import math
from timeit import timeit


def num_digits(n: int) -> int:
    """
    Find the number of digits in a number.

    >>> num_digits(12345)
    5
    >>> num_digits(123)
    3
    """
    digits = 0
    while n > 0:
        n = n // 10
        digits += 1
    return digits


def num_digits_fast(n: int) -> int:
    """
    Find the number of digits in a number.
    abs() is used as logarithm for negative numbers is not defined.

    >>> num_digits_fast(12345)
    5
    >>> num_digits_fast(123)
    3
    """
    return (math.floor(math.log(abs(n), 10) + 1))


def num_digits_faster(n: int) -> int:
    """
    Find the number of digits in a number.
    abs() is used for negative numbers

    >>> num_digits_faster(12345)
    5
    >>> num_digits_faster(123)
    3
    """
    return (len(str(abs(n))))


def benchmark() -> None:
    """
    Benchmark code for comparing 3 functions,
    with 3 different length int values.
    """
    print('\nFor small_num = ', small_num, ':')
    print("> num_digits()",
          '\t\tans =', num_digits(small_num),
          '\ttime =', timeit("z.num_digits(z.small_num)",
                             setup="import __main__ as z"), "seconds")
    print("> num_digits_fast()",
          '\tans =', num_digits_fast(small_num),
          '\ttime =', timeit("z.num_digits_fast(z.small_num)",
                             setup="import __main__ as z"), "seconds")
    print("> num_digits_faster()",
          '\tans =', num_digits_faster(small_num),
          '\ttime =', timeit("z.num_digits_faster(z.small_num)",
                             setup="import __main__ as z"), "seconds")

    print('\nFor medium_num = ', medium_num, ':')
    print("> num_digits()",
          '\t\tans =', num_digits(medium_num),
          '\ttime =', timeit("z.num_digits(z.medium_num)",
                             setup="import __main__ as z"), "seconds")
    print("> num_digits_fast()",
          '\tans =', num_digits_fast(medium_num),
          '\ttime =', timeit("z.num_digits_fast(z.medium_num)",
                             setup="import __main__ as z"), "seconds")
    print("> num_digits_faster()",
          '\tans =', num_digits_faster(medium_num),
          '\ttime =', timeit("z.num_digits_faster(z.medium_num)",
                             setup="import __main__ as z"), "seconds")

    print('\nFor large_num = ', large_num, ':')
    print("> num_digits()",
          '\t\tans =', num_digits(large_num),
          '\ttime =', timeit("z.num_digits(z.large_num)",
                             setup="import __main__ as z"), "seconds")
    print("> num_digits_fast()",
          '\tans =', num_digits_fast(large_num),
          '\ttime =', timeit("z.num_digits_fast(z.large_num)",
                             setup="import __main__ as z"), "seconds")
    print("> num_digits_faster()",
          '\tans =', num_digits_faster(large_num),
          '\ttime =', timeit("z.num_digits_faster(z.large_num)",
                             setup="import __main__ as z"), "seconds")


if __name__ == "__main__":
    small_num = 262144
    medium_num = 1125899906842624
    large_num = 1267650600228229401496703205376
    benchmark()