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 = 1 << 18; // Max DTZ supported, large enough to deal with the syzygy TB limit.
70 enum { BigEndian, LittleEndian };
71 enum TBType { WDL, DTZ }; // Used as template parameter
73 // Each table has a set of flags: all of them refer to DTZ tables, the last one to WDL tables
74 enum TBFlag { STM = 1, Mapped = 2, WinPlies = 4, LossPlies = 8, Wide = 16, SingleValue = 128 };
76 inline WDLScore operator-(WDLScore d) { return WDLScore(-int(d)); }
77 inline Square operator^(Square s, int i) { return Square(int(s) ^ i); }
79 constexpr std::string_view PieceToChar = " PNBRQK pnbrqk";
81 int MapPawns[SQUARE_NB];
82 int MapB1H1H7[SQUARE_NB];
83 int MapA1D1D4[SQUARE_NB];
84 int MapKK[10][SQUARE_NB]; // [MapA1D1D4][SQUARE_NB]
86 int Binomial[6][SQUARE_NB]; // [k][n] k elements from a set of n elements
87 int LeadPawnIdx[6][SQUARE_NB]; // [leadPawnsCnt][SQUARE_NB]
88 int LeadPawnsSize[6][4]; // [leadPawnsCnt][FILE_A..FILE_D]
90 // Comparison function to sort leading pawns in ascending MapPawns[] order
91 bool pawns_comp(Square i, Square j) { return MapPawns[i] < MapPawns[j]; }
92 int off_A1H8(Square sq) { return int(rank_of(sq)) - file_of(sq); }
94 constexpr Value WDL_to_value[] = {
95 -VALUE_MATE + MAX_PLY + 1,
99 VALUE_MATE - MAX_PLY - 1
102 template<typename T, int Half = sizeof(T) / 2, int End = sizeof(T) - 1>
103 inline void swap_endian(T& x)
105 static_assert(std::is_unsigned_v<T>, "Argument of swap_endian not unsigned");
107 uint8_t tmp, *c = (uint8_t*)&x;
108 for (int i = 0; i < Half; ++i)
109 tmp = c[i], c[i] = c[End - i], c[End - i] = tmp;
111 template<> inline void swap_endian<uint8_t>(uint8_t&) {}
113 template<typename T, int LE> T number(void* addr)
117 if (uintptr_t(addr) & (alignof(T) - 1)) // Unaligned pointer (very rare)
118 std::memcpy(&v, addr, sizeof(T));
122 if (LE != IsLittleEndian)
127 // DTZ tables don't store valid scores for moves that reset the rule50 counter
128 // like captures and pawn moves but we can easily recover the correct dtz of the
129 // previous move if we know the position's WDL score.
130 int dtz_before_zeroing(WDLScore wdl) {
131 return wdl == WDLWin ? 1 :
132 wdl == WDLCursedWin ? 101 :
133 wdl == WDLBlessedLoss ? -101 :
134 wdl == WDLLoss ? -1 : 0;
137 // Return the sign of a number (-1, 0, 1)
138 template <typename T> int sign_of(T val) {
139 return (T(0) < val) - (val < T(0));
142 // Numbers in little-endian used by sparseIndex[] to point into blockLength[]
144 char block[4]; // Number of block
145 char offset[2]; // Offset within the block
148 static_assert(sizeof(SparseEntry) == 6, "SparseEntry must be 6 bytes");
150 using Sym = uint16_t; // Huffman symbol
153 enum Side { Left, Right };
155 uint8_t lr[3]; // The first 12 bits is the left-hand symbol, the second 12
156 // bits is the right-hand symbol. If the symbol has length 1,
157 // then the left-hand symbol is the stored value.
160 return S == Left ? ((lr[1] & 0xF) << 8) | lr[0] :
161 S == Right ? (lr[2] << 4) | (lr[1] >> 4) : (assert(false), Sym(-1));
165 static_assert(sizeof(LR) == 3, "LR tree entry must be 3 bytes");
167 // Tablebases data layout is structured as following:
169 // TBFile: memory maps/unmaps the physical .rtbw and .rtbz files
170 // TBTable: one object for each file with corresponding indexing information
171 // TBTables: has ownership of TBTable objects, keeping a list and a hash
173 // class TBFile memory maps/unmaps the single .rtbw and .rtbz files. Files are
174 // memory mapped for best performance. Files are mapped at first access: at init
175 // time only existence of the file is checked.
176 class TBFile : public std::ifstream {
181 // Look for and open the file among the Paths directories where the .rtbw
182 // and .rtbz files can be found. Multiple directories are separated by ";"
183 // on Windows and by ":" on Unix-based operating systems.
186 // C:\tb\wdl345;C:\tb\wdl6;D:\tb\dtz345;D:\tb\dtz6
187 static std::string Paths;
189 TBFile(const std::string& f) {
192 constexpr char SepChar = ':';
194 constexpr char SepChar = ';';
196 std::stringstream ss(Paths);
199 while (std::getline(ss, path, SepChar))
201 fname = path + "/" + f;
202 std::ifstream::open(fname);
208 // Memory map the file and check it.
209 uint8_t* map(void** baseAddress, uint64_t* mapping, TBType type) {
211 close(); // Need to re-open to get native file descriptor
215 int fd = ::open(fname.c_str(), O_RDONLY);
218 return *baseAddress = nullptr, nullptr;
222 if (statbuf.st_size % 64 != 16)
224 std::cerr << "Corrupt tablebase file " << fname << std::endl;
228 *mapping = statbuf.st_size;
229 *baseAddress = mmap(nullptr, statbuf.st_size, PROT_READ, MAP_SHARED, fd, 0);
230 #if defined(MADV_RANDOM)
231 madvise(*baseAddress, statbuf.st_size, MADV_RANDOM);
235 if (*baseAddress == MAP_FAILED)
237 std::cerr << "Could not mmap() " << fname << std::endl;
241 // Note FILE_FLAG_RANDOM_ACCESS is only a hint to Windows and as such may get ignored.
242 HANDLE fd = CreateFileA(fname.c_str(), GENERIC_READ, FILE_SHARE_READ, nullptr,
243 OPEN_EXISTING, FILE_FLAG_RANDOM_ACCESS, nullptr);
245 if (fd == INVALID_HANDLE_VALUE)
246 return *baseAddress = nullptr, nullptr;
249 DWORD size_low = GetFileSize(fd, &size_high);
251 if (size_low % 64 != 16)
253 std::cerr << "Corrupt tablebase file " << fname << std::endl;
257 HANDLE mmap = CreateFileMapping(fd, nullptr, PAGE_READONLY, size_high, size_low, nullptr);
262 std::cerr << "CreateFileMapping() failed" << std::endl;
266 *mapping = uint64_t(mmap);
267 *baseAddress = MapViewOfFile(mmap, FILE_MAP_READ, 0, 0, 0);
271 std::cerr << "MapViewOfFile() failed, name = " << fname
272 << ", error = " << GetLastError() << std::endl;
276 uint8_t* data = (uint8_t*)*baseAddress;
278 constexpr uint8_t Magics[][4] = { { 0xD7, 0x66, 0x0C, 0xA5 },
279 { 0x71, 0xE8, 0x23, 0x5D } };
281 if (memcmp(data, Magics[type == WDL], 4))
283 std::cerr << "Corrupted table in file " << fname << std::endl;
284 unmap(*baseAddress, *mapping);
285 return *baseAddress = nullptr, nullptr;
288 return data + 4; // Skip Magics's header
291 static void unmap(void* baseAddress, uint64_t mapping) {
294 munmap(baseAddress, mapping);
296 UnmapViewOfFile(baseAddress);
297 CloseHandle((HANDLE)mapping);
302 std::string TBFile::Paths;
304 // struct PairsData contains low-level indexing information to access TB data.
