1 /* mpfr_log2 -- log base 2
3 Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011 Free Software Foundation, Inc.
4 Contributed by the Arenaire and Caramel projects, INRIA.
6 This file is part of the GNU MPFR Library.
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.
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.
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. */
23 #define MPFR_NEED_LONGLONG_H
24 #include "mpfr-impl.h"
26 /* The computation of r=log2(a)
27 r=log2(a)=log(a)/log(2) */
30 mpfr_log2 (mpfr_ptr r, mpfr_srcptr a, mpfr_rnd_t rnd_mode)
33 MPFR_SAVE_EXPO_DECL (expo);
36 (("a[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (a), mpfr_log_prec, a, rnd_mode),
37 ("r[%Pu]=%.*Rg inexact=%d", mpfr_get_prec (r), mpfr_log_prec, r,
40 if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (a)))
42 /* If a is NaN, the result is NaN */
48 /* check for infinity before zero */
49 else if (MPFR_IS_INF (a))
57 else /* log(+Inf) = +Inf */
66 MPFR_ASSERTD (MPFR_IS_ZERO (a));
70 MPFR_RET (0); /* log2(0) is an exact -infinity */
74 /* If a is negative, the result is NaN */
75 if (MPFR_UNLIKELY (MPFR_IS_NEG (a)))
81 /* If a is 1, the result is 0 */
82 if (MPFR_UNLIKELY (mpfr_cmp_ui (a, 1) == 0))
86 MPFR_RET (0); /* only "normal" case where the result is exact */
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);
93 MPFR_SAVE_EXPO_MARK (expo);
97 /* Declaration of the intermediary variable */
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);
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);
109 /* initialise of intermediary variable */
113 /* First computation of log2 */
114 MPFR_ZIV_INIT (loop, Nt);
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) */
122 /* estimation of the error */
124 if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
127 /* actualisation of the precision */
128 MPFR_ZIV_NEXT (loop, Nt);
129 mpfr_set_prec (t, Nt);
130 mpfr_set_prec (tt, Nt);
132 MPFR_ZIV_FREE (loop);
134 inexact = mpfr_set (r, t, rnd_mode);
140 MPFR_SAVE_EXPO_FREE (expo);
141 return mpfr_check_range (r, inexact, rnd_mode);