diff options
Diffstat (limited to 'sysdeps/ieee754')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/s_fma.c | 8 | ||||
| -rw-r--r-- | sysdeps/ieee754/ldbl-128/s_fmal.c | 221 | ||||
| -rw-r--r-- | sysdeps/ieee754/ldbl-64-128/s_fmal.c | 5 | ||||
| -rw-r--r-- | sysdeps/ieee754/ldbl-96/s_fma.c | 15 | ||||
| -rw-r--r-- | sysdeps/ieee754/ldbl-96/s_fmal.c | 221 |
5 files changed, 467 insertions, 3 deletions
diff --git a/sysdeps/ieee754/dbl-64/s_fma.c b/sysdeps/ieee754/dbl-64/s_fma.c index 911682eceb..3b0bfd5ce6 100644 --- a/sysdeps/ieee754/dbl-64/s_fma.c +++ b/sysdeps/ieee754/dbl-64/s_fma.c @@ -43,6 +43,12 @@ __fma (double x, double y, double z) || __builtin_expect (u.ieee.exponent + v.ieee.exponent <= IEEE754_DOUBLE_BIAS + DBL_MANT_DIG, 0)) { + /* If z is Inf, but x and y are finite, the result should be + z rather than NaN. */ + if (w.ieee.exponent == 0x7ff + && u.ieee.exponent != 0x7ff + && v.ieee.exponent != 0x7ff) + return (z + x) + y; /* If x or y or z is Inf/NaN, or if fma will certainly overflow, or if x * y is less than half of DBL_DENORM_MIN, compute as x * y + z. */ @@ -165,6 +171,8 @@ __fma (double x, double y, double z) } else { + if ((u.ieee.mantissa1 & 1) == 0) + u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0; v.d = a1 + u.d; int j = fetestexcept (FE_INEXACT) != 0; feupdateenv (&env); diff --git a/sysdeps/ieee754/ldbl-128/s_fmal.c b/sysdeps/ieee754/ldbl-128/s_fmal.c new file mode 100644 index 0000000000..9ec5ba9ee9 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_fmal.c @@ -0,0 +1,221 @@ +/* Compute x * y + z as ternary operation. + Copyright (C) 2010 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jakub@redhat.com>, 2010. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, write to the Free + Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA + 02111-1307 USA. */ + +#include <float.h> +#include <math.h> +#include <fenv.h> +#include <ieee754.h> + +/* This implementation uses rounding to odd to avoid problems with + double rounding. See a paper by Boldo and Melquiond: + http://www.lri.fr/~melquion/doc/08-tc.pdf */ + +long double +__fmal (long double x, long double y, long double z) +{ + union ieee854_long_double u, v, w; + int adjust = 0; + u.d = x; + v.d = y; + w.d = z; + if (__builtin_expect (u.ieee.exponent + v.ieee.exponent + >= 0x7fff + IEEE854_LONG_DOUBLE_BIAS + - LDBL_MANT_DIG, 0) + || __builtin_expect (u.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0) + || __builtin_expect (v.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0) + || __builtin_expect (w.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0) + || __builtin_expect (u.ieee.exponent + v.ieee.exponent + <= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG, 0)) + { + /* If z is Inf, but x and y are finite, the result should be + z rather than NaN. */ + if (w.ieee.exponent == 0x7fff + && u.ieee.exponent != 0x7fff + && v.ieee.exponent != 0x7fff) + return (z + x) + y; + /* If x or y or z is Inf/NaN, or if fma will certainly overflow, + or if x * y is less than half of LDBL_DENORM_MIN, + compute as x * y + z. */ + if (u.ieee.exponent == 0x7fff + || v.ieee.exponent == 0x7fff + || w.ieee.exponent == 0x7fff + || u.ieee.exponent + v.ieee.exponent + > 