2 Stockfish, a UCI chess playing engine derived from Glaurung 2.1
3 Copyright (C) 2004-2023 The Stockfish developers (see AUTHORS file)
5 Stockfish is free software: you can redistribute it and/or modify
6 it under the terms of the GNU General Public License as published by
7 the Free Software Foundation, either version 3 of the License, or
8 (at your option) any later version.
10 Stockfish is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
13 GNU General Public License for more details.
15 You should have received a copy of the GNU General Public License
16 along with this program. If not, see <http://www.gnu.org/licenses/>.
30 #include <initializer_list>
34 #include <string_view>
35 #include <type_traits>
39 #include "../bitboard.h"
41 #include "../movegen.h"
42 #include "../position.h"
43 #include "../search.h"
52 #define WIN32_LEAN_AND_MEAN
54 #define NOMINMAX // Disable macros min() and max()
59 using namespace Stockfish::Tablebases;
61 int Stockfish::Tablebases::MaxCardinality;
67 constexpr int TBPIECES = 7; // Max number of supported pieces
68 constexpr int MAX_DTZ =
69 1 << 18; // Max DTZ supported, large enough to deal with the syzygy TB limit.
78 }; // Used as template parameter
80 // Each table has a set of flags: all of them refer to DTZ tables, the last one to WDL tables
90 inline WDLScore operator-(WDLScore d) { return WDLScore(-int(d)); }
91 inline Square operator^(Square s, int i) { return Square(int(s) ^ i); }
93 constexpr std::string_view PieceToChar = " PNBRQK pnbrqk";
95 int MapPawns[SQUARE_NB];
96 int MapB1H1H7[SQUARE_NB];
97 int MapA1D1D4[SQUARE_NB];
98 int MapKK[10][SQUARE_NB]; // [MapA1D1D4][SQUARE_NB]
100 int Binomial[6][SQUARE_NB]; // [k][n] k elements from a set of n elements
101 int LeadPawnIdx[6][SQUARE_NB]; // [leadPawnsCnt][SQUARE_NB]
102 int LeadPawnsSize[6][4]; // [leadPawnsCnt][FILE_A..FILE_D]
104 // Comparison function to sort leading pawns in ascending MapPawns[] order
105 bool pawns_comp(Square i, Square j) { return MapPawns[i] < MapPawns[j]; }
106 int off_A1H8(Square sq) { return int(rank_of(sq)) - file_of(sq); }
108 constexpr Value WDL_to_value[] = {-VALUE_MATE + MAX_PLY + 1, VALUE_DRAW - 2, VALUE_DRAW,
109 VALUE_DRAW + 2, VALUE_MATE - MAX_PLY - 1};
111 template<typename T, int Half = sizeof(T) / 2, int End = sizeof(T) - 1>
112 inline void swap_endian(T& x) {
113 static_assert(std::is_unsigned_v<T>, "Argument of swap_endian not unsigned");
115 uint8_t tmp, *c = (uint8_t*) &x;
116 for (int i = 0; i < Half; ++i)
117 tmp = c[i], c[i] = c[End - i], c[End - i] = tmp;
120 inline void swap_endian<uint8_t>(uint8_t&) {}
122 template<typename T, int LE>
123 T number(void* addr) {
126 if (uintptr_t(addr) & (alignof(T) - 1)) // Unaligned pointer (very rare)
127 std::memcpy(&v, addr, sizeof(T));
131 if (LE != IsLittleEndian)
136 // DTZ tables don't store valid scores for moves that reset the rule50 counter
137 // like captures and pawn moves but we can easily recover the correct dtz of the
138 // previous move if we know the position's WDL score.
139 int dtz_before_zeroing(WDLScore wdl) {
140 return wdl == WDLWin ? 1
141 : wdl == WDLCursedWin ? 101
142 : wdl == WDLBlessedLoss ? -101
143 : wdl == WDLLoss ? -1
147 // Return the sign of a number (-1, 0, 1)
150 return (T(0) < val) - (val < T(0));
153 // Numbers in little-endian used by sparseIndex[] to point into blockLength[]
155 char block[4]; // Number of block
156 char offset[2]; // Offset within the block
159 static_assert(sizeof(SparseEntry) == 6, "SparseEntry must be 6 bytes");
161 using Sym = uint16_t; // Huffman symbol
169 uint8_t lr[3]; // The first 12 bits is the left-hand symbol, the second 12
170 // bits is the right-hand symbol. If the symbol has length 1,
171 // then the left-hand symbol is the stored value.
174 return S == Left ? ((lr[1] & 0xF) << 8) | lr[0]
175 : S == Right ? (lr[2] << 4) | (lr[1] >> 4)
176 : (assert(false), Sym(-1));
180 static_assert(sizeof(LR) == 3, "LR tree entry must be 3 bytes");
182 // Tablebases data layout is structured as following:
184 // TBFile: memory maps/unmaps the physical .rtbw and .rtbz files
185 // TBTable: one object for each file with corresponding indexing information
186 // TBTables: has ownership of TBTable objects, keeping a list and a hash
188 // class TBFile memory maps/unmaps the single .rtbw and .rtbz files. Files are
189 // memory mapped for best performance. Files are mapped at first access: at init
190 // time only existence of the file is checked.
191 class TBFile: public std::ifstream {
196 // Look for and open the file among the Paths directories where the .rtbw
197 // and .rtbz files can be found. Multiple directories are separated by ";"
198 // on Windows and by ":" on Unix-based operating systems.
201 // C:\tb\wdl345;C:\tb\wdl6;D:\tb\dtz345;D:\tb\dtz6
202 static std::string Paths;
204 TBFile(const std::string& f) {
207 constexpr char SepChar = ':';
209 constexpr char SepChar = ';';
211 std::stringstream ss(Paths);
214 while (std::getline(ss, path, SepChar))
216 fname = path + "/" + f;
217 std::ifstream::open(fname);
223 // Memory map the file and check it.
224 uint8_t* map(void** baseAddress, uint64_t* mapping, TBType type) {
226 close(); // Need to re-open to get native file descriptor
230 int fd = ::open(fname.c_str(), O_RDONLY);
233 return *baseAddress = nullptr, nullptr;
237 if (statbuf.st_size % 64 != 16)
239 std::cerr << "Corrupt tablebase file " << fname << std::endl;
243 *mapping = statbuf.st_size;
244 *baseAddress = mmap(nullptr, statbuf.st_size, PROT_READ, MAP_SHARED, fd, 0);
245 #if defined(MADV_RANDOM)
246 madvise(*baseAddress, statbuf.st_size, MADV_RANDOM);
250 if (*baseAddress == MAP_FAILED)
252 std::cerr << "Could not mmap() " << fname << std::endl;
256 // Note FILE_FLAG_RANDOM_ACCESS is only a hint to Windows and as such may get ignored.
257 HANDLE fd = CreateFileA(fname.c_str(), GENERIC_READ, FILE_SHARE_READ, nullptr,
258 OPEN_EXISTING, FILE_FLAG_RANDOM_ACCESS, nullptr);
260 if (fd == INVALID_HANDLE_VALUE)
261 return *baseAddress = nullptr, nullptr;
264 DWORD size_low = GetFileSize(fd, &size_high);
266 if (size_low % 64 != 16)
268 std::cerr << "Corrupt tablebase file " << fname << std::endl;
272 HANDLE mmap = CreateFileMapping(fd, nullptr, PAGE_READONLY, size_high, size_low, nullptr);
277 std::cerr << "CreateFileMapping() failed" << std::endl;
281 *mapping = uint64_t(mmap);
282 *baseAddress = MapViewOfFile(mmap, FILE_MAP_READ, 0, 0, 0);
286 std::cerr << "MapViewOfFile() failed, name = " << fname
287 << ", error = " << GetLastError() << std::endl;
291 uint8_t* data = (uint8_t*) *baseAddress;
293 constexpr uint8_t Magics[][4] = {{0xD7, 0x66, 0x0C, 0xA5}, {0x71, 0xE8, 0x23, 0x5D}};
295 if (memcmp(data, Magics[type == WDL], 4))
297 std::cerr << "Corrupted table in file " << fname << std::endl;
298 unmap(*baseAddress, *mapping);
299 return *baseAddress = nullptr, nullptr;
302 return data + 4; // Skip Magics's header
305 static void unmap(void* baseAddress, uint64_t mapping) {
308 munmap(baseAddress, mapping);
310 UnmapViewOfFile(baseAddress);
311 CloseHandle((HANDLE) mapping);
316 std::string TBFile::Paths;
318 // struct PairsData contains low-level indexing information to access TB data.
