Magic bitboards can now be found (untested)
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@ -1,19 +1,18 @@
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## Low-level magic bitboard stuff
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# Stolen from this amazing article: https://analog-hors.github.io/site/magic-bitboards/
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# Blatantly stolen from this amazing article: https://analog-hors.github.io/site/magic-bitboards/
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import bitboards
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import pieces
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import std/random
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import std/bitops
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export pieces
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export bitboards
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randomize()
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type
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MagicEntry = object
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@ -23,8 +22,10 @@ type
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indexBits: uint8
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proc generateRookBlockers: array[64, Bitboard] {.compileTime.} =
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## Generates all blocker masks for rooks
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# Yeah uh, don't look too closely at this...
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proc generateRookMasks(blockers: bool = false): array[64, Bitboard] {.compileTime.} =
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## Generates all movement masks for rooks (only generates
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## blocker masks if blockers equals true)
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for rank in 0..7:
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for file in 0..7:
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let
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@ -36,33 +37,37 @@ proc generateRookBlockers: array[64, Bitboard] {.compileTime.} =
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last = makeSquare(rank, 7).toBitboard()
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while true:
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current = current.rightRelativeTo(White)
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if current == last or current == 0:
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if (current == last and blockers) or current == 0:
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break
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result[i] = result[i] or current
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current = bitboard
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last = makeSquare(rank, 0).toBitboard()
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while true:
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current = current.leftRelativeTo(White)
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if current == last or current == 0:
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if (current == last and blockers) or current == 0:
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break
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result[i] = result[i] or current
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current = bitboard
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last = makeSquare(0, file).toBitboard()
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while true:
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current = current.forwardRelativeTo(White)
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if current == last or current == 0:
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if (current == last and blockers) or current == 0:
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break
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result[i] = result[i] or current
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current = bitboard
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last = makeSquare(7, file).toBitboard()
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while true:
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current = current.backwardRelativeTo(White)
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if current == last or current == 0:
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if (current == last and blockers) or current == 0:
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break
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result[i] = result[i] or current
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func generateBishopBlockers: array[64, Bitboard] {.compileTime.} =
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# Okay this is fucking clever tho. Which is obvious, considering I didn't come up with it.
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# Or, well, the trick at the end isn't mine
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func generateBishopMasks(blockers = false): array[64, Bitboard] {.compileTime.} =
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## Generates all movement masks for bishops (only generates
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## blocker masks if blockers equals true)
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for rank in 0..7:
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for file in 0..7:
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# Generate all possible movement masks
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@ -95,11 +100,16 @@ func generateBishopBlockers: array[64, Bitboard] {.compileTime.} =
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if current == 0:
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break
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result[i] = result[i] or current
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# Mask off the edges
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result[i] = result[i] and not getFileMask(0)
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result[i] = result[i] and not getFileMask(7)
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result[i] = result[i] and not getRankMask(0)
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result[i] = result[i] and not getRankMask(7)
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if blockers:
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# Mask off the edges
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# Yeah, this is the trick. I know, not a big deal, but
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# I'm an idiot so what do I know. Credit to @__arandomnoob
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# on the engine programming discord server for the tip!
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result[i] = result[i] and not getFileMask(0)
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result[i] = result[i] and not getFileMask(7)
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result[i] = result[i] and not getRankMask(0)
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result[i] = result[i] and not getRankMask(7)
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func getIndex(magic: MagicEntry, blockers: Bitboard): uint {.inline.} =
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@ -108,7 +118,7 @@ func getIndex(magic: MagicEntry, blockers: Bitboard): uint {.inline.} =
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let
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blockers = blockers and magic.mask
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hash = blockers * magic.value
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index = hash shl (64 - magic.indexBits)
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index = hash shr (64 - magic.indexBits)
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return index.uint
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@ -142,17 +152,109 @@ proc getBishopMoves(square: Square, blockers: Bitboard): Bitboard =
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# are actually able to block the movement of a sliding piece,
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# regardless of color
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const
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ROOK_BLOCKERS* = generateRookBlockers()
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BISHOP_BLOCKERS* = generateBishopBlockers()
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# mfw Nim's compile time VM *graciously* allows me to call perfectly valid code: :D
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ROOK_BLOCKERS = generateRookMasks(blockers=true)
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BISHOP_BLOCKERS = generateBishopMasks(blockers=true)
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ROOK_MOVEMENTS = generateRookMasks()
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BISHOP_MOVEMENTS = generateBishopMasks()
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func getRelevantBlockers(kind: PieceKind, square: Square): Bitboard =
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## Returns the relevant blockers mask for the given piece
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## type at the given square
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case kind:
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of Rook:
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return ROOK_BLOCKERS[square.uint]
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of Bishop:
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return BISHOP_BLOCKERS[square.uint]
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else:
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discard
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proc attemptMagicTableCreation(kind: PieceKind, square: Square, entry: MagicEntry): tuple[success: bool, table: seq[Bitboard]] =
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## Tries to create a magic bitboard table for the given piece
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## at the given square using the provided magic entry. Returns
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## (true, table) if successful, (false, empty) otherwise
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# Initialize a new sequence with capacity 2^indexBits
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result.table = newSeqOfCap[Bitboard](1 shl entry.indexBits)
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result.success = true
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for _ in 0..result.table.capacity:
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result.table.add(Bitboard(0))
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# Iterate all possible blocker configurations
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for blocker in entry.mask.subsets():
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let index = getIndex(entry, blocker)
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# Get the moves the piece can make from the given
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# square with this specific blocker configuration
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var moves: Bitboard
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case kind:
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of Rook:
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moves = ROOK_MOVEMENTS[square.uint]
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of Bishop:
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moves = BISHOP_MOVEMENTS[square.uint]
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else:
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discard
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if result.table[index] == 0:
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# No entry here, yet, so no problem!
