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authorUlrich Drepper <drepper@redhat.com>2004-12-22 20:10:10 +0000
committerUlrich Drepper <drepper@redhat.com>2004-12-22 20:10:10 +0000
commita334319f6530564d22e775935d9c91663623a1b4 (patch)
treeb5877475619e4c938e98757d518bb1e9cbead751 /sysdeps/ia64/fpu/e_powl.S
parent0ecb606cb6cf65de1d9fc8a919bceb4be476c602 (diff)
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(CFLAGS-tst-align.c): Add -mpreferred-stack-boundary=4.
Diffstat (limited to 'sysdeps/ia64/fpu/e_powl.S')
-rw-r--r--sysdeps/ia64/fpu/e_powl.S4080
1 files changed, 2360 insertions, 1720 deletions
diff --git a/sysdeps/ia64/fpu/e_powl.S b/sysdeps/ia64/fpu/e_powl.S
index 3f93f6090e..d286e9abad 100644
--- a/sysdeps/ia64/fpu/e_powl.S
+++ b/sysdeps/ia64/fpu/e_powl.S
@@ -1,10 +1,10 @@
.file "powl.s"
-
-// Copyright (c) 2000 - 2003, Intel Corporation
+// Copyright (C) 2000, 2001, Intel Corporation
// All rights reserved.
-//
-// Contributed 2000 by the Intel Numerics Group, Intel Corporation
+//
+// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story,
+// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
@@ -20,70 +20,61 @@
// * The name of Intel Corporation may not be used to endorse or promote
// products derived from this software without specific prior written
// permission.
-
-// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
-// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
-// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
-// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
-// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
-// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
+// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
-// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
-// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-//
+// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+//
// Intel Corporation is the author of this code, and requests that all
-// problem reports or change requests be submitted to it directly at
-// http://www.intel.com/software/products/opensource/libraries/num.htm.
+// problem reports or change requests be submitted to it directly at
+// http://developer.intel.com/opensource.
//
-//*********************************************************************
+// *********************************************************************
//
// Function: powl(x,y), where
-// y
+// y
// powl(x,y) = x , for double extended precision x and y values
//
-//*********************************************************************
+// *********************************************************************
//
-// History:
-// 02/02/00 (Hand Optimized)
-// 04/04/00 Unwind support added
-// 08/15/00 Bundle added after call to __libm_error_support to properly
+// History:
+// 2/02/00 (Hand Optimized)
+// 4/04/00 Unwind support added
+// 8/15/00 Bundle added after call to __libm_error_support to properly
// set [the previously overwritten] GR_Parameter_RESULT.
-// 01/22/01 Corrected results for powl(1,inf), powl(1,nan), and
+// 1/22/01 Corrected results for powl(1,inf), powl(1,nan), and
// powl(snan,0) to be 1 per C99, not nan. Fixed many flag settings.
-// 02/06/01 Call __libm_error support if over/underflow when y=2.
-// 04/17/01 Support added for y close to 1 and x a non-special value.
-// Shared software under/overflow detection for all paths
-// 02/07/02 Corrected sf3 setting to disable traps
-// 05/13/02 Improved performance of all paths
-// 02/10/03 Reordered header: .section, .global, .proc, .align;
-// used data8 for long double table values
-// 04/17/03 Added missing mutex directive
-// 10/13/03 Corrected .endp names to match .proc names
-//
-//*********************************************************************
+// 2/06/01 Call __libm_error support if over/underflow when y=2.
+//
+// *********************************************************************
//
// Resources Used:
//
-// Floating-Point Registers:
-// f8 (Input x and Return Value)
-// f9 (Input y)
-// f10-f15,f32-f79
+// Floating-Point Registers:
+// f8 (Input and Return Value)
+// f9-f15,f32-f63,f99
//
// General Purpose Registers:
-// Locals r14-24,r32-r65
+// Locals r32 - r61
// Parameters to __libm_error_support r62,r63,r64,r65
//
// Predicate Registers: p6-p15
//
-//*********************************************************************
+// *********************************************************************
//
// Special Cases and IEEE special conditions:
//
// Denormal fault raised on denormal inputs
-// Overflow exceptions raised when appropriate for pow
-// Underflow exceptions raised when appropriate for pow
+// Overflow exceptions raised when appropriate for pow
+// Underflow exceptions raised when appropriate for pow
// (Error Handling Routine called for overflow and Underflow)
// Inexact raised when appropriate by algorithm
//
@@ -111,8 +102,8 @@
// 22. X or Y denorm/unorm and denorm/unorm operand trap is enabled,
// generate denorm/unorm fault except if invalid or div_0 raised.
//
-//*********************************************************************
-//
+// *********************************************************************
+//
// Algorithm
// =========
//
@@ -122,23 +113,23 @@
// If Y = 0.5, return sqrt(X).
//
// Compute log(X) to extra precision.
-//
+//
// ker_log_80( X, logX_hi, logX_lo, Safe );
//
-// ...logX_hi + logX_lo approximates log(X) to roughly 80
+// ...logX_hi + logX_lo approximates log(X) to roughly 80
// ...significant bits of accuracy.
//
// Compute Y*log(X) to extra precision.
//
// P_hi := Y * logX_hi
-// P_lo := Y * logX_hi - P_hi ...using FMA
-// P_lo := Y * logX_lo + P_lo ...using FMA
+// P_lo := Y * logX_hi - P_hi ...using FMA
+// P_lo := Y * logX_lo + P_lo ...using FMA
//
// Compute exp(P_hi + P_lo)
//
-// Flag := 2;
+// Flag := 2;
// Expo_Range := 2; (assuming double-extended power function)
-// ker_exp_64( P_hi, P_lo, Flag, Expo_Range,
+// ker_exp_64( P_hi, P_lo, Flag, Expo_Range,
// Z_hi, Z_lo, scale, Safe )
//
// scale := sgn * scale
@@ -147,7 +138,7 @@
// return scale*Z_hi + (scale*Z_lo)
// quickly
// Else
-// take necessary precaution in computing
+// take necessary precaution in computing
// scale*Z_hi + (scale*Z_lo)
// to set possible exceptions correctly.
// End If
@@ -161,8 +152,8 @@
// If Y is qNaN, return Y without exception.
// If X is qNaN, return X without exception.
//
-// At this point, X is real and Y is +-inf.
-// Thus |X| can only be 1, strictly bigger than 1, or
+// At this point, X is real and Y is +-inf.
+// Thus |X| can only be 1, strictly bigger than 1, or
// strictly less than 1.
//
// If |X| < 1, then
@@ -178,8 +169,8 @@
// ...Note that Y is real, finite, non-zero, and not +1.
//
// If X is qNaN, return X without exception.
-//
-// If X is +-0,
+//
+// If X is +-0,
// return ( Y > 0 ? +0 : +inf )
//
// If X is +inf
@@ -189,11 +180,11 @@
// return -0 ** -Y
// return ( Y > 0 ? +inf : +0 )
//
-// Case_Invalid
+// Case_Invalid
//
// Return 0 * inf to generate a quiet NaN together
// with an invalid exception.
-//
+//
// Implementation
// ==============
//
@@ -202,15 +193,15 @@
//
// STAGE 1
// -------
-// This stage contains two threads.
+// This stage contains two threads.
//
// Stage1.Thread1
//
// fclass.m X_excep, X_ok = X, (NatVal or s/qNaN) or
-// +-0, +-infinity
+// +-0, +-infinity
//
// fclass.nm X_unsupp, X_supp = X, (NatVal or s/qNaN) or
-// +-(0, unnorm, norm, infinity)
+// +-(0, unnorm, norm, infinity)
//
// X_norm := fnorm( X ) with traps disabled
//
@@ -218,26 +209,26 @@
// If (X_unsupp) goto Filtering (Step 2)
//
// Stage1.Thread2
-// ..............
+// ..............
//
// fclass.m Y_excep, Y_ok = Y, (NatVal or s/qNaN) or
-// +-0, +-infinity
+// +-0, +-infinity
//
// fclass.nm Y_unsupp, Y_supp = Y, (NatVal or s/qNaN) or
-// +-(0, unnorm, norm, infinity)
+// +-(0, unnorm, norm, infinity)
//
// Y_norm := fnorm( Y ) with traps disabled
//
// If (Y_excep) goto Filtering (Step 2)
// If (Y_unsupp) goto Filtering (Step 2)
//
-//
+//
// STAGE 2
// -------
// This stage contains two threads.
//
-// Stage2.Thread1
-// ..............
+// Stage2.Thread1
+// ..............
//
// Set X_lt_0 if X < 0 (using fcmp)
// sgn := +1.0
@@ -254,14 +245,14 @@
// This stage contains two threads.
//
//
-// Stage3.Thread1
-// ..............
+// Stage3.Thread1
+// ..............
//
// X := fnorm(X) in prevailing traps
//
//
-// Stage3.Thread2
-// ..............
+// Stage3.Thread2
+// ..............
//
// Y := fnorm(Y) in prevailing traps
//
@@ -271,56 +262,60 @@
// Go to Case_Normal.
//
-
-// ************* DO NOT CHANGE ORDER OF THESE TABLES ********************
-
-// double-extended 1/ln(2)
-// 3fff b8aa 3b29 5c17 f0bb be87fed0691d3e88
-// 3fff b8aa 3b29 5c17 f0bc
-// For speed the significand will be loaded directly with a movl and setf.sig
-// and the exponent will be bias+63 instead of bias+0. Thus subsequent
-// computations need to scale appropriately.
-// The constant 2^12/ln(2) is needed for the computation of N. This is also
-// obtained by scaling the computations.
-//
-// Two shifting constants are loaded directly with movl and setf.d.
-// 1. RSHF_2TO51 = 1.1000..00 * 2^(63-12)
-// This constant is added to x*1/ln2 to shift the integer part of
-// x*2^12/ln2 into the rightmost bits of the significand.
-// The result of this fma is N_signif.
-// 2. RSHF = 1.1000..00 * 2^(63)
-// This constant is subtracted from N_signif * 2^(-51) to give
-// the integer part of N, N_fix, as a floating-point number.
-// The result of this fms is float_N.
-RODATA
-
-.align 16
-// L_hi, L_lo
-LOCAL_OBJECT_START(Constants_exp_64_Arg)
-data8 0xB17217F400000000,0x00003FF2 // L_hi = hi part log(2)/2^12
-data8 0xF473DE6AF278ECE6,0x00003FD4 // L_lo = lo part log(2)/2^12
-LOCAL_OBJECT_END(Constants_exp_64_Arg)
-
-LOCAL_OBJECT_START(Constants_exp_64_A)
-// Reversed
-data8 0xAAAAAAABB1B736A0,0x00003FFA
-data8 0xAAAAAAAB90CD6327,0x00003FFC
-data8 0xFFFFFFFFFFFFFFFF,0x00003FFD
-LOCAL_OBJECT_END(Constants_exp_64_A)
-
-LOCAL_OBJECT_START(Constants_exp_64_P)
-// Reversed
-data8 0xD00D6C8143914A8A,0x00003FF2
-data8 0xB60BC4AC30304B30,0x00003FF5
-data8 0x888888887474C518,0x00003FF8
-data8 0xAAAAAAAA8DAE729D,0x00003FFA
-data8 0xAAAAAAAAAAAAAF61,0x00003FFC
-data8 0x80000000000004C7,0x00003FFE
-LOCAL_OBJECT_END(Constants_exp_64_P)
-
-LOCAL_OBJECT_START(Constants_exp_64_T1)
-data4 0x3F800000,0x3F8164D2,0x3F82CD87,0x3F843A29
-data4 0x3F85AAC3,0x3F871F62,0x3F88980F,0x3F8A14D5
+#include "libm_support.h"
+
+#ifdef _LIBC
+.rodata
+#else
+.data
+#endif
+
+// Inv_L, L_hi, L_lo
+.align 64
+Constants_exp_64_Arg:
+ASM_TYPE_DIRECTIVE(Constants_exp_64_Arg,@object)
+data4 0x5C17F0BC,0xB8AA3B29,0x0000400B,0x00000000
+data4 0x00000000,0xB17217F4,0x00003FF2,0x00000000
+data4 0xF278ECE6,0xF473DE6A,0x00003FD4,0x00000000
+ASM_SIZE_DIRECTIVE(Constants_exp_64_Arg)
+
+.align 64
+Constants_exp_64_Exponents:
+ASM_TYPE_DIRECTIVE(Constants_exp_64_Exponents,@object)
+data4 0x0000007E,0x00000000,0xFFFFFF83,0xFFFFFFFF
+data4 0x000003FE,0x00000000,0xFFFFFC03,0xFFFFFFFF
+data4 0x00003FFE,0x00000000,0xFFFFC003,0xFFFFFFFF
+data4 0x00003FFE,0x00000000,0xFFFFC003,0xFFFFFFFF
+data4 0xFFFFFFE2,0xFFFFFFFF,0xFFFFFFC4,0xFFFFFFFF
+data4 0xFFFFFFBA,0xFFFFFFFF,0xFFFFFFBA,0xFFFFFFFF
+ASM_SIZE_DIRECTIVE(Constants_exp_64_Exponents)
+
+.align 64
+Constants_exp_64_A:
+ASM_TYPE_DIRECTIVE(Constants_exp_64_A,@object)
+// Reversed
+data4 0xB1B736A0,0xAAAAAAAB,0x00003FFA,0x00000000
+data4 0x90CD6327,0xAAAAAAAB,0x00003FFC,0x00000000
+data4 0xFFFFFFFF,0xFFFFFFFF,0x00003FFD,0x00000000
+ASM_SIZE_DIRECTIVE(Constants_exp_64_A)
+
+.align 64
+Constants_exp_64_P:
+ASM_TYPE_DIRECTIVE(Constants_exp_64_P,@object)
+// Reversed
+data4 0x43914A8A,0xD00D6C81,0x00003FF2,0x00000000
+data4 0x30304B30,0xB60BC4AC,0x00003FF5,0x00000000
+data4 0x7474C518,0x88888888,0x00003FF8,0x00000000
+data4 0x8DAE729D,0xAAAAAAAA,0x00003FFA,0x00000000
+data4 0xAAAAAF61,0xAAAAAAAA,0x00003FFC,0x00000000
+data4 0x000004C7,0x80000000,0x00003FFE,0x00000000
+ASM_SIZE_DIRECTIVE(Constants_exp_64_P)
+
+.align 64
+Constants_exp_64_T1:
+ASM_TYPE_DIRECTIVE(Constants_exp_64_T1,@object)
+data4 0x3F800000,0x3F8164D2,0x3F82CD87,0x3F843A29
+data4 0x3F85AAC3,0x3F871F62,0x3F88980F,0x3F8A14D5
data4 0x3F8B95C2,0x3F8D1ADF,0x3F8EA43A,0x3F9031DC
data4 0x3F91C3D3,0x3F935A2B,0x3F94F4F0,0x3F96942D
data4 0x3F9837F0,0x3F99E046,0x3F9B8D3A,0x3F9D3EDA
@@ -335,263 +330,274 @@ data4 0x3FD744FD,0x3FD99D16,0x3FDBFBB8,0x3FDE60F5
data4 0x3FE0CCDF,0x3FE33F89,0x3FE5B907,0x3FE8396A
data4 0x3FEAC0C7,0x3FED4F30,0x3FEFE4BA,0x3FF28177
data4 0x3FF5257D,0x3FF7D0DF,0x3FFA83B3,0x3FFD3E0C
-LOCAL_OBJECT_END(Constants_exp_64_T1)
-
-LOCAL_OBJECT_START(Constants_exp_64_T2)
-data4 0x3F800000,0x3F80058C,0x3F800B18,0x3F8010A4
-data4 0x3F801630,0x3F801BBD,0x3F80214A,0x3F8026D7
-data4 0x3F802C64,0x3F8031F2,0x3F803780,0x3F803D0E
-data4 0x3F80429C,0x3F80482B,0x3F804DB9,0x3F805349
-data4 0x3F8058D8,0x3F805E67,0x3F8063F7,0x3F806987
-data4 0x3F806F17,0x3F8074A8,0x3F807A39,0x3F807FCA
-data4 0x3F80855B,0x3F808AEC,0x3F80907E,0x3F809610
-data4 0x3F809BA2,0x3F80A135,0x3F80A6C7,0x3F80AC5A
-data4 0x3F80B1ED,0x3F80B781,0x3F80BD14,0x3F80C2A8
-data4 0x3F80C83C,0x3F80CDD1,0x3F80D365,0x3F80D8FA
-data4 0x3F80DE8F,0x3F80E425,0x3F80E9BA,0x3F80EF50
-data4 0x3F80F4E6,0x3F80FA7C,0x3F810013,0x3F8105AA
-data4 0x3F810B41,0x3F8110D8,0x3F81166F,0x3F811C07
-data4 0x3F81219F,0x3F812737,0x3F812CD0,0x3F813269
-data4 0x3F813802,0x3F813D9B,0x3F814334,0x3F8148CE
+ASM_SIZE_DIRECTIVE(Constants_exp_64_T1)
+
+.align 64
+Constants_exp_64_T2:
+ASM_TYPE_DIRECTIVE(Constants_exp_64_T2,@object)
+data4 0x3F800000,0x3F80058C,0x3F800B18,0x3F8010A4
+data4 0x3F801630,0x3F801BBD,0x3F80214A,0x3F8026D7
+data4 0x3F802C64,0x3F8031F2,0x3F803780,0x3F803D0E
+data4 0x3F80429C,0x3F80482B,0x3F804DB9,0x3F805349
+data4 0x3F8058D8,0x3F805E67,0x3F8063F7,0x3F806987
+data4 0x3F806F17,0x3F8074A8,0x3F807A39,0x3F807FCA
+data4 0x3F80855B,0x3F808AEC,0x3F80907E,0x3F809610
+data4 0x3F809BA2,0x3F80A135,0x3F80A6C7,0x3F80AC5A
+data4 0x3F80B1ED,0x3F80B781,0x3F80BD14,0x3F80C2A8
+data4 0x3F80C83C,0x3F80CDD1,0x3F80D365,0x3F80D8FA
+data4 0x3F80DE8F,0x3F80E425,0x3F80E9BA,0x3F80EF50
+data4 0x3F80F4E6,0x3F80FA7C,0x3F810013,0x3F8105AA
+data4 0x3F810B41,0x3F8110D8,0x3F81166F,0x3F811C07
+data4 0x3F81219F,0x3F812737,0x3F812CD0,0x3F813269
+data4 0x3F813802,0x3F813D9B,0x3F814334,0x3F8148CE
data4 0x3F814E68,0x3F815402,0x3F81599C,0x3F815F37
-LOCAL_OBJECT_END(Constants_exp_64_T2)
-
-LOCAL_OBJECT_START(Constants_exp_64_W1)
-data8 0x0000000000000000, 0xBE384454171EC4B4
-data8 0xBE6947414AA72766, 0xBE5D32B6D42518F8
-data8 0x3E68D96D3A319149, 0xBE68F4DA62415F36
-data8 0xBE6DDA2FC9C86A3B, 0x3E6B2E50F49228FE
-data8 0xBE49C0C21188B886, 0x3E64BFC21A4C2F1F
-data8 0xBE6A2FBB2CB98B54, 0x3E5DC5DE9A55D329
-data8 0x3E69649039A7AACE, 0x3E54728B5C66DBA5
-data8 0xBE62B0DBBA1C7D7D, 0x3E576E0409F1AF5F
-data8 0x3E6125001A0DD6A1, 0xBE66A419795FBDEF
