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// =================================================================================================
// This file is part of the CLBlast project. The project is licensed under Apache Version 2.0. This
// project loosely follows the Google C++ styleguide and uses a tab-size of two spaces and a max-
// width of 100 characters per line.
//
// Author(s):
// Cedric Nugteren <www.cedricnugteren.nl>
//
// This is part 2 of 2 of the GEMM kernel. See part 1 for more information.
//
// =================================================================================================
// Enables loading of this file using the C++ pre-processor's #include (C++11 standard raw string
// literal). Comment-out this line for syntax-highlighting when developing.
R"(
// =================================================================================================
// The vectorised multiply-add function
inline realM MultiplyAddVector(realM cvec, const realM avec, const real bval) {
#if USE_VECTOR_MAD == 1
cvec += avec * bval;
#else
#if VWM == 1
MultiplyAdd(cvec, avec, bval);
#elif VWM == 2
MultiplyAdd(cvec.x , avec.x, bval);
MultiplyAdd(cvec.y , avec.y, bval);
#elif VWM == 4
MultiplyAdd(cvec.x , avec.x, bval);
MultiplyAdd(cvec.y , avec.y, bval);
MultiplyAdd(cvec.z , avec.z, bval);
MultiplyAdd(cvec.w , avec.w, bval);
#elif VWM == 8
MultiplyAdd(cvec.s0, avec.s0, bval);
MultiplyAdd(cvec.s1, avec.s1, bval);
MultiplyAdd(cvec.s2, avec.s2, bval);
MultiplyAdd(cvec.s3, avec.s3, bval);
MultiplyAdd(cvec.s4, avec.s4, bval);
MultiplyAdd(cvec.s5, avec.s5, bval);
MultiplyAdd(cvec.s6, avec.s6, bval);
MultiplyAdd(cvec.s7, avec.s7, bval);
#elif VWM == 16
MultiplyAdd(cvec.s0, avec.s0, bval);
MultiplyAdd(cvec.s1, avec.s1, bval);
MultiplyAdd(cvec.s2, avec.s2, bval);
MultiplyAdd(cvec.s3, avec.s3, bval);
MultiplyAdd(cvec.s4, avec.s4, bval);
MultiplyAdd(cvec.s5, avec.s5, bval);
MultiplyAdd(cvec.s6, avec.s6, bval);
MultiplyAdd(cvec.s7, avec.s7, bval);
MultiplyAdd(cvec.s8, avec.s8, bval);
MultiplyAdd(cvec.s9, avec.s9, bval);
MultiplyAdd(cvec.sA, avec.sA, bval);
MultiplyAdd(cvec.sB, avec.sB, bval);
MultiplyAdd(cvec.sC, avec.sC, bval);
MultiplyAdd(cvec.sD, avec.sD, bval);
MultiplyAdd(cvec.sE, avec.sE, bval);
MultiplyAdd(cvec.sF, avec.sF, bval);
#endif
#endif
return cvec;
}
// Performs the actual computation: Cpm += Apm * Bpm
inline void MultiplyAccumulate(realM cpm[NWI][MWI/VWM], realM apm[MWI/VWM], realN bpm[NWI/VWN]) {
#pragma unroll
for (int ni=0; ni<NWI/VWN; ++ni) {
#pragma unroll
for (int mi=0; mi<MWI/VWM; ++mi) {
const realM aval = apm[mi];
#if VWN == 1
cpm[ni*VWN + 0][mi] = MultiplyAddVector(cpm[ni*VWN + 0][mi], aval, bpm[ni]);
