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Hadrons: fast A2A matrix contraction kernels
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@ -39,12 +39,7 @@ Author: paboyle <paboyle@ph.ed.ac.uk>
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#include <omp.h>
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// complex reductions
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#pragma omp declare reduction(ComplexPlus: Grid::Complex: omp_out += omp_in)
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#pragma omp declare reduction(GridVComplexPlus: Grid::vComplex: omp_out += omp_in)
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#pragma omp declare reduction(ComplexDPlus: Grid::ComplexD: omp_out += omp_in)
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#pragma omp declare reduction(GridVComplexDPlus: Grid::vComplexD: omp_out += omp_in)
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#pragma omp declare reduction(ComplexFPlus: Grid::ComplexF: omp_out += omp_in)
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#pragma omp declare reduction(GridVComplexFPlus: Grid::vComplexF: omp_out += omp_in)
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#pragma omp declare reduction(ComplexPlus:Grid::ComplexD, Grid::vComplexD, Grid::ComplexF, Grid::vComplexF: omp_out += omp_in)
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#define PARALLEL_FOR_LOOP _Pragma("omp parallel for schedule(static)")
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#define PARALLEL_FOR_LOOP_INTERN _Pragma("omp for schedule(static)")
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@ -32,6 +32,10 @@ See the full license in the file "LICENSE" in the top level distribution directo
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#include <Hadrons/Global.hpp>
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#include <Hadrons/TimerArray.hpp>
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#include <Grid/Eigen/unsupported/CXX11/Tensor>
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#ifdef USE_MKL
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#include "mkl.h"
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#include "mkl_cblas.h"
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#endif
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#ifndef HADRONS_A2AM_NAME
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#define HADRONS_A2AM_NAME "a2aMatrix"
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@ -58,6 +62,9 @@ using A2AMatrixSet = Eigen::TensorMap<Eigen::Tensor<T, 5, Eigen::RowMajor>>;
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template <typename T>
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using A2AMatrix = Eigen::Matrix<T, -1, -1, Eigen::RowMajor>;
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template <typename T>
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using A2AMatrixTr = Eigen::Matrix<T, -1, -1, Eigen::ColMajor>;
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/******************************************************************************
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* Abstract class for A2A kernels *
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******************************************************************************/
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@ -150,6 +157,198 @@ private:
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std::vector<IoHelper> nodeIo_;
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};
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/******************************************************************************
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* A2A matrix contraction kernels *
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******************************************************************************/
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class A2AContraction
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{
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public:
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// accTrMul(acc, a, b): acc += tr(a*b)
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template <typename C, typename MatLeft, typename MatRight>
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static inline void accTrMul(C &acc, const MatLeft &a, const MatRight &b)
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{
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if ((MatLeft::Options == Eigen::RowMajor) and
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(MatRight::Options == Eigen::ColMajor))
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{
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parallel_for_reduce(ComplexPlus, acc) (unsigned int r = 0; r < a.rows(); ++r)
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{
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#ifdef USE_MKL
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ComplexD tmp;
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dotuRow(tmp, r, a, b);
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acc += tmp;
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#else
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acc += a.row(r).conjugate().dot(b.col(r));
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#endif
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}
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}
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else
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{
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parallel_for_reduce(ComplexPlus, acc) (unsigned int c = 0; c < a.cols(); ++c)
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{
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#ifdef USE_MKL
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ComplexD tmp;
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dotuCol(tmp, c, a, b);
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acc += tmp;
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#else
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acc += a.col(c).conjugate().dot(b.row(c));
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#endif
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}
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}
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}
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// mul(res, a, b): res = a*b
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#ifdef USE_MKL
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template <template <class, int...> class Mat, int... Opts>
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static inline void mul(Mat<ComplexD, Opts...> &res,
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const Mat<ComplexD, Opts...> &a,
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const Mat<ComplexD, Opts...> &b)
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{
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static const ComplexD one(1., 0.), zero(0., 0.);
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if (Mat<ComplexD, Opts...>::Options == Eigen::RowMajor)
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{
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cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, a.rows(), b.cols(),
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a.cols(), &one, a.data(), a.cols(), b.data(), b.cols(), &zero,
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res.data(), res.cols());
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}
