#include "rsa.h"
#include "rand.h"
#include <stdbool.h>
#include <stdint.h>

#define NULL ((void *)0)

uint64_t gcd(uint64_t a, uint64_t b) {
    return extended_euclid(a, b, NULL, NULL);
}

int extended_euclid(int a, int b, int *x, int *y) {
    if (b == 0) {
        if (x)
            *x = 1;
        if (y)
            *y = 0;
        return a;
    }

    int x1, y1;
    int gcd = extended_euclid(b, a % b, &x1, &y1);

    if (x)
        *x = y1;
    if (y)
        *y = x1 - (a / b) * y1;

    return gcd;
}

int totient(int n) {
    int result = n;

    // Check for prime factors
    for (int p = 2; p * p <= n; p++) {
        if (n % p == 0) {
            // If p is a prime factor of n, remove all occurrences of p
            while (n % p == 0) {
                n /= p;
            }
            result -= result / p;
        }
    }

    // If n is still greater than 1, then it's a prime factor itself
    if (n > 1) {
        result -= result / n;
    }

    return result;
}

uint64_t mulmod(uint64_t a, uint64_t b, uint64_t m) {
    uint64_t result = 0;
    a %= m;

    while (b > 0) {
        if (b & 1) {
            result = (result + a) % m; // Avoid overflow
        }
        a = (a * 2) % m; // Double a, keep within mod
        b >>= 1;
    }

    return result;
}

uint64_t modexp(uint64_t a, uint64_t b, uint64_t m) {
    uint64_t result = 1;
    a %= m;

    while (b > 0) {
        if (b & 1) {
            result = mulmod(result, a, m);
        }
        b >>= 1;
        a = mulmod(a, a, m);
    }

    return result;
}

uint64_t gen_prime(uint64_t min, uint64_t max) {
    uint64_t cand = 0;
    while (!miller_rabin(cand, 10)) cand = prand_range(min, max);

    return cand;
}

bool is_prime(int n) {
    if (n < 2)
        return false;

    for (int i = 2; i < n / 2 + 1; i++) {
        if (n % i == 0)
            return false;
    }

    return true;
}

bool miller_rabin(uint64_t n, uint64_t k) {
    if (n < 2)
        return false;

    uint64_t d = n - 1;
    uint64_t s = 0;

    while (d % 2 == 0) {
        d /= 2;
        s++;
    }

    for (uint64_t i = 0; i < k; i++) {
        uint64_t a = prand_range(2, n - 2);
        uint64_t x = modexp(a, d, n);

        if (x == 1 || x == n - 1)
            continue;

        for (uint64_t r = 1; r < s; r++) {
            x = modexp(x, 2, n);
            if (x == n - 1)
                break;
        }

        if (x != n - 1)
            return false; // Not prime
    }

    return true; // Likely prime
}

uint64_t mod_inverse(uint64_t a, uint64_t m) {
    uint64_t m0 = m;
    uint64_t y = 0, x = 1;

    if (m == 1)
        return 0;

    while (a > 1) {
        // q is quotient
        uint64_t q = a / m;
        uint64_t t = m;

        // m is remainder now
        m = a % m;
        a = t;
        t = y;

        // Update x and y
        y = x - q * y;
        x = t;
    }

    // Make x positive
    if (x < 0)
        x += m0;

    return x;
}