[CK Tile] Spatially local GEMM tile partitioner. (#1843)

* Add spatially local tile partitioner

* Use 1D Grid size & create partitioner object.

* Docs & use 1D partitioner in example.

* Clang format.

* Change kernel grid size

Now: X is the # of output C-tiles,
     Y is the batch count
     Z is the splitK

* Formatting & more doc.

* Clang format.

* Fix batched gemm test. Use 1d partitioner.

* Move condition.

* FIx ctor.

* clang-format.

example/ck_tile/03_gemm/gemm_basic.cpp

@@ -40,7 +40,7 @@ float gemm_calc(const ck_tile::GemmHostArgs& args, const ck_tile::stream_config&
                                ck_tile::sequence<M_Warp, N_Warp, K_Warp>,
                                ck_tile::sequence<M_Warp_Tile, N_Warp_Tile, K_Warp_Tile>>;
 
-    using TilePartitioner = ck_tile::GemmTile2DPartitioner<CodegenGemmShape>;
+    using TilePartitioner = ck_tile::GemmTile1DPartitioner<CodegenGemmShape>;
 
     using CodegenGemmTraits =
         ck_tile::TileGemmTraits<kPadM, kPadN, kPadK, ALayout, BLayout, CLayout>;

example/ck_tile/03_gemm/gemm_basic.hpp

@@ -79,7 +79,7 @@ auto create_args(int argc, char* argv[])
         .insert("n", "4096", "n dimension")
         .insert("k", "2048", "k dimension")
         .insert("a_layout", "R", "A tensor data layout - Row by default")
-        .insert("b_layout", "R", "B tensor data layout - Row by default")
+        .insert("b_layout", "C", "B tensor data layout - Column by default")
         .insert("c_layout", "R", "C tensor data layout - Row by default")
         .insert("stride_a", "0", "Tensor A stride")
         .insert("stride_b", "0", "Tensor B stride")

example/ck_tile/03_gemm/universal_gemm.cpp

@@ -50,7 +50,9 @@ float gemm_calc(const ck_tile::GemmHostArgs& args, const ck_tile::stream_config&
 
     constexpr bool TransposeC = false;
 
-    constexpr int kBlockPerCu = 1;
+    constexpr int kBlockPerCu                         = 1;
+    constexpr ck_tile::index_t TileParitionerGroupNum = 8;
+    constexpr ck_tile::index_t TileParitionerM01      = 4;
 
     // ===============================================
 
@@ -58,7 +60,8 @@ float gemm_calc(const ck_tile::GemmHostArgs& args, const ck_tile::stream_config&
         ck_tile::TileGemmShape<ck_tile::sequence<M_Tile, N_Tile, K_Tile>,
                                ck_tile::sequence<M_Warp, N_Warp, K_Warp>,
                                ck_tile::sequence<M_Warp_Tile, N_Warp_Tile, K_Warp_Tile>>;
-    using TilePartitioner = ck_tile::GemmTile2DPartitioner<GemmShape>;
+    using TilePartitioner = ck_tile::
+        GemmSpatiallyLocalTilePartitioner<GemmShape, TileParitionerGroupNum, TileParitionerM01>;
 
     using Traits = ck_tile::TileGemmTraits<kPadM, kPadN, kPadK, ALayout, BLayout, CLayout>;
     using GemmUniversalTraits = ck_tile::

example/ck_tile/16_batched_gemm/batched_gemm.cpp

@@ -43,7 +43,7 @@ float batched_gemm(const ck_tile::BatchedGemmHostArgs& args, const ck_tile::stre
                                ck_tile::sequence<M_Warp, N_Warp, K_Warp>,
                                ck_tile::sequence<M_Warp_Tile, N_Warp_Tile, K_Warp_Tile>>;
 
-    using TilePartitioner = ck_tile::GemmTile2DPartitioner<CodegenGemmShape>;
+    using TilePartitioner = ck_tile::GemmTile1DPartitioner<CodegenGemmShape>;
 
     using CodegenGemmTraits =
         ck_tile::TileGemmTraits<kPadM, kPadN, kPadK, ALayout, BLayout, CLayout>;

