The Tor Browser: security/nss/lib/freebl/mpi/utils/pi.c@6474c204b198

Cloned upstream origin tor-browser at tor-browser-31.3.0esr-4.5-1-build1
revision ID fc1c9ff7c1b2defdbc039f12214767608f46423f for hacking purpose.

     1 /*

     2  * pi.c

     3  *

     4  * Compute pi to an arbitrary number of digits.  Uses Machin's formula,

     5  * like everyone else on the planet:

     6  *

     7  *    pi = 16 * arctan(1/5) - 4 * arctan(1/239)

     8  *

     9  * This is pretty effective for up to a few thousand digits, but it

    10  * gets pretty slow after that.

    11  *

    12  * This Source Code Form is subject to the terms of the Mozilla Public

    13  * License, v. 2.0. If a copy of the MPL was not distributed with this

    14  * file, You can obtain one at http://mozilla.org/MPL/2.0/. */

    16 #include <stdio.h>

    17 #include <stdlib.h>

    18 #include <string.h>

    19 #include <limits.h>

    20 #include <time.h>

    22 #include "mpi.h"

    24 mp_err arctan(mp_digit mul, mp_digit x, mp_digit prec, mp_int *sum);

    26 int main(int argc, char *argv[])

    27 {

    28   mp_err       res;

    29   mp_digit     ndigits;

    30   mp_int       sum1, sum2;

    31   clock_t      start, stop;

    32   int          out = 0;

    34   /* Make the user specify precision on the command line */

    35   if(argc < 2) {

    36     fprintf(stderr, "Usage: %s <num-digits>\n", argv[0]);

    37     return 1;

    38   }

    40   if((ndigits = abs(atoi(argv[1]))) == 0) {

    41     fprintf(stderr, "%s: you must request at least 1 digit\n", argv[0]);

    42     return 1;

    43   }

    45   start = clock();

    46   mp_init(&sum1); mp_init(&sum2);

    48   /* sum1 = 16 * arctan(1/5)  */

    49   if((res = arctan(16, 5, ndigits, &sum1)) != MP_OKAY) {

    50     fprintf(stderr, "%s: arctan: %s\n", argv[0], mp_strerror(res));

    51     out = 1; goto CLEANUP;

    52   }

    54   /* sum2 = 4 * arctan(1/239) */

    55   if((res = arctan(4, 239, ndigits, &sum2)) != MP_OKAY) {

    56     fprintf(stderr, "%s: arctan: %s\n", argv[0], mp_strerror(res));

    57     out = 1; goto CLEANUP;

    58   }

    60   /* pi = sum1 - sum2         */

    61   if((res = mp_sub(&sum1, &sum2, &sum1)) != MP_OKAY) {

    62     fprintf(stderr, "%s: mp_sub: %s\n", argv[0], mp_strerror(res));

    63     out = 1; goto CLEANUP;

    64   }

    65   stop = clock();

    67   /* Write the output in decimal */

    68   {

    69     char  *buf = malloc(mp_radix_size(&sum1, 10));

    71     if(buf == NULL) {

    72       fprintf(stderr, "%s: out of memory\n", argv[0]);

    73       out = 1; goto CLEANUP;

    74     }

    75     mp_todecimal(&sum1, buf);

    76     printf("%s\n", buf);

    77     free(buf);

    78   }

    80   fprintf(stderr, "Computation took %.2f sec.\n",

    81 	  (double)(stop - start) / CLOCKS_PER_SEC);

    83  CLEANUP:

    84   mp_clear(&sum1);

    85   mp_clear(&sum2);

    87   return out;

    89 }

    91 /* Compute sum := mul * arctan(1/x), to 'prec' digits of precision */

    92 mp_err arctan(mp_digit mul, mp_digit x, mp_digit prec, mp_int *sum)

    93 {

    94   mp_int   t, v;

    95   mp_digit q = 1, rd;

    96   mp_err   res;

    97   int      sign = 1;

    99   prec += 3;  /* push inaccuracies off the end */

   101   mp_init(&t); mp_set(&t, 10);

   102   mp_init(&v);

   103   if((res = mp_expt_d(&t, prec, &t)) != MP_OKAY ||  /* get 10^prec    */

   104      (res = mp_mul_d(&t, mul, &t)) != MP_OKAY ||    /* ... times mul  */

   105      (res = mp_mul_d(&t, x, &t)) != MP_OKAY)        /* ... times x    */

   106     goto CLEANUP;

   108   /*

   109     The extra multiplication by x in the above takes care of what

   110     would otherwise have to be a special case for 1 / x^1 during the

   111     first loop iteration.  A little sneaky, but effective.

   113     We compute arctan(1/x) by the formula:

   115          1     1       1       1

   116 	 - - ----- + ----- - ----- + ...

   117 	 x   3 x^3   5 x^5   7 x^7

   119     We multiply through by 'mul' beforehand, which gives us a couple

   120     more iterations and more precision

   121    */

   123   x *= x; /* works as long as x < sqrt(RADIX), which it is here */

   125   mp_zero(sum);

   127   do {

   128     if((res = mp_div_d(&t, x, &t, &rd)) != MP_OKAY)

   129       goto CLEANUP;

   131     if(sign < 0 && rd != 0)

   132       mp_add_d(&t, 1, &t);

   134     if((res = mp_div_d(&t, q, &v, &rd)) != MP_OKAY)

   135       goto CLEANUP;

   137     if(sign < 0 && rd != 0)

   138       mp_add_d(&v, 1, &v);

   140     if(sign > 0)

   141       res = mp_add(sum, &v, sum);

   142     else

   143       res = mp_sub(sum, &v, sum);

   145     if(res != MP_OKAY)

   146       goto CLEANUP;

   148     sign *= -1;

   149     q += 2;

   151   } while(mp_cmp_z(&t) != 0);

   153   /* Chop off inaccurate low-order digits */

   154   mp_div_d(sum, 1000, sum, NULL);

   156  CLEANUP:

   157   mp_clear(&v);

   158   mp_clear(&t);

   160   return res;

   161 }

   163 /*------------------------------------------------------------------------*/

   164 /* HERE THERE BE DRAGONS                                                  */

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