mirror of
https://github.com/rn10950/RetroZilla.git
synced 2024-11-16 04:20:32 +01:00
165 lines
4.0 KiB
C
165 lines
4.0 KiB
C
/*
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* pi.c
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*
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* Compute pi to an arbitrary number of digits. Uses Machin's formula,
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* like everyone else on the planet:
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*
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* pi = 16 * arctan(1/5) - 4 * arctan(1/239)
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*
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* This is pretty effective for up to a few thousand digits, but it
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* gets pretty slow after that.
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*
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* This Source Code Form is subject to the terms of the Mozilla Public
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* License, v. 2.0. If a copy of the MPL was not distributed with this
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* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include <limits.h>
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#include <time.h>
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#include "mpi.h"
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mp_err arctan(mp_digit mul, mp_digit x, mp_digit prec, mp_int *sum);
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int main(int argc, char *argv[])
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{
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mp_err res;
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mp_digit ndigits;
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mp_int sum1, sum2;
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clock_t start, stop;
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int out = 0;
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/* Make the user specify precision on the command line */
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if(argc < 2) {
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fprintf(stderr, "Usage: %s <num-digits>\n", argv[0]);
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return 1;
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}
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if((ndigits = abs(atoi(argv[1]))) == 0) {
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fprintf(stderr, "%s: you must request at least 1 digit\n", argv[0]);
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return 1;
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}
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start = clock();
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mp_init(&sum1); mp_init(&sum2);
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/* sum1 = 16 * arctan(1/5) */
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if((res = arctan(16, 5, ndigits, &sum1)) != MP_OKAY) {
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fprintf(stderr, "%s: arctan: %s\n", argv[0], mp_strerror(res));
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out = 1; goto CLEANUP;
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}
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/* sum2 = 4 * arctan(1/239) */
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if((res = arctan(4, 239, ndigits, &sum2)) != MP_OKAY) {
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fprintf(stderr, "%s: arctan: %s\n", argv[0], mp_strerror(res));
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out = 1; goto CLEANUP;
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}
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/* pi = sum1 - sum2 */
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if((res = mp_sub(&sum1, &sum2, &sum1)) != MP_OKAY) {
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fprintf(stderr, "%s: mp_sub: %s\n", argv[0], mp_strerror(res));
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out = 1; goto CLEANUP;
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}
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stop = clock();
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/* Write the output in decimal */
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{
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char *buf = malloc(mp_radix_size(&sum1, 10));
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if(buf == NULL) {
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fprintf(stderr, "%s: out of memory\n", argv[0]);
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out = 1; goto CLEANUP;
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}
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mp_todecimal(&sum1, buf);
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printf("%s\n", buf);
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free(buf);
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}
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fprintf(stderr, "Computation took %.2f sec.\n",
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(double)(stop - start) / CLOCKS_PER_SEC);
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CLEANUP:
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mp_clear(&sum1);
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mp_clear(&sum2);
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return out;
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}
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/* Compute sum := mul * arctan(1/x), to 'prec' digits of precision */
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mp_err arctan(mp_digit mul, mp_digit x, mp_digit prec, mp_int *sum)
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{
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mp_int t, v;
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mp_digit q = 1, rd;
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mp_err res;
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int sign = 1;
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prec += 3; /* push inaccuracies off the end */
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mp_init(&t); mp_set(&t, 10);
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mp_init(&v);
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if((res = mp_expt_d(&t, prec, &t)) != MP_OKAY || /* get 10^prec */
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(res = mp_mul_d(&t, mul, &t)) != MP_OKAY || /* ... times mul */
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(res = mp_mul_d(&t, x, &t)) != MP_OKAY) /* ... times x */
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goto CLEANUP;
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/*
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The extra multiplication by x in the above takes care of what
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would otherwise have to be a special case for 1 / x^1 during the
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first loop iteration. A little sneaky, but effective.
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We compute arctan(1/x) by the formula:
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1 1 1 1
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- - ----- + ----- - ----- + ...
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x 3 x^3 5 x^5 7 x^7
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We multiply through by 'mul' beforehand, which gives us a couple
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more iterations and more precision
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*/
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x *= x; /* works as long as x < sqrt(RADIX), which it is here */
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mp_zero(sum);
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do {
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if((res = mp_div_d(&t, x, &t, &rd)) != MP_OKAY)
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goto CLEANUP;
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if(sign < 0 && rd != 0)
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mp_add_d(&t, 1, &t);
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if((res = mp_div_d(&t, q, &v, &rd)) != MP_OKAY)
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goto CLEANUP;
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if(sign < 0 && rd != 0)
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mp_add_d(&v, 1, &v);
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if(sign > 0)
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res = mp_add(sum, &v, sum);
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else
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res = mp_sub(sum, &v, sum);
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if(res != MP_OKAY)
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goto CLEANUP;
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sign *= -1;
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q += 2;
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} while(mp_cmp_z(&t) != 0);
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/* Chop off inaccurate low-order digits */
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mp_div_d(sum, 1000, sum, NULL);
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CLEANUP:
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mp_clear(&v);
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mp_clear(&t);
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return res;
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}
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/*------------------------------------------------------------------------*/
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/* HERE THERE BE DRAGONS */
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