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-rw-r--r--Build/source/libs/mpfr/mpfr-src/src/const_catalan.c153
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diff --git a/Build/source/libs/mpfr/mpfr-src/src/const_catalan.c b/Build/source/libs/mpfr/mpfr-src/src/const_catalan.c
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index 855e52b7718..00000000000
--- a/Build/source/libs/mpfr/mpfr-src/src/const_catalan.c
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-/* mpfr_const_catalan -- compute Catalan's constant.
-
-Copyright 2005-2020 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
-https://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_catalan, mpfr_const_catalan_internal)
-
-/* Set User Interface */
-#undef mpfr_const_catalan
-int
-mpfr_const_catalan (mpfr_ptr x, mpfr_rnd_t rnd_mode) {
- return mpfr_cache (x, __gmpfr_cache_const_catalan, rnd_mode);
-}
-
-/* return T, Q such that T/Q = sum(k!^2/(2k)!/(2k+1)^2, k=n1..n2-1) */
-static void
-S (mpz_t T, mpz_t P, mpz_t Q, unsigned long n1, unsigned long n2)
-{
- if (n2 == n1 + 1)
- {
- if (n1 == 0)
- {
- mpz_set_ui (P, 1);
- mpz_set_ui (Q, 1);
- }
- else
- {
- mpz_set_ui (P, 2 * n1 - 1);
- mpz_mul_ui (P, P, n1);
- mpz_ui_pow_ui (Q, 2 * n1 + 1, 2);
- mpz_mul_2exp (Q, Q, 1);
- }
- mpz_set (T, P);
- }
- else
- {
- unsigned long m = (n1 + n2) / 2;
- mpz_t T2, P2, Q2;
- S (T, P, Q, n1, m);
- mpz_init (T2);
- mpz_init (P2);
- mpz_init (Q2);
- S (T2, P2, Q2, m, n2);
- mpz_mul (T, T, Q2);
- mpz_mul (T2, T2, P);
- mpz_add (T, T, T2);
- mpz_mul (P, P, P2);
- mpz_mul (Q, Q, Q2);
- mpz_clear (T2);
- mpz_clear (P2);
- mpz_clear (Q2);
- }
-}
-
-/* Don't need to save/restore exponent range: the cache does it.
- Catalan's constant is G = sum((-1)^k/(2*k+1)^2, k=0..infinity).
- We compute it using formula (31) of Victor Adamchik's page
- "33 representations for Catalan's constant"
- http://www-2.cs.cmu.edu/~adamchik/articles/catalan/catalan.htm
-
- G = Pi/8*log(2+sqrt(3)) + 3/8*sum(k!^2/(2k)!/(2k+1)^2,k=0..infinity)
-*/
-int
-mpfr_const_catalan_internal (mpfr_ptr g, mpfr_rnd_t rnd_mode)
-{
- mpfr_t x, y, z;
- mpz_t T, P, Q;
- mpfr_prec_t pg, p;
- int inex;
- MPFR_ZIV_DECL (loop);
- MPFR_GROUP_DECL (group);
-
- MPFR_LOG_FUNC (("rnd_mode=%d", rnd_mode),
- ("g[%Pu]=%.*Rg inex=%d", mpfr_get_prec (g), mpfr_log_prec, g, inex));
-
- /* Here are the WC (max prec = 100.000.000)
- Once we have found a chain of 11, we only look for bigger chain.
- Found 3 '1' at 0
- Found 5 '1' at 9
- Found 6 '0' at 34
- Found 9 '1' at 176
- Found 11 '1' at 705
- Found 12 '0' at 913
- Found 14 '1' at 12762
- Found 15 '1' at 152561
- Found 16 '0' at 171725
- Found 18 '0' at 525355
- Found 20 '0' at 529245
- Found 21 '1' at 6390133
- Found 22 '0' at 7806417
- Found 25 '1' at 11936239
- Found 27 '1' at 51752950
- */
- pg = MPFR_PREC (g);
- p = pg + MPFR_INT_CEIL_LOG2 (pg) + 7;
-
- MPFR_GROUP_INIT_3 (group, p, x, y, z);
- mpz_init (T);
- mpz_init (P);
- mpz_init (Q);
-
- MPFR_ZIV_INIT (loop, p);
- for (;;) {
- mpfr_sqrt_ui (x, 3, MPFR_RNDU);
- mpfr_add_ui (x, x, 2, MPFR_RNDU);
- mpfr_log (x, x, MPFR_RNDU);
- mpfr_const_pi (y, MPFR_RNDU);
- mpfr_mul (x, x, y, MPFR_RNDN);
- S (T, P, Q, 0, (p - 1) / 2);
- mpz_mul_ui (T, T, 3);
- mpfr_set_z (y, T, MPFR_RNDU);
- mpfr_set_z (z, Q, MPFR_RNDD);
- mpfr_div (y, y, z, MPFR_RNDN);
- mpfr_add (x, x, y, MPFR_RNDN);
- mpfr_div_2ui (x, x, 3, MPFR_RNDN);
-
- if (MPFR_LIKELY (MPFR_CAN_ROUND (x, p - 5, pg, rnd_mode)))
- break;
-
- MPFR_ZIV_NEXT (loop, p);
- MPFR_GROUP_REPREC_3 (group, p, x, y, z);
- }
- MPFR_ZIV_FREE (loop);
- inex = mpfr_set (g, x, rnd_mode);
-
- MPFR_GROUP_CLEAR (group);
- mpz_clear (T);
- mpz_clear (P);
- mpz_clear (Q);
-
- return inex;
-}