Subversion Repositories Games.Chess Giants

/*

  Stockfish, a UCI chess playing engine derived from Glaurung 2.1

  Copyright (c) 2013 Ronald de Man

  Copyright (C) 2016-2018 Marco Costalba, Lucas Braesch

  Stockfish is free software: you can redistribute it and/or modify

  it under the terms of the GNU General Public License as published by

  the Free Software Foundation, either version 3 of the License, or

  (at your option) any later version.

  Stockfish is distributed in the hope that it will be useful,

  but WITHOUT ANY WARRANTY; without even the implied warranty of

  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

  GNU General Public License for more details.

  You should have received a copy of the GNU General Public License

  along with this program.  If not, see <http://www.gnu.org/licenses/>.

*/

#include <algorithm>

#include <atomic>

#include <cstdint>

#include <cstring>   // For std::memset

#include <deque>

#include <fstream>

#include <iostream>

#include <list>

#include <sstream>

#include <type_traits>

#include "../bitboard.h"

#include "../movegen.h"

#include "../position.h"

#include "../search.h"

#include "../thread_win32.h"

#include "../types.h"

#include "tbprobe.h"

#ifndef _WIN32

#include <fcntl.h>

#include <unistd.h>

#include <sys/mman.h>

#include <sys/stat.h>

#else

#define WIN32_LEAN_AND_MEAN

#define NOMINMAX

#include <windows.h>

#endif

using namespace Tablebases;

int Tablebases::MaxCardinality;

namespace {

// Each table has a set of flags: all of them refer to DTZ tables, the last one to WDL tables

enum TBFlag { STM = 1, Mapped = 2, WinPlies = 4, LossPlies = 8, SingleValue = 128 };

inline WDLScore operator-(WDLScore d) { return WDLScore(-int(d)); }

inline Square operator^=(Square& s, int i) { return s = Square(int(s) ^ i); }

inline Square operator^(Square s, int i) { return Square(int(s) ^ i); }

// DTZ tables don't store valid scores for moves that reset the rule50 counter

// like captures and pawn moves but we can easily recover the correct dtz of the

// previous move if we know the position's WDL score.

int dtz_before_zeroing(WDLScore wdl) {

    return wdl == WDLWin         ?  1   :

           wdl == WDLCursedWin   ?  101 :

           wdl == WDLBlessedLoss ? -101 :

           wdl == WDLLoss        ? -1   : 0;

}

// Return the sign of a number (-1, 0, 1)

template <typename T> int sign_of(T val) {

    return (T(0) < val) - (val < T(0));

}

// Numbers in little endian used by sparseIndex[] to point into blockLength[]

struct SparseEntry {

    char block[4];   // Number of block

    char offset[2];  // Offset within the block

};

static_assert(sizeof(SparseEntry) == 6, "SparseEntry must be 6 bytes");

typedef uint16_t Sym; // Huffman symbol

struct LR {

    enum Side { Left, Right, Value };

    uint8_t lr[3]; // The first 12 bits is the left-hand symbol, the second 12

                   // bits is the right-hand symbol. If symbol has length 1,

                   // then the first byte is the stored value.

    template<Side S>

    Sym get() {

        return S == Left  ? ((lr[1] & 0xF) << 8) | lr[0] :

               S == Right ?  (lr[2] << 4) | (lr[1] >> 4) :

               S == Value ?   lr[0] : (assert(false), Sym(-1));

    }

};

static_assert(sizeof(LR) == 3, "LR tree entry must be 3 bytes");

const int TBPIECES = 6;

struct PairsData {

    int flags;

    size_t sizeofBlock;            // Block size in bytes

    size_t span;                   // About every span values there is a SparseIndex[] entry

    int blocksNum;                 // Number of blocks in the TB file

    int maxSymLen;                 // Maximum length in bits of the Huffman symbols

    int minSymLen;                 // Minimum length in bits of the Huffman symbols

    Sym* lowestSym;                // lowestSym[l] is the symbol of length l with the lowest value

