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Improve performance of row-major-dense-matrix * vector products for recent CPUs.
This revised version does not bother about aligned loads/stores, and rather processes 8 rows at ones for better instruction pipelining.
This commit is contained in:
Gael Guennebaud
parent
3abc827354
commit
e3f613cbd4
@ -242,253 +242,161 @@ EIGEN_DONT_INLINE static void run(
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template<typename Index, typename LhsScalar, typename LhsMapper, bool ConjugateLhs, typename RhsScalar, typename RhsMapper, bool ConjugateRhs, int Version>
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template<typename Index, typename LhsScalar, typename LhsMapper, bool ConjugateLhs, typename RhsScalar, typename RhsMapper, bool ConjugateRhs, int Version>
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EIGEN_DONT_INLINE void general_matrix_vector_product<Index,LhsScalar,LhsMapper,RowMajor,ConjugateLhs,RhsScalar,RhsMapper,ConjugateRhs,Version>::run(
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EIGEN_DONT_INLINE void general_matrix_vector_product<Index,LhsScalar,LhsMapper,RowMajor,ConjugateLhs,RhsScalar,RhsMapper,ConjugateRhs,Version>::run(
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Index rows, Index cols,
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Index rows, Index cols,
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const LhsMapper& lhs,
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const LhsMapper& alhs,
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const RhsMapper& rhs,
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const RhsMapper& rhs,
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ResScalar* res, Index resIncr,
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ResScalar* res, Index resIncr,
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ResScalar alpha)
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ResScalar alpha)
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{
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{
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// The following copy tells the compiler that lhs's attributes are not modified outside this function
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// This helps GCC to generate propoer code.
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LhsMapper lhs(alhs);
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eigen_internal_assert(rhs.stride()==1);
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eigen_internal_assert(rhs.stride()==1);
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#ifdef _EIGEN_ACCUMULATE_PACKETS
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#error _EIGEN_ACCUMULATE_PACKETS has already been defined
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#endif
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#define _EIGEN_ACCUMULATE_PACKETS(Alignment0,Alignment13,Alignment2) {\
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RhsPacket b = rhs.getVectorMapper(j, 0).template load<RhsPacket, Aligned>(0); \
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ptmp0 = pcj.pmadd(lhs0.template load<LhsPacket, Alignment0>(j), b, ptmp0); \
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ptmp1 = pcj.pmadd(lhs1.template load<LhsPacket, Alignment13>(j), b, ptmp1); \
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ptmp2 = pcj.pmadd(lhs2.template load<LhsPacket, Alignment2>(j), b, ptmp2); \
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ptmp3 = pcj.pmadd(lhs3.template load<LhsPacket, Alignment13>(j), b, ptmp3); }
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conj_helper<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs> cj;
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conj_helper<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs> cj;
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conj_helper<LhsPacket,RhsPacket,ConjugateLhs,ConjugateRhs> pcj;
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conj_helper<LhsPacket,RhsPacket,ConjugateLhs,ConjugateRhs> pcj;
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typedef typename LhsMapper::VectorMapper LhsScalars;
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// TODO: fine tune the following heuristic. The rationale is that if the matrix is very large,
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// processing 8 rows at once might be counter productive wrt cache.
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const Index n8 = lhs.stride()*sizeof(LhsScalar)>32000 ? 0 : rows-7;
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const Index n4 = rows-3;
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const Index n2 = rows-1;
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enum { AllAligned=0, EvenAligned=1, FirstAligned=2, NoneAligned=3 };
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// TODO: for padded aligned inputs, we could enable aligned reads
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const Index rowsAtOnce = 4;
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enum { LhsAlignment = Unaligned };
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const Index peels = 2;
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const Index RhsPacketAlignedMask = RhsPacketSize-1;
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const Index LhsPacketAlignedMask = LhsPacketSize-1;
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const Index depth = cols;
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const Index lhsStride = lhs.stride();
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// How many coeffs of the result do we have to skip to be aligned.
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Index i=0;
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// Here we assume data are at least aligned on the base scalar type
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for(; i<n8; i+=8)
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// if that's not the case then vectorization is discarded, see below.
