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import math

from timeit import timeit

def num_digits(n: int) -> int:

"""

Find the number of digits in a number.

>>> num_digits(12345)

>>> num_digits(123)

>>> num_digits(0)

>>> num_digits(-1)

>>> num_digits(-123456)

>>> num_digits('123') # Raises a TypeError for non-integer input

Traceback (most recent call last):

...

TypeError: Input must be an integer

"""

if not isinstance(n, int):

raise TypeError("Input must be an integer")

digits = 0

n = abs(n)

while True:

n = n // 10

digits += 1

if n == 0:

break

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)

>>> num_digits_fast(123)

>>> num_digits_fast(0)

>>> num_digits_fast(-1)

>>> num_digits_fast(-123456)

>>> num_digits('123') # Raises a TypeError for non-integer input

Traceback (most recent call last):

...

TypeError: Input must be an integer

"""

if not isinstance(n, int):

raise TypeError("Input must be an integer")

return 1 if n == 0 else 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)

>>> num_digits_faster(123)

>>> num_digits_faster(0)

>>> num_digits_faster(-1)

>>> num_digits_faster(-123456)

>>> num_digits('123') # Raises a TypeError for non-integer input

Traceback (most recent call last):

...

TypeError: Input must be an integer

"""

if not isinstance(n, int):

raise TypeError("Input must be an integer")

return len(str(abs(n)))

def benchmark() -> None:

"""

Benchmark multiple functions, with three different length int values.

"""

from collections.abc import Callable

def benchmark_a_function(func: Callable, value: int) -> None:

call = f"{func.__name__}({value})"

timing = timeit(f"__main__.{call}", setup="import __main__")

print(f"{call}: {func(value)} -- {timing} seconds")

for value in (262144, 1125899906842624, 1267650600228229401496703205376):

for func in (num_digits, num_digits_fast, num_digits_faster):

benchmark_a_function(func, value)

print()

if __name__ == "__main__":

import doctest

doctest.testmod()

benchmark()

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