{-# LANGUAGE MultiParamTypeClasses #-}
{-
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 .
-}
{- |
[@AUTHOR@] Dr. Alistair Ward
[@DESCRIPTION@]
* .
* 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(
-- * Type-classes
Hashable1D(..),
Hashable2D(..),
-- * Types
-- ** Data-types
Zobrist(
-- MkZobrist,
getRandomForBlacksMove
-- getRandomByCoordinatesByRankByLogicalColour,
-- getRandomByCastleableRooksXByLogicalColour,
-- getRandomByEnPassantAbscissa
),
-- * Constants
-- combiningOp,
-- * Functions
-- measureHammingDistances,
dereferenceRandomByCoordinatesByRankByLogicalColour,
dereferenceRandomByCastleableRooksXByLogicalColour,
dereferenceRandomByEnPassantAbscissa,
hash2D,
combine,
-- ** Constructors
mkZobrist
) where
import Control.Arrow((***))
import Data.Array.IArray((!))
import qualified BishBosh.Attribute.LogicalColour as Attribute.LogicalColour
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.Data.Exception as Data.Exception
import qualified Control.Exception
import qualified Data.Array.IArray
import qualified Data.Bits
import qualified Data.Default
import qualified Data.Foldable
import qualified Data.List
import qualified System.Random
import qualified ToolShed.System.Random
-- | The random numbers used to generate a hash, which almost uniquely represent a /position/.
data Zobrist x y positionHash = MkZobrist {
getRandomForBlacksMove :: positionHash, -- ^ Defines a random number to apply when the next move is @Black@'s.
getRandomByCoordinatesByRankByLogicalColour :: Attribute.LogicalColour.ByLogicalColour (Attribute.Rank.ByRank (Cartesian.Coordinates.ByCoordinates x y positionHash)), -- ^ Defines random numbers to represent all combinations of each piece at each coordinate; though @Pawn@s can't exist on the terminal ranks.
getRandomByCastleableRooksXByLogicalColour :: Attribute.LogicalColour.ByLogicalColour [(x, positionHash)], -- ^ Defines random numbers to represent all combinations of castleable @Rook@s.
getRandomByEnPassantAbscissa :: Cartesian.Abscissa.ByAbscissa x positionHash -- ^ Defines random numbers to represent any file on which capture en-passant might be available.
} deriving Show
instance Foldable (Zobrist x y) 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 (
flip . Data.Foldable.foldr . flip $ Data.Foldable.foldr f
) (
f randomForBlacksMove i
) randomByCoordinatesByRankByLogicalColour
) randomByCastleableRooksXByLogicalColour
) randomByEnPassantAbscissa
instance (
Data.Array.IArray.Ix x,
Data.Bits.FiniteBits positionHash,
Enum x,
Enum y,
Num positionHash,
Ord y,
System.Random.Random positionHash
) => Data.Default.Default (Zobrist x y positionHash) where
def = mkZobrist Nothing $ System.Random.mkStdGen 0
{- |
* .
* Quantifies the Hamming distance between all combinations of pairs of the random numbers used to compose hashes.
* CAVEAT: a better measure of the suitability of the selected random numbers
-}
measureHammingDistances :: Data.Bits.Bits positionHash => Zobrist x y 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.Array.IArray.Ix x,
Data.Bits.FiniteBits positionHash,
Enum x,
Enum y,
Num positionHash,
Ord y,
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 x y 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 . getNonZeroRandoms *** Attribute.LogicalColour.listArrayByLogicalColour . map (
Attribute.Rank.listArrayByRank . map (
Cartesian.Coordinates.listArrayByCoordinates . getNonZeroRandoms
) . ToolShed.System.Random.randomGens
) . ToolShed.System.Random.randomGens
) . System.Random.split
) *** (
(
Attribute.LogicalColour.listArrayByLogicalColour . map (
zip [Cartesian.Abscissa.xMin, Cartesian.Abscissa.xMax] . getNonZeroRandoms
) . ToolShed.System.Random.randomGens *** Cartesian.Abscissa.listArrayByAbscissa . getNonZeroRandoms
) . System.Random.split
) $ System.Random.split randomGen where
getNonZeroRandoms = filter (/= 0) . System.Random.randoms
zobrist = MkZobrist {
getRandomForBlacksMove = randomForBlacksMove,
getRandomByCoordinatesByRankByLogicalColour = randomByCoordinatesByRankByLogicalColour,
getRandomByCastleableRooksXByLogicalColour = randomByCastleableRooksXByLogicalColour,
getRandomByEnPassantAbscissa = randomByEnPassantAbscissa
}
-- | Dereference 'getRandomByCoordinatesByRankByLogicalColour'.
dereferenceRandomByCoordinatesByRankByLogicalColour :: (
Enum x,
Enum y,
Ord x,
Ord y
)
=> Attribute.LogicalColour.LogicalColour
-> Attribute.Rank.Rank
-> Cartesian.Coordinates.Coordinates x y
-> Zobrist x y positionHash
-> positionHash
dereferenceRandomByCoordinatesByRankByLogicalColour logicalColour rank coordinates MkZobrist { getRandomByCoordinatesByRankByLogicalColour = randomByCoordinatesByRankByLogicalColour } = randomByCoordinatesByRankByLogicalColour ! logicalColour ! rank ! coordinates
-- | Dereference 'getRandomByCastleableRooksXByLogicalColour'.
dereferenceRandomByCastleableRooksXByLogicalColour
:: Eq x
=> Attribute.LogicalColour.LogicalColour
-> x
-> Zobrist x y positionHash
-> Maybe positionHash
dereferenceRandomByCastleableRooksXByLogicalColour logicalColour x MkZobrist { getRandomByCastleableRooksXByLogicalColour = randomByCastleableRooksXByLogicalColour } = lookup x $ randomByCastleableRooksXByLogicalColour ! logicalColour
-- | Dereference 'getRandomByEnPassantAbscissa'.
dereferenceRandomByEnPassantAbscissa
:: Data.Array.IArray.Ix x
=> x
-> Zobrist x y positionHash
-> positionHash
dereferenceRandomByEnPassantAbscissa x MkZobrist { getRandomByEnPassantAbscissa = randomByEnPassantAbscissa } = randomByEnPassantAbscissa ! x
-- | An interface to which 1-D hashable data can conform.
class Hashable1D hashable x {-CAVEAT: MultiParamTypeClasses-} where
listRandoms1D :: hashable x -> Zobrist x y positionHash -> [positionHash]
-- | An interface to which 2-D hashable data can conform.
class Hashable2D hashable x y {-CAVEAT: MultiParamTypeClasses-} where
listRandoms2D :: hashable x y -> Zobrist x y positionHash -> [positionHash]
-- | The operator used when combining random numbers to compose a hash.
combiningOp :: Data.Bits.Bits positionHash => positionHash -> positionHash -> positionHash
combiningOp = Data.Bits.xor
-- | Resolve a hashable into a hash.
hash2D :: (
Data.Bits.Bits positionHash,
Hashable2D hashable x y
)
=> hashable x y
-> Zobrist x y positionHash
-> positionHash
hash2D hashable = Data.List.foldl1' combiningOp . listRandoms2D hashable
-- | Include a list of random numbers in the hash.
combine :: Data.Bits.Bits positionHash => positionHash -> [positionHash] -> positionHash
combine = Data.List.foldl' combiningOp