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Diffstat (limited to 'security/nss/lib/freebl/mpi/utils/pi.c')
| -rw-r--r-- | security/nss/lib/freebl/mpi/utils/pi.c | 194 |
1 files changed, 194 insertions, 0 deletions
diff --git a/security/nss/lib/freebl/mpi/utils/pi.c b/security/nss/lib/freebl/mpi/utils/pi.c new file mode 100644 index 000000000..367118586 --- /dev/null +++ b/security/nss/lib/freebl/mpi/utils/pi.c @@ -0,0 +1,194 @@ +/* + * 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. + * + * The contents of this file are subject to the Mozilla Public + * License Version 1.1 (the "License"); you may not use this file + * except in compliance with the License. You may obtain a copy of + * the License at http://www.mozilla.org/MPL/ + * + * Software distributed under the License is distributed on an "AS + * IS" basis, WITHOUT WARRANTY OF ANY KIND, either express or + * implied. See the License for the specific language governing + * rights and limitations under the License. + * + * The Original Code is the MPI Arbitrary Precision Integer Arithmetic + * library. + * + * The Initial Developer of the Original Code is Michael J. Fromberger. + * Portions created by Michael J. Fromberger are + * Copyright (C) 1999, 2000 Michael J. Fromberger. + * All Rights Reserved. + * + * Contributor(s): + * + * Alternatively, the contents of this file may be used under the + * terms of the GNU General Public License Version 2 or later (the + * "GPL"), in which case the provisions of the GPL are applicable + * instead of those above. If you wish to allow use of your + * version of this file only under the terms of the GPL and not to + * allow others to use your version of this file under the MPL, + * indicate your decision by deleting the provisions above and + * replace them with the notice and other provisions required by + * the GPL. If you do not delete the provisions above, a recipient + * may use your version of this file under either the MPL or the GPL. + * + * $Id$ + */ + +#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 */ |