#elif VWN == 2
cpm[ni*VWN + 0][mi] = MultiplyAddVector(cpm[ni*VWN + 0][mi], aval, bpm[ni].x);
cpm[ni*VWN + 1][mi] = MultiplyAddVector(cpm[ni*VWN + 1][mi], aval, bpm[ni].y);
#elif VWN == 4
cpm[ni*VWN + 0][mi] = MultiplyAddVector(cpm[ni*VWN + 0][mi], aval, bpm[ni].x);
cpm[ni*VWN + 1][mi] = MultiplyAddVector(cpm[ni*VWN + 1][mi], aval, bpm[ni].y);
cpm[ni*VWN + 2][mi] = MultiplyAddVector(cpm[ni*VWN + 2][mi], aval, bpm[ni].z);
cpm[ni*VWN + 3][mi] = MultiplyAddVector(cpm[ni*VWN + 3][mi], aval, bpm[ni].w);
#elif VWN == 8
cpm[ni*VWN + 0][mi] = MultiplyAddVector(cpm[ni*VWN + 0][mi], aval, bpm[ni].s0);
cpm[ni*VWN + 1][mi] = MultiplyAddVector(cpm[ni*VWN + 1][mi], aval, bpm[ni].s1);
cpm[ni*VWN + 2][mi] = MultiplyAddVector(cpm[ni*VWN + 2][mi], aval, bpm[ni].s2);
cpm[ni*VWN + 3][mi] = MultiplyAddVector(cpm[ni*VWN + 3][mi], aval, bpm[ni].s3);
cpm[ni*VWN + 4][mi] = MultiplyAddVector(cpm[ni*VWN + 4][mi], aval, bpm[ni].s4);
cpm[ni*VWN + 5][mi] = MultiplyAddVector(cpm[ni*VWN + 5][mi], aval, bpm[ni].s5);
cpm[ni*VWN + 6][mi] = MultiplyAddVector(cpm[ni*VWN + 6][mi], aval, bpm[ni].s6);
cpm[ni*VWN + 7][mi] = MultiplyAddVector(cpm[ni*VWN + 7][mi], aval, bpm[ni].s7);
#elif VWN == 16
cpm[ni*VWN + 0 ][mi] = MultiplyAddVector(cpm[ni*VWN + 0 ][mi], aval, bpm[ni].s0);
cpm[ni*VWN + 1 ][mi] = MultiplyAddVector(cpm[ni*VWN + 1 ][mi], aval, bpm[ni].s1);
cpm[ni*VWN + 2 ][mi] = MultiplyAddVector(cpm[ni*VWN + 2 ][mi], aval, bpm[ni].s2);
cpm[ni*VWN + 3 ][mi] = MultiplyAddVector(cpm[ni*VWN + 3 ][mi], aval, bpm[ni].s3);
cpm[ni*VWN + 4 ][mi] = MultiplyAddVector(cpm[ni*VWN + 4 ][mi], aval, bpm[ni].s4);
cpm[ni*VWN + 5 ][mi] = MultiplyAddVector(cpm[ni*VWN + 5 ][mi], aval, bpm[ni].s5);
cpm[ni*VWN + 6 ][mi] = MultiplyAddVector(cpm[ni*VWN + 6 ][mi], aval, bpm[ni].s6);
cpm[ni*VWN + 7 ][mi] = MultiplyAddVector(cpm[ni*VWN + 7 ][mi], aval, bpm[ni].s7);
cpm[ni*VWN + 8 ][mi] = MultiplyAddVector(cpm[ni*VWN + 8 ][mi], aval, bpm[ni].s8);
cpm[ni*VWN + 9 ][mi] = MultiplyAddVector(cpm[ni*VWN + 9 ][mi], aval, bpm[ni].s9);
cpm[ni*VWN + 10][mi] = MultiplyAddVector(cpm[ni*VWN + 10][mi], aval, bpm[ni].sA);
cpm[ni*VWN + 11][mi] = MultiplyAddVector(cpm[ni*VWN + 11][mi], aval, bpm[ni].sB);
cpm[ni*VWN + 12][mi] = MultiplyAddVector(cpm[ni*VWN + 12][mi], aval, bpm[ni].sC);
cpm[ni*VWN + 13][mi] = MultiplyAddVector(cpm[ni*VWN + 13][mi], aval, bpm[ni].sD);
cpm[ni*VWN + 14][mi] = MultiplyAddVector(cpm[ni*VWN + 14][mi], aval, bpm[ni].sE);
cpm[ni*VWN + 15][mi] = MultiplyAddVector(cpm[ni*VWN + 15][mi], aval, bpm[ni].sF);
#endif
}
}
}
// =================================================================================================
