2 Stockfish, a UCI chess playing engine derived from Glaurung 2.1
3 Copyright (C) 2004-2021 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/>.
22 #include <cstring> // For std::memset and std::memcpy
28 #include <type_traits>
31 #include "../bitboard.h"
32 #include "../movegen.h"
33 #include "../position.h"
34 #include "../search.h"
46 #define WIN32_LEAN_AND_MEAN
48 # define NOMINMAX // Disable macros min() and max()
53 using namespace Stockfish::Tablebases;
55 int Stockfish::Tablebases::MaxCardinality;
61 constexpr int TBPIECES = 7; // Max number of supported pieces
63 enum { BigEndian, LittleEndian };
64 enum TBType { WDL, DTZ }; // Used as template parameter
66 // Each table has a set of flags: all of them refer to DTZ tables, the last one to WDL tables
67 enum TBFlag { STM = 1, Mapped = 2, WinPlies = 4, LossPlies = 8, Wide = 16, SingleValue = 128 };
69 inline WDLScore operator-(WDLScore d) { return WDLScore(-int(d)); }
70 inline Square operator^(Square s, int i) { return Square(int(s) ^ i); }
72 const std::string PieceToChar = " PNBRQK pnbrqk";
74 int MapPawns[SQUARE_NB];
75 int MapB1H1H7[SQUARE_NB];
76 int MapA1D1D4[SQUARE_NB];
77 int MapKK[10][SQUARE_NB]; // [MapA1D1D4][SQUARE_NB]
79 int Binomial[7][SQUARE_NB]; // [k][n] k elements from a set of n elements
80 int LeadPawnIdx[6][SQUARE_NB]; // [leadPawnsCnt][SQUARE_NB]
81 int LeadPawnsSize[6][4]; // [leadPawnsCnt][FILE_A..FILE_D]
83 // Comparison function to sort leading pawns in ascending MapPawns[] order
84 bool pawns_comp(Square i, Square j) { return MapPawns[i] < MapPawns[j]; }
85 int off_A1H8(Square sq) { return int(rank_of(sq)) - file_of(sq); }
87 constexpr Value WDL_to_value[] = {
88 -VALUE_MATE + MAX_PLY + 1,
92 VALUE_MATE - MAX_PLY - 1
95 template<typename T, int Half = sizeof(T) / 2, int End = sizeof(T) - 1>
96 inline void swap_endian(T& x)
98 static_assert(std::is_unsigned<T>::value, "Argument of swap_endian not unsigned");
100 uint8_t tmp, *c = (uint8_t*)&x;
101 for (int i = 0; i < Half; ++i)
102 tmp = c[i], c[i] = c[End - i], c[End - i] = tmp;
104 template<> inline void swap_endian<uint8_t>(uint8_t&) {}
106 template<typename T, int LE> T number(void* addr)
108 static const union { uint32_t i; char c[4]; } Le = { 0x01020304 };
109 static const bool IsLittleEndian = (Le.c[0] == 4);
113 if ((uintptr_t)addr & (alignof(T) - 1)) // Unaligned pointer (very rare)
114 std::memcpy(&v, addr, sizeof(T));
118 if (LE != IsLittleEndian)
123 // DTZ tables don't store valid scores for moves that reset the rule50 counter
124 // like captures and pawn moves but we can easily recover the correct dtz of the
125 // previous move if we know the position's WDL score.
126 int dtz_before_zeroing(WDLScore wdl) {
127 return wdl == WDLWin ? 1 :
128 wdl == WDLCursedWin ? 101 :
129 wdl == WDLBlessedLoss ? -101 :
130 wdl == WDLLoss ? -1 : 0;
133 // Return the sign of a number (-1, 0, 1)
134 template <typename T> int sign_of(T val) {
135 return (T(0) < val) - (val < T(0));
138 // Numbers in little endian used by sparseIndex[] to point into blockLength[]
140 char block[4]; // Number of block
141 char offset[2]; // Offset within the block
144 static_assert(sizeof(SparseEntry) == 6, "SparseEntry must be 6 bytes");
146 typedef uint16_t Sym; // Huffman symbol
149 enum Side { Left, Right };
151 uint8_t lr[3]; // The first 12 bits is the left-hand symbol, the second 12
152 // bits is the right-hand symbol. If symbol has length 1,
153 // then the left-hand symbol is the stored value.
156 return S == Left ? ((lr[1] & 0xF) << 8) | lr[0] :
157 S == Right ? (lr[2] << 4) | (lr[1] >> 4) : (assert(false), Sym(-1));
161 static_assert(sizeof(LR) == 3, "LR tree entry must be 3 bytes");
163 // Tablebases data layout is structured as following:
165 // TBFile: memory maps/unmaps the physical .rtbw and .rtbz files
166 // TBTable: one object for each file with corresponding indexing information
167 // TBTables: has ownership of TBTable objects, keeping a list and a hash
169 // class TBFile memory maps/unmaps the single .rtbw and .rtbz files. Files are
170 // memory mapped for best performance. Files are mapped at first access: at init
171 // time only existence of the file is checked.
172 class TBFile : public std::ifstream {
177 // Look for and open the file among the Paths directories where the .rtbw
178 // and .rtbz files can be found. Multiple directories are separated by ";"
179 // on Windows and by ":" on Unix-based operating systems.
182 // C:\tb\wdl345;C:\tb\wdl6;D:\tb\dtz345;D:\tb\dtz6
183 static std::string Paths;
185 TBFile(const std::string& f) {
188 constexpr char SepChar = ':';
190 constexpr char SepChar = ';';
192 std::stringstream ss(Paths);
195 while (std::getline(ss, path, SepChar)) {
196 fname = path + "/" + f;
197 std::ifstream::open(fname);
203 // Memory map the file and check it. File should be already open and will be
204 // closed after mapping.
205 uint8_t* map(void** baseAddress, uint64_t* mapping, TBType type) {
209 close(); // Need to re-open to get native file descriptor
213 int fd = ::open(fname.c_str(), O_RDONLY);
216 return *baseAddress = nullptr, nullptr;
220 if (statbuf.st_size % 64 != 16)
222 std::cerr << "Corrupt tablebase file " << fname << std::endl;
226 *mapping = statbuf.st_size;
227 *baseAddress = mmap(nullptr, statbuf.st_size, PROT_READ, MAP_SHARED, fd, 0);
228 #if defined(MADV_RANDOM)
229 madvise(*baseAddress, statbuf.st_size, MADV_RANDOM);
233 if (*baseAddress == MAP_FAILED)
235 std::cerr << "Could not mmap() " << fname << std::endl;
239 // Note FILE_FLAG_RANDOM_ACCESS is only a hint to Windows and as such may get ignored.
240 HANDLE fd = CreateFile(fname.c_str(), GENERIC_READ, FILE_SHARE_READ, nullptr,
241 OPEN_EXISTING, FILE_FLAG_RANDOM_ACCESS, nullptr);
243 if (fd == INVALID_HANDLE_VALUE)
244 return *baseAddress = nullptr, nullptr;
247 DWORD size_low = GetFileSize(fd, &size_high);
249 if (size_low % 64 != 16)
251 std::cerr << "Corrupt tablebase file " << fname << std::endl;
255 HANDLE mmap = CreateFileMapping(fd, nullptr, PAGE_READONLY, size_high, size_low, nullptr);
260 std::cerr << "CreateFileMapping() failed" << std::endl;
264 *mapping = (uint64_t)mmap;
265 *baseAddress = MapViewOfFile(mmap, FILE_MAP_READ, 0, 0, 0);
269 std::cerr << "MapViewOfFile() failed, name = " << fname
270 << ", error = " << GetLastError() << std::endl;
274 uint8_t* data = (uint8_t*)*baseAddress;
276 constexpr uint8_t Magics[][4] = { { 0xD7, 0x66, 0x0C, 0xA5 },
277 { 0x71, 0xE8, 0x23, 0x5D } };
279 if (memcmp(data, Magics[type == WDL], 4))
281 std::cerr << "Corrupted table in file " << fname << std::endl;
282 unmap(*baseAddress, *mapping);
283 return *baseAddress = nullptr, nullptr;
286 return data + 4; // Skip Magics's header
289 static void unmap(void* baseAddress, uint64_t mapping) {
292 munmap(baseAddress, mapping);
294 UnmapViewOfFile(baseAddress);
295 CloseHandle((HANDLE)mapping);
300 std::string TBFile::Paths;
302 // struct PairsData contains low level indexing information to access TB data.
