source/libs/mpfr/mpfr-3.1.3/src/log10.c

   1 /* mpfr_log10 -- logarithm in base 10.
   2
   3 Copyright 2001-2015 Free Software Foundation, Inc.
   4 Contributed by the AriC and Caramel projects, INRIA.
   5
   6 This file is part of the GNU MPFR Library.
   7
   8 The GNU MPFR Library is free software; you can redistribute it and/or modify
   9 it under the terms of the GNU Lesser General Public License as published by
  10 the Free Software Foundation; either version 3 of the License, or (at your
  11 option) any later version.
  12
  13 The GNU MPFR Library is distributed in the hope that it will be useful, but
  14 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  15 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
  16 License for more details.
  17
  18 You should have received a copy of the GNU Lesser General Public License
  19 along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
  20 http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
  21 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
  22
  23 #define MPFR_NEED_LONGLONG_H
  24 #include "mpfr-impl.h"
  25
  26  /* The computation of r=log10(a)
  27
  28     r=log10(a)=log(a)/log(10)
  29  */
  30
  31 int
  32 mpfr_log10 (mpfr_ptr r, mpfr_srcptr a, mpfr_rnd_t rnd_mode)
  33 {
  34   int inexact;
  35   MPFR_SAVE_EXPO_DECL (expo);
  36
  37   MPFR_LOG_FUNC
  38     (("a[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (a), mpfr_log_prec, a, rnd_mode),
  39      ("r[%Pu]=%.*Rg inexact=%d",
  40       mpfr_get_prec (r), mpfr_log_prec, r, inexact));
  41
  42   /* If a is NaN, the result is NaN */
  43   if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (a)))
  44     {
  45       if (MPFR_IS_NAN (a))
  46         {
  47           MPFR_SET_NAN (r);
  48           MPFR_RET_NAN;
  49         }
  50       /* check for infinity before zero */
  51       else if (MPFR_IS_INF (a))
  52         {
  53           if (MPFR_IS_NEG (a))
  54             /* log10(-Inf) = NaN */
  55             {
  56               MPFR_SET_NAN (r);
  57               MPFR_RET_NAN;
  58             }
  59           else /* log10(+Inf) = +Inf */
  60             {
  61               MPFR_SET_INF (r);
  62               MPFR_SET_POS (r);
  63               MPFR_RET (0); /* exact */
  64             }
  65         }
  66       else /* a = 0 */
  67         {
  68           MPFR_ASSERTD (MPFR_IS_ZERO (a));
  69           MPFR_SET_INF (r);
  70           MPFR_SET_NEG (r);
  71           mpfr_set_divby0 ();
  72           MPFR_RET (0); /* log10(0) is an exact -infinity */
  73         }
  74     }
  75
  76   /* If a is negative, the result is NaN */
  77   if (MPFR_UNLIKELY (MPFR_IS_NEG (a)))
  78     {
  79       MPFR_SET_NAN (r);
  80       MPFR_RET_NAN;
  81     }
  82
  83   /* If a is 1, the result is 0 */
  84   if (mpfr_cmp_ui (a, 1) == 0)
  85     {
  86       MPFR_SET_ZERO (r);
  87       MPFR_SET_POS (r);
  88       MPFR_RET (0); /* result is exact */
  89     }
  90
  91   MPFR_SAVE_EXPO_MARK (expo);
  92
  93   /* General case */
  94   {
  95     /* Declaration of the intermediary variable */
  96     mpfr_t t, tt;
  97     MPFR_ZIV_DECL (loop);
  98     /* Declaration of the size variable */
  99     mpfr_prec_t Ny = MPFR_PREC(r);   /* Precision of output variable */
 100     mpfr_prec_t Nt;        /* Precision of the intermediary variable */
 101     mpfr_exp_t  err;                           /* Precision of error */
 102
 103     /* compute the precision of intermediary variable */
 104     /* the optimal number of bits : see algorithms.tex */
 105     Nt = Ny + 4 + MPFR_INT_CEIL_LOG2 (Ny);
 106
 107     /* initialise of intermediary variables */
 108     mpfr_init2 (t, Nt);
 109     mpfr_init2 (tt, Nt);
 110
 111     /* First computation of log10 */
 112     MPFR_ZIV_INIT (loop, Nt);
 113     for (;;)
 114       {
 115         /* compute log10 */
 116         mpfr_set_ui (t, 10, MPFR_RNDN);   /* 10 */
 117         mpfr_log (t, t, MPFR_RNDD);       /* log(10) */
 118         mpfr_log (tt, a, MPFR_RNDN);      /* log(a) */
 119         mpfr_div (t, tt, t, MPFR_RNDN);   /* log(a)/log(10) */
 120
 121         /* estimation of the error */
 122         err = Nt - 4;
 123         if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
 124           break;
 125
 126         /* log10(10^n) is exact:
 127            FIXME: Can we have 10^n exactly representable as a mpfr_t
 128            but n can't fit an unsigned long? */
 129         if (MPFR_IS_POS (t)
 130             && mpfr_integer_p (t) && mpfr_fits_ulong_p (t, MPFR_RNDN)
 131             && !mpfr_ui_pow_ui (tt, 10, mpfr_get_ui (t, MPFR_RNDN), MPFR_RNDN)
 132             && mpfr_cmp (a, tt) == 0)
 133           break;
 134
 135         /* actualisation of the precision */
 136         MPFR_ZIV_NEXT (loop, Nt);
 137         mpfr_set_prec (t, Nt);
 138         mpfr_set_prec (tt, Nt);
 139       }
 140     MPFR_ZIV_FREE (loop);
 141
 142     inexact = mpfr_set (r, t, rnd_mode);
 143
 144     mpfr_clear (t);
 145     mpfr_clear (tt);
 146   }
 147
 148   MPFR_SAVE_EXPO_FREE (expo);
 149   return mpfr_check_range (r, inexact, rnd_mode);
 150 }