-- ---------------------------------------------------------------------------
-- |
-- Module      : Data.Vector.Algorithms.Optimal
-- Copyright   : (c) 2008-2010 Dan Doel
-- Maintainer  : Dan Doel
-- Stability   : Experimental
-- Portability : Portable
--
-- Optimal sorts for very small array sizes, or for small numbers of
-- particular indices in a larger array (to be used, for instance, for
-- sorting a median of 3 values into the lowest position in an array
-- for a median-of-3 quicksort).

-- The code herein was adapted from a C algorithm for optimal sorts
-- of small arrays. The original code was produced for the article
-- /Sorting Revisited/ by Paul Hsieh, available here:
--

--
-- the reference C code.

module Data.Vector.Algorithms.Optimal
( sort2ByIndex
, sort2ByOffset
, sort3ByIndex
, sort3ByOffset
, sort4ByIndex
, sort4ByOffset
, Comparison
) where

import Data.Vector.Generic.Mutable

import Data.Vector.Algorithms.Common (Comparison)

#include "vector.h"

-- | Sorts the elements at the positions 'off' and 'off + 1' in the given
-- array using the comparison.
sort2ByOffset :: (PrimMonad m, MVector v e)
=> Comparison e -> v (PrimState m) e -> Int -> m ()
sort2ByOffset cmp a off = sort2ByIndex cmp a off (off + 1)
{-# INLINABLE sort2ByOffset #-}

-- | Sorts the elements at the two given indices using the comparison. This
-- is essentially a compare-and-swap, although the first index is assumed to
-- be the 'lower' of the two.
sort2ByIndex :: (PrimMonad m, MVector v e)
=> Comparison e -> v (PrimState m) e -> Int -> Int -> m ()
sort2ByIndex cmp a i j = UNSAFE_CHECK(checkIndex) "sort2ByIndex" i (length a)
\$ UNSAFE_CHECK(checkIndex) "sort2ByIndex" j (length a) \$  do
case cmp a0 a1 of
GT -> unsafeWrite a i a1 >> unsafeWrite a j a0
_  -> return ()
{-# INLINABLE sort2ByIndex #-}

-- | Sorts the three elements starting at the given offset in the array.
sort3ByOffset :: (PrimMonad m, MVector v e)
=> Comparison e -> v (PrimState m) e -> Int -> m ()
sort3ByOffset cmp a off = sort3ByIndex cmp a off (off + 1) (off + 2)
{-# INLINABLE sort3ByOffset #-}

-- | Sorts the elements at the three given indices. The indices are assumed
-- to be given from lowest to highest, so if 'l < m < u' then
-- 'sort3ByIndex cmp a m l u' essentially sorts the median of three into the
-- lowest position in the array.
sort3ByIndex :: (PrimMonad m, MVector v e)
=> Comparison e -> v (PrimState m) e -> Int -> Int -> Int -> m ()
sort3ByIndex cmp a i j k = UNSAFE_CHECK(checkIndex) "sort3ByIndex" i (length a)
\$ UNSAFE_CHECK(checkIndex) "sort3ByIndex" j (length a)
\$ UNSAFE_CHECK(checkIndex) "sort3ByIndex" k (length a) \$ do
case cmp a0 a1 of
GT -> case cmp a0 a2 of
GT -> case cmp a2 a1 of
LT -> do unsafeWrite a i a2
unsafeWrite a k a0
_  -> do unsafeWrite a i a1
unsafeWrite a j a2
unsafeWrite a k a0
_  -> do unsafeWrite a i a1
unsafeWrite a j a0
_  -> case cmp a1 a2 of
GT -> case cmp a0 a2 of
GT -> do unsafeWrite a i a2
unsafeWrite a j a0
unsafeWrite a k a1
_  -> do unsafeWrite a j a2
unsafeWrite a k a1
_  -> return ()
{-# INLINABLE sort3ByIndex #-}

-- | Sorts the four elements beginning at the offset.
sort4ByOffset :: (PrimMonad m, MVector v e)
=> Comparison e -> v (PrimState m) e -> Int -> m ()
sort4ByOffset cmp a off = sort4ByIndex cmp a off (off + 1) (off + 2) (off + 3)
{-# INLINABLE sort4ByOffset #-}

-- The horror...

