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/* mpfr_const_log2 -- compute natural logarithm of 2
Copyright 1999, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc.
Contributed by the Arenaire and Cacao 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.LIB. 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 */
MPFR_DECL_INIT_CACHE(__gmpfr_cache_const_log2, mpfr_const_log2_internal);
/* Set User interface */
#undef mpfr_const_log2
int
mpfr_const_log2 (mpfr_ptr x, mp_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_div_2exp (T[0], T[0], v);
mpz_div_2exp (Q[0], Q[0], v);
if (need_P)
mpz_div_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, mp_rnd_t rnd_mode)
{
unsigned long n = MPFR_PREC (x);
mp_prec_t w; /* working precision */
unsigned long N;
mpz_t *T, *P, *Q;
mpfr_t t, q;
int inexact;
int ok = 1; /* ensures that the 1st try will give correct rounding */
unsigned long lgN, i;
MPFR_ZIV_DECL (loop);
MPFR_LOG_FUNC (("rnd_mode=%d", rnd_mode), ("x[%#R]=%R inex=%d",x,x,inexact));
mpfr_init2 (t, MPFR_PREC_MIN);
mpfr_init2 (q, MPFR_PREC_MIN);
if (n < 1253)
w = n + 10; /* ensures correct rounding for the four rounding modes,
together with N = w / 3 + 1 (see below). */
else if (n < 2571)
w = n + 11; /* idem */
else if (n < 3983)
w = n + 12;
else if (n < 4854)
w = n + 13;
else if (n < 26248)
w = n + 14;
else
{
w = n + 15;
ok = 0;
}
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 *) (*__gmp_allocate_func) (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_prec (t, w);
mpfr_set_prec (q, w);
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]);
}
(*__gmp_free_func) (T, 3 * lgN * sizeof (mpz_t));
if (MPFR_LIKELY (ok != 0
|| mpfr_can_round (t, w - 2, MPFR_RNDN, rnd_mode, n)))
break;
MPFR_ZIV_NEXT (loop, w);
}
MPFR_ZIV_FREE (loop);
inexact = mpfr_set (x, t, rnd_mode);
mpfr_clear (t);
mpfr_clear (q);
return inexact;
}
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