303 // There are 8, 4 or 2 PairsData records for each TBTable, according to type of
304 // table and if positions have pawns or not. It is populated at first access.
306 uint8_t flags; // Table flags, see enum TBFlag
307 uint8_t maxSymLen; // Maximum length in bits of the Huffman symbols
308 uint8_t minSymLen; // Minimum length in bits of the Huffman symbols
309 uint32_t blocksNum; // Number of blocks in the TB file
310 size_t sizeofBlock; // Block size in bytes
311 size_t span; // About every span values there is a SparseIndex[] entry
312 Sym* lowestSym; // lowestSym[l] is the symbol of length l with the lowest value
313 LR* btree; // btree[sym] stores the left and right symbols that expand sym
314 uint16_t* blockLength; // Number of stored positions (minus one) for each block: 1..65536
315 uint32_t blockLengthSize; // Size of blockLength[] table: padded so it's bigger than blocksNum
316 SparseEntry* sparseIndex; // Partial indices into blockLength[]
317 size_t sparseIndexSize; // Size of SparseIndex[] table
318 uint8_t* data; // Start of Huffman compressed data
319 std::vector<uint64_t> base64; // base64[l - min_sym_len] is the 64bit-padded lowest symbol of length l
320 std::vector<uint8_t> symlen; // Number of values (-1) represented by a given Huffman symbol: 1..256
321 Piece pieces[TBPIECES]; // Position pieces: the order of pieces defines the groups
322 uint64_t groupIdx[TBPIECES+1]; // Start index used for the encoding of the group's pieces
323 int groupLen[TBPIECES+1]; // Number of pieces in a given group: KRKN -> (3, 1)
324 uint16_t map_idx[4]; // WDLWin, WDLLoss, WDLCursedWin, WDLBlessedLoss (used in DTZ)
327 // struct TBTable contains indexing information to access the corresponding TBFile.
328 // There are 2 types of TBTable, corresponding to a WDL or a DTZ file. TBTable
329 // is populated at init time but the nested PairsData records are populated at
330 // first access, when the corresponding file is memory mapped.
331 template<TBType Type>
333 typedef typename std::conditional<Type == WDL, WDLScore, int>::type Ret;
335 static constexpr int Sides = Type == WDL ? 2 : 1;
337 std::atomic_bool ready;
345 bool hasUniquePieces;
346 uint8_t pawnCount[2]; // [Lead color / other color]
347 PairsData items[Sides][4]; // [wtm / btm][FILE_A..FILE_D or 0]
349 PairsData* get(int stm, int f) {
350 return &items[stm % Sides][hasPawns ? f : 0];
353 TBTable() : ready(false), baseAddress(nullptr) {}
354 explicit TBTable(const std::string& code);
355 explicit TBTable(const TBTable<WDL>& wdl);
359 TBFile::unmap(baseAddress, mapping);
364 TBTable<WDL>::TBTable(const std::string& code) : TBTable() {
369 key = pos.set(code, WHITE, &st).material_key();
370 pieceCount = pos.count<ALL_PIECES>();
371 hasPawns = pos.pieces(PAWN);
373 hasUniquePieces = false;
374 for (Color c : { WHITE, BLACK })
375 for (PieceType pt = PAWN; pt < KING; ++pt)
376 if (popcount(pos.pieces(c, pt)) == 1)
377 hasUniquePieces = true;
379 // Set the leading color. In case both sides have pawns the leading color
380 // is the side with less pawns because this leads to better compression.
381 bool c = !pos.count<PAWN>(BLACK)
382 || ( pos.count<PAWN>(WHITE)
383 && pos.count<PAWN>(BLACK) >= pos.count<PAWN>(WHITE));
385 pawnCount[0] = pos.count<PAWN>(c ? WHITE : BLACK);
386 pawnCount[1] = pos.count<PAWN>(c ? BLACK : WHITE);
388 key2 = pos.set(code, BLACK, &st).material_key();
392 TBTable<DTZ>::TBTable(const TBTable<WDL>& wdl) : TBTable() {
394 // Use the corresponding WDL table to avoid recalculating all from scratch
397 pieceCount = wdl.pieceCount;
398 hasPawns = wdl.hasPawns;
399 hasUniquePieces = wdl.hasUniquePieces;
400 pawnCount[0] = wdl.pawnCount[0];
401 pawnCount[1] = wdl.pawnCount[1];
404 // class TBTables creates and keeps ownership of the TBTable objects, one for
405 // each TB file found. It supports a fast, hash based, table lookup. Populated
406 // at init time, accessed at probe time.
415 template <TBType Type>
416 TBTable<Type>* get() const {
417 return (TBTable<Type>*)(Type == WDL ? (void*)wdl : (void*)dtz);
421 static constexpr int Size = 1 << 12; // 4K table, indexed by key's 12 lsb
422 static constexpr int Overflow = 1; // Number of elements allowed to map to the last bucket
424 Entry hashTable[Size + Overflow];
426 std::deque<TBTable<WDL>> wdlTable;
427 std::deque<TBTable<DTZ>> dtzTable;
429 void insert(Key key, TBTable<WDL>* wdl, TBTable<DTZ>* dtz) {
430 uint32_t homeBucket = (uint32_t)key & (Size - 1);
431 Entry entry{ key, wdl, dtz };
433 // Ensure last element is empty to avoid overflow when looking up
434 for (uint32_t bucket = homeBucket; bucket < Size + Overflow - 1; ++bucket) {
435 Key otherKey = hashTable[bucket].key;
436 if (otherKey == key || !hashTable[bucket].get<WDL>()) {
437 hashTable[bucket] = entry;
441 // Robin Hood hashing: If we've probed for longer than this element,
442 // insert here and search for a new spot for the other element instead.
443 uint32_t otherHomeBucket = (uint32_t)otherKey & (Size - 1);
444 if (otherHomeBucket > homeBucket) {
445 std::swap(entry, hashTable[bucket]);
447 homeBucket = otherHomeBucket;
450 std::cerr << "TB hash table size too low!" << std::endl;
455 template<TBType Type>
456 TBTable<Type>* get(Key key) {
457 for (const Entry* entry = &hashTable[(uint32_t)key & (Size - 1)]; ; ++entry) {
458 if (entry->key == key || !entry->get<Type>())
459 return entry->get<Type>();
464 memset(hashTable, 0, sizeof(hashTable));
468 size_t size() const { return wdlTable.size(); }
469 void add(const std::vector<PieceType>& pieces);
474 // If the corresponding file exists two new objects TBTable<WDL> and TBTable<DTZ>
475 // are created and added to the lists and hash table. Called at init time.