319 // There are 8, 4, or 2 PairsData records for each TBTable, according to the type
320 // of table and if positions have pawns or not. It is populated at first access.
322 uint8_t flags; // Table flags, see enum TBFlag
323 uint8_t maxSymLen; // Maximum length in bits of the Huffman symbols
324 uint8_t minSymLen; // Minimum length in bits of the Huffman symbols
325 uint32_t blocksNum; // Number of blocks in the TB file
326 size_t sizeofBlock; // Block size in bytes
327 size_t span; // About every span values there is a SparseIndex[] entry
328 Sym* lowestSym; // lowestSym[l] is the symbol of length l with the lowest value
329 LR* btree; // btree[sym] stores the left and right symbols that expand sym
330 uint16_t* blockLength; // Number of stored positions (minus one) for each block: 1..65536
331 uint32_t blockLengthSize; // Size of blockLength[] table: padded so it's bigger than blocksNum
332 SparseEntry* sparseIndex; // Partial indices into blockLength[]
333 size_t sparseIndexSize; // Size of SparseIndex[] table
334 uint8_t* data; // Start of Huffman compressed data
335 std::vector<uint64_t>
336 base64; // base64[l - min_sym_len] is the 64bit-padded lowest symbol of length l
338 symlen; // Number of values (-1) represented by a given Huffman symbol: 1..256
339 Piece pieces[TBPIECES]; // Position pieces: the order of pieces defines the groups
340 uint64_t groupIdx[TBPIECES + 1]; // Start index used for the encoding of the group's pieces
341 int groupLen[TBPIECES + 1]; // Number of pieces in a given group: KRKN -> (3, 1)
342 uint16_t map_idx[4]; // WDLWin, WDLLoss, WDLCursedWin, WDLBlessedLoss (used in DTZ)
345 // struct TBTable contains indexing information to access the corresponding TBFile.
346 // There are 2 types of TBTable, corresponding to a WDL or a DTZ file. TBTable
347 // is populated at init time but the nested PairsData records are populated at
348 // first access, when the corresponding file is memory mapped.
349 template<TBType Type>
351 using Ret = std::conditional_t<Type == WDL, WDLScore, int>;
353 static constexpr int Sides = Type == WDL ? 2 : 1;
355 std::atomic_bool ready;
363 bool hasUniquePieces;
364 uint8_t pawnCount[2]; // [Lead color / other color]
365 PairsData items[Sides][4]; // [wtm / btm][FILE_A..FILE_D or 0]
367 PairsData* get(int stm, int f) { return &items[stm % Sides][hasPawns ? f : 0]; }
371 baseAddress(nullptr) {}
372 explicit TBTable(const std::string& code);
373 explicit TBTable(const TBTable<WDL>& wdl);
377 TBFile::unmap(baseAddress, mapping);
382 TBTable<WDL>::TBTable(const std::string& code) :
388 key = pos.set(code, WHITE, &st).material_key();
389 pieceCount = pos.count<ALL_PIECES>();
390 hasPawns = pos.pieces(PAWN);
392 hasUniquePieces = false;
393 for (Color c : {WHITE, BLACK})
394 for (PieceType pt = PAWN; pt < KING; ++pt)
395 if (popcount(pos.pieces(c, pt)) == 1)
396 hasUniquePieces = true;
398 // Set the leading color. In case both sides have pawns the leading color
399 // is the side with fewer pawns because this leads to better compression.
400 bool c = !pos.count<PAWN>(BLACK)
401 || (pos.count<PAWN>(WHITE) && pos.count<PAWN>(BLACK) >= pos.count<PAWN>(WHITE));
403 pawnCount[0] = pos.count<PAWN>(c ? WHITE : BLACK);
404 pawnCount[1] = pos.count<PAWN>(c ? BLACK : WHITE);
406 key2 = pos.set(code, BLACK, &st).material_key();
410 TBTable<DTZ>::TBTable(const TBTable<WDL>& wdl) :
413 // Use the corresponding WDL table to avoid recalculating all from scratch
416 pieceCount = wdl.pieceCount;
417 hasPawns = wdl.hasPawns;
418 hasUniquePieces = wdl.hasUniquePieces;
419 pawnCount[0] = wdl.pawnCount[0];
420 pawnCount[1] = wdl.pawnCount[1];
423 // class TBTables creates and keeps ownership of the TBTable objects, one for
424 // each TB file found. It supports a fast, hash-based, table lookup. Populated
425 // at init time, accessed at probe time.
433 template<TBType Type>
434 TBTable<Type>* get() const {
435 return (TBTable<Type>*) (Type == WDL ? (void*) wdl : (void*) dtz);
439 static constexpr int Size = 1 << 12; // 4K table, indexed by key's 12 lsb
440 static constexpr int Overflow = 1; // Number of elements allowed to map to the last bucket
442 Entry hashTable[Size + Overflow];
444 std::deque<TBTable<WDL>> wdlTable;
445 std::deque<TBTable<DTZ>> dtzTable;
447 void insert(Key key, TBTable<WDL>* wdl, TBTable<DTZ>* dtz) {
448 uint32_t homeBucket = uint32_t(key) & (Size - 1);
449 Entry entry{key, wdl, dtz};
451 // Ensure last element is empty to avoid overflow when looking up
452 for (uint32_t bucket = homeBucket; bucket < Size + Overflow - 1; ++bucket)
454 Key otherKey = hashTable[bucket].key;
455 if (otherKey == key || !hashTable[bucket].get<WDL>())
457 hashTable[bucket] = entry;
461 // Robin Hood hashing: If we've probed for longer than this element,
462 // insert here and search for a new spot for the other element instead.
463 uint32_t otherHomeBucket = uint32_t(otherKey) & (Size - 1);
464 if (otherHomeBucket > homeBucket)
466 std::swap(entry, hashTable[bucket]);
468 homeBucket = otherHomeBucket;
471 std::cerr << "TB hash table size too low!" << std::endl;
476 template<TBType Type>
477 TBTable<Type>* get(Key key) {
478 for (const Entry* entry = &hashTable[uint32_t(key) & (Size - 1)];; ++entry)
480 if (entry->key == key || !entry->get<Type>())
481 return entry->get<Type>();
486 memset(hashTable, 0, sizeof(hashTable));
490 size_t size() const { return wdlTable.size(); }
491 void add(const std::vector<PieceType>& pieces);
496 // If the corresponding file exists two new objects TBTable<WDL> and TBTable<DTZ>
497 // are created and added to the lists and hash table. Called at init time.
498 void TBTables::add(const std::vector<PieceType>& pieces) {
502 for (PieceType pt : pieces)
503 code += PieceToChar[pt];
505 TBFile file(code.insert(code.find('K', 1), "v") + ".rtbw"); // KRK -> KRvK
507 if (!file.is_open()) // Only WDL file is checked
512 MaxCardinality = std::max(int(pieces.size()), MaxCardinality);
514 wdlTable.emplace_back(code);
515 dtzTable.emplace_back(wdlTable.back());
517 // Insert into the hash keys for both colors: KRvK with KR white and black
518 insert(wdlTable.back().key, &wdlTable.back(), &dtzTable.back());
519 insert(wdlTable.back().key2, &wdlTable.back(), &dtzTable.back());
522 // TB tables are compressed with canonical Huffman code. The compressed data is divided into
523 // blocks of size d->sizeofBlock, and each block stores a variable number of symbols.
