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tqcq
515
3party/eigen/Eigen/src/Core/Redux.h
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515
3party/eigen/Eigen/src/Core/Redux.h
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@@ -0,0 +1,515 @@
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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) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
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// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@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_REDUX_H
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#define EIGEN_REDUX_H
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namespace Eigen {
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namespace internal {
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// TODO
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// * implement other kind of vectorization
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// * factorize code
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/***************************************************************************
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* Part 1 : the logic deciding a strategy for vectorization and unrolling
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***************************************************************************/
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template<typename Func, typename Evaluator>
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struct redux_traits
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{
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public:
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typedef typename find_best_packet<typename Evaluator::Scalar,Evaluator::SizeAtCompileTime>::type PacketType;
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enum {
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PacketSize = unpacket_traits<PacketType>::size,
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InnerMaxSize = int(Evaluator::IsRowMajor)
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? Evaluator::MaxColsAtCompileTime
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: Evaluator::MaxRowsAtCompileTime,
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OuterMaxSize = int(Evaluator::IsRowMajor)
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? Evaluator::MaxRowsAtCompileTime
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: Evaluator::MaxColsAtCompileTime,
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SliceVectorizedWork = int(InnerMaxSize)==Dynamic ? Dynamic
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: int(OuterMaxSize)==Dynamic ? (int(InnerMaxSize)>=int(PacketSize) ? Dynamic : 0)
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: (int(InnerMaxSize)/int(PacketSize)) * int(OuterMaxSize)
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};
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enum {
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MightVectorize = (int(Evaluator::Flags)&ActualPacketAccessBit)
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&& (functor_traits<Func>::PacketAccess),
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MayLinearVectorize = bool(MightVectorize) && (int(Evaluator::Flags)&LinearAccessBit),
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MaySliceVectorize = bool(MightVectorize) && (int(SliceVectorizedWork)==Dynamic || int(SliceVectorizedWork)>=3)
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};
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public:
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enum {
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Traversal = int(MayLinearVectorize) ? int(LinearVectorizedTraversal)
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: int(MaySliceVectorize) ? int(SliceVectorizedTraversal)
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: int(DefaultTraversal)
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};
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public:
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enum {
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Cost = Evaluator::SizeAtCompileTime == Dynamic ? HugeCost
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: int(Evaluator::SizeAtCompileTime) * int(Evaluator::CoeffReadCost) + (Evaluator::SizeAtCompileTime-1) * functor_traits<Func>::Cost,
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UnrollingLimit = EIGEN_UNROLLING_LIMIT * (int(Traversal) == int(DefaultTraversal) ? 1 : int(PacketSize))
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};
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public:
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enum {
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Unrolling = Cost <= UnrollingLimit ? CompleteUnrolling : NoUnrolling
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};
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#ifdef EIGEN_DEBUG_ASSIGN
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static void debug()
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{
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std::cerr << "Xpr: " << typeid(typename Evaluator::XprType).name() << std::endl;
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std::cerr.setf(std::ios::hex, std::ios::basefield);
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EIGEN_DEBUG_VAR(Evaluator::Flags)
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std::cerr.unsetf(std::ios::hex);
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EIGEN_DEBUG_VAR(InnerMaxSize)
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EIGEN_DEBUG_VAR(OuterMaxSize)
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EIGEN_DEBUG_VAR(SliceVectorizedWork)
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EIGEN_DEBUG_VAR(PacketSize)
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EIGEN_DEBUG_VAR(MightVectorize)
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EIGEN_DEBUG_VAR(MayLinearVectorize)
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EIGEN_DEBUG_VAR(MaySliceVectorize)
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std::cerr << "Traversal" << " = " << Traversal << " (" << demangle_traversal(Traversal) << ")" << std::endl;
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EIGEN_DEBUG_VAR(UnrollingLimit)
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std::cerr << "Unrolling" << " = " << Unrolling << " (" << demangle_unrolling(Unrolling) << ")" << std::endl;
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std::cerr << std::endl;
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}
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#endif
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};
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/***************************************************************************
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* Part 2 : unrollers
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***************************************************************************/
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/*** no vectorization ***/
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template<typename Func, typename Evaluator, int Start, int Length>
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struct redux_novec_unroller
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{
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enum {
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HalfLength = Length/2
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};
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typedef typename Evaluator::Scalar Scalar;
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EIGEN_DEVICE_FUNC
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static EIGEN_STRONG_INLINE Scalar run(const Evaluator &eval, const Func& func)
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{
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return func(redux_novec_unroller<Func, Evaluator, Start, HalfLength>::run(eval,func),
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redux_novec_unroller<Func, Evaluator, Start+HalfLength, Length-HalfLength>::run(eval,func));
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}
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};
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template<typename Func, typename Evaluator, int Start>
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struct redux_novec_unroller<Func, Evaluator, Start, 1>
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{
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enum {
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outer = Start / Evaluator::InnerSizeAtCompileTime,
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inner = Start % Evaluator::InnerSizeAtCompileTime
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};
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typedef typename Evaluator::Scalar Scalar;
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EIGEN_DEVICE_FUNC
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static EIGEN_STRONG_INLINE Scalar run(const Evaluator &eval, const Func&)
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{
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return eval.coeffByOuterInner(outer, inner);
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}
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};
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// This is actually dead code and will never be called. It is required
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// to prevent false warnings regarding failed inlining though
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// for 0 length run() will never be called at all.
