onnxruntime

include/ck/stream_config.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <hip/hip_runtime.h>
+#include <hip/hip_fp16.h>
+
+struct StreamConfig
+{
+    hipStream_t stream_id_ = nullptr;
+    bool time_kernel_      = false;
+    int log_level_         = 0;
+};

include/ck/tensor/static_tensor.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#ifndef CK_STATIC_TENSOR_HPP
+#define CK_STATIC_TENSOR_HPP
+
+namespace ck {
+
+// StaticTensor for Scalar
+template <AddressSpaceEnum AddressSpace,
+          typename T,
+          typename TensorDesc,
+          bool InvalidElementUseNumericalZeroValue,
+          typename enable_if<TensorDesc::IsKnownAtCompileTime(), bool>::type = false>
+struct StaticTensor
+{
+    static constexpr auto desc_                  = TensorDesc{};
+    static constexpr index_t ndim_               = TensorDesc::GetNumOfDimension();
+    static constexpr index_t element_space_size_ = desc_.GetElementSpaceSize();
+
+    __host__ __device__ constexpr StaticTensor() : invalid_element_scalar_value_{0} {}
+
+    __host__ __device__ constexpr StaticTensor(T invalid_element_value)
+        : invalid_element_scalar_value_{invalid_element_value}
+    {
+    }
+
+    // read access
+    template <typename Idx,
+              typename enable_if<is_known_at_compile_time<Idx>::value && Idx::Size() == ndim_,
+                                 bool>::type = false>
+    __host__ __device__ constexpr const T& operator[](Idx) const
+    {
+        constexpr auto coord = make_tensor_coordinate(desc_, to_multi_index(Idx{}));
+
+        constexpr index_t offset = coord.GetOffset();
+
+        constexpr bool is_valid = coordinate_has_valid_offset(desc_, coord);
+
+        if constexpr(is_valid)
+        {
+            return data_[Number<offset>{}];
+        }
+        else
+        {
+            if constexpr(InvalidElementUseNumericalZeroValue)
+            {
+                return zero_scalar_value_;
+            }
+            else
+            {
+                return invalid_element_scalar_value_;
+            }
+        }
+    }
+
+    // write access
+    template <typename Idx,
+              typename enable_if<is_known_at_compile_time<Idx>::value && Idx::Size() == ndim_,
+                                 bool>::type = false>
+    __host__ __device__ constexpr T& operator()(Idx)
+    {
+        constexpr auto coord = make_tensor_coordinate(desc_, to_multi_index(Idx{}));
+
+        constexpr index_t offset = coord.GetOffset();
+
+        constexpr bool is_valid = coordinate_has_valid_offset(desc_, coord);
+
+        if constexpr(is_valid)
+        {
+            return data_(Number<offset>{});
+        }
+        else
+        {
+            return ignored_element_scalar_;
+        }
+    }
+
+    StaticBuffer<AddressSpace, T, element_space_size_, true> data_;
+    static constexpr T zero_scalar_value_ = T{0};
+    const T invalid_element_scalar_value_;
+    T ignored_element_scalar_;
+};
+
+// StaticTensor for vector
+template <AddressSpaceEnum AddressSpace,
+          typename S,
+          index_t ScalarPerVector,
+          typename TensorDesc,
+          bool InvalidElementUseNumericalZeroValue,
+          typename enable_if<TensorDesc::IsKnownAtCompileTime(), bool>::type = false>
+struct StaticTensorTupleOfVectorBuffer
+{
+    static constexpr auto desc_                  = TensorDesc{};
+    static constexpr index_t ndim_               = TensorDesc::GetNumOfDimension();
+    static constexpr index_t element_space_size_ = desc_.GetElementSpaceSize();
+
+    static constexpr index_t num_of_vector_ =
+        math::integer_divide_ceil(element_space_size_, ScalarPerVector);
+
+    using V = vector_type<S, ScalarPerVector>;
+
+    __host__ __device__ constexpr StaticTensorTupleOfVectorBuffer()
+        : invalid_element_scalar_value_{0}
+    {
+    }
+
+    __host__ __device__ constexpr StaticTensorTupleOfVectorBuffer(S invalid_element_value)
+        : invalid_element_scalar_value_{invalid_element_value}
+    {
+    }
+
+    // Get S
+    // Idx is for S, not V
+    template <typename Idx,
+              typename enable_if<is_known_at_compile_time<Idx>::value && Idx::Size() == ndim_,
+                                 bool>::type = false>
+    __host__ __device__ constexpr const S& operator[](Idx) const
+    {
+        constexpr auto coord = make_tensor_coordinate(desc_, to_multi_index(Idx{}));
+
+        constexpr index_t offset = coord.GetOffset();
+
+        constexpr bool is_valid = coordinate_has_valid_offset(desc_, coord);
+
+        if constexpr(is_valid)
+        {
+            return data_[Number<offset>{}];
+        }
+        else
+        {
+            if constexpr(InvalidElementUseNumericalZeroValue)
+            {
+                return zero_scalar_value_;
+            }
+            else
+            {
+                return invalid_element_scalar_value_;
+            }
+        }
+    }
+
+    // Set S
+    // Idx is for S, not V
+    template <typename Idx,
+              typename enable_if<is_known_at_compile_time<Idx>::value && Idx::Size() == ndim_,
+                                 bool>::type = false>
+    __host__ __device__ constexpr S& operator()(Idx)
+    {
+        constexpr auto coord = make_tensor_coordinate(desc_, to_multi_index(Idx{}));
+
+        constexpr index_t offset = coord.GetOffset();
+
+        constexpr bool is_valid = coordinate_has_valid_offset(desc_, coord);
+
+        if constexpr(is_valid)
+        {
+            return data_(Number<offset>{});
+        }
+        else
+        {
+            return ignored_element_scalar_;
+        }
+    }
+
+    // Get X
+    // Idx is for S, not X. Idx should be aligned with X
+    template <typename X,
+              typename Idx,
+              typename enable_if<has_same_scalar_type<S, X>::value &&
+                                     is_known_at_compile_time<Idx>::value && Idx::Size() == ndim_,
+                                 bool>::type = false>
+    __host__ __device__ constexpr X GetAsType(Idx) const
+    {
+        constexpr auto coord = make_tensor_coordinate(desc_, to_multi_index(Idx{}));
+
+        constexpr index_t offset = coord.GetOffset();
+
+        constexpr bool is_valid = coordinate_has_valid_offset(desc_, coord);
+
+        if constexpr(is_valid)
+        {
+            return data_.template GetAsType<X>(Number<offset>{});
+        }
+        else
+        {
+            if constexpr(InvalidElementUseNumericalZeroValue)
+            {
+                // TODO: is this right way to initialize a vector?
+                return X{0};
+            }
+            else
+            {
+                // TODO: is this right way to initialize a vector?
+                return X{invalid_element_scalar_value_};
+            }
+        }
+    }
+
+    // Set X
+    // Idx is for S, not X. Idx should be aligned with X
+    template <typename X,
+              typename Idx,
+              typename enable_if<has_same_scalar_type<S, X>::value &&
+                                     is_known_at_compile_time<Idx>::value && Idx::Size() == ndim_,
+                                 bool>::type = false>
+    __host__ __device__ constexpr void SetAsType(Idx, X x)
+    {
+        constexpr auto coord = make_tensor_coordinate(desc_, to_multi_index(Idx{}));
+
+        constexpr index_t offset = coord.GetOffset();
+
+        constexpr bool is_valid = coordinate_has_valid_offset(desc_, coord);
+
+        if constexpr(is_valid)
+        {
+            data_.template SetAsType<X>(Number<offset>{}, x);
+        }
+    }
+
+    // Get read access to V. No is_valid check
+    // Idx is for S, not V. Idx should be aligned with V
+    template <typename Idx>
+    __host__ __device__ constexpr const V& GetVectorTypeReference(Idx) const
+    {
+        constexpr auto coord = make_tensor_coordinate(desc_, to_multi_index(Idx{}));
+
+        constexpr index_t offset = coord.GetOffset();
+
+        return data_.GetVectorTypeReference(Number<offset>{});
+    }
+
+    // Get read access to V. No is_valid check
+    // Idx is for S, not V. Idx should be aligned with V
+    template <typename Idx>
+    __host__ __device__ constexpr V& GetVectorTypeReference(Idx)
+    {
+        constexpr auto coord = make_tensor_coordinate(desc_, to_multi_index(Idx{}));
+
+        constexpr index_t offset = coord.GetOffset();
+
+        return data_.GetVectorTypeReference(Number<offset>{});
+    }
+
+    StaticBufferTupleOfVector<AddressSpace, S, num_of_vector_, ScalarPerVector, true> data_;
+    static constexpr S zero_scalar_value_ = S{0};
+    const S invalid_element_scalar_value_ = S{0};
+    S ignored_element_scalar_;
+};
+
+template <AddressSpaceEnum AddressSpace,
+          typename T,
+          typename TensorDesc,
+          typename enable_if<TensorDesc::IsKnownAtCompileTime(), bool>::type = false>
+__host__ __device__ constexpr auto make_static_tensor(TensorDesc)
+{
+    return StaticTensor<AddressSpace, T, TensorDesc, true>{};
+}
+
+template <
+    AddressSpaceEnum AddressSpace,
+    typename T,
+    typename TensorDesc,
+    typename X,
+    typename enable_if<TensorDesc::IsKnownAtCompileTime(), bool>::type                   = false,
+    typename enable_if<is_same<remove_cvref_t<T>, remove_cvref_t<X>>::value, bool>::type = false>
+__host__ __device__ constexpr auto make_static_tensor(TensorDesc, X invalid_element_value)
+{
+    return StaticTensor<AddressSpace, T, TensorDesc, true>{invalid_element_value};
+}
+
+} // namespace ck
+#endif

include/ck/tensor_description/cluster_descriptor.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck/utility/common_header.hpp"
+#include "ck/tensor_description/tensor_adaptor.hpp"
+
+namespace ck {
+
+template <typename Lengths,
+          typename ArrangeOrder = typename arithmetic_sequence_gen<0, Lengths::Size(), 1>::type>
+__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