    LR* btree;                     // btree[sym] stores the left and right symbols that expand sym

    uint16_t* blockLength;         // Number of stored positions (minus one) for each block: 1..65536

    int blockLengthSize;           // Size of blockLength[] table: padded so it's bigger than blocksNum

    SparseEntry* sparseIndex;      // Partial indices into blockLength[]

    size_t sparseIndexSize;        // Size of SparseIndex[] table

    uint8_t* data;                 // Start of Huffman compressed data

    std::vector<uint64_t> base64;  // base64[l - min_sym_len] is the 64bit-padded lowest symbol of length l

    std::vector<uint8_t> symlen;   // Number of values (-1) represented by a given Huffman symbol: 1..256

    Piece pieces[TBPIECES];        // Position pieces: the order of pieces defines the groups

    uint64_t groupIdx[TBPIECES+1]; // Start index used for the encoding of the group's pieces

    int groupLen[TBPIECES+1];      // Number of pieces in a given group: KRKN -> (3, 1)

};

// Helper struct to avoid manually defining entry copy constructor as we

// should because the default one is not compatible with std::atomic_bool.

struct Atomic {

    Atomic() = default;

    Atomic(const Atomic& e) { ready = e.ready.load(); } // MSVC 2013 wants assignment within body

    std::atomic_bool ready;

};

// We define types for the different parts of the WDLEntry and DTZEntry with

// corresponding specializations for pieces or pawns.

struct WDLEntryPiece {

    PairsData* precomp;

};

struct WDLEntryPawn {

    uint8_t pawnCount[2];     // [Lead color / other color]

    WDLEntryPiece file[2][4]; // [wtm / btm][FILE_A..FILE_D]

};

struct DTZEntryPiece {

    PairsData* precomp;

    uint16_t map_idx[4]; // WDLWin, WDLLoss, WDLCursedWin, WDLBlessedLoss

    uint8_t* map;

};

struct DTZEntryPawn {

    uint8_t pawnCount[2];

    DTZEntryPiece file[4];

    uint8_t* map;

};

struct TBEntry : public Atomic {

    void* baseAddress;

    uint64_t mapping;

    Key key;

    Key key2;

    int pieceCount;

    bool hasPawns;

    bool hasUniquePieces;

};

// Now the main types: WDLEntry and DTZEntry

struct WDLEntry : public TBEntry {

    WDLEntry(const std::string& code);

   ~WDLEntry();

    union {

        WDLEntryPiece pieceTable[2]; // [wtm / btm]

        WDLEntryPawn  pawnTable;

    };

};

struct DTZEntry : public TBEntry {

    DTZEntry(const WDLEntry& wdl);

   ~DTZEntry();

    union {

        DTZEntryPiece pieceTable;

        DTZEntryPawn  pawnTable;

    };

};

typedef decltype(WDLEntry::pieceTable) WDLPieceTable;

typedef decltype(DTZEntry::pieceTable) DTZPieceTable;

typedef decltype(WDLEntry::pawnTable ) WDLPawnTable;

typedef decltype(DTZEntry::pawnTable ) DTZPawnTable;

auto item(WDLPieceTable& e, int stm, int  ) -> decltype(e[stm])& { return e[stm]; }

auto item(DTZPieceTable& e, int    , int  ) -> decltype(e)& { return e; }

auto item(WDLPawnTable&  e, int stm, int f) -> decltype(e.file[stm][f])& { return e.file[stm][f]; }

auto item(DTZPawnTable&  e, int    , int f) -> decltype(e.file[f])& { return e.file[f]; }

template<typename E> struct Ret { typedef int type; };

template<> struct Ret<WDLEntry> { typedef WDLScore type; };

int MapPawns[SQUARE_NB];

int MapB1H1H7[SQUARE_NB];

int MapA1D1D4[SQUARE_NB];

int MapKK[10][SQUARE_NB]; // [MapA1D1D4][SQUARE_NB]