305 // There are 8, 4, or 2 PairsData records for each TBTable, according to the type
306 // of table and if positions have pawns or not. It is populated at first access.
308 uint8_t flags; // Table flags, see enum TBFlag
309 uint8_t maxSymLen; // Maximum length in bits of the Huffman symbols
310 uint8_t minSymLen; // Minimum length in bits of the Huffman symbols
311 uint32_t blocksNum; // Number of blocks in the TB file
312 size_t sizeofBlock; // Block size in bytes
313 size_t span; // About every span values there is a SparseIndex[] entry
314 Sym* lowestSym; // lowestSym[l] is the symbol of length l with the lowest value
315 LR* btree; // btree[sym] stores the left and right symbols that expand sym
316 uint16_t* blockLength; // Number of stored positions (minus one) for each block: 1..65536
317 uint32_t blockLengthSize; // Size of blockLength[] table: padded so it's bigger than blocksNum
318 SparseEntry* sparseIndex; // Partial indices into blockLength[]
319 size_t sparseIndexSize; // Size of SparseIndex[] table
320 uint8_t* data; // Start of Huffman compressed data
321 std::vector<uint64_t> base64; // base64[l - min_sym_len] is the 64bit-padded lowest symbol of length l
322 std::vector<uint8_t> symlen; // Number of values (-1) represented by a given Huffman symbol: 1..256
323 Piece pieces[TBPIECES]; // Position pieces: the order of pieces defines the groups
324 uint64_t groupIdx[TBPIECES+1]; // Start index used for the encoding of the group's pieces
325 int groupLen[TBPIECES+1]; // Number of pieces in a given group: KRKN -> (3, 1)
326 uint16_t map_idx[4]; // WDLWin, WDLLoss, WDLCursedWin, WDLBlessedLoss (used in DTZ)
329 // struct TBTable contains indexing information to access the corresponding TBFile.
330 // There are 2 types of TBTable, corresponding to a WDL or a DTZ file. TBTable
331 // is populated at init time but the nested PairsData records are populated at
332 // first access, when the corresponding file is memory mapped.
333 template<TBType Type>
335 using Ret = std::conditional_t<Type == WDL, WDLScore, int>;
337 static constexpr int Sides = Type == WDL ? 2 : 1;
339 std::atomic_bool ready;
347 bool hasUniquePieces;
348 uint8_t pawnCount[2]; // [Lead color / other color]
349 PairsData items[Sides][4]; // [wtm / btm][FILE_A..FILE_D or 0]
351 PairsData* get(int stm, int f) {
352 return &items[stm % Sides][hasPawns ? f : 0];
355 TBTable() : ready(false), baseAddress(nullptr) {}
356 explicit TBTable(const std::string& code);
357 explicit TBTable(const TBTable<WDL>& wdl);
361 TBFile::unmap(baseAddress, mapping);
366 TBTable<WDL>::TBTable(const std::string& code) : TBTable() {
371 key = pos.set(code, WHITE, &st).material_key();
372 pieceCount = pos.count<ALL_PIECES>();
373 hasPawns = pos.pieces(PAWN);
375 hasUniquePieces = false;
376 for (Color c : { WHITE, BLACK })
377 for (PieceType pt = PAWN; pt < KING; ++pt)
378 if (popcount(pos.pieces(c, pt)) == 1)
379 hasUniquePieces = true;
381 // Set the leading color. In case both sides have pawns the leading color
382 // is the side with fewer pawns because this leads to better compression.
383 bool c = !pos.count<PAWN>(BLACK)
384 || ( pos.count<PAWN>(WHITE)
385 && pos.count<PAWN>(BLACK) >= pos.count<PAWN>(WHITE));
387 pawnCount[0] = pos.count<PAWN>(c ? WHITE : BLACK);
388 pawnCount[1] = pos.count<PAWN>(c ? BLACK : WHITE);
390 key2 = pos.set(code, BLACK, &st).material_key();
394 TBTable<DTZ>::TBTable(const TBTable<WDL>& wdl) : TBTable() {
396 // Use the corresponding WDL table to avoid recalculating all from scratch
399 pieceCount = wdl.pieceCount;
400 hasPawns = wdl.hasPawns;
401 hasUniquePieces = wdl.hasUniquePieces;
402 pawnCount[0] = wdl.pawnCount[0];
403 pawnCount[1] = wdl.pawnCount[1];
406 // class TBTables creates and keeps ownership of the TBTable objects, one for
407 // each TB file found. It supports a fast, hash-based, table lookup. Populated
408 // at init time, accessed at probe time.
417 template <TBType Type>
418 TBTable<Type>* get() const {
419 return (TBTable<Type>*)(Type == WDL ? (void*)wdl : (void*)dtz);
423 static constexpr int Size = 1 << 12; // 4K table, indexed by key's 12 lsb
424 static constexpr int Overflow = 1; // Number of elements allowed to map to the last bucket
426 Entry hashTable[Size + Overflow];
428 std::deque<TBTable<WDL>> wdlTable;
429 std::deque<TBTable<DTZ>> dtzTable;
431 void insert(Key key, TBTable<WDL>* wdl, TBTable<DTZ>* dtz) {
432 uint32_t homeBucket = uint32_t(key) & (Size - 1);
433 Entry entry{ key, wdl, dtz };
435 // Ensure last element is empty to avoid overflow when looking up
436 for (uint32_t bucket = homeBucket; bucket < Size + Overflow - 1; ++bucket) {
437 Key otherKey = hashTable[bucket].key;
438 if (otherKey == key || !hashTable[bucket].get<WDL>()) {
439 hashTable[bucket] = entry;
443 // Robin Hood hashing: If we've probed for longer than this element,
444 // insert here and search for a new spot for the other element instead.
445 uint32_t otherHomeBucket = uint32_t(otherKey) & (Size - 1);
446 if (otherHomeBucket > homeBucket) {
447 std::swap(entry, hashTable[bucket]);
449 homeBucket = otherHomeBucket;
452 std::cerr << "TB hash table size too low!" << std::endl;
457 template<TBType Type>
458 TBTable<Type>* get(Key key) {
459 for (const Entry* entry = &hashTable[uint32_t(key) & (Size - 1)]; ; ++entry) {
460 if (entry->key == key || !entry->get<Type>())
461 return entry->get<Type>();
466 memset(hashTable, 0, sizeof(hashTable));
470 size_t size() const { return wdlTable.size(); }
471 void add(const std::vector<PieceType>& pieces);
476 // If the corresponding file exists two new objects TBTable<WDL> and TBTable<DTZ>
477 // are created and added to the lists and hash table. Called at init time.
478 void TBTables::add(const std::vector<PieceType>& pieces) {
482 for (PieceType pt : pieces)
483 code += PieceToChar[pt];
485 TBFile file(code.insert(code.find('K', 1), "v") + ".rtbw"); // KRK -> KRvK
487 if (!file.is_open()) // Only WDL file is checked
492 MaxCardinality = std::max(int(pieces.size()), MaxCardinality);
494 wdlTable.emplace_back(code);
495 dtzTable.emplace_back(wdlTable.back());
497 // Insert into the hash keys for both colors: KRvK with KR white and black
498 insert(wdlTable.back().key , &wdlTable.back(), &dtzTable.back());
499 insert(wdlTable.back().key2, &wdlTable.back(), &dtzTable.back());
502 // TB tables are compressed with canonical Huffman code. The compressed data is divided into
503 // blocks of size d->sizeofBlock, and each block stores a variable number of symbols.
