From d032e0d29b6ed9d3844916ada0ead19c3190ff9a Mon Sep 17 00:00:00 2001 From: Joseph Myers Date: Tue, 25 Sep 2012 19:43:49 +0000 Subject: Fix inaccuracy of clog, clog10 near |z| = 1 (bug 13629). --- sysdeps/generic/math_private.h | 7 ++ sysdeps/i386/fpu/libm-test-ulps | 117 +++++++++++++++++++++++++++++++ sysdeps/ieee754/dbl-64/x2y2m1.c | 111 +++++++++++++++++++++++++++++ sysdeps/ieee754/dbl-64/x2y2m1f.c | 32 +++++++++ sysdeps/ieee754/ldbl-128/x2y2m1l.c | 111 +++++++++++++++++++++++++++++ sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c | 128 ++++++++++++++++++++++++++++++++++ sysdeps/ieee754/ldbl-96/x2y2m1.c | 39 +++++++++++ sysdeps/ieee754/ldbl-96/x2y2m1l.c | 111 +++++++++++++++++++++++++++++ sysdeps/x86_64/fpu/libm-test-ulps | 125 +++++++++++++++++++++++++++++++-- 9 files changed, 777 insertions(+), 4 deletions(-) create mode 100644 sysdeps/ieee754/dbl-64/x2y2m1.c create mode 100644 sysdeps/ieee754/dbl-64/x2y2m1f.c create mode 100644 sysdeps/ieee754/ldbl-128/x2y2m1l.c create mode 100644 sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c create mode 100644 sysdeps/ieee754/ldbl-96/x2y2m1.c create mode 100644 sysdeps/ieee754/ldbl-96/x2y2m1l.c (limited to 'sysdeps') diff --git a/sysdeps/generic/math_private.h b/sysdeps/generic/math_private.h index 5267ec327b..b375bc0c56 100644 --- a/sysdeps/generic/math_private.h +++ b/sysdeps/generic/math_private.h @@ -364,6 +364,13 @@ extern double __slowexp (double __x); extern double __slowpow (double __x, double __y, double __z); extern void __docos (double __x, double __dx, double __v[]); +/* Return X^2 + Y^2 - 1, computed without large cancellation error. + It is given that 1 > X >= Y >= epsilon / 2, and that either X >= + 0.75 or Y >= 0.5. */ +extern float __x2y2m1f (float x, float y); +extern double __x2y2m1 (double x, double y); +extern long double __x2y2m1l (long double x, long double y); + #ifndef math_opt_barrier # define math_opt_barrier(x) \ ({ __typeof (x) __x = (x); __asm ("" : "+m" (__x)); __x; }) diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps index 71b633a3b4..239da44a79 100644 --- a/sysdeps/i386/fpu/libm-test-ulps +++ b/sysdeps/i386/fpu/libm-test-ulps @@ -880,6 +880,12 @@ float: 1 ifloat: 1 ildouble: 1 ldouble: 1 +Test "Real part of: clog (0x0.ffffffffffffffffp0 + 0x0.ffffffffffffffffp-15000 i) == -5.421010862427522170184200798202494495630e-20 + 3.548665303440282824232502561095699343814e-4516 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: clog (0x0.ffffffp0 + 0x0.ffffffp-100 i) == -5.960464655174753498633255797994360530379e-8 + 7.888609052210118054117285652827862296732e-31 i": +float: 1 +ifloat: 1 Test "Real part of: clog (0x1.000566p0 + 0x1.234p-10 i) == 8.298731898331237038231468223024422855654e-5 + 1.110938609507128729312743251313024793990e-3 i": ildouble: 1 ldouble: 1 @@ -904,6 +910,9 @@ ldouble: 1 Test "Real part of: clog (0x1.fp+16383 - 0x1p-16445 i) == 11356.49165759582936919077408168801636572 - 0 i": ildouble: 1 ldouble: 1 +Test "Imaginary part of: clog (0x1367a310575591p-54 + 0x3cfcc0a0541f60p-54 i) == 5.0844550531823026520677817684239496041087e-32 + 1.2627468605458094918919206628466016525397 i": +ildouble: 1 +ldouble: 1 Test "Real part of: clog (0x1p-1074 + 0x1p-1074 i) == -744.0934983311012896593986823853525458290 + pi/4 i": ildouble: 1 ldouble: 1 @@ -922,6 +931,9 @@ ldouble: 1 Test "Real part of: clog (0x1p-16445 - 0x1.fp+16383 i) == 11356.49165759582936919077408168801636572 - pi/2 i": ildouble: 1 ldouble: 1 +Test "Real part of: clog (0x2dd46725bp-35 + 0x7783a1284p-35 i) == 4.4469229730850767799109418892826021157328e-20 + 1.2046235979300843056806465045930070146351 i": +ildouble: 1 +ldouble: 1 Test "Real part of: clog (1.0 + 0x1.234566p-10 i) == 6.172834701221959432440126967147726538097e-7 + 1.111110564353742042376451655136933182201e-3 