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/* mpfr_log1p -- Compute log(1+x)
Copyright 2001, 2002 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 "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"
/* The computation of log1p is done by
log1p(x)=log(1+x)
*/
int
mpfr_log1p (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
int comp, inexact = 0;
if (MPFR_IS_NAN(x))
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
MPFR_CLEAR_NAN(y);
/* check for inf or -inf (result is not defined) */
if (MPFR_IS_INF(x))
{
if (MPFR_SIGN(x) > 0)
{
MPFR_SET_INF(y);
MPFR_SET_POS(y);
MPFR_RET(0);
}
else
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
}
comp = mpfr_cmp_si(x,-1);
/* x<-1 undefined */
if (comp < 0)
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
/* x=0: log1p(-1)=-inf (division by zero) */
if (comp == 0)
{
MPFR_SET_INF(y);
MPFR_SET_POS(y);
MPFR_RET_NAN;
}
MPFR_CLEAR_INF(y);
if (MPFR_IS_ZERO(x))
{
MPFR_SET_ZERO(y); /* log1p(+/- 0) = +/- 0 */
MPFR_SET_SAME_SIGN(y, x);
MPFR_RET(0);
}
/* General case */
{
/* Declaration of the intermediary variable */
mpfr_t t;
/* 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 Nt; /* Precision of the intermediary variable */
long int err; /* Precision of error */
/* compute the precision of intermediary variable */
Nt=MAX(Nx,Ny);
/* the optimal number of bits : see algorithms.ps */
Nt=Nt+5+_mpfr_ceil_log2(Nt);
/* initialise of intermediary variable */
mpfr_init(t);
/* First computation of cosh */
do {
/* reactualisation of the precision */
mpfr_set_prec(t, Nt);
/* compute log1p */
mpfr_add_ui (t, x, 1, GMP_RNDN); /* 1+x */
mpfr_log (t, t, GMP_RNDN); /* log(1+x)*/
/* estimation of the error */
/*err=Nt-(_mpfr_ceil_log2(1+pow(2,1-MPFR_EXP(t))));*/
err=Nt-(MAX(1-MPFR_EXP(t),0)+1);
/* actualisation of the precision */
Nt += 10;
} while ((err<0) || !mpfr_can_round(t, err, GMP_RNDN, rnd_mode, Ny));
inexact = mpfr_set (y, t, rnd_mode);
mpfr_clear(t);
}
return inexact;
}
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