X-Git-Url: https://git.sesse.net/?a=blobdiff_plain;f=src%2Fnnue%2Fnnue_feature_transformer.h;h=b6dd54d3378909ea44c8a1934f3037df2ff97043;hb=93f71ecfe1d26e5ccc813318f420b8363cd26003;hp=4f6a174a486667ea23acab3e3d99c4f1fe13d438;hpb=4766dfc3956f78d853c5e0c4636d6f90fd93df9a;p=stockfish diff --git a/src/nnue/nnue_feature_transformer.h b/src/nnue/nnue_feature_transformer.h index 4f6a174a..b6dd54d3 100644 --- a/src/nnue/nnue_feature_transformer.h +++ b/src/nnue/nnue_feature_transformer.h @@ -1,6 +1,6 @@ /* Stockfish, a UCI chess playing engine derived from Glaurung 2.1 - Copyright (C) 2004-2021 The Stockfish developers (see AUTHORS file) + Copyright (C) 2004-2022 The Stockfish developers (see AUTHORS file) Stockfish is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by @@ -47,12 +47,22 @@ namespace Stockfish::Eval::NNUE { #define vec_store(a,b) _mm512_store_si512(a,b) #define vec_add_16(a,b) _mm512_add_epi16(a,b) #define vec_sub_16(a,b) _mm512_sub_epi16(a,b) + #define vec_mul_16(a,b) _mm512_mullo_epi16(a,b) + #define vec_zero() _mm512_setzero_epi32() + #define vec_set_16(a) _mm512_set1_epi16(a) + #define vec_max_16(a,b) _mm512_max_epi16(a,b) + #define vec_min_16(a,b) _mm512_min_epi16(a,b) + inline vec_t vec_msb_pack_16(vec_t a, vec_t b){ + vec_t compacted = _mm512_packs_epi16(_mm512_srli_epi16(a,7),_mm512_srli_epi16(b,7)); + return _mm512_permutexvar_epi64(_mm512_setr_epi64(0, 2, 4, 6, 1, 3, 5, 7), compacted); + } #define vec_load_psqt(a) _mm256_load_si256(a) #define vec_store_psqt(a,b) _mm256_store_si256(a,b) #define vec_add_psqt_32(a,b) _mm256_add_epi32(a,b) #define vec_sub_psqt_32(a,b) _mm256_sub_epi32(a,b) #define vec_zero_psqt() _mm256_setzero_si256() #define NumRegistersSIMD 32 + #define MaxChunkSize 64 #elif USE_AVX2 typedef __m256i vec_t; @@ -61,12 +71,22 @@ namespace Stockfish::Eval::NNUE { #define vec_store(a,b) _mm256_store_si256(a,b) #define vec_add_16(a,b) _mm256_add_epi16(a,b) #define vec_sub_16(a,b) _mm256_sub_epi16(a,b) + #define vec_mul_16(a,b) _mm256_mullo_epi16(a,b) + #define vec_zero() _mm256_setzero_si256() + #define vec_set_16(a) _mm256_set1_epi16(a) + #define vec_max_16(a,b) _mm256_max_epi16(a,b) + #define vec_min_16(a,b) _mm256_min_epi16(a,b) + inline vec_t vec_msb_pack_16(vec_t a, vec_t b){ + vec_t compacted = _mm256_packs_epi16(_mm256_srli_epi16(a,7), _mm256_srli_epi16(b,7)); + return _mm256_permute4x64_epi64(compacted, 0b11011000); + } #define vec_load_psqt(a) _mm256_load_si256(a) #define vec_store_psqt(a,b) _mm256_store_si256(a,b) #define vec_add_psqt_32(a,b) _mm256_add_epi32(a,b) #define vec_sub_psqt_32(a,b) _mm256_sub_epi32(a,b) #define vec_zero_psqt() _mm256_setzero_si256() #define NumRegistersSIMD 16 + #define MaxChunkSize 32 #elif USE_SSE2 typedef __m128i vec_t; @@ -75,12 +95,19 @@ namespace Stockfish::Eval::NNUE { #define vec_store(a,b) *(a)=(b) #define vec_add_16(a,b) _mm_add_epi16(a,b) #define vec_sub_16(a,b) _mm_sub_epi16(a,b) + #define vec_mul_16(a,b) _mm_mullo_epi16(a,b) + #define vec_zero() _mm_setzero_si128() + #define vec_set_16(a) _mm_set1_epi16(a) + #define vec_max_16(a,b) _mm_max_epi16(a,b) + #define vec_min_16(a,b) _mm_min_epi16(a,b) + #define vec_msb_pack_16(a,b) _mm_packs_epi16(_mm_srli_epi16(a,7),_mm_srli_epi16(b,7)) #define vec_load_psqt(a) (*(a)) #define vec_store_psqt(a,b) *(a)=(b) #define vec_add_psqt_32(a,b) _mm_add_epi32(a,b) #define vec_sub_psqt_32(a,b) _mm_sub_epi32(a,b) #define vec_zero_psqt() _mm_setzero_si128() #define NumRegistersSIMD (Is64Bit ? 