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490 lines
18 KiB
C++
490 lines
18 KiB
C++
// 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) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
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// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
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//
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// Eigen is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 3 of the License, or (at your option) any later version.
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//
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// Alternatively, you can redistribute it and/or
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// modify it under the terms of the GNU General Public License as
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// published by the Free Software Foundation; either version 2 of
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// the License, or (at your option) any later version.
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//
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// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
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// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License and a copy of the GNU General Public License along with
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// Eigen. If not, see <http://www.gnu.org/licenses/>.
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#ifndef EIGEN_PRODUCT_H
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#define EIGEN_PRODUCT_H
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template<int Index, int Size, typename Lhs, typename Rhs>
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struct ei_product_unroller
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{
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inline static void run(int row, int col, const Lhs& lhs, const Rhs& rhs,
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typename Lhs::Scalar &res)
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{
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ei_product_unroller<Index-1, Size, Lhs, Rhs>::run(row, col, lhs, rhs, res);
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res += lhs.coeff(row, Index) * rhs.coeff(Index, col);
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}
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};
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template<int Size, typename Lhs, typename Rhs>
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struct ei_product_unroller<0, Size, Lhs, Rhs>
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{
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inline static void run(int row, int col, const Lhs& lhs, const Rhs& rhs,
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typename Lhs::Scalar &res)
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{
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res = lhs.coeff(row, 0) * rhs.coeff(0, col);
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}
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};
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template<int Index, typename Lhs, typename Rhs>
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struct ei_product_unroller<Index, Dynamic, Lhs, Rhs>
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{
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inline static void run(int, int, const Lhs&, const Rhs&, typename Lhs::Scalar&) {}
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};
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// prevent buggy user code from causing an infinite recursion
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template<int Index, typename Lhs, typename Rhs>
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struct ei_product_unroller<Index, 0, Lhs, Rhs>
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{
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inline static void run(int, int, const Lhs&, const Rhs&, typename Lhs::Scalar&) {}
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};
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template<typename Lhs, typename Rhs>
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struct ei_product_unroller<0, Dynamic, Lhs, Rhs>
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{
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static void run(int, int, const Lhs&, const Rhs&, typename Lhs::Scalar&) {}
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};
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template<bool RowMajor, int Index, int Size, typename Lhs, typename Rhs, typename PacketScalar>
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struct ei_packet_product_unroller;
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template<int Index, int Size, typename Lhs, typename Rhs, typename PacketScalar>
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struct ei_packet_product_unroller<true, Index, Size, Lhs, Rhs, PacketScalar>
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{
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inline static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, PacketScalar &res)
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{
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ei_packet_product_unroller<true, Index-1, Size, Lhs, Rhs, PacketScalar>::run(row, col, lhs, rhs, res);
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res = ei_pmadd(ei_pset1(lhs.coeff(row, Index)), rhs.template packet<Aligned>(Index, col), res);
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}
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};
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template<int Index, int Size, typename Lhs, typename Rhs, typename PacketScalar>
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struct ei_packet_product_unroller<false, Index, Size, Lhs, Rhs, PacketScalar>
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{
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inline static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, PacketScalar &res)
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{
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ei_packet_product_unroller<false, Index-1, Size, Lhs, Rhs, PacketScalar>::run(row, col, lhs, rhs, res);
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res = ei_pmadd(lhs.template packet<Aligned>(row, Index), ei_pset1(rhs.coeff(Index, col)), res);
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}
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};
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template<int Size, typename Lhs, typename Rhs, typename PacketScalar>
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struct ei_packet_product_unroller<true, 0, Size, Lhs, Rhs, PacketScalar>
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{
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inline static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, PacketScalar &res)
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{
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res = ei_pmul(ei_pset1(lhs.coeff(row, 0)),rhs.template packet<Aligned>(0, col));
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}
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};
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template<int Size, typename Lhs, typename Rhs, typename PacketScalar>
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struct ei_packet_product_unroller<false, 0, Size, Lhs, Rhs, PacketScalar>
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{
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inline static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, PacketScalar &res)
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{
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res = ei_pmul(lhs.template packet<Aligned>(row, 0), ei_pset1(rhs.coeff(0, col)));
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}
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};
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template<bool RowMajor, int Index, typename Lhs, typename Rhs, typename PacketScalar>
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struct ei_packet_product_unroller<RowMajor, Index, Dynamic, Lhs, Rhs, PacketScalar>
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{
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inline static void run(int, int, const Lhs&, const Rhs&, PacketScalar&) {}
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};
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template<int Index, typename Lhs, typename Rhs, typename PacketScalar>
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struct ei_packet_product_unroller<false, Index, Dynamic, Lhs, Rhs, PacketScalar>
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{
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inline static void run(int, int, const Lhs&, const Rhs&, PacketScalar&) {}
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};
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template<typename Lhs, typename Rhs, typename PacketScalar>
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struct ei_packet_product_unroller<false, 0, Dynamic, Lhs, Rhs, PacketScalar>
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{
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static void run(int, int, const Lhs&, const Rhs&, PacketScalar&) {}
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};
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template<typename Product, bool RowMajor = true> struct ProductPacketImpl {
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inline static typename Product::PacketScalar execute(const Product& product, int row, int col)
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{ return product._packetRowMajor(row,col); }
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};
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template<typename Product> struct ProductPacketImpl<Product, false> {
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inline static typename Product::PacketScalar execute(const Product& product, int row, int col)
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{ return product._packetColumnMajor(row,col); }
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};
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/** \class Product
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*
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* \brief Expression of the product of two matrices
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*
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* \param Lhs the type of the left-hand side
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* \param Rhs the type of the right-hand side
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* \param EvalMode internal use only
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*
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* This class represents an expression of the product of two matrices.
