acado: SparseLU_gemm_kernel.h Source File

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00001 // This file is part of Eigen, a lightweight C++ template library
00002 // for linear algebra.
00003 //
00004 // Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
00005 //
00006 // This Source Code Form is subject to the terms of the Mozilla
00007 // Public License v. 2.0. If a copy of the MPL was not distributed
00008 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
00009 
00010 #ifndef EIGEN_SPARSELU_GEMM_KERNEL_H
00011 #define EIGEN_SPARSELU_GEMM_KERNEL_H
00012 
00013 namespace Eigen {
00014 
00015 namespace internal {
00016 
00017 
00024 template<typename Scalar,typename Index>
00025 EIGEN_DONT_INLINE
00026 void sparselu_gemm(Index m, Index n, Index d, const Scalar* A, Index lda, const Scalar* B, Index ldb, Scalar* C, Index ldc)
00027 {
00028   using namespace Eigen::internal;
00029   
00030   typedef typename packet_traits<Scalar>::type Packet;
00031   enum {
00032     NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,
00033     PacketSize = packet_traits<Scalar>::size,
00034     PM = 8,                             // peeling in M
00035     RN = 2,                             // register blocking
00036     RK = NumberOfRegisters>=16 ? 4 : 2, // register blocking
00037     BM = 4096/sizeof(Scalar),           // number of rows of A-C per chunk
00038     SM = PM*PacketSize                  // step along M
00039   };
00040   Index d_end = (d/RK)*RK;    // number of columns of A (rows of B) suitable for full register blocking
00041   Index n_end = (n/RN)*RN;    // number of columns of B-C suitable for processing RN columns at once
00042   Index i0 = internal::first_aligned(A,m);
00043   
00044   eigen_internal_assert(((lda%PacketSize)==0) && ((ldc%PacketSize)==0) && (i0==internal::first_aligned(C,m)));
00045   
00046   // handle the non aligned rows of A and C without any optimization:
00047   for(Index i=0; i<i0; ++i)
00048   {
00049     for(Index j=0; j<n; ++j)
00050     {
00051       Scalar c = C[i+j*ldc];
00052       for(Index k=0; k<d; ++k)
00053         c += B[k+j*ldb] * A[i+k*lda];
00054       C[i+j*ldc] = c;
00055     }
00056   }
00057   // process the remaining rows per chunk of BM rows
00058   for(Index ib=i0; ib<m; ib+=BM)
00059   {
00060     Index actual_b = std::min<Index>(BM, m-ib);                 // actual number of rows
00061     Index actual_b_end1 = (actual_b/SM)*SM;                   // actual number of rows suitable for peeling
00062     Index actual_b_end2 = (actual_b/PacketSize)*PacketSize;   // actual number of rows suitable for vectorization
00063     
00064     // Let's process two columns of B-C at once
00065     for(Index j=0; j<n_end; j+=RN)
00066     {
00067       const Scalar* Bc0 = B+(j+0)*ldb;
00068       const Scalar* Bc1 = B+(j+1)*ldb;
00069       
00070       for(Index k=0; k<d_end; k+=RK)
00071       {
00072         
00073         // load and expand a RN x RK block of B
00074         Packet b00, b10, b20, b30, b01, b11, b21, b31;
00075                   b00 = pset1<Packet>(Bc0[0]);
00076                   b10 = pset1<Packet>(Bc0[1]);
00077         if(RK==4) b20 = pset1<Packet>(Bc0[2]);
00078         if(RK==4) b30 = pset1<Packet>(Bc0[3]);
00079                   b01 = pset1<Packet>(Bc1[0]);
00080                   b11 = pset1<Packet>(Bc1[1]);
00081         if(RK==4) b21 = pset1<Packet>(Bc1[2]);
00082         if(RK==4) b31 = pset1<Packet>(Bc1[3]);
00083         
00084         Packet a0, a1, a2, a3, c0, c1, t0, t1;
00085         
00086         const Scalar* A0 = A+ib+(k+0)*lda;
00087         const Scalar* A1 = A+ib+(k+1)*lda;
00088         const Scalar* A2 = A+ib+(k+2)*lda;
00089         const Scalar* A3 = A+ib+(k+3)*lda;
00090         
00091         Scalar* C0 = C+ib+(j+0)*ldc;
00092         Scalar* C1 = C+ib+(j+1)*ldc;
00093         
