* 1.5*2**42 -724*2**-10 */ +/**/ bigv = {{0xfff8016a, 0x4207ffff}}, /* 1.5*2**33-1+362*2**-19 */ +/**/ t52 = {{0x00000000, 0x43300000}}, /* 2**52 */ +/**/ two52e = {{0x000003ff, 0x43300000}}; /* 2**52' */ + +#endif +#endif + +const static double p2=-0.5, p3 = 3.3333333333333333333e-1, p4 = -0.25, + q2 = -0.5, q3 = 3.3333333333331404e-01, q4 = -2.4999999999996436e-01, + q5 = 2.0000010500004459e-01, q6 = -1.6666678916688004e-01, + r3 = 3.33333333333333333372884096563030E-01, + r4 = -2.50000000000000000213574153875908E-01, + r5 = 1.99999999999683593814072199830603E-01, + r6 = -1.66666666666065494878165510225378E-01, + r7 = 1.42857517857114380606360005067609E-01, + r8 = -1.25000449999974370683775964001702E-01, + s3 = 0.333251953125000000e0, + ss3 = 8.138020833333333333e-05, + s4 = -2.500000000000000000e-01, + s5 = 1.999999999999960937e-01, + s6 = -1.666666666666592447e-01, + s7 = 1.428571845238194705e-01, + s8 = -1.250000500000149097e-01; +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/upow.tbl b/REORG.TODO/sysdeps/ieee754/dbl-64/upow.tbl new file mode 100644 index 0000000000..f92c69c521 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/upow.tbl @@ -0,0 +1,10188 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/****************************************************************/ +/* TABLES FOR THE upow() FUNCTION */ +/****************************************************************/ + + + +#ifdef BIG_ENDI +static const union {int4 i[5800]; double x[2900];} ui = { .i = { +/**/ 0x3FF6A000, 0x00000000, +/**/ 0x3F33CD15, 0x3729043E, +/**/ 0xBFD63003, 0x0B3AB000, +/**/ 0x3D2DB623, 0xE731AE00, +/**/ 0x3FF69800, 0x00000000, +/**/ 0x3F33F349, 0xCC7267D0, +/**/ 0xBFD61965, 0xCDB03000, +/**/ 0x3D2F08AD, 0x603C488E, +/**/ 0x3FF69000, 0x00000000, +/**/ 0x3F3473A8, 0x8D0BFD2E, +/**/ 0xBFD602D0, 0x8AF09000, +/**/ 0xBD1EBE91, 0x76DF3F65, +/**/ 0x3FF68800, 0x00000000, +/**/ 0x3F354DD2, 0x390B9ED0, +/**/ 0xBFD5EC43, 0x3D5C3000, +/**/ 0xBD36B71A, 0x1229D17F, +/**/ 0x3FF68000, 0x00000000, +/**/ 0x3F368168, 0x16816817, +/**/ 0xBFD5D5BD, 0xDF596000, +/**/ 0x3D0A0B2A, 0x08A465DC, +/**/ 0x3FF67800, 0x00000000, +/**/ 0x3F380E0B, 0xF08C7765, +/**/ 0xBFD5BF40, 0x6B544000, +/**/ 0x3D227023, 0xEB68981C, +/**/ 0x3FF67000, 0x00000000, +/**/ 0x3F39F360, 0x16719F36, +/**/ 0xBFD5A8CA, 0xDBBEE000, +/**/ 0x3CF7C79B, 0x0AF7ECF8, +/**/ 0x3FF66800, 0x00000000, +/**/ 0x3F3C3107, 0x5AB40167, +/**/ 0xBFD5925D, 0x2B113000, +/**/ 0x3D369BF5, 0xA7A56F34, +/**/ 0x3FF66000, 0x00000000, +/**/ 0x3F3EC6A5, 0x122F9016, +/**/ 0xBFD57BF7, 0x53C8D000, +/**/ 0xBD1FADED, 0xEE5D40EF, +/**/ 0x3FF65C00, 0x00000000, +/**/ 0xBF3E4C22, 0xECCA9097, +/**/ 0xBFD56599, 0x50695000, +/**/ 0xBD14C5FD, 0x2BADC774, +/**/ 0x3FF65400, 0x00000000, +/**/ 0xBF3B07AC, 0x4B55CC62, +/**/ 0xBFD54F43, 0x1B7BE000, +/**/ 0xBD1A8954, 0xC0910952, +/**/ 0x3FF64C00, 0x00000000, +/**/ 0xBF376C52, 0x32DA090E, +/**/ 0xBFD538F4, 0xAF8F7000, +/**/ 0xBD27EC02, 0xE45547CE, +/**/ 0x3FF64400, 0x00000000, +/**/ 0xBF337A6F, 0x4DE9BD38, +/**/ 0xBFD522AE, 0x0738A000, +/**/ 0xBD2EBE70, 0x8164C759, +/**/ 0x3FF63C00, 0x00000000, +/**/ 0xBF2E64BB, 0x923C708B, +/**/ 0xBFD50C6F, 0x1D11C000, +/**/ 0x3D3A0E6B, 0x7E827C2C, +/**/ 0x3FF63400, 0x00000000, +/**/ 0xBF2528EE, 0xA7E43FD4, +/**/ 0xBFD4F637, 0xEBBAA000, +/**/ 0x3D3FC158, 0xCB3124B9, +/**/ 0x3FF62C00, 0x00000000, +/**/ 0xBF168454, 0x86689DF7, +/**/ 0xBFD4E008, 0x6DD8C000, +/**/ 0x3D34D692, 0xA1E44788, +/**/ 0x3FF62400, 0x00000000, +/**/ 0xBED623FA, 0x77016240, +/**/ 0xBFD4C9E0, 0x9E173000, +/**/ 0x3D2E2089, 0x1B0AD8A4, +/**/ 0x3FF61C00, 0x00000000, +/**/ 0x3F151300, 0x58715130, +/**/ 0xBFD4B3C0, 0x77268000, +/**/ 0x3D165B46, 0x81052B9F, +/**/ 0x3FF61400, 0x00000000, +/**/ 0x3F266D06, 0x35D2754E, +/**/ 0xBFD49DA7, 0xF3BCC000, +/**/ 0xBD307B33, 0x4DAF4B9A, +/**/ 0x3FF60C00, 0x00000000, +/**/ 0x3F317C61, 0xDA197F23, +/**/ 0xBFD48797, 0x0E958000, +/**/ 0xBD3DC1B8, 0x465CF25F, +/**/ 0x3FF60400, 0x00000000, +/**/ 0x3F381605, 0x81605816, +/**/ 0xBFD4718D, 0xC271C000, +/**/ 0xBD306C18, 0xFB4C14C5, +/**/ 0x3FF5FC00, 0x00000000, +/**/ 0x3F3F0317, 0xB5C6F559, +/**/ 0xBFD45B8C, 0x0A17E000, +/**/ 0x3D0D9120, 0xE7D0A853, +/**/ 0x3FF5F800, 0x00000000, +/**/ 0xBF39BCBD, 0x6D2041E3, +/**/ 0xBFD44591, 0xE053A000, +/**/ 0x3D06E958, 0x92923D88, +/**/ 0x3FF5F000, 0x00000000, +/**/ 0xBF3229CF, 0x5604CC40, +/**/ 0xBFD42F9F, 0x3FF62000, +/**/ 0xBD390644, 0x0F7D3354, +/**/ 0x3FF5E800, 0x00000000, +/**/ 0xBF2488E5, 0xFD431489, +/**/ 0xBFD419B4, 0x23D5F000, +/**/ 0x3D3CE379, 0x226DE3EC, +/**/ 0x3FF5E000, 0x00000000, +/**/ 0xBF0067E7, 0x6424E9C9, +/**/ 0xBFD403D0, 0x86CEA000, +/**/ 0xBD3E6EF5, 0x74487308, +/**/ 0x3FF5D800, 0x00000000, +/**/ 0x3F19F0FB, 0x38A94D24, +/**/ 0xBFD3EDF4, 0x63C17000, +/**/ 0x3D3F067C, 0x297F2C3F, +/**/ 0x3FF5D000, 0x00000000, +/**/ 0x3F2EADD9, 0x23CAD2AA, +/**/ 0xBFD3D81F, 0xB5947000, +/**/ 0x3D222C7C, 0x2A9D37A4, +/**/ 0x3FF5C800, 0x00000000, +/**/ 0x3F3882B9, 0x31057262, +/**/ 0xBFD3C252, 0x77333000, +/**/ 0xBD183B54, 0xB606BD5C, +/**/ 0x3FF5C400, 0x00000000, +/**/ 0xBF3E00AE, 0x10FFA8F8, +/**/ 0xBFD3AC8C, 0xA38E6000, +/**/ 0x3D2D0BEF, 0xBC02BE4A, +/**/ 0x3FF5BC00, 0x00000000, +/**/ 0xBF34339B, 0x8056EAF3, +/**/ 0xBFD396CE, 0x359BC000, +/**/ 0x3D05839C, 0x5663663D, +/**/ 0x3FF5B400, 0x00000000, +/**/ 0xBF242CC1, 0xF31D7FD5, +/**/ 0xBFD38117, 0x28565000, +/**/ 0x3D2A71E4, 0x93A0702B, +/**/ 0x3FF5AC00, 0x00000000, +/**/ 0x3ED5AC05, 0x6B015AC0, +/**/ 0xBFD36B67, 0x76BE1000, +/**/ 0xBD116ECD, 0xB0F177C8, +/**/ 0x3FF5A400, 0x00000000, +/**/ 0x3F26268D, 0x5BA55E5A, +/**/ 0xBFD355BF, 0x1BD83000, +/**/ 0x3D2BA99B, 0x8964F0E8, +/**/ 0x3FF59C00, 0x00000000, +/**/ 0x3F361F12, 0x3CCAA376, +/**/ 0xBFD3401E, 0x12AED000, +/**/ 0x3D317C73, 0x556E291D, +/**/ 0x3FF59800, 0x00000000, +/**/ 0xBF3E863D, 0x62D32417, +/**/ 0xBFD32A84, 0x56512000, +/**/ 0xBD04F928, 0x139AF5D6, +/**/ 0x3FF59000, 0x00000000, +/**/ 0xBF32DCF7, 0xEA712DCF, +/**/ 0xBFD314F1, 0xE1D36000, +/**/ 0x3D28E27A, 0xD3213CB8, +/**/ 0x3FF58800, 0x00000000, +/**/ 0xBF1B95B2, 0xA0CC87E8, +/**/ 0xBFD2FF66, 0xB04EB000, +/**/ 0x3D38AED2, 0x541E6E2E, +/**/ 0x3FF58000, 0x00000000, +/**/ 0x3F158056, 0x01580560, +/**/ 0xBFD2E9E2, 0xBCE12000, +/**/ 0xBD24300C, 0x128D1DC2, +/**/ 0x3FF57800, 0x00000000, +/**/ 0x3F31F340, 0x15791F34, +/**/ 0xBFD2D466, 0x02ADD000, +/**/ 0x3D288D0D, 0xDCD54196, +/**/ 0x3FF57000, 0x00000000, +/**/ 0x3F3ED3C5, 0x06B39A23, +/**/ 0xBFD2BEF0, 0x7CDC9000, +/**/ 0xBD2A9CFA, 0x4A5004F4, +/**/ 0x3FF56C00, 0x00000000, +/**/ 0xBF33FEA9, 0x53FEA954, +/**/ 0xBFD2A982, 0x269A4000, +/**/ 0x3D22058E, 0x557285CF, +/**/ 0x3FF56400, 0x00000000, +/**/ 0xBF1A1160, 0xEB478503, +/**/ 0xBFD2941A, 0xFB187000, +/**/ 0x3D3210C2, 0xB730E28B, +/**/ 0x3FF55C00, 0x00000000, +/**/ 0x3F1D09AD, 0xE4A18B2E, +/**/ 0xBFD27EBA, 0xF58D9000, +/**/ 0x3D2B1988, 0x00B4BDA7, +/**/ 0x3FF55400, 0x00000000, +/**/ 0x3F355555, 0x55555555, +/**/ 0xBFD26962, 0x1134E000, +/**/ 0x3D31B61F, 0x10522625, +/**/ 0x3FF55000, 0x00000000, +/**/ 0xBF3C4BE6, 0xB319A21F, +/**/ 0xBFD25410, 0x494E5000, +/**/ 0xBD3B1D7A, 0xC0EF77F2, +/**/ 0x3FF54800, 0x00000000, +/**/ 0xBF2B4328, 0x8FA03FD5, +/**/ 0xBFD23EC5, 0x991EC000, +/**/ 0x3D36DBE4, 0x48A2E522, +/**/ 0x3FF54000, 0x00000000, +/**/ 0x3EF54015, 0x40154015, +/**/ 0xBFD22981, 0xFBEF8000, +/**/ 0x3D3A1421, 0x609580DA, +/**/ 0x3FF53800, 0x00000000, +/**/ 0x3F30948F, 0x40FEAC6F, +/**/ 0xBFD21445, 0x6D0EC000, +/**/ 0x3D3CAF04, 0x28B728A3, +/**/ 0x3FF53400, 0x00000000, +/**/ 0xBF3FE034, 0xFD04F7B8, +/**/ 0xBFD1FF0F, 0xE7CF4000, +/**/ 0xBD3E9D5B, 0x513FF0C1, +/**/ 0x3FF52C00, 0x00000000, +/**/ 0xBF300A95, 0x7FAB5403, +/**/ 0xBFD1E9E1, 0x6788A000, +/**/ 0x3D382EAE, 0xD3C8B65E, +/**/ 0x3FF52400, 0x00000000, +/**/ 0x3EB52401, 0x52401524, +/**/ 0xBFD1D4B9, 0xE796C000, +/**/ 0xBD222A66, 0x7C42E56D, +/**/ 0x3FF51C00, 0x00000000, +/**/ 0x3F307EAE, 0x2F8151D0, +/**/ 0xBFD1BF99, 0x635A7000, +/**/ 0x3D31AC89, 0x575C2125, +/**/ 0x3FF51800, 0x00000000, +/**/ 0xBF3ECE3F, 0xEAE9ECE4, +/**/ 0xBFD1AA7F, 0xD638D000, +/**/ 0xBD29F60A, 0x9616F7A0, +/**/ 0x3FF51000, 0x00000000, +/**/ 0xBF2BA3DD, 0xC7675243, +/**/ 0xBFD1956D, 0x3B9BC000, +/**/ 0xBD27D2F7, 0x3AD1AA14, +/**/ 0x3FF50800, 0x00000000, +/**/ 0x3F0B9AC8, 0x764E368D, +/**/ 0xBFD18061, 0x8EF19000, +/**/ 0x3D3482FF, 0xC86D38E5, +/**/ 0x3FF50000, 0x00000000, +/**/ 0x3F350150, 0x15015015, +/**/ 0xBFD16B5C, 0xCBAD0000, +/**/ 0x3D323299, 0x042D74BF, +/**/ 0x3FF4FC00, 0x00000000, +/**/ 0xBF392851, 0x4A683C50, +/**/ 0xBFD1565E, 0xED456000, +/**/ 0x3CEE75AD, 0xFB6ABA25, +/**/ 0x3FF4F400, 0x00000000, +/**/ 0xBF1C2748, 0xACD95EF0, +/**/ 0xBFD14167, 0xEF367000, +/**/ 0xBD3E0C07, 0x824DAAF5, +/**/ 0x3FF4EC00, 0x00000000, +/**/ 0x3F26B90D, 0x67A47465, +/**/ 0xBFD12C77, 0xCD007000, +/**/ 0xBD13B294, 0x8A11F797, +/**/ 0x3FF4E400, 0x00000000, +/**/ 0x3F3E0A72, 0xF0539783, +/**/ 0xBFD1178E, 0x8227E000, +/**/ 0xBD31EF78, 0xCE2D07F2, +/**/ 0x3FF4E000, 0x00000000, +/**/ 0xBF2E00A6, 0xF87FD642, +/**/ 0xBFD102AC, 0x0A35D000, +/**/ 0x3D2F1FBD, 0xDFDFD686, +/**/ 0x3FF4D800, 0x00000000, +/**/ 0x3F10EFB7, 0x0B12E3FD, +/**/ 0xBFD0EDD0, 0x60B78000, +/**/ 0xBD0019B5, 0x2D8435F5, +/**/ 0x3FF4D000, 0x00000000, +/**/ 0x3F37BEF1, 0x5CB4DBE5, +/**/ 0xBFD0D8FB, 0x813EB000, +/**/ 0xBD1EE8C8, 0x8753FA35, +/**/ 0x3FF4CC00, 0x00000000, +/**/ 0xBF34778D, 0xA50918B1, +/**/ 0xBFD0C42D, 0x67616000, +/**/ 0xBD27188B, 0x163CEAE9, +/**/ 0x3FF4C400, 0x00000000, +/**/ 0xBED9F4F7, 0xE37288EC, +/**/ 0xBFD0AF66, 0x0EB9E000, +/**/ 0xBD23C7C3, 0xF528D80A, +/**/ 0x3FF4BC00, 0x00000000, +/**/ 0x3F33EDDA, 0x68FE0E42, +/**/ 0xBFD09AA5, 0x72E6C000, +/**/ 0xBD3B50A1, 0xE1734342, +/**/ 0x3FF4B800, 0x00000000, +/**/ 0xBF3776C6, 0xB72E47D9, +/**/ 0xBFD085EB, 0x8F8AE000, +/**/ 0xBD3E5D51, 0x3F45FE7B, +/**/ 0x3FF4B000, 0x00000000, +/**/ 0xBF04AFD6, 0xA052BF5B, +/**/ 0xBFD07138, 0x604D6000, +/**/ 0x3D3E7632, 0x4E912B17, +/**/ 0x3FF4A800, 0x00000000, +/**/ 0x3F328FFA, 0xD5B5C015, +/**/ 0xBFD05C8B, 0xE0D96000, +/**/ 0xBD2AD0F1, 0xC77CCB58, +/**/ 0x3FF4A400, 0x00000000, +/**/ 0xBF380528, 0x9FEB5D80, +/**/ 0xBFD047E6, 0x0CDE8000, +/**/ 0xBD2DBDF1, 0x0D397F3C, +/**/ 0x3FF49C00, 0x00000000, +/**/ 0xBF02AD3E, 0x25FF5B21, +/**/ 0xBFD03346, 0xE0106000, +/**/ 0xBCF89FF8, 0xA966395C, +/**/ 0x3FF49400, 0x00000000, +/**/ 0x3F339E3B, 0x2D066EA2, +/**/ 0xBFD01EAE, 0x5626C000, +/**/ 0xBD3A43DC, 0xFADE85AE, +/**/ 0x3FF49000, 0x00000000, +/**/ 0xBF3629C1, 0xAFB2E932, +/**/ 0xBFD00A1C, 0x6ADDA000, +/**/ 0xBD31CD8D, 0x688B9E18, +/**/ 0x3FF48800, 0x00000000, +/**/ 0x3ED48805, 0x22014880, +/**/ 0xBFCFEB22, 0x33EA0000, +/**/ 0xBD2F3418, 0xDE00938B, +/**/ 0x3FF48000, 0x00000000, +/**/ 0x3F37119F, 0x3D324D89, +/**/ 0xBFCFC218, 0xBE620000, +/**/ 0xBD34BBA4, 0x6F1CF6A0, +/**/ 0x3FF47C00, 0x00000000, +/**/ 0xBF31EB85, 0x1EB851EC, +/**/ 0xBFCF991C, 0x6CB3C000, +/**/ 0x3D390D04, 0xCD7CC834, +/**/ 0x3FF47400, 0x00000000, +/**/ 0x3F1569C9, 0xAAFC7C01, +/**/ 0xBFCF702D, 0x36778000, +/**/ 0x3D108195, 0x16673E23, +/**/ 0x3FF46C00, 0x00000000, +/**/ 0x3F3CE345, 0x96066250, +/**/ 0xBFCF474B, 0x134E0000, +/**/ 0x3D3BAE49, 0xF1DF7B5E, +/**/ 0x3FF46800, 0x00000000, +/**/ 0xBF26A297, 0x1D02DE87, +/**/ 0xBFCF1E75, 0xFADFA000, +/**/ 0x3D20862B, 0x25D83F6D, +/**/ 0x3FF46000, 0x00000000, +/**/ 0x3F2978FE, 0xB9F34381, +/**/ 0xBFCEF5AD, 0xE4DD0000, +/**/ 0x3CCA2115, 0x65BB8E11, +/**/ 0x3FF45C00, 0x00000000, +/**/ 0xBF3AF398, 0xF6C71366, +/**/ 0xBFCECCF2, 0xC8FEA000, +/**/ 0x3D3BEC63, 0xA3E75640, +/**/ 0x3FF45400, 0x00000000, +/**/ 0xBF030E9C, 0x449AFF5D, +/**/ 0xBFCEA444, 0x9F04A000, +/**/ 0xBD35E916, 0x63732A36, +/**/ 0x3FF44C00, 0x00000000, +/**/ 0x3F367190, 0xF8B42EF3, +/**/ 0xBFCE7BA3, 0x5EB78000, +/**/ 0x3D0D5EEE, 0x23793649, +/**/ 0x3FF44800, 0x00000000, +/**/ 0xBF3079A9, 0xD260511C, +/**/ 0xBFCE530E, 0xFFE72000, +/**/ 0x3D3FDBDB, 0xB13F7C18, +/**/ 0x3FF44000, 0x00000000, +/**/ 0x3F21B87C, 0x0B644FBE, +/**/ 0xBFCE2A87, 0x7A6B2000, +/**/ 0xBD382381, 0x7787081A, +/**/ 0x3FF43C00, 0x00000000, +/**/ 0xBF3D8CF5, 0x411B2E25, +/**/ 0xBFCE020C, 0xC6236000, +/**/ 0x3D252B00, 0xADB91424, +/**/ 0x3FF43400, 0x00000000, +/**/ 0xBF0DAC08, 0xD6A60978, +/**/ 0xBFCDD99E, 0xDAF6E000, +/**/ 0x3D302EC6, 0x69C756EB, +/**/ 0x3FF42C00, 0x00000000, +/**/ 0x3F36625D, 0x51F86EFA, +/**/ 0xBFCDB13D, 0xB0D48000, +/**/ 0xBD32806A, 0x847527E6, +/**/ 0x3FF42800, 0x00000000, +/**/ 0xBF2E8B2D, 0xA8766564, +/**/ 0xBFCD88E9, 0x3FB30000, +/**/ 0x3D375F28, 0x0234BF51, +/**/ 0x3FF42000, 0x00000000, +/**/ 0x3F26A4CB, 0xCB2A247B, +/**/ 0xBFCD60A1, 0x7F904000, +/**/ 0x3D35D6E0, 0x6FC20D39, +/**/ 0x3FF41C00, 0x00000000, +/**/ 0xBF39D5E8, 0xC17DF552, +/**/ 0xBFCD3866, 0x68720000, +/**/ 0x3D373650, 0xB38932BC, +/**/ 0x3FF41400, 0x00000000, +/**/ 0x3EF41414, 0x14141414, +/**/ 0xBFCD1037, 0xF2656000, +/**/ 0x3D084A7E, 0x75B6F6E4, +/**/ 0x3FF40C00, 0x00000000, +/**/ 0x3F3C97A8, 0x43AE87FD, +/**/ 0xBFCCE816, 0x157F2000, +/**/ 0x3D29E0AB, 0xA2099515, +/**/ 0x3FF40800, 0x00000000, +/**/ 0xBF1F4BBC, 0x66A67E6F, +/**/ 0xBFCCC000, 0xC9DB4000, +/**/ 0x3D1D6D58, 0x5D57AFF9, +/**/ 0x3FF40000, 0x00000000, +/**/ 0x3F340140, 0x14014014, +/**/ 0xBFCC97F8, 0x079D4000, +/**/ 0xBD23B161, 0xA8C6E6C5, +/**/ 0x3FF3FC00, 0x00000000, +/**/ 0xBF2FD809, 0xFD809FD8, +/**/ 0xBFCC6FFB, 0xC6F00000, +/**/ 0xBD3EE138, 0xD3A69D43, +/**/ 0x3FF3F400, 0x00000000, +/**/ 0x3F28CA0E, 0x57EE89D2, +/**/ 0xBFCC480C, 0x0005C000, +/**/ 0xBD39A294, 0xD5E44E76, +/**/ 0x3FF3F000, 0x00000000, +/**/ 0xBF370BD5, 0xA50F9260, +/**/ 0xBFCC2028, 0xAB180000, +/**/ 0x3D292E0E, 0xE55C7AC6, +/**/ 0x3FF3E800, 0x00000000, +/**/ 0x3F1704AA, 0x75945FCE, +/**/ 0xBFCBF851, 0xC0676000, +/**/ 0x3D35420E, 0x4C0854AD, +/**/ 0x3FF3E400, 0x00000000, +/**/ 0xBF3D3431, 0xB56FD83C, +/**/ 0xBFCBD087, 0x383BE000, +/**/ 0x3D2D4BC4, 0x595412B6, +/**/ 0x3FF3DC00, 0x00000000, +/**/ 0x3EB3DC01, 0x3DC013DC, +/**/ 0xBFCBA8C9, 0x0AE4A000, +/**/ 0xBD3A32E7, 0xF44432DA, +/**/ 0x3FF3D400, 0x00000000, +/**/ 0x3F3D991A, 0xA75C5BBD, +/**/ 0xBFCB8117, 0x30B82000, +/**/ 0xBD1E9068, 0x3B9CD768, +/**/ 0x3FF3D000, 0x00000000, +/**/ 0xBF1292BA, 0x59C52F5D, +/**/ 0xBFCB5971, 0xA213A000, +/**/ 0xBD39B50E, 0x83AA91DF, +/**/ 0x3FF3C800, 0x00000000, +/**/ 0x3F395A47, 0xBABE7440, +/**/ 0xBFCB31D8, 0x575BC000, +/**/ 0xBD3C794E, 0x562A63CB, +/**/ 0x3FF3C400, 0x00000000, +/**/ 0xBF20D475, 0x58A0943A, +/**/ 0xBFCB0A4B, 0x48FC2000, +/**/ 0x3D22E72D, 0x5C3998ED, +/**/ 0x3FF3BC00, 0x00000000, +/**/ 0x3F360D92, 0x3295482C, +/**/ 0xBFCAE2CA, 0x6F672000, +/**/ 0xBD37A8D5, 0xAE54F550, +/**/ 0x3FF3B800, 0x00000000, +/**/ 0xBF267D12, 0xCAB48651, +/**/ 0xBFCABB55, 0xC316A000, +/**/ 0x3D38A65A, 0xCAF14CD8, +/**/ 0x3FF3B000, 0x00000000, +/**/ 0x3F33B13B, 0x13B13B14, +/**/ 0xBFCA93ED, 0x3C8AE000, +/**/ 0x3D287243, 0x50562169, +/**/ 0x3FF3AC00, 0x00000000, +/**/ 0xBF2A46AF, 0x2C8FD3BF, +/**/ 0xBFCA6C90, 0xD44B8000, +/**/ 0x3D3F63B7, 0xF037B0C6, +/**/ 0x3FF3A400, 0x00000000, +/**/ 0x3F324387, 0xAC822610, +/**/ 0xBFCA4540, 0x82E6A000, +/**/ 0xBD360A77, 0xC81F7171, +/**/ 0x3FF3A000, 0x00000000, +/**/ 0xBF2C34BB, 0xA1923DEE, +/**/ 0xBFCA1DFC, 0x40F1C000, +/**/ 0x3D301E0F, 0x004F3781, +/**/ 0x3FF39800, 0x00000000, +/**/ 0x3F31C2C1, 0x87F63372, +/**/ 0xBFC9F6C4, 0x0708A000, +/**/ 0x3D3337D9, 0x4BCD3F43, +/**/ 0x3FF39400, 0x00000000, +/**/ 0xBF2C4AA0, 0xE11BD52E, +/**/ 0xBFC9CF97, 0xCDCE0000, +/**/ 0xBD3D862F, 0x10C414E3, +/**/ 0x3FF38C00, 0x00000000, +/**/ 0x3F322D36, 0x6088DBF4, +/**/ 0xBFC9A877, 0x8DEBA000, +/**/ 0xBD3470FA, 0x3EFEC390, +/**/ 0x3FF38800, 0x00000000, +/**/ 0xBF2A8BBF, 0x503F774E, +/**/ 0xBFC98163, 0x4011A000, +/**/ 0xBD34EADD, 0x9E9045E2, +/**/ 0x3FF38000, 0x00000000, +/**/ 0x3F338138, 0x13813814, +/**/ 0xBFC95A5A, 0xDCF70000, +/**/ 0xBD07F228, 0x58A0FF6F, +/**/ 0x3FF37C00, 0x00000000, +/**/ 0xBF26FB6F, 0x1B177053, +/**/ 0xBFC9335E, 0x5D594000, +/**/ 0xBD33115C, 0x3ABD47DA, +/**/ 0x3FF37400, 0x00000000, +/**/ 0x3F35BD1C, 0x945EDC20, +/**/ 0xBFC90C6D, 0xB9FCC000, +/**/ 0x3D1935F5, 0x7718D7CA, +/**/ 0x3FF37000, 0x00000000, +/**/ 0xBF219D00, 0x4DBDCC60, +/**/ 0xBFC8E588, 0xEBAC2000, +/**/ 0xBD3B7D5C, 0xAB2D1140, +/**/ 0x3FF36800, 0x00000000, +/**/ 0x3F38DF3D, 0xE0747954, +/**/ 0xBFC8BEAF, 0xEB390000, +/**/ 0x3D073D54, 0xAAE92CD1, +/**/ 0x3FF36400, 0x00000000, +/**/ 0xBF14E775, 0xD9D3C49F, +/**/ 0xBFC897E2, 0xB17B2000, +/**/ 0x3D296B37, 0x380CBE9E, +/**/ 0x3FF35C00, 0x00000000, +/**/ 0x3F3CE5F9, 0xF2AF821E, +/**/ 0xBFC87121, 0x3750E000, +/**/ 0xBD3328EB, 0x42F9AF75, +/**/ 0x3FF35800, 0x00000000, +/**/ 0xBEE82DF0, 0xE34971F2, +/**/ 0xBFC84A6B, 0x759F6000, +/**/ 0x3D3DA280, 0x2ADF8609, +/**/ 0x3FF35400, 0x00000000, +/**/ 0xBF3E304D, 0x4873ECAE, +/**/ 0xBFC823C1, 0x6551A000, +/**/ 0xBD1E0DDB, 0x9A631E83, +/**/ 0x3FF34C00, 0x00000000, +/**/ 0x3F1264B6, 0x1FF659DB, +/**/ 0xBFC7FD22, 0xFF59A000, +/**/ 0x3D158BEB, 0xF457B7D2, +/**/ 0x3FF34800, 0x00000000, +/**/ 0xBF386531, 0xFECB9865, +/**/ 0xBFC7D690, 0x3CAF6000, +/**/ 0x3D24C06B, 0x17C301D7, +/**/ 0x3FF34000, 0x00000000, +/**/ 0x3F25A8C2, 0xEEDA65AE, +/**/ 0xBFC7B009, 0x16516000, +/**/ 0x3D3AE75F, 0xCB067E57, +/**/ 0x3FF33C00, 0x00000000, +/**/ 0xBF31BA4A, 0x8434E1F4, +/**/ 0xBFC7898D, 0x85444000, +/**/ 0xBD38E67B, 0xE3DBAF3F, +/**/ 0x3FF33400, 0x00000000, +/**/ 0x3F31EE97, 0xDBFC660A, +/**/ 0xBFC7631D, 0x82936000, +/**/ 0x3D25E77D, 0xC7C5F3E1, +/**/ 0x3FF33000, 0x00000000, +/**/ 0xBF246252, 0xBC40BFDA, +/**/ 0xBFC73CB9, 0x074FE000, +/**/ 0x3D3D66A9, 0x0D0005A6, +/**/ 0x3FF32800, 0x00000000, +/**/ 0x3F39E640, 0x13299E64, +/**/ 0xBFC71660, 0x0C914000, +/**/ 0xBCE51B15, 0x7CEC3838, +/**/ 0x3FF32400, 0x00000000, +/**/ 0xBEFCB5D4, 0xEF40991F, +/**/ 0xBFC6F012, 0x8B756000, +/**/ 0xBD357739, 0x0D31EF0F, +/**/ 0x3FF32000, 0x00000000, +/**/ 0xBF3D4632, 0xC823D892, +/**/ 0xBFC6C9D0, 0x7D204000, +/**/ 0x3CDC73FA, 0xFD9B2DCA, +/**/ 0x3FF31800, 0x00000000, +/**/ 0x3F1DD63A, 0x7AED804C, +/**/ 0xBFC6A399, 0xDABBE000, +/**/ 0x3D38F934, 0xE66A15A6, +/**/ 0x3FF31400, 0x00000000, +/**/ 0xBF339849, 0xE8C11E1A, +/**/ 0xBFC67D6E, 0x9D786000, +/**/ 0x3D311E88, 0x30A706D3, +/**/ 0x3FF30C00, 0x00000000, +/**/ 0x3F319013, 0x0D190131, +/**/ 0xBFC6574E, 0xBE8C2000, +/**/ 0x3D398C1D, 0x34F0F462, +/**/ 0x3FF30800, 0x00000000, +/**/ 0xBF222315, 0xB47A7FDA, +/**/ 0xBFC6313A, 0x37336000, +/**/ 0x3D144DF5, 0x4F21EA6D, +/**/ 0x3FF30000, 0x00000000, +/**/ 0x3F3C82AC, 0x40260390, +/**/ 0xBFC60B31, 0x00B0A000, +/**/ 0x3D371456, 0xC988F814, +/**/ 0x3FF2FC00, 0x00000000, +/**/ 0x3F026443, 0xA2430A62, +/**/ 0xBFC5E533, 0x144C2000, +/**/ 0x3D31CE0B, 0xF3B290EA, +/**/ 0x3FF2F800, 0x00000000, +/**/ 0xBF37B425, 0xED097B42, +/**/ 0xBFC5BF40, 0x6B544000, +/**/ 0x3D127023, 0xEB68981C, +/**/ 0x3FF2F000, 0x00000000, +/**/ 0x3F2D00E3, 0x4AE0553C, +/**/ 0xBFC59958, 0xFF1D6000, +/**/ 0x3D3A1D05, 0x9769CA05, +/**/ 0x3FF2EC00, 0x00000000, +/**/ 0xBF262BC0, 0x25D69D44, +/**/ 0xBFC5737C, 0xC9018000, +/**/ 0xBD39BAA7, 0xA6B887F6, +/**/ 0x3FF2E400, 0x00000000, +/**/ 0x3F3B88B5, 0xE3103D6B, +/**/ 0xBFC54DAB, 0xC2610000, +/**/ 0xBD2746FE, 0xE5C8D0D8, +/**/ 0x3FF2E000, 0x00000000, +/**/ 0x3F02E025, 0xC04B8097, +/**/ 0xBFC527E5, 0xE4A1C000, +/**/ 0x3D34E60B, 0x8D4B411D, +/**/ 0x3FF2DC00, 0x00000000, +/**/ 0xBF369C22, 0x2C305021, +/**/ 0xBFC5022B, 0x292F6000, +/**/ 0xBD348A05, 0xFF36A25B, +/**/ 0x3FF2D400, 0x00000000, +/**/ 0x3F30A012, 0xD50A012D, +/**/ 0xBFC4DC7B, 0x897BC000, +/**/ 0xBD0C79B6, 0x0AE1FF0F, +/**/ 0x3FF2D000, 0x00000000, +/**/ 0xBF1FBE29, 0xBC66484E, +/**/ 0xBFC4B6D6, 0xFEFE2000, +/**/ 0xBD1522EC, 0xF56E7952, +/**/ 0x3FF2C800, 0x00000000, +/**/ 0x3F3FB4D8, 0x12C9FB4E, +/**/ 0xBFC4913D, 0x8333C000, +/**/ 0x3D353E43, 0x558124C4, +/**/ 0x3FF2C400, 0x00000000, +/**/ 0x3F1E3432, 0x7004B11E, +/**/ 0xBFC46BAF, 0x0F9F6000, +/**/ 0x3D1249CD, 0x0790841A, +/**/ 0x3FF2C000, 0x00000000, +/**/ 0xBF30671A, 0x5C8EF02F, +/**/ 0xBFC4462B, 0x9DC9C000, +/**/ 0x3D384858, 0xA711B062, +/**/ 0x3FF2B800, 0x00000000, +/**/ 0x3F37D835, 0xD548D9AC, +/**/ 0xBFC420B3, 0x27410000, +/**/ 0x3D116282, 0xC85A0884, +/**/ 0x3FF2B400, 0x00000000, +/**/ 0x3ED2B404, 0xAD012B40, +/**/ 0xBFC3FB45, 0xA5992000, +/**/ 0xBD319713, 0xC0CAE559, +/**/ 0x3FF2B000, 0x00000000, +/**/ 0xBF370F78, 0x8E7302A1, +/**/ 0xBFC3D5E3, 0x126BC000, +/**/ 0xBD13FB2F, 0x85096C4B, +/**/ 0x3FF2A800, 0x00000000, +/**/ 0x3F31C92F, 0x3C1053F9, +/**/ 0xBFC3B08B, 0x67580000, +/**/ 0x3D3AADE8, 0xF29320FB, +/**/ 0x3FF2A400, 0x00000000, +/**/ 0xBF14AD94, 0x3DBE2E04, +/**/ 0xBFC38B3E, 0x9E028000, +/**/ 0x3D370EF0, 0x545C17F9, +/**/ 0x3FF2A000, 0x00000000, +/**/ 0xBF3BED61, 0xBED61BED, +/**/ 0xBFC365FC, 0xB015A000, +/**/ 0x3D3FD3A0, 0xAFB9691B, +/**/ 0x3FF29800, 0x00000000, +/**/ 0x3F2B061A, 0x26F004A6, +/**/ 0xBFC340C5, 0x97412000, +/**/ 0x3D37A3DC, 0xF7D9D386, +/**/ 0x3FF29400, 0x00000000, +/**/ 0xBF21B488, 0xFF6B646D, +/**/ 0xBFC31B99, 0x4D3A4000, +/**/ 0xBD3F098E, 0xE3A50810, +/**/ 0x3FF29000, 0x00000000, +/**/ 0xBF3F0582, 0x2CA5D5AC, +/**/ 0xBFC2F677, 0xCBBC0000, +/**/ 0xBD352B30, 0x2160F40D, +/**/ 0x3FF28800, 0x00000000, +/**/ 0x3F260251, 0x16025116, +/**/ 0xBFC2D161, 0x0C868000, +/**/ 0xBD039D6C, 0xCB81B4A1, +/**/ 0x3FF28400, 0x00000000, +/**/ 0xBF258CDF, 0x502065D2, +/**/ 0xBFC2AC55, 0x095F6000, +/**/ 0x3D1D3466, 0xD0C6C8A8, +/**/ 0x3FF27C00, 0x00000000, +/**/ 0x3F3FA38A, 0x1CE4D6F8, +/**/ 0xBFC28753, 0xBC11A000, +/**/ 0xBD37494E, 0x359302E6, +/**/ 0x3FF27800, 0x00000000, +/**/ 0x3F247DD5, 0xDCCA0781, +/**/ 0xBFC2625D, 0x1E6DE000, +/**/ 0x3CF52962, 0xF09E3D82, +/**/ 0x3FF27400, 0x00000000, +/**/ 0xBF25E8EF, 0xDB195E8F, +/**/ 0xBFC23D71, 0x2A49C000, +/**/ 0xBD100D23, 0x8FD3DF5C, +/**/ 0x3FF27000, 0x00000000, +/**/ 0xBF3FF6C8, 0xFFB647FE, +/**/ 0xBFC2188F, 0xD9808000, +/**/ 0x3D3B3A1E, 0x7F50C701, +/**/ 0x3FF26800, 0x00000000, +/**/ 0x3F266F9A, 0xC024D167, +/**/ 0xBFC1F3B9, 0x25F26000, +/**/ 0x3D15F74E, 0x9B083633, +/**/ 0x3FF26400, 0x00000000, +/**/ 0xBF22D1BD, 0xEABD0E14, +/**/ 0xBFC1CEED, 0x09854000, +/**/ 0x3D315C1C, 0x39192AF9, +/**/ 0x3FF26000, 0x00000000, +/**/ 0xBF3DD8F7, 0xF6D0EEC8, +/**/ 0xBFC1AA2B, 0x7E240000, +/**/ 0x3D31AC38, 0xDDE3B366, +/**/ 0x3FF25800, 0x00000000, +/**/ 0x3F2BCEB1, 0x2A241EF6, +/**/ 0xBFC18574, 0x7DBEC000, +/**/ 0xBD3E6744, 0x45BD9B49, +/**/ 0x3FF25400, 0x00000000, +/**/ 0xBF18A05B, 0xA21378D7, +/**/ 0xBFC160C8, 0x024B2000, +/**/ 0xBD2EC2D2, 0xA9009E3D, +/**/ 0x3FF25000, 0x00000000, +/**/ 0xBF3A076F, 0xD6CFA90C, +/**/ 0xBFC13C26, 0x05C3A000, +/**/ 0x3D2CF5FD, 0xD94F6509, +/**/ 0x3FF24800, 0x00000000, +/**/ 0x3F324924, 0x92492492, +/**/ 0xBFC1178E, 0x8227E000, +/**/ 0xBD21EF78, 0xCE2D07F2, +/**/ 0x3FF24400, 0x00000000, +/**/ 0xBEF3682B, 0x6151E899, +/**/ 0xBFC0F301, 0x717D0000, +/**/ 0x3D3E09B4, 0x41AE86C5, +/**/ 0x3FF24000, 0x00000000, +/**/ 0xBF34868E, 0x89FA4C67, +/**/ 0xBFC0CE7E, 0xCDCCC000, +/**/ 0xBD14652D, 0xABFF5447, +/**/ 0x3FF23800, 0x00000000, +/**/ 0x3F3858D8, 0x6B11F09F, +/**/ 0xBFC0AA06, 0x91268000, +/**/ 0x3D345519, 0xD7032129, +/**/ 0x3FF23400, 0x00000000, +/**/ 0x3F159E26, 0xAF37C049, +/**/ 0xBFC08598, 0xB59E4000, +/**/ 0x3D27E5DD, 0x7009902C, +/**/ 0x3FF23000, 0x00000000, +/**/ 0xBF2AB546, 0x2E076329, +/**/ 0xBFC06135, 0x354D4000, +/**/ 0xBD363046, 0x28340EE9, +/**/ 0x3FF22C00, 0x00000000, +/**/ 0xBF3FEDD5, 0xFEDD5FEE, +/**/ 0xBFC03CDC, 0x0A51E000, +/**/ 0xBD381A9C, 0xF169FC5C, +/**/ 0x3FF22400, 0x00000000, +/**/ 0x3F2B5B92, 0x009126D7, +/**/ 0xBFC0188D, 0x2ECF6000, +/**/ 0xBD03F965, 0x1CFF9DFE, +/**/ 0x3FF22000, 0x00000000, +/**/ 0xBF121FB7, 0x8121FB78, +/**/ 0xBFBFE891, 0x39DBC000, +/**/ 0xBD356594, 0xD82F7A82, +/**/ 0x3FF21C00, 0x00000000, +/**/ 0xBF368F22, 0x3A459635, +/**/ 0xBFBFA01C, 0x9DB58000, +/**/ 0x3D08F351, 0xFA48A730, +/**/ 0x3FF21400, 0x00000000, +/**/ 0x3F379804, 0x855E6012, +/**/ 0xBFBF57BC, 0x7D900000, +/**/ 0xBD176A6C, 0x9EA8B04E, +/**/ 0x3FF21000, 0x00000000, +/**/ 0x3F17B57C, 0x78CD7A37, +/**/ 0xBFBF0F70, 0xCDD98000, +/**/ 0xBD32E31F, 0x6C272C1E, +/**/ 0x3FF20C00, 0x00000000, +/**/ 0xBF271E73, 0x07E4EF15, +/**/ 0xBFBEC739, 0x830A0000, +/**/ 0xBD311FCB, 0xA80CDD10, +/**/ 0x3FF20800, 0x00000000, +/**/ 0xBF3CDDEC, 0x49392BA7, +/**/ 0xBFBE7F16, 0x91A34000, +/**/ 0x3D32C1C5, 0x9BC77BFA, +/**/ 0x3FF20000, 0x00000000, +/**/ 0x3F320120, 0x12012012, +/**/ 0xBFBE3707, 0xEE304000, +/**/ 0xBD20F684, 0xE6766ABD, +/**/ 0x3FF1FC00, 0x00000000, +/**/ 0x3EF0DC4F, 0xCE8AD1A2, +/**/ 0xBFBDEF0D, 0x8D468000, +/**/ 0x3D324750, 0x412E9A74, +/**/ 0x3FF1F800, 0x00000000, +/**/ 0xBF2F7047, 0xDC11F704, +/**/ 0xBFBDA727, 0x63844000, +/**/ 0xBD1A8940, 0x1FA71733, +/**/ 0x3FF1F000, 0x00000000, +/**/ 0x3F3FAF3F, 0x16B6419D, +/**/ 0xBFBD5F55, 0x65920000, +/**/ 0xBD30E239, 0xCC185469, +/**/ 0x3FF1EC00, 0x00000000, +/**/ 0x3F2E878F, 0xF70985E2, +/**/ 0xBFBD1797, 0x88218000, +/**/ 0xBD336433, 0xB5EFBEED, +/**/ 0x3FF1E800, 0x00000000, +/**/ 0xBEEF55E4, 0x94D7FDC3, +/**/ 0xBFBCCFED, 0xBFEE0000, +/**/ 0xBD33A823, 0x2FE71256, +/**/ 0x3FF1E400, 0x00000000, +/**/ 0xBF310C4C, 0x0478BBCF, +/**/ 0xBFBC8858, 0x01BC4000, +/**/ 0xBD2646D1, 0xC65AACD3, +/**/ 0x3FF1DC00, 0x00000000, +/**/ 0x3F3F0ECB, 0xCB840C49, +/**/ 0xBFBC40D6, 0x425A4000, +/**/ 0xBD3CB112, 0x1D1930DD, +/**/ 0x3FF1D800, 0x00000000, +/**/ 0x3F2EACE5, 0xC9579074, +/**/ 0xBFBBF968, 0x769FC000, +/**/ 0xBD24218C, 0x8D824283, +/**/ 0x3FF1D400, 0x00000000, +/**/ 0xBECABDFA, 0xFC60F0AE, +/**/ 0xBFBBB20E, 0x936D8000, +/**/ 0x3D368BA8, 0x35459B8E, +/**/ 0x3FF1D000, 0x00000000, +/**/ 0xBF2F2A4B, 0xAFDC61F3, +/**/ 0xBFBB6AC8, 0x8DAD4000, +/**/ 0xBD3B1BDF, 0xF50225C7, +/**/ 0x3FF1CC00, 0x00000000, +/**/ 0xBF3EC8AF, 0xAB802394, +/**/ 0xBFBB2396, 0x5A530000, +/**/ 0x3CEFF64E, 0xEA137079, +/**/ 0x3FF1C400, 0x00000000, +/**/ 0x3F322FC1, 0xCE058D9B, +/**/ 0xBFBADC77, 0xEE5B0000, +/**/ 0x3D3573B2, 0x09C31904, +/**/ 0x3FF1C000, 0x00000000, +/**/ 0x3F0AA04F, 0xE0EFA2CF, +/**/ 0xBFBA956D, 0x3ECAC000, +/**/ 0xBD3E6379, 0x4C02C4AF, +/**/ 0x3FF1BC00, 0x00000000, +/**/ 0xBF26B7F7, 0x225ADFDD, +/**/ 0xBFBA4E76, 0x40B1C000, +/**/ 0x3D0E42B6, 0xB94407C8, +/**/ 0x3FF1B800, 0x00000000, +/**/ 0xBF39E073, 0x217CD13A, +/**/ 0xBFBA0792, 0xE9278000, +/**/ 0x3D0A9CE6, 0xC9AD51BF, +/**/ 0x3FF1B000, 0x00000000, +/**/ 0x3F37C67F, 0x2BAE2B21, +/**/ 0xBFB9C0C3, 0x2D4D4000, +/**/ 0x3D3AB7C0, 0x9E838668, +/**/ 0x3FF1AC00, 0x00000000, +/**/ 0x3F23316E, 0xBD720DCF, +/**/ 0xBFB97A07, 0x024CC000, +/**/ 0x3CF8BCC1, 0x732093CE, +/**/ 0x3FF1A800, 0x00000000, +/**/ 0xBF11A7B9, 0x611A7B96, +/**/ 0xBFB9335E, 0x5D594000, +/**/ 0xBD23115C, 0x3ABD47DA, +/**/ 0x3FF1A400, 0x00000000, +/**/ 0xBF324195, 0xA1C1B8E7, +/**/ 0xBFB8ECC9, 0x33AEC000, +/**/ 0x3D222F39, 0xBE67F7AA, +/**/ 0x3FF1A000, 0x00000000, +/**/ 0xBF3FEE61, 0xFEE61FEE, +/**/ 0xBFB8A647, 0x7A91C000, +/**/ 0xBD3C28C0, 0xAF9BD6DF, +/**/ 0x3FF19800, 0x00000000, +/**/ 0x3F328F89, 0x362B721D, +/**/ 0xBFB85FD9, 0x27508000, +/**/ 0x3D35B818, 0x19970C1C, +/**/ 0x3FF19400, 0x00000000, +/**/ 0x3F14E023, 0x28A70119, +/**/ 0xBFB8197E, 0x2F410000, +/**/ 0x3D3C0FE4, 0x60D20041, +/**/ 0x3FF19000, 0x00000000, +/**/ 0xBF1FD419, 0x3E48FC6F, +/**/ 0xBFB7D336, 0x87C28000, +/**/ 0xBD33C88C, 0x3E706706, +/**/ 0x3FF18C00, 0x00000000, +/**/ 0xBF34F7C6, 0xFD42546B, +/**/ 0xBFB78D02, 0x263D8000, +/**/ 0xBD069B57, 0x94B69FB7, +/**/ 0x3FF18400, 0x00000000, +/**/ 0x3F3E2FA4, 0x01185E30, +/**/ 0xBFB746E1, 0x00228000, +/**/ 0x3D3126D1, 0x6E1E21D2, +/**/ 0x3FF18000, 0x00000000, +/**/ 0x3F318118, 0x11811812, +/**/ 0xBFB700D3, 0x0AEAC000, +/**/ 0xBCEC1E8D, 0xA99DED32, +/**/ 0x3FF17C00, 0x00000000, +/**/ 0x3F13F1CA, 0xFF2E2C43, +/**/ 0xBFB6BAD8, 0x3C188000, +/**/ 0xBD0DAF3C, 0xC08926AE, +/**/ 0x3FF17800, 0x00000000, +/**/ 0xBF1D79B9, 0x0A5EF9FF, +/**/ 0xBFB674F0, 0x89364000, +/**/ 0xBD3A7999, 0x4C9D3302, +/**/ 0x3FF17400, 0x00000000, +/**/ 0xBF338FAD, 0x1ECEA765, +/**/ 0xBFB62F1B, 0xE7D78000, +/**/ 0x3D217995, 0x7ED63C4E, +/**/ 0x3FF17000, 0x00000000, +/**/ 0xBF3F976B, 0xD8C8714B, +/**/ 0xBFB5E95A, 0x4D978000, +/**/ 0xBD31CB7C, 0xE1D17171, +/**/ 0x3FF16800, 0x00000000, +/**/ 0x3F348A33, 0xB08FA497, +/**/ 0xBFB5A3AB, 0xB01AC000, +/**/ 0xBD3E2574, 0x9E6AFA18, +/**/ 0x3FF16400, 0x00000000, +/**/ 0x3F21AA1F, 0x864022C9, +/**/ 0xBFB55E10, 0x050E0000, +/**/ 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0xBD2A47F8, 0x8FCCE5BA, +/**/ 0x3FE87800, 0x00000000, +/**/ 0x3F1A9336, 0xDEECB0A8, +/**/ 0x3FD12A4B, 0xC3912000, +/**/ 0xBD35A750, 0x61473259, +/**/ 0x3FE87800, 0x00000000, +/**/ 0xBF3EC219, 0xFB6A388D, +/**/ 0x3FD13687, 0x0293B000, +/**/ 0xBD3D3E84, 0x99D67123, +/**/ 0x3FE87000, 0x00000000, +/**/ 0xBF106AE7, 0xC1625090, +/**/ 0x3FD142BF, 0xEB9A0000, +/**/ 0x3D31CE61, 0x85B58A9E, +/**/ 0x3FE86800, 0x00000000, +/**/ 0x3F369AE5, 0xACD4200C, +/**/ 0x3FD14EF6, 0x7F887000, +/**/ 0xBD3E97A6, 0x5DFC9794, +/**/ 0x3FE86800, 0x00000000, +/**/ 0xBF2D4286, 0x9389D11C, +/**/ 0x3FD15B2A, 0xBF429000, +/**/ 0xBD2D8E3B, 0x49B629B2, +/**/ 0x3FE86000, 0x00000000, +/**/ 0x3F286186, 0x18618618, +/**/ 0x3FD1675C, 0xABABA000, +/**/ 0x3D38380E, 0x731F55C4, +/**/ 0x3FE86000, 0x00000000, +/**/ 0xBF38EF0F, 0x6AC71708, +/**/ 0x3FD1738C, 0x45A67000, +/**/ 0xBD39C6E9, 0x0032C176, +/**/ 0x3FE85800, 0x00000000, +/**/ 0x3EFFF3D3, 0xE00C2C20, +/**/ 0x3FD17FB9, 0x8E151000, +/**/ 0xBD3A8A8B, 0xA74A2684, +/**/ 0x3FE85000, 0x00000000, +/**/ 0x3F3CFBA0, 0xF9592266, +/**/ 0x3FD18BE4, 0x85D93000, +/**/ 0x3D3C167F, 0x6F3604AB, +/**/ 0x3FE85000, 0x00000000, +/**/ 0xBF1FE7B0, 0xFF3D87FA, +/**/ 0x3FD1980D, 0x2DD42000, +/**/ 0x3D2B7B3A, 0x7A361C9A, +/**/ 0x3FE84800, 0x00000000, +/**/ 0x3F331E8D, 0x918DC223, +/**/ 0x3FD1A433, 0x86E68000, +/**/ 0xBD07A850, 0x634E0AAC, +/**/ 0x3FE84800, 0x00000000, +/**/ 0xBF31BAF9, 0x8D76B549, +/**/ 0x3FD1B057, 0x91F08000, +/**/ 0xBD32DD46, 0x6DC55E2D, +/**/ 0x3FE84000, 0x00000000, +/**/ 0x3F22F2EC, 0xDC90C512, +/**/ 0x3FD1BC79, 0x4FD1D000, +/**/ 0xBD3CCF0C, 0x747BA7BE, +/**/ 0x3FE84000, 0x00000000, +/**/ 0xBF3B442A, 0x6A0916B9, +/**/ 0x3FD1C898, 0xC169A000, +/**/ 0xBD381410, 0xE5C62AFF, +/**/ 0x3FE83800, 0x00000000, +/**/ 0x3EA83801, 0x83801838, +/**/ 0x3FD1D4B5, 0xE796A000, +/**/ 0x3D222A5B, 0xD197BAC2, +/**/ 0x3FE83000, 0x00000000, +/**/ 0x3F3B6A41, 0xCBD11C5C, +/**/ 0x3FD1E0D0, 0xC3371000, +/**/ 0x3D3AF8F2, 0xA9B0D4A0, +/**/ 0x3FE83000, 0x00000000, +/**/ 0xBF225381, 0xCB7A3CD6, +/**/ 0x3FD1ECE9, 0x5528B000, +/**/ 0xBD184E7B, 0x09B4A3B8, +/**/ 0x3FE82800, 0x00000000, +/**/ 0x3F32500C, 0x152500C1, +/**/ 0x3FD1F8FF, 0x9E48A000, +/**/ 0x3D27946C, 0x040CBE77, +/**/ 0x3FE82800, 0x00000000, +/**/ 0xBF32285F, 0x14902134, +/**/ 0x3FD20513, 0x9F73B000, +/**/ 0x3CF6E15E, 0x1609E0A4, +/**/ 0x3FE82000, 0x00000000, +/**/ 0x3F22D9EB, 0xA4018213, +/**/ 0x3FD21125, 0x59861000, +/**/ 0x3D382E78, 0xBA2950C4, +/**/ 0x3FE82000, 0x00000000, +/**/ 0xBF3AEFFC, 0xFC6BBFF4, +/**/ 0x3FD21D34, 0xCD5B9000, +/**/ 0x3D3B552F, 0xB28BADAA, +/**/ 0x3FE81800, 0x00000000, +/**/ 0x3EE81818, 0x18181818, +/**/ 0x3FD22941, 0xFBCF8000, +/**/ 0xBD3A6976, 0xF5EB0963, +/**/ 0x3FE81000, 0x00000000, +/**/ 0x3F3C7F27, 0x4FF0F3C6, +/**/ 0x3FD2354C, 0xE5BC9000, +/**/ 0xBD3D78ED, 0x0602A663, +/**/ 0x3FE81000, 0x00000000, +/**/ 0xBF1ED344, 0x0A86941D, +/**/ 0x3FD24155, 0x8BFD1000, +/**/ 0x3D300FFF, 0x3228FCAD, +/**/ 0x3FE80800, 0x00000000, +/**/ 0x3F3424D0, 0x1B0BD52D, +/**/ 0x3FD24D5B, 0xEF6AF000, +/**/ 0xBCBDD780, 0xFC9FABDD, +/**/ 0x3FE80800, 0x00000000, +/**/ 0xBF2FE7F9, 0xFE7F9FE8, +/**/ 0x3FD25960, 0x10DF7000, +/**/ 0x3D38E7BC, 0x224EA3E3, +/**/ 0x3FE80000, 0x00000000, +/**/ 0x3F280180, 0x18018018, +/**/ 0x3FD26561, 0xF1338000, +/**/ 0x3D38B488, 0x66FAA45F, +/**/ 