524 // Each symbol represents either a WDL or a (remapped) DTZ value, or a pair of other symbols
525 // (recursively). If you keep expanding the symbols in a block, you end up with up to 65536
526 // WDL or DTZ values. Each symbol represents up to 256 values and will correspond after
527 // Huffman coding to at least 1 bit. So a block of 32 bytes corresponds to at most
528 // 32 x 8 x 256 = 65536 values. This maximum is only reached for tables that consist mostly
529 // of draws or mostly of wins, but such tables are actually quite common. In principle, the
530 // blocks in WDL tables are 64 bytes long (and will be aligned on cache lines). But for
531 // mostly-draw or mostly-win tables this can leave many 64-byte blocks only half-filled, so
532 // in such cases blocks are 32 bytes long. The blocks of DTZ tables are up to 1024 bytes long.
533 // The generator picks the size that leads to the smallest table. The "book" of symbols and
534 // Huffman codes are the same for all blocks in the table. A non-symmetric pawnless TB file
535 // will have one table for wtm and one for btm, a TB file with pawns will have tables per
536 // file a,b,c,d also, in this case, one set for wtm and one for btm.
537 int decompress_pairs(PairsData* d, uint64_t idx) {
539 // Special case where all table positions store the same value
540 if (d->flags & TBFlag::SingleValue)
543 // First we need to locate the right block that stores the value at index "idx".
544 // Because each block n stores blockLength[n] + 1 values, the index i of the block
545 // that contains the value at position idx is:
547 // for (i = -1, sum = 0; sum <= idx; i++)
548 // sum += blockLength[i + 1] + 1;
550 // This can be slow, so we use SparseIndex[] populated with a set of SparseEntry that
551 // point to known indices into blockLength[]. Namely SparseIndex[k] is a SparseEntry
552 // that stores the blockLength[] index and the offset within that block of the value
553 // with index I(k), where:
555 // I(k) = k * d->span + d->span / 2 (1)
557 // First step is to get the 'k' of the I(k) nearest to our idx, using definition (1)
558 uint32_t k = uint32_t(idx / d->span);
560 // Then we read the corresponding SparseIndex[] entry
561 uint32_t block = number<uint32_t, LittleEndian>(&d->sparseIndex[k].block);
562 int offset = number<uint16_t, LittleEndian>(&d->sparseIndex[k].offset);
564 // Now compute the difference idx - I(k). From the definition of k, we know that
566 // idx = k * d->span + idx % d->span (2)
568 // So from (1) and (2) we can compute idx - I(K):
569 int diff = idx % d->span - d->span / 2;
571 // Sum the above to offset to find the offset corresponding to our idx
574 // Move to the previous/next block, until we reach the correct block that contains idx,
575 // that is when 0 <= offset <= d->blockLength[block]
577 offset += d->blockLength[--block] + 1;
579 while (offset > d->blockLength[block])
580 offset -= d->blockLength[block++] + 1;
582 // Finally, we find the start address of our block of canonical Huffman symbols
583 uint32_t* ptr = (uint32_t*) (d->data + (uint64_t(block) * d->sizeofBlock));
585 // Read the first 64 bits in our block, this is a (truncated) sequence of
586 // unknown number of symbols of unknown length but we know the first one
587 // is at the beginning of this 64-bit sequence.
588 uint64_t buf64 = number<uint64_t, BigEndian>(ptr);
595 int len = 0; // This is the symbol length - d->min_sym_len
597 // Now get the symbol length. For any symbol s64 of length l right-padded
598 // to 64 bits we know that d->base64[l-1] >= s64 >= d->base64[l] so we
599 // can find the symbol length iterating through base64[].
600 while (buf64 < d->base64[len])
603 // All the symbols of a given length are consecutive integers (numerical
604 // sequence property), so we can compute the offset of our symbol of
605 // length len, stored at the beginning of buf64.
606 sym = Sym((buf64 - d->base64[len]) >> (64 - len - d->minSymLen));
608 // Now add the value of the lowest symbol of length len to get our symbol
609 sym += number<Sym, LittleEndian>(&d->lowestSym[len]);
611 // If our offset is within the number of values represented by symbol sym,
613 if (offset < d->symlen[sym] + 1)
616 // ...otherwise update the offset and continue to iterate
617 offset -= d->symlen[sym] + 1;
618 len += d->minSymLen; // Get the real length
619 buf64 <<= len; // Consume the just processed symbol
623 { // Refill the buffer
625 buf64 |= uint64_t(number<uint32_t, BigEndian>(ptr++)) << (64 - buf64Size);
629 // Now we have our symbol that expands into d->symlen[sym] + 1 symbols.
630 // We binary-search for our value recursively expanding into the left and
631 // right child symbols until we reach a leaf node where symlen[sym] + 1 == 1
632 // that will store the value we need.
633 while (d->symlen[sym])
635 Sym left = d->btree[sym].get<LR::Left>();
637 // If a symbol contains 36 sub-symbols (d->symlen[sym] + 1 = 36) and
638 // expands in a pair (d->symlen[left] = 23, d->symlen[right] = 11), then
639 // we know that, for instance, the tenth value (offset = 10) will be on
640 // the left side because in Recursive Pairing child symbols are adjacent.
641 if (offset < d->symlen[left] + 1)
645 offset -= d->symlen[left] + 1;
646 sym = d->btree[sym].get<LR::Right>();
650 return d->btree[sym].get<LR::Left>();
653 bool check_dtz_stm(TBTable<WDL>*, int, File) { return true; }
655 bool check_dtz_stm(TBTable<DTZ>* entry, int stm, File f) {
657 auto flags = entry->get(stm, f)->flags;
658 return (flags & TBFlag::STM) == stm || ((entry->key == entry->key2) && !entry->hasPawns);
661 // DTZ scores are sorted by frequency of occurrence and then assigned the
662 // values 0, 1, 2, ... in order of decreasing frequency. This is done for each
663 // of the four WDLScore values. The mapping information necessary to reconstruct
664 // the original values are stored in the TB file and read during map[] init.
665 WDLScore map_score(TBTable<WDL>*, File, int value, WDLScore) { return WDLScore(value - 2); }
667 int map_score(TBTable<DTZ>* entry, File f, int value, WDLScore wdl) {
669 constexpr int WDLMap[] = {1, 3, 0, 2, 0};
671 auto flags = entry->get(0, f)->flags;
673 uint8_t* map = entry->map;
674 uint16_t* idx = entry->get(0, f)->map_idx;
675 if (flags & TBFlag::Mapped)
677 if (flags & TBFlag::Wide)
678 value = ((uint16_t*) map)[idx[WDLMap[wdl + 2]] + value];
680 value = map[idx[WDLMap[wdl + 2]] + value];
683 // DTZ tables store distance to zero in number of moves or plies. We
684 // want to return plies, so we have to convert to plies when needed.