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

@@ -70,7 +70,7 @@ struct BatchedGemmKernel : public GemmKernel<TilePartitioner_, GemmPipeline_, Ep
     __host__ static constexpr auto
     GridSize(index_t M, index_t N, index_t KBatch, index_t batch_count)
     {
-        return TilePartitioner::GridSize(M, N, KBatch * batch_count);
+        return dim3(TilePartitioner::GridSize(M, N), batch_count, KBatch);
     }
 
     __host__ static constexpr auto BlockSize() { return dim3(Base::KernelBlockSize); }
@@ -101,14 +101,14 @@ struct BatchedGemmKernel : public GemmKernel<TilePartitioner_, GemmPipeline_, Ep
 
     CK_TILE_DEVICE void operator()(BatchedGemmKernelArgs kargs) const
     {
-        const auto [iM, iN] = TilePartitioner::GetOutputTileIndex(blockIdx.x, blockIdx.y);
+        const auto [iM, iN] = TilePartitioner{kargs.M, kargs.N}.GetOutputTileIndex(blockIdx.x);
         const index_t i_m   = __builtin_amdgcn_readfirstlane(iM * TilePartitioner::MPerBlock);
         const index_t i_n   = __builtin_amdgcn_readfirstlane(iN * TilePartitioner::NPerBlock);
 
-        const auto i_batch = __builtin_amdgcn_readfirstlane(blockIdx.z / kargs.KBatch);
-        const auto i_k     = __builtin_amdgcn_readfirstlane(blockIdx.z - i_batch * kargs.KBatch);
+        const auto i_batch  = __builtin_amdgcn_readfirstlane(blockIdx.y);
+        const auto i_splitk = __builtin_amdgcn_readfirstlane(blockIdx.z);
 
-        const typename Base::SplitKBatchOffset splitk_batch_offset(kargs, i_k);
+        const typename Base::SplitKBatchOffset splitk_batch_offset(kargs, i_splitk);
 
         //  options
         const auto batch_stride_A = __builtin_amdgcn_readfirstlane(kargs.batch_stride_A);
@@ -128,7 +128,7 @@ struct BatchedGemmKernel : public GemmKernel<TilePartitioner_, GemmPipeline_, Ep
         // allocate LDS
         __shared__ char smem_ptr[GetSmemSize()];
 
-        if(kargs.KBatch == 1)
+        if(kargs.k_batch == 1)
         {
             this->RunGemm(a_ptr, b_ptr, c_ptr, smem_ptr, kargs, splitk_batch_offset, i_m, i_n);
         }

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

@@ -75,12 +75,12 @@ struct GemmKernel
     static constexpr auto I1 = number<1>();
     static constexpr auto I2 = number<2>();
 
-    __host__ static constexpr auto GridSize(index_t M, index_t N, index_t KBatch)
+    CK_TILE_HOST static constexpr auto GridSize(index_t M, index_t N, index_t KBatch)
     {
-        return TilePartitioner::GridSize(M, N, KBatch);
+        return dim3(TilePartitioner::GridSize(M, N), 1, KBatch);
     }
 
-    __host__ static constexpr auto BlockSize() { return dim3(KernelBlockSize); }
+    CK_TILE_HOST static constexpr auto BlockSize() { return dim3(KernelBlockSize); }
 
     struct GemmKernelArgs
     {
@@ -93,7 +93,7 @@ struct GemmKernel
         index_t stride_A;
         index_t stride_B;
         index_t stride_C;
-        index_t KBatch;
+        index_t k_batch;
     };
 
     CK_TILE_HOST static constexpr GemmKernelArgs MakeKernelArgs(const GemmHostArgs& hostArgs)
@@ -121,7 +121,7 @@ struct GemmKernel
                                      const std::size_t k_id = blockIdx.z)
         {
             constexpr auto K1   = TilePartitioner::BlockGemmShape::WarpTile::at(number<2>{});
-            const index_t K_t   = kargs.KBatch * K1;
+            const index_t K_t   = kargs.k_batch * K1;
             const index_t KRead = (kargs.K + K_t - 1) / K_t * K1;
 
             if constexpr(std::is_same_v<tensor_layout::gemm::RowMajor, ALayout>)
@@ -142,13 +142,13 @@ struct GemmKernel
                 b_k_split_offset = k_id * KRead;
             }
 
