Merge branch 'develop' into jizhan/reduce_threadwise_multi_d

include/ck_tile/core/numeric/numeric.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include <limits>
+#include <stdint.h>
+
+namespace ck_tile {
+
+// this struct has the information of
+// 1. limit of a certain type, simliar to std::numeric_limits
+// 2. some pre-defined value, zero, one...
+//
+template <typename T>
+struct numeric
+{
+    // minimum finite value, or minimum positive normalized value for float
+    CK_TILE_HOST_DEVICE static constexpr T min() { return std::numeric_limits<T>::min(); }
+
+    // minumum finite value
+    CK_TILE_HOST_DEVICE static constexpr T lowest() { return std::numeric_limits<T>::lowest(); }
+
+    // maximum finite value
+    CK_TILE_HOST_DEVICE static constexpr T max() { return std::numeric_limits<T>::max(); }
+
+    // difference between 1.0 and next value representable by float
+    CK_TILE_HOST_DEVICE static constexpr T epsilon() { return std::numeric_limits<T>::epsilon(); }
+
+    // maximum rounding error
+    CK_TILE_HOST_DEVICE static constexpr T round_error()
+    {
+        return std::numeric_limits<T>::round_error();
+    }
+
+    // positive infinity value
+    CK_TILE_HOST_DEVICE static constexpr T infinity() { return std::numeric_limits<T>::infinity(); }
+
+    // quiet NaN
+    CK_TILE_HOST_DEVICE static constexpr T quiet_NaN()
+    {
+        return std::numeric_limits<T>::quiet_NaN();
+    }
+
+    // signaling NaN
+    CK_TILE_HOST_DEVICE static constexpr T signaling_NaN()
+    {
+        return std::numeric_limits<T>::signaling_NaN();
+    }
+
+    // smallest positive subnormal value
+    CK_TILE_HOST_DEVICE static constexpr T denorm_min()
+    {
+        return std::numeric_limits<T>::denorm_min();
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr T zero() { return static_cast<T>(0); }
+
+    CK_TILE_HOST_DEVICE static constexpr T one() { return static_cast<T>(1); }
+
+#ifndef C_LOG2E
+#define C_LOG2E 1.44269504088896340736 // log2(e)
+#endif
+
+    CK_TILE_HOST_DEVICE static constexpr T log2e()
+    {
+        if constexpr(std::is_same_v<T, float> || std::is_same_v<T, double>)
+        {
+            return static_cast<T>(C_LOG2E);
+        }
+        else
+        {
+            return 0; // TODO: integer?
+        }
+    }
+};
+
+template <typename T>
+struct numeric_traits;
+
+template <>
+struct numeric_traits<float>
+{
+    static constexpr int exp            = 8;
+    static constexpr int mant           = 23;
+    static constexpr int bias           = 127;
+    static constexpr uint32_t nan_mask  = 0x7F800000;
+    static constexpr uint32_t head_mask = 0xFF800000;
+    static constexpr uint32_t mant_mask = 0x7FFFFF;
+    static constexpr uint32_t exp_mask  = 0xFF;
+    static constexpr uint32_t Inf       = 0x7F800000;
+    static constexpr uint32_t NegInf    = 0xFF800000;
+    static constexpr uint32_t NaN       = 0x7F800001;
+    static constexpr uint32_t Neg0      = 0x80000000;
+    using bitwise_type                  = uint32_t;
+};
+
+} // namespace ck_tile
+
+#define CK_TILE_ARITHMETIC_USING_FLOAT(attr_, type_)                 \
+    attr_ bool operator==(const type_& x, const type_& y)            \
+    {                                                                \
+        return static_cast<float>(x) == static_cast<float>(y);       \
+    }                                                                \
+    attr_ bool operator!=(const type_& x, const type_& y)            \
+    {                                                                \
+        return static_cast<float>(x) != static_cast<float>(y);       \
+    }                                                                \
+    attr_ bool operator<(const type_& x, const type_& y)             \
+    {                                                                \
+        return static_cast<float>(x) < static_cast<float>(y);        \
+    }                                                                \
+    attr_ bool operator<=(const type_& x, const type_& y)            \
+    {                                                                \
+        return static_cast<float>(x) <= static_cast<float>(y);       \
+    }                                                                \
+    attr_ bool operator>(const type_& x, const type_& y)             \
+    {                                                                \
+        return static_cast<float>(x) > static_cast<float>(y);        \
+    }                                                                \
+    attr_ bool operator>=(const type_& x, const type_& y)            \
+    {                                                                \
+        return static_cast<float>(x) >= static_cast<float>(y);       \
+    }                                                                \
+    attr_ type_ operator+(const type_& x, const type_& y)            \
+    {                                                                \
+        return type_(static_cast<float>(x) + static_cast<float>(y)); \
+    }                                                                \
+    attr_ type_ operator-(const type_& x)                            \
+    {                                                                \
+        constexpr uint32_t bits = sizeof(type_) * 8;                 \
+        constexpr uint32_t mask = 1 << (bits - 1);                   \
+        type_ y                 = x;                                 \
+        y.data ^= static_cast<typename type_::raw_type>(mask);       \
+        return y;                                                    \
+    }                                                                \
+    attr_ type_ operator-(const type_& x, const type_& y)            \
+    {                                                                \
+        return type_(static_cast<float>(x) - static_cast<float>(y)); \
+    }                                                                \
+    attr_ type_ operator*(const type_& x, const type_& y)            \
+    {                                                                \
+        return type_(static_cast<float>(x) * static_cast<float>(y)); \
+    }                                                                \
+    attr_ type_ operator/(const type_& x, const type_& y)            \
+    {                                                                \
+        return type_(static_cast<float>(x) / static_cast<float>(y)); \
+    }                                                                \
+    attr_ type_& operator+=(type_& x, const type_& y)                \
+    {                                                                \
+        x = type_(static_cast<float>(x) + static_cast<float>(y));    \
+        return x;                                                    \
+    }                                                                \
+    attr_ type_& operator-=(type_& x, const type_& y)                \
+    {                                                                \
+        x = type_(static_cast<float>(x) - static_cast<float>(y));    \
+        return x;                                                    \
+    }                                                                \
+    attr_ type_& operator*=(type_& x, const type_& y)                \
+    {                                                                \
+        x = type_(static_cast<float>(x) * static_cast<float>(y));    \
+        return x;                                                    \
+    }                                                                \
+    attr_ type_& operator/=(type_& x, const type_& y)                \
+    {                                                                \
+        x = type_(static_cast<float>(x) / static_cast<float>(y));    \
+        return x;                                                    \
+    }                                                                \
+    attr_ type_& operator++(type_& x)                                \
+    {                                                                \
+        x = type_(static_cast<float>(x) + 1.f);                      \
+        return x;                                                    \
+    }                                                                \
+    attr_ type_& operator--(type_& x)                                \
+    {                                                                \
+        x = type_(static_cast<float>(x) - 1.f);                      \
+        return x;                                                    \
+    }                                                                \
+    attr_ type_ operator++(type_& x, int)                            \
+    {                                                                \
+        type_ y(x);                                                  \
+        x = type_(static_cast<float>(x) + 1.f);                      \
+        return y;                                                    \
+    }                                                                \
+    attr_ type_ operator--(type_& x, int)                            \
+    {                                                                \
+        type_ y(x);                                                  \
+        x = type_(static_cast<float>(x) - 1.f);                      \
+        return y;                                                    \
+    }

include/ck_tile/core/numeric/type_convert.hpp

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

include/ck_tile/core/numeric/vector_type.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/container/array.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/numeric/float8.hpp"
+#include "ck_tile/core/numeric/half.hpp"
+#include "ck_tile/core/numeric/bfloat16.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+
+namespace ck_tile {
+
+// this structure is used to pick up the <base> type inside
+// using xxx = <base> __attribute__((ext_vector_type(N)));
+// because clang only allow native type + bool in this term (custom type will fail)
+// overload this structure to let proper <base> type
+
+template <typename T>
+struct native_t
+{
+    using type = remove_cvref_t<T>;
+};
+
+// we name this as ext_vector purposely, because clang ext_vector_type extention only accept literay
+// basic type to construct a ext_vector_type you must be very careful using this, or will have lot
+// of compiler errors e.g. struct A; using Ax2_t = A __attribute__((ext_vector_type(2)));  -> will
+// have compiler error
+namespace impl {
+template <typename T_, index_t N_>
+struct ext_vector
+{
+    static constexpr index_t N = N_;
+    using value_type           = typename native_t<remove_cvref_t<T_>>::type;
+    static_assert(!std::is_class_v<value_type>);
+    using type = value_type __attribute__((ext_vector_type(N))); // this is danguous
+};
+
+template <typename V_, index_t Vs_, index_t N_>
+struct ext_vector<V_ __attribute__((ext_vector_type(Vs_))), N_>
+{
+    static constexpr index_t N = Vs_ * N_;
+    using value_type           = typename native_t<remove_cvref_t<V_>>::type;
+    static_assert(!std::is_class_v<value_type>);
+    using type = value_type __attribute__((ext_vector_type(N))); // this is danguous
+};
+
+} // namespace impl
+
+template <typename T, index_t N>
+using ext_vector_t = typename impl::ext_vector<T, N>::type;
+
+// by default, any type will result in a vector_size=1 with scalar_type=T traits.
