diff options
Diffstat (limited to 'REORG.TODO/sysdeps/ieee754/ldbl-128ibm')
104 files changed, 12987 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/Makefile b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/Makefile new file mode 100644 index 0000000000..bdba6cc6b5 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/Makefile @@ -0,0 +1,16 @@ +# The`long double' type is a distinct type we support if +# -mlong-double-128 option is used (or when it becomes a default +# when -mlong-double-64 is not used). +long-double-fcts = yes +sysdep-CFLAGS += -mlong-double-128 + +ifeq ($(subdir),stdlib) +tests += tst-strtold-ldbl-128ibm +$(objpfx)tst-strtold-ldbl-128ibm: $(libm) +endif + +ifeq ($(subdir),math) +tests += test-fmodl-ldbl-128ibm test-remainderl-ldbl-128ibm \ + test-remquol-ldbl-128ibm test-canonical-ldbl-128ibm \ + test-totalorderl-ldbl-128ibm +endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/bits/iscanonical.h b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/bits/iscanonical.h new file mode 100644 index 0000000000..7ddb368d26 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/bits/iscanonical.h @@ -0,0 +1,41 @@ +/* Define iscanonical macro. ldbl-128ibm version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#ifndef _MATH_H +# error "Never use <bits/iscanonical.h> directly; include <math.h> instead." +#endif + +#ifdef __NO_LONG_DOUBLE_MATH +# define iscanonical(x) ((void) (__typeof (x)) (x), 1) +#else +extern int __iscanonicall (long double __x) + __THROW __attribute__ ((__const__)); +# define __iscanonicalf(x) ((void) (__typeof (x)) (x), 1) +# define __iscanonical(x) ((void) (__typeof (x)) (x), 1) +# if __HAVE_DISTINCT_FLOAT128 +# define __iscanonicalf128(x) ((void) (__typeof (x)) (x), 1) +# endif + +/* Return nonzero value if X is canonical. In IEEE interchange binary + formats, all values are canonical, but the argument must still be + converted to its semantic type for any exceptions arising from the + conversion, before being discarded; in IBM long double, there are + encodings that are not consistently handled as corresponding to any + particular value of the type, and we return 0 for those. */ +# define iscanonical(x) __MATH_TG ((x), __iscanonical, (x)) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_acoshl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_acoshl.c new file mode 100644 index 0000000000..cab1da9995 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_acoshl.c @@ -0,0 +1,62 @@ +/* @(#)e_acosh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_acosh(x) + * Method : + * Based on + * acosh(x) = log [ x + sqrt(x*x-1) ] + * we have + * acosh(x) := log(x)+ln2, if x is large; else + * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else + * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. + * + * Special cases: + * acosh(x) is NaN with signal if x<1. + * acosh(NaN) is NaN without signal. + */ + +#include <math.h> +#include <math_private.h> + +static const long double +one = 1.0L, +ln2 = M_LN2l; + +long double +__ieee754_acoshl(long double x) +{ + long double t; + int64_t hx; + uint64_t lx; + double xhi, xlo; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + if(hx<0x3ff0000000000000LL) { /* x < 1 */ + return (x-x)/(x-x); + } else if(hx >=0x4370000000000000LL) { /* x >= 2**56 */ + if(hx >=0x7ff0000000000000LL) { /* x is inf of NaN */ + return x+x; + } else + return __ieee754_logl(x)+ln2; /* acosh(huge)=log(2x) */ + } else if (((hx-0x3ff0000000000000LL)|(lx&0x7fffffffffffffffLL))==0) { + return 0.0; /* acosh(1) = 0 */ + } else if (hx > 0x4000000000000000LL) { /* 2**56 > x > 2 */ + t=x*x; + return __ieee754_logl(2.0*x-one/(x+__ieee754_sqrtl(t-one))); + } else { /* 1<x<2 */ + t = x-one; + return __log1pl(t+__ieee754_sqrtl(2.0*t+t*t)); + } +} +strong_alias (__ieee754_acoshl, __acoshl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_acosl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_acosl.c new file mode 100644 index 0000000000..5974ee1338 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_acosl.c @@ -0,0 +1,316 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + Long double expansions are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* __ieee754_acosl(x) + * Method : + * acos(x) = pi/2 - asin(x) + * acos(-x) = pi/2 + asin(x) + * For |x| <= 0.375 + * acos(x) = pi/2 - asin(x) + * Between .375 and .5 the approximation is + * acos(0.4375 + x) = acos(0.4375) + x P(x) / Q(x) + * Between .5 and .625 the approximation is + * acos(0.5625 + x) = acos(0.5625) + x rS(x) / sS(x) + * For x > 0.625, + * acos(x) = 2 asin(sqrt((1-x)/2)) + * computed with an extended precision square root in the leading term. + * For x < -0.625 + * acos(x) = pi - 2 asin(sqrt((1-|x|)/2)) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + * Functions needed: __ieee754_sqrtl. + */ + +#include <math.h> +#include <math_private.h> + +static const long double + one = 1.0L, + pio2_hi = 1.5707963267948966192313216916397514420986L, + pio2_lo = 4.3359050650618905123985220130216759843812E-35L, + + /* acos(0.5625 + x) = acos(0.5625) + x rS(x) / sS(x) + -0.0625 <= x <= 0.0625 + peak relative error 3.3e-35 */ + + rS0 = 5.619049346208901520945464704848780243887E0L, + rS1 = -4.460504162777731472539175700169871920352E1L, + rS2 = 1.317669505315409261479577040530751477488E2L, + rS3 = -1.626532582423661989632442410808596009227E2L, + rS4 = 3.144806644195158614904369445440583873264E1L, + rS5 = 9.806674443470740708765165604769099559553E1L, + rS6 = -5.708468492052010816555762842394927806920E1L, + rS7 = -1.396540499232262112248553357962639431922E1L, + rS8 = 1.126243289311910363001762058295832610344E1L, + rS9 = 4.956179821329901954211277873774472383512E-1L, + rS10 = -3.313227657082367169241333738391762525780E-1L, + + sS0 = -4.645814742084009935700221277307007679325E0L, + sS1 = 3.879074822457694323970438316317961918430E1L, + sS2 = -1.221986588013474694623973554726201001066E2L, + sS3 = 1.658821150347718105012079876756201905822E2L, + sS4 = -4.804379630977558197953176474426239748977E1L, + sS5 = -1.004296417397316948114344573811562952793E2L, + sS6 = 7.530281592861320234941101403870010111138E1L, + sS7 = 1.270735595411673647119592092304357226607E1L, + sS8 = -1.815144839646376500705105967064792930282E1L, + sS9 = -7.821597334910963922204235247786840828217E-2L, + /* 1.000000000000000000000000000000000000000E0 */ + + acosr5625 = 9.7338991014954640492751132535550279812151E-1L, + pimacosr5625 = 2.1682027434402468335351320579240000860757E0L, + + /* acos(0.4375 + x) = acos(0.4375) + x rS(x) / sS(x) + -0.0625 <= x <= 0.0625 + peak relative error 2.1e-35 */ + + P0 = 2.177690192235413635229046633751390484892E0L, + P1 = -2.848698225706605746657192566166142909573E1L, + P2 = 1.040076477655245590871244795403659880304E2L, + P3 = -1.400087608918906358323551402881238180553E2L, + P4 = 2.221047917671449176051896400503615543757E1L, + P5 = 9.643714856395587663736110523917499638702E1L, + P6 = -5.158406639829833829027457284942389079196E1L, + P7 = -1.578651828337585944715290382181219741813E1L, + P8 = 1.093632715903802870546857764647931045906E1L, + P9 = 5.448925479898460003048760932274085300103E-1L, + P10 = -3.315886001095605268470690485170092986337E-1L, + Q0 = -1.958219113487162405143608843774587557016E0L, + Q1 = 2.614577866876185080678907676023269360520E1L, + Q2 = -9.990858606464150981009763389881793660938E1L, + Q3 = 1.443958741356995763628660823395334281596E2L, + Q4 = -3.206441012484232867657763518369723873129E1L, + Q5 = -1.048560885341833443564920145642588991492E2L, + Q6 = 6.745883931909770880159915641984874746358E1L, + Q7 = 1.806809656342804436118449982647641392951E1L, + Q8 = -1.770150690652438294290020775359580915464E1L, + Q9 = -5.659156469628629327045433069052560211164E-1L, + /* 1.000000000000000000000000000000000000000E0 */ + + acosr4375 = 1.1179797320499710475919903296900511518755E0L, + pimacosr4375 = 2.0236129215398221908706530535894517323217E0L, + + /* asin(x) = x + x^3 pS(x^2) / qS(x^2) + 0 <= x <= 0.5 + peak relative error 1.9e-35 */ + pS0 = -8.358099012470680544198472400254596543711E2L, + pS1 = 3.674973957689619490312782828051860366493E3L, + pS2 = -6.730729094812979665807581609853656623219E3L, + pS3 = 6.643843795209060298375552684423454077633E3L, + pS4 = -3.817341990928606692235481812252049415993E3L, + pS5 = 1.284635388402653715636722822195716476156E3L, + pS6 = -2.410736125231549204856567737329112037867E2L, + pS7 = 2.219191969382402856557594215833622156220E1L, + pS8 = -7.249056260830627156600112195061001036533E-1L, + pS9 = 1.055923570937755300061509030361395604448E-3L, + + qS0 = -5.014859407482408326519083440151745519205E3L, + qS1 = 2.430653047950480068881028451580393430537E4L, + qS2 = -4.997904737193653607449250593976069726962E4L, + qS3 = 5.675712336110456923807959930107347511086E4L, + qS4 = -3.881523118339661268482937768522572588022E4L, + qS5 = 1.634202194895541569749717032234510811216E4L, + qS6 = -4.151452662440709301601820849901296953752E3L, + qS7 = 5.956050864057192019085175976175695342168E2L, + qS8 = -4.175375777334867025769346564600396877176E1L; + /* 1.000000000000000000000000000000000000000E0 */ + +long double +__ieee754_acosl (long double x) +{ + long double a, z, r, w, p, q, s, t, f2; + + if (__glibc_unlikely (isnan (x))) + return x + x; + a = __builtin_fabsl (x); + if (a == 1.0L) + { + if (x > 0.0L) + return 0.0; /* acos(1) = 0 */ + else + return (2.0 * pio2_hi) + (2.0 * pio2_lo); /* acos(-1)= pi */ + } + else if (a > 1.0L) + { + return (x - x) / (x - x); /* acos(|x| > 1) is NaN */ + } + if (a < 0.5L) + { + if (a < 0x1p-106L) + return pio2_hi + pio2_lo; + if (a < 0.4375L) + { + /* Arcsine of x. */ + z = x * x; + p = (((((((((pS9 * z + + pS8) * z + + pS7) * z + + pS6) * z + + pS5) * z + + pS4) * z + + pS3) * z + + pS2) * z + + pS1) * z + + pS0) * z; + q = (((((((( z + + qS8) * z + + qS7) * z + + qS6) * z + + qS5) * z + + qS4) * z + + qS3) * z + + qS2) * z + + qS1) * z + + qS0; + r = x + x * p / q; + z = pio2_hi - (r - pio2_lo); + return z; + } + /* .4375 <= |x| < .5 */ + t = a - 0.4375L; + p = ((((((((((P10 * t + + P9) * t + + P8) * t + + P7) * t + + P6) * t + + P5) * t + + P4) * t + + P3) * t + + P2) * t + + P1) * t + + P0) * t; + + q = (((((((((t + + Q9) * t + + Q8) * t + + Q7) * t + + Q6) * t + + Q5) * t + + Q4) * t + + Q3) * t + + Q2) * t + + Q1) * t + + Q0; + r = p / q; + if (x < 0.0L) + r = pimacosr4375 - r; + else + r = acosr4375 + r; + return r; + } + else if (a < 0.625L) + { + t = a - 0.5625L; + p = ((((((((((rS10 * t + + rS9) * t + + rS8) * t + + rS7) * t + + rS6) * t + + rS5) * t + + rS4) * t + + rS3) * t + + rS2) * t + + rS1) * t + + rS0) * t; + + q = (((((((((t + + sS9) * t + + sS8) * t + + sS7) * t + + sS6) * t + + sS5) * t + + sS4) * t + + sS3) * t + + sS2) * t + + sS1) * t + + sS0; + if (x < 0.0L) + r = pimacosr5625 - p / q; + else + r = acosr5625 + p / q; + return r; + } + else + { /* |x| >= .625 */ + double shi, slo; + + z = (one - a) * 0.5; + s = __ieee754_sqrtl (z); + /* Compute an extended precision square root from + the Newton iteration s -> 0.5 * (s + z / s). + The change w from s to the improved value is + w = 0.5 * (s + z / s) - s = (s^2 + z)/2s - s = (z - s^2)/2s. + Express s = f1 + f2 where f1 * f1 is exactly representable. + w = (z - s^2)/2s = (z - f1^2 - 2 f1 f2 - f2^2)/2s . + s + w has extended precision. */ + ldbl_unpack (s, &shi, &slo); + a = shi; + f2 = slo; + w = z - a * a; + w = w - 2.0 * a * f2; + w = w - f2 * f2; + w = w / (2.0 * s); + /* Arcsine of s. */ + p = (((((((((pS9 * z + + pS8) * z + + pS7) * z + + pS6) * z + + pS5) * z + + pS4) * z + + pS3) * z + + pS2) * z + + pS1) * z + + pS0) * z; + q = (((((((( z + + qS8) * z + + qS7) * z + + qS6) * z + + qS5) * z + + qS4) * z + + qS3) * z + + qS2) * z + + qS1) * z + + qS0; + r = s + (w + s * p / q); + + if (x < 0.0L) + w = pio2_hi + (pio2_lo - r); + else + w = r; + return 2.0 * w; + } +} +strong_alias (__ieee754_acosl, __acosl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_asinl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_asinl.c new file mode 100644 index 0000000000..6ed5e8d68d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_asinl.c @@ -0,0 +1,250 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + Long double expansions are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under the + following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* __ieee754_asin(x) + * Method : + * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ... + * we approximate asin(x) on [0,0.5] by + * asin(x) = x + x*x^2*R(x^2) + * Between .5 and .625 the approximation is + * asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x) + * For x in [0.625,1] + * asin(x) = pi/2-2*asin(sqrt((1-x)/2)) + * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2; + * then for x>0.98 + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo) + * For x<=0.98, let pio4_hi = pio2_hi/2, then + * f = hi part of s; + * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z) + * and + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo) + * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c)) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + */ + + +#include <float.h> +#include <math.h> +#include <math_private.h> +long double sqrtl (long double); + +static const long double + one = 1.0L, + huge = 1.0e+300L, + pio2_hi = 1.5707963267948966192313216916397514420986L, + pio2_lo = 4.3359050650618905123985220130216759843812E-35L, + pio4_hi = 7.8539816339744830961566084581987569936977E-1L, + + /* coefficient for R(x^2) */ + + /* asin(x) = x + x^3 pS(x^2) / qS(x^2) + 0 <= x <= 0.5 + peak relative error 1.9e-35 */ + pS0 = -8.358099012470680544198472400254596543711E2L, + pS1 = 3.674973957689619490312782828051860366493E3L, + pS2 = -6.730729094812979665807581609853656623219E3L, + pS3 = 6.643843795209060298375552684423454077633E3L, + pS4 = -3.817341990928606692235481812252049415993E3L, + pS5 = 1.284635388402653715636722822195716476156E3L, + pS6 = -2.410736125231549204856567737329112037867E2L, + pS7 = 2.219191969382402856557594215833622156220E1L, + pS8 = -7.249056260830627156600112195061001036533E-1L, + pS9 = 1.055923570937755300061509030361395604448E-3L, + + qS0 = -5.014859407482408326519083440151745519205E3L, + qS1 = 2.430653047950480068881028451580393430537E4L, + qS2 = -4.997904737193653607449250593976069726962E4L, + qS3 = 5.675712336110456923807959930107347511086E4L, + qS4 = -3.881523118339661268482937768522572588022E4L, + qS5 = 1.634202194895541569749717032234510811216E4L, + qS6 = -4.151452662440709301601820849901296953752E3L, + qS7 = 5.956050864057192019085175976175695342168E2L, + qS8 = -4.175375777334867025769346564600396877176E1L, + /* 1.000000000000000000000000000000000000000E0 */ + + /* asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x) + -0.0625 <= x <= 0.0625 + peak relative error 3.3e-35 */ + rS0 = -5.619049346208901520945464704848780243887E0L, + rS1 = 4.460504162777731472539175700169871920352E1L, + rS2 = -1.317669505315409261479577040530751477488E2L, + rS3 = 1.626532582423661989632442410808596009227E2L, + rS4 = -3.144806644195158614904369445440583873264E1L, + rS5 = -9.806674443470740708765165604769099559553E1L, + rS6 = 5.708468492052010816555762842394927806920E1L, + rS7 = 1.396540499232262112248553357962639431922E1L, + rS8 = -1.126243289311910363001762058295832610344E1L, + rS9 = -4.956179821329901954211277873774472383512E-1L, + rS10 = 3.313227657082367169241333738391762525780E-1L, + + sS0 = -4.645814742084009935700221277307007679325E0L, + sS1 = 3.879074822457694323970438316317961918430E1L, + sS2 = -1.221986588013474694623973554726201001066E2L, + sS3 = 1.658821150347718105012079876756201905822E2L, + sS4 = -4.804379630977558197953176474426239748977E1L, + sS5 = -1.004296417397316948114344573811562952793E2L, + sS6 = 7.530281592861320234941101403870010111138E1L, + sS7 = 1.270735595411673647119592092304357226607E1L, + sS8 = -1.815144839646376500705105967064792930282E1L, + sS9 = -7.821597334910963922204235247786840828217E-2L, + /* 1.000000000000000000000000000000000000000E0 */ + + asinr5625 = 5.9740641664535021430381036628424864397707E-1L; + + + +long double +__ieee754_asinl (long double x) +{ + long double a, t, w, p, q, c, r, s; + int flag; + + if (__glibc_unlikely (isnan (x))) + return x + x; + flag = 0; + a = __builtin_fabsl (x); + if (a == 1.0L) /* |x|>= 1 */ + return x * pio2_hi + x * pio2_lo; /* asin(1)=+-pi/2 with inexact */ + else if (a >= 1.0L) + return (x - x) / (x - x); /* asin(|x|>1) is NaN */ + else if (a < 0.5L) + { + if (a < 6.938893903907228e-18L) /* |x| < 2**-57 */ + { + math_check_force_underflow (x); + long double force_inexact = huge + x; + math_force_eval (force_inexact); + return x; /* return x with inexact if x!=0 */ + } + else + { + t = x * x; + /* Mark to use pS, qS later on. */ + flag = 1; + } + } + else if (a < 0.625L) + { + t = a - 0.5625; + p = ((((((((((rS10 * t + + rS9) * t + + rS8) * t + + rS7) * t + + rS6) * t + + rS5) * t + + rS4) * t + + rS3) * t + + rS2) * t + + rS1) * t + + rS0) * t; + + q = ((((((((( t + + sS9) * t + + sS8) * t + + sS7) * t + + sS6) * t + + sS5) * t + + sS4) * t + + sS3) * t + + sS2) * t + + sS1) * t + + sS0; + t = asinr5625 + p / q; + if (x > 0.0L) + return t; + else + return -t; + } + else + { + /* 1 > |x| >= 0.625 */ + w = one - a; + t = w * 0.5; + } + + p = (((((((((pS9 * t + + pS8) * t + + pS7) * t + + pS6) * t + + pS5) * t + + pS4) * t + + pS3) * t + + pS2) * t + + pS1) * t + + pS0) * t; + + q = (((((((( t + + qS8) * t + + qS7) * t + + qS6) * t + + qS5) * t + + qS4) * t + + qS3) * t + + qS2) * t + + qS1) * t + + qS0; + + if (flag) /* 2^-57 < |x| < 0.5 */ + { + w = p / q; + return x + x * w; + } + + s = __ieee754_sqrtl (t); + if (a > 0.975L) + { + w = p / q; + t = pio2_hi - (2.0 * (s + s * w) - pio2_lo); + } + else + { + w = ldbl_high (s); + c = (t - w * w) / (s + w); + r = p / q; + p = 2.0 * s * r - (pio2_lo - 2.0 * c); + q = pio4_hi - 2.0 * w; + t = pio4_hi - (p - q); + } + + if (x > 0.0L) + return t; + else + return -t; +} +strong_alias (__ieee754_asinl, __asinl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_atan2l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_atan2l.c new file mode 100644 index 0000000000..b625323df3 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_atan2l.c @@ -0,0 +1,122 @@ +/* e_atan2l.c -- long double version of e_atan2.c. + * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_atan2l(y,x) + * Method : + * 1. Reduce y to positive by atan2l(y,x)=-atan2l(-y,x). + * 2. Reduce x to positive by (if x and y are unexceptional): + * ARG (x+iy) = arctan(y/x) ... if x > 0, + * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, + * + * Special cases: + * + * ATAN2((anything), NaN ) is NaN; + * ATAN2(NAN , (anything) ) is NaN; + * ATAN2(+-0, +(anything but NaN)) is +-0 ; + * ATAN2(+-0, -(anything but NaN)) is +-pi ; + * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; + * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; + * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; + * ATAN2(+-INF,+INF ) is +-pi/4 ; + * ATAN2(+-INF,-INF ) is +-3pi/4; + * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include <math.h> +#include <math_private.h> + +static const long double +tiny = 1.0e-300L, +zero = 0.0, +pi_o_4 = 7.85398163397448309615660845819875699e-01L, /* 3ffe921fb54442d18469898cc51701b8 */ +pi_o_2 = 1.57079632679489661923132169163975140e+00L, /* 3fff921fb54442d18469898cc51701b8 */ +pi = 3.14159265358979323846264338327950280e+00L, /* 4000921fb54442d18469898cc51701b8 */ +pi_lo = 8.67181013012378102479704402604335225e-35L; /* 3f8dcd129024e088a67cc74020bbea64 */ + +long double +__ieee754_atan2l(long double y, long double x) +{ + long double z; + int64_t k,m,hx,hy,ix,iy; + uint64_t lx; + double xhi, xlo, yhi; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + ix = hx&0x7fffffffffffffffLL; + yhi = ldbl_high (y); + EXTRACT_WORDS64 (hy, yhi); + iy = hy&0x7fffffffffffffffLL; + if(((ix)>0x7ff0000000000000LL)|| + ((iy)>0x7ff0000000000000LL)) /* x or y is NaN */ + return x+y; + if(((hx-0x3ff0000000000000LL))==0 + && (lx&0x7fffffffffffffff)==0) return __atanl(y); /* x=1.0L */ + m = ((hy>>63)&1)|((hx>>62)&2); /* 2*sign(x)+sign(y) */ + + /* when y = 0 */ + if(iy==0) { + switch(m) { + case 0: + case 1: return y; /* atan(+-0,+anything)=+-0 */ + case 2: return pi+tiny;/* atan(+0,-anything) = pi */ + case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ + } + } + /* when x = 0 */ + if(ix==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* when x is INF */ + if(ix==0x7ff0000000000000LL) { + if(iy==0x7ff0000000000000LL) { + switch(m) { + case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ + case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ + case 2: return 3.0L*pi_o_4+tiny;/*atan(+INF,-INF)*/ + case 3: return -3.0L*pi_o_4-tiny;/*atan(-INF,-INF)*/ + } + } else { + switch(m) { + case 0: return zero ; /* atan(+...,+INF) */ + case 1: return -zero ; /* atan(-...,+INF) */ + case 2: return pi+tiny ; /* atan(+...,-INF) */ + case 3: return -pi-tiny ; /* atan(-...,-INF) */ + } + } + } + /* when y is INF */ + if(iy==0x7ff0000000000000LL) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* compute y/x */ + k = (iy-ix)>>52; + if(k > 120) z=pi_o_2+0.5L*pi_lo; /* |y/x| > 2**120 */ + else if(hx<0&&k<-120) z=0.0L; /* |y|/x < -2**120 */ + else z=__atanl(fabsl(y/x)); /* safe to do y/x */ + switch (m) { + case 0: return z ; /* atan(+,+) */ + case 1: return -z ; /* atan(-,+) */ + case 2: return pi-(z-pi_lo);/* atan(+,-) */ + default: /* case 3 */ + return (z-pi_lo)-pi;/* atan(-,-) */ + } +} +strong_alias (__ieee754_atan2l, __atan2l_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_atanhl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_atanhl.c new file mode 100644 index 0000000000..b576f42030 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_atanhl.c @@ -0,0 +1,71 @@ +/* @(#)e_atanh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_atanh(x) + * Method : + * 1.Reduced x to positive by atanh(-x) = -atanh(x) + * 2.For x>=0.5 + * 1 2x x + * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) + * 2 1 - x 1 - x + * + * For x<0.5 + * atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) + * + * Special cases: + * atanh(x) is NaN if |x| > 1 with signal; + * atanh(NaN) is that NaN with no signal; + * atanh(+-1) is +-INF with signal. + * + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const long double one = 1.0L, huge = 1e300L; + +static const long double zero = 0.0L; + +long double +__ieee754_atanhl(long double x) +{ + long double t; + int64_t hx,ix; + double xhi; + + xhi = ldbl_high (x); + EXTRACT_WORDS64 (hx, xhi); + ix = hx&0x7fffffffffffffffLL; + if (ix >= 0x3ff0000000000000LL) { /* |x|>=1 */ + if (ix > 0x3ff0000000000000LL) + return (x-x)/(x-x); + t = fabsl (x); + if (t > one) + return (x-x)/(x-x); + if (t == one) + return x/zero; + } + if(ix<0x3c70000000000000LL&&(huge+x)>zero) /* x<2**-56 */ + { + math_check_force_underflow (x); + return x; + } + x = fabsl (x); + if(ix<0x3fe0000000000000LL) { /* x < 0.5 */ + t = x+x; + t = 0.5*__log1pl(t+t*x/(one-x)); + } else + t = 0.5*__log1pl((x+x)/(one-x)); + if(hx>=0) return t; else return -t; +} +strong_alias (__ieee754_atanhl, __atanhl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_coshl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_coshl.c new file mode 100644 index 0000000000..327b2ab960 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_coshl.c @@ -0,0 +1,81 @@ +/* @(#)e_cosh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_cosh(x) + * Method : + * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 + * 1. Replace x by |x| (cosh(x) = cosh(-x)). + * 2. + * [ exp(x) - 1 ]^2 + * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- + * 2*exp(x) + * + * exp(x) + 1/exp(x) + * ln2/2 <= x <= 40 : cosh(x) := ------------------- + * 2 + * 40 <= x <= lnovft : cosh(x) := exp(x)/2 + * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) + * ln2ovft < x : cosh(x) := huge*huge (overflow) + * + * Special cases: + * cosh(x) is |x| if x is +INF, -INF, or NaN. + * only cosh(0)=1 is exact for finite x. + */ + +#include <math.h> +#include <math_private.h> + +static const long double one = 1.0L, half=0.5L, huge = 1.0e300L; + +long double +__ieee754_coshl (long double x) +{ + long double t,w; + int64_t ix; + double xhi; + + /* High word of |x|. */ + xhi = ldbl_high (x); + EXTRACT_WORDS64 (ix, xhi); + ix &= 0x7fffffffffffffffLL; + + /* x is INF or NaN */ + if(ix>=0x7ff0000000000000LL) return x*x; + + /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ + if(ix<0x3fd62e42fefa39efLL) { + if (ix<0x3c80000000000000LL) return one; /* cosh(tiny) = 1 */ + t = __expm1l(fabsl(x)); + w = one+t; + return one+(t*t)/(w+w); + } + + /* |x| in [0.5*ln2,40], return (exp(|x|)+1/exp(|x|)/2; */ + if (ix < 0x4044000000000000LL) { + t = __ieee754_expl(fabsl(x)); + return half*t+half/t; + } + + /* |x| in [40, log(maxdouble)] return half*exp(|x|) */ + if (ix < 0x40862e42fefa39efLL) return half*__ieee754_expl(fabsl(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + if (ix < 0x408633ce8fb9f87fLL) { + w = __ieee754_expl(half*fabsl(x)); + t = half*w; + return t*w; + } + + /* |x| > overflowthresold, cosh(x) overflow */ + return huge*huge; +} +strong_alias (__ieee754_coshl, __coshl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_exp10l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_exp10l.c new file mode 100644 index 0000000000..6c3b6f5589 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_exp10l.c @@ -0,0 +1,48 @@ +/* Copyright (C) 2012-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +static const long double log10_high = 0x2.4d763776aaap+0L; +static const long double log10_low = 0x2.b05ba95b58ae0b4c28a38a3fb4p-48L; + +long double +__ieee754_exp10l (long double arg) +{ + union ibm_extended_long_double u; + long double arg_high, arg_low; + long double exp_high, exp_low; + + if (!isfinite (arg)) + return __ieee754_expl (arg); + if (arg < LDBL_MIN_10_EXP - LDBL_DIG - 10) + return LDBL_MIN * LDBL_MIN; + else if (arg > LDBL_MAX_10_EXP + 1) + return LDBL_MAX * LDBL_MAX; + else if (fabsl (arg) < 0x1p-109L) + return 1.0L; + + u.ld = arg; + arg_high = u.d[0].d; + arg_low = u.d[1].d; + exp_high = arg_high * log10_high; + exp_low = arg_high * log10_low + arg_low * M_LN10l; + return __ieee754_expl (exp_high) * __ieee754_expl (exp_low); +} +strong_alias (__ieee754_exp10l, __exp10l_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_expl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_expl.c new file mode 100644 index 0000000000..10df6bb7d5 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_expl.c @@ -0,0 +1,256 @@ +/* Quad-precision floating point e^x. + Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jj@ultra.linux.cz> + Partly based on double-precision code + by Geoffrey Keating <geoffk@ozemail.com.au> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* The basic design here is from + Abraham Ziv, "Fast Evaluation of Elementary Mathematical Functions with + Correctly Rounded Last Bit", ACM Trans. Math. Soft., 17 (3), September 1991, + pp. 410-423. + + We work with number pairs where the first number is the high part and + the second one is the low part. Arithmetic with the high part numbers must + be exact, without any roundoff errors. + + The input value, X, is written as + X = n * ln(2)_0 + arg1[t1]_0 + arg2[t2]_0 + x + - n * ln(2)_1 + arg1[t1]_1 + arg2[t2]_1 + xl + + where: + - n is an integer, 16384 >= n >= -16495; + - ln(2)_0 is the first 93 bits of ln(2), and |ln(2)_0-ln(2)-ln(2)_1| < 2^-205 + - t1 is an integer, 89 >= t1 >= -89 + - t2 is an integer, 65 >= t2 >= -65 + - |arg1[t1]-t1/256.0| < 2^-53 + - |arg2[t2]-t2/32768.0| < 2^-53 + - x + xl is whatever is left, |x + xl| < 2^-16 + 2^-53 + + Then e^x is approximated as + + e^x = 2^n_1 ( 2^n_0 e^(arg1[t1]_0 + arg1[t1]_1) e^(arg2[t2]_0 + arg2[t2]_1) + + 2^n_0 e^(arg1[t1]_0 + arg1[t1]_1) e^(arg2[t2]_0 + arg2[t2]_1) + * p (x + xl + n * ln(2)_1)) + where: + - p(x) is a polynomial approximating e(x)-1 + - e^(arg1[t1]_0 + arg1[t1]_1) is obtained from a table + - e^(arg2[t2]_0 + arg2[t2]_1) likewise + - n_1 + n_0 = n, so that |n_0| < -LDBL_MIN_EXP-1. + + If it happens that n_1 == 0 (this is the usual case), that multiplication + is omitted. + */ + +#ifndef _GNU_SOURCE +#define _GNU_SOURCE +#endif +#include <float.h> +#include <ieee754.h> +#include <math.h> +#include <fenv.h> +#include <inttypes.h> +#include <math_private.h> + +#define _Float128 long double +#define L(x) x ## L + +#include <sysdeps/ieee754/ldbl-128/t_expl.h> + +static const long double C[] = { +/* Smallest integer x for which e^x overflows. */ +#define himark C[0] + 709.78271289338399678773454114191496482L, + +/* Largest integer x for which e^x underflows. */ +#define lomark C[1] +-744.44007192138126231410729844608163411L, + +/* 3x2^96 */ +#define THREEp96 C[2] + 59421121885698253195157962752.0L, + +/* 3x2^103 */ +#define THREEp103 C[3] + 30423614405477505635920876929024.0L, + +/* 3x2^111 */ +#define THREEp111 C[4] + 7788445287802241442795744493830144.0L, + +/* 1/ln(2) */ +#define M_1_LN2 C[5] + 1.44269504088896340735992468100189204L, + +/* first 93 bits of ln(2) */ +#define M_LN2_0 C[6] + 0.693147180559945309417232121457981864L, + +/* ln2_0 - ln(2) */ +#define M_LN2_1 C[7] +-1.94704509238074995158795957333327386E-31L, + +/* very small number */ +#define TINY C[8] + 1.0e-308L, + +/* 2^16383 */ +#define TWO1023 C[9] + 8.988465674311579538646525953945123668E+307L, + +/* 256 */ +#define TWO8 C[10] + 256.0L, + +/* 32768 */ +#define TWO15 C[11] + 32768.0L, + +/* Chebyshev polynom coefficients for (exp(x)-1)/x */ +#define P1 C[12] +#define P2 C[13] +#define P3 C[14] +#define P4 C[15] +#define P5 C[16] +#define P6 C[17] + 0.5L, + 1.66666666666666666666666666666666683E-01L, + 4.16666666666666666666654902320001674E-02L, + 8.33333333333333333333314659767198461E-03L, + 1.38888888889899438565058018857254025E-03L, + 1.98412698413981650382436541785404286E-04L, +}; + +long double +__ieee754_expl (long double x) +{ + long double result, x22; + union ibm_extended_long_double ex2_u, scale_u; + int unsafe; + + /* Check for usual case. */ + if (isless (x, himark) && isgreater (x, lomark)) + { + int tval1, tval2, n_i, exponent2; + long double n, xl; + + SET_RESTORE_ROUND (FE_TONEAREST); + + n = __roundl (x*M_1_LN2); + x = x-n*M_LN2_0; + xl = n*M_LN2_1; + + tval1 = __roundl (x*TWO8); + x -= __expl_table[T_EXPL_ARG1+2*tval1]; + xl -= __expl_table[T_EXPL_ARG1+2*tval1+1]; + + tval2 = __roundl (x*TWO15); + x -= __expl_table[T_EXPL_ARG2+2*tval2]; + xl -= __expl_table[T_EXPL_ARG2+2*tval2+1]; + + x = x + xl; + + /* Compute ex2 = 2^n_0 e^(argtable[tval1]) e^(argtable[tval2]). */ + ex2_u.ld = (__expl_table[T_EXPL_RES1 + tval1] + * __expl_table[T_EXPL_RES2 + tval2]); + n_i = (int)n; + /* 'unsafe' is 1 iff n_1 != 0. */ + unsafe = fabsl(n_i) >= -LDBL_MIN_EXP - 1; + ex2_u.d[0].ieee.exponent += n_i >> unsafe; + /* Fortunately, there are no subnormal lowpart doubles in + __expl_table, only normal values and zeros. + But after scaling it can be subnormal. */ + exponent2 = ex2_u.d[1].ieee.exponent + (n_i >> unsafe); + if (ex2_u.d[1].ieee.exponent == 0) + /* assert ((ex2_u.d[1].ieee.mantissa0|ex2_u.d[1].ieee.mantissa1) == 0) */; + else if (exponent2 > 0) + ex2_u.d[1].ieee.exponent = exponent2; + else if (exponent2 <= -54) + { + ex2_u.d[1].ieee.exponent = 0; + ex2_u.d[1].ieee.mantissa0 = 0; + ex2_u.d[1].ieee.mantissa1 = 0; + } + else + { + static const double + two54 = 1.80143985094819840000e+16, /* 4350000000000000 */ + twom54 = 5.55111512312578270212e-17; /* 3C90000000000000 */ + ex2_u.d[1].d *= two54; + ex2_u.d[1].ieee.exponent += n_i >> unsafe; + ex2_u.d[1].d *= twom54; + } + + /* Compute scale = 2^n_1. */ + scale_u.ld = 1.0L; + scale_u.d[0].ieee.exponent += n_i - (n_i >> unsafe); + + /* Approximate e^x2 - 1, using a seventh-degree polynomial, + with maximum error in [-2^-16-2^-53,2^-16+2^-53] + less than 4.8e-39. */ + x22 = x + x*x*(P1+x*(P2+x*(P3+x*(P4+x*(P5+x*P6))))); + + /* Now we can test whether the result is ultimate or if we are unsure. + In the later case we should probably call a mpn based routine to give + the ultimate result. + Empirically, this routine is already ultimate in about 99.9986% of + cases, the test below for the round to nearest case will be false + in ~ 99.9963% of cases. + Without proc2 routine maximum error which has been seen is + 0.5000262 ulp. + + union ieee854_long_double ex3_u; + + #ifdef FE_TONEAREST + fesetround (FE_TONEAREST); + #endif + ex3_u.d = (result - ex2_u.d) - x22 * ex2_u.d; + ex2_u.d = result; + ex3_u.ieee.exponent += LDBL_MANT_DIG + 15 + IEEE854_LONG_DOUBLE_BIAS + - ex2_u.ieee.exponent; + n_i = abs (ex3_u.d); + n_i = (n_i + 1) / 2; + fesetenv (&oldenv); + #ifdef FE_TONEAREST + if (fegetround () == FE_TONEAREST) + n_i -= 0x4000; + #endif + if (!n_i) { + return __ieee754_expl_proc2 (origx); + } + */ + } + /* Exceptional cases: */ + else if (isless (x, himark)) + { + if (isinf (x)) + /* e^-inf == 0, with no error. */ + return 0; + else + /* Underflow */ + return TINY * TINY; + } + else + /* Return x, if x is a NaN or Inf; or overflow, otherwise. */ + return TWO1023*x; + + result = x22 * ex2_u.ld + ex2_u.ld; + if (!unsafe) + return result; + return result * scale_u.ld; +} +strong_alias (__ieee754_expl, __expl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_fmodl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_fmodl.c new file mode 100644 index 0000000000..5284fd0fd5 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_fmodl.c @@ -0,0 +1,149 @@ +/* e_fmodl.c -- long double version of e_fmod.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * __ieee754_fmodl(x,y) + * Return x mod y in exact arithmetic + * Method: shift and subtract + */ + +#include <math.h> +#include <math_private.h> +#include <ieee754.h> + +static const long double one = 1.0, Zero[] = {0.0, -0.0,}; + +long double +__ieee754_fmodl (long double x, long double y) +{ + int64_t hx, hy, hz, sx, sy; + uint64_t lx, ly, lz; + int n, ix, iy; + double xhi, xlo, yhi, ylo; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + ldbl_unpack (y, &yhi, &ylo); + EXTRACT_WORDS64 (hy, yhi); + EXTRACT_WORDS64 (ly, ylo); + sx = hx&0x8000000000000000ULL; /* sign of x */ + hx ^= sx; /* |x| */ + sy = hy&0x8000000000000000ULL; /* sign of y */ + hy ^= sy; /* |y| */ + + /* purge off exception values */ + if(__builtin_expect(hy==0 || + (hx>=0x7ff0000000000000LL)|| /* y=0,or x not finite */ + (hy>0x7ff0000000000000LL),0)) /* or y is NaN */ + return (x*y)/(x*y); + if (__glibc_unlikely (hx <= hy)) + { + /* If |x| < |y| return x. */ + if (hx < hy) + return x; + /* At this point the absolute value of the high doubles of + x and y must be equal. */ + if ((lx & 0x7fffffffffffffffLL) == 0 + && (ly & 0x7fffffffffffffffLL) == 0) + /* Both low parts are zero. The result should be an + appropriately signed zero, but the subsequent logic + could treat them as unequal, depending on the signs + of the low parts. */ + return Zero[(uint64_t) sx >> 63]; + /* If the low double of y is the same sign as the high + double of y (ie. the low double increases |y|)... */ + if (((ly ^ sy) & 0x8000000000000000LL) == 0 + /* ... then a different sign low double to high double + for x or same sign but lower magnitude... */ + && (int64_t) (lx ^ sx) < (int64_t) (ly ^ sy)) + /* ... means |x| < |y|. */ + return x; + /* If the low double of x differs in sign to the high + double of x (ie. the low double decreases |x|)... */ + if (((lx ^ sx) & 0x8000000000000000LL) != 0 + /* ... then a different sign low double to high double + for y with lower magnitude (we've already caught + the same sign for y case above)... */ + && (int64_t) (lx ^ sx) > (int64_t) (ly ^ sy)) + /* ... means |x| < |y|. */ + return x; + /* If |x| == |y| return x*0. */ + if ((lx ^ sx) == (ly ^ sy)) + return Zero[(uint64_t) sx >> 63]; + } + + /* Make the IBM extended format 105 bit mantissa look like the ieee854 112 + bit mantissa so the following operations will give the correct + result. */ + ldbl_extract_mantissa(&hx, &lx, &ix, x); + ldbl_extract_mantissa(&hy, &ly, &iy, y); + + if (__glibc_unlikely (ix == -IEEE754_DOUBLE_BIAS)) + { + /* subnormal x, shift x to normal. */ + while ((hx & (1LL << 48)) == 0) + { + hx = (hx << 1) | (lx >> 63); + lx = lx << 1; + ix -= 1; + } + } + + if (__glibc_unlikely (iy == -IEEE754_DOUBLE_BIAS)) + { + /* subnormal y, shift y to normal. */ + while ((hy & (1LL << 48)) == 0) + { + hy = (hy << 1) | (ly >> 63); + ly = ly << 1; + iy -= 1; + } + } + + /* fix point fmod */ + n = ix - iy; + while(n--) { + hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; + if(hz<0){hx = hx+hx+(lx>>63); lx = lx+lx;} + else { + if((hz|lz)==0) /* return sign(x)*0 */ + return Zero[(u_int64_t)sx>>63]; + hx = hz+hz+(lz>>63); lx = lz+lz; + } + } + hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; + if(hz>=0) {hx=hz;lx=lz;} + + /* convert back to floating value and restore the sign */ + if((hx|lx)==0) /* return sign(x)*0 */ + return Zero[(u_int64_t)sx>>63]; + while(hx<0x0001000000000000LL) { /* normalize x */ + hx = hx+hx+(lx>>63); lx = lx+lx; + iy -= 1; + } + if(__builtin_expect(iy>= -1022,0)) { /* normalize output */ + x = ldbl_insert_mantissa((sx>>63), iy, hx, lx); + } else { /* subnormal output */ + n = -1022 - iy; + /* We know 1 <= N <= 52, and that there are no nonzero + bits in places below 2^-1074. */ + lx = (lx >> n) | ((u_int64_t) hx << (64 - n)); + hx >>= n; + x = ldbl_insert_mantissa((sx>>63), -1023, hx, lx); + x *= one; /* create necessary signal */ + } + return x; /* exact output */ +} +strong_alias (__ieee754_fmodl, __fmodl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c new file mode 100644 index 0000000000..81dbe42c79 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c @@ -0,0 +1,218 @@ +/* Implementation of gamma function according to ISO C. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz, 1999. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's + approximation to gamma function. */ + +static const long double gamma_coeff[] = + { + 0x1.555555555555555555555555558p-4L, + -0xb.60b60b60b60b60b60b60b60b6p-12L, + 0x3.4034034034034034034034034p-12L, + -0x2.7027027027027027027027027p-12L, + 0x3.72a3c5631fe46ae1d4e700dca9p-12L, + -0x7.daac36664f1f207daac36664f2p-12L, + 0x1.a41a41a41a41a41a41a41a41a4p-8L, + -0x7.90a1b2c3d4e5f708192a3b4c5ep-8L, + 0x2.dfd2c703c0cfff430edfd2c704p-4L, + -0x1.6476701181f39edbdb9ce625988p+0L, + 0xd.672219167002d3a7a9c886459cp+0L, + -0x9.cd9292e6660d55b3f712eb9e08p+4L, + 0x8.911a740da740da740da740da74p+8L, + }; + +#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0])) + +/* Return gamma (X), for positive X less than 191, in the form R * + 2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to + avoid overflow or underflow in intermediate calculations. */ + +static long double +gammal_positive (long double x, int *exp2_adj) +{ + int local_signgam; + if (x < 0.5L) + { + *exp2_adj = 0; + return __ieee754_expl (__ieee754_lgammal_r (x + 1, &local_signgam)) / x; + } + else if (x <= 1.5L) + { + *exp2_adj = 0; + return __ieee754_expl (__ieee754_lgammal_r (x, &local_signgam)); + } + else if (x < 11.5L) + { + /* Adjust into the range for using exp (lgamma). */ + *exp2_adj = 0; + long double n = __ceill (x - 1.5L); + long double x_adj = x - n; + long double eps; + long double prod = __gamma_productl (x_adj, 0, n, &eps); + return (__ieee754_expl (__ieee754_lgammal_r (x_adj, &local_signgam)) + * prod * (1.0L + eps)); + } + else + { + long double eps = 0; + long double x_eps = 0; + long double x_adj = x; + long double prod = 1; + if (x < 23.0L) + { + /* Adjust into the range for applying Stirling's + approximation. */ + long double n = __ceill (23.0L - x); + x_adj = x + n; + x_eps = (x - (x_adj - n)); + prod = __gamma_productl (x_adj - n, x_eps, n, &eps); + } + /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)). + Compute gamma (X_ADJ + X_EPS) using Stirling's approximation, + starting by computing pow (X_ADJ, X_ADJ) with a power of 2 + factored out. */ + long double exp_adj = -eps; + long double x_adj_int = __roundl (x_adj); + long double x_adj_frac = x_adj - x_adj_int; + int x_adj_log2; + long double x_adj_mant = __frexpl (x_adj, &x_adj_log2); + if (x_adj_mant < M_SQRT1_2l) + { + x_adj_log2--; + x_adj_mant *= 2.0L; + } + *exp2_adj = x_adj_log2 * (int) x_adj_int; + long double ret = (__ieee754_powl (x_adj_mant, x_adj) + * __ieee754_exp2l (x_adj_log2 * x_adj_frac) + * __ieee754_expl (-x_adj) + * __ieee754_sqrtl (2 * M_PIl / x_adj) + / prod); + exp_adj += x_eps * __ieee754_logl (x_adj); + long double bsum = gamma_coeff[NCOEFF - 1]; + long double x_adj2 = x_adj * x_adj; + for (size_t i = 1; i <= NCOEFF - 1; i++) + bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i]; + exp_adj += bsum / x_adj; + return ret + ret * __expm1l (exp_adj); + } +} + +long double +__ieee754_gammal_r (long double x, int *signgamp) +{ + int64_t hx; + double xhi; + long double ret; + + xhi = ldbl_high (x); + EXTRACT_WORDS64 (hx, xhi); + + if ((hx & 0x7fffffffffffffffLL) == 0) + { + /* Return value for x == 0 is Inf with divide by zero exception. */ + *signgamp = 0; + return 1.0 / x; + } + if (hx < 0 && (u_int64_t) hx < 0xfff0000000000000ULL && __rintl (x) == x) + { + /* Return value for integer x < 0 is NaN with invalid exception. */ + *signgamp = 0; + return (x - x) / (x - x); + } + if (hx == 0xfff0000000000000ULL) + { + /* x == -Inf. According to ISO this is NaN. */ + *signgamp = 0; + return x - x; + } + if ((hx & 0x7ff0000000000000ULL) == 0x7ff0000000000000ULL) + { + /* Positive infinity (return positive infinity) or NaN (return + NaN). */ + *signgamp = 0; + return x + x; + } + + if (x >= 172.0L) + { + /* Overflow. */ + *signgamp = 0; + return LDBL_MAX * LDBL_MAX; + } + else + { + SET_RESTORE_ROUNDL (FE_TONEAREST); + if (x > 0.0L) + { + *signgamp = 0; + int exp2_adj; + ret = gammal_positive (x, &exp2_adj); + ret = __scalbnl (ret, exp2_adj); + } + else if (x >= -0x1p-110L) + { + *signgamp = 0; + ret = 1.0L / x; + } + else + { + long double tx = __truncl (x); + *signgamp = (tx == 2.0L * __truncl (tx / 2.0L)) ? -1 : 1; + if (x <= -191.0L) + /* Underflow. */ + ret = LDBL_MIN * LDBL_MIN; + else + { + long double frac = tx - x; + if (frac > 0.5L) + frac = 1.0L - frac; + long double sinpix = (frac <= 0.25L + ? __sinl (M_PIl * frac) + : __cosl (M_PIl * (0.5L - frac))); + int exp2_adj; + ret = M_PIl / (-x * sinpix + * gammal_positive (-x, &exp2_adj)); + ret = __scalbnl (ret, -exp2_adj); + math_check_force_underflow_nonneg (ret); + } + } + } + if (isinf (ret) && x != 0) + { + if (*signgamp < 0) + return -(-__copysignl (LDBL_MAX, ret) * LDBL_MAX); + else + return __copysignl (LDBL_MAX, ret) * LDBL_MAX; + } + else if (ret == 0) + { + if (*signgamp < 0) + return -(-__copysignl (LDBL_MIN, ret) * LDBL_MIN); + else + return __copysignl (LDBL_MIN, ret) * LDBL_MIN; + } + else + return ret; +} +strong_alias (__ieee754_gammal_r, __gammal_r_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c new file mode 100644 index 0000000000..de5a66ab05 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c @@ -0,0 +1,138 @@ +/* @(#)e_hypotl.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_hypotl(x,y) + * + * Method : + * If (assume round-to-nearest) z=x*x+y*y + * has error less than sqrtl(2)/2 ulp, than + * sqrtl(z) has error less than 1 ulp (exercise). + * + * So, compute sqrtl(x*x+y*y) with some care as + * follows to get the error below 1 ulp: + * + * Assume x>y>0; + * (if possible, set rounding to round-to-nearest) + * 1. if x > 2y use + * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y + * where x1 = x with lower 53 bits cleared, x2 = x-x1; else + * 2. if x <= 2y use + * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) + * where t1 = 2x with lower 53 bits cleared, t2 = 2x-t1, + * y1= y with lower 53 bits chopped, y2 = y-y1. + * + * NOTE: scaling may be necessary if some argument is too + * large or too tiny + * + * Special cases: + * hypotl(x,y) is INF if x or y is +INF or -INF; else + * hypotl(x,y) is NAN if x or y is NAN. + * + * Accuracy: + * hypotl(x,y) returns sqrtl(x^2+y^2) with error less + * than 1 ulps (units in the last place) + */ + +#include <math.h> +#include <math_private.h> + +long double +__ieee754_hypotl(long double x, long double y) +{ + long double a,b,a1,a2,b1,b2,w,kld; + int64_t j,k,ha,hb; + double xhi, yhi, hi, lo; + + xhi = ldbl_high (x); + EXTRACT_WORDS64 (ha, xhi); + yhi = ldbl_high (y); + EXTRACT_WORDS64 (hb, yhi); + ha &= 0x7fffffffffffffffLL; + hb &= 0x7fffffffffffffffLL; + if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} + a = fabsl(a); /* a <- |a| */ + b = fabsl(b); /* b <- |b| */ + if((ha-hb)>0x0780000000000000LL) {return a+b;} /* x/y > 2**120 */ + k=0; + kld = 1.0L; + if(ha > 0x5f30000000000000LL) { /* a>2**500 */ + if(ha >= 0x7ff0000000000000LL) { /* Inf or NaN */ + w = a+b; /* for sNaN */ + if (issignaling (a) || issignaling (b)) + return w; + if(ha == 0x7ff0000000000000LL) + w = a; + if(hb == 0x7ff0000000000000LL) + w = b; + return w; + } + /* scale a and b by 2**-600 */ + a *= 0x1p-600L; + b *= 0x1p-600L; + k = 600; + kld = 0x1p+600L; + } + else if(hb < 0x23d0000000000000LL) { /* b < 2**-450 */ + if(hb <= 0x000fffffffffffffLL) { /* subnormal b or 0 */ + if(hb==0) return a; + a *= 0x1p+1022L; + b *= 0x1p+1022L; + k = -1022; + kld = 0x1p-1022L; + } else { /* scale a and b by 2^600 */ + a *= 0x1p+600L; + b *= 0x1p+600L; + k = -600; + kld = 0x1p-600L; + } + } + /* medium size a and b */ + w = a-b; + if (w>b) { + ldbl_unpack (a, &hi, &lo); + a1 = hi; + a2 = lo; + /* a*a + b*b + = (a1+a2)*a + b*b + = a1*a + a2*a + b*b + = a1*(a1+a2) + a2*a + b*b + = a1*a1 + a1*a2 + a2*a + b*b + = a1*a1 + a2*(a+a1) + b*b */ + w = __ieee754_sqrtl(a1*a1-(b*(-b)-a2*(a+a1))); + } else { + a = a+a; + ldbl_unpack (b, &hi, &lo); + b1 = hi; + b2 = lo; + ldbl_unpack (a, &hi, &lo); + a1 = hi; + a2 = lo; + /* a*a + b*b + = a*a + (a-b)*(a-b) - (a-b)*(a-b) + b*b + = a*a + w*w - (a*a - 2*a*b + b*b) + b*b + = w*w + 2*a*b + = w*w + (a1+a2)*b + = w*w + a1*b + a2*b + = w*w + a1*(b1+b2) + a2*b + = w*w + a1*b1 + a1*b2 + a2*b */ + w = __ieee754_sqrtl(a1*b1-(w*(-w)-(a1*b2+a2*b))); + } + if(k!