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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 a generic GEMM kernel that works for all sizes and configurations: it doesn't require any
+// pre and and post-processing kernels.
+//
+// This kernel is seperated into three files. This is part 1 out of 2.
+//
+// =================================================================================================
+
+// 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"(
+
+// Parameters set by the tuner or by the database. Here they are given a basic default value in case
+// this kernel file is used outside of the CLBlast library. Note that all parameters here have a
+// suffix 'D' to denote that they are for the 'direct' version of the GEMM kernel.
+#ifndef WGD
+ #define WGD 8 // Tile-size in dimension M, N, and K (e.g. 8, 16, 32, 64)
+#endif
+#ifndef MDIMCD
+ #define MDIMCD 8 // Threads per workgroup in M-dimension (e.g. 8, 16, 32)
+#endif
+#ifndef NDIMCD
+ #define NDIMCD 8 // Threads per workgroup in N-dimension (e.g. 8, 16, 32)
+#endif
+#ifndef MDIMAD
+ #define MDIMAD 8 // Re-shaped tile dimension of matrix A: KDIMAD * MDIMAD
+#endif
+#ifndef NDIMBD
+ #define NDIMBD 8 // Re-shaped tile dimension of matrix B: KDIMBD * NDIMBD
+#endif
+#ifndef KWID
+ #define KWID 1 // Unroll factor of the WGD loop (smaller or equal than WGD)
+#endif
+#ifndef VWMD
+ #define VWMD 1 // Vector width of matrices A and C
+#endif
+#ifndef VWND
+ #define VWND 1 // Vector width of matrix B
+#endif
+#ifndef PADA
+ #define PADA 1 // Local memory padding for matrix A
+#endif
+#ifndef PADB
+ #define PADB 1 // Local memory padding for matrix B
+#endif
+
+// Helper parameters based on the above tuning parameters
+#define MWID (WGD/MDIMCD) // Work per work-item (M-dimension)
+#define NWID (WGD/NDIMCD) // Work per work-item (N-dimension)
+#define KDIMAD ((MDIMCD*NDIMCD)/(MDIMAD)) // Re-shaped tile dimension of matrix A: KDIMAD * MDIMAD
+#define KDIMBD ((MDIMCD*NDIMCD)/(NDIMBD)) // Re-shaped tile dimension of matrix B: KDIMBD * NDIMBD
+#define MWAD (WGD/MDIMAD) // Amount of loads-per-thread for matrix A (M-dimension)
+#define KWAD (WGD/KDIMAD) // Amount of loads-per-thread for matrix A (K-dimension)
+#define KWBD (WGD/KDIMBD) // Amount of loads-per-thread for matrix B (K-dimension)
+#define NWBD (WGD/NDIMBD) // Amount of loads-per-thread for matrix B (N-dimension)
+
+// =================================================================================================
+
+// Data-widths in dimension M
+#if VWMD == 1
+ typedef real realMD;
+#elif VWMD == 2
+ typedef real2 realMD;
+#elif VWMD == 4
+ typedef real4 realMD;
+#elif VWMD == 8
+ typedef real8 realMD;
+#elif VWMD == 16
+ typedef real16 realMD;
+#endif
+
+// Data-widths in dimension N
+#if VWND == 1
+ typedef real realND;
+#elif VWND == 2
+ typedef real2 realND;
+#elif VWND == 4
+ typedef real4 realND;
+#elif VWND == 8
+ typedef real8 realND;
+#elif VWND == 16
+ typedef real16 realND;
+#endif
+
+// =================================================================================================
+
+// Caches global off-chip memory into local (shared) memory on-chip. This function is specific for
+// caching the A input matrix.
