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/* mpfr_const_log2 -- compute natural logarithm of 2
Copyright 1999, 2001-2017 Free Software Foundation, Inc.
Contributed by the AriC and Caramba projects, INRIA.
This file is part of the GNU MPFR Library.
The GNU MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 3 of the License, or (at your
option) any later version.
The GNU 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 Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see
http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"
/* Declare the cache */
#ifndef MPFR_USE_LOGGING
MPFR_DECL_INIT_CACHE (__gmpfr_cache_const_log2, mpfr_const_log2_internal)
#else
MPFR_DECL_INIT_CACHE (__gmpfr_normal_log2, mpfr_const_log2_internal)
MPFR_DECL_INIT_CACHE (__gmpfr_logging_log2, mpfr_const_log2_internal)
MPFR_THREAD_VAR (mpfr_cache_ptr, __gmpfr_cache_const_log2, __gmpfr_normal_log2)
#endif
/* Set User interface */
#undef mpfr_const_log2
int
mpfr_const_log2 (mpfr_ptr x, mpfr_rnd_t rnd_mode) {
return mpfr_cache (x, __gmpfr_cache_const_log2, rnd_mode);
}
/* Auxiliary function: Compute the terms from n1 to n2 (excluded)
3/4*sum((-1)^n*n!^2/2^n/(2*n+1)!, n = n1..n2-1).
Numerator is T[0], denominator is Q[0],
Compute P[0] only when need_P is non-zero.
Need 1+ceil(log(n2-n1)/log(2)) cells in T[],P[],Q[].
*/
static void
S (mpz_t *T, mpz_t *P, mpz_t *Q, unsigned long n1, unsigned long n2, int need_P)
{
if (n2 == n1 + 1)
{
if (n1 == 0)
mpz_set_ui (P[0], 3);
else
{
mpz_set_ui (P[0], n1);
mpz_neg (P[0], P[0]);
}
if (n1 <= (ULONG_MAX / 4 - 1) / 2)
mpz_set_ui (Q[0], 4 * (2 * n1 + 1));
else /* to avoid overflow in 4 * (2 * n1 + 1) */
{
mpz_set_ui (Q[0], n1);
mpz_mul_2exp (Q[0], Q[0], 1);
mpz_add_ui (Q[0], Q[0], 1);
mpz_mul_2exp (Q[0], Q[0], 2);
}
mpz_set (T[0], P[0]);
}
else
{
unsigned long m = (n1 / 2) + (n2 / 2) + (n1 & 1UL & n2);
unsigned long v, w;
S (T, P, Q, n1, m, 1);
S (T + 1, P + 1, Q + 1, m, n2, need_P);
mpz_mul (T[0], T[0], Q[1]);
mpz_mul (T[1], T[1], P[0]);
mpz_add (T[0], T[0], T[1]);
if (need_P)
mpz_mul (P[0], P[0], P[1]);
mpz_mul (Q[0], Q[0], Q[1]);
/* remove common trailing zeroes if any */
v = mpz_scan1 (T[0], 0);
if (v > 0)
{
w = mpz_scan1 (Q[0], 0);
if (w < v)
v = w;
if (need_P)
{
w = mpz_scan1 (P[0], 0);
if (w < v)
v = w;
}
/* now v = min(val(T), val(Q), val(P)) */
if (v > 0)
{
mpz_fdiv_q_2exp (T[0], T[0], v);
mpz_fdiv_q_2exp (Q[0], Q[0], v);
if (need_P)
mpz_fdiv_q_2exp (P[0], P[0], v);
}
}
}
}
/* Don't need to save / restore exponent range: the cache does it */
int
mpfr_const_log2_internal (mpfr_ptr x, mpfr_rnd_t rnd_mode)
{
unsigned long n = MPFR_PREC (x);
mpfr_prec_t w; /* working precision */
unsigned long N;
mpz_t *T, *P, *Q;
mpfr_t t, q;
int inexact;
unsigned long lgN, i;
MPFR_GROUP_DECL(group);
MPFR_TMP_DECL(marker);
MPFR_ZIV_DECL(loop);
MPFR_LOG_FUNC (
("rnd_mode=%d", rnd_mode),
("x[%Pu]=%.*Rg inex=%d", mpfr_get_prec(x), mpfr_log_prec, x, inexact));
if (n < 1069)
w = n + 9; /* ensures correct rounding for the four rounding modes,
together with N = w / 3 + 1 (see below). */
else
w = n + 10; /* idem at least for prec < 300000 */
MPFR_TMP_MARK(marker);
MPFR_GROUP_INIT_2(group, w, t, q);
MPFR_ZIV_INIT (loop, w);
for (;;)
{
N = w / 3 + 1; /* Warning: do not change that (even increasing N!)
without checking correct rounding in the above
ranges for n. */
/* the following are needed for error analysis (see algorithms.tex) */
MPFR_ASSERTD(w >= 3 && N >= 2);
lgN = MPFR_INT_CEIL_LOG2 (N) + 1;
T = (mpz_t *) MPFR_TMP_ALLOC (3 * lgN * sizeof (mpz_t));
P = T + lgN;
Q = T + 2*lgN;
for (i = 0; i < lgN; i++)
{
mpz_init (T[i]);
mpz_init (P[i]);
mpz_init (Q[i]);
}
S (T, P, Q, 0, N, 0);
mpfr_set_z (t, T[0], MPFR_RNDN);
mpfr_set_z (q, Q[0], MPFR_RNDN);
mpfr_div (t, t, q, MPFR_RNDN);
for (i = 0; i < lgN; i++)
{
mpz_clear (T[i]);
mpz_clear (P[i]);
mpz_clear (Q[i]);
}
/* for prec < 300000 and all rounding modes we checked by exhaustive
search that the rounding is correct */
if (MPFR_LIKELY (n < 300000 || MPFR_CAN_ROUND (t, w - 2, n, rnd_mode)))
break;
MPFR_ZIV_NEXT (loop, w);
MPFR_GROUP_REPREC_2(group, w, t, q);
}
MPFR_ZIV_FREE (loop);
inexact = mpfr_set (x, t, rnd_mode);
MPFR_GROUP_CLEAR(group);
MPFR_TMP_FREE(marker);
return inexact;
}
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