Reorganize project folders (#6)

include/ck_tile/README.md

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+[Back to the main page](../../README.md)
+# Composable Kernel Tile
+## concept
+`ck_tile` provides a programming model with templated abstractions to enable users to implement performance-critical kernels for machine learning workloads. introduces following basic concepts to help users building your own operator
+ - tensor coordinate transformation, this is the core concept of layout/index transform abstraction in both compiler time and run time.
+ - tile-based programming model, including tile-level api and the concept of distributed tensor.
+
+`ck_tile` is independently from the old ck, located under [/include/ck_tile](/include/ck_tile). You don't need to include anything from old CK, `ck_tile` has similiar (indeed almost the same) implementations for users to build operators. We will have a transition period to pull everything from old ck into `ck_tile`, stay tuned.
+
+## component
+`ck_tile` is splitted into several componenets including `core`, `host`, `ops/gemm`, `ops/fmha`... each component you only need to include a single header (e.g `#include "ck_tile/core.hpp"`, `#include "ck_tile/ops/fmha.hpp"`) then you are able to use the function/structure inside (different from old `ck`)  
+
+**[core]**  
+`ck_tile/core` contains all the basic data structure and function to build the kernel, you can only include this header and build your own operators that utilizing all the basic building blocks introduced in ck.
+
+`core/container`
+ - array, store runtime variables with fixed length (tensor index, register buffer, etc...)
+ - tuple, same as std::tuple, hold different type of data, and one of the solution to achieve multiple buffer. 
+ - sequence, compile time integer sequence used to build various internal structures, or to describe tile size
+ - other convenient structure build on top of above 3
+
+`core/numeric`
+ - gpu data type like `fp16_t`, `bf16_t`, `fp8_t`... and the conversion between each other
+ - constexpr integer similiar to std::integral_constant to be used as compile time integer.
+ - math functions and numeric utilities
+
+`core/algorithm`
+ - coordinate transformation system, used to build tensor transform and compile time indexing. This is the core idea introduced in old `ck` to describe how a tensor is build by several basic transform primitives like `merge`/`unmerge`/`embed` etc... and how we indexing into a ND tensor that finally mapped to 1D memory offset.
+
+`core/tensor`
+ - tensor descriptor, to describe how a ND tensor 
+ - distributed tensor, describe the storage of this tensor, and the distribution of how a collection of threads collaborately work for this tensor.
+ - tile level API, including `load_tile`, `store_tile`, `shuffle_tile`, `slice_tile`, etc...
+
+**[host]**  
+`ck_tile/host` contains all the host side utilities to launch a kernel, create the device buffer, and some reference implementations. This can be used to create examples (like that under ck_tile example folder) and simple executable to invoke this kernel, so if you only need `ck_tile` to build your own device library then it's OK to not include this. Based on this, it is recommended to include the specific header you needed under this folder to avoid including unwanted headers (e.g, only include `ck_tile/host/kernel_launch.hpp`), unless you are writing a host executable.
+
+**[ops/gemm, ops/fmha, ops/reduce...]**  
+our implementation of different device operators. 
+ - warp, warp tile level operator
+ - block, block tile level operator
+ - pipeline, pipeline that can achieve a customized tile level mainloop (or epilogue). By switching different pipeline to the kernel template you can have different kind of pipeline optimizations.
+ - kernel, template interface for users to instantiate a particular kernel
+
+**[ops/epilogue]**  
+epilogue part of our kernel. We may extend this epilogue part to let users to build their own cutomized epilogues.
+
+**[ref]**  
+reference implementation of cpu or gpu. This folder is supposed to include a specific header on demand.
+
+## examples
+currently we put all ck_tile related example under [/example/ck_tile](/example/ck_tile/) folder. Please check each example's subfolder.

include/ck_tile/core.hpp

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+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2025, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/algorithm/cluster_descriptor.hpp"
+#include "ck_tile/core/algorithm/coordinate_transform.hpp"
+#include "ck_tile/core/algorithm/indexing_adaptor.hpp"
+#include "ck_tile/core/algorithm/space_filling_curve.hpp"
+#include "ck_tile/core/algorithm/static_encoding_pattern.hpp"
+#include "ck_tile/core/arch/amd_buffer_addressing.hpp"
+#include "ck_tile/core/arch/amd_buffer_addressing_builtins.hpp"
+#include "ck_tile/core/arch/arch.hpp"
+#include "ck_tile/core/arch/generic_memory_space_atomic.hpp"
+#include "ck_tile/core/arch/utility.hpp"
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/container/array.hpp"
+#include "ck_tile/core/container/container_helper.hpp"
+#include "ck_tile/core/container/map.hpp"
+#include "ck_tile/core/container/meta_data_buffer.hpp"
+#include "ck_tile/core/container/multi_index.hpp"
+#include "ck_tile/core/container/sequence.hpp"
+#include "ck_tile/core/container/span.hpp"
+#include "ck_tile/core/container/statically_indexed_array.hpp"
+#include "ck_tile/core/container/thread_buffer.hpp"
+#include "ck_tile/core/container/tuple.hpp"
+#include "ck_tile/core/numeric/bfloat16.hpp"
+#include "ck_tile/core/numeric/float8.hpp"
+#include "ck_tile/core/numeric/half.hpp"
+#include "ck_tile/core/numeric/int8.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/numeric/math.hpp"
+#include "ck_tile/core/numeric/null_type.hpp"
+#include "ck_tile/core/numeric/numeric.hpp"
+#include "ck_tile/core/numeric/pk_int4.hpp"
+#include "ck_tile/core/numeric/type_convert.hpp"
+#include "ck_tile/core/numeric/vector_type.hpp"
+#include "ck_tile/core/tensor/buffer_view.hpp"
+#include "ck_tile/core/tensor/load_tile.hpp"
+#include "ck_tile/core/tensor/null_tensor.hpp"
+#include "ck_tile/core/tensor/null_tile_window.hpp"
+#include "ck_tile/core/tensor/shuffle_tile.hpp"
+#include "ck_tile/core/tensor/slice_tile.hpp"
+#include "ck_tile/core/tensor/static_distributed_tensor.hpp"
+#include "ck_tile/core/tensor/store_tile.hpp"
+#include "ck_tile/core/tensor/sweep_tile.hpp"
+#include "ck_tile/core/tensor/tensor_adaptor.hpp"
+#include "ck_tile/core/tensor/tensor_adaptor_coordinate.hpp"
+#include "ck_tile/core/tensor/tensor_coordinate.hpp"
+#include "ck_tile/core/tensor/tensor_descriptor.hpp"
+#include "ck_tile/core/tensor/tensor_view.hpp"
+#include "ck_tile/core/tensor/tile_distribution.hpp"
+#include "ck_tile/core/tensor/tile_distribution_encoding.hpp"
+#include "ck_tile/core/tensor/tile_elementwise.hpp"
+#include "ck_tile/core/tensor/tile_window.hpp"
+#include "ck_tile/core/tensor/tile_window_linear.hpp"
+#include "ck_tile/core/tensor/tile_window_utils.hpp"
+#include "ck_tile/core/tensor/transpose_tile.hpp"
+#include "ck_tile/core/tensor/update_tile.hpp"
+#include "ck_tile/core/utility/bit_cast.hpp"
+#include "ck_tile/core/utility/env.hpp"
+#include "ck_tile/core/utility/functional.hpp"
+#include "ck_tile/core/utility/functional_with_tuple.hpp"
+#include "ck_tile/core/utility/ignore.hpp"
+#include "ck_tile/core/utility/literals.hpp"
+#include "ck_tile/core/utility/magic_div.hpp"
+#include "ck_tile/core/utility/philox_rand.hpp"
+#include "ck_tile/core/utility/random.hpp"
+#include "ck_tile/core/utility/reduce_operator.hpp"
+#include "ck_tile/core/utility/static_counter.hpp"
+#include "ck_tile/core/utility/to_sequence.hpp"
+#include "ck_tile/core/utility/transpose_vectors.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+#include "ck_tile/core/utility/unary_element_function.hpp"

include/ck_tile/core/README.md

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+# ck_tile/core #
+
+`ck_tile/core` contains every basic functions and structures to create a GPU kernel using `ck_tile`. User should only include `ck_tile/core.hpp` this single header to use all the functionality. Everything is under `ck_tile` namespace. The coding style under this folder should be similar to `std` (`snake_case` for structure/function, Camel for template types...)
+
+```
+algorithm/
+    coordinate transform and some other reusable algorithm
+arch/
+    contains some basic device building block like mma, buffer addressing, etc...
+container/
+    contains basic container data structure, array/sequence/tuple/...
+numeric/
+    data type, and data type related math
+tensor/
+    tensor descriptors and tile level API
+utility/
+    other utility function for both host/device
+```

include/ck_tile/core/algorithm/cluster_descriptor.hpp

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+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/algorithm/coordinate_transform.hpp"
+#include "ck_tile/core/tensor/tensor_adaptor.hpp"
+#include "ck_tile/core/container/container_helper.hpp"
+#include "ck_tile/core/utility/functional.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+
+namespace ck_tile {
+
+template <typename Lengths,
+          typename ArrangeOrder = typename arithmetic_sequence_gen<0, Lengths::size(), 1>::type>
+CK_TILE_HOST_DEVICE constexpr auto make_cluster_descriptor(
+    const Lengths& lengths,
+    ArrangeOrder order = typename arithmetic_sequence_gen<0, Lengths::size(), 1>::type{})
+{
+    constexpr index_t ndim_low = Lengths::size();
+
+    const auto reordered_lengths = container_reorder_given_new2old(lengths, order);
+
+    const auto low_lengths = generate_tuple(
+        [&](auto idim_low) { return reordered_lengths[idim_low]; }, number<ndim_low>{});
+
+    const auto transform = make_merge_transform(low_lengths);
+
+    constexpr auto low_dim_old_top_ids = ArrangeOrder{};
+
+    constexpr auto up_dim_new_top_ids = sequence<0>{};
+
+    return make_single_stage_tensor_adaptor(
+        make_tuple(transform), make_tuple(low_dim_old_top_ids), make_tuple(up_dim_new_top_ids));
+}
+
+} // namespace ck_tile

include/ck_tile/core/algorithm/indexing_adaptor.hpp

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+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/container/multi_index.hpp"
+#include "ck_tile/core/container/container_helper.hpp"
+#include "ck_tile/core/utility/functional.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+
+namespace ck_tile {
+//  pre-defined indexing adaptor used for indexing(scatter/gather)
+
+// this version cache the index inside thread register(which is also prefered in real senario)
+// however it's user's responsibility that each thread only provide one indexing, which means
+// move coordinate will not change on this dim
+template <typename IndexingType>
+struct indexing_adaptor_onshot_cached
+{
+
+    CK_TILE_HOST_DEVICE constexpr indexing_adaptor_onshot_cached() = default;
+    CK_TILE_HOST_DEVICE constexpr indexing_adaptor_onshot_cached(const IndexingType& idx)
+        : cached_idx_(idx)
+    {
+    }
+    IndexingType cached_idx_;
+
+    template <typename LowIdx, typename UpIdx>
+    CK_TILE_HOST_DEVICE constexpr void calculate_lower_index(LowIdx& idx_low,
+                                                             const UpIdx& /*idx_up*/) const
+    {
+        static_assert(LowIdx::size() == 1 && UpIdx::size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        idx_low(number<0>{}) = cached_idx_;
+    }
+
+    template <typename LowIdxDiff, typename UpIdxDiff, typename LowIdx, typename UpIdx>
+    CK_TILE_HOST_DEVICE void update_lower_index(LowIdxDiff& idx_diff_low,
+                                                const UpIdxDiff& idx_diff_up,
+                                                LowIdx& /*idx_low*/,
+                                                const UpIdx& /*idx_up*/) const
+    {
+        // TODO: nonthing changed here
+        static_assert(LowIdxDiff::size() == 1 && UpIdxDiff::size() == 1 && LowIdx::size() == 1 &&
+                          UpIdx::size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        idx_diff_low(number<0>{}) = idx_diff_up[number<0>{}];
+
+        // pass the diff to lower, but not changing the actually index
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr bool is_known_at_compile_time()
+    {
+        return ck_tile::is_known_at_compile_time<IndexingType>::value;
+    }
+};
+} // namespace ck_tile

include/ck_tile/core/algorithm/space_filling_curve.hpp

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+// SPDX-License-Identifier: MIT
+// Copyright (c) 2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/container/multi_index.hpp"
+#include "ck_tile/core/container/container_helper.hpp"
+#include "ck_tile/core/container/statically_indexed_array.hpp"
+#include "ck_tile/core/utility/functional.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+
+namespace ck_tile {
+
+template <typename TensorLengths,
+          typename DimAccessOrder,
+          typename ScalarsPerAccess,
+          bool SnakeCurved = true> // # of scalars per access in each dimension
+struct space_filling_curve
+{
+    static constexpr index_t TensorSize =
+        reduce_on_sequence(TensorLengths{}, multiplies{}, number<1>{});
+    static_assert(0 < TensorSize,
+                  "space_filling_curve should be used to access a non-empty tensor");
+
+    static constexpr index_t nDim = TensorLengths::size();
+
+    using Index = multi_index<nDim>;
+
+    static constexpr index_t ScalarPerVector =
+        reduce_on_sequence(ScalarsPerAccess{}, multiplies{}, number<1>{});
+
+    static constexpr auto access_lengths   = TensorLengths{} / ScalarsPerAccess{};
+    static constexpr auto dim_access_order = DimAccessOrder{};
+    static constexpr auto ordered_access_lengths =
+        container_reorder_given_new2old(access_lengths, dim_access_order);
+
+    static constexpr auto to_index_adaptor = make_single_stage_tensor_adaptor(
+        make_tuple(make_merge_transform(ordered_access_lengths)),
+        make_tuple(typename arithmetic_sequence_gen<0, nDim, 1>::type{}),
+        make_tuple(sequence<0>{}));
+
+    static constexpr auto I0 = number<0>{};
+    static constexpr auto I1 = number<1>{};
+
+    CK_TILE_HOST_DEVICE static constexpr index_t get_num_of_access()
+    {
+        static_assert(TensorLengths::size() == ScalarsPerAccess::size());
+        static_assert(TensorLengths{} % ScalarsPerAccess{} ==
+                      typename uniform_sequence_gen<TensorLengths::size(), 0>::type{});
+
+        return reduce_on_sequence(TensorLengths{}, multiplies{}, number<1>{}) / ScalarPerVector;
+    }
+
+    template <index_t AccessIdx1dHead, index_t AccessIdx1dTail>
+    static CK_TILE_HOST_DEVICE constexpr auto get_step_between(number<AccessIdx1dHead>,
+                                                               number<AccessIdx1dTail>)
+    {
+        static_assert(AccessIdx1dHead >= 0 && AccessIdx1dHead < get_num_of_access(),
+                      "1D index out of range");
+        static_assert(AccessIdx1dTail >= 0 && AccessIdx1dTail < get_num_of_access(),
+                      "1D index out of range");
+
+        constexpr auto idx_head = get_index(number<AccessIdx1dHead>{});
+        constexpr auto idx_tail = get_index(number<AccessIdx1dTail>{});
+        return idx_tail - idx_head;
+    }
+
+    template <index_t AccessIdx1d>
+    static CK_TILE_HOST_DEVICE constexpr auto get_forward_step(number<AccessIdx1d>)
+    {
+        static_assert(AccessIdx1d < get_num_of_access(), "1D index should be larger than 0");
+        return get_step_between(number<AccessIdx1d>{}, number<AccessIdx1d + 1>{});
+    }
+
+    template <index_t AccessIdx1d>
+    static CK_TILE_HOST_DEVICE constexpr auto get_backward_step(number<AccessIdx1d>)
+    {
+        static_assert(AccessIdx1d > 0, "1D index should be larger than 0");
+
+        return get_step_between(number<AccessIdx1d>{}, number<AccessIdx1d - 1>{});
+    }
+
+    // Do not use this function directly!
+    // TODO: can refactor into generic lambda in the future
+    template <index_t AccessIdx1d>
+    static CK_TILE_HOST_DEVICE constexpr Index _get_index(number<AccessIdx1d>)
+    {
+#if 0
+        /*
+         * \todo: tensor_adaptor::calculate_bottom_index does NOT return constexpr as expected.
+         */
+        constexpr auto ordered_access_idx = to_index_adaptor.calculate_bottom_index(make_multi_index(number<AccessIdx1d>{}));
+#else
+
+        constexpr auto access_strides =
+            container_reverse_exclusive_scan(ordered_access_lengths, multiplies{}, number<1>{});
+
+        constexpr auto idx_1d = number<AccessIdx1d>{};
+        // Given tensor strides \p access_lengths, and 1D index of space-filling-curve, compute the
+        // idim-th element of multidimensional index.
+        // All constexpr variables have to be captured by VALUE.
+        constexpr auto compute_index = [ idx_1d, access_strides ](auto idim) constexpr
+        {
+            constexpr auto compute_index_impl = [ idx_1d, access_strides ](auto jdim) constexpr
+            {
+                auto res = idx_1d.value;
+                auto id  = 0;
+
+                static_for<0, jdim.value + 1, 1>{}([&](auto kdim) {
+                    id = res / access_strides[kdim].value;
+                    res -= id * access_strides[kdim].value;
+                });
+
+                return id;
+            };
+
+            constexpr auto id = compute_index_impl(idim);
+            return number<id>{};
+        };
+
+        constexpr auto ordered_access_idx = generate_tuple(compute_index, number<nDim>{});
+#endif
+        constexpr auto forward_sweep = [&]() {
+            statically_indexed_array<bool, nDim> forward_sweep_;
+
+            forward_sweep_(I0) = true;
+
+            static_for<1, nDim, 1>{}([&](auto idim) {
+                index_t tmp = ordered_access_idx[I0];
+
+                static_for<1, idim, 1>{}(
+                    [&](auto j) { tmp = tmp * ordered_access_lengths[j] + ordered_access_idx[j]; });
+
+                forward_sweep_(idim) = tmp % 2 == 0;
+            });
+
+            return forward_sweep_;
+        }();
+
+        // calculate multi-dim tensor index
+        auto idx_md = [&]() {
+            Index ordered_idx;
+
+            static_for<0, nDim, 1>{}([&](auto idim) {
+                ordered_idx(idim) =
+                    !SnakeCurved || forward_sweep[idim]
+                        ? ordered_access_idx[idim]
+                        : ordered_access_lengths[idim] - 1 - ordered_access_idx[idim];
+            });
+
+            return container_reorder_given_old2new(ordered_idx, dim_access_order) *
+                   ScalarsPerAccess{};
+        }();
+        return idx_md;
+    }
+
+    // FIXME: return tuple of number<>, which is compile time only variable
+    template <index_t AccessIdx1d>
+    static CK_TILE_HOST_DEVICE constexpr auto get_index(number<AccessIdx1d>)
+    {
+        constexpr auto idx = _get_index(number<AccessIdx1d>{});
+
+        return generate_tuple([&](auto i) { return number<idx[i]>{}; }, number<nDim>{});
+    }
+};
+
+} // namespace ck_tile

include/ck_tile/core/algorithm/static_encoding_pattern.hpp

@@ -0,0 +1,213 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2025, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/arch/arch.hpp"
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/container/sequence.hpp"
+#include "ck_tile/core/container/tuple.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/tensor/tile_distribution.hpp"
+#include "ck_tile/core/tensor/tile_distribution_encoding.hpp"
+
+namespace ck_tile {
+
+/**
+ * @brief Enumeration describing static tile distribution patterns.
+ *
+ */
+enum struct tile_distribution_pattern
+{
+    /**
+     * @brief Thread raked pattern.
+     *
+     */
+    thread_raked,
+    /**
+     * @brief Warp raked pattern.
+     *
+     */
+    warp_raked,
+    /**
+     * @brief Block raked pattern - aka linear.
+     *
+     */
+    block_raked,
+};
+
+struct TileDistributionEncodingPattern
+{
+};
+
+/**
+ * @brief Class creating 2D static tile distribution with different load/store patterns.
+ *
+ * @note We always assume that Tile is YPerTile x XPerTile where X dim (rightmost)
+ *       is contiguous and we can do vector load on this dimension.
+ *
+ * @tparam BlockSize    Number of threads in a workgroup.
+ * @tparam YPerTile    The tile size of outer/leftmost dimension.
+ * @tparam XPerTile    The tile size of inner/rightmost dimension (contiguous).
+ * @tparam VecSize      The vector access size.
+ * @tparam DistributionPattern The enumeration describing used access pattern.
+ */
+template <index_t BlockSize,
+          index_t YPerTile,
+          index_t XPerTile,
+          index_t VecSize,
+          tile_distribution_pattern DistributionPattern>
+struct TileDistributionEncodingPattern2D : public TileDistributionEncodingPattern
+{
+};
+
+// Thread raked
+template <index_t BlockSize, index_t YPerTile, index_t XPerTile, index_t VecSize>
+struct TileDistributionEncodingPattern2D<BlockSize,
+                                         YPerTile,
+                                         XPerTile,
+                                         VecSize,
+                                         tile_distribution_pattern::thread_raked>
+    : public TileDistributionEncodingPattern
+{
+
+    // TODO: make pattern where below condition does not need to hold - GGemmMultiDSplitk!
+    static_assert(XPerTile % VecSize == 0, "XPerTile must be a multiple of VecSize!");
+    static constexpr index_t warp_size  = get_warp_size();
+    static constexpr index_t num_warps  = BlockSize / get_warp_size();
+    static constexpr index_t LargestVec = (XPerTile * YPerTile) / (num_warps * warp_size);
+    static constexpr index_t X1         = VecSize > LargestVec ? LargestVec : VecSize;
+    static constexpr index_t X0         = XPerTile / X1; // # of threads in X dim
+
+    // # of rows in Y dim accessed by single wavefront in one iteration
+    static constexpr index_t Y1 = warp_size / X0;
+    static_assert(X0 * Y1 == warp_size, "X0 * Y1 must cover whole wavefront!");
+
+    static constexpr index_t Y0 = num_warps;
+    //  YPerWarp = YPerTile / Y0;
+    //  Y2 = YPerWarp / Y1;
+    static constexpr index_t Y2 = YPerTile / (Y1 * Y0); // # of iters within wavefront
+
+    static_assert(X0 * Y1 * Y0 == BlockSize, "X0 * warp_ys * Y0 must cover whole workgroup!");
+    static_assert(Y0 * Y1 * Y2 == YPerTile, "Y0, Y1, Y2 must cover whole YPerTile");
+
+    CK_TILE_HOST_DEVICE static constexpr auto Make2DStaticTileDistribution()
+    {
+        return make_static_tile_distribution(
+            tile_distribution_encoding<sequence<1>,
+                                       tuple<sequence<Y0, Y1, Y2>, sequence<X0, X1>>,
+                                       tuple<sequence<1>, sequence<1, 2>>,
+                                       tuple<sequence<0>, sequence<1, 0>>,
+                                       sequence<1, 2>,
+                                       sequence<2, 1>>{});
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr auto MakeShuffled2DStaticTileDistribution()
+    {
+        return make_static_tile_distribution(
+            tile_distribution_encoding<sequence<1>,
+                                       tuple<sequence<X0, X1>, sequence<Y0, Y1, Y2>>,
+                                       tuple<sequence<2>, sequence<2, 1>>,
+                                       tuple<sequence<0>, sequence<1, 0>>,
+                                       sequence<1, 2>,
+                                       sequence<1, 2>>{});
+    }
+};
+
+// Warp raked
+template <index_t BlockSize, index_t YPerTile, index_t XPerTile, index_t VecSize>
+struct TileDistributionEncodingPattern2D<BlockSize,
+                                         YPerTile,
+                                         XPerTile,
+                                         VecSize,
+                                         tile_distribution_pattern::warp_raked>
+    : public TileDistributionEncodingPattern
+{
+
+    static_assert(XPerTile % VecSize == 0, "XPerTile must be a multiple of VecSize!");
+    static constexpr index_t warp_size  = get_warp_size();
+    static constexpr index_t num_warps  = BlockSize / get_warp_size();
+    static constexpr index_t LargestVec = (XPerTile * YPerTile) / (num_warps * warp_size);
+    static constexpr index_t X1         = VecSize > LargestVec ? LargestVec : VecSize;
+    static constexpr index_t X0         = XPerTile / X1; // # of threads in X dim
+
+    static constexpr index_t Y2 = warp_size / X0; // # of rows in Y dim to cover whole wavefront
+    static_assert(X0 * Y2 == warp_size, "X0 * Y2 must cover whole wavefront!");
+
+    static constexpr index_t Y0 = num_warps;
+    static_assert(X0 * Y2 * Y0 == BlockSize, "X0 * Y2 * Y1 must cover whole workgroup!");
+
+    static constexpr index_t Y1 = YPerTile / (Y2 * Y0); // # of iters within wavefront
+    static_assert(Y0 * Y1 * Y2 == YPerTile, "Y0, Y1, Y2 must cover whole YPerTile");
+
+    CK_TILE_HOST_DEVICE static constexpr auto Make2DStaticTileDistribution()
+    {
+        return make_static_tile_distribution(
+            tile_distribution_encoding<sequence<1>,
+                                       tuple<sequence<Y0, Y1, Y2>, sequence<X0, X1>>,
+                                       tuple<sequence<1>, sequence<1, 2>>,
+                                       tuple<sequence<0>, sequence<2, 0>>,
+                                       sequence<1, 2>,
+                                       sequence<1, 1>>{});
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr auto MakeShuffled2DStaticTileDistribution()
+    {
+        return make_static_tile_distribution(
+            tile_distribution_encoding<sequence<1>,
+                                       tuple<sequence<X0, X1>, sequence<Y0, Y1, Y2>>,
+                                       tuple<sequence<2>, sequence<2, 1>>,
+                                       tuple<sequence<0>, sequence<2, 0>>,
+                                       sequence<1, 2>,
+                                       sequence<1, 1>>{});
+    }
+};
+
+// Block raked
+template <index_t BlockSize, index_t YPerTile, index_t XPerTile, index_t VecSize>
+struct TileDistributionEncodingPattern2D<BlockSize,
+                                         YPerTile,
+                                         XPerTile,
+                                         VecSize,
+                                         tile_distribution_pattern::block_raked>
+    : public TileDistributionEncodingPattern
+{
+
+    // TODO: make pattern where below condition does not need to hold - GGemmMultiDSplitk!
+    static_assert(XPerTile % VecSize == 0, "XPerTile must be a multiple of VecSize!");
+    static constexpr index_t warp_size  = get_warp_size();
+    static constexpr index_t num_warps  = BlockSize / get_warp_size();
+    static constexpr index_t LargestVec = (XPerTile * YPerTile) / (num_warps * warp_size);
+    static constexpr index_t X1         = VecSize > LargestVec ? LargestVec : VecSize;
+    static constexpr index_t X0         = XPerTile / X1; // # of threads in X dim
+    static constexpr index_t Y2 = warp_size / X0; // # of rows in Y dim to cover whole wavefront
+    static_assert(X0 * Y2 == warp_size, "X0 * Y2 must cover whole wavefront!");
+    static constexpr index_t Y1 = num_warps;
+    static_assert(X0 * Y2 * Y1 == BlockSize, "X0 * Y2 * Y1 must cover whole workgroup!");
+    static constexpr index_t Y0 = YPerTile / (Y2 * Y1); // # of iters
+    static_assert(Y0 * Y1 * Y2 == YPerTile, "Y0, Y1, Y2 must cover whole YPerTile");
+
+    CK_TILE_HOST_DEVICE static constexpr auto Make2DStaticTileDistribution()
+    {
+        return make_static_tile_distribution(
+            tile_distribution_encoding<sequence<1>,
+                                       tuple<sequence<Y0, Y1, Y2>, sequence<X0, X1>>,
+                                       tuple<sequence<1>, sequence<1, 2>>,
+                                       tuple<sequence<1>, sequence<2, 0>>,
+                                       sequence<1, 2>,
+                                       sequence<0, 1>>{});
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr auto MakeShuffled2DStaticTileDistribution()
+    {
+        return make_static_tile_distribution(
+            tile_distribution_encoding<sequence<1>,
+                                       tuple<sequence<X0, X1>, sequence<Y0, Y1, Y2>>,
+                                       tuple<sequence<2>, sequence<2, 1>>,
+                                       tuple<sequence<1>, sequence<2, 0>>,
+                                       sequence<1, 2>,
+                                       sequence<1, 0>>{});
+    }
+};
+
+} // namespace ck_tile

include/ck_tile/core/arch/arch.hpp

@@ -0,0 +1,157 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2025, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+// Address Space for AMDGCN
+// https://llvm.org/docs/AMDGPUUsage.html#address-space
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+
+namespace ck_tile {
+
+template <typename, bool>
+struct safe_underlying_type;
+
+template <typename T>
+struct safe_underlying_type<T, true>
+{
+    using type = std::underlying_type_t<T>;
+};
+
+template <typename T>
+struct safe_underlying_type<T, false>
+{
+    using type = void;
+};
+
+template <typename T>
+using safe_underlying_type_t = typename safe_underlying_type<T, std::is_enum<T>::value>::type;
+
+enum struct address_space_enum : std::uint16_t
+{
+    generic = 0,
+    global,
+    lds,
+    sgpr,
+    constant,
+    vgpr
+};
+
+enum struct memory_operation_enum : std::uint16_t
+{
+    set = 0,
+    atomic_add,
+    atomic_max,
+    add
+};
+
+CK_TILE_HOST_DEVICE constexpr index_t get_warp_size()
+{
+    // warpSize is defined by HIP
+    return warpSize;
+}
+
+CK_TILE_DEVICE index_t get_grid_size() { return gridDim.x; }
+
+CK_TILE_DEVICE index_t get_block_size() { return blockDim.x; }
+
+// TODO: deprecate these
+CK_TILE_DEVICE index_t get_thread_local_1d_id() { return threadIdx.x; }
+
+CK_TILE_DEVICE index_t get_thread_global_1d_id() { return blockIdx.x * blockDim.x + threadIdx.x; }
+
+CK_TILE_DEVICE index_t get_block_1d_id() { return blockIdx.x; }
+
+// Use these instead
+CK_TILE_DEVICE index_t get_lane_id() { return __lane_id(); }
+
+CK_TILE_DEVICE index_t get_warp_id()
+{
+    return __builtin_amdgcn_readfirstlane(threadIdx.x / get_warp_size());
+}
+
+CK_TILE_DEVICE index_t get_thread_id() { return threadIdx.x; }
+
+CK_TILE_DEVICE index_t get_block_id() { return blockIdx.x; }
+
+CK_TILE_DEVICE void block_sync_lds()
+{
+#if CK_TILE_EXPERIMENTAL_BLOCK_SYNC_LDS_WITHOUT_SYNC_VMEM
+    // asm volatile("\
+    // s_waitcnt lgkmcnt(0) \n \
+    // s_barrier \
+    // " ::);
+
+    __builtin_amdgcn_s_waitcnt(0xc07f);
+    __builtin_amdgcn_s_barrier();
+#else
+    __syncthreads();
+#endif
+}
+
+CK_TILE_DEVICE void block_sync_load_raw(index_t cnt = 0)
+{
+#ifdef __gfx12__
+    asm volatile("s_wait_loadcnt %0 \n"
+                 "s_barrier_signal -1 \n"
+                 "s_barrier_wait -1"
+                 :
+                 : "n"(cnt)
+                 : "memory");
+#else
+    asm volatile("s_waitcnt vmcnt(%0) \n"
+                 "s_barrier"
+                 :
+                 : "n"(cnt)
+                 : "memory");
+#endif
+}
+
+CK_TILE_DEVICE void block_sync_lds_direct_load()
+{
+    asm volatile("\
+    s_waitcnt vmcnt(0) \n \
+    s_waitcnt lgkmcnt(0) \n \
+    s_barrier \
+    " ::);
+}
+
+CK_TILE_DEVICE void s_nop(index_t cnt = 0)
+{
+#if 1
+    asm volatile("s_nop %0" : : "n"(cnt) :);
+#else
+    __builtin_amdgcn_sched_barrier(cnt);
+#endif
+}
+
+#define CK_CONSTANT_ADDRESS_SPACE \
+    __attribute__((address_space( \
+        static_cast<safe_underlying_type_t<address_space_enum>>(address_space_enum::constant))))
+
+template <typename T>
+__device__ T* cast_pointer_to_generic_address_space(T CK_CONSTANT_ADDRESS_SPACE* p)
+{
+    // cast a pointer in "Constant" address space (4) to "Generic" address space (0)
+    // only c-style pointer cast seems be able to be compiled
+#pragma clang diagnostic push
+#pragma clang diagnostic ignored "-Wold-style-cast"
+    return (T*)(p); // NOLINT(old-style-cast)
+#pragma clang diagnostic pop
+}
+
+template <typename T>
+__host__ __device__ T CK_CONSTANT_ADDRESS_SPACE* cast_pointer_to_constant_address_space(T* p)
+{
+    // cast a pointer in "Generic" address space (0) to "Constant" address space (4)
+    // only c-style pointer cast seems be able to be compiled;
+#pragma clang diagnostic push
+#pragma clang diagnostic ignored "-Wold-style-cast"
+    return (T CK_CONSTANT_ADDRESS_SPACE*)p; // NOLINT(old-style-cast)
+#pragma clang diagnostic pop
+}
+
+} // namespace ck_tile

include/ck_tile/core/arch/generic_memory_space_atomic.hpp

@@ -0,0 +1,458 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2025, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+#include "ck_tile/core/numeric/vector_type.hpp"
+#include "ck_tile/core/numeric/type_convert.hpp"
+#include "ck_tile/core/container/thread_buffer.hpp"
+
+namespace ck_tile {
+
+template <typename T, typename ComputeType>
+CK_TILE_HOST_DEVICE T add(const T& a, const T& b)
+{
+    return type_convert<T>(type_convert<ComputeType>(a) + type_convert<ComputeType>(b));
+}
+
+CK_TILE_HOST_DEVICE bf16x2_t add_bf16x2_t(const bf16x2_t& a, const bf16x2_t& b)
+{
+    bf16x2_t rtn;
+    rtn[0] = add<bf16_t, float>(a[0], b[0]);
+    rtn[1] = add<bf16_t, float>(a[1], b[1]);
+    return rtn;
+}
+
+CK_TILE_HOST_DEVICE bf16x4_t add_bf16x4_t(const bf16x4_t& a, const bf16x4_t& b)
+{
+    bf16x4_t rtn;
+    rtn[0] = add<bf16_t, float>(a[0], b[0]);
+    rtn[1] = add<bf16_t, float>(a[1], b[1]);
+    rtn[2] = add<bf16_t, float>(a[2], b[2]);
+    rtn[3] = add<bf16_t, float>(a[3], b[3]);
+    return rtn;
+}
+
+CK_TILE_HOST_DEVICE fp8x4_t add_fp8x4_t(const fp8x4_t& a, const fp8x4_t& b)
+{
+    fp8x4_t rtn;
+    rtn[0] = add<fp8_t, float>(a[0], b[0]);
+    rtn[1] = add<fp8_t, float>(a[1], b[1]);
+    rtn[2] = add<fp8_t, float>(a[2], b[2]);
+    rtn[3] = add<fp8_t, float>(a[3], b[3]);
+    return rtn;
+}
+
+CK_TILE_HOST_DEVICE fp8x8_t add_fp8x8_t(const fp8x8_t& a, const fp8x8_t& b)
+{
+    fp8x8_t rtn;
+    rtn[0] = add<fp8_t, float>(a[0], b[0]);
+    rtn[1] = add<fp8_t, float>(a[1], b[1]);
+    rtn[2] = add<fp8_t, float>(a[2], b[2]);
+    rtn[3] = add<fp8_t, float>(a[3], b[3]);
+    rtn[4] = add<fp8_t, float>(a[4], b[4]);
+    rtn[5] = add<fp8_t, float>(a[5], b[5]);
+    rtn[6] = add<fp8_t, float>(a[6], b[6]);
+    rtn[7] = add<fp8_t, float>(a[7], b[7]);
+    return rtn;
+}
+
+CK_TILE_HOST_DEVICE bf8x4_t add_bf8x4_t(const bf8x4_t& a, const bf8x4_t& b)
+{
+    bf8x4_t rtn;
+    rtn[0] = add<bf8_t, float>(a[0], b[0]);
+    rtn[1] = add<bf8_t, float>(a[1], b[1]);
+    rtn[2] = add<bf8_t, float>(a[2], b[2]);
+    rtn[3] = add<bf8_t, float>(a[3], b[3]);
+    return rtn;
+}
+
+CK_TILE_HOST_DEVICE bf8x8_t add_bf8x8_t(const bf8x8_t& a, const bf8x8_t& b)
+{
+    bf8x8_t rtn;
+    rtn[0] = add<bf8_t, float>(a[0], b[0]);
+    rtn[1] = add<bf8_t, float>(a[1], b[1]);
+    rtn[2] = add<bf8_t, float>(a[2], b[2]);
+    rtn[3] = add<bf8_t, float>(a[3], b[3]);
+    rtn[4] = add<bf8_t, float>(a[4], b[4]);
+    rtn[5] = add<bf8_t, float>(a[5], b[5]);
+    rtn[6] = add<bf8_t, float>(a[6], b[6]);
+    rtn[7] = add<bf8_t, float>(a[7], b[7]);
+    return rtn;
+}
+
+// Caution: DO NOT REMOVE
+// intentionally have only declaration but no definition to cause compilation failure when trying to
+// instantiate this template. The purpose is to make the implementation of atomic_add explicit for
+// each datatype.
+template <typename X>
+CK_TILE_DEVICE void atomic_add(X* p_dst, const X& x);
+
+template <>
+CK_TILE_DEVICE void atomic_add<bf16x2_t>(bf16x2_t* p_dst, const bf16x2_t& x)
+{
+    union U32BF162_ADDR
+    {
+        uint32_t* u32_a;
+        bf16x2_t* bf162_a;
+    };
+
+    union U32BF162
+    {
+        uint32_t u32;
+        bf16x2_t bf162;
+    };
+
+    U32BF162_ADDR dword_addr;
+    U32BF162 cur_v;
+    U32BF162 new_;
+    uint32_t old_v, new_v;
+    dword_addr.bf162_a = p_dst;
+    cur_v.u32          = *dword_addr.u32_a;
+
+    do
+    {
+        old_v      = cur_v.u32;
+        new_.bf162 = add_bf16x2_t(cur_v.bf162, x);
+        new_v      = new_.u32;
+        cur_v.u32  = atomicCAS(dword_addr.u32_a, old_v, new_v);
+    } while(cur_v.u32 != old_v);
+}
+
+template <>
+CK_TILE_DEVICE void atomic_add<bf16x4_t>(bf16x4_t* p_dst, bf16x4_t const& x)
+{
+    // Union to treat the pointer as either bf16x4_t* or uint64_t*:
+    union U64BF164_ADDR
+    {
+        uint64_t* u64_a;
+        bf16x4_t* bf164_a;
+    };
+
+    // Union to treat the data as either bf16x4_t or 64-bit integer
+    union U64BF164
+    {
+        uint64_t u64;
+        bf16x4_t bf164;
+    };
+
+    U64BF164_ADDR addr;
+    addr.bf164_a = p_dst; // interpret p_dst as a 64-bit location
+
+    // First read (non-atomic) of the old value
+    U64BF164 cur_v;
+    cur_v.u64 = *addr.u64_a;
+
+    U64BF164 new_v_union;
+    uint64_t old_v, new_v;
+
+    do
+    {
+        // old 64 bits
+        old_v = cur_v.u64;
+
+        // Add elementwise in bf16
+        new_v_union.bf164 = add_bf16x4_t(cur_v.bf164, x);
+        new_v             = new_v_union.u64;
+
+        // Attempt the 64-bit CAS
+        cur_v.u64 = atomicCAS(addr.u64_a, old_v, new_v);
+
+    } while(cur_v.u64 != old_v);
+}
+
+template <>
+CK_TILE_DEVICE void atomic_add<fp8x4_t>(fp8x4_t* p_dst, const fp8x4_t& x)
+{
+    union U32FP84_ADDR
+    {
+        uint32_t* u32_a;
+        fp8x4_t* fp84_a;
+    };
+
+    union U32FP84
+    {
+        uint32_t u32;
+        fp8x4_t fp84;
+    };
+
+    U32FP84_ADDR dword_addr;
+    U32FP84 cur_v;
+    U32FP84 new_;
+    uint32_t old_v, new_v;
+
+    dword_addr.fp84_a = p_dst;
+    cur_v.u32         = *dword_addr.u32_a;
+
+    do
+    {
+        old_v     = cur_v.u32;
+        new_.fp84 = add_fp8x4_t(cur_v.fp84, x);
+        new_v     = new_.u32;
+        cur_v.u32 = atomicCAS(dword_addr.u32_a, old_v, new_v);
+    } while(cur_v.u32 != old_v);
+}
+
+template <>
+CK_TILE_DEVICE void atomic_add<bf8x4_t>(bf8x4_t* p_dst, const bf8x4_t& x)
+{
+    union U32BF84_ADDR
+    {
+        uint32_t* u32_a;
+        bf8x4_t* bf84_a;
+    };
+
+    union U32BF84
+    {
+        uint32_t u32;
+        bf8x4_t bf84;
+    };
+
+    U32BF84_ADDR dword_addr;
+    U32BF84 cur_v;
+    U32BF84 new_;
+    uint32_t old_v, new_v;
+
+    dword_addr.bf84_a = p_dst;
+    cur_v.u32         = *dword_addr.u32_a;
+
+    do
+    {
+        old_v     = cur_v.u32;
+        new_.bf84 = add_bf8x4_t(cur_v.bf84, x);
+        new_v     = new_.u32;
+        cur_v.u32 = atomicCAS(dword_addr.u32_a, old_v, new_v);
+    } while(cur_v.u32 != old_v);
+}
+
+//
+// Atomic add for fp8x8_t
+//
+template <>
+CK_TILE_DEVICE void atomic_add<fp8x8_t>(fp8x8_t* p_dst, fp8x8_t const& x)
+{
+    // Union for addressing 64 bits as either "fp8x8_t" or a 64-bit integer.
+    union U64FP88_ADDR
+    {
+        uint64_t* u64_a; // pointer to 64-bit integer
+        fp8x8_t* fp88_a; // pointer to fp8x8_t
+    };
+
+    union U64FP88
+    {
+        uint64_t u64;
+        fp8x8_t fp88;
+    };
+
+    U64FP88_ADDR dword_addr;
+    U64FP88 cur_v;
+    U64FP88 new_v_union;
+    uint64_t old_v, new_v;
+
+    // Point to the destination as both fp8x8_t* and uint64_t*.
+    dword_addr.fp88_a = p_dst;
+    // Initial read of 64 bits from memory
+    cur_v.u64 = *dword_addr.u64_a;
+
+    do
+    {
+        old_v = cur_v.u64;
+        // Add each fp8 element using your add_fp8x8_t(...) routine
+        new_v_union.fp88 = add_fp8x8_t(cur_v.fp88, x);
+        new_v            = new_v_union.u64;
+
+        // Attempt 64-bit CAS
+        cur_v.u64 = atomicCAS(dword_addr.u64_a, old_v, new_v);
+    } while(cur_v.u64 != old_v);
+}
+
+//
+// Atomic add for bf8x8_t
+//
+template <>
+CK_TILE_DEVICE void atomic_add<bf8x8_t>(bf8x8_t* p_dst, bf8x8_t const& x)
+{
+    union U64BF88_ADDR
+    {
+        uint64_t* u64_a;
+        bf8x8_t* bf88_a;
+    };
+
+    union U64BF88
+    {
+        uint64_t u64;
+        bf8x8_t bf88;
+    };
+
+    U64BF88_ADDR dword_addr;
+    U64BF88 cur_v;
+    U64BF88 new_v_union;
+    uint64_t old_v, new_v;
+
+    dword_addr.bf88_a = p_dst;
+    // Read the original 64 bits
+    cur_v.u64 = *dword_addr.u64_a;
+
+    do
+    {
+        old_v = cur_v.u64;
+        // Add each bf8 element using your add_bf8x8_t(...) routine
+        new_v_union.bf88 = add_bf8x8_t(cur_v.bf88, x);
+        new_v            = new_v_union.u64;
+
+        // 64-bit CAS loop
+        cur_v.u64 = atomicCAS(dword_addr.u64_a, old_v, new_v);
+    } while(cur_v.u64 != old_v);
+}
+
+template <typename T, index_t N>
+CK_TILE_DEVICE void atomic_add_g(T* p_dst, const thread_buffer<T, N>& x)
+{
+    static_assert((std::is_same<T, int32_t>::value && (N == 1)) ||
+                      (std::is_same<T, uint32_t>::value && (N == 1)) ||
+                      (std::is_same<T, float>::value && (N == 1 || N == 2)) ||
+                      (std::is_same<T, double>::value && (N == 1 || N == 2)) ||
+                      (std::is_same<T, bf16_t>::value && (N == 2 || N == 4 || N == 8)) ||
+                      (std::is_same<T, fp8_t>::value && (N == 4 || N == 8 || N == 16)) ||
+                      (std::is_same<T, bf8_t>::value && (N == 4 || N == 8 || N == 16)),
+                  "The granularity of the thread buffer is unsupported on the hardware!");
+
+    constexpr auto I0 = number<0>{};
+    constexpr auto I1 = number<1>{};
+
+    if constexpr(std::is_same<T, float>::value)
+    {
+        if constexpr(N == 1)
+        {
+            atomicAdd(p_dst, bit_cast<float>(x));
+        }
+        else if constexpr(N == 2)
+        {
+            atomicAdd(c_style_pointer_cast<float*>(p_dst), x.template get_as<float>()[I0]);
+            atomicAdd(c_style_pointer_cast<float*>(p_dst) + 1, x.template get_as<float>()[I1]);
+        }
+    }
+    else if constexpr(std::is_same<T, double>::value)
+    {
+        if constexpr(N == 1)
+        {
+            return atomicAdd(p_dst, bit_cast<double>(x));
+        }
+        else if constexpr(N == 2)
+        {
+            atomicAdd(c_style_pointer_cast<double*>(p_dst), x.template get_as<double>()[I0]);
+            atomicAdd(c_style_pointer_cast<double*>(p_dst) + 1, x.template get_as<double>()[I1]);
+        }
+    }
+    else if constexpr(std::is_same<T, int32_t>::value)
+    {
+        if constexpr(N == 1)
+        {
+            atomicAdd(p_dst, bit_cast<int32_t>(x));
+        }
+    }
+    else if constexpr(std::is_same<T, uint32_t>::value)
+    {
+        if constexpr(N == 1)
+        {
+            atomicAdd(p_dst, bit_cast<uint32_t>(x));
+        }
+    }
+    else if constexpr(std::is_same<T, bf16_t>::value)
+    {
+        if constexpr(N == 2)
+        {
+            atomic_add(c_style_pointer_cast<bf16x2_t*>(p_dst), x.template get_as<bf16x2_t>()[I0]);
+        }
+        else if constexpr(N == 4)
+        {
+            atomic_add(c_style_pointer_cast<bf16x4_t*>(p_dst), x.template get_as<bf16x4_t>()[I0]);
+        }
+        else if constexpr(N == 8)
+        {
+            atomic_add(c_style_pointer_cast<bf16x4_t*>(p_dst), x.template get_as<bf16x4_t>()[I0]);
+            atomic_add(c_style_pointer_cast<bf16x4_t*>(p_dst) + 1,
+                       x.template get_as<bf16x4_t>()[I1]);
+        }
+    }
+    else if constexpr(std::is_same<T, fp8_t>::value)
+    {
+        if constexpr(N == 4)
+        {
+            atomic_add(c_style_pointer_cast<fp8x4_t*>(p_dst), x.template get_as<fp8x4_t>()[I0]);
+        }
+        if constexpr(N == 8)
+        {
+            atomic_add(c_style_pointer_cast<fp8x8_t*>(p_dst), x.template get_as<fp8x8_t>()[I0]);
+        }
+        if constexpr(N == 16)
+        {
+            atomic_add(c_style_pointer_cast<fp8x8_t*>(p_dst), x.template get_as<fp8x8_t>()[I0]);
+            atomic_add(c_style_pointer_cast<fp8x8_t*>(p_dst) + 1, x.template get_as<fp8x8_t>()[I1]);
+        }
+    }
+    else if constexpr(std::is_same<T, bf8_t>::value)
+    {
+        if constexpr(N == 4)
+        {
+            atomic_add(c_style_pointer_cast<bf8x4_t*>(p_dst), x.template get_as<bf8x4_t>()[I0]);
+        }
+        if constexpr(N == 8)
+        {
+            atomic_add(c_style_pointer_cast<bf8x8_t*>(p_dst), x.template get_as<bf8x8_t>()[I0]);
+        }
+        if constexpr(N == 16)
+        {
+            atomic_add(c_style_pointer_cast<bf8x8_t*>(p_dst), x.template get_as<bf8x8_t>()[I0]);
+            atomic_add(c_style_pointer_cast<bf8x8_t*>(p_dst) + 1, x.template get_as<bf8x8_t>()[I1]);
+        }
+    }
+}
+
+template <typename T, index_t N>
+CK_TILE_DEVICE void atomic_max_g(T* p_dst, const thread_buffer<T, N>& x)
+{
+    static_assert((std::is_same<T, int32_t>::value && (N == 1)) ||
+                      (std::is_same<T, uint32_t>::value && (N == 1)) ||
+                      (std::is_same<T, float>::value && (N == 1 || N == 2)) ||
+                      (std::is_same<T, double>::value && (N == 1)),
+                  "wrong! not implemented");
+
+    constexpr auto I0 = number<0>{};
+    constexpr auto I1 = number<1>{};
+
+    if constexpr(std::is_same<T, float>::value)
+    {
+        if constexpr(N == 1)
+        {
+            atomicMax(p_dst, bit_cast<float>(x));
+        }
+        else if constexpr(N == 2)
+        {
+            atomicMax(c_style_pointer_cast<float*>(p_dst), x.template get_as<float>()[I0]);
+            atomicMax(c_style_pointer_cast<float*>(p_dst) + 1, x.template get_as<float>()[I1]);
+        }
+    }
+    else if constexpr(std::is_same<T, double>::value)
+    {
+        if constexpr(N == 1)
+        {
+            atomicMax(p_dst, bit_cast<double>(x));
+        }
+    }
+    else if constexpr(std::is_same<T, int32_t>::value)
+    {
+        if constexpr(N == 1)
+        {
+            atomicMax(p_dst, bit_cast<int32_t>(x));
+        }
+    }
+    else if constexpr(std::is_same<T, uint32_t>::value)
+    {
+        if constexpr(N == 1)
+        {
+            atomicMax(p_dst, bit_cast<uint32_t>(x));
+        }
+    }
+}
+
+} // namespace ck_tile

include/ck_tile/core/arch/utility.hpp

@@ -0,0 +1,129 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+// Address Space for AMDGCN
+// https://llvm.org/docs/AMDGPUUsage.html#address-space
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/utility/bit_cast.hpp"
+
+#include <stdint.h>
+
+namespace ck_tile {
+
+// TODO: we have "memory" clobber here because this inline asm is used for async copy
+CK_TILE_DEVICE void m0_set_with_memory(index_t v)
+{
+    asm volatile("s_mov_b32 m0, %0" : : "s"(v) : "memory");
+}
+
+// NOTE: this is an immediate value
+CK_TILE_DEVICE void m0_inc_with_memory(index_t v)
+{
+    asm volatile("s_add_u32 m0, %0, m0" : : "n"(v) : "memory");
+}
+
+template <typename T>
+CK_TILE_DEVICE T warp_shuffle_up(const T& v_local, uint32_t lane_delta)
+{
+#if 0
+    return  __shfl_up(v_local, lane_delta);
+#elif 1
+    static_assert(sizeof(T) == sizeof(int32_t), "wrong!");
+
+    const uint32_t wrap_around_lane_delta = warpSize - lane_delta;
+
+    const int32_t v_remote_tmp = __builtin_amdgcn_ds_bpermute(
+        (__lane_id() << 2) + (wrap_around_lane_delta << 2), bit_cast<int32_t>(v_local));
+
+    return bit_cast<T>(v_remote_tmp);
+#endif
+}
+
+template <typename T>
+CK_TILE_DEVICE T warp_shuffle_down(const T& v_local, uint32_t lane_delta)
+{
+#if 0
+    return  __shfl_down(v_local, lane_delta);
+#elif 1
+    static_assert(sizeof(T) == sizeof(int32_t), "wrong!");
+
+    const int32_t v_remote_tmp = __builtin_amdgcn_ds_bpermute(
+        (__lane_id() << 2) + (lane_delta << 2), bit_cast<int32_t>(v_local));
+
+    return bit_cast<T>(v_remote_tmp);
+#endif
+}
+
+template <typename T>
+CK_TILE_DEVICE T warp_shuffle(const T& v_local, uint32_t src_lane)
+{
+#if 0
+    return  __shfl(v_local, src_lane);
+#elif 1
+    if constexpr(sizeof(int32_t) > sizeof(T))
+    {
+        union packet
+        {
+            int32_t x;
+            T v;
+        };
+        packet p;
+        p.v = v_local;
+        packet p_remote;
+        p_remote.x = __builtin_amdgcn_ds_bpermute(src_lane << 2, bit_cast<int32_t>(p));
+
+        return p_remote.v;
+    }
+    else if constexpr(sizeof(int32_t) == sizeof(T))
+    {
+        const int32_t v_remote_tmp =
+            __builtin_amdgcn_ds_bpermute(src_lane << 2, bit_cast<int32_t>(v_local));
+
+        return bit_cast<T>(v_remote_tmp);
+    }
+    else
+    {
+        static_assert(sizeof(T) % sizeof(int32_t) == 0, "wrong!");
+        constexpr index_t elm = sizeof(T) / sizeof(int32_t);
+        using vector_type     = thread_buffer<int32_t, elm>;
+        auto vs               = bit_cast<vector_type>(v_local);
+        auto vs_remote        = vector_type{};
+        static_for<0, elm, 1>{}([&](auto i_e) {
+            int32_t tmp = __builtin_amdgcn_ds_bpermute(src_lane << 2, bit_cast<int32_t>(vs[i_e]));
+            vs_remote(i_e) = tmp;
+        });
+        return bit_cast<T>(vs_remote);
+    }
+#endif
+}
+
+template <typename T>
+CK_TILE_DEVICE auto flag_to_exec(const T& v_flag)
+{
+    static_assert(sizeof(T) == 4);
+    // per-thread v_flag store into 2x sgpr
+    uint32x2_t exec_flag;
+    asm volatile("v_cmp_ge_u32 %[s_exec_flag], %[v_flag], 1"
+                 : [s_exec_flag] "=s"(exec_flag)
+                 : [v_flag] "v"(v_flag));
+    return exec_flag;
+}
+
+template <typename X, typename Y>
+CK_TILE_DEVICE auto cmp_lt_to_exec(const X& x, const Y& y)
+{
+    static_assert(sizeof(X) == 4 && sizeof(Y) == 4);
+    // per-thread cmp store into 2x sgpr
+    uint32x2_t exec_flag;
+    asm volatile("v_cmp_lt_u32 %[s_exec_flag], %[v_x], %[v_y]"
+                 : [s_exec_flag] "=s"(exec_flag)
+                 : [v_x] "v"(x), [v_y] "v"(y));
+    return exec_flag;
+}
+
+} // namespace ck_tile

include/ck_tile/core/config.hpp

@@ -0,0 +1,261 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2025, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#if defined(__gfx908__) || defined(__gfx90a__) || defined(__gfx942__) || defined(__gfx950__)
+#define __gfx9__
+#endif
+#if defined(__gfx942__) || defined(__gfx950__)
+#define __gfx94__
+#endif
+#if defined(__gfx1030__) || defined(__gfx1031__) || defined(__gfx1032__) || \
+    defined(__gfx1034__) || defined(__gfx1035__) || defined(__gfx1036__) || \
+    defined(__gfx10_3_generic__)
+#define __gfx103__
+#endif
+#if defined(__gfx1100__) || defined(__gfx1101__) || defined(__gfx1102__) || \
+    defined(__gfx1103__) || defined(__gfx1150__) || defined(__gfx1151__) || \
+    defined(__gfx1152__) || defined(__gfx11_generic__)
+#define __gfx11__
+#endif
+#if defined(__gfx1200__) || defined(__gfx1201__) || defined(__gfx12_generic__)
+#define __gfx12__
+#endif
+
+#include "hip/hip_version.h"
+#ifndef CK_TILE_DONT_USE_HIP_RUNTIME_HEADERS
+#include "hip/hip_runtime.h"
+#include "hip/hip_fp16.h"
+#endif
+
+#ifdef __HIPCC__
+#define CK_TILE_HOST inline __host__
+#define CK_TILE_DEVICE inline __device__
+#define CK_TILE_HOST_DEVICE inline __host__ __device__
+#define CK_TILE_DEVICE_EXTERN __device__
+#define CK_TILE_HOST_DEVICE_EXTERN __host__ __device__
+#else
+#define CK_TILE_HOST inline
+#define CK_TILE_DEVICE inline
+#define CK_TILE_HOST_DEVICE inline
+#define CK_TILE_DEVICE_EXTERN
+#define CK_TILE_HOST_DEVICE_EXTERN
+#endif
+
+// implementing the "memory address space" attribute
+// https://llvm.org/docs/AMDGPUUsage.html#amdgpu-address-spaces-table
+// WA for https://github.com/ROCm/composable_kernel/issues/1946
+#if 0
+#define CK_TILE_GENERIC_ADDR __attribute__((address_space(0)))
+#define CK_TILE_GLOBAL_ADDR __attribute__((address_space(1)))
+#define CK_TILE_LDS_ADDR __attribute__((address_space(3)))
+#define CK_TILE_BUF_RES_ADDR __attribute__((address_space(8)))
+#else
+#define CK_TILE_GENERIC_ADDR
+#define CK_TILE_GLOBAL_ADDR
+#define CK_TILE_LDS_ADDR
+#define CK_TILE_BUF_RES_ADDR
+#endif
+#ifndef CK_TILE_USE_CUSTOM_DATA_TYPE
+#define CK_TILE_USE_CUSTOM_DATA_TYPE 0 // custom data type will generate extra move/bfi code
+#endif
+
+#define CK_TILE_FLOAT_TO_BFLOAT16_STANDARD 0
+#define CK_TILE_FLOAT_TO_BFLOAT16_TRUNCATE_WITH_NAN 1
+#define CK_TILE_FLOAT_TO_BFLOAT16_TRUNCATE 2
+#define CK_TILE_FLOAT_TO_BFLOAT16_STANDARD_ASM 3
+#define CK_TILE_FLOAT_TO_BFLOAT16_RTA_ASM 4
+
+#ifndef CK_TILE_FLOAT_TO_BFLOAT16_DEFAULT
+#define CK_TILE_FLOAT_TO_BFLOAT16_DEFAULT CK_TILE_FLOAT_TO_BFLOAT16_TRUNCATE
+#endif
+
+#define CK_TILE_FLOAT_TO_FP8_STANDARD 0
+#define CK_TILE_FLOAT_TO_FP8_STOCHASTIC 1
+
+#ifndef CK_TILE_FLOAT_TO_FP8_DEFAULT
+#define CK_TILE_FLOAT_TO_FP8_DEFAULT CK_TILE_FLOAT_TO_FP8_STANDARD
+#endif
+
+// in the old rocm period, we have to use tuple array implementation to implement this
+// so turn on the _USE_TUPLE if meet compiler error, otherwise _USE_ARRAY by default.
+#define CK_TILE_STATICALLY_INDEXED_ARRAY_USE_ARRAY 0
+#define CK_TILE_STATICALLY_INDEXED_ARRAY_USE_TUPLE 1
+#ifndef CK_TILE_STATICALLY_INDEXED_ARRAY_DEFAULT
+#define CK_TILE_STATICALLY_INDEXED_ARRAY_DEFAULT CK_TILE_STATICALLY_INDEXED_ARRAY_USE_TUPLE
+#endif
+
+#define CK_TILE_THREAD_BUFFER_USE_ARRAY 0
+#define CK_TILE_THREAD_BUFFER_USE_TUPLE 1
+#ifndef CK_TILE_THREAD_BUFFER_DEFAULT
+#define CK_TILE_THREAD_BUFFER_DEFAULT CK_TILE_THREAD_BUFFER_USE_ARRAY
+#endif
+
+#ifndef CK_TILE_TUPLE_CTOR_WITH_INITIALIZER_LIST
+#if CK_TILE_THREAD_BUFFER_DEFAULT == CK_TILE_THREAD_BUFFER_USE_TUPLE
+// if using tuple-array as thread_buffer implementation, need to support {} brace init
+// ... with similiar behavior as array
+#define CK_TILE_TUPLE_CTOR_WITH_INITIALIZER_LIST 1
+#else
+#define CK_TILE_TUPLE_CTOR_WITH_INITIALIZER_LIST 0
+#endif
+#endif
+
+#ifndef CK_TILE_USE_LAUNCH_BOUNDS
+#define CK_TILE_USE_LAUNCH_BOUNDS 1
+#endif
+
+#ifndef CK_TILE_TIME_KERNEL
+#define CK_TILE_TIME_KERNEL 1
+#endif
+
+#define CK_TILE_MAX_THREAD_PER_BLOCK 256
+#define CK_TILE_MIN_BLOCK_PER_CU 2
+
+#ifndef CK_TILE_EXPERIMENTAL_USE_BUFFER_LOAD_OOB_CHECK_OFFSET_TRICK
+#define CK_TILE_EXPERIMENTAL_USE_BUFFER_LOAD_OOB_CHECK_OFFSET_TRICK 0
+#endif
+
+#ifndef CK_TILE_EXPERIMENTAL_USE_BUFFER_STORE_OOB_CHECK_OFFSET_TRICK
+#define CK_TILE_EXPERIMENTAL_USE_BUFFER_STORE_OOB_CHECK_OFFSET_TRICK 1
+#endif
+
+#ifndef CK_TILE_EXPERIMENTAL_USE_BUFFER_ATOMIC_ADD_OOB_CHECK_OFFSET_TRICK
+#define CK_TILE_EXPERIMENTAL_USE_BUFFER_ATOMIC_ADD_OOB_CHECK_OFFSET_TRICK 1
+#endif
+
+#ifndef CK_TILE_EXPERIMENTAL_USE_BUFFER_ATOMIC_MAX_OOB_CHECK_OFFSET_TRICK
+#define CK_TILE_EXPERIMENTAL_USE_BUFFER_ATOMIC_MAX_OOB_CHECK_OFFSET_TRICK 1
+#endif
+
+#ifndef CK_TILE_USE_AMD_LDS_DIRECT_LOAD_INLINE_ASM
+#define CK_TILE_USE_AMD_LDS_DIRECT_LOAD_INLINE_ASM 1
+#endif
+
+#ifndef CK_TILE_USE_AMD_BUFFER_LOAD
+#define CK_TILE_USE_AMD_BUFFER_LOAD 1
+#endif
+
+#ifndef CK_TILE_USE_AMD_BUFFER_STORE
+#define CK_TILE_USE_AMD_BUFFER_STORE 1
+#endif
+
+#ifndef CK_TILE_USE_AMD_BUFFER_ATOMIC_ADD_INTEGER
+#define CK_TILE_USE_AMD_BUFFER_ATOMIC_ADD_INTEGER 1
+#endif
+
+#ifndef CK_TILE_USE_PK4_LAYOUT_SHUFFLE
+#define CK_TILE_USE_PK4_LAYOUT_SHUFFLE 1
+#endif
+
+// buffer atomic add: floating point
+#ifndef __HIP_DEVICE_COMPILE__ // for host code
+#define CK_TILE_USE_AMD_BUFFER_ATOMIC_ADD_FLOAT 1
+#elif defined(__gfx9__) // for GPU code
+#define CK_TILE_USE_AMD_BUFFER_ATOMIC_ADD_FLOAT 1
+#else // for GPU code
+#define CK_TILE_USE_AMD_BUFFER_ATOMIC_ADD_FLOAT 0
+#endif
+
+#if(defined(__gfx90a__) || defined(__gfx94__)) // for GPU code
+#define CK_TILE_USE_AMD_BUFFER_ATOMIC_MAX_FLOAT64 1
+#else
+#define CK_TILE_USE_AMD_BUFFER_ATOMIC_MAX_FLOAT64 0
+#endif
+
+#ifndef CK_TILE_EXPERIMENTAL_USE_MEMCPY_FOR_VECTOR_ACCESS
+#define CK_TILE_EXPERIMENTAL_USE_MEMCPY_FOR_VECTOR_ACCESS 0
+#endif
+
+#ifndef CK_TILE_WORKAROUND_SWDEV_XXXXXX_INT8_DS_WRITE_ISSUE
+#define CK_TILE_WORKAROUND_SWDEV_XXXXXX_INT8_DS_WRITE_ISSUE 1
+#endif
+
+#ifndef CK_TILE_WORKAROUND_ROCM_6_1_SCRATCH_MEMORY_ISSUE
+#if HIP_VERSION_MAJOR == 6 && HIP_VERSION_MINOR == 1 && HIP_VERSION_PATCH >= 40091
+#define CK_TILE_WORKAROUND_ROCM_6_1_SCRATCH_MEMORY_ISSUE 1
+#else
+#define CK_TILE_WORKAROUND_ROCM_6_1_SCRATCH_MEMORY_ISSUE 0
+#endif
+#endif
+
+// workaround for ROCm 6.2 and later
+#ifndef CK_TILE_WORKAROUND_ROCM_6_2_SCRATCH_MEMORY_ISSUE
+#if(HIP_VERSION_MAJOR == 6 && HIP_VERSION_MINOR == 2 && HIP_VERSION_PATCH >= 41133) ||  \
+    (HIP_VERSION_MAJOR == 6 && HIP_VERSION_MINOR == 3 && HIP_VERSION_PATCH >= 42131) || \
+    (HIP_VERSION_MAJOR == 6 && HIP_VERSION_MINOR > 3)
+#define CK_TILE_WORKAROUND_ROCM_6_2_SCRATCH_MEMORY_ISSUE 1
+#else
+#define CK_TILE_WORKAROUND_ROCM_6_2_SCRATCH_MEMORY_ISSUE 0
+#endif
+#endif
+
+#ifndef CK_TILE_DEBUG_LOG
+#define CK_TILE_DEBUG_LOG 0
+#endif
+
+#ifndef __HIP_DEVICE_COMPILE__ // for host code
+#define CK_TILE_BUFFER_RESOURCE_3RD_DWORD 0xffffffff
+#elif defined(__gfx803__) || defined(__gfx900__) || defined(__gfx906__) || \
+    defined(__gfx9__) // for GPU code
+#define CK_TILE_BUFFER_RESOURCE_3RD_DWORD 0x00020000
+#elif defined(__gfx103__) // for GPU code
+#define CK_TILE_BUFFER_RESOURCE_3RD_DWORD 0x31014000
+#elif defined(__gfx11__) || defined(__gfx12__) // for GPU code
+#define CK_TILE_BUFFER_RESOURCE_3RD_DWORD 0x31004000
+#endif
+
+#ifndef CK_TILE_EXPERIMENTAL_BLOCK_SYNC_LDS_WITHOUT_SYNC_VMEM
+#define CK_TILE_EXPERIMENTAL_BLOCK_SYNC_LDS_WITHOUT_SYNC_VMEM 1
+#endif
+
+#ifndef CK_TILE_USE_SUBDWORD_TILE_CAST
+#define CK_TILE_USE_SUBDWORD_TILE_CAST 0
+#endif
+
+#ifndef CK_TILE_USE_PK_FP16_TILE_CAST
+#define CK_TILE_USE_PK_FP16_TILE_CAST 0
+#endif
+
+// TODO: better solve this inside compiler
+#ifndef CK_TILE_FMHA_FWD_FAST_EXP2
+#define CK_TILE_FMHA_FWD_FAST_EXP2 0
+#endif
+
+#ifndef CK_TILE_BUFFER_LOAD_RAW_BF16_WA
+#define CK_TILE_BUFFER_LOAD_RAW_BF16_WA 1
+#endif
+
+// workaround: compiler not emiting reciprocal instruction frm __frcp_rn()
+#ifndef CK_TILE_WORKAROUND_SWDEV_383542
+#define CK_TILE_WORKAROUND_SWDEV_383542 1
+#endif
+
+#ifndef CK_TILE_REFERENCE_MOE_SORTING_MOCK_ID
+#define CK_TILE_REFERENCE_MOE_SORTING_MOCK_ID 1
+#endif
+
+#ifndef __HIP_DEVICE_COMPILE__ // for host code
+#ifdef CK_TILE_USE_OCP_FP8
+#define CK_TILE_USE_OCP_FP8 1
+#else
+#define CK_TILE_USE_OCP_FP8 0
+#endif
+#elif defined(__gfx950__) || defined(__gfx12__) // for GPU code
+#define CK_TILE_USE_OCP_FP8 1
+#else // for GPU code
+#define CK_TILE_USE_OCP_FP8 0
+#endif
+
+#ifndef CK_TILE_USE_BUFFER_ADDRESSING_BUILTIN
+#if __clang_major__ == 20
+#define CK_TILE_USE_BUFFER_ADDRESSING_BUILTIN 1
+#else
+#define CK_TILE_USE_BUFFER_ADDRESSING_BUILTIN 0
+#endif
+#endif
+
+#ifndef CK_TILE_WA_ISSUE_2028
+#define CK_TILE_WA_ISSUE_2028 1
+#endif

include/ck_tile/core/container/array.hpp

@@ -0,0 +1,262 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2025, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <initializer_list>
+#include <vector>
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+#include "ck_tile/core/utility/functional.hpp"
+
+namespace ck_tile {
+
+// use aggregate initialization for this type
+// e.g. array<index_t, 4> buf {0};  => {0, 0, 0, 0}, clean
+//      array<index_t, 4> buf {3, 2}; => {3, 2, 2, 2} (not {3,2,0,0})
+// use make_array_with({...}) to construct an array with compatible behavior as old ck
+// TODO: manually added constructor same as old ck
+template <typename T_, index_t N_>
+struct array
+{
+    using value_type           = T_;
+    static constexpr index_t N = N_;
+    // TODO: do we need this?
+    // using bulk_type = uint8_t __attribute__((ext_vector_type(N * sizeof(value_type))));
+    // union {
+    value_type data[N];
+    //     bulk_type __content;
+    //};
+    CK_TILE_HOST_DEVICE constexpr array() : data{} {}
+    // TODO: will initialize the data[] with the last value repeatedly
+    //       behavior different from std
+    CK_TILE_HOST_DEVICE constexpr array(std::initializer_list<value_type> ilist)
+    {
+        constexpr index_t list_size = std::initializer_list<value_type>{}.size();
+        static_assert(list_size <= N, "out of bound");
+
+        index_t i        = 0;
+        value_type vlast = value_type{};
+
+        for(const value_type& val : ilist)
+        {
+            data[i] = val;
+            vlast   = val;
+            ++i;
+        }
+        for(; i < N; ++i)
+        {
+            data[i] = vlast;
+        }
+    }
+
+    template <typename Y,
+              typename = std::enable_if_t<std::is_convertible_v<Y, value_type> ||
+                                          std::is_constructible_v<Y, value_type>>>
+    CK_TILE_HOST_DEVICE explicit constexpr array(Y c)
+    {
+        for(auto i = 0; i < size(); i++)
+            data[i] = static_cast<value_type>(c);
+    }
+
+    // template <typename Y>
+    // CK_TILE_HOST_DEVICE constexpr array(const array& o)
+    // {
+    //     // static_assert(ArrayType::size() == size(), "wrong! size not the same");
+    //     __content = o.__content;
+    // }
+    // CK_TILE_HOST_DEVICE constexpr array& operator=(const array& o)
+    // {
+    //     // static_assert(ArrayType::size() == size(), "wrong! size not the same");
+    //     __content = o.__content;
+    //     return *this;
+    // }
+
+    CK_TILE_HOST_DEVICE static constexpr auto size() { return N; }
+    CK_TILE_HOST_DEVICE static constexpr bool is_static() { return is_static_v<value_type>; }
+
+    // clang-format off
+    CK_TILE_HOST_DEVICE constexpr auto& get()                                           { return data; }
+    CK_TILE_HOST_DEVICE constexpr const auto& get() const                               { return data; }
+    CK_TILE_HOST_DEVICE constexpr auto& get(index_t i)                                  { return data[i]; }
+    CK_TILE_HOST_DEVICE constexpr const auto& get(index_t i) const                      { return data[i]; }
+    template <index_t I> CK_TILE_HOST_DEVICE constexpr auto& get()                      { return data[I]; }
+    template <index_t I> CK_TILE_HOST_DEVICE constexpr const auto& get() const          { return data[I]; }
+    template <index_t I> CK_TILE_HOST_DEVICE constexpr auto& get(number<I>)             { return data[I]; }
+    template <index_t I> CK_TILE_HOST_DEVICE constexpr const auto& get(number<I>) const { return data[I]; }
+
+    CK_TILE_HOST_DEVICE constexpr auto& at(index_t i)                                   { return get(i); }
+    CK_TILE_HOST_DEVICE constexpr const auto& at(index_t i) const                       { return get(i); }
+    template <index_t I> CK_TILE_HOST_DEVICE constexpr auto& at()                       { return get(I); }
+    template <index_t I> CK_TILE_HOST_DEVICE constexpr const auto& at() const           { return get(I); }
+    template <index_t I> CK_TILE_HOST_DEVICE constexpr auto& at(number<I>)              { return get(I); }
+    template <index_t I> CK_TILE_HOST_DEVICE constexpr const auto& at(number<I>) const  { return get(I); }
+
+    CK_TILE_HOST_DEVICE constexpr const value_type& operator[](index_t i) const { return get(i); }
+    CK_TILE_HOST_DEVICE constexpr value_type& operator[](index_t i)             { return get(i); }
+    CK_TILE_HOST_DEVICE constexpr value_type& operator()(index_t i)             { return get(i); }     // TODO: compatible
+#if 0
+    template <typename ArrayLike>
+    CK_TILE_HOST_DEVICE constexpr auto operator=(const ArrayLike& arr)
+    {
+        static_assert(ArrayLike::size() == size(), "wrong! size not the same");
+        for(index_t i = 0; i < size(); ++i)
+        {
+            data[i] = arr[i];
+        }
+        return *this;
+    }
+#endif
+    // type punning (strict aliasing) member functions for read/write
+    // aliasing this array of type "T", "N" elements
+    // as array of type "Tx", sizeof(T)*N/sizeof(Tx) elements
+#define AR_AS_COM_()                                         \
+    static_assert(sizeof(value_type) * N % sizeof(Tx) == 0); \
+    constexpr int vx = sizeof(value_type) * N / sizeof(Tx)
+
+    template <typename Tx> CK_TILE_HOST_DEVICE constexpr auto& get_as()
+            { AR_AS_COM_();    return reinterpret_cast<array<Tx, vx>&>(data); }
+    template <typename Tx> CK_TILE_HOST_DEVICE constexpr const auto& get_as() const
+            { AR_AS_COM_();    return reinterpret_cast<const array<Tx, vx>&>(data); }
+
+    // below index is for index *AFTER* type convert, not before
+    template <typename Tx> CK_TILE_HOST_DEVICE constexpr auto& get_as(index_t i)
+            { AR_AS_COM_();    return reinterpret_cast<array<Tx, vx>&>(data).at(i); }
+    template <typename Tx> CK_TILE_HOST_DEVICE constexpr const auto& get_as(index_t i) const
+            { AR_AS_COM_();    return reinterpret_cast<const array<Tx, vx>&>(data).at(i); }
+    template <typename Tx, index_t I> CK_TILE_HOST_DEVICE constexpr auto& get_as(number<I>)
+            { AR_AS_COM_();    return reinterpret_cast<array<Tx, vx>&>(data).at(number<I>{}); }
+    template <typename Tx, index_t I> CK_TILE_HOST_DEVICE constexpr const auto& get_as(number<I>) const
+            { AR_AS_COM_();    return reinterpret_cast<const array<Tx, vx>&>(data).at(number<I>{}); }
+    
+    template <typename Tx> CK_TILE_HOST_DEVICE constexpr void set_as(index_t i, const Tx & x)
+            { AR_AS_COM_();    reinterpret_cast<array<Tx, vx>&>(data).at(i) = x; }
+    template <typename Tx, index_t I> CK_TILE_HOST_DEVICE constexpr void set_as(number<I>, const Tx & x)
+            { AR_AS_COM_();    reinterpret_cast<array<Tx, vx>&>(data).at(number<I>{}) = x; }
+#undef AR_AS_COM_
+    // clang-format on
+};
+
+// empty Array
+
+template <typename T>
+struct array<T, 0>
+{
+    using value_type = T;
+
+    CK_TILE_HOST_DEVICE constexpr array() {}
+    CK_TILE_HOST_DEVICE static constexpr index_t size() { return 0; }
+    CK_TILE_HOST_DEVICE static constexpr bool is_static() { return is_static_v<T>; };
+    CK_TILE_HOST_DEVICE void print() const { printf("array{size: 0, data: []}"); }
+};
+
+template <typename, typename>
+struct vector_traits;
+
+// specialization for array
+template <typename T, index_t N>
+struct vector_traits<array<T, N>, void>
+{
+    using scalar_type                    = T;
+    static constexpr index_t vector_size = N;
+};
+
+namespace details {
+template <class>
+struct is_ref_wrapper : std::false_type
+{
+};
+template <class T>
+struct is_ref_wrapper<std::reference_wrapper<T>> : std::true_type
+{
+};
+
+template <class T>
+using not_ref_wrapper = std::negation<is_ref_wrapper<std::decay_t<T>>>;
+
+template <class D, class...>
+struct return_type_helper
+{
+    using type = D;
+};
+template <class... Ts>
+struct return_type_helper<void, Ts...> : std::common_type<Ts...>
+{
+    static_assert(std::conjunction_v<not_ref_wrapper<Ts>...>,
+                  "Ts cannot contain reference_wrappers when D is void");
+};
+
+template <class D, class... Ts>
+using return_type = array<typename return_type_helper<D, Ts...>::type, sizeof...(Ts)>;
+} // namespace details
+
+template <typename D = void, typename... Ts>
+CK_TILE_HOST_DEVICE constexpr details::return_type<D, Ts...> make_array(Ts&&... ts)
+{
+    return {std::forward<Ts>(ts)...};
+}
+
+// // make empty array
+// template <typename T>
+// CK_TILE_HOST_DEVICE constexpr auto make_array()
+// {
+//     return array<T, 0>{};
+// }
+
+// compatible with old ck's initializer, make an array and fill it withe the last element from
+// initializer_list
+template <typename T, index_t Size>
+CK_TILE_HOST_DEVICE constexpr auto make_array_with(std::initializer_list<T> ilist)
+{
+    return array<T, Size>(ilist);
+}
+
+template <typename T, index_t Size>
+CK_TILE_HOST_DEVICE constexpr bool operator==(const array<T, Size>& a, const array<T, Size>& b)
+{
+    bool same = true;
+
+    for(index_t i = 0; i < Size; ++i)
+    {
+        if(a[i] != b[i])
+        {
+            same = false;
+            break;
+        }
+    }
+
+    return same;
+}
+
+template <typename T, index_t Size>
+CK_TILE_HOST_DEVICE constexpr bool operator!=(const array<T, Size>& a, const array<T, Size>& b)
+{
+    return !(a == b);
+}
+
+template <typename T, index_t N, typename X>
+CK_TILE_HOST_DEVICE constexpr auto to_array(const std::vector<X>& x)
+{
+    array<T, N> arr;
+
+    static_for<0, N, 1>{}([&x, &arr](auto i) { arr(i) = x[i]; });
+
+    return arr;
+}
+
+template <typename T, index_t N, typename X>
+CK_TILE_HOST_DEVICE constexpr auto to_array(const X& x)
+{
+    static_assert(N <= X::size(), "");
+
+    array<T, N> arr;
+
+    static_for<0, N, 1>{}([&x, &arr](auto i) { arr(i) = x[i]; });
+
+    return arr;
+}
+
+} // namespace ck_tile