=0) + { + w *= kld; + math_check_force_underflow_nonneg (w); + return w; + } + else + return w; +} +strong_alias (__ieee754_hypotl, __hypotl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_ilogbl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_ilogbl.c new file mode 100644 index 0000000000..4088238f30 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_ilogbl.c @@ -0,0 +1,70 @@ +/* s_ilogbl.c -- long double version of s_ilogb.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* ilogbl(long double x) + * return the binary exponent of non-zero x + * ilogbl(0) = FP_ILOGB0 + * ilogbl(NaN) = FP_ILOGBNAN (no signal is raised) + * ilogbl(+-Inf) = INT_MAX (no signal is raised) + */ + +#include <limits.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +int __ieee754_ilogbl(long double x) +{ + int64_t hx, hxs; + int ix; + double xhi, xlo; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + hxs = hx; + hx &= 0x7fffffffffffffffLL; + if(hx <= 0x0010000000000000LL) { + if(hx==0) + return FP_ILOGB0; /* ilogbl(0) = FP_ILOGB0 */ + else /* subnormal x */ + for (ix = -1022, hx<<=11; hx>0; hx<<=1) ix -=1; + return ix; + } + else if (hx < 0x7ff0000000000000LL) + { + int hexp = (hx >> 52) - 0x3ff; + /* If the high part is a power of 2, and the low part is + nonzero with the opposite sign, the low part affects + the exponent. */ + if ((hx & 0x000fffffffffffffLL) == 0) + { + int64_t lx; + EXTRACT_WORDS64 (lx, xlo); + if ((hxs ^ lx) < 0 && (lx & 0x7fffffffffffffffLL) != 0) + hexp--; + } + return hexp; + } + else if (FP_ILOGBNAN != INT_MAX) { + /* ISO C99 requires ilogbl(+-Inf) == INT_MAX. */ + if (hx==0x7ff0000000000000LL) + return INT_MAX; + } + return FP_ILOGBNAN; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_j0l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_j0l.c new file mode 100644 index 0000000000..00bce29284 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_j0l.c @@ -0,0 +1,5 @@ +/* Looks like we can use ieee854 e_j0l.c as is for IBM extended format. */ +#define _Float128 long double +#define L(x) x ## L +#include <sysdeps/ieee754/ldbl-128/e_j0l.c> + diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_j1l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_j1l.c new file mode 100644 index 0000000000..da9fd9eeca --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_j1l.c @@ -0,0 +1,4 @@ +/* Looks like we can use ieee854 e_j1l.c as is for IBM extended format. */ +#define _Float128 long double +#define L(x) x ## L +#include <sysdeps/ieee754/ldbl-128/e_j1l.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_jnl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_jnl.c new file mode 100644 index 0000000000..4a8ccb044e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_jnl.c @@ -0,0 +1,421 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* Modifications for 128-bit long double are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* + * __ieee754_jn(n, x), __ieee754_yn(n, x) + * floating point Bessel's function of the 1st and 2nd kind + * of order n + * + * Special cases: + * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal; + * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. + * Note 2. About jn(n,x), yn(n,x) + * For n=0, j0(x) is called, + * for n=1, j1(x) is called, + * for n<x, forward recursion us used starting + * from values of j0(x) and j1(x). + * for n>x, a continued fraction approximation to + * j(n,x)/j(n-1,x) is evaluated and then backward + * recursion is used starting from a supposed value + * for j(n,x). The resulting value of j(0,x) is + * compared with the actual value to correct the + * supposed value of j(n,x). + * + * yn(n,x) is similar in all respects, except + * that forward recursion is used for all + * values of n>1. + * + */ + +#include <errno.h> +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const long double + invsqrtpi = 5.6418958354775628694807945156077258584405E-1L, + two = 2.0e0L, + one = 1.0e0L, + zero = 0.0L; + + +long double +__ieee754_jnl (int n, long double x) +{ + uint32_t se, lx; + int32_t i, ix, sgn; + long double a, b, temp, di, ret; + long double z, w; + double xhi; + + + /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) + * Thus, J(-n,x) = J(n,-x) + */ + + xhi = ldbl_high (x); + EXTRACT_WORDS (se, lx, xhi); + ix = se & 0x7fffffff; + + /* if J(n,NaN) is NaN */ + if (ix >= 0x7ff00000) + { + if (((ix - 0x7ff00000) | lx) != 0) + return x + x; + } + + if (n < 0) + { + n = -n; + x = -x; + se ^= 0x80000000; + } + if (n == 0) + return (__ieee754_j0l (x)); + if (n == 1) + return (__ieee754_j1l (x)); + sgn = (n & 1) & (se >> 31); /* even n -- 0, odd n -- sign(x) */ + x = fabsl (x); + + { + SET_RESTORE_ROUNDL (FE_TONEAREST); + if (x == 0.0L || ix >= 0x7ff00000) /* if x is 0 or inf */ + return sgn == 1 ? -zero : zero; + else if ((long double) n <= x) + { + /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ + if (ix >= 0x52d00000) + { /* x > 2**302 */ + + /* ??? Could use an expansion for large x here. */ + + /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + long double s; + long double c; + __sincosl (x, &s, &c); + switch (n & 3) + { + case 0: + temp = c + s; + break; + case 1: + temp = -c + s; + break; + case 2: + temp = -c - s; + break; + case 3: + temp = c - s; + break; + } + b = invsqrtpi * temp / __ieee754_sqrtl (x); + } + else + { + a = __ieee754_j0l (x); + b = __ieee754_j1l (x); + for (i = 1; i < n; i++) + { + temp = b; + b = b * ((long double) (i + i) / x) - a; /* avoid underflow */ + a = temp; + } + } + } + else + { + if (ix < 0x3e100000) + { /* x < 2**-29 */ + /* x is tiny, return the first Taylor expansion of J(n,x) + * J(n,x) = 1/n!*(x/2)^n - ... + */ + if (n >= 33) /* underflow, result < 10^-300 */ + b = zero; + else + { + temp = x * 0.5; + b = temp; + for (a = one, i = 2; i <= n; i++) + { + a *= (long double) i; /* a = n! */ + b *= temp; /* b = (x/2)^n */ + } + b = b / a; + } + } + else + { + /* use backward recurrence */ + /* x x^2 x^2 + * J(n,x)/J(n-1,x) = ---- ------ ------ ..... + * 2n - 2(n+1) - 2(n+2) + * + * 1 1 1 + * (for large x) = ---- ------ ------ ..... + * 2n 2(n+1) 2(n+2) + * -- - ------ - ------ - + * x x x + * + * Let w = 2n/x and h=2/x, then the above quotient + * is equal to the continued fraction: + * 1 + * = ----------------------- + * 1 + * w - ----------------- + * 1 + * w+h - --------- + * w+2h - ... + * + * To determine how many terms needed, let + * Q(0) = w, Q(1) = w(w+h) - 1, + * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), + * When Q(k) > 1e4 good for single + * When Q(k) > 1e9 good for double + * When Q(k) > 1e17 good for quadruple + */ + /* determine k */ + long double t, v; + long double q0, q1, h, tmp; + int32_t k, m; + w = (n + n) / (long double) x; + h = 2.0L / (long double) x; + q0 = w; + z = w + h; + q1 = w * z - 1.0L; + k = 1; + while (q1 < 1.0e17L) + { + k += 1; + z += h; + tmp = z * q1 - q0; + q0 = q1; + q1 = tmp; + } + m = n + n; + for (t = zero, i = 2 * (n + k); i >= m; i -= 2) + t = one / (i / x - t); + a = t; + b = one; + /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n) + * Hence, if n*(log(2n/x)) > ... + * single 8.8722839355e+01 + * double 7.09782712893383973096e+02 + * long double 1.1356523406294143949491931077970765006170e+04 + * then recurrent value may overflow and the result is + * likely underflow to zero + */ + tmp = n; + v = two / x; + tmp = tmp * __ieee754_logl (fabsl (v * tmp)); + + if (tmp < 1.1356523406294143949491931077970765006170e+04L) + { + for (i = n - 1, di = (long double) (i + i); i > 0; i--) + { + temp = b; + b *= di; + b = b / x - a; + a = temp; + di -= two; + } + } + else + { + for (i = n - 1, di = (long double) (i + i); i > 0; i--) + { + temp = b; + b *= di; + b = b / x - a; + a = temp; + di -= two; + /* scale b to avoid spurious overflow */ + if (b > 1e100L) + { + a /= b; + t /= b; + b = one; + } + } + } + /* j0() and j1() suffer enormous loss of precision at and + * near zero; however, we know that their zero points never + * coincide, so just choose the one further away from zero. + */ + z = __ieee754_j0l (x); + w = __ieee754_j1l (x); + if (fabsl (z) >= fabsl (w)) + b = (t * z / b); + else + b = (t * w / a); + } + } + if (sgn == 1) + ret = -b; + else + ret = b; + } + if (ret == 0) + { + ret = __copysignl (LDBL_MIN, ret) * LDBL_MIN; + __set_errno (ERANGE); + } + else + math_check_force_underflow (ret); + return ret; +} +strong_alias (__ieee754_jnl, __jnl_finite) + +long double +__ieee754_ynl (int n, long double x) +{ + uint32_t se, lx; + int32_t i, ix; + int32_t sign; + long double a, b, temp, ret; + double xhi; + + xhi = ldbl_high (x); + EXTRACT_WORDS (se, lx, xhi); + ix = se & 0x7fffffff; + + /* if Y(n,NaN) is NaN */ + if (ix >= 0x7ff00000) + { + if (((ix - 0x7ff00000) | lx) != 0) + return x + x; + } + if (x <= 0.0L) + { + if (x == 0.0L) + return ((n < 0 && (n & 1) != 0) ? 1.0L : -1.0L) / 0.0L; + if (se & 0x80000000) + return zero / (zero * x); + } + sign = 1; + if (n < 0) + { + n = -n; + sign = 1 - ((n & 1) << 1); + } + if (n == 0) + return (__ieee754_y0l (x)); + { + SET_RESTORE_ROUNDL (FE_TONEAREST); + if (n == 1) + { + ret = sign * __ieee754_y1l (x); + goto out; + } + if (ix >= 0x7ff00000) + return zero; + if (ix >= 0x52D00000) + { /* x > 2**302 */ + + /* ??? See comment above on the possible futility of this. */ + + /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + long double s; + long double c; + __sincosl (x, &s, &c); + switch (n & 3) + { + case 0: + temp = s - c; + break; + case 1: + temp = -s - c; + break; + case 2: + temp = -s + c; + break; + case 3: + temp = s + c; + break; + } + b = invsqrtpi * temp / __ieee754_sqrtl (x); + } + else + { + a = __ieee754_y0l (x); + b = __ieee754_y1l (x); + /* quit if b is -inf */ + xhi = ldbl_high (b); + GET_HIGH_WORD (se, xhi); + se &= 0xfff00000; + for (i = 1; i < n && se != 0xfff00000; i++) + { + temp = b; + b = ((long double) (i + i) / x) * b - a; + xhi = ldbl_high (b); + GET_HIGH_WORD (se, xhi); + se &= 0xfff00000; + a = temp; + } + } + /* If B is +-Inf, set up errno accordingly. */ + if (! isfinite (b)) + __set_errno (ERANGE); + if (sign > 0) + ret = b; + else + ret = -b; + } + out: + if (isinf (ret)) + ret = __copysignl (LDBL_MAX, ret) * LDBL_MAX; + return ret; +} +strong_alias (__ieee754_ynl, __ynl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_lgammal_r.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_lgammal_r.c new file mode 100644 index 0000000000..8ac8283bd8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_lgammal_r.c @@ -0,0 +1,5 @@ +/* Looks like we can use ieee854 e_lgammal_r.c as is for IBM extended format. */ +#define _Float128 long double +#define L(x) x ## L +#include <sysdeps/ieee754/ldbl-128/e_lgammal_r.c> + diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_log10l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_log10l.c new file mode 100644 index 0000000000..1fbfa48e13 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_log10l.c @@ -0,0 +1,261 @@ +/* log10l.c + * + * Common logarithm, 128-bit long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, log10l(); + * + * y = log10l( x ); + * + * + * + * DESCRIPTION: + * + * Returns the base 10 logarithm of x. + * + * The argument is separated into its exponent and fractional + * parts. If the exponent is between -1 and +1, the logarithm + * of the fraction is approximated by + * + * log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x). + * + * Otherwise, setting z = 2(x-1)/x+1), + * + * log(x) = z + z^3 P(z)/Q(z). + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE 0.5, 2.0 30000 2.3e-34 4.9e-35 + * IEEE exp(+-10000) 30000 1.0e-34 4.1e-35 + * + * In the tests over the interval exp(+-10000), the logarithms + * of the random arguments were uniformly distributed over + * [-10000, +10000]. + * + */ + +/* + Cephes Math Library Release 2.2: January, 1991 + Copyright 1984, 1991 by Stephen L. Moshier + Adapted for glibc November, 2001 + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see <http://www.gnu.org/licenses/>. + */ + +#include <math.h> +#include <math_private.h> + +/* Coefficients for ln(1+x) = x - x**2/2 + x**3 P(x)/Q(x) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 5.3e-37, + * relative peak error spread = 2.3e-14 + */ +static const long double P[13] = +{ + 1.313572404063446165910279910527789794488E4L, + 7.771154681358524243729929227226708890930E4L, + 2.014652742082537582487669938141683759923E5L, + 3.007007295140399532324943111654767187848E5L, + 2.854829159639697837788887080758954924001E5L, + 1.797628303815655343403735250238293741397E5L, + 7.594356839258970405033155585486712125861E4L, + 2.128857716871515081352991964243375186031E4L, + 3.824952356185897735160588078446136783779E3L, + 4.114517881637811823002128927449878962058E2L, + 2.321125933898420063925789532045674660756E1L, + 4.998469661968096229986658302195402690910E-1L, + 1.538612243596254322971797716843006400388E-6L +}; +static const long double Q[12] = +{ + 3.940717212190338497730839731583397586124E4L, + 2.626900195321832660448791748036714883242E5L, + 7.777690340007566932935753241556479363645E5L, + 1.347518538384329112529391120390701166528E6L, + 1.514882452993549494932585972882995548426E6L, + 1.158019977462989115839826904108208787040E6L, + 6.132189329546557743179177159925690841200E5L, + 2.248234257620569139969141618556349415120E5L, + 5.605842085972455027590989944010492125825E4L, + 9.147150349299596453976674231612674085381E3L, + 9.104928120962988414618126155557301584078E2L, + 4.839208193348159620282142911143429644326E1L +/* 1.000000000000000000000000000000000000000E0L, */ +}; + +/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), + * where z = 2(x-1)/(x+1) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 1.1e-35, + * relative peak error spread 1.1e-9 + */ +static const long double R[6] = +{ + 1.418134209872192732479751274970992665513E5L, + -8.977257995689735303686582344659576526998E4L, + 2.048819892795278657810231591630928516206E4L, + -2.024301798136027039250415126250455056397E3L, + 8.057002716646055371965756206836056074715E1L, + -8.828896441624934385266096344596648080902E-1L +}; +static const long double S[6] = +{ + 1.701761051846631278975701529965589676574E6L, + -1.332535117259762928288745111081235577029E6L, + 4.001557694070773974936904547424676279307E5L, + -5.748542087379434595104154610899551484314E4L, + 3.998526750980007367835804959888064681098E3L, + -1.186359407982897997337150403816839480438E2L +/* 1.000000000000000000000000000000000000000E0L, */ +}; + +static const long double +/* log10(2) */ +L102A = 0.3125L, +L102B = -1.14700043360188047862611052755069732318101185E-2L, +/* log10(e) */ +L10EA = 0.5L, +L10EB = -6.570551809674817234887108108339491770560299E-2L, +/* sqrt(2)/2 */ +SQRTH = 7.071067811865475244008443621048490392848359E-1L; + + + +/* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */ + +static long double +neval (long double x, const long double *p, int n) +{ + long double y; + + p += n; + y = *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +/* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */ + +static long double +deval (long double x, const long double *p, int n) +{ + long double y; + + p += n; + y = x + *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + + +long double +__ieee754_log10l (long double x) +{ + long double z; + long double y; + int e; + int64_t hx; + double xhi; + +/* Test for domain */ + xhi = ldbl_high (x); + EXTRACT_WORDS64 (hx, xhi); + if ((hx & 0x7fffffffffffffffLL) == 0) + return (-1.0L / __fabsl (x)); /* log10l(+-0)=-inf */ + if (hx < 0) + return (x - x) / (x - x); + if (hx >= 0x7ff0000000000000LL) + return (x + x); + + if (x == 1.0L) + return 0.0L; + +/* separate mantissa from exponent */ + +/* Note, frexp is used so that denormal numbers + * will be handled properly. + */ + x = __frexpl (x, &e); + + +/* logarithm using log(x) = z + z**3 P(z)/Q(z), + * where z = 2(x-1)/x+1) + */ + if ((e > 2) || (e < -2)) + { + if (x < SQRTH) + { /* 2( 2x-1 )/( 2x+1 ) */ + e -= 1; + z = x - 0.5L; + y = 0.5L * z + 0.5L; + } + else + { /* 2 (x-1)/(x+1) */ + z = x - 0.5L; + z -= 0.5L; + y = 0.5L * x + 0.5L; + } + x = z / y; + z = x * x; + y = x * (z * neval (z, R, 5) / deval (z, S, 5)); + goto done; + } + + +/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */ + + if (x < SQRTH) + { + e -= 1; + x = 2.0 * x - 1.0L; /* 2x - 1 */ + } + else + { + x = x - 1.0L; + } + z = x * x; + y = x * (z * neval (x, P, 12) / deval (x, Q, 11)); + y = y - 0.5 * z; + +done: + + /* Multiply log of fraction by log10(e) + * and base 2 exponent by log10(2). + */ + z = y * L10EB; + z += x * L10EB; + z += e * L102B; + z += y * L10EA; + z += x * L10EA; + z += e * L102A; + return (z); +} +strong_alias (__ieee754_log10l, __log10l_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_log2l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_log2l.c new file mode 100644 index 0000000000..c820dacf08 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_log2l.c @@ -0,0 +1,254 @@ +/* log2l.c + * Base 2 logarithm, 128-bit long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, log2l(); + * + * y = log2l( x ); + * + * + * + * DESCRIPTION: + * + * Returns the base 2 logarithm of x. + * + * The argument is separated into its exponent and fractional + * parts. If the exponent is between -1 and +1, the (natural) + * logarithm of the fraction is approximated by + * + * log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x). + * + * Otherwise, setting z = 2(x-1)/x+1), + * + * log(x) = z + z^3 P(z)/Q(z). + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE 0.5, 2.0 100,000 2.6e-34 4.9e-35 + * IEEE exp(+-10000) 100,000 9.6e-35 4.0e-35 + * + * In the tests over the interval exp(+-10000), the logarithms + * of the random arguments were uniformly distributed over + * [-10000, +10000]. + * + */ + +/* + Cephes Math Library Release 2.2: January, 1991 + Copyright 1984, 1991 by Stephen L. Moshier + Adapted for glibc November, 2001 + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see <http://www.gnu.org/licenses/>. + */ + +#include <math.h> +#include <math_private.h> + +/* Coefficients for ln(1+x) = x - x**2/2 + x**3 P(x)/Q(x) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 5.3e-37, + * relative peak error spread = 2.3e-14 + */ +static const long double P[13] = +{ + 1.313572404063446165910279910527789794488E4L, + 7.771154681358524243729929227226708890930E4L, + 2.014652742082537582487669938141683759923E5L, + 3.007007295140399532324943111654767187848E5L, + 2.854829159639697837788887080758954924001E5L, + 1.797628303815655343403735250238293741397E5L, + 7.594356839258970405033155585486712125861E4L, + 2.128857716871515081352991964243375186031E4L, + 3.824952356185897735160588078446136783779E3L, + 4.114517881637811823002128927449878962058E2L, + 2.321125933898420063925789532045674660756E1L, + 4.998469661968096229986658302195402690910E-1L, + 1.538612243596254322971797716843006400388E-6L +}; +static const long double Q[12] = +{ + 3.940717212190338497730839731583397586124E4L, + 2.626900195321832660448791748036714883242E5L, + 7.777690340007566932935753241556479363645E5L, + 1.347518538384329112529391120390701166528E6L, + 1.514882452993549494932585972882995548426E6L, + 1.158019977462989115839826904108208787040E6L, + 6.132189329546557743179177159925690841200E5L, + 2.248234257620569139969141618556349415120E5L, + 5.605842085972455027590989944010492125825E4L, + 9.147150349299596453976674231612674085381E3L, + 9.104928120962988414618126155557301584078E2L, + 4.839208193348159620282142911143429644326E1L +/* 1.000000000000000000000000000000000000000E0L, */ +}; + +/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), + * where z = 2(x-1)/(x+1) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 1.1e-35, + * relative peak error spread 1.1e-9 + */ +static const long double R[6] = +{ + 1.418134209872192732479751274970992665513E5L, + -8.977257995689735303686582344659576526998E4L, + 2.048819892795278657810231591630928516206E4L, + -2.024301798136027039250415126250455056397E3L, + 8.057002716646055371965756206836056074715E1L, + -8.828896441624934385266096344596648080902E-1L +}; +static const long double S[6] = +{ + 1.701761051846631278975701529965589676574E6L, + -1.332535117259762928288745111081235577029E6L, + 4.001557694070773974936904547424676279307E5L, + -5.748542087379434595104154610899551484314E4L, + 3.998526750980007367835804959888064681098E3L, + -1.186359407982897997337150403816839480438E2L +/* 1.000000000000000000000000000000000000000E0L, */ +}; + +static const long double +/* log2(e) - 1 */ +LOG2EA = 4.4269504088896340735992468100189213742664595E-1L, +/* sqrt(2)/2 */ +SQRTH = 7.071067811865475244008443621048490392848359E-1L; + + +/* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */ + +static long double +neval (long double x, const long double *p, int n) +{ + long double y; + + p += n; + y = *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +/* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */ + +static long double +deval (long double x, const long double *p, int n) +{ + long double y; + + p += n; + y = x + *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + + +long double +__ieee754_log2l (long double x) +{ + long double z; + long double y; + int e; + int64_t hx; + double xhi; + +/* Test for domain */ + xhi = ldbl_high (x); + EXTRACT_WORDS64 (hx, xhi); + if ((hx & 0x7fffffffffffffffLL) == 0) + return (-1.0L / __fabsl (x)); /* log2l(+-0)=-inf */ + if (hx < 0) + return (x - x) / (x - x); + if (hx >= 0x7ff0000000000000LL) + return (x + x); + + if (x == 1.0L) + return 0.0L; + +/* separate mantissa from exponent */ + +/* Note, frexp is used so that denormal numbers + * will be handled properly. + */ + x = __frexpl (x, &e); + + +/* logarithm using log(x) = z + z**3 P(z)/Q(z), + * where z = 2(x-1)/x+1) + */ + if ((e > 2) || (e < -2)) + { + if (x < SQRTH) + { /* 2( 2x-1 )/( 2x+1 ) */ + e -= 1; + z = x - 0.5L; + y = 0.5L * z + 0.5L; + } + else + { /* 2 (x-1)/(x+1) */ + z = x - 0.5L; + z -= 0.5L; + y = 0.5L * x + 0.5L; + } + x = z / y; + z = x * x; + y = x * (z * neval (z, R, 5) / deval (z, S, 5)); + goto done; + } + + +/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */ + + if (x < SQRTH) + { + e -= 1; + x = 2.0 * x - 1.0L; /* 2x - 1 */ + } + else + { + x = x - 1.0L; + } + z = x * x; + y = x * (z * neval (x, P, 12) / deval (x, Q, 11)); + y = y - 0.5 * z; + +done: + +/* Multiply log of fraction by log2(e) + * and base 2 exponent by 1 + */ + z = y * LOG2EA; + z += x * LOG2EA; + z += y; + z += x; + z += e; + return (z); +} +strong_alias (__ieee754_log2l, __log2l_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_logl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_logl.c new file mode 100644 index 0000000000..c44feca65b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_logl.c @@ -0,0 +1,300 @@ +/* logll.c + * + * Natural logarithm for 128-bit long double precision. + * + * + * + * SYNOPSIS: + * + * long double x, y, logl(); + * + * y = logl( x ); + * + * + * + * DESCRIPTION: + * + * Returns the base e (2.718...) logarithm of x. + * + * The argument is separated into its exponent and fractional + * parts. Use of a lookup table increases the speed of the routine. + * The program uses logarithms tabulated at intervals of 1/128 to + * cover the domain from approximately 0.7 to 1.4. + * + * On the interval [-1/128, +1/128] the logarithm of 1+x is approximated by + * log(1+x) = x - 0.5 x^2 + x^3 P(x) . + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE 0.875, 1.125 100000 1.2e-34 4.1e-35 + * IEEE 0.125, 8 100000 1.2e-34 4.1e-35 + * + * + * WARNING: + * + * This program uses integer operations on bit fields of floating-point + * numbers. It does not work with data structures other than the + * structure assumed. + * + */ + +/* Copyright 2001 by Stephen L. Moshier <moshier@na-net.ornl.gov> + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + +/* log(1+x) = x - .5 x^2 + x^3 l(x) + -.0078125 <= x <= +.0078125 + peak relative error 1.2e-37 */ +static const long double +l3 = 3.333333333333333333333333333333336096926E-1L, +l4 = -2.499999999999999999999999999486853077002E-1L, +l5 = 1.999999999999999999999999998515277861905E-1L, +l6 = -1.666666666666666666666798448356171665678E-1L, +l7 = 1.428571428571428571428808945895490721564E-1L, +l8 = -1.249999999999999987884655626377588149000E-1L, +l9 = 1.111111111111111093947834982832456459186E-1L, +l10 = -1.000000000000532974938900317952530453248E-1L, +l11 = 9.090909090915566247008015301349979892689E-2L, +l12 = -8.333333211818065121250921925397567745734E-2L, +l13 = 7.692307559897661630807048686258659316091E-2L, +l14 = -7.144242754190814657241902218399056829264E-2L, +l15 = 6.668057591071739754844678883223432347481E-2L; + +/* Lookup table of ln(t) - (t-1) + t = 0.5 + (k+26)/128) + k = 0, ..., 91 */ +static const long double logtbl[92] = { +-5.5345593589352099112142921677820359632418E-2L, +-5.2108257402767124761784665198737642086148E-2L, +-4.8991686870576856279407775480686721935120E-2L, +-4.5993270766361228596215288742353061431071E-2L, +-4.3110481649613269682442058976885699556950E-2L, +-4.0340872319076331310838085093194799765520E-2L, +-3.7682072451780927439219005993827431503510E-2L, +-3.5131785416234343803903228503274262719586E-2L, +-3.2687785249045246292687241862699949178831E-2L, +-3.0347913785027239068190798397055267411813E-2L, +-2.8110077931525797884641940838507561326298E-2L, +-2.5972247078357715036426583294246819637618E-2L, +-2.3932450635346084858612873953407168217307E-2L, +-2.1988775689981395152022535153795155900240E-2L, +-2.0139364778244501615441044267387667496733E-2L, +-1.8382413762093794819267536615342902718324E-2L, +-1.6716169807550022358923589720001638093023E-2L, +-1.5138929457710992616226033183958974965355E-2L, +-1.3649036795397472900424896523305726435029E-2L, +-1.2244881690473465543308397998034325468152E-2L, +-1.0924898127200937840689817557742469105693E-2L, +-9.6875626072830301572839422532631079809328E-3L, +-8.5313926245226231463436209313499745894157E-3L, +-7.4549452072765973384933565912143044991706E-3L, +-6.4568155251217050991200599386801665681310E-3L, +-5.5356355563671005131126851708522185605193E-3L, +-4.6900728132525199028885749289712348829878E-3L, +-3.9188291218610470766469347968659624282519E-3L, +-3.2206394539524058873423550293617843896540E-3L, +-2.5942708080877805657374888909297113032132E-3L, +-2.0385211375711716729239156839929281289086E-3L, +-1.5522183228760777967376942769773768850872E-3L, +-1.1342191863606077520036253234446621373191E-3L, +-7.8340854719967065861624024730268350459991E-4L, +-4.9869831458030115699628274852562992756174E-4L, +-2.7902661731604211834685052867305795169688E-4L, +-1.2335696813916860754951146082826952093496E-4L, +-3.0677461025892873184042490943581654591817E-5L, +#define ZERO logtbl[38] + 0.0000000000000000000000000000000000000000E0L, +-3.0359557945051052537099938863236321874198E-5L, +-1.2081346403474584914595395755316412213151E-4L, +-2.7044071846562177120083903771008342059094E-4L, +-4.7834133324631162897179240322783590830326E-4L, +-7.4363569786340080624467487620270965403695E-4L, +-1.0654639687057968333207323853366578860679E-3L, +-1.4429854811877171341298062134712230604279E-3L, +-1.8753781835651574193938679595797367137975E-3L, +-2.3618380914922506054347222273705859653658E-3L, +-2.9015787624124743013946600163375853631299E-3L, +-3.4938307889254087318399313316921940859043E-3L, +-4.1378413103128673800485306215154712148146E-3L, +-4.8328735414488877044289435125365629849599E-3L, +-5.5782063183564351739381962360253116934243E-3L, +-6.3731336597098858051938306767880719015261E-3L, +-7.2169643436165454612058905294782949315193E-3L, +-8.1090214990427641365934846191367315083867E-3L, +-9.0486422112807274112838713105168375482480E-3L, +-1.0035177140880864314674126398350812606841E-2L, +-1.1067990155502102718064936259435676477423E-2L, +-1.2146457974158024928196575103115488672416E-2L, +-1.3269969823361415906628825374158424754308E-2L, +-1.4437927104692837124388550722759686270765E-2L, +-1.5649743073340777659901053944852735064621E-2L, +-1.6904842527181702880599758489058031645317E-2L, +-1.8202661505988007336096407340750378994209E-2L, +-1.9542647000370545390701192438691126552961E-2L, +-2.0924256670080119637427928803038530924742E-2L, +-2.2346958571309108496179613803760727786257E-2L, +-2.3810230892650362330447187267648486279460E-2L, +-2.5313561699385640380910474255652501521033E-2L, +-2.6856448685790244233704909690165496625399E-2L, +-2.8438398935154170008519274953860128449036E-2L, +-3.0058928687233090922411781058956589863039E-2L, +-3.1717563112854831855692484086486099896614E-2L, +-3.3413836095418743219397234253475252001090E-2L, +-3.5147290019036555862676702093393332533702E-2L, +-3.6917475563073933027920505457688955423688E-2L, +-3.8723951502862058660874073462456610731178E-2L, +-4.0566284516358241168330505467000838017425E-2L, +-4.2444048996543693813649967076598766917965E-2L, +-4.4356826869355401653098777649745233339196E-2L, +-4.6304207416957323121106944474331029996141E-2L, +-4.8285787106164123613318093945035804818364E-2L, +-5.0301169421838218987124461766244507342648E-2L, +-5.2349964705088137924875459464622098310997E-2L, +-5.4431789996103111613753440311680967840214E-2L, +-5.6546268881465384189752786409400404404794E-2L, +-5.8693031345788023909329239565012647817664E-2L, +-6.0871713627532018185577188079210189048340E-2L, +-6.3081958078862169742820420185833800925568E-2L, +-6.5323413029406789694910800219643791556918E-2L, +-6.7595732653791419081537811574227049288168E-2L +}; + +/* ln(2) = ln2a + ln2b with extended precision. */ +static const long double + ln2a = 6.93145751953125e-1L, + ln2b = 1.4286068203094172321214581765680755001344E-6L; + +static const long double + ldbl_epsilon = 0x1p-106L; + +long double +__ieee754_logl(long double x) +{ + long double z, y, w, t; + unsigned int m; + int k, e; + double xhi; + uint32_t hx, lx; + + xhi = ldbl_high (x); + EXTRACT_WORDS (hx, lx, xhi); + m = hx; + + /* Check for IEEE special cases. */ + k = m & 0x7fffffff; + /* log(0) = -infinity. */ + if ((k | lx) == 0) + { + return -0.5L / ZERO; + } + /* log ( x < 0 ) = NaN */ + if (m & 0x80000000) + { + return (x - x) / ZERO; + } + /* log (infinity or NaN) */ + if (k >= 0x7ff00000) + { + return x + x; + } + + /* On this interval the table is not used due to cancellation error. */ + if ((x <= 1.0078125L) && (x >= 0.9921875L)) + { + if (x == 1.0L) + return 0.0L; + z = x - 1.0L; + k = 64; + t = 1.0L; + e = 0; + } + else + { + /* Extract exponent and reduce domain to 0.703125 <= u < 1.40625 */ + unsigned int w0; + e = (int) (m >> 20) - (int) 0x3fe; + if (e == -1022) + { + x *= 0x1p106L; + xhi = ldbl_high (x); + EXTRACT_WORDS (hx, lx, xhi); + m = hx; + e = (int) (m >> 20) - (int) 0x3fe - 106; + } + m &= 0xfffff; + w0 = m | 0x3fe00000; + m |= 0x100000; + /* Find lookup table index k from high order bits of the significand. */ + if (m < 0x168000) + { + k = (m - 0xff000) >> 13; + /* t is the argument 0.5 + (k+26)/128 + of the nearest item to u in the lookup table. */ + INSERT_WORDS (xhi, 0x3ff00000 + (k << 13), 0); + t = xhi; + w0 += 0x100000; + e -= 1; + k += 64; + } + else + { + k = (m - 0xfe000) >> 14; + INSERT_WORDS (xhi, 0x3fe00000 + (k << 14), 0); + t = xhi; + } + x = __scalbnl (x, ((int) ((w0 - hx) * 2)) >> 21); + /* log(u) = log( t u/t ) = log(t) + log(u/t) + log(t) is tabulated in the lookup table. + Express log(u/t) = log(1+z), where z = u/t - 1 = (u-t)/t. + cf. Cody & Waite. */ + z = (x - t) / t; + } + /* Series expansion of log(1+z). */ + w = z * z; + /* Avoid spurious underflows. */ + if (__glibc_unlikely (fabsl (z) <= ldbl_epsilon)) + y = 0.0L; + else + { + y = ((((((((((((l15 * z + + l14) * z + + l13) * z + + l12) * z + + l11) * z + + l10) * z + + l9) * z + + l8) * z + + l7) * z + + l6) * z + + l5) * z + + l4) * z + + l3) * z * w; + y -= 0.5 * w; + } + y += e * ln2b; /* Base 2 exponent offset times ln(2). */ + y += z; + y += logtbl[k-26]; /* log(t) - (t-1) */ + y += (t - 1.0L); + y += e * ln2a; + return y; +} +strong_alias (__ieee754_logl, __logl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_powl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_powl.c new file mode 100644 index 0000000000..d6fbef6997 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_powl.c @@ -0,0 +1,415 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* Expansions and modifications for 128-bit long double are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* __ieee754_powl(x,y) return x**y + * + * n + * Method: Let x = 2 * (1+f) + * 1. Compute and return log2(x) in two pieces: + * log2(x) = w1 + w2, + * where w1 has 113-53 = 60 bit trailing zeros. + * 2. Perform y*log2(x) = n+y' by simulating muti-precision + * arithmetic, where |y'|<=0.5. + * 3. Return x**y = 2**n*exp(y'*log2) + * + * Special cases: + * 1. (anything) ** 0 is 1 + * 2. (anything) ** 1 is itself + * 3. (anything) ** NAN is NAN + * 4. NAN ** (anything except 0) is NAN + * 5. +-(|x| > 1) ** +INF is +INF + * 6. +-(|x| > 1) ** -INF is +0 + * 7. +-(|x| < 1) ** +INF is +0 + * 8. +-(|x| < 1) ** -INF is +INF + * 9. +-1 ** +-INF is NAN + * 10. +0 ** (+anything except 0, NAN) is +0 + * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 + * 12. +0 ** (-anything except 0, NAN) is +INF + * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF + * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) + * 15. +INF ** (+anything except 0,NAN) is +INF + * 16. +INF ** (-anything except 0,NAN) is +0 + * 17. -INF ** (anything) = -0 ** (-anything) + * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) + * 19. (-anything except 0 and inf) ** (non-integer) is NAN + * + */ + +#include <math.h> +#include <math_private.h> + +static const long double bp[] = { + 1.0L, + 1.5L, +}; + +/* log_2(1.5) */ +static const long double dp_h[] = { + 0.0, + 5.8496250072115607565592654282227158546448E-1L +}; + +/* Low part of log_2(1.5) */ +static const long double dp_l[] = { + 0.0, + 1.0579781240112554492329533686862998106046E-16L +}; + +static const long double zero = 0.0L, + one = 1.0L, + two = 2.0L, + two113 = 1.0384593717069655257060992658440192E34L, + huge = 1.0e300L, + tiny = 1.0e-300L; + +/* 3/2 log x = 3 z + z^3 + z^3 (z^2 R(z^2)) + z = (x-1)/(x+1) + 1 <= x <= 1.25 + Peak relative error 2.3e-37 */ +static const long double LN[] = +{ + -3.0779177200290054398792536829702930623200E1L, + 6.5135778082209159921251824580292116201640E1L, + -4.6312921812152436921591152809994014413540E1L, + 1.2510208195629420304615674658258363295208E1L, + -9.9266909031921425609179910128531667336670E-1L +}; +static const long double LD[] = +{ + -5.129862866715009066465422805058933131960E1L, + 1.452015077564081884387441590064272782044E2L, + -1.524043275549860505277434040464085593165E2L, + 7.236063513651544224319663428634139768808E1L, + -1.494198912340228235853027849917095580053E1L + /* 1.0E0 */ +}; + +/* exp(x) = 1 + x - x / (1 - 2 / (x - x^2 R(x^2))) + 0 <= x <= 0.5 + Peak relative error 5.7e-38 */ +static const long double PN[] = +{ + 5.081801691915377692446852383385968225675E8L, + 9.360895299872484512023336636427675327355E6L, + 4.213701282274196030811629773097579432957E4L, + 5.201006511142748908655720086041570288182E1L, + 9.088368420359444263703202925095675982530E-3L, +}; +static const long double PD[] = +{ + 3.049081015149226615468111430031590411682E9L, + 1.069833887183886839966085436512368982758E8L, + 8.259257717868875207333991924545445705394E5L, + 1.872583833284143212651746812884298360922E3L, + /* 1.0E0 */ +}; + +static const long double + /* ln 2 */ + lg2 = 6.9314718055994530941723212145817656807550E-1L, + lg2_h = 6.9314718055994528622676398299518041312695E-1L, + lg2_l = 2.3190468138462996154948554638754786504121E-17L, + ovt = 8.0085662595372944372e-0017L, + /* 2/(3*log(2)) */ + cp = 9.6179669392597560490661645400126142495110E-1L, + cp_h = 9.6179669392597555432899980587535537779331E-1L, + cp_l = 5.0577616648125906047157785230014751039424E-17L; + +long double +__ieee754_powl (long double x, long double y) +{ + long double z, ax, z_h, z_l, p_h, p_l; + long double y1, t1, t2, r, s, sgn, t, u, v, w; + long double s2, s_h, s_l, t_h, t_l, ay; + int32_t i, j, k, yisint, n; + uint32_t ix, iy; + int32_t hx, hy, hax; + double ohi, xhi, xlo, yhi, ylo; + uint32_t lx, ly, lj; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS (hx, lx, xhi); + ix = hx & 0x7fffffff; + + ldbl_unpack (y, &yhi, &ylo); + EXTRACT_WORDS (hy, ly, yhi); + iy = hy & 0x7fffffff; + + /* y==zero: x**0 = 1 */ + if ((iy | ly) == 0 && !issignaling (x)) + return one; + + /* 1.0**y = 1; -1.0**+-Inf = 1 */ + if (x == one && !issignaling (y)) + return one; + if (x == -1.0L && ((iy - 0x7ff00000) | ly) == 0) + return one; + + /* +-NaN return x+y */ + if ((ix >= 0x7ff00000 && ((ix - 0x7ff00000) | lx) != 0) + || (iy >= 0x7ff00000 && ((iy - 0x7ff00000) | ly) != 0)) + return x + y; + + /* determine if y is an odd int when x < 0 + * yisint = 0 ... y is not an integer + * yisint = 1 ... y is an odd int + * yisint = 2 ... y is an even int + */ + yisint = 0; + if (hx < 0) + { + uint32_t low_ye; + + GET_HIGH_WORD (low_ye, ylo); + if ((low_ye & 0x7fffffff) >= 0x43400000) /* Low part >= 2^53 */ + yisint = 2; /* even integer y */ + else if (iy >= 0x3ff00000) /* 1.0 */ + { + if (__floorl (y) == y) + { + z = 0.5 * y; + if (__floorl (z) == z) + yisint = 2; + else + yisint = 1; + } + } + } + + ax = fabsl (x); + + /* special value of y */ + if (ly == 0) + { + if (iy == 0x7ff00000) /* y is +-inf */ + { + if (ax > one) + /* (|x|>1)**+-inf = inf,0 */ + return (hy >= 0) ? y : zero; + else + /* (|x|<1)**-,+inf = inf,0 */ + return (hy < 0) ? -y : zero; + } + if (ylo == 0.0) + { + if (iy == 0x3ff00000) + { /* y is +-1 */ + if (hy < 0) + return one / x; + else + return x; + } + if (hy == 0x40000000) + return x * x; /* y is 2 */ + if (hy == 0x3fe00000) + { /* y is 0.5 */ + if (hx >= 0) /* x >= +0 */ + return __ieee754_sqrtl (x); + } + } + } + + /* special value of x */ + if (lx == 0) + { + if (ix == 0x7ff00000 || ix == 0 || (ix == 0x3ff00000 && xlo == 0.0)) + { + z = ax; /*x is +-0,+-inf,+-1 */ + if (hy < 0) + z = one / z; /* z = (1/|x|) */ + if (hx < 0) + { + if (((ix - 0x3ff00000) | yisint) == 0) + { + z = (z - z) / (z - z); /* (-1)**non-int is NaN */ + } + else if (yisint == 1) + z = -z; /* (x<0)**odd = -(|x|**odd) */ + } + return z; + } + } + + /* (x<0)**(non-int) is NaN */ + if (((((u_int32_t) hx >> 31) - 1) | yisint) == 0) + return (x - x) / (x - x); + + /* sgn (sign of result -ve**odd) = -1 else = 1 */ + sgn = one; + if (((((u_int32_t) hx >> 31) - 1) | (yisint - 1)) == 0) + sgn = -one; /* (-ve)**(odd int) */ + + /* |y| is huge. + 2^-16495 = 1/2 of smallest representable value. + If (1 - 1/131072)^y underflows, y > 1.4986e9 */ + if (iy > 0x41d654b0) + { + /* if (1 - 2^-113)^y underflows, y > 1.1873e38 */ + if (iy > 0x47d654b0) + { + if (ix <= 0x3fefffff) + return (hy < 0) ? sgn * huge * huge : sgn * tiny * tiny; + if (ix >= 0x3ff00000) + return (hy > 0) ? sgn * huge * huge : sgn * tiny * tiny; + } + /* over/underflow if x is not close to one */ + if (ix < 0x3fefffff) + return (hy < 0) ? sgn * huge * huge : sgn * tiny * tiny; + if (ix > 0x3ff00000) + return (hy > 0) ? sgn * huge * huge : sgn * tiny * tiny; + } + + ay = y > 0 ? y : -y; + if (ay < 0x1p-117) + y = y < 0 ? -0x1p-117 : 0x1p-117; + + n = 0; + /* take care subnormal number */ + if (ix < 0x00100000) + { + ax *= two113; + n -= 113; + ohi = ldbl_high (ax); + GET_HIGH_WORD (ix, ohi); + } + n += ((ix) >> 20) - 0x3ff; + j = ix & 0x000fffff; + /* determine interval */ + ix = j | 0x3ff00000; /* normalize ix */ + if (j <= 0x39880) + k = 0; /* |x|<sqrt(3/2) */ + else if (j < 0xbb670) + k = 1; /* |x|<sqrt(3) */ + else + { + k = 0; + n += 1; + ix -= 0x00100000; + } + + ohi = ldbl_high (ax); + GET_HIGH_WORD (hax, ohi); + ax = __scalbnl (ax, ((int) ((ix - hax) * 2)) >> 21); + + /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ + u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ + v = one / (ax + bp[k]); + s = u * v; + s_h = ldbl_high (s); + + /* t_h=ax+bp[k] High */ + t_h = ax + bp[k]; + t_h = ldbl_high (t_h); + t_l = ax - (t_h - bp[k]); + s_l = v * ((u - s_h * t_h) - s_h * t_l); + /* compute log(ax) */ + s2 = s * s; + u = LN[0] + s2 * (LN[1] + s2 * (LN[2] + s2 * (LN[3] + s2 * LN[4]))); + v = LD[0] + s2 * (LD[1] + s2 * (LD[2] + s2 * (LD[3] + s2 * (LD[4] + s2)))); + r = s2 * s2 * u / v; + r += s_l * (s_h + s); + s2 = s_h * s_h; + t_h = 3.0 + s2 + r; + t_h = ldbl_high (t_h); + t_l = r - ((t_h - 3.0) - s2); + /* u+v = s*(1+...) */ + u = s_h * t_h; + v = s_l * t_h + t_l * s; + /* 2/(3log2)*(s+...) */ + p_h = u + v; + p_h = ldbl_high (p_h); + p_l = v - (p_h - u); + z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */ + z_l = cp_l * p_h + p_l * cp + dp_l[k]; + /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ + t = (long double) n; + t1 = (((z_h + z_l) + dp_h[k]) + t); + t1 = ldbl_high (t1); + t2 = z_l - (((t1 - t) - dp_h[k]) - z_h); + + /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ + y1 = ldbl_high (y); + p_l = (y - y1) * t1 + y * t2; + p_h = y1 * t1; + z = p_l + p_h; + ohi = ldbl_high (z); + EXTRACT_WORDS (j, lj, ohi); + if (j >= 0x40d00000) /* z >= 16384 */ + { + /* if z > 16384 */ + if (((j - 0x40d00000) | lj) != 0) + return sgn * huge * huge; /* overflow */ + else + { + if (p_l + ovt > z - p_h) + return sgn * huge * huge; /* overflow */ + } + } + else if ((j & 0x7fffffff) >= 0x40d01b90) /* z <= -16495 */ + { + /* z < -16495 */ + if (((j - 0xc0d01bc0) | lj) != 0) + return sgn * tiny * tiny; /* underflow */ + else + { + if (p_l <= z - p_h) + return sgn * tiny * tiny; /* underflow */ + } + } + /* compute 2**(p_h+p_l) */ + i = j & 0x7fffffff; + k = (i >> 20) - 0x3ff; + n = 0; + if (i > 0x3fe00000) + { /* if |z| > 0.5, set n = [z+0.5] */ + n = __floorl (z + 0.5L); + t = n; + p_h -= t; + } + t = p_l + p_h; + t = ldbl_high (t); + u = t * lg2_h; + v = (p_l - (t - p_h)) * lg2 + t * lg2_l; + z = u + v; + w = v - (z - u); + /* exp(z) */ + t = z * z; + u = PN[0] + t * (PN[1] + t * (PN[2] + t * (PN[3] + t * PN[4]))); + v = PD[0] + t * (PD[1] + t * (PD[2] + t * (PD[3] + t))); + t1 = z - t * u / v; + r = (z * t1) / (t1 - two) - (w + z * w); + z = one - (r - z); + z = __scalbnl (sgn * z, n); + math_check_force_underflow (z); + return z; +} +strong_alias (__ieee754_powl, __powl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_rem_pio2l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_rem_pio2l.c new file mode 100644 index 0000000000..5aa2c1c007 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_rem_pio2l.c @@ -0,0 +1,279 @@ +/* Quad-precision floating point argument reduction. + Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jj@ultra.linux.cz> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <ieee754.h> + +/* + * Table of constants for 2/pi, 5628 hexadecimal digits of 2/pi + */ +static const int32_t two_over_pi[] = { +0xa2f983, 0x6e4e44, 0x1529fc, 0x2757d1, 0xf534dd, 0xc0db62, +0x95993c, 0x439041, 0xfe5163, 0xabdebb, 0xc561b7, 0x246e3a, +0x424dd2, 0xe00649, 0x2eea09, 0xd1921c, 0xfe1deb, 0x1cb129, +0xa73ee8, 0x8235f5, 0x2ebb44, 0x84e99c, 0x7026b4, 0x5f7e41, +0x3991d6, 0x398353, 0x39f49c, 0x845f8b, 0xbdf928, 0x3b1ff8, +0x97ffde, 0x05980f, 0xef2f11, 0x8b5a0a, 0x6d1f6d, 0x367ecf, +0x27cb09, 0xb74f46, 0x3f669e, 0x5fea2d, 0x7527ba, 0xc7ebe5, +0xf17b3d, 0x0739f7, 0x8a5292, 0xea6bfb, 0x5fb11f, 0x8d5d08, +0x560330, 0x46fc7b, 0x6babf0, 0xcfbc20, 0x9af436, 0x1da9e3, +0x91615e, 0xe61b08, 0x659985, 0x5f14a0, 0x68408d, 0xffd880, +0x4d7327, 0x310606, 0x1556ca, 0x73a8c9, 0x60e27b, 0xc08c6b, +0x47c419, 0xc367cd, 0xdce809, 0x2a8359, 0xc4768b, 0x961ca6, +0xddaf44, 0xd15719, 0x053ea5, 0xff0705, 0x3f7e33, 0xe832c2, +0xde4f98, 0x327dbb, 0xc33d26, 0xef6b1e, 0x5ef89f, 0x3a1f35, +0xcaf27f, 0x1d87f1, 0x21907c, 0x7c246a, 0xfa6ed5, 0x772d30, +0x433b15, 0xc614b5, 0x9d19c3, 0xc2c4ad, 0x414d2c, 0x5d000c, +0x467d86, 0x2d71e3, 0x9ac69b, 0x006233, 0x7cd2b4, 0x97a7b4, +0xd55537, 0xf63ed7, 0x1810a3, 0xfc764d, 0x2a9d64, 0xabd770, +0xf87c63, 0x57b07a, 0xe71517, 0x5649c0, 0xd9d63b, 0x3884a7, +0xcb2324, 0x778ad6, 0x23545a, 0xb91f00, 0x1b0af1, 0xdfce19, +0xff319f, 0x6a1e66, 0x615799, 0x47fbac, 0xd87f7e, 0xb76522, +0x89e832, 0x60bfe6, 0xcdc4ef, 0x09366c, 0xd43f5d, 0xd7de16, +0xde3b58, 0x929bde, 0x2822d2, 0xe88628, 0x4d58e2, 0x32cac6, +0x16e308, 0xcb7de0, 0x50c017, 0xa71df3, 0x5be018, 0x34132e, +0x621283, 0x014883, 0x5b8ef5, 0x7fb0ad, 0xf2e91e, 0x434a48, +0xd36710, 0xd8ddaa, 0x425fae, 0xce616a, 0xa4280a, 0xb499d3, +0xf2a606, 0x7f775c, 0x83c2a3, 0x883c61, 0x78738a, 0x5a8caf, +0xbdd76f, 0x63a62d, 0xcbbff4, 0xef818d, 0x67c126, 0x45ca55, +0x36d9ca, 0xd2a828, 0x8d61c2, 0x77c912, 0x142604, 