include/ck/tensor_description/multi_index_transform.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck/utility/common_header.hpp"
+#include "ck/utility/multi_index.hpp"
+
+namespace ck {
+
+template <typename LowLength>
+struct PassThrough
+{
+    using LowerIndex = MultiIndex<1>;
+    using UpperIndex = MultiIndex<1>;
+
+    using UpLengths = decltype(make_tuple(LowLength{}));
+
+    UpLengths up_lengths_;
+
+    __host__ __device__ constexpr PassThrough() = default;
+
+    __host__ __device__ constexpr PassThrough(const LowLength& low_length)
+        : up_lengths_{make_tuple(low_length)}
+    {
+    }
+
+    __host__ __device__ static constexpr index_t GetNumOfLowerDimension() { return 1; }
+
+    __host__ __device__ static constexpr index_t GetNumOfUpperDimension() { return 1; }
+
+    __host__ __device__ constexpr const auto& GetUpperLengths() const { return up_lengths_; }
+
+    template <typename LowIdx, typename UpIdx>
+    __host__ __device__ static constexpr void CalculateLowerIndex(LowIdx& idx_low,
+                                                                  const UpIdx& idx_up)
+    {
+        static_assert(LowIdx::Size() == 1 && UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        idx_low(Number<0>{}) = idx_up[Number<0>{}];
+    }
+
+    template <typename LowIdxDiff,
+              typename UpIdxDiff,
+              typename LowIdx,
+              typename UpIdx,
+              index_t Hack>
+    __host__ __device__ static void UpdateLowerIndex(LowIdxDiff& idx_diff_low,
+                                                     const UpIdxDiff& idx_diff_up,
+                                                     LowIdx& idx_low,
+                                                     const UpIdx&,
+                                                     Number<Hack>)
+    {
+        static_assert(LowIdxDiff::Size() == 1 && UpIdxDiff::Size() == 1 && LowIdx::Size() == 1 &&
+                          UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        constexpr auto I0 = Number<0>{};
+
+        idx_diff_low(I0) = idx_diff_up[I0];
+
+        idx_low += idx_diff_low;
+    }
+
+    __host__ __device__ static constexpr bool IsLinearTransform() { return true; }
+
+    __host__ __device__ static constexpr bool IsValidUpperIndexAlwaysMappedToValidLowerIndex()
+    {
+        return true;
+    }
+
+    template <typename UpIdx>
+    __host__ __device__ static constexpr bool
+    IsValidUpperIndexMappedToValidLowerIndex(const UpIdx& /* idx_up */)
+    {
+        return true;
+    }
+
+    __host__ __device__ static constexpr bool IsKnownAtCompileTime()
+    {
+        return is_known_at_compile_time<UpLengths>::value;
+    }
+
+    __host__ __device__ void Print() const
+    {
+        printf("{");
+        printf("PassThrough, ");
+        printf("up_lengths_");
+        print_multi_index(up_lengths_);
+        printf("}");
+    }
+};
+
+template <typename LowLength,
+          typename LeftPadLength,
+          typename RightPadLength,
+          bool SkipIsValidCheck = false>
+struct Pad
+{
+    using LowerIndex = MultiIndex<1>;
+    using UpperIndex = MultiIndex<1>;
+
+    using UpLengths = decltype(make_tuple(LowLength{} + LeftPadLength{} + RightPadLength{}));
+
+    UpLengths up_lengths_;
+    LeftPadLength left_pad_length_;
+    RightPadLength right_pad_length_;
+
+    __host__ __device__ constexpr Pad() = default;
+
+    __host__ __device__ constexpr Pad(const LowLength& low_length,
+                                      const LeftPadLength& left_pad_length,
+                                      const RightPadLength& right_pad_length)
+        : up_lengths_{make_tuple(low_length + left_pad_length + right_pad_length)},
+          left_pad_length_{left_pad_length},
+          right_pad_length_{right_pad_length}
+    {
+    }
+
+    __host__ __device__ static constexpr index_t GetNumOfLowerDimension() { return 1; }
+
+    __host__ __device__ static constexpr index_t GetNumOfUpperDimension() { return 1; }
+
+    __host__ __device__ constexpr const auto& GetUpperLengths() const { return up_lengths_; }
+
+    template <typename LowIdx, typename UpIdx>
+    __host__ __device__ constexpr void CalculateLowerIndex(LowIdx& idx_low,
+                                                           const UpIdx& idx_up) const
+    {
+        static_assert(LowIdx::Size() == 1 && UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        idx_low(Number<0>{}) = idx_up[Number<0>{}] - left_pad_length_;
+    }
+
+    template <typename LowIdxDiff,
+              typename UpIdxDiff,
+              typename LowIdx,
+              typename UpIdx,
+              index_t Hack>
+    __host__ __device__ static void UpdateLowerIndex(LowIdxDiff& idx_diff_low,
+                                                     const UpIdxDiff& idx_diff_up,
+                                                     LowIdx& idx_low,
+                                                     const UpIdx&,
+                                                     Number<Hack>)
+    {
+        static_assert(LowIdxDiff::Size() == 1 && UpIdxDiff::Size() == 1 && LowIdx::Size() == 1 &&
+                          UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        constexpr auto I0 = Number<0>{};
+
+        idx_diff_low(I0) = idx_diff_up[I0];
+
+        idx_low += idx_diff_low;
+    }
+
+    __host__ __device__ static constexpr bool IsLinearTransform() { return true; }
+
+    __host__ __device__ static constexpr bool IsValidUpperIndexAlwaysMappedToValidLowerIndex()
+    {
+        return SkipIsValidCheck;
+    }
+
+    template <typename UpIdx>
+    __host__ __device__ constexpr bool
+    IsValidUpperIndexMappedToValidLowerIndex(const UpIdx& idx_up) const
+    {
+        return SkipIsValidCheck ||
+               ((idx_up[Number<0>{}] >= left_pad_length_) &&
+                (idx_up[Number<0>{}] < up_lengths_[Number<0>{}] - right_pad_length_));
+    }
+
+    __host__ __device__ static constexpr bool IsKnownAtCompileTime()
+    {
+        return is_known_at_compile_time<UpLengths>::value &&
+               is_known_at_compile_time<LeftPadLength>::value &&
+               is_known_at_compile_time<RightPadLength>::value;
+    }
+
+    __host__ __device__ void Print() const
+    {
+        printf("{");
+        printf("Pad, ");
+        printf("up_lengths_");
+        print_multi_index(up_lengths_);
+        printf("left_pad_length %d", index_t{left_pad_length_});
+        printf("right_pad_length %d", index_t{right_pad_length_});
+        printf("}");
+    }
+};
+
+template <typename LowLength, typename LeftPadLength, bool SkipIsValidCheck = false>
+struct LeftPad
+{
+    using LowerIndex = MultiIndex<1>;
+    using UpperIndex = MultiIndex<1>;
+
+    using UpLengths = decltype(make_tuple(LowLength{} + LeftPadLength{}));
+
+    UpLengths up_lengths_;
+    LeftPadLength left_pad_length_;
+
+    __host__ __device__ constexpr LeftPad() = default;
+
+    __host__ __device__ constexpr LeftPad(const LowLength& low_length,
+                                          const LeftPadLength& left_pad_length)
+        : up_lengths_{make_tuple(low_length + left_pad_length)}, left_pad_length_{left_pad_length}
+    {
+    }
+
+    __host__ __device__ static constexpr index_t GetNumOfLowerDimension() { return 1; }
+
+    __host__ __device__ static constexpr index_t GetNumOfUpperDimension() { return 1; }
+
+    __host__ __device__ constexpr const auto& GetUpperLengths() const { return up_lengths_; }
+
+    template <typename LowIdx, typename UpIdx>
+    __host__ __device__ constexpr void CalculateLowerIndex(LowIdx& idx_low,
+                                                           const UpIdx& idx_up) const
+    {
+        static_assert(LowIdx::Size() == 1 && UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        idx_low(Number<0>{}) = idx_up[Number<0>{}] - left_pad_length_;
+    }
+
+    template <typename LowIdxDiff,
+              typename UpIdxDiff,
+              typename LowIdx,
+              typename UpIdx,
+              index_t Hack>
+    __host__ __device__ static void UpdateLowerIndex(LowIdxDiff& idx_diff_low,
+                                                     const UpIdxDiff& idx_diff_up,
+                                                     LowIdx& idx_low,
+                                                     const UpIdx&,
+                                                     Number<Hack>)
+    {
+        static_assert(LowIdxDiff::Size() == 1 && UpIdxDiff::Size() == 1 && LowIdx::Size() == 1 &&
+                          UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        constexpr auto I0 = Number<0>{};
+
+        idx_diff_low(I0) = idx_diff_up[I0];
+
+        idx_low += idx_diff_low;
+    }
+
+    __host__ __device__ static constexpr bool IsLinearTransform() { return true; }
+
+    __host__ __device__ static constexpr bool IsValidUpperIndexAlwaysMappedToValidLowerIndex()
+    {
+        return SkipIsValidCheck;
+    }
+
+    template <typename UpIdx>
+    __host__ __device__ constexpr bool
+    IsValidUpperIndexMappedToValidLowerIndex(const UpIdx& idx_up) const
+    {
+        return SkipIsValidCheck || (idx_up[Number<0>{}] >= left_pad_length_);
+    }
+
+    __host__ __device__ static constexpr bool IsKnownAtCompileTime()
+    {
+        return is_known_at_compile_time<UpLengths>::value &&
+               is_known_at_compile_time<LeftPadLength>::value;
+    }
+
+    __host__ __device__ void Print() const
+    {
+        printf("{");
+        printf("LeftPad, ");
+        printf("up_lengths_");
+        print_multi_index(up_lengths_);
+        printf("left_pad_length_ %d", index_t{left_pad_length_});
+        printf("}");
+    }
+};
+
+template <typename LowLength, typename RightPadLength, bool SkipIsValidCheck = false>
+struct RightPad
+{
+    using LowerIndex = MultiIndex<1>;
+    using UpperIndex = MultiIndex<1>;
+
+    using UpLengths = decltype(make_tuple(LowLength{} + RightPadLength{}));
+
+    UpLengths up_lengths_;
+    LowLength low_length_;
+    RightPadLength right_pad_length_;
+
+    __host__ __device__ constexpr RightPad() = default;
+
+    __host__ __device__ constexpr RightPad(const LowLength& low_length,
+                                           const RightPadLength& right_pad_length)
+        : up_lengths_{make_tuple(low_length + right_pad_length)},
+          low_length_{low_length},
+          right_pad_length_{right_pad_length}
+    {
+    }
+
+    __host__ __device__ static constexpr index_t GetNumOfLowerDimension() { return 1; }
+
+    __host__ __device__ static constexpr index_t GetNumOfUpperDimension() { return 1; }
+
+    __host__ __device__ constexpr const auto& GetUpperLengths() const { return up_lengths_; }
+
+    template <typename LowIdx, typename UpIdx>
+    __host__ __device__ static constexpr void CalculateLowerIndex(LowIdx& idx_low,
+                                                                  const UpIdx& idx_up)
+    {
+        static_assert(LowIdx::Size() == 1 && UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        idx_low(Number<0>{}) = idx_up[Number<0>{}];
+    }
+
+    template <typename LowIdxDiff,
+              typename UpIdxDiff,
+              typename LowIdx,
+              typename UpIdx,
+              index_t Hack>
+    __host__ __device__ static void UpdateLowerIndex(LowIdxDiff& idx_diff_low,
+                                                     const UpIdxDiff& idx_diff_up,
+                                                     LowIdx& idx_low,
+                                                     const UpIdx&,
+                                                     Number<Hack>)
+    {
+        static_assert(LowIdxDiff::Size() == 1 && UpIdxDiff::Size() == 1 && LowIdx::Size() == 1 &&
+                          UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        constexpr auto I0 = Number<0>{};
+
+        idx_diff_low(I0) = idx_diff_up[I0];
+
+        idx_low += idx_diff_low;
+    }
+
+    __host__ __device__ static constexpr bool IsLinearTransform() { return true; }
+
+    __host__ __device__ static constexpr bool IsValidUpperIndexAlwaysMappedToValidLowerIndex()
+    {
+        return SkipIsValidCheck;
+    }
+
+    template <typename UpIdx>
+    __host__ __device__ constexpr bool
+    IsValidUpperIndexMappedToValidLowerIndex(const UpIdx& idx_up) const
+    {
+        return SkipIsValidCheck || (idx_up[Number<0>{}] < low_length_);
+    }
+
+    __host__ __device__ static constexpr bool IsKnownAtCompileTime()
+    {
+        return is_known_at_compile_time<UpLengths>::value &&
+               is_known_at_compile_time<LowLength>::value &&
+               is_known_at_compile_time<RightPadLength>::value;
+    }
+
+    __host__ __device__ void Print() const
+    {
+        printf("{");
+        printf("RightPad, ");
+        printf("up_lengths_");
+        print_multi_index(up_lengths_);
+        printf("low_length_ %d", index_t{low_length_});
+        printf("left_pad_length_ %d", index_t{right_pad_length_});
+        printf("}");
+    }
+};
+
+// idx_low = coefficients[0, ...nDimUp-1] * idx_up[0, ...nDimUp-1]
+// UpLengths and Coefficients can be either of the followings:
+//   1) Tuple of index_t, which is known at run-time, or
+//   2) Tuple of Number, which is known at compile-time, or
+//   3) Tuple of mixture of index_t and Number, which is known partially at run-time and partially
+//   at compile-time
+template <typename UpLengths,
+          typename Coefficients,
+          typename enable_if<UpLengths::Size() == Coefficients::Size(), bool>::type = false>
+struct Embed
+{
+    static constexpr index_t NDimUp = UpLengths::Size();
+
+    using LowerIndex = MultiIndex<1>;
+    using UpperIndex = MultiIndex<NDimUp>;
+
+    UpLengths up_lengths_;
+    Coefficients coefficients_;
+
+    __host__ __device__ constexpr Embed() = default;
+
+    __host__ __device__ constexpr Embed(const UpLengths& up_lengths,
+                                        const Coefficients& coefficients)
+        : up_lengths_{up_lengths}, coefficients_{coefficients}
+    {
+    }
+
+    __host__ __device__ static constexpr index_t GetNumOfLowerDimension() { return 1; }
+
+    __host__ __device__ static constexpr index_t GetNumOfUpperDimension() { return NDimUp; }
+
+    __host__ __device__ constexpr const auto& GetUpperLengths() const { return up_lengths_; }
+
+    template <typename LowIdx, typename UpIdx>
+    __host__ __device__ constexpr void CalculateLowerIndex(LowIdx& idx_low,
+                                                           const UpIdx& idx_up) const
+    {
+        static_assert(LowIdx::Size() == 1 && UpIdx::Size() == NDimUp,
+                      "wrong! inconsistent # of dimension");
+
+        idx_low(Number<0>{}) = 0;
+
+        static_for<0, NDimUp, 1>{}([&idx_low, &idx_up, this](auto i) {
+            idx_low(Number<0>{}) += idx_up[i] * this->coefficients_[i];
+        });
+    }
+
+    template <typename LowIdxDiff,
+              typename UpIdxDiff,
+              typename LowIdx,
+              typename UpIdx,
+              index_t Hack>
+    __host__ __device__ void UpdateLowerIndex(LowIdxDiff& idx_diff_low,
+                                              const UpIdxDiff& idx_diff_up,
+                                              LowIdx& idx_low,
+                                              const UpIdx&,
+                                              Number<Hack>) const
+    {
+        static_assert(LowIdxDiff::Size() == 1 && UpIdxDiff::Size() == NDimUp &&
+                          LowIdx::Size() == 1 && UpIdx::Size() == NDimUp,
+                      "wrong! inconsistent # of dimension");
+
+        idx_diff_low(Number<0>{}) = 0;
+
+        static_for<0, NDimUp, 1>{}(
+            [&](auto i) { idx_diff_low(Number<0>{}) += idx_diff_up[i] * coefficients_[i]; });
+
+        idx_low += idx_diff_low;
+    }
+
+    __host__ __device__ static constexpr bool IsLinearTransform() { return true; }
+
+    __host__ __device__ static constexpr bool IsValidUpperIndexAlwaysMappedToValidLowerIndex()
+    {
+        return true;
+    }
+
+    template <typename UpIdx>
+    __host__ __device__ static constexpr bool
+    IsValidUpperIndexMappedToValidLowerIndex(const UpIdx& /* idx_up */)
+    {
+        return true;
+    }
+
+    __host__ __device__ static constexpr bool IsKnownAtCompileTime()
+    {
+        return is_known_at_compile_time<UpLengths>::value &&
+               is_known_at_compile_time<Coefficients>::value;
+    }
+
+    __host__ __device__ void Print() const
+    {
+        printf("{");
+        printf("Embed, ");
+        printf("up_lengths_ ");
+        print_multi_index(up_lengths_);
+        printf("coefficients_ ");
+        print_multi_index(coefficients_);
+        printf("}");
+    }
+};
+
+// Implementation of "Merge" transformation primitive that uses regular to do lowering of
+// multi-index and use carry-and-borrow check to do lowering of multi-index delta
+template <typename LowLengths>
+struct Merge_v1_carry_check
+{
+    static constexpr index_t NDimLow = LowLengths::Size();
+
+    using LowerIndex = MultiIndex<NDimLow>;
+    using UpperIndex = MultiIndex<1>;
+
+    using LowLengthsScan =
+        decltype(container_reverse_exclusive_scan(LowLengths{}, math::multiplies{}, Number<1>{}));
+
+    using UpLengths =
+        decltype(make_tuple(container_reduce(LowLengths{}, math::multiplies{}, Number<1>{})));
+
+    LowLengths low_lengths_;
+    LowLengthsScan low_lengths_scan_;
+    UpLengths up_lengths_;
+
+    __host__ __device__ constexpr Merge_v1_carry_check() = default;
+
+    __host__ __device__ constexpr Merge_v1_carry_check(const LowLengths& low_lengths)
+        : low_lengths_{low_lengths},
+          low_lengths_scan_{
+              container_reverse_exclusive_scan(low_lengths, math::multiplies{}, Number<1>{})},
+          up_lengths_{make_tuple(container_reduce(low_lengths, math::multiplies{}, Number<1>{}))}
+    {
+        static_assert(LowerIndex::Size() == NDimLow, "wrong!");
+    }
+
+    __host__ __device__ static constexpr index_t GetNumOfLowerDimension() { return NDimLow; }
+
+    __host__ __device__ static constexpr index_t GetNumOfUpperDimension() { return 1; }
+
+    __host__ __device__ constexpr const auto& GetUpperLengths() const { return up_lengths_; }
+
+    template <typename LowIdx, typename UpIdx>
+    __host__ __device__ constexpr void CalculateLowerIndex(LowIdx& idx_low,
+                                                           const UpIdx& idx_up) const
+    {
+        static_assert(LowIdx::Size() == NDimLow && UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        index_t tmp = idx_up[Number<0>{}];
+
+        // normal division
+        static_for<0, NDimLow - 1, 1>{}([&](auto i) {
+            idx_low(i) = tmp / this->low_lengths_scan_[i];
+            tmp -= idx_low[i] * this->low_lengths_scan_[i];
+        });
+
+        idx_low(Number<NDimLow - 1>{}) = tmp;
+    }
+
+    template <typename LowIdxDiff,
+              typename UpIdxDiff,
+              typename LowIdx,
+              typename UpIdx,
+              index_t Hack>
+    __host__ __device__ void UpdateLowerIndex_1a(LowIdxDiff& idx_diff_low,
+                                                 const UpIdxDiff& idx_diff_up,
+                                                 LowIdx& idx_low,
+                                                 const UpIdx& /* idx_up_new */,
+                                                 Number<Hack>) const
+    {
+        static_assert(LowIdxDiff::Size() == NDimLow && UpIdxDiff::Size() == 1 &&
+                          LowIdx::Size() == NDimLow && UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        // CalculateLowerIndex(idx_diff_low_const) has multiple integer divisions.
+        // However,
+        //   1) If idx_diff_up is known at compile-time, then idx_diff_low_const
+        //   can be calculated at compile-time.
+        //   2) If idx_diff_up is not known at compile-time, but its value
+        //   doesn't change during the whole kernel execution, then
+        //   idx_diff_low_const also
+        //   doesn't change during the whole kernel execution. Compiler generated
+        //   ISA should
+        //   only caclculate idx_diff_low_const once and save it durinng the whole
+        //   kernel execution
+        // If neither 1) nor 2) is satisfied, then the calculation will also be
+        // computed at
+        //   run-time each time this function is called, and can be very expensive.
+        LowerIndex idx_diff_low_const;
+        LowerIndex idx_low_length_minus_idx_diff_low_const;
+        LowerIndex idx_low_length_plus_idx_diff_low_const;
+
+#if !CK_HACK_MERGE_CALCULATE_IDX_DIFF_LOW_CONST_USE_AMD_GCN_READ_FIRST_LANE
+        index_t tmp = idx_diff_up[Number<0>{}];
+
+        static_for<0, NDimLow - 1, 1>{}([&](auto i) {
+            idx_diff_low_const(i) = tmp / low_lengths_scan_[i];
+            tmp -= idx_diff_low_const[i] * low_lengths_scan_[i];
+        });
+
+        idx_diff_low_const(Number<NDimLow - 1>{}) = tmp;
+
+        static_for<0, NDimLow, 1>{}([&](auto i) {
+            idx_low_length_minus_idx_diff_low_const(i) = low_lengths_[i] - idx_diff_low_const[i];
+
+            idx_low_length_plus_idx_diff_low_const(i) = low_lengths_[i] + idx_diff_low_const[i];
+        });
+#else
+        // Hack: this force result into SGPR. Need to make sure the result is thread invariant
+        index_t tmp = idx_diff_up[Number<0>{}];
+
+        static_for<0, NDimLow - 1, 1>{}([&](auto i) {
+            idx_diff_low_const(i) = __builtin_amdgcn_readfirstlane(tmp / low_lengths_scan_[i]);
+            tmp -= idx_diff_low_const[i] * low_lengths_scan_[i];
+        });
+
+        idx_diff_low_const(Number<NDimLow - 1>{}) = __builtin_amdgcn_readfirstlane(tmp);
+
+        static_for<0, NDimLow, 1>{}([&](auto i) {
+            idx_low_length_minus_idx_diff_low_const(i) =
+                __builtin_amdgcn_readfirstlane(low_lengths_[i] - idx_diff_low_const[i]);
+
+            idx_low_length_plus_idx_diff_low_const(i) =
+                __builtin_amdgcn_readfirstlane(low_lengths_[i] + idx_diff_low_const[i]);
+        });
+#endif
+
+        if constexpr(Hack == 1)
+        {
+            // do carry check on each low dimension in reversed order
+            // do not need to check the first dimension
+            index_t carry = 0;
+
+            static_for<NDimLow - 1, 0, -1>{}([&](auto i) {
+                index_t idx_low_tmp = idx_low[i] + carry;
+
+                bool do_carry = idx_low_tmp >= idx_low_length_minus_idx_diff_low_const[i];
+
+                idx_diff_low(i) =
+                    do_carry ? -idx_low_length_minus_idx_diff_low_const[i] : idx_diff_low_const[i];
+
+                idx_diff_low(i) += carry;
+
+                carry = do_carry ? 1 : 0;
+            });
+
+            idx_diff_low(Number<0>{}) = idx_diff_low_const[Number<0>{}] + carry;
+
+            idx_low += idx_diff_low;
+        }
+        else if constexpr(Hack == 2)
+        {
+            // do carry check on each low dimension in reversed order
+            // do not need to check the first dimension
+            index_t borrow = 0;
+
+            static_for<NDimLow - 1, 0, -1>{}([&](auto i) {
+                index_t idx_low_tmp = idx_low[i] - borrow;
+
+                bool do_borrow = idx_low_tmp < -idx_diff_low_const[i];
+
+                idx_diff_low(i) =
+                    do_borrow ? idx_low_length_plus_idx_diff_low_const[i] : idx_diff_low_const[i];
+
+                idx_diff_low(i) -= borrow;
+
+                borrow = do_borrow ? 1 : 0;
+            });
+
+            idx_diff_low(Number<0>{}) = idx_diff_low_const[Number<0>{}] - borrow;
+
+            idx_low += idx_diff_low;
+        }
+        else
+        {
+            // do carry check on each low dimension in reversed order
+            // do not need to check the first dimension
+            index_t carry = 0;
+
+            static_for<NDimLow - 1, 0, -1>{}([&](auto i) {
+                index_t idx_low_tmp = idx_low[i] + carry;
+
+                bool do_carry  = idx_low_tmp >= idx_low_length_minus_idx_diff_low_const[i];
+                bool do_borrow = idx_low_tmp < -idx_diff_low_const[i];
+
+                idx_diff_low(i) =
+                    do_carry ? -idx_low_length_minus_idx_diff_low_const[i] : idx_diff_low_const[i];
+                idx_diff_low(i) =
+                    do_borrow ? idx_low_length_plus_idx_diff_low_const[i] : idx_diff_low[i];
+
+                idx_diff_low(i) += carry;
+
+                carry = do_carry ? 1 : 0;
+                carry = do_borrow ? -1 : carry;
+            });
+
+            idx_diff_low(Number<0>{}) = idx_diff_low_const[Number<0>{}] + carry;
+
+            idx_low += idx_diff_low;
+        }
+    }
+
+    template <typename LowIdxDiff,
+              typename UpIdxDiff,
+              typename LowIdx,
+              typename UpIdx,
+              index_t Hack>
+    __host__ __device__ void UpdateLowerIndex_1b(LowIdxDiff& idx_diff_low,
+                                                 const UpIdxDiff& idx_diff_up,
+                                                 LowIdx& idx_low,
+                                                 const UpIdx& /* idx_up_new */,
+                                                 Number<Hack>) const
+    {
+        static_assert(LowIdxDiff::Size() == NDimLow && UpIdxDiff::Size() == 1 &&
+                          LowIdx::Size() == NDimLow && UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        // CalculateLowerIndex(idx_diff_low_const) has multiple integer divisions.
+        // However,
+        //   1) If idx_diff_up is known at compile-time, then idx_diff_low_const
+        //   can be calculated at compile-time.
+        //   2) If idx_diff_up is not known at compile-time, but its value
+        //   doesn't change during the whole kernel execution, then
+        //   idx_diff_low_const also
+        //   doesn't change during the whole kernel execution. Compiler generated
+        //   ISA should
+        //   only caclculate idx_diff_low_const once and save it durinng the whole
+        //   kernel execution
+        // If neither 1) nor 2) is satisfied, then the calculation will also be
+        // computed at
+        //   run-time each time this function is called, and can be very expensive.
+        LowerIndex idx_diff_low_const;
+        LowerIndex idx_low_length_minus_idx_diff_low_const;
+        LowerIndex idx_low_length_plus_idx_diff_low_const;
+
+#if !CK_HACK_MERGE_CALCULATE_IDX_DIFF_LOW_CONST_USE_AMD_GCN_READ_FIRST_LANE
+        index_t tmp = idx_diff_up[Number<0>{}];
+
+        static_for<0, NDimLow - 1, 1>{}([&](auto i) {
+            idx_diff_low_const(i) = tmp / low_lengths_scan_[i];
+            tmp -= idx_diff_low_const[i] * low_lengths_scan_[i];
+        });
+
+        idx_diff_low_const(Number<NDimLow - 1>{}) = tmp;
+
+        static_for<0, NDimLow, 1>{}([&](auto i) {
+            idx_low_length_minus_idx_diff_low_const(i) = low_lengths_[i] - idx_diff_low_const[i];
+
+            idx_low_length_plus_idx_diff_low_const(i) = low_lengths_[i] + idx_diff_low_const[i];
+        });
+#else
+        // Hack: this force result into SGPR. Need to make sure the result is thread invariant
+        index_t tmp = idx_diff_up[Number<0>{}];
+
+        static_for<0, NDimLow - 1, 1>{}([&](auto i) {
+            idx_diff_low_const(i) = __builtin_amdgcn_readfirstlane(tmp / low_lengths_scan_[i]);
+            tmp -= idx_diff_low_const[i] * low_lengths_scan_[i];
+        });
+
+        idx_diff_low_const(Number<NDimLow - 1>{}) = __builtin_amdgcn_readfirstlane(tmp);
+
+        static_for<0, NDimLow, 1>{}([&](auto i) {
+            idx_low_length_minus_idx_diff_low_const(i) =
+                __builtin_amdgcn_readfirstlane(low_lengths_[i] - idx_diff_low_const[i]);
+
+            idx_low_length_plus_idx_diff_low_const(i) = low_lengths_[i] + idx_diff_low_const[i];
+        });
+#endif
+
+        if constexpr(Hack == 1)
+        {
+            // do carry check on each low dimension in reversed order
+            // do not need to check the first dimension
+            index_t carry = 0;
+
+            static_for<NDimLow - 1, 0, -1>{}([&](auto i) {
+                index_t idx_low_tmp = idx_low[i] + carry;
+
+                bool do_carry = idx_low_tmp >= idx_low_length_minus_idx_diff_low_const[i];
+
+                idx_diff_low(i) =
+                    do_carry ? -idx_low_length_minus_idx_diff_low_const[i] : idx_diff_low_const[i];
+
+                idx_diff_low(i) += carry;
+
+                carry = do_carry ? 1 : 0;
+            });
+
+            idx_diff_low(Number<0>{}) = idx_diff_low_const[Number<0>{}] + carry;
+
+            idx_low += idx_diff_low;
+        }
+        else if constexpr(Hack == 2)
+        {
+            // do carry check on each low dimension in reversed order
+            // do not need to check the first dimension
+            index_t borrow = 0;
+
+            static_for<NDimLow - 1, 0, -1>{}([&](auto i) {
+                index_t negative_idx_low_tmp = borrow - idx_low[i];
+
+                bool do_borrow = negative_idx_low_tmp > idx_diff_low_const[i];
+
+                idx_diff_low(i) =
+                    do_borrow ? idx_low_length_plus_idx_diff_low_const[i] : idx_diff_low_const[i];
+
+                idx_diff_low(i) -= borrow;
+
+                borrow = do_borrow ? 1 : 0;
+            });
+
+            idx_diff_low(Number<0>{}) = idx_diff_low_const[Number<0>{}] - borrow;
+
+            idx_low += idx_diff_low;
+        }
+        else
+        {
+            // do carry check on each low dimension in reversed order
+            // do not need to check the first dimension
+            index_t carry = 0;
+
+            static_for<NDimLow - 1, 0, -1>{}([&](auto i) {
+                index_t idx_low_tmp = idx_low[i] + carry;
+
+                bool do_carry  = idx_low_tmp >= idx_low_length_minus_idx_diff_low_const[i];
+                bool do_borrow = idx_low_tmp < -idx_diff_low_const[i];
+
+                idx_diff_low(i) =
+                    do_carry ? -idx_low_length_minus_idx_diff_low_const[i] : idx_diff_low_const[i];
+                idx_diff_low(i) =
+                    do_borrow ? idx_low_length_plus_idx_diff_low_const[i] : idx_diff_low[i];
+
+                idx_diff_low(i) += carry;
+
+                carry = do_carry ? 1 : 0;
+                carry = do_borrow ? -1 : carry;
+            });
+
+            idx_diff_low(Number<0>{}) = idx_diff_low_const[Number<0>{}] + carry;
+
+            idx_low += idx_diff_low;
+        }
+    }
+
+    template <typename LowIdxDiff,
+              typename UpIdxDiff,
+              typename LowIdx,
+              typename UpIdx,
+              index_t Hack>
+    __host__ __device__ void UpdateLowerIndex_2(LowIdxDiff& idx_diff_low,
+                                                const UpIdxDiff& idx_diff_up,
+                                                LowIdx& idx_low,
+                                                const UpIdx& /* idx_up_new */,
+                                                Number<Hack>) const
+    {
+        static_assert(LowIdxDiff::Size() == NDimLow && UpIdxDiff::Size() == 1 &&
+                          LowIdx::Size() == NDimLow && UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        // CalculateLowerIndex(idx_diff_low_const) has multiple integer divisions.
+        // However,
+        //   1) If idx_diff_up is known at compile-time, then idx_diff_low_const
+        //   can be calculated at compile-time.
+        //   2) If idx_diff_up is not known at compile-time, but its value
+        //   doesn't change during the whole kernel execution, then
+        //   idx_diff_low_const also
+        //   doesn't change during the whole kernel execution. Compiler generated
+        //   ISA should
+        //   only caclculate idx_diff_low_const once and save it durinng the whole
+        //   kernel execution
+        // If neither 1) nor 2) is satisfied, then the calculation will also be
+        //   computed at run-time each time this function is called, and can be
+        //   very expensive.
+        LowerIndex idx_diff_low_const;
+
+#if !CK_HACK_MERGE_CALCULATE_IDX_DIFF_LOW_CONST_USE_AMD_GCN_READ_FIRST_LANE
+        index_t tmp = idx_diff_up[Number<0>{}];
+
+        static_for<0, NDimLow - 1, 1>{}([&](auto i) {
+            idx_diff_low_const(i) = tmp / low_lengths_scan_[i];
+            tmp -= idx_diff_low_const[i] * low_lengths_scan_[i];
+        });
+
+        idx_diff_low_const(Number<NDimLow - 1>{}) = tmp;
+#else
+        // Hack: this force result into SGPR. Need to make sure the result is thread invariant
+        index_t tmp = idx_diff_up[Number<0>{}];
+
+        static_for<0, NDimLow - 1, 1>{}([&](auto i) {
+            idx_diff_low_const(i) = __builtin_amdgcn_readfirstlane(tmp / low_lengths_scan_[i]);
+            tmp -= idx_diff_low_const[i] * low_lengths_scan_[i];
+        });
+
+        idx_diff_low_const(Number<NDimLow - 1>{}) = __builtin_amdgcn_readfirstlane(tmp);
+#endif
+
+        if constexpr(Hack == 1)
+        {
+            // do carry check on each low dimension in reversed order
+            // do not need to check the first dimension
+            bool do_carry = 0;
+
+            static_for<NDimLow - 1, 0, -1>{}([&](auto i) {
+                idx_diff_low(i) = idx_diff_low_const[i] + do_carry;
+
+                index_t idx_low_tmp = idx_low[i] + idx_diff_low[i];
+
+                do_carry = idx_low_tmp >= low_lengths_[i];
+
+#if 0
+                // TODO: use exec-mask inline asm, which use 1 VALU
+                if(do_carry)
+                {
+                    idx_diff_low(i) -= low_lengths_[i];
+                }
+#elif 1
+                // this use 2 VALU
+                idx_diff_low(i) = do_carry ? idx_diff_low[i] - low_lengths_[i] : idx_diff_low[i];
+#elif 1
+                // this use 2 VALU
+                index_t idx_diff_low_tmp = idx_diff_low[i] - low_lengths_[i];
+                idx_diff_low(i)          = do_carry ? idx_diff_low_tmp : idx_diff_low[i];
+#endif
+
+                idx_low(i) += idx_diff_low[i];
+            });
+
+            constexpr auto I0 = Number<0>{};
+
+            idx_diff_low(I0) = idx_diff_low_const[I0] + do_carry;
+
+            idx_low(I0) += idx_diff_low[I0];
+        }
+        else if constexpr(Hack == 2)
+        {
+            // do borrow check on each low dimension in reversed order
+            // do not need to check the first dimension
+            bool do_borrow = 0;
+
+            static_for<NDimLow - 1, 0, -1>{}([&](auto i) {
+                idx_diff_low(i) = idx_diff_low_const[i] - do_borrow;
+
+                index_t idx_low_tmp = idx_low[i] + idx_diff_low[i];
+
+                do_borrow = idx_low_tmp < 0;
+
+#if 0
+                // TODO: use exec-mask inline asm
+                if(do_borrow)
+                {
+                    idx_diff_low(i) += low_lengths_[i];
+                }
+#elif 1
+                idx_diff_low(i) = do_borrow ? idx_diff_low[i] + low_lengths_[i] : idx_diff_low[i];
+#elif 1
+                index_t idx_diff_low_tmp = idx_diff_low[i] + low_lengths_[i];
+                idx_diff_low(i)          = do_borrow ? idx_diff_low_tmp : idx_diff_low[i];
+#endif
+
+                idx_low(i) += idx_diff_low[i];
+            });
+
+            constexpr auto I0 = Number<0>{};
+
+            idx_diff_low(I0) = idx_diff_low_const[I0] - do_borrow;
+
+            idx_low(I0) += idx_diff_low[I0];
+        }
+        else
+        {
+            // not implemented
+        }
+    }
+
+    template <typename LowIdxDiff,
+              typename UpIdxDiff,
+              typename LowIdx,
+              typename UpIdx,
+              index_t Hack>
+    __host__ __device__ void UpdateLowerIndex(LowIdxDiff& idx_diff_low,
+                                              const UpIdxDiff& idx_diff_up,
+                                              LowIdx& idx_low,
+                                              const UpIdx& idx_up_new,
+                                              Number<Hack>) const
+    {
+#if 1
+        UpdateLowerIndex_1a(idx_diff_low, idx_diff_up, idx_low, idx_up_new, Number<Hack>{});
+#elif 0
+        UpdateLowerIndex_1b(idx_diff_low, idx_diff_up, idx_low, idx_up_new, Number<Hack>{});
+#else
+        UpdateLowerIndex_2(idx_diff_low, idx_diff_up, idx_low, idx_up_new, Number<Hack>{});
+#endif
+    }
+
+    __host__ __device__ static constexpr bool IsLinearTransform() { return false; }
+
+    __host__ __device__ static constexpr bool IsValidUpperIndexAlwaysMappedToValidLowerIndex()
+    {
+        return true;
+    }
+
+    __host__ __device__ static constexpr bool IsKnownAtCompileTime()
+    {
+        return is_known_at_compile_time<LowLengths>::value &&
+               is_known_at_compile_time<LowLengthsScan>::value &&
+               is_known_at_compile_time<UpLengths>::value;
+    }
+
+    template <typename UpIdx>
+    __host__ __device__ static constexpr bool
+    IsValidUpperIndexMappedToValidLowerIndex(const UpIdx& /* idx_up */)
+    {
+        return true;
+    }
+
+    __host__ __device__ void Print() const
+    {
+        printf("{");
+        printf("Merge_v1_carry_check, ");
+        printf("low_lengths_ ");
+        print_multi_index(low_lengths_);
+        printf("low_lengths_scan_ ");
+        print_multi_index(low_lengths_scan_);
+        printf("up_lengths_ ");
+        print_multi_index(up_lengths_);
+        printf("}");
+    }
+};
+
+template <typename LowLengths>
+struct lambda_merge_generate_MagicDivision_calculate_magic_multiplier
+{
+    template <index_t I>
+    __host__ __device__ constexpr auto operator()(Number<I> i) const
+    {
+        return MagicDivision::CalculateMagicMultiplier(LowLengths{}[i]);
+    }
+};
+
+template <typename LowLengths>
+struct lambda_merge_generate_MagicDivision_calculate_magic_shift
+{
+    template <index_t I>
+    __host__ __device__ constexpr auto operator()(Number<I> i) const
+    {
+        return MagicDivision::CalculateMagicShift(LowLengths{}[i]);
+    }
+};
+
+// Implementation of "Merge" transformation primitive that uses magic-number-division to do lowering
+// of both multi-index and delta of multi-index
+// Caution:
+//   1. The magic number division implementation being used would produce correct result if the
+//   dividended is uint32_t and its value is with in 31-bit value range of uint32_t.
+//   2. The 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.
+//   3. For Merge primitive, upper-index is the dividend.
+//   4. When upper-index is uint32_t, its value need to be within 31-bit range.
+//   5. When upper-index is int32_t type (when index_t is int32_t), its value need to be
+//   non-negative.
+template <typename LowLengths>
+struct Merge_v2_magic_division
+{
+    static constexpr index_t NDimLow = LowLengths::Size();
+
+    using LowerIndex = MultiIndex<NDimLow>;
+    using UpperIndex = MultiIndex<1>;
+
+    using UpLengths =
+        decltype(make_tuple(container_reduce(LowLengths{}, math::multiplies{}, Number<1>{})));
+
+    using LowLengthsMagicDivisorMultipiler = decltype(
+        generate_tuple(lambda_merge_generate_MagicDivision_calculate_magic_multiplier<LowLengths>{},
+                       Number<NDimLow>{}));
+
+    using LowLengthsMagicDivisorShift = decltype(
+        generate_tuple(lambda_merge_generate_MagicDivision_calculate_magic_shift<LowLengths>{},
+                       Number<NDimLow>{}));
+
+    LowLengths low_lengths_;
+    LowLengthsMagicDivisorMultipiler low_lengths_magic_divisor_multiplier_;
+    LowLengthsMagicDivisorShift low_lengths_magic_divisor_shift_;
+    UpLengths up_lengths_;
+
+    __host__ __device__ constexpr Merge_v2_magic_division() = default;
+
+    __host__ __device__ constexpr Merge_v2_magic_division(const LowLengths& low_lengths)
+        : low_lengths_{low_lengths},
+          low_lengths_magic_divisor_multiplier_{generate_tuple(
+              [&](auto i) { return MagicDivision::CalculateMagicMultiplier(low_lengths[i]); },
+              Number<NDimLow>{})},
+          low_lengths_magic_divisor_shift_{generate_tuple(
+              [&](auto i) { return MagicDivision::CalculateMagicShift(low_lengths[i]); },
+              Number<NDimLow>{})},
+          up_lengths_{make_tuple(container_reduce(low_lengths, math::multiplies{}, Number<1>{}))}
+    {
+        static_assert(LowerIndex::Size() == NDimLow, "wrong!");
+    }
+
+    __host__ __device__ static constexpr index_t GetNumOfLowerDimension() { return NDimLow; }
+
+    __host__ __device__ static constexpr index_t GetNumOfUpperDimension() { return 1; }
+
+    __host__ __device__ constexpr const auto& GetUpperLengths() const { return up_lengths_; }
+
+    template <typename LowIdx, typename UpIdx>
+    __host__ __device__ constexpr void CalculateLowerIndex(LowIdx& idx_low,
+                                                           const UpIdx& idx_up) const
+    {
+        static_assert(LowIdx::Size() == NDimLow && UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        index_t tmp = idx_up[Number<0>{}];
+
+        static_for<NDimLow - 1, 0, -1>{}([&, this](auto i) {
+            index_t tmp2 =
+                MagicDivision::DoMagicDivision(tmp,
+                                               this->low_lengths_magic_divisor_multiplier_[i],
+                                               this->low_lengths_magic_divisor_shift_[i]);
+            idx_low(i) = tmp - tmp2 * this->low_lengths_[i];
+            tmp        = tmp2;
+        });
+
+        idx_low(Number<0>{}) = tmp;
+    }
+
+    template <typename LowIdxDiff,
+              typename UpIdxDiff,
+              typename LowIdx,
+              typename UpIdx,
+              index_t Hack>
+    __host__ __device__ void UpdateLowerIndex(LowIdxDiff& idx_diff_low,
+                                              const UpIdxDiff&,
+                                              LowIdx& idx_low,
+                                              const UpIdx& idx_up_new,
+                                              Number<Hack>) const
+    {
+        static_assert(LowIdxDiff::Size() == NDimLow && UpIdxDiff::Size() == 1 &&
+                          LowIdx::Size() == NDimLow && UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        index_t tmp = idx_up_new[Number<0>{}];
+
+        static_for<NDimLow - 1, 0, -1>{}([&, this](auto i) {
+            index_t tmp2 =
+                MagicDivision::DoMagicDivision(tmp,
+                                               this->low_lengths_magic_divisor_multiplier_[i],
+                                               this->low_lengths_magic_divisor_shift_[i]);
+
+            index_t idx_low_old = idx_low[i];
+
+            idx_low(i) = tmp - tmp2 * this->low_lengths_[i];
+            tmp        = tmp2;
+
+            idx_diff_low(i) = idx_low[i] - idx_low_old;
+        });
+
+        idx_diff_low(Number<0>{}) = tmp - idx_low(Number<0>{});
+
+        idx_low(Number<0>{}) = tmp;
+    }
+
+    __host__ __device__ static constexpr bool IsLinearTransform() { return false; }
+
+    __host__ __device__ static constexpr bool IsValidUpperIndexAlwaysMappedToValidLowerIndex()
+    {
+        return true;
+    }
+
+    __host__ __device__ static constexpr bool IsKnownAtCompileTime()
+    {
+        return is_known_at_compile_time<LowLengths>::value &&
+               is_known_at_compile_time<LowLengthsMagicDivisorMultipiler>::value &&
+               is_known_at_compile_time<LowLengthsMagicDivisorShift>::value &&
+               is_known_at_compile_time<UpLengths>::value;
+    }
+
+    template <typename UpIdx>
+    __host__ __device__ static constexpr bool
+    IsValidUpperIndexMappedToValidLowerIndex(const UpIdx& /* idx_up */)
+    {
+        return true;
+    }
+
+    __host__ __device__ void Print() const
+    {
+        printf("{");
+        printf("Merge_v2_magic_division, ");
+        printf("low_lengths_ ");
+        print_multi_index(low_lengths_);
+        printf("low_lengths_magic_divisor_multiplier_ ");
+        print_multi_index(low_lengths_magic_divisor_multiplier_);
+        printf("low_lengths_magic_divisor_shift_ ");
+        print_multi_index(low_lengths_magic_divisor_shift_);
+        printf("up_lengths_ ");
+        print_multi_index(up_lengths_);
+        printf("}");
+    }
+};
+
+// Implementation of "Merge" transformation primitive that uses magic-number-division to do lowering
+// of both multi-index and delta of multi-index
+// Caution:
+//   1. The magic number division implementation being used would produce correct result if the
+//   dividended is uint32_t and its value is with in 31-bit value range of uint32_t.
+//   2. The 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.
+//   3. For Merge primitive, upper-index is the dividend.
+//   4. When upper-index is uint32_t, its value need to be within 31-bit range.
+//   5. When upper-index is int32_t type (when index_t is int32_t), its value need to be
+//   non-negative.
+template <typename LowLengths>
+struct Merge_v2r2_magic_division
+{
+    static constexpr index_t NDimLow = LowLengths::Size();
+
+    using LowerIndex = MultiIndex<NDimLow>;
+    using UpperIndex = MultiIndex<1>;
+
+    using LowLengthsScan =
+        decltype(container_reverse_exclusive_scan(LowLengths{}, math::multiplies{}, Number<1>{}));
+
+    using UpLengths =
+        decltype(make_tuple(container_reduce(LowLengths{}, math::multiplies{}, Number<1>{})));
+
+    using LowLengthsScanMagicDivisorMultipiler = decltype(generate_tuple(
+        lambda_merge_generate_MagicDivision_calculate_magic_multiplier<LowLengthsScan>{},
+        Number<NDimLow>{}));
+
+    using LowLengthsScanMagicDivisorShift = decltype(
+        generate_tuple(lambda_merge_generate_MagicDivision_calculate_magic_shift<LowLengthsScan>{},
+                       Number<NDimLow>{}));
+
+    LowLengths low_lengths_;
+    LowLengthsScan low_lengths_scan_;
+    LowLengthsScanMagicDivisorMultipiler low_lengths_scan_magic_divisor_multiplier_;
+    LowLengthsScanMagicDivisorShift low_lengths_scan_magic_divisor_shift_;
+    UpLengths up_lengths_;
+
+    __host__ __device__ constexpr Merge_v2r2_magic_division() = default;
+
+    __host__ __device__ constexpr Merge_v2r2_magic_division(const LowLengths& low_lengths)
+        : low_lengths_{low_lengths},
+          low_lengths_scan_{
+              container_reverse_exclusive_scan(low_lengths, math::multiplies{}, Number<1>{})},
+          low_lengths_scan_magic_divisor_multiplier_{generate_tuple(
+              [&](auto i) { return MagicDivision::CalculateMagicMultiplier(low_lengths_scan_[i]); },
+              Number<NDimLow>{})},
+          low_lengths_scan_magic_divisor_shift_{generate_tuple(
+              [&](auto i) { return MagicDivision::CalculateMagicShift(low_lengths_scan_[i]); },
+              Number<NDimLow>{})},
+          up_lengths_{make_tuple(container_reduce(low_lengths, math::multiplies{}, Number<1>{}))}
+    {
+        static_assert(LowerIndex::Size() == NDimLow, "wrong!");
+    }
+
+    __host__ __device__ static constexpr index_t GetNumOfLowerDimension() { return NDimLow; }
+
+    __host__ __device__ static constexpr index_t GetNumOfUpperDimension() { return 1; }
+
+    __host__ __device__ constexpr const auto& GetUpperLengths() const { return up_lengths_; }
+
+    template <typename LowIdx, typename UpIdx>
+    __host__ __device__ constexpr void CalculateLowerIndex(LowIdx& idx_low,
+                                                           const UpIdx& idx_up) const
+    {
+        static_assert(LowIdx::Size() == NDimLow && UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        index_t tmp = idx_up[Number<0>{}];
+
+        static_for<0, NDimLow - 1, 1>{}([&, this](auto i) {
+            idx_low(i) =
+                MagicDivision::DoMagicDivision(tmp,
+                                               this->low_lengths_scan_magic_divisor_multiplier_[i],
+                                               this->low_lengths_scan_magic_divisor_shift_[i]);
+
+            tmp -= idx_low[i] * this->low_lengths_scan_[i];
+        });
+
+        idx_low(Number<NDimLow - 1>{}) = tmp;
+    }
+
+    template <typename LowIdxDiff,
+              typename UpIdxDiff,
+              typename LowIdx,
+              typename UpIdx,
+              index_t Hack>
+    __host__ __device__ void UpdateLowerIndex(LowIdxDiff& idx_diff_low,
+                                              const UpIdxDiff&,
+                                              LowIdx& idx_low,
+                                              const UpIdx& idx_up_new,
+                                              Number<Hack>) const
+    {
+        static_assert(LowIdxDiff::Size() == NDimLow && UpIdxDiff::Size() == 1 &&
+                          LowIdx::Size() == NDimLow && UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        index_t tmp = idx_up_new[Number<0>{}];
+
+        static_for<0, NDimLow - 1, 1>{}([&, this](auto i) {
+            index_t idx_low_old = idx_low[i];
+
+            idx_low(i) =
+                MagicDivision::DoMagicDivision(tmp,
+                                               this->low_lengths_scan_magic_divisor_multiplier_[i],
+                                               this->low_lengths_scan_magic_divisor_shift_[i]);
+
+            idx_diff_low(i) = idx_low[i] - idx_low_old;
+
+            tmp -= idx_low[i] * this->low_lengths_scan_[i];
+        });
+
+        idx_diff_low(Number<NDimLow - 1>{}) = tmp - idx_low[Number<NDimLow - 1>{}];
+
+        idx_low(Number<NDimLow - 1>{}) = tmp;
+    }
+
+    __host__ __device__ static constexpr bool IsLinearTransform() { return false; }
+
+    __host__ __device__ static constexpr bool IsValidUpperIndexAlwaysMappedToValidLowerIndex()
+    {
+        return true;
+    }
+
+    __host__ __device__ static constexpr bool IsKnownAtCompileTime()
+    {
+        return is_known_at_compile_time<LowLengths>::value &&
+               is_known_at_compile_time<LowLengthsScanMagicDivisorMultipiler>::value &&
+               is_known_at_compile_time<LowLengthsScanMagicDivisorShift>::value &&
+               is_known_at_compile_time<UpLengths>::value;
+    }
+
+    template <typename UpIdx>
+    __host__ __device__ static constexpr bool
+    IsValidUpperIndexMappedToValidLowerIndex(const UpIdx& /* idx_up */)
+    {
+        return true;
+    }
+
+    __host__ __device__ void Print() const
+    {
+        printf("{");
+        printf("Merge_v2r2_magic_division, ");
+        printf("low_lengths_ ");
+        print_multi_index(low_lengths_);
+        printf("low_lengths_scan ");
+        print_multi_index(low_lengths_scan_);
+        printf("low_lengths_scan_magic_divisor_multiplier_ ");
+        print_multi_index(low_lengths_scan_magic_divisor_multiplier_);
+        printf("low_lengths_scan_magic_divisor_shift_ ");
+        print_multi_index(low_lengths_scan_magic_divisor_shift_);
+        printf("up_lengths_ ");
+        print_multi_index(up_lengths_);
+        printf("}");
+    }
+};
+
+// Implementation of "Merge" transformation primitive that uses division and mod. It is supposed to
+// be used for low_lengths that are known at compile time and are power of 2, otherwise performance
+// will be very bad
+template <typename LowLengths>
+struct Merge_v3_division_mod
+{
+    static constexpr index_t NDimLow = LowLengths::Size();
+
+    using LowerIndex = MultiIndex<NDimLow>;
+    using UpperIndex = MultiIndex<1>;
+
+    using LowLengthsScan =
+        decltype(container_reverse_exclusive_scan(LowLengths{}, math::multiplies{}, Number<1>{}));
+
+    using UpLengths =
+        decltype(make_tuple(container_reduce(LowLengths{}, math::multiplies{}, Number<1>{})));
+
+    LowLengths low_lengths_;
+    LowLengthsScan low_lengths_scan_;
+    UpLengths up_lengths_;
+
+    __host__ __device__ constexpr Merge_v3_division_mod() = default;
+
+    __host__ __device__ constexpr Merge_v3_division_mod(const LowLengths& low_lengths)
+        : low_lengths_{low_lengths},
+          low_lengths_scan_{
+              container_reverse_exclusive_scan(low_lengths, math::multiplies{}, Number<1>{})},
+          up_lengths_{make_tuple(container_reduce(low_lengths, math::multiplies{}, Number<1>{}))}
+    {
+        static_assert(LowerIndex::Size() == NDimLow, "wrong!");
+    }
+
+    __host__ __device__ static constexpr index_t GetNumOfLowerDimension() { return NDimLow; }
+
+    __host__ __device__ static constexpr index_t GetNumOfUpperDimension() { return 1; }
+
+    __host__ __device__ constexpr const auto& GetUpperLengths() const { return up_lengths_; }
+
+    template <typename LowIdx, typename UpIdx>
+    __host__ __device__ constexpr void CalculateLowerIndex(LowIdx& idx_low,
+                                                           const UpIdx& idx_up) const
+    {
+        static_assert(LowIdx::Size() == NDimLow && UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        index_t tmp = idx_up[Number<0>{}];
+
+        // division and mod
+        static_for<0, NDimLow - 1, 1>{}([&](auto i) {
+            idx_low(i) = tmp / this->low_lengths_scan_[i];
+            tmp %= this->low_lengths_scan_[i];
+        });
+
+        idx_low(Number<NDimLow - 1>{}) = tmp;
+    }
+
+    template <typename LowIdxDiff,
+              typename UpIdxDiff,
+              typename LowIdx,
+              typename UpIdx,
+              index_t Hack>
+    __host__ __device__ void UpdateLowerIndex(LowIdxDiff& idx_diff_low,
+                                              const UpIdxDiff&,
+                                              LowIdx& idx_low,
+                                              const UpIdx& idx_up_new,
+                                              Number<Hack>) const
+    {
+        static_assert(LowIdxDiff::Size() == NDimLow && UpIdxDiff::Size() == 1 &&
+                          LowIdx::Size() == NDimLow && UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        constexpr auto I0   = Number<0>{};
+        constexpr auto INm1 = Number<NDimLow - 1>{};
+
+        index_t tmp = idx_up_new[I0];
+
+        static_for<0, NDimLow - 1, 1>{}([&](auto i) {
+            const index_t tmp2 = idx_low[i];
+            idx_low(i)         = tmp / this->low_lengths_scan_[i];
+            idx_diff_low(i)    = idx_low[i] - tmp2;
+            tmp %= this->low_lengths_scan_[i];
+        });
+
+        const index_t tmp2 = idx_low[INm1];
+        idx_low(INm1)      = tmp;
+        idx_diff_low(INm1) = idx_low[INm1] - tmp2;
+    }
+
+    __host__ __device__ static constexpr bool IsLinearTransform() { return false; }
+
+    __host__ __device__ static constexpr bool IsValidUpperIndexAlwaysMappedToValidLowerIndex()
+    {
+        return true;
+    }
+
+    __host__ __device__ static constexpr bool IsKnownAtCompileTime()
+    {
+        return is_known_at_compile_time<LowLengths>::value &&
+               is_known_at_compile_time<LowLengthsScan>::value &&
+               is_known_at_compile_time<UpLengths>::value;
+    }
+
+    template <typename UpIdx>
+    __host__ __device__ static constexpr bool
+    IsValidUpperIndexMappedToValidLowerIndex(const UpIdx& /* idx_up */)
+    {
+        return true;
+    }
+
+    __host__ __device__ void Print() const
+    {
+        printf("{");
+        printf("Merge_v3_direct_division_mod, ");
+        printf("low_lengths_ ");
+        print_multi_index(low_lengths_);
+        printf("low_lengths_scan_ ");
+        print_multi_index(low_lengths_scan_);
+        printf("up_lengths_ ");
+        print_multi_index(up_lengths_);
+        printf("}");
+    }
+};
+
+template <typename UpLengths, bool Use24BitIntegerCalculation>
+struct UnMerge
+{
+    static constexpr index_t NDimUp = UpLengths::Size();
+
+    using LowerIndex = MultiIndex<1>;
+    using UpperIndex = MultiIndex<NDimUp>;
+
+    using UpLengthsScan =
+        decltype(container_reverse_exclusive_scan(UpLengths{}, math::multiplies{}, Number<1>{}));
+
+    UpLengths up_lengths_;
+    UpLengthsScan up_lengths_scan_;
+
+    __host__ __device__ constexpr UnMerge() = default;
+
+    __host__ __device__ constexpr UnMerge(const UpLengths& up_lengths)
+        : up_lengths_{up_lengths},
+          up_lengths_scan_{
+              container_reverse_exclusive_scan(up_lengths, math::multiplies{}, Number<1>{})}
+    {
+    }
+
+    __host__ __device__ static constexpr index_t GetNumOfLowerDimension() { return 1; }
+
+    __host__ __device__ static constexpr index_t GetNumOfUpperDimension() { return NDimUp; }
+
+    __host__ __device__ constexpr const auto& GetUpperLengths() const { return up_lengths_; }
+
+    template <typename LowIdx, typename UpIdx>
+    __host__ __device__ constexpr void CalculateLowerIndex(LowIdx& idx_low,
+                                                           const UpIdx& idx_up) const
+    {
+        if constexpr(!Use24BitIntegerCalculation)
+        {
+            idx_low(Number<0>{}) = idx_up[Number<NDimUp - 1>{}];
+
+            static_for<0, NDimUp - 1, 1>{}(
+                [&](auto i) { idx_low(Number<0>{}) += idx_up[i] * up_lengths_scan_[i]; });
+        }
+        else
+        {
+            idx_low(Number<0>{}) = idx_up[Number<NDimUp - 1>{}];
+
+            static_for<0, NDimUp - 1, 1>{}([&](auto i) {
+                idx_low(Number<0>{}) =
+                    (0x00ffffff & idx_low[Number<0>{}]) +
+                    (0x00ffffff & idx_up[i]) * (0x00ffffff & up_lengths_scan_[i]);
+            });
+        }
+    }
+
+    template <typename LowIdxDiff,
+              typename UpIdxDiff,
+              typename LowIdx,
+              typename UpIdx,
+              index_t Hack>
+    __host__ __device__ void UpdateLowerIndex(LowIdxDiff& idx_diff_low,
+                                              const UpIdxDiff& idx_diff_up,
+                                              LowIdx& idx_low,
+                                              const UpIdx&,
+                                              Number<Hack>) const
+    {
+        CalculateLowerIndex(idx_diff_low, idx_diff_up);
+
+        idx_low += idx_diff_low;
+    }
+
+    __host__ __device__ static constexpr bool IsLinearTransform() { return true; }
+
+    __host__ __device__ static constexpr bool IsValidUpperIndexAlwaysMappedToValidLowerIndex()
+    {
+        return true;
+    }
+
+    template <typename UpIdx>
+    __host__ __device__ static constexpr bool
+    IsValidUpperIndexMappedToValidLowerIndex(const UpIdx& /* idx_up */)
+    {
+        return true;
+    }
+
+    __host__ __device__ static constexpr bool IsKnownAtCompileTime()
+    {
+        return is_known_at_compile_time<UpLengths>::value &&
+               is_known_at_compile_time<UpLengthsScan>::value;
+    }
+
+    __host__ __device__ void Print() const
+    {
+        printf("{");
+        printf("UnMerge, ");
+        printf("up_lengths_");
+        print_multi_index(up_lengths_);
+        printf("up_lengths_scan_");
+        print_multi_index(up_lengths_scan_);
+        printf("}");
+    }
+};
+
+template <typename LowerIndex>
+struct Freeze
+{
+    LowerIndex low_idx_;
+
+    __host__ __device__ constexpr Freeze() = default;
+
+    __host__ __device__ constexpr Freeze(const LowerIndex& low_idx) : low_idx_{low_idx} {}
+
+    __host__ __device__ static constexpr index_t GetNumOfLowerDimension() { return 1; }
+
+    __host__ __device__ static constexpr index_t GetNumOfUpperDimension() { return 0; }
+
+    __host__ __device__ static constexpr auto GetUpperLengths() { return Tuple<>{}; }
+
+    template <typename LowIdx, typename UpIdx>
+    __host__ __device__ constexpr void CalculateLowerIndex(LowIdx& idx_low,
+                                                           const UpIdx& /* idx_up */) const
+    {
+        static_assert(LowIdx::Size() == 1 && UpIdx::Size() == 0,
+                      "wrong! inconsistent # of dimension");
+
+        idx_low(Number<0>{}) = low_idx_;
+    }
+
+    template <typename LowIdxDiff,
+              typename UpIdxDiff,
+              typename LowIdx,
+              typename UpIdx,
+              index_t Hack>
+    __host__ __device__ static void UpdateLowerIndex(LowIdxDiff& idx_diff_low,
+                                                     const UpIdxDiff& /* idx_diff_up */,
+                                                     LowIdx& /* idx_low */,
+                                                     const UpIdx& /* idx_up_new */,
+                                                     Number<Hack>)
+    {
+        idx_diff_low(Number<0>{}) = 0;
+    }
+
+    __host__ __device__ static constexpr bool IsLinearTransform() { return true; }
+
+    __host__ __device__ static constexpr bool IsValidUpperIndexAlwaysMappedToValidLowerIndex()
+    {
+        return true;
+    }
+
+    template <typename UpIdx>
+    __host__ __device__ static constexpr bool
+    IsValidUpperIndexMappedToValidLowerIndex(const UpIdx& /* idx_up */)
+    {
+        return true;
+    }
+
+    __host__ __device__ static constexpr bool IsKnownAtCompileTime()
+    {
+        return is_known_at_compile_time<LowerIndex>::value;
+    }
+
+    __host__ __device__ void Print() const
+    {
+        printf("Freeze");
+        printf("low_idx_ %d", index_t{low_idx_});
+    }
+};
+
+// Insert a dangling upper dimension without lower dimension
+template <typename UpperLength>
+struct Insert
+{
+    using UpLengths = decltype(make_tuple(UpperLength{}));
+
+    UpLengths up_lengths_;
+
+    __host__ __device__ constexpr Insert() = default;
+
+    __host__ __device__ constexpr Insert(const UpperLength& up_length)
+        : up_lengths_{make_tuple(up_length)}
+    {
+    }
+
+    __host__ __device__ static constexpr index_t GetNumOfLowerDimension() { return 0; }
+
+    __host__ __device__ static constexpr index_t GetNumOfUpperDimension() { return 1; }
+
+    __host__ __device__ constexpr auto GetUpperLengths() const { return up_lengths_; }
+
+    template <typename LowIdx, typename UpIdx>
+    __host__ __device__ constexpr void CalculateLowerIndex(LowIdx&, const UpIdx&) const
+    {
+        static_assert(LowIdx::Size() == 0 && UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+    }
+
+    template <typename LowIdxDiff,
+              typename UpIdxDiff,
+              typename LowIdx,
+              typename UpIdx,
+              index_t Hack>
+    __host__ __device__ static void
+    UpdateLowerIndex(LowIdxDiff&, const UpIdxDiff&, LowIdx&, const UpIdx&, Number<Hack>)
+    {
+        static_assert(LowIdxDiff::Size() == 0 && UpIdxDiff::Size() == 1 && LowIdx::Size() == 0 &&
+                          UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+    }
+
+    __host__ __device__ static constexpr bool IsLinearTransform() { return true; }
+
+    __host__ __device__ static constexpr bool IsValidUpperIndexAlwaysMappedToValidLowerIndex()
+    {
+        return true;
+    }
+
+    template <typename UpIdx>
+    __host__ __device__ static constexpr bool
+    IsValidUpperIndexMappedToValidLowerIndex(const UpIdx& /* idx_up */)
+    {
+        return true;
+    }
+
+    __host__ __device__ static constexpr bool IsKnownAtCompileTime()
+    {
+        return is_known_at_compile_time<UpperLength>::value;
+    }
+
+    __host__ __device__ void Print() const
+    {
+        printf("Insert");
+        print_multi_index(up_lengths_);
+    }
+};
+
+template <typename VectorSize, typename UpLength>
+struct Vectorize
+{
+    using LowerIndex = MultiIndex<1>;
+    using UpperIndex = MultiIndex<1>;
+
+    using UpLengths = decltype(make_tuple(UpLength{}));
+
+    UpLengths up_lengths_;
+    VectorSize vector_size_;
+
+    __host__ __device__ constexpr Vectorize() = default;
+
+    __host__ __device__ constexpr Vectorize(const VectorSize& vector_size,
+                                            const UpLength& up_length)
+        : vector_size_{vector_size}, up_lengths_{make_tuple(up_length)}
+    {
+    }
+
+    __host__ __device__ static constexpr index_t GetNumOfLowerDimension() { return 1; }
+
+    __host__ __device__ static constexpr index_t GetNumOfUpperDimension() { return 1; }
+
+    __host__ __device__ constexpr const auto& GetUpperLengths() const { return up_lengths_; }
+
+    template <typename LowIdx, typename UpIdx>
+    __host__ __device__ constexpr void CalculateLowerIndex(LowIdx& idx_low,
+                                                           const UpIdx& idx_up) const
+    {
+        static_assert(LowIdx::Size() == 1 && UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        idx_low(Number<0>{}) = vector_size_ * idx_up[Number<0>{}];
+    }
+
+    template <typename LowIdxDiff,
+              typename UpIdxDiff,
+              typename LowIdx,
+              typename UpIdx,
+              index_t Hack>
+    __host__ __device__ void UpdateLowerIndex(LowIdxDiff& idx_diff_low,
+                                              const UpIdxDiff& idx_diff_up,
+                                              LowIdx& idx_low,
+                                              const UpIdx&,
+                                              Number<Hack>) const
+    {
+        static_assert(LowIdxDiff::Size() == 1 && UpIdxDiff::Size() == 1 && LowIdx::Size() == 1 &&
+                          UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        constexpr auto I0 = Number<0>{};
+
+        idx_diff_low(I0) = vector_size_ * idx_diff_up[I0];
+
+        idx_low += idx_diff_low;
+    }
+
+    __host__ __device__ static constexpr bool IsLinearTransform() { return true; }
+
+    __host__ __device__ static constexpr bool IsValidUpperIndexAlwaysMappedToValidLowerIndex()
+    {
+        return true;
+    }
+
+    template <typename UpIdx>
+    __host__ __device__ static constexpr bool
+    IsValidUpperIndexMappedToValidLowerIndex(const UpIdx& /* idx_up */)
+    {
+        return true;
+    }
+
+    __host__ __device__ static constexpr bool IsKnownAtCompileTime()
+    {
+        return is_known_at_compile_time<UpLengths>::value;
+    }
+
+    __host__ __device__ void Print() const
+    {
+        printf("{");
+        printf("Vectorize, ");
+        printf("up_lengths_");
+        print_multi_index(up_lengths_);
+        printf("}");
+    }
+};
+
+template <typename LowLength, typename SliceBegin, typename SliceEnd>
+struct Slice
+{
+    using LowerIndex = MultiIndex<1>;
+    using UpperIndex = MultiIndex<1>;
+
+    using UpLengths = decltype(make_tuple(SliceEnd{} - SliceBegin{}));
+
+    UpLengths up_lengths_;
+    SliceBegin slice_begin_;
+    SliceEnd slice_end_;
+
+    __host__ __device__ constexpr Slice() = default;
+
+    __host__ __device__ constexpr Slice(const LowLength&,
+                                        const SliceBegin& slice_begin,
+                                        const SliceEnd& slice_end)
+        : up_lengths_{make_tuple(slice_end - slice_begin)},
+          slice_begin_{slice_begin},
+          slice_end_{slice_end}
+    {
+    }
+
+    __host__ __device__ static constexpr index_t GetNumOfLowerDimension() { return 1; }
+
+    __host__ __device__ static constexpr index_t GetNumOfUpperDimension() { return 1; }
+
+    __host__ __device__ constexpr const auto& GetUpperLengths() const { return up_lengths_; }
+
+    template <typename LowIdx, typename UpIdx>
+    __host__ __device__ constexpr void CalculateLowerIndex(LowIdx& idx_low,
+                                                           const UpIdx& idx_up) const
+    {
+        static_assert(LowIdx::Size() == 1 && UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        idx_low(Number<0>{}) = idx_up[Number<0>{}] + slice_begin_;
+    }
+
+    template <typename LowIdxDiff,
+              typename UpIdxDiff,
+              typename LowIdx,
+              typename UpIdx,
+              index_t Hack>
+    __host__ __device__ static void UpdateLowerIndex(LowIdxDiff& idx_diff_low,
+                                                     const UpIdxDiff& idx_diff_up,
+                                                     LowIdx& idx_low,
+                                                     const UpIdx&,
+                                                     Number<Hack>)
+    {
+        static_assert(LowIdxDiff::Size() == 1 && UpIdxDiff::Size() == 1 && LowIdx::Size() == 1 &&
+                          UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        constexpr auto I0 = Number<0>{};
+
+        idx_diff_low(I0) = idx_diff_up[I0];
+
+        idx_low += idx_diff_low;
+    }
+
+    __host__ __device__ static constexpr bool IsLinearTransform() { return true; }
+
+    __host__ __device__ static constexpr bool IsValidUpperIndexAlwaysMappedToValidLowerIndex()
+    {
+        return true;
+    }
+
+    template <typename UpIdx>
+    __host__ __device__ constexpr bool IsValidUpperIndexMappedToValidLowerIndex(const UpIdx&) const
+    {
+        return true;
+    }
+
+    __host__ __device__ static constexpr bool IsKnownAtCompileTime()
+    {
+        return is_known_at_compile_time<UpLengths>::value &&
+               is_known_at_compile_time<SliceBegin>::value &&
+               is_known_at_compile_time<SliceEnd>::value;
+    }
+
+    __host__ __device__ void Print() const
+    {
+        printf("{");
+        printf("Slice, ");
+        printf("up_lengths_");
+        print_multi_index(up_lengths_);
+        printf("slice_begin_ %d", index_t{slice_begin_});
+        printf("slice_end %d", index_t{slice_end_});
+        printf("}");
+    }
+};
+
+/*
+ * \brief lower_idx = upper_idx % modulus.
+ * TODO: Need an improved implementation since the modulo operation is expensive.
+ */
+template <typename Modulus, typename UpLength>
+struct Modulo
+{
+    using LowerIndex = MultiIndex<1>;
+    using UpperIndex = MultiIndex<1>;
+    using UpLengths  = decltype(make_tuple(UpLength{}));
+
+    Modulus modulus_;
+    UpLengths up_lengths_;
+
+    __host__ __device__ constexpr Modulo() = default;
+
+    __host__ __device__ constexpr Modulo(const Modulus& modulus, const UpLength& up_length)
+        : modulus_{modulus}, up_lengths_{make_tuple(up_length)}
+    {
+    }
+
+    __host__ __device__ static constexpr index_t GetNumOfLowerDimension() { return 1; }
+
+    __host__ __device__ static constexpr index_t GetNumOfUpperDimension() { return 1; }
+
+    __host__ __device__ constexpr const auto& GetUpperLengths() const { return up_lengths_; }
+
+    template <typename LowIdx, typename UpIdx>
+    __host__ __device__ constexpr void CalculateLowerIndex(LowIdx& idx_low,
+                                                           const UpIdx& idx_up) const
+    {
+        static_assert(LowIdx::Size() == 1 && UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        idx_low(Number<0>{}) = idx_up[Number<0>{}] % modulus_;
+    }
+
+    template <typename LowIdxDiff,
+              typename UpIdxDiff,
+              typename LowIdx,
+              typename UpIdx,
+              index_t Hack>
+    __host__ __device__ void UpdateLowerIndex(LowIdxDiff& idx_diff_low,
+                                              const UpIdxDiff& idx_diff_up,
+                                              LowIdx& idx_low,
+                                              const UpIdx& up_idx,
+                                              Number<Hack>) const
+    {
+        static_assert(LowIdxDiff::Size() == 1 && UpIdxDiff::Size() == 1 && LowIdx::Size() == 1 &&
+                          UpIdx::Size() == 1,
+                      "wrong! inconsistent # of dimension");
+
+        constexpr auto I0 = Number<0>{};
+
+        const auto idx_low_old = idx_low;
+        idx_low(I0)            = (up_idx(I0) + idx_diff_up(I0)) % modulus_;
+        idx_diff_low(I0)       = idx_low - idx_low_old;
+    }
+
+    __host__ __device__ static constexpr bool IsLinearTransform() { return false; }
+
+    __host__ __device__ static constexpr bool IsValidUpperIndexAlwaysMappedToValidLowerIndex()
+    {
+        return true;
+    }
+
+    template <typename UpIdx>
+    __host__ __device__ static constexpr bool
+    IsValidUpperIndexMappedToValidLowerIndex(const UpIdx& /* idx_up */)
+    {
+        return true;
+    }
+
+    __host__ __device__ static constexpr bool IsKnownAtCompileTime()
+    {
+        return is_known_at_compile_time<UpLengths>::value;
+    }
+
+    __host__ __device__ void Print() const
+    {
+        printf("{");
+        printf("Modulus, ");
+        printf("up_lengths_");
+        print_multi_index(up_lengths_);
+        printf("}");
+    }
+};
+} // namespace ck