include/ck_tile/core/container/container_helper.hpp

@@ -0,0 +1,499 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/container/array.hpp"
+#include "ck_tile/core/container/map.hpp"
+#include "ck_tile/core/container/sequence.hpp"
+#include "ck_tile/core/container/tuple.hpp"
+#include "ck_tile/core/utility/functional.hpp"
+
+namespace ck_tile {
+
+template <typename TData, index_t NSize>
+CK_TILE_HOST_DEVICE constexpr auto container_push_back(const array<TData, NSize>& a, const TData& x)
+{
+    array<TData, NSize + 1> r;
+    static_for<0, NSize, 1>{}([&r, &a ](auto i) constexpr { r(i) = a[i]; });
+    r[number<NSize>{}] = x;
+    return r;
+}
+
+template <typename... Ts, typename T>
+CK_TILE_HOST_DEVICE constexpr auto container_push_front(const tuple<Ts...>& a, const T& x)
+{
+    return container_concat(make_tuple(x), a);
+}
+
+template <typename... Ts, typename T>
+CK_TILE_HOST_DEVICE constexpr auto container_push_back(const tuple<Ts...>& a, const T& x)
+{
+    return container_concat(a, make_tuple(x));
+}
+
+// reorder array
+template <typename TData, index_t NSize, index_t... IRs>
+CK_TILE_HOST_DEVICE constexpr auto
+container_reorder_given_new2old(const array<TData, NSize>& old_array, sequence<IRs...> /*new2old*/)
+{
+    static_assert(NSize == sizeof...(IRs), "wrong! size not consistent");
+    static_assert(is_valid_sequence_map<sequence<IRs...>>{}, "wrong! invalid reorder map");
+    return make_array<remove_cvref_t<TData>>(old_array[IRs]...);
+}
+
+template <typename TData, index_t NSize, index_t... IRs>
+CK_TILE_HOST_DEVICE constexpr auto
+container_reorder_given_old2new(const array<TData, NSize>& old_array, sequence<IRs...> old2new)
+{
+    return container_reorder_given_new2old(
+        old_array, typename sequence_map_inverse<decltype(old2new)>::type{});
+}
+
+// reorder array
+template <typename TData, index_t NSize>
+CK_TILE_HOST_DEVICE constexpr auto
+container_reorder_given_new2old(const array<TData, NSize>& old_array,
+                                const map<index_t, index_t>& new2old)
+{
+    array<TData, NSize> new_array;
+
+    for(const auto& [new_pos, old_pos] : new2old)
+    {
+        new_array(new_pos) = old_array[old_pos];
+    }
+
+    return new_array;
+}
+
+template <typename TData, index_t NSize>
+CK_TILE_HOST_DEVICE constexpr auto
+container_reorder_given_old2new(const array<TData, NSize>& old_array,
+                                const map<index_t, index_t>& old2new)
+{
+    array<TData, NSize> new_array;
+
+    for(const auto& [old_pos, new_pos] : old2new)
+    {
+        new_array(new_pos) = old_array[old_pos];
+    }
+
+    return new_array;
+}
+
+// reorder tuple
+template <typename... Ts, index_t... IRs>
+CK_TILE_HOST_DEVICE constexpr auto container_reorder_given_new2old(const tuple<Ts...>& old_tuple,
+                                                                   sequence<IRs...> /*new2old*/)
+{
+    static_assert(sizeof...(Ts) == sizeof...(IRs), "wrong! size not consistent");
+
+    static_assert(is_valid_sequence_map<sequence<IRs...>>{}, "wrong! invalid reorder map");
+
+    return make_tuple(old_tuple[number<IRs>{}]...);
+}
+
+template <typename... Ts, index_t... IRs>
+CK_TILE_HOST_DEVICE constexpr auto container_reorder_given_old2new(const tuple<Ts...>& old_tuple,
+                                                                   sequence<IRs...> old2new)
+{
+    return container_reorder_given_new2old(
+        old_tuple, typename sequence_map_inverse<decltype(old2new)>::type{});
+}
+
+// reorder sequence
+template <index_t... Is, index_t... IRs>
+CK_TILE_HOST_DEVICE constexpr auto container_reorder_given_new2old(sequence<Is...> /* old_seq */,
+                                                                   sequence<IRs...> /*new2old*/)
+{
+    static_assert(sizeof...(Is) == sizeof...(IRs), "wrong! size not consistent");
+
+    static_assert(is_valid_sequence_map<sequence<IRs...>>{}, "wrong! invalid reorder map");
+
+    return sequence<sequence<Is...>::at(number<IRs>{})...>{};
+}
+
+template <index_t... Is, index_t... IRs>
+CK_TILE_HOST_DEVICE constexpr auto container_reorder_given_old2new(sequence<Is...> old_seq,
+                                                                   sequence<IRs...> /* old2new */)
+{
+    static_assert(sizeof...(Is) == sizeof...(IRs), "wrong! size not consistent");
+
+    static_assert(is_valid_sequence_map<sequence<IRs...>>{}, "wrong! invalid reorder map");
+
+    constexpr auto new2old = typename sequence_map_inverse<sequence<IRs...>>::type{};
+
+    return container_reorder_given_new2old(old_seq, new2old);
+}
+
+#if 0
+// rocm-4.1 compiler would crash for recursive lambda
+template <typename Container,
+          typename Reduce,
+          typename Init,
+          index_t IBegin = 0,
+          index_t IEnd   = Container::size(),
+          index_t IStep  = 1>
+CK_TILE_HOST_DEVICE constexpr auto container_reduce(const Container& x,
+                                                    Reduce reduce,
+                                                    Init init,
+                                                    number<IBegin> = number<0>{},
+                                                    number<IEnd>   = number<Container::size()>{},
+                                                    number<IStep>  = number<1>{})
+{
+    static_assert((IEnd - IBegin) % IStep == 0, "wrong!");
+
+    // f is recursive function, fs is a dummy of f
+    // i is index, y_old is current scan, r_old is current reduction
+    auto f = [&](auto fs, auto i, auto r_old) {
+        auto r_new = reduce(x[i], r_old);
+
+        if constexpr(i.value < IEnd - IStep)
+        {
+            // recursively call f/fs
+            return fs(fs, i + number<IStep>{}, r_new);
+        }
+        else
+        {
+            return r_new;
+        }
+    };
+
+    // start recursion
+    return f(f, number<IBegin>{}, init);
+}
+#else
+// i is index, y_old is current scan, r_old is current reduction
+template <typename Container,
+          typename Reduce,
+          typename ROld,
+          index_t I,
+          index_t IEnd,
+          index_t IStep>
+CK_TILE_HOST_DEVICE constexpr auto container_reduce_impl(
+    const Container& x, Reduce reduce, ROld r_old, number<I> i, number<IEnd>, number<IStep>)
+{
+    auto r_new = reduce(x[i], r_old);
+
+    if constexpr(i.value < IEnd - IStep)
+    {
+        return container_reduce_impl(
+            x, reduce, r_new, i + number<IStep>{}, number<IEnd>{}, number<IStep>{});
+    }
+    else
+    {
+        return r_new;
+    }
+}
+
+// rocm-4.1 compiler would crash for recursive lambda
+// container reduce with initial value
+template <typename Container,
+          typename Reduce,
+          typename Init,
+          index_t IBegin = 0,
+          index_t IEnd   = Container::size(),
+          index_t IStep  = 1>
+CK_TILE_HOST_DEVICE constexpr auto container_reduce(const Container& x,
+                                                    Reduce reduce,
+                                                    Init init,
+                                                    number<IBegin> = number<0>{},
+                                                    number<IEnd>   = number<Container::size()>{},
+                                                    number<IStep>  = number<1>{})
+{
+    static_assert((IEnd - IBegin) % IStep == 0, "wrong!");
+
+    if constexpr(IEnd > IBegin)
+    {
+        return container_reduce_impl(
+            x, reduce, init, number<IBegin>{}, number<IEnd>{}, number<IStep>{});
+    }
+    else
+    {
+        return init;
+    }
+}
+#endif
+
+template <typename TData, index_t NSize, typename Reduce>
+CK_TILE_HOST_DEVICE constexpr auto
+container_reverse_inclusive_scan(const array<TData, NSize>& x, Reduce f, TData init)
+{
+    array<TData, NSize> y;
+
+    TData r = init;
+
+    static_for<NSize - 1, 0, -1>{}([&](auto i) {
+        r    = f(r, x[i]);
+        y(i) = r;
+    });
+
+    r              = f(r, x[number<0>{}]);
+    y(number<0>{}) = r;
+
+    return y;
+}
+
+template <typename TData, index_t NSize, typename Reduce, typename Init>
+CK_TILE_HOST_DEVICE constexpr auto
+container_reverse_exclusive_scan(const array<TData, NSize>& x, Reduce f, Init init)
+{
+#if 0
+    array<TData, NSize> y;
+
+    TData r = init;
+
+    static_for<NSize - 1, 0, -1>{}([&](auto i) {
+        y(i) = r;
+        r    = f(r, x[i]);
+    });
+
+    y(number<0>{}) = r;
+
+    return y;
+#else
+    array<TData, NSize> y;
+
+    TData r = init;
+
+    for(index_t i = NSize - 1; i > 0; --i)
+    {
+        y(i) = r;
+        r    = f(r, x[i]);
+    }
+
+    y(0) = r;
+
+    return y;
+#endif
+}
+
+template <index_t... Is, typename Reduce, index_t Init>
+CK_TILE_HOST_DEVICE constexpr auto
+container_reverse_exclusive_scan(const sequence<Is...>& seq, Reduce f, number<Init>)
+{
+    return reverse_exclusive_scan_sequence(seq, f, number<Init>{});
+}
+
+#if 0
+// rocm4.1 compiler would crash with recursive lambda
+template <typename... Xs, typename Reduce, typename Init>
+CK_TILE_HOST_DEVICE constexpr auto
+container_reverse_exclusive_scan(const tuple<Xs...>& x, Reduce reduce, Init init)
+{
+    constexpr index_t NSize = sizeof...(Xs);
+
+    // f is recursive function, fs is a dummy of f
+    // i is index, y_old is current scan, r_old is current reduction
+    auto f = [&](auto fs, auto i, auto y_old, auto r_old) {
+        auto r_new = reduce(x[i], r_old);
+
+        auto y_new = container_push_front(y_old, r_new);
+
+        if constexpr(i.value > 1)
+        {
+            // recursively call f/fs
+            return fs(fs, i - number<1>{}, y_new, r_new);
+        }
+        else
+        {
+            return y_new;
+        }
+    };
+
+    // start recursion
+    return f(f, number<NSize - 1>{}, make_tuple(init), init);
+}
+#else
+// i is index, y_old is current scan, r_old is current reduction
+template <typename... Xs, typename Reduce, index_t I, typename YOld, typename ROld>
+CK_TILE_HOST_DEVICE constexpr auto container_reverse_exclusive_scan_impl(
+    const tuple<Xs...>& x, Reduce reduce, number<I> i, YOld y_old, ROld r_old)
+{
+    auto r_new = reduce(x[i], r_old);
+
+    auto y_new = container_push_front(y_old, r_new);
+
+    if constexpr(i.value > 1)
+    {
+        // recursively call f/fs
+        return container_reverse_exclusive_scan_impl(x, reduce, i - number<1>{}, y_new, r_new);
+    }
+    else
+    {
+        return y_new;
+    }
+}
+
+template <typename... Xs, typename Reduce, typename Init>
+CK_TILE_HOST_DEVICE constexpr auto
+container_reverse_exclusive_scan(const tuple<Xs...>& x, Reduce reduce, Init init)
+{
+    constexpr index_t NSize = sizeof...(Xs);
+
+    return container_reverse_exclusive_scan_impl(
+        x, reduce, number<NSize - 1>{}, make_tuple(init), init);
+}
+#endif
+
+// TODO: update to like container_reverse_exclusive_scan to deal with tuple of Numebr<>
+template <typename... Xs, typename Reduce, typename TData>
+CK_TILE_HOST_DEVICE constexpr auto
+container_reverse_inclusive_scan(const tuple<Xs...>& x, Reduce f, TData init)
+{
+    constexpr index_t NSize = sizeof...(Xs);
+
+    tuple<Xs...> y;
+
+    TData r = init;
+
+    static_for<NSize - 1, 0, -1>{}([&](auto i) {
+        r    = f(r, x[i]);
+        y(i) = r;
+    });
+
+    r              = f(r, x[number<0>{}]);
+    y(number<0>{}) = r;
+
+    return y;
+}
+
+template <typename X, typename... Ys>
+CK_TILE_HOST_DEVICE constexpr auto container_concat(const X& x, const Ys&... ys)
+{
+    return container_concat(x, container_concat(ys...));
+}
+
+template <typename T, index_t NX, index_t NY>
+CK_TILE_HOST_DEVICE constexpr auto container_concat(const array<T, NX>& ax, const array<T, NY>& ay)
+{
+    return unpack2(
+        [&](auto&&... zs) { return make_array<T>(std::forward<decltype(zs)>(zs)...); }, ax, ay);
+}
+
+template <typename... X, typename... Y>
+CK_TILE_HOST_DEVICE constexpr auto container_concat(const tuple<X...>& tx, const tuple<Y...>& ty)
+{
+    return unpack2(
+        [&](auto&&... zs) { return make_tuple(std::forward<decltype(zs)>(zs)...); }, tx, ty);
+}
+
+template <typename Container>
+CK_TILE_HOST_DEVICE constexpr auto container_concat(const Container& x)
+{
+    return x;
+}
+
+template <typename T, index_t N, index_t... Is>
+CK_TILE_HOST_DEVICE constexpr auto get_container_subset(const array<T, N>& arr, sequence<Is...>)
+{
+    static_assert(N >= sizeof...(Is), "wrong! size");
+
+    if constexpr(sizeof...(Is) > 0)
+    {
+        return make_array<T>(arr[Is]...);
+    }
+    else
+    {
+        return array<T, 0>{};
+    }
+}
+
+template <typename... Ts, index_t... Is>
+CK_TILE_HOST_DEVICE constexpr auto get_container_subset(const tuple<Ts...>& tup, sequence<Is...>)
+{
+    static_assert(sizeof...(Ts) >= sizeof...(Is), "wrong! size");
+
+    if constexpr(sizeof...(Is) > 0)
+    {
+        return make_tuple(tup[number<Is>{}]...);
+    }
+    else
+    {
+        return tuple<>{};
+    }
+}
+
+template <typename T, index_t N, index_t... Is>
+CK_TILE_HOST_DEVICE constexpr void
+set_container_subset(array<T, N>& y, sequence<Is...> picks, const array<T, sizeof...(Is)>& x)
+{
+    static_assert(N >= sizeof...(Is), "wrong! size");
+
+    if constexpr(sizeof...(Is) > 0)
+    {
+        for(index_t i = 0; i < picks.size(); ++i)
+        {
+            y(picks[i]) = x[i];
+        }
+    }
+}
+
+template <typename Y, typename X, index_t... Is>
+CK_TILE_HOST_DEVICE constexpr void set_container_subset(Y& y, sequence<Is...> picks, const X& x)
+{
+    static_assert(Y::size() >= sizeof...(Is) && X::size() == sizeof...(Is), "wrong! size");
+
+    if constexpr(sizeof...(Is) > 0)
+    {
+        static_for<0, sizeof...(Is), 1>{}([&](auto i) { y(picks[i]) = x[i]; });
+    }
+}
+
+// return the index of first occurance in the sequence.
+// return seq.size(), if not found
+template <index_t... Is>
+constexpr index_t container_find(sequence<Is...> seq, index_t value)
+{
+    for(auto i = 0; i < seq.size(); i++)
+    {
+        if(seq[i] == value)
+            return i;
+    }
+
+    return seq.size();
+}
+
+template <index_t... Is>
+CK_TILE_HOST_DEVICE constexpr auto sequence_to_tuple_of_number(sequence<Is...>)
+{
+    using Seq = sequence<Is...>;
+
+    return generate_tuple(
+        [&](auto i) {
+            constexpr index_t tmp = Seq::at(i);
+            return number<tmp>{};
+        },
+        number<Seq::size()>{});
+}
+
+#if 0
+#define TO_TUPLE_OF_SEQUENCE(a_of_b_impl, a_size, bs_sizes)             \
+    [a_of_b_impl, a_size, bs_sizes] {                                   \
+        return ck_tile::generate_tuple(                                 \
+            [=](auto i) {                                               \
+                constexpr auto b_impl    = a_of_b_impl[i];              \
+                constexpr index_t b_size = bs_sizes[i];                 \
+                constexpr auto b         = TO_SEQUENCE(b_impl, b_size); \
+                return b;                                               \
+            },                                                          \
+            ck_tile::number<a_size>{});                                 \
+    }()
+#else
+// constexpr index_t can't be captured "-Wunused-lambda-capture"
+// TODO: this is ugly
+#define TO_TUPLE_OF_SEQUENCE(a_of_b_impl, a_size, bs_sizes)             \
+    [a_of_b_impl, bs_sizes] {                                           \
+        return ck_tile::generate_tuple(                                 \
+            [=](auto i) {                                               \
+                constexpr auto b_impl    = a_of_b_impl[i];              \
+                constexpr index_t b_size = bs_sizes[i];                 \
+                constexpr auto b         = TO_SEQUENCE(b_impl, b_size); \
+                return b;                                               \
+            },                                                          \
+            ck_tile::number<a_size>{});                                 \
+    }()
+#endif
+
+} // namespace ck_tile

include/ck_tile/core/container/map.hpp

@@ -0,0 +1,164 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/container/array.hpp"
+#include "ck_tile/core/container/sequence.hpp"
+#include "ck_tile/core/container/tuple.hpp"
+
+namespace ck_tile {
+
+// naive map
+template <typename key, typename data, index_t max_size = 128>
+struct map
+{
+    using pair_type = tuple<key, data>;
+    using impl_type = array<pair_type, max_size>;
+
+    impl_type impl_;
+    index_t size_;
+
+    struct iterator
+    {
+        impl_type& impl_;
+        index_t pos_;
+
+        CK_TILE_HOST_DEVICE constexpr iterator(impl_type& impl, index_t pos)
+            : impl_{impl}, pos_{pos}
+        {
+        }
+
+        CK_TILE_HOST_DEVICE constexpr iterator& operator++()
+        {
+            pos_++;
+            return *this;
+        }
+
+        CK_TILE_HOST_DEVICE constexpr bool operator!=(const iterator& other) const
+        {
+            return other.pos_ != pos_;
+        }
+
+        CK_TILE_HOST_DEVICE constexpr pair_type& operator*() { return impl_.at(pos_); }
+    };
+
+    struct const_iterator
+    {
+        const impl_type& impl_;
+        index_t pos_;
+
+        CK_TILE_HOST_DEVICE constexpr const_iterator(const impl_type& impl, index_t pos)
+            : impl_{impl}, pos_{pos}
+        {
+        }
+
+        CK_TILE_HOST_DEVICE constexpr const_iterator& operator++()
+        {
+            pos_++;
+
+            return *this;
+        }
+
+        CK_TILE_HOST_DEVICE constexpr bool operator!=(const const_iterator& other) const
+        {
+            return other.pos_ != pos_;
+        }
+
+        CK_TILE_HOST_DEVICE constexpr const pair_type& operator*() const { return impl_.at(pos_); }
+    };
+
+    CK_TILE_HOST_DEVICE constexpr map() : impl_{}, size_{0} {}
+
+    CK_TILE_HOST_DEVICE constexpr index_t size() const { return size_; }
+
+    CK_TILE_HOST_DEVICE void clear() { size_ = 0; }
+
+    CK_TILE_HOST_DEVICE constexpr index_t find_position(const key& k) const
+    {
+        for(index_t i = 0; i < size(); i++)
+        {
+            if(impl_[i].template at<0>() == k)
+            {
+                return i;
+            }
+        }
+
+        return size_;
+    }
+
+    CK_TILE_HOST_DEVICE constexpr const_iterator find(const key& k) const
+    {
+        return const_iterator{impl_, find_position(k)};
+    }
+
+    CK_TILE_HOST_DEVICE constexpr iterator find(const key& k)
+    {
+        return iterator{impl_, find_position(k)};
+    }
+
+    CK_TILE_HOST_DEVICE constexpr const data& operator[](const key& k) const
+    {
+        const auto it = find(k);
+
+        // FIXME
+        // assert(it.pos_ < size());
+
+        return impl_[it.pos_].template at<1>();
+    }
+
+    CK_TILE_HOST_DEVICE constexpr data& operator()(const key& k)
+    {
+        auto it = find(k);
+
+        // if entry not found
+        if(it.pos_ == size())
+        {
+            impl_(it.pos_).template at<0>() = k;
+            size_++;
+        }
+
+        // FIXME
+        // assert(size_ <= max_size);
+
+        return impl_(it.pos_).template at<1>();
+    }
+
+    // WARNING: needed by compiler for C++ range-based for loop only, don't use this function!
+    CK_TILE_HOST_DEVICE constexpr const_iterator begin() const { return const_iterator{impl_, 0}; }
+
+    // WARNING: needed by compiler for C++ range-based for loop only, don't use this function!
+    CK_TILE_HOST_DEVICE constexpr const_iterator end() const
+    {
+        return const_iterator{impl_, size_};
+    }
+
+    // WARNING: needed by compiler for C++ range-based for loop only, don't use this function!
+    CK_TILE_HOST_DEVICE constexpr iterator begin() { return iterator{impl_, 0}; }
+
+    // WARNING: needed by compiler for C++ range-based for loop only, don't use this function!
+    CK_TILE_HOST_DEVICE constexpr iterator end() { return iterator{impl_, size_}; }
+
+    CK_TILE_HOST_DEVICE void print() const
+    {
+        printf("map{size_: %d, ", size_);
+        //
+        printf("impl_: [");
+        //
+        for(const auto& [k, d] : *this)
+        {
+            printf("{key: ");
+            print(k);
+            printf(", data: ");
+            print(d);
+            printf("}, ");
+        }
+        //
+        printf("]");
+        //
+        printf("}");
+    }
+};
+
+} // namespace ck_tile

include/ck_tile/core/container/meta_data_buffer.hpp

@@ -0,0 +1,99 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/container/array.hpp"
+#include "ck_tile/core/utility/bit_cast.hpp"
+#include <cstddef>
+
+namespace ck_tile {
+
+// TODO: this structure is not intented to be used by user
+template <index_t MaxSize>
+struct meta_data_buffer
+{
+    CK_TILE_HOST_DEVICE constexpr meta_data_buffer() : buffer_{}, size_{0} {}
+
+    template <typename X, typename... Xs>
+    CK_TILE_HOST_DEVICE constexpr meta_data_buffer(const X& x, const Xs&... xs)
+        : buffer_{}, size_{0}
+    {
+        push(x, xs...);
+    }
+
+    template <typename T>
+    CK_TILE_HOST_DEVICE constexpr void push(const T& data)
+    {
+        if constexpr(!std::is_empty_v<T>)
+        {
+            constexpr index_t size = sizeof(T);
+
+            auto tmp = ck_tile::bit_cast<array<std::byte, size>>(data);
+
+            for(int i = 0; i < size; i++)
+            {
+                buffer_(size_) = tmp[i];
+
+                size_++;
+            }
+        }
+    }
+
+    template <typename X, typename... Xs>
+    CK_TILE_HOST_DEVICE constexpr void push(const X& x, const Xs&... xs)
+    {
+        push(x);
+        push(xs...);
+    }
+
+    template <typename T>
+    CK_TILE_HOST_DEVICE constexpr T pop(index_t& pos) const
+    {
+        T data;
+
+        if constexpr(!std::is_empty_v<T>)
+        {
+            constexpr index_t size = sizeof(T);
+
+            array<std::byte, size> tmp;
+
+            for(int i = 0; i < size; i++)
+            {
+                tmp(i) = buffer_[pos];
+
+                pos++;
+            }
+
+            data = ck_tile::bit_cast<T>(tmp);
+        }
+
+        return data;
+    }
+
+    template <typename T>
+    CK_TILE_HOST_DEVICE constexpr T get(index_t pos) const
+    {
+        constexpr index_t size = sizeof(T);
+
+        array<std::byte, size> tmp;
+
+        for(int i = 0; i < size; i++)
+        {
+            tmp(i) = buffer_[pos];
+
+            pos++;
+        }
+
+        auto data = ck_tile::bit_cast<T>(tmp);
+
+        return data;
+    }
+
+    //
+    array<std::byte, MaxSize> buffer_;
+    index_t size_ = 0;
+};
+
+} // namespace ck_tile

include/ck_tile/core/container/multi_index.hpp

@@ -0,0 +1,100 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/container/array.hpp"
+#include "ck_tile/core/container/sequence.hpp"
+#include "ck_tile/core/container/tuple.hpp"
+#include "ck_tile/core/utility/functional.hpp"
+
+namespace ck_tile {
+
+// Don't use tihs directly. This is for old CK's internal usage,
+// in the future always use array instead
+template <index_t N>
+using multi_index = array<index_t, N>;
+
+template <typename... Xs>
+CK_TILE_HOST_DEVICE constexpr auto make_multi_index(Xs&&... xs)
+{
+    return make_array<index_t>(index_t{xs}...);
+}
+
+template <index_t NSize>
+CK_TILE_HOST_DEVICE constexpr auto make_zero_multi_index()
+{
+    return unpack([](auto... xs) { return make_multi_index(xs...); },
+                  typename uniform_sequence_gen<NSize, 0>::type{});
+}
+
+template <typename T>
+CK_TILE_HOST_DEVICE constexpr auto to_multi_index(const T& x)
+{
+    return unpack([](auto... ys) { return make_multi_index(ys...); }, x);
+}
+
+template <index_t NSize, typename X>
+CK_TILE_HOST_DEVICE constexpr auto operator+=(multi_index<NSize>& y, const X& x)
+{
+    static_assert(X::size() == NSize, "wrong! size not the same");
+    static_for<0, NSize, 1>{}([&](auto i) { y[i] += x[i]; });
+    return y;
+}
+
+template <index_t NSize, typename X>
+CK_TILE_HOST_DEVICE constexpr auto operator-=(multi_index<NSize>& y, const X& x)
+{
+    static_assert(X::size() == NSize, "wrong! size not the same");
+    static_for<0, NSize, 1>{}([&](auto i) { y[i] -= x[i]; });
+    return y;
+}
+
+template <index_t NSize, typename T>
+CK_TILE_HOST_DEVICE constexpr auto operator+(const multi_index<NSize>& a, const T& b)
+{
+    using type = multi_index<NSize>;
+    static_assert(T::size() == NSize, "wrong! size not the same");
+    type r;
+    static_for<0, NSize, 1>{}([&](auto i) { r[i] = a[i] + b[i]; });
+    return r;
+}
+
+template <index_t NSize, typename T>
+CK_TILE_HOST_DEVICE constexpr auto operator-(const multi_index<NSize>& a, const T& b)
+{
+    using type = multi_index<NSize>;
+    static_assert(T::size() == NSize, "wrong! size not the same");
+    type r;
+    static_for<0, NSize, 1>{}([&](auto i) { r[i] = a[i] - b[i]; });
+    return r;
+}
+
+template <index_t NSize, typename T>
+CK_TILE_HOST_DEVICE constexpr auto operator*(const multi_index<NSize>& a, const T& b)
+{
+    using type = multi_index<NSize>;
+    static_assert(T::size() == NSize, "wrong! size not the same");
+    type r;
+    static_for<0, NSize, 1>{}([&](auto i) { r[i] = a[i] * b[i]; });
+    return r;
+}
+
+// multi_index = index_t * multi_index
+template <index_t NSize>
+CK_TILE_HOST_DEVICE constexpr auto operator*(index_t a, const multi_index<NSize>& x)
+{
+    multi_index<NSize> r;
+    static_for<0, NSize, 1>{}([&](auto i) { r[i] = a * x[i]; });
+    return r;
+}
+
+// multi_index = multi_index * index_t
+template <index_t NSize>
+CK_TILE_HOST_DEVICE constexpr auto operator*(const multi_index<NSize>& x, index_t a)
+{
+    return a * x;
+}
+
+} // namespace ck_tile

include/ck_tile/core/container/span.hpp

@@ -0,0 +1,78 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include <cstddef>
+#include <array>
+#include <type_traits>
+
+namespace ck_tile {
+
+// implement the c++20 std::span, lightweight, non-owning reference to a sequence
+// weather it is dynamic or static range. Or can be seen as a view of a contiguous sequence
+// TODO: do we need in device consider this is pointer?
+template <typename T>
+class span
+{
+    public:
+    using element_type    = T;
+    using value_type      = std::remove_cv_t<element_type>;
+    using size_type       = std::size_t;
+    using difference_type = std::ptrdiff_t;
+    using pointer         = element_type*;
+    using const_pointer   = const element_type*;
+    using reference       = element_type&;
+    using const_reference = const element_type&;
+    using iterator        = pointer;
+    using const_iterator  = pointer;
+
+    CK_TILE_HOST_DEVICE constexpr span() : span(nullptr, size_type{0}) {}
+
+    CK_TILE_HOST_DEVICE constexpr span(pointer first, size_type count) : ptr_(first), size_(count)
+    {
+    }
+
+    CK_TILE_HOST_DEVICE constexpr span(pointer first, pointer last) : span(first, last - first) {}
+
+    template <std::size_t N>
+    CK_TILE_HOST_DEVICE constexpr span(element_type (&arr)[N]) noexcept : span(arr, N)
+    {
+    }
+
+    template <std::size_t N>
+    CK_TILE_HOST_DEVICE constexpr span(std::array<value_type, N>& arr) noexcept
+        : span(arr.data(), N)
+    {
+    }
+
+    template <typename Container>
+    CK_TILE_HOST_DEVICE constexpr span(const Container& container)
+        : span(container.data(), container.size())
+    {
+    }
+
+    CK_TILE_HOST_DEVICE constexpr iterator begin() const noexcept { return ptr_; }
+    CK_TILE_HOST_DEVICE constexpr const_iterator cbegin() const noexcept { return begin(); }
+
+    CK_TILE_HOST_DEVICE constexpr iterator end() const noexcept { return begin() + size(); }
+    CK_TILE_HOST_DEVICE constexpr const_iterator cend() const noexcept { return end(); }
+
+    CK_TILE_HOST_DEVICE constexpr reference front() const { return *begin(); }
+    CK_TILE_HOST_DEVICE constexpr reference back() const { return *(--end()); }
+
+    CK_TILE_HOST_DEVICE constexpr reference operator[](size_type idx) const
+    {
+        return *(begin() + idx);
+    }
+    CK_TILE_HOST_DEVICE constexpr pointer data() const noexcept { return ptr_; }
+
+    CK_TILE_HOST_DEVICE constexpr size_type size() const noexcept { return size_; }
+
+    private:
+    pointer ptr_;
+    size_type size_;
+};
+
+} // namespace ck_tile

include/ck_tile/core/container/statically_indexed_array.hpp

@@ -0,0 +1,41 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/container/array.hpp"
+#include "ck_tile/core/container/tuple.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+
+namespace ck_tile {
+
+#if CK_TILE_STATICALLY_INDEXED_ARRAY_DEFAULT == CK_TILE_STATICALLY_INDEXED_ARRAY_USE_TUPLE
+
+template <typename T, index_t N>
+using statically_indexed_array = tuple_array<T, N>;
+
+#else
+
+// consider mark this struct as deprecated
+template <typename T, index_t N>
+using statically_indexed_array = array<T, N>;
+
+#endif
+
+// consider always use ck_tile::array for this purpose
+#if 0
+template <typename X, typename... Xs>
+CK_TILE_HOST_DEVICE constexpr auto make_statically_indexed_array(const X& x, const Xs&... xs)
+{
+    return statically_indexed_array<X, sizeof...(Xs) + 1>(x, static_cast<X>(xs)...);
+}
+
+// make empty statically_indexed_array
+template <typename X>
+CK_TILE_HOST_DEVICE constexpr auto make_statically_indexed_array()
+{
+    return statically_indexed_array<X, 0>();
+}
+#endif
+} // namespace ck_tile

include/ck_tile/core/container/thread_buffer.hpp

@@ -0,0 +1,172 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2025, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/container/array.hpp"
+#include "ck_tile/core/container/tuple.hpp"
+
+namespace ck_tile {
+
+#if CK_TILE_THREAD_BUFFER_DEFAULT == CK_TILE_THREAD_BUFFER_USE_TUPLE
+template <typename T, index_t N>
+using thread_buffer = tuple_array<T, N>;
+
+template <typename... Ts>
+CK_TILE_HOST_DEVICE constexpr auto make_thread_buffer(Ts&&... ts)
+{
+    return make_tuple(ts...);
+}
+#else
+
+#if 0
+template <typename T, index_t N>
+using thread_buffer = array<T, N>;
+
+template <typename... Ts>
+CK_TILE_HOST_DEVICE constexpr auto make_thread_buffer(Ts&&... ts)
+{
+    return make_array(ts...);
+}
+
+#endif
+
+// clang-format off
+template<typename T_, index_t N_>
+struct thread_buffer {
+    using value_type = remove_cvref_t<T_>;
+    static constexpr index_t N = N_;
+
+    value_type data[N];
+
+    // TODO: this ctor can't ignore
+    CK_TILE_HOST_DEVICE constexpr thread_buffer() : data{} {}
+    CK_TILE_HOST_DEVICE constexpr thread_buffer(const value_type & o) : data{o} {}
+
+    CK_TILE_HOST_DEVICE static constexpr auto size() { return N; }
+    CK_TILE_HOST_DEVICE auto & get() {return data; }
+    CK_TILE_HOST_DEVICE const auto & get() const {return data; }
+    CK_TILE_HOST_DEVICE auto & get(index_t i) {return data[i]; }
+    CK_TILE_HOST_DEVICE const auto & get(index_t i) const {return data[i]; }
+    CK_TILE_HOST_DEVICE constexpr const auto& operator[](index_t i) const { return get(i); }
+    CK_TILE_HOST_DEVICE constexpr auto& operator[](index_t i)             { return get(i); }
+    CK_TILE_HOST_DEVICE constexpr auto& operator()(index_t i)             { return get(i); }     // TODO: compatible
+    CK_TILE_HOST_DEVICE constexpr auto& at(index_t i)                                   { return get(i); }
+    CK_TILE_HOST_DEVICE constexpr const auto& at(index_t i) const                       { return get(i); }
+    template <index_t I> CK_TILE_HOST_DEVICE constexpr auto& at()                       { return get(I); }
+    template <index_t I> CK_TILE_HOST_DEVICE constexpr const auto& at() const           { return get(I); }
+    template <index_t I> CK_TILE_HOST_DEVICE constexpr auto& at(number<I>)              { return get(I); }
+    template <index_t I> CK_TILE_HOST_DEVICE constexpr const auto& at(number<I>) const  { return get(I); }
+    
+    template <typename X_,
+              typename std::enable_if<has_same_scalar_type<value_type, X_>::value, bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr auto _get_as() const
+    {
+        using X = remove_cvref_t<X_>;
+
+        constexpr index_t kSPerX = vector_traits<X>::vector_size;
+        static_assert(N % kSPerX == 0);
+
+        union {
+            thread_buffer<X_, N / kSPerX> data {};
+            // tuple_array<value_type, kSPerX> sub_data;
+            value_type sub_data[N];
+        } vx;
+        static_for<0, N, 1>{}(
+            [&](auto j) { vx.sub_data[j] = data[j]; });
+        return vx.data;
+    }
+
+    template <typename X_,
+              index_t Is,
+              typename std::enable_if<has_same_scalar_type<value_type, X_>::value, bool>::type = false>
+    CK_TILE_HOST_DEVICE const constexpr remove_reference_t<X_> _get_as(number<Is> is) const
+    {
+        using X = remove_cvref_t<X_>;
+
+        constexpr index_t kSPerX = vector_traits<X>::vector_size;
+
+        union {
+            X_ data {};
+            tuple_array<value_type, kSPerX> sub_data;
+        } vx;
+        static_for<0, kSPerX, 1>{}(
+            [&](auto j) { vx.sub_data(j) = operator[]((is * number<sizeof(X_)/sizeof(value_type)>{}) + j); });
+        return vx.data;
+    }
+
+#if 0
+    template <typename X_,
+              index_t Is,
+              typename std::enable_if<has_same_scalar_type<value_type, X_>::value, bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr void _set_as(number<Is> is, X_ x)
+    {
+        using X = remove_cvref_t<X_>;
+
+        constexpr index_t kSPerX = vector_traits<X>::vector_size;
+
+        union {
+            X_ data;
+            tuple_array<value_type, kSPerX> sub_data;
+        } vx {x};
+
+        static_for<0, kSPerX, 1>{}(
+           [&](auto j) { operator()((is * number<sizeof(X_)/sizeof(value_type)>{}) + j) = vx.sub_data[j]; });
+    }
+#endif
+
+
+#define TB_COMMON_AS() \
+            static_assert(sizeof(value_type) * N % sizeof(Tx) == 0); \
+            constexpr int vx = sizeof(value_type) * N / sizeof(Tx)
+
+    template<typename Tx>
+    CK_TILE_HOST_DEVICE auto & get_as() {TB_COMMON_AS();
+            return reinterpret_cast<thread_buffer<Tx, vx>&>(data);}
+    template<typename Tx>
+    CK_TILE_HOST_DEVICE constexpr auto get_as() const {TB_COMMON_AS();
+            if constexpr(sizeof(value_type) <= 1 )
+            return _get_as<Tx>();   // TODO: current compiler for 8bit data need use union to get data back, should fix in the future
+            else
+            return reinterpret_cast<const thread_buffer<Tx, vx>&>(data);}
+    template<typename Tx, index_t I>
+    CK_TILE_HOST_DEVICE auto & get_as(number<I>) {TB_COMMON_AS();
+            return reinterpret_cast<thread_buffer<Tx, vx>&>(data).get(number<I>{});}
+    template<typename Tx, index_t I>
+    CK_TILE_HOST_DEVICE constexpr auto get_as(number<I>) const {TB_COMMON_AS();
+            if constexpr(sizeof(value_type) <= 1 )
+            return _get_as<Tx>(number<I>{});   // TODO: current compiler for 8bit data need use union to get data back, should fix in the future
+            else
+            return reinterpret_cast<const thread_buffer<Tx, vx>&>(data).get(number<I>{});}
+
+    template <typename Tx> CK_TILE_HOST_DEVICE constexpr void set_as(index_t i, const Tx & x)
+            { TB_COMMON_AS();    reinterpret_cast<thread_buffer<Tx, vx>&>(data).at(i) = x; }
+    template <typename Tx, index_t I> CK_TILE_HOST_DEVICE constexpr void set_as(number<I>, const Tx & x)
+            { TB_COMMON_AS();    reinterpret_cast<thread_buffer<Tx, vx>&>(data).at(number<I>{}) = x; }
+
+#undef TB_COMMON_AS
+};
+// clang-format on
+
+template <typename, typename>
+struct vector_traits;
+
+// specialization for array
+template <typename T, index_t N>
+struct vector_traits<thread_buffer<T, N>, std::enable_if_t<!std::is_class_v<T>>>
+{
+    using scalar_type                    = T;
+    static constexpr index_t vector_size = N;
+};
+
+template <typename T, index_t N>
+struct vector_traits<thread_buffer<T, N>, std::enable_if_t<std::is_class_v<T>>>
+{
+    using scalar_type                    = typename T::type;
+    static constexpr index_t vector_size = N;
+};
+
+#endif
+
+} // namespace ck_tile

include/ck_tile/core/container/tuple.hpp

@@ -0,0 +1,830 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2025, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/container/sequence.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/numeric/math.hpp"
+#include "ck_tile/core/utility/functional.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+#include <utility>
+#include <initializer_list>
+
+#ifndef CK_TILE_TUPLE_IMPL
+#define CK_TILE_TUPLE_IMPL 1
+#endif
+
+namespace ck_tile {
+
+namespace impl {
+template <typename T, index_t N>
+struct tuple_array_impl;
+}
+
+template <typename T, index_t N>
+using tuple_array = typename impl::tuple_array_impl<T, N>::type;
+
+namespace impl {
+
+// the place where content is stored
+template <index_t idx, typename T, bool is_empty = std::is_empty_v<T>>
+struct tuple_object
+{
+};
+
+template <index_t idx, typename T>
+struct tuple_object<idx, T, true>
+{
+    CK_TILE_HOST_DEVICE constexpr tuple_object() {}
+#if CK_TILE_TUPLE_IMPL == 0
+    template <typename U>
+    CK_TILE_HOST_DEVICE constexpr tuple_object(U&&)
+    {
+    }
+    template <typename U>
+    CK_TILE_HOST_DEVICE constexpr tuple_object(const U&)
+    {
+    }
+    template <typename U>
+    CK_TILE_HOST_DEVICE constexpr tuple_object(U&)
+    {
+    }
+#elif CK_TILE_TUPLE_IMPL == 1
+    template <typename U,
+              typename std::enable_if<!std::is_same<remove_cvref_t<U>, tuple_object>::value,
+                                      bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr tuple_object(U&&)
+    {
+    }
+#endif
+};
+
+template <index_t idx, typename T>
+struct tuple_object<idx, T, false>
+{
+    CK_TILE_HOST_DEVICE constexpr tuple_object() : element{} {}
+#if CK_TILE_TUPLE_IMPL == 0
+    template <typename U>
+    CK_TILE_HOST_DEVICE constexpr tuple_object(U&& e) : element(std::forward<U>(e))
+    {
+    }
+    template <typename U>
+    CK_TILE_HOST_DEVICE constexpr tuple_object(const U& e) : element(e)
+    {
+    }
+    template <typename U>
+    CK_TILE_HOST_DEVICE constexpr tuple_object(U& e) : element(e)
+    {
+    }
+#elif CK_TILE_TUPLE_IMPL == 1
+    template <typename U,
+              typename std::enable_if<!std::is_same<remove_cvref_t<U>, tuple_object>::value,
+                                      bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr tuple_object(U&& e) : element(std::forward<U>(e))
+    {
+    }
+#endif
+    T element;
+};
+
+// NOTE: we return a instance(not a reference) if content is empty
+template <index_t I, class T>
+CK_TILE_HOST_DEVICE constexpr T getv(const tuple_object<I, T, true>&)
+{
+    return {};
+}
+
+template <index_t I, class T>
+CK_TILE_HOST_DEVICE constexpr const T& getv(const tuple_object<I, T, false>& x)
+{
+    return x.element;
+}
+
+template <index_t I, class T>
+CK_TILE_HOST_DEVICE constexpr T& getv(tuple_object<I, T, false>& x)
+{
+    return x.element;
+}
+
+template <index_t I, class T>
+CK_TILE_HOST_DEVICE constexpr T&& getv(tuple_object<I, T, false>&& x)
+{
+    return static_cast<T&&>(x.element);
+}
+
+template <typename index_seq, typename... T>
+struct tuple_base;
+
+template <index_t... I, typename... T>
+struct tuple_base<sequence<I...>, T...> : tuple_object<I, T>...
+{
+    CK_TILE_HOST_DEVICE constexpr tuple_base() = default;
+
+#if CK_TILE_TUPLE_CTOR_WITH_INITIALIZER_LIST
+#define _ILE() (std::initializer_list<U>{}.size() - 1)
+    template <typename U>
+    CK_TILE_HOST_DEVICE constexpr tuple_base(std::initializer_list<U> us)
+        : tuple_object<I, T>(static_cast<T>(*(us.begin() + (I >= _ILE() ? _ILE() : I))))...
+    {
+    }
+#undef _ILE
+#endif
+
+#if CK_TILE_TUPLE_IMPL == 0
+    template <class... U>
+    CK_TILE_HOST_DEVICE constexpr explicit tuple_base(U&&... u)
+        : tuple_object<I, T>(std::forward<U>(u))...
+    {
+    }
+
+    template <class... U>
+    CK_TILE_HOST_DEVICE constexpr explicit tuple_base(const U&... u) : tuple_object<I, T>(u)...
+    {
+    }
+
+    template <class... U>
+    CK_TILE_HOST_DEVICE constexpr explicit tuple_base(U&... u) : tuple_object<I, T>(u)...
+    {
+    }
+
+    template <class... U>
+    CK_TILE_HOST_DEVICE constexpr tuple_base(tuple_base<sequence<I...>, U...>&& u)
+        : tuple_object<I, T>(getv(static_cast<tuple_object<I, U>&&>(u)))...
+    {
+    }
+
+    template <class... U>
+    CK_TILE_HOST_DEVICE constexpr tuple_base(const tuple_base<sequence<I...>, U...>& u)
+        : tuple_object<I, T>(getv(static_cast<const tuple_object<I, U>&>(u)))...
+    {
+    }
+
+    template <class... U>
+    CK_TILE_HOST_DEVICE constexpr tuple_base(tuple_base<sequence<I...>, U...>& u)
+        : tuple_object<I, T>(getv(static_cast<tuple_object<I, U>&>(u)))...
+    {
+    }
+#elif CK_TILE_TUPLE_IMPL == 1
+    template <class U,
+              typename std::enable_if<sizeof...(I) == 1 && sizeof...(T) == 1 &&
+                                          !std::is_same<remove_cvref_t<U>, tuple_base>::value,
+                                      bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr tuple_base(U&& u) : tuple_object<I, T>(std::forward<U>(u))...
+    {
+    }
+
+    template <typename... U, typename std::enable_if<sizeof...(U) >= 2, bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr tuple_base(U&&... u) : tuple_object<I, T>(std::forward<U>(u))...
+    {
+        static_assert(sizeof...(I) == sizeof...(T) && sizeof...(I) == sizeof...(U),
+                      "wrong! inconsistent size");
+    }
+
+#endif
+};
+} // namespace impl
+
+template <class... T>
+struct tuple : impl::tuple_base<make_index_sequence<sizeof...(T)>, T...>
+{
+    CK_TILE_HOST_DEVICE
+    static constexpr auto size() { return sizeof...(T); }
+    using base = impl::tuple_base<make_index_sequence<sizeof...(T)>, T...>;
+    CK_TILE_HOST_DEVICE constexpr tuple() = default;
+
+#if CK_TILE_TUPLE_CTOR_WITH_INITIALIZER_LIST
+    template <typename U>
+    CK_TILE_HOST_DEVICE constexpr tuple(std::initializer_list<U> us) : base(us)
+    {
+    }
+#endif
+
+#if CK_TILE_TUPLE_IMPL == 0
+    template <class... U>
+    CK_TILE_HOST_DEVICE constexpr tuple(U&&... u) : base(std::forward<U>(u)...)
+    {
+    }
+
+    template <class... U>
+    CK_TILE_HOST_DEVICE constexpr tuple(const U&... u) : base(u...)
+    {
+    }
+
+    template <class... U>
+    CK_TILE_HOST_DEVICE constexpr tuple(U&... u) : base(u...)
+    {
+    }
+
+    template <class... U>
+    CK_TILE_HOST_DEVICE constexpr tuple(tuple<U...>&& u)
+        : base(static_cast<impl::tuple_base<make_index_sequence<sizeof...(U)>, U...>&&>(u))
+    {
+    }
+
+    template <class... U>
+    CK_TILE_HOST_DEVICE constexpr tuple(const tuple<U...>& u)
+        : base(static_cast<const impl::tuple_base<make_index_sequence<sizeof...(U)>, U...>&>(u))
+    {
+    }
+
+    template <class... U>
+    CK_TILE_HOST_DEVICE constexpr tuple(tuple<U...>& u)
+        : base(static_cast<impl::tuple_base<make_index_sequence<sizeof...(U)>, U...>&>(u))
+    {
+    }
+#elif CK_TILE_TUPLE_IMPL == 1
+    template <
+        typename U,
+        typename std::enable_if<sizeof...(T) == 1 && !std::is_same<remove_cvref_t<U>, tuple>::value,
+                                bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr tuple(U&& u) : base(std::forward<U>(u))
+    {
+    }
+
+    template <typename... U,
+              typename std::enable_if<sizeof...(U) == sizeof...(T) && sizeof...(U) >= 2,
+                                      bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr tuple(U&&... u) : base(std::forward<U>(u)...)
+    {
+    }
+#endif
+    CK_TILE_HOST_DEVICE static constexpr bool is_static()
+    {
+        bool flag = true;
+
+        static_for<0, sizeof...(T), 1>{}([&flag](auto i) {
+            flag &= is_static_v<remove_cvref_t<__type_pack_element<i.value, T...>>>;
+        });
+
+        return flag;
+    }
+
+#define TP_COM_() static_assert(I < size(), "wrong! out of range")
+    // clang-format off
+    template<index_t I> CK_TILE_HOST_DEVICE constexpr decltype(auto) get() const          { TP_COM_(); return impl::getv<I>(*this); }
+    template<index_t I> CK_TILE_HOST_DEVICE constexpr decltype(auto) get(number<I>) const { TP_COM_(); return get<I>(); }
+    template<index_t I> CK_TILE_HOST_DEVICE constexpr decltype(auto) get()                      { TP_COM_(); return impl::getv<I>(*this); }
+    template<index_t I> CK_TILE_HOST_DEVICE constexpr decltype(auto) get(number<I>)             { TP_COM_(); return get<I>(); }
+
+    template<index_t I> CK_TILE_HOST_DEVICE constexpr decltype(auto) at() const          { TP_COM_(); return impl::getv<I>(*this); }
+    template<index_t I> CK_TILE_HOST_DEVICE constexpr decltype(auto) at(number<I>) const { TP_COM_(); return get<I>(); }
+    template<index_t I> CK_TILE_HOST_DEVICE constexpr decltype(auto) at()                      { TP_COM_(); return impl::getv<I>(*this); }
+    template<index_t I> CK_TILE_HOST_DEVICE constexpr decltype(auto) at(number<I>)             { TP_COM_(); return get<I>(); }
+
+    template<index_t I> CK_TILE_HOST_DEVICE constexpr decltype(auto) operator[](number<I>)             { TP_COM_(); return get<I>(); }
+    template<index_t I> CK_TILE_HOST_DEVICE constexpr decltype(auto) operator[](number<I>) const { TP_COM_(); return get<I>(); }
+    template<index_t I> CK_TILE_HOST_DEVICE constexpr decltype(auto) operator()(number<I>)             { TP_COM_(); return get<I>(); }  // TODO: compatible
+
+    // below function should be used under tuple_array<> type, no extra check will perform here
+    template <typename Tx> CK_TILE_HOST_DEVICE constexpr decltype(auto) get_as()                            { return reinterpret_cast<tuple_array<Tx, size()>&>(*this); }
+    template <typename Tx> CK_TILE_HOST_DEVICE constexpr decltype(auto) get_as() const                      { return reinterpret_cast<const tuple_array<Tx, size()>&>(*this); }
+    // below index is for index *AFTER* type convert, not before
+    //template <typename Tx> CK_TILE_HOST_DEVICE constexpr decltype(auto) get_as(index_t i)                   { TP_COM_(); return reinterpret_cast<tuple_array<Tx, size()>&>(*this).at(i); }
+    //template <typename Tx> CK_TILE_HOST_DEVICE constexpr decltype(auto) get_as(index_t i) const             { TP_COM_(); return reinterpret_cast<const tuple_array<Tx, size()>&>(*this).at(i); }
+    template <typename Tx, index_t I> CK_TILE_HOST_DEVICE constexpr decltype(auto) get_as(number<I>)        { TP_COM_(); return reinterpret_cast<tuple_array<Tx, size()>&>(*this).at(number<I>{}); }
+    template <typename Tx, index_t I> CK_TILE_HOST_DEVICE constexpr decltype(auto) get_as(number<I>) const  { TP_COM_(); return reinterpret_cast<const tuple_array<Tx, size()>&>(*this).at(number<I>{}); }
+    
+    // template <typename Tx> CK_TILE_HOST_DEVICE constexpr void set_as(index_t i, const Tx & x)               { TP_COM_(); reinterpret_cast<tuple_array<Tx, size()>&>(*this).at(i) = x; }
+    template <typename Tx, index_t I> CK_TILE_HOST_DEVICE constexpr void set_as(number<I>, const Tx & x)    { TP_COM_(); reinterpret_cast<tuple_array<Tx, size()>&>(*this).at(number<I>{}) = x; }
+
+    // clang-format on
+#undef TP_COM_
+};
+
+template <typename, typename = void>
+struct vector_traits;
+
+// specialization for array
+template <typename... T>
+struct vector_traits<tuple<T...>>
+{
+    using scalar_type                    = __type_pack_element<0, T...>;
+    static constexpr index_t vector_size = sizeof...(T);
+};
+
+// template <class... T>
+// CK_TILE_HOST_DEVICE constexpr
+// tuple<T...>
+// make_tuple(T const&... t)
+// {
+//     return {t...};
+// }
+template <typename... Xs>
+CK_TILE_HOST_DEVICE constexpr bool operator==(const tuple<Xs...>& a, const tuple<Xs...>& b)
+{
+    bool same = true;
+
+    static_for<0, sizeof...(Xs), 1>{}([&](auto i) {
+        if(a[i] != b[i])
+        {
+            same = false;
+        }
+    });
+
+    return same;
+}
+
+template <typename... Xs>
+CK_TILE_HOST_DEVICE constexpr bool operator!=(const tuple<Xs...>& a, const tuple<Xs...>& b)
+{
+    return !(a == b);
+}
+
+template <typename... Xs>
+CK_TILE_HOST_DEVICE constexpr auto make_tuple(Xs&&... xs)
+{
+    // here xs is always a lvalue as function arg
+    // Xs may deduced as (e.g try to pass in a integer in following cases)
+    //  1). if pass in a rvalue (like function return or int{}) -> Xs is "int"
+    //  2). if pass in a const lvalue -> Xs is "const int &"
+    //  3). if pass in a non-const lvalue -> Xs is "int &"
+    // so the return type of std::forward will dependes on Xs
+    //  1). std::forward -> int&&
+    //  2). std::forward -> const int&
+    //  3). std::forward -> int&
+    return tuple<remove_cvref_t<Xs>...>(std::forward<Xs>(xs)...);
+}
+
+// https://en.cppreference.com/w/cpp/utility/tuple/tie
+template <typename... Args>
+constexpr tuple<Args&...> tie(Args&... args) noexcept
+{
+    return {args...};
+}
+
+template <typename X, typename Y>
+struct tuple_concat;
+
+template <typename... Xs, typename... Ys>
+struct tuple_concat<tuple<Xs...>, tuple<Ys...>>
+{
+    using type = tuple<Xs..., Ys...>;
+};
+
+namespace impl {
+// be very careful using this type (because we want the internal type)
+// template deduction will fail if infering the inner type
+// e.g.
+// template<typename T, index_t N> using some_wrapper = typename tuple_array_impl<T, N>::type;
+// template<typename T, index_t N> void foo(const some_wrapper<T, N>&) {}
+//   -> compiler will fail to deduce this type, because this is under non-deduced context
+//   (https://en.cppreference.com/w/cpp/language/template_argument_deduction, "Non-deduced
+//   contexts")
+//
+// -> use this instead
+// template<typename Tup> void foo(const Tup&) {}
+template <typename T, index_t N>
+struct tuple_array_impl
+{
+    using type = typename tuple_concat<typename tuple_array_impl<T, N / 2>::type,
+                                       typename tuple_array_impl<T, N - N / 2>::type>::type;
+};
+
+template <typename T>
+struct tuple_array_impl<T, 0>
+{
+    using type = tuple<>;
+};
+
+template <typename T>
+struct tuple_array_impl<T, 1>
+{
+    using type = tuple<T>;
+};
+} // namespace impl
+
+template <typename F, index_t... ids>
+CK_TILE_HOST_DEVICE constexpr auto generate_tuple_for(F&& f, sequence<ids...>)
+{
+    return make_tuple(f(number<ids>{})...);
+}
+
+template <typename F, index_t N>
+CK_TILE_HOST_DEVICE constexpr auto generate_tuple(F&& f, number<N>)
+{
+    return generate_tuple_for(f, make_index_sequence<N>{});
+}
+
+template <typename F, index_t N>
+CK_TILE_HOST_DEVICE constexpr auto generate_tie(F&& f, number<N>)
+{
+    return unpack([&f](auto&&... is) { return tie(f(is)...); },
+                  typename arithmetic_sequence_gen<0, N, 1>::type{});
+}
+
+// tx and ty are tuple of references, return type of will tuple of referennce (not rvalue)
+template <typename... X, typename... Y>
+CK_TILE_HOST_DEVICE constexpr auto concat_tuple_of_reference(const tuple<X&...>& tx,
+                                                             const tuple<Y&...>& ty)
+{
+    return unpack2(
+        [&](auto&&... zs) { return tuple<decltype(zs)...>{std::forward<decltype(zs)>(zs)...}; },
+        tx,
+        ty);
+}
+
+template <typename... X, typename... Y>
+CK_TILE_HOST_DEVICE constexpr auto concat_tuple(const tuple<X...>& tx, const tuple<Y...>& ty)
+{
+    return unpack2(
+        [&](auto... zs) { return tuple<decltype(zs)...>{std::forward<decltype(zs)>(zs)...}; },
+        tx,
+        ty);
+}
+
+// Support any number of tuples to concat (also 1)
+template <typename... X>
+CK_TILE_HOST_DEVICE constexpr auto concat_tuple(const tuple<X...>& tx)
+{
+    return tx;
+}
+
+template <typename... X, typename... Tuples>
+CK_TILE_HOST_DEVICE constexpr auto concat_tuple(const tuple<X...>& tx, const Tuples&... tuples)
+{
+    return concat_tuple(tx, concat_tuple(tuples...));
+}
+
+namespace detail {
+
+template <typename F, typename X, index_t... Is>
+CK_TILE_HOST_DEVICE constexpr auto transform_tuples_impl(F f, const X& x, sequence<Is...>)
+{
+    return make_tuple(f(x.at(number<Is>{}))...);
+}
+
+template <typename F, typename X, typename Y, index_t... Is>
+CK_TILE_HOST_DEVICE constexpr auto
+transform_tuples_impl(F f, const X& x, const Y& y, sequence<Is...>)
+{
+    return make_tuple(f(x.at(number<Is>{}), y.at(number<Is>{}))...);
+}
+
+template <typename F, typename X, typename Y, typename Z, index_t... Is>
+CK_TILE_HOST_DEVICE constexpr auto
+transform_tuples_impl(F f, const X& x, const Y& y, const Z& z, sequence<Is...>)
+{
+    return make_tuple(f(x.at(number<Is>{}), y.at(number<Is>{}), z.at(number<Is>{}))...);
+}
+
+} // namespace detail
+
+template <typename F, typename X>
+CK_TILE_HOST_DEVICE constexpr auto transform_tuples(F f, const X& x)
+{
+    return detail::transform_tuples_impl(
+        f, x, typename arithmetic_sequence_gen<0, X::size(), 1>::type{});
+}
+
+template <typename F, typename X, typename Y>
+CK_TILE_HOST_DEVICE constexpr auto transform_tuples(F f, const X& x, const Y& y)
+{
+    return detail::transform_tuples_impl(
+        f, x, y, typename arithmetic_sequence_gen<0, X::size(), 1>::type{});
+}
+
+template <typename F, typename X, typename Y, typename Z>
+CK_TILE_HOST_DEVICE constexpr auto transform_tuples(F f, const X& x, const Y& y, const Z& z)
+{
+    return detail::transform_tuples_impl(
+        f, x, y, z, typename arithmetic_sequence_gen<0, X::size(), 1>::type{});
+}
+
+namespace detail {
+
+template <typename F, typename X, index_t... Is>
+CK_TILE_HOST_DEVICE constexpr auto embed_tuples_impl(F f, const X& x, sequence<Is...>)
+{
+    return concat_tuple(f(x.at(number<Is>{}))...);
+}
+
+} // namespace detail
+
+// make sure F return at least a tuple
+// e.g. x : tuple<X, Y>, f will return tuple<Z, W>
+// this function will return
+template <typename F, typename X>
+CK_TILE_HOST_DEVICE constexpr auto embed_tuples(F f, const X& x)
+{
+    return detail::embed_tuples_impl(
+        f, x, typename arithmetic_sequence_gen<0, X::size(), 1>::type{});
+}
+
+// By default unroll to the flatten
+template <index_t Depth = 0, index_t MaxDepth = -1>
+CK_TILE_HOST_DEVICE constexpr auto unroll_nested_tuple(const tuple<>& t)
+{
+    return t;
+}
+
+template <index_t Depth = 0, index_t MaxDepth = -1, typename T>
+CK_TILE_HOST_DEVICE constexpr auto unroll_nested_tuple(const T& t)
+{
+    return make_tuple(t);
+}
+
+template <index_t Depth = 0, index_t MaxDepth = -1, typename... Ts>
+CK_TILE_HOST_DEVICE constexpr auto unroll_nested_tuple(const tuple<Ts...>& t)
+{
+    if constexpr(Depth == MaxDepth)
+    {
+        return t;
+    }
+    else
+    {
+        return unpack(
+            [&](auto&&... ts) {
+                return concat_tuple(unroll_nested_tuple<Depth + 1, MaxDepth>(ts)...);
+            },
+            t);
+    }
+}
+
+template <typename... Ts>
+CK_TILE_HOST_DEVICE constexpr auto tuple_reverse(const tuple<Ts...>& t)
+{
+    return generate_tuple(
+        [&](auto i) {
+            using Idx = number<tuple<Ts...>::size() - i - 1>;
+            return t.at(Idx{});
+        },
+        number<tuple<Ts...>::size()>{});
+}
+
+// Reduce tuple values in specific range using Function
+template <index_t Idx, index_t End, typename F, typename... Ts>
+CK_TILE_HOST_DEVICE constexpr auto tuple_reduce(F&& f, const tuple<Ts...>& t)
+{
+    static_assert(Idx < End, "Wrong parameters for tuple_reduce");
+    if constexpr(Idx + 1 == End)
+    {
+        return t.at(number<Idx>{});
+    }
+    else
+    {
+        return f(t.at(number<Idx>{}), tuple_reduce<Idx + 1, End>(f, t));
+    }
+}
+
+template <typename T>
+using is_tuple = decltype(std::declval<T&>().IsTuple());
+
+template <typename... Ts>
+CK_TILE_HOST_DEVICE constexpr auto is_nested_tuple(const tuple<Ts...>&)
+{
+    return (is_detected<is_tuple, Ts>::value || ...);
+}
+
+template <index_t depth = 0, typename T>
+CK_TILE_HOST_DEVICE constexpr auto tuple_depth(const T&)
+{
+    return depth;
+}
+
+template <index_t depth = 0, typename... Ts>
+CK_TILE_HOST_DEVICE constexpr auto tuple_depth(const tuple<Ts...>&)
+{
+    return max(tuple_depth<depth + 1>(Ts{})...);
+}
+
+template <typename... Seqs>
+CK_TILE_HOST_DEVICE constexpr auto to_array_of_array(tuple<Seqs...> t_of_s)
+{
+    constexpr index_t n0 = sizeof...(Seqs);
+
+    constexpr index_t max_n1 = [&] {
+        index_t max_n1_ = 0;
+
+        static_for<0, n0, 1>{}([&](auto i0) {
+            constexpr index_t n1 = t_of_s[i0].size();
+
+            max_n1_ = max_n1_ < n1 ? n1 : max_n1_;
+        });
+
+        return max_n1_;
+    }();
+
+    array<array<index_t, max_n1>, n0> a_of_a{{-1}};
+
+    static_for<0, n0, 1>{}([&](auto i0) {
+        constexpr index_t n1 = t_of_s[i0].size();
+
+        static_for<0, n1, 1>{}([&](auto i1) { a_of_a(i0)(i1) = t_of_s[i0][i1]; });
+    });
+
+    return a_of_a;
+}
+
+// Here should use MultiIndex<NSize>, instead of tuple<Ys...>, although the former
+// is the alias of the latter. This is because compiler cannot infer the NSize if
+// using MultiIndex<NSize>
+// TODO: how to fix this?
+template <typename... Ys,
+          typename X,
+          std::enable_if_t<!std::is_integral<X>::value && !std::is_floating_point<X>::value, bool> =
+              false>
+CK_TILE_HOST_DEVICE constexpr auto operator+=(tuple<Ys...>& y, const X& x)
+{
+    static_assert(X::size() == sizeof...(Ys), "wrong! size not the same");
+    constexpr index_t NSize = sizeof...(Ys);
+    static_for<0, NSize, 1>{}([&](auto i) { y[i] += x[i]; });
+    return y;
+}
+
+template <typename... Ys,
+          typename X,
+          std::enable_if_t<!std::is_integral<X>::value && !std::is_floating_point<X>::value, bool> =
+              false>
+CK_TILE_HOST_DEVICE constexpr auto operator-=(tuple<Ys...>& y, const X& x)
+{
+    static_assert(X::size() == sizeof...(Ys), "wrong! size not the same");
+    constexpr index_t NSize = sizeof...(Ys);
+    static_for<0, NSize, 1>{}([&](auto i) { y[i] -= x[i]; });
+    return y;
+}
+
+template <typename... Xs,
+          typename Y,
+          std::enable_if_t<!std::is_integral<Y>::value && !std::is_floating_point<Y>::value, bool> =
+              false>
+CK_TILE_HOST_DEVICE constexpr auto operator+(const tuple<Xs...>& x, const Y& y)
+{
+    static_assert(Y::size() == sizeof...(Xs), "wrong! size not the same");
+    constexpr index_t NSize = sizeof...(Xs);
+
+    tuple<Xs...> r;
+    static_for<0, NSize, 1>{}([&](auto i) { r[i] = x[i] + y[i]; });
+    return r;
+}
+
+template <typename... Xs, typename... Ys>
+CK_TILE_HOST_DEVICE constexpr auto operator+(const tuple<Xs...>& x, const tuple<Ys...>& y)
+{
+    static_assert(sizeof...(Xs) == sizeof...(Ys), "wrong!");
+    constexpr index_t NSize = sizeof...(Xs);
+    return generate_tuple([&](auto i) { return x[i] + y[i]; }, number<NSize>{});
+}
+
+template <typename... Xs,
+          typename Y,
+          std::enable_if_t<!std::is_integral<Y>::value && !std::is_floating_point<Y>::value, bool> =
+              false>
+CK_TILE_HOST_DEVICE constexpr auto operator-(const tuple<Xs...>& x, const Y& y)
+{
+    static_assert(Y::size() == sizeof...(Xs), "wrong! size not the same");
+    constexpr index_t NSize = sizeof...(Xs);
+
+    tuple<Xs...> r;
+    static_for<0, NSize, 1>{}([&](auto i) { r[i] = x[i] - y[i]; });
+    return r;
+}
+
+template <typename... Xs, typename... Ys>
+CK_TILE_HOST_DEVICE constexpr auto operator-(const tuple<Xs...>& x, const tuple<Ys...>& y)
+{
+    static_assert(sizeof...(Xs) == sizeof...(Ys), "wrong!");
+    constexpr index_t NSize = sizeof...(Xs);
+    return generate_tuple([&](auto i) { return x[i] - y[i]; }, number<NSize>{});
+}
+
+template <typename... Xs,
+          typename Y,
+          std::enable_if_t<!std::is_integral<Y>::value && !std::is_floating_point<Y>::value, bool> =
+              false>
+CK_TILE_HOST_DEVICE constexpr auto operator*(const tuple<Xs...>& x, const Y& y)
+{
+    static_assert(Y::size() == sizeof...(Xs), "wrong! size not the same");
+    constexpr index_t NSize = sizeof...(Xs);
+
+    tuple<Xs...> r;
+    static_for<0, NSize, 1>{}([&](auto i) { r[i] = x[i] * y[i]; });
+    return r;
+}
+
+// MultiIndex = scalar * MultiIndex
+template <
+    typename... Xs,
+    typename Y,
+    std::enable_if_t<std::is_integral<Y>::value || std::is_floating_point<Y>::value, bool> = false>
+CK_TILE_HOST_DEVICE constexpr auto operator*(Y a, const tuple<Xs...>& x)
+{
+    constexpr index_t NSize = sizeof...(Xs);
+    tuple<Xs...> r;
+    static_for<0, NSize, 1>{}([&](auto i) { r[i] = a * x[i]; });
+    return r;
+}
+
+// MultiIndex = MultiIndex * scalar
+template <
+    typename... Xs,
+    typename Y,
+    std::enable_if_t<std::is_integral<Y>::value || std::is_floating_point<Y>::value, bool> = false>
+CK_TILE_HOST_DEVICE constexpr auto operator*(const tuple<Xs...>& x, Y a)
+{
+    return a * x;
+}
+
+template <typename... Xs, typename... Ys>
+CK_TILE_HOST_DEVICE constexpr auto operator*(const tuple<Xs...>& x, const tuple<Ys...>& y)
+{
+    static_assert(sizeof...(Xs) == sizeof...(Ys), "wrong!");
+    constexpr index_t NSize = sizeof...(Xs);
+    return generate_tuple([&](auto i) { return x[i] * y[i]; }, number<NSize>{});
+}
+
+template <typename... Xs, typename... Ys>
+CK_TILE_HOST_DEVICE constexpr auto operator/(const tuple<Xs...>& x, const tuple<Ys...>& y)
+{
+    static_assert(sizeof...(Xs) == sizeof...(Ys), "wrong!");
+    constexpr index_t NSize = sizeof...(Xs);
+    return generate_tuple([&](auto i) { return x[i] / y[i]; }, number<NSize>{});
+}
+
+} // namespace ck_tile
+
+#include <tuple>
+// WARNING: needed by compiler for C++ structured binding support only, don't use this
+namespace std {
+
+template <typename... Ts>
+struct tuple_size<ck_tile::tuple<Ts...>> : std::integral_constant<std::size_t, sizeof...(Ts)>
+{
+};
+
+template <std::size_t I, typename... Ts>
+struct tuple_element<I, ck_tile::tuple<Ts...>> : std::tuple_element<I, std::tuple<Ts...>>
+{
+};
+
+template <typename... Ts>
+struct tuple_size<const ck_tile::tuple<Ts...>> : std::integral_constant<std::size_t, sizeof...(Ts)>
+{
+};
+
+template <std::size_t I, typename... Ts>
+struct tuple_element<I, const ck_tile::tuple<Ts...>>
+    : std::tuple_element<I, const std::tuple<Ts...>>
+{
+};
+
+} // namespace std
+
+#if 1
+#define TO_TUPLE_OF_NUMBER(a, n)                                                             \
+    _Pragma("clang diagnostic push") _Pragma(                                                \
+        "clang diagnostic ignored \"-Wc++20-extensions\"")[a]<ck_tile::index_t... IDX_IDX_>( \
+        ck_tile::sequence<IDX_IDX_...>)                                                      \
+    {                                                                                        \
+        return ck_tile::tuple<ck_tile::number<a[ck_tile::number<IDX_IDX_>{}]>...>{};         \
+    }                                                                                        \
+    (ck_tile::make_index_sequence<n>{}) _Pragma("clang diagnostic pop")
+#else
+#define TO_TUPLE_OF_NUMBER(arr, n_)                                                      \
+    [&arr, n_] {                                                                         \
+        static_assert(arr.size() >= n_, "wrong! out of bound");                          \
+                                                                                         \
+        static_assert(n_ < 7, "not implemented");                                        \
+                                                                                         \
+        if constexpr(n_ == 0)                                                            \
+        {                                                                                \
+            return ck_tile::tuple<>{};                                                   \
+        }                                                                                \
+        else if constexpr(n_ == 1)                                                       \
+        {                                                                                \
+            return ck_tile::tuple<number<arr[0]>>{};                                     \
+        }                                                                                \
+        else if constexpr(n_ == 2)                                                       \
+        {                                                                                \
+            return ck_tile::tuple<number<arr[0]>, number<arr[1]>>{};                     \
+        }                                                                                \
+        else if constexpr(n_ == 3)                                                       \
+        {                                                                                \
+            return ck_tile::tuple<number<arr[0]>, number<arr[1]>, number<arr[2]>>{};     \
+        }                                                                                \
+        else if constexpr(n_ == 4)                                                       \
+        {                                                                                \
+            return ck_tile::                                                             \
+                tuple<number<arr[0]>, number<arr[1]>, number<arr[2]>, number<arr[3]>>{}; \
+        }                                                                                \
+        else if constexpr(n_ == 5)                                                       \
+        {                                                                                \
+            return ck_tile::tuple<number<arr[0]>,                                        \
+                                  number<arr[1]>,                                        \
+                                  number<arr[2]>,                                        \
+                                  number<arr[3]>,                                        \
+                                  number<arr[4]>>{};                                     \
+        }                                                                                \
+        else if constexpr(n_ == 6)                                                       \
+        {                                                                                \
+            return ck_tile::tuple<number<arr[0]>,                                        \
+                                  number<arr[1]>,                                        \
+                                  number<arr[2]>,                                        \
+                                  number<arr[3]>,                                        \
+                                  number<arr[4]>,                                        \
+                                  number<arr[5]>>{};                                     \
+        }                                                                                \
+    }()
+#endif

include/ck_tile/core/numeric/bfloat16.hpp

@@ -0,0 +1,423 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2025, Advanced Micro Devices, Inc. All rights reserved.
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/utility/bit_cast.hpp"
+#include "ck_tile/core/numeric/half.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/numeric/numeric.hpp"
+#include <stdint.h>
+
+#pragma once
+
+namespace ck_tile {
+
+enum class bf16_rounding_mode
+{
+    standard = 0, // rtn
+    truncate_with_nan,
+    truncate,
+    standard_asm,
+    rta_asm, // round to nearest away
+};
+
+template <bf16_rounding_mode rounding =
+              static_cast<bf16_rounding_mode>(CK_TILE_FLOAT_TO_BFLOAT16_DEFAULT)>
+CK_TILE_HOST_DEVICE constexpr uint16_t float_to_bf16_raw(float f, constant<rounding> = {});
+
+template <bf16_rounding_mode rounding =
+              static_cast<bf16_rounding_mode>(CK_TILE_FLOAT_TO_BFLOAT16_DEFAULT)>
+CK_TILE_HOST_DEVICE constexpr uint16_t double_to_bf16_raw(double f, constant<rounding> = {});
+
+CK_TILE_HOST_DEVICE
+constexpr float bf16_to_float_raw(uint16_t x);
+
+CK_TILE_HOST_DEVICE
+constexpr double bf16_to_double_raw(uint16_t x);
+
+#if CK_TILE_USE_CUSTOM_DATA_TYPE
+// HIP use __hip_bfloat16 as struct
+struct alignas(2) bfloat16_t
+{
+    using raw_type = uint16_t;
+    raw_type data;
+
+    CK_TILE_HOST_DEVICE
+    static constexpr bfloat16_t bit_cast(raw_type x)
+    {
+        bfloat16_t y;
+        y.data = x;
+        return y;
+    }
+
+    // constructor
+    constexpr bfloat16_t() : data() {}
+
+    // construct from float
+    CK_TILE_HOST_DEVICE
+    explicit constexpr bfloat16_t(const float& x) : data(float_to_bf16_raw(x)) {}
+
+    // construct from double
+    CK_TILE_HOST_DEVICE
+    explicit constexpr bfloat16_t(const double& x) : data(double_to_bf16_raw(x)) {}
+
+    // construct from int
+    CK_TILE_HOST_DEVICE
+    explicit constexpr bfloat16_t(const int& x) : data(float_to_bf16_raw(static_cast<float>(x))) {}
+
+    // construct from unsigned int
+    CK_TILE_HOST_DEVICE
+    explicit constexpr bfloat16_t(const unsigned int& x)
+        : data(float_to_bf16_raw(static_cast<float>(x)))
+    {
+    }
+
+    // cast to float
+    CK_TILE_HOST_DEVICE
+    explicit constexpr operator float() const { return bf16_to_float_raw(data); }
+
+    // cast to float
+    CK_TILE_HOST_DEVICE
+    explicit constexpr operator double() const { return bf16_to_double_raw(data); }
+
+    // cast to int
+    CK_TILE_HOST_DEVICE
+    explicit constexpr operator int() const { return static_cast<int>(bf16_to_float_raw(data)); }
+
+    // internal access
+    CK_TILE_HOST_DEVICE
+    constexpr raw_type& get() { return data; }
+
+    CK_TILE_HOST_DEVICE
+    constexpr raw_type get() const { return data; }
+};
+template <typename>
+struct native_t;
+
+template <>
+struct native_t<bfloat16_t>
+{
+    using type = ushort;
+};
+using bf16_t     = bfloat16_t;
+using bf16_raw_t = typename bf16_t::raw_type;
+#else
+using bfloat16_t = ushort;
+using bf16_t     = bfloat16_t;
+using bf16_raw_t = uint16_t;
+#endif
+// round to nearest
+CK_TILE_HOST_DEVICE
+constexpr uint16_t float_to_bf16_rtn_raw(float f)
+{
+    union
+    {
+        float fp32;
+        uint32_t int32;
+    } u = {f};
+    if(~u.int32 & 0x7f800000)
+    {
+        // When the exponent bits are not all 1s, then the value is zero, normal,
+        // or subnormal. We round the bfloat16 mantissa up by adding 0x7FFF, plus
+        // 1 if the least significant bit of the bfloat16 mantissa is 1 (odd).
+        // This causes the bfloat16's mantissa to be incremented by 1 if the 16
+        // least significant bits of the float mantissa are greater than 0x8000,
+        // or if they are equal to 0x8000 and the least significant bit of the
+        // bfloat16 mantissa is 1 (odd). This causes it to be rounded to even when
+        // the lower 16 bits are exactly 0x8000. If the bfloat16 mantissa already
+        // has the value 0x7f, then incrementing it causes it to become 0x00 and
+        // the exponent is incremented by one, which is the next higher FP value
+        // to the unrounded bfloat16 value. When the bfloat16 value is subnormal
+        // with an exponent of 0x00 and a mantissa of 0x7F, it may be rounded up
+        // to a normal value with an exponent of 0x01 and a mantissa of 0x00.
+        // When the bfloat16 value has an exponent of 0xFE and a mantissa of 0x7F,
+        // incrementing it causes it to become an exponent of 0xFF and a mantissa
+        // of 0x00, which is Inf, the next higher value to the unrounded value.
+        u.int32 += 0x7fff + ((u.int32 >> 16) & 1); // Round to nearest, round to even
+    }
+    else if(u.int32 & 0xffff)
+    {
+        // When all of the exponent bits are 1, the value is Inf or NaN.
+        // Inf is indicated by a zero mantissa. NaN is indicated by any nonzero
+        // mantissa bit. Quiet NaN is indicated by the most significant mantissa
+        // bit being 1. Signaling NaN is indicated by the most significant
+        // mantissa bit being 0 but some other bit(s) being 1. If any of the
+        // lower 16 bits of the mantissa are 1, we set the least significant bit
+        // of the bfloat16 mantissa, in order to preserve signaling NaN in case
+        // the bloat16's mantissa bits are all 0.
+        u.int32 |= 0x10000; // Preserve signaling NaN
+    }
+    return uint16_t(u.int32 >> 16);
+}
+
+CK_TILE_HOST
+constexpr uint16_t float_to_bf16_rtn_asm(float f) { return float_to_bf16_rtn_raw(f); }
+
+CK_TILE_DEVICE
+uint16_t float_to_bf16_rtn_asm(float f)
+{
+    union
+    {
+        float fp32;
+        uint32_t int32;
+    } u = {f};
+
+    static constexpr uint32_t FP32_NAN            = 0x7fff0000;
+    static constexpr uint32_t ROUND_BIAS_FOR_BF16 = 0x7fff;
+
+    using uint32x2_t = uint32_t __attribute__((ext_vector_type(2)));
+    uint32x2_t check_nan;
+    uint32_t tmp;
+    asm volatile("\n \
+            v_cmp_u_f32 %0, %2, %2 \n \
+            v_bfe_u32 %1, %2, 16, 1 \n \
+            v_add3_u32 %1, %2, %1, %3 \n \
+            v_cndmask_b32 %2, %1, %4, %0 \n \
+            v_lshrrev_b32 %2, 16, %2 \n \
+            "
+                 : "=s"(check_nan), "+v"(tmp), "+v"(u.fp32)
+                 : "v"(ROUND_BIAS_FOR_BF16), "v"(FP32_NAN));
+
+    return uint16_t(u.int32);
+}
+
+// TODO: do we need this on host?
+CK_TILE_HOST
+uint16_t float_to_bf16_rta_asm(float f) { return float_to_bf16_rtn_raw(f); }
+
+CK_TILE_DEVICE
+uint16_t float_to_bf16_rta_asm(float f)
+{
+    union
+    {
+        float fp32;
+        struct
+        {
+            uint16_t lo;
+            uint16_t hi;
+        };
+    } u = {f};
+
+    const uint32_t low_nan = 0x7fff;
+    const uint32_t hi_nan  = 0x7fff0000;
+
+    using uint32x2_t = uint32_t __attribute__((ext_vector_type(2)));
+    uint32x2_t check_nan;
+
+    asm volatile("v_cmp_u_f32 %[s_cnan], %[v_x], %[v_x] \n"
+                 "v_add3_u32 %[v_x], %[v_x], %[v_blo], 1 \n"
+                 "v_cndmask_b32 %[v_x], %[v_x], %[v_bhi], %[s_cnan]"
+                 : [s_cnan] "+s"(check_nan), [v_x] "+v"(u.fp32)
+                 : [v_blo] "v"(low_nan), [v_bhi] "v"(hi_nan));
+
+    // Note: in above code snipet, we use hi 16 bit
+    return u.hi;
+}
+
+// Truncate instead of rounding, preserving SNaN
+CK_TILE_HOST_DEVICE
+constexpr uint16_t float_to_bf16_truc_nan_raw(float f)
+{
+    union
+    {
+        float fp32;
+        uint32_t int32;
+    } u = {f};
+    return uint16_t(u.int32 >> 16) | (!(~u.int32 & 0x7f800000) && (u.int32 & 0xffff));
+}
+
+// Fast truncate instead of rounding, RTZ
+CK_TILE_HOST_DEVICE
+constexpr uint16_t float_to_bf16_truc_raw(float f)
+{
+    union
+    {
+        float fp32;
+        uint32_t int32;
+    } u = {f};
+    return uint16_t(u.int32 >> 16);
+}
+
+template <bf16_rounding_mode rounding>
+CK_TILE_HOST_DEVICE constexpr uint16_t float_to_bf16_raw(float f, constant<rounding>)
+{
+    if constexpr(rounding == bf16_rounding_mode::standard)
+        return float_to_bf16_rtn_raw(f);
+    else if constexpr(rounding == bf16_rounding_mode::standard_asm)
+        return float_to_bf16_rtn_asm(f);
+    else if constexpr(rounding == bf16_rounding_mode::truncate_with_nan)
+        return float_to_bf16_truc_nan_raw(f);
+    else if constexpr(rounding == bf16_rounding_mode::rta_asm)
+        return float_to_bf16_rta_asm(f);
+    else
+        return float_to_bf16_truc_raw(f);
+}
+
+template <bf16_rounding_mode rounding>
+CK_TILE_HOST_DEVICE constexpr uint16_t double_to_bf16_raw(double f, constant<rounding>)
+{
+    return float_to_bf16_raw(static_cast<float>(f), constant<rounding>{});
+}
+
+CK_TILE_HOST_DEVICE
+constexpr float bf16_to_float_raw(uint16_t x)
+{
+    union
+    {
+        uint32_t int32;
+        float fp32;
+    } u = {uint32_t(x) << 16};
+    return u.fp32;
+}
+
+CK_TILE_HOST_DEVICE
+constexpr double bf16_to_double_raw(uint16_t x)
+{
+    return static_cast<double>(bf16_to_float_raw(x));
+}
+
+template <bf16_rounding_mode rounding =
+              static_cast<bf16_rounding_mode>(CK_TILE_FLOAT_TO_BFLOAT16_DEFAULT)>
+CK_TILE_HOST_DEVICE constexpr bfloat16_t float_to_bf16(float f, constant<rounding> = {})
+{
+    return bit_cast<bfloat16_t>(float_to_bf16_raw(f, constant<rounding>{}));
+}
+
+template <bf16_rounding_mode rounding =
+              static_cast<bf16_rounding_mode>(CK_TILE_FLOAT_TO_BFLOAT16_DEFAULT)>
+CK_TILE_HOST_DEVICE constexpr bfloat16_t double_to_bf16(double f, constant<rounding> = {})
+{
+    return bit_cast<bfloat16_t>(double_to_bf16_raw(f, constant<rounding>{}));
+}
+
+CK_TILE_HOST_DEVICE
+constexpr float bf16_to_float(bfloat16_t x) { return bf16_to_float_raw(bit_cast<uint16_t>(x)); }
+
+CK_TILE_HOST_DEVICE
+constexpr double bf16_to_double(bfloat16_t x) { return static_cast<double>(bf16_to_float_raw(x)); }
+
+template <bf16_rounding_mode rounding =
+              static_cast<bf16_rounding_mode>(CK_TILE_FLOAT_TO_BFLOAT16_DEFAULT)>
+CK_TILE_HOST_DEVICE bfloat16_t constexpr fp16_to_bf16(half_t f, constant<rounding> = {})
+{
+    return bit_cast<bfloat16_t>(float_to_bf16_raw(static_cast<float>(f), constant<rounding>{}));
+}
+
+CK_TILE_HOST_DEVICE
+constexpr half_t bf16_to_fp16(bfloat16_t x) { return static_cast<fp16_t>(static_cast<float>(x)); }
+
+template <class T>
+struct numeric;
+
+template <>
+struct numeric<bfloat16_t>
+{
+    // minimum finite value, or minimum positive normalized value for float
+    CK_TILE_HOST_DEVICE static constexpr bfloat16_t min()
+    {
+        return bit_cast<bfloat16_t>(static_cast<bf16_raw_t>(0x0080));
+    }
+
+    // minumum finite value
+    CK_TILE_HOST_DEVICE static constexpr bfloat16_t lowest()
+    {
+        return bit_cast<bfloat16_t>(static_cast<bf16_raw_t>(0xff7f));
+    }
+
+    // maximum finite value
+    CK_TILE_HOST_DEVICE static constexpr bfloat16_t max()
+    {
+        return bit_cast<bfloat16_t>(static_cast<bf16_raw_t>(0x7f7f));
+    }
+
+    // difference between 1.0 and next value representable by float
+    CK_TILE_HOST_DEVICE static constexpr bfloat16_t epsilon()
+    {
+        return bit_cast<bfloat16_t>(static_cast<bf16_raw_t>(0x1000));
+    }
+
+    // maximum rounding error
+    // maximum rounding error
+    // bin :  f edcba 9876543210
+    // bits:  s eeeeeeee mmmmmmm
+    //        0 01111110 0000000 (0.5)
+    //
+    CK_TILE_HOST_DEVICE static constexpr bfloat16_t round_error()
+    {
+        return bit_cast<bfloat16_t>(static_cast<bf16_raw_t>(0x3f00));
+    }
+
+    // positive infinity value
+    CK_TILE_HOST_DEVICE static constexpr bfloat16_t infinity()
+    {
+        return bit_cast<bfloat16_t>(static_cast<bf16_raw_t>(0x7f80));
+    }
+
+    // quiet NaN
+    CK_TILE_HOST_DEVICE static constexpr bfloat16_t quiet_NaN()
+    {
+        return bit_cast<bfloat16_t>(static_cast<bf16_raw_t>(0x7FFF));
+    }
+
+    // signaling NaN
+    CK_TILE_HOST_DEVICE static constexpr bfloat16_t signaling_NaN()
+    {
+        return bit_cast<bfloat16_t>(static_cast<bf16_raw_t>(0x7FFF));
+    }
+
+    // smallest positive subnormal value
+    CK_TILE_HOST_DEVICE static constexpr bfloat16_t denorm_min()
+    {
+        return bit_cast<bfloat16_t>(static_cast<bf16_raw_t>(0x0001));
+    }
+    CK_TILE_HOST_DEVICE static constexpr bfloat16_t zero()
+    {
+        return bit_cast<bfloat16_t>(static_cast<bf16_raw_t>(0));
+    }
+};
+
+template <>
+struct numeric_traits<bfloat16_t>
+{
+    static constexpr int exp        = 8;
+    static constexpr int mant       = 7;
+    static constexpr int PackedSize = 1;
+};
+
+#if CK_TILE_USE_CUSTOM_DATA_TYPE
+CK_TILE_ARITHMETIC_USING_FLOAT(CK_TILE_HOST_DEVICE, bfloat16_t)
+#endif
+
+// math
+CK_TILE_HOST_DEVICE
+bfloat16_t abs(const bfloat16_t& x)
+{
+    return bit_cast<bfloat16_t>(static_cast<bf16_raw_t>(bit_cast<bf16_raw_t>(x) & 0x7fff));
+}
+
+CK_TILE_HOST_DEVICE
+bool isnan(const bfloat16_t& x)
+{
+    uint16_t xx = bit_cast<bf16_raw_t>(x);
+    return (xx & 0x7FFF) > 0x7C00;
+}
+
+CK_TILE_DEVICE
+bfloat16_t sqrt(bfloat16_t x)
+{
+    return static_cast<bfloat16_t>(__builtin_amdgcn_sqrtf(static_cast<float>(x)));
+};
+
+CK_TILE_DEVICE
+bfloat16_t exp(bfloat16_t x)
+{
+    return static_cast<bfloat16_t>(__ocml_exp_f32(static_cast<float>(x)));
+};
+
+CK_TILE_DEVICE
+bfloat16_t exp2(bfloat16_t x) { return static_cast<bfloat16_t>(exp2f(static_cast<float>(x))); };
+
+CK_TILE_DEVICE
+bfloat16_t log(bfloat16_t x) { return static_cast<bfloat16_t>(__logf(static_cast<float>(x))); };
+
+} // namespace ck_tile