685 if ((wdl == WDLWin && !(flags & TBFlag::WinPlies))
686 || (wdl == WDLLoss && !(flags & TBFlag::LossPlies)) || wdl == WDLCursedWin
687 || wdl == WDLBlessedLoss)
693 // A temporary fix for the compiler bug with AVX-512. (#4450)
695 #if defined(__clang__) && defined(__clang_major__) && __clang_major__ >= 15
696 #define CLANG_AVX512_BUG_FIX __attribute__((optnone))
700 #ifndef CLANG_AVX512_BUG_FIX
701 #define CLANG_AVX512_BUG_FIX
704 // Compute a unique index out of a position and use it to probe the TB file. To
705 // encode k pieces of the same type and color, first sort the pieces by square in
706 // ascending order s1 <= s2 <= ... <= sk then compute the unique index as:
708 // idx = Binomial[1][s1] + Binomial[2][s2] + ... + Binomial[k][sk]
710 template<typename T, typename Ret = typename T::Ret>
711 CLANG_AVX512_BUG_FIX Ret
712 do_probe_table(const Position& pos, T* entry, WDLScore wdl, ProbeState* result) {
714 Square squares[TBPIECES];
715 Piece pieces[TBPIECES];
717 int next = 0, size = 0, leadPawnsCnt = 0;
719 Bitboard b, leadPawns = 0;
720 File tbFile = FILE_A;
722 // A given TB entry like KRK has associated two material keys: KRvk and Kvkr.
723 // If both sides have the same pieces keys are equal. In this case TB tables
724 // only stores the 'white to move' case, so if the position to lookup has black
725 // to move, we need to switch the color and flip the squares before to lookup.
726 bool symmetricBlackToMove = (entry->key == entry->key2 && pos.side_to_move());
728 // TB files are calculated for white as the stronger side. For instance, we
729 // have KRvK, not KvKR. A position where the stronger side is white will have
730 // its material key == entry->key, otherwise we have to switch the color and
731 // flip the squares before to lookup.
732 bool blackStronger = (pos.material_key() != entry->key);
734 int flipColor = (symmetricBlackToMove || blackStronger) * 8;
735 int flipSquares = (symmetricBlackToMove || blackStronger) * 56;
736 int stm = (symmetricBlackToMove || blackStronger) ^ pos.side_to_move();
738 // For pawns, TB files store 4 separate tables according if leading pawn is on
739 // file a, b, c or d after reordering. The leading pawn is the one with maximum
740 // MapPawns[] value, that is the one most toward the edges and with lowest rank.
744 // In all the 4 tables, pawns are at the beginning of the piece sequence and
745 // their color is the reference one. So we just pick the first one.
746 Piece pc = Piece(entry->get(0, 0)->pieces[0] ^ flipColor);
748 assert(type_of(pc) == PAWN);
750 leadPawns = b = pos.pieces(color_of(pc), PAWN);
752 squares[size++] = pop_lsb(b) ^ flipSquares;
757 std::swap(squares[0], *std::max_element(squares, squares + leadPawnsCnt, pawns_comp));
759 tbFile = File(edge_distance(file_of(squares[0])));
762 // DTZ tables are one-sided, i.e. they store positions only for white to
763 // move or only for black to move, so check for side to move to be stm,
764 // early exit otherwise.
765 if (!check_dtz_stm(entry, stm, tbFile))
766 return *result = CHANGE_STM, Ret();
768 // Now we are ready to get all the position pieces (but the lead pawns) and
769 // directly map them to the correct color and square.
770 b = pos.pieces() ^ leadPawns;
773 Square s = pop_lsb(b);
774 squares[size] = s ^ flipSquares;
775 pieces[size++] = Piece(pos.piece_on(s) ^ flipColor);
780 d = entry->get(stm, tbFile);
782 // Then we reorder the pieces to have the same sequence as the one stored
783 // in pieces[i]: the sequence that ensures the best compression.
784 for (int i = leadPawnsCnt; i < size - 1; ++i)
785 for (int j = i + 1; j < size; ++j)
786 if (d->pieces[i] == pieces[j])
788 std::swap(pieces[i], pieces[j]);
789 std::swap(squares[i], squares[j]);
793 // Now we map again the squares so that the square of the lead piece is in
794 // the triangle A1-D1-D4.
795 if (file_of(squares[0]) > FILE_D)
796 for (int i = 0; i < size; ++i)
797 squares[i] = flip_file(squares[i]);
799 // Encode leading pawns starting with the one with minimum MapPawns[] and
800 // proceeding in ascending order.
803 idx = LeadPawnIdx[leadPawnsCnt][squares[0]];
805 std::stable_sort(squares + 1, squares + leadPawnsCnt, pawns_comp);
807 for (int i = 1; i < leadPawnsCnt; ++i)
808 idx += Binomial[i][MapPawns[squares[i]]];
810 goto encode_remaining; // With pawns we have finished special treatments
813 // In positions without pawns, we further flip the squares to ensure leading
814 // piece is below RANK_5.
815 if (rank_of(squares[0]) > RANK_4)
816 for (int i = 0; i < size; ++i)
817 squares[i] = flip_rank(squares[i]);
819 // Look for the first piece of the leading group not on the A1-D4 diagonal
820 // and ensure it is mapped below the diagonal.
821 for (int i = 0; i < d->groupLen[0]; ++i)
823 if (!off_A1H8(squares[i]))
826 if (off_A1H8(squares[i]) > 0) // A1-H8 diagonal flip: SQ_A3 -> SQ_C1
827 for (int j = i; j < size; ++j)
828 squares[j] = Square(((squares[j] >> 3) | (squares[j] << 3)) & 63);
832 // Encode the leading group.
834 // Suppose we have KRvK. Let's say the pieces are on square numbers wK, wR
835 // and bK (each 0...63). The simplest way to map this position to an index
838 // index = wK * 64 * 64 + wR * 64 + bK;
840 // But this way the TB is going to have 64*64*64 = 262144 positions, with
841 // lots of positions being equivalent (because they are mirrors of each
842 // other) and lots of positions being invalid (two pieces on one square,
843 // adjacent kings, etc.).
844 // Usually the first step is to take the wK and bK together. There are just
845 // 462 ways legal and not-mirrored ways to place the wK and bK on the board.
846 // Once we have placed the wK and bK, there are 62 squares left for the wR
847 // Mapping its square from 0..63 to available squares 0..61 can be done like:
849 // wR -= (wR > wK) + (wR > bK);
851 // In words: if wR "comes later" than wK, we deduct 1, and the same if wR
852 // "comes later" than bK. In case of two same pieces like KRRvK we want to
853 // place the two Rs "together". If we have 62 squares left, we can place two
854 // Rs "together" in 62 * 61 / 2 ways (we divide by 2 because rooks can be
855 // swapped and still get the same position.)
857 // In case we have at least 3 unique pieces (including kings) we encode them
859 if (entry->hasUniquePieces)
862 int adjust1 = squares[1] > squares[0];
863 int adjust2 = (squares[2] > squares[0]) + (squares[2] > squares[1]);
865 // First piece is below a1-h8 diagonal. MapA1D1D4[] maps the b1-d1-d3
866 // triangle to 0...5. There are 63 squares for second piece and and 62
867 // (mapped to 0...61) for the third.
868 if (off_A1H8(squares[0]))
869 idx = (MapA1D1D4[squares[0]] * 63 + (squares[1] - adjust1)) * 62 + squares[2] - adjust2;
871 // First piece is on a1-h8 diagonal, second below: map this occurrence to
872 // 6 to differentiate from the above case, rank_of() maps a1-d4 diagonal
873 // to 0...3 and finally MapB1H1H7[] maps the b1-h1-h7 triangle to 0..27.