504 // Each symbol represents either a WDL or a (remapped) DTZ value, or a pair of other symbols
505 // (recursively). If you keep expanding the symbols in a block, you end up with up to 65536
506 // WDL or DTZ values. Each symbol represents up to 256 values and will correspond after
507 // Huffman coding to at least 1 bit. So a block of 32 bytes corresponds to at most
508 // 32 x 8 x 256 = 65536 values. This maximum is only reached for tables that consist mostly
509 // of draws or mostly of wins, but such tables are actually quite common. In principle, the
510 // blocks in WDL tables are 64 bytes long (and will be aligned on cache lines). But for
511 // mostly-draw or mostly-win tables this can leave many 64-byte blocks only half-filled, so
512 // in such cases blocks are 32 bytes long. The blocks of DTZ tables are up to 1024 bytes long.
513 // The generator picks the size that leads to the smallest table. The "book" of symbols and
514 // Huffman codes are the same for all blocks in the table. A non-symmetric pawnless TB file
515 // will have one table for wtm and one for btm, a TB file with pawns will have tables per
516 // file a,b,c,d also, in this case, one set for wtm and one for btm.
517 int decompress_pairs(PairsData* d, uint64_t idx) {
519 // Special case where all table positions store the same value
520 if (d->flags & TBFlag::SingleValue)
523 // First we need to locate the right block that stores the value at index "idx".
524 // Because each block n stores blockLength[n] + 1 values, the index i of the block
525 // that contains the value at position idx is:
527 // for (i = -1, sum = 0; sum <= idx; i++)
528 // sum += blockLength[i + 1] + 1;
530 // This can be slow, so we use SparseIndex[] populated with a set of SparseEntry that
531 // point to known indices into blockLength[]. Namely SparseIndex[k] is a SparseEntry
532 // that stores the blockLength[] index and the offset within that block of the value
533 // with index I(k), where:
535 // I(k) = k * d->span + d->span / 2 (1)
537 // First step is to get the 'k' of the I(k) nearest to our idx, using definition (1)
538 uint32_t k = uint32_t(idx / d->span);
540 // Then we read the corresponding SparseIndex[] entry
541 uint32_t block = number<uint32_t, LittleEndian>(&d->sparseIndex[k].block);
542 int offset = number<uint16_t, LittleEndian>(&d->sparseIndex[k].offset);
544 // Now compute the difference idx - I(k). From the definition of k, we know that
546 // idx = k * d->span + idx % d->span (2)
548 // So from (1) and (2) we can compute idx - I(K):
549 int diff = idx % d->span - d->span / 2;
551 // Sum the above to offset to find the offset corresponding to our idx
554 // Move to the previous/next block, until we reach the correct block that contains idx,
555 // that is when 0 <= offset <= d->blockLength[block]
557 offset += d->blockLength[--block] + 1;
559 while (offset > d->blockLength[block])
560 offset -= d->blockLength[block++] + 1;
562 // Finally, we find the start address of our block of canonical Huffman symbols
563 uint32_t* ptr = (uint32_t*)(d->data + (uint64_t(block) * d->sizeofBlock));
565 // Read the first 64 bits in our block, this is a (truncated) sequence of
566 // unknown number of symbols of unknown length but we know the first one
567 // is at the beginning of this 64-bit sequence.
568 uint64_t buf64 = number<uint64_t, BigEndian>(ptr); ptr += 2;
574 int len = 0; // This is the symbol length - d->min_sym_len
576 // Now get the symbol length. For any symbol s64 of length l right-padded
577 // to 64 bits we know that d->base64[l-1] >= s64 >= d->base64[l] so we
578 // can find the symbol length iterating through base64[].
579 while (buf64 < d->base64[len])
582 // All the symbols of a given length are consecutive integers (numerical
583 // sequence property), so we can compute the offset of our symbol of
584 // length len, stored at the beginning of buf64.
585 sym = Sym((buf64 - d->base64[len]) >> (64 - len - d->minSymLen));
587 // Now add the value of the lowest symbol of length len to get our symbol
588 sym += number<Sym, LittleEndian>(&d->lowestSym[len]);
590 // If our offset is within the number of values represented by symbol sym,
592 if (offset < d->symlen[sym] + 1)
595 // ...otherwise update the offset and continue to iterate
596 offset -= d->symlen[sym] + 1;
597 len += d->minSymLen; // Get the real length
598 buf64 <<= len; // Consume the just processed symbol
601 if (buf64Size <= 32) { // Refill the buffer
603 buf64 |= uint64_t(number<uint32_t, BigEndian>(ptr++)) << (64 - buf64Size);
607 // Now we have our symbol that expands into d->symlen[sym] + 1 symbols.
608 // We binary-search for our value recursively expanding into the left and
609 // right child symbols until we reach a leaf node where symlen[sym] + 1 == 1
610 // that will store the value we need.
611 while (d->symlen[sym])
613 Sym left = d->btree[sym].get<LR::Left>();
615 // If a symbol contains 36 sub-symbols (d->symlen[sym] + 1 = 36) and
616 // expands in a pair (d->symlen[left] = 23, d->symlen[right] = 11), then
617 // we know that, for instance, the tenth value (offset = 10) will be on
618 // the left side because in Recursive Pairing child symbols are adjacent.
619 if (offset < d->symlen[left] + 1)
622 offset -= d->symlen[left] + 1;
623 sym = d->btree[sym].get<LR::Right>();
627 return d->btree[sym].get<LR::Left>();
630 bool check_dtz_stm(TBTable<WDL>*, int, File) { return true; }
632 bool check_dtz_stm(TBTable<DTZ>* entry, int stm, File f) {
634 auto flags = entry->get(stm, f)->flags;
635 return (flags & TBFlag::STM) == stm
636 || ((entry->key == entry->key2) && !entry->hasPawns);
639 // DTZ scores are sorted by frequency of occurrence and then assigned the
640 // values 0, 1, 2, ... in order of decreasing frequency. This is done for each
641 // of the four WDLScore values. The mapping information necessary to reconstruct
642 // the original values are stored in the TB file and read during map[] init.
643 WDLScore map_score(TBTable<WDL>*, File, int value, WDLScore) { return WDLScore(value - 2); }
645 int map_score(TBTable<DTZ>* entry, File f, int value, WDLScore wdl) {
647 constexpr int WDLMap[] = { 1, 3, 0, 2, 0 };
649 auto flags = entry->get(0, f)->flags;
651 uint8_t* map = entry->map;
652 uint16_t* idx = entry->get(0, f)->map_idx;
653 if (flags & TBFlag::Mapped) {
654 if (flags & TBFlag::Wide)
655 value = ((uint16_t *)map)[idx[WDLMap[wdl + 2]] + value];
657 value = map[idx[WDLMap[wdl + 2]] + value];
660 // DTZ tables store distance to zero in number of moves or plies. We
661 // want to return plies, so we have to convert to plies when needed.
662 if ( (wdl == WDLWin && !(flags & TBFlag::WinPlies))
663 || (wdl == WDLLoss && !(flags & TBFlag::LossPlies))
664 || wdl == WDLCursedWin
665 || wdl == WDLBlessedLoss)
671 // Compute a unique index out of a position and use it to probe the TB file. To
672 // encode k pieces of the same type and color, first sort the pieces by square in
673 // ascending order s1 <= s2 <= ... <= sk then compute the unique index as:
675 // idx = Binomial[1][s1] + Binomial[2][s2] + ... + Binomial[k][sk]
677 template<typename T, typename Ret = typename T::Ret>
678 Ret do_probe_table(const Position& pos, T* entry, WDLScore wdl, ProbeState* result) {
680 Square squares[TBPIECES];
681 Piece pieces[TBPIECES];
683 int next = 0, size = 0, leadPawnsCnt = 0;
685 Bitboard b, leadPawns = 0;
686 File tbFile = FILE_A;
688 // A given TB entry like KRK has associated two material keys: KRvk and Kvkr.