include/ck_tile/core/numeric/half.hpp

@@ -0,0 +1,404 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2025, Advanced Micro Devices, Inc. All rights reserved.
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/utility/bit_cast.hpp"
+#include "ck_tile/core/numeric/numeric.hpp"
+#include <hip/hip_fp16.h>
+
+#pragma once
+
+namespace ck_tile {
+
+using fp16_hip_t = _Float16; // most of hip internal function use this type
+using fp16_raw_t = uint16_t;
+
+CK_TILE_HOST_DEVICE
+constexpr float fp16_to_float_hip(const fp16_hip_t& x);
+
+CK_TILE_HOST_DEVICE
+constexpr double fp16_to_double_hip(const fp16_hip_t& x);
+
+CK_TILE_HOST_DEVICE
+constexpr fp16_hip_t float_to_fp16_hip(const float& x);
+
+CK_TILE_HOST_DEVICE
+constexpr fp16_hip_t double_to_fp16_hip(const double& x);
+
+#if CK_TILE_USE_CUSTOM_DATA_TYPE
+// HIP use fp16_hip_t as interchangable data type for float16
+struct alignas(2) half_t
+{
+    using raw_type = fp16_raw_t;
+    raw_type data;
+
+    CK_TILE_HOST_DEVICE
+    static constexpr half_t bit_cast(raw_type x)
+    {
+        half_t y;
+        y.data = x;
+        return y;
+    }
+
+    CK_TILE_HOST_DEVICE
+    constexpr fp16_hip_t to_fp16() const { return ck_tile::bit_cast<fp16_hip_t>(data); }
+
+    // constructor
+    constexpr half_t() : data{} {}
+
+    // construct from HIP half
+    CK_TILE_HOST_DEVICE
+    explicit constexpr half_t(const fp16_hip_t& x) : data(ck_tile::bit_cast<raw_type>(x)) {}
+
+    // construct from float
+    CK_TILE_HOST_DEVICE
+    explicit constexpr half_t(const float& x) : half_t(float_to_fp16_hip(x)) {}
+
+    // construct from double
+    CK_TILE_HOST_DEVICE
+    explicit constexpr half_t(const double& x) : half_t(double_to_fp16_hip(x)) {}
+
+    // construct from int
+    CK_TILE_HOST_DEVICE
+    explicit constexpr half_t(const int& x) : half_t(static_cast<fp16_hip_t>(__int2half_rn(x))) {}
+
+    // construct from unsigned int
+    CK_TILE_HOST_DEVICE
+    explicit constexpr half_t(const unsigned int& x)
+        : half_t(static_cast<fp16_hip_t>(__uint2half_rn(x)))
+    {
+    }
+
+    // cast to float
+    CK_TILE_HOST_DEVICE
+    explicit constexpr operator float() const { return fp16_to_float_hip(to_fp16()); }
+
+    // cast to double
+    CK_TILE_HOST_DEVICE
+    explicit constexpr operator double() const { return fp16_to_double_hip(to_fp16()); }
+
+    // cast to int
+    CK_TILE_HOST_DEVICE
+    explicit constexpr operator int() const
+    {
+        return static_cast<int>(fp16_to_float_hip(to_fp16()));
+    }
+
+    CK_TILE_HOST_DEVICE
+    explicit constexpr operator fp16_hip_t() const { return ck_tile::bit_cast<fp16_hip_t>(data); }
+
+    // internal access
+    CK_TILE_HOST_DEVICE
+    constexpr raw_type& get() { return data; }
+
+    CK_TILE_HOST_DEVICE
+    constexpr raw_type get() const { return data; }
+};
+
+template <typename>
+struct native_t;
+
+template <>
+struct native_t<half_t>
+{
+    using type = _Float16;
+};
+
+using fp16_t     = half_t;
+using fp16_raw_t = typename half_t::raw_type;
+#else
+using fp16_t     = _Float16;
+using half_t     = _Float16;
+using fp16_raw_t = ushort;
+#endif
+
+// conversions
+CK_TILE_HOST_DEVICE
+constexpr float fp16_to_float_hip(const fp16_hip_t& x)
+{
+    // return __half2float(x);
+    return static_cast<float>(x);
+}
+
+CK_TILE_HOST_DEVICE
+constexpr double fp16_to_double_hip(const fp16_hip_t& x)
+{
+    return static_cast<double>(fp16_to_float_hip(x));
+}
+
+CK_TILE_HOST_DEVICE
+constexpr fp16_hip_t float_to_fp16_hip(const float& x)
+{
+    // return __float2half(x);
+    return static_cast<fp16_hip_t>(x);
+}
+
+CK_TILE_HOST_DEVICE
+constexpr fp16_hip_t double_to_fp16_hip(const double& x)
+{
+    // return __float2half(x);
+    return static_cast<fp16_hip_t>(x);
+}
+
+CK_TILE_HOST_DEVICE
+constexpr float fp16_to_float(const half_t& x) { return static_cast<float>(x); }
+
+CK_TILE_HOST_DEVICE
+constexpr float fp16_to_double(const half_t& x) { return static_cast<float>(x); }
+
+CK_TILE_HOST_DEVICE
+constexpr half_t float_to_fp16(const float& x) { return static_cast<half_t>(x); }
+
+CK_TILE_HOST_DEVICE
+constexpr half_t double_to_fp16(const double& x) { return static_cast<half_t>(x); }
+
+// limits
+template <class T>
+struct numeric;
+
+template <>
+struct numeric<half_t>
+{
+    // minimum finite value, or minimum positive normalized value for float
+    CK_TILE_HOST_DEVICE static constexpr half_t min()
+    {
+        return bit_cast<half_t>(static_cast<fp16_raw_t>(0x0400));
+    }
+
+    // minumum finite value
+    CK_TILE_HOST_DEVICE static constexpr half_t lowest()
+    {
+        return bit_cast<half_t>(static_cast<fp16_raw_t>(0xFBFF));
+    }
+
+    // maximum finite value
+    CK_TILE_HOST_DEVICE static constexpr half_t max()
+    {
+        return bit_cast<half_t>(static_cast<fp16_raw_t>(0x7BFF));
+    }
+
+    // difference between 1.0 and next value representable by float
+    CK_TILE_HOST_DEVICE static constexpr half_t epsilon()
+    {
+        return bit_cast<half_t>(static_cast<fp16_raw_t>(0x1800));
+    }
+
+    // maximum rounding error
+    // bin :  f edcba 9876543210
+    // bits:  s eeeee mmmmmmmmmm
+    //        0 01110 0000000000 (0.5)
+    //
+    CK_TILE_HOST_DEVICE static constexpr half_t round_error()
+    {
+        return bit_cast<half_t>(static_cast<fp16_raw_t>(0x3800));
+    }
+
+    // positive infinity value
+    CK_TILE_HOST_DEVICE static constexpr half_t infinity()
+    {
+        return bit_cast<half_t>(static_cast<fp16_raw_t>(0x7C00));
+    }
+
+    // quiet NaN
+    CK_TILE_HOST_DEVICE static constexpr half_t quiet_NaN()
+    {
+        return bit_cast<half_t>(static_cast<fp16_raw_t>(0x7FFF));
+    }
+
+    // signaling NaN
+    CK_TILE_HOST_DEVICE static constexpr half_t signaling_NaN()
+    {
+        return bit_cast<half_t>(static_cast<fp16_raw_t>(0x7FFF));
+    }
+
+    // smallest positive subnormal value
+    CK_TILE_HOST_DEVICE static constexpr half_t denorm_min()
+    {
+        return bit_cast<half_t>(static_cast<fp16_raw_t>(0x0001));
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr half_t zero()
+    {
+        return bit_cast<half_t>(static_cast<fp16_raw_t>(0));
+    }
+};
+
+template <>
+struct numeric_traits<half_t>
+{
+    static constexpr int exp            = 5;
+    static constexpr int mant           = 10;
+    static constexpr int bias           = 15;
+    static constexpr uint16_t nan_mask  = 0x7C00;
+    static constexpr uint16_t head_mask = 0xFC00;
+    static constexpr uint16_t mant_mask = 0x3FF;
+    static constexpr uint16_t exp_mask  = 0x1F;
+    static constexpr uint16_t abs_mask  = 0x7FFF;
+    static constexpr uint16_t Inf       = 0x7C00;
+    static constexpr uint16_t NegInf    = 0xFC00;
+    static constexpr uint16_t NaN       = 0x7C01;
+    static constexpr uint16_t Neg0      = 0x8000;
+    static constexpr int PackedSize     = 1;
+    using bitwise_type                  = uint16_t;
+};
+
+#if CK_TILE_USE_CUSTOM_DATA_TYPE
+// arithmetic
+CK_TILE_DEVICE bool operator==(const half_t& x, const half_t& y)
+{
+    return __heq(x.to_fp16(), y.to_fp16());
+}
+
+CK_TILE_DEVICE
+bool operator!=(const half_t& x, const half_t& y) { return __hne(x.to_fp16(), y.to_fp16()); }
+
+CK_TILE_DEVICE
+bool operator<(const half_t& x, const half_t& y) { return __hlt(x.to_fp16(), y.to_fp16()); }
+
+CK_TILE_DEVICE
+bool operator<=(const half_t& x, const half_t& y) { return __hle(x.to_fp16(), y.to_fp16()); }
+
+CK_TILE_DEVICE
+bool operator>(const half_t& x, const half_t& y) { return __hgt(x.to_fp16(), y.to_fp16()); }
+
+CK_TILE_DEVICE
+bool operator>=(const half_t& x, const half_t& y) { return __hge(x.to_fp16(), y.to_fp16()); }
+
+#if 0
+CK_TILE_DEVICE
+half_t operator+(const half_t& x, const half_t& y)
+{
+    return half_t(__hadd(x.to_fp16(), y.to_fp16()));
+}
+
+CK_TILE_DEVICE
+half_t operator-(const half_t& x) { return half_t(__hneg(x.to_fp16())); }
+
+CK_TILE_DEVICE
+half_t operator-(const half_t& x, const half_t& y)
+{
+    return half_t(__hsub(x.to_fp16(), y.to_fp16()));
+}
+
+CK_TILE_DEVICE
+half_t operator*(const half_t& x, const half_t& y)
+{
+    return half_t(__hmul(x.to_fp16(), y.to_fp16()));
+}
+
+CK_TILE_DEVICE
+half_t operator/(const half_t& x, const half_t& y)
+{
+    return half_t(__hdiv(x.to_fp16(), y.to_fp16()));
+}
+
+CK_TILE_DEVICE
+half_t& operator+=(half_t& x, const half_t& y)
+{
+    x = half_t(__hadd(x.to_fp16(), y.to_fp16()));
+    return x;
+}
+
+CK_TILE_DEVICE
+half_t& operator-=(half_t& x, const half_t& y)
+{
+    x = half_t(__hsub(x.to_fp16(), y.to_fp16()));
+    return x;
+}
+
+CK_TILE_DEVICE
+half_t& operator*=(half_t& x, const half_t& y)
+{
+    x = half_t(__hmul(x.to_fp16(), y.to_fp16()));
+    return x;
+}
+
+CK_TILE_DEVICE
+half_t& operator/=(half_t& x, const half_t& y)
+{
+    x = half_t(__hdiv(x.to_fp16(), y.to_fp16()));
+    return x;
+}
+
+CK_TILE_DEVICE
+half_t& operator++(half_t& x)
+{
+    x = half_t(__hadd(x.to_fp16(), half_t(1.0f).to_fp16()));
+    return x;
+}
+
+CK_TILE_DEVICE
+half_t& operator--(half_t& x)
+{
+    x = half_t(__hsub(x.to_fp16(), half_t(1.0f).to_fp16()));
+    return x;
+}
+
+CK_TILE_DEVICE
+half_t operator++(half_t& x, int)
+{
+    half_t y(x);
+    x = half_t(__hadd(x.to_fp16(), half_t(1.0f).to_fp16()));
+    return y;
+}
+
+CK_TILE_DEVICE
+half_t operator--(half_t& x, int)
+{
+    half_t y(x);
+    x = half_t(__hsub(x.to_fp16(), half_t(1.0f).to_fp16()));
+    return y;
+}
+#endif
+
+#if CK_TILE_USE_CUSTOM_DATA_TYPE
+CK_TILE_ARITHMETIC_USING_FLOAT(CK_TILE_HOST, half_t)
+#endif
+
+// math
+CK_TILE_HOST_DEVICE
+half_t abs(const half_t& x) { return bit_cast<half_t>(x.get() & 0x7fff); }
+
+CK_TILE_HOST_DEVICE
+bool isnan(const half_t& x)
+{
+    uint16_t xx = x.get();
+    return (xx & 0x7FFF) > 0x7C00;
+}
+
+CK_TILE_DEVICE
+half_t sqrt(half_t x)
+{
+    return static_cast<half_t>(__builtin_amdgcn_sqrtf(static_cast<float>(x)));
+};
+
+CK_TILE_DEVICE
+half_t exp(half_t x) { return static_cast<half_t>(__ocml_exp_f32(static_cast<float>(x))); };
+
+CK_TILE_DEVICE
+half_t exp2(half_t x) { return static_cast<half_t>(exp2f(static_cast<float>(x))); };
+
+CK_TILE_DEVICE
+half_t log(half_t x) { return static_cast<half_t>(__logf(static_cast<float>(x))); };
+#endif
+
+using fp16x2_t = _Float16 __attribute__((ext_vector_type(2)));
+
+CK_TILE_HOST fp16x2_t pk_add_f16(const fp16x2_t& x, const fp16x2_t& y)
+{
+    fp16x2_t vector_res;
+
+    vector_res.x = x.x + y.x;
+    vector_res.y = x.y + y.y;
+
+    return vector_res;
+}
+
+CK_TILE_DEVICE fp16x2_t pk_add_f16(const fp16x2_t& x, const fp16x2_t& y)
+{
+    fp16x2_t c;
+    asm volatile("v_pk_add_f16 %0, %1, %2" : "=v"(c) : "v"(x), "v"(y));
+    return c;
+}
+
+} // namespace ck_tile

include/ck_tile/core/numeric/int8.hpp

@@ -0,0 +1,103 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2025, Advanced Micro Devices, Inc. All rights reserved.
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/half.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/numeric/math.hpp"
+#include "ck_tile/core/numeric/numeric.hpp"
+#include "ck_tile/core/utility/bit_cast.hpp"
+#include "ck_tile/core/utility/random.hpp"
+#include <stdint.h>
+#include <type_traits>
+
+#pragma once
+
+namespace ck_tile {
+
+// use int8_t directly for int8 arithemetic
+// here one can use ck_tile::int8_t to access original int8_t
+using int8_t = int8_t;
+
+// limits
+template <class T>
+struct numeric;
+
+template <>
+struct numeric<int8_t>
+{
+    // minimum finite value, or minimum positive normalized value for float
+    CK_TILE_HOST_DEVICE static constexpr int8_t min() { return int8_t(-128); }
+
+    // minumum finite value
+    CK_TILE_HOST_DEVICE static constexpr int8_t lowest() { return int8_t(-128); }
+
+    // maximum finite value
+    CK_TILE_HOST_DEVICE static constexpr int8_t max() { return int8_t(127); }
+
+    // difference between 1.0 and next value representable by float
+    CK_TILE_HOST_DEVICE static constexpr int8_t epsilon()
+    {
+        return 1; // not used
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr int8_t round_error()
+    {
+        return 1; // not used
+    }
+
+    // positive infinity value
+    CK_TILE_HOST_DEVICE static constexpr int8_t infinity()
+    {
+        return 1; // not used
+    }
+
+    // quiet NaN
+    CK_TILE_HOST_DEVICE static constexpr int8_t quiet_NaN()
+    {
+        return 1; // not used
+    }
+
+    // signaling NaN
+    CK_TILE_HOST_DEVICE static constexpr int8_t signaling_NaN()
+    {
+        return 1; // not used
+    }
+
+    // smallest positive subnormal value
+    CK_TILE_HOST_DEVICE static constexpr int8_t denorm_min()
+    {
+        return 1; // not used
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr int8_t zero() { return 0; }
+};
+
+#if 0
+
+template <>
+struct numeric_traits<int8_t>
+{
+    static constexpr int exp            = 5;
+    static constexpr int mant           = 10;
+    static constexpr int bias           = 15;
+    static constexpr uint16_t nan_mask  = 0x7C00;
+    static constexpr uint16_t head_mask = 0xFC00;
+    static constexpr uint16_t mant_mask = 0x3FF;
+    static constexpr uint16_t exp_mask  = 0x1F;
+    static constexpr uint32_t Inf       = 0x7C00;
+    static constexpr uint32_t NegInf    = 0xFC00;
+    static constexpr uint32_t NaN       = 0x7C01;
+    static constexpr uint32_t Neg0      = 0x8000;
+    static constexpr int PackedSize           = 1;
+    using bitwise_type                  = uint16_t;
+};
+#endif
+
+CK_TILE_HOST_DEVICE
+constexpr float int8_to_float(const int8_t& x) { return static_cast<float>(x); }
+
+CK_TILE_HOST_DEVICE
+constexpr int8_t float_to_int8(const float& x) { return static_cast<int8_t>(x); }
+
+} // namespace ck_tile

include/ck_tile/core/numeric/integer.hpp

@@ -0,0 +1,13 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+#include <stdint.h>
+
+namespace ck_tile {
+
+using index_t      = int32_t;
+using long_index_t = int64_t;
+using int8_t       = int8_t;
+
+} // namespace ck_tile

include/ck_tile/core/numeric/integral_constant.hpp

@@ -0,0 +1,82 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+
+namespace ck_tile {
+
+template <auto v>
+struct constant
+{
+    using value_type                  = decltype(v);
+    using type                        = constant; // using injected-class-name
+    static constexpr value_type value = v;
+    CK_TILE_HOST_DEVICE constexpr operator value_type() const noexcept { return value; }
+    CK_TILE_HOST_DEVICE constexpr value_type operator()() const noexcept { return value; }
+    CK_TILE_HOST_DEVICE static constexpr bool is_static() { return true; }
+};
+
+template <typename T, T v>
+struct integral_constant : constant<v>
+{
+    using value_type         = T;
+    using type               = integral_constant; // using injected-class-name
+    static constexpr T value = v;
+    // constexpr CK_TILE_HOST_DEVICE operator   value_type() const noexcept { return value; }
+    // constexpr CK_TILE_HOST_DEVICE value_type operator()() const noexcept { return value; } //
+};
+
+template <index_t v>
+using number = constant<v>;
+
+template <long_index_t v>
+using long_number = constant<v>;
+
+template <bool b>
+using bool_constant = constant<b>;
+
+#define CK_TILE_LEFT_UNARY_OP(OP)                               \
+    template <auto x>                                           \
+    CK_TILE_HOST_DEVICE constexpr auto operator OP(constant<x>) \
+    {                                                           \
+        return constant<(OP x)>{};                              \
+    }
+
+#define CK_TILE_BINARY_OP(OP)                                                \
+    template <auto x, auto y>                                                \
+    CK_TILE_HOST_DEVICE constexpr auto operator OP(constant<x>, constant<y>) \
+    {                                                                        \
+        return constant<(x OP y)>{};                                         \
+    }
+
+CK_TILE_LEFT_UNARY_OP(+)
+CK_TILE_LEFT_UNARY_OP(-)
+CK_TILE_LEFT_UNARY_OP(~)
+CK_TILE_LEFT_UNARY_OP(!)
+
+CK_TILE_BINARY_OP(+)
+CK_TILE_BINARY_OP(-)
+CK_TILE_BINARY_OP(*)
+CK_TILE_BINARY_OP(/)
+CK_TILE_BINARY_OP(%)
+CK_TILE_BINARY_OP(&)
+CK_TILE_BINARY_OP(|)
+CK_TILE_BINARY_OP(^)
+CK_TILE_BINARY_OP(<<)
+CK_TILE_BINARY_OP(>>)
+CK_TILE_BINARY_OP(&&)
+CK_TILE_BINARY_OP(||)
+CK_TILE_BINARY_OP(==)
+CK_TILE_BINARY_OP(!=)
+CK_TILE_BINARY_OP(>)
+CK_TILE_BINARY_OP(<)
+CK_TILE_BINARY_OP(>=)
+CK_TILE_BINARY_OP(<=)
+
+#undef CK_TILE_LEFT_UNARY_OP
+#undef CK_TILE_BINARY_OP
+
+} // namespace ck_tile

include/ck_tile/core/numeric/null_type.hpp

@@ -0,0 +1,13 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+#include <stdint.h>
+
+namespace ck_tile {
+
+struct null_type
+{
+};
+
+} // namespace ck_tile

include/ck_tile/core/numeric/numeric.hpp

@@ -0,0 +1,196 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2025, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include <limits>
+#include <stdint.h>
+
+namespace ck_tile {
+
+// this struct has the information of
+// 1. limit of a certain type, simliar to std::numeric_limits
+// 2. some pre-defined value, zero, one...
+//
+template <typename T>
+struct numeric
+{
+    // minimum finite value, or minimum positive normalized value for float
+    CK_TILE_HOST_DEVICE static constexpr T min() { return std::numeric_limits<T>::min(); }
+
+    // minumum finite value
+    CK_TILE_HOST_DEVICE static constexpr T lowest() { return std::numeric_limits<T>::lowest(); }
+
+    // maximum finite value
+    CK_TILE_HOST_DEVICE static constexpr T max() { return std::numeric_limits<T>::max(); }
+
+    // difference between 1.0 and next value representable by float
+    CK_TILE_HOST_DEVICE static constexpr T epsilon() { return std::numeric_limits<T>::epsilon(); }
+
+    // maximum rounding error
+    CK_TILE_HOST_DEVICE static constexpr T round_error()
+    {
+        return std::numeric_limits<T>::round_error();
+    }
+
+    // positive infinity value
+    CK_TILE_HOST_DEVICE static constexpr T infinity() { return std::numeric_limits<T>::infinity(); }
+
+    // quiet NaN
+    CK_TILE_HOST_DEVICE static constexpr T quiet_NaN()
+    {
+        return std::numeric_limits<T>::quiet_NaN();
+    }
+
+    // signaling NaN
+    CK_TILE_HOST_DEVICE static constexpr T signaling_NaN()
+    {
+        return std::numeric_limits<T>::signaling_NaN();
+    }
+
+    // smallest positive subnormal value
+    CK_TILE_HOST_DEVICE static constexpr T denorm_min()
+    {
+        return std::numeric_limits<T>::denorm_min();
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr T zero() { return static_cast<T>(0); }
+
+    CK_TILE_HOST_DEVICE static constexpr T one() { return static_cast<T>(1); }
+
+#ifndef C_LOG2E
+#define C_LOG2E 1.44269504088896340736 // log2(e)
+#endif
+
+    CK_TILE_HOST_DEVICE static constexpr T log2e()
+    {
+        if constexpr(std::is_same_v<T, float> || std::is_same_v<T, double>)
+        {
+            return static_cast<T>(C_LOG2E);
+        }
+        else
+        {
+            return 0; // TODO: integer?
+        }
+    }
+};
+
+template <typename T>
+struct numeric_traits
+{
+    static constexpr int PackedSize = 1;
+};
+
+template <>
+struct numeric_traits<float>
+{
+    static constexpr int exp            = 8;
+    static constexpr int mant           = 23;
+    static constexpr int bias           = 127;
+    static constexpr uint32_t nan_mask  = 0x7F800000;
+    static constexpr uint32_t head_mask = 0xFF800000;
+    static constexpr uint32_t mant_mask = 0x7FFFFF;
+    static constexpr uint32_t exp_mask  = 0xFF;
+    static constexpr uint32_t abs_mask  = 0x7FFFFFFF;
+    static constexpr uint32_t Inf       = 0x7F800000;
+    static constexpr uint32_t NegInf    = 0xFF800000;
+    static constexpr uint32_t NaN       = 0x7F800001;
+    static constexpr uint32_t Neg0      = 0x80000000;
+    static constexpr int PackedSize     = 1;
+    using bitwise_type                  = uint32_t;
+};
+
+} // namespace ck_tile
+
+#define CK_TILE_ARITHMETIC_USING_FLOAT(attr_, type_)                 \
+    attr_ bool operator==(const type_& x, const type_& y)            \
+    {                                                                \
+        return static_cast<float>(x) == static_cast<float>(y);       \
+    }                                                                \
+    attr_ bool operator!=(const type_& x, const type_& y)            \
+    {                                                                \
+        return static_cast<float>(x) != static_cast<float>(y);       \
+    }                                                                \
+    attr_ bool operator<(const type_& x, const type_& y)             \
+    {                                                                \
+        return static_cast<float>(x) < static_cast<float>(y);        \
+    }                                                                \
+    attr_ bool operator<=(const type_& x, const type_& y)            \
+    {                                                                \
+        return static_cast<float>(x) <= static_cast<float>(y);       \
+    }                                                                \
+    attr_ bool operator>(const type_& x, const type_& y)             \
+    {                                                                \
+        return static_cast<float>(x) > static_cast<float>(y);        \
+    }                                                                \
+    attr_ bool operator>=(const type_& x, const type_& y)            \
+    {                                                                \
+        return static_cast<float>(x) >= static_cast<float>(y);       \
+    }                                                                \
+    attr_ type_ operator+(const type_& x, const type_& y)            \
+    {                                                                \
+        return type_(static_cast<float>(x) + static_cast<float>(y)); \
+    }                                                                \
+    attr_ type_ operator-(const type_& x)                            \
+    {                                                                \
+        constexpr uint32_t bits = sizeof(type_) * 8;                 \
+        constexpr uint32_t mask = 1 << (bits - 1);                   \
+        type_ y                 = x;                                 \
+        y.data ^= static_cast<typename type_::raw_type>(mask);       \
+        return y;                                                    \
+    }                                                                \
+    attr_ type_ operator-(const type_& x, const type_& y)            \
+    {                                                                \
+        return type_(static_cast<float>(x) - static_cast<float>(y)); \
+    }                                                                \
+    attr_ type_ operator*(const type_& x, const type_& y)            \
+    {                                                                \
+        return type_(static_cast<float>(x) * static_cast<float>(y)); \
+    }                                                                \
+    attr_ type_ operator/(const type_& x, const type_& y)            \
+    {                                                                \
+        return type_(static_cast<float>(x) / static_cast<float>(y)); \
+    }                                                                \
+    attr_ type_& operator+=(type_& x, const type_& y)                \
+    {                                                                \
+        x = type_(static_cast<float>(x) + static_cast<float>(y));    \
+        return x;                                                    \
+    }                                                                \
+    attr_ type_& operator-=(type_& x, const type_& y)                \
+    {                                                                \
+        x = type_(static_cast<float>(x) - static_cast<float>(y));    \
+        return x;                                                    \
+    }                                                                \
+    attr_ type_& operator*=(type_& x, const type_& y)                \
+    {                                                                \
+        x = type_(static_cast<float>(x) * static_cast<float>(y));    \
+        return x;                                                    \
+    }                                                                \
+    attr_ type_& operator/=(type_& x, const type_& y)                \
+    {                                                                \
+        x = type_(static_cast<float>(x) / static_cast<float>(y));    \
+        return x;                                                    \
+    }                                                                \
+    attr_ type_& operator++(type_& x)                                \
+    {                                                                \
+        x = type_(static_cast<float>(x) + 1.f);                      \
+        return x;                                                    \
+    }                                                                \
+    attr_ type_& operator--(type_& x)                                \
+    {                                                                \
+        x = type_(static_cast<float>(x) - 1.f);                      \
+        return x;                                                    \
+    }                                                                \
+    attr_ type_ operator++(type_& x, int)                            \
+    {                                                                \
+        type_ y(x);                                                  \
+        x = type_(static_cast<float>(x) + 1.f);                      \
+        return y;                                                    \
+    }                                                                \
+    attr_ type_ operator--(type_& x, int)                            \
+    {                                                                \
+        type_ y(x);                                                  \
+        x = type_(static_cast<float>(x) - 1.f);                      \
+        return y;                                                    \
+    }

include/ck_tile/core/numeric/pk_int4.hpp

@@ -0,0 +1,150 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2025, Advanced Micro Devices, Inc. All rights reserved.
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/half.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/numeric/math.hpp"
+#include "ck_tile/core/numeric/numeric.hpp"
+#include "ck_tile/core/utility/bit_cast.hpp"
+#include "ck_tile/core/utility/random.hpp"
+#include <stdint.h>
+#include <type_traits>
+#include "ck_tile/core/numeric/int8.hpp"
+
+#pragma once
+
+namespace ck_tile {
+
+// Packed 2xint4
+struct pk_int4_t
+{
+    using type = int8_t;
+    type data;
+    CK_TILE_HOST_DEVICE constexpr pk_int4_t() : data{type{}} {}
+    CK_TILE_HOST_DEVICE constexpr pk_int4_t(type init) : data{init} {}
+};
+
+// limits
+template <class T>
+struct numeric;
+
+template <>
+struct numeric<pk_int4_t>
+{
+    // minimum finite value, or minimum positive normalized value for float
+    CK_TILE_HOST_DEVICE static constexpr pk_int4_t min()
+    {
+        constexpr uint8_t val = 0b10001000;
+        return pk_int4_t(bit_cast<int8_t>(val));
+    }
+
+    // minumum finite value
+    CK_TILE_HOST_DEVICE static constexpr pk_int4_t lowest()
+    {
+        constexpr uint8_t val = 0b10001000;
+        return pk_int4_t(bit_cast<int8_t>(val));
+    }
+
+    // maximum finite value
+    CK_TILE_HOST_DEVICE static constexpr pk_int4_t max()
+    {
+        constexpr uint8_t val = 0b01110111;
+        return pk_int4_t(bit_cast<int8_t>(val));
+    }
+
+    // difference between 1.0 and next value representable by float
+    CK_TILE_HOST_DEVICE static constexpr pk_int4_t epsilon()
+    {
+        return 1; // not used
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr pk_int4_t round_error()
+    {
+        return 1; // not used
+    }
+
+    // positive infinity value
+    CK_TILE_HOST_DEVICE static constexpr pk_int4_t infinity()
+    {
+        return 1; // not used
+    }
+
+    // quiet NaN
+    CK_TILE_HOST_DEVICE static constexpr pk_int4_t quiet_NaN()
+    {
+        return 1; // not used
+    }
+
+    // signaling NaN
+    CK_TILE_HOST_DEVICE static constexpr pk_int4_t signaling_NaN()
+    {
+        return 1; // not used
+    }
+
+    // smallest positive subnormal value
+    CK_TILE_HOST_DEVICE static constexpr pk_int4_t denorm_min()
+    {
+        return 1; // not used
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr pk_int4_t zero() { return 0; }
+};
+
+template <>
+struct numeric_traits<pk_int4_t>
+{
+    static constexpr int PackedSize = 2;
+};
+
+using fp32x2_t = float __attribute__((ext_vector_type(2)));
+using fp16x2_t = _Float16 __attribute__((ext_vector_type(2)));
+using bf16x2_t = bf16_raw_t __attribute__((ext_vector_type(2)));
+
+CK_TILE_HOST_DEVICE fp32x2_t pk_int4_t_to_fp32x2_t(const pk_int4_t& x)
+{
+    uint8_t x_u8 = ck_tile::bit_cast<uint8_t>(x);
+
+    float x_l = ((x_u8 & 0x0f) >> 0) - 8.f;
+    float x_h = ((x_u8 & 0xf0) >> 4) - 8.f;
+
+#ifdef CK_TILE_USE_PK4_LAYOUT_SHUFFLE
+    fp32x2_t res = {x_h, x_l};
+#elif
+    fp32x2_t res = {x_l, x_h};
+#endif
+    return res;
+}
+
+CK_TILE_HOST_DEVICE fp16x2_t pk_int4_t_to_halfx2_t(const pk_int4_t& x)
+{
+    uint8_t x_u8 = ck_tile::bit_cast<uint8_t>(x);
+#ifdef CK_TILE_USE_PK4_LAYOUT_SHUFFLE
+    uint32_t i4s = ((x_u8 & 0x0f) << 16) | ((x_u8 & 0xf0) >> 4);
+#elif
+    uint32_t i4s = ((x_u8 & 0xf0) << 12) | (x_u8 & 0xf);
+#endif
+    const int EX  = 0x64006400;
+    const int SUB = 0xE408E408; //-8
+
+    int lo = i4s | EX;
+
+    return pk_add_f16(bit_cast<fp16x2_t>(lo), bit_cast<fp16x2_t>(SUB));
+}
+
+CK_TILE_HOST_DEVICE bf16x2_t pk_int4_t_to_bfloat16x2_t(const pk_int4_t& x)
+{
+    uint8_t x_u8 = ck_tile::bit_cast<uint8_t>(x);
+
+    float x_l = ((x_u8 & 0x0f) >> 0) - 8.f;
+    float x_h = ((x_u8 & 0xf0) >> 4) - 8.f;
+
+#ifdef CK_TILE_USE_PK4_LAYOUT_SHUFFLE
+    bf16x2_t res = {type_convert<bf16_t>(x_h), type_convert<bf16_t>(x_l)};
+#elif
+    bf16x2_t res = {type_convert<bf16_t>(x_l), type_convert<bf16_t>(x_h)};
+#endif
+    return res;
+}
+
+} // namespace ck_tile

include/ck_tile/core/numeric/type_convert.hpp

@@ -0,0 +1,70 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <stdint.h>
+#include <tuple>
+#include <type_traits>
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/half.hpp"
+#include "ck_tile/core/numeric/bfloat16.hpp"
+#include "ck_tile/core/numeric/float8.hpp"
+#include "ck_tile/core/numeric/int8.hpp"
+
+namespace ck_tile {
+
+#if CK_TILE_USE_CUSTOM_DATA_TYPE
+template <typename Y, typename X>
+CK_TILE_HOST_DEVICE constexpr remove_cvref_t<Y> type_convert(const X& x)
+{
+    return static_cast<Y>(x);
+}
+#else
+// Convert X to Y, both X and Y are non-const data types.
+template <typename Y,
+          typename X,
+          std::enable_if_t<!(std::is_const_v<Y> || std::is_const_v<X>), bool> = false>
+CK_TILE_HOST_DEVICE constexpr Y type_convert(X x)
+{
+    static_assert(!std::is_reference_v<Y> && !std::is_reference_v<X>);
+    return static_cast<Y>(x);
+}
+
+// Convert X to Y, either X or Y is a const data type.
+template <typename Y,
+          typename X,
+          std::enable_if_t<std::is_const_v<Y> || std::is_const_v<X>, bool> = false>
+CK_TILE_HOST_DEVICE constexpr Y type_convert(X x)
+{
+    static_assert(!std::is_reference_v<Y> && !std::is_reference_v<X>);
+
+    using non_const_y = std::remove_const_t<Y>;
+    using non_const_x = std::remove_const_t<X>;
+    return static_cast<Y>(type_convert<non_const_y, non_const_x>(x));
+}
+
+#define CK_TILE_TYPE_CONVERT(dtype_, dname_, stype_, sname_)                    \
+    template <>                                                                 \
+    CK_TILE_HOST_DEVICE constexpr dtype_ type_convert<dtype_, stype_>(stype_ x) \
+    {                                                                           \
+        return sname_##_to_##dname_(x);                                         \
+    }
+
+CK_TILE_TYPE_CONVERT(float, float, fp16_t, fp16)
+CK_TILE_TYPE_CONVERT(float, float, bf16_t, bf16)
+CK_TILE_TYPE_CONVERT(float, float, fp8_t, fp8)
+CK_TILE_TYPE_CONVERT(float, float, bf8_t, bf8)
+
+CK_TILE_TYPE_CONVERT(fp16_t, fp16, float, float)
+CK_TILE_TYPE_CONVERT(bf16_t, bf16, float, float)
+CK_TILE_TYPE_CONVERT(fp8_t, fp8, float, float)
+CK_TILE_TYPE_CONVERT(bf8_t, bf8, float, float)
+
+CK_TILE_TYPE_CONVERT(float, float, int8_t, int8)
+CK_TILE_TYPE_CONVERT(int8_t, int8, float, float)
+
+#undef CK_TILE_TYPE_CONVERT
+#endif
+
+} // namespace ck_tile

include/ck_tile/core/numeric/vector_type.hpp

@@ -0,0 +1,240 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2025, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/container/array.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/numeric/float8.hpp"
+#include "ck_tile/core/numeric/half.hpp"
+#include "ck_tile/core/numeric/bfloat16.hpp"
+#include "ck_tile/core/numeric/pk_int4.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+
+namespace ck_tile {
+
+// this structure is used to pick up the <base> type inside
+// using xxx = <base> __attribute__((ext_vector_type(N)));
+// because clang only allow native type + bool in this term (custom type will fail)
+// overload this structure to let proper <base> type
+
+template <typename T>
+struct native_t
+{
+    using type = remove_cvref_t<T>;
+};
+
+// we name this as ext_vector purposely, because clang ext_vector_type extention only accept literay
+// basic type to construct a ext_vector_type you must be very careful using this, or will have lot
+// of compiler errors e.g. struct A; using Ax2_t = A __attribute__((ext_vector_type(2)));  -> will
+// have compiler error
+namespace impl {
+
+template <typename T_, index_t N_, typename = void>
+struct ext_vector;
+
+template <typename T_, index_t N_>
+struct ext_vector<T_, N_, std::enable_if_t<!std::is_class_v<typename native_t<T_>::type>>>
+{
+    static constexpr index_t N = N_;
+    // struct type is not supported for ext_vector
+    using value_type = typename native_t<T_>::type;
+    static_assert(!std::is_class_v<value_type>);
+    using type = value_type __attribute__((ext_vector_type(N))); // this is danguous
+};
+
+template <typename T_, index_t N_>
+struct ext_vector<T_, N_, std::enable_if_t<std::is_class_v<typename native_t<T_>::type>>>
+{
+    static constexpr index_t N = N_;
+    // struct type is not supported for ext_vector
+    using value_type = typename native_t<T_>::type::type;
+    static_assert(!std::is_class_v<value_type>);
+    using type = value_type __attribute__((ext_vector_type(N))); // this is danguous
+};
+
+template <typename V_, index_t Vs_, index_t N_>
+struct ext_vector<V_ __attribute__((ext_vector_type(Vs_))),
+                  N_,
+                  std::enable_if_t<!std::is_class_v<typename native_t<V_>::type>>>
+{
+    static constexpr index_t N = Vs_ * N_;
+    using value_type           = typename native_t<remove_cvref_t<V_>>::type;
+    static_assert(!std::is_class_v<value_type>);
+    using type = value_type __attribute__((ext_vector_type(N))); // this is danguous
+};
+
+template <typename V_, index_t Vs_, index_t N_>
+struct ext_vector<V_ __attribute__((ext_vector_type(Vs_))),
+                  N_,
+                  std::enable_if_t<std::is_class_v<typename native_t<V_>::type>>>
+{
+    static constexpr index_t N = Vs_ * N_;
+    using value_type           = typename native_t<remove_cvref_t<V_>>::type::type;
+    static_assert(!std::is_class_v<value_type>);
+    using type = value_type __attribute__((ext_vector_type(N))); // this is danguous
+};
+
+} // namespace impl
+
+template <typename T, index_t N>
+using ext_vector_t = typename impl::ext_vector<T, N>::type;
+
+// by default, any type will result in a vector_size=1 with scalar_type=T traits.
+// ... unless we have other vector_traits specialization
+template <typename T, typename>
+struct vector_traits
+{
+    using scalar_type =
+        std::conditional_t<std::is_same_v<remove_cvref_t<T>, pk_int4_t>, int8_t, remove_cvref_t<T>>;
+    static constexpr index_t vector_size = 1;
+};
+
+// specialization for ext_vector_type()
+template <typename T, index_t N>
+struct vector_traits<T __attribute__((ext_vector_type(N)))>
+{
+    using scalar_type = std::conditional_t<std::is_same_v<T, pk_int4_t>, int8_t, T>;
+    static constexpr index_t vector_size = N;
+};
+
+template <typename X, typename Y>
+using has_same_scalar_type = std::is_same<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                          typename vector_traits<remove_cvref_t<Y>>::scalar_type>;
+
+// below are some pre-defines of ext_vector_type
+// attention! 2 vector type could be just the same type
+// fp64
+using fp64_t   = double;
+using fp64x2_t = double __attribute__((ext_vector_type(2)));
+using fp64x4_t = double __attribute__((ext_vector_type(4)));
+
+// fp32
+using fp32_t    = float;
+using fp32x2_t  = float __attribute__((ext_vector_type(2)));
+using fp32x4_t  = float __attribute__((ext_vector_type(4)));
+using fp32x8_t  = float __attribute__((ext_vector_type(8)));
+using fp32x16_t = float __attribute__((ext_vector_type(16)));
+using fp32x32_t = float __attribute__((ext_vector_type(32)));
+using fp32x64_t = float __attribute__((ext_vector_type(64)));
+
+// fp16
+// using fp16_t = ...
+using fp16x2_t  = _Float16 __attribute__((ext_vector_type(2)));
+using fp16x4_t  = _Float16 __attribute__((ext_vector_type(4)));
+using fp16x8_t  = _Float16 __attribute__((ext_vector_type(8)));
+using fp16x16_t = _Float16 __attribute__((ext_vector_type(16)));
+using fp16x32_t = _Float16 __attribute__((ext_vector_type(32)));
+using fp16x64_t = _Float16 __attribute__((ext_vector_type(64)));
+
+// bf16
+// using bf16_t = ...
+using bf16x2_t  = bf16_raw_t __attribute__((ext_vector_type(2)));
+using bf16x4_t  = bf16_raw_t __attribute__((ext_vector_type(4)));
+using bf16x8_t  = bf16_raw_t __attribute__((ext_vector_type(8)));
+using bf16x16_t = bf16_raw_t __attribute__((ext_vector_type(16)));
+using bf16x32_t = bf16_raw_t __attribute__((ext_vector_type(32)));
+using bf16x64_t = bf16_raw_t __attribute__((ext_vector_type(64)));
+
+// i32
+// using int32_t = ...
+using int32x2_t  = int32_t __attribute__((ext_vector_type(2)));
+using int32x4_t  = int32_t __attribute__((ext_vector_type(4)));
+using int32x8_t  = int32_t __attribute__((ext_vector_type(8)));
+using int32x16_t = int32_t __attribute__((ext_vector_type(16)));
+using int32x32_t = int32_t __attribute__((ext_vector_type(32)));
+using int32x64_t = int32_t __attribute__((ext_vector_type(64)));
+
+// u32
+// using uint32_t = ...
+using uint32x2_t  = uint32_t __attribute__((ext_vector_type(2)));
+using uint32x4_t  = uint32_t __attribute__((ext_vector_type(4)));
+using uint32x8_t  = uint32_t __attribute__((ext_vector_type(8)));
+using uint32x16_t = uint32_t __attribute__((ext_vector_type(16)));
+using uint32x32_t = uint32_t __attribute__((ext_vector_type(32)));
+using uint32x64_t = uint32_t __attribute__((ext_vector_type(64)));
+
+// i16
+// using int16_t = ...
+using int16x2_t  = int16_t __attribute__((ext_vector_type(2)));
+using int16x4_t  = int16_t __attribute__((ext_vector_type(4)));
+using int16x8_t  = int16_t __attribute__((ext_vector_type(8)));
+using int16x16_t = int16_t __attribute__((ext_vector_type(16)));
+using int16x32_t = int16_t __attribute__((ext_vector_type(32)));
+using int16x64_t = int16_t __attribute__((ext_vector_type(64)));
+
+// u16
+// using uint16_t
+using uint16x2_t  = uint16_t __attribute__((ext_vector_type(2)));
+using uint16x4_t  = uint16_t __attribute__((ext_vector_type(4)));
+using uint16x8_t  = uint16_t __attribute__((ext_vector_type(8)));
+using uint16x16_t = uint16_t __attribute__((ext_vector_type(16)));
+using uint16x32_t = uint16_t __attribute__((ext_vector_type(32)));
+using uint16x64_t = uint16_t __attribute__((ext_vector_type(64)));
+
+// i8
+// using int8_t
+using int8x2_t  = int8_t __attribute((ext_vector_type(2)));
+using int8x4_t  = int8_t __attribute((ext_vector_type(4)));
+using int8x8_t  = int8_t __attribute((ext_vector_type(8)));
+using int8x16_t = int8_t __attribute((ext_vector_type(16)));
+using int8x32_t = int8_t __attribute((ext_vector_type(32)));
+using int8x64_t = int8_t __attribute((ext_vector_type(64)));
+
+// ui8
+// using uint8_t
+using uint8x2_t  = uint8_t __attribute((ext_vector_type(2)));
+using uint8x4_t  = uint8_t __attribute((ext_vector_type(4)));
+using uint8x8_t  = uint8_t __attribute((ext_vector_type(8)));
+using uint8x16_t = uint8_t __attribute((ext_vector_type(16)));
+using uint8x32_t = uint8_t __attribute((ext_vector_type(32)));
+using uint8x64_t = uint8_t __attribute((ext_vector_type(64)));
+
+#if CK_TILE_USE_CUSTOM_DATA_TYPE
+// f8
+// using fp8_t
+using fp8x2_t  = fp8_raw_t __attribute((ext_vector_type(2)));
+using fp8x4_t  = fp8_raw_t __attribute((ext_vector_type(4)));
+using fp8x8_t  = fp8_raw_t __attribute((ext_vector_type(8)));
+using fp8x16_t = fp8_raw_t __attribute((ext_vector_type(16)));
+using fp8x32_t = fp8_raw_t __attribute((ext_vector_type(32)));
+using fp8x64_t = fp8_raw_t __attribute((ext_vector_type(64)));
+
+// bf8
+// using bf8_t
+using bf8x2_t  = bf8_raw_t __attribute((ext_vector_type(2)));
+using bf8x4_t  = bf8_raw_t __attribute((ext_vector_type(4)));
+using bf8x8_t  = bf8_raw_t __attribute((ext_vector_type(8)));
+using bf8x16_t = bf8_raw_t __attribute((ext_vector_type(16)));
+using bf8x32_t = bf8_raw_t __attribute((ext_vector_type(32)));
+using bf8x64_t = bf8_raw_t __attribute((ext_vector_type(64)));
+#else
+// f8
+// using fp8_t
+using fp8x2_t  = fp8_t __attribute((ext_vector_type(2)));
+using fp8x4_t  = fp8_t __attribute((ext_vector_type(4)));
+using fp8x8_t  = fp8_t __attribute((ext_vector_type(8)));
+using fp8x16_t = fp8_t __attribute((ext_vector_type(16)));
+using fp8x32_t = fp8_t __attribute((ext_vector_type(32)));
+using fp8x64_t = fp8_t __attribute((ext_vector_type(64)));
+
+// bf8
+// using bf8_t
+using bf8x2_t  = bf8_t __attribute((ext_vector_type(2)));
+using bf8x4_t  = bf8_t __attribute((ext_vector_type(4)));
+using bf8x8_t  = bf8_t __attribute((ext_vector_type(8)));
+using bf8x16_t = bf8_t __attribute((ext_vector_type(16)));
+using bf8x32_t = bf8_t __attribute((ext_vector_type(32)));
+using bf8x64_t = bf8_t __attribute((ext_vector_type(64)));
+#endif
+
+// pk_int4_t
+// using pk_int4_t
+using pk_int4x2_t  = int8_t __attribute((ext_vector_type(2)));
+using pk_int4x4_t  = int8_t __attribute((ext_vector_type(4)));
+using pk_int4x8_t  = int8_t __attribute((ext_vector_type(8)));
+using pk_int4x16_t = int8_t __attribute((ext_vector_type(16)));
+using pk_int4x32_t = int8_t __attribute((ext_vector_type(32)));
+} // namespace ck_tile

include/ck_tile/core/tensor/load_tile.hpp

@@ -0,0 +1,203 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/algorithm/coordinate_transform.hpp"
+#include "ck_tile/core/container/container_helper.hpp"
+#include "ck_tile/core/numeric/math.hpp"
+#include "ck_tile/core/tensor/tile_window.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+#include "ck_tile/core/tensor/tile_window.hpp"
+#include "ck_tile/core/tensor/tile_window_linear.hpp"
+#include "ck_tile/core/tensor/null_tile_window.hpp"
+#include "ck_tile/core/tensor/null_tensor.hpp"
+
+namespace ck_tile {
+
+template <typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          index_t NumCoord,
+          index_t i_access           = -1,
+          bool oob_conditional_check = true>
+CK_TILE_DEVICE auto load_tile(const tile_window_with_static_distribution<BottomTensorView_,
+                                                                         WindowLengths_,
+                                                                         TileDistribution_,
+                                                                         NumCoord>& tile_window,
+                              number<i_access>                     = {},
+                              bool_constant<oob_conditional_check> = {})
+{
+    return tile_window.load(number<i_access>{}, bool_constant<oob_conditional_check>{});
+}
+
+template <typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          typename LinearBottomDims_,
+          index_t i_access           = -1,
+          bool oob_conditional_check = true>
+CK_TILE_DEVICE auto load_tile(const tile_window_linear<BottomTensorView_,
+                                                       WindowLengths_,
+                                                       TileDistribution_,
+                                                       LinearBottomDims_>& tile_window,
+                              number<i_access>                     = {},
+                              bool_constant<oob_conditional_check> = {})
+{
+    return tile_window.load(number<i_access>{}, bool_constant<oob_conditional_check>{});
+}
+
+template <typename DistributedTensor_,
+          typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          index_t NumCoord,
+          index_t i_access           = -1,
+          bool oob_conditional_check = true>
+CK_TILE_DEVICE auto load_tile(DistributedTensor_& dst_tile,
+                              const tile_window_with_static_distribution<BottomTensorView_,
+                                                                         WindowLengths_,
+                                                                         TileDistribution_,
+                                                                         NumCoord>& tile_window,
+                              number<i_access>                     = {},
+                              bool_constant<oob_conditional_check> = {})
+{
+    return tile_window.load(dst_tile, number<i_access>{}, bool_constant<oob_conditional_check>{});
+}
+
+template <typename DistributedTensor_,
+          typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          typename LinearBottomDims_,
+          index_t i_access           = -1,
+          bool oob_conditional_check = true>
+CK_TILE_DEVICE auto load_tile(DistributedTensor_& dst_tile,
+                              const tile_window_linear<BottomTensorView_,
+                                                       WindowLengths_,
+                                                       TileDistribution_,
+                                                       LinearBottomDims_>& tile_window,
+                              number<i_access>                     = {},
+                              bool_constant<oob_conditional_check> = {})
+{
+    return tile_window.load(dst_tile, number<i_access>{}, bool_constant<oob_conditional_check>{});
+}
+
+/**
+ * @brief Loads a tile of data using inline assembly.
+ *
+ * @note Bare in mind that loading data this way, you have to manually initialize your
+ *       thread buffer and synchronize load afterwards in order to make sure it's done before
+ *       using loaded data from registers
+ *       @see `tile_window_with_static_distribution::init_raw()` and `buffer_view.hpp`
+ *       @see  `buffer_load_fence()`
+ */
+template <typename T,
+          typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          index_t NumCoord,
+          index_t i_access           = -1,
+          bool oob_conditional_check = true,
+          bool pre_nop               = false>
+CK_TILE_DEVICE auto load_tile_raw(T& tile,
+                                  const tile_window_with_static_distribution<BottomTensorView_,
+                                                                             WindowLengths_,
+                                                                             TileDistribution_,
+                                                                             NumCoord>& tile_window,
+                                  number<i_access>                     = {},
+                                  bool_constant<oob_conditional_check> = {},
+                                  bool_constant<pre_nop>               = {})
+{
+    tile_window.load_raw(
+        tile, number<i_access>{}, bool_constant<oob_conditional_check>{}, bool_constant<pre_nop>{});
+}
+
+template <typename T,
+          typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          typename LinearBottomDims_,
+          index_t i_access           = -1,
+          bool oob_conditional_check = true,
+          bool pre_nop               = false>
+CK_TILE_DEVICE auto load_tile_raw(T& tile,
+                                  const tile_window_linear<BottomTensorView_,
+                                                           WindowLengths_,
+                                                           TileDistribution_,
+                                                           LinearBottomDims_>& tile_window,
+                                  number<i_access>                     = {},
+                                  bool_constant<oob_conditional_check> = {},
+                                  bool_constant<pre_nop>               = {})
+{
+    tile_window.load_raw(
+        tile, number<i_access>{}, bool_constant<oob_conditional_check>{}, bool_constant<pre_nop>{});
+}
+
+template <typename LdsTileWindow_,
+          typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          index_t NumCoord,
+          index_t i_access           = -1,
+          bool oob_conditional_check = true,
+          bool pre_nop               = false>
+CK_TILE_DEVICE auto
+async_load_tile_raw(LdsTileWindow_&& lds_tile,
+                    const tile_window_with_static_distribution<BottomTensorView_,
+                                                               WindowLengths_,
+                                                               TileDistribution_,
+                                                               NumCoord>& tile_window,
+                    number<i_access>                     = {},
+                    bool_constant<oob_conditional_check> = {},
+                    bool_constant<pre_nop>               = {})
+{
+    return tile_window.async_load_raw(lds_tile,
+                                      number<i_access>{},
+                                      bool_constant<oob_conditional_check>{},
+                                      bool_constant<pre_nop>{});
+}
+
+template <typename LdsTileWindow_,
+          typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          typename LinearBottomDims_,
+          index_t i_access           = -1,
+          bool oob_conditional_check = true,
+          bool pre_nop               = false>
+CK_TILE_DEVICE auto async_load_tile_raw(LdsTileWindow_&& lds_tile,
+                                        const tile_window_linear<BottomTensorView_,
+                                                                 WindowLengths_,
+                                                                 TileDistribution_,
+                                                                 LinearBottomDims_>& tile_window,
+                                        number<i_access>                     = {},
+                                        bool_constant<oob_conditional_check> = {},
+                                        bool_constant<pre_nop>               = {})
+{
+    return tile_window.async_load_raw(lds_tile,
+                                      number<i_access>{},
+                                      bool_constant<oob_conditional_check>{},
+                                      bool_constant<pre_nop>{});
+}
+
+CK_TILE_DEVICE auto async_load_fence(index_t cnt = 0)
+{
+    asm volatile("s_waitcnt vmcnt(%0)" : : "n"(cnt) : "memory");
+}
+
+template <typename WindowLengths>
+CK_TILE_DEVICE auto load_tile(const null_tile_window<WindowLengths>&)
+{
+    return null_tensor{};
+}
+
+template <typename T, typename WindowLengths>
+CK_TILE_DEVICE auto load_tile_raw(T& /*null_tile*/, const null_tile_window<WindowLengths>&)
+{
+}
+
+} // namespace ck_tile

include/ck_tile/core/tensor/null_tensor.hpp

@@ -0,0 +1,12 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+namespace ck_tile {
+
+struct null_tensor
+{
+};
+
+} // namespace ck_tile

include/ck_tile/core/tensor/null_tile_window.hpp

@@ -0,0 +1,97 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/numeric/math.hpp"
+#include "ck_tile/core/tensor/tile_window.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+#include "ck_tile/core/tensor/tensor_view.hpp"
+
+namespace ck_tile {
+
+// placeholder type if we want to opt-out a tile window parameter
+template <typename WindowLengths_>
+struct null_tile_window
+{
+    using BottomTensorView = null_tensor_view;
+    using WindowLengths    = remove_cvref_t<WindowLengths_>;
+
+    using BottomTensorIndex = array<index_t, WindowLengths::size()>;
+
+    CK_TILE_DEVICE constexpr null_tile_window() = default;
+
+    CK_TILE_DEVICE constexpr null_tile_window(const WindowLengths& window_lengths)
+        : window_lengths_{window_lengths}
+    {
+    }
+
+    CK_TILE_DEVICE constexpr auto get_window_lengths() const { return window_lengths_; }
+
+    CK_TILE_DEVICE constexpr auto get_bottom_tensor_view() const { return null_tensor_view{}; }
+
+    CK_TILE_DEVICE constexpr auto get_window_origin() const { return BottomTensorIndex{}; }
+
+    CK_TILE_DEVICE void init_raw() {}
+
+    WindowLengths window_lengths_;
+};
+
+// utility to check if this is a Null Tile Window
+namespace impl {
+template <typename>
+struct is_null_tile_window : public std::false_type
+{
+};
+
+template <typename T>
+struct is_null_tile_window<null_tile_window<T>> : public std::true_type
+{
+};
+} // namespace impl
+
+template <typename T>
+CK_TILE_DEVICE constexpr auto is_null_tile_window(const T&)
+{
+    return impl::is_null_tile_window<remove_cvref_t<T>>::value;
+}
+
+template <typename WindowLengths>
+CK_TILE_DEVICE constexpr auto make_null_tile_window(const WindowLengths& window_lengths)
+{
+    static_assert(ck_tile::is_known_at_compile_time<WindowLengths>::value,
+                  "wrong! lengths should be static");
+
+    return null_tile_window<remove_cvref_t<WindowLengths>>{window_lengths};
+}
+
+template <typename WindowLengths, typename... Ts>
+CK_TILE_DEVICE constexpr auto make_tile_window(null_tensor_view,
+                                               const WindowLengths& window_lengths,
+                                               const multi_index<WindowLengths::size()>& /*origin*/,
+                                               Ts&&...)
+{
+    static_assert(ck_tile::is_known_at_compile_time<WindowLengths>::value,
+                  "wrong! lengths should be static");
+
+    return null_tile_window<remove_cvref_t<WindowLengths>>{window_lengths};
+}
+
+template <typename WindowLengths, typename StaticTileDistribution>
+CK_TILE_DEVICE constexpr auto make_tile_window(const null_tile_window<WindowLengths>& t,
+                                               const StaticTileDistribution&)
+{
+    return t;
+}
+
+template <typename WindowLengths>
+CK_TILE_DEVICE void
+move_tile_window(null_tile_window<WindowLengths>&,
+                 const typename null_tile_window<WindowLengths>::BottomTensorIndex&)
+{
+}
+
+} // namespace ck_tile

include/ck_tile/core/tensor/shuffle_tile.hpp

@@ -0,0 +1,177 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/utility/functional.hpp"
+#include "ck_tile/core/algorithm/coordinate_transform.hpp"
+#include "ck_tile/core/algorithm/space_filling_curve.hpp"
+#include "ck_tile/core/container/container_helper.hpp"
+#include "ck_tile/core/container/thread_buffer.hpp"
+#include "ck_tile/core/container/statically_indexed_array.hpp"
+#include "ck_tile/core/numeric/math.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+#include "ck_tile/core/tensor/tile_elementwise.hpp"
+#include "ck_tile/core/utility/transpose_vectors.hpp"
+
+namespace ck_tile {
+namespace detail {
+
+template <typename OutTensor, typename InTensor>
+CK_TILE_DEVICE void shuffle_tile_impl_in_thread(OutTensor& out_tensor, const InTensor& in_tensor)
+{
+    constexpr auto I0 = number<0>{};
+
+    using DataType = typename InTensor::DataType;
+
+    constexpr auto y_in_desc  = InTensor::get_tile_distribution().get_ys_to_d_descriptor();
+    constexpr auto y_out_desc = OutTensor::get_tile_distribution().get_ys_to_d_descriptor();
+
+    // y_dim_out_to_in
+    constexpr auto get_rh_major_minor_to_y = [](auto dstr_tensor) {
+        using DstrEncode = typename decltype(dstr_tensor.get_tile_distribution())::DstrEncode;
+
+        map<array<index_t, 2>, index_t> rh_major_minor_to_y_;
+
+        static_for<0, DstrEncode::NDimY, 1>{}([&](auto i) {
+            constexpr index_t rh_major = DstrEncode::ys_to_rhs_major_[i];
+            constexpr index_t rh_minor = DstrEncode::ys_to_rhs_minor_[i];
+
+            rh_major_minor_to_y_({rh_major, rh_minor}) = i;
+        });
+
+        return rh_major_minor_to_y_;
+    };
+
+    constexpr auto rh_major_minor_to_y_in  = get_rh_major_minor_to_y(InTensor{});
+    constexpr auto rh_major_minor_to_y_out = get_rh_major_minor_to_y(OutTensor{});
+
+    constexpr auto y_dim_out_to_in = [&] {
+        map<index_t, index_t> y_dim_out_to_in_;
+
+        for(const auto& [rh_major_minor, y_out] : rh_major_minor_to_y_out)
+        {
+            y_dim_out_to_in_(y_out) = rh_major_minor_to_y_in[rh_major_minor];
+        }
+
+        return y_dim_out_to_in_;
+    }();
+
+    //
+    constexpr index_t NDimY = InTensor::get_tile_distribution().get_num_of_dimension_y();
+
+    constexpr auto y_lengths = to_sequence(y_in_desc.get_lengths());
+
+    // input and output vector dim in the order of input Y dims
+    constexpr index_t y_dim_vec_in  = NDimY - 1;
+    constexpr index_t y_dim_vec_out = y_dim_out_to_in[NDimY - 1];
+
+    // vector lengths
+    constexpr index_t vec_length_in  = y_lengths[y_dim_vec_in];
+    constexpr index_t vec_length_out = y_lengths[y_dim_vec_out];
+
+    // # of vectors
+    constexpr index_t num_vec_in  = vec_length_out;
+    constexpr index_t num_vec_out = vec_length_in;
+
+    using InVec  = array<DataType, vec_length_in>;
+    using OutVec = array<DataType, vec_length_out>;
+
+    // using InVec  = typename InVec::type;
+    // using OutVec = typename OutVec::type;
+
+    // SFC
+    constexpr auto scalars_per_access_arr = generate_array(
+        [&](auto i) { return (i == y_dim_vec_in or i == y_dim_vec_out) ? y_lengths[i] : 1; },
+        number<NDimY>{});
+
+    constexpr auto scalars_per_access = TO_SEQUENCE(scalars_per_access_arr, NDimY);
+
+    using SFC_Y = space_filling_curve<decltype(y_lengths),
+                                      typename arithmetic_sequence_gen<0, NDimY, 1>::type,
+                                      decltype(scalars_per_access)>;
+
+    constexpr index_t num_access = SFC_Y::get_num_of_access();
+
+    static_assert(num_access > 0, "wrong! num_access should be larger than 0");
+
+    // in/out vectors to be transposed
+    thread_buffer<InVec, num_vec_in> in_vectors;
+    thread_buffer<OutVec, num_vec_out> out_vectors;
+
+    // loop over SFC and do transpose
+    static_for<0, num_access, 1>{}([&](auto iAccess) {
+        // data index [y0, y1, ...] in the order of input tensor
+        constexpr auto idx_y_start = SFC_Y::get_index(iAccess);
+
+        // get input vectors
+        static_for<0, num_vec_in, 1>{}([&](auto i) {
+            constexpr auto idx_y_in = generate_tuple(
+                [&](auto ii) {
+                    return ii == y_dim_vec_out ? idx_y_start[ii] + i : idx_y_start[ii];
+                },
+                number<NDimY>{});
+
+            constexpr index_t in_offset = y_in_desc.calculate_offset(idx_y_in);
+            static_assert(in_offset % vec_length_in == 0);
+
+            in_vectors(i).template get_as<InVec>()(I0) =
+                in_tensor.get_thread_buffer()
+                    .template get_as<InVec>()[number<in_offset / vec_length_in>{}];
+        });
+
+        // transpose
+        transpose_vectors<DataType, num_vec_in, num_vec_out>{}(in_vectors, out_vectors);
+
+        // set output vectors
+        static_for<0, num_vec_out, 1>{}([&](auto i) {
+            constexpr auto idx_y_out_tmp = generate_array(
+                [&](auto ii) { return ii == y_dim_vec_in ? idx_y_start[ii] + i : idx_y_start[ii]; },
+                number<NDimY>{});
+
+            constexpr auto idx_y_out =
+                container_reorder_given_new2old(idx_y_out_tmp, y_dim_out_to_in);
+
+            constexpr index_t out_offset = y_out_desc.calculate_offset(idx_y_out);
+            static_assert(out_offset % vec_length_out == 0);
+
+            out_tensor.get_thread_buffer().template set_as<OutVec>(
+                number<out_offset / vec_length_out>{},
+                out_vectors[i].template get_as<OutVec>()[I0]);
+        });
+    });
+}
+
+} // namespace detail
+
+template <typename OutTensor, typename InTensor>
+CK_TILE_DEVICE void shuffle_tile(OutTensor& out, const InTensor& in)
+{
+    using InDataType  = typename InTensor::DataType;
+    using OutDataType = typename OutTensor::DataType;
+
+    using InDstrEncode  = typename InTensor::StaticTileDistribution::DstrEncode;
+    using OutDstrEncode = typename OutTensor::StaticTileDistribution::DstrEncode;
+
+    // type convert
+    const auto in_tmp = tile_elementwise_in(type_convert<OutDataType, InDataType>, in);
+
+    // shuffle
+    if constexpr(InDstrEncode::rs_lengths_ == OutDstrEncode::rs_lengths_ &&
+                 InDstrEncode::hs_lengthss_ == OutDstrEncode::hs_lengthss_ &&
+                 InDstrEncode::ps_to_rhss_major_ == OutDstrEncode::ps_to_rhss_major_ &&
+                 InDstrEncode::ps_to_rhss_minor_ == OutDstrEncode::ps_to_rhss_minor_ &&
+                 InDstrEncode::NDimY == OutDstrEncode::NDimY)
+    {
+        detail::shuffle_tile_impl_in_thread(out, in_tmp);
+    }
+    else
+    {
+        static_assert(false, "The shuffle should always happen!");
+    }
+}
+
+} // namespace ck_tile

include/ck_tile/core/tensor/slice_tile.hpp

@@ -0,0 +1,92 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/utility/functional.hpp"
+#include "ck_tile/core/algorithm/coordinate_transform.hpp"
+#include "ck_tile/core/container/container_helper.hpp"
+#include "ck_tile/core/numeric/math.hpp"
+#include "ck_tile/core/tensor/tile_window.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+
+namespace ck_tile {
+
+template <typename BottomTensorView_,
+          typename WindowLengths_,
+          index_t... SliceBegins,
+          index_t... SliceEnds>
+CK_TILE_DEVICE constexpr auto
+get_slice_tile(const tile_window_with_static_lengths<BottomTensorView_, WindowLengths_>& tile,
+               sequence<SliceBegins...> slice_begins,
+               sequence<SliceEnds...> slice_ends)
+{
+    using TileWindow = tile_window_with_static_lengths<BottomTensorView_, WindowLengths_>;
+    // NOTE: This API will override the origin of the tile window!
+    static_assert(sizeof...(SliceBegins) == sizeof...(SliceEnds));
+    static_assert(sizeof...(SliceBegins) == TileWindow::get_num_of_dimension());
+
+    constexpr auto slice_lengths = slice_ends - slice_begins;
+
+    return make_tile_window(tile.get_bottom_tensor_view(),
+                            sequence_to_tuple_of_number(slice_lengths),
+                            to_multi_index(slice_begins));
+}
+
+template <typename DataType_,
+          typename StaticTileDistribution_,
+          index_t... SliceBegins,
+          index_t... SliceEnds>
+CK_TILE_DEVICE constexpr auto
+get_slice_tile(const static_distributed_tensor<DataType_, StaticTileDistribution_>& tile,
+               sequence<SliceBegins...> slice_begins,
+               sequence<SliceEnds...> slice_ends)
+{
+    using DataType     = remove_cvref_t<DataType_>;
+    using Distribution = remove_cvref_t<StaticTileDistribution_>;
+
+    constexpr auto sliced_dstr_yidx_ylen =
+        detail::slice_distribution_from_x(Distribution{}, slice_begins, slice_ends);
+
+    constexpr auto sliced_dstr      = sliced_dstr_yidx_ylen.template at<0>();
+    constexpr auto sliced_y_origins = sliced_dstr_yidx_ylen.template at<1>();
+    constexpr auto sliced_y_lengths = sliced_dstr_yidx_ylen.template at<2>();
+
+    auto sliced_tensor = make_static_distributed_tensor<DataType>(sliced_dstr);
+
+    sliced_tensor.get_thread_buffer() =
+        tile.get_y_sliced_thread_data(sliced_y_origins, sliced_y_lengths);
+
+    return sliced_tensor;
+}
+
+template <typename DstDataType_,
+          typename DstStaticTileDistribution_,
+          typename SrcDataType_,
+          typename SrcStaticTileDistribution_,
+          index_t... SliceBegins,
+          index_t... SliceEnds>
+CK_TILE_DEVICE constexpr auto
+set_slice_tile(static_distributed_tensor<DstDataType_, DstStaticTileDistribution_>& dst_tile,
+               const static_distributed_tensor<SrcDataType_, SrcStaticTileDistribution_>& src_tile,
+               sequence<SliceBegins...> slice_begins,
+               sequence<SliceEnds...> slice_ends)
+{
+    using DstDistribution = remove_cvref_t<DstStaticTileDistribution_>;
+
+    constexpr auto sliced_dstr_yidx_ylen =
+        detail::slice_distribution_from_x(DstDistribution{}, slice_begins, slice_ends);
+
+    constexpr auto sliced_dstr      = sliced_dstr_yidx_ylen.template at<0>();
+    constexpr auto sliced_y_origins = sliced_dstr_yidx_ylen.template at<1>();
+    constexpr auto sliced_y_lengths = sliced_dstr_yidx_ylen.template at<2>();
+
+    static_assert(std::is_same_v<decltype(sliced_dstr), DstDistribution>, "wrong!");
+
+    dst_tile.SetSlicedThreadData(sliced_y_origins, sliced_y_lengths, src_tile.get_thread_buffer());
+}
+
+} // namespace ck_tile

include/ck_tile/core/tensor/static_distributed_tensor.hpp

@@ -0,0 +1,235 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2025, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/algorithm/coordinate_transform.hpp"
+#include "ck_tile/core/container/container_helper.hpp"
+#include "ck_tile/core/numeric/math.hpp"
+#include "ck_tile/core/utility/functional.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+#include "ck_tile/core/tensor/tile_distribution.hpp"
+#include "ck_tile/core/container/thread_buffer.hpp"
+
+namespace ck_tile {
+
+template <typename DataType_, typename StaticTileDistribution_>
+struct static_distributed_tensor
+{
+    using DataType               = remove_cvref_t<DataType_>;
+    using StaticTileDistribution = remove_cvref_t<StaticTileDistribution_>;
+
+    static_assert(StaticTileDistribution::is_static(),
+                  "wrong! StaticTileDistribution should be known at compile tile");
+
+    using ThreadTensorDesc =
+        remove_cvref_t<decltype(StaticTileDistribution{}.get_ys_to_d_descriptor())>;
+    static constexpr index_t PackedSize =
+        ck_tile::numeric_traits<remove_cvref_t<DataType>>::PackedSize;
+
+    static constexpr index_t kThreadElementSpaceSize = ThreadTensorDesc{}.get_element_space_size();
+    static_assert(0 < kThreadElementSpaceSize, "Make sure tile distribution is valid");
+
+    CK_TILE_HOST_DEVICE static constexpr auto get_num_of_dimension()
+    {
+        return StaticTileDistribution::get_num_of_dimension_x();
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr auto get_lengths()
+    {
+        return StaticTileDistribution::get_lengths();
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr auto get_tile_distribution()
+    {
+        return StaticTileDistribution{};
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr auto get_distributed_spans()
+    {
+        return StaticTileDistribution::get_distributed_spans();
+    }
+
+    CK_TILE_HOST_DEVICE void initialize(const DataType& x) { thread_buf_.initialize(x); }
+
+    CK_TILE_HOST_DEVICE constexpr const auto& get_thread_buffer() const { return thread_buf_; }
+
+    CK_TILE_HOST_DEVICE constexpr auto& get_thread_buffer() { return thread_buf_; }
+
+    CK_TILE_HOST_DEVICE static constexpr index_t get_thread_buffer_size()
+    {
+        return kThreadElementSpaceSize / PackedSize;
+    }
+
+    template <index_t... YSliceOrigins, index_t... YSliceLengths>
+    CK_TILE_HOST_DEVICE auto get_y_sliced_thread_data(sequence<YSliceOrigins...>,
+                                                      sequence<YSliceLengths...>) const
+    {
+        static_assert(sizeof...(YSliceOrigins) == StaticTileDistribution::NDimY &&
+                          sizeof...(YSliceLengths) == StaticTileDistribution::NDimY,
+                      "wrong!");
+
+        constexpr auto sliced_thread_tensor_desc =
+            make_naive_tensor_descriptor_packed(make_tuple(YSliceLengths...));
+
+        thread_buffer<DataType, sliced_thread_tensor_desc.get_element_space_size()>
+            sliced_thread_data;
+
+        static_ford<sequence<YSliceLengths...>>{}([&](auto idx) {
+            constexpr auto idx_ys = idx + sequence<YSliceOrigins...>{};
+
+            sliced_thread_data(
+                number<sliced_thread_tensor_desc.calculate_offset(idx) / PackedSize>{}) =
+                thread_buf_[number<ThreadTensorDesc{}.calculate_offset(idx_ys) / PackedSize>{}];
+        });
+
+        return sliced_thread_data;
+    }
+
+    template <index_t... YSliceOrigins, index_t... YSliceLengths, typename SlicedThreadData>
+    CK_TILE_HOST_DEVICE void set_y_sliced_thread_data(sequence<YSliceOrigins...>,
+                                                      sequence<YSliceLengths...>,
+                                                      const SlicedThreadData& sliced_thread_data)
+    {
+        static_assert(sizeof...(YSliceOrigins) == StaticTileDistribution::NDimY &&
+                          sizeof...(YSliceLengths) == StaticTileDistribution::NDimY,
+                      "wrong!");
+
+        constexpr auto sliced_thread_tensor_desc =
+            make_naive_tensor_descriptor_packed(make_tuple(YSliceLengths...));
+
+        static_ford<sequence<YSliceLengths...>>{}([&](auto idx) {
+            constexpr auto idx_ys = idx + sequence<YSliceOrigins...>{};
+
+            thread_buf_(number<ThreadTensorDesc{}.calculate_offset(idx_ys) / PackedSize>{}) =
+                sliced_thread_data[number<sliced_thread_tensor_desc.calculate_offset(idx) /
+                                          PackedSize>{}];
+        });
+    }
+
+    template <typename TileDistributedIndices>
+    CK_TILE_HOST_DEVICE constexpr const DataType& operator[](TileDistributedIndices) const
+    {
+        static_assert(is_static_v<TileDistributedIndices>,
+                      "wrong! Tile Distributed Indices should be static");
+
+        constexpr auto y_idx = get_tile_distribution().get_y_indices_from_distributed_indices(
+            TileDistributedIndices{});
+
+        return thread_buf_[number<ThreadTensorDesc{}.calculate_offset(y_idx) / PackedSize>{}];
+    }
+
+    template <typename TileDistributedIndices>
+    CK_TILE_HOST_DEVICE constexpr DataType& operator()(TileDistributedIndices)
+    {
+        static_assert(is_static_v<TileDistributedIndices>,
+                      "wrong! Tile Distributed Indices should be static");
+
+        constexpr auto y_idx = get_tile_distribution().get_y_indices_from_distributed_indices(
+            TileDistributedIndices{});
+
+        return thread_buf_(number<ThreadTensorDesc{}.calculate_offset(y_idx) / PackedSize>{});
+    }
+
+    //
+    thread_buffer<DataType, get_thread_buffer_size()> thread_buf_;
+};
+
+template <typename DataType, typename StaticTileDistribution>
+CK_TILE_HOST_DEVICE constexpr auto make_static_distributed_tensor(const StaticTileDistribution&)
+{
+    return static_distributed_tensor<remove_cvref_t<DataType>,
+                                     remove_cvref_t<StaticTileDistribution>>{};
+}
+
+template <typename DataType, typename StaticTileDistribution, typename ThreadBuffer>
+CK_TILE_HOST_DEVICE constexpr auto make_static_distributed_tensor(const StaticTileDistribution&,
+                                                                  ThreadBuffer&& thread_buffer_)
+{
+    return static_distributed_tensor<remove_cvref_t<DataType>,
+                                     remove_cvref_t<StaticTileDistribution>>{thread_buffer_};
+}
+
+// get X indices from tuple of tile_distributed_index<>
+template <typename StaticTileDistribution, typename DistributedIndices>
+CK_TILE_HOST_DEVICE constexpr auto
+get_x_indices_from_distributed_indices(StaticTileDistribution tile_distribution,
+                                       DistributedIndices distributed_indices)
+{
+    const auto partition_index = detail::get_partition_index(tile_distribution);
+    constexpr auto y_indices =
+        tile_distribution.get_y_indices_from_distributed_indices(distributed_indices);
+
+    const auto x_coord = make_tensor_adaptor_coordinate(
+        tile_distribution.get_ps_ys_to_xs_adaptor(),
+        container_concat(partition_index, to_array<ck_tile::index_t, y_indices.size()>(y_indices)));
+
+    return x_coord.get_bottom_index();
+}
+
+template <typename DataType, typename StaticTileDistribution, typename XIndicesPredicate>
+CK_TILE_HOST_DEVICE void
+set_tile_if(static_distributed_tensor<DataType, StaticTileDistribution>& out_tensor,
+            DataType value,
+            XIndicesPredicate predicate)
+{
+    constexpr auto out_spans =
+        static_distributed_tensor<DataType, StaticTileDistribution>::get_distributed_spans();
+    sweep_tile_span(out_spans[number<0>{}], [&](auto idx0) {
+        sweep_tile_span(out_spans[number<1>{}], [&](auto idx1) {
+            constexpr auto distributed_indices = make_tuple(idx0, idx1);
+            const auto x_indices = get_x_indices_from_distributed_indices(StaticTileDistribution{},
+                                                                          distributed_indices);
+
+            if(predicate(x_indices))
+            {
+                out_tensor(distributed_indices) = value;
+            }
+        });
+    });
+}
+
+// this function used inside span loop over
+template <typename YLengths, index_t XUnpacks>
+CK_TILE_HOST_DEVICE constexpr auto get_y_unpacks_from_x_unpacks(YLengths, number<XUnpacks>)
+{
+    constexpr auto y_size  = reduce_on_sequence(YLengths{}, multiplies{}, number<1>{});
+    constexpr auto y_packs = number<XUnpacks>{};
+    static_assert(y_size % y_packs == 0);
+    constexpr auto y_slice_size = y_size / y_packs;
+
+    constexpr auto slice_info = slice_sequence(YLengths{}, number<y_slice_size>{});
+    constexpr auto unpacks    = slice_info[number<1>{}];
+    return unpacks;
+}
+
+namespace detail {
+
+// check if 2 static_distributed_tensor has same data type and size of element
+// but only difference in distribution
+template <typename X, typename Y>
+struct is_similiar_distributed_tensor
+{
+    static constexpr bool value = false;
+};
+
+template <typename TypeX, typename DistX, typename TypeY, typename DistY>
+struct is_similiar_distributed_tensor<static_distributed_tensor<TypeX, DistX>,
+                                      static_distributed_tensor<TypeY, DistY>>
+{
+    using Tx                    = static_distributed_tensor<TypeX, DistX>;
+    using Ty                    = static_distributed_tensor<TypeY, DistY>;
+    static constexpr bool value = std::is_same_v<typename Tx::DataType, typename Ty::DataType> &&
+                                  Tx::get_thread_buffer_size() == Ty::get_thread_buffer_size();
+};
+
+template <typename X, typename Y>
+inline constexpr bool is_similiar_distributed_tensor_v =
+    is_similiar_distributed_tensor<X, Y>::value;
+
+} // namespace detail
+
+} // namespace ck_tile

include/ck_tile/core/tensor/store_tile.hpp

@@ -0,0 +1,120 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/algorithm/coordinate_transform.hpp"
+#include "ck_tile/core/container/container_helper.hpp"
+#include "ck_tile/core/numeric/math.hpp"
+#include "ck_tile/core/tensor/tile_window.hpp"
+#include "ck_tile/core/tensor/tile_window_linear.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+
+namespace ck_tile {
+
+template <typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          typename DataType_>
+CK_TILE_DEVICE void
+store_tile(tile_window_with_static_lengths<BottomTensorView_, WindowLengths_>& tile_window_tmp,
+           const static_distributed_tensor<DataType_, TileDistribution_>& dstr_tensor)
+{
+    using DataType = remove_cvref_t<typename BottomTensorView_::DataType>;
+    using TileDstr = remove_cvref_t<TileDistribution_>;
+
+    static_assert(std::is_same_v<remove_cvref_t<DataType_>, DataType>, "wrong!");
+
+    constexpr auto tile_dstr = TileDstr{};
+
+    auto tile_window = make_tile_window(tile_window_tmp.get_bottom_tensor_view(),
+                                        tile_window_tmp.get_window_lengths(),
+                                        tile_window_tmp.get_window_origin(),
+                                        tile_dstr);
+
+    tile_window.store(dstr_tensor);
+}
+
+template <typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          typename DataType_>
+CK_TILE_DEVICE void
+store_tile_raw(tile_window_with_static_lengths<BottomTensorView_, WindowLengths_>& tile_window_tmp,
+               const static_distributed_tensor<DataType_, TileDistribution_>& dstr_tensor)
+{
+    using DataType = remove_cvref_t<typename BottomTensorView_::DataType>;
+    using TileDstr = remove_cvref_t<TileDistribution_>;
+
+    static_assert(std::is_same_v<remove_cvref_t<DataType_>, DataType>, "wrong!");
+
+    constexpr auto tile_dstr = TileDstr{};
+
+    auto tile_window = make_tile_window(tile_window_tmp.get_bottom_tensor_view(),
+                                        tile_window_tmp.get_window_lengths(),
+                                        tile_window_tmp.get_window_origin(),
+                                        tile_dstr);
+
+    tile_window.store_raw(dstr_tensor);
+}
+
+template <typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          index_t NumCoord,
+          typename DataType_>
+CK_TILE_DEVICE void
+store_tile(tile_window_with_static_distribution<BottomTensorView_,
+                                                WindowLengths_,
+                                                TileDistribution_,
+                                                NumCoord>& tile_window,
+           const static_distributed_tensor<DataType_, TileDistribution_>& dstr_tensor)
+{
+    tile_window.store(dstr_tensor, number<-1>{});
+}
+
+template <typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          index_t NumCoord,
+          typename DataType_>
+CK_TILE_DEVICE void
+store_tile_raw(tile_window_with_static_distribution<BottomTensorView_,
+                                                    WindowLengths_,
+                                                    TileDistribution_,
+                                                    NumCoord>& tile_window,
+               const static_distributed_tensor<DataType_, TileDistribution_>& dstr_tensor)
+{
+    tile_window.store_raw(dstr_tensor, number<-1>{});
+}
+
+template <typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          typename LinearBottomDims_,
+          typename DataType_>
+CK_TILE_DEVICE void store_tile(
+    tile_window_linear<BottomTensorView_, WindowLengths_, TileDistribution_, LinearBottomDims_>&
+        tile_window,
+    const static_distributed_tensor<DataType_, TileDistribution_>& dstr_tensor)
+{
+    tile_window.store(dstr_tensor, number<-1>{});
+}
+
+template <typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          typename LinearBottomDims_,
+          typename DataType_>
+CK_TILE_DEVICE void store_tile_raw(
+    tile_window_linear<BottomTensorView_, WindowLengths_, TileDistribution_, LinearBottomDims_>&
+        tile_window,
+    const static_distributed_tensor<DataType_, TileDistribution_>& dstr_tensor)
+{
+    tile_window.store_raw(dstr_tensor, number<-1>{});
+}
+
+} // namespace ck_tile

