1 /* mpfr_log10 -- logarithm in base 10.
2
3 Copyright 2001-2023 Free Software Foundation, Inc.
4 Contributed by the AriC and Caramba 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 https://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[%Pd]=%.*Rg rnd=%d", mpfr_get_prec (a), mpfr_log_prec, a, rnd_mode),
39 ("r[%Pd]=%.*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 /* initialize 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_equal_p (a, tt))
133 break;
134
135 /* actualization 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 }