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Better dot products
This commit is contained in:
Charles Schlosser
Rasmus Munk Larsen
parent
134b526d61
commit
fb477b8be1
@ -324,6 +324,7 @@ using std::ptrdiff_t;
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#include "src/Core/CwiseNullaryOp.h"
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#include "src/Core/CwiseUnaryView.h"
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#include "src/Core/SelfCwiseBinaryOp.h"
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#include "src/Core/InnerProduct.h"
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#include "src/Core/Dot.h"
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#include "src/Core/StableNorm.h"
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#include "src/Core/Stride.h"
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@ -17,30 +17,6 @@ namespace Eigen {
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namespace internal {
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// helper function for dot(). The problem is that if we put that in the body of dot(), then upon calling dot
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// with mismatched types, the compiler emits errors about failing to instantiate cwiseProduct BEFORE
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// looking at the static assertions. Thus this is a trick to get better compile errors.
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template <typename T, typename U,
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bool NeedToTranspose = T::IsVectorAtCompileTime && U::IsVectorAtCompileTime &&
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((int(T::RowsAtCompileTime) == 1 && int(U::ColsAtCompileTime) == 1) ||
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(int(T::ColsAtCompileTime) == 1 && int(U::RowsAtCompileTime) == 1))>
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struct dot_nocheck {
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typedef scalar_conj_product_op<typename traits<T>::Scalar, typename traits<U>::Scalar> conj_prod;
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typedef typename conj_prod::result_type ResScalar;
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b) {
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return a.template binaryExpr<conj_prod>(b).sum();
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}
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};
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template <typename T, typename U>
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struct dot_nocheck<T, U, true> {
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typedef scalar_conj_product_op<typename traits<T>::Scalar, typename traits<U>::Scalar> conj_prod;
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typedef typename conj_prod::result_type ResScalar;
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b) {
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return a.transpose().template binaryExpr<conj_prod>(b).sum();
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}
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};
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template <typename Derived, typename Scalar = typename traits<Derived>::Scalar>
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struct squared_norm_impl {
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using Real = typename NumTraits<Scalar>::Real;
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@ -74,18 +50,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
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typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,
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typename internal::traits<OtherDerived>::Scalar>::ReturnType
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MatrixBase<Derived>::dot(const MatrixBase<OtherDerived>& other) const {
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EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
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EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
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EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived, OtherDerived)
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#if !(defined(EIGEN_NO_STATIC_ASSERT) && defined(EIGEN_NO_DEBUG))
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EIGEN_CHECK_BINARY_COMPATIBILIY(
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Eigen::internal::scalar_conj_product_op<Scalar EIGEN_COMMA typename OtherDerived::Scalar>, Scalar,
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typename OtherDerived::Scalar);
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#endif
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eigen_assert(size() == other.size());
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return internal::dot_nocheck<Derived, OtherDerived>::run(*this, other);
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return internal::dot_impl<Derived, OtherDerived>::run(derived(), other.derived());
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}
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//---------- implementation of L2 norm and related functions ----------
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253
Eigen/src/Core/InnerProduct.h
Normal file
253
Eigen/src/Core/InnerProduct.h
Normal file
@ -0,0 +1,253 @@
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2024 Charlie Schlosser <cs.schlosser@gmail.com>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#ifndef EIGEN_INNER_PRODUCT_EVAL_H
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#define EIGEN_INNER_PRODUCT_EVAL_H
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// IWYU pragma: private
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#include "./InternalHeaderCheck.h"
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namespace Eigen {
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namespace internal {
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// recursively searches for the largest simd type that does not exceed Size, or the smallest if no such type exists
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template <typename Scalar, int Size, typename Packet = typename packet_traits<Scalar>::type,
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bool Stop =
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(unpacket_traits<Packet>::size <= Size) || is_same<Packet, typename unpacket_traits<Packet>::half>::value>
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struct find_inner_product_packet_helper;
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template <typename Scalar, int Size, typename Packet>
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struct find_inner_product_packet_helper<Scalar, Size, Packet, false> {
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using type = typename find_inner_product_packet_helper<Scalar, Size, typename unpacket_traits<Packet>::half>::type;
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};
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template <typename Scalar, int Size, typename Packet>
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struct find_inner_product_packet_helper<Scalar, Size, Packet, true> {
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using type = Packet;
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};
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template <typename Scalar, int Size>
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struct find_inner_product_packet : find_inner_product_packet_helper<Scalar, Size> {};
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template <typename Scalar>
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struct find_inner_product_packet<Scalar, Dynamic> {
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using type = typename packet_traits<Scalar>::type;
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};
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template <typename Lhs, typename Rhs>
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struct inner_product_assert {
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EIGEN_STATIC_ASSERT_VECTOR_ONLY(Lhs)
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EIGEN_STATIC_ASSERT_VECTOR_ONLY(Rhs)
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EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Lhs, Rhs)
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#ifndef EIGEN_NO_DEBUG
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static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, const Rhs& rhs) {
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eigen_assert((lhs.size() == rhs.size()) && "Inner product: lhs and rhs vectors must have same size");
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}
