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 "../cluster.h"
33 #include "../movegen.h"
34 #include "../position.h"
35 #include "../search.h"
47 #define WIN32_LEAN_AND_MEAN
49 # define NOMINMAX // Disable macros min() and max()
54 using namespace Stockfish::Tablebases;
56 int Stockfish::Tablebases::MaxCardinality;
62 constexpr int TBPIECES = 7; // Max number of supported pieces
64 enum { BigEndian, LittleEndian };
65 enum TBType { WDL, DTZ }; // Used as template parameter
67 // Each table has a set of flags: all of them refer to DTZ tables, the last one to WDL tables
68 enum TBFlag { STM = 1, Mapped = 2, WinPlies = 4, LossPlies = 8, Wide = 16, SingleValue = 128 };
70 inline WDLScore operator-(WDLScore d) { return WDLScore(-int(d)); }
71 inline Square operator^(Square s, int i) { return Square(int(s) ^ i); }
73 const std::string PieceToChar = " PNBRQK pnbrqk";
75 int MapPawns[SQUARE_NB];
76 int MapB1H1H7[SQUARE_NB];
77 int MapA1D1D4[SQUARE_NB];
78 int MapKK[10][SQUARE_NB]; // [MapA1D1D4][SQUARE_NB]
80 int Binomial[6][SQUARE_NB]; // [k][n] k elements from a set of n elements
81 int LeadPawnIdx[6][SQUARE_NB]; // [leadPawnsCnt][SQUARE_NB]
82 int LeadPawnsSize[6][4]; // [leadPawnsCnt][FILE_A..FILE_D]
84 // Comparison function to sort leading pawns in ascending MapPawns[] order
85 bool pawns_comp(Square i, Square j) { return MapPawns[i] < MapPawns[j]; }
86 int off_A1H8(Square sq) { return int(rank_of(sq)) - file_of(sq); }
88 constexpr Value WDL_to_value[] = {
89 -VALUE_MATE + MAX_PLY + 1,
93 VALUE_MATE - MAX_PLY - 1
96 template<typename T, int Half = sizeof(T) / 2, int End = sizeof(T) - 1>
97 inline void swap_endian(T& x)
99 static_assert(std::is_unsigned<T>::value, "Argument of swap_endian not unsigned");
101 uint8_t tmp, *c = (uint8_t*)&x;
102 for (int i = 0; i < Half; ++i)
103 tmp = c[i], c[i] = c[End - i], c[End - i] = tmp;
105 template<> inline void swap_endian<uint8_t>(uint8_t&) {}
107 template<typename T, int LE> T number(void* addr)
109 static const union { uint32_t i; char c[4]; } Le = { 0x01020304 };
110 static const bool IsLittleEndian = (Le.c[0] == 4);
114 if ((uintptr_t)addr & (alignof(T) - 1)) // Unaligned pointer (very rare)
115 std::memcpy(&v, addr, sizeof(T));
119 if (LE != IsLittleEndian)
124 // DTZ tables don't store valid scores for moves that reset the rule50 counter
125 // like captures and pawn moves but we can easily recover the correct dtz of the
126 // previous move if we know the position's WDL score.
127 int dtz_before_zeroing(WDLScore wdl) {
128 return wdl == WDLWin ? 1 :
129 wdl == WDLCursedWin ? 101 :
130 wdl == WDLBlessedLoss ? -101 :
131 wdl == WDLLoss ? -1 : 0;
134 // Return the sign of a number (-1, 0, 1)
135 template <typename T> int sign_of(T val) {
136 return (T(0) < val) - (val < T(0));
139 // Numbers in little endian used by sparseIndex[] to point into blockLength[]
141 char block[4]; // Number of block
142 char offset[2]; // Offset within the block
145 static_assert(sizeof(SparseEntry) == 6, "SparseEntry must be 6 bytes");
147 typedef uint16_t Sym; // Huffman symbol
150 enum Side { Left, Right };
152 uint8_t lr[3]; // The first 12 bits is the left-hand symbol, the second 12
153 // bits is the right-hand symbol. If symbol has length 1,
154 // then the left-hand symbol is the stored value.
157 return S == Left ? ((lr[1] & 0xF) << 8) | lr[0] :
158 S == Right ? (lr[2] << 4) | (lr[1] >> 4) : (assert(false), Sym(-1));
162 static_assert(sizeof(LR) == 3, "LR tree entry must be 3 bytes");
164 // Tablebases data layout is structured as following:
166 // TBFile: memory maps/unmaps the physical .rtbw and .rtbz files
167 // TBTable: one object for each file with corresponding indexing information
168 // TBTables: has ownership of TBTable objects, keeping a list and a hash
170 // class TBFile memory maps/unmaps the single .rtbw and .rtbz files. Files are
171 // memory mapped for best performance. Files are mapped at first access: at init
172 // time only existence of the file is checked.
173 class TBFile : public std::ifstream {
178 // Look for and open the file among the Paths directories where the .rtbw
179 // and .rtbz files can be found. Multiple directories are separated by ";"
180 // on Windows and by ":" on Unix-based operating systems.
183 // C:\tb\wdl345;C:\tb\wdl6;D:\tb\dtz345;D:\tb\dtz6
184 static std::string Paths;
186 TBFile(const std::string& f) {
189 constexpr char SepChar = ':';
191 constexpr char SepChar = ';';
193 std::stringstream ss(Paths);
196 while (std::getline(ss, path, SepChar)) {
197 fname = path + "/" + f;
198 std::ifstream::open(fname);
204 // Memory map the file and check it. File should be already open and will be
205 // closed after mapping.
206 uint8_t* map(void** baseAddress, uint64_t* mapping, TBType type) {
210 close(); // Need to re-open to get native file descriptor
214 int fd = ::open(fname.c_str(), O_RDONLY);
217 return *baseAddress = nullptr, nullptr;
221 if (statbuf.st_size % 64 != 16)
223 std::cerr << "Corrupt tablebase file " << fname << std::endl;
227 *mapping = statbuf.st_size;
228 *baseAddress = mmap(nullptr, statbuf.st_size, PROT_READ, MAP_SHARED, fd, 0);
229 #if defined(MADV_RANDOM)
230 madvise(*baseAddress, statbuf.st_size, MADV_RANDOM);
234 if (*baseAddress == MAP_FAILED)
236 std::cerr << "Could not mmap() " << fname << std::endl;
240 // Note FILE_FLAG_RANDOM_ACCESS is only a hint to Windows and as such may get ignored.
241 HANDLE fd = CreateFile(fname.c_str(), GENERIC_READ, FILE_SHARE_READ, nullptr,
242 OPEN_EXISTING, FILE_FLAG_RANDOM_ACCESS, nullptr);
244 if (fd == INVALID_HANDLE_VALUE)
245 return *baseAddress = nullptr, nullptr;
248 DWORD size_low = GetFileSize(fd, &size_high);
250 if (size_low % 64 != 16)
252 std::cerr << "Corrupt tablebase file " << fname << std::endl;
256 HANDLE mmap = CreateFileMapping(fd, nullptr, PAGE_READONLY, size_high, size_low, nullptr);
261 std::cerr << "CreateFileMapping() failed" << std::endl;
265 *mapping = (uint64_t)mmap;
266 *baseAddress = MapViewOfFile(mmap, FILE_MAP_READ, 0, 0, 0);
270 std::cerr << "MapViewOfFile() failed, name = " << fname
271 << ", error = " << GetLastError() << std::endl;
275 uint8_t* data = (uint8_t*)*baseAddress;
277 constexpr uint8_t Magics[][4] = { { 0xD7, 0x66, 0x0C, 0xA5 },
278 { 0x71, 0xE8, 0x23, 0x5D } };
280 if (memcmp(data, Magics[type == WDL], 4))
282 std::cerr << "Corrupted table in file " << fname << std::endl;
283 unmap(*baseAddress, *mapping);
284 return *baseAddress = nullptr, nullptr;
287 return data + 4; // Skip Magics's header
290 static void unmap(void* baseAddress, uint64_t mapping) {
293 munmap(baseAddress, mapping);
295 UnmapViewOfFile(baseAddress);
296 CloseHandle((HANDLE)mapping);
301 std::string TBFile::Paths;
303 // struct PairsData contains low level indexing information to access TB data.