i": float: 1 ifloat: 1 @@ -1068,6 +1080,17 @@ idouble: 1 ifloat: 1 ildouble: 1 ldouble: 1 +Test "Real part of: clog10 (0x0.fffffffffffff8p0 + 0x0.fffffffffffff8p-1000 i) == -4.821637332766435821255375046554377090472e-17 + 4.053112396770095089737411317782466262176e-302 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: clog10 (0x0.ffffffffffffffffp0 + 0x0.ffffffffffffffffp-15000 i) == -2.354315103889861110220423157644627849164e-20 + 1.541165759405643564697852372112893034397e-4516 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: clog10 (0x0.ffffffp0 + 0x0.ffffffp-100 i) == -2.588596909321764128428416045209904492216e-8 + 3.425979381266895667295625489912064603415e-31 i": +float: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 Test "Real part of: clog10 (0x1.000566p0 + 0x1.234p-10 i) == 3.604093470239754109961125085078190708674e-5 + 4.824745078422174667425851670822596859720e-4 i": ildouble: 1 ldouble: 1 @@ -1119,6 +1142,29 @@ ldouble: 1 Test "Real part of: clog10 (0x1.fp+16383 - 0x1p-16445 i) == 4932.061660674182269085496060792589701158 - 0 i": ildouble: 1 ldouble: 1 +Test "Real part of: clog10 (0x10673dd0f2481p-51 + 0x7ef1d17cefbd2p-51 i) == 1.3918041236396763648388478552321724382899e-29 + 0.6263795733790237053262025311642907438291 i": +double: 1 +idouble: 1 +Test "Imaginary part of: clog10 (0x11682p-23 + 0x7ffed1p-23 i) == 5.0916490233953865181284669870035717560498e-13 + 0.6784968969384861816694467029319146542069 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: clog10 (0x1367a310575591p-54 + 0x3cfcc0a0541f60p-54 i) == 2.2081507730821788480616336165447731164865e-32 + 0.5484039935757001196548030312819898864760 i": +double: 1 +idouble: 1 +Test "Imaginary part of: clog10 (0x1367a310575591p-54 + 0x3cfcc0a0541f60p-54 i) == 2.2081507730821788480616336165447731164865e-32 + 0.5484039935757001196548030312819898864760 i": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: clog10 (0x164c74eea876p-45 + 0x16f393482f77p-45 i) == -1.3155760824064879362415202279780039150764e-26 + 0.3473590599762514228227328130640352044313 i": +double: 1 +idouble: 1 +Test "Real part of: clog10 (0x1a6p-10 + 0x3a5p-10 i) == -6.2126412844802358329771948751248003038444e-07 + 0.4977135139537443711784513409096950995985 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: clog10 (0x1a6p-10 + 0x3a5p-10 i) == -6.2126412844802358329771948751248003038444e-07 + 0.4977135139537443711784513409096950995985 i": +double: 1 +idouble: 1 Test "Imaginary part of: clog10 (0x1p-1073 + 0x1p-1073 i) == -322.8546703496198318667349645920187712089 + pi/4*log10(e) i": double: 1 idouble: 1 @@ -1199,6 +1245,73 @@ ifloat: 1 Test "Real part of: clog10 (0x1p-8190 + 1.0 i) == 2.920285685286322365786846845062520925172e-4932 + 6.821881769209206737428918127156778851051e-1 i": ildouble: 1 ldouble: 1 +Test "Real part of: clog10 (0x2818p-15 + 0x798fp-15 i) == 6.6737261053986614395049481326819059203910e-09 + 0.5438241985991753781478398141908629586460 i": +float: 1 +ifloat: 1 +Test "Imaginary part of: clog10 (0x2818p-15 + 0x798fp-15 i) == 6.6737261053986614395049481326819059203910e-09 + 0.5438241985991753781478398141908629586460 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: clog10 (0x2dd46725bp-35 + 0x7783a1284p-35 i) == 1.9312741086596516918394613098872836703188e-20 + 0.5231613813514771042838490538484014771862 i": +double: 1 +idouble: 1 +Test "Imaginary part of: clog10 (0x2dd46725bp-35 + 0x7783a1284p-35 i) == 1.9312741086596516918394613098872836703188e-20 + 0.5231613813514771042838490538484014771862 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: clog10 (0x2ede88p-23 + 0x771c3fp-23 i) == -1.9440841725722970687903291200493082253766e-13 + 0.5193774116724956222518530053006822210323 i": +float: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: