eigen/bench/bench_gemm.cpp

// g++-4.4 bench_gemm.cpp -I .. -O2 -DNDEBUG -lrt -fopenmp && OMP_NUM_THREADS=2  ./a.out
// icpc bench_gemm.cpp -I .. -O3 -DNDEBUG -lrt -openmp  && OMP_NUM_THREADS=2  ./a.out

// Compilation options:
//
// -DSCALAR=std::complex<double>
// -DSCALARA=double or -DSCALARB=double
// -DHAVE_BLAS
// -DDECOUPLED
//

#include <iostream>
#include <bench/BenchTimer.h>
#include <Eigen/Core>

using namespace std;
using namespace Eigen;

#ifndef SCALAR
// #define SCALAR std::complex<float>
#define SCALAR float
#endif

#ifndef SCALARA
#define SCALARA SCALAR
#endif

#ifndef SCALARB
#define SCALARB SCALAR
#endif

#ifdef ROWMAJ_A
const int opt_A = RowMajor;
#else
const int opt_A = ColMajor;
#endif

#ifdef ROWMAJ_B
const int opt_B = RowMajor;
#else
const int opt_B = ColMajor;
#endif

typedef SCALAR Scalar;
typedef NumTraits<Scalar>::Real RealScalar;
typedef Matrix<SCALARA, Dynamic, Dynamic, opt_A> A;
typedef Matrix<SCALARB, Dynamic, Dynamic, opt_B> B;
typedef Matrix<Scalar, Dynamic, Dynamic> C;
typedef Matrix<RealScalar, Dynamic, Dynamic> M;

#ifdef HAVE_BLAS

extern "C" {
#include <Eigen/src/misc/blas.h>
}

static float fone = 1;
static float fzero = 0;
static double done = 1;
static double szero = 0;
static std::complex<float> cfone = 1;
static std::complex<float> cfzero = 0;
static std::complex<double> cdone = 1;
static std::complex<double> cdzero = 0;
static char notrans = 'N';
static char trans = 'T';
static char nonunit = 'N';
static char lower = 'L';
static char right = 'R';
static int intone = 1;

#ifdef ROWMAJ_A
const char transA = trans;
#else
const char transA = notrans;
#endif

#ifdef ROWMAJ_B
const char transB = trans;
#else
const char transB = notrans;
#endif

template <typename A, typename B>
void blas_gemm(const A& a, const B& b, MatrixXf& c) {
  int M = c.rows();
  int N = c.cols();
  int K = a.cols();
  int lda = a.outerStride();
  int ldb = b.outerStride();
  int ldc = c.rows();

  sgemm_(&transA, &transB, &M, &N, &K, &fone, const_cast<float*>(a.data()), &lda, const_cast<float*>(b.data()), &ldb,
         &fone, c.data(), &ldc);
}

template <typename A, typename B>
void blas_gemm(const A& a, const B& b, MatrixXd& c) {
  int M = c.rows();
  int N = c.cols();
  int K = a.cols();
  int lda = a.outerStride();
  int ldb = b.outerStride();
  int ldc = c.rows();

  dgemm_(&transA, &transB, &M, &N, &K, &done, const_cast<double*>(a.data()), &lda, const_cast<double*>(b.data()), &ldb,
         &done, c.data(), &ldc);
}

template <typename A, typename B>
void blas_gemm(const A& a, const B& b, MatrixXcf& c) {
  int M = c.rows();
  int N = c.cols();
  int K = a.cols();
  int lda = a.outerStride();
  int ldb = b.outerStride();
  int ldc = c.rows();

  cgemm_(&transA, &transB, &M, &N, &K, (float*)&cfone, const_cast<float*>((const float*)a.data()), &lda,
         const_cast<float*>((const float*)b.data()), &ldb, (float*)&cfone, (float*)c.data(), &ldc);
}

template <typename A, typename B>
void blas_gemm(const A& a, const B& b, MatrixXcd& c) {
  int M = c.rows();
  int N = c.cols();
  int K = a.cols();
  int lda = a.outerStride();
  int ldb = b.outerStride();
  int ldc = c.rows();

  zgemm_(&transA, &transB, &M, &N, &K, (double*)&cdone, const_cast<double*>((const double*)a.data()), &lda,
         const_cast<double*>((const double*)b.data()), &ldb, (double*)&cdone, (double*)c.data(), &ldc);
}

