| Current File : //usr/include/eigen3/Eigen/src/Core/products/GeneralMatrixVector.h |
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// 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_GENERAL_MATRIX_VECTOR_H
#define EIGEN_GENERAL_MATRIX_VECTOR_H
namespace Eigen {
namespace internal {
/* Optimized col-major matrix * vector product:
* This algorithm processes 4 columns at onces that allows to both reduce
* the number of load/stores of the result by a factor 4 and to reduce
* the instruction dependency. Moreover, we know that all bands have the
* same alignment pattern.
*
* Mixing type logic: C += alpha * A * B
* | A | B |alpha| comments
* |real |cplx |cplx | no vectorization
* |real |cplx |real | alpha is converted to a cplx when calling the run function, no vectorization
* |cplx |real |cplx | invalid, the caller has to do tmp: = A * B; C += alpha*tmp
* |cplx |real |real | optimal case, vectorization possible via real-cplx mul
*
* Accesses to the matrix coefficients follow the following logic:
*
* - if all columns have the same alignment then
* - if the columns have the same alignment as the result vector, then easy! (-> AllAligned case)
* - otherwise perform unaligned loads only (-> NoneAligned case)
* - otherwise
* - if even columns have the same alignment then
* // odd columns are guaranteed to have the same alignment too
* - if even or odd columns have the same alignment as the result, then
* // for a register size of 2 scalars, this is guarantee to be the case (e.g., SSE with double)
* - perform half aligned and half unaligned loads (-> EvenAligned case)
* - otherwise perform unaligned loads only (-> NoneAligned case)
* - otherwise, if the register size is 4 scalars (e.g., SSE with float) then
* - one over 4 consecutive columns is guaranteed to be aligned with the result vector,
* perform simple aligned loads for this column and aligned loads plus re-alignment for the other. (-> FirstAligned case)
* // this re-alignment is done by the palign function implemented for SSE in Eigen/src/Core/arch/SSE/PacketMath.h
* - otherwise,
* // if we get here, this means the register size is greater than 4 (e.g., AVX with floats),
* // we currently fall back to the NoneAligned case
*
* The same reasoning apply for the transposed case.
*
* The last case (PacketSize>4) could probably be improved by generalizing the FirstAligned case, but since we do not support AVX yet...
* One might also wonder why in the EvenAligned case we perform unaligned loads instead of using the aligned-loads plus re-alignment
* strategy as in the FirstAligned case. The reason is that we observed that unaligned loads on a 8 byte boundary are not too slow
* compared to unaligned loads on a 4 byte boundary.
*
*/
template<typename Index, typename LhsScalar, typename LhsMapper, bool ConjugateLhs, typename RhsScalar, typename RhsMapper, bool ConjugateRhs, int Version>
struct general_matrix_vector_product<Index,LhsScalar,LhsMapper,ColMajor,ConjugateLhs,RhsScalar,RhsMapper,ConjugateRhs,Version>
{
typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
enum {
Vectorizable = packet_traits<LhsScalar>::Vectorizable && packet_traits<RhsScalar>::Vectorizable
&& int(packet_traits<LhsScalar>::size)==int(packet_traits<RhsScalar>::size),
LhsPacketSize = Vectorizable ? packet_traits<LhsScalar>::size : 1,
RhsPacketSize = Vectorizable ? packet_traits<RhsScalar>::size : 1,
ResPacketSize = Vectorizable ? packet_traits<ResScalar>::size : 1
};
typedef typename packet_traits<LhsScalar>::type _LhsPacket;
typedef typename packet_traits<RhsScalar>::type _RhsPacket;
typedef typename packet_traits<ResScalar>::type _ResPacket;
typedef typename conditional<Vectorizable,_LhsPacket,LhsScalar>::type LhsPacket;