clog10 (0x2ede88p-23 + 0x771c3fp-23 i) == -1.9440841725722970687903291200493082253766e-13 + 0.5193774116724956222518530053006822210323 i": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "Real part of: clog10 (0x4447d7175p-35 + 0x6c445e00ap-35 i) == -6.4375803621988389731799033530075237868110e-21 + 0.4378257977686804492768642780897650927167 i": +double: 1 +idouble: 1 +Test "Imaginary part of: clog10 (0x4447d7175p-35 + 0x6c445e00ap-35 i) == -6.4375803621988389731799033530075237868110e-21 + 0.4378257977686804492768642780897650927167 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: clog10 (0x4d4ep-15 + 0x6605p-15 i) == -7.0781945783414996953799915941870192015212e-09 + 0.4005747524909781155537088181659175147564 i": +float: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: clog10 (0x5b06b680ea2ccp-52 + 0xef452b965da9fp-52 i) == 3.6079845358966994996207055940336690133424e-30 + 0.5243112258263349992771652393178033846555 i": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: clog10 (0x659b70ab7971bp-53 + 0x1f5d111e08abecp-53 i) == -1.0893543813872082317104059174982092534059e-30 + 0.5954257879188711495921161433751775633232 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: clog10 (0x659feap-24 + 0xeaf6f9p-24 i) == 1.6200701438094619117335617123525612051457e-14 + 0.5049027913635038013499728086604870749732 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: clog10 (0x6b10b4f3520217b6p-64 + 0xe8893cbb449253a1p-64 i) == 1.0529283395205396881397407610630442563938e-37 + 0.4947949395762683446121140513971996916447 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: clog10 (0x81b7efa81fc35ad1p-65 + 0x1ef4b835f1c79d812p-65 i) == -4.3074341162203896332989394770760901408798e-39 + 0.5709443672155660428417571212549720987784 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: clog10 (0x8ecbf810c4ae6p-52 + 0xd479468b09a37p-52 i) == -4.2289432987513243393180377141513840878196e-30 + 0.4252020027092323591068799049905597805296 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: clog10 (0x9b57bp-20 + 0xcb7b4p-20 i) == -1.7182001068739620267773842120965071561416e-11 + 0.3990121149225253562859800593935899629087 i": +double: 1 +idouble: 1 +Test "Real part of: clog10 (0xf2p-10 + 0x3e3p-10 i) == 2.6921240173351112953324592659528481616879e-06 + 0.5785726025799636431142862788413361783862 i": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: clog10 (0xf2p-10 + 0x3e3p-10 i) == 2.6921240173351112953324592659528481616879e-06 + 0.5785726025799636431142862788413361783862 i": +double: 1 +idouble: 1 +Test "Imaginary part of: clog10 (0xfe961079616p-45 + 0x1bc37e09e6d1p-45 i) == 2.3329549194675052736016290082882121135546e-26 + 0.4561756099441139182878993697611751382976 i": +double: 1 +idouble: 1 Test "Imaginary part of: clog10 (1.0 + 0x1.234566p-10 i) == 2.680828048441605163181684680300513080769e-7 + 4.825491868832381486767558728169977751564e-4 i": double: 1 idouble: 1 @@ -3271,6 +3384,10 @@ ifloat: 1 ildouble: 1 ldouble: 1 +Function: Imaginary part of "clog": +ildouble: 1 +ldouble: 1 + Function: Real part of "clog10": double: 1 float: 1 diff --git a/sysdeps/ieee754/dbl-64/x2y2m1.c b/sysdeps/ieee754/dbl-64/x2y2m1.c new file mode 100644 index 0000000000..4badde3be4 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/x2y2m1.c @@ -0,0 +1,111 @@ +/* Compute x^2 + y^2 - 1, without large cancellation error. + Copyright (C) 2012 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 + . */ + +#include +#include +#include +#include + +/* 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; +} + +/* Calculate X * Y exactly and store the result in *HI + *LO. It is + given that the values are small enough that no overflow occurs and + large enough (or zero) that no underflow occurs. */ + +static inline