Annotation of OpenXM_contrib/gmp/mpfr/const_log2.c, Revision 1.1
1.1 ! ohara 1: /* mpfr_const_log2 -- compute natural logarithm of 2
! 2:
! 3: Copyright 1999, 2001 Free Software Foundation, Inc.
! 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 Lesser General Public License as published by
! 9: the Free Software Foundation; either version 2.1 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 Lesser General Public
! 15: License for more details.
! 16:
! 17: You should have received a copy of the GNU Lesser 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 "gmp.h"
! 24: #include "gmp-impl.h"
! 25: #include "longlong.h"
! 26: #include "mpfr.h"
! 27: #include "mpfr-impl.h"
! 28:
! 29: mpfr_t __mpfr_const_log2; /* stored value of log(2) */
! 30: mp_prec_t __mpfr_const_log2_prec=0; /* precision of stored value */
! 31: mp_rnd_t __mpfr_const_log2_rnd; /* rounding mode of stored value */
! 32:
! 33: static int mpfr_aux_log2 _PROTO ((mpfr_ptr, mpz_srcptr, int, int));
! 34: static int mpfr_const_aux_log2 _PROTO ((mpfr_ptr, mp_rnd_t));
! 35:
! 36: #define A
! 37: #define A1 1
! 38: #define A2 1
! 39: #undef B
! 40: #define C
! 41: #define C1 2
! 42: #define C2 1
! 43: #define NO_FACTORIAL
! 44: #undef R_IS_RATIONAL
! 45: #define GENERIC mpfr_aux_log2
! 46: #include "generic.c"
! 47: #undef A
! 48: #undef A1
! 49: #undef A2
! 50: #undef NO_FACTORIAL
! 51: #undef GENERIC
! 52: #undef C
! 53: #undef C1
! 54: #undef C2
! 55:
! 56: static int
! 57: mpfr_const_aux_log2 (mpfr_ptr mylog, mp_rnd_t rnd_mode)
! 58: {
! 59: mp_prec_t prec;
! 60: mpfr_t tmp1, tmp2, result,tmp3;
! 61: mpz_t cst;
! 62: int good = 0;
! 63: int logn;
! 64: mp_prec_t prec_i_want = MPFR_PREC(mylog);
! 65: mp_prec_t prec_x;
! 66:
! 67: mpz_init(cst);
! 68: logn = _mpfr_ceil_log2 ((double) MPFR_PREC(mylog));
! 69: prec_x = prec_i_want + logn;
! 70: while (!good){
! 71: prec = _mpfr_ceil_log2 ((double) prec_x);
! 72: mpfr_init2(tmp1, prec_x);
! 73: mpfr_init2(result, prec_x);
! 74: mpfr_init2(tmp2, prec_x);
! 75: mpfr_init2(tmp3, prec_x);
! 76: mpz_set_ui(cst, 1);
! 77: mpfr_aux_log2(tmp1, cst, 4, prec-2);
! 78: mpfr_div_2ui(tmp1, tmp1, 4, GMP_RNDD);
! 79: mpfr_mul_ui(tmp1, tmp1, 15, GMP_RNDD);
! 80:
! 81: mpz_set_ui(cst, 3);
! 82: mpfr_aux_log2(tmp2, cst, 7, prec-2);
! 83: mpfr_div_2ui(tmp2, tmp2, 7, GMP_RNDD);
! 84: mpfr_mul_ui(tmp2, tmp2, 5*3, GMP_RNDD);
! 85: mpfr_sub(result, tmp1, tmp2, GMP_RNDD);
! 86:
! 87: mpz_set_ui(cst, 13);
! 88: mpfr_aux_log2(tmp3, cst, 8, prec-2);
! 89: mpfr_div_2ui(tmp3, tmp3, 8, GMP_RNDD);
! 90: mpfr_mul_ui(tmp3, tmp3, 3*13, GMP_RNDD);
! 91: mpfr_sub(result, result, tmp3, GMP_RNDD);
! 92:
! 93: mpfr_clear(tmp1);
! 94: mpfr_clear(tmp2);
! 95: mpfr_clear(tmp3);
! 96: if (mpfr_can_round(result, prec_x, GMP_RNDD, rnd_mode, prec_i_want)){