-            if(k_id < static_cast<uint32_t>(kargs.KBatch - 1))
+            if(k_id < static_cast<uint32_t>(kargs.k_batch - 1))
             {
                 splitted_k = KRead;
             }
             else
             {
-                splitted_k = kargs.K - KRead * (kargs.KBatch - 1);
+                splitted_k = kargs.K - KRead * (kargs.k_batch - 1);
             }
         }
 
@@ -162,7 +162,7 @@ struct GemmKernel
         if constexpr(EpiloguePipeline::GetVectorSizeC() % 2 != 0 &&
                      is_any_of<CDataType, fp16_t, bf16_t>::value)
         {
-            if(kargs.KBatch != 1)
+            if(kargs.k_batch != 1)
             {
                 std::cerr << "Conditions not met for Kbatch >1 !" << std::endl;
                 return false;
@@ -489,19 +489,14 @@ struct GemmKernel
         // Run Epilogue Pipeline
         auto& c_block_window = gemm_tile_windows.at(I2);
 
-        if constexpr(DstInMemOp == memory_operation_enum::set ||
-                     !(EpiloguePipeline::GetVectorSizeC() % 2 != 0 &&
-                       is_any_of<CDataType, fp16_t, bf16_t>::value))
-        {
-            EpiloguePipeline{}
-                .template operator()<decltype(c_block_window), decltype(c_block_tile), DstInMemOp>(
-                    c_block_window, c_block_tile, smem_ptr);
-        }
+        EpiloguePipeline{}
+            .template operator()<decltype(c_block_window), decltype(c_block_tile), DstInMemOp>(
+                c_block_window, c_block_tile, smem_ptr);
     }
 
     CK_TILE_DEVICE void operator()(GemmKernelArgs kargs) const
     {
-        const auto [iM, iN] = TilePartitioner::GetOutputTileIndex(blockIdx.x, blockIdx.y);
+        const auto [iM, iN] = TilePartitioner{kargs.M, kargs.N}.GetOutputTileIndex(blockIdx.x);
         const index_t i_m   = __builtin_amdgcn_readfirstlane(iM * TilePartitioner::MPerBlock);
         const index_t i_n   = __builtin_amdgcn_readfirstlane(iN * TilePartitioner::NPerBlock);
 
@@ -516,14 +511,20 @@ struct GemmKernel
         // allocate LDS
         __shared__ char smem_ptr[GetSmemSize()];
 
-        if(kargs.KBatch == 1)
+        if(kargs.k_batch == 1)
         {
             RunGemm(a_ptr, b_ptr, c_ptr, smem_ptr, kargs, splitk_batch_offset, i_m, i_n);
         }
         else
         {
-            RunGemm<memory_operation_enum::atomic_add>(
-                a_ptr, b_ptr, c_ptr, smem_ptr, kargs, splitk_batch_offset, i_m, i_n);
+            // Do not compile in case where we have unsupported
+            // VectorSizeC & data type configuration.
+            if constexpr(!(EpiloguePipeline::GetVectorSizeC() % 2 != 0 &&
+                           is_any_of<CDataType, fp16_t, bf16_t>::value))
+            {
+                RunGemm<memory_operation_enum::atomic_add>(
+                    a_ptr, b_ptr, c_ptr, smem_ptr, kargs, splitk_batch_offset, i_m, i_n);
+            }
         }
     }
 };

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

 // SPDX-License-Identifier: MIT
 // Copyright (c) 2018-2025, Advanced Micro Devices, Inc. All rights reserved.
 