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Index alignedStart = rhs.firstAligned(depth);
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Index alignedSize = RhsPacketSize>1 ? alignedStart + ((depth-alignedStart) & ~RhsPacketAlignedMask) : 0;
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const Index peeledSize = alignedSize - RhsPacketSize*peels - RhsPacketSize + 1;
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const Index alignmentStep = LhsPacketSize>1 ? (LhsPacketSize - lhsStride % LhsPacketSize) & LhsPacketAlignedMask : 0;
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Index alignmentPattern = alignmentStep==0 ? AllAligned
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: alignmentStep==(LhsPacketSize/2) ? EvenAligned
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: FirstAligned;
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// we cannot assume the first element is aligned because of sub-matrices
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const Index lhsAlignmentOffset = lhs.firstAligned(depth);
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const Index rhsAlignmentOffset = rhs.firstAligned(rows);
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// find how many rows do we have to skip to be aligned with rhs (if possible)
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Index skipRows = 0;
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// if the data cannot be aligned (TODO add some compile time tests when possible, e.g. for floats)
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if( (sizeof(LhsScalar)!=sizeof(RhsScalar)) ||
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(lhsAlignmentOffset < 0) || (lhsAlignmentOffset == depth) ||
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(rhsAlignmentOffset < 0) || (rhsAlignmentOffset == rows) )
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{
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{
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alignedSize = 0;
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ResPacket c0 = pset1<ResPacket>(ResScalar(0)),
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alignedStart = 0;
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c1 = pset1<ResPacket>(ResScalar(0)),
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alignmentPattern = NoneAligned;
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c2 = pset1<ResPacket>(ResScalar(0)),
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}
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c3 = pset1<ResPacket>(ResScalar(0)),
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else if(LhsPacketSize > 4)
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c4 = pset1<ResPacket>(ResScalar(0)),
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{
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c5 = pset1<ResPacket>(ResScalar(0)),
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// TODO: extend the code to support aligned loads whenever possible when LhsPacketSize > 4.
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c6 = pset1<ResPacket>(ResScalar(0)),
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alignmentPattern = NoneAligned;
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c7 = pset1<ResPacket>(ResScalar(0));
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}
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else if (LhsPacketSize>1)
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{
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// eigen_internal_assert(size_t(firstLhs+lhsAlignmentOffset)%sizeof(LhsPacket)==0 || depth<LhsPacketSize);
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while (skipRows<LhsPacketSize &&
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Index j=0;
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alignedStart != ((lhsAlignmentOffset + alignmentStep*skipRows)%LhsPacketSize))
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for(; j+LhsPacketSize<=cols; j+=LhsPacketSize)
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++skipRows;
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if (skipRows==LhsPacketSize)
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{
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{
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// nothing can be aligned, no need to skip any column
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RhsPacket b0 = rhs.template load<RhsPacket, Unaligned>(j,0);
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alignmentPattern = NoneAligned;
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skipRows = 0;
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c0 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+0,j),b0,c0);
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c1 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+1,j),b0,c1);
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c2 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+2,j),b0,c2);
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c3 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+3,j),b0,c3);
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c4 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+4,j),b0,c4);
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c5 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+5,j),b0,c5);
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c6 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+6,j),b0,c6);
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c7 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+7,j),b0,c7);
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}
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}
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else
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ResScalar cc0 = predux(c0);
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ResScalar cc1 = predux(c1);
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ResScalar cc2 = predux(c2);
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ResScalar cc3 = predux(c3);
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ResScalar cc4 = predux(c4);
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ResScalar cc5 = predux(c5);
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ResScalar cc6 = predux(c6);
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ResScalar cc7 = predux(c7);
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for(; j<cols; ++j)
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{
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{
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skipRows = (std::min)(skipRows,Index(rows));
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RhsScalar b0 = rhs(j,0);
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// note that the skiped columns are processed later.