16 : 8) + #define MaxChunkSize 16 #elif USE_MMX typedef __m64 vec_t; @@ -89,12 +116,26 @@ namespace Stockfish::Eval::NNUE { #define vec_store(a,b) *(a)=(b) #define vec_add_16(a,b) _mm_add_pi16(a,b) #define vec_sub_16(a,b) _mm_sub_pi16(a,b) + #define vec_mul_16(a,b) _mm_mullo_pi16(a,b) + #define vec_zero() _mm_setzero_si64() + #define vec_set_16(a) _mm_set1_pi16(a) + inline vec_t vec_max_16(vec_t a,vec_t b){ + vec_t comparison = _mm_cmpgt_pi16(a,b); + return _mm_or_si64(_mm_and_si64(comparison, a), _mm_andnot_si64(comparison, b)); + } + inline vec_t vec_min_16(vec_t a,vec_t b){ + vec_t comparison = _mm_cmpgt_pi16(a,b); + return _mm_or_si64(_mm_and_si64(comparison, b), _mm_andnot_si64(comparison, a)); + } + #define vec_msb_pack_16(a,b) _mm_packs_pi16(_mm_srli_pi16(a,7),_mm_srli_pi16(b,7)) #define vec_load_psqt(a) (*(a)) #define vec_store_psqt(a,b) *(a)=(b) #define vec_add_psqt_32(a,b) _mm_add_pi32(a,b) #define vec_sub_psqt_32(a,b) _mm_sub_pi32(a,b) #define vec_zero_psqt() _mm_setzero_si64() + #define vec_cleanup() _mm_empty() #define NumRegistersSIMD 8 + #define MaxChunkSize 8 #elif USE_NEON typedef int16x8_t vec_t; @@ -103,12 +144,24 @@ namespace Stockfish::Eval::NNUE { #define vec_store(a,b) *(a)=(b) #define vec_add_16(a,b) vaddq_s16(a,b) #define vec_sub_16(a,b) vsubq_s16(a,b) + #define vec_mul_16(a,b) vmulq_s16(a,b) + #define vec_zero() vec_t{0} + #define vec_set_16(a) vdupq_n_s16(a) + #define vec_max_16(a,b) vmaxq_s16(a,b) + #define vec_min_16(a,b) vminq_s16(a,b) + inline vec_t vec_msb_pack_16(vec_t a, vec_t b){ + const int8x8_t shifta = vshrn_n_s16(a, 7); + const int8x8_t shiftb = vshrn_n_s16(b, 7); + const int8x16_t compacted = vcombine_s8(shifta,shiftb); + return *reinterpret_cast (&compacted); + } #define vec_load_psqt(a) (*(a)) #define vec_store_psqt(a,b) *(a)=(b) #define vec_add_psqt_32(a,b) vaddq_s32(a,b) #define vec_sub_psqt_32(a,b) vsubq_s32(a,b) #define vec_zero_psqt() psqt_vec_t{0} #define NumRegistersSIMD 16 + #define MaxChunkSize 16 #else #undef VECTOR @@ -123,8 +176,10 @@ namespace Stockfish::Eval::NNUE { // We use __m* types as template arguments, which causes GCC to emit warnings // about losing some attribute information. This is irrelevant to us as we // only take their size, so the following pragma are harmless. + #if defined(__GNUC__) #pragma GCC diagnostic push #pragma GCC diagnostic ignored "-Wignored-attributes" + #endif template (); static constexpr int NumPsqtRegs = BestRegisterCount(); - + #if defined(__GNUC__) #pragma GCC diagnostic pop - + #endif #endif @@ -183,7 +238,7 @@ namespace Stockfish::Eval::NNUE { // Number of input/output dimensions static constexpr IndexType InputDimensions = FeatureSet::Dimensions; - static constexpr IndexType OutputDimensions = HalfDimensions * 2; + static constexpr IndexType OutputDimensions = HalfDimensions; // Size of forward propagation buffer static constexpr std::size_t BufferSize = @@ -191,7 +246,7 @@ namespace Stockfish::Eval::NNUE { // Hash value embedded in the evaluation file static constexpr std::uint32_t get_hash_value() { - return FeatureSet::HashValue ^ OutputDimensions; + return FeatureSet::HashValue ^ (OutputDimensions * 2); } // Read