sysdeps/ieee754/ldbl-96/s_fma.c

   1 /* Compute x * y + z as ternary operation.
   2    Copyright (C) 2010-2015 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 #include <math_private.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 (__glibc_unlikely (isinf (z)))
  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   /* Ensure correct sign of exact 0 + 0.  */
  43   if (__glibc_unlikely ((x == 0 || y == 0) && z == 0))
  44     return x * y + z;
  45
  46   fenv_t env;
  47   feholdexcept (&env);
  48   fesetround (FE_TONEAREST);
  49
  50   /* Multiplication m1 + m2 = x * y using Dekker's algorithm.  */
  51 #define C ((1ULL << (LDBL_MANT_DIG + 1) / 2) + 1)
  52   long double x1 = (long double) x * C;
  53   long double y1 = (long double) y * C;
  54   long double m1 = (long double) x * y;
  55   x1 = (x - x1) + x1;
  56   y1 = (y - y1) + y1;
  57   long double x2 = x - x1;
  58   long double y2 = y - y1;
  59   long double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2;
  60
  61   /* Addition a1 + a2 = z + m1 using Knuth's algorithm.  */
  62   long double a1 = z + m1;
  63   long double t1 = a1 - z;
  64   long double t2 = a1 - t1;
  65   t1 = m1 - t1;
  66   t2 = z - t2;
  67   long double a2 = t1 + t2;
  68   /* Ensure the arithmetic is not scheduled after feclearexcept call.  */
  69   math_force_eval (m2);
  70   math_force_eval (a2);
  71   feclearexcept (FE_INEXACT);
  72
  73   /* If the result is an exact zero, ensure it has the correct sign.  */
  74   if (a1 == 0 && m2 == 0)
  75     {
  76       feupdateenv (&env);
  77       /* Ensure that round-to-nearest value of z + m1 is not reused.  */
  78       z = math_opt_barrier (z);
  79       return z + m1;
  80     }
  81
  82   fesetround (FE_TOWARDZERO);
  83   /* Perform m2 + a2 addition with round to odd.  */
  84   a2 = a2 + m2;
  85
  86   /* Add that to a1 again using rounding to odd.  */
  87   union ieee854_long_double u;
  88   u.d = a1 + a2;
  89   if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7fff)
  90     u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0;
  91   feupdateenv (&env);
  92
  93   /* Add finally round to double precision.  */
  94   return u.d;
  95 }
  96 #ifndef __fma
  97 weak_alias (__fma, fma)
  98 #endif