typedef typename conditional<Vectorizable,_RhsPacket,RhsScalar>::type RhsPacket;
typedef typename conditional<Vectorizable,_ResPacket,ResScalar>::type ResPacket;
EIGEN_DONT_INLINE static void run(
Index rows, Index cols,
const LhsMapper& lhs,
const RhsMapper& rhs,
ResScalar* res, Index resIncr,
RhsScalar alpha);
};
template<typename Index, typename LhsScalar, typename LhsMapper, bool ConjugateLhs, typename RhsScalar, typename RhsMapper, bool ConjugateRhs, int Version>
EIGEN_DONT_INLINE void general_matrix_vector_product<Index,LhsScalar,LhsMapper,ColMajor,ConjugateLhs,RhsScalar,RhsMapper,ConjugateRhs,Version>::run(
Index rows, Index cols,
const LhsMapper& lhs,
const RhsMapper& rhs,
ResScalar* res, Index resIncr,
RhsScalar alpha)
{
EIGEN_UNUSED_VARIABLE(resIncr);
eigen_internal_assert(resIncr==1);
#ifdef _EIGEN_ACCUMULATE_PACKETS
#error _EIGEN_ACCUMULATE_PACKETS has already been defined
#endif
#define _EIGEN_ACCUMULATE_PACKETS(Alignment0,Alignment13,Alignment2) \
pstore(&res[j], \
padd(pload<ResPacket>(&res[j]), \
padd( \
padd(pcj.pmul(lhs0.template load<LhsPacket, Alignment0>(j), ptmp0), \
pcj.pmul(lhs1.template load<LhsPacket, Alignment13>(j), ptmp1)), \
padd(pcj.pmul(lhs2.template load<LhsPacket, Alignment2>(j), ptmp2), \
pcj.pmul(lhs3.template load<LhsPacket, Alignment13>(j), ptmp3)) )))
typedef typename LhsMapper::VectorMapper LhsScalars;
conj_helper<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs> cj;
conj_helper<LhsPacket,RhsPacket,ConjugateLhs,ConjugateRhs> pcj;
if(ConjugateRhs)
alpha = numext::conj(alpha);
enum { AllAligned = 0, EvenAligned, FirstAligned, NoneAligned };
const Index columnsAtOnce = 4;
const Index peels = 2;
const Index LhsPacketAlignedMask = LhsPacketSize-1;
const Index ResPacketAlignedMask = ResPacketSize-1;
// const Index PeelAlignedMask = ResPacketSize*peels-1;
const Index size = rows;
const Index lhsStride = lhs.stride();
// How many coeffs of the result do we have to skip to be aligned.
// Here we assume data are at least aligned on the base scalar type.
Index alignedStart = internal::first_default_aligned(res,size);
Index alignedSize = ResPacketSize>1 ? alignedStart + ((size-alignedStart) & ~ResPacketAlignedMask) : 0;
const Index peeledSize = alignedSize - RhsPacketSize*peels - RhsPacketSize + 1;
const Index alignmentStep = LhsPacketSize>1 ? (LhsPacketSize - lhsStride % LhsPacketSize) & LhsPacketAlignedMask : 0;
Index alignmentPattern = alignmentStep==0 ? AllAligned
: alignmentStep==(LhsPacketSize/2) ? EvenAligned
: FirstAligned;
// we cannot assume the first element is aligned because of sub-matrices
const Index lhsAlignmentOffset = lhs.firstAligned(size);
// find how many columns do we have to skip to be aligned with the result (if possible)
Index skipColumns = 0;
// if the data cannot be aligned (TODO add some compile time tests when possible, e.g. for floats)
if( (lhsAlignmentOffset < 0) || (lhsAlignmentOffset == size) || (UIntPtr(res)%sizeof(ResScalar)) )
{
alignedSize = 0;
alignedStart = 0;
alignmentPattern = NoneAligned;
}
else if(LhsPacketSize > 4)
{
// TODO: extend the code to support aligned loads whenever possible when LhsPacketSize > 4.
// Currently, it seems to be better to perform unaligned loads anyway
alignmentPattern = NoneAligned;
}
else if (LhsPacketSize>1)
{
// eigen_internal_assert(size_t(firstLhs+lhsAlignmentOffset)%sizeof(LhsPacket)==0 || size<LhsPacketSize);
while (skipColumns<LhsPacketSize &&
alignedStart != ((lhsAlignmentOffset + alignmentStep*skipColumns)%LhsPacketSize))
++skipColumns;
if (skipColumns==LhsPacketSize)
{
// nothing can be aligned, no need to skip any column
alignmentPattern = NoneAligned;
skipColumns = 0;
}
else
{
skipColumns = (std::min)(skipColumns,cols);
// note that the skiped columns are processed later.
