```{-# LANGUAGE CPP, FlexibleContexts, Rank2Types #-}
-- |
-- Module    : Statistics.Function
-- Copyright : (c) 2009, 2010, 2011 Bryan O'Sullivan
--
-- 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
#if WORD_SIZE_IN_BITS == 64
= 1 + _i32
#else
= 1 + i16
#endif
where
i0   = n - 1
i1   = i0  .|. i0  `shiftR` 1
i2   = i1  .|. i1  `shiftR` 2
i4   = i2  .|. i2  `shiftR` 4
i8   = i4  .|. i4  `shiftR` 8
i16  = i8  .|. i8  `shiftR` 16
_i32 = i16 .|. i16 `shiftR` 32
-- It could be implemented as
--
-- > nextHighestPowerOfTwo n = 1 + foldl' go (n-1) [1, 2, 4, 8, 16, 32]
--     where go m i = m .|. m `shiftR` i
--
-- But GHC do not inline foldl (probably because it's recursive) and
-- as result function walks list of boxed ints. Hand rolled version
-- uses unboxed arithmetic.
```