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+/* Compute x * y + z as ternary operation.
+ Copyright (C) 2010-2017 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_private.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 (isinf (z)))
+ {
+ /* If z is Inf, but x and y are finite, the result should be
+ z rather than NaN. */
+ if (isfinite (x) && isfinite (y))
+ return (z + x) + y;
+ return (x * y) + z;
+ }
+
+ /* 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
+weak_alias (__fma, fma)
+#endif