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template<typename Func, typename Evaluator, int Start>
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struct redux_novec_unroller<Func, Evaluator, Start, 0>
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{
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typedef typename Evaluator::Scalar Scalar;
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EIGEN_DEVICE_FUNC
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static EIGEN_STRONG_INLINE Scalar run(const Evaluator&, const Func&) { return Scalar(); }
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};
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/*** vectorization ***/
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template<typename Func, typename Evaluator, int Start, int Length>
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struct redux_vec_unroller
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{
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template<typename PacketType>
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EIGEN_DEVICE_FUNC
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static EIGEN_STRONG_INLINE PacketType run(const Evaluator &eval, const Func& func)
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{
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enum {
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PacketSize = unpacket_traits<PacketType>::size,
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HalfLength = Length/2
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};
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return func.packetOp(
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redux_vec_unroller<Func, Evaluator, Start, HalfLength>::template run<PacketType>(eval,func),
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redux_vec_unroller<Func, Evaluator, Start+HalfLength, Length-HalfLength>::template run<PacketType>(eval,func) );
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}
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};
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template<typename Func, typename Evaluator, int Start>
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struct redux_vec_unroller<Func, Evaluator, Start, 1>
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{
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template<typename PacketType>
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EIGEN_DEVICE_FUNC
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static EIGEN_STRONG_INLINE PacketType run(const Evaluator &eval, const Func&)
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{
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enum {
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PacketSize = unpacket_traits<PacketType>::size,
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index = Start * PacketSize,
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outer = index / int(Evaluator::InnerSizeAtCompileTime),
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inner = index % int(Evaluator::InnerSizeAtCompileTime),
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alignment = Evaluator::Alignment
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};
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return eval.template packetByOuterInner<alignment,PacketType>(outer, inner);
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}
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};
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/***************************************************************************
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* Part 3 : implementation of all cases
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***************************************************************************/
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template<typename Func, typename Evaluator,
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int Traversal = redux_traits<Func, Evaluator>::Traversal,
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int Unrolling = redux_traits<Func, Evaluator>::Unrolling
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>
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struct redux_impl;
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template<typename Func, typename Evaluator>
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struct redux_impl<Func, Evaluator, DefaultTraversal, NoUnrolling>
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{
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typedef typename Evaluator::Scalar Scalar;
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template<typename XprType>
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EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE
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Scalar run(const Evaluator &eval, const Func& func, const XprType& xpr)
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{
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eigen_assert(xpr.rows()>0 && xpr.cols()>0 && "you are using an empty matrix");
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Scalar res;
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res = eval.coeffByOuterInner(0, 0);
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for(Index i = 1; i < xpr.innerSize(); ++i)
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res = func(res, eval.coeffByOuterInner(0, i));
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for(Index i = 1; i < xpr.outerSize(); ++i)
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for(Index j = 0; j < xpr.innerSize(); ++j)
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res = func(res, eval.coeffByOuterInner(i, j));
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return res;
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}
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};
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template<typename Func, typename Evaluator>
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struct redux_impl<Func,Evaluator, DefaultTraversal, CompleteUnrolling>
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: redux_novec_unroller<Func,Evaluator, 0, Evaluator::SizeAtCompileTime>
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{
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typedef redux_novec_unroller<Func,Evaluator, 0, Evaluator::SizeAtCompileTime> Base;
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typedef typename Evaluator::Scalar Scalar;
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template<typename XprType>
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EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE
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Scalar run(const Evaluator &eval, const Func& func, const XprType& /*xpr*/)
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{
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return Base::run(eval,func);
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}
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};
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template<typename Func, typename Evaluator>
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struct redux_impl<Func, Evaluator, LinearVectorizedTraversal, NoUnrolling>
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{
