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Fix SparseLU special gemm kernel on 32 bits system w/o SSE

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Gael Guennebaud 2013-01-23 19:34:01 +01:00
parent ee36eaefc6
commit 73026eab4d
1 changed files with 85 additions and 70 deletions
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155
Eigen/src/SparseLU/SparseLU_gemm_kernel.h
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@ -29,12 +29,13 @@ void sparselu_gemm(int m, int n, int d, const Scalar* A, int lda, const Scalar*
typedef typename packet_traits<Scalar>::type Packet; typedef typename packet_traits<Scalar>::type Packet;
enum { enum {
NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,
PacketSize = packet_traits<Scalar>::size, PacketSize = packet_traits<Scalar>::size,
PM = 8, // peeling in M PM = 8, // peeling in M
RN = 2, // register blocking RN = 2, // register blocking
RK = 4, // register blocking RK = NumberOfRegisters>=16 ? 4 : 2, // register blocking
BM = 4096/sizeof(Scalar), // number of rows of A-C per chunk BM = 4096/sizeof(Scalar), // number of rows of A-C per chunk
SM = PM*PacketSize // step along M SM = PM*PacketSize // step along M
}; };
int d_end = (d/RK)*RK; // number of columns of A (rows of B) suitable for full register blocking int d_end = (d/RK)*RK; // number of columns of A (rows of B) suitable for full register blocking
int n_end = (n/RN)*RN; // number of columns of B-C suitable for processing RN columns at once int n_end = (n/RN)*RN; // number of columns of B-C suitable for processing RN columns at once
@ -71,14 +72,14 @@ void sparselu_gemm(int m, int n, int d, const Scalar* A, int lda, const Scalar*
// load and expand a RN x RK block of B // load and expand a RN x RK block of B
Packet b00, b10, b20, b30, b01, b11, b21, b31; Packet b00, b10, b20, b30, b01, b11, b21, b31;
b00 = pset1<Packet>(Bc0[0]); b00 = pset1<Packet>(Bc0[0]);
b10 = pset1<Packet>(Bc0[1]); b10 = pset1<Packet>(Bc0[1]);
b20 = pset1<Packet>(Bc0[2]); if(RK==4) b20 = pset1<Packet>(Bc0[2]);
b30 = pset1<Packet>(Bc0[3]); if(RK==4) b30 = pset1<Packet>(Bc0[3]);
b01 = pset1<Packet>(Bc1[0]); b01 = pset1<Packet>(Bc1[0]);
b11 = pset1<Packet>(Bc1[1]); b11 = pset1<Packet>(Bc1[1]);
b21 = pset1<Packet>(Bc1[2]); if(RK==4) b21 = pset1<Packet>(Bc1[2]);
b31 = pset1<Packet>(Bc1[3]); if(RK==4) b31 = pset1<Packet>(Bc1[3]);
Packet a0, a1, a2, a3, c0, c1, t0, t1; Packet a0, a1, a2, a3, c0, c1, t0, t1;
@ -90,46 +91,46 @@ void sparselu_gemm(int m, int n, int d, const Scalar* A, int lda, const Scalar*
Scalar* C0 = C+ib+(j+0)*ldc; Scalar* C0 = C+ib+(j+0)*ldc;
Scalar* C1 = C+ib+(j+1)*ldc; Scalar* C1 = C+ib+(j+1)*ldc;
a0 = pload<Packet>(A0); a0 = pload<Packet>(A0);
a1 = pload<Packet>(A1); a1 = pload<Packet>(A1);
a2 = pload<Packet>(A2); if(RK==4) a2 = pload<Packet>(A2);
a3 = pload<Packet>(A3); if(RK==4) a3 = pload<Packet>(A3);