0x9b4612, +0xc459c4, 0x44c5c8, 0x91b24d, 0xf31700, 0xad43d4, 0xe54929, +0x10d5fd, 0xfcbe00, 0xcc941e, 0xeece70, 0xf53e13, 0x80f1ec, +0xc3e7b3, 0x28f8c7, 0x940593, 0x3e71c1, 0xb3092e, 0xf3450b, +0x9c1288, 0x7b20ab, 0x9fb52e, 0xc29247, 0x2f327b, 0x6d550c, +0x90a772, 0x1fe76b, 0x96cb31, 0x4a1679, 0xe27941, 0x89dff4, +0x9794e8, 0x84e6e2, 0x973199, 0x6bed88, 0x365f5f, 0x0efdbb, +0xb49a48, 0x6ca467, 0x427271, 0x325d8d, 0xb8159f, 0x09e5bc, +0x25318d, 0x3974f7, 0x1c0530, 0x010c0d, 0x68084b, 0x58ee2c, +0x90aa47, 0x02e774, 0x24d6bd, 0xa67df7, 0x72486e, 0xef169f, +0xa6948e, 0xf691b4, 0x5153d1, 0xf20acf, 0x339820, 0x7e4bf5, +0x6863b2, 0x5f3edd, 0x035d40, 0x7f8985, 0x295255, 0xc06437, +0x10d86d, 0x324832, 0x754c5b, 0xd4714e, 0x6e5445, 0xc1090b, +0x69f52a, 0xd56614, 0x9d0727, 0x50045d, 0xdb3bb4, 0xc576ea, +0x17f987, 0x7d6b49, 0xba271d, 0x296996, 0xacccc6, 0x5414ad, +0x6ae290, 0x89d988, 0x50722c, 0xbea404, 0x940777, 0x7030f3, +0x27fc00, 0xa871ea, 0x49c266, 0x3de064, 0x83dd97, 0x973fa3, +0xfd9443, 0x8c860d, 0xde4131, 0x9d3992, 0x8c70dd, 0xe7b717, +0x3bdf08, 0x2b3715, 0xa0805c, 0x93805a, 0x921110, 0xd8e80f, +0xaf806c, 0x4bffdb, 0x0f9038, 0x761859, 0x15a562, 0xbbcb61, +0xb989c7, 0xbd4010, 0x04f2d2, 0x277549, 0xf6b6eb, 0xbb22db, +0xaa140a, 0x2f2689, 0x768364, 0x333b09, 0x1a940e, 0xaa3a51, +0xc2a31d, 0xaeedaf, 0x12265c, 0x4dc26d, 0x9c7a2d, 0x9756c0, +0x833f03, 0xf6f009, 0x8c402b, 0x99316d, 0x07b439, 0x15200c, +0x5bc3d8, 0xc492f5, 0x4badc6, 0xa5ca4e, 0xcd37a7, 0x36a9e6, +0x9492ab, 0x6842dd, 0xde6319, 0xef8c76, 0x528b68, 0x37dbfc, +0xaba1ae, 0x3115df, 0xa1ae00, 0xdafb0c, 0x664d64, 0xb705ed, +0x306529, 0xbf5657, 0x3aff47, 0xb9f96a, 0xf3be75, 0xdf9328, +0x3080ab, 0xf68c66, 0x15cb04, 0x0622fa, 0x1de4d9, 0xa4b33d, +0x8f1b57, 0x09cd36, 0xe9424e, 0xa4be13, 0xb52333, 0x1aaaf0, +0xa8654f, 0xa5c1d2, 0x0f3f0b, 0xcd785b, 0x76f923, 0x048b7b, +0x721789, 0x53a6c6, 0xe26e6f, 0x00ebef, 0x584a9b, 0xb7dac4, +0xba66aa, 0xcfcf76, 0x1d02d1, 0x2df1b1, 0xc1998c, 0x77adc3, +0xda4886, 0xa05df7, 0xf480c6, 0x2ff0ac, 0x9aecdd, 0xbc5c3f, +0x6dded0, 0x1fc790, 0xb6db2a, 0x3a25a3, 0x9aaf00, 0x9353ad, +0x0457b6, 0xb42d29, 0x7e804b, 0xa707da, 0x0eaa76, 0xa1597b, +0x2a1216, 0x2db7dc, 0xfde5fa, 0xfedb89, 0xfdbe89, 0x6c76e4, +0xfca906, 0x70803e, 0x156e85, 0xff87fd, 0x073e28, 0x336761, +0x86182a, 0xeabd4d, 0xafe7b3, 0x6e6d8f, 0x396795, 0x5bbf31, +0x48d784, 0x16df30, 0x432dc7, 0x356125, 0xce70c9, 0xb8cb30, +0xfd6cbf, 0xa200a4, 0xe46c05, 0xa0dd5a, 0x476f21, 0xd21262, +0x845cb9, 0x496170, 0xe0566b, 0x015299, 0x375550, 0xb7d51e, +0xc4f133, 0x5f6e13, 0xe4305d, 0xa92e85, 0xc3b21d, 0x3632a1, +0xa4b708, 0xd4b1ea, 0x21f716, 0xe4698f, 0x77ff27, 0x80030c, +0x2d408d, 0xa0cd4f, 0x99a520, 0xd3a2b3, 0x0a5d2f, 0x42f9b4, +0xcbda11, 0xd0be7d, 0xc1db9b, 0xbd17ab, 0x81a2ca, 0x5c6a08, +0x17552e, 0x550027, 0xf0147f, 0x8607e1, 0x640b14, 0x8d4196, +0xdebe87, 0x2afdda, 0xb6256b, 0x34897b, 0xfef305, 0x9ebfb9, +0x4f6a68, 0xa82a4a, 0x5ac44f, 0xbcf82d, 0x985ad7, 0x95c7f4, +0x8d4d0d, 0xa63a20, 0x5f57a4, 0xb13f14, 0x953880, 0x0120cc, +0x86dd71, 0xb6dec9, 0xf560bf, 0x11654d, 0x6b0701, 0xacb08c, +0xd0c0b2, 0x485551, 0x0efb1e, 0xc37295, 0x3b06a3, 0x3540c0, +0x7bdc06, 0xcc45e0, 0xfa294e, 0xc8cad6, 0x41f3e8, 0xde647c, +0xd8649b, 0x31bed9, 0xc397a4, 0xd45877, 0xc5e369, 0x13daf0, +0x3c3aba, 0x461846, 0x5f7555, 0xf5bdd2, 0xc6926e, 0x5d2eac, +0xed440e, 0x423e1c, 0x87c461, 0xe9fd29, 0xf3d6e7, 0xca7c22, +0x35916f, 0xc5e008, 0x8dd7ff, 0xe26a6e, 0xc6fdb0, 0xc10893, +0x745d7c, 0xb2ad6b, 0x9d6ecd, 0x7b723e, 0x6a11c6, 0xa9cff7, +0xdf7329, 0xbac9b5, 0x5100b7, 0x0db2e2, 0x24ba74, 0x607de5, +0x8ad874, 0x2c150d, 0x0c1881, 0x94667e, 0x162901, 0x767a9f, +0xbefdfd, 0xef4556, 0x367ed9, 0x13d9ec, 0xb9ba8b, 0xfc97c4, +0x27a831, 0xc36ef1, 0x36c594, 0x56a8d8, 0xb5a8b4, 0x0ecccf, +0x2d8912, 0x34576f, 0x89562c, 0xe3ce99, 0xb920d6, 0xaa5e6b, +0x9c2a3e, 0xcc5f11, 0x4a0bfd, 0xfbf4e1, 0x6d3b8e, 0x2c86e2, +0x84d4e9, 0xa9b4fc, 0xd1eeef, 0xc9352e, 0x61392f, 0x442138, +0xc8d91b, 0x0afc81, 0x6a4afb, 0xd81c2f, 0x84b453, 0x8c994e, +0xcc2254, 0xdc552a, 0xd6c6c0, 0x96190b, 0xb8701a, 0x649569, +0x605a26, 0xee523f, 0x0f117f, 0x11b5f4, 0xf5cbfc, 0x2dbc34, +0xeebc34, 0xcc5de8, 0x605edd, 0x9b8e67, 0xef3392, 0xb817c9, +0x9b5861, 0xbc57e1, 0xc68351, 0x103ed8, 0x4871dd, 0xdd1c2d, +0xa118af, 0x462c21, 0xd7f359, 0x987ad9, 0xc0549e, 0xfa864f, +0xfc0656, 0xae79e5, 0x362289, 0x22ad38, 0xdc9367, 0xaae855, +0x382682, 0x9be7ca, 0xa40d51, 0xb13399, 0x0ed7a9, 0x480569, +0xf0b265, 0xa7887f, 0x974c88, 0x36d1f9, 0xb39221, 0x4a827b, +0x21cf98, 0xdc9f40, 0x5547dc, 0x3a74e1, 0x42eb67, 0xdf9dfe, +0x5fd45e, 0xa4677b, 0x7aacba, 0xa2f655, 0x23882b, 0x55ba41, +0x086e59, 0x862a21, 0x834739, 0xe6e389, 0xd49ee5, 0x40fb49, +0xe956ff, 0xca0f1c, 0x8a59c5, 0x2bfa94, 0xc5c1d3, 0xcfc50f, +0xae5adb, 0x86c547, 0x624385, 0x3b8621, 0x94792c, 0x876110, +0x7b4c2a, 0x1a2c80, 0x12bf43, 0x902688, 0x893c78, 0xe4c4a8, +0x7bdbe5, 0xc23ac4, 0xeaf426, 0x8a67f7, 0xbf920d, 0x2ba365, +0xb1933d, 0x0b7cbd, 0xdc51a4, 0x63dd27, 0xdde169, 0x19949a, +0x9529a8, 0x28ce68, 0xb4ed09, 0x209f44, 0xca984e, 0x638270, +0x237c7e, 0x32b90f, 0x8ef5a7, 0xe75614, 0x08f121, 0x2a9db5, +0x4d7e6f, 0x5119a5, 0xabf9b5, 0xd6df82, 0x61dd96, 0x023616, +0x9f3ac4, 0xa1a283, 0x6ded72, 0x7a8d39, 0xa9b882, 0x5c326b, +0x5b2746, 0xed3400, 0x7700d2, 0x55f4fc, 0x4d5901, 0x8071e0, +0xe13f89, 0xb295f3, 0x64a8f1, 0xaea74b, 0x38fc4c, 0xeab2bb, +0x47270b, 0xabc3a7, 0x34ba60, 0x52dd34, 0xf8563a, 0xeb7e8a, +0x31bb36, 0x5895b7, 0x47f7a9, 0x94c3aa, 0xd39225, 0x1e7f3e, +0xd8974e, 0xbba94f, 0xd8ae01, 0xe661b4, 0x393d8e, 0xa523aa, +0x33068e, 0x1633b5, 0x3bb188, 0x1d3a9d, 0x4013d0, 0xcc1be5, +0xf862e7, 0x3bf28f, 0x39b5bf, 0x0bc235, 0x22747e, 0xa247c0, +0xd52d1f, 0x19add3, 0x9094df, 0x9311d0, 0xb42b25, 0x496db2, +0xe264b2, 0x5ef135, 0x3bc6a4, 0x1a4ad0, 0xaac92e, 0x64e886, +0x573091, 0x982cfb, 0x311b1a, 0x08728b, 0xbdcee1, 0x60e142, +0xeb641d, 0xd0bba3, 0xe559d4, 0x597b8c, 0x2a4483, 0xf332ba, +0xf84867, 0x2c8d1b, 0x2fa9b0, 0x50f3dd, 0xf9f573, 0xdb61b4, +0xfe233e, 0x6c41a6, 0xeea318, 0x775a26, 0xbc5e5c, 0xcea708, +0x94dc57, 0xe20196, 0xf1e839, 0xbe4851, 0x5d2d2f, 0x4e9555, +0xd96ec2, 0xe7d755, 0x6304e0, 0xc02e0e, 0xfc40a0, 0xbbf9b3, +0x7125a7, 0x222dfb, 0xf619d8, 0x838c1c, 0x6619e6, 0xb20d55, +0xbb5137, 0x79e809, 0xaf9149, 0x0d73de, 0x0b0da5, 0xce7f58, +0xac1934, 0x724667, 0x7a1a13, 0x9e26bc, 0x4555e7, 0x585cb5, +0x711d14, 0x486991, 0x480d60, 0x56adab, 0xd62f64, 0x96ee0c, +0x212ff3, 0x5d6d88, 0xa67684, 0x95651e, 0xab9e0a, 0x4ddefe, +0x571010, 0x836a39, 0xf8ea31, 0x9e381d, 0xeac8b1, 0xcac96b, +0x37f21e, 0xd505e9, 0x984743, 0x9fc56c, 0x0331b7, 0x3b8bf8, +0x86e56a, 0x8dc343, 0x6230e7, 0x93cfd5, 0x6a8f2d, 0x733005, +0x1af021, 0xa09fcb, 0x7415a1, 0xd56b23, 0x6ff725, 0x2f4bc7, +0xb8a591, 0x7fac59, 0x5c55de, 0x212c38, 0xb13296, 0x5cff50, +0x366262, 0xfa7b16, 0xf4d9a6, 0x2acfe7, 0xf07403, 0xd4d604, +0x6fd916, 0x31b1bf, 0xcbb450, 0x5bd7c8, 0x0ce194, 0x6bd643, +0x4fd91c, 0xdf4543, 0x5f3453, 0xe2b5aa, 0xc9aec8, 0x131485, +0xf9d2bf, 0xbadb9e, 0x76f5b9, 0xaf15cf, 0xca3182, 0x14b56d, +0xe9fe4d, 0x50fc35, 0xf5aed5, 0xa2d0c1, 0xc96057, 0x192eb6, +0xe91d92, 0x07d144, 0xaea3c6, 0x343566, 0x26d5b4, 0x3161e2, +0x37f1a2, 0x209eff, 0x958e23, 0x493798, 0x35f4a6, 0x4bdc02, +0xc2be13, 0xbe80a0, 0x0b72a3, 0x115c5f, 0x1e1bd1, 0x0db4d3, +0x869e85, 0x96976b, 0x2ac91f, 0x8a26c2, 0x3070f0, 0x041412, +0xfc9fa5, 0xf72a38, 0x9c6878, 0xe2aa76, 0x50cfe1, 0x559274, +0x934e38, 0x0a92f7, 0x5533f0, 0xa63db4, 0x399971, 0xe2b755, +0xa98a7c, 0x008f19, 0xac54d2, 0x2ea0b4, 0xf5f3e0, 0x60c849, +0xffd269, 0xae52ce, 0x7a5fdd, 0xe9ce06, 0xfb0ae8, 0xa50cce, +0xea9d3e, 0x3766dd, 0xb834f5, 0x0da090, 0x846f88, 0x4ae3d5, +0x099a03, 0x2eae2d, 0xfcb40a, 0xfb9b33, 0xe281dd, 0x1b16ba, +0xd8c0af, 0xd96b97, 0xb52dc9, 0x9c277f, 0x5951d5, 0x21ccd6, +0xb6496b, 0x584562, 0xb3baf2, 0xa1a5c4, 0x7ca2cf, 0xa9b93d, +0x7b7b89, 0x483d38, +}; + +static const long double c[] = { +/* 106 bits of pi/2 */ +#define PI_2_1 c[0] + 0x1.921fb54442d18469898cc517018p+0L, + +/* pi/2 - PI_2_1 */ +#define PI_2_1t c[1] + 0x3.839a252049c1114cf98e804178p-108L, +}; + +int32_t __ieee754_rem_pio2l(long double x, long double *y) +{ + long double z, w, t; + double tx[8]; + int exp; + int64_t n, ix, hx, ixd; + u_int64_t lxd; + double xhi; + + xhi = ldbl_high (x); + EXTRACT_WORDS64 (hx, xhi); + ix = hx & 0x7fffffffffffffffLL; + if (ix <= 0x3fe921fb54442d10LL) /* x in <-pi/4, pi/4> */ + { + y[0] = x; + y[1] = 0; + return 0; + } + + if (ix < 0x4002d97c7f3321d0LL) /* |x| in <pi/4, 3pi/4) */ + { + if (hx > 0) + { + /* 106 + 106 bit PI is ok */ + z = x - PI_2_1; + y[0] = z - PI_2_1t; + y[1] = (z - y[0]) - PI_2_1t; + return 1; + } + else + { + /* 106 + 106 bit PI is ok */ + z = x + PI_2_1; + y[0] = z + PI_2_1t; + y[1] = (z - y[0]) + PI_2_1t; + return -1; + } + } + + if (ix >= 0x7ff0000000000000LL) /* x is +=oo or NaN */ + { + y[0] = x - x; + y[1] = y[0]; + return 0; + } + + /* Handle large arguments. + We split the 113 bits of the mantissa into 5 24bit integers + stored in a double array. */ + /* Make the IBM extended format 105 bit mantissa look like the ieee854 112 + bit mantissa so the next operation will give the correct result. */ + ldbl_extract_mantissa (&ixd, &lxd, &exp, x); + exp = exp - 23; + /* This is faster than doing this in floating point, because we + have to convert it to integers anyway and like this we can keep + both integer and floating point units busy. */ + tx [0] = (double)(((ixd >> 25) & 0x7fffff) | 0x800000); + tx [1] = (double)((ixd >> 1) & 0xffffff); + tx [2] = (double)(((ixd << 23) | (lxd >> 41)) & 0xffffff); + tx [3] = (double)((lxd >> 17) & 0xffffff); + tx [4] = (double)((lxd << 7) & 0xffffff); + + n = __kernel_rem_pio2 (tx, tx + 5, exp, ((lxd << 7) & 0xffffff) ? 5 : 4, + 3, two_over_pi); + + /* The result is now stored in 3 double values, we need to convert it into + two long double values. */ + t = (long double) tx [6] + (long double) tx [7]; + w = (long double) tx [5]; + + if (hx >= 0) + { + y[0] = w + t; + y[1] = t - (y[0] - w); + return n; + } + else + { + y[0] = -(w + t); + y[1] = -t - (y[0] + w); + return -n; + } +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_remainderl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_remainderl.c new file mode 100644 index 0000000000..68b8fb3519 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_remainderl.c @@ -0,0 +1,81 @@ +/* e_fmodl.c -- long double version of e_fmod.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_remainderl(x,p) + * Return : + * returns x REM p = x - [x/p]*p as if in infinite + * precise arithmetic, where [x/p] is the (infinite bit) + * integer nearest x/p (in half way case choose the even one). + * Method : + * Based on fmodl() return x-[x/p]chopped*p exactlp. + */ + +#include <math.h> +#include <math_private.h> + +static const long double zero = 0.0L; + + +long double +__ieee754_remainderl(long double x, long double p) +{ + int64_t hx,hp; + u_int64_t sx,lx,lp; + long double p_half; + double xhi, xlo, phi, plo; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + ldbl_unpack (p, &phi, &plo); + EXTRACT_WORDS64 (hp, phi); + EXTRACT_WORDS64 (lp, plo); + sx = hx&0x8000000000000000ULL; + lp ^= hp & 0x8000000000000000ULL; + hp &= 0x7fffffffffffffffLL; + lx ^= sx; + hx &= 0x7fffffffffffffffLL; + if (lp == 0x8000000000000000ULL) + lp = 0; + if (lx == 0x8000000000000000ULL) + lx = 0; + + /* purge off exception values */ + if(hp==0) return (x*p)/(x*p); /* p = 0 */ + if((hx>=0x7ff0000000000000LL)|| /* x not finite */ + (hp>0x7ff0000000000000LL)) /* p is NaN */ + return (x*p)/(x*p); + + + if (hp<=0x7fdfffffffffffffLL) x = __ieee754_fmodl(x,p+p); /* now x < 2p */ + if (((hx-hp)|(lx-lp))==0) return zero*x; + x = fabsl(x); + p = fabsl(p); + if (hp<0x0020000000000000LL) { + if(x+x>p) { + x-=p; + if(x+x>=p) x -= p; + } + } else { + p_half = 0.5L*p; + if(x>p_half) { + x-=p; + if(x>=p_half) x -= p; + } + } + if (sx) + x = -x; + return x; +} +strong_alias (__ieee754_remainderl, __remainderl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_sinhl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_sinhl.c new file mode 100644 index 0000000000..67d9d24ce7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_sinhl.c @@ -0,0 +1,79 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + + +/* __ieee754_sinh(x) + * Method : + * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 + * 1. Replace x by |x| (sinh(-x) = -sinh(x)). + * 2. + * E + E/(E+1) + * 0 <= x <= 40 : sinh(x) := --------------, E=expm1(x) + * 2 + * + * 40 <= x <= lnovft : sinh(x) := exp(x)/2 + * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2) + * ln2ovft < x : sinh(x) := x*shuge (overflow) + * + * Special cases: + * sinh(x) is |x| if x is +INF, -INF, or NaN. + * only sinh(0)=0 is exact for finite x. + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const long double one = 1.0, shuge = 1.0e307; + +long double +__ieee754_sinhl(long double x) +{ + long double t,w,h; + int64_t ix,jx; + double xhi; + + /* High word of |x|. */ + xhi = ldbl_high (x); + EXTRACT_WORDS64 (jx, xhi); + ix = jx&0x7fffffffffffffffLL; + + /* x is INF or NaN */ + if(ix>=0x7ff0000000000000LL) return x+x; + + h = 0.5; + if (jx<0) h = -h; + /* |x| in [0,40], return sign(x)*0.5*(E+E/(E+1))) */ + if (ix < 0x4044000000000000LL) { /* |x|<40 */ + if (ix<0x3c90000000000000LL) { /* |x|<2**-54 */ + math_check_force_underflow (x); + if(shuge+x>one) return x;/* sinhl(tiny) = tiny with inexact */ + } + t = __expm1l(fabsl(x)); + if(ix<0x3ff0000000000000LL) return h*(2.0*t-t*t/(t+one)); + w = t/(t+one); + return h*(t+w); + } + + /* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */ + if (ix < 0x40862e42fefa39efLL) return h*__ieee754_expl(fabsl(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + if (ix <= 0x408633ce8fb9f87eLL) { + w = __ieee754_expl(0.5*fabsl(x)); + t = h*w; + return t*w; + } + + /* |x| > overflowthresold, sinh(x) overflow */ + return x*shuge; +} +strong_alias (__ieee754_sinhl, __sinhl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_sqrtl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_sqrtl.c new file mode 100644 index 0000000000..8089090533 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_sqrtl.c @@ -0,0 +1,102 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2.1 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, see <http://www.gnu.org/licenses/>. + */ +/*********************************************************************/ +/* MODULE_NAME: uroot.c */ +/* */ +/* FUNCTION: usqrt */ +/* */ +/* FILES NEEDED: dla.h endian.h mydefs.h uroot.h */ +/* uroot.tbl */ +/* */ +/* An ultimate sqrt routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of square */ +/* root of x. */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round to nearest mode of IEEE 754 standard. */ +/* */ +/*********************************************************************/ + +#include <math_private.h> + +typedef union {int64_t i[2]; long double x; double d[2]; } mynumber; + +static const double + t512 = 0x1p512, + tm256 = 0x1p-256, + two54 = 0x1p54, /* 0x4350000000000000 */ + twom54 = 0x1p-54; /* 0x3C90000000000000 */ + +/*********************************************************************/ +/* An ultimate sqrt routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of square */ +/* root of x. */ +/*********************************************************************/ +long double __ieee754_sqrtl(long double x) +{ + static const long double big = 134217728.0, big1 = 134217729.0; + long double t,s,i; + mynumber a,c; + uint64_t k, l; + int64_t m, n; + double d; + + a.x=x; + k=a.i[0] & INT64_C(0x7fffffffffffffff); + /*----------------- 2^-1022 <= | x |< 2^1024 -----------------*/ + if (k>INT64_C(0x000fffff00000000) && k<INT64_C(0x7ff0000000000000)) { + if (x < 0) return (big1-big1)/(big-big); + l = (k&INT64_C(0x001fffffffffffff))|INT64_C(0x3fe0000000000000); + if ((a.i[1] & INT64_C(0x7fffffffffffffff)) != 0) { + n = (int64_t) ((l - k) * 2) >> 53; + m = (a.i[1] >> 52) & 0x7ff; + if (m == 0) { + a.d[1] *= two54; + m = ((a.i[1] >> 52) & 0x7ff) - 54; + } + m += n; + if (m > 0) + a.i[1] = (a.i[1] & INT64_C(0x800fffffffffffff)) | (m << 52); + else if (m <= -54) { + a.i[1] &= INT64_C(0x8000000000000000); + } else { + m += 54; + a.i[1] = (a.i[1] & INT64_C(0x800fffffffffffff)) | (m << 52); + a.d[1] *= twom54; + } + } + a.i[0] = l; + s = a.x; + d = __ieee754_sqrt (a.d[0]); + c.i[0] = INT64_C(0x2000000000000000)+((k&INT64_C(0x7fe0000000000000))>>1); + c.i[1] = 0; + i = d; + t = 0.5L * (i + s / i); + i = 0.5L * (t + s / t); + return c.x * i; + } + else { + if (k>=INT64_C(0x7ff0000000000000)) + /* sqrt (-Inf) = NaN, sqrt (NaN) = NaN, sqrt (+Inf) = +Inf. */ + return x * x + x; + if (x == 0) return x; + if (x < 0) return (big1-big1)/(big-big); + return tm256*__ieee754_sqrtl(x*t512); + } +} +strong_alias (__ieee754_sqrtl, __sqrtl_finite) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/gamma_productl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/gamma_productl.c new file mode 100644 index 0000000000..7e71cb008a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/gamma_productl.c @@ -0,0 +1,42 @@ +/* Compute a product of X, X+1, ..., with an error estimate. + Copyright (C) 2013-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + +/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N + - 1, in the form R * (1 + *EPS) where the return value R is an + approximation to the product and *EPS is set to indicate the + approximate error in the return value. X is such that all the + values X + 1, ..., X + N - 1 are exactly representable, and X_EPS / + X is small enough that factors quadratic in it can be + neglected. */ + +long double +__gamma_productl (long double x, long double x_eps, int n, long double *eps) +{ + long double ret = x; + *eps = x_eps / x; + for (int i = 1; i < n; i++) + { + *eps += x_eps / (x + i); + ret *= x + i; + /* FIXME: no error estimates for the multiplication. */ + } + return ret; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/ieee754.h b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/ieee754.h new file mode 100644 index 0000000000..7e31128996 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/ieee754.h @@ -0,0 +1,133 @@ +/* Copyright (C) 1992-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#ifndef _IEEE754_H + +#define _IEEE754_H 1 +#include <features.h> + +#include <endian.h> + +__BEGIN_DECLS + +union ieee754_float + { + float f; + + /* This is the IEEE 754 single-precision format. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:8; + unsigned int mantissa:23; +#endif /* Big endian. */ +#if __BYTE_ORDER == __LITTLE_ENDIAN + unsigned int mantissa:23; + unsigned int exponent:8; + unsigned int negative:1; +#endif /* Little endian. */ + } ieee; + + /* This format makes it easier to see if a NaN is a signalling NaN. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:8; + unsigned int quiet_nan:1; + unsigned int mantissa:22; +#endif /* Big endian. */ +#if __BYTE_ORDER == __LITTLE_ENDIAN + unsigned int mantissa:22; + unsigned int quiet_nan:1; + unsigned int exponent:8; + unsigned int negative:1; +#endif /* Little endian. */ + } ieee_nan; + }; + +#define IEEE754_FLOAT_BIAS 0x7f /* Added to exponent. */ + + +union ieee754_double + { + double d; + + /* This is the IEEE 754 double-precision format. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:11; + /* Together these comprise the mantissa. */ + unsigned int mantissa0:20; + unsigned int mantissa1:32; +#endif /* Big endian. */ +#if __BYTE_ORDER == __LITTLE_ENDIAN + /* Together these comprise the mantissa. */ + unsigned int mantissa1:32; + unsigned int mantissa0:20; + unsigned int exponent:11; + unsigned int negative:1; +#endif /* Little endian. */ + } ieee; + + /* This format makes it easier to see if a NaN is a signalling NaN. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:11; + unsigned int quiet_nan:1; + /* Together these comprise the mantissa. */ + unsigned int mantissa0:19; + unsigned int mantissa1:32; +#else + /* Together these comprise the mantissa. */ + unsigned int mantissa1:32; + unsigned int mantissa0:19; + unsigned int quiet_nan:1; + unsigned int exponent:11; + unsigned int negative:1; +#endif + } ieee_nan; + }; + +#define IEEE754_DOUBLE_BIAS 0x3ff /* Added to exponent. */ + + +/* IBM extended format for long double. + + Each long double is made up of two IEEE doubles. The value of the + long double is the sum of the values of the two parts. The most + significant part is required to be the value of the long double + rounded to the nearest double, as specified by IEEE. For Inf + values, the least significant part is required to be one of +0.0 or + -0.0. No other requirements are made; so, for example, 1.0 may be + represented as (1.0, +0.0) or (1.0, -0.0), and the low part of a + NaN is don't-care. */ + +union ibm_extended_long_double + { + long double ld; + union ieee754_double d[2]; + }; + +__END_DECLS + +#endif /* ieee754.h */ diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/include/bits/iscanonical.h b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/include/bits/iscanonical.h new file mode 100644 index 0000000000..bee080bd29 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/include/bits/iscanonical.h @@ -0,0 +1,5 @@ +#include_next <bits/iscanonical.h> + +#ifndef _ISOMAC +libm_hidden_proto (__iscanonicall) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_cosl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_cosl.c new file mode 100644 index 0000000000..0010d6274a --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_cosl.c @@ -0,0 +1,153 @@ +/* Quad-precision floating point cosine on <-pi/4,pi/4>. + Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jj@ultra.linux.cz> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + +static const long double c[] = { +#define ONE c[0] + 1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */ + +/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 ) + x in <0,1/256> */ +#define SCOS1 c[1] +#define SCOS2 c[2] +#define SCOS3 c[3] +#define SCOS4 c[4] +#define SCOS5 c[5] +-5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */ + 4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */ +-1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */ + 2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */ +-2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */ + +/* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 ) + x in <0,0.1484375> */ +#define COS1 c[6] +#define COS2 c[7] +#define COS3 c[8] +#define COS4 c[9] +#define COS5 c[10] +#define COS6 c[11] +#define COS7 c[12] +#define COS8 c[13] +-4.99999999999999999999999999999999759E-01L, /* bffdfffffffffffffffffffffffffffb */ + 4.16666666666666666666666666651287795E-02L, /* 3ffa5555555555555555555555516f30 */ +-1.38888888888888888888888742314300284E-03L, /* bff56c16c16c16c16c16c16a463dfd0d */ + 2.48015873015873015867694002851118210E-05L, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */ +-2.75573192239858811636614709689300351E-07L, /* bfe927e4fb7789f5aa8142a22044b51f */ + 2.08767569877762248667431926878073669E-09L, /* 3fe21eed8eff881d1e9262d7adff4373 */ +-1.14707451049343817400420280514614892E-11L, /* bfda9397496922a9601ed3d4ca48944b */ + 4.77810092804389587579843296923533297E-14L, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */ + +/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 ) + x in <0,1/256> */ +#define SSIN1 c[14] +#define SSIN2 c[15] +#define SSIN3 c[16] +#define SSIN4 c[17] +#define SSIN5 c[18] +-1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */ + 8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */ +-1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */ + 2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */ +-2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */ +}; + +#define SINCOSL_COS_HI 0 +#define SINCOSL_COS_LO 1 +#define SINCOSL_SIN_HI 2 +#define SINCOSL_SIN_LO 3 +extern const long double __sincosl_table[]; + +long double +__kernel_cosl(long double x, long double y) +{ + long double h, l, z, sin_l, cos_l_m1; + int64_t ix; + uint32_t tix, hix, index; + double xhi, hhi; + + xhi = ldbl_high (x); + EXTRACT_WORDS64 (ix, xhi); + tix = ((u_int64_t)ix) >> 32; + tix &= ~0x80000000; /* tix = |x|'s high 32 bits */ + if (tix < 0x3fc30000) /* |x| < 0.1484375 */ + { + /* Argument is small enough to approximate it by a Chebyshev + polynomial of degree 16. */ + if (tix < 0x3c600000) /* |x| < 2^-57 */ + if (!((int)x)) return ONE; /* generate inexact */ + z = x * x; + return ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+ + z*(COS5+z*(COS6+z*(COS7+z*COS8)))))))); + } + else + { + /* So that we don't have to use too large polynomial, we find + l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83 + possible values for h. We look up cosl(h) and sinl(h) in + pre-computed tables, compute cosl(l) and sinl(l) using a + Chebyshev polynomial of degree 10(11) and compute + cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l). */ + int six = tix; + tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000; + index = 0x3ffe - (tix >> 16); + hix = (tix + (0x200 << index)) & (0xfffffc00 << index); + x = fabsl (x); + switch (index) + { + case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break; + case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break; + default: + case 2: index = (hix - 0x3ffc3000) >> 10; break; + } + hix = (hix << 4) & 0x3fffffff; +/* + The following should work for double but generates the wrong index. + For now the code above converts double to ieee extended to compute + the index back to double for the h value. + + index = 0x3fe - (tix >> 20); + hix = (tix + (0x200 << index)) & (0xfffffc00 << index); + if (signbit (x)) + { + x = -x; + y = -y; + } + switch (index) + { + case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break; + case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break; + default: + case 2: index = (hix - 0x3fc30000) >> 14; break; + } +*/ + INSERT_WORDS64 (hhi, ((uint64_t)hix) << 32); + h = hhi; + l = y - (h - x); + z = l * l; + sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5))))); + cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5)))); + return __sincosl_table [index + SINCOSL_COS_HI] + + (__sincosl_table [index + SINCOSL_COS_LO] + - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l + - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1)); + } +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_sincosl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_sincosl.c new file mode 100644 index 0000000000..14b0359c15 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_sincosl.c @@ -0,0 +1,193 @@ +/* Quad-precision floating point sine and cosine on <-pi/4,pi/4>. + Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jj@ultra.linux.cz> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const long double c[] = { +#define ONE c[0] + 1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */ + +/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 ) + x in <0,1/256> */ +#define SCOS1 c[1] +#define SCOS2 c[2] +#define SCOS3 c[3] +#define SCOS4 c[4] +#define SCOS5 c[5] +-5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */ + 4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */ +-1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */ + 2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */ +-2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */ + +/* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 ) + x in <0,0.1484375> */ +#define COS1 c[6] +#define COS2 c[7] +#define COS3 c[8] +#define COS4 c[9] +#define COS5 c[10] +#define COS6 c[11] +#define COS7 c[12] +#define COS8 c[13] +-4.99999999999999999999999999999999759E-01L, /* bffdfffffffffffffffffffffffffffb */ + 4.16666666666666666666666666651287795E-02L, /* 3ffa5555555555555555555555516f30 */ +-1.38888888888888888888888742314300284E-03L, /* bff56c16c16c16c16c16c16a463dfd0d */ + 2.48015873015873015867694002851118210E-05L, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */ +-2.75573192239858811636614709689300351E-07L, /* bfe927e4fb7789f5aa8142a22044b51f */ + 2.08767569877762248667431926878073669E-09L, /* 3fe21eed8eff881d1e9262d7adff4373 */ +-1.14707451049343817400420280514614892E-11L, /* bfda9397496922a9601ed3d4ca48944b */ + 4.77810092804389587579843296923533297E-14L, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */ + +/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 ) + x in <0,1/256> */ +#define SSIN1 c[14] +#define SSIN2 c[15] +#define SSIN3 c[16] +#define SSIN4 c[17] +#define SSIN5 c[18] +-1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */ + 8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */ +-1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */ + 2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */ +-2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */ + +/* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 ) + x in <0,0.1484375> */ +#define SIN1 c[19] +#define SIN2 c[20] +#define SIN3 c[21] +#define SIN4 c[22] +#define SIN5 c[23] +#define SIN6 c[24] +#define SIN7 c[25] +#define SIN8 c[26] +-1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */ + 8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */ +-1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */ + 2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */ +-2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */ + 1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */ +-7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */ + 2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */ +}; + +#define SINCOSL_COS_HI 0 +#define SINCOSL_COS_LO 1 +#define SINCOSL_SIN_HI 2 +#define SINCOSL_SIN_LO 3 +extern const long double __sincosl_table[]; + +void +__kernel_sincosl(long double x, long double y, long double *sinx, long double *cosx, int iy) +{ + long double h, l, z, sin_l, cos_l_m1; + int64_t ix; + uint32_t tix, hix, index; + double xhi, hhi; + + xhi = ldbl_high (x); + EXTRACT_WORDS64 (ix, xhi); + tix = ((uint64_t)ix) >> 32; + tix &= ~0x80000000; /* tix = |x|'s high 32 bits */ + if (tix < 0x3fc30000) /* |x| < 0.1484375 */ + { + /* Argument is small enough to approximate it by a Chebyshev + polynomial of degree 16(17). */ + if (tix < 0x3c600000) /* |x| < 2^-57 */ + { + math_check_force_underflow (x); + if (!((int)x)) /* generate inexact */ + { + *sinx = x; + *cosx = ONE; + return; + } + } + z = x * x; + *sinx = x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+ + z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8))))))))); + *cosx = ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+ + z*(COS5+z*(COS6+z*(COS7+z*COS8)))))))); + } + else + { + /* So that we don't have to use too large polynomial, we find + l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83 + possible values for h. We look up cosl(h) and sinl(h) in + pre-computed tables, compute cosl(l) and sinl(l) using a + Chebyshev polynomial of degree 10(11) and compute + sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l) and + cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l). */ + int six = tix; + tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000; + index = 0x3ffe - (tix >> 16); + hix = (tix + (0x200 << index)) & (0xfffffc00 << index); + x = fabsl (x); + switch (index) + { + case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break; + case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break; + default: + case 2: index = (hix - 0x3ffc3000) >> 10; break; + } + hix = (hix << 4) & 0x3fffffff; +/* + The following should work for double but generates the wrong index. + For now the code above converts double to ieee extended to compute + the index back to double for the h value. + + + index = 0x3fe - (tix >> 20); + hix = (tix + (0x2000 << index)) & (0xffffc000 << index); + if (signbit (x)) + { + x = -x; + y = -y; + } + switch (index) + { + case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break; + case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break; + default: + case 2: index = (hix - 0x3fc30000) >> 14; break; + } +*/ + INSERT_WORDS64 (hhi, ((uint64_t)hix) << 32); + h = hhi; + if (iy) + l = y - (h - x); + else + l = x - h; + z = l * l; + sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5))))); + cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5)))); + z = __sincosl_table [index + SINCOSL_SIN_HI] + + (__sincosl_table [index + SINCOSL_SIN_LO] + + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1) + + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l)); + *sinx = (ix < 0) ? -z : z; + *cosx = __sincosl_table [index + SINCOSL_COS_HI] + + (__sincosl_table [index + SINCOSL_COS_LO] + - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l + - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1)); + } +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_sinl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_sinl.c new file mode 100644 index 0000000000..2138ccf13b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_sinl.c @@ -0,0 +1,157 @@ +/* Quad-precision floating point sine on <-pi/4,pi/4>. + Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jj@ultra.linux.cz> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const long double c[] = { +#define ONE c[0] + 1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */ + +/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 ) + x in <0,1/256> */ +#define SCOS1 c[1] +#define SCOS2 c[2] +#define SCOS3 c[3] +#define SCOS4 c[4] +#define SCOS5 c[5] +-5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */ + 4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */ +-1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */ + 2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */ +-2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */ + +/* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 ) + x in <0,0.1484375> */ +#define SIN1 c[6] +#define SIN2 c[7] +#define SIN3 c[8] +#define SIN4 c[9] +#define SIN5 c[10] +#define SIN6 c[11] +#define SIN7 c[12] +#define SIN8 c[13] +-1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */ + 8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */ +-1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */ + 2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */ +-2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */ + 1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */ +-7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */ + 2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */ + +/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 ) + x in <0,1/256> */ +#define SSIN1 c[14] +#define SSIN2 c[15] +#define SSIN3 c[16] +#define SSIN4 c[17] +#define SSIN5 c[18] +-1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */ + 8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */ +-1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */ + 2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */ +-2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */ +}; + +#define SINCOSL_COS_HI 0 +#define SINCOSL_COS_LO 1 +#define SINCOSL_SIN_HI 2 +#define SINCOSL_SIN_LO 3 +extern const long double __sincosl_table[]; + +long double +__kernel_sinl(long double x, long double y, int iy) +{ + long double h, l, z, sin_l, cos_l_m1; + int64_t ix; + u_int32_t tix, hix, index; + double xhi, hhi; + + xhi = ldbl_high (x); + EXTRACT_WORDS64 (ix, xhi); + tix = ((u_int64_t)ix) >> 32; + tix &= ~0x80000000; /* tix = |x|'s high 32 bits */ + if (tix < 0x3fc30000) /* |x| < 0.1484375 */ + { + /* Argument is small enough to approximate it by a Chebyshev + polynomial of degree 17. */ + if (tix < 0x3c600000) /* |x| < 2^-57 */ + { + math_check_force_underflow (x); + if (!((int)x)) return x; /* generate inexact */ + } + z = x * x; + return x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+ + z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8))))))))); + } + else + { + /* So that we don't have to use too large polynomial, we find + l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83 + possible values for h. We look up cosl(h) and sinl(h) in + pre-computed tables, compute cosl(l) and sinl(l) using a + Chebyshev polynomial of degree 10(11) and compute + sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l). */ + int six = tix; + tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000; + index = 0x3ffe - (tix >> 16); + hix = (tix + (0x200 << index)) & (0xfffffc00 << index); + x = fabsl (x); + switch (index) + { + case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break; + case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break; + default: + case 2: index = (hix - 0x3ffc3000) >> 10; break; + } + hix = (hix << 4) & 0x3fffffff; +/* + The following should work for double but generates the wrong index. + For now the code above converts double to ieee extended to compute + the index back to double for the h value. + + index = 0x3fe - (tix >> 20); + hix = (tix + (0x2000 << index)) & (0xffffc000 << index); + x = fabsl (x); + switch (index) + { + case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break; + case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break; + default: + case 2: index = (hix - 0x3fc30000) >> 14; break; + } +*/ + INSERT_WORDS64 (hhi, ((uint64_t)hix) << 32); + h = hhi; + if (iy) + l = (ix < 0 ? -y : y) - (h - x); + else + l = x - h; + z = l * l; + sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5))))); + cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5)))); + z = __sincosl_table [index + SINCOSL_SIN_HI] + + (__sincosl_table [index + SINCOSL_SIN_LO] + + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1) + + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l)); + return (ix < 0) ? -z : z; + } +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_tanl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_tanl.c new file mode 100644 index 0000000000..232e00c345 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_tanl.c @@ -0,0 +1,166 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + Long double expansions are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* __kernel_tanl( x, y, k ) + * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * Input k indicates whether tan (if k=1) or + * -1/tan (if k= -1) is returned. + * + * Algorithm + * 1. Since tan(-x) = -tan(x), we need only to consider positive x. + * 2. if x < 2^-57, return x with inexact if x!=0. + * 3. tan(x) is approximated by a rational form x + x^3 / 3 + x^5 R(x^2) + * on [0,0.67433]. + * + * Note: tan(x+y) = tan(x) + tan'(x)*y + * ~ tan(x) + (1+x*x)*y + * Therefore, for better accuracy in computing tan(x+y), let + * r = x^3 * R(x^2) + * then + * tan(x+y) = x + (x^3 / 3 + (x^2 *(r+y)+y)) + * + * 4. For x in [0.67433,pi/4], let y = pi/4 - x, then + * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y)) + * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <libc-diag.h> + +static const long double + one = 1.0L, + pio4hi = 7.8539816339744830961566084581987569936977E-1L, + pio4lo = 2.1679525325309452561992610065108379921906E-35L, + + /* tan x = x + x^3 / 3 + x^5 T(x^2)/U(x^2) + 0 <= x <= 0.6743316650390625 + Peak relative error 8.0e-36 */ + TH = 3.333333333333333333333333333333333333333E-1L, + T0 = -1.813014711743583437742363284336855889393E7L, + T1 = 1.320767960008972224312740075083259247618E6L, + T2 = -2.626775478255838182468651821863299023956E4L, + T3 = 1.764573356488504935415411383687150199315E2L, + T4 = -3.333267763822178690794678978979803526092E-1L, + + U0 = -1.359761033807687578306772463253710042010E8L, + U1 = 6.494370630656893175666729313065113194784E7L, + U2 = -4.180787672237927475505536849168729386782E6L, + U3 = 8.031643765106170040139966622980914621521E4L, + U4 = -5.323131271912475695157127875560667378597E2L; + /* 1.000000000000000000000000000000000000000E0 */ + + +long double +__kernel_tanl (long double x, long double y, int iy) +{ + long double z, r, v, w, s; + int32_t ix, sign, hx, lx; + double xhi; + + xhi = ldbl_high (x); + EXTRACT_WORDS (hx, lx, xhi); + ix = hx & 0x7fffffff; + if (ix < 0x3c600000) /* x < 2**-57 */ + { + if ((int) x == 0) /* generate inexact */ + { + if ((ix | lx | (iy + 1)) == 0) + return one / fabs (x); + else if (iy == 1) + { + math_check_force_underflow (x); + return x; + } + else + return -one / x; + } + } + if (ix >= 0x3fe59420) /* |x| >= 0.6743316650390625 */ + { + if ((hx & 0x80000000) != 0) + { + x = -x; + y = -y; + sign = -1; + } + else + sign = 1; + z = pio4hi - x; + w = pio4lo - y; + x = z + w; + y = 0.0; + } + z = x * x; + r = T0 + z * (T1 + z * (T2 + z * (T3 + z * T4))); + v = U0 + z * (U1 + z * (U2 + z * (U3 + z * (U4 + z)))); + r = r / v; + + s = z * x; + r = y + z * (s * r + y); + r += TH * s; + w = x + r; + if (ix >= 0x3fe59420) + { + v = (long double) iy; + w = (v - 2.0 * (x - (w * w / (w + v) - r))); + /* SIGN is set for arguments that reach this code, but not + otherwise, resulting in warnings that it may be used + uninitialized although in the cases where it is used it has + always been set. */ + DIAG_PUSH_NEEDS_COMMENT; + DIAG_IGNORE_NEEDS_COMMENT (5, "-Wmaybe-uninitialized"); + if (sign < 0) + w = -w; + DIAG_POP_NEEDS_COMMENT; + return w; + } + if (iy == 1) + return w; + else + { /* if allow error up to 2 ulp, + simply return -1.0/(x+r) here */ + /* compute -1.0/(x+r) accurately */ + long double u1, z1; + + u1 = ldbl_high (w); + v = r - (u1 - x); /* u1+v = r+x */ + z = -1.0 / w; + z1 = ldbl_high (z); + s = 1.0 + z1 * u1; + return z1 + z * (s + z1 * v); + } +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/ldbl2mpn.