diff options
Diffstat (limited to 'sysdeps/ieee754/dbl-64/s_fma.c')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/s_fma.c | 146 |
1 files changed, 146 insertions, 0 deletions
diff --git a/sysdeps/ieee754/dbl-64/s_fma.c b/sysdeps/ieee754/dbl-64/s_fma.c new file mode 100644 index 0000000000..ca7300c11e --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_fma.c @@ -0,0 +1,146 @@ +/* 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 */ + +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)) + { + /* If x or y or z is Inf/NaN or if fma will certainly overflow, + compute as x * y + z. */ + if (u.ieee.exponent == 0x7ff + || v.ieee.exponent == 0x7ff + || w.ieee.exponent == 0x7ff + || u.ieee.exponent + v.ieee.exponent + > 0x7ff + IEEE754_DOUBLE_BIAS) + return x * y + z; + 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, it doesn't matter if we don't adjust it. */ + 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 + { + v.ieee.exponent -= DBL_MANT_DIG; + if (u.ieee.exponent) + u.ieee.exponent += DBL_MANT_DIG; + else + u.d *= 0x1p53; + } + x = u.d; + y = v.d; + z = w.d; + } + /* 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; + + fenv_t env; + feholdexcept (&env); + fesetround (FE_TOWARDZERO); + /* Perform m2 + a2 addition with round to odd. */ + u.d = a2 + m2; + if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7ff) + u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0; + feupdateenv (&env); + + /* Add that to a1. */ + a1 = a1 + u.d; + + /* And adjust exponent if needed. */ + if (__builtin_expect (adjust, 0)) + a1 *= 0x1p53; + + return a1; +} +#ifndef __fma +weak_alias (__fma, fma) +#endif + +#ifdef NO_LONG_DOUBLE +strong_alias (__fma, __fmal) +weak_alias (__fmal, fmal) +#endif |