Merge branch 'develop' into gemm_bf16_sk_muozturk

include/ck_tile/ops/fused_moe/pipeline/moe_sorting_pipeline.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core.hpp"
+#include "ck_tile/ops/fused_moe/pipeline/moe_sorting_policy.hpp"
+#include <string>
+#include <type_traits>
+
+#ifndef TOPK_SOFTMAX_USE_RAW_TILE_WINDOW
+#define TOPK_SOFTMAX_USE_RAW_TILE_WINDOW 0
+#endif
+
+namespace ck_tile {
+
+// template <typename Problem_, typename Policy_ = MoeSortingPolicy>
+// struct MoeSortingPipeline
+// {
+//     // TODO: this kernel only support warp per row
+//     using Problem    = remove_cvref_t<Problem_>;
+//     using Policy     = remove_cvref_t<Policy_>;
+//     using WeightType = typename Problem::WeightType;
+
+//     template <typename TopkIdWindow, typename WeightWindow>
+//     CK_TILE_DEVICE auto operator()(const TopkIdWindow& topk_id_window,
+//                                    const WeightWindow& weight_window,
+//                                     index_t* p_sorted_token_ids,
+//                                     WeightType* p_sorted_weights,
+//                                     index_t* p_sorted_expert_ids,
+//                                     index_t* p_total_tokens_post_pad,
+//                                     const index_t num_experts,
+//                                     const index_t unit_size,
+//                                     const size_t numel,
+//                                     const index_t topk)
+//     {
+//     }
+// };
+} // namespace ck_tile

include/ck_tile/ops/fused_moe/pipeline/moe_sorting_policy.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core.hpp"
+#include "ck_tile/ops/softmax.hpp"
+#include "ck_tile/ops/topk.hpp"
+
+namespace ck_tile {
+
+struct MoeSortingPolicy
+{
+};
+} // namespace ck_tile

include/ck_tile/ops/fused_moe/pipeline/moe_sorting_problem.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core.hpp"
+#include <string>
+#include <type_traits>
+
+namespace ck_tile {
+
+template <typename IndexType_, typename WeightType_, index_t InternalLoadUnroll_>
+struct MoeSortingProblem
+{
+    // TODO: this kernel only support warp per row
+    using WeightType = remove_cvref_t<WeightType_>;
+    using IndexType  = remove_cvref_t<IndexType_>;
+
+    static constexpr index_t WarpSize           = get_warp_size();
+    static constexpr index_t WarpsPerBlock      = 1;
+    static constexpr index_t InternalLoadUnroll = InternalLoadUnroll_;
+};
+} // namespace ck_tile

include/ck_tile/ops/gemm.hpp

@@ -8,6 +8,7 @@
 #include "ck_tile/ops/gemm/block/block_gemm_areg_breg_creg_v1.hpp"
 #include "ck_tile/ops/gemm/block/block_gemm_areg_breg_creg_v1_custom_policy.hpp"
 #include "ck_tile/ops/gemm/block/block_gemm_areg_breg_creg_v1_default_policy.hpp"
+#include "ck_tile/ops/gemm/block/block_gemm_areg_bsmem_creg_one_warp_v1.hpp"
 #include "ck_tile/ops/gemm/block/block_gemm_areg_bsmem_creg_v1.hpp"
 #include "ck_tile/ops/gemm/block/block_gemm_areg_bsmem_creg_v1_custom_policy.hpp"
 #include "ck_tile/ops/gemm/block/block_gemm_areg_bsmem_creg_v1_default_policy.hpp"
@@ -21,13 +22,21 @@
 #include "ck_tile/ops/gemm/block/block_gemm_asmem_bsmem_creg_v1_custom_policy.hpp"
 #include "ck_tile/ops/gemm/block/block_gemm_asmem_bsmem_creg_v1_default_policy.hpp"
 #include "ck_tile/ops/gemm/block/block_gemm_problem.hpp"
+#include "ck_tile/ops/gemm/block/block_universal_gemm_as_bs_cr.hpp"
 #include "ck_tile/ops/gemm/kernel/gemm_kernel.hpp"
 #include "ck_tile/ops/gemm/kernel/gemm_tile_partitioner.hpp"
+#include "ck_tile/ops/gemm/kernel/grouped_gemm_kernel.hpp"
+#include "ck_tile/ops/gemm/kernel/batched_gemm_kernel.hpp"
+#include "ck_tile/ops/gemm/pipeline/gemm_pipeline_ag_bg_cr_base.hpp"
+#include "ck_tile/ops/gemm/pipeline/gemm_pipeline_ag_bg_cr_comp_v3.hpp"
+#include "ck_tile/ops/gemm/pipeline/gemm_pipeline_ag_bg_cr_mem.hpp"
+#include "ck_tile/ops/gemm/pipeline/gemm_pipeline_ag_bg_cr_scheduler.hpp"
 #include "ck_tile/ops/gemm/pipeline/gemm_pipeline_agmem_bgmem_creg_v1.hpp"
 #include "ck_tile/ops/gemm/pipeline/gemm_pipeline_agmem_bgmem_creg_v1_default_policy.hpp"
 #include "ck_tile/ops/gemm/pipeline/gemm_pipeline_agmem_bgmem_creg_v2.hpp"
 #include "ck_tile/ops/gemm/pipeline/gemm_pipeline_agmem_bgmem_creg_v2_default_policy.hpp"
 #include "ck_tile/ops/gemm/pipeline/gemm_pipeline_problem.hpp"
+#include "ck_tile/ops/gemm/pipeline/gemm_universal_pipeline_ag_bg_cr_policy.hpp"
 #include "ck_tile/ops/gemm/pipeline/tile_gemm_shape.hpp"
 #include "ck_tile/ops/gemm/pipeline/tile_gemm_traits.hpp"
 #include "ck_tile/ops/gemm/warp/warp_gemm.hpp"
@@ -35,4 +44,5 @@
 #include "ck_tile/ops/gemm/warp/warp_gemm_attribute_mfma_impl.hpp"
 #include "ck_tile/ops/gemm/warp/warp_gemm_dispatcher.hpp"
 #include "ck_tile/ops/gemm/warp/warp_gemm_impl.hpp"
+#include "ck_tile/ops/common/generic_2d_block_shape.hpp"
 #include "ck_tile/ops/common/tensor_layout.hpp"

include/ck_tile/ops/gemm/block/block_gemm_areg_bgmem_creg_v1.hpp

@@ -32,7 +32,7 @@ struct BlockGemmARegBGmemCRegV1
         BlockGemmProblem<ADataType, BDataType, CDataType, kBlockSize, BlockGemmShape>,
         BlockGemmARegBGmemCRegV1DefaultPolicy>;
 
-    CK_TILE_HOST_DEVICE static constexpr ck_tile::index_t GetStaticLdsSize()
+    CK_TILE_HOST_DEVICE static constexpr index_t GetStaticLdsSize()
     {
         return sizeof(BDataType) *
                Policy::template MakeBSmemBlockDescriptor<Problem>().get_element_space_size();

include/ck_tile/ops/gemm/block/block_gemm_areg_breg_creg_v1.hpp

@@ -157,7 +157,7 @@ struct BlockGemmARegBRegCRegV1
         });
     }
 
-    CK_TILE_DEVICE constexpr auto MakeCBlockTile() const
+    CK_TILE_DEVICE static constexpr auto MakeCBlockTile()
     {
         constexpr index_t MPerBlock = BlockGemmShape::kM;
         constexpr index_t NPerBlock = BlockGemmShape::kN;

include/ck_tile/ops/gemm/block/block_gemm_areg_bsmem_creg_one_warp_v1.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core.hpp"
+#include "ck_tile/ops/gemm/block/block_gemm_areg_bsmem_creg_v1_default_policy.hpp"
+
+namespace ck_tile {
+
+// A is block distributed tensor
+// B is block window on shared memory
+// C is block distributed tensor
+template <typename Problem_, typename Policy_ = BlockGemmARegBSmemCRegV1DefaultPolicy>
+struct BlockGemmARegBSmemCRegOneWarpV1
+{
+    using Problem        = remove_cvref_t<Problem_>;
+    using Policy         = remove_cvref_t<Policy_>;
+    using ADataType      = remove_cvref_t<typename Problem::ADataType>;
+    using BDataType      = remove_cvref_t<typename Problem::BDataType>;
+    using CDataType      = remove_cvref_t<typename Problem::CDataType>;
+    using BlockGemmShape = remove_cvref_t<typename Problem::BlockGemmShape>;
+
+    static constexpr index_t kBlockSize = Problem::kBlockSize;
+    static_assert(kBlockSize == get_warp_size(), "Check failed!");
+
+    // C += A * B
+    template <typename CBlockTensor, typename ABlockTensorTmp, typename BBlockWindowTmp>
+    CK_TILE_DEVICE void operator()(CBlockTensor& c_block_tensor,
+                                   const ABlockTensorTmp& a_block_tensor_tmp,
+                                   const BBlockWindowTmp& b_block_window_tmp) const
+    {
+        static_assert(
+            std::is_same_v<ADataType, remove_cv_t<typename ABlockTensorTmp::DataType>> &&
+                std::is_same_v<BDataType, remove_cv_t<typename BBlockWindowTmp::DataType>> &&
+                std::is_same_v<CDataType, remove_cv_t<typename CBlockTensor::DataType>>,
+            "wrong!");
+
+        // constexpr index_t MPerBlock = ABlockTensorTmp{}.get_lengths()[number<0>{}];
+        // constexpr index_t NPerBlock = BBlockWindowTmp{}.get_window_lengths()[number<0>{}];
+        // constexpr index_t KPerBlock = ABlockTensorTmp{}.get_lengths()[number<1>{}];
+        constexpr index_t MPerBlock = BlockGemmShape::kM;
+        constexpr index_t NPerBlock = BlockGemmShape::kN;
+        constexpr index_t KPerBlock = BlockGemmShape::kK;
+
+        // static_assert(MPerBlock == BlockGemmShape::kM && NPerBlock == BlockGemmShape::kN &&
+        //                   KPerBlock == BlockGemmShape::kK,
+        //               "wrong!");
+
+        constexpr auto config = Policy::template GetWarpGemmMWarpNWarp<Problem>();
+
+        using WG = remove_cvref_t<decltype(config.template at<0>())>;
+
+        constexpr index_t MWarp = config.template at<1>();
+        constexpr index_t NWarp = config.template at<2>();
+
+        static_assert(MWarp == 1 && NWarp == 1, "Check failed!");
+
+        constexpr index_t MIterPerWarp = MPerBlock / (MWarp * WG::kM);
+        constexpr index_t NIterPerWarp = NPerBlock / (NWarp * WG::kN);
+        constexpr index_t KIterPerWarp = KPerBlock / WG::kK;
+
+        constexpr index_t NPerBlockPerIter = NPerBlock / NIterPerWarp;
+        constexpr index_t KPerBlockPerIter = KPerBlock / KIterPerWarp;
+
+        const index_t iNWarp = 0;
+
+        constexpr auto a_block_outer_dstr_encoding =
+            tile_distribution_encoding<sequence<NWarp>,
+                                       tuple<sequence<MIterPerWarp, MWarp>, sequence<KIterPerWarp>>,
+                                       tuple<sequence<1, 0>>,
+                                       tuple<sequence<1, 0>>,
+                                       sequence<1, 2>,
+                                       sequence<0, 0>>{};
+
+        constexpr auto c_block_outer_dstr_encoding =
+            tile_distribution_encoding<sequence<>,
+                                       tuple<sequence<MIterPerWarp>, sequence<NIterPerWarp>>,
+                                       tuple<>,
+                                       tuple<>,
+                                       sequence<1, 2>,
+                                       sequence<0, 0>>{};
+
+        constexpr auto a_block_dstr_encode = detail::make_embed_tile_distribution_encoding(
+            a_block_outer_dstr_encoding, typename WG::AWarpDstrEncoding{});
+
+        constexpr auto c_block_dstr_encode = detail::make_embed_tile_distribution_encoding(
+            c_block_outer_dstr_encoding, typename WG::CWarpDstrEncoding{});
+
+        constexpr auto a_block_dstr = make_static_tile_distribution(a_block_dstr_encode);
+
+        // constrcut from A-block-tensor from A-Block-tensor-tmp
+        // FIXME: need method to check a_block_tensor and a_block_tensor_tmp have equivalent
+        // distribution
+        auto a_block_tensor =
+            make_static_distributed_tensor<typename ABlockTensorTmp::DataType>(a_block_dstr);
+
+        a_block_tensor.get_thread_buffer() = a_block_tensor_tmp.get_thread_buffer();
+
+        // construct B-warp-window
+        auto b_warp_window_tmp = make_tile_window(
+            b_block_window_tmp.get_bottom_tensor_view(),
+            make_tuple(number<WG::kN>{}, number<WG::kK>{}),
+            b_block_window_tmp.get_window_origin() + multi_index<2>{iNWarp * WG::kN, 0},
+            make_static_tile_distribution(typename WG::BWarpDstrEncoding{}));
+
+#if 0 // FIXME: using array will cause register spill
+        array<array<decltype(b_warp_window_tmp), KIterPerWarp>, NIterPerWarp> b_warp_windows{
+            {b_warp_window_tmp}};
+
+        for(index_t nIter = 0; nIter < NIterPerWarp; nIter++)
+        {
+            for(index_t kIter = 0; kIter < KIterPerWarp; kIter++)
+            {
+                move_tile_window(b_warp_windows(nIter)(kIter),
+                                 {nIter * NPerBlockPerIter, kIter * KPerBlockPerIter});
+            }
+        }
+#else
+        statically_indexed_array<
+            statically_indexed_array<decltype(b_warp_window_tmp), KIterPerWarp>,
+            NIterPerWarp>
+            b_warp_windows;
+
+        static_for<0, NIterPerWarp, 1>{}([&](auto nIter) {
+            static_for<0, KIterPerWarp, 1>{}([&](auto kIter) {
+                b_warp_windows(nIter)(kIter) = b_warp_window_tmp;
+
+                move_tile_window(b_warp_windows(nIter)(kIter),
+                                 {nIter * NPerBlockPerIter, kIter * KPerBlockPerIter});
+            });
+        });
+#endif
+
+        // check C-block-distribution
+        static_assert(
+            std::is_same_v<remove_cvref_t<decltype(c_block_dstr_encode)>,
+                           remove_cvref_t<decltype(CBlockTensor::get_tile_distribution()
+                                                       .get_static_tile_distribution_encoding())>>,
+            "wrong!");
+
+        using AWarpDstr = typename WG::AWarpDstr;
+        using CWarpDstr = typename WG::CWarpDstr;
+
+        using AWarpTensor = typename WG::AWarpTensor;
+        using CWarpTensor = typename WG::CWarpTensor;
+
+        constexpr auto a_warp_y_lengths =
+            to_sequence(AWarpDstr{}.get_ys_to_d_descriptor().get_lengths());
+        constexpr auto c_warp_y_lengths =
+            to_sequence(CWarpDstr{}.get_ys_to_d_descriptor().get_lengths());
+
+        constexpr auto a_warp_y_index_zeros = uniform_sequence_gen_t<AWarpDstr::NDimY, 0>{};
+        constexpr auto c_warp_y_index_zeros = uniform_sequence_gen_t<CWarpDstr::NDimY, 0>{};
+
+        // hot loop:
+        static_for<0, KIterPerWarp, 1>{}([&](auto kIter) {
+            static_for<0, MIterPerWarp, 1>{}([&](auto mIter) {
+                // read A warp tensor from A block tensor
+                AWarpTensor a_warp_tensor;
+
+                a_warp_tensor.get_thread_buffer() = a_block_tensor.get_y_sliced_thread_data(
+                    merge_sequences(sequence<mIter, kIter>{}, a_warp_y_index_zeros),
+                    merge_sequences(sequence<1, 1>{}, a_warp_y_lengths));
+
+                static_for<0, NIterPerWarp, 1>{}([&](auto nIter) {
+                    // read B warp tensor from B Block window
+                    const auto b_warp_tensor = load_tile(b_warp_windows(nIter)(kIter));
+
+                    // read C warp tensor from C block tensor
+                    CWarpTensor c_warp_tensor;
+
+                    c_warp_tensor.get_thread_buffer() = c_block_tensor.get_y_sliced_thread_data(
+                        merge_sequences(sequence<mIter, nIter>{}, c_warp_y_index_zeros),
+                        merge_sequences(sequence<1, 1>{}, c_warp_y_lengths));
+
+                    // warp GEMM
+                    WG{}(c_warp_tensor, a_warp_tensor, b_warp_tensor);
+
+                    // write C warp tensor into C block tensor
+                    c_block_tensor.set_y_sliced_thread_data(
+                        merge_sequences(sequence<mIter, nIter>{}, c_warp_y_index_zeros),
+                        merge_sequences(sequence<1, 1>{}, c_warp_y_lengths),
+                        c_warp_tensor.get_thread_buffer());
+                });
+            });
+        });
+    }
+
+    CK_TILE_DEVICE static constexpr auto MakeCBlockTile()
+    {
+        constexpr index_t MPerBlock = BlockGemmShape::kM;
+        constexpr index_t NPerBlock = BlockGemmShape::kN;
+
+        constexpr auto config = Policy::template GetWarpGemmMWarpNWarp<Problem>();
+
+        using WG = remove_cvref_t<decltype(config.template at<0>())>;
+
+        constexpr index_t MWarp = config.template at<1>();
+        constexpr index_t NWarp = config.template at<2>();
+
+        static_assert(MWarp == 1 && NWarp == 1, "Check failed!");
+
+        constexpr index_t MIterPerWarp = MPerBlock / (MWarp * WG::kM);
+        constexpr index_t NIterPerWarp = NPerBlock / (NWarp * WG::kN);
+        // constexpr index_t KIterPerWarp = KPerBlock / WG::kK;
+
+        constexpr auto c_block_outer_dstr_encoding =
+            tile_distribution_encoding<sequence<>,
+                                       tuple<sequence<MIterPerWarp>, sequence<NIterPerWarp>>,
+                                       tuple<>,
+                                       tuple<>,
+                                       sequence<1, 2>,
+                                       sequence<0, 0>>{};
+
+        constexpr auto c_block_dstr_encode = detail::make_embed_tile_distribution_encoding(
+            c_block_outer_dstr_encoding, typename WG::CWarpDstrEncoding{});
+
+        static_assert(decltype(c_block_dstr_encode)::NDimP == 1, "Check failed!");
+
+        constexpr auto c_block_dstr = make_static_tile_distribution(c_block_dstr_encode);
+        auto c_block_tensor         = make_static_distributed_tensor<CDataType>(c_block_dstr);
+        return c_block_tensor;
+    }
+
+    // C = A * B
+    template <typename ABlockTensorTmp, typename BBlockWindowTmp>
+    CK_TILE_DEVICE auto operator()(const ABlockTensorTmp& a_block_tensor_tmp,
+                                   const BBlockWindowTmp& b_block_window_tmp) const
+    {
+        auto c_block_tensor = MakeCBlockTile();
+        operator()(c_block_tensor, a_block_tensor_tmp, b_block_window_tmp);
+        return c_block_tensor;
+    }
+};
+
+} // namespace ck_tile

include/ck_tile/ops/gemm/block/block_gemm_areg_bsmem_creg_v1.hpp

@@ -181,7 +181,7 @@ struct BlockGemmARegBSmemCRegV1
         });
     }
 
-    CK_TILE_DEVICE constexpr auto MakeCBlockTile() const
+    CK_TILE_DEVICE static constexpr auto MakeCBlockTile()
     {
         constexpr index_t MPerBlock = BlockGemmShape::kM;
         constexpr index_t NPerBlock = BlockGemmShape::kN;

include/ck_tile/ops/gemm/block/block_gemm_areg_bsmem_creg_v2.hpp

@@ -182,7 +182,7 @@ struct BlockGemmARegBSmemCRegV2
         });
     }
 
-    CK_TILE_DEVICE constexpr auto MakeCBlockTile() const
+    CK_TILE_DEVICE static constexpr auto MakeCBlockTile()
     {
         constexpr index_t MPerBlock = BlockGemmShape::kM;
         constexpr index_t NPerBlock = BlockGemmShape::kN;

include/ck_tile/ops/gemm/block/block_gemm_asmem_breg_creg_v1.hpp

@@ -180,7 +180,7 @@ struct BlockGemmASmemBRegCRegV1
         });
     }
 
-    CK_TILE_DEVICE constexpr auto MakeCBlockTile() const
+    CK_TILE_DEVICE static constexpr auto MakeCBlockTile()
     {
         constexpr index_t MPerBlock = BlockGemmShape::kM;
         constexpr index_t NPerBlock = BlockGemmShape::kN;

include/ck_tile/ops/gemm/block/block_gemm_asmem_bsmem_creg_v1.hpp

@@ -24,19 +24,19 @@ struct BlockGemmASmemBSmemCRegV1
     static constexpr index_t kBlockSize = Problem::kBlockSize;
 