-data8 0xBE5CDE8CE1BD41FC, 0xBE621376EA54964F
-data8 0x3E6370BE476E76EE, 0x3E390D1A3427EB92
-data8 0x3E1336DE2BF82BF8, 0xBE5FF1CBD0F7BD9E
-data8 0xBE60A3550CEB09DD, 0xBE5CA37E0980F30D
-data8 0xBE5C541B4C082D25, 0xBE5BBECA3B467D29
-data8 0xBE400D8AB9D946C5, 0xBE5E2A0807ED374A
-data8 0xBE66CB28365C8B0A, 0x3E3AAD5BD3403BCA
-data8 0x3E526055C7EA21E0, 0xBE442C75E72880D6
-data8 0x3E58B2BB85222A43, 0xBE5AAB79522C42BF
-data8 0xBE605CB4469DC2BC, 0xBE589FA7A48C40DC
-data8 0xBE51C2141AA42614, 0xBE48D087C37293F4
-data8 0x3E367A1CA2D673E0, 0xBE51BEBB114F7A38
-data8 0xBE6348E5661A4B48, 0xBDF526431D3B9962
-data8 0x3E3A3B5E35A78A53, 0xBE46C46C1CECD788
-data8 0xBE60B7EC7857D689, 0xBE594D3DD14F1AD7
-data8 0xBE4F9C304C9A8F60, 0xBE52187302DFF9D2
-data8 0xBE5E4C8855E6D68F, 0xBE62140F667F3DC4
-data8 0xBE36961B3BF88747, 0x3E602861C96EC6AA
-data8 0xBE3B5151D57FD718, 0x3E561CD0FC4A627B
-data8 0xBE3A5217CA913FEA, 0x3E40A3CC9A5D193A
-data8 0xBE5AB71310A9C312, 0x3E4FDADBC5F57719
-data8 0x3E361428DBDF59D5, 0x3E5DB5DB61B4180D
-data8 0xBE42AD5F7408D856, 0x3E2A314831B2B707
-LOCAL_OBJECT_END(Constants_exp_64_W1)
-
-LOCAL_OBJECT_START(Constants_exp_64_W2)
-data8 0x0000000000000000, 0xBE641F2537A3D7A2
-data8 0xBE68DD57AD028C40, 0xBE5C77D8F212B1B6
-data8 0x3E57878F1BA5B070, 0xBE55A36A2ECAE6FE
-data8 0xBE620608569DFA3B, 0xBE53B50EA6D300A3
-data8 0x3E5B5EF2223F8F2C, 0xBE56A0D9D6DE0DF4
-data8 0xBE64EEF3EAE28F51, 0xBE5E5AE2367EA80B
-data8 0x3E47CB1A5FCBC02D, 0xBE656BA09BDAFEB7
-data8 0x3E6E70C6805AFEE7, 0xBE6E0509A3415EBA
-data8 0xBE56856B49BFF529, 0x3E66DD3300508651
-data8 0x3E51165FC114BC13, 0x3E53333DC453290F
-data8 0x3E6A072B05539FDA, 0xBE47CD877C0A7696
-data8 0xBE668BF4EB05C6D9, 0xBE67C3E36AE86C93
-data8 0xBE533904D0B3E84B, 0x3E63E8D9556B53CE
-data8 0x3E212C8963A98DC8, 0xBE33138F032A7A22
-data8 0x3E530FA9BC584008, 0xBE6ADF82CCB93C97
-data8 0x3E5F91138370EA39, 0x3E5443A4FB6A05D8
-data8 0x3E63DACD181FEE7A, 0xBE62B29DF0F67DEC
-data8 0x3E65C4833DDE6307, 0x3E5BF030D40A24C1
-data8 0x3E658B8F14E437BE, 0xBE631C29ED98B6C7
-data8 0x3E6335D204CF7C71, 0x3E529EEDE954A79D
-data8 0x3E5D9257F64A2FB8, 0xBE6BED1B854ED06C
-data8 0x3E5096F6D71405CB, 0xBE3D4893ACB9FDF5
-data8 0xBDFEB15801B68349, 0x3E628D35C6A463B9
-data8 0xBE559725ADE45917, 0xBE68C29C042FC476
-data8 0xBE67593B01E511FA, 0xBE4A4313398801ED
-data8 0x3E699571DA7C3300, 0x3E5349BE08062A9E
-data8 0x3E5229C4755BB28E, 0x3E67E42677A1F80D
-data8 0xBE52B33F6B69C352, 0xBE6B3550084DA57F
-data8 0xBE6DB03FD1D09A20, 0xBE60CBC42161B2C1
-data8 0x3E56ED9C78A2B771, 0xBE508E319D0FA795
-data8 0xBE59482AFD1A54E9, 0xBE2A17CEB07FD23E
-data8 0x3E68BF5C17365712, 0x3E3956F9B3785569
-LOCAL_OBJECT_END(Constants_exp_64_W2)
-
-LOCAL_OBJECT_START(Constants_log_80_P)
-// P_8, P_7, ..., P_1
-data8 0xCCCE8B883B1042BC, 0x0000BFFB // P_8
-data8 0xE38997B7CADC2149, 0x00003FFB // P_7
-data8 0xFFFFFFFEB1ACB090, 0x0000BFFB // P_6
-data8 0x9249249806481C81, 0x00003FFC // P_5
-data8 0x0000000000000000, 0x00000000 // Pad for bank conflicts
-data8 0xAAAAAAAAAAAAB0EF, 0x0000BFFC // P_4
-data8 0xCCCCCCCCCCC91416, 0x00003FFC // P_3
-data8 0x8000000000000000, 0x0000BFFD // P_2
-data8 0xAAAAAAAAAAAAAAAB, 0x00003FFD // P_1
-LOCAL_OBJECT_END(Constants_log_80_P)
-
-LOCAL_OBJECT_START(Constants_log_80_Q)
-// log2_hi, log2_lo, Q_6, Q_5, Q_4, Q_3, Q_2, Q_1
-data8 0xB172180000000000,0x00003FFE
-data8 0x82E308654361C4C6,0x0000BFE2
-data8 0x92492453A51BE0AF,0x00003FFC
-data8 0xAAAAAB73A0CFD29F,0x0000BFFC
-data8 0xCCCCCCCCCCCE3872,0x00003FFC
-data8 0xFFFFFFFFFFFFB4FB,0x0000BFFC
-data8 0xAAAAAAAAAAAAAAAB,0x00003FFD
-data8 0x8000000000000000,0x0000BFFE
-LOCAL_OBJECT_END(Constants_log_80_Q)
-
-LOCAL_OBJECT_START(Constants_log_80_Z_G_H_h1)
-// Z1 - 16 bit fixed, G1 and H1 IEEE single, h1 IEEE double
+ASM_SIZE_DIRECTIVE(Constants_exp_64_T2)
+
+.align 64
+Constants_exp_64_W1:
+ASM_TYPE_DIRECTIVE(Constants_exp_64_W1,@object)
+data4 0x00000000,0x00000000,0x171EC4B4,0xBE384454
+data4 0x4AA72766,0xBE694741,0xD42518F8,0xBE5D32B6
+data4 0x3A319149,0x3E68D96D,0x62415F36,0xBE68F4DA
+data4 0xC9C86A3B,0xBE6DDA2F,0xF49228FE,0x3E6B2E50
+data4 0x1188B886,0xBE49C0C2,0x1A4C2F1F,0x3E64BFC2
+data4 0x2CB98B54,0xBE6A2FBB,0x9A55D329,0x3E5DC5DE
+data4 0x39A7AACE,0x3E696490,0x5C66DBA5,0x3E54728B
+data4 0xBA1C7D7D,0xBE62B0DB,0x09F1AF5F,0x3E576E04
+data4 0x1A0DD6A1,0x3E612500,0x795FBDEF,0xBE66A419
+data4 0xE1BD41FC,0xBE5CDE8C,0xEA54964F,0xBE621376
+data4 0x476E76EE,0x3E6370BE,0x3427EB92,0x3E390D1A
+data4 0x2BF82BF8,0x3E1336DE,0xD0F7BD9E,0xBE5FF1CB
+data4 0x0CEB09DD,0xBE60A355,0x0980F30D,0xBE5CA37E
+data4 0x4C082D25,0xBE5C541B,0x3B467D29,0xBE5BBECA
+data4 0xB9D946C5,0xBE400D8A,0x07ED374A,0xBE5E2A08
+data4 0x365C8B0A,0xBE66CB28,0xD3403BCA,0x3E3AAD5B
+data4 0xC7EA21E0,0x3E526055,0xE72880D6,0xBE442C75
+data4 0x85222A43,0x3E58B2BB,0x522C42BF,0xBE5AAB79
+data4 0x469DC2BC,0xBE605CB4,0xA48C40DC,0xBE589FA7
+data4 0x1AA42614,0xBE51C214,0xC37293F4,0xBE48D087
+data4 0xA2D673E0,0x3E367A1C,0x114F7A38,0xBE51BEBB
+data4 0x661A4B48,0xBE6348E5,0x1D3B9962,0xBDF52643
+data4 0x35A78A53,0x3E3A3B5E,0x1CECD788,0xBE46C46C
+data4 0x7857D689,0xBE60B7EC,0xD14F1AD7,0xBE594D3D
+data4 0x4C9A8F60,0xBE4F9C30,0x02DFF9D2,0xBE521873
+data4 0x55E6D68F,0xBE5E4C88,0x667F3DC4,0xBE62140F
+data4 0x3BF88747,0xBE36961B,0xC96EC6AA,0x3E602861
+data4 0xD57FD718,0xBE3B5151,0xFC4A627B,0x3E561CD0
+data4 0xCA913FEA,0xBE3A5217,0x9A5D193A,0x3E40A3CC
+data4 0x10A9C312,0xBE5AB713,0xC5F57719,0x3E4FDADB
+data4 0xDBDF59D5,0x3E361428,0x61B4180D,0x3E5DB5DB
+data4 0x7408D856,0xBE42AD5F,0x31B2B707,0x3E2A3148
+ASM_SIZE_DIRECTIVE(Constants_exp_64_W1)
+
+.align 64
+Constants_exp_64_W2:
+ASM_TYPE_DIRECTIVE(Constants_exp_64_W2,@object)
+data4 0x00000000,0x00000000,0x37A3D7A2,0xBE641F25
+data4 0xAD028C40,0xBE68DD57,0xF212B1B6,0xBE5C77D8
+data4 0x1BA5B070,0x3E57878F,0x2ECAE6FE,0xBE55A36A
+data4 0x569DFA3B,0xBE620608,0xA6D300A3,0xBE53B50E
+data4 0x223F8F2C,0x3E5B5EF2,0xD6DE0DF4,0xBE56A0D9
+data4 0xEAE28F51,0xBE64EEF3,0x367EA80B,0xBE5E5AE2
+data4 0x5FCBC02D,0x3E47CB1A,0x9BDAFEB7,0xBE656BA0
+data4 0x805AFEE7,0x3E6E70C6,0xA3415EBA,0xBE6E0509
+data4 0x49BFF529,0xBE56856B,0x00508651,0x3E66DD33
+data4 0xC114BC13,0x3E51165F,0xC453290F,0x3E53333D
+data4 0x05539FDA,0x3E6A072B,0x7C0A7696,0xBE47CD87
+data4 0xEB05C6D9,0xBE668BF4,0x6AE86C93,0xBE67C3E3
+data4 0xD0B3E84B,0xBE533904,0x556B53CE,0x3E63E8D9
+data4 0x63A98DC8,0x3E212C89,0x032A7A22,0xBE33138F
+data4 0xBC584008,0x3E530FA9,0xCCB93C97,0xBE6ADF82
+data4 0x8370EA39,0x3E5F9113,0xFB6A05D8,0x3E5443A4
+data4 0x181FEE7A,0x3E63DACD,0xF0F67DEC,0xBE62B29D
+data4 0x3DDE6307,0x3E65C483,0xD40A24C1,0x3E5BF030
+data4 0x14E437BE,0x3E658B8F,0xED98B6C7,0xBE631C29
+data4 0x04CF7C71,0x3E6335D2,0xE954A79D,0x3E529EED
+data4 0xF64A2FB8,0x3E5D9257,0x854ED06C,0xBE6BED1B
+data4 0xD71405CB,0x3E5096F6,0xACB9FDF5,0xBE3D4893
+data4 0x01B68349,0xBDFEB158,0xC6A463B9,0x3E628D35
+data4 0xADE45917,0xBE559725,0x042FC476,0xBE68C29C
+data4 0x01E511FA,0xBE67593B,0x398801ED,0xBE4A4313
+data4 0xDA7C3300,0x3E699571,0x08062A9E,0x3E5349BE
+data4 0x755BB28E,0x3E5229C4,0x77A1F80D,0x3E67E426
+data4 0x6B69C352,0xBE52B33F,0x084DA57F,0xBE6B3550
+data4 0xD1D09A20,0xBE6DB03F,0x2161B2C1,0xBE60CBC4
+data4 0x78A2B771,0x3E56ED9C,0x9D0FA795,0xBE508E31
+data4 0xFD1A54E9,0xBE59482A,0xB07FD23E,0xBE2A17CE
+data4 0x17365712,0x3E68BF5C,0xB3785569,0x3E3956F9
+ASM_SIZE_DIRECTIVE(Constants_exp_64_W2)
+
+.align 64
+Constants_log_80_P:
+ASM_TYPE_DIRECTIVE(Constants_log_80_P,@object)
+// 1/2, P_8, P_7, ..., P_1
+data4 0x00000000, 0x80000000, 0x00003FFE, 0x00000000
+data4 0x3B1042BC, 0xCCCE8B88, 0x0000BFFB, 0x00000000
+data4 0xCADC2149, 0xE38997B7, 0x00003FFB, 0x00000000
+data4 0xB1ACB090, 0xFFFFFFFE, 0x0000BFFB, 0x00000000
+data4 0x06481C81, 0x92492498, 0x00003FFC, 0x00000000
+data4 0xAAAAB0EF, 0xAAAAAAAA, 0x0000BFFC, 0x00000000
+data4 0xCCC91416, 0xCCCCCCCC, 0x00003FFC, 0x00000000
+data4 0x00000000, 0x80000000, 0x0000BFFD, 0x00000000
+data4 0xAAAAAAAB, 0xAAAAAAAA, 0x00003FFD
+ASM_SIZE_DIRECTIVE(Constants_log_80_P)
+
+.align 64
+Constants_log_80_Q:
+ASM_TYPE_DIRECTIVE(Constants_log_80_Q,@object)
+// log2_hi, log2_lo, Q_6, Q_5, Q_4, Q_3, Q_2, Q_1
+data4 0x00000000,0xB1721800,0x00003FFE,0x00000000
+data4 0x4361C4C6,0x82E30865,0x0000BFE2,0x00000000
+data4 0xA51BE0AF,0x92492453,0x00003FFC,0x00000000
+data4 0xA0CFD29F,0xAAAAAB73,0x0000BFFC,0x00000000
+data4 0xCCCE3872,0xCCCCCCCC,0x00003FFC,0x00000000
+data4 0xFFFFB4FB,0xFFFFFFFF,0x0000BFFC,0x00000000
+data4 0xAAAAAAAB,0xAAAAAAAA,0x00003FFD,0x00000000
+data4 0x00000000,0x80000000,0x0000BFFE,0x00000000
+ASM_SIZE_DIRECTIVE(Constants_log_80_Q)
+
+.align 64
+Constants_log_80_Z_G_H_h1:
+ASM_TYPE_DIRECTIVE(Constants_log_80_Z_G_H_h1,@object)
+// Z1 - 16 bit fixed, G1 and H1 IEEE single, h1 IEEE double
data4 0x00008000,0x3F800000,0x00000000,0x00000000
-data4 0x00000000,0x00000000,0x00000000,0x00000000
+data4 0x00000000,0x00000000,0x00000000,0x00000000
data4 0x00007879,0x3F70F0F0,0x3D785196,0x00000000
data4 0xEBA0E0D1,0x8B1D330B,0x00003FDA,0x00000000
data4 0x000071C8,0x3F638E38,0x3DF13843,0x00000000
data4 0x9EADD553,0xE2AF365E,0x00003FE2,0x00000000
data4 0x00006BCB,0x3F579430,0x3E2FF9A0,0x00000000
-data4 0x752F34A2,0xF585FEC3,0x0000BFE3,0x00000000
+data4 0x752F34A2,0xF585FEC3,0x0000BFE3,0x00000000
data4 0x00006667,0x3F4CCCC8,0x3E647FD6,0x00000000
-data4 0x893B03F3,0xF3546435,0x00003FE2,0x00000000
-data4 0x00006187,0x3F430C30,0x3E8B3AE7,0x00000000
-data4 0x39CDD2AC,0xBABA62E0,0x00003FE4,0x00000000
-data4 0x00005D18,0x3F3A2E88,0x3EA30C68,0x00000000
+data4 0x893B03F3,0xF3546435,0x00003FE2,0x00000000
+data4 0x00006187,0x3F430C30,0x3E8B3AE7,0x00000000
+data4 0x39CDD2AC,0xBABA62E0,0x00003FE4,0x00000000
+data4 0x00005D18,0x3F3A2E88,0x3EA30C68,0x00000000
data4 0x457978A1,0x8718789F,0x00003FE2,0x00000000
-data4 0x0000590C,0x3F321640,0x3EB9CEC8,0x00000000
-data4 0x3185E56A,0x9442DF96,0x0000BFE4,0x00000000
-data4 0x00005556,0x3F2AAAA8,0x3ECF9927,0x00000000
-data4 0x2BBE2CBD,0xCBF9A4BF,0x00003FE4,0x00000000
-data4 0x000051EC,0x3F23D708,0x3EE47FC5,0x00000000
-data4 0x852D5935,0xF3537535,0x00003FE3,0x00000000
-data4 0x00004EC5,0x3F1D89D8,0x3EF8947D,0x00000000
-data4 0x46CDF32F,0xA1F1E699,0x0000BFDF,0x00000000
-data4 0x00004BDB,0x3F17B420,0x3F05F3A1,0x00000000
-data4 0xD8484CE3,0x84A61856,0x00003FE4,0x00000000
+data4 0x0000590C,0x3F321640,0x3EB9CEC8,0x00000000
+data4 0x3185E56A,0x9442DF96,0x0000BFE4,0x00000000
+data4 0x00005556,0x3F2AAAA8,0x3ECF9927,0x00000000
+data4 0x2BBE2CBD,0xCBF9A4BF,0x00003FE4,0x00000000
+data4 0x000051EC,0x3F23D708,0x3EE47FC5,0x00000000
+data4 0x852D5935,0xF3537535,0x00003FE3,0x00000000
+data4 0x00004EC5,0x3F1D89D8,0x3EF8947D,0x00000000
+data4 0x46CDF32F,0xA1F1E699,0x0000BFDF,0x00000000
+data4 0x00004BDB,0x3F17B420,0x3F05F3A1,0x00000000
+data4 0xD8484CE3,0x84A61856,0x00003FE4,0x00000000
data4 0x00004925,0x3F124920,0x3F0F4303,0x00000000
-data4 0xFF28821B,0xC7DD97E0,0x0000BFE2,0x00000000
-data4 0x0000469F,0x3F0D3DC8,0x3F183EBF,0x00000000
-data4 0xEF1FD32F,0xD3C4A887,0x00003FE3,0x00000000
-data4 0x00004445,0x3F088888,0x3F20EC80,0x00000000
-data4 0x464C76DA,0x84672BE6,0x00003FE5,0x00000000
+data4 0xFF28821B,0xC7DD97E0,0x0000BFE2,0x00000000
+data4 0x0000469F,0x3F0D3DC8,0x3F183EBF,0x00000000
+data4 0xEF1FD32F,0xD3C4A887,0x00003FE3,0x00000000
+data4 0x00004445,0x3F088888,0x3F20EC80,0x00000000
+data4 0x464C76DA,0x84672BE6,0x00003FE5,0x00000000
data4 0x00004211,0x3F042108,0x3F29516A,0x00000000
-data4 0x18835FB9,0x9A43A511,0x0000BFE5,0x00000000
-LOCAL_OBJECT_END(Constants_log_80_Z_G_H_h1)
-
-LOCAL_OBJECT_START(Constants_log_80_Z_G_H_h2)
-// Z2 - 16 bit fixed, G2 and H2 IEEE single, h2 IEEE double
-data4 0x00008000,0x3F800000,0x00000000,0x00000000
-data4 0x00000000,0x00000000,0x00000000,0x00000000
-data4 0x00007F81,0x3F7F00F8,0x3B7F875D,0x00000000
+data4 0x18835FB9,0x9A43A511,0x0000BFE5,0x00000000
+ASM_SIZE_DIRECTIVE(Constants_log_80_Z_G_H_h1)
+
+.align 64
+Constants_log_80_Z_G_H_h2:
+ASM_TYPE_DIRECTIVE(Constants_log_80_Z_G_H_h2,@object)
+// Z2 - 16 bit fixed, G2 and H2 IEEE single, h2 IEEE double
+data4 0x00008000,0x3F800000,0x00000000,0x00000000
+data4 0x00000000,0x00000000,0x00000000,0x00000000
+data4 0x00007F81,0x3F7F00F8,0x3B7F875D,0x00000000
data4 0x211398BF,0xAD08B116,0x00003FDB,0x00000000
-data4 0x00007F02,0x3F7E03F8,0x3BFF015B,0x00000000
-data4 0xC376958E,0xB106790F,0x00003FDE,0x00000000
-data4 0x00007E85,0x3F7D08E0,0x3C3EE393,0x00000000
-data4 0x79A7679A,0xFD03F242,0x0000BFDA,0x00000000
-data4 0x00007E08,0x3F7C0FC0,0x3C7E0586,0x00000000
-data4 0x05E7AE08,0xF03F81C3,0x0000BFDF,0x00000000
-data4 0x00007D8D,0x3F7B1880,0x3C9E75D2,0x00000000
+data4 0x00007F02,0x3F7E03F8,0x3BFF015B,0x00000000
+data4 0xC376958E,0xB106790F,0x00003FDE,0x00000000
+data4 0x00007E85,0x3F7D08E0,0x3C3EE393,0x00000000
+data4 0x79A7679A,0xFD03F242,0x0000BFDA,0x00000000
+data4 0x00007E08,0x3F7C0FC0,0x3C7E0586,0x00000000
+data4 0x05E7AE08,0xF03F81C3,0x0000BFDF,0x00000000
+data4 0x00007D8D,0x3F7B1880,0x3C9E75D2,0x00000000
data4 0x049EB22F,0xD1B87D3C,0x00003FDE,0x00000000
-data4 0x00007D12,0x3F7A2328,0x3CBDC97A,0x00000000
-data4 0x3A9E81E0,0xFABC8B95,0x00003FDF,0x00000000
+data4 0x00007D12,0x3F7A2328,0x3CBDC97A,0x00000000
+data4 0x3A9E81E0,0xFABC8B95,0x00003FDF,0x00000000
data4 0x00007C98,0x3F792FB0,0x3CDCFE47,0x00000000
-data4 0x7C4B5443,0xF5F3653F,0x00003FDF,0x00000000
-data4 0x00007C20,0x3F783E08,0x3CFC15D0,0x00000000
-data4 0xF65A1773,0xE78AB204,0x00003FE0,0x00000000
-data4 0x00007BA8,0x3F774E38,0x3D0D874D,0x00000000
-data4 0x7B8EF695,0xDB7CBFFF,0x0000BFE0,0x00000000
-data4 0x00007B31,0x3F766038,0x3D1CF49B,0x00000000
-data4 0xCF773FB3,0xC0241AEA,0x0000BFE0,0x00000000
-data4 0x00007ABB,0x3F757400,0x3D2C531D,0x00000000
-data4 0xC9539FDF,0xFC8F4D48,0x00003FE1,0x00000000
-data4 0x00007A45,0x3F748988,0x3D3BA322,0x00000000
-data4 0x954665C2,0x9CD035FB,0x0000BFE1,0x00000000
-data4 0x000079D1,0x3F73A0D0,0x3D4AE46F,0x00000000
-data4 0xDD367A30,0xEC9017C7,0x00003FE1,0x00000000
-data4 0x0000795D,0x3F72B9D0,0x3D5A1756,0x00000000
-data4 0xCB11189C,0xEE6625D3,0x0000BFE1,0x00000000
-data4 0x000078EB,0x3F71D488,0x3D693B9D,0x00000000
+data4 0x7C4B5443,0xF5F3653F,0x00003FDF,0x00000000
+data4 0x00007C20,0x3F783E08,0x3CFC15D0,0x00000000
+data4 0xF65A1773,0xE78AB204,0x00003FE0,0x00000000
+data4 0x00007BA8,0x3F774E38,0x3D0D874D,0x00000000
+data4 0x7B8EF695,0xDB7CBFFF,0x0000BFE0,0x00000000
+data4 0x00007B31,0x3F766038,0x3D1CF49B,0x00000000
+data4 0xCF773FB3,0xC0241AEA,0x0000BFE0,0x00000000
+data4 0x00007ABB,0x3F757400,0x3D2C531D,0x00000000
+data4 0xC9539FDF,0xFC8F4D48,0x00003FE1,0x00000000
+data4 0x00007A45,0x3F748988,0x3D3BA322,0x00000000
+data4 0x954665C2,0x9CD035FB,0x0000BFE1,0x00000000
+data4 0x000079D1,0x3F73A0D0,0x3D4AE46F,0x00000000
+data4 0xDD367A30,0xEC9017C7,0x00003FE1,0x00000000
+data4 0x0000795D,0x3F72B9D0,0x3D5A1756,0x00000000
+data4 0xCB11189C,0xEE6625D3,0x0000BFE1,0x00000000
+data4 0x000078EB,0x3F71D488,0x3D693B9D,0x00000000
data4 0xBE11C424,0xA49C8DB5,0x0000BFE0,0x00000000
-LOCAL_OBJECT_END(Constants_log_80_Z_G_H_h2)
-
