arithmoi- Efficient basic number-theoretic functions. Primes, powers, integer logarithms.

PortabilityNon-portable (GHC extensions)
MaintainerDaniel Fischer <>
Safe HaskellNone



Potentially faster power function for Integer base and Int or Word exponent.



integerPower :: Integer -> Int -> IntegerSource

Power of an Integer by the left-to-right repeated squaring algorithm. This needs two multiplications in each step while the right-to-left algorithm needs only one multiplication for 0-bits, but here the two factors always have approximately the same size, which on average gains a bit when the result is large.

For small results, it is unlikely to be any faster than '(^)', quite possibly slower (though the difference shouldn't be large), and for exponents with few bits set, the same holds. But for exponents with many bits set, the speedup can be significant.

Warning: No check for the negativity of the exponent is performed, a negative exponent is interpreted as a large positive exponent.

integerWordPower :: Integer -> Word -> IntegerSource

Same as integerPower, but for exponents of type Word.