476 void TBTables::add(const std::vector<PieceType>& pieces) {
480 for (PieceType pt : pieces)
481 code += PieceToChar[pt];
483 TBFile file(code.insert(code.find('K', 1), "v") + ".rtbw"); // KRK -> KRvK
485 if (!file.is_open()) // Only WDL file is checked
490 MaxCardinality = std::max((int)pieces.size(), MaxCardinality);
492 wdlTable.emplace_back(code);
493 dtzTable.emplace_back(wdlTable.back());
495 // Insert into the hash keys for both colors: KRvK with KR white and black
496 insert(wdlTable.back().key , &wdlTable.back(), &dtzTable.back());
497 insert(wdlTable.back().key2, &wdlTable.back(), &dtzTable.back());
500 // TB tables are compressed with canonical Huffman code. The compressed data is divided into
501 // blocks of size d->sizeofBlock, and each block stores a variable number of symbols.
502 // Each symbol represents either a WDL or a (remapped) DTZ value, or a pair of other symbols
503 // (recursively). If you keep expanding the symbols in a block, you end up with up to 65536
504 // WDL or DTZ values. Each symbol represents up to 256 values and will correspond after
505 // Huffman coding to at least 1 bit. So a block of 32 bytes corresponds to at most
506 // 32 x 8 x 256 = 65536 values. This maximum is only reached for tables that consist mostly
507 // of draws or mostly of wins, but such tables are actually quite common. In principle, the
508 // blocks in WDL tables are 64 bytes long (and will be aligned on cache lines). But for
509 // mostly-draw or mostly-win tables this can leave many 64-byte blocks only half-filled, so
510 // in such cases blocks are 32 bytes long. The blocks of DTZ tables are up to 1024 bytes long.
511 // The generator picks the size that leads to the smallest table. The "book" of symbols and
512 // Huffman codes is the same for all blocks in the table. A non-symmetric pawnless TB file
513 // will have one table for wtm and one for btm, a TB file with pawns will have tables per
514 // file a,b,c,d also in this case one set for wtm and one for btm.
515 int decompress_pairs(PairsData* d, uint64_t idx) {
517 // Special case where all table positions store the same value
518 if (d->flags & TBFlag::SingleValue)
521 // First we need to locate the right block that stores the value at index "idx".
522 // Because each block n stores blockLength[n] + 1 values, the index i of the block
523 // that contains the value at position idx is:
525 // for (i = -1, sum = 0; sum <= idx; i++)
526 // sum += blockLength[i + 1] + 1;
528 // This can be slow, so we use SparseIndex[] populated with a set of SparseEntry that
529 // point to known indices into blockLength[]. Namely SparseIndex[k] is a SparseEntry
530 // that stores the blockLength[] index and the offset within that block of the value
531 // with index I(k), where:
533 // I(k) = k * d->span + d->span / 2 (1)
535 // First step is to get the 'k' of the I(k) nearest to our idx, using definition (1)
536 uint32_t k = uint32_t(idx / d->span);
538 // Then we read the corresponding SparseIndex[] entry
539 uint32_t block = number<uint32_t, LittleEndian>(&d->sparseIndex[k].block);
540 int offset = number<uint16_t, LittleEndian>(&d->sparseIndex[k].offset);
542 // Now compute the difference idx - I(k). From definition of k we know that
544 // idx = k * d->span + idx % d->span (2)
546 // So from (1) and (2) we can compute idx - I(K):
547 int diff = idx % d->span - d->span / 2;
549 // Sum the above to offset to find the offset corresponding to our idx
552 // Move to previous/next block, until we reach the correct block that contains idx,
553 // that is when 0 <= offset <= d->blockLength[block]
555 offset += d->blockLength[--block] + 1;
557 while (offset > d->blockLength[block])
558 offset -= d->blockLength[block++] + 1;
560 // Finally, we find the start address of our block of canonical Huffman symbols
561 uint32_t* ptr = (uint32_t*)(d->data + ((uint64_t)block * d->sizeofBlock));
563 // Read the first 64 bits in our block, this is a (truncated) sequence of
564 // unknown number of symbols of unknown length but we know the first one
565 // is at the beginning of this 64 bits sequence.
566 uint64_t buf64 = number<uint64_t, BigEndian>(ptr); ptr += 2;
571 int len = 0; // This is the symbol length - d->min_sym_len
573 // Now get the symbol length. For any symbol s64 of length l right-padded
574 // to 64 bits we know that d->base64[l-1] >= s64 >= d->base64[l] so we
575 // can find the symbol length iterating through base64[].
576 while (buf64 < d->base64[len])
579 // All the symbols of a given length are consecutive integers (numerical
580 // sequence property), so we can compute the offset of our symbol of
581 // length len, stored at the beginning of buf64.
582 sym = Sym((buf64 - d->base64[len]) >> (64 - len - d->minSymLen));
584 // Now add the value of the lowest symbol of length len to get our symbol
585 sym += number<Sym, LittleEndian>(&d->lowestSym[len]);
587 // If our offset is within the number of values represented by symbol sym
589 if (offset < d->symlen[sym] + 1)
592 // ...otherwise update the offset and continue to iterate
593 offset -= d->symlen[sym] + 1;
594 len += d->minSymLen; // Get the real length
595 buf64 <<= len; // Consume the just processed symbol
598 if (buf64Size <= 32) { // Refill the buffer
600 buf64 |= (uint64_t)number<uint32_t, BigEndian>(ptr++) << (64 - buf64Size);
604 // Ok, now we have our symbol that expands into d->symlen[sym] + 1 symbols.
605 // We binary-search for our value recursively expanding into the left and
606 // right child symbols until we reach a leaf node where symlen[sym] + 1 == 1
607 // that will store the value we need.
608 while (d->symlen[sym]) {
610 Sym left = d->btree[sym].get<LR::Left>();
612 // If a symbol contains 36 sub-symbols (d->symlen[sym] + 1 = 36) and
613 // expands in a pair (d->symlen[left] = 23, d->symlen[right] = 11), then
614 // we know that, for instance the ten-th value (offset = 10) will be on
615 // the left side because in Recursive Pairing child symbols are adjacent.
616 if (offset < d->symlen[left] + 1)
619 offset -= d->symlen[left] + 1;
620 sym = d->btree[sym].get<LR::Right>();
624 return d->btree[sym].get<LR::Left>();
627 bool check_dtz_stm(TBTable<WDL>*, int, File) { return true; }
629 bool check_dtz_stm(TBTable<DTZ>* entry, int stm, File f) {
631 auto flags = entry->get(stm, f)->flags;
632 return (flags & TBFlag::STM) == stm
633 || ((entry->key == entry->key2) && !entry->hasPawns);
636 // DTZ scores are sorted by frequency of occurrence and then assigned the
637 // values 0, 1, 2, ... in order of decreasing frequency. This is done for each
638 // of the four WDLScore values. The mapping information necessary to reconstruct
639 // the original values is stored in the TB file and read during map[] init.
640 WDLScore map_score(TBTable<WDL>*, File, int value, WDLScore) { return WDLScore(value - 2); }
642 int map_score(TBTable<DTZ>* entry, File f, int value, WDLScore wdl) {
644 constexpr int WDLMap[] = { 1, 3, 0, 2, 0 };
646 auto flags = entry->get(0, f)->flags;
648 uint8_t* map = entry->map;
649 uint16_t* idx = entry->get(0, f)->map_idx;
650 if (flags & TBFlag::Mapped) {
651 if (flags & TBFlag::Wide)
652 value = ((uint16_t *)map)[idx[WDLMap[wdl + 2]] + value];
654 value = map[idx[WDLMap[wdl + 2]] + value];
657 // DTZ tables store distance to zero in number of moves or plies. We
658 // want to return plies, so we have convert to plies when needed.