     // C += A * B
-    template <typename CBlockTensor, typename ABlockWindowTmp, typename BBlockWindowTmp>
+    template <typename CBlockTensor, typename ABlockWindow, typename BBlockWindow>
     CK_TILE_DEVICE void operator()(CBlockTensor& c_block_tensor,
-                                   const ABlockWindowTmp& a_block_window_tmp,
-                                   const BBlockWindowTmp& b_block_window_tmp) const
+                                   const ABlockWindow& a_block_window,
+                                   const BBlockWindow& b_block_window) const
     {
-        static_assert(std::is_same_v<ADataType, typename ABlockWindowTmp::DataType> &&
-                          std::is_same_v<BDataType, typename BBlockWindowTmp::DataType> &&
+        static_assert(std::is_same_v<ADataType, typename ABlockWindow::DataType> &&
+                          std::is_same_v<BDataType, typename BBlockWindow::DataType> &&
                           std::is_same_v<CDataType, typename CBlockTensor::DataType>,
                       "wrong!");
 
-        constexpr index_t MPerBlock = ABlockWindowTmp{}.get_window_lengths()[number<0>{}];
-        constexpr index_t NPerBlock = BBlockWindowTmp{}.get_window_lengths()[number<0>{}];
-        constexpr index_t KPerBlock = ABlockWindowTmp{}.get_window_lengths()[number<1>{}];
+        constexpr index_t MPerBlock = ABlockWindow{}.get_window_lengths()[number<0>{}];
+        constexpr index_t NPerBlock = BBlockWindow{}.get_window_lengths()[number<0>{}];
+        constexpr index_t KPerBlock = ABlockWindow{}.get_window_lengths()[number<1>{}];
 
         static_assert(MPerBlock == BlockGemmShape::kM && NPerBlock == BlockGemmShape::kN &&
                           KPerBlock == BlockGemmShape::kK,
@@ -62,9 +62,9 @@ struct BlockGemmASmemBSmemCRegV1
 
         // construct A-warp-window
         auto a_warp_window_tmp = make_tile_window(
-            a_block_window_tmp.get_bottom_tensor_view(),
+            a_block_window.get_bottom_tensor_view(),
             make_tuple(number<WG::kM>{}, number<WG::kK>{}),
-            a_block_window_tmp.get_window_origin() + multi_index<2>{iMWarp * WG::kM, 0},
+            a_block_window.get_window_origin() + multi_index<2>{iMWarp * WG::kM, 0},
             make_static_tile_distribution(typename WG::AWarpDstrEncoding{}));
 
 #if 0 // FIXME: using array will cause register spill
@@ -97,9 +97,9 @@ struct BlockGemmASmemBSmemCRegV1
 
         // construct B-warp-window
         auto b_warp_window_tmp = make_tile_window(
-            b_block_window_tmp.get_bottom_tensor_view(),
+            b_block_window.get_bottom_tensor_view(),
             make_tuple(number<WG::kN>{}, number<WG::kK>{}),
-            b_block_window_tmp.get_window_origin() + multi_index<2>{iNWarp * WG::kN, 0},
+            b_block_window.get_window_origin() + multi_index<2>{iNWarp * WG::kN, 0},
             make_static_tile_distribution(typename WG::BWarpDstrEncoding{}));
 
 #if 0 // FIXME: using array will cause register spill
@@ -167,7 +167,7 @@ struct BlockGemmASmemBSmemCRegV1
         });
     }
 
-    CK_TILE_DEVICE constexpr auto MakeCBlockTile() const
+    CK_TILE_DEVICE static constexpr auto MakeCBlockTile()
     {
         constexpr index_t MPerBlock = BlockGemmShape::kM;
         constexpr index_t NPerBlock = BlockGemmShape::kN;
@@ -200,12 +200,12 @@ struct BlockGemmASmemBSmemCRegV1
     }
 
     // C = A * B
-    template <typename ABlockTensorTmp, typename BBlockWindowTmp>
+    template <typename ABlockTensorTmp, typename BBlockWindow>
     CK_TILE_DEVICE auto operator()(const ABlockTensorTmp& a_block_tensor_tmp,
-                                   const BBlockWindowTmp& b_block_window_tmp) const
+                                   const BBlockWindow& b_block_window) const
     {
         auto c_block_tensor = MakeCBlockTile();
-        operator()(c_block_tensor, a_block_tensor_tmp, b_block_window_tmp);
+        operator()(c_block_tensor, a_block_tensor_tmp, b_block_window);
         return c_block_tensor;
     }
 };