include/ck/tensor_description/multi_index_transform_helper.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck/utility/common_header.hpp"
+#include "ck/tensor_description/multi_index_transform.hpp"
+
+namespace ck {
+
+template <typename LowLength>
+__host__ __device__ constexpr auto make_pass_through_transform(const LowLength& low_length)
+{
+    return PassThrough<LowLength>{low_length};
+}
+
+template <typename LowLength, typename LeftPad, typename RightPad, bool SkipIsValidCheck = false>
+__host__ __device__ constexpr auto
+make_pad_transform(const LowLength& low_length,
+                   const LeftPad& left_pad,
+                   const RightPad& right_pad,
+                   integral_constant<bool, SkipIsValidCheck> = integral_constant<bool, false>{})
+{
+    return Pad<LowLength, LeftPad, RightPad, SkipIsValidCheck>{low_length, left_pad, right_pad};
+}
+
+template <typename LowLength, typename LeftPadLength, bool SkipIsValidCheck = false>
+__host__ __device__ constexpr auto make_left_pad_transform(
+    const LowLength& low_length,
+    const LeftPadLength& left_pad,
+    integral_constant<bool, SkipIsValidCheck> = integral_constant<bool, false>{})
+{
+    return LeftPad<LowLength, LeftPadLength, SkipIsValidCheck>{low_length, left_pad};
+}
+
+template <typename LowLength, typename RightPadLength, bool SkipIsValidCheck = false>
+__host__ __device__ constexpr auto make_right_pad_transform(
+    const LowLength& low_length,
+    const RightPadLength& right_pad,
+    integral_constant<bool, SkipIsValidCheck> = integral_constant<bool, false>{})
+{
+    return RightPad<LowLength, RightPadLength, SkipIsValidCheck>{low_length, right_pad};
+}
+
+template <typename UpLengths,
+          typename Coefficients,
+          typename enable_if<UpLengths::Size() == Coefficients::Size(), bool>::type = false>
+__host__ __device__ constexpr auto make_embed_transform(const UpLengths& up_lengths,
+                                                        const Coefficients& coefficients)
+{
+    return Embed<UpLengths, Coefficients>{up_lengths, coefficients};
+}
+
+template <typename LowLengths>
+__host__ __device__ constexpr auto make_merge_transform(const LowLengths& low_lengths)
+{
+#if CK_EXPERIMENTAL_MERGE_USE_MAGIC_DIVISION
+    return make_merge_transform_v2_magic_division(low_lengths);
+#else
+    return make_merge_transform_v1_carry_check(low_lengths);
+#endif
+}
+
+template <typename LowLengths>
+__host__ __device__ constexpr auto
+make_merge_transform_v1_carry_check(const LowLengths& low_lengths)
+{
+    return Merge_v1_carry_check<LowLengths>{low_lengths};
+}
+
+template <typename LowLengths>
+__host__ __device__ constexpr auto
+make_merge_transform_v2_magic_division(const LowLengths& low_lengths)
+{
+#if 1
+    return Merge_v2_magic_division<LowLengths>{low_lengths};
+#else
+    return Merge_v2r2_magic_division<LowLengths>{low_lengths};
+#endif
+}
+
+template <typename LowLengths>
+__host__ __device__ constexpr auto
+make_merge_transform_v3_division_mod(const LowLengths& low_lengths)
+{
+    return Merge_v3_division_mod<LowLengths>{low_lengths};
+}
+
+template <typename UpLengths, bool Use24BitIntegerCalculation = false>
+__host__ __device__ constexpr auto make_unmerge_transform(
+    const UpLengths& up_lengths,
+    integral_constant<bool, Use24BitIntegerCalculation> = integral_constant<bool, false>{})
+{
+    return UnMerge<UpLengths, Use24BitIntegerCalculation>{up_lengths};
+}
+
+template <typename LowerIndex>
+__host__ __device__ constexpr auto make_freeze_transform(const LowerIndex& low_idx)
+{
+    return Freeze<LowerIndex>{low_idx};
+}
+
+template <typename UpperIndex>
+__host__ __device__ constexpr auto make_insert_transform(const UpperIndex& up_idx)
+{
+    return Insert<UpperIndex>{up_idx};
+}
+
+template <typename LowLength, typename SliceBegin, typename SliceEnd>
+__host__ __device__ constexpr auto make_slice_transform(const LowLength& low_length,
+                                                        const SliceBegin& slice_begin,
+                                                        const SliceEnd& slice_end)
+{
+    return Slice<LowLength, SliceBegin, SliceEnd>{low_length, slice_begin, slice_end};
+}
+
+template <typename VectorSize, typename UpLength>
+__host__ __device__ constexpr auto make_vectorize_transform(const VectorSize& vector_size,
+                                                            const UpLength& up_length)
+{
+    return Vectorize<VectorSize, UpLength>{vector_size, up_length};
+}
+
+template <typename Modulus, typename UpLength>
+__host__ __device__ constexpr auto make_modulo_transform(const Modulus& modulus,
+                                                         const UpLength& up_length)
+{
+    return Modulo<Modulus, UpLength>{modulus, up_length};
+}
+} // namespace ck

include/ck/tensor_description/tensor_adaptor.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck/utility/common_header.hpp"
+#include "ck/tensor_description/tensor_descriptor.hpp"
+#include "ck/tensor_description/tensor_descriptor_helper.hpp"
+
+namespace ck {
+
+// 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 TensorAdaptor
+{
+    __host__ __device__ static constexpr index_t GetNumOfTransform() { return Transforms::Size(); }
+
+    __host__ __device__ constexpr const auto& GetTransforms() const { return transforms_; }
+
+    __host__ __device__ static constexpr auto GetLowerDimensionHiddenIdss()
+    {
+        return LowerDimensionHiddenIdss{};
+    }
+
+    __host__ __device__ static constexpr auto GetUpperDimensionHiddenIdss()
+    {
+        return UpperDimensionHiddenIdss{};
+    }
+
+    __host__ __device__ static constexpr auto GetTopDimensionHiddenIds()
+    {
+        return TopDimensionHiddenIds{};
+    }
+
+    __host__ __device__ static constexpr auto GetBottomDimensionHiddenIds()
+    {
+        return BottomDimensionHiddenIds{};
+    }
+
+    __host__ __device__ static constexpr auto InitializeElementSize(const Transforms& transforms)
+    {
+        const auto lengths = generate_tuple(
+            [&](auto idim_top) {
+                constexpr auto tmp = GetTransformAndItsUpperDimension(idim_top);
+
+                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>{}].GetUpperLengths()[Number<idim_up>{}];
+
+                return length;
+            },
+            Number<ndim_top_>{});
+
+        // TODO: make container_reduce support tuple of Number and index_t
+        return container_reduce(lengths, math::multiplies{}, Number<1>{});
+    }
+
+    template <index_t IDim>
+    __host__ __device__ static constexpr auto GetTransformAndItsUpperDimension(Number<IDim>)
+    {
+        constexpr auto idim_top = Number<IDim>{};
+
+        constexpr index_t idim_hidden = TopDimensionHiddenIds::At(idim_top);
+
+        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] == idim_hidden)
+                {
+                    itran_found   = itran;
+                    idim_up_found = idim_up;
+                    found         = true;
+                }
+            });
+        });
+
+        return make_tuple(itran_found, idim_up_found, found);
+    }
+
+    __host__ __device__ static constexpr index_t GetNumOfBottomDimension()
+    {
+        return BottomDimensionHiddenIds::Size();
+    }
+
+    __host__ __device__ static constexpr index_t GetNumOfTopDimension()
+    {
+        return TopDimensionHiddenIds::Size();
+    }
+
+    __host__ __device__ static constexpr index_t GetNumOfHiddenDimension()
+    {
+        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),
+                                                                      math::less<index_t>,
+                                                                      math::equal<index_t>>::type;
+
+        return unique_sort_all_dim_ids::Size();
+    }
+
+    constexpr static index_t ntransform_  = GetNumOfTransform();
+    constexpr static index_t ndim_hidden_ = GetNumOfHiddenDimension();
+    constexpr static index_t ndim_bottom_ = GetNumOfBottomDimension();
+    constexpr static index_t ndim_top_    = GetNumOfTopDimension();
+
+    using HiddenIndex = MultiIndex<ndim_hidden_>;
+    using BottomIndex = MultiIndex<ndim_bottom_>;
+    using TopIndex    = MultiIndex<ndim_top_>;
+
+    // may be index_t or Number<>
+    using ElementSize = remove_cv_t<decltype(InitializeElementSize(Transforms{}))>;
+
+    public:
+#if 0 // workaround compiler complaint about constexpr
+    __host__ __device__ constexpr TensorAdaptor() = default;
+#else
+    __host__ __device__ constexpr TensorAdaptor() : transforms_{}, element_size_{} {}
+#endif
+
+    __host__ __device__ constexpr TensorAdaptor(const Transforms& transforms)
+        : transforms_{transforms}, element_size_{InitializeElementSize(transforms)}
+    {
+        static_assert(Transforms::Size() == ntransform_ &&
+                          LowerDimensionHiddenIdss::Size() == ntransform_ &&
+                          UpperDimensionHiddenIdss::Size() == ntransform_,
+                      "wrong! inconsistent # of transformations");
+
+        // TODO check dependency of dimensions is valid
+    }
+
+    __host__ __device__ constexpr auto GetElementSize() const { return element_size_; }
+
+#if 0 // debug
+    template <index_t I>
+    __host__ __device__ constexpr index_t GetTopDimensionLength(Number<I> idim) const
+    {
+        // TODO: not implemented
+    }
+
+    template <index_t I>
+    __host__ __device__ constexpr index_t GetBottomDimensionLength(Number<I> idim) const
+    {
+        // TODO: not implemented
+    }
+#endif
+
+    template <typename TopIdx>
+    __host__ __device__ constexpr auto CalculateBottomIndex(const TopIdx& idx_top) const
+    {
+        static_assert(TopIdx::Size() == TopDimensionHiddenIds::Size(),
+                      "wrong! # of dimension inconsistent");
+
+        constexpr index_t ntransform  = GetNumOfTransform();
+        constexpr index_t ndim_hidden = GetNumOfHiddenDimension();
+
+        MultiIndex<ndim_hidden> idx_hidden;
+
+        // initialize uppest index
+        set_container_subset(idx_hidden, GetTopDimensionHiddenIds(), idx_top);
+
+        // calculate hidden index
+        static_for<ntransform, 0, -1>{}([&](auto itran_p1) {
+            auto itran              = itran_p1 - Number<1>{};
+            const auto& tran        = GetTransforms().At(itran);
+            constexpr auto dims_low = GetLowerDimensionHiddenIdss().At(itran);
+            constexpr auto dims_up  = GetUpperDimensionHiddenIdss().At(itran);
+
+            const auto idx_up = get_container_subset(idx_hidden, dims_up);
+
+            MultiIndex<dims_low.Size()> idx_low;
+
+            tran.CalculateLowerIndex(idx_low, idx_up);
+
+            set_container_subset(idx_hidden, dims_low, idx_low);
+        });
+
+        return get_container_subset(idx_hidden, BottomDimensionHiddenIds{});
+    }
+
+    __host__ __device__ static constexpr bool IsKnownAtCompileTime()
+    {
+        bool is_known = true;
+
+        static_for<0, Transforms::Size(), 1>{}([&](auto i) {
+            is_known &= remove_cvref_t<decltype(Transforms{}[i])>::IsKnownAtCompileTime();
+        });
+
+        return is_known && is_known_at_compile_time<ElementSize>::value;
+    }
+
+    __host__ __device__ void Print() const
+    {
+        printf("{");
+        printf("TensorAdaptor, ");
+        static_for<0, ntransform_, 1>{}([&](auto i) {
+            printf("transforms: ");
+            transforms_[i].Print();
+            printf("LowerDimensionHiddenIds:");
+            LowerDimensionHiddenIdss{}.At(i).Print();
+            printf("UpperDimensionHiddenIds:");
+            UpperDimensionHiddenIdss{}.At(i).Print();
+        });
+
+        printf("BottomDimensionHiddenIds:");
+        BottomDimensionHiddenIds::Print();
+        printf("TopDimensionHiddenIds:");
+        TopDimensionHiddenIds::Print();
+
+        printf("}");
+    }
+
+    private:
+    Transforms transforms_;
+    ElementSize element_size_;
+};
+
+template <typename TensorAdaptor0, typename TensorAdaptor1>
+__host__ __device__ constexpr auto chain_tensor_adaptors(const TensorAdaptor0& adaptor0,
+                                                         const TensorAdaptor1& adaptor1)
+{
+    static_assert(TensorAdaptor0::GetNumOfTopDimension() ==
+                      TensorAdaptor1::GetNumOfBottomDimension(),
+                  "wrong!");
+
+    // all_transforms = transform0 + transform1
+    const auto all_transforms =
+        container_concat(adaptor0.GetTransforms(), adaptor1.GetTransforms());
+
+    // shift
+    constexpr index_t adaptor0_max_hidden_id = [&]() {
+        index_t adaptor0_max_hidden_id_ = NumericLimits<index_t>::Min();
+
+        static_for<0, TensorAdaptor0::GetNumOfTransform(), 1>{}([&](auto itran) {
+            constexpr index_t ndim_low =
+                TensorAdaptor0{}.GetTransforms()[itran].GetNumOfLowerDimension();
+
+            static_for<0, ndim_low, 1>{}([&](auto idim_low) {
+                adaptor0_max_hidden_id_ =
+                    math::max(adaptor0_max_hidden_id_,
+                              TensorAdaptor0::GetLowerDimensionHiddenIdss()[itran][idim_low].value);
+            });
+
+            constexpr index_t ndim_up =
+                TensorAdaptor0{}.GetTransforms()[itran].GetNumOfUpperDimension();
+
+            static_for<0, ndim_up, 1>{}([&](auto idim_up) {
+                adaptor0_max_hidden_id_ =
+                    math::max(adaptor0_max_hidden_id_,
+                              TensorAdaptor0::GetUpperDimensionHiddenIdss()[itran][idim_up].value);
+            });
+        });
+
+        return adaptor0_max_hidden_id_;
+    }();
+
+    constexpr index_t adaptor1_min_hidden_id = [&]() {
+        index_t adaptor1_min_hidden_id_ = NumericLimits<index_t>::Max();
+
+        static_for<0, TensorAdaptor1::GetNumOfTransform(), 1>{}([&](auto itran) {
+            constexpr index_t ndim_low =
+                TensorAdaptor1{}.GetTransforms()[itran].GetNumOfLowerDimension();
+
+            // 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::GetLowerDimensionHiddenIdss()[itran][idim_low].value;
+
+                bool is_bottom_dim = false;
+                static_for<0, TensorAdaptor1::GetNumOfBottomDimension(), 1>{}([&](auto i) {
+                    if constexpr(low_dim_hidden_id ==
+                                 TensorAdaptor1::GetBottomDimensionHiddenIds()[i])
+                    {
+                        is_bottom_dim = true;
+                    }
+                });
+
+                if(!is_bottom_dim)
+                {
+                    adaptor1_min_hidden_id_ = math::min(adaptor1_min_hidden_id_, low_dim_hidden_id);
+                }
+            });
+
+            constexpr index_t ndim_up =
+                TensorAdaptor1{}.GetTransforms()[itran].GetNumOfUpperDimension();
+
+            // get the min of all upper dimensions
+            static_for<0, ndim_up, 1>{}([&](auto idim_up) {
+                adaptor1_min_hidden_id_ =
+                    math::min(adaptor1_min_hidden_id_,
+                              TensorAdaptor1::GetUpperDimensionHiddenIdss()[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::GetNumOfBottomDimension();
+
+    // 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::GetLowerDimensionHiddenIdss()[itran].Size();
+
+            constexpr auto low_dim_hidden_ids_1 =
+                TensorAdaptor1::GetLowerDimensionHiddenIdss()[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::GetBottomDimensionHiddenIds()[idim_bottom_1])
+                        {
+                            low_dim_hidden_ids_1_mod_(idim_low_1) =
+                                TensorAdaptor0::GetTopDimensionHiddenIds()[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::GetNumOfTransform()>{});
+
+    constexpr auto all_low_dim_hidden_idss =
+        container_concat(TensorAdaptor0::GetLowerDimensionHiddenIdss(), 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::GetUpperDimensionHiddenIdss()[itran].Size();
+
+            constexpr auto up_dim_hidden_ids_1 =
+                TensorAdaptor1::GetUpperDimensionHiddenIdss()[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::GetNumOfTransform()>{});
+
+    constexpr auto all_up_dim_hidden_idss =
+        container_concat(TensorAdaptor0::GetUpperDimensionHiddenIdss(), up_dim_hidden_idss_1);
+
+    // bottom_dim_hidden_ids = bottom_dim_hidden_ids_0
+    constexpr auto bottom_dim_hidden_ids = TensorAdaptor0::GetBottomDimensionHiddenIds();
+
+    // top_dim_hidden_ids = shift_hidden_id(top_dim_hidden_ids_1)
+    constexpr auto top_dim_hidden_ids =
+        TensorAdaptor1::GetTopDimensionHiddenIds() + Number<adaptor1_hidden_id_shift>{};
+
+    // put everything together
+    return TensorAdaptor<remove_cv_t<decltype(all_transforms)>,
+                         remove_cv_t<decltype(all_low_dim_hidden_idss)>,
+                         remove_cv_t<decltype(all_up_dim_hidden_idss)>,
+                         remove_cv_t<decltype(bottom_dim_hidden_ids)>,
+                         remove_cv_t<decltype(top_dim_hidden_ids)>>{all_transforms};
+}
+
+// Transforms: Tuple<transforms...>
+// LowerDimensionOldTopIdss: Tuple<Sequence<...>, ...>
+// UpperDimensionNewTopIdss: Tuple<Sequence<...>, ...>
+template <typename Transforms, typename LowerDimensionOldTopIdss, typename UpperDimensionNewTopIdss>
+__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 TensorAdaptor<remove_cv_t<Transforms>,
+                         remove_cv_t<decltype(low_dim_hidden_idss)>,
+                         remove_cv_t<decltype(up_dim_hidden_idss)>,
+                         remove_cv_t<decltype(bottom_dim_hidden_ids)>,
+                         remove_cv_t<decltype(top_dim_hidden_ids)>>{transforms};
+}
+
+template <typename X, typename... Xs, typename enable_if<sizeof...(Xs) >= 2, bool>::type = false>
+__host__ __device__ constexpr auto chain_tensor_adaptors(const X& x, const Xs&... xs)
+{
+    return chain_tensor_adaptors(x, chain_tensor_adaptors(xs...));
+}
+
+} // namespace ck