659 if ( (wdl == WDLWin && !(flags & TBFlag::WinPlies))
660 || (wdl == WDLLoss && !(flags & TBFlag::LossPlies))
661 || wdl == WDLCursedWin
662 || wdl == WDLBlessedLoss)
668 // Compute a unique index out of a position and use it to probe the TB file. To
669 // encode k pieces of same type and color, first sort the pieces by square in
670 // ascending order s1 <= s2 <= ... <= sk then compute the unique index as:
672 // idx = Binomial[1][s1] + Binomial[2][s2] + ... + Binomial[k][sk]
674 template<typename T, typename Ret = typename T::Ret>
675 Ret do_probe_table(const Position& pos, T* entry, WDLScore wdl, ProbeState* result) {
677 Square squares[TBPIECES];
678 Piece pieces[TBPIECES];
680 int next = 0, size = 0, leadPawnsCnt = 0;
682 Bitboard b, leadPawns = 0;
683 File tbFile = FILE_A;
685 // A given TB entry like KRK has associated two material keys: KRvk and Kvkr.
686 // If both sides have the same pieces keys are equal. In this case TB tables
687 // only store the 'white to move' case, so if the position to lookup has black
688 // to move, we need to switch the color and flip the squares before to lookup.
689 bool symmetricBlackToMove = (entry->key == entry->key2 && pos.side_to_move());
691 // TB files are calculated for white as stronger side. For instance we have
692 // KRvK, not KvKR. A position where stronger side is white will have its
693 // material key == entry->key, otherwise we have to switch the color and
694 // flip the squares before to lookup.
695 bool blackStronger = (pos.material_key() != entry->key);
697 int flipColor = (symmetricBlackToMove || blackStronger) * 8;
698 int flipSquares = (symmetricBlackToMove || blackStronger) * 56;
699 int stm = (symmetricBlackToMove || blackStronger) ^ pos.side_to_move();
701 // For pawns, TB files store 4 separate tables according if leading pawn is on
702 // file a, b, c or d after reordering. The leading pawn is the one with maximum
703 // MapPawns[] value, that is the one most toward the edges and with lowest rank.
704 if (entry->hasPawns) {
706 // In all the 4 tables, pawns are at the beginning of the piece sequence and
707 // their color is the reference one. So we just pick the first one.
708 Piece pc = Piece(entry->get(0, 0)->pieces[0] ^ flipColor);
710 assert(type_of(pc) == PAWN);
712 leadPawns = b = pos.pieces(color_of(pc), PAWN);
714 squares[size++] = pop_lsb(&b) ^ flipSquares;
719 std::swap(squares[0], *std::max_element(squares, squares + leadPawnsCnt, pawns_comp));
721 tbFile = File(edge_distance(file_of(squares[0])));
724 // DTZ tables are one-sided, i.e. they store positions only for white to
725 // move or only for black to move, so check for side to move to be stm,
726 // early exit otherwise.
727 if (!check_dtz_stm(entry, stm, tbFile))
728 return *result = CHANGE_STM, Ret();
730 // Now we are ready to get all the position pieces (but the lead pawns) and
731 // directly map them to the correct color and square.
732 b = pos.pieces() ^ leadPawns;
734 Square s = pop_lsb(&b);
735 squares[size] = s ^ flipSquares;
736 pieces[size++] = Piece(pos.piece_on(s) ^ flipColor);
741 d = entry->get(stm, tbFile);
743 // Then we reorder the pieces to have the same sequence as the one stored
744 // in pieces[i]: the sequence that ensures the best compression.
745 for (int i = leadPawnsCnt; i < size - 1; ++i)
746 for (int j = i + 1; j < size; ++j)
747 if (d->pieces[i] == pieces[j])
749 std::swap(pieces[i], pieces[j]);
750 std::swap(squares[i], squares[j]);
754 // Now we map again the squares so that the square of the lead piece is in
755 // the triangle A1-D1-D4.
756 if (file_of(squares[0]) > FILE_D)
757 for (int i = 0; i < size; ++i)
758 squares[i] = flip_file(squares[i]);
760 // Encode leading pawns starting with the one with minimum MapPawns[] and
761 // proceeding in ascending order.
762 if (entry->hasPawns) {
763 idx = LeadPawnIdx[leadPawnsCnt][squares[0]];
765 std::stable_sort(squares + 1, squares + leadPawnsCnt, pawns_comp);
767 for (int i = 1; i < leadPawnsCnt; ++i)
768 idx += Binomial[i][MapPawns[squares[i]]];
770 goto encode_remaining; // With pawns we have finished special treatments
773 // In positions withouth pawns, we further flip the squares to ensure leading
774 // piece is below RANK_5.
775 if (rank_of(squares[0]) > RANK_4)
776 for (int i = 0; i < size; ++i)
777 squares[i] = flip_rank(squares[i]);
779 // Look for the first piece of the leading group not on the A1-D4 diagonal
780 // and ensure it is mapped below the diagonal.
781 for (int i = 0; i < d->groupLen[0]; ++i) {
782 if (!off_A1H8(squares[i]))
785 if (off_A1H8(squares[i]) > 0) // A1-H8 diagonal flip: SQ_A3 -> SQ_C1
786 for (int j = i; j < size; ++j)
787 squares[j] = Square(((squares[j] >> 3) | (squares[j] << 3)) & 63);
791 // Encode the leading group.
793 // Suppose we have KRvK. Let's say the pieces are on square numbers wK, wR
794 // and bK (each 0...63). The simplest way to map this position to an index
797 // index = wK * 64 * 64 + wR * 64 + bK;
799 // But this way the TB is going to have 64*64*64 = 262144 positions, with
800 // lots of positions being equivalent (because they are mirrors of each
801 // other) and lots of positions being invalid (two pieces on one square,
802 // adjacent kings, etc.).
803 // Usually the first step is to take the wK and bK together. There are just
804 // 462 ways legal and not-mirrored ways to place the wK and bK on the board.
805 // Once we have placed the wK and bK, there are 62 squares left for the wR
806 // Mapping its square from 0..63 to available squares 0..61 can be done like:
808 // wR -= (wR > wK) + (wR > bK);
810 // In words: if wR "comes later" than wK, we deduct 1, and the same if wR
811 // "comes later" than bK. In case of two same pieces like KRRvK we want to
812 // place the two Rs "together". If we have 62 squares left, we can place two
813 // Rs "together" in 62 * 61 / 2 ways (we divide by 2 because rooks can be
814 // swapped and still get the same position.)
816 // In case we have at least 3 unique pieces (inlcuded kings) we encode them
818 if (entry->hasUniquePieces) {
820 int adjust1 = squares[1] > squares[0];
821 int adjust2 = (squares[2] > squares[0]) + (squares[2] > squares[1]);
823 // First piece is below a1-h8 diagonal. MapA1D1D4[] maps the b1-d1-d3
824 // triangle to 0...5. There are 63 squares for second piece and and 62
825 // (mapped to 0...61) for the third.
826 if (off_A1H8(squares[0]))
827 idx = ( MapA1D1D4[squares[0]] * 63
828 + (squares[1] - adjust1)) * 62
829 + squares[2] - adjust2;
831 // First piece is on a1-h8 diagonal, second below: map this occurence to
832 // 6 to differentiate from the above case, rank_of() maps a1-d4 diagonal
833 // to 0...3 and finally MapB1H1H7[] maps the b1-h1-h7 triangle to 0..27.