#endif

void matlab_cplx_cplx(const M& ar, const M& ai, const M& br, const M& bi, M& cr, M& ci) {
  cr.noalias() += ar * br;
  cr.noalias() -= ai * bi;
  ci.noalias() += ar * bi;
  ci.noalias() += ai * br;
  // [cr ci] += [ar ai] * br + [-ai ar] * bi
}

void matlab_real_cplx(const M& a, const M& br, const M& bi, M& cr, M& ci) {
  cr.noalias() += a * br;
  ci.noalias() += a * bi;
}

void matlab_cplx_real(const M& ar, const M& ai, const M& b, M& cr, M& ci) {
  cr.noalias() += ar * b;
  ci.noalias() += ai * b;
}

template <typename A, typename B, typename C>
EIGEN_DONT_INLINE void gemm(const A& a, const B& b, C& c) {
  c.noalias() += a * b;
}

int main(int argc, char** argv) {
  std::ptrdiff_t l1 = internal::queryL1CacheSize();
  std::ptrdiff_t l2 = internal::queryTopLevelCacheSize();
  std::cout << "L1 cache size     = " << (l1 > 0 ? l1 / 1024 : -1) << " KB\n";
  std::cout << "L2/L3 cache size  = " << (l2 > 0 ? l2 / 1024 : -1) << " KB\n";
  typedef internal::gebp_traits<Scalar, Scalar> Traits;
  std::cout << "Register blocking = " << Traits::mr << " x " << Traits::nr << "\n";

  int rep = 1;    // number of repetitions per try
  int tries = 2;  // number of tries, we keep the best

  int s = 2048;
  int m = s;
  int n = s;
  int p = s;
  int cache_size1 = -1, cache_size2 = l2, cache_size3 = 0;

  bool need_help = false;
  for (int i = 1; i < argc;) {
    if (argv[i][0] == '-') {
      if (argv[i][1] == 's') {
        ++i;
        s = atoi(argv[i++]);
        m = n = p = s;
        if (argv[i][0] != '-') {
          n = atoi(argv[i++]);
          p = atoi(argv[i++]);
        }
      } else if (argv[i][1] == 'c') {
        ++i;
        cache_size1 = atoi(argv[i++]);
        if (argv[i][0] != '-') {
          cache_size2 = atoi(argv[i++]);
          if (argv[i][0] != '-') cache_size3 = atoi(argv[i++]);
        }
      } else if (argv[i][1] == 't') {
        tries = atoi(argv[++i]);
        ++i;
      } else if (argv[i][1] == 'p') {
        ++i;
        rep = atoi(argv[i++]);
      }
    } else {
      need_help = true;
      break;
    }
  }

  if (need_help) {
    std::cout << argv[0] << " -s <matrix sizes> -c <cache sizes> -t <nb tries> -p <nb repeats>\n";
    std::cout << "   <matrix sizes> : size\n";
    std::cout << "   <matrix sizes> : rows columns depth\n";
    return 1;
  }

#if EIGEN_VERSION_AT_LEAST(3, 2, 90)
  if (cache_size1 > 0) setCpuCacheSizes(cache_size1, cache_size2, cache_size3);
#endif

  A a(m, p);
  a.setRandom();
  B b(p, n);
  b.setRandom();
  C c(m, n);
  c.setOnes();
  C rc = c;

  std::cout << "Matrix sizes = " << m << "x" << p << " * " << p << "x" << n << "\n";
  std::ptrdiff_t mc(m), nc(n), kc(p);
  internal::computeProductBlockingSizes<Scalar, Scalar>(kc, mc, nc);
  std::cout << "blocking size (mc x kc) = " << mc << " x " << kc << " x " << nc << "\n";

  C r = c;