874 else if (off_A1H8(squares[1]))
875 idx = (6 * 63 + rank_of(squares[0]) * 28 + MapB1H1H7[squares[1]]) * 62 + squares[2]
878 // First two pieces are on a1-h8 diagonal, third below
879 else if (off_A1H8(squares[2]))
880 idx = 6 * 63 * 62 + 4 * 28 * 62 + rank_of(squares[0]) * 7 * 28
881 + (rank_of(squares[1]) - adjust1) * 28 + MapB1H1H7[squares[2]];
883 // All 3 pieces on the diagonal a1-h8
885 idx = 6 * 63 * 62 + 4 * 28 * 62 + 4 * 7 * 28 + rank_of(squares[0]) * 7 * 6
886 + (rank_of(squares[1]) - adjust1) * 6 + (rank_of(squares[2]) - adjust2);
889 // We don't have at least 3 unique pieces, like in KRRvKBB, just map
891 idx = MapKK[MapA1D1D4[squares[0]]][squares[1]];
894 idx *= d->groupIdx[0];
895 Square* groupSq = squares + d->groupLen[0];
897 // Encode remaining pawns and then pieces according to square, in ascending order
898 bool remainingPawns = entry->hasPawns && entry->pawnCount[1];
900 while (d->groupLen[++next])
902 std::stable_sort(groupSq, groupSq + d->groupLen[next]);
905 // Map down a square if "comes later" than a square in the previous
906 // groups (similar to what was done earlier for leading group pieces).
907 for (int i = 0; i < d->groupLen[next]; ++i)
909 auto f = [&](Square s) { return groupSq[i] > s; };
910 auto adjust = std::count_if(squares, groupSq, f);
911 n += Binomial[i + 1][groupSq[i] - adjust - 8 * remainingPawns];
914 remainingPawns = false;
915 idx += n * d->groupIdx[next];
916 groupSq += d->groupLen[next];
919 // Now that we have the index, decompress the pair and get the score
920 return map_score(entry, tbFile, decompress_pairs(d, idx), wdl);
923 // Group together pieces that will be encoded together. The general rule is that
924 // a group contains pieces of the same type and color. The exception is the leading
925 // group that, in case of positions without pawns, can be formed by 3 different
926 // pieces (default) or by the king pair when there is not a unique piece apart
927 // from the kings. When there are pawns, pawns are always first in pieces[].
929 // As example KRKN -> KRK + N, KNNK -> KK + NN, KPPKP -> P + PP + K + K
931 // The actual grouping depends on the TB generator and can be inferred from the
932 // sequence of pieces in piece[] array.
934 void set_groups(T& e, PairsData* d, int order[], File f) {
936 int n = 0, firstLen = e.hasPawns ? 0 : e.hasUniquePieces ? 3 : 2;
939 // Number of pieces per group is stored in groupLen[], for instance in KRKN
940 // the encoder will default on '111', so groupLen[] will be (3, 1).
941 for (int i = 1; i < e.pieceCount; ++i)
942 if (--firstLen > 0 || d->pieces[i] == d->pieces[i - 1])
945 d->groupLen[++n] = 1;
947 d->groupLen[++n] = 0; // Zero-terminated
949 // The sequence in pieces[] defines the groups, but not the order in which
950 // they are encoded. If the pieces in a group g can be combined on the board
951 // in N(g) different ways, then the position encoding will be of the form:
953 // g1 * N(g2) * N(g3) + g2 * N(g3) + g3
955 // This ensures unique encoding for the whole position. The order of the
956 // groups is a per-table parameter and could not follow the canonical leading
957 // pawns/pieces -> remaining pawns -> remaining pieces. In particular the
958 // first group is at order[0] position and the remaining pawns, when present,
959 // are at order[1] position.
960 bool pp = e.hasPawns && e.pawnCount[1]; // Pawns on both sides
961 int next = pp ? 2 : 1;
962 int freeSquares = 64 - d->groupLen[0] - (pp ? d->groupLen[1] : 0);
965 for (int k = 0; next < n || k == order[0] || k == order[1]; ++k)
966 if (k == order[0]) // Leading pawns or pieces
968 d->groupIdx[0] = idx;
969 idx *= e.hasPawns ? LeadPawnsSize[d->groupLen[0]][f] : e.hasUniquePieces ? 31332 : 462;
971 else if (k == order[1]) // Remaining pawns
973 d->groupIdx[1] = idx;
974 idx *= Binomial[d->groupLen[1]][48 - d->groupLen[0]];
976 else // Remaining pieces
978 d->groupIdx[next] = idx;
979 idx *= Binomial[d->groupLen[next]][freeSquares];
980 freeSquares -= d->groupLen[next++];
983 d->groupIdx[n] = idx;
986 // In Recursive Pairing each symbol represents a pair of children symbols. So
987 // read d->btree[] symbols data and expand each one in his left and right child
988 // symbol until reaching the leaves that represent the symbol value.
989 uint8_t set_symlen(PairsData* d, Sym s, std::vector<bool>& visited) {
991 visited[s] = true; // We can set it now because tree is acyclic
992 Sym sr = d->btree[s].get<LR::Right>();
997 Sym sl = d->btree[s].get<LR::Left>();
1000 d->symlen[sl] = set_symlen(d, sl, visited);
1003 d->symlen[sr] = set_symlen(d, sr, visited);
1005 return d->symlen[sl] + d->symlen[sr] + 1;
1008 uint8_t* set_sizes(PairsData* d, uint8_t* data) {
1012 if (d->flags & TBFlag::SingleValue)
1014 d->blocksNum = d->blockLengthSize = 0;
1015 d->span = d->sparseIndexSize = 0; // Broken MSVC zero-init
1016 d->minSymLen = *data++; // Here we store the single value
1020 // groupLen[] is a zero-terminated list of group lengths, the last groupIdx[]
1021 // element stores the biggest index that is the tb size.
1022 uint64_t tbSize = d->groupIdx[std::find(d->groupLen, d->groupLen + 7, 0) - d->groupLen];
1024 d->sizeofBlock = 1ULL << *data++;
1025 d->span = 1ULL << *data++;
1026 d->sparseIndexSize = size_t((tbSize + d->span - 1) / d->span); // Round up
1027 auto padding = number<uint8_t, LittleEndian>(data++);
1028 d->blocksNum = number<uint32_t, LittleEndian>(data);
1029 data += sizeof(uint32_t);
1030 d->blockLengthSize = d->blocksNum + padding; // Padded to ensure SparseIndex[]
1031 // does not point out of range.
1032 d->maxSymLen = *data++;
1033 d->minSymLen = *data++;
1034 d->lowestSym = (Sym*) data;
1035 d->base64.resize(d->maxSymLen - d->minSymLen + 1);
1037 // See https://en.wikipedia.org/wiki/Huffman_coding
1038 // The canonical code is ordered such that longer symbols (in terms of
1039 // the number of bits of their Huffman code) have a lower numeric value,
1040 // so that d->lowestSym[i] >= d->lowestSym[i+1] (when read as LittleEndian).
1041 // Starting from this we compute a base64[] table indexed by symbol length
1042 // and containing 64 bit values so that d->base64[i] >= d->base64[i+1].
1044 // Implementation note: we first cast the unsigned size_t "base64.size()"
1045 // to a signed int "base64_size" variable and then we are able to subtract 2,
1046 // avoiding unsigned overflow warnings.
1048 int base64_size = static_cast<int>(d->base64.size());
1049 for (int i = base64_size - 2; i >= 0; --i)
1051 d->base64[i] = (d->base64[i + 1] + number<Sym, LittleEndian>(&d->lowestSym[i])
1052 - number<Sym, LittleEndian>(&d->lowestSym[i + 1]))
1055 assert(d->base64[i] * 2 >= d->base64[i + 1]);
1058 // Now left-shift by an amount so that d->base64[i] gets shifted 1 bit more
1059 // than d->base64[i+1] and given the above assert condition, we ensure that
1060 // d->base64[i] >= d->base64[i+1]. Moreover for any symbol s64 of length i
1061 // and right-padded to 64 bits holds d->base64[i-1] >= s64 >= d->base64[i].