include/ck_tile/core/tensor/sweep_tile.hpp

@@ -0,0 +1,308 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/tensor/tile_distribution.hpp"
+#include "ck_tile/core/utility/functional.hpp"
+#include "ck_tile/core/utility/functional_with_tuple.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+
+namespace ck_tile {
+
+// sweep over a span of a distribted tile and apply lambda function F
+template <typename TileDistributedSpan_, // tile_distributed_span<...>
+          typename F                     // signature: F(tile_distributed_index<...>)
+          >
+CK_TILE_DEVICE void sweep_tile_span(TileDistributedSpan_, const F& f)
+{
+    using DstrSpan = remove_cvref_t<TileDistributedSpan_>;
+
+    static_ford<typename DstrSpan::Impl>{}([&](auto dstr_idx_impl) {
+        constexpr auto dstr_idx = detail::make_tile_distributed_index(dstr_idx_impl);
+
+        f(dstr_idx);
+    });
+}
+
+// unpacked span, this version support span with unpack(multi-arg) functor
+//
+template <
+    typename TileDistributedSpan_, // tile_distributed_span<...>
+    typename F,                    // signature: F(tile_distributed_index<...>)
+    typename Unpacks = typename uniform_sequence_gen<TileDistributedSpan_::Impl::size(), 1>::type>
+CK_TILE_DEVICE void sweep_tile_uspan(TileDistributedSpan_, const F& f, Unpacks = {})
+{
+    using DstrSpan = remove_cvref_t<TileDistributedSpan_>;
+
+    static_uford<typename DstrSpan::Impl, Unpacks>{}(
+        [&](auto... dstr_idx_impl) { f(detail::make_tile_distributed_index(dstr_idx_impl)...); });
+}
+
+namespace impl {
+
+template <typename, typename, typename>
+struct sweep_tile_impl;
+
+template <typename DistributedTensor, typename UnpacksPerXDim, index_t I, index_t... Is>
+struct sweep_tile_impl<DistributedTensor, UnpacksPerXDim, sequence<I, Is...>>
+{
+    CK_TILE_HOST_DEVICE constexpr auto get_y_unpacks() const
+    {
+        constexpr auto spans     = DistributedTensor::get_distributed_spans();
+        constexpr auto y_lengths = typename decltype(spans[number<I>{}])::Impl{};
+        constexpr auto x_unpacks = number<UnpacksPerXDim{}.at(number<I>{})>{};
+        constexpr auto y_unpacks = get_y_unpacks_from_x_unpacks(y_lengths, x_unpacks);
+        return y_unpacks;
+    }
+    CK_TILE_HOST_DEVICE constexpr index_t get_num_of_access() const
+    {
+        constexpr auto spans = DistributedTensor::get_distributed_spans();
+        constexpr auto u =
+            static_uford<typename decltype(spans[number<I>{}])::Impl, decltype(get_y_unpacks())>{};
+        return u.get_num_of_access() *
+               sweep_tile_impl<DistributedTensor, UnpacksPerXDim, sequence<Is...>>{}
+                   .get_num_of_access();
+    }
+    template <typename F, typename SpanIdx>
+    CK_TILE_HOST_DEVICE constexpr void operator()(const F& f, const SpanIdx& span_idx) const
+    {
+        constexpr auto spans = DistributedTensor::get_distributed_spans();
+
+        sweep_tile_uspan(
+            spans[number<I>{}],
+            [&](auto... i_idx) {
+                const auto next_span_idx = embed_tuples(
+                    [&](auto si) { return make_tuple(concat_tuple(si, make_tuple(i_idx))...); },
+                    span_idx);
+                sweep_tile_impl<DistributedTensor, UnpacksPerXDim, sequence<Is...>>{}(
+                    f, next_span_idx);
+            },
+            get_y_unpacks());
+    }
+    template <typename F, typename SpanIdx, index_t i_access>
+    CK_TILE_HOST_DEVICE constexpr void
+    operator()(const F& f, const SpanIdx& span_idx, number<i_access>) const
+    {
+        constexpr auto spans = DistributedTensor::get_distributed_spans();
+        constexpr auto u =
+            static_uford<typename decltype(spans[number<I>{}])::Impl, decltype(get_y_unpacks())>{};
+        constexpr auto access_stride =
+            sweep_tile_impl<DistributedTensor, UnpacksPerXDim, sequence<Is...>>{}
+                .get_num_of_access();
+        constexpr auto curr_i_access = number<i_access / access_stride>{};
+        constexpr auto next_i_access = number<i_access % access_stride>{};
+        u(
+            [&](auto... i_idx) {
+                const auto next_span_idx = embed_tuples(
+                    [&](auto si) {
+                        return make_tuple(concat_tuple(
+                            si, make_tuple(detail::make_tile_distributed_index(i_idx)))...);
+                    },
+                    span_idx);
+                sweep_tile_impl<DistributedTensor, UnpacksPerXDim, sequence<Is...>>{}(
+                    f, next_span_idx, next_i_access);
+            },
+            curr_i_access);
+    }
+};
+
+template <typename DistributedTensor, typename UnpacksPerXDim>
+struct sweep_tile_impl<DistributedTensor, UnpacksPerXDim, sequence<>>
+{
+    CK_TILE_HOST_DEVICE constexpr index_t get_num_of_access() const { return 1; }
+    template <typename F, typename SpanIdx>
+    CK_TILE_HOST_DEVICE constexpr void operator()(const F& f, const SpanIdx& span_idx) const
+    {
+        unpack(f, span_idx);
+    }
+    template <typename F, typename SpanIdx, index_t i_access>
+    CK_TILE_HOST_DEVICE constexpr void
+    operator()(const F& f, const SpanIdx& span_idx, number<i_access>) const
+    {
+        unpack(f, span_idx);
+    }
+};
+
+template <typename, typename, typename>
+struct sweep_tile_impl_0;
+
+// TODO: support empty tuple to remove this "entry-point" like function
+template <typename DistributedTensor, typename UnpacksPerXDim, index_t I, index_t... Is>
+struct sweep_tile_impl_0<DistributedTensor, UnpacksPerXDim, sequence<I, Is...>>
+{
+    CK_TILE_HOST_DEVICE constexpr auto get_y_unpacks() const
+    {
+        constexpr auto spans     = DistributedTensor::get_distributed_spans();
+        constexpr auto y_lengths = typename decltype(spans[number<I>{}])::Impl{};
+        constexpr auto x_unpacks = number<UnpacksPerXDim{}.at(number<I>{})>{};
+        constexpr auto y_unpacks = get_y_unpacks_from_x_unpacks(y_lengths, x_unpacks);
+        return y_unpacks;
+    }
+    CK_TILE_HOST_DEVICE constexpr index_t get_num_of_access() const
+    {
+        constexpr auto spans = DistributedTensor::get_distributed_spans();
+        constexpr auto u =
+            static_uford<typename decltype(spans[number<I>{}])::Impl, decltype(get_y_unpacks())>{};
+        return u.get_num_of_access() *
+               sweep_tile_impl<DistributedTensor, UnpacksPerXDim, sequence<Is...>>{}
+                   .get_num_of_access();
+    }
+    template <typename F>
+    CK_TILE_HOST_DEVICE constexpr void operator()(const F& f) const
+    {
+        constexpr auto spans = DistributedTensor::get_distributed_spans();
+        sweep_tile_uspan(
+            spans[number<I>{}],
+            [&](auto... i_idx) {
+                constexpr auto next_span_idx = make_tuple(make_tuple(i_idx)...);
+                sweep_tile_impl<DistributedTensor, UnpacksPerXDim, sequence<Is...>>{}(
+                    f, next_span_idx);
+            },
+            get_y_unpacks());
+    }
+    template <typename F, index_t i_access>
+    CK_TILE_HOST_DEVICE constexpr void operator()(const F& f, number<i_access>) const
+    {
+        constexpr auto spans = DistributedTensor::get_distributed_spans();
+        constexpr auto u =
+            static_uford<typename decltype(spans[number<I>{}])::Impl, decltype(get_y_unpacks())>{};
+        constexpr auto access_stride =
+            sweep_tile_impl<DistributedTensor, UnpacksPerXDim, sequence<Is...>>{}
+                .get_num_of_access();
+        constexpr auto curr_i_access = number<i_access / access_stride>{};
+        constexpr auto next_i_access = number<i_access % access_stride>{};
+        u(
+            [&](auto... i_idx) {
+                constexpr auto next_span_idx =
+                    make_tuple(make_tuple(detail::make_tile_distributed_index(i_idx))...);
+                sweep_tile_impl<DistributedTensor, UnpacksPerXDim, sequence<Is...>>{}(
+                    f, next_span_idx, next_i_access);
+            },
+            curr_i_access);
+    }
+};
+
+} // namespace impl
+
+/*
+ * Enhanced sweep-tile utility, can control unpacks along each X-dim
+ * the lambda function argument is the distributed-idx, which can directly
+ * plugged into the distributed tensor as setter/getter
+ *
+ * e.g. below function, y with the type DistributedTensor, r is row scale
+ *
+ * // sweep tile 1 by 1
+ * sweep_tile<DistributedTensor>([&](auto idx) {
+ *     constexpr auto row_id = make_tuple(idx[number<0>{}]);
+ *     y(idx)                = y(idx) * r(row_id);
+ * });
+ *
+ * // sweep tile with 2 pixel from last dim each function call
+ * sweep_tile<DistributedTensor>(
+ *     [&](auto idx_0, auto idx_1) {
+ *         constexpr auto row_id = make_tuple(idx_0[number<0>{}]);
+ *         y(idx_0)              = y(idx_0) * r(row_id);
+ *         y(idx_1)              = y(idx_1) * r(row_id);
+ *     },
+ *     sequence<1, 2>{});
+ *
+ * // sweep tile with 2x2 pixel each function call
+ * sweep_tile<DistributedTensor>(
+ *     [&](auto idx_00, auto idx_01, auto idx_10, auto idx_11) {
+ *         constexpr auto row_id0 = make_tuple(idx_00[number<0>{}]);
+ *         constexpr auto row_id1 = make_tuple(idx_10[number<0>{}]);
+ *         y(idx_00)              = y(idx_00) * r(row_id0);
+ *         y(idx_01)              = y(idx_01) * r(row_id0);
+ *         y(idx_10)              = y(idx_10) * r(row_id1);
+ *         y(idx_11)              = y(idx_11) * r(row_id1);
+ *     },
+ *     sequence<2, 2>{});
+ *
+ * TODO: do we need constexpr? lambda function could be non-constexpr
+ */
+template <typename DistributedTensor,
+          typename F,
+          typename UnpacksPerXDim =
+              typename uniform_sequence_gen<DistributedTensor::get_num_of_dimension(), 1>::type>
+CK_TILE_HOST_DEVICE constexpr void sweep_tile(const F& f, UnpacksPerXDim = {})
+{
+    constexpr auto spans = DistributedTensor::get_distributed_spans();
+
+    impl::sweep_tile_impl_0<DistributedTensor,
+                            UnpacksPerXDim,
+                            typename arithmetic_sequence_gen<0, spans.size(), 1>::type>{}(f);
+}
+
+template <typename DistributedTensor,
+          typename F,
+          typename UnpacksPerXDim =
+              typename uniform_sequence_gen<DistributedTensor::get_num_of_dimension(), 1>::type>
+CK_TILE_HOST_DEVICE constexpr void
+sweep_tile(const DistributedTensor&, const F& f, UnpacksPerXDim = {})
+{
+    sweep_tile<DistributedTensor, F, UnpacksPerXDim>(f, UnpacksPerXDim{});
+}
+
+/*
+ * construct a sweep tile instance, which support issue the lambda one by one
+ * Note that this struct will hold the lambda functor, but will not hold the distributed tensor
+ * the functionality is the same as sweep_tile()
+ */
+template <typename DistributedTensor_,
+          typename F_,
+          typename UnpacksPerXDim_ =
+              typename uniform_sequence_gen<DistributedTensor_::get_num_of_dimension(), 1>::type>
+struct tile_sweeper
+{
+    using DistributedTensor = remove_cvref_t<DistributedTensor_>;
+    using F                 = remove_cvref_t<F_>;
+    using UnpacksPerXDim    = remove_cvref_t<UnpacksPerXDim_>;
+
+    CK_TILE_HOST_DEVICE tile_sweeper(const F& f_, UnpacksPerXDim = {}) : f(f_) {}
+    CK_TILE_HOST_DEVICE tile_sweeper(const DistributedTensor&, const F& f_, UnpacksPerXDim = {})
+        : f(f_)
+    {
+    }
+    CK_TILE_HOST_DEVICE static constexpr index_t get_num_of_access()
+    {
+        constexpr auto spans = DistributedTensor::get_distributed_spans();
+        constexpr auto tmp =
+            impl::sweep_tile_impl_0<DistributedTensor,
+                                    UnpacksPerXDim,
+                                    typename arithmetic_sequence_gen<0, spans.size(), 1>::type>{};
+        return tmp.get_num_of_access();
+    }
+
+    CK_TILE_HOST_DEVICE void operator()() const
+    {
+        sweep_tile<DistributedTensor>(f, UnpacksPerXDim{});
+    }
+
+    template <index_t i_access>
+    CK_TILE_HOST_DEVICE void operator()(number<i_access>) const
+    {
+        constexpr auto spans = DistributedTensor::get_distributed_spans();
+
+        impl::sweep_tile_impl_0<DistributedTensor,
+                                UnpacksPerXDim,
+                                typename arithmetic_sequence_gen<0, spans.size(), 1>::type>{}(
+            f, number<i_access>{});
+    }
+    F f;
+};
+
+// partial deduction is not allowed
+// template <typename T, typename F, typename U>
+// CK_TILE_HOST_DEVICE_EXTERN tile_sweeper(const F&, U = {})->tile_sweeper<T, F, U>;
+
+// deduction guide
+template <typename T,
+          typename F,
+          typename U = typename uniform_sequence_gen<T::get_num_of_dimension(), 1>::type>
+CK_TILE_HOST_DEVICE_EXTERN tile_sweeper(const T&, const F&, U = {})->tile_sweeper<T, F, U>;
+
+} // namespace ck_tile

include/ck_tile/core/tensor/tensor_adaptor.hpp

@@ -0,0 +1,945 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/algorithm/coordinate_transform.hpp"
+#include "ck_tile/core/container/container_helper.hpp"
+#include "ck_tile/core/numeric/math.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+#include "ck_tile/core/numeric/numeric.hpp"
+
+namespace ck_tile {
+
+// Transforms: Tuple<transforms...>
+// LowerDimensionHiddenIdss : Tuple<Sequence<...>, ...>
+// UpperDimensionHiddenIdss : Tuple<Sequence<...>, ...>
+// BottomDimensionHiddenIds : Sequence<...>
+// TopDimensionHiddenIds : Sequence<...>
+template <typename Transforms,
+          typename LowerDimensionHiddenIdss,
+          typename UpperDimensionHiddenIdss,
+          typename BottomDimensionHiddenIds,
+          typename TopDimensionHiddenIds>
+struct tensor_adaptor
+{
+    CK_TILE_HOST_DEVICE static constexpr index_t get_num_of_transform()
+    {
+        return Transforms::size();
+    }
+
+    CK_TILE_HOST_DEVICE constexpr const auto& get_transforms() const { return transforms_; }
+
+    CK_TILE_HOST_DEVICE static constexpr auto get_lower_dimension_hidden_idss()
+    {
+        return LowerDimensionHiddenIdss{};
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr auto get_upper_dimension_hidden_idss()
+    {
+        return UpperDimensionHiddenIdss{};
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr auto get_bottom_dimension_hidden_ids()
+    {
+        return BottomDimensionHiddenIds{};
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr auto get_top_dimension_hidden_ids()
+    {
+        return TopDimensionHiddenIds{};
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr auto initialize_element_size(const Transforms& transforms)
+    {
+        const auto lengths = generate_tuple(
+            [&](auto idim_top) {
+                constexpr index_t idim_hidden = TopDimensionHiddenIds::at(idim_top);
+
+                constexpr auto tmp = get_transform_and_its_upper_dimension(number<idim_hidden>{});
+
+                constexpr index_t itran   = tmp[number<0>{}];
+                constexpr index_t idim_up = tmp[number<1>{}];
+                constexpr bool found      = tmp[number<2>{}];
+
+                static_assert(found == true,
+                              "wrong! not found matching transformation and upper-dimension");
+
+                const auto length =
+                    transforms[number<itran>{}].get_upper_lengths()[number<idim_up>{}];
+
+                return length;
+            },
+            number<ndim_top_>{});
+
+        // TODO: make container_reduce support tuple of number and index_t
+        return container_reduce(lengths, multiplies{}, number<1>{});
+    }
+
+    template <index_t IDimHidden>
+    CK_TILE_HOST_DEVICE static constexpr auto
+        get_transform_and_its_upper_dimension(number<IDimHidden>)
+    {
+        // FIXME: length of bottom dimension is not known, since info about lower dim length are not
+        // saved in transformation
+        static_assert(IDimHidden >= ndim_bottom_, "wrong! not implemented");
+
+        index_t itran_found   = 0;
+        index_t idim_up_found = 0;
+        bool found            = false;
+
+        static_for<0, ntransform_, 1>{}([&](auto itran) {
+            constexpr auto up_dim_ids = UpperDimensionHiddenIdss{}[itran];
+
+            static_for<0, up_dim_ids.size(), 1>{}([&](auto idim_up) {
+                if constexpr(up_dim_ids[idim_up] == IDimHidden)
+                {
+                    itran_found   = itran;
+                    idim_up_found = idim_up;
+                    found         = true;
+                }
+            });
+        });
+
+        return make_tuple(itran_found, idim_up_found, found);
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr index_t get_num_of_bottom_dimension()
+    {
+        return BottomDimensionHiddenIds::size();
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr index_t get_num_of_top_dimension()
+    {
+        return TopDimensionHiddenIds::size();
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr index_t get_num_of_hidden_dimension()
+    {
+        constexpr auto all_low_dim_ids = unpack(
+            [](auto&&... xs) constexpr { return merge_sequences(xs...); },
+            LowerDimensionHiddenIdss{});
+
+        constexpr auto all_up_dim_ids = unpack(
+            [](auto&&... xs) constexpr { return merge_sequences(xs...); },
+            UpperDimensionHiddenIdss{});
+
+        constexpr auto all_dim_ids = merge_sequences(all_low_dim_ids, all_up_dim_ids);
+
+        using unique_sort_all_dim_ids = typename sequence_unique_sort<decltype(all_dim_ids),
+                                                                      less<index_t>,
+                                                                      equal<index_t>>::type;
+
+        return unique_sort_all_dim_ids::size();
+    }
+
+    constexpr static index_t ntransform_  = get_num_of_transform();
+    constexpr static index_t ndim_hidden_ = get_num_of_hidden_dimension();
+    constexpr static index_t ndim_bottom_ = get_num_of_bottom_dimension();
+    constexpr static index_t ndim_top_    = get_num_of_top_dimension();
+
+    using HiddenIndex = multi_index<ndim_hidden_>;
+    using BottomIndex = multi_index<ndim_bottom_>;
+    using TopIndex    = multi_index<ndim_top_>;
+
+    // may be index_t or number<>
+    using ElementSize = remove_cv_t<decltype(initialize_element_size(Transforms{}))>;
+
+    public:
+    CK_TILE_HOST_DEVICE constexpr tensor_adaptor() = default;
+
+    CK_TILE_HOST_DEVICE constexpr tensor_adaptor(const Transforms& transforms)
+        : transforms_{transforms}, element_size_{initialize_element_size(transforms)}
+    {
+        static_assert(Transforms::size() == ntransform_ &&
+                          LowerDimensionHiddenIdss::size() == ntransform_ &&
+                          UpperDimensionHiddenIdss::size() == ntransform_,
+                      "wrong! inconsistent # of transformations");
+
+        // TODO check dependency of dimensions is valid
+    }
+
+    CK_TILE_HOST_DEVICE constexpr auto get_element_size() const { return element_size_; }
+
+    // FIXME: this logic is wrong when getting bottome dimension lengths
+    template <index_t IDimHidden>
+    CK_TILE_HOST_DEVICE constexpr auto get_hidden_dimension_length(number<IDimHidden>) const
+    {
+        static_assert(IDimHidden >= 0 && IDimHidden < ndim_hidden_, "wrong! out of range");
+
+        constexpr auto tmp = get_transform_and_its_upper_dimension(number<IDimHidden>{});
+
+        constexpr index_t itran   = tmp[number<0>{}];
+        constexpr index_t idim_up = tmp[number<1>{}];
+        constexpr bool found      = tmp[number<2>{}];
+
+        static_assert(found == true,
+                      "wrong! not found matching transformation and upper-dimension");
+
+        return transforms_[number<itran>{}].get_upper_lengths()[number<idim_up>{}];
+    }
+
+    template <index_t IDimTop>
+    CK_TILE_HOST_DEVICE constexpr auto get_top_dimension_length(number<IDimTop> idim_top) const
+    {
+        return get_hidden_dimension_length(TopDimensionHiddenIds::at(idim_top));
+    }
+
+#if 0
+    // FIXME: get_hidden_dimension_length is wrong when getting bottome dimension lengths
+    template <index_t IDimBottom>
+    CK_TILE_HOST_DEVICE constexpr index_t
+    get_bottom_dimension_length(number<IDimBottom> idim_bottom) const
+    {
+        return get_hidden_dimension_length(TopDimensionHiddenIds::at(idim_bottom));
+    }
+#endif
+
+    CK_TILE_HOST_DEVICE constexpr auto get_top_dimension_lengths() const
+    {
+        return generate_tuple([&](auto i) { return get_top_dimension_length(i); },
+                              number<ndim_top_>{});
+    }
+
+#if 0
+    // FIXME: get_hidden_dimension_length is wrong when getting bottome dimension lengths
+    CK_TILE_HOST_DEVICE constexpr auto GetBottomDimensionLengths() const
+    {
+        return generate_tuple([&](auto i) { return get_bottom_dimension_length(i); },
+                              number<ndim_bottom_>{});
+    }
+#endif
+
+    template <typename TopIdx>
+    CK_TILE_HOST_DEVICE constexpr auto calculate_bottom_index(const TopIdx& idx_top) const
+    {
+        static_assert(TopIdx::size() == TopDimensionHiddenIds::size(),
+                      "wrong! # of dimension inconsistent");
+
+        constexpr index_t ntransform  = get_num_of_transform();
+        constexpr index_t ndim_hidden = get_num_of_hidden_dimension();
+
+        multi_index<ndim_hidden> idx_hidden;
+
+        // initialize uppest index
+        set_container_subset(idx_hidden, get_top_dimension_hidden_ids(), idx_top);
+
+        // calculate hidden index
+        static_for<ntransform, 0, -1>{}([&](auto itran_p1) {
+            auto itran              = itran_p1 - number<1>{};
+            const auto& tran        = get_transforms().at(itran);
+            constexpr auto dims_low = get_lower_dimension_hidden_idss().at(itran);
+            constexpr auto dims_up  = get_upper_dimension_hidden_idss().at(itran);
+
+            const auto idx_up = get_container_subset(idx_hidden, dims_up);
+
+            multi_index<dims_low.size()> idx_low;
+
+            tran.calculate_lower_index(idx_low, idx_up);
+
+            set_container_subset(idx_hidden, dims_low, idx_low);
+        });
+
+        return get_container_subset(idx_hidden, BottomDimensionHiddenIds{});
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr bool is_static()
+    {
+        bool is_known = true;
+
+        static_for<0, Transforms::size(), 1>{}([&](auto i) {
+            is_known &= remove_cvref_t<decltype(Transforms{}[i])>::is_known_at_compile_time();
+        });
+
+        return is_known && ck_tile::is_known_at_compile_time<ElementSize>::value;
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr bool is_known_at_compile_time() { return is_static(); }
+
+    CK_TILE_HOST_DEVICE static constexpr auto get_top_dimension_safe_vector_length_strides(
+        const array<index_t, ndim_hidden_>& guaranteed_vector_lengths,
+        const array<index_t, ndim_hidden_>& guaranteed_vector_strides)
+    {
+        auto vector_lengths = guaranteed_vector_lengths;
+        auto vector_strides = guaranteed_vector_strides;
+
+        static_for<0, get_num_of_transform(), 1>{}([&](auto itran) {
+            constexpr auto low_dims = get_lower_dimension_hidden_idss().at(itran);
+            constexpr auto up_dims  = get_upper_dimension_hidden_idss().at(itran);
+
+            const auto up_guaranteed_vector_lengths =
+                get_container_subset(guaranteed_vector_lengths, up_dims);
+            const auto up_guaranteed_vector_strides =
+                get_container_subset(guaranteed_vector_strides, up_dims);
+
+            // only need type of transform
+            auto [up_vector_lengths, up_vector_strides] =
+                Transforms{}.at(itran).calculate_upper_dimension_safe_vector_length_strides(
+                    get_container_subset(vector_lengths, low_dims),
+                    get_container_subset(vector_strides, low_dims));
+
+            if constexpr(up_dims.size() > 0)
+            {
+                for(index_t i = 0; i < up_dims.size(); ++i)
+                {
+                    up_vector_lengths(i) = (up_guaranteed_vector_lengths[i] != -1)
+                                               ? up_guaranteed_vector_lengths[i]
+                                               : up_vector_lengths[i];
+
+                    up_vector_strides(i) = (up_guaranteed_vector_strides[i] != -1)
+                                               ? up_guaranteed_vector_strides[i]
+                                               : up_vector_strides[i];
+                }
+            }
+
+            set_container_subset(vector_lengths, up_dims, up_vector_lengths);
+            set_container_subset(vector_strides, up_dims, up_vector_strides);
+        });
+
+        constexpr auto top_dims = TopDimensionHiddenIds{};
+
+        return make_tuple(get_container_subset(vector_lengths, top_dims),
+                          get_container_subset(vector_strides, top_dims));
+    }
+
+    CK_TILE_HOST_DEVICE void print() const
+    {
+        printf("tensor_adaptor{");
+
+        //
+        printf("transforms: ");
+        print(transforms_);
+        printf(", ");
+
+        //
+        printf("LowerDimensionHiddenIds: ");
+        print(LowerDimensionHiddenIdss{});
+        printf(", ");
+
+        //
+        printf("UpperDimensionHiddenIds: ");
+        print(UpperDimensionHiddenIdss{});
+        printf(", ");
+
+        //
+        printf("BottomDimensionHiddenIds: ");
+        print(BottomDimensionHiddenIds{});
+        printf(", ");
+
+        //
+        printf("TopDimensionHiddenIds: ");
+        print(TopDimensionHiddenIds{});
+
+        printf("}");
+    }
+
+    private:
+    Transforms transforms_;
+    ElementSize element_size_;
+};
+
+// Transforms: Tuple<transforms...>
+// LowerDimensionOldTopIdss: Tuple<Sequence<...>, ...>
+// UpperDimensionNewTopIdss: Tuple<Sequence<...>, ...>
+template <typename Transforms, typename LowerDimensionOldTopIdss, typename UpperDimensionNewTopIdss>
+CK_TILE_HOST_DEVICE constexpr auto make_single_stage_tensor_adaptor(const Transforms& transforms,
+                                                                    LowerDimensionOldTopIdss,
+                                                                    UpperDimensionNewTopIdss)
+{
+    constexpr index_t ntransform = Transforms::size();
+
+    static_assert(LowerDimensionOldTopIdss::size() == ntransform &&
+                      UpperDimensionNewTopIdss::size() == ntransform,
+                  "wrong!");
+
+    // sanity check on LowerDimensionOldTopIdss and UpperDimensionNewTopIdss
+    constexpr auto all_low_dim_old_top_ids = unpack(
+        [](auto&&... xs) constexpr { return merge_sequences(xs...); }, LowerDimensionOldTopIdss{});
+
+    constexpr auto all_up_dim_new_top_ids = unpack(
+        [](auto&&... xs) constexpr { return merge_sequences(xs...); }, UpperDimensionNewTopIdss{});
+
+    static_assert(is_valid_sequence_map<decltype(all_low_dim_old_top_ids)>::value &&
+                      is_valid_sequence_map<decltype(all_up_dim_new_top_ids)>::value,
+                  "wrong!");
+
+    constexpr index_t ndim_old_top = all_low_dim_old_top_ids.size();
+    constexpr index_t ndim_new_top = all_up_dim_new_top_ids.size();
+
+    // low_dim_hidden_idss
+    constexpr auto low_dim_hidden_idss = LowerDimensionOldTopIdss{};
+
+    // up_dim_hidden_idss: shift UpperDimensionNewTopIdss by ndim_bottom
+    constexpr auto up_dim_hidden_idss = generate_tuple(
+        [](auto itran) { return UpperDimensionNewTopIdss{}[itran] + number<ndim_old_top>{}; },
+        number<ntransform>{});
+
+    // bottom_dim_hidden_ids
+    constexpr auto bottom_dim_hidden_ids =
+        typename arithmetic_sequence_gen<0, ndim_old_top, 1>::type{};
+
+    // top_dim_hidden_ids
+    constexpr auto top_dim_hidden_ids =
+        typename arithmetic_sequence_gen<0, ndim_new_top, 1>::type{} + number<ndim_old_top>{};
+
+    return tensor_adaptor<remove_cvref_t<Transforms>,
+                          remove_cvref_t<decltype(low_dim_hidden_idss)>,
+                          remove_cvref_t<decltype(up_dim_hidden_idss)>,
+                          remove_cvref_t<decltype(bottom_dim_hidden_ids)>,
+                          remove_cvref_t<decltype(top_dim_hidden_ids)>>{transforms};
+}
+
+// TODO: How to fix this? It uses an struct instead of lambda because lambda
+// doesn't have constructor, and to put it outside the scope where it is used
+// (transform_tensor_adaptor) because template cannot be defined inside a function
+// template
+template <typename NewTransforms>
+struct lambda_get_up_dim_num
+{
+    template <typename I>
+    CK_TILE_HOST_DEVICE constexpr auto operator()(I) const
+    {
+        using Tran = remove_reference_t<decltype(NewTransforms{}.at(I{}))>;
+        return number<Tran::get_num_of_upper_dimension()>{};
+    }
+};
+
+template <typename OldTensorAdaptor,
+          typename NewTransforms,
+          typename NewLowerDimensionOldTopIdss,
+          typename NewUpperDimensionNewTopIdss>
+CK_TILE_HOST_DEVICE constexpr auto
+transform_tensor_adaptor(const OldTensorAdaptor& old_tensor_adaptor,
+                         const NewTransforms& new_transforms,
+                         NewLowerDimensionOldTopIdss,
+                         NewUpperDimensionNewTopIdss)
+{
+    // sanity check
+    {
+        static_assert(NewTransforms::size() == NewLowerDimensionOldTopIdss::size() &&
+                          NewTransforms::size() == NewUpperDimensionNewTopIdss::size(),
+                      "wrong! inconsitent number of transform");
+
+        constexpr auto all_old_top_ids = unpack([](auto... xs) { return merge_sequences(xs...); },
+                                                NewLowerDimensionOldTopIdss{});
+
+        constexpr auto all_new_top_ids = unpack([](auto... xs) { return merge_sequences(xs...); },
+                                                NewUpperDimensionNewTopIdss{});
+
+        static_assert(is_valid_sequence_map<decltype(all_old_top_ids)>::value &&
+                          is_valid_sequence_map<decltype(all_new_top_ids)>::value,
+                      "wrong!");
+    }
+
+    // lower dimension's hidden idss
+    // convert lower dimension top idss (tuple of sequences) to hidden idss (tuple of
+    // sequences)
+    constexpr auto low_dim_hidden_idss = transform_tuples(
+        // convert lower dimension top ids (a sequence) to hidden ids (a sequence)
+        [](auto low_dim_top_ids) constexpr {
+            return transform_sequences(
+                // convert lower dimension top id to hidden id
+                [](auto low_dim_top_id) constexpr {
+                    return OldTensorAdaptor::get_top_dimension_hidden_ids()[low_dim_top_id];
+                },
+                low_dim_top_ids);
+        },
+        NewLowerDimensionOldTopIdss{});
+
+    constexpr index_t num_new_transform = NewTransforms::size();
+
+    // upper dimension's hidden idss
+    constexpr index_t old_hidden_dim_number = OldTensorAdaptor::get_num_of_hidden_dimension();
+
+    constexpr auto up_dim_numbers =
+        generate_sequence(lambda_get_up_dim_num<NewTransforms>{}, number<num_new_transform>{});
+
+    constexpr auto up_dim_numbers_scan = merge_sequences(
+        sequence<0>{}, inclusive_scan_sequence(up_dim_numbers, plus<index_t>{}, number<0>{}));
+
+    constexpr auto up_dim_hidden_idss = generate_tuple(
+        [ old_hidden_dim_number, up_dim_numbers_scan ](auto i) constexpr {
+            return
+                typename arithmetic_sequence_gen<old_hidden_dim_number + up_dim_numbers_scan[i],
+                                                 old_hidden_dim_number + up_dim_numbers_scan[i + 1],
+                                                 1>::type{};
+        },
+        number<num_new_transform>{});
+
+    // new top dimension's hidden ids
+    constexpr auto unordered_new_top_dim_hidden_ids = unpack(
+        [](auto... xs) constexpr { return merge_sequences(xs...); }, up_dim_hidden_idss);
+
+    constexpr auto new_top_dim_unordered2ordered = unpack(
+        [](auto... xs) constexpr { return merge_sequences(xs...); }, NewUpperDimensionNewTopIdss{});
+
+    constexpr auto new_top_dim_hidden_ids =
+        unordered_new_top_dim_hidden_ids.reorder_old_to_new(new_top_dim_unordered2ordered);
+
+    // put everything together
+    const auto all_transforms =
+        container_concat(old_tensor_adaptor.get_transforms(), new_transforms);
+
+    constexpr auto all_low_dim_hidden_idss =
+        container_concat(OldTensorAdaptor::get_lower_dimension_hidden_idss(), low_dim_hidden_idss);
+
+    constexpr auto all_up_dim_hidden_idss =
+        container_concat(OldTensorAdaptor::get_upper_dimension_hidden_idss(), up_dim_hidden_idss);
+
+    return tensor_adaptor<
+        remove_cvref_t<decltype(all_transforms)>,
+        remove_cvref_t<decltype(all_low_dim_hidden_idss)>,
+        remove_cvref_t<decltype(all_up_dim_hidden_idss)>,
+        remove_cvref_t<decltype(OldTensorAdaptor::get_bottom_dimension_hidden_ids())>,
+        remove_cvref_t<decltype(new_top_dim_hidden_ids)>>{all_transforms};
+}
+
+template <typename TensorAdaptor0, typename TensorAdaptor1>
+CK_TILE_HOST_DEVICE constexpr auto chain_tensor_adaptors(const TensorAdaptor0& adaptor0,
+                                                         const TensorAdaptor1& adaptor1)
+{
+    static_assert(TensorAdaptor0::get_num_of_top_dimension() ==
+                      TensorAdaptor1::get_num_of_bottom_dimension(),
+                  "wrong!");
+
+    // all_transforms = transform0 + transform1
+    const auto all_transforms =
+        container_concat(adaptor0.get_transforms(), adaptor1.get_transforms());
+
+    // shift
+    constexpr index_t adaptor0_max_hidden_id = [&]() {
+        index_t adaptor0_max_hidden_id_ = numeric<index_t>::min();
+
+        static_for<0, TensorAdaptor0::get_num_of_transform(), 1>{}([&](auto itran) {
+            constexpr index_t ndim_low =
+                TensorAdaptor0{}.get_transforms()[itran].get_num_of_lower_dimension();
+
+            static_for<0, ndim_low, 1>{}([&](auto idim_low) {
+                adaptor0_max_hidden_id_ =
+                    max(adaptor0_max_hidden_id_,
+                        TensorAdaptor0::get_lower_dimension_hidden_idss()[itran][idim_low].value);
+            });
+
+            constexpr index_t ndim_up =
+                TensorAdaptor0{}.get_transforms()[itran].get_num_of_upper_dimension();
+
+            static_for<0, ndim_up, 1>{}([&](auto idim_up) {
+                adaptor0_max_hidden_id_ =
+                    max(adaptor0_max_hidden_id_,
+                        TensorAdaptor0::get_upper_dimension_hidden_idss()[itran][idim_up].value);
+            });
+        });
+
+        return adaptor0_max_hidden_id_;
+    }();
+
+    constexpr index_t adaptor1_min_hidden_id = [&]() {
+        index_t adaptor1_min_hidden_id_ = numeric<index_t>::max();
+
+        static_for<0, TensorAdaptor1::get_num_of_transform(), 1>{}([&](auto itran) {
+            constexpr index_t ndim_low =
+                TensorAdaptor1{}.get_transforms()[itran].get_num_of_lower_dimension();
+
+            // get the min of all lower dimenions, but not bottom dimension (because their id will
+            // be matched with top id from adaptor0)
+            static_for<0, ndim_low, 1>{}([&](auto idim_low) {
+                constexpr index_t low_dim_hidden_id =
+                    TensorAdaptor1::get_lower_dimension_hidden_idss()[itran][idim_low].value;
+
+                bool is_bottom_dim = false;
+                static_for<0, TensorAdaptor1::get_num_of_bottom_dimension(), 1>{}([&](auto i) {
+                    if constexpr(low_dim_hidden_id ==
+                                 TensorAdaptor1::get_bottom_dimension_hidden_ids()[i])
+                    {
+                        is_bottom_dim = true;
+                    }
+                });
+
+                if(!is_bottom_dim)
+                {
+                    adaptor1_min_hidden_id_ = min(adaptor1_min_hidden_id_, low_dim_hidden_id);
+                }
+            });
+
+            constexpr index_t ndim_up =
+                TensorAdaptor1{}.get_transforms()[itran].get_num_of_upper_dimension();
+
+            // get the min of all upper dimensions
+            static_for<0, ndim_up, 1>{}([&](auto idim_up) {
+                adaptor1_min_hidden_id_ =
+                    min(adaptor1_min_hidden_id_,
+                        TensorAdaptor1::get_upper_dimension_hidden_idss()[itran][idim_up].value);
+            });
+        });
+
+        return adaptor1_min_hidden_id_;
+    }();
+
+    constexpr index_t adaptor1_hidden_id_shift =
+        adaptor0_max_hidden_id + 1 - adaptor1_min_hidden_id;
+
+    constexpr index_t ndim_bottom_1 = TensorAdaptor1::get_num_of_bottom_dimension();
+
+    // all_low_dim_hidden_idss =
+    // low_dim_hidden_idss_0 + match_hidden_id_for_1(shift_hidden_id_for_1(low_dim_hiden_idss_1))
+    constexpr auto low_dim_hidden_idss_1 = generate_tuple(
+        // generate sequence of ids for a transform
+        [&](auto itran) {
+            constexpr auto ndim_low_1 =
+                TensorAdaptor1::get_lower_dimension_hidden_idss()[itran].size();
+
+            constexpr auto low_dim_hidden_ids_1 =
+                TensorAdaptor1::get_lower_dimension_hidden_idss()[itran];
+
+            // sequence in, sequence out
+            constexpr auto low_dim_hidden_ids_1_mod = [&]() constexpr
+            {
+                auto low_dim_hidden_ids_1_mod_ = to_multi_index(low_dim_hidden_ids_1);
+
+                // shift hidden id so every dim id is unique
+                static_for<0, ndim_low_1, 1>{}([&](auto idim_low_1) {
+                    low_dim_hidden_ids_1_mod_(idim_low_1) += adaptor1_hidden_id_shift;
+                });
+
+                // match hidden id
+                static_for<0, ndim_low_1, 1>{}([&](auto idim_low_1) {
+                    static_for<0, ndim_bottom_1, 1>{}([&](auto idim_bottom_1) {
+                        // if this low dim is bottom dim, then do id matching
+                        if constexpr(low_dim_hidden_ids_1[idim_low_1] ==
+                                     TensorAdaptor1::get_bottom_dimension_hidden_ids()
+                                         [idim_bottom_1])
+                        {
+                            low_dim_hidden_ids_1_mod_(idim_low_1) =
+                                TensorAdaptor0::get_top_dimension_hidden_ids()[idim_bottom_1];
+                        }
+                    });
+                });
+
+                return low_dim_hidden_ids_1_mod_;
+            }
+            ();
+
+            return generate_sequence_v2(
+                [&](auto i) constexpr { return number<low_dim_hidden_ids_1_mod[i]>{}; },
+                number<ndim_low_1>{});
+        },
+        number<TensorAdaptor1::get_num_of_transform()>{});
+
+    constexpr auto all_low_dim_hidden_idss =
+        container_concat(TensorAdaptor0::get_lower_dimension_hidden_idss(), low_dim_hidden_idss_1);
+
+    // all_up_dim_hidden_idss =
+    // up_dim_hidden_idss_0 + shift_hidden_id_for_1(up_dim_hiden_idss_1)
+    constexpr auto up_dim_hidden_idss_1 = generate_tuple(
+        // generate sequence of ids for a transform
+        [&](auto itran) {
+            constexpr auto ndim_up_1 =
+                TensorAdaptor1::get_upper_dimension_hidden_idss()[itran].size();
+
+            constexpr auto up_dim_hidden_ids_1 =
+                TensorAdaptor1::get_upper_dimension_hidden_idss()[itran];
+
+            // sequence in, constexpr tuple out
+            constexpr auto up_dim_hidden_ids_1_mod = [&]() constexpr
+            {
+                auto up_dim_hidden_ids_1_mod_ = to_multi_index(up_dim_hidden_ids_1);
+
+                // shift hidden id
+                static_for<0, ndim_up_1, 1>{}([&](auto idim_up_1) {
+                    up_dim_hidden_ids_1_mod_(idim_up_1) += adaptor1_hidden_id_shift;
+                });
+
+                return up_dim_hidden_ids_1_mod_;
+            }
+            ();
+
+            // constexpr tuple to sequence
+            return generate_sequence_v2(
+                [&](auto i) constexpr { return number<up_dim_hidden_ids_1_mod[i]>{}; },
+                number<ndim_up_1>{});
+        },
+        number<TensorAdaptor1::get_num_of_transform()>{});
+
+    constexpr auto all_up_dim_hidden_idss =
+        container_concat(TensorAdaptor0::get_upper_dimension_hidden_idss(), up_dim_hidden_idss_1);
+
+    // bottom_dim_hidden_ids = bottom_dim_hidden_ids_0
+    constexpr auto bottom_dim_hidden_ids = TensorAdaptor0::get_bottom_dimension_hidden_ids();
+
+    // top_dim_hidden_ids = shift_hidden_id(top_dim_hidden_ids_1)
+    constexpr auto top_dim_hidden_ids =
+        TensorAdaptor1::get_top_dimension_hidden_ids() + number<adaptor1_hidden_id_shift>{};
+
+    // put everything together
+    return tensor_adaptor<remove_cvref_t<decltype(all_transforms)>,
+                          remove_cvref_t<decltype(all_low_dim_hidden_idss)>,
+                          remove_cvref_t<decltype(all_up_dim_hidden_idss)>,
+                          remove_cvref_t<decltype(bottom_dim_hidden_ids)>,
+                          remove_cvref_t<decltype(top_dim_hidden_ids)>>{all_transforms};
+}
+
+template <typename X,
+          typename... Xs,
+          typename std::enable_if<sizeof...(Xs) >= 2, bool>::type = false>
+CK_TILE_HOST_DEVICE constexpr auto chain_tensor_adaptors(const X& x, const Xs&... xs)
+{
+    return chain_tensor_adaptors(x, chain_tensor_adaptors(xs...));
+}
+
+} // namespace ck_tile
+
+// Macro function
+// construct constexpr tensor_adaptor from constexpr encoding
+// encoded_tensor_adaptor are Tuple of following objects:
+//    1. encoded transforms (array of fixed size). Each encoded transform is a Tuple of following:
+//           1.1 name (coord_transform_enum)
+//           1.2 meta data for constructor of the transform
+//           1.3 num of lower dimension (index_t)
+//           1.4 lower dimension Ids (array of fixed size)
+//           1.5 num of up dimension (index_t)
+//           1.6 upper dimension Ids (array of fixed size)
+//    2. num of transforms (index_t)
+//    3. encoded bottom dimension Ids (array of fixed size)
+//    4. num of bottom dimension (index_t)
+//    5. encoded top dimension Ids (array of fixed size)
+//    6. num of top dimension (index_t)
+#define CONSTRUCT_TENSOR_ADAPTOR_FROM_ENCODING(encoded_tensor_adaptor)                            \
+    [encoded_tensor_adaptor]() {                                                                  \
+        using namespace ck_tile;                                                                  \
+                                                                                                  \
+        constexpr auto encoded_transforms  = encoded_tensor_adaptor.template at<0>();             \
+        constexpr index_t num_transform    = encoded_tensor_adaptor.template at<1>();             \
+        constexpr auto encoded_bottom_dims = encoded_tensor_adaptor.template at<2>();             \
+        constexpr index_t num_bottom_dim   = encoded_tensor_adaptor.template at<3>();             \
+        constexpr auto encoded_top_dims    = encoded_tensor_adaptor.template at<4>();             \
+        constexpr index_t num_top_dim      = encoded_tensor_adaptor.template at<5>();             \
+                                                                                                  \
+        constexpr auto trans = [&encoded_transforms]() {                                          \
+            return generate_tuple(                                                                \
+                [&encoded_transforms](auto i) constexpr {                                         \
+                    constexpr auto name        = encoded_transforms[i].template at<0>();          \
+                    constexpr auto meta_data   = encoded_transforms[i].template at<1>();          \
+                    constexpr auto num_low_dim = encoded_transforms[i].template at<2>();          \
+                    constexpr auto num_up_dim  = encoded_transforms[i].template at<4>();          \
+                                                                                                  \
+                    static_assert(name == coord_transform_enum::pass_through ||                   \
+                                      name == coord_transform_enum::pad ||                        \
+                                      name == coord_transform_enum::embed ||                      \
+                                      name == coord_transform_enum::merge ||                      \
+                                      name == coord_transform_enum::unmerge ||                    \
+                                      name == coord_transform_enum::replicate,                    \
+                                  "");                                                            \
+                                                                                                  \
+                    if constexpr(name == coord_transform_enum::pass_through)                      \
+                    {                                                                             \
+                        index_t pos  = 0;                                                         \
+                        auto low_len = meta_data.template pop<index_t>(pos);                      \
+                                                                                                  \
+                        return make_pass_through_transform(low_len);                              \
+                    }                                                                             \
+                    else if constexpr(name == coord_transform_enum::pad)                          \
+                    {                                                                             \
+                        index_t pos    = 0;                                                       \
+                        auto low_len   = meta_data.template pop<index_t>(pos);                    \
+                        auto left_pad  = meta_data.template pop<index_t>(pos);                    \
+                        auto right_pad = meta_data.template pop<index_t>(pos);                    \
+                                                                                                  \
+                        return make_pad_transform(low_len, left_pad, right_pad);                  \
+                    }                                                                             \
+                    else if constexpr(name == coord_transform_enum::embed)                        \
+                    {                                                                             \
+                        index_t pos  = 0;                                                         \
+                        auto up_lens = meta_data.template pop<array<index_t, num_up_dim>>(pos);   \
+                        auto coefficients =                                                       \
+                            meta_data.template pop<array<index_t, num_up_dim>>(pos);              \
+                                                                                                  \
+                        return make_embed_transform(up_lens, coefficients);                       \
+                    }                                                                             \
+                    else if constexpr(name == coord_transform_enum::merge)                        \
+                    {                                                                             \
+                        index_t pos   = 0;                                                        \
+                        auto low_lens = meta_data.template pop<array<index_t, num_low_dim>>(pos); \
+                                                                                                  \
+                        return make_merge_transform(low_lens);                                    \
+                    }                                                                             \
+                    else if constexpr(name == coord_transform_enum::unmerge)                      \
+                    {                                                                             \
+                        index_t pos  = 0;                                                         \
+                        auto up_lens = meta_data.template pop<array<index_t, num_up_dim>>(pos);   \
+                                                                                                  \
+                        return make_unmerge_transform(up_lens);                                   \
+                    }                                                                             \
+                    else if constexpr(name == coord_transform_enum::replicate)                    \
+                    {                                                                             \
+                        index_t pos  = 0;                                                         \
+                        auto up_lens = meta_data.template pop<array<index_t, num_up_dim>>(pos);   \
+                                                                                                  \
+                        return make_replicate_transform(up_lens);                                 \
+                    }                                                                             \
+                },                                                                                \
+                number<num_transform>{});                                                         \
+        }();                                                                                      \
+                                                                                                  \
+        constexpr auto low_dim_idss = [&encoded_transforms, &num_transform]() {                   \
+            return generate_tuple(                                                                \
+                [&encoded_transforms](auto i) {                                                   \
+                    constexpr auto num_low_dim = encoded_transforms[i].template at<2>();          \
+                    constexpr auto low_dims    = encoded_transforms[i].template at<3>();          \
+                                                                                                  \
+                    return TO_SEQUENCE(low_dims, num_low_dim);                                    \
+                },                                                                                \
+                number<num_transform>());                                                         \
+        }();                                                                                      \
+                                                                                                  \
+        constexpr auto up_dim_idss = [&encoded_transforms, &num_transform] {                      \
+            return generate_tuple(                                                                \
+                [&encoded_transforms](auto i) {                                                   \
+                    constexpr auto num_up_dim = encoded_transforms[i].template at<4>();           \
+                    constexpr auto up_dims    = encoded_transforms[i].template at<5>();           \
+                                                                                                  \
+                    return TO_SEQUENCE(up_dims, num_up_dim);                                      \
+                },                                                                                \
+                number<num_transform>());                                                         \
+        }();                                                                                      \
+                                                                                                  \
+        constexpr auto bottom_dim_ids = TO_SEQUENCE(encoded_bottom_dims, num_bottom_dim);         \
+        constexpr auto top_dim_ids    = TO_SEQUENCE(encoded_top_dims, num_top_dim);               \
+                                                                                                  \
+        return tensor_adaptor<remove_cvref_t<decltype(trans)>,                                    \
+                              remove_cvref_t<decltype(low_dim_idss)>,                             \
+                              remove_cvref_t<decltype(up_dim_idss)>,                              \
+                              remove_cvref_t<decltype(bottom_dim_ids)>,                           \
+                              remove_cvref_t<decltype(top_dim_ids)>>{trans};                      \
+    }()
+
+// Macro function
+// construct static tensor_adaptor from constexpr encoding
+// encoded_tensor_adaptor are Tuple of following objects:
+//    1. encoded transforms (array of fixed size). Each encoded transform is a Tuple of following:
+//           1.1 name (coord_transform_enum)
+//           1.2 meta data for constructor of the transform
+//           1.3 num of lower dimension (index_t)
+//           1.4 lower dimension Ids (array of fixed size)
+//           1.5 num of up dimension (index_t)
+//           1.6 upper dimension Ids (array of fixed size)
+//    2. num of transforms (index_t)
+//    3. encoded bottom dimension Ids (array of fixed size)
+//    4. num of bottom dimension (index_t)
+//    5. encoded top dimension Ids (array of fixed size)
+//    6. num of top dimension (index_t)
+#define CONSTRUCT_STATIC_TENSOR_ADAPTOR_FROM_ENCODING(encoded_tensor_adaptor)                      \
+    [encoded_tensor_adaptor]() {                                                                   \
+        using namespace ck_tile;                                                                   \
+                                                                                                   \
+        constexpr auto encoded_transforms  = encoded_tensor_adaptor.template at<0>();              \
+        constexpr index_t num_transform    = encoded_tensor_adaptor.template at<1>();              \
+        constexpr auto encoded_bottom_dims = encoded_tensor_adaptor.template at<2>();              \
+        constexpr index_t num_bottom_dim   = encoded_tensor_adaptor.template at<3>();              \
+        constexpr auto encoded_top_dims    = encoded_tensor_adaptor.template at<4>();              \
+        constexpr index_t num_top_dim      = encoded_tensor_adaptor.template at<5>();              \
+                                                                                                   \
+        constexpr auto trans = [&encoded_transforms]() {                                           \
+            return generate_tuple(                                                                 \
+                [&encoded_transforms](auto i) constexpr {                                          \
+                    constexpr auto name        = encoded_transforms[i].template at<0>();           \
+                    constexpr auto meta_data   = encoded_transforms[i].template at<1>();           \
+                    constexpr auto num_low_dim = encoded_transforms[i].template at<2>();           \
+                    constexpr auto num_up_dim  = encoded_transforms[i].template at<4>();           \
+                                                                                                   \
+                    static_assert(name == coord_transform_enum::pass_through ||                    \
+                                      name == coord_transform_enum::pad ||                         \
+                                      name == coord_transform_enum::embed ||                       \
+                                      name == coord_transform_enum::merge ||                       \
+                                      name == coord_transform_enum::unmerge ||                     \
+                                      name == coord_transform_enum::replicate,                     \
+                                  "");                                                             \
+                                                                                                   \
+                    if constexpr(name == coord_transform_enum::pass_through)                       \
+                    {                                                                              \
+                        constexpr index_t low_len = meta_data.template get<index_t>(0);            \
+                                                                                                   \
+                        return make_pass_through_transform(number<low_len>{});                     \
+                    }                                                                              \
+                    else if constexpr(name == coord_transform_enum::pad)                           \
+                    {                                                                              \
+                        constexpr index_t low_len = meta_data.template get<index_t>(0);            \
+                                                                                                   \
+                        constexpr index_t left_pad =                                               \
+                            meta_data.template get<index_t>(sizeof(low_len));                      \
+                                                                                                   \
+                        constexpr index_t right_pad =                                              \
+                            meta_data.template pop<index_t>(sizeof(low_len) + sizeof(left_pad));   \
+                                                                                                   \
+                        return make_pad_transform(                                                 \
+                            number<low_len>{}, number<left_pad>{}, number<right_pad>{});           \
+                    }                                                                              \
+                    else if constexpr(name == coord_transform_enum::embed)                         \
+                    {                                                                              \
+                        constexpr auto up_lens =                                                   \
+                            meta_data.template get<array<index_t, num_up_dim>>(0);                 \
+                                                                                                   \
+                        constexpr auto coefficients =                                              \
+                            meta_data.template get<array<index_t, num_up_dim>>(sizeof(up_lens));   \
+                                                                                                   \
+                        return make_embed_transform(TO_TUPLE_OF_NUMBER(up_lens, num_up_dim),       \
+                                                    TO_TUPLE_OF_NUMBER(coefficients, num_up_dim)); \
+                    }                                                                              \
+                    else if constexpr(name == coord_transform_enum::merge)                         \
+                    {                                                                              \
+                        constexpr auto low_lens =                                                  \
+                            meta_data.template get<array<index_t, num_low_dim>>(0);                \
+                                                                                                   \
+                        return make_merge_transform(TO_TUPLE_OF_NUMBER(low_lens, num_low_dim));    \
+                    }                                                                              \
+                    else if constexpr(name == coord_transform_enum::unmerge)                       \
+                    {                                                                              \
+                        constexpr auto up_lens =                                                   \
+                            meta_data.template get<array<index_t, num_up_dim>>(0);                 \
+                                                                                                   \
+                        return make_unmerge_transform(TO_TUPLE_OF_NUMBER(up_lens, num_up_dim));    \
+                    }                                                                              \
+                    else if constexpr(name == coord_transform_enum::replicate)                     \
+                    {                                                                              \
+                        constexpr auto up_lens =                                                   \
+                            meta_data.template get<array<index_t, num_up_dim>>(0);                 \
+                                                                                                   \
+                        return make_replicate_transform(TO_TUPLE_OF_NUMBER(up_lens, num_up_dim));  \
+                    }                                                                              \
+                },                                                                                 \
+                number<num_transform>{});                                                          \
+        }();                                                                                       \
+                                                                                                   \
+        constexpr auto low_dim_idss = [&encoded_transforms]() {                                    \
+            return generate_tuple(                                                                 \
+                [&encoded_transforms](auto i) {                                                    \
+                    constexpr auto num_low_dim = encoded_transforms[i].template at<2>();           \
+                    constexpr auto low_dims    = encoded_transforms[i].template at<3>();           \
+                                                                                                   \
+                    return TO_SEQUENCE(low_dims, num_low_dim);                                     \
+                },                                                                                 \
+                number<num_transform>());                                                          \
+        }();                                                                                       \
+                                                                                                   \
+        constexpr auto up_dim_idss = [&encoded_transforms] {                                       \
+            return generate_tuple(                                                                 \
+                [&encoded_transforms](auto i) {                                                    \
+                    constexpr auto num_up_dim = encoded_transforms[i].template at<4>();            \
+                    constexpr auto up_dims    = encoded_transforms[i].template at<5>();            \
+                                                                                                   \
+                    return TO_SEQUENCE(up_dims, num_up_dim);                                       \
+                },                                                                                 \
+                number<num_transform>());                                                          \
+        }();                                                                                       \
+                                                                                                   \
+        constexpr auto bottom_dim_ids = TO_SEQUENCE(encoded_bottom_dims, num_bottom_dim);          \
+        constexpr auto top_dim_ids    = TO_SEQUENCE(encoded_top_dims, num_top_dim);                \
+                                                                                                   \
+        return tensor_adaptor<remove_cvref_t<decltype(trans)>,                                     \
+                              remove_cvref_t<decltype(low_dim_idss)>,                              \
+                              remove_cvref_t<decltype(up_dim_idss)>,                               \
+                              remove_cvref_t<decltype(bottom_dim_ids)>,                            \
+                              remove_cvref_t<decltype(top_dim_ids)>>{trans};                       \
+    }()

include/ck_tile/core/tensor/tensor_adaptor_coordinate.hpp

@@ -0,0 +1,257 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/algorithm/coordinate_transform.hpp"
+#include "ck_tile/core/tensor/tensor_adaptor.hpp"
+#include "ck_tile/core/container/container_helper.hpp"
+#include "ck_tile/core/container/multi_index.hpp"
+#include "ck_tile/core/numeric/math.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+
+namespace ck_tile {
+
+template <index_t NDimHidden, typename BottomDimensionHiddenIds, typename TopDimensionHiddenIds>
+struct tensor_adaptor_coordinate
+{
+    static constexpr index_t ndim_bottom_ = BottomDimensionHiddenIds::size();
+    static constexpr index_t ndim_top_    = TopDimensionHiddenIds::size();
+
+    using HiddenIndex = multi_index<NDimHidden>;
+    using BottomIndex = multi_index<ndim_bottom_>;
+    using TopIndex    = multi_index<ndim_top_>;
+
+    public:
+    CK_TILE_HOST_DEVICE constexpr tensor_adaptor_coordinate() = default;
+
+    CK_TILE_HOST_DEVICE constexpr tensor_adaptor_coordinate(const HiddenIndex& idx_hidden)
+        : idx_hidden_{idx_hidden}
+    {
+    }
+
+    CK_TILE_HOST_DEVICE constexpr auto get_top_index() const
+    {
+        return get_container_subset(idx_hidden_, TopDimensionHiddenIds{});
+    }
+
+    CK_TILE_HOST_DEVICE constexpr auto get_bottom_index() const
+    {
+        return get_container_subset(idx_hidden_, BottomDimensionHiddenIds{});
+    }
+
+    CK_TILE_HOST_DEVICE constexpr const auto& get_hidden_index() const { return idx_hidden_; }
+
+    CK_TILE_HOST_DEVICE constexpr auto& get_hidden_index() { return idx_hidden_; }
+
+    //
+    HiddenIndex idx_hidden_;
+};
+
+template <typename Adaptor, typename TopIndex>
+CK_TILE_HOST_DEVICE constexpr auto make_tensor_adaptor_coordinate(const Adaptor& adaptor,
+                                                                  const TopIndex& idx_top)
+{
+    static_assert(Adaptor::get_num_of_top_dimension() == TopIndex::size(),
+                  "wrong! # of dimension inconsistent");
+
+    constexpr index_t ntransform  = Adaptor::get_num_of_transform();
+    constexpr index_t ndim_hidden = Adaptor::get_num_of_hidden_dimension();
+    constexpr auto bottom_dim_ids = Adaptor::get_bottom_dimension_hidden_ids();
+    constexpr auto top_dim_ids    = Adaptor::get_top_dimension_hidden_ids();
+
+    multi_index<ndim_hidden> idx_hidden;
+
+    // initialize visible index
+    set_container_subset(idx_hidden, top_dim_ids, idx_top);
+
+    // calculate hidden index
+    static_for<ntransform, 0, -1>{}([&adaptor, &idx_hidden](auto itran_p1) {
+        auto itran              = itran_p1 - number<1>{};
+        const auto& tran        = adaptor.get_transforms().at(itran);
+        constexpr auto dims_low = Adaptor::get_lower_dimension_hidden_idss().at(itran);
+        constexpr auto dims_up  = Adaptor::get_upper_dimension_hidden_idss().at(itran);
+
+        const auto idx_up = get_container_subset(idx_hidden, dims_up);
+
+        multi_index<dims_low.size()> idx_low;
+
+        tran.calculate_lower_index(idx_low, idx_up);
+
+        set_container_subset(idx_hidden, dims_low, idx_low);
+    });
+
+    return tensor_adaptor_coordinate<ndim_hidden,
+                                     remove_cvref_t<decltype(bottom_dim_ids)>,
+                                     remove_cvref_t<decltype(top_dim_ids)>>{idx_hidden};
+}
+
+template <bool JudgeDoTransforms = true,
+          typename Adaptor,
+          typename AdaptorCoord,
+          typename TopIndex,
+          typename BottomIndex>
+CK_TILE_HOST_DEVICE constexpr void move_tensor_adaptor_coordinate(const Adaptor& adaptor,
+                                                                  AdaptorCoord& coord,
+                                                                  const TopIndex& idx_diff_top,
+                                                                  BottomIndex& idx_diff_bottom)
+{
+    constexpr index_t ndim_hidden = Adaptor::get_num_of_hidden_dimension();
+    constexpr index_t ndim_top    = Adaptor::get_num_of_top_dimension();
+    //  constexpr index_t ndim_bottom = Adaptor::get_num_of_bottom_dimension();
+    constexpr index_t ntransform = Adaptor::get_num_of_transform();
+
+    //  static_assert(TopIndex::size() == ndim_top && BottomIndex::size() == ndim_bottom, "");
+
+    // judge whether calculation of lower diff is needed for each transform
+    // use index_t for boolean type
+    auto do_transforms = make_zero_multi_index<ntransform>();
+
+    if constexpr(JudgeDoTransforms)
+    {
+        auto is_non_zero_diff = make_zero_multi_index<ndim_hidden>();
+
+        // decide do_transform by checkout non-zero index diff components
+        multi_index<ndim_top> non_zero_diff_pick_top;
+
+        static_for<0, ndim_top, 1>{}(
+            [&](auto i) { non_zero_diff_pick_top(i) = (idx_diff_top[i] != 0); });
+
+        set_container_subset(
+            is_non_zero_diff, Adaptor::get_top_dimension_hidden_ids(), non_zero_diff_pick_top);
+
+        static_for<ntransform - 1, -1, -1>{}([&](auto itran) {
+            constexpr auto dims_low = Adaptor::get_lower_dimension_hidden_idss().at(itran);
+            constexpr auto dims_up  = Adaptor::get_upper_dimension_hidden_idss().at(itran);
+
+            const auto non_zero_diff_pick_up = get_container_subset(is_non_zero_diff, dims_up);
+
+            multi_index<dims_low.size()> non_zero_diff_pick_low;
+
+            // if any of upper index diff components is non-zero, then
+            //   1) Need to do this transform
+            //   2) all components of lower index diff will assume to be non-zero and need to be
+            //   computed
+            const bool idx_diff_up_has_non_zero = container_reduce(
+                non_zero_diff_pick_up, [](auto a, auto b) constexpr { return a or b; }, false);
+
+            do_transforms(itran) = idx_diff_up_has_non_zero;
+
+            static_for<0, dims_low.size(), 1>{}(
+                [&](auto i) { non_zero_diff_pick_low(i) = idx_diff_up_has_non_zero; });
+
+            set_container_subset(is_non_zero_diff, dims_low, non_zero_diff_pick_low);
+        });
+    }
+    else
+    {
+        static_for<ntransform - 1, -1, -1>{}([&](auto itran) { do_transforms(itran) = 1; });
+    }
+
+    // this is what needs to be calculated
+    auto idx_diff_hidden = make_zero_multi_index<ndim_hidden>();
+
+    // initialize top index diff
+    set_container_subset(idx_diff_hidden, Adaptor::get_top_dimension_hidden_ids(), idx_diff_top);
+
+    // this is what needs to be updated
+    auto& idx_hidden = coord.get_hidden_index();
+
+    // update top index
+    auto idx_hidden_pick_top =
+        get_container_subset(idx_hidden, Adaptor::get_top_dimension_hidden_ids());
+
+    idx_hidden_pick_top += idx_diff_top;
+
+    set_container_subset(idx_hidden, Adaptor::get_top_dimension_hidden_ids(), idx_hidden_pick_top);
+
+    // update rest of hidden index
+    static_for<ntransform - 1, -1, -1>{}([&](auto itran) {
+        if(do_transforms[itran])
+        {
+            const auto& tran        = adaptor.get_transforms().at(itran);
+            constexpr auto dims_low = Adaptor::get_lower_dimension_hidden_idss().at(itran);
+            constexpr auto dims_up  = Adaptor::get_upper_dimension_hidden_idss().at(itran);
+
+            const auto idx_up_new  = get_container_subset(idx_hidden, dims_up);
+            auto idx_low           = get_container_subset(idx_hidden, dims_low);
+            const auto idx_diff_up = get_container_subset(idx_diff_hidden, dims_up);
+
+            multi_index<dims_low.size()> idx_diff_low;
+
+            tran.update_lower_index(idx_diff_low, idx_diff_up, idx_low, idx_up_new);
+
+            set_container_subset(idx_diff_hidden, dims_low, idx_diff_low);
+            set_container_subset(idx_hidden, dims_low, idx_low);
+        }
+    });
+
+    // set bottom index diff
+    idx_diff_bottom =
+        get_container_subset(idx_diff_hidden, Adaptor::get_bottom_dimension_hidden_ids());
+}
+
+template <bool JudgeDoTransforms = true, typename Adaptor, typename AdaptorCoord, typename TopIndex>
+CK_TILE_HOST_DEVICE constexpr void move_tensor_adaptor_coordinate(const Adaptor& adaptor,
+                                                                  AdaptorCoord& coord,
+                                                                  const TopIndex& idx_diff_top)
+{
+    constexpr index_t ndim_bottom = Adaptor::get_num_of_bottom_dimension();
+
+    multi_index<ndim_bottom> tmp;
+
+    move_tensor_adaptor_coordinate<JudgeDoTransforms>(adaptor, coord, idx_diff_top, tmp);
+}
+
+template <typename Adaptor, typename AdaptorCoord>
+CK_TILE_HOST_DEVICE constexpr bool
+adaptor_coordinate_is_valid_assuming_top_index_is_valid(const Adaptor& adaptor,
+                                                        const AdaptorCoord& coord)
+{
+    bool valid = true;
+
+    constexpr index_t ntransform = Adaptor::get_num_of_transform();
+
+    const auto& idx_hidden = coord.get_hidden_index();
+
+    static_for<ntransform - 1, -1, -1>{}([&adaptor, &idx_hidden, &valid](auto itran) {
+        const auto tran = adaptor.get_transforms().at(itran);
+
+        // check validity, only if current transformation does not always has a valid mapping
+        if constexpr(!decltype(tran)::is_valid_upper_index_always_mapped_to_valid_lower_index())
+        {
+            const auto idx_up = get_container_subset(
+                idx_hidden, Adaptor::get_upper_dimension_hidden_idss().at(itran));
+
+            // Comment: using valid = valid && .. will result in weird control flow in ISA
+            valid &= tran.is_valid_upper_index_mapped_to_valid_lower_index(idx_up);
+        }
+    });
+
+    return valid;
+}
+
+template <typename Adaptor, typename AdpatorCoord>
+CK_TILE_HOST_DEVICE constexpr bool adaptor_coordinate_is_valid(const Adaptor& adaptor,
+                                                               const AdpatorCoord& coord)
+{
+    // check top index
+    const auto& idx_top = coord.get_top_index();
+
+    bool is_top_index_valid = true;
+
+    static_for<0, Adaptor::get_num_of_dimension(), 1>{}(
+        [&is_top_index_valid, &idx_top, &adaptor](auto i) {
+            is_top_index_valid =
+                is_top_index_valid && (idx_top[i] >= 0 && idx_top[i] < adaptor.get_length(i));
+        });
+
+    // check other hidden index
+    return is_top_index_valid &&
+           adaptor_coordinate_is_valid_assuming_top_index_is_valid(adaptor, coord);
+}
+
+} // namespace ck_tile

include/ck_tile/core/tensor/tensor_coordinate.hpp

@@ -0,0 +1,92 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/algorithm/coordinate_transform.hpp"
+#include "ck_tile/core/tensor/tensor_adaptor.hpp"
+#include "ck_tile/core/tensor/tensor_adaptor_coordinate.hpp"
+#include "ck_tile/core/container/container_helper.hpp"
+#include "ck_tile/core/container/multi_index.hpp"
+#include "ck_tile/core/numeric/math.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+
+namespace ck_tile {
+
+template <index_t NDimHidden, typename TopDimensionHiddenIds>
+struct tensor_coordinate
+    : public tensor_adaptor_coordinate<NDimHidden, sequence<0>, TopDimensionHiddenIds>
+{
+    using Base = tensor_adaptor_coordinate<NDimHidden, sequence<0>, TopDimensionHiddenIds>;
+
+    // TODO make these private
+    static constexpr index_t ndim_top_ = TopDimensionHiddenIds::size();
+
+    using HiddenIndex = multi_index<NDimHidden>;
+    using TopIndex    = multi_index<ndim_top_>;
+
+    public:
+    CK_TILE_HOST_DEVICE constexpr tensor_coordinate() = default;
+
+    CK_TILE_HOST_DEVICE constexpr tensor_coordinate(const HiddenIndex& idx_hidden)
+        : Base{idx_hidden}
+    {
+    }
+
+    // construct from TensorAdaptorCoordinte base class
+    CK_TILE_HOST_DEVICE constexpr tensor_coordinate(const Base& adaptor_coord) : Base{adaptor_coord}
+    {
+    }
+
+    CK_TILE_HOST_DEVICE constexpr auto get_index() const { return Base::get_top_index(); }
+
+    CK_TILE_HOST_DEVICE constexpr index_t get_offset() const
+    {
+        return Base::get_bottom_index()[number<0>{}];
+    }
+
+    CK_TILE_HOST_DEVICE constexpr const auto& get_hidden_index() const
+    {
+        return Base::get_hidden_index();
+    }
+
+    CK_TILE_HOST_DEVICE auto& get_hidden_index() { return Base::get_hidden_index(); }
+};
+
+template <typename TensorDesc, typename TopIndex>
+CK_TILE_HOST_DEVICE constexpr auto make_tensor_coordinate(const TensorDesc& tensor_desc,
+                                                          const TopIndex& idx_top)
+{
+    const auto adaptor_coord = make_tensor_adaptor_coordinate(tensor_desc, idx_top);
+
+    return tensor_coordinate<TensorDesc::get_num_of_hidden_dimension(),
+                             remove_cvref_t<decltype(TensorDesc::get_top_dimension_hidden_ids())>>{
+        adaptor_coord};
+}
+
+template <bool JudgeDoTransforms = true, typename TensorDesc, typename TensorCoord, typename Index>
+CK_TILE_HOST_DEVICE constexpr void
+move_tensor_coordinate(const TensorDesc& tensor_desc, TensorCoord& coord, const Index& coord_step)
+{
+    move_tensor_adaptor_coordinate(tensor_desc, coord, coord_step);
+}
+
+template <typename TensorDesc, typename TensorCoord>
+CK_TILE_HOST_DEVICE constexpr bool
+coordinate_has_valid_offset_assuming_top_index_is_valid(const TensorDesc& tensor_desc,
+                                                        const TensorCoord& coord)
+{
+    return adaptor_coordinate_is_valid_assuming_top_index_is_valid(tensor_desc, coord);
+}
+
+template <typename TensorDesc, typename TensorCoord>
+CK_TILE_HOST_DEVICE constexpr bool coordinate_has_valid_offset(const TensorDesc& tensor_desc,
+                                                               const TensorCoord& coord)
+{
+    return adaptor_coordinate_is_valid(tensor_desc, coord);
+}
+
+} // namespace ck_tile

include/ck_tile/core/tensor/tensor_descriptor.hpp

@@ -0,0 +1,467 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/algorithm/coordinate_transform.hpp"
+#include "ck_tile/core/tensor/tensor_adaptor.hpp"
+#include "ck_tile/core/container/container_helper.hpp"
+#include "ck_tile/core/container/multi_index.hpp"
+#include "ck_tile/core/numeric/math.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+
+namespace ck_tile {
+
+// Transforms: Tuple<transforms...>
+// LowerDimensionHiddenIdss : Tuple<sequence<...>, ...>
+// UpperDimensionHiddenIdss : Tuple<sequence<...>, ...>
+// TopDimensionHiddenIds> : sequence<...>
+template <typename Transforms,
+          typename LowerDimensionHiddenIdss,
+          typename UpperDimensionHiddenIdss,
+          typename TopDimensionHiddenIds,
+          typename ElementSpaceSize,
+          typename GuaranteedVectorLengths_,
+          typename GuaranteedVectorSrides_>
+struct tensor_descriptor : public tensor_adaptor<Transforms,
+                                                 LowerDimensionHiddenIdss,
+                                                 UpperDimensionHiddenIdss,
+                                                 sequence<0>,
+                                                 TopDimensionHiddenIds>
+{
+    using Base = tensor_adaptor<Transforms,
+                                LowerDimensionHiddenIdss,
+                                UpperDimensionHiddenIdss,
+                                sequence<0>,
+                                TopDimensionHiddenIds>;
+
+    using ElementSpaceSizeType = ElementSpaceSize;
+
+    constexpr static index_t ntransform_  = Base::get_num_of_transform();
+    constexpr static index_t ndim_hidden_ = Base::get_num_of_hidden_dimension();
+    constexpr static index_t ndim_top_    = Base::get_num_of_top_dimension();
+
+    using GuaranteedVectorLengths = GuaranteedVectorLengths_;
+    using GuaranteedVectorStrides = GuaranteedVectorSrides_;
+
+    static_assert(GuaranteedVectorLengths::size() == ndim_hidden_ &&
+                      GuaranteedVectorStrides::size() == ndim_hidden_,
+                  "wrong! inconsistent # of hidden dimensions");
+
+    using TopIndex    = multi_index<ndim_top_>;
+    using HiddenIndex = multi_index<ndim_hidden_>;
+
+    public:
+    CK_TILE_HOST_DEVICE constexpr tensor_descriptor() = default;
+
+    CK_TILE_HOST_DEVICE constexpr tensor_descriptor(const Transforms& transforms,
+                                                    ElementSpaceSize element_space_size)
+        : Base{transforms}, element_space_size_{element_space_size}
+
+    {
+        static_assert(Transforms::size() == ntransform_ &&
+                          LowerDimensionHiddenIdss::size() == ntransform_ &&
+                          UpperDimensionHiddenIdss::size() == ntransform_,
+                      "wrong! inconsistent # of transformations");
+
+        // TODO check dependency of dimensions is valid
+    }
+
+    // construct from tensor_adaptor base class
+    CK_TILE_HOST_DEVICE constexpr tensor_descriptor(const Base& adaptor,
+                                                    ElementSpaceSize element_space_size)
+        : Base{adaptor}, element_space_size_{element_space_size}
+    {
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr index_t get_num_of_dimension()
+    {
+        return Base::get_num_of_top_dimension();
+    }
+
+    template <index_t IDim>
+    CK_TILE_HOST_DEVICE constexpr auto get_length(number<IDim> idim) const
+    {
+        return Base::get_top_dimension_length(idim);
+    }
+
+    CK_TILE_HOST_DEVICE constexpr auto get_lengths() const
+    {
+        return Base::get_top_dimension_lengths();
+    }
+
+    CK_TILE_HOST_DEVICE constexpr auto get_element_space_size() const
+    {
+        return element_space_size_;
+    }
+
+    template <typename Idx>
+    CK_TILE_HOST_DEVICE constexpr index_t calculate_offset(const Idx& idx) const
+    {
+        return Base::calculate_bottom_index(idx)[number<0>{}];
+    }
+
+    // TODO make these private
+    CK_TILE_HOST_DEVICE constexpr const auto& get_transforms() const
+    {
+        return Base::get_transforms();
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr auto get_lower_dimension_hidden_idss()
+    {
+        return Base::get_lower_dimension_hidden_idss();
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr auto get_upper_dimension_hidden_idss()
+    {
+        return Base::get_upper_dimension_hidden_idss();
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr auto get_top_dimension_hidden_ids()
+    {
+        return Base::get_top_dimension_hidden_ids();
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr bool is_static()
+    {
+        return Base::is_known_at_compile_time() &&
+               ck_tile::is_known_at_compile_time<ElementSpaceSize>::value;
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr bool is_known_at_compile_time() { return is_static(); }
+
+    CK_TILE_HOST_DEVICE static constexpr auto get_top_dimension_safe_vector_length_strides()
+    {
+        return Base::get_top_dimension_safe_vector_length_strides(
+            to_array<index_t, ndim_hidden_>(GuaranteedVectorLengths{}),
+            to_array<index_t, ndim_hidden_>(GuaranteedVectorStrides{}));
+    }
+
+    CK_TILE_HOST_DEVICE void print() const
+    {
+        printf("tensor_descriptor{");
+
+        // tensor_adaptor
+        Base::print();
+        printf(", ");
+
+        // element_space_size_
+        printf("element_space_size_: ");
+        print(element_space_size_);
+
+        printf("}");
+    }
+
+    // TODO make these private
+    ElementSpaceSize element_space_size_;
+};
+
+template <typename Adaptor, typename ElementSpaceSize>
+CK_TILE_HOST_DEVICE constexpr auto
+make_tensor_descriptor_from_adaptor(const Adaptor& adaptor,
+                                    const ElementSpaceSize& element_space_size)
+{
+    constexpr index_t NDimHidden = Adaptor::get_num_of_hidden_dimension();
+
+    return tensor_descriptor<remove_cvref_t<decltype(adaptor.get_transforms())>,
+                             remove_cvref_t<decltype(adaptor.get_lower_dimension_hidden_idss())>,
+                             remove_cvref_t<decltype(adaptor.get_upper_dimension_hidden_idss())>,
+                             remove_cvref_t<decltype(adaptor.get_top_dimension_hidden_ids())>,
+                             remove_cvref_t<decltype(element_space_size)>,
+                             typename uniform_sequence_gen<NDimHidden, -1>::type,
+                             typename uniform_sequence_gen<NDimHidden, -1>::type>{
+        adaptor, element_space_size};
+}
+
+template <typename OldTensorDescriptor,
+          typename NewTransforms,
+          typename NewLowerDimensionOldTopIdss,
+          typename NewUpperDimensionNewTopIdss>
+CK_TILE_HOST_DEVICE constexpr auto
+transform_tensor_descriptor(const OldTensorDescriptor& old_tensor_desc,
+                            const NewTransforms& new_transforms,
+                            NewLowerDimensionOldTopIdss,
+                            NewUpperDimensionNewTopIdss)
+{
+    const auto element_space_size = old_tensor_desc.get_element_space_size();
+
+    const auto new_tensor_adaptor = transform_tensor_adaptor(old_tensor_desc,
+                                                             new_transforms,
+                                                             NewLowerDimensionOldTopIdss{},
+                                                             NewUpperDimensionNewTopIdss{});
+
+    constexpr index_t NDimHiddenOld = OldTensorDescriptor::get_num_of_hidden_dimension();
+    constexpr index_t NDimHiddenNew = decltype(new_tensor_adaptor)::get_num_of_hidden_dimension();
+
+    using NewGuaranteedVectorLengths = typename sequence_merge<
+        typename OldTensorDescriptor::GuaranteedVectorLengths,
+        typename uniform_sequence_gen<NDimHiddenNew - NDimHiddenOld, -1>::type>::type;
+
+    using NewGuaranteedVectorStrides = typename sequence_merge<
+        typename OldTensorDescriptor::GuaranteedVectorStrides,
+        typename uniform_sequence_gen<NDimHiddenNew - NDimHiddenOld, -1>::type>::type;
+
+    return tensor_descriptor<
+        remove_cvref_t<decltype(new_tensor_adaptor.get_transforms())>,
+        remove_cvref_t<decltype(new_tensor_adaptor.get_lower_dimension_hidden_idss())>,
+        remove_cvref_t<decltype(new_tensor_adaptor.get_upper_dimension_hidden_idss())>,
+        remove_cvref_t<decltype(new_tensor_adaptor.get_top_dimension_hidden_ids())>,
+        remove_cvref_t<decltype(element_space_size)>,
+        NewGuaranteedVectorLengths,
+        NewGuaranteedVectorStrides>{new_tensor_adaptor, element_space_size};
+}
+
+namespace detail {
+
+template <typename Lengths, typename Strides, index_t I, typename AccOld>
+CK_TILE_HOST_DEVICE constexpr auto calculate_element_space_size_impl(const Lengths& lengths,
+                                                                     const Strides& strides,
+                                                                     number<I> i,
+                                                                     AccOld acc_old)
+{
+    auto acc_new = acc_old + (lengths[i] - number<1>{}) * strides[i];
+
+    if constexpr(i.value < Lengths::size() - 1)
+    {
+        return calculate_element_space_size_impl(lengths, strides, i + number<1>{}, acc_new);
+    }
+    else
+    {
+        return acc_new;
+    }
+}
+
+} // namespace detail
+
+/*
+ * These functions create naive tensor descriptor
+ */
+
+// Lengths..., Strides... could be:
+//   1) index_t, which is known at run-time, or
+//   2) number<>, which is known at compile-time
+// element_space_size could be:
+//   1) long_index_t, or
+//   2) long_number<>
+template <typename... Lengths,
+          typename... Strides,
+          index_t GuaranteedLastDimensionVectorLength                                   = -1,
+          index_t GuaranteedLastDimensionVectorStride                                   = -1,
+          typename std::enable_if<sizeof...(Lengths) == sizeof...(Strides), bool>::type = false>
+CK_TILE_HOST_DEVICE constexpr auto
+make_naive_tensor_descriptor(const tuple<Lengths...>& lengths,
+                             const tuple<Strides...>& strides,
+                             number<GuaranteedLastDimensionVectorLength> = number<-1>{},
+                             number<GuaranteedLastDimensionVectorStride> = number<-1>{})
+{
+    constexpr index_t N = sizeof...(Lengths);
+
+    const auto transforms = make_tuple(make_embed_transform(lengths, strides));
+
+    constexpr auto low_dim_hidden_idss = make_tuple(sequence<0>{});
+
+    constexpr auto up_dim_hidden_idss =
+        make_tuple(typename arithmetic_sequence_gen<1, N + 1, 1>::type{});
+
+    constexpr auto visible_dim_hidden_ids = typename arithmetic_sequence_gen<1, N + 1, 1>::type{};
+
+    const auto element_space_size =
+        detail::calculate_element_space_size_impl(lengths, strides, number<0>{}, long_number<1>{});
+
+    using GuaranteedVectorLengths =
+        typename sequence_merge<typename uniform_sequence_gen<N, -1>::type,
+                                sequence<GuaranteedLastDimensionVectorLength>>::type;
+
+    using GuaranteedVectorStrides =
+        typename sequence_merge<typename uniform_sequence_gen<N, -1>::type,
+                                sequence<GuaranteedLastDimensionVectorStride>>::type;
+
+    return tensor_descriptor<remove_cv_t<decltype(transforms)>,
+                             remove_cv_t<decltype(low_dim_hidden_idss)>,
+                             remove_cv_t<decltype(up_dim_hidden_idss)>,
+                             remove_cv_t<decltype(visible_dim_hidden_ids)>,
+                             remove_cv_t<decltype(element_space_size)>,
+                             GuaranteedVectorLengths,
+                             GuaranteedVectorStrides>{transforms, element_space_size};
+}
+
+// tensor descriptor with offset, the offset will not be added into element space size
+// only have an information of the starting offset, and will impact on offset calculation
+template <typename... Lengths,
+          typename... Strides,
+          typename offset,
+          index_t GuaranteedLastDimensionVectorLength                                   = -1,
+          index_t GuaranteedLastDimensionVectorStride                                   = -1,
+          typename std::enable_if<sizeof...(Lengths) == sizeof...(Strides), bool>::type = false>
+CK_TILE_HOST_DEVICE constexpr auto
+make_naive_tensor_descriptor_with_offset(const tuple<Lengths...>& lengths,
+                                         const tuple<Strides...>& strides,
+                                         const offset& os,
+                                         number<GuaranteedLastDimensionVectorLength> = number<-1>{},
+                                         number<GuaranteedLastDimensionVectorStride> = number<-1>{})
+{
+    const auto desc_0 = [&]() {
+        const auto element_space_size = detail::calculate_element_space_size_impl(
+            lengths, strides, number<0>{}, long_number<1>{});
+
+        const auto transforms = make_tuple(make_offset_transform(element_space_size, os));
+
+        constexpr auto low_dim_hidden_idss = make_tuple(sequence<0>{});
+
+        constexpr auto up_dim_hidden_idss = make_tuple(sequence<1>{});
+
+        constexpr auto visible_dim_hidden_ids = sequence<1>{};
+
+        using GuaranteedVectorLengths =
+            typename sequence_merge<typename uniform_sequence_gen<1, -1>::type,
+                                    sequence<GuaranteedLastDimensionVectorLength>>::type;
+
+        using GuaranteedVectorStrides =
+            typename sequence_merge<typename uniform_sequence_gen<1, -1>::type,
+                                    sequence<GuaranteedLastDimensionVectorStride>>::type;
+
+        return tensor_descriptor<remove_cv_t<decltype(transforms)>,
+                                 remove_cv_t<decltype(low_dim_hidden_idss)>,
+                                 remove_cv_t<decltype(up_dim_hidden_idss)>,
+                                 remove_cv_t<decltype(visible_dim_hidden_ids)>,
+                                 remove_cv_t<decltype(element_space_size)>,
+                                 GuaranteedVectorLengths,
+                                 GuaranteedVectorStrides>{transforms, element_space_size};
+    }();
+
+    constexpr index_t N = sizeof...(Lengths);
+
+    return transform_tensor_descriptor(
+        desc_0,
+        make_tuple(make_embed_transform(lengths, strides)),
+        make_tuple(sequence<0>{}),
+        make_tuple(typename arithmetic_sequence_gen<0, N, 1>::type{}));
+}
+
+// Lengths... could be:
+//   1) index_t, which is known at run-time, or
+//   2) number<>, which is known at compile-time
+// element_space_size could be:
+//   1) long_index_t, or
+//   2) long_number<>
+template <typename... Lengths, index_t GuaranteedLastDimensionVectorLength = -1>
+CK_TILE_HOST_DEVICE constexpr auto
+make_naive_tensor_descriptor_packed(const tuple<Lengths...>& lengths,
+                                    number<GuaranteedLastDimensionVectorLength> = number<-1>{})
+{
+    constexpr index_t N = sizeof...(Lengths);
+
+    const auto transforms = make_tuple(make_unmerge_transform(lengths));
+
+    constexpr auto low_dim_hidden_idss = make_tuple(sequence<0>{});
+
+    constexpr auto up_dim_hidden_idss =
+        make_tuple(typename arithmetic_sequence_gen<1, N + 1, 1>::type{});
+
+    constexpr auto visible_dim_hidden_ids = typename arithmetic_sequence_gen<1, N + 1, 1>::type{};
+
+    const auto element_space_size = container_reduce(lengths, multiplies{}, long_number<1>{});
+
+    using GuaranteedVectorLengths =
+        typename sequence_merge<typename uniform_sequence_gen<N, -1>::type,
+                                sequence<GuaranteedLastDimensionVectorLength>>::type;
+
+    using GuaranteedVectorStrides =
+        typename sequence_merge<typename uniform_sequence_gen<N, -1>::type, sequence<1>>::type;
+
+    return tensor_descriptor<remove_cv_t<decltype(transforms)>,
+                             remove_cv_t<decltype(low_dim_hidden_idss)>,
+                             remove_cv_t<decltype(up_dim_hidden_idss)>,
+                             remove_cv_t<decltype(visible_dim_hidden_ids)>,
+                             remove_cv_t<decltype(element_space_size)>,
+                             GuaranteedVectorLengths,
+                             GuaranteedVectorStrides>{transforms, element_space_size};
+}
+
+template <typename... Lengths,
+          typename... Strides,
+          typename Offset,
+          index_t GuaranteedLastDimensionVectorLength                                   = -1,
+          typename std::enable_if<sizeof...(Lengths) == sizeof...(Strides), bool>::type = false>
+CK_TILE_HOST_DEVICE constexpr auto make_naive_tensor_descriptor_packed_with_offset(
+    const tuple<Lengths...>& lengths,
+    const Offset& offset,
+    number<GuaranteedLastDimensionVectorLength> = number<-1>{})
+{
+    const auto desc_0 = [&]() {
+        const auto element_space_size = container_reduce(lengths, multiplies{}, long_number<1>{});
+
+        const auto transforms = make_tuple(make_offset_transform(element_space_size, offset));
+
+        constexpr auto low_dim_hidden_idss = make_tuple(sequence<0>{});
+
+        constexpr auto up_dim_hidden_idss = make_tuple(sequence<1>{});
+
+        constexpr auto visible_dim_hidden_ids = sequence<1>{};
+
+        using GuaranteedVectorLengths =
+            typename sequence_merge<typename uniform_sequence_gen<1, -1>::type,
+                                    sequence<GuaranteedLastDimensionVectorLength>>::type;
+
+        using GuaranteedVectorStrides =
+            typename sequence_merge<typename uniform_sequence_gen<1, -1>::type, sequence<1>>::type;
+
+        return tensor_descriptor<remove_cv_t<decltype(transforms)>,
+                                 remove_cv_t<decltype(low_dim_hidden_idss)>,
+                                 remove_cv_t<decltype(up_dim_hidden_idss)>,
+                                 remove_cv_t<decltype(visible_dim_hidden_ids)>,
+                                 remove_cv_t<decltype(element_space_size)>,
+                                 GuaranteedVectorLengths,
+                                 GuaranteedVectorStrides>{transforms, element_space_size};
+    }();
+
+    constexpr index_t N = sizeof...(Lengths);
+
+    return transform_tensor_descriptor(
+        desc_0,
+        make_tuple(make_unmerge_transform(lengths)),
+        make_tuple(sequence<0>{}),
+        make_tuple(typename arithmetic_sequence_gen<0, N, 1>::type{}));
+}
+
+// Lengths... could be:
+//   1) index_t, which is known at run-time, or
+//   2) number<>, which is known at compile-time
+// align could be:
+//   1) index_t, or
+//   2) number<>
+template <typename... Lengths, typename Align>
+CK_TILE_HOST_DEVICE constexpr auto
+make_naive_tensor_descriptor_aligned(const tuple<Lengths...>& lengths, Align align)
+{
+    constexpr auto I1 = number<1>{};
+
+    constexpr index_t N = sizeof...(Lengths);
+
+    const auto stride_n_minus_2 = integer_least_multiple(lengths[number<N - 1>{}], align);
+
+    auto strides = generate_tuple(
+        [&](auto i) {
+            if constexpr(i.value == N - 1)
+            {
+                return I1;
+            }
+            else if constexpr(i.value == N - 2)
+            {
+                return number<stride_n_minus_2>{};
+            }
+            else
+            {
+                return container_reduce(
+                    lengths, multiplies{}, number<stride_n_minus_2>{}, i + I1, number<N - 1>{}, I1);
+            }
+        },
+        number<N>{});
+
+    return make_naive_tensor_descriptor(lengths, strides);
+}
+
+} // namespace ck_tile

