Efficient way to compute p^q (exponentiation), where q is an integer

Question

What is an efficient way to compute p^q, where q is an integer?

Answer 1

I assume by ^ you mean power function, and not bitwise xor.

The development of an efficient power function for any type of p and any positive integral q is the subject of an entire section, 3.2, in Stepanov's and McJones's book Elements of Programming. The language in the book is not C++, but is very easily translated into C++.

It covers several optimizations, including exponentiation by squaring, conversion to tail recursion then iteration, and accumulation-variable elimination, and relates the optimizations to the notions of type regularity and associative operations to prove it works for all such types.