834 else if (off_A1H8(squares[1]))
835 idx = ( 6 * 63 + rank_of(squares[0]) * 28
836 + MapB1H1H7[squares[1]]) * 62
837 + squares[2] - adjust2;
839 // First two pieces are on a1-h8 diagonal, third below
840 else if (off_A1H8(squares[2]))
841 idx = 6 * 63 * 62 + 4 * 28 * 62
842 + rank_of(squares[0]) * 7 * 28
843 + (rank_of(squares[1]) - adjust1) * 28
844 + MapB1H1H7[squares[2]];
846 // All 3 pieces on the diagonal a1-h8
848 idx = 6 * 63 * 62 + 4 * 28 * 62 + 4 * 7 * 28
849 + rank_of(squares[0]) * 7 * 6
850 + (rank_of(squares[1]) - adjust1) * 6
851 + (rank_of(squares[2]) - adjust2);
853 // We don't have at least 3 unique pieces, like in KRRvKBB, just map
855 idx = MapKK[MapA1D1D4[squares[0]]][squares[1]];
858 idx *= d->groupIdx[0];
859 Square* groupSq = squares + d->groupLen[0];
861 // Encode remainig pawns then pieces according to square, in ascending order
862 bool remainingPawns = entry->hasPawns && entry->pawnCount[1];
864 while (d->groupLen[++next])
866 std::stable_sort(groupSq, groupSq + d->groupLen[next]);
869 // Map down a square if "comes later" than a square in the previous
870 // groups (similar to what done earlier for leading group pieces).
871 for (int i = 0; i < d->groupLen[next]; ++i)
873 auto f = [&](Square s) { return groupSq[i] > s; };
874 auto adjust = std::count_if(squares, groupSq, f);
875 n += Binomial[i + 1][groupSq[i] - adjust - 8 * remainingPawns];
878 remainingPawns = false;
879 idx += n * d->groupIdx[next];
880 groupSq += d->groupLen[next];
883 // Now that we have the index, decompress the pair and get the score
884 return map_score(entry, tbFile, decompress_pairs(d, idx), wdl);
887 // Group together pieces that will be encoded together. The general rule is that
888 // a group contains pieces of same type and color. The exception is the leading
889 // group that, in case of positions withouth pawns, can be formed by 3 different
890 // pieces (default) or by the king pair when there is not a unique piece apart
891 // from the kings. When there are pawns, pawns are always first in pieces[].
893 // As example KRKN -> KRK + N, KNNK -> KK + NN, KPPKP -> P + PP + K + K
895 // The actual grouping depends on the TB generator and can be inferred from the
896 // sequence of pieces in piece[] array.
898 void set_groups(T& e, PairsData* d, int order[], File f) {
900 int n = 0, firstLen = e.hasPawns ? 0 : e.hasUniquePieces ? 3 : 2;
903 // Number of pieces per group is stored in groupLen[], for instance in KRKN
904 // the encoder will default on '111', so groupLen[] will be (3, 1).
905 for (int i = 1; i < e.pieceCount; ++i)
906 if (--firstLen > 0 || d->pieces[i] == d->pieces[i - 1])
909 d->groupLen[++n] = 1;
911 d->groupLen[++n] = 0; // Zero-terminated
913 // The sequence in pieces[] defines the groups, but not the order in which
914 // they are encoded. If the pieces in a group g can be combined on the board
915 // in N(g) different ways, then the position encoding will be of the form:
917 // g1 * N(g2) * N(g3) + g2 * N(g3) + g3
919 // This ensures unique encoding for the whole position. The order of the
920 // groups is a per-table parameter and could not follow the canonical leading
921 // pawns/pieces -> remainig pawns -> remaining pieces. In particular the
922 // first group is at order[0] position and the remaining pawns, when present,
923 // are at order[1] position.
924 bool pp = e.hasPawns && e.pawnCount[1]; // Pawns on both sides
925 int next = pp ? 2 : 1;
926 int freeSquares = 64 - d->groupLen[0] - (pp ? d->groupLen[1] : 0);
929 for (int k = 0; next < n || k == order[0] || k == order[1]; ++k)
930 if (k == order[0]) // Leading pawns or pieces
932 d->groupIdx[0] = idx;
933 idx *= e.hasPawns ? LeadPawnsSize[d->groupLen[0]][f]
934 : e.hasUniquePieces ? 31332 : 462;
936 else if (k == order[1]) // Remaining pawns
938 d->groupIdx[1] = idx;
939 idx *= Binomial[d->groupLen[1]][48 - d->groupLen[0]];
941 else // Remainig pieces
943 d->groupIdx[next] = idx;
944 idx *= Binomial[d->groupLen[next]][freeSquares];
945 freeSquares -= d->groupLen[next++];
948 d->groupIdx[n] = idx;
951 // In Recursive Pairing each symbol represents a pair of childern symbols. So
952 // read d->btree[] symbols data and expand each one in his left and right child
953 // symbol until reaching the leafs that represent the symbol value.
954 uint8_t set_symlen(PairsData* d, Sym s, std::vector<bool>& visited) {
956 visited[s] = true; // We can set it now because tree is acyclic
957 Sym sr = d->btree[s].get<LR::Right>();
962 Sym sl = d->btree[s].get<LR::Left>();
965 d->symlen[sl] = set_symlen(d, sl, visited);
968 d->symlen[sr] = set_symlen(d, sr, visited);
970 return d->symlen[sl] + d->symlen[sr] + 1;
973 uint8_t* set_sizes(PairsData* d, uint8_t* data) {
977 if (d->flags & TBFlag::SingleValue) {
978 d->blocksNum = d->blockLengthSize = 0;
979 d->span = d->sparseIndexSize = 0; // Broken MSVC zero-init
980 d->minSymLen = *data++; // Here we store the single value
984 // groupLen[] is a zero-terminated list of group lengths, the last groupIdx[]
985 // element stores the biggest index that is the tb size.
986 uint64_t tbSize = d->groupIdx[std::find(d->groupLen, d->groupLen + 7, 0) - d->groupLen];
988 d->sizeofBlock = 1ULL << *data++;
989 d->span = 1ULL << *data++;
990 d->sparseIndexSize = size_t((tbSize + d->span - 1) / d->span); // Round up
991 auto padding = number<uint8_t, LittleEndian>(data++);
992 d->blocksNum = number<uint32_t, LittleEndian>(data); data += sizeof(uint32_t);
993 d->blockLengthSize = d->blocksNum + padding; // Padded to ensure SparseIndex[]
994 // does not point out of range.
995 d->maxSymLen = *data++;
996 d->minSymLen = *data++;
997 d->lowestSym = (Sym*)data;
998 d->base64.resize(d->maxSymLen - d->minSymLen + 1);
1000 // The canonical code is ordered such that longer symbols (in terms of
1001 // the number of bits of their Huffman code) have lower numeric value,
1002 // so that d->lowestSym[i] >= d->lowestSym[i+1] (when read as LittleEndian).
1003 // Starting from this we compute a base64[] table indexed by symbol length
1004 // and containing 64 bit values so that d->base64[i] >= d->base64[i+1].
1005 // See https://en.wikipedia.org/wiki/Huffman_coding
1006 for (int i = d->base64.size() - 2; i >= 0; --i) {
1007 d->base64[i] = (d->base64[i + 1] + number<Sym, LittleEndian>(&d->lowestSym[i])
1008 - number<Sym, LittleEndian>(&d->lowestSym[i + 1])) / 2;
1010 assert(d->base64[i] * 2 >= d->base64[i+1]);
1013 // Now left-shift by an amount so that d->base64[i] gets shifted 1 bit more
1014 // than d->base64[i+1] and given the above assert condition, we ensure that
1015 // d->base64[i] >= d->base64[i+1]. Moreover for any symbol s64 of length i
1016 // and right-padded to 64 bits holds d->base64[i-1] >= s64 >= d->base64[i].
