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/* 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
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