c - Trouble with Bailey-Borwein-Plouffe formula -


i trying implement bbp formula. wrote following quick , dirty test code, based on paper paul h. bailey (that found here):

#include <stdio.h> #include <stdlib.h> #include <math.h> #include <gmp.h> #include <limits.h>  long bin_exp_mod_k(int base, int exponent, int div) {     long expmod = 1;     long t;      t = (long) pow(2, floor(log(exponent)/log(2.0)));      while(42) {         if(exponent >= t) {             expmod = (base * expmod) % div;             exponent -= t;         }          t = t/2;          if(t >= 1) {             expmod = ((long)pow(expmod, 2)) % div;         } else             break;     }      return expmod; }  void bbp_part(mpf_t rop, int base, int index, int digit_index, int num_iter) {     const int knum = num_iter;     int k;     long ldiv;     mpf_t fbase;     mpf_t fst_sum;     mpf_t fst_sum_int;     mpf_t snd_sum;     mpf_t powval;     mpf_t div;      mpf_init(fst_sum);     mpf_init(snd_sum);     mpf_init(fst_sum_int);     mpf_init(powval);     mpf_init(div);     mpf_init(rop);     mpf_init_set_si(fbase, base);      for(k = 0;k <= digit_index;k++) {         ldiv = 8 * k + index;         mpf_set_si(powval, bin_exp_mod_k(base, digit_index - k, ldiv));         mpf_set_si(div, ldiv);         mpf_div(powval, powval, div);         mpf_add(fst_sum, fst_sum, powval);     }      mpf_trunc(fst_sum_int, fst_sum);     mpf_sub(fst_sum, fst_sum, fst_sum_int);      for(k = digit_index + 1;k < knum;k++) {         ldiv = 8 * k + index;         mpf_set_si(div, ldiv);         mpf_pow_ui(powval, fbase, digit_index - k);         mpf_div(powval, powval, div);         mpf_add(snd_sum, snd_sum, powval);     }      mpf_set(rop, fst_sum);     mpf_add(fst_sum, fst_sum, snd_sum);      printf("s%i: %.20lf\n", index, mpf_get_d(rop));      mpf_clear(fst_sum);     mpf_clear(snd_sum);     mpf_clear(fbase);     mpf_clear(fst_sum_int);     mpf_clear(powval);     mpf_clear(div); }  int main(int argc, char **argv) {     const int base = 16;     int d;     int num_iter;     mpf_t pi_digits;     mpf_t part1;     mpf_t part1_int;     mpf_t part4;     mpf_t part4_int;     mpf_t part5;     mpf_t part5_int;     mpf_t part6;     mpf_t part6_int;      if(argc == 1) {         return -1;     }      d = atoi(argv[1]);      if(argc == 3) {         num_iter = atoi(argv[2]);     } else {         num_iter = int_max;     }      mpf_set_default_prec(128);      mpf_init(pi_digits);      mpf_init(part1_int);            mpf_init(part4_int);     mpf_init(part5_int);     mpf_init(part6_int);      bbp_part(part1, base, 1, d, num_iter);     bbp_part(part4, base, 4, d, num_iter);     bbp_part(part5, base, 5, d, num_iter);     bbp_part(part6, base, 6, d, num_iter);      mpf_trunc(part1_int, part1);     mpf_trunc(part4_int, part4);     mpf_trunc(part5_int, part5);     mpf_trunc(part6_int, part6);      mpf_sub(part1, part1, part1_int);     mpf_sub(part4, part4, part4_int);     mpf_sub(part5, part5, part5_int);     mpf_sub(part6, part6, part6_int);      mpf_mul_ui(part1, part1, 4l);     mpf_mul_ui(part4, part4, 2l);      mpf_set(pi_digits, part1);     mpf_sub(pi_digits, pi_digits, part4);     mpf_sub(pi_digits, pi_digits, part5);     mpf_sub(pi_digits, pi_digits, part6);      mpf_clear(pi_digits);     mpf_clear(part1);     mpf_clear(part4);     mpf_clear(part5);     mpf_clear(part6);     mpf_clear(part1_int);     mpf_clear(part4_int);     mpf_clear(part5_int);     mpf_clear(part6_int);      return 0; }

and seems correct, because according paper partial results s1, s4, s5 , s6 are, small precision difference, same ones noted.

however, can't figure out did miss "combining results" part. no matter do, 0.57... instead of 0.42... written on paper.

can see missing here?


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