// This file is part of Eigen, a lightweight C++ template library // for linear algebra. // // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr> // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com> // // This Source Code Form is subject to the terms of the Mozilla // Public License v. 2.0. If a copy of the MPL was not distributed // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. #ifndef EIGEN_REDUX_H #define EIGEN_REDUX_H namespace Eigen { namespace internal { // TODO // * implement other kind of vectorization // * factorize code /*************************************************************************** * Part 1 : the logic deciding a strategy for vectorization and unrolling ***************************************************************************/ template<typename Func, typename Derived> struct redux_traits { public: typedef typename find_best_packet<typename Derived::Scalar,Derived::SizeAtCompileTime>::type PacketType; enum { PacketSize = unpacket_traits<PacketType>::size, InnerMaxSize = int(Derived::IsRowMajor) ? Derived::MaxColsAtCompileTime : Derived::MaxRowsAtCompileTime }; enum { MightVectorize = (int(Derived::Flags)&ActualPacketAccessBit) && (functor_traits<Func>::PacketAccess), MayLinearVectorize = bool(MightVectorize) && (int(Derived::Flags)&LinearAccessBit), MaySliceVectorize = bool(MightVectorize) && int(InnerMaxSize)>=3*PacketSize }; public: enum { Traversal = int(MayLinearVectorize) ? int(LinearVectorizedTraversal) : int(MaySliceVectorize) ? int(SliceVectorizedTraversal) : int(DefaultTraversal) }; public: enum { Cost = Derived::SizeAtCompileTime == Dynamic ? HugeCost : Derived::SizeAtCompileTime * Derived::CoeffReadCost + (Derived::SizeAtCompileTime-1) * functor_traits<Func>::Cost, UnrollingLimit = EIGEN_UNROLLING_LIMIT * (int(Traversal) == int(DefaultTraversal) ? 1 : int(PacketSize)) }; public: enum { Unrolling = Cost <= UnrollingLimit ? CompleteUnrolling : NoUnrolling }; #ifdef EIGEN_DEBUG_ASSIGN static void debug() { std::cerr << "Xpr: " << typeid(typename Derived::XprType).name() << std::endl; std::cerr.setf(std::ios::hex, std::ios::basefield); EIGEN_DEBUG_VAR(Derived::Flags) std::cerr.unsetf(std::ios::hex); EIGEN_DEBUG_VAR(InnerMaxSize) EIGEN_DEBUG_VAR(PacketSize) EIGEN_DEBUG_VAR(MightVectorize) EIGEN_DEBUG_VAR(MayLinearVectorize) EIGEN_DEBUG_VAR(MaySliceVectorize) EIGEN_DEBUG_VAR(Traversal) EIGEN_DEBUG_VAR(UnrollingLimit) EIGEN_DEBUG_VAR(Unrolling) std::cerr << std::endl; } #endif }; /*************************************************************************** * Part 2 : unrollers ***************************************************************************/ /*** no vectorization ***/ template<typename Func, typename Derived, int Start, int Length> struct redux_novec_unroller { enum { HalfLength = Length/2 }; typedef typename Derived::Scalar Scalar; EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(const Derived &mat, const Func& func) { return func(redux_novec_unroller<Func, Derived, Start, HalfLength>::run(mat,func), redux_novec_unroller<Func, Derived, Start+HalfLength, Length-HalfLength>::run(mat,func)); } }; template<typename Func, typename Derived, int Start> struct redux_novec_unroller<Func, Derived, Start, 1> { enum { outer = Start / Derived::InnerSizeAtCompileTime, inner = Start % Derived::InnerSizeAtCompileTime }; typedef typename Derived::Scalar Scalar; EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(const Derived &mat, const Func&) { return mat.coeffByOuterInner(outer, inner); } }; // This is actually dead code and will never be called. It is required // to prevent false warnings regarding failed inlining though // for 0 length run() will never be called at all. template<typename Func, typename Derived, int Start> struct redux_novec_unroller<Func, Derived, Start, 0> { typedef typename Derived::Scalar Scalar; EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(const Derived&, const Func&) { return Scalar(); } }; /*** vectorization ***/ template<typename Func, typename Derived, int Start, int Length> struct redux_vec_unroller { enum { PacketSize = redux_traits<Func, Derived>::PacketSize, HalfLength = Length/2 }; typedef typename Derived::Scalar Scalar; typedef typename redux_traits<Func, Derived>::PacketType PacketScalar; static EIGEN_STRONG_INLINE PacketScalar run(const Derived &mat, const Func& func) { return func.packetOp( redux_vec_unroller<Func, Derived, Start, HalfLength>::run(mat,func), redux_vec_unroller<Func, Derived, Start+HalfLength, Length-HalfLength>::run(mat,func) ); } }; template<typename Func, typename Derived, int Start> struct redux_vec_unroller<Func, Derived, Start, 1> { enum { index = Start * redux_traits<Func, Derived>::PacketSize, outer = index / int(Derived::InnerSizeAtCompileTime), inner = index % int(Derived::InnerSizeAtCompileTime), alignment = Derived::Alignment }; typedef typename Derived::Scalar Scalar; typedef typename redux_traits<Func, Derived>::PacketType PacketScalar; static EIGEN_STRONG_INLINE PacketScalar run(const Derived &mat, const Func&) { return mat.template packetByOuterInner<alignment,PacketScalar>(outer, inner); } }; /*************************************************************************** * Part 3 : implementation of all cases ***************************************************************************/ template<typename Func, typename Derived, int Traversal = redux_traits<Func, Derived>::Traversal, int Unrolling = redux_traits<Func, Derived>::Unrolling > struct redux_impl; template<typename Func, typename Derived> struct redux_impl<Func, Derived, DefaultTraversal, NoUnrolling> { typedef typename Derived::Scalar Scalar; EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(const Derived &mat, const Func& func) { eigen_assert(mat.rows()>0 && mat.cols()>0 && "you are using an empty matrix"); Scalar res; res = mat.coeffByOuterInner(0, 0); for(Index i = 1; i < mat.innerSize(); ++i) res = func(res, mat.coeffByOuterInner(0, i)); for(Index i = 1; i < mat.outerSize(); ++i) for(Index j = 0; j < mat.innerSize(); ++j) res = func(res, mat.coeffByOuterInner(i, j)); return res; } }; template<typename Func, typename Derived> struct redux_impl<Func,Derived, DefaultTraversal, CompleteUnrolling> : public redux_novec_unroller<Func,Derived, 0, Derived::SizeAtCompileTime> {}; template<typename Func, typename Derived> struct redux_impl<Func, Derived, LinearVectorizedTraversal, NoUnrolling> { typedef typename Derived::Scalar Scalar; typedef typename redux_traits<Func, Derived>::PacketType PacketScalar; static Scalar run(const Derived &mat, const Func& func) { const Index size = mat.size(); const Index packetSize = redux_traits<Func, Derived>::PacketSize; const int packetAlignment = unpacket_traits<PacketScalar>::alignment; enum { alignment0 = (bool(Derived::Flags & DirectAccessBit) && bool(packet_traits<Scalar>::AlignedOnScalar)) ? int(packetAlignment) : int(Unaligned), alignment = EIGEN_PLAIN_ENUM_MAX(alignment0, Derived::Alignment) }; const Index alignedStart = internal::first_default_aligned(mat.nestedExpression()); const Index alignedSize2 = ((size-alignedStart)/(2*packetSize))*(2*packetSize); const Index alignedSize = ((size-alignedStart)/(packetSize))*(packetSize); const Index alignedEnd2 = alignedStart + alignedSize2; const Index alignedEnd = alignedStart + alignedSize; Scalar res; if(alignedSize) { PacketScalar packet_res0 = mat.template packet<alignment,PacketScalar>(alignedStart); if(alignedSize>packetSize) // we have at least two packets to partly unroll the loop { PacketScalar packet_res1 = mat.template packet<alignment,PacketScalar>(alignedStart+packetSize); for(Index index = alignedStart + 2*packetSize; index < alignedEnd2; index += 2*packetSize) { packet_res0 = func.packetOp(packet_res0, mat.template packet<alignment,PacketScalar>(index)); packet_res1 = func.packetOp(packet_res1, mat.template packet<alignment,PacketScalar>(index+packetSize)); } packet_res0 = func.packetOp(packet_res0,packet_res1); if(alignedEnd>alignedEnd2) packet_res0 = func.packetOp(packet_res0, mat.template packet<alignment,PacketScalar>(alignedEnd2)); } res = func.predux(packet_res0); for(Index index = 0; index < alignedStart; ++index) res = func(res,mat.coeff(index)); for(Index index = alignedEnd; index < size; ++index) res = func(res,mat.coeff(index)); } else // too small to vectorize anything. // since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize. { res = mat.coeff(0); for(Index index = 1; index < size; ++index) res = func(res,mat.coeff(index)); } return res; } }; // NOTE: for SliceVectorizedTraversal we simply bypass unrolling template<typename Func, typename Derived, int Unrolling> struct redux_impl<Func, Derived, SliceVectorizedTraversal, Unrolling> { typedef typename Derived::Scalar Scalar; typedef typename redux_traits<Func, Derived>::PacketType PacketType; EIGEN_DEVICE_FUNC static Scalar run(const Derived &mat, const Func& func) { eigen_assert(mat.rows()>0 && mat.cols()>0 && "you are using an empty matrix"); const Index innerSize = mat.innerSize(); const Index outerSize = mat.outerSize(); enum { packetSize = redux_traits<Func, Derived>::PacketSize }; const Index packetedInnerSize = ((innerSize)/packetSize)*packetSize; Scalar res; if(packetedInnerSize) { PacketType packet_res = mat.template packet<Unaligned,PacketType>(0,0); for(Index j=0; j<outerSize; ++j) for(Index i=(j==0?packetSize:0); i<packetedInnerSize; i+=Index(packetSize)) packet_res = func.packetOp(packet_res, mat.template packetByOuterInner<Unaligned,PacketType>(j,i)); res = func.predux(packet_res); for(Index