+/**
+ * @file
+ * GemmTilePartitioner allows customized mapping between a workgroup and the C-tile it computes.
+ */
+
 #pragma once
 
 #include "ck_tile/core.hpp"
 
 namespace ck_tile {
 
-/** @brief Struct representing 2D block index mapping into 3D output tile space. */
+/**
+ * @brief Class providing 2D workgroup index mapping into 2D output GEMM C-tile space.
+ *
+ */
 template <typename BlockGemmShapeType>
 struct GemmTile2DPartitioner
 {
@@ -17,21 +25,32 @@ struct GemmTile2DPartitioner
     static constexpr index_t NPerBlock = BlockGemmShape::kN;
     static constexpr index_t KPerBlock = BlockGemmShape::kK;
 
-    /** @brief Returns 3D grid size. */
-    CK_TILE_HOST static constexpr auto GridSize(index_t M, index_t N, index_t batch_size) noexcept(
-        noexcept(MPerBlock != 0 && NPerBlock != 0)) -> dim3
+    CK_TILE_HOST_DEVICE GemmTile2DPartitioner() noexcept = delete;
+    CK_TILE_HOST_DEVICE GemmTile2DPartitioner([[maybe_unused]] index_t M,
+                                              [[maybe_unused]] index_t N) noexcept;
+
+    /**
+     * @brief Calculates GEMM kernel grid size.
+     *
+     * @param M     GEMM's M dimension.
+     * @param N     GEMM's N dimension.
+     * @return dim3 Structure holding grid's X,Y and Z dimensions.
+     */
+    CK_TILE_HOST static auto
+    GridSize(index_t M, index_t N) noexcept(noexcept(MPerBlock != 0 && NPerBlock != 0)) -> dim3
     {
         const index_t GridDimX = (M + MPerBlock - 1) / MPerBlock;
         const index_t GridDimY = (N + NPerBlock - 1) / NPerBlock;
-        const index_t GridDimZ = batch_size;
-        return dim3(GridDimX, GridDimY, GridDimZ);
+        return dim3(GridDimX, GridDimY, 1);
     }
 
     /**
-     * @brief Returns the number of loops.
-     * @param [in] K is dimension
+     * @brief Calculate number of loop iterations over GEMM's K dimension.
+     *
+     * @param K         GEMM's K dimension.
+     * @return index_t  The number of loop iterations over K dimension.
      */
-    CK_TILE_HOST_DEVICE static constexpr auto GetLoopNum(index_t K) noexcept -> index_t
+    CK_TILE_HOST_DEVICE static auto GetLoopNum(index_t K) noexcept -> index_t
     {
         return integer_divide_ceil(K, KPerBlock);
     }
@@ -42,8 +61,15 @@ struct GemmTile2DPartitioner
      * @param [in] blockIdy is blockIdx.y
      * @return Returns the output tile indexes.
      */
-    CK_TILE_DEVICE static constexpr auto GetOutputTileIndex(index_t blockIdx,
-                                                            index_t blockIdy) noexcept
+
+    /**
+     * @brief Calculate workgroup 2D index mapping into 2D output C-tile space.
+     *
+     * @param blockIdx      WGP's X index.
+     * @param blockIdy      WGP's Y index.
+     * @return const tuple<index_t, index_t>    Tuple containing 2D output C-tile index.
+     */
+    CK_TILE_DEVICE static auto GetOutputTileIndex(index_t blockIdx, index_t blockIdy) noexcept
         -> const tuple<index_t, index_t>
     {
         const index_t iM = __builtin_amdgcn_readfirstlane(blockIdx);
@@ -53,61 +79,71 @@ struct GemmTile2DPartitioner
 };
 
 /**
- * @brief Struct representing 1D block index mapping into 2D output tile space.
+ * @brief Class providing 1D WGP index mapping into 2D output C-tile space.
+ *
+ * @tparam BlockGemmShape_  A class providing basic GEMM parameters. \link TileGemmShape
  */
-template <typename BlockGemmShapeType>
+template <typename BlockGemmShape_>
 struct GemmTile1DPartitioner
 {
-    using BlockGemmShape = remove_cvref_t<BlockGemmShapeType>;
+    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;
 
