The (^) operator sometimes uses one (*) more than needed.

The implementation of integer exponentiation is suboptimal. By inserting a trace in (*) you can easily observe that, e.g., exponent 4 uses 3 multiplications instead of 2.

Here's a different version:

(^)		:: (Num a, Integral b) => a -> b -> a
_ ^ 0		=  1
x ^ n | n > 0	=  g x n
		   where g b i | even i  = g (b*b) (i `quot` 2)
			       | otherwise = f b (i-1) b
                         f _ 0 y = y
		         f a d y | even d = f (a*a) (d `quot` 2) y
                                 | otherwise = f a (d-1) (a * y)
_ ^ _		= error "Prelude.^: negative exponent"

Trac metadata

Trac field	Value
Version	6.8.2
Type	Bug
TypeOfFailure	OtherFailure
Priority	normal
Resolution	Unresolved
Component	Prelude
Test case
Differential revisions
BlockedBy
Related
Blocking
CC	lennart.augustsson@credit-suisse.com
Operating system	Unknown
Architecture	Unknown