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typedef typename Evaluator::Scalar Scalar;
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typedef typename redux_traits<Func, Evaluator>::PacketType PacketScalar;
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template<typename XprType>
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static Scalar run(const Evaluator &eval, const Func& func, const XprType& xpr)
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{
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const Index size = xpr.size();
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const Index packetSize = redux_traits<Func, Evaluator>::PacketSize;
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const int packetAlignment = unpacket_traits<PacketScalar>::alignment;
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enum {
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alignment0 = (bool(Evaluator::Flags & DirectAccessBit) && bool(packet_traits<Scalar>::AlignedOnScalar)) ? int(packetAlignment) : int(Unaligned),
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alignment = EIGEN_PLAIN_ENUM_MAX(alignment0, Evaluator::Alignment)
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};
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const Index alignedStart = internal::first_default_aligned(xpr);
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const Index alignedSize2 = ((size-alignedStart)/(2*packetSize))*(2*packetSize);
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const Index alignedSize = ((size-alignedStart)/(packetSize))*(packetSize);
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const Index alignedEnd2 = alignedStart + alignedSize2;
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const Index alignedEnd = alignedStart + alignedSize;
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Scalar res;
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if(alignedSize)
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{
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PacketScalar packet_res0 = eval.template packet<alignment,PacketScalar>(alignedStart);
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if(alignedSize>packetSize) // we have at least two packets to partly unroll the loop
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{
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PacketScalar packet_res1 = eval.template packet<alignment,PacketScalar>(alignedStart+packetSize);
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for(Index index = alignedStart + 2*packetSize; index < alignedEnd2; index += 2*packetSize)
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{
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packet_res0 = func.packetOp(packet_res0, eval.template packet<alignment,PacketScalar>(index));
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packet_res1 = func.packetOp(packet_res1, eval.template packet<alignment,PacketScalar>(index+packetSize));
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}
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packet_res0 = func.packetOp(packet_res0,packet_res1);
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if(alignedEnd>alignedEnd2)
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packet_res0 = func.packetOp(packet_res0, eval.template packet<alignment,PacketScalar>(alignedEnd2));
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}
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res = func.predux(packet_res0);
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for(Index index = 0; index < alignedStart; ++index)
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res = func(res,eval.coeff(index));
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for(Index index = alignedEnd; index < size; ++index)
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res = func(res,eval.coeff(index));
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}
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else // too small to vectorize anything.
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// since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize.
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{
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res = eval.coeff(0);
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for(Index index = 1; index < size; ++index)
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res = func(res,eval.coeff(index));
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}
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return res;
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}
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};
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// NOTE: for SliceVectorizedTraversal we simply bypass unrolling
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template<typename Func, typename Evaluator, int Unrolling>
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struct redux_impl<Func, Evaluator, SliceVectorizedTraversal, Unrolling>
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{
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typedef typename Evaluator::Scalar Scalar;
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typedef typename redux_traits<Func, Evaluator>::PacketType PacketType;
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template<typename XprType>
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EIGEN_DEVICE_FUNC static Scalar run(const Evaluator &eval, const Func& func, const XprType& xpr)
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{
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eigen_assert(xpr.rows()>0 && xpr.cols()>0 && "you are using an empty matrix");
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const Index innerSize = xpr.innerSize();
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const Index outerSize = xpr.outerSize();
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enum {
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packetSize = redux_traits<Func, Evaluator>::PacketSize
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};
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const Index packetedInnerSize = ((innerSize)/packetSize)*packetSize;
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Scalar res;
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if(packetedInnerSize)
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{
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PacketType packet_res = eval.template packet<Unaligned,PacketType>(0,0);
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for(Index j=0; j<outerSize; ++j)
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for(Index i=(j==0?packetSize:0); i<packetedInnerSize; i+=Index(packetSize))
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packet_res = func.packetOp(packet_res, eval.template packetByOuterInner<Unaligned,PacketType>(j,i));
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||||
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||||
res = func.predux(packet_res);
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||||
for(Index j=0; j<outerSize; ++j)
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||||
for(Index i=packetedInnerSize; i<innerSize; ++i)
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res = func(res, eval.coeffByOuterInner(j,i));
|
||||
}
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||||
else // too small to vectorize anything.