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/ldbl2mpn.c new file mode 100644 index 0000000000..4146e5c2d4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/ldbl2mpn.c @@ -0,0 +1,197 @@ +/* Copyright (C) 1995-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "gmp.h" +#include "gmp-impl.h" +#include "longlong.h" +#include <ieee754.h> +#include <float.h> +#include <math.h> +#include <stdlib.h> + +/* Convert a `long double' in IBM extended format to a multi-precision + integer representing the significand scaled up by its number of + bits (106 for long double) and an integral power of two (MPN + frexpl). */ + + +/* When signs differ, the actual value is the difference between the + significant double and the less significant double. Sometimes a + bit can be lost when we borrow from the significant mantissa. */ +#define EXTRA_INTERNAL_PRECISION (7) + +mp_size_t +__mpn_extract_long_double (mp_ptr res_ptr, mp_size_t size, + int *expt, int *is_neg, + long double value) +{ + union ibm_extended_long_double u; + unsigned long long hi, lo; + int ediff; + + u.ld = value; + + *is_neg = u.d[0].ieee.negative; + *expt = (int) u.d[0].ieee.exponent - IEEE754_DOUBLE_BIAS; + + lo = ((long long) u.d[1].ieee.mantissa0 << 32) | u.d[1].ieee.mantissa1; + hi = ((long long) u.d[0].ieee.mantissa0 << 32) | u.d[0].ieee.mantissa1; + + /* Hold 7 extra bits of precision in the mantissa. This allows + the normalizing shifts below to prevent losing precision when + the signs differ and the exponents are sufficiently far apart. */ + lo <<= EXTRA_INTERNAL_PRECISION; + + /* If the lower double is not a denormal or zero then set the hidden + 53rd bit. */ + if (u.d[1].ieee.exponent != 0) + lo |= 1ULL << (52 + EXTRA_INTERNAL_PRECISION); + else + lo = lo << 1; + + /* The lower double is normalized separately from the upper. We may + need to adjust the lower manitissa to reflect this. */ + ediff = u.d[0].ieee.exponent - u.d[1].ieee.exponent - 53; + if (ediff > 0) + { + if (ediff < 64) + lo = lo >> ediff; + else + lo = 0; + } + else if (ediff < 0) + lo = lo << -ediff; + + /* The high double may be rounded and the low double reflects the + difference between the long double and the rounded high double + value. This is indicated by a differnce between the signs of the + high and low doubles. */ + if (u.d[0].ieee.negative != u.d[1].ieee.negative + && lo != 0) + { + lo = (1ULL << (53 + EXTRA_INTERNAL_PRECISION)) - lo; + if (hi == 0) + { + /* we have a borrow from the hidden bit, so shift left 1. */ + hi = 0x000ffffffffffffeLL | (lo >> (52 + EXTRA_INTERNAL_PRECISION)); + lo = 0x0fffffffffffffffLL & (lo << 1); + (*expt)--; + } + else + hi--; + } +#if BITS_PER_MP_LIMB == 32 + /* Combine the mantissas to be contiguous. */ + res_ptr[0] = lo >> EXTRA_INTERNAL_PRECISION; + res_ptr[1] = (hi << (53 - 32)) | (lo >> (32 + EXTRA_INTERNAL_PRECISION)); + res_ptr[2] = hi >> 11; + res_ptr[3] = hi >> (32 + 11); + #define N 4 +#elif BITS_PER_MP_LIMB == 64 + /* Combine the two mantissas to be contiguous. */ + res_ptr[0] = (hi << 53) | (lo >> EXTRA_INTERNAL_PRECISION); + res_ptr[1] = hi >> 11; + #define N 2 +#else + #error "mp_limb size " BITS_PER_MP_LIMB "not accounted for" +#endif +/* The format does not fill the last limb. There are some zeros. */ +#define NUM_LEADING_ZEROS (BITS_PER_MP_LIMB \ + - (LDBL_MANT_DIG - ((N - 1) * BITS_PER_MP_LIMB))) + + if (u.d[0].ieee.exponent == 0) + { + /* A biased exponent of zero is a special case. + Either it is a zero or it is a denormal number. */ + if (res_ptr[0] == 0 && res_ptr[1] == 0 + && res_ptr[N - 2] == 0 && res_ptr[N - 1] == 0) /* Assumes N<=4. */ + /* It's zero. */ + *expt = 0; + else + { + /* It is a denormal number, meaning it has no implicit leading + one bit, and its exponent is in fact the format minimum. We + use DBL_MIN_EXP instead of LDBL_MIN_EXP below because the + latter describes the properties of both parts together, but + the exponent is computed from the high part only. */ + int cnt; + +#if N == 2 + if (res_ptr[N - 1] != 0) + { + count_leading_zeros (cnt, res_ptr[N - 1]); + cnt -= NUM_LEADING_ZEROS; + res_ptr[N - 1] = res_ptr[N - 1] << cnt + | (res_ptr[0] >> (BITS_PER_MP_LIMB - cnt)); + res_ptr[0] <<= cnt; + *expt = DBL_MIN_EXP - 1 - cnt; + } + else + { + count_leading_zeros (cnt, res_ptr[0]); + if (cnt >= NUM_LEADING_ZEROS) + { + res_ptr[N - 1] = res_ptr[0] << (cnt - NUM_LEADING_ZEROS); + res_ptr[0] = 0; + } + else + { + res_ptr[N - 1] = res_ptr[0] >> (NUM_LEADING_ZEROS - cnt); + res_ptr[0] <<= BITS_PER_MP_LIMB - (NUM_LEADING_ZEROS - cnt); + } + *expt = DBL_MIN_EXP - 1 + - (BITS_PER_MP_LIMB - NUM_LEADING_ZEROS) - cnt; + } +#else + int j, k, l; + + for (j = N - 1; j > 0; j--) + if (res_ptr[j] != 0) + break; + + count_leading_zeros (cnt, res_ptr[j]); + cnt -= NUM_LEADING_ZEROS; + l = N - 1 - j; + if (cnt < 0) + { + cnt += BITS_PER_MP_LIMB; + l--; + } + if (!cnt) + for (k = N - 1; k >= l; k--) + res_ptr[k] = res_ptr[k-l]; + else + { + for (k = N - 1; k > l; k--) + res_ptr[k] = res_ptr[k-l] << cnt + | res_ptr[k-l-1] >> (BITS_PER_MP_LIMB - cnt); + res_ptr[k--] = res_ptr[0] << cnt; + } + + for (; k >= 0; k--) + res_ptr[k] = 0; + *expt = DBL_MIN_EXP - 1 - l * BITS_PER_MP_LIMB - cnt; +#endif + } + } + else + /* Add the implicit leading one bit for a normalized number. */ + res_ptr[N - 1] |= (mp_limb_t) 1 << (LDBL_MANT_DIG - 1 + - ((N - 1) * BITS_PER_MP_LIMB)); + + return N; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/lgamma_negl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/lgamma_negl.c new file mode 100644 index 0000000000..638812c50b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/lgamma_negl.c @@ -0,0 +1,532 @@ +/* lgammal expanding around zeros. + Copyright (C) 2015-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const long double lgamma_zeros[][2] = + { + { -0x2.74ff92c01f0d82abec9f315f1ap+0L, -0x7.12c334804d9a79cb5d46094d46p-112L }, + { -0x2.bf6821437b20197995a4b4641fp+0L, 0x5.140b4ff4b7d6069e1bd7acc196p-108L }, + { -0x3.24c1b793cb35efb8be699ad3dap+0L, 0x4.59abab3480539f1c0e926287cp-108L }, + { -0x3.f48e2a8f85fca170d456129123p+0L, -0x6.cc320a4887d1cb4c711828a75ep-108L }, + { -0x4.0a139e16656030c39f0b0de182p+0L, 0xe.d53e84029416e1242006b2b3dp-108L }, + { -0x4.fdd5de9bbabf3510d0aa407698p+0L, -0x8.501d7d78125286f78d1e501f14p-108L }, + { -0x5.021a95fc2db6432a4c56e5953ap+0L, 0xb.2133950fbcf2b01a8b9058dcccp-108L }, + { -0x5.ffa4bd647d0357dd4ed62cbd32p+0L, 0x1.2071c071a2145d2982428f2269p-108L }, + { -0x6.005ac9625f233b607c2d96d164p+0L, 0x7.a347953a96cbf30e1a0db20856p-108L }, + { -0x6.fff2fddae1bbff3d626b65c24p+0L, 0x2.de0bfcff5c457ebcf4d3ad9674p-108L }, + { -0x7.000cff7b7f87adf4482dcdb988p+0L, 0x7.d54d99e35a74d6407b80292df2p-108L }, + { -0x7.fffe5fe05673c3ca9e82b522bp+0L, -0xc.a9d2e8837cd1f14bd3d05002e4p-108L }, + { -0x8.0001a01459fc9f60cb3cec1cecp+0L, -0x8.576677ca538d88084310983b8p-108L }, + { -0x8.ffffd1c425e80ffc864e957494p+0L, 0x1.a6181dfdef1807e3087e4bb163p-104L }, + { -0x9.00002e3bb47d86d6d843fedc34p+0L, -0x1.1deb7ad09ec5e9d6e8ae2d548bp-104L }, + { -0x9.fffffb606bdfdcd062ae77a504p+0L, -0x1.47c69d2eb6f33d170fce38ff818p-104L }, + { -0xa.0000049f93bb9927b45d95e154p+0L, -0x4.1e03086db9146a9287bd4f2172p-108L }, + { -0xa.ffffff9466e9f1b36dacd2adbcp+0L, -0x1.18d05a4e458062f3f95345a4dap-104L }, + { -0xb.0000006b9915315d965a6ffea4p+0L, -0xe.4bea39000dcc1848023c5f6bdcp-112L }, + { -0xb.fffffff7089387387de41acc3cp+0L, -0x1.3c978bd839c8c428b5efcf91ef8p-104L }, + { -0xc.00000008f76c7731567c0f025p+0L, -0xf.387920df5675833859190eb128p-108L }, + { -0xc.ffffffff4f6dcf617f97a5ffc8p+0L, 0xa.82ab72d76f32eaee2d1a42ed5p-108L }, + { -0xd.00000000b092309c06683dd1b8p+0L, -0x1.03e3700857a15c19ac5a611de98p-104L }, + { -0xd.fffffffff36345ab9e184a3e08p+0L, -0x1.d1176dc48e47f62d917973dd45p-104L }, + { -0xe.000000000c9cba545e94e75ec4p+0L, -0x1.718f753e2501e757a17cf2ecbfp-104L }, + { -0xe.ffffffffff28c060c6604ef304p+0L, 0x8.e0762c8ca8361c23e8393919c4p-108L }, + { -0xf.0000000000d73f9f399bd0e42p+0L, -0xf.85e9ee31b0b890744fc0e3fbcp-108L }, + { -0xf.fffffffffff28c060c6621f514p+0L, 0x1.18d1b2eec9d960bd9adc5be5f6p-104L }, + { -0x1.000000000000d73f9f399da1428p+4L, 0x3.406c46e0e88305d2800f0e414cp-104L }, + { -0x1.0ffffffffffff3569c47e7a93ep+4L, -0x1.c46a08a2e008a998ebabb8087fp-104L }, + { -0x1.1000000000000ca963b81856888p+4L, -0x7.6ca5a3a64ec15db0a95caf2cap-108L }, + { -0x1.1fffffffffffff4bec3ce23413p+4L, -0x2.d08b2b726187c841cb92cd5222p-104L }, + { -0x1.20000000000000b413c31dcbec8p+4L, -0x2.4c3b2ffacbb4932f18dceedfd7p-104L }, + { -0x1.2ffffffffffffff685b25cbf5f8p+4L, 0x2.ba3126cd1c7b7a0822d694705cp-104L }, + { -0x1.30000000000000097a4da340a08p+4L, -0x2.b81b7b1f1f001c72bf914141efp-104L }, + { -0x1.3fffffffffffffff86af516ff8p+4L, 0x8.9429818df2a87abafd48248a2p-108L }, + { -0x1.40000000000000007950ae9008p+4L, -0x8.9413ccc8a353fda263f8ce973cp-108L }, + { -0x1.4ffffffffffffffffa391c4249p+4L, 0x3.d5c63022b62b5484ba346524dbp-104L }, + { -0x1.500000000000000005c6e3bdb7p+4L, -0x3.d5c62f55ed5322b2685c5e9a52p-104L }, + { -0x1.5fffffffffffffffffbcc71a49p+4L, -0x2.01eb5aeb96c74d7ad25e060529p-104L }, + { -0x1.6000000000000000004338e5b7p+4L, 0x2.01eb5aec04b2f2eb663e4e3d8ap-104L }, + { -0x1.6ffffffffffffffffffd13c97d8p+4L, -0x1.d38fcc4d08d6fe5aa56ab04308p-104L }, + { -0x1.70000000000000000002ec36828p+4L, 0x1.d38fcc4d090cee2f5d0b69a99cp-104L }, + { -0x1.7fffffffffffffffffffe0d31p+4L, 0x1.972f577cca4b4c8cb1dc14001bp-104L }, + { -0x1.800000000000000000001f2cfp+4L, -0x1.972f577cca4b3442e35f0040b38p-104L }, + { -0x1.8ffffffffffffffffffffec0c3p+4L, -0x3.22e9a0572b1bb5b95f346a92d6p-104L }, + { -0x1.90000000000000000000013f3dp+4L, 0x3.22e9a0572b1bb5c371ddb35617p-104L }, + { -0x1.9ffffffffffffffffffffff3b88p+4L, -0x3.d01cad8d32e386fd783e97296dp-104L }, + { -0x1.a0000000000000000000000c478p+4L, 0x3.d01cad8d32e386fd7c1ab8c1fep-104L }, + { -0x1.afffffffffffffffffffffff8b8p+4L, -0x1.538f48cc5737d5979c39db806c8p-104L }, + { -0x1.b00000000000000000000000748p+4L, 0x1.538f48cc5737d5979c3b3a6bdap-104L }, + { -0x1.bffffffffffffffffffffffffcp+4L, 0x2.862898d42174dcf171470d8c8cp-104L }, + { -0x1.c0000000000000000000000004p+4L, -0x2.862898d42174dcf171470d18bap-104L }, + { -0x1.dp+4L, 0x2.4b3f31686b15af57c61ceecdf4p-104L }, + { -0x1.dp+4L, -0x2.4b3f31686b15af57c61ceecdd1p-104L }, + { -0x1.ep+4L, 0x1.3932c5047d60e60caded4c298ap-108L }, + { -0x1.ep+4L, -0x1.3932c5047d60e60caded4c29898p-108L }, + { -0x1.fp+4L, 0xa.1a6973c1fade2170f7237d36p-116L }, + { -0x1.fp+4L, -0xa.1a6973c1fade2170f7237d36p-116L }, + { -0x2p+4L, 0x5.0d34b9e0fd6f10b87b91be9bp-120L }, + { -0x2p+4L, -0x5.0d34b9e0fd6f10b87b91be9bp-120L }, + { -0x2.1p+4L, 0x2.73024a9ba1aa36a7059bff52e8p-124L }, + { -0x2.1p+4L, -0x2.73024a9ba1aa36a7059bff52e8p-124L }, + { -0x2.2p+4L, 0x1.2710231c0fd7a13f8a2b4af9d68p-128L }, + { -0x2.2p+4L, -0x1.2710231c0fd7a13f8a2b4af9d68p-128L }, + { -0x2.3p+4L, 0x8.6e2ce38b6c8f9419e3fad3f03p-136L }, + { -0x2.3p+4L, -0x8.6e2ce38b6c8f9419e3fad3f03p-136L }, + { -0x2.4p+4L, 0x3.bf30652185952560d71a254e4fp-140L }, + { -0x2.4p+4L, -0x3.bf30652185952560d71a254e4fp-140L }, + { -0x2.5p+4L, 0x1.9ec8d1c94e85af4c78b15c3d8ap-144L }, + { -0x2.5p+4L, -0x1.9ec8d1c94e85af4c78b15c3d8ap-144L }, + { -0x2.6p+4L, 0xa.ea565ce061d57489e9b8527628p-152L }, + { -0x2.6p+4L, -0xa.ea565ce061d57489e9b8527628p-152L }, + { -0x2.7p+4L, 0x4.7a6512692eb37804111dabad3p-156L }, + { -0x2.7p+4L, -0x4.7a6512692eb37804111dabad3p-156L }, + { -0x2.8p+4L, 0x1.ca8ed42a12ae3001a07244abadp-160L }, + { -0x2.8p+4L, -0x1.ca8ed42a12ae3001a07244abadp-160L }, + { -0x2.9p+4L, 0xb.2f30e1ce812063f12e7e8d8d98p-168L }, + { -0x2.9p+4L, -0xb.2f30e1ce812063f12e7e8d8d98p-168L }, + { -0x2.ap+4L, 0x4.42bd49d4c37a0db136489772e4p-172L }, + { -0x2.ap+4L, -0x4.42bd49d4c37a0db136489772e4p-172L }, + { -0x2.bp+4L, 0x1.95db45257e5122dcbae56def37p-176L }, + { -0x2.bp+4L, -0x1.95db45257e5122dcbae56def37p-176L }, + { -0x2.cp+4L, 0x9.3958d81ff63527ecf993f3fb7p-184L }, + { -0x2.cp+4L, -0x9.3958d81ff63527ecf993f3fb7p-184L }, + { -0x2.dp+4L, 0x3.47970e4440c8f1c058bd238c99p-188L }, + { -0x2.dp+4L, -0x3.47970e4440c8f1c058bd238c99p-188L }, + { -0x2.ep+4L, 0x1.240804f65951062ca46e4f25c6p-192L }, + { -0x2.ep+4L, -0x1.240804f65951062ca46e4f25c6p-192L }, + { -0x2.fp+4L, 0x6.36a382849fae6de2d15362d8a4p-200L }, + { -0x2.fp+4L, -0x6.36a382849fae6de2d15362d8a4p-200L }, + { -0x3p+4L, 0x2.123680d6dfe4cf4b9b1bcb9d8cp-204L }, + }; + +static const long double e_hi = 0x2.b7e151628aed2a6abf7158809dp+0L; +static const long double e_lo = -0xb.0c389d18e9f0c74b25a9587b28p-112L; + +/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) in Stirling's + approximation to lgamma function. */ + +static const long double lgamma_coeff[] = + { + 0x1.555555555555555555555555558p-4L, + -0xb.60b60b60b60b60b60b60b60b6p-12L, + 0x3.4034034034034034034034034p-12L, + -0x2.7027027027027027027027027p-12L, + 0x3.72a3c5631fe46ae1d4e700dca9p-12L, + -0x7.daac36664f1f207daac36664f2p-12L, + 0x1.a41a41a41a41a41a41a41a41a4p-8L, + -0x7.90a1b2c3d4e5f708192a3b4c5ep-8L, + 0x2.dfd2c703c0cfff430edfd2c704p-4L, + -0x1.6476701181f39edbdb9ce625988p+0L, + 0xd.672219167002d3a7a9c886459cp+0L, + -0x9.cd9292e6660d55b3f712eb9e08p+4L, + 0x8.911a740da740da740da740da74p+8L, + -0x8.d0cc570e255bf59ff6eec24b48p+12L, + 0xa.8d1044d3708d1c219ee4fdc448p+16L, + -0xe.8844d8a169abbc406169abbc4p+20L, + 0x1.6d29a0f6433b79890cede624338p+28L, + -0x2.88a233b3c8cddaba9809357126p+32L, + 0x5.0dde6f27500939a85c40939a86p+36L, + -0xb.4005bde03d4642a243581714bp+40L, + 0x1.bc8cd6f8f1f755c78753cdb5d6p+48L, + -0x4.bbebb143bb94de5a0284fa7ec4p+52L, + 0xe.2e1337f5af0bed90b6b0a352d4p+56L, + -0x2.e78250162b62405ad3e4bfe61bp+64L, + 0xa.5f7eef9e71ac7c80326ab4cc8cp+68L, + -0x2.83be0395e550213369924971b2p+76L, + }; + +#define NCOEFF (sizeof (lgamma_coeff) / sizeof (lgamma_coeff[0])) + +/* Polynomial approximations to (|gamma(x)|-1)(x-n)/(x-x0), where n is + the integer end-point of the half-integer interval containing x and + x0 is the zero of lgamma in that half-integer interval. Each + polynomial is expressed in terms of x-xm, where xm is the midpoint + of the interval for which the polynomial applies. */ + +static const long double poly_coeff[] = + { + /* Interval [-2.125, -2] (polynomial degree 21). */ + -0x1.0b71c5c54d42eb6c17f30b7aa9p+0L, + -0xc.73a1dc05f34951602554c6d76cp-4L, + -0x1.ec841408528b51473e6c42f1c58p-4L, + -0xe.37c9da26fc3c9a3c1844c04b84p-4L, + -0x1.03cd87c519305703b00b046ce4p-4L, + -0xe.ae9ada65e09aa7f1c817c91048p-4L, + 0x9.b11855a4864b571b6a4f571c88p-8L, + -0xe.f28c133e697a95ba2dabb97584p-4L, + 0x2.6ec14a1c586a7ddb6c4be90fe1p-4L, + -0xf.57cab973e14496f0900851c0d4p-4L, + 0x4.5b0fc25f16b0df37175495c70cp-4L, + -0xf.f50e59f1a8fb8c402091e3cd3cp-4L, + 0x6.5f5eae1681d1e50e575c3d4d36p-4L, + -0x1.0d2422dac7ea8a52db6bf0d14fp+0L, + 0x8.820008f221eae5a36e15913bacp-4L, + -0x1.1f492eec53b9481ea23a7e944ep+0L, + 0xa.cb55b4d662945e8cf1f81ee5b4p-4L, + -0x1.3616863983e131d7935700ccd48p+0L, + 0xd.43c783ebab66074d18709d5cap-4L, + -0x1.51d5dbc56bc85976871c6e51f78p+0L, + 0x1.06253af656eb6b2ed998387aabp+0L, + -0x1.7d910a0aadc63d7a1ef7690dbb8p+0L, + /* Interval [-2.25, -2.125] (polynomial degree 22). */ + -0xf.2930890d7d675a80c36afb0fd4p-4L, + -0xc.a5cfde054eab5c6770daeca684p-4L, + 0x3.9c9e0fdebb07cdf89c61d434adp-4L, + -0x1.02a5ad35605fcf4af65a67fe8a8p+0L, + 0x9.6e9b1185bb48be9de18d8bbeb8p-4L, + -0x1.4d8332f3cfbfa116fdf648372cp+0L, + 0x1.1c0c8cb4d9f4b1d495142b53ebp+0L, + -0x1.c9a6f5ae9130ccfb9b7e39136f8p+0L, + 0x1.d7e9307fd58a2e85209d0e83eap+0L, + -0x2.921cb3473d96462f22c171712fp+0L, + 0x2.e8d59113b6f3fc1ed3b556b62cp+0L, + -0x3.cbab931624e3b6cf299cea1213p+0L, + 0x4.7d9f0f05d2c4cf91e41ea1f048p+0L, + -0x5.ade9cba31affa276fe516135eep+0L, + 0x6.dc983a62cf6ddc935ae3c5b9ap+0L, + -0x8.8d9ed100b2a7813f82cbd83e3cp+0L, + 0xa.6fa0926892835a9a29c9b8db8p+0L, + -0xc.ebc90aff4ffe319d70bef0d61p+0L, + 0xf.d69cf50ab226bacece014c0b44p+0L, + -0x1.389964ac7cfef4578eec028e5c8p+4L, + 0x1.7ff0d2090164e25901f97cab3bp+4L, + -0x1.e9e6d282da6bd004619d073071p+4L, + 0x2.5d719ab6ad4be8b5c32b0fba2ap+4L, + /* Interval [-2.375, -2.25] (polynomial degree 24). */ + -0xd.7d28d505d6181218a25f31d5e4p-4L, + -0xe.69649a3040985140cdf946827cp-4L, + 0xb.0d74a2827d053a8d4459500f88p-4L, + -0x1.924b0922853617cac181b097e48p+0L, + 0x1.d49b12bccf0a568582e2dbf8ep+0L, + -0x3.0898bb7d8c4093e6360d26bbc5p+0L, + 0x4.207a6cac711cb538684f74619ep+0L, + -0x6.39ee63ea4fb1dcac86ab337e3cp+0L, + 0x8.e2e2556a797b64a1b9328a3978p+0L, + -0xd.0e83ac82552ee5596df1706ff4p+0L, + 0x1.2e4525e0ce666e48fac68ddcdep+4L, + -0x1.b8e350d6a8f6597ed2eb3c2eff8p+4L, + 0x2.805cd69b9197ee0089dd1b1c46p+4L, + -0x3.a42585423e4d00db075f2d687ep+4L, + 0x5.4b4f409f874e2a7dcd8aa4a62ap+4L, + -0x7.b3c5829962ca1b95535db9cc4ep+4L, + 0xb.33b7b928986ec6b219e2e15a98p+4L, + -0x1.04b76dec4115106bb16316d9cd8p+8L, + 0x1.7b366d8d46f179d5c5302d6534p+8L, + -0x2.2799846ddc54813d40da622b99p+8L, + 0x3.2253a862c1078a3ccabac65bebp+8L, + -0x4.8d92cebc90a4a29816f4952f4ep+8L, + 0x6.9ebb8f9d72c66c80c4f4492e7ap+8L, + -0xa.2850a483f9ba0e43f5848b5cd8p+8L, + 0xe.e1b6bdce83b27944edab8c428p+8L, + /* Interval [-2.5, -2.375] (polynomial degree 25). */ + -0xb.74ea1bcfff94b2c01afba9daa8p-4L, + -0x1.2a82bd590c37538cab143308e3p+0L, + 0x1.88020f828b966fec66b8648d16p+0L, + -0x3.32279f040eb694970e9db0308bp+0L, + 0x5.57ac82517767e68a72142041b4p+0L, + -0x9.c2aedcfe22833de438786dc658p+0L, + 0x1.12c132f1f5577f99dbfb7ecb408p+4L, + -0x1.ea94e26628a3de3557dc349db8p+4L, + 0x3.66b4ac4fa582f5cbe7e19d10c6p+4L, + -0x6.0cf746a9cf4cbcb0004cb01f66p+4L, + 0xa.c102ef2c20d5a313cbfd37f5b8p+4L, + -0x1.31ebff06e8f08f58d1c35eacfdp+8L, + 0x2.1fd6f0c0e788660ba1f1573722p+8L, + -0x3.c6d760404305e75356a86a11d6p+8L, + 0x6.b6d18e0c31a2ba4d5b5ac78676p+8L, + -0xb.efaf5426343e6b41a823ed6c44p+8L, + 0x1.53852db2fe01305b9f336d132d8p+12L, + -0x2.5b977cb2b568382e71ca93a36bp+12L, + 0x4.310d090a6119c7d85a2786a616p+12L, + -0x7.73a518387ef1d4d04917dfb25cp+12L, + 0xd.3f965798601aabd24bdaa6e68cp+12L, + -0x1.78db20b0b166480c93cf0031198p+16L, + 0x2.9be0068b65cf13bd1cf71f0eccp+16L, + -0x4.a221230466b9cd51d5b811d6b6p+16L, + 0x8.f6f8c13e2b52aa3e30a4ce6898p+16L, + -0x1.02145337ff16b44fa7c2adf7f28p+20L, + /* Interval [-2.625, -2.5] (polynomial degree 26). */ + -0x3.d10108c27ebafad533c20eac33p-4L, + 0x1.cd557caff7d2b2085f41dbec538p+0L, + 0x3.819b4856d399520dad9776ebb9p+0L, + 0x6.8505cbad03dc34c5e42e89c4b4p+0L, + 0xb.c1b2e653a9e38f82b3997134a8p+0L, + 0x1.50a53a38f1481381051544750ep+4L, + 0x2.57ae00cbe5232cbeef4e94eb2cp+4L, + 0x4.2b156301b8604db82856d5767p+4L, + 0x7.6989ed23ca3ca751fc9c32eb88p+4L, + 0xd.2dd29765579396f3a456772c44p+4L, + 0x1.76e1c3430eb8630991d1aa8a248p+8L, + 0x2.9a77bf548873743fe65d025f56p+8L, + 0x4.a0d62ed7266389753842d7be74p+8L, + 0x8.3a6184dd32d31ec73fc6f2d37cp+8L, + 0xe.a0ade153a3bf0247db49e11ae8p+8L, + 0x1.a01359fa74d4eaf8858bbc35f68p+12L, + 0x2.e3b0a32845cbc135bae4a5216cp+12L, + 0x5.23012653815fe88456170a7dc6p+12L, + 0x9.21c92dcde748ec199bc9c65738p+12L, + 0x1.03c0f3621b4c67d2d86e5e813d8p+16L, + 0x1.cdc884edcc9f5404f2708551cb8p+16L, + 0x3.35025f0b1624d1ffc86688bf03p+16L, + 0x5.b3bd9562ebf2409c5ce99929ep+16L, + 0xa.1a229b1986d9f89cb80abccfdp+16L, + 0x1.1e69136ebd520146d51837f3308p+20L, + 0x2.2d2738c72449db2524171b9271p+20L, + 0x4.036e80cc6621b836f94f426834p+20L, + /* Interval [-2.75, -2.625] (polynomial degree 24). */ + -0x6.b5d252a56e8a75458a27ed1c2ep-4L, + 0x1.28d60383da3ac721aed3c57949p+0L, + 0x1.db6513ada8a66ea77d87d9a796p+0L, + 0x2.e217118f9d348a27f7506c4b4fp+0L, + 0x4.450112c5cbf725a0fb982fc44cp+0L, + 0x6.4af99151eae7810a75a5fceac8p+0L, + 0x9.2db598b4a97a7f69ab7be31128p+0L, + 0xd.62bef9c22471f5f17955733c6p+0L, + 0x1.379f294e412bd6255506135f4a8p+4L, + 0x1.c5827349d8865d858d4f85f3c38p+4L, + 0x2.93a7e7a75b755bbea1785a1349p+4L, + 0x3.bf9bb882afed66a08b22ed7a45p+4L, + 0x5.73c737828d2044aca95fdef33ep+4L, + 0x7.ee46534920f1c81574db260f0ep+4L, + 0xb.891c6b837b513eaf1592fe78ccp+4L, + 0x1.0c775d815bf741526a3dd66ded8p+8L, + 0x1.867ee44cf11f26455a8924a56bp+8L, + 0x2.37fe968baa1018e55cae680f1dp+8L, + 0x3.3a2c557f686679eb5d8e960fd1p+8L, + 0x4.b1ba0539d4d80cc9174738b992p+8L, + 0x6.d3fd80155b6d2211956cb6bc5ap+8L, + 0x9.eb5a96b0ee3d9ca523f5fbc1fp+8L, + 0xe.6b37429c1acc7dc19ef312dda4p+8L, + 0x1.621132d6aa138b203a28e4792fp+12L, + 0x2.09610219270e2ce11a985d4d36p+12L, + /* Interval [-2.875, -2.75] (polynomial degree 23). */ + -0x8.a41b1e4f36ff88dc820815607cp-4L, + 0xc.da87d3b69dc0f2f9c6f368b8c8p-4L, + 0x1.1474ad5c36158a7bea04fd30b28p+0L, + 0x1.761ecb90c555df6555b7dbb9ce8p+0L, + 0x1.d279bff9ae291caf6c4b17497f8p+0L, + 0x2.4e5d00559a6e2b9b5d7e35b575p+0L, + 0x2.d57545a75cee8743b1ff6e22b8p+0L, + 0x3.8514eee3aac88b89d2d4ddef4ep+0L, + 0x4.5235e3b6e1891fd9c975383318p+0L, + 0x5.562acdb10eef3c14a780490e3cp+0L, + 0x6.8ec8965c76f0b261bc41b5e532p+0L, + 0x8.15251aca144a98a1e1c0981388p+0L, + 0x9.f08d56ab9e7eee9515a457214cp+0L, + 0xc.3dbbeda2620d5be4fe8621ce6p+0L, + 0xf.0f5bfd65b3feb6d745a2cdbf9cp+0L, + 0x1.28a6ccd8dd27fb90fcaa31d37dp+4L, + 0x1.6d0a3a3091c3d64cfd1a3c5769p+4L, + 0x1.c1570107e02d5ab0b8bea6d6c98p+4L, + 0x2.28fc9b295b583fa469de7acceap+4L, + 0x2.a8a4cac0217026bbdbce34f4adp+4L, + 0x3.4532c98bce75262ac0ede53edep+4L, + 0x4.062fd9ba18e00e55c25a4f0688p+4L, + 0x5.22e00e6d9846a3451fad5587f8p+4L, + 0x6.5d0f7ce92a0bf928d4a30e92c6p+4L, + /* Interval [-3, -2.875] (polynomial degree 22). */ + -0xa.046d667e468f3e44dcae1afcc8p-4L, + 0x9.70b88dcc006c214d8d996fdf7p-4L, + 0xa.a8a39421c86d3ff24931a093c4p-4L, + 0xd.2f4d1363f324da2b357c850124p-4L, + 0xd.ca9aa1a3a5c00de11bf5d7047p-4L, + 0xf.cf09c31eeb52a45dfb25e50ebcp-4L, + 0x1.04b133a39ed8a096914cc78812p+0L, + 0x1.22b547a06edda9447f516a2ee7p+0L, + 0x1.2c57fce7db86a91c8d0f12077b8p+0L, + 0x1.4aade4894708fb8b78365e9bf88p+0L, + 0x1.579c8b7b67ec5179ecc4e9c7dp+0L, + 0x1.776820e7fc7361c50e7ef40a88p+0L, + 0x1.883ab28c72ef238ada6c480ab18p+0L, + 0x1.aa2ef6e1d11b9fcea06a1dcab1p+0L, + 0x1.bf4ad50f2dd2aeb02395ea08648p+0L, + 0x1.e40206a5477615838e02279dfc8p+0L, + 0x1.fdcbcfd4b0777fb173b85d5b398p+0L, + 0x2.25e32b3b3c89e833029169a17bp+0L, + 0x2.44ce344ff0bda6570fe3d0a76dp+0L, + 0x2.70bfba6fa079faf2dbf31d2216p+0L, + 0x2.953e22a97725cc179ad21024fap+0L, + 0x2.d8ccc51524659a499eee0f267p+0L, + 0x3.080fbb09c14936c2171c8a51bcp+0L, + }; + +static const size_t poly_deg[] = + { + 21, + 22, + 24, + 25, + 26, + 24, + 23, + 22, + }; + +static const size_t poly_end[] = + { + 21, + 44, + 69, + 95, + 122, + 147, + 171, + 194, + }; + +/* Compute sin (pi * X) for -0.25 <= X <= 0.5. */ + +static long double +lg_sinpi (long double x) +{ + if (x <= 0.25L) + return __sinl (M_PIl * x); + else + return __cosl (M_PIl * (0.5L - x)); +} + +/* Compute cos (pi * X) for -0.25 <= X <= 0.5. */ + +static long double +lg_cospi (long double x) +{ + if (x <= 0.25L) + return __cosl (M_PIl * x); + else + return __sinl (M_PIl * (0.5L - x)); +} + +/* Compute cot (pi * X) for -0.25 <= X <= 0.5. */ + +static long double +lg_cotpi (long double x) +{ + return lg_cospi (x) / lg_sinpi (x); +} + +/* Compute lgamma of a negative argument -48 < X < -2, setting + *SIGNGAMP accordingly. */ + +long double +__lgamma_negl (long double x, int *signgamp) +{ + /* Determine the half-integer region X lies in, handle exact + integers and determine the sign of the result. */ + int i = __floorl (-2 * x); + if ((i & 1) == 0 && i == -2 * x) + return 1.0L / 0.0L; + long double xn = ((i & 1) == 0 ? -i / 2 : (-i - 1) / 2); + i -= 4; + *signgamp = ((i & 2) == 0 ? -1 : 1); + + SET_RESTORE_ROUNDL (FE_TONEAREST); + + /* Expand around the zero X0 = X0_HI + X0_LO. */ + long double x0_hi = lgamma_zeros[i][0], x0_lo = lgamma_zeros[i][1]; + long double xdiff = x - x0_hi - x0_lo; + + /* For arguments in the range -3 to -2, use polynomial + approximations to an adjusted version of the gamma function. */ + if (i < 2) + { + int j = __floorl (-8 * x) - 16; + long double xm = (-33 - 2 * j) * 0.0625L; + long double x_adj = x - xm; + size_t deg = poly_deg[j]; + size_t end = poly_end[j]; + long double g = poly_coeff[end]; + for (size_t j = 1; j <= deg; j++) + g = g * x_adj + poly_coeff[end - j]; + return __log1pl (g * xdiff / (x - xn)); + } + + /* The result we want is log (sinpi (X0) / sinpi (X)) + + log (gamma (1 - X0) / gamma (1 - X)). */ + long double x_idiff = fabsl (xn - x), x0_idiff = fabsl (xn - x0_hi - x0_lo); + long double log_sinpi_ratio; + if (x0_idiff < x_idiff * 0.5L) + /* Use log not log1p to avoid inaccuracy from log1p of arguments + close to -1. */ + log_sinpi_ratio = __ieee754_logl (lg_sinpi (x0_idiff) + / lg_sinpi (x_idiff)); + else + { + /* Use log1p not log to avoid inaccuracy from log of arguments + close to 1. X0DIFF2 has positive sign if X0 is further from + XN than X is from XN, negative sign otherwise. */ + long double x0diff2 = ((i & 1) == 0 ? xdiff : -xdiff) * 0.5L; + long double sx0d2 = lg_sinpi (x0diff2); + long double cx0d2 = lg_cospi (x0diff2); + log_sinpi_ratio = __log1pl (2 * sx0d2 + * (-sx0d2 + cx0d2 * lg_cotpi (x_idiff))); + } + + long double log_gamma_ratio; + long double y0 = 1 - x0_hi; + long double y0_eps = -x0_hi + (1 - y0) - x0_lo; + long double y = 1 - x; + long double y_eps = -x + (1 - y); + /* We now wish to compute LOG_GAMMA_RATIO + = log (gamma (Y0 + Y0_EPS) / gamma (Y + Y_EPS)). XDIFF + accurately approximates the difference Y0 + Y0_EPS - Y - + Y_EPS. Use Stirling's approximation. First, we may need to + adjust into the range where Stirling's approximation is + sufficiently accurate. */ + long double log_gamma_adj = 0; + if (i < 18) + { + int n_up = (19 - i) / 2; + long double ny0, ny0_eps, ny, ny_eps; + ny0 = y0 + n_up; + ny0_eps = y0 - (ny0 - n_up) + y0_eps; + y0 = ny0; + y0_eps = ny0_eps; + ny = y + n_up; + ny_eps = y - (ny - n_up) + y_eps; + y = ny; + y_eps = ny_eps; + long double prodm1 = __lgamma_productl (xdiff, y - n_up, y_eps, n_up); + log_gamma_adj = -__log1pl (prodm1); + } + long double log_gamma_high + = (xdiff * __log1pl ((y0 - e_hi - e_lo + y0_eps) / e_hi) + + (y - 0.5L + y_eps) * __log1pl (xdiff / y) + log_gamma_adj); + /* Compute the sum of (B_2k / 2k(2k-1))(Y0^-(2k-1) - Y^-(2k-1)). */ + long double y0r = 1 / y0, yr = 1 / y; + long double y0r2 = y0r * y0r, yr2 = yr * yr; + long double rdiff = -xdiff / (y * y0); + long double bterm[NCOEFF]; + long double dlast = rdiff, elast = rdiff * yr * (yr + y0r); + bterm[0] = dlast * lgamma_coeff[0]; + for (size_t j = 1; j < NCOEFF; j++) + { + long double dnext = dlast * y0r2 + elast; + long double enext = elast * yr2; + bterm[j] = dnext * lgamma_coeff[j]; + dlast = dnext; + elast = enext; + } + long double log_gamma_low = 0; + for (size_t j = 0; j < NCOEFF; j++) + log_gamma_low += bterm[NCOEFF - 1 - j]; + log_gamma_ratio = log_gamma_high + log_gamma_low; + + return log_sinpi_ratio + log_gamma_ratio; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/lgamma_productl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/lgamma_productl.c new file mode 100644 index 0000000000..92c1cffd67 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/lgamma_productl.c @@ -0,0 +1,38 @@ +/* Compute a product of 1 + (T/X), 1 + (T/(X+1)), .... + Copyright (C) 2015-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +/* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS + + 1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1. X is such that + all the values X + 1, ..., X + N - 1 are exactly representable, and + X_EPS / X is small enough that factors quadratic in it can be + neglected. */ + +long double +__lgamma_productl (long double t, long double x, long double x_eps, int n) +{ + long double x_full = x + x_eps; + long double ret = 0; + for (int i = 0; i < n; i++) + /* FIXME: no extra precision used. */ + ret += (t / (x_full + i)) * (1 + ret); + return ret; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/math_ldbl.h b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/math_ldbl.h new file mode 100644 index 0000000000..8f2984e924 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/math_ldbl.h @@ -0,0 +1,290 @@ +/* Manipulation of the bit representation of 'long double' quantities. + Copyright (C) 2006-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#ifndef _MATH_LDBL_H_ +#define _MATH_LDBL_H_ 1 + +#include <ieee754.h> +#include <stdint.h> + +/* To suit our callers we return *hi64 and *lo64 as if they came from + an ieee854 112 bit mantissa, that is, 48 bits in *hi64 (plus one + implicit bit) and 64 bits in *lo64. */ + +static inline void +ldbl_extract_mantissa (int64_t *hi64, uint64_t *lo64, int *exp, long double x) +{ + /* We have 105 bits of mantissa plus one implicit digit. Since + 106 bits are representable we use the first implicit digit for + the number before the decimal point and the second implicit bit + as bit 53 of the mantissa. */ + uint64_t hi, lo; + union ibm_extended_long_double u; + + u.ld = x; + *exp = u.d[0].ieee.exponent - IEEE754_DOUBLE_BIAS; + + lo = ((uint64_t) u.d[1].ieee.mantissa0 << 32) | u.d[1].ieee.mantissa1; + hi = ((uint64_t) u.d[0].ieee.mantissa0 << 32) | u.d[0].ieee.mantissa1; + + if (u.d[0].ieee.exponent != 0) + { + int ediff; + + /* If not a denormal or zero then we have an implicit 53rd bit. */ + hi |= (uint64_t) 1 << 52; + + if (u.d[1].ieee.exponent != 0) + lo |= (uint64_t) 1 << 52; + else + /* A denormal is to be interpreted as having a biased exponent + of 1. */ + lo = lo << 1; + + /* We are going to shift 4 bits out of hi later, because we only + want 48 bits in *hi64. That means we want 60 bits in lo, but + we currently only have 53. Shift the value up. */ + lo = lo << 7; + + /* The lower double is normalized separately from the upper. + We may need to adjust the lower mantissa to reflect this. + The difference between the exponents can be larger than 53 + when the low double is much less than 1ULP of the upper + (in which case there are significant bits, all 0's or all + 1's, between the two significands). The difference between + the exponents can be less than 53 when the upper double + exponent is nearing its minimum value (in which case the low + double is denormal ie. has an exponent of zero). */ + ediff = u.d[0].ieee.exponent - u.d[1].ieee.exponent - 53; + if (ediff > 0) + { + if (ediff < 64) + lo = lo >> ediff; + else + lo = 0; + } + else if (ediff < 0) + lo = lo << -ediff; + + if (u.d[0].ieee.negative != u.d[1].ieee.negative + && lo != 0) + { + hi--; + lo = ((uint64_t) 1 << 60) - lo; + if (hi < (uint64_t) 1 << 52) + { + /* We have a borrow from the hidden bit, so shift left 1. */ + hi = (hi << 1) | (lo >> 59); + lo = (((uint64_t) 1 << 60) - 1) & (lo << 1); + *exp = *exp - 1; + } + } + } + else + /* If the larger magnitude double is denormal then the smaller + one must be zero. */ + hi = hi << 1; + + *lo64 = (hi << 60) | lo; + *hi64 = hi >> 4; +} + +static inline long double +ldbl_insert_mantissa (int sign, int exp, int64_t hi64, uint64_t lo64) +{ + union ibm_extended_long_double u; + int expnt2; + uint64_t hi, lo; + + u.d[0].ieee.negative = sign; + u.d[1].ieee.negative = sign; + u.d[0].ieee.exponent = exp + IEEE754_DOUBLE_BIAS; + u.d[1].ieee.exponent = 0; + expnt2 = exp - 53 + IEEE754_DOUBLE_BIAS; + + /* Expect 113 bits (112 bits + hidden) right justified in two longs. + The low order 53 bits (52 + hidden) go into the lower double */ + lo = (lo64 >> 7) & (((uint64_t) 1 << 53) - 1); + /* The high order 53 bits (52 + hidden) go into the upper double */ + hi = lo64 >> 60; + hi |= hi64 << 4; + + if (lo != 0) + { + int lzcount; + + /* hidden bit of low double controls rounding of the high double. + If hidden is '1' and either the explicit mantissa is non-zero + or hi is odd, then round up hi and adjust lo (2nd mantissa) + plus change the sign of the low double to compensate. */ + if ((lo & ((uint64_t) 1 << 52)) != 0 + && ((hi & 1) != 0 || (lo & (((uint64_t) 1 << 52) - 1)) != 0)) + { + hi++; + if ((hi & ((uint64_t) 1 << 53)) != 0) + { + hi = hi >> 1; + u.d[0].ieee.exponent++; + } + u.d[1].ieee.negative = !sign; + lo = ((uint64_t) 1 << 53) - lo; + } + + /* Normalize the low double. Shift the mantissa left until + the hidden bit is '1' and adjust the exponent accordingly. */ + + if (sizeof (lo) == sizeof (long)) + lzcount = __builtin_clzl (lo); + else if ((lo >> 32) != 0) + lzcount = __builtin_clzl ((long) (lo >> 32)); + else + lzcount = __builtin_clzl ((long) lo) + 32; + lzcount = lzcount - (64 - 53); + lo <<= lzcount; + expnt2 -= lzcount; + + if (expnt2 >= 1) + /* Not denormal. */ + u.d[1].ieee.exponent = expnt2; + else + { + /* Is denormal. Note that biased exponent of 0 is treated + as if it was 1, hence the extra shift. */ + if (expnt2 > -53) + lo >>= 1 - expnt2; + else + lo = 0; + } + } + else + u.d[1].ieee.negative = 0; + + u.d[1].ieee.mantissa1 = lo; + u.d[1].ieee.mantissa0 = lo >> 32; + u.d[0].ieee.mantissa1 = hi; + u.d[0].ieee.mantissa0 = hi >> 32; + return u.ld; +} + +/* Handy utility functions to pack/unpack/cononicalize and find the nearbyint + of long double implemented as double double. */ +static inline long double +default_ldbl_pack (double a, double aa) +{ + union ibm_extended_long_double u; + u.d[0].d = a; + u.d[1].d = aa; + return u.ld; +} + +static inline void +default_ldbl_unpack (long double l, double *a, double *aa) +{ + union ibm_extended_long_double u; + u.ld = l; + *a = u.d[0].d; + *aa = u.d[1].d; +} + +#ifndef ldbl_pack +# define ldbl_pack default_ldbl_pack +#endif +#ifndef ldbl_unpack +# define ldbl_unpack default_ldbl_unpack +#endif + +/* Extract high double. */ +#define ldbl_high(x) ((double) x) + +/* Convert a finite long double to canonical form. + Does not handle +/-Inf properly. */ +static inline void +ldbl_canonicalize (double *a, double *aa) +{ + double xh, xl; + + xh = *a + *aa; + xl = (*a - xh) + *aa; + *a = xh; + *aa = xl; +} + +/* Simple inline nearbyint (double) function. + Only works in the default rounding mode + but is useful in long double rounding functions. */ +static inline double +ldbl_nearbyint (double a) +{ + double two52 = 0x1p52; + + if (__glibc_likely ((__builtin_fabs (a) < two52))) + { + if (__glibc_likely ((a > 0.0))) + { + a += two52; + a -= two52; + } + else if (__glibc_likely ((a < 0.0))) + { + a = two52 - a; + a = -(a - two52); + } + } + return a; +} + +/* Canonicalize a result from an integer rounding function, in any + rounding mode. *A and *AA are finite and integers, with *A being + nonzero; if the result is not already canonical, *AA is plus or + minus a power of 2 that does not exceed the least set bit in + *A. */ +static inline void +ldbl_canonicalize_int (double *a, double *aa) +{ + /* Previously we used EXTRACT_WORDS64 from math_private.h, but in order + to avoid including internal headers we duplicate that code here. */ + uint64_t ax, aax; + union { double value; uint64_t word; } extractor; + extractor.value = *a; + ax = extractor.word; + extractor.value = *aa; + aax = extractor.word; + + int expdiff = ((ax >> 52) & 0x7ff) - ((aax >> 52) & 0x7ff); + if (expdiff <= 53) + { + if (expdiff == 53) + { + /* Half way between two double values; noncanonical iff the + low bit of A's mantissa is 1. */ + if ((ax & 1) != 0) + { + *a += 2 * *aa; + *aa = -*aa; + } + } + else + { + /* The sum can be represented in a single double. */ + *a += *aa; + *aa = 0; + } + } +} + +#endif /* math_ldbl.h */ diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/mpn2ldbl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/mpn2ldbl.c new file mode 100644 index 0000000000..92b28b8b5d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/mpn2ldbl.c @@ -0,0 +1,161 @@ +/* Copyright (C) 1995-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <ieee754.h> +#include <errno.h> +#include <float.h> +#include <math.h> + +/* Need to set this when including gmp headers after system headers. */ +#define HAVE_ALLOCA 1 + +#include "gmp.h" +#include "gmp-impl.h" + +/* Convert a multi-precision integer of the needed number of bits (106 + for long double) and an integral power of two to a `long double' in + IBM extended format. */ + +long double +__mpn_construct_long_double (mp_srcptr frac_ptr, int expt, int sign) +{ + union ibm_extended_long_double u; + unsigned long lzcount; + unsigned long long hi, lo; + int exponent2; + + u.d[0].ieee.negative = sign; + u.d[1].ieee.negative = sign; + u.d[0].ieee.exponent = expt + IEEE754_DOUBLE_BIAS; + u.d[1].ieee.exponent = 0; + exponent2 = expt - 53 + IEEE754_DOUBLE_BIAS; + +#if BITS_PER_MP_LIMB == 32 + /* The low order 53 bits (52 + hidden) go into the lower double */ + lo = frac_ptr[0]; + lo |= (frac_ptr[1] & ((1LL << (53 - 32)) - 1)) << 32; + /* The high order 53 bits (52 + hidden) go into the upper double */ + hi = (frac_ptr[1] >> (53 - 32)) & ((1 << 11) - 1); + hi |= ((unsigned long long) frac_ptr[2]) << 11; + hi |= ((unsigned long long) frac_ptr[3]) << (32 + 11); +#elif BITS_PER_MP_LIMB == 64 + /* The low order 53 bits (52 + hidden) go into the lower double */ + lo = frac_ptr[0] & (((mp_limb_t) 1 << 53) - 1); + /* The high order 53 bits (52 + hidden) go into the upper double */ + hi = (frac_ptr[0] >> 53) & (((mp_limb_t) 1 << 11) - 1); + hi |= (frac_ptr[1] << 11); +#else + #error "mp_limb size " BITS_PER_MP_LIMB "not accounted for" +#endif + + if ((hi & (1LL << 52)) == 0 && (hi | lo) != 0) + { + /* denormal number */ + unsigned long long val = hi ? hi : lo; + + if (sizeof (val) == sizeof (long)) + lzcount = __builtin_clzl (val); + else if ((val >> 32) != 0) + lzcount = __builtin_clzl ((long) (val >> 32)); + else + lzcount = __builtin_clzl ((long) val) + 32; + if (hi) + lzcount = lzcount - (64 - 53); + else + lzcount = lzcount + 53 - (64 - 53); + + if (lzcount > u.d[0].ieee.exponent) + { + lzcount = u.d[0].ieee.exponent; + u.d[0].ieee.exponent = 0; + exponent2 -= lzcount; + } + else + { + u.d[0].ieee.exponent -= (lzcount - 1); + exponent2 -= (lzcount - 1); + } + + if (lzcount <= 53) + { + hi = (hi << lzcount) | (lo >> (53 - lzcount)); + lo = (lo << lzcount) & ((1LL << 53) - 1); + } + else + { + hi = lo << (lzcount - 53); + lo = 0; + } + } + + if (lo != 0) + { + /* hidden bit of low double controls rounding of the high double. + If hidden is '1' and either the explicit mantissa is non-zero + or hi is odd, then round up hi and adjust lo (2nd mantissa) + plus change the sign of the low double to compensate. */ + if ((lo & (1LL << 52)) != 0 + && ((hi & 1) != 0 || (lo & ((1LL << 52) - 1)) != 0)) + { + hi++; + if ((hi & (1LL << 53)) != 0) + { + hi >>= 1; + u.d[0].ieee.exponent++; + if (u.d[0].ieee.exponent == IEEE754_DOUBLE_BIAS + DBL_MAX_EXP) + { + /* Overflow. The appropriate overflowed result must + be produced (if an infinity, that means the low + part must be zero). */ + __set_errno (ERANGE); + return (sign ? -LDBL_MAX : LDBL_MAX) * LDBL_MAX; + } + } + u.d[1].ieee.negative = !sign; + lo = (1LL << 53) - lo; + } + + /* Normalize the low double. Shift the mantissa left until + the hidden bit is '1' and adjust the exponent accordingly. */ + + if (sizeof (lo) == sizeof (long)) + lzcount = __builtin_clzl (lo); + else if ((lo >> 32) != 0) + lzcount = __builtin_clzl ((long) (lo >> 32)); + else + lzcount = __builtin_clzl ((long) lo) + 32; + lzcount = lzcount - (64 - 53); + lo <<= lzcount; + exponent2 -= lzcount; + + if (exponent2 > 0) + u.d[1].ieee.exponent = exponent2; + else if (exponent2 > -53) + lo >>= 1 - exponent2; + else + lo = 0; + } + else + u.d[1].ieee.negative = 0; + + u.d[1].ieee.mantissa1 = lo; + u.d[1].ieee.mantissa0 = lo >> 32; + u.d[0].ieee.mantissa1 = hi; + u.d[0].ieee.mantissa0 = hi >> 32; + + return u.ld; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/printf_fphex.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/printf_fphex.c new file mode 100644 index 0000000000..2f87ec17cc --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/printf_fphex.c @@ -0,0 +1,139 @@ +/* Print floating point number in hexadecimal notation according to ISO C99. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define PRINT_FPHEX_LONG_DOUBLE \ +do { \ + /* We have 105 bits of mantissa plus one implicit digit. Since \ + 106 bits are representable without rest using hexadecimal \ + digits we use only the implicit digits for the number before \ + the decimal point. */ \ + unsigned long long int num0, num1; \ + unsigned long long hi, lo; \ + int ediff; \ + union ibm_extended_long_double u; \ + u.ld = fpnum.ldbl; \ + \ + assert (sizeof (long double) == 16); \ + \ + lo = ((long long)u.d[1].ieee.mantissa0 << 32) | u.d[1].ieee.mantissa1; \ + hi = ((long long)u.d[0].ieee.mantissa0 << 32) | u.d[0].ieee.mantissa1; \ + lo <<= 7; /* pre-shift lo to match ieee854. */ \ + /* If the lower double is not a denormal or zero then set the hidden \ + 53rd bit. */ \ + if (u.d[1].ieee.exponent != 0) \ + lo |= (1ULL << (52 + 7)); \ + else \ + lo <<= 1; \ + /* The lower double is normalized separately from the upper. We \ + may need to adjust the lower manitissa to reflect this. */ \ + ediff = u.d[0].ieee.exponent - u.d[1].ieee.exponent - 53; \ + if (ediff > 63) \ + lo = 0; \ + else if (ediff > 0) \ + lo = lo >> ediff; \ + else if (ediff < 0) \ + lo = lo << -ediff; \ + if (u.d[0].ieee.negative != u.d[1].ieee.negative \ + && lo != 0) \ + { \ + lo = (1ULL << 60) - lo; \ + if (hi == 0L) \ + { \ + /* we have a borrow from the hidden bit, so shift left 1. */ \ + hi = 0xffffffffffffeLL | (lo >> 59); \ + lo = 0xfffffffffffffffLL & (lo << 1); \ + u.d[0].ieee.exponent--; \ + } \ + else \ + hi--; \ + } \ + num1 = (hi << 60) | lo; \ + num0 = hi >> 4; \ + \ + zero_mantissa = (num0|num1) == 0; \ + \ + if (sizeof (unsigned long int) > 6) \ + { \ + numstr = _itoa_word (num1, numbuf + sizeof numbuf, 16, \ + info->spec == 'A'); \ + wnumstr = _itowa_word (num1, \ + wnumbuf + sizeof (wnumbuf) / sizeof (wchar_t),\ + 16, info->spec == 'A'); \ + } \ + else \ + { \ + numstr = _itoa (num1, numbuf + sizeof numbuf, 16, \ + info->spec == 'A'); \ + wnumstr = _itowa (num1, \ + wnumbuf + sizeof (wnumbuf) / sizeof (wchar_t), \ + 16, info->spec == 'A'); \ + } \ + \ + while (numstr > numbuf + (sizeof numbuf - 64 / 4)) \ + { \ + *--numstr = '0'; \ + *--wnumstr = L'0'; \ + } \ + \ + if (sizeof (unsigned long int) > 6) \ + { \ + numstr = _itoa_word (num0, numstr, 16, info->spec == 'A'); \ + wnumstr = _itowa_word (num0, wnumstr, 16, info->spec == 'A'); \ + } \ + else \ + { \ + numstr = _itoa (num0, numstr, 16, info->spec == 'A'); \ + wnumstr = _itowa (num0, wnumstr, 16, info->spec == 'A'); \ + } \ + \ + /* Fill with zeroes. */ \ + while (numstr > numbuf + (sizeof numbuf - 112 / 4)) \ + { \ + *--numstr = '0'; \ + *--wnumstr = L'0'; \ + } \ + \ + leading = u.d[0].ieee.exponent == 0 ? '0' : '1'; \ + \ + exponent = u.d[0].ieee.exponent; \ + \ + if (exponent == 0) \ + { \ + if (zero_mantissa) \ + expnegative = 0; \ + else \ + { \ + /* This is a denormalized number. */ \ + expnegative = 1; \ + exponent = IEEE754_DOUBLE_BIAS - 1; \ + } \ + } \ + else if (exponent >= IEEE754_DOUBLE_BIAS) \ + { \ + expnegative = 0; \ + exponent -= IEEE754_DOUBLE_BIAS; \ + } \ + else \ + { \ + expnegative = 1; \ + exponent = -(exponent - IEEE754_DOUBLE_BIAS); \ + } \ +} while (0) + +#include <stdio-common/printf_fphex.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_asinhl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_asinhl.c new file mode 100644 index 0000000000..aa9a9ba213 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_asinhl.c @@ -0,0 +1,63 @@ +/* @(#)s_asinh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_asinh.c,v 1.9 1995/05/12 04:57:37 jtc Exp $"; +#endif + +/* asinh(x) + * Method : + * Based on + * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] + * we have + * asinh(x) := x if 1+x*x=1, + * := sign(x)*(log(x)+ln2)) for large |x|, else + * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else + * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +static const long double +one = 1.00000000000000000000e+00L, /* 0x3ff0000000000000, 0 */ +ln2 = 0.6931471805599453094172321214581766L, /* 0x3fe62e42fefa39ef, 0x3c7abc9e3b398040 */ +huge= 1.00000000000000000000e+300L; + +long double __asinhl(long double x) +{ + long double t,w; + int64_t hx,ix; + double xhi; + + xhi = ldbl_high (x); + EXTRACT_WORDS64 (hx, xhi); + ix = hx&0x7fffffffffffffffLL; + if(ix>=0x7ff0000000000000LL) return x+x; /* x is inf or NaN */ + if(ix< 0x3c70000000000000LL) { /* |x|<2**-56 */ + math_check_force_underflow (x); + if(huge+x>one) return x; /* return x inexact except 0 */ + } + if(ix>0x4370000000000000LL) { /* |x| > 2**56 */ + w = __ieee754_logl(fabsl(x))+ln2; + } else if (ix>0x4000000000000000LL) { /* 2**56 >= |x| > 2.0 */ + t = fabs(x); + w = __ieee754_logl(2.0*t+one/(__ieee754_sqrtl(x*x+one)+t)); + } else { /* 2.0 >= |x| >= 2**-56 */ + t = x*x; + w =__log1pl(fabsl(x)+t/(one+__ieee754_sqrtl(one+t))); + } + if(hx>0) return w; else return -w; +} +long_double_symbol (libm, __asinhl, asinhl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_atanl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_atanl.c new file mode 100644 index 0000000000..0560d820ae --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_atanl.c @@ -0,0 +1,250 @@ +/* s_atanl.c + * + * Inverse circular tangent for 128-bit long double precision + * (arctangent) + * + * + * + * SYNOPSIS: + * + * long double x, y, atanl(); + * + * y = atanl( x ); + * + * + * + * DESCRIPTION: + * + * Returns radian angle between -pi/2 and +pi/2 whose tangent is x. + * + * The function uses a rational approximation of the form + * t + t^3 P(t^2)/Q(t^2), optimized for |t| < 0.09375. + * + * The argument is reduced using the identity + * arctan x - arctan u = arctan ((x-u)/(1 + ux)) + * and an 83-entry lookup table for arctan u, with u = 0, 1/8, ..., 10.25. + * Use of the table improves the execution speed of the routine. + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -19, 19 4e5 1.7e-34 5.4e-35 + * + * + * WARNING: + * + * This program uses integer operations on bit fields of floating-point + * numbers. It does not work with data structures other than the + * structure assumed. + * + */ + +/* Copyright 2001 by Stephen L. Moshier <moshier@na-net.ornl.gov> + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + + +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +/* arctan(k/8), k = 0, ..., 82 */ +static const long double atantbl[84] = { + 0.0000000000000000000000000000000000000000E0L, + 1.2435499454676143503135484916387102557317E-1L, /* arctan(0.125) */ + 2.4497866312686415417208248121127581091414E-1L, + 3.5877067027057222039592006392646049977698E-1L, + 4.6364760900080611621425623146121440202854E-1L, + 5.5859931534356243597150821640166127034645E-1L, + 6.4350110879328438680280922871732263804151E-1L, + 7.1882999962162450541701415152590465395142E-1L, + 7.8539816339744830961566084581987572104929E-1L, + 8.4415398611317100251784414827164750652594E-1L, + 8.9605538457134395617480071802993782702458E-1L, + 9.4200004037946366473793717053459358607166E-1L, + 9.8279372324732906798571061101466601449688E-1L, + 1.0191413442663497346383429170230636487744E0L, + 1.0516502125483736674598673120862998296302E0L, + 1.0808390005411683108871567292171998202703E0L, + 1.1071487177940905030170654601785370400700E0L, + 1.1309537439791604464709335155363278047493E0L, + 1.1525719972156675180401498626127513797495E0L, + 1.1722738811284763866005949441337046149712E0L, + 1.1902899496825317329277337748293183376012E0L, + 1.2068173702852525303955115800565576303133E0L, + 1.2220253232109896370417417439225704908830E0L, + 1.2360594894780819419094519711090786987027E0L, + 1.2490457723982544258299170772810901230778E0L, + 1.2610933822524404193139408812473357720101E0L, + 1.2722973952087173412961937498224804940684E0L, + 1.2827408797442707473628852511364955306249E0L, + 1.2924966677897852679030914214070816845853E0L, + 1.3016288340091961438047858503666855921414E0L, + 1.3101939350475556342564376891719053122733E0L, + 1.3182420510168370498593302023271362531155E0L, + 1.3258176636680324650592392104284756311844E0L, + 1.3329603993374458675538498697331558093700E0L, + 1.3397056595989995393283037525895557411039E0L, + 1.3460851583802539310489409282517796256512E0L, + 1.3521273809209546571891479413898128509842E0L, + 1.3578579772154994751124898859640585287459E0L, + 1.3633001003596939542892985278250991189943E0L, + 1.3684746984165928776366381936948529556191E0L, + 1.3734007669450158608612719264449611486510E0L, + 1.3780955681325110444536609641291551522494E0L, + 1.3825748214901258580599674177685685125566E0L, + 1.3868528702577214543289381097042486034883E0L, + 1.3909428270024183486427686943836432060856E0L, + 1.3948567013423687823948122092044222644895E0L, + 1.3986055122719575950126700816114282335732E0L, + 1.4021993871854670105330304794336492676944E0L, + 1.4056476493802697809521934019958079881002E0L, + 1.4089588955564736949699075250792569287156E0L, + 1.4121410646084952153676136718584891599630E0L, + 1.4152014988178669079462550975833894394929E0L, + 1.4181469983996314594038603039700989523716E0L, + 1.4209838702219992566633046424614466661176E0L, + 1.4237179714064941189018190466107297503086E0L, + 1.4263547484202526397918060597281265695725E0L, + 1.4288992721907326964184700745371983590908E0L, + 1.4313562697035588982240194668401779312122E0L, + 1.4337301524847089866404719096698873648610E0L, + 1.4360250423171655234964275337155008780675E0L, + 1.4382447944982225979614042479354815855386E0L, + 1.4403930189057632173997301031392126865694E0L, + 1.4424730991091018200252920599377292525125E0L, + 1.4444882097316563655148453598508037025938E0L, + 1.4464413322481351841999668424758804165254E0L, + 1.4483352693775551917970437843145232637695E0L, + 1.4501726582147939000905940595923466567576E0L, + 1.4519559822271314199339700039142990228105E0L, + 1.4536875822280323362423034480994649820285E0L, + 1.4553696664279718992423082296859928222270E0L, + 1.4570043196511885530074841089245667532358E0L, + 1.4585935117976422128825857356750737658039E0L, + 1.4601391056210009726721818194296893361233E0L, + 1.4616428638860188872060496086383008594310E0L, + 1.4631064559620759326975975316301202111560E0L, + 1.4645314639038178118428450961503371619177E0L, + 1.4659193880646627234129855241049975398470E0L, + 1.4672716522843522691530527207287398276197E0L, + 1.4685896086876430842559640450619880951144E0L, + 1.4698745421276027686510391411132998919794E0L, + 1.4711276743037345918528755717617308518553E0L, + 1.4723501675822635384916444186631899205983E0L, + 1.4735431285433308455179928682541563973416E0L, /* arctan(10.25) */ + 1.5707963267948966192313216916397514420986E0L /* pi/2 */ +}; + + +/* arctan t = t + t^3 p(t^2) / q(t^2) + |t| <= 0.09375 + peak relative error 5.3e-37 */ + +static const long double + p0 = -4.283708356338736809269381409828726405572E1L, + p1 = -8.636132499244548540964557273544599863825E1L, + p2 = -5.713554848244551350855604111031839613216E1L, + p3 = -1.371405711877433266573835355036413750118E1L, + p4 = -8.638214309119210906997318946650189640184E-1L, + q0 = 1.285112506901621042780814422948906537959E2L, + q1 = 3.361907253914337187957855834229672347089E2L, + q2 = 3.180448303864130128268191635189365331680E2L, + q3 = 1.307244136980865800160844625025280344686E2L, + q4 = 2.173623741810414221251136181221172551416E1L; + /* q5 = 1.000000000000000000000000000000000000000E0 */ + + +long double +__atanl (long double x) +{ + int32_t k, sign, lx; + long double t, u, p, q; + double xhi; + + xhi = ldbl_high (x); + EXTRACT_WORDS (k, lx, xhi); + sign = k & 0x80000000; + + /* Check for IEEE special cases. */ + k &= 0x7fffffff; + if (k >= 0x7ff00000) + { + /* NaN. */ + if (((k - 0x7ff00000) | lx) != 0) + return (x + x); + + /* Infinity. */ + if (sign) + return -atantbl[83]; + else + return atantbl[83]; + } + + if (k <= 0x3c800000) /* |x| <= 2**-55. */ + { + math_check_force_underflow (x); + /* Raise inexact. */ + if (1e300L + x > 0.0) + return x; + } + + if (k >= 0x46c00000) /* |x| >= 2**109. */ + { + /* Saturate result to {-,+}pi/2. */ + if (sign) + return -atantbl[83]; + else + return atantbl[83]; + } + + if (sign) + x = -x; + + if (k >= 0x40248000) /* 10.25 */ + { + k = 83; + t = -1.0/x; + } + else + { + /* Index of nearest table element. + Roundoff to integer is asymmetrical to avoid cancellation when t < 0 + (cf. fdlibm). */ + k = 8.0 * x + 0.25; + u = 0.125 * k; + /* Small arctan argument. */ + t = (x - u) / (1.0 + x * u); + } + + /* Arctan of small argument t. */ + u = t * t; + p = ((((p4 * u) + p3) * u + p2) * u + p1) * u + p0; + q = ((((u + q4) * u + q3) * u + q2) * u + q1) * u + q0; + u = t * u * p / q + t; + + /* arctan x = arctan u + arctan t */ + u = atantbl[k] + u; + if (sign) + return (-u); + else + return u; +} + +long_double_symbol (libm, __atanl, atanl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_cbrtl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_cbrtl.c new file mode 100644 index 0000000000..64bfc46414 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_cbrtl.c @@ -0,0 +1,10 @@ +/* Looks like we can use ieee854 s_cbrtl.c as is for IBM extended format. */ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) + +#define _Float128 long double +#define L(x) x ## L + +#include <sysdeps/ieee754/ldbl-128/s_cbrtl.c> +long_double_symbol (libm, __cbrtl, cbrtl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_ceill.