include/ck_tile/core/tensor/tensor_view.hpp

@@ -0,0 +1,533 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2025, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/arch/arch.hpp"
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/algorithm/coordinate_transform.hpp"
+#include "ck_tile/core/container/container_helper.hpp"
+#include "ck_tile/core/numeric/math.hpp"
+#include "ck_tile/core/tensor/tensor_descriptor.hpp"
+#include "ck_tile/core/utility/functional.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+
+namespace ck_tile {
+
+/*
+ * tensor_view
+ * abstract the underneath memory buffer(global, LDS, etc...)
+ * and provide a unified get/set function for access
+ *
+ * For addressing into the buffer we use 2 variable to control:
+ * coord : ND tensor coordinate, will calculate the actual offset inside
+ * linear_offset : 1D offset, will be used in the immediate field of
+ *   the buffer instruction to help reduce register usage
+ *
+ * User can use either of the field, or both to indexing into the tensor
+ *
+ * We usually provide 2 set of API for buffer get/set, e.g.
+ * get_vectorized_elements()/get_vectorized_elements_raw()
+ * the former usually will call intrinsic or normal C function, the later
+ * usually will call inline-asm function
+ *
+ */
+template <typename BufferView_,
+          typename TensorDesc_,
+          memory_operation_enum DstInMemOp_ = memory_operation_enum::set>
+struct tensor_view
+{
+    using buffer_view = remove_reference_t<BufferView_>;
+    using DataType    = typename buffer_view::type;
+    using TensorDesc  = remove_cvref_t<TensorDesc_>;
+    using TensorIndex = array<index_t, TensorDesc::get_num_of_top_dimension()>;
+    using TensorCoord = decltype(make_tensor_coordinate(TensorDesc{}, TensorIndex{}));
+    static constexpr auto DstInMemOp = DstInMemOp_;
+    static constexpr index_t PackedSize =
+        ck_tile::numeric_traits<remove_cvref_t<DataType>>::PackedSize;
+
+    CK_TILE_HOST_DEVICE constexpr tensor_view() = default;
+
+    CK_TILE_HOST_DEVICE constexpr tensor_view(const buffer_view& buffer_view,
+                                              const TensorDesc& desc)
+        : buf_{buffer_view}, desc_{desc}
+    {
+    }
+
+    CK_TILE_HOST_DEVICE void init_raw() { buf_.init_raw(); }
+
+    CK_TILE_HOST_DEVICE constexpr auto& get_tensor_descriptor() const { return desc_; }
+
+    CK_TILE_HOST_DEVICE static constexpr index_t get_num_of_dimension()
+    {
+        return TensorDesc::get_num_of_top_dimension();
+    }
+
+    CK_TILE_HOST_DEVICE constexpr const auto& get_buffer_view() const { return buf_; }
+
+    CK_TILE_HOST_DEVICE constexpr auto& get_buffer_view() { return buf_; }
+
+    // X is vector of DataType.
+    // "coord" is coordinate of DataType, not X. "coord" should be aligned to X
+    template <typename X,
+              bool oob_conditional_check = true,
+              typename std::enable_if<
+                  std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                 typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
+                  bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr remove_cvref_t<X>
+    get_vectorized_elements(const TensorCoord& coord,
+                            index_t linear_offset,
+                            bool_constant<oob_conditional_check> = {}) const
+    {
+        return buf_.template get<X>(
+            coord.get_offset() / PackedSize,
+            linear_offset / PackedSize,
+            coordinate_has_valid_offset_assuming_top_index_is_valid(desc_, coord),
+            bool_constant<oob_conditional_check>{});
+    }
+
+    template <typename X,
+              bool oob_conditional_check = true,
+              typename std::enable_if<
+                  std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                 typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
+                  bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr remove_cvref_t<X>
+    get_vectorized_elements(const TensorCoord& coord,
+                            index_t linear_offset,
+                            bool is_valid_element, // flag
+                            bool_constant<oob_conditional_check> = {}) const
+    {
+        return buf_.template get<X>(coord.get_offset() / PackedSize,
+                                    linear_offset / PackedSize,
+                                    is_valid_element,
+                                    bool_constant<oob_conditional_check>{});
+    }
+
+    // X is vector of DataType.
+    // "coord" is coordinate of DataType, not X. "coord" should be aligned to X
+    template <typename X,
+              bool oob_conditional_check = true,
+              bool pre_nop               = false,
+              typename std::enable_if<
+                  std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                 typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
+                  bool>::type = false>
+    CK_TILE_HOST_DEVICE void get_vectorized_elements_raw(remove_cvref_t<X>& dst,
+                                                         const TensorCoord& coord,
+                                                         index_t linear_offset,
+                                                         bool_constant<oob_conditional_check> = {},
+                                                         bool_constant<pre_nop> = {}) const
+    {
+        return buf_.template get_raw<X, oob_conditional_check, pre_nop>(
+            dst,
+            coord.get_offset() / PackedSize,
+            linear_offset / PackedSize,
+            coordinate_has_valid_offset_assuming_top_index_is_valid(desc_, coord),
+            bool_constant<pre_nop>{});
+    }
+
+    template <typename X,
+              bool oob_conditional_check = true,
+              bool pre_nop               = false,
+              typename std::enable_if<
+                  std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                 typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
+                  bool>::type = false>
+    CK_TILE_HOST_DEVICE void get_vectorized_elements_raw(remove_cvref_t<X>& dst,
+                                                         const TensorCoord& coord,
+                                                         index_t linear_offset,
+                                                         bool is_valid_element,
+                                                         bool_constant<oob_conditional_check> = {},
+                                                         bool_constant<pre_nop> = {}) const
+    {
+        return buf_.template get_raw<X, oob_conditional_check, pre_nop>(dst,
+                                                                        coord.get_offset() /
+                                                                            PackedSize,
+                                                                        linear_offset / PackedSize,
+                                                                        is_valid_element,
+                                                                        bool_constant<pre_nop>{});
+    }
+
+    template <typename X,
+              bool oob_conditional_check = true,
+              typename std::enable_if<
+                  std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                 typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
+                  bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr void
+    async_get_vectorized_elements(CK_TILE_LDS_ADDR remove_cvref_t<DataType>* smem,
+                                  const TensorCoord& coord,
+                                  index_t linear_offset) const
+    {
+        return buf_.template async_get<X>(
+            smem,
+            coord.get_offset() / PackedSize,
+            linear_offset / PackedSize,
+            coordinate_has_valid_offset_assuming_top_index_is_valid(desc_, coord),
+            bool_constant<oob_conditional_check>{});
+    }
+
+    template <typename X,
+              bool oob_conditional_check = true,
+              typename std::enable_if<
+                  std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                 typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
+                  bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr void
+    async_get_vectorized_elements(CK_TILE_LDS_ADDR remove_cvref_t<DataType>* smem,
+                                  const TensorCoord& coord,
+                                  index_t linear_offset,
+                                  bool is_valid_element) const
+    {
+        return buf_.template async_get<X>(smem,
+                                          coord.get_offset() / PackedSize,
+                                          linear_offset / PackedSize,
+                                          is_valid_element,
+                                          bool_constant<oob_conditional_check>{});
+    }
+
+    template <typename X,
+              bool pre_nop = false,
+              typename std::enable_if<
+                  std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                 typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
+                  bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr void
+    async_get_vectorized_elements_raw(remove_cvref_t<DataType>* smem,
+                                      const TensorCoord& coord,
+                                      index_t linear_offset,
+                                      bool_constant<pre_nop> = {}) const
+    {
+        return buf_.template async_get_raw<X>(
+            smem,
+            coord.get_offset() / PackedSize,
+            linear_offset / PackedSize,
+            coordinate_has_valid_offset_assuming_top_index_is_valid(desc_, coord),
+            bool_constant<pre_nop>{});
+    }
+
+    template <typename X,
+              bool pre_nop = false,
+              typename std::enable_if<
+                  std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                 typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
+                  bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr void
+    async_get_vectorized_elements_raw(remove_cvref_t<DataType>* smem,
+                                      const TensorCoord& coord,
+                                      index_t linear_offset,
+                                      bool is_valid_element,
+                                      bool_constant<pre_nop> = {}) const
+    {
+        return buf_.template async_get_raw<X>(smem,
+                                              coord.get_offset() / PackedSize,
+                                              linear_offset / PackedSize,
+                                              is_valid_element,
+                                              bool_constant<pre_nop>{});
+    }
+
+    // X is vector of DataType.
+    // "coord" is coordinate of DataType, not X. "coord" should be aligned to X
+    template <typename X,
+              bool oob_conditional_check = true,
+              typename std::enable_if<
+                  std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                 typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
+                  bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr void
+    set_vectorized_elements(const TensorCoord& coord,
+                            index_t linear_offset,
+                            const X& x,
+                            bool_constant<oob_conditional_check> = {})
+    {
+        buf_.template set<X, oob_conditional_check>(
+            coord.get_offset() / PackedSize,
+            linear_offset / PackedSize,
+            coordinate_has_valid_offset_assuming_top_index_is_valid(desc_, coord),
+            x);
+    }
+
+    template <typename X,
+              bool oob_conditional_check = true,
+              typename std::enable_if<
+                  std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                 typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
+                  bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr void
+    set_vectorized_elements(const TensorCoord& coord,
+                            index_t linear_offset,
+                            bool is_valid_element,
+                            const X& x,
+                            bool_constant<oob_conditional_check> = {})
+    {
+        buf_.template set<X, oob_conditional_check>(
+            coord.get_offset(), linear_offset, is_valid_element, x);
+    }
+
+    template <typename X,
+              bool oob_conditional_check = true,
+              typename std::enable_if<
+                  std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                 typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
+                  bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr void
+    set_vectorized_elements_raw(const TensorCoord& coord,
+                                index_t linear_offset,
+                                const X& x,
+                                bool_constant<oob_conditional_check> = {})
+    {
+        buf_.template set_raw<X, oob_conditional_check>(
+            coord.get_offset() / PackedSize,
+            linear_offset / PackedSize,
+            coordinate_has_valid_offset_assuming_top_index_is_valid(desc_, coord),
+            x);
+    }
+
+    template <typename X,
+              bool oob_conditional_check = true,
+              typename std::enable_if<
+                  std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                 typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
+                  bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr void
+    set_vectorized_elements_raw(const TensorCoord& coord,
+                                index_t linear_offset,
+                                bool is_valid_element,
+                                const X& x,
+                                bool_constant<oob_conditional_check> = {})
+    {
+        buf_.template set_raw<X, oob_conditional_check>(
+            coord.get_offset() / PackedSize, linear_offset / PackedSize, is_valid_element, x);
+    }
+
+    // X is vector of DataType.
+    // "coord" is coordinate of DataType, not X. "coord" should be aligned to X
+    template <typename X,
+              bool oob_conditional_check = true,
+              typename std::enable_if<
+                  std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                 typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
+                  bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr void
+    update_vectorized_elements(const TensorCoord& coord,
+                               index_t linear_offset,
+                               const X& x,
+                               bool_constant<oob_conditional_check> = {})
+    {
+        buf_.template update<DstInMemOp, X, oob_conditional_check>(
+            coord.get_offset() / PackedSize,
+            linear_offset / PackedSize,
+            coordinate_has_valid_offset_assuming_top_index_is_valid(desc_, coord),
+            x);
+    }
+
+    template <typename X,
+              bool oob_conditional_check = true,
+              typename std::enable_if<
+                  std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                 typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
+                  bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr void
+    update_vectorized_elements(const TensorCoord& coord,
+                               index_t linear_offset,
+                               bool is_valid_element,
+                               const X& x,
+                               bool_constant<oob_conditional_check> = {})
+    {
+        buf_.template update<DstInMemOp, X, oob_conditional_check>(
+            coord.get_offset() / PackedSize, linear_offset / PackedSize, is_valid_element, x);
+    }
+
+    // X is vector of DataType.
+    // "coord" is coordinate of DataType, not X. "coord" should be aligned to X
+    template <typename X,
+              bool oob_conditional_check = true,
+              bool pre_nop               = false,
+              typename std::enable_if<
+                  std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                 typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
+                  bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr void
+    update_vectorized_elements_raw(const TensorCoord& coord,
+                                   index_t linear_offset,
+                                   const X& x,
+                                   bool_constant<oob_conditional_check> = {},
+                                   bool_constant<pre_nop>               = {})
+    {
+        buf_.template update_raw<DstInMemOp, X, oob_conditional_check, pre_nop>(
+            coord.get_offset() / PackedSize,
+            linear_offset / PackedSize,
+            coordinate_has_valid_offset_assuming_top_index_is_valid(desc_, coord),
+            x);
+    }
+
+    template <typename X,
+              bool oob_conditional_check = true,
+              bool pre_nop               = false,
+              typename std::enable_if<
+                  std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                 typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
+                  bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr void
+    update_vectorized_elements_raw(const TensorCoord& coord,
+                                   index_t linear_offset,
+                                   bool is_valid_element,
+                                   const X& x,
+                                   bool_constant<oob_conditional_check> = {},
+                                   bool_constant<pre_nop>               = {})
+    {
+        buf_.template update_raw<DstInMemOp, X, oob_conditional_check, pre_nop>(
+            coord.get_offset() / PackedSize, linear_offset / PackedSize, is_valid_element, x);
+    }
+
+    CK_TILE_HOST_DEVICE void print() const
+    {
+        printf("tensor_view{");
+
+        // buf_
+        printf("buf_: ");
+        print(buf_);
+        printf(", ");
+
+        // desc_
+        printf("desc_: ");
+        print(desc_);
+
+        printf("}");
+    }
+
+    // member
+    buffer_view buf_;
+    TensorDesc desc_;
+};
+
+// placeholder type if we want to opt-out a tile view parameter
+struct null_tensor_view
+{
+};
+
+template <address_space_enum BufferAddressSpace = address_space_enum::generic,
+          amd_buffer_coherence_enum Coherence   = amd_buffer_coherence_enum::coherence_default,
+          typename DataType,
+          typename... Ts>
+CK_TILE_HOST_DEVICE constexpr auto make_tensor_view(DataType* p,
+                                                    const tensor_descriptor<Ts...>& desc)
+{
+    auto buffer_view =
+        make_buffer_view<BufferAddressSpace, Coherence>(p, desc.get_element_space_size());
+
+    return tensor_view<decltype(buffer_view), decltype(desc)>{buffer_view, desc};
+}
+
+template <address_space_enum BufferAddressSpace = address_space_enum::generic,
+          memory_operation_enum DstInMemOp      = memory_operation_enum::set,
+          amd_buffer_coherence_enum Coherence   = amd_buffer_coherence_enum::coherence_default,
+          typename DataType,
+          typename... Lengths,
+          typename... Strides,
+          index_t GuaranteedLastDimensionVectorLength                                   = -1,
+          index_t GuaranteedLastDimensionVectorStride                                   = -1,
+          typename std::enable_if<sizeof...(Lengths) == sizeof...(Strides), bool>::type = false>
+CK_TILE_HOST_DEVICE constexpr auto
+make_naive_tensor_view(DataType* p,
+                       const tuple<Lengths...>& lengths,
+                       const tuple<Strides...>& strides,
+                       number<GuaranteedLastDimensionVectorLength> = number<-1>{},
+                       number<GuaranteedLastDimensionVectorStride> = number<-1>{})
+{
+    auto desc = make_naive_tensor_descriptor(lengths,
+                                             strides,
+                                             number<GuaranteedLastDimensionVectorLength>{},
+                                             number<GuaranteedLastDimensionVectorStride>{});
+
+    auto buffer_view =
+        make_buffer_view<BufferAddressSpace, Coherence>(p, desc.get_element_space_size());
+
+    return tensor_view<decltype(buffer_view), decltype(desc), DstInMemOp>{buffer_view, desc};
+}
+
+template <address_space_enum BufferAddressSpace = address_space_enum::generic,
+          amd_buffer_coherence_enum Coherence   = amd_buffer_coherence_enum::coherence_default,
+          typename DataType,
+          typename... Lengths,
+          index_t GuaranteedLastDimensionVectorLength = -1>
+CK_TILE_HOST_DEVICE constexpr auto
+make_naive_tensor_view_packed(DataType* p,
+                              const tuple<Lengths...>& lengths,
+                              number<GuaranteedLastDimensionVectorLength> = number<-1>{})
+{
+    auto desc =
+        make_naive_tensor_descriptor_packed(lengths, number<GuaranteedLastDimensionVectorLength>{});
+
+    auto buffer_view =
+        make_buffer_view<BufferAddressSpace, Coherence>(p, desc.get_element_space_size());
+
+    return tensor_view<decltype(buffer_view), decltype(desc)>{buffer_view, desc};
+}
+
+template <typename OldTensorView,
+          typename NewTransforms,
+          typename NewLowerDimensionOldVisibleIdss,
+          typename NewUpperDimensionNewVisibleIdss>
+CK_TILE_HOST_DEVICE constexpr auto transform_tensor_view(const OldTensorView& old_tensor_view,
+                                                         const NewTransforms& new_transforms,
+                                                         NewLowerDimensionOldVisibleIdss,
+                                                         NewUpperDimensionNewVisibleIdss)
+{
+    auto new_desc = transform_tensor_descriptor(old_tensor_view.desc_,
+                                                new_transforms,
+                                                NewLowerDimensionOldVisibleIdss{},
+                                                NewUpperDimensionNewVisibleIdss{});
+
+    return tensor_view<typename OldTensorView::buffer_view,
+                       remove_cvref_t<decltype(new_desc)>,
+                       remove_cvref_t<OldTensorView>::DstInMemOp>{old_tensor_view.buf_, new_desc};
+}
+
+template <typename TensorView,
+          typename TileLengths, // tuple<...>
+          typename DoPads>      // sequence<bool, bool, ...>
+CK_TILE_HOST_DEVICE constexpr auto
+pad_tensor_view(const TensorView& tensor_view, const TileLengths& tile_lengths, DoPads)
+{
+    constexpr index_t num_dim = DoPads::size();
+
+    static_assert(num_dim == TileLengths::size() && num_dim == TensorView::get_num_of_dimension(),
+                  "wrong! inconsistent # of dimensions");
+
+    // transforms
+    const auto transforms = generate_tuple(
+        [&](auto idim) {
+            const auto old_length = tensor_view.get_tensor_descriptor().get_length(idim);
+
+            const auto tile_length = tile_lengths[idim];
+
+            const auto new_length = integer_divide_ceil(old_length, tile_length) * tile_length;
+
+            const auto pad_length = new_length - old_length;
+
+            constexpr bool DoPad = DoPads::at(idim);
+
+            const auto transform =
+                conditional_expr<DoPad>(make_right_pad_transform(old_length, pad_length),
+                                        make_pass_through_transform(old_length));
+
+            return transform;
+        },
+        number<num_dim>{});
+
+    // lower dimension Id
+    const auto lower_dimss =
+        generate_tuple([&](auto idim) { return sequence<idim.value>{}; }, number<num_dim>{});
+
+    // upper dimension Id
+    const auto upper_dimss = lower_dimss;
+
+    return transform_tensor_view(tensor_view, transforms, lower_dimss, upper_dimss);
+}
+
+} // namespace ck_tile

include/ck_tile/core/tensor/tile_distribution.hpp

@@ -0,0 +1,673 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/arch/arch.hpp"
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/container/array.hpp"
+#include "ck_tile/core/container/sequence.hpp"
+#include "ck_tile/core/container/tuple.hpp"
+#include "ck_tile/core/container/container_helper.hpp"
+#include "ck_tile/core/container/meta_data_buffer.hpp"
+#include "ck_tile/core/tensor/tensor_adaptor.hpp"
+#include "ck_tile/core/tensor/tile_distribution_encoding.hpp"
+#include "ck_tile/core/utility/functional.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+
+namespace ck_tile {
+
+namespace detail {
+template <typename Distribution>
+CK_TILE_HOST_DEVICE auto get_partition_index(Distribution)
+{
+    return Distribution::_get_partition_index();
+}
+} // namespace detail
+
+// distributed span
+template <index_t... PartialHsLengths>
+struct tile_distributed_span
+{
+    using Impl = sequence<PartialHsLengths...>;
+
+    static constexpr auto impl_ = Impl{};
+
+    CK_TILE_HOST_DEVICE static constexpr bool is_static() { return true; }
+};
+
+// distributed index
+template <index_t... PartialHsIndices>
+struct tile_distributed_index
+{
+    using Impl = sequence<PartialHsIndices...>;
+
+    static constexpr auto impl_ = Impl{};
+
+    CK_TILE_HOST_DEVICE static constexpr bool is_static() { return true; }
+};
+
+namespace detail {
+
+template <index_t... Is>
+CK_TILE_HOST_DEVICE constexpr auto make_tile_distributed_span(sequence<Is...>)
+{
+    return tile_distributed_span<Is...>{};
+}
+
+template <index_t... Is>
+CK_TILE_HOST_DEVICE constexpr auto make_tile_distributed_index(sequence<Is...>)
+{
+    return tile_distributed_index<Is...>{};
+}
+
+} // namespace detail
+
+template <typename PsYs2XsAdaptor_,
+          typename Ys2DDescriptor_,
+          typename StaticTileDistributionEncoding_,
+          typename TileDistributionDetail_> // FIXME: this is for hold ad-hoc but useful info,
+                                            // should be more elegnat
+struct tile_distribution
+{
+    using PsYs2XsAdaptor = remove_cvref_t<PsYs2XsAdaptor_>;
+    using Ys2DDescriptor = remove_cvref_t<Ys2DDescriptor_>;
+    using DstrEncode     = remove_cvref_t<StaticTileDistributionEncoding_>;
+    using DstrDetail     = remove_cvref_t<TileDistributionDetail_>;
+
+    static_assert(PsYs2XsAdaptor::is_static() && Ys2DDescriptor::is_static(),
+                  "wrong! should be static");
+
+    static constexpr index_t NDimX = PsYs2XsAdaptor::get_num_of_bottom_dimension();
+    static constexpr index_t NDimY = Ys2DDescriptor::get_num_of_top_dimension();
+    static constexpr index_t NDimP = PsYs2XsAdaptor::get_num_of_top_dimension() - NDimY;
+    static constexpr index_t NDimR = StaticTileDistributionEncoding_::NDimR;
+
+    PsYs2XsAdaptor ps_ys_to_xs_;
+    Ys2DDescriptor ys_to_d_;
+
+    CK_TILE_HOST_DEVICE static constexpr index_t get_num_of_dimension_x() { return NDimX; }
+    CK_TILE_HOST_DEVICE static constexpr index_t get_num_of_dimension_y() { return NDimY; }
+    CK_TILE_HOST_DEVICE static constexpr index_t get_num_of_dimension_p() { return NDimP; }
+    CK_TILE_HOST_DEVICE static constexpr index_t get_num_of_dimension_r() { return NDimR; }
+
+    CK_TILE_HOST_DEVICE static auto _get_partition_index()
+    {
+        // only support warp-tile and block-tile
+        static_assert(NDimP == 1 or NDimP == 2, "wrong!");
+
+        if constexpr(NDimP == 1)
+        {
+            return array<index_t, 1>{get_lane_id()};
+        }
+        else if constexpr(NDimP == 2)
+        {
+            return array<index_t, 2>{get_warp_id(), get_lane_id()};
+        }
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr auto get_lengths()
+    {
+#if 0
+        // FIXME: tensor_adaptor::GetBottomDimensionLengths is wrong. re-enable this after it's fixed
+        ps_ys_to_xs_.GetBottomDimensionLengths();
+#else
+        return generate_tuple(
+            [&](auto i) {
+                constexpr index_t x_length =
+                    container_reduce(typename DstrEncode::HsLengthss{}[i], multiplies{}, 1);
+
+                return number<x_length>{};
+            },
+            number<NDimX>{});
+#endif
+    }
+
+    CK_TILE_HOST_DEVICE constexpr const auto& get_ps_ys_to_xs_adaptor() const
+    {
+        return ps_ys_to_xs_;
+    }
+
+    CK_TILE_HOST_DEVICE constexpr const auto& get_ys_to_d_descriptor() const { return ys_to_d_; }
+
+    CK_TILE_HOST_DEVICE static constexpr auto get_static_tile_distribution_encoding()
+    {
+        return DstrEncode{};
+    }
+
+#if 1
+    // Calculate Replication index [R0, R1, ...] based on Partion index
+    // FIXME: very nasty implementation
+    template <typename PartitionIndex>
+    CK_TILE_HOST_DEVICE auto calculate_rs_index_from_ps_index(const PartitionIndex& ps_idx) const
+    {
+        static_assert(PartitionIndex::size() == NDimP, "wrong!");
+
+        const auto ps_ys_idx = container_concat(ps_idx, array<index_t, NDimY>{0});
+
+        const auto dummy_adaptor_coord = make_tensor_adaptor_coordinate(ps_ys_to_xs_, ps_ys_idx);
+
+        array<index_t, NDimR> rs_idx;
+
+        static_for<0, NDimP, 1>{}([&](auto idim_p) {
+            constexpr index_t ndim_low = DstrEncode::ps_to_rhss_major_[idim_p].size();
+
+            static_for<0, ndim_low, 1>{}([&](auto i) {
+                constexpr index_t rh_major = DstrEncode::ps_to_rhss_major_[idim_p][i];
+                constexpr index_t rh_minor = DstrEncode::ps_to_rhss_minor_[idim_p][i];
+
+                // 0-th rh_major is the replicate dimension
+                if constexpr(rh_major == 0)
+                {
+                    constexpr index_t adaptor_hidden_id =
+                        DstrDetail::rh_major_minor_to_adaptor_hidden_idss_[rh_major][rh_minor];
+
+                    // fill in
+                    rs_idx(rh_minor) = dummy_adaptor_coord.get_hidden_index()[adaptor_hidden_id];
+                }
+            });
+        });
+
+        return rs_idx;
+    }
+#endif
+
+    template <typename PartitionIndex = decltype(_get_partition_index())>
+    CK_TILE_HOST_DEVICE auto
+    calculate_index(const PartitionIndex& ps_idx = _get_partition_index()) const
+    {
+        const auto ps_ys_idx = container_concat(ps_idx, array<index_t, NDimY>{0});
+        const auto window_adaptor_thread_coord_tmp =
+            make_tensor_adaptor_coordinate(ps_ys_to_xs_, ps_ys_idx);
+        return window_adaptor_thread_coord_tmp.get_bottom_index();
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr auto get_distributed_spans()
+    {
+        constexpr auto distributed_spans_impl = DstrEncode::detail::distributed_spans_lengthss_;
+        constexpr auto ndims_spans_minor      = DstrEncode::detail::ndims_distributed_spans_minor_;
+
+        return generate_tuple(
+            [&](auto i) {
+                constexpr auto span_impl          = distributed_spans_impl[i];
+                constexpr index_t ndim_span_minor = ndims_spans_minor[i];
+
+                constexpr auto span = TO_SEQUENCE(span_impl, ndim_span_minor);
+
+                return detail::make_tile_distributed_span(span);
+            },
+            number<NDimX>{});
+    }
+
+    // FIXME: it's hacky to get Y index from Distributed-Index
+    template <typename DistributedIndices>
+    CK_TILE_HOST_DEVICE static constexpr auto
+        get_y_indices_from_distributed_indices(DistributedIndices)
+    {
+        constexpr auto ys_idx_arr = [] {
+            array<index_t, NDimY> ys_idx;
+
+            static_for<0, NDimY, 1>{}([&](auto i) {
+                constexpr index_t span_major = DstrEncode::detail::ys_to_span_major_[i];
+                constexpr index_t span_minor = DstrEncode::detail::ys_to_span_minor_[i];
+
+                constexpr auto dstr_index = DistributedIndices{}[number<span_major>{}];
+
+                ys_idx(i) = dstr_index.impl_[span_minor];
+            });
+
+            return ys_idx;
+        }();
+
+        constexpr index_t ndim_y = NDimY;
+
+        return TO_SEQUENCE(ys_idx_arr, ndim_y);
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr bool is_static()
+    {
+        return PsYs2XsAdaptor::is_static() && Ys2DDescriptor::is_static();
+    }
+
+    CK_TILE_HOST_DEVICE void print() const
+    {
+        printf("tile_distribution{");
+        //
+        printf("tile_distribution_encoding: ");
+        print(DstrEncode{});
+        printf(", ");
+        //
+        printf("ps_ys_to_xs_: ");
+        print(ps_ys_to_xs_);
+        printf(", ");
+        //
+        printf("ys_to_d_: ");
+        print(ys_to_d_);
+        //
+        printf("}");
+    }
+};
+
+namespace detail {
+
+template <index_t NDimMax>
+CK_TILE_HOST_DEVICE constexpr auto make_sequential_index(index_t ibegin, index_t iend)
+{
+    array<index_t, NDimMax> arr{0};
+
+    for(index_t i = 0; i < iend - ibegin; ++i)
+    {
+        arr(i) = ibegin + i;
+    }
+
+    return arr;
+}
+
+// this returns a constexpr encoding of tile_distribution
+template <typename StaticTileDistributionEncoding_>
+CK_TILE_HOST_DEVICE constexpr auto
+    make_adaptor_encoding_for_tile_distribution(StaticTileDistributionEncoding_)
+{
+    using RsLengths    = typename StaticTileDistributionEncoding_::RsLengths;
+    using HsLengthss   = typename StaticTileDistributionEncoding_::HsLengthss;
+    using Ps2RHssMajor = typename StaticTileDistributionEncoding_::Ps2RHssMajor;
+    using Ps2RHssMinor = typename StaticTileDistributionEncoding_::Ps2RHssMinor;
+    using Ys2RHsMajor  = typename StaticTileDistributionEncoding_::Ys2RHsMajor;
+    using Ys2RHsMinor  = typename StaticTileDistributionEncoding_::Ys2RHsMinor;
+
+    // FIXME: increase max value if fail
+    constexpr index_t kMaxNumTransforms = 20;
+    constexpr index_t kMaxMetaDataSize  = 128;
+    constexpr index_t kMaxNumDim        = 10;
+
+    using Name     = coord_transform_enum;
+    using MetaData = meta_data_buffer<kMaxMetaDataSize>;
+    using NumDim   = index_t;
+    using Dims     = array<index_t, kMaxNumDim>;
+    using Lengths  = array<index_t, kMaxNumDim>;
+
+    // Tile Adaptor
+    //   bottom dims [x0, x1, x2, ...]
+    //   top dims [p0, p1, ..., y0, y1, ...]
+    constexpr index_t ndim_x = HsLengthss::size();
+
+    // Dim Ids: [idim_x_major, idim_x_minor] to [idim_hidden]
+    array<array<index_t, kMaxNumDim>, ndim_x + 1> rh_major_minor_to_hidden_ids;
+    array<array<index_t, kMaxNumDim>, ndim_x + 1> rh_major_minor_to_hidden_lengths;
+
+    auto trans = array<tuple<Name, MetaData, NumDim, Dims, NumDim, Dims>, kMaxNumTransforms>{};
+
+    index_t num_tran       = 0;
+    index_t hidden_dim_cnt = ndim_x;
+
+    // this is replicate transform
+    {
+        constexpr index_t ndim_r_minor = RsLengths::size();
+
+        constexpr auto r_minor_lengths = RsLengths{};
+
+        trans(num_tran++) = {
+            coord_transform_enum::replicate,
+            MetaData{to_array<index_t, ndim_r_minor>(r_minor_lengths)},
+            NumDim{0},
+            Dims{},
+            NumDim{ndim_r_minor},
+            make_sequential_index<kMaxNumDim>(hidden_dim_cnt, hidden_dim_cnt + ndim_r_minor)};
+
+        for(index_t i = 0; i < ndim_r_minor; ++i)
+        {
+            rh_major_minor_to_hidden_ids(0)(i)     = hidden_dim_cnt;
+            rh_major_minor_to_hidden_lengths(0)(i) = r_minor_lengths[i];
+
+            hidden_dim_cnt++;
+        }
+    };
+
+    // these are Unmerge transforms for X dimesions
+    static_for<0, ndim_x, 1>{}([&trans,
+                                &num_tran,
+                                &hidden_dim_cnt,
+                                &rh_major_minor_to_hidden_ids,
+                                &rh_major_minor_to_hidden_lengths](auto idim_x) {
+        // typename HsLengthss::base{}.foo();
+        constexpr auto h_minor_lengths =
+            HsLengthss{}.get(idim_x); // std::tuple_element_t<idim_x, HsLengthss>{};
+        // constexpr auto h_minor_lengths = impl::getv<idim_x>(HsLengthss{});
+
+        constexpr index_t ndim_h_minor = h_minor_lengths.size();
+
+        trans(num_tran++) = {
+            coord_transform_enum::unmerge,
+            MetaData{to_array<index_t, ndim_h_minor>(h_minor_lengths)},
+            NumDim{1},
+            Dims{idim_x},
+            NumDim{ndim_h_minor},
+            make_sequential_index<kMaxNumDim>(hidden_dim_cnt, hidden_dim_cnt + ndim_h_minor)};
+
+        for(index_t i = 0; i < ndim_h_minor; ++i)
+        {
+            rh_major_minor_to_hidden_ids(idim_x + 1)(i)     = hidden_dim_cnt;
+            rh_major_minor_to_hidden_lengths(idim_x + 1)(i) = h_minor_lengths[i];
+
+            hidden_dim_cnt++;
+        }
+    });
+
+    // transform: P dimensions
+    constexpr index_t ndim_p = Ps2RHssMajor::size();
+
+    Dims hidden_dim_id_ps;
+
+    static_for<0, ndim_p, 1>{}([&](auto iDimP) {
+        //
+        index_t hidden_dim_id_p = hidden_dim_cnt++;
+
+        hidden_dim_id_ps(iDimP) = hidden_dim_id_p;
+
+        constexpr auto p2RHsMajor = Ps2RHssMajor{}[iDimP];
+        constexpr auto p2RHsMinor = Ps2RHssMinor{}[iDimP];
+
+        static_assert(p2RHsMajor.size() == p2RHsMinor.size(), "wrong!");
+
+        constexpr index_t ndim_low = p2RHsMajor.size();
+
+        Dims low_dims;
+        Lengths low_lengths;
+
+        for(index_t i = 0; i < ndim_low; ++i)
+        {
+            index_t rh_major = p2RHsMajor[i];
+            index_t rh_minor = p2RHsMinor[i];
+            low_dims(i)      = rh_major_minor_to_hidden_ids[rh_major][rh_minor];
+            low_lengths(i)   = rh_major_minor_to_hidden_lengths[rh_major][rh_minor];
+        }
+
+        trans(num_tran++) = {coord_transform_enum::merge,
+                             MetaData{to_array<index_t, ndim_low>(low_lengths)},
+                             NumDim{ndim_low},
+                             low_dims,
+                             NumDim{1},
+                             Dims{hidden_dim_id_p}};
+    });
+
+    constexpr index_t ndim_bottom = ndim_x;
+
+    constexpr auto bottom_dim_ids = make_sequential_index<kMaxNumDim>(0, ndim_bottom);
+
+    constexpr auto ys_to_rhs_major = Ys2RHsMajor{};
+    constexpr auto ys_to_rhs_minor = Ys2RHsMinor{};
+
+    constexpr index_t ndim_y   = Ys2RHsMajor::size();
+    constexpr index_t ndim_top = ndim_p + ndim_y;
+
+    auto top_dim_ids = hidden_dim_id_ps;
+
+    {
+        for(index_t i = 0; i < ndim_y; ++i)
+        {
+            index_t rh_major        = ys_to_rhs_major[i];
+            index_t rh_minor        = ys_to_rhs_minor[i];
+            top_dim_ids(ndim_p + i) = rh_major_minor_to_hidden_ids[rh_major][rh_minor];
+        }
+    }
+
+    //
+    const auto ps_ys_to_xs_adaptor_encoding =
+        make_tuple(trans, num_tran, bottom_dim_ids, ndim_bottom, top_dim_ids, ndim_top);
+
+    // descriptor: [y0, y1, ...] to [d]
+    Lengths y_lengths;
+    index_t d_length = 1;
+
+    for(index_t i = 0; i < ndim_y; ++i)
+    {
+        index_t rh_major = ys_to_rhs_major[i];
+        index_t rh_minor = ys_to_rhs_minor[i];
+        index_t y_length = rh_major_minor_to_hidden_lengths[rh_major][rh_minor];
+        y_lengths(i)     = y_length;
+        d_length *= y_length;
+    }
+
+    auto tran = make_tuple(coord_transform_enum::unmerge,
+                           MetaData{to_array<index_t, ndim_y>(y_lengths)},
+                           NumDim{1},
+                           Dims{0},
+                           NumDim{ndim_y},
+                           make_sequential_index<kMaxNumDim>(1, ndim_y + 1));
+
+    const auto ys_to_d_adaptor_encoding = make_tuple(
+        make_tuple(tran), 1, Dims{0}, 1, make_sequential_index<kMaxNumDim>(1, ndim_y + 1), ndim_y);
+
+    return make_tuple(ps_ys_to_xs_adaptor_encoding,
+                      ys_to_d_adaptor_encoding,
+                      d_length,
+                      rh_major_minor_to_hidden_ids);
+}
+
+// FIXME: this is nasty. Move it inside TileDistributionEncoding::detail
+template <typename RhMajorMinor2AdaptorHiddenIdss> // tuple<sequence<...>, ...>
+struct tile_distribution_detail
+{
+    static constexpr auto rh_major_minor_to_adaptor_hidden_idss_ =
+        to_array_of_array(RhMajorMinor2AdaptorHiddenIdss{});
+};
+
+} // namespace detail
+
+#if 0
+// this returns a constexpr tile_distribution
+template <typename StaticTileDistributionEncoding_>
+CK_TILE_HOST_DEVICE constexpr auto make_tile_distribution(StaticTileDistributionEncoding_)
+{
+    using DstrEncode = remove_cvref_t<StaticTileDistributionEncoding_>;
+
+    constexpr auto adaptor_impl =
+        detail::make_adaptor_encoding_for_tile_distribution(StaticTileDistributionEncoding_{});
+
+    constexpr auto ps_ys_to_xs_adaptor_impl          = adaptor_impl.template at<0>();
+    constexpr auto ys_to_d_adaptor_impl              = adaptor_impl.template at<1>();
+    constexpr index_t d_length                       = adaptor_impl.template at<2>();
+    constexpr auto rh_major_minor_to_hidden_ids_impl = adaptor_impl.template at<3>();
+
+    constexpr auto ps_ys_to_xs_adaptor =
+        CONSTRUCT_TENSOR_ADAPTOR_FROM_ENCODING(ps_ys_to_xs_adaptor_impl);
+
+    constexpr auto ys_to_d_adaptor = CONSTRUCT_TENSOR_ADAPTOR_FROM_ENCODING(ys_to_d_adaptor_impl);
+
+    constexpr auto ys_to_d_descriptor =
+        make_tensor_descriptor_from_adaptor(ys_to_d_adaptor, d_length);
+
+    //
+    constexpr index_t ndim_rh_major = DstrEncode::detail::ndim_rh_major_;
+    constexpr auto ndims_rhs_minor  = DstrEncode::detail::ndims_rhs_minor_;
+
+    constexpr auto rh_major_minor_to_hidden_ids =
+        TO_TUPLE_OF_SEQUENCE(rh_major_minor_to_hidden_ids_impl, ndim_rh_major, ndims_rhs_minor);
+
+    return tile_distribution<
+        remove_cvref_t<decltype(ps_ys_to_xs_adaptor)>,
+        remove_cvref_t<decltype(ys_to_d_descriptor)>,
+        remove_cvref_t<DstrEncode>,
+        detail::tile_distribution_detail<remove_cvref_t<decltype(rh_major_minor_to_hidden_ids)>>>{
+        ps_ys_to_xs_adaptor, ys_to_d_descriptor};
+}
+#endif
+
+// this returns a static tile_distribution
+template <typename StaticTileDistributionEncoding_>
+CK_TILE_HOST_DEVICE constexpr auto make_static_tile_distribution(StaticTileDistributionEncoding_)
+{
+    using DstrEncode = remove_cvref_t<StaticTileDistributionEncoding_>;
+
+    constexpr auto adaptor_impl =
+        detail::make_adaptor_encoding_for_tile_distribution(StaticTileDistributionEncoding_{});
+
+    constexpr auto ps_ys_to_xs_adaptor_impl          = adaptor_impl.template at<0>();
+    constexpr auto ys_to_d_adaptor_impl              = adaptor_impl.template at<1>();
+    constexpr index_t d_length                       = adaptor_impl.template at<2>();
+    constexpr auto rh_major_minor_to_hidden_ids_impl = adaptor_impl.template at<3>();
+
+    constexpr auto ps_ys_to_xs_adaptor =
+        CONSTRUCT_STATIC_TENSOR_ADAPTOR_FROM_ENCODING(ps_ys_to_xs_adaptor_impl);
+
+    constexpr auto ys_to_d_adaptor =
+        CONSTRUCT_STATIC_TENSOR_ADAPTOR_FROM_ENCODING(ys_to_d_adaptor_impl);
+
+    constexpr auto ys_to_d_descriptor =
+        make_tensor_descriptor_from_adaptor(ys_to_d_adaptor, number<d_length>{});
+
+    //
+    constexpr index_t ndim_rh_major = DstrEncode::detail::ndim_rh_major_;
+    constexpr auto ndims_rhs_minor  = DstrEncode::detail::ndims_rhs_minor_;
+
+    constexpr auto rh_major_minor_to_hidden_ids =
+        TO_TUPLE_OF_SEQUENCE(rh_major_minor_to_hidden_ids_impl, ndim_rh_major, ndims_rhs_minor);
+
+    return tile_distribution<
+        remove_cvref_t<decltype(ps_ys_to_xs_adaptor)>,
+        remove_cvref_t<decltype(ys_to_d_descriptor)>,
+        remove_cvref_t<DstrEncode>,
+        detail::tile_distribution_detail<remove_cvref_t<decltype(rh_major_minor_to_hidden_ids)>>>{
+        ps_ys_to_xs_adaptor, ys_to_d_descriptor};
+}
+
+//***********************************************************************************
+
+namespace detail {
+//
+// slice tensor from x_dim, result in split in y_dim, not p_dim.
+// We don't support slice cross p_dim (aka, slice different threads)
+// also, sliced along y_dim need be the first dim of current dim.
+// Multiply Y dim before sliced dim does not make sense
+//
+// e.g
+//       X0           X1
+//       <1, 4, 32> - <4, 1, 4, 2, 4>  | slice origin:<0, 0>, len:<0, 32>, (0 means all length)
+//        Y  P  P      Y  P  Y  P  Y
+//   =>  <1, 4, 32> - <1, 1, 4, 2, 4> -> OK
+//                     |--> slice along this Y dim, is the first dim of X1, totally 4 slices
+//
+//       X0           X1
+//       <1, 4, 32> - <4, 1, 4, 2, 4>  | slice origin:<0, 0>, len:<0, 8>, (0 means all length)
+//        Y  P  P      Y  P  Y  P  Y
+//   =>  <1, 4, 32> - <1, 1, 1, 2, 4> -> OK
+//                           |--> slice along this Y dim, the P dim is 1 in the left, so is OK
+//                                 totally 16 slices
+//
+//       X0           X1
+//       <1, 4, 32> - <4, 1, 4, 2, 4>  | slice origin:<0, 0>, len:<0, 4>, (0 means all length)
+//        Y  P  P      Y  P  Y  P  Y
+//   =>  <1, 4, 32> - <1, 1, 1, 1, 4> -> Fail
+//                              |--> slice along this P dim, will split threads, not supported
+//
+//       X0           X1
+//       <1, 4, 32> - <4, 1, 4, 2, 4>  | slice origin:<0, 0>, len:<0, 16>, (0 means all length)
+//        Y  P  P      Y  P  Y  P  Y
+//   =>  <1, 4, 32> - <1, 1, 2, 2, 4> -> OK
+//                           |--> slice along this Y dim, but this Y sim need to split into 2
+//                           subdime
+//                                the P dim in the left is 1, means actually not crossing P
+//
+template <typename Distribution, index_t... XSliceBegins, index_t... XSliceEnds>
+CK_TILE_HOST_DEVICE constexpr auto slice_distribution_from_x(
+    Distribution, sequence<XSliceBegins...> x_slice_begins, sequence<XSliceEnds...> x_slice_ends)
+{
+    // NOTE: this function need to be called under constexpr context,
+    // due to https://wg21.link/p2280r0 we have to use non-reference type for distribution
+    using Encoding = decltype(Distribution::get_static_tile_distribution_encoding());
+
+    static_assert(sizeof...(XSliceBegins) == sizeof...(XSliceEnds));
+
+    constexpr auto x_slice_lengths = x_slice_ends - x_slice_begins;
+
+    constexpr auto src_h_prefix_sum = Encoding::detail::get_h_dim_lengths_prefix_sum();
+    constexpr auto src_y_info       = Encoding::detail::get_sorted_y_info();
+    constexpr auto src_y_dims       = src_y_info[number<0>{}];
+    constexpr auto src_y_maps       = src_y_info[number<1>{}];
+    constexpr auto src_y_prefix_sum = src_y_info[number<2>{}];
+
+    constexpr auto sliced_hlen_yidx_ylen = [&]() constexpr
+    {
+        auto y_slice_sorted_origins = make_zero_multi_index<Encoding::NDimY>();
+        auto y_slice_lengths        = Encoding::detail::ys_lengths_;
+
+        // This lambda will modify some value outside, so c++ will not treat return value as
+        // constexpr
+        // TODO: ugly
+        auto new_h_lengths = transform_tuples(
+            [&](auto h_len, auto id) {
+                constexpr auto sliced_h =
+                    reverse_slice_sequence(h_len, number<x_slice_lengths[id]>{});
+
+                constexpr auto sliced_h_lens  = sliced_h[number<0>{}];
+                constexpr auto sliced_h_index = sliced_h[number<2>{}];
+
+                // update y_slice_lengths
+                constexpr auto uniformed_h_index = sliced_h_index + number<src_h_prefix_sum[id]>{};
+                constexpr auto found_y_index     = container_find(src_y_dims, uniformed_h_index);
+
+                static_assert(found_y_index >= 0 && found_y_index < src_y_dims.size(),
+                              "not sliced at y dim, please check");
+
+                static_for<0, sliced_h_index + 1, 1>{}([&](auto i) {
+                    y_slice_lengths(src_y_maps[found_y_index - i]) =
+                        sliced_h_lens[sliced_h_index - i];
+                });
+                // TODO: add validations not across p dim
+
+                // NOTE: this y_origin is for all dims, not only current dim
+                //       will later use pick to select target dim
+                constexpr auto y_origin = [&]() {
+                    constexpr auto h_trans = make_merge_transform_v3_division_mod(h_len);
+                    auto h_origin_         = make_zero_multi_index<h_trans.NDimLow>();
+                    h_trans.calculate_lower_index(h_origin_, sequence<x_slice_begins[id].value>{});
+
+                    auto y_origin_ = make_zero_multi_index<Encoding::NDimY>();
+                    static_for<0, sliced_h_index + 1, 1>{}([&](auto i) {
+                        y_origin_(found_y_index - i) = h_origin_[sliced_h_index - i];
+                    });
+                    return y_origin_;
+                }();
+
+                constexpr auto y_picks = typename arithmetic_sequence_gen<src_y_prefix_sum[id],
+                                                                          src_y_prefix_sum[id + 1],
+                                                                          1>::type{};
+
+                set_container_subset(
+                    y_slice_sorted_origins, y_picks, get_container_subset(y_origin, y_picks));
+                return sliced_h_lens;
+            },
+            typename Encoding::HsLengthss{},
+            typename arithmetic_sequence_gen<0, Encoding::HsLengthss::size(), 1>::type{});
+
+        auto y_slice_origins = container_reorder_given_old2new(y_slice_sorted_origins, src_y_maps);
+
+        return make_tuple(new_h_lengths, y_slice_origins, y_slice_lengths);
+    }
+    ();
+
+    constexpr auto sliced_h_lengths       = sliced_hlen_yidx_ylen[number<0>{}];
+    constexpr auto sliced_y_origins_array = sliced_hlen_yidx_ylen[number<1>{}];
+    constexpr auto sliced_y_origins_size  = sliced_y_origins_array.size();
+    constexpr auto sliced_y_lengths_array = sliced_hlen_yidx_ylen[number<2>{}];
+    constexpr auto sliced_y_lengths_size  = sliced_y_lengths_array.size();
+
+    constexpr auto sliced_y_origins = TO_SEQUENCE(sliced_y_origins_array, sliced_y_origins_size);
+    constexpr auto sliced_y_lengths = TO_SEQUENCE(sliced_y_lengths_array, sliced_y_lengths_size);
+
+    return make_tuple(
+        make_static_tile_distribution(
+            tile_distribution_encoding<typename Encoding::RsLengths,
+                                       remove_cvref_t<decltype(sliced_h_lengths)>, // only need to
+                                                                                   // change the
+                                                                                   // h_lengths type
+                                       typename Encoding::Ps2RHssMajor,
+                                       typename Encoding::Ps2RHssMinor,
+                                       typename Encoding::Ys2RHsMajor,
+                                       typename Encoding::Ys2RHsMinor>{}),
+        sliced_y_origins,
+        sliced_y_lengths);
+}
+
+} // namespace detail
+} // namespace ck_tile

include/ck_tile/core/tensor/tile_distribution_encoding.hpp

@@ -0,0 +1,760 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/algorithm/coordinate_transform.hpp"
+#include "ck_tile/core/tensor/tensor_adaptor.hpp"
+#include "ck_tile/core/tensor/tensor_adaptor_coordinate.hpp"
+#include "ck_tile/core/container/container_helper.hpp"
+#include "ck_tile/core/container/multi_index.hpp"
+#include "ck_tile/core/numeric/math.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+
+namespace ck_tile {
+
+template <typename RsLengths_,    // sequence<...>
+          typename HsLengthss_,   // tuple<sequence<...>, ...>
+          typename Ps2RHssMajor_, // tuple<sequence<...>, ...>
+          typename Ps2RHssMinor_, // tuple<sequence<...>, ...>
+          typename Ys2RHsMajor_,  // sequence<...>
+          typename Ys2RHsMinor_>  // sequence<...>
+struct tile_distribution_encoding
+{
+    using RsLengths    = remove_cvref_t<RsLengths_>;
+    using HsLengthss   = remove_cvref_t<HsLengthss_>;
+    using Ps2RHssMajor = remove_cvref_t<Ps2RHssMajor_>;
+    using Ps2RHssMinor = remove_cvref_t<Ps2RHssMinor_>;
+    using Ys2RHsMajor  = remove_cvref_t<Ys2RHsMajor_>;
+    using Ys2RHsMinor  = remove_cvref_t<Ys2RHsMinor_>;
+
+    static_assert(Ps2RHssMajor::size() == Ps2RHssMinor::size(), "wrong!");
+    static_assert(Ys2RHsMajor::size() == Ys2RHsMinor::size(), "wrong!");
+
+    static constexpr index_t NDimX = HsLengthss::size();
+    static constexpr index_t NDimP = Ps2RHssMajor::size();
+    static constexpr index_t NDimY = Ys2RHsMajor::size();
+    static constexpr index_t NDimR = RsLengths::size();
+
+    // FIXME: move into detail
+    static constexpr auto rs_lengths_       = RsLengths{};
+    static constexpr auto hs_lengthss_      = HsLengthss{};
+    static constexpr auto ps_to_rhss_major_ = Ps2RHssMajor{};
+    static constexpr auto ps_to_rhss_minor_ = Ps2RHssMinor{};
+    static constexpr auto ys_to_rhs_major_  = Ys2RHsMajor{};
+    static constexpr auto ys_to_rhs_minor_  = Ys2RHsMinor{};
+
+    // redundant but useful info
+    // TODO: really bad code, should be over-hauled
+    struct detail
+    {
+        // ndim_rh_major_, ndim_span_mainor_
+        static constexpr index_t ndim_rh_major_   = NDimX + 1;
+        static constexpr index_t ndim_span_major_ = NDimX;
+
+        // ndims_rhs_minor_[ndim_rh_major_]
+        static constexpr auto ndims_rhs_minor_ = generate_array(
+            [](auto i) {
+                if constexpr(i.value == 0)
+                {
+                    return rs_lengths_.size();
+                }
+                else
+                {
+                    return hs_lengthss_[i - number<1>{}].size();
+                }
+            },
+            number<ndim_rh_major_>{});
+
+        // max_ndim_rh_minor_
+        static constexpr index_t max_ndim_rh_minor_ =
+            container_reduce(ndims_rhs_minor_, maximize<index_t>{}, 0);
+
+        // rhs_lengthss_[ndim_rh_major_][max_ndim_rh_minor_]
+        static constexpr auto rhs_lengthss_ =
+            to_array_of_array(container_concat(make_tuple(rs_lengths_), hs_lengthss_));
+
+        // ys_lengths_
+        static constexpr auto ys_lengths_ = [] {
+            array<index_t, NDimY> ys_lengths_tmp{-1};
+
+            for(index_t i = 0; i < NDimY; i++)
+            {
+                index_t rh_major = ys_to_rhs_major_[i];
+                index_t rh_minor = ys_to_rhs_minor_[i];
+
+                ys_lengths_tmp(i) = rhs_lengthss_[rh_major][rh_minor];
+            }
+
+            return ys_lengths_tmp;
+        }();
+
+        // rhs_major_minor_to_ys_[ndim_rh_majpr_][max_ndim_rh_minor_]
+        static constexpr auto rhs_major_minor_to_ys_ = [] {
+            array<array<index_t, max_ndim_rh_minor_>, NDimX + 1> rhs_major_minor_to_ys_tmp{{-1}};
+
+            static_for<0, NDimY, 1>{}([&](auto i) {
+                constexpr index_t rh_major = ys_to_rhs_major_[i];
+                constexpr index_t rh_minor = ys_to_rhs_minor_[i];
+
+                rhs_major_minor_to_ys_tmp(rh_major)(rh_minor) = i;
+            });
+
+            return rhs_major_minor_to_ys_tmp;
+        }();
+
+        // ndims_span_minor_[NDimY]
+        static constexpr auto ndims_span_minor_ = [] {
+            array<index_t, NDimX> ndims_span_minor{0};
+
+            for(index_t i = 0; i < NDimY; i++)
+            {
+                const index_t span_major = ys_to_rhs_major_[i] - 1;
+
+                ndims_span_minor(span_major)++;
+            }
+
+            return ndims_span_minor;
+        }();
+
+        // max_ndim_span_minor_
+        static constexpr index_t max_ndim_span_minor_ =
+            container_reduce(ndims_span_minor_, maximize<index_t>{}, 0);
+
+        // rhs_major_minor_to_span_minor_ [ndim_rh_major_][max_ndim_rh_minor_]
+        static constexpr auto rhs_major_minor_to_span_minor_ = [] {
+            array<array<index_t, max_ndim_rh_minor_>, ndim_rh_major_> rhs_major_minor_to_span_minor{
+                {-1}};
+
+            static_for<0, ndim_rh_major_, 1>{}([&](auto rh_major) {
+                constexpr index_t ndim_rh_minor = ndims_rhs_minor_[rh_major];
+
+                index_t cnt_ndim_span_minor = 0;
+
+                static_for<0, ndim_rh_minor, 1>{}([&](auto rh_minor) {
+                    constexpr index_t idim_y = rhs_major_minor_to_ys_[rh_major][rh_minor];
+
+                    if(idim_y >= 0)
+                    {
+                        rhs_major_minor_to_span_minor(rh_major)(rh_minor) = cnt_ndim_span_minor;
+
+                        cnt_ndim_span_minor++;
+                    }
+                });
+            });
+
+            return rhs_major_minor_to_span_minor;
+        }();
+
+        // ys_to_span_major_[NDimY]
+        static constexpr auto ys_to_span_major_ =
+            generate_array([](auto i) { return ys_to_rhs_major_[i] - 1; }, number<NDimY>{});
+
+        // ys_to_span_minor_[NDimY]
+        static constexpr auto ys_to_span_minor_ = generate_array(
+            [](auto i) {
+                return rhs_major_minor_to_span_minor_[ys_to_rhs_major_[i]][ys_to_rhs_minor_[i]];
+            },
+            number<NDimY>{});
+
+        // distributed_spans_lengthss_[ndim_span_major_][max_ndim_span_minor_]
+        static constexpr auto distributed_spans_lengthss_ = [] {
+            array<array<index_t, max_ndim_span_minor_>, ndim_span_major_>
+                distributed_spans_lengthss{{-1}};
+
+            static_for<0, NDimY, 1>{}([&](auto i) {
+                const index_t rh_major = ys_to_rhs_major_[i];
+                const index_t rh_minor = ys_to_rhs_minor_[i];
+
+                const index_t h_length = hs_lengthss_[number<rh_major - 1>{}][rh_minor];
+
+                const index_t span_major = rh_major - 1;
+                const index_t span_minor = rhs_major_minor_to_span_minor_[rh_major][rh_minor];
+
+                distributed_spans_lengthss(span_major)(span_minor) = h_length;
+            });
+
+            return distributed_spans_lengthss;
+        }();
+
+        // ndims_distributed_spans_minor_[ndim_span_major_]
+        static constexpr auto ndims_distributed_spans_minor_ = [] {
+            array<index_t, ndim_span_major_> ndims_distributed_spans_minor{0};
+
+            static_for<0, NDimY, 1>{}([&](auto i) {
+                const index_t span_major = ys_to_rhs_major_[i] - 1;
+
+                ndims_distributed_spans_minor(span_major)++;
+            });
+
+            return ndims_distributed_spans_minor;
+        }();
+
+        // does_p_own_r_[NDimP][NDimR]
+        static constexpr auto does_p_own_r_ = [] {
+            if constexpr(NDimR > 0)
+            {
+                array<array<bool, NDimR>, NDimP> does_p_own_r{{false}};
+
+                static_for<0, NDimP, 1>{}([&](auto idim_p) {
+                    constexpr index_t ndim_low = ps_to_rhss_major_[idim_p].size();
+
+                    static_for<0, ndim_low, 1>{}([&](auto idim_low) {
+                        constexpr index_t rh_major = ps_to_rhss_major_[idim_p][idim_low];
+                        constexpr index_t rh_minor = ps_to_rhss_minor_[idim_p][idim_low];
+
+                        if constexpr(rh_major == 0)
+                        {
+                            does_p_own_r(idim_p)(rh_minor) = true;
+                        }
+                    });
+                });
+
+                return does_p_own_r;
+            }
+            else
+            {
+                return array<array<bool, NDimR>, NDimP>{};
+            }
+        }();
+
+        // ps_over_rs_derivative_[NDimP][NDimR]
+        static constexpr auto ps_over_rs_derivative_ = [] {
+            if constexpr(NDimR > 0)
+            {
+                array<array<index_t, NDimR>, NDimP> ps_over_rs_derivative{{0}};
+
+                static_for<0, NDimP, 1>{}([&](auto idim_p) {
+                    constexpr index_t ndim_low = ps_to_rhss_major_[idim_p].size();
+
+                    index_t p_over_rh_derivative = 1;
+
+                    static_for<ndim_low - 1, -1, -1>{}([&](auto idim_low) {
+                        constexpr index_t rh_major = ps_to_rhss_major_[idim_p][idim_low];
+                        constexpr index_t rh_minor = ps_to_rhss_minor_[idim_p][idim_low];
+
+                        constexpr index_t rh_length = rhs_lengthss_[rh_major][rh_minor];
+
+                        if constexpr(rh_major == 0)
+                        {
+                            ps_over_rs_derivative(idim_p)(rh_minor) = p_over_rh_derivative;
+                        }
+
+                        p_over_rh_derivative *= rh_length;
+                    });
+                });
+
+                return ps_over_rs_derivative;
+            }
+            else
+            {
+                return array<array<index_t, NDimR>, NDimP>{};
+            }
+        }();
+
+        // e.g. tuple<seq<1, 4, 32>, seq<4, 1, 4, 2, 4>> --> seq<3, 5> --> seq<0, 3, 8>
+        CK_TILE_HOST_DEVICE static constexpr auto get_h_dim_lengths_prefix_sum()
+        {
+            // <len_d0, len_d1, ...>
+            // e.g. tuple<seq<1, 4, 32>, seq<4, 1, 4, 2, 4>> --> seq<3, 5>
+            constexpr auto uniformed_h_dim_lengths = generate_sequence_v2(
+                [&](auto i) {
+                    constexpr index_t size = HsLengthss{}[i].size();
+                    return number<size>{};
+                },
+                number<NDimX>{});
+
+            // <0, len_d0, len_d0+len_d1, ...>
+            // e.g. seq<3, 5> --> seq<0, 3, 8>
+            constexpr auto h_dim_prefix_sum = prefix_sum_sequence(uniformed_h_dim_lengths);
+
+            return h_dim_prefix_sum;
+        }
+
+        CK_TILE_HOST_DEVICE static constexpr auto get_uniformed_idx_y_to_h()
+        {
+            constexpr auto all_ys_2_rhss = transform_sequences(
+                [](auto major, auto minor) constexpr {
+                    // <0, 0, len_d0, len_d0+len_d1, ...>
+                    constexpr auto x_dim_prefix_sum = merge_sequences(
+                        sequence<0>{} /*for R dims*/, get_h_dim_lengths_prefix_sum());
+                    return x_dim_prefix_sum.at(major) + minor;
+                },
+                Ys2RHsMajor{},
+                Ys2RHsMinor{});
+
+            return all_ys_2_rhss;
+        }
+
+        // return tuple<sorted_dims, sorted_maps, sorted_prefix_sum>
+        template <typename IdxSeq, typename PrefixSumSeq>
+        CK_TILE_HOST_DEVICE static constexpr auto get_sorted_info(IdxSeq, PrefixSumSeq)
+        {
+            using sorted_idx = sequence_unique_sort<IdxSeq, less<index_t>, equal<index_t>>;
+
+            constexpr auto sorted_dims = typename sorted_idx::type{};
+            constexpr auto sorted_maps = typename sorted_idx::sorted2unsorted_map{};
+
+            constexpr auto sorted_histogram =
+                histogram_sorted_sequence(sorted_dims, PrefixSumSeq{});
+            constexpr auto sorted_prefix_sum = prefix_sum_sequence(sorted_histogram);
+
+            return make_tuple(sorted_dims, sorted_maps, sorted_prefix_sum);
+        }
+
+        CK_TILE_HOST_DEVICE static constexpr auto get_sorted_y_info()
+        {
+            return get_sorted_info(get_uniformed_idx_y_to_h(), get_h_dim_lengths_prefix_sum());
+        }
+
+        CK_TILE_HOST_DEVICE void print() const
+        {
+            printf("tile_distribution_encoding::detail{");
+            //
+            printf("ndim_rh_major_: ");
+            print(ndim_rh_major_);
+            printf(", ");
+            //
+            printf("ndim_span_major_: ");
+            print(ndim_span_major_);
+            printf(", ");
+            //
+            printf("ndims_rhs_minor_: ");
+            print(ndims_rhs_minor_);
+            printf(", ");
+            //
+            printf("ndim_rh_major_: ");
+            print(ndim_rh_major_);
+            printf(", ");
+            //
+            printf("max_ndim_rh_minor_: ");
+            print(max_ndim_rh_minor_);
+            printf(", ");
+            //
+            printf("rhs_lengthss_: ");
+            print(rhs_lengthss_);
+            printf(", ");
+            //
+            printf("ys_lengths_: ");
+            print(ys_lengths_);
+            printf(", ");
+            //
+            printf("rhs_major_minor_to_ys_: ");
+            print(rhs_major_minor_to_ys_);
+            printf(", ");
+            //
+            printf("ndims_span_minor_: ");
+            print(ndims_span_minor_);
+            printf(", ");
+            //
+            printf("max_ndim_span_minor_: ");
+            print(max_ndim_span_minor_);
+            printf(", ");
+            //
+            printf("ys_to_span_major_: ");
+            print(ys_to_span_major_);
+            printf(", ");
+            //
+            printf("ys_to_span_minor_: ");
+            print(ys_to_span_minor_);
+            printf(", ");
+            //
+            printf("distributed_spans_lengthss_: ");
+            print(distributed_spans_lengthss_);
+            printf(", ");
+            //
+            printf("ndims_distributed_spans_minor_: ");
+            print(ndims_distributed_spans_minor_);
+            printf(", ");
+            //
+            printf("ps_over_rs_derivative_: ");
+            print(ps_over_rs_derivative_);
+            //
+            printf("}");
+        }
+    };
+
+    CK_TILE_HOST_DEVICE void print() const
+    {
+        printf("tile_distribution_encoding{");
+        //
+        printf("NDimX: %d, NDimP: %d, NDimY: %d, ", NDimX, NDimP, NDimY);
+        //
+        printf("rs_lengths_: ");
+        print(rs_lengths_);
+        printf(", ");
+        //
+        printf("hs_lengthss_: ");
+        print(hs_lengthss_);
+        printf(", ");
+        //
+        printf("ps_to_rhss_major_: ");
+        print(ps_to_rhss_major_);
+        printf(", ");
+        //
+        printf("ps_to_rhss_minor_: ");
+        print(ps_to_rhss_minor_);
+        printf(", ");
+        //
+        printf("ys_to_rhs_major_: ");
+        print(ys_to_rhs_major_);
+        printf(", ");
+        //
+        printf("ys_to_rhs_minor_: ");
+        print(ys_to_rhs_minor_);
+        printf(", ");
+        //
+        printf("detail: ");
+        print(detail{});
+        //
+        printf("}");
+    }
+};
+
+namespace detail {
+
+template <typename OuterDstr, typename InnerDstr>
+CK_TILE_HOST_DEVICE constexpr auto make_embed_tile_distribution_encoding(OuterDstr, InnerDstr)
+{
+    static_assert(OuterDstr::NDimX == InnerDstr::NDimX, "wrong!");
+
+    constexpr index_t NDimHMajor = OuterDstr::NDimX;
+
+    using RsLengths =
+        sequence_merge_t<typename OuterDstr::RsLengths, typename InnerDstr::RsLengths>;
+
+    constexpr auto hs_lengthss = generate_tuple(
+        [&](auto i) {
+            return merge_sequences(typename OuterDstr::HsLengthss{}[i],
+                                   typename InnerDstr::HsLengthss{}[i]);
+        },
+        number<NDimHMajor>{});
+
+    //
+    constexpr auto rhs_major_2_ndim_outer_rhs_minor = [&]() {
+        array<index_t, NDimHMajor + 1> rhs_major_2_ndim_outer_rhs_minor_;
+
+        // R dimension
+        rhs_major_2_ndim_outer_rhs_minor_(0) = OuterDstr::RsLengths::size();
+
+        // Hs dimensions
+        static_for<0, NDimHMajor, 1>{}([&](auto i) {
+            rhs_major_2_ndim_outer_rhs_minor_(i + 1) = typename OuterDstr::HsLengthss{}[i].size();
+        });
+
+        return rhs_major_2_ndim_outer_rhs_minor_;
+    }();
+
+    // Ps2RHssMinor
+    constexpr auto updated_inner_ps_2_rhss_minor = generate_tuple(
+        [&](auto p) {
+            constexpr auto inner_p_2_rhss_major = typename InnerDstr::Ps2RHssMajor{}[p];
+            constexpr auto inner_p_2_rhss_minor = typename InnerDstr::Ps2RHssMinor{}[p];
+
+            constexpr index_t ndim_tmp = inner_p_2_rhss_minor.size();
+
+            constexpr auto updated_inner_p_2_rhss_minor = [&]() {
+                array<index_t, ndim_tmp> updated_inner_p_2_rhss_minor_;
+
+                for(index_t i = 0; i < ndim_tmp; i++)
+                {
+                    index_t rh_major = inner_p_2_rhss_major[i];
+
+                    index_t ndim_outer_h_minor = rhs_major_2_ndim_outer_rhs_minor[rh_major];
+
+                    updated_inner_p_2_rhss_minor_(i) = inner_p_2_rhss_minor[i] + ndim_outer_h_minor;
+                }
+
+                return updated_inner_p_2_rhss_minor_;
+            }();
+
+            return TO_SEQUENCE(updated_inner_p_2_rhss_minor, ndim_tmp);
+        },
+        number<InnerDstr::NDimP>{});
+
+    // Ys2RHsMinor
+    constexpr auto updated_inner_ys_2_rhs_minor = [&]() {
+        constexpr auto inner_ys_2_rhs_major = typename InnerDstr::Ys2RHsMajor{};
+        constexpr auto inner_ys_2_rhs_minor = typename InnerDstr::Ys2RHsMinor{};
+
+        constexpr index_t ndim_tmp = inner_ys_2_rhs_minor.size();
+
+        constexpr auto updated_inner_ys_2_rhs_minor_ = [&]() {
+            array<index_t, ndim_tmp> updated_inner_ys_2_rhs_minor__;
+
+            for(index_t i = 0; i < ndim_tmp; i++)
+            {
+                index_t rh_major = inner_ys_2_rhs_major[i];
+
+                index_t ndim_outer_h_minor = rhs_major_2_ndim_outer_rhs_minor[rh_major];
+
+                updated_inner_ys_2_rhs_minor__(i) = inner_ys_2_rhs_minor[i] + ndim_outer_h_minor;
+            }
+
+            return updated_inner_ys_2_rhs_minor__;
+        }();
+
+        return TO_SEQUENCE(updated_inner_ys_2_rhs_minor_, ndim_tmp);
+    }();
+
+    //
+    constexpr auto ps_2_rhss_major =
+        container_concat(typename OuterDstr::Ps2RHssMajor{}, typename InnerDstr::Ps2RHssMajor{});
+
+    constexpr auto ps_2_rhss_minor =
+        container_concat(typename OuterDstr::Ps2RHssMinor{}, updated_inner_ps_2_rhss_minor);
+
+    //
+    constexpr auto ys_2_rhs_major =
+        merge_sequences(typename OuterDstr::Ys2RHsMajor{}, typename InnerDstr::Ys2RHsMajor{});
+
+    constexpr auto ys_2_rhs_minor =
+        merge_sequences(typename OuterDstr::Ys2RHsMinor{}, updated_inner_ys_2_rhs_minor);
+
+    return tile_distribution_encoding<RsLengths,
+                                      remove_cvref_t<decltype(hs_lengthss)>,
+                                      remove_cvref_t<decltype(ps_2_rhss_major)>,
+                                      remove_cvref_t<decltype(ps_2_rhss_minor)>,
+                                      remove_cvref_t<decltype(ys_2_rhs_major)>,
+                                      remove_cvref_t<decltype(ys_2_rhs_minor)>>{};
+}
+
+template <typename InDstr, index_t... InReduceDimXs>
+CK_TILE_HOST_DEVICE constexpr auto
+make_reduce_tile_distribution_encoding_impl(InDstr, sequence<InReduceDimXs...> reduce_dim_xs_in)
+{
+    constexpr auto I1 = number<1>{};
+
+    // FIXME: increase if fail
+    constexpr index_t max_ndim_r_out = 20;
+    constexpr index_t max_ndim_y_out = 20;
+
+    //
+    constexpr index_t ndim_p               = InDstr::NDimP;
+    constexpr index_t ndim_x_in            = InDstr::NDimX;
+    constexpr index_t ndim_y_in            = InDstr::NDimY;
+    constexpr index_t ndim_rh_major_in     = InDstr::NDimX + 1;
+    constexpr index_t ndim_x_out           = ndim_x_in - sizeof...(InReduceDimXs);
+    constexpr index_t max_ndim_rh_minor_in = InDstr::detail::max_ndim_rh_minor_;
+
+    // ndims_ps_low
+    constexpr auto ndims_ps_low = generate_array(
+        [&](auto i) { return InDstr::ps_to_rhss_major_[i].size(); }, number<ndim_p>{});
+
+    // is_rh_major_in_for_reduce
+    array<bool, ndim_rh_major_in> is_rh_major_in_for_reduce{false};
+
+    for(index_t i = 0; i < reduce_dim_xs_in.size(); i++)
+    {
+        index_t rh_major = reduce_dim_xs_in[i] + 1;
+
+        is_rh_major_in_for_reduce(rh_major) = true;
+    }
+
+    // is_y_in_for_reduce
+    array<bool, ndim_y_in> is_y_in_for_reduce{false};
+
+    for(index_t i = 0; i < ndim_y_in; i++)
+    {
+        index_t rh_major = InDstr::ys_to_rhs_major_[i];
+
+        if(is_rh_major_in_for_reduce[rh_major])
+        {
+            is_y_in_for_reduce(i) = true;
+        }
+    }
+
+    // is_rh_minor_in_for_y_reduce
+    array<array<bool, max_ndim_rh_minor_in>, ndim_rh_major_in> is_rh_minor_in_for_y_reduce{{false}};
+
+    static_for<0, ndim_y_in, 1>{}([&](auto i) {
+        index_t rh_major = InDstr::ys_to_rhs_major_[i];
+        index_t rh_minor = InDstr::ys_to_rhs_minor_[i];
+
+        if(is_y_in_for_reduce[i])
+        {
+            is_rh_minor_in_for_y_reduce(rh_major)(rh_minor) = true;
+        }
+    });
+
+    // in2out_rh_major
+    array<index_t, ndim_rh_major_in> in2out_rh_major{-1};
+    index_t cnt_ndim_rh_major_out = 0;
+
+    for(index_t i = 0; i < ndim_rh_major_in; i++)
+    {
+        if(is_rh_major_in_for_reduce[i])
+        {
+            in2out_rh_major(i) = 0;
+        }
+        else
+        {
+            in2out_rh_major(i) = cnt_ndim_rh_major_out;
+
+            cnt_ndim_rh_major_out++;
+        }
+    }
+
+    // rs_lengths_out, in2out_rh_minor
+    array<index_t, max_ndim_r_out> rs_lengths_out{-1};
+    array<array<index_t, max_ndim_rh_minor_in>, ndim_rh_major_in> in2out_rh_minor{{-1}};
+
+    // loop over input R dim
+    for(index_t i = 0; i < InDstr::rs_lengths_.size(); i++)
+    {
+        // rs_lengths_out
+        rs_lengths_out(i) = InDstr::rs_lengths_[i];
+
+        // in2out_rh_minor
+        in2out_rh_minor(0)(i) = i;
+    }
+
+    // loop over input H Dim
+    index_t cnt_ndim_r_out = InDstr::rs_lengths_.size();
+
+    static_for<1, ndim_rh_major_in, 1>{}([&](auto rh_major_in) {
+        constexpr auto h_major_in = rh_major_in - I1;
+
+        constexpr index_t ndim_rh_minor_in = InDstr::hs_lengthss_[h_major_in].size();
+
+        if(is_rh_major_in_for_reduce[rh_major_in])
+        {
+            for(index_t rh_minor_in = 0; rh_minor_in < ndim_rh_minor_in; rh_minor_in++)
+            {
+                if(not is_rh_minor_in_for_y_reduce[rh_major_in][rh_minor_in])
+                {
+                    // rs_lengths_out
+                    rs_lengths_out(cnt_ndim_r_out) = InDstr::hs_lengthss_[h_major_in][rh_minor_in];
+
+                    // in2out_rh_minor
+                    in2out_rh_minor(rh_major_in)(rh_minor_in) = cnt_ndim_r_out;
+
+                    cnt_ndim_r_out++;
+                }
+            }
+        }
+        else
+        {
+            for(index_t rh_minor_in = 0; rh_minor_in < ndim_rh_minor_in; rh_minor_in++)
+            {
+                // in2out_rh_minor
+                in2out_rh_minor(rh_major_in)(rh_minor_in) = rh_minor_in;
+            }
+        }
+    });
+
+    // ndim_r_out
+    const index_t ndim_r_out = cnt_ndim_r_out;
+
+    // ndims_hs_minor_out, hs_lengthss_out
+    array<index_t, ndim_x_out> ndims_hs_minor_out{-1};
+    array<array<index_t, max_ndim_rh_minor_in>, ndim_x_out> hs_lengthss_out{{-1}};
+
+    index_t cnt_ndim_x_out = 0;
+
+    static_for<0, ndim_x_in, 1>{}([&](auto i) {
+        if(not is_rh_major_in_for_reduce[i + I1])
+        {
+            // ndims_hs_minor_out
+            ndims_hs_minor_out(cnt_ndim_x_out) = InDstr::hs_lengthss_[i].size();
+
+            // hs_lengthss_out
+            static_for<0, InDstr::hs_lengthss_[i].size(), 1>{}(
+                [&](auto j) { hs_lengthss_out(cnt_ndim_x_out)(j) = InDstr::hs_lengthss_[i][j]; });
+
+            cnt_ndim_x_out++;
+        }
+    });
+
+    // ps_to_rhss_major_out, ps_to_rhss_minor_out
+    array<array<index_t, max_ndim_rh_minor_in>, ndim_p> ps_to_rhss_major_out{{-1}};
+    array<array<index_t, max_ndim_rh_minor_in>, ndim_p> ps_to_rhss_minor_out{{-1}};
+
+    static_for<0, ndim_p, 1>{}([&](auto idim_p) {
+        static_for<0, InDstr::ps_to_rhss_major_[idim_p].size(), 1>{}([&](auto idim_low) {
+            index_t rh_major_in = InDstr::ps_to_rhss_major_[idim_p][idim_low];
+            index_t rh_minor_in = InDstr::ps_to_rhss_minor_[idim_p][idim_low];
+
+            ps_to_rhss_major_out(idim_p)(idim_low) = in2out_rh_major[rh_major_in];
+            ps_to_rhss_minor_out(idim_p)(idim_low) = in2out_rh_minor[rh_major_in][rh_minor_in];
+        });
+    });
+
+    // ys_to_rhs_major_out, ys_to_rhs_minor_out
+    array<index_t, max_ndim_y_out> ys_to_rhs_major_out{-1};
+    array<index_t, max_ndim_y_out> ys_to_rhs_minor_out{-1};
+
+    index_t cnt_ndim_y_out = 0;
+
+    static_for<0, ndim_y_in, 1>{}([&](auto i) {
+        if(not is_y_in_for_reduce[i])
+        {
+            index_t rh_major_in = InDstr::ys_to_rhs_major_[i];
+            index_t rh_minor_in = InDstr::ys_to_rhs_minor_[i];
+
+            ys_to_rhs_major_out(cnt_ndim_y_out) = in2out_rh_major[rh_major_in];
+            ys_to_rhs_minor_out(cnt_ndim_y_out) = in2out_rh_minor[rh_major_in][rh_minor_in];
+
+            cnt_ndim_y_out++;
+        }
+    });
+
+    // ndim_y_out
+    const index_t ndim_y_out = cnt_ndim_y_out;
+
+    //
+    return make_tuple(ndim_x_out,
+                      ndim_p,
+                      ndim_y_out,
+                      ndim_r_out,
+                      ndims_hs_minor_out,
+                      ndims_ps_low,
+                      rs_lengths_out,
+                      hs_lengthss_out,
+                      ps_to_rhss_major_out,
+                      ps_to_rhss_minor_out,
+                      ys_to_rhs_major_out,
+                      ys_to_rhs_minor_out);
+}
+
+template <typename InDstr, index_t... InReduceDimXs>
+CK_TILE_HOST_DEVICE constexpr auto
+make_reduce_tile_distribution_encoding(InDstr, sequence<InReduceDimXs...> reduce_dim_xs_in)
+{
+    constexpr auto impl = make_reduce_tile_distribution_encoding_impl(InDstr{}, reduce_dim_xs_in);
+
+    constexpr index_t ndim_x             = impl.template at<0>();
+    constexpr index_t ndim_p             = impl.template at<1>();
+    constexpr index_t ndim_y             = impl.template at<2>();
+    constexpr index_t ndim_r             = impl.template at<3>();
+    constexpr auto ndims_hs_minor        = impl.template at<4>();
+    constexpr auto ndims_ps_low          = impl.template at<5>();
+    constexpr auto rs_lengths_impl       = impl.template at<6>();
+    constexpr auto hs_lengthss_impl      = impl.template at<7>();
+    constexpr auto ps_to_rhss_major_impl = impl.template at<8>();
+    constexpr auto ps_to_rhss_minor_impl = impl.template at<9>();
+    constexpr auto ys_to_rhs_major_impl  = impl.template at<10>();
+    constexpr auto ys_to_rhs_minor_impl  = impl.template at<11>();
+
+    constexpr auto rs_lengths  = TO_SEQUENCE(rs_lengths_impl, ndim_r);
+    constexpr auto hs_lengthss = TO_TUPLE_OF_SEQUENCE(hs_lengthss_impl, ndim_x, ndims_hs_minor);
+    constexpr auto ps_to_rhss_major =
+        TO_TUPLE_OF_SEQUENCE(ps_to_rhss_major_impl, ndim_p, ndims_ps_low);
+    constexpr auto ps_to_rhss_minor =
+        TO_TUPLE_OF_SEQUENCE(ps_to_rhss_minor_impl, ndim_p, ndims_ps_low);
+    constexpr auto ys_to_rhs_major = TO_SEQUENCE(ys_to_rhs_major_impl, ndim_y);
+    constexpr auto ys_to_rhs_minor = TO_SEQUENCE(ys_to_rhs_minor_impl, ndim_y);
+
+    return tile_distribution_encoding<remove_cvref_t<decltype(rs_lengths)>,
+                                      remove_cvref_t<decltype(hs_lengthss)>,
+                                      remove_cvref_t<decltype(ps_to_rhss_major)>,
+                                      remove_cvref_t<decltype(ps_to_rhss_minor)>,
+                                      remove_cvref_t<decltype(ys_to_rhs_major)>,
+                                      remove_cvref_t<decltype(ys_to_rhs_minor)>>{};
+}
+
+} // namespace detail
+} // namespace ck_tile