689 // If both sides have the same pieces keys are equal. In this case TB tables
690 // only stores the 'white to move' case, so if the position to lookup has black
691 // to move, we need to switch the color and flip the squares before to lookup.
692 bool symmetricBlackToMove = (entry->key == entry->key2 && pos.side_to_move());
694 // TB files are calculated for white as the stronger side. For instance, we
695 // have KRvK, not KvKR. A position where the stronger side is white will have
696 // its material key == entry->key, otherwise we have to switch the color and
697 // flip the squares before to lookup.
698 bool blackStronger = (pos.material_key() != entry->key);
700 int flipColor = (symmetricBlackToMove || blackStronger) * 8;
701 int flipSquares = (symmetricBlackToMove || blackStronger) * 56;
702 int stm = (symmetricBlackToMove || blackStronger) ^ pos.side_to_move();
704 // For pawns, TB files store 4 separate tables according if leading pawn is on
705 // file a, b, c or d after reordering. The leading pawn is the one with maximum
706 // MapPawns[] value, that is the one most toward the edges and with lowest rank.
707 if (entry->hasPawns) {
709 // In all the 4 tables, pawns are at the beginning of the piece sequence and
710 // their color is the reference one. So we just pick the first one.
711 Piece pc = Piece(entry->get(0, 0)->pieces[0] ^ flipColor);
713 assert(type_of(pc) == PAWN);
715 leadPawns = b = pos.pieces(color_of(pc), PAWN);
717 squares[size++] = pop_lsb(b) ^ flipSquares;
722 std::swap(squares[0], *std::max_element(squares, squares + leadPawnsCnt, pawns_comp));
724 tbFile = File(edge_distance(file_of(squares[0])));
727 // DTZ tables are one-sided, i.e. they store positions only for white to
728 // move or only for black to move, so check for side to move to be stm,
729 // early exit otherwise.
730 if (!check_dtz_stm(entry, stm, tbFile))
731 return *result = CHANGE_STM, Ret();
733 // Now we are ready to get all the position pieces (but the lead pawns) and
734 // directly map them to the correct color and square.
735 b = pos.pieces() ^ leadPawns;
737 Square s = pop_lsb(b);
738 squares[size] = s ^ flipSquares;
739 pieces[size++] = Piece(pos.piece_on(s) ^ flipColor);
744 d = entry->get(stm, tbFile);
746 // Then we reorder the pieces to have the same sequence as the one stored
747 // in pieces[i]: the sequence that ensures the best compression.
748 for (int i = leadPawnsCnt; i < size - 1; ++i)
749 for (int j = i + 1; j < size; ++j)
750 if (d->pieces[i] == pieces[j])
752 std::swap(pieces[i], pieces[j]);
753 std::swap(squares[i], squares[j]);
757 // Now we map again the squares so that the square of the lead piece is in
758 // the triangle A1-D1-D4.
759 if (file_of(squares[0]) > FILE_D)
760 for (int i = 0; i < size; ++i)
761 squares[i] = flip_file(squares[i]);
763 // Encode leading pawns starting with the one with minimum MapPawns[] and
764 // proceeding in ascending order.
765 if (entry->hasPawns) {
766 idx = LeadPawnIdx[leadPawnsCnt][squares[0]];
768 std::stable_sort(squares + 1, squares + leadPawnsCnt, pawns_comp);
770 for (int i = 1; i < leadPawnsCnt; ++i)
771 idx += Binomial[i][MapPawns[squares[i]]];
773 goto encode_remaining; // With pawns we have finished special treatments
776 // In positions without pawns, we further flip the squares to ensure leading
777 // piece is below RANK_5.
778 if (rank_of(squares[0]) > RANK_4)
779 for (int i = 0; i < size; ++i)
780 squares[i] = flip_rank(squares[i]);
782 // Look for the first piece of the leading group not on the A1-D4 diagonal
783 // and ensure it is mapped below the diagonal.
784 for (int i = 0; i < d->groupLen[0]; ++i) {
785 if (!off_A1H8(squares[i]))
788 if (off_A1H8(squares[i]) > 0) // A1-H8 diagonal flip: SQ_A3 -> SQ_C1
789 for (int j = i; j < size; ++j)
790 squares[j] = Square(((squares[j] >> 3) | (squares[j] << 3)) & 63);
794 // Encode the leading group.
796 // Suppose we have KRvK. Let's say the pieces are on square numbers wK, wR
797 // and bK (each 0...63). The simplest way to map this position to an index
800 // index = wK * 64 * 64 + wR * 64 + bK;
802 // But this way the TB is going to have 64*64*64 = 262144 positions, with
803 // lots of positions being equivalent (because they are mirrors of each
804 // other) and lots of positions being invalid (two pieces on one square,
805 // adjacent kings, etc.).
806 // Usually the first step is to take the wK and bK together. There are just
807 // 462 ways legal and not-mirrored ways to place the wK and bK on the board.
808 // Once we have placed the wK and bK, there are 62 squares left for the wR
809 // Mapping its square from 0..63 to available squares 0..61 can be done like:
811 // wR -= (wR > wK) + (wR > bK);
813 // In words: if wR "comes later" than wK, we deduct 1, and the same if wR
814 // "comes later" than bK. In case of two same pieces like KRRvK we want to
815 // place the two Rs "together". If we have 62 squares left, we can place two
816 // Rs "together" in 62 * 61 / 2 ways (we divide by 2 because rooks can be
817 // swapped and still get the same position.)
819 // In case we have at least 3 unique pieces (including kings) we encode them
821 if (entry->hasUniquePieces) {
823 int adjust1 = squares[1] > squares[0];
824 int adjust2 = (squares[2] > squares[0]) + (squares[2] > squares[1]);
826 // First piece is below a1-h8 diagonal. MapA1D1D4[] maps the b1-d1-d3
827 // triangle to 0...5. There are 63 squares for second piece and and 62
828 // (mapped to 0...61) for the third.
829 if (off_A1H8(squares[0]))
830 idx = ( MapA1D1D4[squares[0]] * 63
831 + (squares[1] - adjust1)) * 62
832 + squares[2] - adjust2;
834 // First piece is on a1-h8 diagonal, second below: map this occurrence to
835 // 6 to differentiate from the above case, rank_of() maps a1-d4 diagonal
836 // to 0...3 and finally MapB1H1H7[] maps the b1-h1-h7 triangle to 0..27.
837 else if (off_A1H8(squares[1]))
838 idx = ( 6 * 63 + rank_of(squares[0]) * 28
839 + MapB1H1H7[squares[1]]) * 62
840 + squares[2] - adjust2;
842 // First two pieces are on a1-h8 diagonal, third below
843 else if (off_A1H8(squares[2]))
844 idx = 6 * 63 * 62 + 4 * 28 * 62
845 + rank_of(squares[0]) * 7 * 28
846 + (rank_of(squares[1]) - adjust1) * 28
847 + MapB1H1H7[squares[2]];
849 // All 3 pieces on the diagonal a1-h8
851 idx = 6 * 63 * 62 + 4 * 28 * 62 + 4 * 7 * 28
852 + rank_of(squares[0]) * 7 * 6
853 + (rank_of(squares[1]) - adjust1) * 6
854 + (rank_of(squares[2]) - adjust2);
856 // We don't have at least 3 unique pieces, like in KRRvKBB, just map
858 idx = MapKK[MapA1D1D4[squares[0]]][squares[1]];
861 idx *= d->groupIdx[0];
862 Square* groupSq = squares + d->groupLen[0];
864 // Encode remaining pawns and then pieces according to square, in ascending order
865 bool remainingPawns = entry->hasPawns && entry->pawnCount[1];
867 while (d->groupLen[++next])
869 std::stable_sort(groupSq, groupSq + d->groupLen[next]);
872 // Map down a square if "comes later" than a square in the previous
873 // groups (similar to what was done earlier for leading group pieces).
