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/* mpfr_const_log2 -- compute natural logarithm of 2
Copyright (C) 1999 PolKA project, Inria Lorraine and Loria
This file is part of the MPFR Library.
The MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Library General Public License as published by
the Free Software Foundation; either version 2 of the License, or (at your
option) any later version.
The MPFR Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library General Public
License for more details.
You should have received a copy of the GNU Library General Public License
along with the MPFR Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */
#include <stdio.h>
#include <math.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
#include "mpfr.h"
mpfr_t __mpfr_const_log2; /* stored value of log(2) */
int __mpfr_const_log2_prec=0; /* precision of stored value */
mp_rnd_t __mpfr_const_log2_rnd; /* rounding mode of stored value */
#define A
#define A1 1
#define A2 1
#undef B
#define C
#define C1 2
#define C2 1
#define NO_FACTORIAL
#undef R_IS_RATIONAL
#define GENERIC mpfr_aux_log2
#include "generic.c"
#undef A
#undef A1
#undef A2
#undef NO_FACTORIAL
#undef GENERIC
#undef C
#undef C1
#undef C2
int
#if __STDC__
mpfr_const_aux_log2(mpfr_ptr mylog, mp_rnd_t rnd_mode)
#else
mpfr_const_aux_log2(mylog, rnd_mode) mpfr_ptr mylog; mp_rnd_t rnd_mode;
#endif
{
int prec;
mpfr_t tmp1, tmp2, result,tmp3;
mpz_t cst;
int good = 0;
int logn;
int prec_i_want = MPFR_PREC(mylog);
int prec_x;
mpz_init(cst);
logn = (int) ceil(log
((double) MPFR_PREC(mylog))
/log(2.0));
prec_x = prec_i_want + logn;
while (!good){
prec = (int) ceil(log
((double) (prec_x))
/log(2.0));
mpfr_init2(tmp1, prec_x);
mpfr_init2(result, prec_x);
mpfr_init2(tmp2, prec_x);
mpfr_init2(tmp3, prec_x);
mpz_set_ui(cst, 1);
mpfr_aux_log2(tmp1, cst, 4, prec-2);
mpfr_div_2exp(tmp1, tmp1, 4,GMP_RNDD);
mpfr_mul_ui(tmp1, tmp1, 15,GMP_RNDD);
mpz_set_ui(cst, 3);
mpfr_aux_log2(tmp2, cst, 7, prec-2);
mpfr_div_2exp(tmp2, tmp2, 7,GMP_RNDD);
mpfr_mul_ui(tmp2, tmp2, 5*3,GMP_RNDD);
mpfr_sub(result, tmp1, tmp2, GMP_RNDD);
mpz_set_ui(cst, 13);
mpfr_aux_log2(tmp3, cst, 8, prec-2);
mpfr_div_2exp(tmp3, tmp3, 8,GMP_RNDD);
mpfr_mul_ui(tmp3, tmp3, 3*13,GMP_RNDD);
mpfr_sub(result, result, tmp3, GMP_RNDD);
mpfr_clear(tmp1);
mpfr_clear(tmp2);
mpfr_clear(tmp3);
if (mpfr_can_round(result, prec_x, GMP_RNDD, rnd_mode, prec_i_want)){
mpfr_set(mylog, result, rnd_mode);
good = 1;
} else
{
prec_x += logn;
}
mpfr_clear(result);
}
mpz_clear(cst);
return 0;
}
/* set x to log(2) rounded to precision MPFR_PREC(x) with direction rnd_mode
use formula log(2) = sum(1/k/2^k, k=1..infinity)
whence 2^N*log(2) = S(N) + R(N)
where S(N) = sum(2^(N-k)/k, k=1..N-1)
and R(N) = sum(1/k/2^(k-N), k=N..infinity) < 2/N
Let S'(N) = sum(floor(2^(N-k)/k), k=1..N-1)
Then 2^N*log(2)-S'(N) <= N-1+2/N <= N for N>=2.
*/
void
#if __STDC__
mpfr_const_log2(mpfr_ptr x, mp_rnd_t rnd_mode)
#else
mpfr_const_log2(x, rnd_mode) mpfr_ptr x; mp_rnd_t rnd_mode;
#endif
{
int N, oldN, k, precx; mpz_t s, t, u;
precx = MPFR_PREC(x);
/* has stored value enough precision ? */
if (precx <= __mpfr_const_log2_prec) {
if (rnd_mode==__mpfr_const_log2_rnd || mpfr_can_round(__mpfr_const_log2,
__mpfr_const_log2_prec, __mpfr_const_log2_rnd, rnd_mode, precx))
{
mpfr_set(x, __mpfr_const_log2, rnd_mode); return;
}
}
/* need to recompute */
if (precx < 30000){ /* use nai"ve Taylor series evaluation */
N=2;
do {
oldN = N;
N = precx + (int)ceil(log((double)N)/log(2.0));
} while (N != oldN);
mpz_init_set_ui(s,0);
mpz_init(u);
mpz_init_set_ui(t,1);
#if 0
/* use log(2) = sum(1/k/2^k, k=1..infinity) */
mpz_mul_2exp(t, t, N);
for (k=1;k<N;k++) {
mpz_div_2exp(t, t, 1);
mpz_fdiv_q_ui(u, t, k);
mpz_add(s, s, u);
}
#else
/* use log(2) = sum((6*k-1)/(2*k^2-k)/2^(2*k+1), k=1..infinity) */
mpz_mul_2exp(t, t, N-1);
for (k=1;k<N/2;k++) {
mpz_div_2exp(t, t, 2);
mpz_mul_ui(u, t, 6*k-1);
mpz_fdiv_q_ui(u, u, k*(2*k-1));
mpz_add(s, s, u);
}
#endif
mpfr_set_z(x, s, rnd_mode);
MPFR_EXP(x) -= N;
mpz_clear(s); mpz_clear(t); mpz_clear(u);
} else
{
/* use binary splitting method */
mpfr_const_aux_log2(x, rnd_mode);
}
/* store computed value */
if (__mpfr_const_log2_prec==0) mpfr_init2(__mpfr_const_log2, precx);
else mpfr_set_prec(__mpfr_const_log2, precx);
mpfr_set(__mpfr_const_log2, x, rnd_mode);
__mpfr_const_log2_prec=precx;
__mpfr_const_log2_rnd=rnd_mode;
}
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