bench_gemm.cpp
Go to the documentation of this file.
1 
2 // g++-4.4 bench_gemm.cpp -I .. -O2 -DNDEBUG -lrt -fopenmp && OMP_NUM_THREADS=2 ./a.out
3 // icpc bench_gemm.cpp -I .. -O3 -DNDEBUG -lrt -openmp && OMP_NUM_THREADS=2 ./a.out
4 
5 // Compilation options:
6 //
7 // -DSCALAR=std::complex<double>
8 // -DSCALARA=double or -DSCALARB=double
9 // -DHAVE_BLAS
10 // -DDECOUPLED
11 //
12 
13 #include <iostream>
14 #include <bench/BenchTimer.h>
15 #include <Eigen/Core>
16 
17 
18 using namespace std;
19 using namespace Eigen;
20 
21 #ifndef SCALAR
22 // #define SCALAR std::complex<float>
23 #define SCALAR float
24 #endif
25 
26 #ifndef SCALARA
27 #define SCALARA SCALAR
28 #endif
29 
30 #ifndef SCALARB
31 #define SCALARB SCALAR
32 #endif
33 
34 #ifdef ROWMAJ_A
35 const int opt_A = RowMajor;
36 #else
37 const int opt_A = ColMajor;
38 #endif
39 
40 #ifdef ROWMAJ_B
41 const int opt_B = RowMajor;
42 #else
43 const int opt_B = ColMajor;
44 #endif
45 
46 typedef SCALAR Scalar;
47 typedef NumTraits<Scalar>::Real RealScalar;
48 typedef Matrix<SCALARA,Dynamic,Dynamic,opt_A> A;
49 typedef Matrix<SCALARB,Dynamic,Dynamic,opt_B> B;
50 typedef Matrix<Scalar,Dynamic,Dynamic> C;
51 typedef Matrix<RealScalar,Dynamic,Dynamic> M;
52 
53 #ifdef HAVE_BLAS
54 
55 extern "C" {
56  #include <Eigen/src/misc/blas.h>
57 }
58 
59 static float fone = 1;
60 static float fzero = 0;
61 static double done = 1;
62 static double szero = 0;
63 static std::complex<float> cfone = 1;
64 static std::complex<float> cfzero = 0;
65 static std::complex<double> cdone = 1;
66 static std::complex<double> cdzero = 0;
67 static char notrans = 'N';
68 static char trans = 'T';
69 static char nonunit = 'N';
70 static char lower = 'L';
71 static char right = 'R';
72 static int intone = 1;
73 
74 #ifdef ROWMAJ_A
75 const char transA = trans;
76 #else
77 const char transA = notrans;
78 #endif
79 
80 #ifdef ROWMAJ_B
81 const char transB = trans;
82 #else
83 const char transB = notrans;
84 #endif
85 
86 template<typename A,typename B>
87 void blas_gemm(const A& a, const B& b, MatrixXf& c)
88 {
89  int M = c.rows(); int N = c.cols(); int K = a.cols();
90  int lda = a.outerStride(); int ldb = b.outerStride(); int ldc = c.rows();
91 
92  sgemm_(&transA,&transB,&M,&N,&K,&fone,
93  const_cast<float*>(a.data()),&lda,
94  const_cast<float*>(b.data()),&ldb,&fone,
95  c.data(),&ldc);
96 }
97 
98 template<typename A,typename B>
99 void blas_gemm(const A& a, const B& b, MatrixXd& c)
100 {
101  int M = c.rows(); int N = c.cols(); int K = a.cols();
102  int lda = a.outerStride(); int ldb = b.outerStride(); int ldc = c.rows();
103 
104  dgemm_(&transA,&transB,&M,&N,&K,&done,
105  const_cast<double*>(a.data()),&lda,
106  const_cast<double*>(b.data()),&ldb,&done,
107  c.data(),&ldc);
108 }
109 
110 template<typename A,typename B>
111 void blas_gemm(const A& a, const B& b, MatrixXcf& c)
112 {
113  int M = c.rows(); int N = c.cols(); int K = a.cols();
114  int lda = a.outerStride(); int ldb = b.outerStride(); int ldc = c.rows();
115 
116  cgemm_(&transA,&transB,&M,&N,&K,(float*)&cfone,
117  const_cast<float*>((const float*)a.data()),&lda,
118  const_cast<float*>((const float*)b.data()),&ldb,(float*)&cfone,
119  (float*)c.data(),&ldc);
120 }
121 
122 template<typename A,typename B>
123 void blas_gemm(const A& a, const B& b, MatrixXcd& c)
124 {
125  int M = c.rows(); int N = c.cols(); int K = a.cols();
126  int lda = a.outerStride(); int ldb = b.outerStride(); int ldc = c.rows();
127 
128  zgemm_(&transA,&transB,&M,&N,&K,(double*)&cdone,
129  const_cast<double*>((const double*)a.data()),&lda,
130  const_cast<double*>((const double*)b.data()),&ldb,(double*)&cdone,
131  (double*)c.data(),&ldc);
132 }
133 
134 
135 
136 #endif
137 
138 void matlab_cplx_cplx(const M& ar, const M& ai, const M& br, const M& bi, M& cr, M& ci)