include/ck/tensor_description/tensor_descriptor.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck/utility/common_header.hpp"
+#include "ck/utility/sequence_helper.hpp"
+#include "ck/tensor_description/multi_index_transform.hpp"
+
+namespace ck {
+
+template <index_t NDimHidden, typename VisibleDimensionIds>
+struct TensorCoordinate;
+
+template <index_t NTransform, index_t NDimVisible, typename UpdateLowerIndexHack>
+struct TensorCoordinateStep;
+
+// Transforms: Tuple<transforms...>
+// LowerDimensionIdss : Tuple<Sequence<...>, ...>
+// UpperDimensionIdss : Tuple<Sequence<...>, ...>
+// VisibleDimensionIds> : Sequence<...>
+template <typename Transforms,
+          typename LowerDimensionIdss,
+          typename UpperDimensionIdss,
+          typename VisibleDimensionIds,
+          typename ElementSpaceSize>
+struct TensorDescriptor
+{
+    // TODO make these private
+    __host__ __device__ static constexpr index_t GetNumOfTransform() { return Transforms::Size(); }
+
+    __host__ __device__ static constexpr index_t GetNumOfVisibleDimension()
+    {
+        return VisibleDimensionIds::Size();
+    }
+
+    __host__ __device__ static constexpr index_t GetNumOfHiddenDimension()
+    {
+        constexpr auto all_low_dim_ids = unpack(
+            [](auto&&... xs) constexpr { return merge_sequences(xs...); }, LowerDimensionIdss{});
+
+        constexpr auto all_up_dim_ids = unpack(
+            [](auto&&... xs) constexpr { return merge_sequences(xs...); }, UpperDimensionIdss{});
+
+        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),
+                                                                      math::less<index_t>,
+                                                                      math::equal<index_t>>::type;
+
+        return unique_sort_all_dim_ids::Size();
+    }
+
+    __host__ __device__ static constexpr auto InitializeElementSize(const Transforms& transforms)
+    {
+        const auto lengths = generate_tuple(
+            [&](auto idim_visible) {
+                constexpr auto tmp = GetTransformAndItsUpperDimension(idim_visible);
+
+                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>{}].GetUpperLengths()[Number<idim_up>{}];
+
+                return length;
+            },
+            Number<ndim_visible_>{});
+
+        // TODO: make container_reduce support tuple of Number and index_t
+        return container_reduce(lengths, math::multiplies{}, Number<1>{});
+    }
+
+    template <index_t IDim>
+    __host__ __device__ static constexpr auto GetTransformAndItsUpperDimension(Number<IDim>)
+    {
+        constexpr auto idim_visible = Number<IDim>{};
+
+        constexpr index_t idim_hidden = VisibleDimensionIds::At(idim_visible);
+
+        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 = UpperDimensionIdss{}[itran];
+
+            static_for<0, up_dim_ids.Size(), 1>{}([&](auto idim_up) {
+                if constexpr(up_dim_ids[idim_up] == idim_hidden)
+                {
+                    itran_found   = itran;
+                    idim_up_found = idim_up;
+                    found         = true;
+                }
+            });
+        });
+
+        return make_tuple(itran_found, idim_up_found, found);
+    }
+
+    constexpr static index_t ntransform_   = GetNumOfTransform();
+    constexpr static index_t ndim_visible_ = GetNumOfVisibleDimension();
+    constexpr static index_t ndim_hidden_  = GetNumOfHiddenDimension();
+
+    using VisibleIndex = MultiIndex<ndim_visible_>;
+    using HiddenIndex  = MultiIndex<ndim_hidden_>;
+    using Coordinate   = TensorCoordinate<ndim_hidden_, VisibleDimensionIds>;
+
+    // may be index_t or Number<>
+    using ElementSize = remove_cv_t<decltype(InitializeElementSize(Transforms{}))>;
+
+    public:
+#if 0 // workaround compiler complaint about constexpr
+    __host__ __device__ constexpr TensorDescriptor() = default;
+#else
+    __host__ __device__ constexpr TensorDescriptor()
+        : transforms_{}, element_size_{}, element_space_size_{}
+    {
+    }
+#endif
+
+    __host__ __device__ constexpr TensorDescriptor(const Transforms& transforms,
+                                                   ElementSpaceSize element_space_size)
+        : transforms_{transforms},
+          element_size_{InitializeElementSize(transforms)},
+          element_space_size_{element_space_size}
+
+    {
+        static_assert(Transforms::Size() == ntransform_ &&
+                          LowerDimensionIdss::Size() == ntransform_ &&
+                          UpperDimensionIdss::Size() == ntransform_,
+                      "wrong! inconsistent # of transformations");
+
+        // TODO check dependency of dimensions is valid
+    }
+
+    __host__ __device__ static constexpr index_t GetNumOfDimension()
+    {
+        return GetNumOfVisibleDimension();
+    }
+
+    template <index_t IDim>
+    __host__ __device__ constexpr auto GetLength(Number<IDim>) const
+    {
+        static_assert(IDim >= 0 && IDim < ndim_visible_, "wrong! out of range");
+
+        constexpr auto tmp = GetTransformAndItsUpperDimension(Number<IDim>{});
+
+        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>{}].GetUpperLengths()[Number<idim_up>{}];
+    }
+
+    __host__ __device__ constexpr auto GetLengths() const
+    {
+        // FIXME: use Tuple of reference instead
+        return generate_sequence_v2([&](auto I) { return GetLength(I); }, Number<ndim_visible_>{});
+    }
+
+    __host__ __device__ constexpr auto GetElementSize() const { return element_size_; }
+
+    __host__ __device__ constexpr auto GetElementSpaceSize() const { return element_space_size_; }
+
+    template <typename Idx>
+    __host__ __device__ constexpr index_t CalculateOffset(const Idx& idx) const
+    {
+        static_assert(Idx::Size() == GetNumOfDimension(), "wrong! inconsistent # of dimension");
+
+        return make_tensor_coordinate(*this, idx).GetOffset();
+    }
+
+    // TODO make these private
+    __host__ __device__ constexpr const auto& GetTransforms() const { return transforms_; }
+
+    __host__ __device__ static constexpr auto GetLowerDimensionIdss()
+    {
+        return LowerDimensionIdss{};
+    }
+
+    __host__ __device__ static constexpr auto GetUpperDimensionIdss()
+    {
+        return UpperDimensionIdss{};
+    }
+
+    __host__ __device__ static constexpr auto GetVisibleDimensionIds()
+    {
+        return VisibleDimensionIds{};
+    }
+
+    __host__ __device__ static constexpr bool IsKnownAtCompileTime()
+    {
+        bool is_known = true;
+
+        static_for<0, Transforms::Size(), 1>{}([&](auto i) {
+            is_known &= remove_cvref_t<decltype(Transforms{}[i])>::IsKnownAtCompileTime();
+        });
+
+        return is_known && is_known_at_compile_time<ElementSize>::value &&
+               is_known_at_compile_time<ElementSpaceSize>::value;
+    }
+
+    __host__ __device__ void Print() const
+    {
+        printf("{");
+        printf("TensorDescriptor, ");
+        static_for<0, ntransform_, 1>{}([&](auto i) {
+            printf("transforms: ");
+            transforms_[i].Print();
+            printf("LowerDimensionIds:");
+            LowerDimensionIdss{}.At(i).Print();
+            printf("UpperDimensionIds:");
+            UpperDimensionIdss{}.At(i).Print();
+        });
+        printf("}");
+
+        VisibleDimensionIds::Print();
+    }
+
+    // TODO make these private
+    Transforms transforms_;
+    ElementSize element_size_;
+    ElementSpaceSize element_space_size_;
+};
+
+template <index_t NDimHidden, typename VisibleDimensionIds>
+struct TensorCoordinate
+{
+    // TODO make these private
+    static constexpr index_t ndim_visible_ = VisibleDimensionIds::Size();
+
+    using HiddenIndex  = MultiIndex<NDimHidden>;
+    using VisibleIndex = MultiIndex<ndim_visible_>;
+
+    public:
+    __host__ __device__ constexpr TensorCoordinate() = default;
+
+    __host__ __device__ constexpr TensorCoordinate(const HiddenIndex& idx_hidden)
+        : idx_hidden_{idx_hidden}
+    {
+    }
+
+    __host__ __device__ constexpr auto GetIndex() const { return GetVisibleIndex(); }
+
+    __host__ __device__ constexpr index_t GetOffset() const { return idx_hidden_[Number<0>{}]; }
+
+    // TODO make these private
+    __host__ __device__ constexpr const auto& GetHiddenIndex() const { return idx_hidden_; }
+
+    __host__ __device__ auto& GetHiddenIndex() { return idx_hidden_; }
+
+    __host__ __device__ constexpr auto GetVisibleIndex() const
+    {
+        return get_container_subset(idx_hidden_, VisibleDimensionIds{});
+    }
+
+    // TODO make these private
+    HiddenIndex idx_hidden_;
+};
+
+template <index_t NTransform, index_t NDimVisible, typename UpdateLowerIndexHack>
+struct TensorCoordinateStep
+{
+    // TODO make these private
+    using VisibleIndex = MultiIndex<NDimVisible>;
+
+    public:
+    __host__ __device__ constexpr TensorCoordinateStep() = default;
+
+    __host__ __device__ constexpr TensorCoordinateStep(const VisibleIndex& idx_diff_visible,
+                                                       const MultiIndex<NTransform>& do_transforms)
+        : idx_diff_visible_{idx_diff_visible}, do_transforms_{do_transforms}
+    {
+    }
+
+    __host__ __device__ constexpr const auto& GetIndexDiff() const { return GetVisibleIndexDiff(); }
+
+    // TODO make these private
+    __host__ __device__ constexpr const auto& GetVisibleIndexDiff() const
+    {
+        return idx_diff_visible_;
+    }
+
+    VisibleIndex idx_diff_visible_;
+    MultiIndex<NTransform> do_transforms_;
+
+    // HACK: control UpdateLowerIndex()
+    static constexpr UpdateLowerIndexHack update_lower_index_hack_;
+};
+
+// 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_descriptor) because template cannot be defined inside a function
+// template
+template <typename NewTransforms>
+struct lambda_get_up_dim_num
+{
+    template <typename I>
+    __host__ __device__ constexpr auto operator()(I) const
+    {
+        using Tran = remove_reference_t<decltype(NewTransforms{}.At(I{}))>;
+        return Number<Tran::GetNumOfUpperDimension()>{};
+    }
+};
+
+template <typename OldTensorDescriptor,
+          typename NewTransforms,
+          typename NewLowerDimensionOldVisibleIdss,
+          typename NewUpperDimensionNewVisibleIdss>
+__host__ __device__ constexpr auto
+transform_tensor_descriptor(const OldTensorDescriptor& old_tensor_desc,
+                            const NewTransforms& new_transforms,
+                            NewLowerDimensionOldVisibleIdss,
+                            NewUpperDimensionNewVisibleIdss)
+{
+    // sanity check
+    {
+        static_assert(NewTransforms::Size() == NewLowerDimensionOldVisibleIdss::Size() &&
+                          NewTransforms::Size() == NewUpperDimensionNewVisibleIdss::Size(),
+                      "wrong! inconsitent number of transform");
+
+        constexpr auto all_old_top_ids = unpack([](auto... xs) { return merge_sequences(xs...); },
+                                                NewLowerDimensionOldVisibleIdss{});
+
+        constexpr auto all_new_top_ids = unpack([](auto... xs) { return merge_sequences(xs...); },
+                                                NewUpperDimensionNewVisibleIdss{});
+
+        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 visible idss (tuple of sequences) to hidden idss (tuple of
+    // sequences)
+    constexpr auto low_dim_hidden_idss = transform_tuples(
+        // convert lower dimension visible ids (a sequence) to hidden ids (a sequence)
+        [](auto low_dim_visible_ids) constexpr {
+            return transform_sequences(
+                // convert lower dimension visible id to hidden id
+                [](auto low_dim_visible_id) constexpr {
+                    return OldTensorDescriptor::GetVisibleDimensionIds()[low_dim_visible_id];
+                },
+                low_dim_visible_ids);
+        },
+        NewLowerDimensionOldVisibleIdss{});
+
+    constexpr index_t num_new_transform = NewTransforms::Size();
+
+    // upper dimension's hidden idss
+    constexpr index_t old_hidden_dim_number = OldTensorDescriptor::GetNumOfHiddenDimension();
+
+    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, math::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 visible dimension's hidden ids
+    constexpr auto unordered_new_visible_dim_hidden_ids = unpack(
+        [](auto... xs) constexpr { return merge_sequences(xs...); }, up_dim_hidden_idss);
+
+    constexpr auto new_visible_dim_unordered2ordered = unpack(
+        [](auto... xs) constexpr { return merge_sequences(xs...); },
+        NewUpperDimensionNewVisibleIdss{});
+
+    constexpr auto new_visible_dim_hidden_ids =
+        unordered_new_visible_dim_hidden_ids.ReorderGivenOld2New(new_visible_dim_unordered2ordered);
+
+    // put everything together
+    const auto all_transforms = container_concat(old_tensor_desc.GetTransforms(), new_transforms);
+
+    constexpr auto all_low_dim_hidden_idss =
+        container_concat(OldTensorDescriptor::GetLowerDimensionIdss(), low_dim_hidden_idss);
+
+    constexpr auto all_up_dim_hidden_idss =
+        container_concat(OldTensorDescriptor::GetUpperDimensionIdss(), up_dim_hidden_idss);
+
+    const auto element_space_size = old_tensor_desc.GetElementSpaceSize();
+
+    return TensorDescriptor<remove_cv_t<decltype(all_transforms)>,
+                            remove_cv_t<decltype(all_low_dim_hidden_idss)>,
+                            remove_cv_t<decltype(all_up_dim_hidden_idss)>,
+                            remove_cv_t<decltype(new_visible_dim_hidden_ids)>,
+                            remove_cv_t<decltype(element_space_size)>>{all_transforms,
+                                                                       element_space_size};
+}
+
+template <typename TensorDesc, typename VisibleIndex>
+__host__ __device__ constexpr auto make_tensor_coordinate(const TensorDesc& tensor_desc,
+                                                          const VisibleIndex& idx_visible)
+{
+    static_assert(TensorDesc::GetNumOfDimension() == VisibleIndex::Size(),
+                  "wrong! # of dimension inconsistent");
+
+    constexpr index_t ntransform   = TensorDesc::GetNumOfTransform();
+    constexpr index_t ndim_hidden  = TensorDesc::GetNumOfHiddenDimension();
+    constexpr auto visible_dim_ids = TensorDesc::GetVisibleDimensionIds();
+
+    MultiIndex<ndim_hidden> idx_hidden;
+
+    // initialize visible index
+    set_container_subset(idx_hidden, visible_dim_ids, idx_visible);
+
+    // calculate hidden index
+    static_for<ntransform, 0, -1>{}([&tensor_desc, &idx_hidden](auto itran_p1) {
+        auto itran              = itran_p1 - Number<1>{};
+        const auto& tran        = tensor_desc.GetTransforms().At(itran);
+        constexpr auto dims_low = TensorDesc::GetLowerDimensionIdss().At(itran);
+        constexpr auto dims_up  = TensorDesc::GetUpperDimensionIdss().At(itran);
+
+        const auto idx_up = get_container_subset(idx_hidden, dims_up);
+
+        MultiIndex<dims_low.Size()> idx_low;
+
+        tran.CalculateLowerIndex(idx_low, idx_up);
+
+        set_container_subset(idx_hidden, dims_low, idx_low);
+    });
+
+    return TensorCoordinate<ndim_hidden, decltype(visible_dim_ids)>{idx_hidden};
+}
+
+// UpdateLowerIndexHack: Sequence<...>
+// HACK: control UpdateLowerIndex
+template <typename TensorDesc, typename VisibleIndex, typename UpdateLowerIndexHack>
+__host__ __device__ constexpr auto make_tensor_coordinate_step(const TensorDesc&,
+                                                               const VisibleIndex& idx_diff_visible,
+                                                               UpdateLowerIndexHack)
+{
+    static_assert(TensorDesc::GetNumOfDimension() == VisibleIndex::Size(),
+                  "wrong! # of dimension inconsistent");
+
+    constexpr index_t ntransform   = TensorDesc::GetNumOfTransform();
+    constexpr index_t ndim_hidden  = TensorDesc::GetNumOfHiddenDimension();
+    constexpr index_t ndim_visible = TensorDesc::GetNumOfVisibleDimension();
+    constexpr auto visible_dim_ids = TensorDesc::GetVisibleDimensionIds();
+
+    static_assert(UpdateLowerIndexHack::Size() == ntransform, "wrong!");
+
+    // use index_t for boolean type
+    auto do_transforms    = make_zero_multi_index<ntransform>();
+    auto is_non_zero_diff = make_zero_multi_index<ndim_hidden>();
+
+    // decide do_transform by checkout non-zero index diff components
+    MultiIndex<VisibleIndex::Size()> non_zero_diff_pick_visible;
+
+    static_for<0, ndim_visible, 1>{}(
+        [&](auto i) { non_zero_diff_pick_visible(i) = (idx_diff_visible[i] != 0); });
+
+    set_container_subset(is_non_zero_diff, visible_dim_ids, non_zero_diff_pick_visible);
+
+    static_for<ntransform - 1, -1, -1>{}([&](auto itran) {
+        constexpr auto dims_low = TensorDesc::GetLowerDimensionIdss().At(itran);
+        constexpr auto dims_up  = TensorDesc::GetUpperDimensionIdss().At(itran);
+
+        const auto non_zero_diff_pick_up = get_container_subset(is_non_zero_diff, dims_up);
+
+        MultiIndex<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);
+    });
+
+    return TensorCoordinateStep<ntransform, ndim_visible, UpdateLowerIndexHack>{idx_diff_visible,
+                                                                                do_transforms};
+}
+
+template <typename TensorDesc, typename VisibleIndex>
+__host__ __device__ constexpr auto make_tensor_coordinate_step(const TensorDesc&,
+                                                               const VisibleIndex& idx_diff_visible)
+{
+    constexpr index_t ntransform = TensorDesc::GetNumOfTransform();
+
+    return make_tensor_coordinate_step(
+        TensorDesc{}, idx_diff_visible, typename uniform_sequence_gen<ntransform, 0>::type{});
+}
+
+template <typename TensorDesc, typename TensorCoord, typename TensorCoordStep>
+__host__ __device__ constexpr void move_tensor_coordinate(const TensorDesc& tensor_desc,
+                                                          TensorCoord& coord,
+                                                          const TensorCoordStep& coord_step)
+{
+    constexpr index_t ndim_hidden = TensorDesc::GetNumOfHiddenDimension();
+    constexpr index_t ntransform  = TensorDesc::GetNumOfTransform();
+
+    // this is what needs to be calculated
+    auto idx_diff_hidden = make_zero_multi_index<ndim_hidden>();
+
+    // initialize visible index diff
+    set_container_subset(
+        idx_diff_hidden, TensorDesc::GetVisibleDimensionIds(), coord_step.GetVisibleIndexDiff());
+
+    // this is what needs to be updated
+    auto& idx_hidden = coord.GetHiddenIndex();
+
+    // update visible index
+    auto idx_hidden_pick_visible =
+        get_container_subset(idx_hidden, TensorDesc::GetVisibleDimensionIds());
+
+    idx_hidden_pick_visible += coord_step.GetIndexDiff();
+
+    set_container_subset(idx_hidden, TensorDesc::GetVisibleDimensionIds(), idx_hidden_pick_visible);
+
+    // update rest of hidden index
+    static_for<ntransform - 1, -1, -1>{}([&](auto itran) {
+        if(coord_step.do_transforms_[itran])
+        {
+            const auto& tran        = tensor_desc.GetTransforms().At(itran);
+            constexpr auto dims_low = TensorDesc::GetLowerDimensionIdss().At(itran);
+            constexpr auto dims_up  = TensorDesc::GetUpperDimensionIdss().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);
+
+            MultiIndex<dims_low.Size()> idx_diff_low;
+
+            // HACK: control UpdateLowerIndex for Merge using hack
+            constexpr index_t Hack = decltype(coord_step.update_lower_index_hack_)::At(itran);
+
+            tran.UpdateLowerIndex(idx_diff_low, idx_diff_up, idx_low, idx_up_new, Number<Hack>{});
+
+            set_container_subset(idx_diff_hidden, dims_low, idx_diff_low);
+            set_container_subset(idx_hidden, dims_low, idx_low);
+        }
+    });
+}
+
+template <typename TensorDesc, typename TensorCoord>
+__host__ __device__ constexpr bool
+coordinate_has_valid_offset_assuming_visible_index_is_valid(const TensorDesc& tensor_desc,
+                                                            const TensorCoord& coord)
+{
+    bool valid = true;
+
+    constexpr index_t ntransform = TensorDesc::GetNumOfTransform();
+
+    const auto& idx_hidden = coord.GetHiddenIndex();
+
+    static_for<ntransform - 1, -1, -1>{}([&tensor_desc, &idx_hidden, &valid](auto itran) {
+        const auto tran = tensor_desc.GetTransforms().At(itran);
+
+        // check validity, only if current transformation does not always has a valid mapping
+        if constexpr(!decltype(tran)::IsValidUpperIndexAlwaysMappedToValidLowerIndex())
+        {
+            const auto idx_up =
+                get_container_subset(idx_hidden, TensorDesc::GetUpperDimensionIdss().At(itran));
+
+            // Comment: using valid = valid && .. will result in weird control flow in ISA
+            valid &= tran.IsValidUpperIndexMappedToValidLowerIndex(idx_up);
+        }
+    });
+
+    return valid;
+}
+
+template <typename TensorDesc, typename TensorCoord>
+__host__ __device__ constexpr bool coordinate_has_valid_offset(const TensorDesc& tensor_desc,
+                                                               const TensorCoord& coord)
+{
+    // check visible index
+    const auto& idx_visible = coord.GetVisibleIndex();
+
+    bool is_visible_index_valid = true;
+
+    static_for<0, TensorDesc::GetNumOfDimension(), 1>{}(
+        [&is_visible_index_valid, &idx_visible, &tensor_desc](auto i) {
+            is_visible_index_valid =
+                is_visible_index_valid &&
+                (idx_visible[i] >= 0 && idx_visible[i] < tensor_desc.GetLength(i));
+        });
+
+    // check other hidden index
+    return is_visible_index_valid &&
+           coordinate_has_valid_offset_assuming_visible_index_is_valid(tensor_desc, coord);
+}
+
+template <typename TensorDesc>
+using TensorCoordinate_t = decltype(make_tensor_coordinate(
+    TensorDesc{}, MultiIndex<remove_cvref_t<TensorDesc>::GetNumOfDimension()>{}));
+
+template <typename TensorDesc>
+using TensorCoordinateStep_t = decltype(make_tensor_coordinate_step(
+    TensorDesc{}, MultiIndex<remove_cvref_t<TensorDesc>::GetNumOfDimension()>{}));
+
+} // namespace ck

include/ck/tensor_description/tensor_descriptor_helper.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck/utility/common_header.hpp"
+#include "ck/tensor_description/tensor_descriptor.hpp"
+#include "ck/tensor_description/multi_index_transform_helper.hpp"
+
+namespace ck {
+
+/*
+ * These functions create tensor descriptor at runtime. If they are not constexpr, you will
+ * likely see usage of scratch memory during construction of these tensor descriptors. So
+ * it's better to call these functions on host and then pass the constructed tensor descritpors
+ * to GPU. If the tensor descritpors being constructed are constexpr, then you can call these
+ * functions on GPU without worrying about scratch memory usage.
+ */
+
+#if CK_WORKAROUND_SWDEV_275126
+template <typename Lengths, typename Strides, index_t I, typename AccOld>
+__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;
+    }
+}
+#endif
+
+// 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) LongNumber<>
+template <typename... Lengths,
+          typename... Strides,
+          typename enable_if<sizeof...(Lengths) == sizeof...(Strides), bool>::type = false>
+__host__ __device__ constexpr auto make_naive_tensor_descriptor(const Tuple<Lengths...>& lengths,
+                                                                const Tuple<Strides...>& strides)
+{
+    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{};
+
+#if !CK_WORKAROUND_SWDEV_275126
+    // rocm-4.1 compiler would crash for recursive labmda
+    // recursive function for reduction
+    auto f = [&](auto fs, auto i, auto acc_old) {
+        auto acc_new = acc_old + (lengths[i] - Number<1>{}) * strides[i];
+
+        if constexpr(i.value < N - 1)
+        {
+            return fs(fs, i + Number<1>{}, acc_new);
+        }
+        else
+        {
+            return acc_new;
+        }
+    };
+
+    const auto element_space_size = f(f, Number<0>{}, LongNumber<1>{});
+#else
+    const auto element_space_size =
+        calculate_element_space_size_impl(lengths, strides, Number<0>{}, LongNumber<1>{});
+#endif
+
+    return TensorDescriptor<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)>>{transforms,
+                                                                       element_space_size};
+}
+
+// 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) LongNumber<>
+template <typename... Lengths>
+__host__ __device__ constexpr auto
+make_naive_tensor_descriptor_packed(const Tuple<Lengths...>& lengths)
+{
+    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, math::multiplies{}, LongNumber<1>{});
+
+    return TensorDescriptor<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)>>{transforms,
+                                                                       element_space_size};
+}
+
+// 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>
+__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 = math::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,
+                                        math::multiplies{},
+                                        Number<stride_n_minus_2>{},
+                                        i + I1,
+                                        Number<N - 1>{},
+                                        I1);
+            }
+        },
+        Number<N>{});
+
+    return make_naive_tensor_descriptor(lengths, strides);
+}
+
+} // namespace ck

include/ck/tensor_description/tensor_space_filling_curve.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck/utility/math.hpp"
+#include "ck/utility/sequence.hpp"
+#include "ck/utility/sequence_helper.hpp"
+#include "ck/utility/statically_indexed_array_multi_index.hpp"
+#include "ck/utility/tuple_helper.hpp"
+#include "ck/tensor_description/tensor_adaptor.hpp"
+
+namespace ck {
+
+template <typename TensorLengths,
+          typename DimAccessOrder,
+          typename ScalarsPerAccess,
+          bool SnakeCurved = true> // # of scalars per access in each dimension
+struct SpaceFillingCurve
+{
+    static constexpr index_t nDim = TensorLengths::Size();
+
+    using Index = MultiIndex<nDim>;
+
+    static constexpr index_t ScalarPerVector =
+        reduce_on_sequence(ScalarsPerAccess{}, math::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>{};
+
+    __host__ __device__ static constexpr index_t GetNumOfAccess()
+    {
+        static_assert(TensorLengths::Size() == ScalarsPerAccess::Size());
+        static_assert(TensorLengths{} % ScalarsPerAccess{} ==
+                      typename uniform_sequence_gen<TensorLengths::Size(), 0>::type{});
+
+        return reduce_on_sequence(TensorLengths{}, math::multiplies{}, Number<1>{}) /
+               ScalarPerVector;
+    }
+
+    template <index_t AccessIdx1dBegin, index_t AccessIdx1dEnd>
+    static __device__ __host__ constexpr auto GetStepBetween(Number<AccessIdx1dBegin>,
+                                                             Number<AccessIdx1dEnd>)
+    {
+        static_assert(AccessIdx1dBegin >= 0, "1D index should be non-negative");
+        static_assert(AccessIdx1dBegin < GetNumOfAccess(), "1D index should be larger than 0");
+        static_assert(AccessIdx1dEnd >= 0, "1D index should be non-negative");
+        static_assert(AccessIdx1dEnd < GetNumOfAccess(), "1D index should be larger than 0");
+
+        constexpr auto idx_begin = GetIndex(Number<AccessIdx1dBegin>{});
+        constexpr auto idx_end   = GetIndex(Number<AccessIdx1dEnd>{});
+        return idx_end - idx_begin;
+    }
+
+    template <index_t AccessIdx1d>
+    static __device__ __host__ constexpr auto GetForwardStep(Number<AccessIdx1d>)
+    {
+        static_assert(AccessIdx1d < GetNumOfAccess(), "1D index should be larger than 0");
+        return GetStepBetween(Number<AccessIdx1d>{}, Number<AccessIdx1d + 1>{});
+    }
+
+    template <index_t AccessIdx1d>
+    static __device__ __host__ constexpr auto GetBackwardStep(Number<AccessIdx1d>)
+    {
+        static_assert(AccessIdx1d > 0, "1D index should be larger than 0");
+
+        return GetStepBetween(Number<AccessIdx1d>{}, Number<AccessIdx1d - 1>{});
+    }
+
+    template <index_t AccessIdx1d>
+    static __device__ __host__ constexpr Index GetIndex(Number<AccessIdx1d>)
+    {
+#if 0
+        /*
+         * \todo: TensorAdaptor::CalculateBottomIndex does NOT return constexpr as expected.
+         */
+        constexpr auto ordered_access_idx = to_index_adaptor.CalculateBottomIndex(make_multi_index(Number<AccessIdx1d>{}));
+#else
+
+        constexpr auto access_strides = container_reverse_exclusive_scan(
+            ordered_access_lengths, math::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 = [&]() {
+            StaticallyIndexedArray<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: rename this function
+    template <index_t AccessIdx1d>
+    static __device__ __host__ constexpr auto GetIndexTupleOfNumber(Number<AccessIdx1d>)
+    {
+        constexpr auto idx = GetIndex(Number<AccessIdx1d>{});
+
+        return generate_tuple([&](auto i) { return Number<idx[i]>{}; }, Number<nDim>{});
+    }
+};
+
+} // namespace ck

include/ck/tensor_operation/gpu/block/blockwise_gemm_dl_v2r3.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck/utility/common_header.hpp"
+#include "ck/tensor_description/tensor_adaptor.hpp"
+#include "ck/tensor_operation/gpu/thread/threadwise_tensor_slice_transfer_v4r1.hpp"
+#include "ck/tensor_operation/gpu/thread/threadwise_contraction_dl.hpp"
+
+namespace ck {
+
+// C[BM0, BM1, BN0, BN1] += transpose(A[K, BM0, BM1]) * B[K, BN0, BN1]
+// A and B are visable to the whole block, C is distributed among each thread
+// Assume:
+//   1. A:
+//     1. ABlockDesc_BK0_BM_BK1 is known at compile-time
+//     2. ABlockBuffer is DynamicBuffer
+//   2. B:
+//     1. BBlockDesc_BK0_BN_BK1 is known at compile-time
+//     2. BBlockBuffer is DynamicBuffer
+//   3. C:
+//     1. CThreadDesc_BM0_BM11_BN0_BN11 is known at compile-time
+//     2. CThreadBuffer is StaticBuffer
+// Also assume:
+//   BM10BN10ThreadClusterBM10Xs::Size() = BM10BN10ThreadClusterBN10Xs::Size() == 2
+//   BM0 = BN0 = 2. It will do 2x2 pipelined read and fma (ABBA optimization)
+template <index_t BlockSize,
+          typename FloatA,
+          typename FloatB,
+          typename FloatC,
+          typename ABlockDesc_BK0_BM_BK1,
+          typename BBlockDesc_BK0_BN_BK1,
+          index_t BM1PerThreadBM11,
+          index_t BN1PerThreadBN11,
+          index_t BK0PerThread,
+          typename BM10BN10ThreadClusterBM10Xs, // Sequence<BM10BN10ThreadClusterBM100,
+                                                //          BM10BN10ThreadClusterBM101, ...>
+          typename BM10BN10ThreadClusterBN10Xs, // Sequence<BM10BN10ThreadClusterBN100,
+                                                //          BM10BN10ThreadClusterBN101, ...>
+          index_t AThreadCopyScalarPerVector_BM11,
+          index_t BThreadCopyScalarPerVector_BN11,
+          typename enable_if<ABlockDesc_BK0_BM_BK1::IsKnownAtCompileTime() &&
+                                 BBlockDesc_BK0_BN_BK1::IsKnownAtCompileTime(),
+                             bool>::type = false>
+struct BlockwiseGemmDl_A_BK0_BM_BK1_B_BK0_BN_BK1_C_BM0_BM1_BN0_BN1_pipeline_BM0_2_BN0_2
+{
+    using AIndex = MultiIndex<3>;
+    using BIndex = MultiIndex<3>;
+    using CIndex = MultiIndex<4>;
+
+    static constexpr auto I0 = Number<0>{};
+    static constexpr auto I1 = Number<1>{};
+    static constexpr auto I2 = Number<2>{};
+    static constexpr auto I3 = Number<3>{};
+
+    static constexpr index_t BK0 = ABlockDesc_BK0_BM_BK1{}.GetLength(I0);
+    static constexpr index_t BK1 = ABlockDesc_BK0_BM_BK1{}.GetLength(I2);
+    static constexpr index_t BM  = ABlockDesc_BK0_BM_BK1{}.GetLength(I1);
+    static constexpr index_t BN  = BBlockDesc_BK0_BN_BK1{}.GetLength(I1);
+
+    static constexpr index_t BM100 = BM10BN10ThreadClusterBM10Xs{}[I0];
+    static constexpr index_t BN100 = BM10BN10ThreadClusterBN10Xs{}[I0];
+
+    static constexpr index_t BM101 = BM10BN10ThreadClusterBM10Xs{}[I1];
+    static constexpr index_t BN101 = BM10BN10ThreadClusterBN10Xs{}[I1];
+
+    static constexpr index_t BM11 = BM1PerThreadBM11;
+    static constexpr index_t BN11 = BN1PerThreadBN11;
+
+    static constexpr index_t BM1 = BM100 * BM101 * BM11;
+    static constexpr index_t BN1 = BN100 * BN101 * BN11;
+
+    static constexpr index_t BM0 = BM / BM1;
+    static constexpr index_t BN0 = BN / BN1;
+
+    __host__ __device__ static constexpr auto
+    MakeABlockDescriptor_BK0_BM0_BM1_BK1(const ABlockDesc_BK0_BM_BK1& a_block_desc_bk0_bm_bk1)
+    {
+        const auto a_block_bk0_bm0_bm1_bk1 = transform_tensor_descriptor(
+            a_block_desc_bk0_bm_bk1,
+            make_tuple(make_pass_through_transform(Number<BK0>{}),
+                       make_unmerge_transform(make_tuple(Number<BM0>{}, Number<BM1>{})),
+                       make_pass_through_transform(Number<BK1>{})),
+            make_tuple(Sequence<0>{}, Sequence<1>{}, Sequence<2>{}),
+            make_tuple(Sequence<0>{}, Sequence<1, 2>{}, Sequence<3>{}));
+
+        return a_block_bk0_bm0_bm1_bk1;
+    }
+
+    __host__ __device__ static constexpr auto
+    MakeBBlockDescriptor_BK0_BN0_BN1_BK1(const BBlockDesc_BK0_BN_BK1& b_block_desc_bk0_bn_bk1)
+    {
+        const auto b_block_desc_bk0_bn0_bn1_bk1 = transform_tensor_descriptor(
+            b_block_desc_bk0_bn_bk1,
+            make_tuple(make_pass_through_transform(Number<BK0>{}),
+                       make_unmerge_transform(make_tuple(Number<BN0>{}, Number<BN1>{})),
+                       make_pass_through_transform(Number<BK1>{})),
+            make_tuple(Sequence<0>{}, Sequence<1>{}, Sequence<2>{}),
+            make_tuple(Sequence<0>{}, Sequence<1, 2>{}, Sequence<3>{}));
+
+        return b_block_desc_bk0_bn0_bn1_bk1;
+    }
+
+    __host__ __device__ static constexpr auto
+    MakeCBlockAdaptor_BM0_BM100_BM101_BM11_BN0_BN100_BN101_BN11_To_BM_BN()
+    {
+        // upper: [BM0, BM100, BM101, BM11, BN0, BN100, BN101, BN11]
+        // lower: [BM, BN]
+        constexpr auto c_block_adaptor_m0_m100_m101_m11_n0_n100_n101_n11_to_m_n =
+            make_single_stage_tensor_adaptor(
+                make_tuple(make_unmerge_transform(make_tuple(
+                               Number<BM0>{}, Number<BM100>{}, Number<BM101>{}, Number<BM11>{})),
+                           make_unmerge_transform(make_tuple(
+                               Number<BN0>{}, Number<BN100>{}, Number<BN101>{}, Number<BN11>{}))),
+                make_tuple(Sequence<0>{}, Sequence<1>{}),
+                make_tuple(Sequence<0, 1, 2, 3>{}, Sequence<4, 5, 6, 7>{}));
+
+        return c_block_adaptor_m0_m100_m101_m11_n0_n100_n101_n11_to_m_n;
+    }
+
+    __host__ __device__ static constexpr auto
+    MakeCBlockAdaptor_BM0_BM100_BM101_BM11_BN0_BN100_BN101_BN11_To_BM0_BM1_BN0_BN1()
+    {
+        // upper: [BM0, BM100, BM101, BM11, BN0, BN100, BN101, BN11]
+        // lower: [BM0, BM1, BN0, BN1]
+        constexpr auto c_block_adaptor_m0_m100_m101_m11_n0_n100_n101_n11_to_m0_m1_n0_n1 =
+            make_single_stage_tensor_adaptor(
+                make_tuple(make_pass_through_transform(Number<BM0>{}),
+                           make_unmerge_transform(
+                               make_tuple(Number<BM100>{}, Number<BM101>{}, Number<BM11>{})),
+                           make_pass_through_transform(Number<BN0>{}),
+                           make_unmerge_transform(
+                               make_tuple(Number<BN100>{}, Number<BN101>{}, Number<BN11>{}))),
+                make_tuple(Sequence<0>{}, Sequence<1>{}, Sequence<2>{}, Sequence<3>{}),
+                make_tuple(Sequence<0>{}, Sequence<1, 2, 3>{}, Sequence<4>{}, Sequence<5, 6, 7>{}));
+
+        return c_block_adaptor_m0_m100_m101_m11_n0_n100_n101_n11_to_m0_m1_n0_n1;
+    }
+
+    __host__ __device__ static constexpr auto GetCThreadTensorLengths_BM0_BM1_BN0_BN1()
+    {
+        return Sequence<BM0, BM11, BN0, BN11>{};
+    }
+
+    static constexpr auto a_block_desc_bk0_bm0_bm1_bk1_ =
+        MakeABlockDescriptor_BK0_BM0_BM1_BK1(ABlockDesc_BK0_BM_BK1{});
+
+    static constexpr auto b_block_desc_bk0_bn0_bn1_bk1_ =
+        MakeBBlockDescriptor_BK0_BN0_BN1_BK1(BBlockDesc_BK0_BN_BK1{});
+
+    public:
+    __device__ BlockwiseGemmDl_A_BK0_BM_BK1_B_BK0_BN_BK1_C_BM0_BM1_BN0_BN1_pipeline_BM0_2_BN0_2()
+        : c_thread_origin_data_idx_{CalculateCThreadOriginOnBlock_BM0_BM1_BN0_BN1(
+              get_thread_local_1d_id())},
+          a_thread_copy_{
+              make_tuple(0, c_thread_origin_data_idx_[I0], c_thread_origin_data_idx_[I1], 0)},
+          b_thread_copy_{
+              make_tuple(0, c_thread_origin_data_idx_[I2], c_thread_origin_data_idx_[I3], 0)}
+    {
+        static_assert(ABlockDesc_BK0_BM_BK1::IsKnownAtCompileTime() &&
+                          BBlockDesc_BK0_BN_BK1::IsKnownAtCompileTime(),
+                      "wrong! Desc should be known at compile-time");
+
+        static_assert(BlockSize == BM101 * BM100 * BN101 * BN100,
+                      "wrong! blocksize and cluster size not consistent");
+
+        static_assert(BM % BM1 == 0 && BN % BN1 == 0, "wrong!");
+
+        static_assert(ABlockDesc_BK0_BM_BK1{}.GetLength(I0) ==
+                          BBlockDesc_BK0_BN_BK1{}.GetLength(I0),
+                      "wrong! K dimension not consistent");
+
+        // TODO remove this restriction
+        static_assert(BM10BN10ThreadClusterBM10Xs::Size() == 2 &&
+                          BM10BN10ThreadClusterBN10Xs::Size() == 2,
+                      "wrong!");
+
+        // TODO: remove this restriction
+        static_assert(BM0 == 2, "wrong");
+        static_assert(BM0 == 2 && BN0 == 2, "wrong");
+    }
+
+    __device__ static CIndex CalculateCThreadOriginOnBlock_BM0_BM1_BN0_BN1(index_t thread_id)
+    {
+        // lower: [BM0, BM1, BN0, BN1]
+        // upper: [BM0, BM100, BM101, BM11, BN0, BN100, BN101, BN11]
+        constexpr auto adaptor0 =
+            MakeCBlockAdaptor_BM0_BM100_BM101_BM11_BN0_BN100_BN101_BN11_To_BM0_BM1_BN0_BN1();
+
+        // lower: [BM0, BM100, BM101, BM11, BN0, BN100, BN101, BN11]
+        // upper: [Tid, BM0, BM11, BN0, BN11]
+        constexpr auto adaptor1 = make_single_stage_tensor_adaptor(
+            make_tuple(make_merge_transform(make_tuple(BM100, BN100, BM101, BN101)),
+                       make_pass_through_transform(BM0),
+                       make_pass_through_transform(BM11),
+                       make_pass_through_transform(BN0),
+                       make_pass_through_transform(BN11)),
+            make_tuple(
+                Sequence<1, 5, 2, 6>{}, Sequence<0>{}, Sequence<3>{}, Sequence<4>{}, Sequence<7>{}),
+            make_tuple(Sequence<0>{}, Sequence<1>{}, Sequence<2>{}, Sequence<3>{}, Sequence<4>{}));
+
+        constexpr auto adaptor = chain_tensor_adaptors(adaptor0, adaptor1);
+
+        return adaptor.CalculateBottomIndex(make_multi_index(thread_id, 0, 0, 0, 0));
+    }
+
+    template <typename CThreadDesc_BM0_BM11_BN0_BN11,
+              typename ABlockBuffer,
+              typename BBlockBuffer,
+              typename CThreadBuffer>
+    __device__ void Run(const CThreadDesc_BM0_BM11_BN0_BN11&,
+                        const ABlockBuffer& a_block_buf,
+                        const BBlockBuffer& b_block_buf,
+                        CThreadBuffer& c_thread_buf) const
+    {
+        static_assert(CThreadDesc_BM0_BM11_BN0_BN11::IsKnownAtCompileTime(),
+                      "wrong! Desc should be known at compile-time");
+
+        // TODO: remove this restriction
+        static_assert(BM0 == 2 && BN0 == 2 &&
+                          CThreadDesc_BM0_BM11_BN0_BN11{}.GetLength(I0) == BM0 &&
+                          CThreadDesc_BM0_BM11_BN0_BN11{}.GetLength(I2) == BN0,
+                      "wrong");
+
+        auto a_thread_buf = make_static_buffer<AddressSpaceEnum::Vgpr, FloatA>(
+            a_thread_desc_bk0_bm0_bm1_bk1_.GetElementSpaceSize());
+        auto b_thread_buf = make_static_buffer<AddressSpaceEnum::Vgpr, FloatB>(
+            b_thread_desc_bk0_bn0_bn1_bk1_.GetElementSpaceSize());
+
+        constexpr auto threadwise_contraction =
+            ThreadwiseContractionDl_A_TK0_TM0_TM1_TK1_B_TK0_TN0_TN1_TK1_C_TM0_TM1_TN0_TN1<
+                FloatA,
+                FloatB,
+                FloatC,
+                decltype(a_thread_desc_bk0_bm0_bm1_bk1_),
+                decltype(b_thread_desc_bk0_bn0_bn1_bk1_),
+                CThreadDesc_BM0_BM11_BN0_BN11,
+                Sequence<BK0PerThread, BK1>,
+                Sequence<1, BM1PerThreadBM11>,
+                Sequence<1, BN1PerThreadBN11>>{};
+
+        // read A_sub_0
+        a_thread_copy_.Run(a_block_desc_bk0_bm0_bm1_bk1_,
+                           make_tuple(I0, I0, I0, I0),
+                           a_block_buf,
+                           a_thread_desc_bk0_bm0_bm1_bk1_,
+                           make_tuple(I0, I0, I0, I0),
+                           a_thread_buf);
+
+        // read B_sub_0
+        b_thread_copy_.Run(b_block_desc_bk0_bn0_bn1_bk1_,
+                           make_tuple(I0, I0, I0, I0),
+                           b_block_buf,
+                           b_thread_desc_bk0_bn0_bn1_bk1_,
+                           make_tuple(I0, I0, I0, I0),
+                           b_thread_buf);
+
+        // read B_sub_1
+        b_thread_copy_.Run(b_block_desc_bk0_bn0_bn1_bk1_,
+                           make_tuple(I0, I1, I0, I0),
+                           b_block_buf,
+                           b_thread_desc_bk0_bn0_bn1_bk1_,
+                           make_tuple(I0, I1, I0, I0),
+                           b_thread_buf);
+
+        // read A_sub_1
+        a_thread_copy_.Run(a_block_desc_bk0_bm0_bm1_bk1_,
+                           make_tuple(I0, I1, I0, I0),
+                           a_block_buf,
+                           a_thread_desc_bk0_bm0_bm1_bk1_,
+                           make_tuple(I0, I1, I0, I0),
+                           a_thread_buf);
+
+        // C_sub_00 += transpose(A_sub_0) * B_sub_0
+        threadwise_contraction.Run(a_thread_buf,
+                                   make_tuple(I0, I0, I0, I0),
+                                   b_thread_buf,
+                                   make_tuple(I0, I0, I0, I0),
+                                   c_thread_buf,
+                                   make_tuple(I0, I0, I0, I0));
+
+        // C_sub_01 += transpose(A_sub_0) * B_sub_1
+        threadwise_contraction.Run(a_thread_buf,
+                                   make_tuple(I0, I0, I0, I0),
+                                   b_thread_buf,
+                                   make_tuple(I0, I1, I0, I0),
+                                   c_thread_buf,
+                                   make_tuple(I0, I0, I1, I0));
+
+        // loop over rest of bk0
+        static_for<BK0PerThread, BK0, BK0PerThread>{}([&](auto bk0) {
+            // read A_sub_0
+            a_thread_copy_.Run(a_block_desc_bk0_bm0_bm1_bk1_,
+                               make_tuple(bk0, I0, I0, I0),
+                               a_block_buf,
+                               a_thread_desc_bk0_bm0_bm1_bk1_,
+                               make_tuple(I0, I0, I0, I0),
+                               a_thread_buf);
+
+            // C_sub_10 += transpose(A_sub_1) * B_sub_0
+            threadwise_contraction.Run(a_thread_buf,
+                                       make_tuple(I0, I1, I0, I0),
+                                       b_thread_buf,
+                                       make_tuple(I0, I0, I0, I0),
+                                       c_thread_buf,
+                                       make_tuple(I1, I0, I0, I0));
+
+            // read B_sub_0
+            b_thread_copy_.Run(b_block_desc_bk0_bn0_bn1_bk1_,
+                               make_tuple(bk0, I0, I0, I0),
+                               b_block_buf,
+                               b_thread_desc_bk0_bn0_bn1_bk1_,
+                               make_tuple(I0, I0, I0, I0),
+                               b_thread_buf);
+
+            // C_sub_11 += transpose(A_sub_1) * B_sub_1
+            threadwise_contraction.Run(a_thread_buf,
+                                       make_tuple(I0, I1, I0, I0),
+                                       b_thread_buf,
+                                       make_tuple(I0, I1, I0, I0),
+                                       c_thread_buf,
+                                       make_tuple(I1, I0, I1, I0));
+
+            // read B_sub_1
+            b_thread_copy_.Run(b_block_desc_bk0_bn0_bn1_bk1_,
+                               make_tuple(bk0, I1, I0, I0),
+                               b_block_buf,
+                               b_thread_desc_bk0_bn0_bn1_bk1_,
+                               make_tuple(I0, I1, I0, I0),
+                               b_thread_buf);
+
+            // read A_sub_1
+            a_thread_copy_.Run(a_block_desc_bk0_bm0_bm1_bk1_,
+                               make_tuple(bk0, I1, I0, I0),
+                               a_block_buf,
+                               a_thread_desc_bk0_bm0_bm1_bk1_,
+                               make_tuple(I0, I1, I0, I0),
+                               a_thread_buf);
+
+            // C_sub_00 += transpose(A_sub_0) * B_sub_0
+            threadwise_contraction.Run(a_thread_buf,
+                                       make_tuple(I0, I0, I0, I0),
+                                       b_thread_buf,
+                                       make_tuple(I0, I0, I0, I0),
+                                       c_thread_buf,
+                                       make_tuple(I0, I0, I0, I0));
+
+            // C_sub_01 += transpose(A_sub_0) * B_sub_1
+            threadwise_contraction.Run(a_thread_buf,
+                                       make_tuple(I0, I0, I0, I0),
+                                       b_thread_buf,
+                                       make_tuple(I0, I1, I0, I0),
+                                       c_thread_buf,
+                                       make_tuple(I0, I0, I1, I0));
+        });
+
+        // C_sub_10 += transpose(A_sub_1) * B_sub_0
+        threadwise_contraction.Run(a_thread_buf,
+                                   make_tuple(I0, I1, I0, I0),
+                                   b_thread_buf,
+                                   make_tuple(I0, I0, I0, I0),
+                                   c_thread_buf,
+                                   make_tuple(I1, I0, I0, I0));
+
+        // C_sub_11 += transpose(A_sub_1) * B_sub_1
+        threadwise_contraction.Run(a_thread_buf,
+                                   make_tuple(I0, I1, I0, I0),
+                                   b_thread_buf,
+                                   make_tuple(I0, I1, I0, I0),
+                                   c_thread_buf,
+                                   make_tuple(I1, I0, I1, I0));
+    }
+
+    private:
+    // A[BK0, BM0, BM1, BK1]
+    static constexpr auto a_thread_desc_bk0_bm0_bm1_bk1_ =
+        make_naive_tensor_descriptor_packed(make_tuple(
+            Number<BK0PerThread>{}, Number<BM0>{}, Number<BM1PerThreadBM11>{}, Number<BK1>{}));
+
+    // B[BK0, BN0, BN1, BK1]
+    static constexpr auto b_thread_desc_bk0_bn0_bn1_bk1_ =
+        make_naive_tensor_descriptor_packed(make_tuple(
+            Number<BK0PerThread>{}, Number<BN0>{}, Number<BN1PerThreadBN11>{}, Number<BK1>{}));
+
+    using AThreadCopy = ThreadwiseTensorSliceTransfer_v4r1<
+        FloatA,
+        FloatA,
+        decltype(a_block_desc_bk0_bm0_bm1_bk1_),
+        decltype(a_thread_desc_bk0_bm0_bm1_bk1_),
+        Sequence<BK0PerThread, 1, BM1PerThreadBM11, BK1>, // SliceLengths
+        Sequence<0, 1, 2, 3>,                             // DimAccessOrder
+        Sequence<1, 1, BM1PerThreadBM11, BK1>,            // SrcVectorTensorLengths
+        Sequence<0, 1, 2, 3>>;                            // SrcVectorTensorContiguousDimOrder
+
+    using BThreadCopy = ThreadwiseTensorSliceTransfer_v4r1<
+        FloatB,
+        FloatB,
+        decltype(b_block_desc_bk0_bn0_bn1_bk1_),
+        decltype(b_thread_desc_bk0_bn0_bn1_bk1_),
+        Sequence<BK0PerThread, 1, BN1PerThreadBN11, BK1>, // SliceLengths
+        Sequence<0, 1, 2, 3>,                             // DimAccessOrder
+        Sequence<1, 1, BN1PerThreadBN11, BK1>,            // SrcVectorTensorLengths
+        Sequence<0, 1, 2, 3>>;                            // SrcVectorTensorContiguousDimOrder
+
+    CIndex c_thread_origin_data_idx_;
+
+    AThreadCopy a_thread_copy_;
+    BThreadCopy b_thread_copy_;
+};
+
+} // namespace ck