1062 for (int i = 0; i < base64_size; ++i)
1063 d->base64[i] <<= 64 - i - d->minSymLen; // Right-padding to 64 bits
1065 data += base64_size * sizeof(Sym);
1066 d->symlen.resize(number<uint16_t, LittleEndian>(data));
1067 data += sizeof(uint16_t);
1068 d->btree = (LR*) data;
1070 // The compression scheme used is "Recursive Pairing", that replaces the most
1071 // frequent adjacent pair of symbols in the source message by a new symbol,
1072 // reevaluating the frequencies of all of the symbol pairs with respect to
1073 // the extended alphabet, and then repeating the process.
1074 // See https://web.archive.org/web/20201106232444/http://www.larsson.dogma.net/dcc99.pdf
1075 std::vector<bool> visited(d->symlen.size());
1077 for (Sym sym = 0; sym < d->symlen.size(); ++sym)
1079 d->symlen[sym] = set_symlen(d, sym, visited);
1081 return data + d->symlen.size() * sizeof(LR) + (d->symlen.size() & 1);
1084 uint8_t* set_dtz_map(TBTable<WDL>&, uint8_t* data, File) { return data; }
1086 uint8_t* set_dtz_map(TBTable<DTZ>& e, uint8_t* data, File maxFile) {
1090 for (File f = FILE_A; f <= maxFile; ++f)
1092 auto flags = e.get(0, f)->flags;
1093 if (flags & TBFlag::Mapped)
1095 if (flags & TBFlag::Wide)
1097 data += uintptr_t(data) & 1; // Word alignment, we may have a mixed table
1098 for (int i = 0; i < 4; ++i)
1099 { // Sequence like 3,x,x,x,1,x,0,2,x,x
1100 e.get(0, f)->map_idx[i] = uint16_t((uint16_t*) data - (uint16_t*) e.map + 1);
1101 data += 2 * number<uint16_t, LittleEndian>(data) + 2;
1106 for (int i = 0; i < 4; ++i)
1108 e.get(0, f)->map_idx[i] = uint16_t(data - e.map + 1);
1115 return data += uintptr_t(data) & 1; // Word alignment
1118 // Populate entry's PairsData records with data from the just memory-mapped file.
1119 // Called at first access.
1120 template<typename T>
1121 void set(T& e, uint8_t* data) {
1130 assert(e.hasPawns == bool(*data & HasPawns));
1131 assert((e.key != e.key2) == bool(*data & Split));
1133 data++; // First byte stores flags
1135 const int sides = T::Sides == 2 && (e.key != e.key2) ? 2 : 1;
1136 const File maxFile = e.hasPawns ? FILE_D : FILE_A;
1138 bool pp = e.hasPawns && e.pawnCount[1]; // Pawns on both sides
1140 assert(!pp || e.pawnCount[0]);
1142 for (File f = FILE_A; f <= maxFile; ++f)
1145 for (int i = 0; i < sides; i++)
1146 *e.get(i, f) = PairsData();
1148 int order[][2] = {{*data & 0xF, pp ? *(data + 1) & 0xF : 0xF},
1149 {*data >> 4, pp ? *(data + 1) >> 4 : 0xF}};
1152 for (int k = 0; k < e.pieceCount; ++k, ++data)
1153 for (int i = 0; i < sides; i++)
1154 e.get(i, f)->pieces[k] = Piece(i ? *data >> 4 : *data & 0xF);
1156 for (int i = 0; i < sides; ++i)
1157 set_groups(e, e.get(i, f), order[i], f);
1160 data += uintptr_t(data) & 1; // Word alignment
1162 for (File f = FILE_A; f <= maxFile; ++f)
1163 for (int i = 0; i < sides; i++)
1164 data = set_sizes(e.get(i, f), data);
1166 data = set_dtz_map(e, data, maxFile);
1168 for (File f = FILE_A; f <= maxFile; ++f)
1169 for (int i = 0; i < sides; i++)
1171 (d = e.get(i, f))->sparseIndex = (SparseEntry*) data;
1172 data += d->sparseIndexSize * sizeof(SparseEntry);
1175 for (File f = FILE_A; f <= maxFile; ++f)
1176 for (int i = 0; i < sides; i++)
1178 (d = e.get(i, f))->blockLength = (uint16_t*) data;
1179 data += d->blockLengthSize * sizeof(uint16_t);
1182 for (File f = FILE_A; f <= maxFile; ++f)
1183 for (int i = 0; i < sides; i++)
1185 data = (uint8_t*) ((uintptr_t(data) + 0x3F) & ~0x3F); // 64 byte alignment
1186 (d = e.get(i, f))->data = data;
1187 data += d->blocksNum * d->sizeofBlock;
1191 // If the TB file corresponding to the given position is already memory-mapped
1192 // then return its base address, otherwise, try to memory map and init it. Called
1193 // at every probe, memory map, and init only at first access. Function is thread
1194 // safe and can be called concurrently.
1195 template<TBType Type>
1196 void* mapped(TBTable<Type>& e, const Position& pos) {
1198 static std::mutex mutex;
1200 // Use 'acquire' to avoid a thread reading 'ready' == true while
1201 // another is still working. (compiler reordering may cause this).
1202 if (e.ready.load(std::memory_order_acquire))
1203 return e.baseAddress; // Could be nullptr if file does not exist
1205 std::scoped_lock<std::mutex> lk(mutex);
1207 if (e.ready.load(std::memory_order_relaxed)) // Recheck under lock
1208 return e.baseAddress;
1210 // Pieces strings in decreasing order for each color, like ("KPP","KR")
1211 std::string fname, w, b;
1212 for (PieceType pt = KING; pt >= PAWN; --pt)
1214 w += std::string(popcount(pos.pieces(WHITE, pt)), PieceToChar[pt]);
1215 b += std::string(popcount(pos.pieces(BLACK, pt)), PieceToChar[pt]);
1219 (e.key == pos.material_key() ? w + 'v' + b : b + 'v' + w) + (Type == WDL ? ".rtbw" : ".rtbz");
1221 uint8_t* data = TBFile(fname).map(&e.baseAddress, &e.mapping, Type);
1226 e.ready.store(true, std::memory_order_release);
1227 return e.baseAddress;
1230 template<TBType Type, typename Ret = typename TBTable<Type>::Ret>
1231 Ret probe_table(const Position& pos, ProbeState* result, WDLScore wdl = WDLDraw) {
1233 if (pos.count<ALL_PIECES>() == 2) // KvK
1234 return Ret(WDLDraw);
1236 TBTable<Type>* entry = TBTables.get<Type>(pos.material_key());
1238 if (!entry || !mapped(*entry, pos))
1239 return *result = FAIL, Ret();
1241 return do_probe_table(pos, entry, wdl, result);
1244 // For a position where the side to move has a winning capture it is not necessary
1245 // to store a winning value so the generator treats such positions as "don't care"
1246 // and tries to assign to it a value that improves the compression ratio. Similarly,
1247 // if the side to move has a drawing capture, then the position is at least drawn.
1248 // If the position is won, then the TB needs to store a win value. But if the
1249 // position is drawn, the TB may store a loss value if that is better for compression.
1250 // All of this means that during probing, the engine must look at captures and probe
1251 // their results and must probe the position itself. The "best" result of these
1252 // probes is the correct result for the position.
1253 // DTZ tables do not store values when a following move is a zeroing winning move
1254 // (winning capture or winning pawn move). Also, DTZ store wrong values for positions
1255 // where the best move is an ep-move (even if losing). So in all these cases set
1256 // the state to ZEROING_BEST_MOVE.
