Algorithms: Number Theory

int factorial(int n) {
    int alg_error = 0;
    int alg_result = INT_MIN;
    errno = 0;
    if (!(((n >= 0) && (n <= 1000000)))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    if (!(((n >= 0) && (n <= 12)))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int result = 1;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int i = 2;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }

def factorial(n: int) -> int:
    alg_require(type(n) is int and -2147483648 <= n <= 2147483647)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(n >= 0 and n <= 12)
    result: int = 1
    i: int = 2
    while i <= n:
        result *= i
        i += 1
    return result

n = 0

function gcd(int $a, int $b): int {
    alg_require((($a >= 0) && ($b >= 0)));
    $remainder = 0;
    while (($b != 0)) {
        $remainder = ($a % $b);
        $a = $b;
        $b = $remainder;
    }
    return $a;
}

$a = 48;

    static int factorial(int n) {
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require(((n >= 0) && (n <= 12)));
        int result = 1;
        int i = 2;
        while ((i <= n)) {
            result = Math.multiplyExact(result, i);
            i = Math.addExact(i, 1);
        }
        return result;
    }

function factorial(n) {
    alg_require(Number.isInteger(n) && n >= -2147483648 && n <= 2147483647);
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((n >= 0) && (n <= 12)));
    let result = 1;
    let i = 2;
    while ((i <= n)) {
        result = alg_mul(result, i);
        i = alg_add(i, 1);
    }
    return result;
}