include/ck/tensor_operation/gpu/block/blockwise_gemm_dlops_v2r2.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#ifndef CK_BLOCKWISE_GEMM_DLOPS_V2R2_HPP
+#define CK_BLOCKWISE_GEMM_DLOPS_V2R2_HPP
+
+#include "common_header.hpp"
+#include "tensor_adaptor.hpp"
+#include "threadwise_tensor_slice_transfer.hpp"
+#include "threadwise_contraction_dlops.hpp"
+
+namespace ck {
+
+// C[M0, M1, N0, N1] += transpose(A[K, M0, M1]) * B[K, N0, N1]
+// A and B are visable to the whole block, C is distributed among each thread
+// Assume:
+//   1. A:
+//     1. AKMBlockDesc is known at compile-time
+//     2. ABlockBuffer is DynamicBuffer
+//   2. B:
+//     1. BKNBlockDesc is known at compile-time
+//     2. BBlockBuffer is DynamicBuffer
+//   3. C:
+//     1. CM0M1N0N1ThreadDesc is known at compile-time
+//     2. CThreadBuffer is StaticBuffer
+// Also assume:
+//   M0 = N0 = 2. It will do 2x2 pipelined read and fma (ABBA optimization)
+template <
+    index_t BlockSize,
+    typename FloatA,
+    typename FloatB,
+    typename FloatC,
+    typename AKMBlockDesc,
+    typename BKNBlockDesc,
+    index_t M1PerThreadM11,
+    index_t N1PerThreadN11,
+    index_t KPerThread,
+    index_t M1N1ThreadClusterM100,
+    index_t M1N1ThreadClusterN100,
+    index_t M1N1ThreadClusterM101,
+    index_t M1N1ThreadClusterN101,
+    index_t AThreadCopyScalarPerVector_M11,
+    index_t BThreadCopyScalarPerVector_N11,
+    typename enable_if<AKMBlockDesc::IsKnownAtCompileTime() && BKNBlockDesc::IsKnownAtCompileTime(),
+                       bool>::type = false>
+struct BlockwiseGemmDlops_km_kn_m0m1n0n1_v2r2_pipeline_2x2
+{
+    using AIndex = MultiIndex<3>;
+    using BIndex = MultiIndex<3>;
+    using CIndex = MultiIndex<4>;
+
+    static constexpr auto I0 = Number<0>{};
+    static constexpr auto I1 = Number<1>{};
+    static constexpr auto I2 = Number<2>{};
+    static constexpr auto I3 = Number<3>{};
+
+    static constexpr index_t K = AKMBlockDesc{}.GetLength(I0);
+    static constexpr index_t M = AKMBlockDesc{}.GetLength(I1);
+    static constexpr index_t N = BKNBlockDesc{}.GetLength(I1);
+
+    static constexpr index_t M100 = M1N1ThreadClusterM100;
+    static constexpr index_t N100 = M1N1ThreadClusterN100;
+
+    static constexpr index_t M101 = M1N1ThreadClusterM101;
+    static constexpr index_t N101 = M1N1ThreadClusterN101;
+
+    static constexpr index_t M11 = M1PerThreadM11;
+    static constexpr index_t N11 = N1PerThreadN11;
+
+    static constexpr index_t M1 = M1N1ThreadClusterM100 * M1N1ThreadClusterM101 * M1PerThreadM11;
+    static constexpr index_t N1 = M1N1ThreadClusterN100 * M1N1ThreadClusterN101 * N1PerThreadN11;
+
+    static constexpr index_t M0 = M / M1;
+    static constexpr index_t N0 = N / N1;
+
+    __host__ __device__ static constexpr auto
+    MakeAKM0M1BlockDescriptor(const AKMBlockDesc& /* a_k_m_block_desc */)
+    {
+        const auto a_k_m0_m1_block_desc = transform_tensor_descriptor(
+            AKMBlockDesc{},
+            make_tuple(make_pass_through_transform(Number<K>{}),
+                       make_unmerge_transform(make_tuple(Number<M0>{}, Number<M1>{}))),
+            make_tuple(Sequence<0>{}, Sequence<1>{}),
+            make_tuple(Sequence<0>{}, Sequence<1, 2>{}));
+
+        return a_k_m0_m1_block_desc;
+    }
+
+    __host__ __device__ static constexpr auto
+    MakeBKN0N1BlockDescriptor(const BKNBlockDesc& /* b_k_n_block_desc */)
+    {
+        const auto b_k_n0_n1_block_desc = transform_tensor_descriptor(
+            BKNBlockDesc{},
+            make_tuple(make_pass_through_transform(Number<K>{}),
+                       make_unmerge_transform(make_tuple(Number<N0>{}, Number<N1>{}))),
+            make_tuple(Sequence<0>{}, Sequence<1>{}),
+            make_tuple(Sequence<0>{}, Sequence<1, 2>{}));
+
+        return b_k_n0_n1_block_desc;
+    }
+
+    __host__ __device__ static constexpr auto MakeCM0M100M101M11N0N100N101N11ToMNBlockAdaptor()
+    {
+        // upper: [M0, M100, M101, M11, N0, N100, N101, N11]
+        // lower: [M, N]
+        constexpr auto c_m0_m100_m101_m11_n0_n100_n101_n11_to_m_n_block_adaptor =
+            make_single_stage_tensor_adaptor(
+                make_tuple(make_unmerge_transform(make_tuple(
+                               Number<M0>{}, Number<M100>{}, Number<M101>{}, Number<M11>{})),
+                           make_unmerge_transform(make_tuple(
+                               Number<N0>{}, Number<N100>{}, Number<N101>{}, Number<N11>{}))),
+                make_tuple(Sequence<0>{}, Sequence<1>{}),
+                make_tuple(Sequence<0, 1, 2, 3>{}, Sequence<4, 5, 6, 7>{}));
+
+        return c_m0_m100_m101_m11_n0_n100_n101_n11_to_m_n_block_adaptor;
+    }
+
+    __host__ __device__ static constexpr auto
+    MakeCM0M100M101M11N0N100N101N11ToM0M1N0N1BlockAdaptor()
+    {
+        // upper: [M0, M100, M101, M11, N0, N100, N101, N11]
+        // lower: [M0, M1, N0, N1]
+        constexpr auto c_m0_m100_m101_m11_n0_n100_n101_n11_to_m0_m1_n0_n1_block_adaptor =
+            make_single_stage_tensor_adaptor(
+                make_tuple(make_pass_through_transform(Number<M0>{}),
+                           make_unmerge_transform(
+                               make_tuple(Number<M100>{}, Number<M101>{}, Number<M11>{})),
+                           make_pass_through_transform(Number<N0>{}),
+                           make_unmerge_transform(
+                               make_tuple(Number<N100>{}, Number<N101>{}, Number<N11>{}))),
+                make_tuple(Sequence<0>{}, Sequence<1>{}, Sequence<2>{}, Sequence<3>{}),
+                make_tuple(Sequence<0>{}, Sequence<1, 2, 3>{}, Sequence<4>{}, Sequence<5, 6, 7>{}));
+
+        return c_m0_m100_m101_m11_n0_n100_n101_n11_to_m0_m1_n0_n1_block_adaptor;
+    }
+
+    __host__ __device__ static constexpr auto GetCM0M1N0N1ThreadTensorLengths()
+    {
+        return Sequence<M0, M11, N0, N11>{};
+    }
+
+    static constexpr auto a_k_m0_m1_block_desc_ = MakeAKM0M1BlockDescriptor(AKMBlockDesc{});
+    static constexpr auto b_k_n0_n1_block_desc_ = MakeBKN0N1BlockDescriptor(BKNBlockDesc{});
+
+    public:
+    __device__ BlockwiseGemmDlops_km_kn_m0m1n0n1_v2r2_pipeline_2x2()
+        : c_thread_origin_data_idx_{CalculateCM0M1N0N1ThreadOriginOnBlock(
+              get_thread_local_1d_id())},
+          a_thread_copy_{
+              make_tuple(0, c_thread_origin_data_idx_[I0], c_thread_origin_data_idx_[I1])},
+          b_thread_copy_{
+              make_tuple(0, c_thread_origin_data_idx_[I2], c_thread_origin_data_idx_[I3])}
+    {
+        static_assert(AKMBlockDesc::IsKnownAtCompileTime() && BKNBlockDesc::IsKnownAtCompileTime(),
+                      "wrong! Desc should be known at compile-time");
+
+        static_assert(BlockSize == M101 * M100 * N101 * N100,
+                      "wrong! blocksize and cluster size not consistent");
+
+        static_assert(M % M1 == 0 && N % N1 == 0, "wrong!");
+
+        static_assert(AKMBlockDesc{}.GetLength(I0) == BKNBlockDesc{}.GetLength(I0),
+                      "wrong! K dimension not consistent");
+
+        // TODO: remove this restriction
+        static_assert(M0 == 2 && N0 == 2, "wrong");
+    }
+
+    __device__ static CIndex CalculateCM0M1N0N1ThreadOriginOnBlock(index_t thread_id)
+    {
+        // lower: [M0, M1, N0, N1]
+        // upper: [M0, M100, M101, M11, N0, N100, N101, N11]
+        constexpr auto adaptor0 = MakeCM0M100M101M11N0N100N101N11ToM0M1N0N1BlockAdaptor();
+
+        // lower: [M0, M100, M101, M11, N0, N100, N101, N11]
+        // upper: [Tid, M0, M11, N0, N11]
+        constexpr auto adaptor1 = make_single_stage_tensor_adaptor(
+            make_tuple(make_merge_transform(make_tuple(M100, N100, M101, N101)),
+                       make_pass_through_transform(M0),
+                       make_pass_through_transform(M11),
+                       make_pass_through_transform(N0),
+                       make_pass_through_transform(N11)),
+            make_tuple(
+                Sequence<1, 5, 2, 6>{}, Sequence<0>{}, Sequence<3>{}, Sequence<4>{}, Sequence<7>{}),
+            make_tuple(Sequence<0>{}, Sequence<1>{}, Sequence<2>{}, Sequence<3>{}, Sequence<4>{}));
+
+        constexpr auto adaptor = chain_tensor_adaptors(adaptor0, adaptor1);
+
+        return adaptor.CalculateBottomIndex(make_multi_index(thread_id, 0, 0, 0, 0));
+    }
+
+    __host__ __device__ static constexpr index_t GetABlockAlignment() { return M1PerThreadM11; }
+
+    __host__ __device__ static constexpr auto GetBBlockAlignment() { return N1PerThreadN11; }
+
+    template <typename CM0M1N0N1ThreadDesc,
+              typename ABlockBuffer,
+              typename BBlockBuffer,
+              typename CThreadBuffer>
+    __device__ void Run(const CM0M1N0N1ThreadDesc& /* c_m0_m1_n0_n1_thread_desc */,
+                        const ABlockBuffer& a_block_buf,
+                        const BBlockBuffer& b_block_buf,
+                        CThreadBuffer& c_thread_buf) const
+    {
+        static_assert(CM0M1N0N1ThreadDesc::IsKnownAtCompileTime(),
+                      "wrong! Desc should be known at compile-time");
+
+        // TODO: remove this restriction
+        static_assert(M0 == 2 && N0 == 2 && CM0M1N0N1ThreadDesc{}.GetLength(I0) == M0 &&
+                          CM0M1N0N1ThreadDesc{}.GetLength(I2) == N0,
+                      "wrong");
+
+        auto a_thread_buf = make_static_buffer<AddressSpaceEnum::Vgpr, FloatA>(
+            a_k_m0_m1_thread_desc_.GetElementSpaceSize());
+        auto b_thread_buf = make_static_buffer<AddressSpaceEnum::Vgpr, FloatB>(
+            b_k_n0_n1_thread_desc_.GetElementSpaceSize());
+
+        constexpr auto threadwise_gemm =
+            ThreadwiseGemmDlops_km0m1_kn0n1_m0m1n0n1<FloatA,
+                                                     FloatB,
+                                                     FloatC,
+                                                     decltype(a_k_m0_m1_thread_desc_),
+                                                     decltype(b_k_n0_n1_thread_desc_),
+                                                     CM0M1N0N1ThreadDesc,
+                                                     Sequence<KPerThread>,
+                                                     Sequence<1, M1PerThreadM11>,
+                                                     Sequence<1, N1PerThreadN11>>{};
+
+        // read A_sub_0
+        a_thread_copy_.Run(a_k_m0_m1_block_desc_,
+                           make_tuple(I0, I0, I0),
+                           a_block_buf,
+                           a_k_m0_m1_thread_desc_,
+                           make_tuple(I0, I0, I0),
+                           a_thread_buf);
+
+        // read B_sub_0
+        b_thread_copy_.Run(b_k_n0_n1_block_desc_,
+                           make_tuple(I0, I0, I0),
+                           b_block_buf,
+                           b_k_n0_n1_thread_desc_,
+                           make_tuple(I0, I0, I0),
+                           b_thread_buf);
+
+        // read B_sub_1
+        b_thread_copy_.Run(b_k_n0_n1_block_desc_,
+                           make_tuple(I0, I1, I0),
+                           b_block_buf,
+                           b_k_n0_n1_thread_desc_,
+                           make_tuple(I0, I1, I0),
+                           b_thread_buf);
+
+        // read A_sub_1
+        a_thread_copy_.Run(a_k_m0_m1_block_desc_,
+                           make_tuple(I0, I1, I0),
+                           a_block_buf,
+                           a_k_m0_m1_thread_desc_,
+                           make_tuple(I0, I1, I0),
+                           a_thread_buf);
+
+        // C_sub_00 += transpose(A_sub_0) * B_sub_0
+        threadwise_gemm.Run(a_thread_buf,
+                            make_tuple(I0, I0, I0),
+                            b_thread_buf,
+                            make_tuple(I0, I0, I0),
+                            c_thread_buf,
+                            make_tuple(I0, I0, I0, I0));
+
+        // C_sub_01 += transpose(A_sub_0) * B_sub_1
+        threadwise_gemm.Run(a_thread_buf,
+                            make_tuple(I0, I0, I0),
+                            b_thread_buf,
+                            make_tuple(I0, I1, I0),
+                            c_thread_buf,
+                            make_tuple(I0, I0, I1, I0));
+
+        // loop over rest of k
+        static_for<KPerThread, K, KPerThread>{}([&](auto k) {
+            // read A_sub_0
+            a_thread_copy_.Run(a_k_m0_m1_block_desc_,
+                               make_tuple(k, I0, I0),
+                               a_block_buf,
+                               a_k_m0_m1_thread_desc_,
+                               make_tuple(I0, I0, I0),
+                               a_thread_buf);
+
+            // C_sub_10 += transpose(A_sub_1) * B_sub_0
+            threadwise_gemm.Run(a_thread_buf,
+                                make_tuple(I0, I1, I0),
+                                b_thread_buf,
+                                make_tuple(I0, I0, I0),
+                                c_thread_buf,
+                                make_tuple(I1, I0, I0, I0));
+
+            // read B_sub_0
+            b_thread_copy_.Run(b_k_n0_n1_block_desc_,
+                               make_tuple(k, I0, I0),
+                               b_block_buf,
+                               b_k_n0_n1_thread_desc_,
+                               make_tuple(I0, I0, I0),
+                               b_thread_buf);
+
+            // C_sub_11 += transpose(A_sub_1) * B_sub_1
+            threadwise_gemm.Run(a_thread_buf,
+                                make_tuple(I0, I1, I0),
+                                b_thread_buf,
+                                make_tuple(I0, I1, I0),
+                                c_thread_buf,
+                                make_tuple(I1, I0, I1, I0));
+
+            // read B_sub_1
+            b_thread_copy_.Run(b_k_n0_n1_block_desc_,
+                               make_tuple(k, I1, I0),
+                               b_block_buf,
+                               b_k_n0_n1_thread_desc_,
+                               make_tuple(I0, I1, I0),
+                               b_thread_buf);
+
+            // read A_sub_1
+            a_thread_copy_.Run(a_k_m0_m1_block_desc_,
+                               make_tuple(k, I1, I0),
+                               a_block_buf,
+                               a_k_m0_m1_thread_desc_,
+                               make_tuple(I0, I1, I0),
+                               a_thread_buf);
+
+            // C_sub_00 += transpose(A_sub_0) * B_sub_0
+            threadwise_gemm.Run(a_thread_buf,
+                                make_tuple(I0, I0, I0),
+                                b_thread_buf,
+                                make_tuple(I0, I0, I0),
+                                c_thread_buf,
+                                make_tuple(I0, I0, I0, I0));
+
+            // C_sub_01 += transpose(A_sub_0) * B_sub_1
+            threadwise_gemm.Run(a_thread_buf,
+                                make_tuple(I0, I0, I0),
+                                b_thread_buf,
+                                make_tuple(I0, I1, I0),
+                                c_thread_buf,
+                                make_tuple(I0, I0, I1, I0));
+        });
+
+        // C_sub_10 += transpose(A_sub_1) * B_sub_0
+        threadwise_gemm.Run(a_thread_buf,
+                            make_tuple(I0, I1, I0),
+                            b_thread_buf,
+                            make_tuple(I0, I0, I0),
+                            c_thread_buf,
+                            make_tuple(I1, I0, I0, I0));
+
+        // C_sub_11 += transpose(A_sub_1) * B_sub_1
+        threadwise_gemm.Run(a_thread_buf,
+                            make_tuple(I0, I1, I0),
+                            b_thread_buf,
+                            make_tuple(I0, I1, I0),
+                            c_thread_buf,
+                            make_tuple(I1, I0, I1, I0));
+    }
+
+    private:
+    // A[K, M0, M1]
+    static constexpr auto a_k_m0_m1_thread_desc_ = make_naive_tensor_descriptor_packed(
+        make_tuple(Number<KPerThread>{}, Number<M0>{}, Number<M1PerThreadM11>{}));
+
+    // B[K, N0, N1]
+    static constexpr auto b_k_n0_n1_thread_desc_ = make_naive_tensor_descriptor_packed(
+        make_tuple(Number<KPerThread>{}, Number<N0>{}, Number<N1PerThreadN11>{}));
+
+    using AThreadCopy = ThreadwiseTensorSliceTransfer_v4<FloatA,
+                                                         FloatA,
+                                                         decltype(a_k_m0_m1_block_desc_),
+                                                         decltype(a_k_m0_m1_thread_desc_),
+                                                         Sequence<KPerThread, 1, M1PerThreadM11>,
+                                                         Sequence<0, 1, 2>,
+                                                         2,
+                                                         AThreadCopyScalarPerVector_M11,
+                                                         1>;
+
+    using BThreadCopy = ThreadwiseTensorSliceTransfer_v4<FloatB,
+                                                         FloatB,
+                                                         decltype(b_k_n0_n1_block_desc_),
+                                                         decltype(b_k_n0_n1_thread_desc_),
+                                                         Sequence<KPerThread, 1, N1PerThreadN11>,
+                                                         Sequence<0, 1, 2>,
+                                                         2,
+                                                         BThreadCopyScalarPerVector_N11,
+                                                         1>;
+
+    CIndex c_thread_origin_data_idx_;
+
+    AThreadCopy a_thread_copy_;
+    BThreadCopy b_thread_copy_;
+};
+
+} // namespace ck
+#endif

include/ck/tensor_operation/gpu/block/blockwise_gemm_dlops_v3.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#ifndef CK_BLOCKWISE_GEMM_DLOPS_V3_HPP
+#define CK_BLOCKWISE_GEMM_DLOPS_V3_HPP
+
+#include "common_header.hpp"
+#include "threadwise_gemm_dlops_v3.hpp"
+
+namespace ck {
+
+template <index_t BlockSize,
+          typename FloatA,
+          typename FloatB,
+          typename FloatC,
+          typename ABlockDesc_E1_K1_E2,
+          typename BBlockDesc_E1_N_Ho_Wo_E2,
+          typename CThreadDesc_K_N_Ho_Wo,
+          index_t EPerThreadLoop,
+          index_t KPerThreadLoop>
+struct BlockwiseGemmDlops_km_kn_m0m1n0n1_v3
+{
+    static constexpr auto I0 = Number<0>{};
+    static constexpr auto I1 = Number<1>{};
+    static constexpr auto I2 = Number<2>{};
+    static constexpr auto I3 = Number<3>{};
+    static constexpr auto I4 = Number<4>{};
+
+    using AIndex = MultiIndex<3>;
+    using BIndex = MultiIndex<3>;
+    using CIndex = MultiIndex<4>;
+
+    static constexpr auto E1        = ABlockDesc_E1_K1_E2{}.GetLength(I0);
+    static constexpr auto KPerBlock = ABlockDesc_E1_K1_E2{}.GetLength(I1);
+    static constexpr auto E2        = ABlockDesc_E1_K1_E2{}.GetLength(I2);
+
+    static constexpr auto HoPerBlock = BBlockDesc_E1_N_Ho_Wo_E2{}.GetLength(I2);
+    static constexpr auto WoPerBlock = BBlockDesc_E1_N_Ho_Wo_E2{}.GetLength(I3);
+
+    static constexpr auto KPerThread  = CThreadDesc_K_N_Ho_Wo{}.GetLength(I0);
+    static constexpr auto HoPerThread = CThreadDesc_K_N_Ho_Wo{}.GetLength(I2);
+    static constexpr auto WoPerThread = CThreadDesc_K_N_Ho_Wo{}.GetLength(I3);
+
+    static constexpr auto a_thread_mtx_ = make_naive_tensor_descriptor_packed(
+        make_tuple(Number<EPerThreadLoop>{}, Number<KPerThreadLoop>{}, Number<E2>{}));
+
+    static constexpr auto b_thread_mtx_ =
+        make_naive_tensor_descriptor_packed(make_tuple(Number<EPerThreadLoop>{},
+                                                       Number<1>{},
+                                                       Number<HoPerThread>{},
+                                                       Number<WoPerThread>{},
+                                                       Number<E2>{}));
+
+    static constexpr auto c_thread_mtx_ = make_naive_tensor_descriptor_packed(make_tuple(
+        Number<KPerThreadLoop>{}, Number<1>{}, Number<HoPerThread>{}, Number<WoPerThread>{}));
+
+    __device__ BlockwiseGemmDlops_km_kn_m0m1n0n1_v3()
+        : c_thread_origin_data_idx_{GetBeginOfCThreadDesc_K_N_Ho_Wo(get_thread_local_1d_id())},
+          a_thread_copy_{make_tuple(0, c_thread_origin_data_idx_[I0] * KPerThread, 0)}
+    {
+        static_assert(ABlockDesc_E1_K1_E2::IsKnownAtCompileTime() &&
+                          BBlockDesc_E1_N_Ho_Wo_E2::IsKnownAtCompileTime() &&
+                          CThreadDesc_K_N_Ho_Wo::IsKnownAtCompileTime(),
+                      "wrong! Desc should be known at compile-time");
+
+        static_assert(
+            ABlockDesc_E1_K1_E2{}.GetLength(I0) == BBlockDesc_E1_N_Ho_Wo_E2{}.GetLength(I0) &&
+                ABlockDesc_E1_K1_E2{}.GetLength(I2) == BBlockDesc_E1_N_Ho_Wo_E2{}.GetLength(I4),
+            "wrong! E dimension not consistent\n");
+
+        static_assert(E1 % EPerThreadLoop == 0, "");
+        static_assert(KPerThread % KPerThreadLoop == 0, "");
+
+        static_assert(KPerBlock % KPerThread == 0 && HoPerBlock % HoPerThread == 0 &&
+                          WoPerBlock % WoPerThread == 0,
+                      "wrong! Cannot evenly divide work among\n");
+
+        constexpr auto KThreadCluster = KPerBlock / KPerThread;
+        constexpr auto HThreadCluster = HoPerBlock / HoPerThread;
+        constexpr auto WThreadCluster = WoPerBlock / WoPerThread;
+
+        static_assert(BlockSize == KThreadCluster * HThreadCluster * WThreadCluster,
+                      "wrong! wrong blocksize\n");
+    }
+
+    __device__ static constexpr auto GetCThreadDesc_K_N_Ho_WoLengths()
+    {
+        return Sequence<KPerThread, I1, HoPerThread, WoPerThread>{};
+    }
+
+    __device__ static CIndex GetBeginOfCThreadDesc_K_N_Ho_Wo(index_t thread_id)
+    {
+        constexpr auto K0 = KPerBlock / KPerThread;
+        constexpr auto N0 = I1;
+        constexpr auto H0 = HoPerBlock / HoPerThread;
+        constexpr auto W0 = WoPerBlock / WoPerThread;
+
+        constexpr auto c_threadid_to_k_n_h_w_thread_cluster_adaptor =
+            make_single_stage_tensor_adaptor(
+                make_tuple(make_merge_transform(make_tuple(K0, N0, H0, W0))),
+                make_tuple(Sequence<0, 1, 2, 3>{}),
+                make_tuple(Sequence<0>{}));
+
+        const auto c_k_n_h_w_thread_cluster_idx =
+            c_threadid_to_k_n_h_w_thread_cluster_adaptor.CalculateBottomIndex(
+                make_multi_index(thread_id));
+
+        return c_k_n_h_w_thread_cluster_idx;
+    }
+
+    template <typename ABlockBuffer, typename BThreadBuffer, typename CThreadBuffer>
+    __device__ void Run(const ABlockBuffer& a_block_buf,
+                        const BThreadBuffer& b_thread_buf,
+                        CThreadBuffer& c_thread_buf) const
+    {
+        static_assert(
+            is_same<remove_cvref_t<typename ABlockBuffer::type>, remove_cvref_t<FloatA>>::value &&
+            is_same<remove_cvref_t<typename BThreadBuffer::type>, remove_cvref_t<FloatB>>::value &&
+            is_same<remove_cvref_t<typename CThreadBuffer::type>, remove_cvref_t<FloatC>>::value &&
+            "wrong! inconsistent type");
+
+        constexpr auto a_block_mtx = ABlockDesc_E1_K1_E2{};
+
+        // thread A buffer for GEMM
+        StaticBuffer<AddressSpaceEnum::Vgpr, FloatA, a_thread_mtx_.GetElementSpaceSize(), true>
+            a_thread_buf;
+
+        constexpr auto threadwise_gemm = ThreadwiseGemmDlops_km_kn_mn_v3<FloatA,
+                                                                         FloatB,
+                                                                         FloatC,
+                                                                         decltype(a_thread_mtx_),
+                                                                         decltype(b_thread_mtx_),
+                                                                         decltype(c_thread_mtx_)>{};
+
+        static_for<0, E1, EPerThreadLoop>{}([&](auto e_begin) {
+            static_for<0, KPerThread, KPerThreadLoop>{}([&](auto k_begin) {
+                a_thread_copy_.Run(a_block_mtx,
+                                   make_tuple(e_begin, k_begin, I0),
+                                   a_block_buf,
+                                   a_thread_mtx_,
+                                   make_tuple(I0, I0, I0),
+                                   a_thread_buf);
+
+                threadwise_gemm.Run(a_thread_buf,
+                                    make_tuple(I0, I0, I0),
+                                    b_thread_buf,
+                                    make_tuple(e_begin, I0, I0, I0, I0),
+                                    c_thread_buf,
+                                    make_tuple(k_begin, I0, I0, I0));
+            });
+        });
+    }
+
+    template <typename ABlockSliceMoveStepIdx>
+    __device__ void MoveABlockSliceWindow(const ABlockSliceMoveStepIdx& a_block_slice_move_step_idx)
+    {
+        a_thread_copy_.MoveSrcSliceWindow(ABlockDesc_E1_K1_E2{}, a_block_slice_move_step_idx);
+    }
+
+    private:
+    using AThreadCopy =
+        ThreadwiseTensorSliceTransfer_v4<FloatA,
+                                         FloatA,
+                                         ABlockDesc_E1_K1_E2,
+                                         decltype(a_thread_mtx_),
+                                         Sequence<EPerThreadLoop, KPerThreadLoop, E2>,
+                                         Sequence<0, 1, 2>,
+                                         2,
+                                         E2,
+                                         E2>;
+
+    CIndex c_thread_origin_data_idx_;
+
+    AThreadCopy a_thread_copy_;
+};
+
+} // namespace ck
+#endif