+inline void GlobalToLocalDirectA(const __global realMD* restrict agm, __local real* alm,
+ const int a_ld, const int a_offset, const int kwg,
+ const int a_transpose, const int a_conjugate) {
+ #if MDIMCD == MDIMAD
+ const int la0 = get_local_id(0);
+ const int la1 = get_local_id(1);
+ #else
+ const int tid = get_local_id(0) + MDIMCD*get_local_id(1);
+ const int la0 = tid % MDIMAD;
+ const int la1 = tid / MDIMAD;
+ #endif
+ #pragma unroll
+ for (int mia=0; mia<MWAD/VWMD; ++mia) {
+ #pragma unroll
+ for (int kia=0; kia<KWAD; ++kia) {
+
+ // Computes the indices for the global memory
+ int mg = mia + la0*(MWAD/VWMD);
+ int kg = kia + la1*KWAD;
+ int idm = (a_transpose) ? mg + kwg/VWMD : mg + GetGroupID0()*(WGD/VWMD);
+ int idk = (a_transpose) ? kg + GetGroupID0()*WGD : kg + kwg;
+
+ // Loads the data from global memory into the local memory
+ const realMD avec = agm[idk*(a_ld/VWMD) + idm + a_offset];
+ #if VWMD == 1
+ alm[kg*(WGD + PADA) + mg] = avec;
+ #elif VWMD == 2
+ alm[kg*(WGD + PADA) + mg*VWMD + 0] = avec.x;
+ alm[kg*(WGD + PADA) + mg*VWMD + 1] = avec.y;
+ #elif VWMD == 4
+ alm[kg*(WGD + PADA) + mg*VWMD + 0] = avec.x;
+ alm[kg*(WGD + PADA) + mg*VWMD + 1] = avec.y;
+ alm[kg*(WGD + PADA) + mg*VWMD + 2] = avec.z;
+ alm[kg*(WGD + PADA) + mg*VWMD + 3] = avec.w;
+ #elif VWMD == 8
+ alm[kg*(WGD + PADA) + mg*VWMD + 0] = avec.s0;
+ alm[kg*(WGD + PADA) + mg*VWMD + 1] = avec.s1;
+ alm[kg*(WGD + PADA) + mg*VWMD + 2] = avec.s2;
+ alm[kg*(WGD + PADA) + mg*VWMD + 3] = avec.s3;
+ alm[kg*(WGD + PADA) + mg*VWMD + 4] = avec.s4;
+ alm[kg*(WGD + PADA) + mg*VWMD + 5] = avec.s5;
+ alm[kg*(WGD + PADA) + mg*VWMD + 6] = avec.s6;
+ alm[kg*(WGD + PADA) + mg*VWMD + 7] = avec.s7;
+ #elif VWMD == 16
+ alm[kg*(WGD + PADA) + mg*VWMD + 0] = avec.s0;
+ alm[kg*(WGD + PADA) + mg*VWMD + 1] = avec.s1;
+ alm[kg*(WGD + PADA) + mg*VWMD + 2] = avec.s2;
+ alm[kg*(WGD + PADA) + mg*VWMD + 3] = avec.s3;
+ alm[kg*(WGD + PADA) + mg*VWMD + 4] = avec.s4;
+ alm[kg*(WGD + PADA) + mg*VWMD + 5] = avec.s5;
+ alm[kg*(WGD + PADA) + mg*VWMD + 6] = avec.s6;
+ alm[kg*(WGD + PADA) + mg*VWMD + 7] = avec.s7;
+ alm[kg*(WGD + PADA) + mg*VWMD + 8] = avec.s8;
+ alm[kg*(WGD + PADA) + mg*VWMD + 9] = avec.s9;
+ alm[kg*(WGD + PADA) + mg*VWMD + 10] = avec.sA;
+ alm[kg*(WGD + PADA) + mg*VWMD + 11] = avec.sB;
+ alm[kg*(WGD + PADA) + mg*VWMD + 12] = avec.sC;
+ alm[kg*(WGD + PADA) + mg*VWMD + 13] = avec.sD;
+ alm[kg*(WGD + PADA) + mg*VWMD + 14] = avec.sE;
+ alm[kg*(WGD + PADA) + mg*VWMD + 15] = avec.sF;
+ #endif
+ if (a_conjugate) {
+ for (int vm=0; vm<VWMD; ++vm) {
+ COMPLEX_CONJUGATE(alm[kg*(WGD + PADA) + mg*VWMD + vm]);
+ }
+ }
+ }
+ }
+}
+
+// Same as above, but now for the B input matrix
+inline void GlobalToLocalDirectB(const __global realND* restrict bgm, __local real* blm,
+ const int b_ld, const int b_offset, const int kwg,
+ const int b_transpose, const int b_conjugate) {
+ #if MDIMCD == NDIMBD
+ const int lb0 = get_local_id(0);
+ const int lb1 = get_local_id(1);
+ #else
+ const int tid = get_local_id(0) + MDIMCD*get_local_id(1);
+ const int lb0 = tid % NDIMBD;
+ const int lb1 = tid / NDIMBD;
+ #endif
+ #pragma unroll
+ for (int kib=0; kib<KWBD; ++kib) {
+ #pragma unroll
+ for (int nib=0; nib<NWBD/VWND; ++nib) {
+
+ // Computes the indices for the global memory
+ int ng = nib + lb0*(NWBD/VWND);
+ int kg = kib + lb1*KWBD;
+ int idn = (b_transpose) ? ng + kwg/VWND : ng + GetGroupID1()*(WGD/VWND);
+ int idk = (b_transpose) ? kg + GetGroupID1()*WGD : kg + kwg;
+
+ // Loads the data from global memory into the local memory
+ const realND bvec = bgm[idk*(b_ld/VWND) + idn + b_offset];
+ #if VWND == 1
+ blm[kg*(WGD + PADB) + ng] = bvec;
