sysdeps/ieee754/ldbl-96/s_fma.c

   1 /* Compute x * y + z as ternary operation.
   2    Copyright (C) 2010-2023 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 #define NO_MATH_REDIRECT
  20 #include <float.h>
  21 #define dfmal __hide_dfmal
  22 #define f32xfmaf64 __hide_f32xfmaf64
  23 #include <math.h>
  24 #undef dfmal
  25 #undef f32xfmaf64
  26 #include <fenv.h>
  27 #include <ieee754.h>
  28 #include <math-barriers.h>
  29 #include <libm-alias-double.h>
  30 #include <math-narrow-alias.h>
  31
  32 /* This implementation uses rounding to odd to avoid problems with
  33    double rounding.  See a paper by Boldo and Melquiond:
  34    http://www.lri.fr/~melquion/doc/08-tc.pdf  */
  35
  36 double
  37 __fma (double x, double y, double z)
  38 {
  39   if (__glibc_unlikely (!isfinite (x) || !isfinite (y)))
  40     return x * y + z;
  41   else if (__glibc_unlikely (!isfinite (z)))
  42     /* If z is Inf, but x and y are finite, the result should be z
  43        rather than NaN.  */
  44     return (z + x) + y;
  45
  46   /* Ensure correct sign of exact 0 + 0.  */
  47   if (__glibc_unlikely ((x == 0 || y == 0) && z == 0))
  48     {
  49       x = math_opt_barrier (x);
  50       return x * y + z;
  51     }
  52
  53   fenv_t env;
  54   feholdexcept (&env);
  55   fesetround (FE_TONEAREST);
  56
  57   /* Multiplication m1 + m2 = x * y using Dekker's algorithm.  */
  58 #define C ((1ULL << (LDBL_MANT_DIG + 1) / 2) + 1)
  59   long double x1 = (long double) x * C;
  60   long double y1 = (long double) y * C;
  61   long double m1 = (long double) x * y;
  62   x1 = (x - x1) + x1;
  63   y1 = (y - y1) + y1;
  64   long double x2 = x - x1;
  65   long double y2 = y - y1;
  66   long double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2;
  67
  68   /* Addition a1 + a2 = z + m1 using Knuth's algorithm.  */
  69   long double a1 = z + m1;
  70   long double t1 = a1 - z;
  71   long double t2 = a1 - t1;
  72   t1 = m1 - t1;
  73   t2 = z - t2;
  74   long double a2 = t1 + t2;
  75   /* Ensure the arithmetic is not scheduled after feclearexcept call.  */
  76   math_force_eval (m2);
  77   math_force_eval (a2);
  78   feclearexcept (FE_INEXACT);
  79
  80   /* If the result is an exact zero, ensure it has the correct sign.  */
  81   if (a1 == 0 && m2 == 0)
  82     {
  83       feupdateenv (&env);
  84       /* Ensure that round-to-nearest value of z + m1 is not reused.  */
  85       z = math_opt_barrier (z);
  86       return z + m1;
  87     }
  88
  89   fesetround (FE_TOWARDZERO);
  90   /* Perform m2 + a2 addition with round to odd.  */
  91   a2 = a2 + m2;
  92
  93   /* Add that to a1 again using rounding to odd.  */
  94   union ieee854_long_double u;
  95   u.d = a1 + a2;
  96   if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7fff)
  97     u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0;
  98   feupdateenv (&env);
  99
 100   /* Add finally round to double precision.  */
 101   return u.d;
 102 }
 103 #ifndef __fma
 104 libm_alias_double (__fma, fma)
 105 libm_alias_double_narrow (__fma, fma)
 106 #endif