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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: }