Annotation of OpenXM_contrib/gmp/mpfr/log2.c, Revision 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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