void +mul_split (double *hi, double *lo, double x, double y) +{ +#ifdef __FP_FAST_FMA + /* Fast built-in fused multiply-add. */ + *hi = x * y; + *lo = __builtin_fma (x, y, -*hi); +#elif defined FP_FAST_FMA + /* Fast library fused multiply-add, compiler before GCC 4.6. */ + *hi = x * y; + *lo = __fma (x, y, -*hi); +#else + /* Apply Dekker's algorithm. */ + *hi = x * y; +# define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1) + double x1 = x * C; + double y1 = y * C; +# undef C + x1 = (x - x1) + x1; + y1 = (y - y1) + y1; + double x2 = x - x1; + double y2 = y - y1; + *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2; +#endif +} + +/* 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 either X >= + 0.75 or Y >= 0.5. */ + +double +__x2y2m1 (double x, double y) +{ + double vals[4]; + SET_RESTORE_ROUND (FE_TONEAREST); + mul_split (&vals[1], &vals[0], x, x); + mul_split (&vals[3], &vals[2], y, y); + if (x >= 0.75) + vals[1] -= 1.0; + else + { + vals[1] -= 0.5; + vals[3] -= 0.5; + } + qsort (vals, 4, 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 <= 2; i++) + { + add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]); + qsort (vals + i + 1, 3 - i, sizeof (double), compare); + } + /* Now any error from this addition will be small. */ + return vals[3] + vals[2] + vals[1] + vals[0]; +} diff --git a/sysdeps/ieee754/dbl-64/x2y2m1f.c b/sysdeps/ieee754/dbl-64/x2y2m1f.c new file mode 100644 index 0000000000..fcaa70851c --- /dev/null +++ b/sysdeps/ieee754/dbl-64/x2y2m1f.c @@ -0,0 +1,32 @@ +/* Compute x^2 + y^2 - 1, without large cancellation error. + Copyright (C) 2012 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 + . */ + +#include +#include +#include + +/* Return X^2 + Y^2 - 1, computed without large cancellation error. + It is given that 1 > X >= Y >= epsilon / 2, and that either X >= + 0.75 or Y >= 0.5. */ + +float +__x2y2m1f (float x, float y) +{ + double dx = x, dy = y; + return (float) ((dx - 1) * (dx + 1) + dy * dy); +} diff --git a/sysdeps/ieee754/ldbl-128/x2y2m1l.c b/sysdeps/ieee754/ldbl-128/x2y2m1l.c new file mode 100644 index 0000000000..a249cd3479 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/x2y2m1l.c @@ -0,0 +1,111 @@ +/* Compute x^2 + y^2 - 1, without large cancellation error. + Copyright (C) 2012 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 + . */ + +#include +#include +#include +#include + +/* 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 (long double *hi, long double *lo, long double x, long double y) +{ + /* Apply Dekker's algorithm. */ + *hi = x + y; + *lo = (x - *hi) + y; +} + +/* Calculate X * Y exactly and store the result in *HI + *LO. It is + given that the values are small enough that no overflow occurs and + large enough (or zero) that no underflow occurs. */ + +static inline void +mul_split (long double *hi, long double *lo, long double x, long double y) +{ +#ifdef __FP_FAST_FMAL + /* Fast built-in fused multiply-add. */ + *hi = x * y; + *lo = __builtin_fmal (x, y, -*hi); +#elif defined FP_FAST_FMAL + /* Fast library fused multiply-add, compiler before GCC 4.6. */ + *hi = x * y; + *lo = __fmal (x, y, -*hi); +#else + /* Apply Dekker's algorithm. */ + *hi = x * y; +# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1) + long double x1 = x * C; + long double y1 = y * C; +# undef C + x1 = (x - x1) + x1; + y1 = (y - y1) + y1; + long double x2 = x - x1; + long double y2 = y - y1; + *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2; +#endif +} + +/* Compare absolute values of floating-point values pointed to by P + and Q for qsort. */ + +static int +compare (const void *p, const void *q) +{ + long double pld = fabsl (*(const long double *) p); + long double qld = fabsl (*(const long double *) q); + if (pld < qld) + return -1; + else