Annotation of OpenXM_contrib/gmp/mpfr/log2.c, Revision 1.1.1.1
1.1 maekawa 1: /* mpfr_log2 -- compute natural logarithm of 2
2:
3: Copyright (C) 1999 PolKA project, Inria Lorraine and Loria
4:
5: This file is part of the MPFR Library.
6:
7: The MPFR Library is free software; you can redistribute it and/or modify
8: it under the terms of the GNU Library General Public License as published by
9: the Free Software Foundation; either version 2 of the License, or (at your
10: option) any later version.
11:
12: The MPFR Library is distributed in the hope that it will be useful, but
13: WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
14: or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library General Public
15: License for more details.
16:
17: You should have received a copy of the GNU Library General Public License
18: along with the MPFR Library; see the file COPYING.LIB. If not, write to
19: the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
20: MA 02111-1307, USA. */
21:
22: #include <stdio.h>
23: #include <math.h>
24: #include "gmp.h"
25: #include "gmp-impl.h"
26: #include "longlong.h"
27: #include "mpfr.h"
28:
29: mpfr_t __mpfr_log2; /* stored value of log(2) with rnd_mode=GMP_RNDZ */
30: int __mpfr_log2_prec=0; /* precision of stored value */
31:
32: /* set x to log(2) rounded to precision PREC(x) with direction rnd_mode
33:
34: use formula log(2) = sum(1/k/2^k, k=1..infinity)
35:
36: whence 2^N*log(2) = S(N) + R(N)
37:
38: where S(N) = sum(2^(N-k)/k, k=1..N-1)
39: and R(N) = sum(1/k/2^(k-N), k=N..infinity) < 2/N
40:
41: Let S'(N) = sum(floor(2^(N-k)/k), k=1..N-1)
42:
43: Then 2^N*log(2)-S'(N) <= N-1+2/N <= N for N>=2.
44: */
45: void
46: #if __STDC__
47: mpfr_log2(mpfr_ptr x, unsigned char rnd_mode)
48: #else
49: mpfr_log2(x, rnd_mode) mpfr_ptr x; unsigned char rnd_mode;
50: #endif
51: {
52: int N, oldN, k, precx; mpz_t s, t, u;
53:
54: precx = PREC(x);
55:
56: /* has stored value enough precision ? */
57: if (precx <= __mpfr_log2_prec) {
58: if (rnd_mode==GMP_RNDZ || rnd_mode==GMP_RNDD ||
59: mpfr_can_round(__mpfr_log2, __mpfr_log2_prec, GMP_RNDZ, rnd_mode, precx))
60: {
61: mpfr_set(x, __mpfr_log2, rnd_mode); return;
62: }
63: }
64:
65: /* need to recompute */
66: N=2;
67: do {
68: oldN = N;
69: N = precx + (int)ceil(log((double)N)/log(2.0));
70: } while (N != oldN);
71: mpz_init_set_ui(s,0);
72: mpz_init(u);
73: mpz_init_set_ui(t,1);
74: #if 0
75: /* use log(2) = sum(1/k/2^k, k=1..infinity) */
76: mpz_mul_2exp(t, t, N);
77: for (k=1;k<N;k++) {
78: mpz_div_2exp(t, t, 1);
79: mpz_fdiv_q_ui(u, t, k);
80: mpz_add(s, s, u);
81: }
82: #else
83: /* use log(2) = sum((6*k-1)/(2*k^2-k)/2^(2*k+1), k=1..infinity) */
84: mpz_mul_2exp(t, t, N-1);
85: for (k=1;k<N/2;k++) {
86: mpz_div_2exp(t, t, 2);
87: mpz_mul_ui(u, t, 6*k-1);
88: mpz_fdiv_q_ui(u, u, k*(2*k-1));
89: mpz_add(s, s, u);
90: }
91: #endif
92: mpfr_set_z(x, s, rnd_mode);
93: EXP(x) -= N;
94:
95: /* stored computed value */
96: if (__mpfr_log2_prec==0) mpfr_init2(__mpfr_log2, precx);
97: else mpfr_set_prec(__mpfr_log2, precx);
98: mpfr_set(__mpfr_log2, x, GMP_RNDZ);
99: __mpfr_log2_prec=precx;
100:
101: mpz_clear(s); mpz_clear(t); mpz_clear(u);
102: }
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