1017 for (size_t i = 0; i < d->base64.size(); ++i)
1018 d->base64[i] <<= 64 - i - d->minSymLen; // Right-padding to 64 bits
1020 data += d->base64.size() * sizeof(Sym);
1021 d->symlen.resize(number<uint16_t, LittleEndian>(data)); data += sizeof(uint16_t);
1022 d->btree = (LR*)data;
1024 // The compression scheme used is "Recursive Pairing", that replaces the most
1025 // frequent adjacent pair of symbols in the source message by a new symbol,
1026 // reevaluating the frequencies of all of the symbol pairs with respect to
1027 // the extended alphabet, and then repeating the process.
1028 // See http://www.larsson.dogma.net/dcc99.pdf
1029 std::vector<bool> visited(d->symlen.size());
1031 for (Sym sym = 0; sym < d->symlen.size(); ++sym)
1033 d->symlen[sym] = set_symlen(d, sym, visited);
1035 return data + d->symlen.size() * sizeof(LR) + (d->symlen.size() & 1);
1038 uint8_t* set_dtz_map(TBTable<WDL>&, uint8_t* data, File) { return data; }
1040 uint8_t* set_dtz_map(TBTable<DTZ>& e, uint8_t* data, File maxFile) {
1044 for (File f = FILE_A; f <= maxFile; ++f) {
1045 auto flags = e.get(0, f)->flags;
1046 if (flags & TBFlag::Mapped) {
1047 if (flags & TBFlag::Wide) {
1048 data += (uintptr_t)data & 1; // Word alignment, we may have a mixed table
1049 for (int i = 0; i < 4; ++i) { // Sequence like 3,x,x,x,1,x,0,2,x,x
1050 e.get(0, f)->map_idx[i] = (uint16_t)((uint16_t *)data - (uint16_t *)e.map + 1);
1051 data += 2 * number<uint16_t, LittleEndian>(data) + 2;
1055 for (int i = 0; i < 4; ++i) {
1056 e.get(0, f)->map_idx[i] = (uint16_t)(data - e.map + 1);
1063 return data += (uintptr_t)data & 1; // Word alignment
1066 // Populate entry's PairsData records with data from the just memory mapped file.
1067 // Called at first access.
1068 template<typename T>
1069 void set(T& e, uint8_t* data) {
1073 enum { Split = 1, HasPawns = 2 };
1075 assert(e.hasPawns == bool(*data & HasPawns));
1076 assert((e.key != e.key2) == bool(*data & Split));
1078 data++; // First byte stores flags
1080 const int sides = T::Sides == 2 && (e.key != e.key2) ? 2 : 1;
1081 const File maxFile = e.hasPawns ? FILE_D : FILE_A;
1083 bool pp = e.hasPawns && e.pawnCount[1]; // Pawns on both sides
1085 assert(!pp || e.pawnCount[0]);
1087 for (File f = FILE_A; f <= maxFile; ++f) {
1089 for (int i = 0; i < sides; i++)
1090 *e.get(i, f) = PairsData();
1092 int order[][2] = { { *data & 0xF, pp ? *(data + 1) & 0xF : 0xF },
1093 { *data >> 4, pp ? *(data + 1) >> 4 : 0xF } };
1096 for (int k = 0; k < e.pieceCount; ++k, ++data)
1097 for (int i = 0; i < sides; i++)
1098 e.get(i, f)->pieces[k] = Piece(i ? *data >> 4 : *data & 0xF);
1100 for (int i = 0; i < sides; ++i)
1101 set_groups(e, e.get(i, f), order[i], f);
1104 data += (uintptr_t)data & 1; // Word alignment
1106 for (File f = FILE_A; f <= maxFile; ++f)
1107 for (int i = 0; i < sides; i++)
1108 data = set_sizes(e.get(i, f), data);
1110 data = set_dtz_map(e, data, maxFile);
1112 for (File f = FILE_A; f <= maxFile; ++f)
1113 for (int i = 0; i < sides; i++) {
1114 (d = e.get(i, f))->sparseIndex = (SparseEntry*)data;
1115 data += d->sparseIndexSize * sizeof(SparseEntry);
1118 for (File f = FILE_A; f <= maxFile; ++f)
1119 for (int i = 0; i < sides; i++) {
1120 (d = e.get(i, f))->blockLength = (uint16_t*)data;
1121 data += d->blockLengthSize * sizeof(uint16_t);
1124 for (File f = FILE_A; f <= maxFile; ++f)
1125 for (int i = 0; i < sides; i++) {
1126 data = (uint8_t*)(((uintptr_t)data + 0x3F) & ~0x3F); // 64 byte alignment
1127 (d = e.get(i, f))->data = data;
1128 data += d->blocksNum * d->sizeofBlock;
1132 // If the TB file corresponding to the given position is already memory mapped
1133 // then return its base address, otherwise try to memory map and init it. Called
1134 // at every probe, memory map and init only at first access. Function is thread
1135 // safe and can be called concurrently.
1136 template<TBType Type>
1137 void* mapped(TBTable<Type>& e, const Position& pos) {
1139 static std::mutex mutex;
1141 // Use 'acquire' to avoid a thread reading 'ready' == true while
1142 // another is still working. (compiler reordering may cause this).
1143 if (e.ready.load(std::memory_order_acquire))
1144 return e.baseAddress; // Could be nullptr if file does not exist
1146 std::scoped_lock<std::mutex> lk(mutex);
1148 if (e.ready.load(std::memory_order_relaxed)) // Recheck under lock
1149 return e.baseAddress;
1151 // Pieces strings in decreasing order for each color, like ("KPP","KR")
1152 std::string fname, w, b;
1153 for (PieceType pt = KING; pt >= PAWN; --pt) {
1154 w += std::string(popcount(pos.pieces(WHITE, pt)), PieceToChar[pt]);
1155 b += std::string(popcount(pos.pieces(BLACK, pt)), PieceToChar[pt]);
1158 fname = (e.key == pos.material_key() ? w + 'v' + b : b + 'v' + w)
1159 + (Type == WDL ? ".rtbw" : ".rtbz");
1161 uint8_t* data = TBFile(fname).map(&e.baseAddress, &e.mapping, Type);
1166 e.ready.store(true, std::memory_order_release);
1167 return e.baseAddress;
1170 template<TBType Type, typename Ret = typename TBTable<Type>::Ret>
1171 Ret probe_table(const Position& pos, ProbeState* result, WDLScore wdl = WDLDraw) {
1173 if (pos.count<ALL_PIECES>() == 2) // KvK
1174 return Ret(WDLDraw);
1176 TBTable<Type>* entry = TBTables.get<Type>(pos.material_key());
1178 if (!entry || !mapped(*entry, pos))
1179 return *result = FAIL, Ret();
1181 return do_probe_table(pos, entry, wdl, result);
1184 // For a position where the side to move has a winning capture it is not necessary
1185 // to store a winning value so the generator treats such positions as "don't cares"
1186 // and tries to assign to it a value that improves the compression ratio. Similarly,
1187 // if the side to move has a drawing capture, then the position is at least drawn.
1188 // If the position is won, then the TB needs to store a win value. But if the
1189 // position is drawn, the TB may store a loss value if that is better for compression.
1190 // All of this means that during probing, the engine must look at captures and probe
1191 // their results and must probe the position itself. The "best" result of these
1192 // probes is the correct result for the position.
1193 // DTZ tables do not store values when a following move is a zeroing winning move
1194 // (winning capture or winning pawn move). Also DTZ store wrong values for positions
1195 // where the best move is an ep-move (even if losing). So in all these cases set
1196 // the state to ZEROING_BEST_MOVE.
