    -- |
    -- Module:      Math.NumberTheory.Powers.Natural
    -- Copyright:   (c) 2011-2014 Daniel Fischer
    -- Licence:     MIT
    -- Maintainer:  Daniel Fischer <daniel.is.fischer@googlemail.com>
    -- Stability:   Provisional
    -- Portability: Non-portable (GHC extensions)
    --
    -- Potentially faster power function for 'Natural' base and 'Int'
    -- or 'Word' exponent.
    --
    {-# LANGUAGE Safe #-}
    module Math.NumberTheory.Powers.Natural
        {-# DEPRECATED "It is no faster than (^)" #-}
        ( naturalPower
        , naturalWordPower
        ) where

    import Numeric.Natural (Natural)

    -- | Power of an 'Natural' 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.
    naturalPower :: Natural -> Int -> Natural
    naturalPower :: Natural -> Int -> Natural
    naturalPower = Natural -> Int -> Natural
    forall a b. (Num a, Integral b) => a -> b -> a
    (^)
    {-# DEPRECATED naturalPower "Use (^) instead" #-}

    -- | Same as 'naturalPower', but for exponents of type 'Word'.
    naturalWordPower :: Natural -> Word -> Natural
    naturalWordPower :: Natural -> Word -> Natural
    naturalWordPower = Natural -> Word -> Natural
    forall a b. (Num a, Integral b) => a -> b -> a
    (^)
    {-# DEPRECATED naturalWordPower "Use (^) instead" #-}