! 97: mpfr_set(mylog, result, rnd_mode);
! 98: good = 1;
! 99: } else
! 100: {
! 101: prec_x += logn;
! 102: }
! 103: mpfr_clear(result);
! 104: }
! 105: mpz_clear(cst);
! 106: return 0;
! 107: }
! 108:
! 109: /* Cross-over point from nai"ve Taylor series to binary splitting,
! 110: obtained experimentally on a Pentium II. Optimal value for
! 111: target machine should be determined by tuneup. */
! 112: #define LOG2_THRESHOLD 25000
! 113:
! 114: /* set x to log(2) rounded to precision MPFR_PREC(x) with direction rnd_mode
! 115:
! 116: use formula log(2) = sum(1/k/2^k, k=1..infinity)
! 117:
! 118: whence 2^N*log(2) = S(N) + R(N)
! 119:
! 120: where S(N) = sum(2^(N-k)/k, k=1..N-1)
! 121: and R(N) = sum(1/k/2^(k-N), k=N..infinity) < 2/N
! 122:
! 123: Let S'(N) = sum(floor(2^(N-k)/k), k=1..N-1)
! 124:
! 125: Then 2^N*log(2)-S'(N) <= N-1+2/N <= N for N>=2.
! 126: */
! 127: void
! 128: mpfr_const_log2 (mpfr_ptr x, mp_rnd_t rnd_mode)
! 129: {
! 130: mp_prec_t N, k, precx;
! 131: mpz_t s, t, u;
! 132:
! 133: precx = MPFR_PREC(x);
! 134: MPFR_CLEAR_FLAGS(x);
! 135:
! 136: /* has stored value enough precision ? */
! 137: if (precx <= __mpfr_const_log2_prec)
! 138: {
! 139: if ((rnd_mode == __mpfr_const_log2_rnd) ||
! 140: mpfr_can_round (__mpfr_const_log2, __mpfr_const_log2_prec - 1,
! 141: __mpfr_const_log2_rnd, rnd_mode, precx))
! 142: {
! 143: mpfr_set (x, __mpfr_const_log2, rnd_mode);
! 144: return;
! 145: }
! 146: }
! 147:
! 148: /* need to recompute */
! 149: if (precx < LOG2_THRESHOLD) /* use nai"ve Taylor series evaluation */
! 150: {
! 151: /* the following was checked by exhaustive search to give a correct
! 152: result for all 4 rounding modes up to precx = 13500 */
! 153: N = precx + 2 * _mpfr_ceil_log2 ((double) precx) + 1;
! 154:
! 155: mpz_init (s); /* set to zero */
! 156: mpz_init (u);
! 157: mpz_init_set_ui (t, 1);
! 158:
! 159: /* use log(2) = sum((6*k-1)/(2*k^2-k)/2^(2*k+1), k=1..infinity) */
! 160: mpz_mul_2exp (t, t, N-1);
! 161: for (k=1; k<=N/2; k++)
! 162: {
! 163: mpz_div_2exp (t, t, 2);
! 164: mpz_mul_ui (u, t, 6*k-1);
! 165: mpz_fdiv_q_ui (u, u, k*(2*k-1));
! 166: mpz_add (s, s, u);
! 167: }
! 168:
! 169: mpfr_set_z (x, s, rnd_mode);
! 170: MPFR_EXP(x) -= N;
! 171: mpz_clear (s);
! 172: mpz_clear (t);
! 173: mpz_clear (u);
! 174: }
! 175: else /* use binary splitting method */
! 176: mpfr_const_aux_log2(x, rnd_mode);
! 177:
! 178: /* store computed value */
! 179: if (__mpfr_const_log2_prec == 0)
! 180: mpfr_init2 (__mpfr_const_log2, precx);
! 181: else
! 182: mpfr_set_prec (__mpfr_const_log2, precx);
! 183:
! 184: mpfr_set (__mpfr_const_log2, x, rnd_mode);
! 185: __mpfr_const_log2_prec = precx;
! 186: __mpfr_const_log2_rnd = rnd_mode;
! 187: }
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