0x3FE80000, 0x00000000, +/**/ 0xBF37FD00, 0x5FF40180, +/**/ 0x3FD27161, 0x913F8000, +/**/ 0x3D34F4F1, 0xF61564B4, +/**/ 0x3FE7F800, 0x00000000, +/**/ 0x3F104AE8, 0x9750B6C7, +/**/ 0x3FD27D5E, 0xF1DB6000, +/**/ 0xBD092374, 0x78CAC9F4, +/**/ 0x3FE7F800, 0x00000000, +/**/ 0xBF3FD017, 0xF405FD01, +/**/ 0x3FD2895A, 0x13DE8000, +/**/ 0x3D3A8D7A, 0xD24C13F0, +/**/ 0x3FE7F000, 0x00000000, +/**/ 0xBF0D2BF1, 0xC9C5485E, +/**/ 0x3FD29552, 0xF81FF000, +/**/ 0x3D348D30, 0x1771C408, +/**/ 0x3FE7E800, 0x00000000, +/**/ 0x3F38927F, 0xD029DB60, +/**/ 0x3FD2A149, 0x9F763000, +/**/ 0xBD30DBBF, 0x51F3AADC, +/**/ 0x3FE7E800, 0x00000000, +/**/ 0xBF26504A, 0xB0A45169, +/**/ 0x3FD2AD3E, 0x0AB73000, +/**/ 0x3D2B972E, 0x488C359F, +/**/ 0x3FE7E000, 0x00000000, +/**/ 0x3F312A8A, 0xD278E8DD, +/**/ 0x3FD2B930, 0x3AB8A000, +/**/ 0xBD26DB12, 0xD6BFB0A5, +/**/ 0x3FE7E000, 0x00000000, +/**/ 0xBF327577, 0x24BB32E7, +/**/ 0x3FD2C520, 0x304F8000, +/**/ 0x3D230852, 0x8C342F39, +/**/ 0x3FE7D800, 0x00000000, +/**/ 0x3F23EF9A, 0xA4B45AEC, +/**/ 0x3FD2D10D, 0xEC508000, +/**/ 0x3D360C61, 0xF7088353, +/**/ 0x3FE7D800, 0x00000000, +/**/ 0xBF398DAF, 0x32748CC1, +/**/ 0x3FD2DCF9, 0x6F8FD000, +/**/ 0x3D20B4A2, 0x8E33C9CE, +/**/ 0x3FE7D000, 0x00000000, +/**/ 0x3F07D05F, 0x417D05F4, +/**/ 0x3FD2E8E2, 0xBAE12000, +/**/ 0xBD267B1E, 0x99B72BD8, +/**/ 0x3FE7C800, 0x00000000, +/**/ 0x3F3F8EF7, 0x431D3027, +/**/ 0x3FD2F4C9, 0xCF17A000, +/**/ 0x3D371F04, 0x9374B87B, +/**/ 0x3FE7C800, 0x00000000, +/**/ 0xBF0E77A3, 0xDAD83E6C, +/**/ 0x3FD300AE, 0xAD063000, +/**/ 0x3D342F56, 0x8B75FCAC, +/**/ 0x3FE7C000, 0x00000000, +/**/ 0x3F38E041, 0x588D1676, +/**/ 0x3FD30C91, 0x557F2000, +/**/ 0xBD142958, 0xA1451755, +/**/ 0x3FE7C000, 0x00000000, +/**/ 0xBF24C6DD, 0x1FE8414C, +/**/ 0x3FD31871, 0xC9544000, +/**/ 0x3D184FAB, 0x94CECFD9, +/**/ 0x3FE7B800, 0x00000000, +/**/ 0x3F3265F4, 0x81C2D3B2, +/**/ 0x3FD32450, 0x09570000, +/**/ 0x3D3D271B, 0x9BDAE59D, +/**/ 0x3FE7B800, 0x00000000, +/**/ 0xBF30C39C, 0xB6466407, +/**/ 0x3FD3302C, 0x16586000, +/**/ 0x3D36217D, 0xC2A3E08B, +/**/ 0x3FE7B000, 0x00000000, +/**/ 0x3F283FAD, 0x12B21224, +/**/ 0x3FD33C05, 0xF128E000, +/**/ 0xBD22B906, 0x380E1A7D, +/**/ 0x3FE7B000, 0x00000000, +/**/ 0xBF36EFB8, 0xF899E55D, +/**/ 0x3FD347DD, 0x9A988000, +/**/ 0xBD25594D, 0xD4C58092, +/**/ 0x3FE7A800, 0x00000000, +/**/ 0x3F1836B6, 0x3FF42B9F, +/**/ 0x3FD353B3, 0x1376E000, +/**/ 0xBD1331AF, 0xE6C26D9B, +/**/ 0x3FE7A800, 0x00000000, +/**/ 0xBF3CE7FD, 0x0B739FF4, +/**/ 0x3FD35F86, 0x5C933000, +/**/ 0xBD3B07DE, 0x4EA1A54A, +/**/ 0x3FE7A000, 0x00000000, +/**/ 0x3EC7A005, 0xE8017A00, +/**/ 0x3FD36B57, 0x76BC1000, +/**/ 0x3D116978, 0x5A9C223F, +/**/ 0x3FE79800, 0x00000000, +/**/ 0x3F3D535D, 0xB1CC5B7B, +/**/ 0x3FD37726, 0x62BFE000, +/**/ 0xBD3E9436, 0xAC53B023, +/**/ 0x3FE79800, 0x00000000, +/**/ 0xBF15EEAC, 0xE0DA37A9, +/**/ 0x3FD382F3, 0x216C5000, +/**/ 0xBD1061D2, 0x1D1A7F6D, +/**/ 0x3FE79000, 0x00000000, +/**/ 0x3F37C21E, 0x344E16D6, +/**/ 0x3FD38EBD, 0xB38ED000, +/**/ 0x3D290582, 0xE67D4CA0, +/**/ 0x3FE79000, 0x00000000, +/**/ 0xBF25E69A, 0x39C9E465, +/**/ 0x3FD39A86, 0x19F45000, +/**/ 0x3D18EE51, 0x937354F5, +/**/ 0x3FE78800, 0x00000000, +/**/ 0x3F32640B, 0xC52640BC, +/**/ 0x3FD3A64C, 0x55694000, +/**/ 0x3D37A71C, 0xBCD735D0, +/**/ 0x3FE78800, 0x00000000, +/**/ 0xBF3037DE, 0x2F6A09ED, +/**/ 0x3FD3B210, 0x66B9C000, +/**/ 0xBD33C1ED, 0x9811560E, +/**/ 0x3FE78000, 0x00000000, +/**/ 0x3F2A71DC, 0x01781A72, +/**/ 0x3FD3BDD2, 0x4EB15000, +/**/ 0xBD3257B4, 0x970E6ED9, +/**/ 0x3FE78000, 0x00000000, +/**/ 0xBF354996, 0xA9EEBFF4, +/**/ 0x3FD3C992, 0x0E1B2000, +/**/ 0x3D141C28, 0xAA680B76, +/**/ 0x3FE77800, 0x00000000, +/**/ 0x3F208119, 0xAC60D341, +/**/ 0x3FD3D54F, 0xA5C1F000, +/**/ 0x3D3C3E1C, 0xD9A395E3, +/**/ 0x3FE77800, 0x00000000, +/**/ 0xBF3A28AE, 0x742E2DD0, +/**/ 0x3FD3E10B, 0x16701000, +/**/ 0x3D3F3BCF, 0x145429C7, +/**/ 0x3FE77000, 0x00000000, +/**/ 0x3F0BD584, 0x36340177, +/**/ 0x3FD3ECC4, 0x60EF6000, +/**/ 0xBD060286, 0x27C1300F, +/**/ 0x3FE77000, 0x00000000, +/**/ 0xBF3ED55D, 0x240C7174, +/**/ 0x3FD3F87B, 0x86094000, +/**/ 0xBD35DFD7, 0x54589889, +/**/ 0x3FE76800, 0x00000000, +/**/ 0xBEF18DE5, 0xAB277F45, +/**/ 0x3FD40430, 0x8686A000, +/**/ 0x3D3F8EF4, 0x3049F7D3, +/**/ 0x3FE76000, 0x00000000, +/**/ 0x3F3CB026, 0x01D3C7B8, +/**/ 0x3FD40FE3, 0x63303000, +/**/ 0x3D3E5C5F, 0xE79F05C6, +/**/ 0x3FE76000, 0x00000000, +/**/ 0xBF15E95B, 0xA9D08664, +/**/ 0x3FD41B94, 0x1CCE1000, +/**/ 0xBD304690, 0x13E43FC9, +/**/ 0x3FE75800, 0x00000000, +/**/ 0x3F3867A4, 0x097CFD43, +/**/ 0x3FD42742, 0xB427E000, +/**/ 0xBD398727, 0x02B82675, +/**/ 0x3FE75800, 0x00000000, +/**/ 0xBF2353DF, 0xE8A9353E, +/**/ 0x3FD432EF, 0x2A04F000, +/**/ 0xBD3FB129, 0x931715AD, +/**/ 0x3FE75000, 0x00000000, +/**/ 0x3F3450E6, 0x4F13DC4A, +/**/ 0x3FD43E99, 0x7F2C1000, +/**/ 0x3D1C3F72, 0x40C41A04, +/**/ 0x3FE75000, 0x00000000, +/**/ 0xBF2B4FBF, 0xE8B1B4FC, +/**/ 0x3FD44A41, 0xB463C000, +/**/ 0x3D31EE28, 0xF37CF612, +/**/ 0x3FE74800, 0x00000000, +/**/ 0x3F306BB6, 0x7E458100, +/**/ 0x3FD455E7, 0xCA720000, +/**/ 0x3D1AD8C6, 0x36629AED, +/**/ 0x3FE74800, 0x00000000, +/**/ 0xBF31745D, 0x1745D174, +/**/ 0x3FD4618B, 0xC21C6000, +/**/ 0xBD13D82F, 0x484C84CC, +/**/ 0x3FE74000, 0x00000000, +/**/ 0x3F296FBD, 0x236DEC04, +/**/ 0x3FD46D2D, 0x9C280000, +/**/ 0x3D359B27, 0x5F67F75A, +/**/ 0x3FE74000, 0x00000000, +/**/ 0xBF350F9D, 0x3B304B87, +/**/ 0x3FD478CD, 0x5959B000, +/**/ 0x3D2EC89B, 0xF0C8D098, +/**/ 0x3FE73800, 0x00000000, +/**/ 0x3F226A51, 0xA4EBDC70, +/**/ 0x3FD4846A, 0xFA75C000, +/**/ 0xBD263EA2, 0xE3798DCE, +/**/ 0x3FE73800, 0x00000000, +/**/ 0xBF3879D5, 0xF00B9A78, +/**/ 0x3FD49006, 0x80401000, +/**/ 0xBD38BCCF, 0xFE1A0F8C, +/**/ 0x3FE73000, 0x00000000, +/**/ 0x3F178D7F, 0x5DAAD90C, +/**/ 0x3FD49B9F, 0xEB7C1000, +/**/ 0x3D3DAC1C, 0x58AB60D7, +/**/ 0x3FE73000, 0x00000000, +/**/ 0xBF3BB33C, 0x783709C7, +/**/ 0x3FD4A737, 0x3CED0000, +/**/ 0xBD39A234, 0xEBF35449, +/**/ 0x3FE72800, 0x00000000, +/**/ 0x3F061274, 0x265AD23A, +/**/ 0x3FD4B2CC, 0x75556000, +/**/ 0xBD380FCB, 0xC78BFA4B, +/**/ 0x3FE72800, 0x00000000, +/**/ 0xBF3EBC05, 0xC90A1FD2, +/**/ 0x3FD4BE5F, 0x95778000, +/**/ 0xBD3D7C92, 0xCD9AD824, +/**/ 0x3FE72000, 0x00000000, +/**/ 0xBEC71FFA, 0x38017200, +/**/ 0x3FD4C9F0, 0x9E153000, +/**/ 0xBD2E1DDE, 0x70E02DE0, +/**/ 0x3FE71800, 0x00000000, +/**/ 0x3F3E6B99, 0x74A050E1, +/**/ 0x3FD4D57F, 0x8FEFE000, +/**/ 0x3D23F926, 0x7FD06868, +/**/ 0x3FE71800, 0x00000000, +/**/ 0xBF077400, 0xB8BD1180, +/**/ 0x3FD4E10C, 0x6BC8A000, +/**/ 0x3CF8283F, 0x1636F061, +/**/ 0x3FE71000, 0x00000000, +/**/ 0x3F3BC36C, 0xE3E0453A, +/**/ 0x3FD4EC97, 0x32600000, +/**/ 0x3D234D7A, 0xAF04D104, +/**/ 0x3FE71000, 0x00000000, +/**/ 0xBF15FA98, 0x6935DDC5, +/**/ 0x3FD4F81F, 0xE4764000, +/**/ 0xBD27FCF6, 0x434FF08D, +/**/ 0x3FE70800, 0x00000000, +/**/ 0x3F394B40, 0x7337CF08, +/**/ 0x3FD503A6, 0x82CB2000, +/**/ 0xBD2A68C8, 0xF16F9B5D, +/**/ 0x3FE70800, 0x00000000, +/**/ 0xBF1F7B97, 0xA835403A, +/**/ 0x3FD50F2B, 0x0E1E0000, +/**/ 0x3D3A0940, 0x8C47B8D8, +/**/ 0x3FE70000, 0x00000000, +/**/ 0x3F3702E0, 0x5C0B8170, +/**/ 0x3FD51AAD, 0x872E0000, +/**/ 0xBD3F4BD8, 0xDB0A7CC1, +/**/ 0x3FE70000, 0x00000000, +/**/ 0xBF241EE6, 0x4F67A855, +/**/ 0x3FD5262D, 0xEEB99000, +/**/ 0xBD3E1B9F, 0x70894A01, +/**/ 0x3FE6F800, 0x00000000, +/**/ 0x3F34EA19, 0x221C0170, +/**/ 0x3FD531AC, 0x457EE000, +/**/ 0x3D3DF83B, 0x7D931501, +/**/ 0x3FE6F800, 0x00000000, +/**/ 0xBF282102, 0x5508CA5C, +/**/ 0x3FD53D28, 0x8C3BE000, +/**/ 0xBD111397, 0xEB6DFAC5, +/**/ 0x3FE6F000, 0x00000000, +/**/ 0x3F3300B7, 0x9300B793, +/**/ 0x3FD548A2, 0xC3ADD000, +/**/ 0x3D23167E, 0x63081CF7, +/**/ 0x3FE6F000, 0x00000000, +/**/ 0xBF2BC486, 0x005BB90F, +/**/ 0x3FD5541A, 0xEC91C000, +/**/ 0xBCF816AA, 0xDC72EEBA, +/**/ 0x3FE6E800, 0x00000000, +/**/ 0x3F314688, 0xC5A3A00B, +/**/ 0x3FD55F91, 0x07A44000, +/**/ 0xBD11E647, 0x78DF4A62, +/**/ 0x3FE6E800, 0x00000000, +/**/ 0xBF2F09D6, 0xDA9C5AE1, +/**/ 0x3FD56B05, 0x15A18000, +/**/ 0x3D29247B, 0xBC4A23FC, +/**/ 0x3FE6E000, 0x00000000, +/**/ 0x3F2F76B4, 0x337C6CB1, +/**/ 0x3FD57677, 0x17456000, +/**/ 0xBD364EAD, 0x9524D7CA, +/**/ 0x3FE6E000, 0x00000000, +/**/ 0xBF30F8AC, 0xEDF4EC87, +/**/ 0x3FD581E7, 0x0D4B3000, +/**/ 0xBD1F31E1, 0xB12D8F1D, +/**/ 0x3FE6D800, 0x00000000, +/**/ 0x3F2CBDF2, 0x6EAEF381, +/**/ 0x3FD58D54, 0xF86E0000, +/**/ 0x3D2791F3, 0x0A795215, +/**/ 0x3FE6D800, 0x00000000, +/**/ 0xBF323DB9, 0xB624BFF5, +/**/ 0x3FD598C0, 0xD9688000, +/**/ 0xBD385F49, 0x70D96DA4, +/**/ 0x3FE6D000, 0x00000000, +/**/ 0x3F2A6268, 0x1C860FB0, +/**/ 0x3FD5A42A, 0xB0F4D000, +/**/ 0xBCDE63AF, 0x2DF7BA69, +/**/ 0x3FE6D000, 0x00000000, +/**/ 0xBF335443, 0xB253BAE1, +/**/ 0x3FD5AF92, 0x7FCCE000, +/**/ 0xBD1C032F, 0xF5FFC77A, +/**/ 0x3FE6C800, 0x00000000, +/**/ 0x3F2863B1, 0xAB4294D4, +/**/ 0x3FD5BAF8, 0x46AA2000, +/**/ 0xBD339AE8, 0xF873FA41, +/**/ 0x3FE6C800, 0x00000000, +/**/ 0xBF343C7C, 0x87EAA6DF, +/**/ 0x3FD5C65C, 0x0645A000, +/**/ 0xBD39FE06, 0x0180EE65, +/**/ 0x3FE6C000, 0x00000000, +/**/ 0x3F26C16C, 0x16C16C17, +/**/ 0x3FD5D1BD, 0xBF581000, +/**/ 0xBD38D6BD, 0xC9C7C238, +/**/ 0x3FE6C000, 0x00000000, +/**/ 0xBF34F695, 0x95C33E00, +/**/ 0x3FD5DD1D, 0x7299C000, +/**/ 0xBD38AF61, 0x8815CE17, +/**/ 0x3FE6B800, 0x00000000, +/**/ 0x3F257B34, 0xE7802D73, +/**/ 0x3FD5E87B, 0x20C29000, +/**/ 0x3D3527D1, 0x8F7738FA, +/**/ 0x3FE6B800, 0x00000000, +/**/ 0xBF3582BF, 0xF4A5582C, +/**/ 0x3FD5F3D6, 0xCA8A2000, +/**/ 0x3D37AF84, 0x8E19CC75, +/**/ 0x3FE6B000, 0x00000000, +/**/ 0x3F2490AA, 0x31A3CFC7, +/**/ 0x3FD5FF30, 0x70A79000, +/**/ 0x3D2E9E43, 0x9F105039, +/**/ 0x3FE6B000, 0x00000000, +/**/ 0xBF35E12C, 0x77C30E5A, +/**/ 0x3FD60A88, 0x13D1A000, +/**/ 0x3D36E9B9, 0xC879AF55, +/**/ 0x3FE6A800, 0x00000000, +/**/ 0x3F24016A, 0x94016A94, +/**/ 0x3FD615DD, 0xB4BEC000, +/**/ 0x3D13C7CA, 0x90BC04B2, +/**/ 0x3FE6A800, 0x00000000, +/**/ 0xBF36120B, 0xAD33D63F, +/**/ 0x3FD62131, 0x5424F000, +/**/ 0xBD3382FC, 0x4AA68669, +/**/ 0x3FE6A000, 0x00000000, +/**/ 0x3F23CD15, 0x3729043E, +/**/ 0x3FD62C82, 0xF2B9C000, +/**/ 0x3D3E54BD, 0xBD7C8A98 } }; + +static const union {int4 i[4350]; double x[2175]; } vj = { .i = { +/**/ 0x3F46A400, 0x7D161C28, +/**/ 0xBF46A200, 0x20600000, +/**/ 0x3D27DC4E, 0xAA7623D9, +/**/ 0x3F4693FA, 0xD596E639, +/**/ 0xBF4691FD, 0x4CE00000, +/**/ 0x3D26B0CF, 0x29C3F0AD, +/**/ 0x3F4683F5, 0x3219CE89, +/**/ 0xBF4681FA, 0x7B600000, +/**/ 0x3D22B290, 0x95B9FDCC, +/**/ 0x3F4673EF, 0x929ED397, +/**/ 0xBF4671F7, 0xABE00000, +/**/ 0x3D17C727, 0xFA2F2D87, +/**/ 0x3F4663E9, 0xF725F3E2, +/**/ 0xBF4661F4, 0xDE600000, +/**/ 0x3CF22ED3, 0x6EDBFF1C, +/**/ 0x3F4653E4, 0x5FAF2DE9, +/**/ 0xBF4651F2, 0x12E00000, +/**/ 0xBD144936, 0x157812BB, +/**/ 0x3F4643DE, 0xCC3A802B, +/**/ 0xBF4641EF, 0x49600000, +/**/ 0xBD2959CB, 0x60314E05, +/**/ 0x3F4633D9, 0x3CC7E927, +/**/ 0xBF4631EC, 0x81E00000, +/**/ 0xBD35ABDA, 0xC3638E99, +/**/ 0x3F4623D3, 0xB157675C, +/**/ 0xBF4621E9, 0xBC800000, +/**/ 0x3D3FF1D3, 0xC63F9A21, +/**/ 0x3F4613CE, 0x29E8F948, +/**/ 0xBF4611E6, 0xF9000000, +/**/ 0x3D342D26, 0x71EEE611, +/**/ 0x3F4603C8, 0xA67C9D6B, +/**/ 0xBF4601E4, 0x37800000, +/**/ 0x3D1C1C77, 0x11A09689, +/**/ 0x3F45F3C3, 0x27125244, +/**/ 0xBF45F1E1, 0x78000000, +/**/ 0xBD1DFD16, 0xF7DC643C, +/**/ 0x3F45E3BD, 0xABAA1651, +/**/ 0xBF45E1DE, 0xBA800000, +/**/ 0xBD376503, 0x91318A02, +/**/ 0x3F45D3B8, 0x3443E812, +/**/ 0xBF45D1DB, 0xFF200000, +/**/ 0x3D3756E4, 0xCE55DCDD, +/**/ 0x3F45C3B2, 0xC0DFC606, +/**/ 0xBF45C1D9, 0x45A00000, +/**/ 0x3D12D5CF, 0x8F6F8FA0, +/**/ 0x3F45B3AD, 0x517DAEAB, +/**/ 0xBF45B1D6, 0x8E200000, +/**/ 0xBD2E90AB, 0x9B85DC2C, +/**/ 0x3F45A3A7, 0xE61DA081, +/**/ 0xBF45A1D3, 0xD8C00000, +/**/ 0x3D3B5E88, 0x3BF5AC54, +/**/ 0x3F4593A2, 0x7EBF9A07, +/**/ 0xBF4591D1, 0x25400000, +/**/ 0x3D12AC3A, 0x0C86DDB1, +/**/ 0x3F45839D, 0x1B6399BB, +/**/ 0xBF4581CE, 0x73C00000, +/**/ 0xBD3361C2, 0x76830985, +/**/ 0x3F457397, 0xBC099E1C, +/**/ 0xBF4571CB, 0xC4600000, +/**/ 0x3D333915, 0xD062EBFF, +/**/ 0x3F456392, 0x60B1A5AA, +/**/ 0xBF4561C9, 0x16E00000, +/**/ 0xBD1E0DA0, 0x9CC4988F, +/**/ 0x3F45538D, 0x095BAEE4, +/**/ 0xBF4551C6, 0x6B800000, +/**/ 0x3D3C69C4, 0x235BC18A, +/**/ 0x3F454387, 0xB607B848, +/**/ 0xBF4541C3, 0xC2000000, +/**/ 0xBCEFCC99, 0xF7737723, +/**/ 0x3F453382, 0x66B5C056, +/**/ 0xBF4531C1, 0x1A800000, +/**/ 0xBD3FBAE2, 0x809CBCBB, +/**/ 0x3F45237D, 0x1B65C58C, +/**/ 0xBF4521BE, 0x75200000, +/**/ 0x3CCAA5C8, 0x194FEE63, +/**/ 0x3F451377, 0xD417C66A, +/**/ 0xBF4511BB, 0xD1C00000, +/**/ 0x3D3ED325, 0xE1CC7BBC, +/**/ 0x3F450372, 0x90CBC16E, +/**/ 0xBF4501B9, 0x30400000, +/**/ 0xBD0F0298, 0x68AB3742, +/**/ 0x3F44F36D, 0x5181B517, +/**/ 0xBF44F1B6, 0x90E00000, +/**/ 0x3D381BE1, 0x41E67AD9, +/**/ 0x3F44E368, 0x16399FE6, +/**/ 0xBF44E1B3, 0xF3600000, +/**/ 0xBD2A6E79, 0x668D3662, +/**/ 0x3F44D362, 0xDEF38058, +/**/ 0xBF44D1B1, 0x58000000, +/**/ 0x3D284EA7, 0x21F8B7C2, +/**/ 0x3F44C35D, 0xABAF54EC, +/**/ 0xBF44C1AE, 0xBE800000, +/**/ 0xBD3BC76D, 0x7417D9C5, +/**/ 0x3F44B358, 0x7C6D1C22, +/**/ 0xBF44B1AC, 0x27200000, +/**/ 0xBD1409FD, 0x16AAD1FC, +/**/ 0x3F44A353, 0x512CD479, +/**/ 0xBF44A1A9, 0x91C00000, +/**/ 0x3D30771E, 0x98BC14FD, +/**/ 0x3F44934E, 0x29EE7C70, +/**/ 0xBF4491A6, 0xFE400000, +/**/ 0xBD3B5993, 0x5CCB7232, +/**/ 0x3F448349, 0x06B21285, +/**/ 0xBF4481A4, 0x6CE00000, +/**/ 0xBD20E729, 0x5512F9C2, +/**/ 0x3F447343, 0xE7779538, +/**/ 0xBF4471A1, 0xDD800000, +/**/ 0x3D225436, 0x55B30899, +/**/ 0x3F44633E, 0xCC3F0308, +/**/ 0xBF44619F, 0x50200000, +/**/ 0x3D39807C, 0x9E54E31F, +/**/ 0x3F445339, 0xB5085A73, +/**/ 0xBF44519C, 0xC4A00000, +/**/ 0xBD376F6F, 0xD5804C0E, +/**/ 0x3F444334, 0xA1D399FA, +/**/ 0xBF44419A, 0x3B400000, +/**/ 0xBD234953, 0x6CDE6425, +/**/ 0x3F44332F, 0x92A0C01A, +/**/ 0xBF443197, 0xB3E00000, +/**/ 0x3D070E7B, 0xAAF6596F, +/**/ 0x3F44232A, 0x876FCB54, +/**/ 0xBF442195, 0x2E800000, +/**/ 0x3D2C49F8, 0x4EC011F1, +/**/ 0x3F441325, 0x8040BA25, +/**/ 0xBF441192, 0xAB200000, +/**/ 0x3D3825DC, 0xD8AAA7EB, +/**/ 0x3F440320, 0x7D138B0E, +/**/ 0xBF440190, 0x29A00000, +/**/ 0xBD3F1A8D, 0xFE0B73D6, +/**/ 0x3F43F31B, 0x7DE83C8C, +/**/ 0xBF43F18D, 0xAA400000, +/**/ 0xBD379B43, 0xE46CA26B, +/**/ 0x3F43E316, 0x82BECD20, +/**/ 0xBF43E18B, 0x2CE00000, +/**/ 0xBD315B44, 0x6283780D, +/**/ 0x3F43D311, 0x8B973B49, +/**/ 0xBF43D188, 0xB1800000, +/**/ 0xBD28B31E, 0x017589BE, +/**/ 0x3F43C30C, 0x98718584, +/**/ 0xBF43C186, 0x38200000, +/**/ 0xBD212A46, 0x8FBB296E, +/**/ 0x3F43B307, 0xA94DAA52, +/**/ 0xBF43B183, 0xC0C00000, +/**/ 0xBD183403, 0x045CBBD2, +/**/ 0x3F43A302, 0xBE2BA832, +/**/ 0xBF43A181, 0x4B600000, +/**/ 0xBD13009B, 0xD7CC5936, +/**/ 0x3F4392FD, 0xD70B7DA2, +/**/ 0xBF43917E, 0xD8000000, +/**/ 0xBD12B655, 0xC1742279, +/**/ 0x3F4382F8, 0xF3ED2921, +/**/ 0xBF43817C, 0x66A00000, +/**/ 0xBD17512E, 0xEA83FAE8, +/**/ 0x3F4372F4, 0x14D0A930, +/**/ 0xBF437179, 0xF7400000, +/**/ 0xBD206692, 0xBED65875, +/**/ 0x3F4362EF, 0x39B5FC4C, +/**/ 0xBF436177, 0x89E00000, +/**/ 0xBD27931B, 0xD38FFE9E, +/**/ 0x3F4352EA, 0x629D20F5, +/**/ 0xBF435175, 0x1E800000, +/**/ 0xBD309618, 0xE524208F, +/**/ 0x3F4342E5, 0x8F8615AA, +/**/ 0xBF434172, 0xB5200000, +/**/ 0xBD3697E9, 0xDD4C72C5, +/**/ 0x3F4332E0, 0xC070D8EB, +/**/ 0xBF433170, 0x4DC00000, +/**/ 0xBD3DCE00, 0x5E6E12C3, +/**/ 0x3F4322DB, 0xF55D6935, +/**/ 0xBF43216D, 0xE8800000, +/**/ 0x3D39C8A4, 0x0AE9A8CE, +/**/ 0x3F4312D7, 0x2E4BC509, +/**/ 0xBF43116B, 0x85200000, +/**/ 0x3D302D03, 0xD1CD2FA1, +/**/ 0x3F4302D2, 0x6B3BEAE5, +/**/ 0xBF430169, 0x23C00000, +/**/ 0x3D15807D, 0xA3BADFD1, +/**/ 0x3F42F2CD, 0xAC2DD949, +/**/ 0xBF42F166, 0xC4600000, +/**/ 0xBD1A7422, 0xF57F0504, +/**/ 0x3F42E2C8, 0xF1218EB3, +/**/ 0xBF42E164, 0x67000000, +/**/ 0xBD33C974, 0x2F2C781C, +/**/ 0x3F42D2C4, 0x3A1709A3, +/**/ 0xBF42D162, 0x0BC00000, +/**/ 0x3D3DDBDD, 0x851A1E61, +/**/ 0x3F42C2BF, 0x870E4898, +/**/ 0xBF42C15F, 0xB2600000, +/**/ 0x3D2CA7D9, 0xA14AA8FD, +/**/ 0x3F42B2BA, 0xD8074A10, +/**/ 0xBF42B15D, 0x5B000000, +/**/ 0xBD03022E, 0xDDCDDFF5, +/**/ 0x3F42A2B6, 0x2D020C8C, +/**/ 0xBF42A15B, 0x05A00000, +/**/ 0xBD343FBA, 0x0F9231A8, +/**/ 0x3F4292B1, 0x85FE8E8A, +/**/ 0xBF429158, 0xB2600000, +/**/ 0x3D38B690, 0xA52C9CCF, +/**/ 0x3F4282AC, 0xE2FCCE8A, +/**/ 0xBF428156, 0x61000000, +/**/ 0x3D120E6A, 0xC8CC82EB, +/**/ 0x3F4272A8, 0x43FCCB0A, +/**/ 0xBF427154, 0x11A00000, +/**/ 0xBD30D79B, 0x792E6C51, +/**/ 0x3F4262A3, 0xA8FE8289, +/**/ 0xBF426151, 0xC4600000, +/**/ 0x3D38A5EE, 0x91F7F7AA, +/**/ 0x3F42529F, 0x1201F387, +/**/ 0xBF42514F, 0x79000000, +/**/ 0x3CEFA728, 0x46C2E8BA, +/**/ 0x3F42429A, 0x7F071C84, +/**/ 0xBF42414D, 0x2FA00000, +/**/ 0xBD37D0BA, 0xFA447A17, +/**/ 0x3F423295, 0xF00DFBFD, +/**/ 0xBF42314A, 0xE8600000, +/**/ 0x3D2C7A24, 0x94AF3FED, +/**/ 0x3F422291, 0x65169072, +/**/ 0xBF422148, 0xA3000000, +/**/ 0xBD29B0BD, 0x050CEA04, +/**/ 0x3F42128C, 0xDE20D863, +/**/ 0xBF421146, 0x5FC00000, +/**/ 0x3D36EFF3, 0x0C3035EB, +/**/ 0x3F420288, 0x5B2CD24E, +/**/ 0xBF420144, 0x1E600000, +/**/ 0xBD19A3E2, 0x73569B27, +/**/ 0x3F41F283, 0xDC3A7CB2, +/**/ 0xBF41F141, 0xDF200000, +/**/ 0x3D3B1DDE, 0xEEB67715, +/**/ 0x3F41E27F, 0x6149D610, +/**/ 0xBF41E13F, 0xA1C00000, +/**/ 0xBD11EA17, 0x94F49154, +/**/ 0x3F41D27A, 0xEA5ADCE5, +/**/ 0xBF41D13D, 0x66800000, +/**/ 0x3D3ACED9, 0x52DD9D37, +/**/ 0x3F41C276, 0x776D8FB1, +/**/ 0xBF41C13B, 0x2D200000, +/**/ 0xBD1C140B, 0xF72D8EEB, +/**/ 0x3F41B272, 0x0881ECF4, +/**/ 0xBF41B138, 0xF5E00000, +/**/ 0x3D360AE5, 0x939583E1, +/**/ 0x3F41A26D, 0x9D97F32C, +/**/ 0xBF41A136, 0xC0800000, +/**/ 0xBD2C00D9, 0x1D246C7C, +/**/ 0x3F419269, 0x36AFA0D9, +/**/ 0xBF419134, 0x8D400000, +/**/ 0x3D29B40E, 0x0B955CFB, +/**/ 0x3F418264, 0xD3C8F479, +/**/ 0xBF418132, 0x5BE00000, +/**/ 0xBD3964BF, 0x45A6C249, +/**/ 0x3F417260, 0x74E3EC8D, +/**/ 0xBF417130, 0x2CA00000, +/**/ 0xBCE777E0, 0xF3363612, +/**/ 0x3F41625C, 0x1A008792, +/**/ 0xBF41612D, 0xFF600000, +/**/ 0x3D36D608, 0x28DE8296, +/**/ 0x3F415257, 0xC31EC409, +/**/ 0xBF41512B, 0xD4000000, +/**/ 0xBD32AE69, 0x4BB1B788, +/**/ 0x3F414253, 0x703EA071, +/**/ 0xBF414129, 0xAAC00000, +/**/ 0x3D05BF68, 0x170ECD8C, +/**/ 0x3F41324F, 0x21601B48, +/**/ 0xBF413127, 0x83800000, +/**/ 0x3D370A0B, 0x7C653BFC, +/**/ 0x3F41224A, 0xD683330E, +/**/ 0xBF412125, 0x5E200000, +/**/ 0xBD35B70D, 0x77BBBEBF, +/**/ 0x3F411246, 0x8FA7E642, +/**/ 0xBF411123, 0x3AE00000, +/**/ 0xBD0C52EB, 0x93ABC1CD, +/**/ 0x3F410242, 0x4CCE3363, +/**/ 0xBF410121, 0x19A00000, +/**/ 0x3D2B2237, 0xE5C6F4C7, +/**/ 0x3F40F23E, 0x0DF618F1, +/**/ 0xBF40F11E, 0xFA600000, +/**/ 0x3D3D9C5F, 0x1E9A50AD, +/**/ 0x3F40E239, 0xD31F956A, +/**/ 0xBF40E11C, 0xDD000000, +/**/ 0xBD336793, 0x8965F0DA, +/**/ 0x3F40D235, 0x9C4AA74E, +/**/ 0xBF40D11A, 0xC1C00000, +/**/ 0xBD15E6EE, 0x7E49E231, +/**/ 0x3F40C231, 0x69774D1D, +/**/ 0xBF40C118, 0xA8800000, +/**/ 0x3D1D9B9D, 0x04FD621C, +/**/ 0x3F40B22D, 0x3AA58554, +/**/ 0xBF40B116, 0x91400000, +/**/ 0x3D333B55, 0x7DD9EED3, +/**/ 0x3F40A229, 0x0FD54E74, +/**/ 0xBF40A114, 0x7C000000, +/**/ 0x3D3E048F, 0x7AA78478, +/**/ 0x3F409224, 0xE906A6FC, +/**/ 0xBF409112, 0x68A00000, +/**/ 0xBD383C6A, 0x644DDE88, +/**/ 0x3F408220, 0xC6398D6B, +/**/ 0xBF408110, 0x57600000, +/**/ 0xBD2F0D2F, 0x76B8C83A, +/**/ 0x3F40721C, 0xA76E0040, +/**/ 0xBF40710E, 0x48200000, +/**/ 0xBD1F63E0, 0x9CE99FD3, +/**/ 0x3F406218, 0x8CA3FDFB, +/**/ 0xBF40610C, 0x3AE00000, +/**/ 0xBCF328B4, 0x4FE774F2, +/**/ 0x3F405214, 0x75DB851A, +/**/ 0xBF40510A, 0x2FA00000, +/**/ 0x3D11B6BD, 0x3782BCD4, +/**/ 0x3F404210, 0x6314941D, +/**/ 0xBF404108, 0x26600000, +/**/ 0x3D22116F, 0xE7183792, +/**/ 0x3F40320C, 0x544F2983, +/**/ 0xBF403106, 0x1F200000, +/**/ 0x3D293F1E, 0x1B995B3D, +/**/ 0x3F402208, 0x498B43CB, +/**/ 0xBF402104, 0x19E00000, +/**/ 0x3D2E6669, 0xFC162630, +/**/ 0x3F401204, 0x42C8E175, +/**/ 0xBF401102, 0x16A00000, +/**/ 0x3D30C4AA, 0x254FC9F8, +/**/ 0x3F400200, 0x40080100, +/**/ 0xBF400100, 0x15600000, +/**/ 0x3D3154EE, 0xE4431F92, +/**/ 0x3F3FE3F8, 0x829141D6, +/**/ 0xBF3FE1FC, 0x2C400000, +/**/ 0x3D30E503, 0x9B2D30FB, +/**/ 0x3F3FC3F0, 0x8D157F6B, +/**/ 0xBF3FC1F8, 0x31C00000, +/**/ 0x3D2EEBD1, 0x53EBD670, +/**/ 0x3F3FA3E8, 0x9F9CB7BC, +/**/ 0xBF3FA1F4, 0x3B400000, +/**/ 0x3D2A113C, 0xE04A16E0, +/**/ 0x3F3F83E0, 0xBA26E7CA, +/**/ 0xBF3F81F0, 0x48C00000, +/**/ 0x3D233C4A, 0x99C43E34, +/**/ 0x3F3F63D8, 0xDCB40C91, +/**/ 0xBF3F61EC, 0x5A400000, +/**/ 0x3D14DDF6, 0x7BD210C1, +/**/ 0x3F3F43D1, 0x07442311, +/**/ 0xBF3F41E8, 0x6FC00000, +/**/ 0xBCC52C1D, 0x9E4B51C8, +/**/ 0x3F3F23C9, 0x39D72849, +/**/ 0xBF3F21E4, 0x89400000, +/**/ 0xBD1A196F, 0x8EA8C754, +/**/ 0x3F3F03C1, 0x746D1936, +/**/ 0xBF3F01E0, 0xA6C00000, +/**/ 0xBD2BB719, 0xF95AF98D, +/**/ 0x3F3EE3B9, 0xB705F2D8, +/**/ 0xBF3EE1DC, 0xC8400000, +/**/ 0xBD3628EB, 0x28FFD598, +/**/ 0x3F3EC3B2, 0x01A1B22C, +/**/ 0xBF3EC1D8, 0xEDC00000, +/**/ 0xBD3F6D76, 0x0BBAC8F8, +/**/ 0x3F3EA3AA, 0x54405432, +/**/ 0xBF3EA1D5, 0x17800000, +/**/ 0x3D3657D2, 0xB7A7EE0D, +/**/ 0x3F3E83A2, 0xAEE1D5E8, +/**/ 0xBF3E81D1, 0x45000000, +/**/ 0x3D264FDE, 0xFA9CCC78, +/**/ 0x3F3E639B, 0x1186344C, +/**/ 0xBF3E61CD, 0x76800000, +/**/ 0xBCEF83EB, 0xE02EF455, +/**/ 0x3F3E4393, 0x7C2D6C5E, +/**/ 0xBF3E41C9, 0xAC000000, +/**/ 0xBD2C26B3, 0x03C3E129, +/**/ 0x3F3E238B, 0xEED77B1B, +/**/ 0xBF3E21C5, 0xE5800000, +/**/ 0xBD3C1CBE, 0x904D773D, +/**/ 0x3F3E0384, 0x69845D83, +/**/ 0xBF3E01C2, 0x23400000, +/**/ 0x3D34E8B1, 0xD0615454, +/**/ 0x3F3DE37C, 0xEC341093, +/**/ 0xBF3DE1BE, 0x64C00000, +/**/ 0x3D13F7DF, 0xE9BE933E, +/**/ 0x3F3DC375, 0x76E6914B, +/**/ 0xBF3DC1BA, 0xAA400000, +/**/ 0xBD27B7D7, 0x707B004A, +/**/ 0x3F3DA36E, 0x099BDCA9, +/**/ 0xBF3DA1B6, 0xF3C00000, +/**/ 0xBD3DA3F8, 0xEE2141C3, +/**/ 0x3F3D8366, 0xA453EFAC, +/**/ 0xBF3D81B3, 0x41800000, +/**/ 0x3D2F4DA1, 0x63D21825, +/**/ 0x3F3D635F, 0x470EC752, +/**/ 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0xBF2C80CB, 0x17800000, +/**/ 0xBD12D119, 0x8D8D1C8F, +/**/ 0x3F2C418F, 0x1E05880E, +/**/ 0xBF2C40C7, 0x8B800000, +/**/ 0x3D347649, 0x544D2574, +/**/ 0x3F2C0188, 0x15712C30, +/**/ 0xBF2C00C4, 0x07000000, +/**/ 0xBD32D030, 0x4EEA9E68, +/**/ 0x3F2BC181, 0x1CDF709C, +/**/ 0xBF2BC0C0, 0x8B000000, +/**/ 0x3D15E533, 0x74A84109, +/**/ 0x3F2B817A, 0x34504F50, +/**/ 0xBF2B80BD, 0x17000000, +/**/ 0x3D3D53C1, 0x025FBF68, +/**/ 0x3F2B4173, 0x5BC3C24B, +/**/ 0xBF2B40B9, 0xAA800000, +/**/ 0xBD267FA7, 0x6BAA2FA8, +/**/ 0x3F2B016C, 0x9339C38C, +/**/ 0xBF2B00B6, 0x46800000, +/**/ 0x3D277F1D, 0xBB3FDE1E, +/**/ 0x3F2AC165, 0xDAB24D11, +/**/ 0xBF2AC0B2, 0xEA000000, +/**/ 0xBD3DAD17, 0x1A8CDBE2, +/**/ 0x3F2A815F, 0x322D58D9, +/**/ 0xBF2A80AF, 0x96000000, +/**/ 0xBD1E1315, 0xD81CF36E, +/**/ 0x3F2A4158, 0x99AAE0E3, +/**/ 0xBF2A40AC, 0x4A000000, +/**/ 0x3D2C7307, 0xE649E7B4, +/**/ 0x3F2A0152, 0x112ADF2D, +/**/ 0xBF2A00A9, 0x05800000, +/**/ 0xBD3C713A, 0xB77435EC, +/**/ 0x3F29C14B, 0x98AD4DB7, +/**/ 0xBF29C0A5, 0xC9800000, +/**/ 0xBD1E1005, 0x3A7AE827, +/**/ 0x3F298145, 0x3032267F, +/**/ 0xBF2980A2, 0x95800000, +/**/ 0x3D2A0460, 0xA8F2A842, +/**/ 0x3F29413E, 0xD7B96385, +/**/ 0xBF29409F, 0x69000000, +/**/ 0xBD3EDDA5, 0xA7B8321E, +/**/ 0x3F290138, 0x8F42FEC5, +/**/ 0xBF29009C, 0x45000000, +/**/ 0xBD264506, 0x3A3F0D33, +/**/ 0x3F28C132, 0x56CEF241, +/**/ 0xBF28C099, 0x29000000, +/**/ 0x3D206930, 0x33EE13CD, +/**/ 0x3F28812C, 0x2E5D37F6, +/**/ 0xBF288096, 0x15000000, +/**/ 0x3D3B28AC, 0x22DF1FDA, +/**/ 0x3F284126, 0x15EDC9E3, +/**/ 0xBF284093, 0x08800000, +/**/ 0xBD324546, 0xDD73B6DB, +/**/ 0x3F280120, 0x0D80A208, +/**/ 0xBF280090, 0x04800000, +/**/ 0xBCB440C2, 0x6DFEB485, +/**/ 0x3F27C11A, 0x1515BA62, +/**/ 0xBF27C08D, 0x08800000, +/**/ 0x3D31BCBE, 0x9823B19D, +/**/ 0x3F278114, 0x2CAD0CF1, +/**/ 0xBF27808A, 0x14000000, +/**/ 0xBD3CD148, 0xA9EB4E97, +/**/ 0x3F27410E, 0x544693B4, +/**/ 0xBF274087, 0x28000000, +/**/ 0xBD277AAC, 0xCA4F73AA, +/**/ 0x3F270108, 0x8BE248AA, +/**/ 0xBF270084, 0x44000000, +/**/ 0x3D13E656, 0x26068EF7, +/**/ 0x3F26C102, 0xD38025D2, +/**/ 0xBF26C081, 0x68000000, +/**/ 0x3D35547B, 0x44C3EC8A, +/**/ 0x3F2680FD, 0x2B20252A, +/**/ 0xBF26807E, 0x93800000, +/**/ 0xBD3AABA5, 0x110DCE4B, +/**/ 0x3F2640F7, 0x92C240B1, +/**/ 0xBF26407B, 0xC7800000, +/**/ 0xBD260B96, 0xAC011956, +/**/ 0x3F2600F2, 0x0A667267, +/**/ 0xBF260079, 0x03800000, +/**/ 0x3D111C22, 0x5DFA826E, +/**/ 0x3F25C0EC, 0x920CB44A, +/**/ 0xBF25C076, 0x47800000, +/**/ 0x3D333BD6, 0xD8A2980A, +/**/ 0x3F2580E7, 0x29B5005A, +/**/ 0xBF258073, 0x93000000, +/**/ 0xBD3E2660, 0x71C1D861, +/**/ 0x3F2540E1, 0xD15F5095, +/**/ 0xBF254070, 0xE7000000, +/**/ 0xBD2FBD3A, 0x4E77E5EE, +/**/ 0x3F2500DC, 0x890B9EFA, +/**/ 0xBF25006E, 0x43000000, +/**/ 0xBCFEBDF2, 0x7B90A2D9, +/**/ 0x3F24C0D7, 0x50B9E589, +/**/ 0xBF24C06B, 0xA7000000, +/**/ 0x3D2765B3, 0x58F2FF2C, +/**/ 0x3F2480D2, 0x286A1E40, +/**/ 0xBF248069, 0x13000000, +/**/ 0x3D38FE8D, 0x74AE382C, +/**/ 0x3F2440CD, 0x101C431E, +/**/ 0xBF244066, 0x86800000, +/**/ 0xBD3A07C3, 0xB0286224, +/**/ 0x3F2400C8, 0x07D04E23, +/**/ 0xBF240064, 0x02800000, +/**/ 0xBD2ABE33, 0x46EFC0EC, +/**/ 0x3F23C0C3, 0x0F86394D, +/**/ 0xBF23C061, 0x86800000, +/**/ 0xBCF06744, 0x70DE3151, +/**/ 0x3F2380BE, 0x273DFE9C, +/**/ 0xBF23805F, 0x12800000, +/**/ 0x3D260659, 0x05CFCD61, +/**/ 0x3F2340B9, 0x4EF7980F, +/**/ 0xBF23405C, 0xA6800000, +/**/ 0x3D36BEC8, 0xD7DBBEBC, +/**/ 0x3F2300B4, 0x86B2FFA4, +/**/ 0xBF23005A, 0x42000000, +/**/ 0xBD3DD29F, 0x2B2027B4, +/**/ 0x3F22C0AF, 0xCE702F5C, +/**/ 0xBF22C057, 0xE6000000, +/**/ 0xBD32B00B, 0x6959A7D0, +/**/ 0x3F2280AB, 0x262F2134, +/**/ 0xBF228055, 0x92000000, +/**/ 0xBD1F61EF, 0x19FAAC2D, +/**/ 0x3F2240A6, 0x8DEFCF2C, +/**/ 0xBF224053, 0x46000000, +/**/ 0x3D05A87E, 0xCB16B8A8, +/**/ 0x3F2200A2, 0x05B23344, +/**/ 0xBF220051, 0x02000000, +/**/ 0x3D29F32F, 0x23B9B257, +/**/ 0x3F21C09D, 0x8D76477A, +/**/ 0xBF21C04E, 0xC6000000, +/**/ 0x3D36F61B, 0x7E214821, +/**/ 0x3F218099, 0x253C05CD, +/**/ 0xBF21804C, 0x91800000, +/**/ 0xBD3F5464, 0x46FDFCA2, +/**/ 0x3F214094, 0xCD03683D, +/**/ 0xBF21404A, 0x65800000, +/**/ 0xBD35E4E7, 0xA30F2308, +/**/ 0x3F210090, 0x84CC68C9, +/**/ 0xBF210048, 0x41800000, +/**/ 0xBD2974DC, 0xF800CC34, +/**/ 0x3F20C08C, 0x4C970171, +/**/ 0xBF20C046, 0x25800000, +/**/ 0xBD0E9FC5, 0xC1006E9D, +/**/ 0x3F208088, 0x24632C32, +/**/ 0xBF208044, 0x11800000, +/**/ 0x3D133DE7, 0x078E4438, +/**/ 0x3F204084, 0x0C30E30D, +/**/ 0xBF204042, 0x05800000, +/**/ 0x3D2A61D2, 0x15F82A7B, +/**/ 0x3F200080, 0x04002001, +/**/ 0xBF200040, 0x01800000, +/**/ 0x3D355155, 0x3BBB110C, +/**/ 0x3F1F80F8, 0x17A1BA1A, +/**/ 0xBF1F807C, 0x0B000000, +/**/ 0x3D3D31BE, 0x6C520A9B, +/**/ 0x3F1F00F0, 0x47462860, +/**/ 0xBF1F0078, 0x22000000, +/**/ 0xBD3B2CDB, 0x4B6D83F6, +/**/ 0x3F1E80E8, 0x96ED7ED3, +/**/ 0xBF1E8074, 0x4A000000, +/**/ 0xBD33C977, 0xD4122C5A, +/**/ 0x3F1E00E1, 0x0697B172, +/**/ 0xBF1E0070, 0x82000000, +/**/ 0xBD29462E, 0x2D1517C4, +/**/ 0x3F1D80D9, 0x9644B43B, +/**/ 0xBF1D806C, 0xCA000000, +/**/ 0xBD16E2E3, 0xF0952D45, +/**/ 0x3F1D00D2, 0x45F47B2C, +/**/ 0xBF1D0069, 0x22000000, +/**/ 0x3CEED452, 0x2DDC2A8D, +/**/ 0x3F1C80CB, 0x15A6FA46, +/**/ 0xBF1C8065, 0x8A000000, +/**/ 0x3D1DAFEE, 0xA08CEBE8, +/**/ 0x3F1C00C4, 0x055C2585, +/**/ 0xBF1C0062, 0x02000000, +/**/ 0x3D2B50A4, 0xBB11EF55, +/**/ 0x3F1B80BD, 0x1513F0E9, +/**/ 0xBF1B805E, 0x8A000000, +/**/ 0x3D33ACA6, 0xC6D142BF, +/**/ 0x3F1B00B6, 0x44CE5071, +/**/ 0xBF1B005B, 0x22000000, +/**/ 0x3D3979F8, 0xF8CD3D11, +/**/ 0x3F1A80AF, 0x948B381A, +/**/ 0xBF1A8057, 0xCA000000, +/**/ 0x3D3F1149, 0x07EDFD29, +/**/ 0x3F1A00A9, 0x044A9BE5, +/**/ 0xBF1A0054, 0x81000000, +/**/ 0xBD3B8C68, 0xF7BB7092, +/**/ 0x3F1980A2, 0x940C6FCF, +/**/ 0xBF198051, 0x49000000, +/**/ 0xBD365E1C, 0xF27E09A9, +/**/ 0x3F19009C, 0x43D0A7D8, +/**/ 0xBF19004E, 0x21000000, +/**/ 0xBD3162D2, 0xD508D564, +/**/ 0x3F188096, 0x139737FE, +/**/ 0xBF18804B, 0x09000000, +/**/ 0xBD293315, 0x18D5C93E, +/**/ 0x3F180090, 0x03601440, +/**/ 0xBF180048, 0x01000000, +/**/ 0xBD200288, 0x0C26A328, +/**/ 0x3F17808A, 0x132B309E, +/**/ 0xBF178045, 0x09000000, +/**/ 0xBD0CC7F9, 0x7E89FD6F, +/**/ 0x3F170084, 0x42F88115, +/**/ 0xBF170042, 0x21000000, +/**/ 0x3CE40881, 0x058494DC, +/**/ 0x3F16807E, 0x92C7F9A5, +/**/ 0xBF16803F, 0x49000000, +/**/ 0x3D12AE16, 0xCD5698B9, +/**/ 0x3F160079, 0x02998E4D, +/**/ 0xBF16003C, 0x81000000, +/**/ 0x3D21138B, 0xC5780E17, +/**/ 0x3F158073, 0x926D330B, +/**/ 0xBF158039, 0xC9000000, +/**/ 0x3D287809, 0x4E2001E2, +/**/ 0x3F15006E, 0x4242DBDF, +/**/ 0xBF150037, 0x21000000, +/**/ 0x3D2F8684, 0x21448AA2, +/**/ 0x3F148069, 0x121A7CC8, +/**/ 0xBF148034, 0x89000000, +/**/ 0x3D33207E, 0x2F637D8E, +/**/ 0x3F140064, 0x01F409C4, +/**/ 0xBF140032, 0x01000000, +/**/ 0x3D3654B9, 0x12E44B29, +/**/ 0x3F13805F, 0x11CF76D3, +/**/ 0xBF13802F, 0x89000000, +/**/ 0x3D3960F2, 0xCA5547F3, +/**/ 0x3F13005A, 0x41ACB7F4, +/**/ 0xBF13002D, 0x21000000, +/**/ 0x3D3C462B, 0x6487063D, +/**/ 0x3F128055, 0x918BC126, +/**/ 0xBF12802A, 0xC9000000, +/**/ 0x3D3F0562, 0xEFEA1107, +/**/ 0x3F120051, 0x016C8668, +/**/ 0xBF120028, 0x80000000, +/**/ 0xBD3E6066, 0x857113CE, +/**/ 0x3F11804C, 0x914EFBBA, +/**/ 0xBF118026, 0x48000000, +/**/ 0xBD3BEA30, 0xEDD9EB54, +/**/ 0x3F110048, 0x41331519, +/**/ 0xBF110024, 0x20000000, +/**/ 0xBD3996FC, 0x3BFFFF5A, +/**/ 0x3F108044, 0x1118C686, +/**/ 0xBF108022, 0x08000000, +/**/ 0xBD3765C8, 0x62F2E042, +/**/ 0x3F100040, 0x01000400, +/**/ 0xBF100020, 0x00000000, +/**/ 0xBD355595, 0x562224CD, +/**/ 0x3F0F0078, 0x21D1830C, +/**/ 0xBF0F003C, 0x10000000, +/**/ 0xBD336563, 0x095D69EB, +/**/ 0x3F0E0070, 0x81A5E62E, +/**/ 0xBF0E0038, 0x40000000, +/**/ 0xBD319431, 0x70D45290, +/**/ 0x3F0D0069, 0x217D1965, +/**/ 0xBF0D0034, 0x90000000, +/**/ 0xBD2FC201, 0x022D0EF6, +/**/ 0x3F0C0062, 0x015704B1, +/**/ 0xBF0C0031, 0x00000000, +/**/ 0xBD2C95A0, 0x5E276E21, +/**/ 0x3F0B005B, 0x2133900E, +/**/ 0xBF0B002D, 0x90000000, +/**/ 0xBD29A140, 0xE0372A42, +/**/ 0x3F0A0054, 0x8112A37D, +/**/ 0xBF0A002A, 0x40000000, +/**/ 0xBD26E2E2, 0x73BBB580, +/**/ 0x3F09004E, 0x20F426FB, +/**/ 0xBF090027, 0x10000000, +/**/ 0xBD245885, 0x04D48C20, +/**/ 0x3F080048, 0x00D80288, +/**/ 0xBF080024, 0x00000000, +/**/ 0xBD220028, 0x80613426, +/**/ 0x3F070042, 0x20BE1E23, +/**/ 0xBF070021, 0x10000000, +/**/ 0xBD1FAF99, 0xA80279F3, +/**/ 0x3F06003C, 0x80A661CA, +/**/ 0xBF06001E, 0x40000000, +/**/ 0xBD1BBAE3, 0xDC287DFE, +/**/ 0x3F050037, 0x2090B57C, +/**/ 0xBF05001B, 0x90000000, +/**/ 0xBD181E2F, 0x7B73B67C, +/**/ 0x3F040032, 0x007D0139, +/**/ 0xBF040019, 0x00000000, +/**/ 0xBD14D57C, 0x65A375F8, +/**/ 0x3F03002D, 0x206B2CFF, +/**/ 0xBF030016, 0x90000000, +/**/ 0xBD11DCCA, 0x7BF71EC1, +/**/ 0x3F020028, 0x805B20CD, +/**/ 0xBF020014, 0x40000000, +/**/ 0xBD0E6033, 0x425C4447, +/**/ 0x3F010024, 0x204CC4A3, +/**/ 0xBF010012, 0x10000000, +/**/ 0xBD0996D3, 0x730FFF5C, +/**/ 0x3F000020, 0x00400080, +/**/ 0xBF000010, 0x00000000, +/**/ 0xBD055575, 0x558888DE, +/**/ 0x3EFE0038, 0x406978C6, +/**/ 0xBEFE001C, 0x20000000, +/**/ 0xBD019418, 0xB845146A, +/**/ 0x3EFC0031, 0x0055C096, +/**/ 0xBEFC0018, 0x80000000, +/**/ 0xBCFC957A, 0xD989DB3C, +/**/ 0x3EFA002A, 0x4044A870, +/**/ 0xBEFA0015, 0x20000000, +/**/ 0xBCF6E2C6, 0x8F0EED2F, +/**/ 0x3EF80024, 0x00360051, +/**/ 0xBEF80012, 0x00000000, +/**/ 0xBCF20014, 0x40184CEB, +/**/ 0x3EF6001E, 0x40299839, +/**/ 0xBEF6000F, 0x20000000, +/**/ 0xBCEBBAC7, 0x434A1F5C, +/**/ 0x3EF40019, 0x001F4027, +/**/ 0xBEF4000C, 0x80000000, +/**/ 0xBCE4D568, 0xDD68DD6A, +/**/ 0x3EF20014, 0x4016C81A, +/**/ 0xBEF2000A, 0x20000000, +/**/ 0xBCDE6019, 0xA11710FC, +/**/ 0x3EF00010, 0x00100010, +/**/ 