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cc0 += cj.pmul(lhs(i+0,j), b0);
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cc1 += cj.pmul(lhs(i+1,j), b0);
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cc2 += cj.pmul(lhs(i+2,j), b0);
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cc3 += cj.pmul(lhs(i+3,j), b0);
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cc4 += cj.pmul(lhs(i+4,j), b0);
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cc5 += cj.pmul(lhs(i+5,j), b0);
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cc6 += cj.pmul(lhs(i+6,j), b0);
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cc7 += cj.pmul(lhs(i+7,j), b0);
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}
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}
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/* eigen_internal_assert( alignmentPattern==NoneAligned
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res[(i+0)*resIncr] += alpha*cc0;
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|| LhsPacketSize==1
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res[(i+1)*resIncr] += alpha*cc1;
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|| (skipRows + rowsAtOnce >= rows)
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res[(i+2)*resIncr] += alpha*cc2;
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|| LhsPacketSize > depth
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res[(i+3)*resIncr] += alpha*cc3;
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|| (size_t(firstLhs+alignedStart+lhsStride*skipRows)%sizeof(LhsPacket))==0);*/
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res[(i+4)*resIncr] += alpha*cc4;
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res[(i+5)*resIncr] += alpha*cc5;
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res[(i+6)*resIncr] += alpha*cc6;
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res[(i+7)*resIncr] += alpha*cc7;
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}
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}
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else if(Vectorizable)
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for(; i<n4; i+=4)
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{
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{
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alignedStart = 0;
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ResPacket c0 = pset1<ResPacket>(ResScalar(0)),
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alignedSize = depth;
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c1 = pset1<ResPacket>(ResScalar(0)),
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alignmentPattern = AllAligned;
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c2 = pset1<ResPacket>(ResScalar(0)),
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c3 = pset1<ResPacket>(ResScalar(0));
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Index j=0;
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for(; j+LhsPacketSize<=cols; j+=LhsPacketSize)
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{
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RhsPacket b0 = rhs.template load<RhsPacket, Unaligned>(j,0);
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c0 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+0,j),b0,c0);
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c1 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+1,j),b0,c1);
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c2 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+2,j),b0,c2);
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c3 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+3,j),b0,c3);
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}
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ResScalar cc0 = predux(c0);
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ResScalar cc1 = predux(c1);
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ResScalar cc2 = predux(c2);
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ResScalar cc3 = predux(c3);
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for(; j<cols; ++j)
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{
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RhsScalar b0 = rhs(j,0);
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cc0 += cj.pmul(lhs(i+0,j), b0);
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cc1 += cj.pmul(lhs(i+1,j), b0);
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cc2 += cj.pmul(lhs(i+2,j), b0);
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cc3 += cj.pmul(lhs(i+3,j), b0);
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}
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res[(i+0)*resIncr] += alpha*cc0;
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res[(i+1)*resIncr] += alpha*cc1;
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res[(i+2)*resIncr] += alpha*cc2;
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res[(i+3)*resIncr] += alpha*cc3;
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}
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}
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for(; i<n2; i+=2)
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const Index offset1 = (FirstAligned && alignmentStep==1)?3:1;
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const Index offset3 = (FirstAligned && alignmentStep==1)?1:3;
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Index rowBound = ((rows-skipRows)/rowsAtOnce)*rowsAtOnce + skipRows;
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for (Index i=skipRows; i<rowBound; i+=rowsAtOnce)
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{
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{
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// FIXME: what is the purpose of this EIGEN_ALIGN_DEFAULT ??
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ResPacket c0 = pset1<ResPacket>(ResScalar(0)),
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EIGEN_ALIGN_MAX ResScalar tmp0 = ResScalar(0);
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c1 = pset1<ResPacket>(ResScalar(0));
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ResScalar tmp1 = ResScalar(0), tmp2 = ResScalar(0), tmp3 = ResScalar(0);
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// this helps the compiler generating good binary code
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Index j=0;
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const LhsScalars lhs0 = lhs.getVectorMapper(i+0, 0), lhs1 = lhs.getVectorMapper(i+offset1, 0),
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for(; j+LhsPacketSize<=cols; j+=LhsPacketSize)
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lhs2 = lhs.getVectorMapper(i+2, 0), lhs3 = lhs.getVectorMapper(i+offset3, 0);
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if (Vectorizable)
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{
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{
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/* explicit vectorization */
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RhsPacket b0 = rhs.template load<RhsPacket, Unaligned>(j,0);
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ResPacket ptmp0 = pset1<ResPacket>(ResScalar(0)), ptmp1 = pset1<ResPacket>(ResScalar(0)),
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ptmp2 = pset1<ResPacket>(ResScalar(0)), ptmp3 = pset1<ResPacket>(ResScalar(0));
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// process initial unaligned coeffs
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c0 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+0,j),b0,c0);
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// FIXME this loop get vectorized by the compiler !