304 // There are 8, 4 or 2 PairsData records for each TBTable, according to type of
305 // table and if positions have pawns or not. It is populated at first access.
307 uint8_t flags; // Table flags, see enum TBFlag
308 uint8_t maxSymLen; // Maximum length in bits of the Huffman symbols
309 uint8_t minSymLen; // Minimum length in bits of the Huffman symbols
310 uint32_t blocksNum; // Number of blocks in the TB file
311 size_t sizeofBlock; // Block size in bytes
312 size_t span; // About every span values there is a SparseIndex[] entry
313 Sym* lowestSym; // lowestSym[l] is the symbol of length l with the lowest value
314 LR* btree; // btree[sym] stores the left and right symbols that expand sym
315 uint16_t* blockLength; // Number of stored positions (minus one) for each block: 1..65536
316 uint32_t blockLengthSize; // Size of blockLength[] table: padded so it's bigger than blocksNum
317 SparseEntry* sparseIndex; // Partial indices into blockLength[]
318 size_t sparseIndexSize; // Size of SparseIndex[] table
319 uint8_t* data; // Start of Huffman compressed data
320 std::vector<uint64_t> base64; // base64[l - min_sym_len] is the 64bit-padded lowest symbol of length l
321 std::vector<uint8_t> symlen; // Number of values (-1) represented by a given Huffman symbol: 1..256
322 Piece pieces[TBPIECES]; // Position pieces: the order of pieces defines the groups
323 uint64_t groupIdx[TBPIECES+1]; // Start index used for the encoding of the group's pieces
324 int groupLen[TBPIECES+1]; // Number of pieces in a given group: KRKN -> (3, 1)
325 uint16_t map_idx[4]; // WDLWin, WDLLoss, WDLCursedWin, WDLBlessedLoss (used in DTZ)
328 // struct TBTable contains indexing information to access the corresponding TBFile.
329 // There are 2 types of TBTable, corresponding to a WDL or a DTZ file. TBTable
330 // is populated at init time but the nested PairsData records are populated at
331 // first access, when the corresponding file is memory mapped.
332 template<TBType Type>
334 typedef typename std::conditional<Type == WDL, WDLScore, int>::type Ret;
336 static constexpr int Sides = Type == WDL ? 2 : 1;
338 std::atomic_bool ready;
346 bool hasUniquePieces;
347 uint8_t pawnCount[2]; // [Lead color / other color]
348 PairsData items[Sides][4]; // [wtm / btm][FILE_A..FILE_D or 0]
350 PairsData* get(int stm, int f) {
351 return &items[stm % Sides][hasPawns ? f : 0];
354 TBTable() : ready(false), baseAddress(nullptr) {}
355 explicit TBTable(const std::string& code);
356 explicit TBTable(const TBTable<WDL>& wdl);
360 TBFile::unmap(baseAddress, mapping);
365 TBTable<WDL>::TBTable(const std::string& code) : TBTable() {
370 key = pos.set(code, WHITE, &st).material_key();
371 pieceCount = pos.count<ALL_PIECES>();
372 hasPawns = pos.pieces(PAWN);
374 hasUniquePieces = false;
375 for (Color c : { WHITE, BLACK })
376 for (PieceType pt = PAWN; pt < KING; ++pt)
377 if (popcount(pos.pieces(c, pt)) == 1)
378 hasUniquePieces = true;
380 // Set the leading color. In case both sides have pawns the leading color
381 // is the side with less pawns because this leads to better compression.
382 bool c = !pos.count<PAWN>(BLACK)
383 || ( pos.count<PAWN>(WHITE)
384 && pos.count<PAWN>(BLACK) >= pos.count<PAWN>(WHITE));
386 pawnCount[0] = pos.count<PAWN>(c ? WHITE : BLACK);
387 pawnCount[1] = pos.count<PAWN>(c ? BLACK : WHITE);
389 key2 = pos.set(code, BLACK, &st).material_key();
393 TBTable<DTZ>::TBTable(const TBTable<WDL>& wdl) : TBTable() {
395 // Use the corresponding WDL table to avoid recalculating all from scratch
398 pieceCount = wdl.pieceCount;
399 hasPawns = wdl.hasPawns;
400 hasUniquePieces = wdl.hasUniquePieces;
401 pawnCount[0] = wdl.pawnCount[0];
402 pawnCount[1] = wdl.pawnCount[1];
405 // class TBTables creates and keeps ownership of the TBTable objects, one for
406 // each TB file found. It supports a fast, hash based, table lookup. Populated
407 // at init time, accessed at probe time.
416 template <TBType Type>
417 TBTable<Type>* get() const {
418 return (TBTable<Type>*)(Type == WDL ? (void*)wdl : (void*)dtz);
422 static constexpr int Size = 1 << 12; // 4K table, indexed by key's 12 lsb
423 static constexpr int Overflow = 1; // Number of elements allowed to map to the last bucket
425 Entry hashTable[Size + Overflow];
427 std::deque<TBTable<WDL>> wdlTable;
428 std::deque<TBTable<DTZ>> dtzTable;
430 void insert(Key key, TBTable<WDL>* wdl, TBTable<DTZ>* dtz) {
431 uint32_t homeBucket = (uint32_t)key & (Size - 1);
432 Entry entry{ key, wdl, dtz };
434 // Ensure last element is empty to avoid overflow when looking up
435 for (uint32_t bucket = homeBucket; bucket < Size + Overflow - 1; ++bucket) {
436 Key otherKey = hashTable[bucket].key;
437 if (otherKey == key || !hashTable[bucket].get<WDL>()) {
438 hashTable[bucket] = entry;
442 // Robin Hood hashing: If we've probed for longer than this element,
443 // insert here and search for a new spot for the other element instead.
444 uint32_t otherHomeBucket = (uint32_t)otherKey & (Size - 1);
445 if (otherHomeBucket > homeBucket) {
446 std::swap(entry, hashTable[bucket]);
448 homeBucket = otherHomeBucket;
451 std::cerr << "TB hash table size too low!" << std::endl;
456 template<TBType Type>
457 TBTable<Type>* get(Key key) {
458 for (const Entry* entry = &hashTable[(uint32_t)key & (Size - 1)]; ; ++entry) {
459 if (entry->key == key || !entry->get<Type>())
460 return entry->get<Type>();
465 memset(hashTable, 0, sizeof(hashTable));
469 size_t size() const { return wdlTable.size(); }
470 void add(const std::vector<PieceType>& pieces);
475 // If the corresponding file exists two new objects TBTable<WDL> and TBTable<DTZ>
476 // are created and added to the lists and hash table. Called at init time.