-LOCAL_OBJECT_START(Constants_log_80_h3_G_H)
-// h3 IEEE double extended, H3 and G3 IEEE single
-data4 0x112666B0,0xAAACAAB1,0x00003FD3,0x3F7FFC00
+ASM_SIZE_DIRECTIVE(Constants_log_80_Z_G_H_h2)
+
+.align 64
+Constants_log_80_h3_G_H:
+ASM_TYPE_DIRECTIVE(Constants_log_80_h3_G_H,@object)
+// h3 IEEE double extended, H3 and G3 IEEE single
+data4 0x112666B0,0xAAACAAB1,0x00003FD3,0x3F7FFC00
data4 0x9B7FAD21,0x90051030,0x00003FD8,0x3F7FF400
-data4 0xF4D783C4,0xA6B46F46,0x00003FDA,0x3F7FEC00
-data4 0x11C6DDCA,0xDA148D88,0x0000BFD8,0x3F7FE400
+data4 0xF4D783C4,0xA6B46F46,0x00003FDA,0x3F7FEC00
+data4 0x11C6DDCA,0xDA148D88,0x0000BFD8,0x3F7FE400
data4 0xCA964D95,0xCE65C1D8,0x0000BFD8,0x3F7FDC00
-data4 0x23412D13,0x883838EE,0x0000BFDB,0x3F7FD400
-data4 0x983ED687,0xB7E5CFA1,0x00003FDB,0x3F7FCC08
-data4 0xE3C3930B,0xDBE23B16,0x0000BFD9,0x3F7FC408
-data4 0x48AA4DFC,0x9B92F1FC,0x0000BFDC,0x3F7FBC10
-data4 0xCE9C8F7E,0x9A8CEB15,0x0000BFD9,0x3F7FB410
-data4 0x0DECE74A,0x8C220879,0x00003FDC,0x3F7FAC18
+data4 0x23412D13,0x883838EE,0x0000BFDB,0x3F7FD400
+data4 0x983ED687,0xB7E5CFA1,0x00003FDB,0x3F7FCC08
+data4 0xE3C3930B,0xDBE23B16,0x0000BFD9,0x3F7FC408
+data4 0x48AA4DFC,0x9B92F1FC,0x0000BFDC,0x3F7FBC10
+data4 0xCE9C8F7E,0x9A8CEB15,0x0000BFD9,0x3F7FB410
+data4 0x0DECE74A,0x8C220879,0x00003FDC,0x3F7FAC18
data4 0x2F053150,0xB25CA912,0x0000BFDA,0x3F7FA420
-data4 0xD9A5BE20,0xA5876555,0x00003FDB,0x3F7F9C20
-data4 0x2053F087,0xC919BB6E,0x00003FD9,0x3F7F9428
-data4 0x041E9A77,0xB70BDA79,0x00003FDC,0x3F7F8C30
-data4 0xEA1C9C30,0xF18A5C08,0x00003FDA,0x3F7F8438
-data4 0x796D89E5,0xA3790D84,0x0000BFDD,0x3F7F7C40
-data4 0xA2915A3A,0xE1852369,0x0000BFDD,0x3F7F7448
-data4 0xA39ED868,0xD803858F,0x00003FDC,0x3F7F6C50
-data4 0x9417EBB7,0xB2EEE356,0x0000BFDD,0x3F7F6458
-data4 0x9BB0D07F,0xED5C1F8A,0x0000BFDC,0x3F7F5C68
-data4 0xE87C740A,0xD6D201A0,0x0000BFDD,0x3F7F5470
-data4 0x1CA74025,0xE8DEBF5E,0x00003FDC,0x3F7F4C78
+data4 0xD9A5BE20,0xA5876555,0x00003FDB,0x3F7F9C20
+data4 0x2053F087,0xC919BB6E,0x00003FD9,0x3F7F9428
+data4 0x041E9A77,0xB70BDA79,0x00003FDC,0x3F7F8C30
+data4 0xEA1C9C30,0xF18A5C08,0x00003FDA,0x3F7F8438
+data4 0x796D89E5,0xA3790D84,0x0000BFDD,0x3F7F7C40
+data4 0xA2915A3A,0xE1852369,0x0000BFDD,0x3F7F7448
+data4 0xA39ED868,0xD803858F,0x00003FDC,0x3F7F6C50
+data4 0x9417EBB7,0xB2EEE356,0x0000BFDD,0x3F7F6458
+data4 0x9BB0D07F,0xED5C1F8A,0x0000BFDC,0x3F7F5C68
+data4 0xE87C740A,0xD6D201A0,0x0000BFDD,0x3F7F5470
+data4 0x1CA74025,0xE8DEBF5E,0x00003FDC,0x3F7F4C78
data4 0x1F34A7EB,0x9A995A97,0x0000BFDC,0x3F7F4488
-data4 0x359EED97,0x9CB0F742,0x0000BFDA,0x3F7F3C90
-data4 0xBBC6A1C8,0xD6F833C2,0x0000BFDD,0x3F7F34A0
-data4 0xE71090EC,0xE1F68F2A,0x00003FDC,0x3F7F2CA8
-data4 0xC160A74F,0xD1881CF1,0x0000BFDB,0x3F7F24B8
-data4 0xD78CB5A4,0x9AD05AE2,0x00003FD6,0x3F7F1CC8
-data4 0x9A77DC4B,0xE658CB8E,0x0000BFDD,0x3F7F14D8
-data4 0x6BD6D312,0xBA281296,0x00003FDC,0x3F7F0CE0
-data4 0xF95210D0,0xB478BBEB,0x0000BFDB,0x3F7F04F0
-data4 0x38800100,0x39400480,0x39A00640,0x39E00C41 // H's start here
-data4 0x3A100A21,0x3A300F22,0x3A4FF51C,0x3A6FFC1D
+data4 0x359EED97,0x9CB0F742,0x0000BFDA,0x3F7F3C90
+data4 0xBBC6A1C8,0xD6F833C2,0x0000BFDD,0x3F7F34A0
+data4 0xE71090EC,0xE1F68F2A,0x00003FDC,0x3F7F2CA8
+data4 0xC160A74F,0xD1881CF1,0x0000BFDB,0x3F7F24B8
+data4 0xD78CB5A4,0x9AD05AE2,0x00003FD6,0x3F7F1CC8
+data4 0x9A77DC4B,0xE658CB8E,0x0000BFDD,0x3F7F14D8
+data4 0x6BD6D312,0xBA281296,0x00003FDC,0x3F7F0CE0
+data4 0xF95210D0,0xB478BBEB,0x0000BFDB,0x3F7F04F0
+data4 0x38800100,0x39400480,0x39A00640,0x39E00C41 // H's start here
+data4 0x3A100A21,0x3A300F22,0x3A4FF51C,0x3A6FFC1D
data4 0x3A87F20B,0x3A97F68B,0x3AA7EB86,0x3AB7E101
-data4 0x3AC7E701,0x3AD7DD7B,0x3AE7D474,0x3AF7CBED
-data4 0x3B03E1F3,0x3B0BDE2F,0x3B13DAAA,0x3B1BD766
-data4 0x3B23CC5C,0x3B2BC997,0x3B33C711,0x3B3BBCC6
-data4 0x3B43BAC0,0x3B4BB0F4,0x3B53AF6D,0x3B5BA620
-data4 0x3B639D12,0x3B6B9444,0x3B7393BC,0x3B7B8B6D
-LOCAL_OBJECT_END(Constants_log_80_h3_G_H)
-
-GR_sig_inv_ln2 = r14
-GR_rshf_2to51 = r15
-GR_exp_2tom51 = r16
-GR_rshf = r17
-GR_exp_half = r18
-GR_sign_mask = r19
-GR_exp_square_oflow = r20
-GR_exp_square_uflow = r21
-GR_exp_ynear1_oflow = r22
-GR_exp_ynear1_uflow = r23
-GR_signif_Z = r24
-
-GR_signexp_x = r32
-
-GR_exp_x = r33
-
+data4 0x3AC7E701,0x3AD7DD7B,0x3AE7D474,0x3AF7CBED
+data4 0x3B03E1F3,0x3B0BDE2F,0x3B13DAAA,0x3B1BD766
+data4 0x3B23CC5C,0x3B2BC997,0x3B33C711,0x3B3BBCC6
+data4 0x3B43BAC0,0x3B4BB0F4,0x3B53AF6D,0x3B5BA620
+data4 0x3B639D12,0x3B6B9444,0x3B7393BC,0x3B7B8B6D
+ASM_SIZE_DIRECTIVE(Constants_log_80_h3_G_H)
+
+.align 64
+Constant_half:
+ASM_TYPE_DIRECTIVE(Constant_half,@object)
+data4 0x00000000,0x80000000,0x00003FFE
+ASM_SIZE_DIRECTIVE(Constant_half)
+
+GR_Expo_Range = r32
+GR_Flag = r33
GR_Table_Ptr = r34
GR_Table_Ptr1 = r35
+GR_BIAS = r35
GR_Index1 = r36
+GR_sign_mask = r36
GR_Index2 = r37
GR_Expo_X = r37
+GR_signif_Z = r38
GR_M = r38
GR_X_0 = r39
@@ -614,49 +620,45 @@ GR_k = r44
GR_Big_Pos_Exp = r45
-GR_exp_pos_max = r46
-GR_exp_bias_p_k = r47
+GR_BIAS_p_k = r47
+GR_BIASed_exp_y = r47
+GR_Big_Neg_Exp = r48
GR_Index3 = r48
GR_temp = r48
GR_vsm_expo = r49
+GR_y_sign = r49
GR_T1_ptr = r50
-GR_P_ptr1 = r50
GR_T2_ptr = r51
-GR_P_ptr2 = r51
GR_N_fix = r52
GR_exp_y = r53
GR_signif_y = r54
-GR_signexp_y = r55
-GR_fraction_y = r55
+GR_exp_and_sign_y = r55
GR_low_order_bit = r56
-GR_exp_mask = r57
-GR_exp_bias = r58
-GR_y_sign = r59
-GR_table_base = r60
-GR_ptr_exp_Arg = r61
-GR_Delta_Exp = r62
-GR_Special_Exp = r63
-GR_exp_neg_max = r64
-GR_Big_Neg_Exp = r65
-
-//** Registers for unwind support
+GR_get_exp_mask = r57
+GR_exponent_zero = r58
+
+// ** Registers for unwind support
GR_SAVE_PFS = r59
GR_SAVE_B0 = r60
GR_SAVE_GP = r61
-GR_Parameter_X = r62
-GR_Parameter_Y = r63
-GR_Parameter_RESULT = r64
-GR_Parameter_TAG = r65
+GR_Parameter_X = r62
+GR_Parameter_Y = r63
+GR_Parameter_RESULT = r64
+GR_Parameter_TAG = r65
-//**
+FR_X = f8
+FR_Y = f9
+FR_RESULT = f99
+
+// **
FR_Input_X = f8
-FR_Result = f8
+FR_Output = f8
FR_Input_Y = f9
FR_Neg = f10
@@ -669,6 +671,7 @@ FR_poly_hi = f11
FR_Sgn = f12
+FR_Neg_X = f13
FR_half_W = f13
FR_X_cor = f14
@@ -695,11 +698,13 @@ FR_Scale = f36
FR_G_1 = f37
FR_G = f37
FR_Wsq = f37
+FR_L_Inv = f37
FR_temp = f37
FR_H_1 = f38
FR_H = f38
FR_W4 = f38
+FR_float_N = f38
FR_h = f39
FR_h_1 = f39
@@ -715,7 +720,9 @@ FR_L_lo = f41
FR_A_1 = f41
FR_h_2 = f42
+FR_P_6 = f42
+FR_abs_W = f43
FR_W1 = f43
FR_G_3 = f44
@@ -733,6 +740,7 @@ FR_H_3 = f47
FR_float_N = f48
+FR_P_4 = f49
FR_A_2 = f49
FR_Q_4 = f50
@@ -760,6 +768,7 @@ FR_Two = f56
FR_Big = f57
FR_neg_2_mK = f58
+FR_NBig = f58
FR_r = f59
@@ -768,1253 +777,1652 @@ FR_poly_lo = f60
FR_poly = f61
FR_P_5 = f62
-FR_Result_small = f62
FR_rsq = f63
-FR_Delta = f64
-
-FR_save_Input_X = f65
-FR_norm_X = f66
-FR_norm_Y = f67
-FR_Y_lo_2 = f68
-
-FR_P_6 = f69
-FR_Result_big = f69
-
-FR_RSHF_2TO51 = f70
-FR_INV_LN2_2TO63 = f71
-FR_2TOM51 = f72
-FR_RSHF = f73
-FR_TMP1 = f74
-FR_TMP2 = f75
-FR_TMP3 = f76
-FR_Tscale = f77
-FR_P_4 = f78
-FR_NBig = f79
-
+FR_Result = f99
+FR_Result_small = f100
+FR_Result_big = f101
.section .text
-GLOBAL_LIBM_ENTRY(powl)
-//
-// Get significand of x. It is the critical path.
-//
+.proc powl#
+.global powl#
+.align 64
+
+powl:
{ .mfi
- getf.sig GR_signif_Z = FR_Input_X // Get significand of x
- fclass.m p11, p12 = FR_Input_X, 0x0b // Test x unorm
- nop.i 999
+alloc GR_Expo_Range = ar.pfs,0,30,4,0
+(p0) fclass.m.unc p7, p13 = FR_Input_Y, 0x1E7
+nop.i 0
}
{ .mfi
- nop.m 999
- fnorm.s1 FR_norm_X = FR_Input_X // Normalize x
- mov GR_exp_half = 0xffff - 1 // Exponent for 0.5
-}
-;;
-
+(p0) getf.exp GR_exp_and_sign_y = FR_Input_Y
+//
+// Save State
+//
+(p0) fclass.m.unc p6, p12 = FR_Input_X, 0x1E7
+nop.i 0
+};;
{ .mfi
- alloc r32 = ar.pfs,0,30,4,0
- fclass.m p7, p0 = FR_Input_Y, 0x1E7 // Test y natval, nan, inf, zero
- mov GR_exp_pos_max = 0x13fff // Max exponent for pos oflow test
+(p0) getf.sig GR_signif_y = FR_Input_Y
+(p0) fcmp.eq.unc.s1 p12, p13 = FR_Input_X, f1
+nop.i 0
}
{ .mfi
- addl GR_table_base = @ltoff(Constants_exp_64_Arg#), gp // Ptr to tables
- fnorm.s1 FR_norm_Y = FR_Input_Y // Normalize y
- mov GR_exp_neg_max = 0x33fff // Max exponent for neg oflow test
+ nop.m 999
+//
+// Check for y = 1
+// Identify EM unsupporteds.
+// Load FR_half = .5
+//
+(p0) fadd.s1 FR_Two = f1, f1
+//
+// Load 1/2 in GP register
+//
+nop.i 0
}
;;
-{ .mfi
- getf.exp GR_signexp_y = FR_Input_Y // Get sign and exp of y
-(p12) fclass.m p11, p0 = FR_Input_Y, 0x0b // Test y unorm
- mov GR_sign_mask = 0x20000 // Sign mask
-}
-{ .mfi
- ld8 GR_table_base = [GR_table_base] // Get base address for tables
- fadd.s1 FR_Two = f1, f1 // Form 2.0 for square test
- mov GR_exp_mask = 0x1FFFF // Exponent mask
+{ .mmi
+ nop.m 999
+(p0) addl GR_Table_Ptr = @ltoff(Constant_half#), gp
+ nop.i 999
}
;;
-{ .mfi
- getf.sig GR_signif_y = FR_Input_Y // Get significand of y
- fclass.m p6, p0 = FR_Input_X, 0x1E7 // Test x natval, nan, inf, zero
+{ .mmi
+ ld8 GR_Table_Ptr = [GR_Table_Ptr]
+ nop.m 999
nop.i 999
}
;;
+{ .mlx
+(p0) ldfe FR_Half =[GR_Table_Ptr],0
+(p0) movl GR_get_exp_mask = 0x1FFFF ;;
+}
+
{ .mfi
- getf.exp GR_signexp_x = FR_Input_X // Get signexp of x
- fmerge.s FR_save_Input_X = FR_Input_X, FR_Input_X
- extr.u GR_Index1 = GR_signif_Z, 59, 4 // Extract upper 4 signif bits of x
+ nop.m 999
+(p0) fclass.nm.unc p9, p15 = FR_Input_Y, 0x1FF
+//
+// Create FR_Two = 2
+// Get exp and significand of Y
+// Crate Masks
+// sgn = 1
+//
+(p0) and GR_exp_y = GR_get_exp_mask,GR_exp_and_sign_y
}
-{ .mfb
- setf.exp FR_Half = GR_exp_half // Load half
- nop.f 999
-(p11) br.cond.spnt POWL_DENORM // Branch if x or y denorm/unorm
+{ .mlx
+ nop.m 999
+(p0) movl GR_exponent_zero = 0xFFFF ;;
}
-;;
-
-// Return here from POWL_DENORM
-POWL_COMMON:
{ .mfi
- setf.exp FR_Big = GR_exp_pos_max // Form big pos value for oflow test
- fclass.nm p11, p0 = FR_Input_Y, 0x1FF // Test Y unsupported
- shl GR_Index1 = GR_Index1,5 // Adjust index1 pointer x 32
+ nop.m 999
+(p0) mov FR_Sgn = f1
+ nop.i 999
}
{ .mfi
- add GR_Table_Ptr = 0x7c0, GR_table_base // Constants_log_80_Z_G_H_h1
- fma.s1 FR_Sgn = f1,f1,f0 // Assume result positive
- mov GR_exp_bias = 0xFFFF // Form exponent bias
+ nop.m 999
+(p0) fcmp.eq.unc.s1 p10, p11 = FR_Input_Y, f1
+ nop.i 999 ;;
}
-;;
-
+{ .mfb
+ nop.m 999
//
// Identify NatVals, NaNs, Infs, and Zeros.
+// Load Half
//
-//
+(p0) fclass.nm.unc p8, p14 = FR_Input_X, 0x1FF
+//
// Remove sign bit from exponent of y.
-// Check for x = 1
+// Check for x = 1
+//
+(p6) br.cond.spnt L(POWL_64_SPECIAL) ;;
+}
+{ .mib
+ nop.m 999
+ nop.i 999
+(p7) br.cond.spnt L(POWL_64_SPECIAL) ;;
+}
+{ .mib
+ nop.m 999
+ nop.i 999
+(p8) br.cond.spnt L(POWL_64_UNSUPPORT) ;;
+}
+{ .mib
+ nop.m 999
+ nop.i 999
+(p9) br.cond.spnt L(POWL_64_UNSUPPORT) ;;
+}
+{ .mfi
+(p0) cmp.lt.unc p9, p0 = GR_exp_y,GR_exponent_zero
+(p0) fcmp.lt.unc.s1 p6, p13 = FR_Input_X, f0
+//
// Branch on Infs, Nans, Zeros, and Natvals
// Check to see that exponent < 0
//
+(p0) sub GR_exp_y = GR_exp_y,GR_exponent_zero
+}
+// x not zero, is y ==2?
{ .mfi
- setf.exp FR_NBig = GR_exp_neg_max // Form big neg value for oflow test
- fclass.nm p8, p0 = FR_Input_X, 0x1FF // Test X unsupported
- and GR_exp_y = GR_exp_mask,GR_signexp_y // Get biased exponent of y
+ nop.m 999
+(p11) fcmp.eq.unc.s1 p7, p14 = FR_Input_Y, FR_Two
+ nop.i 999 ;;
}
{ .mfb
- add GR_Index1 = GR_Index1,GR_Table_Ptr
- nop.f 999
-(p6) br.cond.spnt POWL_64_SPECIAL // Branch if x natval, nan, inf, zero
+ nop.m 999
+(p9) fcmp.lt.unc.s1 p9, p0 = FR_Input_X, f0
+(p7) br.cond.spnt L(POWL_64_SQUARE) ;; // Branch if x not zero and y=2
}
-;;
-
-// load Z_1 from Index1
-
-// There is logic starting here to determine if y is an integer when x < 0.
-// If 0 < |y| < 1 then clearly y is not an integer.
-// If |y| > 1, then the significand of y is shifted left by the size of
-// the exponent of y. This preserves the lsb of the integer part + the
-// fractional bits. The lsb of the integer can be tested to determine if
-// the integer is even or odd. The fractional bits can be tested. If zero,
-// then y is an integer.
+{ .mfi
+ nop.m 999
+(p6) fmerge.ns FR_Neg_X = FR_Input_X, FR_Input_X
+ nop.i 999 ;;
+}
+{ .mfi
+ nop.m 999
+(p10) fmpy.s0 FR_Result = FR_Input_X, f1
//
+// For y = 1, compute result = x
+// For x = 1, compute 1
+// When Y is one return X and possible raise
+// denormal operand exception.
+// Remove exponent BIAS
+//
+(p6) shl GR_exp_and_sign_y= GR_signif_y,GR_exp_y ;;
+}
{ .mfi
- ld2 GR_Z_1 =[GR_Index1],4 // Load Z_1
- fmerge.s FR_Z = f0, FR_norm_X // Z = |x|
- extr.u GR_X_0 = GR_signif_Z, 49, 15 // Extract X_0 from significand
+(p9) or GR_exp_and_sign_y = 0xF,GR_signif_y
+(p12) fma.s0 FR_Result = FR_Input_Y, f0, f1
+ nop.i 999 ;;
}
-{ .mfb
- cmp.lt p9, p0 = GR_exp_y,GR_exp_bias // Test 0 < |y| < 1
- nop.f 999
-(p7) br.cond.spnt POWL_64_SPECIAL // Branch if y natval, nan, inf, zero
+{ .mii
+ nop.m 999
+(p6) extr.u GR_exp_y = GR_exp_and_sign_y,63,1 ;;
+(p6) cmp.ne.unc p9, p0 = GR_exp_y, r0
}
-;;
-
-{ .mfb
- ldfs FR_G_1 = [GR_Index1],4 // Load G_1
- fcmp.eq.s1 p10, p0 = FR_Input_Y, f1 // Test Y = +1.0
-(p8) br.cond.spnt POWL_64_UNSUPPORT // Branch if x unsupported
+{ .mii
+ nop.m 999
+//
+// Both predicates can be set.
+// Don't consider y's < 1.
+//
+(p6) shl GR_signif_y= GR_exp_and_sign_y,1 ;;
+//
+// Is shift off integer part of y.
+// Get y's even or odd bit.
+//
+(p6) cmp.ne.unc p8, p0 = GR_signif_y, r0
}
-;;
-
+{ .mib
+ nop.m 999
+ nop.i 999
//
-// X_0 = High order 15 bit of Z
+// Is the fractional part of the y = 0?
+// Is the integer even or odd.
//
-{ .mfb
- ldfs FR_H_1 = [GR_Index1],8 // Load H_1
-(p9) fcmp.lt.unc.s1 p9, p0 = FR_Input_X, f0 // Test x<0, 0 <|y|<1
-(p11) br.cond.spnt POWL_64_UNSUPPORT // Branch if y unsupported
+(p10) br.cond.spnt L(POWL_64_RETURN) ;;
+}
+{ .mib
+ nop.m 999
+ nop.i 999
+(p12) br.cond.spnt L(POWL_64_RETURN) ;;
+}
+{ .mib
+ nop.m 999
+ nop.i 999
+(p8) br.cond.spnt L(POWL_64_XNEG) ;;
}
-;;
-
{ .mfi
- ldfe FR_h_1 = [GR_Index1] // Load h_1
- fcmp.eq.s1 p7, p0 = FR_Input_Y, FR_Two // Test y = 2.0
- pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 // X_1 = X_0 * Z_1 (bits 15-30)
- // Wait 4 cycles to use result
+ nop.m 999
+(p9) fmerge.ns FR_Sgn = FR_Sgn, FR_Sgn
+ nop.i 999
}
{ .mfi
- add GR_Table_Ptr = 0x9c0, GR_table_base // Constants_log_80_Z_G_H_h2
- nop.f 999
- sub GR_exp_y = GR_exp_y,GR_exp_bias // Get true exponent of y
+ nop.m 999
+(p0) fcmp.eq.unc.s0 p11, p0 = FR_Input_Y, FR_Half
+ nop.i 999 ;;
}
-;;
-
//
-// Branch for (x < 0) and Y not an integer.
+// Raise possible denormal operand exception for both
+// X and Y.
//
{ .mfb
- nop.m 999
- fcmp.lt.s1 p6, p0 = FR_Input_X, f0 // Test x < 0
-(p9) br.cond.spnt POWL_64_XNEG // Branch if x < 0, 0 < |y| < 1
+ nop.m 999
+//
+// Branch for (x < 0) and Y not an integer.
+//
+(p0) fcmp.eq.unc.s0 p12, p0 = FR_Input_X, f1
+//
+// For x < 0 and y integer, make x positive
+// For x < 0 and y odd integer,, set sign = -1.