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_ceill.c new file mode 100644 index 0000000000..c451825c62 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_ceill.c @@ -0,0 +1,62 @@ +/* Ceil (round to +inf) long double floating-point values. + IBM extended format long double version. + Copyright (C) 2006-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_ldbl_opt.h> +#include <float.h> +#include <ieee754.h> + + +long double +__ceill (long double x) +{ + double xh, xl, hi, lo; + + ldbl_unpack (x, &xh, &xl); + + /* Return Inf, Nan, +/-0 unchanged. */ + if (__builtin_expect (xh != 0.0 + && __builtin_isless (__builtin_fabs (xh), + __builtin_inf ()), 1)) + { + hi = __ceil (xh); + if (hi != xh) + { + /* The high part is not an integer; the low part does not + affect the result. */ + xh = hi; + xl = 0; + } + else + { + /* The high part is a nonzero integer. */ + lo = __ceil (xl); + xh = hi; + xl = lo; + ldbl_canonicalize_int (&xh, &xl); + } + } + else + /* Quiet signaling NaN arguments. */ + xh += xh; + + return ldbl_pack (xh, xl); +} + +long_double_symbol (libm, __ceill, ceill); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_copysignl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_copysignl.c new file mode 100644 index 0000000000..3b8ec1a74d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_copysignl.c @@ -0,0 +1,41 @@ +/* s_copysignl.c -- long double version of s_copysign.c. + * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * copysignl(long double x, long double y) + * copysignl(x,y) returns a value with the magnitude of x and + * with the sign bit of y. + */ + +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +long double __copysignl(long double x, long double y) +{ + if (signbit (x) != signbit (y)) + x = -x; + return x; +} + +#if IS_IN (libm) +long_double_symbol (libm, __copysignl, copysignl); +#else +long_double_symbol (libc, __copysignl, copysignl); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_cosl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_cosl.c new file mode 100644 index 0000000000..54c6cc77d2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_cosl.c @@ -0,0 +1,88 @@ +/* s_cosl.c -- long double version of s_cos.c. + * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* cosl(x) + * Return cosine function of x. + * + * kernel function: + * __kernel_sinl ... sine function on [-pi/4,pi/4] + * __kernel_cosl ... cosine function on [-pi/4,pi/4] + * __ieee754_rem_pio2l ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include <errno.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +long double __cosl(long double x) +{ + long double y[2],z=0.0L; + int64_t n, ix; + double xhi; + + /* High word of x. */ + xhi = ldbl_high (x); + EXTRACT_WORDS64 (ix, xhi); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffffffffffffLL; + if(ix <= 0x3fe921fb54442d18LL) + return __kernel_cosl(x,z); + + /* cos(Inf or NaN) is NaN */ + else if (ix>=0x7ff0000000000000LL) { + if (ix == 0x7ff0000000000000LL) + __set_errno (EDOM); + return x-x; + } + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2l(x,y); + switch(n&3) { + case 0: + return __kernel_cosl(y[0],y[1]); + case 1: + return -__kernel_sinl(y[0],y[1],1); + case 2: + return -__kernel_cosl(y[0],y[1]); + default: + return __kernel_sinl(y[0],y[1],1); + } + } +} +long_double_symbol (libm, __cosl, cosl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_erfl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_erfl.c new file mode 100644 index 0000000000..7b761b0afa --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_erfl.c @@ -0,0 +1,970 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* Modifications and expansions for 128-bit long double are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* double erf(double x) + * double erfc(double x) + * x + * 2 |\ + * erf(x) = --------- | exp(-t*t)dt + * sqrt(pi) \| + * 0 + * + * erfc(x) = 1-erf(x) + * Note that + * erf(-x) = -erf(x) + * erfc(-x) = 2 - erfc(x) + * + * Method: + * 1. erf(x) = x + x*R(x^2) for |x| in [0, 7/8] + * Remark. The formula is derived by noting + * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....) + * and that + * 2/sqrt(pi) = 1.128379167095512573896158903121545171688 + * is close to one. + * + * 1a. erf(x) = 1 - erfc(x), for |x| > 1.0 + * erfc(x) = 1 - erf(x) if |x| < 1/4 + * + * 2. For |x| in [7/8, 1], let s = |x| - 1, and + * c = 0.84506291151 rounded to single (24 bits) + * erf(s + c) = sign(x) * (c + P1(s)/Q1(s)) + * Remark: here we use the taylor series expansion at x=1. + * erf(1+s) = erf(1) + s*Poly(s) + * = 0.845.. + P1(s)/Q1(s) + * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25] + * + * 3. For x in [1/4, 5/4], + * erfc(s + const) = erfc(const) + s P1(s)/Q1(s) + * for const = 1/4, 3/8, ..., 9/8 + * and 0 <= s <= 1/8 . + * + * 4. For x in [5/4, 107], + * erfc(x) = (1/x)*exp(-x*x-0.5625 + R(z)) + * z=1/x^2 + * The interval is partitioned into several segments + * of width 1/8 in 1/x. + * erf(x) = 1.0 - erfc(x) if x < 25.6283 else + * erf(x) = sign(x)*(1.0 - tiny) + * + * Note1: + * To compute exp(-x*x-0.5625+R/S), let s be a single + * precision number and s := x; then + * -x*x = -s*s + (s-x)*(s+x) + * exp(-x*x-0.5626+R/S) = + * exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S); + * Note2: + * Here 4 and 5 make use of the asymptotic series + * exp(-x*x) + * erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) ) + * x*sqrt(pi) + * + * Note3: + * For x higher than 25.6283, erf(x) underflows. + * + * 5. For inf > x >= 107 + * erf(x) = sign(x) *(1 - tiny) (raise inexact) + * erfc(x) = tiny*tiny (raise underflow) if x > 0 + * = 2 - tiny if x<0 + * + * 7. Special case: + * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, + * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, + * erfc/erf(NaN) is NaN + */ + +#include <errno.h> +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> +#include <fix-int-fp-convert-zero.h> + +/* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */ + +static long double +neval (long double x, const long double *p, int n) +{ + long double y; + + p += n; + y = *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +/* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */ + +static long double +deval (long double x, const long double *p, int n) +{ + long double y; + + p += n; + y = x + *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + + +static const long double +tiny = 1e-300L, + one = 1.0L, + two = 2.0L, + /* 2/sqrt(pi) - 1 */ + efx = 1.2837916709551257389615890312154517168810E-1L; + + +/* erf(x) = x + x R(x^2) + 0 <= x <= 7/8 + Peak relative error 1.8e-35 */ +#define NTN1 8 +static const long double TN1[NTN1 + 1] = +{ + -3.858252324254637124543172907442106422373E10L, + 9.580319248590464682316366876952214879858E10L, + 1.302170519734879977595901236693040544854E10L, + 2.922956950426397417800321486727032845006E9L, + 1.764317520783319397868923218385468729799E8L, + 1.573436014601118630105796794840834145120E7L, + 4.028077380105721388745632295157816229289E5L, + 1.644056806467289066852135096352853491530E4L, + 3.390868480059991640235675479463287886081E1L +}; +#define NTD1 8 +static const long double TD1[NTD1 + 1] = +{ + -3.005357030696532927149885530689529032152E11L, + -1.342602283126282827411658673839982164042E11L, + -2.777153893355340961288511024443668743399E10L, + -3.483826391033531996955620074072768276974E9L, + -2.906321047071299585682722511260895227921E8L, + -1.653347985722154162439387878512427542691E7L, + -6.245520581562848778466500301865173123136E5L, + -1.402124304177498828590239373389110545142E4L, + -1.209368072473510674493129989468348633579E2L +/* 1.0E0 */ +}; + + +/* erf(z+1) = erf_const + P(z)/Q(z) + -.125 <= z <= 0 + Peak relative error 7.3e-36 */ +static const long double erf_const = 0.845062911510467529296875L; +#define NTN2 8 +static const long double TN2[NTN2 + 1] = +{ + -4.088889697077485301010486931817357000235E1L, + 7.157046430681808553842307502826960051036E3L, + -2.191561912574409865550015485451373731780E3L, + 2.180174916555316874988981177654057337219E3L, + 2.848578658049670668231333682379720943455E2L, + 1.630362490952512836762810462174798925274E2L, + 6.317712353961866974143739396865293596895E0L, + 2.450441034183492434655586496522857578066E1L, + 5.127662277706787664956025545897050896203E-1L +}; +#define NTD2 8 +static const long double TD2[NTD2 + 1] = +{ + 1.731026445926834008273768924015161048885E4L, + 1.209682239007990370796112604286048173750E4L, + 1.160950290217993641320602282462976163857E4L, + 5.394294645127126577825507169061355698157E3L, + 2.791239340533632669442158497532521776093E3L, + 8.989365571337319032943005387378993827684E2L, + 2.974016493766349409725385710897298069677E2L, + 6.148192754590376378740261072533527271947E1L, + 1.178502892490738445655468927408440847480E1L + /* 1.0E0 */ +}; + + +/* erfc(x + 0.25) = erfc(0.25) + x R(x) + 0 <= x < 0.125 + Peak relative error 1.4e-35 */ +#define NRNr13 8 +static const long double RNr13[NRNr13 + 1] = +{ + -2.353707097641280550282633036456457014829E3L, + 3.871159656228743599994116143079870279866E2L, + -3.888105134258266192210485617504098426679E2L, + -2.129998539120061668038806696199343094971E1L, + -8.125462263594034672468446317145384108734E1L, + 8.151549093983505810118308635926270319660E0L, + -5.033362032729207310462422357772568553670E0L, + -4.253956621135136090295893547735851168471E-2L, + -8.098602878463854789780108161581050357814E-2L +}; +#define NRDr13 7 +static const long double RDr13[NRDr13 + 1] = +{ + 2.220448796306693503549505450626652881752E3L, + 1.899133258779578688791041599040951431383E2L, + 1.061906712284961110196427571557149268454E3L, + 7.497086072306967965180978101974566760042E1L, + 2.146796115662672795876463568170441327274E2L, + 1.120156008362573736664338015952284925592E1L, + 2.211014952075052616409845051695042741074E1L, + 6.469655675326150785692908453094054988938E-1L + /* 1.0E0 */ +}; +/* erfc(0.25) = C13a + C13b to extra precision. */ +static const long double C13a = 0.723663330078125L; +static const long double C13b = 1.0279753638067014931732235184287934646022E-5L; + + +/* erfc(x + 0.375) = erfc(0.375) + x R(x) + 0 <= x < 0.125 + Peak relative error 1.2e-35 */ +#define NRNr14 8 +static const long double RNr14[NRNr14 + 1] = +{ + -2.446164016404426277577283038988918202456E3L, + 6.718753324496563913392217011618096698140E2L, + -4.581631138049836157425391886957389240794E2L, + -2.382844088987092233033215402335026078208E1L, + -7.119237852400600507927038680970936336458E1L, + 1.313609646108420136332418282286454287146E1L, + -6.188608702082264389155862490056401365834E0L, + -2.787116601106678287277373011101132659279E-2L, + -2.230395570574153963203348263549700967918E-2L +}; +#define NRDr14 7 +static const long double RDr14[NRDr14 + 1] = +{ + 2.495187439241869732696223349840963702875E3L, + 2.503549449872925580011284635695738412162E2L, + 1.159033560988895481698051531263861842461E3L, + 9.493751466542304491261487998684383688622E1L, + 2.276214929562354328261422263078480321204E2L, + 1.367697521219069280358984081407807931847E1L, + 2.276988395995528495055594829206582732682E1L, + 7.647745753648996559837591812375456641163E-1L + /* 1.0E0 */ +}; +/* erfc(0.375) = C14a + C14b to extra precision. */ +static const long double C14a = 0.5958709716796875L; +static const long double C14b = 1.2118885490201676174914080878232469565953E-5L; + +/* erfc(x + 0.5) = erfc(0.5) + x R(x) + 0 <= x < 0.125 + Peak relative error 4.7e-36 */ +#define NRNr15 8 +static const long double RNr15[NRNr15 + 1] = +{ + -2.624212418011181487924855581955853461925E3L, + 8.473828904647825181073831556439301342756E2L, + -5.286207458628380765099405359607331669027E2L, + -3.895781234155315729088407259045269652318E1L, + -6.200857908065163618041240848728398496256E1L, + 1.469324610346924001393137895116129204737E1L, + -6.961356525370658572800674953305625578903E0L, + 5.145724386641163809595512876629030548495E-3L, + 1.990253655948179713415957791776180406812E-2L +}; +#define NRDr15 7 +static const long double RDr15[NRDr15 + 1] = +{ + 2.986190760847974943034021764693341524962E3L, + 5.288262758961073066335410218650047725985E2L, + 1.363649178071006978355113026427856008978E3L, + 1.921707975649915894241864988942255320833E2L, + 2.588651100651029023069013885900085533226E2L, + 2.628752920321455606558942309396855629459E1L, + 2.455649035885114308978333741080991380610E1L, + 1.378826653595128464383127836412100939126E0L + /* 1.0E0 */ +}; +/* erfc(0.5) = C15a + C15b to extra precision. */ +static const long double C15a = 0.4794921875L; +static const long double C15b = 7.9346869534623172533461080354712635484242E-6L; + +/* erfc(x + 0.625) = erfc(0.625) + x R(x) + 0 <= x < 0.125 + Peak relative error 5.1e-36 */ +#define NRNr16 8 +static const long double RNr16[NRNr16 + 1] = +{ + -2.347887943200680563784690094002722906820E3L, + 8.008590660692105004780722726421020136482E2L, + -5.257363310384119728760181252132311447963E2L, + -4.471737717857801230450290232600243795637E1L, + -4.849540386452573306708795324759300320304E1L, + 1.140885264677134679275986782978655952843E1L, + -6.731591085460269447926746876983786152300E0L, + 1.370831653033047440345050025876085121231E-1L, + 2.022958279982138755020825717073966576670E-2L, +}; +#define NRDr16 7 +static const long double RDr16[NRDr16 + 1] = +{ + 3.075166170024837215399323264868308087281E3L, + 8.730468942160798031608053127270430036627E2L, + 1.458472799166340479742581949088453244767E3L, + 3.230423687568019709453130785873540386217E2L, + 2.804009872719893612081109617983169474655E2L, + 4.465334221323222943418085830026979293091E1L, + 2.612723259683205928103787842214809134746E1L, + 2.341526751185244109722204018543276124997E0L, + /* 1.0E0 */ +}; +/* erfc(0.625) = C16a + C16b to extra precision. */ +static const long double C16a = 0.3767547607421875L; +static const long double C16b = 4.3570693945275513594941232097252997287766E-6L; + +/* erfc(x + 0.75) = erfc(0.75) + x R(x) + 0 <= x < 0.125 + Peak relative error 1.7e-35 */ +#define NRNr17 8 +static const long double RNr17[NRNr17 + 1] = +{ + -1.767068734220277728233364375724380366826E3L, + 6.693746645665242832426891888805363898707E2L, + -4.746224241837275958126060307406616817753E2L, + -2.274160637728782675145666064841883803196E1L, + -3.541232266140939050094370552538987982637E1L, + 6.988950514747052676394491563585179503865E0L, + -5.807687216836540830881352383529281215100E0L, + 3.631915988567346438830283503729569443642E-1L, + -1.488945487149634820537348176770282391202E-2L +}; +#define NRDr17 7 +static const long double RDr17[NRDr17 + 1] = +{ + 2.748457523498150741964464942246913394647E3L, + 1.020213390713477686776037331757871252652E3L, + 1.388857635935432621972601695296561952738E3L, + 3.903363681143817750895999579637315491087E2L, + 2.784568344378139499217928969529219886578E2L, + 5.555800830216764702779238020065345401144E1L, + 2.646215470959050279430447295801291168941E1L, + 2.984905282103517497081766758550112011265E0L, + /* 1.0E0 */ +}; +/* erfc(0.75) = C17a + C17b to extra precision. */ +static const long double C17a = 0.2888336181640625L; +static const long double C17b = 1.0748182422368401062165408589222625794046E-5L; + + +/* erfc(x + 0.875) = erfc(0.875) + x R(x) + 0 <= x < 0.125 + Peak relative error 2.2e-35 */ +#define NRNr18 8 +static const long double RNr18[NRNr18 + 1] = +{ + -1.342044899087593397419622771847219619588E3L, + 6.127221294229172997509252330961641850598E2L, + -4.519821356522291185621206350470820610727E2L, + 1.223275177825128732497510264197915160235E1L, + -2.730789571382971355625020710543532867692E1L, + 4.045181204921538886880171727755445395862E0L, + -4.925146477876592723401384464691452700539E0L, + 5.933878036611279244654299924101068088582E-1L, + -5.557645435858916025452563379795159124753E-2L +}; +#define NRDr18 7 +static const long double RDr18[NRDr18 + 1] = +{ + 2.557518000661700588758505116291983092951E3L, + 1.070171433382888994954602511991940418588E3L, + 1.344842834423493081054489613250688918709E3L, + 4.161144478449381901208660598266288188426E2L, + 2.763670252219855198052378138756906980422E2L, + 5.998153487868943708236273854747564557632E1L, + 2.657695108438628847733050476209037025318E1L, + 3.252140524394421868923289114410336976512E0L, + /* 1.0E0 */ +}; +/* erfc(0.875) = C18a + C18b to extra precision. */ +static const long double C18a = 0.215911865234375L; +static const long double C18b = 1.3073705765341685464282101150637224028267E-5L; + +/* erfc(x + 1.0) = erfc(1.0) + x R(x) + 0 <= x < 0.125 + Peak relative error 1.6e-35 */ +#define NRNr19 8 +static const long double RNr19[NRNr19 + 1] = +{ + -1.139180936454157193495882956565663294826E3L, + 6.134903129086899737514712477207945973616E2L, + -4.628909024715329562325555164720732868263E2L, + 4.165702387210732352564932347500364010833E1L, + -2.286979913515229747204101330405771801610E1L, + 1.870695256449872743066783202326943667722E0L, + -4.177486601273105752879868187237000032364E0L, + 7.533980372789646140112424811291782526263E-1L, + -8.629945436917752003058064731308767664446E-2L +}; +#define NRDr19 7 +static const long double RDr19[NRDr19 + 1] = +{ + 2.744303447981132701432716278363418643778E3L, + 1.266396359526187065222528050591302171471E3L, + 1.466739461422073351497972255511919814273E3L, + 4.868710570759693955597496520298058147162E2L, + 2.993694301559756046478189634131722579643E2L, + 6.868976819510254139741559102693828237440E1L, + 2.801505816247677193480190483913753613630E1L, + 3.604439909194350263552750347742663954481E0L, + /* 1.0E0 */ +}; +/* erfc(1.0) = C19a + C19b to extra precision. */ +static const long double C19a = 0.15728759765625L; +static const long double C19b = 1.1609394035130658779364917390740703933002E-5L; + +/* erfc(x + 1.125) = erfc(1.125) + x R(x) + 0 <= x < 0.125 + Peak relative error 3.6e-36 */ +#define NRNr20 8 +static const long double RNr20[NRNr20 + 1] = +{ + -9.652706916457973956366721379612508047640E2L, + 5.577066396050932776683469951773643880634E2L, + -4.406335508848496713572223098693575485978E2L, + 5.202893466490242733570232680736966655434E1L, + -1.931311847665757913322495948705563937159E1L, + -9.364318268748287664267341457164918090611E-2L, + -3.306390351286352764891355375882586201069E0L, + 7.573806045289044647727613003096916516475E-1L, + -9.611744011489092894027478899545635991213E-2L +}; +#define NRDr20 7 +static const long double RDr20[NRDr20 + 1] = +{ + 3.032829629520142564106649167182428189014E3L, + 1.659648470721967719961167083684972196891E3L, + 1.703545128657284619402511356932569292535E3L, + 6.393465677731598872500200253155257708763E2L, + 3.489131397281030947405287112726059221934E2L, + 8.848641738570783406484348434387611713070E1L, + 3.132269062552392974833215844236160958502E1L, + 4.430131663290563523933419966185230513168E0L + /* 1.0E0 */ +}; +/* erfc(1.125) = C20a + C20b to extra precision. */ +static const long double C20a = 0.111602783203125L; +static const long double C20b = 8.9850951672359304215530728365232161564636E-6L; + +/* erfc(1/x) = 1/x exp (-1/x^2 - 0.5625 + R(1/x^2)) + 7/8 <= 1/x < 1 + Peak relative error 1.4e-35 */ +#define NRNr8 9 +static const long double RNr8[NRNr8 + 1] = +{ + 3.587451489255356250759834295199296936784E1L, + 5.406249749087340431871378009874875889602E2L, + 2.931301290625250886238822286506381194157E3L, + 7.359254185241795584113047248898753470923E3L, + 9.201031849810636104112101947312492532314E3L, + 5.749697096193191467751650366613289284777E3L, + 1.710415234419860825710780802678697889231E3L, + 2.150753982543378580859546706243022719599E2L, + 8.740953582272147335100537849981160931197E0L, + 4.876422978828717219629814794707963640913E-2L +}; +#define NRDr8 8 +static const long double RDr8[NRDr8 + 1] = +{ + 6.358593134096908350929496535931630140282E1L, + 9.900253816552450073757174323424051765523E2L, + 5.642928777856801020545245437089490805186E3L, + 1.524195375199570868195152698617273739609E4L, + 2.113829644500006749947332935305800887345E4L, + 1.526438562626465706267943737310282977138E4L, + 5.561370922149241457131421914140039411782E3L, + 9.394035530179705051609070428036834496942E2L, + 6.147019596150394577984175188032707343615E1L + /* 1.0E0 */ +}; + +/* erfc(1/x) = 1/x exp (-1/x^2 - 0.5625 + R(1/x^2)) + 0.75 <= 1/x <= 0.875 + Peak relative error 2.0e-36 */ +#define NRNr7 9 +static const long double RNr7[NRNr7 + 1] = +{ + 1.686222193385987690785945787708644476545E1L, + 1.178224543567604215602418571310612066594E3L, + 1.764550584290149466653899886088166091093E4L, + 1.073758321890334822002849369898232811561E5L, + 3.132840749205943137619839114451290324371E5L, + 4.607864939974100224615527007793867585915E5L, + 3.389781820105852303125270837910972384510E5L, + 1.174042187110565202875011358512564753399E5L, + 1.660013606011167144046604892622504338313E4L, + 6.700393957480661937695573729183733234400E2L +}; +#define NRDr7 9 +static const long double RDr7[NRDr7 + 1] = +{ +-1.709305024718358874701575813642933561169E3L, +-3.280033887481333199580464617020514788369E4L, +-2.345284228022521885093072363418750835214E5L, +-8.086758123097763971926711729242327554917E5L, +-1.456900414510108718402423999575992450138E6L, +-1.391654264881255068392389037292702041855E6L, +-6.842360801869939983674527468509852583855E5L, +-1.597430214446573566179675395199807533371E5L, +-1.488876130609876681421645314851760773480E4L, +-3.511762950935060301403599443436465645703E2L + /* 1.0E0 */ +}; + +/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2)) + 5/8 <= 1/x < 3/4 + Peak relative error 1.9e-35 */ +#define NRNr6 9 +static const long double RNr6[NRNr6 + 1] = +{ + 1.642076876176834390623842732352935761108E0L, + 1.207150003611117689000664385596211076662E2L, + 2.119260779316389904742873816462800103939E3L, + 1.562942227734663441801452930916044224174E4L, + 5.656779189549710079988084081145693580479E4L, + 1.052166241021481691922831746350942786299E5L, + 9.949798524786000595621602790068349165758E4L, + 4.491790734080265043407035220188849562856E4L, + 8.377074098301530326270432059434791287601E3L, + 4.506934806567986810091824791963991057083E2L +}; +#define NRDr6 9 +static const long double RDr6[NRDr6 + 1] = +{ +-1.664557643928263091879301304019826629067E2L, +-3.800035902507656624590531122291160668452E3L, +-3.277028191591734928360050685359277076056E4L, +-1.381359471502885446400589109566587443987E5L, +-3.082204287382581873532528989283748656546E5L, +-3.691071488256738343008271448234631037095E5L, +-2.300482443038349815750714219117566715043E5L, +-6.873955300927636236692803579555752171530E4L, +-8.262158817978334142081581542749986845399E3L, +-2.517122254384430859629423488157361983661E2L + /* 1.00 */ +}; + +/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2)) + 1/2 <= 1/x < 5/8 + Peak relative error 4.6e-36 */ +#define NRNr5 10 +static const long double RNr5[NRNr5 + 1] = +{ +-3.332258927455285458355550878136506961608E-3L, +-2.697100758900280402659586595884478660721E-1L, +-6.083328551139621521416618424949137195536E0L, +-6.119863528983308012970821226810162441263E1L, +-3.176535282475593173248810678636522589861E2L, +-8.933395175080560925809992467187963260693E2L, +-1.360019508488475978060917477620199499560E3L, +-1.075075579828188621541398761300910213280E3L, +-4.017346561586014822824459436695197089916E2L, +-5.857581368145266249509589726077645791341E1L, +-2.077715925587834606379119585995758954399E0L +}; +#define NRDr5 9 +static const long double RDr5[NRDr5 + 1] = +{ + 3.377879570417399341550710467744693125385E-1L, + 1.021963322742390735430008860602594456187E1L, + 1.200847646592942095192766255154827011939E2L, + 7.118915528142927104078182863387116942836E2L, + 2.318159380062066469386544552429625026238E3L, + 4.238729853534009221025582008928765281620E3L, + 4.279114907284825886266493994833515580782E3L, + 2.257277186663261531053293222591851737504E3L, + 5.570475501285054293371908382916063822957E2L, + 5.142189243856288981145786492585432443560E1L + /* 1.0E0 */ +}; + +/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2)) + 3/8 <= 1/x < 1/2 + Peak relative error 2.0e-36 */ +#define NRNr4 10 +static const long double RNr4[NRNr4 + 1] = +{ + 3.258530712024527835089319075288494524465E-3L, + 2.987056016877277929720231688689431056567E-1L, + 8.738729089340199750734409156830371528862E0L, + 1.207211160148647782396337792426311125923E2L, + 8.997558632489032902250523945248208224445E2L, + 3.798025197699757225978410230530640879762E3L, + 9.113203668683080975637043118209210146846E3L, + 1.203285891339933238608683715194034900149E4L, + 8.100647057919140328536743641735339740855E3L, + 2.383888249907144945837976899822927411769E3L, + 2.127493573166454249221983582495245662319E2L +}; +#define NRDr4 10 +static const long double RDr4[NRDr4 + 1] = +{ +-3.303141981514540274165450687270180479586E-1L, +-1.353768629363605300707949368917687066724E1L, +-2.206127630303621521950193783894598987033E2L, +-1.861800338758066696514480386180875607204E3L, +-8.889048775872605708249140016201753255599E3L, +-2.465888106627948210478692168261494857089E4L, +-3.934642211710774494879042116768390014289E4L, +-3.455077258242252974937480623730228841003E4L, +-1.524083977439690284820586063729912653196E4L, +-2.810541887397984804237552337349093953857E3L, +-1.343929553541159933824901621702567066156E2L + /* 1.0E0 */ +}; + +/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2)) + 1/4 <= 1/x < 3/8 + Peak relative error 8.4e-37 */ +#define NRNr3 11 +static const long double RNr3[NRNr3 + 1] = +{ +-1.952401126551202208698629992497306292987E-6L, +-2.130881743066372952515162564941682716125E-4L, +-8.376493958090190943737529486107282224387E-3L, +-1.650592646560987700661598877522831234791E-1L, +-1.839290818933317338111364667708678163199E0L, +-1.216278715570882422410442318517814388470E1L, +-4.818759344462360427612133632533779091386E1L, +-1.120994661297476876804405329172164436784E2L, +-1.452850765662319264191141091859300126931E2L, +-9.485207851128957108648038238656777241333E1L, +-2.563663855025796641216191848818620020073E1L, +-1.787995944187565676837847610706317833247E0L +}; +#define NRDr3 10 +static const long double RDr3[NRDr3 + 1] = +{ + 1.979130686770349481460559711878399476903E-4L, + 1.156941716128488266238105813374635099057E-2L, + 2.752657634309886336431266395637285974292E-1L, + 3.482245457248318787349778336603569327521E0L, + 2.569347069372696358578399521203959253162E1L, + 1.142279000180457419740314694631879921561E2L, + 3.056503977190564294341422623108332700840E2L, + 4.780844020923794821656358157128719184422E2L, + 4.105972727212554277496256802312730410518E2L, + 1.724072188063746970865027817017067646246E2L, + 2.815939183464818198705278118326590370435E1L + /* 1.0E0 */ +}; + +/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2)) + 1/8 <= 1/x < 1/4 + Peak relative error 1.5e-36 */ +#define NRNr2 11 +static const long double RNr2[NRNr2 + 1] = +{ +-2.638914383420287212401687401284326363787E-8L, +-3.479198370260633977258201271399116766619E-6L, +-1.783985295335697686382487087502222519983E-4L, +-4.777876933122576014266349277217559356276E-3L, +-7.450634738987325004070761301045014986520E-2L, +-7.068318854874733315971973707247467326619E-1L, +-4.113919921935944795764071670806867038732E0L, +-1.440447573226906222417767283691888875082E1L, +-2.883484031530718428417168042141288943905E1L, +-2.990886974328476387277797361464279931446E1L, +-1.325283914915104866248279787536128997331E1L, +-1.572436106228070195510230310658206154374E0L +}; +#define NRDr2 10 +static const long double RDr2[NRDr2 + 1] = +{ + 2.675042728136731923554119302571867799673E-6L, + 2.170997868451812708585443282998329996268E-4L, + 7.249969752687540289422684951196241427445E-3L, + 1.302040375859768674620410563307838448508E-1L, + 1.380202483082910888897654537144485285549E0L, + 8.926594113174165352623847870299170069350E0L, + 3.521089584782616472372909095331572607185E1L, + 8.233547427533181375185259050330809105570E1L, + 1.072971579885803033079469639073292840135E2L, + 6.943803113337964469736022094105143158033E1L, + 1.775695341031607738233608307835017282662E1L + /* 1.0E0 */ +}; + +/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2)) + 1/128 <= 1/x < 1/8 + Peak relative error 2.2e-36 */ +#define NRNr1 9 +static const long double RNr1[NRNr1 + 1] = +{ +-4.250780883202361946697751475473042685782E-8L, +-5.375777053288612282487696975623206383019E-6L, +-2.573645949220896816208565944117382460452E-4L, +-6.199032928113542080263152610799113086319E-3L, +-8.262721198693404060380104048479916247786E-2L, +-6.242615227257324746371284637695778043982E-1L, +-2.609874739199595400225113299437099626386E0L, +-5.581967563336676737146358534602770006970E0L, +-5.124398923356022609707490956634280573882E0L, +-1.290865243944292370661544030414667556649E0L +}; +#define NRDr1 8 +static const long double RDr1[NRDr1 + 1] = +{ + 4.308976661749509034845251315983612976224E-6L, + 3.265390126432780184125233455960049294580E-4L, + 9.811328839187040701901866531796570418691E-3L, + 1.511222515036021033410078631914783519649E-1L, + 1.289264341917429958858379585970225092274E0L, + 6.147640356182230769548007536914983522270E0L, + 1.573966871337739784518246317003956180750E1L, + 1.955534123435095067199574045529218238263E1L, + 9.472613121363135472247929109615785855865E0L + /* 1.0E0 */ +}; + + +long double +__erfl (long double x) +{ + long double a, y, z; + int32_t i, ix, hx; + double xhi; + + xhi = ldbl_high (x); + GET_HIGH_WORD (hx, xhi); + ix = hx & 0x7fffffff; + + if (ix >= 0x7ff00000) + { /* erf(nan)=nan */ + i = ((uint32_t) hx >> 31) << 1; + return (long double) (1 - i) + one / x; /* erf(+-inf)=+-1 */ + } + + if (ix >= 0x3ff00000) /* |x| >= 1.0 */ + { + if (ix >= 0x4039A0DE) + { + /* __erfcl (x) underflows if x > 25.6283 */ + if ((hx & 0x80000000) == 0) + return one-tiny; + else + return tiny-one; + } + else + { + y = __erfcl (x); + return (one - y); + } + } + a = x; + if ((hx & 0x80000000) != 0) + a = -a; + z = x * x; + if (ix < 0x3fec0000) /* a < 0.875 */ + { + if (ix < 0x3c600000) /* |x|<2**-57 */ + { + if (ix < 0x00800000) + { + /* erf (-0) = -0. Unfortunately, for IBM extended double + 0.0625 * (16.0 * x + (16.0 * efx) * x) for x = -0 + evaluates to 0. */ + if (x == 0) + return x; + long double ret = 0.0625 * (16.0 * x + (16.0 * efx) * x); + math_check_force_underflow (ret); + return ret; + } + return x + efx * x; + } + y = a + a * neval (z, TN1, NTN1) / deval (z, TD1, NTD1); + } + else + { + a = a - one; + y = erf_const + neval (a, TN2, NTN2) / deval (a, TD2, NTD2); + } + + if (hx & 0x80000000) /* x < 0 */ + y = -y; + return( y ); +} + +long_double_symbol (libm, __erfl, erfl); +long double +__erfcl (long double x) +{ + long double y, z, p, r; + int32_t i, ix; + uint32_t hx; + double xhi; + + xhi = ldbl_high (x); + GET_HIGH_WORD (hx, xhi); + ix = hx & 0x7fffffff; + + if (ix >= 0x7ff00000) + { /* erfc(nan)=nan */ + /* erfc(+-inf)=0,2 */ + long double ret = (long double) ((hx >> 31) << 1) + one / x; + if (FIX_INT_FP_CONVERT_ZERO && ret == 0.0L) + return 0.0L; + return ret; + } + + if (ix < 0x3fd00000) /* |x| <1/4 */ + { + if (ix < 0x38d00000) /* |x|<2**-114 */ + return one - x; + return one - __erfl (x); + } + if (ix < 0x3ff40000) /* 1.25 */ + { + if ((hx & 0x80000000) != 0) + x = -x; + i = 8.0 * x; + switch (i) + { + case 2: + z = x - 0.25L; + y = C13b + z * neval (z, RNr13, NRNr13) / deval (z, RDr13, NRDr13); + y += C13a; + break; + case 3: + z = x - 0.375L; + y = C14b + z * neval (z, RNr14, NRNr14) / deval (z, RDr14, NRDr14); + y += C14a; + break; + case 4: + z = x - 0.5L; + y = C15b + z * neval (z, RNr15, NRNr15) / deval (z, RDr15, NRDr15); + y += C15a; + break; + case 5: + z = x - 0.625L; + y = C16b + z * neval (z, RNr16, NRNr16) / deval (z, RDr16, NRDr16); + y += C16a; + break; + case 6: + z = x - 0.75L; + y = C17b + z * neval (z, RNr17, NRNr17) / deval (z, RDr17, NRDr17); + y += C17a; + break; + case 7: + z = x - 0.875L; + y = C18b + z * neval (z, RNr18, NRNr18) / deval (z, RDr18, NRDr18); + y += C18a; + break; + case 8: + z = x - 1.0L; + y = C19b + z * neval (z, RNr19, NRNr19) / deval (z, RDr19, NRDr19); + y += C19a; + break; + default: /* i == 9. */ + z = x - 1.125L; + y = C20b + z * neval (z, RNr20, NRNr20) / deval (z, RDr20, NRDr20); + y += C20a; + break; + } + if (hx & 0x80000000) + y = 2.0L - y; + return y; + } + /* 1.25 < |x| < 107 */ + if (ix < 0x405ac000) + { + /* x < -9 */ + if (hx >= 0xc0220000) + return two - tiny; + + if ((hx & 0x80000000) != 0) + x = -x; + z = one / (x * x); + i = 8.0 / x; + switch (i) + { + default: + case 0: + p = neval (z, RNr1, NRNr1) / deval (z, RDr1, NRDr1); + break; + case 1: + p = neval (z, RNr2, NRNr2) / deval (z, RDr2, NRDr2); + break; + case 2: + p = neval (z, RNr3, NRNr3) / deval (z, RDr3, NRDr3); + break; + case 3: + p = neval (z, RNr4, NRNr4) / deval (z, RDr4, NRDr4); + break; + case 4: + p = neval (z, RNr5, NRNr5) / deval (z, RDr5, NRDr5); + break; + case 5: + p = neval (z, RNr6, NRNr6) / deval (z, RDr6, NRDr6); + break; + case 6: + p = neval (z, RNr7, NRNr7) / deval (z, RDr7, NRDr7); + break; + case 7: + p = neval (z, RNr8, NRNr8) / deval (z, RDr8, NRDr8); + break; + } + z = (float) x; + r = __ieee754_expl (-z * z - 0.5625) * + __ieee754_expl ((z - x) * (z + x) + p); + if ((hx & 0x80000000) == 0) + { + long double ret = r / x; + if (ret == 0) + __set_errno (ERANGE); + return ret; + } + else + return two - r / x; + } + else + { + if ((hx & 0x80000000) == 0) + { + __set_errno (ERANGE); + return tiny * tiny; + } + else + return two - tiny; + } +} + +long_double_symbol (libm, __erfcl, erfcl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_expm1l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_expm1l.c new file mode 100644 index 0000000000..42d57c6eec --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_expm1l.c @@ -0,0 +1,152 @@ +/* expm1l.c + * + * Exponential function, minus 1 + * 128-bit long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, expm1l(); + * + * y = expm1l( x ); + * + * + * + * DESCRIPTION: + * + * Returns e (2.71828...) raised to the x power, minus one. + * + * Range reduction is accomplished by separating the argument + * into an integer k and fraction f such that + * + * x k f + * e = 2 e. + * + * An expansion x + .5 x^2 + x^3 R(x) approximates exp(f) - 1 + * in the basic range [-0.5 ln 2, 0.5 ln 2]. + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -79,+MAXLOG 100,000 1.7e-34 4.5e-35 + * + */ + +/* Copyright 2001 by Stephen L. Moshier + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <errno.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +/* exp(x) - 1 = x + 0.5 x^2 + x^3 P(x)/Q(x) + -.5 ln 2 < x < .5 ln 2 + Theoretical peak relative error = 8.1e-36 */ + +static const long double + P0 = 2.943520915569954073888921213330863757240E8L, + P1 = -5.722847283900608941516165725053359168840E7L, + P2 = 8.944630806357575461578107295909719817253E6L, + P3 = -7.212432713558031519943281748462837065308E5L, + P4 = 4.578962475841642634225390068461943438441E4L, + P5 = -1.716772506388927649032068540558788106762E3L, + P6 = 4.401308817383362136048032038528753151144E1L, + P7 = -4.888737542888633647784737721812546636240E-1L, + Q0 = 1.766112549341972444333352727998584753865E9L, + Q1 = -7.848989743695296475743081255027098295771E8L, + Q2 = 1.615869009634292424463780387327037251069E8L, + Q3 = -2.019684072836541751428967854947019415698E7L, + Q4 = 1.682912729190313538934190635536631941751E6L, + Q5 = -9.615511549171441430850103489315371768998E4L, + Q6 = 3.697714952261803935521187272204485251835E3L, + Q7 = -8.802340681794263968892934703309274564037E1L, + /* Q8 = 1.000000000000000000000000000000000000000E0 */ +/* C1 + C2 = ln 2 */ + + C1 = 6.93145751953125E-1L, + C2 = 1.428606820309417232121458176568075500134E-6L, +/* ln 2^-114 */ + minarg = -7.9018778583833765273564461846232128760607E1L, big = 1e290L; + + +long double +__expm1l (long double x) +{ + long double px, qx, xx; + int32_t ix, lx, sign; + int k; + double xhi; + + /* Detect infinity and NaN. */ + xhi = ldbl_high (x); + EXTRACT_WORDS (ix, lx, xhi); + sign = ix & 0x80000000; + ix &= 0x7fffffff; + if (!sign && ix >= 0x40600000) + return __expl (x); + if (ix >= 0x7ff00000) + { + /* Infinity (which must be negative infinity). */ + if (((ix - 0x7ff00000) | lx) == 0) + return -1.0L; + /* NaN. Invalid exception if signaling. */ + return x + x; + } + + /* expm1(+- 0) = +- 0. */ + if ((ix | lx) == 0) + return x; + + /* Minimum value. */ + if (x < minarg) + return (4.0/big - 1.0L); + + /* Express x = ln 2 (k + remainder), remainder not exceeding 1/2. */ + xx = C1 + C2; /* ln 2. */ + px = __floorl (0.5 + x / xx); + k = px; + /* remainder times ln 2 */ + x -= px * C1; + x -= px * C2; + + /* Approximate exp(remainder ln 2). */ + px = (((((((P7 * x + + P6) * x + + P5) * x + P4) * x + P3) * x + P2) * x + P1) * x + P0) * x; + + qx = (((((((x + + Q7) * x + + Q6) * x + Q5) * x + Q4) * x + Q3) * x + Q2) * x + Q1) * x + Q0; + + xx = x * x; + qx = x + (0.5 * xx + xx * px / qx); + + /* exp(x) = exp(k ln 2) exp(remainder ln 2) = 2^k exp(remainder ln 2). + + We have qx = exp(remainder ln 2) - 1, so + exp(x) - 1 = 2^k (qx + 1) - 1 + = 2^k qx + 2^k - 1. */ + + px = __ldexpl (1.0L, k); + x = px * qx + (px - 1.0); + return x; +} +libm_hidden_def (__expm1l) +long_double_symbol (libm, __expm1l, expm1l); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fabsl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fabsl.c new file mode 100644 index 0000000000..c801c97065 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fabsl.c @@ -0,0 +1,44 @@ +/* s_fabsl.c -- long double version of s_fabs.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + + +/* + * fabsl(x) returns the absolute value of x. + */ + +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +long double __fabsl(long double x) +{ + u_int64_t hx, lx; + double xhi, xlo; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + lx = lx ^ ( hx & 0x8000000000000000LL ); + hx = hx & 0x7fffffffffffffffLL; + INSERT_WORDS64 (xhi, hx); + INSERT_WORDS64 (xlo, lx); + x = ldbl_pack (xhi, xlo); + return x; +} +long_double_symbol (libm, __fabsl, fabsl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_finitel.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_finitel.c new file mode 100644 index 0000000000..3b9e3de292 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_finitel.c @@ -0,0 +1,49 @@ +/* s_finitel.c -- long double version of s_finite.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * finitel(x) returns 1 is x is finite, else 0; + * no branching! + */ + +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +int +___finitel (long double x) +{ + uint64_t hx; + double xhi; + + xhi = ldbl_high (x); + EXTRACT_WORDS64 (hx, xhi); + hx &= 0x7ff0000000000000LL; + hx -= 0x7ff0000000000000LL; + return hx >> 63; +} +hidden_ver (___finitel, __finitel) +weak_alias (___finitel, ____finitel) +#if IS_IN (libm) +long_double_symbol (libm, ____finitel, finitel); +long_double_symbol (libm, ___finitel, __finitel); +#else +long_double_symbol (libc, ____finitel, finitel); +long_double_symbol (libc, ___finitel, __finitel); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_floorl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_floorl.c new file mode 100644 index 0000000000..6b837c7bcd --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_floorl.c @@ -0,0 +1,62 @@ +/* Round to int long double floating-point values. + IBM extended format long double version. + Copyright (C) 2006-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_ldbl_opt.h> +#include <float.h> +#include <ieee754.h> + + +long double +__floorl (long double x) +{ + double xh, xl, hi, lo; + + ldbl_unpack (x, &xh, &xl); + + /* Return Inf, Nan, +/-0 unchanged. */ + if (__builtin_expect (xh != 0.0 + && __builtin_isless (__builtin_fabs (xh), + __builtin_inf ()), 1)) + { + hi = __floor (xh); + if (hi != xh) + { + /* The high part is not an integer; the low part does not + affect the result. */ + xh = hi; + xl = 0; + } + else + { + /* The high part is a nonzero integer. */ + lo = __floor (xl); + xh = hi; + xl = lo; + ldbl_canonicalize_int (&xh, &xl); + } + } + else + /* Quiet signaling NaN arguments. */ + xh += xh; + + return ldbl_pack (xh, xl); +} + +long_double_symbol (libm, __floorl, floorl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fmal.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fmal.c new file mode 100644 index 0000000000..9098e79df9 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fmal.c @@ -0,0 +1,257 @@ +/* Compute x * y + z as ternary operation. + Copyright (C) 2011-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by David Flaherty <flaherty@linux.vnet.ibm.com>. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> +#include <mul_split.h> +#include <stdlib.h> + +/* Calculate X + Y exactly and store the result in *HI + *LO. It is + given that |X| >= |Y| and the values are small enough that no + overflow occurs. */ + +static void +add_split (double *hi, double *lo, double x, double y) +{ + /* Apply Dekker's algorithm. */ + *hi = x + y; + *lo = (x - *hi) + y; +} + +/* Value with extended range, used in intermediate computations. */ +typedef struct +{ + /* Value in [0.5, 1), as from frexp, or 0. */ + double val; + /* Exponent of power of 2 it is multiplied by, or 0 for zero. */ + int exp; +} ext_val; + +/* Store D as an ext_val value. */ + +static void +store_ext_val (ext_val *v, double d) +{ + v->val = __frexp (d, &v->exp); +} + +/* Store X * Y as ext_val values *V0 and *V1. */ + +static void +mul_ext_val (ext_val *v0, ext_val *v1, double x, double y) +{ + int xexp, yexp; + x = __frexp (x, &xexp); + y = __frexp (y, &yexp); + double hi, lo; + mul_split (&hi, &lo, x, y); + store_ext_val (v0, hi); + if (hi != 0) + v0->exp += xexp + yexp; + store_ext_val (v1, lo); + if (lo != 0) + v1->exp += xexp + yexp; +} + +/* Compare absolute values of ext_val values pointed to by P and Q for + qsort. */ + +static int +compare (const void *p, const void *q) +{ + const ext_val *pe = p; + const ext_val *qe = q; + if (pe->val == 0) + return qe->val == 0 ? 