+// ... unless we have other vector_traits specialization
+template <typename T>
+struct vector_traits
+{
+    using scalar_type                    = remove_cvref_t<T>;
+    static constexpr index_t vector_size = 1;
+};
+
+// specialization for ext_vector_type()
+template <typename T, index_t N>
+struct vector_traits<T __attribute__((ext_vector_type(N)))>
+{
+    using scalar_type                    = T;
+    static constexpr index_t vector_size = N;
+};
+
+template <typename X, typename Y>
+using has_same_scalar_type = std::is_same<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                          typename vector_traits<remove_cvref_t<Y>>::scalar_type>;
+
+// below are some pre-defines of ext_vector_type
+// attention! 2 vector type could be just the same type
+// fp64
+using fp64_t   = double;
+using fp64x2_t = double __attribute__((ext_vector_type(2)));
+using fp64x4_t = double __attribute__((ext_vector_type(4)));
+
+// fp32
+using fp32_t    = float;
+using fp32x2_t  = float __attribute__((ext_vector_type(2)));
+using fp32x4_t  = float __attribute__((ext_vector_type(4)));
+using fp32x8_t  = float __attribute__((ext_vector_type(8)));
+using fp32x16_t = float __attribute__((ext_vector_type(16)));
+using fp32x32_t = float __attribute__((ext_vector_type(32)));
+using fp32x64_t = float __attribute__((ext_vector_type(64)));
+
+// fp16
+// using fp16_t = ...
+using fp16x2_t  = _Float16 __attribute__((ext_vector_type(2)));
+using fp16x4_t  = _Float16 __attribute__((ext_vector_type(4)));
+using fp16x8_t  = _Float16 __attribute__((ext_vector_type(8)));
+using fp16x16_t = _Float16 __attribute__((ext_vector_type(16)));
+using fp16x32_t = _Float16 __attribute__((ext_vector_type(32)));
+using fp16x64_t = _Float16 __attribute__((ext_vector_type(64)));
+
+// bf16
+// using bf16_t = ...
+using bf16x2_t  = bf16_raw_t __attribute__((ext_vector_type(2)));
+using bf16x4_t  = bf16_raw_t __attribute__((ext_vector_type(4)));
+using bf16x8_t  = bf16_raw_t __attribute__((ext_vector_type(8)));
+using bf16x16_t = bf16_raw_t __attribute__((ext_vector_type(16)));
+using bf16x32_t = bf16_raw_t __attribute__((ext_vector_type(32)));
+using bf16x64_t = bf16_raw_t __attribute__((ext_vector_type(64)));
+
+// i32
+// using int32_t = ...
+using int32x2_t  = int32_t __attribute__((ext_vector_type(2)));
+using int32x4_t  = int32_t __attribute__((ext_vector_type(4)));
+using int32x8_t  = int32_t __attribute__((ext_vector_type(8)));
+using int32x16_t = int32_t __attribute__((ext_vector_type(16)));
+using int32x32_t = int32_t __attribute__((ext_vector_type(32)));
+using int32x64_t = int32_t __attribute__((ext_vector_type(64)));
+
+// i16
+// using int16_t = ...
+using int16x2_t  = int16_t __attribute__((ext_vector_type(2)));
+using int16x4_t  = int16_t __attribute__((ext_vector_type(4)));
+using int16x8_t  = int16_t __attribute__((ext_vector_type(8)));
+using int16x16_t = int16_t __attribute__((ext_vector_type(16)));
+using int16x32_t = int16_t __attribute__((ext_vector_type(32)));
+using int16x64_t = int16_t __attribute__((ext_vector_type(64)));
+
+// u16
+// using uint16_t
+using uint16x2_t  = uint16_t __attribute__((ext_vector_type(2)));
+using uint16x4_t  = uint16_t __attribute__((ext_vector_type(4)));
+using uint16x8_t  = uint16_t __attribute__((ext_vector_type(8)));
+using uint16x16_t = uint16_t __attribute__((ext_vector_type(16)));
+using uint16x32_t = uint16_t __attribute__((ext_vector_type(32)));
+using uint16x64_t = uint16_t __attribute__((ext_vector_type(64)));
+
+// i8
+// using int8_t
+using int8x2_t  = int8_t __attribute((ext_vector_type(2)));
+using int8x4_t  = int8_t __attribute((ext_vector_type(4)));
+using int8x8_t  = int8_t __attribute((ext_vector_type(8)));
+using int8x16_t = int8_t __attribute((ext_vector_type(16)));
+using int8x32_t = int8_t __attribute((ext_vector_type(32)));
+using int8x64_t = int8_t __attribute((ext_vector_type(64)));
+
+#if CK_TILE_USE_CUSTOM_DATA_TYPE
+// f8
+// using fp8_t
+using fp8x2_t  = fp8_raw_t __attribute((ext_vector_type(2)));
+using fp8x4_t  = fp8_raw_t __attribute((ext_vector_type(4)));
+using fp8x8_t  = fp8_raw_t __attribute((ext_vector_type(8)));
+using fp8x16_t = fp8_raw_t __attribute((ext_vector_type(16)));
+using fp8x32_t = fp8_raw_t __attribute((ext_vector_type(32)));
+using fp8x64_t = fp8_raw_t __attribute((ext_vector_type(64)));
+
+// bf8
+// using bf8_t
+using bf8x2_t  = bf8_raw_t __attribute((ext_vector_type(2)));
+using bf8x4_t  = bf8_raw_t __attribute((ext_vector_type(4)));
+using bf8x8_t  = bf8_raw_t __attribute((ext_vector_type(8)));
+using bf8x16_t = bf8_raw_t __attribute((ext_vector_type(16)));
+using bf8x32_t = bf8_raw_t __attribute((ext_vector_type(32)));
+using bf8x64_t = bf8_raw_t __attribute((ext_vector_type(64)));
+#else
+// f8
+// using fp8_t
+using fp8x2_t  = fp8_t __attribute((ext_vector_type(2)));
+using fp8x4_t  = fp8_t __attribute((ext_vector_type(4)));
+using fp8x8_t  = fp8_t __attribute((ext_vector_type(8)));
+using fp8x16_t = fp8_t __attribute((ext_vector_type(16)));
+using fp8x32_t = fp8_t __attribute((ext_vector_type(32)));
+using fp8x64_t = fp8_t __attribute((ext_vector_type(64)));
+
+// bf8
+// using bf8_t
+using bf8x2_t  = bf8_t __attribute((ext_vector_type(2)));
+using bf8x4_t  = bf8_t __attribute((ext_vector_type(4)));
+using bf8x8_t  = bf8_t __attribute((ext_vector_type(8)));
+using bf8x16_t = bf8_t __attribute((ext_vector_type(16)));
+using bf8x32_t = bf8_t __attribute((ext_vector_type(32)));
+using bf8x64_t = bf8_t __attribute((ext_vector_type(64)));
+#endif
+
+} // namespace ck_tile

include/ck_tile/core/tensor/buffer_view.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/arch/arch.hpp"
+#include "ck_tile/core/arch/amd_buffer_addressing.hpp"
+#include "ck_tile/core/container/array.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/numeric/float8.hpp"
+#include "ck_tile/core/numeric/half.hpp"
+#include "ck_tile/core/numeric/bfloat16.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+
+namespace ck_tile {
+
+// T may be scalar or vector
+// X may be scalar or vector
+// T and X have same scalar type
+// X contains multiple T
+// FIXME: InvalidElementUseNumericalZeroValue and invalid_element_value_ should be a property of
+//        transforms of tensor_view/Tensor
+// FIXME: amd_buffer_coherence_enum is only meaningful for buffer addressing. Need to split
+// buffer_view definition for different memory address space (Global/GenericLds/Vgpr)
+template <address_space_enum BufferAddressSpace,
+          typename T,
+          typename BufferSizeType,
+          bool InvalidElementUseNumericalZeroValue,
+          amd_buffer_coherence_enum Coherence = amd_buffer_coherence_enum::coherence_default>
+struct buffer_view;
+
+// Address Space: generic
+// T may be scalar or vector
+// X may be scalar or vector
+// T and X have same scalar type
+// X contains multiple T
+// FIXME: InvalidElementUseNumericalZeroValue and invalid_element_value_ should be a property of
+//        transforms of tensor_view/Tensor
+template <typename T, typename BufferSizeType, bool InvalidElementUseNumericalZeroValue>
+struct buffer_view<address_space_enum::generic,
+                   T,
+                   BufferSizeType,
+                   InvalidElementUseNumericalZeroValue,
+                   amd_buffer_coherence_enum::coherence_default>
+{
+    using type = T;
+
+    T* p_data_ = nullptr;
+    BufferSizeType buffer_size_;
+    remove_cvref_t<T> invalid_element_value_ = T{0};
+
+    CK_TILE_HOST_DEVICE constexpr buffer_view()
+        : p_data_{}, buffer_size_{}, invalid_element_value_{}
+    {
+    }
+
+    CK_TILE_HOST_DEVICE constexpr buffer_view(T* p_data, BufferSizeType buffer_size)
+        : p_data_{p_data}, buffer_size_{buffer_size}, invalid_element_value_{0}
+    {
+    }
+
+    CK_TILE_HOST_DEVICE constexpr buffer_view(T* p_data,
+                                              BufferSizeType buffer_size,
+                                              T invalid_element_value)
+        : p_data_{p_data}, buffer_size_{buffer_size}, invalid_element_value_{invalid_element_value}
+    {
+    }
+
+    CK_TILE_DEVICE static constexpr address_space_enum get_address_space()
+    {
+        return address_space_enum::generic;
+    }
+
+    // i is offset of T
+    // FIXME: doesn't do is_valid check
+    CK_TILE_DEVICE constexpr const T& operator[](index_t i) const { return p_data_[i]; }
+
+    // i is offset of T
+    // FIXME: doesn't do is_valid check
+    CK_TILE_DEVICE constexpr T& operator()(index_t i) { return p_data_[i]; }
+
+    // i is offset of T, not X. i should be aligned to X
+    template <typename X,
+              bool oob_conditional_check = true,
+              typename std::enable_if<
+                  std::is_same<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                               typename vector_traits<remove_cvref_t<T>>::scalar_type>::value,
+                  bool>::type = false>
+    CK_TILE_DEVICE constexpr auto
+    get(index_t i, bool is_valid_element, bool_constant<oob_conditional_check> = {}) const
+    {
+        // X contains multiple T