include/ck_tile/ops/gemm/block/block_universal_gemm_as_bs_cr.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core.hpp"
+#include "ck_tile/ops/gemm/block/block_gemm_asmem_bsmem_creg_v1_default_policy.hpp"
+#include "ck_tile/ops/gemm/pipeline/gemm_pipeline_ag_bg_cr_scheduler.hpp"
+
+namespace ck_tile {
+
+// A is block window on shared memory
+// B is block window on shared memory
+// C is block distributed tensor
+template <typename Problem_, typename Policy_ = BlockGemmASmemBSmemCRegV1DefaultPolicy>
+struct BlockUniversalGemmAsBsCr
+{
+    private:
+    // TODO: This should be in Policy - UniversalGemmPolicyBase ?
+    template <typename PipelineProblem_, typename GemmPolicy_>
+    struct GemmTraits_
+    {
+        using Problem        = remove_cvref_t<PipelineProblem_>;
+        using Policy         = remove_cvref_t<GemmPolicy_>;
+        using ADataType      = remove_cvref_t<typename Problem::ADataType>;
+        using BDataType      = remove_cvref_t<typename Problem::BDataType>;
+        using CDataType      = remove_cvref_t<typename Problem::CDataType>;
+        using BlockGemmShape = remove_cvref_t<typename Problem::BlockGemmShape>;
+
+        static constexpr index_t kBlockSize = Problem::kBlockSize;
+        static constexpr auto Scheduler     = Problem::Scheduler;
+
+        static constexpr index_t MPerBlock = BlockGemmShape::kM;
+        static constexpr index_t NPerBlock = BlockGemmShape::kN;
+        static constexpr index_t KPerBlock = BlockGemmShape::kK;
+
+        static constexpr auto config = Policy::template GetWarpGemmMWarpNWarp<Problem>();
+
+        using WarpGemm = remove_cvref_t<decltype(config.template at<0>())>;
+
+        static constexpr index_t MWarp = config.template at<1>();
+        static constexpr index_t NWarp = config.template at<2>();
+
+        using I0 = number<0>;
+        using I1 = number<1>;
+
+        static_assert(MWarp == BlockGemmShape::BlockWarps::at(I0{}),
+                      "Error! WarpGemm's MWarp is not consisten with BlockGemmShape!");
+        static_assert(NWarp == BlockGemmShape::BlockWarps::at(I1{}),
+                      "Error! WarpGemm's NWarp is not consisten with BlockGemmShape!");
+        static_assert(WarpGemm::kM == BlockGemmShape::WarpTile::at(I0{}),
+                      "Error! WarpGemm's M is not consisten with BlockGemmShape!");
+        static_assert(WarpGemm::kN == BlockGemmShape::WarpTile::at(I1{}),
+                      "Error! WarpGemm's N is not consisten with BlockGemmShape!");
+
+        static constexpr index_t MIterPerWarp = MPerBlock / (MWarp * WarpGemm::kM);
+        static constexpr index_t NIterPerWarp = NPerBlock / (NWarp * WarpGemm::kN);
+        static constexpr index_t KIterPerWarp = KPerBlock / WarpGemm::kK;
+
+        static_assert(MIterPerWarp * MWarp * WarpGemm::kM == MPerBlock,
+                      "Error! Warps should cover all Block tile!");
+        static_assert(NIterPerWarp * NWarp * WarpGemm::kN == NPerBlock,
+                      "Error! Warps should cover all Block tile!");
+
+        static constexpr index_t MPerBlockPerIter = MWarp * WarpGemm::kM;
+        static constexpr index_t NPerBlockPerIter = NWarp * WarpGemm::kN;
+        static constexpr index_t KPerBlockPerIter = WarpGemm::kK;
+
+        using AWarpTileDistr = remove_cvref_t<decltype(make_static_tile_distribution(
+            typename WarpGemm::AWarpDstrEncoding{}))>;
+        using BWarpTileDistr = remove_cvref_t<decltype(make_static_tile_distribution(
+            typename WarpGemm::BWarpDstrEncoding{}))>;
+
+        using AWarpTile =
+            remove_cvref_t<decltype(make_static_distributed_tensor<ADataType>(AWarpTileDistr{}))>;
+        using BWarpTile =
+            remove_cvref_t<decltype(make_static_distributed_tensor<BDataType>(BWarpTileDistr{}))>;
+
+        // TODO: Should we have two policies? Interwave & Intrawave ??
+        static constexpr index_t InterWaveSchedulingMacClusters = 1;
+
+        static constexpr index_t KPack      = WarpGemm::kKPerThread;
+        static constexpr index_t KPerThread = KPerBlock / WarpGemm::kK * KPack;
+        static constexpr index_t KRepeat    = KPerThread / KPack;
+    };
+
+    public:
+    using Traits = GemmTraits_<Problem_, Policy_>;
+
+    using ADataType = remove_cvref_t<typename Traits::ADataType>;
+    using BDataType = remove_cvref_t<typename Traits::BDataType>;
+    using CDataType = remove_cvref_t<typename Traits::CDataType>;
+
+    using WarpGemm = remove_cvref_t<typename Traits::WarpGemm>;
+
+    static constexpr index_t KIterPerWarp = Traits::KIterPerWarp;
+    static constexpr index_t MIterPerWarp = Traits::MIterPerWarp;
+    static constexpr index_t NIterPerWarp = Traits::NIterPerWarp;
+
+    static constexpr index_t MWarp = Traits::MWarp;
+    static constexpr index_t NWarp = Traits::NWarp;
+
+    static constexpr auto Scheduler = Traits::Scheduler;
+
+    using I0 = number<0>;
+    using I1 = number<1>;
+
+    private:
+    template <GemmPipelineScheduler Scheduler, typename GemmTraits>
+    struct BlockGemmImpl
+    {
+    };
+
+    template <typename GemmTraits>
+    struct BlockGemmImpl<GemmPipelineScheduler::Default, GemmTraits>
+    {
+        // C += A * B
+        template <typename CBlockTensor, typename ASmemBlockWindow, typename BSmemBlockWindow>
+        CK_TILE_DEVICE void operator()(CBlockTensor& c_block_tensor,
+                                       const ASmemBlockWindow& a_block_window,
+                                       const BSmemBlockWindow& b_block_window)
+        {
+            static_assert(std::is_same_v<CDataType, typename CBlockTensor::DataType>,
+                          "The CDataType as defined in traits should be the same as correspoinding "
+                          "C block tensor data type!");
+            static_assert(std::is_same_v<ADataType, typename ASmemBlockWindow::DataType> &&
+                              std::is_same_v<BDataType, typename BSmemBlockWindow::DataType>,
+                          "The ADataType and BDataType as defined in "
+                          "traits should be the same as correspoinding block window data type!");
+
+            static_assert(
+                GemmTraits::MPerBlock == ASmemBlockWindow{}.get_window_lengths()[I0{}] &&
+                    GemmTraits::NPerBlock == BSmemBlockWindow{}.get_window_lengths()[I0{}] &&
+                    GemmTraits::KPerBlock == ASmemBlockWindow{}.get_window_lengths()[I1{}],
+                "MPerBlock, NPerBlock, KPerBlock defined in "
+                " BlockGemmShape are different from A/B block smem windows apropriate dims!");
+
+            const index_t iMWarp = get_warp_id() / NWarp;
+            const index_t iNWarp = get_warp_id() - (iMWarp * NWarp);
+
+            // TODO: refactor warp_window tile type to class member as it should be
+            // compile-time known information.
+            auto a_warp_window_tmp = make_tile_window(
+                a_block_window.get_bottom_tensor_view(),
+                make_tuple(number<WarpGemm::kM>{}, number<WarpGemm::kK>{}),
+                a_block_window.get_window_origin() + multi_index<2>{iMWarp * WarpGemm::kM, 0},
+                make_static_tile_distribution(typename WarpGemm::AWarpDstrEncoding{}));
+
+            using AWarpWindow = remove_cvref_t<decltype(a_warp_window_tmp)>;
+
+            static_assert(GemmTraits::AWarpTile::get_num_of_dimension() ==
+                              AWarpWindow::get_num_of_dimension(),
+                          "AWarpWindow number of dimensions must be equal to "
+                          "AWarpTile number of dimensions!");
+            static_assert(GemmTraits::AWarpTile::get_lengths() ==
+                              AWarpWindow{}.get_window_lengths(),
+                          "AWarpWindow lengths must be equal to AWarpTile lengths!");
+
+            statically_indexed_array<
+                statically_indexed_array<AWarpWindow, GemmTraits::KIterPerWarp>,
+                MIterPerWarp>
+                a_warp_windows;
+
+            // construct B-warp-window
+            auto b_warp_window_tmp = make_tile_window(
+                b_block_window.get_bottom_tensor_view(),
+                make_tuple(number<WarpGemm::kN>{}, number<WarpGemm::kK>{}),
+                b_block_window.get_window_origin() + multi_index<2>{iNWarp * WarpGemm::kN, 0},
+                make_static_tile_distribution(typename WarpGemm::BWarpDstrEncoding{}));
+
+            using BWarpWindow = remove_cvref_t<decltype(b_warp_window_tmp)>;
+
+            static_assert(GemmTraits::BWarpTile::get_num_of_dimension() ==
+                              BWarpWindow::get_num_of_dimension(),
+                          "BWarpWindow number of dimensions must be equal to "
+                          "BWarpTile number of dimensions!");
+            static_assert(GemmTraits::BWarpTile::get_lengths() ==
+                              BWarpWindow{}.get_window_lengths(),
+                          "BWarpWindow lengths must be equal to BWarpTile lengths!");
+
+            statically_indexed_array<
+                statically_indexed_array<BWarpWindow, GemmTraits::KIterPerWarp>,
+                NIterPerWarp>
+                b_warp_windows;
+
+            static_for<0, MIterPerWarp, 1>{}([&](auto mIter) {
+                static_for<0, GemmTraits::KIterPerWarp, 1>{}([&](auto kIter) {
+                    a_warp_windows(mIter)(kIter) = a_warp_window_tmp;
+
+                    // TODO: I don't have to move 0,0 window!
+                    move_tile_window(a_warp_windows(mIter)(kIter),
+                                     {mIter * GemmTraits::MPerBlockPerIter,
+                                      kIter * GemmTraits::KPerBlockPerIter});
+                });
+            });
+
+            static_for<0, NIterPerWarp, 1>{}([&](auto nIter) {
+                static_for<0, GemmTraits::KIterPerWarp, 1>{}([&](auto kIter) {
+                    b_warp_windows(nIter)(kIter) = b_warp_window_tmp;
+
+                    move_tile_window(b_warp_windows(nIter)(kIter),
+                                     {nIter * GemmTraits::NPerBlockPerIter,
+                                      kIter * GemmTraits::KPerBlockPerIter});
+                });
+            });
+
+            using CWarpDstr   = typename WarpGemm::CWarpDstr;
+            using CWarpTensor = typename WarpGemm::CWarpTensor;
+
+            constexpr auto c_warp_y_lengths =
+                to_sequence(CWarpDstr{}.get_ys_to_d_descriptor().get_lengths());
+            constexpr auto c_warp_y_index_zeros = uniform_sequence_gen_t<CWarpDstr::NDimY, 0>{};
+
+            // hot loop:
+            static_for<0, GemmTraits::KIterPerWarp, 1>{}([&](auto kIter) {
+                static_for<0, MIterPerWarp, 1>{}([&](auto mIter) {
+                    const auto a_warp_tile = load_tile(a_warp_windows(mIter)(kIter));
+
+                    static_for<0, NIterPerWarp, 1>{}([&](auto nIter) {
+                        const auto b_warp_tile = load_tile(b_warp_windows(nIter)(kIter));
+
+                        // read C warp tensor from C block tensor-
+                        CWarpTensor c_warp_tensor;
+
+                        c_warp_tensor.get_thread_buffer() = c_block_tensor.get_y_sliced_thread_data(
+                            merge_sequences(sequence<mIter, nIter>{}, c_warp_y_index_zeros),
+                            merge_sequences(sequence<1, 1>{}, c_warp_y_lengths));
+
+                        // warp GEMM
+                        WarpGemm{}(c_warp_tensor, a_warp_tile, b_warp_tile);
+
+                        // write C warp tensor into C block tensor
+                        c_block_tensor.set_y_sliced_thread_data(
+                            merge_sequences(sequence<mIter, nIter>{}, c_warp_y_index_zeros),
+                            merge_sequences(sequence<1, 1>{}, c_warp_y_lengths),
+                            c_warp_tensor.get_thread_buffer());
+                    });
+                });
+            });
+        }
+    };
+
+    template <typename GemmTraits>
+    struct BlockGemmImpl<GemmPipelineScheduler::Intrawave, GemmTraits>
+    {
+        statically_indexed_array<
+            statically_indexed_array<typename GemmTraits::AWarpTile, KIterPerWarp>,
+            MIterPerWarp>
+            a_warp_tiles_;
+
+        statically_indexed_array<
+            statically_indexed_array<typename GemmTraits::BWarpTile, KIterPerWarp>,
+            NIterPerWarp>
+            b_warp_tiles_;
+
+        template <typename ASmemBlockWindow, typename BSmemBlockWindow>
+        CK_TILE_DEVICE void LocalPrefetch(const ASmemBlockWindow& a_block_window,
+                                          const BSmemBlockWindow& b_block_window)
+        {
+            static_assert(
+                GemmTraits::MPerBlock == ASmemBlockWindow{}.get_window_lengths()[I0{}] &&
+                    GemmTraits::NPerBlock == BSmemBlockWindow{}.get_window_lengths()[I0{}] &&
+                    GemmTraits::KPerBlock == ASmemBlockWindow{}.get_window_lengths()[I1{}],
+                "MPerBlock, NPerBlock, KPerBlock defined in "
+                " BlockGemmShape are different from A/B block smem windows apropriate dims!");
+
+            static_assert(std::is_same_v<ADataType, typename ASmemBlockWindow::DataType> &&
+                              std::is_same_v<BDataType, typename BSmemBlockWindow::DataType>,
+                          "The ADataType and BDataType as defined in "
+                          "traits should be the same as correspoinding block window data type!");
+
+            const index_t iMWarp = get_warp_id() / NWarp;
+            const index_t iNWarp = get_warp_id() - (iMWarp * NWarp);
+
+            // TODO: refactor warp_window tile type to class member as it should be
+            // compile-time known information.
+            auto a_warp_window_tmp = make_tile_window(
+                a_block_window.get_bottom_tensor_view(),
+                make_tuple(number<WarpGemm::kM>{}, number<WarpGemm::kK>{}),
+                a_block_window.get_window_origin() + multi_index<2>{iMWarp * WarpGemm::kM, 0},
+                make_static_tile_distribution(typename WarpGemm::AWarpDstrEncoding{}));
+
+            using AWarpWindow = remove_cvref_t<decltype(a_warp_window_tmp)>;
+
+            static_assert(GemmTraits::AWarpTile::get_num_of_dimension() ==
+                              AWarpWindow::get_num_of_dimension(),
+                          "AWarpWindow number of dimensions must be equal to "
+                          "AWarpTile number of dimensions!");
+            static_assert(GemmTraits::AWarpTile::get_lengths() ==
+                              AWarpWindow{}.get_window_lengths(),
+                          "AWarpWindow lengths must be equal to AWarpTile lengths!");
+
+            statically_indexed_array<statically_indexed_array<AWarpWindow, KIterPerWarp>,
+                                     MIterPerWarp>
+                a_warp_windows;
+
+            // construct B-warp-window
+            auto b_warp_window_tmp = make_tile_window(
+                b_block_window.get_bottom_tensor_view(),
+                make_tuple(number<WarpGemm::kN>{}, number<WarpGemm::kK>{}),
+                b_block_window.get_window_origin() + multi_index<2>{iNWarp * WarpGemm::kN, 0},
+                make_static_tile_distribution(typename WarpGemm::BWarpDstrEncoding{}));
+
+            using BWarpWindow = remove_cvref_t<decltype(b_warp_window_tmp)>;
+
+            static_assert(GemmTraits::BWarpTile::get_num_of_dimension() ==
+                              BWarpWindow::get_num_of_dimension(),
+                          "BWarpWindow number of dimensions must be equal to "
+                          "BWarpTile number of dimensions!");
+            static_assert(GemmTraits::BWarpTile::get_lengths() ==
+                              BWarpWindow{}.get_window_lengths(),
+                          "BWarpWindow lengths must be equal to BWarpTile lengths!");
+
+            statically_indexed_array<statically_indexed_array<BWarpWindow, KIterPerWarp>,
+                                     NIterPerWarp>
+                b_warp_windows;
+
+            static_for<0, MIterPerWarp, 1>{}([&](auto mIter) {
+                static_for<0, KIterPerWarp, 1>{}([&](auto kIter) {
+                    a_warp_windows(mIter)(kIter) = a_warp_window_tmp;
+
+                    // TODO: I don't have to move 0,0 window!
+                    move_tile_window(a_warp_windows(mIter)(kIter),
+                                     {mIter * GemmTraits::MPerBlockPerIter,
+                                      kIter * GemmTraits::KPerBlockPerIter});
+                });
+            });
+
+            static_for<0, NIterPerWarp, 1>{}([&](auto nIter) {
+                static_for<0, KIterPerWarp, 1>{}([&](auto kIter) {
+                    b_warp_windows(nIter)(kIter) = b_warp_window_tmp;
+
+                    move_tile_window(b_warp_windows(nIter)(kIter),
+                                     {nIter * GemmTraits::NPerBlockPerIter,
+                                      kIter * GemmTraits::KPerBlockPerIter});
+                });
+            });
+
+            static_for<0, KIterPerWarp, 1>{}([&](auto kIter) {
+                static_for<0, MIterPerWarp, 1>{}([&](auto mIter) {
+                    // read A warp tensor from A block window
+                    load_tile(a_warp_tiles_(mIter)(kIter), a_warp_windows(mIter)(kIter));
+                });
+                static_for<0, NIterPerWarp, 1>{}([&](auto nIter) {
+                    // read B warp tensor from B Block window
+                    load_tile(b_warp_tiles_(nIter)(kIter), b_warp_windows(nIter)(kIter));
+                });
+            });
+        }
+
+        // C += A * B
+        template <typename CBlockTensor, typename ASmemBlockWindow, typename BSmemBlockWindow>
+        CK_TILE_DEVICE void operator()(CBlockTensor& c_block_tensor,
+                                       [[maybe_unused]] const ASmemBlockWindow& a_block_window,
+                                       [[maybe_unused]] const BSmemBlockWindow& b_block_window)
+        {
+            static_assert(std::is_same_v<CDataType, typename CBlockTensor::DataType>,
+                          "The CDataType as defined in traits should be the same as correspoinding "
+                          "C block tensor data type!");
+
+            using CWarpDstr   = typename WarpGemm::CWarpDstr;
+            using CWarpTensor = typename WarpGemm::CWarpTensor;
+
+            constexpr auto c_warp_y_lengths =
+                to_sequence(CWarpDstr{}.get_ys_to_d_descriptor().get_lengths());
+            constexpr auto c_warp_y_index_zeros = uniform_sequence_gen_t<CWarpDstr::NDimY, 0>{};
+
+            // hot loop:
+            static_for<0, KIterPerWarp, 1>{}([&](auto kIter) {
+                static_for<0, MIterPerWarp, 1>{}([&](auto mIter) {
+                    static_for<0, NIterPerWarp, 1>{}([&](auto nIter) {
+                        // read C warp tensor from C block tensor-
+                        CWarpTensor c_warp_tensor;
+
+                        c_warp_tensor.get_thread_buffer() = c_block_tensor.get_y_sliced_thread_data(
+                            merge_sequences(sequence<mIter, nIter>{}, c_warp_y_index_zeros),
+                            merge_sequences(sequence<1, 1>{}, c_warp_y_lengths));
+
+                        // warp GEMM
+                        WarpGemm{}(c_warp_tensor,
+                                   a_warp_tiles_[mIter][kIter],
+                                   b_warp_tiles_[nIter][kIter]);
+
+                        // write C warp tensor into C block tensor
+                        c_block_tensor.set_y_sliced_thread_data(
+                            merge_sequences(sequence<mIter, nIter>{}, c_warp_y_index_zeros),
+                            merge_sequences(sequence<1, 1>{}, c_warp_y_lengths),
+                            c_warp_tensor.get_thread_buffer());
+                    });
+                });
+            });
+        }
+    };
+
+    template <typename GemmTraits>
+    struct BlockGemmImpl<GemmPipelineScheduler::Interwave, GemmTraits>
+    {
+        static constexpr index_t KPerThread     = GemmTraits::KPerThread;
+        static constexpr index_t NumMacClusters = GemmTraits::InterWaveSchedulingMacClusters;
+        static constexpr index_t KPerInnerLoop =
+            ck_tile::max(KPerThread / NumMacClusters, GemmTraits::KPack);
+        // TODO: do we really need this?? Are there any cases when this would be >=1 ??
+        // Would we need InterWaveSchedulingMacClusters > 1 ???
+        static constexpr index_t KRepeat        = KPerThread / KPerInnerLoop;
+        static constexpr index_t KInnerLoopIter = KPerInnerLoop / GemmTraits::KPack;
+
+        statically_indexed_array<
+            statically_indexed_array<typename GemmTraits::AWarpTile, KInnerLoopIter>,
+            MIterPerWarp>
+            a_warp_tiles_;
+
+        statically_indexed_array<
+            statically_indexed_array<typename GemmTraits::BWarpTile, KInnerLoopIter>,
+            NIterPerWarp>
+            b_warp_tiles_;
+
+        template <index_t KIdx, typename ASmemBlockWindow, typename BSmemBlockWindow>
+        CK_TILE_DEVICE void LocalPrefetch(const ASmemBlockWindow& a_block_window,
+                                          const BSmemBlockWindow& b_block_window)
+        {
+            static_assert(
+                GemmTraits::MPerBlock == ASmemBlockWindow{}.get_window_lengths()[I0{}] &&
+                    GemmTraits::NPerBlock == BSmemBlockWindow{}.get_window_lengths()[I0{}] &&
+                    GemmTraits::KPerBlock == ASmemBlockWindow{}.get_window_lengths()[I1{}],
+                "MPerBlock, NPerBlock, KPerBlock defined in "
+                " BlockGemmShape are different from A/B block smem windows apropriate dims!");
+
+            static_assert(std::is_same_v<ADataType, typename ASmemBlockWindow::DataType> &&
+                              std::is_same_v<BDataType, typename BSmemBlockWindow::DataType>,
+                          "The ADataType and BDataType as defined in "
+                          "traits should be the same as correspoinding block window data type!");
+
+            const index_t iMWarp = get_warp_id() / NWarp;
+            const index_t iNWarp = get_warp_id() - (iMWarp * NWarp);
+
+            // TODO: refactor warp_window tile type to class member as it should be
+            // compile-time known information.
+            auto a_warp_window_tmp = make_tile_window(
+                a_block_window.get_bottom_tensor_view(),
+                make_tuple(number<WarpGemm::kM>{}, number<WarpGemm::kK>{}),
+                a_block_window.get_window_origin() +
+                    multi_index<2>{iMWarp * WarpGemm::kM, KIdx * KPerInnerLoop},
+                make_static_tile_distribution(typename WarpGemm::AWarpDstrEncoding{}));
+
+            using AWarpWindow = remove_cvref_t<decltype(a_warp_window_tmp)>;
+
+            static_assert(GemmTraits::AWarpTile::get_num_of_dimension() ==
+                              AWarpWindow::get_num_of_dimension(),
+                          "AWarpWindow number of dimensions must be equal to "
+                          "AWarpTile number of dimensions!");
+            static_assert(GemmTraits::AWarpTile::get_lengths() ==
+                              AWarpWindow{}.get_window_lengths(),
+                          "AWarpWindow lengths must be equal to AWarpTile lengths!");
+
+            statically_indexed_array<statically_indexed_array<AWarpWindow, KInnerLoopIter>,
+                                     MIterPerWarp>
+                a_warp_windows;
+
+            // construct B-warp-window
+            auto b_warp_window_tmp = make_tile_window(
+                b_block_window.get_bottom_tensor_view(),
+                make_tuple(number<WarpGemm::kN>{}, number<WarpGemm::kK>{}),
+                b_block_window.get_window_origin() +
+                    multi_index<2>{iNWarp * WarpGemm::kN, KIdx * KPerInnerLoop},
+                make_static_tile_distribution(typename WarpGemm::BWarpDstrEncoding{}));
+
+            using BWarpWindow = remove_cvref_t<decltype(b_warp_window_tmp)>;
+
+            static_assert(GemmTraits::BWarpTile::get_num_of_dimension() ==
+                              BWarpWindow::get_num_of_dimension(),
+                          "BWarpWindow number of dimensions must be equal to "
+                          "BWarpTile number of dimensions!");
+            static_assert(GemmTraits::BWarpTile::get_lengths() ==
+                              BWarpWindow{}.get_window_lengths(),
+                          "BWarpWindow lengths must be equal to BWarpTile lengths!");
+
+            statically_indexed_array<statically_indexed_array<BWarpWindow, KInnerLoopIter>,
+                                     NIterPerWarp>
+                b_warp_windows;
+
+            static_for<0, MIterPerWarp, 1>{}([&](auto mIter) {
+                static_for<0, KInnerLoopIter, 1>{}([&](auto kIter) {
+                    a_warp_windows(mIter)(kIter) = a_warp_window_tmp;
+
+                    move_tile_window(a_warp_windows(mIter)(kIter),
+                                     {mIter * GemmTraits::MPerBlockPerIter,
+                                      kIter * GemmTraits::KPerBlockPerIter});
+                });
+            });
+
+            static_for<0, NIterPerWarp, 1>{}([&](auto nIter) {
+                static_for<0, KInnerLoopIter, 1>{}([&](auto kIter) {
+                    b_warp_windows(nIter)(kIter) = b_warp_window_tmp;
+
+                    move_tile_window(b_warp_windows(nIter)(kIter),
+                                     {nIter * GemmTraits::NPerBlockPerIter,
+                                      kIter * GemmTraits::KPerBlockPerIter});
+                });
+            });
+
+            // TODO check if a_warp_tiles has same desc as a_warp_window
+            static_for<0, KInnerLoopIter, 1>{}([&](auto kIter) {
+                static_for<0, MIterPerWarp, 1>{}([&](auto mIter) {
+                    // read A warp tensor from A block window
+                    load_tile(a_warp_tiles_(mIter)(kIter), a_warp_windows(mIter)(kIter));
+                });
+                static_for<0, NIterPerWarp, 1>{}([&](auto nIter) {
+                    // read B warp tensor from B Block window
+                    load_tile(b_warp_tiles_(nIter)(kIter), b_warp_windows(nIter)(kIter));
+                });
+            });
+        }
+
+        // C += A * B
+        template <typename CBlockTensor, typename ASmemBlockWindow, typename BSmemBlockWindow>
+        CK_TILE_DEVICE void operator()(CBlockTensor& c_block_tensor,
+                                       const ASmemBlockWindow& a_block_window,
+                                       const BSmemBlockWindow& b_block_window)
+        {
+            static_assert(std::is_same_v<CDataType, typename CBlockTensor::DataType>,
+                          "The CDataType as defined in traits should be the same as correspoinding "
+                          "C block tensor data type!");
+
+            using CWarpDstr   = typename WarpGemm::CWarpDstr;
+            using CWarpTensor = typename WarpGemm::CWarpTensor;
+
+            constexpr auto c_warp_y_lengths =
+                to_sequence(CWarpDstr{}.get_ys_to_d_descriptor().get_lengths());
+            constexpr auto c_warp_y_index_zeros = uniform_sequence_gen_t<CWarpDstr::NDimY, 0>{};
+
+            // hot loop:
+            static_for<0, KRepeat, 1>{}([&](auto kIter) {
+                LocalPrefetch<kIter.value>(a_block_window, b_block_window);
+                __builtin_amdgcn_sched_barrier(0);
+                // NOTE: Synchronize threads in a workgroup at the start of each MAC
+                // cluster, but except the first, as we can shorten non-MAC cluster a bit
+                // and there's no observable negative impact. The desired effect is waves in
+                // a workgroup executing MAC in sync. This avoids some out-of-sync waves
+                // hijacking MAC resource from other workgroups and reducing the chance of
+                // latency hiding by waiting for the rest of the workgroup at the eventual
+                // sync point.
+                if constexpr(kIter.value != 0 || KRepeat == 1)
+                {
+                    __builtin_amdgcn_s_barrier();
+                    __builtin_amdgcn_sched_barrier(0);
+                }
+
+                static_for<0, KInnerLoopIter, 1>{}([&](auto kInnerIter) {
+                    static_for<0, MIterPerWarp, 1>{}([&](auto mIter) {
+                        static_for<0, NIterPerWarp, 1>{}([&](auto nIter) {
+                            // read C warp tensor from C block tensor-
+                            CWarpTensor c_warp_tensor;
+
+                            c_warp_tensor.get_thread_buffer() =
+                                c_block_tensor.get_y_sliced_thread_data(
+                                    merge_sequences(sequence<mIter, nIter>{}, c_warp_y_index_zeros),
+                                    merge_sequences(sequence<1, 1>{}, c_warp_y_lengths));
+
+                            // The block_sync_lds() here performs double duty:
+                            // A) safeguard against data hazard because barrier from
+                            // blockwise_gemm is moved here B) reduce VMEM FIFO congestion
+                            // by applying small delays to different wavefronts It is
+                            // performed near the end of MAC cluster to minimize lgkmcnt
+                            // penalty
+                            if constexpr(kIter.value == KRepeat - 1 &&
+                                         kInnerIter.value == KInnerLoopIter - 1 &&
+                                         mIter.value == MIterPerWarp - 1 &&
+                                         nIter.value == NIterPerWarp - 1)
+                            {
+                                __builtin_amdgcn_sched_barrier(0);
+                                block_sync_lds();
+                                __builtin_amdgcn_sched_barrier(0);
+                            }
+                            // warp GEMM
+                            WarpGemm{}(c_warp_tensor,
+                                       a_warp_tiles_[mIter][kInnerIter],
+                                       b_warp_tiles_[nIter][kInnerIter]);
+
+                            // write C warp tensor into C block tensor
+                            c_block_tensor.set_y_sliced_thread_data(
+                                merge_sequences(sequence<mIter, nIter>{}, c_warp_y_index_zeros),
+                                merge_sequences(sequence<1, 1>{}, c_warp_y_lengths),
+                                c_warp_tensor.get_thread_buffer());
+
+                            if constexpr(kInnerIter.value == 0 && mIter.value == 0 &&
+                                         nIter.value == 0)
+                            {
+                                __builtin_amdgcn_sched_barrier(0);
+                                __builtin_amdgcn_s_setprio(1);
+                                __builtin_amdgcn_sched_barrier(0);
+                            }
+                        });
+                    });
+                });
+
+                __builtin_amdgcn_sched_barrier(0);
+                __builtin_amdgcn_s_setprio(0);
+                __builtin_amdgcn_sched_barrier(0);
+            });
+        }
+    };
+
+    public:
+    CK_TILE_DEVICE static constexpr auto MakeCBlockTile()
+    {
+        constexpr auto c_block_outer_dstr_encoding = tile_distribution_encoding<
+            sequence<>,
+            tuple<sequence<MIterPerWarp, MWarp>, sequence<NIterPerWarp, NWarp>>,
+            tuple<sequence<1, 2>>,
+            tuple<sequence<1, 1>>,
+            sequence<1, 2>,
+            sequence<0, 0>>{};
+
+        constexpr auto c_block_dstr_encode = detail::make_embed_tile_distribution_encoding(
+            c_block_outer_dstr_encoding, typename WarpGemm::CWarpDstrEncoding{});
+        constexpr auto c_block_dstr = make_static_tile_distribution(c_block_dstr_encode);
+        auto c_block_tensor         = make_static_distributed_tensor<CDataType>(c_block_dstr);
+
+        return c_block_tensor;
+    }
+
+    template <typename ASmemBlockWindow, typename BSmemBlockWindow>
+    CK_TILE_DEVICE void LocalPrefetch(const ASmemBlockWindow& a_block_window,
+                                      const BSmemBlockWindow& b_block_window)
+    {
+        block_gemm_impl_.LocalPrefetch(a_block_window, b_block_window);
+    }
+
+    // C += A * B
+    template <typename CBlockTensor, typename ASmemBlockWindow, typename BSmemBlockWindow>
+    CK_TILE_DEVICE void operator()(CBlockTensor& c_block_tensor,
+                                   const ASmemBlockWindow& a_block_window,
+                                   const BSmemBlockWindow& b_block_window)
+    {
+        block_gemm_impl_(c_block_tensor, a_block_window, b_block_window);
+    }
+
+    // C = A * B
+    template <typename ASmemBlockWindow, typename BSmemBlockWindow>
+    CK_TILE_DEVICE auto operator()(const ASmemBlockWindow& a_block_window,
+                                   const BSmemBlockWindow& b_block_window)
+    {
+        auto c_block_tensor = MakeCBlockTile();
+        block_gemm_impl_(c_block_tensor, a_block_window, b_block_window);
+        return c_block_tensor;
+    }
+
+    private:
+    BlockGemmImpl<Scheduler, Traits> block_gemm_impl_{};
+};
+
+} // namespace ck_tile