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* It is the return type of the operator* between matrices, and most of the time
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* this is the only way it is used.
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*
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* \sa class Sum, class Difference
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*/
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template<typename Lhs, typename Rhs> struct ei_product_eval_mode
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{
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enum{ value = Lhs::MaxRowsAtCompileTime >= EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
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&& Rhs::MaxColsAtCompileTime >= EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
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&& (!( (Lhs::Flags&RowMajorBit) && ((Rhs::Flags&RowMajorBit) ^ RowMajorBit)))
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? CacheFriendlyProduct : NormalProduct };
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};
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template<typename Lhs, typename Rhs, int EvalMode>
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struct ei_traits<Product<Lhs, Rhs, EvalMode> >
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{
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typedef typename Lhs::Scalar Scalar;
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typedef typename ei_nested<Lhs,Rhs::ColsAtCompileTime>::type LhsNested;
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typedef typename ei_nested<Rhs,Lhs::RowsAtCompileTime>::type RhsNested;
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typedef typename ei_unref<LhsNested>::type _LhsNested;
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typedef typename ei_unref<RhsNested>::type _RhsNested;
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enum {
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LhsCoeffReadCost = _LhsNested::CoeffReadCost,
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RhsCoeffReadCost = _RhsNested::CoeffReadCost,
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LhsFlags = _LhsNested::Flags,
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RhsFlags = _RhsNested::Flags,
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RowsAtCompileTime = Lhs::RowsAtCompileTime,
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ColsAtCompileTime = Rhs::ColsAtCompileTime,
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MaxRowsAtCompileTime = Lhs::MaxRowsAtCompileTime,
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MaxColsAtCompileTime = Rhs::MaxColsAtCompileTime,
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_RhsPacketAccess = (RhsFlags & RowMajorBit) && (RhsFlags & PacketAccessBit) && (ColsAtCompileTime % ei_packet_traits<Scalar>::size == 0),
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_LhsPacketAccess = (!(LhsFlags & RowMajorBit)) && (LhsFlags & PacketAccessBit) && (RowsAtCompileTime % ei_packet_traits<Scalar>::size == 0),
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_PacketAccess = (_LhsPacketAccess || _RhsPacketAccess) ? 1 : 0,
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_RowMajor = (RhsFlags & RowMajorBit)
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&& (EvalMode==(int)CacheFriendlyProduct ? (int)LhsFlags & RowMajorBit : (!_LhsPacketAccess)),
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_LostBits = HereditaryBits & ~(
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(_RowMajor ? 0 : RowMajorBit)
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| ((RowsAtCompileTime == Dynamic || ColsAtCompileTime == Dynamic) ? 0 : LargeBit)),
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Flags = ((unsigned int)(LhsFlags | RhsFlags) & _LostBits)
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| EvalBeforeAssigningBit
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| EvalBeforeNestingBit
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| (_PacketAccess ? PacketAccessBit : 0),
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CoeffReadCost
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= Lhs::ColsAtCompileTime == Dynamic
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? Dynamic
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: Lhs::ColsAtCompileTime
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* (NumTraits<Scalar>::MulCost + LhsCoeffReadCost + RhsCoeffReadCost)
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+ (Lhs::ColsAtCompileTime - 1) * NumTraits<Scalar>::AddCost
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};
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};
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template<typename Lhs, typename Rhs, int EvalMode> class Product : ei_no_assignment_operator,
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public MatrixBase<Product<Lhs, Rhs, EvalMode> >
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{
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public:
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EIGEN_GENERIC_PUBLIC_INTERFACE(Product)
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friend class ProductPacketImpl<Product,Flags&RowMajorBit>;
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typedef typename ei_traits<Product>::LhsNested LhsNested;
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typedef typename ei_traits<Product>::RhsNested RhsNested;
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typedef typename ei_traits<Product>::_LhsNested _LhsNested;
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typedef typename ei_traits<Product>::_RhsNested _RhsNested;
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inline Product(const Lhs& lhs, const Rhs& rhs)
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: m_lhs(lhs), m_rhs(rhs)
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{
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ei_assert(lhs.cols() == rhs.rows());
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}
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/** \internal */
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template<typename DestDerived, int AlignedMode>