}
/* eigen_internal_assert( (alignmentPattern==NoneAligned)
|| (skipColumns + columnsAtOnce >= cols)
|| LhsPacketSize > size
|| (size_t(firstLhs+alignedStart+lhsStride*skipColumns)%sizeof(LhsPacket))==0);*/
}
else if(Vectorizable)
{
alignedStart = 0;
alignedSize = size;
alignmentPattern = AllAligned;
}
const Index offset1 = (alignmentPattern==FirstAligned && alignmentStep==1)?3:1;
const Index offset3 = (alignmentPattern==FirstAligned && alignmentStep==1)?1:3;
Index columnBound = ((cols-skipColumns)/columnsAtOnce)*columnsAtOnce + skipColumns;
for (Index i=skipColumns; i<columnBound; i+=columnsAtOnce)
{
RhsPacket ptmp0 = pset1<RhsPacket>(alpha*rhs(i, 0)),
ptmp1 = pset1<RhsPacket>(alpha*rhs(i+offset1, 0)),
ptmp2 = pset1<RhsPacket>(alpha*rhs(i+2, 0)),
ptmp3 = pset1<RhsPacket>(alpha*rhs(i+offset3, 0));
// this helps a lot generating better binary code
const LhsScalars lhs0 = lhs.getVectorMapper(0, i+0), lhs1 = lhs.getVectorMapper(0, i+offset1),
lhs2 = lhs.getVectorMapper(0, i+2), lhs3 = lhs.getVectorMapper(0, i+offset3);
if (Vectorizable)
{
/* explicit vectorization */
// process initial unaligned coeffs
for (Index j=0; j<alignedStart; ++j)
{
res[j] = cj.pmadd(lhs0(j), pfirst(ptmp0), res[j]);
res[j] = cj.pmadd(lhs1(j), pfirst(ptmp1), res[j]);
res[j] = cj.pmadd(lhs2(j), pfirst(ptmp2), res[j]);
res[j] = cj.pmadd(lhs3(j), pfirst(ptmp3), res[j]);
}
if (alignedSize>alignedStart)
{
switch(alignmentPattern)
{
case AllAligned:
for (Index j = alignedStart; j<alignedSize; j+=ResPacketSize)
_EIGEN_ACCUMULATE_PACKETS(Aligned,Aligned,Aligned);
break;
case EvenAligned:
for (Index j = alignedStart; j<alignedSize; j+=ResPacketSize)
_EIGEN_ACCUMULATE_PACKETS(Aligned,Unaligned,Aligned);
break;
case FirstAligned:
{
Index j = alignedStart;
if(peels>1)
{
LhsPacket A00, A01, A02, A03, A10, A11, A12, A13;
ResPacket T0, T1;
A01 = lhs1.template load<LhsPacket, Aligned>(alignedStart-1);
A02 = lhs2.template load<LhsPacket, Aligned>(alignedStart-2);
A03 = lhs3.template load<LhsPacket, Aligned>(alignedStart-3);
for (; j<peeledSize; j+=peels*ResPacketSize)
{
A11 = lhs1.template load<LhsPacket, Aligned>(j-1+LhsPacketSize); palign<1>(A01,A11);
A12 = lhs2.template load<LhsPacket, Aligned>(j-2+LhsPacketSize); palign<2>(A02,A12);
A13 = lhs3.template load<LhsPacket, Aligned>(j-3+LhsPacketSize); palign<3>(A03,A13);
A00 = lhs0.template load<LhsPacket, Aligned>(j);
A10 = lhs0.template load<LhsPacket, Aligned>(j+LhsPacketSize);
T0 = pcj.pmadd(A00, ptmp0, pload<ResPacket>(&res[j]));
T1 = pcj.pmadd(A10, ptmp0, pload<ResPacket>(&res[j+ResPacketSize]));