include/ck_tile/ops/gemm/kernel/batched_gemm_kernel.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <iostream>
+#include <string>
+
+#include "ck_tile/core.hpp"
+#include "ck_tile/ops/common.hpp"
+
+namespace ck_tile {
+
+struct BatchedGemmHostArgs
+{
+    const void* a_ptr;
+    const void* b_ptr;
+    void* c_ptr;
+    index_t M;
+    index_t N;
+    index_t K;
+    index_t stride_A;
+    index_t stride_B;
+    index_t stride_C;
+    index_t batch_stride_A;
+    index_t batch_stride_B;
+    index_t batch_stride_C;
+    index_t batch_count;
+};
+
+template <typename TilePartitioner_, typename GemmPipeline_, typename EpiloguePipeline_>
+struct BatchedGemmKernel
+{
+    using TilePartitioner                    = remove_cvref_t<TilePartitioner_>;
+    using GemmPipeline                       = remove_cvref_t<GemmPipeline_>;
+    using EpiloguePipeline                   = remove_cvref_t<EpiloguePipeline_>;
+    using ALayout                            = remove_cvref_t<typename GemmPipeline::ALayout>;
+    using BLayout                            = remove_cvref_t<typename GemmPipeline::BLayout>;
+    using CLayout                            = remove_cvref_t<typename GemmPipeline::CLayout>;
+    static constexpr index_t KernelBlockSize = GemmPipeline::BlockSize;
+
+    using ADataType = remove_cvref_t<typename GemmPipeline::ADataType>;
+    using BDataType = remove_cvref_t<typename GemmPipeline::BDataType>;
+    using CDataType = remove_cvref_t<typename EpiloguePipeline::ODataType>;
+
+    struct BatchedGemmKargs
+    {
+        const void* a_ptr;
+        const void* b_ptr;
+        void* c_ptr;
+        index_t M;
+        index_t N;
+        index_t K;
+        index_t stride_A;
+        index_t stride_B;
+        index_t stride_C;
+        index_t batch_stride_A;
+        index_t batch_stride_B;
+        index_t batch_stride_C;
+        index_t batch_count;
+    };
+
+    using Kargs = BatchedGemmKargs;
+    using Hargs = BatchedGemmHostArgs;
+
+    __host__ static constexpr auto GridSize(const Hargs& h)
+    {
+        return TilePartitioner::GridSize(h.M, h.N, h.batch_count);
+    }
+
+    __host__ static constexpr auto BlockSize() { return dim3(KernelBlockSize); }
+
+    CK_TILE_HOST static constexpr BatchedGemmKargs MakeKargs(const Hargs& h)
+    {
+        Kargs k;
+        k.a_ptr          = h.a_ptr;
+        k.b_ptr          = h.b_ptr;
+        k.c_ptr          = h.c_ptr;
+        k.M              = h.M;
+        k.N              = h.N;
+        k.K              = h.K;
+        k.stride_A       = h.stride_A;
+        k.stride_B       = h.stride_B;
+        k.stride_C       = h.stride_C;
+        k.batch_stride_A = h.batch_stride_A;
+        k.batch_stride_B = h.batch_stride_B;
+        k.batch_stride_C = h.batch_stride_C;
+        k.batch_count    = h.batch_count;
+        return k;
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr index_t GetSmemSize()
+    {
+        return max(GemmPipeline::GetSmemSize(), EpiloguePipeline::GetSmemSize());
+    }
+
+    CK_TILE_DEVICE void operator()(Kargs kargs) const
+    {
+        const auto [i_m, i_n] = TilePartitioner{}();
+        const auto i_batch    = __builtin_amdgcn_readfirstlane(blockIdx.z);
+
+        //  options
+        const auto batch_stride_A = __builtin_amdgcn_readfirstlane(kargs.batch_stride_A);
+        const auto batch_offset_A = __builtin_amdgcn_readfirstlane(i_batch * batch_stride_A);
+        const ADataType* a_start  = static_cast<const ADataType*>(kargs.a_ptr);
+
+        const auto batch_stride_B = __builtin_amdgcn_readfirstlane(kargs.batch_stride_B);
+        const auto batch_offset_B = __builtin_amdgcn_readfirstlane(i_batch * batch_stride_B);
+        const BDataType* b_start  = static_cast<const BDataType*>(kargs.b_ptr);
+
+        // Convert pointers to tensor views
+        auto a_tensor_view = [&]() {
+            if constexpr(std::is_same_v<ALayout, tensor_layout::gemm::RowMajor>)
+            {
+                return make_naive_tensor_view<address_space_enum::global>(
+                    a_start + batch_offset_A,
+                    make_tuple(kargs.M, kargs.K),
+                    make_tuple(kargs.stride_A, 1),
+                    number<GemmPipeline::VectorSizeA>{},
+                    number<1>{});
+            }
+            else
+            {
+                return make_naive_tensor_view<address_space_enum::global>(
+                    a_start + batch_offset_A,
+                    make_tuple(kargs.M, kargs.K),
+                    make_tuple(1, kargs.stride_A),
+                    number<1>{},
+                    number<1>{});
+            }
+        }();
+
+        auto b_tensor_view = [&]() {
+            if constexpr(std::is_same_v<BLayout, tensor_layout::gemm::RowMajor>)
+            {
+                return make_naive_tensor_view<address_space_enum::global>(
+                    b_start + batch_offset_B,
+                    make_tuple(kargs.N, kargs.K),
+                    make_tuple(1, kargs.stride_B),
+                    number<1>{},
+                    number<1>{});
+            }
+            else
+            {
+                return make_naive_tensor_view<address_space_enum::global>(
+                    b_start + batch_offset_B,
+                    make_tuple(kargs.N, kargs.K),
+                    make_tuple(kargs.stride_B, 1),
+                    number<GemmPipeline::VectorSizeB>{},
+                    number<1>{});
+            }
+        }();
+
+        auto a_pad_view = [&]() {
+            if constexpr(std::is_same_v<ALayout, tensor_layout::gemm::RowMajor>)
+            {
+                return pad_tensor_view(
+                    a_tensor_view,
+                    make_tuple(number<TilePartitioner::kM>{}, number<TilePartitioner::kK>{}),
+                    sequence<false, GemmPipeline::kPadK>{});
+            }
+            else
+            {
+                return pad_tensor_view(
+                    a_tensor_view,
+                    make_tuple(number<TilePartitioner::kM>{}, number<TilePartitioner::kK>{}),
+                    sequence<GemmPipeline::kPadM, false>{});
+            }
+        }();
+        // clang-format on
+
+        auto a_block_window = make_tile_window(
+            a_pad_view,
+            make_tuple(number<TilePartitioner::kM>{}, number<TilePartitioner::kK>{}),
+            {i_m, 0});
+
+        auto b_pad_view = [&]() {
+            if constexpr(std::is_same_v<BLayout, tensor_layout::gemm::ColumnMajor>)
+            {
+                return pad_tensor_view(
+                    b_tensor_view,
+                    make_tuple(number<TilePartitioner::kN>{}, number<TilePartitioner::kK>{}),
+                    sequence<false, GemmPipeline::kPadK>{});
+            }
+            else
+            {
+                return pad_tensor_view(
+                    b_tensor_view,
+                    make_tuple(number<TilePartitioner::kN>{}, number<TilePartitioner::kK>{}),
+                    sequence<GemmPipeline::kPadN, false>{});
+            }
+        }();
+        // clang-format on
+
+        auto b_block_window = make_tile_window(
+            b_pad_view,
+            make_tuple(number<TilePartitioner::kN>{}, number<TilePartitioner::kK>{}),
+            {i_n, 0});
+
+        // allocate LDS
+        __shared__ char smem_ptr[GetSmemSize()];
+
+        const index_t num_loop = TilePartitioner::GetLoopNum(kargs.K);
+
+        // Run GEMM cooperatively by whole wokrgroup.
+        auto c_block_tile =
+            GemmPipeline{}.template operator()(a_block_window, b_block_window, num_loop, smem_ptr);
+
+        const auto batch_stride_C = __builtin_amdgcn_readfirstlane(kargs.batch_stride_C);
+        const auto batch_offset_C = __builtin_amdgcn_readfirstlane(i_batch * batch_stride_C);
+        CDataType* c_start        = static_cast<CDataType*>(kargs.c_ptr);
+        auto c_tensor_view        = [&]() {
+            if constexpr(std::is_same_v<CLayout, tensor_layout::gemm::RowMajor>)
+            {
+                return make_naive_tensor_view<address_space_enum::global>(
+                    c_start + batch_offset_C,
+                    make_tuple(kargs.M, kargs.N),
+                    make_tuple(kargs.stride_C, 1),
+                    number<GemmPipeline::VectorSizeC>{},
+                    number<1>{});
+            }
+            else
+            {
+                return make_naive_tensor_view<address_space_enum::global>(
+                    c_start + batch_offset_C,
+                    make_tuple(kargs.M, kargs.N),
+                    make_tuple(1, kargs.stride_C),
+                    number<1>{},
+                    number<1>{});
+            }
+        }();
+
+        auto c_pad_view = [&]() {
+            if constexpr(std::is_same_v<CLayout, tensor_layout::gemm::RowMajor>)
+            {
+                return pad_tensor_view(
+                    c_tensor_view,
+                    make_tuple(number<TilePartitioner::kM>{}, number<TilePartitioner::kN>{}),
+                    sequence<false, GemmPipeline::kPadN>{});
+            }
+            else
+            {
+                return pad_tensor_view(
+                    c_tensor_view,
+                    make_tuple(number<TilePartitioner::kM>{}, number<TilePartitioner::kN>{}),
+                    sequence<GemmPipeline::kPadM, false>{});
+            }
+        }();
+        auto c_block_window = make_tile_window(
+            c_pad_view,
+            make_tuple(number<TilePartitioner::kM>{}, number<TilePartitioner::kN>{}),
+            {i_m, i_n});
+
+        EpiloguePipeline{}(c_block_window, c_block_tile);
+    }
+};
+
+} // namespace ck_tile

include/ck_tile/ops/gemm/kernel/gemm_kernel.hpp

@@ -3,12 +3,13 @@
 
 #pragma once
 
-#include "ck_tile/core.hpp"
-#include "ck_tile/ops/common.hpp"
 #include <iostream>
-
 #include <string>
 
+#include "ck_tile/core.hpp"
+#include "ck_tile/ops/common.hpp"
+#include "ck_tile/ops/gemm/pipeline/gemm_pipeline_ag_bg_cr_scheduler.hpp"
+
 namespace ck_tile {
 
 template <typename TilePartitioner_, typename GemmPipeline_, typename EpiloguePipeline_>
@@ -17,20 +18,19 @@ struct GemmKernel
     using TilePartitioner                    = remove_cvref_t<TilePartitioner_>;
     using GemmPipeline                       = remove_cvref_t<GemmPipeline_>;
     using EpiloguePipeline                   = remove_cvref_t<EpiloguePipeline_>;
-    static constexpr index_t KernelBlockSize = GemmPipeline::kBlockSize;
-
-    using ADataType    = remove_cvref_t<typename GemmPipeline::ADataType>;
-    using BDataType    = remove_cvref_t<typename GemmPipeline::BDataType>;
-    using CAccDataType = remove_cvref_t<typename GemmPipeline::CDataType>;
-    using CODataType   = remove_cvref_t<typename EpiloguePipeline::ODataType>;
+    using ALayout                            = remove_cvref_t<typename GemmPipeline::ALayout>;
+    using BLayout                            = remove_cvref_t<typename GemmPipeline::BLayout>;
+    using CLayout                            = remove_cvref_t<typename GemmPipeline::CLayout>;
+    static constexpr index_t KernelBlockSize = GemmPipeline::BlockSize;
 
-    using LayoutA = remove_cvref_t<typename GemmPipeline::LayoutA>;
-    using LayoutB = remove_cvref_t<typename GemmPipeline::LayoutB>;
-    using LayoutC = remove_cvref_t<typename GemmPipeline::LayoutC>;
+    using ADataType = remove_cvref_t<typename GemmPipeline::ADataType>;
+    using BDataType = remove_cvref_t<typename GemmPipeline::BDataType>;
+    // using CAccDataType = remove_cvref_t<typename GemmPipeline::CDataType>;
+    using CDataType = remove_cvref_t<typename EpiloguePipeline::ODataType>;
 
-    __host__ static constexpr auto GridSize(index_t M_size, index_t N_size, index_t Batch_size)
+    __host__ static constexpr auto GridSize(index_t M, index_t N, index_t KBatch)
     {
-        return TilePartitioner::GridSize(M_size, N_size, Batch_size);
+        return TilePartitioner::GridSize(M, N, KBatch);
     }
 
     __host__ static constexpr auto BlockSize() { return dim3(KernelBlockSize); }
@@ -40,34 +40,103 @@ struct GemmKernel
         const void* a_ptr;
         const void* b_ptr;
         void* c_ptr;
-
-        float epsilon;
-
-        ck_tile::index_t M;
-        ck_tile::index_t N;
-        ck_tile::index_t K;
-        ck_tile::index_t stride_A;
-        ck_tile::index_t stride_B;
-        ck_tile::index_t stride_C;
+        index_t M;
+        index_t N;
+        index_t K;
+        index_t stride_A;
+        index_t stride_B;
+        index_t stride_C;
     };
 
     CK_TILE_HOST static constexpr GemmCommonKargs MakeKargs(const void* a_ptr,
                                                             const void* b_ptr,
                                                             void* c_ptr,
-                                                            float epsilon,
-                                                            ck_tile::index_t M,
-                                                            ck_tile::index_t N,
-                                                            ck_tile::index_t K,
-                                                            ck_tile::index_t stride_A,
-                                                            ck_tile::index_t stride_B,
-                                                            ck_tile::index_t stride_C)
+                                                            index_t M,
+                                                            index_t N,
+                                                            index_t K,
+                                                            index_t stride_A,
+                                                            index_t stride_B,
+                                                            index_t stride_C)
     {
-        return GemmCommonKargs{a_ptr, b_ptr, c_ptr, epsilon, M, N, K, stride_A, stride_B, stride_C};
+        return GemmCommonKargs{a_ptr, b_ptr, c_ptr, M, N, K, stride_A, stride_B, stride_C};
     }
 
