Implement accurate fma.

5 files changed, 268 insertions, 2 deletions

diff --git a/sysdeps/ieee754/dbl-64/s_fma.c b/sysdeps/ieee754/dbl-64/s_fma.c
new file mode 100644
index 0000000000..ca7300c11e
--- /dev/null
+++ b/sysdeps/ieee754/dbl-64/s_fma.c
@@ -0,0 +1,146 @@
+/* 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)
+{
+  union ieee754_double u, v, w;
+  int adjust = 0;
+  u.d = x;
+  v.d = y;
+  w.d = z;
+  if (__builtin_expect (u.ieee.exponent + v.ieee.exponent
+			>= 0x7ff + IEEE754_DOUBLE_BIAS - DBL_MANT_DIG, 0)
+      || __builtin_expect (u.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0)
+      || __builtin_expect (v.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0)
+      || __builtin_expect (w.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0))
+    {
+      /* If x or y or z is Inf/NaN or if fma will certainly overflow,
+	 compute as x * y + z.  */
+      if (u.ieee.exponent == 0x7ff
+	  || v.ieee.exponent == 0x7ff
+	  || w.ieee.exponent == 0x7ff
+	  || u.ieee.exponent + v.ieee.exponent
+	     > 0x7ff + IEEE754_DOUBLE_BIAS)
+	return x * y + z;
+      if (u.ieee.exponent + v.ieee.exponent
+	  >= 0x7ff + IEEE754_DOUBLE_BIAS - DBL_MANT_DIG)
+	{
+	  /* Compute 1p-53 times smaller result and multiply
+	     at the end.  */
+	  if (u.ieee.exponent > v.ieee.exponent)
+	    u.ieee.exponent -= DBL_MANT_DIG;
+	  else
+	    v.ieee.exponent -= DBL_MANT_DIG;
+	  /* If x + y exponent is very large and z exponent is very small,
+	     it doesn't matter if we don't adjust it.  */
+	  if (w.ieee.exponent > DBL_MANT_DIG)
+	    w.ieee.exponent -= DBL_MANT_DIG;
+	  adjust = 1;
+	}
+      else if (w.ieee.exponent >= 0x7ff - DBL_MANT_DIG)
+	{
+	  /* Similarly.
+	     If z exponent is very large and x and y exponents are
+	     very small, it doesn't matter if we don't adjust it.  */
+	  if (u.ieee.exponent > v.ieee.exponent)
+	    {
+	      if (u.ieee.exponent > DBL_MANT_DIG)
+		u.ieee.exponent -= DBL_MANT_DIG;
+	    }
+	  else if (v.ieee.exponent > DBL_MANT_DIG)
+	    v.ieee.exponent -= DBL_MANT_DIG;
+	  w.ieee.exponent -= DBL_MANT_DIG;
+	  adjust = 1;
+	}
+      else if (u.ieee.exponent >= 0x7ff - DBL_MANT_DIG)
+	{
+	  u.ieee.exponent -= DBL_MANT_DIG;
+	  if (v.ieee.exponent)
+	    v.ieee.exponent += DBL_MANT_DIG;
+	  else
+	    v.d *= 0x1p53;
+	}
+      else
+	{
+	  v.ieee.exponent -= DBL_MANT_DIG;
+	  if (u.ieee.exponent)
+	    u.ieee.exponent += DBL_MANT_DIG;
+	  else
+	    u.d *= 0x1p53;
+	}
+      x = u.d;
+      y = v.d;
+      z = w.d;
+    }
+  /* Multiplication m1 + m2 = x * y using Dekker's algorithm.  */
+#define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1)
+  double x1 = x * C;
+  double y1 = y * C;
+  double m1 = x * y;
+  x1 = (x - x1) + x1;
+  y1 = (y - y1) + y1;
+  double x2 = x - x1;
+  double y2 = y - y1;
+  double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2;
+
+  /* Addition a1 + a2 = z + m1 using Knuth's algorithm.  */
+  double a1 = z + m1;
+  double t1 = a1 - z;
+  double t2 = a1 - t1;
+  t1 = m1 - t1;
+  t2 = z - t2;
+  double a2 = t1 + t2;
+
+  fenv_t env;
+  feholdexcept (&env);
+  fesetround (FE_TOWARDZERO);
+  /* Perform m2 + a2 addition with round to odd.  */
+  u.d = a2 + m2;
+  if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7ff)
+    u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0;
+  feupdateenv (&env);
+
+  /* Add that to a1.  */
+  a1 = a1 + u.d;
+
+  /* And adjust exponent if needed.  */
+  if (__builtin_expect (adjust, 0))
+    a1 *= 0x1p53;
+
+  return a1;
+}
+#ifndef __fma
+weak_alias (__fma, fma)
+#endif
+
+#ifdef NO_LONG_DOUBLE
+strong_alias (__fma, __fmal)
+weak_alias (__fmal, fmal)
+#endif
diff --git a/sysdeps/ieee754/dbl-64/s_fmaf.c b/sysdeps/ieee754/dbl-64/s_fmaf.c
index 9721876601..cd16cd1dce 100644
--- a/sysdeps/ieee754/dbl-64/s_fmaf.c
+++ b/sysdeps/ieee754/dbl-64/s_fmaf.c
@@ -39,7 +39,7 @@ __fmaf (float x, float y, float z)
   fesetround (FE_TOWARDZERO);
   /* Perform addition with round to odd.  */
   u.d = temp + (double) z;
-  if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0xff)
+  if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7ff)
     u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0;
   feupdateenv (&env);
   /* And finally truncation with round to nearest.  */
diff --git a/sysdeps/ieee754/ldbl-128/s_fma.c b/sysdeps/ieee754/ldbl-128/s_fma.c
new file mode 100644
index 0000000000..78055e5c6c
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-128/s_fma.c
@@ -0,0 +1,50 @@
+/* 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 <math.h>
+#include <fenv.h>
+#include <ieee754.h>
+
+/* This implementation relies on long double being more than twice as
+   precise as double and uses rounding to odd in order 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)
+{
+  fenv_t env;
+  /* Multiplication is always exact.  */
+  long double temp = (long double) x * (long double) y;
+  union ieee854_long_double u;
+  feholdexcept (&env);
+  fesetround (FE_TOWARDZERO);
+  /* Perform addition with round to odd.  */
+  u.d = temp + (long double) z;
+  if ((u.ieee.mantissa3 & 1) == 0 && u.ieee.exponent != 0x7fff)
+    u.ieee.mantissa3 |= fetestexcept (FE_INEXACT) != 0;
+  feupdateenv (&env);
+  /* And finally truncation with round to nearest.  */
+  return (double) u.d;
+}
+#ifndef __fma
+weak_alias (__fma, fma)
+#endif
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
diff --git a/sysdeps/ieee754/ldbl-opt/s_fma.c b/sysdeps/ieee754/ldbl-opt/s_fma.c
index 2ee7214131..1723c5c306 100644
--- a/sysdeps/ieee754/ldbl-opt/s_fma.c
+++ b/sysdeps/ieee754/ldbl-opt/s_fma.c
@@ -1,5 +1,5 @@
 #include <math_ldbl_opt.h>
-#include <math/s_fma.c>
+#include <sysdeps/ieee754/dbl-64/s_fma.c>
 #if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1)
 compat_symbol (libm, __fma, fmal, GLIBC_2_1);
 #endif