#include <stdio.h>
#include <math.h>
#include <gmp.h>

/*
    n! の近似値と桁数
*/
void fact_digits(unsigned int ni)
{
    double n = ni;
    double afa, dfa;
    afa = sqrt(M_TWOPI * n) * pow(n, n) * exp(-n);
    /* dfa = 0.5 * log10(M_TWOPI * n) + n * log10(n) + log10(exp(-n)); */
    dfa = 0.5 * log10(M_TWOPI * n) + n * log10(n/M_E);
    printf("%d: n! approx = %g, %.0f digits\n", ni, afa, dfa + 0.5);
}

/*
    n! の値と使用している limb の数
*/
int fact_value(unsigned int n, mpz_t result)
{
    unsigned int m = 2;
    if (n < m) {
        mpz_set_ui(result, 1);
        return 0;
    }
    printf("mp_bits_per_limb %d\n", mp_bits_per_limb);
    mpz_set_ui(result, m);
    while (++m <= n) {
        fact_digits(m);
        mpz_mul_ui(result, result, m);
        gmp_printf("  %Zd (%u limbs, %u bits)\n", result, mpz_size(result),
           mp_bits_per_limb * mpz_size(result));
        /* printf("  _mp_alloc %d, _mp_size %d\n",
            result[0]._mp_alloc, result[0]._mp_size); */
    }
    return 0;
}

int main(int argc, char* argv[])
{
    unsigned int n = 24;
    mpz_t result;
    mpz_init(result);
    fact_value(n, result); 
    mpz_clear(result);
    return 0;
}