// Merges the results in Cpm with the global array in Cgm. This also performs the multiplication
// with the constants: Cgm = alpha*A*B + beta*Cgm = alpha*Cpm + beta*Cgm
inline void StoreResults(__global realM* cgm, realM cpm[NWI][MWI/VWM], const int kSizeM,
const real alpha, const real beta) {
#pragma unroll
for (int ni=0; ni<NWI; ++ni) {
#pragma unroll
for (int mi=0; mi<MWI/VWM; ++mi) {
#if STRM == 0
int mg = mi + get_local_id(0)*(MWI/VWM);
#elif STRM == 1
int mg = get_local_id(0) + mi*MDIMC;
#endif
#if STRN == 0
int ng = ni + get_local_id(1)*NWI;
#elif STRN == 1
int ng = ni%VWN + get_local_id(1)*VWN + (ni/VWN)*VWN*NDIMC;
#endif
int idm = mg + GetGroupID0() * (MWG/VWM);
int idn = ng + GetGroupID1() * NWG;
// The final multiplication with alpha and the addition with beta*C
int index = idn*(kSizeM/VWM) + idm;
realM result;
realM xval = cpm[ni][mi];
realM yval = cgm[index];
#if VWM == 1
AXPBY(result, alpha, xval, beta, yval);
#elif VWM == 2
AXPBY(result.x, alpha, xval.x, beta, yval.x);
AXPBY(result.y, alpha, xval.y, beta, yval.y);
#elif VWM == 4
AXPBY(result.x, alpha, xval.x, beta, yval.x);
AXPBY(result.y, alpha, xval.y, beta, yval.y);
AXPBY(result.z, alpha, xval.z, beta, yval.z);
AXPBY(result.w, alpha, xval.w, beta, yval.w);
#elif VWM == 8
AXPBY(result.s0, alpha, xval.s0, beta, yval.s0);
AXPBY(result.s1, alpha, xval.s1, beta, yval.s1);
AXPBY(result.s2, alpha, xval.s2, beta, yval.s2);
AXPBY(result.s3, alpha, xval.s3, beta, yval.s3);
AXPBY(result.s4, alpha, xval.s4, beta, yval.s4);
AXPBY(result.s5, alpha, xval.s5, beta, yval.s5);
AXPBY(result.s6, alpha, xval.s6, beta, yval.s6);
AXPBY(result.s7, alpha, xval.s7, beta, yval.s7);
#elif VWM == 16
AXPBY(result.s0, alpha, xval.s0, beta, yval.s0);
AXPBY(result.s1, alpha, xval.s1, beta, yval.s1);
AXPBY(result.s2, alpha, xval.s2, beta, yval.s2);
AXPBY(result.s3, alpha, xval.s3, beta, yval.s3);
AXPBY(result.s4, alpha, xval.s4, beta, yval.s4);
AXPBY(result.s5, alpha, xval.s5, beta, yval.s5);
AXPBY(result.s6, alpha, xval.s6, beta, yval.s6);
AXPBY(result.s7, alpha, xval.s7, beta, yval.s7);
AXPBY(result.s8, alpha, xval.s8, beta, yval.s8);
AXPBY(result.s9, alpha, xval.s9, beta, yval.s9);
AXPBY(result.sA, alpha, xval.sA, beta, yval.sA);
AXPBY(result.sB, alpha, xval.sB, beta, yval.sB);
AXPBY(result.sC, alpha, xval.sC, beta, yval.sC);
AXPBY(result.sD, alpha, xval.sD, beta, yval.sD);
AXPBY(result.sE, alpha, xval.sE, beta, yval.sE);
AXPBY(result.sF, alpha, xval.sF, beta, yval.sF);
#endif
cgm[index] = result;
}
}
}
// =================================================================================================
// Main body of the matrix-multiplication algorithm. It calls the (inlined) functions above.