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||||
// since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize.
|
||||
{
|
||||
res = redux_impl<Func, Evaluator, DefaultTraversal, NoUnrolling>::run(eval, func, xpr);
|
||||
}
|
||||
|
||||
return res;
|
||||
}
|
||||
};
|
||||
|
||||
template<typename Func, typename Evaluator>
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||||
struct redux_impl<Func, Evaluator, LinearVectorizedTraversal, CompleteUnrolling>
|
||||
{
|
||||
typedef typename Evaluator::Scalar Scalar;
|
||||
|
||||
typedef typename redux_traits<Func, Evaluator>::PacketType PacketType;
|
||||
enum {
|
||||
PacketSize = redux_traits<Func, Evaluator>::PacketSize,
|
||||
Size = Evaluator::SizeAtCompileTime,
|
||||
VectorizedSize = (int(Size) / int(PacketSize)) * int(PacketSize)
|
||||
};
|
||||
|
||||
template<typename XprType>
|
||||
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE
|
||||
Scalar run(const Evaluator &eval, const Func& func, const XprType &xpr)
|
||||
{
|
||||
EIGEN_ONLY_USED_FOR_DEBUG(xpr)
|
||||
eigen_assert(xpr.rows()>0 && xpr.cols()>0 && "you are using an empty matrix");
|
||||
if (VectorizedSize > 0) {
|
||||
Scalar res = func.predux(redux_vec_unroller<Func, Evaluator, 0, Size / PacketSize>::template run<PacketType>(eval,func));
|
||||
if (VectorizedSize != Size)
|
||||
res = func(res,redux_novec_unroller<Func, Evaluator, VectorizedSize, Size-VectorizedSize>::run(eval,func));
|
||||
return res;
|
||||
}
|
||||
else {
|
||||
return redux_novec_unroller<Func, Evaluator, 0, Size>::run(eval,func);
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
// evaluator adaptor
|
||||
template<typename _XprType>
|
||||
class redux_evaluator : public internal::evaluator<_XprType>
|
||||
{
|
||||
typedef internal::evaluator<_XprType> Base;
|
||||
public:
|
||||
typedef _XprType XprType;
|
||||
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
|
||||
explicit redux_evaluator(const XprType &xpr) : Base(xpr) {}
|
||||
|
||||
typedef typename XprType::Scalar Scalar;
|
||||
typedef typename XprType::CoeffReturnType CoeffReturnType;
|
||||
typedef typename XprType::PacketScalar PacketScalar;
|
||||
|
||||
enum {
|
||||
MaxRowsAtCompileTime = XprType::MaxRowsAtCompileTime,
|
||||
MaxColsAtCompileTime = XprType::MaxColsAtCompileTime,
|
||||
// TODO we should not remove DirectAccessBit and rather find an elegant way to query the alignment offset at runtime from the evaluator
|
||||
Flags = Base::Flags & ~DirectAccessBit,
|
||||
IsRowMajor = XprType::IsRowMajor,
|
||||
SizeAtCompileTime = XprType::SizeAtCompileTime,
|
||||
InnerSizeAtCompileTime = XprType::InnerSizeAtCompileTime
|
||||
};
|
||||
|
||||
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
|
||||
CoeffReturnType coeffByOuterInner(Index outer, Index inner) const
|
||||
{ return Base::coeff(IsRowMajor ? outer : inner, IsRowMajor ? inner : outer); }
|
||||
|
||||
template<int LoadMode, typename PacketType>
|
||||
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
|
||||
PacketType packetByOuterInner(Index outer, Index inner) const
|
||||
{ return Base::template packet<LoadMode,PacketType>(IsRowMajor ? outer : inner, IsRowMajor ? inner : outer); }
|
||||
|
||||
};
|
||||
|
||||
} // end namespace internal
|
||||
|
||||
/***************************************************************************
|
||||
* Part 4 : public API
|
||||
***************************************************************************/
|
||||
|
||||
|
||||
/** \returns the result of a full redux operation on the whole matrix or vector using \a func
|
||||
*
|
||||
* The template parameter \a BinaryOp is the type of the functor \a func which must be
|
||||
* an associative operator. Both current C++98 and C++11 functor styles are handled.
|
||||
*
|
||||
* \warning the matrix must be not empty, otherwise an assertion is triggered.
|
||||
*
|
||||
* \sa DenseBase::sum(), DenseBase::minCoeff(), DenseBase::maxCoeff(), MatrixBase::colwise(), MatrixBase::rowwise()
|
||||
*/
|
||||
template<typename Derived>
|
||||
template<typename Func>
|
||||
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
|
||||
DenseBase<Derived>::redux(const Func& func) const
|
||||
{
|
||||
eigen_assert(this->rows()>0 && this->cols()>0 && "you are using an empty matrix");
|
||||
|
||||
typedef typename internal::redux_evaluator<Derived> ThisEvaluator;
|
||||
ThisEvaluator thisEval(derived());
|
||||
|
||||
// The initial expression is passed to the reducer as an additional argument instead of
|
||||
// passing it as a member of redux_evaluator to help
|
||||
return internal::redux_impl<Func, ThisEvaluator>::run(thisEval, func, derived());
|
||||
}
|
||||
|
||||
/** \returns the minimum of all coefficients of \c *this.