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else if (Mat<ComplexD, Opts...>::Options == Eigen::ColMajor)
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{
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cblas_zgemm(CblasColMajor, CblasNoTrans, CblasNoTrans, a.rows(), b.cols(),
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a.cols(), &one, a.data(), a.rows(), b.data(), b.rows(), &zero,
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res.data(), res.rows());
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}
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}
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template <template <class, int...> class Mat, int... Opts>
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static inline void mul(Mat<ComplexF, Opts...> &res,
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const Mat<ComplexF, Opts...> &a,
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const Mat<ComplexF, Opts...> &b)
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{
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static const ComplexF one(1., 0.), zero(0., 0.);
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if (Mat<ComplexF, Opts...>::Options == Eigen::RowMajor)
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{
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cblas_cgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, a.rows(), b.cols(),
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a.cols(), &one, a.data(), a.cols(), b.data(), b.cols(), &zero,
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res.data(), res.cols());
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}
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else if (Mat<ComplexF, Opts...>::Options == Eigen::ColMajor)
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{
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cblas_cgemm(CblasColMajor, CblasNoTrans, CblasNoTrans, a.rows(), b.cols(),
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a.cols(), &one, a.data(), a.rows(), b.data(), b.rows(), &zero,
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res.data(), res.rows());
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}
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}
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#else
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template <typename Mat>
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static inline void mul(Mat &res, const Mat &a, const Mat &b)
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{
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res = a*b;
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}
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#endif
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private:
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template <typename C, typename MatLeft, typename MatRight>
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static inline void makeDotRowPt(C * &aPt, unsigned int &aInc, C * &bPt,
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unsigned int &bInc, const unsigned int aRow,
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const MatLeft &a, const MatRight &b)
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{
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if (MatLeft::Options == Eigen::RowMajor)
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{
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aPt = a.data() + aRow*a.cols();
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aInc = 1;
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}
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else if (MatLeft::Options == Eigen::ColMajor)
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{
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aPt = a.data() + aRow;
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aInc = a.rows();
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}
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if (MatRight::Options == Eigen::RowMajor)
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{
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bPt = b.data() + aRow;
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bInc = b.cols();
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}
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else if (MatRight::Options == Eigen::ColMajor)
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{
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bPt = b.data() + aRow*b.rows();
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bInc = 1;
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}
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}
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#ifdef USE_MKL
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template <typename C, typename MatLeft, typename MatRight>
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static inline void makeDotColPt(C * &aPt, unsigned int &aInc, C * &bPt,
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unsigned int &bInc, const unsigned int aCol,
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const MatLeft &a, const MatRight &b)
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{
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if (MatLeft::Options == Eigen::RowMajor)
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{
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aPt = a.data() + aCol;
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aInc = a.cols();
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}
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else if (MatLeft::Options == Eigen::ColMajor)
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{
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aPt = a.data() + aCol*a.rows();
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aInc = 1;
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}
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if (MatRight::Options == Eigen::RowMajor)
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{
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bPt = b.data() + aCol*b.cols();
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bInc = 1;
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}
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else if (MatRight::Options == Eigen::ColMajor)
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{
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bPt = b.data() + aCol;
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bInc = b.rows();
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}
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}
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template <typename MatLeft, typename MatRight>
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static inline void dotuRow(ComplexF &res, const unsigned int aRow,
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const MatLeft &a, const MatRight &b)
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{
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const ComplexF *aPt, *bPt;
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unsigned int aInc, bInc;
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makeDotRowPt(aPt, aInc, bPt, bInc, aRow, a, b);
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cblas_cdotu_sub(a.cols(), aPt, aInc, bPt, bInc, &res);
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}
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template <typename MatLeft, typename MatRight>