#define KMADD(c, a, b, tmp) tmp = b; tmp = pmul(a,tmp); c = padd(c,tmp); #define KMADD(c, a, b, tmp) tmp = b; tmp = pmul(a,tmp); c = padd(c,tmp);
#define WORK(I) \ #define WORK(I) \
c0 = pload<Packet>(C0+i+(I)*PacketSize); \ c0 = pload<Packet>(C0+i+(I)*PacketSize); \
c1 = pload<Packet>(C1+i+(I)*PacketSize); \ c1 = pload<Packet>(C1+i+(I)*PacketSize); \
KMADD(c0, a0, b00, t0); \ KMADD(c0, a0, b00, t0); \
KMADD(c1, a0, b01, t1); \ KMADD(c1, a0, b01, t1); \
a0 = pload<Packet>(A0+i+(I+1)*PacketSize); \ a0 = pload<Packet>(A0+i+(I+1)*PacketSize); \
KMADD(c0, a1, b10, t0); \ KMADD(c0, a1, b10, t0); \
KMADD(c1, a1, b11, t1); \ KMADD(c1, a1, b11, t1); \
a1 = pload<Packet>(A1+i+(I+1)*PacketSize); \ a1 = pload<Packet>(A1+i+(I+1)*PacketSize); \
KMADD(c0, a2, b20, t0); \ if(RK==4) KMADD(c0, a2, b20, t0); \
KMADD(c1, a2, b21, t1); \ if(RK==4) KMADD(c1, a2, b21, t1); \
a2 = pload<Packet>(A2+i+(I+1)*PacketSize); \ if(RK==4) a2 = pload<Packet>(A2+i+(I+1)*PacketSize); \
KMADD(c0, a3, b30, t0); \ if(RK==4) KMADD(c0, a3, b30, t0); \
KMADD(c1, a3, b31, t1); \ if(RK==4) KMADD(c1, a3, b31, t1); \
a3 = pload<Packet>(A3+i+(I+1)*PacketSize); \ if(RK==4) a3 = pload<Packet>(A3+i+(I+1)*PacketSize); \
pstore(C0+i+(I)*PacketSize, c0); \ pstore(C0+i+(I)*PacketSize, c0); \
pstore(C1+i+(I)*PacketSize, c1) pstore(C1+i+(I)*PacketSize, c1)
// process rows of A' - C' with aggressive vectorization and peeling // process rows of A' - C' with aggressive vectorization and peeling
for(int i=0; i<actual_b_end1; i+=PacketSize*8) for(int i=0; i<actual_b_end1; i+=PacketSize*8)
{ {
EIGEN_ASM_COMMENT("SPARSELU_GEMML_KERNEL1"); EIGEN_ASM_COMMENT("SPARSELU_GEMML_KERNEL1");
_mm_prefetch((const char*)(A0+i+(5)*PacketSize), _MM_HINT_T0); prefetch((A0+i+(5)*PacketSize));
_mm_prefetch((const char*)(A1+i+(5)*PacketSize), _MM_HINT_T0); prefetch((A1+i+(5)*PacketSize));
_mm_prefetch((const char*)(A2+i+(5)*PacketSize), _MM_HINT_T0); if(RK==4) prefetch((A2+i+(5)*PacketSize));
_mm_prefetch((const char*)(A3+i+(5)*PacketSize), _MM_HINT_T0); if(RK==4) prefetch((A3+i+(5)*PacketSize));
WORK(0); WORK(0);
WORK(1); WORK(1);
WORK(2); WORK(2);
WORK(3); WORK(3);
WORK(4); WORK(4);
WORK(5); WORK(5);
WORK(6); WORK(6);
WORK(7); WORK(7);
} }
// process the remaining rows with vectorization only // process the remaining rows with vectorization only
for(int i=actual_b_end1; i<actual_b_end2; i+=PacketSize) for(int i=actual_b_end1; i<actual_b_end2; i+=PacketSize)
@ -139,8 +140,16 @@ void sparselu_gemm(int m, int n, int d, const Scalar* A, int lda, const Scalar*
// process the remaining rows without vectorization // process the remaining rows without vectorization
for(int i=actual_b_end2; i<actual_b; ++i) for(int i=actual_b_end2; i<actual_b; ++i)
{ {
C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1]+A2[i]*Bc0[2]+A3[i]*Bc0[3]; if(RK==4)
C1[i] += A0[i]*Bc1[0]+A1[i]*Bc1[1]+A2[i]*Bc1[2]+A3[i]*Bc1[3]; {
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; Bc0 += RK;