477 void TBTables::add(const std::vector<PieceType>& pieces) {
481 for (PieceType pt : pieces)
482 code += PieceToChar[pt];
484 TBFile file(code.insert(code.find('K', 1), "v") + ".rtbw"); // KRK -> KRvK
486 if (!file.is_open()) // Only WDL file is checked
491 MaxCardinality = std::max((int)pieces.size(), MaxCardinality);
493 wdlTable.emplace_back(code);
494 dtzTable.emplace_back(wdlTable.back());
496 // Insert into the hash keys for both colors: KRvK with KR white and black
497 insert(wdlTable.back().key , &wdlTable.back(), &dtzTable.back());
498 insert(wdlTable.back().key2, &wdlTable.back(), &dtzTable.back());
501 // TB tables are compressed with canonical Huffman code. The compressed data is divided into
502 // blocks of size d->sizeofBlock, and each block stores a variable number of symbols.
503 // Each symbol represents either a WDL or a (remapped) DTZ value, or a pair of other symbols
504 // (recursively). If you keep expanding the symbols in a block, you end up with up to 65536
505 // WDL or DTZ values. Each symbol represents up to 256 values and will correspond after
506 // Huffman coding to at least 1 bit. So a block of 32 bytes corresponds to at most
507 // 32 x 8 x 256 = 65536 values. This maximum is only reached for tables that consist mostly
508 // of draws or mostly of wins, but such tables are actually quite common. In principle, the
509 // blocks in WDL tables are 64 bytes long (and will be aligned on cache lines). But for
510 // mostly-draw or mostly-win tables this can leave many 64-byte blocks only half-filled, so
511 // in such cases blocks are 32 bytes long. The blocks of DTZ tables are up to 1024 bytes long.
512 // The generator picks the size that leads to the smallest table. The "book" of symbols and
513 // Huffman codes is the same for all blocks in the table. A non-symmetric pawnless TB file
514 // will have one table for wtm and one for btm, a TB file with pawns will have tables per
515 // file a,b,c,d also in this case one set for wtm and one for btm.
516 int decompress_pairs(PairsData* d, uint64_t idx) {
518 // Special case where all table positions store the same value
519 if (d->flags & TBFlag::SingleValue)
522 // First we need to locate the right block that stores the value at index "idx".
523 // Because each block n stores blockLength[n] + 1 values, the index i of the block
524 // that contains the value at position idx is:
526 // for (i = -1, sum = 0; sum <= idx; i++)
527 // sum += blockLength[i + 1] + 1;
529 // This can be slow, so we use SparseIndex[] populated with a set of SparseEntry that
530 // point to known indices into blockLength[]. Namely SparseIndex[k] is a SparseEntry
531 // that stores the blockLength[] index and the offset within that block of the value
532 // with index I(k), where:
534 // I(k) = k * d->span + d->span / 2 (1)
536 // First step is to get the 'k' of the I(k) nearest to our idx, using definition (1)
537 uint32_t k = uint32_t(idx / d->span);
539 // Then we read the corresponding SparseIndex[] entry
540 uint32_t block = number<uint32_t, LittleEndian>(&d->sparseIndex[k].block);
541 int offset = number<uint16_t, LittleEndian>(&d->sparseIndex[k].offset);
543 // Now compute the difference idx - I(k). From definition of k we know that
545 // idx = k * d->span + idx % d->span (2)
547 // So from (1) and (2) we can compute idx - I(K):
548 int diff = idx % d->span - d->span / 2;
550 // Sum the above to offset to find the offset corresponding to our idx
553 // Move to previous/next block, until we reach the correct block that contains idx,
554 // that is when 0 <= offset <= d->blockLength[block]
556 offset += d->blockLength[--block] + 1;
558 while (offset > d->blockLength[block])
559 offset -= d->blockLength[block++] + 1;
561 // Finally, we find the start address of our block of canonical Huffman symbols
562 uint32_t* ptr = (uint32_t*)(d->data + ((uint64_t)block * d->sizeofBlock));
564 // Read the first 64 bits in our block, this is a (truncated) sequence of
565 // unknown number of symbols of unknown length but we know the first one
566 // is at the beginning of this 64 bits sequence.
567 uint64_t buf64 = number<uint64_t, BigEndian>(ptr); ptr += 2;
572 int len = 0; // This is the symbol length - d->min_sym_len
574 // Now get the symbol length. For any symbol s64 of length l right-padded
575 // to 64 bits we know that d->base64[l-1] >= s64 >= d->base64[l] so we
576 // can find the symbol length iterating through base64[].
577 while (buf64 < d->base64[len])
580 // All the symbols of a given length are consecutive integers (numerical
581 // sequence property), so we can compute the offset of our symbol of
582 // length len, stored at the beginning of buf64.
583 sym = Sym((buf64 - d->base64[len]) >> (64 - len - d->minSymLen));
585 // Now add the value of the lowest symbol of length len to get our symbol
586 sym += number<Sym, LittleEndian>(&d->lowestSym[len]);
588 // If our offset is within the number of values represented by symbol sym
590 if (offset < d->symlen[sym] + 1)
593 // ...otherwise update the offset and continue to iterate
594 offset -= d->symlen[sym] + 1;
595 len += d->minSymLen; // Get the real length
596 buf64 <<= len; // Consume the just processed symbol
599 if (buf64Size <= 32) { // Refill the buffer
601 buf64 |= (uint64_t)number<uint32_t, BigEndian>(ptr++) << (64 - buf64Size);
605 // Ok, now we have our symbol that expands into d->symlen[sym] + 1 symbols.
606 // We binary-search for our value recursively expanding into the left and
607 // right child symbols until we reach a leaf node where symlen[sym] + 1 == 1
608 // that will store the value we need.
609 while (d->symlen[sym]) {
611 Sym left = d->btree[sym].get<LR::Left>();
613 // If a symbol contains 36 sub-symbols (d->symlen[sym] + 1 = 36) and
614 // expands in a pair (d->symlen[left] = 23, d->symlen[right] = 11), then
615 // we know that, for instance the ten-th value (offset = 10) will be on
616 // the left side because in Recursive Pairing child symbols are adjacent.
617 if (offset < d->symlen[left] + 1)
620 offset -= d->symlen[left] + 1;
621 sym = d->btree[sym].get<LR::Right>();
625 return d->btree[sym].get<LR::Left>();
628 bool check_dtz_stm(TBTable<WDL>*, int, File) { return true; }
630 bool check_dtz_stm(TBTable<DTZ>* entry, int stm, File f) {
632 auto flags = entry->get(stm, f)->flags;
633 return (flags & TBFlag::STM) == stm
634 || ((entry->key == entry->key2) && !entry->hasPawns);
637 // DTZ scores are sorted by frequency of occurrence and then assigned the
638 // values 0, 1, 2, ... in order of decreasing frequency. This is done for each
639 // of the four WDLScore values. The mapping information necessary to reconstruct
640 // the original values is stored in the TB file and read during map[] init.
641 WDLScore map_score(TBTable<WDL>*, File, int value, WDLScore) { return WDLScore(value - 2); }
643 int map_score(TBTable<DTZ>* entry, File f, int value, WDLScore wdl) {
645 constexpr int WDLMap[] = { 1, 3, 0, 2, 0 };
647 auto flags = entry->get(0, f)->flags;
649 uint8_t* map = entry->map;
650 uint16_t* idx = entry->get(0, f)->map_idx;
651 if (flags & TBFlag::Mapped) {
652 if (flags & TBFlag::Wide)
653 value = ((uint16_t *)map)[idx[WDLMap[wdl + 2]] + value];
655 value = map[idx[WDLMap[wdl + 2]] + value];
658 // DTZ tables store distance to zero in number of moves or plies. We
659 // want to return plies, so we have convert to plies when needed.