// Comparison function to sort leading pawns in ascending MapPawns[] order

bool pawns_comp(Square i, Square j) { return MapPawns[i] < MapPawns[j]; }

int off_A1H8(Square sq) { return int(rank_of(sq)) - file_of(sq); }

const Value WDL_to_value[] = {

   -VALUE_MATE + MAX_PLY + 1,

    VALUE_DRAW - 2,

    VALUE_DRAW,

    VALUE_DRAW + 2,

    VALUE_MATE - MAX_PLY - 1

};

const std::string PieceToChar = " PNBRQK  pnbrqk";

int Binomial[6][SQUARE_NB];    // [k][n] k elements from a set of n elements

int LeadPawnIdx[5][SQUARE_NB]; // [leadPawnsCnt][SQUARE_NB]

int LeadPawnsSize[5][4];       // [leadPawnsCnt][FILE_A..FILE_D]

enum { BigEndian, LittleEndian };

template<typename T, int Half = sizeof(T) / 2, int End = sizeof(T) - 1>

inline void swap_byte(T& x)

{

    char tmp, *c = (char*)&x;

    for (int i = 0; i < Half; ++i)

        tmp = c[i], c[i] = c[End - i], c[End - i] = tmp;

}

template<> inline void swap_byte<uint8_t, 0, 0>(uint8_t&) {}

template<typename T, int LE> T number(void* addr)

{

    const union { uint32_t i; char c[4]; } Le = { 0x01020304 };

    const bool IsLittleEndian = (Le.c[0] == 4);

    T v;

    if ((uintptr_t)addr & (alignof(T) - 1)) // Unaligned pointer (very rare)

        std::memcpy(&v, addr, sizeof(T));

    else

        v = *((T*)addr);

    if (LE != IsLittleEndian)

        swap_byte(v);

    return v;

}

class HashTable {

    typedef std::pair<WDLEntry*, DTZEntry*> EntryPair;

    typedef std::pair<Key, EntryPair> Entry;

    static const int TBHASHBITS = 10;

    static const int HSHMAX     = 5;

    Entry hashTable[1 << TBHASHBITS][HSHMAX];

    std::deque<WDLEntry> wdlTable;

    std::deque<DTZEntry> dtzTable;

    void insert(Key key, WDLEntry* wdl, DTZEntry* dtz) {

        Entry* entry = hashTable[key >> (64 - TBHASHBITS)];

        for (int i = 0; i < HSHMAX; ++i, ++entry)

            if (!entry->second.first || entry->first == key) {

                *entry = std::make_pair(key, std::make_pair(wdl, dtz));

                return;

            }

        std::cerr << "HSHMAX too low!" << std::endl;

        exit(1);

    }

public:

    template<typename E, int I = std::is_same<E, WDLEntry>::value ? 0 : 1>

    E* get(Key key) {

      Entry* entry = hashTable[key >> (64 - TBHASHBITS)];

      for (int i = 0; i < HSHMAX; ++i, ++entry)

          if (entry->first == key)

              return std::get<I>(entry->second);

      return nullptr;

  }

  void clear() {

      std::memset(hashTable, 0, sizeof(hashTable));

      wdlTable.clear();

      dtzTable.clear();

  }

  size_t size() const { return wdlTable.size(); }

  void insert(const std::vector<PieceType>& pieces);

};

HashTable EntryTable;

class TBFile : public std::ifstream {

    std::string fname;

public:

    // Look for and open the file among the Paths directories where the .rtbw

    // and .rtbz files can be found. Multiple directories are separated by ";"

    // on Windows and by ":" on Unix-based operating systems.

    //

    // Example:

    // C:\tb\wdl345;C:\tb\wdl6;D:\tb\dtz345;D:\tb\dtz6

    static std::string Paths;

    TBFile(const std::string& f) {

#ifndef _WIN32

        const char SepChar = ':';

#else

        const char SepChar = ';';

#endif

        std::stringstream ss(Paths);

        std::string path;

        while (std::getline(ss, path, SepChar)) {

            fname = path + "/" + f;

            std::ifstream::open(fname);

            if (is_open())

                return;

        }

    }

    // Memory map the file and check it. File should be already open and will be

    // closed after mapping.