-- | Sorts the elements at the four given indices. Like the 2 and 3 element
-- versions, this assumes that the indices are given in increasing order, so
-- it can be used to sort medians into particular positions and so on.
sort4ByIndex :: (PrimMonad m, MVector v e)
=> Comparison e -> v (PrimState m) e -> Int -> Int -> Int -> Int -> m ()
sort4ByIndex cmp a i j k l = UNSAFE_CHECK(checkIndex) "sort4ByIndex" i (length a)
\$ UNSAFE_CHECK(checkIndex) "sort4ByIndex" j (length a)
\$ UNSAFE_CHECK(checkIndex) "sort4ByIndex" k (length a)
\$ UNSAFE_CHECK(checkIndex) "sort4ByIndex" l (length a) \$ do
case cmp a0 a1 of
GT -> case cmp a0 a2 of
GT -> case cmp a1 a2 of
GT -> case cmp a1 a3 of
GT -> case cmp a2 a3 of
GT -> do unsafeWrite a i a3
unsafeWrite a j a2
unsafeWrite a k a1
unsafeWrite a l a0
_  -> do unsafeWrite a i a2
unsafeWrite a j a3
unsafeWrite a k a1
unsafeWrite a l a0
_  -> case cmp a0 a3 of
GT -> do unsafeWrite a i a2
unsafeWrite a j a1
unsafeWrite a k a3
unsafeWrite a l a0
_  -> do unsafeWrite a i a2
unsafeWrite a j a1
unsafeWrite a k a0
unsafeWrite a l a3
_ -> case cmp a2 a3 of
GT -> case cmp a1 a3 of
GT -> do unsafeWrite a i a3
unsafeWrite a j a1
unsafeWrite a k a2
unsafeWrite a l a0
_  -> do unsafeWrite a i a1
unsafeWrite a j a3
unsafeWrite a k a2
unsafeWrite a l a0
_  -> case cmp a0 a3 of
GT -> do unsafeWrite a i a1
unsafeWrite a j a2
unsafeWrite a k a3
unsafeWrite a l a0
_  -> do unsafeWrite a i a1
unsafeWrite a j a2
unsafeWrite a k a0
-- unsafeWrite a l a3
_  -> case cmp a0 a3 of
GT -> case cmp a1 a3 of
GT -> do unsafeWrite a i a3
-- unsafeWrite a j a1
unsafeWrite a k a0
unsafeWrite a l a2
_  -> do unsafeWrite a i a1
unsafeWrite a j a3
unsafeWrite a k a0
unsafeWrite a l a2
_  -> case cmp a2 a3 of
GT -> do unsafeWrite a i a1
unsafeWrite a j a0
unsafeWrite a k a3
unsafeWrite a l a2
_  -> do unsafeWrite a i a1
unsafeWrite a j a0
-- unsafeWrite a k a2
-- unsafeWrite a l a3
_  -> case cmp a1 a2 of
GT -> case cmp a0 a2 of
GT -> case cmp a0 a3 of
GT -> case cmp a2 a3 of
GT -> do unsafeWrite a i a3
unsafeWrite a j a2
unsafeWrite a k a0
unsafeWrite a l a1
_  -> do unsafeWrite a i a2
unsafeWrite a j a3
unsafeWrite a k a0
unsafeWrite a l a1
_  -> case cmp a1 a3 of
GT -> do unsafeWrite a i a2
unsafeWrite a j a0
unsafeWrite a k a3
unsafeWrite a l a1
_  -> do unsafeWrite a i a2
unsafeWrite a j a0
unsafeWrite a k a1
-- unsafeWrite a l a3
_  -> case cmp a2 a3 of
GT -> case cmp a0 a3 of
GT -> do unsafeWrite a i a3
unsafeWrite a j a0
-- unsafeWrite a k a2
unsafeWrite a l a1
_  -> do -- unsafeWrite a i a0
unsafeWrite a j a3
-- unsafeWrite a k a2
unsafeWrite a l a1
_  -> case cmp a1 a3 of
GT -> do -- unsafeWrite a i a0
unsafeWrite a j a2
unsafeWrite a k a3
unsafeWrite a l a1
_  -> do -- unsafeWrite a i a0
unsafeWrite a j a2
unsafeWrite a k a1
-- unsafeWrite a l a3
_  -> case cmp a1 a3 of
GT -> case cmp a0 a3 of
GT -> do unsafeWrite a i a3
unsafeWrite a j a0
unsafeWrite a k a1
unsafeWrite a l a2
_  -> do -- unsafeWrite a i a0
unsafeWrite a j a3
unsafeWrite a k a1
unsafeWrite a l a2
_  -> case cmp a2 a3 of
GT -> do -- unsafeWrite a i a0
-- unsafeWrite a j a1
unsafeWrite a k a3
unsafeWrite a l a2
_  -> do -- unsafeWrite a i a0
-- unsafeWrite a j a1
-- unsafeWrite a k a2
-- unsafeWrite a l a3
return ()
{-# INLINABLE sort4ByIndex #-}