+        constexpr index_t scalar_per_t_vector = vector_traits<remove_cvref_t<T>>::vector_size;
+
+        constexpr index_t scalar_per_x_vector = vector_traits<remove_cvref_t<X>>::vector_size;
+
+        static_assert(scalar_per_x_vector % scalar_per_t_vector == 0,
+                      "wrong! X should contain multiple T");
+
+        if(is_valid_element)
+        {
+#if CK_TILE_EXPERIMENTAL_USE_MEMCPY_FOR_VECTOR_ACCESS
+            X tmp;
+
+            __builtin_memcpy(&tmp, &(p_data_[i]), sizeof(X));
+
+            return tmp;
+#else
+            return *c_style_pointer_cast<const X*>(&p_data_[i]);
+#endif
+        }
+        else
+        {
+            if constexpr(InvalidElementUseNumericalZeroValue)
+            {
+                return X{numeric<remove_cvref_t<T>>::zero()};
+            }
+            else
+            {
+                return X{invalid_element_value_};
+            }
+        }
+    }
+
+    // i is offset of T, not X. i should be aligned to X
+    template <memory_operation_enum Op,
+              typename X,
+              typename std::enable_if<
+                  std::is_same<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                               typename vector_traits<remove_cvref_t<T>>::scalar_type>::value,
+                  bool>::type = false>
+    CK_TILE_DEVICE void update(index_t i, bool is_valid_element, const X& x)
+    {
+        if constexpr(Op == memory_operation_enum::set)
+        {
+            this->template set<X>(i, is_valid_element, x);
+        }
+        // FIXME: remove memory_operation_enum::add
+        else if constexpr(Op == memory_operation_enum::add)
+        {
+            auto tmp = this->template get<X>(i, is_valid_element);
+            this->template set<X>(i, is_valid_element, x + tmp);
+        }
+    }
+
+    // i is offset of T, not X. i should be aligned to X
+    template <typename X,
+              typename std::enable_if<
+                  std::is_same<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                               typename vector_traits<remove_cvref_t<T>>::scalar_type>::value,
+                  bool>::type = false>
+    CK_TILE_DEVICE void set(index_t i, bool is_valid_element, const X& x)
+    {
+        // X contains multiple T
+        constexpr index_t scalar_per_t_vector = vector_traits<remove_cvref_t<T>>::vector_size;
+
+        constexpr index_t scalar_per_x_vector = vector_traits<remove_cvref_t<X>>::vector_size;
+
+        static_assert(scalar_per_x_vector % scalar_per_t_vector == 0,
+                      "wrong! X should contain multiple T");
+
+        if(is_valid_element)
+        {
+#if CK_TILE_EXPERIMENTAL_USE_MEMCPY_FOR_VECTOR_ACCESS
+            X tmp = x;
+
+            __builtin_memcpy(&(p_data_[i]), &tmp, sizeof(X));
+#else
+            *c_style_pointer_cast<X*>(&p_data_[i]) = x;
+#endif
+        }
+    }
+
+    // FIXME: remove
+    CK_TILE_DEVICE static constexpr bool is_static_buffer() { return false; }
+
+    // FIXME: remove
+    CK_TILE_DEVICE static constexpr bool is_dynamic_buffer() { return true; }
+
+    CK_TILE_HOST_DEVICE void print() const
+    {
+        printf("buffer_view{");
+
+        // AddressSpace
+        printf("AddressSpace: generic, ");
+
+        // p_data_
+        printf("p_data_: %p, ", static_cast<void*>(const_cast<remove_cvref_t<T>*>(p_data_)));
+
+        // buffer_size_
+        printf("buffer_size_: ");
+        print(buffer_size_);
+        printf(", ");
+
+        // invalid_element_value_
+        printf("invalid_element_value_: ");
+        print(invalid_element_value_);
+
+        printf("}");
+    }
+};
+
+// Address Space: Global
+// T may be scalar or vector
+// X may be scalar or vector
+// T and X have same scalar type
+// X contains multiple T
+// FIXME: InvalidElementUseNumericalZeroValue and invalid_element_value_ should be a property of
+//        transforms of tensor_view/Tensor
+template <typename T,
+          typename BufferSizeType,
+          bool InvalidElementUseNumericalZeroValue,
+          amd_buffer_coherence_enum Coherence>
+struct buffer_view<address_space_enum::global,
+                   T,
+                   BufferSizeType,
+                   InvalidElementUseNumericalZeroValue,
+                   Coherence>
+{
+    using type = T;
+
+    T* p_data_ = nullptr;
+    BufferSizeType buffer_size_;
+    remove_cvref_t<T> invalid_element_value_ = T{0};
+
+    CK_TILE_HOST_DEVICE constexpr buffer_view()
+        : p_data_{}, buffer_size_{}, invalid_element_value_{}
+    {
+    }
+
+    CK_TILE_HOST_DEVICE constexpr buffer_view(T* p_data, BufferSizeType buffer_size)
+        : p_data_{p_data}, buffer_size_{buffer_size}, invalid_element_value_{0}
+    {
+    }
+
+    CK_TILE_HOST_DEVICE constexpr buffer_view(T* p_data,
+                                              BufferSizeType buffer_size,
+                                              T invalid_element_value)
+        : p_data_{p_data}, buffer_size_{buffer_size}, invalid_element_value_{invalid_element_value}
+    {
+    }
+
+    CK_TILE_DEVICE static constexpr address_space_enum get_address_space()
+    {
+        return address_space_enum::global;
+    }
+
+    // i is offset of T
+    // FIXME: doesn't do is_valid check
+    CK_TILE_DEVICE constexpr const T& operator[](index_t i) const { return p_data_[i]; }
+
+    // i is offset of T
+    // FIXME: doesn't do is_valid check
+    CK_TILE_DEVICE constexpr T& operator()(index_t i) { return p_data_[i]; }
+
+    // i is offset of T, not X. i should be aligned to X
+    template <typename X,
+              bool oob_conditional_check = true,
+              typename std::enable_if<
+                  std::is_same<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                               typename vector_traits<remove_cvref_t<T>>::scalar_type>::value,
+                  bool>::type = false>
+    CK_TILE_DEVICE constexpr auto
+    get(index_t i, bool is_valid_element, bool_constant<oob_conditional_check> = {}) const
+    {
+        // X contains multiple T
+        constexpr index_t scalar_per_t_vector = vector_traits<remove_cvref_t<T>>::vector_size;
+
+        constexpr index_t scalar_per_x_vector = vector_traits<remove_cvref_t<X>>::vector_size;
+
+        static_assert(scalar_per_x_vector % scalar_per_t_vector == 0,
+                      "wrong! X should contain multiple T");
+
+#if CK_TILE_USE_AMD_BUFFER_LOAD
+        bool constexpr use_amd_buffer_addressing = true;
+#else
+        bool constexpr use_amd_buffer_addressing = false;
+#endif
+
+        if constexpr(use_amd_buffer_addressing)
+        {
+            constexpr index_t t_per_x = scalar_per_x_vector / scalar_per_t_vector;
+
+            if constexpr(InvalidElementUseNumericalZeroValue)
+            {
+                return amd_buffer_load_invalid_element_return_zero<remove_cvref_t<T>,
+                                                                   t_per_x,
+                                                                   Coherence,
+                                                                   oob_conditional_check>(
+                    p_data_, i, is_valid_element, buffer_size_);
+            }
+            else
+            {
+                return amd_buffer_load_invalid_element_return_customized_value<
+                    remove_cvref_t<T>,
+                    t_per_x,
+                    Coherence,
+                    oob_conditional_check>(
+                    p_data_, i, is_valid_element, buffer_size_, invalid_element_value_);
+            }
+        }
+        else
+        {
+            if(is_valid_element)
+            {
+#if CK_TILE_EXPERIMENTAL_USE_MEMCPY_FOR_VECTOR_ACCESS
+                X tmp;
+
+                __builtin_memcpy(&tmp, &(p_data_[i]), sizeof(X));
+
+                return tmp;
+#else
+                return *c_style_pointer_cast<const X*>(&p_data_[i]);
+#endif
+            }
+            else
+            {
+                if constexpr(InvalidElementUseNumericalZeroValue)
+                {
+                    return X{numeric<remove_cvref_t<T>>::zero()};
+                }
+                else
+                {
+                    return X{invalid_element_value_};
+                }
+            }
+        }
+    }
+
+    // i is offset of T, not X. i should be aligned to X
+    template <typename X,
+              bool oob_conditional_check = true,
+              typename std::enable_if<
+                  std::is_same<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                               typename vector_traits<remove_cvref_t<T>>::scalar_type>::value,
+                  bool>::type = false>
+    CK_TILE_DEVICE constexpr auto
+    get_raw(remove_cvref_t<X>& dst, index_t i, bool is_valid_element) const
+    {
+        constexpr index_t scalar_per_t_vector = vector_traits<remove_cvref_t<T>>::vector_size;
+
+        constexpr index_t scalar_per_x_vector = vector_traits<remove_cvref_t<X>>::vector_size;
+
+        static_assert(scalar_per_x_vector % scalar_per_t_vector == 0,
+                      "wrong! X should contain multiple T");