0xBEF00008, 0x00000000, +/**/ 0xBCD55565, 0x5562222D, +/**/ 0x3EEC0018, 0x80157013, +/**/ 0xBEEC000C, 0x40000000, +/**/ 0xBCCC9568, 0x176276C5, +/**/ 0x3EE80012, 0x000D800A, +/**/ 0xBEE80009, 0x00000000, +/**/ 0xBCC2000A, 0x20061337, +/**/ 0x3EE4000C, 0x8007D005, +/**/ 0xBEE40006, 0x40000000, +/**/ 0xBCB4D55F, 0x195A3758, +/**/ 0x3EE00008, 0x00040002, +/**/ 0xBEE00004, 0x00000000, +/**/ 0xBCA5555D, 0x5558888A, +/**/ 0x3ED80009, 0x00036001, +/**/ 0xBED80004, 0x80000000, +/**/ 0xBC920005, 0x100184CD, +/**/ 0x3ED00004, 0x00010000, +/**/ 0xBED00002, 0x00000000, +/**/ 0xBC755559, 0x55562222, +/**/ 0x3EC00002, 0x00004000, +/**/ 0xBEC00001, 0x00000000, +/**/ 0xBC455557, 0x55558889, +/**/ 0x00000000, 0x00000000, +/**/ 0x00000000, 0x00000000, +/**/ 0x00000000, 0x00000000, +/**/ 0xBEBFFFFC, 0x00008000, +/**/ 0x3EBFFFFE, 0x00000000, +/**/ 0x3C455553, 0x55558889, +/**/ 0xBECFFFF8, 0x00020000, +/**/ 0x3ECFFFFC, 0x00000000, +/**/ 0x3C755551, 0x55562222, +/**/ 0xBED7FFF7, 0x00035FFF, +/**/ 0x3ED7FFFB, 0x80000000, +/**/ 0x3C91FFFA, 0xF00184CC, +/**/ 0xBEDFFFF0, 0x0007FFFC, +/**/ 0x3EDFFFF8, 0x00000000, +/**/ 0x3CA5554D, 0x55588887, +/**/ 0xBEE3FFF3, 0x8007CFFB, +/**/ 0x3EE3FFF9, 0xC0000000, +/**/ 0x3CB4D54B, 0x915A3753, +/**/ 0xBEE7FFEE, 0x000D7FF6, +/**/ 0x3EE7FFF7, 0x00000000, +/**/ 0x3CC1FFF5, 0xE006132F, +/**/ 0xBEEBFFE7, 0x80156FED, +/**/ 0x3EEBFFF3, 0xC0000000, +/**/ 0x3CCC9542, 0x936276B2, +/**/ 0xBEEFFFE0, 0x001FFFE0, +/**/ 0x3EEFFFF0, 0x00000000, +/**/ 0x3CD55545, 0x55622217, +/**/ 0xBEF1FFEB, 0xC016C7E6, +/**/ 0x3EF1FFF5, 0xE0000000, +/**/ 0x3CDE5FE6, 0x5F1710D1, +/**/ 0xBEF3FFE7, 0x001F3FD9, +/**/ 0x3EF3FFF3, 0x80000000, +/**/ 0x3CE4D541, 0xCD68DD41, +/**/ 0xBEF5FFE1, 0xC02997C7, +/**/ 0x3EF5FFF0, 0xE0000000, +/**/ 0x3CEBBA8E, 0x124A1F13, +/**/ 0xBEF7FFDC, 0x0035FFAF, +/**/ 0x3EF7FFEE, 0x00000000, +/**/ 0x3CF1FFEB, 0xC0184CAE, +/**/ 0xBEF9FFD5, 0xC044A790, +/**/ 0x3EF9FFEA, 0xE0000000, +/**/ 0x3CF6E28E, 0xC68EECCD, +/**/ 0xBEFBFFCF, 0x0055BF6A, +/**/ 0x3EFBFFE7, 0x80000000, +/**/ 0x3CFC952F, 0xD189DAA2, +/**/ 0xBEFDFFC7, 0xC069773A, +/**/ 0x3EFDFFE3, 0xE0000000, +/**/ 0x3D0193E7, 0x480513F6, +/**/ 0xBEFFFFC0, 0x007FFF00, +/**/ 0x3EFFFFE0, 0x00000000, +/**/ 0x3D055535, 0x55888833, +/**/ 0xBF00FFDB, 0xE04CC35D, +/**/ 0x3F00FFED, 0xF0000000, +/**/ 0x3D099681, 0xE2CFFE66, +/**/ 0xBF01FFD7, 0x805B1F33, +/**/ 0x3F01FFEB, 0xC0000000, +/**/ 0x3D0E5FCC, 0xBE5C42ED, +/**/ 0xBF02FFD2, 0xE06B2B01, +/**/ 0x3F02FFE9, 0x70000000, +/**/ 0x3D11DC8A, 0xD9D71DD1, +/**/ 0xBF03FFCE, 0x007CFEC8, +/**/ 0x3F03FFE7, 0x00000000, +/**/ 0x3D14D52E, 0x45A374B3, +/**/ 0xBF04FFC8, 0xE090B284, +/**/ 0x3F04FFE4, 0x70000000, +/**/ 0x3D181DD0, 0x8553B4C7, +/**/ 0xBF05FFC3, 0x80A65E36, +/**/ 0x3F05FFE1, 0xC0000000, +/**/ 0x3D1BBA71, 0x7A287BBE, +/**/ 0xBF06FFBD, 0xE0BE19DD, +/**/ 0x3F06FFDE, 0xF0000000, +/**/ 0x3D1FAF11, 0x03E27702, +/**/ 0xBF07FFB8, 0x00D7FD78, +/**/ 0x3F07FFDC, 0x00000000, +/**/ 0x3D21FFD7, 0x80613240, +/**/ 0xBF08FFB1, 0xE0F42105, +/**/ 0x3F08FFD8, 0xF0000000, +/**/ 0x3D245825, 0xA6C489B3, +/**/ 0xBF09FFAB, 0x81129C84, +/**/ 0x3F09FFD5, 0xC0000000, +/**/ 0x3D26E272, 0xE2BBB26F, +/**/ 0xBF0AFFA4, 0xE13387F2, +/**/ 0x3F0AFFD2, 0x70000000, +/**/ 0x3D29A0BF, 0x21272669, +/**/ 0xBF0BFF9E, 0x0156FB50, +/**/ 0x3F0BFFCF, 0x00000000, +/**/ 0x3D2C950A, 0x4E276957, +/**/ 0xBF0CFF96, 0xE17D0E9B, +/**/ 0x3F0CFFCB, 0x70000000, +/**/ 0x3D2FC154, 0x551D090E, +/**/ 0xBF0DFF8F, 0x81A5D9D2, +/**/ 0x3F0DFFC7, 0xC0000000, +/**/ 0x3D3193CE, 0x90544EF1, +/**/ 0xBF0EFF87, 0xE1D174F4, +/**/ 0x3F0EFFC3, 0xF0000000, +/**/ 0x3D3364F2, 0x4D556583, +/**/ 0xBF0FFF80, 0x01FFF800, +/**/ 0x3F0FFFC0, 0x00000000, +/**/ 0x3D355515, 0x56221F78, +/**/ 0xBF107FBB, 0xF118BD7A, +/**/ 0x3F107FDD, 0xF8000000, +/**/ 0x3D376537, 0x9EEAD9D8, +/**/ 0xBF10FFB7, 0xC1330AE7, +/**/ 0x3F10FFDB, 0xE0000000, +/**/ 0x3D399659, 0x1B7FF7AE, +/**/ 0xBF117FB3, 0x714EF047, +/**/ 0x3F117FD9, 0xB8000000, +/**/ 0x3D3BE979, 0xBF51E233, +/**/ 0xBF11FFAF, 0x016C7998, +/**/ 0x3F11FFD7, 0x80000000, +/**/ 0x3D3E5F99, 0x7D7108FF, +/**/ 0xBF127FAA, 0x718BB2DA, +/**/ 0x3F127FD5, 0x39000000, +/**/ 0xBD3F0647, 0xB7721DC6, +/**/ 0xBF12FFA5, 0xC1ACA80C, +/**/ 0x3F12FFD2, 0xE1000000, +/**/ 0xBD3C4729, 0xED071532, +/**/ 0xBF137FA0, 0xF1CF652D, +/**/ 0x3F137FD0, 0x79000000, +/**/ 0xBD39620D, 0x315D596D, +/**/ 0xBF13FF9C, 0x01F3F63C, +/**/ 0x3F13FFCE, 0x01000000, +/**/ 0xBD3655F1, 0x92E45F81, +/**/ 0xBF147F96, 0xF21A6739, +/**/ 0x3F147FCB, 0x79000000, +/**/ 0xBD3321D7, 0x206B9526, +/**/ 0xBF14FF91, 0xC242C421, +/**/ 0x3F14FFC8, 0xE1000000, +/**/ 0xBD2F897B, 0xD244C12A, +/**/ 0xBF157F8C, 0x726D18F6, +/**/ 0x3F157FC6, 0x39000000, +/**/ 0xBD287B4B, 0xF93040AE, +/**/ 0xBF15FF87, 0x029971B4, +/**/ 0x3F15FFC3, 0x81000000, +/**/ 0xBD21171E, 0xD578562C, +/**/ 0xBF167F81, 0x72C7DA5C, +/**/ 0x3F167FC0, 0xB9000000, +/**/ 0xBD12B5E9, 0x0F773DB4, +/**/ 0xBF16FF7B, 0xC2F85EEC, +/**/ 0x3F16FFBD, 0xE1000000, +/**/ 0xBCE44CD3, 0x158A76C2, +/**/ 0xBF177F75, 0xF32B0B63, +/**/ 0x3F177FBA, 0xF9000000, +/**/ 0x3D0CB55C, 0x2E48511B, +/**/ 0xBF17FF70, 0x035FEBC0, +/**/ 0x3F17FFB8, 0x01000000, +/**/ 0x3D1FFAF0, 0x184C534F, +/**/ 0xBF187F69, 0xF3970C03, +/**/ 0x3F187FB4, 0xF9000000, +/**/ 0x3D292D95, 0xACC53FBE, +/**/ 0xBF18FF63, 0xC3D07829, +/**/ 0x3F18FFB1, 0xE1000000, +/**/ 0x3D315FD7, 0xE48887C8, +/**/ 0xBF197F5D, 0x740C3C32, +/**/ 0x3F197FAE, 0xB9000000, +/**/ 0x3D365AE3, 0x1DF5B242, +/**/ 0xBF19FF57, 0x044A641C, +/**/ 0x3F19FFAB, 0x81000000, +/**/ 0x3D3B88EC, 0x6FBB0E5F, +/**/ 0xBF1A7F50, 0x748AFBE7, +/**/ 0x3F1A7FA8, 0x3A000000, +/**/ 0xBD3F150C, 0x39766B40, +/**/ 0xBF1AFF49, 0xC4CE0F91, +/**/ 0x3F1AFFA4, 0xE2000000, +/**/ 0xBD397E06, 0xF14DB839, +/**/ 0xBF1B7F42, 0xF513AB19, +/**/ 0x3F1B7FA1, 0x7A000000, +/**/ 0xBD33B103, 0xCBD9CC3D, +/**/ 0xBF1BFF3C, 0x055BDA7D, +/**/ 0x3F1BFF9E, 0x02000000, +/**/ 0xBD2B5A05, 0xBB1321B5, +/**/ 0xBF1C7F34, 0xF5A6A9BD, +/**/ 0x3F1C7F9A, 0x7A000000, +/**/ 0xBD1DC410, 0xECAF9551, +/**/ 0xBF1CFF2D, 0xC5F424D6, +/**/ 0x3F1CFF96, 0xE2000000, +/**/ 0xBCEF80FF, 0x3DF3CD68, +/**/ 0xBF1D7F26, 0x764457C8, +/**/ 0x3F1D7F93, 0x3A000000, +/**/ 0x3D16CBC7, 0x4271E737, +/**/ 0xBF1DFF1F, 0x06974E91, +/**/ 0x3F1DFF8F, 0x82000000, +/**/ 0x3D2939D2, 0x1D134848, +/**/ 0xBF1E7F17, 0x76ED1530, +/**/ 0x3F1E7F8B, 0xBA000000, +/**/ 0x3D33C2DD, 0xA9892C73, +/**/ 0xBF1EFF0F, 0xC745B7A4, +/**/ 0x3F1EFF87, 0xE2000000, +/**/ 0x3D3B25CF, 0x8AEC69D5, +/**/ 0xBF1F7F07, 0xF7A141EA, +/**/ 0x3F1F7F83, 0xFB000000, +/**/ 0xBD3D3941, 0x645B412A, +/**/ 0xBF1FFF00, 0x07FFC002, +/**/ 0x3F1FFF80, 0x03000000, +/**/ 0xBD355955, 0x3BBC6662, +/**/ 0xBF203F7B, 0xFC309EF5, +/**/ 0x3F203FBD, 0xFD800000, +/**/ 0xBD2A72D8, 0x260B17B3, +/**/ 0xBF207F77, 0xE462E3D0, +/**/ 0x3F207FBB, 0xF1800000, +/**/ 0xBD136218, 0x0994AE68, +/**/ 0xBF20BF73, 0xBC96B492, +/**/ 0x3F20BFB9, 0xDD800000, +/**/ 0x3D0E52E6, 0xECB2641F, +/**/ 0xBF20FF6F, 0x84CC1739, +/**/ 0x3F20FFB7, 0xC1800000, +/**/ 0x3D296078, 0xE7FCF60B, +/**/ 0xBF213F6B, 0x3D0311C6, +/**/ 0x3F213FB5, 0x9D800000, +/**/ 0x3D35DA18, 0xA7850AFF, +/**/ 0xBF217F66, 0xE53BAA36, +/**/ 0x3F217FB3, 0x71800000, +/**/ 0x3D3F48F1, 0x5E7BB444, +/**/ 0xBF21BF62, 0x7D75E68A, +/**/ 0x3F21BFB1, 0x3E000000, +/**/ 0xBD370239, 0x812BC469, +/**/ 0xBF21FF5E, 0x05B1CCC0, +/**/ 0x3F21FFAF, 0x02000000, +/**/ 0xBD2A0CD0, 0x23BF1A4D, +/**/ 0xBF223F59, 0x7DEF62D8, +/**/ 0x3F223FAC, 0xBE000000, +/**/ 0xBD0614D3, 0x736E3623, +/**/ 0xBF227F54, 0xE62EAED0, +/**/ 0x3F227FAA, 0x72000000, +/**/ 0x3D1F28BD, 0x37EDEDB0, +/**/ 0xBF22BF50, 0x3E6FB6A9, +/**/ 0x3F22BFA8, 0x1E000000, +/**/ 0x3D32A0F5, 0x07CE33C8, +/**/ 0xBF22FF4B, 0x86B28060, +/**/ 0x3F22FFA5, 0xC2000000, +/**/ 0x3D3DC2B6, 0xA31C6A8D, +/**/ 0xBF233F46, 0xBEF711F6, +/**/ 0x3F233FA3, 0x5E800000, +/**/ 0xBD36CF8B, 0xFC67C9FB, +/**/ 0xBF237F41, 0xE73D7169, +/**/ 0x3F237FA0, 0xF2800000, +/**/ 0xBD2629A5, 0xE6D88A89, +/**/ 0xBF23BF3C, 0xFF85A4B8, +/**/ 0x3F23BF9E, 0x7E800000, +/**/ 0x3CEE7C34, 0x202574EC, +/**/ 0xBF23FF38, 0x07CFB1E3, +/**/ 0x3F23FF9C, 0x02800000, +/**/ 0x3D2A9723, 0x46E594C1, +/**/ 0xBF243F33, 0x001B9EE8, +/**/ 0x3F243F99, 0x7E800000, +/**/ 0x3D39F33C, 0xF61AE74C, +/**/ 0xBF247F2D, 0xE86971C7, +/**/ 0x3F247F96, 0xF3000000, +/**/ 0xBD39141C, 0x85341E31, +/**/ 0xBF24BF28, 0xC0B9307F, +/**/ 0x3F24BF94, 0x5F000000, +/**/ 0xBD2792F5, 0xDA0FAF09, +/**/ 0xBF24FF23, 0x890AE10E, +/**/ 0x3F24FF91, 0xC3000000, +/**/ 0x3CFD4219, 0xFB239430, +/**/ 0xBF253F1E, 0x415E8974, +/**/ 0x3F253F8F, 0x1F000000, +/**/ 0x3D2F8B72, 0x0359434A, +/**/ 0xBF257F18, 0xE9B42FAF, +/**/ 0x3F257F8C, 0x73000000, +/**/ 0x3D3E0C4B, 0x1939FEDF, +/**/ 0xBF25BF13, 0x820BD9BF, +/**/ 0x3F25BF89, 0xBF800000, +/**/ 0xBD335728, 0x39B301E2, +/**/ 0xBF25FF0E, 0x0A658DA3, +/**/ 0x3F25FF87, 0x03800000, +/**/ 0xBD118E84, 0x5E1E8D4F, +/**/ 0xBF263F08, 0x82C15159, +/**/ 0x3F263F84, 0x3F800000, +/**/ 0x3D25CFC0, 0xBDDDD045, +/**/ 0xBF267F02, 0xEB1F2AE1, +/**/ 0x3F267F81, 0x73800000, +/**/ 0x3D3A8C5C, 0x08837E99, +/**/ 0xBF26BEFD, 0x437F203A, +/**/ 0x3F26BF7E, 0xA0000000, +/**/ 0xBD35752E, 0x3C56F12D, +/**/ 0xBF26FEF7, 0x8BE13762, +/**/ 0x3F26FF7B, 0xC4000000, +/**/ 0xBD146EFA, 0x46359E28, +/**/ 0xBF273EF1, 0xC4457659, +/**/ 0x3F273F78, 0xE0000000, +/**/ 0x3D273355, 0xCD265865, +/**/ 0xBF277EEB, 0xECABE31C, +/**/ 0x3F277F75, 0xF4000000, +/**/ 0x3D3CAC0E, 0x095DEBF8, +/**/ 0xBF27BEE6, 0x051483AC, +/**/ 0x3F27BF73, 0x00800000, +/**/ 0xBD31E395, 0x4C39F4DB, +/**/ 0xBF27FEE0, 0x0D7F5E08, +/**/ 0x3F27FF70, 0x04800000, +/**/ 0xBCB43F3D, 0xA1314B81, +/**/ 0xBF283EDA, 0x05EC782D, +/**/ 0x3F283F6D, 0x00800000, +/**/ 0x3D321B10, 0x115B8D70, +/**/ 0xBF287ED3, 0xEE5BD81B, +/**/ 0x3F287F69, 0xF5000000, +/**/ 0xBD3B54A7, 0x83704FE1, +/**/ 0xBF28BECD, 0xC6CD83D1, +/**/ 0x3F28BF66, 0xE1000000, +/**/ 0xBD20C4CC, 0x41229C91, +/**/ 0xBF28FEC7, 0x8F41814D, +/**/ 0x3F28FF63, 0xC5000000, +/**/ 0x3D25E5A8, 0x2A183F17, +/**/ 0xBF293EC1, 0x47B7D68F, +/**/ 0x3F293F60, 0xA1000000, +/**/ 0x3D3EAC06, 0xF81B997D, +/**/ 0xBF297EBA, 0xF0308995, +/**/ 0x3F297F5D, 0x75800000, +/**/ 0xBD2A6B9B, 0x3A1E5BAD, +/**/ 0xBF29BEB4, 0x88ABA05E, +/**/ 0x3F29BF5A, 0x41800000, +/**/ 0x3D1D3958, 0xBDFE3C77, +/**/ 0xBF29FEAE, 0x112920E9, +/**/ 0x3F29FF57, 0x05800000, +/**/ 0x3D3C3972, 0x375BA904, +/**/ 0xBF2A3EA7, 0x89A91135, +/**/ 0x3F2A3F53, 0xC2000000, +/**/ 0xBD2CE6F3, 0x588DE85B, +/**/ 0xBF2A7EA0, 0xF22B7740, +/**/ 0x3F2A7F50, 0x76000000, +/**/ 0x3D1D2249, 0x75AEDBFD, +/**/ 0xBF2ABE9A, 0x4AB05909, +/**/ 0x3F2ABF4D, 0x22000000, +/**/ 0x3D3D6E96, 0x2CE7BDAC, +/**/ 0xBF2AFE93, 0x9337BC90, +/**/ 0x3F2AFF49, 0xC6800000, +/**/ 0xBD2800DC, 0xCB7D724C, +/**/ 0xBF2B3E8C, 0xCBC1A7D1, +/**/ 0x3F2B3F46, 0x62800000, +/**/ 0x3D25F908, 0xFA591B29, +/**/ 0xBF2B7E85, 0xF44E20CE, +/**/ 0x3F2B7F42, 0xF7000000, +/**/ 0xBD3D9991, 0x53021ED8, +/**/ 0xBF2BBE7F, 0x0CDD2D83, +/**/ 0x3F2BBF3F, 0x83000000, +/**/ 0xBD1706BF, 0xFD596AD6, +/**/ 0xBF2BFE78, 0x156ED3F0, +/**/ 0x3F2BFF3C, 0x07000000, +/**/ 0x3D328528, 0x4EC45253, +/**/ 0xBF2C3E71, 0x0E031A14, +/**/ 0x3F2C3F38, 0x83800000, +/**/ 0xBD34C408, 0x927D8A9E, +/**/ 0xBF2C7E69, 0xF69A05ED, +/**/ 0x3F2C7F34, 0xF7800000, +/**/ 0x3D118EF4, 0xCAE2C25F, +/**/ 0xBF2CBE62, 0xCF339D7A, +/**/ 0x3F2CBF31, 0x63800000, +/**/ 0x3D3DFD79, 0x73DBBB41, +/**/ 0xBF2CFE5B, 0x97CFE6B9, +/**/ 0x3F2CFF2D, 0xC8000000, +/**/ 0xBD1FD74F, 0xE7FE77E6, +/**/ 0xBF2D3E54, 0x506EE7AA, +/**/ 0x3F2D3F2A, 0x24000000, +/**/ 0x3D328AD4, 0xBDDB871F, +/**/ 0xBF2D7E4C, 0xF910A64A, +/**/ 0x3F2D7F26, 0x78800000, +/**/ 0xBD327F8C, 0x903DDD81, +/**/ 0xBF2DBE45, 0x91B52899, +/**/ 0x3F2DBF22, 0xC4800000, +/**/ 0x3D21D80F, 0xDF52840A, +/**/ 0xBF2DFE3E, 0x1A5C7495, +/**/ 0x3F2DFF1F, 0x09000000, +/**/ 0xBD3B316D, 0xEED9F651, +/**/ 0xBF2E3E36, 0x9306903D, +/**/ 0x3F2E3F1B, 0x45000000, +/**/ 0x3CF2911A, 0x76DB3C6B, +/**/ 0xBF2E7E2E, 0xFBB3818F, +/**/ 0x3F2E7F17, 0x79000000, +/**/ 0x3D3DFC86, 0x85559113, +/**/ 0xBF2EBE27, 0x54634E89, +/**/ 0x3F2EBF13, 0xA5800000, +/**/ 0xBD12D83E, 0x0AB3DBE7, +/**/ 0xBF2EFE1F, 0x9D15FD2B, +/**/ 0x3F2EFF0F, 0xC9800000, +/**/ 0x3D39124F, 0x617B99F1, +/**/ 0xBF2F3E17, 0xD5CB9373, +/**/ 0x3F2F3F0B, 0xE6000000, +/**/ 0xBD2152B9, 0xF8F64DA1, +/**/ 0xBF2F7E0F, 0xFE841760, +/**/ 0x3F2F7F07, 0xFA000000, +/**/ 0x3D3617EB, 0x34C4735B, +/**/ 0xBF2FBE08, 0x173F8EEF, +/**/ 0x3F2FBF04, 0x06800000, +/**/ 0xBD2551B0, 0x739FA712, +/**/ 0xBF2FFE00, 0x1FFE0020, +/**/ 0x3F2FFF00, 0x0A800000, +/**/ 0x3D351558, 0x885DE027, +/**/ 0xBF301EFC, 0x0C5FB879, +/**/ 0x3F301F7E, 0x03800000, +/**/ 0xBD255905, 0x68F8FC50, +/**/ 0xBF303EF8, 0x00C1F3B0, +/**/ 0x3F303F7B, 0xFD800000, +/**/ 0x3D361295, 0xDF771CF4, +/**/ 0xBF305EF3, 0xED25B4B7, +/**/ 0x3F305F79, 0xF3C00000, +/**/ 0xBD2158BB, 0xD8A255DB, +/**/ 0xBF307EEF, 0xD18AFE8B, +/**/ 0x3F307F77, 0xE5C00000, +/**/ 0x3D3917A1, 0xB740E625, +/**/ 0xBF309EEB, 0xADF1D42C, +/**/ 0x3F309F75, 0xD4000000, +/**/ 0xBD1281AD, 0x9C716D59, +/**/ 0xBF30BEE7, 0x825A3899, +/**/ 0x3F30BF73, 0xBE000000, +/**/ 0x3D3E2C7A, 0x86ED7DDC, +/**/ 0xBF30DEE3, 0x4EC42ED1, +/**/ 0x3F30DF71, 0xA4400000, +/**/ 0x3CF7F534, 0xF54F7E28, +/**/ 0xBF30FEDF, 0x132FB9D5, +/**/ 0x3F30FF6F, 0x86800000, +/**/ 0xBD3AA6E1, 0x404F4E01, +/**/ 0xBF311EDA, 0xCF9CDCA2, +/**/ 0x3F311F6D, 0x64800000, +/**/ 0x3D2375B9, 0x4A6EC981, +/**/ 0xBF313ED6, 0x840B9A38, +/**/ 0x3F313F6B, 0x3EC00000, +/**/ 0xBD315A73, 0x33401DD0, +/**/ 0xBF315ED2, 0x307BF596, +/**/ 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0x3F3DBE45, 0x9A400000, +/**/ 0x3D1787DF, 0x67DCC15E, +/**/ 0xBF3DDC83, 0xE41BC143, +/**/ 0x3F3DDE41, 0xE0C00000, +/**/ 0xBD262398, 0x352F961F, +/**/ 0xBF3DFC7C, 0x696BA563, +/**/ 0x3F3DFE3E, 0x23400000, +/**/ 0xBD3B16B9, 0xDEDD373A, +/**/ 0xBF3E1C74, 0xE6BE58DA, +/**/ 0x3F3E1E3A, 0x61800000, +/**/ 0x3D35D42E, 0x336BE94B, +/**/ 0xBF3E3C6D, 0x5C13DEA7, +/**/ 0x3F3E3E36, 0x9C000000, +/**/ 0x3D1EBFAF, 0x08A303A2, +/**/ 0xBF3E5C65, 0xC96C39C9, +/**/ 0x3F3E5E32, 0xD2800000, +/**/ 0xBD160A06, 0x34856362, +/**/ 0xBF3E7C5E, 0x2EC76D3D, +/**/ 0x3F3E7E2F, 0x05000000, +/**/ 0xBD31C21A, 0x154CDF1A, +/**/ 0xBF3E9C56, 0x8C257C04, +/**/ 0x3F3E9E2B, 0x33800000, +/**/ 0xBD3D0DDE, 0x31941F7F, +/**/ 0xBF3EBC4E, 0xE186691B, +/**/ 0x3F3EBE27, 0x5DC00000, +/**/ 0x3D389B31, 0xC26EC60D, +/**/ 0xBF3EDC47, 0x2EEA3781, +/**/ 0x3F3EDE23, 0x84400000, +/**/ 0x3D2E742A, 0xD583BEF8, +/**/ 0xBF3EFC3F, 0x7450EA34, +/**/ 0x3F3EFE1F, 0xA6C00000, +/**/ 0x3D1B3F31, 0xAC2DA351, +/**/ 0xBF3F1C37, 0xB1BA8433, +/**/ 0x3F3F1E1B, 0xC5400000, +/**/ 0xBCE45533, 0x2DC67430, +/**/ 0xBF3F3C2F, 0xE727087C, +/**/ 0x3F3F3E17, 0xDFC00000, +/**/ 0xBD1C7133, 0xFF1174AE, +/**/ 0xBF3F5C28, 0x14967A0F, +/**/ 0x3F3F5E13, 0xF6400000, +/**/ 0xBD29383C, 0x4AE098DC, +/**/ 0xBF3F7C20, 0x3A08DBE9, +/**/ 0x3F3F7E10, 0x08C00000, +/**/ 0xBD31211D, 0x684B0B3B, +/**/ 0xBF3F9C18, 0x577E3109, +/**/ 0x3F3F9E0C, 0x17400000, +/**/ 0xBD34AA4B, 0x268D7464, +/**/ 0xBF3FBC10, 0x6CF67C6E, +/**/ 0x3F3FBE08, 0x21C00000, +/**/ 0xBD3736A7, 0xBED03388, +/**/ 0xBF3FDC08, 0x7A71C116, +/**/ 0x3F3FDE04, 0x28400000, +/**/ 0xBD38C533, 0x900BC4E5, +/**/ 0xBF3FFC00, 0x7FF00200, +/**/ 0x3F3FFE00, 0x2AC00000, +/**/ 0xBD3954EE, 0xF9987527, +/**/ 0xBF400DFC, 0x3EB8A115, +/**/ 0x3F400EFE, 0x14A00000, +/**/ 0xBD38E4DA, 0x5B2E613B, +/**/ 0xBF401DF8, 0x397AC249, +/**/ 0x3F401EFC, 0x11E00000, +/**/ 0xBD3773F6, 0x14E5761B, +/**/ 0xBF402DF4, 0x303E661C, +/**/ 0x3F402EFA, 0x0D200000, +/**/ 0xBD350142, 0x873570A0, +/**/ 0xBF403DF0, 0x23038E0C, +/**/ 0x3F403EF8, 0x06600000, +/**/ 0xBD318BC0, 0x12F5DD53, +/**/ 0xBF404DEC, 0x11CA3B9A, +/**/ 0x3F404EF5, 0xFDA00000, +/**/ 0xBD2A24DE, 0x32BC307C, +/**/ 0xBF405DE7, 0xFC927044, +/**/ 0x3F405EF3, 0xF2E00000, +/**/ 0xBD1E513F, 0xF01532DA, +/**/ 0xBF406DE3, 0xE35C2D8A, +/**/ 0x3F406EF1, 0xE6200000, +/**/ 0xBCF10631, 0xCE27534E, +/**/ 0xBF407DDF, 0xC62774EA, +/**/ 0x3F407EEF, 0xD7600000, +/**/ 0x3D19E95C, 0x86CE9380, +/**/ 0xBF408DDB, 0xA4F447E4, +/**/ 0x3F408EED, 0xC6A00000, +/**/ 0x3D2E19BC, 0xBA0CD2C3, +/**/ 0xBF409DD7, 0x7FC2A7F8, +/**/ 0x3F409EEB, 0xB3E00000, +/**/ 0x3D38A832, 0x31FF7199, +/**/ 0xBF40ADD3, 0x569296A4, +/**/ 0x3F40AEE9, 0x9F400000, +/**/ 0xBD3CB2AD, 0xC2D77791, +/**/ 0xBF40BDCF, 0x29641567, +/**/ 0x3F40BEE7, 0x88800000, +/**/ 0xBD3102C1, 0xE5545563, +/**/ 0xBF40CDCA, 0xF83725C2, +/**/ 0x3F40CEE5, 0x6FC00000, +/**/ 0xBD111C2A, 0x66B3E48D, +/**/ 0xBF40DDC6, 0xC30BC932, +/**/ 0x3F40DEE3, 0x55000000, +/**/ 0x3D2302EF, 0x7711FC2A, +/**/ 0xBF40EDC2, 0x89E20138, +/**/ 0x3F40EEE1, 0x38400000, +/**/ 0x3D3857C4, 0xB558238E, +/**/ 0xBF40FDBE, 0x4CB9CF52, +/**/ 0x3F40FEDF, 0x19A00000, +/**/ 0xBD37C324, 0x1194C2E1, +/**/ 0xBF410DBA, 0x0B933501, +/**/ 0x3F410EDC, 0xF8E00000, +/**/ 0xBD1B390B, 0xFBCAF285, +/**/ 0xBF411DB5, 0xC66E33C2, +/**/ 0x3F411EDA, 0xD6200000, +/**/ 0x3D266ECF, 0x0E52C3A4, +/**/ 0xBF412DB1, 0x7D4ACD15, +/**/ 0x3F412ED8, 0xB1600000, +/**/ 0x3D3E4EDB, 0x1A4AF71D, +/**/ 0xBF413DAD, 0x30290279, +/**/ 0x3F413ED6, 0x8AC00000, +/**/ 0xBD2B0DD1, 0x58C4D599, +/**/ 0xBF414DA8, 0xDF08D56E, +/**/ 0x3F414ED4, 0x62000000, +/**/ 0x3D1EDC6F, 0x2FB4061D, +/**/ 0xBF415DA4, 0x89EA4773, +/**/ 0x3F415ED2, 0x37400000, +/**/ 0x3D3E09E8, 0x1BA53538, +/**/ 0xBF416DA0, 0x30CD5A06, +/**/ 0x3F416ED0, 0x0AA00000, +/**/ 0xBD251B08, 0x4A5B4574, +/**/ 0xBF417D9B, 0xD3B20EA8, +/**/ 0x3F417ECD, 0xDBE00000, +/**/ 0x3D2BE3AD, 0x4241B57B, +/**/ 0xBF418D97, 0x729866D7, +/**/ 0x3F418ECB, 0xAB400000, +/**/ 0xBD387707, 0xFA22BD16, +/**/ 0xBF419D93, 0x0D806412, +/**/ 0x3F419EC9, 0x78800000, +/**/ 0x3D01C6FC, 0xFFA2FC2F, +/**/ 0xBF41AD8E, 0xA46A07D9, +/**/ 0x3F41AEC7, 0x43C00000, +/**/ 0x3D3E028D, 0x05F32EE8, +/**/ 0xBF41BD8A, 0x375553AB, +/**/ 0x3F41BEC5, 0x0D200000, +/**/ 0xBD146400, 0xC7E46F2B, +/**/ 0xBF41CD85, 0xC6424907, +/**/ 0x3F41CEC2, 0xD4600000, +/**/ 0x3D38E737, 0x8DFCE791, +/**/ 0xBF41DD81, 0x5130E96B, +/**/ 0x3F41DEC0, 0x99C00000, +/**/ 0xBD1FEF30, 0x92F4A6CE, +/**/ 0xBF41ED7C, 0xD8213659, +/**/ 0x3F41EEBE, 0x5D000000, +/**/ 0x3D383EF4, 0x4AE68315, +/**/ 0xBF41FD78, 0x5B13314D, +/**/ 0x3F41FEBC, 0x1E600000, +/**/ 0xBD199E1E, 0x39A8276A, +/**/ 0xBF420D73, 0xDA06DBC8, +/**/ 0x3F420EB9, 0xDDA00000, +/**/ 0x3D3C11BF, 0xE39F6D77, +/**/ 0xBF421D6F, 0x54FC3749, +/**/ 0x3F421EB7, 0x9B000000, +/**/ 0xBCD50D72, 0xC3A8C440, +/**/ 0xBF422D6A, 0xCBF3454F, +/**/ 0x3F422EB5, 0x56600000, +/**/ 0xBD3B9869, 0x06E59170, +/**/ 0xBF423D66, 0x3EEC0759, +/**/ 0x3F423EB3, 0x0FA00000, +/**/ 0x3D248C4B, 0x86930551, +/**/ 0xBF424D61, 0xADE67EE6, +/**/ 0x3F424EB0, 0xC7000000, +/**/ 0xBD2D6F13, 0xB3649FF7, +/**/ 0xBF425D5D, 0x18E2AD76, +/**/ 0x3F425EAE, 0x7C400000, +/**/ 0x3D396F87, 0xB496441D, +/**/ 0xBF426D58, 0x7FE09487, +/**/ 0x3F426EAC, 0x2FA00000, +/**/ 0x3D05E2D0, 0x01961A2F, +/**/ 0xBF427D53, 0xE2E03598, +/**/ 0x3F427EA9, 0xE1000000, +/**/ 0xBD32D013, 0x652D1720, +/**/ 0xBF428D4F, 0x41E1922A, +/**/ 0x3F428EA7, 0x90400000, +/**/ 0x3D38CB3F, 0x15C6A78A, +/**/ 0xBF429D4A, 0x9CE4ABBA, +/**/ 0x3F429EA5, 0x3DA00000, +/**/ 0x3D163D44, 0x07F8A52A, +/**/ 0xBF42AD45, 0xF3E983C8, +/**/ 0x3F42AEA2, 0xE9000000, +/**/ 0xBD2905BC, 0x1FEC6070, +/**/ 0xBF42BD41, 0x46F01BD4, +/**/ 0x3F42BEA0, 0x92600000, +/**/ 0xBD3D6A4E, 0x8FE5CB8E, +/**/ 0xBF42CD3C, 0x95F8755C, +/**/ 0x3F42CE9E, 0x39A00000, +/**/ 0x3D32D9FF, 0x120028B6, +/**/ 0xBF42DD37, 0xE10291DF, +/**/ 0x3F42DE9B, 0xDF000000, +/**/ 0x3D112C29, 0x94B2D8A6, +/**/ 0xBF42ED33, 0x280E72DD, +/**/ 0x3F42EE99, 0x82600000, +/**/ 0xBD222C5A, 0x0E9DC27F, +/**/ 0xBF42FD2E, 0x6B1C19D4, +/**/ 0x3F42FE97, 0x23C00000, +/**/ 0xBD3548A7, 0xA4C12307, +/**/ 0xBF430D29, 0xAA2B8844, +/**/ 0x3F430E94, 0xC3000000, +/**/ 0x3D3FB49A, 0x1B27A40C, +/**/ 0xBF431D24, 0xE53CBFAC, +/**/ 0x3F431E92, 0x60600000, +/**/ 0x3D35E297, 0xC65D601D, +/**/ 0xBF432D20, 0x1C4FC18B, +/**/ 0x3F432E8F, 0xFBC00000, +/**/ 0x3D2A84A1, 0xD4E46CD5, +/**/ 0xBF433D1B, 0x4F648F60, +/**/ 0x3F433E8D, 0x95200000, +/**/ 0x3D175314, 0x526215F8, +/**/ 0xBF434D16, 0x7E7B2AAB, +/**/ 0x3F434E8B, 0x2C800000, +/**/ 0xBCD9430B, 0x9746A94C, +/**/ 0xBF435D11, 0xA99394E9, +/**/ 0x3F435E88, 0xC1E00000, +/**/ 0xBD15A88D, 0x47EF6144, +/**/ 0xBF436D0C, 0xD0ADCF9B, +/**/ 0x3F436E86, 0x55400000, +/**/ 0xBD227301, 0x94614FFB, +/**/ 0xBF437D07, 0xF3C9DC3F, +/**/ 0x3F437E83, 0xE6A00000, +/**/ 0xBD27A44A, 0x16908831, +/**/ 0xBF438D03, 0x12E7BC55, +/**/ 0x3F438E81, 0x76000000, +/**/ 0xBD2A6621, 0x13DE59AC, +/**/ 0xBF439CFE, 0x2E07715C, +/**/ 0x3F439E7F, 0x03600000, +/**/ 0xBD2AB687, 0x76635000, +/**/ 0xBF43ACF9, 0x4528FCD2, +/**/ 0x3F43AE7C, 0x8EC00000, +/**/ 0xBD28937E, 0x28F7818F, +/**/ 0xBF43BCF4, 0x584C6037, +/**/ 0x3F43BE7A, 0x18200000, +/**/ 0xBD23FB06, 0x17328F27, +/**/ 0xBF43CCEF, 0x67719D0A, +/**/ 0x3F43CE77, 0x9F800000, +/**/ 0xBD19D640, 0x5AD74747, +/**/ 0xBF43DCEA, 0x7298B4CA, +/**/ 0x3F43DE75, 0x24E00000, +/**/ 0xBCFB0E6A, 0xC5CB9C74, +/**/ 0xBF43ECE5, 0x79C1A8F6, +/**/ 0x3F43EE72, 0xA8400000, +/**/ 0x3D1145E2, 0xF21B8682, +/**/ 0xBF43FCE0, 0x7CEC7B0D, +/**/ 0x3F43FE70, 0x29A00000, +/**/ 0x3D27251B, 0x59543A06, +/**/ 0xBF440CDB, 0x7C192C8E, +/**/ 0x3F440E6D, 0xA9000000, +/**/ 0x3D341357, 0xAC6250B6, +/**/ 0xBF441CD6, 0x7747BEF8, +/**/ 0x3F441E6B, 0x26600000, +/**/ 0x3D3DD4D6, 0x43A510F7, +/**/ 0xBF442CD1, 0x6E7833CB, +/**/ 0x3F442E68, 0xA1E00000, +/**/ 0xBD3727F7, 0x05F7D1E1, +/**/ 0xBF443CCC, 0x61AA8C85, +/**/ 0x3F443E66, 0x1B400000, +/**/ 0xBD25C421, 0x527C9668, +/**/ 0xBF444CC7, 0x50DECAA5, +/**/ 0x3F444E63, 0x92A00000, +/**/ 0x3D053C47, 0x053F70AC, +/**/ 0xBF445CC2, 0x3C14EFAB, +/**/ 0x3F445E61, 0x08000000, +/**/ 0x3D3175D5, 0x1E315FBB, +/**/ 0xBF446CBD, 0x234CFD15, +/**/ 0x3F446E5E, 0x7B800000, +/**/ 0xBD3E762C, 0x6A8B33AC, +/**/ 0xBF447CB8, 0x0686F463, +/**/ 0x3F447E5B, 0xECE00000, +/**/ 0xBD2A36F8, 0x67AD9900, +/**/ 0xBF448CB2, 0xE5C2D713, +/**/ 0x3F448E59, 0x5C400000, +/**/ 0x3D161B95, 0x1E974853, +/**/ 0xBF449CAD, 0xC100A6A5, +/**/ 0x3F449E56, 0xC9A00000, +/**/ 0x3D3971F7, 0x8CE22250, +/**/ 0xBF44ACA8, 0x98406498, +/**/ 0x3F44AE54, 0x35200000, +/**/ 0xBD315945, 0xDF8A23F8, +/**/ 0xBF44BCA3, 0x6B82126A, +/**/ 0x3F44BE51, 0x9E800000, +/**/ 0x3D1498B2, 0x1A63D360, +/**/ 0xBF44CC9E, 0x3AC5B19B, +/**/ 0x3F44CE4F, 0x05E00000, +/**/ 0x3D3CF14E, 0x4323A054, +/**/ 0xBF44DC99, 0x060B43AA, +/**/ 0x3F44DE4C, 0x6B600000, +/**/ 0xBD23EDC2, 0x4CE35F94, +/**/ 0xBF44EC93, 0xCD52CA15, +/**/ 0x3F44EE49, 0xCEC00000, +/**/ 0x3D306E9D, 0xCCF1B48E, +/**/ 0xBF44FC8E, 0x909C465C, +/**/ 0x3F44FE47, 0x30400000, +/**/ 0xBD33DD35, 0x5FF9440B, +/**/ 0xBF450C89, 0x4FE7B9FF, +/**/ 0x3F450E44, 0x8FA00000, +/**/ 0x3D224D49, 0xAA4D276D, +/**/ 0xBF451C84, 0x0B35267A, +/**/ 0x3F451E41, 0xED200000, +/**/ 0xBD3884D4, 0x11B557F9, +/**/ 0xBF452C7E, 0xC2848D4F, +/**/ 0x3F452E3F, 0x48800000, +/**/ 0x3D1C857D, 0xB43290C4, +/**/ 0xBF453C79, 0x75D5EFFC, +/**/ 0x3F453E3C, 0xA2000000, +/**/ 0xBD37E5C1, 0x2D598D3C, +/**/ 0xBF454C74, 0x25294FFF, +/**/ 0x3F454E39, 0xF9600000, +/**/ 0x3D24CD93, 0x3FE47B89, +/**/ 0xBF455C6E, 0xD07EAED8, +/**/ 0x3F455E37, 0x4EE00000, +/**/ 0xBD31F800, 0xAA959122, +/**/ 0xBF456C69, 0x77D60E06, +/**/ 0x3F456E34, 0xA2400000, +/**/ 0x3D32FEDF, 0x7329AF92, +/**/ 0xBF457C64, 0x1B2F6F08, +/**/ 0x3F457E31, 0xF3C00000, +/**/ 0xBD1ACE5A, 0x1C545A6F, +/**/ 0xBF458C5E, 0xBA8AD35D, +/**/ 0x3F458E2F, 0x43400000, +/**/ 0xBD3F0E63, 0x19F6B9EF, +/**/ 0xBF459C59, 0x55E83C84, +/**/ 0x3F459E2C, 0x90A00000, +/**/ 0x3D23DEF2, 0x73005F6F, +/**/ 0xBF45AC53, 0xED47ABFB, +/**/ 0x3F45AE29, 0xDC200000, +/**/ 0xBD277204, 0x1C295DE7, +/**/ 0xBF45BC4E, 0x80A92343, +/**/ 0x3F45BE27, 0x25800000, +/**/ 0x3D3FF92A, 0x8D869589, +/**/ 0xBF45CC49, 0x100CA3D9, +/**/ 0x3F45CE24, 0x6D000000, +/**/ 0x3D2A0DFD, 0x145C5335, +/**/ 0xBF45DC43, 0x9B722F3C, +/**/ 0x3F45DE21, 0xB2800000, +/**/ 0xBD123A1A, 0x6A8614B3, +/**/ 0xBF45EC3E, 0x22D9C6ED, +/**/ 0x3F45EE1E, 0xF6000000, +/**/ 0xBD34C665, 0x63CBC7E7, +/**/ 0xBF45FC38, 0xA6436C69, +/**/ 0x3F45FE1C, 0x37600000, +/**/ 0x3D3C6061, 0xAB6C51D7, +/**/ 0xBF460C33, 0x25AF2130, +/**/ 0x3F460E19, 0x76E00000, +/**/ 0x3D2DCD9C, 0x1EC7F453, +/**/ 0xBF461C2D, 0xA11CE6C1, +/**/ 0x3F461E16, 0xB4600000, +/**/ 0x3D066EFA, 0x20C52899, +/**/ 0xBF462C28, 0x188CBE9A, +/**/ 0x3F462E13, 0xEFE00000, +/**/ 0xBD1FA5AC, 0xEB5FDD5C, +/**/ 0xBF463C22, 0x8BFEAA3B, +/**/ 0x3F463E11, 0x29600000, +/**/ 0xBD313E11, 0xF22FE2BC, +/**/ 0xBF464C1C, 0xFB72AB23, +/**/ 0x3F464E0E, 0x60E00000, +/**/ 0xBD392F15, 0x6710E251, +/**/ 0xBF465C17, 0x66E8C2D0, +/**/ 0x3F465E0B, 0x96600000, +/**/ 0xBD3FBB76, 0x1EFC78A7, +/**/ 0xBF466C11, 0xCE60F2C1, +/**/ 0x3F466E08, 0xC9C00000, +/**/ 0x3D3B1DCB, 0x602C1A84, +/**/ 0xBF467C0C, 0x31DB3C76, +/**/ 0x3F467E05, 0xFB400000, +/**/ 0x3D375DAE, 0x9027DA74, +/**/ 0xBF468C06, 0x9157A16E, +/**/ 0x3F468E03, 0x2AC00000, +/**/ 0x3D350532, 0xEA560DA0, +/**/ 0xBF469C00, 0xECD62326, +/**/ 0x3F469E00, 0x58400000, +/**/ 0x3D341557, 0xE7B63DE2 } }; + +#else +#ifdef LITTLE_ENDI +static const union {int4 i[5800]; double x[2900];} ui = { .i = { +/**/ 0x00000000, 0x3FF6A000, +/**/ 0x3729043E, 0x3F33CD15, +/**/ 0x0B3AB000, 0xBFD63003, +/**/ 0xE731AE00, 0x3D2DB623, +/**/ 0x00000000, 0x3FF69800, +/**/ 0xCC7267D0, 0x3F33F349, +/**/ 0xCDB03000, 0xBFD61965, +/**/ 0x603C488E, 0x3D2F08AD, +/**/ 0x00000000, 0x3FF69000, +/**/ 0x8D0BFD2E, 0x3F3473A8, +/**/ 0x8AF09000, 0xBFD602D0, +/**/ 0x76DF3F65, 0xBD1EBE91, +/**/ 0x00000000, 0x3FF68800, +/**/ 0x390B9ED0, 0x3F354DD2, +/**/ 0x3D5C3000, 0xBFD5EC43, +/**/ 0x1229D17F, 0xBD36B71A, +/**/ 0x00000000, 0x3FF68000, +/**/ 0x16816817, 0x3F368168, +/**/ 0xDF596000, 0xBFD5D5BD, +/**/ 0x08A465DC, 0x3D0A0B2A, +/**/ 0x00000000, 0x3FF67800, +/**/ 0xF08C7765, 0x3F380E0B, +/**/ 0x6B544000, 0xBFD5BF40, +/**/ 0xEB68981C, 0x3D227023, +/**/ 0x00000000, 0x3FF67000, +/**/ 0x16719F36, 0x3F39F360, +/**/ 0xDBBEE000, 0xBFD5A8CA, +/**/ 0x0AF7ECF8, 0x3CF7C79B, +/**/ 0x00000000, 0x3FF66800, +/**/ 0x5AB40167, 0x3F3C3107, +/**/ 0x2B113000, 0xBFD5925D, +/**/ 0xA7A56F34, 0x3D369BF5, +/**/ 0x00000000, 0x3FF66000, +/**/ 0x122F9016, 0x3F3EC6A5, +/**/ 0x53C8D000, 0xBFD57BF7, +/**/ 0xEE5D40EF, 0xBD1FADED, +/**/ 0x00000000, 0x3FF65C00, +/**/ 0xECCA9097, 0xBF3E4C22, +/**/ 0x50695000, 0xBFD56599, +/**/ 0x2BADC774, 0xBD14C5FD, +/**/ 0x00000000, 0x3FF65400, +/**/ 0x4B55CC62, 0xBF3B07AC, +/**/ 0x1B7BE000, 0xBFD54F43, +/**/ 0xC0910952, 0xBD1A8954, +/**/ 0x00000000, 0x3FF64C00, +/**/ 0x32DA090E, 0xBF376C52, +/**/ 0xAF8F7000, 0xBFD538F4, +/**/ 0xE45547CE, 0xBD27EC02, +/**/ 0x00000000, 0x3FF64400, +/**/ 0x4DE9BD38, 0xBF337A6F, +/**/ 0x0738A000, 0xBFD522AE, +/**/ 0x8164C759, 0xBD2EBE70, +/**/ 0x00000000, 0x3FF63C00, +/**/ 0x923C708B, 0xBF2E64BB, +/**/ 0x1D11C000, 0xBFD50C6F, +/**/ 0x7E827C2C, 0x3D3A0E6B, +/**/ 0x00000000, 0x3FF63400, +/**/ 0xA7E43FD4, 0xBF2528EE, +/**/ 0xEBBAA000, 0xBFD4F637, +/**/ 0xCB3124B9, 0x3D3FC158, +/**/ 0x00000000, 0x3FF62C00, +/**/ 0x86689DF7, 0xBF168454, +/**/ 0x6DD8C000, 0xBFD4E008, +/**/ 0xA1E44788, 0x3D34D692, +/**/ 0x00000000, 0x3FF62400, +/**/ 0x77016240, 0xBED623FA, +/**/ 0x9E173000, 0xBFD4C9E0, +/**/ 0x1B0AD8A4, 0x3D2E2089, +/**/ 0x00000000, 0x3FF61C00, +/**/ 0x58715130, 0x3F151300, +/**/ 0x77268000, 0xBFD4B3C0, +/**/ 0x81052B9F, 0x3D165B46, +/**/ 0x00000000, 0x3FF61400, +/**/ 0x35D2754E, 0x3F266D06, +/**/ 0xF3BCC000, 0xBFD49DA7, +/**/ 0x4DAF4B9A, 0xBD307B33, +/**/ 0x00000000, 0x3FF60C00, +/**/ 0xDA197F23, 0x3F317C61, +/**/ 0x0E958000, 0xBFD48797, +/**/ 0x465CF25F, 0xBD3DC1B8, +/**/ 0x00000000, 0x3FF60400, +/**/ 0x81605816, 0x3F381605, +/**/ 0xC271C000, 0xBFD4718D, +/**/ 0xFB4C14C5, 0xBD306C18, +/**/ 0x00000000, 0x3FF5FC00, +/**/ 0xB5C6F559, 0x3F3F0317, +/**/ 0x0A17E000, 0xBFD45B8C, +/**/ 0xE7D0A853, 0x3D0D9120, +/**/ 0x00000000, 0x3FF5F800, +/**/ 0x6D2041E3, 0xBF39BCBD, +/**/ 0xE053A000, 0xBFD44591, +/**/ 0x92923D88, 0x3D06E958, +/**/ 0x00000000, 0x3FF5F000, +/**/ 0x5604CC40, 0xBF3229CF, +/**/ 0x3FF62000, 0xBFD42F9F, +/**/ 0x0F7D3354, 0xBD390644, +/**/ 0x00000000, 0x3FF5E800, +/**/ 0xFD431489, 0xBF2488E5, +/**/ 0x23D5F000, 0xBFD419B4, +/**/ 0x226DE3EC, 0x3D3CE379, +/**/ 0x00000000, 0x3FF5E000, +/**/ 0x6424E9C9, 0xBF0067E7, +/**/ 0x86CEA000, 0xBFD403D0, +/**/ 0x74487308, 0xBD3E6EF5, +/**/ 0x00000000, 0x3FF5D800, +/**/ 0x38A94D24, 0x3F19F0FB, +/**/ 0x63C17000, 0xBFD3EDF4, +/**/ 0x297F2C3F, 0x3D3F067C, +/**/ 0x00000000, 0x3FF5D000, +/**/ 0x23CAD2AA, 0x3F2EADD9, +/**/ 0xB5947000, 0xBFD3D81F, +/**/ 0x2A9D37A4, 0x3D222C7C, +/**/ 0x00000000, 0x3FF5C800, +/**/ 0x31057262, 0x3F3882B9, +/**/ 0x77333000, 0xBFD3C252, +/**/ 0xB606BD5C, 0xBD183B54, +/**/ 0x00000000, 0x3FF5C400, +/**/ 0x10FFA8F8, 0xBF3E00AE, +/**/ 0xA38E6000, 0xBFD3AC8C, +/**/ 0xBC02BE4A, 0x3D2D0BEF, +/**/ 0x00000000, 0x3FF5BC00, +/**/ 0x8056EAF3, 0xBF34339B, +/**/ 0x359BC000, 0xBFD396CE, +/**/ 0x5663663D, 0x3D05839C, +/**/ 0x00000000, 0x3FF5B400, +/**/ 0xF31D7FD5, 0xBF242CC1, +/**/ 0x28565000, 0xBFD38117, +/**/ 0x93A0702B, 0x3D2A71E4, +/**/ 0x00000000, 0x3FF5AC00, +/**/ 0x6B015AC0, 0x3ED5AC05, +/**/ 0x76BE1000, 0xBFD36B67, +/**/ 0xB0F177C8, 0xBD116ECD, +/**/ 0x00000000, 0x3FF5A400, +/**/ 0x5BA55E5A, 0x3F26268D, +/**/ 0x1BD83000, 0xBFD355BF, +/**/ 0x8964F0E8, 0x3D2BA99B, +/**/ 0x00000000, 0x3FF59C00, +/**/ 0x3CCAA376, 0x3F361F12, +/**/ 0x12AED000, 0xBFD3401E, +/**/ 0x556E291D, 0x3D317C73, +/**/ 0x00000000, 0x3FF59800, +/**/ 0x62D32417, 0xBF3E863D, +/**/ 0x56512000, 0xBFD32A84, +/**/ 0x139AF5D6, 0xBD04F928, +/**/ 0x00000000, 0x3FF59000, +/**/ 0xEA712DCF, 0xBF32DCF7, +/**/ 0xE1D36000, 0xBFD314F1, +/**/ 0xD3213CB8, 0x3D28E27A, +/**/ 0x00000000, 0x3FF58800, +/**/ 0xA0CC87E8, 0xBF1B95B2, +/**/ 0xB04EB000, 0xBFD2FF66, +/**/ 0x541E6E2E, 0x3D38AED2, +/**/ 0x00000000, 0x3FF58000, +/**/ 0x01580560, 0x3F158056, +/**/ 0xBCE12000, 0xBFD2E9E2, +/**/ 0x128D1DC2, 0xBD24300C, +/**/ 0x00000000, 0x3FF57800, +/**/ 0x15791F34, 0x3F31F340, +/**/ 0x02ADD000, 0xBFD2D466, +/**/ 0xDCD54196, 0x3D288D0D, +/**/ 0x00000000, 0x3FF57000, +/**/ 0x06B39A23, 0x3F3ED3C5, +/**/ 0x7CDC9000, 0xBFD2BEF0, +/**/ 0x4A5004F4, 0xBD2A9CFA, +/**/ 0x00000000, 0x3FF56C00, +/**/ 0x53FEA954, 0xBF33FEA9, +/**/ 0x269A4000, 0xBFD2A982, +/**/ 0x557285CF, 0x3D22058E, +/**/ 0x00000000, 0x3FF56400, +/**/ 0xEB478503, 0xBF1A1160, +/**/ 0xFB187000, 0xBFD2941A, +/**/ 0xB730E28B, 0x3D3210C2, +/**/ 0x00000000, 0x3FF55C00, +/**/ 0xE4A18B2E, 0x3F1D09AD, +/**/ 0xF58D9000, 0xBFD27EBA, +/**/ 0x00B4BDA7, 0x3D2B1988, +/**/ 0x00000000, 0x3FF55400, +/**/ 0x55555555, 0x3F355555, +/**/ 0x1134E000, 0xBFD26962, +/**/ 0x10522625, 0x3D31B61F, +/**/ 0x00000000, 0x3FF55000, +/**/ 0xB319A21F, 0xBF3C4BE6, +/**/ 0x494E5000, 0xBFD25410, +/**/ 0xC0EF77F2, 0xBD3B1D7A, +/**/ 0x00000000, 0x3FF54800, +/**/ 0x8FA03FD5, 0xBF2B4328, +/**/ 0x991EC000, 0xBFD23EC5, +/**/ 0x48A2E522, 0x3D36DBE4, +/**/ 0x00000000, 0x3FF54000, +/**/ 0x40154015, 0x3EF54015, +/**/ 0xFBEF8000, 0xBFD22981, +/**/ 0x609580DA, 0x3D3A1421, +/**/ 0x00000000, 0x3FF53800, +/**/ 0x40FEAC6F, 0x3F30948F, +/**/ 0x6D0EC000, 0xBFD21445, +/**/ 0x28B728A3, 0x3D3CAF04, +/**/ 0x00000000, 0x3FF53400, +/**/ 0xFD04F7B8, 0xBF3FE034, +/**/ 0xE7CF4000, 0xBFD1FF0F, +/**/ 0x513FF0C1, 0xBD3E9D5B, +/**/ 0x00000000, 0x3FF52C00, +/**/ 0x7FAB5403, 0xBF300A95, +/**/ 0x6788A000, 0xBFD1E9E1, +/**/ 0xD3C8B65E, 0x3D382EAE, +/**/ 0x00000000, 0x3FF52400, +/**/ 0x52401524, 0x3EB52401, +/**/ 0xE796C000, 0xBFD1D4B9, +/**/ 0x7C42E56D, 0xBD222A66, +/**/ 0x00000000, 0x3FF51C00, +/**/ 0x2F8151D0, 0x3F307EAE, +/**/ 0x635A7000, 0xBFD1BF99, +/**/ 0x575C2125, 0x3D31AC89, +/**/ 0x00000000, 0x3FF51800, +/**/ 0xEAE9ECE4, 0xBF3ECE3F, +/**/ 0xD638D000, 0xBFD1AA7F, +/**/ 0x9616F7A0, 0xBD29F60A, +/**/ 0x00000000, 