660 if ( (wdl == WDLWin && !(flags & TBFlag::WinPlies))
661 || (wdl == WDLLoss && !(flags & TBFlag::LossPlies))
662 || wdl == WDLCursedWin
663 || wdl == WDLBlessedLoss)
669 // Compute a unique index out of a position and use it to probe the TB file. To
670 // encode k pieces of same type and color, first sort the pieces by square in
671 // ascending order s1 <= s2 <= ... <= sk then compute the unique index as:
673 // idx = Binomial[1][s1] + Binomial[2][s2] + ... + Binomial[k][sk]
675 template<typename T, typename Ret = typename T::Ret>
676 Ret do_probe_table(const Position& pos, T* entry, WDLScore wdl, ProbeState* result) {
678 Square squares[TBPIECES];
679 Piece pieces[TBPIECES];
681 int next = 0, size = 0, leadPawnsCnt = 0;
683 Bitboard b, leadPawns = 0;
684 File tbFile = FILE_A;
686 // A given TB entry like KRK has associated two material keys: KRvk and Kvkr.
687 // If both sides have the same pieces keys are equal. In this case TB tables
688 // only store the 'white to move' case, so if the position to lookup has black
689 // to move, we need to switch the color and flip the squares before to lookup.
690 bool symmetricBlackToMove = (entry->key == entry->key2 && pos.side_to_move());
692 // TB files are calculated for white as stronger side. For instance we have
693 // KRvK, not KvKR. A position where stronger side is white will have its
694 // material key == entry->key, otherwise we have to switch the color and
695 // flip the squares before to lookup.
696 bool blackStronger = (pos.material_key() != entry->key);
698 int flipColor = (symmetricBlackToMove || blackStronger) * 8;
699 int flipSquares = (symmetricBlackToMove || blackStronger) * 56;
700 int stm = (symmetricBlackToMove || blackStronger) ^ pos.side_to_move();
702 // For pawns, TB files store 4 separate tables according if leading pawn is on
703 // file a, b, c or d after reordering. The leading pawn is the one with maximum
704 // MapPawns[] value, that is the one most toward the edges and with lowest rank.
705 if (entry->hasPawns) {
707 // In all the 4 tables, pawns are at the beginning of the piece sequence and
708 // their color is the reference one. So we just pick the first one.
709 Piece pc = Piece(entry->get(0, 0)->pieces[0] ^ flipColor);
711 assert(type_of(pc) == PAWN);
713 leadPawns = b = pos.pieces(color_of(pc), PAWN);
715 squares[size++] = pop_lsb(&b) ^ flipSquares;
720 std::swap(squares[0], *std::max_element(squares, squares + leadPawnsCnt, pawns_comp));
722 tbFile = File(edge_distance(file_of(squares[0])));
725 // DTZ tables are one-sided, i.e. they store positions only for white to
726 // move or only for black to move, so check for side to move to be stm,
727 // early exit otherwise.
728 if (!check_dtz_stm(entry, stm, tbFile))
729 return *result = CHANGE_STM, Ret();
731 // Now we are ready to get all the position pieces (but the lead pawns) and
732 // directly map them to the correct color and square.
733 b = pos.pieces() ^ leadPawns;
735 Square s = pop_lsb(&b);
736 squares[size] = s ^ flipSquares;
737 pieces[size++] = Piece(pos.piece_on(s) ^ flipColor);
742 d = entry->get(stm, tbFile);
744 // Then we reorder the pieces to have the same sequence as the one stored
745 // in pieces[i]: the sequence that ensures the best compression.
746 for (int i = leadPawnsCnt; i < size - 1; ++i)
747 for (int j = i + 1; j < size; ++j)
748 if (d->pieces[i] == pieces[j])
750 std::swap(pieces[i], pieces[j]);
751 std::swap(squares[i], squares[j]);
755 // Now we map again the squares so that the square of the lead piece is in
756 // the triangle A1-D1-D4.
757 if (file_of(squares[0]) > FILE_D)
758 for (int i = 0; i < size; ++i)
759 squares[i] = flip_file(squares[i]);
761 // Encode leading pawns starting with the one with minimum MapPawns[] and
762 // proceeding in ascending order.
763 if (entry->hasPawns) {
764 idx = LeadPawnIdx[leadPawnsCnt][squares[0]];
766 std::stable_sort(squares + 1, squares + leadPawnsCnt, pawns_comp);
768 for (int i = 1; i < leadPawnsCnt; ++i)
769 idx += Binomial[i][MapPawns[squares[i]]];
771 goto encode_remaining; // With pawns we have finished special treatments
774 // In positions withouth pawns, we further flip the squares to ensure leading
775 // piece is below RANK_5.
776 if (rank_of(squares[0]) > RANK_4)
777 for (int i = 0; i < size; ++i)
778 squares[i] = flip_rank(squares[i]);
780 // Look for the first piece of the leading group not on the A1-D4 diagonal
781 // and ensure it is mapped below the diagonal.
782 for (int i = 0; i < d->groupLen[0]; ++i) {
783 if (!off_A1H8(squares[i]))
786 if (off_A1H8(squares[i]) > 0) // A1-H8 diagonal flip: SQ_A3 -> SQ_C1
787 for (int j = i; j < size; ++j)
788 squares[j] = Square(((squares[j] >> 3) | (squares[j] << 3)) & 63);
792 // Encode the leading group.
794 // Suppose we have KRvK. Let's say the pieces are on square numbers wK, wR
795 // and bK (each 0...63). The simplest way to map this position to an index
798 // index = wK * 64 * 64 + wR * 64 + bK;
800 // But this way the TB is going to have 64*64*64 = 262144 positions, with
801 // lots of positions being equivalent (because they are mirrors of each
802 // other) and lots of positions being invalid (two pieces on one square,
803 // adjacent kings, etc.).
804 // Usually the first step is to take the wK and bK together. There are just
805 // 462 ways legal and not-mirrored ways to place the wK and bK on the board.
806 // Once we have placed the wK and bK, there are 62 squares left for the wR
807 // Mapping its square from 0..63 to available squares 0..61 can be done like:
809 // wR -= (wR > wK) + (wR > bK);
811 // In words: if wR "comes later" than wK, we deduct 1, and the same if wR
812 // "comes later" than bK. In case of two same pieces like KRRvK we want to
813 // place the two Rs "together". If we have 62 squares left, we can place two
814 // Rs "together" in 62 * 61 / 2 ways (we divide by 2 because rooks can be
815 // swapped and still get the same position.)
817 // In case we have at least 3 unique pieces (inlcuded kings) we encode them
819 if (entry->hasUniquePieces) {
821 int adjust1 = squares[1] > squares[0];
822 int adjust2 = (squares[2] > squares[0]) + (squares[2] > squares[1]);
824 // First piece is below a1-h8 diagonal. MapA1D1D4[] maps the b1-d1-d3
825 // triangle to 0...5. There are 63 squares for second piece and and 62
826 // (mapped to 0...61) for the third.
827 if (off_A1H8(squares[0]))
828 idx = ( MapA1D1D4[squares[0]] * 63
829 + (squares[1] - adjust1)) * 62
830 + squares[2] - adjust2;
832 // First piece is on a1-h8 diagonal, second below: map this occurence to
833 // 6 to differentiate from the above case, rank_of() maps a1-d4 diagonal
834 // to 0...3 and finally MapB1H1H7[] maps the b1-h1-h7 triangle to 0..27.