include/ck_tile/core/tensor/tile_elementwise.hpp

@@ -0,0 +1,342 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/container/array.hpp"
+#include "ck_tile/core/container/sequence.hpp"
+#include "ck_tile/core/container/tuple.hpp"
+#include "ck_tile/core/container/container_helper.hpp"
+#include "ck_tile/core/tensor/tensor_adaptor.hpp"
+#include "ck_tile/core/tensor/null_tensor.hpp"
+#include "ck_tile/core/utility/functional.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+
+namespace ck_tile {
+
+// TODO: support tensors with different distribution
+template <typename InOutElementFunc,
+          typename... InOutDstrTensors,
+          typename = std::enable_if_t<std::conjunction_v<
+              std::negation<std::is_same<std::remove_const_t<InOutDstrTensors>, null_tensor>>...>>>
+CK_TILE_DEVICE void tile_elementwise_inout(const InOutElementFunc& inout_element_func,
+                                           InOutDstrTensors&... inout_dstr_tensors)
+{
+    // TODO: make sure all distributed tensors have same lengths and distribution
+    // static_assert(xxx);
+
+    constexpr index_t thread_buffer_size =
+        __type_pack_element<0, InOutDstrTensors...>::get_thread_buffer_size();
+
+    static_for<0, thread_buffer_size, 1>{}(
+        [&](auto i) { inout_element_func(inout_dstr_tensors.get_thread_buffer().at(i)...); });
+}
+
+template <typename InElementFunc,
+          typename... InTensor,
+          typename = std::enable_if_t<
+              std::conjunction_v<std::negation<std::is_same<InTensor, null_tensor>>...>>>
+CK_TILE_DEVICE auto tile_elementwise_in(const InElementFunc& in_element_func,
+                                        const InTensor&... in_dstr_tensors)
+{
+    using OutDataType = decltype(in_element_func(typename InTensor::DataType{}...));
+
+    // TODO: make sure all distributed tensors have same lengths and distribution
+    // static_assert(xxx);
+    constexpr auto in_tile_dstr = __type_pack_element<0, InTensor...>::get_tile_distribution();
+
+    constexpr index_t thread_buffer_size =
+        __type_pack_element<0, InTensor...>::get_thread_buffer_size();
+
+    auto out_dstr_tensor = make_static_distributed_tensor<OutDataType>(in_tile_dstr);
+
+    static_for<0, thread_buffer_size, 1>{}([&](auto i) {
+        out_dstr_tensor.get_thread_buffer()(i) =
+            in_element_func(in_dstr_tensors.get_thread_buffer()[i]...);
+    });
+
+    return out_dstr_tensor;
+}
+
+template <typename DstrTensors, typename T>
+CK_TILE_DEVICE void set_tile(DstrTensors& dstr_tensor, const T& value)
+{
+    tile_elementwise_inout(
+        [&value](auto& x) {
+            x = type_convert<typename DstrTensors::DataType, remove_cvref_t<T>>(value);
+        },
+        dstr_tensor);
+}
+
+template <typename T>
+CK_TILE_DEVICE void set_tile(null_tensor&, const T&)
+{
+}
+
+// TODO: prefer to use per-dword value to set a tensor, in case compiler not doing well with
+// sub-dword tensor...
+template <typename DstrTensors, index_t v, bool skip_subdword_opt = false>
+CK_TILE_DEVICE void
+set_tile(DstrTensors& dstr_tensor, number<v>, bool_constant<skip_subdword_opt> = {})
+{
+    using elem_type             = typename DstrTensors::DataType;
+    constexpr index_t elem_size = sizeof(elem_type);
+
+    constexpr index_t tensor_bytes = DstrTensors::get_thread_buffer_size() * elem_size;
+
+    // # bytes per write = 4
+    if constexpr(v == 0 && tensor_bytes % 4 == 0 && !skip_subdword_opt)
+    {
+#if CK_TILE_WORKAROUND_ROCM_6_1_SCRATCH_MEMORY_ISSUE
+        auto& buffer = dstr_tensor.get_thread_buffer();
+
+        static_for<0, tensor_bytes / 4, 1>{}([&](auto i_write) {
+            if constexpr(elem_size == 1)
+            {
+                // # elements per write = 4
+                constexpr auto values = ext_vector_t<elem_type, 4>{0, 0, 0, 0};
+
+                buffer[i_write * 4 + 0] = values.x;
+                buffer[i_write * 4 + 1] = values.y;
+                buffer[i_write * 4 + 2] = values.z;
+                buffer[i_write * 4 + 3] = values.w;
+            }
+            else if constexpr(elem_size == 2)
+            {
+                // # elements per write = 2
+                constexpr auto values = ext_vector_t<elem_type, 2>{0, 0};
+
+                buffer[i_write * 2 + 0] = values.x;
+                buffer[i_write * 2 + 1] = values.y;
+            }
+            else if constexpr(elem_size == 4)
+            {
+                // # elements per write = 1
+                constexpr elem_type value = 0;
+
+                buffer[i_write] = value;
+            }
+            else
+            {
+                static_assert(false, "type not supported");
+            }
+        });
+#else
+        using dvec_t = array<index_t, tensor_bytes / 4>;
+        auto& tensor = reinterpret_cast<dvec_t&>(dstr_tensor.get_thread_buffer());
+        for(auto i = 0; i < tensor.size(); i++)
+            tensor.get(i) = v;
+#endif
+    }
+    else
+    {
+        tile_elementwise_inout([](auto& x) { x = type_convert<elem_type, index_t>(v); },
+                               dstr_tensor);
+    }
+}
+
+template <index_t v>
+CK_TILE_DEVICE void set_tile(null_tensor&, number<v>)
+{
+}
+
+template <typename DstrTensors>
+CK_TILE_DEVICE void clear_tile(DstrTensors& dstr_tensor)
+{
+    set_tile(dstr_tensor, 0);
+}
+
+namespace impl {
+// TODO: this is ugly
+template <typename OutDataType, typename InTensor>
+CK_TILE_DEVICE auto cast_tile_pk_fp8_fp32(const InTensor& in_dstr_tensors)
+{
+#if defined(__gfx94__)
+    // This API is designed to use the _pk_ serious of function
+    constexpr auto in_tile_dstr = InTensor::get_tile_distribution();
+
+    constexpr index_t thread_buffer_size = InTensor::get_thread_buffer_size();
+    static_assert(thread_buffer_size % 4 == 0);
+    constexpr index_t thread_buffer_size_pk = thread_buffer_size / 4;
+
+    auto out_dstr_tensor = make_static_distributed_tensor<OutDataType>(in_tile_dstr);
+#pragma clang diagnostic push
+#pragma clang diagnostic ignored "-Wuninitialized"
+    // __builtin_amdgcn_cvt_pk_fp8_f32() this builtin require the old value, and
+    // will generate a v_mov_b32 vxxx [old] before cvt, which result in unwanted ISA
+    // so we prepare an uninitialized variable purposely, and turn off the warning
+    int dummy_old;
+    static_for<0, thread_buffer_size_pk, 1>{}([&](auto i) {
+        uint32_t x = __builtin_amdgcn_cvt_pk_fp8_f32(
+            in_dstr_tensors.get_thread_buffer()[number<4 * i + 0>{}],
+            in_dstr_tensors.get_thread_buffer()[number<4 * i + 1>{}],
+            dummy_old,
+            false); // false -> WORD0
+
+        uint32_t y = __builtin_amdgcn_cvt_pk_fp8_f32(
+            in_dstr_tensors.get_thread_buffer()[number<4 * i + 2>{}],
+            in_dstr_tensors.get_thread_buffer()[number<4 * i + 3>{}],
+            dummy_old,
+            false); // false -> WORD0
+
+        constexpr int32_t m0 = 0x05040100;
+        using vec_t          = array<OutDataType, 4>;
+
+        vec_t d = bit_cast<vec_t>(__builtin_amdgcn_perm(y, x, m0));
+        out_dstr_tensor.get_thread_buffer().template set_as<vec_t>(number<i>{}, d);
+    });
+#pragma clang diagnostic pop
+
+    return out_dstr_tensor;
+#else
+    // fallback
+    return tile_elementwise_in(type_convert<OutDataType, typename InTensor::DataType>,
+                               in_dstr_tensors);
+#endif
+}
+
+template <typename OutDataType, typename InTensor>
+CK_TILE_DEVICE auto cast_tile_pk_fp16_fp32(const InTensor& in_dstr_tensors)
+{
+#if defined(__gfx908__) || defined(__gfx90a__) || defined(__gfx94__)
+    // This API is designed to use the _pk_ serious of function
+    constexpr auto in_tile_dstr = InTensor::get_tile_distribution();
+
+    constexpr index_t thread_buffer_size = InTensor::get_thread_buffer_size();
+    static_assert(thread_buffer_size % 2 == 0);
+    constexpr index_t thread_buffer_size_pk = thread_buffer_size / 2;
+
+    auto out_dstr_tensor = make_static_distributed_tensor<OutDataType>(in_tile_dstr);
+
+    // TODO: this is rtz cvt, need be very careful
+    for(index_t i = 0; i < thread_buffer_size_pk; i++)
+    {
+        auto o = __builtin_amdgcn_cvt_pkrtz(in_dstr_tensors.get_thread_buffer()[2 * i + 0],
+                                            in_dstr_tensors.get_thread_buffer()[2 * i + 1]);
+
+        out_dstr_tensor.get_thread_buffer().at(2 * i + 0) = o.x;
+        out_dstr_tensor.get_thread_buffer().at(2 * i + 1) = o.y;
+    }
+
+    return out_dstr_tensor;
+#else
+    // fallback
+    return tile_elementwise_in(type_convert<OutDataType, typename InTensor::DataType>,
+                               in_dstr_tensors);
+#endif
+}
+
+#if CK_TILE_USE_SUBDWORD_TILE_CAST
+// this function assume either src or dst (or both) date type is under 1 dword
+// we pack subdword value into 1 dword to avoid compiler's default subdword behavior(which is buggy)
+template <typename OutDataType, typename InTensor>
+CK_TILE_DEVICE auto cast_tile_opt_subdword(const InTensor& in_dstr_tensors)
+{
+    constexpr auto in_tile_dstr = InTensor::get_tile_distribution();
+
+    auto out_dstr_tensor = make_static_distributed_tensor<OutDataType>(in_tile_dstr);
+
+    using i_type                   = remove_cvref_t<typename InTensor::DataType>;
+    using o_type                   = remove_cvref_t<OutDataType>;
+    constexpr index_t i_elem_bytes = sizeof(i_type);
+    constexpr index_t o_elem_bytes = sizeof(o_type);
+    static_assert(i_elem_bytes < 4 || o_elem_bytes < 4);
+
+    constexpr index_t bulk_size =
+        (i_elem_bytes >= o_elem_bytes) ? (4 / o_elem_bytes) : (4 / i_elem_bytes);
+    static_assert(bulk_size != 0);
+
+    using o_bulk_type =
+        std::conditional_t<i_elem_bytes >= o_elem_bytes, float, array<o_type, bulk_size>>;
+
+    constexpr index_t thread_buffer_size = InTensor::get_thread_buffer_size();
+
+    constexpr index_t iters = thread_buffer_size / bulk_size;
+    constexpr index_t rems  = thread_buffer_size % bulk_size;
+
+    // cast the sequence per-bulk
+    static_for<0, iters, 1>{}([&](auto i) {
+        union bulk_wrapper
+        {
+            o_bulk_type bulk{};
+            o_type data[bulk_size];
+        } o_bulk;
+
+        // TODO: should use below function, but somehow will result in spill (same as c-forloop)
+        static_for<0, bulk_size, 1>{}([&o_bulk, &in_dstr_tensors, &i](auto ib) {
+            o_bulk.data[ib.value] = static_cast<o_type>(
+                in_dstr_tensors.get_thread_buffer()
+                    .template get_as<i_type>()[number<bulk_size * i.value + ib.value>{}]);
+        });
+
+        // TODO: fixme, should use above!
+        // static_assert(sizeof(i_type) / sizeof(o_type) == 2);
+        // o_bulk.data[0] = static_cast<o_type>(
+        //     in_dstr_tensors.get_thread_buffer().template get_as<i_type>()[number<2 * i + 0>{}]);
+        // o_bulk.data[1] = static_cast<o_type>(
+        //     in_dstr_tensors.get_thread_buffer().template get_as<i_type>()[number<2 * i + 1>{}]);
+
+        out_dstr_tensor.get_thread_buffer().template set_as<o_bulk_type>(i, o_bulk.bulk);
+    });
+
+    static_for<0, rems, 1>{}([&](auto r) {
+        // TODO: introducing local scratch pad?
+        auto idx = number<iters * bulk_size + r>{};
+        out_dstr_tensor.get_thread_buffer().at(idx) =
+            static_cast<o_type>(in_dstr_tensors.get_thread_buffer().at(idx));
+    });
+
+    return out_dstr_tensor;
+}
+#endif
+} // namespace impl
+
+template <typename DstType, typename SrcTensor>
+CK_TILE_DEVICE auto cast_tile(const SrcTensor& src_tensor)
+{
+    if constexpr((std::is_same_v<DstType, fp8_t> ||
+                  std::is_same_v<DstType, bf8_t>)&&std::is_same_v<typename SrcTensor::DataType,
+                                                                  float> &&
+                 (SrcTensor::get_thread_buffer_size() % 4 == 0))
+    {
+        return impl::cast_tile_pk_fp8_fp32<DstType, SrcTensor>(src_tensor);
+    }
+#if CK_TILE_USE_PK_FP16_TILE_CAST
+    else if constexpr(std::is_same_v<DstType, fp16_t> &&
+                      std::is_same_v<typename SrcTensor::DataType, float> &&
+                      (SrcTensor::get_thread_buffer_size() % 2 == 0))
+    {
+        return impl::cast_tile_pk_fp16_fp32<DstType, SrcTensor>(src_tensor);
+    }
+#endif
+#if CK_TILE_USE_SUBDWORD_TILE_CAST
+    else if constexpr(sizeof(DstType) < 4 || sizeof(typename SrcTensor::DataType) < 4)
+    {
+        return impl::cast_tile_opt_subdword<DstType, SrcTensor>(src_tensor);
+    }
+#endif
+    else
+        return tile_elementwise_in(type_convert<DstType, typename SrcTensor::DataType>, src_tensor);
+}
+
+// no-op function for null_tensor arguments
+template <typename InOutElementFunc,
+          typename... MaybeNullTensor,
+          typename = std::enable_if_t<
+              std::disjunction_v<std::is_same<remove_cvref_t<MaybeNullTensor>, null_tensor>...>>>
+CK_TILE_DEVICE void tile_elementwise_inout(const InOutElementFunc&, MaybeNullTensor&&...)
+{
+}
+
+// no-op function for null_tensor arguments
+template <typename InElementFunc,
+          typename... MaybeNullTensor,
+          typename = std::enable_if_t<
+              std::disjunction_v<std::is_same<remove_cvref_t<MaybeNullTensor>, null_tensor>...>>>
+CK_TILE_DEVICE auto tile_elementwise_in(const InElementFunc&, MaybeNullTensor&&...)
+{
+    return null_tensor{};
+}
+
+} // namespace ck_tile

include/ck_tile/core/tensor/tile_window_utils.hpp

@@ -0,0 +1,54 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#include "ck_tile/core/arch/arch.hpp"
+#include "ck_tile/core/arch/utility.hpp"
+#include "ck_tile/core/algorithm/space_filling_curve.hpp"
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/container/array.hpp"
+#include "ck_tile/core/container/sequence.hpp"
+#include "ck_tile/core/container/tuple.hpp"
+#include "ck_tile/core/container/container_helper.hpp"
+#include "ck_tile/core/tensor/static_distributed_tensor.hpp"
+#include "ck_tile/core/tensor/tensor_adaptor.hpp"
+#include "ck_tile/core/tensor/tile_distribution.hpp"
+#include "ck_tile/core/utility/functional.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+
+#pragma once
+namespace ck_tile {
+
+// input a lds store tile, extract some information from it
+// used to set m0 value for gfx9 serious
+template <typename LdsTileWindow_>
+CK_TILE_DEVICE auto get_async_store_smem_info(LdsTileWindow_&& lds_tile)
+{
+    using LdsTileWindow = remove_cvref_t<LdsTileWindow_>;
+    using LdsDataType   = typename LdsTileWindow::DataType;
+
+    // issues * warps * lanes
+    static_assert(LdsTileWindow::get_num_of_dimension() == 3); // TODO: hard coded
+
+    const index_t size_per_buf =
+        lds_tile.get_bottom_tensor_view().get_tensor_descriptor().calculate_offset(
+            make_tuple(number<0>{}, number<0>{}, number<0>{})) *
+        sizeof(LdsDataType);
+
+    const index_t size_per_wave =
+        lds_tile.get_bottom_tensor_view().get_tensor_descriptor().calculate_offset(
+            make_tuple(number<0>{}, number<1>{}, number<0>{})) *
+            sizeof(LdsDataType) -
+        size_per_buf;
+
+    const index_t size_per_issue =
+        lds_tile.get_bottom_tensor_view().get_tensor_descriptor().calculate_offset(
+            make_tuple(number<1>{}, number<0>{}, number<0>{})) *
+            sizeof(LdsDataType) -
+        size_per_buf;
+
+    const index_t m0_init_value = size_per_buf + size_per_wave * get_warp_id();
+
+    return make_tuple(m0_init_value, size_per_issue);
+}
+
+} // namespace ck_tile

include/ck_tile/core/tensor/transpose_tile.hpp

@@ -0,0 +1,232 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2025, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/utility/functional.hpp"
+#include "ck_tile/core/algorithm/coordinate_transform.hpp"
+#include "ck_tile/core/algorithm/space_filling_curve.hpp"
+#include "ck_tile/core/container/container_helper.hpp"
+#include "ck_tile/core/container/thread_buffer.hpp"
+#include "ck_tile/core/container/statically_indexed_array.hpp"
+#include "ck_tile/core/numeric/math.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+#include "ck_tile/core/tensor/tile_elementwise.hpp"
+#include "ck_tile/core/utility/transpose_vectors.hpp"
+
+namespace ck_tile {
+namespace detail {
+
+template <typename OutTensor, typename InTensor>
+CK_TILE_DEVICE void transpose_tile2d_impl_in_thread(OutTensor& out_tensor,
+                                                    const InTensor& in_tensor)
+{
+    constexpr auto I0 = number<0>{};
+
+    static_assert(std::is_same_v<typename InTensor::DataType, typename OutTensor::DataType>,
+                  "Data type for InTensor and OutTensor must be the same!");
+
+    using DataType = typename InTensor::DataType;
+
+    constexpr auto y_in_desc  = InTensor::get_tile_distribution().get_ys_to_d_descriptor();
+    constexpr auto y_out_desc = OutTensor::get_tile_distribution().get_ys_to_d_descriptor();
+
+    // y_dim_out_to_in
+    // For swapped Hs tile case I need only get_rh_minor_to_y
+    // since rh_major are already swapped due to swapped Hs.
+    constexpr auto get_rh_minor_to_y = [](auto dstr_tensor) {
+        using DstrEncode = typename decltype(dstr_tensor.get_tile_distribution())::DstrEncode;
+
+        map<index_t, index_t> rh_minor_to_y_;
+
+        static_for<0, DstrEncode::NDimY, 1>{}([&](auto i) {
+            constexpr index_t rh_minor = DstrEncode::ys_to_rhs_minor_[i];
+
+            rh_minor_to_y_(rh_minor) = i;
+        });
+
+        return rh_minor_to_y_;
+    };
+
+    // In swapped Hs case <Y,X> -> <X,Y> tile
+    // we have same rh_major, but reversed rh_minor!
+    constexpr auto rh_minor_to_y_in  = get_rh_minor_to_y(InTensor{});
+    constexpr auto rh_minor_to_y_out = get_rh_minor_to_y(OutTensor{});
+
+    // Is this really needed?? Should we have simple reverse here??
+    constexpr auto y_dim_out_to_in = [&] {
+        map<index_t, index_t> y_dim_out_to_in_;
+
+        for(const auto& [rh_minor, y_out] : rh_minor_to_y_out)
+        {
+            y_dim_out_to_in_(y_out) = rh_minor_to_y_in[rh_minor];
+        }
+
+        return y_dim_out_to_in_;
+    }();
+
+    constexpr index_t NDimY  = InTensor::get_tile_distribution().get_num_of_dimension_y();
+    constexpr auto y_lengths = to_sequence(y_in_desc.get_lengths());
+
+    // input and output vector dim in the order of input Y dims
+    constexpr index_t y_dim_vec_in  = NDimY - 1;
+    constexpr index_t y_dim_vec_out = y_dim_out_to_in[NDimY - 1];
+
+    // vector lengths
+    constexpr index_t vec_length_in  = y_lengths[y_dim_vec_in];
+    constexpr index_t vec_length_out = y_lengths[y_dim_vec_out];
+
+    // # of vectors
+    constexpr index_t num_vec_in  = vec_length_out;
+    constexpr index_t num_vec_out = vec_length_in;
+
+    // SFC
+    constexpr auto scalars_per_access_arr = generate_array(
+        [&](auto i) { return (i == y_dim_vec_in or i == y_dim_vec_out) ? y_lengths[i] : 1; },
+        number<NDimY>{});
+
+    constexpr auto scalars_per_access = TO_SEQUENCE(scalars_per_access_arr, NDimY);
+
+    using SFC_Y = space_filling_curve<decltype(y_lengths),
+                                      typename arithmetic_sequence_gen<0, NDimY, 1>::type,
+                                      decltype(scalars_per_access)>;
+
+    constexpr index_t num_access = SFC_Y::get_num_of_access();
+
+    static_assert(num_access > 0, "wrong! num_access should be larger than 0");
+
+    if constexpr(num_vec_in == 1 || num_vec_out == 1)
+    {
+        // loop over SFC
+        static_for<0, num_access, 1>{}([&](auto iAccess) {
+            // data index [y0, y1, ...] in the order of input tensor
+            constexpr auto idx_y = SFC_Y::get_index(iAccess);
+
+            constexpr index_t in_offset  = y_in_desc.calculate_offset(idx_y);
+            constexpr index_t out_offset = y_out_desc.calculate_offset(idx_y);
+
+            if constexpr(vec_length_in == 1)
+            {
+                out_tensor.get_thread_buffer()[number<out_offset>{}] =
+                    in_tensor.get_thread_buffer()[number<in_offset>{}];
+            }
+            else
+            {
+                using Vec = array<DataType, vec_length_in>;
+                out_tensor.get_thread_buffer().template get_as<Vec>(
+                    number<out_offset / vec_length_in>{}) =
+                    in_tensor.get_thread_buffer().template get_as<Vec>(
+                        number<in_offset / vec_length_in>{});
+            }
+        });
+    }
+    else
+    {
+        using InVec  = array<DataType, vec_length_in>;
+        using OutVec = array<DataType, vec_length_out>;
+
+        // in/out vectors to be transposed
+        thread_buffer<InVec, num_vec_in> in_vectors;
+        thread_buffer<OutVec, num_vec_out> out_vectors;
+
+        // loop over SFC and do transpose
+        static_for<0, num_access, 1>{}([&](auto iAccess) {
+            // data index [y0, y1, ...] in the order of input tensor
+            constexpr auto idx_y_start = SFC_Y::get_index(iAccess);
+
+            // get input vectors
+            static_for<0, num_vec_in, 1>{}([&](auto i) {
+                constexpr auto idx_y_in = generate_tuple(
+                    [&](auto ii) {
+                        return ii == y_dim_vec_out ? idx_y_start[ii] + i : idx_y_start[ii];
+                    },
+                    number<NDimY>{});
+
+                constexpr index_t in_offset = y_in_desc.calculate_offset(idx_y_in);
+                static_assert(in_offset % vec_length_in == 0);
+
+                in_vectors(i).template get_as<InVec>()(I0) =
+                    in_tensor.get_thread_buffer()
+                        .template get_as<InVec>()[number<in_offset / vec_length_in>{}];
+            });
+
+            // transpose
+            transpose_vectors<DataType, num_vec_in, num_vec_out>{}(in_vectors, out_vectors);
+
+            // set output vectors
+            static_for<0, num_vec_out, 1>{}([&](auto i) {
+                constexpr auto idx_y_out_tmp = generate_array(
+                    [&](auto ii) {
+                        return ii == y_dim_vec_in ? idx_y_start[ii] + i : idx_y_start[ii];
+                    },
+                    number<NDimY>{});
+
+                constexpr auto idx_y_out =
+                    container_reorder_given_new2old(idx_y_out_tmp, y_dim_out_to_in);
+
+                constexpr index_t out_offset = y_out_desc.calculate_offset(idx_y_out);
+                static_assert(out_offset % vec_length_out == 0);
+
+                out_tensor.get_thread_buffer().template set_as<OutVec>(
+                    number<out_offset / vec_length_out>{},
+                    out_vectors[i].template get_as<OutVec>()[I0]);
+            });
+        });
+    }
+}
+
+} // namespace detail
+
+template <typename OutTensor, typename InTensor>
+CK_TILE_DEVICE void transpose_tile2d(OutTensor& out, const InTensor& in)
+{
+    using InDataType  = typename InTensor::DataType;
+    using OutDataType = typename OutTensor::DataType;
+
+    using InTileDistr  = typename InTensor::StaticTileDistribution;
+    using OutTileDistr = typename OutTensor::StaticTileDistribution;
+
+    using InDstrEncode  = typename InTileDistr::DstrEncode;
+    using OutDstrEncode = typename OutTileDistr::DstrEncode;
+
+    using InThreadTensorDesc  = typename InTensor::ThreadTensorDesc;
+    using OutThreadTensorDesc = typename OutTensor::ThreadTensorDesc;
+
+    // Ys:
+    constexpr auto in_thread_desc_lengths  = InThreadTensorDesc{}.get_lengths();
+    constexpr auto out_thread_desc_lengths = OutThreadTensorDesc{}.get_lengths();
+
+    // type convert
+    const auto in_tmp = [&]() {
+        if constexpr(std::is_same_v<OutDataType, InDataType>)
+        {
+            return in;
+        }
+        else
+        {
+            return tile_elementwise_in(type_convert<OutDataType, InDataType>, in);
+        }
+    }();
+
+    // Scenario where we switch from tile <Y, X> -> <X, Y> - only 2D tiles!
+    // we preserve Ps but swap Ys: <Y1, Y0> -> <Y0, Y1>
+    if constexpr(InDstrEncode::rs_lengths_ == OutDstrEncode::rs_lengths_ &&
+                 InDstrEncode::hs_lengthss_ == tuple_reverse(OutDstrEncode::hs_lengthss_) &&
+                 InDstrEncode::NDimY == OutDstrEncode::NDimY && InDstrEncode::NDimY == 2 &&
+                 in_thread_desc_lengths == tuple_reverse(out_thread_desc_lengths))
+    // Any condition on Ps ??
+    //  InDstrEncode::ps_to_rhss_major_ == OutDstrEncode::ps_to_rhss_major_ &&
+    //  InDstrEncode::ps_to_rhss_minor_ == OutDstrEncode::ps_to_rhss_minor_ &&
+    {
+        detail::transpose_tile2d_impl_in_thread(out, in_tmp);
+    }
+    else
+    {
+        static_assert(false, "Provided tensors could not be transposed!");
+    }
+}
+
+} // namespace ck_tile

include/ck_tile/core/tensor/update_tile.hpp

@@ -0,0 +1,105 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/algorithm/coordinate_transform.hpp"
+#include "ck_tile/core/container/container_helper.hpp"
+#include "ck_tile/core/numeric/math.hpp"
+#include "ck_tile/core/tensor/tile_window.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+
+namespace ck_tile {
+
+template <typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          typename DataType_>
+CK_TILE_DEVICE void
+update_tile(tile_window_with_static_lengths<BottomTensorView_, WindowLengths_>& tile_window_tmp,
+            const static_distributed_tensor<DataType_, TileDistribution_>& dstr_tensor)
+{
+    using DataType = remove_cvref_t<typename BottomTensorView_::DataType>;
+    using TileDstr = remove_cvref_t<TileDistribution_>;
+
+    static_assert(std::is_same_v<remove_cvref_t<DataType_>, DataType>, "wrong!");
+
+    constexpr auto tile_dstr = TileDstr{};
+
+    auto tile_window = make_tile_window(tile_window_tmp.get_bottom_tensor_view(),
+                                        tile_window_tmp.get_window_lengths(),
+                                        tile_window_tmp.get_window_origin(),
+                                        tile_dstr);
+
+    tile_window.update(dstr_tensor);
+}
+
+template <typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          index_t NumCoord,
+          typename DataType_,
+          index_t i_access           = -1,
+          bool oob_conditional_check = true>
+CK_TILE_DEVICE void
+update_tile(tile_window_with_static_distribution<BottomTensorView_,
+                                                 WindowLengths_,
+                                                 TileDistribution_,
+                                                 NumCoord>& tile_window,
+            const static_distributed_tensor<DataType_, TileDistribution_>& dstr_tensor,
+            number<i_access>                     = {},
+            bool_constant<oob_conditional_check> = {})
+{
+    tile_window.update(dstr_tensor, number<i_access>{}, bool_constant<oob_conditional_check>{});
+}
+
+template <typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          index_t NumCoord,
+          typename DataType_,
+          index_t i_access           = -1,
+          bool oob_conditional_check = true,
+          bool pre_nop               = false>
+CK_TILE_DEVICE void
+update_tile_raw(tile_window_with_static_distribution<BottomTensorView_,
+                                                     WindowLengths_,
+                                                     TileDistribution_,
+                                                     NumCoord>& tile_window,
+                const static_distributed_tensor<DataType_, TileDistribution_>& dstr_tensor,
+                number<i_access>                     = {},
+                bool_constant<oob_conditional_check> = {},
+                bool_constant<pre_nop>               = {})
+{
+    tile_window.update_raw(dstr_tensor,
+                           number<i_access>{},
+                           bool_constant<oob_conditional_check>{},
+                           bool_constant<pre_nop>{});
+}
+
+template <typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          typename LinearBottomDims_,
+          typename DataType_,
+          index_t i_access           = -1,
+          bool oob_conditional_check = true,
+          bool pre_nop               = false>
+CK_TILE_DEVICE auto update_tile_raw(
+    tile_window_linear<BottomTensorView_, WindowLengths_, TileDistribution_, LinearBottomDims_>&
+        tile_window,
+    const static_distributed_tensor<DataType_, TileDistribution_>& dstr_tensor,
+    number<i_access>                     = {},
+    bool_constant<oob_conditional_check> = {},
+    bool_constant<pre_nop>               = {})
+{
+    tile_window.update_raw(dstr_tensor,
+                           number<i_access>{},
+                           bool_constant<oob_conditional_check>{},
+                           bool_constant<pre_nop>{});
+}
+
+} // namespace ck_tile

include/ck_tile/core/utility/bit_cast.hpp

@@ -0,0 +1,19 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+
+namespace ck_tile {
+
+template <typename Y, typename X>
+CK_TILE_HOST_DEVICE constexpr Y bit_cast(const X& x)
+{
+    static_assert(__has_builtin(__builtin_bit_cast), "");
+    static_assert(sizeof(X) == sizeof(Y), "Do not support cast between different size of type");
+
+    return __builtin_bit_cast(Y, x);
+}
+
+} // namespace ck_tile

include/ck_tile/core/utility/env.hpp

@@ -0,0 +1,208 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2025, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <iostream>
+#include <string>
+
+namespace ck_tile {
+
+template <typename... Args>
+void CK_TILE_ERROR(Args&&... args) noexcept
+{
+    std::ostringstream oss;
+    (oss << ... << args);
+    std::cerr << "[ERROR] " << oss.str() << std::endl;
+}
+
+namespace internal {
+
+template <size_t N>
+bool is_any_of(const char* const (&names)[N], const std::string& str)
+{
+    return std::any_of(std::begin(names), std::end(names), [&](const char* inner_str) {
+        return str == inner_str;
+    });
+};
+
+template <typename T>
+struct ParseEnvVal
+{
+};
+template <>
+struct ParseEnvVal<bool>
+{
+    static bool parse_env_var_value(const char* vp)
+    {
+        std::string value_env_str{vp};
+
+        for(auto& c : value_env_str)
+        {
+            if(std::isalpha(c) != 0)
+            {
+                c = std::tolower(static_cast<unsigned char>(c));
+            }
+        }
+
+        if(is_any_of(enabled_names, value_env_str))
+        {
+            return true;
+        }
+        else if(is_any_of(disabled_names, value_env_str))
+        {
+            return false;
+        }
+        else
+        {
+            throw std::runtime_error("Invalid value for env variable");
+        }
+
+        return false;
+    }
+
+    private:
+    static constexpr const char* enabled_names[]  = {"enable", "enabled", "1", "yes", "on", "true"};
+    static constexpr const char* disabled_names[] = {
+        "disable", "disabled", "0", "no", "off", "false"};
+};
+
+// Supports hexadecimals (with leading "0x"), octals (if prefix is "0") and decimals (default).
+// Returns 0 if environment variable is in wrong format (strtoull fails to parse the string).
+template <>
+struct ParseEnvVal<uint64_t>
+{
+    static uint64_t parse_env_var_value(const char* vp) { return std::strtoull(vp, nullptr, 0); }
+};
+
+template <>
+struct ParseEnvVal<std::string>
+{
+    static std::string parse_env_var_value(const char* vp) { return std::string{vp}; }
+};
+
+template <typename T>
+struct EnvVar
+{
+    private:
+    T value{};
+    bool is_unset = true;
+
+    public:
+    const T& GetValue() const { return value; }
+
+    bool IsUnset() const { return is_unset; }
+
+    void Unset() { is_unset = true; }
+
+    void UpdateValue(const T& val)
+    {
+        is_unset = false;
+        value    = val;
+    }
+
+    explicit EnvVar(const char* const name, const T& def_val)
+    {
+        // NOLINTNEXTLINE (concurrency-mt-unsafe)
+        const char* vp = std::getenv(name);
+        if(vp != nullptr) // a value was provided
+        {
+            is_unset = false;
+            value    = ParseEnvVal<T>::parse_env_var_value(vp);
+        }
+        else // no value provided, use default value
+        {
+            value = def_val;
+        }
+    }
+};
+} // end namespace internal
+
+// Static inside function hides the variable and provides
+// thread-safety/locking
+// Used in global namespace
+#define CK_TILE_DECLARE_ENV_VAR(name, type, default_val)                            \
+    namespace ck_tile::env {                                                        \
+    struct name                                                                     \
+    {                                                                               \
+        static_assert(std::is_same_v<name, ::ck_tile::env::name>,                   \
+                      "CK_TILE_DECLARE_ENV* must be used in the global namespace"); \
+        using value_type = type;                                                    \
+        static ck_tile::internal::EnvVar<type>& Ref()                               \
+        {                                                                           \
+            static ck_tile::internal::EnvVar<type> var{#name, default_val};         \
+            return var;                                                             \
+        }                                                                           \
+    };                                                                              \
+    }
+
+#define CK_TILE_DECLARE_ENV_VAR_BOOL(name) CK_TILE_DECLARE_ENV_VAR(name, bool, false)
+
+#define CK_TILE_DECLARE_ENV_VAR_UINT64(name) CK_TILE_DECLARE_ENV_VAR(name, uint64_t, 0)
+
+#define CK_TILE_DECLARE_ENV_VAR_STR(name) CK_TILE_DECLARE_ENV_VAR(name, std::string, "")
+
+#define CK_TILE_ENV(name) \
+    ck_tile::env::name {}
+
+template <class EnvVar>
+inline const std::string& EnvGetString(EnvVar)
+{
+    static_assert(std::is_same_v<typename EnvVar::value_type, std::string>);
+    return EnvVar::Ref().GetValue();
+}
+
+template <class EnvVar>
+inline bool EnvIsEnabled(EnvVar)
+{
+    static_assert(std::is_same_v<typename EnvVar::value_type, bool>);
+    return !EnvVar::Ref().IsUnset() && EnvVar::Ref().GetValue();
+}
+
+template <class EnvVar>
+inline bool EnvIsDisabled(EnvVar)
+{
+    static_assert(std::is_same_v<typename EnvVar::value_type, bool>);
+    return !EnvVar::Ref().IsUnset() && !EnvVar::Ref().GetValue();
+}
+
+template <class EnvVar>
+inline uint64_t EnvValue(EnvVar)
+{
+    static_assert(std::is_same_v<typename EnvVar::value_type, uint64_t>);
+    return EnvVar::Ref().GetValue();
+}
+
+template <class EnvVar>
+inline bool EnvIsUnset(EnvVar)
+{
+    return EnvVar::Ref().IsUnset();
+}
+
+template <class EnvVar>
+void EnvUnset(EnvVar)
+{
+    EnvVar::Ref().Unset();
+}
+
+/// Updates the cached value of an environment variable
+template <typename EnvVar, typename ValueType>
+void UpdateEnvVar(EnvVar, const ValueType& val)
+{
+    static_assert(std::is_same_v<typename EnvVar::value_type, ValueType>);
+    EnvVar::Ref().UpdateValue(val);
+}
+
+template <typename EnvVar>
+void UpdateEnvVar(EnvVar, const std::string_view& val)
+{
+    EnvVar::Ref().UpdateValue(
+        ck_tile::internal::ParseEnvVal<typename EnvVar::value_type>::parse_env_var_value(
+            val.data()));
+}
+
+} // namespace ck_tile
+
+// environment variable to enable logging:
+// export CK_TILE_LOGGING=ON or CK_TILE_LOGGING=1 or CK_TILE_LOGGING=ENABLED
+CK_TILE_DECLARE_ENV_VAR_BOOL(CK_TILE_LOGGING)

include/ck_tile/core/utility/functional.hpp

@@ -0,0 +1,232 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/container/sequence.hpp"
+#include <stdint.h>
+#include <utility>
+
+namespace ck_tile {
+
+namespace detail {
+
+struct swallow
+{
+    template <typename... Ts>
+    CK_TILE_HOST_DEVICE constexpr swallow(Ts&&...)
+    {
+    }
+};
+
+template <class>
+struct static_for_impl;
+
+template <index_t... Is>
+struct static_for_impl<sequence<Is...>>
+{
+    template <class F>
+    CK_TILE_HOST_DEVICE constexpr void operator()(F f) const
+    {
+        swallow{(f(number<Is>{}), 0)...};
+    }
+};
+
+} // namespace detail
+
+// F signature: F(number<Iter>)
+template <index_t NBegin, index_t NEnd, index_t Increment>
+struct static_for
+{
+    CK_TILE_HOST_DEVICE constexpr static_for()
+    {
+        static_assert(Increment != 0 && (NEnd - NBegin) % Increment == 0,
+                      "Wrong! should satisfy (NEnd - NBegin) % Increment == 0");
+        static_assert((Increment > 0 && NBegin <= NEnd) || (Increment < 0 && NBegin >= NEnd),
+                      "wrongs! should (Increment > 0 && NBegin <= NEnd) || (Increment < 0 && "
+                      "NBegin >= NEnd)");
+    }
+
+    template <class F>
+    CK_TILE_HOST_DEVICE constexpr void operator()(F f) const
+    {
+        detail::static_for_impl<typename arithmetic_sequence_gen<NBegin, NEnd, Increment>::type>{}(
+            f);
+    }
+};
+
+namespace detail {
+
+template <typename T, T... Is>
+struct applier
+{
+    template <typename F>
+    CK_TILE_HOST_DEVICE constexpr void operator()(F f) const
+    {
+        // tweak -fbracket-depth if compilation fails. Clang default limit is 256
+        (f(number<Is>{}), ...);
+    }
+};
+
+template <int32_t Size> // == sizeof...(Is)
+using make_applier = __make_integer_seq<applier, index_t, Size>;
+
+} // namespace detail
+
+template <index_t N>
+struct static_for<0, N, 1> : detail::make_applier<N>
+{
+    using detail::make_applier<N>::operator();
+};
+
+struct identity
+{
+    template <typename T>
+    CK_TILE_HOST_DEVICE constexpr T&& operator()(T&& arg) const noexcept
+    {
+        return std::forward<T>(arg);
+    }
+};
+
+namespace detail {
+
+// RemainLengths: sequence<...>
+// Orders: sequence<...>
+template <class RemainLengths, class Orders>
+struct static_ford_impl
+{
+    CK_TILE_HOST_DEVICE constexpr static_ford_impl()
+    {
+        static_assert(RemainLengths::size() > 0, "wrong! should not get here");
+    }
+
+    // F signature: F(sequence<...>)
+    // CurrentOrderedId: sequence<...>
+    template <class F, class CurrentOrderedId>
+    CK_TILE_HOST_DEVICE constexpr void operator()(F f, CurrentOrderedId) const
+    {
+        static_for<0, RemainLengths::front(), 1>{}([=](auto I) {
+            static_ford_impl<decltype(RemainLengths::pop_front()), Orders>{}(
+                f, CurrentOrderedId::push_back(I));
+        });
+    }
+};
+
+template <class Orders>
+struct static_ford_impl<sequence<>, Orders>
+{
+    // F signature: F(sequence<...>)
+    // OrderedId: sequence<...>
+    template <class F, class OrderedId>
+    CK_TILE_HOST_DEVICE constexpr void operator()(F f, OrderedId) const
+    {
+        // retrive unordered Id
+        f(OrderedId::reorder_old_to_new(Orders{}));
+    }
+};
+
+} // namespace detail
+
+// Lengths is sequence<...>, it is the length of each dimension for
+// N-dimensional loop
+// Orders is sequence<...>, it is the order of dimension in which static_ford
+// will loop over each
+// dimension
+template <class Lengths,
+          class Orders = typename arithmetic_sequence_gen<0, Lengths::size(), 1>::type>
+struct static_ford
+{
+    CK_TILE_HOST_DEVICE constexpr static_ford()
+    {
+        static_assert(Lengths::size() > 0, "wrong! Lengths is empty");
+        static_assert(Lengths::size() == Orders::size(), "wrong! inconsistent size");
+    }
+
+    // F signature: F(sequence<...> multi_id)
+    // multi_id is the unordered multi-index
+    template <class F>
+    CK_TILE_HOST_DEVICE constexpr void operator()(F f) const
+    {
+        constexpr auto ordered_lengths = Lengths::reorder_new_to_old(Orders{});
+        detail::static_ford_impl<decltype(ordered_lengths), Orders>{}(f, sequence<>{});
+    }
+};
+
+namespace detail {
+
+template <typename Indices>
+struct unpack_impl;
+
+template <index_t... Is>
+struct unpack_impl<sequence<Is...>>
+{
+    template <typename F, typename X>
+    CK_TILE_HOST_DEVICE constexpr auto operator()(F&& f, X&& x) const
+    {
+#if 0
+        return std::forward<F>(f)(std::forward<X>(x).at(number<Is>{})...);
+#else
+        return std::forward<F>(f)(std::forward<X>(x).template at<Is>()...);
+#endif
+    }
+};
+
+template <typename Seq0, typename Seq1>
+struct unpack2_impl;
+
+// TODO: remove this, after properly implementing unpack that takes any number of containers
+template <index_t... Is, index_t... Js>
+struct unpack2_impl<sequence<Is...>, sequence<Js...>>
+{
+    template <typename F, typename X, typename Y>
+    CK_TILE_HOST_DEVICE constexpr auto operator()(F&& f, X&& x, Y&& y) const
+    {
+#if 0
+        return std::forward<F>(f)(std::forward<X>(x).at(number<Is>{})...,
+                                  std::forward<Y>(y).at(number<Js>{})...);
+#else
+        return std::forward<F>(f)(std::forward<X>(x).template at<Is>()...,
+                                  std::forward<Y>(y).template at<Js>()...);
+#endif
+    }
+};
+
+} // namespace detail
+
+template <typename F, typename X>
+CK_TILE_HOST_DEVICE constexpr auto unpack(F&& f, X&& x)
+{
+    using X_ = remove_reference_t<X>;
+    return detail::unpack_impl<typename arithmetic_sequence_gen<0, X_::size(), 1>::type>{}(
+        std::forward<F>(f), std::forward<X>(x));
+}
+
+// TODO: properly implement unpack that takes any number of containers
+template <typename F, typename X, typename Y>
+CK_TILE_HOST_DEVICE constexpr auto unpack2(F&& f, X&& x, Y&& y)
+{
+    using X_ = remove_reference_t<X>;
+    using Y_ = remove_reference_t<Y>;
+    return detail::unpack2_impl<typename arithmetic_sequence_gen<0, X_::size(), 1>::type,
+                                typename arithmetic_sequence_gen<0, Y_::size(), 1>::type>{}(
+        std::forward<F>(f), std::forward<X>(x), std::forward<Y>(y));
+}
+
+// z = predicate ? x : y
+template <bool predicate, typename X, typename Y>
+constexpr auto conditional_expr(X&& x, Y&& y)
+{
+    if constexpr(predicate)
+    {
+        return std::forward<X>(x);
+    }
+    else
+    {
+        return std::forward<Y>(y);
+    }
+}
+
+} // namespace ck_tile

include/ck_tile/core/utility/functional_with_tuple.hpp

@@ -0,0 +1,173 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+// This file should not be included inside tuple.hpp!
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/numeric/math.hpp"
+#include "ck_tile/core/container/sequence.hpp"
+#include "ck_tile/core/container/tuple.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+#include <stdint.h>
+#include <utility>
+
+namespace ck_tile {
+
+namespace detail {
+
+// RemainLengths: sequence<...>
+// Orders: sequence<...>
+template <class RemainLengths, class RamainUnpacks, class Orders>
+struct static_uford_impl
+{
+    CK_TILE_HOST_DEVICE constexpr static_uford_impl()
+    {
+        static_assert(RemainLengths::size() > 0, "wrong! should not get here");
+        static_assert(RamainUnpacks::size() > 0, "wrong! should not get here");
+    }
+
+    template <class F, class CurrentUnpackIds>
+    CK_TILE_HOST_DEVICE constexpr void operator()(F f, CurrentUnpackIds) const
+    {
+        constexpr index_t pack_len = RamainUnpacks::front();
+        static_for<0, RemainLengths::front(), pack_len>{}([=](auto I) {
+            constexpr auto new_pack = generate_tuple(
+                [&](auto idx_) {
+                    constexpr auto i_new_pack = number<I + idx_ % pack_len>{};
+                    constexpr auto i_pre_pack = number<idx_ / pack_len>{};
+                    return CurrentUnpackIds{}.at(i_pre_pack).push_back(i_new_pack);
+                },
+                number<CurrentUnpackIds::size() * pack_len>{});
+
+            static_uford_impl<decltype(RemainLengths::pop_front()),
+                              decltype(RamainUnpacks::pop_front()),
+                              Orders>{}(f, new_pack);
+        });
+    }
+};
+
+template <class Orders>
+struct static_uford_impl<sequence<>, sequence<>, Orders>
+{
+    template <class F, class PackedId>
+    CK_TILE_HOST_DEVICE constexpr void operator()(F f, PackedId) const
+    {
+        constexpr auto origin_packs = transform_tuples(
+            [](auto pack_) { return decltype(pack_)::reorder_old_to_new(Orders{}); }, PackedId{});
+        unpack(f, origin_packs);
+    }
+};
+
+template <class RemainLengths, class RamainUnpacks, class Orders>
+struct static_uford_one_shot_impl
+{
+    template <class F, class CurrentUnpackIds, index_t current_acc>
+    CK_TILE_HOST_DEVICE constexpr void operator()(F f, CurrentUnpackIds, number<current_acc>) const
+    {
+        constexpr auto r_lens_stride =
+            reverse_exclusive_scan_sequence(RemainLengths{}, multiplies{}, number<1>{});
+        constexpr auto r_upks_stride =
+            reverse_exclusive_scan_sequence(RamainUnpacks{}, multiplies{}, number<1>{});
+
+        constexpr index_t current_stride = r_lens_stride.front() / r_upks_stride.front();
+        constexpr index_t pack_len       = RamainUnpacks::front();
+        constexpr index_t current_idx    = (current_acc / current_stride) * pack_len;
+
+        constexpr auto new_pack = generate_tuple(
+            [&](auto idx_) {
+                constexpr auto i_new_pack = number<current_idx + idx_ % pack_len>{};
+                constexpr auto i_pre_pack = number<idx_ / pack_len>{};
+                return CurrentUnpackIds{}.at(i_pre_pack).push_back(i_new_pack);
+            },
+            number<CurrentUnpackIds::size() * pack_len>{});
+
+        static_uford_one_shot_impl<decltype(RemainLengths::pop_front()),
+                                   decltype(RamainUnpacks::pop_front()),
+                                   Orders>{}(f, new_pack, number<current_acc % current_stride>{});
+    }
+};
+
+template <class Orders>
+struct static_uford_one_shot_impl<sequence<>, sequence<>, Orders>
+{
+    template <class F, class PackedId, index_t current_acc>
+    CK_TILE_HOST_DEVICE constexpr void operator()(F f, PackedId, number<current_acc>) const
+    {
+        constexpr auto origin_packs = transform_tuples(
+            [](auto pack_) { return decltype(pack_)::reorder_old_to_new(Orders{}); }, PackedId{});
+        unpack(f, origin_packs);
+    }
+};
+
+} // namespace detail
+
+// TODO: we may unify static_ford/static_uford in the future
+//
+// loop over nd space(sequence) with packs
+// you must make sure the function passed in has same number of argument
+//
+// e.g.
+// Lengths=seq<2, 3, 4>, Unpacks=<1, 1, 2>
+// static_uford<Lengths, Unpacks>{}([&](auto i_0, auto i_1){}); // require 2 args(packs)
+//
+// loop #0, i_0=seq<0, 0, 0>, i_1=<0, 0, 1>
+// loop #1, i_0=seq<0, 0, 2>, i_1=<0, 0, 3>
+// loop #2, i_0=seq<0, 1, 0>, i_1=<0, 1, 1>
+// loop #3, i_0=seq<0, 1, 2>, i_1=<0, 1, 3>
+// loop #4, i_0=seq<0, 2, 0>, i_1=<0, 2, 1>
+// loop #5, i_0=seq<0, 2, 2>, i_1=<0, 2, 3>
+// loop #6, i_0=seq<1, 0, 0>, i_1=<1, 0, 1>
+// ...
+template <class Lengths,
+          class Unpacks = typename uniform_sequence_gen<Lengths::size(), 1>::type,
+          class Orders  = typename arithmetic_sequence_gen<0, Lengths::size(), 1>::type>
+struct static_uford
+{
+    static constexpr index_t num_packs = reduce_on_sequence(Unpacks{}, multiplies{}, number<1>{});
+
+    CK_TILE_HOST_DEVICE constexpr static_uford()
+    {
+        static_assert(Lengths::size() > 0, "wrong! Lengths is empty");
+        static_assert(Lengths::size() == Unpacks::size(), "wrong! inconsistent size");
+        static_assert(Lengths::size() == Orders::size(), "wrong! inconsistent size");
+        static_for<0, Lengths::size(), 1>{}(
+            [&](auto i) { static_assert(Lengths{}.at(i) % Unpacks{}.at(i) == 0); });
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr index_t get_num_of_access()
+    {
+        using L_ = decltype(Lengths{} / Unpacks{});
+
+        return reduce_on_sequence(L_{}, multiplies{}, number<1>{});
+    }
+
+    // F signature: F(sequence<...> multi_id...)
+    // multi_id is the unordered multi-index
+    template <class F>
+    CK_TILE_HOST_DEVICE constexpr void operator()(F f) const
+    {
+        constexpr auto ordered_lengths = Lengths::reorder_new_to_old(Orders{});
+        constexpr auto ordered_unpacks = Unpacks::reorder_new_to_old(Orders{});
+        detail::static_uford_impl<decltype(ordered_lengths), decltype(ordered_unpacks), Orders>{}(
+            f, make_tuple(sequence<>{}));
+    }
+
+    // this version is friendly for issue function one by one
+    template <class F, index_t i_access>
+    CK_TILE_HOST_DEVICE constexpr void operator()(F f, number<i_access>) const
+    {
+        static_assert(i_access < get_num_of_access());
+        constexpr auto ordered_lengths = Lengths::reorder_new_to_old(Orders{});
+        constexpr auto ordered_unpacks = Unpacks::reorder_new_to_old(Orders{});
+        detail::static_uford_one_shot_impl<decltype(ordered_lengths),
+                                           decltype(ordered_unpacks),
+                                           Orders>{}(
+            f, make_tuple(sequence<>{}), number<i_access>{});
+    }
+};
+
+} // namespace ck_tile

include/ck_tile/core/utility/ignore.hpp

@@ -0,0 +1,22 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+// https://en.cppreference.com/w/cpp/utility/tuple/ignore
+
+namespace ck_tile {
+
+namespace detail {
+struct ignore_t
+{
+    template <typename T>
+    constexpr void operator=(T&&) const noexcept
+    {
+    }
+};
+} // namespace detail
+
+inline constexpr detail::ignore_t ignore;
+
+} // namespace ck_tile

include/ck_tile/core/utility/literals.hpp

@@ -0,0 +1,22 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <cstdlib>
+
+namespace ck_tile {
+namespace literals {
+// [P0330] Literal Suffix for (signed) size_t (C++23)
+// ref: https://wg21.link/p0330r8
+inline constexpr std::size_t operator""_uz(unsigned long long size)
+{
+    return static_cast<std::size_t>(size);
+}
+
+inline constexpr std::size_t operator""_zu(unsigned long long size)
+{
+    return static_cast<std::size_t>(size);
+}
+} // namespace literals
+} // namespace ck_tile

include/ck_tile/core/utility/magic_div.hpp

@@ -0,0 +1,257 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/container/tuple.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/utility/bit_cast.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+#include <stdint.h>
+
+namespace ck_tile {
+
+// magic number division
+// Caution:
+//   1. For uint32_t as dividend: magic number division implementation being used would produce
+//   correct result if the dividend is uint32_t and its value is within 31-bit value range.
+//   2. For int32_t as dividendd: magic number division for int32_t dividened has not been
+//   implemented, the int32_t dividend would be bit-wise interpreted as uint32_t and magic number
+//   division implementation for uint32_t is then used. Therefore, dividend value need to be
+//   non-negative.
+// TODO:
+//   1. Implement magic number divison for int32_t
+//   2. Implement magic number divison for unit32_t with 32-bit value range
+struct magic_division32_bit_range
+{
+    // uint32_t
+    CK_TILE_HOST_DEVICE static constexpr auto calculate_magic_numbers(uint32_t divisor)
+    {
+        // WARNING: magic division is only valid for division inside this range.
+        // assert(divisor >= 1 && divisor <= INT32_MAX)
+
+        uint32_t shift_u32 = 0;
+
+        while((1U << shift_u32) < divisor)
+        {
+            shift_u32++;
+        };
+
+        uint64_t tmp_u64        = static_cast<uint64_t>((1UL << shift_u32) - divisor) << 32;
+        uint32_t multiplier_u32 = tmp_u64 / divisor + 1;
+
+        return make_tuple(multiplier_u32, shift_u32);
+    }
+
+    template <auto Divisor, typename = std::enable_if_t<(0 < Divisor)>>
+    CK_TILE_HOST_DEVICE static constexpr auto calculate_magic_numbers(constant<Divisor>)
+    {
+        constexpr auto tmp = calculate_magic_numbers(uint32_t{Divisor});
+
+        constexpr uint32_t multiplier = tmp[number<0>{}];
+        constexpr uint32_t shift      = tmp[number<1>{}];
+
+        return make_tuple(constant<multiplier>{}, constant<shift>{});
+    }
+
+    // magic division for uint32_t
+    CK_TILE_DEVICE static constexpr uint32_t
+    do_magic_division(uint32_t dividend, uint32_t multiplier, uint32_t shift)
+    {
+        if(__builtin_is_constant_evaluated())
+        {
+            uint32_t tmp = (static_cast<uint64_t>(dividend) * multiplier) >> 32;
+            return (tmp + dividend) >> shift;
+        }
+        else
+        {
+            uint32_t tmp = __umulhi(dividend, multiplier);
+            return (tmp + dividend) >> shift;
+        }
+    }
+
+    CK_TILE_HOST static constexpr uint32_t
+    do_magic_division(uint32_t dividend, uint32_t multiplier, uint32_t shift)
+    {
+        uint32_t tmp = (static_cast<uint64_t>(dividend) * multiplier) >> 32;
+        return (tmp + dividend) >> shift;
+    }
+
+    // magic division for int32_t
+    // HACK: use dividend_i32 as if it's uint32_t, dividend_i32 need to be
+    // non-negative for result to be correct
+    // TODO: figure out how to do magic number divison for int32_t as dividended
+    CK_TILE_DEVICE static constexpr int32_t
+    do_magic_division(int32_t dividend_i32, uint32_t multiplier, uint32_t shift)
+    {
+        if(__builtin_is_constant_evaluated())
+        {
+            uint32_t dividend_u32 = bit_cast<uint32_t>(dividend_i32);
+            uint32_t tmp          = (static_cast<uint64_t>(dividend_u32) * multiplier) >> 32;
+            return (tmp + dividend_u32) >> shift;
+        }
+        else
+        {
+            uint32_t dividend_u32 = bit_cast<uint32_t>(dividend_i32);
+            uint32_t tmp          = __umulhi(dividend_u32, multiplier);
+            return (tmp + dividend_u32) >> shift;
+        }
+    }
+
+    CK_TILE_HOST static constexpr int32_t
+    do_magic_division(int32_t dividend_i32, uint32_t multiplier, uint32_t shift)
+    {
+        uint32_t dividend_u32 = bit_cast<uint32_t>(dividend_i32);
+        uint32_t tmp          = (static_cast<uint64_t>(dividend_u32) * multiplier) >> 32;
+        return (tmp + dividend_u32) >> shift;
+    }
+};
+
+// magic number division
+// This version on works for divisor and dividended between [0, 1 << 16]
+struct magic_division16_bit_range
+{
+    // uint32_t
+    CK_TILE_HOST_DEVICE static constexpr auto calculate_magic_numbers(uint32_t divisor)
+    {
+        // WARNING: magic division is only valid for division inside this range.
+        // assert(divisor >= 1 && divisor <= (1U << 16));
+
+        uint32_t shift_u32 = 0;
+
+        while((1U << shift_u32) < divisor)
+        {
+            shift_u32++;
+        };
+
+        uint32_t one            = 1;
+        uint32_t multiplier_u32 = ((one << 16) * ((one << shift_u32) - divisor)) / divisor + 1;
+
+        return make_tuple(multiplier_u32, shift_u32);
+    }
+
+    // integral_constant<uint32_t, .>
+    template <auto Divisor>
+    CK_TILE_HOST_DEVICE static constexpr auto calculate_magic_numbers(constant<Divisor>)
+    {
+        constexpr auto tmp = calculate_magic_numbers(uint32_t{Divisor});
+
+        constexpr uint32_t multiplier = tmp[number<0>{}];
+        constexpr uint32_t shift      = tmp[number<1>{}];
+
+        return make_tuple(constant<multiplier>{}, constant<shift>{});
+    }
+
+    // magic division for uint32_t
+    CK_TILE_DEVICE static constexpr uint32_t
+    do_magic_division(uint32_t dividend, uint32_t multiplier, uint32_t shift)
+    {
+        uint32_t tmp = (dividend * multiplier) >> 16;
+        return (tmp + dividend) >> shift;
+    }
+
+    CK_TILE_HOST static constexpr uint32_t
+    do_magic_division(uint32_t dividend, uint32_t multiplier, uint32_t shift)
+    {
+        uint32_t tmp = (dividend * multiplier) >> 16;
+        return (tmp + dividend) >> shift;
+    }
+
+    // magic division for int32_t
+    // HACK: use dividend_i32 as if it's uint32_t, dividend_i32 need to be
+    // non-negative for result to be correct
+    // TODO: figure out how to do magic number divison for int32_t as dividended
+    CK_TILE_DEVICE static constexpr int32_t
+    do_magic_division(int32_t dividend_i32, uint32_t multiplier, uint32_t shift)
+    {
+        uint32_t dividend_u32 = bit_cast<uint32_t>(dividend_i32);
+        uint32_t tmp          = (dividend_u32 * multiplier) >> 16;
+        return (tmp + dividend_u32) >> shift;
+    }
+
+    CK_TILE_HOST static constexpr int32_t
+    do_magic_division(int32_t dividend_i32, uint32_t multiplier, uint32_t shift)
+    {
+        uint32_t dividend_u32 = bit_cast<uint32_t>(dividend_i32);
+        uint32_t tmp          = (dividend_u32 * multiplier) >> 16;
+        return (tmp + dividend_u32) >> shift;
+    }
+};
+
+// use 32bit version
+using magic_division = magic_division32_bit_range;
+
+struct mdiv
+{
+    // 1 dword -> 3 dword storage
+    uint32_t divisor;
+    uint32_t multiplier;
+    uint32_t shift; // TODO: 8 bit is enough
+
+    // prefer construct on host
+    CK_TILE_HOST_DEVICE mdiv(uint32_t divisor_) : divisor(divisor_)
+    {
+        auto tmp = magic_division::calculate_magic_numbers(divisor_);
+
+        multiplier = tmp[number<0>{}];
+        shift      = tmp[number<1>{}];
+    }
+
+    CK_TILE_HOST_DEVICE mdiv() : divisor(0), multiplier(0), shift(0) {}
+
+    CK_TILE_HOST_DEVICE void update(uint32_t divisor_)
+    {
+        divisor  = divisor_;
+        auto tmp = magic_division::calculate_magic_numbers(divisor_);
+
+        multiplier = tmp[number<0>{}];
+        shift      = tmp[number<1>{}];
+    }
+
+    CK_TILE_HOST_DEVICE uint32_t div(uint32_t dividend_) const
+    {
+        return magic_division::do_magic_division(dividend_, multiplier, shift);
+    }
+
+    CK_TILE_HOST_DEVICE void
+    divmod(uint32_t dividend_, uint32_t& quotient_, uint32_t& remainder_) const
+    {
+        quotient_  = div(dividend_);
+        remainder_ = dividend_ - (quotient_ * divisor);
+    }
+
+    CK_TILE_HOST_DEVICE uint32_t get() const { return divisor; }
+};
+
+struct mdiv2
+{
+    // 1 dword -> 2 dword storage, divisor need compute from runtime
+    uint32_t multiplier;
+    uint32_t shift; // TODO: 8 bit is enough
+
+    // prefer construct on host
+    CK_TILE_HOST_DEVICE mdiv2(uint32_t divisor_)
+    {
+        auto tmp = magic_division::calculate_magic_numbers(divisor_);
+
+        multiplier = tmp[number<0>{}];
+        shift      = tmp[number<1>{}];
+    }
+
+    CK_TILE_HOST_DEVICE mdiv2() : multiplier(0), shift(0) {}
+
+    CK_TILE_HOST_DEVICE uint32_t div(uint32_t dividend_) const
+    {
+        return magic_division::do_magic_division(dividend_, multiplier, shift);
+    }
+
+    CK_TILE_HOST_DEVICE void
+    divmod(uint32_t dividend_, uint32_t divisor_, uint32_t& quotient_, uint32_t& remainder_) const
+    {
+        quotient_  = div(dividend_);
+        remainder_ = dividend_ - (quotient_ * divisor_);
+    }
+};
+
+} // namespace ck_tile

include/ck_tile/core/utility/philox_rand.hpp

@@ -0,0 +1,122 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+
+namespace ck_tile {
+
+// Reference: https://github.com/Dao-AILab/flash-attention/blob/main/csrc/flash_attn/src/philox.cuh
+class philox
+{
+    public:
+    CK_TILE_HOST_DEVICE philox(unsigned long long seed_, unsigned long long offset_)
+        : seed(reinterpret_cast<const uint2&>(seed_))
+    {
+
+        ull2* tmp = reinterpret_cast<ull2*>(&counter);
+        tmp->x    = offset_;
+    }
+
+    CK_TILE_HOST_DEVICE uint4 get_philox_4x32(const unsigned long long subsequence) const
+    {
+
+        uint4 counter_ = counter;
+        ull2* tmp      = reinterpret_cast<ull2*>(&counter_);
+        tmp->y         = subsequence;
+
+        uint2 key_ = seed;
+// 7-round philox
+#pragma unroll
+        for(int i = 0; i < 6; i++)
+        {
+            counter_ = philox_single_round(counter_, key_);
+            key_.x += kPhilox10A;
+            key_.y += kPhilox10B;
+        }
+        uint4 output = philox_single_round(counter_, key_);
+        return output;
+    }
+
+    CK_TILE_HOST_DEVICE void get_random_16x8(uint8_t* out,
+                                             const unsigned long long subsequence) const
+    {
+        uint4 tmp_ph;
+        tmp_ph = get_philox_4x32(subsequence);
+
+        uint32_t* out_tmp = reinterpret_cast<uint32_t*>(&out[0]);
+
+        out_tmp[0] = tmp_ph.x;
+        out_tmp[1] = tmp_ph.y;
+        out_tmp[2] = tmp_ph.z;
+        out_tmp[3] = tmp_ph.w;
+    }
+
+    CK_TILE_HOST_DEVICE void get_random_8x8(uint8_t* out,
+                                            const unsigned long long subsequence,
+                                            const index_t start_idx) const
+    {
+        uint4 tmp_ph;
+        tmp_ph = get_philox_4x32(subsequence);
+
+        uint32x4_t tmp;
+        tmp[0]            = tmp_ph.x;
+        tmp[1]            = tmp_ph.y;
+        tmp[2]            = tmp_ph.z;
+        tmp[3]            = tmp_ph.w;
+        uint32_t* out_tmp = reinterpret_cast<uint32_t*>(&out[0]);
+        out_tmp[0]        = tmp[start_idx];
+        out_tmp[1]        = tmp[start_idx + 2];
+    }
+
+    CK_TILE_HOST_DEVICE void get_random_4x8(uint8_t* out,
+                                            const unsigned long long subsequence,
+                                            const index_t start_idx) const
+    {
+        uint4 tmp_ph;
+        tmp_ph = get_philox_4x32(subsequence);
+
+        uint32x4_t tmp;
+        tmp[0]            = tmp_ph.x;
+        tmp[1]            = tmp_ph.y;
+        tmp[2]            = tmp_ph.z;
+        tmp[3]            = tmp_ph.w;
+        uint32_t* out_tmp = reinterpret_cast<uint32_t*>(&out[0]);
+        out_tmp[0]        = tmp[start_idx];
+    }
+
+    private:
+    struct ull2
+    {
+        uint64_t x;
+        uint64_t y;
+    };
+    uint4 counter;
+    const uint2 seed;
+
+    CK_TILE_HOST_DEVICE uint2 mulhilo32(const unsigned int a, const unsigned int b) const
+    {
+        uint2* res;
+        unsigned long long tmp;
+        tmp = static_cast<unsigned long long>(a) * b;
+        res = reinterpret_cast<uint2*>(&tmp);
+        return *res;
+    }
+
+    CK_TILE_HOST_DEVICE uint4 philox_single_round(const uint4 ctr, const uint2 key) const
+    {
+
+        uint2 res0 = mulhilo32(kPhiloxSA, ctr.x);
+        uint2 res1 = mulhilo32(kPhiloxSB, ctr.z);
+        uint4 ret  = {res1.y ^ ctr.y ^ key.x, res1.x, res0.y ^ ctr.w ^ key.y, res0.x};
+        return ret;
+    }
+
+    static const unsigned long kPhilox10A = 0x9E3779B9;
+    static const unsigned long kPhilox10B = 0xBB67AE85;
+    static const unsigned long kPhiloxSA  = 0xD2511F53;
+    static const unsigned long kPhiloxSB  = 0xCD9E8D57;
+};
+
+} // namespace ck_tile

include/ck_tile/core/utility/random.hpp

@@ -0,0 +1,58 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/half.hpp"
+#include <stdint.h>
+#include <tuple>
+#include <type_traits>
+
+namespace ck_tile {
+
+// return 0 if data is not fp16 or fp32
+template <typename T, uint32_t seed_>
+struct prand_generator_t
+{
+    CK_TILE_HOST_DEVICE uint32_t operator()(int, T, uint32_t = seed_) { return 0; }
+};
+
+// version for fp32
+template <uint32_t seed_>
+struct prand_generator_t<float, seed_>
+{
+    CK_TILE_HOST_DEVICE uint32_t operator()(int id, float val, uint32_t seed = seed_)
+    {
+        uint32_t x         = *(reinterpret_cast<uint32_t*>(&val));
+        uint32_t drop_bits = uint32_t(x) & 0xFFFFu;
+        drop_bits ^= x >> 16;
+        drop_bits = ((drop_bits & 31) << 11) | (drop_bits >> 5);
+        drop_bits *= 0x7000149;
+        // NOTE: If id is in 64 bit, we are only using lower 32 bit.
+        //       So, it can have an effect of using same id for multiple elements when the id is
+        //       very large!
+        uint32_t rng = (drop_bits ^ 0x13371337 ^ (id * 229791) ^ seed);
+        return rng;
+    }
+};
+
+// version for fp16
+template <uint32_t seed_>
+struct prand_generator_t<half_t, seed_>
+{
+    CK_TILE_HOST_DEVICE uint32_t operator()(int id, half_t val, uint32_t seed = seed_)
+    {
+        uint16_t x         = *(reinterpret_cast<uint16_t*>(&val));
+        uint32_t drop_bits = uint32_t(x) & 0xFFFFu;
+        drop_bits          = ((drop_bits & 31) << 11) | (drop_bits >> 5);
+        drop_bits *= 0x7000149;
+        // NOTE: If id is in 64 bit, we are only using lower 32 bit.
+        //       So, it can have an effect of using same id for multiple elements when the id is
+        //       very large!
+        uint32_t rng = (drop_bits ^ 0x13371337 ^ (id * 229791) ^ seed);
+        return rng;
+    }
+};
+
+} // namespace ck_tile

include/ck_tile/core/utility/reduce_operator.hpp

@@ -0,0 +1,95 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+
+namespace ck_tile {
+
+namespace ReduceOp {
+// y = ReduceOp(y, x);
+struct Add
+{
+    template <typename T>
+    CK_TILE_HOST_DEVICE static constexpr T GetIdentityValue()
+    {
+        return type_convert<T>(0.0f);
+    };
+
+    template <typename T,
+              typename = std::enable_if_t<std::is_same_v<T, float> || std::is_same_v<T, double> ||
+                                          std::is_same_v<T, int32_t> || std::is_same_v<T, int8_t>>>
+    CK_TILE_HOST_DEVICE constexpr T operator()(const T& y, const T x) const
+    {
+        return y + x;
+    }
+
+    template <typename T,
+              typename = std::enable_if_t<std::is_same_v<T, half_t> || std::is_same_v<T, bf16_t>>>
+    CK_TILE_HOST_DEVICE constexpr T operator()(T& y, T x) const
+    {
+        float y_ = type_convert<float>(y);
+        float x_ = type_convert<float>(x);
+
+        return type_convert<T>(y_ + x_);
+    }
+};
+
+struct SquareAdd
+{
+    template <typename T>
+    CK_TILE_HOST_DEVICE static constexpr T GetIdentityValue()
+    {
+        return type_convert<T>(0.0f);
+    };
+
+    template <typename T,
+              typename = std::enable_if_t<std::is_same_v<T, float> || std::is_same_v<T, double> ||
+                                          std::is_same_v<T, int32_t> || std::is_same_v<T, int8_t>>>
+    CK_TILE_HOST_DEVICE constexpr T operator()(const T& y, const T x) const
+    {
+        return y + (x * x);
+    }
+};
+
+struct Max
+{
+    template <typename T,
+              typename = std::enable_if_t<std::is_same_v<T, float> || std::is_same_v<T, double> ||
+                                          std::is_same_v<T, int32_t> || std::is_same_v<T, int8_t>>>
+    CK_TILE_HOST_DEVICE static constexpr T GetIdentityValue()
+    {
+        return numeric<T>::min();
+    };
+
+    template <typename T,
+              typename = std::enable_if_t<std::is_same_v<T, float> || std::is_same_v<T, double> ||
+                                          std::is_same_v<T, int32_t> || std::is_same_v<T, int8_t>>>
+    CK_TILE_HOST_DEVICE constexpr T operator()(const T& y, const T x) const
+    {
+        return max(y, x);
+    }
+};
+
+struct AbsMax
+{
+    template <typename T,
+              typename = std::enable_if_t<std::is_same_v<T, float> || std::is_same_v<T, double> ||
+                                          std::is_same_v<T, int32_t> || std::is_same_v<T, int8_t>>>
+    CK_TILE_HOST_DEVICE static constexpr T GetIdentityValue()
+    {
+        return numeric<T>::min();
+    };
+
+    template <typename T,
+              typename = std::enable_if_t<std::is_same_v<T, float> || std::is_same_v<T, double> ||
+                                          std::is_same_v<T, int32_t> || std::is_same_v<T, int8_t>>>
+    CK_TILE_HOST_DEVICE constexpr T operator()(const T& y, const T x) const
+    {
+        return max(y, abs(x));
+    }
+};
+
+} // namespace ReduceOp
+} // namespace ck_tile

include/ck_tile/core/utility/static_counter.hpp

@@ -0,0 +1,116 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+
+namespace ck_tile {
+
+template <typename Context, index_t Start = 0, index_t Step = 1>
+struct static_counter
+{
+    public:
+    template <typename Unique>
+    static constexpr index_t next()
+    {
+        return next<Unique>(0) * Step + Start;
+    }
+
+    template <unsigned long long>
+    static constexpr index_t next()
+    {
+        struct Unique
+        {
+        };
+        return next<Unique>(0) * Step + Start;
+    }
+
+    template <typename Unique>
+    static constexpr index_t current()
+    {
+        return current<Unique>(0) * Step + Start;
+    }
+
+    template <unsigned long long>
+    static constexpr index_t current()
+    {
+        struct Unique
+        {
+        };
+        return current<Unique>(0) * Step + Start;
+    }
+
+    private:
+    template <index_t I>
+    struct slot
+    {
+        _Pragma("GCC diagnostic push");
+        _Pragma("GCC diagnostic ignored \"-Wundefined-internal\"");
+        friend constexpr bool slot_allocated(slot<I>);
+        _Pragma("GCC diagnostic pop");
+    };
+
+    template <index_t I>
+    struct allocate_slot
+    {
+        friend constexpr bool slot_allocated(slot<I>) { return true; }
+        enum
+        {
+            value = I
+        };
+    };
+
+    // If slot_allocated(slot<I>) has NOT been defined, then SFINAE will keep this function out of
+    // the overload set...
+    template <typename Unique, index_t I = 0, bool = slot_allocated(slot<I>())>
+    static constexpr index_t next(index_t)
+    {
+        return next<Unique, I + 1>(0);
+    }
+
+    // ...And this function will be used, instead, which will define slot_allocated(slot<I>) via
+    // allocate_slot<I>.
+    template <typename Unique, index_t I = 0>
+    static constexpr index_t next(double)
+    {
+        return allocate_slot<I>::value;
+    }
+
+    // If slot_allocated(slot<I>) has NOT been defined, then SFINAE will keep this function out of
+    // the overload set...
+    template <typename Unique, index_t I = Start, bool = slot_allocated(slot<I>())>
+    static constexpr index_t current(index_t)
+    {
+        return current<Unique, I + 1>(0);
+    }
+
+    // ...And this function will be used, instead, which will return the current counter, or assert
+    // in case next() hasn't been called yet.
+    template <typename Unique, index_t I = Start>
+    static constexpr index_t current(double)
+    {
+        static_assert(I != 0, "You must invoke next() first");
+
+        return I - 1;
+    }
+};
+
+namespace impl {
+template <int I>
+struct static_counter_uniq_;
+}
+
+#define MAKE_SC() \
+    ck_tile::static_counter<ck_tile::impl::static_counter_uniq_<__COUNTER__>> {}
+#define MAKE_SC_WITH(start_, step_) \
+    ck_tile::static_counter<ck_tile::impl::static_counter_uniq_<__COUNTER__>, start_, step_> {}
+#define NEXT_SC(c_) c_.next<__COUNTER__>()
+#define NEXT_SCI(c_, static_i_) c_.next<__COUNTER__ + static_i_>()
+
+// Usage:
+// constexpr auto c = MAKE_SC()
+// NEXT_SC(c)    // -> constexpr 0
+// NEXT_SC(c)    // -> constexpr 1
+// NEXT_SC(c)    // -> constexpr 2
+} // namespace ck_tile

include/ck_tile/core/utility/to_sequence.hpp

@@ -0,0 +1,73 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+#include "ck_tile/core/container/sequence.hpp"
+// TODO: use c++20 nontype template with struct to implement this
+
+#if 1
+// clang happen to support this feature (__cpp_generic_lambdas >= 201707) in c++17 mode
+#define TO_SEQUENCE(a, n)                                                                    \
+    _Pragma("clang diagnostic push") _Pragma(                                                \
+        "clang diagnostic ignored \"-Wc++20-extensions\"")[a]<ck_tile::index_t... IDX_IDX_>( \
+        ck_tile::sequence<IDX_IDX_...>)                                                      \
+    {                                                                                        \
+        return ck_tile::sequence<a.at(ck_tile::number<IDX_IDX_>{})...>{};                    \
+    }                                                                                        \
+    (ck_tile::make_index_sequence<n>{});                                                     \
+    _Pragma("clang diagnostic pop")
+
+#else
+// Macro function
+// convert constexpr array to sequence, both a/n need to be constexpr (can't be a rvalue like 2)
+#define TO_SEQUENCE(a, n)                                                                     \
+    [a, n] {                                                                                  \
+        static_assert(a.size() >= n, "wrong! out of bound");                                  \
+        static_assert(n <= 10, "not implemented");                                            \
+        if constexpr(n == 0)                                                                  \
+        {                                                                                     \
+            return ck_tile::sequence<>{};                                                     \
+        }                                                                                     \
+        else if constexpr(n == 1)                                                             \
+        {                                                                                     \
+            return ck_tile::sequence<a[0]>{};                                                 \
+        }                                                                                     \
+        else if constexpr(n == 2)                                                             \
+        {                                                                                     \
+            return ck_tile::sequence<a[0], a[1]>{};                                           \
+        }                                                                                     \
+        else if constexpr(n == 3)                                                             \
+        {                                                                                     \
+            return ck_tile::sequence<a[0], a[1], a[2]>{};                                     \
+        }                                                                                     \
+        else if constexpr(n == 4)                                                             \
+        {                                                                                     \
+            return ck_tile::sequence<a[0], a[1], a[2], a[3]>{};                               \
+        }                                                                                     \
+        else if constexpr(n == 5)                                                             \
+        {                                                                                     \
+            return ck_tile::sequence<a[0], a[1], a[2], a[3], a[4]>{};                         \
+        }                                                                                     \
+        else if constexpr(n == 6)                                                             \
+        {                                                                                     \
+            return ck_tile::sequence<a[0], a[1], a[2], a[3], a[4], a[5]>{};                   \
+        }                                                                                     \
+        else if constexpr(n == 7)                                                             \
+        {                                                                                     \
+            return ck_tile::sequence<a[0], a[1], a[2], a[3], a[4], a[5], a[6]>{};             \
+        }                                                                                     \
+        else if constexpr(n == 8)                                                             \
+        {                                                                                     \
+            return ck_tile::sequence<a[0], a[1], a[2], a[3], a[4], a[5], a[6], a[7]>{};       \
+        }                                                                                     \
+        else if constexpr(n == 9)                                                             \
+        {                                                                                     \
+            return ck_tile::sequence<a[0], a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8]>{}; \
+        }                                                                                     \
+        else if constexpr(n == 10)                                                            \
+        {                                                                                     \
+            return ck_tile::                                                                  \
+                sequence<a[0], a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8], a[9]>{};       \
+        }                                                                                     \
+    }()
+#endif