139 {
140  cr.noalias() += ar * br;
141  cr.noalias() -= ai * bi;
142  ci.noalias() += ar * bi;
143  ci.noalias() += ai * br;
144  // [cr ci] += [ar ai] * br + [-ai ar] * bi
145 }
146 
147 void matlab_real_cplx(const M& a, const M& br, const M& bi, M& cr, M& ci)
148 {
149  cr.noalias() += a * br;
150  ci.noalias() += a * bi;
151 }
152 
153 void matlab_cplx_real(const M& ar, const M& ai, const M& b, M& cr, M& ci)
154 {
155  cr.noalias() += ar * b;
156  ci.noalias() += ai * b;
157 }
158 
159 
160 
161 template<typename A, typename B, typename C>
162 EIGEN_DONT_INLINE void gemm(const A& a, const B& b, C& c)
163 {
164  c.noalias() += a * b;
165 }
166 
167 int main(int argc, char ** argv)
168 {
169  std::ptrdiff_t l1 = internal::queryL1CacheSize();
170  std::ptrdiff_t l2 = internal::queryTopLevelCacheSize();
171  std::cout << "L1 cache size = " << (l1>0 ? l1/1024 : -1) << " KB\n";
172  std::cout << "L2/L3 cache size = " << (l2>0 ? l2/1024 : -1) << " KB\n";
173  typedef internal::gebp_traits<Scalar,Scalar> Traits;
174  std::cout << "Register blocking = " << Traits::mr << " x " << Traits::nr << "\n";
175 
176  int rep = 1; // number of repetitions per try
177  int tries = 2; // number of tries, we keep the best
178 
179  int s = 2048;
180  int m = s;
181  int n = s;
182  int p = s;
183  int cache_size1=-1, cache_size2=l2, cache_size3 = 0;
184 
185  bool need_help = false;
186  for (int i=1; i<argc;)
187  {
188  if(argv[i][0]=='-')
189  {
190  if(argv[i][1]=='s')
191  {
192  ++i;
193  s = atoi(argv[i++]);
194  m = n = p = s;
195  if(argv[i][0]!='-')
196  {
197  n = atoi(argv[i++]);
198  p = atoi(argv[i++]);
199  }
200  }
201  else if(argv[i][1]=='c')
202  {
203  ++i;
204  cache_size1 = atoi(argv[i++]);
205  if(argv[i][0]!='-')
206  {
207  cache_size2 = atoi(argv[i++]);
208  if(argv[i][0]!='-')
209  cache_size3 = atoi(argv[i++]);
210  }
211  }
212  else if(argv[i][1]=='t')
213  {
214  tries = atoi(argv[++i]);
215  ++i;
216  }
217  else if(argv[i][1]=='p')
218  {
219  ++i;
220  rep = atoi(argv[i++]);
221  }
222  }
223  else
224  {
225  need_help = true;
226  break;
227  }
228  }
229 
230  if(need_help)
231  {
232  std::cout << argv[0] << " -s <matrix sizes> -c <cache sizes> -t <nb tries> -p <nb repeats>\n";
233  std::cout << " <matrix sizes> : size\n";
234  std::cout << " <matrix sizes> : rows columns depth\n";
235  return 1;
236  }
237 
238 #if EIGEN_VERSION_AT_LEAST(3,2,90)
239  if(cache_size1>0)
240  setCpuCacheSizes(cache_size1,cache_size2,cache_size3);
241 #endif
242 
243  A a(m,p); a.setRandom();
244  B b(p,n); b.setRandom();
245  C c(m,n); c.setOnes();
246  C rc = c;
247 
248  std::cout << "Matrix sizes = " << m << "x" << p << " * " << p << "x" << n << "\n";
249  std::ptrdiff_t mc(m), nc(n), kc(p);
250  internal::computeProductBlockingSizes<Scalar,Scalar>(kc, mc, nc);
251  std::cout << "blocking size (mc x kc) = " << mc << " x " << kc << " x " << nc << "\n";
252 
253  C r = c;
254 
255  // check the parallel product is correct
256  #if defined EIGEN_HAS_OPENMP
257  Eigen::initParallel();
258  int procs = omp_get_max_threads();
259  if(procs>1)
260  {
261  #ifdef HAVE_BLAS
262  blas_gemm(a,b,r);
263  #else
264  omp_set_num_threads(1);
265  r.noalias() += a * b;
266  omp_set_num_threads(procs);
267  #endif
268  c.noalias() += a * b;
269  if(!r.isApprox(c)) std::cerr << "Warning, your parallel product is crap!\n\n";
270  }
271  #elif defined HAVE_BLAS
272  blas_gemm(a,b,r);
273  c.noalias() += a * b;
274  if(!r.isApprox(c)) {
275  std::cout << (r - c).norm()/r.norm() << "\n";
276  std::cerr << "Warning, your product is crap!\n\n";
277  }
278  #else
279  if(1.*m*n*p<2000.*2000*2000)
280  {
281  gemm(a,b,c);
282  r.noalias() += a.cast<Scalar>() .lazyProduct( b.cast<Scalar>() );
