Update tuning parameters to get better performance

src/interface/extension/backend/amd_gpu.hpp

@@ -153,7 +153,7 @@ typename sb_handle_t::event_t _axpy_batch(
   const auto nWG = (_N + local_size - 1) / local_size;
   // the limit for _N*batch_size is taken empirically from test on AMDW6800
   const index_t global_size =
-      (_N * _batch_size >= 327680)
+      (_N * _batch_size >= 163840)
           ? (_N > (1 << 19)) ? (local_size * nWG) / 4 : local_size * nWG
           : local_size * nWG * _batch_size;
   return blas::internal::_axpy_batch_impl<256, 32>(

src/interface/extension/backend/default_cpu.hpp

@@ -124,11 +124,10 @@ typename sb_handle_t::event_t _axpy_batch(
   // local_size taken empirically
   constexpr index_t local_size = static_cast<index_t>(256);
   const auto nWG = (_N + local_size - 1) / local_size;
-  // the limit for _N*batch_size is taken empirically from test on AMDW6800
-  const index_t global_size =
-      (_N * _batch_size >= 327680)
-          ? (_N > (1 << 19)) ? (local_size * nWG) / 4 : local_size * nWG
-          : local_size * nWG * _batch_size;
+  // the limit for _N*batch_size is taken empirically from test on i9 CPU
+  const index_t global_size = (_N * _batch_size >= 163840)
+                                  ? local_size * nWG
+                                  : local_size * nWG * _batch_size;
   return blas::internal::_axpy_batch_impl<256, 32>(
       sb_handle, _N, _alpha, _vx, _incx, _stride_x, _vy, _incy, _stride_y,
       _batch_size, _dependencies, global_size);

src/interface/extension/backend/intel_gpu.hpp

@@ -146,11 +146,10 @@ typename sb_handle_t::event_t _axpy_batch(
   constexpr index_t local_size = static_cast<index_t>(256);
   const auto nWG = (_N + local_size - 1) / local_size;
   // the limit for _N*batch_size is taken empirically from test on intelGPU
-  const index_t global_size =
-      (_N * _batch_size >= 327680)
-          ? (_N > (1 << 19)) ? (local_size * nWG) / 4 : local_size * nWG
-          : local_size * nWG * _batch_size;
-  return blas::internal::_axpy_batch_impl<256, 32>(
+  const index_t global_size = (_N * _batch_size > 327680)
+                                  ? local_size * nWG
+                                  : local_size * nWG * _batch_size;
+  return blas::internal::_axpy_batch_impl<256, 128>(
       sb_handle, _N, _alpha, _vx, _incx, _stride_x, _vy, _incy, _stride_y,
       _batch_size, _dependencies, global_size);
 }

src/interface/extension/backend/nvidia_gpu.hpp

@@ -151,14 +151,23 @@ typename sb_handle_t::event_t _axpy_batch(
   // local_size taken empirically
   constexpr index_t local_size = static_cast<index_t>(256);
   const auto nWG = (_N + local_size - 1) / local_size;
-  // the limit for _N*batch_size is taken empirically from test on AMDW6800
-  const index_t global_size =
-      (_N * _batch_size >= 327680)
-          ? (_N > (1 << 19)) ? (local_size * nWG) / 4 : local_size * nWG
-          : local_size * nWG * _batch_size;
-  return blas::internal::_axpy_batch_impl<256, 32>(
-      sb_handle, _N, _alpha, _vx, _incx, _stride_x, _vy, _incy, _stride_y,
-      _batch_size, _dependencies, global_size);
+  // the limit for _N*batch_size is taken empirically from test on A100
+  if (_N * _batch_size <= 81920) {
+    const index_t global_size = local_size * nWG * _batch_size;
+    return blas::internal::_axpy_batch_impl<256, 32>(
+        sb_handle, _N, _alpha, _vx, _incx, _stride_x, _vy, _incy, _stride_y,
+        _batch_size, _dependencies, global_size);
+  } else if (_N <= (1 << 19)) {
+    const index_t global_size = local_size * nWG;
+    return blas::internal::_axpy_batch_impl<256, 64>(
+        sb_handle, _N, _alpha, _vx, _incx, _stride_x, _vy, _incy, _stride_y,
+        _batch_size, _dependencies, global_size);
+  } else {
+    const index_t global_size = (local_size * nWG);
+    return blas::internal::_axpy_batch_impl<256, 128>(
+        sb_handle, _N, _alpha, _vx, _incx, _stride_x, _vy, _incy, _stride_y,
+        _batch_size, _dependencies, global_size);
+  }
 }
 }  // namespace backend
 }  // namespace axpy_batch