-    CK_TILE_HOST_DEVICE static constexpr ck_tile::index_t GetSmemSize()
+    CK_TILE_HOST_DEVICE static constexpr index_t GetSmemSize()
     {
-        return ck_tile::max(GemmPipeline::GetSmemSize(), EpiloguePipeline::GetSmemSize());
+        return max(GemmPipeline::GetSmemSize(), EpiloguePipeline::GetSmemSize());
+    }
+
+    CK_TILE_HOST static bool IsSupportedArgument(const GemmCommonKargs& kargs)
+    {
+        if constexpr(std::is_same_v<ALayout, tensor_layout::gemm::RowMajor>)
+        {
+            if(kargs.K % TilePartitioner::kK != 0 && GemmPipeline::kPadK == false)
+            {
+                return false;
+            }
+            if(kargs.K % GemmPipeline::VectorSizeA != 0)
+            {
+                return false;
+            }
+        }
+        else
+        {
+            if(kargs.M % TilePartitioner::kM != 0 && GemmPipeline::kPadM == false)
+            {
+                return false;
+            }
+            if(kargs.M % GemmPipeline::VectorSizeA != 0)
+            {
+                return false;
+            }
+        }
+
+        if constexpr(std::is_same_v<BLayout, tensor_layout::gemm::RowMajor>)
+        {
+            if(kargs.N % TilePartitioner::kN != 0 && GemmPipeline::kPadN == false)
+            {
+                return false;
+            }
+            if(kargs.N % GemmPipeline::VectorSizeB != 0)
+            {
+                return false;
+            }
+        }
+        else
+        {
+            if(kargs.K % TilePartitioner::kK != 0 && GemmPipeline::kPadK == false)
+            {
+                return false;
+            }
+            if(kargs.K % GemmPipeline::VectorSizeB != 0)
+            {
+                return false;
+            }
+        }
+
+        if constexpr(std::is_same_v<CLayout, tensor_layout::gemm::RowMajor>)
+        {
+            if(kargs.N % TilePartitioner::kN != 0 && GemmPipeline::kPadN == false)
+            {
+                return false;
+            }
+            if(kargs.N % GemmPipeline::VectorSizeC != 0)
+            {
+                return false;
+            }
+        }
+        else
+        {
+            if(kargs.M % TilePartitioner::kM != 0 && GemmPipeline::kPadM == false)
+            {
+                return false;
+            }
+            if(kargs.M % GemmPipeline::VectorSizeC != 0)
+            {
+                return false;
+            }
+        }
+        return true;
     }
 
     CK_TILE_DEVICE void operator()(GemmCommonKargs kargs) const
@@ -78,13 +147,13 @@ struct GemmKernel
         const BDataType* b_start = static_cast<const BDataType*>(kargs.b_ptr);
         // Convert pointers to tensor views
         auto a_tensor_view = [&]() {
-            if constexpr(std::is_same_v<LayoutA, tensor_layout::gemm::ColumnMajor>)
+            if constexpr(std::is_same_v<ALayout, tensor_layout::gemm::RowMajor>)
             {
                 return make_naive_tensor_view<address_space_enum::global>(
                     a_start,
                     make_tuple(kargs.M, kargs.K),
-                    make_tuple(1, kargs.stride_A),
-                    number<GemmPipeline::AlignmentA>{},
+                    make_tuple(kargs.stride_A, 1),
+                    number<GemmPipeline::VectorSizeA>{},
                     number<1>{});
             }
             else
@@ -92,51 +161,74 @@ struct GemmKernel
                 return make_naive_tensor_view<address_space_enum::global>(
                     a_start,
                     make_tuple(kargs.M, kargs.K),
-                    make_tuple(kargs.stride_A, 1),
-                    number<GemmPipeline::AlignmentA>{},
+                    make_tuple(1, kargs.stride_A),
+                    number<1>{},
                     number<1>{});
             }
         }();
 
         auto b_tensor_view = [&]() {
-            if constexpr(std::is_same_v<LayoutB, tensor_layout::gemm::RowMajor>)
+            if constexpr(std::is_same_v<BLayout, tensor_layout::gemm::RowMajor>)
             {
                 return make_naive_tensor_view<address_space_enum::global>(
                     b_start,
                     make_tuple(kargs.N, kargs.K),
                     make_tuple(1, kargs.stride_B),
-                    number<GemmPipeline::AlignmentB>{},
+                    number<1>{},
                     number<1>{});
             }
             else
-            { // Default NK layout
+            {
                 return make_naive_tensor_view<address_space_enum::global>(
                     b_start,
                     make_tuple(kargs.N, kargs.K),
                     make_tuple(kargs.stride_B, 1),
-                    number<GemmPipeline::AlignmentB>{},
+                    number<GemmPipeline::VectorSizeB>{},
                     number<1>{});
             }
         }();
 
-        auto a_pad_view = pad_tensor_view(
-            a_tensor_view,
-            make_tuple(number<TilePartitioner::kM>{}, number<TilePartitioner::kK>{}),
-            sequence < 0,
-            GemmPipeline::kPadA ? 1 : 0 > {});
+        auto a_pad_view = [&]() {
+            if constexpr(std::is_same_v<ALayout, tensor_layout::gemm::RowMajor>)
+            {
+                return pad_tensor_view(
+                    a_tensor_view,
+                    make_tuple(number<TilePartitioner::kM>{}, number<TilePartitioner::kK>{}),
+                    sequence<false, GemmPipeline::kPadK>{});
+            }
+            else
+            {
+                return pad_tensor_view(
+                    a_tensor_view,
+                    make_tuple(number<TilePartitioner::kM>{}, number<TilePartitioner::kK>{}),
+                    sequence<GemmPipeline::kPadM, false>{});
+            }
+        }();
+        // clang-format on
 
-        auto ABlockWindow = make_tile_window(
+        auto a_block_window = make_tile_window(
             a_pad_view,
             make_tuple(number<TilePartitioner::kM>{}, number<TilePartitioner::kK>{}),
             {i_m, 0});
 
-        auto b_pad_view = pad_tensor_view(
-            b_tensor_view,
-            make_tuple(number<TilePartitioner::kN>{}, number<TilePartitioner::kK>{}),
-            sequence < 0,
-            GemmPipeline::kPadB ? 1 : 0 > {});
+        auto b_pad_view = [&]() {
+            if constexpr(std::is_same_v<BLayout, tensor_layout::gemm::ColumnMajor>)
+            {
+                return pad_tensor_view(
+                    b_tensor_view,
+                    make_tuple(number<TilePartitioner::kN>{}, number<TilePartitioner::kK>{}),
+                    sequence<false, GemmPipeline::kPadK>{});
+            }
+            else
+            {
+                return pad_tensor_view(
+                    b_tensor_view,
+                    make_tuple(number<TilePartitioner::kN>{}, number<TilePartitioner::kK>{}),
+                    sequence<GemmPipeline::kPadN, false>{});
+            }
+        }();
 
-        auto BBlockWindow = make_tile_window(
+        auto b_block_window = make_tile_window(
             b_pad_view,
             make_tuple(number<TilePartitioner::kN>{}, number<TilePartitioner::kK>{}),
             {i_n, 0});
@@ -144,20 +236,21 @@ struct GemmKernel
         // allocate LDS
         __shared__ char smem_ptr[GetSmemSize()];
 
-        const index_t num_loop = (kargs.K + TilePartitioner::kK - 1) / TilePartitioner::kK;
+        const index_t num_loop = TilePartitioner::GetLoopNum(kargs.K);
 
-        auto acc = GemmPipeline{}(ABlockWindow, BBlockWindow, num_loop, smem_ptr);
-
-        CODataType* c_start = static_cast<CODataType*>(kargs.c_ptr);
+        // Run GEMM cooperatively by whole wokrgroup.
+        auto c_block_tile =
+            GemmPipeline{}.template operator()(a_block_window, b_block_window, num_loop, smem_ptr);
 
+        CDataType* c_start = static_cast<CDataType*>(kargs.c_ptr);
         auto c_tensor_view = [&]() {
-            if constexpr(std::is_same_v<LayoutC, tensor_layout::gemm::ColumnMajor>)
+            if constexpr(std::is_same_v<CLayout, tensor_layout::gemm::RowMajor>)
             {
                 return make_naive_tensor_view<address_space_enum::global>(
                     c_start,
                     make_tuple(kargs.M, kargs.N),
-                    make_tuple(1, kargs.stride_C),
-                    number<GemmPipeline::AlignmentC>{},
+                    make_tuple(kargs.stride_C, 1),
+                    number<GemmPipeline::VectorSizeC>{},
                     number<1>{});
             }
             else
@@ -165,23 +258,34 @@ struct GemmKernel
                 return make_naive_tensor_view<address_space_enum::global>(
                     c_start,
                     make_tuple(kargs.M, kargs.N),
-                    make_tuple(kargs.stride_C, 1),
-                    number<GemmPipeline::AlignmentC>{},
+                    make_tuple(1, kargs.stride_C),
+                    number<1>{},
                     number<1>{});
             }
         }();
 
-        auto c_pad_view = pad_tensor_view(
-            c_tensor_view,
-            make_tuple(number<TilePartitioner::kM>{}, number<TilePartitioner::kN>{}),
-            sequence < 0,
-            GemmPipeline::kPadC ? 1 : 0 > {});
+        auto c_pad_view = [&]() {
+            if constexpr(std::is_same_v<CLayout, tensor_layout::gemm::RowMajor>)
+            {
+                return pad_tensor_view(
+                    c_tensor_view,
+                    make_tuple(number<TilePartitioner::kM>{}, number<TilePartitioner::kN>{}),
+                    sequence<false, GemmPipeline::kPadN>{});
+            }
+            else
+            {
+                return pad_tensor_view(
+                    c_tensor_view,
+                    make_tuple(number<TilePartitioner::kM>{}, number<TilePartitioner::kN>{}),
+                    sequence<GemmPipeline::kPadM, false>{});
+            }
+        }();
         auto CBlockWindow_pad = make_tile_window(
             c_pad_view,
             make_tuple(number<TilePartitioner::kM>{}, number<TilePartitioner::kN>{}),
             {i_m, i_n});
 
-        EpiloguePipeline{}(CBlockWindow_pad, acc);
+        EpiloguePipeline{}(CBlockWindow_pad, c_block_tile);
     }
 };
 

include/ck_tile/ops/gemm/kernel/gemm_tile_partitioner.hpp

@@ -9,26 +9,66 @@ namespace ck_tile {
 template <typename BlockGemmShape_>
 struct GemmTilePartitioner
 {
-    using BlockGemmShape = ck_tile::remove_cvref_t<BlockGemmShape_>;
+    using BlockGemmShape = remove_cvref_t<BlockGemmShape_>;
 
-    static constexpr ck_tile::index_t kM = BlockGemmShape::kM;
-    static constexpr ck_tile::index_t kN = BlockGemmShape::kN;
-    static constexpr ck_tile::index_t kK = BlockGemmShape::kK;
+    static constexpr index_t kM = BlockGemmShape::kM;
+    static constexpr index_t kN = BlockGemmShape::kN;
+    static constexpr index_t kK = BlockGemmShape::kK;
 
-    CK_TILE_HOST static constexpr auto
-    GridSize(ck_tile::index_t M, ck_tile::index_t N, ck_tile::index_t batch_size)
+    CK_TILE_HOST static constexpr auto GridSize(index_t M, index_t N, index_t batch_size)
     {
-        ck_tile::index_t GridDimX = (M + kM - 1) / kM;
-        ck_tile::index_t GridDimY = (N + kN - 1) / kN;
-        ck_tile::index_t GridDimZ = batch_size;
+        index_t GridDimX = (M + kM - 1) / kM;
+        index_t GridDimY = (N + kN - 1) / kN;
+        index_t GridDimZ = batch_size;
         return dim3(GridDimX, GridDimY, GridDimZ);
     }
 
+    CK_TILE_HOST_DEVICE static constexpr auto GetLoopNum(index_t K)
+    {
+        return integer_divide_ceil(K, kK);
+    }
+
     CK_TILE_DEVICE auto operator()()
     {
         const index_t iM = __builtin_amdgcn_readfirstlane(blockIdx.x * kM);
         const index_t iN = __builtin_amdgcn_readfirstlane(blockIdx.y * kN);
-        return ck_tile::make_tuple(iM, iN);
+        return make_tuple(iM, iN);
+    }
+};
+
+template <typename BlockGemmShape_>
+struct GemmTile1DPartitioner
+{
+    using BlockGemmShape = remove_cvref_t<BlockGemmShape_>;
+
+    static constexpr index_t MPerBlock = BlockGemmShape::kM;
+    static constexpr index_t NPerBlock = BlockGemmShape::kN;
+    static constexpr index_t KPerBlock = BlockGemmShape::kK;
+
+    CK_TILE_HOST static constexpr auto GridSize(index_t M, index_t N)
+    {
+        index_t GridDimX = (M + MPerBlock - 1) / MPerBlock;
+        index_t GridDimY = (N + NPerBlock - 1) / NPerBlock;
+        return dim3(GridDimX * GridDimY, 1, 1);
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr auto GetNBlock(index_t N)
+    {
+        return integer_divide_ceil(N, NPerBlock);
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr auto GetLoopNum(index_t K)
+    {
+        return integer_divide_ceil(K, KPerBlock);
+    }
+
+    CK_TILE_DEVICE auto operator()(index_t blockOffset, index_t NBlockSize)
+    {
+        index_t iM = __builtin_amdgcn_readfirstlane((blockIdx.x - blockOffset) /
+                                                    GetNBlock(NBlockSize) * MPerBlock);
+        index_t iN = __builtin_amdgcn_readfirstlane((blockIdx.x - blockOffset) %
+                                                    GetNBlock(NBlockSize) * NPerBlock);
+        return make_tuple(iM, iN);
     }
 };
 } // namespace ck_tile