T0 = pcj.pmadd(A01, ptmp1, T0);
A01 = lhs1.template load<LhsPacket, Aligned>(j-1+2*LhsPacketSize); palign<1>(A11,A01);
T0 = pcj.pmadd(A02, ptmp2, T0);
A02 = lhs2.template load<LhsPacket, Aligned>(j-2+2*LhsPacketSize); palign<2>(A12,A02);
T0 = pcj.pmadd(A03, ptmp3, T0);
pstore(&res[j],T0);
A03 = lhs3.template load<LhsPacket, Aligned>(j-3+2*LhsPacketSize); palign<3>(A13,A03);
T1 = pcj.pmadd(A11, ptmp1, T1);
T1 = pcj.pmadd(A12, ptmp2, T1);
T1 = pcj.pmadd(A13, ptmp3, T1);
pstore(&res[j+ResPacketSize],T1);
}
}
for (; j<alignedSize; j+=ResPacketSize)
_EIGEN_ACCUMULATE_PACKETS(Aligned,Unaligned,Unaligned);
break;
}
default:
for (Index j = alignedStart; j<alignedSize; j+=ResPacketSize)
_EIGEN_ACCUMULATE_PACKETS(Unaligned,Unaligned,Unaligned);
break;
}
}
} // end explicit vectorization
/* process remaining coeffs (or all if there is no explicit vectorization) */
for (Index j=alignedSize; j<size; ++j)
{
res[j] = cj.pmadd(lhs0(j), pfirst(ptmp0), res[j]);
res[j] = cj.pmadd(lhs1(j), pfirst(ptmp1), res[j]);
res[j] = cj.pmadd(lhs2(j), pfirst(ptmp2), res[j]);
res[j] = cj.pmadd(lhs3(j), pfirst(ptmp3), res[j]);
}
}
// process remaining first and last columns (at most columnsAtOnce-1)
Index end = cols;
Index start = columnBound;
do
{
for (Index k=start; k<end; ++k)
{
RhsPacket ptmp0 = pset1<RhsPacket>(alpha*rhs(k, 0));
const LhsScalars lhs0 = lhs.getVectorMapper(0, k);
if (Vectorizable)
{
/* explicit vectorization */
// process first unaligned result's coeffs
for (Index j=0; j<alignedStart; ++j)
res[j] += cj.pmul(lhs0(j), pfirst(ptmp0));
// process aligned result's coeffs
if (lhs0.template aligned<LhsPacket>(alignedStart))
for (Index i = alignedStart;i<alignedSize;i+=ResPacketSize)
pstore(&res[i], pcj.pmadd(lhs0.template load<LhsPacket, Aligned>(i), ptmp0, pload<ResPacket>(&res[i])));
else
for (Index i = alignedStart;i<alignedSize;i+=ResPacketSize)
pstore(&res[i], pcj.pmadd(lhs0.template load<LhsPacket, Unaligned>(i), ptmp0, pload<ResPacket>(&res[i])));
}
// process remaining scalars (or all if no explicit vectorization)
for (Index i=alignedSize; i<size; ++i)
res[i] += cj.pmul(lhs0(i), pfirst(ptmp0));
}
if (skipColumns)
{
start = 0;
end = skipColumns;
skipColumns = 0;
}
else
break;
} while(Vectorizable);
#undef _EIGEN_ACCUMULATE_PACKETS
}
/* Optimized row-major matrix * vector product:
* This algorithm processes 4 rows at onces that allows to both reduce
* the number of load/stores of the result by a factor 4 and to reduce
* the instruction dependency. Moreover, we know that all bands have the
* same alignment pattern.