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#else
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static EIGEN_DEVICE_FUNC void run(const Lhs&, const Rhs&) {}
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#endif
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};
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template <typename Func, typename Lhs, typename Rhs>
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struct inner_product_evaluator {
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static constexpr int LhsFlags = evaluator<Lhs>::Flags, RhsFlags = evaluator<Rhs>::Flags,
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SizeAtCompileTime = min_size_prefer_fixed(Lhs::SizeAtCompileTime, Rhs::SizeAtCompileTime),
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LhsAlignment = evaluator<Lhs>::Alignment, RhsAlignment = evaluator<Rhs>::Alignment;
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using Scalar = typename Func::result_type;
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using Packet = typename find_inner_product_packet<Scalar, SizeAtCompileTime>::type;
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static constexpr bool Vectorize =
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bool(LhsFlags & RhsFlags & PacketAccessBit) && Func::PacketAccess &&
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((SizeAtCompileTime == Dynamic) || (unpacket_traits<Packet>::size <= SizeAtCompileTime));
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit inner_product_evaluator(const Lhs& lhs, const Rhs& rhs,
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Func func = Func())
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: m_func(func), m_lhs(lhs), m_rhs(rhs), m_size(lhs.size()) {
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inner_product_assert<Lhs, Rhs>::run(lhs, rhs);
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}
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index size() const { return m_size.value(); }
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(Index index) const {
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return m_func.coeff(m_lhs.coeff(index), m_rhs.coeff(index));
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}
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(const Scalar& value, Index index) const {
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return m_func.coeff(value, m_lhs.coeff(index), m_rhs.coeff(index));
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}
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template <typename PacketType, int LhsMode = LhsAlignment, int RhsMode = RhsAlignment>
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EIGEN_STRONG_INLINE PacketType packet(Index index) const {
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return m_func.packet(m_lhs.template packet<LhsMode, PacketType>(index),
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m_rhs.template packet<RhsMode, PacketType>(index));
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}
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template <typename PacketType, int LhsMode = LhsAlignment, int RhsMode = RhsAlignment>
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EIGEN_STRONG_INLINE PacketType packet(const PacketType& value, Index index) const {
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return m_func.packet(value, m_lhs.template packet<LhsMode, PacketType>(index),
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m_rhs.template packet<RhsMode, PacketType>(index));
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}
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const Func m_func;
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const evaluator<Lhs> m_lhs;
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const evaluator<Rhs> m_rhs;
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const variable_if_dynamic<Index, SizeAtCompileTime> m_size;
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};
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template <typename Evaluator, bool Vectorize = Evaluator::Vectorize>
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struct inner_product_impl;
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// scalar loop
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template <typename Evaluator>
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struct inner_product_impl<Evaluator, false> {
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using Scalar = typename Evaluator::Scalar;
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static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run(const Evaluator& eval) {
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const Index size = eval.size();
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if (size == 0) return Scalar(0);
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Scalar result = eval.coeff(0);
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for (Index k = 1; k < size; k++) {
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result = eval.coeff(result, k);
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}
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return result;
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}
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};
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// vector loop
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template <typename Evaluator>
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struct inner_product_impl<Evaluator, true> {
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using UnsignedIndex = std::make_unsigned_t<Index>;
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using Scalar = typename Evaluator::Scalar;
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using Packet = typename Evaluator::Packet;
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static constexpr int PacketSize = unpacket_traits<Packet>::size;
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static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run(const Evaluator& eval) {
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const UnsignedIndex size = static_cast<UnsignedIndex>(eval.size());
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if (size < PacketSize) return inner_product_impl<Evaluator, false>::run(eval);
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const UnsignedIndex packetEnd = numext::round_down(size, PacketSize);
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const UnsignedIndex numPackets = size / PacketSize;
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Packet presult0 = eval.template packet<Packet>(0 * PacketSize);
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Packet presult1 = pzero(Packet());
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Packet presult2 = pzero(Packet());
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Packet presult3 = pzero(Packet());
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if (numPackets >= 2) presult1 = eval.template packet<Packet>(1 * PacketSize);
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if (numPackets >= 3) presult2 = eval.template packet<Packet>(2 * PacketSize);
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if (numPackets >= 4) {
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presult3 = eval.template packet<Packet>(3 * PacketSize);
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const UnsignedIndex numRemPackets = (numPackets - 4) % 4;
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const UnsignedIndex quadStart = 4 * PacketSize;
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const UnsignedIndex quadEnd = (numPackets - numRemPackets) * PacketSize;
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for (UnsignedIndex k = quadStart; k < quadEnd; k += 4 * PacketSize) {
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presult0 = eval.packet(presult0, k + 0 * PacketSize);
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presult1 = eval.packet(presult1, k + 1 * PacketSize);
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presult2 = eval.packet(presult2, k + 2 * PacketSize);
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presult3 = eval.packet(presult3, k + 3 * PacketSize);
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}
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if (numRemPackets >= 1) presult0 = eval.packet(presult0, quadEnd + 0 * PacketSize);
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if (numRemPackets >= 2) presult1 = eval.packet(presult1, quadEnd + 1 * PacketSize);
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if (numRemPackets == 3) presult2 = eval.packet(presult2, quadEnd + 2 * PacketSize);
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}
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Scalar result = predux(padd(padd(presult0, presult1), padd(presult2, presult3)));
