Python3确定对数是否“完美”，即浮点数没有余数

Question

Problem statement:

I am trying to determine if a logarithm is "perfect," ie, there is no remainder. The issue I am having is that math.log() always returns a float.

I read this: https://docs.python.org/3/tutorial/floatingpoint.html

Here is my current solution:

import sys
import math


def is_even_log(argument, base):
    x = math.log(argument, base)  # yields float

    numerator, denominator = x.as_integer_ratio()

    print(
        f"numeratorerator: {numerator}, "
        f"denominatorominator: {denominator}")

    if numerator % denominator == 0:
        print(f"Log base {base} of {argument} is even")
        return True
    else:
        print(f"Log base {base} of {argument} is not even")
        return False


is_even_log(int(sys.argv[1]), int(sys.argv[2]))

Question

Just curious if anyone has better way to do this? I would imagine that I could access some property of the PyObject which indicates if there is a remainder or not.

Answer 1

You can round the logarithm to the nearest integer, and check if it's correct by exponentiating back up again:

def is_even_log(argument, base):
    return argument == base**round(math.log(argument, base))

Answer 2

Log b in base i equals x is equivalent to b equals i to the power x. So the code would be:

def is_even_log(arg, base):
    x = math.log(arg, base)
    return arg == base ** int(x+1/2) 

As the int function returns the truncation of a float, int(x+1/2) returns the rounded number. This solution works for integers (both arg and base) because in this case the if statement is a comparaison between integers

Testing the equality of floats is not recommended anyways because of the approximations.