+//
+(p11) br.cond.spnt L(POWL_64_SQRT) ;;
+}
+{ .mmf
+(p0) cmp.eq.unc p15, p14 = r0, r0
+ nop.m 999
+(p13) fnorm.s1 FR_Z = FR_Input_X ;;
+}
+{ .mfi
+ nop.m 999
+(p6) fnorm.s1 FR_Z = FR_Neg_X
+ nop.i 999
}
;;
-{ .mfi
+//
+// Branch to embedded sqrt(x)
+//
+//
+// Computes ln( x ) to extra precision
+// Input FR 1: FR_X
+// Output FR 2: FR_Y_hi
+// Output FR 3: FR_Y_lo
+// Output PR 1: PR_Safe
+//
+
+{ .mmi
nop.m 999
- fcmp.eq.s1 p12, p0 = FR_Input_X, f1 // Test x=+1.0
+(p0) addl GR_Table_Ptr = @ltoff(Constants_log_80_Z_G_H_h1#), gp
nop.i 999
}
-{ .mfb
- nop.m 999
- fsub.s1 FR_W = FR_Z, f1 // W = Z - 1
-(p7) br.cond.spnt POWL_64_SQUARE // Branch if y=2
-}
;;
-{ .mfi
+{ .mmi
+ ld8 GR_Table_Ptr = [GR_Table_Ptr]
nop.m 999
-(p10) fmpy.s0 FR_Result = FR_Input_X, f1 // If y=+1.0, result=x
-(p6) shl GR_fraction_y= GR_signif_y,GR_exp_y // Get lsb of int + fraction
- // Wait 4 cycles to use result
+ nop.i 999
}
;;
+
+{ .mlx
+ nop.m 999
+(p0) movl GR_BIAS = 0x000000000000FFFF ;;
+}
{ .mfi
- nop.m 999
-(p12) fma.s0 FR_Result = FR_Input_Y, f0, f1 // If x=1.0, result=1, chk denorm
- extr.u GR_Index2 = GR_X_1, 6, 4 // Extract index2
+ nop.m 999
+(p0) fsub.s1 FR_W = FR_Z, f1
+ nop.i 999 ;;
}
-;;
-
-//
-// N = exponent of Z
-//
-{ .mib
- getf.exp GR_N = FR_Z // Get exponent of Z (also x)
- shl GR_Index2=GR_Index2,5 // Index2 x 32 bytes
-(p10) br.ret.spnt b0 // Exit if y=+1.0
+//
+// Z = Norm(X) - both + and - case
+// Set Safe = True
+//
+{ .mmb
+(p0) getf.sig GR_signif_Z = FR_Z
+(p0) getf.exp GR_N = FR_Z
+ nop.b 999 ;;
+}
+{ .mii
+ nop.m 999
+//
+// Get significand of Z
+// W = Z - 1
+//
+(p0) extr.u GR_Index1 = GR_signif_Z, 59, 4 ;;
+//
+// Index1 = High order 4 bits of Z
+// X_0 = High order 15 bit of Z
+//
+(p0) shl GR_Index1 = GR_Index1,5 ;;
+}
+{ .mfi
+ nop.m 999
+//
+// Add offset to Index1 ptr.
+//
+(p0) fabs FR_abs_W = FR_W
+//
+// BIAS = 0x000...FFFF
+// Adjust Index1 ptr ( x 32) .
+//
+(p0) add GR_Index1 = GR_Index1,GR_Table_Ptr
+}
+{ .mmi
+ nop.m 999 ;;
+(p0) ld2 GR_Z_1 =[GR_Index1],4
+(p0) extr.u GR_X_0 = GR_signif_Z, 49, 15
}
;;
-{ .mib
- add GR_Index2 = GR_Index2, GR_Table_Ptr // Pointer to table 2
+{ .mmi
+ nop.m 999
+(p0) addl GR_Table_Ptr = @ltoff(Constants_log_80_Z_G_H_h2#), gp
nop.i 999
-(p12) br.ret.spnt b0 // Exit if x=+1.0
}
;;
{ .mmi
- ld2 GR_Z_2 =[GR_Index2],4 // Load Z_2
-;;
- ldfs FR_G_2 = [GR_Index2],4 // Load G_2
+ ld8 GR_Table_Ptr = [GR_Table_Ptr]
+ nop.m 999
nop.i 999
}
;;
-{ .mii
- ldfs FR_H_2 = [GR_Index2],8 // Load H_2
-(p6) tbit.nz.unc p9, p0 = GR_fraction_y, 63 // Test x<0 and y odd integer
- add GR_Table_Ptr = 0xbcc, GR_table_base // Constants_log_80_h3_G_H, G_3
-}
-;;
+{ .mmi
+(p0) ldfs FR_G_1 = [GR_Index1],4 ;;
+(p0) ldfs FR_H_1 = [GR_Index1],8
+ nop.i 999 ;;
+}
//
-// For x < 0 and y odd integer,, set sign = -1.
+// Adjust Index2 (x 32).
//
{ .mfi
- getf.exp GR_M = FR_W // Get signexp of W
- nop.f 999
- pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 // X_2 = X_1 * Z_2 (bits 15-30)
+(p0) ldfe FR_h_1 = [GR_Index1],0
+ nop.f 999
+(p0) pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 ;;
}
-{ .mfi
- ldfe FR_h_2 = [GR_Index2] // Load h_2
-(p9) fnma.s1 FR_Sgn = f1, f1, f0 // If x<0, y odd int, result negative
- sub GR_N = GR_N, GR_exp_bias // Get true exponent of x = N
+{ .mmi
+ nop.m 999 ;;
+//
+// load Z_1 from Index1
+// abs_W = |W|
+// Point to Table2
+//
+(p0) getf.exp GR_M = FR_abs_W
+//
+// M = M - BIAS
+// Load G_1
+// N = exponent of Z
+//
+ nop.i 999;;
}
-;;
-
-{ .mfi
- add GR_Table_Ptr1 = 0xdc0, GR_table_base // Ptr to H_3
- fcmp.eq.s0 p11, p0 = FR_Input_Y, FR_Half // Test y=0.5, also set denorm
-(p6) shl GR_fraction_y= GR_fraction_y, 1 // Shift left 1 to get fraction
+{ .mmi
+ nop.m 999
+ nop.m 999
+ nop.i 999;;
}
-;;
-
-{ .mmb
- setf.sig FR_float_N = GR_N
-(p6) cmp.ne.unc p8, p0 = GR_fraction_y, r0 // Test x<0 and y not integer
-(p8) br.cond.spnt POWL_64_XNEG // Branch if x<0 and y not int
+{ .mmi
+ nop.m 999
+ nop.m 999
+ nop.i 999;;
}
-;;
-
+{ .mmi
+ nop.m 999
+ nop.m 999
+(p0) extr.u GR_Index2 = GR_X_1, 6, 4 ;;
+}
+{ .mii
+ nop.m 999
+//
+// Extract Index2
+// Load H_1
+// Is -8 > M ?
//
-// Raise possible denormal operand exception for both X and Y.
-// Set pointers in case |x| near 1
-// Branch to embedded sqrt(x) if y=0.5
+(p0) shl GR_Index2=GR_Index2,5 ;;
+(p0) add GR_Index2 = GR_Index2, GR_Table_Ptr
+}
//
-{ .mfi
- add GR_P_ptr1 = 0x6b0, GR_table_base // Constants_log_80_P, P8, NEAR path
- fcmp.eq.s0 p12, p0 = FR_Input_X, FR_Input_Y // Dummy to set denormal
- add GR_P_ptr2 = 0x700, GR_table_base // Constants_log_80_P, P4, NEAR path
+// M = exponent of abs_W
+// X_1 = X_0 * Z_1
+//
+{ .mii
+(p0) sub GR_M = GR_M, GR_BIAS
+ nop.i 999 ;;
+(p0) cmp.gt.unc p7, p14 = -8, GR_M
}
-{ .mfb
- cmp.eq p15, p14 = r0, r0 // Assume result safe (no over/under)
- fsub.s1 FR_Delta = FR_Input_Y,f1 // Delta = y - 1.0
-(p11) br.cond.spnt POWL_64_SQRT // Branch if y=0.5
+{ .mib
+ nop.m 999
+ nop.i 999
+(p7) br.cond.spnt L(LOGL80_NEAR) ;;
}
-;;
-
//
-// Computes ln( x ) to extra precision
-// Input FR 1: FR_X
-// Output FR 2: FR_Y_hi
-// Output FR 3: FR_Y_lo
-// Output PR 1: PR_Safe
+// Load h_1
+// Possible branch out.
+// Add offset of table to Index2
//
{ .mfi
- and GR_M = GR_exp_mask, GR_M // Mask to get exponent of W
- nop.f 999
- extr.u GR_Index3 = GR_X_2, 1, 5 // Get index3
+(p0) ld2 GR_Z_2 =[GR_Index2],4
+(p0) fmerge.se FR_S = f1,FR_Z
+(p0) sub GR_N = GR_N, GR_BIAS
}
;;
{ .mmi
- shladd GR_Table_Ptr1 = GR_Index3,2,GR_Table_Ptr1 // Ptr to H_3
- shladd GR_Index3 = GR_Index3,4,GR_Table_Ptr // Ptr to G_3
- sub GR_M = GR_M, GR_exp_bias // Get true exponent of W
-}
-;;
-
-{ .mib
- ldfs FR_G_3 = [GR_Index3],-12 // Load G_3
- cmp.gt p7, p14 = -8, GR_M // Test if |x-1| < 2^-8
-(p7) br.cond.spnt LOGL80_NEAR // Branch if |x-1| < 2^-8
-}
-;;
-
-// Here if |x-1| >= 2^-8
-{ .mmf
- ldfs FR_H_3 = [GR_Table_Ptr1] // Load H_3
nop.m 999
- nop.f 999
+(p0) addl GR_Table_Ptr = @ltoff(Constants_log_80_h3_G_H#), gp
+ nop.i 999
}
;;
-{ .mfi
- ldfe FR_h_3 = [GR_Index3] // Load h_3
- fmerge.se FR_S = f1,FR_Z // S = merge of 1.0 and signif(Z)
- nop.i 999
-}
-{ .mfi
- add GR_Table_Ptr = 0x740, GR_table_base // Constants_log_80_Q
- fmpy.s1 FR_G = FR_G_1, FR_G_2 // G = G_1 * G_2
+{ .mmi
+ ld8 GR_Table_Ptr = [GR_Table_Ptr]
+ nop.m 999
nop.i 999
}
;;
+//
+// load Z_2
+// N - BIAS
+// Point to Table 3.
+// S = merging of Z and 1.0
+//
+{ .mmi
+(p0) ldfs FR_G_2 = [GR_Index2],4
+(p0) setf.sig FR_float_N = GR_N
+(p0) add GR_Table_Ptr1 = 0x200,GR_Table_Ptr ;;
+}
//
-// Begin Loading Q's - load log2_hi part
+// load G_2
+// X_2 = X_1 * Z_2
+// Add offset to Table 2 ptr.
+// float_N = significand of N
//
-{ .mfi
- ldfe FR_log2_hi = [GR_Table_Ptr],16 // Load log2_hi
- fadd.s1 FR_H = FR_H_1, FR_H_2 // H = H_1 + H_2
- nop.i 999
-};;
-
+{ .mmi
+(p0) ldfs FR_H_2 = [GR_Index2],8 ;;
//
-// h = h_1 + h_2
+// load H_2
+// G = G * G_2
//
+(p0) ldfe FR_h_2 = [GR_Index2],0
+(p0) pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 ;;
+}
+{ .mmi
+ nop.m 999
+ nop.m 999
+ nop.i 999;;
+}
+{ .mmi
+ nop.m 999
+ nop.m 999
+ nop.i 999;;
+}
+{ .mmi
+ nop.m 999
+ nop.m 999
+ nop.i 999;;
+}
+{ .mii
+ nop.m 999
+ nop.i 999 ;;
+(p0) extr.u GR_Index3 = GR_X_2, 1, 5 ;;
+}
{ .mfi
- ldfe FR_log2_lo = [GR_Table_Ptr],16 // Load log2_lo
- fadd.s1 FR_h = FR_h_1, FR_h_2 // h = h_1 + h_2
- nop.i 999
+(p0) shladd GR_Table_Ptr1 = GR_Index3,2,GR_Table_Ptr1
+ nop.f 999
+//
+// h = h_1 + h_2
+// Adjust Index3
+//
+(p0) shladd GR_Index3 = GR_Index3,4,GR_Table_Ptr ;;
+}
+{ .mmb
+ nop.m 999
+(p0) ldfe FR_h_3 = [GR_Index3],12
+ nop.b 999 ;;
+}
+{ .mmf
+(p0) ldfs FR_H_3 = [GR_Table_Ptr1],0
+//
+// float_N = Make N a fp number
+// Load h_3
+// Get pointer to Q table.
+//
+(p0) ldfs FR_G_3 = [GR_Index3],0
+(p0) fmpy.s1 FR_G = FR_G_1, FR_G_2
}
;;
-{ .mfi
- ldfe FR_Q_6 = [GR_Table_Ptr],16 // Load Q_6
- fcvt.xf FR_float_N = FR_float_N
+{ .mmi
+ nop.m 999
+(p0) addl GR_Table_Ptr = @ltoff(Constants_log_80_Q#), gp
nop.i 999
}
;;
-{ .mfi
- ldfe FR_Q_5 = [GR_Table_Ptr],16 // Load Q_5
- nop.f 999
+{ .mmi
+ ld8 GR_Table_Ptr = [GR_Table_Ptr]
+ nop.m 999
nop.i 999
}
;;
+
+
+{ .mfi
+(p0) ldfe FR_log2_hi = [GR_Table_Ptr],16
+(p0) fadd.s1 FR_H = FR_H_1, FR_H_2
+ nop.i 999 ;;
+}
+{ .mmf
+ nop.m 999
//
-// G = G_1 * G_2 * G_3
+// G = G_1 * G_2 * G_3
//
-{ .mfi
- ldfe FR_Q_4 = [GR_Table_Ptr],16 // Load Q_4
- fmpy.s1 FR_G = FR_G, FR_G_3
- nop.i 999
+(p0) ldfe FR_log2_lo = [GR_Table_Ptr],16
+//
+// load h_2
+// H = H_1 + H_2
+// Get Index3
+//
+(p0) fadd.s1 FR_h = FR_h_1, FR_h_2 ;;
}
-;;
-
//
-// H = H_1 + H_2 + H_3
+// Load log2_lo part
+// r = G*S -1
//
{ .mfi
- ldfe FR_Q_3 = [GR_Table_Ptr],16 // Load Q_3
- fadd.s1 FR_H = FR_H, FR_H_3
- nop.i 999
+(p0) ldfe FR_Q_6 = [GR_Table_Ptr],16
+//
+// Load H_3
+//
+(p0) fcvt.xf FR_float_N = FR_float_N
+ nop.i 999 ;;
}
-;;
-
//
-// Y_lo = poly + Y_lo
+// Load Q_6
//
-// h = h_1 + h_2 + h_3
+{ .mmi
+(p0) ldfe FR_Q_5 = [GR_Table_Ptr],16 ;;
+(p0) ldfe FR_Q_4 = [GR_Table_Ptr],16
+ nop.i 999 ;;
+}
+{ .mmi
+(p0) ldfe FR_Q_3 = [GR_Table_Ptr],16 ;;
+(p0) ldfe FR_Q_2 = [GR_Table_Ptr],16
+ nop.i 999 ;;
+}
+{ .mmf
+ nop.m 999
//
+// poly_lo = Q_5 + r * Q_6
+// Load Q_2
+// rsq = r * r
+//
+(p0) ldfe FR_Q_1 = [GR_Table_Ptr],16
+//
+// h = h_1 + h_2 + h_3
+// H = H_1 + H_2 + H_3
+// Load G_3.
+// Begin Loading Q's - load log2_hi part
+//
+(p0) fmpy.s1 FR_G = FR_G, FR_G_3
+}
{ .mfi
- ldfe FR_Q_2 = [GR_Table_Ptr],16 // Load Q_2
- fadd.s1 FR_h = FR_h, FR_h_3
- nop.i 999
+ nop.m 999
+(p0) fadd.s1 FR_H = FR_H, FR_H_3
+ nop.i 999
}
;;
//
-// GS_hi = G*S
-// r = G*S -1
+// Y_lo = poly + Y_lo
//
-{ .mfi
- ldfe FR_Q_1 = [GR_Table_Ptr],16 // Load Q_1
- fmpy.s1 FR_GS_hi = FR_G, FR_S
+
+{ .mmi
+ nop.m 999
+(p0) addl GR_Table_Ptr = @ltoff(Constants_exp_64_Arg#), gp
nop.i 999
}
-{ .mfi
+;;
+
+{ .mmi
+ ld8 GR_Table_Ptr = [GR_Table_Ptr]
nop.m 999
- fms.s1 FR_r = FR_G, FR_S, f1
nop.i 999
}
;;
+
+{ .mfi
+ nop.m 999
+(p0) fadd.s1 FR_h = FR_h, FR_h_3
+ nop.i 999 ;;
+}
+{ .mfi
+ nop.m 999
//
-// poly_lo = Q_5 + r * Q_6
+// Load Q_5
//
+(p0) fmpy.s1 FR_GS_hi = FR_G, FR_S
+ nop.i 999
+}
{ .mfi
- getf.exp GR_Delta_Exp = FR_Delta // Get signexp of y-1 for exp calc
- fma.s1 FR_poly_lo = FR_r, FR_Q_6, FR_Q_5
- nop.i 999
+ nop.m 999
+(p0) fms.s1 FR_r = FR_G, FR_S, f1
+ nop.i 999 ;;
}
+{ .mfi
+ nop.m 999
+(p0) fma.s1 FR_poly_lo = FR_r, FR_Q_6, FR_Q_5
+ nop.i 999
+}
+{ .mfi
+ nop.m 999
//
-// r_cor = GS_hi -1
+// GS_hi = G*S
+// Load Q_4
//
+(p0) fsub.s1 FR_r_cor = FR_GS_hi, f1
+ nop.i 999 ;;
+}
{ .mfi
- nop.m 999
- fsub.s1 FR_r_cor = FR_GS_hi, f1
- nop.i 999
+ nop.m 999
+(p0) fms.s1 FR_GS_lo = FR_G, FR_S, FR_GS_hi
+ nop.i 999
}
-;;
-
+{ .mfi
+ nop.m 999
+(p0) fma.s1 FR_poly = FR_r, FR_Q_2, FR_Q_1
+ nop.i 999 ;;
+}
+{ .mfi
+ nop.m 999
//
+// Load Q_3
+// r_cor = GS_hi -1
// GS_lo = G*S - GS_hi
//
+(p0) fmpy.s1 FR_rsq = FR_r, FR_r
+ nop.i 999
+}
{ .mfi
- nop.m 999
- fms.s1 FR_GS_lo = FR_G, FR_S, FR_GS_hi
- nop.i 999
+ nop.m 999
+(p0) fma.s1 FR_G = FR_float_N, FR_log2_hi, FR_H
+ nop.i 999 ;;
}
-;;
-
+{ .mfi
+ nop.m 999
//
-// rsq = r * r
+// poly = poly_hi + rsq * poly_lo
+// Tbl = float_N*log2_hi + H
//
-{ .mfi
- nop.m 999
- fmpy.s1 FR_rsq = FR_r, FR_r
- nop.i 999
+(p0) fma.s1 FR_Y_lo = FR_float_N, FR_log2_lo, FR_h
+ nop.i 999 ;;
}
+{ .mfi
+ nop.m 999
//
-// G = float_N*log2_hi + H
+// r_cor = r_cor - r
+// poly_hi = r * Q_2 + Q_1
//
-{ .mfi
- nop.m 999
- fma.s1 FR_G = FR_float_N, FR_log2_hi, FR_H
- nop.i 999
+(p0) fma.s1 FR_poly_lo = FR_r, FR_poly_lo, FR_Q_4
+ nop.i 999
}
-;;
-
+{ .mfi
+ nop.m 999
//
-// Y_lo = float_N*log2_lo + h
+// Load Q_1
//
+(p0) fsub.s1 FR_r_cor = FR_r_cor, FR_r
+ nop.i 999 ;;
+}
{ .mfi
- nop.m 999
- fma.s1 FR_Y_lo = FR_float_N, FR_log2_lo, FR_h
- nop.i 999
+ nop.m 999
+//
+// Y_lo = float_N*log2_lo + h
+//
+(p0) fadd.s1 FR_Y_hi = FR_G, FR_r
+ nop.i 999 ;;
}
-;;
-
+{ .mfi
+ nop.m 999
//
-// poly_lo = Q_4 + r * poly_lo
-// r_cor = r_cor - r
+// poly_lo = Q_4 + r * poly_lo;;
+// r_cor = r_cor + GS_lo;;
//
+(p0) fma.s1 FR_poly_lo = FR_r, FR_poly_lo, FR_Q_3
+ nop.i 999
+}
{ .mfi
- nop.m 999
- fma.s1 FR_poly_lo = FR_r, FR_poly_lo, FR_Q_4
- nop.i 999
+ nop.m 999
+(p0) fadd.s1 FR_r_cor = FR_r_cor, FR_GS_lo
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
- fsub.s1 FR_r_cor = FR_r_cor, FR_r
- nop.i 999
+ nop.m 999
+(p0) fadd.s1 FR_r_cor = FR_r_cor, FR_Y_lo
+ nop.i 999
}
-;;
-
+{ .mfi
+ nop.m 999
//
-// poly_hi = r * Q_2 + Q_1
-// Y_hi = G + r
+// poly_lo = Q_3 + r * poly_lo;;
//
+(p0) fma.s1 FR_poly = FR_rsq, FR_poly_lo, FR_poly
+ nop.i 999 ;;
+}
{ .mfi
- nop.m 999
- fma.s1 FR_poly = FR_r, FR_Q_2, FR_Q_1
- nop.i 999
+ nop.m 999
+(p0) fsub.s1 FR_Y_lo = FR_G, FR_Y_hi
+ nop.i 999
+}
+{ .mmi
+(p0) ldfe FR_L_Inv = [GR_Table_Ptr],16 ;;
+(p0) ldfe FR_L_hi = [GR_Table_Ptr],16
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
- fadd.s1 FR_Y_hi = FR_G, FR_r
- nop.i 999
+(p0) ldfe FR_L_lo = [GR_Table_Ptr],16
+ nop.f 999
+ nop.i 999 ;;
}
-;;
-
+{ .mfi
+ nop.m 999
//
-// poly_lo = Q_3 + r * poly_lo
-// r_cor = r_cor + GS_lo
+// Y_hi = Tbl + r
+// r_cor = r_cor + Y_lo
//
-{ .mfi
- nop.m 999
- fma.s1 FR_poly_lo = FR_r, FR_poly_lo, FR_Q_3
- nop.i 999
+(p0) fma.s1 FR_poly = FR_rsq, FR_poly, FR_r_cor
+ nop.i 999 ;;
}
{ .mfi
+ nop.m 999
+// Y_lo = Tbl - Y_hi
+// poly = rsq * poly + r_cor
+//
+(p0) fadd.s1 FR_Y_lo = FR_Y_lo, FR_r
+ nop.i 999 ;;
+}
+{ .mfb
+ nop.m 999
+//
+// Y_lo = Y_lo + r
+//
+(p0) fadd.s1 FR_Y_lo = FR_Y_lo, FR_poly
+//
+// Load L_Inv
+// Load L_hi
+// Load L_lo
+// all long before they are needed.
