bench/bench_gemm.cpp - mirror - Git at Google


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

 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

 typedef SCALAR Scalar;
 typedef NumTraits<Scalar>::Real RealScalar;
 typedef Matrix<SCALARA,Dynamic,Dynamic> A;
 typedef Matrix<SCALARB,Dynamic,Dynamic> 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;

 void blas_gemm(const MatrixXf& a, const MatrixXf& b, MatrixXf& c)
 {
   int M = c.rows(); int N = c.cols(); int K = a.cols();
   int lda = a.rows(); int ldb = b.rows(); int ldc = c.rows();

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

 EIGEN_DONT_INLINE void blas_gemm(const MatrixXd& a, const MatrixXd& b, MatrixXd& c)
 {
   int M = c.rows(); int N = c.cols(); int K = a.cols();
   int lda = a.rows(); int ldb = b.rows(); int ldc = c.rows();

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

 void blas_gemm(const MatrixXcf& a, const MatrixXcf& b, MatrixXcf& c)
 {
   int M = c.rows(); int N = c.cols(); int K = a.cols();
   int lda = a.rows(); int ldb = b.rows(); int ldc = c.rows();

   cgemm_(&notrans,&notrans,&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);
 }

 void blas_gemm(const MatrixXcd& a, const MatrixXcd& b, MatrixXcd& c)
 {
   int M = c.rows(); int N = c.cols(); int K = a.cols();
   int lda = a.rows(); int ldb = b.rows(); int ldc = c.rows();

   zgemm_(&notrans,&notrans,&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;
 }

 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')
       {
         ++i;
         tries = atoi(argv[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(cache_size1>0)
    setCpuCacheSizes(cache_size1,cache_size2,cache_size3);


   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 << "\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 << "\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 << "\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

   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;
 }

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

	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

	typedef SCALAR Scalar;
	typedef NumTraits<Scalar>::Real RealScalar;
	typedef Matrix<SCALARA,Dynamic,Dynamic> A;
	typedef Matrix<SCALARB,Dynamic,Dynamic> 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;

	void blas_gemm(const MatrixXf& a, const MatrixXf& b, MatrixXf& c)
	{
	int M = c.rows(); int N = c.cols(); int K = a.cols();
	int lda = a.rows(); int ldb = b.rows(); int ldc = c.rows();

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

	EIGEN_DONT_INLINE void blas_gemm(const MatrixXd& a, const MatrixXd& b, MatrixXd& c)
	{
	int M = c.rows(); int N = c.cols(); int K = a.cols();
	int lda = a.rows(); int ldb = b.rows(); int ldc = c.rows();

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

	void blas_gemm(const MatrixXcf& a, const MatrixXcf& b, MatrixXcf& c)
	{
	int M = c.rows(); int N = c.cols(); int K = a.cols();
	int lda = a.rows(); int ldb = b.rows(); int ldc = c.rows();

	cgemm_(&notrans,&notrans,&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);
	}

	void blas_gemm(const MatrixXcd& a, const MatrixXcd& b, MatrixXcd& c)
	{
	int M = c.rows(); int N = c.cols(); int K = a.cols();
	int lda = a.rows(); int ldb = b.rows(); int ldc = c.rows();

	zgemm_(&notrans,&notrans,&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;
	}

	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')
	{
	++i;
	tries = atoi(argv[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(cache_size1>0)
	setCpuCacheSizes(cache_size1,cache_size2,cache_size3);


	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 << "\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 << "\n";
	std::cerr << "Warning, your product is crap!\n\n";
	}
	#else
	if(1.mnp<2000.2000*2000)
	{
	gemm(a,b,c);
	r.noalias() += a.cast<Scalar>() .lazyProduct( b.cast<Scalar>() );
	if(!r.isApprox(c)) {
	std::cout << r - c << "\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)nprep2/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)nprep2/tblas.best(REAL_TIMER))*1e-9 << " GFLOPS \t(" << tblas.total(REAL_TIMER) << "s)\n";
	#endif

	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)nprep2/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)nprep2/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)nprep2/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)nprep2/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.mnp<3030*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)nprep2/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)nprep2/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)nprep2/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)nprep2/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)nprep2/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)nprep2/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)nprep2/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)nprep2/t.best(REAL_TIMER))*1e-9 << " GFLOPS \t(" << t.total(REAL_TIMER) << "s)\n";
	}
	#endif

	return 0;
	}