"""Tests for factor.py"""
import random
from factor import is_prime, factor, totient


def _trial_prime(n):
    if n < 2:
        return False
    if n < 4:
        return True
    if n % 2 == 0:
        return False
    i = 3
    while i * i <= n:
        if n % i == 0:
            return False
        i += 2
    return True


def test_small_primes():
    for n in range(2, 3000):
        assert is_prime(n) == _trial_prime(n), n


def test_carmichaels():
    for c in [561, 1105, 1729, 2465, 2821, 6601, 8911, 10585, 15841, 29341, 41041, 46657, 52633, 62745, 63973]:
        assert not is_prime(c), c


def test_large_known_primes():
    for p in [2**31 - 1, 2**61 - 1, 999999999999999989, 32416190071]:
        assert is_prime(p), p


def test_factor_small():
    for n in range(2, 1000):
        fs = factor(n)
        prod = 1
        for f in fs:
            prod *= f
            assert is_prime(f)
        assert prod == n
        assert fs == sorted(fs)


def test_factor_random_large():
    random.seed(42)
    for _ in range(300):
        def rnd_prime(lo, hi):
            while True:
                x = random.randrange(lo, hi)
                if is_prime(x):
                    return x
        a = rnd_prime(1000, 100000)
        b = rnd_prime(1000, 100000)
        n = a * b
        fs = factor(n)
        assert sorted(fs) == sorted([a, b]), (n, fs)


def test_factor_powers():
    for base in [2, 3, 5, 7, 11]:
        for e in [1, 2, 3, 5, 8, 12]:
            n = base ** e
            fs = factor(n)
            assert fs == [base] * e


def test_totient():
    assert totient(1) == 1
    assert totient(2) == 1
    assert totient(10) == 4
    assert totient(12) == 4
    assert totient(30) == 8


def test_edge():
    assert factor(0) == []
    assert factor(1) == []
    assert factor(-12) == [2, 2, 3]
    assert is_prime(0) is False
    assert is_prime(1) is False
    assert is_prime(2) is True
    assert is_prime(999999999999999937 * 2) is False