include/ck/tensor_operation/gpu/block/blockwise_gemm_xdlops.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck/utility/common_header.hpp"
+#include "ck/tensor_operation/gpu/thread/threadwise_tensor_slice_transfer.hpp"
+#include "ck/tensor_operation/gpu/warp/xdlops_gemm.hpp"
+#include "ck/tensor_description/tensor_adaptor.hpp"
+
+namespace ck {
+
+enum struct LoopScheduler
+{
+    Default,
+    Interwave,
+};
+
+constexpr LoopScheduler make_default_loop_scheduler()
+{
+#if CK_EXPERIMENTAL_DEFAULT_TO_INTER_WAVE_SCHEDULING
+    return LoopScheduler::Interwave;
+#else
+    return LoopScheduler::Default;
+#endif // if CK_EXPERIMENTAL_DEFAULT_TO_INTER_WAVE_SCHEDULING
+}
+
+template <index_t MNXdlPerWave, index_t MNWaves, index_t MNPerXdl, typename TileDesc_K0_MN_K1>
+__host__ __device__ static constexpr auto
+MakeGemmMmaTileDescriptor_MN0_MN1_MN2_K(const TileDesc_K0_MN_K1&)
+{
+    constexpr index_t K0 = TileDesc_K0_MN_K1{}.GetLength(Number<0>{});
+    constexpr index_t K1 = TileDesc_K0_MN_K1{}.GetLength(Number<2>{});
+
+    return transform_tensor_descriptor(
+        TileDesc_K0_MN_K1{},
+        make_tuple(make_merge_transform_v3_division_mod(make_tuple(Number<K0>{}, Number<K1>{})),
+                   make_unmerge_transform(
+                       make_tuple(Number<MNXdlPerWave>{}, Number<MNWaves>{}, Number<MNPerXdl>{}))),
+        make_tuple(Sequence<0, 2>{}, Sequence<1>{}),
+        make_tuple(Sequence<3>{}, Sequence<0, 1, 2>{}));
+}
+
+template <index_t BlockSize,
+          typename FloatAB,
+          typename FloatAcc,
+          typename AK0MK1BlockDesc,
+          typename BK0NK1BlockDesc,
+          index_t MPerXDL,
+          index_t NPerXDL,
+          index_t MRepeat,
+          index_t NRepeat,
+          index_t KPack>
+struct BlockwiseGemmXdlops_k0mk1_k0nk1_m0n0m1n1m2m3m4n2_v1
+{
+    static constexpr auto I0 = Number<0>{};
+    static constexpr auto I1 = Number<1>{};
+    static constexpr auto I2 = Number<2>{};
+    static constexpr auto I3 = Number<3>{};
+
+    using ThisThreadBlock = ThisThreadBlock<BlockSize>;
+
+    static constexpr index_t WaveSize = get_warp_size();
+
+    static constexpr index_t MPerBlock = AK0MK1BlockDesc{}.GetLength(I1);
+    static constexpr index_t NPerBlock = BK0NK1BlockDesc{}.GetLength(I1);
+    static constexpr index_t KPerBlock =
+        BK0NK1BlockDesc{}.GetLength(I0) * BK0NK1BlockDesc{}.GetLength(I2);
+
+    static constexpr index_t A_K0 = AK0MK1BlockDesc{}.GetLength(I0);
+    static constexpr index_t B_K0 = BK0NK1BlockDesc{}.GetLength(I0);
+    static constexpr index_t A_K1 = AK0MK1BlockDesc{}.GetLength(I2);
+    static constexpr index_t B_K1 = BK0NK1BlockDesc{}.GetLength(I2);
+
+    static constexpr auto xdlops_gemm = XdlopsGemm<FloatAB, MPerXDL, NPerXDL, KPack>{};
+
+    static constexpr index_t KPerThread = KPerBlock / xdlops_gemm.K0PerXdlops;
+
+    static constexpr index_t MWaves = MPerBlock / (MRepeat * MPerXDL);
+    static constexpr index_t NWaves = NPerBlock / (NRepeat * NPerXDL);
+
+    StaticBufferTupleOfVector<AddressSpaceEnum::Vgpr,
+                              FloatAcc,
+                              MRepeat * NRepeat,
+                              xdlops_gemm.GetRegSizePerXdlops(),
+                              true>
+        c_thread_buf_;
+
+    __host__ __device__ constexpr auto& GetCThreadBuffer() { return c_thread_buf_; }
+
+    __device__ static auto GetWaveIdx()
+    {
+        const index_t thread_id = ThisThreadBlock::GetThreadId();
+
+        constexpr auto threadid_to_wave_idx_adaptor = make_single_stage_tensor_adaptor(
+            make_tuple(make_merge_transform(make_tuple(MWaves, NWaves, WaveSize))),
+            make_tuple(Sequence<0, 1, 2>{}),
+            make_tuple(Sequence<0>{}));
+
+        return threadid_to_wave_idx_adaptor.CalculateBottomIndex(make_multi_index(thread_id));
+    }
+
+    __device__ static auto CalculateAThreadOriginDataIndex()
+    {
+        const auto wave_idx = GetWaveIdx();
+
+        const auto waveId_m = wave_idx[I0];
+
+        const auto xdlops_a_idx = xdlops_gemm.CalculateAThreadOriginDataIndex();
+
+        return make_tuple(0, waveId_m, xdlops_a_idx[I1], KPerThread * xdlops_a_idx[I0]);
+    }
+
+    __device__ static auto CalculateBThreadOriginDataIndex()
+    {
+        const auto wave_idx = GetWaveIdx();
+
+        const auto waveId_n = wave_idx[I1];
+
+        const auto xdlops_b_idx = xdlops_gemm.CalculateBThreadOriginDataIndex();
+
+        return make_tuple(0, waveId_n, xdlops_b_idx[I1], KPerThread * xdlops_b_idx[I0]);
+    }
+
+    template <index_t m0, index_t n0, index_t xdlops_i, index_t blk_i>
+    __device__ static auto
+        CalculateCThreadOriginDataIndex(Number<m0>, Number<n0>, Number<xdlops_i>, Number<blk_i>)
+    {
+        const auto wave_idx = GetWaveIdx();
+
+        const auto waveId_m = wave_idx[I0];
+        const auto waveId_n = wave_idx[I1];
+
+        const auto blk_idx = xdlops_gemm.GetBeginOfThreadBlk(xdlops_i, blk_i);
+
+        constexpr auto mrepeat_mwave_mperxdl_to_m_adaptor = make_single_stage_tensor_adaptor(
+            make_tuple(make_unmerge_transform(make_tuple(MRepeat, MWaves, MPerXDL))),
+            make_tuple(Sequence<0>{}),
+            make_tuple(Sequence<0, 1, 2>{}));
+
+        constexpr auto nrepeat_nwave_nperxdl_to_n_adaptor = make_single_stage_tensor_adaptor(
+            make_tuple(make_unmerge_transform(make_tuple(NRepeat, NWaves, NPerXDL))),
+            make_tuple(Sequence<0>{}),
+            make_tuple(Sequence<0, 1, 2>{}));
+
+        const index_t c_thread_m = mrepeat_mwave_mperxdl_to_m_adaptor.CalculateBottomIndex(
+            make_tuple(m0, waveId_m, blk_idx[I0]))[I0];
+        const index_t c_thread_n = nrepeat_nwave_nperxdl_to_n_adaptor.CalculateBottomIndex(
+            make_tuple(n0, waveId_n, blk_idx[I1]))[I0];
+
+        return make_tuple(c_thread_m, c_thread_n);
+    }
+
+    template <index_t m0, index_t n0, index_t xdlops_i, index_t blk_i>
+    __device__ static auto
+        CalculateCThreadOriginDataIndex8D(Number<m0>, Number<n0>, Number<xdlops_i>, Number<blk_i>)
+    {
+        const auto wave_idx = GetWaveIdx();
+
+        const auto waveId_m = wave_idx[I0];
+        const auto waveId_n = wave_idx[I1];
+
+        const auto blk_idx = xdlops_gemm.GetBeginOfThreadBlk4D(xdlops_i, blk_i);
+
+        return make_tuple(Number<m0>{},
+                          Number<n0>{},
+                          waveId_m,
+                          waveId_n,
+                          blk_idx[I0],
+                          blk_idx[I1],
+                          blk_idx[I2],
+                          blk_idx[I3]);
+    }
+
+    __host__ __device__ BlockwiseGemmXdlops_k0mk1_k0nk1_m0n0m1n1m2m3m4n2_v1()
+    {
+        static_assert(AK0MK1BlockDesc::IsKnownAtCompileTime() &&
+                          BK0NK1BlockDesc::IsKnownAtCompileTime(),
+                      "wrong! Desc should be known at compile-time");
+
+        static_assert(ThisThreadBlock::GetNumOfThread() == MWaves * NWaves * WaveSize,
+                      "ThisThreadBlock::GetNumOfThread() != MWaves * NWaves * WaveSize\n");
+
+        static_assert(MPerBlock % (MPerXDL * MRepeat) == 0 && NPerBlock % (NPerXDL * NRepeat) == 0,
+                      "wrong!");
+    }
+
+    __host__ __device__ static constexpr auto GetCThreadDescriptor_M0_N0_M1_N1_M2_M3_M4_N2()
+    {
+        constexpr auto c_m0_m1_m2_n_tblk_lens = xdlops_gemm.GetCM0M1M2NThreadBlkLengths();
+
+        constexpr auto M0 = c_m0_m1_m2_n_tblk_lens[I0];
+        constexpr auto M1 = c_m0_m1_m2_n_tblk_lens[I1];
+        constexpr auto M2 = c_m0_m1_m2_n_tblk_lens[I2];
+        constexpr auto N  = c_m0_m1_m2_n_tblk_lens[I3];
+
+        return make_naive_tensor_descriptor_packed(
+            make_tuple(Number<MRepeat>{}, Number<NRepeat>{}, I1, I1, M0, M1, M2, N));
+    }
+
+    __host__ __device__ static constexpr auto GetCThreadDescriptor_G_M0_N0_M1_N1_M2_M3_M4_N2()
+    {
+        constexpr auto c_m0_m1_m2_n_tblk_lens = xdlops_gemm.GetCM0M1M2NThreadBlkLengths();
+
+        constexpr auto M0 = c_m0_m1_m2_n_tblk_lens[I0];
+        constexpr auto M1 = c_m0_m1_m2_n_tblk_lens[I1];
+        constexpr auto M2 = c_m0_m1_m2_n_tblk_lens[I2];
+        constexpr auto N  = c_m0_m1_m2_n_tblk_lens[I3];
+
+        return make_naive_tensor_descriptor_packed(
+            make_tuple(I1, Number<MRepeat>{}, Number<NRepeat>{}, I1, I1, M0, M1, M2, N));
+    }
+
+    __host__ __device__ static constexpr auto GetCBlockDescriptor_M0_N0_M1_N1_M2_M3_M4_N2()
+    {
+        constexpr auto c_block_desc_m0_n0_m1_n1_m2_n2 =
+            make_naive_tensor_descriptor_packed(make_tuple(Number<MRepeat>{},
+                                                           Number<NRepeat>{},
+                                                           Number<MWaves>{},
+                                                           Number<NWaves>{},
+                                                           Number<MPerXDL>{},
+                                                           Number<NPerXDL>{}));
+
+        return xdlops_gemm.MakeCDescriptor_M0_N0_M1_N1_M2_M3_M4_N2(c_block_desc_m0_n0_m1_n1_m2_n2);
+    }
+
+    __host__ __device__ static constexpr auto GetCBlockDescriptor_G_M0_N0_M1_N1_M2_M3_M4_N2()
+    {
+        constexpr auto c_block_desc_g_m0_n0_m1_n1_m2_n2 =
+            make_naive_tensor_descriptor_packed(make_tuple(I1,
+                                                           Number<MRepeat>{},
+                                                           Number<NRepeat>{},
+                                                           Number<MWaves>{},
+                                                           Number<NWaves>{},
+                                                           Number<MPerXDL>{},
+                                                           Number<NPerXDL>{}));
+
+        return xdlops_gemm.MakeCDescriptor_G_M0_N0_M1_N1_M2_M3_M4_N2(
+            c_block_desc_g_m0_n0_m1_n1_m2_n2);
+    }
+
+    template <typename CGridDesc_M_N>
+    __host__ __device__ static constexpr auto
+    MakeCGridDescriptor_M0_N0_M1_N1_M2_M3_M4_N2(const CGridDesc_M_N& c_grid_desc_m_n)
+    {
+        const auto M = c_grid_desc_m_n.GetLength(I0);
+        const auto N = c_grid_desc_m_n.GetLength(I1);
+
+        const auto c_grid_desc_m0_n0_m1_n1_m2_n2 = transform_tensor_descriptor(
+            c_grid_desc_m_n,
+            make_tuple(make_unmerge_transform(make_tuple(M / (MWaves * MPerXDL), MWaves, MPerXDL)),
+                       make_unmerge_transform(make_tuple(N / (NWaves * NPerXDL), NWaves, NPerXDL))),
+            make_tuple(Sequence<0>{}, Sequence<1>{}),
+            make_tuple(Sequence<0, 2, 4>{}, Sequence<1, 3, 5>{}));
+
+        return xdlops_gemm.MakeCDescriptor_M0_N0_M1_N1_M2_M3_M4_N2(c_grid_desc_m0_n0_m1_n1_m2_n2);
+    }
+
+    template <typename CGridDesc_G_M_N>
+    __host__ __device__ static constexpr auto
+    MakeCGridDescriptor_G_M0_N0_M1_N1_M2_M3_M4_N2(const CGridDesc_G_M_N& c_grid_desc_g_m_n)
+    {
+        const auto G = c_grid_desc_g_m_n.GetLength(I0);
+        const auto M = c_grid_desc_g_m_n.GetLength(I1);
+        const auto N = c_grid_desc_g_m_n.GetLength(I2);
+
+        const auto c_grid_desc_g_m0_n0_m1_n1_m2_n2 = transform_tensor_descriptor(
+            c_grid_desc_g_m_n,
+            make_tuple(make_pass_through_transform(G),
+                       make_unmerge_transform(make_tuple(M / (MWaves * MPerXDL), MWaves, MPerXDL)),
+                       make_unmerge_transform(make_tuple(N / (NWaves * NPerXDL), NWaves, NPerXDL))),
+            make_tuple(Sequence<0>{}, Sequence<1>{}, Sequence<2>{}),
+            make_tuple(Sequence<0>{}, Sequence<1, 3, 5>{}, Sequence<2, 4, 6>{}));
+
+        return xdlops_gemm.MakeCDescriptor_G_M0_N0_M1_N1_M2_M3_M4_N2(
+            c_grid_desc_g_m0_n0_m1_n1_m2_n2);
+    }
+
+    __host__ __device__ static constexpr auto MakeABlockDescriptor_M0_M1_M2_K()
+    {
+        return transform_tensor_descriptor(
+            AK0MK1BlockDesc{},
+            make_tuple(
+                make_merge_transform_v3_division_mod(make_tuple(Number<A_K0>{}, Number<A_K1>{})),
+                make_unmerge_transform(
+                    make_tuple(Number<MRepeat>{}, Number<MWaves>{}, Number<MPerXDL>{}))),
+            make_tuple(Sequence<0, 2>{}, Sequence<1>{}),
+            make_tuple(Sequence<3>{}, Sequence<0, 1, 2>{}));
+    }
+
+    __host__ __device__ static constexpr auto MakeBBlockDescriptor_N0_N1_N2_K()
+    {
+        return transform_tensor_descriptor(
+            BK0NK1BlockDesc{},
+            make_tuple(
+                make_merge_transform_v3_division_mod(make_tuple(Number<B_K0>{}, Number<B_K1>{})),
+                make_unmerge_transform(
+                    make_tuple(Number<NRepeat>{}, Number<NWaves>{}, Number<NPerXDL>{}))),
+            make_tuple(Sequence<0, 2>{}, Sequence<1>{}),
+            make_tuple(Sequence<3>{}, Sequence<0, 1, 2>{}));
+    }
+
+    static constexpr auto a_block_desc_m0_m1_m2_k = MakeABlockDescriptor_M0_M1_M2_K();
+    static constexpr auto b_block_desc_n0_n1_n2_k = MakeBBlockDescriptor_N0_N1_N2_K();
+
+    template <typename ABlockBuffer, typename BBlockBuffer, typename CThreadBuffer>
+    __device__ void Run(const ABlockBuffer& a_block_buf,
+                        const BBlockBuffer& b_block_buf,
+                        CThreadBuffer& c_thread_buf) const
+    {
+        auto a_thread_buf = make_static_buffer<AddressSpaceEnum::Vgpr, FloatAB>(
+            a_thread_desc_.GetElementSpaceSize());
+        auto b_thread_buf = make_static_buffer<AddressSpaceEnum::Vgpr, FloatAB>(
+            b_thread_desc_.GetElementSpaceSize());
+
+        static_for<0, MRepeat, 1>{}([&](auto m0) {
+            // read A
+            a_thread_copy_.Run(a_block_desc_m0_m1_m2_k,
+                               make_tuple(m0, I0, I0, I0),
+                               a_block_buf,
+                               a_thread_desc_,
+                               make_tuple(I0, I0, I0, I0),
+                               a_thread_buf);
+
+            static_for<0, NRepeat, 1>{}([&](auto n0) {
+                // read B
+                b_thread_copy_.Run(b_block_desc_n0_n1_n2_k,
+                                   make_tuple(n0, I0, I0, I0),
+                                   b_block_buf,
+                                   b_thread_desc_,
+                                   make_tuple(I0, I0, I0, I0),
+                                   b_thread_buf);
+
+                static_for<0, KPerThread, KPack>{}([&](auto k) {
+                    vector_type<FloatAB, KPack> a_thread_vec;
+                    vector_type<FloatAB, KPack> b_thread_vec;
+
+                    static_for<0, KPack, 1>{}([&](auto i) {
+                        a_thread_vec.template AsType<FloatAB>()(i) = a_thread_buf
+                            [Number<a_thread_desc_.CalculateOffset(make_tuple(0, 0, 0, k + i))>{}];
+                        b_thread_vec.template AsType<FloatAB>()(i) = b_thread_buf
+                            [Number<b_thread_desc_.CalculateOffset(make_tuple(0, 0, 0, k + i))>{}];
+                    });
+
+                    using mfma_input_type =
+                        typename vector_type<FloatAB, xdlops_gemm.K1PerXdlops>::type;
+
+                    constexpr index_t c_offset =
+                        c_thread_desc_.CalculateOffset(make_tuple(m0, n0, 0));
+
+                    xdlops_gemm.template Run(
+                        a_thread_vec.template AsType<mfma_input_type>(),
+                        b_thread_vec.template AsType<mfma_input_type>(),
+                        c_thread_buf.GetVectorTypeReference(Number<c_offset>{}));
+                });
+            });
+        });
+    }
+
+    protected:
+    // A[M0, M1, M2, KPerThread]
+    static constexpr auto a_thread_desc_ =
+        make_naive_tensor_descriptor_packed(make_tuple(I1, I1, I1, Number<KPerThread>{}));
+
+    // B[N0, N1, N2, KPerThread]
+    static constexpr auto b_thread_desc_ =
+        make_naive_tensor_descriptor_packed(make_tuple(I1, I1, I1, Number<KPerThread>{}));
+
+    // C[M, N, NumRegXdlops]
+    static constexpr auto c_thread_desc_ = make_naive_tensor_descriptor_packed(
+        make_tuple(Number<MRepeat>{}, Number<NRepeat>{}, xdlops_gemm.GetRegSizePerXdlops()));
+
+    using AThreadCopy = ThreadwiseTensorSliceTransfer_v4<FloatAB,
+                                                         FloatAB,
+                                                         decltype(a_block_desc_m0_m1_m2_k),
+                                                         decltype(a_thread_desc_),
+                                                         Sequence<1, 1, 1, KPerThread>,
+                                                         Sequence<0, 1, 2, 3>,
+                                                         3,
+                                                         A_K1,
+                                                         A_K1>;
+
+    using BThreadCopy = ThreadwiseTensorSliceTransfer_v4<FloatAB,
+                                                         FloatAB,
+                                                         decltype(b_block_desc_n0_n1_n2_k),
+                                                         decltype(b_thread_desc_),
+                                                         Sequence<1, 1, 1, KPerThread>,
+                                                         Sequence<0, 1, 2, 3>,
+                                                         3,
+                                                         B_K1,
+                                                         B_K1>;
+
+    AThreadCopy a_thread_copy_{CalculateAThreadOriginDataIndex()};
+    BThreadCopy b_thread_copy_{CalculateBThreadOriginDataIndex()};
+};
+
+// Note: To facilitate the inter-wave loop scheduler, we need to explicitly set the macro
+// CK_EXPERIMENTAL_INTER_WAVE_SCHEDULING=1 as a few intrinsics are not yet available in
+// the latest ROCm release. For unsupported compilers, inter-wave loop scheduler falls back to the
+// default loop scheduler which is given by the macro CK_EXPERIMENTAL_INTER_WAVE_SCHEDULING=0
+template <index_t BlockSize,
+          typename FloatAB,
+          typename FloatAcc,
+          typename AK0MK1BlockDesc,
+          typename BK0NK1BlockDesc,
+          index_t MPerXDL,
+          index_t NPerXDL,
+          index_t MRepeat,
+          index_t NRepeat,
+          index_t KPack,
+          index_t NumMacClusters = CK_EXPERIMENTAL_INTER_WAVE_SCHEDULING_MAC_CLUSTERS>
+struct BlockwiseGemmXdlopsInterwave_k0mk1_k0nk1_m0n0m1n1m2m3m4n2_v1
+    : public BlockwiseGemmXdlops_k0mk1_k0nk1_m0n0m1n1m2m3m4n2_v1<BlockSize,
+                                                                 FloatAB,
+                                                                 FloatAcc,
+                                                                 AK0MK1BlockDesc,
+                                                                 BK0NK1BlockDesc,
+                                                                 MPerXDL,
+                                                                 NPerXDL,
+                                                                 MRepeat,
+                                                                 NRepeat,
+                                                                 KPack>
+{
+    using Base = BlockwiseGemmXdlops_k0mk1_k0nk1_m0n0m1n1m2m3m4n2_v1<BlockSize,
+                                                                     FloatAB,
+                                                                     FloatAcc,
+                                                                     AK0MK1BlockDesc,
+                                                                     BK0NK1BlockDesc,
+                                                                     MPerXDL,
+                                                                     NPerXDL,
+                                                                     MRepeat,
+                                                                     NRepeat,
+                                                                     KPack>;
+
+#if CK_EXPERIMENTAL_INTER_WAVE_SCHEDULING
+    using Base::a_block_desc_m0_m1_m2_k;
+    using Base::A_K1;
+    using Base::b_block_desc_n0_n1_n2_k;
+    using Base::B_K1;
+    using Base::c_thread_buf_;
+    using Base::c_thread_desc_;
+    using Base::CalculateAThreadOriginDataIndex;
+    using Base::CalculateBThreadOriginDataIndex;
+    using Base::I0;
+    using Base::I1;
+    using Base::KPerThread;
+    using Base::xdlops_gemm;
+
+    static constexpr index_t KPerInnerLoop = math::max(KPerThread / NumMacClusters, KPack);
+
+    // 2-wave optimized blockwise gemm
+    template <typename ABlockBuffer, typename BBlockBuffer, typename CThreadBuffer>
+    __device__ void Run(const ABlockBuffer& a_block_buf,
+                        const BBlockBuffer& b_block_buf,
+                        CThreadBuffer& c_thread_buf) const
+    {
+        auto a_thread_buf = make_static_buffer<AddressSpaceEnum::Vgpr, FloatAB>(
+            a_thread_desc_.GetElementSpaceSize());
+        auto b_thread_buf = make_static_buffer<AddressSpaceEnum::Vgpr, FloatAB>(
+            b_thread_desc_.GetElementSpaceSize());
+
+        static_for<0, KPerThread, KPerInnerLoop>{}([&](auto k) {
+            static_for<0, MRepeat, 1>{}([&](auto m0) {
+                // read A
+                a_thread_copy_.Run(a_block_desc_m0_m1_m2_k,
+                                   make_tuple(m0, I0, I0, k),
+                                   a_block_buf,
+                                   a_thread_desc_,
+                                   make_tuple(m0, I0, I0, I0),
+                                   a_thread_buf);
+            });
+            static_for<0, NRepeat, 1>{}([&](auto n0) {
+                // read B
+                b_thread_copy_.Run(b_block_desc_n0_n1_n2_k,
+                                   make_tuple(n0, I0, I0, k),
+                                   b_block_buf,
+                                   b_thread_desc_,
+                                   make_tuple(n0, I0, I0, I0),
+                                   b_thread_buf);
+            });
+            __builtin_amdgcn_sched_barrier(0);
+            // NOTE: Synchronize threads in a workgroup at the start of each MAC cluster, but except
+            // the first, as we can shorten non-MAC cluster a bit and there's no observable negative
+            // impact. The desired effect is waves in a workgroup executing MAC in sync. This avoids
+            // some out-of-sync waves hijacking MAC resource from other workgroups and reducing the
+            // chance of latency hiding by waiting for the rest of the workgroup at the eventual
+            // sync point.
+            if constexpr(k.value != 0 || KPerInnerLoop == KPerThread)
+            {
+                asm volatile("s_barrier" ::);
+                __builtin_amdgcn_sched_barrier(0);
+            }
+            static_for<0, KPerInnerLoop, KPack>{}([&](auto k_) {
+                static_for<0, MRepeat, 1>{}([&](auto m0) {
+                    static_for<0, NRepeat, 1>{}([&](auto n0) {
+                        vector_type<FloatAB, KPack> a_thread_vec;
+                        vector_type<FloatAB, KPack> b_thread_vec;
+
+                        static_for<0, KPack, 1>{}([&](auto i) {
+                            a_thread_vec.template AsType<FloatAB>()(i) =
+                                a_thread_buf[Number<a_thread_desc_.CalculateOffset(
+                                    make_tuple(m0, 0, 0, k_ + i))>{}];
+                            b_thread_vec.template AsType<FloatAB>()(i) =
+                                b_thread_buf[Number<b_thread_desc_.CalculateOffset(
+                                    make_tuple(n0, 0, 0, k_ + i))>{}];
+                        });
+
+                        using mfma_input_type =
+                            typename vector_type<FloatAB, xdlops_gemm.K1PerXdlops>::type;
+
+                        constexpr index_t c_offset =
+                            c_thread_desc_.CalculateOffset(make_tuple(m0, n0, 0));
+
+                        // The block_sync_lds() here performs double duty:
+                        // A) safeguard against data hazard because barrier from blockwise_gemm is
+                        // moved here B) reduce VMEM FIFO congestion by applying small delays to
+                        // different wavefronts It is performed near the end of MAC cluster to
+                        // minimize lgkmcnt penalty
+                        if constexpr(k.value == KPerThread - KPerInnerLoop &&
+                                     k_.value == KPerInnerLoop - KPack && m0.value == MRepeat - 1 &&
+                                     n0.value == NRepeat - 1)
+                        {
+                            __builtin_amdgcn_sched_barrier(0);
+                            block_sync_lds();
+                            __builtin_amdgcn_sched_barrier(0);
+                        }
+
+                        // TODO: insert setprio in more precise manner since we
+                        // could have more than >1 MFMA instructions in single call
+                        xdlops_gemm.template Run(
+                            a_thread_vec.template AsType<mfma_input_type>(),
+                            b_thread_vec.template AsType<mfma_input_type>(),
+                            c_thread_buf.GetVectorTypeReference(Number<c_offset>{}));
+                        if constexpr(k_.value == 0 && m0.value == 0 && n0.value == 0)
+                        {
+                            __builtin_amdgcn_sched_barrier(0);
+                            __builtin_amdgcn_s_setprio(1);
+                            __builtin_amdgcn_sched_barrier(0);
+                        }
+                    });
+                });
+            });
+            __builtin_amdgcn_sched_barrier(0);
+            __builtin_amdgcn_s_setprio(0);
+            __builtin_amdgcn_sched_barrier(0);
+        });
+    }
+
+    protected:
+    // A[M0, M1, M2, KPerInnerLoop]
+    static constexpr auto a_thread_desc_ = make_naive_tensor_descriptor_packed(
+        make_tuple(Number<MRepeat>{}, I1, I1, Number<KPerInnerLoop>{}));
+
+    // B[N0, N1, N2, KPerInnerLoop]
+    static constexpr auto b_thread_desc_ = make_naive_tensor_descriptor_packed(
+        make_tuple(Number<NRepeat>{}, I1, I1, Number<KPerInnerLoop>{}));
+
+    using AThreadCopy = ThreadwiseTensorSliceTransfer_v4<FloatAB,
+                                                         FloatAB,
+                                                         decltype(a_block_desc_m0_m1_m2_k),
+                                                         decltype(a_thread_desc_),
+                                                         Sequence<1, 1, 1, KPerInnerLoop>,
+                                                         Sequence<0, 1, 2, 3>,
+                                                         3,
+                                                         A_K1,
+                                                         A_K1>;
+
+    using BThreadCopy = ThreadwiseTensorSliceTransfer_v4<FloatAB,
+                                                         FloatAB,
+                                                         decltype(b_block_desc_n0_n1_n2_k),
+                                                         decltype(b_thread_desc_),
+                                                         Sequence<1, 1, 1, KPerInnerLoop>,
+                                                         Sequence<0, 1, 2, 3>,
+                                                         3,
+                                                         B_K1,
+                                                         B_K1>;
+
+    AThreadCopy a_thread_copy_{CalculateAThreadOriginDataIndex()};
+    BThreadCopy b_thread_copy_{CalculateBThreadOriginDataIndex()};
+
+#endif // #if CK_EXPERIMENTAL_INTER_WAVE_SCHEDULING
+};
+
+template <index_t BlockSize,
+          typename FloatAB,
+          typename FloatAcc,
+          typename AK0MK1BlockDesc,
+          typename BK0NK1BlockDesc,
+          index_t MPerXDL,
+          index_t NPerXDL,
+          index_t MRepeat,
+          index_t NRepeat,
+          index_t KPack,
+          LoopScheduler LoopSched>
+constexpr auto BlockwiseGemmXdlops_k0mk1_k0nk1_m0n0m1n1m2m3m4n2_Selector()
+{
+    if constexpr(LoopSched == LoopScheduler::Default)
+    {
+        return BlockwiseGemmXdlops_k0mk1_k0nk1_m0n0m1n1m2m3m4n2_v1<BlockSize,
+                                                                   FloatAB,
+                                                                   FloatAcc,
+                                                                   AK0MK1BlockDesc,
+                                                                   BK0NK1BlockDesc,
+                                                                   MPerXDL,
+                                                                   NPerXDL,
+                                                                   MRepeat,
+                                                                   NRepeat,
+                                                                   KPack>{};
+    }
+    else if constexpr(LoopSched == LoopScheduler::Interwave)
+    {
+        return BlockwiseGemmXdlopsInterwave_k0mk1_k0nk1_m0n0m1n1m2m3m4n2_v1<BlockSize,
+                                                                            FloatAB,
+                                                                            FloatAcc,
+                                                                            AK0MK1BlockDesc,
+                                                                            BK0NK1BlockDesc,
+                                                                            MPerXDL,
+                                                                            NPerXDL,
+                                                                            MRepeat,
+                                                                            NRepeat,
+                                                                            KPack>{};
+    }
+};
+
+// Blockwise gemm supporting
+// 1. regular XDL output M2_M3_M4_M2 and transposed XDL output M2_N2_N3_N4
+// 2. decoupled input tile descriptor and mma tile descriptor in order to support both vgpr and LDS
+// source buffer
+// 3. configurable k index starting position and step size after each FMA/XDL instruction
+template <index_t BlockSize,
+          typename FloatAB,
+          typename FloatAcc,
+          typename ATileDesc,
+          typename BTileDesc,
+          typename AMmaTileDesc,
+          typename BMmaTileDesc,
+          index_t MPerBlock,
+          index_t NPerBlock,
+          index_t KPerBlock,
+          index_t MPerXDL,
+          index_t NPerXDL,
+          index_t MRepeat,
+          index_t NRepeat,
+          index_t KPack,
+          bool TransposeC = false,
+          index_t AMmaKStride =
+              KPack* XdlopsGemm<FloatAB, MPerXDL, NPerXDL, KPack, TransposeC>{}.K0PerXdlops,
+          index_t BMmaKStride =
+              KPack* XdlopsGemm<FloatAB, MPerXDL, NPerXDL, KPack, TransposeC>{}.K0PerXdlops>
+struct BlockwiseGemmXdlops_v2
+{
+    static constexpr auto I0 = Number<0>{};
+    static constexpr auto I1 = Number<1>{};
+    static constexpr auto I2 = Number<2>{};
+    static constexpr auto I3 = Number<3>{};
+
+    using ThisThreadBlock = ThisThreadBlock<BlockSize>;
+
+    static constexpr index_t WaveSize = get_warp_size();
+
+    static constexpr index_t A_K0 = ATileDesc{}.GetLength(I0);
+    static constexpr index_t B_K0 = BTileDesc{}.GetLength(I0);
+    static constexpr index_t A_K1 = ATileDesc{}.GetLength(I2);
+    static constexpr index_t B_K1 = BTileDesc{}.GetLength(I2);
+
+    static constexpr auto xdlops_gemm = XdlopsGemm<FloatAB, MPerXDL, NPerXDL, KPack, TransposeC>{};
+
+    static constexpr index_t KPerThread = KPerBlock / xdlops_gemm.K0PerXdlops;
+
+    static constexpr index_t MWaves = MPerBlock / (MRepeat * MPerXDL);
+    static constexpr index_t NWaves = NPerBlock / (NRepeat * NPerXDL);
+
+    static_assert(KPerThread % KPack == 0,
+                  "Wrong KPack setting; try increasing KPerThread or decreasing KPack");
+
+    StaticBufferTupleOfVector<AddressSpaceEnum::Vgpr,
+                              FloatAcc,
+                              MRepeat * NRepeat,
+                              xdlops_gemm.GetRegSizePerXdlops(),
+                              true>
+        c_thread_buf_;
+
+    __host__ __device__ constexpr auto& GetCThreadBuffer() { return c_thread_buf_; }
+
+    __device__ static auto GetWaveIdx()
+    {
+        const index_t thread_id = ThisThreadBlock::GetThreadId();
+
+        constexpr auto threadid_to_wave_idx_adaptor = make_single_stage_tensor_adaptor(
+            make_tuple(make_merge_transform(make_tuple(MWaves, NWaves, WaveSize))),
+            make_tuple(Sequence<0, 1, 2>{}),
+            make_tuple(Sequence<0>{}));
+
+        return threadid_to_wave_idx_adaptor.CalculateBottomIndex(make_multi_index(thread_id));
+    }
+
+    __device__ static auto CalculateAThreadOriginDataIndex()
+    {
+        const auto wave_idx = GetWaveIdx();
+
+        const auto waveId_m = wave_idx[I0];
+
+        const auto xdlops_a_idx = xdlops_gemm.CalculateAThreadOriginDataIndex();
+
+        return make_tuple(0, waveId_m, xdlops_a_idx[I1], KPack * xdlops_a_idx[I0]);
+    }
+
+    __device__ static auto CalculateBThreadOriginDataIndex()
+    {
+        const auto wave_idx = GetWaveIdx();
+
+        const auto waveId_n = wave_idx[I1];
+
+        const auto xdlops_b_idx = xdlops_gemm.CalculateBThreadOriginDataIndex();
+
+        return make_tuple(0, waveId_n, xdlops_b_idx[I1], KPack * xdlops_b_idx[I0]);
+    }
+
+    template <index_t m0, index_t n0, index_t xdlops_i, index_t blk_i>
+    __device__ static auto
+        CalculateCThreadOriginDataIndex(Number<m0>, Number<n0>, Number<xdlops_i>, Number<blk_i>)
+    {
+        const auto wave_idx = GetWaveIdx();
+
+        const auto waveId_m = wave_idx[I0];
+        const auto waveId_n = wave_idx[I1];
+
+        const auto blk_idx = xdlops_gemm.GetBeginOfThreadBlk(xdlops_i, blk_i);
+
+        constexpr auto mrepeat_mwave_mperxdl_to_m_adaptor = make_single_stage_tensor_adaptor(
+            make_tuple(make_unmerge_transform(make_tuple(MRepeat, MWaves, MPerXDL))),
+            make_tuple(Sequence<0>{}),
+            make_tuple(Sequence<0, 1, 2>{}));
+
+        constexpr auto nrepeat_nwave_nperxdl_to_n_adaptor = make_single_stage_tensor_adaptor(
+            make_tuple(make_unmerge_transform(make_tuple(NRepeat, NWaves, NPerXDL))),
+            make_tuple(Sequence<0>{}),
+            make_tuple(Sequence<0, 1, 2>{}));
+
+        const index_t c_thread_m = mrepeat_mwave_mperxdl_to_m_adaptor.CalculateBottomIndex(
+            make_tuple(m0, waveId_m, blk_idx[I0]))[I0];
+        const index_t c_thread_n = nrepeat_nwave_nperxdl_to_n_adaptor.CalculateBottomIndex(
+            make_tuple(n0, waveId_n, blk_idx[I1]))[I0];
+
+        return make_tuple(c_thread_m, c_thread_n);
+    }
+
+    template <index_t m0, index_t n0, index_t xdlops_i, index_t blk_i>
+    __device__ static auto
+        CalculateCThreadOriginDataIndex8D(Number<m0>, Number<n0>, Number<xdlops_i>, Number<blk_i>)
+    {
+        const auto wave_idx = GetWaveIdx();
+
+        const auto waveId_m = wave_idx[I0];
+        const auto waveId_n = wave_idx[I1];
+
+        const auto blk_idx = xdlops_gemm.GetBeginOfThreadBlk4D(xdlops_i, blk_i);
+
+        return make_tuple(
+            m0, n0, waveId_m, waveId_n, blk_idx[I0], blk_idx[I1], blk_idx[I2], blk_idx[I3]);
+    }
+
+    using Tuple4 = decltype(CalculateAThreadOriginDataIndex());
+
+    __host__ __device__ BlockwiseGemmXdlops_v2(Tuple4 a_origin = CalculateAThreadOriginDataIndex(),
+                                               Tuple4 b_origin = CalculateBThreadOriginDataIndex())
+        : a_thread_copy_(a_origin), b_thread_copy_(b_origin)
+    {
+        static_assert(AMmaTileDesc::IsKnownAtCompileTime() && BMmaTileDesc::IsKnownAtCompileTime(),
+                      "wrong! Desc should be known at compile-time");
+
+        static_assert(ThisThreadBlock::GetNumOfThread() == MWaves * NWaves * WaveSize,
+                      "ThisThreadBlock::GetNumOfThread() != MWaves * NWaves * WaveSize\n");
+
+        static_assert(MPerBlock % (MPerXDL * MRepeat) == 0 && NPerBlock % (NPerXDL * NRepeat) == 0,
+                      "wrong!");
+    }
+
+    __host__ __device__ BlockwiseGemmXdlops_v2(const BlockwiseGemmXdlops_v2& other)
+        : a_thread_copy_(other.a_origin), b_thread_copy_(other.b_origin)
+    {
+    }
+
+    // transposed XDL output supporting C_xdl' = B_xdl' * A_xdl'
+    __host__ __device__ static constexpr auto GetCThreadDescriptor_M0_N0_M1_N1_M2_N2_N3_N4()
+    {
+        constexpr auto c_m0_m1_m2_n_tblk_lens = xdlops_gemm.GetCM0M1M2NThreadBlkLengths();
+
+        constexpr auto M0 = c_m0_m1_m2_n_tblk_lens[I0];
+        constexpr auto M1 = c_m0_m1_m2_n_tblk_lens[I1];
+        constexpr auto M2 = c_m0_m1_m2_n_tblk_lens[I2];
+        constexpr auto N  = c_m0_m1_m2_n_tblk_lens[I3];
+
+        return make_naive_tensor_descriptor_packed(
+            make_tuple(Number<MRepeat>{}, Number<NRepeat>{}, I1, I1, N, M0, M1, M2));
+    }
+
+    // XDL output supporting C_xdl = A_xdl * B_xdl
+    __host__ __device__ static constexpr auto GetCThreadDescriptor_M0_N0_M1_N1_M2_M3_M4_N2()
+    {
+        constexpr auto c_m0_m1_m2_n_tblk_lens = xdlops_gemm.GetCM0M1M2NThreadBlkLengths();
+
+        constexpr auto M0 = c_m0_m1_m2_n_tblk_lens[I0];
+        constexpr auto M1 = c_m0_m1_m2_n_tblk_lens[I1];
+        constexpr auto M2 = c_m0_m1_m2_n_tblk_lens[I2];
+        constexpr auto N  = c_m0_m1_m2_n_tblk_lens[I3];
+
+        return make_naive_tensor_descriptor_packed(
+            make_tuple(Number<MRepeat>{}, Number<NRepeat>{}, I1, I1, M0, M1, M2, N));
+    }
+
+    __host__ __device__ static constexpr auto GetCThreadDescriptor_G_M0_N0_M1_N1_M2_M3_M4_N2()
+    {
+        constexpr auto c_m0_m1_m2_n_tblk_lens = xdlops_gemm.GetCM0M1M2NThreadBlkLengths();
+
+        constexpr auto M0 = c_m0_m1_m2_n_tblk_lens[I0];
+        constexpr auto M1 = c_m0_m1_m2_n_tblk_lens[I1];
+        constexpr auto M2 = c_m0_m1_m2_n_tblk_lens[I2];
+        constexpr auto N  = c_m0_m1_m2_n_tblk_lens[I3];
+
+        return make_naive_tensor_descriptor_packed(
+            make_tuple(I1, Number<MRepeat>{}, Number<NRepeat>{}, I1, I1, M0, M1, M2, N));
+    }
+
+    // transposed XDL output supporting C_xdl' = B_xdl' * A_xdl'
+    __host__ __device__ static constexpr auto GetCBlockDescriptor_M0_N0_M1_N1_M2_N2_N3_N4()
+    {
+        constexpr auto c_block_desc_m0_n0_m1_n1_m2_n2 =
+            make_naive_tensor_descriptor_packed(make_tuple(Number<MRepeat>{},
+                                                           Number<NRepeat>{},
+                                                           Number<MWaves>{},
+                                                           Number<NWaves>{},
+                                                           Number<MPerXDL>{},
+                                                           Number<NPerXDL>{}));
+
+        return xdlops_gemm.MakeCDescriptor_M0_N0_M1_N1_M2_N2_N3_N4(c_block_desc_m0_n0_m1_n1_m2_n2);
+    }
+
+    // XDL output supporting C_xdl = A_xdl * B_xdl
+    __host__ __device__ static constexpr auto GetCBlockDescriptor_M0_N0_M1_N1_M2_M3_M4_N2()
+    {
+        constexpr auto c_block_desc_m0_n0_m1_n1_m2_n2 =
+            make_naive_tensor_descriptor_packed(make_tuple(Number<MRepeat>{},
+                                                           Number<NRepeat>{},
+                                                           Number<MWaves>{},
+                                                           Number<NWaves>{},
+                                                           Number<MPerXDL>{},
+                                                           Number<NPerXDL>{}));
+
+        return xdlops_gemm.MakeCDescriptor_M0_N0_M1_N1_M2_M3_M4_N2(c_block_desc_m0_n0_m1_n1_m2_n2);
+    }
+
+    __host__ __device__ static constexpr auto GetCBlockDescriptor_G_M0_N0_M1_N1_M2_M3_M4_N2()
+    {
+        constexpr auto c_block_desc_g_m0_n0_m1_n1_m2_n2 =
+            make_naive_tensor_descriptor_packed(make_tuple(I1,
+                                                           Number<MRepeat>{},
+                                                           Number<NRepeat>{},
+                                                           Number<MWaves>{},
+                                                           Number<NWaves>{},
+                                                           Number<MPerXDL>{},
+                                                           Number<NPerXDL>{}));
+
+        return xdlops_gemm.MakeCDescriptor_G_M0_N0_M1_N1_M2_M3_M4_N2(
+            c_block_desc_g_m0_n0_m1_n1_m2_n2);
+    }
+
+    template <typename CGridDesc_M_N>
+    __host__ __device__ static constexpr auto
+    MakeCGridDescriptor_M0_N0_M1_N1_M2_M3_M4_N2(const CGridDesc_M_N& c_grid_desc_m_n)
+    {
+        const auto M = c_grid_desc_m_n.GetLength(I0);
+        const auto N = c_grid_desc_m_n.GetLength(I1);
+
+        const auto c_grid_desc_m0_n0_m1_n1_m2_n2 = transform_tensor_descriptor(
+            c_grid_desc_m_n,
+            make_tuple(make_unmerge_transform(make_tuple(M / (MWaves * MPerXDL), MWaves, MPerXDL)),
+                       make_unmerge_transform(make_tuple(N / (NWaves * NPerXDL), NWaves, NPerXDL))),
+            make_tuple(Sequence<0>{}, Sequence<1>{}),
+            make_tuple(Sequence<0, 2, 4>{}, Sequence<1, 3, 5>{}));
+
+        return xdlops_gemm.MakeCDescriptor_M0_N0_M1_N1_M2_M3_M4_N2(c_grid_desc_m0_n0_m1_n1_m2_n2);
+    }
+
+    template <typename CGridDesc_G_M_N>
+    __host__ __device__ static constexpr auto
+    MakeCGridDescriptor_G_M0_N0_M1_N1_M2_M3_M4_N2(const CGridDesc_G_M_N& c_grid_desc_g_m_n)
+    {
+        const auto G = c_grid_desc_g_m_n.GetLength(I0);
+        const auto M = c_grid_desc_g_m_n.GetLength(I1);
+        const auto N = c_grid_desc_g_m_n.GetLength(I2);
+
+        const auto c_grid_desc_g_m0_n0_m1_n1_m2_n2 = transform_tensor_descriptor(
+            c_grid_desc_g_m_n,
+            make_tuple(make_pass_through_transform(G),
+                       make_unmerge_transform(make_tuple(M / (MWaves * MPerXDL), MWaves, MPerXDL)),
+                       make_unmerge_transform(make_tuple(N / (NWaves * NPerXDL), NWaves, NPerXDL))),
+            make_tuple(Sequence<0>{}, Sequence<1>{}, Sequence<2>{}),
+            make_tuple(Sequence<0>{}, Sequence<1, 3, 5>{}, Sequence<2, 4, 6>{}));
+
+        return xdlops_gemm.MakeCDescriptor_G_M0_N0_M1_N1_M2_M3_M4_N2(
+            c_grid_desc_g_m0_n0_m1_n1_m2_n2);
+    }
+
+    static constexpr AMmaTileDesc a_block_desc_m0_m1_m2_k;
+    static constexpr BMmaTileDesc b_block_desc_n0_n1_n2_k;
+
+    template <typename ABlockBuffer, typename BBlockBuffer, typename CThreadBuffer>
+    __device__ void Run(const ABlockBuffer& a_block_buf,
+                        const BBlockBuffer& b_block_buf,
+                        CThreadBuffer& c_thread_buf) const
+    {
+        auto a_thread_buf = make_static_buffer<AddressSpaceEnum::Vgpr, FloatAB>(
+            a_thread_desc_.GetElementSpaceSize());
+        auto b_thread_buf = make_static_buffer<AddressSpaceEnum::Vgpr, FloatAB>(
+            b_thread_desc_.GetElementSpaceSize());
+
+        static_for<0, KPerThread / KPack, 1>{}([&](auto k) { // k=0,1,2 instead of k=0,kpack*1, ...
+            static_for<0, MRepeat, 1>{}([&](auto m0) {
+                // read A
+                a_thread_copy_.Run(a_block_desc_m0_m1_m2_k,
+                                   make_tuple(m0, I0, I0, Number<k * AMmaKStride>{}),
+                                   a_block_buf,
+                                   a_thread_desc_,
+                                   make_tuple(I0, I0, I0, I0),
+                                   a_thread_buf);
+
+                static_for<0, NRepeat, 1>{}([&](auto n0) {
+                    // read B
+                    b_thread_copy_.Run(b_block_desc_n0_n1_n2_k,
+                                       make_tuple(n0, I0, I0, Number<k * BMmaKStride>{}),
+                                       b_block_buf,
+                                       b_thread_desc_,
+                                       make_tuple(I0, I0, I0, I0),
+                                       b_thread_buf);
+                    vector_type<FloatAB, KPack> a_thread_vec;
+                    vector_type<FloatAB, KPack> b_thread_vec;
+
+                    static_for<0, KPack, 1>{}([&](auto i) {
+                        a_thread_vec.template AsType<FloatAB>()(i) = a_thread_buf
+                            [Number<a_thread_desc_.CalculateOffset(make_tuple(0, 0, 0, i))>{}];
+                        b_thread_vec.template AsType<FloatAB>()(i) = b_thread_buf
+                            [Number<b_thread_desc_.CalculateOffset(make_tuple(0, 0, 0, i))>{}];
+                    });
+
+                    using mfma_input_type =
+                        typename vector_type<FloatAB, xdlops_gemm.K1PerXdlops>::type;
+
+                    constexpr index_t c_offset =
+                        c_thread_desc_.CalculateOffset(make_tuple(m0, n0, 0));
+
+                    xdlops_gemm.template Run(
+                        a_thread_vec.template AsType<mfma_input_type>(),
+                        b_thread_vec.template AsType<mfma_input_type>(),
+                        c_thread_buf.GetVectorTypeReference(Number<c_offset>{}));
+                });
+            });
+        });
+    }
+
+    protected:
+    // A[M0, M1, M2, KPack]
+    static constexpr auto a_thread_desc_ =
+        make_naive_tensor_descriptor_packed(make_tuple(I1, I1, I1, Number<KPack>{}));
+
+    // B[N0, N1, N2, KPack]
+    static constexpr auto b_thread_desc_ =
+        make_naive_tensor_descriptor_packed(make_tuple(I1, I1, I1, Number<KPack>{}));
+
+    // C[M, N, NumRegXdlops]
+    static constexpr auto c_thread_desc_ = make_naive_tensor_descriptor_packed(
+        make_tuple(Number<MRepeat>{}, Number<NRepeat>{}, xdlops_gemm.GetRegSizePerXdlops()));
+
+    using AThreadCopy = ThreadwiseTensorSliceTransfer_v4<FloatAB,
+                                                         FloatAB,
+                                                         decltype(a_block_desc_m0_m1_m2_k),
+                                                         decltype(a_thread_desc_),
+                                                         Sequence<1, 1, 1, KPack>,
+                                                         Sequence<0, 1, 2, 3>,
+                                                         3,
+                                                         A_K1,
+                                                         A_K1>;
+
+    using BThreadCopy = ThreadwiseTensorSliceTransfer_v4<FloatAB,
+                                                         FloatAB,
+                                                         decltype(b_block_desc_n0_n1_n2_k),
+                                                         decltype(b_thread_desc_),
+                                                         Sequence<1, 1, 1, KPack>,
+                                                         Sequence<0, 1, 2, 3>,
+                                                         3,
+                                                         B_K1,
+                                                         B_K1>;
+
+    AThreadCopy a_thread_copy_;
+    BThreadCopy b_thread_copy_;
+};
+
+} // namespace ck