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void _cacheOptimalEval(DestDerived& res, ei_meta_false) const;
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#ifdef EIGEN_VECTORIZE
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template<typename DestDerived, int AlignedMode>
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void _cacheOptimalEval(DestDerived& res, ei_meta_true) const;
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#endif
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private:
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inline int _rows() const { return m_lhs.rows(); }
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inline int _cols() const { return m_rhs.cols(); }
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const Scalar _coeff(int row, int col) const
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{
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Scalar res;
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const bool unroll = CoeffReadCost <= EIGEN_UNROLLING_LIMIT;
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if(unroll)
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{
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ei_product_unroller<Lhs::ColsAtCompileTime-1,
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unroll ? Lhs::ColsAtCompileTime : Dynamic,
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_LhsNested, _RhsNested>
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::run(row, col, m_lhs, m_rhs, res);
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}
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else
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{
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res = m_lhs.coeff(row, 0) * m_rhs.coeff(0, col);
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for(int i = 1; i < m_lhs.cols(); i++)
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res += m_lhs.coeff(row, i) * m_rhs.coeff(i, col);
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}
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return res;
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}
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template<int LoadMode>
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const PacketScalar _packet(int row, int col) const
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{
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if(Lhs::ColsAtCompileTime <= EIGEN_UNROLLING_LIMIT)
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{
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PacketScalar res;
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ei_packet_product_unroller<Flags&RowMajorBit, Lhs::ColsAtCompileTime-1,
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Lhs::ColsAtCompileTime <= EIGEN_UNROLLING_LIMIT
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? Lhs::ColsAtCompileTime : Dynamic,
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_LhsNested, _RhsNested, PacketScalar>
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::run(row, col, m_lhs, m_rhs, res);
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return res;
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}
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else
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return ProductPacketImpl<Product,Flags&RowMajorBit>::execute(*this, row, col);
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}
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const PacketScalar _packetRowMajor(int row, int col) const
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{
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PacketScalar res;
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res = ei_pmul(ei_pset1(m_lhs.coeff(row, 0)),m_rhs.template packet<Aligned>(0, col));
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for(int i = 1; i < m_lhs.cols(); i++)
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res = ei_pmadd(ei_pset1(m_lhs.coeff(row, i)), m_rhs.template packet<Aligned>(i, col), res);
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return res;
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}
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const PacketScalar _packetColumnMajor(int row, int col) const
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{
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PacketScalar res;
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res = ei_pmul(m_lhs.template packet<Aligned>(row, 0), ei_pset1(m_rhs.coeff(0, col)));
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for(int i = 1; i < m_lhs.cols(); i++)
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res = ei_pmadd(m_lhs.template packet<Aligned>(row, i), ei_pset1(m_rhs.coeff(i, col)), res);
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return res;
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// const PacketScalar tmp[4];
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// ei_punpack(m_rhs.packet(0,col), tmp);
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//
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// return
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// ei_pmadd(m_lhs.packet(row, 0), tmp[0],
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// ei_pmadd(m_lhs.packet(row, 1), tmp[1],
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// ei_pmadd(m_lhs.packet(row, 2), tmp[2]
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// ei_pmul(m_lhs.packet(row, 3), tmp[3]))));
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}
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protected:
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const LhsNested m_lhs;
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const RhsNested m_rhs;
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};
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/** \returns the matrix product of \c *this and \a other.
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*
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* \note This function causes an immediate evaluation. If you want to perform a matrix product
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* without immediate evaluation, call .lazy() on one of the matrices before taking the product.