    uint8_t* map(void** baseAddress, uint64_t* mapping, const uint8_t* TB_MAGIC) {

        assert(is_open());

        close(); // Need to re-open to get native file descriptor

#ifndef _WIN32

        struct stat statbuf;

        int fd = ::open(fname.c_str(), O_RDONLY);

        if (fd == -1)

            return *baseAddress = nullptr, nullptr;

        fstat(fd, &statbuf);

        *mapping = statbuf.st_size;

        *baseAddress = mmap(nullptr, statbuf.st_size, PROT_READ, MAP_SHARED, fd, 0);

        ::close(fd);

        if (*baseAddress == MAP_FAILED) {

            std::cerr << "Could not mmap() " << fname << std::endl;

            exit(1);

        }

#else

        HANDLE fd = CreateFile(fname.c_str(), GENERIC_READ, FILE_SHARE_READ, nullptr,

                               OPEN_EXISTING, FILE_ATTRIBUTE_NORMAL, nullptr);

        if (fd == INVALID_HANDLE_VALUE)

            return *baseAddress = nullptr, nullptr;

        DWORD size_high;

        DWORD size_low = GetFileSize(fd, &size_high);

        HANDLE mmap = CreateFileMapping(fd, nullptr, PAGE_READONLY, size_high, size_low, nullptr);

        CloseHandle(fd);

        if (!mmap) {

            std::cerr << "CreateFileMapping() failed" << std::endl;

            exit(1);

        }

        *mapping = (uint64_t)mmap;

        *baseAddress = MapViewOfFile(mmap, FILE_MAP_READ, 0, 0, 0);

        if (!*baseAddress) {

            std::cerr << "MapViewOfFile() failed, name = " << fname

                      << ", error = " << GetLastError() << std::endl;

            exit(1);

        }

#endif

        uint8_t* data = (uint8_t*)*baseAddress;

        if (   *data++ != *TB_MAGIC++

            || *data++ != *TB_MAGIC++

            || *data++ != *TB_MAGIC++

            || *data++ != *TB_MAGIC) {

            std::cerr << "Corrupted table in file " << fname << std::endl;

            unmap(*baseAddress, *mapping);

            return *baseAddress = nullptr, nullptr;

        }

        return data;

    }

    static void unmap(void* baseAddress, uint64_t mapping) {

#ifndef _WIN32

        munmap(baseAddress, mapping);

#else

        UnmapViewOfFile(baseAddress);

        CloseHandle((HANDLE)mapping);

#endif

    }

};

std::string TBFile::Paths;

WDLEntry::WDLEntry(const std::string& code) {

    StateInfo st;

    Position pos;

    memset(this, 0, sizeof(WDLEntry));

    ready = false;

    key = pos.set(code, WHITE, &st).material_key();

    pieceCount = popcount(pos.pieces());

    hasPawns = pos.pieces(PAWN);

    for (Color c = WHITE; c <= BLACK; ++c)

        for (PieceType pt = PAWN; pt < KING; ++pt)

            if (popcount(pos.pieces(c, pt)) == 1)

                hasUniquePieces = true;

    if (hasPawns) {

        // Set the leading color. In case both sides have pawns the leading color

        // is the side with less pawns because this leads to better compression.

        bool c =   !pos.count<PAWN>(BLACK)

                || (   pos.count<PAWN>(WHITE)

                    && pos.count<PAWN>(BLACK) >= pos.count<PAWN>(WHITE));

        pawnTable.pawnCount[0] = pos.count<PAWN>(c ? WHITE : BLACK);

        pawnTable.pawnCount[1] = pos.count<PAWN>(c ? BLACK : WHITE);

    }

    key2 = pos.set(code, BLACK, &st).material_key();

}

WDLEntry::~WDLEntry() {

    if (baseAddress)

        TBFile::unmap(baseAddress, mapping);

    for (int i = 0; i < 2; ++i)

        if (hasPawns)

            for (File f = FILE_A; f <= FILE_D; ++f)

                delete pawnTable.file[i][f].precomp;

        else

            delete pieceTable[i].precomp;