if (pld == qld) + 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 either X >= + 0.75 or Y >= 0.5. */ + +long double +__x2y2m1l (long double x, long double y) +{ + long double vals[4]; + SET_RESTORE_ROUNDL (FE_TONEAREST); + mul_split (&vals[1], &vals[0], x, x); + mul_split (&vals[3], &vals[2], y, y); + if (x >= 0.75L) + vals[1] -= 1.0L; + else + { + vals[1] -= 0.5L; + vals[3] -= 0.5L; + } + qsort (vals, 4, sizeof (long 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 <= 2; i++) + { + add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]); + qsort (vals + i + 1, 3 - i, sizeof (long double), compare); + } + /* Now any error from this addition will be small. */ + return vals[3] + vals[2] + vals[1] + vals[0]; +} diff --git a/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c b/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c new file mode 100644 index 0000000000..4379b68c3c --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c @@ -0,0 +1,128 @@ +/* Compute x^2 + y^2 - 1, without large cancellation error. + Copyright (C) 2012 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 + . */ + +#include +#include +#include + +/* 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; +} + +/* Calculate X * Y exactly and store the result in *HI + *LO. It is + given that the values are small enough that no overflow occurs and + large enough (or zero) that no underflow occurs. */ + +static inline void +mul_split (double *hi, double *lo, double x, double y) +{ +#ifdef __FP_FAST_FMA + /* Fast built-in fused multiply-add. */ + *hi = x * y; + *lo = __builtin_fma (x, y, -*hi); +#elif defined FP_FAST_FMA + /* Fast library fused multiply-add, compiler before GCC 4.6. */ + *hi = x * y; + *lo = __fma (x, y, -*hi); +#else + /* Apply Dekker's algorithm. */ + *hi = x * y; +# define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1) + double x1 = x * C; + double y1 = y * C; +# undef C + x1 = (x - x1) + x1; + y1 = (y - y1) + y1; + double x2 = x - x1; + double y2 = y - y1; + *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2; +#endif +} + +/* 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 either X >= + 0.75 or Y >= 0.5. */ + +long double +__x2y2m1l (long double x, long double y) +{ + double vals[12]; + SET_RESTORE_ROUND (FE_TONEAREST); + union ibm_extended_long_double xu, yu; + xu.d = x; + yu.d = y; + if (fabs (xu.dd[1]) < 0x1p-500) + xu.dd[1] = 0.0; + if (fabs (yu.dd[1]) < 0x1p-500) + yu.dd[1] = 0.0; + mul_split (&vals[1], &vals[0], xu.dd[0], xu.dd[0]); + mul_split (&vals[3], &vals[2], xu.dd[0], xu.dd[1]); + vals[2] *= 2.0; + vals[3] *= 2.0; + mul_split (&vals[5], &vals[4], xu.dd[1], xu.dd[1]); + mul_split (&vals[7], &vals[6], yu.dd[0], yu.dd[0]); + mul_split (&vals[9], &vals[8], yu.dd[0], yu.dd[1]); + vals[8] *= 2.0; + vals[9] *= 2.0; + mul_split (&vals[11], &vals[10], yu.dd[1], yu.dd[1]); + if (xu.dd[0] >= 0.75) + vals[1] -= 1.0; + else + { + vals[1] -= 0.5; + vals[7] -= 0.5; + } + qsort (vals, 12, 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 <= 10; i++) + { + add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]); + qsort (vals + i + 1, 11 - i, sizeof (double), compare); + } + /* Now any error from this addition will be small. */ + long double retval = (long double) vals[11]; + for (size_t i = 10; i != (size_t) -1; i--) + retval += (long double) vals[i]; + return retval; +} diff --git a/sysdeps/ieee754/ldbl-96/x2y2m1.c b/sysdeps/ieee754/ldbl-96/x2y2m1.c new file mode 100644 index 0000000000..3086fa2c80 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/x2y2m1.c @@ -0,0 +1,39 @@ +/* Compute x^2 + y^2 - 1, without large cancellation error. + Copyright (C) 2012 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 + . */ + +#include +#include +#include + +#if FLT_EVAL_METHOD == 