From 798d32edad091b6faaa1627a7514868fc28c5fd9 Mon Sep 17 00:00:00 2001
From: Cedric Nugteren <web@cedricnugteren.nl>
Date: Sun, 17 Jul 2016 14:36:51 +0200
Subject: Improved the GEMM direct kernel by adding register blocking. Still
 not fast though

---
 src/kernels/level3/xgemm_direct.opencl | 190 ++++++++++++++++++++++++++++-----
 1 file changed, 161 insertions(+), 29 deletions(-)

(limited to 'src/kernels')

diff --git a/src/kernels/level3/xgemm_direct.opencl b/src/kernels/level3/xgemm_direct.opencl
index 9d2a55c8..a5e8ca3d 100644
--- a/src/kernels/level3/xgemm_direct.opencl
+++ b/src/kernels/level3/xgemm_direct.opencl
@@ -18,48 +18,180 @@ R"(
 
 // =================================================================================================
 
-// Main entry point of the kernel. This is the direct version.
-__attribute__((reqd_work_group_size(16, 16, 1)))
+// Initializes the accumulation registers to zero
+inline void InitAccRegistersDirect(real cpm[NWI][MWI]) {
+  #pragma unroll
+  for (int mi=0; mi<MWI; ++mi) {
+    #pragma unroll
+    for (int ni=0; ni<NWI; ++ni) {
+      SetToZero(cpm[ni][mi]);
+    }
+  }
+}
+// =================================================================================================
+
+// Performs the actual computation: Cpm += Apm * Bpm
+inline void MultiplyAccumulateDirect(real cpm[NWI][MWI], real apm[MWI], real bpm[NWI]) {
+  #pragma unroll
+  for (int ni=0; ni<NWI; ++ni) {
+    #pragma unroll
+    for (int mi=0; mi<MWI; ++mi) {
+      MultiplyAdd(cpm[ni][mi], apm[mi], bpm[ni]);
+    }
+  }
+}
+
+// =================================================================================================
+
+// 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 StoreResultsDirect(__global real* cgm, real cpm[NWI][MWI],
+                               const int kSizeM, const int kSizeN,
+                               const real alpha, const real beta,
+                               const int c_ld, const int c_offset, const int c_transpose) {
+  #pragma unroll
+  for (int ni=0; ni<NWI; ++ni) {
+    #pragma unroll
+    for (int mi=0; mi<MWI; ++mi) {
+      int mg = mi + get_local_id(0)*MWI;
+      int ng = ni + get_local_id(1)*NWI;
+      int idm = mg + GetGroupID0() * MWG;
+      int idn = ng + GetGroupID1() * NWG;
+
+      // Determines the destination index
+      const int c_index = (c_transpose) ? idm*c_ld + idn : idn*c_ld + idm;
+
+      // The final multiplication with alpha and the addition with beta*C
+      real result;
+      AXPBY(result, alpha, cpm[ni][mi], beta, cgm[c_index + c_offset]);
+      cgm[c_index + c_offset] = result;
+    }
+  }
+}
+
+// =================================================================================================
+
+// Main entry point of the kernel. This is the direct version without restrictions.
+__attribute__((reqd_work_group_size(MDIMC, NDIMC, 1)))
 __kernel void XgemmDirect(const int kSizeM, const int kSizeN, const int kSizeK,
                           const real_arg arg_alpha,
                           const real_arg arg_beta,
-                          const __global real* restrict agm, const int a_offset, const int a_ld,
-                          const __global real* restrict bgm, const int b_offset, const int b_ld,
+                          const __global realM* restrict agm, const int a_offset, const int a_ld,
+                          const __global realN* restrict bgm, const int b_offset, const int b_ld,
                           __global real* cgm, const int c_offset, const int c_ld,
                           const int a_transpose, const int b_transpose, const int c_transpose,
                           const int a_conjugate, const int b_conjugate) {
   const real alpha = GetRealArg(arg_alpha);
   const real beta = GetRealArg(arg_beta);
 