0 : -1; + else if (qe->val == 0) + return 1; + else if (pe->exp < qe->exp) + return -1; + else if (pe->exp > qe->exp) + return 1; + else + { + double pd = fabs (pe->val); + double qd = fabs (qe->val); + if (pd < qd) + return -1; + else if (pd == qd) + return 0; + else + return 1; + } +} + +/* Calculate *X + *Y exactly, storing the high part in *X (rounded to + nearest) and the low part in *Y. It is given that |X| >= |Y|. */ + +static void +add_split_ext (ext_val *x, ext_val *y) +{ + int xexp = x->exp, yexp = y->exp; + if (y->val == 0 || xexp - yexp > 53) + return; + double hi = x->val; + double lo = __scalbn (y->val, yexp - xexp); + add_split (&hi, &lo, hi, lo); + store_ext_val (x, hi); + if (hi != 0) + x->exp += xexp; + store_ext_val (y, lo); + if (lo != 0) + y->exp += xexp; +} + +long double +__fmal (long double x, long double y, long double z) +{ + double xhi, xlo, yhi, ylo, zhi, zlo; + int64_t hx, hy, hz; + int xexp, yexp, zexp; + double scale_val; + int scale_exp; + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + xexp = (hx & 0x7ff0000000000000LL) >> 52; + ldbl_unpack (y, &yhi, &ylo); + EXTRACT_WORDS64 (hy, yhi); + yexp = (hy & 0x7ff0000000000000LL) >> 52; + ldbl_unpack (z, &zhi, &zlo); + EXTRACT_WORDS64 (hz, zhi); + zexp = (hz & 0x7ff0000000000000LL) >> 52; + + /* If z is Inf or NaN, but x and y are finite, avoid any exceptions + from computing x * y. */ + if (zexp == 0x7ff && xexp != 0x7ff && yexp != 0x7ff) + return (z + x) + y; + + /* If z is zero and x are y are nonzero, compute the result as x * y + to avoid the wrong sign of a zero result if x * y underflows to + 0. */ + if (z == 0 && x != 0 && y != 0) + return x * y; + + /* If x or y or z is Inf/NaN, or if x * y is zero, compute as x * y + + z. */ + if (xexp == 0x7ff || yexp == 0x7ff || zexp == 0x7ff + || x == 0 || y == 0) + return (x * y) + z; + + { + SET_RESTORE_ROUND (FE_TONEAREST); + + ext_val vals[10]; + store_ext_val (&vals[0], zhi); + store_ext_val (&vals[1], zlo); + mul_ext_val (&vals[2], &vals[3], xhi, yhi); + mul_ext_val (&vals[4], &vals[5], xhi, ylo); + mul_ext_val (&vals[6], &vals[7], xlo, yhi); + mul_ext_val (&vals[8], &vals[9], xlo, ylo); + qsort (vals, 10, sizeof (ext_val), compare); + /* Add up the values so that each element of VALS has absolute + value at most equal to the last set bit of the next nonzero + element. */ + for (size_t i = 0; i <= 8; i++) + { + add_split_ext (&vals[i + 1], &vals[i]); + qsort (vals + i + 1, 9 - i, sizeof (ext_val), compare); + } + /* Add up the values in the other direction, so that each element + of VALS has absolute value less than 5ulp of the next + value. */ + size_t dstpos = 9; + for (size_t i = 1; i <= 9; i++) + { + if (vals[dstpos].val == 0) + { + vals[dstpos] = vals[9 - i]; + vals[9 - i].val = 0; + vals[9 - i].exp = 0; + } + else + { + add_split_ext (&vals[dstpos], &vals[9 - i]); + if (vals[9 - i].val != 0) + { + if (9 - i < dstpos - 1) + { + vals[dstpos - 1] = vals[9 - i]; + vals[9 - i].val = 0; + vals[9 - i].exp = 0; + } + dstpos--; + } + } + } + /* If the result is an exact zero, it results from adding two + values with opposite signs; recompute in the original rounding + mode. */ + if (vals[9].val == 0) + goto zero_out; + /* Adding the top three values will now give a result as accurate + as the underlying long double arithmetic. */ + add_split_ext (&vals[9], &vals[8]); + if (compare (&vals[8], &vals[7]) < 0) + { + ext_val tmp = vals[7]; + vals[7] = vals[8]; + vals[8] = tmp; + } + add_split_ext (&vals[8], &vals[7]); + add_split_ext (&vals[9], &vals[8]); + if (vals[9].exp > DBL_MAX_EXP || vals[9].exp < DBL_MIN_EXP) + { + /* Overflow or underflow, with the result depending on the + original rounding mode, but not on the low part computed + here. */ + scale_val = vals[9].val; + scale_exp = vals[9].exp; + goto scale_out; + } + double hi = __scalbn (vals[9].val, vals[9].exp); + double lo = __scalbn (vals[8].val, vals[8].exp); + /* It is possible that the low part became subnormal and was + rounded so that the result is no longer canonical. */ + ldbl_canonicalize (&hi, &lo); + long double ret = ldbl_pack (hi, lo); + math_check_force_underflow (ret); + return ret; + } + + scale_out: + scale_val = math_opt_barrier (scale_val); + scale_val = __scalbn (scale_val, scale_exp); + if (fabs (scale_val) == DBL_MAX) + return __copysignl (LDBL_MAX, scale_val); + math_check_force_underflow (scale_val); + return scale_val; + + zero_out:; + double zero = 0.0; + zero = math_opt_barrier (zero); + return zero - zero; +} +#if IS_IN (libm) +long_double_symbol (libm, __fmal, fmal); +#else +long_double_symbol (libc, __fmal, fmal); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fpclassifyl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fpclassifyl.c new file mode 100644 index 0000000000..82d520bc7f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fpclassifyl.c @@ -0,0 +1,97 @@ +/* Return classification value corresponding to argument. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz>, 1999. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> +#include <math_ldbl_opt.h> + + /* + * hx lx + * +NaN 7ffn nnnn nnnn nnnn xxxx xxxx xxxx xxxx + * -NaN fffn nnnn nnnn nnnn xxxx xxxx xxxx xxxx + * +Inf 7ff0 0000 0000 0000 xxxx xxxx xxxx xxxx + * -Inf fff0 0000 0000 0000 xxxx xxxx xxxx xxxx + * +0 0000 0000 0000 0000 xxxx xxxx xxxx xxxx + * -0 8000 0000 0000 0000 xxxx xxxx xxxx xxxx + * +normal 0360 0000 0000 0000 0000 0000 0000 0000 (smallest) + * -normal 8360 0000 0000 0000 0000 0000 0000 0000 (smallest) + * +normal 7fef ffff ffff ffff 7c8f ffff ffff fffe (largest) + * +normal ffef ffff ffff ffff fc8f ffff ffff fffe (largest) + * +denorm 0360 0000 0000 0000 8000 0000 0000 0001 (largest) + * -denorm 8360 0000 0000 0000 0000 0000 0000 0001 (largest) + * +denorm 000n nnnn nnnn nnnn xxxx xxxx xxxx xxxx + * -denorm 800n nnnn nnnn nnnn xxxx xxxx xxxx xxxx + */ + +int +___fpclassifyl (long double x) +{ + u_int64_t hx, lx; + int retval = FP_NORMAL; + double xhi, xlo; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + if ((hx & 0x7ff0000000000000ULL) == 0x7ff0000000000000ULL) { + /* +/-NaN or +/-Inf */ + if (hx & 0x000fffffffffffffULL) { + /* +/-NaN */ + retval = FP_NAN; + } else { + retval = FP_INFINITE; + } + } else { + /* +/-zero or +/- normal or +/- denormal */ + if (hx & 0x7fffffffffffffffULL) { + /* +/- normal or +/- denormal */ + if ((hx & 0x7ff0000000000000ULL) > 0x0360000000000000ULL) { + /* +/- normal */ + retval = FP_NORMAL; + } else { + if ((hx & 0x7ff0000000000000ULL) == 0x0360000000000000ULL) { + EXTRACT_WORDS64 (lx, xlo); + if ((lx & 0x7fffffffffffffff) /* lower is non-zero */ + && ((lx^hx) & 0x8000000000000000ULL)) { /* and sign differs */ + /* +/- denormal */ + retval = FP_SUBNORMAL; + } else { + /* +/- normal */ + retval = FP_NORMAL; + } + } else { + /* +/- denormal */ + retval = FP_SUBNORMAL; + } + } + } else { + /* +/- zero */ + retval = FP_ZERO; + } + } + + return retval; +} +long_double_symbol (libm, ___fpclassifyl, __fpclassifyl); +#ifdef __LONG_DOUBLE_MATH_OPTIONAL +libm_hidden_ver (___fpclassifyl, __fpclassifyl) +#else +libm_hidden_def (__fpclassifyl) +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_frexpl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_frexpl.c new file mode 100644 index 0000000000..210c5d2ed4 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_frexpl.c @@ -0,0 +1,148 @@ +/* s_frexpl.c -- long double version of s_frexp.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * for non-zero x + * x = frexpl(arg,&exp); + * return a long double fp quantity x such that 0.5 <= |x| <1.0 + * and the corresponding binary exponent "exp". That is + * arg = x*2^exp. + * If arg is inf, 0.0, or NaN, then frexpl(arg,&exp) returns arg + * with *exp=0. + */ + +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +long double __frexpl(long double x, int *eptr) +{ + uint64_t hx, lx, ix, ixl; + int64_t explo, expon; + double xhi, xlo; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + ixl = 0x7fffffffffffffffULL & lx; + ix = 0x7fffffffffffffffULL & hx; + expon = 0; + if (ix >= 0x7ff0000000000000ULL || ix == 0) + { + /* 0,inf,nan. */ + *eptr = expon; + return x + x; + } + expon = ix >> 52; + if (expon == 0) + { + /* Denormal high double, the low double must be 0.0. */ + int cnt; + + /* Normalize. */ + if (sizeof (ix) == sizeof (long)) + cnt = __builtin_clzl (ix); + else if ((ix >> 32) != 0) + cnt = __builtin_clzl ((long) (ix >> 32)); + else + cnt = __builtin_clzl ((long) ix) + 32; + cnt = cnt - 12; + expon -= cnt; + ix <<= cnt + 1; + } + expon -= 1022; + ix &= 0x000fffffffffffffULL; + hx &= 0x8000000000000000ULL; + hx |= (1022LL << 52) | ix; + + if (ixl != 0) + { + /* If the high double is an exact power of two and the low + double has the opposite sign, then the exponent calculated + from the high double is one too big. */ + if (ix == 0 + && (int64_t) (hx ^ lx) < 0) + { + hx += 1LL << 52; + expon -= 1; + } + + explo = ixl >> 52; + if (explo == 0) + { + /* The low double started out as a denormal. Normalize its + mantissa and adjust the exponent. */ + int cnt; + + if (sizeof (ixl) == sizeof (long)) + cnt = __builtin_clzl (ixl); + else if ((ixl >> 32) != 0) + cnt = __builtin_clzl ((long) (ixl >> 32)); + else + cnt = __builtin_clzl ((long) ixl) + 32; + cnt = cnt - 12; + explo -= cnt; + ixl <<= cnt + 1; + } + + /* With variable precision we can't assume much about the + magnitude of the returned low double. It may even be a + denormal. */ + explo -= expon; + ixl &= 0x000fffffffffffffULL; + lx &= 0x8000000000000000ULL; + if (explo <= 0) + { + /* Handle denormal low double. */ + if (explo > -52) + { + ixl |= 1LL << 52; + ixl >>= 1 - explo; + } + else + { + ixl = 0; + lx = 0; + if ((hx & 0x7ff0000000000000ULL) == (1023LL << 52)) + { + /* Oops, the adjustment we made above for values a + little smaller than powers of two turned out to + be wrong since the returned low double will be + zero. This can happen if the input was + something weird like 0x1p1000 - 0x1p-1000. */ + hx -= 1LL << 52; + expon += 1; + } + } + explo = 0; + } + lx |= (explo << 52) | ixl; + } + + INSERT_WORDS64 (xhi, hx); + INSERT_WORDS64 (xlo, lx); + x = ldbl_pack (xhi, xlo); + *eptr = expon; + return x; +} +#if IS_IN (libm) +long_double_symbol (libm, __frexpl, frexpl); +#else +long_double_symbol (libc, __frexpl, frexpl); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fromfpl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fromfpl.c new file mode 100644 index 0000000000..e323b4c25b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fromfpl.c @@ -0,0 +1,4 @@ +#define UNSIGNED 0 +#define INEXACT 0 +#define FUNC fromfpl +#include <s_fromfpl_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fromfpl_main.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fromfpl_main.c new file mode 100644 index 0000000000..8b9108e84d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fromfpl_main.c @@ -0,0 +1,147 @@ +/* Round to integer type. ldbl-128ibm version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <errno.h> +#include <fenv.h> +#include <math.h> +#include <math_private.h> +#include <stdbool.h> +#include <stdint.h> + +#define BIAS 0x3ff +#define MANT_DIG 53 + +#if UNSIGNED +# define RET_TYPE uintmax_t +#else +# define RET_TYPE intmax_t +#endif + +#include <fromfp.h> + +RET_TYPE +FUNC (long double x, int round, unsigned int width) +{ + double hi, lo; + if (width > INTMAX_WIDTH) + width = INTMAX_WIDTH; + uint64_t hx, lx; + ldbl_unpack (x, &hi, &lo); + EXTRACT_WORDS64 (hx, hi); + EXTRACT_WORDS64 (lx, lo); + bool negative = (hx & 0x8000000000000000ULL) != 0; + bool lo_negative = (lx & 0x8000000000000000ULL) != 0; + if (width == 0) + return fromfp_domain_error (negative, width); + hx &= 0x7fffffffffffffffULL; + lx &= 0x7fffffffffffffffULL; + if ((hx | lx) == 0) + return 0; + int hi_exponent = hx >> (MANT_DIG - 1); + hi_exponent -= BIAS; + int exponent = hi_exponent; + hx &= ((1ULL << (MANT_DIG - 1)) - 1); + if (hx == 0 && lx != 0 && lo_negative != negative) + exponent--; + int max_exponent = fromfp_max_exponent (negative, width); + if (exponent > max_exponent) + return fromfp_domain_error (negative, width); + int lo_exponent = lx >> (MANT_DIG - 1); + lo_exponent -= BIAS; + + /* Convert the high part to integer. */ + hx |= 1ULL << (MANT_DIG - 1); + uintmax_t uret; + bool half_bit, more_bits; + if (hi_exponent >= MANT_DIG - 1) + { + uret = hx; + uret <<= hi_exponent - (MANT_DIG - 1); + half_bit = false; + more_bits = false; + } + else if (hi_exponent >= -1) + { + uint64_t h = 1ULL << (MANT_DIG - 2 - hi_exponent); + half_bit = (hx & h) != 0; + more_bits = (hx & (h - 1)) != 0; + uret = hx >> (MANT_DIG - 1 - hi_exponent); + } + else + { + uret = 0; + half_bit = false; + more_bits = true; + } + + /* Likewise, the low part. */ + if (lx != 0) + { + uintmax_t lo_uret; + bool lo_half_bit, lo_more_bits; + lx &= ((1ULL << (MANT_DIG - 1)) - 1); + lx |= 1ULL << (MANT_DIG - 1); + /* The high part exponent is at most 64, so the low part + exponent is at most 11. */ + if (lo_exponent >= -1) + { + uint64_t h = 1ULL << (MANT_DIG - 2 - lo_exponent); + lo_half_bit = (lx & h) != 0; + lo_more_bits = (lx & (h - 1)) != 0; + lo_uret = lx >> (MANT_DIG - 1 - lo_exponent); + } + else + { + lo_uret = 0; + lo_half_bit = false; + lo_more_bits = true; + } + if (lo_negative == negative) + { + uret += lo_uret; + half_bit |= lo_half_bit; + more_bits |= lo_more_bits; + } + else + { + uret -= lo_uret; + if (lo_half_bit) + { + uret--; + half_bit = true; + } + if (lo_more_bits && !more_bits) + { + if (half_bit) + { + half_bit = false; + more_bits = true; + } + else + { + uret--; + half_bit = true; + more_bits = true; + } + } + } + } + + return fromfp_round_and_return (negative, uret, half_bit, more_bits, round, + exponent, max_exponent, width); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fromfpxl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fromfpxl.c new file mode 100644 index 0000000000..2f3189d7de --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_fromfpxl.c @@ -0,0 +1,4 @@ +#define UNSIGNED 0 +#define INEXACT 1 +#define FUNC fromfpxl +#include <s_fromfpl_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_getpayloadl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_getpayloadl.c new file mode 100644 index 0000000000..420b17837e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_getpayloadl.c @@ -0,0 +1,34 @@ +/* Get NaN payload. ldbl-128ibm version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fix-int-fp-convert-zero.h> +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +long double +getpayloadl (const long double *x) +{ + double xhi = ldbl_high (*x); + uint64_t ix; + EXTRACT_WORDS64 (ix, xhi); + ix &= 0x7ffffffffffffULL; + if (FIX_INT_FP_CONVERT_ZERO && ix == 0) + return 0.0L; + return (long double) ix; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_iscanonicall.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_iscanonicall.c new file mode 100644 index 0000000000..24999a920d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_iscanonicall.c @@ -0,0 +1,60 @@ +/* Test whether long double value is canonical. ldbl-128ibm version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +int +__iscanonicall (long double x) +{ + double xhi, xlo; + uint64_t hx, lx; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + int64_t ix = hx & 0x7fffffffffffffffULL; + int64_t iy = lx & 0x7fffffffffffffffULL; + int hexp = (ix & 0x7ff0000000000000LL) >> 52; + int lexp = (iy & 0x7ff0000000000000LL) >> 52; + + if (iy == 0) + /* Low part 0 is always OK. */ + return 1; + + if (hexp == 0x7ff) + /* If a NaN, the low part does not matter. If an infinity, the + low part must be 0, in which case we have already returned. */ + return ix != 0x7ff0000000000000LL; + + /* The high part is finite and the low part is nonzero. There must + be sufficient difference between the exponents. */ + bool low_p2; + if (lexp == 0) + { + /* Adjust the exponent for subnormal low part. */ + lexp = 12 - __builtin_clzll (iy); + low_p2 = iy == (1LL << (51 + lexp)); + } + else + low_p2 = (iy & 0xfffffffffffffLL) == 0; + int expdiff = hexp - lexp; + return expdiff > 53 || (expdiff == 53 && low_p2 && (ix & 1) == 0); +} +libm_hidden_def (__iscanonicall) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_isinfl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_isinfl.c new file mode 100644 index 0000000000..730aa4d8d1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_isinfl.c @@ -0,0 +1,40 @@ +/* + * Written by J.T. Conklin <jtc@netbsd.org>. + * Change for long double by Jakub Jelinek <jj@ultra.linux.cz> + * Public domain. + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * isinfl(x) returns 1 if x is inf, -1 if x is -inf, else 0; + * no branching! + * slightly dodgy in relying on signed shift right copying sign bit + */ + +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +int +___isinfl (long double x) +{ + double xhi; + int64_t hx, mask; + + xhi = ldbl_high (x); + EXTRACT_WORDS64 (hx, xhi); + + mask = (hx & 0x7fffffffffffffffLL) ^ 0x7ff0000000000000LL; + mask |= -mask; + mask >>= 63; + return ~mask & (hx >> 62); +} +hidden_ver (___isinfl, __isinfl) +#if !IS_IN (libm) +weak_alias (___isinfl, ____isinfl) +long_double_symbol (libc, ___isinfl, isinfl); +long_double_symbol (libc, ____isinfl, __isinfl); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_isnanl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_isnanl.c new file mode 100644 index 0000000000..9980875df2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_isnanl.c @@ -0,0 +1,46 @@ +/* s_isnanl.c -- long double version of s_isnan.c. + * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * isnanl(x) returns 1 is x is nan, else 0; + * no branching! + */ + +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +int +___isnanl (long double x) +{ + uint64_t hx; + double xhi; + + xhi = ldbl_high (x); + EXTRACT_WORDS64 (hx, xhi); + hx &= 0x7fffffffffffffffLL; + hx = 0x7ff0000000000000LL - hx; + return (int) (hx >> 63); +} +hidden_ver (___isnanl, __isnanl) +#if !IS_IN (libm) +weak_alias (___isnanl, ____isnanl) +long_double_symbol (libc, ___isnanl, isnanl); +long_double_symbol (libc, ____isnanl, __isnanl); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_issignalingl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_issignalingl.c new file mode 100644 index 0000000000..feb7edea5d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_issignalingl.c @@ -0,0 +1,49 @@ +/* Test for signaling NaN. + Copyright (C) 2013-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> + +int +__issignalingl (long double x) +{ + uint64_t xi; + /* For inspecting NaN status, we only have to look at the first of the pair + of IEEE 754 64-bit precision numbers. */ + double xhi; + + xhi = ldbl_high (x); + EXTRACT_WORDS64 (xi, xhi); +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN +# error untested + /* We only have to care about the high-order bit of x's significand, because + having it set (sNaN) already makes the significand different from that + used to designate infinity. */ + return (xi & UINT64_C (0x7ff8000000000000)) == UINT64_C (0x7ff8000000000000); +#else + /* To keep the following comparison simple, toggle the quiet/signaling bit, + so that it is set for sNaNs. This is inverse to IEEE 754-2008 (as well as + common practice for IEEE 754-1985). */ + xi ^= UINT64_C (0x0008000000000000); + /* We have to compare for greater (instead of greater or equal), because x's + significand being all-zero designates infinity not NaN. */ + return (xi & UINT64_C (0x7fffffffffffffff)) > UINT64_C (0x7ff8000000000000); +#endif +} +libm_hidden_def (__issignalingl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_llrintl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_llrintl.c new file mode 100644 index 0000000000..fbf38bf717 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_llrintl.c @@ -0,0 +1,140 @@ +/* Round to long long int long double floating-point values. + IBM extended format long double version. + Copyright (C) 2006-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <fenv.h> +#include <math_ldbl_opt.h> +#include <float.h> +#include <ieee754.h> + + +long long +__llrintl (long double x) +{ + double xh, xl; + long long res, hi, lo; + int save_round; + + ldbl_unpack (x, &xh, &xl); + + /* Limit the range of values handled by the conversion to long long. + We do this because we aren't sure whether that conversion properly + raises FE_INVALID. */ + if (__builtin_expect + ((__builtin_fabs (xh) <= -(double) (-__LONG_LONG_MAX__ - 1)), 1) +#if !defined (FE_INVALID) + || 1 +#endif + ) + { + save_round = fegetround (); + + if (__glibc_unlikely ((xh == -(double) (-__LONG_LONG_MAX__ - 1)))) + { + /* When XH is 9223372036854775808.0, converting to long long will + overflow, resulting in an invalid operation. However, XL might + be negative and of sufficient magnitude that the overall long + double is in fact in range. Avoid raising an exception. In any + case we need to convert this value specially, because + the converted value is not exactly represented as a double + thus subtracting HI from XH suffers rounding error. */ + hi = __LONG_LONG_MAX__; + xh = 1.0; + } + else + { + hi = (long long) xh; + xh -= hi; + } + ldbl_canonicalize (&xh, &xl); + + lo = (long long) xh; + + /* Peg at max/min values, assuming that the above conversions do so. + Strictly speaking, we can return anything for values that overflow, + but this is more useful. */ + res = hi + lo; + + /* This is just sign(hi) == sign(lo) && sign(res) != sign(hi). */ + if (__glibc_unlikely (((~(hi ^ lo) & (res ^ hi)) < 0))) + goto overflow; + + xh -= lo; + ldbl_canonicalize (&xh, &xl); + + hi = res; + switch (save_round) + { + case FE_TONEAREST: + if (fabs (xh) < 0.5 + || (fabs (xh) == 0.5 + && ((xh > 0.0 && xl < 0.0) + || (xh < 0.0 && xl > 0.0) + || (xl == 0.0 && (res & 1) == 0)))) + return res; + + if (xh < 0.0) + res -= 1; + else + res += 1; + break; + + case FE_TOWARDZERO: + if (res > 0 && (xh < 0.0 || (xh == 0.0 && xl < 0.0))) + res -= 1; + else if (res < 0 && (xh > 0.0 || (xh == 0.0 && xl > 0.0))) + res += 1; + return res; + break; + + case FE_UPWARD: + if (xh > 0.0 || (xh == 0.0 && xl > 0.0)) + res += 1; + break; + + case FE_DOWNWARD: + if (xh < 0.0 || (xh == 0.0 && xl < 0.0)) + res -= 1; + break; + } + + if (__glibc_unlikely (((~(hi ^ (res - hi)) & (res ^ hi)) < 0))) + goto overflow; + + return res; + } + else + { + if (xh > 0.0) + hi = __LONG_LONG_MAX__; + else if (xh < 0.0) + hi = -__LONG_LONG_MAX__ - 1; + else + /* Nan */ + hi = 0; + } + +overflow: +#ifdef FE_INVALID + feraiseexcept (FE_INVALID); +#endif + return hi; +} + +long_double_symbol (libm, __llrintl, llrintl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_llroundl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_llroundl.c new file mode 100644 index 0000000000..609cc864de --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_llroundl.c @@ -0,0 +1,120 @@ +/* Round to long long int long double floating-point values. + IBM extended format long double version. + Copyright (C) 2006-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <fenv.h> +#include <math_ldbl_opt.h> +#include <float.h> +#include <ieee754.h> + +long long +__llroundl (long double x) +{ + double xh, xl; + long long res, hi, lo; + + ldbl_unpack (x, &xh, &xl); + + /* Limit the range of values handled by the conversion to long long. + We do this because we aren't sure whether that conversion properly + raises FE_INVALID. */ + if (__builtin_expect + ((__builtin_fabs (xh) <= -(double) (-__LONG_LONG_MAX__ - 1)), 1) +#if !defined (FE_INVALID) + || 1 +#endif + ) + { + if (__glibc_unlikely ((xh == -(double) (-__LONG_LONG_MAX__ - 1)))) + { + /* When XH is 9223372036854775808.0, converting to long long will + overflow, resulting in an invalid operation. However, XL might + be negative and of sufficient magnitude that the overall long + double is in fact in range. Avoid raising an exception. In any + case we need to convert this value specially, because + the converted value is not exactly represented as a double + thus subtracting HI from XH suffers rounding error. */ + hi = __LONG_LONG_MAX__; + xh = 1.0; + } + else + { + hi = (long long) xh; + xh -= hi; + } + ldbl_canonicalize (&xh, &xl); + + lo = (long long) xh; + + /* Peg at max/min values, assuming that the above conversions do so. + Strictly speaking, we can return anything for values that overflow, + but this is more useful. */ + res = hi + lo; + + /* This is just sign(hi) == sign(lo) && sign(res) != sign(hi). */ + if (__glibc_unlikely (((~(hi ^ lo) & (res ^ hi)) < 0))) + goto overflow; + + xh -= lo; + ldbl_canonicalize (&xh, &xl); + + hi = res; + if (xh > 0.5) + { + res += 1; + } + else if (xh == 0.5) + { + if (xl > 0.0 || (xl == 0.0 && res >= 0)) + res += 1; + } + else if (-xh > 0.5) + { + res -= 1; + } + else if (-xh == 0.5) + { + if (xl < 0.0 || (xl == 0.0 && res <= 0)) + res -= 1; + } + + if (__glibc_unlikely (((~(hi ^ (res - hi)) & (res ^ hi)) < 0))) + goto overflow; + + return res; + } + else + { + if (xh > 0.0) + hi = __LONG_LONG_MAX__; + else if (xh < 0.0) + hi = -__LONG_LONG_MAX__ - 1; + else + /* Nan */ + hi = 0; + } + +overflow: +#ifdef FE_INVALID + feraiseexcept (FE_INVALID); +#endif + return hi; +} + +long_double_symbol (libm, __llroundl, llroundl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_log1pl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_log1pl.c new file mode 100644 index 0000000000..5457892a98 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_log1pl.c @@ -0,0 +1,249 @@ +/* log1pl.c + * + * Relative error logarithm + * Natural logarithm of 1+x, 128-bit long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, log1pl(); + * + * y = log1pl( x ); + * + * + * + * DESCRIPTION: + * + * Returns the base e (2.718...) logarithm of 1+x. + * + * The argument 1+x is separated into its exponent and fractional + * parts. If the exponent is between -1 and +1, the logarithm + * of the fraction is approximated by + * + * log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x). + * + * Otherwise, setting z = 2(w-1)/(w+1), + * + * log(w) = z + z^3 P(z)/Q(z). + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -1, 8 100000 1.9e-34 4.3e-35 + */ + +/* Copyright 2001 by Stephen L. Moshier + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + + +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +/* Coefficients for log(1+x) = x - x^2 / 2 + x^3 P(x)/Q(x) + * 1/sqrt(2) <= 1+x < sqrt(2) + * Theoretical peak relative error = 5.3e-37, + * relative peak error spread = 2.3e-14 + */ +static const long double + P12 = 1.538612243596254322971797716843006400388E-6L, + P11 = 4.998469661968096229986658302195402690910E-1L, + P10 = 2.321125933898420063925789532045674660756E1L, + P9 = 4.114517881637811823002128927449878962058E2L, + P8 = 3.824952356185897735160588078446136783779E3L, + P7 = 2.128857716871515081352991964243375186031E4L, + P6 = 7.594356839258970405033155585486712125861E4L, + P5 = 1.797628303815655343403735250238293741397E5L, + P4 = 2.854829159639697837788887080758954924001E5L, + P3 = 3.007007295140399532324943111654767187848E5L, + P2 = 2.014652742082537582487669938141683759923E5L, + P1 = 7.771154681358524243729929227226708890930E4L, + P0 = 1.313572404063446165910279910527789794488E4L, + /* Q12 = 1.000000000000000000000000000000000000000E0L, */ + Q11 = 4.839208193348159620282142911143429644326E1L, + Q10 = 9.104928120962988414618126155557301584078E2L, + Q9 = 9.147150349299596453976674231612674085381E3L, + Q8 = 5.605842085972455027590989944010492125825E4L, + Q7 = 2.248234257620569139969141618556349415120E5L, + Q6 = 6.132189329546557743179177159925690841200E5L, + Q5 = 1.158019977462989115839826904108208787040E6L, + Q4 = 1.514882452993549494932585972882995548426E6L, + Q3 = 1.347518538384329112529391120390701166528E6L, + Q2 = 7.777690340007566932935753241556479363645E5L, + Q1 = 2.626900195321832660448791748036714883242E5L, + Q0 = 3.940717212190338497730839731583397586124E4L; + +/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), + * where z = 2(x-1)/(x+1) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 1.1e-35, + * relative peak error spread 1.1e-9 + */ +static const long double + R5 = -8.828896441624934385266096344596648080902E-1L, + R4 = 8.057002716646055371965756206836056074715E1L, + R3 = -2.024301798136027039250415126250455056397E3L, + R2 = 2.048819892795278657810231591630928516206E4L, + R1 = -8.977257995689735303686582344659576526998E4L, + R0 = 1.418134209872192732479751274970992665513E5L, + /* S6 = 1.000000000000000000000000000000000000000E0L, */ + S5 = -1.186359407982897997337150403816839480438E2L, + S4 = 3.998526750980007367835804959888064681098E3L, + S3 = -5.748542087379434595104154610899551484314E4L, + S2 = 4.001557694070773974936904547424676279307E5L, + S1 = -1.332535117259762928288745111081235577029E6L, + S0 = 1.701761051846631278975701529965589676574E6L; + +/* C1 + C2 = ln 2 */ +static const long double C1 = 6.93145751953125E-1L; +static const long double C2 = 1.428606820309417232121458176568075500134E-6L; + +static const long double sqrth = 0.7071067811865475244008443621048490392848L; +/* ln (2^16384 * (1 - 2^-113)) */ +static const long double zero = 0.0L; + + +long double +__log1pl (long double xm1) +{ + long double x, y, z, r, s; + double xhi; + int32_t hx, lx; + int e; + + /* Test for NaN or infinity input. */ + xhi = ldbl_high (xm1); + EXTRACT_WORDS (hx, lx, xhi); + if (hx >= 0x7ff00000) + return xm1 + xm1; + + /* log1p(+- 0) = +- 0. */ + if (((hx & 0x7fffffff) | lx) == 0) + return xm1; + + if (xm1 >= 0x1p107L) + x = xm1; + else + x = xm1 + 1.0L; + + /* log1p(-1) = -inf */ + if (x <= 0.0L) + { + if (x == 0.0L) + return (-1.0L / 0.0L); + else + return (zero / (x - x)); + } + + /* Separate mantissa from exponent. */ + + /* Use frexp used so that denormal numbers will be handled properly. */ + x = __frexpl (x, &e); + + /* Logarithm using log(x) = z + z^3 P(z^2)/Q(z^2), + where z = 2(x-1)/x+1). */ + if ((e > 2) || (e < -2)) + { + if (x < sqrth) + { /* 2( 2x-1 )/( 2x+1 ) */ + e -= 1; + z = x - 0.5L; + y = 0.5L * z + 0.5L; + } + else + { /* 2 (x-1)/(x+1) */ + z = x - 0.5L; + z -= 0.5L; + y = 0.5L * x + 0.5L; + } + x = z / y; + z = x * x; + r = ((((R5 * z + + R4) * z + + R3) * z + + R2) * z + + R1) * z + + R0; + s = (((((z + + S5) * z + + S4) * z + + S3) * z + + S2) * z + + S1) * z + + S0; + z = x * (z * r / s); + z = z + e * C2; + z = z + x; + z = z + e * C1; + return (z); + } + + + /* Logarithm using log(1+x) = x - .5x^2 + x^3 P(x)/Q(x). */ + + if (x < sqrth) + { + e -= 1; + if (e != 0) + x = 2.0L * x - 1.0L; /* 2x - 1 */ + else + x = xm1; + } + else + { + if (e != 0) + x = x - 1.0L; + else + x = xm1; + } + z = x * x; + r = (((((((((((P12 * x + + P11) * x + + P10) * x + + P9) * x + + P8) * x + + P7) * x + + P6) * x + + P5) * x + + P4) * x + + P3) * x + + P2) * x + + P1) * x + + P0; + s = (((((((((((x + + Q11) * x + + Q10) * x + + Q9) * x + + Q8) * x + + Q7) * x + + Q6) * x + + Q5) * x + + Q4) * x + + Q3) * x + + Q2) * x + + Q1) * x + + Q0; + y = x * (z * r / s); + y = y + e * C2; + z = y - 0.5L * z; + z = z + x; + z = z + e * C1; + return (z); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_logbl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_logbl.c new file mode 100644 index 0000000000..3c07c5e8e2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_logbl.c @@ -0,0 +1,63 @@ +/* s_logbl.c -- long double version of s_logb.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * long double logbl(x) + * IEEE 754 logb. Included to pass IEEE test suite. Not recommend. + * Use ilogb instead. + */ + +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> +#include <fix-int-fp-convert-zero.h> + +long double +__logbl (long double x) +{ + int64_t hx, hxs, rhx; + double xhi, xlo; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + hxs = hx; + hx &= 0x7fffffffffffffffLL; /* high |x| */ + if (hx == 0) + return -1.0 / fabs (x); + if (hx >= 0x7ff0000000000000LL) + return x * x; + if (__glibc_unlikely ((rhx = hx >> 52) == 0)) + { + /* POSIX specifies that denormal number is treated as + though it were normalized. */ + rhx -= __builtin_clzll (hx) - 12; + } + else if ((hx & 0x000fffffffffffffLL) == 0) + { + /* If the high part is a power of 2, and the low part is nonzero + with the opposite sign, the low part affects the + exponent. */ + int64_t lx; + EXTRACT_WORDS64 (lx, xlo); + if ((hxs ^ lx) < 0 && (lx & 0x7fffffffffffffffLL) != 0) + rhx--; + } + if (FIX_INT_FP_CONVERT_ZERO && rhx == 1023) + return 0.0L; + return (long double) (rhx - 1023); +} +#ifndef __logbl +long_double_symbol (libm, __logbl, logbl); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_lrintl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_lrintl.c new file mode 100644 index 0000000000..b404cab8e3 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_lrintl.c @@ -0,0 +1,155 @@ +/* Round to long int long double floating-point values. + IBM extended format long double version. + Copyright (C) 2006-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <fenv.h> +#include <math_ldbl_opt.h> +#include <float.h> +#include <ieee754.h> + + +long +__lrintl (long double x) +{ + double xh, xl; + long res, hi, lo; + int save_round; + + ldbl_unpack (x, &xh, &xl); + + /* Limit the range of values handled by the conversion to long. + We do this because we aren't sure whether that conversion properly + raises FE_INVALID. */ + if ( +#if __LONG_MAX__ == 2147483647 + __builtin_expect + ((__builtin_fabs (xh) <= (double) __LONG_MAX__ + 2), 1) +#else + __builtin_expect + ((__builtin_fabs (xh) <= -(double) (-__LONG_MAX__ - 1)), 1) +#endif +#if !defined (FE_INVALID) + || 1 +#endif + ) + { + save_round = fegetround (); + +#if __LONG_MAX__ == 2147483647 + long long llhi = (long long) xh; + if (llhi != (long) llhi) + hi = llhi < 0 ? -__LONG_MAX__ - 1 : __LONG_MAX__; + else + hi = llhi; + xh -= hi; +#else + if (__glibc_unlikely ((xh == -(double) (-__LONG_MAX__ - 1)))) + { + /* When XH is 9223372036854775808.0, converting to long long will + overflow, resulting in an invalid operation. However, XL might + be negative and of sufficient magnitude that the overall long + double is in fact in range. Avoid raising an exception. In any + case we need to convert this value specially, because + the converted value is not exactly represented as a double + thus subtracting HI from XH suffers rounding error. */ + hi = __LONG_MAX__; + xh = 1.0; + } + else + { + hi = (long) xh; + xh -= hi; + } +#endif + ldbl_canonicalize (&xh, &xl); + + lo = (long) xh; + + /* Peg at max/min values, assuming that the above conversions do so. + Strictly speaking, we can return anything for values that overflow, + but this is more useful. */ + res = hi + lo; + + /* This is just sign(hi) == sign(lo) && sign(res) != sign(hi). */ + if (__glibc_unlikely (((~(hi ^ lo) & (res ^ hi)) < 0))) + goto overflow; + + xh -= lo; + ldbl_canonicalize (&xh, &xl); + + hi = res; + switch (save_round) + { + case FE_TONEAREST: + if (fabs (xh) < 0.5 + || (fabs (xh) == 0.5 + && ((xh > 0.0 && xl < 0.0) + || (xh < 0.0 && xl > 0.0) + || (xl == 0.0 && (res & 1) == 0)))) + return res; + + if (xh < 0.0) + res -= 1; + else + res += 1; + break; + + case FE_TOWARDZERO: + if (res > 0 && (xh < 0.0 || (xh == 0.0 && xl < 0.0))) + res -= 1; + else if (res < 0 && (xh > 0.0 || (xh == 0.0 && xl > 0.0))) + res += 1; + return res; + break; + + case FE_UPWARD: + if (xh > 0.0 || (xh == 0.0 && xl > 0.0)) + res += 1; + break; + + case FE_DOWNWARD: + if (xh < 0.0 || (xh == 0.0 && xl < 0.0)) + res -= 1; + break; + } + + if (__glibc_unlikely (((~(hi ^ (res - hi)) & (res ^ hi)) < 0))) + goto overflow; + + return res; + } + else + { + if (xh > 0.0) + hi = __LONG_MAX__; + else if (xh < 0.0) + hi = -__LONG_MAX__ - 1; + else + /* Nan */ + hi = 0; + } + +overflow: +#ifdef FE_INVALID + feraiseexcept (FE_INVALID); +#endif + return hi; +} + +long_double_symbol (libm, __lrintl, lrintl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_lroundl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_lroundl.c new file mode 100644 index 0000000000..f9ae37e844 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_lroundl.c @@ -0,0 +1,135 @@ +/* Round to long int long double floating-point values. + IBM extended format long double version. + Copyright (C) 2006-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <fenv.h> +#include <math_ldbl_opt.h> +#include <float.h> +#include <ieee754.h> + +long +__lroundl (long double x) +{ + double xh, xl; + long res, hi, lo; + + ldbl_unpack (x, &xh, &xl); + + /* Limit the range of values handled by the conversion to long. + We do this because we aren't sure whether that conversion properly + raises FE_INVALID. */ + if ( +#if __LONG_MAX__ == 2147483647 + __builtin_expect + ((__builtin_fabs (xh) <= (double) __LONG_MAX__ + 2), 1) +#else + __builtin_expect + ((__builtin_fabs (xh) <= -(double) (-__LONG_MAX__ - 1)), 1) +#endif +#if !defined (FE_INVALID) + || 1 +#endif + ) + { +#if __LONG_MAX__ == 2147483647 + long long llhi = (long long) xh; + if (llhi != (long) llhi) + hi = llhi < 0 ? -__LONG_MAX__ - 1 : __LONG_MAX__; + else + hi = llhi; + xh -= hi; +#else + if (__glibc_unlikely ((xh == -(double) (-__LONG_MAX__ - 1)))) + { + /* When XH is 9223372036854775808.0, converting to long long will + overflow, resulting in an invalid operation. However, XL might + be negative and of sufficient magnitude that the overall long + double is in fact in range. Avoid raising an exception. In any + case we need to convert this value specially, because + the converted value is not exactly represented as a double + thus subtracting HI from XH suffers rounding error. */ + hi = __LONG_MAX__; + xh = 1.0; + } + else + { + hi = (long) xh; + xh -= hi; + } +#endif + ldbl_canonicalize (&xh, &xl); + + lo = (long) xh; + + /* Peg at max/min values, assuming that the above conversions do so. + Strictly speaking, we can return anything for values that overflow, + but this is more useful. */ + res = hi + lo; + + /* This is just sign(hi) == sign(lo) && sign(res) != sign(hi). */ + if (__glibc_unlikely (((~(hi ^ lo) & (res ^ hi)) < 0))) + goto overflow; + + xh -= lo; + ldbl_canonicalize (&xh, &xl); + + hi = res; + if (xh > 0.5) + { + res += 1; + } + else if (xh == 0.5) + { + if (xl > 0.0 || (xl == 0.0 && res >= 0)) + res += 1; + } + else if (-xh > 0.5) + { + res -= 1; + } + else if (-xh == 0.5) + { + if (xl < 0.0 || (xl == 0.0 && res <= 0)) + res -= 1; + } + + if (__glibc_unlikely (((~(hi ^ (res - hi)) & (res ^ hi)) < 0))) + goto overflow; + + return res; + } + else + { + if (xh > 0.0) + hi = __LONG_MAX__; + else if (xh < 0.0) + hi = -__LONG_MAX__ - 1; + else + /* Nan */ + hi = 0; + } + +overflow: +#ifdef FE_INVALID + feraiseexcept (FE_INVALID); +#endif + return hi; +} + +long_double_symbol (libm, __lroundl, lroundl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_modfl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_modfl.c new file mode 100644 index 0000000000..260cc3e33c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_modfl.c @@ -0,0 +1,96 @@ +/* s_modfl.c -- long double version of s_modf.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * modfl(long double x, long double *iptr) + * return fraction part of x, and return x's integral part in *iptr. + * Method: + * Bit twiddling. + * + * Exception: + * No exception. + */ + +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +static const long double one = 1.0; + +long double __modfl(long double x, long double *iptr) +{ + int64_t i0,i1,j0; + u_int64_t i; + double xhi, xlo; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (i0, xhi); + EXTRACT_WORDS64 (i1, xlo); + i1 &= 0x000fffffffffffffLL; + j0 = ((i0>>52)&0x7ff)-0x3ff; /* exponent of x */ + if(j0<52) { /* integer part in high x */ + if(j0<0) { /* |x|<1 */ + /* *iptr = +-0 */ + INSERT_WORDS64 (xhi, i0&0x8000000000000000ULL); + *iptr = xhi; + return x; + } else { + i = (0x000fffffffffffffLL)>>j0; + if(((i0&i)|(i1&0x7fffffffffffffffLL))==0) { /* x is integral */ + *iptr = x; + /* return +-0 */ + INSERT_WORDS64 (xhi, i0&0x8000000000000000ULL); + x = xhi; + return x; + } else { + INSERT_WORDS64 (xhi, i0&(~i)); + *iptr = xhi; + return x - *iptr; + } + } + } else if (j0>103) { /* no fraction part */ + *iptr = x*one; + /* We must handle NaNs separately. */ + if ((i0 & 0x7fffffffffffffffLL) > 0x7ff0000000000000LL) + return x*one; + /* return +-0 */ + INSERT_WORDS64 (xhi, i0&0x8000000000000000ULL); + x = xhi; + return x; + } else { /* fraction part in low x */ + i = -1ULL>>(j0-52); + if((i1&i)==0) { /* x is integral */ + *iptr = x; + /* return +-0 */ + INSERT_WORDS64 (xhi, i0&0x8000000000000000ULL); + x = xhi; + return x; + } else { + INSERT_WORDS64 (xhi, i0); + INSERT_WORDS64 (xlo, i1&(~i)); + *iptr = ldbl_pack (xhi, xlo); + return x - *iptr; + } + } +} +#if IS_IN (libm) +long_double_symbol (libm, __modfl, modfl); +#else +long_double_symbol (libc, __modfl, modfl); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nearbyintl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nearbyintl.c new file mode 100644 index 0000000000..18b052cecb --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nearbyintl.c @@ -0,0 +1,21 @@ +/* Round to int long double floating-point values without raising inexact. + IBM extended format long double version. + Copyright (C) 2006-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define USE_AS_NEARBYINTL +#include "s_rintl.c" diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nextafterl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nextafterl.c new file mode 100644 index 0000000000..0d6469d548 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nextafterl.c @@ -0,0 +1,160 @@ +/* s_nextafterl.c -- long double version of s_nextafter.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* IEEE functions + * nextafterl(x,y) + * return the next machine floating-point number of x in the + * direction toward y. + * Special cases: + */ + +#include <errno.h> +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +long double __nextafterl(long double x, long double y) +{ + int64_t hx, hy, ihx, ihy, lx; + double xhi, xlo, yhi; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + yhi = ldbl_high (y); + EXTRACT_WORDS64 (hy, yhi); + ihx = hx&0x7fffffffffffffffLL; /* |hx| */ + ihy = hy&0x7fffffffffffffffLL; /* |hy| */ + + if((ihx>0x7ff0000000000000LL) || /* x is nan */ + (ihy>0x7ff0000000000000LL)) /* y is nan */ + return x+y; /* signal the nan */ + if(x==y) + return y; /* x=y, return y */ + if(ihx == 0) { /* x == 0 */ + long double u; /* return +-minsubnormal */ + hy = (hy & 0x8000000000000000ULL) | 1; + INSERT_WORDS64 (yhi, hy); + x = yhi; + u = math_opt_barrier (x); + u = u * u; + math_force_eval (u); /* raise underflow flag */ + return x; + } + + long double u; + if(x > y) { /* x > y, x -= ulp */ + /* This isn't the largest magnitude correctly rounded + long double as you can see from the lowest mantissa + bit being zero. It is however the largest magnitude + long double with a 106 bit mantissa, and nextafterl + is insane with variable precision. So to make + nextafterl sane we assume 106 bit precision. */ + if((hx==0xffefffffffffffffLL)&&(lx==0xfc8ffffffffffffeLL)) { + u = x+x; /* overflow, return -inf */ + math_force_eval (u); + __set_errno (ERANGE); + return y; + } + if (hx >= 0x7ff0000000000000LL) { + u = 0x1.fffffffffffff7ffffffffffff8p+1023L; + return u; + } + if(ihx <= 0x0360000000000000LL) { /* x <= LDBL_MIN */ + u = math_opt_barrier (x); + x -= LDBL_TRUE_MIN; + if (ihx < 0x0360000000000000LL + || (hx > 0 && lx <= 0) + || (hx < 0 && lx > 1)) { + u = u * u; + math_force_eval (u); /* raise underflow flag */ + __set_errno (ERANGE); + } + /* Avoid returning -0 in FE_DOWNWARD mode. */ + if (x == 0.0L) + return 0.0L; + return x; + } + /* If the high double is an exact power of two and the low + double is the opposite sign, then 1ulp is one less than + what we might determine from the high double. Similarly + if X is an exact power of two, and positive, because + making it a little smaller will result in the exponent + decreasing by one and normalisation of the mantissa. */ + if ((hx & 0x000fffffffffffffLL) == 0 + && ((lx != 0 && (hx ^ lx) < 0) + || (lx == 0 && hx >= 0))) + ihx -= 1LL << 52; + if (ihx < (106LL << 52)) { /* ulp will denormal */ + INSERT_WORDS64 (yhi, ihx & (0x7ffLL<<52)); + u = yhi * 0x1p-105; + } else { + INSERT_WORDS64 (yhi, (ihx & (0x7ffLL<<52))-(105LL<<52)); + u = yhi; + } + return x - u; + } else { /* x < y, x += ulp */ + if((hx==0x7fefffffffffffffLL)&&(lx==0x7c8ffffffffffffeLL)) { + u = x+x; /* overflow, return +inf */ + math_force_eval (u); + __set_errno (ERANGE); + return y; + } + if ((uint64_t) hx >= 0xfff0000000000000ULL) { + u = -0x1.fffffffffffff7ffffffffffff8p+1023L; + return u; + } + if(ihx <= 0x0360000000000000LL) { /* x <= LDBL_MIN */ + u = math_opt_barrier (x); + x += LDBL_TRUE_MIN; + if (ihx < 0x0360000000000000LL + || (hx > 0 && lx < 0 && lx != 0x8000000000000001LL) + || (hx < 0 && lx >= 0)) { + u = u * u; + math_force_eval (u); /* raise underflow flag */ + __set_errno (ERANGE); + } + if (x == 0.0L) /* handle negative LDBL_TRUE_MIN case */ + x = -0.0L; + return x; + } + /* If the high double is an exact power of two and the low + double is the opposite sign, then 1ulp is one less than + what we might determine from the high double. Similarly + if X is an exact power of two, and negative, because + making it a little larger will result in the exponent + decreasing by one and normalisation of the mantissa. */ + if ((hx & 0x000fffffffffffffLL) == 0 + && ((lx != 0 && (hx ^ lx) < 0) + || (lx == 0 && hx < 0))) + ihx -= 1LL << 52; + if (ihx < (106LL << 52)) { /* ulp will denormal */ + INSERT_WORDS64 (yhi, ihx & (0x7ffLL<<52)); + u = yhi * 0x1p-105; + } else { + INSERT_WORDS64 (yhi, (ihx & (0x7ffLL<<52))-(105LL<<52)); + u = yhi; + } + return x + u; + } +} +strong_alias (__nextafterl, __nexttowardl) +long_double_symbol (libm, __nextafterl, nextafterl); +long_double_symbol (libm, __nexttowardl, nexttowardl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nexttoward.