// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_SPARSELU_GEMM_KERNEL_H
#define EIGEN_SPARSELU_GEMM_KERNEL_H
namespace Eigen {
namespace internal {
/** \internal
* A general matrix-matrix product kernel optimized for the SparseLU factorization.
* - A, B, and C must be column major
* - lda and ldc must be multiples of the respective packet size
* - C must have the same alignment as A
*/
template<typename Scalar,typename Index>
EIGEN_DONT_INLINE
void sparselu_gemm(Index m, Index n, Index d, const Scalar* A, Index lda, const Scalar* B, Index ldb, Scalar* C, Index ldc)
{
using namespace Eigen::internal;
typedef typename packet_traits<Scalar>::type Packet;
enum {
NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,
PacketSize = packet_traits<Scalar>::size,
PM = 8, // peeling in M
RN = 2, // register blocking
RK = NumberOfRegisters>=16 ? 4 : 2, // register blocking
BM = 4096/sizeof(Scalar), // number of rows of A-C per chunk
SM = PM*PacketSize // step along M
};
Index d_end = (d/RK)*RK; // number of columns of A (rows of B) suitable for full register blocking
Index n_end = (n/RN)*RN; // number of columns of B-C suitable for processing RN columns at once
Index i0 = internal::first_aligned(A,m);
eigen_internal_assert(((lda%PacketSize)==0) && ((ldc%PacketSize)==0) && (i0==internal::first_aligned(C,m)));
// handle the non aligned rows of A and C without any optimization:
for(Index i=0; i<i0; ++i)
{
for(Index j=0; j<n; ++j)
{
Scalar c = C[i+j*ldc];
for(Index k=0; k<d; ++k)
c += B[k+j*ldb] * A[i+k*lda];
C[i+j*ldc] = c;
}
}
// process the remaining rows per chunk of BM rows
for(Index ib=i0; ib<m; ib+=BM)
{
Index actual_b = std::min<Index>(BM, m-ib); // actual number of rows
Index actual_b_end1 = (actual_b/SM)*SM; // actual number of rows suitable for peeling
Index actual_b_end2 = (actual_b/PacketSize)*PacketSize; // actual number of rows suitable for vectorization
// Let's process two columns of B-C at once
for(Index j=0; j<n_end; j+=RN)
{
const Scalar* Bc0 = B+(j+0)*ldb;
const Scalar* Bc1 = B+(j+1)*ldb;
for(Index k=0; k<d_end; k+=RK)
{
// load and expand a RN x RK block of B
Packet b00, b10, b20, b30, b01, b11, b21, b31;
b00 = pset1<Packet>(Bc0[0]);
b10 = pset1<Packet>(Bc0[1]);
if(RK==4) b20 = pset1<Packet>(Bc0[2]);
if(RK==4) b30 = pset1<Packet>(Bc0[3]);
b01 = pset1<Packet>(Bc1[0]);
b11 = pset1<Packet>(Bc1[1]);
if(RK==4) b21 = pset1<Packet>(Bc1[2]);
if(RK==4) b31 = pset1<Packet>(Bc1[3]);
Packet a0, a1, a2, a3, c0, c1, t0, t1;
const Scalar* A0 = A+ib+(k+0)*lda;
const Scalar* A1 = A+ib+(k+1)*lda;
const Scalar* A2 = A+ib+(k+2)*lda;
const Scalar* A3 = A+ib+(k+3)*lda;
Scalar* C0 = C+ib+(j+0)*ldc;
Scalar* C1 = C+ib+(j+1)*ldc;
a0 = pload<Packet>(A0);
a1 = pload<Packet>(A1);
if(RK==4)
{
a2 = pload<Packet>(A2);
a3 = pload<Packet>(A3);
}
else
{
// workaround "may be used uninitialized in this function" warning
a2 = a3 = a0;
}
#define KMADD(c, a, b, tmp) {tmp = b; tmp = pmul(a,tmp); c = padd(c,tmp);}
#define WORK(I) \
c0 = pload<Packet>(C0+i+(I)*PacketSize); \
c1 = pload<Packet>(C1+i+(I)*PacketSize); \
KMADD(c0, a0, b00, t0) \
KMADD(c1, a0, b01, t1) \
a0 = pload<Packet>(A0+i+(I+1)*PacketSize); \
KMADD(c0, a1, b10, t0) \
KMADD(c1, a1, b11, t1) \
a1 = pload<Packet>(A1+i+(I+1)*PacketSize); \
if(RK==4) KMADD(c0, a2, b20, t0) \
if(RK==4) KMADD(c1, a2, b21, t1) \
if(RK==4) a2 = pload<Packet>(A2+i+(I+1)*PacketSize); \
if(RK==4) KMADD(c0, a3, b30, t0) \
if(RK==4) KMADD(c1, a3, b31, t1) \
if(RK==4) a3 = pload<Packet>(A3+i+(I+1)*PacketSize); \
pstore(C0+i+(I)*PacketSize, c0); \
pstore(C1+i+(I)*PacketSize, c1)