network parameters @@ -216,8 +271,8 @@ namespace Stockfish::Eval::NNUE { // Convert input features std::int32_t transform(const Position& pos, OutputType* output, int bucket) const { - update_accumulator(pos, WHITE); - update_accumulator(pos, BLACK); + update_accumulator(pos); + update_accumulator(pos); const Color perspectives[2] = {pos.side_to_move(), ~pos.side_to_move()}; const auto& accumulation = pos.state()->accumulator.accumulation; @@ -229,149 +284,62 @@ namespace Stockfish::Eval::NNUE { ) / 2; - #if defined(USE_AVX512) - - constexpr IndexType NumChunks = HalfDimensions / (SimdWidth * 2); - static_assert(HalfDimensions % (SimdWidth * 2) == 0); - const __m512i Control = _mm512_setr_epi64(0, 2, 4, 6, 1, 3, 5, 7); - const __m512i Zero = _mm512_setzero_si512(); - for (IndexType p = 0; p < 2; ++p) { - const IndexType offset = HalfDimensions * p; - auto out = reinterpret_cast<__m512i*>(&output[offset]); - for (IndexType j = 0; j < NumChunks; ++j) - { - __m512i sum0 = _mm512_load_si512(&reinterpret_cast - (accumulation[perspectives[p]])[j * 2 + 0]); - __m512i sum1 = _mm512_load_si512(&reinterpret_cast - (accumulation[perspectives[p]])[j * 2 + 1]); + const IndexType offset = (HalfDimensions / 2) * p; - _mm512_store_si512(&out[j], _mm512_permutexvar_epi64(Control, - _mm512_max_epi8(_mm512_packs_epi16(sum0, sum1), Zero))); - } - } - return psqt; +#if defined(VECTOR) - #elif defined(USE_AVX2) + constexpr IndexType OutputChunkSize = MaxChunkSize; + static_assert((HalfDimensions / 2) % OutputChunkSize == 0); + constexpr IndexType NumOutputChunks = HalfDimensions / 2 / OutputChunkSize; - constexpr IndexType NumChunks = HalfDimensions / SimdWidth; - constexpr int Control = 0b11011000; - const __m256i Zero = _mm256_setzero_si256(); + vec_t Zero = vec_zero(); + vec_t One = vec_set_16(127); - for (IndexType p = 0; p < 2; ++p) - { - const IndexType offset = HalfDimensions * p; - auto out = reinterpret_cast<__m256i*>(&output[offset]); - for (IndexType j = 0; j < NumChunks; ++j) - { - __m256i sum0 = _mm256_load_si256(&reinterpret_cast - (accumulation[perspectives[p]])[j * 2 + 0]); - __m256i sum1 = _mm256_load_si256(&reinterpret_cast - (accumulation[perspectives[p]])[j * 2 + 1]); + const vec_t* in0 = reinterpret_cast(&(accumulation[perspectives[p]][0])); + const vec_t* in1 = reinterpret_cast(&(accumulation[perspectives[p]][HalfDimensions / 2])); + vec_t* out = reinterpret_cast< vec_t*>(output + offset); - _mm256_store_si256(&out[j], _mm256_permute4x64_epi64( - _mm256_max_epi8(_mm256_packs_epi16(sum0, sum1), Zero), Control)); - } - } - return psqt; - - #elif defined(USE_SSE2) - - #ifdef USE_SSE41 - constexpr IndexType NumChunks = HalfDimensions / SimdWidth; - const __m128i Zero = _mm_setzero_si128(); - #else - constexpr IndexType NumChunks = HalfDimensions / SimdWidth; - const __m128i k0x80s = _mm_set1_epi8(-128); - #endif - - for (IndexType p = 0; p < 2; ++p) - { - const IndexType offset = HalfDimensions * p; - auto out = reinterpret_cast<__m128i*>(&output[offset]); - for (IndexType j = 0; j < NumChunks; ++j) + for (IndexType j = 0; j < NumOutputChunks; j += 1) { - __m128i sum0 = _mm_load_si128(&reinterpret_cast - (accumulation[perspectives[p]])[j * 2 + 0]); - __m128i sum1 = _mm_load_si128(&reinterpret_cast - (accumulation[perspectives[p]])[j * 2 + 1]); - const __m128i