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nexttoward.c new file mode 100644 index 0000000000..d8f4fc6523 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nexttoward.c @@ -0,0 +1,90 @@ +/* s_nexttoward.c + * Conversion from s_nextafter.c by Ulrich Drepper, Cygnus Support, + * drepper@cygnus.com and Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* IEEE functions + * nexttoward(x,y) + * return the next machine floating-point number of x in the + * direction toward y. + * Special cases: + */ + +#include <errno.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> +#include <float.h> + +double __nexttoward(double x, long double y) +{ + int32_t hx,ix; + int64_t hy,iy; + uint32_t lx; + double yhi; + + EXTRACT_WORDS(hx,lx,x); + yhi = ldbl_high (y); + EXTRACT_WORDS64(hy,yhi); + ix = hx&0x7fffffff; /* |x| */ + iy = hy&0x7fffffffffffffffLL; /* |y| */ + + if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */ + iy>0x7ff0000000000000LL) /* y is nan */ + return x+y; + if((long double) x==y) return y; /* x=y, return y */ + if((ix|lx)==0) { /* x == 0 */ + double u; + INSERT_WORDS(x,(uint32_t)((hy>>32)&0x80000000),1);/* return +-minsub */ + u = math_opt_barrier (x); + u = u * u; + math_force_eval (u); /* raise underflow flag */ + return x; + } + if(hx>=0) { /* x > 0 */ + if (x > y) { /* x > 0 */ + if(lx==0) hx -= 1; + lx -= 1; + } else { /* x < y, x += ulp */ + lx += 1; + if(lx==0) hx += 1; + } + } else { /* x < 0 */ + if (x < y) { /* x < 0 */ + if(lx==0) hx -= 1; + lx -= 1; + } else { /* x > y, x += ulp */ + lx += 1; + if(lx==0) hx += 1; + } + } + hy = hx&0x7ff00000; + if(hy>=0x7ff00000) { + double u = x+x; /* overflow */ + math_force_eval (u); + __set_errno (ERANGE); + } + if(hy<0x00100000) { + double u = x*x; /* underflow */ + math_force_eval (u); /* raise underflow flag */ + __set_errno (ERANGE); + } + INSERT_WORDS(x,hx,lx); + return x; +} +long_double_symbol (libm, __nexttoward, nexttoward); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c new file mode 100644 index 0000000000..7c5d1cc112 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c @@ -0,0 +1,79 @@ +/* s_nexttowardf.c -- float version of s_nextafter.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com + * and Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +#include <errno.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> +#include <float.h> + +float __nexttowardf(float x, long double y) +{ + int32_t hx,ix; + int64_t hy,iy; + double yhi; + + GET_FLOAT_WORD(hx,x); + yhi = ldbl_high (y); + EXTRACT_WORDS64 (hy, yhi); + ix = hx&0x7fffffff; /* |x| */ + iy = hy&0x7fffffffffffffffLL; /* |y| */ + + if((ix>0x7f800000) || /* x is nan */ + (iy>0x7ff0000000000000LL)) + /* y is nan */ + return x+y; + if((long double) x==y) return y; /* x=y, return y */ + if(ix==0) { /* x == 0 */ + float u; + SET_FLOAT_WORD(x,(u_int32_t)((hy>>32)&0x80000000)|1);/* return +-minsub*/ + u = math_opt_barrier (x); + u = u * u; + math_force_eval (u); /* raise underflow flag */ + return x; + } + if(hx>=0) { /* x > 0 */ + if(x > y) { /* x -= ulp */ + hx -= 1; + } else { /* x < y, x += ulp */ + hx += 1; + } + } else { /* x < 0 */ + if(x < y) { /* x -= ulp */ + hx -= 1; + } else { /* x > y, x += ulp */ + hx += 1; + } + } + hy = hx&0x7f800000; + if(hy>=0x7f800000) { + float u = x+x; /* overflow */ + math_force_eval (u); + __set_errno (ERANGE); + } + if(hy<0x00800000) { /* underflow */ + float u = x*x; + math_force_eval (u); /* raise underflow flag */ + __set_errno (ERANGE); + } + SET_FLOAT_WORD(x,hx); + return x; +} +long_double_symbol (libm, __nexttowardf, nexttowardf); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nextupl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nextupl.c new file mode 100644 index 0000000000..bf74f0e1ab --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_nextupl.c @@ -0,0 +1,78 @@ +/* Return the least floating-point number greater than X. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +/* Return the least floating-point number greater than X. */ +long double +__nextupl (long double x) +{ + int64_t hx, ihx, lx; + double xhi, xlo, yhi; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + ihx = hx & 0x7fffffffffffffffLL; + + if (ihx > 0x7ff0000000000000LL) /* x is nan. */ + return x + x; /* Signal the nan. */ + if (ihx == 0) + return LDBL_TRUE_MIN; + + long double u; + if ((hx == 0x7fefffffffffffffLL) && (lx == 0x7c8ffffffffffffeLL)) + return INFINITY; + if ((uint64_t) hx >= 0xfff0000000000000ULL) + { + u = -0x1.fffffffffffff7ffffffffffff8p+1023L; + return u; + } + if (ihx <= 0x0360000000000000LL) + { /* x <= LDBL_MIN. */ + x += LDBL_TRUE_MIN; + if (x == 0.0L) /* Handle negative LDBL_TRUE_MIN case. */ + x = -0.0L; + return x; + } + /* If the high double is an exact power of two and the low + double is the opposite sign, then 1ulp is one less than + what we might determine from the high double. Similarly + if X is an exact power of two, and negative, because + making it a little larger will result in the exponent + decreasing by one and normalisation of the mantissa. */ + if ((hx & 0x000fffffffffffffLL) == 0 + && ((lx != 0 && lx != 0x8000000000000000LL && (hx ^ lx) < 0) + || ((lx == 0 || lx == 0x8000000000000000LL) && hx < 0))) + ihx -= 1LL << 52; + if (ihx < (106LL << 52)) + { /* ulp will denormal. */ + INSERT_WORDS64 (yhi, ihx & (0x7ffLL << 52)); + u = yhi * 0x1p-105; + } + else + { + INSERT_WORDS64 (yhi, (ihx & (0x7ffLL << 52)) - (105LL << 52)); + u = yhi; + } + return x + u; +} + +weak_alias (__nextupl, nextupl) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_remquol.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_remquol.c new file mode 100644 index 0000000000..9b6ec09d41 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_remquol.c @@ -0,0 +1,119 @@ +/* Compute remainder and a congruent to the quotient. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz>, 1999. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +#include <math_private.h> +#include <math_ldbl_opt.h> + + +static const long double zero = 0.0; + + +long double +__remquol (long double x, long double y, int *quo) +{ + int64_t hx,hy; + u_int64_t sx,lx,ly,qs; + int cquo; + double xhi, xlo, yhi, ylo; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + ldbl_unpack (y, &yhi, &ylo); + EXTRACT_WORDS64 (hy, yhi); + EXTRACT_WORDS64 (ly, ylo); + sx = hx & 0x8000000000000000ULL; + qs = sx ^ (hy & 0x8000000000000000ULL); + ly ^= hy & 0x8000000000000000ULL; + hy &= 0x7fffffffffffffffLL; + lx ^= sx; + hx &= 0x7fffffffffffffffLL; + + /* Purge off exception values. */ + if (hy == 0) + return (x * y) / (x * y); /* y = 0 */ + if ((hx >= 0x7ff0000000000000LL) /* x not finite */ + || (hy > 0x7ff0000000000000LL)) /* y is NaN */ + return (x * y) / (x * y); + + if (hy <= 0x7fbfffffffffffffLL) + x = __ieee754_fmodl (x, 8 * y); /* now x < 8y */ + + if (((hx - hy) | (lx - ly)) == 0) + { + *quo = qs ? -1 : 1; + return zero * x; + } + + x = fabsl (x); + y = fabsl (y); + cquo = 0; + + if (hy <= 0x7fcfffffffffffffLL && x >= 4 * y) + { + x -= 4 * y; + cquo += 4; + } + if (hy <= 0x7fdfffffffffffffLL && x >= 2 * y) + { + x -= 2 * y; + cquo += 2; + } + + if (hy < 0x0020000000000000LL) + { + if (x + x > y) + { + x -= y; + ++cquo; + if (x + x >= y) + { + x -= y; + ++cquo; + } + } + } + else + { + long double y_half = 0.5L * y; + if (x > y_half) + { + x -= y; + ++cquo; + if (x >= y_half) + { + x -= y; + ++cquo; + } + } + } + + *quo = qs ? -cquo : cquo; + + /* Ensure correct sign of zero result in round-downward mode. */ + if (x == 0.0L) + x = 0.0L; + if (sx) + x = -x; + return x; +} +long_double_symbol (libm, __remquol, remquol); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_rintl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_rintl.c new file mode 100644 index 0000000000..ea8c2bca0e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_rintl.c @@ -0,0 +1,129 @@ +/* Round to int long double floating-point values. + IBM extended format long double version. + Copyright (C) 2006-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* This has been coded in assembler because GCC makes such a mess of it + when it's coded in C. */ + +#include <math.h> +#include <fenv.h> +#include <math_ldbl_opt.h> +#include <float.h> +#include <ieee754.h> + +#ifdef USE_AS_NEARBYINTL +# define rintl nearbyintl +# define __rintl __nearbyintl +#endif + + +long double +__rintl (long double x) +{ + double xh, xl, hi, lo; + + ldbl_unpack (x, &xh, &xl); + + /* Return Inf, Nan, +/-0 unchanged. */ + if (__builtin_expect (xh != 0.0 + && __builtin_isless (__builtin_fabs (xh), + __builtin_inf ()), 1)) + { + double orig_xh; + int save_round = fegetround (); + + /* Long double arithmetic, including the canonicalisation below, + only works in round-to-nearest mode. */ +#ifdef USE_AS_NEARBYINTL + SET_RESTORE_ROUND_NOEX (FE_TONEAREST); +#else + fesetround (FE_TONEAREST); +#endif + + /* Convert the high double to integer. */ + orig_xh = xh; + hi = ldbl_nearbyint (xh); + + /* Subtract integral high part from the value. If the low double + happens to be exactly 0.5 or -0.5, you might think that this + subtraction could result in an incorrect conversion. For + instance, subtracting an odd number would cause this function + to round in the wrong direction. However, if we have a + canonical long double with the low double 0.5 or -0.5, then the + high double must be even. */ + xh -= hi; + ldbl_canonicalize (&xh, &xl); + + /* Now convert the low double, adjusted for any remainder from the + high double. */ + lo = ldbl_nearbyint (xh); + + xh -= lo; + ldbl_canonicalize (&xh, &xl); + + switch (save_round) + { + case FE_TONEAREST: + if (xl > 0.0 && xh == 0.5) + lo += 1.0; + else if (xl < 0.0 && -xh == 0.5) + lo -= 1.0; + break; + + case FE_TOWARDZERO: + if (orig_xh < 0.0) + goto do_up; + /* Fall thru */ + + case FE_DOWNWARD: + if (xh < 0.0 || (xh == 0.0 && xl < 0.0)) + lo -= 1.0; + break; + + case FE_UPWARD: + do_up: + if (xh > 0.0 || (xh == 0.0 && xl > 0.0)) + lo += 1.0; + break; + } + + /* Ensure the final value is canonical. In certain cases, + rounding causes hi,lo calculated so far to be non-canonical. */ + xh = hi; + xl = lo; + ldbl_canonicalize (&xh, &xl); + + /* Ensure we return -0 rather than +0 when appropriate. */ + if (orig_xh < 0.0) + xh = -__builtin_fabs (xh); + +#ifdef USE_AS_NEARBYINTL + math_force_eval (xh); + math_force_eval (xl); +#else + fesetround (save_round); +#endif + } + else + /* Quiet signaling NaN arguments. */ + xh += xh; + + return ldbl_pack (xh, xl); +} + +long_double_symbol (libm, __rintl, rintl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_roundevenl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_roundevenl.c new file mode 100644 index 0000000000..f4221cda4b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_roundevenl.c @@ -0,0 +1,69 @@ +/* Round to nearest integer value, rounding halfway cases to even. + ldbl-128ibm version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + +long double +roundevenl (long double x) +{ + double xh, xl, hi; + + ldbl_unpack (x, &xh, &xl); + + if (xh != 0 && isfinite (xh)) + { + hi = roundeven (xh); + if (hi != xh) + { + /* The high part is not an integer; the low part only + affects the result if the high part is exactly half way + between two integers and the low part is nonzero in the + opposite direction to the rounding of the high part. */ + double diff = hi - xh; + if (fabs (diff) == 0.5) + { + if (xl < 0 && diff > 0) + xh = hi - 1; + else if (xl > 0 && diff < 0) + xh = hi + 1; + else + xh = hi; + } + else + xh = hi; + xl = 0; + } + else + { + /* The high part is a nonzero integer. Rounding the low + part to nearest, ties round to even, is always correct, + as a high part that is an odd integer together with a low + part with magnitude 0.5 is not a valid long double. */ + xl = roundeven (xl); + xh = hi; + ldbl_canonicalize_int (&xh, &xl); + } + } + else + /* Quiet signaling NaN arguments. */ + xh += xh; + + return ldbl_pack (xh, xl); +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_roundl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_roundl.c new file mode 100644 index 0000000000..0b70e24637 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_roundl.c @@ -0,0 +1,87 @@ +/* Round to int long double floating-point values. + IBM extended format long double version. + Copyright (C) 2006-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* This has been coded in assembler because GCC makes such a mess of it + when it's coded in C. */ + +#include <math.h> +#include <math_ldbl_opt.h> +#include <float.h> +#include <ieee754.h> + + +long double +__roundl (long double x) +{ + double xh, xl, hi, lo; + + ldbl_unpack (x, &xh, &xl); + + /* Return Inf, Nan, +/-0 unchanged. */ + if (__builtin_expect (xh != 0.0 + && __builtin_isless (__builtin_fabs (xh), + __builtin_inf ()), 1)) + { + hi = __round (xh); + if (hi != xh) + { + /* The high part is not an integer; the low part only + affects the result if the high part is exactly half way + between two integers and the low part is nonzero with the + opposite sign. */ + if (fabs (hi - xh) == 0.5) + { + if (xh > 0 && xl < 0) + xh = hi - 1; + else if (xh < 0 && xl > 0) + xh = hi + 1; + else + xh = hi; + } + else + xh = hi; + xl = 0; + } + else + { + /* The high part is a nonzero integer. */ + lo = __round (xl); + if (fabs (lo - xl) == 0.5) + { + if (xh > 0 && xl < 0) + xl = lo + 1; + else if (xh < 0 && lo > 0) + xl = lo - 1; + else + xl = lo; + } + else + xl = lo; + xh = hi; + ldbl_canonicalize_int (&xh, &xl); + } + } + else + /* Quiet signaling NaN arguments. */ + xh += xh; + + return ldbl_pack (xh, xl); +} + +long_double_symbol (libm, __roundl, roundl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_scalblnl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_scalblnl.c new file mode 100644 index 0000000000..031635267f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_scalblnl.c @@ -0,0 +1,104 @@ +/* s_scalblnl.c -- long double version of s_scalbln.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* @(#)s_scalbln.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * scalblnl (long double x, long int n) + * scalblnl(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +static const long double +twolm54 = 5.55111512312578270212e-17, /* 0x3C90000000000000, 0 */ +huge = 1.0E+300L, +tiny = 1.0E-300L; +static const double +two54 = 1.80143985094819840000e+16, /* 0x4350000000000000 */ +twom54 = 5.55111512312578270212e-17; /* 0x3C90000000000000 */ + +long double __scalblnl (long double x, long int n) +{ + int64_t k,l,hx,lx; + union { int64_t i; double d; } u; + double xhi, xlo; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + k = (hx>>52)&0x7ff; /* extract exponent */ + l = (lx>>52)&0x7ff; + if (k==0) { /* 0 or subnormal x */ + if ((hx&0x7fffffffffffffffULL)==0) return x; /* +-0 */ + u.i = hx; + u.d *= two54; + hx = u.i; + k = ((hx>>52)&0x7ff) - 54; + } + else if (k==0x7ff) return x+x; /* NaN or Inf */ + if (n< -50000) return tiny*__copysignl(tiny,x); /*underflow */ + if (n> 50000 || k+n > 0x7fe) + return huge*__copysignl(huge,x); /* overflow */ + /* Now k and n are bounded we know that k = k+n does not + overflow. */ + k = k+n; + if (k > 0) { /* normal result */ + hx = (hx&0x800fffffffffffffULL)|(k<<52); + if ((lx & 0x7fffffffffffffffULL) == 0) { /* low part +-0 */ + INSERT_WORDS64 (xhi, hx); + INSERT_WORDS64 (xlo, lx); + x = ldbl_pack (xhi, xlo); + return x; + } + if (l == 0) { /* low part subnormal */ + u.i = lx; + u.d *= two54; + lx = u.i; + l = ((lx>>52)&0x7ff) - 54; + } + l = l + n; + if (l > 0) + lx = (lx&0x800fffffffffffffULL)|(l<<52); + else if (l <= -54) + lx = (lx&0x8000000000000000ULL); + else { + l += 54; + u.i = (lx&0x800fffffffffffffULL)|(l<<52); + u.d *= twom54; + lx = u.i; + } + INSERT_WORDS64 (xhi, hx); + INSERT_WORDS64 (xlo, lx); + x = ldbl_pack (xhi, xlo); + return x; + } + if (k <= -54) + return tiny*__copysignl(tiny,x); /*underflow*/ + k += 54; /* subnormal result */ + lx &= 0x8000000000000000ULL; + hx &= 0x800fffffffffffffULL; + INSERT_WORDS64 (xhi, hx|(k<<52)); + INSERT_WORDS64 (xlo, lx); + x = ldbl_pack (xhi, xlo); + return x*twolm54; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_scalbnl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_scalbnl.c new file mode 100644 index 0000000000..0c4508835e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_scalbnl.c @@ -0,0 +1,104 @@ +/* s_scalbnl.c -- long double version of s_scalbn.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* @(#)s_scalbn.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * scalbnl (long double x, int n) + * scalbnl(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +static const long double +twolm54 = 5.55111512312578270212e-17, /* 0x3C90000000000000, 0 */ +huge = 1.0E+300L, +tiny = 1.0E-300L; +static const double +two54 = 1.80143985094819840000e+16, /* 0x4350000000000000 */ +twom54 = 5.55111512312578270212e-17; /* 0x3C90000000000000 */ + +long double __scalbnl (long double x, int n) +{ + int64_t k,l,hx,lx; + union { int64_t i; double d; } u; + double xhi, xlo; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + k = (hx>>52)&0x7ff; /* extract exponent */ + l = (lx>>52)&0x7ff; + if (k==0) { /* 0 or subnormal x */ + if ((hx&0x7fffffffffffffffULL)==0) return x; /* +-0 */ + u.i = hx; + u.d *= two54; + hx = u.i; + k = ((hx>>52)&0x7ff) - 54; + } + else if (k==0x7ff) return x+x; /* NaN or Inf */ + if (n< -50000) return tiny*__copysignl(tiny,x); /*underflow */ + if (n> 50000 || k+n > 0x7fe) + return huge*__copysignl(huge,x); /* overflow */ + /* Now k and n are bounded we know that k = k+n does not + overflow. */ + k = k+n; + if (k > 0) { /* normal result */ + hx = (hx&0x800fffffffffffffULL)|(k<<52); + if ((lx & 0x7fffffffffffffffULL) == 0) { /* low part +-0 */ + INSERT_WORDS64 (xhi, hx); + INSERT_WORDS64 (xlo, lx); + x = ldbl_pack (xhi, xlo); + return x; + } + if (l == 0) { /* low part subnormal */ + u.i = lx; + u.d *= two54; + lx = u.i; + l = ((lx>>52)&0x7ff) - 54; + } + l = l + n; + if (l > 0) + lx = (lx&0x800fffffffffffffULL)|(l<<52); + else if (l <= -54) + lx = (lx&0x8000000000000000ULL); + else { + l += 54; + u.i = (lx&0x800fffffffffffffULL)|(l<<52); + u.d *= twom54; + lx = u.i; + } + INSERT_WORDS64 (xhi, hx); + INSERT_WORDS64 (xlo, lx); + x = ldbl_pack (xhi, xlo); + return x; + } + if (k <= -54) + return tiny*__copysignl(tiny,x); /*underflow*/ + k += 54; /* subnormal result */ + lx &= 0x8000000000000000ULL; + hx &= 0x800fffffffffffffULL; + INSERT_WORDS64 (xhi, hx|(k<<52)); + INSERT_WORDS64 (xlo, lx); + x = ldbl_pack (xhi, xlo); + return x*twolm54; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_setpayloadl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_setpayloadl.c new file mode 100644 index 0000000000..1aba33e6e2 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_setpayloadl.c @@ -0,0 +1,3 @@ +#define SIG 0 +#define FUNC setpayloadl +#include <s_setpayloadl_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_setpayloadl_main.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_setpayloadl_main.c new file mode 100644 index 0000000000..9aa02cdf93 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_setpayloadl_main.c @@ -0,0 +1,60 @@ +/* Set NaN payload. ldbl-128ibm version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +#define SET_HIGH_BIT (HIGH_ORDER_BIT_IS_SET_FOR_SNAN ? SIG : !SIG) +#define BIAS 0x3ff +#define PAYLOAD_DIG 51 +#define EXPLICIT_MANT_DIG 52 + +int +FUNC (long double *x, long double payload) +{ + double hi, lo; + uint64_t hx, lx; + + ldbl_unpack (payload, &hi, &lo); + EXTRACT_WORDS64 (hx, hi); + EXTRACT_WORDS64 (lx, lo); + int exponent = hx >> EXPLICIT_MANT_DIG; + /* Test if argument is (a) negative or too large; (b) too small, + except for 0 when allowed; (c) not an integer. All valid + arguments have the low part zero. */ + if ((lx & 0x7fffffffffffffffULL) != 0 + || exponent >= BIAS + PAYLOAD_DIG + || (exponent < BIAS && !(SET_HIGH_BIT && hx == 0)) + || (hx & ((1ULL << (BIAS + EXPLICIT_MANT_DIG - exponent)) - 1)) != 0) + { + *x = 0.0L; + return 1; + } + if (hx != 0) + { + hx &= (1ULL << EXPLICIT_MANT_DIG) - 1; + hx |= 1ULL << EXPLICIT_MANT_DIG; + hx >>= BIAS + EXPLICIT_MANT_DIG - exponent; + } + hx |= 0x7ff0000000000000ULL | (SET_HIGH_BIT ? 0x8000000000000ULL : 0); + INSERT_WORDS64 (hi, hx); + *x = ldbl_pack (hi, 0.0); + return 0; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_setpayloadsigl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_setpayloadsigl.c new file mode 100644 index 0000000000..d97e2c8206 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_setpayloadsigl.c @@ -0,0 +1,3 @@ +#define SIG 1 +#define FUNC setpayloadsigl +#include <s_setpayloadl_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_signbitl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_signbitl.c new file mode 100644 index 0000000000..d6ceede69f --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_signbitl.c @@ -0,0 +1,32 @@ +/* Return nonzero value if number is negative. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_ldbl_opt.h> + +int +___signbitl (long double x) +{ + return __builtin_signbitl (x); +} +#if IS_IN (libm) +long_double_symbol (libm, ___signbitl, __signbitl); +#else +long_double_symbol (libc, ___signbitl, __signbitl); +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_sincosl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_sincosl.c new file mode 100644 index 0000000000..8329979931 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_sincosl.c @@ -0,0 +1,76 @@ +/* Compute sine and cosine of argument. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz>. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <errno.h> +#include <math.h> + +#include <math_private.h> +#include <math_ldbl_opt.h> + +void +__sincosl (long double x, long double *sinx, long double *cosx) +{ + int64_t ix; + double xhi; + + /* High word of x. */ + xhi = ldbl_high (x); + EXTRACT_WORDS64 (ix, xhi); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffffffffffffLL; + if (ix <= 0x3fe921fb54442d10LL) + __kernel_sincosl (x, 0.0L, sinx, cosx, 0); + else if (ix >= 0x7ff0000000000000LL) + { + /* sin(Inf or NaN) is NaN */ + *sinx = *cosx = x - x; + if (isinf (x)) + __set_errno (EDOM); + } + else + { + /* Argument reduction needed. */ + long double y[2]; + int n; + + n = __ieee754_rem_pio2l (x, y); + switch (n & 3) + { + case 0: + __kernel_sincosl (y[0], y[1], sinx, cosx, 1); + break; + case 1: + __kernel_sincosl (y[0], y[1], cosx, sinx, 1); + *cosx = -*cosx; + break; + case 2: + __kernel_sincosl (y[0], y[1], sinx, cosx, 1); + *sinx = -*sinx; + *cosx = -*cosx; + break; + default: + __kernel_sincosl (y[0], y[1], cosx, sinx, 1); + *sinx = -*sinx; + break; + } + } +} +long_double_symbol (libm, __sincosl, sincosl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_sinl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_sinl.c new file mode 100644 index 0000000000..087921a913 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_sinl.c @@ -0,0 +1,85 @@ +/* s_sinl.c -- long double version of s_sin.c. + * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* sinl(x) + * Return sine function of x. + * + * kernel function: + * __kernel_sinl ... sine function on [-pi/4,pi/4] + * __kernel_cosl ... cose function on [-pi/4,pi/4] + * __ieee754_rem_pio2l ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include <errno.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +long double __sinl(long double x) +{ + long double y[2],z=0.0L; + int64_t n, ix; + double xhi; + + /* High word of x. */ + xhi = ldbl_high (x); + EXTRACT_WORDS64 (ix, xhi); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffffffffffffLL; + if(ix <= 0x3fe921fb54442d10LL) + return __kernel_sinl(x,z,0); + + /* sin(Inf or NaN) is NaN */ + else if (ix>=0x7ff0000000000000LL) { + if (ix == 0x7ff0000000000000LL) + __set_errno (EDOM); + return x-x; + } + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2l(x,y); + switch(n&3) { + case 0: return __kernel_sinl(y[0],y[1],1); + case 1: return __kernel_cosl(y[0],y[1]); + case 2: return -__kernel_sinl(y[0],y[1],1); + default: + return -__kernel_cosl(y[0],y[1]); + } + } +} +long_double_symbol (libm, __sinl, sinl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_tanhl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_tanhl.c new file mode 100644 index 0000000000..e6457a1c1c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_tanhl.c @@ -0,0 +1,87 @@ +/* @(#)s_tanh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_tanh.c,v 1.7 1995/05/10 20:48:22 jtc Exp $"; +#endif + +/* Tanh(x) + * Return the Hyperbolic Tangent of x + * + * Method : + * x -x + * e - e + * 0. tanh(x) is defined to be ----------- + * x -x + * e + e + * 1. reduce x to non-negative by tanh(-x) = -tanh(x). + * 2. 0 <= x <= 2**-57 : tanh(x) := x*(one+x) + * -t + * 2**-57 < x <= 1 : tanh(x) := -----; t = expm1(-2x) + * t + 2 + * 2 + * 1 <= x <= 40.0 : tanh(x) := 1- ----- ; t=expm1(2x) + * t + 2 + * 40.0 < x <= INF : tanh(x) := 1. + * + * Special cases: + * tanh(NaN) is NaN; + * only tanh(0)=0 is exact for finite argument. + */ + +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +static const long double one=1.0L, two=2.0L, tiny = 1.0e-300L; + +long double __tanhl(long double x) +{ + long double t,z; + int64_t jx,ix; + double xhi; + + /* High word of |x|. */ + xhi = ldbl_high (x); + EXTRACT_WORDS64 (jx, xhi); + ix = jx&0x7fffffffffffffffLL; + + /* x is INF or NaN */ + if(ix>=0x7ff0000000000000LL) { + if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ + else return one/x-one; /* tanh(NaN) = NaN */ + } + + /* |x| < 40 */ + if (ix < 0x4044000000000000LL) { /* |x|<40 */ + if (ix == 0) + return x; /* x == +-0 */ + if (ix<0x3c60000000000000LL) /* |x|<2**-57 */ + { + math_check_force_underflow (x); + return x; /* tanh(small) = small */ + } + if (ix>=0x3ff0000000000000LL) { /* |x|>=1 */ + t = __expm1l(two*fabsl(x)); + z = one - two/(t+two); + } else { + t = __expm1l(-two*fabsl(x)); + z= -t/(t+two); + } + /* |x| > 40, return +-1 */ + } else { + z = one - tiny; /* raised inexact flag */ + } + return (jx>=0)? z: -z; +} +long_double_symbol (libm, __tanhl, tanhl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_tanl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_tanl.c new file mode 100644 index 0000000000..66b8a0621e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_tanl.c @@ -0,0 +1,79 @@ +/* s_tanl.c -- long double version of s_tan.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* @(#)s_tan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* tanl(x) + * Return tangent function of x. + * + * kernel function: + * __kernel_tanl ... tangent function on [-pi/4,pi/4] + * __ieee754_rem_pio2l ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include <errno.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +long double __tanl(long double x) +{ + long double y[2],z=0.0L; + int64_t n, ix; + double xhi; + + /* High word of x. */ + xhi = ldbl_high (x); + EXTRACT_WORDS64 (ix, xhi); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffffffffffffLL; + if(ix <= 0x3fe921fb54442d10LL) return __kernel_tanl(x,z,1); + + /* tanl(Inf or NaN) is NaN */ + else if (ix>=0x7ff0000000000000LL) { + if (ix == 0x7ff0000000000000LL) + __set_errno (EDOM); + return x-x; /* NaN */ + } + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2l(x,y); + return __kernel_tanl(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even + -1 -- n odd */ + } +} +long_double_symbol (libm, __tanl, tanl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_totalorderl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_totalorderl.c new file mode 100644 index 0000000000..963376a7cf --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_totalorderl.c @@ -0,0 +1,62 @@ +/* Total order operation. ldbl-128ibm version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +int +totalorderl (long double x, long double y) +{ + double xhi, xlo, yhi, ylo; + int64_t hx, hy, lx, ly; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + ldbl_unpack (y, &yhi, &ylo); + EXTRACT_WORDS64 (hy, yhi); +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN +# error not implemented +#endif + uint64_t hx_sign = hx >> 63; + uint64_t hy_sign = hy >> 63; + int64_t hx_adj = hx ^ (hx_sign >> 1); + int64_t hy_adj = hy ^ (hy_sign >> 1); + if (hx_adj < hy_adj) + return 1; + else if (hx_adj > hy_adj) + return 0; + + /* The high doubles are identical. If they are NaNs or both the low + parts are zero, the low parts are not significant (and if they + are infinities, both the low parts must be zero). */ + if ((hx & 0x7fffffffffffffffULL) >= 0x7ff0000000000000ULL) + return 1; + EXTRACT_WORDS64 (lx, xlo); + EXTRACT_WORDS64 (ly, ylo); + if (((lx | ly) & 0x7fffffffffffffffULL) == 0) + return 1; + + /* Otherwise compare the low parts. */ + uint64_t lx_sign = lx >> 63; + uint64_t ly_sign = ly >> 63; + lx ^= lx_sign >> 1; + ly ^= ly_sign >> 1; + return lx <= ly; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_totalordermagl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_totalordermagl.c new file mode 100644 index 0000000000..f7480909df --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_totalordermagl.c @@ -0,0 +1,64 @@ +/* Total order operation on absolute values. ldbl-128ibm version. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +int +totalordermagl (long double x, long double y) +{ + double xhi, xlo, yhi, ylo; + int64_t hx, hy, lx, ly; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + ldbl_unpack (y, &yhi, &ylo); + EXTRACT_WORDS64 (hy, yhi); +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN +# error not implemented +#endif + uint64_t x_sign = hx & 0x8000000000000000ULL; + uint64_t y_sign = hy & 0x8000000000000000ULL; + hx ^= x_sign; + hy ^= y_sign; + if (hx < hy) + return 1; + else if (hx > hy) + return 0; + + /* The high doubles are identical. If they are NaNs or both the low + parts are zero, the low parts are not significant (and if they + are infinities, both the low parts must be zero). */ + if (hx >= 0x7ff0000000000000ULL) + return 1; + EXTRACT_WORDS64 (lx, xlo); + EXTRACT_WORDS64 (ly, ylo); + if (((lx | ly) & 0x7fffffffffffffffULL) == 0) + return 1; + lx ^= x_sign; + ly ^= y_sign; + + /* Otherwise compare the low parts. */ + uint64_t lx_sign = lx >> 63; + uint64_t ly_sign = ly >> 63; + lx ^= lx_sign >> 1; + ly ^= ly_sign >> 1; + return lx <= ly; +} diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_truncl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_truncl.c new file mode 100644 index 0000000000..ecabf9d711 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_truncl.c @@ -0,0 +1,62 @@ +/* Truncate (toward zero) long double floating-point values. + IBM extended format long double version. + Copyright (C) 2006-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_ldbl_opt.h> +#include <float.h> +#include <ieee754.h> + + +long double +__truncl (long double x) +{ + double xh, xl, hi, lo; + + ldbl_unpack (x, &xh, &xl); + + /* Return Inf, Nan, +/-0 unchanged. */ + if (__builtin_expect (xh != 0.0 + && __builtin_isless (__builtin_fabs (xh), + __builtin_inf ()), 1)) + { + hi = __trunc (xh); + if (hi != xh) + { + /* The high part is not an integer; the low part does not + affect the result. */ + xh = hi; + xl = 0; + } + else + { + /* The high part is a nonzero integer. */ + lo = xh > 0 ? __floor (xl) : __ceil (xl); + xh = hi; + xl = lo; + ldbl_canonicalize_int (&xh, &xl); + } + } + else + /* Quiet signaling NaN arguments. */ + xh += xh; + + return ldbl_pack (xh, xl); +} + +long_double_symbol (libm, __truncl, truncl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_ufromfpl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_ufromfpl.c new file mode 100644 index 0000000000..c686daa4a7 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_ufromfpl.c @@ -0,0 +1,4 @@ +#define UNSIGNED 1 +#define INEXACT 0 +#define FUNC ufromfpl +#include <s_fromfpl_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_ufromfpxl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_ufromfpxl.c new file mode 100644 index 0000000000..906066c83c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_ufromfpxl.c @@ -0,0 +1,4 @@ +#define UNSIGNED 1 +#define INEXACT 1 +#define FUNC ufromfpxl +#include <s_fromfpl_main.c> diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/strtod_nan_ldouble.h b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/strtod_nan_ldouble.h new file mode 100644 index 0000000000..198fe48f5c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/strtod_nan_ldouble.h @@ -0,0 +1,30 @@ +/* Convert string for NaN payload to corresponding NaN. For ldbl-128ibm. + Copyright (C) 1997-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define FLOAT long double +#define SET_MANTISSA(flt, mant) \ + do \ + { \ + union ibm_extended_long_double u; \ + u.ld = (flt); \ + u.d[0].ieee_nan.mantissa0 = (mant) >> 32; \ + u.d[0].ieee_nan.mantissa1 = (mant); \ + if ((u.d[0].ieee.mantissa0 | u.d[0].ieee.mantissa1) != 0) \ + (flt) = u.ld; \ + } \ + while (0) diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/strtold_l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/strtold_l.c new file mode 100644 index 0000000000..37034cb254 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/strtold_l.c @@ -0,0 +1,60 @@ +/* Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <stdlib.h> +#include <wchar.h> +#include <xlocale.h> + +/* The actual implementation for all floating point sizes is in strtod.c. + These macros tell it to produce the `long double' version, `strtold'. */ + +#define FLOAT long double +#define FLT LDBL +#ifdef USE_WIDE_CHAR +extern long double ____new_wcstold_l (const wchar_t *, wchar_t **, __locale_t); +# define STRTOF __new_wcstold_l +# define __STRTOF ____new_wcstold_l +# define ____STRTOF_INTERNAL ____wcstold_l_internal +# define STRTOF_NAN __wcstold_nan +#else +extern long double ____new_strtold_l (const char *, char **, __locale_t); +# define STRTOF __new_strtold_l +# define __STRTOF ____new_strtold_l +# define ____STRTOF_INTERNAL ____strtold_l_internal +# define STRTOF_NAN __strtold_nan +#endif +extern __typeof (__STRTOF) STRTOF; +libc_hidden_proto (__STRTOF) +libc_hidden_proto (STRTOF) +#define MPN2FLOAT __mpn_construct_long_double +#define FLOAT_HUGE_VAL HUGE_VALL + +#include <strtod_l.c> + +#ifdef __LONG_DOUBLE_MATH_OPTIONAL +# include <math_ldbl_opt.h> +# ifdef USE_WIDE_CHAR +weak_alias (____new_wcstold_l, ___new_wcstold_l); +long_double_symbol (libc, ___new_wcstold_l, wcstold_l); +long_double_symbol (libc, ____new_wcstold_l, __wcstold_l); +# else +weak_alias (____new_strtold_l, ___new_strtold_l); +long_double_symbol (libc, ___new_strtold_l, strtold_l); +long_double_symbol (libc, ____new_strtold_l, __strtold_l); +# endif +#endif diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/t_sincosl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/t_sincosl.c new file mode 100644 index 0000000000..22c59150be --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/t_sincosl.c @@ -0,0 +1,693 @@ +/* Quad-precision floating point sine and cosine tables. + Copyright (C) 1999-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jj@ultra.linux.cz> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* For 0.1484375 + n/128.0, n=0..82 this table contains + first 113 bits of cosine, then at least 113 additional + bits and the same for sine. + 0.1484375+82.0/128.0 is the smallest number among above defined numbers + larger than pi/4. + Computed using gmp. + */ + +const long double __sincosl_table[] = { + +/* x = 1.48437500000000000000000000000000000e-01L 3ffc3000000000000000000000000000 */ +/* cos(x) = 0.fd2f5320e1b790209b4dda2f98 f79caaa7b873aff1014b0fbc52 43766d03cb006bc837c4358 */ + 0x0.fd2f5320e1b790209b4dda2f98p0L, + 0x0.f79caaa7b873aff1014b0fbc52p-104L, +/* sin(x) = 0.25dc50bc95711d0d9787d108fd 438cf5959ee0bfb7a1e36e8b1a 112968f356657420e9cc9ea */ + 0x0.25dc50bc95711d0d9787d108fdp0L, + 0x0.438cf5959ee0bfb7a1e36e8b1ap-104L, + +/* x = 1.56250000000000000000000000000000000e-01 3ffc4000000000000000000000000000 */ +/* cos(x) = 0.fce1a053e621438b6d60c76e8c 45bf0a9dc71aa16f922acc10e9 5144ec796a249813c9cb649 */ + 0x0.fce1a053e621438b6d60c76e8cp0L, + 0x0.45bf0a9dc71aa16f922acc10e9p-104L, +/* sin(x) = 0.27d66258bacd96a3eb335b365c 87d59438c5142bb56a489e9b8d b9d36234ffdebb6bdc22d8e */ + 0x0.27d66258bacd96a3eb335b365cp0L, + 0x0.87d59438c5142bb56a489e9b8dp-104L, + +/* x = 1.64062500000000000000000000000000000e-01 3ffc5000000000000000000000000000 */ +/* cos(x) = 0.fc8ffa01ba6807417e05962b0d 9fdf1fddb0cc4c07d22e19e080 19bffa50a6c7acdb40307a3 */ + 0x0.fc8ffa01ba6807417e05962b0dp0L, + 0x0.9fdf1fddb0cc4c07d22e19e080p-104L, +/* sin(x) = 0.29cfd49b8be4f665276cab01cb f0426934906c3dd105473b226e 410b1450f62e53ff7c6cce1 */ + 0x0.29cfd49b8be4f665276cab01cbp0L, + 0x0.f0426934906c3dd105473b226ep-104L, + +/* x = 1.71875000000000000000000000000000000e-01 3ffc6000000000000000000000000000 */ +/* cos(x) = 0.fc3a6170f767ac735d63d99a9d 439e1db5e59d3ef153a4265d58 55850ed82b536bf361b80e3 */ + 0x0.fc3a6170f767ac735d63d99a9dp0L, + 0x0.439e1db5e59d3ef153a4265d58p-104L, +/* sin(x) = 0.2bc89f9f424de5485de7ce03b2 514952b9faf5648c3244d4736f eb95dbb9da49f3b58a9253b */ + 0x0.2bc89f9f424de5485de7ce03b2p0L, + 0x0.514952b9faf5648c3244d4736fp-104L, + +/* x = 1.79687500000000000000000000000000000e-01 3ffc7000000000000000000000000000 */ +/* cos(x) = 0.fbe0d7f7fef11e70aa43b8abf4 f6a457cea20c8f3f676b47781f 9821bbe9ce04b3c7b981c0b */ + 0x0.fbe0d7f7fef11e70aa43b8abf4p0L, + 0x0.f6a457cea20c8f3f676b47781fp-104L, +/* sin(x) = 0.2dc0bb80b49a97ffb34e8dd1f8 db9df7af47ed2dcf58b12c8e78 27e048cae929da02c04ecac */ + 0x0.2dc0bb80b49a97ffb34e8dd1f8p0L, + 0x0.db9df7af47ed2dcf58b12c8e78p-104L, + +/* x = 1.87500000000000000000000000000000000e-01 3ffc8000000000000000000000000000 */ +/* cos(x) = 0.fb835efcf670dd2ce6fe792469 7eea13ea358867e9cdb3899b78 3f4f9f43aa5626e8b67b3bc */ + 0x0.fb835efcf670dd2ce6fe792469p0L, + 0x0.7eea13ea358867e9cdb3899b78p-104L, +/* sin(x) = 0.2fb8205f75e56a2b56a1c4792f 856258769af396e0189ef72c05 e4df59a6b00e4b44a6ea515 */ + 0x0.2fb8205f75e56a2b56a1c4792fp0L, + 0x0.856258769af396e0189ef72c05p-104L, + +/* x = 1.95312500000000000000000000000000000e-01 3ffc9000000000000000000000000000 */ +/* cos(x) = 0.fb21f7f5c156696b00ac1fe28a c5fd76674a92b4df80d9c8a46c 684399005deccc41386257c */ + 0x0.fb21f7f5c156696b00ac1fe28ap0L, + 0x0.c5fd76674a92b4df80d9c8a46cp-104L, +/* sin(x) = 0.31aec65df552876f82ece9a235 6713246eba6799983d7011b0b3 698d6e1da919c15d57c30c1 */ + 0x0.31aec65df552876f82ece9a235p0L, + 0x0.6713246eba6799983d7011b0b3p-104L, + +/* x = 2.03125000000000000000000000000000000e-01 3ffca000000000000000000000000000 */ +/* cos(x) = 0.fabca467fb3cb8f1d069f01d8e a33ade5bfd68296ecd1cc9f7b7 609bbcf3676e726c3301334 */ + 0x0.fabca467fb3cb8f1d069f01d8ep0L, + 0x0.a33ade5bfd68296ecd1cc9f7b7p-104L, +/* sin(x) = 0.33a4a5a19d86246710f602c44d f4fa513f4639ce938477aeeabb 82e8e0a7ed583a188879fd4 */ + 0x0.33a4a5a19d86246710f602c44dp0L, + 0x0.f4fa513f4639ce938477aeeabbp-104L, + +/* x = 2.10937500000000000000000000000000000e-01 3ffcb000000000000000000000000000 */ +/* cos(x) = 0.fa5365e8f1d3ca27be1db5d76a e64d983d7470a4ab0f4ccf65a2 b8c67a380df949953a09bc1 */ + 0x0.fa5365e8f1d3ca27be1db5d76ap0L, + 0x0.e64d983d7470a4ab0f4ccf65a2p-104L, +/* sin(x) = 0.3599b652f40ec999df12a0a4c8 561de159c98d4e54555de518b9 7f48886f715d8df5f4f093e */ + 0x0.3599b652f40ec999df12a0a4c8p0L, + 0x0.561de159c98d4e54555de518b9p-104L, + +/* x = 2.18750000000000000000000000000000000e-01 3ffcc000000000000000000000000000 */ +/* cos(x) = 0.f9e63e1d9e8b6f6f2e296bae5b 5ed9c11fd7fa2fe11e09fc7bde 901abed24b6365e72f7db4e */ + 0x0.f9e63e1d9e8b6f6f2e296bae5bp0L, + 0x0.5ed9c11fd7fa2fe11e09fc7bdep-104L, +/* sin(x) = 0.378df09db8c332ce0d2b53d865 582e4526ea336c768f68c32b49 6c6d11c1cd241bb9f1da523 */ + 0x0.378df09db8c332ce0d2b53d865p0L, + 0x0.582e4526ea336c768f68c32b49p-104L, + +/* x = 2.26562500000000000000000000000000000e-01 3ffcd000000000000000000000000000 */ +/* cos(x) = 0.f9752eba9fff6b98842beadab0 54a932fb0f8d5b875ae63d6b22 88d09b148921aeb6e52f61b */ + 0x0.f9752eba9fff6b98842beadab0p0L, + 0x0.54a932fb0f8d5b875ae63d6b22p-104L, +/* sin(x) = 0.39814cb10513453cb97b21bc1c a6a337b150c21a675ab85503bc 09a436a10ab1473934e20c8 */ + 0x0.39814cb10513453cb97b21bc1cp0L, + 0x0.a6a337b150c21a675ab85503bcp-104L, + +/* x = 2.34375000000000000000000000000000000e-01 3ffce000000000000000000000000000 */ +/* cos(x) = 0.f90039843324f9b940416c1984 b6cbed1fc733d97354d4265788 a86150493ce657cae032674 */ + 0x0.f90039843324f9b940416c1984p0L, + 0x0.b6cbed1fc733d97354d4265788p-104L, +/* sin(x) = 0.3b73c2bf6b4b9f668ef9499c81 f0d965087f1753fa64b086e58c b8470515c18c1412f8c2e02 */ + 0x0.3b73c2bf6b4b9f668ef9499c81p0L, + 0x0.f0d965087f1753fa64b086e58cp-104L, + +/* x = 2.42187500000000000000000000000000000e-01 3ffcf000000000000000000000000000 */ +/* cos(x) = 0.f887604e2c39dbb20e4ec58250 59a789ffc95b275ad9954078ba 8a28d3fcfe9cc2c1d49697b */ + 0x0.f887604e2c39dbb20e4ec58250p0L, + 0x0.59a789ffc95b275ad9954078bap-104L, +/* sin(x) = 0.3d654aff15cb457a0fca854698 aba33039a8a40626609204472d 9d40309b626eccc6dff0ffa */ + 0x0.3d654aff15cb457a0fca854698p0L, + 0x0.aba33039a8a40626609204472dp-104L, + +/* x = 2.50000000000000000000000000000000000e-01 3ffd0000000000000000000000000000 */ +/* cos(x) = 0.f80aa4fbef750ba783d33cb95f 94f8a41426dbe79edc4a023ef9 ec13c944551c0795b84fee1 */ + 0x0.f80aa4fbef750ba783d33cb95fp0L, + 0x0.94f8a41426dbe79edc4a023ef9p-104L, +/* sin(x) = 0.3f55dda9e62aed7513bd7b8e6a 3d1635dd5676648d7db525898d 7086af9330f03c7f285442a */ + 0x0.3f55dda9e62aed7513bd7b8e6ap0L, + 0x0.3d1635dd5676648d7db525898dp-104L, + +/* x = 2.57812500000000000000000000000000000e-01 3ffd0800000000000000000000000000 */ +/* cos(x) = 0.f78a098069792daabc9ee42591 b7c5a68cb1ab822aeb446b3311 b4ba5371b8970e2c1547ad7 */ + 0x0.f78a098069792daabc9ee42591p0L, + 0x0.b7c5a68cb1ab822aeb446b3311p-104L, +/* sin(x) = 0.414572fd94556e6473d6202713 88dd47c0ba050cdb5270112e3e 370e8c4705ae006426fb5d5 */ + 0x0.414572fd94556e6473d6202713p0L, + 0x0.88dd47c0ba050cdb5270112e3ep-104L, + +/* x = 2.65625000000000000000000000000000000e-01 3ffd1000000000000000000000000000 */ +/* cos(x) = 0.f7058fde0788dfc805b8fe8878 9e4f4253e3c50afe8b22f41159 620ab5940ff7df9557c0d1f */ + 0x0.f7058fde0788dfc805b8fe8878p0L, + 0x0.9e4f4253e3c50afe8b22f41159p-104L, +/* sin(x) = 0.4334033bcd90d6604f5f36c1d4 b84451a87150438275b77470b5 0e5b968fa7962b5ffb379b7 */ + 0x0.4334033bcd90d6604f5f36c1d4p0L, + 0x0.b84451a87150438275b77470b5p-104L, + +/* x = 2.73437500000000000000000000000000000e-01 3ffd1800000000000000000000000000 */ +/* cos(x) = 0.f67d3a26af7d07aa4bd6d42af8 c0067fefb96d5b46c031eff536 27f215ea3242edc3f2e13eb */ + 0x0.f67d3a26af7d07aa4bd6d42af8p0L, + 0x0.c0067fefb96d5b46c031eff536p-104L, +/* sin(x) = 0.452186aa5377ab20bbf2524f52 e3a06a969f47166ab88cf88c11 1ad12c55941021ef3317a1a */ + 0x0.452186aa5377ab20bbf2524f52p0L, + 0x0.e3a06a969f47166ab88cf88c11p-104L, + +/* x = 2.81250000000000000000000000000000000e-01 3ffd2000000000000000000000000000 */ +/* cos(x) = 0.f5f10a7bb77d3dfa0c1da8b578 42783280d01ce3c0f82bae3b9d 623c168d2e7c29977994451 */ + 0x0.f5f10a7bb77d3dfa0c1da8b578p0L, + 0x0.42783280d01ce3c0f82bae3b9dp-104L, +/* sin(x) = 0.470df5931ae1d946076fe0dcff 47fe31bb2ede618ebc607821f8 462b639e1f4298b5ae87fd3 */ + 0x0.470df5931ae1d946076fe0dcffp0L, + 0x0.47fe31bb2ede618ebc607821f8p-104L, + +/* x = 2.89062500000000000000000000000000000e-01 3ffd2800000000000000000000000000 */ +/* cos(x) = 0.f561030ddd7a78960ea9f4a32c 6521554995667f5547bafee9ec 48b3155cdb0f7fd00509713 */ + 0x0.f561030ddd7a78960ea9f4a32cp0L, + 0x0.6521554995667f5547bafee9ecp-104L, +/* sin(x) = 0.48f948446abcd6b0f7fccb100e 7a1b26eccad880b0d24b59948c 7cdd49514d44b933e6985c2 */ + 0x0.48f948446abcd6b0f7fccb100ep0L, + 0x0.7a1b26eccad880b0d24b59948cp-104L, + +/* x = 2.96875000000000000000000000000000000e-01 3ffd3000000000000000000000000000 */ +/* cos(x) = 0.f4cd261d3e6c15bb369c875863 0d2ac00b7ace2a51c0631bfeb3 9ed158ba924cc91e259c195 */ + 0x0.f4cd261d3e6c15bb369c875863p0L, + 0x0.0d2ac00b7ace2a51c0631bfeb3p-104L, +/* sin(x) = 0.4ae37710fad27c8aa9c4cf96c0 3519b9ce07dc08a1471775499f 05c29f86190aaebaeb9716e */ + 0x0.4ae37710fad27c8aa9c4cf96c0p0L, + 0x0.3519b9ce07dc08a1471775499fp-104L, + +/* x = 3.04687500000000000000000000000000000e-01 3ffd3800000000000000000000000000 */ +/* cos(x) = 0.f43575f94d4f6b272f5fb76b14 d2a64ab52df1ee8ddf7c651034 