sysdeps/ieee754/ldbl-96/s_fma.c

   1 /* Compute x * y + z as ternary operation.
   2    Copyright (C) 2010 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, write to the Free
  18    Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
  19    02111-1307 USA.  */
  20
  21 #include <float.h>
  22 #include <math.h>
  23 #include <fenv.h>
  24 #include <ieee754.h>
  25
  26 /* This implementation uses rounding to odd to avoid problems with
  27    double rounding.  See a paper by Boldo and Melquiond:
  28    http://www.lri.fr/~melquion/doc/08-tc.pdf  */
  29
  30 double
  31 __fma (double x, double y, double z)
  32 {
  33   if (__builtin_expect (isinf (z), 0))
  34     {
  35       /* If z is Inf, but x and y are finite, the result should be
  36          z rather than NaN.  */
  37       if (finite (x) && finite (y))
  38         return (z + x) + y;
  39       return (x * y) + z;
  40     }
  41
  42   /* Multiplication m1 + m2 = x * y using Dekker's algorithm.  */
  43 #define C ((1ULL << (LDBL_MANT_DIG + 1) / 2) + 1)
  44   long double x1 = (long double) x * C;
  45   long double y1 = (long double) y * C;
  46   long double m1 = (long double) x * y;
  47   x1 = (x - x1) + x1;
  48   y1 = (y - y1) + y1;
  49   long double x2 = x - x1;
  50   long double y2 = y - y1;
  51   long double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2;
  52
  53   /* Addition a1 + a2 = z + m1 using Knuth's algorithm.  */
  54   long double a1 = z + m1;
  55   long double t1 = a1 - z;
  56   long double t2 = a1 - t1;
  57   t1 = m1 - t1;
  58   t2 = z - t2;
  59   long double a2 = t1 + t2;
  60
  61   fenv_t env;
  62   feholdexcept (&env);
  63   fesetround (FE_TOWARDZERO);
  64   /* Perform m2 + a2 addition with round to odd.  */
  65   a2 = a2 + m2;
  66
  67   /* Add that to a1 again using rounding to odd.  */
  68   union ieee854_long_double u;
  69   u.d = a1 + a2;
  70   if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7fff)
  71     u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0;
  72   feupdateenv (&env);
  73
  74   /* Add finally round to double precision.  */
  75   return u.d;
  76 }
  77 #ifndef __fma
  78 weak_alias (__fma, fma)
  79 #endif