include/ck/tensor_operation/gpu/block/blockwise_gemm_xdlops_skip_b_lds.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck/utility/common_header.hpp"
+#include "ck/tensor_operation/gpu/thread/threadwise_tensor_slice_transfer.hpp"
+#include "ck/tensor_operation/gpu/warp/xdlops_gemm.hpp"
+#include "ck/tensor_description/tensor_adaptor.hpp"
+
+namespace ck {
+
+template <index_t BlockSize,
+          typename FloatAB,
+          typename FloatAcc,
+          typename AK0MK1BlockDesc,
+          typename BK0K0BN0N1N2N3K1BlockDesc,
+          index_t MPerBlock,
+          index_t NPerBlock,
+          index_t K0PerBlock,
+          index_t MPerXDL,
+          index_t NPerXDL,
+          index_t MRepeat,
+          index_t NRepeat,
+          index_t KPack>
+struct BlockwiseGemmXdlops_k0mk1_k0nk1_m0n0m1n1m2m3m4n2_v1r1
+{
+    static constexpr auto I0 = Number<0>{};
+    static constexpr auto I1 = Number<1>{};
+    static constexpr auto I2 = Number<2>{};
+    static constexpr auto I3 = Number<3>{};
+
+    static constexpr index_t WaveSize = 64;
+
+    static constexpr index_t KPerBlock = K0PerBlock * KPack;
+
+    static constexpr index_t A_K0 = AK0MK1BlockDesc{}.GetLength(I0);
+    static constexpr index_t A_K1 = AK0MK1BlockDesc{}.GetLength(I2);
+
+    static constexpr auto xdlops_gemm = XdlopsGemm<FloatAB, MPerXDL, NPerXDL, KPack>{};
+
+    static constexpr index_t KPerThread  = KPerBlock / xdlops_gemm.K0PerXdlops;
+    static constexpr index_t K0PerThread = K0PerBlock / xdlops_gemm.K0PerXdlops;
+
+    static constexpr index_t MWaves = MPerBlock / (MRepeat * MPerXDL);
+    static constexpr index_t NWaves = NPerBlock / (NRepeat * NPerXDL);
+
+    StaticBufferTupleOfVector<AddressSpaceEnum::Vgpr,
+                              FloatAcc,
+                              MRepeat * NRepeat,
+                              xdlops_gemm.GetRegSizePerXdlops(),
+                              true>
+        c_thread_buf_;
+
+    __host__ __device__ constexpr auto& GetCThreadBuffer() { return c_thread_buf_; }
+
+    __device__ static auto GetWaveIdx()
+    {
+        const index_t thread_id = get_thread_local_1d_id();
+
+        constexpr auto threadid_to_wave_idx_adaptor = make_single_stage_tensor_adaptor(
+            make_tuple(make_merge_transform(make_tuple(MWaves, NWaves, WaveSize))),
+            make_tuple(Sequence<0, 1, 2>{}),
+            make_tuple(Sequence<0>{}));
+
+        return threadid_to_wave_idx_adaptor.CalculateBottomIndex(make_multi_index(thread_id));
+    }
+
+    __device__ static auto CalculateAThreadOriginDataIndex()
+    {
+        const auto wave_idx = GetWaveIdx();
+
+        const auto waveId_m = wave_idx[I0];
+
+        const auto xdlops_a_idx = xdlops_gemm.CalculateAThreadOriginDataIndex();
+
+        return make_tuple(0, waveId_m, xdlops_a_idx[I1], KPerThread * xdlops_a_idx[I0]);
+    }
+
+    __device__ static auto CalculateBThreadOriginDataIndex()
+    {
+        const auto wave_idx = GetWaveIdx();
+
+        const auto waveId_n = wave_idx[I1];
+
+        const auto xdlops_b_idx = xdlops_gemm.CalculateBThreadOriginDataIndex();
+
+        return make_tuple(0, waveId_n, xdlops_b_idx[I1], KPerThread * xdlops_b_idx[I0]);
+    }
+
+    template <index_t m0, index_t n0, index_t xdlops_i, index_t blk_i>
+    __device__ static auto
+        CalculateCThreadOriginDataIndex(Number<m0>, Number<n0>, Number<xdlops_i>, Number<blk_i>)
+    {
+        const auto wave_idx = GetWaveIdx();
+
+        const auto waveId_m = wave_idx[I0];
+        const auto waveId_n = wave_idx[I1];
+
+        const auto blk_idx = xdlops_gemm.GetBeginOfThreadBlk(xdlops_i, blk_i);
+
+        constexpr auto mrepeat_mwave_mperxdl_to_m_adaptor = make_single_stage_tensor_adaptor(
+            make_tuple(make_unmerge_transform(make_tuple(MRepeat, MWaves, MPerXDL))),
+            make_tuple(Sequence<0>{}),
+            make_tuple(Sequence<0, 1, 2>{}));
+
+        constexpr auto nrepeat_nwave_nperxdl_to_n_adaptor = make_single_stage_tensor_adaptor(
+            make_tuple(make_unmerge_transform(make_tuple(NRepeat, NWaves, NPerXDL))),
+            make_tuple(Sequence<0>{}),
+            make_tuple(Sequence<0, 1, 2>{}));
+
+        const index_t c_thread_m = mrepeat_mwave_mperxdl_to_m_adaptor.CalculateBottomIndex(
+            make_tuple(m0, waveId_m, blk_idx[I0]))[I0];
+        const index_t c_thread_n = nrepeat_nwave_nperxdl_to_n_adaptor.CalculateBottomIndex(
+            make_tuple(n0, waveId_n, blk_idx[I1]))[I0];
+
+        return make_tuple(c_thread_m, c_thread_n);
+    }
+
+    __host__ __device__ BlockwiseGemmXdlops_k0mk1_k0nk1_m0n0m1n1m2m3m4n2_v1r1()
+    {
+        static_assert(AK0MK1BlockDesc::IsKnownAtCompileTime() &&
+                          BK0K0BN0N1N2N3K1BlockDesc::IsKnownAtCompileTime(),
+                      "wrong! Desc should be known at compile-time");
+
+        static_assert(BlockSize == MWaves * NWaves * WaveSize,
+                      "BlockSize != MWaves * NWaves * WaveSize\n");
+
+        static_assert(MPerBlock % (MPerXDL * MRepeat) == 0 && NPerBlock % (NPerXDL * NRepeat) == 0,
+                      "wrong!");
+    }
+
+    __host__ __device__ static constexpr auto GetCThreadDescriptor_M0_N0_M1_N1_M2_M3_M4_N2()
+    {
+        constexpr auto c_m0_m1_m2_n_tblk_lens = xdlops_gemm.GetCM0M1M2NThreadBlkLengths();
+
+        constexpr auto M0 = c_m0_m1_m2_n_tblk_lens[I0];
+        constexpr auto M1 = c_m0_m1_m2_n_tblk_lens[I1];
+        constexpr auto M2 = c_m0_m1_m2_n_tblk_lens[I2];
+        constexpr auto N  = c_m0_m1_m2_n_tblk_lens[I3];
+
+        return make_naive_tensor_descriptor_packed(
+            make_tuple(Number<MRepeat>{}, Number<NRepeat>{}, I1, I1, M0, M1, M2, N));
+    }
+
+    __host__ __device__ static constexpr auto GetCThreadDescriptor_G_M0_N0_M1_N1_M2_M3_M4_N2()
+    {
+        constexpr auto c_m0_m1_m2_n_tblk_lens = xdlops_gemm.GetCM0M1M2NThreadBlkLengths();
+
+        constexpr auto M0 = c_m0_m1_m2_n_tblk_lens[I0];
+        constexpr auto M1 = c_m0_m1_m2_n_tblk_lens[I1];
+        constexpr auto M2 = c_m0_m1_m2_n_tblk_lens[I2];
+        constexpr auto N  = c_m0_m1_m2_n_tblk_lens[I3];
+
+        return make_naive_tensor_descriptor_packed(
+            make_tuple(I1, Number<MRepeat>{}, Number<NRepeat>{}, I1, I1, M0, M1, M2, N));
+    }
+
+    __host__ __device__ static constexpr auto GetCBlockDescriptor_M0_N0_M1_N1_M2_M3_M4_N2()
+    {
+        constexpr auto c_block_desc_m0_n0_m1_n1_m2_n2 =
+            make_naive_tensor_descriptor_packed(make_tuple(Number<MRepeat>{},
+                                                           Number<NRepeat>{},
+                                                           Number<MWaves>{},
+                                                           Number<NWaves>{},
+                                                           Number<MPerXDL>{},
+                                                           Number<NPerXDL>{}));
+
+        return xdlops_gemm.MakeCDescriptor_M0_N0_M1_N1_M2_M3_M4_N2(c_block_desc_m0_n0_m1_n1_m2_n2);
+    }
+
+    __host__ __device__ static constexpr auto GetCBlockDescriptor_G_M0_N0_M1_N1_M2_M3_M4_N2()
+    {
+        constexpr auto c_block_desc_g_m0_n0_m1_n1_m2_n2 =
+            make_naive_tensor_descriptor_packed(make_tuple(I1,
+                                                           Number<MRepeat>{},
+                                                           Number<NRepeat>{},
+                                                           Number<MWaves>{},
+                                                           Number<NWaves>{},
+                                                           Number<MPerXDL>{},
+                                                           Number<NPerXDL>{}));
+
+        return xdlops_gemm.MakeCDescriptor_G_M0_N0_M1_N1_M2_M3_M4_N2(
+            c_block_desc_g_m0_n0_m1_n1_m2_n2);
+    }
+
+    template <typename CGridDesc_M_N>
+    __host__ __device__ static constexpr auto
+    MakeCGridDescriptor_M0_N0_M1_N1_M2_M3_M4_N2(const CGridDesc_M_N& c_grid_desc_m_n)
+    {
+        const auto M = c_grid_desc_m_n.GetLength(I0);
+        const auto N = c_grid_desc_m_n.GetLength(I1);
+
+        const auto c_grid_desc_m0_n0_m1_n1_m2_n2 = transform_tensor_descriptor(
+            c_grid_desc_m_n,
+            make_tuple(make_unmerge_transform(make_tuple(M / (MWaves * MPerXDL), MWaves, MPerXDL)),
+                       make_unmerge_transform(make_tuple(N / (NWaves * NPerXDL), NWaves, NPerXDL))),
+            make_tuple(Sequence<0>{}, Sequence<1>{}),
+            make_tuple(Sequence<0, 2, 4>{}, Sequence<1, 3, 5>{}));
+
+        return xdlops_gemm.MakeCDescriptor_M0_N0_M1_N1_M2_M3_M4_N2(c_grid_desc_m0_n0_m1_n1_m2_n2);
+    }
+
+    template <typename CGridDesc_G_M_N>
+    __host__ __device__ static constexpr auto
+    MakeCGridDescriptor_G_M0_N0_M1_N1_M2_M3_M4_N2(const CGridDesc_G_M_N& c_grid_desc_g_m_n)
+    {
+        const auto G = c_grid_desc_g_m_n.GetLength(I0);
+        const auto M = c_grid_desc_g_m_n.GetLength(I1);
+        const auto N = c_grid_desc_g_m_n.GetLength(I2);
+
+        const auto c_grid_desc_g_m0_n0_m1_n1_m2_n2 = transform_tensor_descriptor(
+            c_grid_desc_g_m_n,
+            make_tuple(make_pass_through_transform(G),
+                       make_unmerge_transform(make_tuple(M / (MWaves * MPerXDL), MWaves, MPerXDL)),
+                       make_unmerge_transform(make_tuple(N / (NWaves * NPerXDL), NWaves, NPerXDL))),
+            make_tuple(Sequence<0>{}, Sequence<1>{}, Sequence<2>{}),
+            make_tuple(Sequence<0>{}, Sequence<1, 3, 5>{}, Sequence<2, 4, 6>{}));
+
+        return xdlops_gemm.MakeCDescriptor_G_M0_N0_M1_N1_M2_M3_M4_N2(
+            c_grid_desc_g_m0_n0_m1_n1_m2_n2);
+    }
+
+    __host__ __device__ static constexpr auto MakeABlockDescriptor_M0_M1_M2_K()
+    {
+        return transform_tensor_descriptor(
+            AK0MK1BlockDesc{},
+            make_tuple(
+                make_merge_transform_v3_division_mod(make_tuple(Number<A_K0>{}, Number<A_K1>{})),
+                make_unmerge_transform(
+                    make_tuple(Number<MRepeat>{}, Number<MWaves>{}, Number<MPerXDL>{}))),
+            make_tuple(Sequence<0, 2>{}, Sequence<1>{}),
+            make_tuple(Sequence<3>{}, Sequence<0, 1, 2>{}));
+    }
+
+    __device__ void MoveABlockSliceWindow()
+    {
+        a_thread_copy_.MoveSrcSliceWindow(a_block_desc_m0_m1_m2_k,
+                                          make_multi_index(0, 0, 0, K0PerBlock * KPack));
+    }
+    __device__ void ResetABlockStartWindow()
+    {
+        a_thread_copy_.SetSrcCoord(CalculateAThreadOriginDataIndex());
+    }
+
+    static constexpr auto a_block_desc_m0_m1_m2_k = MakeABlockDescriptor_M0_M1_M2_K();
+
+    template <typename ABlockBuffer, typename BBlockBuffer, typename CThreadBuffer>
+    __device__ void Run(const ABlockBuffer& a_block_buf,
+                        const BBlockBuffer& b_thread_buf,
+                        CThreadBuffer& c_thread_buf) const
+    {
+        auto a_thread_buf = make_static_buffer<AddressSpaceEnum::Vgpr, FloatAB>(
+            a_thread_desc_.GetElementSpaceSize());
+
+        static_for<0, MRepeat, 1>{}([&](auto m0) {
+            // read A
+            a_thread_copy_.Run(a_block_desc_m0_m1_m2_k,
+                               make_tuple(m0, I0, I0, I0),
+                               a_block_buf,
+                               a_thread_desc_,
+                               make_tuple(I0, I0, I0, I0),
+                               a_thread_buf);
+
+            static_for<0, NRepeat, 1>{}([&](auto n0) {
+                // read B
+                static_for<0, KPerThread, KPack>{}([&](auto k) {
+                    vector_type<FloatAB, KPack> a_thread_vec;
+                    vector_type<FloatAB, KPack> b_thread_vec;
+                    constexpr index_t k0 = k / KPack;
+                    static_for<0, KPack, 1>{}([&](auto i) {
+                        a_thread_vec.template AsType<FloatAB>()(i) = a_thread_buf
+                            [Number<a_thread_desc_.CalculateOffset(make_tuple(0, 0, 0, k + i))>{}];
+                        b_thread_vec.template AsType<FloatAB>()(i) = b_thread_buf
+                            [Number<b_thread_desc_.CalculateOffset(make_tuple(k0, n0, i))>{}];
+                    });
+
+                    using mfma_input_type =
+                        typename vector_type<FloatAB, xdlops_gemm.K1PerXdlops>::type;
+
+                    constexpr index_t c_offset =
+                        c_thread_desc_.CalculateOffset(make_tuple(m0, n0, 0));
+
+                    xdlops_gemm.template Run(
+                        a_thread_vec.template AsType<mfma_input_type>(),
+                        b_thread_vec.template AsType<mfma_input_type>(),
+                        c_thread_buf.GetVectorTypeReference(Number<c_offset>{}));
+                });
+            });
+        });
+    }
+
+    private:
+    // A[M0, M1, M2, KPerThread]
+    static constexpr auto a_thread_desc_ =
+        make_naive_tensor_descriptor_packed(make_tuple(I1, I1, I1, Number<KPerThread>{}));
+
+    // B[N0, N1, N2, KPerThread]
+    static constexpr auto b_thread_desc_ =
+        make_naive_tensor_descriptor_packed(make_tuple(Number<K0PerThread>{}, // KPerThread
+                                                       Number<NRepeat>{},     // repeat
+                                                       Number<KPack>{}));
+
+    // C[M, N, NumRegXdlops]
+    static constexpr auto c_thread_desc_ = make_naive_tensor_descriptor_packed(
+        make_tuple(Number<MRepeat>{}, Number<NRepeat>{}, xdlops_gemm.GetRegSizePerXdlops()));
+
+    using AThreadCopy = ThreadwiseTensorSliceTransfer_v4<FloatAB,
+                                                         FloatAB,
+                                                         decltype(a_block_desc_m0_m1_m2_k),
+                                                         decltype(a_thread_desc_),
+                                                         Sequence<1, 1, 1, KPerThread>,
+                                                         Sequence<0, 1, 2, 3>,
+                                                         3,
+                                                         A_K1,
+                                                         A_K1>;
+
+    AThreadCopy a_thread_copy_{CalculateAThreadOriginDataIndex()};
+};
+
+} // namespace ck

include/ck/tensor_operation/gpu/block/blockwise_softmax.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck/utility/data_type.hpp"
+#include "ck/utility/reduction_common.hpp"
+#include "ck/utility/reduction_operator.hpp"
+#include "ck/utility/reduction_functions_accumulate.hpp"
+#include "ck/tensor_operation/gpu/block/reduction_functions_blockwise.hpp"
+#include "ck/tensor_operation/gpu/thread/reduction_functions_threadwise.hpp"
+
+namespace ck {
+
+template <index_t BlockSize,
+          typename AccDataType,
+          typename ThreadMap_M_K, // thread_id to m_k
+          typename ThreadClusterDesc_M_K,
+          typename ThreadSliceDesc_M_K,
+          bool IgnoreNaN = false>
+struct BlockwiseSoftmax
+{
+    static constexpr auto I0         = Number<0>{};
+    static constexpr auto I1         = Number<1>{};
+    static constexpr index_t MRepeat = ThreadSliceDesc_M_K{}.GetLength(I0);
+    static constexpr index_t KRepeat = ThreadSliceDesc_M_K{}.GetLength(I1);
+
+    using ThreadSliceDesc_M = decltype(
+        make_naive_tensor_descriptor_packed(make_tuple(ThreadSliceDesc_M_K{}.GetLength(I0))));
+
+    using ThreadwiseMaxReduce = typename conditional<
+        IgnoreNaN,
+        ThreadwiseReduction<AccDataType,
+                            ThreadSliceDesc_M_K,
+                            ThreadSliceDesc_M,
+                            reduce::Max,
+                            false,
+                            detail::AccumulateWithNanIgnore<reduce::Max, AccDataType>>,
+        ThreadwiseReduction<AccDataType,
+                            ThreadSliceDesc_M_K,
+                            ThreadSliceDesc_M,
+                            reduce::Max,
+                            false>>::type;
+
+    using ThreadwiseSumReduce = typename conditional<
+        IgnoreNaN,
+        ThreadwiseReduction<AccDataType,
+                            ThreadSliceDesc_M_K,
+                            ThreadSliceDesc_M,
+                            reduce::Add,
+                            false,
+                            detail::AccumulateWithNanIgnore<reduce::Add, AccDataType>>,
+        ThreadwiseReduction<AccDataType,
+                            ThreadSliceDesc_M_K,
+                            ThreadSliceDesc_M,
+                            reduce::Add,
+                            false>>::type;
+
+    using ThreadClusterLengths_M_K = decltype(ThreadClusterDesc_M_K{}.GetLengths());
+
+    using BlockwiseMaxReduce = PartitionedBlockwiseReduction_v2<AccDataType,
+                                                                BlockSize,
+                                                                ThreadClusterLengths_M_K,
+                                                                ThreadMap_M_K,
+                                                                reduce::Max,
+                                                                false>;
+
+    using BlockwiseSumReduce = PartitionedBlockwiseReduction_v2<AccDataType,
+                                                                BlockSize,
+                                                                ThreadClusterLengths_M_K,
+                                                                ThreadMap_M_K,
+                                                                reduce::Add,
+                                                                false>;
+
+    using BufferType = StaticBuffer<AddressSpaceEnum::Vgpr, AccDataType, MRepeat, true>;
+
+    template <typename CThreadBuffer, typename WorkspaceBuffer>
+    __host__ __device__ void Run(CThreadBuffer& in_thread_buf, WorkspaceBuffer& reduce_work_buf)
+    {
+        // find max value
+        static_for<0, MRepeat, 1>{}([&](auto I) {
+            max_value_buf(I) = reduce::Max::template GetIdentityValue<AccDataType>();
+        });
+        ThreadwiseMaxReduce::Reduce(in_thread_buf, max_value_buf);
+        static_for<0, MRepeat, 1>{}([&](auto I) {
+            BlockwiseMaxReduce::Reduce(reduce_work_buf, max_value_buf(I));
+            block_sync_lds();
+        });
+
+        // calculate exp for elements, P=exp(s-max)
+        static_for<0, MRepeat, 1>{}([&](auto iM) {
+            static_for<0, KRepeat, 1>{}([&](auto iK) {
+                auto offset = Number<ThreadSliceDesc_M_K{}.CalculateOffset(make_tuple(iM, iK))>{};
+                in_thread_buf(offset) = IgnoreNaN && ck::math::isnan(in_thread_buf[offset])
+                                            ? 0
+                                            : math::exp(in_thread_buf[offset] - max_value_buf(iM));
+            });
+        });
+
+        // sum data
+        static_for<0, MRepeat, 1>{}([&](auto I) {
+            sum_value_buf(I) = reduce::Add::template GetIdentityValue<AccDataType>();
+        });
+        ThreadwiseSumReduce::Reduce(in_thread_buf, sum_value_buf);
+        static_for<0, MRepeat, 1>{}([&](auto I) {
+            BlockwiseSumReduce::Reduce(reduce_work_buf, sum_value_buf(I));
+            block_sync_lds();
+        });
+    }
+
+    BufferType max_value_buf;
+    BufferType sum_value_buf;
+};
+
+} // namespace ck