+
+        constexpr index_t t_per_x = scalar_per_x_vector / scalar_per_t_vector;
+
+        amd_buffer_load_raw<remove_cvref_t<T>, t_per_x, Coherence, oob_conditional_check>(
+            dst, p_data_, i, buffer_size_, is_valid_element);
+    }
+
+    // i is offset of T, not X. i should be aligned to X
+    template <typename X,
+              typename std::enable_if<
+                  std::is_same<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                               typename vector_traits<remove_cvref_t<T>>::scalar_type>::value,
+                  bool>::type = false>
+    CK_TILE_DEVICE constexpr auto
+    async_get(remove_cvref_t<T>* smem, index_t i, bool /*is_valid_element*/) const
+    {
+        // X is vector of T
+        constexpr index_t scalar_per_t_vector = vector_traits<remove_cvref_t<T>>::vector_size;
+        constexpr index_t scalar_per_x_vector = vector_traits<remove_cvref_t<X>>::vector_size;
+
+        static_assert(scalar_per_x_vector % scalar_per_t_vector == 0,
+                      "wrong! X should contain multiple T");
+
+        constexpr index_t t_per_x = scalar_per_x_vector / scalar_per_t_vector;
+
+        amd_async_buffer_load_with_oob<remove_cvref_t<T>, t_per_x, Coherence>(
+            smem, p_data_, i, buffer_size_);
+    }
+
+    // i is offset of T, not X. i should be aligned to X
+    template <memory_operation_enum Op,
+              typename X,
+              typename std::enable_if<
+                  std::is_same<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                               typename vector_traits<remove_cvref_t<T>>::scalar_type>::value,
+                  bool>::type = false>
+    CK_TILE_DEVICE void update(index_t i, bool is_valid_element, const X& x)
+    {
+        if constexpr(Op == memory_operation_enum::set)
+        {
+            this->template set<X>(i, is_valid_element, x);
+        }
+        else if constexpr(Op == memory_operation_enum::atomic_add)
+        {
+            this->template atomic_add<X>(i, is_valid_element, x);
+        }
+        else if constexpr(Op == memory_operation_enum::atomic_max)
+        {
+            this->template atomic_max<X>(i, is_valid_element, x);
+        }
+        // FIXME: remove memory_operation_enum::add
+        else if constexpr(Op == memory_operation_enum::add)
+        {
+            auto tmp = this->template get<X>(i, is_valid_element);
+            this->template set<X>(i, is_valid_element, x + tmp);
+            // tmp += x;
+            // this->template set<X>(i, is_valid_element, tmp);
+        }
+    }
+
+    // i is offset of T, not X. i should be aligned to X
+    template <typename X,
+              bool oob_conditional_check = true,
+              typename std::enable_if<
+                  std::is_same<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                               typename vector_traits<remove_cvref_t<T>>::scalar_type>::value,
+                  bool>::type = false>
+    CK_TILE_DEVICE void set(index_t i, bool is_valid_element, const X& x)
+    {
+        // X contains multiple T
+        constexpr index_t scalar_per_t_vector = vector_traits<remove_cvref_t<T>>::vector_size;
+
+        constexpr index_t scalar_per_x_vector = vector_traits<remove_cvref_t<X>>::vector_size;
+
+        static_assert(scalar_per_x_vector % scalar_per_t_vector == 0,
+                      "wrong! X should contain multiple T");
+
+#if CK_TILE_USE_AMD_BUFFER_STORE
+        bool constexpr use_amd_buffer_addressing = true;
+#else
+        bool constexpr use_amd_buffer_addressing = false;
+#endif
+
+        if constexpr(use_amd_buffer_addressing)
+        {
+            constexpr index_t t_per_x = scalar_per_x_vector / scalar_per_t_vector;
+
+            amd_buffer_store<remove_cvref_t<T>, t_per_x, Coherence>(
+                x, p_data_, i, is_valid_element, buffer_size_);
+        }
+        else
+        {
+            if(is_valid_element)
+            {
+#if CK_TILE_EXPERIMENTAL_USE_MEMCPY_FOR_VECTOR_ACCESS
+                X tmp = x;
+
+                __builtin_memcpy(&(p_data_[i]), &tmp, sizeof(X));
+#else
+                *c_style_pointer_cast<X*>(&p_data_[i]) = x;
+#endif
+            }
+        }
+    }
+
+    // i is offset of T, not X. i should be aligned to X
+    template <typename X,
+              bool oob_conditional_check = true,
+              typename std::enable_if<
+                  std::is_same<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                               typename vector_traits<remove_cvref_t<T>>::scalar_type>::value,
+                  bool>::type = false>
+    CK_TILE_DEVICE void set_raw(index_t i, bool is_valid_element, const X& x)
+    {
+        // X contains multiple T
+        constexpr index_t scalar_per_t_vector = vector_traits<remove_cvref_t<T>>::vector_size;
+
+        constexpr index_t scalar_per_x_vector = vector_traits<remove_cvref_t<X>>::vector_size;
+
+        static_assert(scalar_per_x_vector % scalar_per_t_vector == 0,
+                      "wrong! X should contain multiple T");
+
+        constexpr index_t t_per_x = scalar_per_x_vector / scalar_per_t_vector;
+        amd_buffer_store_raw<remove_cvref_t<T>, t_per_x, Coherence, oob_conditional_check>(
+            x, p_data_, i, is_valid_element, buffer_size_);
+    }
+
+    template <typename X,
+              typename std::enable_if<
+                  std::is_same<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                               typename vector_traits<remove_cvref_t<T>>::scalar_type>::value,
+                  bool>::type = false>
+    CK_TILE_DEVICE void atomic_add(index_t i, bool is_valid_element, const X& x)
+    {
+        using scalar_t = typename vector_traits<remove_cvref_t<T>>::scalar_type;
+
+        // X contains multiple T
+        constexpr index_t scalar_per_t_vector = vector_traits<remove_cvref_t<T>>::vector_size;
+
+        constexpr index_t scalar_per_x_vector = vector_traits<remove_cvref_t<X>>::vector_size;
+
+        static_assert(scalar_per_x_vector % scalar_per_t_vector == 0,
+                      "wrong! X should contain multiple T");
+
+        static_assert(get_address_space() == address_space_enum::global, "only support global mem");
+
+#if CK_TILE_USE_AMD_BUFFER_ATOMIC_ADD_INTEGER && CK_TILE_USE_AMD_BUFFER_ATOMIC_ADD_FLOAT
+        bool constexpr use_amd_buffer_addressing =
+            std::is_same_v<remove_cvref_t<scalar_t>, int32_t> ||
+            std::is_same_v<remove_cvref_t<scalar_t>, float> ||
+            (std::is_same_v<remove_cvref_t<scalar_t>, half_t> && scalar_per_x_vector % 2 == 0);
+#elif CK_TILE_USE_AMD_BUFFER_ATOMIC_ADD_INTEGER && (!CK_TILE_USE_AMD_BUFFER_ATOMIC_ADD_FLOAT)
+        bool constexpr use_amd_buffer_addressing =
+            std::is_same_v<remove_cvref_t<scalar_t>, int32_t>;
+#elif(!CK_TILE_USE_AMD_BUFFER_ATOMIC_ADD_INTEGER) && CK_TILE_USE_AMD_BUFFER_ATOMIC_ADD_FLOAT
+        bool constexpr use_amd_buffer_addressing =
+            std::is_same_v<remove_cvref_t<scalar_t>, float> ||
+            (std::is_same_v<remove_cvref_t<scalar_t>, half_t> && scalar_per_x_vector % 2 == 0);
+#else
+        bool constexpr use_amd_buffer_addressing = false;
+#endif
+
+        if constexpr(use_amd_buffer_addressing)
+        {
+            constexpr index_t t_per_x = scalar_per_x_vector / scalar_per_t_vector;
+
+            amd_buffer_atomic_add<remove_cvref_t<T>, t_per_x>(
+                x, p_data_, i, is_valid_element, buffer_size_);
+        }
+        else
+        {
+            if(is_valid_element)
+            {
+                atomic_add<X>(c_style_pointer_cast<X*>(&p_data_[i]), x);
+            }
+        }
+    }
+
+    template <typename X,
+              typename std::enable_if<
+                  std::is_same<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                               typename vector_traits<remove_cvref_t<T>>::scalar_type>::value,
+                  bool>::type = false>
+    CK_TILE_DEVICE void atomic_max(index_t i, bool is_valid_element, const X& x)
+    {
+        // X contains multiple T
+        constexpr index_t scalar_per_t_vector = vector_traits<remove_cvref_t<T>>::vector_size;
+
+        constexpr index_t scalar_per_x_vector = vector_traits<remove_cvref_t<X>>::vector_size;
+
+        static_assert(scalar_per_x_vector % scalar_per_t_vector == 0,
+                      "wrong! X should contain multiple T");
+
+        static_assert(get_address_space() == address_space_enum::global, "only support global mem");
+
+#if CK_TILE_USE_AMD_BUFFER_ATOMIC_MAX_FLOAT64
+        using scalar_t = typename vector_traits<remove_cvref_t<T>>::scalar_type;
+        bool constexpr use_amd_buffer_addressing = std::is_same_v<remove_cvref_t<scalar_t>, double>;
+#else
+        bool constexpr use_amd_buffer_addressing = false;
+#endif
+
+        if constexpr(use_amd_buffer_addressing)
+        {
+            constexpr index_t t_per_x = scalar_per_x_vector / scalar_per_t_vector;
+
+            amd_buffer_atomic_max<remove_cvref_t<T>, t_per_x>(
+                x, p_data_, i, is_valid_element, buffer_size_);
