sysdeps/ieee754/ldbl-96/s_fma.c

   1 /* Compute x * y + z as ternary operation.
   2    Copyright (C) 2010-2014 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4    Contributed by Jakub Jelinek <jakub@redhat.com>, 2010.
   5
   6    The GNU C Library is free software; you can redistribute it and/or
   7    modify it under the terms of the GNU Lesser General Public
   8    License as published by the Free Software Foundation; either
   9    version 2.1 of the License, or (at your option) any later version.
  10
  11    The GNU C Library is distributed in the hope that it will be useful,
  12    but WITHOUT ANY WARRANTY; without even the implied warranty of
  13    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  14    Lesser General Public License for more details.
  15
  16    You should have received a copy of the GNU Lesser General Public
  17    License along with the GNU C Library; if not, see
  18    <http://www.gnu.org/licenses/>.  */
  19
  20 #include <float.h>
  21 #include <math.h>
  22 #include <fenv.h>
  23 #include <ieee754.h>
  24
  25 /* This implementation uses rounding to odd to avoid problems with
  26    double rounding.  See a paper by Boldo and Melquiond:
  27    http://www.lri.fr/~melquion/doc/08-tc.pdf  */
  28
  29 double
  30 __fma (double x, double y, double z)
  31 {
  32   if (__builtin_expect (isinf (z), 0))
  33     {
  34       /* If z is Inf, but x and y are finite, the result should be
  35          z rather than NaN.  */
  36       if (finite (x) && finite (y))
  37         return (z + x) + y;
  38       return (x * y) + z;
  39     }
  40
  41   /* Ensure correct sign of exact 0 + 0.  */
  42   if (__builtin_expect ((x == 0 || y == 0) && z == 0, 0))
  43     return x * y + z;
  44
  45   fenv_t env;
  46   feholdexcept (&env);
  47   fesetround (FE_TONEAREST);
  48
  49   /* Multiplication m1 + m2 = x * y using Dekker's algorithm.  */
  50 #define C ((1ULL << (LDBL_MANT_DIG + 1) / 2) + 1)
  51   long double x1 = (long double) x * C;
  52   long double y1 = (long double) y * C;
  53   long double m1 = (long double) x * y;
  54   x1 = (x - x1) + x1;
  55   y1 = (y - y1) + y1;
  56   long double x2 = x - x1;
  57   long double y2 = y - y1;
  58   long double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2;
  59
  60   /* Addition a1 + a2 = z + m1 using Knuth's algorithm.  */
  61   long double a1 = z + m1;
  62   long double t1 = a1 - z;
  63   long double t2 = a1 - t1;
  64   t1 = m1 - t1;
  65   t2 = z - t2;
  66   long double a2 = t1 + t2;
  67   feclearexcept (FE_INEXACT);
  68
  69   /* If the result is an exact zero, ensure it has the correct
  70      sign.  */
  71   if (a1 == 0 && m2 == 0)
  72     {
  73       feupdateenv (&env);
  74       /* Ensure that round-to-nearest value of z + m1 is not
  75          reused.  */
  76       asm volatile ("" : "=m" (z) : "m" (z));
  77       return z + m1;
  78     }
  79
  80   fesetround (FE_TOWARDZERO);
  81   /* Perform m2 + a2 addition with round to odd.  */
  82   a2 = a2 + m2;
  83
  84   /* Add that to a1 again using rounding to odd.  */
  85   union ieee854_long_double u;
  86   u.d = a1 + a2;
  87   if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7fff)
  88     u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0;
  89   feupdateenv (&env);
  90
  91   /* Add finally round to double precision.  */
  92   return u.d;
  93 }
  94 #ifndef __fma
  95 weak_alias (__fma, fma)
  96 #endif