Which is faster: x*x or x**2?

Question

I am trying to optimize my Python code. Between:

y = x*x

or

y = x**2

if I need one trillion iterations in a speed-critical program, which one should I choose?

Staford

@ChrisHayes: I actually done it for Gauss-Legendre Algorithm in python. At the time x*x was faster than x**2. – Photogene

@TonyHopkinson Python is used in a lot of scientific computing, despite being agonizingly slow (usually it is used to call optimized libraries like numpy). – Improvised

You ever see the code the mathmeticians and engineers write? Microoptimisation is the least of their problems. :( – Separable

@roippi et al. even after more than 4 years, I'm yet to understand why this question is "off-topic". Someone plz enlighten me or remove the "off-topic" honor. – Staford

This seems like a legitimate question. On Python 3.6, x*x is about 3.5x faster than x**2. Although lines of opcodes are equal via dis module, the implementations differ. In CPython ceval.c, x*x uses PyNumber_Multiply and binary_op1 while x**2 uses PyNumber_Power and ternary_op. It's not clear to me where the slow down occurs, but the latter is more complex. – Kathikathiawar

Answer 1

x**2 is faster than x*x.

Implementation of exponent has some overhead in Python, so it is usually faster to use your custom multiplication O(n) with small multiplication count. x*x*x*x*x is way faster than x**5. Exponent time is a sort of constant. Your multiplication time is increasing with exponent parameter, so with a large parameter it is better to use exponent. However, with really very small parameter (2, in your case), exponent is faster than multiplication. And x**2 is faster than x*x, although x**3 is way slower than x*x*x. You can find a nice benchmark in this answer.

Gauntry

x*x can be faster than x**2. It seems you meant the reverse of what you said. – Photogene

x**2 is a special case, and the speed difference in my tests was pretty small. So I guess it can also depend on x. – Gauntry