e5b2889305a9ea9015d758a */ + 0x0.f43575f94d4f6b272f5fb76b14p0L, + 0x0.d2a64ab52df1ee8ddf7c651034p-104L, +/* sin(x) = 0.4ccc7a50127e1de0cb6b40c302 c651f7bded4f9e7702b0471ae0 288d091a37391950907202f */ + 0x0.4ccc7a50127e1de0cb6b40c302p0L, + 0x0.c651f7bded4f9e7702b0471ae0p-104L, + +/* x = 3.12500000000000000000000000000000000e-01 3ffd4000000000000000000000000000 */ +/* cos(x) = 0.f399f500c9e9fd37ae9957263d ab8877102beb569f101ee44953 50868e5847d181d50d3cca2 */ + 0x0.f399f500c9e9fd37ae9957263dp0L, + 0x0.ab8877102beb569f101ee44953p-104L, +/* sin(x) = 0.4eb44a5da74f600207aaa090f0 734e288603ffadb3eb2542a469 77b105f8547128036dcf7f0 */ + 0x0.4eb44a5da74f600207aaa090f0p0L, + 0x0.734e288603ffadb3eb2542a469p-104L, + +/* x = 3.20312500000000000000000000000000000e-01 3ffd4800000000000000000000000000 */ +/* cos(x) = 0.f2faa5a1b74e82fd61fa05f917 7380e8e69b7b15a945e8e5ae11 24bf3d12b0617e03af4fab5 */ + 0x0.f2faa5a1b74e82fd61fa05f917p0L, + 0x0.7380e8e69b7b15a945e8e5ae11p-104L, +/* sin(x) = 0.509adf9a7b9a5a0f638a8fa3a6 0a199418859f18b37169a644fd b986c21ecb00133853bc35b */ + 0x0.509adf9a7b9a5a0f638a8fa3a6p0L, + 0x0.0a199418859f18b37169a644fdp-104L, + +/* x = 3.28125000000000000000000000000000000e-01 3ffd5000000000000000000000000000 */ +/* cos(x) = 0.f2578a595224dd2e6bfa2eb2f9 9cc674f5ea6f479eae2eb58018 6897ae3f893df1113ca06b8 */ + 0x0.f2578a595224dd2e6bfa2eb2f9p0L, + 0x0.9cc674f5ea6f479eae2eb58018p-104L, +/* sin(x) = 0.5280326c3cf481823ba6bb08ea c82c2093f2bce3c4eb4ee3dec7 df41c92c8a4226098616075 */ + 0x0.5280326c3cf481823ba6bb08eap0L, + 0x0.c82c2093f2bce3c4eb4ee3dec7p-104L, + +/* x = 3.35937500000000000000000000000000000e-01 3ffd5800000000000000000000000000 */ +/* cos(x) = 0.f1b0a5b406b526d886c55feadc 8d0dcc8eb9ae2ac707051771b4 8e05b25b000009660bdb3e3 */ + 0x0.f1b0a5b406b526d886c55feadcp0L, + 0x0.8d0dcc8eb9ae2ac707051771b4p-104L, +/* sin(x) = 0.54643b3da29de9b357155eef0f 332fb3e66c83bf4dddd9491c5e b8e103ccd92d6175220ed51 */ + 0x0.54643b3da29de9b357155eef0fp0L, + 0x0.332fb3e66c83bf4dddd9491c5ep-104L, + +/* x = 3.43750000000000000000000000000000000e-01 3ffd6000000000000000000000000000 */ +/* cos(x) = 0.f105fa4d66b607a67d44e04272 5204435142ac8ad54dfb0907a4 f6b56b06d98ee60f19e557a */ + 0x0.f105fa4d66b607a67d44e04272p0L, + 0x0.5204435142ac8ad54dfb0907a4p-104L, +/* sin(x) = 0.5646f27e8bd65cbe3a5d61ff06 572290ee826d9674a00246b05a e26753cdfc90d9ce81a7d02 */ + 0x0.5646f27e8bd65cbe3a5d61ff06p0L, + 0x0.572290ee826d9674a00246b05ap-104L, + +/* x = 3.51562500000000000000000000000000000e-01 3ffd6800000000000000000000000000 */ +/* cos(x) = 0.f0578ad01ede707fa39c09dc6b 984afef74f3dc8d0efb0f4c5a6 b13771145b3e0446fe33887 */ + 0x0.f0578ad01ede707fa39c09dc6bp0L, + 0x0.984afef74f3dc8d0efb0f4c5a6p-104L, +/* sin(x) = 0.582850a41e1dd46c7f602ea244 cdbbbfcdfa8f3189be794dda42 7ce090b5f85164f1f80ac13 */ + 0x0.582850a41e1dd46c7f602ea244p0L, + 0x0.cdbbbfcdfa8f3189be794dda42p-104L, + +/* x = 3.59375000000000000000000000000000000e-01 3ffd7000000000000000000000000000 */ +/* cos(x) = 0.efa559f5ec3aec3a4eb0331927 8a2d41fcf9189462261125fe61 47b078f1daa0b06750a1654 */ + 0x0.efa559f5ec3aec3a4eb0331927p0L, + 0x0.8a2d41fcf9189462261125fe61p-104L, +/* sin(x) = 0.5a084e28e35fda2776dfdbbb55 31d74ced2b5d17c0b1afc46475 29d50c295e36d8ceec126c1 */ + 0x0.5a084e28e35fda2776dfdbbb55p0L, + 0x0.31d74ced2b5d17c0b1afc46475p-104L, + +/* x = 3.67187500000000000000000000000000000e-01 3ffd7800000000000000000000000000 */ +/* cos(x) = 0.eeef6a879146af0bf9b95ea2ea 0ac0d3e2e4d7e15d93f48cbd41 bf8e4fded40bef69e19eafa */ + 0x0.eeef6a879146af0bf9b95ea2eap0L, + 0x0.0ac0d3e2e4d7e15d93f48cbd41p-104L, +/* sin(x) = 0.5be6e38ce8095542bc14ee9da0 d36483e6734bcab2e07624188a f5653f114eeb46738fa899d */ + 0x0.5be6e38ce8095542bc14ee9da0p0L, + 0x0.d36483e6734bcab2e07624188ap-104L, + +/* x = 3.75000000000000000000000000000000000e-01 3ffd8000000000000000000000000000 */ +/* cos(x) = 0.ee35bf5ccac89052cd91ddb734 d3a47e262e3b609db604e21705 3803be0091e76daf28a89b7 */ + 0x0.ee35bf5ccac89052cd91ddb734p0L, + 0x0.d3a47e262e3b609db604e21705p-104L, +/* sin(x) = 0.5dc40955d9084f48a94675a249 8de5d851320ff5528a6afb3f2e 24de240fce6cbed1ba0ccd6 */ + 0x0.5dc40955d9084f48a94675a249p0L, + 0x0.8de5d851320ff5528a6afb3f2ep-104L, + +/* x = 3.82812500000000000000000000000000000e-01 3ffd8800000000000000000000000000 */ +/* cos(x) = 0.ed785b5c44741b4493c56bcb9d 338a151c6f6b85d8f8aca658b2 8572c162b199680eb9304da */ + 0x0.ed785b5c44741b4493c56bcb9dp0L, + 0x0.338a151c6f6b85d8f8aca658b2p-104L, +/* sin(x) = 0.5f9fb80f21b53649c432540a50 e22c53057ff42ae0fdf1307760 dc0093f99c8efeb2fbd7073 */ + 0x0.5f9fb80f21b53649c432540a50p0L, + 0x0.e22c53057ff42ae0fdf1307760p-104L, + +/* x = 3.90625000000000000000000000000000000e-01 3ffd9000000000000000000000000000 */ +/* cos(x) = 0.ecb7417b8d4ee3fec37aba4073 aa48f1f14666006fb431d96713 03c8100d10190ec8179c41d */ + 0x0.ecb7417b8d4ee3fec37aba4073p0L, + 0x0.aa48f1f14666006fb431d96713p-104L, +/* sin(x) = 0.6179e84a09a5258a40e9b5face 03e525f8b5753cd0105d93fe62 98010c3458e84d75fe420e9 */ + 0x0.6179e84a09a5258a40e9b5facep0L, + 0x0.03e525f8b5753cd0105d93fe62p-104L, + +/* x = 3.98437500000000000000000000000000000e-01 3ffd9800000000000000000000000000 */ +/* cos(x) = 0.ebf274bf0bda4f62447e56a093 626798d3013b5942b1abfd155a acc9dc5c6d0806a20d6b9c1 */ + 0x0.ebf274bf0bda4f62447e56a093p0L, + 0x0.626798d3013b5942b1abfd155ap-104L, +/* sin(x) = 0.6352929dd264bd44a02ea76632 5d8aa8bd9695fc8def3caefba5 b94c9a3c873f7b2d3776ead */ + 0x0.6352929dd264bd44a02ea76632p0L, + 0x0.5d8aa8bd9695fc8def3caefba5p-104L, + +/* x = 4.06250000000000000000000000000000000e-01 3ffda000000000000000000000000000 */ +/* cos(x) = 0.eb29f839f201fd13b937968279 16a78f15c85230a4e8ea4b2155 8265a14367e1abb4c30695a */ + 0x0.eb29f839f201fd13b937968279p0L, + 0x0.16a78f15c85230a4e8ea4b2155p-104L, +/* sin(x) = 0.6529afa7d51b129631ec197c0a 840a11d7dc5368b0a47956feb2 85caa8371c4637ef17ef01b */ + 0x0.6529afa7d51b129631ec197c0ap0L, + 0x0.840a11d7dc5368b0a47956feb2p-104L, + +/* x = 4.14062500000000000000000000000000000e-01 3ffda800000000000000000000000000 */ +/* cos(x) = 0.ea5dcf0e30cf03e6976ef0b1ec 26515fba47383855c3b4055a99 b5e86824b2cd1a691fdca7b */ + 0x0.ea5dcf0e30cf03e6976ef0b1ecp0L, + 0x0.26515fba47383855c3b4055a99p-104L, +/* sin(x) = 0.66ff380ba0144109e39a320b0a 3fa5fd65ea0585bcbf9b1a769a 9b0334576c658139e1a1cbe */ + 0x0.66ff380ba0144109e39a320b0ap0L, + 0x0.3fa5fd65ea0585bcbf9b1a769ap-104L, + +/* x = 4.21875000000000000000000000000000000e-01 3ffdb000000000000000000000000000 */ +/* cos(x) = 0.e98dfc6c6be031e60dd3089cbd d18a75b1f6b2c1e97f79225202 f03dbea45b07a5ec4efc062 */ + 0x0.e98dfc6c6be031e60dd3089cbdp0L, + 0x0.d18a75b1f6b2c1e97f79225202p-104L, +/* sin(x) = 0.68d32473143327973bc712bcc4 ccddc47630d755850c0655243b 205934dc49ffed8eb76adcb */ + 0x0.68d32473143327973bc712bcc4p0L, + 0x0.ccddc47630d755850c0655243bp-104L, + +/* x = 4.29687500000000000000000000000000000e-01 3ffdb800000000000000000000000000 */ +/* cos(x) = 0.e8ba8393eca7821aa563d83491 b6101189b3b101c3677f73d7ba d7c10f9ee02b7ab4009739a */ + 0x0.e8ba8393eca7821aa563d83491p0L, + 0x0.b6101189b3b101c3677f73d7bap-104L, +/* sin(x) = 0.6aa56d8e8249db4eb60a761fe3 f9e559be456b9e13349ca99b0b fb787f22b95db3b70179615 */ + 0x0.6aa56d8e8249db4eb60a761fe3p0L, + 0x0.f9e559be456b9e13349ca99b0bp-104L, + +/* x = 4.37500000000000000000000000000000000e-01 3ffdc000000000000000000000000000 */ +/* cos(x) = 0.e7e367d2956cfb16b6aa11e541 9cd0057f5c132a6455bf064297 e6a76fe2b72bb630d6d50ff */ + 0x0.e7e367d2956cfb16b6aa11e541p0L, + 0x0.9cd0057f5c132a6455bf064297p-104L, +/* sin(x) = 0.6c760c14c8585a51dbd34660ae 6c52ac7036a0b40887a0b63724 f8b4414348c3063a637f457 */ + 0x0.6c760c14c8585a51dbd34660aep0L, + 0x0.6c52ac7036a0b40887a0b63724p-104L, + +/* x = 4.45312500000000000000000000000000000e-01 3ffdc800000000000000000000000000 */ +/* cos(x) = 0.e708ac84d4172a3e2737662213 429e14021074d7e702e77d72a8 f1101a7e70410df8273e9aa */ + 0x0.e708ac84d4172a3e2737662213p0L, + 0x0.429e14021074d7e702e77d72a8p-104L, +/* sin(x) = 0.6e44f8c36eb10a1c752d093c00 f4d47ba446ac4c215d26b03164 42f168459e677d06e7249e3 */ + 0x0.6e44f8c36eb10a1c752d093c00p0L, + 0x0.f4d47ba446ac4c215d26b03164p-104L, + +/* x = 4.53125000000000000000000000000000000e-01 3ffdd000000000000000000000000000 */ +/* cos(x) = 0.e62a551594b970a770b15d41d4 c0e483e47aca550111df6966f9 e7ac3a94ae49e6a71eb031e */ + 0x0.e62a551594b970a770b15d41d4p0L, + 0x0.c0e483e47aca550111df6966f9p-104L, +/* sin(x) = 0.70122c5ec5028c8cff33abf4fd 340ccc382e038379b09cf04f9a 52692b10b72586060cbb001 */ + 0x0.70122c5ec5028c8cff33abf4fdp0L, + 0x0.340ccc382e038379b09cf04f9ap-104L, + +/* x = 4.60937500000000000000000000000000000e-01 3ffdd800000000000000000000000000 */ +/* cos(x) = 0.e54864fe33e8575cabf5bd0e5c f1b1a8bc7c0d5f61702450fa6b 6539735820dd2603ae355d5 */ + 0x0.e54864fe33e8575cabf5bd0e5cp0L, + 0x0.f1b1a8bc7c0d5f61702450fa6bp-104L, +/* sin(x) = 0.71dd9fb1ff4677853acb970a9f 6729c6e3aac247b1c57cea66c7 7413f1f98e8b9e98e49d851 */ + 0x0.71dd9fb1ff4677853acb970a9fp0L, + 0x0.6729c6e3aac247b1c57cea66c7p-104L, + +/* x = 4.68750000000000000000000000000000000e-01 3ffde000000000000000000000000000 */ +/* cos(x) = 0.e462dfc670d421ab3d1a159012 28f146a0547011202bf5ab01f9 14431859aef577966bc4fa4 */ + 0x0.e462dfc670d421ab3d1a159012p0L, + 0x0.28f146a0547011202bf5ab01f9p-104L, +/* sin(x) = 0.73a74b8f52947b681baf6928eb 3fb021769bf4779bad0e3aa9b1 cdb75ec60aad9fc63ff19d5 */ + 0x0.73a74b8f52947b681baf6928ebp0L, + 0x0.3fb021769bf4779bad0e3aa9b1p-104L, + +/* x = 4.76562500000000000000000000000000000e-01 3ffde800000000000000000000000000 */ +/* cos(x) = 0.e379c9045f29d517c4808aa497 c2057b2b3d109e76c0dc302d4d 0698b36e3f0bdbf33d8e952 */ + 0x0.e379c9045f29d517c4808aa497p0L, + 0x0.c2057b2b3d109e76c0dc302d4dp-104L, +/* sin(x) = 0.756f28d011d98528a44a75fc29 c779bd734ecdfb582fdb74b68a 4c4c4be54cfd0b2d3ad292f */ + 0x0.756f28d011d98528a44a75fc29p0L, + 0x0.c779bd734ecdfb582fdb74b68ap-104L, + +/* x = 4.84375000000000000000000000000000000e-01 3ffdf000000000000000000000000000 */ +/* cos(x) = 0.e28d245c58baef72225e232abc 003c4366acd9eb4fc2808c2ab7 fe7676cf512ac7f945ae5fb */ + 0x0.e28d245c58baef72225e232abcp0L, + 0x0.003c4366acd9eb4fc2808c2ab7p-104L, +/* sin(x) = 0.77353054ca72690d4c6e171fd9 9e6b39fa8e1ede5f052fd29645 34c75340970a3a9cd3c5c32 */ + 0x0.77353054ca72690d4c6e171fd9p0L, + 0x0.9e6b39fa8e1ede5f052fd29645p-104L, + +/* x = 4.92187500000000000000000000000000000e-01 3ffdf800000000000000000000000000 */ +/* cos(x) = 0.e19cf580eeec046aa1422fa748 07ecefb2a1911c94e7b5f20a00 f70022d940193691e5bd790 */ + 0x0.e19cf580eeec046aa1422fa748p0L, + 0x0.07ecefb2a1911c94e7b5f20a00p-104L, +/* sin(x) = 0.78f95b0560a9a3bd6df7bd981d c38c61224d08bc20631ea932e6 05e53b579e9e0767dfcbbcb */ + 0x0.78f95b0560a9a3bd6df7bd981dp0L, + 0x0.c38c61224d08bc20631ea932e6p-104L, + +/* x = 5.00000000000000000000000000000000000e-01 3ffe0000000000000000000000000000 */ +/* cos(x) = 0.e0a94032dbea7cedbddd9da2fa fad98556566b3a89f43eabd723 50af3e8b19e801204d8fe2e */ + 0x0.e0a94032dbea7cedbddd9da2fap0L, + 0x0.fad98556566b3a89f43eabd723p-104L, +/* sin(x) = 0.7abba1d12c17bfa1d92f0d93f6 0ded9992f45b4fcaf13cd58b30 3693d2a0db47db35ae8a3a9 */ + 0x0.7abba1d12c17bfa1d92f0d93f6p0L, + 0x0.0ded9992f45b4fcaf13cd58b30p-104L, + +/* x = 5.07812500000000000000000000000000000e-01 3ffe0400000000000000000000000000 */ +/* cos(x) = 0.dfb20840f3a9b36f7ae2c51534 2890b5ec583b8366cc2b55029e 95094d31112383f2553498b */ + 0x0.dfb20840f3a9b36f7ae2c51534p0L, + 0x0.2890b5ec583b8366cc2b55029ep-104L, +/* sin(x) = 0.7c7bfdaf13e5ed17212f8a7525 bfb113aba6c0741b5362bb8d59 282a850b63716bca0c910f0 */ + 0x0.7c7bfdaf13e5ed17212f8a7525p0L, + 0x0.bfb113aba6c0741b5362bb8d59p-104L, + +/* x = 5.15625000000000000000000000000000000e-01 3ffe0800000000000000000000000000 */ +/* cos(x) = 0.deb7518814a7a931bbcc88c109 cd41c50bf8bb48f20ae8c36628 d1d3d57574f7dc58f27d91c */ + 0x0.deb7518814a7a931bbcc88c109p0L, + 0x0.cd41c50bf8bb48f20ae8c36628p-104L, +/* sin(x) = 0.7e3a679daaf25c676542bcb402 8d0964172961c921823a4ef0c3 a9070d886dbd073f6283699 */ + 0x0.7e3a679daaf25c676542bcb402p0L, + 0x0.8d0964172961c921823a4ef0c3p-104L, + +/* x = 5.23437500000000000000000000000000000e-01 3ffe0c00000000000000000000000000 */ +/* cos(x) = 0.ddb91ff318799172bd2452d0a3 889f5169c64a0094bcf0b8aa7d cf0d7640a2eba68955a80be */ + 0x0.ddb91ff318799172bd2452d0a3p0L, + 0x0.889f5169c64a0094bcf0b8aa7dp-104L, +/* sin(x) = 0.7ff6d8a34bd5e8fa54c97482db 5159df1f24e8038419c0b448b9 eea8939b5d4dfcf40900257 */ + 0x0.7ff6d8a34bd5e8fa54c97482dbp0L, + 0x0.5159df1f24e8038419c0b448b9p-104L, + +/* x = 5.31250000000000000000000000000000000e-01 3ffe1000000000000000000000000000 */ +/* cos(x) = 0.dcb7777ac420705168f31e3eb7 80ce9c939ecada62843b54522f 5407eb7f21e556059fcd734 */ + 0x0.dcb7777ac420705168f31e3eb7p0L, + 0x0.80ce9c939ecada62843b54522fp-104L, +/* sin(x) = 0.81b149ce34caa5a4e650f8d09f d4d6aa74206c32ca951a93074c 83b2d294d25dbb0f7fdfad2 */ + 0x0.81b149ce34caa5a4e650f8d09fp0L, + 0x0.d4d6aa74206c32ca951a93074cp-104L, + +/* x = 5.39062500000000000000000000000000000e-01 3ffe1400000000000000000000000000 */ +/* cos(x) = 0.dbb25c25b8260c14f6e7bc98ec 991b70c65335198b0ab628bad2 0cc7b229d4dd62183cfa055 */ + 0x0.dbb25c25b8260c14f6e7bc98ecp0L, + 0x0.991b70c65335198b0ab628bad2p-104L, +/* sin(x) = 0.8369b434a372da7eb5c8a71fe3 6ce1e0b2b493f6f5cb2e38bcae c2a556b3678c401940d1c3c */ + 0x0.8369b434a372da7eb5c8a71fe3p0L, + 0x0.6ce1e0b2b493f6f5cb2e38bcaep-104L, + +/* x = 5.46875000000000000000000000000000000e-01 3ffe1800000000000000000000000000 */ +/* cos(x) = 0.daa9d20860827063fde51c09e8 55e9932e1b17143e7244fd267a 899d41ae1f3bc6a0ec42e27 */ + 0x0.daa9d20860827063fde51c09e8p0L, + 0x0.55e9932e1b17143e7244fd267ap-104L, +/* sin(x) = 0.852010f4f0800521378bd8dd61 4753d080c2e9e0775ffc609947 b9132f5357404f464f06a58 */ + 0x0.852010f4f0800521378bd8dd61p0L, + 0x0.4753d080c2e9e0775ffc609947p-104L, + +/* x = 5.54687500000000000000000000000000000e-01 3ffe1c00000000000000000000000000 */ +/* cos(x) = 0.d99ddd44e44a43d4d4a3a3ed95 204106fd54d78e8c7684545c0d a0b7c2c72be7a89b7c182ad */ + 0x0.d99ddd44e44a43d4d4a3a3ed95p0L, + 0x0.204106fd54d78e8c7684545c0dp-104L, +/* sin(x) = 0.86d45935ab396cb4e421e822de e54f3562dfcefeaa782184c234 01d231f5ad981a1cc195b18 */ + 0x0.86d45935ab396cb4e421e822dep0L, + 0x0.e54f3562dfcefeaa782184c234p-104L, + +/* x = 5.62500000000000000000000000000000000e-01 3ffe2000000000000000000000000000 */ +/* cos(x) = 0.d88e820b1526311dd561efbc0c 1a9a5375eb26f65d246c5744b1 3ca26a7e0fd42556da843c8 */ + 0x0.d88e820b1526311dd561efbc0cp0L, + 0x0.1a9a5375eb26f65d246c5744b1p-104L, +/* sin(x) = 0.88868625b4e1dbb23133101330 22527200c143a5cb16637cb7da f8ade82459ff2e98511f40f */ + 0x0.88868625b4e1dbb23133101330p0L, + 0x0.22527200c143a5cb16637cb7dap-104L, + +/* x = 5.70312500000000000000000000000000000e-01 3ffe2400000000000000000000000000 */ +/* cos(x) = 0.d77bc4985e93a607c9d868b906 bbc6bbe3a04258814acb035846 8b826fc91bd4d814827f65e */ + 0x0.d77bc4985e93a607c9d868b906p0L, + 0x0.bbc6bbe3a04258814acb035846p-104L, +/* sin(x) = 0.8a3690fc5bfc11bf9535e2739a 8512f448a41251514bbed7fc18 d530f9b4650fcbb2861b0aa */ + 0x0.8a3690fc5bfc11bf9535e2739ap0L, + 0x0.8512f448a41251514bbed7fc18p-104L, + +/* x = 5.78125000000000000000000000000000000e-01 3ffe2800000000000000000000000000 */ +/* cos(x) = 0.d665a937b4ef2b1f6d51bad6d9 88a4419c1d7051faf31a9efa15 1d7631117efac03713f950a */ + 0x0.d665a937b4ef2b1f6d51bad6d9p0L, + 0x0.88a4419c1d7051faf31a9efa15p-104L, +/* sin(x) = 0.8be472f9776d809af2b8817124 3d63d66dfceeeb739cc894e023 fbc165a0e3f26ff729c5d57 */ + 0x0.8be472f9776d809af2b8817124p0L, + 0x0.3d63d66dfceeeb739cc894e023p-104L, + +/* x = 5.85937500000000000000000000000000000e-01 3ffe2c00000000000000000000000000 */ +/* cos(x) = 0.d54c3441844897fc8f853f0655 f1ba695eba9fbfd7439dbb1171 d862d9d9146ca5136f825ac */ + 0x0.d54c3441844897fc8f853f0655p0L, + 0x0.f1ba695eba9fbfd7439dbb1171p-104L, +/* sin(x) = 0.8d902565817ee7839bce3cd128 060119492cd36d42d82ada30d7 f8bde91324808377ddbf5d4 */ + 0x0.8d902565817ee7839bce3cd128p0L, + 0x0.060119492cd36d42d82ada30d7p-104L, + +/* x = 5.93750000000000000000000000000000000e-01 3ffe3000000000000000000000000000 */ +/* cos(x) = 0.d42f6a1b9f0168cdf031c2f63c 8d9304d86f8d34cb1d5fccb68c a0f2241427fc18d1fd5bbdf */ + 0x0.d42f6a1b9f0168cdf031c2f63cp0L, + 0x0.8d9304d86f8d34cb1d5fccb68cp-104L, +/* sin(x) = 0.8f39a191b2ba6122a3fa4f41d5 a3ffd421417d46f19a22230a14 f7fcc8fce5c75b4b28b29d1 */ + 0x0.8f39a191b2ba6122a3fa4f41d5p0L, + 0x0.a3ffd421417d46f19a22230a14p-104L, + +/* x = 6.01562500000000000000000000000000000e-01 3ffe3400000000000000000000000000 */ +/* cos(x) = 0.d30f4f392c357ab0661c5fa8a7 d9b26627846fef214b1d19a223 79ff9eddba087cf410eb097 */ + 0x0.d30f4f392c357ab0661c5fa8a7p0L, + 0x0.d9b26627846fef214b1d19a223p-104L, +/* sin(x) = 0.90e0e0d81ca678796cc92c8ea8 c2815bc72ca78abe571bfa8576 aacc571e096a33237e0e830 */ + 0x0.90e0e0d81ca678796cc92c8ea8p0L, + 0x0.c2815bc72ca78abe571bfa8576p-104L, + +/* x = 6.09375000000000000000000000000000000e-01 3ffe3800000000000000000000000000 */ +/* cos(x) = 0.d1ebe81a95ee752e48a26bcd32 d6e922d7eb44b8ad2232f69307 95e84b56317269b9dd1dfa6 */ + 0x0.d1ebe81a95ee752e48a26bcd32p0L, + 0x0.d6e922d7eb44b8ad2232f69307p-104L, +/* sin(x) = 0.9285dc9bc45dd9ea3d02457bcc e59c4175aab6ff7929a8d28719 5525fdace200dba032874fb */ + 0x0.9285dc9bc45dd9ea3d02457bccp0L, + 0x0.e59c4175aab6ff7929a8d28719p-104L, + +/* x = 6.17187500000000000000000000000000000e-01 3ffe3c00000000000000000000000000 */ +/* cos(x) = 0.d0c5394d772228195e25736c03 574707de0af1ca344b13bd3914 bfe27518e9e426f5deff1e1 */ + 0x0.d0c5394d772228195e25736c03p0L, + 0x0.574707de0af1ca344b13bd3914p-104L, +/* sin(x) = 0.94288e48bd0335fc41c4cbd292 0497a8f5d1d8185c99fa0081f9 0c27e2a53ffdd208a0dbe69 */ + 0x0.94288e48bd0335fc41c4cbd292p0L, + 0x0.0497a8f5d1d8185c99fa0081f9p-104L, + +/* x = 6.25000000000000000000000000000000000e-01 3ffe4000000000000000000000000000 */ +/* cos(x) = 0.cf9b476c897c25c5bfe750dd3f 308eaf7bcc1ed00179a256870f 4200445043dcdb1974b5878 */ + 0x0.cf9b476c897c25c5bfe750dd3fp0L, + 0x0.308eaf7bcc1ed00179a256870fp-104L, +/* sin(x) = 0.95c8ef544210ec0b91c49bd2aa 09e8515fa61a156ebb10f5f8c2 32a6445b61ebf3c2ec268f9 */ + 0x0.95c8ef544210ec0b91c49bd2aap0L, + 0x0.09e8515fa61a156ebb10f5f8c2p-104L, + +/* x = 6.32812500000000000000000000000000000e-01 3ffe4400000000000000000000000000 */ +/* cos(x) = 0.ce6e171f92f2e27f32225327ec 440ddaefae248413efc0e58cee e1ae369aabe73f88c87ed1a */ + 0x0.ce6e171f92f2e27f32225327ecp0L, + 0x0.440ddaefae248413efc0e58ceep-104L, +/* sin(x) = 0.9766f93cd18413a6aafc1cfc6f c28abb6817bf94ce349901ae3f 48c3215d3eb60acc5f78903 */ + 0x0.9766f93cd18413a6aafc1cfc6fp0L, + 0x0.c28abb6817bf94ce349901ae3fp-104L, + +/* x = 6.40625000000000000000000000000000000e-01 3ffe4800000000000000000000000000 */ +/* cos(x) = 0.cd3dad1b5328a2e459f993f4f5 108819faccbc4eeba9604e81c7 adad51cc8a2561631a06826 */ + 0x0.cd3dad1b5328a2e459f993f4f5p0L, + 0x0.108819faccbc4eeba9604e81c7p-104L, +/* sin(x) = 0.9902a58a45e27bed68412b426b 675ed503f54d14c8172e0d373f 42cadf04daf67319a7f94be */ + 0x0.9902a58a45e27bed68412b426bp0L, + 0x0.675ed503f54d14c8172e0d373fp-104L, + +/* x = 6.48437500000000000000000000000000000e-01 3ffe4c00000000000000000000000000 */ +/* cos(x) = 0.cc0a0e21709883a3ff00911e11 a07ee3bd7ea2b04e081be99be0 264791170761ae64b8b744a */ + 0x0.cc0a0e21709883a3ff00911e11p0L, + 0x0.a07ee3bd7ea2b04e081be99be0p-104L, +/* sin(x) = 0.9a9bedcdf01b38d993f3d78207 81de292033ead73b89e28f3931 3dbe3a6e463f845b5fa8490 */ + 0x0.9a9bedcdf01b38d993f3d78207p0L, + 0x0.81de292033ead73b89e28f3931p-104L, + +/* x = 6.56250000000000000000000000000000000e-01 3ffe5000000000000000000000000000 */ +/* cos(x) = 0.cad33f00658fe5e8204bbc0f3a 66a0e6a773f87987a780b243d7 be83b3db1448ca0e0e62787 */ + 0x0.cad33f00658fe5e8204bbc0f3ap0L, + 0x0.66a0e6a773f87987a780b243d7p-104L, +/* sin(x) = 0.9c32cba2b14156ef05256c4f85 7991ca6a547cd7ceb1ac8a8e62 a282bd7b9183648a462bd04 */ + 0x0.9c32cba2b14156ef05256c4f85p0L, + 0x0.7991ca6a547cd7ceb1ac8a8e62p-104L, + +/* x = 6.64062500000000000000000000000000000e-01 3ffe5400000000000000000000000000 */ +/* cos(x) = 0.c99944936cf48c8911ff93fe64 b3ddb7981e414bdaf6aae12035 77de44878c62bc3bc9cf7b9 */ + 0x0.c99944936cf48c8911ff93fe64p0L, + 0x0.b3ddb7981e414bdaf6aae12035p-104L, +/* sin(x) = 0.9dc738ad14204e689ac582d0f8 5826590feece34886cfefe2e08 cf2bb8488d55424dc9d3525 */ + 0x0.9dc738ad14204e689ac582d0f8p0L, + 0x0.5826590feece34886cfefe2e08p-104L, + +/* x = 6.71875000000000000000000000000000000e-01 3ffe5800000000000000000000000000 */ +/* cos(x) = 0.c85c23c26ed7b6f014ef546c47 929682122876bfbf157de0aff3 c4247d820c746e32cd4174f */ + 0x0.c85c23c26ed7b6f014ef546c47p0L, + 0x0.929682122876bfbf157de0aff3p-104L, +/* sin(x) = 0.9f592e9b66a9cf906a3c7aa3c1 0199849040c45ec3f0a7475973 11038101780c5f266059dbf */ + 0x0.9f592e9b66a9cf906a3c7aa3c1p0L, + 0x0.0199849040c45ec3f0a7475973p-104L, + +/* x = 6.79687500000000000000000000000000000e-01 3ffe5c00000000000000000000000000 */ +/* cos(x) = 0.c71be181ecd6875ce2da5615a0 3cca207d9adcb9dfb0a1d6c40a 4f0056437f1a59ccddd06ee */ + 0x0.c71be181ecd6875ce2da5615a0p0L, + 0x0.3cca207d9adcb9dfb0a1d6c40ap-104L, +/* sin(x) = 0.a0e8a725d33c828c11fa50fd9e 9a15ffecfad43f3e534358076b 9b0f6865694842b1e8c67dc */ + 0x0.a0e8a725d33c828c11fa50fd9ep0L, + 0x0.9a15ffecfad43f3e534358076bp-104L, + +/* x = 6.87500000000000000000000000000000000e-01 3ffe6000000000000000000000000000 */ +/* cos(x) = 0.c5d882d2ee48030c7c07d28e98 1e34804f82ed4cf93655d23653 89b716de6ad44676a1cc5da */ + 0x0.c5d882d2ee48030c7c07d28e98p0L, + 0x0.1e34804f82ed4cf93655d23653p-104L, +/* sin(x) = 0.a2759c0e79c35582527c32b55f 5405c182c66160cb1d9eb7bb0b 7cdf4ad66f317bda4332914 */ + 0x0.a2759c0e79c35582527c32b55fp0L, + 0x0.5405c182c66160cb1d9eb7bb0bp-104L, + +/* x = 6.95312500000000000000000000000000000e-01 3ffe6400000000000000000000000000 */ +/* cos(x) = 0.c4920cc2ec38fb891b38827db0 8884fc66371ac4c2052ca8885b 981bbcfd3bb7b093ee31515 */ + 0x0.c4920cc2ec38fb891b38827db0p0L, + 0x0.8884fc66371ac4c2052ca8885bp-104L, +/* sin(x) = 0.a400072188acf49cd6b173825e 038346f105e1301afe642bcc36 4cea455e21e506e3e927ed8 */ + 0x0.a400072188acf49cd6b173825ep0L, + 0x0.038346f105e1301afe642bcc36p-104L, + +/* x = 7.03125000000000000000000000000000000e-01 3ffe6800000000000000000000000000 */ +/* cos(x) = 0.c348846bbd3631338ffe2bfe9d d1381a35b4e9c0c51b4c13fe37 6bad1bf5caacc4542be0aa9 */ + 0x0.c348846bbd3631338ffe2bfe9dp0L, + 0x0.d1381a35b4e9c0c51b4c13fe37p-104L, +/* sin(x) = 0.a587e23555bb08086d02b9c662 cdd29316c3e9bd08d93793634a 21b1810cce73bdb97a99b9e */ + 0x0.a587e23555bb08086d02b9c662p0L, + 0x0.cdd29316c3e9bd08d93793634ap-104L, + +/* x = 7.10937500000000000000000000000000000e-01 3ffe6c00000000000000000000000000 */ +/* cos(x) = 0.c1fbeef380e4ffdd5a613ec872 2f643ffe814ec2343e53adb549 627224fdc9f2a7b77d3d69f */ + 0x0.c1fbeef380e4ffdd5a613ec872p0L, + 0x0.2f643ffe814ec2343e53adb549p-104L, +/* sin(x) = 0.a70d272a76a8d4b6da0ec90712 bb748b96dabf88c3079246f3db 7eea6e58ead4ed0e2843303 */ + 0x0.a70d272a76a8d4b6da0ec90712p0L, + 0x0.bb748b96dabf88c3079246f3dbp-104L, + +/* x = 7.18750000000000000000000000000000000e-01 3ffe7000000000000000000000000000 */ +/* cos(x) = 0.c0ac518c8b6ae710ba37a3eeb9 0cb15aebcb8bed4356fb507a48 a6e97de9aa6d9660116b436 */ + 0x0.c0ac518c8b6ae710ba37a3eeb9p0L, + 0x0.0cb15aebcb8bed4356fb507a48p-104L, +/* sin(x) = 0.a88fcfebd9a8dd47e2f3c76ef9 e2439920f7e7fbe735f8bcc985 491ec6f12a2d4214f8cfa99 */ + 0x0.a88fcfebd9a8dd47e2f3c76ef9p0L, + 0x0.e2439920f7e7fbe735f8bcc985p-104L, + +/* x = 7.26562500000000000000000000000000000e-01 3ffe7400000000000000000000000000 */ +/* cos(x) = 0.bf59b17550a440687596929656 7cf3e3b4e483061877c02811c6 cae85fad5a6c3da58f49292 */ + 0x0.bf59b17550a440687596929656p0L, + 0x0.7cf3e3b4e483061877c02811c6p-104L, +/* sin(x) = 0.aa0fd66eddb921232c28520d39 11b8a03193b47f187f1471ac21 6fbcd5bb81029294d3a73f1 */ + 0x0.aa0fd66eddb921232c28520d39p0L, + 0x0.11b8a03193b47f187f1471ac21p-104L, + +/* x = 7.34375000000000000000000000000000000e-01 3ffe7800000000000000000000000000 */ +/* cos(x) = 0.be0413f84f2a771c614946a88c bf4da1d75a5560243de8f2283f efa0ea4a48468a52d51d8b3 */ + 0x0.be0413f84f2a771c614946a88cp0L, + 0x0.bf4da1d75a5560243de8f2283fp-104L, +/* sin(x) = 0.ab8d34b36acd987210ed343ec6 5d7e3adc2e7109fce43d55c8d5 7dfdf55b9e01d2cc1f1b9ec */ + 0x0.ab8d34b36acd987210ed343ec6p0L, + 0x0.5d7e3adc2e7109fce43d55c8d5p-104L, + +/* x = 7.42187500000000000000000000000000000e-01 3ffe7c00000000000000000000000000 */ +/* cos(x) = 0.bcab7e6bfb2a14a9b122c574a3 76bec98ab14808c64a4e731b34 047e217611013ac99c0f25d */ + 0x0.bcab7e6bfb2a14a9b122c574a3p0L, + 0x0.76bec98ab14808c64a4e731b34p-104L, +/* sin(x) = 0.ad07e4c409d08c4fa3a9057bb0 ac24b8636e74e76f51e09bd6b2 319707cbd9f5e254643897a */ + 0x0.ad07e4c409d08c4fa3a9057bb0p0L, + 0x0.ac24b8636e74e76f51e09bd6b2p-104L, + +/* x = 7.50000000000000000000000000000000000e-01 3ffe8000000000000000000000000000 */ +/* cos(x) = 0.bb4ff632a908f73ec151839cb9 d993b4e0bfb8f20e7e44e6e4ae e845e35575c3106dbe6fd06 */ + 0x0.bb4ff632a908f73ec151839cb9p0L, + 0x0.d993b4e0bfb8f20e7e44e6e4aep-104L, +/* sin(x) = 0.ae7fe0b5fc786b2d966e1d6af1 40a488476747c2646425fc7533 f532cd044cb10a971a49a6a */ + 0x0.ae7fe0b5fc786b2d966e1d6af1p0L, + 0x0.40a488476747c2646425fc7533p-104L, + +/* x = 7.57812500000000000000000000000000000e-01 3ffe8400000000000000000000000000 */ +/* cos(x) = 0.b9f180ba77dd0751628e135a95 08299012230f14becacdd14c3f 8862d122de5b56d55b53360 */ + 0x0.b9f180ba77dd0751628e135a95p0L, + 0x0.08299012230f14becacdd14c3fp-104L, +/* sin(x) = 0.aff522a954f2ba16d9defdc416 e33f5e9a5dfd5a6c228e0abc4d 521327ff6e2517a7b3851dd */ + 0x0.aff522a954f2ba16d9defdc416p0L, + 0x0.e33f5e9a5dfd5a6c228e0abc4dp-104L, + +/* x = 7.65625000000000000000000000000000000e-01 3ffe8800000000000000000000000000 */ +/* cos(x) = 0.b890237d3bb3c284b614a05390 16bfa1053730bbdf940fa895e1 85f8e58884d3dda15e63371 */ + 0x0.b890237d3bb3c284b614a05390p0L, + 0x0.16bfa1053730bbdf940fa895e1p-104L, +/* sin(x) = 0.b167a4c90d63c4244cf5493b7c c23bd3c3c1225e078baa0c53d6 d400b926281f537a1a260e6 */ + 0x0.b167a4c90d63c4244cf5493b7cp0L, + 0x0.c23bd3c3c1225e078baa0c53d6p-104L, + +/* x = 7.73437500000000000000000000000000000e-01 3ffe8c00000000000000000000000000 */ +/* cos(x) = 0.b72be40067aaf2c050dbdb7a14 c3d7d4f203f6b3f0224a4afe55 d6ec8e92b508fd5c5984b3b */ + 0x0.b72be40067aaf2c050dbdb7a14p0L, + 0x0.c3d7d4f203f6b3f0224a4afe55p-104L, +/* sin(x) = 0.b2d7614b1f3aaa24df2d6e20a7 7e1ca3e6d838c03e29c1bcb026 e6733324815fadc9eb89674 */ + 0x0.b2d7614b1f3aaa24df2d6e20a7p0L, + 0x0.7e1ca3e6d838c03e29c1bcb026p-104L, + +/* x = 7.81250000000000000000000000000000000e-01 3ffe9000000000000000000000000000 */ +/* cos(x) = 0.b5c4c7d4f7dae915ac786ccf4b 1a498d3e73b6e5e74fe7519d9c 53ee6d6b90e881bddfc33e1 */ + 0x0.b5c4c7d4f7dae915ac786ccf4bp0L, + 0x0.1a498d3e73b6e5e74fe7519d9cp-104L, +/* sin(x) = 0.b44452709a5975290591376543 4a59d111f0433eb2b133f7d103 207e2aeb4aae111ddc385b3 */ + 0x0.b44452709a5975290591376543p0L, + 0x0.4a59d111f0433eb2b133f7d103p-104L, + +/* x = 7.89062500000000000000000000000000000e-01 3ffe9400000000000000000000000000 */ +/* cos(x) = 0.b45ad4975b1294cadca4cf40ec 8f22a68cd14b175835239a37e6 3acb85e8e9505215df18140 */ + 0x0.b45ad4975b1294cadca4cf40ecp0L, + 0x0.8f22a68cd14b175835239a37e6p-104L, +/* sin(x) = 0.b5ae7285bc10cf515753847e8f 8b7a30e0a580d929d770103509 880680f7b8b0e8ad23b65d8 */ + 0x0.b5ae7285bc10cf515753847e8fp0L, + 0x0.8b7a30e0a580d929d770103509p-104L +}; diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-canonical-ldbl-128ibm.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-canonical-ldbl-128ibm.c new file mode 100644 index 0000000000..75735db18e --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-canonical-ldbl-128ibm.c @@ -0,0 +1,230 @@ +/* Test iscanonical and canonicalizel for ldbl-128ibm. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <math_ldbl.h> +#include <stdbool.h> +#include <stdio.h> + +struct test +{ + double hi, lo; + bool canonical; +}; + +static const struct test tests[] = + { + { __builtin_nan (""), 0.0, true }, + { __builtin_nan (""), DBL_MAX, true }, + { __builtin_nan (""), __builtin_inf (), true }, + { __builtin_nan (""), __builtin_nan (""), true }, + { __builtin_nan (""), __builtin_nans (""), true }, + { __builtin_nans (""), 0.0, true }, + { __builtin_nans (""), DBL_MAX, true }, + { __builtin_nans (""), __builtin_inf (), true }, + { __builtin_nans (""), __builtin_nan (""), true }, + { __builtin_nans (""), __builtin_nans (""), true }, + { __builtin_inf (), 0.0, true }, + { __builtin_inf (), -0.0, true }, + { -__builtin_inf (), 0.0, true }, + { -__builtin_inf (), -0.0, true }, + { __builtin_inf (), DBL_TRUE_MIN, false }, + { __builtin_inf (), -DBL_TRUE_MIN, false }, + { -__builtin_inf (), DBL_TRUE_MIN, false }, + { -__builtin_inf (), -DBL_TRUE_MIN, false }, + { __builtin_inf (), DBL_MIN, false }, + { __builtin_inf (), -DBL_MIN, false }, + { -__builtin_inf (), DBL_MIN, false }, + { -__builtin_inf (), -DBL_MIN, false }, + { __builtin_inf (), __builtin_inf (), false }, + { __builtin_inf (), -__builtin_inf (), false }, + { -__builtin_inf (), __builtin_inf (), false }, + { -__builtin_inf (), -__builtin_inf (), false }, + { __builtin_inf (), __builtin_nan (""), false }, + { __builtin_inf (), -__builtin_nan (""), false }, + { -__builtin_inf (), __builtin_nan (""), false }, + { -__builtin_inf (), -__builtin_nan (""), false }, + { 0.0, 0.0, true }, + { 0.0, -0.0, true }, + { -0.0, 0.0, true }, + { -0.0, -0.0, true }, + { 0.0, DBL_TRUE_MIN, false }, + { 0.0, -DBL_TRUE_MIN, false }, + { -0.0, DBL_TRUE_MIN, false }, + { -0.0, -DBL_TRUE_MIN, false }, + { 0.0, DBL_MAX, false }, + { 0.0, -DBL_MAX, false }, + { -0.0, DBL_MAX, false }, + { -0.0, -DBL_MAX, false }, + { 0.0, __builtin_inf (), false }, + { 0.0, -__builtin_inf (), false }, + { -0.0, __builtin_inf (), false }, + { -0.0, -__builtin_inf (), false }, + { 0.0, __builtin_nan (""), false }, + { 0.0, -__builtin_nan (""), false }, + { -0.0, __builtin_nan (""), false }, + { -0.0, -__builtin_nan (""), false }, + { 1.0, 0.0, true }, + { 1.0, -0.0, true }, + { -1.0, 0.0, true }, + { -1.0, -0.0, true }, + { 1.0, DBL_TRUE_MIN, true }, + { 1.0, -DBL_TRUE_MIN, true }, + { -1.0, DBL_TRUE_MIN, true }, + { -1.0, -DBL_TRUE_MIN, true }, + { 1.0, DBL_MAX, false }, + { 1.0, -DBL_MAX, false }, + { -1.0, DBL_MAX, false }, + { -1.0, -DBL_MAX, false }, + { 1.0, __builtin_inf (), false }, + { 1.0, -__builtin_inf (), false }, + { -1.0, __builtin_inf (), false }, + { -1.0, -__builtin_inf (), false }, + { 1.0, __builtin_nan (""), false }, + { 1.0, -__builtin_nan (""), false }, + { -1.0, __builtin_nan (""), false }, + { -1.0, -__builtin_nan (""), false }, + { 0x1p1023, 0x1.1p969, true }, + { 0x1p1023, -0x1.1p969, true }, + { -0x1p1023, 0x1.1p969, true }, + { -0x1p1023, -0x1.1p969, true }, + { 0x1p1023, 0x1.1p970, false }, + { 0x1p1023, -0x1.1p970, false }, + { -0x1p1023, 0x1.1p970, false }, + { -0x1p1023, -0x1.1p970, false }, + { 0x1p1023, 0x1p970, true }, + { 0x1p1023, -0x1p970, true }, + { -0x1p1023, 0x1p970, true }, + { -0x1p1023, -0x1p970, true }, + { 0x1.0000000000001p1023, 0x1p970, false }, + { 0x1.0000000000001p1023, -0x1p970, false }, + { -0x1.0000000000001p1023, 0x1p970, false }, + { -0x1.0000000000001p1023, -0x1p970, false }, + { 0x1p-969, 0x1.1p-1023, true }, + { 0x1p-969, -0x1.1p-1023, true }, + { -0x1p-969, 0x1.1p-1023, true }, + { -0x1p-969, -0x1.1p-1023, true }, + { 0x1p-969, 0x1.1p-1022, false }, + { 0x1p-969, -0x1.1p-1022, false }, + { -0x1p-969, 0x1.1p-1022, false }, + { -0x1p-969, -0x1.1p-1022, false }, + { 0x1p-969, 0x1p-1022, true }, + { 0x1p-969, -0x1p-1022, true }, + { -0x1p-969, 0x1p-1022, true }, + { -0x1p-969, -0x1p-1022, true }, + { 0x1.0000000000001p-969, 0x1p-1022, false }, + { 0x1.0000000000001p-969, -0x1p-1022, false }, + { -0x1.0000000000001p-969, 0x1p-1022, false }, + { -0x1.0000000000001p-969, -0x1p-1022, false }, + { 0x1p-970, 0x1.1p-1024, true }, + { 0x1p-970, -0x1.1p-1024, true }, + { -0x1p-970, 0x1.1p-1024, true }, + { -0x1p-970, -0x1.1p-1024, true }, + { 0x1p-970, 0x1.1p-1023, false }, + { 0x1p-970, -0x1.1p-1023, false }, + { -0x1p-970, 0x1.1p-1023, false }, + { -0x1p-970, -0x1.1p-1023, false }, + { 0x1p-970, 0x1p-1023, true }, + { 0x1p-970, -0x1p-1023, true }, + { -0x1p-970, 0x1p-1023, true }, + { -0x1p-970, -0x1p-1023, true }, + { 0x1.0000000000001p-970, 0x1p-1023, false }, + { 0x1.0000000000001p-970, -0x1p-1023, false }, + { -0x1.0000000000001p-970, 0x1p-1023, false }, + { -0x1.0000000000001p-970, -0x1p-1023, false }, + { 0x1p-1000, 0x1.1p-1054, true }, + { 0x1p-1000, -0x1.1p-1054, true }, + { -0x1p-1000, 0x1.1p-1054, true }, + { -0x1p-1000, -0x1.1p-1054, true }, + { 0x1p-1000, 0x1.1p-1053, false }, + { 0x1p-1000, -0x1.1p-1053, false }, + { -0x1p-1000, 0x1.1p-1053, false }, + { -0x1p-1000, -0x1.1p-1053, false }, + { 0x1p-1000, 0x1p-1053, true }, + { 0x1p-1000, -0x1p-1053, true }, + { -0x1p-1000, 0x1p-1053, true }, + { -0x1p-1000, -0x1p-1053, true }, + { 0x1.0000000000001p-1000, 0x1p-1053, false }, + { 0x1.0000000000001p-1000, -0x1p-1053, false }, + { -0x1.0000000000001p-1000, 0x1p-1053, false }, + { -0x1.0000000000001p-1000, -0x1p-1053, false }, + { 0x1p-1021, 0x1p-1074, true }, + { 0x1p-1021, -0x1p-1074, true }, + { -0x1p-1021, 0x1p-1074, true }, + { -0x1p-1021, -0x1p-1074, true }, + { 0x1.0000000000001p-1021, 0x1p-1074, false }, + { 0x1.0000000000001p-1021, -0x1p-1074, false }, + { -0x1.0000000000001p-1021, 0x1p-1074, false }, + { -0x1.0000000000001p-1021, -0x1p-1074, false }, + { 0x1p-1022, 0x1p-1074, false }, + { 0x1p-1022, -0x1p-1074, false }, + { -0x1p-1022, 0x1p-1074, false }, + { -0x1p-1022, -0x1p-1074, false }, + }; + +static int +do_test (void) +{ + int result = 0; + + for (size_t i = 0; i < sizeof (tests) / sizeof (tests[0]); i++) + { + long double ld = ldbl_pack (tests[i].hi, tests[i].lo); + bool canonical = iscanonical (ld); + if (canonical == tests[i].canonical) + { + printf ("PASS: iscanonical test %zu\n", i); + long double ldc = 12345.0L; + bool canonicalize_ret = canonicalizel (&ldc, &ld); + if (canonicalize_ret == !canonical) + { + printf ("PASS: canonicalizel test %zu\n", i); + bool canon_ok; + if (!canonical) + canon_ok = ldc == 12345.0L; + else if (isnan (ld)) + canon_ok = isnan (ldc) && !issignaling (ldc); + else + canon_ok = ldc == ld; + if (canon_ok) + printf ("PASS: canonicalized value test %zu\n", i); + else + { + printf ("FAIL: canonicalized value test %zu\n", i); + result = 1; + } + } + else + { + printf ("FAIL: canonicalizel test %zu\n", i); + result = 1; + } + } + else + { + printf ("FAIL: iscanonical test %zu\n", i); + result = 1; + } + } + + return result; +} + +#define TEST_FUNCTION do_test () +#include "../test-skeleton.c" diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-fmodl-ldbl-128ibm.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-fmodl-ldbl-128ibm.c new file mode 100644 index 0000000000..c9bfcfc5a8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-fmodl-ldbl-128ibm.c @@ -0,0 +1,21 @@ +/* Test for ldbl-128ibm fmodl handling of equal values (bug 19602). + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define FUNC fmodl +#define SETUP +#include "test-fmodrem-ldbl-128ibm.c" diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-fmodrem-ldbl-128ibm.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-fmodrem-ldbl-128ibm.c new file mode 100644 index 0000000000..a7cc042a15 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-fmodrem-ldbl-128ibm.c @@ -0,0 +1,84 @@ +/* Test for ldbl-128ibm fmodl etc. handling of equal values. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <fenv.h> +#include <float.h> +#include <math.h> +#include <stdio.h> + +/* FUNC is defined to be the name of the function to test. */ +#define STRX(x) #x +#define STR(x) STRX (x) +#define SFUNC STR (FUNC) + +union u +{ + long double ld; + double d[2]; +}; + +volatile union u p1 = { .d = { DBL_MIN, 0.0 } }; +volatile union u p2 = { .d = { DBL_MIN, -0.0 } }; +volatile union u m1 = { .d = { -DBL_MIN, 0.0 } }; +volatile union u m2 = { .d = { -DBL_MIN, -0.0 } }; + +static int +test_func (const char *s, long double x, long double y, long double expected) +{ + volatile long double r; + r = FUNC (x, y); + if (r != expected || copysignl (1.0, r) != copysignl (1.0, expected)) + { + printf ("FAIL: " SFUNC " (%s)\n", s); + return 1; + } + else + { + printf ("PASS: " SFUNC " (%s)\n", s); + return 0; + } +} + +#define TEST_FUNC(a, b, e) test_func (#a ", " #b, a, b, e) + +static int +do_test (void) +{ + int result = 0; + SETUP; + result |= TEST_FUNC (p1.ld, p1.ld, 0.0L); + result |= TEST_FUNC (p1.ld, p2.ld, 0.0L); + result |= TEST_FUNC (p1.ld, m1.ld, 0.0L); + result |= TEST_FUNC (p1.ld, m2.ld, 0.0L); + result |= TEST_FUNC (p2.ld, p1.ld, 0.0L); + result |= TEST_FUNC (p2.ld, p2.ld, 0.0L); + result |= TEST_FUNC (p2.ld, m1.ld, 0.0L); + result |= TEST_FUNC (p2.ld, m2.ld, 0.0L); + result |= TEST_FUNC (m1.ld, p1.ld, -0.0L); + result |= TEST_FUNC (m1.ld, p2.ld, -0.0L); + result |= TEST_FUNC (m1.ld, m1.ld, -0.0L); + result |= TEST_FUNC (m1.ld, m2.ld, -0.0L); + result |= TEST_FUNC (m2.ld, p1.ld, -0.0L); + result |= TEST_FUNC (m2.ld, p2.ld, -0.0L); + result |= TEST_FUNC (m2.ld, m1.ld, -0.0L); + result |= TEST_FUNC (m2.ld, m2.ld, -0.0L); + return result; +} + +#define TEST_FUNCTION do_test () +#include "../../../test-skeleton.c" diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-remainderl-ldbl-128ibm.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-remainderl-ldbl-128ibm.c new file mode 100644 index 0000000000..32b18be741 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-remainderl-ldbl-128ibm.c @@ -0,0 +1,21 @@ +/* Test for ldbl-128ibm remainderl handling of equal values (bug 19677). + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define FUNC remainderl +#define SETUP fesetround (FE_DOWNWARD) +#include "test-fmodrem-ldbl-128ibm.c" diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-remquol-ldbl-128ibm.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-remquol-ldbl-128ibm.c new file mode 100644 index 0000000000..f0d48420b8 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-remquol-ldbl-128ibm.c @@ -0,0 +1,30 @@ +/* Test for ldbl-128ibm remquol handling of equal values (bug 19677). + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> + +static long double +wrap_remquol (long double x, long double y) +{ + int quo; + return remquol (x, y, &quo); +} + +#define FUNC wrap_remquol +#define SETUP fesetround (FE_DOWNWARD) +#include "test-fmodrem-ldbl-128ibm.c" diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-totalorderl-ldbl-128ibm.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-totalorderl-ldbl-128ibm.c new file mode 100644 index 0000000000..eaada2f848 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/test-totalorderl-ldbl-128ibm.c @@ -0,0 +1,73 @@ +/* Test totalorderl and totalordermagl for ldbl-128ibm. + Copyright (C) 2016-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_ldbl.h> +#include <stdbool.h> +#include <stdio.h> + +struct test +{ + double hi, lo1, lo2; +}; + +static const struct test tests[] = + { + { __builtin_nan (""), 1, __builtin_nans ("") }, + { -__builtin_nan (""), 1, __builtin_nans ("") }, + { __builtin_nans (""), 1, __builtin_nan ("") }, + { -__builtin_nans (""), 1, __builtin_nan ("") }, + { __builtin_inf (), 0.0, -0.0 }, + { -__builtin_inf (), 0.0, -0.0 }, + { 1.5, 0.0, -0.0 }, + }; + +static int +do_test (void) +{ + int result = 0; + + for (size_t i = 0; i < sizeof (tests) / sizeof (tests[0]); i++) + { + long double ldx = ldbl_pack (tests[i].hi, tests[i].lo1); + long double ldy = ldbl_pack (tests[i].hi, tests[i].lo2); + bool to1 = totalorderl (ldx, ldy); + bool to2 = totalorderl (ldy, ldx); + if (to1 && to2) + printf ("PASS: test %zu\n", i); + else + { + printf ("FAIL: test %zu\n", i); + result = 1; + } + to1 = totalordermagl (ldx, ldy); + to2 = totalordermagl (ldy, ldx); + if (to1 && to2) + printf ("PASS: test %zu (totalordermagl)\n", i); + else + { + printf ("FAIL: test %zu (totalordermagl)\n", i); + result = 1; + } + } + + return result; +} + +#define TEST_FUNCTION do_test () +#include "../test-skeleton.c" diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/tst-strtold-ldbl-128ibm.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/tst-strtold-ldbl-128ibm.c new file mode 100644 index 0000000000..1181892165 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/tst-strtold-ldbl-128ibm.c @@ -0,0 +1,85 @@ +/* Test for ldbl-128ibm strtold overflow to infinity (bug 14551). + Copyright (C) 2015-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <errno.h> +#include <fenv.h> +#include <math.h> +#include <stdio.h> +#include <stdlib.h> + +static int +test_strtold_value (const char *s, double exp_hi, double exp_lo, int exp_exc, + int exp_errno) +{ + int result = 0; + union { long double ld; double d[2]; } x; + feclearexcept (FE_ALL_EXCEPT); + errno = 0; + x.ld = strtold (s, NULL); + int exc = fetestexcept (FE_ALL_EXCEPT); + int new_errno = errno; + printf ("strtold (\"%s\") returned (%a, %a), exceptions 0x%x, errno %d\n", + s, x.d[0], x.d[1], exc, new_errno); + if (x.d[0] == exp_hi) + printf ("PASS: strtold (\"%s\") high == %a\n", s, exp_hi); + else + { + printf ("FAIL: strtold (\"%s\") high == %a\n", s, exp_hi); + result = 1; + } + if (x.d[1] == exp_lo) + printf ("PASS: strtold (\"%s\") low == %a\n", s, exp_lo); + else + { + printf ("FAIL: strtold (\"%s\") low == %a\n", s, exp_lo); + result = 1; + } + if (exc == exp_exc) + printf ("PASS: strtold (\"%s\") exceptions 0x%x\n", s, exp_exc); + else + { + printf ("FAIL: strtold (\"%s\") exceptions 0x%x\n", s, exp_exc); + result = 1; + } + if (new_errno == exp_errno) + printf ("PASS: strtold (\"%s\") errno %d\n", s, exp_errno); + else + { + printf ("FAIL: strtold (\"%s\") errno %d\n", s, exp_errno); + result = 1; + } + return result; +} + +static int +do_test (void) +{ + int result = 0; + result |= test_strtold_value ("0x1.fffffffffffff8p+1023", INFINITY, 0, + FE_OVERFLOW | FE_INEXACT, ERANGE); + result |= test_strtold_value ("-0x1.fffffffffffff8p+1023", -INFINITY, 0, + FE_OVERFLOW | FE_INEXACT, ERANGE); + result |= test_strtold_value ("0x1.ffffffffffffffp+1023", INFINITY, 0, + FE_OVERFLOW | FE_INEXACT, ERANGE); + result |= test_strtold_value ("-0x1.ffffffffffffffp+1023", -INFINITY, 0, + FE_OVERFLOW | FE_INEXACT, ERANGE); + return result; +} + +#define TEST_FUNCTION do_test () +#include "../../../test-skeleton.c" diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/w_expl_compat.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/w_expl_compat.c new file mode 100644 index 0000000000..c9d44b61dd --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/w_expl_compat.c @@ -0,0 +1,21 @@ +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +long double __expl(long double x) /* wrapper exp */ +{ + long double z; + z = __ieee754_expl(x); + if (_LIB_VERSION == _IEEE_) + return z; + if (isfinite(x)) + { + if (!isfinite (z)) + return __kernel_standard_l(x,x,206); /* exp overflow */ + else if (z == 0.0L) + return __kernel_standard_l(x,x,207); /* exp underflow */ + } + return z; +} +hidden_def (__expl) +long_double_symbol (libm, __expl, expl); diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c new file mode 100644 index 0000000000..0bdb9a1848 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c @@ -0,0 +1,93 @@ +/* Compute x^2 + y^2 - 1, without large cancellation error. + Copyright (C) 2012-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <mul_split.h> +#include <stdlib.h> + +/* Calculate X + Y exactly and store the result in *HI + *LO. It is + given that |X| >= |Y| and the values are small enough that no + overflow occurs. */ + +static inline void +add_split (double *hi, double *lo, double x, double y) +{ + /* Apply Dekker's algorithm. */ + *hi = x + y; + *lo = (x - *hi) + y; +} + +/* Compare absolute values of floating-point values pointed to by P + and Q for qsort. */ + +static int +compare (const void *p, const void *q) +{ + double pd = fabs (*(const double *) p); + double qd = fabs (*(const double *) q); + if (pd < qd) + return -1; + else if (pd == qd) + return 0; + else + return 1; +} + +/* Return X^2 + Y^2 - 1, computed without large cancellation error. + It is given that 1 > X >= Y >= epsilon / 2, and that X^2 + Y^2 >= + 0.5. */ + +long double +__x2y2m1l (long double x, long double y) +{ + double vals[13]; + SET_RESTORE_ROUND (FE_TONEAREST); + union ibm_extended_long_double xu, yu; + xu.ld = x; + yu.ld = y; + if (fabs (xu.d[1].d) < 0x1p-500) + xu.d[1].d = 0.0; + if (fabs (yu.d[1].d) < 0x1p-500) + yu.d[1].d = 0.0; + mul_split (&vals[1], &vals[0], xu.d[0].d, xu.d[0].d); + mul_split (&vals[3], &vals[2], xu.d[0].d, xu.d[1].d); + vals[2] *= 2.0; + vals[3] *= 2.0; + mul_split (&vals[5], &vals[4], xu.d[1].d, xu.d[1].d); + mul_split (&vals[7], &vals[6], yu.d[0].d, yu.d[0].d); + mul_split (&vals[9], &vals[8], yu.d[0].d, yu.d[1].d); + vals[8] *= 2.0; + vals[9] *= 2.0; + mul_split (&vals[11], &vals[10], yu.d[1].d, yu.d[1].d); + vals[12] = -1.0; + qsort (vals, 13, sizeof (double), compare); + /* Add up the values so that each element of VALS has absolute value + at most equal to the last set bit of the next nonzero + element. */ + for (size_t i = 0; i <= 11; i++) + { + add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]); + qsort (vals + i + 1, 12 - i, sizeof (double), compare); + } + /* Now any error from this addition will be small. */ + long double retval = (long double) vals[12]; + for (size_t i = 11; i != (size_t) -1; i--) + retval += (long double) vals[i]; + return retval; +} |