0x7fff + IEEE854_LONG_DOUBLE_BIAS + || u.ieee.exponent + v.ieee.exponent + < IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG - 2) + return x * y + z; + if (u.ieee.exponent + v.ieee.exponent + >= 0x7fff + IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG) + { + /* Compute 1p-113 times smaller result and multiply + at the end. */ + if (u.ieee.exponent > v.ieee.exponent) + u.ieee.exponent -= LDBL_MANT_DIG; + else + v.ieee.exponent -= LDBL_MANT_DIG; + /* If x + y exponent is very large and z exponent is very small, + it doesn't matter if we don't adjust it. */ + if (w.ieee.exponent > LDBL_MANT_DIG) + w.ieee.exponent -= LDBL_MANT_DIG; + adjust = 1; + } + else if (w.ieee.exponent >= 0x7fff - LDBL_MANT_DIG) + { + /* Similarly. + If z exponent is very large and x and y exponents are + very small, it doesn't matter if we don't adjust it. */ + if (u.ieee.exponent > v.ieee.exponent) + { + if (u.ieee.exponent > LDBL_MANT_DIG) + u.ieee.exponent -= LDBL_MANT_DIG; + } + else if (v.ieee.exponent > LDBL_MANT_DIG) + v.ieee.exponent -= LDBL_MANT_DIG; + w.ieee.exponent -= LDBL_MANT_DIG; + adjust = 1; + } + else if (u.ieee.exponent >= 0x7fff - LDBL_MANT_DIG) + { + u.ieee.exponent -= LDBL_MANT_DIG; + if (v.ieee.exponent) + v.ieee.exponent += LDBL_MANT_DIG; + else + v.d *= 0x1p113L; + } + else if (v.ieee.exponent >= 0x7fff - LDBL_MANT_DIG) + { + v.ieee.exponent -= LDBL_MANT_DIG; + if (u.ieee.exponent) + u.ieee.exponent += LDBL_MANT_DIG; + else + u.d *= 0x1p113L; + } + else /* if (u.ieee.exponent + v.ieee.exponent + <= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG) */ + { + if (u.ieee.exponent > v.ieee.exponent) + u.ieee.exponent += 2 * LDBL_MANT_DIG; + else + v.ieee.exponent += 2 * LDBL_MANT_DIG; + if (w.ieee.exponent <= 4 * LDBL_MANT_DIG + 4) + { + if (w.ieee.exponent) + w.ieee.exponent += 2 * LDBL_MANT_DIG; + else + w.d *= 0x1p226L; + adjust = -1; + } + /* Otherwise x * y should just affect inexact + and nothing else. */ + } + x = u.d; + y = v.d; + z = w.d; + } + /* Multiplication m1 + m2 = x * y using Dekker's algorithm. */ +#define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1) + long double x1 = x * C; + long double y1 = y * C; + long double m1 = x * y; + x1 = (x - x1) + x1; + y1 = (y - y1) + y1; + long double x2 = x - x1; + long double y2 = y - y1; + long double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2; + + /* Addition a1 + a2 = z + m1 using Knuth's algorithm. */ + long double a1 = z + m1; + long double t1 = a1 - z; + long double t2 = a1 - t1; + t1 = m1 - t1; + t2 = z - t2; + long double a2 = t1 + t2; + + fenv_t env; + feholdexcept (&env); + fesetround (FE_TOWARDZERO); + /* Perform m2 + a2 addition with round to odd. */ + u.d = a2 + m2; + + if (__builtin_expect (adjust == 0, 1)) + { + if ((u.ieee.mantissa3 & 1) == 0 && u.ieee.exponent != 0x7fff) + u.ieee.mantissa3 |= fetestexcept (FE_INEXACT) != 0; + feupdateenv (&env); + /* Result is a1 + u.d. */ + return a1 + u.d; + } + else if (__builtin_expect (adjust > 0, 1)) + { + if ((u.ieee.mantissa3 & 1) == 0 && u.ieee.exponent != 0x7fff) + u.ieee.mantissa3 |= fetestexcept (FE_INEXACT) != 0; + feupdateenv (&env); + /* Result is a1 + u.d, scaled up. */ + return (a1 + u.d) * 0x1p113L; + } + else + { + if ((u.ieee.mantissa3 & 1) == 0) + u.ieee.mantissa3 |= fetestexcept (FE_INEXACT) != 0; + v.d = a1 + u.d; + int j = fetestexcept (FE_INEXACT) != 0; + feupdateenv (&env); + /* Ensure the following computations are performed in default rounding + mode instead of just reusing the round to zero computation. */ + asm volatile ("" : "=m" (u) : "m" (u)); + /* If a1 + u.d is exact, the only rounding happens during + scaling down. */ + if (j == 0) + return v.d * 0x1p-226L; + /* If result rounded to zero is not subnormal, no double + rounding will occur. */ + if (v.ieee.exponent > 226) + return (a1 + u.d) * 0x1p-226L; + /* If v.d * 0x1p-226L with round to zero is a subnormal above + or equal to LDBL_MIN / 2, then v.d * 0x1p-226L shifts mantissa + down just by 1 bit, which means v.ieee.mantissa3 |= j would + change the round bit, not sticky or guard bit. + v.d * 0x1p-226L never normalizes by shifting up, + so round bit plus sticky bit should be already enough + for proper rounding. */ + if (v.ieee.exponent == 226) + { + /* v.ieee.mantissa3 & 2 is LSB bit of the result before rounding, + v.ieee.mantissa3 & 1 is the round bit and j is our sticky + bit. In round-to-nearest 001 rounds down like 00, + 011 rounds up, even though 01 rounds down (thus we need + to adjust), 101 rounds down like 10 and 111 rounds up + like 11. */ + if ((v.ieee.mantissa3 & 3) == 1) + { + v.d *= 0x1p-226L; + if (v.ieee.negative) + return v.d - 0x1p-16493L /* __LDBL_DENORM_MIN__ */; + else + return v.d + 0x1p-16493L /* __LDBL_DENORM_MIN__ */; + } + else + return v.d * 0x1p-226L; + } + v.ieee.mantissa3 |= j; + return v.d * 0x1p-226L; + } +} +weak_alias (__fmal, fmal) diff --git a/sysdeps/ieee754/ldbl-64-128/s_fmal.c b/sysdeps/ieee754/ldbl-64-128/s_fmal.c new file mode 100644 index 0000000000..218aa52b35 --- /dev/null +++ b/sysdeps/ieee754/ldbl-64-128/s_fmal.c @@ -0,0 +1,5 @@ +#include <math_ldbl_opt.h> +#undef weak_alias +#define weak_alias(n,a) +#include <sysdeps/ieee754/ldbl-128/s_fmal.c> +long_double_symbol (libm, __fmal, fmal); diff --git a/sysdeps/ieee754/ldbl-96/s_fma.c b/sysdeps/ieee754/ldbl-96/s_fma.c index 90c6d1f29d..6c7e9d0d36 100644 --- a/sysdeps/ieee754/ldbl-96/s_fma.c +++ b/sysdeps/ieee754/ldbl-96/s_fma.c @@ -30,11 +30,20 @@ double __fma (double x, double y, double z) { + if (__builtin_expect (isinf (z), 0)) + { + /* If z is Inf, but x and y are finite, the result should be + z rather than NaN. */ + if (finite (x) && finite (y)) + return (z + x) + y; + return (x * y) + z; + } + /* Multiplication m1 + m2 = x * y using Dekker's algorithm. */ #define C ((1ULL << (LDBL_MANT_DIG + 1) / 2) + 1) - long double x1 = x * C; - long double y1 = y * C; - long double m1 = x * y; + long double x1 = (long double) x * C; + long double y1 = (long double) y * C; + long double m1 = (long double) x * y; x1 = (x - x1) + x1; y1 = (y - y1) + y1; long double x2 = x - x1; diff --git a/sysdeps/ieee754/ldbl-96/s_fmal.c b/sysdeps/ieee754/ldbl-96/s_fmal.c new file mode 100644 index 0000000000..340f02536c --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_fmal.c @@ -0,0 +1,221 @@ +/* Compute x * y + z as ternary operation. + Copyright (C) 2010 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jakub@redhat.com>, 2010. