Zobrist.hs

{-
	Copyright (C) 2018 Dr. Alistair Ward

	This file is part of BishBosh.

	BishBosh is free software: you can redistribute it and/or modify
	it under the terms of the GNU General Public License as published by
	the Free Software Foundation, either version 3 of the License, or
	(at your option) any later version.

	BishBosh is distributed in the hope that it will be useful,
	but WITHOUT ANY WARRANTY; without even the implied warranty of
	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
	GNU General Public License for more details.

	You should have received a copy of the GNU General Public License
	along with BishBosh.  If not, see <http://www.gnu.org/licenses/>.
-}
{- |
 [@AUTHOR@]	Dr. Alistair Ward

 [@DESCRIPTION@]

	* <https://www.chessprogramming.org/Zobrist_Hashing>.

	* Defines the random-numbers required to construct a hash of a chess-position.

	* Facilitates the construction of a hash from arbitrary data.
-}

module BishBosh.Component.Zobrist(
-- * Types
-- ** Type-synonyms
--	Index,
-- ** Data-types
	Zobrist(
--		MkZobrist,
		getRandomForBlacksMove
--		getRandomByCoordinatesByRankByLogicalColour,
--		getRandomByCastleableRooksXByLogicalColour,
--		getRandomByEnPassantAbscissa
	),
-- * Functions
--	measureHammingDistances,
	dereferenceRandomByCoordinatesByRankByLogicalColour,
	dereferenceRandomByCastleableRooksXByLogicalColour,
	dereferenceRandomByEnPassantAbscissa,
-- ** Constructors
	mkZobrist
) where

import			Control.Arrow((***))
import			Data.Array.IArray((!))
import qualified	BishBosh.Attribute.Rank		as Attribute.Rank
import qualified	BishBosh.Cartesian.Abscissa	as Cartesian.Abscissa
import qualified	BishBosh.Cartesian.Coordinates	as Cartesian.Coordinates
import qualified	BishBosh.Colour.LogicalColour	as Colour.LogicalColour
import qualified	BishBosh.Data.Exception		as Data.Exception
import qualified	BishBosh.Type.Length		as Type.Length
import qualified	Control.Exception
import qualified	Data.Array.IArray
import qualified	Data.Bits
import qualified	Data.Default
import qualified	Data.Foldable
import qualified	System.Random
import qualified	ToolShed.System.Random

-- | Used as an index into 'getRandomByCoordinatesByRankByLogicalColour'.
type Index	= (Colour.LogicalColour.LogicalColour, Attribute.Rank.Rank, Cartesian.Coordinates.Coordinates)

-- | The random numbers used to generate a hash, which almost uniquely represent a /position/.
data Zobrist positionHash	= MkZobrist {
	getRandomForBlacksMove				:: positionHash,								-- ^ Defines a random number to apply when the next move is @Black@'s.
	getRandomByCoordinatesByRankByLogicalColour	:: Data.Array.IArray.Array {-Boxed-} Index positionHash,			-- ^ Defines random numbers to represent all combinations of each piece at each coordinate; though @Pawn@s can't exist on the terminal ranks. N.B.: regrettably the array can't be unboxed, because 'Data.Array.Unboxed.UArray' isn't 'Foldable'; cf. 'Data.Array.IArray.Array'.

	getRandomByCastleableRooksXByLogicalColour	:: Colour.LogicalColour.ArrayByLogicalColour [(Type.Length.X, positionHash)],	-- ^ Defines random numbers to represent all combinations of castleable @Rook@s.
	getRandomByEnPassantAbscissa			:: Data.Array.IArray.Array Type.Length.X positionHash				-- ^ Defines random numbers to represent any file on which capture en-passant might be available.
} deriving Show

instance Foldable Zobrist where
	foldr f i MkZobrist {
		getRandomForBlacksMove				= randomForBlacksMove,
		getRandomByCoordinatesByRankByLogicalColour	= randomByCoordinatesByRankByLogicalColour,
		getRandomByCastleableRooksXByLogicalColour	= randomByCastleableRooksXByLogicalColour,
		getRandomByEnPassantAbscissa			= randomByEnPassantAbscissa
	} = Data.Foldable.foldr f (
		Data.Foldable.foldr (
			flip . foldr $ f . snd
		) (
			Data.Foldable.foldr f (
				f randomForBlacksMove i
			) randomByCoordinatesByRankByLogicalColour
		) randomByCastleableRooksXByLogicalColour
	 ) randomByEnPassantAbscissa

instance (
	Data.Bits.FiniteBits	positionHash,
	System.Random.Random	positionHash
 ) => Data.Default.Default (Zobrist positionHash) where
	def	= mkZobrist Nothing $ System.Random.mkStdGen 0

{- |
	* <https://www.chessprogramming.org/Population_Count#HammingDistance>.