1197 template<bool CheckZeroingMoves>
1198 WDLScore search(Position& pos, ProbeState* result) {
1200 WDLScore value, bestValue = WDLLoss;
1203 auto moveList = MoveList<LEGAL>(pos);
1204 size_t totalCount = moveList.size(), moveCount = 0;
1206 for (const Move move : moveList)
1208 if ( !pos.capture(move)
1209 && (!CheckZeroingMoves || type_of(pos.moved_piece(move)) != PAWN))
1214 pos.do_move(move, st);
1215 value = -search<false>(pos, result);
1216 pos.undo_move(move);
1218 if (*result == FAIL)
1221 if (value > bestValue)
1225 if (value >= WDLWin)
1227 *result = ZEROING_BEST_MOVE; // Winning DTZ-zeroing move
1233 // In case we have already searched all the legal moves we don't have to probe
1234 // the TB because the stored score could be wrong. For instance TB tables
1235 // do not contain information on position with ep rights, so in this case
1236 // the result of probe_wdl_table is wrong. Also in case of only capture
1237 // moves, for instance here 4K3/4q3/6p1/2k5/6p1/8/8/8 w - - 0 7, we have to
1238 // return with ZEROING_BEST_MOVE set.
1239 bool noMoreMoves = (moveCount && moveCount == totalCount);
1245 value = probe_table<WDL>(pos, result);
1247 if (*result == FAIL)
1251 // DTZ stores a "don't care" value if bestValue is a win
1252 if (bestValue >= value)
1253 return *result = ( bestValue > WDLDraw
1254 || noMoreMoves ? ZEROING_BEST_MOVE : OK), bestValue;
1256 return *result = OK, value;
1262 /// Tablebases::init() is called at startup and after every change to
1263 /// "SyzygyPath" UCI option to (re)create the various tables. It is not thread
1264 /// safe, nor it needs to be.
1265 void Tablebases::init(const std::string& paths) {
1269 TBFile::Paths = paths;
1271 if (paths.empty() || paths == "<empty>")
1274 // MapB1H1H7[] encodes a square below a1-h8 diagonal to 0..27
1276 for (Square s = SQ_A1; s <= SQ_H8; ++s)
1277 if (off_A1H8(s) < 0)
1278 MapB1H1H7[s] = code++;
1280 // MapA1D1D4[] encodes a square in the a1-d1-d4 triangle to 0..9
1281 std::vector<Square> diagonal;
1283 for (Square s = SQ_A1; s <= SQ_D4; ++s)
1284 if (off_A1H8(s) < 0 && file_of(s) <= FILE_D)
1285 MapA1D1D4[s] = code++;
1287 else if (!off_A1H8(s) && file_of(s) <= FILE_D)
1288 diagonal.push_back(s);
1290 // Diagonal squares are encoded as last ones
1291 for (auto s : diagonal)
1292 MapA1D1D4[s] = code++;
1294 // MapKK[] encodes all the 461 possible legal positions of two kings where
1295 // the first is in the a1-d1-d4 triangle. If the first king is on the a1-d4
1296 // diagonal, the other one shall not to be above the a1-h8 diagonal.
1297 std::vector<std::pair<int, Square>> bothOnDiagonal;
1299 for (int idx = 0; idx < 10; idx++)
1300 for (Square s1 = SQ_A1; s1 <= SQ_D4; ++s1)
1301 if (MapA1D1D4[s1] == idx && (idx || s1 == SQ_B1)) // SQ_B1 is mapped to 0
1303 for (Square s2 = SQ_A1; s2 <= SQ_H8; ++s2)
1304 if ((PseudoAttacks[KING][s1] | s1) & s2)
1305 continue; // Illegal position
1307 else if (!off_A1H8(s1) && off_A1H8(s2) > 0)
1308 continue; // First on diagonal, second above
1310 else if (!off_A1H8(s1) && !off_A1H8(s2))
1311 bothOnDiagonal.emplace_back(idx, s2);
1314 MapKK[idx][s2] = code++;
1317 // Legal positions with both kings on diagonal are encoded as last ones
1318 for (auto p : bothOnDiagonal)
1319 MapKK[p.first][p.second] = code++;
1321 // Binomial[] stores the Binomial Coefficents using Pascal rule. There
1322 // are Binomial[k][n] ways to choose k elements from a set of n elements.
1325 for (int n = 1; n < 64; n++) // Squares
1326 for (int k = 0; k < 7 && k <= n; ++k) // Pieces
1327 Binomial[k][n] = (k > 0 ? Binomial[k - 1][n - 1] : 0)
1328 + (k < n ? Binomial[k ][n - 1] : 0);
1330 // MapPawns[s] encodes squares a2-h7 to 0..47. This is the number of possible
1331 // available squares when the leading one is in 's'. Moreover the pawn with
1332 // highest MapPawns[] is the leading pawn, the one nearest the edge and,
1333 // among pawns with same file, the one with lowest rank.
1334 int availableSquares = 47; // Available squares when lead pawn is in a2
1336 // Init the tables for the encoding of leading pawns group: with 7-men TB we
1337 // can have up to 5 leading pawns (KPPPPPK).
1338 for (int leadPawnsCnt = 1; leadPawnsCnt <= 5; ++leadPawnsCnt)
1339 for (File f = FILE_A; f <= FILE_D; ++f)
1341 // Restart the index at every file because TB table is splitted
1342 // by file, so we can reuse the same index for different files.
1345 // Sum all possible combinations for a given file, starting with
1346 // the leading pawn on rank 2 and increasing the rank.
1347 for (Rank r = RANK_2; r <= RANK_7; ++r)
1349 Square sq = make_square(f, r);
1351 // Compute MapPawns[] at first pass.
1352 // If sq is the leading pawn square, any other pawn cannot be
1353 // below or more toward the edge of sq. There are 47 available
1354 // squares when sq = a2 and reduced by 2 for any rank increase
1355 // due to mirroring: sq == a3 -> no a2, h2, so MapPawns[a3] = 45
1356 if (leadPawnsCnt == 1)
1358 MapPawns[sq] = availableSquares--;
1359 MapPawns[flip_file(sq)] = availableSquares--;
1361 LeadPawnIdx[leadPawnsCnt][sq] = idx;
1362 idx += Binomial[leadPawnsCnt - 1][MapPawns[sq]];
1364 // After a file is traversed, store the cumulated per-file index
1365 LeadPawnsSize[leadPawnsCnt][f] = idx;
1368 // Add entries in TB tables if the corresponding ".rtbw" file exists
1369 for (PieceType p1 = PAWN; p1 < KING; ++p1) {
1370 TBTables.add({KING, p1, KING});
1372 for (PieceType p2 = PAWN; p2 <= p1; ++p2) {
1373 TBTables.add({KING, p1, p2, KING});
1374 TBTables.add({KING, p1, KING, p2});
1376 for (PieceType p3 = PAWN; p3 < KING; ++p3)
1377 TBTables.add({KING, p1, p2, KING, p3});
1379 for (PieceType p3 = PAWN; p3 <= p2; ++p3) {
1380 TBTables.add({KING, p1, p2, p3, KING});
1382 for (PieceType p4 = PAWN; p4 <= p3; ++p4) {
1383 TBTables.add({KING, p1, p2, p3, p4, KING});
1385 for (PieceType p5 = PAWN; p5 <= p4; ++p5)
1386 TBTables.add({KING, p1, p2, p3, p4, p5, KING});
1388 for (PieceType p5 = PAWN; p5 < KING; ++p5)
1389 TBTables.add({KING, p1, p2, p3, p4, KING, p5});
1392 for (PieceType p4 = PAWN; p4 < KING; ++p4) {
1393 TBTables.add({KING, p1, p2, p3, KING, p4});
1395 for (PieceType p5 = PAWN; p5 <= p4; ++p5)
1396 TBTables.add({KING, p1, p2, p3, KING, p4, p5});
1400 for (PieceType p3 = PAWN; p3 <= p1; ++p3)
1401 for (PieceType p4 = PAWN; p4 <= (p1 == p3 ? p2 : p3); ++p4)
1402 TBTables.add({KING, p1, p2, KING, p3, p4});
1406 sync_cout << "info string Found " << TBTables.size() << " tablebases" << sync_endl;
1409 // Probe the WDL table for a particular position.
