// Copyright 2024 Google LLC // SPDX-License-Identifier: Apache-2.0 // // Licensed under the Apache License, Version 2.0 (the "License"); // you may not use this file except in compliance with the License. // You may obtain a copy of the License at // // https://www.apache.org/licenses/LICENSE-2.0 // // Unless required by applicable law or agreed to in writing, software // distributed under the License is distributed on an "AS IS" BASIS, // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. // See the License for the specific language governing permissions and // limitations under the License. #include #include #include "compression/compress.h" #include "hwy/base.h" // Include guard for (potentially) SIMD code. #if defined(THIRD_PARTY_GEMMA_CPP_DOT_TOGGLE) == defined(HWY_TARGET_TOGGLE) #ifdef THIRD_PARTY_GEMMA_CPP_DOT_TOGGLE #undef THIRD_PARTY_GEMMA_CPP_DOT_TOGGLE #else #define THIRD_PARTY_GEMMA_CPP_DOT_TOGGLE #endif #include "hwy/highway.h" // After highway.h #include "compression/compress-inl.h" #include "ops/fp_arith-inl.h" #include "hwy/contrib/math/math-inl.h" #include "hwy/profiler.h" // also uses SIMD HWY_BEFORE_NAMESPACE(); namespace gcpp { namespace HWY_NAMESPACE { namespace hn = hwy::HWY_NAMESPACE; //------------------------------------------------------------------------------ // Returns 2 * sum(|w.*v|) / |sum(w.*v)|. This is large when there are many // similar-magnitude and opposite-sign elements. See // https://en.wikipedia.org/wiki/Condition_number. template HWY_MAYBE_UNUSED double ConditionNumber(const WeightT* HWY_RESTRICT w, const VecT* HWY_RESTRICT v, size_t num) { PROFILER_FUNC; const hn::ScalableTag df; using VF = hn::Vec; const size_t N = hn::Lanes(df); VF sum = hn::Zero(df); VF sum_err = hn::Zero(df); VF sum_abs = hn::Zero(df); VF sum_abs_err = hn::Zero(df); const auto packed_w = MakeSpan(w, num); const auto packed_v = MakeSpan(v, num); size_t i = 0; if (num >= 2 * N) { for (; i <= num - 2 * N; i += 2 * N) { VF w0, w1, v0, v1; Decompress2(df, packed_w, i, w0, w1); Decompress2(df, packed_v, i, v0, v1); const VF mul0 = hn::Mul(w0, v0); const VF mul1 = hn::Mul(w1, v1); UpdateCascadedSums(df, mul0, sum, sum_err); UpdateCascadedSums(df, mul1, sum, sum_err); UpdateCascadedSums(df, hn::Abs(mul0), sum_abs, sum_abs_err); UpdateCascadedSums(df, hn::Abs(mul1), sum_abs, sum_abs_err); } } size_t remaining = num - i; HWY_DASSERT(remaining < 2 * N); if (HWY_UNLIKELY(remaining != 0)) { HWY_ALIGN float padded_w[2 * hn::MaxLanes(df)]; HWY_ALIGN float padded_v[2 * hn::MaxLanes(df)]; DecompressAndZeroPad(df, packed_w, i, padded_w, remaining); DecompressAndZeroPad(df, packed_v, i, padded_v, remaining); // 1..2 whole vectors, possibly zero-padded. for (size_t padded_pos = 0; padded_pos < remaining; padded_pos += N) { const VF w0 = hn::Load(df, padded_w + padded_pos); const VF v0 = hn::Load(df, padded_v + padded_pos); const VF mul = hn::Mul(w0, v0); UpdateCascadedSums(df, mul, sum, sum_err); UpdateCascadedSums(df, hn::Abs(mul), sum_abs, sum_abs_err); } } const