}

DTZEntry::DTZEntry(const WDLEntry& wdl) {

    memset(this, 0, sizeof(DTZEntry));

    ready = false;

    key = wdl.key;

    key2 = wdl.key2;

    pieceCount = wdl.pieceCount;

    hasPawns = wdl.hasPawns;

    hasUniquePieces = wdl.hasUniquePieces;

    if (hasPawns) {

        pawnTable.pawnCount[0] = wdl.pawnTable.pawnCount[0];

        pawnTable.pawnCount[1] = wdl.pawnTable.pawnCount[1];

    }

}

DTZEntry::~DTZEntry() {

    if (baseAddress)

        TBFile::unmap(baseAddress, mapping);

    if (hasPawns)

        for (File f = FILE_A; f <= FILE_D; ++f)

            delete pawnTable.file[f].precomp;

    else

        delete pieceTable.precomp;

}

void HashTable::insert(const std::vector<PieceType>& pieces) {

    std::string code;

    for (PieceType pt : pieces)

        code += PieceToChar[pt];

    TBFile file(code.insert(code.find('K', 1), "v") + ".rtbw"); // KRK -> KRvK

    if (!file.is_open()) // Only WDL file is checked

        return;

    file.close();

    MaxCardinality = std::max((int)pieces.size(), MaxCardinality);

    wdlTable.emplace_back(code);

    dtzTable.emplace_back(wdlTable.back());

    insert(wdlTable.back().key , &wdlTable.back(), &dtzTable.back());

    insert(wdlTable.back().key2, &wdlTable.back(), &dtzTable.back());

}

// TB tables are compressed with canonical Huffman code. The compressed data is divided into

// blocks of size d->sizeofBlock, and each block stores a variable number of symbols.

// Each symbol represents either a WDL or a (remapped) DTZ value, or a pair of other symbols

// (recursively). If you keep expanding the symbols in a block, you end up with up to 65536

// WDL or DTZ values. Each symbol represents up to 256 values and will correspond after

// Huffman coding to at least 1 bit. So a block of 32 bytes corresponds to at most

// 32 x 8 x 256 = 65536 values. This maximum is only reached for tables that consist mostly

// of draws or mostly of wins, but such tables are actually quite common. In principle, the

// blocks in WDL tables are 64 bytes long (and will be aligned on cache lines). But for

// mostly-draw or mostly-win tables this can leave many 64-byte blocks only half-filled, so

// in such cases blocks are 32 bytes long. The blocks of DTZ tables are up to 1024 bytes long.

// The generator picks the size that leads to the smallest table. The "book" of symbols and

// Huffman codes is the same for all blocks in the table. A non-symmetric pawnless TB file

// will have one table for wtm and one for btm, a TB file with pawns will have tables per

// file a,b,c,d also in this case one set for wtm and one for btm.

int decompress_pairs(PairsData* d, uint64_t idx) {

    // Special case where all table positions store the same value

    if (d->flags & TBFlag::SingleValue)

        return d->minSymLen;

    // First we need to locate the right block that stores the value at index "idx".

    // Because each block n stores blockLength[n] + 1 values, the index i of the block

    // that contains the value at position idx is:

    //

    //                    for (i = -1, sum = 0; sum <= idx; i++)

    //                        sum += blockLength[i + 1] + 1;

    //

    // This can be slow, so we use SparseIndex[] populated with a set of SparseEntry that

    // point to known indices into blockLength[]. Namely SparseIndex[k] is a SparseEntry

    // that stores the blockLength[] index and the offset within that block of the value

    // with index I(k), where:

    //

    //       I(k) = k * d->span + d->span / 2      (1)

    // First step is to get the 'k' of the I(k) nearest to our idx, using definition (1)

    uint32_t k = (uint32_t) (idx / d->span); // Pierre-Marie Baty -- added type cast

    // Then we read the corresponding SparseIndex[] entry

    uint32_t block = number<uint32_t, LittleEndian>(&d->sparseIndex[k].block);

    int offset     = number<uint16_t, LittleEndian>(&d->sparseIndex[k].offset);