874 for (int i = 0; i < d->groupLen[next]; ++i)
876 auto f = [&](Square s) { return groupSq[i] > s; };
877 auto adjust = std::count_if(squares, groupSq, f);
878 n += Binomial[i + 1][groupSq[i] - adjust - 8 * remainingPawns];
881 remainingPawns = false;
882 idx += n * d->groupIdx[next];
883 groupSq += d->groupLen[next];
886 // Now that we have the index, decompress the pair and get the score
887 return map_score(entry, tbFile, decompress_pairs(d, idx), wdl);
890 // Group together pieces that will be encoded together. The general rule is that
891 // a group contains pieces of the same type and color. The exception is the leading
892 // group that, in case of positions without pawns, can be formed by 3 different
893 // pieces (default) or by the king pair when there is not a unique piece apart
894 // from the kings. When there are pawns, pawns are always first in pieces[].
896 // As example KRKN -> KRK + N, KNNK -> KK + NN, KPPKP -> P + PP + K + K
898 // The actual grouping depends on the TB generator and can be inferred from the
899 // sequence of pieces in piece[] array.
901 void set_groups(T& e, PairsData* d, int order[], File f) {
903 int n = 0, firstLen = e.hasPawns ? 0 : e.hasUniquePieces ? 3 : 2;
906 // Number of pieces per group is stored in groupLen[], for instance in KRKN
907 // the encoder will default on '111', so groupLen[] will be (3, 1).
908 for (int i = 1; i < e.pieceCount; ++i)
909 if (--firstLen > 0 || d->pieces[i] == d->pieces[i - 1])
912 d->groupLen[++n] = 1;
914 d->groupLen[++n] = 0; // Zero-terminated
916 // The sequence in pieces[] defines the groups, but not the order in which
917 // they are encoded. If the pieces in a group g can be combined on the board
918 // in N(g) different ways, then the position encoding will be of the form:
920 // g1 * N(g2) * N(g3) + g2 * N(g3) + g3
922 // This ensures unique encoding for the whole position. The order of the
923 // groups is a per-table parameter and could not follow the canonical leading
924 // pawns/pieces -> remaining pawns -> remaining pieces. In particular the
925 // first group is at order[0] position and the remaining pawns, when present,
926 // are at order[1] position.
927 bool pp = e.hasPawns && e.pawnCount[1]; // Pawns on both sides
928 int next = pp ? 2 : 1;
929 int freeSquares = 64 - d->groupLen[0] - (pp ? d->groupLen[1] : 0);
932 for (int k = 0; next < n || k == order[0] || k == order[1]; ++k)
933 if (k == order[0]) // Leading pawns or pieces
935 d->groupIdx[0] = idx;
936 idx *= e.hasPawns ? LeadPawnsSize[d->groupLen[0]][f]
937 : e.hasUniquePieces ? 31332 : 462;
939 else if (k == order[1]) // Remaining pawns
941 d->groupIdx[1] = idx;
942 idx *= Binomial[d->groupLen[1]][48 - d->groupLen[0]];
944 else // Remaining pieces
946 d->groupIdx[next] = idx;
947 idx *= Binomial[d->groupLen[next]][freeSquares];
948 freeSquares -= d->groupLen[next++];
951 d->groupIdx[n] = idx;
954 // In Recursive Pairing each symbol represents a pair of children symbols. So
955 // read d->btree[] symbols data and expand each one in his left and right child
956 // symbol until reaching the leaves that represent the symbol value.
957 uint8_t set_symlen(PairsData* d, Sym s, std::vector<bool>& visited) {
959 visited[s] = true; // We can set it now because tree is acyclic
960 Sym sr = d->btree[s].get<LR::Right>();
965 Sym sl = d->btree[s].get<LR::Left>();
968 d->symlen[sl] = set_symlen(d, sl, visited);
971 d->symlen[sr] = set_symlen(d, sr, visited);
973 return d->symlen[sl] + d->symlen[sr] + 1;
976 uint8_t* set_sizes(PairsData* d, uint8_t* data) {
980 if (d->flags & TBFlag::SingleValue) {
981 d->blocksNum = d->blockLengthSize = 0;
982 d->span = d->sparseIndexSize = 0; // Broken MSVC zero-init
983 d->minSymLen = *data++; // Here we store the single value
987 // groupLen[] is a zero-terminated list of group lengths, the last groupIdx[]
988 // element stores the biggest index that is the tb size.
989 uint64_t tbSize = d->groupIdx[std::find(d->groupLen, d->groupLen + 7, 0) - d->groupLen];
991 d->sizeofBlock = 1ULL << *data++;
992 d->span = 1ULL << *data++;
993 d->sparseIndexSize = size_t((tbSize + d->span - 1) / d->span); // Round up
994 auto padding = number<uint8_t, LittleEndian>(data++);
995 d->blocksNum = number<uint32_t, LittleEndian>(data); data += sizeof(uint32_t);
996 d->blockLengthSize = d->blocksNum + padding; // Padded to ensure SparseIndex[]
997 // does not point out of range.
998 d->maxSymLen = *data++;
999 d->minSymLen = *data++;
1000 d->lowestSym = (Sym*)data;
1001 d->base64.resize(d->maxSymLen - d->minSymLen + 1);
1003 // See https://en.wikipedia.org/wiki/Huffman_coding
1004 // The canonical code is ordered such that longer symbols (in terms of
1005 // the number of bits of their Huffman code) have a lower numeric value,
1006 // so that d->lowestSym[i] >= d->lowestSym[i+1] (when read as LittleEndian).
1007 // Starting from this we compute a base64[] table indexed by symbol length
1008 // and containing 64 bit values so that d->base64[i] >= d->base64[i+1].
1010 // Implementation note: we first cast the unsigned size_t "base64.size()"
1011 // to a signed int "base64_size" variable and then we are able to subtract 2,
1012 // avoiding unsigned overflow warnings.
1014 int base64_size = static_cast<int>(d->base64.size());
1015 for (int i = base64_size - 2; i >= 0; --i) {
1016 d->base64[i] = (d->base64[i + 1] + number<Sym, LittleEndian>(&d->lowestSym[i])
1017 - number<Sym, LittleEndian>(&d->lowestSym[i + 1])) / 2;
1019 assert(d->base64[i] * 2 >= d->base64[i+1]);
1022 // Now left-shift by an amount so that d->base64[i] gets shifted 1 bit more
1023 // than d->base64[i+1] and given the above assert condition, we ensure that
1024 // d->base64[i] >= d->base64[i+1]. Moreover for any symbol s64 of length i
1025 // and right-padded to 64 bits holds d->base64[i-1] >= s64 >= d->base64[i].
1026 for (int i = 0; i < base64_size; ++i)
1027 d->base64[i] <<= 64 - i - d->minSymLen; // Right-padding to 64 bits
1029 data += base64_size * sizeof(Sym);
1030 d->symlen.resize(number<uint16_t, LittleEndian>(data)); data += sizeof(uint16_t);
1031 d->btree = (LR*)data;
1033 // The compression scheme used is "Recursive Pairing", that replaces the most
1034 // frequent adjacent pair of symbols in the source message by a new symbol,
1035 // reevaluating the frequencies of all of the symbol pairs with respect to
1036 // the extended alphabet, and then repeating the process.