835 else if (off_A1H8(squares[1]))
836 idx = ( 6 * 63 + rank_of(squares[0]) * 28
837 + MapB1H1H7[squares[1]]) * 62
838 + squares[2] - adjust2;
840 // First two pieces are on a1-h8 diagonal, third below
841 else if (off_A1H8(squares[2]))
842 idx = 6 * 63 * 62 + 4 * 28 * 62
843 + rank_of(squares[0]) * 7 * 28
844 + (rank_of(squares[1]) - adjust1) * 28
845 + MapB1H1H7[squares[2]];
847 // All 3 pieces on the diagonal a1-h8
849 idx = 6 * 63 * 62 + 4 * 28 * 62 + 4 * 7 * 28
850 + rank_of(squares[0]) * 7 * 6
851 + (rank_of(squares[1]) - adjust1) * 6
852 + (rank_of(squares[2]) - adjust2);
854 // We don't have at least 3 unique pieces, like in KRRvKBB, just map
856 idx = MapKK[MapA1D1D4[squares[0]]][squares[1]];
859 idx *= d->groupIdx[0];
860 Square* groupSq = squares + d->groupLen[0];
862 // Encode remainig pawns then pieces according to square, in ascending order
863 bool remainingPawns = entry->hasPawns && entry->pawnCount[1];
865 while (d->groupLen[++next])
867 std::stable_sort(groupSq, groupSq + d->groupLen[next]);
870 // Map down a square if "comes later" than a square in the previous
871 // groups (similar to what done earlier for leading group pieces).
872 for (int i = 0; i < d->groupLen[next]; ++i)
874 auto f = [&](Square s) { return groupSq[i] > s; };
875 auto adjust = std::count_if(squares, groupSq, f);
876 n += Binomial[i + 1][groupSq[i] - adjust - 8 * remainingPawns];
879 remainingPawns = false;
880 idx += n * d->groupIdx[next];
881 groupSq += d->groupLen[next];
884 // Now that we have the index, decompress the pair and get the score
885 return map_score(entry, tbFile, decompress_pairs(d, idx), wdl);
888 // Group together pieces that will be encoded together. The general rule is that
889 // a group contains pieces of same type and color. The exception is the leading
890 // group that, in case of positions withouth pawns, can be formed by 3 different
891 // pieces (default) or by the king pair when there is not a unique piece apart
892 // from the kings. When there are pawns, pawns are always first in pieces[].
894 // As example KRKN -> KRK + N, KNNK -> KK + NN, KPPKP -> P + PP + K + K
896 // The actual grouping depends on the TB generator and can be inferred from the
897 // sequence of pieces in piece[] array.
899 void set_groups(T& e, PairsData* d, int order[], File f) {
901 int n = 0, firstLen = e.hasPawns ? 0 : e.hasUniquePieces ? 3 : 2;
904 // Number of pieces per group is stored in groupLen[], for instance in KRKN
905 // the encoder will default on '111', so groupLen[] will be (3, 1).
906 for (int i = 1; i < e.pieceCount; ++i)
907 if (--firstLen > 0 || d->pieces[i] == d->pieces[i - 1])
910 d->groupLen[++n] = 1;
912 d->groupLen[++n] = 0; // Zero-terminated
914 // The sequence in pieces[] defines the groups, but not the order in which
915 // they are encoded. If the pieces in a group g can be combined on the board
916 // in N(g) different ways, then the position encoding will be of the form:
918 // g1 * N(g2) * N(g3) + g2 * N(g3) + g3
920 // This ensures unique encoding for the whole position. The order of the
921 // groups is a per-table parameter and could not follow the canonical leading
922 // pawns/pieces -> remainig pawns -> remaining pieces. In particular the
923 // first group is at order[0] position and the remaining pawns, when present,
924 // are at order[1] position.
925 bool pp = e.hasPawns && e.pawnCount[1]; // Pawns on both sides
926 int next = pp ? 2 : 1;
927 int freeSquares = 64 - d->groupLen[0] - (pp ? d->groupLen[1] : 0);
930 for (int k = 0; next < n || k == order[0] || k == order[1]; ++k)
931 if (k == order[0]) // Leading pawns or pieces
933 d->groupIdx[0] = idx;
934 idx *= e.hasPawns ? LeadPawnsSize[d->groupLen[0]][f]
935 : e.hasUniquePieces ? 31332 : 462;
937 else if (k == order[1]) // Remaining pawns
939 d->groupIdx[1] = idx;
940 idx *= Binomial[d->groupLen[1]][48 - d->groupLen[0]];
942 else // Remainig pieces
944 d->groupIdx[next] = idx;
945 idx *= Binomial[d->groupLen[next]][freeSquares];
946 freeSquares -= d->groupLen[next++];
949 d->groupIdx[n] = idx;
952 // In Recursive Pairing each symbol represents a pair of childern symbols. So
953 // read d->btree[] symbols data and expand each one in his left and right child
954 // symbol until reaching the leafs that represent the symbol value.
955 uint8_t set_symlen(PairsData* d, Sym s, std::vector<bool>& visited) {
957 visited[s] = true; // We can set it now because tree is acyclic
958 Sym sr = d->btree[s].get<LR::Right>();
963 Sym sl = d->btree[s].get<LR::Left>();
966 d->symlen[sl] = set_symlen(d, sl, visited);
969 d->symlen[sr] = set_symlen(d, sr, visited);
971 return d->symlen[sl] + d->symlen[sr] + 1;
974 uint8_t* set_sizes(PairsData* d, uint8_t* data) {
978 if (d->flags & TBFlag::SingleValue) {
979 d->blocksNum = d->blockLengthSize = 0;
980 d->span = d->sparseIndexSize = 0; // Broken MSVC zero-init
981 d->minSymLen = *data++; // Here we store the single value
985 // groupLen[] is a zero-terminated list of group lengths, the last groupIdx[]
986 // element stores the biggest index that is the tb size.
987 uint64_t tbSize = d->groupIdx[std::find(d->groupLen, d->groupLen + 7, 0) - d->groupLen];
989 d->sizeofBlock = 1ULL << *data++;
990 d->span = 1ULL << *data++;
991 d->sparseIndexSize = size_t((tbSize + d->span - 1) / d->span); // Round up
992 auto padding = number<uint8_t, LittleEndian>(data++);
993 d->blocksNum = number<uint32_t, LittleEndian>(data); data += sizeof(uint32_t);
994 d->blockLengthSize = d->blocksNum + padding; // Padded to ensure SparseIndex[]
995 // does not point out of range.
996 d->maxSymLen = *data++;
997 d->minSymLen = *data++;
998 d->lowestSym = (Sym*)data;
999 d->base64.resize(d->maxSymLen - d->minSymLen + 1);
1001 // The canonical code is ordered such that longer symbols (in terms of
1002 // the number of bits of their Huffman code) have lower numeric value,
1003 // so that d->lowestSym[i] >= d->lowestSym[i+1] (when read as LittleEndian).
1004 // Starting from this we compute a base64[] table indexed by symbol length
1005 // and containing 64 bit values so that d->base64[i] >= d->base64[i+1].
1006 // See https://en.wikipedia.org/wiki/Huffman_coding
1007 for (int i = d->base64.size() - 2; i >= 0; --i) {
1008 d->base64[i] = (d->base64[i + 1] + number<Sym, LittleEndian>(&d->lowestSym[i])
1009 - number<Sym, LittleEndian>(&d->lowestSym[i + 1])) / 2;
1011 assert(d->base64[i] * 2 >= d->base64[i+1]);
1014 // Now left-shift by an amount so that d->base64[i] gets shifted 1 bit more
1015 // than d->base64[i+1] and given the above assert condition, we ensure that
1016 // d->base64[i] >= d->base64[i+1]. Moreover for any symbol s64 of length i
1017 // and right-padded to 64 bits holds d->base64[i-1] >= s64 >= d->base64[i].
