#!/usr/bin/env python3
"""Functional Python Programming
Chapter 12, Example Set 1
"""
import math
def some_function(n: float) -> float:
"""
An approximation of the gamma function.
>>> round(some_function(4), 3)
24.0
"""
s = sum(
(
1,
1/((2**1)*(6*n)**1),
1/((2**3)*(6*n)**2),
-139/((2**3)*(2*3*5)*(6*n)**3),
-571/((2**6)*(2*3*5)*(6*n)**4),
)
)
return math.sqrt(2*math.pi*n)*(n/math.e)**n*s
def test():
import doctest
doctest.testmod()
def performance():
import dis
dis.disassemble(some_function.__code__)
size = len(some_function.__code__.co_code)
print(f"size {size} bytes")
import timeit
t = timeit.timeit(
"""some_function(4)""",
"""from Chapter_12.ch12_ex1 import some_function"""
)
print(f"total time {t:.3f} sec. for 1,000,000 iterations")
rate = 1_000_000*size/t
print(f"rate {rate:,.0f} bytes/sec")
print(f"rate {rate/1_000_000:,.1f} Mbytes/sec")
if __name__ == "__main__":
test()
performance()