+// They are used in LOGL_RETURN PATH
+//
+br.cond.sptk L(LOGL_RETURN) ;;
+}
+L(LOGL80_NEAR):
+//
+// Branch LOGL80_NEAR
+//
+
+{ .mmi
nop.m 999
- fadd.s1 FR_r_cor = FR_r_cor, FR_GS_lo
+(p0) addl GR_Table_Ptr = @ltoff(Constants_log_80_P#), gp
nop.i 999
}
;;
-//
-// Y_lo = G - Y_hi
-//
-{ .mfi
+{ .mmi
+ ld8 GR_Table_Ptr = [GR_Table_Ptr]
nop.m 999
- fsub.s1 FR_Y_lo_2 = FR_G, FR_Y_hi
nop.i 999
}
;;
+{ .mfi
+ nop.m 999
+(p0) fmpy.s1 FR_Wsq = FR_W, FR_W
+(p0) add GR_Table_Ptr1 = 0x50,GR_Table_Ptr
+}
//
-// r_cor = r_cor + Y_lo
-// poly = poly_hi + rsq * poly_lo
+// Adjust ptr to 1/2
+// Adjust Ptr1 to P_4
//
-{ .mfi
- add GR_Table_Ptr = 0x0, GR_table_base // Constants_exp_64_Arg
- fadd.s1 FR_r_cor = FR_r_cor, FR_Y_lo
- nop.i 999
+{ .mmi
+(p0) ldfe FR_Half = [GR_Table_Ptr],16 ;;
+(p0) ldfe FR_P_4 = [GR_Table_Ptr1],16
+ nop.i 999
}
-{ .mfi
- nop.m 999
- fma.s1 FR_poly = FR_rsq, FR_poly_lo, FR_poly
- nop.i 999
+//
+// Load 1/2
+//
+{ .mmi
+(p0) ldfe FR_P_8 = [GR_Table_Ptr],16 ;;
+(p0) ldfe FR_P_3 = [GR_Table_Ptr1],16
+ nop.i 999
+}
+{ .mmi
+(p0) ldfe FR_P_7 = [GR_Table_Ptr],16 ;;
+(p0) ldfe FR_P_2 = [GR_Table_Ptr1],16
+ nop.i 999
}
-;;
-
//
-// Load L_hi
-// Load L_lo
-// all long before they are needed.
-// They are used in LOGL_RETURN PATH
+// Load P_7
+// half_W = .5 * W
+// Load P_3
//
-// Y_lo = Y_lo + r
-// poly = rsq * poly + r_cor
+{ .mmi
+(p0) ldfe FR_P_6 = [GR_Table_Ptr],16 ;;
+(p0) ldfe FR_P_1 = [GR_Table_Ptr1],16
+ nop.i 999 ;;
+}
+//
+// Load P_6
+// Wsq = w * w
+// poly = w*P_4 + P_3
+// Load P_2
//
{ .mfi
- ldfe FR_L_hi = [GR_Table_Ptr],16 // Load L_hi
- fadd.s1 FR_Y_lo = FR_Y_lo_2, FR_r
- nop.i 999
+(p0) ldfe FR_P_5 = [GR_Table_Ptr],16
+//
+// Load P_5
+// poly_lo = w * P_8 + P_7
+// Y_hi = w - (1/2)w*w
+// Load P_1
+//
+(p0) fmpy.s1 FR_W4 = FR_Wsq, FR_Wsq
+ nop.i 999
}
{ .mfi
- nop.m 999
- fma.s1 FR_poly = FR_rsq, FR_poly, FR_r_cor
- nop.i 999
+ nop.m 999
+(p0) fmpy.s1 FR_W3 = FR_Wsq, FR_W
+ nop.i 999
}
;;
-{ .mfb
- ldfe FR_L_lo = [GR_Table_Ptr],16 // Load L_lo
- fadd.s1 FR_Y_lo = FR_Y_lo, FR_poly
- br.cond.sptk LOGL_RETURN // Branch to common code
-}
-;;
-
-
-LOGL80_NEAR:
-// Here if |x-1| < 2^-8
//
-// Branch LOGL80_NEAR
+// Y_lo = W3 * poly + Y_lo
//
-{ .mmf
- ldfe FR_P_8 = [GR_P_ptr1],16 // Load P_8
- ldfe FR_P_4 = [GR_P_ptr2],16 // Load P_4
- fmpy.s1 FR_Wsq = FR_W, FR_W
-}
-;;
-
{ .mmi
- ldfe FR_P_7 = [GR_P_ptr1],16 // Load P_7
- ldfe FR_P_3 = [GR_P_ptr2],16 // Load P_3
+ nop.m 999
+(p0) addl GR_Table_Ptr = @ltoff(Constants_exp_64_Arg#), gp
nop.i 999
}
;;
{ .mmi
- ldfe FR_P_6 = [GR_P_ptr1],16 // Load P_6
- ldfe FR_P_2 = [GR_P_ptr2],16 // Load P_2
+ ld8 GR_Table_Ptr = [GR_Table_Ptr]
+ nop.m 999
nop.i 999
}
;;
+
{ .mmi
- ldfe FR_P_5 = [GR_P_ptr1],16 // Load P_5
- ldfe FR_P_1 = [GR_P_ptr2],16 // Load P_1
- nop.i 999
+(p0) ldfe FR_L_Inv = [GR_Table_Ptr],16 ;;
+(p0) ldfe FR_L_hi = [GR_Table_Ptr],16
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- getf.exp GR_Delta_Exp = FR_Delta // Get signexp of y-1 for exp calc
- fmpy.s1 FR_W4 = FR_Wsq, FR_Wsq
- nop.i 999
+(p0) ldfe FR_L_lo = [GR_Table_Ptr],16
+//
+// Load P_8
+// Load P_4
+//
+(p0) fmpy.s1 FR_half_W = FR_Half, FR_W
+ nop.i 999 ;;
}
{ .mfi
- add GR_Table_Ptr = 0x0, GR_table_base // Constants_exp_64_Arg
- fmpy.s1 FR_W3 = FR_Wsq, FR_W
- nop.i 999
+ nop.m 999
+(p0) fma.s1 FR_poly_lo = FR_W, FR_P_8,FR_P_7
+ nop.i 999
}
-;;
-
{ .mfi
- nop.m 999
- fmpy.s1 FR_half_W = FR_Half, FR_W
- nop.i 999
+ nop.m 999
+(p0) fma.s1 FR_poly = FR_W, FR_P_4, FR_P_3
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- ldfe FR_L_hi = [GR_Table_Ptr],16
- fma.s1 FR_poly_lo = FR_W, FR_P_8,FR_P_7
- nop.i 999
+ nop.m 999
+(p0) fnma.s1 FR_Y_hi = FR_W, FR_half_W, FR_W
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
- fma.s1 FR_poly = FR_W, FR_P_4, FR_P_3
- nop.i 999
+ nop.m 999
+//
+// W4 = Wsq * Wsq
+// poly = w *poly + P_2
+//
+(p0) fma.s1 FR_poly_lo = FR_W, FR_poly_lo, FR_P_6
+ nop.i 999
}
-;;
-
{ .mfi
- ldfe FR_L_lo = [GR_Table_Ptr],16
- fnma.s1 FR_Y_hi = FR_W, FR_half_W, FR_W
- nop.i 999
+ nop.m 999
+(p0) fma.s1 FR_poly = FR_W, FR_poly, FR_P_2
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 999
- fma.s1 FR_poly_lo = FR_W, FR_poly_lo, FR_P_6
- nop.i 999
+ nop.m 999
+(p0) fsub.s1 FR_Y_lo = FR_W, FR_Y_hi
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
- fma.s1 FR_poly = FR_W, FR_poly, FR_P_2
- nop.i 999
+ nop.m 999
+//
+// poly = w * poly + P_1
+// w3 = wsq * w
+//
+(p0) fma.s1 FR_poly_lo = FR_W, FR_poly_lo, FR_P_5
+ nop.i 999
}
-;;
-
{ .mfi
- nop.m 999
- fsub.s1 FR_Y_lo = FR_W, FR_Y_hi
- nop.i 999
+ nop.m 999
+//
+// poly_lo = w * poly_lo + P_6
+// Y_lo = W - Y_hi
+//
+(p0) fma.s1 FR_poly = FR_W, FR_poly, FR_P_1
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 999
- fma.s1 FR_poly_lo = FR_W, FR_poly_lo, FR_P_5
- nop.i 999
+ nop.m 999
+(p0) fnma.s1 FR_Y_lo = FR_W, FR_half_W, FR_Y_lo
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
- fma.s1 FR_poly = FR_W, FR_poly, FR_P_1
- nop.i 999
+ nop.m 999
+//
+// poly_lo = w * poly_lo +
+// Y_lo = Y_lo - w * (1/2)w
+//
+(p0) fma.s1 FR_poly = FR_poly_lo, FR_W4, FR_poly
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 999
- fnma.s1 FR_Y_lo = FR_W, FR_half_W, FR_Y_lo
- nop.i 999
+ nop.m 999
+//
+// Y_lo = (W-Y_hi) - w * (1/2)w
+// poly = W4* poly_lo + poly
+//
+(p0) fma.s1 FR_Y_lo = FR_poly, FR_W3, FR_Y_lo
+ nop.i 999 ;;
+}
+L(LOGL_RETURN):
+{ .mfi
+(p0) add GR_Expo_Range = 0x2,r0
+//
+// Load L_Inv
+// Load L_hi
+// Load L_lo
+// all long before they are needed.
+//
+//
+// kernel_log_80 computed ln(X)
+// and return logX_hi and logX_lo as results.
+// PR_pow_Safe set as well.
+//
+(p0) fmpy.s1 FR_X_lo = FR_Input_Y, FR_logx_lo
+//
+// Compute Y * (logX_hi + logX_lo)
+// P_hi -> X
+// P_lo -> X_cor
+// (Manipulate names so that inputs are in
+// the place kernel_exp expects them)
+// Set GR_Flag to 2
+// Set GR_Expo_Range to Double
+//
+// This function computes exp( x + x_cor)
+// Input FR 1: FR_X
+// Input FR 2: FR_X_cor
+// Input GR 1: GR_Flag
+// Input GR 2: GR_Expo_Range
+// Output FR 3: FR_Y_hi
+// Output FR 4: FR_Y_lo
+// Output FR 5: FR_Scale
+// Output PR 1: PR_Safe
+//
+(p0) cmp.eq.unc p15, p0 = r0, r0
}
;;
-{ .mfi
- nop.m 999
- fma.s1 FR_poly = FR_poly_lo, FR_W4, FR_poly
- nop.i 999
+{ .mmi
+(p0) addl GR_W1_ptr = @ltoff(Constants_exp_64_W1#), gp
+(p0) addl GR_W2_ptr = @ltoff(Constants_exp_64_W2#), gp
+(p0) add GR_Flag = 0x2,r0
}
;;
-{ .mfi
- nop.m 999
- fma.s1 FR_Y_lo = FR_poly, FR_W3, FR_Y_lo
- nop.i 999
+{ .mmi
+ ld8 GR_W1_ptr = [GR_W1_ptr]
+ ld8 GR_W2_ptr = [GR_W2_ptr]
+(p0) cmp.ne.unc p7, p0 = 0x1, GR_Flag
}
;;
+{ .mlx
+ nop.m 999
+(p0) movl GR_Mask = 0x1FFFF ;;
+}
-LOGL_RETURN:
-// Common code for completion of both logx paths
+{ .mlx
+ nop.m 999
+(p0) movl GR_BIAS = 0x0FFFF ;;
+}
+{ .mfi
+ nop.m 999
//
-// L_hi, L_lo already loaded.
-//
-//
-// kernel_log_80 computed ln(X)
-// and return logX_hi and logX_lo as results.
-// PR_pow_Safe set as well.
+// X_lo = Y * logX_lo
//
+(p0) fma.s1 FR_P_hi = FR_Input_Y, FR_logx_hi,FR_X_lo
+ nop.i 999 ;;
+}
+{ .mfi
+ nop.m 999
//
-// Compute Y * (logX_hi + logX_lo)
-// P_hi -> X
-// P_lo -> X_cor
-// (Manipulate names so that inputs are in
-// the place kernel_exp expects them)
+// Set Safe=True
+// Flag is always 2 for this routine
//
-// This function computes exp( x + x_cor)
-// Input FR 1: FR_X
-// Input FR 2: FR_X_cor
-// Output FR 3: FR_Y_hi
-// Output FR 4: FR_Y_lo
-// Output FR 5: FR_Scale
-// Output PR 1: PR_Safe
+(p0) fmpy.s1 FR_float_N = FR_X, FR_L_Inv
+ nop.i 999
+}
+{ .mfi
+ nop.m 999
//
-// P15 is True
+// X_hi = Y * logX_hi + X_lo
+// Set GR_Flag = 2 for exp(x + xcor)
//
-// Load constants used in computing N using right-shift technique
-{ .mlx
- mov GR_exp_2tom51 = 0xffff-51
- movl GR_sig_inv_ln2 = 0xb8aa3b295c17f0bc // significand of 1/ln2
+(p0) fms.s1 FR_P_lo= FR_Input_Y, FR_logx_hi, FR_P_hi
+ nop.i 999 ;;
}
-{ .mlx
- add GR_Special_Exp = -50,GR_exp_bias
- movl GR_rshf_2to51 = 0x4718000000000000 // 1.10000 2^(63+51)
+{ .mmi
+ nop.m 999 ;;
+(p0) getf.exp GR_Expo_X = FR_X
+ nop.i 999 ;;
}
-;;
-
+{ .mfi
+(p0) and GR_Expo_X = GR_Expo_X, GR_Mask
//
+// Calculate unBIASed exponent of X
// Point to Table of W1s
// Point to Table of W2s
//
-{ .mmi
- add GR_W1_ptr = 0x2b0, GR_table_base // Constants_exp_64_W1
- add GR_W2_ptr = 0x4b0, GR_table_base // Constants_exp_64_W2
- cmp.le p6,p0= GR_Delta_Exp,GR_Special_Exp
-};;
-
-// Form two constants we need
-// 1/ln2 * 2^63 to compute w = x * 1/ln2 * 128
-// 1.1000..000 * 2^(63+63-12) to right shift int(N) into the significand
-
+(p0) fcvt.fx.s1 FR_N = FR_float_N
+ nop.i 999 ;;
+}
{ .mfi
- setf.sig FR_INV_LN2_2TO63 = GR_sig_inv_ln2 // form 1/ln2 * 2^63
- nop.f 999
- and GR_Delta_Exp=GR_Delta_Exp,GR_exp_mask // Get exponent of y-1
+ nop.m 999
+(p0) fadd.s1 FR_P_lo = FR_P_lo, FR_X_lo
+//
+// Float_N = X * L_Inv
+// Create exponent BIAS
+// Get BIASed exponent of X
+//
+(p0) sub GR_Expo_X = GR_Expo_X, GR_BIAS ;;
}
-{ .mlx
- setf.d FR_RSHF_2TO51 = GR_rshf_2to51 // Form const 1.1000 * 2^(63+51)
- movl GR_rshf = 0x43e8000000000000 // 1.10000 2^63 for right shift
+{ .mib
+(p0) cmp.gt.unc p9, p0 = -6, GR_Expo_X
+ nop.i 999
+//
+// N = fcvt.fx(float_N)
+// If -6 > Expo_X, set P9
+//
+(p9) br.cond.spnt L(EXPL_SMALL)
}
;;
-{ .mfi
- nop.m 999
- fmpy.s1 FR_X_lo = FR_Input_Y, FR_logx_lo // logx_lo is Y_lo
- cmp.eq p15, p0= r0, r0 // Set p15, assume safe
-};;
-
+//
+// If expo_X < -6 goto exp_small
+//
{ .mmi
- setf.exp FR_2TOM51 = GR_exp_2tom51 // Form 2^-51 for scaling float_N
- setf.d FR_RSHF = GR_rshf // Form right shift const 1.1000 * 2^63
- add GR_Table_Ptr1 = 0x50, GR_table_base // Constants_exp_64_P for
- // EXPL_SMALL path
+ nop.m 999
+(p0) addl GR_T1_ptr = @ltoff(Constants_exp_64_T1#), gp
+(p0) cmp.lt.unc p10, p0 = 14, GR_Expo_X
}
;;
{ .mmi
- ldfe FR_P_6 = [GR_Table_Ptr1],16 // Load P_6 for EXPL_SMALL path
-;;
- ldfe FR_P_5 = [GR_Table_Ptr1],16 // Load P_5 for EXPL_SMALL path
+ ld8 GR_T1_ptr = [GR_T1_ptr]
+ nop.m 999
nop.i 999
}
;;
-{ .mfi
- ldfe FR_P_4 = [GR_Table_Ptr1],16 // Load P_4 for EXPL_SMALL path
- fma.s1 FR_P_hi = FR_Input_Y, FR_logx_hi,FR_X_lo // logx_hi ix Y_hi
- nop.i 999
+{ .mib
+ nop.m 999
+ nop.i 999
+//
+// If 14 < Expo_X, set P10
+// Create pointer to T1 table
+//
+(p10) br.cond.spnt L(EXPL_HUGE) ;;
}
-;;
+
{ .mmi
- ldfe FR_P_3 = [GR_Table_Ptr1],16 // Load P_3 for EXPL_SMALL path
-;;
- ldfe FR_P_2 = [GR_Table_Ptr1],16 // Load P_2 for EXPL_SMALL path
+(p0) addl GR_Table_Ptr = @ltoff(Constants_exp_64_Exponents#), gp
+(p0) addl GR_T2_ptr = @ltoff(Constants_exp_64_T2#), gp
nop.i 999
}
;;
-// N = X * Inv_log2_by_2^12
-// By adding 1.10...0*2^63 we shift and get round_int(N_signif) in significand.
-// We actually add 1.10...0*2^51 to X * Inv_log2 to do the same thing.
-{ .mfi
- ldfe FR_P_1 = [GR_Table_Ptr1] // Load P_1 for EXPL_SMALL path
- fma.s1 FR_N = FR_X, FR_INV_LN2_2TO63, FR_RSHF_2TO51
- nop.i 999
-}
-{ .mfb
- nop.m 999
- fms.s1 FR_P_lo= FR_Input_Y, FR_logx_hi, FR_P_hi // P_hi is X
-(p6) br.cond.spnt POWL_Y_ALMOST_1 // Branch if |y-1| < 2^-50
-}
-;;
-
{ .mmi
- getf.exp GR_Expo_X = FR_X
- add GR_T1_ptr = 0x0b0, GR_table_base // Constants_exp_64_T1
- add GR_T2_ptr = 0x1b0, GR_table_base // Constants_exp_64_T2
+ ld8 GR_Table_Ptr = [GR_Table_Ptr]
+ ld8 GR_T2_ptr = [GR_T2_ptr]
+ nop.i 999
}
;;
-// float_N = round_int(N)
-// The signficand of N contains the rounded integer part of X * 2^12/ln2,
-// as a twos complement number in the lower bits (that is, it may be negative).
-// That twos complement number (called N) is put into GR_N_fix.
-
-// Since N is scaled by 2^51, it must be multiplied by 2^-51
-// before the shift constant 1.10000 * 2^63 is subtracted to yield float_N.
-// Thus, float_N contains the floating point version of N
-
-{ .mfi
- add GR_Table_Ptr = 0x20, GR_table_base // Constants_exp_64_A
- fms.s1 FR_float_N = FR_N, FR_2TOM51, FR_RSHF // Form float_N
- nop.i 999
-}
-// Create low part of Y(ln(x)_hi + ln(x)_lo) as P_lo
-{ .mfi
- mov GR_Big_Pos_Exp = 0x3ffe // 16382, largest safe exponent
- fadd.s1 FR_P_lo = FR_P_lo, FR_X_lo
- mov GR_Big_Neg_Exp = -0x3ffd // -16381 smallest safe exponent
-};;
-
-{ .mfi
- nop.m 999
- fmpy.s1 FR_rsq = FR_X, FR_X // rsq = X*X for EXPL_SMALL path
- mov GR_vsm_expo = -70 // Exponent for very small path
+{ .mmi
+(p0) shladd GR_Table_Ptr = GR_Expo_Range,4,GR_Table_Ptr ;;
+//
+// Adjust T1_ptr by x 4 for single-precision values
+// Adjust T2_ptr by x 4 for single-precision values
+//
+(p0) ld8 GR_Big_Pos_Exp = [GR_Table_Ptr],8
+ nop.i 999 ;;
}
+//
+// Load double W1
+// Load +max exponent
+//
{ .mfi
- nop.m 999
- fma.s1 FR_poly_lo = FR_P_6, FR_X, FR_P_5 // poly_lo for EXPL_SMALL path
- add GR_temp = 0x1,r0 // For tiny signif if small path
+(p0) ld8 GR_Big_Neg_Exp = [GR_Table_Ptr],0
+//
+// If 14 < Expo_X, goto exp_huge
+//
+(p0) fcvt.xf FR_float_N = FR_N
+ nop.i 999
}
;;
//
-// If expo_X < -6 goto exp_small
+// Load double W2
+// Load -max exponent
+// Load ptr to A's
//
+
{ .mmi
- getf.sig GR_N_fix = FR_N
- ldfe FR_A_3 = [GR_Table_Ptr],16 // Load A_3
- and GR_Expo_X = GR_Expo_X, GR_exp_mask // Get exponent of X
+(p0) getf.sig GR_N_fix = FR_N
+(p0) addl GR_Table_Ptr = @ltoff(Constants_exp_64_A#), gp
+ nop.i 999
}
;;
-{ .mfi
- ldfe FR_A_2 = [GR_Table_Ptr],16 // Load A_2
- nop.f 999
- sub GR_Expo_X = GR_Expo_X, GR_exp_bias // Get true exponent of X
+{ .mmi
+ ld8 GR_Table_Ptr = [GR_Table_Ptr]
+ nop.m 999
+ nop.i 999
}
;;
//
-// If -6 > Expo_X, set P9 and branch
+// Load single T1
+// Load single T2
+// W_1_p1 = W_1 + 1
//
-{ .mfb
- cmp.gt p9, p0 = -6, GR_Expo_X
- fnma.s1 FR_r = FR_L_hi, FR_float_N, FR_X // r = X - L_hi * float_N
-(p9) br.cond.spnt EXPL_SMALL // Branch if |X| < 2^-6
+{ .mmi
+(p0) ldfe FR_A_3 = [GR_Table_Ptr],16 ;;
+//
+// Load A_3
+// if k > big_pos_exp, set p14 and Safe=False
+//
+(p0) ldfe FR_A_2 = [GR_Table_Ptr],16
+(p0) extr.u GR_M1 = GR_N_fix, 6, 6
}
-;;
-
+{ .mmi
+ nop.m 999 ;;
+(p0) shladd GR_W1_ptr = GR_M1,3,GR_W1_ptr
//
-// If 14 <= Expo_X, set P10
+// float_N = fcvt.xf(N)
+// N_fix = significand of N
+// Create pointer to T2 table
//
-{ .mib
- cmp.le p10, p0 = 14, GR_Expo_X
- nop.i 999
-(p10) br.cond.spnt EXPL_HUGE // Branch if |X| >= 2^14
+(p0) extr.u GR_M2 = GR_N_fix, 0, 6
}
-;;
-
//
-// Load single T1
-// Load single T2
-// W_1_p1 = W_1 + 1
+// r = r + X_cor
+// Adjust W1_ptr by x 8 for double-precision values
+// Adjust W2_ptr by x 8 for double-precision values
+// Adjust Table_ptr by Expo_Rangex16
//
{ .mmi
- nop.m 999
- nop.m 999
- extr.u GR_M1 = GR_N_fix, 6, 6 // Extract index M_1
+(p0) shladd GR_T1_ptr = GR_M1,2,GR_T1_ptr ;;
+(p0) ldfd FR_W1 = [GR_W1_ptr],0
+(p0) shladd GR_W2_ptr = GR_M2,3,GR_W2_ptr
}
-;;
-
//
-// k = extr.u(N_fix,0,6)
+// Load ptr to A's
//
-{ .mmi
- shladd GR_W1_ptr = GR_M1,3,GR_W1_ptr // Point to W1
- shladd GR_T1_ptr = GR_M1,2,GR_T1_ptr // Point to T1
- extr.u GR_M2 = GR_N_fix, 0, 6 // Extract index M_2
+{ .mfi
+(p0) ldfs FR_T1 = [GR_T1_ptr],0
+(p0) fnma.s1 FR_r = FR_L_hi, FR_float_N, FR_X
+(p0) shladd GR_T2_ptr = GR_M2,2,GR_T2_ptr ;;
}
-;;
-
-// N_fix is only correct up to 50 bits because of our right shift technique.