1257 template<bool CheckZeroingMoves>
1258 WDLScore search(Position& pos, ProbeState* result) {
1260 WDLScore value, bestValue = WDLLoss;
1263 auto moveList = MoveList<LEGAL>(pos);
1264 size_t totalCount = moveList.size(), moveCount = 0;
1266 for (const Move move : moveList)
1268 if (!pos.capture(move) && (!CheckZeroingMoves || type_of(pos.moved_piece(move)) != PAWN))
1273 pos.do_move(move, st);
1274 value = -search<false>(pos, result);
1275 pos.undo_move(move);
1277 if (*result == FAIL)
1280 if (value > bestValue)
1284 if (value >= WDLWin)
1286 *result = ZEROING_BEST_MOVE; // Winning DTZ-zeroing move
1292 // In case we have already searched all the legal moves we don't have to probe
1293 // the TB because the stored score could be wrong. For instance TB tables
1294 // do not contain information on position with ep rights, so in this case
1295 // the result of probe_wdl_table is wrong. Also in case of only capture
1296 // moves, for instance here 4K3/4q3/6p1/2k5/6p1/8/8/8 w - - 0 7, we have to
1297 // return with ZEROING_BEST_MOVE set.
1298 bool noMoreMoves = (moveCount && moveCount == totalCount);
1304 value = probe_table<WDL>(pos, result);
1306 if (*result == FAIL)
1310 // DTZ stores a "don't care" value if bestValue is a win
1311 if (bestValue >= value)
1312 return *result = (bestValue > WDLDraw || noMoreMoves ? ZEROING_BEST_MOVE : OK), bestValue;
1314 return *result = OK, value;
1320 // Called at startup and after every change to
1321 // "SyzygyPath" UCI option to (re)create the various tables. It is not thread
1322 // safe, nor it needs to be.
1323 void Tablebases::init(const std::string& paths) {
1327 TBFile::Paths = paths;
1329 if (paths.empty() || paths == "<empty>")
1332 // MapB1H1H7[] encodes a square below a1-h8 diagonal to 0..27
1334 for (Square s = SQ_A1; s <= SQ_H8; ++s)
1335 if (off_A1H8(s) < 0)
1336 MapB1H1H7[s] = code++;
1338 // MapA1D1D4[] encodes a square in the a1-d1-d4 triangle to 0..9
1339 std::vector<Square> diagonal;
1341 for (Square s = SQ_A1; s <= SQ_D4; ++s)
1342 if (off_A1H8(s) < 0 && file_of(s) <= FILE_D)
1343 MapA1D1D4[s] = code++;
1345 else if (!off_A1H8(s) && file_of(s) <= FILE_D)
1346 diagonal.push_back(s);
1348 // Diagonal squares are encoded as last ones
1349 for (auto s : diagonal)
1350 MapA1D1D4[s] = code++;
1352 // MapKK[] encodes all the 462 possible legal positions of two kings where
1353 // the first is in the a1-d1-d4 triangle. If the first king is on the a1-d4
1354 // diagonal, the other one shall not be above the a1-h8 diagonal.
1355 std::vector<std::pair<int, Square>> bothOnDiagonal;
1357 for (int idx = 0; idx < 10; idx++)
1358 for (Square s1 = SQ_A1; s1 <= SQ_D4; ++s1)
1359 if (MapA1D1D4[s1] == idx && (idx || s1 == SQ_B1)) // SQ_B1 is mapped to 0
1361 for (Square s2 = SQ_A1; s2 <= SQ_H8; ++s2)
1362 if ((PseudoAttacks[KING][s1] | s1) & s2)
1363 continue; // Illegal position
1365 else if (!off_A1H8(s1) && off_A1H8(s2) > 0)
1366 continue; // First on diagonal, second above
1368 else if (!off_A1H8(s1) && !off_A1H8(s2))
1369 bothOnDiagonal.emplace_back(idx, s2);
1372 MapKK[idx][s2] = code++;
1375 // Legal positions with both kings on a diagonal are encoded as last ones
1376 for (auto p : bothOnDiagonal)
1377 MapKK[p.first][p.second] = code++;
1379 // Binomial[] stores the Binomial Coefficients using Pascal rule. There
1380 // are Binomial[k][n] ways to choose k elements from a set of n elements.
1383 for (int n = 1; n < 64; n++) // Squares
1384 for (int k = 0; k < 6 && k <= n; ++k) // Pieces
1386 (k > 0 ? Binomial[k - 1][n - 1] : 0) + (k < n ? Binomial[k][n - 1] : 0);
1388 // MapPawns[s] encodes squares a2-h7 to 0..47. This is the number of possible
1389 // available squares when the leading one is in 's'. Moreover the pawn with
1390 // highest MapPawns[] is the leading pawn, the one nearest the edge, and
1391 // among pawns with the same file, the one with the lowest rank.
1392 int availableSquares = 47; // Available squares when lead pawn is in a2
1394 // Init the tables for the encoding of leading pawns group: with 7-men TB we
1395 // can have up to 5 leading pawns (KPPPPPK).
1396 for (int leadPawnsCnt = 1; leadPawnsCnt <= 5; ++leadPawnsCnt)
1397 for (File f = FILE_A; f <= FILE_D; ++f)
1399 // Restart the index at every file because TB table is split
1400 // by file, so we can reuse the same index for different files.
1403 // Sum all possible combinations for a given file, starting with
1404 // the leading pawn on rank 2 and increasing the rank.
1405 for (Rank r = RANK_2; r <= RANK_7; ++r)
1407 Square sq = make_square(f, r);
1409 // Compute MapPawns[] at first pass.
1410 // If sq is the leading pawn square, any other pawn cannot be
1411 // below or more toward the edge of sq. There are 47 available
1412 // squares when sq = a2 and reduced by 2 for any rank increase
1413 // due to mirroring: sq == a3 -> no a2, h2, so MapPawns[a3] = 45
1414 if (leadPawnsCnt == 1)
1416 MapPawns[sq] = availableSquares--;
1417 MapPawns[flip_file(sq)] = availableSquares--;
1419 LeadPawnIdx[leadPawnsCnt][sq] = idx;
1420 idx += Binomial[leadPawnsCnt - 1][MapPawns[sq]];
1422 // After a file is traversed, store the cumulated per-file index
1423 LeadPawnsSize[leadPawnsCnt][f] = idx;
1426 // Add entries in TB tables if the corresponding ".rtbw" file exists
1427 for (PieceType p1 = PAWN; p1 < KING; ++p1)
1429 TBTables.add({KING, p1, KING});
1431 for (PieceType p2 = PAWN; p2 <= p1; ++p2)
1433 TBTables.add({KING, p1, p2, KING});
1434 TBTables.add({KING, p1, KING, p2});
1436 for (PieceType p3 = PAWN; p3 < KING; ++p3)
1437 TBTables.add({KING, p1, p2, KING, p3});
1439 for (PieceType p3 = PAWN; p3 <= p2; ++p3)
1441 TBTables.add({KING, p1, p2, p3, KING});
1443 for (PieceType p4 = PAWN; p4 <= p3; ++p4)
1445 TBTables.add({KING, p1, p2, p3, p4, KING});
1447 for (PieceType p5 = PAWN; p5 <= p4; ++p5)
1448 TBTables.add({KING, p1, p2, p3, p4, p5, KING});
1450 for (PieceType p5 = PAWN; p5 < KING; ++p5)
1451 TBTables.add({KING, p1, p2, p3, p4, KING, p5});
1454 for (PieceType p4 = PAWN; p4 < KING; ++p4)
1456 TBTables.add({KING, p1, p2, p3, KING, p4});
1458 for (PieceType p5 = PAWN; p5 <= p4; ++p5)
1459 TBTables.add({KING, p1, p2, p3, KING, p4, p5});
1463 for (PieceType p3 = PAWN; p3 <= p1; ++p3)
1464 for (PieceType p4 = PAWN; p4 <= (p1 == p3 ? p2 : p3); ++p4)
1465 TBTables.add({KING, p1, p2, KING, p3, p4});
1469 sync_cout << "info string Found " << TBTables.size() << " tablebases" << sync_endl;
1472 // Probe the WDL table for a particular position.