283  if(!r.isApprox(c)) {
284  std::cout << (r - c).norm()/r.norm() << "\n";
285  std::cerr << "Warning, your product is crap!\n\n";
286  }
287  }
288  #endif
289 
290  #ifdef HAVE_BLAS
291  BenchTimer tblas;
292  c = rc;
293  BENCH(tblas, tries, rep, blas_gemm(a,b,c));
294  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";
295  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";
296  #endif
297 
298  // warm start
299  if(b.norm()+a.norm()==123.554) std::cout << "\n";
300 
301  BenchTimer tmt;
302  c = rc;
303  BENCH(tmt, tries, rep, gemm(a,b,c));
304  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";
305  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";
306 
307  #ifdef EIGEN_HAS_OPENMP
308  if(procs>1)
309  {
310  BenchTimer tmono;
311  omp_set_num_threads(1);
312  Eigen::setNbThreads(1);
313  c = rc;
314  BENCH(tmono, tries, rep, gemm(a,b,c));
315  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";
316  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";
317  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";
318  }
319  #endif
320 
321  if(1.*m*n*p<30*30*30)
322  {
323  BenchTimer tmt;
324  c = rc;
325  BENCH(tmt, tries, rep, c.noalias()+=a.lazyProduct(b));
326  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";
327  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";
328  }
329 
330  #ifdef DECOUPLED
331  if((NumTraits<A::Scalar>::IsComplex) && (NumTraits<B::Scalar>::IsComplex))
332  {
333  M ar(m,p); ar.setRandom();
334  M ai(m,p); ai.setRandom();
335  M br(p,n); br.setRandom();
336  M bi(p,n); bi.setRandom();
337  M cr(m,n); cr.setRandom();
338  M ci(m,n); ci.setRandom();
339 
340  BenchTimer t;
341  BENCH(t, tries, rep, matlab_cplx_cplx(ar,ai,br,bi,cr,ci));
342  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";
343  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";
344  }
345  if((!NumTraits<A::Scalar>::IsComplex) && (NumTraits<B::Scalar>::IsComplex))
346  {
347  M a(m,p); a.setRandom();
348  M br(p,n); br.setRandom();
349  M bi(p,n); bi.setRandom();
350  M cr(m,n); cr.setRandom();
351  M ci(m,n); ci.setRandom();
352 
353  BenchTimer t;
354  BENCH(t, tries, rep, matlab_real_cplx(a,br,bi,cr,ci));
355  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";
356  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";
357  }
358  if((NumTraits<A::Scalar>::IsComplex) && (!NumTraits<B::Scalar>::IsComplex))
359  {
360  M ar(m,p); ar.setRandom();
361  M ai(m,p); ai.setRandom();
362  M b(p,n); b.setRandom();
363  M cr(m,n); cr.setRandom();
364  M ci(m,n); ci.setRandom();
365 
366  BenchTimer t;
367  BENCH(t, tries, rep, matlab_cplx_real(ar,ai,b,cr,ci));
368  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";
369  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";
370  }
371  #endif
372 
373  return 0;
374 }
375 
B
Matrix< SCALARB, Dynamic, Dynamic, opt_B > B
Definition: bench_gemm.cpp:49
m
Matrix3f m
Definition: AngleAxis_mimic_euler.cpp:1
Eigen::setCpuCacheSizes
void setCpuCacheSizes(std::ptrdiff_t l1, std::ptrdiff_t l2, std::ptrdiff_t l3)
Definition: products/GeneralBlockPanelKernel.h:2638
Scalar
SCALAR Scalar
Definition: bench_gemm.cpp:46
M
Matrix< RealScalar, Dynamic, Dynamic > M
Definition: bench_gemm.cpp:51
Eigen::initParallel
void initParallel()
Definition: Parallelizer.h:53
lower
static char lower
Definition: blas_interface.hh:60
Eigen::ColMajor
Definition: Constants.h:319
b
Scalar * b
Definition: benchVecAdd.cpp:17
opt_A
const int opt_A
Definition: bench_gemm.cpp:37
n
int n
Definition: BiCGSTAB_simple.cpp:1
c
Scalar Scalar * c
Definition: benchVecAdd.cpp:17
l2
gtsam::Key l2
Definition: testLinearContainerFactor.cpp:24
intone
static int intone
Definition: blas_interface.hh:63
Eigen
Namespace containing all symbols from the Eigen library.
