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/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 +++++++++++++++++++++++++++++ 6 files changed, 532 insertions(+) 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/ieee754') 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]; +} -- cgit 1.4.1