1037 // See https://web.archive.org/web/20201106232444/http://www.larsson.dogma.net/dcc99.pdf
1038 std::vector<bool> visited(d->symlen.size());
1040 for (Sym sym = 0; sym < d->symlen.size(); ++sym)
1042 d->symlen[sym] = set_symlen(d, sym, visited);
1044 return data + d->symlen.size() * sizeof(LR) + (d->symlen.size() & 1);
1047 uint8_t* set_dtz_map(TBTable<WDL>&, uint8_t* data, File) { return data; }
1049 uint8_t* set_dtz_map(TBTable<DTZ>& e, uint8_t* data, File maxFile) {
1053 for (File f = FILE_A; f <= maxFile; ++f) {
1054 auto flags = e.get(0, f)->flags;
1055 if (flags & TBFlag::Mapped) {
1056 if (flags & TBFlag::Wide) {
1057 data += uintptr_t(data) & 1; // Word alignment, we may have a mixed table
1058 for (int i = 0; i < 4; ++i) { // Sequence like 3,x,x,x,1,x,0,2,x,x
1059 e.get(0, f)->map_idx[i] = uint16_t((uint16_t*)data - (uint16_t*)e.map + 1);
1060 data += 2 * number<uint16_t, LittleEndian>(data) + 2;
1064 for (int i = 0; i < 4; ++i) {
1065 e.get(0, f)->map_idx[i] = uint16_t(data - e.map + 1);
1072 return data += uintptr_t(data) & 1; // Word alignment
1075 // Populate entry's PairsData records with data from the just memory-mapped file.
1076 // Called at first access.
1077 template<typename T>
1078 void set(T& e, uint8_t* data) {
1082 enum { Split = 1, HasPawns = 2 };
1084 assert(e.hasPawns == bool(*data & HasPawns));
1085 assert((e.key != e.key2) == bool(*data & Split));
1087 data++; // First byte stores flags
1089 const int sides = T::Sides == 2 && (e.key != e.key2) ? 2 : 1;
1090 const File maxFile = e.hasPawns ? FILE_D : FILE_A;
1092 bool pp = e.hasPawns && e.pawnCount[1]; // Pawns on both sides
1094 assert(!pp || e.pawnCount[0]);
1096 for (File f = FILE_A; f <= maxFile; ++f) {
1098 for (int i = 0; i < sides; i++)
1099 *e.get(i, f) = PairsData();
1101 int order[][2] = { { *data & 0xF, pp ? *(data + 1) & 0xF : 0xF },
1102 { *data >> 4, pp ? *(data + 1) >> 4 : 0xF } };
1105 for (int k = 0; k < e.pieceCount; ++k, ++data)
1106 for (int i = 0; i < sides; i++)
1107 e.get(i, f)->pieces[k] = Piece(i ? *data >> 4 : *data & 0xF);
1109 for (int i = 0; i < sides; ++i)
1110 set_groups(e, e.get(i, f), order[i], f);
1113 data += uintptr_t(data) & 1; // Word alignment
1115 for (File f = FILE_A; f <= maxFile; ++f)
1116 for (int i = 0; i < sides; i++)
1117 data = set_sizes(e.get(i, f), data);
1119 data = set_dtz_map(e, data, maxFile);
1121 for (File f = FILE_A; f <= maxFile; ++f)
1122 for (int i = 0; i < sides; i++) {
1123 (d = e.get(i, f))->sparseIndex = (SparseEntry*)data;
1124 data += d->sparseIndexSize * sizeof(SparseEntry);
1127 for (File f = FILE_A; f <= maxFile; ++f)
1128 for (int i = 0; i < sides; i++) {
1129 (d = e.get(i, f))->blockLength = (uint16_t*)data;
1130 data += d->blockLengthSize * sizeof(uint16_t);
1133 for (File f = FILE_A; f <= maxFile; ++f)
1134 for (int i = 0; i < sides; i++) {
1135 data = (uint8_t*)((uintptr_t(data) + 0x3F) & ~0x3F); // 64 byte alignment
1136 (d = e.get(i, f))->data = data;
1137 data += d->blocksNum * d->sizeofBlock;
1141 // If the TB file corresponding to the given position is already memory-mapped
1142 // then return its base address, otherwise, try to memory map and init it. Called
1143 // at every probe, memory map, and init only at first access. Function is thread
1144 // safe and can be called concurrently.
1145 template<TBType Type>
1146 void* mapped(TBTable<Type>& e, const Position& pos) {
1148 static std::mutex mutex;
1150 // Use 'acquire' to avoid a thread reading 'ready' == true while
1151 // another is still working. (compiler reordering may cause this).
1152 if (e.ready.load(std::memory_order_acquire))
1153 return e.baseAddress; // Could be nullptr if file does not exist
1155 std::scoped_lock<std::mutex> lk(mutex);
1157 if (e.ready.load(std::memory_order_relaxed)) // Recheck under lock
1158 return e.baseAddress;
1160 // Pieces strings in decreasing order for each color, like ("KPP","KR")
1161 std::string fname, w, b;
1162 for (PieceType pt = KING; pt >= PAWN; --pt) {
1163 w += std::string(popcount(pos.pieces(WHITE, pt)), PieceToChar[pt]);
1164 b += std::string(popcount(pos.pieces(BLACK, pt)), PieceToChar[pt]);
1167 fname = (e.key == pos.material_key() ? w + 'v' + b : b + 'v' + w)
1168 + (Type == WDL ? ".rtbw" : ".rtbz");
1170 uint8_t* data = TBFile(fname).map(&e.baseAddress, &e.mapping, Type);
1175 e.ready.store(true, std::memory_order_release);
1176 return e.baseAddress;
1179 template<TBType Type, typename Ret = typename TBTable<Type>::Ret>
1180 Ret probe_table(const Position& pos, ProbeState* result, WDLScore wdl = WDLDraw) {
1182 if (pos.count<ALL_PIECES>() == 2) // KvK
1183 return Ret(WDLDraw);
1185 TBTable<Type>* entry = TBTables.get<Type>(pos.material_key());
1187 if (!entry || !mapped(*entry, pos))
1188 return *result = FAIL, Ret();
1190 return do_probe_table(pos, entry, wdl, result);
1193 // For a position where the side to move has a winning capture it is not necessary
1194 // to store a winning value so the generator treats such positions as "don't care"
1195 // and tries to assign to it a value that improves the compression ratio. Similarly,
1196 // if the side to move has a drawing capture, then the position is at least drawn.
1197 // If the position is won, then the TB needs to store a win value. But if the
1198 // position is drawn, the TB may store a loss value if that is better for compression.
1199 // All of this means that during probing, the engine must look at captures and probe
1200 // their results and must probe the position itself. The "best" result of these
1201 // probes is the correct result for the position.
1202 // DTZ tables do not store values when a following move is a zeroing winning move
1203 // (winning capture or winning pawn move). Also, DTZ store wrong values for positions
1204 // where the best move is an ep-move (even if losing). So in all these cases set
1205 // the state to ZEROING_BEST_MOVE.
1206 template<bool CheckZeroingMoves>
1207 WDLScore search(Position& pos, ProbeState* result) {
1209 WDLScore value, bestValue = WDLLoss;
1212 auto moveList = MoveList<LEGAL>(pos);
1213 size_t totalCount = moveList.size(), moveCount = 0;
1215 for (const Move move : moveList)
1217 if ( !pos.capture(move)
1218 && (!CheckZeroingMoves || type_of(pos.moved_piece(move)) != PAWN))
1223 pos.do_move(move, st);
1224 value = -search<false>(pos, result);
1225 pos.undo_move(move);
1227 if (*result == FAIL)
1230 if (value > bestValue)
1234 if (value >= WDLWin)
1236 *result = ZEROING_BEST_MOVE; // Winning DTZ-zeroing move
1242 // In case we have already searched all the legal moves we don't have to probe
1243 // the TB because the stored score could be wrong. For instance TB tables
1244 // do not contain information on position with ep rights, so in this case
1245 // the result of probe_wdl_table is wrong. Also in case of only capture
1246 // moves, for instance here 4K3/4q3/6p1/2k5/6p1/8/8/8 w - - 0 7, we have to
1247 // return with ZEROING_BEST_MOVE set.