-// Actually in the normal path we will have restricted K to about 14 bits.
-// Somewhat arbitrarily we extract 32 bits.
{ .mmi
- ldfd FR_W1 = [GR_W1_ptr]
- shladd GR_W2_ptr = GR_M2,3,GR_W2_ptr // Point to W2
- extr GR_k = GR_N_fix, 12, 32 // Extract k
+(p0) ldfd FR_W2 = [GR_W2_ptr],0
+(p0) ldfs FR_T2 = [GR_T2_ptr],0
+//
+// r = x - L_hi * float_N
+// M2 = extr.u(N_fix,0,6)
+// M1 = extr.u(N_fix,6,6)
+//
+(p0) extr GR_k = GR_N_fix, 12, 52 ;;
}
-;;
-
+//
+// Load A_1
+// poly = A_3 * r + A_2
+// rsq = r*r
+//
+{ .mii
+(p0) add GR_BIAS_p_k = GR_BIAS, GR_k
+(p0) cmp.gt.unc p14,p15 = GR_k,GR_Big_Pos_Exp ;;
+(p15) cmp.lt p14,p15 = GR_k,GR_Big_Neg_Exp
+}
+//
+// BIAS_p_K = BIAS + k
+// T = T1 * T2
+//
{ .mfi
- ldfs FR_T1 = [GR_T1_ptr]
- fnma.s1 FR_r = FR_L_lo, FR_float_N, FR_r
- shladd GR_T2_ptr = GR_M2,2,GR_T2_ptr // Point to T2
+(p0) setf.exp FR_Scale = GR_BIAS_p_k
+ nop.f 999
+ nop.i 999 ;;
}
{ .mfi
- add GR_exp_bias_p_k = GR_exp_bias, GR_k
- nop.f 999
- cmp.gt p14,p15 = GR_k,GR_Big_Pos_Exp
+ nop.m 999
+(p0) fnma.s1 FR_r = FR_L_lo, FR_float_N, FR_r
+ nop.i 999
}
-;;
-
//
-// if k < big_neg_exp, set p14 and Safe=False
+// W = W_1_p1 * W2 + W1
//
-{ .mmi
- ldfs FR_T2 = [GR_T2_ptr]
-(p15) cmp.lt p14,p15 = GR_k,GR_Big_Neg_Exp
- nop.i 999
+{ .mfi
+(p0) ldfe FR_A_1 = [GR_Table_Ptr],16
+ nop.f 999
+ nop.i 999 ;;
}
-;;
-
-{ .mmi
- setf.exp FR_Scale = GR_exp_bias_p_k
- ldfd FR_W2 = [GR_W2_ptr]
- nop.i 999
+{ .mfi
+ nop.m 999
+(p0) fadd.s1 FR_W_1_p1 = FR_W1, f1
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- ldfe FR_A_1 = [GR_Table_Ptr],16
- fadd.s1 FR_r = FR_r, FR_X_cor
- nop.i 999
+ nop.m 999
+//
+// k = extr.u(N_fix,0,6)
+// r = r - N * L_lo
+// Load ptr to Table of exponent thresholds.
+//
+(p0) fadd.s1 FR_r = FR_r, FR_X_cor
+ nop.i 999
}
-;;
-
{ .mfi
- nop.m 999
- fadd.s1 FR_W_1_p1 = FR_W1, f1
- nop.i 999
+ nop.m 999
+(p0) fmpy.s1 FR_T = FR_T1, FR_T2
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 999
- fma.s1 FR_poly = FR_r, FR_A_3, FR_A_2
- nop.i 999
+ nop.m 999
+//
+// if k < big_neg_exp, set p14 and Safe=False
+// Load A_2
+//
+(p0) fma.s1 FR_W = FR_W2, FR_W_1_p1, FR_W1
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
- fmpy.s1 FR_rsq = FR_r, FR_r
- nop.i 999
+ nop.m 999
+(p0) fma.s1 FR_poly = FR_r, FR_A_3, FR_A_2
+ nop.i 999
}
-;;
-
{ .mfi
- nop.m 999
- fmpy.s1 FR_T = FR_T1, FR_T2
- nop.i 999
+ nop.m 999
+(p0) fmpy.s1 FR_rsq = FR_r, FR_r
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 999
- fma.s1 FR_W = FR_W2, FR_W_1_p1, FR_W1
- nop.i 999
+ nop.m 999
+(p0) mov FR_Y_hi = FR_T
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 999
- fma.s1 FR_TMP1 = FR_Scale, FR_Sgn, f0
- nop.i 999
+ nop.m 999
+//
+// Scale = set_exp(BIAS_p_k)
+// poly = r * poly + A_1
+//
+(p0) fadd.s1 FR_Wp1 = FR_W, f1
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 999
- fma.s1 FR_poly = FR_r, FR_poly, FR_A_1
- nop.i 999
+ nop.m 999
+(p0) fma.s1 FR_poly = FR_r, FR_poly, FR_A_1
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 999
- fma.s1 FR_TMP2 = FR_T, f1, f0 // TMP2 = Y_hi = T
- nop.i 999
+ nop.m 999
+(p0) fma.s1 FR_poly = FR_rsq, FR_poly,FR_r
+ nop.i 999 ;;
}
-;;
-
{ .mfi
+ nop.m 999
+//
+// Wp1 = W + 1
+// poly = rsq * poly + rk
+//
+(p0) fma.s1 FR_Y_lo = FR_Wp1, FR_poly, FR_W
+ nop.i 999 ;;
+}
+{ .mfb
+ nop.m 999
+//
+// Y_lo = poly * Wp1 + W
+// Y_hi = T
+//
+(p0) fmpy.s1 FR_Y_lo = FR_Y_lo, FR_T
+//
+// Y_lo = T * Y_lo
+//
+(p0) br.cond.sptk L(EXPL_RETURN) ;;
+}
+
+L(EXPL_SMALL):
+
+//
+// r4 = rsq * rsq
+//
+
+{ .mmi
nop.m 999
- fadd.s1 FR_Wp1 = FR_W, f1
+(p0) addl GR_Table_Ptr1 = @ltoff(Constants_exp_64_P), gp
nop.i 999
}
;;
-{ .mfi
+{ .mmi
+ ld8 GR_Table_Ptr1 = [GR_Table_Ptr1]
nop.m 999
- fma.s1 FR_poly = FR_rsq, FR_poly,FR_r
nop.i 999
}
;;
-{ .mfi
- nop.m 999
- fma.s1 FR_Tscale = FR_T, FR_TMP1, f0 // Scale * Sgn * T
- nop.i 999
+{ .mmf
+ nop.m 999
+(p0) ldfe FR_P_6 = [GR_Table_Ptr1],16
+//
+// Return
+//
+(p0) fadd.s1 FR_r = FR_X,f0 ;;
}
-{ .mfi
+
+{ .mmi
nop.m 999
- fma.s1 FR_Y_lo = FR_Wp1, FR_poly, FR_W
+(p0) addl GR_Table_Ptr = @ltoff(Constants_exp_64_Exponents#), gp
nop.i 999
}
;;
-{ .mfb
- nop.m 999
- fmpy.s1 FR_TMP3 = FR_Y_lo, FR_Tscale
- br.cond.sptk POWL_64_SHARED
+{ .mmi
+ ld8 GR_Table_Ptr = [GR_Table_Ptr]
+(p0) ldfe FR_P_5 = [GR_Table_Ptr1],16
+ nop.i 999
}
;;
-
-EXPL_SMALL:
-// Here if |ylogx| < 2^-6
//
-// Begin creating lsb to perturb final result
+// Is input very small?
+// Load P_5
+//
+{ .mii
+(p0) ldfe FR_P_4 = [GR_Table_Ptr1],16
+(p0) add GR_Table_Ptr = 0x040,GR_Table_Ptr ;;
+(p0) shladd GR_Table_Ptr = GR_Expo_Range,3,GR_Table_Ptr ;;
+}
+{ .mmb
+(p0) ldfe FR_P_3 = [GR_Table_Ptr1],16
//
+// Adjust ptr.
+//
+(p0) ld8 GR_vsm_expo = [GR_Table_Ptr],0
+ nop.b 999 ;;
+}
{ .mfi
- setf.sig FR_temp = GR_temp
- fma.s1 FR_poly_lo = FR_poly_lo, FR_X, FR_P_4
- cmp.lt p12, p0 = GR_Expo_X, GR_vsm_expo // Test |ylogx| < 2^-70
+ nop.m 999
+//
+// r = X (don't seem to need X_Cor)
+// Load the threshold exponents
+//
+(p0) fmpy.s1 FR_rsq = FR_r, FR_r
+ nop.i 999 ;;
}
+//
+// Load the negative integer
+// Load P_5
+//
{ .mfi
- nop.m 999
- fma.s1 FR_poly_hi = FR_P_2, FR_X, FR_P_1
- nop.i 999
+(p0) cmp.lt.unc p12, p0 = GR_Expo_X, GR_vsm_expo
+ nop.f 999
+ nop.i 999 ;;
+}
+{ .mfb
+ nop.m 999
+//
+// rsq = r * r
+// Offset into exponents
+//
+(p0) fmpy.s1 FR_r4 = FR_rsq, FR_rsq
+(p12) br.cond.spnt L(EXPL_VERY_SMALL) ;;
}
-;;
-
{ .mfi
- nop.m 999
- fmpy.s1 FR_TMP2 = f1, f1
- nop.i 999
+(p0) ldfe FR_P_2 = [GR_Table_Ptr1],16
+//
+// Load p4,p3,p2,p1
+//
+(p0) fma.s1 FR_poly_lo = FR_P_6, FR_r, FR_P_5
+//
+// Y_lo = r4 * poly_lo + poly_hi
+// Scale = 1.0
+//
+(p0) add GR_temp = 0x1,r0 ;;
}
+{ .mmf
+ nop.m 999
+(p0) ldfe FR_P_1 = [GR_Table_Ptr1],0
+(p0) mov FR_Scale = f1
+}
+//
+// Begin creating lsb to perturb final result
+//
{ .mfi
- nop.m 999
- fmpy.s1 FR_TMP1 = FR_Sgn, f1
- nop.i 999
+(p0) setf.sig FR_temp = GR_temp
+(p0) mov FR_Y_hi = f1
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 999
- fmpy.s1 FR_r4 = FR_rsq, FR_rsq
-(p12) cmp.eq p15, p0 = r0, r0 // Set safe if |ylogx| < 2^-70
+ nop.m 999
+//
+// poly_lo = p_5 + p_6 * r
+// poly_hi = p_1 + p_2 * r
+//
+(p0) fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_P_4
+ nop.i 999 ;;
}
-{ .mfb
- nop.m 999
-(p12) fmpy.s1 FR_TMP3 = FR_Sgn, FR_X
-(p12) br.cond.spnt POWL_64_SHARED // Branch if |ylogx| < 2^-70
+{ .mfi
+ nop.m 999
+//
+// poly_lo = p_4 + poly_lo * r
+// poly_hi = r + poly_hi * rsq
+//
+(p0) fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_P_3
+ nop.i 999
}
-;;
-
{ .mfi
- nop.m 999
- fma.s1 FR_poly_lo = FR_poly_lo, FR_X, FR_P_3
- nop.i 999
+ nop.m 999
+(p0) fma.s1 FR_poly_hi = FR_P_2, FR_r, FR_P_1
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
- fma.s1 FR_poly_hi = FR_poly_hi, FR_rsq, FR_X
- nop.i 999
+ nop.m 999
+(p0) fma.s1 FR_poly_hi = FR_poly_hi, FR_rsq, FR_r
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 999
- fma.s1 FR_Y_lo = FR_poly_lo, FR_r4, FR_poly_hi
- nop.i 999
+ nop.m 999
+//
+// poly_lo = p_3 + poly_lo * r
+// Y_hi = 1, always
+//
+(p0) fma.s1 FR_Y_lo = FR_poly_lo, FR_r4, FR_poly_hi
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 999
- fmpy.s1 FR_TMP3 = FR_Y_lo, FR_TMP1 // Add sign info
- nop.i 999
+ nop.m 999
+//
+// Set lsb in fp register
+//
+(p0) for FR_temp = FR_Y_lo,FR_temp
+ nop.i 999 ;;
}
-;;
-
+{ .mfb
+ nop.m 999
//
// Toggle on last bit of Y_lo
+//
+(p0) fmerge.se FR_Y_lo = FR_Y_lo,FR_temp
+//
// Set lsb of Y_lo to 1
//
+(p0) br.cond.sptk L(EXPL_RETURN) ;;
+}
+L(EXPL_VERY_SMALL):
{ .mfi
- nop.m 999
- for FR_temp = FR_Y_lo,FR_temp
- nop.i 999
+ nop.m 999
+(p0) mov FR_Y_lo = FR_r
+(p0) cmp.eq.unc p15, p0 = r0, r0
}
-;;
-
+{ .mfi
+ nop.m 999
+(p0) mov FR_Scale = f1
+ nop.i 999
+};;
{ .mfb
- nop.m 999
- fmerge.se FR_TMP3 = FR_TMP3,FR_temp
- br.cond.sptk POWL_64_SHARED
+ nop.m 999
+(p0) mov FR_Y_hi = f1
+//
+// If flag_not_1,
+// Y_hi = 1.0
+// Y_lo = X + X_cor
+// PR_Safe = true
+//
+(p0) br.cond.sptk L(EXPL_RETURN) ;;
}
-;;
-
-
-EXPL_HUGE:
-// Here if |ylogx| >= 2^14
+L(EXPL_HUGE):
{ .mfi
- mov GR_temp = 0x0A1DC // If X < 0, exponent -24100
- fcmp.gt.s1 p12, p13 = FR_X, f0 // Test X > 0
- cmp.eq p14, p15 = r0, r0 // Set Safe to false
+ nop.m 999
+//
+// Return for flag=2
+//
+(p0) fcmp.gt.unc.s1 p12, p13 = FR_X, f0
+(p0) cmp.eq.unc p14, p15 = r0, r0 ;;
}
-;;
-
-{ .mmi
-(p12) mov GR_Mask = 0x15DC0 // If X > 0, exponent +24000
-(p13) mov GR_Mask = 0x0A240 // If X < 0, exponent -24000
- nop.i 999
+{ .mlx
+ nop.m 999
+//
+// Set Safe to false
+// Is x > 0
+//
+(p12) movl GR_Mask = 0x15DC0 ;;
}
-;;
-
-{ .mmf
- setf.exp FR_TMP2 = GR_Mask // Form Y_hi = TMP2
-(p13) setf.exp FR_Y_lo = GR_temp // If X < 0, Y_lo = 2^-24100
-(p12) mov FR_Y_lo = f1 // IF X > 0, Y_lo = 1.0
+{ .mlx
+(p12) setf.exp FR_Y_hi = GR_Mask
+(p13) movl GR_Mask = 0xA240 ;;
+}
+{ .mlx
+(p13) setf.exp FR_Y_hi = GR_Mask
+//
+// x > 0: Create mask for Y_hi = 2**(24,000)
+// x <= 0: Create mask for Y_hi = 2**(-24,000)
+//
+(p13) movl GR_temp = 0xA1DC ;;
}
-;;
-
{ .mfi
- nop.m 999
- fmpy.s1 FR_TMP1 = FR_TMP2, FR_Sgn // TMP1 = Y_hi * Sgn
- nop.i 999
+(p13) setf.exp FR_Y_lo = GR_temp
+//
+// x < =0: Create mask for 2**(-24,100)
+// x <= 0: Y_lo = w**(-24,100)
+//
+(p12) mov FR_Y_lo = f1
+ nop.i 999 ;;
}
-;;
-
-{ .mfb
- nop.m 999
- fmpy.s1 FR_TMP3 = FR_Y_lo,FR_TMP1 // TMP3 = Y_lo * (Y_hi * Sgn)
- br.cond.sptk POWL_64_SHARED
+{ .mfi
+ nop.m 999
+(p12) mov FR_Scale = FR_Y_hi
+ nop.i 999 ;;
}
-;;
-
-POWL_Y_ALMOST_1:
-// Here if delta = |y-1| < 2^-50
+{ .mfi
+ nop.m 999
//
-// x**(1 + delta) = x * e (ln(x)*delta) = x ( 1 + ln(x) * delta)
+// x > 0: Y_lo = 1.0
+// x > 0: Scale = 2**(24,000)
//
-// Computation will be safe for 2^-16381 <= x < 2^16383
-
+(p13) mov FR_Scale = FR_Y_hi
+ nop.i 999 ;;
+}
+L(EXPL_RETURN):
{ .mfi
- mov GR_exp_ynear1_oflow = 0xffff + 16383
- fma.s1 FR_TMP1 = FR_Input_X,FR_Delta,f0
- and GR_exp_x = GR_exp_mask, GR_signexp_x
+ nop.m 999
+//
+// Scale = 2**(24,000)
+//
+//
+// exp(y *ln(x)) almost complete
+// FR_Scale is Scale
+// f34 is Z_hi
+// f35 is Z_lo
+//
+(p0) fmpy.s1 FR_Sgn = FR_Scale, FR_Sgn
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- cmp.lt p15, p14 = GR_exp_x, GR_exp_ynear1_oflow
- fma.s1 FR_TMP2 = FR_logx_hi,f1,FR_X_lo
- mov GR_exp_ynear1_uflow = 0xffff - 16381
+ nop.m 999
+//
+// sgn * scale
+//
+(p0) fmpy.s1 FR_Y_lo = FR_Y_lo,FR_Sgn
+ nop.i 999 ;;
}
-;;
-
{ .mfb
-(p15) cmp.ge p15, p14 = GR_exp_x, GR_exp_ynear1_uflow
- fma.s1 FR_TMP3 = FR_Input_X,f1,f0
- br.cond.sptk POWL_64_SHARED
-};;
-
-POWL_64_SQUARE:
+ nop.m 999
+//
+// Z_lo * (sgn * scale)
//
-// Here if x not zero and y=2.
+(p0) fma.s0 FR_Result = FR_Y_hi, FR_Sgn, FR_Y_lo
//
-// Setup for multipath code
+// Z_hi * (sgn * scale) + Z_lo
//
+(p15) br.cond.sptk L(POWL_64_RETURN) ;;
+}
{ .mfi
- mov GR_exp_square_oflow = 0xffff + 8192 // Exponent where x*x overflows
- fmerge.se FR_TMP1 = FR_Input_X, FR_Input_X
- and GR_exp_x = GR_exp_mask, GR_signexp_x // Get exponent of x
+ nop.m 999
+(p0) fsetc.s3 0x7F,0x01
+ nop.i 999
+}
+{ .mlx
+ nop.m 999
+//
+// Z_hi * (sgn * scale) + Z_lo with wre & td
+// Z_hi * (sgn * scale) + Z_lo with fz & td
+//
+(p0) movl GR_T1_ptr = 0x00000000013FFF ;;
}
-;;
-
{ .mfi
- cmp.lt p15, p14 = GR_exp_x, GR_exp_square_oflow // Decide safe/unsafe
- fmerge.se FR_TMP2 = FR_Input_X, FR_Input_X
- mov GR_exp_square_uflow = 0xffff - 8191 // Exponent where x*x underflows
+ nop.m 999
+(p0) fma.s3 FR_Result_small = FR_Y_hi, FR_Sgn, FR_Y_lo
+ nop.i 999
}
-;;
-
{ .mfi
-(p15) cmp.ge p15, p14 = GR_exp_x, GR_exp_square_uflow // Decide safe/unsafe
- fma.s1 FR_TMP3 = f0,f0,f0
- nop.i 999
+ nop.m 999
+(p0) fsetc.s3 0x7F,0x40
+ nop.i 999 ;;
}
-;;
-
+{ .mfi
+ nop.m 999
//
-// This is the shared path that will set overflow and underflow.
+// Return if no danger of over of underflow.
//
-POWL_64_SHARED:
-
+(p0) fsetc.s2 0x7F,0x42
+ nop.i 999;;
+}
+{ .mfi
+ nop.m 999
//
-// Return if no danger of over or underflow.
+// S0 user supplied status
+// S2 user supplied status + WRE + TD (Overflows)
+// S3 user supplied status + FZ + TD (Underflows)
//
-{ .mfb
- nop.m 999
- fma.s0 FR_Result = FR_TMP1, FR_TMP2, FR_TMP3
-(p15) br.ret.sptk b0 // Main path return if certain no over/underflow
+(p0) fma.s2 FR_Result_big = FR_Y_hi, FR_Sgn, FR_Y_lo
+ nop.i 999 ;;
}
-;;
-
//
-// S0 user supplied status
-// S2 user supplied status + WRE + TD (Overflows)
-// S2 user supplied status + FZ + TD (Underflows)
+// S0 user supplied status
+// S2 user supplied status + WRE + TD (Overflows)
+// S3 user supplied status + FZ + TD (Underflows)
//
//
// If (Safe) is true, then
@@ -2022,742 +2430,973 @@ POWL_64_SHARED:
// No overflow or underflow here, but perhaps inexact.
// Return
// Else
-// Determine if overflow or underflow was raised.
-// Fetch +/- overflow threshold for IEEE double extended
-
+// Determine if overflow or underflow was raised.
+// Fetch +/- overflow threshold for IEEE single, double,
+// double extended
+//
{ .mfi
- nop.m 999
- fsetc.s2 0x7F,0x41 // For underflow test, set S2=User+TD+FTZ
- nop.i 999
+(p0) setf.exp FR_Big = GR_T1_ptr
+(p0) fsetc.s2 0x7F,0x40
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 999
- fma.s2 FR_Result_small = FR_TMP1, FR_TMP2, FR_TMP3
- nop.i 999
+ nop.m 999
+(p0) fclass.m.unc p11, p0 = FR_Result_small, 0x00F
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 999
- fsetc.s2 0x7F,0x42 // For overflow test, set S2=User+TD+WRE
- nop.i 999
+ nop.m 999
+(p0) fmerge.ns FR_NBig = FR_Big, FR_Big
+ nop.i 999
}
-;;
-
{ .mfi
- nop.m 999
- fma.s2 FR_Result_big = FR_TMP1, FR_TMP2,FR_TMP3
- nop.i 999
+ nop.m 999
+//
+// Create largest double exponent + 1.
+// Create smallest double exponent - 1.
