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