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Diffstat (limited to 'src/const_pi.c')
| -rw-r--r-- | src/const_pi.c | 128 |
1 files changed, 128 insertions, 0 deletions
diff --git a/src/const_pi.c b/src/const_pi.c new file mode 100644 index 0000000..046ccc4 --- /dev/null +++ b/src/const_pi.c @@ -0,0 +1,128 @@ +/* mpfr_const_pi -- compute Pi + +Copyright 1999, 2000, 2001, 2002, 2003, 2004, 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. */ + +#include "mpfr-impl.h" + +/* Declare the cache */ +#ifndef MPFR_USE_LOGGING +MPFR_DECL_INIT_CACHE(__gmpfr_cache_const_pi, mpfr_const_pi_internal); +#else +MPFR_DECL_INIT_CACHE(__gmpfr_normal_pi, mpfr_const_pi_internal); +MPFR_DECL_INIT_CACHE(__gmpfr_logging_pi, mpfr_const_pi_internal); +mpfr_cache_ptr MPFR_THREAD_ATTR __gmpfr_cache_const_pi = __gmpfr_normal_pi; +#endif + +/* Set User Interface */ +#undef mpfr_const_pi +int +mpfr_const_pi (mpfr_ptr x, mpfr_rnd_t rnd_mode) { + return mpfr_cache (x, __gmpfr_cache_const_pi, rnd_mode); +} + +/* Don't need to save/restore exponent range: the cache does it */ +int +mpfr_const_pi_internal (mpfr_ptr x, mpfr_rnd_t rnd_mode) +{ + mpfr_t a, A, B, D, S; + mpfr_prec_t px, p, cancel, k, kmax; + MPFR_ZIV_DECL (loop); + int inex; + + MPFR_LOG_FUNC + (("rnd_mode=%d", rnd_mode), + ("x[%Pu]=%.*Rg inexact=%d", mpfr_get_prec(x), mpfr_log_prec, x, inex)); + + px = MPFR_PREC (x); + + /* we need 9*2^kmax - 4 >= px+2*kmax+8 */ + for (kmax = 2; ((px + 2 * kmax + 12) / 9) >> kmax; kmax ++); + + p = px + 3 * kmax + 14; /* guarantees no recomputation for px <= 10000 */ + + mpfr_init2 (a, p); + mpfr_init2 (A, p); + mpfr_init2 (B, p); + mpfr_init2 (D, p); + mpfr_init2 (S, p); + + MPFR_ZIV_INIT (loop, p); + for (;;) { + mpfr_set_ui (a, 1, MPFR_RNDN); /* a = 1 */ + mpfr_set_ui (A, 1, MPFR_RNDN); /* A = a^2 = 1 */ + mpfr_set_ui_2exp (B, 1, -1, MPFR_RNDN); /* B = b^2 = 1/2 */ + mpfr_set_ui_2exp (D, 1, -2, MPFR_RNDN); /* D = 1/4 */ + +#define b B +#define ap a +#define Ap A +#define Bp B + for (k = 0; ; k++) + { + /* invariant: 1/2 <= B <= A <= a < 1 */ + mpfr_add (S, A, B, MPFR_RNDN); /* 1 <= S <= 2 */ + mpfr_div_2ui (S, S, 2, MPFR_RNDN); /* exact, 1/4 <= S <= 1/2 */ + mpfr_sqrt (b, B, MPFR_RNDN); /* 1/2 <= b <= 1 */ + mpfr_add (ap, a, b, MPFR_RNDN); /* 1 <= ap <= 2 */ + mpfr_div_2ui (ap, ap, 1, MPFR_RNDN); /* exact, 1/2 <= ap <= 1 */ + mpfr_mul (Ap, ap, ap, MPFR_RNDN); /* 1/4 <= Ap <= 1 */ + mpfr_sub (Bp, Ap, S, MPFR_RNDN); /* -1/4 <= Bp <= 3/4 */ + mpfr_mul_2ui (Bp, Bp, 1, MPFR_RNDN); /* -1/2 <= Bp <= 3/2 */ + mpfr_sub (S, Ap, Bp, MPFR_RNDN); + MPFR_ASSERTN (mpfr_cmp_ui (S, 1) < 0); + cancel = mpfr_cmp_ui (S, 0) ? (mpfr_uexp_t) -mpfr_get_exp(S) : p; + /* MPFR_ASSERTN (cancel >= px || cancel >= 9 * (1 << k) - 4); */ + mpfr_mul_2ui (S, S, k, MPFR_RNDN); + mpfr_sub (D, D, S, MPFR_RNDN); + /* stop when |A_k - B_k| <= 2^(k-p) i.e. cancel >= p-k */ + if (cancel + k >= p) + break; + } +#undef b +#undef ap +#undef Ap +#undef Bp + + mpfr_div (A, B, D, MPFR_RNDN); + + /* MPFR_ASSERTN(p >= 2 * k + 8); */ + if (MPFR_LIKELY (MPFR_CAN_ROUND (A, p - 2 * k - 8, px, rnd_mode))) + break; + + p += kmax; + MPFR_ZIV_NEXT (loop, p); + mpfr_set_prec (a, p); + mpfr_set_prec (A, p); + mpfr_set_prec (B, p); + mpfr_set_prec (D, p); + mpfr_set_prec (S, p); + } + MPFR_ZIV_FREE (loop); + inex = mpfr_set (x, A, rnd_mode); + + mpfr_clear (a); + mpfr_clear (A); + mpfr_clear (B); + mpfr_clear (D); + mpfr_clear (S); + + return inex; +} |