/* mpfr_log10 -- logarithm in base 10.

Copyright 2001, 2002, 2003, 2004, 2005 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. */

#define MPFR_NEED_LONGLONG_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;
  MPFR_SAVE_EXPO_DECL (expo);

  /* If a is NaN, the result is NaN */
  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (a)))
    {
      if (MPFR_IS_NAN (a))
	{
	  MPFR_SET_NAN (r);
	  MPFR_RET_NAN;
	}
      /* check for infinity before zero */
      else if (MPFR_IS_INF (a))
	{
	  if (MPFR_IS_NEG (a))
	    /* 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 */
	    }
	}
      else /* a = 0 */
	{
          MPFR_ASSERTD (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_UNLIKELY (MPFR_IS_NEG (a)))
    {
      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 */
    }
  MPFR_SAVE_EXPO_MARK (expo);

  /* General case */
  {
    /* Declaration of the intermediary variable */
    mpfr_t t, tt;
    MPFR_ZIV_DECL (loop);
    /* Declaration of the size variable */
    mp_prec_t Ny = MPFR_PREC(r);   /* Precision of output variable */
    mp_prec_t Nt;        /* Precision of the intermediary variable */
    mp_exp_t  err;                           /* Precision of error */

    /* compute the precision of intermediary variable */
    /* the optimal number of bits : see algorithms.tex */
    Nt = Ny + 4+ MPFR_INT_CEIL_LOG2 (Ny);

    /* initialise of intermediary variables */
    mpfr_init2 (t, Nt);
    mpfr_init2 (tt, Nt);

    /* First computation of log10 */
    MPFR_ZIV_INIT (loop, Nt);
    for(;;) {
      /* 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;
      if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
	break;

      /* log10(10^n) is exact:
	 FIXME: Can we have 10^n exactly representable as a mpfr_t
	 but n can't fit an unsigned long? */
      if (MPFR_IS_POS (t) 
	  && mpfr_integer_p (t) && mpfr_fits_ulong_p (t, GMP_RNDN)
	  && !mpfr_ui_pow_ui (tt, 10, mpfr_get_ui (t, GMP_RNDN), GMP_RNDN)
          && mpfr_cmp (a, tt) == 0)
	break;

      /* actualisation of the precision */
      MPFR_ZIV_NEXT (loop, Nt);
      mpfr_set_prec (t, Nt);
      mpfr_set_prec (tt, Nt);
    }
    MPFR_ZIV_FREE (loop);

    inexact = mpfr_set (r, t, rnd_mode);

    mpfr_clear (t);
    mpfr_clear (tt);
  }

  MPFR_SAVE_EXPO_FREE (expo);
  return mpfr_check_range (r, inexact, rnd_mode);
}