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Initial revision

/* 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_d1 (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;
}