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/* mpfr_fma -- Floating multiply-add
Copyright (C) 2001 Free Software Foundation, Inc.
This file is part of the MPFR Library.
The MPFR 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 MPFR 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 MPFR Library; see
the file COPYING.LIB. If not, write to the Free Software
Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */
#include <stdio.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"
/* The computation of fma of x y and u is done by
fma(s,x,y,z)= z + x*y = s
*/
int
mpfr_fma (mpfr_ptr s, mpfr_srcptr x ,mpfr_srcptr y ,mpfr_srcptr z , mp_rnd_t rnd_mode)
{
int inexact =0;
/* Flag calcul exacte */
int not_exact=0;
/* particular cases */
if (MPFR_IS_NAN(x) || MPFR_IS_NAN(y) || MPFR_IS_NAN(z))
{
MPFR_SET_NAN(s);
return 1;
}
/* cases Inf*0+z, 0*Inf+z, Inf-Inf */
if ((MPFR_IS_INF(x) && MPFR_IS_ZERO(y)) ||
(MPFR_IS_INF(y) && MPFR_IS_ZERO(x)) ||
((MPFR_IS_INF(x) || MPFR_IS_INF(y)) && MPFR_IS_INF(z) &&
((MPFR_SIGN(x) * MPFR_SIGN(y)) != MPFR_SIGN(z))))
{
MPFR_SET_NAN(s);
return 1;
}
MPFR_CLEAR_NAN(s);
if (MPFR_IS_INF(x) || MPFR_IS_INF(y))
{
if (MPFR_IS_INF(z)) /* case Inf-Inf already checked above */
{
MPFR_SET_INF(s);
MPFR_SET_SAME_SIGN(s, z);
return 0;
}
else /* z is finite */
{
MPFR_SET_INF(s);
if (MPFR_SIGN(s) != (MPFR_SIGN(x) * MPFR_SIGN(y)))
MPFR_CHANGE_SIGN(s);
return 0;
}
}
/* now x and y are finite */
if (MPFR_IS_INF(z))
{
MPFR_SET_INF(s);
MPFR_SET_SAME_SIGN(s, z);
return 0;
}
MPFR_CLEAR_INF(s);
if(!MPFR_NOTZERO(x) || !MPFR_NOTZERO(y))
return mpfr_set (s, z, rnd_mode);
if (!MPFR_NOTZERO(z))
return mpfr_mul (s, x, y, rnd_mode);
/* General case */
/* Detail of the compute */
/* u <- x*y */
/* t <- z+u */
{
/* Declaration of the intermediary variable */
mpfr_t t, u;
int d,fl1,fl2;
int accu=0;
/* Declaration of the size variable */
mp_prec_t Nx = MPFR_PREC(x); /* Precision of input variable */
mp_prec_t Ny = MPFR_PREC(y); /* Precision of input variable */
mp_prec_t Nz = MPFR_PREC(z); /* Precision of input variable */
mp_prec_t Ns = MPFR_PREC(s); /* Precision of output variable */
int Nt; /* Precision of the intermediary variable */
long int err; /* Precision of error */
unsigned int first_pass=0; /* temporary precision */
/* compute the precision of intermediary variable */
Nt=MAX(MAX(Nx,Ny),Nz);
/* the optimal number of bits is MPFR_EXP(u)-MPFR_EXP(v)+1 */
/* but u and v are not yet compute, also we take in account */
/* just one bit */
Nt=Nt+1+_mpfr_ceil_log2(Nt)+20;
/* initialise the intermediary variables */
mpfr_init(u);
mpfr_init(t);
/* First computation of fma */
do {
if(accu++ >2)
{
mpfr_clear(t);
mpfr_clear(u);
goto fma_paul;
}
not_exact=0;
/* reactualisation of the precision */
mpfr_set_prec(u,Nt);
mpfr_set_prec(t,Nt);
/* computations */
fl1=mpfr_mul(u,x,y,GMP_RNDN);
if(fl1) not_exact=1;
fl2=mpfr_add(t,z,u,GMP_RNDN);
if(fl2) not_exact=1;
/*Nt=Nt+(d+1)+_mpfr_ceil_log2(Nt); */
d = MPFR_EXP(u)-MPFR_EXP(t);
/* estimation of the error */
err=Nt-(d+1);
/* actualisation of the precision */
Nt +=(1-first_pass)*d + first_pass*10;
if(Nt<0)Nt=0;
first_pass=1;
} while ( (fl1!=fl2) || (err <0) || ((!mpfr_can_round(t,err,GMP_RNDN,rnd_mode,Ns)) && not_exact ));
inexact = mpfr_set (s, t, rnd_mode);
mpfr_clear(t);
mpfr_clear(u);
goto fin;
}
fma_paul:
/* General case */
/* Detail of the compute */
/* u <- x*y exact */
/* s <- z+u */
{
mpfr_t u;
/* if we take prec(u) >= prec(x) + prec(y), the product
u <- x*y is always exact */
mpfr_init2 (u, MPFR_PREC(x) + MPFR_PREC(y));
mpfr_mul (u, x, y, GMP_RNDN); /* always exact */
inexact = mpfr_add (s, z, u, rnd_mode);
mpfr_clear(u);
}
return inexact;
fin:
if (not_exact == 0 && inexact == 0)
return 0;
if (not_exact != 0 && inexact == 0)
return 1;
return inexact;
}
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