0x3FF51000, +/**/ 0xC7675243, 0xBF2BA3DD, +/**/ 0x3B9BC000, 0xBFD1956D, +/**/ 0x3AD1AA14, 0xBD27D2F7, +/**/ 0x00000000, 0x3FF50800, +/**/ 0x764E368D, 0x3F0B9AC8, +/**/ 0x8EF19000, 0xBFD18061, +/**/ 0xC86D38E5, 0x3D3482FF, +/**/ 0x00000000, 0x3FF50000, +/**/ 0x15015015, 0x3F350150, +/**/ 0xCBAD0000, 0xBFD16B5C, +/**/ 0x042D74BF, 0x3D323299, +/**/ 0x00000000, 0x3FF4FC00, +/**/ 0x4A683C50, 0xBF392851, +/**/ 0xED456000, 0xBFD1565E, +/**/ 0xFB6ABA25, 0x3CEE75AD, +/**/ 0x00000000, 0x3FF4F400, +/**/ 0xACD95EF0, 0xBF1C2748, +/**/ 0xEF367000, 0xBFD14167, +/**/ 0x824DAAF5, 0xBD3E0C07, +/**/ 0x00000000, 0x3FF4EC00, +/**/ 0x67A47465, 0x3F26B90D, +/**/ 0xCD007000, 0xBFD12C77, +/**/ 0x8A11F797, 0xBD13B294, +/**/ 0x00000000, 0x3FF4E400, +/**/ 0xF0539783, 0x3F3E0A72, +/**/ 0x8227E000, 0xBFD1178E, +/**/ 0xCE2D07F2, 0xBD31EF78, +/**/ 0x00000000, 0x3FF4E000, +/**/ 0xF87FD642, 0xBF2E00A6, +/**/ 0x0A35D000, 0xBFD102AC, +/**/ 0xDFDFD686, 0x3D2F1FBD, +/**/ 0x00000000, 0x3FF4D800, +/**/ 0x0B12E3FD, 0x3F10EFB7, +/**/ 0x60B78000, 0xBFD0EDD0, +/**/ 0x2D8435F5, 0xBD0019B5, +/**/ 0x00000000, 0x3FF4D000, +/**/ 0x5CB4DBE5, 0x3F37BEF1, +/**/ 0x813EB000, 0xBFD0D8FB, +/**/ 0x8753FA35, 0xBD1EE8C8, +/**/ 0x00000000, 0x3FF4CC00, +/**/ 0xA50918B1, 0xBF34778D, +/**/ 0x67616000, 0xBFD0C42D, +/**/ 0x163CEAE9, 0xBD27188B, +/**/ 0x00000000, 0x3FF4C400, +/**/ 0xE37288EC, 0xBED9F4F7, +/**/ 0x0EB9E000, 0xBFD0AF66, +/**/ 0xF528D80A, 0xBD23C7C3, +/**/ 0x00000000, 0x3FF4BC00, +/**/ 0x68FE0E42, 0x3F33EDDA, +/**/ 0x72E6C000, 0xBFD09AA5, +/**/ 0xE1734342, 0xBD3B50A1, +/**/ 0x00000000, 0x3FF4B800, +/**/ 0xB72E47D9, 0xBF3776C6, +/**/ 0x8F8AE000, 0xBFD085EB, +/**/ 0x3F45FE7B, 0xBD3E5D51, +/**/ 0x00000000, 0x3FF4B000, +/**/ 0xA052BF5B, 0xBF04AFD6, +/**/ 0x604D6000, 0xBFD07138, +/**/ 0x4E912B17, 0x3D3E7632, +/**/ 0x00000000, 0x3FF4A800, +/**/ 0xD5B5C015, 0x3F328FFA, +/**/ 0xE0D96000, 0xBFD05C8B, +/**/ 0xC77CCB58, 0xBD2AD0F1, +/**/ 0x00000000, 0x3FF4A400, +/**/ 0x9FEB5D80, 0xBF380528, +/**/ 0x0CDE8000, 0xBFD047E6, +/**/ 0x0D397F3C, 0xBD2DBDF1, +/**/ 0x00000000, 0x3FF49C00, +/**/ 0x25FF5B21, 0xBF02AD3E, +/**/ 0xE0106000, 0xBFD03346, +/**/ 0xA966395C, 0xBCF89FF8, +/**/ 0x00000000, 0x3FF49400, +/**/ 0x2D066EA2, 0x3F339E3B, +/**/ 0x5626C000, 0xBFD01EAE, +/**/ 0xFADE85AE, 0xBD3A43DC, +/**/ 0x00000000, 0x3FF49000, +/**/ 0xAFB2E932, 0xBF3629C1, +/**/ 0x6ADDA000, 0xBFD00A1C, +/**/ 0x688B9E18, 0xBD31CD8D, +/**/ 0x00000000, 0x3FF48800, +/**/ 0x22014880, 0x3ED48805, +/**/ 0x33EA0000, 0xBFCFEB22, +/**/ 0xDE00938B, 0xBD2F3418, +/**/ 0x00000000, 0x3FF48000, +/**/ 0x3D324D89, 0x3F37119F, +/**/ 0xBE620000, 0xBFCFC218, +/**/ 0x6F1CF6A0, 0xBD34BBA4, +/**/ 0x00000000, 0x3FF47C00, +/**/ 0x1EB851EC, 0xBF31EB85, +/**/ 0x6CB3C000, 0xBFCF991C, +/**/ 0xCD7CC834, 0x3D390D04, +/**/ 0x00000000, 0x3FF47400, +/**/ 0xAAFC7C01, 0x3F1569C9, +/**/ 0x36778000, 0xBFCF702D, +/**/ 0x16673E23, 0x3D108195, +/**/ 0x00000000, 0x3FF46C00, +/**/ 0x96066250, 0x3F3CE345, +/**/ 0x134E0000, 0xBFCF474B, +/**/ 0xF1DF7B5E, 0x3D3BAE49, +/**/ 0x00000000, 0x3FF46800, +/**/ 0x1D02DE87, 0xBF26A297, +/**/ 0xFADFA000, 0xBFCF1E75, +/**/ 0x25D83F6D, 0x3D20862B, +/**/ 0x00000000, 0x3FF46000, +/**/ 0xB9F34381, 0x3F2978FE, +/**/ 0xE4DD0000, 0xBFCEF5AD, +/**/ 0x65BB8E11, 0x3CCA2115, +/**/ 0x00000000, 0x3FF45C00, +/**/ 0xF6C71366, 0xBF3AF398, +/**/ 0xC8FEA000, 0xBFCECCF2, +/**/ 0xA3E75640, 0x3D3BEC63, +/**/ 0x00000000, 0x3FF45400, +/**/ 0x449AFF5D, 0xBF030E9C, +/**/ 0x9F04A000, 0xBFCEA444, +/**/ 0x63732A36, 0xBD35E916, +/**/ 0x00000000, 0x3FF44C00, +/**/ 0xF8B42EF3, 0x3F367190, +/**/ 0x5EB78000, 0xBFCE7BA3, +/**/ 0x23793649, 0x3D0D5EEE, +/**/ 0x00000000, 0x3FF44800, +/**/ 0xD260511C, 0xBF3079A9, +/**/ 0xFFE72000, 0xBFCE530E, +/**/ 0xB13F7C18, 0x3D3FDBDB, +/**/ 0x00000000, 0x3FF44000, +/**/ 0x0B644FBE, 0x3F21B87C, +/**/ 0x7A6B2000, 0xBFCE2A87, +/**/ 0x7787081A, 0xBD382381, +/**/ 0x00000000, 0x3FF43C00, +/**/ 0x411B2E25, 0xBF3D8CF5, +/**/ 0xC6236000, 0xBFCE020C, +/**/ 0xADB91424, 0x3D252B00, +/**/ 0x00000000, 0x3FF43400, +/**/ 0xD6A60978, 0xBF0DAC08, +/**/ 0xDAF6E000, 0xBFCDD99E, +/**/ 0x69C756EB, 0x3D302EC6, +/**/ 0x00000000, 0x3FF42C00, +/**/ 0x51F86EFA, 0x3F36625D, +/**/ 0xB0D48000, 0xBFCDB13D, +/**/ 0x847527E6, 0xBD32806A, +/**/ 0x00000000, 0x3FF42800, +/**/ 0xA8766564, 0xBF2E8B2D, +/**/ 0x3FB30000, 0xBFCD88E9, +/**/ 0x0234BF51, 0x3D375F28, +/**/ 0x00000000, 0x3FF42000, +/**/ 0xCB2A247B, 0x3F26A4CB, +/**/ 0x7F904000, 0xBFCD60A1, +/**/ 0x6FC20D39, 0x3D35D6E0, +/**/ 0x00000000, 0x3FF41C00, +/**/ 0xC17DF552, 0xBF39D5E8, +/**/ 0x68720000, 0xBFCD3866, +/**/ 0xB38932BC, 0x3D373650, +/**/ 0x00000000, 0x3FF41400, +/**/ 0x14141414, 0x3EF41414, +/**/ 0xF2656000, 0xBFCD1037, +/**/ 0x75B6F6E4, 0x3D084A7E, +/**/ 0x00000000, 0x3FF40C00, +/**/ 0x43AE87FD, 0x3F3C97A8, +/**/ 0x157F2000, 0xBFCCE816, +/**/ 0xA2099515, 0x3D29E0AB, +/**/ 0x00000000, 0x3FF40800, +/**/ 0x66A67E6F, 0xBF1F4BBC, +/**/ 0xC9DB4000, 0xBFCCC000, +/**/ 0x5D57AFF9, 0x3D1D6D58, +/**/ 0x00000000, 0x3FF40000, +/**/ 0x14014014, 0x3F340140, +/**/ 0x079D4000, 0xBFCC97F8, +/**/ 0xA8C6E6C5, 0xBD23B161, +/**/ 0x00000000, 0x3FF3FC00, +/**/ 0xFD809FD8, 0xBF2FD809, +/**/ 0xC6F00000, 0xBFCC6FFB, +/**/ 0xD3A69D43, 0xBD3EE138, +/**/ 0x00000000, 0x3FF3F400, +/**/ 0x57EE89D2, 0x3F28CA0E, +/**/ 0x0005C000, 0xBFCC480C, +/**/ 0xD5E44E76, 0xBD39A294, +/**/ 0x00000000, 0x3FF3F000, +/**/ 0xA50F9260, 0xBF370BD5, +/**/ 0xAB180000, 0xBFCC2028, +/**/ 0xE55C7AC6, 0x3D292E0E, +/**/ 0x00000000, 0x3FF3E800, +/**/ 0x75945FCE, 0x3F1704AA, +/**/ 0xC0676000, 0xBFCBF851, +/**/ 0x4C0854AD, 0x3D35420E, +/**/ 0x00000000, 0x3FF3E400, +/**/ 0xB56FD83C, 0xBF3D3431, +/**/ 0x383BE000, 0xBFCBD087, +/**/ 0x595412B6, 0x3D2D4BC4, +/**/ 0x00000000, 0x3FF3DC00, +/**/ 0x3DC013DC, 0x3EB3DC01, +/**/ 0x0AE4A000, 0xBFCBA8C9, +/**/ 0xF44432DA, 0xBD3A32E7, +/**/ 0x00000000, 0x3FF3D400, +/**/ 0xA75C5BBD, 0x3F3D991A, +/**/ 0x30B82000, 0xBFCB8117, +/**/ 0x3B9CD768, 0xBD1E9068, +/**/ 0x00000000, 0x3FF3D000, +/**/ 0x59C52F5D, 0xBF1292BA, +/**/ 0xA213A000, 0xBFCB5971, +/**/ 0x83AA91DF, 0xBD39B50E, +/**/ 0x00000000, 0x3FF3C800, +/**/ 0xBABE7440, 0x3F395A47, +/**/ 0x575BC000, 0xBFCB31D8, +/**/ 0x562A63CB, 0xBD3C794E, +/**/ 0x00000000, 0x3FF3C400, +/**/ 0x58A0943A, 0xBF20D475, +/**/ 0x48FC2000, 0xBFCB0A4B, +/**/ 0x5C3998ED, 0x3D22E72D, +/**/ 0x00000000, 0x3FF3BC00, +/**/ 0x3295482C, 0x3F360D92, +/**/ 0x6F672000, 0xBFCAE2CA, +/**/ 0xAE54F550, 0xBD37A8D5, +/**/ 0x00000000, 0x3FF3B800, +/**/ 0xCAB48651, 0xBF267D12, +/**/ 0xC316A000, 0xBFCABB55, +/**/ 0xCAF14CD8, 0x3D38A65A, +/**/ 0x00000000, 0x3FF3B000, +/**/ 0x13B13B14, 0x3F33B13B, +/**/ 0x3C8AE000, 0xBFCA93ED, +/**/ 0x50562169, 0x3D287243, +/**/ 0x00000000, 0x3FF3AC00, +/**/ 0x2C8FD3BF, 0xBF2A46AF, +/**/ 0xD44B8000, 0xBFCA6C90, +/**/ 0xF037B0C6, 0x3D3F63B7, +/**/ 0x00000000, 0x3FF3A400, +/**/ 0xAC822610, 0x3F324387, +/**/ 0x82E6A000, 0xBFCA4540, +/**/ 0xC81F7171, 0xBD360A77, +/**/ 0x00000000, 0x3FF3A000, +/**/ 0xA1923DEE, 0xBF2C34BB, +/**/ 0x40F1C000, 0xBFCA1DFC, +/**/ 0x004F3781, 0x3D301E0F, +/**/ 0x00000000, 0x3FF39800, +/**/ 0x87F63372, 0x3F31C2C1, +/**/ 0x0708A000, 0xBFC9F6C4, +/**/ 0x4BCD3F43, 0x3D3337D9, +/**/ 0x00000000, 0x3FF39400, +/**/ 0xE11BD52E, 0xBF2C4AA0, +/**/ 0xCDCE0000, 0xBFC9CF97, +/**/ 0x10C414E3, 0xBD3D862F, +/**/ 0x00000000, 0x3FF38C00, +/**/ 0x6088DBF4, 0x3F322D36, +/**/ 0x8DEBA000, 0xBFC9A877, +/**/ 0x3EFEC390, 0xBD3470FA, +/**/ 0x00000000, 0x3FF38800, +/**/ 0x503F774E, 0xBF2A8BBF, +/**/ 0x4011A000, 0xBFC98163, +/**/ 0x9E9045E2, 0xBD34EADD, +/**/ 0x00000000, 0x3FF38000, +/**/ 0x13813814, 0x3F338138, +/**/ 0xDCF70000, 0xBFC95A5A, +/**/ 0x58A0FF6F, 0xBD07F228, +/**/ 0x00000000, 0x3FF37C00, +/**/ 0x1B177053, 0xBF26FB6F, +/**/ 0x5D594000, 0xBFC9335E, +/**/ 0x3ABD47DA, 0xBD33115C, +/**/ 0x00000000, 0x3FF37400, +/**/ 0x945EDC20, 0x3F35BD1C, +/**/ 0xB9FCC000, 0xBFC90C6D, +/**/ 0x7718D7CA, 0x3D1935F5, +/**/ 0x00000000, 0x3FF37000, +/**/ 0x4DBDCC60, 0xBF219D00, +/**/ 0xEBAC2000, 0xBFC8E588, +/**/ 0xAB2D1140, 0xBD3B7D5C, +/**/ 0x00000000, 0x3FF36800, +/**/ 0xE0747954, 0x3F38DF3D, +/**/ 0xEB390000, 0xBFC8BEAF, +/**/ 0xAAE92CD1, 0x3D073D54, +/**/ 0x00000000, 0x3FF36400, +/**/ 0xD9D3C49F, 0xBF14E775, +/**/ 0xB17B2000, 0xBFC897E2, +/**/ 0x380CBE9E, 0x3D296B37, +/**/ 0x00000000, 0x3FF35C00, +/**/ 0xF2AF821E, 0x3F3CE5F9, +/**/ 0x3750E000, 0xBFC87121, +/**/ 0x42F9AF75, 0xBD3328EB, +/**/ 0x00000000, 0x3FF35800, +/**/ 0xE34971F2, 0xBEE82DF0, +/**/ 0x759F6000, 0xBFC84A6B, +/**/ 0x2ADF8609, 0x3D3DA280, +/**/ 0x00000000, 0x3FF35400, +/**/ 0x4873ECAE, 0xBF3E304D, +/**/ 0x6551A000, 0xBFC823C1, +/**/ 0x9A631E83, 0xBD1E0DDB, +/**/ 0x00000000, 0x3FF34C00, +/**/ 0x1FF659DB, 0x3F1264B6, +/**/ 0xFF59A000, 0xBFC7FD22, +/**/ 0xF457B7D2, 0x3D158BEB, +/**/ 0x00000000, 0x3FF34800, +/**/ 0xFECB9865, 0xBF386531, +/**/ 0x3CAF6000, 0xBFC7D690, +/**/ 0x17C301D7, 0x3D24C06B, +/**/ 0x00000000, 0x3FF34000, +/**/ 0xEEDA65AE, 0x3F25A8C2, +/**/ 0x16516000, 0xBFC7B009, +/**/ 0xCB067E57, 0x3D3AE75F, +/**/ 0x00000000, 0x3FF33C00, +/**/ 0x8434E1F4, 0xBF31BA4A, +/**/ 0x85444000, 0xBFC7898D, +/**/ 0xE3DBAF3F, 0xBD38E67B, +/**/ 0x00000000, 0x3FF33400, +/**/ 0xDBFC660A, 0x3F31EE97, +/**/ 0x82936000, 0xBFC7631D, +/**/ 0xC7C5F3E1, 0x3D25E77D, +/**/ 0x00000000, 0x3FF33000, +/**/ 0xBC40BFDA, 0xBF246252, +/**/ 0x074FE000, 0xBFC73CB9, +/**/ 0x0D0005A6, 0x3D3D66A9, +/**/ 0x00000000, 0x3FF32800, +/**/ 0x13299E64, 0x3F39E640, +/**/ 0x0C914000, 0xBFC71660, +/**/ 0x7CEC3838, 0xBCE51B15, +/**/ 0x00000000, 0x3FF32400, +/**/ 0xEF40991F, 0xBEFCB5D4, +/**/ 0x8B756000, 0xBFC6F012, +/**/ 0x0D31EF0F, 0xBD357739, +/**/ 0x00000000, 0x3FF32000, +/**/ 0xC823D892, 0xBF3D4632, +/**/ 0x7D204000, 0xBFC6C9D0, +/**/ 0xFD9B2DCA, 0x3CDC73FA, +/**/ 0x00000000, 0x3FF31800, +/**/ 0x7AED804C, 0x3F1DD63A, +/**/ 0xDABBE000, 0xBFC6A399, +/**/ 0xE66A15A6, 0x3D38F934, +/**/ 0x00000000, 0x3FF31400, +/**/ 0xE8C11E1A, 0xBF339849, +/**/ 0x9D786000, 0xBFC67D6E, +/**/ 0x30A706D3, 0x3D311E88, +/**/ 0x00000000, 0x3FF30C00, +/**/ 0x0D190131, 0x3F319013, +/**/ 0xBE8C2000, 0xBFC6574E, +/**/ 0x34F0F462, 0x3D398C1D, +/**/ 0x00000000, 0x3FF30800, +/**/ 0xB47A7FDA, 0xBF222315, +/**/ 0x37336000, 0xBFC6313A, +/**/ 0x4F21EA6D, 0x3D144DF5, +/**/ 0x00000000, 0x3FF30000, +/**/ 0x40260390, 0x3F3C82AC, +/**/ 0x00B0A000, 0xBFC60B31, +/**/ 0xC988F814, 0x3D371456, +/**/ 0x00000000, 0x3FF2FC00, +/**/ 0xA2430A62, 0x3F026443, +/**/ 0x144C2000, 0xBFC5E533, +/**/ 0xF3B290EA, 0x3D31CE0B, +/**/ 0x00000000, 0x3FF2F800, +/**/ 0xED097B42, 0xBF37B425, +/**/ 0x6B544000, 0xBFC5BF40, +/**/ 0xEB68981C, 0x3D127023, +/**/ 0x00000000, 0x3FF2F000, +/**/ 0x4AE0553C, 0x3F2D00E3, +/**/ 0xFF1D6000, 0xBFC59958, +/**/ 0x9769CA05, 0x3D3A1D05, +/**/ 0x00000000, 0x3FF2EC00, +/**/ 0x25D69D44, 0xBF262BC0, +/**/ 0xC9018000, 0xBFC5737C, +/**/ 0xA6B887F6, 0xBD39BAA7, +/**/ 0x00000000, 0x3FF2E400, +/**/ 0xE3103D6B, 0x3F3B88B5, +/**/ 0xC2610000, 0xBFC54DAB, +/**/ 0xE5C8D0D8, 0xBD2746FE, +/**/ 0x00000000, 0x3FF2E000, +/**/ 0xC04B8097, 0x3F02E025, +/**/ 0xE4A1C000, 0xBFC527E5, +/**/ 0x8D4B411D, 0x3D34E60B, +/**/ 0x00000000, 0x3FF2DC00, +/**/ 0x2C305021, 0xBF369C22, +/**/ 0x292F6000, 0xBFC5022B, +/**/ 0xFF36A25B, 0xBD348A05, +/**/ 0x00000000, 0x3FF2D400, +/**/ 0xD50A012D, 0x3F30A012, +/**/ 0x897BC000, 0xBFC4DC7B, +/**/ 0x0AE1FF0F, 0xBD0C79B6, +/**/ 0x00000000, 0x3FF2D000, +/**/ 0xBC66484E, 0xBF1FBE29, +/**/ 0xFEFE2000, 0xBFC4B6D6, +/**/ 0xF56E7952, 0xBD1522EC, +/**/ 0x00000000, 0x3FF2C800, +/**/ 0x12C9FB4E, 0x3F3FB4D8, +/**/ 0x8333C000, 0xBFC4913D, +/**/ 0x558124C4, 0x3D353E43, +/**/ 0x00000000, 0x3FF2C400, +/**/ 0x7004B11E, 0x3F1E3432, +/**/ 0x0F9F6000, 0xBFC46BAF, +/**/ 0x0790841A, 0x3D1249CD, +/**/ 0x00000000, 0x3FF2C000, +/**/ 0x5C8EF02F, 0xBF30671A, +/**/ 0x9DC9C000, 0xBFC4462B, +/**/ 0xA711B062, 0x3D384858, +/**/ 0x00000000, 0x3FF2B800, +/**/ 0xD548D9AC, 0x3F37D835, +/**/ 0x27410000, 0xBFC420B3, +/**/ 0xC85A0884, 0x3D116282, +/**/ 0x00000000, 0x3FF2B400, +/**/ 0xAD012B40, 0x3ED2B404, +/**/ 0xA5992000, 0xBFC3FB45, +/**/ 0xC0CAE559, 0xBD319713, +/**/ 0x00000000, 0x3FF2B000, +/**/ 0x8E7302A1, 0xBF370F78, +/**/ 0x126BC000, 0xBFC3D5E3, +/**/ 0x85096C4B, 0xBD13FB2F, +/**/ 0x00000000, 0x3FF2A800, +/**/ 0x3C1053F9, 0x3F31C92F, +/**/ 0x67580000, 0xBFC3B08B, +/**/ 0xF29320FB, 0x3D3AADE8, +/**/ 0x00000000, 0x3FF2A400, +/**/ 0x3DBE2E04, 0xBF14AD94, +/**/ 0x9E028000, 0xBFC38B3E, +/**/ 0x545C17F9, 0x3D370EF0, +/**/ 0x00000000, 0x3FF2A000, +/**/ 0xBED61BED, 0xBF3BED61, +/**/ 0xB015A000, 0xBFC365FC, +/**/ 0xAFB9691B, 0x3D3FD3A0, +/**/ 0x00000000, 0x3FF29800, +/**/ 0x26F004A6, 0x3F2B061A, +/**/ 0x97412000, 0xBFC340C5, +/**/ 0xF7D9D386, 0x3D37A3DC, +/**/ 0x00000000, 0x3FF29400, +/**/ 0xFF6B646D, 0xBF21B488, +/**/ 0x4D3A4000, 0xBFC31B99, +/**/ 0xE3A50810, 0xBD3F098E, +/**/ 0x00000000, 0x3FF29000, +/**/ 0x2CA5D5AC, 0xBF3F0582, +/**/ 0xCBBC0000, 0xBFC2F677, +/**/ 0x2160F40D, 0xBD352B30, +/**/ 0x00000000, 0x3FF28800, +/**/ 0x16025116, 0x3F260251, +/**/ 0x0C868000, 0xBFC2D161, +/**/ 0xCB81B4A1, 0xBD039D6C, +/**/ 0x00000000, 0x3FF28400, +/**/ 0x502065D2, 0xBF258CDF, +/**/ 0x095F6000, 0xBFC2AC55, +/**/ 0xD0C6C8A8, 0x3D1D3466, +/**/ 0x00000000, 0x3FF27C00, +/**/ 0x1CE4D6F8, 0x3F3FA38A, +/**/ 0xBC11A000, 0xBFC28753, +/**/ 0x359302E6, 0xBD37494E, +/**/ 0x00000000, 0x3FF27800, +/**/ 0xDCCA0781, 0x3F247DD5, +/**/ 0x1E6DE000, 0xBFC2625D, +/**/ 0xF09E3D82, 0x3CF52962, +/**/ 0x00000000, 0x3FF27400, +/**/ 0xDB195E8F, 0xBF25E8EF, +/**/ 0x2A49C000, 0xBFC23D71, +/**/ 0x8FD3DF5C, 0xBD100D23, +/**/ 0x00000000, 0x3FF27000, +/**/ 0xFFB647FE, 0xBF3FF6C8, +/**/ 0xD9808000, 0xBFC2188F, +/**/ 0x7F50C701, 0x3D3B3A1E, +/**/ 0x00000000, 0x3FF26800, +/**/ 0xC024D167, 0x3F266F9A, +/**/ 0x25F26000, 0xBFC1F3B9, +/**/ 0x9B083633, 0x3D15F74E, +/**/ 0x00000000, 0x3FF26400, +/**/ 0xEABD0E14, 0xBF22D1BD, +/**/ 0x09854000, 0xBFC1CEED, +/**/ 0x39192AF9, 0x3D315C1C, +/**/ 0x00000000, 0x3FF26000, +/**/ 0xF6D0EEC8, 0xBF3DD8F7, +/**/ 0x7E240000, 0xBFC1AA2B, +/**/ 0xDDE3B366, 0x3D31AC38, +/**/ 0x00000000, 0x3FF25800, +/**/ 0x2A241EF6, 0x3F2BCEB1, +/**/ 0x7DBEC000, 0xBFC18574, +/**/ 0x45BD9B49, 0xBD3E6744, +/**/ 0x00000000, 0x3FF25400, +/**/ 0xA21378D7, 0xBF18A05B, +/**/ 0x024B2000, 0xBFC160C8, +/**/ 0xA9009E3D, 0xBD2EC2D2, +/**/ 0x00000000, 0x3FF25000, +/**/ 0xD6CFA90C, 0xBF3A076F, +/**/ 0x05C3A000, 0xBFC13C26, +/**/ 0xD94F6509, 0x3D2CF5FD, +/**/ 0x00000000, 0x3FF24800, +/**/ 0x92492492, 0x3F324924, +/**/ 0x8227E000, 0xBFC1178E, +/**/ 0xCE2D07F2, 0xBD21EF78, +/**/ 0x00000000, 0x3FF24400, +/**/ 0x6151E899, 0xBEF3682B, +/**/ 0x717D0000, 0xBFC0F301, +/**/ 0x41AE86C5, 0x3D3E09B4, +/**/ 0x00000000, 0x3FF24000, +/**/ 0x89FA4C67, 0xBF34868E, +/**/ 0xCDCCC000, 0xBFC0CE7E, +/**/ 0xABFF5447, 0xBD14652D, +/**/ 0x00000000, 0x3FF23800, +/**/ 0x6B11F09F, 0x3F3858D8, +/**/ 0x91268000, 0xBFC0AA06, +/**/ 0xD7032129, 0x3D345519, +/**/ 0x00000000, 0x3FF23400, +/**/ 0xAF37C049, 0x3F159E26, +/**/ 0xB59E4000, 0xBFC08598, +/**/ 0x7009902C, 0x3D27E5DD, +/**/ 0x00000000, 0x3FF23000, +/**/ 0x2E076329, 0xBF2AB546, +/**/ 0x354D4000, 0xBFC06135, +/**/ 0x28340EE9, 0xBD363046, +/**/ 0x00000000, 0x3FF22C00, +/**/ 0xFEDD5FEE, 0xBF3FEDD5, +/**/ 0x0A51E000, 0xBFC03CDC, +/**/ 0xF169FC5C, 0xBD381A9C, +/**/ 0x00000000, 0x3FF22400, +/**/ 0x009126D7, 0x3F2B5B92, +/**/ 0x2ECF6000, 0xBFC0188D, +/**/ 0x1CFF9DFE, 0xBD03F965, +/**/ 0x00000000, 0x3FF22000, +/**/ 0x8121FB78, 0xBF121FB7, +/**/ 0x39DBC000, 0xBFBFE891, +/**/ 0xD82F7A82, 0xBD356594, +/**/ 0x00000000, 0x3FF21C00, +/**/ 0x3A459635, 0xBF368F22, +/**/ 0x9DB58000, 0xBFBFA01C, +/**/ 0xFA48A730, 0x3D08F351, +/**/ 0x00000000, 0x3FF21400, +/**/ 0x855E6012, 0x3F379804, +/**/ 0x7D900000, 0xBFBF57BC, +/**/ 0x9EA8B04E, 0xBD176A6C, +/**/ 0x00000000, 0x3FF21000, +/**/ 0x78CD7A37, 0x3F17B57C, +/**/ 0xCDD98000, 0xBFBF0F70, +/**/ 0x6C272C1E, 0xBD32E31F, +/**/ 0x00000000, 0x3FF20C00, +/**/ 0x07E4EF15, 0xBF271E73, +/**/ 0x830A0000, 0xBFBEC739, +/**/ 0xA80CDD10, 0xBD311FCB, +/**/ 0x00000000, 0x3FF20800, +/**/ 0x49392BA7, 0xBF3CDDEC, +/**/ 0x91A34000, 0xBFBE7F16, +/**/ 0x9BC77BFA, 0x3D32C1C5, +/**/ 0x00000000, 0x3FF20000, +/**/ 0x12012012, 0x3F320120, +/**/ 0xEE304000, 0xBFBE3707, +/**/ 0xE6766ABD, 0xBD20F684, +/**/ 0x00000000, 0x3FF1FC00, +/**/ 0xCE8AD1A2, 0x3EF0DC4F, +/**/ 0x8D468000, 0xBFBDEF0D, +/**/ 0x412E9A74, 0x3D324750, +/**/ 0x00000000, 0x3FF1F800, +/**/ 0xDC11F704, 0xBF2F7047, +/**/ 0x63844000, 0xBFBDA727, +/**/ 0x1FA71733, 0xBD1A8940, +/**/ 0x00000000, 0x3FF1F000, +/**/ 0x16B6419D, 0x3F3FAF3F, +/**/ 0x65920000, 0xBFBD5F55, +/**/ 0xCC185469, 0xBD30E239, +/**/ 0x00000000, 0x3FF1EC00, +/**/ 0xF70985E2, 0x3F2E878F, +/**/ 0x88218000, 0xBFBD1797, +/**/ 0xB5EFBEED, 0xBD336433, +/**/ 0x00000000, 0x3FF1E800, +/**/ 0x94D7FDC3, 0xBEEF55E4, +/**/ 0xBFEE0000, 0xBFBCCFED, +/**/ 0x2FE71256, 0xBD33A823, +/**/ 0x00000000, 0x3FF1E400, +/**/ 0x0478BBCF, 0xBF310C4C, +/**/ 0x01BC4000, 0xBFBC8858, +/**/ 0xC65AACD3, 0xBD2646D1, +/**/ 0x00000000, 0x3FF1DC00, +/**/ 0xCB840C49, 0x3F3F0ECB, +/**/ 0x425A4000, 0xBFBC40D6, +/**/ 0x1D1930DD, 0xBD3CB112, +/**/ 0x00000000, 0x3FF1D800, +/**/ 0xC9579074, 0x3F2EACE5, +/**/ 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0xEB7C1000, 0x3FD49B9F, +/**/ 0x58AB60D7, 0x3D3DAC1C, +/**/ 0x00000000, 0x3FE73000, +/**/ 0x783709C7, 0xBF3BB33C, +/**/ 0x3CED0000, 0x3FD4A737, +/**/ 0xEBF35449, 0xBD39A234, +/**/ 0x00000000, 0x3FE72800, +/**/ 0x265AD23A, 0x3F061274, +/**/ 0x75556000, 0x3FD4B2CC, +/**/ 0xC78BFA4B, 0xBD380FCB, +/**/ 0x00000000, 0x3FE72800, +/**/ 0xC90A1FD2, 0xBF3EBC05, +/**/ 0x95778000, 0x3FD4BE5F, +/**/ 0xCD9AD824, 0xBD3D7C92, +/**/ 0x00000000, 0x3FE72000, +/**/ 0x38017200, 0xBEC71FFA, +/**/ 0x9E153000, 0x3FD4C9F0, +/**/ 0x70E02DE0, 0xBD2E1DDE, +/**/ 0x00000000, 0x3FE71800, +/**/ 0x74A050E1, 0x3F3E6B99, +/**/ 0x8FEFE000, 0x3FD4D57F, +/**/ 0x7FD06868, 0x3D23F926, +/**/ 0x00000000, 0x3FE71800, +/**/ 0xB8BD1180, 0xBF077400, +/**/ 0x6BC8A000, 0x3FD4E10C, +/**/ 0x1636F061, 0x3CF8283F, +/**/ 0x00000000, 0x3FE71000, +/**/ 0xE3E0453A, 0x3F3BC36C, +/**/ 0x32600000, 0x3FD4EC97, +/**/ 0xAF04D104, 0x3D234D7A, +/**/ 0x00000000, 0x3FE71000, +/**/ 0x6935DDC5, 0xBF15FA98, +/**/ 0xE4764000, 0x3FD4F81F, +/**/ 0x434FF08D, 0xBD27FCF6, +/**/ 0x00000000, 0x3FE70800, +/**/ 0x7337CF08, 0x3F394B40, +/**/ 0x82CB2000, 0x3FD503A6, +/**/ 0xF16F9B5D, 0xBD2A68C8, +/**/ 0x00000000, 0x3FE70800, +/**/ 0xA835403A, 0xBF1F7B97, +/**/ 0x0E1E0000, 0x3FD50F2B, +/**/ 0x8C47B8D8, 0x3D3A0940, +/**/ 0x00000000, 0x3FE70000, +/**/ 0x5C0B8170, 0x3F3702E0, +/**/ 0x872E0000, 0x3FD51AAD, +/**/ 0xDB0A7CC1, 0xBD3F4BD8, +/**/ 0x00000000, 0x3FE70000, +/**/ 0x4F67A855, 0xBF241EE6, +/**/ 0xEEB99000, 0x3FD5262D, +/**/ 0x70894A01, 0xBD3E1B9F, +/**/ 0x00000000, 0x3FE6F800, +/**/ 0x221C0170, 0x3F34EA19, +/**/ 0x457EE000, 0x3FD531AC, +/**/ 0x7D931501, 0x3D3DF83B, +/**/ 0x00000000, 0x3FE6F800, +/**/ 0x5508CA5C, 0xBF282102, +/**/ 0x8C3BE000, 0x3FD53D28, +/**/ 0xEB6DFAC5, 0xBD111397, +/**/ 0x00000000, 0x3FE6F000, +/**/ 0x9300B793, 0x3F3300B7, +/**/ 0xC3ADD000, 0x3FD548A2, +/**/ 0x63081CF7, 0x3D23167E, +/**/ 0x00000000, 0x3FE6F000, +/**/ 0x005BB90F, 0xBF2BC486, +/**/ 0xEC91C000, 0x3FD5541A, +/**/ 0xDC72EEBA, 0xBCF816AA, +/**/ 0x00000000, 0x3FE6E800, +/**/ 0xC5A3A00B, 0x3F314688, +/**/ 0x07A44000, 0x3FD55F91, +/**/ 0x78DF4A62, 0xBD11E647, +/**/ 0x00000000, 0x3FE6E800, +/**/ 0xDA9C5AE1, 0xBF2F09D6, +/**/ 0x15A18000, 0x3FD56B05, +/**/ 0xBC4A23FC, 0x3D29247B, +/**/ 0x00000000, 0x3FE6E000, +/**/ 0x337C6CB1, 0x3F2F76B4, +/**/ 0x17456000, 0x3FD57677, +/**/ 0x9524D7CA, 0xBD364EAD, +/**/ 0x00000000, 0x3FE6E000, +/**/ 0xEDF4EC87, 0xBF30F8AC, +/**/ 0x0D4B3000, 0x3FD581E7, +/**/ 0xB12D8F1D, 0xBD1F31E1, +/**/ 0x00000000, 0x3FE6D800, +/**/ 0x6EAEF381, 0x3F2CBDF2, +/**/ 0xF86E0000, 0x3FD58D54, +/**/ 0x0A795215, 0x3D2791F3, +/**/ 0x00000000, 0x3FE6D800, +/**/ 0xB624BFF5, 0xBF323DB9, +/**/ 0xD9688000, 0x3FD598C0, +/**/ 0x70D96DA4, 0xBD385F49, +/**/ 0x00000000, 0x3FE6D000, +/**/ 0x1C860FB0, 0x3F2A6268, +/**/ 0xB0F4D000, 0x3FD5A42A, +/**/ 0x2DF7BA69, 0xBCDE63AF, +/**/ 0x00000000, 0x3FE6D000, +/**/ 0xB253BAE1, 0xBF335443, +/**/ 0x7FCCE000, 0x3FD5AF92, +/**/ 0xF5FFC77A, 0xBD1C032F, +/**/ 0x00000000, 0x3FE6C800, +/**/ 0xAB4294D4, 0x3F2863B1, +/**/ 0x46AA2000, 0x3FD5BAF8, +/**/ 0xF873FA41, 0xBD339AE8, +/**/ 0x00000000, 0x3FE6C800, +/**/ 0x87EAA6DF, 0xBF343C7C, +/**/ 0x0645A000, 0x3FD5C65C, +/**/ 0x0180EE65, 0xBD39FE06, +/**/ 0x00000000, 0x3FE6C000, +/**/ 0x16C16C17, 0x3F26C16C, +/**/ 0xBF581000, 0x3FD5D1BD, +/**/ 0xC9C7C238, 0xBD38D6BD, +/**/ 0x00000000, 0x3FE6C000, +/**/ 0x95C33E00, 0xBF34F695, +/**/ 0x7299C000, 0x3FD5DD1D, +/**/ 0x8815CE17, 0xBD38AF61, +/**/ 0x00000000, 0x3FE6B800, +/**/ 0xE7802D73, 0x3F257B34, +/**/ 0x20C29000, 0x3FD5E87B, +/**/ 0x8F7738FA, 0x3D3527D1, +/**/ 0x00000000, 0x3FE6B800, +/**/ 0xF4A5582C, 0xBF3582BF, +/**/ 0xCA8A2000, 0x3FD5F3D6, +/**/ 0x8E19CC75, 0x3D37AF84, +/**/ 0x00000000, 0x3FE6B000, +/**/ 0x31A3CFC7, 0x3F2490AA, +/**/ 0x70A79000, 0x3FD5FF30, +/**/ 0x9F105039, 0x3D2E9E43, +/**/ 0x00000000, 0x3FE6B000, +/**/ 0x77C30E5A, 0xBF35E12C, +/**/ 0x13D1A000, 0x3FD60A88, +/**/ 0xC879AF55, 0x3D36E9B9, +/**/ 0x00000000, 0x3FE6A800, +/**/ 0x94016A94, 0x3F24016A, +/**/ 0xB4BEC000, 0x3FD615DD, +/**/ 0x90BC04B2, 0x3D13C7CA, +/**/ 0x00000000, 0x3FE6A800, +/**/ 0xAD33D63F, 0xBF36120B, +/**/ 0x5424F000, 0x3FD62131, +/**/ 0x4AA68669, 0xBD3382FC, +/**/ 0x00000000, 0x3FE6A000, +/**/ 0x3729043E, 0x3F23CD15, +/**/ 0xF2B9C000, 0x3FD62C82, +/**/ 0xBD7C8A98, 0x3D3E54BD } }; + +static const union {int4 i[4350]; double x[2175]; } vj = { .i = { +/**/ 0x7D161C28, 0x3F46A400, +/**/ 0x20600000, 0xBF46A200, +/**/ 0xAA7623D9, 0x3D27DC4E, +/**/ 0xD596E639, 0x3F4693FA, +/**/ 0x4CE00000, 0xBF4691FD, +/**/ 0x29C3F0AD, 0x3D26B0CF, +/**/ 0x3219CE89, 0x3F4683F5, +/**/ 0x7B600000, 0xBF4681FA, +/**/ 0x95B9FDCC, 0x3D22B290, +/**/ 0x929ED397, 0x3F4673EF, +/**/ 0xABE00000, 0xBF4671F7, +/**/ 0xFA2F2D87, 0x3D17C727, +/**/ 0xF725F3E2, 0x3F4663E9, +/**/ 0xDE600000, 0xBF4661F4, +/**/ 0x6EDBFF1C, 0x3CF22ED3, +/**/ 0x5FAF2DE9, 0x3F4653E4, +/**/ 0x12E00000, 0xBF4651F2, +/**/ 0x157812BB, 0xBD144936, +/**/ 0xCC3A802B, 0x3F4643DE, +/**/ 0x49600000, 0xBF4641EF, +/**/ 0x60314E05, 0xBD2959CB, +/**/ 0x3CC7E927, 0x3F4633D9, +/**/ 0x81E00000, 0xBF4631EC, +/**/ 0xC3638E99, 0xBD35ABDA, +/**/ 0xB157675C, 0x3F4623D3, +/**/ 0xBC800000, 0xBF4621E9, +/**/ 0xC63F9A21, 0x3D3FF1D3, +/**/ 0x29E8F948, 0x3F4613CE, +/**/ 0xF9000000, 0xBF4611E6, +/**/ 0x71EEE611, 0x3D342D26, +/**/ 0xA67C9D6B, 0x3F4603C8, +/**/ 0x37800000, 0xBF4601E4, +/**/ 0x11A09689, 0x3D1C1C77, +/**/ 0x27125244, 0x3F45F3C3, +/**/ 0x78000000, 0xBF45F1E1, +/**/ 0xF7DC643C, 0xBD1DFD16, +/**/ 0xABAA1651, 0x3F45E3BD, +/**/ 0xBA800000, 0xBF45E1DE, +/**/ 0x91318A02, 0xBD376503, +/**/ 0x3443E812, 0x3F45D3B8, +/**/ 0xFF200000, 0xBF45D1DB, +/**/ 0xCE55DCDD, 0x3D3756E4, +/**/ 0xC0DFC606, 0x3F45C3B2, +/**/ 0x45A00000, 0xBF45C1D9, +/**/ 0x8F6F8FA0, 0x3D12D5CF, +/**/ 0x517DAEAB, 0x3F45B3AD, +/**/ 0x8E200000, 0xBF45B1D6, +/**/ 0x9B85DC2C, 0xBD2E90AB, +/**/ 0xE61DA081, 0x3F45A3A7, +/**/ 0xD8C00000, 0xBF45A1D3, +/**/ 0x3BF5AC54, 0x3D3B5E88, +/**/ 0x7EBF9A07, 0x3F4593A2, +/**/ 0x25400000, 0xBF4591D1, +/**/ 0x0C86DDB1, 0x3D12AC3A, +/**/ 0x1B6399BB, 0x3F45839D, +/**/ 0x73C00000, 0xBF4581CE, +/**/ 0x76830985, 0xBD3361C2, +/**/ 0xBC099E1C, 0x3F457397, +/**/ 0xC4600000, 0xBF4571CB, +/**/ 0xD062EBFF, 0x3D333915, +/**/ 0x60B1A5AA, 0x3F456392, +/**/ 0x16E00000, 0xBF4561C9, +/**/ 0x9CC4988F, 0xBD1E0DA0, +/**/ 0x095BAEE4, 0x3F45538D, +/**/ 0x6B800000, 0xBF4551C6, +/**/ 0x235BC18A, 0x3D3C69C4, +/**/ 0xB607B848, 0x3F454387, +/**/ 0xC2000000, 0xBF4541C3, +/**/ 0xF7737723, 0xBCEFCC99, +/**/ 0x66B5C056, 0x3F453382, +/**/ 0x1A800000, 0xBF4531C1, +/**/ 0x809CBCBB, 0xBD3FBAE2, +/**/ 0x1B65C58C, 0x3F45237D, +/**/ 0x75200000, 0xBF4521BE, +/**/ 0x194FEE63, 0x3CCAA5C8, +/**/ 0xD417C66A, 0x3F451377, +/**/ 0xD1C00000, 0xBF4511BB, +/**/ 0xE1CC7BBC, 0x3D3ED325, +/**/ 0x90CBC16E, 0x3F450372, +/**/ 0x30400000, 0xBF4501B9, +/**/ 0x68AB3742, 0xBD0F0298, +/**/ 0x5181B517, 0x3F44F36D, +/**/ 0x90E00000, 0xBF44F1B6, +/**/ 0x41E67AD9, 0x3D381BE1, +/**/ 0x16399FE6, 0x3F44E368, +/**/ 0xF3600000, 0xBF44E1B3, +/**/ 0x668D3662, 0xBD2A6E79, +/**/ 0xDEF38058, 0x3F44D362, +/**/ 0x58000000, 0xBF44D1B1, +/**/ 0x21F8B7C2, 0x3D284EA7, +/**/ 0xABAF54EC, 0x3F44C35D, +/**/ 0xBE800000, 0xBF44C1AE, +/**/ 0x7417D9C5, 0xBD3BC76D, +/**/ 0x7C6D1C22, 0x3F44B358, +/**/ 0x27200000, 0xBF44B1AC, +/**/ 0x16AAD1FC, 0xBD1409FD, +/**/ 0x512CD479, 0x3F44A353, +/**/ 0x91C00000, 0xBF44A1A9, +/**/ 0x98BC14FD, 0x3D30771E, +/**/ 0x29EE7C70, 0x3F44934E, +/**/ 0xFE400000, 0xBF4491A6, +/**/ 0x5CCB7232, 0xBD3B5993, +/**/ 0x06B21285, 0x3F448349, +/**/ 0x6CE00000, 0xBF4481A4, +/**/ 0x5512F9C2, 0xBD20E729, +/**/ 0xE7779538, 0x3F447343, +/**/ 0xDD800000, 0xBF4471A1, +/**/ 0x55B30899, 0x3D225436, +/**/ 0xCC3F0308, 0x3F44633E, +/**/ 0x50200000, 0xBF44619F, +/**/ 0x9E54E31F, 0x3D39807C, +/**/ 0xB5085A73, 0x3F445339, +/**/ 0xC4A00000, 0xBF44519C, +/**/ 0xD5804C0E, 0xBD376F6F, +/**/ 0xA1D399FA, 0x3F444334, +/**/ 0x3B400000, 0xBF44419A, +/**/ 0x6CDE6425, 0xBD234953, +/**/ 0x92A0C01A, 0x3F44332F, +/**/ 0xB3E00000, 0xBF443197, +/**/ 0xAAF6596F, 0x3D070E7B, +/**/ 0x876FCB54, 0x3F44232A, +/**/ 0x2E800000, 0xBF442195, +/**/ 0x4EC011F1, 0x3D2C49F8, +/**/ 0x8040BA25, 0x3F441325, +/**/ 0xAB200000, 0xBF441192, +/**/ 0xD8AAA7EB, 0x3D3825DC, +/**/ 0x7D138B0E, 0x3F440320, +/**/ 0x29A00000, 0xBF440190, +/**/ 0xFE0B73D6, 0xBD3F1A8D, +/**/ 0x7DE83C8C, 0x3F43F31B, +/**/ 0xAA400000, 0xBF43F18D, +/**/ 0xE46CA26B, 0xBD379B43, +/**/ 0x82BECD20, 0x3F43E316, +/**/ 0x2CE00000, 0xBF43E18B, +/**/ 0x6283780D, 0xBD315B44, +/**/ 0x8B973B49, 0x3F43D311, +/**/ 0xB1800000, 0xBF43D188, +/**/ 0x017589BE, 0xBD28B31E, +/**/ 0x98718584, 0x3F43C30C, +/**/ 0x38200000, 0xBF43C186, +/**/ 0x8FBB296E, 0xBD212A46, +/**/ 0xA94DAA52, 0x3F43B307, +/**/ 0xC0C00000, 0xBF43B183, +/**/ 0x045CBBD2, 0xBD183403, +/**/ 0xBE2BA832, 0x3F43A302, +/**/ 0x4B600000, 0xBF43A181, +/**/ 0xD7CC5936, 0xBD13009B, +/**/ 0xD70B7DA2, 0x3F4392FD, +/**/ 0xD8000000, 0xBF43917E, +/**/ 0xC1742279, 0xBD12B655, +/**/ 0xF3ED2921, 0x3F4382F8, +/**/ 0x66A00000, 0xBF43817C, +/**/ 0xEA83FAE8, 0xBD17512E, +/**/ 0x14D0A930, 0x3F4372F4, +/**/ 0xF7400000, 0xBF437179, +/**/ 0xBED65875, 0xBD206692, +/**/ 0x39B5FC4C, 0x3F4362EF, +/**/ 0x89E00000, 0xBF436177, +/**/ 0xD38FFE9E, 0xBD27931B, +/**/ 0x629D20F5, 0x3F4352EA, +/**/ 0x1E800000, 0xBF435175, +/**/ 0xE524208F, 0xBD309618, +/**/ 0x8F8615AA, 0x3F4342E5, +/**/ 0xB5200000, 0xBF434172, +/**/ 0xDD4C72C5, 0xBD3697E9, +/**/ 0xC070D8EB, 0x3F4332E0, +/**/ 0x4DC00000, 0xBF433170, +/**/ 0x5E6E12C3, 0xBD3DCE00, +/**/ 0xF55D6935, 0x3F4322DB, +/**/ 0xE8800000, 0xBF43216D, +/**/ 0x0AE9A8CE, 0x3D39C8A4, +/**/ 0x2E4BC509, 0x3F4312D7, +/**/ 0x85200000, 0xBF43116B, +/**/ 0xD1CD2FA1, 0x3D302D03, +/**/ 0x6B3BEAE5, 0x3F4302D2, +/**/ 0x23C00000, 0xBF430169, +/**/ 0xA3BADFD1, 0x3D15807D, +/**/ 0xAC2DD949, 0x3F42F2CD, +/**/ 0xC4600000, 0xBF42F166, +/**/ 0xF57F0504, 0xBD1A7422, +/**/ 0xF1218EB3, 0x3F42E2C8, +/**/ 0x67000000, 0xBF42E164, +/**/ 0x2F2C781C, 0xBD33C974, +/**/ 0x3A1709A3, 0x3F42D2C4, +/**/ 0x0BC00000, 0xBF42D162, +/**/ 0x851A1E61, 0x3D3DDBDD, +/**/ 0x870E4898, 0x3F42C2BF, +/**/ 0xB2600000, 0xBF42C15F, +/**/ 0xA14AA8FD, 0x3D2CA7D9, +/**/ 0xD8074A10, 0x3F42B2BA, +/**/ 0x5B000000, 0xBF42B15D, +/**/ 0xDDCDDFF5, 0xBD03022E, +/**/ 0x2D020C8C, 0x3F42A2B6, +/**/ 0x05A00000, 0xBF42A15B, +/**/ 0x0F9231A8, 0xBD343FBA, +/**/ 0x85FE8E8A, 0x3F4292B1, +/**/ 0xB2600000, 0xBF429158, +/**/ 0xA52C9CCF, 0x3D38B690, +/**/ 0xE2FCCE8A, 0x3F4282AC, +/**/ 0x61000000, 0xBF428156, +/**/ 0xC8CC82EB, 0x3D120E6A, +/**/ 0x43FCCB0A, 0x3F4272A8, +/**/ 0x11A00000, 0xBF427154, +/**/ 0x792E6C51, 0xBD30D79B, +/**/ 0xA8FE8289, 0x3F4262A3, +/**/ 0xC4600000, 0xBF426151, +/**/ 0x91F7F7AA, 0x3D38A5EE, +/**/ 0x1201F387, 0x3F42529F, +/**/ 0x79000000, 0xBF42514F, +/**/ 0x46C2E8BA, 0x3CEFA728, +/**/ 0x7F071C84, 0x3F42429A, +/**/ 0x2FA00000, 0xBF42414D, +/**/ 0xFA447A17, 0xBD37D0BA, +/**/ 0xF00DFBFD, 0x3F423295, +/**/ 0xE8600000, 0xBF42314A, +/**/ 0x94AF3FED, 0x3D2C7A24, +/**/ 0x65169072, 0x3F422291, +/**/ 0xA3000000, 0xBF422148, +/**/ 0x050CEA04, 0xBD29B0BD, +/**/ 0xDE20D863, 0x3F42128C, +/**/ 0x5FC00000, 0xBF421146, +/**/ 0x0C3035EB, 0x3D36EFF3, +/**/ 0x5B2CD24E, 0x3F420288, +/**/ 0x1E600000, 0xBF420144, +/**/ 0x73569B27, 0xBD19A3E2, +/**/ 0xDC3A7CB2, 0x3F41F283, +/**/ 0xDF200000, 0xBF41F141, +/**/ 0xEEB67715, 0x3D3B1DDE, +/**/ 0x6149D610, 0x3F41E27F, +/**/ 0xA1C00000, 0xBF41E13F, +/**/ 0x94F49154, 0xBD11EA17, +/**/ 0xEA5ADCE5, 0x3F41D27A, +/**/ 0x66800000, 0xBF41D13D, +/**/ 0x52DD9D37, 0x3D3ACED9, +/**/ 0x776D8FB1, 0x3F41C276, +/**/ 0x2D200000, 0xBF41C13B, +/**/ 0xF72D8EEB, 0xBD1C140B, +/**/ 0x0881ECF4, 0x3F41B272, +/**/ 0xF5E00000, 0xBF41B138, +/**/ 0x939583E1, 0x3D360AE5, +/**/ 0x9D97F32C, 0x3F41A26D, +/**/ 0xC0800000, 0xBF41A136, +/**/ 0x1D246C7C, 0xBD2C00D9, +/**/ 0x36AFA0D9, 0x3F419269, +/**/ 0x8D400000, 0xBF419134, +/**/ 0x0B955CFB, 0x3D29B40E, +/**/ 0xD3C8F479, 0x3F418264, +/**/ 0x5BE00000, 0xBF418132, +/**/ 0x45A6C249, 0xBD3964BF, +/**/ 0x74E3EC8D, 0x3F417260, +/**/ 0x2CA00000, 0xBF417130, +/**/ 0xF3363612, 0xBCE777E0, +/**/ 0x1A008792, 0x3F41625C, +/**/ 0xFF600000, 0xBF41612D, +/**/ 0x28DE8296, 0x3D36D608, +/**/ 0xC31EC409, 0x3F415257, +/**/ 0xD4000000, 0xBF41512B, +/**/ 0x4BB1B788, 0xBD32AE69, +/**/ 0x703EA071, 0x3F414253, +/**/ 0xAAC00000, 0xBF414129, +/**/ 0x170ECD8C, 0x3D05BF68, +/**/ 0x21601B48, 0x3F41324F, +/**/ 0x83800000, 0xBF413127, +/**/ 0x7C653BFC, 0x3D370A0B, +/**/ 0xD683330E, 0x3F41224A, +/**/ 0x5E200000, 0xBF412125, +/**/ 0x77BBBEBF, 0xBD35B70D, +/**/ 0x8FA7E642, 0x3F411246, +/**/ 0x3AE00000, 0xBF411123, +/**/ 0x93ABC1CD, 0xBD0C52EB, +/**/ 0x4CCE3363, 0x3F410242, +/**/ 0x19A00000, 0xBF410121, +/**/ 0xE5C6F4C7, 0x3D2B2237, +/**/ 0x0DF618F1, 0x3F40F23E, +/**/ 0xFA600000, 0xBF40F11E, +/**/ 0x1E9A50AD, 0x3D3D9C5F, +/**/ 0xD31F956A, 0x3F40E239, +/**/ 0xDD000000, 0xBF40E11C, +/**/ 0x8965F0DA, 0xBD336793, +/**/ 0x9C4AA74E, 0x3F40D235, +/**/ 0xC1C00000, 0xBF40D11A, +/**/ 0x7E49E231, 0xBD15E6EE, +/**/ 0x69774D1D, 0x3F40C231, +/**/ 0xA8800000, 0xBF40C118, +/**/ 0x04FD621C, 0x3D1D9B9D, +/**/ 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0x132B309E, 0x3F17808A, +/**/ 0x09000000, 0xBF178045, +/**/ 0x7E89FD6F, 0xBD0CC7F9, +/**/ 0x42F88115, 0x3F170084, +/**/ 0x21000000, 0xBF170042, +/**/ 0x058494DC, 0x3CE40881, +/**/ 0x92C7F9A5, 0x3F16807E, +/**/ 0x49000000, 0xBF16803F, +/**/ 0xCD5698B9, 0x3D12AE16, +/**/ 0x02998E4D, 0x3F160079, +/**/ 0x81000000, 0xBF16003C, +/**/ 0xC5780E17, 0x3D21138B, +/**/ 0x926D330B, 0x3F158073, +/**/ 0xC9000000, 0xBF158039, +/**/ 0x4E2001E2, 0x3D287809, +/**/ 0x4242DBDF, 0x3F15006E, +/**/ 0x21000000, 0xBF150037, +/**/ 0x21448AA2, 0x3D2F8684, +/**/ 0x121A7CC8, 0x3F148069, +/**/ 0x89000000, 0xBF148034, +/**/ 0x2F637D8E, 0x3D33207E, +/**/ 0x01F409C4, 0x3F140064, +/**/ 0x01000000, 0xBF140032, +/**/ 0x12E44B29, 0x3D3654B9, +/**/ 0x11CF76D3, 0x3F13805F, +/**/ 0x89000000, 0xBF13802F, +/**/ 0xCA5547F3, 0x3D3960F2, +/**/ 0x41ACB7F4, 0x3F13005A, +/**/ 0x21000000, 0xBF13002D, +/**/ 0x6487063D, 0x3D3C462B, +/**/ 0x918BC126, 0x3F128055, +/**/ 0xC9000000, 0xBF12802A, +/**/ 0xEFEA1107, 0x3D3F0562, +/**/ 0x016C8668, 0x3F120051, +/**/ 0x80000000, 0xBF120028, +/**/ 0x857113CE, 0xBD3E6066, +/**/ 0x914EFBBA, 0x3F11804C, +/**/ 0x48000000, 0xBF118026, +/**/ 0xEDD9EB54, 0xBD3BEA30, +/**/ 0x41331519, 0x3F110048, +/**/ 0x20000000, 0xBF110024, +/**/ 0x3BFFFF5A, 