source/libs/mpfr/mpfr-3.1.3/src/const_pi.c

   1 /* mpfr_const_pi -- compute Pi
   2
   3 Copyright 1999-2015 Free Software Foundation, Inc.
   4 Contributed by the AriC and Caramel projects, INRIA.
   5
   6 This file is part of the GNU MPFR Library.
   7
   8 The GNU MPFR Library is free software; you can redistribute it and/or modify
   9 it under the terms of the GNU Lesser General Public License as published by
  10 the Free Software Foundation; either version 3 of the License, or (at your
  11 option) any later version.
  12
  13 The GNU MPFR Library is distributed in the hope that it will be useful, but
  14 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  15 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
  16 License for more details.
  17
  18 You should have received a copy of the GNU Lesser General Public License
  19 along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
  20 http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
  21 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
  22
  23 #include "mpfr-impl.h"
  24
  25 /* Declare the cache */
  26 #ifndef MPFR_USE_LOGGING
  27 MPFR_DECL_INIT_CACHE(__gmpfr_cache_const_pi, mpfr_const_pi_internal);
  28 #else
  29 MPFR_DECL_INIT_CACHE(__gmpfr_normal_pi, mpfr_const_pi_internal);
  30 MPFR_DECL_INIT_CACHE(__gmpfr_logging_pi, mpfr_const_pi_internal);
  31 mpfr_cache_ptr MPFR_THREAD_ATTR __gmpfr_cache_const_pi = __gmpfr_normal_pi;
  32 #endif
  33
  34 /* Set User Interface */
  35 #undef mpfr_const_pi
  36 int
  37 mpfr_const_pi (mpfr_ptr x, mpfr_rnd_t rnd_mode) {
  38   return mpfr_cache (x, __gmpfr_cache_const_pi, rnd_mode);
  39 }
  40
  41 /* Don't need to save/restore exponent range: the cache does it */
  42 int
  43 mpfr_const_pi_internal (mpfr_ptr x, mpfr_rnd_t rnd_mode)
  44 {
  45   mpfr_t a, A, B, D, S;
  46   mpfr_prec_t px, p, cancel, k, kmax;
  47   MPFR_ZIV_DECL (loop);
  48   int inex;
  49
  50   MPFR_LOG_FUNC
  51     (("rnd_mode=%d", rnd_mode),
  52      ("x[%Pu]=%.*Rg inexact=%d", mpfr_get_prec(x), mpfr_log_prec, x, inex));
  53
  54   px = MPFR_PREC (x);
  55
  56   /* we need 9*2^kmax - 4 >= px+2*kmax+8 */
  57   for (kmax = 2; ((px + 2 * kmax + 12) / 9) >> kmax; kmax ++);
  58
  59   p = px + 3 * kmax + 14; /* guarantees no recomputation for px <= 10000 */
  60
  61   mpfr_init2 (a, p);
  62   mpfr_init2 (A, p);
  63   mpfr_init2 (B, p);
  64   mpfr_init2 (D, p);
  65   mpfr_init2 (S, p);
  66
  67   MPFR_ZIV_INIT (loop, p);
  68   for (;;) {
  69     mpfr_set_ui (a, 1, MPFR_RNDN);          /* a = 1 */
  70     mpfr_set_ui (A, 1, MPFR_RNDN);          /* A = a^2 = 1 */
  71     mpfr_set_ui_2exp (B, 1, -1, MPFR_RNDN); /* B = b^2 = 1/2 */
  72     mpfr_set_ui_2exp (D, 1, -2, MPFR_RNDN); /* D = 1/4 */
  73
  74 #define b B
  75 #define ap a
  76 #define Ap A
  77 #define Bp B
  78     for (k = 0; ; k++)
  79       {
  80         /* invariant: 1/2 <= B <= A <= a < 1 */
  81         mpfr_add (S, A, B, MPFR_RNDN); /* 1 <= S <= 2 */
  82         mpfr_div_2ui (S, S, 2, MPFR_RNDN); /* exact, 1/4 <= S <= 1/2 */
  83         mpfr_sqrt (b, B, MPFR_RNDN); /* 1/2 <= b <= 1 */
  84         mpfr_add (ap, a, b, MPFR_RNDN); /* 1 <= ap <= 2 */
  85         mpfr_div_2ui (ap, ap, 1, MPFR_RNDN); /* exact, 1/2 <= ap <= 1 */
  86         mpfr_mul (Ap, ap, ap, MPFR_RNDN); /* 1/4 <= Ap <= 1 */
  87         mpfr_sub (Bp, Ap, S, MPFR_RNDN); /* -1/4 <= Bp <= 3/4 */
  88         mpfr_mul_2ui (Bp, Bp, 1, MPFR_RNDN); /* -1/2 <= Bp <= 3/2 */
  89         mpfr_sub (S, Ap, Bp, MPFR_RNDN);
  90         MPFR_ASSERTN (mpfr_cmp_ui (S, 1) < 0);
  91         cancel = mpfr_cmp_ui (S, 0) ? (mpfr_uexp_t) -mpfr_get_exp(S) : p;
  92         /* MPFR_ASSERTN (cancel >= px || cancel >= 9 * (1 << k) - 4); */
  93         mpfr_mul_2ui (S, S, k, MPFR_RNDN);
  94         mpfr_sub (D, D, S, MPFR_RNDN);
  95         /* stop when |A_k - B_k| <= 2^(k-p) i.e. cancel >= p-k */
  96         if (cancel + k >= p)
  97           break;
  98       }
  99 #undef b
 100 #undef ap
 101 #undef Ap
 102 #undef Bp
 103
 104       mpfr_div (A, B, D, MPFR_RNDN);
 105
 106       /* MPFR_ASSERTN(p >= 2 * k + 8); */
 107       if (MPFR_LIKELY (MPFR_CAN_ROUND (A, p - 2 * k - 8, px, rnd_mode)))
 108         break;
 109
 110       p += kmax;
 111       MPFR_ZIV_NEXT (loop, p);
 112       mpfr_set_prec (a, p);
 113       mpfr_set_prec (A, p);
 114       mpfr_set_prec (B, p);
 115       mpfr_set_prec (D, p);
 116       mpfr_set_prec (S, p);
 117   }
 118   MPFR_ZIV_FREE (loop);
 119   inex = mpfr_set (x, A, rnd_mode);
 120
 121   mpfr_clear (a);
 122   mpfr_clear (A);
 123   mpfr_clear (B);
 124   mpfr_clear (D);
 125   mpfr_clear (S);
 126
 127   return inex;
 128 }