Exponentials in python x.**y vs math.pow(x, y)

Question

Which one is more efficient using math.pow or the ** operator? When should I use one over the other?

So far I know that x**y can return an int

Answer 1

Just for the protocol: The ** operator calls the built-in pow function which accepts an optional third argument (modulus) if the first two arguments are integer types.

So, if you intend to calculate remainders from powers, use the built-in function. The math.pow may give you false results:

import math

base = 13
exp = 100
mod = 2
print math.pow(base, exp) % mod
print pow(base, exp, mod)

When I ran this, I got 0.0 in the first case which obviously cannot be true, because 13 is odd (and therefore all of it's integral powers). The math.pow version uses limited accuracy which causes an error.

For sake of fairness, we must say, math.pow can be much faster:

import timeit
print timeit.timeit("math.pow(2, 100)",setup='import math')
print timeit.timeit("pow(2, 100)")

Here is what I'm getting as output:

0.240936803195
1.4775809183

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Some online examples

• http://ideone.com/qaDWRd (wrong remainder with math.pow)
• http://ideone.com/g7J9Un (lower performance with pow on int values)
• http://ideone.com/KnEtXj (slightly lower performance with pow on float values)