1473 // If *result != FAIL, the probe was successful.
1474 // The return value is from the point of view of the side to move:
1476 // -1 : loss, but draw under 50-move rule
1478 // 1 : win, but draw under 50-move rule
1480 WDLScore Tablebases::probe_wdl(Position& pos, ProbeState* result) {
1483 return search<false>(pos, result);
1486 // Probe the DTZ table for a particular position.
1487 // If *result != FAIL, the probe was successful.
1488 // The return value is from the point of view of the side to move:
1489 // n < -100 : loss, but draw under 50-move rule
1490 // -100 <= n < -1 : loss in n ply (assuming 50-move counter == 0)
1491 // -1 : loss, the side to move is mated
1493 // 1 < n <= 100 : win in n ply (assuming 50-move counter == 0)
1494 // 100 < n : win, but draw under 50-move rule
1496 // The return value n can be off by 1: a return value -n can mean a loss
1497 // in n+1 ply and a return value +n can mean a win in n+1 ply. This
1498 // cannot happen for tables with positions exactly on the "edge" of
1499 // the 50-move rule.
1501 // This implies that if dtz > 0 is returned, the position is certainly
1502 // a win if dtz + 50-move-counter <= 99. Care must be taken that the engine
1503 // picks moves that preserve dtz + 50-move-counter <= 99.
1505 // If n = 100 immediately after a capture or pawn move, then the position
1506 // is also certainly a win, and during the whole phase until the next
1507 // capture or pawn move, the inequality to be preserved is
1508 // dtz + 50-move-counter <= 100.
1510 // In short, if a move is available resulting in dtz + 50-move-counter <= 99,
1511 // then do not accept moves leading to dtz + 50-move-counter == 100.
1512 int Tablebases::probe_dtz(Position& pos, ProbeState* result) {
1515 WDLScore wdl = search<true>(pos, result);
1517 if (*result == FAIL || wdl == WDLDraw) // DTZ tables don't store draws
1520 // DTZ stores a 'don't care value in this case, or even a plain wrong
1521 // one as in case the best move is a losing ep, so it cannot be probed.
1522 if (*result == ZEROING_BEST_MOVE)
1523 return dtz_before_zeroing(wdl);
1525 int dtz = probe_table<DTZ>(pos, result, wdl);
1527 if (*result == FAIL)
1530 if (*result != CHANGE_STM)
1531 return (dtz + 100 * (wdl == WDLBlessedLoss || wdl == WDLCursedWin)) * sign_of(wdl);
1533 // DTZ stores results for the other side, so we need to do a 1-ply search and
1534 // find the winning move that minimizes DTZ.
1536 int minDTZ = 0xFFFF;
1538 for (const Move move : MoveList<LEGAL>(pos))
1540 bool zeroing = pos.capture(move) || type_of(pos.moved_piece(move)) == PAWN;
1542 pos.do_move(move, st);
1544 // For zeroing moves we want the dtz of the move _before_ doing it,
1545 // otherwise we will get the dtz of the next move sequence. Search the
1546 // position after the move to get the score sign (because even in a
1547 // winning position we could make a losing capture or go for a draw).
1548 dtz = zeroing ? -dtz_before_zeroing(search<false>(pos, result)) : -probe_dtz(pos, result);
1550 // If the move mates, force minDTZ to 1
1551 if (dtz == 1 && pos.checkers() && MoveList<LEGAL>(pos).size() == 0)
1554 // Convert result from 1-ply search. Zeroing moves are already accounted
1555 // by dtz_before_zeroing() that returns the DTZ of the previous move.
1557 dtz += sign_of(dtz);
1559 // Skip the draws and if we are winning only pick positive dtz
1560 if (dtz < minDTZ && sign_of(dtz) == sign_of(wdl))
1563 pos.undo_move(move);
1565 if (*result == FAIL)
1569 // When there are no legal moves, the position is mate: we return -1
1570 return minDTZ == 0xFFFF ? -1 : minDTZ;
1574 // Use the DTZ tables to rank root moves.
1576 // A return value false indicates that not all probes were successful.
1577 bool Tablebases::root_probe(Position& pos, Search::RootMoves& rootMoves) {
1579 ProbeState result = OK;
1582 // Obtain 50-move counter for the root position
1583 int cnt50 = pos.rule50_count();
1585 // Check whether a position was repeated since the last zeroing move.
1586 bool rep = pos.has_repeated();
1588 int dtz, bound = Options["Syzygy50MoveRule"] ? (MAX_DTZ - 100) : 1;
1590 // Probe and rank each move
1591 for (auto& m : rootMoves)
1593 pos.do_move(m.pv[0], st);
1595 // Calculate dtz for the current move counting from the root position
1596 if (pos.rule50_count() == 0)
1598 // In case of a zeroing move, dtz is one of -101/-1/0/1/101
1599 WDLScore wdl = -probe_wdl(pos, &result);
1600 dtz = dtz_before_zeroing(wdl);
1602 else if (pos.is_draw(1))
1604 // In case a root move leads to a draw by repetition or 50-move rule,
1605 // we set dtz to zero. Note: since we are only 1 ply from the root,
1606 // this must be a true 3-fold repetition inside the game history.
1611 // Otherwise, take dtz for the new position and correct by 1 ply
1612 dtz = -probe_dtz(pos, &result);
1613 dtz = dtz > 0 ? dtz + 1 : dtz < 0 ? dtz - 1 : dtz;
1616 // Make sure that a mating move is assigned a dtz value of 1
1617 if (pos.checkers() && dtz == 2 && MoveList<LEGAL>(pos).size() == 0)
1620 pos.undo_move(m.pv[0]);
1625 // Better moves are ranked higher. Certain wins are ranked equally.
1626 // Losing moves are ranked equally unless a 50-move draw is in sight.
1627 int r = dtz > 0 ? (dtz + cnt50 <= 99 && !rep ? MAX_DTZ : MAX_DTZ - (dtz + cnt50))
1628 : dtz < 0 ? (-dtz * 2 + cnt50 < 100 ? -MAX_DTZ : -MAX_DTZ + (-dtz + cnt50))
1632 // Determine the score to be displayed for this move. Assign at least
1633 // 1 cp to cursed wins and let it grow to 49 cp as the positions gets
1634 // closer to a real win.
1635 m.tbScore = r >= bound ? VALUE_MATE - MAX_PLY - 1
1636 : r > 0 ? Value((std::max(3, r - (MAX_DTZ - 200)) * int(PawnValue)) / 200)
1637 : r == 0 ? VALUE_DRAW
1638 : r > -bound ? Value((std::min(-3, r + (MAX_DTZ - 200)) * int(PawnValue)) / 200)
1639 : -VALUE_MATE + MAX_PLY + 1;
1646 // Use the WDL tables to rank root moves.
1647 // This is a fallback for the case that some or all DTZ tables are missing.
1649 // A return value false indicates that not all probes were successful.
1650 bool Tablebases::root_probe_wdl(Position& pos, Search::RootMoves& rootMoves) {
1652 static const int WDL_to_rank[] = {-MAX_DTZ, -MAX_DTZ + 101, 0, MAX_DTZ - 101, MAX_DTZ};
1654 ProbeState result = OK;
1658 bool rule50 = Options["Syzygy50MoveRule"];
1660 // Probe and rank each move
1661 for (auto& m : rootMoves)
1663 pos.do_move(m.pv[0], st);
1668 wdl = -probe_wdl(pos, &result);
1670 pos.undo_move(m.pv[0]);
1675 m.tbRank = WDL_to_rank[wdl + 2];
1678 wdl = wdl > WDLDraw ? WDLWin : wdl < WDLDraw ? WDLLoss : WDLDraw;
1679 m.tbScore = WDL_to_value[wdl + 2];
1685 } // namespace Stockfish