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maths/number_of_digits.py: Streamline benchmarks (#7913)

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* maths/number_of_digits.py: Streamline benchmarks

```
num_digits(262144): 6 -- 0.2226011250168085 seconds
num_digits_fast(262144): 6 -- 0.13145116699161008 seconds
num_digits_faster(262144): 6 -- 0.09273383300751448 seconds

num_digits(1125899906842624): 16 -- 0.6056742920191027 seconds
num_digits_fast(1125899906842624): 16 -- 0.15698366600554436 seconds
num_digits_faster(1125899906842624): 16 -- 0.1027024170034565 seconds

num_digits(1267650600228229401496703205376): 31 -- 1.1957934170495719 seconds
num_digits_fast(1267650600228229401496703205376): 31 -- 0.15552304196171463 seconds
num_digits_faster(1267650600228229401496703205376): 31 -- 0.13062308297958225 seconds
```

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* Update number_of_digits.py

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maths/number_of_digits.py
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@ -67,93 +67,23 @@ def num_digits_faster(n: int) -> int:
def benchmark() -> None:
"""
Benchmark code for comparing 3 functions,
with 3 different length int values.
Benchmark multiple functions, with three 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",
)
from collections.abc import Callable
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",
)
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")
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",
)
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__":
small_num = 262144
medium_num = 1125899906842624
large_num = 1267650600228229401496703205376
benchmark()
import doctest
doctest.testmod()
benchmark()