include/ck_tile/ops/gemm/kernel/grouped_gemm_kernel.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <iostream>
+#include <string>
+
+#include "ck_tile/core/numeric/math.hpp"
+#include "ck_tile/core/utility/literals.hpp"
+#include "ck_tile/core/utility/amd_address_space.hpp"
+#include "ck_tile/ops/gemm/pipeline/gemm_pipeline_ag_bg_cr_scheduler.hpp"
+#include "ck_tile/core.hpp"
+#include "ck_tile/ops/common.hpp"
+#include "ck_tile/host.hpp"
+
+namespace ck_tile {
+
+struct GroupedGemmHostArgs
+{
+    const void* a_ptr;
+    const void* b_ptr;
+    void* c_ptr;
+    index_t M;
+    index_t N;
+    index_t K;
+    index_t stride_A;
+    index_t stride_B;
+    index_t stride_C;
+};
+
+template <typename TilePartitioner_, typename GemmPipeline_, typename EpiloguePipeline_>
+struct GroupedGemmKernel
+{
+    using TilePartitioner                    = remove_cvref_t<TilePartitioner_>;
+    using GemmPipeline                       = remove_cvref_t<GemmPipeline_>;
+    using EpiloguePipeline                   = remove_cvref_t<EpiloguePipeline_>;
+    using ALayout                            = remove_cvref_t<typename GemmPipeline::ALayout>;
+    using BLayout                            = remove_cvref_t<typename GemmPipeline::BLayout>;
+    using CLayout                            = remove_cvref_t<typename GemmPipeline::CLayout>;
+    static constexpr index_t KernelBlockSize = GemmPipeline::BlockSize;
+
+    using ADataType = remove_cvref_t<typename GemmPipeline::ADataType>;
+    using BDataType = remove_cvref_t<typename GemmPipeline::BDataType>;
+    using CDataType = remove_cvref_t<typename EpiloguePipeline::ODataType>;
+
+    struct GemmTransKernelArg
+    {
+        GroupedGemmHostArgs group_karg;
+        ck_tile::index_t block_start;
+        ck_tile::index_t block_end;
+
+        GemmTransKernelArg() = default;
+        GemmTransKernelArg(GroupedGemmHostArgs&& karg, index_t bl_start, index_t bl_end)
+            : group_karg{karg}, block_start{bl_start}, block_end{bl_end}
+        {
+        }
+    };
+
+    __host__ static size_t GetWorkSpaceSize(const std::vector<GroupedGemmHostArgs>& gemm_descs)
+    {
+        return gemm_descs.size() * sizeof(GemmTransKernelArg);
+    }
+
+    __host__ static constexpr auto BlockSize() { return dim3(KernelBlockSize); }
+
+    using Hargs = GroupedGemmHostArgs;
+
+    __host__ static constexpr auto GridSize(const std::vector<Hargs>& gemm_descs)
+    {
+        index_t grid_size = 0;
+        for(const auto& it_desc : gemm_descs)
+        {
+            const auto dim3 = TilePartitioner::GridSize(it_desc.M, it_desc.N);
+            grid_size += dim3.x * dim3.y * 1;
+        }
+        return dim3(grid_size, 1, 1);
+    }
+
+    CK_TILE_HOST static auto MakeKargs(const std::vector<Hargs>& gemm_descs)
+    {
+        std::vector<GemmTransKernelArg> gemm_kernel_args_;
+        index_t group_count = ck_tile::type_convert<ck_tile::index_t>(gemm_descs.size());
+        index_t grid_size   = 0;
+        gemm_kernel_args_.reserve(group_count);
+
+        for(std::size_t i = 0; i < gemm_descs.size(); ++i)
+        {
+            const index_t M = gemm_descs[i].M;
+            const index_t N = gemm_descs[i].N;
+            const index_t K = gemm_descs[i].K;
+
+            if(M == 0 || N == 0 || K == 0)
+            {
+                continue;
+            }
+
+            const index_t stride_a = gemm_descs[i].stride_A;
+            const index_t stride_b = gemm_descs[i].stride_B;
+            const index_t stride_c = gemm_descs[i].stride_C;
+
+            const auto dim3             = TilePartitioner::GridSize(M, N);
+            const index_t grid_size_grp = dim3.x * 1 * 1;
+
+            const index_t block_start = grid_size;
+            const index_t block_end   = grid_size + grid_size_grp;
+
+            grid_size += grid_size_grp;
+
+            auto karg = GroupedGemmHostArgs{type_convert<const ADataType*>(gemm_descs[i].a_ptr),
+                                            type_convert<const BDataType*>(gemm_descs[i].b_ptr),
+                                            type_convert<CDataType*>(gemm_descs[i].c_ptr),
+                                            M,
+                                            N,
+                                            K,
+                                            stride_a,
+                                            stride_b,
+                                            stride_c};
+
+            gemm_kernel_args_.emplace_back(std::move(karg), block_start, block_end);
+        }
+
+        return gemm_kernel_args_;
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr index_t GetSmemSize()
+    {
+        return max(GemmPipeline::GetSmemSize(), EpiloguePipeline::GetSmemSize());
+    }
+
+    CK_TILE_DEVICE void Run(const Hargs& kargs, const index_t block_start) const
+    {
+        const auto [i_m, i_n] = TilePartitioner{}(block_start, kargs.N);
+        // options
+        const ADataType* a_start = static_cast<const ADataType*>(kargs.a_ptr);
+        const BDataType* b_start = static_cast<const BDataType*>(kargs.b_ptr);
+        // Convert pointers to tensor views
+        auto a_tensor_view = [&]() {
+            if constexpr(std::is_same_v<ALayout, tensor_layout::gemm::RowMajor>)
+            {
+                return make_naive_tensor_view<address_space_enum::global>(
+                    a_start,
+                    make_tuple(kargs.M, kargs.K),
+                    make_tuple(kargs.stride_A, 1),
+                    number<GemmPipeline::VectorSizeA>{},
+                    number<1>{});
+            }
+            else
+            {
+                return make_naive_tensor_view<address_space_enum::global>(
+                    a_start,
+                    make_tuple(kargs.M, kargs.K),
+                    make_tuple(1, kargs.stride_A),
+                    number<1>{},
+                    number<1>{});
+            }
+        }();
+
+        auto b_tensor_view = [&]() {
+            if constexpr(std::is_same_v<BLayout, tensor_layout::gemm::RowMajor>)
+            {
+                return make_naive_tensor_view<address_space_enum::global>(
+                    b_start,
+                    make_tuple(kargs.N, kargs.K),
+                    make_tuple(1, kargs.stride_B),
+                    number<1>{},
+                    number<1>{});
+            }
+            else
+            {
+                return make_naive_tensor_view<address_space_enum::global>(
+                    b_start,
+                    make_tuple(kargs.N, kargs.K),
+                    make_tuple(kargs.stride_B, 1),
+                    number<GemmPipeline::VectorSizeB>{},
+                    number<1>{});
+            }
+        }();
+
+        auto a_pad_view = [&]() {
+            if constexpr(std::is_same_v<ALayout, tensor_layout::gemm::RowMajor>)
+            {
+                return pad_tensor_view(a_tensor_view,
+                                       make_tuple(number<TilePartitioner::MPerBlock>{},
+                                                  number<TilePartitioner::KPerBlock>{}),
+                                       sequence<false, GemmPipeline::kPadK>{});
+            }
+            else
+            {
+                return pad_tensor_view(a_tensor_view,
+                                       make_tuple(number<TilePartitioner::MPerBlock>{},
+                                                  number<TilePartitioner::KPerBlock>{}),
+                                       sequence<GemmPipeline::kPadM, false>{});
+            }
+        }();
+        // clang-format on
+
+        auto a_block_window = make_tile_window(
+            a_pad_view,
+            make_tuple(number<TilePartitioner::MPerBlock>{}, number<TilePartitioner::KPerBlock>{}),
+            {i_m, 0});
+
+        auto b_pad_view = [&]() {
+            if constexpr(std::is_same_v<BLayout, tensor_layout::gemm::ColumnMajor>)
+            {
+                return pad_tensor_view(b_tensor_view,
+                                       make_tuple(number<TilePartitioner::NPerBlock>{},
+                                                  number<TilePartitioner::KPerBlock>{}),
+                                       sequence<false, GemmPipeline::kPadK>{});
+            }
+            else
+            {
+                return pad_tensor_view(b_tensor_view,
+                                       make_tuple(number<TilePartitioner::NPerBlock>{},
+                                                  number<TilePartitioner::KPerBlock>{}),
+                                       sequence<GemmPipeline::kPadN, false>{});
+            }
+        }();
+
+        auto b_block_window = make_tile_window(
+            b_pad_view,
+            make_tuple(number<TilePartitioner::NPerBlock>{}, number<TilePartitioner::KPerBlock>{}),
+            {i_n, 0});
+
+        // allocate LDS
+        __shared__ char smem_ptr[GetSmemSize()];
+
+        const index_t num_loop = TilePartitioner::GetLoopNum(kargs.K);
+
+        // Run GEMM cooperatively by whole wokrgroup.
+        auto c_block_tile =
+            GemmPipeline{}.template operator()(a_block_window, b_block_window, num_loop, smem_ptr);
+
+        CDataType* c_start = static_cast<CDataType*>(kargs.c_ptr);
+        auto c_tensor_view = [&]() {
+            if constexpr(std::is_same_v<CLayout, tensor_layout::gemm::RowMajor>)
+            {
+                return make_naive_tensor_view<address_space_enum::global>(
+                    c_start,
+                    make_tuple(kargs.M, kargs.N),
+                    make_tuple(kargs.stride_C, 1),
+                    number<GemmPipeline::VectorSizeC>{},
+                    number<1>{});
+            }
+            else
+            {
+                return make_naive_tensor_view<address_space_enum::global>(
+                    c_start,
+                    make_tuple(kargs.M, kargs.N),
+                    make_tuple(1, kargs.stride_C),
+                    number<1>{},
+                    number<1>{});
+            }
+        }();
+
+        auto c_pad_view = [&]() {
+            if constexpr(std::is_same_v<CLayout, tensor_layout::gemm::RowMajor>)
+            {
+                return pad_tensor_view(c_tensor_view,
+                                       make_tuple(number<TilePartitioner::MPerBlock>{},
+                                                  number<TilePartitioner::NPerBlock>{}),
+                                       sequence<false, GemmPipeline::kPadN>{});
+            }
+            else
+            {
+                return pad_tensor_view(c_tensor_view,
+                                       make_tuple(number<TilePartitioner::MPerBlock>{},
+                                                  number<TilePartitioner::NPerBlock>{}),
+                                       sequence<GemmPipeline::kPadM, false>{});
+            }
+        }();
+        auto CBlockWindow_pad = make_tile_window(
+            c_pad_view,
+            make_tuple(number<TilePartitioner::MPerBlock>{}, number<TilePartitioner::NPerBlock>{}),
+            {i_m, i_n});
+
+        EpiloguePipeline{}(CBlockWindow_pad, c_block_tile);
+    }
+
+    CK_TILE_DEVICE void operator()(const void CK_CONSTANT_ADDRESS_SPACE* gemm_descs_const,
+                                   int group_count) const
+    {
+        const index_t block_id   = ck_tile::get_block_1d_id();
+        const auto gemm_desc_ptr = reinterpret_cast<const GemmTransKernelArg*>(
+            cast_pointer_to_generic_address_space(gemm_descs_const));
+
+        index_t left     = 0;
+        index_t right    = group_count;
+        index_t group_id = index_t((left + right) / 2);
+
+        while((!(block_id >= gemm_desc_ptr[group_id].block_start &&
+                 block_id < gemm_desc_ptr[group_id].block_end)) &&
+              left <= right)
+        {
+            if(block_id < gemm_desc_ptr[group_id].block_start)
+            {
+                right = group_id;
+            }
+            else
+            {
+                left = group_id;
+            }
+            group_id = index_t((left + right) / 2);
+        }
+
+        Run(gemm_desc_ptr[group_id].group_karg, gemm_desc_ptr[group_id].block_start);
+    }
+};
+
+} // namespace ck_tile

include/ck_tile/ops/gemm/pipeline/gemm_pipeline_ag_bg_cr_base.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core.hpp"
+
+namespace ck_tile {
+
+template <typename Problem, typename Policy>
+struct GemmPipelineAgBgCrImplBase
+{
+    using ADataType      = remove_cvref_t<typename Problem::ADataType>;
+    using BDataType      = remove_cvref_t<typename Problem::BDataType>;
+    using BlockGemmShape = remove_cvref_t<typename Problem::BlockGemmShape>;
+
+    static constexpr index_t MPerBlock = BlockGemmShape::kM;
+    static constexpr index_t NPerBlock = BlockGemmShape::kN;
+    static constexpr index_t KPerBlock = BlockGemmShape::kK;
+
+    template <typename DstBlockTile, typename SrcTileWindow>
+    CK_TILE_DEVICE void GlobalPrefetch(DstBlockTile& dst_block_tile,
+                                       SrcTileWindow& dram_tile_window) const
+    {
+        load_tile(dst_block_tile, dram_tile_window);
+        move_tile_window(dram_tile_window, {0, KPerBlock});
+    }
+
+    template <typename DstTileWindow, typename SrcBlockTile, typename ElementFunction>
+    CK_TILE_DEVICE void LocalPrefill(DstTileWindow& lds_tile_window,
+                                     const SrcBlockTile& src_block_tile,
+                                     const ElementFunction& element_func) const
+    {
+        const auto block_tile_tmp = tile_elementwise_in(element_func, src_block_tile);
+        store_tile(lds_tile_window, block_tile_tmp);
+    }
+
+    CK_TILE_DEVICE auto GetABLdsTensorViews(void* p_smem) const
+    {
+        // A tile in LDS
+        ADataType* p_a_lds              = static_cast<ADataType*>(p_smem);
+        constexpr auto a_lds_block_desc = Policy::template MakeALdsBlockDescriptor<Problem>();
+        auto a_lds_block = make_tensor_view<address_space_enum::lds>(p_a_lds, a_lds_block_desc);
+
+        // TODO: LDS alignment should come from Policy!
+        constexpr index_t a_lds_block_space_size_aligned =
+            integer_divide_ceil(sizeof(ADataType) * a_lds_block_desc.get_element_space_size(), 16) *
+            16;
+
+        // B tile in LDS
+        BDataType* p_b_lds = static_cast<BDataType*>(
+            static_cast<void*>(static_cast<char*>(p_smem) + a_lds_block_space_size_aligned));
+        constexpr auto b_lds_block_desc = Policy::template MakeBLdsBlockDescriptor<Problem>();
+        auto b_lds_block = make_tensor_view<address_space_enum::lds>(p_b_lds, b_lds_block_desc);
+
+        return make_tuple(std::move(a_lds_block), std::move(b_lds_block));
+    }
+
+    template <typename ADramBlockWindowTmp, typename ALdsTensorView>
+    CK_TILE_DEVICE auto GetAWindows(const ADramBlockWindowTmp& a_dram_block_window_tmp,
+                                    const ALdsTensorView& a_lds_block_view) const
+    {
+        // A DRAM tile window for load
+        auto a_copy_dram_window =
+            make_tile_window(a_dram_block_window_tmp.get_bottom_tensor_view(),
+                             make_tuple(number<MPerBlock>{}, number<KPerBlock>{}),
+                             a_dram_block_window_tmp.get_window_origin(),
+                             Policy::template MakeADramTileDistribution<Problem>());
+
+        // A LDS tile window for store
+        auto a_copy_lds_window =
+            make_tile_window(a_lds_block_view,
+                             make_tuple(number<MPerBlock>{}, number<KPerBlock>{}),
+                             {0, 0},
+                             a_copy_dram_window.get_tile_distribution());
+
+        auto a_lds_gemm_window = make_tile_window(
+            a_lds_block_view, make_tuple(number<MPerBlock>{}, number<KPerBlock>{}), {0, 0});
+
+        return make_tuple(std::move(a_copy_dram_window),
+                          std::move(a_copy_lds_window),
+                          std::move(a_lds_gemm_window));
+    }
+
+    template <typename BDramBlockWindowTmp, typename BLdsTensorView>
+    CK_TILE_DEVICE auto GetBWindows(const BDramBlockWindowTmp& b_dram_block_window_tmp,
+                                    const BLdsTensorView& b_lds_block_view) const
+    {
+        auto b_copy_dram_window =
+            make_tile_window(b_dram_block_window_tmp.get_bottom_tensor_view(),
+                             make_tuple(number<NPerBlock>{}, number<KPerBlock>{}),
+                             b_dram_block_window_tmp.get_window_origin(),
+                             Policy::template MakeBDramTileDistribution<Problem>());
+
+        // B LDS tile window for store
+        auto b_copy_lds_window =
+            make_tile_window(b_lds_block_view,
+                             make_tuple(number<NPerBlock>{}, number<KPerBlock>{}),
+                             {0, 0},
+                             b_copy_dram_window.get_tile_distribution());
+
+        auto b_lds_gemm_window = make_tile_window(
+            b_lds_block_view, make_tuple(number<NPerBlock>{}, number<KPerBlock>{}), {0, 0});
+
+        return make_tuple(std::move(b_copy_dram_window),
+                          std::move(b_copy_lds_window),
+                          std::move(b_lds_gemm_window));
+    }
+};
+
+} // namespace ck_tile