// check the parallel product is correct
#if defined EIGEN_HAS_OPENMP
  Eigen::initParallel();
  int procs = omp_get_max_threads();
  if (procs > 1) {
#ifdef HAVE_BLAS
    blas_gemm(a, b, r);
#else
    omp_set_num_threads(1);
    r.noalias() += a * b;
    omp_set_num_threads(procs);
#endif
    c.noalias() += a * b;
    if (!r.isApprox(c)) std::cerr << "Warning, your parallel product is crap!\n\n";
  }
#elif defined HAVE_BLAS
  blas_gemm(a, b, r);
  c.noalias() += a * b;
  if (!r.isApprox(c)) {
    std::cout << (r - c).norm() / r.norm() << "\n";
    std::cerr << "Warning, your product is crap!\n\n";
  }
#else
  if (1. * m * n * p < 2000. * 2000 * 2000) {
    gemm(a, b, c);
    r.noalias() += a.cast<Scalar>().lazyProduct(b.cast<Scalar>());
    if (!r.isApprox(c)) {
      std::cout << (r - c).norm() / r.norm() << "\n";
      std::cerr << "Warning, your product is crap!\n\n";
    }
  }
#endif

#ifdef HAVE_BLAS
  BenchTimer tblas;
  c = rc;
  BENCH(tblas, tries, rep, blas_gemm(a, b, c));
  std::cout << "blas  cpu         " << tblas.best(CPU_TIMER) / rep << "s  \t"
            << (double(m) * n * p * rep * 2 / tblas.best(CPU_TIMER)) * 1e-9 << " GFLOPS \t(" << tblas.total(CPU_TIMER)
            << "s)\n";
  std::cout << "blas  real        " << tblas.best(REAL_TIMER) / rep << "s  \t"
            << (double(m) * n * p * rep * 2 / tblas.best(REAL_TIMER)) * 1e-9 << " GFLOPS \t(" << tblas.total(REAL_TIMER)
            << "s)\n";
#endif

  // warm start
  if (b.norm() + a.norm() == 123.554) std::cout << "\n";

  BenchTimer tmt;
  c = rc;
  BENCH(tmt, tries, rep, gemm(a, b, c));
  std::cout << "eigen cpu         " << tmt.best(CPU_TIMER) / rep << "s  \t"
            << (double(m) * n * p * rep * 2 / tmt.best(CPU_TIMER)) * 1e-9 << " GFLOPS \t(" << tmt.total(CPU_TIMER)
            << "s)\n";
  std::cout << "eigen real        " << tmt.best(REAL_TIMER) / rep << "s  \t"
            << (double(m) * n * p * rep * 2 / tmt.best(REAL_TIMER)) * 1e-9 << " GFLOPS \t(" << tmt.total(REAL_TIMER)
            << "s)\n";

#ifdef EIGEN_HAS_OPENMP
  if (procs > 1) {
    BenchTimer tmono;
    omp_set_num_threads(1);
    Eigen::setNbThreads(1);
    c = rc;
    BENCH(tmono, tries, rep, gemm(a, b, c));
    std::cout << "eigen mono cpu    " << tmono.best(CPU_TIMER) / rep << "s  \t"
              << (double(m) * n * p * rep * 2 / tmono.best(CPU_TIMER)) * 1e-9 << " GFLOPS \t(" << tmono.total(CPU_TIMER)
              << "s)\n";
    std::cout << "eigen mono real   " << tmono.best(REAL_TIMER) / rep << "s  \t"
              << (double(m) * n * p * rep * 2 / tmono.best(REAL_TIMER)) * 1e-9 << " GFLOPS \t("
              << tmono.total(REAL_TIMER) << "s)\n";
    std::cout << "mt speed up x" << tmono.best(CPU_TIMER) / tmt.best(REAL_TIMER) << " => "
              << (100.0 * tmono.best(CPU_TIMER) / tmt.best(REAL_TIMER)) / procs << "%\n";
  }
#endif