Definition: jet.h:637
K
static Cal3_S2 K(500, 500, 0.1, 640/2, 480/2)
std
Definition: BFloat16.h:88
trans
static char trans
Definition: blas_interface.hh:58
Eigen::NumTraits
Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...
Definition: NumTraits.h:232
A
Matrix< SCALARA, Dynamic, Dynamic, opt_A > A
Definition: bench_gemm.cpp:48
N
#define N
Definition: gksort.c:12
EIGEN_DONT_INLINE
#define EIGEN_DONT_INLINE
Definition: Macros.h:940
Eigen::BenchTimer::best
double best(int TIMER=CPU_TIMER) const
Definition: BenchTimer.h:111
notrans
static char notrans
Definition: blas_interface.hh:57
Eigen::internal::queryL1CacheSize
int queryL1CacheSize()
Definition: Memory.h:1143
omp_set_num_threads
void omp_set_num_threads(int num_threads)
e
Array< double, 1, 3 > e(1./3., 0.5, 2.)
s
RealScalar s
Definition: level1_cplx_impl.h:126
lda
* lda
Definition: eigenvalues.cpp:59
opt_B
const int opt_B
Definition: bench_gemm.cpp:43
right
static char right
Definition: blas_interface.hh:61
RealScalar
NumTraits< Scalar >::Real RealScalar
Definition: bench_gemm.cpp:47
gemm
EIGEN_DONT_INLINE void gemm(const A &a, const B &b, C &c)
Definition: bench_gemm.cpp:162
C
Matrix< Scalar, Dynamic, Dynamic > C
Definition: bench_gemm.cpp:50
l1
gtsam::Key l1
Definition: testLinearContainerFactor.cpp:24
main
int main(int argc, char **argv)
Definition: bench_gemm.cpp:167
nonunit
static char nonunit
Definition: blas_interface.hh:59
matlab_cplx_cplx
void matlab_cplx_cplx(const M &ar, const M &ai, const M &br, const M &bi, M &cr, M &ci)
Definition: bench_gemm.cpp:138
matlab_real_cplx
void matlab_real_cplx(const M &a, const M &br, const M &bi, M &cr, M &ci)
Definition: bench_gemm.cpp:147
Eigen::setNbThreads
void setNbThreads(int v)
Definition: Parallelizer.h:72
omp_get_max_threads
int omp_get_max_threads(void)
SCALAR
#define SCALAR
Definition: bench_gemm.cpp:23
test_virtual_functions.nc
nc
Definition: test_virtual_functions.py:206
Eigen::RowMajor
Definition: Constants.h:321
p
float * p
Definition: Tutorial_Map_using.cpp:9
a
ArrayXXi a
Definition: Array_initializer_list_23_cxx11.cpp:1
BENCH
#define BENCH(TIMER, TRIES, REP, CODE)
Definition: BenchTimer.h:174
Eigen::Matrix
The matrix class, also used for vectors and row-vectors.
Definition: 3rdparty/Eigen/Eigen/src/Core/Matrix.h:178
i
int i
Definition: BiCGSTAB_step_by_step.cpp:9
matlab_cplx_real
void matlab_cplx_real(const M &ar, const M &ai, const M &b, M &cr, M &ci)
Definition: bench_gemm.cpp:153
Eigen::internal::queryTopLevelCacheSize
int queryTopLevelCacheSize()
Definition: Memory.h:1152
Eigen::BenchTimer::total
double total(int TIMER=CPU_TIMER) const
Definition: BenchTimer.h:125
align_3::t
Point2 t(10, 10)

gtsam
Author(s):
autogenerated on Tue Jul 4 2023 02:33:57