Implement accurate fma.

1 files changed, 70 insertions, 0 deletions

diff --git a/sysdeps/ieee754/ldbl-96/s_fma.c b/sysdeps/ieee754/ldbl-96/s_fma.c
new file mode 100644
index 0000000000..90c6d1f29d
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-96/s_fma.c
@@ -0,0 +1,70 @@
+/* Compute x * y + z as ternary operation.
+   Copyright (C) 2010 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, write to the Free
+   Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
+   02111-1307 USA.  */
+
+#include <float.h>
+#include <math.h>
+#include <fenv.h>
+#include <ieee754.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)
+{
+  /* Multiplication m1 + m2 = x * y using Dekker's algorithm.  */
+#define C ((1ULL << (LDBL_MANT_DIG + 1) / 2) + 1)
+  long double x1 = x * C;
+  long double y1 = y * C;
+  long double m1 = 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;
+
+  fenv_t env;
+  feholdexcept (&env);
+  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