	* Quantifies the Hamming distance between all combinations of pairs of the random numbers used to compose hashes.

	* CAVEAT: <https://en.wikipedia.org/wiki/Linear_independence> a better measure of the suitability of the selected random numbers
-}
measureHammingDistances :: Data.Bits.Bits positionHash => Zobrist positionHash -> [Int]
measureHammingDistances	= map (Data.Bits.popCount . uncurry Data.Bits.xor) . getCombinations . Data.Foldable.toList where
	getCombinations :: [a] -> [(a, a)]
	getCombinations (x : remainder)	= map ((,) x) remainder ++ getCombinations remainder	-- CAVEAT: O(n^2) time-complexity.
	getCombinations _		= []

-- | Smart constructor.
mkZobrist :: (
	Data.Bits.FiniteBits	positionHash,
	System.Random.RandomGen randomGen,
	System.Random.Random	positionHash
 )
	=> Maybe Int	-- ^ The optional minimum acceptable Hamming-distance between any two of the selected random numbers.
	-> randomGen
	-> Zobrist positionHash
mkZobrist maybeMinimumHammingDistance randomGen
	| Just minimumHammingDistance <- maybeMinimumHammingDistance
	, let minimumHammingDistance'	= minimum $ measureHammingDistances zobrist
	, minimumHammingDistance' < minimumHammingDistance	= Control.Exception.throw . Data.Exception.mkRequestFailure . showString "BishBosh.Component.Zobrist.mkZobrist:\tthe minimum Hamming-distance between the selected random numbers doesn't reach the configured minimum " . shows (minimumHammingDistance', minimumHammingDistance) . showString " => use more than " $ shows (Data.Bits.finiteBitSize randomForBlacksMove) " bits, or re-seed the generator & hope."
	| otherwise						= zobrist
	where
		((randomForBlacksMove, randomByCoordinatesByRankByLogicalColour), (randomByCastleableRooksXByLogicalColour, randomByEnPassantAbscissa))	= (
			(
				head . System.Random.randoms *** Data.Array.IArray.listArray (minBound, maxBound) . System.Random.randoms
			) . System.Random.split
		 ) *** (
			(
				Colour.LogicalColour.listArrayByLogicalColour . map (
					zip [Cartesian.Abscissa.xMin, Cartesian.Abscissa.xMax] . System.Random.randoms
				) . ToolShed.System.Random.randomGens *** Cartesian.Abscissa.listArrayByAbscissa . System.Random.randoms
			) . System.Random.split
		 ) $ System.Random.split randomGen

		zobrist	= MkZobrist {
			getRandomForBlacksMove				= randomForBlacksMove,
			getRandomByCoordinatesByRankByLogicalColour	= randomByCoordinatesByRankByLogicalColour,
			getRandomByCastleableRooksXByLogicalColour	= randomByCastleableRooksXByLogicalColour,
			getRandomByEnPassantAbscissa			= randomByEnPassantAbscissa
		}

-- | Dereferences 'getRandomByCoordinatesByRankByLogicalColour' using the specified index.
dereferenceRandomByCoordinatesByRankByLogicalColour :: Zobrist positionHash -> Index -> positionHash
dereferenceRandomByCoordinatesByRankByLogicalColour MkZobrist { getRandomByCoordinatesByRankByLogicalColour = randomByCoordinatesByRankByLogicalColour }	= (randomByCoordinatesByRankByLogicalColour !)

-- | Dereferences 'getRandomByCastleableRooksXByLogicalColour' using the specified abscissa.
dereferenceRandomByCastleableRooksXByLogicalColour
	:: Zobrist positionHash
	-> Colour.LogicalColour.LogicalColour
	-> Type.Length.X
	-> Maybe positionHash	-- ^ The existence of a result depends on whether there remain any Rooks which can castle.
dereferenceRandomByCastleableRooksXByLogicalColour MkZobrist { getRandomByCastleableRooksXByLogicalColour = randomByCastleableRooksXByLogicalColour } logicalColour x	= lookup x $ randomByCastleableRooksXByLogicalColour ! logicalColour

-- | Dereferences 'getRandomByEnPassantAbscissa' using the specified abscissa.
dereferenceRandomByEnPassantAbscissa :: Zobrist positionHash -> Type.Length.X -> positionHash
dereferenceRandomByEnPassantAbscissa MkZobrist { getRandomByEnPassantAbscissa = randomByEnPassantAbscissa }	= (randomByEnPassantAbscissa !)