1018 for (size_t i = 0; i < d->base64.size(); ++i)
1019 d->base64[i] <<= 64 - i - d->minSymLen; // Right-padding to 64 bits
1021 data += d->base64.size() * sizeof(Sym);
1022 d->symlen.resize(number<uint16_t, LittleEndian>(data)); data += sizeof(uint16_t);
1023 d->btree = (LR*)data;
1025 // The compression scheme used is "Recursive Pairing", that replaces the most
1026 // frequent adjacent pair of symbols in the source message by a new symbol,
1027 // reevaluating the frequencies of all of the symbol pairs with respect to
1028 // the extended alphabet, and then repeating the process.
1029 // See http://www.larsson.dogma.net/dcc99.pdf
1030 std::vector<bool> visited(d->symlen.size());
1032 for (Sym sym = 0; sym < d->symlen.size(); ++sym)
1034 d->symlen[sym] = set_symlen(d, sym, visited);
1036 return data + d->symlen.size() * sizeof(LR) + (d->symlen.size() & 1);
1039 uint8_t* set_dtz_map(TBTable<WDL>&, uint8_t* data, File) { return data; }
1041 uint8_t* set_dtz_map(TBTable<DTZ>& e, uint8_t* data, File maxFile) {
1045 for (File f = FILE_A; f <= maxFile; ++f) {
1046 auto flags = e.get(0, f)->flags;
1047 if (flags & TBFlag::Mapped) {
1048 if (flags & TBFlag::Wide) {
1049 data += (uintptr_t)data & 1; // Word alignment, we may have a mixed table
1050 for (int i = 0; i < 4; ++i) { // Sequence like 3,x,x,x,1,x,0,2,x,x
1051 e.get(0, f)->map_idx[i] = (uint16_t)((uint16_t *)data - (uint16_t *)e.map + 1);
1052 data += 2 * number<uint16_t, LittleEndian>(data) + 2;
1056 for (int i = 0; i < 4; ++i) {
1057 e.get(0, f)->map_idx[i] = (uint16_t)(data - e.map + 1);
1064 return data += (uintptr_t)data & 1; // Word alignment
1067 // Populate entry's PairsData records with data from the just memory mapped file.
1068 // Called at first access.
1069 template<typename T>
1070 void set(T& e, uint8_t* data) {
1074 enum { Split = 1, HasPawns = 2 };
1076 assert(e.hasPawns == bool(*data & HasPawns));
1077 assert((e.key != e.key2) == bool(*data & Split));
1079 data++; // First byte stores flags
1081 const int sides = T::Sides == 2 && (e.key != e.key2) ? 2 : 1;
1082 const File maxFile = e.hasPawns ? FILE_D : FILE_A;
1084 bool pp = e.hasPawns && e.pawnCount[1]; // Pawns on both sides
1086 assert(!pp || e.pawnCount[0]);
1088 for (File f = FILE_A; f <= maxFile; ++f) {
1090 for (int i = 0; i < sides; i++)
1091 *e.get(i, f) = PairsData();
1093 int order[][2] = { { *data & 0xF, pp ? *(data + 1) & 0xF : 0xF },
1094 { *data >> 4, pp ? *(data + 1) >> 4 : 0xF } };
1097 for (int k = 0; k < e.pieceCount; ++k, ++data)
1098 for (int i = 0; i < sides; i++)
1099 e.get(i, f)->pieces[k] = Piece(i ? *data >> 4 : *data & 0xF);
1101 for (int i = 0; i < sides; ++i)
1102 set_groups(e, e.get(i, f), order[i], f);
1105 data += (uintptr_t)data & 1; // Word alignment
1107 for (File f = FILE_A; f <= maxFile; ++f)
1108 for (int i = 0; i < sides; i++)
1109 data = set_sizes(e.get(i, f), data);
1111 data = set_dtz_map(e, data, maxFile);
1113 for (File f = FILE_A; f <= maxFile; ++f)
1114 for (int i = 0; i < sides; i++) {
1115 (d = e.get(i, f))->sparseIndex = (SparseEntry*)data;
1116 data += d->sparseIndexSize * sizeof(SparseEntry);
1119 for (File f = FILE_A; f <= maxFile; ++f)
1120 for (int i = 0; i < sides; i++) {
1121 (d = e.get(i, f))->blockLength = (uint16_t*)data;
1122 data += d->blockLengthSize * sizeof(uint16_t);
1125 for (File f = FILE_A; f <= maxFile; ++f)
1126 for (int i = 0; i < sides; i++) {
1127 data = (uint8_t*)(((uintptr_t)data + 0x3F) & ~0x3F); // 64 byte alignment
1128 (d = e.get(i, f))->data = data;
1129 data += d->blocksNum * d->sizeofBlock;
1133 // If the TB file corresponding to the given position is already memory mapped
1134 // then return its base address, otherwise try to memory map and init it. Called
1135 // at every probe, memory map and init only at first access. Function is thread
1136 // safe and can be called concurrently.
1137 template<TBType Type>
1138 void* mapped(TBTable<Type>& e, const Position& pos) {
1140 static std::mutex mutex;
1142 // Use 'acquire' to avoid a thread reading 'ready' == true while
1143 // another is still working. (compiler reordering may cause this).
1144 if (e.ready.load(std::memory_order_acquire))
1145 return e.baseAddress; // Could be nullptr if file does not exist
1147 std::scoped_lock<std::mutex> lk(mutex);
1149 if (e.ready.load(std::memory_order_relaxed)) // Recheck under lock
1150 return e.baseAddress;
1152 // Pieces strings in decreasing order for each color, like ("KPP","KR")
1153 std::string fname, w, b;
1154 for (PieceType pt = KING; pt >= PAWN; --pt) {
1155 w += std::string(popcount(pos.pieces(WHITE, pt)), PieceToChar[pt]);
1156 b += std::string(popcount(pos.pieces(BLACK, pt)), PieceToChar[pt]);
1159 fname = (e.key == pos.material_key() ? w + 'v' + b : b + 'v' + w)
1160 + (Type == WDL ? ".rtbw" : ".rtbz");
1162 uint8_t* data = TBFile(fname).map(&e.baseAddress, &e.mapping, Type);
1167 e.ready.store(true, std::memory_order_release);
1168 return e.baseAddress;
1171 template<TBType Type, typename Ret = typename TBTable<Type>::Ret>
1172 Ret probe_table(const Position& pos, ProbeState* result, WDLScore wdl = WDLDraw) {
1174 if (pos.count<ALL_PIECES>() == 2) // KvK
1175 return Ret(WDLDraw);
1177 TBTable<Type>* entry = TBTables.get<Type>(pos.material_key());
1179 if (!entry || !mapped(*entry, pos))
1180 return *result = FAIL, Ret();
1182 return do_probe_table(pos, entry, wdl, result);
1185 // For a position where the side to move has a winning capture it is not necessary
1186 // to store a winning value so the generator treats such positions as "don't cares"
1187 // and tries to assign to it a value that improves the compression ratio. Similarly,
1188 // if the side to move has a drawing capture, then the position is at least drawn.
1189 // If the position is won, then the TB needs to store a win value. But if the
1190 // position is drawn, the TB may store a loss value if that is better for compression.
1191 // All of this means that during probing, the engine must look at captures and probe
1192 // their results and must probe the position itself. The "best" result of these
1193 // probes is the correct result for the position.
1194 // DTZ tables do not store values when a following move is a zeroing winning move
1195 // (winning capture or winning pawn move). Also DTZ store wrong values for positions
1196 // where the best move is an ep-move (even if losing). So in all these cases set
1197 // the state to ZEROING_BEST_MOVE.
