Improve index generation

The speedup seems to vary by machine.  The indexing function can be changed w/o needing to understand intrinsics.

Result of 100 runs
==================
base (...ish_baseline) =    1719637  +/- 3233
test (./stockfish    ) =    1734245  +/- 3534
diff                   =     +14608  +/- 4868

speedup        = +0.0085
P(speedup > 0) =  1.0000

closes https://github.com/official-stockfish/Stockfish/pull/6366

No functional change

src/nnue/nnue_accumulator.cpp

@@ -18,9 +18,9 @@
 
 #include "nnue_accumulator.h"
 
+#include <algorithm>
 #include <cassert>
 #include <cstdint>
-#include <initializer_list>
 #include <type_traits>
 
 #include "../bitboard.h"
@@ -362,6 +362,29 @@ void update_accumulator_incremental(
     (target_state.acc<TransformedFeatureDimensions>()).computed[Perspective] = true;
 }
 
+Bitboard get_changed_pieces(const Piece old[SQUARE_NB], const Piece new_[SQUARE_NB]) {
+#if defined(USE_AVX512) || defined(USE_AVX2)
+    static_assert(sizeof(Piece) == 1);
+    Bitboard same_bb = 0;
+    for (int i = 0; i < 64; i += 32)
+    {
+        const __m256i       old_v = _mm256_loadu_si256(reinterpret_cast<const __m256i*>(old + i));
+        const __m256i       new_v = _mm256_loadu_si256(reinterpret_cast<const __m256i*>(new_ + i));
+        const __m256i       cmp_equal  = _mm256_cmpeq_epi8(old_v, new_v);
+        const std::uint32_t equal_mask = _mm256_movemask_epi8(cmp_equal);
+        same_bb |= static_cast<Bitboard>(equal_mask) << i;
+    }
+    return ~same_bb;
+#else
+    Bitboard changed = 0;
+    for (Square sq = SQUARE_ZERO; sq < SQUARE_NB; ++sq)
+    {
+        changed |= static_cast<Bitboard>(old[sq] != new_[sq]) << sq;
+    }
+    return changed;
+#endif
+}
+
 template<Color Perspective, IndexType Dimensions>
 void update_accumulator_refresh_cache(const FeatureTransformer<Dimensions>& featureTransformer,
                                       const Position&                       pos,
@@ -374,29 +397,24 @@ void update_accumulator_refresh_cache(const FeatureTransformer<Dimensions>& feat
     auto&                 entry = cache[ksq][Perspective];
     FeatureSet::IndexList removed, added;
 
-    for (Color c : {WHITE, BLACK})
+    const Bitboard changed_bb = get_changed_pieces(entry.pieces, pos.piece_array());
-    {
+    Bitboard       removed_bb = changed_bb & entry.pieceBB;
-        for (PieceType pt = PAWN; pt <= KING; ++pt)
+    Bitboard       added_bb   = changed_bb & pos.pieces();
-        {
-            const Piece    piece    = make_piece(c, pt);
-            const Bitboard oldBB    = entry.byColorBB[c] & entry.byTypeBB[pt];
-            const Bitboard newBB    = pos.pieces(c, pt);
-            Bitboard       toRemove = oldBB & ~newBB;
-            Bitboard       toAdd    = newBB & ~oldBB;
 
-            while (toRemove)
+    while (removed_bb)
     {
-                Square sq = pop_lsb(toRemove);
+        Square sq = pop_lsb(removed_bb);
-                removed.push_back(FeatureSet::make_index<Perspective>(sq, piece, ksq));
+        removed.push_back(FeatureSet::make_index<Perspective>(sq, entry.pieces[sq], ksq));
     }
-            while (toAdd)
+    while (added_bb)
     {
-                Square sq = pop_lsb(toAdd);
+        Square sq = pop_lsb(added_bb);
-                added.push_back(FeatureSet::make_index<Perspective>(sq, piece, ksq));
+        added.push_back(FeatureSet::make_index<Perspective>(sq, pos.piece_on(sq), ksq));
-            }
-        }
     }
 
+    entry.pieceBB = pos.pieces();
+    std::copy_n(pos.piece_array(), SQUARE_NB, entry.pieces);
+
     auto& accumulator                 = accumulatorState.acc<Dimensions>();
     accumulator.computed[Perspective] = true;
 
@@ -518,12 +536,6 @@ void update_accumulator_refresh_cache(const FeatureTransformer<Dimensions>& feat
     std::memcpy(accumulator.psqtAccumulation[Perspective], entry.psqtAccumulation,
                 sizeof(int32_t) * PSQTBuckets);
 #endif
-
-    for (Color c : {WHITE, BLACK})
-        entry.byColorBB[c] = pos.pieces(c);
-
-    for (PieceType pt = PAWN; pt <= KING; ++pt)
-        entry.byTypeBB[pt] = pos.pieces(pt);
 }
 
 }

src/nnue/nnue_accumulator.h

@@ -71,8 +71,8 @@ struct AccumulatorCaches {
         struct alignas(CacheLineSize) Entry {
             BiasType       accumulation[Size];
             PSQTWeightType psqtAccumulation[PSQTBuckets];
-            Bitboard       byColorBB[COLOR_NB];
+            Piece          pieces[SQUARE_NB];
-            Bitboard       byTypeBB[PIECE_TYPE_NB];
+            Bitboard       pieceBB;
 
             // To initialize a refresh entry, we set all its bitboards empty,
             // so we put the biases in the accumulation, without any weights on top

src/position.h

@@ -93,6 +93,7 @@ class Position {
     template<typename... PieceTypes>
     Bitboard     pieces(Color c, PieceTypes... pts) const;
     Piece        piece_on(Square s) const;
+    const Piece* piece_array() const;
     Square       ep_square() const;
     bool         empty(Square s) const;
     template<PieceType Pt>
@@ -208,6 +209,8 @@ inline Piece Position::piece_on(Square s) const {
     return board[s];
 }
 
+inline const Piece* Position::piece_array() const { return board; }
+
 inline bool Position::empty(Square s) const { return piece_on(s) == NO_PIECE; }
 
 inline Piece Position::moved_piece(Move m) const { return piece_on(m.from_sq()); }