include/ck_tile/ops/gemm/pipeline/gemm_pipeline_ag_bg_cr_comp_v3.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core.hpp"
+#include "ck_tile/ops/gemm/pipeline/gemm_pipeline_agmem_bgmem_creg_v1_default_policy.hpp"
+#include "ck_tile/ops/gemm/pipeline/gemm_pipeline_ag_bg_cr_scheduler.hpp"
+#include "ck_tile/ops/gemm/pipeline/gemm_pipeline_ag_bg_cr_base.hpp"
+
+namespace ck_tile {
+
+//  A Tile Window: global memory
+//  B Tile Window: global memory
+//  C Distributed tensor: register
+template <typename Problem>
+struct BaseGemmPipelineAgBgCrCompV3
+{
+    static constexpr index_t PrefetchStages  = 2;
+    static constexpr index_t PrefillStages   = 1;
+    static constexpr index_t GlobalBufferNum = 1;
+
+    CK_TILE_HOST static constexpr bool BlockHasHotloop(index_t num_loop)
+    {
+        return num_loop > PrefetchStages;
+    }
+
+    CK_TILE_HOST static constexpr TailNumber GetBlockLoopTailNum(index_t num_loop)
+    {
+        ignore = num_loop;
+        return TailNumber::Full;
+    }
+};
+
+// Compute optimized pipeline
+// GlobalPrefetchStages: 2
+// LocalPreFillStages: 1
+// LocalPreFetchStages: 1
+// LocalSharedMemoryBuffer: 1
+template <typename Problem, typename Policy = GemmPipelineAGmemBGmemCRegV1DefaultPolicy>
+struct GemmPipelineAgBgCrCompV3 : public BaseGemmPipelineAgBgCrCompV3<Problem>
+{
+    using Base             = BaseGemmPipelineAgBgCrCompV3<Problem>;
+    using PipelineImplBase = GemmPipelineAgBgCrImplBase<Problem, Policy>;
+
+    using ADataType      = remove_cvref_t<typename Problem::ADataType>;
+    using BDataType      = remove_cvref_t<typename Problem::BDataType>;
+    using CDataType      = remove_cvref_t<typename Problem::CDataType>;
+    using BlockGemmShape = remove_cvref_t<typename Problem::BlockGemmShape>;
+
+    using ALayout = remove_cvref_t<typename Problem::ALayout>;
+    using BLayout = remove_cvref_t<typename Problem::BLayout>;
+    using CLayout = remove_cvref_t<typename Problem::CLayout>;
+
+    using BlockGemm = remove_cvref_t<decltype(Policy::template GetBlockGemm<Problem>())>;
+    using I0        = number<0>;
+    using I1        = number<1>;
+    using I2        = number<2>;
+
+    static constexpr index_t BlockSize = Problem::kBlockSize;
+    static constexpr index_t MPerBlock = BlockGemmShape::kM;
+    static constexpr index_t NPerBlock = BlockGemmShape::kN;
+    static constexpr index_t KPerBlock = BlockGemmShape::kK;
+
+    static constexpr index_t VectorSizeA = Problem::VectorSizeA;
+    static constexpr index_t VectorSizeB = Problem::VectorSizeB;
+    static constexpr index_t VectorSizeC = Problem::VectorSizeC;
+
+    static constexpr bool kPadM = Problem::kPadM;
+    static constexpr bool kPadN = Problem::kPadN;
+    static constexpr bool kPadK = Problem::kPadK;
+
+    // Where is the right place for HasHotLoop and TailNum ???
+    static constexpr bool HasHotLoop = Problem::HasHotLoop;
+    static constexpr auto TailNum    = Problem::TailNum;
+    static constexpr auto Scheduler  = Problem::Scheduler;
+
+    using Base::PrefetchStages;
+
+    CK_TILE_HOST_DEVICE static constexpr index_t GetSmemSize()
+    {
+        return Policy::template GetSmemSize<Problem>();
+    }
+
+    template <GemmPipelineScheduler Scheduler>
+    struct PipelineImpl : public PipelineImplBase
+    {
+    };
+
+    template <>
+    struct PipelineImpl<GemmPipelineScheduler::Intrawave> : public PipelineImplBase
+    {
+        using Base = PipelineImplBase;
+
+        CK_TILE_DEVICE static constexpr auto HotLoopScheduler()
+        {
+            constexpr index_t MPerXDL = BlockGemmShape::WarpTile::at(I0{});
+            constexpr index_t NPerXDL = BlockGemmShape::WarpTile::at(I1{});
+            constexpr index_t KPerXDL = BlockGemmShape::WarpTile::at(I2{});
+
+            constexpr index_t WaveSize = 64;
+            constexpr index_t WaveNumM = BlockGemmShape::BlockWarps::at(I0{});
+            constexpr index_t WaveNumN = BlockGemmShape::BlockWarps::at(I1{});
+
+            constexpr index_t A_LDS_Read_Width = KPerXDL;
+            constexpr index_t B_LDS_Read_Width = KPerXDL;
+
+            constexpr index_t A_Buffer_Load_Inst_Num =
+                MPerBlock * KPerBlock / (BlockSize * VectorSizeA);
+            constexpr index_t B_Buffer_Load_Inst_Num =
+                NPerBlock * KPerBlock / (BlockSize * VectorSizeB);
+
+            constexpr index_t A_LDS_Write_Inst_Num = MPerBlock * KPerBlock / (BlockSize * KPerXDL);
+            constexpr index_t B_LDS_Write_Inst_Num = NPerBlock * KPerBlock / (BlockSize * KPerXDL);
+
+            constexpr index_t A_LDS_Read_Inst_Num =
+                WaveNumN * MPerBlock * KPerBlock / (BlockSize * KPerXDL);
+            constexpr index_t B_LDS_Read_Inst_Num =
+                WaveNumM * MPerBlock * KPerBlock / (BlockSize * KPerXDL);
+
+            constexpr index_t C_MFMA_Inst_Num = MPerBlock * NPerBlock * KPerBlock /
+                                                (BlockSize / WaveSize) /
+                                                (MPerXDL * NPerXDL * KPerXDL);
+
+            // A/B split schedule
+            // compiler is likely to use ds_read2 when instruction width smaller than 16bytes
+            constexpr auto num_ds_read_inst_a = A_LDS_Read_Width * sizeof(ADataType) == 16
+                                                    ? A_LDS_Read_Inst_Num
+                                                    : A_LDS_Read_Inst_Num / 2;
+            constexpr auto num_ds_read_inst_b = B_LDS_Read_Width * sizeof(BDataType) == 16
+                                                    ? B_LDS_Read_Inst_Num
+                                                    : B_LDS_Read_Inst_Num / 2;
+
+            constexpr auto num_ds_write_inst_a = A_LDS_Write_Inst_Num;
+            constexpr auto num_ds_write_inst_b = B_LDS_Write_Inst_Num;
+
+            constexpr auto num_buffer_load_inst_a = A_Buffer_Load_Inst_Num;
+            constexpr auto num_buffer_load_inst_b = B_Buffer_Load_Inst_Num;
+
+            constexpr auto num_mfma_inst = C_MFMA_Inst_Num;
+
+            constexpr auto mfma_cycle = NPerXDL == 16 ? 16 : 32;
+            constexpr auto ds_read_a_issue_cycle =
+                A_LDS_Read_Width * sizeof(ADataType) == 16 ? 8 : 4;
+            constexpr auto ds_read_b_issue_cycle =
+                B_LDS_Read_Width * sizeof(BDataType) == 16 ? 8 : 4;
+            constexpr auto ds_read_a_mfma_rate =
+                (mfma_cycle - 4 + 2 * ds_read_a_issue_cycle - 1) / (2 * ds_read_a_issue_cycle);
+            constexpr auto ds_read_b_mfma_rate =
+                (mfma_cycle - 4 + 2 * ds_read_b_issue_cycle - 1) / (2 * ds_read_b_issue_cycle);
+
+            constexpr auto num_dsread_a_mfma =
+                (num_ds_read_inst_a + ds_read_a_mfma_rate - 1) / ds_read_a_mfma_rate;
+            constexpr auto num_dsread_b_mfma =
+                (num_ds_read_inst_b + ds_read_b_mfma_rate - 1) / ds_read_b_mfma_rate;
+
+            // stage 1
+            // Separate this part?
+            // constexpr auto num_mfma_per_ds_read = sizeof(ComputeDataType) / sizeof(ADataType) >
+            //                                               sizeof(ComputeDataType) /
+            //                                               sizeof(BDataType)
+            //                                           ? sizeof(ComputeDataType) /
+            //                                           sizeof(ADataType) : sizeof(ComputeDataType)
+            //                                           / sizeof(BDataType);
+            constexpr auto num_mfma_stage1 =
+                num_mfma_inst - (num_dsread_a_mfma + num_dsread_b_mfma);
+            constexpr auto num_mfma_per_issue =
+                num_mfma_stage1 / (num_buffer_load_inst_a + num_buffer_load_inst_b);
+            constexpr auto num_dswrite_per_issue_a = num_ds_write_inst_a / num_buffer_load_inst_a;
+            constexpr auto num_dswrite_per_issue_b = num_ds_write_inst_b / num_buffer_load_inst_b;
+
+            static_for<0, num_buffer_load_inst_a, 1>{}([&](auto i) {
+                ignore = i;
+                static_for<0, num_dswrite_per_issue_a, 1>{}([&](auto idswrite) {
+                    ignore = idswrite;
+                    __builtin_amdgcn_sched_group_barrier(0x200, 1, 0); // DS write
+                    __builtin_amdgcn_sched_group_barrier(0x008, 1, 0); // MFMA
+                });
+                __builtin_amdgcn_sched_group_barrier(0x020, 1, 0); // VMEM read
+                __builtin_amdgcn_sched_group_barrier(
+                    0x008, num_mfma_per_issue - num_dswrite_per_issue_a, 0); // MFMA
+            });
+            static_for<0, num_buffer_load_inst_b, 1>{}([&](auto i) {
+                ignore = i;
+                static_for<0, num_dswrite_per_issue_b, 1>{}([&](auto idswrite) {
+                    ignore = idswrite;
+                    __builtin_amdgcn_sched_group_barrier(0x200, 1, 0); // DS write
+                    __builtin_amdgcn_sched_group_barrier(0x008, 1, 0); // MFMA
+                });
+                __builtin_amdgcn_sched_group_barrier(0x020, 1, 0); // VMEM read
+                __builtin_amdgcn_sched_group_barrier(
+                    0x008, num_mfma_per_issue - num_dswrite_per_issue_b, 0); // MFMA
+            });
+
+            // stage 2
+            static_for<0, num_dsread_a_mfma, 1>{}([&](auto i) {
+                if constexpr((num_ds_read_inst_a - (i + 1) * ds_read_a_mfma_rate) >=
+                             ds_read_a_mfma_rate)
+                {
+                    __builtin_amdgcn_sched_group_barrier(0x100, ds_read_a_mfma_rate, 0); // DS read
+                }
+                else
+                {
+                    __builtin_amdgcn_sched_group_barrier(
+                        0x100,
+                        num_ds_read_inst_a - (num_dsread_a_mfma - 1) * ds_read_a_mfma_rate,
+                        0); // DS read
+                }
+                __builtin_amdgcn_sched_group_barrier(0x008, 1, 0); // MFMA
+            });
+
+            static_for<0, num_dsread_b_mfma, 1>{}([&](auto i) {
+                if constexpr((num_ds_read_inst_b - (i + 1) * ds_read_b_mfma_rate) >=
+                             ds_read_b_mfma_rate)
+                {
+                    __builtin_amdgcn_sched_group_barrier(0x100, ds_read_b_mfma_rate, 0); // DS read
+                }
+                else
+                {
+                    __builtin_amdgcn_sched_group_barrier(
+                        0x100,
+                        num_ds_read_inst_b - (num_dsread_b_mfma - 1) * ds_read_b_mfma_rate,
+                        0); // DS read
+                }
+                __builtin_amdgcn_sched_group_barrier(0x008, 1, 0); // MFMA
+            });
+        }
+
+        template <bool HasHotLoop,
+                  TailNumber TailNum,
+                  typename ADramBlockWindowTmp,
+                  typename BDramBlockWindowTmp,
+                  typename AElementFunction,
+                  typename BElementFunction>
+        CK_TILE_DEVICE auto operator()(const ADramBlockWindowTmp& a_dram_block_window_tmp,
+                                       const AElementFunction& a_element_func,
+                                       const BDramBlockWindowTmp& b_dram_block_window_tmp,
+                                       const BElementFunction& b_element_func,
+                                       index_t num_loop,
+                                       void* p_smem) const
+        {
+            static_assert(
+                std::is_same_v<ADataType, remove_cvref_t<typename ADramBlockWindowTmp::DataType>> &&
+                    std::is_same_v<BDataType,
+                                   remove_cvref_t<typename BDramBlockWindowTmp::DataType>>,
+                "A/B Dram block window should have the same data type as appropriate "
+                "([A|B]DataType) defined in Problem definition!");
+
+            static_assert(MPerBlock == ADramBlockWindowTmp{}.get_window_lengths()[I0{}] &&
+                              NPerBlock == BDramBlockWindowTmp{}.get_window_lengths()[I0{}] &&
+                              KPerBlock == ADramBlockWindowTmp{}.get_window_lengths()[I1{}],
+                          "A/B block window appropriate sizes must be equal to MPerBlock/NPerblock"
+                          " or KPerBlock!");
+
+            // ------------------------------------------------------------------------------------
+            // Definitions of all needed tiles
+
+            // A/B tiles in LDS
+            auto&& [a_lds_block, b_lds_block] = Base::GetABLdsTensorViews(p_smem);
+
+            // A DRAM tile window for load
+            // A LDS tile window for store
+            // A LDS tile for block GEMM
+            auto&& [a_copy_dram_window, a_copy_lds_window, a_lds_gemm_window] =
+                Base::GetAWindows(a_dram_block_window_tmp, a_lds_block);
+
+            // B DRAM tile window for load
+            // B LDS tile window for store
+            // B LDS tile for block GEMM
+            auto&& [b_copy_dram_window, b_copy_lds_window, b_lds_gemm_window] =
+                Base::GetBWindows(b_dram_block_window_tmp, b_lds_block);
+
+            // Block GEMM
+            auto block_gemm   = BlockGemm();
+            auto c_block_tile = block_gemm.MakeCBlockTile();
+
+            using ABlockTileDistr = decltype(a_copy_dram_window.get_tile_distribution());
+            using BBlockTileDistr = decltype(b_copy_dram_window.get_tile_distribution());
+
+            using ABlockTile =
+                decltype(make_static_distributed_tensor<ADataType>(ABlockTileDistr{}));
+            using BBlockTile =
+                decltype(make_static_distributed_tensor<BDataType>(BBlockTileDistr{}));
+
+            ABlockTile a_block_tile;
+            BBlockTile b_block_tile;
+
+            // -----------------------------------------------------------------------------------------
+            // Gemm pipeline start
+
+            // prefetch
+            // global read 0
+            Base::GlobalPrefetch(a_block_tile, a_copy_dram_window);
+            Base::GlobalPrefetch(b_block_tile, b_copy_dram_window);
+
+            // initialize C
+            tile_elementwise_inout([](auto& c) { c = 0; }, c_block_tile);
+
+            // LDS write 0
+            Base::LocalPrefill(a_copy_lds_window, a_block_tile, a_element_func);
+            Base::LocalPrefill(b_copy_lds_window, b_block_tile, b_element_func);
+
+            Base::GlobalPrefetch(a_block_tile, a_copy_dram_window);
+            Base::GlobalPrefetch(b_block_tile, b_copy_dram_window);
+
+            block_sync_lds();
+            block_gemm.LocalPrefetch(a_lds_gemm_window, b_lds_gemm_window);
+
+            __builtin_amdgcn_sched_barrier(0);
+
+            // main body
+            if constexpr(HasHotLoop)
+            {
+                index_t i = 0;
+                do
+                {
+                    block_sync_lds();
+
+                    Base::LocalPrefill(a_copy_lds_window, a_block_tile, a_element_func);
+                    Base::LocalPrefill(b_copy_lds_window, b_block_tile, b_element_func);
+
+                    Base::GlobalPrefetch(a_block_tile, a_copy_dram_window);
+                    Base::GlobalPrefetch(b_block_tile, b_copy_dram_window);
+
+                    block_gemm(c_block_tile, a_lds_gemm_window, b_lds_gemm_window);
+
+                    block_sync_lds();
+                    block_gemm.LocalPrefetch(a_lds_gemm_window, b_lds_gemm_window);
+                    HotLoopScheduler();
+                    __builtin_amdgcn_sched_barrier(0);
+
+                    i += 1;
+                } while(i < (num_loop - 1));
+            }
+            // tail
+            if constexpr(TailNum == TailNumber::Full)
+            {
+                block_gemm(c_block_tile, a_lds_gemm_window, b_lds_gemm_window);
+            }
+            // Let's leak last MFMA block to epilogue region, cover the potential lds-shuffle
+            // latency
+            // __builtin_amdgcn_sched_barrier(0);
+            return c_block_tile;
+        }
+    };
+
+    template <typename ADramBlockWindowTmp,
+              typename BDramBlockWindowTmp,
+              typename AElementFunction,
+              typename BElementFunction>
+    CK_TILE_DEVICE auto operator()(const ADramBlockWindowTmp& a_dram_block_window_tmp,
+                                   const AElementFunction& a_element_func,
+                                   const BDramBlockWindowTmp& b_dram_block_window_tmp,
+                                   const BElementFunction& b_element_func,
+                                   index_t num_loop,
+                                   void* p_smem) const
+    {
+        return PipelineImpl<Scheduler>{}.template operator()<HasHotLoop, TailNum>(
+            a_dram_block_window_tmp,
+            a_element_func,
+            b_dram_block_window_tmp,
+            b_element_func,
+            num_loop,
+            p_smem);
+    }
+
+    template <typename ADramBlockWindowTmp, typename BDramBlockWindowTmp>
+    CK_TILE_DEVICE auto operator()(const ADramBlockWindowTmp& a_dram_block_window_tmp,
+                                   const BDramBlockWindowTmp& b_dram_block_window_tmp,
+                                   index_t num_loop,
+                                   void* p_smem) const
+    {
+        return PipelineImpl<Scheduler>{}.template operator()<HasHotLoop, TailNum>(
+            a_dram_block_window_tmp,
+            [](const ADataType& a) { return a; },
+            b_dram_block_window_tmp,
+            [](const BDataType& b) { return b; },
+            num_loop,
+            p_smem);
+    }
+};
+
+} // namespace ck_tile