+        }
+        else if(is_valid_element)
+        {
+            atomic_max<X>(c_style_pointer_cast<X*>(&p_data_[i]), x);
+        }
+    }
+
+    // FIXME: remove
+    CK_TILE_DEVICE static constexpr bool is_static_buffer() { return false; }
+
+    // FIXME: remove
+    CK_TILE_DEVICE static constexpr bool is_dynamic_buffer() { return true; }
+
+    CK_TILE_HOST_DEVICE void print() const
+    {
+        printf("buffer_view{");
+
+        // AddressSpace
+        printf("AddressSpace: Global, ");
+
+        // p_data_
+        printf("p_data_: %p, ", static_cast<void*>(const_cast<remove_cvref_t<T>*>(p_data_)));
+
+        // buffer_size_
+        printf("buffer_size_: ");
+        print(buffer_size_);
+        printf(", ");
+
+        // invalid_element_value_
+        printf("invalid_element_value_: ");
+        print(invalid_element_value_);
+
+        printf("}");
+    }
+};
+
+// Address Space: LDS
+// T may be scalar or vector
+// X may be scalar or vector
+// T and X have same scalar type
+// X contains multiple T
+// FIXME: InvalidElementUseNumericalZeroValue and invalid_element_value_ should be a property of
+//        transforms of tensor_view/Tensor
+template <typename T, typename BufferSizeType, bool InvalidElementUseNumericalZeroValue>
+struct buffer_view<address_space_enum::lds,
+                   T,
+                   BufferSizeType,
+                   InvalidElementUseNumericalZeroValue,
+                   amd_buffer_coherence_enum::coherence_default>
+{
+    using type = T;
+
+    T* p_data_ = nullptr;
+    BufferSizeType buffer_size_;
+    remove_cvref_t<T> invalid_element_value_ = T{0};
+
+    CK_TILE_HOST_DEVICE constexpr buffer_view()
+        : p_data_{}, buffer_size_{}, invalid_element_value_{}
+    {
+    }
+
+    CK_TILE_HOST_DEVICE constexpr buffer_view(T* p_data, BufferSizeType buffer_size)
+        : p_data_{p_data}, buffer_size_{buffer_size}, invalid_element_value_{0}
+    {
+    }
+
+    CK_TILE_HOST_DEVICE constexpr buffer_view(T* p_data,
+                                              BufferSizeType buffer_size,
+                                              T invalid_element_value)
+        : p_data_{p_data}, buffer_size_{buffer_size}, invalid_element_value_{invalid_element_value}
+    {
+    }
+
+    CK_TILE_DEVICE static constexpr address_space_enum get_address_space()
+    {
+        return address_space_enum::lds;
+    }
+
+    // i is offset of T
+    // FIXME: doesn't do is_valid check
+    CK_TILE_DEVICE constexpr const T& operator[](index_t i) const { return p_data_[i]; }
+
+    // i is offset of T
+    // FIXME: doesn't do is_valid check
+    CK_TILE_DEVICE constexpr T& operator()(index_t i) { return p_data_[i]; }
+
+    // i is offset of T, not X. i should be aligned to X
+    template <typename X,
+              bool oob_conditional_check = true,
+              typename std::enable_if<
+                  std::is_same<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                               typename vector_traits<remove_cvref_t<T>>::scalar_type>::value,
+                  bool>::type = false>
+    CK_TILE_DEVICE constexpr auto
+    get(index_t i, bool is_valid_element, bool_constant<oob_conditional_check> = {}) const
+    {
+        // X contains multiple T
+        constexpr index_t scalar_per_t_vector = vector_traits<remove_cvref_t<T>>::vector_size;
+
+        constexpr index_t scalar_per_x_vector = vector_traits<remove_cvref_t<X>>::vector_size;
+
+        static_assert(scalar_per_x_vector % scalar_per_t_vector == 0,
+                      "wrong! X should contain multiple T");
+
+        if(is_valid_element)
+        {
+#if CK_TILE_EXPERIMENTAL_USE_MEMCPY_FOR_VECTOR_ACCESS
+            X tmp;
+
+            __builtin_memcpy(&tmp, &(p_data_[i]), sizeof(X));
+
+            return tmp;
+#else
+            using buf_t = ext_vector_t<typename vector_traits<remove_cvref_t<T>>::scalar_type,
+                                       scalar_per_t_vector * scalar_per_x_vector>;
+            // using buf_t = ushort __attribute__((ext_vector_type(8)));
+            auto rtn = *c_style_pointer_cast<const buf_t*>(&p_data_[i]);
+            return bit_cast<X>(rtn);
+#endif
+        }
+        else
+        {
+            if constexpr(InvalidElementUseNumericalZeroValue)
+            {
+                return X{numeric<remove_cvref_t<T>>::zero()};
+            }
+            else
+            {
+                return X{invalid_element_value_};
+            }
+        }
+    }
+
+    // i is offset of T, not X. i should be aligned to X
+    template <memory_operation_enum Op,
+              typename X,
+              typename std::enable_if<
+                  std::is_same<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                               typename vector_traits<remove_cvref_t<T>>::scalar_type>::value,
+                  bool>::type = false>
+    CK_TILE_DEVICE void update(index_t i, bool is_valid_element, const X& x)
+    {
+        if constexpr(Op == memory_operation_enum::set)
+        {
+            this->template set<X>(i, is_valid_element, x);
+        }
+        // FIXME: remove memory_operation_enum::add
+        else if constexpr(Op == memory_operation_enum::add)
+        {
+            auto tmp = this->template get<X>(i, is_valid_element);
+            this->template set<X>(i, is_valid_element, x + tmp);
+        }
+    }
+
+    // i is offset of T, not X. i should be aligned to X
+    template <typename X,
+              typename std::enable_if<
+                  std::is_same<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                               typename vector_traits<remove_cvref_t<T>>::scalar_type>::value,
+                  bool>::type = false>
+    CK_TILE_DEVICE void set(index_t i, bool is_valid_element, const X& x)
+    {
+        // X contains multiple T
+        constexpr index_t scalar_per_t_vector = vector_traits<remove_cvref_t<T>>::vector_size;
+
+        constexpr index_t scalar_per_x_vector = vector_traits<remove_cvref_t<X>>::vector_size;
+
+        static_assert(scalar_per_x_vector % scalar_per_t_vector == 0,
+                      "wrong! X should contain multiple T");
+
+#if CK_TILE_WORKAROUND_SWDEV_XXXXXX_INT8_DS_WRITE_ISSUE
+        bool constexpr workaround_int8_ds_write_issue = true;
+#else
+        bool constexpr workaround_int8_ds_write_issue = false;
+#endif
+
+        if constexpr(std::is_same<typename vector_traits<remove_cvref_t<T>>::scalar_type,
+                                  int8_t>::value &&
+                     workaround_int8_ds_write_issue)
+        {
+            if(is_valid_element)
+            {
+                // HACK: compiler would lower IR "store<i8, 16> address_space(3)" into inefficient
+                // ISA, so I try to let compiler emit IR "store<i32, 4>" which would be lower to
+                // ds_write_b128
+                // TODO: remove this after compiler fix
+                static_assert((std::is_same<remove_cvref_t<T>, int8_t>::value &&
+                               std::is_same<remove_cvref_t<X>, int8_t>::value) ||
+                                  (std::is_same<remove_cvref_t<T>, int8_t>::value &&
+                                   std::is_same<remove_cvref_t<X>, int8x2_t>::value) ||
+                                  (std::is_same<remove_cvref_t<T>, int8_t>::value &&
+                                   std::is_same<remove_cvref_t<X>, int8x4_t>::value) ||
+                                  (std::is_same<remove_cvref_t<T>, int8_t>::value &&
+                                   std::is_same<remove_cvref_t<X>, int8x8_t>::value) ||
+                                  (std::is_same<remove_cvref_t<T>, int8_t>::value &&
+                                   std::is_same<remove_cvref_t<X>, int8x16_t>::value) ||
+                                  (std::is_same<remove_cvref_t<T>, int8x4_t>::value &&
+                                   std::is_same<remove_cvref_t<X>, int8x4_t>::value) ||
+                                  (std::is_same<remove_cvref_t<T>, int8x8_t>::value &&
+                                   std::is_same<remove_cvref_t<X>, int8x8_t>::value) ||
+                                  (std::is_same<remove_cvref_t<T>, int8x16_t>::value &&
+                                   std::is_same<remove_cvref_t<X>, int8x16_t>::value),
+                              "wrong! not implemented for this combination, please add "
+                              "implementation");
+
+                if constexpr(std::is_same<remove_cvref_t<T>, int8_t>::value &&
+                             std::is_same<remove_cvref_t<X>, int8_t>::value)
+                {
+                    // HACK: cast pointer of x is bad
+                    // TODO: remove this after compiler fix
+                    *c_style_pointer_cast<int8_t*>(&p_data_[i]) =
+                        *c_style_pointer_cast<const int8_t*>(&x);
+                }
+                else if constexpr(std::is_same<remove_cvref_t<T>, int8_t>::value &&
+                                  std::is_same<remove_cvref_t<X>, int8x2_t>::value)