0 + +# include + +#else + +/* Return X^2 + Y^2 - 1, computed without large cancellation error. + It is given that 1 > X >= Y >= epsilon / 2, and that either X >= + 0.75 or Y >= 0.5. */ + +double +__x2y2m1 (double x, double y) +{ + return (double) __x2y2m1l (x, y); +} + +#endif diff --git a/sysdeps/ieee754/ldbl-96/x2y2m1l.c b/sysdeps/ieee754/ldbl-96/x2y2m1l.c new file mode 100644 index 0000000000..a249cd3479 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/x2y2m1l.c @@ -0,0 +1,111 @@ +/* Compute x^2 + y^2 - 1, without large cancellation error. + Copyright (C) 2012 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 + . */ + +#include +#include +#include +#include + +/* 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 (long double *hi, long double *lo, long double x, long double y) +{ + /* Apply Dekker's algorithm. */ + *hi = x + y; + *lo = (x - *hi) + y; +} + +/* Calculate X * Y exactly and store the result in *HI + *LO. It is + given that the values are small enough that no overflow occurs and + large enough (or zero) that no underflow occurs. */ + +static inline void +mul_split (long double *hi, long double *lo, long double x, long double y) +{ +#ifdef __FP_FAST_FMAL + /* Fast built-in fused multiply-add. */ + *hi = x * y; + *lo = __builtin_fmal (x, y, -*hi); +#elif defined FP_FAST_FMAL + /* Fast library fused multiply-add, compiler before GCC 4.6. */ + *hi = x * y; + *lo = __fmal (x, y, -*hi); +#else + /* Apply Dekker's algorithm. */ + *hi = x * y; +# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1) + long double x1 = x * C; + long double y1 = y * C; +# undef C + x1 = (x - x1) + x1; + y1 = (y - y1) + y1; + long double x2 = x - x1; + long double y2 = y - y1; + *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2; +#endif +} + +/* Compare absolute values of floating-point values pointed to by P + and Q for qsort. */ + +static int +compare (const void *p, const void *q) +{ + long double pld = fabsl (*(const long double *) p); + long double qld = fabsl (*(const long double *) q); + if (pld < qld) + return -1; + else if (pld == qld) + 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 either X >= + 0.75 or Y >= 0.5. */ + +long double +__x2y2m1l (long double x, long double y) +{ + long double vals[4]; + SET_RESTORE_ROUNDL (FE_TONEAREST); + mul_split (&vals[1], &vals[0], x, x); + mul_split (&vals[3], &vals[2], y, y); + if (x >= 0.75L) + vals[1] -= 1.0L; + else + { + vals[1] -= 0.5L; + vals[3] -= 0.5L; + } + qsort (vals, 4, sizeof (long 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 <= 2; i++) + { + add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]); + qsort (vals + i + 1, 3 - i, sizeof (long double), compare); + } + /* Now any error from this addition will be small. */ + return vals[3] + vals[2] + vals[1] + vals[0]; +} diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps index d79578ce41..714b6b633c 100644 --- a/sysdeps/x86_64/fpu/libm-test-ulps +++ b/sysdeps/x86_64/fpu/libm-test-ulps @@ -812,6 +812,12 @@ float: 1 ifloat: 1 ildouble: 1 ldouble: 1 +Test "Real part of: clog (0x0.ffffffffffffffffp0 + 0x0.ffffffffffffffffp-15000 i) == -5.421010862427522170184200798202494495630e-20 + 3.548665303440282824232502561095699343814e-4516 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: clog (0x0.ffffffp0 + 0x0.ffffffp-100 i) == -5.960464655174753498633255797994360530379e-8 + 7.888609052210118054117285652827862296732e-31 i": +float: 1 +ifloat: 1 Test "Real part of: clog (0x1.000566p0 + 0x1.234p-10 i) == 8.298731898331237038231468223024422855654e-5 + 1.110938609507128729312743251313024793990e-3 i": float: 1 ifloat: 1 @@ -868,6 +874,12 @@ ldouble: 1 Test "Real part of: clog (0x1p-16445 - 0x1.fp+16383 i) == 11356.49165759582936919077408168801636572 - pi/2 i": ildouble: 1 ldouble: 