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/* Compute x * y + z as ternary operation.
Copyright (C) 2010-2021 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<https://www.gnu.org/licenses/>. */
#define NO_MATH_REDIRECT
#include <float.h>
#include <math.h>
#include <fenv.h>
#include <ieee754.h>
#include <math-barriers.h>
#include <libm-alias-double.h>
/* This implementation uses rounding to odd to avoid problems with
double rounding. See a paper by Boldo and Melquiond:
http://www.lri.fr/~melquion/doc/08-tc.pdf */
double
__fma (double x, double y, double z)
{
if (__glibc_unlikely (!isfinite (x) || !isfinite (y)))
return x * y + z;
else if (__glibc_unlikely (!isfinite (z)))
/* If z is Inf, but x and y are finite, the result should be z
rather than NaN. */
return (z + x) + y;
/* Ensure correct sign of exact 0 + 0. */
if (__glibc_unlikely ((x == 0 || y == 0) && z == 0))
{
x = math_opt_barrier (x);
return x * y + z;
}
fenv_t env;
feholdexcept (&env);
fesetround (FE_TONEAREST);
/* Multiplication m1 + m2 = x * y using Dekker's algorithm. */
#define C ((1ULL << (LDBL_MANT_DIG + 1) / 2) + 1)
long double x1 = (long double) x * C;
long double y1 = (long double) y * C;
long double m1 = (long double) x * y;
x1 = (x - x1) + x1;
y1 = (y - y1) + y1;
long double x2 = x - x1;
long double y2 = y - y1;
long double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2;
/* Addition a1 + a2 = z + m1 using Knuth's algorithm. */
long double a1 = z + m1;
long double t1 = a1 - z;
long double t2 = a1 - t1;
t1 = m1 - t1;
t2 = z - t2;
long double a2 = t1 + t2;
/* Ensure the arithmetic is not scheduled after feclearexcept call. */
math_force_eval (m2);
math_force_eval (a2);
feclearexcept (FE_INEXACT);
/* If the result is an exact zero, ensure it has the correct sign. */
if (a1 == 0 && m2 == 0)
{
feupdateenv (&env);
/* Ensure that round-to-nearest value of z + m1 is not reused. */
z = math_opt_barrier (z);
return z + m1;
}
fesetround (FE_TOWARDZERO);
/* Perform m2 + a2 addition with round to odd. */
a2 = a2 + m2;
/* Add that to a1 again using rounding to odd. */
union ieee854_long_double u;
u.d = a1 + a2;
if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7fff)
u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0;
feupdateenv (&env);
/* Add finally round to double precision. */
return u.d;
}
#ifndef __fma
libm_alias_double (__fma, fma)
#endif
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