-    /** @brief delete default ctr with no any object */
-    constexpr GemmTile1DPartitioner() noexcept = delete;
-
-    /** @brief constructs an object that does contain a N value. */
-    constexpr GemmTile1DPartitioner(index_t N) noexcept { N_ = N; }
+    CK_TILE_HOST_DEVICE GemmTile1DPartitioner() noexcept = delete;
 
-    /** @brief Returns 1D grid size. */
-    CK_TILE_HOST static constexpr auto
-    GridSize(index_t M, index_t N) noexcept(noexcept(MPerBlock != 0 && NPerBlock != 0)) -> dim3
+    /**
+     * @brief Construct a new GemmTile1DPartitioner object.
+     *
+     * @param M     GEMM's M dimension.
+     * @param N     GEMM's N dimension.
+     */
+    CK_TILE_HOST_DEVICE GemmTile1DPartitioner([[maybe_unused]] index_t M, index_t N) noexcept
     {
-        const index_t GridDimX = (M + MPerBlock - 1) / MPerBlock;
-        const index_t GridDimY = (N + NPerBlock - 1) / NPerBlock;
-        return dim3(GridDimX * GridDimY, 1, 1);
+        N_ = N;
     }
 
     /**
-     * @brief Returns the number of blocks in N.
-     * @param [in] N is dimension
+     * @brief Calculates GEMM kernel grid size.
+     *
+     * @param M     GEMM's M dimension.
+     * @param N     GEMM's N dimension.
+     * @return dim3 Structure holding grid's X,Y and Z dimensions.
      */
-    CK_TILE_HOST_DEVICE static constexpr auto GetNBlock(index_t N) noexcept -> index_t
+    CK_TILE_HOST static auto
+    GridSize(index_t M, index_t N) noexcept(noexcept(MPerBlock != 0 && NPerBlock != 0)) -> index_t
     {
-        return integer_divide_ceil(N, NPerBlock);
+        const index_t GridDimX = (M + MPerBlock - 1) / MPerBlock;
+        const index_t GridDimY = (N + NPerBlock - 1) / NPerBlock;
+        return GridDimX * GridDimY;
     }
 
     /**
-     * @brief Returns the number of loops.
-     * @param [in] K is dimension
+     * @brief Calculate number of loop iterations over GEMM's K dimension.
+     *
+     * @param K         GEMM's K dimension.
+     * @return index_t  The number of loop iterations over K dimension.
      */
-    CK_TILE_HOST_DEVICE static constexpr auto GetLoopNum(index_t K) noexcept -> index_t
+    CK_TILE_HOST_DEVICE static auto GetLoopNum(index_t K) noexcept -> index_t
     {
         return integer_divide_ceil(K, KPerBlock);
     }
 
     /**
-     * @brief The function returns 2D output tile space.
-     * @param [in] blockIdx is blockIdx.x - block_start.
-     * */
-    CK_TILE_DEVICE static constexpr auto GetOutputTileIndex(index_t blockIdx) noexcept
+     * @brief Calculate workgroup 1D index mapping into 2D output C-tile space.
+     *
+     * @param blockIdx      WGP's index.
+     * @return const tuple<index_t, index_t>    Tuple containing 2D output C-tile index.
+     */
+    CK_TILE_DEVICE static auto GetOutputTileIndex(index_t blockIdx) noexcept
         -> const tuple<index_t, index_t>
     {
-        const index_t NBlock = GetNBlock(N_);
+        const index_t NBlocks = integer_divide_ceil(N_, NPerBlock);
 
-        const index_t iM = __builtin_amdgcn_readfirstlane(blockIdx / NBlock);
-        const index_t iN = __builtin_amdgcn_readfirstlane(blockIdx - (iM)*NBlock);
+        const index_t iM = __builtin_amdgcn_readfirstlane(blockIdx / NBlocks);
+        const index_t iN = __builtin_amdgcn_readfirstlane(blockIdx - iM * NBlocks);
         return make_tuple(iM, iN);
     }
 