+                {
+                    // HACK: cast pointer of x is bad
+                    // TODO: remove this after compiler fix
+                    *c_style_pointer_cast<int16_t*>(&p_data_[i]) =
+                        *c_style_pointer_cast<const int16_t*>(&x);
+                }
+                else if constexpr(std::is_same<remove_cvref_t<T>, int8_t>::value &&
+                                  std::is_same<remove_cvref_t<X>, int8x4_t>::value)
+                {
+                    // HACK: cast pointer of x is bad
+                    // TODO: remove this after compiler fix
+                    *c_style_pointer_cast<int32_t*>(&p_data_[i]) =
+                        *c_style_pointer_cast<const int32_t*>(&x);
+                }
+                else if constexpr(std::is_same<remove_cvref_t<T>, int8_t>::value &&
+                                  std::is_same<remove_cvref_t<X>, int8x8_t>::value)
+                {
+                    // HACK: cast pointer of x is bad
+                    // TODO: remove this after compiler fix
+                    *c_style_pointer_cast<int32x2_t*>(&p_data_[i]) =
+                        *c_style_pointer_cast<const int32x2_t*>(&x);
+                }
+                else if constexpr(std::is_same<remove_cvref_t<T>, int8_t>::value &&
+                                  std::is_same<remove_cvref_t<X>, int8x16_t>::value)
+                {
+                    // HACK: cast pointer of x is bad
+                    // TODO: remove this after compiler fix
+                    *c_style_pointer_cast<int32x4_t*>(&p_data_[i]) =
+                        *c_style_pointer_cast<const int32x4_t*>(&x);
+                }
+                else if constexpr(std::is_same<remove_cvref_t<T>, int8x4_t>::value &&
+                                  std::is_same<remove_cvref_t<X>, int8x4_t>::value)
+                {
+                    // HACK: cast pointer of x is bad
+                    // TODO: remove this after compiler fix
+                    *c_style_pointer_cast<int32_t*>(&p_data_[i]) =
+                        *c_style_pointer_cast<const int32_t*>(&x);
+                }
+                else if constexpr(std::is_same<remove_cvref_t<T>, int8x8_t>::value &&
+                                  std::is_same<remove_cvref_t<X>, int8x8_t>::value)
+                {
+                    // HACK: cast pointer of x is bad
+                    // TODO: remove this after compiler fix
+                    *c_style_pointer_cast<int32x2_t*>(&p_data_[i]) =
+                        *c_style_pointer_cast<const int32x2_t*>(&x);
+                }
+                else if constexpr(std::is_same<remove_cvref_t<T>, int8x16_t>::value &&
+                                  std::is_same<remove_cvref_t<X>, int8x16_t>::value)
+                {
+                    // HACK: cast pointer of x is bad
+                    // TODO: remove this after compiler fix
+                    *c_style_pointer_cast<int32x4_t*>(&p_data_[i]) =
+                        *c_style_pointer_cast<const int32x4_t*>(&x);
+                }
+            }
+        }
+        else
+        {
+            if(is_valid_element)
+            {
+#if CK_TILE_EXPERIMENTAL_USE_MEMCPY_FOR_VECTOR_ACCESS
+                X tmp = x;
+
+                __builtin_memcpy(&(p_data_[i]), &tmp, sizeof(X));
+#else
+                using buf_t = ext_vector_t<typename vector_traits<remove_cvref_t<T>>::scalar_type,
+                                           scalar_per_t_vector * scalar_per_x_vector>;
+
+                *c_style_pointer_cast<buf_t*>(&p_data_[i]) = reinterpret_cast<const buf_t&>(x);
+#endif
+            }
+        }
+    }
+
+    // FIXME: remove
+    CK_TILE_DEVICE static constexpr bool is_static_buffer() { return false; }
+
+    // FIXME: remove
+    CK_TILE_DEVICE static constexpr bool is_dynamic_buffer() { return true; }
+
+    CK_TILE_HOST_DEVICE void print() const
+    {
+        printf("buffer_view{");
+
+        // AddressSpace
+        printf("AddressSpace: Lds, ");
+
+        // p_data_
+        printf("p_data_: %p, ", static_cast<void*>(const_cast<remove_cvref_t<T>*>(p_data_)));
+
+        // buffer_size_
+        printf("buffer_size_: ");
+        print(buffer_size_);
+        printf(", ");
+
+        // invalid_element_value_
+        printf("invalid_element_value_: ");
+        print(invalid_element_value_);
+
+        printf("}");
+    }
+};
+
+// Address Space: Vgpr
+// T may be scalar or vector
+// X may be scalar or vector
+// T and X have same scalar type
+// X contains multiple T
+// FIXME: InvalidElementUseNumericalZeroValue and invalid_element_value_ should be a property of
+//        transforms of tensor_view/Tensor
+template <typename T, typename BufferSizeType, bool InvalidElementUseNumericalZeroValue>
+struct buffer_view<address_space_enum::vgpr,
+                   T,
+                   BufferSizeType,
+                   InvalidElementUseNumericalZeroValue,
+                   amd_buffer_coherence_enum::coherence_default>
+{
+    using type = T;
+
+    T* p_data_ = nullptr;
+    BufferSizeType buffer_size_;
+    remove_cvref_t<T> invalid_element_value_ = T{0};
+
+    CK_TILE_HOST_DEVICE constexpr buffer_view()
+        : p_data_{}, buffer_size_{}, invalid_element_value_{}
+    {
+    }
+
+    CK_TILE_HOST_DEVICE constexpr buffer_view(T* p_data, BufferSizeType buffer_size)
+        : p_data_{p_data}, buffer_size_{buffer_size}, invalid_element_value_{0}
+    {
+    }
+
+    CK_TILE_HOST_DEVICE constexpr buffer_view(T* p_data,
+                                              BufferSizeType buffer_size,
+                                              T invalid_element_value)
+        : p_data_{p_data}, buffer_size_{buffer_size}, invalid_element_value_{invalid_element_value}
+    {
+    }
+
+    CK_TILE_DEVICE static constexpr address_space_enum get_address_space()
+    {
+        return address_space_enum::vgpr;
+    }
+
+    // i is offset of T
+    // FIXME: doesn't do is_valid check
+    CK_TILE_DEVICE constexpr const T& operator[](index_t i) const { return p_data_[i]; }
+
+    // i is offset of T
+    // FIXME: doesn't do is_valid check
+    CK_TILE_DEVICE constexpr T& operator()(index_t i) { return p_data_[i]; }
+
+    // i is offset of T, not X. i should be aligned to X
+    template <typename X,
+              bool oob_conditional_check = true,
+              typename std::enable_if<
+                  std::is_same<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                               typename vector_traits<remove_cvref_t<T>>::scalar_type>::value,
+                  bool>::type = false>
+    CK_TILE_DEVICE constexpr auto
+    get(index_t i, bool is_valid_element, bool_constant<oob_conditional_check> = {}) const
+    {
+        // X contains multiple T
+        constexpr index_t scalar_per_t_vector = vector_traits<remove_cvref_t<T>>::vector_size;
+
+        constexpr index_t scalar_per_x_vector = vector_traits<remove_cvref_t<X>>::vector_size;
+
+        static_assert(scalar_per_x_vector % scalar_per_t_vector == 0,
+                      "wrong! X should contain multiple T");
+
+        if(is_valid_element)
+        {
+#if CK_TILE_EXPERIMENTAL_USE_MEMCPY_FOR_VECTOR_ACCESS
+            X tmp;
+
+            __builtin_memcpy(&tmp, &(p_data_[i]), sizeof(X));
+
+            return tmp;
+#else
+            return *c_style_pointer_cast<const X*>(&p_data_[i]);
+#endif
+        }
+        else
+        {
+            if constexpr(InvalidElementUseNumericalZeroValue)
+            {
+                return X{numeric<remove_cvref_t<T>>::zero()};
+            }
+            else
+            {
+                return X{invalid_element_value_};
+            }
+        }
+    }
+
+    // i is offset of T, not X. i should be aligned to X
+    template <memory_operation_enum Op,
+              typename X,
+              typename std::enable_if<
+                  std::is_same<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                               typename vector_traits<remove_cvref_t<T>>::scalar_type>::value,
+                  bool>::type = false>
+    CK_TILE_DEVICE void update(index_t i, bool is_valid_element, const X& x)
+    {
+        if constexpr(Op == memory_operation_enum::set)
+        {
+            this->template set<X>(i, is_valid_element, x);
+        }
+        // FIXME: remove memory_operation_enum::add
+        else if constexpr(Op == memory_operation_enum::add)
+        {
+            auto tmp = this->template get<X>(i, is_valid_element);
+            this->template set<X>(i, is_valid_element, x + tmp);
+        }
+    }
+
+    // i is offset of T, not X. i should be aligned to X
+    template <typename X,
+              typename std::enable_if<
+                  std::is_same<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                               typename vector_traits<remove_cvref_t<T>>::scalar_type>::value,
+                  bool>::type = false>
+    CK_TILE_DEVICE void set(index_t i, bool is_valid_element, const X& x)
+    {
+        // X contains multiple T