00094                   a0 = pload<Packet>(A0);
00095                   a1 = pload<Packet>(A1);
00096         if(RK==4)
00097         {
00098           a2 = pload<Packet>(A2);
00099           a3 = pload<Packet>(A3);
00100         }
00101         else
00102         {
00103           // workaround "may be used uninitialized in this function" warning
00104           a2 = a3 = a0;
00105         }
00106         
00107 #define KMADD(c, a, b, tmp) {tmp = b; tmp = pmul(a,tmp); c = padd(c,tmp);}
00108 #define WORK(I)  \
00109                     c0 = pload<Packet>(C0+i+(I)*PacketSize);   \
00110                     c1 = pload<Packet>(C1+i+(I)*PacketSize);   \
00111                     KMADD(c0, a0, b00, t0)      \
00112                     KMADD(c1, a0, b01, t1)      \
00113                     a0 = pload<Packet>(A0+i+(I+1)*PacketSize); \
00114                     KMADD(c0, a1, b10, t0)      \
00115                     KMADD(c1, a1, b11, t1)       \
00116                     a1 = pload<Packet>(A1+i+(I+1)*PacketSize); \
00117           if(RK==4) KMADD(c0, a2, b20, t0)       \
00118           if(RK==4) KMADD(c1, a2, b21, t1)       \
00119           if(RK==4) a2 = pload<Packet>(A2+i+(I+1)*PacketSize); \
00120           if(RK==4) KMADD(c0, a3, b30, t0)       \
00121           if(RK==4) KMADD(c1, a3, b31, t1)       \
00122           if(RK==4) a3 = pload<Packet>(A3+i+(I+1)*PacketSize); \
00123                     pstore(C0+i+(I)*PacketSize, c0);           \
00124                     pstore(C1+i+(I)*PacketSize, c1)
00125         
00126         // process rows of A' - C' with aggressive vectorization and peeling 
00127         for(Index i=0; i<actual_b_end1; i+=PacketSize*8)
00128         {
00129           EIGEN_ASM_COMMENT("SPARSELU_GEMML_KERNEL1");
00130                     prefetch((A0+i+(5)*PacketSize));
00131                     prefetch((A1+i+(5)*PacketSize));
00132           if(RK==4) prefetch((A2+i+(5)*PacketSize));
00133           if(RK==4) prefetch((A3+i+(5)*PacketSize));
00134                     WORK(0);
00135                     WORK(1);
00136                     WORK(2);
00137                     WORK(3);
00138                     WORK(4);
00139                     WORK(5);
00140                     WORK(6);
00141                     WORK(7);
00142         }
00143         // process the remaining rows with vectorization only
00144         for(Index i=actual_b_end1; i<actual_b_end2; i+=PacketSize)
00145         {
00146           WORK(0);
00147         }
00148 #undef WORK
00149         // process the remaining rows without vectorization
00150         for(Index i=actual_b_end2; i<actual_b; ++i)
00151         {
00152           if(RK==4)
00153           {
00154             C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1]+A2[i]*Bc0[2]+A3[i]*Bc0[3];
00155             C1[i] += A0[i]*Bc1[0]+A1[i]*Bc1[1]+A2[i]*Bc1[2]+A3[i]*Bc1[3];
00156           }
00157           else
00158           {
00159             C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1];
00160             C1[i] += A0[i]*Bc1[0]+A1[i]*Bc1[1];
00161           }
00162         }
00163         
00164         Bc0 += RK;
00165         Bc1 += RK;
00166       } // peeled loop on k
00167     } // peeled loop on the columns j
00168     // process the last column (we now perform a matrux-vector product)
00169     if((n-n_end)>0)
00170     {
00171       const Scalar* Bc0 = B+(n-1)*ldb;
00172       
00173       for(Index k=0; k<d_end; k+=RK)
00174       {
00175         
00176         // load and expand a 1 x RK block of B
00177         Packet b00, b10, b20, b30;
00178                   b00 = pset1<Packet>(Bc0[0]);
00179                   b10 = pset1<Packet>(Bc0[1]);
00180         if(RK==4) b20 = pset1<Packet>(Bc0[2]);
00181         if(RK==4) b30 = pset1<Packet>(Bc0[3]);
00182         
00183         Packet a0, a1, a2, a3, c0, t0/*, t1*/;