@ -156,12 +165,12 @@ void sparselu_gemm(int m, int n, int d, const Scalar* A, int lda, const Scalar*
for(int k=0; k<d_end; k+=RK) for(int k=0; k<d_end; k+=RK)
{ {
// load and expand a RN x RK block of B // load and expand a 1 x RK block of B
Packet b00, b10, b20, b30; Packet b00, b10, b20, b30;
b00 = pset1<Packet>(Bc0[0]); b00 = pset1<Packet>(Bc0[0]);
b10 = pset1<Packet>(Bc0[1]); b10 = pset1<Packet>(Bc0[1]);
b20 = pset1<Packet>(Bc0[2]); if(RK==4) b20 = pset1<Packet>(Bc0[2]);
b30 = pset1<Packet>(Bc0[3]); if(RK==4) b30 = pset1<Packet>(Bc0[3]);
Packet a0, a1, a2, a3, c0, t0/*, t1*/; Packet a0, a1, a2, a3, c0, t0/*, t1*/;
@ -172,22 +181,22 @@ void sparselu_gemm(int m, int n, int d, const Scalar* A, int lda, const Scalar*
Scalar* C0 = C+ib+(n_end)*ldc; Scalar* C0 = C+ib+(n_end)*ldc;
a0 = pload<Packet>(A0); a0 = pload<Packet>(A0);
a1 = pload<Packet>(A1); a1 = pload<Packet>(A1);
a2 = pload<Packet>(A2); if(RK==4) a2 = pload<Packet>(A2);
a3 = pload<Packet>(A3); if(RK==4) a3 = pload<Packet>(A3);
#define WORK(I) \ #define WORK(I) \
c0 = pload<Packet>(C0+i+(I)*PacketSize); \ c0 = pload<Packet>(C0+i+(I)*PacketSize); \
KMADD(c0, a0, b00, t0); \ KMADD(c0, a0, b00, t0); \
a0 = pload<Packet>(A0+i+(I+1)*PacketSize); \ a0 = pload<Packet>(A0+i+(I+1)*PacketSize); \
KMADD(c0, a1, b10, t0); \ KMADD(c0, a1, b10, t0); \
a1 = pload<Packet>(A1+i+(I+1)*PacketSize); \ a1 = pload<Packet>(A1+i+(I+1)*PacketSize); \
KMADD(c0, a2, b20, t0); \ if(RK==4) KMADD(c0, a2, b20, t0); \
a2 = pload<Packet>(A2+i+(I+1)*PacketSize); \ if(RK==4) a2 = pload<Packet>(A2+i+(I+1)*PacketSize); \
KMADD(c0, a3, b30, t0); \ if(RK==4) KMADD(c0, a3, b30, t0); \
a3 = pload<Packet>(A3+i+(I+1)*PacketSize); \ if(RK==4) a3 = pload<Packet>(A3+i+(I+1)*PacketSize); \
pstore(C0+i+(I)*PacketSize, c0); pstore(C0+i+(I)*PacketSize, c0);
// agressive vectorization and peeling // agressive vectorization and peeling
for(int i=0; i<actual_b_end1; i+=PacketSize*8) for(int i=0; i<actual_b_end1; i+=PacketSize*8)
@ -210,7 +219,10 @@ void sparselu_gemm(int m, int n, int d, const Scalar* A, int lda, const Scalar*
// remaining scalars // remaining scalars
for(int i=actual_b_end2; i<actual_b; ++i) for(int i=actual_b_end2; i<actual_b; ++i)
{ {
C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1]+A2[i]*Bc0[2]+A3[i]*Bc0[3]; 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; Bc0 += RK;
@ -224,9 +236,12 @@ void sparselu_gemm(int m, int n, int d, const Scalar* A, int lda, const Scalar*
{ {
for(int j=0; j<n; ++j) for(int j=0; j<n; ++j)
{ {
typedef Map<Matrix<Scalar,Dynamic,1>, Aligned > MapVector; enum {
typedef Map<const Matrix<Scalar,Dynamic,1>, Aligned > ConstMapVector; Alignment = PacketSize>1 ? Aligned : 0
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); };
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) 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); + B[1+d_end+j*ldb] * ConstMapVector(A+(d_end+1)*lda+ib, actual_b);