+        constexpr index_t scalar_per_t_vector = vector_traits<remove_cvref_t<T>>::vector_size;
+
+        constexpr index_t scalar_per_x_vector = vector_traits<remove_cvref_t<X>>::vector_size;
+
+        static_assert(scalar_per_x_vector % scalar_per_t_vector == 0,
+                      "wrong! X should contain multiple T");
+
+        if(is_valid_element)
+        {
+#if CK_TILE_EXPERIMENTAL_USE_MEMCPY_FOR_VECTOR_ACCESS
+            X tmp = x;
+
+            __builtin_memcpy(&(p_data_[i]), &tmp, sizeof(X));
+#else
+            *c_style_pointer_cast<X*>(&p_data_[i]) = x;
+#endif
+        }
+    }
+
+    // FIXME: remove
+    CK_TILE_DEVICE static constexpr bool is_static_buffer() { return false; }
+
+    // FIXME: remove
+    CK_TILE_DEVICE static constexpr bool is_dynamic_buffer() { return true; }
+
+    CK_TILE_HOST_DEVICE void print() const
+    {
+        printf("buffer_view{");
+
+        // AddressSpace
+        printf("AddressSpace: Vgpr, ");
+
+        // p_data_
+        printf("p_data_: %p, ", static_cast<void*>(const_cast<remove_cvref_t<T>*>(p_data_)));
+
+        // buffer_size_
+        printf("buffer_size_: ");
+        print(buffer_size_);
+        printf(", ");
+
+        // invalid_element_value_
+        printf("invalid_element_value_: ");
+        print(invalid_element_value_);
+
+        printf("}");
+    }
+};
+
+template <address_space_enum BufferAddressSpace,
+          amd_buffer_coherence_enum Coherence = amd_buffer_coherence_enum::coherence_default,
+          typename T,
+          typename BufferSizeType>
+CK_TILE_HOST_DEVICE constexpr auto make_buffer_view(T* p, BufferSizeType buffer_size)
+{
+    return buffer_view<BufferAddressSpace, T, BufferSizeType, true, Coherence>{p, buffer_size};
+}
+
+template <address_space_enum BufferAddressSpace,
+          amd_buffer_coherence_enum Coherence = amd_buffer_coherence_enum::coherence_default,
+          typename T,
+          typename BufferSizeType,
+          typename X,
+          typename std::enable_if<std::is_same<remove_cvref_t<T>, remove_cvref_t<X>>::value,
+                                  bool>::type = false>
+CK_TILE_HOST_DEVICE constexpr auto
+make_buffer_view(T* p, BufferSizeType buffer_size, X invalid_element_value)
+{
+    return buffer_view<BufferAddressSpace, T, BufferSizeType, false, Coherence>{
+        p, buffer_size, invalid_element_value};
+}
+
+} // namespace ck_tile

include/ck_tile/core/tensor/load_tile.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/algorithm/coordinate_transform.hpp"
+#include "ck_tile/core/container/container_helper.hpp"
+#include "ck_tile/core/numeric/math.hpp"
+#include "ck_tile/core/tensor/tile_window.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+#include "ck_tile/core/tensor/tile_window.hpp"
+#include "ck_tile/core/tensor/null_tile_window.hpp"
+#include "ck_tile/core/tensor/null_tensor.hpp"
+
+namespace ck_tile {
+
+template <typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          index_t NumCoord,
+          bool oob_conditional_check = true>
+CK_TILE_DEVICE auto load_tile(const tile_window_with_static_distribution<BottomTensorView_,
+                                                                         WindowLengths_,
+                                                                         TileDistribution_,
+                                                                         NumCoord>& tile_window,
+                              bool_constant<oob_conditional_check> = {})
+{
+    return tile_window.load(bool_constant<oob_conditional_check>{});
+}
+
+template <typename T,
+          typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          index_t NumCoord,
+          bool oob_conditional_check = true>
+CK_TILE_DEVICE auto load_tile_raw(T& tile,
+                                  const tile_window_with_static_distribution<BottomTensorView_,
+                                                                             WindowLengths_,
+                                                                             TileDistribution_,
+                                                                             NumCoord>& tile_window,
+                                  bool_constant<oob_conditional_check> = {})
+{
+    tile_window.load_raw(tile, bool_constant<oob_conditional_check>{});
+}
+
+template <typename LdsTileWindow_,
+          typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          index_t NumCoord>
+CK_TILE_DEVICE auto
+async_load_tile_raw(LdsTileWindow_&& lds_tile,
+                    const tile_window_with_static_distribution<BottomTensorView_,
+                                                               WindowLengths_,
+                                                               TileDistribution_,
+                                                               NumCoord>& tile_window)
+{
+    return tile_window.async_load(lds_tile);
+}
+
+CK_TILE_DEVICE auto async_load_fence(index_t cnt = 0)
+{
+    asm volatile("s_waitcnt vmcnt(%0)" : : "n"(cnt) : "memory");
+}
+
+template <typename WindowLengths>
+CK_TILE_DEVICE auto load_tile(const null_tile_window<WindowLengths>&)
+{
+    return null_tensor{};
+}
+
+template <typename T, typename WindowLengths>
+CK_TILE_DEVICE auto load_tile_raw(T& /*null_tile*/, const null_tile_window<WindowLengths>&)
+{
+}
+
+} // namespace ck_tile

include/ck_tile/core/tensor/null_tensor.hpp

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

include/ck_tile/core/tensor/null_tile_window.hpp

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

include/ck_tile/core/tensor/shuffle_tile.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/utility/functional.hpp"
+#include "ck_tile/core/algorithm/coordinate_transform.hpp"
+#include "ck_tile/core/algorithm/space_filling_curve.hpp"
+#include "ck_tile/core/container/container_helper.hpp"
+#include "ck_tile/core/container/thread_buffer.hpp"
+#include "ck_tile/core/container/statically_indexed_array.hpp"
+#include "ck_tile/core/numeric/math.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+#include "ck_tile/core/tensor/tile_elementwise.hpp"
+#include "ck_tile/core/utility/transpose_vectors.hpp"
+
+namespace ck_tile {
+namespace detail {
+
+template <typename OutTensor, typename InTensor>
+CK_TILE_DEVICE void shuffle_tile_impl_in_thread(OutTensor& out_tensor, const InTensor& in_tensor)
+{
+    constexpr auto I0 = number<0>{};
+
+    using DataType = typename InTensor::DataType;
+
+    constexpr auto y_in_desc  = InTensor::get_tile_distribution().get_ys_to_d_descriptor();
+    constexpr auto y_out_desc = OutTensor::get_tile_distribution().get_ys_to_d_descriptor();
+
+    // y_dim_out_to_in
+    constexpr auto get_rh_major_minor_to_y = [](auto dstr_tensor) {
+        using DstrEncode = typename decltype(dstr_tensor.get_tile_distribution())::DstrEncode;
+
+        map<array<index_t, 2>, index_t> rh_major_minor_to_y_;
+
+        static_for<0, DstrEncode::NDimY, 1>{}([&](auto i) {
+            constexpr index_t rh_major = DstrEncode::ys_to_rhs_major_[i];
+            constexpr index_t rh_minor = DstrEncode::ys_to_rhs_minor_[i];
+
+            rh_major_minor_to_y_({rh_major, rh_minor}) = i;
+        });
+
+        return rh_major_minor_to_y_;
+    };
+
+    constexpr auto rh_major_minor_to_y_in  = get_rh_major_minor_to_y(InTensor{});
+    constexpr auto rh_major_minor_to_y_out = get_rh_major_minor_to_y(OutTensor{});
+
+    constexpr auto y_dim_out_to_in = [&] {
+        map<index_t, index_t> y_dim_out_to_in_;
+
+        for(const auto& [rh_major_minor, y_out] : rh_major_minor_to_y_out)
+        {
+            y_dim_out_to_in_(y_out) = rh_major_minor_to_y_in[rh_major_minor];
+        }
+
+        return y_dim_out_to_in_;
+    }();
+
+    //
+    constexpr index_t NDimY = InTensor::get_tile_distribution().get_num_of_dimension_y();
+
+    constexpr auto y_lengths = to_sequence(y_in_desc.get_lengths());
+
+    // input and output vector dim in the order of input Y dims
+    constexpr index_t y_dim_vec_in  = NDimY - 1;
+    constexpr index_t y_dim_vec_out = y_dim_out_to_in[NDimY - 1];
+
+    // vector lengths
+    constexpr index_t vec_length_in  = y_lengths[y_dim_vec_in];
+    constexpr index_t vec_length_out = y_lengths[y_dim_vec_out];
+
+    // # of vectors
+    constexpr index_t num_vec_in  = vec_length_out;
+    constexpr index_t num_vec_out = vec_length_in;
+
+    using InVec  = array<DataType, vec_length_in>;
+    using OutVec = array<DataType, vec_length_out>;
+
+    // using InVec  = typename InVec::type;
+    // using OutVec = typename OutVec::type;
+
+    // SFC
+    constexpr auto scalars_per_access_arr = generate_array(
+        [&](auto i) { return (i == y_dim_vec_in or i == y_dim_vec_out) ? y_lengths[i] : 1; },
+        number<NDimY>{});
+
+    constexpr auto scalars_per_access = TO_SEQUENCE(scalars_per_access_arr, NDimY);
+
+    using SFC_Y = space_filling_curve<decltype(y_lengths),
+                                      typename arithmetic_sequence_gen<0, NDimY, 1>::type,
+                                      decltype(scalars_per_access)>;
+
+    constexpr index_t num_access = SFC_Y::get_num_of_access();