@@ -141,21 +177,176 @@ struct HasFnOneArgImpl<T, std::void_t<decltype(std::declval<T>().GetOutputTileIn
  * enable-if `GetOutputTileIndex`-fn is std::true_type when `GetOutputTileIndex`-fn is well-formed,
  * otherwise std::false_type.
  */
-template <typename PartitionerFn,
-          typename = typename std::enable_if_t<HasFnOneArgImpl<PartitionerFn>{}>>
+template <typename TilePartitioner,
+          typename = typename std::enable_if_t<HasFnOneArgImpl<TilePartitioner>{}>>
 struct OffsettedTile1DPartitioner
 {
     /**
      * @brief The function subtracts the block's start (offset) from 1D raw-indexes.
-     * @param [in] block_start is `blockIdx.x - block_start`.
-     * @return Returns a `tuple` [Im, In] shifted index, used to shift 1d-tile index.
+     * @param [in] block_start Workgroup offset.
+     * @param [in] M           Gemm's M dimension.
+     * @param [in] N           Gemm's N dimension.
+     * @return Returns a `tuple` [Im, In] with shifted index.
      */
-    [[nodiscard]] CK_TILE_DEVICE static constexpr auto GetOffsetedTileIndex(index_t block_start,
-                                                                            index_t N) noexcept
+    [[nodiscard]] CK_TILE_DEVICE static auto
+    GetOffsetedTileIndex(index_t block_start, index_t M, index_t N) noexcept
         -> const tuple<index_t, index_t>
     {
-        const auto [iM, iN] = PartitionerFn(N).GetOutputTileIndex(blockIdx.x - block_start);
+        const auto [iM, iN] = TilePartitioner{M, N}.GetOutputTileIndex(blockIdx.x - block_start);
         return make_tuple(iM, iN);
     }
 };
+
+/**
+ * @brief Class mapping 1D block index into 2D output tile space.
+ *
+ * @note It groups spatially workgroups in order to better utilize caches.
+ *       It is using grouped Rows of column-vectors WGP pattern. It's optimized
+ *       for gfx94x-like multiple-die chip.
+ *
+ * @tparam GroupNum - The number of big groups.
+ * @tparam M01      - The number of groups in M dim within spatially local WGPs,
+ *
+ */
+template <typename BlockGemmShapeType, index_t GroupNum, index_t M01>
+struct GemmSpatiallyLocalTilePartitioner
+{
+    using BlockGemmShape = remove_cvref_t<BlockGemmShapeType>;
+
+    static constexpr index_t MPerBlock = BlockGemmShape::kM;
+    static constexpr index_t NPerBlock = BlockGemmShape::kN;
+    static constexpr index_t KPerBlock = BlockGemmShape::kK;
+
+    CK_TILE_HOST_DEVICE GemmSpatiallyLocalTilePartitioner() noexcept = delete;
+    CK_TILE_HOST_DEVICE GemmSpatiallyLocalTilePartitioner(index_t M_, index_t N_) noexcept
+        : M(M_), N(N_)
+    {
+    }
+
+    /**
+     * @brief Calculates GEMM kernel grid size.
+     *
+     * @param M     GEMM's M dimension.
+     * @param N     GEMM's N dimension.
+     * @return index_t A total number of workgroups.
+     */
+    CK_TILE_HOST static auto
+    GridSize(index_t M, index_t N) noexcept(noexcept(MPerBlock != 0 && NPerBlock != 0)) -> index_t
+    {
+        const index_t GridDimX = integer_divide_ceil(M, MPerBlock);
+        const index_t GridDimY = integer_divide_ceil(N, NPerBlock);
+        return GridDimX * GridDimY;
+    }
+
+    /**
+     * @brief Calculate number of loop iterations over GEMM's K dimension.
+     *
+     * @param K         GEMM's K dimension.
+     * @return index_t  The number of loop iterations over K dimension.
+     */
+    CK_TILE_HOST_DEVICE static auto GetLoopNum(index_t K) noexcept -> index_t
+    {
+        return integer_divide_ceil(K, KPerBlock);
+    }
+
+    /**
+     * @brief Calculate workgroup 1D index mapping into 2D output C-tile space.
+     *
+     * @param [in] block_1d_id      WGP's index.
+     * @return const tuple<index_t, index_t>    Tuple containing 2D output C-tile index.
+     */
+    CK_TILE_DEVICE auto GetOutputTileIndex(index_t block_1d_id) noexcept
+        -> const tuple<index_t, index_t>
+    {
+        const auto M0 = integer_divide_ceil(M, MPerBlock);
+        const auto N0 = integer_divide_ceil(N, NPerBlock);
+
+        if(M0 == 1)
+        {
+            return make_tuple(0, block_1d_id);
