#include <inttypes.h>
#include <math.h>
#include <stdbool.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>

int *dec_to_bin(int d, int *length) {
    int *binary_form = calloc(20, sizeof(int));
    int index = 0;
    while (d != 0) {
        binary_form[index] = d % 2;
        d /= 2;
        index++;
    }

    *length = index;

    for (int i = index; i >= 0; i--) {
        printf("%d", binary_form[i]);
    }
    printf(" index: %d\n", index);

    return binary_form;
}

uint64_t quick_pow(int *d_binary, int a, int n, int length) {
    uint64_t *powed = calloc(20, sizeof(uint64_t));

    powed[0] = a;
    for (int i = 1; i <= length; i++) {
        powed[i] = (powed[i - 1] * powed[i - 1]) % n;
        printf("powed: %ju, index: %d; ", powed[i], (i));
    }

    // check where in the binary are ones
    uint64_t multiplied = 1;
    for (int i = 0; i < length; i++) {
        if (d_binary[i] == 1) {
            multiplied *= powed[i];
        }
    }

    printf("\nbm quick math: %ju; %d ", multiplied, n);
    multiplied = multiplied % n;
    printf("quick math: %ju", multiplied);

    free(powed);

    return multiplied;
}

bool prime_test(uint64_t n) {
    printf("\n\nprime test: %jd\n", n);
    // Miller Rabin prime test
    // choose a base: a, which should be a prime so that (n, a) = 1
    // then do 2 rounds of tests provided the first one did not fail
    // 1: a^d =k 1 mod n
    // 2: a^(d * 2^r) =k n-1 mod n
    // d = n-1 / 2^S (where S means how many time did we divide the number till we reached the first odd number)
    // S: see above
    // r = {0,... S-1}

    int a = 2;
    int d = n - 1;
    int S = 0;
    int r = S - 1; // this stores the number of elements from 0 to S-1

    while (d % 2 == 0) {
        d = floor((double)d / 2.0);
        S++;
        printf("%d ", d);
    }
    printf("S: %d", S);
    printf("\n");

    // round 1
    // 1: a^d =k 1 mod n
    int length;
    int *d_binary = dec_to_bin(d, &length);

    if (quick_pow(d_binary, a, n, length) == 1) {
        free(d_binary);
        return true;
    }

    printf("\n\n");
    free(d_binary);
    return false;
}

int main() {
    prime_test(111);
    prime_test(29);
    prime_test(27);

    return 0;
}