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/* mpfr_log10 -- logarithm in base 10.
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=log10(a)
r=log10(a)=log(a)/log(10)
*/
int
mpfr_log10 (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) /* log10(-Inf) = NaN */
{
MPFR_SET_NAN(r);
MPFR_RET_NAN;
}
else /* log10(+Inf) = +Inf */
{
MPFR_SET_INF(r);
MPFR_SET_POS(r);
MPFR_RET(0); /* exact */
}
}
/* 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_NEG(r);
MPFR_RET(0); /* log10(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); /* result is exact */
}
/* General case */
{
/* Declaration of the intermediary variable */
mpfr_t t, tt;
int ok;
/* 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 output 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 + 4+ _mpfr_ceil_log2 (Nt);
/* initialise of intermediary variables */
mpfr_init (t);
mpfr_init (tt);
/* First computation of log10 */
do {
/* reactualisation of the precision */
mpfr_set_prec (t, Nt);
mpfr_set_prec (tt, Nt);
/* compute log10 */
mpfr_set_ui (t, 10, GMP_RNDN); /* 10 */
mpfr_log (t, t, GMP_RNDD); /* log(10) */
mpfr_log (tt, a, GMP_RNDN); /* log(a) */
mpfr_div (t, tt, t, GMP_RNDN); /* log(a)/log(10) */
/* estimation of the error */
err = Nt - 4;
ok = mpfr_can_round (t, err, GMP_RNDN, rnd_mode, Ny);
/* log10(10^n) is exact */
if ((MPFR_SIGN(t) > 0) && mpfr_isinteger(t))
if (mpfr_ui_pow_ui (tt, 10, (unsigned long int) mpfr_get_d (t) + 0.5,
GMP_RNDN) == 0)
if (mpfr_cmp (a, tt) == 0)
ok = 1;
/* actualisation of the precision */
Nt += 10;
} while ((err < 0) || !ok);
inexact = mpfr_set (r, t, rnd_mode);
mpfr_clear (t);
mpfr_clear (tt);
}
return inexact;
}
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