mirror of https://github.com/macssh/macssh.git
103 lines
2.8 KiB
C
Executable File
103 lines
2.8 KiB
C
Executable File
/* mpfr_log2 -- compute natural logarithm of 2
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Copyright (C) 1999 PolKA project, Inria Lorraine and Loria
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This file is part of the MPFR Library.
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The MPFR Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Library General Public License as published by
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the Free Software Foundation; either version 2 of the License, or (at your
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option) any later version.
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The MPFR Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library General Public
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License for more details.
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You should have received a copy of the GNU Library General Public License
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along with the MPFR Library; see the file COPYING.LIB. If not, write to
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the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
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MA 02111-1307, USA. */
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#include <stdio.h>
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#include <math.h>
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#include "gmp.h"
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#include "gmp-impl.h"
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#include "longlong.h"
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#include "mpfr.h"
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mpfr_t __mpfr_log2; /* stored value of log(2) with rnd_mode=GMP_RNDZ */
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int __mpfr_log2_prec=0; /* precision of stored value */
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/* set x to log(2) rounded to precision PREC(x) with direction rnd_mode
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use formula log(2) = sum(1/k/2^k, k=1..infinity)
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whence 2^N*log(2) = S(N) + R(N)
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where S(N) = sum(2^(N-k)/k, k=1..N-1)
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and R(N) = sum(1/k/2^(k-N), k=N..infinity) < 2/N
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Let S'(N) = sum(floor(2^(N-k)/k), k=1..N-1)
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Then 2^N*log(2)-S'(N) <= N-1+2/N <= N for N>=2.
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*/
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void
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#if __STDC__
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mpfr_log2(mpfr_ptr x, unsigned char rnd_mode)
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#else
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mpfr_log2(x, rnd_mode) mpfr_ptr x; unsigned char rnd_mode;
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#endif
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{
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int N, oldN, k, precx; mpz_t s, t, u;
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precx = PREC(x);
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/* has stored value enough precision ? */
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if (precx <= __mpfr_log2_prec) {
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if (rnd_mode==GMP_RNDZ || rnd_mode==GMP_RNDD ||
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mpfr_can_round(__mpfr_log2, __mpfr_log2_prec, GMP_RNDZ, rnd_mode, precx))
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{
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mpfr_set(x, __mpfr_log2, rnd_mode); return;
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}
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}
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/* need to recompute */
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N=2;
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do {
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oldN = N;
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N = precx + (int)ceil(log((double)N)/log(2.0));
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} while (N != oldN);
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mpz_init_set_ui(s,0);
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mpz_init(u);
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mpz_init_set_ui(t,1);
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#if 0
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/* use log(2) = sum(1/k/2^k, k=1..infinity) */
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mpz_mul_2exp(t, t, N);
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for (k=1;k<N;k++) {
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mpz_div_2exp(t, t, 1);
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mpz_fdiv_q_ui(u, t, k);
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mpz_add(s, s, u);
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}
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#else
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/* use log(2) = sum((6*k-1)/(2*k^2-k)/2^(2*k+1), k=1..infinity) */
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mpz_mul_2exp(t, t, N-1);
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for (k=1;k<N/2;k++) {
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mpz_div_2exp(t, t, 2);
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mpz_mul_ui(u, t, 6*k-1);
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mpz_fdiv_q_ui(u, u, k*(2*k-1));
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mpz_add(s, s, u);
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}
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#endif
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mpfr_set_z(x, s, rnd_mode);
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EXP(x) -= N;
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/* stored computed value */
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if (__mpfr_log2_prec==0) mpfr_init2(__mpfr_log2, precx);
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else mpfr_set_prec(__mpfr_log2, precx);
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mpfr_set(__mpfr_log2, x, GMP_RNDZ);
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__mpfr_log2_prec=precx;
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mpz_clear(s); mpz_clear(t); mpz_clear(u);
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}
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