*
* Mixing type logic:
* - alpha is always a complex (or converted to a complex)
* - no vectorization
*/
template<typename Index, typename LhsScalar, typename LhsMapper, bool ConjugateLhs, typename RhsScalar, typename RhsMapper, bool ConjugateRhs, int Version>
struct general_matrix_vector_product<Index,LhsScalar,LhsMapper,RowMajor,ConjugateLhs,RhsScalar,RhsMapper,ConjugateRhs,Version>
{
typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
enum {
Vectorizable = packet_traits<LhsScalar>::Vectorizable && packet_traits<RhsScalar>::Vectorizable
&& int(packet_traits<LhsScalar>::size)==int(packet_traits<RhsScalar>::size),
LhsPacketSize = Vectorizable ? packet_traits<LhsScalar>::size : 1,
RhsPacketSize = Vectorizable ? packet_traits<RhsScalar>::size : 1,
ResPacketSize = Vectorizable ? packet_traits<ResScalar>::size : 1
};
typedef typename packet_traits<LhsScalar>::type _LhsPacket;
typedef typename packet_traits<RhsScalar>::type _RhsPacket;
typedef typename packet_traits<ResScalar>::type _ResPacket;
typedef typename conditional<Vectorizable,_LhsPacket,LhsScalar>::type LhsPacket;
typedef typename conditional<Vectorizable,_RhsPacket,RhsScalar>::type RhsPacket;
typedef typename conditional<Vectorizable,_ResPacket,ResScalar>::type ResPacket;
EIGEN_DONT_INLINE static void run(
Index rows, Index cols,
const LhsMapper& lhs,
const RhsMapper& rhs,
ResScalar* res, Index resIncr,
ResScalar alpha);
};
template<typename Index, typename LhsScalar, typename LhsMapper, bool ConjugateLhs, typename RhsScalar, typename RhsMapper, bool ConjugateRhs, int Version>
EIGEN_DONT_INLINE void general_matrix_vector_product<Index,LhsScalar,LhsMapper,RowMajor,ConjugateLhs,RhsScalar,RhsMapper,ConjugateRhs,Version>::run(
Index rows, Index cols,
const LhsMapper& lhs,
const RhsMapper& rhs,
ResScalar* res, Index resIncr,
ResScalar alpha)
{
eigen_internal_assert(rhs.stride()==1);
#ifdef _EIGEN_ACCUMULATE_PACKETS
#error _EIGEN_ACCUMULATE_PACKETS has already been defined
#endif
#define _EIGEN_ACCUMULATE_PACKETS(Alignment0,Alignment13,Alignment2) {\
RhsPacket b = rhs.getVectorMapper(j, 0).template load<RhsPacket, Aligned>(0); \
ptmp0 = pcj.pmadd(lhs0.template load<LhsPacket, Alignment0>(j), b, ptmp0); \
ptmp1 = pcj.pmadd(lhs1.template load<LhsPacket, Alignment13>(j), b, ptmp1); \
ptmp2 = pcj.pmadd(lhs2.template load<LhsPacket, Alignment2>(j), b, ptmp2); \
ptmp3 = pcj.pmadd(lhs3.template load<LhsPacket, Alignment13>(j), b, ptmp3); }
conj_helper<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs> cj;
conj_helper<LhsPacket,RhsPacket,ConjugateLhs,ConjugateRhs> pcj;
typedef typename LhsMapper::VectorMapper LhsScalars;
enum { AllAligned=0, EvenAligned=1, FirstAligned=2, NoneAligned=3 };
const Index rowsAtOnce = 4;
const Index peels = 2;
const Index RhsPacketAlignedMask = RhsPacketSize-1;
const Index LhsPacketAlignedMask = LhsPacketSize-1;
const Index depth = cols;
const Index lhsStride = lhs.stride();
// How many coeffs of the result do we have to skip to be aligned.
// Here we assume data are at least aligned on the base scalar type
// if that's not the case then vectorization is discarded, see below.
Index alignedStart = rhs.firstAligned(depth);
Index alignedSize = RhsPacketSize>1 ? alignedStart + ((depth-alignedStart) & ~RhsPacketAlignedMask) : 0;
const Index peeledSize = alignedSize - RhsPacketSize*peels - RhsPacketSize + 1;
const Index alignmentStep = LhsPacketSize>1 ? (LhsPacketSize - lhsStride % LhsPacketSize) & LhsPacketAlignedMask : 0;
Index alignmentPattern = alignmentStep==0 ? AllAligned
: alignmentStep==(LhsPacketSize/2) ? EvenAligned
: FirstAligned;
// we cannot assume the first element is aligned because of sub-matrices
const Index lhsAlignmentOffset = lhs.firstAligned(depth);
const Index rhsAlignmentOffset = rhs.firstAligned(rows);
// find how many rows do we have to skip to be aligned with rhs (if possible)
Index skipRows = 0;
// if the data cannot be aligned (TODO add some compile time tests when possible, e.g. for floats)
if( (sizeof(LhsScalar)!=sizeof(RhsScalar)) ||
(lhsAlignmentOffset < 0) || (lhsAlignmentOffset == depth) ||
(rhsAlignmentOffset < 0) || (rhsAlignmentOffset == rows) )
{
alignedSize = 0;
alignedStart = 0;
alignmentPattern = NoneAligned;
}
else if(LhsPacketSize > 4)
{
// TODO: extend the code to support aligned loads whenever possible when LhsPacketSize > 4.