    // Now compute the difference idx - I(k). From definition of k we know that

    //

    //       idx = k * d->span + idx % d->span    (2)

    //

    // So from (1) and (2) we can compute idx - I(K):

    int diff = idx % d->span - d->span / 2;

    // Sum the above to offset to find the offset corresponding to our idx

    offset += diff;

    // Move to previous/next block, until we reach the correct block that contains idx,

    // that is when 0 <= offset <= d->blockLength[block]

    while (offset < 0)

        offset += d->blockLength[--block] + 1;

    while (offset > d->blockLength[block])

        offset -= d->blockLength[block++] + 1;

    // Finally, we find the start address of our block of canonical Huffman symbols

    uint32_t* ptr = (uint32_t*)(d->data + block * d->sizeofBlock);

    // Read the first 64 bits in our block, this is a (truncated) sequence of

    // unknown number of symbols of unknown length but we know the first one

    // is at the beginning of this 64 bits sequence.

    uint64_t buf64 = number<uint64_t, BigEndian>(ptr); ptr += 2;

    int buf64Size = 64;

    Sym sym;

    while (true) {

        int len = 0; // This is the symbol length - d->min_sym_len

        // Now get the symbol length. For any symbol s64 of length l right-padded

        // to 64 bits we know that d->base64[l-1] >= s64 >= d->base64[l] so we

        // can find the symbol length iterating through base64[].

        while (buf64 < d->base64[len])

            ++len;

        // All the symbols of a given length are consecutive integers (numerical

        // sequence property), so we can compute the offset of our symbol of

        // length len, stored at the beginning of buf64.

        sym = (Sym) ((buf64 - d->base64[len]) >> (64 - len - d->minSymLen)); // Pierre-Marie Baty -- added type cast

        // Now add the value of the lowest symbol of length len to get our symbol

        sym += number<Sym, LittleEndian>(&d->lowestSym[len]);

        // If our offset is within the number of values represented by symbol sym

        // we are done...

        if (offset < d->symlen[sym] + 1)

            break;

        // ...otherwise update the offset and continue to iterate

        offset -= d->symlen[sym] + 1;

        len += d->minSymLen; // Get the real length

        buf64 <<= len;       // Consume the just processed symbol

        buf64Size -= len;

        if (buf64Size <= 32) { // Refill the buffer

            buf64Size += 32;

            buf64 |= (uint64_t)number<uint32_t, BigEndian>(ptr++) << (64 - buf64Size);

        }

    }

    // Ok, now we have our symbol that expands into d->symlen[sym] + 1 symbols.

    // We binary-search for our value recursively expanding into the left and

    // right child symbols until we reach a leaf node where symlen[sym] + 1 == 1

    // that will store the value we need.

    while (d->symlen[sym]) {

        Sym left = d->btree[sym].get<LR::Left>();

        // If a symbol contains 36 sub-symbols (d->symlen[sym] + 1 = 36) and

        // expands in a pair (d->symlen[left] = 23, d->symlen[right] = 11), then

        // we know that, for instance the ten-th value (offset = 10) will be on

        // the left side because in Recursive Pairing child symbols are adjacent.

        if (offset < d->symlen[left] + 1)

            sym = left;

        else {

            offset -= d->symlen[left] + 1;

            sym = d->btree[sym].get<LR::Right>();

        }

    }

    return d->btree[sym].get<LR::Value>();

}

bool check_dtz_stm(WDLEntry*, int, File) { return true; }

bool check_dtz_stm(DTZEntry* entry, int stm, File f) {

    int flags = entry->hasPawns ? entry->pawnTable.file[f].precomp->flags

                                : entry->pieceTable.precomp->flags;

    return   (flags & TBFlag::STM) == stm

          || ((entry->key == entry->key2) && !entry->hasPawns);

}

// DTZ scores are sorted by frequency of occurrence and then assigned the

// values 0, 1, 2, ... in order of decreasing frequency. This is done for each

// of the four WDLScore values. The mapping information necessary to reconstruct

// the original values is stored in the TB file and read during map[] init.