0xBD3996FC, +/**/ 0x1118C686, 0x3F108044, +/**/ 0x08000000, 0xBF108022, +/**/ 0x62F2E042, 0xBD3765C8, +/**/ 0x01000400, 0x3F100040, +/**/ 0x00000000, 0xBF100020, +/**/ 0x562224CD, 0xBD355595, +/**/ 0x21D1830C, 0x3F0F0078, +/**/ 0x10000000, 0xBF0F003C, +/**/ 0x095D69EB, 0xBD336563, +/**/ 0x81A5E62E, 0x3F0E0070, +/**/ 0x40000000, 0xBF0E0038, +/**/ 0x70D45290, 0xBD319431, +/**/ 0x217D1965, 0x3F0D0069, +/**/ 0x90000000, 0xBF0D0034, +/**/ 0x022D0EF6, 0xBD2FC201, +/**/ 0x015704B1, 0x3F0C0062, +/**/ 0x00000000, 0xBF0C0031, +/**/ 0x5E276E21, 0xBD2C95A0, +/**/ 0x2133900E, 0x3F0B005B, +/**/ 0x90000000, 0xBF0B002D, +/**/ 0xE0372A42, 0xBD29A140, +/**/ 0x8112A37D, 0x3F0A0054, +/**/ 0x40000000, 0xBF0A002A, +/**/ 0x73BBB580, 0xBD26E2E2, +/**/ 0x20F426FB, 0x3F09004E, +/**/ 0x10000000, 0xBF090027, +/**/ 0x04D48C20, 0xBD245885, +/**/ 0x00D80288, 0x3F080048, +/**/ 0x00000000, 0xBF080024, +/**/ 0x80613426, 0xBD220028, +/**/ 0x20BE1E23, 0x3F070042, +/**/ 0x10000000, 0xBF070021, +/**/ 0xA80279F3, 0xBD1FAF99, +/**/ 0x80A661CA, 0x3F06003C, +/**/ 0x40000000, 0xBF06001E, +/**/ 0xDC287DFE, 0xBD1BBAE3, +/**/ 0x2090B57C, 0x3F050037, +/**/ 0x90000000, 0xBF05001B, +/**/ 0x7B73B67C, 0xBD181E2F, +/**/ 0x007D0139, 0x3F040032, +/**/ 0x00000000, 0xBF040019, +/**/ 0x65A375F8, 0xBD14D57C, +/**/ 0x206B2CFF, 0x3F03002D, +/**/ 0x90000000, 0xBF030016, +/**/ 0x7BF71EC1, 0xBD11DCCA, +/**/ 0x805B20CD, 0x3F020028, +/**/ 0x40000000, 0xBF020014, +/**/ 0x425C4447, 0xBD0E6033, +/**/ 0x204CC4A3, 0x3F010024, +/**/ 0x10000000, 0xBF010012, +/**/ 0x730FFF5C, 0xBD0996D3, +/**/ 0x00400080, 0x3F000020, +/**/ 0x00000000, 0xBF000010, +/**/ 0x558888DE, 0xBD055575, +/**/ 0x406978C6, 0x3EFE0038, +/**/ 0x20000000, 0xBEFE001C, +/**/ 0xB845146A, 0xBD019418, +/**/ 0x0055C096, 0x3EFC0031, +/**/ 0x80000000, 0xBEFC0018, +/**/ 0xD989DB3C, 0xBCFC957A, +/**/ 0x4044A870, 0x3EFA002A, +/**/ 0x20000000, 0xBEFA0015, +/**/ 0x8F0EED2F, 0xBCF6E2C6, +/**/ 0x00360051, 0x3EF80024, +/**/ 0x00000000, 0xBEF80012, +/**/ 0x40184CEB, 0xBCF20014, +/**/ 0x40299839, 0x3EF6001E, +/**/ 0x20000000, 0xBEF6000F, +/**/ 0x434A1F5C, 0xBCEBBAC7, +/**/ 0x001F4027, 0x3EF40019, +/**/ 0x80000000, 0xBEF4000C, +/**/ 0xDD68DD6A, 0xBCE4D568, +/**/ 0x4016C81A, 0x3EF20014, +/**/ 0x20000000, 0xBEF2000A, +/**/ 0xA11710FC, 0xBCDE6019, +/**/ 0x00100010, 0x3EF00010, +/**/ 0x00000000, 0xBEF00008, +/**/ 0x5562222D, 0xBCD55565, +/**/ 0x80157013, 0x3EEC0018, +/**/ 0x40000000, 0xBEEC000C, +/**/ 0x176276C5, 0xBCCC9568, +/**/ 0x000D800A, 0x3EE80012, +/**/ 0x00000000, 0xBEE80009, +/**/ 0x20061337, 0xBCC2000A, +/**/ 0x8007D005, 0x3EE4000C, +/**/ 0x40000000, 0xBEE40006, +/**/ 0x195A3758, 0xBCB4D55F, +/**/ 0x00040002, 0x3EE00008, +/**/ 0x00000000, 0xBEE00004, +/**/ 0x5558888A, 0xBCA5555D, +/**/ 0x00036001, 0x3ED80009, +/**/ 0x80000000, 0xBED80004, +/**/ 0x100184CD, 0xBC920005, +/**/ 0x00010000, 0x3ED00004, +/**/ 0x00000000, 0xBED00002, +/**/ 0x55562222, 0xBC755559, +/**/ 0x00004000, 0x3EC00002, +/**/ 0x00000000, 0xBEC00001, +/**/ 0x55558889, 0xBC455557, +/**/ 0x00000000, 0x00000000, +/**/ 0x00000000, 0x00000000, +/**/ 0x00000000, 0x00000000, +/**/ 0x00008000, 0xBEBFFFFC, +/**/ 0x00000000, 0x3EBFFFFE, +/**/ 0x55558889, 0x3C455553, +/**/ 0x00020000, 0xBECFFFF8, +/**/ 0x00000000, 0x3ECFFFFC, +/**/ 0x55562222, 0x3C755551, +/**/ 0x00035FFF, 0xBED7FFF7, +/**/ 0x80000000, 0x3ED7FFFB, +/**/ 0xF00184CC, 0x3C91FFFA, +/**/ 0x0007FFFC, 0xBEDFFFF0, +/**/ 0x00000000, 0x3EDFFFF8, +/**/ 0x55588887, 0x3CA5554D, +/**/ 0x8007CFFB, 0xBEE3FFF3, +/**/ 0xC0000000, 0x3EE3FFF9, +/**/ 0x915A3753, 0x3CB4D54B, +/**/ 0x000D7FF6, 0xBEE7FFEE, +/**/ 0x00000000, 0x3EE7FFF7, +/**/ 0xE006132F, 0x3CC1FFF5, +/**/ 0x80156FED, 0xBEEBFFE7, +/**/ 0xC0000000, 0x3EEBFFF3, +/**/ 0x936276B2, 0x3CCC9542, +/**/ 0x001FFFE0, 0xBEEFFFE0, +/**/ 0x00000000, 0x3EEFFFF0, +/**/ 0x55622217, 0x3CD55545, +/**/ 0xC016C7E6, 0xBEF1FFEB, +/**/ 0xE0000000, 0x3EF1FFF5, +/**/ 0x5F1710D1, 0x3CDE5FE6, +/**/ 0x001F3FD9, 0xBEF3FFE7, +/**/ 0x80000000, 0x3EF3FFF3, +/**/ 0xCD68DD41, 0x3CE4D541, +/**/ 0xC02997C7, 0xBEF5FFE1, +/**/ 0xE0000000, 0x3EF5FFF0, +/**/ 0x124A1F13, 0x3CEBBA8E, +/**/ 0x0035FFAF, 0xBEF7FFDC, +/**/ 0x00000000, 0x3EF7FFEE, +/**/ 0xC0184CAE, 0x3CF1FFEB, +/**/ 0xC044A790, 0xBEF9FFD5, +/**/ 0xE0000000, 0x3EF9FFEA, +/**/ 0xC68EECCD, 0x3CF6E28E, +/**/ 0x0055BF6A, 0xBEFBFFCF, +/**/ 0x80000000, 0x3EFBFFE7, +/**/ 0xD189DAA2, 0x3CFC952F, +/**/ 0xC069773A, 0xBEFDFFC7, +/**/ 0xE0000000, 0x3EFDFFE3, +/**/ 0x480513F6, 0x3D0193E7, +/**/ 0x007FFF00, 0xBEFFFFC0, +/**/ 0x00000000, 0x3EFFFFE0, +/**/ 0x55888833, 0x3D055535, +/**/ 0xE04CC35D, 0xBF00FFDB, +/**/ 0xF0000000, 0x3F00FFED, +/**/ 0xE2CFFE66, 0x3D099681, +/**/ 0x805B1F33, 0xBF01FFD7, +/**/ 0xC0000000, 0x3F01FFEB, +/**/ 0xBE5C42ED, 0x3D0E5FCC, +/**/ 0xE06B2B01, 0xBF02FFD2, +/**/ 0x70000000, 0x3F02FFE9, +/**/ 0xD9D71DD1, 0x3D11DC8A, +/**/ 0x007CFEC8, 0xBF03FFCE, +/**/ 0x00000000, 0x3F03FFE7, +/**/ 0x45A374B3, 0x3D14D52E, +/**/ 0xE090B284, 0xBF04FFC8, +/**/ 0x70000000, 0x3F04FFE4, +/**/ 0x8553B4C7, 0x3D181DD0, +/**/ 0x80A65E36, 0xBF05FFC3, +/**/ 0xC0000000, 0x3F05FFE1, +/**/ 0x7A287BBE, 0x3D1BBA71, +/**/ 0xE0BE19DD, 0xBF06FFBD, +/**/ 0xF0000000, 0x3F06FFDE, +/**/ 0x03E27702, 0x3D1FAF11, +/**/ 0x00D7FD78, 0xBF07FFB8, +/**/ 0x00000000, 0x3F07FFDC, +/**/ 0x80613240, 0x3D21FFD7, +/**/ 0xE0F42105, 0xBF08FFB1, +/**/ 0xF0000000, 0x3F08FFD8, +/**/ 0xA6C489B3, 0x3D245825, +/**/ 0x81129C84, 0xBF09FFAB, +/**/ 0xC0000000, 0x3F09FFD5, +/**/ 0xE2BBB26F, 0x3D26E272, +/**/ 0xE13387F2, 0xBF0AFFA4, +/**/ 0x70000000, 0x3F0AFFD2, +/**/ 0x21272669, 0x3D29A0BF, +/**/ 0x0156FB50, 0xBF0BFF9E, +/**/ 0x00000000, 0x3F0BFFCF, +/**/ 0x4E276957, 0x3D2C950A, +/**/ 0xE17D0E9B, 0xBF0CFF96, +/**/ 0x70000000, 0x3F0CFFCB, +/**/ 0x551D090E, 0x3D2FC154, +/**/ 0x81A5D9D2, 0xBF0DFF8F, +/**/ 0xC0000000, 0x3F0DFFC7, +/**/ 0x90544EF1, 0x3D3193CE, +/**/ 0xE1D174F4, 0xBF0EFF87, +/**/ 0xF0000000, 0x3F0EFFC3, +/**/ 0x4D556583, 0x3D3364F2, +/**/ 0x01FFF800, 0xBF0FFF80, +/**/ 0x00000000, 0x3F0FFFC0, +/**/ 0x56221F78, 0x3D355515, +/**/ 0xF118BD7A, 0xBF107FBB, +/**/ 0xF8000000, 0x3F107FDD, +/**/ 0x9EEAD9D8, 0x3D376537, +/**/ 0xC1330AE7, 0xBF10FFB7, +/**/ 0xE0000000, 0x3F10FFDB, +/**/ 0x1B7FF7AE, 0x3D399659, +/**/ 0x714EF047, 0xBF117FB3, +/**/ 0xB8000000, 0x3F117FD9, +/**/ 0xBF51E233, 0x3D3BE979, +/**/ 0x016C7998, 0xBF11FFAF, +/**/ 0x80000000, 0x3F11FFD7, +/**/ 0x7D7108FF, 0x3D3E5F99, +/**/ 0x718BB2DA, 0xBF127FAA, +/**/ 0x39000000, 0x3F127FD5, +/**/ 0xB7721DC6, 0xBD3F0647, +/**/ 0xC1ACA80C, 0xBF12FFA5, +/**/ 0xE1000000, 0x3F12FFD2, +/**/ 0xED071532, 0xBD3C4729, +/**/ 0xF1CF652D, 0xBF137FA0, +/**/ 0x79000000, 0x3F137FD0, +/**/ 0x315D596D, 0xBD39620D, +/**/ 0x01F3F63C, 0xBF13FF9C, +/**/ 0x01000000, 0x3F13FFCE, +/**/ 0x92E45F81, 0xBD3655F1, +/**/ 0xF21A6739, 0xBF147F96, +/**/ 0x79000000, 0x3F147FCB, +/**/ 0x206B9526, 0xBD3321D7, +/**/ 0xC242C421, 0xBF14FF91, +/**/ 0xE1000000, 0x3F14FFC8, +/**/ 0xD244C12A, 0xBD2F897B, +/**/ 0x726D18F6, 0xBF157F8C, +/**/ 0x39000000, 0x3F157FC6, +/**/ 0xF93040AE, 0xBD287B4B, +/**/ 0x029971B4, 0xBF15FF87, +/**/ 0x81000000, 0x3F15FFC3, +/**/ 0xD578562C, 0xBD21171E, +/**/ 0x72C7DA5C, 0xBF167F81, +/**/ 0xB9000000, 0x3F167FC0, +/**/ 0x0F773DB4, 0xBD12B5E9, +/**/ 0xC2F85EEC, 0xBF16FF7B, +/**/ 0xE1000000, 0x3F16FFBD, +/**/ 0x158A76C2, 0xBCE44CD3, +/**/ 0xF32B0B63, 0xBF177F75, +/**/ 0xF9000000, 0x3F177FBA, +/**/ 0x2E48511B, 0x3D0CB55C, +/**/ 0x035FEBC0, 0xBF17FF70, +/**/ 0x01000000, 0x3F17FFB8, +/**/ 0x184C534F, 0x3D1FFAF0, +/**/ 0xF3970C03, 0xBF187F69, +/**/ 0xF9000000, 0x3F187FB4, +/**/ 0xACC53FBE, 0x3D292D95, +/**/ 0xC3D07829, 0xBF18FF63, +/**/ 0xE1000000, 0x3F18FFB1, +/**/ 0xE48887C8, 0x3D315FD7, +/**/ 0x740C3C32, 0xBF197F5D, +/**/ 0xB9000000, 0x3F197FAE, +/**/ 0x1DF5B242, 0x3D365AE3, +/**/ 0x044A641C, 0xBF19FF57, +/**/ 0x81000000, 0x3F19FFAB, +/**/ 0x6FBB0E5F, 0x3D3B88EC, +/**/ 0x748AFBE7, 0xBF1A7F50, +/**/ 0x3A000000, 0x3F1A7FA8, +/**/ 0x39766B40, 0xBD3F150C, +/**/ 0xC4CE0F91, 0xBF1AFF49, +/**/ 0xE2000000, 0x3F1AFFA4, +/**/ 0xF14DB839, 0xBD397E06, +/**/ 0xF513AB19, 0xBF1B7F42, +/**/ 0x7A000000, 0x3F1B7FA1, +/**/ 0xCBD9CC3D, 0xBD33B103, +/**/ 0x055BDA7D, 0xBF1BFF3C, +/**/ 0x02000000, 0x3F1BFF9E, +/**/ 0xBB1321B5, 0xBD2B5A05, +/**/ 0xF5A6A9BD, 0xBF1C7F34, +/**/ 0x7A000000, 0x3F1C7F9A, +/**/ 0xECAF9551, 0xBD1DC410, +/**/ 0xC5F424D6, 0xBF1CFF2D, +/**/ 0xE2000000, 0x3F1CFF96, +/**/ 0x3DF3CD68, 0xBCEF80FF, +/**/ 0x764457C8, 0xBF1D7F26, +/**/ 0x3A000000, 0x3F1D7F93, +/**/ 0x4271E737, 0x3D16CBC7, +/**/ 0x06974E91, 0xBF1DFF1F, +/**/ 0x82000000, 0x3F1DFF8F, +/**/ 0x1D134848, 0x3D2939D2, +/**/ 0x76ED1530, 0xBF1E7F17, +/**/ 0xBA000000, 0x3F1E7F8B, +/**/ 0xA9892C73, 0x3D33C2DD, +/**/ 0xC745B7A4, 0xBF1EFF0F, +/**/ 0xE2000000, 0x3F1EFF87, +/**/ 0x8AEC69D5, 0x3D3B25CF, +/**/ 0xF7A141EA, 0xBF1F7F07, +/**/ 0xFB000000, 0x3F1F7F83, +/**/ 0x645B412A, 0xBD3D3941, +/**/ 0x07FFC002, 0xBF1FFF00, +/**/ 0x03000000, 0x3F1FFF80, +/**/ 0x3BBC6662, 0xBD355955, +/**/ 0xFC309EF5, 0xBF203F7B, +/**/ 0xFD800000, 0x3F203FBD, +/**/ 0x260B17B3, 0xBD2A72D8, +/**/ 0xE462E3D0, 0xBF207F77, +/**/ 0xF1800000, 0x3F207FBB, +/**/ 0x0994AE68, 0xBD136218, +/**/ 0xBC96B492, 0xBF20BF73, +/**/ 0xDD800000, 0x3F20BFB9, +/**/ 0xECB2641F, 0x3D0E52E6, +/**/ 0x84CC1739, 0xBF20FF6F, +/**/ 0xC1800000, 0x3F20FFB7, +/**/ 0xE7FCF60B, 0x3D296078, +/**/ 0x3D0311C6, 0xBF213F6B, +/**/ 0x9D800000, 0x3F213FB5, +/**/ 0xA7850AFF, 0x3D35DA18, +/**/ 0xE53BAA36, 0xBF217F66, +/**/ 0x71800000, 0x3F217FB3, +/**/ 0x5E7BB444, 0x3D3F48F1, +/**/ 0x7D75E68A, 0xBF21BF62, +/**/ 0x3E000000, 0x3F21BFB1, +/**/ 0x812BC469, 0xBD370239, +/**/ 0x05B1CCC0, 0xBF21FF5E, +/**/ 0x02000000, 0x3F21FFAF, +/**/ 0x23BF1A4D, 0xBD2A0CD0, +/**/ 0x7DEF62D8, 0xBF223F59, +/**/ 0xBE000000, 0x3F223FAC, +/**/ 0x736E3623, 0xBD0614D3, +/**/ 0xE62EAED0, 0xBF227F54, +/**/ 0x72000000, 0x3F227FAA, +/**/ 0x37EDEDB0, 0x3D1F28BD, +/**/ 0x3E6FB6A9, 0xBF22BF50, +/**/ 0x1E000000, 0x3F22BFA8, +/**/ 0x07CE33C8, 0x3D32A0F5, +/**/ 0x86B28060, 0xBF22FF4B, +/**/ 0xC2000000, 0x3F22FFA5, +/**/ 0xA31C6A8D, 0x3D3DC2B6, +/**/ 0xBEF711F6, 0xBF233F46, +/**/ 0x5E800000, 0x3F233FA3, +/**/ 0xFC67C9FB, 0xBD36CF8B, +/**/ 0xE73D7169, 0xBF237F41, +/**/ 0xF2800000, 0x3F237FA0, +/**/ 0xE6D88A89, 0xBD2629A5, +/**/ 0xFF85A4B8, 0xBF23BF3C, +/**/ 0x7E800000, 0x3F23BF9E, +/**/ 0x202574EC, 0x3CEE7C34, +/**/ 0x07CFB1E3, 0xBF23FF38, +/**/ 0x02800000, 0x3F23FF9C, +/**/ 0x46E594C1, 0x3D2A9723, +/**/ 0x001B9EE8, 0xBF243F33, +/**/ 0x7E800000, 0x3F243F99, +/**/ 0xF61AE74C, 0x3D39F33C, +/**/ 0xE86971C7, 0xBF247F2D, +/**/ 0xF3000000, 0x3F247F96, +/**/ 0x85341E31, 0xBD39141C, +/**/ 0xC0B9307F, 0xBF24BF28, +/**/ 0x5F000000, 0x3F24BF94, +/**/ 0xDA0FAF09, 0xBD2792F5, +/**/ 0x890AE10E, 0xBF24FF23, +/**/ 0xC3000000, 0x3F24FF91, +/**/ 0xFB239430, 0x3CFD4219, +/**/ 0x415E8974, 0xBF253F1E, +/**/ 0x1F000000, 0x3F253F8F, +/**/ 0x0359434A, 0x3D2F8B72, +/**/ 0xE9B42FAF, 0xBF257F18, +/**/ 0x73000000, 0x3F257F8C, +/**/ 0x1939FEDF, 0x3D3E0C4B, +/**/ 0x820BD9BF, 0xBF25BF13, +/**/ 0xBF800000, 0x3F25BF89, +/**/ 0x39B301E2, 0xBD335728, +/**/ 0x0A658DA3, 0xBF25FF0E, +/**/ 0x03800000, 0x3F25FF87, +/**/ 0x5E1E8D4F, 0xBD118E84, +/**/ 0x82C15159, 0xBF263F08, +/**/ 0x3F800000, 0x3F263F84, +/**/ 0xBDDDD045, 0x3D25CFC0, +/**/ 0xEB1F2AE1, 0xBF267F02, +/**/ 0x73800000, 0x3F267F81, +/**/ 0x08837E99, 0x3D3A8C5C, +/**/ 0x437F203A, 0xBF26BEFD, +/**/ 0xA0000000, 0x3F26BF7E, +/**/ 0x3C56F12D, 0xBD35752E, +/**/ 0x8BE13762, 0xBF26FEF7, +/**/ 0xC4000000, 0x3F26FF7B, +/**/ 0x46359E28, 0xBD146EFA, +/**/ 0xC4457659, 0xBF273EF1, +/**/ 0xE0000000, 0x3F273F78, +/**/ 0xCD265865, 0x3D273355, +/**/ 0xECABE31C, 0xBF277EEB, +/**/ 0xF4000000, 0x3F277F75, +/**/ 0x095DEBF8, 0x3D3CAC0E, +/**/ 0x051483AC, 0xBF27BEE6, +/**/ 0x00800000, 0x3F27BF73, +/**/ 0x4C39F4DB, 0xBD31E395, +/**/ 0x0D7F5E08, 0xBF27FEE0, +/**/ 0x04800000, 0x3F27FF70, +/**/ 0xA1314B81, 0xBCB43F3D, +/**/ 0x05EC782D, 0xBF283EDA, +/**/ 0x00800000, 0x3F283F6D, +/**/ 0x115B8D70, 0x3D321B10, +/**/ 0xEE5BD81B, 0xBF287ED3, +/**/ 0xF5000000, 0x3F287F69, +/**/ 0x83704FE1, 0xBD3B54A7, +/**/ 0xC6CD83D1, 0xBF28BECD, +/**/ 0xE1000000, 0x3F28BF66, +/**/ 0x41229C91, 0xBD20C4CC, +/**/ 0x8F41814D, 0xBF28FEC7, +/**/ 0xC5000000, 0x3F28FF63, +/**/ 0x2A183F17, 0x3D25E5A8, +/**/ 0x47B7D68F, 0xBF293EC1, +/**/ 0xA1000000, 0x3F293F60, +/**/ 0xF81B997D, 0x3D3EAC06, +/**/ 0xF0308995, 0xBF297EBA, +/**/ 0x75800000, 0x3F297F5D, +/**/ 0x3A1E5BAD, 0xBD2A6B9B, +/**/ 0x88ABA05E, 0xBF29BEB4, +/**/ 0x41800000, 0x3F29BF5A, +/**/ 0xBDFE3C77, 0x3D1D3958, +/**/ 0x112920E9, 0xBF29FEAE, +/**/ 0x05800000, 0x3F29FF57, +/**/ 0x375BA904, 0x3D3C3972, +/**/ 0x89A91135, 0xBF2A3EA7, +/**/ 0xC2000000, 0x3F2A3F53, +/**/ 0x588DE85B, 0xBD2CE6F3, +/**/ 0xF22B7740, 0xBF2A7EA0, +/**/ 0x76000000, 0x3F2A7F50, +/**/ 0x75AEDBFD, 0x3D1D2249, +/**/ 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0x234CFD15, 0xBF446CBD, +/**/ 0x7B800000, 0x3F446E5E, +/**/ 0x6A8B33AC, 0xBD3E762C, +/**/ 0x0686F463, 0xBF447CB8, +/**/ 0xECE00000, 0x3F447E5B, +/**/ 0x67AD9900, 0xBD2A36F8, +/**/ 0xE5C2D713, 0xBF448CB2, +/**/ 0x5C400000, 0x3F448E59, +/**/ 0x1E974853, 0x3D161B95, +/**/ 0xC100A6A5, 0xBF449CAD, +/**/ 0xC9A00000, 0x3F449E56, +/**/ 0x8CE22250, 0x3D3971F7, +/**/ 0x98406498, 0xBF44ACA8, +/**/ 0x35200000, 0x3F44AE54, +/**/ 0xDF8A23F8, 0xBD315945, +/**/ 0x6B82126A, 0xBF44BCA3, +/**/ 0x9E800000, 0x3F44BE51, +/**/ 0x1A63D360, 0x3D1498B2, +/**/ 0x3AC5B19B, 0xBF44CC9E, +/**/ 0x05E00000, 0x3F44CE4F, +/**/ 0x4323A054, 0x3D3CF14E, +/**/ 0x060B43AA, 0xBF44DC99, +/**/ 0x6B600000, 0x3F44DE4C, +/**/ 0x4CE35F94, 0xBD23EDC2, +/**/ 0xCD52CA15, 0xBF44EC93, +/**/ 0xCEC00000, 0x3F44EE49, +/**/ 0xCCF1B48E, 0x3D306E9D, +/**/ 0x909C465C, 0xBF44FC8E, +/**/ 0x30400000, 0x3F44FE47, +/**/ 0x5FF9440B, 0xBD33DD35, +/**/ 0x4FE7B9FF, 0xBF450C89, +/**/ 0x8FA00000, 0x3F450E44, +/**/ 0xAA4D276D, 0x3D224D49, +/**/ 0x0B35267A, 0xBF451C84, +/**/ 0xED200000, 0x3F451E41, +/**/ 0x11B557F9, 0xBD3884D4, +/**/ 0xC2848D4F, 0xBF452C7E, +/**/ 0x48800000, 0x3F452E3F, +/**/ 0xB43290C4, 0x3D1C857D, +/**/ 0x75D5EFFC, 0xBF453C79, +/**/ 0xA2000000, 0x3F453E3C, +/**/ 0x2D598D3C, 0xBD37E5C1, +/**/ 0x25294FFF, 0xBF454C74, +/**/ 0xF9600000, 0x3F454E39, +/**/ 0x3FE47B89, 0x3D24CD93, +/**/ 0xD07EAED8, 0xBF455C6E, +/**/ 0x4EE00000, 0x3F455E37, +/**/ 0xAA959122, 0xBD31F800, +/**/ 0x77D60E06, 0xBF456C69, +/**/ 0xA2400000, 0x3F456E34, +/**/ 0x7329AF92, 0x3D32FEDF, +/**/ 0x1B2F6F08, 0xBF457C64, +/**/ 0xF3C00000, 0x3F457E31, +/**/ 0x1C545A6F, 0xBD1ACE5A, +/**/ 0xBA8AD35D, 0xBF458C5E, +/**/ 0x43400000, 0x3F458E2F, +/**/ 0x19F6B9EF, 0xBD3F0E63, +/**/ 0x55E83C84, 0xBF459C59, +/**/ 0x90A00000, 0x3F459E2C, +/**/ 0x73005F6F, 0x3D23DEF2, +/**/ 0xED47ABFB, 0xBF45AC53, +/**/ 0xDC200000, 0x3F45AE29, +/**/ 0x1C295DE7, 0xBD277204, +/**/ 0x80A92343, 0xBF45BC4E, +/**/ 0x25800000, 0x3F45BE27, +/**/ 0x8D869589, 0x3D3FF92A, +/**/ 0x100CA3D9, 0xBF45CC49, +/**/ 0x6D000000, 0x3F45CE24, +/**/ 0x145C5335, 0x3D2A0DFD, +/**/ 0x9B722F3C, 0xBF45DC43, +/**/ 0xB2800000, 0x3F45DE21, +/**/ 0x6A8614B3, 0xBD123A1A, +/**/ 0x22D9C6ED, 0xBF45EC3E, +/**/ 0xF6000000, 0x3F45EE1E, +/**/ 0x63CBC7E7, 0xBD34C665, +/**/ 0xA6436C69, 0xBF45FC38, +/**/ 0x37600000, 0x3F45FE1C, +/**/ 0xAB6C51D7, 0x3D3C6061, +/**/ 0x25AF2130, 0xBF460C33, +/**/ 0x76E00000, 0x3F460E19, +/**/ 0x1EC7F453, 0x3D2DCD9C, +/**/ 0xA11CE6C1, 0xBF461C2D, +/**/ 0xB4600000, 0x3F461E16, +/**/ 0x20C52899, 0x3D066EFA, +/**/ 0x188CBE9A, 0xBF462C28, +/**/ 0xEFE00000, 0x3F462E13, +/**/ 0xEB5FDD5C, 0xBD1FA5AC, +/**/ 0x8BFEAA3B, 0xBF463C22, +/**/ 0x29600000, 0x3F463E11, +/**/ 0xF22FE2BC, 0xBD313E11, +/**/ 0xFB72AB23, 0xBF464C1C, +/**/ 0x60E00000, 0x3F464E0E, +/**/ 0x6710E251, 0xBD392F15, +/**/ 0x66E8C2D0, 0xBF465C17, +/**/ 0x96600000, 0x3F465E0B, +/**/ 0x1EFC78A7, 0xBD3FBB76, +/**/ 0xCE60F2C1, 0xBF466C11, +/**/ 0xC9C00000, 0x3F466E08, +/**/ 0x602C1A84, 0x3D3B1DCB, +/**/ 0x31DB3C76, 0xBF467C0C, +/**/ 0xFB400000, 0x3F467E05, +/**/ 0x9027DA74, 0x3D375DAE, +/**/ 0x9157A16E, 0xBF468C06, +/**/ 0x2AC00000, 0x3F468E03, +/**/ 0xEA560DA0, 0x3D350532, +/**/ 0xECD62326, 0xBF469C00, +/**/ 0x58400000, 0x3F469E00, +/**/ 0xE7B63DE2, 0x3D341557 } }; + +#endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/urem.h b/REORG.TODO/sysdeps/ieee754/dbl-64/urem.h new file mode 100644 index 0000000000..d9e5696fdd --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/urem.h @@ -0,0 +1,46 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/************************************************************************/ +/* MODULE_NAME: urem.h */ +/* */ +/* */ +/* common data and variables definition for BIG or LITTLE ENDIAN */ +/************************************************************************/ + +#ifndef UREM_H +#define UREM_H + +#ifdef BIG_ENDI +static const mynumber big = {{0x43380000, 0}}, /* 6755399441055744 */ + t128 = {{0x47f00000, 0}}, /* 2^ 128 */ + tm128 = {{0x37f00000, 0}}, /* 2^-128 */ + ZERO = {{0, 0}}, /* 0.0 */ + nZERO = {{0x80000000, 0}}; /* -0.0 */ +#else +#ifdef LITTLE_ENDI +static const mynumber big = {{0, 0x43380000}}, /* 6755399441055744 */ + t128 = {{0, 0x47f00000}}, /* 2^ 128 */ + tm128 = {{0, 0x37f00000}}, /* 2^-128 */ + ZERO = {{0, 0}}, /* 0.0 */ + nZERO = {{0, 0x80000000}}; /* -0.0 */ +#endif +#endif + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/usncs.h b/REORG.TODO/sysdeps/ieee754/dbl-64/usncs.h new file mode 100644 index 0000000000..09f76ae8ea --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/usncs.h @@ -0,0 +1,48 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/************************************************************************/ +/* MODULE_NAME: dosincos.h */ +/* */ +/* */ +/* common data and variables definition for BIG or LITTLE ENDIAN */ +/************************************************************************/ + +#ifndef USNCS_H +#define USNCS_H + +static const double s1 = -0x1.5555555555555p-3; /* -0.16666666666666666 */ +static const double s2 = 0x1.1111111110ECEp-7; /* 0.0083333333333323288 */ +static const double s3 = -0x1.A01A019DB08B8p-13; /* -0.00019841269834414642 */ +static const double s4 = 0x1.71DE27B9A7ED9p-19; /* 2.755729806860771e-06 */ +static const double s5 = -0x1.ADDFFC2FCDF59p-26; /* -2.5022014848318398e-08 */ +static const double aa = -0x1.5558000000000p-3; /* -0.1666717529296875 */ +static const double bb = 0x1.5555555556E24p-18; /* 5.0862630208387126e-06 */ +static const double big = 0x1.8000000000000p45; /* 52776558133248 */ +static const double hp0 = 0x1.921FB54442D18p0; /* 1.5707963267948966 */ +static const double hp1 = 0x1.1A62633145C07p-54; /* 6.123233995736766e-17 */ +static const double mp1 = 0x1.921FB58000000p0; /* 1.5707963407039642 */ +static const double mp2 = -0x1.DDE973C000000p-27; /* -1.3909067564377153e-08 */ +static const double mp3 = -0x1.CB3B399D747F2p-55; /* -4.9789962505147994e-17 */ +static const double pp3 = -0x1.CB3B398000000p-55; /* -4.9789962314799099e-17 */ +static const double pp4 = -0x1.d747f23e32ed7p-83; /* -1.9034889620193266e-25 */ +static const double hpinv = 0x1.45F306DC9C883p-1; /* 0.63661977236758138 */ +static const double toint = 0x1.8000000000000p52; /* 6755399441055744 */ + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/utan.h b/REORG.TODO/sysdeps/ieee754/dbl-64/utan.h new file mode 100644 index 0000000000..b34e52f1fb --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/utan.h @@ -0,0 +1,265 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/******************************************************************/ +/* */ +/* MODULE_NAME:utan.h */ +/* */ +/* common data and variables prototype and definition */ +/******************************************************************/ + +#ifndef UTAN_H +#define UTAN_H + +#ifdef BIG_ENDI + static const number + /* polynomial I */ +/**/ d3 = {{0x3FD55555, 0x55555555} }, /* 0.333... */ +/**/ d5 = {{0x3FC11111, 0x111107C6} }, /* 0.133... */ +/**/ d7 = {{0x3FABA1BA, 0x1CDB8745} }, /* . */ +/**/ d9 = {{0x3F9664ED, 0x49CFC666} }, /* . */ +/**/ d11 = {{0x3F82385A, 0x3CF2E4EA} }, /* . */ + /* polynomial II */ +/**/ a3 = {{0x3fd55555, 0x55555555} }, /* 1/3 */ +/**/ aa3 = {{0x3c755555, 0x55555555} }, /* 1/3-a3 */ +/**/ a5 = {{0x3fc11111, 0x11111111} }, /* 2/15 */ +/**/ aa5 = {{0x3c411111, 0x11111111} }, /* 2/15-a5 */ +/**/ a7 = {{0x3faba1ba, 0x1ba1ba1c} }, /* 17/315 */ +/**/ aa7 = {{0xbc479179, 0x17917918} }, /* ()-a7 */ +/**/ a9 = {{0x3f9664f4, 0x882c10fa} }, /* 62/2835 */ +/**/ aa9 = {{0xbc09a528, 0x8b6c44fd} }, /* ()-a9 */ +/**/ a11 = {{0x3f8226e3, 0x55e6c23d} }, /* . */ +/**/ aa11 = {{0xbc2c292b, 0x8f1a2c13} }, /* . */ +/**/ a13 = {{0x3f6d6d3d, 0x0e157de0} }, /* . */ +/**/ aa13 = {{0xbc0280cf, 0xc968d971} }, /* . */ +/**/ a15 = {{0x3f57da36, 0x452b75e3} }, /* . */ +#if 0 +/**/ aa15 = {{0xbbf25789, 0xb285d2ed} }, /* . */ +#endif +/**/ a17 = {{0x3f435582, 0x48036744} }, /* . */ +#if 0 +/**/ aa17 = {{0x3be488d9, 0x563f1f23} }, /* . */ +#endif +/**/ a19 = {{0x3f2f57d7, 0x734d1664} }, /* . */ +#if 0 +/**/ aa19 = {{0x3bb0d55a, 0x913ccb50} }, /* . */ +#endif +/**/ a21 = {{0x3f1967e1, 0x8afcafad} }, /* . */ +#if 0 +/**/ aa21 = {{0xbbbd7614, 0xa42d44e6} }, /* . */ +#endif +/**/ a23 = {{0x3f0497d8, 0xeea25259} }, /* . */ +#if 0 +/**/ aa23 = {{0x3b99f2d0, 0x2e4d2863} }, /* . */ +#endif +/**/ a25 = {{0x3ef0b132, 0xd39a6050} }, /* . */ +#if 0 +/**/ aa25 = {{0x3b93b274, 0xc2c19614} }, /* . */ +#endif +/**/ a27 = {{0x3edb0f72, 0xd3ee24e9} }, /* . */ +#if 0 +/**/ aa27 = {{0x3b61688d, 0xdd595609} }, /* . */ +#endif + /* polynomial III */ +/**/ e0 = {{0x3FD55555, 0x55554DBD} }, /* . */ +/**/ e1 = {{0x3FC11112, 0xE0A6B45F} }, /* . */ + + /* constants */ +/**/ mfftnhf = {{0xc02f0000, 0x00000000} }, /*-15.5 */ + +/**/ g1 = {{0x3e4b096c, 0x00000000} }, /* 1.259e-8 */ +/**/ g2 = {{0x3faf212d, 0x00000000} }, /* 0.0608 */ +/**/ g3 = {{0x3fe92f1a, 0x00000000} }, /* 0.787 */ +/**/ g4 = {{0x40390000, 0x00000000} }, /* 25.0 */ +/**/ g5 = {{0x4197d784, 0x00000000} }, /* 1e8 */ +/**/ gy1 = {{0x3e7ad7f2, 0x9abcaf48} }, /* 1e-7 */ +/**/ gy2 = {{0x3faf212d, 0x00000000} }, /* 0.0608 */ + +/**/ u1 = {{0x3cc8c33a, 0x00000000} }, /* 6.873e-16 */ +/**/ u2 = {{0x3983dc4d, 0x00000000} }, /* 1.224e-31 */ +/**/ u3 = {{0x3c78e14b, 0x00000000} }, /* 2.158e-17 */ +/**/ ua3 = {{0x3bfd8b58, 0x00000000} }, /* 1.001e-19 */ +/**/ ub3 = {{0x3cc81898, 0x00000000} }, /* 6.688e-16 */ +/**/ u4 = {{0x399856c2, 0x00000000} }, /* 3e-31 */ +/**/ u5 = {{0x3c39d80a, 0x00000000} }, /* 1.401e-18 */ +/**/ u6 = {{0x3c374c5a, 0x00000000} }, /* 1.263e-18 */ +/**/ u7 = {{0x39903beb, 0x00000000} }, /* 2.001e-31 */ +/**/ u8 = {{0x399c56ae, 0x00000000} }, /* 3.493e-31 */ +/**/ u9 = {{0x3c7d0ac7, 0x00000000} }, /* 2.519e-17 */ +/**/ ua9 = {{0x3bfd8b58, 0x00000000} }, /* 1.001e-19 */ +/**/ ub9 = {{0x3ccc2375, 0x00000000} }, /* 7.810e-16 */ +/**/ u10 = {{0x3c7e40af, 0x00000000} }, /* 2.624e-17 */ +/**/ ua10 = {{0x3bfd8b58, 0x00000000} }, /* 1.001e-19 */ +/**/ ub10 = {{0x3ccc6405, 0x00000000} }, /* 7.880e-16 */ +/**/ u11 = {{0x39e509b6, 0x00000000} }, /* 8.298e-30 */ +/**/ u12 = {{0x39e509b6, 0x00000000} }, /* 8.298e-30 */ +/**/ u13 = {{0x3c39d80a, 0x00000000} }, /* 1.401e-18 */ +/**/ u14 = {{0x3c374c5a, 0x00000000} }, /* 1.263e-18 */ +/**/ u15 = {{0x3ab5767a, 0x00000000} }, /* 6.935e-26 */ +/**/ u16 = {{0x3ab57744, 0x00000000} }, /* 6.936e-26 */ +/**/ u17 = {{0x3c7d0ac7, 0x00000000} }, /* 2.519e-17 */ +/**/ ua17 = {{0x3bfdb11f, 0x00000000} }, /* 1.006e-19 */ +/**/ ub17 = {{0x3ccc2375, 0x00000000} }, /* 7.810e-16 */ +/**/ u18 = {{0x3c7e40af, 0x00000000} }, /* 2.624e-17 */ +/**/ ua18 = {{0x3bfdb11f, 0x00000000} }, /* 1.006e-19 */ +/**/ ub18 = {{0x3ccc6405, 0x00000000} }, /* 7.880e-16 */ +/**/ u19 = {{0x39a13b61, 0x00000000} }, /* 4.248e-31 */ +/**/ u20 = {{0x39a13b61, 0x00000000} }, /* 4.248e-31 */ +/**/ u21 = {{0x3c3bb9b8, 0x00000000} }, /* 1.503e-18 */ +/**/ u22 = {{0x3c392e08, 0x00000000} }, /* 1.365e-18 */ +/**/ u23 = {{0x3a0ce706, 0x00000000} }, /* 4.560e-29 */ +/**/ u24 = {{0x3a0cff5d, 0x00000000} }, /* 4.575e-29 */ +/**/ u25 = {{0x3c7d0ac7, 0x00000000} }, /* 2.519e-17 */ +/**/ ua25 = {{0x3bfd8b58, 0x00000000} }, /* 1.001e-19 */ +/**/ ub25 = {{0x3ccc2375, 0x00000000} }, /* 7.810e-16 */ +/**/ u26 = {{0x3c7e40af, 0x00000000} }, /* 2.624e-17 */ +/**/ ua26 = {{0x3bfd8b58, 0x00000000} }, /* 1.001e-19 */ +/**/ ub26 = {{0x3ccc6405, 0x00000000} }, /* 7.880e-16 */ +/**/ u27 = {{0x3ad421cb, 0x00000000} }, /* 2.602e-25 */ +/**/ u28 = {{0x3ad421cb, 0x00000000} }, /* 2.602e-25 */ + +/**/ mp1 = {{0x3FF921FB, 0x58000000} }, +/**/ mp2 = {{0xBE4DDE97, 0x3C000000} }, +/**/ mp3 = {{0xBC8CB3B3, 0x99D747F2} }, +/**/ pp3 = {{0xBC8CB3B3, 0x98000000} }, +/**/ pp4 = {{0xbacd747f, 0x23e32ed7} }, +/**/ hpinv = {{0x3FE45F30, 0x6DC9C883} }, +/**/ toint = {{0x43380000, 0x00000000} }; + +#else +#ifdef LITTLE_ENDI + + static const number + /* polynomial I */ +/**/ d3 = {{0x55555555, 0x3FD55555} }, /* 0.333... */ +/**/ d5 = {{0x111107C6, 0x3FC11111} }, /* 0.133... */ +/**/ d7 = {{0x1CDB8745, 0x3FABA1BA} }, /* . */ +/**/ d9 = {{0x49CFC666, 0x3F9664ED} }, /* . */ +/**/ d11 = {{0x3CF2E4EA, 0x3F82385A} }, /* . */ + /* polynomial II */ +/**/ a3 = {{0x55555555, 0x3fd55555} }, /* 1/3 */ +/**/ aa3 = {{0x55555555, 0x3c755555} }, /* 1/3-a3 */ +/**/ a5 = {{0x11111111, 0x3fc11111} }, /* 2/15 */ +/**/ aa5 = {{0x11111111, 0x3c411111} }, /* 2/15-a5 */ +/**/ a7 = {{0x1ba1ba1c, 0x3faba1ba} }, /* 17/315 */ +/**/ aa7 = {{0x17917918, 0xbc479179} }, /* ()-a7 */ +/**/ a9 = {{0x882c10fa, 0x3f9664f4} }, /* 62/2835 */ +/**/ aa9 = {{0x8b6c44fd, 0xbc09a528} }, /* ()-a9 */ +/**/ a11 = {{0x55e6c23d, 0x3f8226e3} }, /* . */ +/**/ aa11 = {{0x8f1a2c13, 0xbc2c292b} }, /* . */ +/**/ a13 = {{0x0e157de0, 0x3f6d6d3d} }, /* . */ +/**/ aa13 = {{0xc968d971, 0xbc0280cf} }, /* . */ +/**/ a15 = {{0x452b75e3, 0x3f57da36} }, /* . */ +#if 0 +/**/ aa15 = {{0xb285d2ed, 0xbbf25789} }, /* . */ +#endif +/**/ a17 = {{0x48036744, 0x3f435582} }, /* . */ +#if 0 +/**/ aa17 = {{0x563f1f23, 0x3be488d9} }, /* . */ +#endif +/**/ a19 = {{0x734d1664, 0x3f2f57d7} }, /* . */ +#if 0 +/**/ aa19 = {{0x913ccb50, 0x3bb0d55a} }, /* . */ +#endif +/**/ a21 = {{0x8afcafad, 0x3f1967e1} }, /* . */ +#if 0 +/**/ aa21 = {{0xa42d44e6, 0xbbbd7614} }, /* . */ +#endif +/**/ a23 = {{0xeea25259, 0x3f0497d8} }, /* . */ +#if 0 +/**/ aa23 = {{0x2e4d2863, 0x3b99f2d0} }, /* . */ +#endif +/**/ a25 = {{0xd39a6050, 0x3ef0b132} }, /* . */ +#if 0 +/**/ aa25 = {{0xc2c19614, 0x3b93b274} }, /* . */ +#endif +/**/ a27 = {{0xd3ee24e9, 0x3edb0f72} }, /* . */ +#if 0 +/**/ aa27 = {{0xdd595609, 0x3b61688d} }, /* . */ +#endif + /* polynomial III */ +/**/ e0 = {{0x55554DBD, 0x3FD55555} }, /* . */ +/**/ e1 = {{0xE0A6B45F, 0x3FC11112} }, /* . */ + + /* constants */ +/**/ mfftnhf = {{0x00000000, 0xc02f0000} }, /*-15.5 */ + +/**/ g1 = {{0x00000000, 0x3e4b096c} }, /* 1.259e-8 */ +/**/ g2 = {{0x00000000, 0x3faf212d} }, /* 0.0608 */ +/**/ g3 = {{0x00000000, 0x3fe92f1a} }, /* 0.787 */ +/**/ g4 = {{0x00000000, 0x40390000} }, /* 25.0 */ +/**/ g5 = {{0x00000000, 0x4197d784} }, /* 1e8 */ +/**/ gy1 = {{0x9abcaf48, 0x3e7ad7f2} }, /* 1e-7 */ +/**/ gy2 = {{0x00000000, 0x3faf212d} }, /* 0.0608 */ + +/**/ u1 = {{0x00000000, 0x3cc8c33a} }, /* 6.873e-16 */ +/**/ u2 = {{0x00000000, 0x3983dc4d} }, /* 1.224e-31 */ +/**/ u3 = {{0x00000000, 0x3c78e14b} }, /* 2.158e-17 */ +/**/ ua3 = {{0x00000000, 0x3bfd8b58} }, /* 1.001e-19 */ +/**/ ub3 = {{0x00000000, 0x3cc81898} }, /* 6.688e-16 */ +/**/ u4 = {{0x00000000, 0x399856c2} }, /* 3e-31 */ +/**/ u5 = {{0x00000000, 0x3c39d80a} }, /* 1.401e-18 */ +/**/ u6 = {{0x00000000, 0x3c374c5a} }, /* 1.263e-18 */ +/**/ u7 = {{0x00000000, 0x39903beb} }, /* 2.001e-31 */ +/**/ u8 = {{0x00000000, 0x399c56ae} }, /* 3.493e-31 */ +/**/ u9 = {{0x00000000, 0x3c7d0ac7} }, /* 2.519e-17 */ +/**/ ua9 = {{0x00000000, 0x3bfd8b58} }, /* 1.001e-19 */ +/**/ ub9 = {{0x00000000, 0x3ccc2375} }, /* 7.810e-16 */ +/**/ u10 = {{0x00000000, 0x3c7e40af} }, /* 2.624e-17 */ +/**/ ua10 = {{0x00000000, 0x3bfd8b58} }, /* 1.001e-19 */ +/**/ ub10 = {{0x00000000, 0x3ccc6405} }, /* 7.880e-16 */ +/**/ u11 = {{0x00000000, 0x39e509b6} }, /* 8.298e-30 */ +/**/ u12 = {{0x00000000, 0x39e509b6} }, /* 8.298e-30 */ +/**/ u13 = {{0x00000000, 0x3c39d80a} }, /* 1.401e-18 */ +/**/ u14 = {{0x00000000, 0x3c374c5a} }, /* 1.263e-18 */ +/**/ u15 = {{0x00000000, 0x3ab5767a} }, /* 6.935e-26 */ +/**/ u16 = {{0x00000000, 0x3ab57744} }, /* 6.936e-26 */ +/**/ u17 = {{0x00000000, 0x3c7d0ac7} }, /* 2.519e-17 */ +/**/ ua17 = {{0x00000000, 0x3bfdb11f} }, /* 1.006e-19 */ +/**/ ub17 = {{0x00000000, 0x3ccc2375} }, /* 7.810e-16 */ +/**/ u18 = {{0x00000000, 0x3c7e40af} }, /* 2.624e-17 */ +/**/ ua18 = {{0x00000000, 0x3bfdb11f} }, /* 1.006e-19 */ +/**/ ub18 = {{0x00000000, 0x3ccc6405} }, /* 7.880e-16 */ +/**/ u19 = {{0x00000000, 0x39a13b61} }, /* 4.248e-31 */ +/**/ u20 = {{0x00000000, 0x39a13b61} }, /* 4.248e-31 */ +/**/ u21 = {{0x00000000, 0x3c3bb9b8} }, /* 1.503e-18 */ +/**/ u22 = {{0x00000000, 0x3c392e08} }, /* 1.365e-18 */ +/**/ u23 = {{0x00000000, 0x3a0ce706} }, /* 4.560e-29 */ +/**/ u24 = {{0x00000000, 0x3a0cff5d} }, /* 4.575e-29 */ +/**/ u25 = {{0x00000000, 0x3c7d0ac7} }, /* 2.519e-17 */ +/**/ ua25 = {{0x00000000, 0x3bfd8b58} }, /* 1.001e-19 */ +/**/ ub25 = {{0x00000000, 0x3ccc2375} }, /* 7.810e-16 */ +/**/ u26 = {{0x00000000, 0x3c7e40af} }, /* 2.624e-17 */ +/**/ ua26 = {{0x00000000, 0x3bfd8b58} }, /* 1.001e-19 */ +/**/ ub26 = {{0x00000000, 0x3ccc6405} }, /* 7.880e-16 */ +/**/ u27 = {{0x00000000, 0x3ad421cb} }, /* 2.602e-25 */ +/**/ u28 = {{0x00000000, 0x3ad421cb} }, /* 2.602e-25 */ + +/**/ mp1 = {{0x58000000, 0x3FF921FB} }, +/**/ mp2 = {{0x3C000000, 0xBE4DDE97} }, +/**/ mp3 = {{0x99D747F2, 0xBC8CB3B3} }, +/**/ pp3 = {{0x98000000, 0xBC8CB3B3} }, +/**/ pp4 = {{0x23e32ed7, 0xbacd747f} }, +/**/ hpinv = {{0x6DC9C883, 0x3FE45F30} }, +/**/ toint = {{0x00000000, 0x43380000} }; + +#endif +#endif + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/utan.tbl b/REORG.TODO/sysdeps/ieee754/dbl-64/utan.tbl new file mode 100644 index 0000000000..8b536e9235 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/utan.tbl @@ -0,0 +1,1525 @@ +/* + * IBM Accurate Mathematical Library + * Written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ + +/****************************************************************/ +/* TABLES FOR THE utan() FUNCTION */ +/****************************************************************/ + + +#ifdef BIG_ENDI +static const number + xfg[186][4] = { /* xi,Fi,Gi,FFi, i=16..201 */ +/**/ {{{0x3fb00000, 0x1e519d60} }, +/**/ {{0x3fb00557, 0x96c4e240} }, +/**/ {{0x402ff554, 0x628127b7} }, +/**/ {{0xbb9a1dee, 0x9e355b06} },}, +/**/ {{{0x3fb10000, 0x1b1a7010} }, +/**/ {{0x3fb10668, 0xaab892b7} }, +/**/ {{0x402e12c7, 0xbe3fdf74} }, +/**/ {{0x3ba89234, 0x037da741} },}, +/**/ {{{0x3fb20000, 0x2505e350} }, +/**/ {{0x3fb2079b, 0xff547824} }, +/**/ {{0x402c65c5, 0xde853633} }, +/**/ {{0x3bb7486e, 0xe9614250} },}, +/**/ {{{0x3fb2ffff, 0xfcdc4252} }, +/**/ {{0x3fb308f3, 0x5eb16c68} }, +/**/ {{0x402ae5da, 0xe56be74f} }, +/**/ {{0xbb82c726, 0x91a23034} },}, +/**/ {{{0x3fb3ffff, 0xe3ff849f} }, +/**/ {{0x3fb40a71, 0x154999cc} }, +/**/ {{0x40298c43, 0x046b7352} }, +/**/ {{0x3b9aceaf, 0x3843738f} },}, +/**/ {{{0x3fb4ffff, 0xedc9590f} }, +/**/ {{0x3fb50c17, 0x429bdd80} }, +/**/ {{0x40285384, 0x91b5d674} }, +/**/ {{0xbbc1d02d, 0xb4403d22} },}, +/**/ {{{0x3fb60000, 0x00ee83f7} }, +/**/ {{0x3fb60de7, 0xda80cc21} }, +/**/ {{0x40273724, 0xef21a2a7} }, +/**/ {{0xbb95e53c, 0x72523ffd} },}, +/**/ {{{0x3fb6ffff, 0xeb05ea41} }, +/**/ {{0x3fb70fe4, 0xb8c51bea} }, +/**/ {{0x40263370, 0xfae562ff} }, +/**/ {{0xbb99ad0e, 0x8ffe0626} },}, +/**/ {{{0x3fb7ffff, 0xdc0515f7} }, +/**/ {{0x3fb81210, 0x1db54498} }, +/**/ {{0x40254553, 0x0e7eab5c} }, +/**/ {{0xbb914c87, 0xd62ed686} },}, +/**/ {{{0x3fb8ffff, 0xe384d7ab} }, +/**/ {{0x3fb9146c, 0x2a8d3727} }, +/**/ {{0x40246a33, 0xfd57f3fd} }, +/**/ {{0xbbbbda8d, 0x5381e06d} },}, +/**/ {{{0x3fb9ffff, 0xe4832347} }, +/**/ {{0x3fba16fa, 0xd50e1050} }, +/**/ {{0x40239fe2, 0xc5537a96} }, +/**/ {{0x3bc7f695, 0xc111eabb} },}, +/**/ {{{0x3fbb0000, 0x274540e3} }, +/**/ {{0x3fbb19be, 0x7ae68517} }, +/**/ {{0x4022e481, 0x3637e946} }, +/**/ {{0x3bc307f8, 0x8dbd9d93} },}, +/**/ {{{0x3fbbffff, 0xfebf2e9b} }, +/**/ {{0x3fbc1cb8, 0x8369cd19} }, +/**/ {{0x40223676, 0x17aef223} }, +/**/ {{0x3bc50038, 0x424a9cf3} },}, +/**/ {{{0x3fbd0000, 0x23529045} }, +/**/ {{0x3fbd1feb, 0xc11d7ef7} }, +/**/ {{0x4021945f, 0xb8e43d4e} }, +/**/ {{0x3b812007, 0x52a6f224} },}, +/**/ {{{0x3fbdffff, 0xd872a829} }, +/**/ {{0x3fbe2359, 0x8ee4d6b7} }, +/**/ {{0x4020fd0c, 0x76195d5f} }, +/**/ {{0xbbb4d9ab, 0x85fdca85} },}, +/**/ {{{0x3fbeffff, 0xff323b84} }, +/**/ {{0x3fbf2704, 0xec9073e5} }, +/**/ {{0x40206f71, 0x3020200f} }, +/**/ {{0x3bb77aa2, 0x12836992} },}, +/**/ {{{0x3fc00000, 0x0ce79195} }, +/**/ {{0x3fc01577, 0xbc30cc61} }, +/**/ {{0x401fd549, 0xd6564a88} }, +/**/ {{0xbbc8926f, 0x965c0ad0} },}, +/**/ {{{0x3fc07fff, 0xee40e918} }, +/**/ {{0x3fc0978d, 0x8279ac01} }, +/**/ {{0x401edbb5, 0x9294bc03} }, +/**/ {{0xbb80a533, 0x4aae45d6} },}, +/**/ {{{0x3fc10000, 0x0cc091fd} }, +/**/ {{0x3fc119c5, 0x44dfb2f7} }, +/**/ {{0x401df0bb, 0x067d8e18} }, +/**/ {{0xbbcc2c18, 0x4ff642a4} },}, +/**/ {{{0x3fc18000, 0x0d9936a1} }, +/**/ {{0x3fc19c1f, 0xb9085a4b} }, +/**/ {{0x401d131a, 0x71ce3629} }, +/**/ {{0xbbc36553, 0x0669355b} },}, +/**/ {{{0x3fc1ffff, 0xed5f3188} }, +/**/ {{0x3fc21e9d, 0xee74bf2d} }, +/**/ {{0x401c41b6, 0xff0cd655} }, +/**/ {{0x3b8867f5, 0x478ecfc5} },}, +/**/ {{{0x3fc28000, 0x05f06a51} }, +/**/ {{0x3fc2a141, 0x550b313f} }, +/**/ {{0x401b7b92, 0x1702e6d2} }, +/**/ {{0xbbadab51, 0x380131fe} },}, +/**/ {{{0x3fc2ffff, 0xfe3d339e} }, +/**/ {{0x3fc3240a, 0xa75f76df} }, +/**/ {{0x401abfc8, 0xfcb6409d} }, +/**/ {{0x3bc60bcf, 0x0d291d83} },}, +/**/ {{{0x3fc37fff, 0xed888d6f} }, +/**/ {{0x3fc3a6fb, 0x13cc5db7} }, +/**/ {{0x401a0d8f, 0x8ed5320d} }, +/**/ {{0x3bb8a48e, 0x4eef03ab} },}, +/**/ {{{0x3fc40000, 0x02ca050d} }, +/**/ {{0x3fc42a13, 0xe25776bb} }, +/**/ {{0x4019642d, 0xfa84c2bc} }, +/**/ {{0xbbd0bd5d, 0xcc56516f} },}, +/**/ {{{0x3fc47fff, 0xf2531f5c} }, +/**/ {{0x3fc4ad55, 0xdeb73404} }, +/**/ {{0x4018c2fe, 0xf86e9035} }, +/**/ {{0x3b9cffe7, 0x5aa287c8} },}, +/**/ {{{0x3fc50000, 0x13774992} }, +/**/ {{0x3fc530c2, 0x7d0ee307} }, +/**/ {{0x4018296c, 0x370caf35} }, +/**/ {{0xbbcf75d1, 0xf91d6532} },}, +/**/ {{{0x3fc57fff, 0xedddcb2d} }, +/**/ {{0x3fc5b45a, 0x5db4347d} }, +/**/ {{0x401796ee, 0x52190c0e} }, +/**/ {{0x3b88a25f, 0x17d5d076} },}, +/**/ {{{0x3fc5ffff, 0xf41949a0} }, +/**/ {{0x3fc6381f, 0x13bf986a} }, +/**/ {{0x40170b09, 0x2d2255fd} }, +/**/ {{0xbb9bfb23, 0xb1bcd5e7} },}, +/**/ {{{0x3fc67fff, 0xf834d3a1} }, +/**/ {{0x3fc6bc11, 0x8ec85952} }, +/**/ {{0x4016854c, 0x62cf2268} }, +/**/ {{0x3b9ee53b, 0x82e39e04} },}, +/**/ {{{0x3fc6ffff, 0xfd9106ea} }, +/**/ {{0x3fc74032, 0xf298f6f7} }, +/**/ {{0x40160551, 0x1f4f84a9} }, +/**/ {{0xbbb59c4a, 0x112634b8} },}, +/**/ {{{0x3fc78000, 0x0f649a4f} }, +/**/ {{0x3fc7c484, 0x6ca53abc} }, +/**/ {{0x40158ab9, 0x4809d175} }, +/**/ {{0x3bc91c75, 0x73d3cd2e} },}, +/**/ {{{0x3fc7ffff, 0xef06bbd8} }, +/**/ {{0x3fc84906, 0xdf7d76ad} }, +/**/ {{0x4015152e, 0xdd2b30a6} }, +/**/ {{0xbbbfa2da, 0x084c3eef} },}, +/**/ {{{0x3fc88000, 0x021c6334} }, +/**/ {{0x3fc8cdbb, 0xd965f986} }, +/**/ {{0x4014a462, 0x51b74296} }, +/**/ {{0xbb9ec02e, 0x74dcfe0b} },}, +/**/ {{{0x3fc8ffff, 0xf38d0756} }, +/**/ {{0x3fc952a4, 0x28e173c7} }, +/**/ {{0x4014380b, 0x17b59ebd} }, +/**/ {{0xbbcd0f1c, 0xb77589f0} },}, +/**/ {{{0x3fc98000, 0x104efca1} }, +/**/ {{0x3fc9d7c1, 0x4644d23c} }, +/**/ {{0x4013cfe5, 0xcb1eabd5} }, +/**/ {{0xbbd5d6f7, 0xea188d9e} },}, +/**/ {{{0x3fca0000, 0x09417b30} }, +/**/ {{0x3fca5d14, 0x096d76aa} }, +/**/ {{0x40136bb4, 0xb3723db0} }, +/**/ {{0x3bbe3e0d, 0xfbf3979c} },}, +/**/ {{{0x3fca7fff, 0xeb1c23ec} }, +/**/ {{0x3fcae29d, 0xab60288d} }, +/**/ {{0x40130b3e, 0x783071d7} }, +/**/ {{0xbbc7dd82, 0x3d5384bf} },}, +/**/ {{{0x3fcaffff, 0xfb171c13} }, +/**/ {{0x3fcb685f, 0xa221a96b} }, +/**/ {{0x4012ae4d, 0xd8c0747d} }, +/**/ {{0x3bd4644b, 0xd5554972} },}, +/**/ {{{0x3fcb8000, 0x0aba44be} }, +/**/ {{0x3fcbee5a, 0xecdf241f} }, +/**/ {{0x401254b1, 0xc6fad63b} }, +/**/ {{0x3ba41916, 0xd092b85a} },}, +/**/ {{{0x3fcc0000, 0x113d2a3e} }, +/**/ {{0x3fcc7490, 0xb3e92543} }, +/**/ {{0x4011fe3c, 0x9a62c035} }, +/**/ {{0xbba3cc39, 0x41a03739} },}, +/**/ {{{0x3fcc7fff, 0xf49e00ce} }, +/**/ {{0x3fccfb02, 0x0f59eab0} }, +/**/ {{0x4011aac3, 0xe956a631} }, +/**/ {{0xbbb7a383, 0xbfa8cb5b} },}, +/**/ {{{0x3fcd0000, 0x05f611ab} }, +/**/ {{0x3fcd81b0, 0x89e6844e} }, +/**/ {{0x40115a1f, 0xf391268d} }, +/**/ {{0x3bd39b5c, 0xb2dc91f3} },}, +/**/ {{{0x3fcd8000, 0x14764ceb} }, +/**/ {{0x3fce089d, 0x27debf0d} }, +/**/ {{0x40110c2b, 0xfbc84740} }, +/**/ {{0x3bc14d4d, 0x84712510} },}, +/**/ {{{0x3fce0000, 0x14bcea76} }, +/**/ {{0x3fce8fc9, 0x16dbc820} }, +/**/ {{0x4010c0c5, 0xa00ca48e} }, +/**/ {{0xbbd33788, 0x640f1b9e} },}, +/**/ {{{0x3fce7fff, 0xfd7995bd} }, +/**/ {{0x3fcf1735, 0x88b50424} }, +/**/ {{0x401077cc, 0xbe02169a} }, +/**/ {{0xbbb61fee, 0x221fdf77} },}, +/**/ {{{0x3fcf0000, 0x0cc35436} }, +/**/ {{0x3fcf9ee3, 0xfd21a40b} }, +/**/ {{0x40103123, 0x1ee7ffe8} }, +/**/ {{0x3bd427e3, 0xc79ff5c1} },}, +/**/ {{{0x3fcf8000, 0x01d1da33} }, +/**/ {{0x3fd0136a, 0xb7dbe15c} }, +/**/ {{0x400fd959, 0x77d559e5} }, +/**/ {{0x3bb0c6a1, 0xd67948d7} },}, +/**/ {{{0x3fd00000, 0x060c13b2} }, +/**/ {{0x3fd05785, 0xaaad4f18} }, +/**/ {{0x400f549e, 0x2675d182} }, +/**/ {{0xbbc15208, 0x18f0dd10} },}, +/**/ {{{0x3fd04000, 0x03885492} }, +/**/ {{0x3fd09bc3, 0x660542d7} }, +/**/ {{0x400ed3e2, 0xdf3f5fec} }, +/**/ {{0xbbd95657, 0xb883ae62} },}, +/**/ {{{0x3fd08000, 0x052f5a13} }, +/**/ {{0x3fd0e024, 0x9a195045} }, +/**/ {{0x400e56f8, 0xfa68f2c8} }, +/**/ {{0x3bded7ba, 0x5a543e8e} },}, +/**/ {{{0x3fd0c000, 0x02ba1af5} }, +/**/ {{0x3fd124a9, 0xe2e7f24b} }, +/**/ {{0x400dddb4, 0xbffe633f} }, +/**/ {{0xbbdcba86, 0x0c60278f} },}, +/**/ {{{0x3fd0ffff, 0xf76642c1} }, +/**/ {{0x3fd16953, 0xe162ffe6} }, +/**/ {{0x400d67ed, 0x0311d5d5} }, +/**/ {{0x3b7b1f4a, 0xe40c5f9e} },}, +/**/ {{{0x3fd14000, 0x033602f0} }, +/**/ {{0x3fd1ae23, 0x5f49508e} }, +/**/ {{0x400cf57a, 0xb8708266} }, +/**/ {{0xbbd6a6c2, 0x8620f301} },}, +/**/ {{{0x3fd17fff, 0xfefd1a13} }, +/**/ {{0x3fd1f318, 0xdb2a9ba1} }, +/**/ {{0x400c8639, 0x8d11009e} }, +/**/ {{0x3bd3a9c6, 0x69b21d3b} },}, +/**/ {{{0x3fd1bfff, 0xf718365d} }, +/**/ {{0x3fd23835, 0x0c41e3ac} }, +/**/ {{0x400c1a06, 0xe02be47c} }, +/**/ {{0x3bdb961a, 0x129e8cd1} },}, +/**/ {{{0x3fd1ffff, 0xff001e00} }, +/**/ {{0x3fd27d78, 0xb2f6395e} }, +/**/ {{0x400bb0c1, 0xf2fe9a85} }, +/**/ {{0x3be074a9, 0xe68fd7d8} },}, +/**/ {{{0x3fd23fff, 0xfe425a6a} }, +/**/ {{0x3fd2c2e4, 0x618faabe} }, +/**/ {{0x400b4a4c, 0x190b18df} }, +/**/ {{0xbbdf0d1f, 0xf615aad1} },}, +/**/ {{{0x3fd28000, 0x059ec1db} }, +/**/ {{0x3fd30878, 0xd8583884} }, +/**/ {{0x400ae688, 0x0cd82bc2} }, +/**/ {{0xbbd563c3, 0x141c1f8d} },}, +/**/ {{{0x3fd2c000, 0x000dd081} }, +/**/ {{0x3fd34e36, 0xaffdb6d8} }, +/**/ {{0x400a855a, 0x5270fc15} }, +/**/ {{0xbbc6d88d, 0x9f2cdafd} },}, +/**/ {{{0x3fd2ffff, 0xfc1dcd2b} }, +/**/ {{0x3fd3941e, 0xa95875bc} }, +/**/ {{0x400a26a8, 0xaa9502b6} }, +/**/ {{0xbbe13cad, 0x8389b15c} },}, +/**/ {{{0x3fd33fff, 0xf6c0d4a0} }, +/**/ {{0x3fd3da31, 0x739845f5} }, +/**/ {{0x4009ca5a, 0x4d2573a0} }, +/**/ {{0xbbc71636, 0xacaee379} },}, +/**/ {{{0x3fd38000, 0x06b16793} }, +/**/ {{0x3fd4206f, 0xdbc088f0} }, +/**/ {{0x40097057, 0x9344e33a} }, +/**/ {{0xbbc2c052, 0x1d7a4f81} },}, +/**/ {{{0x3fd3c000, 0x07358fa3} }, +/**/ {{0x3fd466da, 0x6f23311d} }, +/**/ {{0x4009188a, 0x5aa612ea} }, +/**/ {{0x3b8653a5, 0x685e8edc} },}, +/**/ {{{0x3fd3ffff, 0xfc3b18cf} }, +/**/ {{0x3fd4ad71, 0xe9282e6b} }, +/**/ {{0x4008c2dd, 0x641e643d} }, +/**/ {{0x3b95f0ef, 0x3f567c64} },}, +/**/ {{{0x3fd44000, 0x000dd2a8} }, +/**/ {{0x3fd4f437, 0x1fa3f2d1} }, +/**/ {{0x40086f3c, 0x6072f821} }, +/**/ {{0x3bb68efa, 0x95ff68b5} },}, +/**/ {{{0x3fd47fff, 0xfbb43713} }, +/**/ {{0x3fd53b2a, 0xb3ac333c} }, +/**/ {{0x40081d94, 0x3da56692} }, +/**/ {{0xbbbf4d7f, 0x2985fd3f} },}, +/**/ {{{0x3fd4bfff, 0xfb113bf4} }, +/**/ {{0x3fd5824d, 0x6e8ed9c2} }, +/**/ {{0x4007cdd2, 0xa8add00f} }, +/**/ {{0x3bcf478a, 0x1c9b3657} },}, +/**/ {{{0x3fd4ffff, 0xf7f087c9} }, +/**/ {{0x3fd5c9a0, 0x07446496} }, +/**/ {{0x40077fe6, 0x444588eb} }, +/**/ {{0xbbc177dc, 0xa4eabb0c} },}, +/**/ {{{0x3fd54000, 0x088b3814} }, +/**/ {{0x3fd61123, 0x564125f9} }, +/**/ {{0x400733be, 0x6281a765} }, +/**/ {{0xbbc2c52c, 0xf57051c4} },}, +/**/ {{{0x3fd57fff, 0xf7d55966} }, +/**/ {{0x3fd658d7, 0xe194a5d5} }, +/**/ {{0x4006e94b, 0x73b47d1f} }, +/**/ {{0x3bda2fcf, 0xf9996dc6} },}, +/**/ {{{0x3fd5c000, 0x08bf2490} }, +/**/ {{0x3fd6a0be, 0xb775b28d} }, +/**/ {{0x4006a07e, 0x15b6ec28} }, +/**/ {{0xbbe0ca90, 0xaa5285b8} },}, +/**/ {{{0x3fd60000, 0x09fa853f} }, +/**/ {{0x3fd6e8d8, 0x65a66cfd} }, +/**/ {{0x40065948, 0x1c701269} }, +/**/ {{0x3bd9ea95, 0x8591e13a} },}, +/**/ {{{0x3fd64000, 0x07595fca} }, +/**/ {{0x3fd73125, 0xc0556a7c} }, +/**/ {{0x4006139b, 0xbaae9d02} }, +/**/ {{0x3bd88aff, 0x40152b83} },}, +/**/ {{{0x3fd68000, 0x031687da} }, +/**/ {{0x3fd779a7, 0x92e2cfd0} }, +/**/ {{0x4005cf6b, 0xcae0882b} }, +/**/ {{0xbbd8a4a2, 0x9f439451} },}, +/**/ {{{0x3fd6bfff, 0xf5c8cfe2} }, +/**/ {{0x3fd7c25e, 0x9fb452ed} }, +/**/ {{0x40058cab, 0xc561f1cd} }, +/**/ {{0xbbe371a6, 0xf6a37d74} },}, +/**/ {{{0x3fd6ffff, 0xf81df231} }, +/**/ {{0x3fd80b4b, 0xcfb4dab5} }, +/**/ {{0x40054b4f, 0x8d3ca5d3} }, +/**/ {{0x3bcb4686, 0x679dc99f} },}, +/**/ {{{0x3fd73fff, 0xfa71385e} }, +/**/ {{0x3fd8546f, 0xe007a9b6} }, +/**/ {{0x40050b4b, 0xb3b22176} }, +/**/ {{0xbbcd1540, 0xa5c73477} },}, +/**/ {{{0x3fd78000, 0x024a9c2b} }, +/**/ {{0x3fd89dcb, 0xa7fcf5cf} }, +/**/ {{0x4004cc95, 0x3159cbe1} }, +/**/ {{0xbbdc25ea, 0xd58a6ad0} },}, +/**/ {{{0x3fd7c000, 0x02eb62b8} }, +/**/ {{0x3fd8e75f, 0xec0ba5cf} }, +/**/ {{0x40048f21, 0x8731eeea} }, +/**/ {{0xbbc1cb73, 0xcc1adafb} },}, +/**/ {{{0x3fd80000, 0x054a52d1} }, +/**/ {{0x3fd9312d, 0x8bb822e9} }, +/**/ {{0x400452e6, 0x9170a729} }, +/**/ {{0xbbd8bb17, 0xeac002ee} },}, +/**/ {{{0x3fd83fff, 0xf93a00a3} }, +/**/ {{0x3fd97b35, 0x4bb9ad2a} }, +/**/ {{0x400417da, 0xae924e7f} }, +/**/ {{0x3bd4b800, 0x9a378cc7} },}, +/**/ {{{0x3fd87fff, 0xfbdc91c1} }, +/**/ {{0x3fd9c578, 0x2771b601} }, +/**/ {{0x4003ddf4, 0x78855799} }, +/**/ {{0x3bd9077d, 0xa00445d9} },}, +/**/ {{{0x3fd8bfff, 0xf6d215e6} }, +/**/ {{0x3fda0ff6, 0xe0ea4a0b} }, +/**/ {{0x4003a52b, 0x189a0989} }, +/**/ {{0xbbda6831, 0x89c0613d} },}, +/**/ {{{0x3fd90000, 0x02f734ef} }, +/**/ {{0x3fda5ab2, 0x736bf579} }, +/**/ {{0x40036d75, 0xe9244ca6} }, +/**/ {{0x3be3a6d8, 0x4b722377} },}, +/**/ {{{0x3fd94000, 0x04eef8b4} }, +/**/ {{0x3fdaa5ab, 0x9fb6e3d0} }, +/**/ {{0x400336cc, 0xc9089cb7} }, +/**/ {{0x3b9f6963, 0x22cc00bb} },}, +/**/ {{{0x3fd98000, 0x041ec76a} }, +/**/ {{0x3fdaf0e3, 0x5176c7e4} }, +/**/ {{0x40030127, 0xcb0b9506} }, +/**/ {{0x3bb1ffdb, 0x5385a849} },}, +/**/ {{{0x3fd9c000, 0x08044e47} }, +/**/ {{0x3fdb3c5a, 0x77071224} }, +/**/ {{0x4002cc7f, 0x50d75ec7} }, +/**/ {{0xbbb0fade, 0x78effc8a} },}, +/**/ {{{0x3fda0000, 0x01f8235b} }, +/**/ {{0x3fdb8811, 0xe725782e} }, +/**/ {{0x400298cc, 0x18fbfb37} }, +/**/ {{0xbbe55ed3, 0x3b50e71b} },}, +/**/ {{{0x3fda3fff, 0xfb8c6f08} }, +/**/ {{0x3fdbd40a, 0x97b086f3} }, +/**/ {{0x40026607, 0x154de04b} }, +/**/ {{0xbbdec65e, 0x455faae3} },}, +/**/ {{{0x3fda7fff, 0xfb3d63e1} }, +/**/ {{0x3fdc2045, 0x7d9a3b8a} }, +/**/ {{0x40023429, 0x7e60bfbb} }, +/**/ {{0x3be3001c, 0x154ebd33} },}, +/**/ {{{0x3fdabfff, 0xf5f45c48} }, +/**/ {{0x3fdc6cc3, 0x7b8d45e6} }, +/**/ {{0x4002032c, 0xdb1ace69} }, +/**/ {{0xbbe5ebf8, 0x3ed33616} },}, +/**/ {{{0x3fdb0000, 0x0508b34c} }, +/**/ {{0x3fdcb985, 0xa27e8d37} }, +/**/ {{0x4001d30a, 0xd4459a2b} }, +/**/ {{0xbbd01432, 0xae61e2d1} },}, +/**/ {{{0x3fdb4000, 0x0a84710c} }, +/**/ {{0x3fdd068c, 0xc3e50155} }, +/**/ {{0x4001a3bd, 0x775034dd} }, +/**/ {{0xbbe80b1e, 0x58e0e228} },}, +/**/ {{{0x3fdb7fff, 0xf692e9d8} }, +/**/ {{0x3fdd53d9, 0xc49d6627} }, +/**/ {{0x4001753e, 0xfe18066a} }, +/**/ {{0xbbb004c8, 0xf760d33e} },}, +/**/ {{{0x3fdbc000, 0x0280f14d} }, +/**/ {{0x3fdda16d, 0xe4e81013} }, +/**/ {{0x40014789, 0xa38ea052} }, +/**/ {{0x3be848bc, 0x27c9c4ea} },}, +/**/ {{{0x3fdc0000, 0x001121d1} }, +/**/ {{0x3fddef49, 0xeac018f0} }, +/**/ {{0x40011a98, 0x20b8be0c} }, +/**/ {{0xbbe1527e, 0xd0d6010e} },}, +/**/ {{{0x3fdc3fff, 0xfef662aa} }, +/**/ {{0x3fde3d6e, 0xea0c7070} }, +/**/ {{0x4000ee65, 0x32f46ccd} }, +/**/ {{0x3be8d241, 0x189a000d} },}, +/**/ {{{0x3fdc8000, 0x09845818} }, +/**/ {{0x3fde8bdd, 0xf36a8b1b} }, +/**/ {{0x4000c2eb, 0xcac73476} }, +/**/ {{0x3bd221f7, 0x12bed284} },}, +/**/ {{{0x3fdcbfff, 0xfb0493bf} }, +/**/ {{0x3fdeda97, 0xe0c60d10} }, +/**/ {{0x40009827, 0x251c7836} }, +/**/ {{0xbbe0bd54, 0x6eec41b7} },}, +/**/ {{{0x3fdcffff, 0xfd52961f} }, +/**/ {{0x3fdf299d, 0xefb3e44b} }, +/**/ {{0x40006e12, 0x74e459f5} }, +/**/ {{0xbbd93f77, 0xe969c82f} },}, +/**/ {{{0x3fdd3fff, 0xfe2319a4} }, +/**/ {{0x3fdf78f1, 0x17139490} }, +/**/ {{0x400044a9, 0x3e737e94} }, +/**/ {{0xbb91e7cc, 0x49594b7a} },}, +/**/ {{{0x3fdd7fff, 0xfa4de596} }, +/**/ {{0x3fdfc892, 0x638f49e8} }, +/**/ {{0x40001be7, 0x231057a5} }, +/**/ {{0x3bd482b0, 0xf5af9f5f} },}, +/**/ {{{0x3fddbfff, 0xfe729a69} }, +/**/ {{0x3fe00c41, 0x7c6ab019} }, +/**/ {{0x3fffe78f, 0xbf612660} }, +/**/ {{0x3bea5cda, 0x00da681e} },}, +/**/ {{{0x3fde0000, 0x09d66802} }, +/**/ {{0x3fe03461, 0xf6b883cf} }, +/**/ {{0x3fff988e, 0xbc05a87c} }, +/**/ {{0xbbe06c33, 0xf2372669} },}, +/**/ {{{0x3fde3fff, 0xfb211657} }, +/**/ {{0x3fe05cab, 0x191db8e8} }, +/**/ {{0x3fff4ac3, 0x7bcfe6be} }, +/**/ {{0xbbd5d51f, 0x5ed8d35b} },}, +/**/ {{{0x3fde8000, 0x0a3f068a} }, +/**/ {{0x3fe0851d, 0x95fb54f0} }, +/**/ {{0x3ffefe26, 0x144ca408} }, +/**/ {{0xbbc7c894, 0xa2c169c5} },}, +/**/ {{{0x3fdec000, 0x01adb060} }, +/**/ {{0x3fe0adb9, 0xdc7b54f9} }, +/**/ {{0x3ffeb2af, 0x5ebe52a7} }, +/**/ {{0x3bd4e740, 0x312c5ffd} },}, +/**/ {{{0x3fdeffff, 0xff5c0d01} }, +/**/ {{0x3fe0d680, 0x92550a8d} }, +/**/ {{0x3ffe6858, 0x0d71fdf0} }, +/**/ {{0x3bddd8a6, 0x96b35499} },}, +/**/ {{{0x3fdf3fff, 0xf93d5fcc} }, +/**/ {{0x3fe0ff72, 0x45cb4374} }, +/**/ {{0x3ffe1f19, 0x3cce5040} }, +/**/ {{0xbbc9f0ec, 0x7c1efab4} },}, +/**/ {{{0x3fdf7fff, 0xfa0dd18f} }, +/**/ {{0x3fe1288f, 0x944dd508} }, +/**/ {{0x3ffdd6ec, 0x298b874d} }, +/**/ {{0x3bea6ebd, 0x9642a0a6} },}, +/**/ {{{0x3fdfbfff, 0xfd3a9f1a} }, +/**/ {{0x3fe151d9, 0x13750f3e} }, +/**/ {{0x3ffd8fca, 0x5806a27e} }, +/**/ {{0x3bda2a03, 0xfc65ac7a} },}, +/**/ {{{0x3fdfffff, 0xfc481400} }, +/**/ {{0x3fe17b4f, 0x598944ca} }, +/**/ {{0x3ffd49ad, 0x82532170} }, +/**/ {{0x3bc4412e, 0x3d236dc3} },}, +/**/ {{{0x3fe01fff, 0xff53786c} }, +/**/ {{0x3fe1a4f3, 0x07d83d47} }, +/**/ {{0x3ffd048f, 0x851bffeb} }, +/**/ {{0x3bd1589d, 0x29f81b14} },}, +/**/ {{{0x3fe03fff, 0xfee301b7} }, +/**/ {{0x3fe1cec4, 0xb8a6a382} }, +/**/ {{0x3ffcc06a, 0x7c519db6} }, +/**/ {{0x3bd370e6, 0x5b24d6b2} },}, +/**/ {{{0x3fe06000, 0x006e36bf} }, +/**/ {{0x3fe1f8c5, 0x114eb8be} }, +/**/ {{0x3ffc7d38, 0xa34d6786} }, +/**/ {{0xbbea92de, 0x4b98c1d4} },}, +/**/ {{{0x3fe07fff, 0xfd60aa43} }, +/**/ {{0x3fe222f4, 0xabeccecb} }, +/**/ {{0x3ffc3af4, 0x77342ac4} }, +/**/ {{0xbbdd47f6, 0x03a5c2c2} },}, +/**/ {{{0x3fe0a000, 0x037762e8} }, +/**/ {{0x3fe24d54, 0x3f99efe8} }, +/**/ {{0x3ffbf998, 0x75f54fab} }, +/**/ {{0x3bedf7f4, 0x15771a46} },}, +/**/ {{{0x3fe0bfff, 0xff1c6921} }, +/**/ {{0x3fe277e4, 0x598e35d0} }, +/**/ {{0x3ffbb91f, 0x8addd186} }, +/**/ {{0x3be0f16c, 0x5e0e5a73} },}, +/**/ {{{0x3fe0dfff, 0xff07154b} }, +/**/ {{0x3fe2a2a5, 0xb6bc3986} }, +/**/ {{0x3ffb7984, 0x8301646d} }, +/**/ {{0xbbf02dd0, 0xbbaa5310} },}, +/**/ {{{0x3fe10000, 0x02fcdda4} }, +/**/ {{0x3fe2cd99, 0x02a59f1e} }, +/**/ {{0x3ffb3ac2, 0x705219bf} }, +/**/ {{0xbbe59357, 0x112fa616} },}, +/**/ {{{0x3fe12000, 0x01ce1140} }, +/**/ {{0x3fe2f8be, 0xdf0a67c2} }, +/**/ {{0x3ffafcd4, 0x9ab8ae2a} }, +/**/ {{0x3be2c542, 0x9303f346} },}, +/**/ {{{0x3fe14000, 0x04d0f355} }, +/**/ {{0x3fe32418, 0x08fcc7bf} }, +/**/ {{0x3ffabfb6, 0x497b9a36} }, +/**/ {{0x3bebc044, 0xb5a59234} },}, +/**/ {{{0x3fe16000, 0x00fb0c8a} }, +/**/ {{0x3fe34fa5, 0x2471618b} }, +/**/ {{0x3ffa8363, 0x0d26d117} }, +/**/ {{0xbbdbfbb2, 0x3f7bb7c9} },}, +/**/ {{{0x3fe18000, 0x026f10b3} }, +/**/ {{0x3fe37b66, 0xf7579056} }, +/**/ {{0x3ffa47d6, 0x6b4cf4b1} }, +/**/ {{0x3bf0f6b4, 0xaf0b5de9} },}, +/**/ {{{0x3fe19fff, 0xfd0978f8} }, +/**/ {{0x3fe3a75e, 0x290cc78c} }, +/**/ {{0x3ffa0d0c, 0x36c21315} }, +/**/ {{0x3beb2129, 0xa296b262} },}, +/**/ {{{0x3fe1bfff, 0xfd94840b} }, +/**/ {{0x3fe3d38b, 0x85b4e4a4} }, +/**/ {{0x3ff9d300, 0x32f2ecef} }, +/**/ {{0xbbdbab1a, 0xb9bb7d74} },}, +/**/ {{{0x3fe1dfff, 0xfbda1ea1} }, +/**/ {{0x3fe3ffef, 0xbf3cee2f} }, +/**/ {{0x3ff999ae, 0x6770fed8} }, +/**/ {{0x3bda0bdc, 0xb4ace9a4} },}, +/**/ {{{0x3fe1ffff, 0xfc989533} }, +/**/ {{0x3fe42c8b, 0x9c27900c} }, +/**/ {{0x3ff96112, 0xe0d9f1ac} }, +/**/ {{0xbbee19eb, 0x2fa2d81a} },}, +/**/ {{{0x3fe22000, 0x012b8d26} }, +/**/ {{0x3fe4595f, 0xe11975ca} }, +/**/ {{0x3ff92929, 0xcdaa4e80} }, +/**/ {{0x3bf23382, 0xacc82d4b} },}, +/**/ {{{0x3fe24000, 0x04f4d6af} }, +/**/ {{0x3fe4866d, 0x4d224131} }, +/**/ {{0x3ff8f1ef, 0x815c34e8} }, +/**/ {{0xbbd0c6ff, 0x3b740a99} },}, +/**/ {{{0x3fe25fff, 0xfcc07bda} }, +/**/ {{0x3fe4b3b4, 0x98b7d010} }, +/**/ {{0x3ff8bb60, 0x73e7ffa1} }, +/**/ {{0x3bebc31b, 0x1ad7a9c2} },}, +/**/ {{{0x3fe28000, 0x042d9639} }, +/**/ {{0x3fe4e136, 0xb64540d1} }, +/**/ {{0x3ff88578, 0xf4374938} }, +/**/ {{0x3be36de9, 0x1b85e901} },}, +/**/ {{{0x3fe2a000, 0x03be29a0} }, +/**/ {{0x3fe50ef4, 0x52bffd96} }, +/**/ {{0x3ff85035, 0xc0042c06} }, +/**/ {{0x3be15d01, 0x76f5efbd} },}, +/**/ {{{0x3fe2bfff, 0xfaa91f12} }, +/**/ {{0x3fe53cee, 0x3e2f4e0d} }, +/**/ {{0x3ff81b93, 0x8542df07} }, +/**/ {{0x3be555cd, 0x17662a2b} },}, +/**/ {{{0x3fe2dfff, 0xfe884891} }, +/**/ {{0x3fe56b25, 0x6c1a2470} }, +/**/ {{0x3ff7e78e, 0xe422ea70} }, +/**/ {{0x3bf03504, 0xbd030c11} },}, +/**/ {{{0x3fe2ffff, 0xfe87152b} }, +/**/ {{0x3fe5999a, 0x9beaaaa1} }, +/**/ {{0x3ff7b424, 0xd18fe9b3} }, +/**/ {{0xbb649a5f, 0x773e0e64} },}, +/**/ {{{0x3fe31fff, 0xffc1a721} }, +/**/ {{0x3fe5c84e, 0xafe0e564} }, +/**/ {{0x3ff78152, 0x338db8d4} }, +/**/ {{0x3beaf428, 0x5da8e935} },}, +/**/ {{{0x3fe33fff, 0xff70a372} }, +/**/ {{0x3fe5f742, 0x82191d64} }, +/**/ {{0x3ff74f14, 0x1122bcae} }, +/**/ {{0x3bdb1c4b, 0xdee4bfaf} },}, +/**/ {{{0x3fe36000, 0x0436e836} }, +/**/ {{0x3fe62676, 0xfde6ccff} }, +/**/ {{0x3ff71d67, 0x7644252c} }, +/**/ {{0xbbec3d10, 0xe08c3afb} },}, +/**/ {{{0x3fe37fff, 0xfcbe9641} }, +/**/ {{0x3fe655ec, 0xee9ffdaf} }, +/**/ {{0x3ff6ec49, 0xa6fc0515} }, +/**/ {{0x3bdda453, 0x2ed29567} },}, +/**/ {{{0x3fe39fff, 0xffb6d6ca} }, +/**/ {{0x3fe685a5, 0x5e67a1e1} }, +/**/ {{0x3ff6bbb7, 0xbc2ae969} }, +/**/ {{0x3becbf7b, 0x2ef43882} },}, +/**/ {{{0x3fe3c000, 0x04934fec} }, +/**/ {{0x3fe6b5a1, 0x2cc07d75} }, +/**/ {{0x3ff68baf, 0x10b02ef8} }, +/**/ {{0xbbe7c8fb, 0xfeb7cabd} },}, +/**/ {{{0x3fe3e000, 0x03f5cf7f} }, +/**/ {{0x3fe6e5e1, 0x3e59def6} }, +/**/ {{0x3ff65c2d, 0x0e61500f} }, +/**/ {{0xbbe30ba4, 0x035f7845} },}, +/**/ {{{0x3fe40000, 0x05280ad9} }, +/**/ {{0x3fe71666, 0x91ab4c3e} }, +/**/ {{0x3ff62d2f, 0x19f01c90} }, +/**/ {{0xbbf1e9f5, 0xffe95f6a} },}, +/**/ {{{0x3fe42000, 0x049efb65} }, +/**/ {{0x3fe74732, 0x18af3b9d} }, +/**/ {{0x3ff5feb2, 0xb86465e4} }, +/**/ {{0x3bc4cad7, 0x280d591e} },}, +/**/ {{{0x3fe44000, 0x0035ccb6} }, +/**/ {{0x3fe77844, 0xcb4ff1e5} }, +/**/ {{0x3ff5d0b5, 0x7c455428} }, +/**/ {{0x3bed8c18, 0x7ba5617c} },}, +/**/ {{{0x3fe46000, 0x03346717} }, +/**/ {{0x3fe7a99f, 0xba258778} }, +/**/ {{0x3ff5a334, 0xf4392254} }, +/**/ {{0xbbefd14a, 0xfc84a570} },}, +/**/ {{{0x3fe48000, 0x03002575} }, +/**/ {{0x3fe7db43, 0xd836768f} }, +/**/ {{0x3ff5762e, 0xdcf97e0c} }, +/**/ {{0xbbdd7eba, 0x5f5df49e} },}, +/**/ {{{0x3fe4a000, 0x055bf381} }, +/**/ {{0x3fe80d32, 0x35edeefa} }, +/**/ {{0x3ff549a0, 0xea46e31f} }, +/**/ {{0xbbdba522, 0x76823eac} },}, +/**/ {{{0x3fe4c000, 0x04ce10e3} }, +/**/ {{0x3fe83f6b, 0xd67dc1a8} }, +/**/ {{0x3ff51d88, 0xed82bcc4} }, +/**/ {{0xbbeae92d, 0x077d29ea} },}, +/**/ {{{0x3fe4e000, 0x016c60e1} }, +/**/ {{0x3fe871f1, 0xca0aaf31} }, +/**/ {{0x3ff4f1e4, 0xbdacbf16} }, +/**/ {{0x3be82958, 0x46ee425e} },}, +/**/ {{{0x3fe4ffff, 0xff966f0a} }, +/**/ {{0x3fe8a4c5, 0x2bff2dae} }, +/**/ {{0x3ff4c6b2, 0x3917657e} }, +/**/ {{0xbbf127c2, 0x5c86c705} },}, +/**/ {{{0x3fe52000, 0x0076e6eb} }, +/**/ {{0x3fe8d7e7, 0x175651e8} }, +/**/ {{0x3ff49bef, 0x4f459b05} }, +/**/ {{0xbbb1e9d1, 0x4181bbfc} },}, +/**/ {{{0x3fe54000, 0x03d12d3b} }, +/**/ {{0x3fe90b58, 0xa976ed56} }, +/**/ {{0x3ff47199, 0xfdf24af4} }, +/**/ {{0x3be38c17, 0xc30decaf} },}, +/**/ {{{0x3fe55fff, 0xfce7fa8d} }, +/**/ {{0x3fe93f1a, 0xf03a3a09} }, +/**/ {{0x3ff447b0, 0x5f13234b} }, +/**/ {{0x3bf1b8b2, 0x70df7e20} },}, +/**/ {{{0x3fe58000, 0x0331b46a} }, +/**/ {{0x3fe9732f, 0x38e83134} }, +/**/ {{0x3ff41e30, 0x68d8b41b} }, +/**/ {{0xbbee24d8, 0xb90bc28b} },}, +/**/ {{{0x3fe59fff, 0xfc14848e} }, +/**/ {{0x3fe9a796, 0x8471b489} }, +/**/ {{0x3ff3f518, 0x5de3aa73} }, +/**/ {{0xbbecacd9, 0xe0761536} },}, +/**/ {{{0x3fe5bfff, 0xfb7cd395} }, +/**/ {{0x3fe9dc52, 0x24a8b955} }, +/**/ {{0x3ff3cc66, 0x4f8fff15} }, +/**/ {{0xbbf67c97, 0x82045611} },}, +/**/ {{{0x3fe5e000, 0x000dcc40} }, +/**/ {{0x3fea1163, 0x4df5b93e} }, +/**/ {{0x3ff3a418, 0x75853228} }, +/**/ {{0xbbf585da, 0xd481f350} },}, +/**/ {{{0x3fe60000, 0x02efd2fc} }, +/**/ {{0x3fea46cb, 0x30d16323} }, +/**/ {{0x3ff37c2d, 0x187962ae} }, +/**/ {{0x3bf004c3, 0xa5f77bb0} },}, +/**/ {{{0x3fe61fff, 0xfeb8088a} }, +/**/ {{0x3fea7c8b, 0x053920c0} }, +/**/ {{0x3ff354a2, 0x891769a9} }, +/**/ {{0x3bbc6b30, 0x3fee3029} },}, +/**/ {{{0x3fe64000, 0x00f3ca06} }, +/**/ {{0x3feab2a4, 0x28a1911a} }, +/**/ {{0x3ff32d77, 0x0a6f0a4a} }, +/**/ {{0x3bf2a6f8, 0xfac5081a} },}, +/**/ {{{0x3fe65fff, 0xfe9ec2f4} }, +/**/ {{0x3feae917, 0xd4ce7239} }, +/**/ {{0x3ff306a9, 0x0751a948} }, +/**/ {{0xbbe950b5, 0x51ab9dbd} },}, +/**/ {{{0x3fe68000, 0x03d43966} }, +/**/ {{0x3feb1fe7, 0x708b998a} }, +/**/ {{0x3ff2e036, 0xd7a153c7} }, +/**/ {{0x3bdd36e2, 0xa1e4a14e} },}, +/**/ {{{0x3fe69fff, 0xfab67783} }, +/**/ {{0x3feb5714, 0x2e575464} }, +/**/ {{0x3ff2ba1f, 0x05006cb6} }, +/**/ {{0x3bea9a4a, 0x473c2e31} },}, +/**/ {{{0x3fe6bfff, 0xfcb65f89} }, +/**/ {{0x3feb8e9f, 0x981efd2f} }, +/**/ {{0x3ff2945f, 0xe948d9f7} }, +/**/ {{0xbbca5294, 0xe802df72} },}, +/**/ {{{0x3fe6dfff, 0xfc5609a9} }, +/**/ {{0x3febc68a, 0xfaed6ff1} }, +/**/ {{0x3ff26ef8, 0x1533411e} }, +/**/ {{0xbbf89153, 0xf51bc566} },}, +/**/ {{{0x3fe6ffff, 0xfc4eef86} }, +/**/ {{0x3febfed7, 0xc62205fe} }, +/**/ {{0x3ff249e6, 0x0e70978c} }, +/**/ {{0x3bc39021, 0xa2b9ff56} },}, +/**/ {{{0x3fe72000, 0x004d98b3} }, +/**/ {{0x3fec3787, 0x716968ad} }, +/**/ {{0x3ff22528, 0x61be7751} }, +/**/ {{0x3befc9c5, 0x74ee2211} },}, +/**/ {{{0x3fe73fff, 0xfc155075} }, +/**/ {{0x3fec709b, 0x5ec6fd4e} }, +/**/ {{0x3ff200bd, 0xb5d53311} }, +/**/ {{0x3be28a4d, 0xa269ae63} },}, +/**/ {{{0x3fe76000, 0x0498c203} }, +/**/ {{0x3fecaa15, 0x323d08c1} }, +/**/ {{0x3ff1dca4, 0x93433f65} }, +/**/ {{0x3bf8cae4, 0x14a28fb7} },}, +/**/ {{{0x3fe77fff, 0xff1e5636} }, +/**/ {{0x3fece3f6, 0x4147c12c} }, +/**/ {{0x3ff1b8db, 0xbfe294a8} }, +/**/ {{0xbbe7e19c, 0x4b56a744} },}, +/**/ {{{0x3fe7a000, 0x0226d45a} }, +/**/ {{0x3fed1e40, 0x4120eb7f} }, +/**/ {{0x3ff19561, 0xd15f8278} }, +/**/ {{0x3be64b28, 0x032c5d4c} },}, +/**/ {{{0x3fe7c000, 0x0250a5aa} }, +/**/ {{0x3fed58f4, 0xb112a1e1} }, +/**/ {{0x3ff17235, 0x8a59d565} }, +/**/ {{0xbbe716de, 0xb8dc7867} },}, +/**/ {{{0x3fe7e000, 0x0482f82e} }, +/**/ {{0x3fed9415, 0x3576bdf0} }, +/**/ {{0x3ff14f55, 0xa22a1c5b} }, +/**/ {{0x3bf207e1, 0xe1305604} },}, +/**/ {{{0x3fe80000, 0x0205003e} }, +/**/ {{0x3fedcfa3, 0x64d69ff7} }, +/**/ {{0x3ff12cc0, 0xe37eb26f} }, +/**/ {{0xbbd52ec6, 0xe32395f8} },}, +/**/ {{{0x3fe81fff, 0xfbf99411} }, +/**/ {{0x3fee0ba0, 0xebf98f51} }, +/**/ {{0x3ff10a76, 0x16ddd5d6} }, +/**/ {{0xbbece0d6, 0x59866045} },}, +/**/ {{{0x3fe84000, 0x0248e3a3} }, +/**/ {{0x3fee480f, 0x9bb7f565} }, +/**/ {{0x3ff0e873, 0xfb84e05c} }, +/**/ {{0x3bf4e5e8, 0x1595df92} },}, +/**/ {{{0x3fe86000, 0x0145c157} }, +/**/ {{0x3fee84f1, 0x0a10b3ab} }, +/**/ {{0x3ff0c6b9, 0x7cbd7b1e} }, +/**/ {{0xbbe19de6, 0xd5f121d0} },}, +/**/ {{{0x3fe88000, 0x022631b9} }, +/**/ {{0x3feec247, 0x0be1f047} }, +/**/ {{0x3ff0a545, 0x6d0b3ee6} }, +/**/ {{0xbbc272b1, 0xa3ba2c6f} },}, +/**/ {{{0x3fe8a000, 0x045f7828} }, +/**/ {{0x3fef0013, 0x6c45ba1c} }, +/**/ {{0x3ff08416, 0xaf2a0f09} }, +/**/ {{0x3be82b56, 0x5b63c799} },}, +/**/ {{{0x3fe8bfff, 0xffc686cf} }, +/**/ {{0x3fef3e57, 0xf03c824b} }, +/**/ {{0x3ff0632c, 0x33502220} }, +/**/ {{0xbbd039ad, 0x2dbeeb25} },}, +/**/ {{{0x3fe8dfff, 0xfd8644c6} }, +/**/ {{0x3fef7d16, 0x8774261d} }, +/**/ {{0x3ff04284, 0xdd5b3019} }, +/**/ {{0x3bd79f33, 0xe1eba933} },}, +/**/ {{{0x3fe8ffff, 0xfe4e7937} }, +/**/ {{0x3fefbc51, 0x1a99a641} }, +/**/ {{0x3ff0221f, 0x9f69840b} }, +/**/ {{0xbbea9e84, 0x7beee018} },}, +/**/ {{{0x3fe92000, 0x0435251f} }, +/**/ {{0x3feffc09, 0x9eb22390} }, +/**/ {{0x3ff001fb, 0x6f7c51e8} }, +/**/ {{0xbb5a12e7, 0x31032e0a} },}, + }; + +#else +#ifdef LITTLE_ENDI +static const number + xfg[186][4] = { /* xi,Fi,Gi,FFi, i=16..201 */ +/**/ {{{0x1e519d60, 0x3fb00000} }, +/**/ {{0x96c4e240, 0x3fb00557} }, +/**/ {{0x628127b7, 0x402ff554} }, +/**/ {{0x9e355b06, 0xbb9a1dee} },}, +/**/ {{{0x1b1a7010, 0x3fb10000} }, +/**/ {{0xaab892b7, 0x3fb10668} }, +/**/ {{0xbe3fdf74, 0x402e12c7} }, +/**/ {{0x037da741, 0x3ba89234} },}, +/**/ {{{0x2505e350, 0x3fb20000} }, +/**/ {{0xff547824, 0x3fb2079b} }, +/**/ {{0xde853633, 0x402c65c5} }, +/**/ {{0xe9614250, 0x3bb7486e} },}, +/**/ {{{0xfcdc4252, 0x3fb2ffff} }, +/**/ {{0x5eb16c68, 0x3fb308f3} }, +/**/ {{0xe56be74f, 0x402ae5da} }, +/**/ {{0x91a23034, 0xbb82c726} },}, +/**/ {{{0xe3ff849f, 0x3fb3ffff} }, +/**/ {{0x154999cc, 0x3fb40a71} }, +/**/ {{0x046b7352, 0x40298c43} }, +/**/ {{0x3843738f, 0x3b9aceaf} },}, +/**/ {{{0xedc9590f, 0x3fb4ffff} }, +/**/ {{0x429bdd80, 0x3fb50c17} }, +/**/ {{0x91b5d674, 0x40285384} }, +/**/ {{0xb4403d22, 0xbbc1d02d} },}, +/**/ {{{0x00ee83f7, 0x3fb60000} }, +/**/ {{0xda80cc21, 0x3fb60de7} }, +/**/ {{0xef21a2a7, 0x40273724} }, +/**/ {{0x72523ffd, 0xbb95e53c} },}, +/**/ {{{0xeb05ea41, 0x3fb6ffff} }, +/**/ {{0xb8c51bea, 0x3fb70fe4} }, +/**/ {{0xfae562ff, 0x40263370} }, +/**/ {{0x8ffe0626, 0xbb99ad0e} },}, +/**/ {{{0xdc0515f7, 0x3fb7ffff} }, +/**/ {{0x1db54498, 0x3fb81210} }, +/**/ {{0x0e7eab5c, 0x40254553} }, +/**/ {{0xd62ed686, 0xbb914c87} },}, +/**/ {{{0xe384d7ab, 0x3fb8ffff} }, +/**/ {{0x2a8d3727, 0x3fb9146c} }, +/**/ {{0xfd57f3fd, 0x40246a33} }, +/**/ {{0x5381e06d, 0xbbbbda8d} },}, +/**/ {{{0xe4832347, 0x3fb9ffff} }, +/**/ {{0xd50e1050, 0x3fba16fa} }, +/**/ {{0xc5537a96, 0x40239fe2} }, +/**/ {{0xc111eabb, 0x3bc7f695} },}, +/**/ {{{0x274540e3, 0x3fbb0000} }, +/**/ {{0x7ae68517, 0x3fbb19be} }, +/**/ {{0x3637e946, 0x4022e481} }, +/**/ {{0x8dbd9d93, 0x3bc307f8} },}, +/**/ {{{0xfebf2e9b, 0x3fbbffff} }, +/**/ {{0x8369cd19, 0x3fbc1cb8} }, +/**/ {{0x17aef223, 0x40223676} }, +/**/ {{0x424a9cf3, 0x3bc50038} },}, +/**/ {{{0x23529045, 0x3fbd0000} }, +/**/ {{0xc11d7ef7, 0x3fbd1feb} }, +/**/ {{0xb8e43d4e, 0x4021945f} }, +/**/ {{0x52a6f224, 0x3b812007} },}, +/**/ {{{0xd872a829, 0x3fbdffff} }, +/**/ {{0x8ee4d6b7, 0x3fbe2359} }, +/**/ {{0x76195d5f, 0x4020fd0c} }, +/**/ {{0x85fdca85, 0xbbb4d9ab} },}, +/**/ {{{0xff323b84, 0x3fbeffff} }, +/**/ {{0xec9073e5, 0x3fbf2704} }, +/**/ {{0x3020200f, 0x40206f71} }, +/**/ {{0x12836992, 0x3bb77aa2} },}, +/**/ {{{0x0ce79195, 0x3fc00000} }, +/**/ {{0xbc30cc61, 0x3fc01577} }, +/**/ {{0xd6564a88, 0x401fd549} }, +/**/ {{0x965c0ad0, 0xbbc8926f} },}, +/**/ {{{0xee40e918, 0x3fc07fff} }, +/**/ {{0x8279ac01, 0x3fc0978d} }, +/**/ {{0x9294bc03, 0x401edbb5} }, +/**/ {{0x4aae45d6, 0xbb80a533} },}, +/**/ {{{0x0cc091fd, 0x3fc10000} }, +/**/ {{0x44dfb2f7, 0x3fc119c5} }, +/**/ {{0x067d8e18, 0x401df0bb} }, +/**/ {{0x4ff642a4, 0xbbcc2c18} },}, +/**/ {{{0x0d9936a1, 0x3fc18000} }, +/**/ {{0xb9085a4b, 0x3fc19c1f} }, +/**/ {{0x71ce3629, 0x401d131a} }, +/**/ {{0x0669355b, 0xbbc36553} },}, +/**/ {{{0xed5f3188, 0x3fc1ffff} }, +/**/ {{0xee74bf2d, 0x3fc21e9d} }, +/**/ {{0xff0cd655, 0x401c41b6} }, +/**/ {{0x478ecfc5, 0x3b8867f5} },}, +/**/ {{{0x05f06a51, 0x3fc28000} }, +/**/ {{0x550b313f, 0x3fc2a141} }, +/**/ {{0x1702e6d2, 0x401b7b92} }, +/**/ {{0x380131fe, 0xbbadab51} },}, +/**/ {{{0xfe3d339e, 0x3fc2ffff} }, +/**/ {{0xa75f76df, 0x3fc3240a} }, +/**/ {{0xfcb6409d, 0x401abfc8} }, +/**/ {{0x0d291d83, 0x3bc60bcf} },}, +/**/ {{{0xed888d6f, 0x3fc37fff} }, +/**/ {{0x13cc5db7, 0x3fc3a6fb} }, +/**/ {{0x8ed5320d, 0x401a0d8f} }, +/**/ {{0x4eef03ab, 0x3bb8a48e} },}, +/**/ {{{0x02ca050d, 0x3fc40000} }, +/**/ {{0xe25776bb, 0x3fc42a13} }, +/**/ {{0xfa84c2bc, 0x4019642d} }, +/**/ {{0xcc56516f, 0xbbd0bd5d} },}, +/**/ {{{0xf2531f5c, 0x3fc47fff} }, +/**/ {{0xdeb73404, 0x3fc4ad55} }, +/**/ {{0xf86e9035, 0x4018c2fe} }, +/**/ {{0x5aa287c8, 0x3b9cffe7} },}, +/**/ {{{0x13774992, 0x3fc50000} }, +/**/ {{0x7d0ee307, 0x3fc530c2} }, +/**/ {{0x370caf35, 0x4018296c} }, +/**/ {{0xf91d6532, 0xbbcf75d1} },}, +/**/ {{{0xedddcb2d, 0x3fc57fff} }, +/**/ {{0x5db4347d, 0x3fc5b45a} }, +/**/ {{0x52190c0e, 0x401796ee} }, +/**/ {{0x17d5d076, 0x3b88a25f} },}, +/**/ {{{0xf41949a0, 0x3fc5ffff} }, +/**/ {{0x13bf986a, 0x3fc6381f} }, +/**/ {{0x2d2255fd, 0x40170b09} }, +/**/ {{0xb1bcd5e7, 0xbb9bfb23} },}, +/**/ {{{0xf834d3a1, 0x3fc67fff} }, +/**/ {{0x8ec85952, 0x3fc6bc11} }, +/**/ {{0x62cf2268, 0x4016854c} }, +/**/ {{0x82e39e04, 0x3b9ee53b} },}, +/**/ {{{0xfd9106ea, 0x3fc6ffff} }, +/**/ {{0xf298f6f7, 0x3fc74032} }, +/**/ {{0x1f4f84a9, 0x40160551} }, +/**/ {{0x112634b8, 0xbbb59c4a} },}, +/**/ {{{0x0f649a4f, 0x3fc78000} }, +/**/ {{0x6ca53abc, 0x3fc7c484} }, +/**/ {{0x4809d175, 0x40158ab9} }, +/**/ {{0x73d3cd2e, 0x3bc91c75} },}, +/**/ {{{0xef06bbd8, 0x3fc7ffff} }, +/**/ {{0xdf7d76ad, 0x3fc84906} }, +/**/ {{0xdd2b30a6, 0x4015152e} }, +/**/ {{0x084c3eef, 0xbbbfa2da} },}, +/**/ {{{0x021c6334, 0x3fc88000} }, +/**/ {{0xd965f986, 0x3fc8cdbb} }, +/**/ {{0x51b74296, 0x4014a462} }, +/**/ {{0x74dcfe0b, 0xbb9ec02e} },}, +/**/ {{{0xf38d0756, 0x3fc8ffff} }, +/**/ {{0x28e173c7, 0x3fc952a4} }, +/**/ {{0x17b59ebd, 0x4014380b} }, +/**/ {{0xb77589f0, 0xbbcd0f1c} },}, +/**/ {{{0x104efca1, 0x3fc98000} }, +/**/ {{0x4644d23c, 0x3fc9d7c1} }, +/**/ {{0xcb1eabd5, 0x4013cfe5} }, +/**/ {{0xea188d9e, 0xbbd5d6f7} },}, +/**/ {{{0x09417b30, 0x3fca0000} }, +/**/ {{0x096d76aa, 0x3fca5d14} }, +/**/ {{0xb3723db0, 0x40136bb4} }, +/**/ {{0xfbf3979c, 0x3bbe3e0d} },}, +/**/ {{{0xeb1c23ec, 0x3fca7fff} }, +/**/ {{0xab60288d, 