/* Compute x * y + z as ternary operation.

   Copyright (C) 2010-2018 Free Software Foundation, Inc.

   This file is part of the GNU C Library.

   Contributed by Jakub Jelinek <jakub@redhat.com>, 2010.

   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

   <http://www.gnu.org/licenses/>.  */

#include <float.h>

#include <math.h>

#include <fenv.h>

#include <ieee754.h>

#include <math-barriers.h>

#include <math_private.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