1248 bool noMoreMoves = (moveCount && moveCount == totalCount);
1254 value = probe_table<WDL>(pos, result);
1256 if (*result == FAIL)
1260 // DTZ stores a "don't care" value if bestValue is a win
1261 if (bestValue >= value)
1262 return *result = ( bestValue > WDLDraw
1263 || noMoreMoves ? ZEROING_BEST_MOVE : OK), bestValue;
1265 return *result = OK, value;
1271 // Tablebases::init() is called at startup and after every change to
1272 // "SyzygyPath" UCI option to (re)create the various tables. It is not thread
1273 // safe, nor it needs to be.
1274 void Tablebases::init(const std::string& paths) {
1278 TBFile::Paths = paths;
1280 if (paths.empty() || paths == "<empty>")
1283 // MapB1H1H7[] encodes a square below a1-h8 diagonal to 0..27
1285 for (Square s = SQ_A1; s <= SQ_H8; ++s)
1286 if (off_A1H8(s) < 0)
1287 MapB1H1H7[s] = code++;
1289 // MapA1D1D4[] encodes a square in the a1-d1-d4 triangle to 0..9
1290 std::vector<Square> diagonal;
1292 for (Square s = SQ_A1; s <= SQ_D4; ++s)
1293 if (off_A1H8(s) < 0 && file_of(s) <= FILE_D)
1294 MapA1D1D4[s] = code++;
1296 else if (!off_A1H8(s) && file_of(s) <= FILE_D)
1297 diagonal.push_back(s);
1299 // Diagonal squares are encoded as last ones
1300 for (auto s : diagonal)
1301 MapA1D1D4[s] = code++;
1303 // MapKK[] encodes all the 462 possible legal positions of two kings where
1304 // the first is in the a1-d1-d4 triangle. If the first king is on the a1-d4
1305 // diagonal, the other one shall not be above the a1-h8 diagonal.
1306 std::vector<std::pair<int, Square>> bothOnDiagonal;
1308 for (int idx = 0; idx < 10; idx++)
1309 for (Square s1 = SQ_A1; s1 <= SQ_D4; ++s1)
1310 if (MapA1D1D4[s1] == idx && (idx || s1 == SQ_B1)) // SQ_B1 is mapped to 0
1312 for (Square s2 = SQ_A1; s2 <= SQ_H8; ++s2)
1313 if ((PseudoAttacks[KING][s1] | s1) & s2)
1314 continue; // Illegal position
1316 else if (!off_A1H8(s1) && off_A1H8(s2) > 0)
1317 continue; // First on diagonal, second above
1319 else if (!off_A1H8(s1) && !off_A1H8(s2))
1320 bothOnDiagonal.emplace_back(idx, s2);
1323 MapKK[idx][s2] = code++;
1326 // Legal positions with both kings on a diagonal are encoded as last ones
1327 for (auto p : bothOnDiagonal)
1328 MapKK[p.first][p.second] = code++;
1330 // Binomial[] stores the Binomial Coefficients using Pascal rule. There
1331 // are Binomial[k][n] ways to choose k elements from a set of n elements.
1334 for (int n = 1; n < 64; n++) // Squares
1335 for (int k = 0; k < 6 && k <= n; ++k) // Pieces
1336 Binomial[k][n] = (k > 0 ? Binomial[k - 1][n - 1] : 0)
1337 + (k < n ? Binomial[k ][n - 1] : 0);
1339 // MapPawns[s] encodes squares a2-h7 to 0..47. This is the number of possible
1340 // available squares when the leading one is in 's'. Moreover the pawn with
1341 // highest MapPawns[] is the leading pawn, the one nearest the edge, and
1342 // among pawns with the same file, the one with the lowest rank.
1343 int availableSquares = 47; // Available squares when lead pawn is in a2
1345 // Init the tables for the encoding of leading pawns group: with 7-men TB we
1346 // can have up to 5 leading pawns (KPPPPPK).
1347 for (int leadPawnsCnt = 1; leadPawnsCnt <= 5; ++leadPawnsCnt)
1348 for (File f = FILE_A; f <= FILE_D; ++f)
1350 // Restart the index at every file because TB table is split
1351 // by file, so we can reuse the same index for different files.
1354 // Sum all possible combinations for a given file, starting with
1355 // the leading pawn on rank 2 and increasing the rank.
1356 for (Rank r = RANK_2; r <= RANK_7; ++r)
1358 Square sq = make_square(f, r);
1360 // Compute MapPawns[] at first pass.
1361 // If sq is the leading pawn square, any other pawn cannot be
1362 // below or more toward the edge of sq. There are 47 available
1363 // squares when sq = a2 and reduced by 2 for any rank increase
1364 // due to mirroring: sq == a3 -> no a2, h2, so MapPawns[a3] = 45
1365 if (leadPawnsCnt == 1)
1367 MapPawns[sq] = availableSquares--;
1368 MapPawns[flip_file(sq)] = availableSquares--;
1370 LeadPawnIdx[leadPawnsCnt][sq] = idx;
1371 idx += Binomial[leadPawnsCnt - 1][MapPawns[sq]];
1373 // After a file is traversed, store the cumulated per-file index
1374 LeadPawnsSize[leadPawnsCnt][f] = idx;
1377 // Add entries in TB tables if the corresponding ".rtbw" file exists
1378 for (PieceType p1 = PAWN; p1 < KING; ++p1) {
1379 TBTables.add({KING, p1, KING});
1381 for (PieceType p2 = PAWN; p2 <= p1; ++p2) {
1382 TBTables.add({KING, p1, p2, KING});
1383 TBTables.add({KING, p1, KING, p2});
1385 for (PieceType p3 = PAWN; p3 < KING; ++p3)
1386 TBTables.add({KING, p1, p2, KING, p3});
1388 for (PieceType p3 = PAWN; p3 <= p2; ++p3) {
1389 TBTables.add({KING, p1, p2, p3, KING});
1391 for (PieceType p4 = PAWN; p4 <= p3; ++p4) {
1392 TBTables.add({KING, p1, p2, p3, p4, KING});
1394 for (PieceType p5 = PAWN; p5 <= p4; ++p5)
1395 TBTables.add({KING, p1, p2, p3, p4, p5, KING});
1397 for (PieceType p5 = PAWN; p5 < KING; ++p5)
1398 TBTables.add({KING, p1, p2, p3, p4, KING, p5});
1401 for (PieceType p4 = PAWN; p4 < KING; ++p4) {
1402 TBTables.add({KING, p1, p2, p3, KING, p4});
1404 for (PieceType p5 = PAWN; p5 <= p4; ++p5)
1405 TBTables.add({KING, p1, p2, p3, KING, p4, p5});
1409 for (PieceType p3 = PAWN; p3 <= p1; ++p3)
1410 for (PieceType p4 = PAWN; p4 <= (p1 == p3 ? p2 : p3); ++p4)
1411 TBTables.add({KING, p1, p2, KING, p3, p4});
1415 sync_cout << "info string Found " << TBTables.size() << " tablebases" << sync_endl;
1418 // Probe the WDL table for a particular position.
1419 // If *result != FAIL, the probe was successful.