j=0; j<outerSize; ++j) for(Index i=packetedInnerSize; i<innerSize; ++i) res = func(res, mat.coeffByOuterInner(j,i)); } else // too small to vectorize anything. // since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize. { res = redux_impl<Func, Derived, DefaultTraversal, NoUnrolling>::run(mat, func); } return res; } }; template<typename Func, typename Derived> struct redux_impl<Func, Derived, LinearVectorizedTraversal, CompleteUnrolling> { typedef typename Derived::Scalar Scalar; typedef typename redux_traits<Func, Derived>::PacketType PacketScalar; enum { PacketSize = redux_traits<Func, Derived>::PacketSize, Size = Derived::SizeAtCompileTime, VectorizedSize = (Size / PacketSize) * PacketSize }; EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(const Derived &mat, const Func& func) { eigen_assert(mat.rows()>0 && mat.cols()>0 && "you are using an empty matrix"); if (VectorizedSize > 0) { Scalar res = func.predux(redux_vec_unroller<Func, Derived, 0, Size / PacketSize>::run(mat,func)); if (VectorizedSize != Size) res = func(res,redux_novec_unroller<Func, Derived, VectorizedSize, Size-VectorizedSize>::run(mat,func)); return res; } else { return redux_novec_unroller<Func, Derived, 0, Size>::run(mat,func); } } }; // evaluator adaptor template<typename _XprType> class redux_evaluator { public: typedef _XprType XprType; EIGEN_DEVICE_FUNC explicit redux_evaluator(const XprType &xpr) : m_evaluator(xpr), m_xpr(xpr) {} typedef typename XprType::Scalar Scalar; typedef typename XprType::CoeffReturnType CoeffReturnType; typedef typename XprType::PacketScalar PacketScalar; typedef typename XprType::PacketReturnType PacketReturnType; 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 = evaluator<XprType>::Flags & ~DirectAccessBit, IsRowMajor = XprType::IsRowMajor, SizeAtCompileTime = XprType::SizeAtCompileTime, InnerSizeAtCompileTime = XprType::InnerSizeAtCompileTime, CoeffReadCost = evaluator<XprType>::CoeffReadCost, Alignment = evaluator<XprType>::Alignment }; EIGEN_DEVICE_FUNC Index rows() const { return m_xpr.rows(); } EIGEN_DEVICE_FUNC Index cols() const { return m_xpr.cols(); } EIGEN_DEVICE_FUNC Index size() const { return m_xpr.size(); } EIGEN_DEVICE_FUNC Index innerSize() const { return m_xpr.innerSize(); } EIGEN_DEVICE_FUNC Index outerSize() const { return m_xpr.outerSize(); } EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index row, Index col) const { return m_evaluator.coeff(row, col); } EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const { return m_evaluator.coeff(index); } template<int LoadMode, typename PacketType> PacketType packet(Index row, Index col) const { return m_evaluator.template packet<LoadMode,PacketType>(row, col); } template<int LoadMode, typename PacketType> PacketType packet(Index index) const { return m_evaluator.template packet<LoadMode,PacketType>(index); } EIGEN_DEVICE_FUNC CoeffReturnType coeffByOuterInner(Index outer, Index inner) const { return m_evaluator.coeff(IsRowMajor ? outer : inner, IsRowMajor ? inner : outer); } template<int LoadMode, typename PacketType> PacketType packetByOuterInner(Index outer, Index inner) const { return m_evaluator.template packet<LoadMode,PacketType>(IsRowMajor ? outer : inner, IsRowMajor ? inner : outer); } const XprType & nestedExpression() const { return m_xpr; } protected: internal::evaluator<XprType> m_evaluator; const XprType &m_xpr; }; } // 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. * * \sa DenseBase::sum(), DenseBase::minCoeff(), DenseBase::maxCoeff(), MatrixBase::colwise(), MatrixBase::rowwise() */ template<typename Derived> template<typename Func> 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()); return internal::redux_impl<Func, ThisEvaluator>::run(thisEval, func); } /** \returns the minimum of all coefficients of \c *this. * \warning the result is undefined if \c *this contains NaN. */ template<typename Derived> EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar DenseBase<Derived>::minCoeff() const { return derived().redux(Eigen::internal::scalar_min_op<Scalar,Scalar>()); } /** \returns the maximum of all coefficients of \c *this. * \warning the result is undefined if \c *this contains NaN. */ template<typename Derived> EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar DenseBase<Derived>::maxCoeff() const { return derived().redux(Eigen::internal::scalar_max_op<Scalar,Scalar>()); } /** \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_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_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_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_STRONG_INLINE typename internal::traits<Derived>::Scalar MatrixBase<Derived>::trace() const { return derived().diagonal().sum(); } } // end namespace Eigen #endif // EIGEN_REDUX_H