-  // Thread identifiers
-  const int mid = get_global_id(0); // Row ID of cgm
-  const int nid = get_global_id(1); // Col ID of cgm
-
-  // Allows for incomplete workgroups
-  if (mid < kSizeM && nid < kSizeN) {
-
-    // Computes a single element
-    real acc;
-    SetToZero(acc);
-    for (int k=0; k<kSizeK; ++k) {
-      const int a_index = (a_transpose) ? mid*a_ld + k : k*a_ld + mid;
-      const int b_index = (b_transpose) ? nid*b_ld + k : k*b_ld + nid;
-      real a_val = agm[a_index + a_offset];
-      real b_val = bgm[b_index + b_offset];
-      if (a_conjugate) { COMPLEX_CONJUGATE(a_val); }
-      if (b_conjugate) { COMPLEX_CONJUGATE(b_val); }
-      MultiplyAdd(acc, a_val, b_val);
+  // Extra pointers to scalar versions of global memory
+  const __global real* restrict agms = (const __global real* restrict) agm;
+  const __global real* restrict bgms = (const __global real* restrict) bgm;
+
+  // Allocates workitem-private memory (registers)
+  real apm[MWI];
+  real bpm[NWI];
+  real cpm[NWI][MWI];
+
+  // Initializes the accumulation registers
+  InitAccRegistersDirect(cpm);
+
+  // The faster version of GEMM is not allowed on the (incomplete) borders. Therefore, this section
+  // processes only the main parts: output blocks of NWI by MWI.
+  const int idm = get_local_id(0) * MWI + GetGroupID0() * MWG;
+  const int idn = get_local_id(1) * NWI + GetGroupID1() * NWG;
+  if ((idm < kSizeM - MWI) && (idn < kSizeN - NWI)) {
+
+    // Loops over all complete workgroup tiles
+    int kwg = 0;
+    // TODO: Implement a faster version with local memory and vector loads
+    // for (; kwg < kSizeK - KWG; kwg+=KWG) { }
+
+    // Loop over the remaining part (incomplete tile in K-dimension)
+    for (; kwg < kSizeK; ++kwg) {
+      const int idk = kwg;
+
+      // Loads A into register memory
+      #pragma unroll
+      for (int mi=0; mi<MWI; ++mi) {
+        const int a_index = (a_transpose) ? (idm + mi)*a_ld + idk : idk*a_ld + (idm + mi);
+        apm[mi] = agms[a_index + a_offset];
+        if (a_conjugate) { COMPLEX_CONJUGATE(apm[mi]); }
+      }
+
+      // Loads B into register memory
+      #pragma unroll
+      for (int ni=0; ni<NWI; ++ni) {
+        const int b_index = (b_transpose) ? (idn + ni)*b_ld + idk : idk*b_ld + (idn + ni);
+        bpm[ni] = bgms[b_index + b_offset];
+        if (b_conjugate) { COMPLEX_CONJUGATE(bpm[ni]); }
+      }
+
+      // Performs the accumulation (Cpm += Apm * Bpm)
+      MultiplyAccumulateDirect(cpm, apm, bpm);
+    }
+
+    #if GLOBAL_MEM_FENCE == 1
+      barrier(CLK_GLOBAL_MEM_FENCE);
+    #endif
+
+    // Stores a tile of results and performs the multiplication with alpha and beta
+    StoreResultsDirect(cgm, cpm, kSizeM, kSizeN, alpha, beta, c_ld, c_offset, c_transpose);
+  }
+
+  // Simple but slow version for the parts on the edge (incomplete tiles in M and N-dimensions)
+  else {
+
+    // Loop over the K-dimension
+    for (int idk = 0; idk < kSizeK; ++idk) {
+
+      // Loads A into register memory
+      #pragma unroll
+      for (int mi=0; mi<MWI; ++mi) {
+        if (idm + mi < kSizeM) {
+          const int a_index = (a_transpose) ? (idm + mi)*a_ld + idk : idk*a_ld + (idm + mi);
+          apm[mi] = agms[a_index + a_offset];
+          if (a_conjugate) { COMPLEX_CONJUGATE(apm[mi]); }
+        }
+        else {
+          SetToZero(apm[mi]);
+        }
+      }
+
+      // Loads B into register memory
+      #pragma unroll
+      for (int ni=0; ni<NWI; ++ni) {
+        if (idn + ni < kSizeN) {
+          const int b_index = (b_transpose) ? (idn + ni)*b_ld + idk : idk*b_ld + (idn + ni);
+          bpm[ni] = bgms[b_index + b_offset];
+          if (b_conjugate) { COMPLEX_CONJUGATE(bpm[ni]); }
+        }
+        else {
+          SetToZero(bpm[ni]);
+        }
+      }
+
+      // Performs the accumulation (Cpm += Apm * Bpm)
+      MultiplyAccumulateDirect(cpm, apm, bpm);
     }
 
-    // Determines the destination index
-    const int c_index = (c_transpose) ? mid*c_ld + nid : nid*c_ld + mid;
+    // Stores the results
+    #pragma unroll
+    for (int ni=0; ni<NWI; ++ni) {
+      #pragma unroll
+      for (int mi=0; mi<MWI; ++mi) {
+        if ((idm + mi) < kSizeM && (idn + ni) < kSizeN) {
 
-    // Computes the result
-    real result;
-    AXPBY(result, alpha, acc, beta, cgm[c_index + c_offset]);
+          // Determines the destination index
+          const int c_index = (c_transpose) ? (idm + mi)*c_ld + (idn + ni) : (idn + ni)*c_ld + (idm + mi);
 
-    // Stores the result
-    cgm[c_index + c_offset] = result;
+          // Computes and stores the result
+          real result;
+          AXPBY(result, alpha, cpm[ni][mi], beta, cgm[c_index + c_offset]);
+          cgm[c_index + c_offset] = result;
+        }
+      }
+    }
   }
 }
 
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