|
||||
* In case \c *this contains NaN, NaNPropagation determines the behavior:
|
||||
* NaNPropagation == PropagateFast : undefined
|
||||
* NaNPropagation == PropagateNaN : result is NaN
|
||||
* NaNPropagation == PropagateNumbers : result is minimum of elements that are not NaN
|
||||
* \warning the matrix must be not empty, otherwise an assertion is triggered.
|
||||
*/
|
||||
template<typename Derived>
|
||||
template<int NaNPropagation>
|
||||
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
|
||||
DenseBase<Derived>::minCoeff() const
|
||||
{
|
||||
return derived().redux(Eigen::internal::scalar_min_op<Scalar,Scalar, NaNPropagation>());
|
||||
}
|
||||
|
||||
/** \returns the maximum of all coefficients of \c *this.
|
||||
* In case \c *this contains NaN, NaNPropagation determines the behavior:
|
||||
* NaNPropagation == PropagateFast : undefined
|
||||
* NaNPropagation == PropagateNaN : result is NaN
|
||||
* NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN
|
||||
* \warning the matrix must be not empty, otherwise an assertion is triggered.
|
||||
*/
|
||||
template<typename Derived>
|
||||
template<int NaNPropagation>
|
||||
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
|
||||
DenseBase<Derived>::maxCoeff() const
|
||||
{
|
||||
return derived().redux(Eigen::internal::scalar_max_op<Scalar,Scalar, NaNPropagation>());
|
||||
}
|
||||
|
||||
/** \returns the sum of all coefficients of \c *this
|
||||
*
|
||||
* If \c *this is empty, then the value 0 is returned.
|
||||
*
|
||||
* \sa trace(), prod(), mean()
|
||||
*/
|
||||
template<typename Derived>
|
||||
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
|
||||
DenseBase<Derived>::sum() const
|
||||
{
|
||||
if(SizeAtCompileTime==0 || (SizeAtCompileTime==Dynamic && size()==0))
|
||||
return Scalar(0);
|
||||
return derived().redux(Eigen::internal::scalar_sum_op<Scalar,Scalar>());
|
||||
}
|
||||
|
||||
/** \returns the mean of all coefficients of *this
|
||||
*
|
||||
* \sa trace(), prod(), sum()
|
||||
*/
|
||||
template<typename Derived>
|
||||
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
|
||||
DenseBase<Derived>::mean() const
|
||||
{
|
||||
#ifdef __INTEL_COMPILER
|
||||
#pragma warning push
|
||||
#pragma warning ( disable : 2259 )
|
||||
#endif
|
||||
return Scalar(derived().redux(Eigen::internal::scalar_sum_op<Scalar,Scalar>())) / Scalar(this->size());
|
||||
#ifdef __INTEL_COMPILER
|
||||
#pragma warning pop
|
||||
#endif
|
||||
}
|
||||
|
||||
/** \returns the product of all coefficients of *this
|
||||
*
|
||||
* Example: \include MatrixBase_prod.cpp
|
||||
* Output: \verbinclude MatrixBase_prod.out
|
||||
*
|
||||
* \sa sum(), mean(), trace()
|
||||
*/
|
||||
template<typename Derived>
|
||||
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
|
||||
DenseBase<Derived>::prod() const
|
||||
{
|
||||
if(SizeAtCompileTime==0 || (SizeAtCompileTime==Dynamic && size()==0))
|
||||
return Scalar(1);
|
||||
return derived().redux(Eigen::internal::scalar_product_op<Scalar>());
|
||||
}
|
||||
|
||||
/** \returns the trace of \c *this, i.e. the sum of the coefficients on the main diagonal.
|
||||
*
|
||||
* \c *this can be any matrix, not necessarily square.
|
||||
*
|
||||
* \sa diagonal(), sum()
|
||||
*/
|
||||
template<typename Derived>
|
||||
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
|
||||
MatrixBase<Derived>::trace() const
|
||||
{
|
||||
return derived().diagonal().sum();
|
||||
}
|
||||
|
||||
} // end namespace Eigen
|
||||
|
||||
#endif // EIGEN_REDUX_H
|
||||
Reference in New Issue
Block a user