0x3fcae29d} }, +/**/ {{0x783071d7, 0x40130b3e} }, +/**/ {{0x3d5384bf, 0xbbc7dd82} },}, +/**/ {{{0xfb171c13, 0x3fcaffff} }, +/**/ {{0xa221a96b, 0x3fcb685f} }, +/**/ {{0xd8c0747d, 0x4012ae4d} }, +/**/ {{0xd5554972, 0x3bd4644b} },}, +/**/ {{{0x0aba44be, 0x3fcb8000} }, +/**/ {{0xecdf241f, 0x3fcbee5a} }, +/**/ {{0xc6fad63b, 0x401254b1} }, +/**/ {{0xd092b85a, 0x3ba41916} },}, +/**/ {{{0x113d2a3e, 0x3fcc0000} }, +/**/ {{0xb3e92543, 0x3fcc7490} }, +/**/ {{0x9a62c035, 0x4011fe3c} }, +/**/ {{0x41a03739, 0xbba3cc39} },}, +/**/ {{{0xf49e00ce, 0x3fcc7fff} }, +/**/ {{0x0f59eab0, 0x3fccfb02} }, +/**/ {{0xe956a631, 0x4011aac3} }, +/**/ {{0xbfa8cb5b, 0xbbb7a383} },}, +/**/ {{{0x05f611ab, 0x3fcd0000} }, +/**/ {{0x89e6844e, 0x3fcd81b0} }, +/**/ {{0xf391268d, 0x40115a1f} }, +/**/ {{0xb2dc91f3, 0x3bd39b5c} },}, +/**/ {{{0x14764ceb, 0x3fcd8000} }, +/**/ {{0x27debf0d, 0x3fce089d} }, +/**/ {{0xfbc84740, 0x40110c2b} }, +/**/ {{0x84712510, 0x3bc14d4d} },}, +/**/ {{{0x14bcea76, 0x3fce0000} }, +/**/ {{0x16dbc820, 0x3fce8fc9} }, +/**/ {{0xa00ca48e, 0x4010c0c5} }, +/**/ {{0x640f1b9e, 0xbbd33788} },}, +/**/ {{{0xfd7995bd, 0x3fce7fff} }, +/**/ {{0x88b50424, 0x3fcf1735} }, +/**/ {{0xbe02169a, 0x401077cc} }, +/**/ {{0x221fdf77, 0xbbb61fee} },}, +/**/ {{{0x0cc35436, 0x3fcf0000} }, +/**/ {{0xfd21a40b, 0x3fcf9ee3} }, +/**/ {{0x1ee7ffe8, 0x40103123} }, +/**/ {{0xc79ff5c1, 0x3bd427e3} },}, +/**/ {{{0x01d1da33, 0x3fcf8000} }, +/**/ {{0xb7dbe15c, 0x3fd0136a} }, +/**/ {{0x77d559e5, 0x400fd959} }, +/**/ {{0xd67948d7, 0x3bb0c6a1} },}, +/**/ {{{0x060c13b2, 0x3fd00000} }, +/**/ {{0xaaad4f18, 0x3fd05785} }, +/**/ {{0x2675d182, 0x400f549e} }, +/**/ {{0x18f0dd10, 0xbbc15208} },}, +/**/ {{{0x03885492, 0x3fd04000} }, +/**/ {{0x660542d7, 0x3fd09bc3} }, +/**/ {{0xdf3f5fec, 0x400ed3e2} }, +/**/ {{0xb883ae62, 0xbbd95657} },}, +/**/ {{{0x052f5a13, 0x3fd08000} }, +/**/ {{0x9a195045, 0x3fd0e024} }, +/**/ {{0xfa68f2c8, 0x400e56f8} }, +/**/ {{0x5a543e8e, 0x3bded7ba} },}, +/**/ {{{0x02ba1af5, 0x3fd0c000} }, +/**/ {{0xe2e7f24b, 0x3fd124a9} }, +/**/ {{0xbffe633f, 0x400dddb4} }, +/**/ {{0x0c60278f, 0xbbdcba86} },}, +/**/ {{{0xf76642c1, 0x3fd0ffff} }, +/**/ {{0xe162ffe6, 0x3fd16953} }, +/**/ {{0x0311d5d5, 0x400d67ed} }, +/**/ {{0xe40c5f9e, 0x3b7b1f4a} },}, +/**/ {{{0x033602f0, 0x3fd14000} }, +/**/ {{0x5f49508e, 0x3fd1ae23} }, +/**/ {{0xb8708266, 0x400cf57a} }, +/**/ {{0x8620f301, 0xbbd6a6c2} },}, +/**/ {{{0xfefd1a13, 0x3fd17fff} }, +/**/ {{0xdb2a9ba1, 0x3fd1f318} }, +/**/ {{0x8d11009e, 0x400c8639} }, +/**/ {{0x69b21d3b, 0x3bd3a9c6} },}, +/**/ {{{0xf718365d, 0x3fd1bfff} }, +/**/ {{0x0c41e3ac, 0x3fd23835} }, +/**/ {{0xe02be47c, 0x400c1a06} }, +/**/ {{0x129e8cd1, 0x3bdb961a} },}, +/**/ {{{0xff001e00, 0x3fd1ffff} }, +/**/ {{0xb2f6395e, 0x3fd27d78} }, +/**/ {{0xf2fe9a85, 0x400bb0c1} }, +/**/ {{0xe68fd7d8, 0x3be074a9} },}, +/**/ {{{0xfe425a6a, 0x3fd23fff} }, +/**/ {{0x618faabe, 0x3fd2c2e4} }, +/**/ {{0x190b18df, 0x400b4a4c} }, +/**/ {{0xf615aad1, 0xbbdf0d1f} },}, +/**/ {{{0x059ec1db, 0x3fd28000} }, +/**/ {{0xd8583884, 0x3fd30878} }, +/**/ {{0x0cd82bc2, 0x400ae688} }, +/**/ {{0x141c1f8d, 0xbbd563c3} },}, +/**/ {{{0x000dd081, 0x3fd2c000} }, +/**/ {{0xaffdb6d8, 0x3fd34e36} }, +/**/ {{0x5270fc15, 0x400a855a} }, +/**/ {{0x9f2cdafd, 0xbbc6d88d} },}, +/**/ {{{0xfc1dcd2b, 0x3fd2ffff} }, +/**/ {{0xa95875bc, 0x3fd3941e} }, +/**/ {{0xaa9502b6, 0x400a26a8} }, +/**/ {{0x8389b15c, 0xbbe13cad} },}, +/**/ {{{0xf6c0d4a0, 0x3fd33fff} }, +/**/ {{0x739845f5, 0x3fd3da31} }, +/**/ {{0x4d2573a0, 0x4009ca5a} }, +/**/ {{0xacaee379, 0xbbc71636} },}, +/**/ {{{0x06b16793, 0x3fd38000} }, +/**/ {{0xdbc088f0, 0x3fd4206f} }, +/**/ {{0x9344e33a, 0x40097057} }, +/**/ {{0x1d7a4f81, 0xbbc2c052} },}, +/**/ {{{0x07358fa3, 0x3fd3c000} }, +/**/ {{0x6f23311d, 0x3fd466da} }, +/**/ {{0x5aa612ea, 0x4009188a} }, +/**/ {{0x685e8edc, 0x3b8653a5} },}, +/**/ {{{0xfc3b18cf, 0x3fd3ffff} }, +/**/ {{0xe9282e6b, 0x3fd4ad71} }, +/**/ {{0x641e643d, 0x4008c2dd} }, +/**/ {{0x3f567c64, 0x3b95f0ef} },}, +/**/ {{{0x000dd2a8, 0x3fd44000} }, +/**/ {{0x1fa3f2d1, 0x3fd4f437} }, +/**/ {{0x6072f821, 0x40086f3c} }, +/**/ {{0x95ff68b5, 0x3bb68efa} },}, +/**/ {{{0xfbb43713, 0x3fd47fff} }, +/**/ {{0xb3ac333c, 0x3fd53b2a} }, +/**/ {{0x3da56692, 0x40081d94} }, +/**/ {{0x2985fd3f, 0xbbbf4d7f} },}, +/**/ {{{0xfb113bf4, 0x3fd4bfff} }, +/**/ {{0x6e8ed9c2, 0x3fd5824d} }, +/**/ {{0xa8add00f, 0x4007cdd2} }, +/**/ {{0x1c9b3657, 0x3bcf478a} },}, +/**/ {{{0xf7f087c9, 0x3fd4ffff} }, +/**/ {{0x07446496, 0x3fd5c9a0} }, +/**/ {{0x444588eb, 0x40077fe6} }, +/**/ {{0xa4eabb0c, 0xbbc177dc} },}, +/**/ {{{0x088b3814, 0x3fd54000} }, +/**/ {{0x564125f9, 0x3fd61123} }, +/**/ {{0x6281a765, 0x400733be} }, +/**/ {{0xf57051c4, 0xbbc2c52c} },}, +/**/ {{{0xf7d55966, 0x3fd57fff} }, +/**/ {{0xe194a5d5, 0x3fd658d7} }, +/**/ {{0x73b47d1f, 0x4006e94b} }, +/**/ {{0xf9996dc6, 0x3bda2fcf} },}, +/**/ {{{0x08bf2490, 0x3fd5c000} }, +/**/ {{0xb775b28d, 0x3fd6a0be} }, +/**/ {{0x15b6ec28, 0x4006a07e} }, +/**/ {{0xaa5285b8, 0xbbe0ca90} },}, +/**/ {{{0x09fa853f, 0x3fd60000} }, +/**/ {{0x65a66cfd, 0x3fd6e8d8} }, +/**/ {{0x1c701269, 0x40065948} }, +/**/ {{0x8591e13a, 0x3bd9ea95} },}, +/**/ {{{0x07595fca, 0x3fd64000} }, +/**/ {{0xc0556a7c, 0x3fd73125} }, +/**/ {{0xbaae9d02, 0x4006139b} }, +/**/ {{0x40152b83, 0x3bd88aff} },}, +/**/ {{{0x031687da, 0x3fd68000} }, +/**/ {{0x92e2cfd0, 0x3fd779a7} }, +/**/ {{0xcae0882b, 0x4005cf6b} }, +/**/ {{0x9f439451, 0xbbd8a4a2} },}, +/**/ {{{0xf5c8cfe2, 0x3fd6bfff} }, +/**/ {{0x9fb452ed, 0x3fd7c25e} }, +/**/ {{0xc561f1cd, 0x40058cab} }, +/**/ {{0xf6a37d74, 0xbbe371a6} },}, +/**/ {{{0xf81df231, 0x3fd6ffff} }, +/**/ {{0xcfb4dab5, 0x3fd80b4b} }, +/**/ {{0x8d3ca5d3, 0x40054b4f} }, +/**/ {{0x679dc99f, 0x3bcb4686} },}, +/**/ {{{0xfa71385e, 0x3fd73fff} }, +/**/ {{0xe007a9b6, 0x3fd8546f} }, +/**/ {{0xb3b22176, 0x40050b4b} }, +/**/ {{0xa5c73477, 0xbbcd1540} },}, +/**/ {{{0x024a9c2b, 0x3fd78000} }, +/**/ {{0xa7fcf5cf, 0x3fd89dcb} }, +/**/ {{0x3159cbe1, 0x4004cc95} }, +/**/ {{0xd58a6ad0, 0xbbdc25ea} },}, +/**/ {{{0x02eb62b8, 0x3fd7c000} }, +/**/ {{0xec0ba5cf, 0x3fd8e75f} }, +/**/ {{0x8731eeea, 0x40048f21} }, +/**/ {{0xcc1adafb, 0xbbc1cb73} },}, +/**/ {{{0x054a52d1, 0x3fd80000} }, +/**/ {{0x8bb822e9, 0x3fd9312d} }, +/**/ {{0x9170a729, 0x400452e6} }, +/**/ {{0xeac002ee, 0xbbd8bb17} },}, +/**/ {{{0xf93a00a3, 0x3fd83fff} }, +/**/ {{0x4bb9ad2a, 0x3fd97b35} }, +/**/ {{0xae924e7f, 0x400417da} }, +/**/ {{0x9a378cc7, 0x3bd4b800} },}, +/**/ {{{0xfbdc91c1, 0x3fd87fff} }, +/**/ {{0x2771b601, 0x3fd9c578} }, +/**/ {{0x78855799, 0x4003ddf4} }, +/**/ {{0xa00445d9, 0x3bd9077d} },}, +/**/ {{{0xf6d215e6, 0x3fd8bfff} }, +/**/ {{0xe0ea4a0b, 0x3fda0ff6} }, +/**/ {{0x189a0989, 0x4003a52b} }, +/**/ {{0x89c0613d, 0xbbda6831} },}, +/**/ {{{0x02f734ef, 0x3fd90000} }, +/**/ {{0x736bf579, 0x3fda5ab2} }, +/**/ {{0xe9244ca6, 0x40036d75} }, +/**/ {{0x4b722377, 0x3be3a6d8} },}, +/**/ {{{0x04eef8b4, 0x3fd94000} }, +/**/ {{0x9fb6e3d0, 0x3fdaa5ab} }, +/**/ {{0xc9089cb7, 0x400336cc} }, +/**/ {{0x22cc00bb, 0x3b9f6963} },}, +/**/ {{{0x041ec76a, 0x3fd98000} }, +/**/ {{0x5176c7e4, 0x3fdaf0e3} }, +/**/ {{0xcb0b9506, 0x40030127} }, +/**/ {{0x5385a849, 0x3bb1ffdb} },}, +/**/ {{{0x08044e47, 0x3fd9c000} }, +/**/ {{0x77071224, 0x3fdb3c5a} }, +/**/ {{0x50d75ec7, 0x4002cc7f} }, +/**/ {{0x78effc8a, 0xbbb0fade} },}, +/**/ {{{0x01f8235b, 0x3fda0000} }, +/**/ {{0xe725782e, 0x3fdb8811} }, +/**/ {{0x18fbfb37, 0x400298cc} }, +/**/ {{0x3b50e71b, 0xbbe55ed3} },}, +/**/ {{{0xfb8c6f08, 0x3fda3fff} }, +/**/ {{0x97b086f3, 0x3fdbd40a} }, +/**/ {{0x154de04b, 0x40026607} }, +/**/ {{0x455faae3, 0xbbdec65e} },}, +/**/ {{{0xfb3d63e1, 0x3fda7fff} }, +/**/ {{0x7d9a3b8a, 0x3fdc2045} }, +/**/ {{0x7e60bfbb, 0x40023429} }, +/**/ {{0x154ebd33, 0x3be3001c} },}, +/**/ {{{0xf5f45c48, 0x3fdabfff} }, +/**/ {{0x7b8d45e6, 0x3fdc6cc3} }, +/**/ {{0xdb1ace69, 0x4002032c} }, +/**/ {{0x3ed33616, 0xbbe5ebf8} },}, +/**/ {{{0x0508b34c, 0x3fdb0000} }, +/**/ {{0xa27e8d37, 0x3fdcb985} }, +/**/ {{0xd4459a2b, 0x4001d30a} }, +/**/ {{0xae61e2d1, 0xbbd01432} },}, +/**/ {{{0x0a84710c, 0x3fdb4000} }, +/**/ {{0xc3e50155, 0x3fdd068c} }, +/**/ {{0x775034dd, 0x4001a3bd} }, +/**/ {{0x58e0e228, 0xbbe80b1e} },}, +/**/ {{{0xf692e9d8, 0x3fdb7fff} }, +/**/ {{0xc49d6627, 0x3fdd53d9} }, +/**/ {{0xfe18066a, 0x4001753e} }, +/**/ {{0xf760d33e, 0xbbb004c8} },}, +/**/ {{{0x0280f14d, 0x3fdbc000} }, +/**/ {{0xe4e81013, 0x3fdda16d} }, +/**/ {{0xa38ea052, 0x40014789} }, +/**/ {{0x27c9c4ea, 0x3be848bc} },}, +/**/ {{{0x001121d1, 0x3fdc0000} }, +/**/ {{0xeac018f0, 0x3fddef49} }, +/**/ {{0x20b8be0c, 0x40011a98} }, +/**/ {{0xd0d6010e, 0xbbe1527e} },}, +/**/ {{{0xfef662aa, 0x3fdc3fff} }, +/**/ {{0xea0c7070, 0x3fde3d6e} }, +/**/ {{0x32f46ccd, 0x4000ee65} }, +/**/ {{0x189a000d, 0x3be8d241} },}, +/**/ {{{0x09845818, 0x3fdc8000} }, +/**/ {{0xf36a8b1b, 0x3fde8bdd} }, +/**/ {{0xcac73476, 0x4000c2eb} }, +/**/ {{0x12bed284, 0x3bd221f7} },}, +/**/ {{{0xfb0493bf, 0x3fdcbfff} }, +/**/ {{0xe0c60d10, 0x3fdeda97} }, +/**/ {{0x251c7836, 0x40009827} }, +/**/ {{0x6eec41b7, 0xbbe0bd54} },}, +/**/ {{{0xfd52961f, 0x3fdcffff} }, +/**/ {{0xefb3e44b, 0x3fdf299d} }, +/**/ {{0x74e459f5, 0x40006e12} }, +/**/ {{0xe969c82f, 0xbbd93f77} },}, +/**/ {{{0xfe2319a4, 0x3fdd3fff} }, +/**/ {{0x17139490, 0x3fdf78f1} }, +/**/ {{0x3e737e94, 0x400044a9} }, +/**/ {{0x49594b7a, 0xbb91e7cc} },}, +/**/ {{{0xfa4de596, 0x3fdd7fff} }, +/**/ {{0x638f49e8, 0x3fdfc892} }, +/**/ {{0x231057a5, 0x40001be7} }, +/**/ {{0xf5af9f5f, 0x3bd482b0} },}, +/**/ {{{0xfe729a69, 0x3fddbfff} }, +/**/ {{0x7c6ab019, 0x3fe00c41} }, +/**/ {{0xbf612660, 0x3fffe78f} }, +/**/ {{0x00da681e, 0x3bea5cda} },}, +/**/ {{{0x09d66802, 0x3fde0000} }, +/**/ {{0xf6b883cf, 0x3fe03461} }, +/**/ {{0xbc05a87c, 0x3fff988e} }, +/**/ {{0xf2372669, 0xbbe06c33} },}, +/**/ {{{0xfb211657, 0x3fde3fff} }, +/**/ {{0x191db8e8, 0x3fe05cab} }, +/**/ {{0x7bcfe6be, 0x3fff4ac3} }, +/**/ {{0x5ed8d35b, 0xbbd5d51f} },}, +/**/ {{{0x0a3f068a, 0x3fde8000} }, +/**/ {{0x95fb54f0, 0x3fe0851d} }, +/**/ {{0x144ca408, 0x3ffefe26} }, +/**/ {{0xa2c169c5, 0xbbc7c894} },}, +/**/ {{{0x01adb060, 0x3fdec000} }, +/**/ {{0xdc7b54f9, 0x3fe0adb9} }, +/**/ {{0x5ebe52a7, 0x3ffeb2af} }, +/**/ {{0x312c5ffd, 0x3bd4e740} },}, +/**/ {{{0xff5c0d01, 0x3fdeffff} }, +/**/ {{0x92550a8d, 0x3fe0d680} }, +/**/ {{0x0d71fdf0, 0x3ffe6858} }, +/**/ {{0x96b35499, 0x3bddd8a6} },}, +/**/ {{{0xf93d5fcc, 0x3fdf3fff} }, +/**/ {{0x45cb4374, 0x3fe0ff72} }, +/**/ {{0x3cce5040, 0x3ffe1f19} }, +/**/ {{0x7c1efab4, 0xbbc9f0ec} },}, +/**/ {{{0xfa0dd18f, 0x3fdf7fff} }, +/**/ {{0x944dd508, 0x3fe1288f} }, +/**/ {{0x298b874d, 0x3ffdd6ec} }, +/**/ {{0x9642a0a6, 0x3bea6ebd} },}, +/**/ {{{0xfd3a9f1a, 0x3fdfbfff} }, +/**/ {{0x13750f3e, 0x3fe151d9} }, +/**/ {{0x5806a27e, 0x3ffd8fca} }, +/**/ {{0xfc65ac7a, 0x3bda2a03} },}, +/**/ {{{0xfc481400, 0x3fdfffff} }, +/**/ {{0x598944ca, 0x3fe17b4f} }, +/**/ {{0x82532170, 0x3ffd49ad} }, +/**/ {{0x3d236dc3, 0x3bc4412e} },}, +/**/ {{{0xff53786c, 0x3fe01fff} }, +/**/ {{0x07d83d47, 0x3fe1a4f3} }, +/**/ {{0x851bffeb, 0x3ffd048f} }, +/**/ {{0x29f81b14, 0x3bd1589d} },}, +/**/ {{{0xfee301b7, 0x3fe03fff} }, +/**/ {{0xb8a6a382, 0x3fe1cec4} }, +/**/ {{0x7c519db6, 0x3ffcc06a} }, +/**/ {{0x5b24d6b2, 0x3bd370e6} },}, +/**/ {{{0x006e36bf, 0x3fe06000} }, +/**/ {{0x114eb8be, 0x3fe1f8c5} }, +/**/ {{0xa34d6786, 0x3ffc7d38} }, +/**/ {{0x4b98c1d4, 0xbbea92de} },}, +/**/ {{{0xfd60aa43, 0x3fe07fff} }, +/**/ {{0xabeccecb, 0x3fe222f4} }, +/**/ {{0x77342ac4, 0x3ffc3af4} }, +/**/ {{0x03a5c2c2, 0xbbdd47f6} },}, +/**/ {{{0x037762e8, 0x3fe0a000} }, +/**/ {{0x3f99efe8, 0x3fe24d54} }, +/**/ {{0x75f54fab, 0x3ffbf998} }, +/**/ {{0x15771a46, 0x3bedf7f4} },}, +/**/ {{{0xff1c6921, 0x3fe0bfff} }, +/**/ {{0x598e35d0, 0x3fe277e4} }, +/**/ {{0x8addd186, 0x3ffbb91f} }, +/**/ {{0x5e0e5a73, 0x3be0f16c} },}, +/**/ {{{0xff07154b, 0x3fe0dfff} }, +/**/ {{0xb6bc3986, 0x3fe2a2a5} }, +/**/ {{0x8301646d, 0x3ffb7984} }, +/**/ {{0xbbaa5310, 0xbbf02dd0} },}, +/**/ {{{0x02fcdda4, 0x3fe10000} }, +/**/ {{0x02a59f1e, 0x3fe2cd99} }, +/**/ {{0x705219bf, 0x3ffb3ac2} }, +/**/ {{0x112fa616, 0xbbe59357} },}, +/**/ {{{0x01ce1140, 0x3fe12000} }, +/**/ {{0xdf0a67c2, 0x3fe2f8be} }, +/**/ {{0x9ab8ae2a, 0x3ffafcd4} }, +/**/ {{0x9303f346, 0x3be2c542} },}, +/**/ {{{0x04d0f355, 0x3fe14000} }, +/**/ {{0x08fcc7bf, 0x3fe32418} }, +/**/ {{0x497b9a36, 0x3ffabfb6} }, +/**/ {{0xb5a59234, 0x3bebc044} },}, +/**/ {{{0x00fb0c8a, 0x3fe16000} }, +/**/ {{0x2471618b, 0x3fe34fa5} }, +/**/ {{0x0d26d117, 0x3ffa8363} }, +/**/ {{0x3f7bb7c9, 0xbbdbfbb2} },}, +/**/ {{{0x026f10b3, 0x3fe18000} }, +/**/ {{0xf7579056, 0x3fe37b66} }, +/**/ {{0x6b4cf4b1, 0x3ffa47d6} }, +/**/ {{0xaf0b5de9, 0x3bf0f6b4} },}, +/**/ {{{0xfd0978f8, 0x3fe19fff} }, +/**/ {{0x290cc78c, 0x3fe3a75e} }, +/**/ {{0x36c21315, 0x3ffa0d0c} }, +/**/ {{0xa296b262, 0x3beb2129} },}, +/**/ {{{0xfd94840b, 0x3fe1bfff} }, +/**/ {{0x85b4e4a4, 0x3fe3d38b} }, +/**/ {{0x32f2ecef, 0x3ff9d300} }, +/**/ {{0xb9bb7d74, 0xbbdbab1a} },}, +/**/ {{{0xfbda1ea1, 0x3fe1dfff} }, +/**/ {{0xbf3cee2f, 0x3fe3ffef} }, +/**/ {{0x6770fed8, 0x3ff999ae} }, +/**/ {{0xb4ace9a4, 0x3bda0bdc} },}, +/**/ {{{0xfc989533, 0x3fe1ffff} }, +/**/ {{0x9c27900c, 0x3fe42c8b} }, +/**/ {{0xe0d9f1ac, 0x3ff96112} }, +/**/ {{0x2fa2d81a, 0xbbee19eb} },}, +/**/ {{{0x012b8d26, 0x3fe22000} }, +/**/ {{0xe11975ca, 0x3fe4595f} }, +/**/ {{0xcdaa4e80, 0x3ff92929} }, +/**/ {{0xacc82d4b, 0x3bf23382} },}, +/**/ {{{0x04f4d6af, 0x3fe24000} }, +/**/ {{0x4d224131, 0x3fe4866d} }, +/**/ {{0x815c34e8, 0x3ff8f1ef} }, +/**/ {{0x3b740a99, 0xbbd0c6ff} },}, +/**/ {{{0xfcc07bda, 0x3fe25fff} }, +/**/ {{0x98b7d010, 0x3fe4b3b4} }, +/**/ {{0x73e7ffa1, 0x3ff8bb60} }, +/**/ 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{{0xe802df72, 0xbbca5294} },}, +/**/ {{{0xfc5609a9, 0x3fe6dfff} }, +/**/ {{0xfaed6ff1, 0x3febc68a} }, +/**/ {{0x1533411e, 0x3ff26ef8} }, +/**/ {{0xf51bc566, 0xbbf89153} },}, +/**/ {{{0xfc4eef86, 0x3fe6ffff} }, +/**/ {{0xc62205fe, 0x3febfed7} }, +/**/ {{0x0e70978c, 0x3ff249e6} }, +/**/ {{0xa2b9ff56, 0x3bc39021} },}, +/**/ {{{0x004d98b3, 0x3fe72000} }, +/**/ {{0x716968ad, 0x3fec3787} }, +/**/ {{0x61be7751, 0x3ff22528} }, +/**/ {{0x74ee2211, 0x3befc9c5} },}, +/**/ {{{0xfc155075, 0x3fe73fff} }, +/**/ {{0x5ec6fd4e, 0x3fec709b} }, +/**/ {{0xb5d53311, 0x3ff200bd} }, +/**/ {{0xa269ae63, 0x3be28a4d} },}, +/**/ {{{0x0498c203, 0x3fe76000} }, +/**/ {{0x323d08c1, 0x3fecaa15} }, +/**/ {{0x93433f65, 0x3ff1dca4} }, +/**/ {{0x14a28fb7, 0x3bf8cae4} },}, +/**/ {{{0xff1e5636, 0x3fe77fff} }, +/**/ {{0x4147c12c, 0x3fece3f6} }, +/**/ {{0xbfe294a8, 0x3ff1b8db} }, +/**/ {{0x4b56a744, 0xbbe7e19c} },}, +/**/ {{{0x0226d45a, 0x3fe7a000} }, +/**/ {{0x4120eb7f, 0x3fed1e40} }, +/**/ {{0xd15f8278, 0x3ff19561} }, +/**/ {{0x032c5d4c, 0x3be64b28} },}, +/**/ {{{0x0250a5aa, 0x3fe7c000} }, +/**/ {{0xb112a1e1, 0x3fed58f4} }, +/**/ {{0x8a59d565, 0x3ff17235} }, +/**/ {{0xb8dc7867, 0xbbe716de} },}, +/**/ {{{0x0482f82e, 0x3fe7e000} }, +/**/ {{0x3576bdf0, 0x3fed9415} }, +/**/ {{0xa22a1c5b, 0x3ff14f55} }, +/**/ {{0xe1305604, 0x3bf207e1} },}, +/**/ {{{0x0205003e, 0x3fe80000} }, +/**/ {{0x64d69ff7, 0x3fedcfa3} }, +/**/ {{0xe37eb26f, 0x3ff12cc0} }, +/**/ {{0xe32395f8, 0xbbd52ec6} },}, +/**/ {{{0xfbf99411, 0x3fe81fff} }, +/**/ {{0xebf98f51, 0x3fee0ba0} }, +/**/ {{0x16ddd5d6, 0x3ff10a76} }, +/**/ {{0x59866045, 0xbbece0d6} },}, +/**/ {{{0x0248e3a3, 0x3fe84000} }, +/**/ {{0x9bb7f565, 0x3fee480f} }, +/**/ {{0xfb84e05c, 0x3ff0e873} }, +/**/ {{0x1595df92, 0x3bf4e5e8} },}, +/**/ {{{0x0145c157, 0x3fe86000} }, +/**/ {{0x0a10b3ab, 0x3fee84f1} }, +/**/ {{0x7cbd7b1e, 0x3ff0c6b9} }, +/**/ {{0xd5f121d0, 0xbbe19de6} },}, +/**/ {{{0x022631b9, 0x3fe88000} }, +/**/ {{0x0be1f047, 0x3feec247} }, +/**/ {{0x6d0b3ee6, 0x3ff0a545} }, +/**/ {{0xa3ba2c6f, 0xbbc272b1} },}, +/**/ {{{0x045f7828, 0x3fe8a000} }, +/**/ {{0x6c45ba1c, 0x3fef0013} }, +/**/ {{0xaf2a0f09, 0x3ff08416} }, +/**/ {{0x5b63c799, 0x3be82b56} },}, +/**/ {{{0xffc686cf, 0x3fe8bfff} }, +/**/ {{0xf03c824b, 0x3fef3e57} }, +/**/ {{0x33502220, 0x3ff0632c} }, +/**/ {{0x2dbeeb25, 0xbbd039ad} },}, +/**/ {{{0xfd8644c6, 0x3fe8dfff} }, +/**/ {{0x8774261d, 0x3fef7d16} }, +/**/ {{0xdd5b3019, 0x3ff04284} }, +/**/ {{0xe1eba933, 0x3bd79f33} },}, +/**/ {{{0xfe4e7937, 0x3fe8ffff} }, +/**/ {{0x1a99a641, 0x3fefbc51} }, +/**/ {{0x9f69840b, 0x3ff0221f} }, +/**/ {{0x7beee018, 0xbbea9e84} },}, +/**/ {{{0x0435251f, 0x3fe92000} }, +/**/ {{0x9eb22390, 0x3feffc09} }, +/**/ {{0x6f7c51e8, 0x3ff001fb} }, +/**/ {{0x31032e0a, 0xbb5a12e7} },}, + }; + +#endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/w_exp_compat.c b/REORG.TODO/sysdeps/ieee754/dbl-64/w_exp_compat.c new file mode 100644 index 0000000000..e61e03b335 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/w_exp_compat.c @@ -0,0 +1,38 @@ +/* Copyright (C) 2011-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@gmail.com>, 2011. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + +/* wrapper exp */ +double +__exp (double x) +{ + double z = __ieee754_exp (x); + if (__builtin_expect (!isfinite (z) || z == 0, 0) + && isfinite (x) && _LIB_VERSION != _IEEE_) + return __kernel_standard (x, x, 6 + !!signbit (x)); + + return z; +} +hidden_def (__exp) +weak_alias (__exp, exp) +#ifdef NO_LONG_DOUBLE +strong_alias (__exp, __expl) +weak_alias (__exp, expl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_acosh.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_acosh.c new file mode 100644 index 0000000000..ccccdaf106 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_acosh.c @@ -0,0 +1,67 @@ +/* Optimized for 64-bit by Ulrich Drepper <drepper@gmail.com>, 2012 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_acosh(x) + * Method : + * Based on + * acosh(x) = log [ x + sqrt(x*x-1) ] + * we have + * acosh(x) := log(x)+ln2, if x is large; else + * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else + * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. + * + * Special cases: + * acosh(x) is NaN with signal if x<1. + * acosh(NaN) is NaN without signal. + */ + +#include <math.h> +#include <math_private.h> + +static const double +one = 1.0, +ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ + +double +__ieee754_acosh (double x) +{ + int64_t hx; + EXTRACT_WORDS64 (hx, x); + + if (hx > INT64_C (0x4000000000000000)) + { + if (__glibc_unlikely (hx >= INT64_C (0x41b0000000000000))) + { + /* x > 2**28 */ + if (hx >= INT64_C (0x7ff0000000000000)) + /* x is inf of NaN */ + return x + x; + else + return __ieee754_log (x) + ln2;/* acosh(huge)=log(2x) */ + } + + /* 2**28 > x > 2 */ + double t = x * x; + return __ieee754_log (2.0 * x - one / (x + __ieee754_sqrt (t - one))); + } + else if (__glibc_likely (hx > INT64_C (0x3ff0000000000000))) + { + /* 1<x<2 */ + double t = x - one; + return __log1p (t + __ieee754_sqrt (2.0 * t + t * t)); + } + else if (__glibc_likely (hx == INT64_C (0x3ff0000000000000))) + return 0.0; /* acosh(1) = 0 */ + else /* x < 1 */ + return (x - x) / (x - x); +} +strong_alias (__ieee754_acosh, __acosh_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_cosh.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_cosh.c new file mode 100644 index 0000000000..fca80b13f9 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_cosh.c @@ -0,0 +1,84 @@ +/* Optimized by Ulrich Drepper <drepper@gmail.com>, 2011 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_cosh(x) + * Method : + * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 + * 1. Replace x by |x| (cosh(x) = cosh(-x)). + * 2. + * [ exp(x) - 1 ]^2 + * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- + * 2*exp(x) + * + * exp(x) + 1/exp(x) + * ln2/2 <= x <= 22 : cosh(x) := ------------------- + * 2 + * 22 <= x <= lnovft : cosh(x) := exp(x)/2 + * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) + * ln2ovft < x : cosh(x) := huge*huge (overflow) + * + * Special cases: + * cosh(x) is |x| if x is +INF, -INF, or NaN. + * only cosh(0)=1 is exact for finite x. + */ + +#include <math.h> +#include <math_private.h> + +static const double one = 1.0, half=0.5, huge = 1.0e300; + +double +__ieee754_cosh (double x) +{ + double t,w; + int32_t ix; + + /* High word of |x|. */ + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + + /* |x| in [0,22] */ + if (ix < 0x40360000) { + /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ + if(ix<0x3fd62e43) { + if (ix<0x3c800000) /* cosh(tiny) = 1 */ + return one; + t = __expm1(fabs(x)); + w = one+t; + return one+(t*t)/(w+w); + } + + /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ + t = __ieee754_exp(fabs(x)); + return half*t+half/t; + } + + /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ + if (ix < 0x40862e42) return half*__ieee754_exp(fabs(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + int64_t fix; + EXTRACT_WORDS64(fix, x); + fix &= UINT64_C(0x7fffffffffffffff); + if (fix <= UINT64_C(0x408633ce8fb9f87d)) { + w = __ieee754_exp(half*fabs(x)); + t = half*w; + return t*w; + } + + /* x is INF or NaN */ + if(ix>=0x7ff00000) return x*x; + + /* |x| > overflowthresold, cosh(x) overflow */ + return huge*huge; +} +strong_alias (__ieee754_cosh, __cosh_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_fmod.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_fmod.c new file mode 100644 index 0000000000..f686bb6706 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_fmod.c @@ -0,0 +1,105 @@ +/* Rewritten for 64-bit machines by Ulrich Drepper <drepper@gmail.com>. */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * __ieee754_fmod(x,y) + * Return x mod y in exact arithmetic + * Method: shift and subtract + */ + +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +static const double one = 1.0, Zero[] = {0.0, -0.0,}; + +double +__ieee754_fmod (double x, double y) +{ + int32_t n,ix,iy; + int64_t hx,hy,hz,sx,i; + + EXTRACT_WORDS64(hx,x); + EXTRACT_WORDS64(hy,y); + sx = hx&UINT64_C(0x8000000000000000); /* sign of x */ + hx ^=sx; /* |x| */ + hy &= UINT64_C(0x7fffffffffffffff); /* |y| */ + + /* purge off exception values */ + if(__builtin_expect(hy==0 + || hx >= UINT64_C(0x7ff0000000000000) + || hy > UINT64_C(0x7ff0000000000000), 0)) + /* y=0,or x not finite or y is NaN */ + return (x*y)/(x*y); + if(__builtin_expect(hx<=hy, 0)) { + if(hx<hy) return x; /* |x|<|y| return x */ + return Zero[(uint64_t)sx>>63]; /* |x|=|y| return x*0*/ + } + + /* determine ix = ilogb(x) */ + if(__builtin_expect(hx<UINT64_C(0x0010000000000000), 0)) { + /* subnormal x */ + for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1; + } else ix = (hx>>52)-1023; + + /* determine iy = ilogb(y) */ + if(__builtin_expect(hy<UINT64_C(0x0010000000000000), 0)) { /* subnormal y */ + for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1; + } else iy = (hy>>52)-1023; + + /* set up hx, hy and align y to x */ + if(__builtin_expect(ix >= -1022, 1)) + hx = UINT64_C(0x0010000000000000)|(UINT64_C(0x000fffffffffffff)&hx); + else { /* subnormal x, shift x to normal */ + n = -1022-ix; + hx<<=n; + } + if(__builtin_expect(iy >= -1022, 1)) + hy = UINT64_C(0x0010000000000000)|(UINT64_C(0x000fffffffffffff)&hy); + else { /* subnormal y, shift y to normal */ + n = -1022-iy; + hy<<=n; + } + + /* fix point fmod */ + n = ix - iy; + while(n--) { + hz=hx-hy; + if(hz<0){hx = hx+hx;} + else { + if(hz==0) /* return sign(x)*0 */ + return Zero[(uint64_t)sx>>63]; + hx = hz+hz; + } + } + hz=hx-hy; + if(hz>=0) {hx=hz;} + + /* convert back to floating value and restore the sign */ + if(hx==0) /* return sign(x)*0 */ + return Zero[(uint64_t)sx>>63]; + while(hx<UINT64_C(0x0010000000000000)) { /* normalize x */ + hx = hx+hx; + iy -= 1; + } + if(__builtin_expect(iy>= -1022, 1)) { /* normalize output */ + hx = ((hx-UINT64_C(0x0010000000000000))|((uint64_t)(iy+1023)<<52)); + INSERT_WORDS64(x,hx|sx); + } else { /* subnormal output */ + n = -1022 - iy; + hx>>=n; + INSERT_WORDS64(x,hx|sx); + x *= one; /* create necessary signal */ + } + return x; /* exact output */ +} +strong_alias (__ieee754_fmod, __fmod_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_log10.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_log10.c new file mode 100644 index 0000000000..4f5a81669e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_log10.c @@ -0,0 +1,87 @@ +/* @(#)e_log10.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_log10(x) + * Return the base 10 logarithm of x + * + * Method : + * Let log10_2hi = leading 40 bits of log10(2) and + * log10_2lo = log10(2) - log10_2hi, + * ivln10 = 1/log(10) rounded. + * Then + * n = ilogb(x), + * if(n<0) n = n+1; + * x = scalbn(x,-n); + * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) + * + * Note 1: + * To guarantee log10(10**n)=n, where 10**n is normal, the rounding + * mode must set to Round-to-Nearest. + * Note 2: + * [1/log(10)] rounded to 53 bits has error .198 ulps; + * log10 is monotonic at all binary break points. + * + * Special cases: + * log10(x) is NaN with signal if x < 0; + * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; + * log10(NaN) is that NaN with no signal; + * log10(10**N) = N for N=0,1,...,22. + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +static const double two54 = 1.80143985094819840000e+16; /* 0x4350000000000000 */ +static const double ivln10 = 4.34294481903251816668e-01; /* 0x3FDBCB7B1526E50E */ +static const double log10_2hi = 3.01029995663611771306e-01; /* 0x3FD34413509F6000 */ +static const double log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF311F12B36 */ + +double +__ieee754_log10 (double x) +{ + double y, z; + int64_t i, hx; + int32_t k; + + EXTRACT_WORDS64 (hx, x); + + k = 0; + if (hx < INT64_C(0x0010000000000000)) + { /* x < 2**-1022 */ + if (__glibc_unlikely ((hx & UINT64_C(0x7fffffffffffffff)) == 0)) + return -two54 / (x - x); /* log(+-0)=-inf */ + if (__glibc_unlikely (hx < 0)) + return (x - x) / (x - x); /* log(-#) = NaN */ + k -= 54; + x *= two54; /* subnormal number, scale up x */ + EXTRACT_WORDS64 (hx, x); + } + /* scale up resulted in a NaN number */ + if (__glibc_unlikely (hx >= UINT64_C(0x7ff0000000000000))) + return x + x; + k += (hx >> 52) - 1023; + i = ((uint64_t) k & UINT64_C(0x8000000000000000)) >> 63; + hx = (hx & UINT64_C(0x000fffffffffffff)) | ((0x3ff - i) << 52); + y = (double) (k + i); + INSERT_WORDS64 (x, hx); + z = y * log10_2lo + ivln10 * __ieee754_log (x); + return z + y * log10_2hi; +} + +strong_alias (__ieee754_log10, __log10_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_log2.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_log2.c new file mode 100644 index 0000000000..5ccb78cf03 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/e_log2.c @@ -0,0 +1,128 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_log2(x) + * Return the logarithm to base 2 of x + * + * Method : + * 1. Argument Reduction: find k and f such that + * x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * 2. Approximation of log(1+f). + * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * = 2s + s*R + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error + * of this polynomial approximation is bounded by 2**-58.45. In + * other words, + * 2 4 6 8 10 12 14 + * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s + * (the values of Lg1 to Lg7 are listed in the program) + * and + * | 2 14 | -58.45 + * | Lg1*s +...+Lg7*s - R(z) | <= 2 + * | | + * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. + * In order to guarantee error in log below 1ulp, we compute log + * by + * log(1+f) = f - s*(f - R) (if f is not too large) + * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) + * + * 3. Finally, log(x) = k + log(1+f). + * = k+(f-(hfsq-(s*(hfsq+R)))) + * + * Special cases: + * log2(x) is NaN with signal if x < 0 (including -INF) ; + * log2(+INF) is +INF; log(0) is -INF with signal; + * log2(NaN) is that NaN with no signal. + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include <math.h> +#include <math_private.h> + +static const double ln2 = 0.69314718055994530942; +static const double two54 = 1.80143985094819840000e+16; /* 4350000000000000 */ +static const double Lg1 = 6.666666666666735130e-01; /* 3FE5555555555593 */ +static const double Lg2 = 3.999999999940941908e-01; /* 3FD999999997FA04 */ +static const double Lg3 = 2.857142874366239149e-01; /* 3FD2492494229359 */ +static const double Lg4 = 2.222219843214978396e-01; /* 3FCC71C51D8E78AF */ +static const double Lg5 = 1.818357216161805012e-01; /* 3FC7466496CB03DE */ +static const double Lg6 = 1.531383769920937332e-01; /* 3FC39A09D078C69F */ +static const double Lg7 = 1.479819860511658591e-01; /* 3FC2F112DF3E5244 */ + +static const double zero = 0.0; + +double +__ieee754_log2 (double x) +{ + double hfsq, f, s, z, R, w, t1, t2, dk; + int64_t hx, i, j; + int32_t k; + + EXTRACT_WORDS64 (hx, x); + + k = 0; + if (hx < INT64_C(0x0010000000000000)) + { /* x < 2**-1022 */ + if (__glibc_unlikely ((hx & UINT64_C(0x7fffffffffffffff)) == 0)) + return -two54 / (x - x); /* log(+-0)=-inf */ + if (__glibc_unlikely (hx < 0)) + return (x - x) / (x - x); /* log(-#) = NaN */ + k -= 54; + x *= two54; /* subnormal number, scale up x */ + EXTRACT_WORDS64 (hx, x); + } + if (__glibc_unlikely (hx >= UINT64_C(0x7ff0000000000000))) + return x + x; + k += (hx >> 52) - 1023; + hx &= UINT64_C(0x000fffffffffffff); + i = (hx + UINT64_C(0x95f6400000000)) & UINT64_C(0x10000000000000); + /* normalize x or x/2 */ + INSERT_WORDS64 (x, hx | (i ^ UINT64_C(0x3ff0000000000000))); + k += (i >> 52); + dk = (double) k; + f = x - 1.0; + if ((UINT64_C(0x000fffffffffffff) & (2 + hx)) < 3) + { /* |f| < 2**-20 */ + if (f == zero) + return dk; + R = f * f * (0.5 - 0.33333333333333333 * f); + return dk - (R - f) / ln2; + } + s = f / (2.0 + f); + z = s * s; + i = hx - UINT64_C(0x6147a00000000); + w = z * z; + j = UINT64_C(0x6b85100000000) - hx; + t1 = w * (Lg2 + w * (Lg4 + w * Lg6)); + t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7))); + i |= j; + R = t2 + t1; + if (i > 0) + { + hfsq = 0.5 * f * f; + return dk - ((hfsq - (s * (hfsq + R))) - f) / ln2; + } + else + { + return dk - ((s * (f - R)) - f) / ln2; + } +} + +strong_alias (__ieee754_log2, __log2_finite) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_ceil.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_ceil.c new file mode 100644 index 0000000000..faaaf90208 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_ceil.c @@ -0,0 +1,54 @@ +/* @(#)s_ceil.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * ceil(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + */ + +#include <math.h> +#include <math_private.h> + +double +__ceil(double x) +{ + int64_t i0,i; + int32_t j0; + EXTRACT_WORDS64(i0,x); + j0 = ((i0>>52)&0x7ff)-0x3ff; + if(j0<=51) { + if(j0<0) { + /* return 0*sign(x) if |x|<1 */ + if(i0<0) {i0=INT64_C(0x8000000000000000);} + else if(i0!=0) { i0=INT64_C(0x3ff0000000000000);} + } else { + i = INT64_C(0x000fffffffffffff)>>j0; + if((i0&i)==0) return x; /* x is integral */ + if(i0>0) i0 += UINT64_C(0x0010000000000000)>>j0; + i0 &= (~i); + } + } else { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + INSERT_WORDS64(x,i0); + return x; +} +#ifndef __ceil +weak_alias (__ceil, ceil) +# ifdef NO_LONG_DOUBLE +strong_alias (__ceil, __ceill) +weak_alias (__ceil, ceill) +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_finite.