logarithms.c

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

#define L2_INFILE "ln_2.txt"

void taylor_log(mpf_t, const mpf_t, const mpf_t);
void hyperbolic_log(mpf_t, const mpf_t, const mpf_t);

int main(int argc, char **argv)
{
    unsigned long p, n, e, c;
    mpf_t N, T, R, V, nlog2, tmp;
    FILE *l_2_in;

    sscanf(argv[3], "%lu", &p);
    mpf_set_default_prec(p);

    l_2_in = fopen(L2_INFILE, "r");
    mpf_init(nlog2);
    mpf_inp_str(nlog2, l_2_in, 10);
    fclose(l_2_in);

    mpf_init_set_str(N, argv[1], 10);

    sscanf(argv[2], "%lu", &n);
    mpf_init_set_ui(T, 10);
    mpf_pow_ui(T, T, n);
    mpf_ui_div(T, 1, T);

    mpf_init(V);
    mpf_set_d(V, mpf_get_d_2exp(&e, N));

    mpf_init(R);
    mpf_init(tmp);

    printf("%ld\n", e);
    gmp_printf("%.*Ff\n", 20, V);
    sscanf(argv[4], "%lu", &c);
    switch(c)
    {
        case 1:
            printf("Case 1\n");
            taylor_log(R, V, T);
            break;
        case 2:
            printf("Case 2\n");
            hyperbolic_log(R, V, T);
            break;
        default:
            printf("ERROR: Incorrect choice of function\n");
            printf("Please choose from the following options\n");
            printf("1:\tTaylor expansion method\n");
            printf("2:\tHyperbolic expansion method\n");
            return 1;
    }
    mpf_mul_ui(tmp, nlog2, e);
    mpf_add(R, R, tmp);
    gmp_printf("%.*Ff\n", n, R);
}

void taylor_log(mpf_t R,
                const mpf_t N,
                const mpf_t T)
{
    mpf_t x, y, r, pr, tmp, d;
    int n = 1;
    mpf_init(x);
    mpf_init(y);
    mpf_init(tmp);
    mpf_init(d);

    mpf_sub_ui(x, N, 1);
    mpf_init_set(y, x);

    mpf_init_set(r, x);
    mpf_init_set_ui(pr, 0);

    mpf_sub(d, r, pr);
    mpf_abs(d, d);
    while(mpf_cmp(d, T) > 0)
    {
        mpf_set(pr, r);

        mpf_mul(y, y, x);
        mpf_div_ui(tmp, y, ++n);
        mpf_sub(r, r, tmp);

        mpf_mul(y, y, x);
        mpf_div_ui(tmp, y, ++n);
        mpf_add(r, r, tmp);

        mpf_sub(d, r, pr);
        mpf_abs(d,d);
    }
    printf("%d\n", n);
    mpf_set(R, r);
}

void hyperbolic_log(mpf_t R,
                    const mpf_t N,
                    const mpf_t T)
{
    mpf_t x, x2, r, pr, tmp, d;
    int n = 1;
    mpf_init(x);
    mpf_init(x2);
    mpf_init(tmp);
    mpf_init(d);

    mpf_sub_ui(x, N, 1);
    mpf_add_ui(tmp, N, 1);
    mpf_div(x, x, tmp);

    mpf_init_set(r, x);
    mpf_init_set_ui(pr, 0);

    mpf_mul(x2, x, x);

    mpf_sub(d, r, pr);
    mpf_abs(d,d);
    while(mpf_cmp(d, T) > 0)
    {
        mpf_set(pr, r);
        ++n;

        mpf_mul(x, x, x2);
        mpf_div_ui(tmp, x, ++n);
        mpf_add(r, r, tmp);

        mpf_sub(d, r, pr);
        mpf_abs(d,d);
    }
    printf("%d\n", n);
    mpf_mul_ui(R, r, 2);
}