Copyright | (c) 2011-2014 Daniel Fischer |
---|---|

License | MIT |

Maintainer | Daniel Fischer <daniel.is.fischer@googlemail.com> |

Stability | Provisional |

Portability | Non-portable (GHC extensions) |

Safe Haskell | Safe |

Language | Haskell2010 |

## Synopsis

- naturalPower :: Natural -> Int -> Natural
- naturalWordPower :: Natural -> Word -> Natural

# Documentation

naturalPower :: Natural -> Int -> 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.

naturalWordPower :: Natural -> Word -> Natural #

Same as `naturalPower`

, but for exponents of type `Word`

.