00184         
00185         const Scalar* A0 = A+ib+(k+0)*lda;
00186         const Scalar* A1 = A+ib+(k+1)*lda;
00187         const Scalar* A2 = A+ib+(k+2)*lda;
00188         const Scalar* A3 = A+ib+(k+3)*lda;
00189         
00190         Scalar* C0 = C+ib+(n_end)*ldc;
00191         
00192                   a0 = pload<Packet>(A0);
00193                   a1 = pload<Packet>(A1);
00194         if(RK==4)
00195         {
00196           a2 = pload<Packet>(A2);
00197           a3 = pload<Packet>(A3);
00198         }
00199         else
00200         {
00201           // workaround "may be used uninitialized in this function" warning
00202           a2 = a3 = a0;
00203         }
00204         
00205 #define WORK(I) \
00206                   c0 = pload<Packet>(C0+i+(I)*PacketSize);   \
00207                   KMADD(c0, a0, b00, t0)       \
00208                   a0 = pload<Packet>(A0+i+(I+1)*PacketSize); \
00209                   KMADD(c0, a1, b10, t0)       \
00210                   a1 = pload<Packet>(A1+i+(I+1)*PacketSize); \
00211         if(RK==4) KMADD(c0, a2, b20, t0)       \
00212         if(RK==4) a2 = pload<Packet>(A2+i+(I+1)*PacketSize); \
00213         if(RK==4) KMADD(c0, a3, b30, t0)       \
00214         if(RK==4) a3 = pload<Packet>(A3+i+(I+1)*PacketSize); \
00215                   pstore(C0+i+(I)*PacketSize, c0);
00216         
00217         // agressive vectorization and peeling
00218         for(Index i=0; i<actual_b_end1; i+=PacketSize*8)
00219         {
00220           EIGEN_ASM_COMMENT("SPARSELU_GEMML_KERNEL2");
00221           WORK(0);
00222           WORK(1);
00223           WORK(2);
00224           WORK(3);
00225           WORK(4);
00226           WORK(5);
00227           WORK(6);
00228           WORK(7);
00229         }
00230         // vectorization only
00231         for(Index i=actual_b_end1; i<actual_b_end2; i+=PacketSize)
00232         {
00233           WORK(0);
00234         }
00235         // remaining scalars
00236         for(Index i=actual_b_end2; i<actual_b; ++i)
00237         {
00238           if(RK==4) 
00239             C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1]+A2[i]*Bc0[2]+A3[i]*Bc0[3];
00240           else
00241             C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1];
00242         }
00243         
00244         Bc0 += RK;
00245 #undef WORK
00246       }
00247     }
00248     
00249     // process the last columns of A, corresponding to the last rows of B
00250     Index rd = d-d_end;
00251     if(rd>0)
00252     {
00253       for(Index j=0; j<n; ++j)
00254       {
00255         enum {
00256           Alignment = PacketSize>1 ? Aligned : 0
00257         };
00258         typedef Map<Matrix<Scalar,Dynamic,1>, Alignment > MapVector;
00259         typedef Map<const Matrix<Scalar,Dynamic,1>, Alignment > ConstMapVector;
00260         if(rd==1)       MapVector(C+j*ldc+ib,actual_b) += B[0+d_end+j*ldb] * ConstMapVector(A+(d_end+0)*lda+ib, actual_b);
00261         
00262         else if(rd==2)  MapVector(C+j*ldc+ib,actual_b) += B[0+d_end+j*ldb] * ConstMapVector(A+(d_end+0)*lda+ib, actual_b)
00263                                                         + B[1+d_end+j*ldb] * ConstMapVector(A+(d_end+1)*lda+ib, actual_b);
00264         
00265         else            MapVector(C+j*ldc+ib,actual_b) += B[0+d_end+j*ldb] * ConstMapVector(A+(d_end+0)*lda+ib, actual_b)
00266                                                         + B[1+d_end+j*ldb] * ConstMapVector(A+(d_end+1)*lda+ib, actual_b)
00267                                                         + B[2+d_end+j*ldb] * ConstMapVector(A+(d_end+2)*lda+ib, actual_b);
00268       }
00269     }
00270   
00271   } // blocking on the rows of A and C
00272 }
00273 #undef KMADD
00274 
00275 } // namespace internal
00276 
00277 } // namespace Eigen
00278 
00279 #endif // EIGEN_SPARSELU_GEMM_KERNEL_H