+// Identify denormals
+//
+(p0) fcmp.ge.unc.s1 p8, p0 = FR_Result_big , FR_Big
+ nop.i 999 ;;
+}
+{ .mii
+ nop.m 999
+ nop.i 999 ;;
+//
+// fcmp: resultS2 <= - overflow threshold
+// fclass: resultS3 is denorm/unorm/0
+//
+(p8) mov GR_Parameter_TAG = 18 ;;
+}
+{ .mfb
+ nop.m 999
+//
+// fcmp: resultS2 >= + overflow threshold
+//
+(p0) fcmp.le.unc.s1 p9, p0 = FR_Result_big, FR_NBig
+(p8) br.cond.spnt __libm_error_region ;;
+}
+{ .mii
+ nop.m 999
+ nop.i 999 ;;
+(p9) mov GR_Parameter_TAG = 18
+}
+{ .mib
+ nop.m 999
+ nop.i 999
+(p9) br.cond.spnt __libm_error_region ;;
+}
+//
+// Report that pow overflowed - either +Inf, or -Inf
+//
+{ .mmb
+(p11) mov GR_Parameter_TAG = 19
+ nop.m 999
+(p11) br.cond.spnt __libm_error_region ;;
+}
+{ .mib
+ nop.m 999
+ nop.i 999
+//
+// Report that pow underflowed
+//
+(p0) br.cond.sptk L(POWL_64_RETURN) ;;
}
-;;
+
+L(POWL_64_SQUARE):
+// Here if x not zero and y=2.
+// Must call __libm_error_support for overflow or underflow
+//
+// S0 user supplied status
+// S2 user supplied status + WRE + TD (Overflows)
+// S3 user supplied status + FZ + TD (Underflows)
+//
{ .mfi
- nop.m 999
- fsetc.s2 0x7F,0x40 // Reset S2=User
- nop.i 999
+ nop.m 999
+(p0) fma.s0 FR_Result = FR_Input_X, FR_Input_X, f0
+ nop.i 999
}
-;;
-
{ .mfi
- nop.m 999
- fclass.m p11, p0 = FR_Result_small, 0x00F // Test small result unorm/zero
- nop.i 999
+ nop.m 999
+(p0) fsetc.s3 0x7F,0x01
+ nop.i 999
+}
+{ .mlx
+ nop.m 999
+(p0) movl GR_T1_ptr = 0x00000000013FFF ;;
}
-;;
-
{ .mfi
- nop.m 999
- fcmp.ge.s1 p8, p0 = FR_Result_big , FR_Big // Test >= + oflow threshold
- nop.i 999
+ nop.m 999
+(p0) fma.s3 FR_Result_small = FR_Input_X, FR_Input_X, f0
+ nop.i 999
}
-;;
-
-{ .mfb
-(p11) mov GR_Parameter_TAG = 19 // Set tag for underflow
- fcmp.le.s1 p9, p0 = FR_Result_big, FR_NBig // Test <= - oflow threshold
-(p11) br.cond.spnt __libm_error_region // Branch if pow underflowed
+{ .mfi
+ nop.m 999
+(p0) fsetc.s3 0x7F,0x40
+ nop.i 999 ;;
+}
+{ .mfi
+ nop.m 999
+//
+// Return if no danger of over of underflow.
+//
+(p0) fsetc.s2 0x7F,0x42
+ nop.i 999;;
+}
+{ .mfi
+ nop.m 999
+(p0) fma.s2 FR_Result_big = FR_Input_X, FR_Input_X, f0
+ nop.i 999 ;;
+}
+//
+// S0 user supplied status
+// S2 user supplied status + WRE + TD (Overflows)
+// S3 user supplied status + FZ + TD (Underflows)
+//
+//
+// If (Safe) is true, then
+// Compute result using user supplied status field.
+// No overflow or underflow here, but perhaps inexact.
+// Return
+// Else
+// Determine if overflow or underflow was raised.
+// Fetch +/- overflow threshold for IEEE single, double,
+// double extended
+//
+{ .mfi
+(p0) setf.exp FR_Big = GR_T1_ptr
+(p0) fsetc.s2 0x7F,0x40
+ nop.i 999 ;;
+}
+{ .mfi
+ nop.m 999
+(p0) fclass.m.unc p11, p0 = FR_Result_small, 0x00F
+ nop.i 999 ;;
+}
+{ .mfi
+ nop.m 999
+(p0) fmerge.ns FR_NBig = FR_Big, FR_Big
+ nop.i 999
+}
+{ .mfi
+ nop.m 999
+//
+// Create largest double exponent + 1.
+// Create smallest double exponent - 1.
+// Identify denormals
+//
+(p0) fcmp.ge.unc.s1 p8, p0 = FR_Result_big , FR_Big
+ nop.i 999 ;;
+}
+{ .mii
+ nop.m 999
+ nop.i 999 ;;
+//
+// fcmp: resultS2 <= - overflow threshold
+// fclass: resultS3 is denorm/unorm/0
+//
+(p8) mov GR_Parameter_TAG = 18 ;;
}
-;;
-
{ .mfb
-(p8) mov GR_Parameter_TAG = 18 // Set tag for overflow
- nop.f 999
-(p8) br.cond.spnt __libm_error_region // Branch if pow +overflow
+ nop.m 999
+//
+// fcmp: resultS2 >= + overflow threshold
+//
+(p0) fcmp.le.unc.s1 p9, p0 = FR_Result_big, FR_NBig
+(p8) br.cond.spnt __libm_error_region ;;
}
-;;
-
-{ .mbb
-(p9) mov GR_Parameter_TAG = 18 // Set tag for overflow
-(p9) br.cond.spnt __libm_error_region // Branch if pow -overflow
- br.ret.sptk b0 // Branch if result really ok
+{ .mii
+ nop.m 999
+ nop.i 999 ;;
+(p9) mov GR_Parameter_TAG = 18
}
-;;
+{ .mib
+ nop.m 999
+ nop.i 999
+(p9) br.cond.spnt __libm_error_region ;;
+}
+//
+// Report that pow overflowed - either +Inf, or -Inf
+//
+{ .mmb
+(p11) mov GR_Parameter_TAG = 19
+ nop.m 999
+(p11) br.cond.spnt __libm_error_region ;;
+}
+{ .mib
+ nop.m 999
+ nop.i 999
+//
+// Report that pow underflowed
+//
+(p0) br.cond.sptk L(POWL_64_RETURN) ;;
+}
+
-POWL_64_SPECIAL:
-// Here if x or y is NatVal, nan, inf, or zero
+
+L(POWL_64_SPECIAL):
{ .mfi
- nop.m 999
- fcmp.eq.s1 p15, p0 = FR_Input_X, f1 // Test x=+1
- nop.i 999
+ nop.m 999
+(p0) fcmp.eq.s1 p15, p0 = FR_Input_X, f1 // Is x=+1
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 999
- fclass.m p8, p0 = FR_Input_X, 0x143 // Test x natval, snan
- nop.i 999
+ nop.m 999
+(p0) fclass.m.unc p14, p0 = FR_Input_Y, 0x023
+ nop.i 999 ;;
}
-;;
{ .mfi
- nop.m 999
-(p15) fcmp.eq.unc.s0 p6,p0 = FR_Input_Y, f0 // If x=1, flag invalid if y=SNaN
- nop.i 999
+ nop.m 999
+(p15) fcmp.eq.unc.s0 p6,p0 = FR_Input_Y, f0 // If x=1, flag invalid if y=SNaN
+ nop.i 999
}
{ .mfb
- nop.m 999
-(p15) fmpy.s0 FR_Result = f1,f1 // If x=1, result=1
-(p15) br.ret.spnt b0 // Exit if x=1
+ nop.m 999
+(p15) fmpy.s0 FR_Result = f1,f1 // If x=1, result=1
+(p15) br.cond.spnt L(POWL_64_RETURN) ;; // Exit if x=1
}
-;;
{ .mfi
- nop.m 999
- fclass.m p6, p0 = FR_Input_Y, 0x007 // Test y zero
- nop.i 999
+ nop.m 999
+(p0) fclass.m.unc p13, p0 = FR_Input_X, 0x023
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 999
- fclass.m p9, p0 = FR_Input_Y, 0x143 // Test y natval, snan
- nop.i 999
+ nop.m 999
+(p0) fclass.m.unc p8, p0 = FR_Input_X, 0x143
+ nop.i 999
}
-;;
-
{ .mfi
- nop.m 999
- fclass.m p10, p0 = FR_Input_X, 0x083 // Test x qnan
- nop.i 999
+ nop.m 999
+(p0) fclass.m.unc p9, p0 = FR_Input_Y, 0x143
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p8) fmpy.s0 FR_Result = FR_Input_Y, FR_Input_X // If x=snan, result=qnan
-(p6) cmp.ne p8,p0 = r0,r0 // Don't exit if x=snan, y=0 ==> result=+1
+ nop.m 999
+(p0) fclass.m.unc p10, p0 = FR_Input_X, 0x083
+ nop.i 999
}
-;;
-
{ .mfi
- nop.m 999
-(p6) fclass.m.unc p15, p0 = FR_Input_X,0x007 // Test x=0, y=0
- nop.i 999
+ nop.m 999
+(p0) fclass.m.unc p11, p0 = FR_Input_Y, 0x083
+ nop.i 999 ;;
}
-{ .mfb
- nop.m 999
-(p9) fmpy.s0 FR_Result = FR_Input_Y, FR_Input_X // If y=snan, result=qnan
-(p8) br.ret.spnt b0 // Exit if x=snan, y not 0,
- // result=qnan
+{ .mfi
+ nop.m 999
+(p0) fclass.m.unc p6, p0 = FR_Input_Y, 0x007
+ nop.i 999
}
-;;
-
{ .mfi
- nop.m 999
- fcmp.eq.s1 p7, p0 = FR_Input_Y, f1 // Test y +1.0
- nop.i 999
+ nop.m 999
+(p0) fcmp.eq.unc.s1 p7, p0 = FR_Input_Y, f1
+ nop.i 999 ;;
+}
+{ .mfi
+ nop.m 999
+//
+// set p13 if x +/- Inf
+// set p14 if y +/- Inf
+// set p8 if x Natval or +/-SNaN
+// set p9 if y Natval or +/-SNaN
+// set p10 if x QNaN
+// set p11 if y QNaNs
+// set p6 if y is +/-0
+// set p7 if y is 1
+//
+(p8) fmpy.s0 FR_Result = FR_Input_Y, FR_Input_X
+(p6) cmp.ne p8,p0 = r0,r0 ;; // Don't exit if x=snan, y=0 ==> result=+1
}
{ .mfb
- nop.m 999
-(p10) fmpy.s0 FR_Result = FR_Input_X, f0 // If x=qnan, result=qnan
-(p9) br.ret.spnt b0 // Exit if y=snan, result=qnan
+ nop.m 999
+(p9) fmpy.s0 FR_Result = FR_Input_Y, FR_Input_X
+(p8) br.cond.spnt L(POWL_64_RETURN) ;;
+}
+{ .mfb
+ nop.m 999
+(p10) fmpy.s0 FR_Result = FR_Input_X, f0
+(p9) br.cond.spnt L(POWL_64_RETURN) ;;
}
-;;
-
{ .mfi
- nop.m 999
-(p6) fclass.m.unc p8, p0 = FR_Input_X,0x0C3 // Test x=nan, y=0
- nop.i 999
+ nop.m 999
+//
+// Produce result for SNaN and NatVals and return
+//
+(p6) fclass.m.unc p15, p0 = FR_Input_X,0x007
+ nop.i 999
+}
+{ .mfi
+ nop.m 999
+//
+// If Y +/- 0, set p15 if x +/- 0
+//
+(p6) fclass.m.unc p8, p0 = FR_Input_X,0x0C3
+ nop.i 999 ;;
}
-;;
{ .mfi
- nop.m 999
-(p6) fcmp.eq.s0 p9,p0 = FR_Input_X, f0 // If y=0, flag if x denormal
- nop.i 999
+ nop.m 999
+(p6) fcmp.eq.s0 p9,p0 = FR_Input_X, f0 // If y=0, flag if x denormal
+ nop.i 999
}
{ .mfi
- nop.m 999
-(p6) fadd.s0 FR_Result = f1, f0 // If y=0, result=1
- nop.i 999
+ nop.m 999
+(p6) fadd.s0 FR_Result = f1, f0
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 999
- fclass.m p11, p0 = FR_Input_Y, 0x083 // Test y qnan
- nop.i 999
+ nop.m 999
+//
+// Set p8 if y = +/-0 and X is a QNaN/SNaN
+// If y = +/-0, let result = 1.0
+//
+(p7) fmpy.s0 FR_Result = FR_Input_X,f1
+//
+// If y == 1, result = x * 1
+//
+(p15) mov GR_Parameter_TAG = 20
}
-{ .mfb
-(p15) mov GR_Parameter_TAG = 20 // Error tag for x=0, y=0
-(p7) fmpy.s0 FR_Result = FR_Input_X,f1 // If y=1, result=x
-(p15) br.cond.spnt __libm_error_region // Branch if x=0, y=0, result=1
+{ .mib
+ nop.m 999
+ nop.i 999
+(p15) br.cond.spnt __libm_error_region ;;
}
-;;
-
-{ .mfb
-(p8) mov GR_Parameter_TAG = 23 // Error tag for x=nan, y=0
- fclass.m p14, p0 = FR_Input_Y, 0x023 // Test y inf
-(p8) br.cond.spnt __libm_error_region // Branch if x=snan, y=0,
- // result=1
+{ .mib
+ nop.m 999
+//
+// If x and y are both zero, result = 1.0 and call error
+// support.
+//
+(p8) mov GR_Parameter_TAG = 23
+(p8) br.cond.spnt __libm_error_region ;;
}
-;;
-
-{ .mfb
- nop.m 999
- fclass.m p13, p0 = FR_Input_X, 0x023 // Test x inf
-(p6) br.ret.spnt b0 // Exit y=0, x not nan or 0,
- // result=1
+{ .mib
+ nop.m 999
+ nop.i 999
+//
+// If y = +/-0 and x is a QNaN, result = 1.0 and call error
+// support.
+//
+(p6) br.cond.spnt L(POWL_64_RETURN) ;;
}
-;;
+// If x=0, y=-inf, go to the X_IS_ZERO path
{ .mfb
- nop.m 999
-(p14) fcmp.eq.unc.s1 p0,p14 = FR_Input_X,f0 // Test x not 0, y=inf
-(p7) br.ret.spnt b0 // Exit y=1, x not snan,
- // result=x
+ nop.m 999
+(p14) fcmp.eq.unc.s1 p0,p14 = FR_Input_X,f0
+(p7) br.cond.spnt L(POWL_64_RETURN) ;;
}
-;;
-{ .mfb
- nop.m 999
-(p10) fmpy.s0 FR_Result = FR_Input_Y,FR_Input_X // If x=qnan, y not snan,
- // result=qnan
-(p10) br.ret.spnt b0 // Exit x=qnan, y not snan,
- // result=qnan
+{ .mfi
+ nop.m 999
+//
+// Produce all results for x**0 and x**1
+// Let all the result x ** 0 == 1 and return
+// Let all x ** 1 == x and return
+//
+(p10) fmpy.s0 FR_Result = FR_Input_Y,FR_Input_X
+ nop.i 999 ;;
}
-;;
-
{ .mfb
- nop.m 999
-(p11) fmpy.s0 FR_Result = FR_Input_Y,FR_Input_X // If y=qnan, x not nan or 1,
- // result=qnan
-(p11) br.ret.spnt b0 // Exit y=qnan, x not nan or 1,
- // result=qnan
+ nop.m 999
+(p11) fmpy.s0 FR_Result = FR_Input_Y,FR_Input_X
+(p10) br.cond.spnt L(POWL_64_RETURN) ;;
}
-;;
-
-{ .mbb
- nop.m 999
-(p14) br.cond.spnt POWL_64_Y_IS_INF // Branch if y=inf, x not 1 or nan
-(p13) br.cond.spnt POWL_64_X_IS_INF // Branch if x=inf, y not 1 or nan
+{ .mib
+ nop.m 999
+ nop.i 999
+(p11) br.cond.spnt L(POWL_64_RETURN) ;;
}
-;;
-
-
-POWL_64_X_IS_ZERO:
-// Here if x=0, y not nan or 1 or inf or 0
-
-// There is logic starting here to determine if y is an integer when x = 0.
-// If 0 < |y| < 1 then clearly y is not an integer.
-// If |y| > 1, then the significand of y is shifted left by the size of
-// the exponent of y. This preserves the lsb of the integer part + the
-// fractional bits. The lsb of the integer can be tested to determine if
-// the integer is even or odd. The fractional bits can be tested. If zero,
-// then y is an integer.
+{ .mib
+ nop.m 999
+ nop.i 999
+//
+// Return result for x or y QNaN input with QNaN result
+//
+(p14) br.cond.spnt L(POWL_64_Y_IS_INF) ;;
+}
+{ .mib
+ nop.m 999
+ nop.i 999
+(p13) br.cond.spnt L(POWL_64_X_IS_INF) ;;
+}
+L(POWL_64_X_IS_ZERO):
+{ .mmb
+(p0) getf.sig GR_signif_y = FR_Input_Y
+(p0) getf.exp GR_BIASed_exp_y = FR_Input_Y
+ nop.b 999 ;;
+}
+{ .mlx
+ nop.m 999
+(p0) movl GR_Mask = 0x1FFFF
+}
+{ .mlx
+ nop.m 999
+(p0) movl GR_y_sign = 0x20000 ;;
+}
+//
+// Get BIASed exp and significand of y
//
{ .mfi
- and GR_exp_y = GR_exp_mask,GR_signexp_y // Get biased exponent of y
- nop.f 999
- and GR_y_sign = GR_sign_mask,GR_signexp_y // Get sign of y
+(p0) and GR_exp_y = GR_Mask,GR_BIASed_exp_y
+ nop.f 999
+(p0) and GR_y_sign = GR_y_sign,GR_BIASed_exp_y
}
-;;
-
+{ .mlx
+ nop.m 999
+(p0) movl GR_BIAS = 0xFFFF ;;
+}
+{ .mfi
+(p0) cmp.lt.unc p9, p8 = GR_exp_y,GR_BIAS
+ nop.f 999
//
// Maybe y is < 1 already, so
// can never be an integer.
+// Remove sign bit from exponent.
+//
+(p0) sub GR_exp_y = GR_exp_y,GR_BIAS ;;
+}
+{ .mii
+ nop.m 999
+ nop.i 999 ;;
+//
+// Remove exponent BIAS
//
+(p8) shl GR_exp_y= GR_signif_y,GR_exp_y ;;
+}
{ .mfi
- cmp.lt p9, p8 = GR_exp_y,GR_exp_bias // Test 0 < |y| < 1
- nop.f 999
- sub GR_exp_y = GR_exp_y,GR_exp_bias // Get true exponent of y
+(p9) or GR_exp_y= 0xF,GR_signif_y
+ nop.f 999
+ nop.i 999 ;;
}
-;;
-
+{ .mii
+ nop.m 999
//
// Shift significand of y looking for nonzero bits
// For y > 1, shift signif_y exp_y bits to the left
-// For y < 1, turn on 4 low order bits of significand of y
+// For y < 1, turn on 4 low order bits of significand of y
// so that the fraction will always be non-zero
//
-{ .mmi
-(p9) or GR_exp_y= 0xF,GR_signif_y // Force nonzero fraction if y<1
-;;
- nop.m 999
-(p8) shl GR_exp_y= GR_signif_y,GR_exp_y // Get lsb of int + fraction
- // Wait 4 cycles to use result
+(p0) shl GR_signif_y= GR_exp_y,1 ;;
+(p0) extr.u GR_low_order_bit = GR_exp_y,63,1
}
-;;
-
-{ .mmi
- nop.m 999
-;;
- nop.m 999
- nop.i 999
-}
-;;
-
-{ .mmi
- nop.m 999
-;;
- nop.m 999
- shl GR_fraction_y= GR_exp_y,1 // Shift left 1 to get fraction
-}
-;;
-
//
// Integer part of y shifted off.
// Get y's low even or odd bit - y might not be an int.
//
{ .mii
- cmp.eq p13,p0 = GR_fraction_y, r0 // Test for y integer
- cmp.eq p8,p0 = GR_y_sign, r0 // Test for y > 0
-;;
-(p13) tbit.nz.unc p13,p0 = GR_exp_y, 63 // Test if y an odd integer
-}
-;;
-
-{ .mfi
-(p13) cmp.eq.unc p13,p14 = GR_y_sign, r0 // Test y pos odd integer
-(p8) fcmp.eq.s0 p12,p0 = FR_Input_Y, f0 // If x=0 and y>0 flag if y denormal
- nop.i 999
+(p0) cmp.eq.unc p13,p0 = GR_signif_y, r0
+(p0) cmp.eq.unc p8,p9 = GR_y_sign, r0 ;;
+//
+// Is y an int?
+// Is y positive
+//
+(p13) cmp.ne.unc p13,p0 = GR_low_order_bit, r0 ;;
}
-;;
-
//
-// Return +/-0 when x=+/-0 and y is positive odd integer
+// Is y and int and odd?
//
{ .mfb
- nop.m 999
-(p13) mov FR_Result = FR_Input_X // If x=0, y pos odd int, result=x
-(p13) br.ret.spnt b0 // Exit x=0, y pos odd int, result=x
+(p13) cmp.eq.unc p13,p14 = GR_y_sign, r0
+(p8) fcmp.eq.s0 p12,p0 = FR_Input_Y, f0 // If x=0 and y>0 flag if y denormal
+ nop.b 999 ;;
}
-;;
-
+{ .mfb
+ nop.m 999
//
-// Return +/-inf when x=+/-0 and y is negative odd int
+// Is y and int and odd and positive?
//
-{ .mfb
-(p14) mov GR_Parameter_TAG = 21
-(p14) frcpa.s0 FR_Result, p0 = f1, FR_Input_X // Result +-inf, set Z flag
-(p14) br.cond.spnt __libm_error_region
+(p13) mov FR_Result = FR_Input_X
+(p13) br.cond.sptk L(POWL_64_RETURN) ;;
}
-;;
-
+{ .mfi
+ nop.m 999
//
-// Return +0 when x=+/-0 and y positive and not an odd integer
+// Return +/-0 when x=+/-0 and y is and odd pos. int
//
-{ .mfb
- nop.m 999
-(p8) mov FR_Result = f0 // If x=0, y>0 and not odd integer, result=+0
-(p8) br.ret.sptk b0 // Exit x=0, y>0 and not odd integer, result=+0
+(p14) frcpa.s0 FR_Result, p10 = f1, FR_Input_X
+(p14) mov GR_Parameter_TAG = 21
+}
+{ .mib
+ nop.m 999
+ nop.i 999
+(p14) br.cond.spnt __libm_error_region ;;
}
-;;
+{ .mfb
+ nop.m 999
//
-// Return +inf when x=+/-0 and y is negative and not odd int
+// Return +/-0 when x=+/-Inf and y is and odd neg int
+// and raise dz exception
//
-{ .mfb
- mov GR_Parameter_TAG = 21
- frcpa.s0 FR_Result, p10 = f1,f0 // Result +inf, raise Z flag
- br.cond.sptk __libm_error_region
+(p8) mov FR_Result = f0
+(p8) br.cond.sptk L(POWL_64_RETURN) ;;
}
-;;
-
-
-POWL_64_X_IS_INF:
+{ .mfi
+ nop.m 999
//
-// Here if x=inf, y not 1 or nan
+// Return +0 when x=+/-0 and y > 0 and not odd.
