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Diffstat (limited to 'sysdeps/ieee754/dbl-64/s_fma.c')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/s_fma.c | 301 |
1 files changed, 0 insertions, 301 deletions
diff --git a/sysdeps/ieee754/dbl-64/s_fma.c b/sysdeps/ieee754/dbl-64/s_fma.c deleted file mode 100644 index 68c8515fb1..0000000000 --- a/sysdeps/ieee754/dbl-64/s_fma.c +++ /dev/null @@ -1,301 +0,0 @@ -/* Compute x * y + z as ternary operation. - Copyright (C) 2010-2017 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, see - <http://www.gnu.org/licenses/>. */ - -#include <float.h> -#include <math.h> -#include <fenv.h> -#include <ieee754.h> -#include <math_private.h> -#include <tininess.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 */ - -double -__fma (double x, double y, double z) -{ - union ieee754_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 - >= 0x7ff + IEEE754_DOUBLE_BIAS - DBL_MANT_DIG, 0) - || __builtin_expect (u.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0) - || __builtin_expect (v.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0) - || __builtin_expect (w.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0) - || __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 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 (u.ieee.exponent == 0x7ff - || v.ieee.exponent == 0x7ff - || w.ieee.exponent == 0x7ff - || x == 0 - || y == 0) - return x * y + z; - /* If fma will certainly overflow, compute as x * y. */ - if (u.ieee.exponent + v.ieee.exponent > 0x7ff + IEEE754_DOUBLE_BIAS) - return x * y; - /* If x * y is less than 1/4 of DBL_TRUE_MIN, neither the - result nor whether there is underflow depends on its exact - value, only on its sign. */ - if (u.ieee.exponent + v.ieee.exponent - < IEEE754_DOUBLE_BIAS - DBL_MANT_DIG - 2) - { - int neg = u.ieee.negative ^ v.ieee.negative; - double tiny = neg ? -0x1p-1074 : 0x1p-1074; - if (w.ieee.exponent >= 3) - return tiny + z; - /* Scaling up, adding TINY and scaling down produces the - correct result, because in round-to-nearest mode adding - TINY has no effect and in other modes double rounding is - harmless. But it may not produce required underflow - exceptions. */ - v.d = z * 0x1p54 + tiny; - if (TININESS_AFTER_ROUNDING - ? v.ieee.exponent < 55 - : (w.ieee.exponent == 0 - || (w.ieee.exponent == 1 - && w.ieee.negative != neg - && w.ieee.mantissa1 == 0 - && w.ieee.mantissa0 == 0))) - { - double force_underflow = x * y; - math_force_eval (force_underflow); - } - return v.d * 0x1p-54; - } - if (u.ieee.exponent + v.ieee.exponent - >= 0x7ff + IEEE754_DOUBLE_BIAS - DBL_MANT_DIG) - { - /* Compute 1p-53 times smaller result and multiply - at the end. */ - if (u.ieee.exponent > v.ieee.exponent) - u.ieee.exponent -= DBL_MANT_DIG; - else - v.ieee.exponent -= DBL_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 > DBL_MANT_DIG) - w.ieee.exponent -= DBL_MANT_DIG; - adjust = 1; - } - else if (w.ieee.exponent >= 0x7ff - DBL_MANT_DIG) - { - /* Similarly. - If z exponent is very large and x and y exponents are - very small, adjust them up to avoid spurious underflows, - rather than down. */ - if (u.ieee.exponent + v.ieee.exponent - <= IEEE754_DOUBLE_BIAS + 2 * DBL_MANT_DIG) - { - if (u.ieee.exponent > v.ieee.exponent) - u.ieee.exponent += 2 * DBL_MANT_DIG + 2; - else - v.ieee.exponent += 2 * DBL_MANT_DIG + 2; - } - else if (u.ieee.exponent > v.ieee.exponent) - { - if (u.ieee.exponent > DBL_MANT_DIG) - u.ieee.exponent -= DBL_MANT_DIG; - } - else if (v.ieee.exponent > DBL_MANT_DIG) - v.ieee.exponent -= DBL_MANT_DIG; - w.ieee.exponent -= DBL_MANT_DIG; - adjust = 1; - } - else if (u.ieee.exponent >= 0x7ff - DBL_MANT_DIG) - { - u.ieee.exponent -= DBL_MANT_DIG; - if (v.ieee.exponent) - v.ieee.exponent += DBL_MANT_DIG; - else - v.d *= 0x1p53; - } - else if (v.ieee.exponent >= 0x7ff - DBL_MANT_DIG) - { - v.ieee.exponent -= DBL_MANT_DIG; - if (u.ieee.exponent) - u.ieee.exponent += DBL_MANT_DIG; - else - u.d *= 0x1p53; - } - else /* if (u.ieee.exponent + v.ieee.exponent - <= IEEE754_DOUBLE_BIAS + DBL_MANT_DIG) */ - { - if (u.ieee.exponent > v.ieee.exponent) - u.ieee.exponent += 2 * DBL_MANT_DIG + 2; - else - v.ieee.exponent += 2 * DBL_MANT_DIG + 2; - if (w.ieee.exponent <= 4 * DBL_MANT_DIG + 6) - { - if (w.ieee.exponent) - w.ieee.exponent += 2 * DBL_MANT_DIG + 2; - else - w.d *= 0x1p108; - adjust = -1; - } - /* Otherwise x * y should just affect inexact - and nothing else. */ - } - x = u.d; - y = v.d; - z = w.d; - } - - /* Ensure correct sign of exact 0 + 0. */ - if (__glibc_unlikely ((x == 0 || y == 0) && z == 0)) - { - x = math_opt_barrier (x); - return x * y + z; - } - - fenv_t env; - libc_feholdexcept_setround (&env, FE_TONEAREST); - - /* Multiplication m1 + m2 = x * y using Dekker's algorithm. */ -#define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1) - double x1 = x * C; - double y1 = y * C; - double m1 = x * y; - x1 = (x - x1) + x1; - y1 = (y - y1) + y1; - double x2 = x - x1; - double y2 = y - y1; - double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2; - - /* Addition a1 + a2 = z + m1 using Knuth's algorithm. */ - double a1 = z + m1; - double t1 = a1 - z; - double t2 = a1 - t1; - t1 = m1 - t1; - t2 = z - t2; - double a2 = t1 + t2; - /* Ensure the arithmetic is not scheduled after feclearexcept call. */ - math_force_eval (m2); - math_force_eval (a2); - feclearexcept (FE_INEXACT); - - /* If the result is an exact zero, ensure it has the correct sign. */ - if (a1 == 0 && m2 == 0) - { - libc_feupdateenv (&env); - /* Ensure that round-to-nearest value of z + m1 is not reused. */ - z = math_opt_barrier (z); - return z + m1; - } - - libc_fesetround (FE_TOWARDZERO); - - /* Perform m2 + a2 addition with round to odd. */ - u.d = a2 + m2; - - if (__glibc_unlikely (adjust < 0)) - { - if ((u.ieee.mantissa1 & 1) == 0) - u.ieee.mantissa1 |= libc_fetestexcept (FE_INEXACT) != 0; - v.d = a1 + u.d; - /* Ensure the addition is not scheduled after fetestexcept call. */ - math_force_eval (v.d); - } - - /* Reset rounding mode and test for inexact simultaneously. */ - int j = libc_feupdateenv_test (&env, FE_INEXACT) != 0; - - if (__glibc_likely (adjust == 0)) - { - if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7ff) - u.ieee.mantissa1 |= j; - /* Result is a1 + u.d. */ - return a1 + u.d; - } - else if (__glibc_likely (adjust > 0)) - { - if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7ff) - u.ieee.mantissa1 |= j; - /* Result is a1 + u.d, scaled up. */ - return (a1 + u.d) * 0x1p53; - } - else - { - /* If a1 + u.d is exact, the only rounding happens during - scaling down. */ - if (j == 0) - return v.d * 0x1p-108; - /* If result rounded to zero is not subnormal, no double - rounding will occur. */ - if (v.ieee.exponent > 108) - return (a1 + u.d) * 0x1p-108; - /* If v.d * 0x1p-108 with round to zero is a subnormal above - or equal to DBL_MIN / 2, then v.d * 0x1p-108 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-108 never normalizes by shifting up, - so round bit plus sticky bit should be already enough - for proper rounding. */ - if (v.ieee.exponent == 108) - { - /* If the exponent would be in the normal range when - rounding to normal precision with unbounded exponent - range, the exact result is known and spurious underflows - must be avoided on systems detecting tininess after - rounding. */ - if (TININESS_AFTER_ROUNDING) - { - w.d = a1 + u.d; - if (w.ieee.exponent == 109) - return w.d * 0x1p-108; - } - /* 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. */ - w.d = 0.0; - w.ieee.mantissa1 = ((v.ieee.mantissa1 & 3) << 1) | j; - w.ieee.negative = v.ieee.negative; - v.ieee.mantissa1 &= ~3U; - v.d *= 0x1p-108; - w.d *= 0x1p-2; - return v.d + w.d; - } - v.ieee.mantissa1 |= j; - return v.d * 0x1p-108; - } -} -#ifndef __fma -weak_alias (__fma, fma) -#endif - -#ifdef NO_LONG_DOUBLE -strong_alias (__fma, __fmal) -weak_alias (__fmal, fmal) -#endif |