packedbytes = _mm_packs_epi16(sum0, sum1); - - #ifdef USE_SSE41 - _mm_store_si128(&out[j], _mm_max_epi8(packedbytes, Zero)); - #else - _mm_store_si128(&out[j], _mm_subs_epi8(_mm_adds_epi8(packedbytes, k0x80s), k0x80s)); - #endif - } - } - return psqt; + const vec_t sum0a = vec_max_16(vec_min_16(in0[j * 2 + 0], One), Zero); + const vec_t sum0b = vec_max_16(vec_min_16(in0[j * 2 + 1], One), Zero); + const vec_t sum1a = vec_max_16(vec_min_16(in1[j * 2 + 0], One), Zero); + const vec_t sum1b = vec_max_16(vec_min_16(in1[j * 2 + 1], One), Zero); - #elif defined(USE_MMX) + const vec_t pa = vec_mul_16(sum0a, sum1a); + const vec_t pb = vec_mul_16(sum0b, sum1b); - constexpr IndexType NumChunks = HalfDimensions / SimdWidth; - const __m64 k0x80s = _mm_set1_pi8(-128); - - for (IndexType p = 0; p < 2; ++p) - { - const IndexType offset = HalfDimensions * p; - auto out = reinterpret_cast<__m64*>(&output[offset]); - for (IndexType j = 0; j < NumChunks; ++j) - { - __m64 sum0 = *(&reinterpret_cast(accumulation[perspectives[p]])[j * 2 + 0]); - __m64 sum1 = *(&reinterpret_cast(accumulation[perspectives[p]])[j * 2 + 1]); - const __m64 packedbytes = _mm_packs_pi16(sum0, sum1); - out[j] = _mm_subs_pi8(_mm_adds_pi8(packedbytes, k0x80s), k0x80s); + out[j] = vec_msb_pack_16(pa, pb); } - } - _mm_empty(); - return psqt; - - #elif defined(USE_NEON) - - constexpr IndexType NumChunks = HalfDimensions / (SimdWidth / 2); - const int8x8_t Zero = {0}; - - for (IndexType p = 0; p < 2; ++p) - { - const IndexType offset = HalfDimensions * p; - const auto out = reinterpret_cast(&output[offset]); - constexpr IndexType UnrollFactor = 16; - static_assert(UnrollFactor % UnrollFactor == 0); - for (IndexType j = 0; j < NumChunks; j += UnrollFactor) - { - int16x8_t sums[UnrollFactor]; - for (IndexType i = 0; i < UnrollFactor; ++i) - sums[i] = reinterpret_cast(accumulation[perspectives[p]])[j+i]; +#else - for (IndexType i = 0; i < UnrollFactor; ++i) - out[j+i] = vmax_s8(vqmovn_s16(sums[i]), Zero); + for (IndexType j = 0; j < HalfDimensions / 2; ++j) { + BiasType sum0 = accumulation[static_cast(perspectives[p])][j + 0]; + BiasType sum1 = accumulation[static_cast(perspectives[p])][j + HalfDimensions / 2]; + sum0 = std::max(0, std::min(127, sum0)); + sum1 = std::max(0, std::min(127, sum1)); + output[offset + j] = static_cast(sum0 * sum1 / 128); } + +#endif } - return psqt; - #else +#if defined(vec_cleanup) + vec_cleanup(); +#endif - for (IndexType p = 0; p < 2; ++p) - { - const IndexType offset = HalfDimensions * p; - for (IndexType j = 0; j < HalfDimensions; ++j) - { - BiasType sum = accumulation[perspectives[p]][j]; - output[offset + j] = static_cast(std::max(0, std::min(127, sum))); - } - } return psqt; - #endif - } // end of function transform() private: - void update_accumulator(const Position& pos, const Color perspective) const { + template + void update_accumulator(const Position& pos) const { // The size must be enough to contain the largest possible update. // That might depend on the feature set and generally relies on the @@ -389,18 +357,18 @@ namespace Stockfish::Eval::NNUE { // of the estimated gain in terms of features to be added/subtracted. StateInfo *st = pos.state(), *next = nullptr; int gain = FeatureSet::refresh_cost(pos); - while (st->previous && !st->accumulator.computed[perspective]) + while (st->previous && !st->accumulator.computed[Perspective]) { // This governs when a full feature refresh is needed and how many // updates are better than just one full refresh. - if ( FeatureSet::requires_refresh(st, perspective) + if ( FeatureSet::requires_refresh(st, Perspective) || (gain -= FeatureSet::update_cost(st) + 1) < 0) break; next = st; st = st->previous; } - if (st->accumulator.computed[perspective]) + if (st->accumulator.computed[Perspective]) { if (next == nullptr) return; @@ -409,17 +377,17 @@ namespace Stockfish::Eval::NNUE { // accumulator. Then, we update the current accumulator (pos.state()). // Gather all features to be updated. - const Square ksq = pos.square(perspective); + const Square ksq = pos.square(Perspective); FeatureSet::IndexList removed[2], added[2]; - FeatureSet::append_changed_indices( - ksq, next->dirtyPiece, perspective, removed[0], added[0]); + FeatureSet::append_changed_indices( + ksq, next->dirtyPiece, removed[0], added[0]); for (StateInfo *st2 = pos.state(); st2 != next; st2 = st2->previous) - FeatureSet::append_changed_indices( - ksq, st2->dirtyPiece, perspective, removed[1], added[1]); + FeatureSet::append_changed_indices( + ksq, st2->dirtyPiece, removed[1], added[1]); // Mark the accumulators as computed. - next->accumulator.computed[perspective] = true; - pos.state()->accumulator.computed[perspective] = true; + next->accumulator.computed[Perspective] = true; + pos.state()->accumulator.computed[Perspective] = true; // Now update the accumulators listed in states_to_update[], where the last element is a sentinel. StateInfo *states_to_update[3] = @@ -429,7 +397,7 @@ namespace Stockfish::Eval::NNUE { { // Load accumulator auto accTile = reinterpret_cast( - &st->accumulator.accumulation[perspective][j * TileHeight]); + &st->accumulator.accumulation[Perspective][j * TileHeight]); for (IndexType k = 0; k < NumRegs; ++k) acc[k] = vec_load(&accTile[k]); @@ -455,7 +423,7 @@ namespace Stockfish::Eval::NNUE { // Store accumulator accTile = reinterpret_cast( - &states_to_update[i]->accumulator.accumulation[perspective][j * TileHeight]); + &states_to_update[i]->accumulator.accumulation[Perspective][j * TileHeight]); for (IndexType k = 0; k < NumRegs; ++k) vec_store(&accTile[k], acc[k]); } @@ -465,7 +433,7 @@ namespace Stockfish::Eval::NNUE { { // Load accumulator auto accTilePsqt = reinterpret_cast( - &st->accumulator.psqtAccumulation[perspective][j * PsqtTileHeight]); + &st->accumulator.psqtAccumulation[Perspective][j * PsqtTileHeight]); for (std::size_t k = 0; k < NumPsqtRegs; ++k) psqt[k] = vec_load_psqt(&accTilePsqt[k]); @@ -491,7 +459,7 @@ namespace Stockfish::Eval::NNUE { // Store accumulator accTilePsqt = reinterpret_cast( - &states_to_update[i]->accumulator.psqtAccumulation[perspective][j * PsqtTileHeight]); + &states_to_update[i]->accumulator.psqtAccumulation[Perspective][j * PsqtTileHeight]); for (std::size_t k = 0; k < NumPsqtRegs; ++k) vec_store_psqt(&accTilePsqt[k], psqt[k]); } @@ -500,12 +468,12 @@ namespace Stockfish::Eval::NNUE { #else for (IndexType i = 0; states_to_update[i]; ++i) { - std::memcpy(states_to_update[i]->accumulator.accumulation[perspective], - st->accumulator.accumulation[perspective], + std::memcpy(states_to_update[i]->accumulator.accumulation[Perspective], + st->accumulator.accumulation[Perspective], HalfDimensions * sizeof(BiasType)); for (std::size_t k = 0; k < PSQTBuckets; ++k) - states_to_update[i]->accumulator.psqtAccumulation[perspective][k] = st->accumulator.psqtAccumulation[perspective][k]; + states_to_update[i]->accumulator.psqtAccumulation[Perspective][k] = st->accumulator.psqtAccumulation[Perspective][k]; st = states_to_update[i]; @@ -515,10 +483,10 @@ namespace Stockfish::Eval::NNUE { const IndexType offset = HalfDimensions * index; for (IndexType j = 0; j < HalfDimensions; ++j) - st->accumulator.accumulation[perspective][j] -= weights[offset + j]; + st->accumulator.accumulation[Perspective][j] -= weights[offset + j]; for (std::size_t k = 0; k < PSQTBuckets; ++k) - st->accumulator.psqtAccumulation[perspective][k] -= psqtWeights[index * PSQTBuckets + k]; + st->accumulator.psqtAccumulation[Perspective][k] -= psqtWeights[index * PSQTBuckets + k]; } // Difference calculation for the activated features @@ -527,10 +495,10 @@ namespace Stockfish::Eval::NNUE { const IndexType offset = HalfDimensions * index; for (IndexType j = 0; j < HalfDimensions; ++j) - st->accumulator.accumulation[perspective][j] += weights[offset + j]; + st->accumulator.accumulation[Perspective][j] += weights[offset + j]; for (std::size_t k = 0; k < PSQTBuckets; ++k) - st->accumulator.psqtAccumulation[perspective][k] += psqtWeights[index * PSQTBuckets + k]; + st->accumulator.psqtAccumulation[Perspective][k] += psqtWeights[index * PSQTBuckets + k]; } } #endif @@ -539,9 +507,9 @@ namespace Stockfish::Eval::NNUE { { // Refresh the accumulator auto& accumulator = pos.state()->accumulator; - accumulator.computed[perspective] = true; + accumulator.computed[Perspective] = true; FeatureSet::IndexList active; - FeatureSet::append_active_indices(pos, perspective, active); + FeatureSet::append_active_indices(pos, active); #ifdef VECTOR for (IndexType j = 0; j < HalfDimensions / TileHeight; ++j) @@ -561,7 +529,7 @@ namespace Stockfish::Eval::NNUE { } auto accTile = reinterpret_cast( - &accumulator.accumulation[perspective][j * TileHeight]); + &accumulator.accumulation[Perspective][j * TileHeight]); for (unsigned k = 0; k < NumRegs; k++) vec_store(&accTile[k], acc[k]); } @@ -581,27 +549,27 @@ namespace Stockfish::Eval::NNUE { } auto accTilePsqt = reinterpret_cast( - &accumulator.psqtAccumulation[perspective][j * PsqtTileHeight]); + &accumulator.psqtAccumulation[Perspective][j * PsqtTileHeight]); for (std::size_t k = 0; k < NumPsqtRegs; ++k) vec_store_psqt(&accTilePsqt[k], psqt[k]); } #else - std::memcpy(accumulator.accumulation[perspective], biases, + std::memcpy(accumulator.accumulation[Perspective], biases, HalfDimensions * sizeof(BiasType)); for (std::size_t k = 0; k < PSQTBuckets; ++k) - accumulator.psqtAccumulation[perspective][k] = 0; + accumulator.psqtAccumulation[Perspective][k] = 0; for (const auto index : active) { const IndexType offset = HalfDimensions * index; for (IndexType j = 0; j < HalfDimensions; ++j) - accumulator.accumulation[perspective][j] += weights[offset + j]; + accumulator.accumulation[Perspective][j] += weights[offset + j]; for (std::size_t k = 0; k < PSQTBuckets; ++k) - accumulator.psqtAccumulation[perspective][k] += psqtWeights[index * PSQTBuckets + k]; + accumulator.psqtAccumulation[Perspective][k] += psqtWeights[index * PSQTBuckets + k]; } #endif }