1410 // If *result != FAIL, the probe was successful.
1411 // The return value is from the point of view of the side to move:
1413 // -1 : loss, but draw under 50-move rule
1415 // 1 : win, but draw under 50-move rule
1417 WDLScore Tablebases::probe_wdl(Position& pos, ProbeState* result) {
1420 return search<false>(pos, result);
1423 // Probe the DTZ table for a particular position.
1424 // If *result != FAIL, the probe was successful.
1425 // The return value is from the point of view of the side to move:
1426 // n < -100 : loss, but draw under 50-move rule
1427 // -100 <= n < -1 : loss in n ply (assuming 50-move counter == 0)
1428 // -1 : loss, the side to move is mated
1430 // 1 < n <= 100 : win in n ply (assuming 50-move counter == 0)
1431 // 100 < n : win, but draw under 50-move rule
1433 // The return value n can be off by 1: a return value -n can mean a loss
1434 // in n+1 ply and a return value +n can mean a win in n+1 ply. This
1435 // cannot happen for tables with positions exactly on the "edge" of
1436 // the 50-move rule.
1438 // This implies that if dtz > 0 is returned, the position is certainly
1439 // a win if dtz + 50-move-counter <= 99. Care must be taken that the engine
1440 // picks moves that preserve dtz + 50-move-counter <= 99.
1442 // If n = 100 immediately after a capture or pawn move, then the position
1443 // is also certainly a win, and during the whole phase until the next
1444 // capture or pawn move, the inequality to be preserved is
1445 // dtz + 50-move-counter <= 100.
1447 // In short, if a move is available resulting in dtz + 50-move-counter <= 99,
1448 // then do not accept moves leading to dtz + 50-move-counter == 100.
1449 int Tablebases::probe_dtz(Position& pos, ProbeState* result) {
1452 WDLScore wdl = search<true>(pos, result);
1454 if (*result == FAIL || wdl == WDLDraw) // DTZ tables don't store draws
1457 // DTZ stores a 'don't care' value in this case, or even a plain wrong
1458 // one as in case the best move is a losing ep, so it cannot be probed.
1459 if (*result == ZEROING_BEST_MOVE)
1460 return dtz_before_zeroing(wdl);
1462 int dtz = probe_table<DTZ>(pos, result, wdl);
1464 if (*result == FAIL)
1467 if (*result != CHANGE_STM)
1468 return (dtz + 100 * (wdl == WDLBlessedLoss || wdl == WDLCursedWin)) * sign_of(wdl);
1470 // DTZ stores results for the other side, so we need to do a 1-ply search and
1471 // find the winning move that minimizes DTZ.
1473 int minDTZ = 0xFFFF;
1475 for (const Move move : MoveList<LEGAL>(pos))
1477 bool zeroing = pos.capture(move) || type_of(pos.moved_piece(move)) == PAWN;
1479 pos.do_move(move, st);
1481 // For zeroing moves we want the dtz of the move _before_ doing it,
1482 // otherwise we will get the dtz of the next move sequence. Search the
1483 // position after the move to get the score sign (because even in a
1484 // winning position we could make a losing capture or going for a draw).
1485 dtz = zeroing ? -dtz_before_zeroing(search<false>(pos, result))
1486 : -probe_dtz(pos, result);
1488 // If the move mates, force minDTZ to 1
1489 if (dtz == 1 && pos.checkers() && MoveList<LEGAL>(pos).size() == 0)
1492 // Convert result from 1-ply search. Zeroing moves are already accounted
1493 // by dtz_before_zeroing() that returns the DTZ of the previous move.
1495 dtz += sign_of(dtz);
1497 // Skip the draws and if we are winning only pick positive dtz
1498 if (dtz < minDTZ && sign_of(dtz) == sign_of(wdl))
1501 pos.undo_move(move);
1503 if (*result == FAIL)
1507 // When there are no legal moves, the position is mate: we return -1
1508 return minDTZ == 0xFFFF ? -1 : minDTZ;
1512 // Use the DTZ tables to rank root moves.
1514 // A return value false indicates that not all probes were successful.
1515 bool Tablebases::root_probe(Position& pos, Search::RootMoves& rootMoves) {
1520 // Obtain 50-move counter for the root position
1521 int cnt50 = pos.rule50_count();
1523 // Check whether a position was repeated since the last zeroing move.
1524 bool rep = pos.has_repeated();
1526 int dtz, bound = Options["Syzygy50MoveRule"] ? 900 : 1;
1528 // Probe and rank each move
1529 for (auto& m : rootMoves)
1531 pos.do_move(m.pv[0], st);
1533 // Calculate dtz for the current move counting from the root position
1534 if (pos.rule50_count() == 0)
1536 // In case of a zeroing move, dtz is one of -101/-1/0/1/101
1537 WDLScore wdl = -probe_wdl(pos, &result);
1538 dtz = dtz_before_zeroing(wdl);
1542 // Otherwise, take dtz for the new position and correct by 1 ply
1543 dtz = -probe_dtz(pos, &result);
1544 dtz = dtz > 0 ? dtz + 1
1545 : dtz < 0 ? dtz - 1 : dtz;
1548 // Make sure that a mating move is assigned a dtz value of 1
1551 && MoveList<LEGAL>(pos).size() == 0)
1554 pos.undo_move(m.pv[0]);
1559 // Better moves are ranked higher. Certain wins are ranked equally.
1560 // Losing moves are ranked equally unless a 50-move draw is in sight.
1561 int r = dtz > 0 ? (dtz + cnt50 <= 99 && !rep ? 1000 : 1000 - (dtz + cnt50))
1562 : dtz < 0 ? (-dtz * 2 + cnt50 < 100 ? -1000 : -1000 + (-dtz + cnt50))
1566 // Determine the score to be displayed for this move. Assign at least
1567 // 1 cp to cursed wins and let it grow to 49 cp as the positions gets
1568 // closer to a real win.
1569 m.tbScore = r >= bound ? VALUE_MATE - MAX_PLY - 1
1570 : r > 0 ? Value((std::max( 3, r - 800) * int(PawnValueEg)) / 200)
1571 : r == 0 ? VALUE_DRAW
1572 : r > -bound ? Value((std::min(-3, r + 800) * int(PawnValueEg)) / 200)
1573 : -VALUE_MATE + MAX_PLY + 1;
1580 // Use the WDL tables to rank root moves.
1581 // This is a fallback for the case that some or all DTZ tables are missing.
1583 // A return value false indicates that not all probes were successful.
1584 bool Tablebases::root_probe_wdl(Position& pos, Search::RootMoves& rootMoves) {
1586 static const int WDL_to_rank[] = { -1000, -899, 0, 899, 1000 };
1591 bool rule50 = Options["Syzygy50MoveRule"];
1593 // Probe and rank each move
1594 for (auto& m : rootMoves)
1596 pos.do_move(m.pv[0], st);
1598 WDLScore wdl = -probe_wdl(pos, &result);
1600 pos.undo_move(m.pv[0]);
1605 m.tbRank = WDL_to_rank[wdl + 2];
1608 wdl = wdl > WDLDraw ? WDLWin
1609 : wdl < WDLDraw ? WDLLoss : WDLDraw;
1610 m.tbScore = WDL_to_value[wdl + 2];
1616 } // namespace Stockfish