1/* mpfr_log10 -- logarithm in base 10.
2
3Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc.
4Contributed by the AriC and Caramel projects, INRIA.
5
6This file is part of the GNU MPFR Library.
7
8The GNU MPFR Library is free software; you can redistribute it and/or modify
9it under the terms of the GNU Lesser General Public License as published by
10the Free Software Foundation; either version 3 of the License, or (at your
11option) any later version.
12
13The GNU MPFR Library is distributed in the hope that it will be useful, but
14WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
15or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
16License for more details.
17
18You should have received a copy of the GNU Lesser General Public License
19along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
20http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
2151 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
31int
32mpfr_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}
151