include/ck_tile/core/utility/transpose_vectors.hpp

@@ -0,0 +1,155 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/container/array.hpp"
+#include "ck_tile/core/container/thread_buffer.hpp"
+#include "ck_tile/core/utility/bit_cast.hpp"
+#include "ck_tile/core/utility/functional.hpp"
+
+namespace ck_tile {
+
+// S: scalar type (or it can be non-scalar type)
+// NX: # of vector before transpose
+// NY: # of vector after transpose
+// we got [NX, NY] amount of S data to be transposed into [NY, NX] amount of S data
+template <typename S_, index_t NX, index_t NY>
+struct transpose_vectors
+{
+    static constexpr index_t s_per_x = NY;
+    static constexpr index_t s_per_y = NX;
+
+    using S = remove_cvref_t<S_>;
+
+    using VX = array<S, s_per_x>;
+    using VY = array<S, s_per_y>;
+
+    CK_TILE_DEVICE void operator()(const thread_buffer<VX, NX>& vx_tuple,
+                                   thread_buffer<VY, NY>& vy_tuple)
+    {
+        constexpr auto I1 = number<1>{};
+        constexpr auto I2 = number<2>{};
+        constexpr auto I3 = number<3>{};
+        constexpr auto I4 = number<4>{};
+
+        if constexpr(sizeof(S) == 2)
+        {
+            static_assert((NX % 2 == 0 && NY % 2 == 0), "wrong!");
+
+            using S2 = array<S, 2>; // typename array<S, 2>::type;
+
+            // loop over 2x2 tile and transpose data from vx_tuple into vy_tuple
+            static_for<0, NY, 2>{}([&](auto iy) {
+                static_for<0, NX, 2>{}([&](auto ix) {
+                    // 2 16bitx2 data from vx_tuple to be transposed
+                    const int32_t x_s2_0 =
+                        bit_cast<int32_t>(vx_tuple[ix].template get_as<S2>()[iy / I2]);
+                    const int32_t x_s2_1 =
+                        bit_cast<int32_t>(vx_tuple[ix + I1].template get_as<S2>()[iy / I2]);
+
+                    constexpr int32_t m0 = 0x05040100;
+                    constexpr int32_t m1 = 0x07060302;
+
+                    // transpose 2x2 16bit
+                    // ex: v_perm_b32(0x 11 22 33 44, 0x 55 66 77 88, 0x 05 01 04 00) -> 0x33774488
+                    //                   -- -- -- --     -- -- -- --      -  -  -  -
+                    //             index  7  6  5  4      3  2  1  0     33 77 44 88
+                    // index is reversed because of little endianness (least significant bits first)
+                    const int32_t y_s2_0 = __builtin_amdgcn_perm(x_s2_1, x_s2_0, m0);
+                    const int32_t y_s2_1 = __builtin_amdgcn_perm(x_s2_1, x_s2_0, m1);
+
+                    // 2 16bitx2 data after transposed
+                    vy_tuple(iy).template get_as<S2>()(ix / I2)      = bit_cast<S2>(y_s2_0);
+                    vy_tuple(iy + I1).template get_as<S2>()(ix / I2) = bit_cast<S2>(y_s2_1);
+                });
+            });
+        }
+        else if constexpr(sizeof(S) == 1)
+        {
+            static_assert(((NX % 4 == 0 && NY % 4 == 0) || (NX % 2 == 0 && NY % 2 == 0)), "wrong!");
+
+            using S4 = array<S, 4>; // typename array<S, 4>::type;
+            using S2 = array<S, 2>; // typename array<S, 4>::type;
+
+            if constexpr(NX % 4 == 0 && NY % 4 == 0)
+            {
+                // loop over 4x4 tile and transpose data from vx_tuple into vy_tuple
+                static_for<0, NY, 4>{}([&](auto iy) {
+                    static_for<0, NX, 4>{}([&](auto ix) {
+                        // 4 int8x4 data from vx_tuple
+                        const int32_t x_s4_0 =
+                            bit_cast<int32_t>(vx_tuple[ix].template get_as<S4>()[iy / I4]);
+                        const int32_t x_s4_1 =
+                            bit_cast<int32_t>(vx_tuple[ix + I1].template get_as<S4>()[iy / I4]);
+                        const int32_t x_s4_2 =
+                            bit_cast<int32_t>(vx_tuple[ix + I2].template get_as<S4>()[iy / I4]);
+                        const int32_t x_s4_3 =
+                            bit_cast<int32_t>(vx_tuple[ix + I3].template get_as<S4>()[iy / I4]);
+
+                        // transpose
+                        int32_t t_s4_0, t_s4_1;
+                        int32_t y_s4_0, y_s4_1, y_s4_2, y_s4_3;
+
+                        constexpr int32_t m0 = 0x05010400;
+                        constexpr int32_t m1 = 0x05040100;
+                        constexpr int32_t m2 = 0x07060302;
+                        constexpr int32_t m3 = 0x07030602;
+
+                        // ex: v_perm_b32(0x 11 22 33 44, 0x 55 66 77 88, 0x 05 01 04 00) ->
+                        // 0x33774488
+                        //                   -- -- -- --     -- -- -- --      -  -  -  -
+                        //             index  7  6  5  4      3  2  1  0     33 77 44 88
+                        // index is reversed because of little endianness (least significant bits
+                        // first)
+                        t_s4_0 = __builtin_amdgcn_perm(x_s4_1, x_s4_0, m0);
+                        t_s4_1 = __builtin_amdgcn_perm(x_s4_3, x_s4_2, m0);
+                        y_s4_0 = __builtin_amdgcn_perm(t_s4_1, t_s4_0, m1);
+                        y_s4_1 = __builtin_amdgcn_perm(t_s4_1, t_s4_0, m2);
+                        t_s4_0 = __builtin_amdgcn_perm(x_s4_1, x_s4_0, m3);
+                        t_s4_1 = __builtin_amdgcn_perm(x_s4_3, x_s4_2, m3);
+                        y_s4_2 = __builtin_amdgcn_perm(t_s4_1, t_s4_0, m1);
+                        y_s4_3 = __builtin_amdgcn_perm(t_s4_1, t_s4_0, m2);
+
+                        // 4 int8x4 data from vy_tuple
+                        vy_tuple(iy).template get_as<S4>()(ix / I4)      = bit_cast<S4>(y_s4_0);
+                        vy_tuple(iy + I1).template get_as<S4>()(ix / I4) = bit_cast<S4>(y_s4_1);
+                        vy_tuple(iy + I2).template get_as<S4>()(ix / I4) = bit_cast<S4>(y_s4_2);
+                        vy_tuple(iy + I3).template get_as<S4>()(ix / I4) = bit_cast<S4>(y_s4_3);
+                    });
+                });
+            }
+            else if constexpr(NX % 2 == 0 && NY % 2 == 0)
+            {
+                static_for<0, NY, 2>{}([&](auto ix) {
+                    static_for<0, NX, 2>{}([&](auto iy) {
+                        const int16_t x_s2_0 =
+                            bit_cast<int16_t>(vx_tuple[ix].template get_as<S2>()[iy / I2]);
+                        const int16_t x_s2_1 =
+                            bit_cast<int16_t>(vx_tuple[ix + I1].template get_as<S2>()[iy / I2]);
+                        constexpr int32_t m0 = 0x05040100;
+                        constexpr int32_t m1 = 0x07060302;
+
+                        const int32_t x0_32 = static_cast<int32_t>(x_s2_0 & 0xFFFF);
+                        const int32_t x1_32 = static_cast<int32_t>(x_s2_1 & 0xFFFF);
+
+                        const int32_t y_s2_0 = __builtin_amdgcn_perm(x1_32, x0_32, m0);
+                        const int32_t y_s2_1 = __builtin_amdgcn_perm(x1_32, x0_32, m1);
+
+                        vy_tuple(iy).template get_as<S2>()[ix / I2] =
+                            bit_cast<S2>(static_cast<int16_t>(y_s2_0 & 0xFFFF));
+                        vy_tuple(iy + I1).template get_as<S2>()[ix / I2] =
+                            bit_cast<S2>(static_cast<int16_t>(y_s2_1 & 0xFFFF));
+                    });
+                });
+            }
+        }
+        else
+        {
+            static_assert(false, "not implemented");
+        }
+    }
+};
+
+} // namespace ck_tile

include/ck_tile/core/utility/type_traits.hpp

@@ -0,0 +1,130 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include <type_traits>
+#include <stdint.h>
+
+namespace ck_tile {
+
+// remove_cvref_t
+template <typename T>
+using remove_reference_t = typename std::remove_reference<T>::type;
+
+template <typename T>
+using remove_cv_t = typename std::remove_cv<T>::type;
+
+template <typename T>
+using remove_cvref_t = remove_cv_t<std::remove_reference_t<T>>;
+
+template <typename T>
+using remove_pointer_t = typename std::remove_pointer<T>::type;
+
+template <typename From, typename To>
+struct copy_const
+{
+    static_assert(!std::is_const_v<From>);
+
+    using type = To;
+};
+
+template <typename From, typename To>
+struct copy_const<const From, To>
+{
+    using type = std::add_const_t<typename copy_const<From, To>::type>;
+};
+
+template <typename From, typename To>
+using copy_const_t = typename copy_const<From, To>::type;
+
+namespace detail {
+template <class Default, class AlwaysVoid, template <class...> class Op, class... Args>
+struct detector
+{
+    using value_t = std::false_type;
+    using type    = Default;
+};
+
+template <class Default, template <class...> class Op, class... Args>
+struct detector<Default, std::void_t<Op<Args...>>, Op, Args...>
+{
+    using value_t = std::true_type;
+    using type    = Op<Args...>;
+};
+} // namespace detail
+
+struct nonesuch
+{
+    ~nonesuch()               = delete;
+    nonesuch(nonesuch const&) = delete;
+    void operator=(nonesuch const&) = delete;
+};
+
+template <template <class...> class Op, class... Args>
+using is_detected = typename detail::detector<nonesuch, void, Op, Args...>::value_t;
+
+namespace impl {
+
+template <typename T>
+using has_is_static = decltype(T::is_static());
+
+template <typename T>
+struct is_static_impl
+{
+    static constexpr bool value = []() {
+        if constexpr(is_detected<has_is_static, T>{})
+            return T::is_static();
+        else
+            return std::is_arithmetic<T>::value;
+    }();
+};
+} // namespace impl
+
+template <typename T>
+using is_static = impl::is_static_impl<remove_cvref_t<T>>;
+
+template <typename T>
+inline constexpr bool is_static_v = is_static<T>::value;
+
+// TODO: deprecate this
+template <typename T>
+using is_known_at_compile_time = is_static<T>;
+// TODO: if evaluating a rvalue, e.g. a const integer
+// , this helper will also return false, which is not good(?)
+//       do we need something like is_constexpr()?
+
+// FIXME: do we need this anymore?
+template <
+    typename PY,
+    typename PX,
+    typename std::enable_if<std::is_pointer_v<PY> && std::is_pointer_v<PX>, bool>::type = false>
+CK_TILE_HOST_DEVICE PY c_style_pointer_cast(PX p_x)
+{
+#pragma clang diagnostic push
+#pragma clang diagnostic ignored "-Wold-style-cast"
+#pragma clang diagnostic ignored "-Wcast-align"
+    return (PY)p_x; // NOLINT(old-style-cast, cast-align)
+#pragma clang diagnostic pop
+}
+
+template <typename CompareTo, typename... Rest>
+struct is_any_of : std::false_type
+{
+};
+
+template <typename CompareTo, typename FirstType>
+struct is_any_of<CompareTo, FirstType> : std::is_same<CompareTo, FirstType>
+{
+};
+
+template <typename CompareTo, typename FirstType, typename... Rest>
+struct is_any_of<CompareTo, FirstType, Rest...>
+    : std::integral_constant<bool,
+                             std::is_same<CompareTo, FirstType>::value ||
+                                 is_any_of<CompareTo, Rest...>::value>
+{
+};
+
+} // namespace ck_tile

include/ck_tile/core/utility/unary_element_function.hpp

@@ -0,0 +1,69 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core.hpp"
+
+namespace ck_tile {
+
+template <typename F, typename... Fs>
+struct composes : private composes<F>
+{
+    template <typename FirstArg, typename... RestArgs>
+    CK_TILE_HOST_DEVICE constexpr explicit composes(FirstArg&& firstArg, RestArgs&&... restArgs)
+        : composes<F>(std::forward<FirstArg>(firstArg)), inner_(std::forward<RestArgs>(restArgs)...)
+    {
+    }
+
+    template <typename Arg>
+    CK_TILE_HOST_DEVICE constexpr auto operator()(Arg&& arg) const
+    {
+        return static_cast<const composes<F>&>(*this)(inner_(std::forward<Arg>(arg)));
+    }
+
+    private:
+    composes<Fs...> inner_;
+};
+
+template <typename F>
+struct composes<F>
+{
+    static_assert(!std::is_reference_v<F>);
+
+    template <typename Arg, typename = std::enable_if_t<std::is_constructible_v<F, Arg>>>
+    CK_TILE_HOST_DEVICE constexpr explicit composes(Arg&& arg) : f_(std::forward<Arg>(arg))
+    {
+    }
+
+    template <typename Arg,
+              typename = std::enable_if_t<std::is_invocable_v<std::add_const_t<F>&, Arg>>>
+    CK_TILE_HOST_DEVICE constexpr auto operator()(Arg&& arg) const
+    {
+        return f_(std::forward<Arg>(arg));
+    }
+
+    private:
+    F f_;
+};
+
+/// FIXME: create macro to replace '__host__ __device__' and nothing more
+template <typename... Ts>
+__host__ __device__ composes(Ts&&...)->composes<remove_cvref_t<Ts>...>;
+
+template <typename SaturateType>
+struct saturates
+{
+    // NOTE: this function does not return SaturateType value
+    // it is user's responsiblity to do further cast or not
+    template <typename AccType>
+    CK_TILE_HOST_DEVICE constexpr auto operator()(const AccType& a_) const
+        -> std::enable_if_t<std::is_arithmetic_v<AccType>, AccType>
+    {
+        return clamp(a_,
+                     type_convert<AccType>(numeric<SaturateType>::lowest()),
+                     type_convert<AccType>(numeric<SaturateType>::max()));
+    }
+};
+
+} // namespace ck_tile

include/ck_tile/host.hpp

@@ -0,0 +1,38 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2025, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/host/arg_parser.hpp"
+#include "ck_tile/host/check_err.hpp"
+#include "ck_tile/host/concat.hpp"
+#include "ck_tile/host/convolution_host_tensor_descriptor_helper.hpp"
+#include "ck_tile/host/convolution_parameter.hpp"
+#include "ck_tile/host/device_memory.hpp"
+#include "ck_tile/host/fill.hpp"
+#include "ck_tile/host/hip_check_error.hpp"
+#include "ck_tile/host/host_tensor.hpp"
+#include "ck_tile/host/joinable_thread.hpp"
+#include "ck_tile/host/kernel_launch.hpp"
+#include "ck_tile/host/ranges.hpp"
+#include "ck_tile/host/reference/reference_batched_dropout.hpp"
+#include "ck_tile/host/reference/reference_batched_elementwise.hpp"
+#include "ck_tile/host/reference/reference_batched_gemm.hpp"
+#include "ck_tile/host/reference/reference_batched_masking.hpp"
+#include "ck_tile/host/reference/reference_batched_rotary_position_embedding.hpp"
+#include "ck_tile/host/reference/reference_batched_softmax.hpp"
+#include "ck_tile/host/reference/reference_batched_transpose.hpp"
+#include "ck_tile/host/reference/reference_elementwise.hpp"
+#include "ck_tile/host/reference/reference_fused_moe.hpp"
+#include "ck_tile/host/reference/reference_gemm.hpp"
+#include "ck_tile/host/reference/reference_im2col.hpp"
+#include "ck_tile/host/reference/reference_layernorm2d_fwd.hpp"
+#include "ck_tile/host/reference/reference_moe_sorting.hpp"
+#include "ck_tile/host/reference/reference_permute.hpp"
+#include "ck_tile/host/reference/reference_reduce.hpp"
+#include "ck_tile/host/reference/reference_rmsnorm2d_fwd.hpp"
+#include "ck_tile/host/reference/reference_rowwise_quantization2d.hpp"
+#include "ck_tile/host/reference/reference_softmax.hpp"
+#include "ck_tile/host/reference/reference_topk.hpp"
+#include "ck_tile/host/stream_config.hpp"
+#include "ck_tile/host/timer.hpp"

include/ck_tile/host/arg_parser.hpp

@@ -0,0 +1,236 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <string>
+
+#include <iomanip>
+#include <iostream>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string>
+#include <unordered_map>
+#include <vector>
+
+namespace ck_tile {
+/*
+ * a host side utility, arg parser for, either
+ * -[key0] = [value0, value1, value2]
+ * or
+ * -[key0]=[value0] -[key1]=[value1] ...
+ */
+class ArgParser
+{
+
+    public:
+    class Arg
+    {
+        public:
+        std::string name;
+        std::string value;
+        std::string help_text;
+    };
+
+    ArgParser() {}
+    ArgParser& insert(const std::string& _name,
+                      const std::string& _default_value,
+                      const std::string& _help_text)
+    {
+        Arg in;
+        in.name      = _name;
+        in.value     = _default_value;
+        in.help_text = _help_text;
+
+        if(input_map.count(_name) != 0)
+        {
+            printf("arg:%s already exist\n", _name.c_str());
+        }
+        else
+        {
+            input_map[_name] = in;
+            keys.push_back(_name);
+        }
+        return *this;
+    }
+    void print() const
+    {
+        // find max key length
+        std::string::size_type max_key_length = 11;
+        for(auto& key : keys)
+        {
+            if(max_key_length < key.length())
+            {
+                max_key_length = key.length();
+            }
+        }
+
+        printf("args:\n");
+        for(auto& key : keys)
+        {
+            auto value = input_map.at(key);
+            std::vector<std::string> help_text_lines;
+            size_t pos = 0;
+            for(size_t next_pos = value.help_text.find('\n', pos); next_pos != std::string::npos;)
+            {
+                help_text_lines.push_back(std::string(value.help_text.begin() + pos,
+                                                      value.help_text.begin() + next_pos++));
+                pos      = next_pos;
+                next_pos = value.help_text.find('\n', pos);
+            }
+            help_text_lines.push_back(
+                std::string(value.help_text.begin() + pos, value.help_text.end()));
+
+            std::string default_value = std::string("(default:") + value.value + std::string(")");
+            std::cout << std::setw(1 + max_key_length - value.name.length()) << "-" << key
+                      << std::setw(4) << " " << help_text_lines[0] << " " << default_value
+                      << std::endl;
+
+            for(auto help_next_line = std::next(help_text_lines.begin());
+                help_next_line != help_text_lines.end();
+                ++help_next_line)
+            {
+                std::cout << std::setw(1 + max_key_length + 4) << " " << *help_next_line
+                          << std::endl;
+            }
+        }
+    }
+    bool parse(int argc, char* argv[], int start_index = 1)
+    {
+        if(argc < start_index)
+        {
+            printf("not enough args\n");
+            return false;
+        }
+        for(int i = start_index; i < argc; i++)
+        {
+            char* cur_arg = argv[i];
+            if(cur_arg[0] != '-')
+            {
+                printf("illegal input\n");
+                print();
+                return false;
+            }
+            else
+            {
+                std::string text(cur_arg + 1);
+                if(text == "?")
+                {
+                    print();
+                    return false;
+                }
+                auto pos = text.find('=');
+                if(pos == std::string::npos)
+                {
+                    printf("arg should be [key]=[value] pair, here:%s\n", text.c_str());
+                    return false;
+                }
+                if(pos >= (text.size() - 1))
+                {
+                    printf("cant find value after \"=\", here:%s\n", text.c_str());
+                    return false;
+                }
+                auto key   = text.substr(0, pos);
+                auto value = text.substr(pos + 1);
+                if(input_map.count(key) == 0)
+                {
+                    printf("no such arg:%s\n", key.c_str());
+                    return false;
+                }
+                input_map[key].value = value;
+            }
+        }
+        return true;
+    }
+
+    std::string get_str(const std::string& name) const
+    {
+        std::string value = input_map.at(name).value;
+        return value;
+    }
+
+    int get_int(const std::string& name) const
+    {
+        int value = atoi(input_map.at(name).value.c_str());
+        return value;
+    }
+
+    uint32_t get_uint32(const std::string& name) const
+    {
+        uint32_t value = strtoul(input_map.at(name).value.c_str(), nullptr, 10);
+        return value;
+    }
+
+    uint64_t get_uint64(const std::string& name) const
+    {
+        uint64_t value = strtoull(input_map.at(name).value.c_str(), nullptr, 10);
+        return value;
+    }
+
+    bool get_bool(const std::string& name) const
+    {
+        auto v = input_map.at(name).value;
+        if(v.compare("t") == 0 || v.compare("true") == 0)
+            return true;
+        if(v.compare("f") == 0 || v.compare("false") == 0)
+            return false;
+        int value = atoi(v.c_str());
+        return value == 0 ? false : true;
+    }
+
+    float get_float(const std::string& name) const
+    {
+        double value = atof(input_map.at(name).value.c_str());
+        return static_cast<float>(value);
+    }
+
+    double get_double(const std::string& name) const
+    {
+        double value = atof(input_map.at(name).value.c_str());
+        return value;
+    }
+
+    std::vector<std::string> get_string_vec(const std::string& name,
+                                            const std::string& delimiter = ",") const
+    {
+        if(get_str(name).empty())
+        {
+            return {};
+        }
+        std::string s = get_str(name);
+        std::vector<std::string> tokens;
+        size_t pos = 0;
+        std::string token;
+        while((pos = s.find(delimiter)) != std::string::npos)
+        {
+            token = s.substr(0, pos);
+            tokens.push_back(token);
+            s.erase(0, pos + delimiter.length());
+        }
+        tokens.push_back(s);
+
+        return tokens;
+    }
+
+    std::vector<int> get_int_vec(const std::string& name, const std::string& delimiter = ",") const
+    {
+        if(get_str(name).empty())
+        {
+            return {};
+        }
+        const std::vector<std::string> args = get_string_vec(name, delimiter);
+        std::vector<int> tokens;
+        tokens.reserve(static_cast<int>(args.size()));
+        for(const std::string& token : args)
+        {
+            int value = atoi(token.c_str());
+            tokens.push_back(value);
+        }
+        return tokens;
+    }
+
+    private:
+    std::unordered_map<std::string, Arg> input_map;
+    std::vector<std::string> keys;
+};
+} // namespace ck_tile

include/ck_tile/host/check_err.hpp

@@ -0,0 +1,517 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2025, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <algorithm>
+#include <cmath>
+#include <cstdlib>
+#include <iostream>
+#include <iomanip>
+#include <iterator>
+#include <limits>
+#include <type_traits>
+#include <vector>
+
+#include "ck_tile/core.hpp"
+#include "ck_tile/host/ranges.hpp"
+
+namespace ck_tile {
+
+template <typename ComputeDataType, typename OutDataType, typename AccDataType = ComputeDataType>
+double get_relative_threshold(const int number_of_accumulations = 1)
+{
+    using F8   = ck_tile::fp8_t;
+    using BF8  = ck_tile::bf8_t;
+    using F16  = ck_tile::half_t;
+    using BF16 = ck_tile::bf16_t;
+    using F32  = float;
+    using I8   = int8_t;
+    using I32  = int32_t;
+
+    static_assert(
+        is_any_of<ComputeDataType, F8, BF8, F16, BF16, F32, pk_int4_t, I8, I32, int>::value,
+        "Warning: Unhandled ComputeDataType for setting up the relative threshold!");
+
+    double compute_error = 0;
+    if constexpr(is_any_of<ComputeDataType, pk_int4_t, I8, I32, int>::value)
+    {
+        return 0;
+    }
+    else
+    {
+        compute_error = std::pow(2, -numeric_traits<ComputeDataType>::mant) * 0.5;
+    }
+
+    static_assert(is_any_of<OutDataType, F8, BF8, F16, BF16, F32, pk_int4_t, I8, I32, int>::value,
+                  "Warning: Unhandled OutDataType for setting up the relative threshold!");
+
+    double output_error = 0;
+    if constexpr(is_any_of<OutDataType, pk_int4_t, I8, I32, int>::value)
+    {
+        return 0;
+    }
+    else
+    {
+        output_error = std::pow(2, -numeric_traits<OutDataType>::mant) * 0.5;
+    }
+    double midway_error = std::max(compute_error, output_error);
+
+    static_assert(is_any_of<AccDataType, F8, BF8, F16, BF16, F32, pk_int4_t, I8, I32, int>::value,
+                  "Warning: Unhandled AccDataType for setting up the relative threshold!");
+
+    double acc_error = 0;
+    if constexpr(is_any_of<AccDataType, pk_int4_t, I8, I32, int>::value)
+    {
+        return 0;
+    }
+    else
+    {
+        acc_error = std::pow(2, -numeric_traits<AccDataType>::mant) * 0.5 * number_of_accumulations;
+    }
+    return std::max(acc_error, midway_error);
+}
+
+template <typename ComputeDataType, typename OutDataType, typename AccDataType = ComputeDataType>
+double get_absolute_threshold(const double max_possible_num, const int number_of_accumulations = 1)
+{
+    using F8   = ck_tile::fp8_t;
+    using BF8  = ck_tile::bf8_t;
+    using F16  = ck_tile::half_t;
+    using BF16 = ck_tile::bf16_t;
+    using F32  = float;
+    using I8   = int8_t;
+    using I32  = int32_t;
+
+    static_assert(
+        is_any_of<ComputeDataType, F8, BF8, F16, BF16, F32, pk_int4_t, I8, I32, int>::value,
+        "Warning: Unhandled ComputeDataType for setting up the absolute threshold!");
+
+    auto expo            = std::log2(std::abs(max_possible_num));
+    double compute_error = 0;
+    if constexpr(is_any_of<ComputeDataType, pk_int4_t, I8, I32, int>::value)
+    {
+        return 0;
+    }
+    else
+    {
+        compute_error = std::pow(2, expo - numeric_traits<ComputeDataType>::mant) * 0.5;
+    }
+
+    static_assert(is_any_of<OutDataType, F8, BF8, F16, BF16, F32, pk_int4_t, I8, I32, int>::value,
+                  "Warning: Unhandled OutDataType for setting up the absolute threshold!");
+
+    double output_error = 0;
+    if constexpr(is_any_of<OutDataType, pk_int4_t, I8, I32, int>::value)
+    {
+        return 0;
+    }
+    else
+    {
+        output_error = std::pow(2, expo - numeric_traits<OutDataType>::mant) * 0.5;
+    }
+    double midway_error = std::max(compute_error, output_error);
+
+    static_assert(is_any_of<AccDataType, F8, BF8, F16, BF16, F32, pk_int4_t, I8, I32, int>::value,
+                  "Warning: Unhandled AccDataType for setting up the absolute threshold!");
+
+    double acc_error = 0;
+    if constexpr(is_any_of<AccDataType, pk_int4_t, I8, I32, int>::value)
+    {
+        return 0;
+    }
+    else
+    {
+        acc_error =
+            std::pow(2, expo - numeric_traits<AccDataType>::mant) * 0.5 * number_of_accumulations;
+    }
+    return std::max(acc_error, midway_error);
+}
+
+template <typename T>
+std::ostream& operator<<(std::ostream& os, const std::vector<T>& v)
+{
+    using size_type = typename std::vector<T>::size_type;
+
+    os << "[";
+    for(size_type idx = 0; idx < v.size(); ++idx)
+    {
+        if(0 < idx)
+        {
+            os << ", ";
+        }
+        os << v[idx];
+    }
+    return os << "]";
+}
+
+template <typename Range, typename RefRange>
+typename std::enable_if<
+    std::is_same_v<ranges::range_value_t<Range>, ranges::range_value_t<RefRange>> &&
+        std::is_floating_point_v<ranges::range_value_t<Range>> &&
+        !std::is_same_v<ranges::range_value_t<Range>, half_t>,
+    bool>::type CK_TILE_HOST
+check_err(const Range& out,
+          const RefRange& ref,
+          const std::string& msg  = "Error: Incorrect results!",
+          double rtol             = 1e-5,
+          double atol             = 3e-6,
+          bool allow_infinity_ref = false)
+{
+    if(out.size() != ref.size())
+    {
+        std::cerr << msg << " out.size() != ref.size(), :" << out.size() << " != " << ref.size()
+                  << std::endl;
+        return false;
+    }
+
+    const auto is_infinity_error = [=](auto o, auto r) {
+        const bool either_not_finite = !std::isfinite(o) || !std::isfinite(r);
+        const bool both_infinite_and_same =
+            std::isinf(o) && std::isinf(r) && (bit_cast<uint64_t>(o) == bit_cast<uint64_t>(r));
+
+        return either_not_finite && !(allow_infinity_ref && both_infinite_and_same);
+    };
+
+    bool res{true};
+    int err_count  = 0;
+    double err     = 0;
+    double max_err = std::numeric_limits<double>::min();
+    for(std::size_t i = 0; i < ref.size(); ++i)
+    {
+        const double o = *std::next(std::begin(out), i);
+        const double r = *std::next(std::begin(ref), i);
+        err            = std::abs(o - r);
+        if(err > atol + rtol * std::abs(r) || is_infinity_error(o, r))
+        {
+            max_err = err > max_err ? err : max_err;
+            err_count++;
+            if(err_count < 5)
+            {
+                std::cerr << msg << std::setw(12) << std::setprecision(7) << " out[" << i
+                          << "] != ref[" << i << "]: " << o << " != " << r << std::endl;
+            }
+            res = false;
+        }
+    }
+    if(!res)
+    {
+        const float error_percent =
+            static_cast<float>(err_count) / static_cast<float>(out.size()) * 100.f;
+        std::cerr << "max err: " << max_err;
+        std::cerr << ", number of errors: " << err_count;
+        std::cerr << ", " << error_percent << "% wrong values" << std::endl;
+    }
+    return res;
+}
+
+template <typename Range, typename RefRange>
+typename std::enable_if<
+    std::is_same_v<ranges::range_value_t<Range>, ranges::range_value_t<RefRange>> &&
+        std::is_same_v<ranges::range_value_t<Range>, bf16_t>,
+    bool>::type CK_TILE_HOST
+check_err(const Range& out,
+          const RefRange& ref,
+          const std::string& msg  = "Error: Incorrect results!",
+          double rtol             = 1e-3,
+          double atol             = 1e-3,
+          bool allow_infinity_ref = false)
+{
+    if(out.size() != ref.size())
+    {
+        std::cerr << msg << " out.size() != ref.size(), :" << out.size() << " != " << ref.size()
+                  << std::endl;
+        return false;
+    }
+
+    const auto is_infinity_error = [=](auto o, auto r) {
+        const bool either_not_finite = !std::isfinite(o) || !std::isfinite(r);
+        const bool both_infinite_and_same =
+            std::isinf(o) && std::isinf(r) && (bit_cast<uint64_t>(o) == bit_cast<uint64_t>(r));
+
+        return either_not_finite && !(allow_infinity_ref && both_infinite_and_same);
+    };
+
+    bool res{true};
+    int err_count = 0;
+    double err    = 0;
+    // TODO: This is a hack. We should have proper specialization for bf16_t data type.
+    double max_err = std::numeric_limits<float>::min();
+    for(std::size_t i = 0; i < ref.size(); ++i)
+    {
+        const double o = type_convert<float>(*std::next(std::begin(out), i));
+        const double r = type_convert<float>(*std::next(std::begin(ref), i));
+        err            = std::abs(o - r);
+        if(err > atol + rtol * std::abs(r) || is_infinity_error(o, r))
+        {
+            max_err = err > max_err ? err : max_err;
+            err_count++;
+            if(err_count < 5)
+            {
+                std::cerr << msg << std::setw(12) << std::setprecision(7) << " out[" << i
+                          << "] != ref[" << i << "]: " << o << " != " << r << std::endl;
+            }
+            res = false;
+        }
+    }
+    if(!res)
+    {
+        const float error_percent =
+            static_cast<float>(err_count) / static_cast<float>(out.size()) * 100.f;
+        std::cerr << "max err: " << max_err;
+        std::cerr << ", number of errors: " << err_count;
+        std::cerr << ", " << error_percent << "% wrong values" << std::endl;
+    }
+    return res;
+}
+
+template <typename Range, typename RefRange>
+typename std::enable_if<
+    std::is_same_v<ranges::range_value_t<Range>, ranges::range_value_t<RefRange>> &&
+        std::is_same_v<ranges::range_value_t<Range>, half_t>,
+    bool>::type CK_TILE_HOST
+check_err(const Range& out,
+          const RefRange& ref,
+          const std::string& msg  = "Error: Incorrect results!",
+          double rtol             = 1e-3,
+          double atol             = 1e-3,
+          bool allow_infinity_ref = false)
+{
+    if(out.size() != ref.size())
+    {
+        std::cerr << msg << " out.size() != ref.size(), :" << out.size() << " != " << ref.size()
+                  << std::endl;
+        return false;
+    }
+
+    const auto is_infinity_error = [=](auto o, auto r) {
+        const bool either_not_finite = !std::isfinite(o) || !std::isfinite(r);
+        const bool both_infinite_and_same =
+            std::isinf(o) && std::isinf(r) && (bit_cast<uint64_t>(o) == bit_cast<uint64_t>(r));
+
+        return either_not_finite && !(allow_infinity_ref && both_infinite_and_same);
+    };
+
+    bool res{true};
+    int err_count  = 0;
+    double err     = 0;
+    double max_err = static_cast<double>(std::numeric_limits<ranges::range_value_t<Range>>::min());
+    for(std::size_t i = 0; i < ref.size(); ++i)
+    {
+        const double o = type_convert<float>(*std::next(std::begin(out), i));
+        const double r = type_convert<float>(*std::next(std::begin(ref), i));
+        err            = std::abs(o - r);
+        if(err > atol + rtol * std::abs(r) || is_infinity_error(o, r))
+        {
+            max_err = err > max_err ? err : max_err;
+            err_count++;
+            if(err_count < 5)
+            {
+                std::cerr << msg << std::setw(12) << std::setprecision(7) << " out[" << i
+                          << "] != ref[" << i << "]: " << o << " != " << r << std::endl;
+            }
+            res = false;
+        }
+    }
+    if(!res)
+    {
+        const float error_percent =
+            static_cast<float>(err_count) / static_cast<float>(out.size()) * 100.f;
+        std::cerr << "max err: " << max_err;
+        std::cerr << ", number of errors: " << err_count;
+        std::cerr << ", " << error_percent << "% wrong values" << std::endl;
+    }
+    return res;
+}
+
+template <typename Range, typename RefRange>
+std::enable_if_t<(std::is_same_v<ranges::range_value_t<Range>, ranges::range_value_t<RefRange>> &&
+                  std::is_integral_v<ranges::range_value_t<Range>> &&
+                  !std::is_same_v<ranges::range_value_t<Range>, bf16_t>)
+#ifdef CK_EXPERIMENTAL_BIT_INT_EXTENSION_INT4
+                     || std::is_same_v<ranges::range_value_t<Range>, int4_t>
+#endif
+                 ,
+                 bool>
+    CK_TILE_HOST check_err(const Range& out,
+                           const RefRange& ref,
+                           const std::string& msg = "Error: Incorrect results!",
+                           double                 = 0,
+                           double atol            = 0)
+{
+    if(out.size() != ref.size())
+    {
+        std::cerr << msg << " out.size() != ref.size(), :" << out.size() << " != " << ref.size()
+                  << std::endl;
+        return false;
+    }
+
+    bool res{true};
+    int err_count   = 0;
+    int64_t err     = 0;
+    int64_t max_err = std::numeric_limits<int64_t>::min();
+    for(std::size_t i = 0; i < ref.size(); ++i)
+    {
+        const int64_t o = *std::next(std::begin(out), i);
+        const int64_t r = *std::next(std::begin(ref), i);
+        err             = std::abs(o - r);
+
+        if(err > atol)
+        {
+            max_err = err > max_err ? err : max_err;
+            err_count++;
+            if(err_count < 5)
+            {
+                std::cerr << msg << " out[" << i << "] != ref[" << i << "]: " << o << " != " << r
+                          << std::endl;
+            }
+            res = false;
+        }
+    }
+    if(!res)
+    {
+        const float error_percent =
+            static_cast<float>(err_count) / static_cast<float>(out.size()) * 100.f;
+        std::cerr << "max err: " << max_err;
+        std::cerr << ", number of errors: " << err_count;
+        std::cerr << ", " << error_percent << "% wrong values" << std::endl;
+    }
+    return res;
+}
+
+template <typename Range, typename RefRange>
+std::enable_if_t<(std::is_same_v<ranges::range_value_t<Range>, ranges::range_value_t<RefRange>> &&
+                  std::is_same_v<ranges::range_value_t<Range>, fp8_t>),
+                 bool>
+    CK_TILE_HOST check_err(const Range& out,
+                           const RefRange& ref,
+                           const std::string& msg               = "Error: Incorrect results!",
+                           unsigned max_rounding_point_distance = 1,
+                           double atol                          = 1e-1,
+                           bool allow_infinity_ref              = false)
+{
+    if(out.size() != ref.size())
+    {
+        std::cerr << msg << " out.size() != ref.size(), :" << out.size() << " != " << ref.size()
+                  << std::endl;
+        return false;
+    }
+
+    const auto is_infinity_error = [=](auto o, auto r) {
+        const bool either_not_finite = !std::isfinite(o) || !std::isfinite(r);
+        const bool both_infinite_and_same =
+            std::isinf(o) && std::isinf(r) && (bit_cast<uint64_t>(o) == bit_cast<uint64_t>(r));
+
+        return either_not_finite && !(allow_infinity_ref && both_infinite_and_same);
+    };
+
+    static const auto get_rounding_point_distance = [](fp8_t o, fp8_t r) -> unsigned {
+        static const auto get_sign_bit = [](fp8_t v) -> bool {
+            return 0x80 & bit_cast<uint8_t>(v);
+        };
+
+        if(get_sign_bit(o) ^ get_sign_bit(r))
+        {
+            return std::numeric_limits<unsigned>::max();
+        }
+        else
+        {
+            return std::abs(bit_cast<int8_t>(o) - bit_cast<int8_t>(r));
+        }
+    };
+
+    bool res{true};
+    int err_count  = 0;
+    double err     = 0;
+    double max_err = std::numeric_limits<float>::min();
+    for(std::size_t i = 0; i < ref.size(); ++i)
+    {
+        const fp8_t o_fp8   = *std::next(std::begin(out), i);
+        const fp8_t r_fp8   = *std::next(std::begin(ref), i);
+        const double o_fp64 = type_convert<float>(o_fp8);
+        const double r_fp64 = type_convert<float>(r_fp8);
+        err                 = std::abs(o_fp64 - r_fp64);
+        if(!(less_equal<double>{}(err, atol) ||
+             get_rounding_point_distance(o_fp8, r_fp8) <= max_rounding_point_distance) ||
+           is_infinity_error(o_fp64, r_fp64))
+        {
+            max_err = err > max_err ? err : max_err;
+            err_count++;
+            if(err_count < 5)
+            {
+                std::cerr << msg << std::setw(12) << std::setprecision(7) << " out[" << i
+                          << "] != ref[" << i << "]: " << o_fp64 << " != " << r_fp64 << std::endl;
+            }
+            res = false;
+        }
+    }
+    if(!res)
+    {
+        const float error_percent =
+            static_cast<float>(err_count) / static_cast<float>(out.size()) * 100.f;
+        std::cerr << "max err: " << max_err;
+        std::cerr << ", number of errors: " << err_count;
+        std::cerr << ", " << error_percent << "% wrong values" << std::endl;
+    }
+    return res;
+}
+
+template <typename Range, typename RefRange>
+std::enable_if_t<(std::is_same_v<ranges::range_value_t<Range>, ranges::range_value_t<RefRange>> &&
+                  std::is_same_v<ranges::range_value_t<Range>, bf8_t>),
+                 bool>
+    CK_TILE_HOST check_err(const Range& out,
+                           const RefRange& ref,
+                           const std::string& msg  = "Error: Incorrect results!",
+                           double rtol             = 1e-3,
+                           double atol             = 1e-3,
+                           bool allow_infinity_ref = false)
+{
+    if(out.size() != ref.size())
+    {
+        std::cerr << msg << " out.size() != ref.size(), :" << out.size() << " != " << ref.size()
+                  << std::endl;
+        return false;
+    }
+
+    const auto is_infinity_error = [=](auto o, auto r) {
+        const bool either_not_finite = !std::isfinite(o) || !std::isfinite(r);
+        const bool both_infinite_and_same =
+            std::isinf(o) && std::isinf(r) && (bit_cast<uint64_t>(o) == bit_cast<uint64_t>(r));
+
+        return either_not_finite && !(allow_infinity_ref && both_infinite_and_same);
+    };
+
+    bool res{true};
+    int err_count  = 0;
+    double err     = 0;
+    double max_err = std::numeric_limits<float>::min();
+    for(std::size_t i = 0; i < ref.size(); ++i)
+    {
+        const double o = type_convert<float>(*std::next(std::begin(out), i));
+        const double r = type_convert<float>(*std::next(std::begin(ref), i));
+        err            = std::abs(o - r);
+        if(err > atol + rtol * std::abs(r) || is_infinity_error(o, r))
+        {
+            max_err = err > max_err ? err : max_err;
+            err_count++;
+            if(err_count < 5)
+            {
+                std::cerr << msg << std::setw(12) << std::setprecision(7) << " out[" << i
+                          << "] != ref[" << i << "]: " << o << " != " << r << std::endl;
+            }
+            res = false;
+        }
+    }
+    if(!res)
+    {
+        const float error_percent =
+            static_cast<float>(err_count) / static_cast<float>(out.size()) * 100.f;
+        std::cerr << "max err: " << max_err;
+        std::cerr << ", number of errors: " << err_count;
+        std::cerr << ", " << error_percent << "% wrong values" << std::endl;
+    }
+    return res;
+}
+
+} // namespace ck_tile

include/ck_tile/host/concat.hpp

@@ -0,0 +1,122 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2025, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/ops/gemm/pipeline/gemm_pipeline_ag_bg_cr_scheduler.hpp"
+
+namespace ck_tile {
+
+template <typename T>
+struct IsCharArray : std::false_type
+{
+};
+
+template <std::size_t N>
+struct IsCharArray<char[N]> : std::true_type
+{
+};
+
+template <std::size_t N>
+struct IsCharArray<const char[N]> : std::true_type
+{
+};
+
+template <std::size_t N>
+struct IsCharArray<char (&)[N]> : std::true_type
+{
+};
+
+template <std::size_t N>
+struct IsCharArray<const char (&)[N]> : std::true_type
+{
+};
+
+template <typename... Ts>
+inline constexpr bool AllConvertibleToStringView = ((std::is_convertible_v<Ts, std::string_view> ||
+                                                     IsCharArray<Ts>::value ||
+                                                     std::is_same_v<Ts, char>)&&...);
+
+template <typename... Ts>
+[[nodiscard]] auto concat(const Ts&... xs)
+    -> std::enable_if_t<!AllConvertibleToStringView<Ts...>, std::string>
+{
+    using ::operator<<;
+    thread_local std::ostringstream oss;
+    oss.str("");
+
+    (oss << ... << xs);
+    return oss.str();
+}
+
+template <std::size_t N>
+[[nodiscard]] constexpr inline std::size_t getSize(char (&)[N]) noexcept
+{
+    return N;
+}
+
+template <std::size_t N>
+[[nodiscard]] constexpr inline std::size_t getSize(const char (&)[N]) noexcept
+{
+    return N;
+}
+
+[[nodiscard]] constexpr inline std::size_t getSize(const char* s) noexcept
+{
+    const char* end = s;
+    while(*end++ != 0) {}
+    return end - s - 1;
+}
+
+[[nodiscard]] constexpr inline std::size_t getSize(const char&) noexcept { return 1; }
+
+[[nodiscard]] inline std::size_t getSize(const std::string& s) noexcept { return s.size(); }
+
+[[nodiscard]] constexpr inline std::size_t getSize(const std::string_view& s) noexcept
+{
+    return s.size();
+}
+
+template <typename... Ts>
+auto concatInto(std::string& result, const Ts&... xs)
+    -> std::enable_if_t<AllConvertibleToStringView<Ts...>, void>
+{
+    const std::size_t space = (1 + ... + getSize(xs));
+    result.reserve(result.size() + space);
+    ((result += xs), ...);
+}
+
+template <typename... Ts>
+[[nodiscard]] auto concat(const Ts&... xs)
+    -> std::enable_if_t<AllConvertibleToStringView<Ts...>, std::string>
+{
+    std::string result;
+    concatInto(result, xs...);
+    return result;
+}
+
+// Function for types convertible to std::string_view
+template <typename Sep, typename First, typename... Rest>
+[[nodiscard]] auto concat(Sep sep, const First& first, const Rest&... rest)
+    -> std::enable_if_t<AllConvertibleToStringView<First, Rest...>, std::string>
+{
+    std::string result;
+    result += first;
+    ((result += sep, result += rest), ...);
+    return result;
+}
+
+// Function for other types
+template <typename Sep, typename First, typename... Rest>
+[[nodiscard]] auto concat(Sep sep, const First& first, const Rest&... rest)
+    -> std::enable_if_t<!AllConvertibleToStringView<First, Rest...>, std::string>
+{
+    using ::operator<<;
+    thread_local std::ostringstream oss;
+    oss.str("");
+    oss << first;
+    ((oss << sep << rest), ...);
+    return oss.str();
+}
+
+} // namespace ck_tile

include/ck_tile/host/convolution_host_tensor_descriptor_helper.hpp

@@ -0,0 +1,236 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/ops/common/tensor_layout.hpp"
+#include "ck_tile/host/convolution_parameter.hpp"
+#include "ck_tile/host/host_tensor.hpp"
+
+namespace ck_tile {
+namespace conv {
+namespace detail {
+
+template <typename OldLayout>
+CK_TILE_HOST std::vector<std::size_t> get_layout_transpose_gnchw_to_old()
+{
+    using namespace ck_tile::tensor_layout::convolution;
+
+    if constexpr(is_any_of<OldLayout, GNCW, GKCX, GNKW>::value)
+    {
+        return {0, 1, 2, 3};
+    }
+    else if constexpr(is_any_of<OldLayout, GNCHW, GKCYX, GNKHW>::value)
+    {
+        return {0, 1, 2, 3, 4};
+    }
+    else if constexpr(is_any_of<OldLayout, GNCDHW, GKCZYX, GNKDHW>::value)
+    {
+        return {0, 1, 2, 3, 4, 5};
+    }
+    if constexpr(is_any_of<OldLayout, GNWC, GKXC, GNWK>::value)
+    {
+        return {0, 1, 3, 2};
+    }
+    else if constexpr(is_any_of<OldLayout, GNHWC, GKYXC, GNHWK>::value)
+    {
+        return {0, 1, 4, 2, 3};
+    }
+    else if constexpr(is_any_of<OldLayout, GNDHWC, GKZYXC, GNDHWK>::value)
+    {
+        return {0, 1, 5, 2, 3, 4};
+    }
+    else if constexpr(is_any_of<OldLayout, NWGC, KXGC, NWGK>::value)
+    {
+        return {2, 0, 3, 1};
+    }
+    else if constexpr(is_any_of<OldLayout, NHWGC, KYXGC, NHWGK>::value)
+    {
+        return {3, 0, 4, 1, 2};
+    }
+    else if constexpr(is_any_of<OldLayout, NDHWGC, KZYXGC, NDHWGK>::value)
+    {
+        return {4, 0, 5, 1, 2, 3};
+    }
+    else
+    {
+        printf("%s\n", __func__);
+        throw std::runtime_error("wrong! unsupported layout");
+    }
+}
+
+} // namespace detail
+
+// make tensor descriptor for packed input tensor, and order the dimension in the order of GNCHW
+// regardless of physical layout
+template <typename InLayout>
+CK_TILE_HOST HostTensorDescriptor
+make_input_host_tensor_descriptor_g_n_c_wis_packed(const ck_tile::conv::ConvParam& param)
+{
+    using namespace ck_tile::tensor_layout::convolution;
+
+    std::vector<std::size_t> physical_lengths;
+
+    if constexpr(is_any_of<InLayout, GNCW, GNCHW, GNCDHW>::value)
+    {
+        physical_lengths = std::vector<std::size_t>{static_cast<std::size_t>(param.G_),
+                                                    static_cast<std::size_t>(param.N_),
+                                                    static_cast<std::size_t>(param.C_)};
+
+        physical_lengths.insert(physical_lengths.end(),
+                                param.input_spatial_lengths_.begin(),
+                                param.input_spatial_lengths_.begin() + param.num_dim_spatial_);
+    }
+    else if constexpr(is_any_of<InLayout, GNWC, GNHWC, GNDHWC>::value)
+    {
+        physical_lengths = std::vector<std::size_t>{static_cast<std::size_t>(param.G_),
+                                                    static_cast<std::size_t>(param.N_),
+                                                    static_cast<std::size_t>(param.C_)};
+
+        physical_lengths.insert(physical_lengths.begin() + 2,
+                                param.input_spatial_lengths_.begin(),
+                                param.input_spatial_lengths_.begin() + param.num_dim_spatial_);
+    }
+    else if constexpr(is_any_of<InLayout, NWGC, NHWGC, NDHWGC>::value)
+    {
+        physical_lengths = std::vector<std::size_t>{static_cast<std::size_t>(param.N_),
+                                                    static_cast<std::size_t>(param.G_),
+                                                    static_cast<std::size_t>(param.C_)};
+
+        physical_lengths.insert(physical_lengths.begin() + 1,
+                                param.input_spatial_lengths_.begin(),
+                                param.input_spatial_lengths_.begin() + param.num_dim_spatial_);
+    }
+    else
+    {
+        printf("%s\n", __func__);
+        printf("%s\n", InLayout::name);
+        throw std::runtime_error("wrong! unsupported layout");
+    }
+
+    return transpose_host_tensor_descriptor_given_new2old(
+        HostTensorDescriptor(physical_lengths),
+        detail::get_layout_transpose_gnchw_to_old<InLayout>());
+}
+
+// make tensor descriptor for packed weight tensor, and order the dimension in the order of GKCYX
+// regardless of physical layout
+template <typename WeiLayout>
+CK_TILE_HOST HostTensorDescriptor
+make_weight_host_tensor_descriptor_g_k_c_xs_packed(const ck_tile::conv::ConvParam& param)
+{
+    using namespace ck_tile::tensor_layout::convolution;
+
+    std::vector<std::size_t> physical_lengths;
+
+    if constexpr(is_any_of<WeiLayout, KXC, KYXC, KZYXC>::value)
+    {
+        if(param.G_ != 1)
+        {
+            throw std::runtime_error("wrong! G != 1");
+        }
+
+        physical_lengths = std::vector<std::size_t>{static_cast<std::size_t>(param.K_),
+                                                    static_cast<std::size_t>(param.C_)};
+
+        physical_lengths.insert(physical_lengths.end(),
+                                param.filter_spatial_lengths_.begin(),
+                                param.filter_spatial_lengths_.begin() + param.num_dim_spatial_);
+    }
+    else if constexpr(is_any_of<WeiLayout, GKCX, GKCYX, GKCZYX>::value)
+    {
+        physical_lengths = std::vector<std::size_t>{static_cast<std::size_t>(param.G_),
+                                                    static_cast<std::size_t>(param.K_),
+                                                    static_cast<std::size_t>(param.C_)};
+
+        physical_lengths.insert(physical_lengths.end(),
+                                param.filter_spatial_lengths_.begin(),
+                                param.filter_spatial_lengths_.begin() + param.num_dim_spatial_);
+    }
+    else if constexpr(is_any_of<WeiLayout, GKXC, GKYXC, GKZYXC>::value)
+    {
+        physical_lengths = std::vector<std::size_t>{static_cast<std::size_t>(param.G_),
+                                                    static_cast<std::size_t>(param.K_),
+                                                    static_cast<std::size_t>(param.C_)};
+
+        physical_lengths.insert(physical_lengths.begin() + 2,
+                                param.filter_spatial_lengths_.begin(),
+                                param.filter_spatial_lengths_.begin() + param.num_dim_spatial_);
+    }
+    else if constexpr(is_any_of<WeiLayout, KXGC, KYXGC, KZYXGC>::value)
+    {
+        physical_lengths = std::vector<std::size_t>{static_cast<std::size_t>(param.K_),
+                                                    static_cast<std::size_t>(param.G_),
+                                                    static_cast<std::size_t>(param.C_)};
+
+        physical_lengths.insert(physical_lengths.begin() + 1,
+                                param.filter_spatial_lengths_.begin(),
+                                param.filter_spatial_lengths_.begin() + param.num_dim_spatial_);
+    }
+    else
+    {
+        printf("%s\n", __func__);
+        printf("%s\n", WeiLayout::name);
+        throw std::runtime_error("wrong! unsupported layout");
+    }
+
+    return transpose_host_tensor_descriptor_given_new2old(
+        HostTensorDescriptor(physical_lengths),
+        detail::get_layout_transpose_gnchw_to_old<WeiLayout>());
+}
+
+// make tensor descriptor for packed output tensor, and order the dimension in the order of GNKHW
+// regardless of physical layout
+template <typename OutLayout>
+CK_TILE_HOST HostTensorDescriptor
+make_output_host_tensor_descriptor_g_n_k_wos_packed(const ck_tile::conv::ConvParam& param)
+{
+    using namespace ck_tile::tensor_layout::convolution;
+
+    std::vector<std::size_t> physical_lengths;
+
+    if constexpr(is_any_of<OutLayout, GNKW, GNKHW, GNKDHW>::value)
+    {
+        physical_lengths = std::vector<std::size_t>{static_cast<std::size_t>(param.G_),
+                                                    static_cast<std::size_t>(param.N_),
+                                                    static_cast<std::size_t>(param.K_)};
+
+        physical_lengths.insert(physical_lengths.end(),
+                                param.output_spatial_lengths_.begin(),
+                                param.output_spatial_lengths_.begin() + param.num_dim_spatial_);
+    }
+    // separate from legacy code above
+    else if constexpr(is_any_of<OutLayout, GNWK, GNHWK, GNDHWK>::value)
+    {
+        physical_lengths = std::vector<std::size_t>{static_cast<std::size_t>(param.G_),
+                                                    static_cast<std::size_t>(param.N_),
+                                                    static_cast<std::size_t>(param.K_)};
+
+        physical_lengths.insert(physical_lengths.begin() + 2,
+                                param.output_spatial_lengths_.begin(),
+                                param.output_spatial_lengths_.begin() + param.num_dim_spatial_);
+    }
+    else if constexpr(is_any_of<OutLayout, NWGK, NHWGK, NDHWGK>::value)
+    {
+        physical_lengths = std::vector<std::size_t>{static_cast<std::size_t>(param.N_),
+                                                    static_cast<std::size_t>(param.G_),
+                                                    static_cast<std::size_t>(param.K_)};
+
+        physical_lengths.insert(physical_lengths.begin() + 1,
+                                param.output_spatial_lengths_.begin(),
+                                param.output_spatial_lengths_.begin() + param.num_dim_spatial_);
+    }
+    else
+    {
+        printf("%s\n", __func__);
+        printf("%s\n", OutLayout::name);
+        throw std::runtime_error("wrong! unsupported layout");
+    }
+
+    return transpose_host_tensor_descriptor_given_new2old(
+        HostTensorDescriptor(physical_lengths),
+        detail::get_layout_transpose_gnchw_to_old<OutLayout>());
+}
+
+} // namespace conv
+} // namespace ck_tile

include/ck_tile/host/convolution_parameter.hpp

@@ -0,0 +1,277 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <cstdlib>
+#include <numeric>
+#include <iterator>
+#include <vector>
+
+namespace ck_tile {
+namespace conv {
+
+struct ConvParam
+{
+    ConvParam(ck_tile::index_t n_dim,
+              ck_tile::index_t group_count,
+              ck_tile::index_t n_batch,
+              ck_tile::index_t n_out_channels,
+              ck_tile::index_t n_in_channels,
+              const std::vector<ck_tile::index_t>& filters_len,
+              const std::vector<ck_tile::index_t>& input_len,
+              const std::vector<ck_tile::index_t>& strides,
+              const std::vector<ck_tile::index_t>& dilations,
+              const std::vector<ck_tile::index_t>& left_pads,
+              const std::vector<ck_tile::index_t>& right_pads)
+        : num_dim_spatial_(static_cast<ck_tile::long_index_t>(n_dim)),
+          G_(static_cast<ck_tile::long_index_t>(group_count)),
+          N_(static_cast<ck_tile::long_index_t>(n_batch)),
+          K_(static_cast<ck_tile::long_index_t>(n_out_channels)),
+          C_(static_cast<ck_tile::long_index_t>(n_in_channels)),
+          filter_spatial_lengths_(num_dim_spatial_),
+          input_spatial_lengths_(num_dim_spatial_),
+          output_spatial_lengths_(num_dim_spatial_),
+          conv_filter_strides_(num_dim_spatial_),
+          conv_filter_dilations_(num_dim_spatial_),
+          input_left_pads_(num_dim_spatial_),
+          input_right_pads_(num_dim_spatial_)
+    {
+        if(static_cast<ck_tile::index_t>(filter_spatial_lengths_.size()) != num_dim_spatial_ ||
+           static_cast<ck_tile::index_t>(input_spatial_lengths_.size()) != num_dim_spatial_ ||
+           static_cast<ck_tile::index_t>(conv_filter_strides_.size()) != num_dim_spatial_ ||
+           static_cast<ck_tile::index_t>(conv_filter_dilations_.size()) != num_dim_spatial_ ||
+           static_cast<ck_tile::index_t>(input_left_pads_.size()) != num_dim_spatial_ ||
+           static_cast<ck_tile::index_t>(input_right_pads_.size()) != num_dim_spatial_)
+        {
+            throw(std::runtime_error(
+                "ConvParam::ConvParam: "
+                "parameter size is different from number of declared dimensions!"));
+        }
+
+        for(ck_tile::index_t i = 0; i < num_dim_spatial_; ++i)
+        {
+            filter_spatial_lengths_[i] = static_cast<ck_tile::long_index_t>(filters_len[i]);
+            input_spatial_lengths_[i]  = static_cast<ck_tile::long_index_t>(input_len[i]);
+            conv_filter_strides_[i]    = static_cast<ck_tile::long_index_t>(strides[i]);
+            conv_filter_dilations_[i]  = static_cast<ck_tile::long_index_t>(dilations[i]);
+            input_left_pads_[i]        = static_cast<ck_tile::long_index_t>(left_pads[i]);
+            input_right_pads_[i]       = static_cast<ck_tile::long_index_t>(right_pads[i]);
+
+            // XEff = (X - 1) * conv_dilation_w + 1;
+            // Wo = (Wi + in_left_pad_w + in_right_pad_w - XEff) / conv_stride_w + 1;
+            const ck_tile::long_index_t x_eff =
+                (filter_spatial_lengths_[i] - 1) * conv_filter_dilations_[i] + 1;
+
+            output_spatial_lengths_[i] =
+                (input_spatial_lengths_[i] + input_left_pads_[i] + input_right_pads_[i] - x_eff) /
+                    conv_filter_strides_[i] +
+                1;
+        }
+    }
+
+    ConvParam(ck_tile::long_index_t n_dim,
+              ck_tile::long_index_t group_count,
+              ck_tile::long_index_t n_batch,
+              ck_tile::long_index_t n_out_channels,
+              ck_tile::long_index_t n_in_channels,
+              const std::vector<ck_tile::long_index_t>& filters_len,
+              const std::vector<ck_tile::long_index_t>& input_len,
+              const std::vector<ck_tile::long_index_t>& strides,
+              const std::vector<ck_tile::long_index_t>& dilations,
+              const std::vector<ck_tile::long_index_t>& left_pads,
+              const std::vector<ck_tile::long_index_t>& right_pads)
+        : num_dim_spatial_(n_dim),
+          G_(group_count),
+          N_(n_batch),
+          K_(n_out_channels),
+          C_(n_in_channels),
+          filter_spatial_lengths_(filters_len),
+          input_spatial_lengths_(input_len),
+          output_spatial_lengths_(num_dim_spatial_),
+          conv_filter_strides_(strides),
+          conv_filter_dilations_(dilations),
+          input_left_pads_(left_pads),
+          input_right_pads_(right_pads)
+    {
+        if(static_cast<ck_tile::index_t>(filter_spatial_lengths_.size()) != num_dim_spatial_ ||
+           static_cast<ck_tile::index_t>(input_spatial_lengths_.size()) != num_dim_spatial_ ||
+           static_cast<ck_tile::index_t>(conv_filter_strides_.size()) != num_dim_spatial_ ||
+           static_cast<ck_tile::index_t>(conv_filter_dilations_.size()) != num_dim_spatial_ ||
+           static_cast<ck_tile::index_t>(input_left_pads_.size()) != num_dim_spatial_ ||
+           static_cast<ck_tile::index_t>(input_right_pads_.size()) != num_dim_spatial_)
+        {
+            throw(std::runtime_error(
+                "ConvParam::ConvParam: "
+                "parameter size is different from number of declared dimensions!"));
+        }
+
+        for(ck_tile::index_t i = 0; i < num_dim_spatial_; ++i)
+        {
+            // XEff = (X - 1) * conv_dilation_w + 1;
+            // Wo = (Wi + in_left_pad_w + in_right_pad_w - XEff) / conv_stride_w + 1;
+            const ck_tile::long_index_t x_eff =
+                (filter_spatial_lengths_[i] - 1) * conv_filter_dilations_[i] + 1;
+
+            output_spatial_lengths_[i] =
+                (input_spatial_lengths_[i] + input_left_pads_[i] + input_right_pads_[i] - x_eff) /
+                    conv_filter_strides_[i] +
+                1;
+        }
+    }
+
+    ck_tile::long_index_t num_dim_spatial_;
+    ck_tile::long_index_t G_;
+    ck_tile::long_index_t N_;
+    ck_tile::long_index_t K_;
+    ck_tile::long_index_t C_;
+
+    std::vector<ck_tile::long_index_t> filter_spatial_lengths_;
+    std::vector<ck_tile::long_index_t> input_spatial_lengths_;
+    std::vector<ck_tile::long_index_t> output_spatial_lengths_;
+
+    std::vector<ck_tile::long_index_t> conv_filter_strides_;
+    std::vector<ck_tile::long_index_t> conv_filter_dilations_;
+
+    std::vector<ck_tile::long_index_t> input_left_pads_;
+    std::vector<ck_tile::long_index_t> input_right_pads_;
+
+    std::vector<ck_tile::long_index_t> GetOutputSpatialLengths() const
+    {
+        return output_spatial_lengths_;
+    }
+
+    std::size_t GetFlops() const
+    {
+        // 2 * G * N * K * C * <output spatial lengths product> * <filter spatial lengths product>
+        return static_cast<std::size_t>(2) * G_ * N_ * K_ * C_ *
+               std::accumulate(std::begin(output_spatial_lengths_),
+                               std::next(std::begin(output_spatial_lengths_), num_dim_spatial_),
+                               1,
+                               std::multiplies<>()) *
+               std::accumulate(std::begin(filter_spatial_lengths_),
+                               std::next(std::begin(filter_spatial_lengths_), num_dim_spatial_),
+                               1,
+                               std::multiplies<>());
+    }
+
+    template <typename InDataType>
+    std::size_t GetInputByte() const
+    {
+        // sizeof(InDataType) * (G * N * C * <input spatial lengths product>) +
+        return sizeof(InDataType) *
+               (G_ * N_ * C_ *
+                std::accumulate(std::begin(input_spatial_lengths_),
+                                std::next(std::begin(input_spatial_lengths_), num_dim_spatial_),
+                                1,
+                                std::multiplies<>()));
+    }
+
+    template <typename WeiDataType>
+    std::size_t GetWeightByte() const
+    {
+        // sizeof(WeiDataType) * (G * K * C * <filter spatial lengths product>) +
+        return sizeof(WeiDataType) *
+               (G_ * K_ * C_ *
+                std::accumulate(std::begin(filter_spatial_lengths_),
+                                std::next(std::begin(filter_spatial_lengths_), num_dim_spatial_),
+                                1,
+                                std::multiplies<>()));
+    }
+
+    template <typename OutDataType>
+    std::size_t GetOutputByte() const
+    {
+        // sizeof(OutDataType) * (G * N * K * <output spatial lengths product>);
+        return sizeof(OutDataType) * (G_ * N_ * K_ *
+                                      std::accumulate(std::begin(output_spatial_lengths_),
+                                                      std::end(output_spatial_lengths_),
+                                                      static_cast<std::size_t>(1),
+                                                      std::multiplies<std::size_t>()));
+    }
+
+    template <typename InDataType, typename WeiDataType, typename OutDataType>
+    std::size_t GetByte() const
+    {
+        return GetInputByte<InDataType>() + GetWeightByte<WeiDataType>() +
+               GetOutputByte<OutDataType>();
+    }
+};
+
+CK_TILE_HOST std::string get_conv_param_parser_helper_msg()
+{
+    std::string msg;
+
+    msg += "Following arguments (depending on number of spatial dims):\n"
+           " Number of spatial dimensions (1=Conv1d, 2=Conv2d, 3=Conv3d)\n"
+           " G, N, K, C, \n"
+           " <filter spatial dimensions>, (ie Y, X for 2D)\n"
+           " <input image spatial dimensions>, (ie Hi, Wi for 2D)\n"
+           " <strides>, (ie Sy, Sx for 2D)\n"
+           " <dilations>, (ie Dy, Dx for 2D)\n"
+           " <left padding>, (ie LeftPy, LeftPx for 2D)\n"
+           " <right padding>, (ie RightPy, RightPx for 2D)\n";
+
+    return msg;
+}
+
+CK_TILE_HOST ck_tile::conv::ConvParam
+parse_conv_param(int num_dim_spatial, int arg_idx, char* const argv[])
+{
+    const ck_tile::long_index_t G = std::stol(argv[arg_idx++]);
+    const ck_tile::long_index_t N = std::stol(argv[arg_idx++]);
+    const ck_tile::long_index_t K = std::stol(argv[arg_idx++]);
+    const ck_tile::long_index_t C = std::stol(argv[arg_idx++]);
+
+    std::vector<ck_tile::long_index_t> filter_spatial_lengths(num_dim_spatial);
+    std::vector<ck_tile::long_index_t> input_spatial_lengths(num_dim_spatial);
+    std::vector<ck_tile::long_index_t> conv_filter_strides(num_dim_spatial);
+    std::vector<ck_tile::long_index_t> conv_filter_dilations(num_dim_spatial);
+    std::vector<ck_tile::long_index_t> input_left_pads(num_dim_spatial);
+    std::vector<ck_tile::long_index_t> input_right_pads(num_dim_spatial);
+
+    for(int i = 0; i < num_dim_spatial; ++i)
+    {
+        filter_spatial_lengths[i] = std::stol(argv[arg_idx++]);
+    }
+
+    for(int i = 0; i < num_dim_spatial; ++i)
+    {
+        input_spatial_lengths[i] = std::stol(argv[arg_idx++]);
+    }
+
+    for(int i = 0; i < num_dim_spatial; ++i)
+    {
+        conv_filter_strides[i] = std::stol(argv[arg_idx++]);
+    }
+
+    for(int i = 0; i < num_dim_spatial; ++i)
+    {
+        conv_filter_dilations[i] = std::stol(argv[arg_idx++]);
+    }
+
+    for(int i = 0; i < num_dim_spatial; ++i)
+    {
+        input_left_pads[i] = std::stol(argv[arg_idx++]);
+    }
+
+    for(int i = 0; i < num_dim_spatial; ++i)
+    {
+        input_right_pads[i] = std::stol(argv[arg_idx++]);
+    }
+
+    return ck_tile::conv::ConvParam{num_dim_spatial,
+                                    G,
+                                    N,
+                                    K,
+                                    C,
+                                    filter_spatial_lengths,
+                                    input_spatial_lengths,
+                                    conv_filter_strides,
+                                    conv_filter_dilations,
+                                    input_left_pads,
+                                    input_right_pads};
+}
+
+} // namespace conv
+} // namespace ck_tile

include/ck_tile/host/device_memory.hpp

@@ -0,0 +1,170 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <hip/hip_runtime.h>
+#include <stdint.h>
+#include <stdexcept>
+#include "ck_tile/host/hip_check_error.hpp"
+#include "ck_tile/host/host_tensor.hpp"
+
+namespace ck_tile {
+template <typename T>
+__global__ void set_buffer_value(T* p, T x, uint64_t buffer_element_size)
+{
+    for(uint64_t i = threadIdx.x; i < buffer_element_size; i += blockDim.x)
+    {
+        p[i] = x;
+    }
+}
+
+/**
+ * @brief Container for storing data in GPU device memory
+ *
+ */
+struct DeviceMem
+{
+    DeviceMem() : mpDeviceBuf(nullptr), mMemSize(0) {}
+    DeviceMem(std::size_t mem_size) : mMemSize(mem_size)
+    {
+        if(mMemSize != 0)
+        {
+            HIP_CHECK_ERROR(hipMalloc(static_cast<void**>(&mpDeviceBuf), mMemSize));
+        }
+        else
+        {
+            mpDeviceBuf = nullptr;
+        }
+    }
+    template <typename T>
+    DeviceMem(const HostTensor<T>& t) : mMemSize(t.get_element_space_size_in_bytes())
+    {
+        if(mMemSize != 0)
+        {
+            HIP_CHECK_ERROR(hipMalloc(static_cast<void**>(&mpDeviceBuf), mMemSize));
+        }
+        else
+        {
+            mpDeviceBuf = nullptr;
+        }
+        ToDevice(t.data());
+    }
+    void Realloc(std::size_t mem_size)
+    {
+        if(mpDeviceBuf)
+        {
+            HIP_CHECK_ERROR(hipFree(mpDeviceBuf));
+        }
+        mMemSize = mem_size;
+        if(mMemSize != 0)
+        {
+            HIP_CHECK_ERROR(hipMalloc(static_cast<void**>(&mpDeviceBuf), mMemSize));
+        }
+        else
+        {
+            mpDeviceBuf = nullptr;
+        }
+    }
+    void* GetDeviceBuffer() const { return mpDeviceBuf; }
+    std::size_t GetBufferSize() const { return mMemSize; }
+    void ToDevice(const void* p) const
+    {
+        if(mpDeviceBuf)
+        {
+            HIP_CHECK_ERROR(
+                hipMemcpy(mpDeviceBuf, const_cast<void*>(p), mMemSize, hipMemcpyHostToDevice));
+        }
+        // else
+        // {
+        //     throw std::runtime_error("ToDevice with an empty pointer");
+        // }
+    }
+    void ToDevice(const void* p, const std::size_t cpySize) const
+    {
+        if(mpDeviceBuf)
+        {
+            HIP_CHECK_ERROR(
+                hipMemcpy(mpDeviceBuf, const_cast<void*>(p), cpySize, hipMemcpyHostToDevice));
+        }
+    }
+    void FromDevice(void* p) const
+    {
+        if(mpDeviceBuf)
+        {
+            HIP_CHECK_ERROR(hipMemcpy(p, mpDeviceBuf, mMemSize, hipMemcpyDeviceToHost));
+        }
+        // else
+        // {
+        //     throw std::runtime_error("FromDevice with an empty pointer");
+        // }
+    }
+    void FromDevice(void* p, const std::size_t cpySize) const
+    {
+        if(mpDeviceBuf)
+        {
+            HIP_CHECK_ERROR(hipMemcpy(p, mpDeviceBuf, cpySize, hipMemcpyDeviceToHost));
+        }
+    }
+
+    // construct a host tensor with type T
+    template <typename T>
+    HostTensor<T> ToHost(std::size_t cpySize)
+    {
+        // TODO: host tensor could be slightly larger than the device tensor
+        // we just copy all data from GPU buffer
+        std::size_t host_elements = (cpySize + sizeof(T) - 1) / sizeof(T);
+        HostTensor<T> h_({host_elements});
+        if(mpDeviceBuf)
+        {
+            HIP_CHECK_ERROR(hipMemcpy(h_.data(), mpDeviceBuf, cpySize, hipMemcpyDeviceToHost));
+        }
+        return h_;
+    }
+    template <typename T>
+    HostTensor<T> ToHost()
+    {
+        return ToHost<T>(mMemSize);
+    }
+
+    void SetZero() const
+    {
+        if(mpDeviceBuf)
+        {
+            HIP_CHECK_ERROR(hipMemset(mpDeviceBuf, 0, mMemSize));
+        }
+    }
+    template <typename T>
+    void SetValue(T x) const
+    {
+        if(mpDeviceBuf)
+        {
+            if(mMemSize % sizeof(T) != 0)
+            {
+                throw std::runtime_error("wrong! not entire DeviceMem will be set");
+            }
+
+            // TODO: call a gpu kernel to set the value (?)
+            set_buffer_value<T><<<1, 1024>>>(static_cast<T*>(mpDeviceBuf), x, mMemSize / sizeof(T));
+        }
+    }
+    ~DeviceMem()
+    {
+        if(mpDeviceBuf)
+        {
+            try
+            {
+                HIP_CHECK_ERROR(hipFree(mpDeviceBuf));
+            }
+            catch(std::runtime_error& re)
+            {
+                std::cerr << re.what() << std::endl;
+            }
+        }
+    }
+
+    void* mpDeviceBuf;
+    std::size_t mMemSize;
+};
+
+} // namespace ck_tile

include/ck_tile/host/fill.hpp

@@ -0,0 +1,451 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2025, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <algorithm>
+#include <cmath>
+#include <iterator>
+#include <optional>
+#include <random>
+#include <type_traits>
+#include <utility>
+#include <unordered_set>
+
+#include "ck_tile/core.hpp"
+#include "ck_tile/host/joinable_thread.hpp"
+
+namespace ck_tile {
+
+template <typename T>
+struct FillUniformDistribution
+{
+    float a_{-5.f};
+    float b_{5.f};
+    std::optional<uint32_t> seed_{11939};
+    // ATTENTION: threaded does not guarantee the distribution between thread
+    bool threaded = false;
+
+    template <typename ForwardIter>
+    void operator()(ForwardIter first, ForwardIter last) const
+    {
+        if(threaded)
+        {
+            uint32_t num_thread  = std::thread::hardware_concurrency();
+            auto total           = static_cast<std::size_t>(std::distance(first, last));
+            auto work_per_thread = static_cast<std::size_t>((total + num_thread - 1) / num_thread);
+
+            std::vector<joinable_thread> threads(num_thread);
+            for(std::size_t it = 0; it < num_thread; ++it)
+            {
+                std::size_t iw_begin = it * work_per_thread;
+                std::size_t iw_end   = std::min((it + 1) * work_per_thread, total);
+                auto thread_f        = [this, total, iw_begin, iw_end, &first] {
+                    if(iw_begin > total || iw_end > total)
+                        return;
+                    // need to make each thread unique, add an offset to current seed
+                    std::mt19937 gen(seed_.has_value() ? (*seed_ + iw_begin)
+                                                              : std::random_device{}());
+                    std::uniform_real_distribution<float> dis(a_, b_);
+                    std::generate(first + iw_begin, first + iw_end, [&dis, &gen]() {
+                        return ck_tile::type_convert<T>(dis(gen));
+                    });
+                };
+                threads[it] = joinable_thread(thread_f);
+            }
+        }
+        else
+        {
+            std::mt19937 gen(seed_.has_value() ? *seed_ : std::random_device{}());
+            std::uniform_real_distribution<float> dis(a_, b_);
+            std::generate(
+                first, last, [&dis, &gen]() { return ck_tile::type_convert<T>(dis(gen)); });
+        }
+    }
+
+    template <typename ForwardRange>
+    auto operator()(ForwardRange&& range) const
+        -> std::void_t<decltype(std::declval<const FillUniformDistribution&>()(
+            std::begin(std::forward<ForwardRange>(range)),
+            std::end(std::forward<ForwardRange>(range))))>
+    {
+        (*this)(std::begin(std::forward<ForwardRange>(range)),
+                std::end(std::forward<ForwardRange>(range)));
+    }
+};
+
+namespace impl {
+
+// clang-format off
+template<index_t bytes> struct RawIntegerType_ {};
+template<> struct RawIntegerType_<1> { using type = uint8_t;};
+template<> struct RawIntegerType_<2> { using type = uint16_t;};
+template<> struct RawIntegerType_<4> { using type = uint32_t;};
+template<> struct RawIntegerType_<8> { using type = uint64_t;};
+// clang-format on
+
+template <typename T>
+using RawIntegerType = typename RawIntegerType_<sizeof(T)>::type;
+} // namespace impl
+
+// Note: this struct will have no const-ness will generate random
+template <typename T>
+struct FillUniformDistribution_Unique
+{
+    float a_{-5.f};
+    float b_{5.f};
+    std::optional<uint32_t> seed_{11939};
+
+    std::mt19937 gen_{};
+    std::unordered_set<impl::RawIntegerType<T>> set_{};
+
+    FillUniformDistribution_Unique(float a                      = -5.f,
+                                   float b                      = 5.f,
+                                   std::optional<uint32_t> seed = {11939})
+        : a_(a),
+          b_(b),
+          seed_(seed),
+          gen_{seed_.has_value() ? *seed_ : std::random_device{}()},
+          set_{}
+    {
+    }
+
+    template <typename ForwardIter>
+    void operator()(ForwardIter first, ForwardIter last)
+    {
+        std::mt19937& gen = gen_;
+        std::uniform_real_distribution<float> dis(a_, b_);
+        auto& set = set_;
+        std::generate(first, last, [&dis, &gen, &set]() {
+            T v = static_cast<T>(0);
+            do
+            {
+                v = ck_tile::type_convert<T>(dis(gen));
+            } while(set.count(bit_cast<impl::RawIntegerType<T>>(v)) == 1);
+            set.insert(bit_cast<impl::RawIntegerType<T>>(v));
+
+            return v;
+        });
+    }
+
+    template <typename ForwardRange>
+    auto operator()(ForwardRange&& range)
+        -> std::void_t<decltype(std::declval<FillUniformDistribution_Unique&>()(
+            std::begin(std::forward<ForwardRange>(range)),
+            std::end(std::forward<ForwardRange>(range))))>
+    {
+        (*this)(std::begin(std::forward<ForwardRange>(range)),
+                std::end(std::forward<ForwardRange>(range)));
+    }
+
+    void clear() { set_.clear(); }
+};
+
+template <typename T>
+struct FillNormalDistribution
+{
+    float mean_{0.f};
+    float variance_{1.f};
+    std::optional<uint32_t> seed_{11939};
+    // ATTENTION: threaded does not guarantee the distribution between thread
+    bool threaded = false;
+
+    template <typename ForwardIter>
+    void operator()(ForwardIter first, ForwardIter last) const
+    {
+        if(threaded)
+        {
+            uint32_t num_thread  = std::thread::hardware_concurrency();
+            auto total           = static_cast<std::size_t>(std::distance(first, last));
+            auto work_per_thread = static_cast<std::size_t>((total + num_thread - 1) / num_thread);
+
+            std::vector<joinable_thread> threads(num_thread);
+            for(std::size_t it = 0; it < num_thread; ++it)
+            {
+                std::size_t iw_begin = it * work_per_thread;
+                std::size_t iw_end   = std::min((it + 1) * work_per_thread, total);
+                auto thread_f        = [this, total, iw_begin, iw_end, &first] {
+                    if(iw_begin > total || iw_end > total)
+                        return;
+                    // need to make each thread unique, add an offset to current seed
+                    std::mt19937 gen(seed_.has_value() ? (*seed_ + iw_begin)
+                                                              : std::random_device{}());
+                    std::normal_distribution<float> dis(mean_, std::sqrt(variance_));
+                    std::generate(first + iw_begin, first + iw_end, [&dis, &gen]() {
+                        return ck_tile::type_convert<T>(dis(gen));
+                    });
+                };
+                threads[it] = joinable_thread(thread_f);
+            }
+        }
+        else
+        {
+            std::mt19937 gen(seed_.has_value() ? *seed_ : std::random_device{}());
+            std::normal_distribution<float> dis(mean_, std::sqrt(variance_));
+            std::generate(
+                first, last, [&dis, &gen]() { return ck_tile::type_convert<T>(dis(gen)); });
+        }
+    }
+
+    template <typename ForwardRange>
+    auto operator()(ForwardRange&& range) const
+        -> std::void_t<decltype(std::declval<const FillNormalDistribution&>()(
+            std::begin(std::forward<ForwardRange>(range)),
+            std::end(std::forward<ForwardRange>(range))))>
+    {
+        (*this)(std::begin(std::forward<ForwardRange>(range)),
+                std::end(std::forward<ForwardRange>(range)));
+    }
+};
+
+// Normally FillUniformDistributionIntegerValue should use std::uniform_int_distribution as below.
+// However this produces segfaults in std::mt19937 which look like inifite loop.
+//      template <typename T>
+//      struct FillUniformDistributionIntegerValue
+//      {
+//          int a_{-5};
+//          int b_{5};
+//
+//          template <typename ForwardIter>
+//          void operator()(ForwardIter first, ForwardIter last) const
+//          {
+//              std::mt19937 gen(11939);
+//              std::uniform_int_distribution<int> dis(a_, b_);
+//              std::generate(
+//                  first, last, [&dis, &gen]() { return ck_tile::type_convert<T>(dis(gen)); });
+//          }
+//      };
+
+// Workaround for uniform_int_distribution not working as expected. See note above.<
+template <typename T>
+struct FillUniformDistributionIntegerValue
+{
+    float a_{-5.f};
+    float b_{5.f};
+    std::optional<uint32_t> seed_{11939};
+
+    template <typename ForwardIter>
+    void operator()(ForwardIter first, ForwardIter last) const
+    {
+        std::mt19937 gen(seed_.has_value() ? *seed_ : std::random_device{}());
+        std::uniform_real_distribution<float> dis(a_, b_);
+        std::generate(
+            first, last, [&dis, &gen]() { return ck_tile::type_convert<T>(std::round(dis(gen))); });
+    }
+
+    template <typename ForwardRange>
+    auto operator()(ForwardRange&& range) const
+        -> std::void_t<decltype(std::declval<const FillUniformDistributionIntegerValue&>()(
+            std::begin(std::forward<ForwardRange>(range)),
+            std::end(std::forward<ForwardRange>(range))))>
+    {
+        (*this)(std::begin(std::forward<ForwardRange>(range)),
+                std::end(std::forward<ForwardRange>(range)));
+    }
+};
+
+template <typename T>
+struct FillNormalDistributionIntegerValue
+{
+    float mean_{0.f};
+    float variance_{1.f};
+    std::optional<uint32_t> seed_{11939};
+
+    template <typename ForwardIter>
+    void operator()(ForwardIter first, ForwardIter last) const
+    {
+        std::mt19937 gen(seed_.has_value() ? *seed_ : std::random_device{}());
+        std::normal_distribution<float> dis(mean_, std::sqrt(variance_));
+        std::generate(
+            first, last, [&dis, &gen]() { return ck_tile::type_convert<T>(std::round(dis(gen))); });
+    }
+
+    template <typename ForwardRange>
+    auto operator()(ForwardRange&& range) const
+        -> std::void_t<decltype(std::declval<const FillNormalDistributionIntegerValue&>()(
+            std::begin(std::forward<ForwardRange>(range)),
+            std::end(std::forward<ForwardRange>(range))))>
+    {
+        (*this)(std::begin(std::forward<ForwardRange>(range)),
+                std::end(std::forward<ForwardRange>(range)));
+    }
+};
+
+template <typename T>
+struct FillMonotonicSeq
+{
+    T init_value_{0};
+    T step_{1};
+
+    template <typename ForwardIter>
+    void operator()(ForwardIter first, ForwardIter last) const
+    {
+        std::generate(first, last, [=, *this, n = init_value_]() mutable {
+            auto tmp = n;
+            if constexpr(std::is_same_v<decltype(tmp), pk_int4_t>)
+            {
+                n.data += step_.data;
+            }
+            else
+            {
+                n += step_;
+            }
+            return tmp;
+        });
+    }
+
+    template <typename ForwardRange>
+    auto operator()(ForwardRange&& range) const
+        -> std::void_t<decltype(std::declval<const FillMonotonicSeq&>()(
+            std::begin(std::forward<ForwardRange>(range)),
+            std::end(std::forward<ForwardRange>(range))))>
+    {
+        (*this)(std::begin(std::forward<ForwardRange>(range)),
+                std::end(std::forward<ForwardRange>(range)));
+    }
+};
+
+template <typename T, bool IsAscending = true>
+struct FillStepRange
+{
+    float start_value_{0};
+    float end_value_{3};
+    float step_{1};
+
+    template <typename ForwardIter>
+    void operator()(ForwardIter first, ForwardIter last) const
+    {
+        std::generate(first, last, [=, *this, n = start_value_]() mutable {
+            auto tmp = n;
+            n += step_;
+            if constexpr(IsAscending)
+            {
+                if(n > end_value_)
+                    n = start_value_;
+            }
+            else
+            {
+                if(n < end_value_)
+                    n = start_value_;
+            }
+
+            return type_convert<T>(tmp);
+        });
+    }
+
+    template <typename ForwardRange>
+    auto operator()(ForwardRange&& range) const -> std::void_t<
+        decltype(std::declval<const FillStepRange&>()(std::begin(std::forward<ForwardRange>(range)),
+                                                      std::end(std::forward<ForwardRange>(range))))>
+    {
+        (*this)(std::begin(std::forward<ForwardRange>(range)),
+                std::end(std::forward<ForwardRange>(range)));
+    }
+};
+
+template <typename T>
+struct FillConstant
+{
+    T value_{0};
+
+    template <typename ForwardIter>
+    void operator()(ForwardIter first, ForwardIter last) const
+    {
+        std::fill(first, last, value_);
+    }
+
+    template <typename ForwardRange>
+    auto operator()(ForwardRange&& range) const -> std::void_t<
+        decltype(std::declval<const FillConstant&>()(std::begin(std::forward<ForwardRange>(range)),
+                                                     std::end(std::forward<ForwardRange>(range))))>
+    {
+        (*this)(std::begin(std::forward<ForwardRange>(range)),
+                std::end(std::forward<ForwardRange>(range)));
+    }
+};
+
+//----------------------------------------------------------------------------------------------
+/// @brief      Transforms given input to fit 2:4 structured sparsity pattern so
+///             every subgroup of 4 elements contain at most 2 non-zero elements
+template <typename T>
+struct AdjustToStructuredSparsity
+{
+    size_t start{0};
+    // masks represent all valid 2:4 structured sparsity permutations
+    // clang-format off
+    static constexpr int32_t masks[] = {0, 0, 1, 1,
+                                        0, 1, 0, 1,
+                                        0, 1, 1, 0,
+                                        1, 0, 0, 1,
+                                        1, 0, 1, 0,
+                                        1, 1, 0, 0,
+                                        0, 0, 0, 1,
+                                        0, 0, 1, 0,
+                                        0, 1, 0, 0,
+                                        1, 0, 0, 0};
+    // clang-format on
+
+    template <typename ForwardIter>
+    void operator()(ForwardIter first, ForwardIter last) const
+    {
+        std::transform(first, last, first, [=, *this, index = start](T val) mutable {
+            auto tmp = val * masks[index % (sizeof(masks) / sizeof(int32_t))];
+            index += 1;
+
+            return type_convert<T>(tmp);
+        });
+    }
+
+    template <typename ForwardRange>
+    auto operator()(ForwardRange&& range) const
+        -> std::void_t<decltype(std::declval<const AdjustToStructuredSparsity&>()(
+            std::begin(std::forward<ForwardRange>(range)),
+            std::end(std::forward<ForwardRange>(range))))>
+    {
+        (*this)(std::begin(std::forward<ForwardRange>(range)),
+                std::end(std::forward<ForwardRange>(range)));
+    }
+};
+
+template <typename T, bool UseCos = true, bool UseAbs = false>
+struct FillTrigValue
+{
+    template <typename T_, bool UseCos_ = true, bool UseAbs_ = false>
+    struct LinearTrigGen
+    {
+        int i{0};
+        auto operator()()
+        {
+            float v = 0;
+            if constexpr(UseCos_)
+            {
+                v = cos(i);
+            }
+            else
+            {
+                v = sin(i);
+            }
+            if constexpr(UseAbs_)
+                v = abs(v);
+            i++;
+            return ck_tile::type_convert<T_>(v);
+        }
+    };
+    template <typename ForwardIter>
+    void operator()(ForwardIter first, ForwardIter last) const
+    {
+        LinearTrigGen<T, UseCos, UseAbs> gen;
+        std::generate(first, last, gen);
+    }
+
+    template <typename ForwardRange>
+    auto operator()(ForwardRange&& range) const -> std::void_t<
+        decltype(std::declval<const FillTrigValue&>()(std::begin(std::forward<ForwardRange>(range)),
+                                                      std::end(std::forward<ForwardRange>(range))))>
+    {
+        (*this)(std::begin(std::forward<ForwardRange>(range)),
+                std::end(std::forward<ForwardRange>(range)));
+    }
+};
+
+} // namespace ck_tile

