Allow TT entries with key16==0 to be fetched

Fix the issue where a TT entry with key16==0 would always be reported
as a miss. Instead, we'll use depth8 to detect whether the TT entry is
occupied. In order to do that, we'll change DEPTH_OFFSET to -7
(depth8==0) to distinguish between an unoccupied entry and the
otherwise lowest possible depth, i.e., DEPTH_NONE (depth8==1).

To prevent a performance regression, we'll reorder the TT entry fields
by the access order of TranspositionTable::probe(). Memory in general
works fastest when accessed in sequential order. We'll also match the
store order in TTEntry::save() with the entry field order, and
re-order the 'if-or' expressions in TTEntry::save() from the cheapest
to the most expensive.

Finally, as we now have a proper TT entry occupancy test, we'll fix a
minor corner case with hashfull reporting. To reproduce:
- Use a big hash
- Either:
  a. Start 31 very quick searches (this wraparounds generation to 0); or
  b. Force generation of the first search to 0.
- go depth infinite

Before the fix, hashfull would incorrectly report nearly full hash
immediately after the search start, since
TranspositionTable::hashfull() used to consider only the entry
generation and not whether the entry was actually occupied.

STC:
LLR: 2.95 (-2.94,2.94) {-0.25,1.25}
Total: 36848 W: 4091 L: 3898 D: 28859
Ptnml(0-2): 158, 2996, 11972, 3091, 207
https://tests.stockfishchess.org/tests/view/5f3f98d5dc02a01a0c2881f7

LTC:
LLR: 2.95 (-2.94,2.94) {0.25,1.25}
Total: 32280 W: 1828 L: 1653 D: 28799
Ptnml(0-2): 34, 1428, 13051, 1583, 44
https://tests.stockfishchess.org/tests/view/5f3fe77a87a5c3c63d8f5332

closes https://github.com/official-stockfish/Stockfish/pull/3048

Bench: 3760677

src/tt.cpp

@@ -37,18 +37,19 @@ void TTEntry::save(Key k, Value v, bool pv, Bound b, Depth d, Move m, Value ev)
   if (m || (uint16_t)k != key16)
       move16 = (uint16_t)m;
 
-  // Overwrite less valuable entries
-  if ((uint16_t)k != key16
-      || d - DEPTH_OFFSET > depth8 - 4
-      || b == BOUND_EXACT)
+  // Overwrite less valuable entries (cheapest checks first)
+  if (b == BOUND_EXACT
+      || (uint16_t)k != key16
+      || d - DEPTH_OFFSET > depth8 - 4)
   {
-      assert(d >= DEPTH_OFFSET);
+      assert(d > DEPTH_OFFSET);
+      assert(d < 256 + DEPTH_OFFSET);
 
       key16     = (uint16_t)k;
+      depth8    = (uint8_t)(d - DEPTH_OFFSET);
+      genBound8 = (uint8_t)(TT.generation8 | uint8_t(pv) << 2 | b);
       value16   = (int16_t)v;
       eval16    = (int16_t)ev;
-      genBound8 = (uint8_t)(TT.generation8 | uint8_t(pv) << 2 | b);
-      depth8    = (uint8_t)(d - DEPTH_OFFSET);
   }
 }
 
@@ -119,11 +120,11 @@ TTEntry* TranspositionTable::probe(const Key key, bool& found) const {
   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)
+      if (tte[i].key16 == key16 || !tte[i].depth8)
       {
           tte[i].genBound8 = uint8_t(generation8 | (tte[i].genBound8 & 0x7)); // Refresh
 
-          return found = (bool)tte[i].key16, &tte[i];
+          return found = (bool)tte[i].depth8, &tte[i];
       }
 
   // Find an entry to be replaced according to the replacement strategy
@@ -149,7 +150,7 @@ int TranspositionTable::hashfull() const {
   int cnt = 0;
   for (int i = 0; i < 1000; ++i)
       for (int j = 0; j < ClusterSize; ++j)
-          cnt += (table[i].entry[j].genBound8 & 0xF8) == generation8;
+          cnt += table[i].entry[j].depth8 && (table[i].entry[j].genBound8 & 0xF8) == generation8;
 
   return cnt / ClusterSize;
 }

src/tt.h

@@ -25,13 +25,13 @@
 /// TTEntry struct is the 10 bytes transposition table entry, defined as below:
 ///
 /// key        16 bit
-/// move       16 bit
-/// value      16 bit
-/// eval value 16 bit
+/// depth       8 bit
 /// generation  5 bit
 /// pv node     1 bit
 /// bound type  2 bit
-/// depth       8 bit
+/// move       16 bit
+/// value      16 bit
+/// eval value 16 bit
 
 struct TTEntry {
 
@@ -47,11 +47,11 @@ private:
   friend class TranspositionTable;
 
   uint16_t key16;
+  uint8_t  depth8;
+  uint8_t  genBound8;
   uint16_t move16;
   int16_t  value16;
   int16_t  eval16;
-  uint8_t  genBound8;
-  uint8_t  depth8;
 };
 
 

src/types.h

@@ -232,7 +232,8 @@ enum : int {
   DEPTH_QS_RECAPTURES = -5,
 
   DEPTH_NONE   = -6,
-  DEPTH_OFFSET = DEPTH_NONE
+
+  DEPTH_OFFSET = -7 // value used only for TT entry occupancy check
 };
 
 enum Square : int {