+        }
+        else if(N0 == 1)
+        {
+            return make_tuple(block_1d_id, 0);
+        }
+        // block_1d_id = block_1d_id % (M0 * N0); // swallow batch index
+        else
+        {
+            const auto group_size    = integer_divide_ceil(M0 * N0, GroupNum);
+            const auto big_group_num = GroupNum - (group_size * GroupNum - M0 * N0);
+            const auto group_id_y    = block_1d_id / GroupNum;
+            const auto group_id_x    = block_1d_id - group_id_y * GroupNum;
+            const auto remap_block_1d_id =
+                group_id_x <= big_group_num
+                    ? group_id_x * group_size + group_id_y
+                    : group_id_x * group_size + big_group_num - group_id_x + group_id_y;
+
+            const index_t idx_M0 = remap_block_1d_id / N0;
+            const index_t idx_N0 = remap_block_1d_id - idx_M0 * N0;
+
+            const index_t M0_tmp     = M0 / M01;
+            const index_t M0_mod_M01 = M0 - M0_tmp * M01;
+
+            const auto M01_adapt = (idx_M0 < M0 - M0_mod_M01) ? M01 : M0_mod_M01;
+
+            const index_t idx_M00          = idx_M0 / M01;
+            const index_t idx_M01          = idx_M0 - idx_M00 * M01;
+            const index_t idx_N0_M01_local = idx_N0 + idx_M01 * N0;
+
+            /**
+             *                        idxN0
+             *
+             *           |<               mtx   N                 >|
+             *
+             *             NPerBlock   NPerBlock   NPerBlock   NPerBlock
+             *                N_0         N_1        N_2         N_3
+             *       -   |-----------|-----------|-----------|-----|-----|-
+             *       ^   | -   -  0  |/---->  2  |           |     |     |
+             *           | |   |     /     |     |           |     |     |  M_0  MPerBlock
+             *           | M   |    /|     |     |           |     |     |
+             *           |-0---|---/-|-----|-----|-----------|-----|-----|-
+             *           | 1   |  /  |     |     |  blockid  |     |     |
+             * idxM0     | |   | /   |     V     |     5     |     |     |  M_1  MPerBlock
+             *           | -   V   1 |     -  3  |           |     |     |
+             *           |-----------|-----------|-----------|-----|-----|-
+             *    mtx M  |           |           |           |     |     |
+             *           |           |           |           |     |     |  M_2  MPerBlock
+             *           |           |           |           |     |     |
+             *           |-----------|-----------|-----------|-----|-----|-
+             *           |           |           |           |     |     |
+             *           |           |           |           |     |     |  M_3  MPerBlock
+             *           |           |           |           |     |     |
+             *           |-----------|-----------|-----------|-----|-----|-
+             *       V   |           |           |           |     |     |
+             *       -   |-----------|-----------|-----------|-----|-----|- M_4  MPerBlock
+             *           |           |           |           |     |     |
+             *           |-----------|-----------|-----------|-----|-----|-
+             *  Example:
+             *   assume:
+             *      M0 = 5
+             *      N0 = 4
+             *      block_1d_id = 5
+             *      M01 = 2
+             *
+             *   idx_N0 = 1
+             *   idx_M0 = 1
+             *   M01_adapt = 2
+             *   idx_M00 = 0
+             *   idx_M01 = 1
+             *   idx_N0_M01_local = 5
+             *   output {1, 2}
+             */
+
+            const index_t N_out           = idx_N0_M01_local / M01_adapt;
+            const index_t idx_loc_mod_M01 = idx_N0_M01_local - N_out * M01_adapt;
+
+            return make_tuple(idx_loc_mod_M01 + idx_M00 * M01, N_out);
+        }
+    }
+
+    private:
+    index_t M;
+    index_t N;
+};
+
 } // namespace ck_tile

