    {-# LANGUAGE CPP, FlexibleContexts, Rank2Types #-}
    -- |
    -- Module    : Statistics.Function
    -- Copyright : (c) 2009, 2010, 2011 Bryan O'Sullivan
    -- License   : BSD3
    --
    -- Maintainer  : bos@serpentine.com
    -- Stability   : experimental
    -- Portability : portable
    --
    -- Useful functions.

    module Statistics.Function
        (
        -- * Scanning
          minMax
        -- * Sorting
        , sort
        , sortBy
        , partialSort
        -- * Indexing
        , indexed
        , indices
        -- * Bit twiddling
        , nextHighestPowerOfTwo
        -- * Comparison
        , within
        ) where

    #include "MachDeps.h"

    import Data.Bits ((.|.), shiftR)
    import qualified Data.Vector.Algorithms.Intro as I
    import qualified Data.Vector.Generic as G
    import Statistics.Function.Comparison (within)

    -- | Sort a vector.
    sort :: (Ord e, G.Vector v e) => v e -> v e
    sort = G.modify I.sort
    {-# INLINE sort #-}

    -- | Sort a vector using a custom ordering.
    sortBy :: (G.Vector v e) => I.Comparison e -> v e -> v e
    sortBy f = G.modify $ I.sortBy f
    {-# INLINE sortBy #-}

    -- | Partially sort a vector, such that the least /k/ elements will be
    -- at the front.
    partialSort :: (G.Vector v e, Ord e) =>
                   Int -- ^ The number /k/ of least elements.
                -> v e
                -> v e
    partialSort k = G.modify (`I.partialSort` k)
    {-# INLINE partialSort #-}

    -- | Return the indices of a vector.
    indices :: (G.Vector v a, G.Vector v Int) => v a -> v Int
    indices a = G.enumFromTo 0 (G.length a - 1)
    {-# INLINE indices #-}

    -- | Zip a vector with its indices.
    indexed :: (G.Vector v e, G.Vector v Int, G.Vector v (Int,e)) => v e -> v (Int,e)
    indexed a = G.zip (indices a) a
    {-# INLINE indexed #-}

    data MM = MM {-# UNPACK #-} !Double {-# UNPACK #-} !Double

    -- | Compute the minimum and maximum of a vector in one pass.
    minMax :: (G.Vector v Double) => v Double -> (Double, Double)
    minMax = fini . G.foldl' go (MM (1/0) (-1/0))
      where
        go (MM lo hi) k = MM (min lo k) (max hi k)
        fini (MM lo hi) = (lo, hi)
    {-# INLINE minMax #-}

    -- | Efficiently compute the next highest power of two for a
    -- non-negative integer.  If the given value is already a power of
    -- two, it is returned unchanged.  If negative, zero is returned.
    nextHighestPowerOfTwo :: Int -> Int
    nextHighestPowerOfTwo n = o + 1
        where m = n - 1
              o = m
                  .|. (m `shiftR` 1)
                  .|. (m `shiftR` 2)
                  .|. (m `shiftR` 4)
                  .|. (m `shiftR` 8)
                  .|. (m `shiftR` 16)
    #if WORD_SIZE_IN_BITS == 64
                  .|. (m `shiftR` 32)
    #endif