Kod: Zaznacz cały
https://www.mpfr.org/
To listing tego pliku const_pi .c
Kod: Zaznacz cały
/* mpfr_const_pi -- compute Pi
Copyright 1999-2023 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. */
#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_THREAD_VAR (mpfr_cache_ptr, __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);
}
/* The algorithm used here is taken from Section 8.2.5 of the book
"Fast Algorithms: A Multitape Turing Machine Implementation"
by A. Schönhage, A. F. W. Grotefeld and E. Vetter, 1994.
It is a clever form of Brent-Salamin formula. */
/* 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_GROUP_DECL (group);
MPFR_ZIV_DECL (loop);
int inex;
MPFR_LOG_FUNC
(("rnd_mode=%d", rnd_mode),
("x[%Pd]=%.*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_GROUP_INIT_5 (group, p, a, A, B, D, S);
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_sqr (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_ASSERTD (mpfr_cmp_ui (S, 1) < 0);
cancel = MPFR_NOTZERO (S) ? (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 >= p - k)
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_GROUP_REPREC_5 (group, p, a, A, B, D, S);
}
MPFR_ZIV_FREE (loop);
inex = mpfr_set (x, A, rnd_mode);
MPFR_GROUP_CLEAR (group);
return inex;
}
Napisałem zgrabniejszy i sprytniejszy algorytm do obliczania samej wartości liczby Pi. Nazwałem go FFCPI aka FCPI co jest skrótem od Fibonacci Fast Compute Pi.
Kod: Zaznacz cały
// Calculate real value of PI with use large numbers of Fibonacci sequence
// FCPI algorithm
// Author: Sylwester Bogusiak aka Sylvi91
// This is free code to calculate pi value to an arbitrary degree of precision.
// There is no warranty or guarantee of any kind.
// The mpfr library has further restrictions.
// To Compile:
// gcc -o cpi cpi.c -lmpfr
// Usage in command line:
// ./cpi 1000000000
#include <stdio.h>
#include <mpfr.h>
#include <stdlib.h>
#include <assert.h>
#include <math.h>
#include <time.h>
void fcpi(int n) {
int i;
mpfr_t pi, f_n, f_n_minus_1, temp;
mpfr_inits2(1000, pi, f_n, f_n_minus_1, temp);
// Initialize Fibonacci numbers
mpfr_set_ui(f_n, 1, MPFR_RNDN);
mpfr_set_ui(f_n_minus_1, 0, MPFR_RNDN);
// Compute consecutive Fibonacci numbers
for (i = 2; i < n; i++) {
mpfr_add(temp, f_n, f_n_minus_1, MPFR_RNDN);
// Swap Fibonacci numbers
mpfr_set(f_n_minus_1, f_n, MPFR_RNDN);
mpfr_set(f_n, temp, MPFR_RNDN);
}
// Compute Pi using Fibonacci numbers and other natural numbers
mpfr_div(pi, f_n, f_n_minus_1, MPFR_RNDN);
mpfr_sqr(pi, pi, MPFR_RNDN);
mpfr_mul_ui(pi, pi, 6, MPFR_RNDN);
mpfr_div_ui(pi, pi, 5, MPFR_RNDN);
// Set the precision for the result
mpfr_prec_round(pi, 1000, MPFR_RNDN);
printf ("\n For f(%d) Pi = ", i );
// Print the calculated value of Pi
mpfr_out_str(stdout, 10, 0, pi, MPFR_RNDN);
printf("\n");
// Clean up
mpfr_clears(pi, f_n, f_n_minus_1, temp, NULL);
}
int main(int argc, char * argv[]) {
int n;
if (argc <= 1){
printf ("Usage: %s <number of iterations>\n", argv[0]);
return 1;
}
n = atoi(argv[1]);
assert( n >= 1);
time_t start; // system time var
time_t end; // system time var
time(&start); // Get the begining system time
fcpi(n); // Change the argument to adjust the number of iterations
time(&end); // Get the end system time
double dif;
dif = difftime (end,start); // calculate the diff
printf ("\nYour calculations took %.2lf seconds to run.\n", dif ); // time
return 0;
}
// Bye, bye ;) My computer with Fibonacci compute Pi ;) FCPI AKA FFCPI - fibonacci fast compute pi