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if (size > packetEnd) {
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Scalar scalarAccum = eval.coeff(packetEnd);
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for (UnsignedIndex k = packetEnd + 1; k < size; k++) {
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scalarAccum = eval.coeff(scalarAccum, k);
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}
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result += scalarAccum;
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}
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return result;
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}
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};
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template <typename Scalar, bool Conj>
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struct conditional_conj;
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template <typename Scalar>
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struct conditional_conj<Scalar, true> {
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static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(const Scalar& a) { return numext::conj(a); }
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template <typename Packet>
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static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packet(const Packet& a) {
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return pconj(a);
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}
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};
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template <typename Scalar>
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struct conditional_conj<Scalar, false> {
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static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(const Scalar& a) { return a; }
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template <typename Packet>
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static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packet(const Packet& a) {
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return a;
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}
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};
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template <typename LhsScalar, typename RhsScalar, bool Conj>
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struct scalar_inner_product_op {
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using result_type = typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType;
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using conj_helper = conditional_conj<LhsScalar, Conj>;
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type coeff(const LhsScalar& a, const RhsScalar& b) const {
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return (conj_helper::coeff(a) * b);
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}
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type coeff(const result_type& accum, const LhsScalar& a,
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const RhsScalar& b) const {
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return (conj_helper::coeff(a) * b) + accum;
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}
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static constexpr bool PacketAccess = false;
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};
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template <typename Scalar, bool Conj>
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struct scalar_inner_product_op<Scalar, Scalar, Conj> {
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using result_type = Scalar;
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using conj_helper = conditional_conj<Scalar, Conj>;
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(const Scalar& a, const Scalar& b) const {
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return pmul(conj_helper::coeff(a), b);
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}
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(const Scalar& accum, const Scalar& a, const Scalar& b) const {
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return pmadd(conj_helper::coeff(a), b, accum);
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}
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template <typename Packet>
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packet(const Packet& a, const Packet& b) const {
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return pmul(conj_helper::packet(a), b);
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}
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template <typename Packet>
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packet(const Packet& accum, const Packet& a, const Packet& b) const {
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return pmadd(conj_helper::packet(a), b, accum);
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}
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static constexpr bool PacketAccess = packet_traits<Scalar>::HasMul && packet_traits<Scalar>::HasAdd;
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};
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template <typename Lhs, typename Rhs, bool Conj>
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struct default_inner_product_impl {
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using LhsScalar = typename traits<Lhs>::Scalar;
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using RhsScalar = typename traits<Rhs>::Scalar;
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using Op = scalar_inner_product_op<LhsScalar, RhsScalar, Conj>;
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using Evaluator = inner_product_evaluator<Op, Lhs, Rhs>;
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using result_type = typename Evaluator::Scalar;
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static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type run(const MatrixBase<Lhs>& a, const MatrixBase<Rhs>& b) {
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Evaluator eval(a.derived(), b.derived(), Op());
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return inner_product_impl<Evaluator>::run(eval);
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}
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};
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template <typename Lhs, typename Rhs>
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struct dot_impl : default_inner_product_impl<Lhs, Rhs, true> {};
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} // namespace internal
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} // namespace Eigen
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#endif // EIGEN_INNER_PRODUCT_EVAL_H
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@ -235,19 +235,20 @@ EIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(sub_assign_op, scalar_difference_op, add_assig
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template <typename Lhs, typename Rhs>
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struct generic_product_impl<Lhs, Rhs, DenseShape, DenseShape, InnerProduct> {
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using impl = default_inner_product_impl<Lhs, Rhs, false>;
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template <typename Dst>
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static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs) {
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dst.coeffRef(0, 0) = (lhs.transpose().cwiseProduct(rhs)).sum();
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dst.coeffRef(0, 0) = impl::run(lhs, rhs);
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}
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template <typename Dst>
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static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs) {
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dst.coeffRef(0, 0) += (lhs.transpose().cwiseProduct(rhs)).sum();
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dst.coeffRef(0, 0) += impl::run(lhs, rhs);
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}
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template <typename Dst>
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static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs) {
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dst.coeffRef(0, 0) -= (lhs.transpose().cwiseProduct(rhs)).sum();
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dst.coeffRef(0, 0) -= impl::run(lhs, rhs);
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}
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};
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