1198 template<bool CheckZeroingMoves>
1199 WDLScore search(Position& pos, ProbeState* result) {
1201 WDLScore value, bestValue = WDLLoss;
1204 auto moveList = MoveList<LEGAL>(pos);
1205 size_t totalCount = moveList.size(), moveCount = 0;
1207 for (const Move move : moveList)
1209 if ( !pos.capture(move)
1210 && (!CheckZeroingMoves || type_of(pos.moved_piece(move)) != PAWN))
1215 pos.do_move(move, st);
1216 value = -search<false>(pos, result);
1217 pos.undo_move(move);
1219 if (*result == FAIL)
1222 if (value > bestValue)
1226 if (value >= WDLWin)
1228 *result = ZEROING_BEST_MOVE; // Winning DTZ-zeroing move
1234 // In case we have already searched all the legal moves we don't have to probe
1235 // the TB because the stored score could be wrong. For instance TB tables
1236 // do not contain information on position with ep rights, so in this case
1237 // the result of probe_wdl_table is wrong. Also in case of only capture
1238 // moves, for instance here 4K3/4q3/6p1/2k5/6p1/8/8/8 w - - 0 7, we have to
1239 // return with ZEROING_BEST_MOVE set.
1240 bool noMoreMoves = (moveCount && moveCount == totalCount);
1246 value = probe_table<WDL>(pos, result);
1248 if (*result == FAIL)
1252 // DTZ stores a "don't care" value if bestValue is a win
1253 if (bestValue >= value)
1254 return *result = ( bestValue > WDLDraw
1255 || noMoreMoves ? ZEROING_BEST_MOVE : OK), bestValue;
1257 return *result = OK, value;
1263 /// Tablebases::init() is called at startup and after every change to
1264 /// "SyzygyPath" UCI option to (re)create the various tables. It is not thread
1265 /// safe, nor it needs to be.
1266 void Tablebases::init(const std::string& paths) {
1270 TBFile::Paths = paths;
1272 if (paths.empty() || paths == "<empty>")
1275 // MapB1H1H7[] encodes a square below a1-h8 diagonal to 0..27
1277 for (Square s = SQ_A1; s <= SQ_H8; ++s)
1278 if (off_A1H8(s) < 0)
1279 MapB1H1H7[s] = code++;
1281 // MapA1D1D4[] encodes a square in the a1-d1-d4 triangle to 0..9
1282 std::vector<Square> diagonal;
1284 for (Square s = SQ_A1; s <= SQ_D4; ++s)
1285 if (off_A1H8(s) < 0 && file_of(s) <= FILE_D)
1286 MapA1D1D4[s] = code++;
1288 else if (!off_A1H8(s) && file_of(s) <= FILE_D)
1289 diagonal.push_back(s);
1291 // Diagonal squares are encoded as last ones
1292 for (auto s : diagonal)
1293 MapA1D1D4[s] = code++;
1295 // MapKK[] encodes all the 461 possible legal positions of two kings where
1296 // the first is in the a1-d1-d4 triangle. If the first king is on the a1-d4
1297 // diagonal, the other one shall not to be above the a1-h8 diagonal.
1298 std::vector<std::pair<int, Square>> bothOnDiagonal;
1300 for (int idx = 0; idx < 10; idx++)
1301 for (Square s1 = SQ_A1; s1 <= SQ_D4; ++s1)
1302 if (MapA1D1D4[s1] == idx && (idx || s1 == SQ_B1)) // SQ_B1 is mapped to 0
1304 for (Square s2 = SQ_A1; s2 <= SQ_H8; ++s2)
1305 if ((PseudoAttacks[KING][s1] | s1) & s2)
1306 continue; // Illegal position
1308 else if (!off_A1H8(s1) && off_A1H8(s2) > 0)
1309 continue; // First on diagonal, second above
1311 else if (!off_A1H8(s1) && !off_A1H8(s2))
1312 bothOnDiagonal.emplace_back(idx, s2);
1315 MapKK[idx][s2] = code++;
1318 // Legal positions with both kings on diagonal are encoded as last ones
1319 for (auto p : bothOnDiagonal)
1320 MapKK[p.first][p.second] = code++;
1322 // Binomial[] stores the Binomial Coefficents using Pascal rule. There
1323 // are Binomial[k][n] ways to choose k elements from a set of n elements.
1326 for (int n = 1; n < 64; n++) // Squares
1327 for (int k = 0; k < 6 && k <= n; ++k) // Pieces
1328 Binomial[k][n] = (k > 0 ? Binomial[k - 1][n - 1] : 0)
1329 + (k < n ? Binomial[k ][n - 1] : 0);
1331 // MapPawns[s] encodes squares a2-h7 to 0..47. This is the number of possible
1332 // available squares when the leading one is in 's'. Moreover the pawn with
1333 // highest MapPawns[] is the leading pawn, the one nearest the edge and,
1334 // among pawns with same file, the one with lowest rank.
1335 int availableSquares = 47; // Available squares when lead pawn is in a2
1337 // Init the tables for the encoding of leading pawns group: with 7-men TB we
1338 // can have up to 5 leading pawns (KPPPPPK).
1339 for (int leadPawnsCnt = 1; leadPawnsCnt <= 5; ++leadPawnsCnt)
1340 for (File f = FILE_A; f <= FILE_D; ++f)
1342 // Restart the index at every file because TB table is splitted
1343 // by file, so we can reuse the same index for different files.
1346 // Sum all possible combinations for a given file, starting with
1347 // the leading pawn on rank 2 and increasing the rank.
1348 for (Rank r = RANK_2; r <= RANK_7; ++r)
1350 Square sq = make_square(f, r);
1352 // Compute MapPawns[] at first pass.
1353 // If sq is the leading pawn square, any other pawn cannot be
1354 // below or more toward the edge of sq. There are 47 available
1355 // squares when sq = a2 and reduced by 2 for any rank increase
1356 // due to mirroring: sq == a3 -> no a2, h2, so MapPawns[a3] = 45
1357 if (leadPawnsCnt == 1)
1359 MapPawns[sq] = availableSquares--;
1360 MapPawns[flip_file(sq)] = availableSquares--;
1362 LeadPawnIdx[leadPawnsCnt][sq] = idx;
1363 idx += Binomial[leadPawnsCnt - 1][MapPawns[sq]];
1365 // After a file is traversed, store the cumulated per-file index
1366 LeadPawnsSize[leadPawnsCnt][f] = idx;
1369 // Add entries in TB tables if the corresponding ".rtbw" file exists
1370 for (PieceType p1 = PAWN; p1 < KING; ++p1) {
1371 TBTables.add({KING, p1, KING});
1373 for (PieceType p2 = PAWN; p2 <= p1; ++p2) {
1374 TBTables.add({KING, p1, p2, KING});
1375 TBTables.add({KING, p1, KING, p2});
1377 for (PieceType p3 = PAWN; p3 < KING; ++p3)
1378 TBTables.add({KING, p1, p2, KING, p3});
1380 for (PieceType p3 = PAWN; p3 <= p2; ++p3) {
1381 TBTables.add({KING, p1, p2, p3, KING});
1383 for (PieceType p4 = PAWN; p4 <= p3; ++p4) {
1384 TBTables.add({KING, p1, p2, p3, p4, KING});
1386 for (PieceType p5 = PAWN; p5 <= p4; ++p5)
1387 TBTables.add({KING, p1, p2, p3, p4, p5, KING});
1389 for (PieceType p5 = PAWN; p5 < KING; ++p5)
1390 TBTables.add({KING, p1, p2, p3, p4, KING, p5});
1393 for (PieceType p4 = PAWN; p4 < KING; ++p4) {
1394 TBTables.add({KING, p1, p2, p3, KING, p4});
1396 for (PieceType p5 = PAWN; p5 <= p4; ++p5)
1397 TBTables.add({KING, p1, p2, p3, KING, p4, p5});
1401 for (PieceType p3 = PAWN; p3 <= p1; ++p3)
1402 for (PieceType p4 = PAWN; p4 <= (p1 == p3 ? p2 : p3); ++p4)
1403 TBTables.add({KING, p1, p2, KING, p3, p4});
1407 if (Cluster::is_root())
1408 sync_cout << "info string Found " << TBTables.size() << " tablebases" << sync_endl;
1411 // Probe the WDL table for a particular position.
