machin_like_formula.cpp

#include<cmath>
#include<iomanip>
#include<iostream>
#include<gmpxx.h>

int main() {
    unsigned digit = 10000;
    mpf_set_default_prec((digit + 1) * log2(10));
    mpf_class pi = 0;
    unsigned m = digit / 4;
    
    mpz_class p5 = 5;
    for (unsigned n = 0; n < 3 * m + 2; n++) {
        pi += (n % 2 == 0 ? 16_mpf : -16_mpf) / ((2 * n + 1) * p5);
        p5 *= 25;
    }

    mpz_class p239 = 239;
    for (unsigned n = 0; n < m; n++) {
        pi += (n % 2 == 1 ? 4_mpf : -4_mpf) / ((2 * n + 1) * p239);
        p239 *= 57121;
    }

    std::cout << std::fixed << std::setprecision(digit + 1) << pi << std::endl;
}

g++ calc_10000_digits_of_pi.cpp -o calc_10000_digits_of_pi -lmpfr -lgmp