+ #elif VWND == 2
+ blm[kg*(WGD + PADB) + ng*VWND + 0] = bvec.x;
+ blm[kg*(WGD + PADB) + ng*VWND + 1] = bvec.y;
+ #elif VWND == 4
+ blm[kg*(WGD + PADB) + ng*VWND + 0] = bvec.x;
+ blm[kg*(WGD + PADB) + ng*VWND + 1] = bvec.y;
+ blm[kg*(WGD + PADB) + ng*VWND + 2] = bvec.z;
+ blm[kg*(WGD + PADB) + ng*VWND + 3] = bvec.w;
+ #elif VWND == 8
+ blm[kg*(WGD + PADB) + ng*VWND + 0] = bvec.s0;
+ blm[kg*(WGD + PADB) + ng*VWND + 1] = bvec.s1;
+ blm[kg*(WGD + PADB) + ng*VWND + 2] = bvec.s2;
+ blm[kg*(WGD + PADB) + ng*VWND + 3] = bvec.s3;
+ blm[kg*(WGD + PADB) + ng*VWND + 4] = bvec.s4;
+ blm[kg*(WGD + PADB) + ng*VWND + 5] = bvec.s5;
+ blm[kg*(WGD + PADB) + ng*VWND + 6] = bvec.s6;
+ blm[kg*(WGD + PADB) + ng*VWND + 7] = bvec.s7;
+ #elif VWND == 16
+ blm[kg*(WGD + PADB) + ng*VWND + 0] = bvec.s0;
+ blm[kg*(WGD + PADB) + ng*VWND + 1] = bvec.s1;
+ blm[kg*(WGD + PADB) + ng*VWND + 2] = bvec.s2;
+ blm[kg*(WGD + PADB) + ng*VWND + 3] = bvec.s3;
+ blm[kg*(WGD + PADB) + ng*VWND + 4] = bvec.s4;
+ blm[kg*(WGD + PADB) + ng*VWND + 5] = bvec.s5;
+ blm[kg*(WGD + PADB) + ng*VWND + 6] = bvec.s6;
+ blm[kg*(WGD + PADB) + ng*VWND + 7] = bvec.s7;
+ blm[kg*(WGD + PADB) + ng*VWND + 8] = bvec.s8;
+ blm[kg*(WGD + PADB) + ng*VWND + 9] = bvec.s9;
+ blm[kg*(WGD + PADB) + ng*VWND + 10] = bvec.sA;
+ blm[kg*(WGD + PADB) + ng*VWND + 11] = bvec.sB;
+ blm[kg*(WGD + PADB) + ng*VWND + 12] = bvec.sC;
+ blm[kg*(WGD + PADB) + ng*VWND + 13] = bvec.sD;
+ blm[kg*(WGD + PADB) + ng*VWND + 14] = bvec.sE;
+ blm[kg*(WGD + PADB) + ng*VWND + 15] = bvec.sF;
+ #endif
+ if (b_conjugate) {
+ for (int vn=0; vn<VWND; ++vn) {
+ COMPLEX_CONJUGATE(blm[kg*(WGD + PADB) + ng*VWND + vn]);
+ }
+ }
+ }
+ }
+}
+
+// =================================================================================================
+
+// Caches on-chip local memory into per-thread private memory (registers). This function is specific
+// for caching the A input matrix.
+inline void LocalToPrivateDirectA(__local real* alm, real apm[MWID], const int kg,
+ const int a_transpose) {
+ #pragma unroll
+ for (int mi=0; mi<MWID; ++mi) {
+ const int mg = mi + get_local_id(0)*MWID;
+ const int index = (a_transpose) ? mg*(WGD + PADA) + kg : kg*(WGD + PADA) + mg;
+ apm[mi] = alm[index];
+ }
+}
+
+// Same as above, but now for the B input matrix
+inline void LocalToPrivateDirectB(__local real* blm, real bpm[NWID], const int kg,
+ const int b_transpose) {
+ #pragma unroll
+ for (int ni=0; ni<NWID; ++ni) {
+ const int ng = ni + get_local_id(1)*NWID;
+ const int index = (b_transpose) ? ng*(WGD + PADB) + kg : kg*(WGD + PADB) + ng;
+ bpm[ni] = blm[index];
+ }
+}
+
+// =================================================================================================
+
+// Initializes the accumulation registers to zero
+inline void InitAccRegistersDirect(real cpm[NWID][MWID]) {
+ #pragma unroll
+ for (int mi=0; mi<MWID; ++mi) {
+ #pragma unroll
+ for (int ni=0; ni<NWID; ++ni) {
+ SetToZero(cpm[ni][mi]);
+ }
+ }
+}
+
+// =================================================================================================
+
+// Performs the actual computation: Cpm += Apm * Bpm
+inline void MultiplyAccumulateDirect(real cpm[NWID][MWID], real apm[MWID], real bpm[NWID]) {
+ #pragma unroll
+ for (int ni=0; ni<NWID; ++ni) {
+ #pragma unroll
+ for (int mi=0; mi<MWID; ++mi) {
+ MultiplyAdd(cpm[ni][mi], apm[mi], bpm[ni]);
+ }
+ }
+}
+
+// =================================================================================================
+
+// End of the C++11 raw string literal
+)"
+
+// =================================================================================================