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>
blas_gemm(const A & a,const B & b,MatrixXf & c)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>
blas_gemm(const A & a,const B & b,MatrixXd & c)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>
blas_gemm(const A & a,const B & b,MatrixXcf & c)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>
blas_gemm(const A & a,const B & b,MatrixXcd & c)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
matlab_cplx_cplx(const M & ar,const M & ai,const M & br,const M & bi,M & cr,M & ci)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
matlab_real_cplx(const M & a,const M & br,const M & bi,M & cr,M & ci)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
matlab_cplx_real(const M & ar,const M & ai,const M & b,M & cr,M & ci)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>
gemm(const A & a,const B & b,C & c)162 EIGEN_DONT_INLINE void gemm(const A& a, const B& b, C& c)
163 {
164 c.noalias() += a * b;
165 }
166
main(int argc,char ** argv)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
376