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*
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* \sa lazy(), operator*=(const MatrixBase&)
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*/
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template<typename Derived>
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template<typename OtherDerived>
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inline const Product<Derived,OtherDerived>
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MatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const
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{
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return Product<Derived,OtherDerived>(derived(), other.derived());
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}
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/** replaces \c *this by \c *this * \a other.
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*
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* \returns a reference to \c *this
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*/
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template<typename Derived>
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template<typename OtherDerived>
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inline Derived &
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MatrixBase<Derived>::operator*=(const MatrixBase<OtherDerived> &other)
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{
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return *this = *this * other;
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}
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template<typename Derived>
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template<typename Lhs, typename Rhs>
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inline Derived& MatrixBase<Derived>::lazyAssign(const Product<Lhs,Rhs,CacheFriendlyProduct>& product)
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{
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product.template _cacheOptimalEval<Derived, Aligned>(derived(),
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#ifdef EIGEN_VECTORIZE
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typename ei_meta_if<Flags & PacketAccessBit, ei_meta_true, ei_meta_false>::ret()
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#else
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ei_meta_false()
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#endif
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);
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return derived();
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}
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template<typename Lhs, typename Rhs, int EvalMode>
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template<typename DestDerived, int AlignedMode>
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void Product<Lhs,Rhs,EvalMode>::_cacheOptimalEval(DestDerived& res, ei_meta_false) const
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{
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res.setZero();
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const int cols4 = m_lhs.cols() & 0xfffffffC;
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if (Lhs::Flags&RowMajorBit)
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{
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// std::cout << "opt rhs\n";
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int j=0;
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for(; j<cols4; j+=4)
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{
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for(int k=0; k<this->rows(); ++k)
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{
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const Scalar tmp0 = m_lhs.coeff(k,j );
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const Scalar tmp1 = m_lhs.coeff(k,j+1);
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const Scalar tmp2 = m_lhs.coeff(k,j+2);
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const Scalar tmp3 = m_lhs.coeff(k,j+3);
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for (int i=0; i<this->cols(); ++i)
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res.coeffRef(k,i) += tmp0 * m_rhs.coeff(j+0,i) + tmp1 * m_rhs.coeff(j+1,i)
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+ tmp2 * m_rhs.coeff(j+2,i) + tmp3 * m_rhs.coeff(j+3,i);
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}
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}
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for(; j<m_lhs.cols(); ++j)
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{
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for(int k=0; k<this->rows(); ++k)
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{
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const Scalar tmp = m_rhs.coeff(k,j);
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for (int i=0; i<this->cols(); ++i)
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res.coeffRef(k,i) += tmp * m_lhs.coeff(j,i);
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}
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}
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}
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else
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{
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// std::cout << "opt lhs\n";
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int j = 0;
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for(; j<cols4; j+=4)
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{
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for(int k=0; k<this->cols(); ++k)
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{
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const Scalar tmp0 = m_rhs.coeff(j ,k);