include/ck_tile/host/hip_check_error.hpp

@@ -0,0 +1,36 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include <sstream>
+#include <stdexcept>
+#include <hip/hip_runtime.h>
+
+namespace ck_tile {
+// To be removed, which really does not tell the location of failed HIP functional call
+CK_TILE_HOST void hip_check_error(hipError_t x)
+{
+    if(x != hipSuccess)
+    {
+        std::ostringstream ss;
+        ss << "HIP runtime error: " << hipGetErrorString(x) << ". " << __FILE__ << ": " << __LINE__
+           << "in function: " << __func__;
+        throw std::runtime_error(ss.str());
+    }
+}
+} // namespace ck_tile
+
+#define HIP_CHECK_ERROR(retval_or_funcall)                                         \
+    do                                                                             \
+    {                                                                              \
+        hipError_t _tmpVal = retval_or_funcall;                                    \
+        if(_tmpVal != hipSuccess)                                                  \
+        {                                                                          \
+            std::ostringstream ostr;                                               \
+            ostr << "HIP Function Failed (" << __FILE__ << "," << __LINE__ << ") " \
+                 << hipGetErrorString(_tmpVal);                                    \
+            throw std::runtime_error(ostr.str());                                  \
+        }                                                                          \
+    } while(0)

include/ck_tile/host/host_tensor.hpp

@@ -0,0 +1,722 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2025, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <algorithm>
+#include <cassert>
+#include <iostream>
+#include <iomanip>
+#include <numeric>
+#include <utility>
+#include <vector>
+#include <functional>
+#include <fstream>
+
+#include "ck_tile/core.hpp"
+#include "ck_tile/host/joinable_thread.hpp"
+#include "ck_tile/host/ranges.hpp"
+
+namespace ck_tile {
+
+template <typename Range>
+CK_TILE_HOST std::ostream& LogRange(std::ostream& os,
+                                    Range&& range,
+                                    std::string delim,
+                                    int precision = std::cout.precision(),
+                                    int width     = 0)
+{
+    bool first = true;
+    for(auto&& v : range)
+    {
+        if(first)
+            first = false;
+        else
+            os << delim;
+        os << std::setw(width) << std::setprecision(precision) << v;
+    }
+    return os;
+}
+
+template <typename T, typename Range>
+CK_TILE_HOST std::ostream& LogRangeAsType(std::ostream& os,
+                                          Range&& range,
+                                          std::string delim,
+                                          int precision = std::cout.precision(),
+                                          int width     = 0)
+{
+    bool first = true;
+    for(auto&& v : range)
+    {
+        if(first)
+            first = false;
+        else
+            os << delim;
+        os << std::setw(width) << std::setprecision(precision) << static_cast<T>(v);
+    }
+    return os;
+}
+
+template <typename F, typename T, std::size_t... Is>
+CK_TILE_HOST auto call_f_unpack_args_impl(F f, T args, std::index_sequence<Is...>)
+{
+    return f(std::get<Is>(args)...);
+}
+
+template <typename F, typename T>
+CK_TILE_HOST auto call_f_unpack_args(F f, T args)
+{
+    constexpr std::size_t N = std::tuple_size<T>{};
+
+    return call_f_unpack_args_impl(f, args, std::make_index_sequence<N>{});
+}
+
+template <typename F, typename T, std::size_t... Is>
+CK_TILE_HOST auto construct_f_unpack_args_impl(T args, std::index_sequence<Is...>)
+{
+    return F(std::get<Is>(args)...);
+}
+
+template <typename F, typename T>
+CK_TILE_HOST auto construct_f_unpack_args(F, T args)
+{
+    constexpr std::size_t N = std::tuple_size<T>{};
+
+    return construct_f_unpack_args_impl<F>(args, std::make_index_sequence<N>{});
+}
+
+struct HostTensorDescriptor
+{
+    HostTensorDescriptor() = default;
+
+    void CalculateStrides()
+    {
+        mStrides.clear();
+        mStrides.resize(mLens.size(), 0);
+        if(mStrides.empty())
+            return;
+
+        mStrides.back() = 1;
+        std::partial_sum(mLens.rbegin(),
+                         mLens.rend() - 1,
+                         mStrides.rbegin() + 1,
+                         std::multiplies<std::size_t>());
+    }
+
+    template <typename X, typename = std::enable_if_t<std::is_convertible_v<X, std::size_t>>>
+    HostTensorDescriptor(const std::initializer_list<X>& lens) : mLens(lens.begin(), lens.end())
+    {
+        this->CalculateStrides();
+    }
+
+    template <typename Lengths,
+              typename = std::enable_if_t<
+                  std::is_convertible_v<ck_tile::ranges::range_value_t<Lengths>, std::size_t>>>
+    HostTensorDescriptor(const Lengths& lens) : mLens(lens.begin(), lens.end())
+    {
+        this->CalculateStrides();
+    }
+
+    template <typename X,
+              typename Y,
+              typename = std::enable_if_t<std::is_convertible_v<X, std::size_t> &&
+                                          std::is_convertible_v<Y, std::size_t>>>
+    HostTensorDescriptor(const std::initializer_list<X>& lens,
+                         const std::initializer_list<Y>& strides)
+        : mLens(lens.begin(), lens.end()), mStrides(strides.begin(), strides.end())
+    {
+    }
+
+    template <typename Lengths,
+              typename Strides,
+              typename = std::enable_if_t<
+                  std::is_convertible_v<ck_tile::ranges::range_value_t<Lengths>, std::size_t> &&
+                  std::is_convertible_v<ck_tile::ranges::range_value_t<Strides>, std::size_t>>>
+    HostTensorDescriptor(const Lengths& lens, const Strides& strides)
+        : mLens(lens.begin(), lens.end()), mStrides(strides.begin(), strides.end())
+    {
+    }
+
+    std::size_t get_num_of_dimension() const { return mLens.size(); }
+    std::size_t get_element_size() const
+    {
+        assert(mLens.size() == mStrides.size());
+        return std::accumulate(
+            mLens.begin(), mLens.end(), std::size_t{1}, std::multiplies<std::size_t>());
+    }
+    std::size_t get_element_space_size() const
+    {
+        std::size_t space = 1;
+        for(std::size_t i = 0; i < mLens.size(); ++i)
+        {
+            if(mLens[i] == 0)
+                continue;
+
+            space += (mLens[i] - 1) * mStrides[i];
+        }
+        return space;
+    }
+
+    std::size_t get_length(std::size_t dim) const { return mLens[dim]; }
+
+    const std::vector<std::size_t>& get_lengths() const { return mLens; }
+
+    std::size_t get_stride(std::size_t dim) const { return mStrides[dim]; }
+
+    const std::vector<std::size_t>& get_strides() const { return mStrides; }
+
+    template <typename... Is>
+    std::size_t GetOffsetFromMultiIndex(Is... is) const
+    {
+        assert(sizeof...(Is) == this->get_num_of_dimension());
+        std::initializer_list<std::size_t> iss{static_cast<std::size_t>(is)...};
+        return std::inner_product(iss.begin(), iss.end(), mStrides.begin(), std::size_t{0});
+    }
+
+    std::size_t GetOffsetFromMultiIndex(std::vector<std::size_t> iss) const
+    {
+        return std::inner_product(iss.begin(), iss.end(), mStrides.begin(), std::size_t{0});
+    }
+
+    friend std::ostream& operator<<(std::ostream& os, const HostTensorDescriptor& desc)
+    {
+        os << "dim " << desc.get_num_of_dimension() << ", ";
+
+        os << "lengths {";
+        LogRange(os, desc.get_lengths(), ", ");
+        os << "}, ";
+
+        os << "strides {";
+        LogRange(os, desc.get_strides(), ", ");
+        os << "}";
+
+        return os;
+    }
+
+    private:
+    std::vector<std::size_t> mLens;
+    std::vector<std::size_t> mStrides;
+};
+
+template <typename New2Old>
+CK_TILE_HOST HostTensorDescriptor transpose_host_tensor_descriptor_given_new2old(
+    const HostTensorDescriptor& a, const New2Old& new2old)
+{
+    std::vector<std::size_t> new_lengths(a.get_num_of_dimension());
+    std::vector<std::size_t> new_strides(a.get_num_of_dimension());
+
+    for(std::size_t i = 0; i < a.get_num_of_dimension(); i++)
+    {
+        new_lengths[i] = a.get_lengths()[new2old[i]];
+        new_strides[i] = a.get_strides()[new2old[i]];
+    }
+
+    return HostTensorDescriptor(new_lengths, new_strides);
+}
+
+template <typename F, typename... Xs>
+struct ParallelTensorFunctor
+{
+    F mF;
+    static constexpr std::size_t NDIM = sizeof...(Xs);
+    std::array<std::size_t, NDIM> mLens;
+    std::array<std::size_t, NDIM> mStrides;
+    std::size_t mN1d;
+
+    ParallelTensorFunctor(F f, Xs... xs) : mF(f), mLens({static_cast<std::size_t>(xs)...})
+    {
+        mStrides.back() = 1;
+        std::partial_sum(mLens.rbegin(),
+                         mLens.rend() - 1,
+                         mStrides.rbegin() + 1,
+                         std::multiplies<std::size_t>());
+        mN1d = mStrides[0] * mLens[0];
+    }
+
+    std::array<std::size_t, NDIM> GetNdIndices(std::size_t i) const
+    {
+        std::array<std::size_t, NDIM> indices;
+
+        for(std::size_t idim = 0; idim < NDIM; ++idim)
+        {
+            indices[idim] = i / mStrides[idim];
+            i -= indices[idim] * mStrides[idim];
+        }
+
+        return indices;
+    }
+
+    void operator()(std::size_t num_thread = 1) const
+    {
+        std::size_t work_per_thread = (mN1d + num_thread - 1) / num_thread;
+
+        std::vector<joinable_thread> threads(num_thread);
+
+        for(std::size_t it = 0; it < num_thread; ++it)
+        {
+            std::size_t iw_begin = it * work_per_thread;
+            std::size_t iw_end   = std::min((it + 1) * work_per_thread, mN1d);
+
+            auto f = [this, iw_begin, iw_end] {
+                for(std::size_t iw = iw_begin; iw < iw_end; ++iw)
+                {
+                    call_f_unpack_args(this->mF, this->GetNdIndices(iw));
+                }
+            };
+            threads[it] = joinable_thread(f);
+        }
+    }
+};
+
+template <typename F, typename... Xs>
+CK_TILE_HOST auto make_ParallelTensorFunctor(F f, Xs... xs)
+{
+    return ParallelTensorFunctor<F, Xs...>(f, xs...);
+}
+
+template <typename T>
+struct HostTensor
+{
+    using Descriptor = HostTensorDescriptor;
+    using Data       = std::vector<T>;
+
+    template <typename X>
+    HostTensor(std::initializer_list<X> lens) : mDesc(lens), mData(get_element_space_size())
+    {
+    }
+
+    template <typename X, typename Y>
+    HostTensor(std::initializer_list<X> lens, std::initializer_list<Y> strides)
+        : mDesc(lens, strides), mData(get_element_space_size())
+    {
+    }
+
+    template <typename Lengths>
+    HostTensor(const Lengths& lens) : mDesc(lens), mData(get_element_space_size())
+    {
+    }
+
+    template <typename Lengths, typename Strides>
+    HostTensor(const Lengths& lens, const Strides& strides)
+        : mDesc(lens, strides), mData(get_element_space_size())
+    {
+    }
+
+    HostTensor(const Descriptor& desc) : mDesc(desc), mData(get_element_space_size()) {}
+
+    template <typename OutT>
+    HostTensor<OutT> CopyAsType() const
+    {
+        HostTensor<OutT> ret(mDesc);
+        std::transform(mData.cbegin(), mData.cend(), ret.mData.begin(), [](auto value) {
+            return ck_tile::type_convert<OutT>(value);
+        });
+        return ret;
+    }
+
+    HostTensor()                  = delete;
+    HostTensor(const HostTensor&) = default;
+    HostTensor(HostTensor&&)      = default;
+
+    ~HostTensor() = default;
+
+    HostTensor& operator=(const HostTensor&) = default;
+    HostTensor& operator=(HostTensor&&) = default;
+
+    template <typename FromT>
+    explicit HostTensor(const HostTensor<FromT>& other) : HostTensor(other.template CopyAsType<T>())
+    {
+    }
+
+    std::size_t get_length(std::size_t dim) const { return mDesc.get_length(dim); }
+
+    decltype(auto) get_lengths() const { return mDesc.get_lengths(); }
+
+    std::size_t get_stride(std::size_t dim) const { return mDesc.get_stride(dim); }
+
+    decltype(auto) get_strides() const { return mDesc.get_strides(); }
+
+    std::size_t get_num_of_dimension() const { return mDesc.get_num_of_dimension(); }
+
+    std::size_t get_element_size() const { return mDesc.get_element_size(); }
+
+    std::size_t get_element_space_size() const
+    {
+        constexpr index_t PackedSize = ck_tile::numeric_traits<remove_cvref_t<T>>::PackedSize;
+        return mDesc.get_element_space_size() / PackedSize;
+    }
+
+    std::size_t get_element_space_size_in_bytes() const
+    {
+        return sizeof(T) * get_element_space_size();
+    }
+
+    // void SetZero() { ck_tile::ranges::fill<T>(mData, 0); }
+    void SetZero() { std::fill(mData.begin(), mData.end(), 0); }
+
+    template <typename F>
+    void ForEach_impl(F&& f, std::vector<size_t>& idx, size_t rank)
+    {
+        if(rank == mDesc.get_num_of_dimension())
+        {
+            f(*this, idx);
+            return;
+        }
+        // else
+        for(size_t i = 0; i < mDesc.get_lengths()[rank]; i++)
+        {
+            idx[rank] = i;
+            ForEach_impl(std::forward<F>(f), idx, rank + 1);
+        }
+    }
+
+    template <typename F>
+    void ForEach(F&& f)
+    {
+        std::vector<size_t> idx(mDesc.get_num_of_dimension(), 0);
+        ForEach_impl(std::forward<F>(f), idx, size_t(0));
+    }
+
+    template <typename F>
+    void ForEach_impl(const F&& f, std::vector<size_t>& idx, size_t rank) const
+    {
+        if(rank == mDesc.get_num_of_dimension())
+        {
+            f(*this, idx);
+            return;
+        }
+        // else
+        for(size_t i = 0; i < mDesc.get_lengths()[rank]; i++)
+        {
+            idx[rank] = i;
+            ForEach_impl(std::forward<const F>(f), idx, rank + 1);
+        }
+    }
+
+    template <typename F>
+    void ForEach(const F&& f) const
+    {
+        std::vector<size_t> idx(mDesc.get_num_of_dimension(), 0);
+        ForEach_impl(std::forward<const F>(f), idx, size_t(0));
+    }
+
+    template <typename G>
+    void GenerateTensorValue(G g, std::size_t num_thread = 1)
+    {
+        switch(mDesc.get_num_of_dimension())
+        {
+        case 1: {
+            auto f = [&](auto i) { (*this)(i) = g(i); };
+            make_ParallelTensorFunctor(f, mDesc.get_lengths()[0])(num_thread);
+            break;
+        }
+        case 2: {
+            auto f = [&](auto i0, auto i1) { (*this)(i0, i1) = g(i0, i1); };
+            make_ParallelTensorFunctor(f, mDesc.get_lengths()[0], mDesc.get_lengths()[1])(
+                num_thread);
+            break;
+        }
+        case 3: {
+            auto f = [&](auto i0, auto i1, auto i2) { (*this)(i0, i1, i2) = g(i0, i1, i2); };
+            make_ParallelTensorFunctor(f,
+                                       mDesc.get_lengths()[0],
+                                       mDesc.get_lengths()[1],
+                                       mDesc.get_lengths()[2])(num_thread);
+            break;
+        }
+        case 4: {
+            auto f = [&](auto i0, auto i1, auto i2, auto i3) {
+                (*this)(i0, i1, i2, i3) = g(i0, i1, i2, i3);
+            };
+            make_ParallelTensorFunctor(f,
+                                       mDesc.get_lengths()[0],
+                                       mDesc.get_lengths()[1],
+                                       mDesc.get_lengths()[2],
+                                       mDesc.get_lengths()[3])(num_thread);
+            break;
+        }
+        case 5: {
+            auto f = [&](auto i0, auto i1, auto i2, auto i3, auto i4) {
+                (*this)(i0, i1, i2, i3, i4) = g(i0, i1, i2, i3, i4);
+            };
+            make_ParallelTensorFunctor(f,
+                                       mDesc.get_lengths()[0],
+                                       mDesc.get_lengths()[1],
+                                       mDesc.get_lengths()[2],
+                                       mDesc.get_lengths()[3],
+                                       mDesc.get_lengths()[4])(num_thread);
+            break;
+        }
+        case 6: {
+            auto f = [&](auto i0, auto i1, auto i2, auto i3, auto i4, auto i5) {
+                (*this)(i0, i1, i2, i3, i4, i5) = g(i0, i1, i2, i3, i4, i5);
+            };
+            make_ParallelTensorFunctor(f,
+                                       mDesc.get_lengths()[0],
+                                       mDesc.get_lengths()[1],
+                                       mDesc.get_lengths()[2],
+                                       mDesc.get_lengths()[3],
+                                       mDesc.get_lengths()[4],
+                                       mDesc.get_lengths()[5])(num_thread);
+            break;
+        }
+        default: throw std::runtime_error("unspported dimension");
+        }
+    }
+
+    template <typename... Is>
+    std::size_t GetOffsetFromMultiIndex(Is... is) const
+    {
+        constexpr index_t PackedSize = ck_tile::numeric_traits<remove_cvref_t<T>>::PackedSize;
+        return mDesc.GetOffsetFromMultiIndex(is...) / PackedSize;
+    }
+
+    template <typename... Is>
+    T& operator()(Is... is)
+    {
+        return mData[GetOffsetFromMultiIndex(is...)];
+    }
+
+    template <typename... Is>
+    const T& operator()(Is... is) const
+    {
+        return mData[GetOffsetFromMultiIndex(is...)];
+    }
+
+    T& operator()(std::vector<std::size_t> idx) { return mData[GetOffsetFromMultiIndex(idx)]; }
+
+    const T& operator()(std::vector<std::size_t> idx) const
+    {
+        return mData[GetOffsetFromMultiIndex(idx)];
+    }
+
+    HostTensor<T> transpose(std::vector<size_t> axes = {}) const
+    {
+        if(axes.empty())
+        {
+            axes.resize(this->get_num_of_dimension());
+            std::iota(axes.rbegin(), axes.rend(), 0);
+        }
+        if(axes.size() != mDesc.get_num_of_dimension())
+        {
+            throw std::runtime_error(
+                "HostTensor::transpose(): size of axes must match tensor dimension");
+        }
+        std::vector<size_t> tlengths, tstrides;
+        for(const auto& axis : axes)
+        {
+            tlengths.push_back(get_lengths()[axis]);
+            tstrides.push_back(get_strides()[axis]);
+        }
+        HostTensor<T> ret(*this);
+        ret.mDesc = HostTensorDescriptor(tlengths, tstrides);
+        return ret;
+    }
+
+    HostTensor<T> transpose(std::vector<size_t> axes = {})
+    {
+        return const_cast<HostTensor<T> const*>(this)->transpose(axes);
+    }
+
+    typename Data::iterator begin() { return mData.begin(); }
+
+    typename Data::iterator end() { return mData.end(); }
+
+    typename Data::pointer data() { return mData.data(); }
+
+    typename Data::const_iterator begin() const { return mData.begin(); }
+
+    typename Data::const_iterator end() const { return mData.end(); }
+
+    typename Data::const_pointer data() const { return mData.data(); }
+
+    typename Data::size_type size() const { return mData.size(); }
+
+    // return a slice of this tensor
+    // for simplicity we just copy the data and return a new tensor
+    auto slice(std::vector<size_t> s_begin, std::vector<size_t> s_end) const
+    {
+        assert(s_begin.size() == s_end.size());
+        assert(s_begin.size() == get_num_of_dimension());
+
+        std::vector<size_t> s_len(s_begin.size());
+        std::transform(
+            s_end.begin(), s_end.end(), s_begin.begin(), s_len.begin(), std::minus<size_t>{});
+        HostTensor<T> sliced_tensor(s_len);
+
+        sliced_tensor.ForEach([&](auto& self, auto idx) {
+            std::vector<size_t> src_idx(idx.size());
+            std::transform(
+                idx.begin(), idx.end(), s_begin.begin(), src_idx.begin(), std::plus<size_t>{});
+            self(idx) = operator()(src_idx);
+        });
+
+        return sliced_tensor;
+    }
+
+    template <typename U = T>
+    auto AsSpan() const
+    {
+        constexpr std::size_t FromSize = sizeof(T);
+        constexpr std::size_t ToSize   = sizeof(U);
+
+        using Element = std::add_const_t<std::remove_reference_t<U>>;
+        return ck_tile::span<Element>{reinterpret_cast<Element*>(data()),
+                                      size() * FromSize / ToSize};
+    }
+
+    template <typename U = T>
+    auto AsSpan()
+    {
+        constexpr std::size_t FromSize = sizeof(T);
+        constexpr std::size_t ToSize   = sizeof(U);
+
+        using Element = std::remove_reference_t<U>;
+        return ck_tile::span<Element>{reinterpret_cast<Element*>(data()),
+                                      size() * FromSize / ToSize};
+    }
+
+    friend std::ostream& operator<<(std::ostream& os, const HostTensor<T>& t)
+    {
+        os << t.mDesc;
+        os << "[";
+        for(typename Data::size_type idx = 0; idx < t.mData.size(); ++idx)
+        {
+            if(0 < idx)
+            {
+                os << ", ";
+            }
+            if constexpr(std::is_same_v<T, bf16_t> || std::is_same_v<T, fp16_t>)
+            {
+                os << type_convert<float>(t.mData[idx]) << " #### ";
+            }
+            else
+            {
+                os << t.mData[idx];
+            }
+        }
+        os << "]";
+        return os;
+    }
+
+    // read data from a file, as dtype
+    // the file could dumped from torch as (targeting tensor is t here)
+    // numpy.savetxt("f.txt", t.view(-1).numpy())
+    // numpy.savetxt("f.txt", t.cpu().view(-1).numpy()) # from cuda to cpu to save
+    // numpy.savetxt("f.txt", t.cpu().view(-1).numpy(), fmt="%d")   # save as int
+    // will output f.txt, each line is a value
+    // dtype=float or int, internally will cast to real type
+    void loadtxt(std::string file_name, std::string dtype = "float")
+    {
+        std::ifstream file(file_name);
+
+        if(file.is_open())
+        {
+            std::string line;
+
+            index_t cnt = 0;
+            while(std::getline(file, line))
+            {
+                if(cnt >= static_cast<index_t>(mData.size()))
+                {
+                    throw std::runtime_error(std::string("data read from file:") + file_name +
+                                             " is too big");
+                }
+
+                if(dtype == "float")
+                {
+                    mData[cnt] = type_convert<T>(std::stof(line));
+                }
+                else if(dtype == "int" || dtype == "int32")
+                {
+                    mData[cnt] = type_convert<T>(std::stoi(line));
+                }
+                cnt++;
+            }
+            file.close();
+            if(cnt < static_cast<index_t>(mData.size()))
+            {
+                std::cerr << "Warning! reading from file:" << file_name
+                          << ", does not match the size of this tensor" << std::endl;
+            }
+        }
+        else
+        {
+            // Print an error message to the standard error
+            // stream if the file cannot be opened.
+            throw std::runtime_error(std::string("unable to open file:") + file_name);
+        }
+    }
+
+    // can save to a txt file and read from torch as:
+    // torch.from_numpy(np.loadtxt('f.txt', dtype=np.int32/np.float32...)).view([...]).contiguous()
+    void savetxt(std::string file_name, std::string dtype = "float")
+    {
+        std::ofstream file(file_name);
+
+        if(file.is_open())
+        {
+            for(auto& itm : mData)
+            {
+                if(dtype == "float")
+                    file << type_convert<float>(itm) << std::endl;
+                else if(dtype == "int")
+                    file << type_convert<int>(itm) << std::endl;
+                else
+                    // TODO: we didn't implement operator<< for all custom
+                    // data types, here fall back to float in case compile error
+                    file << type_convert<float>(itm) << std::endl;
+            }
+            file.close();
+        }
+        else
+        {
+            // Print an error message to the standard error
+            // stream if the file cannot be opened.
+            throw std::runtime_error(std::string("unable to open file:") + file_name);
+        }
+    }
+
+    Descriptor mDesc;
+    Data mData;
+};
+
+template <bool is_row_major>
+auto host_tensor_descriptor(std::size_t row,
+                            std::size_t col,
+                            std::size_t stride,
+                            bool_constant<is_row_major>)
+{
+    using namespace ck_tile::literals;
+
+    if constexpr(is_row_major)
+    {
+        return HostTensorDescriptor({row, col}, {stride, 1_uz});
+    }
+    else
+    {
+        return HostTensorDescriptor({row, col}, {1_uz, stride});
+    }
+}
+template <bool is_row_major>
+auto get_default_stride(std::size_t row,
+                        std::size_t col,
+                        std::size_t stride,
+                        bool_constant<is_row_major>)
+{
+    if(stride == 0)
+    {
+        if constexpr(is_row_major)
+        {
+            return col;
+        }
+        else
+        {
+            return row;
+        }
+    }
+    else
+        return stride;
+}
+
+} // namespace ck_tile

include/ck_tile/host/joinable_thread.hpp

@@ -0,0 +1,27 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <thread>
+#include <utility>
+
+namespace ck_tile {
+
+struct joinable_thread : std::thread
+{
+    template <typename... Xs>
+    joinable_thread(Xs&&... xs) : std::thread(std::forward<Xs>(xs)...)
+    {
+    }
+
+    joinable_thread(joinable_thread&&) = default;
+    joinable_thread& operator=(joinable_thread&&) = default;
+
+    ~joinable_thread()
+    {
+        if(this->joinable())
+            this->join();
+    }
+};
+} // namespace ck_tile

include/ck_tile/host/kernel_launch.hpp

@@ -0,0 +1,117 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/host/stream_config.hpp"
+#include "ck_tile/host/hip_check_error.hpp"
+#include "ck_tile/host/timer.hpp"
+#include <hip/hip_runtime.h>
+#include <cstddef>
+
+namespace ck_tile {
+template <int MaxThreadPerBlock, int MinBlockPerCu, typename Kernel, typename... Args>
+#if CK_TILE_USE_LAUNCH_BOUNDS
+__launch_bounds__(MaxThreadPerBlock, MinBlockPerCu)
+#endif
+    __global__ void kentry(Args... args)
+{
+    Kernel{}(args...);
+}
+
+//
+// return a anonymous functor(lambda) to be called later
+// the KernelImpl should be a class without non-static data member, or let's say
+// can be instantiate with "KernelImpl{}"
+//
+// the "static __device__ operator()(some_arg)" is the entry point of KernelImpl
+//
+template <int MaxThreadPerBlock = CK_TILE_MAX_THREAD_PER_BLOCK,
+          int MinBlockPerCu     = CK_TILE_MIN_BLOCK_PER_CU,
+          typename KernelImpl,
+          typename... Args>
+CK_TILE_HOST auto
+make_kernel(KernelImpl /*f*/, dim3 grid_dim, dim3 block_dim, std::size_t lds_byte, Args... args)
+{
+    const auto kernel = kentry<MaxThreadPerBlock, MinBlockPerCu, KernelImpl, Args...>;
+
+    return [=](const stream_config& s) {
+        kernel<<<grid_dim, block_dim, lds_byte, s.stream_id_>>>(args...);
+    };
+}
+
+template <typename... Callables>
+CK_TILE_HOST void launch_and_check(const stream_config& sc, Callables&&... callables)
+{
+    // abort the sequence in case of intermediate error
+    if(!((static_cast<void>(callables(sc)), hipPeekAtLastError() == hipSuccess) && ...))
+    {
+        HIP_CHECK_ERROR(hipGetLastError());
+    }
+}
+
+// clang-format off
+/*
+ * launch_kernel()
+ *
+ * this is the function to launch arbitrary number of kernels with optional timer(selected by stream_config)
+ * the callables should have signature as "operator()(const stream_config& s){ ... }" to call
+ * 
+ * the simplest way is pass in a lambda function, with "[=](const stream_config& s){ call_your_kernel_here() }"
+ * as signature, for the callable (pay attention to the capture list)
+ * 
+ * e.g.
+ *  ck_tile::launch_kernel(s,
+ *                      [=](const stream_config& s){ hipMemset(ptr, 0, size) },
+ *                      [=](const stream_config& s){ some_kernel<<<grids, blocks>>>(arg); }
+ *                      );
+ * 
+ * if you use ck_tile kernel, or similiar to this style (structure with "static __device__ operator()(...){}")
+ * you can pass your kernel to ck_tile::make_kernel(), which will create a anonymous functor for you,
+ * then pass it to ck_tile::launch_kernel()
+ * 
+ * e.g.
+ *  ck_tile::launch_kernel(s,
+ *                      ck_tile::make_kernel<T0, B0>(kernel_0{}, grids0, blocks0, 0, kargs0),
+ *                      ck_tile::make_kernel<T0, B1>(kernel_1{}, grids1, blocks1, 0, kargs1),
+ *                       ...);
+ **/
+// clang-format on
+template <typename... Callables>
+CK_TILE_HOST float launch_kernel(const stream_config& s, Callables&&... callables)
+{
+    if(!s.time_kernel_)
+    {
+        launch_and_check(s, std::forward<Callables>(callables)...);
+        return 0;
+    }
+
+    auto time_launches = [&](auto timer) {
+        // warmup
+        for(int i = 0; i < s.cold_niters_; i++)
+        {
+            launch_and_check(s, std::forward<Callables>(callables)...);
+        }
+
+        timer.start(s.stream_id_);
+        for(int i = 0; i < s.nrepeat_; i++)
+        {
+            launch_and_check(s, std::forward<Callables>(callables)...);
+        }
+        timer.stop(s.stream_id_);
+
+        return timer.duration() / s.nrepeat_;
+    };
+
+    if(s.is_gpu_timer_)
+    {
+        return time_launches(gpu_timer{});
+    }
+    else
+    {
+        return time_launches(cpu_timer{});
+    }
+}
+
+} // namespace ck_tile

include/ck_tile/host/ranges.hpp

@@ -0,0 +1,69 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <iterator>
+#include <type_traits>
+#include <utility>
+
+// ranges implementation are not intented to be used by user
+// TODO: do we need this?
+namespace ck_tile {
+
+template <typename T>
+using iter_value_t = typename std::iterator_traits<remove_cvref_t<T>>::value_type;
+
+template <typename T>
+using iter_reference_t = decltype(*std::declval<T&>());
+
+template <typename T>
+using iter_difference_t = typename std::iterator_traits<remove_cvref_t<T>>::difference_type;
+
+namespace ranges {
+template <typename R>
+using iterator_t = decltype(std::begin(std::declval<R&>()));
+
+template <typename R>
+using sentinel_t = decltype(std::end(std::declval<R&>()));
+
+template <typename R>
+using range_size_t = decltype(std::size(std::declval<R&>()));
+
+template <typename R>
+using range_difference_t = ck_tile::iter_difference_t<ranges::iterator_t<R>>;
+
+template <typename R>
+using range_value_t = iter_value_t<ranges::iterator_t<R>>;
+
+template <typename R>
+using range_reference_t = iter_reference_t<ranges::iterator_t<R>>;
+
+template <typename T, typename = void>
+struct is_range : std::false_type
+{
+};
+
+template <typename T>
+struct is_range<
+    T,
+    std::void_t<decltype(std::begin(std::declval<T&>())), decltype(std::end(std::declval<T&>()))>>
+    : std::true_type
+{
+};
+
+template <typename T>
+inline constexpr bool is_range_v = is_range<T>::value;
+
+template <typename T, typename = void>
+struct is_sized_range : std::false_type
+{
+};
+
+template <typename T>
+struct is_sized_range<T, std::void_t<decltype(std::size(std::declval<T&>()))>>
+    : std::bool_constant<is_range_v<T>>
+{
+};
+} // namespace ranges
+} // namespace ck_tile

include/ck_tile/host/reference/reference_batched_dropout.hpp

@@ -0,0 +1,33 @@
+// 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/host/host_tensor.hpp"
+#include <thread>
+
+namespace ck_tile {
+
+template <typename DataType, typename RandValOutputDataType>
+CK_TILE_HOST void reference_batched_dropout(HostTensor<DataType>& in_out_b_m_n,
+                                            const HostTensor<RandValOutputDataType>& randval_b_m_n,
+                                            const uint8_t& p_undrop_in_uint8_t,
+                                            const float scale)
+{
+    const int N = in_out_b_m_n.mDesc.get_lengths()[2];
+    auto f      = [&](auto batch, auto m) {
+        for(int n = 0; n < N; ++n)
+        {
+            float tmp = ck_tile::type_convert<float>(in_out_b_m_n(batch, m, n)) * scale;
+            in_out_b_m_n(batch, m, n) = randval_b_m_n(batch, m, n) <= p_undrop_in_uint8_t
+                                                 ? ck_tile::type_convert<DataType>(tmp)
+                                                 : DataType(0);
+        }
+    };
+
+    make_ParallelTensorFunctor(
+        f, randval_b_m_n.mDesc.get_lengths()[0], randval_b_m_n.mDesc.get_lengths()[1])(
+        std::thread::hardware_concurrency());
+}
+} // namespace ck_tile

include/ck_tile/host/reference/reference_batched_elementwise.hpp

@@ -0,0 +1,64 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core.hpp"
+#include "ck_tile/host/host_tensor.hpp"
+#include <thread>
+
+namespace ck_tile {
+
+template <typename ADataType,
+          typename BDataType,
+          typename AccDataType,
+          typename CDataType,
+          typename AElementOp      = ck_tile::identity,
+          typename BElementOp      = ck_tile::identity,
+          typename BinaryElementOp = ck_tile::plus<AccDataType>>
+CK_TILE_HOST void reference_batched_elementwise(const HostTensor<ADataType>& a_b_m_n,
+                                                const HostTensor<BDataType>& b_b_m_n,
+                                                HostTensor<CDataType>& c_b_m_n,
+                                                const AElementOp& a_element_op           = {},
+                                                const BElementOp& b_element_op           = {},
+                                                const BinaryElementOp& binary_element_op = {})
+{
+    const ck_tile::index_t N = c_b_m_n.mDesc.get_lengths()[2];
+
+    const bool broadcast_a_dim_b = (a_b_m_n.get_lengths()[0] == 1);
+    const bool broadcast_a_dim_m = (a_b_m_n.get_lengths()[1] == 1);
+    const bool broadcast_a_dim_n = (a_b_m_n.get_lengths()[2] == 1);
+
+    const bool broadcast_b_dim_b = (b_b_m_n.get_lengths()[0] == 1);
+    const bool broadcast_b_dim_m = (b_b_m_n.get_lengths()[1] == 1);
+    const bool broadcast_b_dim_n = (b_b_m_n.get_lengths()[2] == 1);
+
+    auto f = [&](auto batch, auto m) {
+        for(ck_tile::index_t n = 0; n < N; ++n)
+        {
+            AccDataType v_a{};
+            {
+                ck_tile::index_t i_b = (broadcast_a_dim_b ? 0 : batch);
+                ck_tile::index_t i_m = (broadcast_a_dim_m ? 0 : m);
+                ck_tile::index_t i_n = (broadcast_a_dim_n ? 0 : n);
+
+                v_a = ck_tile::type_convert<AccDataType>(a_element_op(a_b_m_n(i_b, i_m, i_n)));
+            }
+
+            AccDataType v_b{};
+            {
+                ck_tile::index_t i_b = (broadcast_b_dim_b ? 0 : batch);
+                ck_tile::index_t i_m = (broadcast_b_dim_m ? 0 : m);
+                ck_tile::index_t i_n = (broadcast_b_dim_n ? 0 : n);
+
+                v_b = ck_tile::type_convert<AccDataType>(b_element_op(b_b_m_n(i_b, i_m, i_n)));
+            }
+
+            c_b_m_n(batch, m, n) = ck_tile::type_convert<CDataType>(binary_element_op(v_a, v_b));
+        }
+    };
+
+    make_ParallelTensorFunctor(f, c_b_m_n.mDesc.get_lengths()[0], c_b_m_n.mDesc.get_lengths()[1])(
+        std::thread::hardware_concurrency());
+}
+} // namespace ck_tile

include/ck_tile/host/reference/reference_batched_gemm.hpp

@@ -0,0 +1,50 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core.hpp"
+#include "ck_tile/host/host_tensor.hpp"
+#include <thread>
+
+namespace ck_tile {
+
+template <typename ADataType,
+          typename BDataType,
+          typename AccDataType,
+          typename CDataType,
+          typename AElementOp   = ck_tile::identity,
+          typename BElementOp   = ck_tile::identity,
+          typename ACCElementOp = ck_tile::identity>
+CK_TILE_HOST void reference_batched_gemm(const HostTensor<ADataType>& a_b_m_k,
+                                         const HostTensor<BDataType>& b_b_n_k,
+                                         HostTensor<CDataType>& c_b_m_n,
+                                         const AElementOp& a_element_op     = {},
+                                         const BElementOp& b_element_op     = {},
+                                         const ACCElementOp& acc_element_op = {})
+{
+    const int N = b_b_n_k.mDesc.get_lengths()[1];
+    const int K = b_b_n_k.mDesc.get_lengths()[2];
+
+    auto f = [&](auto batch, auto m) {
+        for(int n = 0; n < N; ++n)
+        {
+            AccDataType v_acc = 0;
+
+            for(int k = 0; k < K; ++k)
+            {
+                ADataType v_a = a_element_op(a_b_m_k(batch, m, k));
+                BDataType v_b = b_element_op(b_b_n_k(batch, n, k));
+
+                v_acc += ck_tile::type_convert<AccDataType>(v_a) *
+                         ck_tile::type_convert<AccDataType>(v_b);
+            }
+
+            c_b_m_n(batch, m, n) = ck_tile::type_convert<CDataType>(acc_element_op(v_acc));
+        }
+    };
+
+    make_ParallelTensorFunctor(f, c_b_m_n.mDesc.get_lengths()[0], c_b_m_n.mDesc.get_lengths()[1])(
+        std::thread::hardware_concurrency());
+}
+} // namespace ck_tile

include/ck_tile/host/reference/reference_batched_masking.hpp

@@ -0,0 +1,32 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core.hpp"
+#include "ck_tile/host/host_tensor.hpp"
+#include <thread>
+
+namespace ck_tile {
+
+template <typename CDataType, typename MaskingType>
+CK_TILE_HOST void reference_batched_masking(HostTensor<CDataType>& c_b_m_n, const MaskingType& mask)
+{
+    const int M = c_b_m_n.mDesc.get_lengths()[1];
+    const int N = c_b_m_n.mDesc.get_lengths()[2];
+
+    auto f = [&](auto batch) {
+        for(int n = 0; n < N; ++n)
+        {
+            for(int m = 0; m < M; ++m)
+            {
+                if(mask.IsOutOfBound(m, n))
+                    c_b_m_n(batch, m, n) = -ck_tile::numeric<CDataType>::infinity();
+            }
+        }
+    };
+
+    make_ParallelTensorFunctor(f,
+                               c_b_m_n.mDesc.get_lengths()[0])(std::thread::hardware_concurrency());
+}
+} // namespace ck_tile

include/ck_tile/host/reference/reference_batched_rotary_position_embedding.hpp

@@ -0,0 +1,73 @@
+// 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/host/host_tensor.hpp"
+
+#include <cassert>
+#include <thread>
+
+namespace ck_tile {
+
+template <typename DataType, typename ComputeDataType = float>
+CK_TILE_HOST void reference_batched_rotary_position_embedding(const HostTensor<DataType>& input_bsd,
+                                                              const HostTensor<DataType>& cos_sd,
+                                                              const HostTensor<DataType>& sin_sd,
+                                                              bool interleaved,
+                                                              HostTensor<DataType>& output_bsd,
+                                                              bool use_1_row_sin_cos = false)
+{
+    assert(cos_sd.get_num_of_dimension() == 2 && sin_sd.get_num_of_dimension() == 2);
+    assert(cos_sd.get_length(0) == sin_sd.get_length(0) &&
+           cos_sd.get_length(1) == sin_sd.get_length(1));
+
+    const index_t rotary_dim = cos_sd.get_length(1) * 2;
+    assert(static_cast<std::size_t>(rotary_dim) <= input_bsd.get_length(2));
+
+    output_bsd.ForEach([&](auto& self, auto i) {
+        const index_t i_d = i[2];
+        if(rotary_dim <= i_d)
+        {
+            self(i) = input_bsd(i);
+            return;
+        }
+        assert(i_d < rotary_dim);
+
+        const index_t i_s         = i[1];
+        const index_t i_s_cos_sin = (use_1_row_sin_cos ? 0 : i_s);
+
+        const ComputeDataType cos = type_convert<ComputeDataType>(
+            interleaved ? cos_sd(i_s_cos_sin, i_d / 2)
+                        : cos_sd(i_s_cos_sin, i_d % cos_sd.get_length(1)));
+        const ComputeDataType sin = type_convert<ComputeDataType>(
+            interleaved ? sin_sd(i_s_cos_sin, i_d / 2)
+                        : sin_sd(i_s_cos_sin, i_d % sin_sd.get_length(1)));
+
+        const ComputeDataType half_rotated_input = [&] {
+            const index_t i_b = i[0];
+
+            if(interleaved)
+            {
+                const bool is_even         = (i_d % 2 == 0);
+                const index_t pos          = i_d + (is_even ? 1 : -1);
+                const ComputeDataType sign = (is_even ? -1 : 1);
+                return sign * type_convert<ComputeDataType>(input_bsd(i_b, i_s, pos));
+            }
+            else
+            {
+                const index_t half_rdim    = (rotary_dim / 2);
+                const index_t pos          = (i_d + half_rdim) % rotary_dim;
+                const ComputeDataType sign = (pos < half_rdim ? 1 : -1);
+                return sign * type_convert<ComputeDataType>(input_bsd(i_b, i_s, pos));
+            }
+        }();
+        ComputeDataType result =
+            type_convert<ComputeDataType>(input_bsd(i)) * cos + half_rotated_input * sin;
+
+        self(i) = type_convert<DataType>(result);
+    });
+}
+
+} // namespace ck_tile

include/ck_tile/host/reference/reference_batched_softmax.hpp

@@ -0,0 +1,71 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core.hpp"
+#include "ck_tile/host/host_tensor.hpp"
+#include <thread>
+
+namespace ck_tile {
+
+template <typename ADataType,
+          typename CompDataType,
+          typename BDataType,
+          typename CompElementOp = ck_tile::identity>
+CK_TILE_HOST void reference_batched_softmax(
+    const HostTensor<ADataType>& a_b_m_n,
+    HostTensor<BDataType>& b_b_m_n,
+    const CompElementOp& comp_element_op                                    = {},
+    std::optional<std::reference_wrapper<HostTensor<CompDataType>>> lse_b_m = std::nullopt)
+{
+    const int N = a_b_m_n.mDesc.get_lengths()[2];
+
+    auto f = [&](auto batch, auto m) {
+        CompDataType v_max = -ck_tile::numeric<CompDataType>::infinity();
+
+        // max
+        for(int n = 0; n < N; ++n)
+        {
+            const CompDataType v_a = ck_tile::type_convert<CompDataType>(a_b_m_n(batch, m, n));
+
+            v_max = v_max < v_a ? v_a : v_max;
+        }
+
+        CompDataType v_exp_sum = 0;
+        // validate v_max if all the elements within a row are -INF
+        if(std::isinf(v_max) && v_max < 0)
+        {
+            v_max = ck_tile::type_convert<CompDataType>(0.f);
+        }
+
+        // sum
+        for(int n = 0; n < N; ++n)
+        {
+            const CompDataType v_a = ck_tile::type_convert<CompDataType>(a_b_m_n(batch, m, n));
+
+            v_exp_sum += ck_tile::exp(v_a - v_max);
+        }
+
+        // if sum is zero(masked), or nan/inf(other computation error), don't do divide
+        CompDataType inv_sum = (v_exp_sum == 0.f ? 1.f : 1.f / v_exp_sum);
+
+        // elementwise
+        for(int n = 0; n < N; ++n)
+        {
+            const CompDataType v_a = ck_tile::type_convert<CompDataType>(a_b_m_n(batch, m, n));
+            const CompDataType v_b = ck_tile::exp(v_a - v_max) * inv_sum;
+
+            b_b_m_n(batch, m, n) = ck_tile::type_convert<BDataType>(comp_element_op(v_b));
+        }
+        // lse
+        if(lse_b_m)
+        {
+            lse_b_m->get()(batch, m) = v_max + ck_tile::log(v_exp_sum);
+        }
+    };
+
+    make_ParallelTensorFunctor(f, b_b_m_n.mDesc.get_lengths()[0], b_b_m_n.mDesc.get_lengths()[1])(
+        std::thread::hardware_concurrency());
+}
+} // namespace ck_tile

include/ck_tile/host/reference/reference_batched_transpose.hpp

@@ -0,0 +1,59 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core.hpp"
+#include "ck_tile/host/host_tensor.hpp"
+#include <thread>
+
+namespace ck_tile {
+
+template <typename Type>
+CK_TILE_HOST void reference_batched_transpose(const HostTensor<Type>& x,
+                                              HostTensor<Type>& y,
+                                              std::string layout_in  = "NCHW",
+                                              std::string layout_out = "NHWC")
+{
+    const int N = x.mDesc.get_lengths()[0];
+
+    auto f = [&](auto batch) {
+        if(layout_in == "NCHW" && layout_out == "NHWC")
+        {
+            const int C = x.mDesc.get_lengths()[1];
+            const int H = x.mDesc.get_lengths()[2];
+            const int W = x.mDesc.get_lengths()[3];
+            for(int c = 0; c < C; ++c)
+            {
+                for(int h = 0; h < H; ++h)
+                {
+                    for(int w = 0; w < W; ++w)
+                    {
+                        Type v_x          = x(batch, c, h, w);
+                        y(batch, h, w, c) = v_x;
+                    }
+                }
+            }
+        }
+        else if(layout_in == "NHWC" && layout_out == "NCHW")
+        {
+            const int H = x.mDesc.get_lengths()[1];
+            const int W = x.mDesc.get_lengths()[2];
+            const int C = x.mDesc.get_lengths()[3];
+            for(int h = 0; h < H; ++h)
+            {
+                for(int w = 0; w < W; ++w)
+                {
+                    for(int c = 0; c < C; ++c)
+                    {
+                        Type v_x          = x(batch, h, w, c);
+                        y(batch, c, h, w) = v_x;
+                    }
+                }
+            }
+        }
+    };
+
+    make_ParallelTensorFunctor(f, N)(std::thread::hardware_concurrency());
+}
+} // namespace ck_tile

include/ck_tile/host/reference/reference_elementwise.hpp

@@ -0,0 +1,47 @@
+// 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/host/host_tensor.hpp"
+#include <thread>
+
+namespace ck_tile {
+template <typename ADataType, typename BDataType, typename ComputeDataType, typename ElementOp>
+CK_TILE_HOST void reference_unary_elementwise(const HostTensor<ADataType>& a,
+                                              HostTensor<BDataType>& b,
+                                              ElementOp element_op)
+{
+    // TODO: imeplement gpu version reference function
+    auto f = [&](auto i) {
+        auto v_a   = type_convert<ComputeDataType>(a.mData[i]);
+        auto v_b   = element_op(v_a);
+        b.mData[i] = ck_tile::type_convert<BDataType>(v_b);
+    };
+
+    make_ParallelTensorFunctor(f, b.get_element_space_size())(std::thread::hardware_concurrency());
+}
+
+template <typename ADataType,
+          typename BDataType,
+          typename CDataType,
+          typename ComputeDataType,
+          typename ElementOp>
+CK_TILE_HOST void reference_binary_elementwise(const HostTensor<ADataType>& a,
+                                               const HostTensor<BDataType>& b,
+                                               HostTensor<CDataType>& c,
+                                               ElementOp element_op)
+{
+    // TODO: imeplement gpu version reference function
+    auto f = [&](auto i) {
+        auto v_a   = type_convert<ComputeDataType>(a.mData[i]);
+        auto v_b   = type_convert<ComputeDataType>(b.mData[i]);
+        auto v_c   = element_op(v_a, v_b);
+        c.mData[i] = ck_tile::type_convert<CDataType>(v_c);
+    };
+
+    make_ParallelTensorFunctor(f, c.get_element_space_size())(std::thread::hardware_concurrency());
+}
+
+} // namespace ck_tile

include/ck_tile/host/reference/reference_fused_moe.hpp

@@ -0,0 +1,205 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core.hpp"
+#include "ck_tile/host/host_tensor.hpp"
+
+namespace ck_tile {
+// [indexing implementation-1]
+// using M_a as constexpr block_size to partition all tokens into different slices
+// each slice map to one expert, and one expert can have multiple slices
+// e.g. num_experts = 6, topk=3, M_a = 4, input_tokens = 5
+// before sort, topk_ids is : [[0, 3, 5], [2, 3, 5], [1, 3, 5], [1, 2, 3], [1, 3, 5]]
+//                            tok-0      tok-1      tok-2      tok-3      tok-4
+//           topk_weight is : [[a, b, c], [d, e, f], [g, h, i], [j, k, l], [m, n, o]] (some float
+//           number)
+//
+// token_id_per_expert is : [[0], [2, 3, 4], [1, 3], [0, 1, 2, 3, 4], [], [0, 1, 2, 5]]
+//  (only for reference)    exp-0  exp-1     exp-2   exp-3          exp-4  exp-5
+// weight_id_per_expert is: [[a], [g, j, m], [d, k], [b, e, h, l, n], [], [c, f, i, o]]
+//
+// max_num_tokens_padded : topk * input_tokens + num_experts * (M_a - 1)
+// max_num_tokens_padded : topk * input_tokens + num_experts * M_a - topk (updated)
+// * this could be larger than actual, since actual tokens are on GPU
+//
+// sorted_token_ids_ptr   : [0, 6, 6, 6, 2, 3, 4, 6, 1, 3, 6, 6, 0, 1, 2, 3, 4, 6, 6, 6, 6, 6, 6, 6,
+// 0, 1, 2, 5]
+//                          |-  exp-0  -|-  exp-1  -|-  exp-2  -|-      exp-3          -|-  exp-4
+//                          -|-  exp-5  -|
+// sorted_weight_ptr      : [a, *, *, *, g, j, m, *, d, k, *, *, b, e, h, l, n, *, *, *, *, *, *, *,
+// c, f, i, o]
+//
+// * length is max_num_tokens_padded, actual size is num_tokens_post_padded_ptr
+//
+// sorted_expert_ids_ptr  : [0, 1, 2, 3, 3, 4, 5]
+// * length is (max_num_tokens_padded + block_size - 1) / block_size
+///
+// num_tokens_post_padded_ptr : [28]
+// num_sorted_tiles_ptr : [7]
+
+template <typename AccDataType, // you only need to explcitly set this one
+          typename Activation,  // ck_tile::element_wise::Gelu
+          typename ADataType,
+          typename GDataType,
+          typename DDataType,
+          typename ODataType,
+          typename AScaleDataType,
+          typename GScaleDataType,
+          typename DScaleDataType,
+          typename YSmoothScaleDataType,
+          typename TopkWeightDataType,
+          typename IndexDataType>
+void reference_fused_moe(
+    const ck_tile::HostTensor<ADataType>& a_host,       // [tokens, hidden_size]
+    const ck_tile::HostTensor<GDataType>& g_host,       // [experts, interme_size_0, hidden_size]
+    const ck_tile::HostTensor<DDataType>& d_host,       // [experts, hidden_size, interme_size_1]
+    const ck_tile::HostTensor<AScaleDataType>& sa_host, // [tokens, 1],
+    const ck_tile::HostTensor<GScaleDataType>& sg_host, // [experts, 1, interme_size_0]
+    const ck_tile::HostTensor<DScaleDataType>& sd_host, // [experts, 1, hidden_size],
+    const ck_tile::HostTensor<YSmoothScaleDataType>& sy_host,        // [experts, 1, interme_size_0]
+    ck_tile::HostTensor<ODataType>& o_host,                          // [tokens, hidden_size]
+    const ck_tile::HostTensor<IndexDataType>& sorted_token_ids_host, // [max_num_tokens_padded]
+    const ck_tile::HostTensor<TopkWeightDataType>& sorted_weight_host, // [max_num_tokens_padded]
+    const ck_tile::HostTensor<IndexDataType>&
+        sorted_expert_ids_host, // [(max_num_tokens_padded + block_size - 1) / block_size]
+    const ck_tile::HostTensor<IndexDataType>& num_sorted_tiles_host, // [1]
+
+    const ck_tile::HostTensor<IndexDataType>&
+        token_ids_host, // [tokens, topk] --> ugly!!! remove in the future
+
+    ck_tile::index_t block_m,
+    ck_tile::index_t tokens,
+    ck_tile::index_t experts,
+    ck_tile::index_t hidden_size,
+    ck_tile::index_t intermediate_size, // this size is for gate/up/down
+    ck_tile::index_t topk,
+    ck_tile::index_t gate_only)
+{
+    assert(sorted_token_ids_host.get_num_of_dimension() == 1);
+    assert(sorted_weight_host.get_num_of_dimension() == 1);
+    assert(sorted_expert_ids_host.get_num_of_dimension() == 1);
+    assert(num_sorted_tiles_host.get_element_size() == 1);
+    ck_tile::index_t num_sorted_tiles    = num_sorted_tiles_host.mData[0] / block_m;
+    ck_tile::index_t intermediate_size_0 = intermediate_size * (gate_only ? 1 : 2);
+    ck_tile::index_t intermediate_size_1 = intermediate_size;
+
+    ck_tile::HostTensor<AccDataType> out_topk_tokens({tokens, topk, hidden_size});
+
+    int max_num_tokens_padded = topk * tokens + experts * block_m - topk;
+    // assert();
+    auto f = [&](auto i_flatten) {
+        ck_tile::index_t i_tile = i_flatten / block_m;
+        if(i_tile >= num_sorted_tiles)
+            return;
+        ck_tile::index_t i_expert = sorted_expert_ids_host.mData[i_tile];
+
+#if CK_TILE_REFERENCE_MOE_SORTING_MOCK_ID
+        ck_tile::index_t i_token = sorted_token_ids_host.mData[i_flatten];
+        ck_tile::index_t i_topk  = i_token >> 24;
+        i_token &= 0xffffff;
+        if(i_token >= tokens)
+            return;
+        (void)token_ids_host;
+#else
+        // TODO: better remove this in the future, or modify the token_id value
+        auto get_topk_id = [&](ck_tile::index_t token_id_, ck_tile::index_t expert_id_) {
+            for(ck_tile::index_t i_ = 0; i_ < topk; i_++)
+            {
+                if(token_ids_host(token_id_, i_) == expert_id_)
+                    return i_;
+            }
+            throw std::runtime_error("not correct token/expert pair\n");
+            return -1; // TODO: not correct!!
+        };
+        ck_tile::index_t i_token = sorted_token_ids_host.mData[i_flatten];
+        if(i_token >= tokens)
+            return;
+        ck_tile::index_t i_topk = get_topk_id(i_token, i_expert); // TODO: ugly
+#endif
+        auto weight = sorted_weight_host.mData[i_flatten];
+
+        ck_tile::HostTensor<AccDataType> acc_0({1, intermediate_size_0});
+        // first gemm
+        for(ck_tile::index_t i_n = 0; i_n < intermediate_size_0; i_n++)
+        {
+            AccDataType acc = static_cast<AccDataType>(0);
+            for(ck_tile::index_t i_k = 0; i_k < hidden_size; i_k++)
+            {
+                acc += type_convert<AccDataType>(a_host(i_token, i_k)) *
+                       type_convert<AccDataType>(g_host(i_expert, i_n, i_k));
+            }
+            acc_0(0, i_n) = acc;
+            // printf("ie:%2d, it:%3d, in:%d, %f\n", i_expert, i_token, i_n, acc);
+        }
+
+        ck_tile::HostTensor<AccDataType> y({1, intermediate_size_1});
+        if(gate_only)
+        {
+            if(intermediate_size_1 != intermediate_size_0)
+                throw std::runtime_error(
+                    "intermediate_size not correct, 0:" + std::to_string(intermediate_size_0) +
+                    ", 1:" + std::to_string(intermediate_size_1));
+            for(ck_tile::index_t i_n = 0; i_n < intermediate_size_1; i_n++)
+            {
+                Activation{}(y(0, i_n), acc_0(0, i_n));
+                // printf("ie:%2d, it:%3d, in:%d, %f\n", i_expert, i_token, i_n, y(0, i_n));
+            }
+        }
+        else
+        {
+            if(intermediate_size_1 * 2 != intermediate_size_0)
+                throw std::runtime_error(
+                    "intermediate_size not correct, 0:" + std::to_string(intermediate_size_0) +
+                    ", 1:" + std::to_string(intermediate_size_1));
+            for(ck_tile::index_t i_n = 0; i_n < intermediate_size_1; i_n++)
+            {
+                AccDataType tmp;
+                Activation{}(tmp, acc_0(0, i_n));
+                y(0, i_n) = tmp * acc_0(0, i_n + intermediate_size_1); // TODO: elementwise mul
+            }
+        }
+
+        // second gemm, loop along gemm-n
+        ck_tile::HostTensor<AccDataType> acc_1({1, hidden_size});
+        for(ck_tile::index_t i_n = 0; i_n < hidden_size; i_n++)
+        {
+            AccDataType acc = static_cast<AccDataType>(0);
+            for(ck_tile::index_t i_k = 0; i_k < intermediate_size_1; i_k++)
+            {
+                acc += y(0, i_k) * type_convert<AccDataType>(d_host(i_expert, i_n, i_k));
+            }
+            acc_1(0, i_n) = acc * weight; // multiple weight here
+        }
+
+        for(ck_tile::index_t i_n = 0; i_n < hidden_size; i_n++)
+        {
+            out_topk_tokens(i_token, i_topk, i_n) = acc_1(0, i_n);
+        }
+    };
+
+    // make_ParallelTensorFunctor(f, max_num_tokens_padded)(std::thread::hardware_concurrency());
+    make_ParallelTensorFunctor(f, max_num_tokens_padded)(1);
+
+    // reduce
+    auto r = [&](auto i_token) {
+        for(ck_tile::index_t i_n = 0; i_n < hidden_size; i_n++)
+        {
+            AccDataType acc = type_convert<AccDataType>(0);
+            for(ck_tile::index_t i_topk = 0; i_topk < topk; i_topk++)
+            {
+                acc += out_topk_tokens(i_token, i_topk, i_n);
+            }
+            o_host(i_token, i_n) = type_convert<ODataType>(acc);
+        }
+    };
+    make_ParallelTensorFunctor(r, tokens)(std::thread::hardware_concurrency());
+
+    (void)num_sorted_tiles_host;
+    (void)sa_host;
+    (void)sg_host;
+    (void)sd_host;
+    (void)sy_host;
+}
+} // namespace ck_tile

include/ck_tile/host/reference/reference_gemm.hpp

@@ -0,0 +1,211 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2025, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <cstdlib>
+#include <thread>
+
+#include "ck_tile/core.hpp"
+#include "ck_tile/host/host_tensor.hpp"
+
+namespace ck_tile {
+
+template <typename ADataType,
+          typename BDataType,
+          typename AccDataType,
+          typename CDataType,
+          typename AElementOp   = ck_tile::identity,
+          typename BElementOp   = ck_tile::identity,
+          typename ACCElementOp = ck_tile::identity>
+CK_TILE_HOST void reference_gemm(const HostTensor<ADataType>& a_m_k,
+                                 const HostTensor<BDataType>& b_k_n,
+                                 HostTensor<CDataType>& c_m_n,
+                                 const AElementOp& a_element_op     = {},
+                                 const BElementOp& b_element_op     = {},
+                                 const ACCElementOp& acc_element_op = {})
+{
+    const std::size_t M = a_m_k.get_length(0);
+    const std::size_t N = b_k_n.get_length(1);
+    const std::size_t K = a_m_k.get_length(1);
+
+    auto f_mn = [&](auto m, auto n) {
+        AccDataType v_acc = 0;
+
+        for(std::size_t k = 0; k < K; ++k)
+        {
+            AccDataType v_a;
+            AccDataType v_b;
+            if constexpr(std::is_same_v<ADataType, pk_int4_t>)
+            {
+                const pk_int4_t pk_val  = a_element_op(a_m_k(m, k));
+                const fp32x2_t fp32_val = pk_int4_t_to_fp32x2_t(pk_val);
+                if(k % 2 == 1)
+                    v_a = fp32_val.hi;
+                else
+                    v_a = fp32_val.lo;
+            }
+            else
+            {
+                v_a = ck_tile::type_convert<AccDataType>(a_element_op(a_m_k(m, k)));
+            }
+            if constexpr(std::is_same_v<BDataType, pk_int4_t>)
+            {
+                const pk_int4_t pk_val  = b_element_op(b_k_n(k, n));
+                const fp32x2_t fp32_val = pk_int4_t_to_fp32x2_t(pk_val);
+                if(k % 2 == 1)
+                    v_b = fp32_val.hi;
+                else
+                    v_b = fp32_val.lo;
+            }
+            else
+            {
+                v_b = ck_tile::type_convert<AccDataType>(b_element_op(b_k_n(k, n)));
+            }
+            v_acc += v_a * v_b;
+        }
+
+        c_m_n(m, n) = ck_tile::type_convert<CDataType>(acc_element_op(v_acc));
+    };
+
+    make_ParallelTensorFunctor(f_mn, M, N)(std::thread::hardware_concurrency());
+}
+
+template <typename ADataType,
+          typename BDataType,
+          typename AccDataType,
+          typename CDataType,
+          typename LayoutA,
+          typename LayoutB,
+          typename LayoutC>
+__global__ void naive_gemm_kernel(ADataType* A,
+                                  BDataType* B,
+                                  CDataType* C,
+                                  ck_tile::index_t M,
+                                  ck_tile::index_t N,
+                                  ck_tile::index_t K,
+                                  ck_tile::index_t strideA,
+                                  ck_tile::index_t strideB,
+                                  ck_tile::index_t strideC)
+{
+    int idx = blockIdx.x * blockDim.x + threadIdx.x;
+    int row = idx / N; // Compute row index
+    int col = idx % N; // Compute column index
+
+    if(row < M && col < N)
+    {
+        AccDataType acc = 0.0;
+        for(int k = 0; k < K; ++k)
+        {
+            constexpr index_t packed_size_a = ck_tile::numeric_traits<ADataType>::PackedSize;
+            constexpr index_t packed_size_b = ck_tile::numeric_traits<BDataType>::PackedSize;
+            // Adjust indexing based on matrix layout
+            int a_index = (std::is_same_v<LayoutA, tensor_layout::gemm::RowMajor>)
+                              ? row * strideA + k
+                              : k * strideA + row;
+            int b_index = (std::is_same_v<LayoutB, tensor_layout::gemm::ColumnMajor>)
+                              ? col * strideB + k
+                              : k * strideB + col;
+
+            AccDataType v_a;
+            AccDataType v_b;
+            if constexpr(std::is_same_v<ADataType, pk_int4_t>)
+            {
+                const fp32x2_t fp32_val = pk_int4_t_to_fp32x2_t(A[a_index / packed_size_a]);
+                if(k % 2 == 1)
+                    v_a = fp32_val.hi;
+                else
+                    v_a = fp32_val.lo;
+            }
+            else
+            {
+                v_a = ck_tile::type_convert<AccDataType>(A[a_index]);
+            }
+            if constexpr(std::is_same_v<BDataType, pk_int4_t>)
+            {
+                const fp32x2_t fp32_val = pk_int4_t_to_fp32x2_t(B[b_index / packed_size_b]);
+                if(k % 2 == 1)
+                    v_b = fp32_val.hi;
+                else
+                    v_b = fp32_val.lo;
+            }
+            else
+            {
+                v_b = ck_tile::type_convert<AccDataType>(B[b_index]);
+            }
+            acc += v_a * v_b;
+        }
+
+        int c_index = (std::is_same_v<LayoutC, tensor_layout::gemm::RowMajor>)
+                          ? row * strideC + col
+                          : col * strideC + row;
+        C[c_index]  = ck_tile::type_convert<CDataType>(acc);
+    }
+}
+
+template <typename ADataType,
+          typename BDataType,
+          typename AccDataType,
+          typename CDataType,
+          typename LayoutA,
+          typename LayoutB,
+          typename LayoutC>
+void reference_gemm_gpu(ADataType* a_ptr,
+                        BDataType* b_ptr,
+                        CDataType* c_ptr,
+                        index_t M,
+                        index_t N,
+                        index_t K,
+                        index_t stride_a,
+                        index_t stride_b,
+                        index_t stride_c)
+{
+    int totalElements      = M * N;
+    int numThreadsPerBlock = 256; // Common choice for threads per block
+    int numBlocks          = (totalElements + numThreadsPerBlock - 1) / numThreadsPerBlock;
+
+    naive_gemm_kernel<ADataType, BDataType, AccDataType, CDataType, LayoutA, LayoutB, LayoutC>
+        <<<numBlocks, numThreadsPerBlock>>>(
+            a_ptr, b_ptr, c_ptr, M, N, K, stride_a, stride_b, stride_c);
+
+    return;
+}
+
+template <typename ADataType,
+          typename BDataType,
+          typename AccDataType,
+          typename CDataType,
+          typename LayoutA,
+          typename LayoutB,
+          typename LayoutC>
+void reference_batched_gemm_gpu(ADataType* a_ptr,
+                                BDataType* b_ptr,
+                                CDataType* 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)
+{
+    int totalElements      = M * N;
+    int numThreadsPerBlock = 256; // Common choice for threads per block
+    int numBlocks          = (totalElements + numThreadsPerBlock - 1) / numThreadsPerBlock;
+
+    for(index_t batch_id = 0; batch_id < batch_count; ++batch_id)
+    {
+        ADataType* d_ATemp = a_ptr + batch_id * batch_stride_A;
+        BDataType* d_BTemp = b_ptr + batch_id * batch_stride_B;
+        CDataType* d_CTemp = c_ptr + batch_id * batch_stride_C;
+        naive_gemm_kernel<ADataType, BDataType, AccDataType, CDataType, LayoutA, LayoutB, LayoutC>
+            <<<numBlocks, numThreadsPerBlock>>>(
+                d_ATemp, d_BTemp, d_CTemp, M, N, K, stride_a, stride_b, stride_c);
+    }
+
+    return;
+}
+} // namespace ck_tile

include/ck_tile/host/reference/reference_im2col.hpp

@@ -0,0 +1,133 @@
+// 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/host/host_tensor.hpp"
+#include <thread>
+
+namespace ck_tile {
+
+template <typename InDataType, typename OutDataType, index_t NDimSpatial>
+CK_TILE_HOST void reference_im2col(const HostTensor<InDataType>& in_host,
+                                   HostTensor<OutDataType>& out_host,
+                                   const ck_tile::conv::ConvParam& conv_params)
+{
+    const long_index_t G = in_host.get_lengths()[0];
+    const long_index_t N = in_host.get_lengths()[1];
+    const long_index_t C = in_host.get_lengths()[2];
+
+    if constexpr(NDimSpatial == 1)
+    {
+        const long_index_t Wo = conv_params.output_spatial_lengths_[0];
+        auto func             = [&](auto g, auto n, auto wo) {
+            long_index_t row    = n * Wo + wo;
+            long_index_t column = 0;
+
+            for(long_index_t x = 0; x < conv_params.filter_spatial_lengths_[0]; ++x)
+            {
+                auto wi = static_cast<long_index_t>(wo * conv_params.conv_filter_strides_[0]) +
+                          static_cast<long_index_t>(x * conv_params.conv_filter_dilations_[0]) -
+                          static_cast<long_index_t>(conv_params.input_left_pads_[0]);
+
+                for(long_index_t c = 0; c < C; ++c)
+                {
+                    if(wi >= 0 && type_convert<std::size_t>(wi) < in_host.get_lengths()[3])
+                    {
+                        InDataType v_in          = in_host(g, n, c, wi);
+                        out_host(g, row, column) = type_convert<OutDataType>(v_in);
+                    }
+                    column++;
+                }
+            }
+        };
+
+        make_ParallelTensorFunctor(func, G, N, Wo)(std::thread::hardware_concurrency());
+    }
+    else if constexpr(NDimSpatial == 2)
+    {
+        const long_index_t Ho = conv_params.output_spatial_lengths_[0];
+        const long_index_t Wo = conv_params.output_spatial_lengths_[1];
+
+        auto func = [&](auto g, auto n, auto ho, auto wo) {
+            long_index_t row    = n * Ho * Wo + ho * Wo + wo;
+            long_index_t column = 0;
+
+            for(long_index_t y = 0; y < conv_params.filter_spatial_lengths_[0]; ++y)
+            {
+                auto hi = static_cast<long_index_t>(ho * conv_params.conv_filter_strides_[0]) +
+                          static_cast<long_index_t>(y * conv_params.conv_filter_dilations_[0]) -
+                          static_cast<long_index_t>(conv_params.input_left_pads_[0]);
+
+                for(long_index_t x = 0; x < conv_params.filter_spatial_lengths_[1]; ++x)
+                {
+                    auto wi = static_cast<long_index_t>(wo * conv_params.conv_filter_strides_[1]) +
+                              static_cast<long_index_t>(x * conv_params.conv_filter_dilations_[1]) -
+                              static_cast<long_index_t>(conv_params.input_left_pads_[1]);
+
+                    for(long_index_t c = 0; c < C; ++c)
+                    {
+
+                        if(hi >= 0 && type_convert<std::size_t>(hi) < in_host.get_lengths()[3] &&
+                           wi >= 0 && type_convert<std::size_t>(wi) < in_host.get_lengths()[4])
+                        {
+                            InDataType v_in          = in_host(g, n, c, hi, wi);
+                            out_host(g, row, column) = type_convert<OutDataType>(v_in);
+                        }
+                        column++;
+                    }
+                }
+            }
+        };
+
+        make_ParallelTensorFunctor(func, G, N, Ho, Wo)(std::thread::hardware_concurrency());
+    }
+    else if constexpr(NDimSpatial == 3)
+    {
+        const long_index_t Do = conv_params.output_spatial_lengths_[0];
+        const long_index_t Ho = conv_params.output_spatial_lengths_[1];
+        const long_index_t Wo = conv_params.output_spatial_lengths_[2];
+
+        auto func = [&](auto g, auto n, auto d_o, auto ho, auto wo) {
+            long_index_t row    = n * Do * Ho * Wo + d_o * Ho * Wo + ho * Wo + wo;
+            long_index_t column = 0;
+
+            for(long_index_t z = 0; z < conv_params.filter_spatial_lengths_[0]; ++z)
+            {
+                auto di = static_cast<long_index_t>(d_o * conv_params.conv_filter_strides_[0]) +
+                          static_cast<long_index_t>(z * conv_params.conv_filter_dilations_[0]) -
+                          static_cast<long_index_t>(conv_params.input_left_pads_[0]);
+                for(long_index_t y = 0; y < conv_params.filter_spatial_lengths_[1]; ++y)
+                {
+                    auto hi = static_cast<long_index_t>(ho * conv_params.conv_filter_strides_[1]) +
+                              static_cast<long_index_t>(y * conv_params.conv_filter_dilations_[1]) -
+                              static_cast<long_index_t>(conv_params.input_left_pads_[1]);
+                    for(long_index_t x = 0; x < conv_params.filter_spatial_lengths_[2]; ++x)
+                    {
+                        auto wi =
+                            static_cast<long_index_t>(wo * conv_params.conv_filter_strides_[2]) +
+                            static_cast<long_index_t>(x * conv_params.conv_filter_dilations_[2]) -
+                            static_cast<long_index_t>(conv_params.input_left_pads_[2]);
+                        for(long_index_t c = 0; c < C; ++c)
+                        {
+                            if(di >= 0 &&
+                               type_convert<std::size_t>(di) < in_host.get_lengths()[3] &&
+                               hi >= 0 &&
+                               type_convert<std::size_t>(hi) < in_host.get_lengths()[4] &&
+                               wi >= 0 && type_convert<std::size_t>(wi) < in_host.get_lengths()[5])
+                            {
+                                InDataType v_in          = in_host(g, n, c, di, hi, wi);
+                                out_host(g, row, column) = type_convert<OutDataType>(v_in);
+                            }
+                            column++;
+                        }
+                    }
+                }
+            }
+        };
+
+        make_ParallelTensorFunctor(func, G, N, Do, Ho, Wo)(std::thread::hardware_concurrency());
+    }
+}
+} // namespace ck_tile

include/ck_tile/host/reference/reference_layernorm2d_fwd.hpp

@@ -0,0 +1,96 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core.hpp"
+#include "ck_tile/host/host_tensor.hpp"
+
+namespace ck_tile {
+
+// Note: for simplicity, each functor only care about single M
+struct reference_layernorm2d_default_epilogue
+{
+    template <typename OutDataType, typename AccDataType>
+    void operator()(int m, HostTensor<OutDataType>& o, const HostTensor<AccDataType>& acc)
+    {
+        const int N = acc.mDesc.get_lengths()[1];
+        for(int n = 0; n < N; ++n)
+        {
+            o(m, n) = ck_tile::type_convert<OutDataType>(acc(m, n));
+        }
+    }
+
+    template <typename OutDataType, typename AccDataType>
+    auto operator()(int m, const HostTensor<AccDataType>& acc)
+    {
+        HostTensor<OutDataType> o(acc.get_lengths(), acc.get_strides());
+        operator()(m, o, acc);
+        return o;
+    }
+};
+
+template <typename XDataType,
+          typename GammaDataType,
+          typename BetaDataType,
+          typename ComputeDataType,
+          typename YDataType,
+          typename MeanDataType,
+          typename InvStdDataType,
+          typename Epilogue = reference_layernorm2d_default_epilogue>
+void reference_layernorm2d_fwd(const HostTensor<XDataType>& x_m_n,
+                               const HostTensor<GammaDataType>& gamma_n,
+                               const HostTensor<BetaDataType>& beta_n,
+                               HostTensor<YDataType>& y_m_n,
+                               HostTensor<MeanDataType>& mean_m,
+                               HostTensor<InvStdDataType>& invStd_m,
+                               ComputeDataType epsilon,
+                               Epilogue epilogue_functor = {})
+{
+    auto layernorm2d_fwd_func = [&](auto m) {
+        const int N = x_m_n.mDesc.get_lengths()[1];
+
+        int count                = 0;
+        ComputeDataType mean     = 0;
+        ComputeDataType variance = 0;
+        ComputeDataType divisor  = 0;
+
+        for(int n = 0; n < N; ++n)
+        {
+            ++count;
+            ComputeDataType x     = ck_tile::type_convert<ComputeDataType>(x_m_n(m, n));
+            ComputeDataType delta = x - mean;
+            mean += delta / count;
+            ComputeDataType delta2 = x - mean;
+            variance += delta * delta2;
+        }
+
+        // actual variance
+        variance = variance / count;
+        divisor  = ck_tile::type_convert<ComputeDataType>(1) / ck_tile::sqrt(variance + epsilon);
+
+        if constexpr(!std::is_same_v<MeanDataType, ck_tile::null_type>)
+            mean_m(m) = ck_tile::type_convert<MeanDataType>(mean);
+
+        if constexpr(!std::is_same_v<InvStdDataType, ck_tile::null_type>)
+            invStd_m(m) = ck_tile::type_convert<InvStdDataType>(divisor);
+
+        HostTensor<ComputeDataType> acc(x_m_n.get_lengths(), x_m_n.get_strides());
+        for(int n = 0; n < N; ++n)
+        {
+            ComputeDataType x     = ck_tile::type_convert<ComputeDataType>(x_m_n(m, n));
+            ComputeDataType gamma = ck_tile::type_convert<ComputeDataType>(gamma_n(n));
+            ComputeDataType beta  = ck_tile::type_convert<ComputeDataType>(beta_n(n));
+            auto a_               = (x - mean) * divisor;
+            a_                    = a_ * gamma + beta;
+
+            acc(m, n) = a_;
+        }
+
+        epilogue_functor(m, y_m_n, acc);
+    };
+
+    make_ParallelTensorFunctor(layernorm2d_fwd_func,
+                               mean_m.mDesc.get_lengths()[0])(std::thread::hardware_concurrency());
+}
+} // namespace ck_tile

include/ck_tile/host/reference/reference_moe_sorting.hpp

@@ -0,0 +1,119 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core.hpp"
+#include "ck_tile/host/host_tensor.hpp"
+
+namespace ck_tile {
+
+#define MOE_SORTING_MOCK_ID(token_id_, topk_id_) \
+    static_cast<uint32_t>(((token_id_)&0x00ffffff) | (((topk_id_)&0xff) << 24))
+
+template <typename WeightType, typename IndexType = index_t>
+CK_TILE_HOST void reference_moe_sorting(const HostTensor<IndexType>& topk_ids,
+                                        const HostTensor<WeightType>& weights,
+                                        const HostTensor<IndexType>& local_expert_mask,
+                                        HostTensor<IndexType>& p_sorted_token_ids,
+                                        HostTensor<WeightType>& sorted_weight,
+                                        HostTensor<IndexType>& sorted_expert_ids,
+                                        index_t& unit_cnt,
+                                        const index_t experts,
+                                        const index_t unit_size,
+                                        bool local_expert_masking,
+                                        bool skip_experts_with_zero_token = true)
+{
+    const index_t num_token = topk_ids.mDesc.get_lengths()[0];
+    const index_t topk      = topk_ids.mDesc.get_lengths()[1];
+    // allocate a temp buffer, and fill the value with [number_token|topk]
+    std::vector<std::vector<IndexType>> expert_tokens(
+        experts,
+#if CK_TILE_REFERENCE_MOE_SORTING_MOCK_ID
+        std::vector<IndexType>(unit_size, MOE_SORTING_MOCK_ID(num_token, topk)));
+#else
+        std::vector<IndexType>(unit_size, num_token));
+#endif
+    std::vector<std::vector<WeightType>> expert_token_weights(
+        experts, std::vector<WeightType>(unit_size, 0));
+    // count number of unit-size slices in this expert
+    std::vector<IndexType> expert_slices(experts, 1);
+    // count the tokens used in this expert
+    std::vector<IndexType> expert_slice_idxs(experts, 0);
+    // TODO: above 2 buffer seems duplicated
+
+    for(index_t t = 0; t < num_token; t++)
+    {
+        for(index_t k = 0; k < topk; k++)
+        {
+            IndexType e  = topk_ids(t, k);
+            WeightType w = weights(t, k);
+            index_t idx  = expert_slice_idxs[e];
+            if(idx > expert_slices[e] * unit_size - 1)
+            {
+                expert_slices[e]++;
+                index_t new_size = expert_slices[e] * unit_size;
+                expert_tokens[e].resize(new_size);
+                expert_token_weights[e].resize(new_size);
+                for(index_t i = (expert_slices[e] - 1) * unit_size; i < new_size; i++)
+                {
+#if CK_TILE_REFERENCE_MOE_SORTING_MOCK_ID
+                    expert_tokens[e][i] = MOE_SORTING_MOCK_ID(num_token, topk);
+#else
+                    expert_tokens[e][i] = num_token;
+#endif
+                    expert_token_weights[e][i] = 0;
+                }
+            }
+#if CK_TILE_REFERENCE_MOE_SORTING_MOCK_ID
+            expert_tokens[e][idx] = MOE_SORTING_MOCK_ID(t, k);
+#else
+            expert_tokens[e][idx] = t;
+#endif
+            expert_token_weights[e][idx] = w;
+            expert_slice_idxs[e]++;
+        }
+    }
+
+    IndexType* out_tokens    = p_sorted_token_ids.data();
+    WeightType* out_weights  = sorted_weight.data();
+    IndexType* out_expert_id = sorted_expert_ids.data();
+    int curr_expert_id       = 0;
+    for(index_t e = 0; e < experts; e++)
+    {
+        if(local_expert_masking)
+        {
+            if(local_expert_mask(e) == 0)
+                continue;
+        }
+        if(skip_experts_with_zero_token)
+        {
+            if(expert_slice_idxs[e] == 0)
+            {
+                curr_expert_id++;
+                continue;
+            }
+        }
+
+        memcpy(out_tokens, expert_tokens[e].data(), sizeof(index_t) * expert_slices[e] * unit_size);
+        out_tokens += expert_slices[e] * unit_size;
+        memcpy(out_weights,
+               expert_token_weights[e].data(),
+               sizeof(WeightType) * expert_slices[e] * unit_size);
+        out_weights += expert_slices[e] * unit_size;
+
+        for(index_t s = 0; s < expert_slices[e]; s++)
+        {
+            out_expert_id[s] = curr_expert_id;
+            unit_cnt++;
+        }
+        out_expert_id += expert_slices[e];
+        curr_expert_id++;
+    }
+    unit_cnt *= unit_size;
+    return;
+}
+
+#undef MOE_SORTING_MOCK_ID
+
+} // namespace ck_tile

include/ck_tile/host/reference/reference_permute.hpp

@@ -0,0 +1,76 @@
+// 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/host/host_tensor.hpp"
+#include <thread>
+#include <numeric>
+#include <functional>
+
+namespace ck_tile {
+
+/*
+    this will do permute + contiguous like functionality in pytorch
+*/
+template <typename DataType>
+CK_TILE_HOST void
+reference_permute(const HostTensor<DataType>& x, HostTensor<DataType>& y, std::vector<index_t> perm)
+{
+    const auto x_len = x.mDesc.get_lengths();
+    const auto y_len = y.mDesc.get_lengths();
+    assert(x_len.size() == y_len.size());
+    index_t rank     = x_len.size();
+    const auto x_elm = std::accumulate(x_len.begin(), x_len.end(), 1, std::multiplies<index_t>());
+    const auto y_elm = std::accumulate(y_len.begin(), y_len.end(), 1, std::multiplies<index_t>());
+    assert(x_elm == y_elm);
+    (void)y_elm;
+
+    auto f = [&](auto i_element) {
+        std::vector<size_t> y_coord = [&]() {
+            std::vector<size_t> tmp(rank, 0);
+            size_t r = i_element;
+            for(index_t i = rank - 1; i >= 0; i--)
+            {
+                tmp[i] = r % y_len[i];
+                r      = r / y_len[i];
+            }
+            return tmp;
+        }();
+
+        std::vector<size_t> x_coord = [&]() {
+            std::vector<size_t> tmp(rank, 0);
+            for(index_t i = 0; i < rank; i++)
+            {
+                tmp[perm[i]] = y_coord[i];
+            }
+            return tmp;
+        }();
+
+        // do permute
+        y(y_coord) = x(x_coord);
+    };
+
+    make_ParallelTensorFunctor(f, x_elm)(std::thread::hardware_concurrency());
+}
+
+template <typename DataType>
+CK_TILE_HOST auto reference_permute(const HostTensor<DataType>& x, std::vector<index_t> perm)
+{
+    auto x_shape                          = x.get_lengths();
+    ck_tile::index_t rank                 = perm.size();
+    std::vector<ck_tile::index_t> y_shape = [&]() {
+        std::vector<ck_tile::index_t> tmp(rank, 0);
+        for(int i = 0; i < static_cast<int>(rank); i++)
+        {
+            tmp[i] = x_shape[perm[i]];
+        }
+        return tmp;
+    }();
+
+    HostTensor<DataType> y(y_shape);
+    reference_permute(x, y, perm);
+    return y;
+}
+} // namespace ck_tile