alignmentPattern = NoneAligned;
}
else if (LhsPacketSize>1)
{
// eigen_internal_assert(size_t(firstLhs+lhsAlignmentOffset)%sizeof(LhsPacket)==0 || depth<LhsPacketSize);
while (skipRows<LhsPacketSize &&
alignedStart != ((lhsAlignmentOffset + alignmentStep*skipRows)%LhsPacketSize))
++skipRows;
if (skipRows==LhsPacketSize)
{
// nothing can be aligned, no need to skip any column
alignmentPattern = NoneAligned;
skipRows = 0;
}
else
{
skipRows = (std::min)(skipRows,Index(rows));
// note that the skiped columns are processed later.
}
/* eigen_internal_assert( alignmentPattern==NoneAligned
|| LhsPacketSize==1
|| (skipRows + rowsAtOnce >= rows)
|| LhsPacketSize > depth
|| (size_t(firstLhs+alignedStart+lhsStride*skipRows)%sizeof(LhsPacket))==0);*/
}
else if(Vectorizable)
{
alignedStart = 0;
alignedSize = depth;
alignmentPattern = AllAligned;
}
const Index offset1 = (alignmentPattern==FirstAligned && alignmentStep==1)?3:1;
const Index offset3 = (alignmentPattern==FirstAligned && alignmentStep==1)?1:3;
Index rowBound = ((rows-skipRows)/rowsAtOnce)*rowsAtOnce + skipRows;
for (Index i=skipRows; i<rowBound; i+=rowsAtOnce)
{
// FIXME: what is the purpose of this EIGEN_ALIGN_DEFAULT ??
EIGEN_ALIGN_MAX ResScalar tmp0 = ResScalar(0);
ResScalar tmp1 = ResScalar(0), tmp2 = ResScalar(0), tmp3 = ResScalar(0);
// this helps the compiler generating good binary code
const LhsScalars lhs0 = lhs.getVectorMapper(i+0, 0), lhs1 = lhs.getVectorMapper(i+offset1, 0),
lhs2 = lhs.getVectorMapper(i+2, 0), lhs3 = lhs.getVectorMapper(i+offset3, 0);
if (Vectorizable)
{
/* explicit vectorization */
ResPacket ptmp0 = pset1<ResPacket>(ResScalar(0)), ptmp1 = pset1<ResPacket>(ResScalar(0)),
ptmp2 = pset1<ResPacket>(ResScalar(0)), ptmp3 = pset1<ResPacket>(ResScalar(0));
// process initial unaligned coeffs
// FIXME this loop get vectorized by the compiler !
for (Index j=0; j<alignedStart; ++j)
{
RhsScalar b = rhs(j, 0);
tmp0 += cj.pmul(lhs0(j),b); tmp1 += cj.pmul(lhs1(j),b);
tmp2 += cj.pmul(lhs2(j),b); tmp3 += cj.pmul(lhs3(j),b);
}
if (alignedSize>alignedStart)
{
switch(alignmentPattern)
{
case AllAligned:
for (Index j = alignedStart; j<alignedSize; j+=RhsPacketSize)
_EIGEN_ACCUMULATE_PACKETS(Aligned,Aligned,Aligned);
break;
case EvenAligned:
for (Index j = alignedStart; j<alignedSize; j+=RhsPacketSize)
_EIGEN_ACCUMULATE_PACKETS(Aligned,Unaligned,Aligned);
break;
case FirstAligned:
{
Index j = alignedStart;
if (peels>1)
{
/* Here we proccess 4 rows with with two peeled iterations to hide
* the overhead of unaligned loads. Moreover unaligned loads are handled
* using special shift/move operations between the two aligned packets
* overlaping the desired unaligned packet. This is *much* more efficient
* than basic unaligned loads.
