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/* mpfr_log2 -- log base 2
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 <stdio.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"
/* The computation of r=log2(a)
r=log2(a)=log(a)/log(2)
*/
int
mpfr_log2 (mpfr_ptr r, mpfr_srcptr a, mp_rnd_t rnd_mode)
{
int inexact = 0;
/* If a is NaN, the result is NaN */
if (MPFR_IS_NAN(a))
{
MPFR_SET_NAN(r);
MPFR_RET_NAN;
}
MPFR_CLEAR_NAN(r);
/* check for infinity before zero */
if (MPFR_IS_INF(a))
{
if (MPFR_SIGN(a) < 0) /* log(-Inf) = NaN */
{
MPFR_SET_NAN(r);
MPFR_RET_NAN;
}
else /* log(+Inf) = +Inf */
{
MPFR_SET_INF(r);
MPFR_SET_POS(r);
MPFR_RET(0);
}
}
/* Now we can clear the flags without damage even if r == a */
MPFR_CLEAR_INF(r);
if (MPFR_IS_ZERO(a))
{
MPFR_SET_INF(r);
MPFR_SET_POS(r);
MPFR_RET(0); /* log(0) is an exact infinity */
}
/* If a is negative, the result is NaN */
if (MPFR_SIGN(a) < 0)
{
MPFR_SET_NAN(r);
MPFR_RET_NAN;
}
/* If a is 1, the result is 0 */
if (mpfr_cmp_ui(a, 1) == 0)
{
MPFR_SET_ZERO(r);
MPFR_SET_POS(r);
MPFR_RET(0); /* only "normal" case where the result is exact */
}
/* If a is integer, log2(a) is exact*/
if (mpfr_cmp_ui_2exp(a,1,MPFR_EXP(a)-1) == 0)
return mpfr_set_si(r,MPFR_EXP(a)-1,rnd_mode);
/* General case */
{
/* Declaration of the intermediary variable */
mpfr_t t, tt;
/* Declaration of the size variable */
mp_prec_t Nx = MPFR_PREC(a); /* Precision of input variable */
mp_prec_t Ny = MPFR_PREC(r); /* 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+3+_mpfr_ceil_log2(Nt);
/* initialise of intermediary variable */
mpfr_init(t);
mpfr_init(tt);
/* First computation of log2 */
do {
/* reactualisation of the precision */
mpfr_set_prec(t,Nt);
mpfr_set_prec(tt,Nt);
/* compute log2 */
mpfr_const_log2(t,GMP_RNDD); /* log(2) */
mpfr_log(tt,a,GMP_RNDN); /* log(a) */
mpfr_div(t,tt,t,GMP_RNDN); /* log(a)/log(2) */
/* estimation of the error */
err=Nt-3;
/* actualisation of the precision */
Nt += 10;
} while ((err<0) || !mpfr_can_round(t,err,GMP_RNDN,rnd_mode,Ny));
inexact = mpfr_set(r,t,rnd_mode);
mpfr_clear(t);
mpfr_clear(tt);
}
return inexact;
}
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