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c1 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+1,j),b0,c1);
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for (Index j=0; j<alignedStart; ++j)
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{
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RhsScalar b = rhs(j, 0);
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tmp0 += cj.pmul(lhs0(j),b); tmp1 += cj.pmul(lhs1(j),b);
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tmp2 += cj.pmul(lhs2(j),b); tmp3 += cj.pmul(lhs3(j),b);
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}
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if (alignedSize>alignedStart)
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{
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switch(alignmentPattern)
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{
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case AllAligned:
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for (Index j = alignedStart; j<alignedSize; j+=RhsPacketSize)
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_EIGEN_ACCUMULATE_PACKETS(Aligned,Aligned,Aligned);
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break;
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case EvenAligned:
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for (Index j = alignedStart; j<alignedSize; j+=RhsPacketSize)
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_EIGEN_ACCUMULATE_PACKETS(Aligned,Unaligned,Aligned);
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break;
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case FirstAligned:
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{
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Index j = alignedStart;
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if (peels>1)
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{
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/* Here we proccess 4 rows with with two peeled iterations to hide
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* the overhead of unaligned loads. Moreover unaligned loads are handled
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* using special shift/move operations between the two aligned packets
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* overlaping the desired unaligned packet. This is *much* more efficient
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* than basic unaligned loads.
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*/
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LhsPacket A01, A02, A03, A11, A12, A13;
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A01 = lhs1.template load<LhsPacket, Aligned>(alignedStart-1);
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A02 = lhs2.template load<LhsPacket, Aligned>(alignedStart-2);
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A03 = lhs3.template load<LhsPacket, Aligned>(alignedStart-3);
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for (; j<peeledSize; j+=peels*RhsPacketSize)
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{
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RhsPacket b = rhs.getVectorMapper(j, 0).template load<RhsPacket, Aligned>(0);
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A11 = lhs1.template load<LhsPacket, Aligned>(j-1+LhsPacketSize); palign<1>(A01,A11);
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A12 = lhs2.template load<LhsPacket, Aligned>(j-2+LhsPacketSize); palign<2>(A02,A12);
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A13 = lhs3.template load<LhsPacket, Aligned>(j-3+LhsPacketSize); palign<3>(A03,A13);
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ptmp0 = pcj.pmadd(lhs0.template load<LhsPacket, Aligned>(j), b, ptmp0);
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ptmp1 = pcj.pmadd(A01, b, ptmp1);
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A01 = lhs1.template load<LhsPacket, Aligned>(j-1+2*LhsPacketSize); palign<1>(A11,A01);
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ptmp2 = pcj.pmadd(A02, b, ptmp2);
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A02 = lhs2.template load<LhsPacket, Aligned>(j-2+2*LhsPacketSize); palign<2>(A12,A02);
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ptmp3 = pcj.pmadd(A03, b, ptmp3);
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A03 = lhs3.template load<LhsPacket, Aligned>(j-3+2*LhsPacketSize); palign<3>(A13,A03);
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b = rhs.getVectorMapper(j+RhsPacketSize, 0).template load<RhsPacket, Aligned>(0);
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ptmp0 = pcj.pmadd(lhs0.template load<LhsPacket, Aligned>(j+LhsPacketSize), b, ptmp0);
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ptmp1 = pcj.pmadd(A11, b, ptmp1);
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ptmp2 = pcj.pmadd(A12, b, ptmp2);
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ptmp3 = pcj.pmadd(A13, b, ptmp3);
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}
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}
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for (; j<alignedSize; j+=RhsPacketSize)
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_EIGEN_ACCUMULATE_PACKETS(Aligned,Unaligned,Unaligned);
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break;
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}
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default:
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for (Index j = alignedStart; j<alignedSize; j+=RhsPacketSize)
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_EIGEN_ACCUMULATE_PACKETS(Unaligned,Unaligned,Unaligned);
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break;
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}
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tmp0 += predux(ptmp0);
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tmp1 += predux(ptmp1);
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tmp2 += predux(ptmp2);
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tmp3 += predux(ptmp3);
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}
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} // end explicit vectorization
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// process remaining coeffs (or all if no explicit vectorization)
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// FIXME this loop get vectorized by the compiler !
