Number of Digits

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A
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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)
5
>>> num_digits(123)
3
>>> num_digits(0)
1
>>> num_digits(-1)
1
>>> num_digits(-123456)
6
"""
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)
5
>>> num_digits_fast(123)
3
>>> num_digits_fast(0)
1
>>> num_digits_fast(-1)
1
>>> num_digits_fast(-123456)
6
"""
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)
5
>>> num_digits_faster(123)
3
>>> num_digits_faster(0)
1
>>> num_digits_faster(-1)
1
>>> num_digits_faster(-123456)
6
"""
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()
```