//
+(p9) frcpa.s0 FR_Result, p10 = f1,f0
+(p9) mov GR_Parameter_TAG = 21
+}
+{ .mib
+ nop.m 999
+ nop.i 999
+(p9) br.cond.sptk __libm_error_region ;;
+}
+L(POWL_64_X_IS_INF):
{ .mfi
- and GR_exp_y = GR_exp_mask,GR_signexp_y // Get biased exponent y
- fclass.m p13, p0 = FR_Input_X,0x022 // Test x=-inf
- nop.i 999
+(p0) getf.exp GR_exp_y = FR_Input_Y
+(p0) fclass.m.unc p13, p0 = FR_Input_X,0x022
+(p0) mov GR_Mask = 0x1FFFF ;;
}
-;;
{ .mfi
- and GR_y_sign = GR_sign_mask,GR_signexp_y // Get sign of y
- fcmp.eq.s0 p9,p0 = FR_Input_Y, f0 // Dummy to set flag if y denorm
- nop.i 999
+(p0) getf.sig GR_signif_y = FR_Input_Y
+(p0) fcmp.eq.s0 p9,p0 = FR_Input_Y, f0 // Flag if y denormal
+ nop.i 999 ;;
}
-;;
//
-// Maybe y is < 1 already, so
-// isn't an int.
+// Get exp and significand of y
+// Create exponent mask and sign mask
//
-{ .mfi
-(p13) cmp.lt.unc p9, p8 = GR_exp_y,GR_exp_bias // Test 0 < |y| < 1 if x=-inf
- fclass.m p11, p0 = FR_Input_X,0x021 // Test x=+inf
- sub GR_exp_y = GR_exp_y,GR_exp_bias // Get true exponent y
+{ .mlx
+(p0) and GR_low_order_bit = GR_Mask,GR_exp_y
+(p0) movl GR_BIAS = 0xFFFF
}
-;;
-
+{ .mmi
+ nop.m 999 ;;
//
-// Shift significand of y looking for nonzero bits
-// For y > 1, shift signif_y exp_y bits to the left
-// For y < 1, turn on 4 low order bits of significand of y
-// so that the fraction will always be non-zero
+// Remove sign bit from exponent.
//
-{ .mmi
-(p9) or GR_exp_y= 0xF,GR_signif_y // Force nonzero fraction if y<1
-;;
-(p11) cmp.eq.unc p14,p12 = GR_y_sign, r0 // Test x=+inf, y>0
-(p8) shl GR_exp_y= GR_signif_y,GR_exp_y // Get lsb of int + fraction
- // Wait 4 cycles to use result
-}
-;;
-
+(p0) cmp.lt.unc p9, p8 = GR_low_order_bit,GR_BIAS
//
-// Return +inf for x=+inf, y > 0
-// Return +0 for x=+inf, y < 0
+// Maybe y is < 1 already, so
+// isn't an int.
//
-{ .mfi
- nop.m 999
-(p12) mov FR_Result = f0 // If x=+inf, y<0, result=+0
- nop.i 999
+(p0) sub GR_low_order_bit = GR_low_order_bit,GR_BIAS
}
-{ .mfb
- nop.m 999
-(p14) fma.s0 FR_Result = FR_Input_X,f1,f0 // If x=+inf, y>0, result=+inf
-(p11) br.ret.sptk b0 // Exit x=+inf
+{ .mlx
+ nop.m 999
+(p0) movl GR_sign_mask = 0x20000 ;;
}
-;;
-
+{ .mfi
+(p0) and GR_sign_mask = GR_sign_mask,GR_exp_y
//
-// Here only if x=-inf. Wait until can use result of shl...
+// Return +Inf when x=+/-0 and y < 0 and not odd and raise
+// divide-by-zero exception.
//
+(p0) fclass.m.unc p11, p0 = FR_Input_X,0x021
+ nop.i 999 ;;
+}
{ .mmi
- nop.m 999
-;;
- nop.m 999
- nop.i 999
+ nop.m 999 ;;
+//
+// Is shift off integer part of y.
+// Get y's even or odd bit - y might not be an int.
+//
+(p11) cmp.eq.unc p11,p12 = GR_sign_mask, r0
+//
+// Remove exponent BIAS
+//
+(p8) shl GR_exp_y = GR_signif_y,GR_low_order_bit ;;
}
-;;
-
{ .mfi
- cmp.eq p8,p9 = GR_y_sign, r0 // Test y pos
- nop.f 999
- shl GR_fraction_y = GR_exp_y,1 // Shift left 1 to get fraction
+(p9) or GR_exp_y = 0xF,GR_signif_y
+//
+// Is y positive or negative when x is +Inf?
+// Is y and int when x = -Inf
+//
+(p11) mov FR_Result = FR_Input_X
+ nop.i 999 ;;
}
-;;
-
-{ .mmi
- cmp.eq p13,p0 = GR_fraction_y, r0 // Test y integer
-;;
- nop.m 999
-(p13) tbit.nz.unc p13,p0 = GR_exp_y, 63 // Test y odd integer
+{ .mfi
+ nop.m 999
+(p12) mov FR_Result = f0
+ nop.i 999 ;;
}
-;;
-
+{ .mii
+ nop.m 999
//
-// Is y even or odd?
+// Shift signficand looking for nonzero bits
+// For y non-ints, upset the significand.
//
+(p0) shl GR_signif_y = GR_exp_y,1 ;;
+(p13) cmp.eq.unc p13,p0 = GR_signif_y, r0
+}
{ .mii
-(p13) cmp.eq.unc p14,p10 = GR_y_sign, r0 // Test x=-inf, y pos odd int
-(p13) cmp.ne.and p8,p9 = r0,r0 // If y odd int, turn off p8,p9
- nop.i 999
+ nop.m 999
+(p0) extr.u GR_low_order_bit = GR_exp_y,63,1 ;;
+(p13) cmp.ne.unc p13,p0 = GR_low_order_bit, r0
+}
+{ .mib
+ nop.m 999
+ nop.i 999
+(p11) br.cond.sptk L(POWL_64_RETURN) ;;
+}
+{ .mib
+ nop.m 999
+ nop.i 999
+(p12) br.cond.sptk L(POWL_64_RETURN) ;;
}
-;;
-
//
-// Return -0 for x = -inf and y < 0 and odd int.
-// Return -Inf for x = -inf and y > 0 and odd int.
+// Return Inf for y > 0
+// Return +0 for y < 0
+// Is y even or odd?
//
-{ .mfi
- nop.m 999
-(p10) fmerge.ns FR_Result = f0, f0 // If x=-inf, y neg odd int, result=-0
- nop.i 999
+{ .mii
+(p13) cmp.eq.unc p13,p10 = GR_sign_mask, r0
+(p0) cmp.eq.unc p8,p9 = GR_sign_mask, r0 ;;
+ nop.i 999
}
{ .mfi
- nop.m 999
-(p14) fmpy.s0 FR_Result = FR_Input_X,f1 // If x=-inf, y pos odd int, result=-inf
- nop.i 999
-}
-;;
-
+ nop.m 999
//
-// Return Inf for x = -inf and y > 0 not an odd int.
-// Return +0 for x = -inf and y < 0 not an odd int.
+// For x = -inf, y is and int, positive
+// and odd
+// Is y positive in general?
//
-.pred.rel "mutex",p8,p9
-{ .mfi
- nop.m 999
-(p8) fmerge.ns FR_Result = FR_Input_X, FR_Input_X // If x=-inf, y>0 not odd int
- // result=+inf
- nop.i 999
+(p13) mov FR_Result = FR_Input_X
+ nop.i 999 ;;
}
{ .mfb
- nop.m 999
-(p9) fmpy.s0 FR_Result = f0,f0 // If x=-inf, y<0 not odd int
- // result=+0
- br.ret.sptk b0 // Exit for x=-inf
+ nop.m 999
+(p10) fmerge.ns FR_Result = f0, f0
+(p13) br.cond.sptk L(POWL_64_RETURN) ;;
}
-;;
-
-
-POWL_64_Y_IS_INF:
-// Here if y=inf, x not 1 or nan
+{ .mib
+ nop.m 999
+ nop.i 999
+(p10) br.cond.sptk L(POWL_64_RETURN) ;;
+}
+{ .mfi
+ nop.m 999
//
-// For y = +Inf and |x| < 1 returns 0
-// For y = +Inf and |x| > 1 returns Inf
-// For y = -Inf and |x| < 1 returns Inf
-// For y = -Inf and |x| > 1 returns 0
-// For y = Inf and |x| = 1 returns 1
+// Return -Inf for x = -inf and y > 0 and odd int.
+// Return -0 for x = -inf and y < 0 and odd int.
//
-{ .mfi
- nop.m 999
- fclass.m p8, p0 = FR_Input_Y, 0x021 // Test y=+inf
- nop.i 999
+(p8) fmerge.ns FR_Result = FR_Input_X, FR_Input_X
+ nop.i 999 ;;
}
-;;
-
-{ .mfi
- nop.m 999
- fclass.m p9, p0 = FR_Input_Y, 0x022 // Test y=-inf
- nop.i 999
+{ .mfb
+ nop.m 999
+(p9) mov FR_Result = f0
+(p8) br.cond.sptk L(POWL_64_RETURN) ;;
}
-;;
-
+{ .mib
+ nop.m 999
+ nop.i 999
+(p9) br.cond.sptk L(POWL_64_RETURN) ;;
+}
+L(POWL_64_Y_IS_INF):
{ .mfi
- nop.m 999
- fabs FR_X = FR_Input_X // Form |x|
- nop.i 999
+ nop.m 999
+//
+// Return Inf for x = -inf and y > 0 not an odd int.
+// Return +0 for x = -inf and y < 0 and not an odd int.
+//
+(p0) fclass.m.unc p8, p0 = FR_Input_Y, 0x021
+ nop.i 999
}
-;;
-
{ .mfi
- nop.m 999
- fcmp.eq.s0 p10,p0 = FR_Input_X, f0 // flag if x denormal
- nop.i 999
+ nop.m 999
+(p0) fclass.m.unc p9, p0 = FR_Input_Y, 0x022
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 999
-(p8) fcmp.lt.unc.s1 p6, p0 = FR_X, f1 // Test y=+inf, |x|<1
- nop.i 999
+ nop.m 999
+(p0) fabs FR_X = FR_Input_X
+ nop.i 999 ;;
}
-;;
{ .mfi
- nop.m 999
-(p8) fcmp.gt.unc.s1 p7, p0 = FR_X, f1 // Test y=+inf, |x|>1
- nop.i 999
+ nop.m 999
+(p0) fcmp.eq.s0 p10,p0 = FR_Input_X, f0 // flag if x denormal
+ nop.i 999 ;;
}
-;;
{ .mfi
- nop.m 999
-(p9) fcmp.lt.unc.s1 p12, p0 = FR_X, f1 // Test y=-inf, |x|<1
- nop.i 999
+ nop.m 999
+//
+// Find y = +/- Inf
+// Compute |x|
+//
+(p8) fcmp.lt.unc.s1 p6, p0 = FR_X, f1
+ nop.i 999
}
{ .mfi
- nop.m 999
-(p6) fmpy.s0 FR_Result = f0,f0 // If y=+inf, |x|<1, result=+0
- nop.i 999
+ nop.m 999
+(p8) fcmp.gt.unc.s1 p7, p0 = FR_X, f1
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 999
-(p9) fcmp.gt.unc.s1 p13, p0 = FR_X, f1 // Test y=-inf, |x|>1
- nop.i 999
+ nop.m 999
+(p9) fcmp.lt.unc.s1 p12, p0 = FR_X, f1
+ nop.i 999
}
{ .mfi
- nop.m 999
-(p7) fmpy.s0 FR_Result = FR_Input_Y, f1 // If y=+inf, |x|>1, result=+inf
- nop.i 999
+ nop.m 999
+(p9) fcmp.gt.unc.s1 p13, p0 = FR_X, f1
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 999
- fcmp.eq.s1 p14, p0 = FR_X, f1 // Test y=inf, |x|=1
- nop.i 999
+ nop.m 999
+//
+// For y = +Inf and |x| < 1 returns 0
+// For y = +Inf and |x| > 1 returns Inf
+// For y = -Inf and |x| < 1 returns Inf
+// For y = -Inf and |x| > 1 returns 0
+//
+(p6) mov FR_Result = f0
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p12) fnma.s0 FR_Result = FR_Input_Y, f1, f0 // If y=-inf, |x|<1, result=+inf
- nop.i 999
+ nop.m 999
+(p7) mov FR_Result = FR_Input_Y
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 999
-(p13) mov FR_Result = f0 // If y=-inf, |x|>1, result=+0
- nop.i 999
+ nop.m 999
+(p12) fmpy.s0 FR_Result = FR_Input_Y, FR_Input_Y
+ nop.i 999 ;;
}
-;;
-
{ .mfb
- nop.m 999
-(p14) fmpy.s0 FR_Result = f1,f1 // If y=inf, |x|=1, result=+1
- br.ret.sptk b0 // Common return for y=inf
+ nop.m 999
+(p13) mov FR_Result = f0
+//
+// Produce x ** +/- Inf results
+//
+(p6) br.cond.spnt L(POWL_64_RETURN) ;;
}
-;;
-
-
-// Here if x or y denorm/unorm
-POWL_DENORM:
-{ .mmi
- getf.sig GR_signif_Z = FR_norm_X // Get significand of x
-;;
- getf.exp GR_signexp_y = FR_norm_Y // Get sign and exp of y
- nop.i 999
+{ .mib
+ nop.m 999
+ nop.i 999
+(p7) br.cond.spnt L(POWL_64_RETURN) ;;
}
-;;
-
-{ .mfi
- getf.sig GR_signif_y = FR_norm_Y // Get significand of y
- nop.f 999
- nop.i 999
+{ .mib
+ nop.m 999
+ nop.i 999
+(p12) br.cond.spnt L(POWL_64_RETURN) ;;
}
-;;
-
{ .mib
- getf.exp GR_signexp_x = FR_norm_X // Get sign and exp of x
- extr.u GR_Index1 = GR_signif_Z, 59, 4 // Extract upper 4 signif bits of x
- br.cond.sptk POWL_COMMON // Branch back to main path
+ nop.m 999
+ nop.i 999
+(p13) br.cond.spnt L(POWL_64_RETURN) ;;
}
-;;
-
-
-POWL_64_UNSUPPORT:
+{ .mfb
+ nop.m 999
//
-// Raise exceptions for specific
-// values - pseudo NaN and
-// infinities.
-// Return NaN and raise invalid
+// +/-1 ** +/-Inf, result is +1
//
-{ .mfb
- nop.m 999
- fmpy.s0 FR_Result = FR_Input_X,f0
- br.ret.sptk b0
+(p0) fmpy.s0 FR_Result = f1,f1
+(p0) br.cond.sptk L(POWL_64_RETURN) ;;
}
-;;
-
-POWL_64_XNEG:
+L(POWL_64_UNSUPPORT):
+{ .mfb
+ nop.m 999
//
-// Raise invalid for x < 0 and
-// y not an integer
+// Return NaN and raise invalid
//
+(p0) fmpy.s0 FR_Result = FR_Input_X,f0
+//
+// Raise exceptions for specific
+// values - pseudo NaN and
+// infinities.
+//
+(p0) br.cond.sptk L(POWL_64_RETURN) ;;
+}
+L(POWL_64_XNEG):
{ .mfi
- nop.m 999
- frcpa.s0 FR_Result, p8 = f0, f0
- mov GR_Parameter_TAG = 22
+ nop.m 999
+(p0) frcpa.s0 FR_Result, p8 = f0, f0
+//
+// Raise invalid for x < 0 and
+// y not an integer and
+//
+(p0) mov GR_Parameter_TAG = 22
}
{ .mib
- nop.m 999
- nop.i 999
- br.cond.sptk __libm_error_region
+ nop.m 999
+ nop.i 999
+(p0) br.cond.sptk __libm_error_region ;;
}
-;;
-
-POWL_64_SQRT:
+L(POWL_64_SQRT):
{ .mfi
- nop.m 999
- frsqrta.s0 FR_Result,p10 = FR_save_Input_X
- nop.i 999 ;;
+ nop.m 999
+(p0) frsqrta.s0 FR_Result,p10 = FR_Input_X
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p10) fma.s1 f62=FR_Half,FR_save_Input_X,f0
- nop.i 999 ;;
+ nop.m 999
+(p10) fma.s1 f62=FR_Half,FR_Input_X,f0
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p10) fma.s1 f63=FR_Result,FR_Result,f0
- nop.i 999 ;;
+ nop.m 999
+//
+// Step (2)
+// h = 1/2 * a in f9
+//
+(p10) fma.s1 f63=FR_Result,FR_Result,f0
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p10) fnma.s1 f32=f63,f62,FR_Half
- nop.i 999 ;;
+ nop.m 999
+//
+// Step (3)
+// t1 = y0 * y0 in f10
+//
+(p10) fnma.s1 f32=f63,f62,f11
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p10) fma.s1 f33=f32,FR_Result,FR_Result
- nop.i 999 ;;
+ nop.m 999
+//
+// Step (4)
+// t2 = 1/2 - t1 * h in f10
+//
+(p10) fma.s1 f33=f32,FR_Result,FR_Result
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p10) fma.s1 f34=f33,f62,f0
- nop.i 999 ;;
+ nop.m 999
+//
+// Step (5)
+// y1 = y0 + t2 * y0 in f13
+//
+(p10) fma.s1 f34=f33,f62,f0
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p10) fnma.s1 f35=f34,f33,FR_Half
- nop.i 999 ;;
+ nop.m 999
+//
+// Step (6)
+// t3 = y1 * h in f10
+//
+(p10) fnma.s1 f35=f34,f33,f11
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p10) fma.s1 f63=f35,f33,f33
- nop.i 999 ;;
+ nop.m 999
+//
+// Step (7)
+// t4 = 1/2 - t3 * y1 in f10
+//
+(p10) fma.s1 f63=f35,f33,f33
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p10) fma.s1 f32=FR_save_Input_X,f63,f0
- nop.i 999
+ nop.m 999
+//
+// Step (8)
+// y2 = y1 + t4 * y1 in f13
+//
+(p10) fma.s1 f32=FR_Input_X,f63,f0
+ nop.i 999
}
{ .mfi
- nop.m 999
-(p10) fma.s1 FR_Result=f63,f62,f0
- nop.i 999 ;;
+ nop.m 999
+//
+// Step (9)
+// S = a * y2 in f10
+//
+(p10) fma.s1 FR_Result=f63,f62,f0
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p10) fma.s1 f33=f11,f63,f0
- nop.i 999 ;;
+ nop.m 999
+//
+// Step (10)
+// t5 = y2 * h in f9
+//
+(p10) fma.s1 f33=f11,f63,f0
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p10) fnma.s1 f34=f32,f32,FR_save_Input_X
- nop.i 999
+ nop.m 999
+//
+// Step (11)
+// H = 1/2 * y2 in f11
+//
+(p10) fnma.s1 f34=f32,f32,f8
+ nop.i 999
}
{ .mfi
- nop.m 999
-(p10) fnma.s1 f35=FR_Result,f63,FR_Half
- nop.i 999 ;;
+ nop.m 999
+//
+// Step (12)
+// d = a - S * S in f12
+//
+(p10) fnma.s1 f35=FR_Result,f63,f11
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p10) fma.s1 f62=f33,f34,f32
- nop.i 999
+ nop.m 999
+//
+// Step (13)
+// t6 = 1/2 - t5 * y2 in f7
+//
+(p10) fma.s1 f62=f33,f34,f32
+ nop.i 999
}
{ .mfi
- nop.m 999
-(p10) fma.s1 f63=f33,f35,f33
- nop.i 999 ;;
+ nop.m 999
+//
+// Step (14)
+// S1 = S + d * H in f13
+//
+(p10) fma.s1 f63=f33,f35,f33
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p10) fnma.s1 f32=f62,f62,FR_save_Input_X
- nop.i 999 ;;
+ nop.m 999
+//
+// Step (15)
+// H1 = H + t6 * h in f7
+//
+(p10) fnma.s1 f32=f62,f62,FR_Input_X
+ nop.i 999 ;;
}
{ .mfb
- nop.m 999
-(p10) fma.s0 FR_Result=f32,f63,f62
- br.ret.sptk b0 // Exit for x > 0, y = 0.5
+ nop.m 999
+//
+// Step (16)
+// d1 = a - S1 * S1
+//
+(p10) fma.s0 FR_Result=f32,f63,f62
+//
+// Step (17)
+// R = S1 + d1 * H1
+//
+(p10) br.cond.sptk L(POWL_64_RETURN) ;;
}
-;;
-
-GLOBAL_LIBM_END(powl)
+{ .mib
+ nop.m 999
+ nop.i 999
+//
+// Do the Newton-Raphson iteration from the EAS.
+//
+(p0) br.cond.sptk L(POWL_64_RETURN) ;;
+}
+//
+// Take care of the degenerate cases.
+//
+L(POWL_64_RETURN):
+{ .mfb
+ nop.m 999
+(p0) mov FR_Output = FR_Result
+(p0) br.ret.sptk b0 ;;
+}
+.endp powl
+ASM_SIZE_DIRECTIVE(powl)
-LOCAL_LIBM_ENTRY(__libm_error_region)
+.proc __libm_error_region
+__libm_error_region:
.prologue
{ .mfi
add GR_Parameter_Y=-32,sp // Parameter 2 value
@@ -2772,32 +3411,32 @@ LOCAL_LIBM_ENTRY(__libm_error_region)
mov GR_SAVE_GP=gp // Save gp
};;
{ .mmi
- stfe [GR_Parameter_Y] = FR_Input_Y,16 // Save Parameter 2 on stack
+ stfe [GR_Parameter_Y] = FR_Y,16 // Save Parameter 2 on stack
add GR_Parameter_X = 16,sp // Parameter 1 address
.save b0, GR_SAVE_B0
mov GR_SAVE_B0=b0 // Save b0
};;
.body
{ .mib
- stfe [GR_Parameter_X] = FR_save_Input_X // Store Parameter 1 on stack
+ stfe [GR_Parameter_X] = FR_X // Store Parameter 1 on stack
add GR_Parameter_RESULT = 0,GR_Parameter_Y
nop.b 0 // Parameter 3 address
}
{ .mib
- stfe [GR_Parameter_Y] = FR_Result // Store Parameter 3 on stack
+ stfe [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack
add GR_Parameter_Y = -16,GR_Parameter_Y
- br.call.sptk b0=__libm_error_support# // Call error handling function
+ br.call.sptk b0=__libm_error_support# // Call error handling function
};;
{ .mmi
- add GR_Parameter_RESULT = 48,sp
nop.m 0
- nop.i 0
+ nop.m 0
+ add GR_Parameter_RESULT = 48,sp
};;
{ .mmi
- ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack
+ ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack
.restore sp
- add sp = 64,sp // Restore stack pointer
- mov b0 = GR_SAVE_B0 // Restore return address
+ add sp = 64,sp // Restore stack pointer
+ mov b0 = GR_SAVE_B0 // Restore return address
};;
{ .mib
mov gp = GR_SAVE_GP // Restore gp
@@ -2805,6 +3444,7 @@ LOCAL_LIBM_ENTRY(__libm_error_region)
br.ret.sptk b0 // Return
};;
-LOCAL_LIBM_END(__libm_error_region#)
+.endp __libm_error_region
+ASM_SIZE_DIRECTIVE(__libm_error_region)
.type __libm_error_support#,@function
.global __libm_error_support#
generated by cgit v1.2.3 (git 2.25.1) at 2024-11-10 22:03:23 +0000