float div = hwy::ScalarAbs(ReduceCascadedSums(df, sum, sum_err)); if (div == 0.0f) return hn::GetLane(hn::Inf(df)); const double cond = 2.0 * ReduceCascadedSums(df, sum_abs, sum_abs_err) / static_cast(div); HWY_ASSERT(cond >= 0.0); return cond; } // Same, but for a single vector - just skips the product. template HWY_MAYBE_UNUSED double ConditionNumber(const VecT* HWY_RESTRICT v, size_t num) { PROFILER_FUNC; const hn::ScalableTag df; using VF = hn::Vec; const size_t N = hn::Lanes(df); VF sum = hn::Zero(df); VF sum_err = hn::Zero(df); VF sum_abs = hn::Zero(df); VF sum_abs_err = hn::Zero(df); const auto packed_v = MakeSpan(v, num); size_t i = 0; if (num >= 2 * N) { for (; i <= num - 2 * N; i += 2 * N) { VF v0, v1; Decompress2(df, packed_v, i, v0, v1); UpdateCascadedSums(df, v0, sum, sum_err); UpdateCascadedSums(df, v1, sum, sum_err); UpdateCascadedSums(df, hn::Abs(v0), sum_abs, sum_abs_err); UpdateCascadedSums(df, hn::Abs(v1), sum_abs, sum_abs_err); } } size_t remaining = num - i; HWY_DASSERT(remaining < 2 * N); if (HWY_UNLIKELY(remaining != 0)) { HWY_ALIGN float padded_v[2 * hn::MaxLanes(df)]; DecompressAndZeroPad(df, packed_v, i, padded_v, remaining); // 1..2 whole vectors, possibly zero-padded. for (size_t padded_pos = 0; padded_pos < remaining; padded_pos += N) { const VF v0 = hn::Load(df, padded_v + padded_pos); UpdateCascadedSums(df, v0, sum, sum_err); UpdateCascadedSums(df, hn::Abs(v0), sum_abs, sum_abs_err); } } const float div = hwy::ScalarAbs(ReduceCascadedSums(df, sum, sum_err)); if (div == 0.0f) return hn::GetLane(hn::Inf(df)); const double cond = 2.0 * ReduceCascadedSums(df, sum_abs, sum_abs_err) / static_cast(div); HWY_ASSERT(cond >= 0.0); return cond; } // Algorithm 6.15 from Handbook of Floating-Point Arithmetic. 10 ops is too slow // for compute-limited Matmul but might be OK for attention. // Also supports bf16 inputs, used by matvec-inl.h. struct DotKernelCompensated { template , HWY_IF_F32_D(DF)> HWY_INLINE void Update4(DF df, const VF w0, const VF w1, const VF w2, const VF w3, const VF v0, const VF v1, const VF v2, const VF v3, VF& sum0, VF& sum1, VF& sum2, VF& sum3, VF& comp0, VF& comp1, VF& comp2, VF& comp3) const { VF perr0, perr1, perr2, perr3; const VF prod0 = TwoProducts(df, w0, v0, perr0); const VF prod1 = TwoProducts(df, w1, v1, perr1); const VF prod2 = TwoProducts(df, w2, v2, perr2); const VF prod3 = TwoProducts(df, w3, v3, perr3); VF serr0, serr1, serr2, serr3; sum0 = TwoSums(df, prod0, sum0, serr0); sum1 = TwoSums(df, prod1, sum1, serr1); sum2 = TwoSums(df, prod2, sum2, serr2); sum3 = TwoSums(df, prod3, sum3, serr3); comp0 = hn::Add(comp0, hn::Add(perr0, serr0)); comp1 = hn::Add(comp1, hn::Add(perr1, serr1)); comp2 = hn::Add(comp2, hn::Add(perr2, serr2)); comp3 = hn::Add(comp3, hn::Add(perr3, serr3)); } template , HWY_IF_BF16_D(DBF), class DF = hn::Repartition, class VF = hn::Vec> HWY_INLINE void Update4(DBF /*dbf*/, const VBF w0, const VBF w1, const VBF w2, const VBF w3, const VBF v0, const VBF v1, const VBF v2, const VBF v3, VF& sum0, VF& sum1, VF& sum2, VF& sum3, VF& comp0, VF& comp1, VF& comp2, VF& comp3) const { const DF df; const VF prod0 = WidenMulPairwiseAdd(df, w0, v0); const VF prod1 = WidenMulPairwiseAdd(df, w1, v1); const VF prod2 = WidenMulPairwiseAdd(df, w2, v2); const VF prod3 = WidenMulPairwiseAdd(df, w3, v3); VF serr0, serr1, serr2, serr3; sum0 = TwoSums(df, prod0, sum0, serr0); sum1 = TwoSums(df, prod1, sum1, serr1); sum2 = TwoSums(df, prod2, sum2, serr2); sum3 = TwoSums(df, prod3, sum3, serr3); comp0 = hn::Add(comp0, serr0); comp1 = hn::Add(comp1, serr1); comp2 = hn::Add(comp2, serr2); comp3 = hn::Add(comp3, serr3); } template , HWY_IF_F32_D(DF)> HWY_INLINE void Update1(DF df, const VF w0, const VF v0, VF& sum0, VF& comp0) const { VF perr0; const VF prod0 = TwoProducts(df, w0, v0, perr0); VF serr0; sum0 = TwoSums(df, prod0, sum0, serr0); comp0 = hn::Add(comp0, hn::Add(perr0, serr0)); } template , HWY_IF_BF16_D(DBF), class DF = hn::Repartition, class VF = hn::Vec> HWY_INLINE void Update1(DBF /*dbf*/, const VBF w0, const VBF v0, VF& sum0, VF& comp0) const { const DF df; const VF prod0 = WidenMulPairwiseAdd(df, w0, v0); VF serr0; sum0 = TwoSums(df, prod0, sum0, serr0); comp0 = hn::Add(comp0, serr0); } template > HWY_INLINE float Reduce(DF df, VF& sum0, VF& sum1, VF& sum2, VF& sum3, VF& comp0, VF& comp1, VF& comp2, VF& comp3) const { // Reduction tree: sum of all accumulators by pairs, then across lanes. AssimilateCascadedSums(df, sum1, comp1, sum0, comp0); AssimilateCascadedSums(df, sum3, comp3, sum2, comp2); AssimilateCascadedSums(df, sum2, comp2, sum0, comp0); return ReduceCascadedSums(df, sum0, comp0); } }; // Default kernel template HWY_INLINE float Dot(D d, const PackedSpan& w, size_t w_ofs, const VecT* HWY_RESTRICT vec_aligned, size_t num) { return DecompressAndCall(d, w, w_ofs, vec_aligned, num, DotKernelCompensated()); } // Adapter for a single pointer, no bounds checking. template HWY_INLINE float Dot(const WeightT* HWY_RESTRICT w, const VecT* vec_aligned, size_t num) { const hn::ScalableTag d; return Dot(d, MakeConstSpan(w, num), /*w_ofs=*/0, vec_aligned, num); } // Adapter for use by matvec-inl.h. TODO: remove when that is no longer used. template HWY_INLINE float Dot(const std::array& w, size_t w_ofs, const VecT* vec_aligned, size_t num) { const hn::ScalableTag d; return Dot(d, MakeConstSpan(w.data(), kCapacity), w_ofs, vec_aligned, num); } // Adapter for use by matvec-inl.h. TODO: remove when that is no longer used. template HWY_INLINE float Dot(const CompressedArray& w, size_t w_ofs, const VecT* vec_aligned, size_t num) { const hn::ScalableTag d; return w.scale() * Dot(d, MakeConstSpan(w.data(), kCapacity), w_ofs, vec_aligned, num); } // NOLINTNEXTLINE(google-readability-namespace-comments) } // namespace HWY_NAMESPACE } // namespace gcpp HWY_AFTER_NAMESPACE(); #endif // NOLINT