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for (Index j=alignedSize; j<depth; ++j)
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{
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RhsScalar b = rhs(j, 0);
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tmp0 += cj.pmul(lhs0(j),b); tmp1 += cj.pmul(lhs1(j),b);
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tmp2 += cj.pmul(lhs2(j),b); tmp3 += cj.pmul(lhs3(j),b);
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}
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}
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res[i*resIncr] += alpha*tmp0;
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ResScalar cc0 = predux(c0);
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res[(i+offset1)*resIncr] += alpha*tmp1;
|
ResScalar cc1 = predux(c1);
|
||||||
res[(i+2)*resIncr] += alpha*tmp2;
|
for(; j<cols; ++j)
|
||||||
res[(i+offset3)*resIncr] += alpha*tmp3;
|
{
|
||||||
|
RhsScalar b0 = rhs(j,0);
|
||||||
|
|
||||||
|
cc0 += cj.pmul(lhs(i+0,j), b0);
|
||||||
|
cc1 += cj.pmul(lhs(i+1,j), b0);
|
||||||
|
}
|
||||||
|
res[(i+0)*resIncr] += alpha*cc0;
|
||||||
|
res[(i+1)*resIncr] += alpha*cc1;
|
||||||
}
|
}
|
||||||
|
for(; i<rows; ++i)
|
||||||
// process remaining first and last rows (at most columnsAtOnce-1)
|
|
||||||
Index end = rows;
|
|
||||||
Index start = rowBound;
|
|
||||||
do
|
|
||||||
{
|
{
|
||||||
for (Index i=start; i<end; ++i)
|
ResPacket c0 = pset1<ResPacket>(ResScalar(0));
|
||||||
|
Index j=0;
|
||||||
|
for(; j+LhsPacketSize<=cols; j+=LhsPacketSize)
|
||||||
{
|
{
|
||||||
EIGEN_ALIGN_MAX ResScalar tmp0 = ResScalar(0);
|
RhsPacket b0 = rhs.template load<RhsPacket,Unaligned>(j,0);
|
||||||
ResPacket ptmp0 = pset1<ResPacket>(tmp0);
|
c0 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i,j),b0,c0);
|
||||||
const LhsScalars lhs0 = lhs.getVectorMapper(i, 0);
|
|
||||||
// process first unaligned result's coeffs
|
|
||||||
// FIXME this loop get vectorized by the compiler !
|
|
||||||
for (Index j=0; j<alignedStart; ++j)
|
|
||||||
tmp0 += cj.pmul(lhs0(j), rhs(j, 0));
|
|
||||||
|
|
||||||
if (alignedSize>alignedStart)
|
|
||||||
{
|
|
||||||
// process aligned rhs coeffs
|
|
||||||
if (lhs0.template aligned<LhsPacket>(alignedStart))
|
|
||||||
for (Index j = alignedStart;j<alignedSize;j+=RhsPacketSize)
|
|
||||||
ptmp0 = pcj.pmadd(lhs0.template load<LhsPacket, Aligned>(j), rhs.getVectorMapper(j, 0).template load<RhsPacket, Aligned>(0), ptmp0);
|
|
||||||
else
|
|
||||||
for (Index j = alignedStart;j<alignedSize;j+=RhsPacketSize)
|
|
||||||
ptmp0 = pcj.pmadd(lhs0.template load<LhsPacket, Unaligned>(j), rhs.getVectorMapper(j, 0).template load<RhsPacket, Aligned>(0), ptmp0);
|
|
||||||
tmp0 += predux(ptmp0);
|
|
||||||
}
|
|
||||||
|
|
||||||
// process remaining scalars
|
|
||||||
// FIXME this loop get vectorized by the compiler !
|
|
||||||
for (Index j=alignedSize; j<depth; ++j)
|
|
||||||
tmp0 += cj.pmul(lhs0(j), rhs(j, 0));
|
|
||||||
res[i*resIncr] += alpha*tmp0;
|
|
||||||
}
|
}
|
||||||
if (skipRows)
|
ResScalar cc0 = predux(c0);
|
||||||
|
for(; j<cols; ++j)
|
||||||
{
|
{
|
||||||
start = 0;
|
cc0 += cj.pmul(lhs(i,j), rhs(j,0));
|
||||||
end = skipRows;
|
|
||||||
skipRows = 0;
|
|
||||||
}
|
}
|
||||||
else
|
res[i*resIncr] += alpha*cc0;
|
||||||
break;
|
}
|
||||||
} while(Vectorizable);
|
#endif
|
||||||
|
|
||||||
#undef _EIGEN_ACCUMULATE_PACKETS
|
|
||||||
}
|
}
|
||||||
|
|
||||||
} // end namespace internal
|
} // end namespace internal
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user