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static inline void dotuCol(ComplexF &res, const unsigned int aCol,
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const MatLeft &a, const MatRight &b)
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{
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const ComplexF *aPt, *bPt;
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unsigned int aInc, bInc;
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makeDotColPt(aPt, aInc, bPt, bInc, aCol, a, b);
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cblas_cdotu_sub(a.rows(), aPt, aInc, bPt, bInc, &res);
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}
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template <typename MatLeft, typename MatRight>
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static inline void dotuRow(ComplexD &res, const unsigned int aRow,
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const MatLeft &a, const MatRight &b)
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{
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const ComplexD *aPt, *bPt;
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unsigned int aInc, bInc;
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makeDotRowPt(aPt, aInc, bPt, bInc, aRow, a, b);
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cblas_zdotu_sub(a.cols(), aPt, aInc, bPt, bInc, &res);
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}
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template <typename MatLeft, typename MatRight>
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static inline void dotuCol(ComplexD &res, const unsigned int aCol,
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const MatLeft &a, const MatRight &b)
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{
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const ComplexD *aPt, *bPt;
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unsigned int aInc, bInc;
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makeDotColPt(aPt, aInc, bPt, bInc, aCol, a, b);
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cblas_zdotu_sub(a.rows(), aPt, aInc, bPt, bInc, &res);
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}
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#endif
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};
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/******************************************************************************
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* A2AMatrixIo template implementation *
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******************************************************************************/
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@ -1,16 +1,12 @@
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#include <Hadrons/Global.hpp>
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#include <Hadrons/A2AMatrix.hpp>
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#ifdef USE_MKL
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#include "mkl.h"
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#include "mkl_cblas.h"
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#endif
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#ifdef AVX2
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#include <immintrin.h>
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#endif
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using namespace Grid;
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typedef Eigen::Matrix<ComplexD, -1, -1, Eigen::RowMajor> RMCMat;
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typedef Eigen::Matrix<ComplexD, -1, -1, Eigen::ColMajor> CMCMat;
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using namespace Hadrons;
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#ifdef GRID_COMMS_MPI3
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#define GET_RANK(rank, nMpi) \
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@ -50,7 +46,7 @@ inline void trBenchmark(const std::string name, const MatLeft &left,
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if (rank == 0)
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{
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std::cout << std::setw(30) << name << ": diff= "
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std::cout << std::setw(34) << name << ": diff= "
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<< std::setw(12) << std::norm(buf-ref)
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<< std::setw(10) << t/1.0e6 << " sec "
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<< std::setw(10) << flops/t/1.0e3 << " GFlop/s "
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@ -85,16 +81,17 @@ inline void mulBenchmark(const std::string name, const MatV &left,
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if (rank == 0)
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{
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std::cout << std::setw(30) << name << ": diff= "
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<< std::setw(12) << (buf-ref).squaredNorm()
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<< std::setw(10) << t/1.0e6 << " sec "
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<< std::setw(10) << flops/t/1.0e3 << " GFlop/s "
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<< std::setw(10) << bytes/t*1.0e6/1024/1024/1024 << " GB/s "
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<< std::endl;
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std::cout << std::setw(34) << name << ": diff= "
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<< std::setw(12) << (buf-ref).squaredNorm()
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<< std::setw(10) << t/1.0e6 << " sec "
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<< std::setw(10) << flops/t/1.0e3 << " GFlop/s "
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<< std::setw(10) << bytes/t*1.0e6/1024/1024/1024 << " GB/s "
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<< std::endl;
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}
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::sleep(1);
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}
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#ifdef USE_MKL
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template <typename MatLeft, typename MatRight>
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static inline void zdotuRow(ComplexD &res, const unsigned int aRow,
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const MatLeft &a, const MatRight &b)
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@ -154,6 +151,7 @@ static inline void zdotuCol(ComplexD &res, const unsigned int aCol,
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}
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cblas_zdotu_sub(a.rows(), aPt, aInc, bPt, bInc, &res);
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}
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#endif
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template <typename MatLeft, typename MatRight>
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void fullTrBenchmark(const unsigned int ni, const unsigned int nj, const unsigned int nMat)
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@ -192,12 +190,18 @@ void fullTrBenchmark(const unsigned int ni, const unsigned int nj, const unsigne
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}
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BARRIER();
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ref = (left.back()*right.back()).trace();