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

@@ -77,8 +77,8 @@ struct GroupedGemmKernel : public GemmKernel<TilePartitioner_, GemmPipeline_, Ep
         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;
+            const auto local_grid_size = TilePartitioner::GridSize(it_desc.M, it_desc.N);
+            grid_size += local_grid_size * it_desc.k_batch;
         }
         return dim3(grid_size, 1, 1);
     }
@@ -106,8 +106,7 @@ struct GroupedGemmKernel : public GemmKernel<TilePartitioner_, GemmPipeline_, Ep
             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;
+            const index_t grid_size_grp = TilePartitioner::GridSize(M, N) * gemm_descs[i].k_batch;
 
             const index_t block_start = grid_size;
             const index_t block_end   = grid_size + grid_size_grp;
@@ -138,8 +137,8 @@ struct GroupedGemmKernel : public GemmKernel<TilePartitioner_, GemmPipeline_, Ep
 
     CK_TILE_DEVICE void Run(const GemmTransKernelArg& kargs) const
     {
-        const auto [iM, iN] =
-            OffsetTile1DPartitioner::GetOffsetedTileIndex(kargs.block_start, kargs.group_karg.N);
+        const auto [iM, iN] = OffsetTile1DPartitioner::GetOffsetedTileIndex(
+            kargs.block_start, kargs.group_karg.M, kargs.group_karg.N);
 
         const index_t i_m = __builtin_amdgcn_readfirstlane(iM * TilePartitioner::MPerBlock);
         const index_t i_n = __builtin_amdgcn_readfirstlane(iN * TilePartitioner::NPerBlock);

test/ck_tile/batched_gemm/test_batched_gemm_util.hpp

@@ -53,7 +53,7 @@ class TestCkTileBatchedGemm : public ::testing::Test
                                    ck_tile::sequence<M_Warp, N_Warp, K_Warp>,
                                    ck_tile::sequence<M_Warp_Tile, N_Warp_Tile, K_Warp_Tile>>;
 
-        using TilePartitioner = ck_tile::GemmTile2DPartitioner<CodegenGemmShape>;
+        using TilePartitioner = ck_tile::GemmTile1DPartitioner<CodegenGemmShape>;
 
         using CodegenGemmTraits =
             ck_tile::TileGemmTraits<kPadM, kPadN, kPadK, ALayout, BLayout, CLayout>;

test/ck_tile/gemm/test_gemm_pipeline_util.hpp

@@ -55,7 +55,9 @@ class TestCkTileGemmPipeline : public ::testing::Test
         // TODO: For now - but this should also be a test parameter
         constexpr bool TransposeC = false;
 
-        constexpr int kBlockPerCu = 1;
+        constexpr int kBlockPerCu                         = 1;
+        constexpr ck_tile::index_t TileParitionerGroupNum = 8;
+        constexpr ck_tile::index_t TileParitionerM01      = 4;
 
         // ===============================================
 
@@ -63,7 +65,8 @@ class TestCkTileGemmPipeline : public ::testing::Test
             ck_tile::TileGemmShape<ck_tile::sequence<M_Tile, N_Tile, K_Tile>,
                                    ck_tile::sequence<M_Warp, N_Warp, K_Warp>,
                                    ck_tile::sequence<M_Warp_Tile, N_Warp_Tile, K_Warp_Tile>>;
-        using TilePartitioner = ck_tile::GemmTile2DPartitioner<GemmShape>;
+        using TilePartitioner = ck_tile::
+            GemmSpatiallyLocalTilePartitioner<GemmShape, TileParitionerGroupNum, TileParitionerM01>;
 
         using Traits = ck_tile::TileGemmTraits<kPadM, kPadN, kPadK, ALayout, BLayout, CLayout>;
         using GemmUniversalTraits = ck_tile::