include/ck_tile/ops/gemm/pipeline/gemm_pipeline_ag_bg_cr_mem.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core.hpp"
+#include "ck_tile/ops/gemm/pipeline/gemm_pipeline_agmem_bgmem_creg_v1_default_policy.hpp"
+#include "ck_tile/ops/gemm/pipeline/gemm_pipeline_ag_bg_cr_scheduler.hpp"
+#include "ck_tile/ops/gemm/pipeline/gemm_pipeline_ag_bg_cr_base.hpp"
+
+namespace ck_tile {
+
+//  A Tile Window: global memory
+//  B Tile Window: global memory
+//  C Distributed tensor: register
+template <typename Problem>
+struct BaseGemmPipelineAgBgCrMem
+{
+    using ADataType      = remove_cvref_t<typename Problem::ADataType>;
+    using BDataType      = remove_cvref_t<typename Problem::BDataType>;
+    using BlockGemmShape = remove_cvref_t<typename Problem::BlockGemmShape>;
+
+    static constexpr index_t BlockSize = Problem::kBlockSize;
+    static constexpr index_t MPerBlock = BlockGemmShape::kM;
+    static constexpr index_t NPerBlock = BlockGemmShape::kN;
+    static constexpr index_t KPerBlock = BlockGemmShape::kK;
+
+    // TODO: Is this 32K value gfx9 arch specific?
+    static constexpr index_t MinMemInFlyBytes = 32768;
+
+    static constexpr index_t WgpPerCU =
+        (4 * get_warp_size() / BlockSize) >= 1 ? 4 * get_warp_size() / BlockSize : 1;
+    static constexpr index_t FullMemBandPrefetchStages = integer_divide_ceil(
+        MinMemInFlyBytes / WgpPerCU,
+        (MPerBlock * sizeof(ADataType) + NPerBlock * sizeof(BDataType)) * KPerBlock);
+    static constexpr index_t PrefetchStages =
+        FullMemBandPrefetchStages >= 2
+            ? FullMemBandPrefetchStages <= 8 ? FullMemBandPrefetchStages : 8
+            : 2;
+
+    static constexpr index_t LocalPrefillStages = 1;
+    static constexpr index_t GlobalBufferNum    = PrefetchStages;
+
+    CK_TILE_HOST static constexpr bool BlockHasHotloop(index_t num_loop)
+    {
+        return num_loop > PrefetchStages;
+    }
+
+    CK_TILE_HOST static constexpr TailNumber GetBlockLoopTailNum(index_t num_loop)
+    {
+        if(num_loop % PrefetchStages == 1)
+        {
+            return TailNumber::One;
+        }
+        else if(num_loop % PrefetchStages == 2)
+        {
+            return TailNumber::Two;
+        }
+        else if(num_loop % PrefetchStages == 3)
+        {
+            return TailNumber::Three;
+        }
+        else if(num_loop % PrefetchStages == 4)
+        {
+            return TailNumber::Four;
+        }
+        else if(num_loop % PrefetchStages == 5)
+        {
+            return TailNumber::Five;
+        }
+        else if(num_loop % PrefetchStages == 6)
+        {
+            return TailNumber::Six;
+        }
+        else if(num_loop % PrefetchStages == 7)
+        {
+            return TailNumber::Seven;
+        }
+        else
+        {
+            return TailNumber::Full;
+        }
+    }
+};
+
+// Maximum Global Memory throughput pipeline with >=32KB data in fly
+// GlobalPrefetchStages: >=2
+// LocalPreFillStages: 1
+// LocalPreFetchStages: 0
+// LocalSharedMemoryBuffer: 1
+template <typename Problem, typename Policy = GemmPipelineAGmemBGmemCRegV1DefaultPolicy>
+struct GemmPipelineAgBgCrMem : public BaseGemmPipelineAgBgCrMem<Problem>
+{
+    using Base             = BaseGemmPipelineAgBgCrMem<Problem>;
+    using PipelineImplBase = GemmPipelineAgBgCrImplBase<Problem, Policy>;
+
+    using ADataType      = remove_cvref_t<typename Problem::ADataType>;
+    using BDataType      = remove_cvref_t<typename Problem::BDataType>;
+    using CDataType      = remove_cvref_t<typename Problem::CDataType>;
+    using BlockGemmShape = remove_cvref_t<typename Problem::BlockGemmShape>;
+
+    using ALayout = remove_cvref_t<typename Problem::ALayout>;
+    using BLayout = remove_cvref_t<typename Problem::BLayout>;
+    using CLayout = remove_cvref_t<typename Problem::CLayout>;
+
+    using BlockGemm = remove_cvref_t<decltype(Policy::template GetBlockGemm<Problem>())>;
+    using I0        = number<0>;
+    using I1        = number<1>;
+    using I2        = number<2>;
+
+    static constexpr index_t MPerBlock = BlockGemmShape::kM;
+    static constexpr index_t NPerBlock = BlockGemmShape::kN;
+    static constexpr index_t KPerBlock = BlockGemmShape::kK;
+
+    static constexpr index_t VectorSizeA = Problem::VectorSizeA;
+    static constexpr index_t VectorSizeB = Problem::VectorSizeB;
+    static constexpr index_t VectorSizeC = Problem::VectorSizeC;
+
+    static constexpr bool kPadM = Problem::kPadM;
+    static constexpr bool kPadN = Problem::kPadN;
+    static constexpr bool kPadK = Problem::kPadK;
+
+    // Where is the right place for HasHotLoop and TailNum ???
+    static constexpr bool HasHotLoop = Problem::HasHotLoop;
+    static constexpr auto TailNum    = Problem::TailNum;
+    static constexpr auto Scheduler  = Problem::Scheduler;
+
+    using Base::PrefetchStages;
+
+    CK_TILE_HOST_DEVICE static constexpr index_t GetSmemSize()
+    {
+        return Policy::template GetSmemSize<Problem>();
+    }
+
+    template <GemmPipelineScheduler Scheduler>
+    struct PipelineImpl : public PipelineImplBase
+    {
+    };
+
+    template <>
+    struct PipelineImpl<GemmPipelineScheduler::Intrawave> : public PipelineImplBase
+    {
+        using Base = PipelineImplBase;
+
+        template <bool HasHotLoop,
+                  TailNumber TailNum,
+                  typename ADramBlockWindowTmp,
+                  typename BDramBlockWindowTmp,
+                  typename AElementFunction,
+                  typename BElementFunction>
+        CK_TILE_DEVICE auto operator()(const ADramBlockWindowTmp& a_dram_block_window_tmp,
+                                       const AElementFunction& a_element_func,
+                                       const BDramBlockWindowTmp& b_dram_block_window_tmp,
+                                       const BElementFunction& b_element_func,
+                                       index_t num_loop,
+                                       void* p_smem) const
+        {
+            static_assert(
+                std::is_same_v<ADataType, remove_cvref_t<typename ADramBlockWindowTmp::DataType>> &&
+                    std::is_same_v<BDataType,
+                                   remove_cvref_t<typename BDramBlockWindowTmp::DataType>>,
+                "A/B Dram block window should have the same data type as appropriate "
+                "([A|B]DataType) defined in Problem definition!");
+
+            static_assert(MPerBlock == ADramBlockWindowTmp{}.get_window_lengths()[I0{}] &&
+                              NPerBlock == BDramBlockWindowTmp{}.get_window_lengths()[I0{}] &&
+                              KPerBlock == ADramBlockWindowTmp{}.get_window_lengths()[I1{}],
+                          "A/B block window appropriate sizes must be equal to MPerBlock/NPerblock"
+                          " or KPerBlock!");
+
+            // ------------------------------------------------------------------------------------
+            // Definitions of all needed tiles
+
+            // A/B tiles in LDS
+            // With c++20 could simplify to below line.
+            // Currently get error: captured structured bindings are a C++20 extension
+            // auto&& [a_lds_block, b_lds_block] = Base::GetABLdsTensorViews(p_smem);
+            auto ab_lds_blocks = Base::GetABLdsTensorViews(p_smem);
+            auto& a_lds_block  = ab_lds_blocks.at(I0{});
+            auto& b_lds_block  = ab_lds_blocks.at(I1{});
+
+            // A DRAM tile window for load
+            // A LDS tile window for store
+            // A LDS tile for block GEMM
+            auto a_windows           = Base::GetAWindows(a_dram_block_window_tmp, a_lds_block);
+            auto& a_copy_dram_window = a_windows.at(I0{});
+            auto& a_copy_lds_window  = a_windows.at(I1{});
+            auto& a_lds_gemm_window  = a_windows.at(I2{});
+
+            // B DRAM tile window for load
+            // B LDS tile window for store
+            // B LDS tile for block GEMM
+            auto b_windows           = Base::GetBWindows(b_dram_block_window_tmp, b_lds_block);
+            auto& b_copy_dram_window = b_windows.at(I0{});
+            auto& b_copy_lds_window  = b_windows.at(I1{});
+            auto& b_lds_gemm_window  = b_windows.at(I2{});
+
+            // Block GEMM
+            auto block_gemm   = BlockGemm();
+            auto c_block_tile = block_gemm.MakeCBlockTile();
+
+            using ABlockTileDistr = decltype(a_copy_dram_window.get_tile_distribution());
+            using BBlockTileDistr = decltype(b_copy_dram_window.get_tile_distribution());
+
+            using ABlockTile =
+                decltype(make_static_distributed_tensor<ADataType>(ABlockTileDistr{}));
+            using BBlockTile =
+                decltype(make_static_distributed_tensor<BDataType>(BBlockTileDistr{}));
+
+            tuple_array<ABlockTile, PrefetchStages> a_block_tiles;
+            tuple_array<BBlockTile, PrefetchStages> b_block_tiles;
+
+            // -----------------------------------------------------------------------------------------
+            // Gemm pipeline start
+
+            // prefetch
+            // global read 0
+            Base::GlobalPrefetch(a_block_tiles.get(I0{}), a_copy_dram_window);
+            Base::GlobalPrefetch(b_block_tiles.get(I0{}), b_copy_dram_window);
+
+            // initialize C
+            tile_elementwise_inout([](auto& c) { c = 0; }, c_block_tile);
+
+            // LDS write 0
+            Base::LocalPrefill(a_copy_lds_window, a_block_tiles.get(I0{}), a_element_func);
+            Base::LocalPrefill(b_copy_lds_window, b_block_tiles.get(I0{}), b_element_func);
+
+            // Global prefetch [1, PrefetchStages]
+            static_for<1, PrefetchStages, 1>{}([&](auto prefetch_idx) {
+                Base::GlobalPrefetch(a_block_tiles.get(number<prefetch_idx>{}), a_copy_dram_window);
+                Base::GlobalPrefetch(b_block_tiles.get(number<prefetch_idx>{}), b_copy_dram_window);
+            });
+
+            // main body
+            if constexpr(HasHotLoop)
+            {
+                index_t i = 0;
+                do
+                {
+                    static_for<0, PrefetchStages, 1>{}([&](auto prefetch_idx) {
+                        block_sync_lds();
+                        block_gemm.LocalPrefetch(a_lds_gemm_window, b_lds_gemm_window);
+                        block_gemm(c_block_tile, a_lds_gemm_window, b_lds_gemm_window);
+
+                        block_sync_lds();
+
+                        Base::LocalPrefill(
+                            a_copy_lds_window,
+                            a_block_tiles.get(number<(prefetch_idx + 1) % PrefetchStages>{}),
+                            a_element_func);
+                        Base::LocalPrefill(
+                            b_copy_lds_window,
+                            b_block_tiles.get(number<(prefetch_idx + 1) % PrefetchStages>{}),
+                            b_element_func);
+
+                        Base::GlobalPrefetch(a_block_tiles.get(number<prefetch_idx>{}),
+                                             a_copy_dram_window);
+                        Base::GlobalPrefetch(b_block_tiles.get(number<prefetch_idx>{}),
+                                             b_copy_dram_window);
+                    });
+
+                    i += PrefetchStages;
+                } while(i < (num_loop - PrefetchStages));
+            }
+
+            auto HotLoopTail = [&](auto tail_num) {
+                static_for<1, tail_num, 1>{}([&](auto prefetch_idx) {
+                    block_sync_lds();
+
+                    block_gemm.LocalPrefetch(a_lds_gemm_window, b_lds_gemm_window);
+                    block_gemm(c_block_tile, a_lds_gemm_window, b_lds_gemm_window);
+
+                    block_sync_lds();
+
+                    Base::LocalPrefill(a_copy_lds_window,
+                                       a_block_tiles.get(number<prefetch_idx>{}),
+                                       a_element_func);
+                    Base::LocalPrefill(b_copy_lds_window,
+                                       b_block_tiles.get(number<prefetch_idx>{}),
+                                       b_element_func);
+                });
+
+                block_sync_lds();
+                block_gemm.LocalPrefetch(a_lds_gemm_window, b_lds_gemm_window);
+                block_gemm(c_block_tile, a_lds_gemm_window, b_lds_gemm_window);
+            };
+
+            if constexpr(TailNum == TailNumber::One)
+            {
+                block_sync_lds();
+                block_gemm.LocalPrefetch(a_lds_gemm_window, b_lds_gemm_window);
+                block_gemm(c_block_tile, a_lds_gemm_window, b_lds_gemm_window);
+            }
+            else if constexpr(TailNum == TailNumber::Two)
+            {
+                HotLoopTail(number<2>{});
+            }
+            else if constexpr(TailNum == TailNumber::Three)
+            {
+                HotLoopTail(number<3>{});
+            }
+            else if constexpr(TailNum == TailNumber::Four)
+            {
+                HotLoopTail(number<4>{});
+            }
+            else if constexpr(TailNum == TailNumber::Five)
+            {
+                HotLoopTail(number<5>{});
+            }
+            else if constexpr(TailNum == TailNumber::Six)
+            {
+                HotLoopTail(number<6>{});
+            }
+            else if constexpr(TailNum == TailNumber::Seven)
+            {
+                HotLoopTail(number<7>{});
+            }
+            else if constexpr(TailNum == TailNumber::Full)
+            {
+                HotLoopTail(number<PrefetchStages>{});
+            }
+
+            return c_block_tile;
+        }
+    };
+
+    template <>
+    struct PipelineImpl<GemmPipelineScheduler::Interwave> : public PipelineImplBase
+    {
+        using Base = PipelineImplBase;
+
+        template <bool HasHotLoop,
+                  TailNumber TailNum,
+                  typename ADramBlockWindowTmp,
+                  typename BDramBlockWindowTmp,
+                  typename AElementFunction,
+                  typename BElementFunction>
+        CK_TILE_DEVICE auto operator()(const ADramBlockWindowTmp& a_dram_block_window_tmp,
+                                       const AElementFunction& a_element_func,
+                                       const BDramBlockWindowTmp& b_dram_block_window_tmp,
+                                       const BElementFunction& b_element_func,
+                                       index_t num_loop,
+                                       void* p_smem) const
+        {
+            static_assert(
+                std::is_same_v<ADataType, remove_cvref_t<typename ADramBlockWindowTmp::DataType>> &&
+                    std::is_same_v<BDataType,
+                                   remove_cvref_t<typename BDramBlockWindowTmp::DataType>>,
+                "A/B Dram block window should have the same data type as appropriate "
+                "([A|B]DataType) defined in Problem definition!");
+
+            static_assert(MPerBlock == ADramBlockWindowTmp{}.get_window_lengths()[I0{}] &&
+                              NPerBlock == BDramBlockWindowTmp{}.get_window_lengths()[I0{}] &&
+                              KPerBlock == ADramBlockWindowTmp{}.get_window_lengths()[I1{}],
+                          "A/B block window appropriate sizes must be equal to MPerBlock/NPerblock"
+                          " or KPerBlock!");
+
+            // ------------------------------------------------------------------------------------
+            // Definitions of all needed tiles
+
+            // A/B tiles in LDS
+            // With c++20 could simplify to below line.
+            // Currently get error: captured structured bindings are a C++20 extension
+            // auto&& [a_lds_block, b_lds_block] = Base::GetABLdsTensorViews(p_smem);
+            auto ab_lds_blocks = Base::GetABLdsTensorViews(p_smem);
+            auto& a_lds_block  = ab_lds_blocks.at(I0{});
+            auto& b_lds_block  = ab_lds_blocks.at(I1{});
+
+            // A DRAM tile window for load
+            // A LDS tile window for store
+            // A LDS tile for block GEMM
+            auto a_windows           = Base::GetAWindows(a_dram_block_window_tmp, a_lds_block);
+            auto& a_copy_dram_window = a_windows.at(I0{});
+            auto& a_copy_lds_window  = a_windows.at(I1{});
+            auto& a_lds_gemm_window  = a_windows.at(I2{});
+
+            // B DRAM tile window for load
+            // B LDS tile window for store
+            // B LDS tile for block GEMM
+            auto b_windows           = Base::GetBWindows(b_dram_block_window_tmp, b_lds_block);
+            auto& b_copy_dram_window = b_windows.at(I0{});
+            auto& b_copy_lds_window  = b_windows.at(I1{});
+            auto& b_lds_gemm_window  = b_windows.at(I2{});
+
+            // Block GEMM
+            auto block_gemm   = BlockGemm();
+            auto c_block_tile = block_gemm.MakeCBlockTile();
+
+            using ABlockTileDistr = decltype(a_copy_dram_window.get_tile_distribution());
+            using BBlockTileDistr = decltype(b_copy_dram_window.get_tile_distribution());
+
+            using ABlockTile =
+                decltype(make_static_distributed_tensor<ADataType>(ABlockTileDistr{}));
+            using BBlockTile =
+                decltype(make_static_distributed_tensor<BDataType>(BBlockTileDistr{}));
+
+            tuple_array<ABlockTile, PrefetchStages> a_block_tiles;
+            tuple_array<BBlockTile, PrefetchStages> b_block_tiles;
+
+            // -----------------------------------------------------------------------------------------
+            // Gemm pipeline start
+
+            // prefetch
+            // global read 0
+            Base::GlobalPrefetch(a_block_tiles.get(I0{}), a_copy_dram_window);
+            Base::GlobalPrefetch(b_block_tiles.get(I0{}), b_copy_dram_window);
+
+            // initialize C
+            tile_elementwise_inout([](auto& c) { c = 0; }, c_block_tile);
+
+            // LDS write 0
+            Base::LocalPrefill(a_copy_lds_window, a_block_tiles.get(I0{}), a_element_func);
+            Base::LocalPrefill(b_copy_lds_window, b_block_tiles.get(I0{}), b_element_func);
+
+            // Global prefetch [1, PrefetchStages]
+            static_for<1, PrefetchStages, 1>{}([&](auto prefetch_idx) {
+                Base::GlobalPrefetch(a_block_tiles.get(number<prefetch_idx>{}), a_copy_dram_window);
+                Base::GlobalPrefetch(b_block_tiles.get(number<prefetch_idx>{}), b_copy_dram_window);
+            });
+
+            // main body
+            if constexpr(HasHotLoop)
+            {
+                index_t i = 0;
+                do
+                {
+                    static_for<0, PrefetchStages, 1>{}([&](auto prefetch_idx) {
+                        block_sync_lds();
+                        block_gemm(c_block_tile, a_lds_gemm_window, b_lds_gemm_window);
+                        // no second block_sync_lds because it's interwave
+
+                        Base::LocalPrefill(
+                            a_copy_lds_window,
+                            a_block_tiles.get(number<(prefetch_idx + 1) % PrefetchStages>{}),
+                            a_element_func);
+                        Base::LocalPrefill(
+                            b_copy_lds_window,
+                            b_block_tiles.get(number<(prefetch_idx + 1) % PrefetchStages>{}),
+                            b_element_func);
+
+                        Base::GlobalPrefetch(a_block_tiles.get(number<prefetch_idx>{}),
+                                             a_copy_dram_window);
+                        Base::GlobalPrefetch(b_block_tiles.get(number<prefetch_idx>{}),
+                                             b_copy_dram_window);
+                    });
+
+                    i += PrefetchStages;
+                } while(i < (num_loop - PrefetchStages));
+            }
+
+            auto HotLoopTail = [&](auto tail_num) {
+                static_for<1, tail_num, 1>{}([&](auto prefetch_idx) {
+                    block_sync_lds();
+                    block_gemm(c_block_tile, a_lds_gemm_window, b_lds_gemm_window);
+                    // no second block_sync_lds because it's interwave
+
+                    Base::LocalPrefill(a_copy_lds_window,
+                                       a_block_tiles.get(number<prefetch_idx>{}),
+                                       a_element_func);
+                    Base::LocalPrefill(b_copy_lds_window,
+                                       b_block_tiles.get(number<prefetch_idx>{}),
+                                       b_element_func);
+                });
+
+                block_sync_lds();
+                block_gemm(c_block_tile, a_lds_gemm_window, b_lds_gemm_window);
+            };
+
+            if constexpr(TailNum == TailNumber::One)
+            {
+                block_sync_lds();
+                block_gemm(c_block_tile, a_lds_gemm_window, b_lds_gemm_window);
+            }
+            else if constexpr(TailNum == TailNumber::Two)
+            {
+                HotLoopTail(number<2>{});
+            }
+            else if constexpr(TailNum == TailNumber::Three)
+            {
+                HotLoopTail(number<3>{});
+            }
+            else if constexpr(TailNum == TailNumber::Four)
+            {
+                HotLoopTail(number<4>{});
+            }
+            else if constexpr(TailNum == TailNumber::Five)
+            {
+                HotLoopTail(number<5>{});
+            }
+            else if constexpr(TailNum == TailNumber::Six)
+            {
+                HotLoopTail(number<6>{});
+            }
+            else if constexpr(TailNum == TailNumber::Seven)
+            {
+                HotLoopTail(number<7>{});
+            }
+            else if constexpr(TailNum == TailNumber::Full)
+            {
+                HotLoopTail(number<PrefetchStages>{});
+            }
+
+            return c_block_tile;
+        }
+    };
+
+    template <typename ADramBlockWindowTmp,
+              typename BDramBlockWindowTmp,
+              typename AElementFunction,
+              typename BElementFunction>
+    CK_TILE_DEVICE auto operator()(const ADramBlockWindowTmp& a_dram_block_window_tmp,
+                                   const AElementFunction& a_element_func,
+                                   const BDramBlockWindowTmp& b_dram_block_window_tmp,
+                                   const BElementFunction& b_element_func,
+                                   index_t num_loop,
+                                   void* p_smem) const
+    {
+        return PipelineImpl<Scheduler>{}.template operator()<HasHotLoop, TailNum>(
+            a_dram_block_window_tmp,
+            a_element_func,
+            b_dram_block_window_tmp,
+            b_element_func,
+            num_loop,
+            p_smem);
+    }
+
+    template <typename ADramBlockWindowTmp, typename BDramBlockWindowTmp>
+    CK_TILE_DEVICE auto operator()(const ADramBlockWindowTmp& a_dram_block_window_tmp,
+                                   const BDramBlockWindowTmp& b_dram_block_window_tmp,
+                                   index_t num_loop,
+                                   void* p_smem) const
+    {
+        return PipelineImpl<Scheduler>{}.template operator()<HasHotLoop, TailNum>(
+            a_dram_block_window_tmp,
+            [](const ADataType& a) { return a; },
+            b_dram_block_window_tmp,
+            [](const BDataType& b) { return b; },
+            num_loop,
+            p_smem);
+    }
+};
+
+} // namespace ck_tile

include/ck_tile/ops/gemm/pipeline/gemm_pipeline_ag_bg_cr_scheduler.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <ostream>
+
+#include "ck_tile/core.hpp"
+
+namespace ck_tile {
+
+enum struct GemmPipelineScheduler
+{
+    Default,
+    Intrawave,
+    Interwave,
+};
+
+enum struct TailNumber
+{
+    // Single / Double buffer pipeline
+    Odd,
+    Even,
+
+    // Long prefetch pipeline, up to 8
+    One,
+    Two,
+    Three,
+    Four,
+    Five,
+    Six,
+    Seven,
+
+    // Unroll stages > Prefetch stages, number of loop is multiple of unroll stages
+    Empty,
+    // Unroll stages <= Prefetch stages, number of loop is multiple of unroll stages add
+    // prefetchstages
+    Full,
+};
+
+} // namespace ck_tile
+
+inline std::ostream& operator<<(std::ostream& os, const ck_tile::GemmPipelineScheduler& s)
+{
+    switch(s)
+    {
+    case ck_tile::GemmPipelineScheduler::Default: os << "Default"; break;
+    case ck_tile::GemmPipelineScheduler::Intrawave: os << "Intrawave"; break;
+    case ck_tile::GemmPipelineScheduler::Interwave: os << "Interwave"; break;
+    default: os << "";
+    }
+    return os;
+}
+
+inline std::ostream& operator<<(std::ostream& os, const ck_tile::TailNumber& s)
+{
+    switch(s)
+    {
+    case ck_tile::TailNumber::Odd: os << "Odd"; break;
+    case ck_tile::TailNumber::Even: os << "Even"; break;
+    case ck_tile::TailNumber::One: os << "One"; break;
+    case ck_tile::TailNumber::Two: os << "Two"; break;
+    case ck_tile::TailNumber::Three: os << "Three"; break;
+    case ck_tile::TailNumber::Four: os << "Four"; break;
+    case ck_tile::TailNumber::Five: os << "Five"; break;
+    case ck_tile::TailNumber::Six: os << "Six"; break;
+    case ck_tile::TailNumber::Seven: os << "Seven"; break;
+    case ck_tile::TailNumber::Empty: os << "Empty"; break;
+    case ck_tile::TailNumber::Full: os << "Full"; break;
+    default: os << "";
+    }
+    return os;
+}