Use 128 bit multiply for TT index

Remove super cluster stuff from TT and just use a 128 bit multiply.

STC https://tests.stockfishchess.org/tests/view/5ee719b3aae8aec816ab7548
LLR: 2.94 (-2.94,2.94) {-1.50,0.50}
Total: 12736 W: 2502 L: 2333 D: 7901
Ptnml(0-2): 191, 1452, 2944, 1559, 222

LTC https://tests.stockfishchess.org/tests/view/5ee732d1aae8aec816ab7556
LLR: 2.93 (-2.94,2.94) {-1.50,0.50}
Total: 27584 W: 3431 L: 3350 D: 20803
Ptnml(0-2): 173, 2500, 8400, 2511, 208

Scheme back to being derived from https://lemire.me/blog/2016/06/27/a-fast-alternative-to-the-modulo-reduction/

Also the default optimized version of the index calculation now uses fewer instructions.
https://godbolt.org/z/Tktxbv
Might benefit from mulx (requires -mbmi2)

closes #2744

bench: 4320954

src/misc.h

@@ -110,6 +110,19 @@ class PRNG {
   { return T(rand64() & rand64() & rand64()); }
 };
 
+inline uint64_t mul_hi64(uint64_t a, uint64_t b) {
+#if defined(__GNUC__) && defined(IS_64BIT)
+    __extension__ typedef unsigned __int128 uint128;
+    return ((uint128)a * (uint128)b) >> 64;
+#else
+    uint64_t aL = (uint32_t)a, aH = a >> 32;
+    uint64_t bL = (uint32_t)b, bH = b >> 32;
+    uint64_t c1 = (aL * bL) >> 32;
+    uint64_t c2 = aH * bL + c1;
+    uint64_t c3 = aL * bH + (uint32_t)c2;
+    return aH * bH + (c2 >> 32) + (c3 >> 32);
+#endif
+}
 
 /// Under Windows it is not possible for a process to run on more than one
 /// logical processor group. This usually means to be limited to use max 64

src/search.cpp

@@ -662,7 +662,7 @@ namespace {
     // search to overwrite a previous full search TT value, so we use a different
     // position key in case of an excluded move.
     excludedMove = ss->excludedMove;
-    posKey = pos.key() ^ Key(excludedMove << 16); // Isn't a very good hash
+    posKey = pos.key() ^ (Key(excludedMove) << 48); // Isn't a very good hash
     tte = TT.probe(posKey, ttHit);
     ttValue = ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
     ttMove =  rootNode ? thisThread->rootMoves[thisThread->pvIdx].pv[0]

src/tt.cpp

@@ -36,17 +36,17 @@ TranspositionTable TT; // Our global transposition table
 void TTEntry::save(Key k, Value v, bool pv, Bound b, Depth d, Move m, Value ev) {
 
   // Preserve any existing move for the same position
-  if (m || (k >> 48) != key16)
+  if (m || (uint16_t)k != key16)
       move16 = (uint16_t)m;
 
   // Overwrite less valuable entries
-  if (  (k >> 48) != key16
+  if ((uint16_t)k != key16
       || d - DEPTH_OFFSET > depth8 - 4
       || b == BOUND_EXACT)
   {
       assert(d >= DEPTH_OFFSET);
 
-      key16     = (uint16_t)(k >> 48);
+      key16     = (uint16_t)k;
       value16   = (int16_t)v;
       eval16    = (int16_t)ev;
       genBound8 = (uint8_t)(TT.generation8 | uint8_t(pv) << 2 | b);
@@ -65,10 +65,8 @@ void TranspositionTable::resize(size_t mbSize) {
 
   aligned_ttmem_free(mem);
 
-  superClusterCount = mbSize * 1024 * 1024 / (sizeof(Cluster) * ClustersPerSuperCluster);
-
-  table = static_cast<Cluster*>(
-      aligned_ttmem_alloc(superClusterCount * ClustersPerSuperCluster * sizeof(Cluster), mem));
+  clusterCount = mbSize * 1024 * 1024 / sizeof(Cluster);
+  table = static_cast<Cluster*>(aligned_ttmem_alloc(clusterCount * sizeof(Cluster), mem));
   if (!mem)
   {
       std::cerr << "Failed to allocate " << mbSize
@@ -91,8 +89,6 @@ void TranspositionTable::clear() {
   {
       threads.emplace_back([this, idx]() {
 
-          const size_t clusterCount = superClusterCount * ClustersPerSuperCluster;
-
           // Thread binding gives faster search on systems with a first-touch policy
           if (Options["Threads"] > 8)
               WinProcGroup::bindThisThread(idx);
@@ -121,7 +117,7 @@ void TranspositionTable::clear() {
 TTEntry* TranspositionTable::probe(const Key key, bool& found) const {
 
   TTEntry* const tte = first_entry(key);
-  const uint16_t key16 = key >> 48;  // Use the high 16 bits as key inside the cluster
+  const uint16_t key16 = (uint16_t)key;  // Use the low 16 bits as key inside the cluster
 
   for (int i = 0; i < ClusterSize; ++i)
       if (!tte[i].key16 || tte[i].key16 == key16)

src/tt.h

@@ -66,7 +66,6 @@ struct TTEntry {
 class TranspositionTable {
 
   static constexpr int ClusterSize = 3;
-  static constexpr int ClustersPerSuperCluster = 256;
 
   struct Cluster {
     TTEntry entry[ClusterSize];
@@ -84,20 +83,13 @@ class TranspositionTable {
   void clear();
 
   TTEntry* first_entry(const Key key) const {
-
-    // The index is computed from
-    // Idx = (K48 * SCC) / 2^40, with K48 the 48 lowest bits swizzled.
-
-    const uint64_t firstTerm =  uint32_t(key) * uint64_t(superClusterCount);
-    const uint64_t secondTerm = (uint16_t(key >> 32) * uint64_t(superClusterCount)) >> 16;
-
-    return &table[(firstTerm + secondTerm) >> 24].entry[0];
+    return &table[mul_hi64(key, clusterCount)].entry[0];
   }
 
 private:
   friend struct TTEntry;
 
-  size_t superClusterCount;
+  size_t clusterCount;
   Cluster* table;
   void* mem;
   uint8_t generation8; // Size must be not bigger than TTEntry::genBound8

src/ucioption.cpp

@@ -56,7 +56,6 @@ bool CaseInsensitiveLess::operator() (const string& s1, const string& s2) const
 
 void init(OptionsMap& o) {
 
-  // At most 2^32 superclusters. Supercluster = 8 kB
   constexpr int MaxHashMB = Is64Bit ? 33554432 : 2048;
 
   o["Debug Log File"]        << Option("", on_logger);