1420 // The return value is from the point of view of the side to move:
1422 // -1 : loss, but draw under 50-move rule
1424 // 1 : win, but draw under 50-move rule
1426 WDLScore Tablebases::probe_wdl(Position& pos, ProbeState* result) {
1429 return search<false>(pos, result);
1432 // Probe the DTZ table for a particular position.
1433 // If *result != FAIL, the probe was successful.
1434 // The return value is from the point of view of the side to move:
1435 // n < -100 : loss, but draw under 50-move rule
1436 // -100 <= n < -1 : loss in n ply (assuming 50-move counter == 0)
1437 // -1 : loss, the side to move is mated
1439 // 1 < n <= 100 : win in n ply (assuming 50-move counter == 0)
1440 // 100 < n : win, but draw under 50-move rule
1442 // The return value n can be off by 1: a return value -n can mean a loss
1443 // in n+1 ply and a return value +n can mean a win in n+1 ply. This
1444 // cannot happen for tables with positions exactly on the "edge" of
1445 // the 50-move rule.
1447 // This implies that if dtz > 0 is returned, the position is certainly
1448 // a win if dtz + 50-move-counter <= 99. Care must be taken that the engine
1449 // picks moves that preserve dtz + 50-move-counter <= 99.
1451 // If n = 100 immediately after a capture or pawn move, then the position
1452 // is also certainly a win, and during the whole phase until the next
1453 // capture or pawn move, the inequality to be preserved is
1454 // dtz + 50-move-counter <= 100.
1456 // In short, if a move is available resulting in dtz + 50-move-counter <= 99,
1457 // then do not accept moves leading to dtz + 50-move-counter == 100.
1458 int Tablebases::probe_dtz(Position& pos, ProbeState* result) {
1461 WDLScore wdl = search<true>(pos, result);
1463 if (*result == FAIL || wdl == WDLDraw) // DTZ tables don't store draws
1466 // DTZ stores a 'don't care value in this case, or even a plain wrong
1467 // one as in case the best move is a losing ep, so it cannot be probed.
1468 if (*result == ZEROING_BEST_MOVE)
1469 return dtz_before_zeroing(wdl);
1471 int dtz = probe_table<DTZ>(pos, result, wdl);
1473 if (*result == FAIL)
1476 if (*result != CHANGE_STM)
1477 return (dtz + 100 * (wdl == WDLBlessedLoss || wdl == WDLCursedWin)) * sign_of(wdl);
1479 // DTZ stores results for the other side, so we need to do a 1-ply search and
1480 // find the winning move that minimizes DTZ.
1482 int minDTZ = 0xFFFF;
1484 for (const Move move : MoveList<LEGAL>(pos))
1486 bool zeroing = pos.capture(move) || type_of(pos.moved_piece(move)) == PAWN;
1488 pos.do_move(move, st);
1490 // For zeroing moves we want the dtz of the move _before_ doing it,
1491 // otherwise we will get the dtz of the next move sequence. Search the
1492 // position after the move to get the score sign (because even in a
1493 // winning position we could make a losing capture or go for a draw).
1494 dtz = zeroing ? -dtz_before_zeroing(search<false>(pos, result))
1495 : -probe_dtz(pos, result);
1497 // If the move mates, force minDTZ to 1
1498 if (dtz == 1 && pos.checkers() && MoveList<LEGAL>(pos).size() == 0)
1501 // Convert result from 1-ply search. Zeroing moves are already accounted
1502 // by dtz_before_zeroing() that returns the DTZ of the previous move.
1504 dtz += sign_of(dtz);
1506 // Skip the draws and if we are winning only pick positive dtz
1507 if (dtz < minDTZ && sign_of(dtz) == sign_of(wdl))
1510 pos.undo_move(move);
1512 if (*result == FAIL)
1516 // When there are no legal moves, the position is mate: we return -1
1517 return minDTZ == 0xFFFF ? -1 : minDTZ;
1521 // Use the DTZ tables to rank root moves.
1523 // A return value false indicates that not all probes were successful.
1524 bool Tablebases::root_probe(Position& pos, Search::RootMoves& rootMoves) {
1526 ProbeState result = OK;
1529 // Obtain 50-move counter for the root position
1530 int cnt50 = pos.rule50_count();
1532 // Check whether a position was repeated since the last zeroing move.
1533 bool rep = pos.has_repeated();
1535 int dtz, bound = Options["Syzygy50MoveRule"] ? (MAX_DTZ - 100) : 1;
1537 // Probe and rank each move
1538 for (auto& m : rootMoves)
1540 pos.do_move(m.pv[0], st);
1542 // Calculate dtz for the current move counting from the root position
1543 if (pos.rule50_count() == 0)
1545 // In case of a zeroing move, dtz is one of -101/-1/0/1/101
1546 WDLScore wdl = -probe_wdl(pos, &result);
1547 dtz = dtz_before_zeroing(wdl);
1549 else if (pos.is_draw(1))
1551 // In case a root move leads to a draw by repetition or 50-move rule,
1552 // we set dtz to zero. Note: since we are only 1 ply from the root,
1553 // this must be a true 3-fold repetition inside the game history.
1558 // Otherwise, take dtz for the new position and correct by 1 ply
1559 dtz = -probe_dtz(pos, &result);
1560 dtz = dtz > 0 ? dtz + 1
1561 : dtz < 0 ? dtz - 1 : dtz;
1564 // Make sure that a mating move is assigned a dtz value of 1
1567 && MoveList<LEGAL>(pos).size() == 0)
1570 pos.undo_move(m.pv[0]);
1575 // Better moves are ranked higher. Certain wins are ranked equally.
1576 // Losing moves are ranked equally unless a 50-move draw is in sight.
1577 int r = dtz > 0 ? (dtz + cnt50 <= 99 && !rep ? MAX_DTZ : MAX_DTZ - (dtz + cnt50))
1578 : dtz < 0 ? (-dtz * 2 + cnt50 < 100 ? -MAX_DTZ : -MAX_DTZ + (-dtz + cnt50))
1582 // Determine the score to be displayed for this move. Assign at least
1583 // 1 cp to cursed wins and let it grow to 49 cp as the positions gets
1584 // closer to a real win.
1585 m.tbScore = r >= bound ? VALUE_MATE - MAX_PLY - 1
1586 : r > 0 ? Value((std::max( 3, r - (MAX_DTZ - 200)) * int(PawnValue)) / 200)
1587 : r == 0 ? VALUE_DRAW
1588 : r > -bound ? Value((std::min(-3, r + (MAX_DTZ - 200)) * int(PawnValue)) / 200)
1589 : -VALUE_MATE + MAX_PLY + 1;
1596 // Use the WDL tables to rank root moves.
1597 // This is a fallback for the case that some or all DTZ tables are missing.
1599 // A return value false indicates that not all probes were successful.
1600 bool Tablebases::root_probe_wdl(Position& pos, Search::RootMoves& rootMoves) {
1602 static const int WDL_to_rank[] = { -MAX_DTZ, -MAX_DTZ + 101, 0, MAX_DTZ - 101, MAX_DTZ };
1604 ProbeState result = OK;
1608 bool rule50 = Options["Syzygy50MoveRule"];
1610 // Probe and rank each move
1611 for (auto& m : rootMoves)
1613 pos.do_move(m.pv[0], st);
1618 wdl = -probe_wdl(pos, &result);
1620 pos.undo_move(m.pv[0]);
1625 m.tbRank = WDL_to_rank[wdl + 2];
1628 wdl = wdl > WDLDraw ? WDLWin
1629 : wdl < WDLDraw ? WDLLoss : WDLDraw;
1630 m.tbScore = WDL_to_value[wdl + 2];
1636 } // namespace Stockfish