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_finite.c new file mode 100644 index 0000000000..ef51608f6e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_finite.c @@ -0,0 +1,42 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * finite(x) returns 1 is x is finite, else 0; + * no branching! + */ + +#include <math.h> +#include <math_private.h> +#include <shlib-compat.h> +#include <stdint.h> + +#undef __finite +int +__finite(double x) +{ + int64_t lx; + EXTRACT_WORDS64(lx,x); + return (int)((uint64_t)((lx&INT64_C(0x7ff0000000000000))-INT64_C(0x7ff0000000000000))>>63); +} +hidden_def (__finite) +weak_alias (__finite, finite) +#ifdef NO_LONG_DOUBLE +# ifdef LDBL_CLASSIFY_COMPAT +# if SHLIB_COMPAT (libc, GLIBC_2_0, GLIBC_2_23) +compat_symbol (libc, __finite, __finitel, GLIBC_2_0); +# endif +# if SHLIB_COMPAT (libm, GLIBC_2_1, GLIBC_2_23) +compat_symbol (libm, __finite, __finitel, GLIBC_2_1); +# endif +# endif +weak_alias (__finite, finitel) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_floor.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_floor.c new file mode 100644 index 0000000000..1b99fffc30 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_floor.c @@ -0,0 +1,74 @@ +/* Round double to integer away from zero. + Copyright (C) 2011-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 2011. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* Based on a version which carries the following copyright: */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +/* + * floor(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + */ + + +double +__floor (double x) +{ + int64_t i0; + EXTRACT_WORDS64(i0,x); + int32_t j0 = ((i0>>52)&0x7ff)-0x3ff; + if(__builtin_expect(j0<52, 1)) { + if(j0<0) { + /* return 0*sign(x) if |x|<1 */ + if(i0>=0) {i0=0;} + else if((i0&0x7fffffffffffffffl)!=0) + { i0=0xbff0000000000000l;} + } else { + uint64_t i = (0x000fffffffffffffl)>>j0; + if((i0&i)==0) return x; /* x is integral */ + if(i0<0) i0 += (0x0010000000000000l)>>j0; + i0 &= (~i); + } + INSERT_WORDS64(x,i0); + } else if (j0==0x400) + return x+x; /* inf or NaN */ + return x; +} +#ifndef __floor +weak_alias (__floor, floor) +# ifdef NO_LONG_DOUBLE +strong_alias (__floor, __floorl) +weak_alias (__floor, floorl) +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_frexp.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_frexp.c new file mode 100644 index 0000000000..5e8bc64711 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_frexp.c @@ -0,0 +1,69 @@ +/* Copyright (C) 2011-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@gmail.com>, 2011. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <inttypes.h> +#include <math.h> +#include <math_private.h> + +/* + * for non-zero, finite x + * x = frexp(arg,&exp); + * return a double fp quantity x such that 0.5 <= |x| <1.0 + * and the corresponding binary exponent "exp". That is + * arg = x*2^exp. + * If arg is inf, 0.0, or NaN, then frexp(arg,&exp) returns arg + * with *exp=0. + */ + + +double +__frexp (double x, int *eptr) +{ + int64_t ix; + EXTRACT_WORDS64 (ix, x); + int32_t ex = 0x7ff & (ix >> 52); + int e = 0; + + if (__glibc_likely (ex != 0x7ff && x != 0.0)) + { + /* Not zero and finite. */ + e = ex - 1022; + if (__glibc_unlikely (ex == 0)) + { + /* Subnormal. */ + x *= 0x1p54; + EXTRACT_WORDS64 (ix, x); + ex = 0x7ff & (ix >> 52); + e = ex - 1022 - 54; + } + + ix = (ix & INT64_C (0x800fffffffffffff)) | INT64_C (0x3fe0000000000000); + INSERT_WORDS64 (x, ix); + } + else + /* Quiet signaling NaNs. */ + x += x; + + *eptr = e; + return x; +} +weak_alias (__frexp, frexp) +#ifdef NO_LONG_DOUBLE +strong_alias (__frexp, __frexpl) +weak_alias (__frexp, frexpl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_getpayload.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_getpayload.c new file mode 100644 index 0000000000..fbcd75b8bd --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_getpayload.c @@ -0,0 +1,33 @@ +/* Get NaN payload. dbl-64/wordsize-64 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +double +getpayload (const double *x) +{ + uint64_t ix; + EXTRACT_WORDS64 (ix, *x); + ix &= 0x7ffffffffffffULL; + return (double) ix; +} +#ifdef NO_LONG_DOUBLE +weak_alias (getpayload, getpayloadl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_isinf.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_isinf.c new file mode 100644 index 0000000000..951fb73239 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_isinf.c @@ -0,0 +1,33 @@ +/* + * Written by J.T. Conklin <jtc@netbsd.org>. + * Changed to return -1 for -Inf by Ulrich Drepper <drepper@cygnus.com>. + * Public domain. + */ + +/* + * isinf(x) returns 1 is x is inf, -1 if x is -inf, else 0; + * no branching! + */ + +#include <math.h> +#include <math_private.h> +#include <shlib-compat.h> + +int +__isinf (double x) +{ + int64_t ix; + EXTRACT_WORDS64(ix,x); + int64_t t = ix & UINT64_C(0x7fffffffffffffff); + t ^= UINT64_C(0x7ff0000000000000); + t |= -t; + return ~(t >> 63) & (ix >> 62); +} +hidden_def (__isinf) +weak_alias (__isinf, isinf) +#ifdef NO_LONG_DOUBLE +# if defined LDBL_CLASSIFY_COMPAT && SHLIB_COMPAT (libc, GLIBC_2_0, GLIBC_2_23) +compat_symbol (libc, __isinf, __isinfl, GLIBC_2_0); +# endif +weak_alias (__isinf, isinfl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_isnan.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_isnan.c new file mode 100644 index 0000000000..bcff9e3b67 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_isnan.c @@ -0,0 +1,39 @@ +/* @(#)s_isnan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * isnan(x) returns 1 is x is nan, else 0; + * no branching! + */ + +#include <math.h> +#include <math_private.h> +#include <shlib-compat.h> +#include <stdint.h> + +#undef __isnan +int __isnan(double x) +{ + int64_t hx; + EXTRACT_WORDS64(hx,x); + hx &= UINT64_C(0x7fffffffffffffff); + hx = UINT64_C(0x7ff0000000000000) - hx; + return (int)(((uint64_t)hx)>>63); +} +hidden_def (__isnan) +weak_alias (__isnan, isnan) +#ifdef NO_LONG_DOUBLE +# if defined LDBL_CLASSIFY_COMPAT && SHLIB_COMPAT (libc, GLIBC_2_0, GLIBC_2_23) +compat_symbol (libc, __isnan, __isnanl, GLIBC_2_0); +# endif +weak_alias (__isnan, isnanl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_issignaling.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_issignaling.c new file mode 100644 index 0000000000..117f64bede --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_issignaling.c @@ -0,0 +1,43 @@ +/* Test for signaling NaN. + Copyright (C) 2013-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> + +int +__issignaling (double x) +{ + u_int64_t xi; + EXTRACT_WORDS64 (xi, x); +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN + /* We only have to care about the high-order bit of x's significand, because + having it set (sNaN) already makes the significand different from that + used to designate infinity. */ + return (xi & UINT64_C (0x7ff8000000000000)) == UINT64_C (0x7ff8000000000000); +#else + /* To keep the following comparison simple, toggle the quiet/signaling bit, + so that it is set for sNaNs. This is inverse to IEEE 754-2008 (as well as + common practice for IEEE 754-1985). */ + xi ^= UINT64_C (0x0008000000000000); + /* We have to compare for greater (instead of greater or equal), because x's + significand being all-zero designates infinity not NaN. */ + return (xi & UINT64_C (0x7fffffffffffffff)) > UINT64_C (0x7ff8000000000000); +#endif +} +libm_hidden_def (__issignaling) diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_llround.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_llround.c new file mode 100644 index 0000000000..86a791111e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_llround.c @@ -0,0 +1,82 @@ +/* Round double value to long long int. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define lround __hidden_lround +#define __lround __hidden___lround + +#include <math.h> +#include <sysdep.h> + +#include <math_private.h> + + +long long int +__llround (double x) +{ + int32_t j0; + int64_t i0; + long long int result; + int sign; + + EXTRACT_WORDS64 (i0, x); + j0 = ((i0 >> 52) & 0x7ff) - 0x3ff; + sign = i0 < 0 ? -1 : 1; + i0 &= UINT64_C(0xfffffffffffff); + i0 |= UINT64_C(0x10000000000000); + + if (j0 < (int32_t) (8 * sizeof (long long int)) - 1) + { + if (j0 < 0) + return j0 < -1 ? 0 : sign; + else if (j0 >= 52) + result = i0 << (j0 - 52); + else + { + i0 += UINT64_C(0x8000000000000) >> j0; + + result = i0 >> (52 - j0); + } + } + else + { + /* The number is too large. It is left implementation defined + what happens. */ + return (long long int) x; + } + + return sign * result; +} + +weak_alias (__llround, llround) +#ifdef NO_LONG_DOUBLE +strong_alias (__llround, __llroundl) +weak_alias (__llround, llroundl) +#endif + +/* long has the same width as long long on LP64 machines, so use an alias. */ +#undef lround +#undef __lround +#ifdef _LP64 +strong_alias (__llround, __lround) +weak_alias (__llround, lround) +# ifdef NO_LONG_DOUBLE +strong_alias (__llround, __lroundl) +weak_alias (__llround, lroundl) +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_logb.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_logb.c new file mode 100644 index 0000000000..c65cd52208 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_logb.c @@ -0,0 +1,48 @@ +/* Compute radix independent exponent. + Copyright (C) 2011-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@gmail.com>, 2011. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> + + +double +__logb (double x) +{ + int64_t ix, ex; + + EXTRACT_WORDS64 (ix, x); + ix &= UINT64_C(0x7fffffffffffffff); + if (ix == 0) + return -1.0 / fabs (x); + ex = ix >> 52; + if (ex == 0x7ff) + return x * x; + if (__glibc_unlikely (ex == 0)) + { + int m = __builtin_clzll (ix); + ex -= m - 12; + } + return (double) (ex - 1023); +} +weak_alias (__logb, logb) +#ifdef NO_LONG_DOUBLE +strong_alias (__logb, __logbl) +weak_alias (__logb, logbl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_lround.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_lround.c new file mode 100644 index 0000000000..02b01aa00d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_lround.c @@ -0,0 +1,89 @@ +/* Round double value to long int. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <limits.h> +#include <math.h> + +#include <math_private.h> + +/* For LP64, lround is an alias for llround. */ +#ifndef _LP64 + +long int +__lround (double x) +{ + int32_t j0; + int64_t i0; + long int result; + int sign; + + EXTRACT_WORDS64 (i0, x); + j0 = ((i0 >> 52) & 0x7ff) - 0x3ff; + sign = i0 < 0 ? -1 : 1; + i0 &= UINT64_C(0xfffffffffffff); + i0 |= UINT64_C(0x10000000000000); + + if (j0 < (int32_t) (8 * sizeof (long int)) - 1) + { + if (j0 < 0) + return j0 < -1 ? 0 : sign; + else if (j0 >= 52) + result = i0 << (j0 - 52); + else + { + i0 += UINT64_C(0x8000000000000) >> j0; + + result = i0 >> (52 - j0); +#ifdef FE_INVALID + if (sizeof (long int) == 4 + && sign == 1 + && result == LONG_MIN) + /* Rounding brought the value out of range. */ + feraiseexcept (FE_INVALID); +#endif + } + } + else + { + /* The number is too large. Unless it rounds to LONG_MIN, + FE_INVALID must be raised and the return value is + unspecified. */ +#ifdef FE_INVALID + if (sizeof (long int) == 4 + && x <= (double) LONG_MIN - 0.5) + { + /* If truncation produces LONG_MIN, the cast will not raise + the exception, but may raise "inexact". */ + feraiseexcept (FE_INVALID); + return LONG_MIN; + } +#endif + return (long int) x; + } + + return sign * result; +} + +weak_alias (__lround, lround) +# ifdef NO_LONG_DOUBLE +strong_alias (__lround, __lroundl) +weak_alias (__lround, lroundl) +# endif + +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_modf.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_modf.c new file mode 100644 index 0000000000..c309e56272 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_modf.c @@ -0,0 +1,66 @@ +/* Rewritten for 64-bit machines by Ulrich Drepper <drepper@gmail.com>. */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * modf(double x, double *iptr) + * return fraction part of x, and return x's integral part in *iptr. + * Method: + * Bit twiddling. + * + * Exception: + * No exception. + */ + +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +static const double one = 1.0; + +double +__modf(double x, double *iptr) +{ + int64_t i0; + int32_t j0; + EXTRACT_WORDS64(i0,x); + j0 = ((i0>>52)&0x7ff)-0x3ff; /* exponent of x */ + if(j0<52) { /* integer part in x */ + if(j0<0) { /* |x|<1 */ + /* *iptr = +-0 */ + INSERT_WORDS64(*iptr,i0&UINT64_C(0x8000000000000000)); + return x; + } else { + uint64_t i = UINT64_C(0x000fffffffffffff)>>j0; + if((i0&i)==0) { /* x is integral */ + *iptr = x; + /* return +-0 */ + INSERT_WORDS64(x,i0&UINT64_C(0x8000000000000000)); + return x; + } else { + INSERT_WORDS64(*iptr,i0&(~i)); + return x - *iptr; + } + } + } else { /* no fraction part */ + *iptr = x*one; + /* We must handle NaNs separately. */ + if (j0 == 0x400 && (i0 & UINT64_C(0xfffffffffffff))) + return x*one; + INSERT_WORDS64(x,i0&UINT64_C(0x8000000000000000)); /* return +-0 */ + return x; + } +} +weak_alias (__modf, modf) +#ifdef NO_LONG_DOUBLE +strong_alias (__modf, __modfl) +weak_alias (__modf, modfl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_nearbyint.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_nearbyint.c new file mode 100644 index 0000000000..8293819981 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_nearbyint.c @@ -0,0 +1,66 @@ +/* Adapted for use as nearbyint by Ulrich Drepper <drepper@cygnus.com>. */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * rint(x) + * Return x rounded to integral value according to the prevailing + * rounding mode. + * Method: + * Using floating addition. + * Exception: + * Inexact flag raised if x not equal to rint(x). + */ + +#include <fenv.h> +#include <math.h> +#include <math_private.h> + +static const double +TWO52[2]={ + 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ + -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ +}; + +double +__nearbyint(double x) +{ + fenv_t env; + int64_t i0,sx; + int32_t j0; + EXTRACT_WORDS64(i0,x); + sx = (i0>>63)&1; + j0 = ((i0>>52)&0x7ff)-0x3ff; + if(__builtin_expect(j0<52, 1)) { + if(j0<0) { + libc_feholdexcept (&env); + double w = TWO52[sx]+x; + double t = w-TWO52[sx]; + math_opt_barrier(t); + libc_fesetenv (&env); + return __copysign (t, x); + } + } else { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + libc_feholdexcept (&env); + double w = TWO52[sx]+x; + double t = w-TWO52[sx]; + math_opt_barrier (t); + libc_fesetenv (&env); + return t; +} +weak_alias (__nearbyint, nearbyint) +#ifdef NO_LONG_DOUBLE +strong_alias (__nearbyint, __nearbyintl) +weak_alias (__nearbyint, nearbyintl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_remquo.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_remquo.c new file mode 100644 index 0000000000..37a823c075 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_remquo.c @@ -0,0 +1,114 @@ +/* Compute remainder and a congruent to the quotient. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> +#include <stdint.h> + +static const double zero = 0.0; + + +double +__remquo (double x, double y, int *quo) +{ + int64_t hx, hy; + uint64_t sx, qs; + int cquo; + + EXTRACT_WORDS64 (hx, x); + EXTRACT_WORDS64 (hy, y); + sx = hx & UINT64_C(0x8000000000000000); + qs = sx ^ (hy & UINT64_C(0x8000000000000000)); + hy &= UINT64_C(0x7fffffffffffffff); + hx &= UINT64_C(0x7fffffffffffffff); + + /* Purge off exception values. */ + if (__glibc_unlikely (hy == 0)) + return (x * y) / (x * y); /* y = 0 */ + if (__builtin_expect (hx >= UINT64_C(0x7ff0000000000000) /* x not finite */ + || hy > UINT64_C(0x7ff0000000000000), 0))/* y is NaN */ + return (x * y) / (x * y); + + if (hy <= UINT64_C(0x7fbfffffffffffff)) + x = __ieee754_fmod (x, 8 * y); /* now x < 8y */ + + if (__glibc_unlikely (hx == hy)) + { + *quo = qs ? -1 : 1; + return zero * x; + } + + x = fabs (x); + INSERT_WORDS64 (y, hy); + cquo = 0; + + if (hy <= UINT64_C(0x7fcfffffffffffff) && x >= 4 * y) + { + x -= 4 * y; + cquo += 4; + } + if (hy <= UINT64_C(0x7fdfffffffffffff) && x >= 2 * y) + { + x -= 2 * y; + cquo += 2; + } + + if (hy < UINT64_C(0x0020000000000000)) + { + if (x + x > y) + { + x -= y; + ++cquo; + if (x + x >= y) + { + x -= y; + ++cquo; + } + } + } + else + { + double y_half = 0.5 * y; + if (x > y_half) + { + x -= y; + ++cquo; + if (x >= y_half) + { + x -= y; + ++cquo; + } + } + } + + *quo = qs ? -cquo : cquo; + + /* Ensure correct sign of zero result in round-downward mode. */ + if (x == 0.0) + x = 0.0; + if (sx) + x = -x; + return x; +} +weak_alias (__remquo, remquo) +#ifdef NO_LONG_DOUBLE +strong_alias (__remquo, __remquol) +weak_alias (__remquo, remquol) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_rint.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_rint.c new file mode 100644 index 0000000000..87b2339d43 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_rint.c @@ -0,0 +1,60 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * rint(x) + * Return x rounded to integral value according to the prevailing + * rounding mode. + * Method: + * Using floating addition. + * Exception: + * Inexact flag raised if x not equal to rint(x). + */ + +#include <math.h> +#include <math_private.h> + +static const double +TWO52[2]={ + 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ + -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ +}; + +double +__rint(double x) +{ + int64_t i0,sx; + int32_t j0; + EXTRACT_WORDS64(i0,x); + sx = (i0>>63)&1; + j0 = ((i0>>52)&0x7ff)-0x3ff; + if(j0<52) { + if(j0<0) { + double w = TWO52[sx]+x; + double t = w-TWO52[sx]; + EXTRACT_WORDS64(i0,t); + INSERT_WORDS64(t,(i0&UINT64_C(0x7fffffffffffffff))|(sx<<63)); + return t; + } + } else { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + double w = TWO52[sx]+x; + return w-TWO52[sx]; +} +#ifndef __rint +weak_alias (__rint, rint) +# ifdef NO_LONG_DOUBLE +strong_alias (__rint, __rintl) +weak_alias (__rint, rintl) +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_round.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_round.c new file mode 100644 index 0000000000..0e3738b6ef --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_round.c @@ -0,0 +1,68 @@ +/* Round double to integer away from zero. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> +#include <stdint.h> + + +double +__round (double x) +{ + int64_t i0, j0; + + EXTRACT_WORDS64 (i0, x); + j0 = ((i0 >> 52) & 0x7ff) - 0x3ff; + if (__glibc_likely (j0 < 52)) + { + if (j0 < 0) + { + i0 &= UINT64_C(0x8000000000000000); + if (j0 == -1) + i0 |= UINT64_C(0x3ff0000000000000); + } + else + { + uint64_t i = UINT64_C(0x000fffffffffffff) >> j0; + if ((i0 & i) == 0) + /* X is integral. */ + return x; + + i0 += UINT64_C(0x0008000000000000) >> j0; + i0 &= ~i; + } + } + else + { + if (j0 == 0x400) + /* Inf or NaN. */ + return x + x; + else + return x; + } + + INSERT_WORDS64 (x, i0); + return x; +} +weak_alias (__round, round) +#ifdef NO_LONG_DOUBLE +strong_alias (__round, __roundl) +weak_alias (__round, roundl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_roundeven.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_roundeven.c new file mode 100644 index 0000000000..d13ee25cea --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_roundeven.c @@ -0,0 +1,72 @@ +/* Round to nearest integer value, rounding halfway cases to even. + dbl-64/wordsize-64 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +#define BIAS 0x3ff +#define MANT_DIG 53 +#define MAX_EXP (2 * BIAS + 1) + +double +roundeven (double x) +{ + uint64_t ix, ux; + EXTRACT_WORDS64 (ix, x); + ux = ix & 0x7fffffffffffffffULL; + int exponent = ux >> (MANT_DIG - 1); + if (exponent >= BIAS + MANT_DIG - 1) + { + /* Integer, infinity or NaN. */ + if (exponent == MAX_EXP) + /* Infinity or NaN; quiet signaling NaNs. */ + return x + x; + else + return x; + } + else if (exponent >= BIAS) + { + /* At least 1; not necessarily an integer. Locate the bits with + exponents 0 and -1 (when the unbiased exponent is 0, the bit + with exponent 0 is implicit, but as the bias is odd it is OK + to take it from the low bit of the exponent). */ + int int_pos = (BIAS + MANT_DIG - 1) - exponent; + int half_pos = int_pos - 1; + uint64_t half_bit = 1ULL << half_pos; + uint64_t int_bit = 1ULL << int_pos; + if ((ix & (int_bit | (half_bit - 1))) != 0) + /* Carry into the exponent works correctly. No need to test + whether HALF_BIT is set. */ + ix += half_bit; + ix &= ~(int_bit - 1); + } + else if (exponent == BIAS - 1 && ux > 0x3fe0000000000000ULL) + /* Interval (0.5, 1). */ + ix = (ix & 0x8000000000000000ULL) | 0x3ff0000000000000ULL; + else + /* Rounds to 0. */ + ix &= 0x8000000000000000ULL; + INSERT_WORDS64 (x, ix); + return x; +} +hidden_def (roundeven) +#ifdef NO_LONG_DOUBLE +weak_alias (roundeven, roundevenl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_scalbln.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_scalbln.c new file mode 100644 index 0000000000..8dce51e928 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_scalbln.c @@ -0,0 +1,60 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * scalbn (double x, int n) + * scalbn(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include <math.h> +#include <math_private.h> + +static const double +two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ +twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ +huge = 1.0e+300, +tiny = 1.0e-300; + +double +__scalbln (double x, long int n) +{ + int64_t ix; + int64_t k; + EXTRACT_WORDS64(ix,x); + k = (ix >> 52) & 0x7ff; /* extract exponent */ + if (__builtin_expect(k==0, 0)) { /* 0 or subnormal x */ + if ((ix & UINT64_C(0xfffffffffffff))==0) return x; /* +-0 */ + x *= two54; + EXTRACT_WORDS64(ix,x); + k = ((ix >> 52) & 0x7ff) - 54; + } + if (__builtin_expect(k==0x7ff, 0)) return x+x; /* NaN or Inf */ + if (__builtin_expect(n< -50000, 0)) + return tiny*__copysign(tiny,x); /*underflow*/ + if (__builtin_expect(n> 50000 || k+n > 0x7fe, 0)) + return huge*__copysign(huge,x); /* overflow */ + /* Now k and n are bounded we know that k = k+n does not + overflow. */ + k = k+n; + if (__builtin_expect(k > 0, 1)) /* normal result */ + {INSERT_WORDS64(x,(ix&UINT64_C(0x800fffffffffffff))|(k<<52)); + return x;} + if (k <= -54) + return tiny*__copysign(tiny,x); /*underflow*/ + k += 54; /* subnormal result */ + INSERT_WORDS64(x,(ix&INT64_C(0x800fffffffffffff))|(k<<52)); + return x*twom54; +} +#ifdef NO_LONG_DOUBLE +strong_alias (__scalbln, __scalblnl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_scalbn.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_scalbn.c new file mode 100644 index 0000000000..d517a919c8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_scalbn.c @@ -0,0 +1,60 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * scalbn (double x, int n) + * scalbn(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include <math.h> +#include <math_private.h> + +static const double +two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ +twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ +huge = 1.0e+300, +tiny = 1.0e-300; + +double +__scalbn (double x, int n) +{ + int64_t ix; + int64_t k; + EXTRACT_WORDS64(ix,x); + k = (ix >> 52) & 0x7ff; /* extract exponent */ + if (__builtin_expect(k==0, 0)) { /* 0 or subnormal x */ + if ((ix & UINT64_C(0xfffffffffffff))==0) return x; /* +-0 */ + x *= two54; + EXTRACT_WORDS64(ix,x); + k = ((ix >> 52) & 0x7ff) - 54; + } + if (__builtin_expect(k==0x7ff, 0)) return x+x; /* NaN or Inf */ + if (__builtin_expect(n< -50000, 0)) + return tiny*__copysign(tiny,x); /*underflow*/ + if (__builtin_expect(n> 50000 || k+n > 0x7fe, 0)) + return huge*__copysign(huge,x); /* overflow */ + /* Now k and n are bounded we know that k = k+n does not + overflow. */ + k = k+n; + if (__builtin_expect(k > 0, 1)) /* normal result */ + {INSERT_WORDS64(x,(ix&UINT64_C(0x800fffffffffffff))|(k<<52)); + return x;} + if (k <= -54) + return tiny*__copysign(tiny,x); /*underflow*/ + k += 54; /* subnormal result */ + INSERT_WORDS64(x,(ix&INT64_C(0x800fffffffffffff))|(k<<52)); + return x*twom54; +} +#ifdef NO_LONG_DOUBLE +strong_alias (__scalbn, __scalbnl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_setpayload_main.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_setpayload_main.c new file mode 100644 index 0000000000..d4f6d55432 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_setpayload_main.c @@ -0,0 +1,53 @@ +/* Set NaN payload. dbl-64/wordsize-64 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +#define SET_HIGH_BIT (HIGH_ORDER_BIT_IS_SET_FOR_SNAN ? SIG : !SIG) +#define BIAS 0x3ff +#define PAYLOAD_DIG 51 +#define EXPLICIT_MANT_DIG 52 + +int +FUNC (double *x, double payload) +{ + uint64_t ix; + EXTRACT_WORDS64 (ix, payload); + int exponent = ix >> EXPLICIT_MANT_DIG; + /* Test if argument is (a) negative or too large; (b) too small, + except for 0 when allowed; (c) not an integer. */ + if (exponent >= BIAS + PAYLOAD_DIG + || (exponent < BIAS && !(SET_HIGH_BIT && ix == 0)) + || (ix & ((1ULL << (BIAS + EXPLICIT_MANT_DIG - exponent)) - 1)) != 0) + { + INSERT_WORDS64 (*x, 0); + return 1; + } + if (ix != 0) + { + ix &= (1ULL << EXPLICIT_MANT_DIG) - 1; + ix |= 1ULL << EXPLICIT_MANT_DIG; + ix >>= BIAS + EXPLICIT_MANT_DIG - exponent; + } + ix |= 0x7ff0000000000000ULL | (SET_HIGH_BIT ? 0x8000000000000ULL : 0); + INSERT_WORDS64 (*x, ix); + return 0; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_totalorder.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_totalorder.c new file mode 100644 index 0000000000..1e8d57f32b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_totalorder.c @@ -0,0 +1,50 @@ +/* Total order operation. dbl-64/wordsize-64 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +int +totalorder (double x, double y) +{ + int64_t ix, iy; + EXTRACT_WORDS64 (ix, x); + EXTRACT_WORDS64 (iy, y); +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN + /* For the preferred quiet NaN convention, this operation is a + comparison of the representations of the arguments interpreted as + sign-magnitude integers. If both arguments are NaNs, invert the + quiet/signaling bit so comparing that way works. */ + if ((ix & 0x7fffffffffffffffULL) > 0x7ff0000000000000ULL + && (iy & 0x7fffffffffffffffULL) > 0x7ff0000000000000ULL) + { + ix ^= 0x0008000000000000ULL; + iy ^= 0x0008000000000000ULL; + } +#endif + uint64_t ix_sign = ix >> 63; + uint64_t iy_sign = iy >> 63; + ix ^= ix_sign >> 1; + iy ^= iy_sign >> 1; + return ix <= iy; +} +#ifdef NO_LONG_DOUBLE +weak_alias (totalorder, totalorderl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_totalordermag.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_totalordermag.c new file mode 100644 index 0000000000..47a077f18b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_totalordermag.c @@ -0,0 +1,47 @@ +/* Total order operation on absolute values. dbl-64/wordsize-64 version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +int +totalordermag (double x, double y) +{ + uint64_t ix, iy; + EXTRACT_WORDS64 (ix, x); + EXTRACT_WORDS64 (iy, y); + ix &= 0x7fffffffffffffffULL; + iy &= 0x7fffffffffffffffULL; +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN + /* For the preferred quiet NaN convention, this operation is a + comparison of the representations of the absolute values of the + arguments. If both arguments are NaNs, invert the + quiet/signaling bit so comparing that way works. */ + if (ix > 0x7ff0000000000000ULL && iy > 0x7ff0000000000000ULL) + { + ix ^= 0x0008000000000000ULL; + iy ^= 0x0008000000000000ULL; + } +#endif + return ix <= iy; +} +#ifdef NO_LONG_DOUBLE +weak_alias (totalordermag, totalordermagl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_trunc.c b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_trunc.c new file mode 100644 index 0000000000..050ec0016a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/wordsize-64/s_trunc.c @@ -0,0 +1,57 @@ +/* Truncate argument to nearest integral value not larger than the argument. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> + + +double +__trunc (double x) +{ + int64_t i0, j0; + int64_t sx; + + EXTRACT_WORDS64 (i0, x); + sx = i0 & UINT64_C(0x8000000000000000); + j0 = ((i0 >> 52) & 0x7ff) - 0x3ff; + if (j0 < 52) + { + if (j0 < 0) + /* The magnitude of the number is < 1 so the result is +-0. */ + INSERT_WORDS64 (x, sx); + else + INSERT_WORDS64 (x, sx | (i0 & ~(UINT64_C(0x000fffffffffffff) >> j0))); + } + else + { + if (j0 == 0x400) + /* x is inf or NaN. */ + return x + x; + } + + return x; +} +#ifndef __trunc +weak_alias (__trunc, trunc) +# ifdef NO_LONG_DOUBLE +strong_alias (__trunc, __truncl) +weak_alias (__trunc, truncl) +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/x2y2m1.c b/REORG.TODO/sysdeps/ieee754/dbl-64/x2y2m1.c new file mode 100644 index 0000000000..70d33de74c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/x2y2m1.c @@ -0,0 +1,75 @@ +/* Compute x^2 + y^2 - 1, without large cancellation error. + Copyright (C) 2012-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <mul_split.h> +#include <stdlib.h> + +/* Calculate X + Y exactly and store the result in *HI + *LO. It is + given that |X| >= |Y| and the values are small enough that no + overflow occurs. */ + +static inline void +add_split (double *hi, double *lo, double x, double y) +{ + /* Apply Dekker's algorithm. */ + *hi = x + y; + *lo = (x - *hi) + y; +} + +/* Compare absolute values of floating-point values pointed to by P + and Q for qsort. */ + +static int +compare (const void *p, const void *q) +{ + double pd = fabs (*(const double *) p); + double qd = fabs (*(const double *) q); + if (pd < qd) + return -1; + else if (pd == qd) + return 0; + else + return 1; +} + +/* Return X^2 + Y^2 - 1, computed without large cancellation error. + It is given that 1 > X >= Y >= epsilon / 2, and that X^2 + Y^2 >= + 0.5. */ + +double +__x2y2m1 (double x, double y) +{ + double vals[5]; + SET_RESTORE_ROUND (FE_TONEAREST); + mul_split (&vals[1], &vals[0], x, x); + mul_split (&vals[3], &vals[2], y, y); + vals[4] = -1.0; + qsort (vals, 5, sizeof (double), compare); + /* Add up the values so that each element of VALS has absolute value + at most equal to the last set bit of the next nonzero + element. */ + for (size_t i = 0; i <= 3; i++) + { + add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]); + qsort (vals + i + 1, 4 - i, sizeof (double), compare); + } + /* Now any error from this addition will be small. */ + return vals[4] + vals[3] + vals[2] + vals[1] + vals[0]; +} diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/x2y2m1f.c b/REORG.TODO/sysdeps/ieee754/dbl-64/x2y2m1f.c new file mode 100644 index 0000000000..17bc435a62 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/x2y2m1f.c @@ -0,0 +1,32 @@ +/* Compute x^2 + y^2 - 1, without large cancellation error. + Copyright (C) 2012-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +/* Return X^2 + Y^2 - 1, computed without large cancellation error. + It is given that 1 > X >= Y >= epsilon / 2, and that X^2 + Y^2 >= + 0.5. */ + +float +__x2y2m1f (float x, float y) +{ + double dx = x, dy = y; + return (float) ((dx - 1) * (dx + 1) + dy * dy); +} |