inline void XgemmBody(const int kSizeM, const int kSizeN, const int kSizeK,
const __global realM* restrict agm, const __global realN* restrict bgm,
__global realM* cgm, realM cpm[NWI][MWI/VWM]
#if SA == 1 && SB == 1
, __local realM* alm, __local realN* blm
#elif SA == 1
, __local realM* alm
#elif SB == 1
, __local realN* blm
#endif
) {
// Allocates workitem-private memory (registers)
realM apm[MWI/VWM];
realN bpm[NWI/VWN];
// Combined thread identifier (volatile to disable caching)
#if SA == 1 || SB == 1
volatile int tid = get_local_id(0) + MDIMC*get_local_id(1);
#endif
// Initializes the accumulation registers
InitAccRegisters(cpm);
// Loops over all workgroup tiles
for (int kwg=0; kwg<kSizeK; kwg+=KWG) {
// Loads data: off-chip --> local (matrix A)
#if SA == 1
GlobalToLocalA(agm, alm, kSizeM, tid, kwg);
#endif
// Loads data: off-chip --> local (matrix B)
#if SB == 1
GlobalToLocalB(bgm, blm, kSizeN, tid, kwg);
#endif
#if SA == 1 || SB == 1
barrier(CLK_LOCAL_MEM_FENCE);
#endif
// Loops over all workitem tiles, unrolled by a factor KWI
for (int pwi=0; pwi<KWG; pwi+=KWI) {
#pragma unroll
for (int pit=0; pit<KWI; ++pit) {
#if SA == 0 || SB == 0
int idk = kwg + pwi + pit;
#endif
#if SA == 1 || SB == 1
int kg = pwi+pit;
#endif
// Loads data: local --> private (matrix A)
#if SA == 1
LocalToPrivateA(alm, apm, kg);
// Loads data: off-chip --> private (matrix A)
#else
GlobalToPrivateA(agm, apm, kSizeM, idk, kwg);
#endif
// Loads data: local --> private (matrix B)
#if SB == 1
LocalToPrivateB(blm, bpm, kg);
// Loads data: off-chip --> private (matrix B)
#else
GlobalToPrivateB(bgm, bpm, kSizeN, idk);
#endif
// Performs the accumulation (Cpm += Apm * Bpm)
MultiplyAccumulate(cpm, apm, bpm);
}
}
#if SA == 1 || SB == 1
barrier(CLK_LOCAL_MEM_FENCE);
#endif
}
#if GLOBAL_MEM_FENCE == 1
barrier(CLK_GLOBAL_MEM_FENCE);
#endif
}
// =================================================================================================
// The upper-triangular and lower-triangular kernels are only used in special cases
#if defined(ROUTINE_SYRK) || defined(ROUTINE_HERK) || defined(ROUTINE_SYR2K) || defined(ROUTINE_HER2K)
// Main entry point of the kernel. This is the upper-triangular version.
__attribute__((reqd_work_group_size(MDIMC, NDIMC, 1)))
__kernel void XgemmUpper(const int kSizeN, const int kSizeK,
const __constant real* restrict arg_alpha,
const __constant real* restrict arg_beta,
const __global realM* restrict agm,
const __global realN* restrict bgm,
__global realM* cgm) {
const real alpha = arg_alpha[0];
const real beta = arg_beta[0];
// Skip these threads if they do not contain threads contributing to the upper-triangle
if (GetGroupID1()*NWG < GetGroupID0()*MWG) {
return;
}
// Allocates workgroup-private memory (local memory)
#if SA == 1
__local realM alm[KWG * MWG/VWM];
#endif
#if SB == 1
__local realN blm[KWG * NWG/VWN];
#endif
// Computes the matrix-multiplication and stores the result in register memory
realM cpm[NWI][MWI/VWM];
#if SA == 1 && SB == 1
XgemmBody(kSizeN, kSizeN, kSizeK, agm, bgm, cgm, cpm, alm, blm);
#elif SA == 1
XgemmBody(kSizeN, kSizeN, kSizeK, agm, bgm, cgm, cpm, alm);
#elif SB == 1
XgemmBody(kSizeN, kSizeN, kSizeK, agm, bgm, cgm, cpm, blm);
#else
XgemmBody(kSizeN, kSizeN, kSizeK, agm, bgm, cgm, cpm);
#endif
// Stores an MWG * NWG tile of results and performs the multiplication with alpha and beta
StoreResults(cgm, cpm, kSizeN, alpha, beta);
}
// Main entry point of the kernel. This is the lower-triangular version.
