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Diffstat (limited to 'src/const_catalan.c')
| -rw-r--r-- | src/const_catalan.c | 153 |
1 files changed, 153 insertions, 0 deletions
diff --git a/src/const_catalan.c b/src/const_catalan.c new file mode 100644 index 0000000..c8929c1 --- /dev/null +++ b/src/const_catalan.c @@ -0,0 +1,153 @@ +/* mpfr_const_catalan -- compute Catalan's constant. + +Copyright 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc. +Contributed by the AriC and Caramel 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 */ +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; +} |