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

License | MIT |

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

Stability | Provisional |

Portability | Non-portable (GHC extensions) |

Safe Haskell | None |

Language | Haskell98 |

Functions dealing with cubes. Moderately efficient calculation of integer cube roots and testing for cubeness.

- integerCubeRoot :: Integral a => a -> a
- integerCubeRoot' :: Integral a => a -> a
- exactCubeRoot :: Integral a => a -> Maybe a
- isCube :: Integral a => a -> Bool
- isCube' :: Integral a => a -> Bool
- isPossibleCube :: Integral a => a -> Bool

# Documentation

integerCubeRoot :: Integral a => a -> a Source

Calculate the integer cube root of an integer `n`

,
that is the largest integer `r`

such that `r^3 <= n`

.
Note that this is not symmetric about `0`

, for example
`integerCubeRoot (-2) = (-2)`

while `integerCubeRoot 2 = 1`

.

integerCubeRoot' :: Integral a => a -> a Source

Calculate the integer cube root of a nonnegative integer `n`

,
that is, the largest integer `r`

such that `r^3 <= n`

.
The precondition `n >= 0`

is not checked.

exactCubeRoot :: Integral a => a -> Maybe a Source

Returns `Nothing`

if the argument is not a cube,
`Just r`

if `n == r^3`

.

isCube' :: Integral a => a -> Bool Source

Test whether a nonnegative integer is a cube.
Before `integerCubeRoot`

is calculated, a few tests
of remainders modulo small primes weed out most non-cubes.
For testing many numbers, most of which aren't cubes,
this is much faster than `let r = cubeRoot n in r*r*r == n`

.
The condition `n >= 0`

is *not* checked.

isPossibleCube :: Integral a => a -> Bool Source

Test whether a nonnegative number is possibly a cube.
Only about 0.08% of all numbers pass this test.
The precondition `n >= 0`

is *not* checked.