1 +Test "Imaginary part of: clog (0x2818p-15 + 0x798fp-15 i) == 1.5366822245016167178749091974664853785194e-08 + 1.2522014929038946066987318471922169174157 i": +float: 1 +ifloat: 1 +Test "Real part of: clog (0x2dd46725bp-35 + 0x7783a1284p-35 i) == 4.4469229730850767799109418892826021157328e-20 + 1.2046235979300843056806465045930070146351 i": +ildouble: 1 +ldouble: 1 Test "Real part of: clog (1.0 + 0x1.234566p-10 i) == 6.172834701221959432440126967147726538097e-7 + 1.111110564353742042376451655136933182201e-3 i": float: 1 ifloat: 1 @@ -1009,6 +1021,21 @@ idouble: 1 ifloat: 1 ildouble: 1 ldouble: 1 +Test "Real part of: clog10 (0x0.fffffffffffff8p0 + 0x0.fffffffffffff8p-1000 i) == -4.821637332766435821255375046554377090472e-17 + 4.053112396770095089737411317782466262176e-302 i": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "Real part of: clog10 (0x0.ffffffffffffffffp0 + 0x0.ffffffffffffffffp-15000 i) == -2.354315103889861110220423157644627849164e-20 + 1.541165759405643564697852372112893034397e-4516 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: clog10 (0x0.ffffffp0 + 0x0.ffffffp-100 i) == -2.588596909321764128428416045209904492216e-8 + 3.425979381266895667295625489912064603415e-31 i": +double: 1 +float: 2 +idouble: 1 +ifloat: 2 +ildouble: 1 +ldouble: 1 Test "Real part of: clog10 (0x1.000566p0 + 0x1.234p-10 i) == 3.604093470239754109961125085078190708674e-5 + 4.824745078422174667425851670822596859720e-4 i": float: 1 ifloat: 1 @@ -1068,6 +1095,27 @@ ldouble: 1 Test "Real part of: clog10 (0x1.fp+16383 - 0x1p-16445 i) == 4932.061660674182269085496060792589701158 - 0 i": ildouble: 1 ldouble: 1 +Test "Real part of: clog10 (0x10673dd0f2481p-51 + 0x7ef1d17cefbd2p-51 i) == 1.3918041236396763648388478552321724382899e-29 + 0.6263795733790237053262025311642907438291 i": +double: 1 +idouble: 1 +Test "Imaginary part of: clog10 (0x11682p-23 + 0x7ffed1p-23 i) == 5.0916490233953865181284669870035717560498e-13 + 0.6784968969384861816694467029319146542069 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: clog10 (0x1367a310575591p-54 + 0x3cfcc0a0541f60p-54 i) == 2.2081507730821788480616336165447731164865e-32 + 0.5484039935757001196548030312819898864760 i": +double: 1 +idouble: 1 +Test "Imaginary part of: clog10 (0x1367a310575591p-54 + 0x3cfcc0a0541f60p-54 i) == 2.2081507730821788480616336165447731164865e-32 + 0.5484039935757001196548030312819898864760 i": +double: 1 +idouble: 1 +Test "Imaginary part of: clog10 (0x164c74eea876p-45 + 0x16f393482f77p-45 i) == -1.3155760824064879362415202279780039150764e-26 + 0.3473590599762514228227328130640352044313 i": +double: 1 +idouble: 1 +Test "Real part of: clog10 (0x1a6p-10 + 0x3a5p-10 i) == -6.2126412844802358329771948751248003038444e-07 + 0.4977135139537443711784513409096950995985 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: clog10 (0x1a6p-10 + 0x3a5p-10 i) == -6.2126412844802358329771948751248003038444e-07 + 0.4977135139537443711784513409096950995985 i": +double: 1 +idouble: 1 Test "Imaginary part of: clog10 (0x1p-1073 + 0x1p-1073 i) == -322.8546703496198318667349645920187712089 + pi/4*log10(e) i": double: 1 idouble: 1 @@ -1151,6 +1199,75 @@ ifloat: 1 Test "Real part of: clog10 (0x1p-8190 + 1.0 i) == 2.920285685286322365786846845062520925172e-4932 + 6.821881769209206737428918127156778851051e-1 i": ildouble: 1 ldouble: 1 +Test "Real part of: clog10 (0x2818p-15 + 0x798fp-15 i) == 6.6737261053986614395049481326819059203910e-09 + 0.5438241985991753781478398141908629586460 i": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +Test "Imaginary part of: clog10 (0x2818p-15 + 0x798fp-15 i) == 6.6737261053986614395049481326819059203910e-09 + 0.5438241985991753781478398141908629586460 i": +float: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "Real part of: clog10 (0x2dd46725bp-35 + 0x7783a1284p-35 i) == 1.9312741086596516918394613098872836703188e-20 + 0.5231613813514771042838490538484014771862 i": +double: 1 +idouble: 1 +Test "Imaginary part of: clog10 (0x2dd46725bp-35 + 0x7783a1284p-35 i) == 1.9312741086596516918394613098872836703188e-20 + 0.5231613813514771042838490538484014771862 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: clog10 (0x2ede88p-23 + 0x771c3fp-23 i) == -1.9440841725722970687903291200493082253766e-13 + 0.5193774116724956222518530053006822210323 i": +float: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: clog10 (0x2ede88p-23 + 0x771c3fp-23 i) == -1.9440841725722970687903291200493082253766e-13 + 0.5193774116724956222518530053006822210323 i": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "Real part of: clog10 (0x4447d7175p-35 + 0x6c445e00ap-35 i) == -6.4375803621988389731799033530075237868110e-21 + 0.4378257977686804492768642780897650927167 i": +double: 1 +idouble: 1 +Test "Imaginary part of: clog10 (0x4447d7175p-35 + 0x6c445e00ap-35 i) == -6.4375803621988389731799033530075237868110e-21 + 0.4378257977686804492768642780897650927167 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: clog10 (0x4d4ep-15 + 0x6605p-15 i) == -7.0781945783414996953799915941870192015212e-09 + 0.4005747524909781155537088181659175147564 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: clog10 (0x5b06b680ea2ccp-52 + 0xef452b965da9fp-52 i) == 3.6079845358966994996207055940336690133424e-30 + 0.5243112258263349992771652393178033846555 i": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: clog10 (0x659b70ab7971bp-53 + 0x1f5d111e08abecp-53 i) == -1.0893543813872082317104059174982092534059e-30 + 0.5954257879188711495921161433751775633232 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: clog10 (0x659feap-24 + 0xeaf6f9p-24 i) == 1.6200701438094619117335617123525612051457e-14 + 0.5049027913635038013499728086604870749732 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: clog10 (0x6b10b4f3520217b6p-64 + 0xe8893cbb449253a1p-64 i) == 1.0529283395205396881397407610630442563938e-37 + 0.4947949395762683446121140513971996916447 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: clog10 (0x81b7efa81fc35ad1p-65 + 0x1ef4b835f1c79d812p-65 i) == -4.3074341162203896332989394770760901408798e-39 + 0.5709443672155660428417571212549720987784 i": +ildouble: 1 +ldouble: 1 +Test "Real part of: clog10 (0x8ecbf810c4ae6p-52 + 0xd479468b09a37p-52 i) == -4.2289432987513243393180377141513840878196e-30 + 0.4252020027092323591068799049905597805296 i": +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: clog10 (0x9b57bp-20 + 0xcb7b4p-20 i) == -1.7182001068739620267773842120965071561416e-11 + 0.3990121149225253562859800593935899629087 i": +double: 1 +idouble: 1 +Test "Real part of: clog10 (0xf2p-10 + 0x3e3p-10 i) == 2.6921240173351112953324592659528481616879e-06 + 0.5785726025799636431142862788413361783862 i": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: clog10 (0xf2p-10 + 0x3e3p-10 i) == 2.6921240173351112953324592659528481616879e-06 + 0.5785726025799636431142862788413361783862 i": +double: 1 +idouble: 1 +Test "Imaginary part of: clog10 (0xfe961079616p-45 + 0x1bc37e09e6d1p-45 i) == 2.3329549194675052736016290082882121135546e-26 + 0.4561756099441139182878993697611751382976 i": +double: 1 +idouble: 1 Test "Imaginary part of: clog10 (1.0 + 0x1.234566p-10 i) == 2.680828048441605163181684680300513080769e-7 + 4.825491868832381486767558728169977751564e-4 i": double: 1 idouble: 1 @@ -3050,17 +3167,17 @@ ifloat: 3 Function: Real part of "clog10": double: 2 -float: 1 +float: 2 idouble: 2 -ifloat: 1 +ifloat: 2 ildouble: 1 ldouble: 1 Function: Imaginary part of "clog10": double: 1 -float: 5 +float: 1 idouble: 1 -ifloat: 5 +ifloat: 1 ildouble: 1 ldouble: 1 -- cgit 1.4.1