*/
LhsPacket A01, A02, A03, A11, A12, A13;
A01 = lhs1.template load<LhsPacket, Aligned>(alignedStart-1);
A02 = lhs2.template load<LhsPacket, Aligned>(alignedStart-2);
A03 = lhs3.template load<LhsPacket, Aligned>(alignedStart-3);
for (; j<peeledSize; j+=peels*RhsPacketSize)
{
RhsPacket b = rhs.getVectorMapper(j, 0).template load<RhsPacket, Aligned>(0);
A11 = lhs1.template load<LhsPacket, Aligned>(j-1+LhsPacketSize); palign<1>(A01,A11);
A12 = lhs2.template load<LhsPacket, Aligned>(j-2+LhsPacketSize); palign<2>(A02,A12);
A13 = lhs3.template load<LhsPacket, Aligned>(j-3+LhsPacketSize); palign<3>(A03,A13);
ptmp0 = pcj.pmadd(lhs0.template load<LhsPacket, Aligned>(j), b, ptmp0);
ptmp1 = pcj.pmadd(A01, b, ptmp1);
A01 = lhs1.template load<LhsPacket, Aligned>(j-1+2*LhsPacketSize); palign<1>(A11,A01);
ptmp2 = pcj.pmadd(A02, b, ptmp2);
A02 = lhs2.template load<LhsPacket, Aligned>(j-2+2*LhsPacketSize); palign<2>(A12,A02);
ptmp3 = pcj.pmadd(A03, b, ptmp3);
A03 = lhs3.template load<LhsPacket, Aligned>(j-3+2*LhsPacketSize); palign<3>(A13,A03);
b = rhs.getVectorMapper(j+RhsPacketSize, 0).template load<RhsPacket, Aligned>(0);
ptmp0 = pcj.pmadd(lhs0.template load<LhsPacket, Aligned>(j+LhsPacketSize), b, ptmp0);
ptmp1 = pcj.pmadd(A11, b, ptmp1);
ptmp2 = pcj.pmadd(A12, b, ptmp2);
ptmp3 = pcj.pmadd(A13, b, ptmp3);
}
}
for (; j<alignedSize; j+=RhsPacketSize)
_EIGEN_ACCUMULATE_PACKETS(Aligned,Unaligned,Unaligned);
break;
}
default:
for (Index j = alignedStart; j<alignedSize; j+=RhsPacketSize)
_EIGEN_ACCUMULATE_PACKETS(Unaligned,Unaligned,Unaligned);
break;
}
tmp0 += predux(ptmp0);
tmp1 += predux(ptmp1);
tmp2 += predux(ptmp2);
tmp3 += predux(ptmp3);
}
} // end explicit vectorization
// process remaining coeffs (or all if no explicit vectorization)
// FIXME this loop get vectorized by the compiler !
for (Index j=alignedSize; j<depth; ++j)
{
RhsScalar b = rhs(j, 0);
tmp0 += cj.pmul(lhs0(j),b); tmp1 += cj.pmul(lhs1(j),b);
tmp2 += cj.pmul(lhs2(j),b); tmp3 += cj.pmul(lhs3(j),b);
}
res[i*resIncr] += alpha*tmp0;
res[(i+offset1)*resIncr] += alpha*tmp1;
res[(i+2)*resIncr] += alpha*tmp2;
res[(i+offset3)*resIncr] += alpha*tmp3;
}
// process remaining first and last rows (at most columnsAtOnce-1)
Index end = rows;
Index start = rowBound;
do
{
for (Index i=start; i<end; ++i)
{
EIGEN_ALIGN_MAX ResScalar tmp0 = ResScalar(0);
ResPacket ptmp0 = pset1<ResPacket>(tmp0);
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)
{
start = 0;
end = skipRows;
skipRows = 0;
}
else
break;
} while(Vectorizable);
#undef _EIGEN_ACCUMULATE_PACKETS
}
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_GENERAL_MATRIX_VECTOR_H