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result.table[index] = moves
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elif (result.table[index] or blocker) != moves:
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# We found a non-constructive collision, fail :(
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# Notes for future self: A "constructive" collision
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# is one which doesn't affect the result, because some
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# blocker configurations will map to the same set of
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# resulting moves. This actually improves our chances
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# of building our lovely perfect-hash-function-as-a-table
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# because we don't actually need to map *all* blocker
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# configurations uniquely, just the ones that lead to
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# a different set of moves. This happens because we are
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# keeping track of a lot of redundant blockers that are
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# beyond squares a slider piece could go to: we could reduce
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# the table size if we didn't account for those, but this
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# would require us to have a loop going in every sliding
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# direction to find what pieces are actually blocking the
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# the slider's path and which aren't for every single lookup,
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# which is the whole thing we're trying to avoid by doing all
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# this magic bitboard stuff and it is basically how the old mailbox
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# move generator worked anyway (thanks to Sebastian Lague on YouTube
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# for the insight)
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return (false, @[])
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# We have found a constructive collision: all good
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proc findMagic(kind: PieceKind, square: Square, indexBits: uint8): tuple[entry: MagicEntry, table: seq[Bitboard]] =
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## Constructs a (sort of) perfect hash function that fits all
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## the possible blocking configurations for the given piece at
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## the given square into a table of size 2^indexBits
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let mask = kind.getRelevantBlockers(square)
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# The best way to find a good magic number? Literally just
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# bruteforce the shit out of it!
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var rand = initRand()
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while true:
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# Again, this is stolen from the article. A magic number
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# is only useful if it is small (i.e. has a low number of
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# bits set), so we AND together 3 random numbers to get a
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# number with (hopefully) not that many bits set
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let
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magic = rand.next() and rand.next() and rand.next()
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entry = MagicEntry(mask: mask, value: magic, indexBits: indexBits)
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var attempt = attemptMagicTableCreation(kind, square, entry)
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if attempt.success:
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return (entry, attempt.table)
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# Not successful? No problem, we'll just try again until
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# the heat death of the universe!
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import std/strformat
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# func findMagic(slider: PieceKind, square: Square, indexBits: uint8): tuple[magic: MagicEntry, moves: seq[Bitboard]] =
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# ## Given a slider piece, its starting square and the number of desired
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# ## index bits, find a magic number that perfectly maps all the possible
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# ## sliding moves for that piece at that square into an appropriately sized
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# ## perfect hash table with at most 2^indexBits entries
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# var mask: Bitboard
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# case slider:
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# of Rook:
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# mask = ROOK_BLOCKERS[square.uint]
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for i in 0..63:
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let square = Square(i)
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var result = findMagic(Rook, square, Rook.getRelevantBlockers(square).uint64.countSetBits().uint8)
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echo &"Found magic bitboard for rooks at {square}"
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ROOK_MAGICS.add(result.entry)
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ROOK_MOVES[i] = result.table
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result = findMagic(Bishop, square, Bishop.getRelevantBlockers(square).uint64.countSetBits().uint8)
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echo &"Found magic bitboard for bishops at {square}"
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BISHOP_MAGICS.add(result.entry)
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BISHOP_MOVES[i] = result.table
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