sysdeps/ieee754/ldbl-96/s_fma.c

   1 /* Compute x * y + z as ternary operation.
   2    Copyright (C) 2010-2021 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4
   5    The GNU C Library is free software; you can redistribute it and/or
   6    modify it under the terms of the GNU Lesser General Public
   7    License as published by the Free Software Foundation; either
   8    version 2.1 of the License, or (at your option) any later version.
   9
  10    The GNU C Library is distributed in the hope that it will be useful,
  11    but WITHOUT ANY WARRANTY; without even the implied warranty of
  12    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  13    Lesser General Public License for more details.
  14
  15    You should have received a copy of the GNU Lesser General Public
  16    License along with the GNU C Library; if not, see
  17    <https://www.gnu.org/licenses/>.  */
  18
  19 #include <float.h>
  20 #include <math.h>
  21 #include <fenv.h>
  22 #include <ieee754.h>
  23 #include <math-barriers.h>
  24 #include <libm-alias-double.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 (!isfinite (x) || !isfinite (y)))
  34     return x * y + z;
  35   else if (__glibc_unlikely (!isfinite (z)))
  36     /* If z is Inf, but x and y are finite, the result should be z
  37        rather than NaN.  */
  38     return (z + x) + y;
  39
  40   /* Ensure correct sign of exact 0 + 0.  */
  41   if (__glibc_unlikely ((x == 0 || y == 0) && z == 0))
  42     {
  43       x = math_opt_barrier (x);
  44       return x * y + z;
  45     }
  46
  47   fenv_t env;
  48   feholdexcept (&env);
  49   fesetround (FE_TONEAREST);
  50
  51   /* Multiplication m1 + m2 = x * y using Dekker's algorithm.  */
  52 #define C ((1ULL << (LDBL_MANT_DIG + 1) / 2) + 1)
  53   long double x1 = (long double) x * C;
  54   long double y1 = (long double) y * C;
  55   long double m1 = (long double) x * y;
  56   x1 = (x - x1) + x1;
  57   y1 = (y - y1) + y1;
  58   long double x2 = x - x1;
  59   long double y2 = y - y1;
  60   long double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2;
  61
  62   /* Addition a1 + a2 = z + m1 using Knuth's algorithm.  */
  63   long double a1 = z + m1;
  64   long double t1 = a1 - z;
  65   long double t2 = a1 - t1;
  66   t1 = m1 - t1;
  67   t2 = z - t2;
  68   long double a2 = t1 + t2;
  69   /* Ensure the arithmetic is not scheduled after feclearexcept call.  */
  70   math_force_eval (m2);
  71   math_force_eval (a2);
  72   feclearexcept (FE_INEXACT);
  73
  74   /* If the result is an exact zero, ensure it has the correct sign.  */
  75   if (a1 == 0 && m2 == 0)
  76     {
  77       feupdateenv (&env);
  78       /* Ensure that round-to-nearest value of z + m1 is not reused.  */
  79       z = math_opt_barrier (z);
  80       return z + m1;
  81     }
  82
  83   fesetround (FE_TOWARDZERO);
  84   /* Perform m2 + a2 addition with round to odd.  */
  85   a2 = a2 + m2;
  86
  87   /* Add that to a1 again using rounding to odd.  */
  88   union ieee854_long_double u;
  89   u.d = a1 + a2;
  90   if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7fff)
  91     u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0;
  92   feupdateenv (&env);
  93
  94   /* Add finally round to double precision.  */
  95   return u.d;
  96 }
  97 #ifndef __fma
  98 libm_alias_double (__fma, fma)
  99 #endif