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const Scalar tmp1 = m_rhs.coeff(j+1,k);
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const Scalar tmp2 = m_rhs.coeff(j+2,k);
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const Scalar tmp3 = m_rhs.coeff(j+3,k);
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for (int i=0; i<this->rows(); ++i)
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res.coeffRef(i,k) += tmp0 * m_lhs.coeff(i,j+0) + tmp1 * m_lhs.coeff(i,j+1)
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+ tmp2 * m_lhs.coeff(i,j+2) + tmp3 * m_lhs.coeff(i,j+3);
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}
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}
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for(; j<m_lhs.cols(); ++j)
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{
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for(int k=0; k<this->cols(); ++k)
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{
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const Scalar tmp = m_rhs.coeff(j,k);
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for (int i=0; i<this->rows(); ++i)
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res.coeffRef(i,k) += tmp * m_lhs.coeff(i,j);
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}
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}
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}
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}
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#ifdef EIGEN_VECTORIZE
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template<typename Lhs, typename Rhs, int EvalMode>
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template<typename DestDerived, int AlignedMode>
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void Product<Lhs,Rhs,EvalMode>::_cacheOptimalEval(DestDerived& res, ei_meta_true) const
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{
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if (((Lhs::Flags&RowMajorBit) && (_cols() % ei_packet_traits<Scalar>::size != 0))
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|| (_rows() % ei_packet_traits<Scalar>::size != 0))
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{
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return _cacheOptimalEval<DestDerived, AlignedMode>(res, ei_meta_false());
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}
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res.setZero();
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const int cols4 = m_lhs.cols() & 0xfffffffC;
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if (Lhs::Flags&RowMajorBit)
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{
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// std::cout << "packet rhs\n";
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int j=0;
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for(; j<cols4; j+=4)
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{
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for(int k=0; k<this->rows(); k++)
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{
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const typename ei_packet_traits<Scalar>::type tmp0 = ei_pset1(m_lhs.coeff(k,j+0));
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const typename ei_packet_traits<Scalar>::type tmp1 = ei_pset1(m_lhs.coeff(k,j+1));
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const typename ei_packet_traits<Scalar>::type tmp2 = ei_pset1(m_lhs.coeff(k,j+2));
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const typename ei_packet_traits<Scalar>::type tmp3 = ei_pset1(m_lhs.coeff(k,j+3));
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for (int i=0; i<this->cols(); i+=ei_packet_traits<Scalar>::size)
|
|
{
|
|
res.template writePacket<AlignedMode>(k,i,
|
|
ei_pmadd(tmp0, m_rhs.template packet<AlignedMode>(j+0,i),
|
|
ei_pmadd(tmp1, m_rhs.template packet<AlignedMode>(j+1,i),
|
|
ei_pmadd(tmp2, m_rhs.template packet<AlignedMode>(j+2,i),
|
|
ei_pmadd(tmp3, m_rhs.template packet<AlignedMode>(j+3,i),
|
|
res.template packet<AlignedMode>(k,i)))))
|
|
);
|
|
}
|
|
}
|
|
}
|
|
for(; j<m_lhs.cols(); ++j)
|
|
{
|
|
for(int k=0; k<this->rows(); k++)
|
|
{
|
|
const typename ei_packet_traits<Scalar>::type tmp = ei_pset1(m_lhs.coeff(k,j));
|
|
for (int i=0; i<this->cols(); i+=ei_packet_traits<Scalar>::size)
|
|
res.template writePacket<AlignedMode>(k,i,
|
|
ei_pmadd(tmp, m_rhs.template packet<AlignedMode>(j,i), res.template packet<AlignedMode>(k,i)));
|
|
}
|
|
}
|
|
}
|
|
else
|
|
{
|
|
// std::cout << "packet lhs\n";
|
|
int k=0;
|
|
for(; k<cols4; k+=4)
|
|
{
|
|
for(int j=0; j<this->cols(); j+=1)
|
|
{
|
|
const typename ei_packet_traits<Scalar>::type tmp0 = ei_pset1(m_rhs.coeff(k+0,j));
|
|
const typename ei_packet_traits<Scalar>::type tmp1 = ei_pset1(m_rhs.coeff(k+1,j));
|
|
const typename ei_packet_traits<Scalar>::type tmp2 = ei_pset1(m_rhs.coeff(k+2,j));
|
|
const typename ei_packet_traits<Scalar>::type tmp3 = ei_pset1(m_rhs.coeff(k+3,j));
|
|
|
|
for (int i=0; i<this->rows(); i+=ei_packet_traits<Scalar>::size)
|
|
{
|
|
res.template writePacket<AlignedMode>(i,j,
|
|
ei_pmadd(tmp0, m_lhs.template packet<AlignedMode>(i,k),
|
|
ei_pmadd(tmp1, m_lhs.template packet<AlignedMode>(i,k+1),
|
|
ei_pmadd(tmp2, m_lhs.template packet<AlignedMode>(i,k+2),
|
|
ei_pmadd(tmp3, m_lhs.template packet<AlignedMode>(i,k+3),
|
|
res.template packet<AlignedMode>(i,j)))))
|
|
);
|
|
}
|
|
}
|
|
}
|
|
for(; k<m_lhs.cols(); ++k)
|
|
{
|
|
for(int j=0; j<this->cols(); j++)
|
|
{
|
|
const typename ei_packet_traits<Scalar>::type tmp = ei_pset1(m_rhs.coeff(k,j));
|
|
for (int i=0; i<this->rows(); i+=ei_packet_traits<Scalar>::size)
|
|
res.template writePacket<AlignedMode>(k,j,
|
|
ei_pmadd(tmp, m_lhs.template packet<AlignedMode>(i,k), res.template packet<AlignedMode>(i,j)));
|
|
}
|
|
}
|
|
}
|
|
}
|
|
#endif // EIGEN_VECTORIZE
|
|
|
|
#endif // EIGEN_PRODUCT_H
|