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trBenchmark("Hadrons A2AContraction::accTrMul", left, right, ref,
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[](ComplexD &res, const MatLeft &a, const MatRight &b)
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{
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res = 0.;
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A2AContraction::accTrMul(res, a, b);
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});
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trBenchmark("Naive loop rows first", left, right, ref,
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[](ComplexD &res, const MatLeft &a, const MatRight &b)
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{
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res = 0.;
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auto nr = a.rows(), nc = a.cols();
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parallel_for_reduce(ComplexDPlus, res) (unsigned int i = 0; i < nr; ++i)
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parallel_for_reduce(ComplexPlus, res) (unsigned int i = 0; i < nr; ++i)
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for (unsigned int j = 0; j < nc; ++j)
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{
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res += a(i, j)*b(j, i);
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@ -208,7 +212,7 @@ void fullTrBenchmark(const unsigned int ni, const unsigned int nj, const unsigne
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{
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res = 0.;
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auto nr = a.rows(), nc = a.cols();
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parallel_for_reduce(ComplexDPlus, res) (unsigned int j = 0; j < nc; ++j)
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parallel_for_reduce(ComplexPlus, res) (unsigned int j = 0; j < nc; ++j)
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for (unsigned int i = 0; i < nr; ++i)
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{
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res += a(i, j)*b(j, i);
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@ -224,7 +228,7 @@ void fullTrBenchmark(const unsigned int ni, const unsigned int nj, const unsigne
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{
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res = 0.;
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parallel_for_reduce(ComplexDPlus, res) (unsigned int r = 0; r < a.rows(); ++r)
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parallel_for_reduce(ComplexPlus, res) (unsigned int r = 0; r < a.rows(); ++r)
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{
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res += a.row(r).conjugate().dot(b.col(r));
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}
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@ -234,7 +238,7 @@ void fullTrBenchmark(const unsigned int ni, const unsigned int nj, const unsigne
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{
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res = 0.;
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parallel_for_reduce(ComplexDPlus, res) (unsigned int c = 0; c < a.cols(); ++c)
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parallel_for_reduce(ComplexPlus, res) (unsigned int c = 0; c < a.cols(); ++c)
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{
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res += a.col(c).conjugate().dot(b.row(c));
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}
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@ -250,7 +254,7 @@ void fullTrBenchmark(const unsigned int ni, const unsigned int nj, const unsigne
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{
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res = 0.;
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parallel_for_reduce(ComplexDPlus, res) (unsigned int r = 0; r < a.rows(); ++r)
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parallel_for_reduce(ComplexPlus, res) (unsigned int r = 0; r < a.rows(); ++r)
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{
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ComplexD tmp;
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@ -263,7 +267,7 @@ void fullTrBenchmark(const unsigned int ni, const unsigned int nj, const unsigne
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{
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res = 0.;
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parallel_for_reduce(ComplexDPlus, res) (unsigned int c = 0; c < a.cols(); ++c)
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parallel_for_reduce(ComplexPlus, res) (unsigned int c = 0; c < a.cols(); ++c)
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{
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ComplexD tmp;
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@ -305,6 +309,11 @@ void fullMulBenchmark(const unsigned int ni, const unsigned int nj, const unsign
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}
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BARRIER();
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ref = left.back()*right.back();
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mulBenchmark("Hadrons A2AContraction::mul", left, right, ref,
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[](Mat &res, const Mat &a, const Mat &b)
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{
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A2AContraction::mul(res, a, b);
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});
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mulBenchmark("Eigen A*B", left, right, ref,
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[](Mat &res, const Mat &a, const Mat &b)
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{
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@ -381,12 +390,12 @@ int main(int argc, char *argv[])
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std::cout << std::endl;
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}
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fullTrBenchmark<RMCMat, RMCMat>(ni, nj, nMat);
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fullTrBenchmark<RMCMat, CMCMat>(ni, nj, nMat);
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fullTrBenchmark<CMCMat, RMCMat>(ni, nj, nMat);
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fullTrBenchmark<CMCMat, CMCMat>(ni, nj, nMat);
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fullMulBenchmark<RMCMat>(ni, nj, nMat);
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fullMulBenchmark<CMCMat>(ni, nj, nMat);
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fullTrBenchmark<A2AMatrix<ComplexD>, A2AMatrix<ComplexD>>(ni, nj, nMat);
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fullTrBenchmark<A2AMatrix<ComplexD>, A2AMatrixTr<ComplexD>>(ni, nj, nMat);
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fullTrBenchmark<A2AMatrixTr<ComplexD>, A2AMatrix<ComplexD>>(ni, nj, nMat);
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fullTrBenchmark<A2AMatrixTr<ComplexD>, A2AMatrixTr<ComplexD>>(ni, nj, nMat);
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fullMulBenchmark<A2AMatrix<ComplexD>>(ni, nj, nMat);
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fullMulBenchmark<A2AMatrixTr<ComplexD>>(ni, nj, nMat);
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FINALIZE();
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return EXIT_SUCCESS;
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