  if (1. * m * n * p < 30 * 30 * 30) {
    BenchTimer tmt;
    c = rc;
    BENCH(tmt, tries, rep, c.noalias() += a.lazyProduct(b));
    std::cout << "lazy cpu         " << tmt.best(CPU_TIMER) / rep << "s  \t"
              << (double(m) * n * p * rep * 2 / tmt.best(CPU_TIMER)) * 1e-9 << " GFLOPS \t(" << tmt.total(CPU_TIMER)
              << "s)\n";
    std::cout << "lazy real        " << tmt.best(REAL_TIMER) / rep << "s  \t"
              << (double(m) * n * p * rep * 2 / tmt.best(REAL_TIMER)) * 1e-9 << " GFLOPS \t(" << tmt.total(REAL_TIMER)
              << "s)\n";
  }

#ifdef DECOUPLED
  if ((NumTraits<A::Scalar>::IsComplex) && (NumTraits<B::Scalar>::IsComplex)) {
    M ar(m, p);
    ar.setRandom();
    M ai(m, p);
    ai.setRandom();
    M br(p, n);
    br.setRandom();
    M bi(p, n);
    bi.setRandom();
    M cr(m, n);
    cr.setRandom();
    M ci(m, n);
    ci.setRandom();

    BenchTimer t;
    BENCH(t, tries, rep, matlab_cplx_cplx(ar, ai, br, bi, cr, ci));
    std::cout << "\"matlab\" cpu    " << t.best(CPU_TIMER) / rep << "s  \t"
              << (double(m) * n * p * rep * 2 / t.best(CPU_TIMER)) * 1e-9 << " GFLOPS \t(" << t.total(CPU_TIMER)
              << "s)\n";
    std::cout << "\"matlab\" real   " << t.best(REAL_TIMER) / rep << "s  \t"
              << (double(m) * n * p * rep * 2 / t.best(REAL_TIMER)) * 1e-9 << " GFLOPS \t(" << t.total(REAL_TIMER)
              << "s)\n";
  }
  if ((!NumTraits<A::Scalar>::IsComplex) && (NumTraits<B::Scalar>::IsComplex)) {
    M a(m, p);
    a.setRandom();
    M br(p, n);
    br.setRandom();
    M bi(p, n);
    bi.setRandom();
    M cr(m, n);
    cr.setRandom();
    M ci(m, n);
    ci.setRandom();

    BenchTimer t;
    BENCH(t, tries, rep, matlab_real_cplx(a, br, bi, cr, ci));
    std::cout << "\"matlab\" cpu    " << t.best(CPU_TIMER) / rep << "s  \t"
              << (double(m) * n * p * rep * 2 / t.best(CPU_TIMER)) * 1e-9 << " GFLOPS \t(" << t.total(CPU_TIMER)
              << "s)\n";
    std::cout << "\"matlab\" real   " << t.best(REAL_TIMER) / rep << "s  \t"
              << (double(m) * n * p * rep * 2 / t.best(REAL_TIMER)) * 1e-9 << " GFLOPS \t(" << t.total(REAL_TIMER)
              << "s)\n";
  }
  if ((NumTraits<A::Scalar>::IsComplex) && (!NumTraits<B::Scalar>::IsComplex)) {
    M ar(m, p);
    ar.setRandom();
    M ai(m, p);
    ai.setRandom();
    M b(p, n);
    b.setRandom();
    M cr(m, n);
    cr.setRandom();
    M ci(m, n);
    ci.setRandom();

    BenchTimer t;
    BENCH(t, tries, rep, matlab_cplx_real(ar, ai, b, cr, ci));
    std::cout << "\"matlab\" cpu    " << t.best(CPU_TIMER) / rep << "s  \t"
              << (double(m) * n * p * rep * 2 / t.best(CPU_TIMER)) * 1e-9 << " GFLOPS \t(" << t.total(CPU_TIMER)
              << "s)\n";
    std::cout << "\"matlab\" real   " << t.best(REAL_TIMER) / rep << "s  \t"
              << (double(m) * n * p * rep * 2 / t.best(REAL_TIMER)) * 1e-9 << " GFLOPS \t(" << t.total(REAL_TIMER)
              << "s)\n";
  }
#endif

  return 0;
}