__attribute__((reqd_work_group_size(MDIMC, NDIMC, 1)))
__kernel void XgemmLower(const int kSizeN, const int kSizeK,
const __constant real* restrict arg_alpha,
const __constant real* restrict arg_beta,
const __global realM* restrict agm,
const __global realN* restrict bgm,
__global realM* cgm) {
const real alpha = arg_alpha[0];
const real beta = arg_beta[0];
// Skip these threads if they do not contain threads contributing to the lower-triangle
if (GetGroupID1()*NWG > GetGroupID0()*MWG) {
return;
}
// Allocates workgroup-private memory (local memory)
#if SA == 1
__local realM alm[KWG * MWG/VWM];
#endif
#if SB == 1
__local realN blm[KWG * NWG/VWN];
#endif
// Computes the matrix-multiplication and stores the result in register memory
realM cpm[NWI][MWI/VWM];
#if SA == 1 && SB == 1
XgemmBody(kSizeN, kSizeN, kSizeK, agm, bgm, cgm, cpm, alm, blm);
#elif SA == 1
XgemmBody(kSizeN, kSizeN, kSizeK, agm, bgm, cgm, cpm, alm);
#elif SB == 1
XgemmBody(kSizeN, kSizeN, kSizeK, agm, bgm, cgm, cpm, blm);
#else
XgemmBody(kSizeN, kSizeN, kSizeK, agm, bgm, cgm, cpm);
#endif
// Stores an MWG * NWG tile of results and performs the multiplication with alpha and beta
StoreResults(cgm, cpm, kSizeN, alpha, beta);
}
// =================================================================================================
// If not using a triangular version, include the regular kernel
#else
// Main entry point of the kernel. This is the regular full version.
__attribute__((reqd_work_group_size(MDIMC, NDIMC, 1)))
__kernel void Xgemm(const int kSizeM, const int kSizeN, const int kSizeK,
const __constant real* restrict arg_alpha,
const __constant real* restrict arg_beta,
const __global realM* restrict agm,
const __global realN* restrict bgm,
__global realM* cgm) {
const real alpha = arg_alpha[0];
const real beta = arg_beta[0];
// Allocates workgroup-private memory (local memory)
#if SA == 1
__local realM alm[KWG * MWG/VWM];
#endif
#if SB == 1
__local realN blm[KWG * NWG/VWN];
#endif
// Computes the matrix-multiplication and stores the result in register memory
realM cpm[NWI][MWI/VWM];
#if SA == 1 && SB == 1
XgemmBody(kSizeM, kSizeN, kSizeK, agm, bgm, cgm, cpm, alm, blm);
#elif SA == 1
XgemmBody(kSizeM, kSizeN, kSizeK, agm, bgm, cgm, cpm, alm);
#elif SB == 1
XgemmBody(kSizeM, kSizeN, kSizeK, agm, bgm, cgm, cpm, blm);
#else
XgemmBody(kSizeM, kSizeN, kSizeK, agm, bgm, cgm, cpm);
#endif
// Stores an MWG * NWG tile of results and performs the multiplication with alpha and beta
StoreResults(cgm, cpm, kSizeM, alpha, beta);
}
#endif
// =================================================================================================
// End of the C++11 raw string literal
)"
// =================================================================================================
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