1412 // If *result != FAIL, the probe was successful.
1413 // The return value is from the point of view of the side to move:
1415 // -1 : loss, but draw under 50-move rule
1417 // 1 : win, but draw under 50-move rule
1419 WDLScore Tablebases::probe_wdl(Position& pos, ProbeState* result) {
1422 return search<false>(pos, result);
1425 // Probe the DTZ table for a particular position.
1426 // If *result != FAIL, the probe was successful.
1427 // The return value is from the point of view of the side to move:
1428 // n < -100 : loss, but draw under 50-move rule
1429 // -100 <= n < -1 : loss in n ply (assuming 50-move counter == 0)
1430 // -1 : loss, the side to move is mated
1432 // 1 < n <= 100 : win in n ply (assuming 50-move counter == 0)
1433 // 100 < n : win, but draw under 50-move rule
1435 // The return value n can be off by 1: a return value -n can mean a loss
1436 // in n+1 ply and a return value +n can mean a win in n+1 ply. This
1437 // cannot happen for tables with positions exactly on the "edge" of
1438 // the 50-move rule.
1440 // This implies that if dtz > 0 is returned, the position is certainly
1441 // a win if dtz + 50-move-counter <= 99. Care must be taken that the engine
1442 // picks moves that preserve dtz + 50-move-counter <= 99.
1444 // If n = 100 immediately after a capture or pawn move, then the position
1445 // is also certainly a win, and during the whole phase until the next
1446 // capture or pawn move, the inequality to be preserved is
1447 // dtz + 50-move-counter <= 100.
1449 // In short, if a move is available resulting in dtz + 50-move-counter <= 99,
1450 // then do not accept moves leading to dtz + 50-move-counter == 100.
1451 int Tablebases::probe_dtz(Position& pos, ProbeState* result) {
1454 WDLScore wdl = search<true>(pos, result);
1456 if (*result == FAIL || wdl == WDLDraw) // DTZ tables don't store draws
1459 // DTZ stores a 'don't care' value in this case, or even a plain wrong
1460 // one as in case the best move is a losing ep, so it cannot be probed.
1461 if (*result == ZEROING_BEST_MOVE)
1462 return dtz_before_zeroing(wdl);
1464 int dtz = probe_table<DTZ>(pos, result, wdl);
1466 if (*result == FAIL)
1469 if (*result != CHANGE_STM)
1470 return (dtz + 100 * (wdl == WDLBlessedLoss || wdl == WDLCursedWin)) * sign_of(wdl);
1472 // DTZ stores results for the other side, so we need to do a 1-ply search and
1473 // find the winning move that minimizes DTZ.
1475 int minDTZ = 0xFFFF;
1477 for (const Move move : MoveList<LEGAL>(pos))
1479 bool zeroing = pos.capture(move) || type_of(pos.moved_piece(move)) == PAWN;
1481 pos.do_move(move, st);
1483 // For zeroing moves we want the dtz of the move _before_ doing it,
1484 // otherwise we will get the dtz of the next move sequence. Search the
1485 // position after the move to get the score sign (because even in a
1486 // winning position we could make a losing capture or going for a draw).
1487 dtz = zeroing ? -dtz_before_zeroing(search<false>(pos, result))
1488 : -probe_dtz(pos, result);
1490 // If the move mates, force minDTZ to 1
1491 if (dtz == 1 && pos.checkers() && MoveList<LEGAL>(pos).size() == 0)
1494 // Convert result from 1-ply search. Zeroing moves are already accounted
1495 // by dtz_before_zeroing() that returns the DTZ of the previous move.
1497 dtz += sign_of(dtz);
1499 // Skip the draws and if we are winning only pick positive dtz
1500 if (dtz < minDTZ && sign_of(dtz) == sign_of(wdl))
1503 pos.undo_move(move);
1505 if (*result == FAIL)
1509 // When there are no legal moves, the position is mate: we return -1
1510 return minDTZ == 0xFFFF ? -1 : minDTZ;
1514 // Use the DTZ tables to rank root moves.
1516 // A return value false indicates that not all probes were successful.
1517 bool Tablebases::root_probe(Position& pos, Search::RootMoves& rootMoves) {
1522 // Obtain 50-move counter for the root position
1523 int cnt50 = pos.rule50_count();
1525 // Check whether a position was repeated since the last zeroing move.
1526 bool rep = pos.has_repeated();
1528 int dtz, bound = Options["Syzygy50MoveRule"] ? 900 : 1;
1530 // Probe and rank each move
1531 for (auto& m : rootMoves)
1533 pos.do_move(m.pv[0], st);
1535 // Calculate dtz for the current move counting from the root position
1536 if (pos.rule50_count() == 0)
1538 // In case of a zeroing move, dtz is one of -101/-1/0/1/101
1539 WDLScore wdl = -probe_wdl(pos, &result);
1540 dtz = dtz_before_zeroing(wdl);
1544 // Otherwise, take dtz for the new position and correct by 1 ply
1545 dtz = -probe_dtz(pos, &result);
1546 dtz = dtz > 0 ? dtz + 1
1547 : dtz < 0 ? dtz - 1 : dtz;
1550 // Make sure that a mating move is assigned a dtz value of 1
1553 && MoveList<LEGAL>(pos).size() == 0)
1556 pos.undo_move(m.pv[0]);
1561 // Better moves are ranked higher. Certain wins are ranked equally.
1562 // Losing moves are ranked equally unless a 50-move draw is in sight.
1563 int r = dtz > 0 ? (dtz + cnt50 <= 99 && !rep ? 1000 : 1000 - (dtz + cnt50))
1564 : dtz < 0 ? (-dtz * 2 + cnt50 < 100 ? -1000 : -1000 + (-dtz + cnt50))
1568 // Determine the score to be displayed for this move. Assign at least
1569 // 1 cp to cursed wins and let it grow to 49 cp as the positions gets
1570 // closer to a real win.
1571 m.tbScore = r >= bound ? VALUE_MATE - MAX_PLY - 1
1572 : r > 0 ? Value((std::max( 3, r - 800) * int(PawnValueEg)) / 200)
1573 : r == 0 ? VALUE_DRAW
1574 : r > -bound ? Value((std::min(-3, r + 800) * int(PawnValueEg)) / 200)
1575 : -VALUE_MATE + MAX_PLY + 1;
1582 // Use the WDL tables to rank root moves.
1583 // This is a fallback for the case that some or all DTZ tables are missing.
1585 // A return value false indicates that not all probes were successful.
1586 bool Tablebases::root_probe_wdl(Position& pos, Search::RootMoves& rootMoves) {
1588 static const int WDL_to_rank[] = { -1000, -899, 0, 899, 1000 };
1593 bool rule50 = Options["Syzygy50MoveRule"];
1595 // Probe and rank each move
1596 for (auto& m : rootMoves)
1598 pos.do_move(m.pv[0], st);
1600 WDLScore wdl = -probe_wdl(pos, &result);
1602 pos.undo_move(m.pv[0]);
1607 m.tbRank = WDL_to_rank[wdl + 2];
1610 wdl = wdl > WDLDraw ? WDLWin
1611 : wdl < WDLDraw ? WDLLoss : WDLDraw;
1612 m.tbScore = WDL_to_value[wdl + 2];
1618 } // namespace Stockfish