include/ck/tensor_operation/gpu/block/blockwise_tensor_slice_transfer_v5r1.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck/utility/common_header.hpp"
+#include "ck/tensor_description/tensor_descriptor.hpp"
+#include "ck/tensor_description/tensor_descriptor_helper.hpp"
+#include "ck/tensor_description/cluster_descriptor.hpp"
+#include "ck/tensor_operation/gpu/thread/threadwise_tensor_slice_transfer_v5r1.hpp"
+
+namespace ck {
+
+// this version does following things to avoid scratch memory issue
+// 1. Use StaticallyIndexedArray instead of C array for thread buffer
+// 2. ThreadwiseTensorSliceTransfer_v3 does not keep reference to tensor descriptor
+// 3. ThreadwiseTensorSliceTransfer_v3::Run() does not construct new tensor coordinate
+template <index_t BlockSize,
+          InMemoryDataOperationEnum DstInMemOp,
+          typename BlockSliceLengths,
+          typename ThreadSliceLengths,
+          typename ThreadClusterLengths,
+          typename ThreadClusterArrangeOrder,
+          typename SrcData,
+          typename DstData,
+          typename SrcDesc,
+          typename DstDesc,
+          typename SrcDimAccessOrder,
+          typename DstDimAccessOrder,
+          typename SrcVectorTensorLengths,
+          typename DstVectorTensorLengths,
+          typename SrcVectorTensorContiguousDimOrder,
+          typename DstVectorTensorContiguousDimOrder,
+          bool ThreadTransferSrcResetCoordinateAfterRun,
+          bool ThreadTransferDstResetCoordinateAfterRun>
+struct BlockwiseTensorSliceTransfer_v5r1
+{
+    static constexpr index_t nDim = remove_reference_t<SrcDesc>::GetNumOfDimension();
+
+    using Index = MultiIndex<nDim>;
+
+    __device__ constexpr BlockwiseTensorSliceTransfer_v5r1(const SrcDesc& src_desc,
+                                                           const Index& src_block_slice_origin,
+                                                           const DstDesc& dst_desc,
+                                                           const Index& dst_block_slice_origin)
+        : threadwise_transfer_(
+              src_desc, make_zero_multi_index<nDim>(), dst_desc, make_zero_multi_index<nDim>())
+
+    {
+        static_assert(nDim == remove_cvref_t<SrcDesc>::GetNumOfDimension() &&
+                          nDim == remove_cvref_t<DstDesc>::GetNumOfDimension() &&
+                          nDim == BlockSliceLengths::Size() && nDim == ThreadSliceLengths::Size() &&
+                          nDim == ThreadClusterLengths::Size() &&
+                          nDim == ThreadClusterArrangeOrder::Size() &&
+                          nDim == SrcDimAccessOrder::Size() && nDim == DstDimAccessOrder::Size(),
+                      "wrong! nDim not consistent");
+
+        static_assert(
+            is_same<BlockSliceLengths, decltype(ThreadSliceLengths{} * ThreadClusterLengths{})>{},
+            "wrong! threads should be mapped to cover entire slicing window");
+
+        static_assert(BlockSize >= thread_cluster_desc_.GetElementSize(),
+                      "wrong! BlockSize too small");
+
+        if(BlockSize == thread_cluster_desc_.GetElementSize() or
+           get_thread_local_1d_id() < thread_cluster_desc_.GetElementSize())
+        {
+            const auto thread_cluster_idx = thread_cluster_desc_.CalculateBottomIndex(
+                make_multi_index(get_thread_local_1d_id()));
+
+            const auto thread_data_idx_begin = thread_cluster_idx * ThreadSliceLengths{};
+
+            threadwise_transfer_.SetSrcSliceOrigin(src_desc,
+                                                   src_block_slice_origin + thread_data_idx_begin);
+            threadwise_transfer_.SetDstSliceOrigin(dst_desc,
+                                                   dst_block_slice_origin + thread_data_idx_begin);
+        }
+    }
+
+    template <typename SrcBuffer>
+    __device__ void RunRead(const SrcDesc& src_desc, const SrcBuffer& src_buf)
+    {
+        if(BlockSize == thread_cluster_desc_.GetElementSize() or
+           get_thread_local_1d_id() < thread_cluster_desc_.GetElementSize())
+        {
+            threadwise_transfer_.RunRead(src_desc, src_buf);
+        }
+    }
+
+    template <typename DstBuffer>
+    __device__ void RunWrite(const DstDesc& dst_desc, DstBuffer& dst_buf)
+    {
+        if(BlockSize == thread_cluster_desc_.GetElementSize() or
+           get_thread_local_1d_id() < thread_cluster_desc_.GetElementSize())
+        {
+            threadwise_transfer_.RunWrite(dst_desc, dst_buf);
+        }
+    }
+
+    __device__ void MoveSrcSliceWindow(const SrcDesc& src_desc, const Index& step)
+    {
+        if(BlockSize == thread_cluster_desc_.GetElementSize() or
+           get_thread_local_1d_id() < thread_cluster_desc_.GetElementSize())
+        {
+            threadwise_transfer_.MoveSrcSliceWindow(src_desc, step);
+        }
+    }
+
+    // SrcMoveSliceWindowStepHack to control index calculation move slice window
+    template <typename SrcMoveSliceWindowStepHack>
+    __device__ void
+    MoveSrcSliceWindow(const SrcDesc& src_desc,
+                       const Index& step,
+                       const SrcMoveSliceWindowStepHack& src_move_slice_window_step_hack)
+    {
+        if(BlockSize == thread_cluster_desc_.GetElementSize() or
+           get_thread_local_1d_id() < thread_cluster_desc_.GetElementSize())
+        {
+            threadwise_transfer_.MoveSrcSliceWindow(
+                src_desc, step, src_move_slice_window_step_hack);
+        }
+    }
+
+    __device__ void MoveDstSliceWindow(const DstDesc& dst_desc, const Index& step)
+    {
+        if(BlockSize == thread_cluster_desc_.GetElementSize() or
+           get_thread_local_1d_id() < thread_cluster_desc_.GetElementSize())
+        {
+            threadwise_transfer_.MoveDstSliceWindow(dst_desc, step);
+        }
+    }
+
+    private:
+    static constexpr auto thread_cluster_desc_ =
+        make_cluster_descriptor(ThreadClusterLengths{}, ThreadClusterArrangeOrder{});
+
+    using ThreadwiseTransfer =
+        ThreadwiseTensorSliceTransfer_v5r1<ThreadSliceLengths,
+                                           DstInMemOp,
+                                           SrcData,
+                                           DstData,
+                                           SrcDesc,
+                                           DstDesc,
+                                           SrcDimAccessOrder,
+                                           DstDimAccessOrder,
+                                           SrcVectorTensorLengths,
+                                           DstVectorTensorLengths,
+                                           SrcVectorTensorContiguousDimOrder,
+                                           DstVectorTensorContiguousDimOrder,
+                                           ThreadTransferSrcResetCoordinateAfterRun,
+                                           ThreadTransferDstResetCoordinateAfterRun>;
+
+    ThreadwiseTransfer threadwise_transfer_;
+};
+
+} // namespace ck

include/ck/tensor_operation/gpu/block/blockwise_welford.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck/tensor_description/cluster_descriptor.hpp"
+#include "ck/utility/reduction_common.hpp"
+
+namespace ck {
+
+// clang-format off
+// Assume:
+//  1) work_buffer is buffer (typically LDS) allocated outside as workspace
+//  2) work_buffer has T elements, and space size is no less than 3*BlockSize
+//  3) mean_value, var_value and count is the input data in vgpr from each thread
+//  4) mean_value, var_value and count is the over-written reduced output in vgpr for each thread
+//  5) Merge mean and M from ThreadwiseWelford
+// clang-format on
+template <typename T,
+          index_t BlockSize,
+          typename ThreadClusterLengths_M_K,
+          typename ThreadClusterArrangeOrder,
+          bool GetActualVariance = true>
+struct BlockwiseWelford
+{
+    static_assert(BlockSize == ThreadClusterLengths_M_K::At(0) * ThreadClusterLengths_M_K::At(1),
+                  "The product of cluster lengths should be same as BlockSize!");
+
+    static constexpr auto BufferLength_M = ThreadClusterLengths_M_K::At(0);
+    static constexpr auto BufferLength_K = ThreadClusterLengths_M_K::At(1);
+
+    static constexpr auto block_buf_desc_m_k = make_naive_tensor_descriptor_packed(
+        make_tuple(Number<BufferLength_M>{}, Number<BufferLength_K>{}));
+
+    static constexpr auto thread_cluster_desc =
+        make_cluster_descriptor(ThreadClusterLengths_M_K{}, ThreadClusterArrangeOrder{});
+
+    __device__ static inline void
+    Merge(T& mean_a, T& var_a, int& count_a, T mean_b, T var_b, int count_b)
+    {
+        int count            = count_a + count_b;
+        T count_b_over_count = count == 0 ? type_convert<T>(0) : type_convert<T>(count_b) / count;
+        T delta              = mean_b - mean_a;
+        mean_a += delta * count_b_over_count;
+        var_a += var_b + delta * delta * count_a * count_b_over_count;
+        count_a = count;
+    }
+
+    __device__ static void Run(T& mean_value, T& var_value, int& count)
+    {
+        __shared__ T mean_block_buf[BlockSize];
+        __shared__ T var_block_buf[BlockSize];
+        __shared__ int count_block_buf[BlockSize];
+
+        constexpr auto cluster_len_shift = get_shift<BufferLength_K>();
+
+        const auto thread_cluster_idx =
+            thread_cluster_desc.CalculateBottomIndex(make_multi_index(get_thread_local_1d_id()));
+
+        const auto thread_m_cluster_id = thread_cluster_idx[Number<0>{}];
+        const auto thread_k_cluster_id = thread_cluster_idx[Number<1>{}];
+
+        index_t offset1 = block_buf_desc_m_k.CalculateOffset(thread_cluster_idx);
+
+        mean_block_buf[offset1]  = mean_value;
+        var_block_buf[offset1]   = var_value;
+        count_block_buf[offset1] = count;
+
+        block_sync_lds();
+
+        static_for<0, cluster_len_shift, 1>{}([&](auto I) {
+            constexpr index_t indOffset = 1 << (cluster_len_shift - 1 - I());
+
+            if(thread_k_cluster_id < indOffset)
+            {
+                index_t offset2 = block_buf_desc_m_k.CalculateOffset(thread_cluster_idx +
+                                                                     make_tuple(0, indOffset));
+
+                T mean1    = mean_block_buf[offset1];
+                T var1     = var_block_buf[offset1];
+                int count1 = count_block_buf[offset1];
+
+                T mean2    = mean_block_buf[offset2];
+                T var2     = var_block_buf[offset2];
+                int count2 = count_block_buf[offset2];
+
+                Merge(mean1, var1, count1, mean2, var2, count2);
+
+                mean_block_buf[offset1]  = mean1;
+                var_block_buf[offset1]   = var1;
+                count_block_buf[offset1] = count1;
+            }
+
+            block_sync_lds();
+        });
+
+        index_t offset = block_buf_desc_m_k.CalculateOffset(make_tuple(thread_m_cluster_id, 0));
+
+        count      = count_block_buf[offset];
+        mean_value = mean_block_buf[offset];
+
+        if constexpr(GetActualVariance)
+            var_value = var_block_buf[offset] / count;
+        else
+            var_value = var_block_buf[offset];
+    };
+};
+} // namespace ck

include/ck/tensor_operation/gpu/block/reduction_functions_blockwise.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck/tensor_description/cluster_descriptor.hpp"
+#include "ck/utility/reduction_common.hpp"
+#include "ck/utility/reduction_functions_accumulate.hpp"
+
+namespace ck {
+
+// clang-format off
+// Assume:
+//  1) work_buffer is buffer (typically LDS) allocated outside as workspace, does not include any in/out data
+//  2) work_buffer has AccDataType elements, and space size is no less than BlockSize
+//  3) in_out_value is the input data in vgpr from each thread
+//  4) in_out_value is the over-written reduced output in vgpr for each thread
+// clang-format on
+template <typename AccDataType,
+          index_t BlockSize,
+          typename ThreadClusterLengths_M_K,
+          typename ThreadClusterArrangeOrder,
+          typename OpReduce,
+          bool PropagateNan,
+          typename Accumulation =
+              detail::AccumulateWithNanCheck<PropagateNan, OpReduce, AccDataType>>
+struct PartitionedBlockwiseReduction
+{
+    static_assert(BlockSize == ThreadClusterLengths_M_K::At(0) * ThreadClusterLengths_M_K::At(1),
+                  "The product of cluster lengths should be same as BlockSize!");
+
+    static constexpr auto BufferLength_M = ThreadClusterLengths_M_K::At(0);
+    static constexpr auto BufferLength_K = ThreadClusterLengths_M_K::At(1);
+
+    static_assert(BufferLength_K > 1, "Parallel reduction need work on at least two elements");
+
+    static constexpr auto block_buf_desc_m_k = make_naive_tensor_descriptor_packed(
+        make_tuple(Number<BufferLength_M>{}, Number<BufferLength_K>{}));
+
+    static constexpr auto thread_cluster_desc =
+        make_cluster_descriptor(ThreadClusterLengths_M_K{}, ThreadClusterArrangeOrder{});
+
+    template <typename BufferType>
+    __device__ static void Reduce(BufferType& work_buffer, AccDataType& in_out_value)
+    {
+        static_assert(is_same<typename BufferType::type, AccDataType>{},
+                      "Buffer data type should be consistent as AccDataType!");
+
+        constexpr auto cluster_len_shift = get_shift<BufferLength_K>();
+
+        const auto thread_cluster_idx =
+            thread_cluster_desc.CalculateBottomIndex(make_multi_index(get_thread_local_1d_id()));
+
+        const auto thread_m_cluster_id = thread_cluster_idx[Number<0>{}];
+        const auto thread_k_cluster_id = thread_cluster_idx[Number<1>{}];
+
+        work_buffer(block_buf_desc_m_k.CalculateOffset(thread_cluster_idx)) = in_out_value;
+
+        __syncthreads();
+
+        static_for<0, cluster_len_shift, 1>{}([&](auto I) {
+            constexpr index_t indOffset = 1 << (cluster_len_shift - 1 - I());
+
+            if(thread_k_cluster_id < indOffset)
+            {
+                index_t offset1 = block_buf_desc_m_k.CalculateOffset(thread_cluster_idx);
+                index_t offset2 = block_buf_desc_m_k.CalculateOffset(thread_cluster_idx +
+                                                                     make_tuple(0, indOffset));
+
+                AccDataType opData1 = work_buffer[offset1];
+                AccDataType opData2 = work_buffer[offset2];
+                Accumulation::Calculate(opData1, opData2);
+                work_buffer(offset1) = opData1;
+            }
+
+            __syncthreads();
+        });
+
+        index_t offset = block_buf_desc_m_k.CalculateOffset(make_tuple(thread_m_cluster_id, 0));
+
+        in_out_value = work_buffer[offset];
+    };
+};
+
+// clang-format off
+// Assume:
+//  1) work_buffer is buffer (typically LDS) allocated outside as workspace, does not include any in/out data
+//  2) work_buffer has AccDataType elements, and space size is no less than BlockSize
+//  3) in_out_value is the input data in vgpr from each thread
+//  4) in_out_value is the over-written reduced output in vgpr for each thread
+// clang-format on
+template <typename AccDataType,
+          index_t BlockSize,
+          typename ThreadClusterLengths_M_K,
+          typename ThreadClusterDesc,
+          typename OpReduce,
+          bool PropagateNan,
+          typename Accumulation =
+              detail::AccumulateWithNanCheck<PropagateNan, OpReduce, AccDataType>>
+struct PartitionedBlockwiseReduction_v2
+{
+    static_assert(BlockSize == ThreadClusterLengths_M_K::At(0) * ThreadClusterLengths_M_K::At(1),
+                  "The product of cluster lengths should be same as BlockSize!");
+
+    static constexpr auto BufferLength_M = ThreadClusterLengths_M_K::At(0);
+    static constexpr auto BufferLength_K = ThreadClusterLengths_M_K::At(1);
+
+    static_assert(BufferLength_K > 1, "Parallel reduction need work on at least two elements");
+
+    static constexpr auto block_buf_desc_m_k = make_naive_tensor_descriptor_packed(
+        make_tuple(Number<BufferLength_M>{}, Number<BufferLength_K>{}));
+
+    static constexpr auto thread_cluster_desc = ThreadClusterDesc{};
+
+    template <typename BufferType>
+    __device__ static void Reduce(BufferType& work_buffer, AccDataType& in_out_value)
+    {
+        static_assert(is_same<typename BufferType::type, AccDataType>{},
+                      "Buffer data type should be consistent as AccDataType!");
+
+        constexpr auto cluster_len_shift = get_shift<BufferLength_K>();
+
+        const auto thread_cluster_idx =
+            thread_cluster_desc.CalculateBottomIndex(make_multi_index(get_thread_local_1d_id()));
+
+        const auto thread_m_cluster_id = thread_cluster_idx[Number<0>{}];
+        const auto thread_k_cluster_id = thread_cluster_idx[Number<1>{}];
+
+        work_buffer(block_buf_desc_m_k.CalculateOffset(thread_cluster_idx)) = in_out_value;
+
+        __syncthreads();
+
+        static_for<0, cluster_len_shift, 1>{}([&](auto I) {
+            constexpr index_t indOffset = 1 << (cluster_len_shift - 1 - I());
+
+            if(thread_k_cluster_id < indOffset)
+            {
+                index_t offset1 = block_buf_desc_m_k.CalculateOffset(thread_cluster_idx);
+                index_t offset2 = block_buf_desc_m_k.CalculateOffset(thread_cluster_idx +
+                                                                     make_tuple(0, indOffset));
+
+                AccDataType opData1 = work_buffer[offset1];
+                AccDataType opData2 = work_buffer[offset2];
+                Accumulation::Calculate(opData1, opData2);
+                work_buffer(offset1) = opData1;
+            }
+
+            __syncthreads();
+        });
+
+        index_t offset = block_buf_desc_m_k.CalculateOffset(make_tuple(thread_m_cluster_id, 0));
+
+        in_out_value = work_buffer[offset];
+    };
+};
+
+// clang-format off
+// Assume:
+//  1) work_val_buffer/work_idx_buffer is buffer (typically LDS) allocated outside as workspace, does not include any in/out data
+//  2) work_val_buffer/work_idx_buffer has AccDataType/IndexDataType elements, and space size is no less than BlockSize
+//  3) in_out_value/in_out_index is the input data in vgpr from each thread
+//  4) in_out_value/in_out_index is the over-written reduced output in vgpr for each thread
+// clang-format on
+template <
+    typename AccDataType,
+    typename IndexDataType,
+    index_t BlockSize,
+    typename ThreadClusterLengths_M_K,
+    typename ThreadClusterArrangeOrder,
+    typename OpReduce,
+    bool PropagateNan,
+    typename Accumulation =
+        detail::AccumulateWithIndexAndNanCheck<PropagateNan, OpReduce, AccDataType, IndexDataType>>
+struct PartitionedBlockwiseReductionWithIndex
+{
+    static_assert(BlockSize == ThreadClusterLengths_M_K::At(0) * ThreadClusterLengths_M_K::At(1),
+                  "The product of cluster lengths should be same as BlockSize!");
+
+    static constexpr auto BufferLength_M = ThreadClusterLengths_M_K::At(0);
+    static constexpr auto BufferLength_K = ThreadClusterLengths_M_K::At(1);
+
+    static_assert(BufferLength_K > 1, "Parallel reduction need work on at least two elements");
+
+    static constexpr auto block_buf_desc_m_k = make_naive_tensor_descriptor_packed(
+        make_tuple(Number<BufferLength_M>{}, Number<BufferLength_K>{}));
+
+    static constexpr auto thread_cluster_desc =
+        make_cluster_descriptor(ThreadClusterLengths_M_K{}, ThreadClusterArrangeOrder{});
+
+    // This interface accumulates on both data values and indices
+    template <typename BufferType, typename IdxBufferType>
+    __device__ static void Reduce(BufferType& work_val_buffer,
+                                  IdxBufferType& work_idx_buffer,
+                                  AccDataType& in_out_value,
+                                  IndexDataType& in_out_index)
+    {
+        static_assert(is_same<typename BufferType::type, AccDataType>{},
+                      "Buffer data type should be consistent as AccDataType!");
+        static_assert(is_same<typename IdxBufferType::type, IndexDataType>{},
+                      "Buffer data type should be consistent as IndexDataType!");
+
+        constexpr auto cluster_len_shift = get_shift<BufferLength_K>();
+
+        const auto thread_cluster_idx =
+            thread_cluster_desc.CalculateBottomIndex(make_multi_index(get_thread_local_1d_id()));
+
+        const auto thread_m_cluster_id = thread_cluster_idx[Number<0>{}];
+        const auto thread_k_cluster_id = thread_cluster_idx[Number<1>{}];
+
+        work_val_buffer(block_buf_desc_m_k.CalculateOffset(thread_cluster_idx)) = in_out_value;
+        work_idx_buffer(block_buf_desc_m_k.CalculateOffset(thread_cluster_idx)) = in_out_index;
+
+        __syncthreads();
+
+        static_for<0, cluster_len_shift, 1>{}([&](auto I) {
+            constexpr index_t indOffset = 1 << I();
+
+            if(thread_k_cluster_id % (indOffset * 2) == 0)
+            {
+                index_t offset1 = block_buf_desc_m_k.CalculateOffset(thread_cluster_idx);
+                index_t offset2 = block_buf_desc_m_k.CalculateOffset(thread_cluster_idx +
+                                                                     make_tuple(0, indOffset));
+
+                AccDataType opData1      = work_val_buffer[offset1];
+                AccDataType opData2      = work_val_buffer[offset2];
+                IndexDataType currIndex1 = work_idx_buffer[offset1];
+                IndexDataType currIndex2 = work_idx_buffer[offset2];
+
+                Accumulation::Calculate(opData1, opData2, currIndex1, currIndex2);
+                work_val_buffer(offset1) = opData1;
+                work_idx_buffer(offset1) = currIndex1;
+            }
+
+            __syncthreads();
+        });
+
+        index_t offset = block_buf_desc_m_k.CalculateOffset(make_tuple(thread_m_cluster_id, 0));
+
+        in_out_value = work_val_buffer[offset];
+        in_out_index = work_idx_buffer[offset];
+    };
+};
+
+} // namespace ck

include/ck/tensor_operation/gpu/block/thread_group_tensor_slice_transfer_v4r1.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck/utility/common_header.hpp"
+#include "ck/tensor_description/tensor_descriptor.hpp"
+#include "ck/tensor_description/tensor_descriptor_helper.hpp"
+#include "ck/tensor_description/cluster_descriptor.hpp"
+#include "ck/tensor_operation/gpu/thread/threadwise_tensor_slice_transfer_v3r1.hpp"
+
+namespace ck {
+
+// this version does following things to avoid scratch memory issue
+// 1. Use StaticallyIndexedArray instead of C array for thread buffer
+// 2. ThreadwiseTensorSliceTransfer_v3 does not keep reference to tensor descriptor
+// 3. ThreadwiseTensorSliceTransfer_v3::Run() does not construct new tensor coordinate
+template <typename ThreadGroup,
+          typename SrcElementwiseOperation,
+          typename DstElementwiseOperation,
+          InMemoryDataOperationEnum DstInMemOp,
+          typename BlockSliceLengths,
+          typename ThreadClusterLengths,
+          typename ThreadClusterArrangeOrder,
+          typename SrcData,
+          typename DstData,
+          typename SrcDesc,
+          typename DstDesc,
+          typename SrcDimAccessOrder,
+          typename DstDimAccessOrder,
+          index_t SrcVectorDim,
+          index_t DstVectorDim,
+          index_t SrcScalarPerVector,
+          index_t DstScalarPerVector,
+          index_t SrcScalarStrideInVector,
+          index_t DstScalarStrideInVector,
+          bool ThreadTransferSrcResetCoordinateAfterRun,
+          bool ThreadTransferDstResetCoordinateAfterRun,
+          index_t NumThreadScratch = 1>
+struct ThreadGroupTensorSliceTransfer_v4r1
+{
+    static constexpr index_t nDim = remove_reference_t<SrcDesc>::GetNumOfDimension();
+
+    static constexpr auto thread_slice_lengths = BlockSliceLengths{} / ThreadClusterLengths{};
+
+    using Index = MultiIndex<nDim>;
+
+    __device__ constexpr ThreadGroupTensorSliceTransfer_v4r1(
+        const SrcDesc& src_desc,
+        const Index& src_block_slice_origin,
+        const SrcElementwiseOperation& src_element_op,
+        const DstDesc& dst_desc,
+        const Index& dst_block_slice_origin,
+        const DstElementwiseOperation& dst_element_op)
+        : threadwise_transfer_(src_desc,
+                               make_zero_multi_index<nDim>(),
+                               src_element_op,
+                               dst_desc,
+                               make_zero_multi_index<nDim>(),
+                               dst_element_op)
+
+    {
+        static_assert(nDim == remove_cvref_t<SrcDesc>::GetNumOfDimension() &&
+                          nDim == remove_cvref_t<DstDesc>::GetNumOfDimension() &&
+                          nDim == ThreadClusterLengths::Size() &&
+                          nDim == ThreadClusterArrangeOrder::Size() &&
+                          nDim == SrcDimAccessOrder::Size() && nDim == DstDimAccessOrder::Size(),
+                      "wrong! nDim not consistent");
+
+        static_assert(
+            is_same<BlockSliceLengths, decltype(thread_slice_lengths * ThreadClusterLengths{})>{},
+            "wrong! threads should be mapped to cover entire slicing window");
+
+        static_assert(ThreadGroup::GetNumOfThread() >= thread_cluster_desc_.GetElementSize(),
+                      "wrong! ThreadGroup::GetNumOfThread() too small");
+
+        if(ThreadGroup::GetNumOfThread() == thread_cluster_desc_.GetElementSize() or
+           ThreadGroup::GetThreadId() < thread_cluster_desc_.GetElementSize())
+        {
+            const auto thread_cluster_idx = thread_cluster_desc_.CalculateBottomIndex(
+                make_multi_index(ThreadGroup::GetThreadId()));
+
+            const auto thread_data_idx_begin = thread_cluster_idx * thread_slice_lengths;
+
+            threadwise_transfer_.SetSrcSliceOrigin(src_desc,
+                                                   src_block_slice_origin + thread_data_idx_begin);
+            threadwise_transfer_.SetDstSliceOrigin(dst_desc,
+                                                   dst_block_slice_origin + thread_data_idx_begin);
+        }
+    }
+
+    template <typename SrcBuffer, index_t ThreadScratchId = 0>
+    __device__ void RunRead(const SrcDesc& src_desc,
+                            const SrcBuffer& src_buf,
+                            Number<ThreadScratchId> thread_scratch_id = Number<ThreadScratchId>{})
+    {
+        if(ThreadGroup::GetNumOfThread() == thread_cluster_desc_.GetElementSize() or
+           ThreadGroup::GetThreadId() < thread_cluster_desc_.GetElementSize())
+        {
+            threadwise_transfer_.RunRead(src_desc, src_buf, thread_scratch_id);
+        }
+    }
+
+    template <typename DstBuffer, index_t ThreadScratchId = 0>
+    __device__ void RunWrite(const DstDesc& dst_desc,
+                             DstBuffer& dst_buf,
+                             Number<ThreadScratchId> thread_scratch_id = Number<ThreadScratchId>{})
+    {
+        if(ThreadGroup::GetNumOfThread() == thread_cluster_desc_.GetElementSize() or
+           ThreadGroup::GetThreadId() < thread_cluster_desc_.GetElementSize())
+        {
+            threadwise_transfer_.RunWrite(dst_desc, dst_buf, thread_scratch_id);
+        }
+    }
+
+    template <typename SrcBuffer, typename DstBuffer, index_t ThreadScratchId>
+    __device__ void Run(const SrcDesc& src_desc,
+                        const SrcBuffer& src_buf,
+                        const DstDesc& dst_desc,
+                        DstBuffer& dst_buf,
+                        Number<ThreadScratchId> thread_scratch_id)
+    {
+        RunRead(src_desc, src_buf, thread_scratch_id);
+        RunWrite(dst_desc, dst_buf, thread_scratch_id);
+    }
+
+    __device__ void MoveSrcSliceWindow(const SrcDesc& src_desc, const Index& step)
+    {
+        if(ThreadGroup::GetNumOfThread() == thread_cluster_desc_.GetElementSize() or
+           ThreadGroup::GetThreadId() < thread_cluster_desc_.GetElementSize())
+        {
+            threadwise_transfer_.MoveSrcSliceWindow(src_desc, step);
+        }
+    }
+
+    __device__ void MoveDstSliceWindow(const DstDesc& dst_desc, const Index& step)
+    {
+        if(ThreadGroup::GetNumOfThread() == thread_cluster_desc_.GetElementSize() or
+           ThreadGroup::GetThreadId() < thread_cluster_desc_.GetElementSize())
+        {
+            threadwise_transfer_.MoveDstSliceWindow(dst_desc, step);
+        }
+    }
+
+    private:
+    static constexpr auto thread_cluster_desc_ =
+        make_cluster_descriptor(ThreadClusterLengths{}, ThreadClusterArrangeOrder{});
+
+    using ThreadwiseTransfer =
+        ThreadwiseTensorSliceTransfer_v3r1<decltype(thread_slice_lengths),
+                                           SrcElementwiseOperation,
+                                           DstElementwiseOperation,
+                                           DstInMemOp,
+                                           SrcData,
+                                           DstData,
+                                           SrcDesc,
+                                           DstDesc,
+                                           SrcDimAccessOrder,
+                                           DstDimAccessOrder,
+                                           SrcVectorDim,
+                                           DstVectorDim,
+                                           SrcScalarPerVector,
+                                           DstScalarPerVector,
+                                           SrcScalarStrideInVector,
+                                           DstScalarStrideInVector,
+                                           ThreadTransferSrcResetCoordinateAfterRun,
+                                           ThreadTransferDstResetCoordinateAfterRun,
+                                           NumThreadScratch>;
+
+    ThreadwiseTransfer threadwise_transfer_;
+};
+
+} // namespace ck

include/ck/tensor_operation/gpu/block/thread_group_tensor_slice_transfer_v6r1.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck/utility/common_header.hpp"
+#include "ck/tensor_description/tensor_descriptor.hpp"
+#include "ck/tensor_description/tensor_descriptor_helper.hpp"
+#include "ck/tensor_description/cluster_descriptor.hpp"
+#include "ck/tensor_operation/gpu/thread/threadwise_tensor_slice_transfer_v6r1.hpp"
+
+namespace ck {
+
+// this version does following things to avoid scratch memory issue
+// 1. Use StaticallyIndexedArray instead of C array for thread buffer
+// 2. ThreadwiseTensorSliceTransfer_v3 does not keep reference to tensor descriptor
+// 3. ThreadwiseTensorSliceTransfer_v3::Run() does not construct new tensor coordinate
+template <typename ThreadGroup,
+          typename ElementwiseOperation,
+          InMemoryDataOperationEnum DstInMemOp,
+          typename SliceLengths,
+          typename ThreadClusterLengths,
+          typename ThreadClusterArrangeOrder,
+          typename SrcData,
+          typename DstData,
+          typename SrcDesc,
+          typename DstDesc,
+          typename DimAccessOrder,
+          index_t VectorDim,
+          index_t ScalarPerVector,
+          bool ThreadTransferSrcResetCoordinateAfterRun,
+          bool ThreadTransferDstResetCoordinateAfterRun>
+struct ThreadGroupTensorSliceTransfer_v6r1
+{
+    static constexpr index_t nDim = remove_reference_t<SrcDesc>::GetNumOfDimension();
+
+    static constexpr auto thread_slice_lengths = SliceLengths{} / ThreadClusterLengths{};
+
+    using Index = MultiIndex<nDim>;
+
+    __device__ constexpr ThreadGroupTensorSliceTransfer_v6r1(const SrcDesc& src_desc,
+                                                             const Index& src_block_slice_origin,
+                                                             const DstDesc& dst_desc,
+                                                             const Index& dst_block_slice_origin,
+                                                             const ElementwiseOperation& element_op)
+        : threadwise_transfer_(src_desc,
+                               make_zero_multi_index<nDim>(),
+                               dst_desc,
+                               make_zero_multi_index<nDim>(),
+                               element_op)
+
+    {
+        static_assert(nDim == remove_cvref_t<SrcDesc>::GetNumOfDimension() &&
+                          nDim == remove_cvref_t<DstDesc>::GetNumOfDimension() &&
+                          nDim == ThreadClusterLengths::Size() &&
+                          nDim == ThreadClusterArrangeOrder::Size() &&
+                          nDim == DimAccessOrder::Size(),
+                      "wrong! nDim not consistent");
+
+        static_assert(
+            is_same<SliceLengths, decltype(thread_slice_lengths * ThreadClusterLengths{})>{},
+            "wrong! threads should be mapped to cover entire slicing window");
+
+        static_assert(ThreadGroup::GetNumOfThread() >= thread_cluster_desc_.GetElementSize(),
+                      "wrong! ThreadGroup::GetNumOfThread() too small");
+
+        if(ThreadGroup::GetNumOfThread() == thread_cluster_desc_.GetElementSize() or
+           ThreadGroup::GetThreadId() < thread_cluster_desc_.GetElementSize())
+        {
+            const auto thread_cluster_idx = thread_cluster_desc_.CalculateBottomIndex(
+                make_multi_index(ThreadGroup::GetThreadId()));
+
+            const auto thread_data_idx_begin = thread_cluster_idx * thread_slice_lengths;
+
+            threadwise_transfer_.SetSrcSliceOrigin(src_desc,
+                                                   src_block_slice_origin + thread_data_idx_begin);
+            threadwise_transfer_.SetDstSliceOrigin(dst_desc,
+                                                   dst_block_slice_origin + thread_data_idx_begin);
+        }
+    }
+
+    template <typename SrcBuffer, typename DstBuffer>
+    __device__ void Run(const SrcDesc& src_desc,
+                        const SrcBuffer& src_buf,
+                        const DstDesc& dst_desc,
+                        DstBuffer& dst_buf)
+    {
+        if(ThreadGroup::GetNumOfThread() == thread_cluster_desc_.GetElementSize() or
+           ThreadGroup::GetThreadId() < thread_cluster_desc_.GetElementSize())
+        {
+            threadwise_transfer_.Run(src_desc, src_buf, dst_desc, dst_buf);
+        }
+    }
+
+    __device__ void MoveSrcSliceWindow(const SrcDesc& src_desc, const Index& step)
+    {
+        if(ThreadGroup::GetNumOfThread() == thread_cluster_desc_.GetElementSize() or
+           ThreadGroup::GetThreadId() < thread_cluster_desc_.GetElementSize())
+        {
+            threadwise_transfer_.MoveSrcSliceWindow(src_desc, step);
+        }
+    }
+
+    __device__ void MoveDstSliceWindow(const DstDesc& dst_desc, const Index& step)
+    {
+        if(ThreadGroup::GetNumOfThread() == thread_cluster_desc_.GetElementSize() or
+           ThreadGroup::GetThreadId() < thread_cluster_desc_.GetElementSize())
+        {
+            threadwise_transfer_.MoveDstSliceWindow(dst_desc, step);
+        }
+    }
+
+    private:
+    static constexpr auto thread_cluster_desc_ =
+        make_cluster_descriptor(ThreadClusterLengths{}, ThreadClusterArrangeOrder{});
+
+    using ThreadwiseTransfer =
+        ThreadwiseTensorSliceTransfer_v6r1<SrcData,
+                                           DstData,
+                                           SrcDesc,
+                                           DstDesc,
+                                           ElementwiseOperation,
+                                           decltype(thread_slice_lengths),
+                                           DimAccessOrder,
+                                           VectorDim,
+                                           ScalarPerVector,
+                                           DstInMemOp,
+                                           ThreadTransferSrcResetCoordinateAfterRun,
+                                           ThreadTransferDstResetCoordinateAfterRun>;
+
+    ThreadwiseTransfer threadwise_transfer_;
+};
+
+} // namespace ck