--- /dev/null
+/* mpfr_const_catalan -- compute Catalan's constant.
+
+Copyright 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 2.1 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, 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, mp_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, mp_rnd_t rnd_mode)
+{
+ mpfr_t x, y, z;
+ mpz_t T, P, Q;
+ mp_prec_t pg, p;
+ int inex;
+ MPFR_ZIV_DECL (loop);
+ MPFR_GROUP_DECL (group);
+
+ MPFR_LOG_FUNC (("rnd_mode=%d", rnd_mode), ("g[%#R]=%R inex=%d", g, 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 + 9;
+ p += MPFR_INT_CEIL_LOG2 (p);
+
+ 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, GMP_RNDU);
+ mpfr_add_ui (x, x, 2, GMP_RNDU);
+ mpfr_log (x, x, GMP_RNDU);
+ mpfr_const_pi (y, GMP_RNDU);
+ mpfr_mul (x, x, y, GMP_RNDN);
+ S (T, P, Q, 0, (p - 1) / 2);
+ mpz_mul_ui (T, T, 3);
+ mpfr_set_z (y, T, GMP_RNDU);
+ mpfr_set_z (z, Q, GMP_RNDD);
+ mpfr_div (y, y, z, GMP_RNDN);
+ mpfr_add (x, x, y, GMP_RNDN);
+ mpfr_div_2ui (x, x, 3, GMP_RNDN);
+
+ if (MPFR_LIKELY (MPFR_CAN_ROUND (x, p - 5, pg, rnd_mode)))
+ break;
+ /* Fixme: Is it possible? */
+ 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;
+}
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