Discrete inverse factorial, with "floor" and "round" rounding-modes

inv!.py

def factorial(n: int):
	if n < 0:
		raise ValueError('undefined')
	out = 1
	while n >= 1:
		out *= n
		n -= 1
	return out

def inv_factorial(n: int, round: bool):
	'''
	if `round` is `False`, floors instead
	'''
	if n <= 0:
		raise ValueError('undefined')
	# solutions of x! = x: 1, 2.
	# solutions of x! = 1: 0, 1.
	if n <= 2:
		return n
	i = 2
	while True:
		n //= i
		if n <= (1 if round else i):
			return i
		i += 1

def tests():
	for i, v in enumerate((1, 1, 2, 6, 24, 120)):
		assert factorial(i) == v
	for i in range(1, 1 << 8, 1):
		assert inv_factorial(factorial(i), False) == i
		assert inv_factorial(factorial(i), True) == i

tests()

# LICENSE: https://unlicense.org