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, write to the Free + Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA + 02111-1307 USA. */ + +#include <float.h> +#include <math.h> +#include <fenv.h> +#include <ieee754.h> + +/* This implementation uses rounding to odd to avoid problems with + double rounding. See a paper by Boldo and Melquiond: + http://www.lri.fr/~melquion/doc/08-tc.pdf */ + +long double +__fmal (long double x, long double y, long double z) +{ + union ieee854_long_double u, v, w; + int adjust = 0; + u.d = x; + v.d = y; + w.d = z; + if (__builtin_expect (u.ieee.exponent + v.ieee.exponent + >= 0x7fff + IEEE854_LONG_DOUBLE_BIAS + - LDBL_MANT_DIG, 0) + || __builtin_expect (u.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0) + || __builtin_expect (v.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0) + || __builtin_expect (w.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0) + || __builtin_expect (u.ieee.exponent + v.ieee.exponent + <= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG, 0)) + { + /* If z is Inf, but x and y are finite, the result should be + z rather than NaN. */ + if (w.ieee.exponent == 0x7fff + && u.ieee.exponent != 0x7fff + && v.ieee.exponent != 0x7fff) + return (z + x) + y; + /* If x or y or z is Inf/NaN, or if fma will certainly overflow, + or if x * y is less than half of LDBL_DENORM_MIN, + compute as x * y + z. */ + if (u.ieee.exponent == 0x7fff + || v.ieee.exponent == 0x7fff + || w.ieee.exponent == 0x7fff + || u.ieee.exponent + v.ieee.exponent + > 0x7fff + IEEE854_LONG_DOUBLE_BIAS + || u.ieee.exponent + v.ieee.exponent + < IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG - 2) + return x * y + z; + if (u.ieee.exponent + v.ieee.exponent + >= 0x7fff + IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG) + { + /* Compute 1p-64 times smaller result and multiply + at the end. */ + if (u.ieee.exponent > v.ieee.exponent) + u.ieee.exponent -= LDBL_MANT_DIG; + else + v.ieee.exponent -= LDBL_MANT_DIG; + /* If x + y exponent is very large and z exponent is very small, + it doesn't matter if we don't adjust it. */ + if (w.ieee.exponent > LDBL_MANT_DIG) + w.ieee.exponent -= LDBL_MANT_DIG; + adjust = 1; + } + else if (w.ieee.exponent >= 0x7fff - LDBL_MANT_DIG) + { + /* Similarly. + If z exponent is very large and x and y exponents are + very small, it doesn't matter if we don't adjust it. */ + if (u.ieee.exponent > v.ieee.exponent) + { + if (u.ieee.exponent > LDBL_MANT_DIG) + u.ieee.exponent -= LDBL_MANT_DIG; + } + else if (v.ieee.exponent > LDBL_MANT_DIG) + v.ieee.exponent -= LDBL_MANT_DIG; + w.ieee.exponent -= LDBL_MANT_DIG; + adjust = 1; + } + else if (u.ieee.exponent >= 0x7fff - LDBL_MANT_DIG) + { + u.ieee.exponent -= LDBL_MANT_DIG; + if (v.ieee.exponent) + v.ieee.exponent += LDBL_MANT_DIG; + else + v.d *= 0x1p64L; + } + else if (v.ieee.exponent >= 0x7fff - LDBL_MANT_DIG) + { + v.ieee.exponent -= LDBL_MANT_DIG; + if (u.ieee.exponent) + u.ieee.exponent += LDBL_MANT_DIG; + else + u.d *= 0x1p64L; + } + else /* if (u.ieee.exponent + v.ieee.exponent + <= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG) */ + { + if (u.ieee.exponent > v.ieee.exponent) + u.ieee.exponent += 2 * LDBL_MANT_DIG; + else + v.ieee.exponent += 2 * LDBL_MANT_DIG; + if (w.ieee.exponent <= 4 * LDBL_MANT_DIG + 4) + { + if (w.ieee.exponent) + w.ieee.exponent += 2 * LDBL_MANT_DIG; + else + w.d *= 0x1p128L; + adjust = -1; + } + /* Otherwise x * y should just affect inexact + and nothing else. */ + } + x = u.d; + y = v.d; + z = w.d; + } + /* Multiplication m1 + m2 = x * y using Dekker's algorithm. */ +#define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1) + long double x1 = x * C; + long double y1 = y * C; + long double m1 = x * y; + x1 = (x - x1) + x1; + y1 = (y - y1) + y1; + long double x2 = x - x1; + long double y2 = y - y1; + long double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2; + + /* Addition a1 + a2 = z + m1 using Knuth's algorithm. */ + long double a1 = z + m1; + long double t1 = a1 - z; + long double t2 = a1 - t1; + t1 = m1 - t1; + t2 = z - t2; + long double a2 = t1 + t2; + + fenv_t env; + feholdexcept (&env); + fesetround (FE_TOWARDZERO); + /* Perform m2 + a2 addition with round to odd. */ + u.d = a2 + m2; + + if (__builtin_expect (adjust == 0, 1)) + { + if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7fff) + u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0; + feupdateenv (&env); + /* Result is a1 + u.d. */ + return a1 + u.d; + } + else if (__builtin_expect (adjust > 0, 1)) + { + if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7fff) + u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0; + feupdateenv (&env); + /* Result is a1 + u.d, scaled up. */ + return (a1 + u.d) * 0x1p64L; + } + else + { + if ((u.ieee.mantissa1 & 1) == 0) + u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0; + v.d = a1 + u.d; + int j = fetestexcept (FE_INEXACT) != 0; + feupdateenv (&env); + /* Ensure the following computations are performed in default rounding + mode instead of just reusing the round to zero computation. */ + asm volatile ("" : "=m" (u) : "m" (u)); + /* If a1 + u.d is exact, the only rounding happens during + scaling down. */ + if (j == 0) + return v.d * 0x1p-128L; + /* If result rounded to zero is not subnormal, no double + rounding will occur. */ + if (v.ieee.exponent > 128) + return (a1 + u.d) * 0x1p-128L; + /* If v.d * 0x1p-128L with round to zero is a subnormal above + or equal to LDBL_MIN / 2, then v.d * 0x1p-128L shifts mantissa + down just by 1 bit, which means v.ieee.mantissa1 |= j would + change the round bit, not sticky or guard bit. + v.d * 0x1p-128L never normalizes by shifting up, + so round bit plus sticky bit should be already enough + for proper rounding. */ + if (v.ieee.exponent == 128) + { + /* v.ieee.mantissa1 & 2 is LSB bit of the result before rounding, + v.ieee.mantissa1 & 1 is the round bit and j is our sticky + bit. In round-to-nearest 001 rounds down like 00, + 011 rounds up, even though 01 rounds down (thus we need + to adjust), 101 rounds down like 10 and 111 rounds up + like 11. */ + if ((v.ieee.mantissa1 & 3) == 1) + { + v.d *= 0x1p-128L; + if (v.ieee.negative) + return v.d - 0x1p-16445L /* __LDBL_DENORM_MIN__ */; + else + return v.d + 0x1p-16445L /* __LDBL_DENORM_MIN__ */; + } + else + return v.d * 0x1p-128L; + } + v.ieee.mantissa1 |= j; + return v.d * 0x1p-128L; + } +} +weak_alias (__fmal, fmal) |