1 /* mpfr_log2 -- log base 2
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=log2(a)
27 r=log2(a)=log(a)/log(2) */
28
29 int
30 mpfr_log2 (mpfr_ptr r, mpfr_srcptr a, mpfr_rnd_t rnd_mode)
31 {
32 int inexact;
33 MPFR_SAVE_EXPO_DECL (expo);
34
35 MPFR_LOG_FUNC
36 (("a[%Pd]=%.*Rg rnd=%d", mpfr_get_prec (a), mpfr_log_prec, a, rnd_mode),
37 ("r[%Pd]=%.*Rg inexact=%d", mpfr_get_prec (r), mpfr_log_prec, r,
38 inexact));
39
40 if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (a)))
41 {
42 /* If a is NaN, the result is NaN */
43 if (MPFR_IS_NAN (a))
44 {
45 MPFR_SET_NAN (r);
46 MPFR_RET_NAN;
47 }
48 /* check for infinity before zero */
49 else if (MPFR_IS_INF (a))
50 {
51 if (MPFR_IS_NEG (a))
52 /* log(-Inf) = NaN */
53 {
54 MPFR_SET_NAN (r);
55 MPFR_RET_NAN;
56 }
57 else /* log(+Inf) = +Inf */
58 {
59 MPFR_SET_INF (r);
60 MPFR_SET_POS (r);
61 MPFR_RET (0);
62 }
63 }
64 else /* a is zero */
65 {
66 MPFR_ASSERTD (MPFR_IS_ZERO (a));
67 MPFR_SET_INF (r);
68 MPFR_SET_NEG (r);
69 MPFR_SET_DIVBY0 ();
70 MPFR_RET (0); /* log2(0) is an exact -infinity */
71 }
72 }
73
74 /* If a is negative, the result is NaN */
75 if (MPFR_UNLIKELY (MPFR_IS_NEG (a)))
76 {
77 MPFR_SET_NAN (r);
78 MPFR_RET_NAN;
79 }
80
81 /* If a is 1, the result is 0 */
82 if (MPFR_UNLIKELY (mpfr_cmp_ui (a, 1) == 0))
83 {
84 MPFR_SET_ZERO (r);
85 MPFR_SET_POS (r);
86 MPFR_RET (0); /* only "normal" case where the result is exact */
87 }
88
89 /* If a is 2^N, log2(a) is exact*/
90 if (MPFR_UNLIKELY (mpfr_cmp_ui_2exp (a, 1, MPFR_GET_EXP (a) - 1) == 0))
91 return mpfr_set_si(r, MPFR_GET_EXP (a) - 1, rnd_mode);
92
93 MPFR_SAVE_EXPO_MARK (expo);
94
95 /* General case */
96 {
97 /* Declaration of the intermediary variable */
98 mpfr_t t, tt;
99 /* Declaration of the size variable */
100 mpfr_prec_t Ny = MPFR_PREC(r); /* target precision */
101 mpfr_prec_t Nt; /* working precision */
102 mpfr_exp_t err; /* error */
103 MPFR_ZIV_DECL (loop);
104
105 /* compute the precision of intermediary variable */
106 /* the optimal number of bits : see algorithms.tex */
107 Nt = Ny + 3 + MPFR_INT_CEIL_LOG2 (Ny);
108
109 /* initialize of intermediary variable */
110 mpfr_init2 (t, Nt);
111 mpfr_init2 (tt, Nt);
112
113 /* First computation of log2 */
114 MPFR_ZIV_INIT (loop, Nt);
115 for (;;)
116 {
117 /* compute log2 */
118 mpfr_const_log2(t,MPFR_RNDD); /* log(2) */
119 mpfr_log(tt,a,MPFR_RNDN); /* log(a) */
120 mpfr_div(t,tt,t,MPFR_RNDN); /* log(a)/log(2) */
121
122 /* estimation of the error */
123 err = Nt-3;
124 if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
125 break;
126
127 /* actualization of the precision */
128 MPFR_ZIV_NEXT (loop, Nt);
129 mpfr_set_prec (t, Nt);
130 mpfr_set_prec (tt, Nt);
131 }
132 MPFR_ZIV_FREE (loop);
133
134 inexact = mpfr_set (r, t, rnd_mode);
135
136 mpfr_clear (t);
137 mpfr_clear (tt);
138 }
139
140 MPFR_SAVE_EXPO_FREE (expo);
141 return mpfr_check_range (r, inexact, rnd_mode);
142 }