WDLScore map_score(WDLEntry*, File, int value, WDLScore) { return WDLScore(value - 2); }

int map_score(DTZEntry* entry, File f, int value, WDLScore wdl) {

    const int WDLMap[] = { 1, 3, 0, 2, 0 };

    int flags = entry->hasPawns ? entry->pawnTable.file[f].precomp->flags

                                : entry->pieceTable.precomp->flags;

    uint8_t* map = entry->hasPawns ? entry->pawnTable.map

                                   : entry->pieceTable.map;

    uint16_t* idx = entry->hasPawns ? entry->pawnTable.file[f].map_idx

                                    : entry->pieceTable.map_idx;

    if (flags & TBFlag::Mapped)

        value = map[idx[WDLMap[wdl + 2]] + value];

    // DTZ tables store distance to zero in number of moves or plies. We

    // want to return plies, so we have convert to plies when needed.

    if (   (wdl == WDLWin  && !(flags & TBFlag::WinPlies))

        || (wdl == WDLLoss && !(flags & TBFlag::LossPlies))

        ||  wdl == WDLCursedWin

        ||  wdl == WDLBlessedLoss)

        value *= 2;

    return value + 1;

}

// Compute a unique index out of a position and use it to probe the TB file. To

// encode k pieces of same type and color, first sort the pieces by square in

// ascending order s1 <= s2 <= ... <= sk then compute the unique index as:

//

//      idx = Binomial[1][s1] + Binomial[2][s2] + ... + Binomial[k][sk]

//

template<typename Entry, typename T = typename Ret<Entry>::type>

T do_probe_table(const Position& pos, Entry* entry, WDLScore wdl, ProbeState* result) {

    const bool IsWDL = std::is_same<Entry, WDLEntry>::value;

    Square squares[TBPIECES];

    Piece pieces[TBPIECES];

    uint64_t idx;

    int next = 0, size = 0, leadPawnsCnt = 0;

    PairsData* d;

    Bitboard b, leadPawns = 0;

    File tbFile = FILE_A;

    // A given TB entry like KRK has associated two material keys: KRvk and Kvkr.

    // If both sides have the same pieces keys are equal. In this case TB tables

    // only store the 'white to move' case, so if the position to lookup has black

    // to move, we need to switch the color and flip the squares before to lookup.

    bool symmetricBlackToMove = (entry->key == entry->key2 && pos.side_to_move());

    // TB files are calculated for white as stronger side. For instance we have

    // KRvK, not KvKR. A position where stronger side is white will have its

    // material key == entry->key, otherwise we have to switch the color and

    // flip the squares before to lookup.

    bool blackStronger = (pos.material_key() != entry->key);

    int flipColor   = (symmetricBlackToMove || blackStronger) * 8;

    int flipSquares = (symmetricBlackToMove || blackStronger) * 070;

    int stm         = (symmetricBlackToMove || blackStronger) ^ pos.side_to_move();

    // For pawns, TB files store 4 separate tables according if leading pawn is on

    // file a, b, c or d after reordering. The leading pawn is the one with maximum

    // MapPawns[] value, that is the one most toward the edges and with lowest rank.

    if (entry->hasPawns) {

        // In all the 4 tables, pawns are at the beginning of the piece sequence and

        // their color is the reference one. So we just pick the first one.

        Piece pc = Piece(item(entry->pawnTable, 0, 0).precomp->pieces[0] ^ flipColor);

        assert(type_of(pc) == PAWN);

        leadPawns = b = pos.pieces(color_of(pc), PAWN);

        do

            squares[size++] = pop_lsb(&b) ^ flipSquares;

        while (b);

        leadPawnsCnt = size;

        std::swap(squares[0], *std::max_element(squares, squares + leadPawnsCnt, pawns_comp));

        tbFile = file_of(squares[0]);

        if (tbFile > FILE_D)

            tbFile = file_of(squares[0] ^ 7); // Horizontal flip: SQ_H1 -> SQ_A1