// process rows of A' - C' with aggressive vectorization and peeling
for(Index i=0; i<actual_b_end1; i+=PacketSize*8)
{
EIGEN_ASM_COMMENT("SPARSELU_GEMML_KERNEL1");
prefetch((A0+i+(5)*PacketSize));
prefetch((A1+i+(5)*PacketSize));
if(RK==4) prefetch((A2+i+(5)*PacketSize));
if(RK==4) prefetch((A3+i+(5)*PacketSize));
WORK(0);
WORK(1);
WORK(2);
WORK(3);
WORK(4);
WORK(5);
WORK(6);
WORK(7);
}
// process the remaining rows with vectorization only
for(Index i=actual_b_end1; i<actual_b_end2; i+=PacketSize)
{
WORK(0);
}
#undef WORK
// process the remaining rows without vectorization
for(Index i=actual_b_end2; i<actual_b; ++i)
{
if(RK==4)
{
C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1]+A2[i]*Bc0[2]+A3[i]*Bc0[3];
C1[i] += A0[i]*Bc1[0]+A1[i]*Bc1[1]+A2[i]*Bc1[2]+A3[i]*Bc1[3];
}
else
{
C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1];
C1[i] += A0[i]*Bc1[0]+A1[i]*Bc1[1];
}
}
Bc0 += RK;
Bc1 += RK;
} // peeled loop on k
} // peeled loop on the columns j
// process the last column (we now perform a matrux-vector product)
if((n-n_end)>0)
{
const Scalar* Bc0 = B+(n-1)*ldb;
for(Index k=0; k<d_end; k+=RK)
{
// load and expand a 1 x RK block of B
Packet b00, b10, b20, b30;
b00 = pset1<Packet>(Bc0[0]);
b10 = pset1<Packet>(Bc0[1]);
if(RK==4) b20 = pset1<Packet>(Bc0[2]);
if(RK==4) b30 = pset1<Packet>(Bc0[3]);
Packet a0, a1, a2, a3, c0, t0/*, t1*/;
const Scalar* A0 = A+ib+(k+0)*lda;
const Scalar* A1 = A+ib+(k+1)*lda;
const Scalar* A2 = A+ib+(k+2)*lda;
const Scalar* A3 = A+ib+(k+3)*lda;
Scalar* C0 = C+ib+(n_end)*ldc;
a0 = pload<Packet>(A0);
a1 = pload<Packet>(A1);
if(RK==4)
{
a2 = pload<Packet>(A2);
a3 = pload<Packet>(A3);
}
else
{
// workaround "may be used uninitialized in this function" warning
a2 = a3 = a0;
}
#define WORK(I) \
c0 = pload<Packet>(C0+i+(I)*PacketSize); \
KMADD(c0, a0, b00, t0) \
a0 = pload<Packet>(A0+i+(I+1)*PacketSize); \
KMADD(c0, a1, b10, t0) \
a1 = pload<Packet>(A1+i+(I+1)*PacketSize); \
if(RK==4) KMADD(c0, a2, b20, t0) \
if(RK==4) a2 = pload<Packet>(A2+i+(I+1)*PacketSize); \
if(RK==4) KMADD(c0, a3, b30, t0) \
if(RK==4) a3 = pload<Packet>(A3+i+(I+1)*PacketSize); \
pstore(C0+i+(I)*PacketSize, c0);
// agressive vectorization and peeling
for(Index i=0; i<actual_b_end1; i+=PacketSize*8)
{
EIGEN_ASM_COMMENT("SPARSELU_GEMML_KERNEL2");
WORK(0);
WORK(1);
WORK(2);
WORK(3);
WORK(4);
WORK(5);
WORK(6);
WORK(7);
}
// vectorization only
for(Index i=actual_b_end1; i<actual_b_end2; i+=PacketSize)
{
WORK(0);
}
// remaining scalars
for(Index i=actual_b_end2; i<actual_b; ++i)
{
if(RK==4)
C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1]+A2[i]*Bc0[2]+A3[i]*Bc0[3];
else
C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1];
}
Bc0 += RK;
#undef WORK
}
}
// process the last columns of A, corresponding to the last rows of B
Index rd = d-d_end;
if(rd>0)
{
for(Index j=0; j<n; ++j)
{
enum {
Alignment = PacketSize>1 ? Aligned : 0
};
typedef Map<Matrix<Scalar,Dynamic,1>, Alignment > MapVector;
typedef Map<const Matrix<Scalar,Dynamic,1>, Alignment > ConstMapVector;
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);
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)
+ B[1+d_end+j*ldb] * ConstMapVector(A+(d_end+1)*lda+ib, actual_b);
else MapVector(C+j*ldc+ib,actual_b) += B[0+d_end+j*ldb] * ConstMapVector(A+(d_end+0)*lda+ib, actual_b)
+ B[1+d_end+j*ldb] * ConstMapVector(A+(d_end+1)*lda+ib, actual_b)
+ B[2+d_end+j*ldb] * ConstMapVector(A+(d_end+2)*lda+ib, actual_b);
}
}
} // blocking on the rows of A and C
}
#undef KMADD
} // namespace internal
} // namespace Eigen
#endif // EIGEN_SPARSELU_GEMM_KERNEL_H