+
+    static_assert(num_access > 0, "wrong! num_access should be larger than 0");
+
+    // in/out vectors to be transposed
+    thread_buffer<InVec, num_vec_in> in_vectors;
+    thread_buffer<OutVec, num_vec_out> out_vectors;
+
+    // loop over SFC and do transpose
+    static_for<0, num_access, 1>{}([&](auto iAccess) {
+        // data index [y0, y1, ...] in the order of input tensor
+        constexpr auto idx_y_start = SFC_Y::get_index(iAccess);
+
+        // get input vectors
+        static_for<0, num_vec_in, 1>{}([&](auto i) {
+            constexpr auto idx_y_in = generate_array(
+                [&](auto ii) {
+                    return ii == y_dim_vec_out ? idx_y_start[ii] + i : idx_y_start[ii];
+                },
+                number<NDimY>{});
+
+            constexpr index_t in_offset = y_in_desc.calculate_offset(idx_y_in);
+            static_assert(in_offset % vec_length_in == 0);
+
+            in_vectors(i).template get_as<InVec>()(I0) =
+                in_tensor.get_thread_buffer()
+                    .template get_as<InVec>()[number<in_offset / vec_length_in>{}];
+        });
+
+        // transpose
+        transpose_vectors<DataType, num_vec_in, num_vec_out>{}(in_vectors, out_vectors);
+
+        // set output vectors
+        static_for<0, num_vec_out, 1>{}([&](auto i) {
+            constexpr auto idx_y_out_tmp = generate_array(
+                [&](auto ii) { return ii == y_dim_vec_in ? idx_y_start[ii] + i : idx_y_start[ii]; },
+                number<NDimY>{});
+
+            constexpr auto idx_y_out =
+                container_reorder_given_new2old(idx_y_out_tmp, y_dim_out_to_in);
+
+            constexpr index_t out_offset = y_out_desc.calculate_offset(idx_y_out);
+            static_assert(out_offset % vec_length_out == 0);
+
+            out_tensor.get_thread_buffer().template set_as<OutVec>(
+                number<out_offset / vec_length_out>{},
+                out_vectors[i].template get_as<OutVec>()[I0]);
+        });
+    });
+}
+
+} // namespace detail
+
+template <typename OutTensor, typename InTensor>
+CK_TILE_DEVICE void shuffle_tile(OutTensor& out, const InTensor& in)
+{
+    using InDataType  = typename InTensor::DataType;
+    using OutDataType = typename OutTensor::DataType;
+
+    using InDstrEncode  = typename InTensor::StaticTileDistribution::DstrEncode;
+    using OutDstrEncode = typename OutTensor::StaticTileDistribution::DstrEncode;
+
+    // type convert
+    const auto in_tmp = tile_elementwise_in(type_convert<OutDataType, InDataType>, in);
+
+    // shuffle
+    if constexpr(InDstrEncode::rs_lengths_ == OutDstrEncode::rs_lengths_ &&
+                 InDstrEncode::hs_lengthss_ == OutDstrEncode::hs_lengthss_ &&
+                 InDstrEncode::ps_to_rhss_major_ == OutDstrEncode::ps_to_rhss_major_ &&
+                 InDstrEncode::ps_to_rhss_minor_ == OutDstrEncode::ps_to_rhss_minor_ &&
+                 InDstrEncode::NDimY == OutDstrEncode::NDimY)
+    {
+        detail::shuffle_tile_impl_in_thread(out, in_tmp);
+    }
+    else
+    {
+        // NOT implemented
+    }
+}
+
+} // namespace ck_tile

include/ck_tile/core/tensor/slice_tile.hpp

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

include/ck_tile/core/tensor/static_distributed_tensor.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/algorithm/coordinate_transform.hpp"
+#include "ck_tile/core/container/container_helper.hpp"
+#include "ck_tile/core/numeric/math.hpp"
+#include "ck_tile/core/utility/functional.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+#include "ck_tile/core/tensor/tile_distribution.hpp"
+#include "ck_tile/core/container/thread_buffer.hpp"
+
+namespace ck_tile {
+
+template <typename DataType_, typename StaticTileDistribution_>
+struct static_distributed_tensor
+{
+    using DataType               = remove_cvref_t<DataType_>;
+    using StaticTileDistribution = remove_cvref_t<StaticTileDistribution_>;
+
+    static_assert(StaticTileDistribution::is_static(),
+                  "wrong! StaticTileDistribution should be known at compile tile");
+
+    using ThreadTensorDesc =
+        remove_cvref_t<decltype(StaticTileDistribution{}.get_ys_to_d_descriptor())>;
+
+    static constexpr index_t kThreadElementSpaceSize = ThreadTensorDesc{}.get_element_space_size();
+
+    CK_TILE_HOST_DEVICE static constexpr auto get_num_of_dimension()
+    {
+        return StaticTileDistribution::get_num_of_dimension_x();
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr auto get_lengths()
+    {
+        return StaticTileDistribution::get_lengths();
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr auto get_tile_distribution()
+    {
+        return StaticTileDistribution{};
+    }
+
+    CK_TILE_HOST_DEVICE static constexpr auto get_distributed_spans()
+    {
+        return StaticTileDistribution::get_distributed_spans();
+    }
+
+    CK_TILE_HOST_DEVICE void initialize(const DataType& x) { thread_buf_.initialize(x); }
+
+    CK_TILE_HOST_DEVICE constexpr const auto& get_thread_buffer() const { return thread_buf_; }
+
+    CK_TILE_HOST_DEVICE constexpr auto& get_thread_buffer() { return thread_buf_; }
+
+    CK_TILE_HOST_DEVICE static constexpr index_t get_thread_buffer_size()
+    {
+        return kThreadElementSpaceSize;
+    }
+
+    template <index_t... YSliceOrigins, index_t... YSliceLengths>
+    CK_TILE_HOST_DEVICE auto get_y_sliced_thread_data(sequence<YSliceOrigins...>,
+                                                      sequence<YSliceLengths...>) const
+    {
+        static_assert(sizeof...(YSliceOrigins) == StaticTileDistribution::NDimY &&
+                          sizeof...(YSliceLengths) == StaticTileDistribution::NDimY,
+                      "wrong!");
+
+        constexpr auto sliced_thread_tensor_desc =
+            make_naive_tensor_descriptor_packed(make_tuple(YSliceLengths...));
+
+        thread_buffer<DataType, sliced_thread_tensor_desc.get_element_space_size()>
+            sliced_thread_data;
+
+        static_ford<sequence<YSliceLengths...>>{}([&](auto idx) {
+            constexpr auto idx_ys = idx + sequence<YSliceOrigins...>{};
+
+            sliced_thread_data(number<sliced_thread_tensor_desc.calculate_offset(idx)>{}) =
+                thread_buf_[number<ThreadTensorDesc{}.calculate_offset(idx_ys)>{}];
+        });
+
+        return sliced_thread_data;
+    }
+
+    template <index_t... YSliceOrigins, index_t... YSliceLengths, typename SlicedThreadData>
+    CK_TILE_HOST_DEVICE void set_y_sliced_thread_data(sequence<YSliceOrigins...>,
+                                                      sequence<YSliceLengths...>,
+                                                      const SlicedThreadData& sliced_thread_data)
+    {
+        static_assert(sizeof...(YSliceOrigins) == StaticTileDistribution::NDimY &&
+                          sizeof...(YSliceLengths) == StaticTileDistribution::NDimY,
+                      "wrong!");
+
+        constexpr auto sliced_thread_tensor_desc =
+            make_naive_tensor_descriptor_packed(make_tuple(YSliceLengths...));
+
+        static_ford<sequence<YSliceLengths...>>{}([&](auto idx) {
+            constexpr auto idx_ys = idx + sequence<YSliceOrigins...>{};
+
+            thread_buf_(number<ThreadTensorDesc{}.calculate_offset(idx_ys)>{}) =
+                sliced_thread_data[number<sliced_thread_tensor_desc.calculate_offset(idx)>{}];
+        });
+    }
+
+    template <typename TileDistributedIndices>
+    CK_TILE_HOST_DEVICE constexpr const DataType& operator[](TileDistributedIndices) const
+    {
+        static_assert(is_static_v<TileDistributedIndices>,
+                      "wrong! Tile Distributed Indices should be static");
+
+        constexpr auto y_idx = get_tile_distribution().get_y_indices_from_distributed_indices(
+            TileDistributedIndices{});
+
+        return thread_buf_[number<ThreadTensorDesc{}.calculate_offset(y_idx)>{}];
+    }
+
+    template <typename TileDistributedIndices>
+    CK_TILE_HOST_DEVICE constexpr DataType& operator()(TileDistributedIndices)
+    {
+        static_assert(is_static_v<TileDistributedIndices>,
+                      "wrong! Tile Distributed Indices should be static");
+
+        constexpr auto y_idx = get_tile_distribution().get_y_indices_from_distributed_indices(
+            TileDistributedIndices{});
+
+        return thread_buf_(number<ThreadTensorDesc{}.calculate_offset(y_idx)>{});
+    }
+
+    //
+    thread_buffer<DataType, kThreadElementSpaceSize> thread_buf_;
+};
+
+template <typename DataType, typename StaticTileDistribution>
+CK_TILE_HOST_DEVICE constexpr auto make_static_distributed_tensor(const StaticTileDistribution&)
+{
+    return static_distributed_tensor<remove_cvref_t<DataType>,
+                                     remove_cvref_t<StaticTileDistribution>>{};
+}
+
+template <typename DataType, typename StaticTileDistribution, typename ThreadBuffer>
+CK_TILE_HOST_DEVICE constexpr auto make_static_distributed_tensor(const StaticTileDistribution&,
+                                                                  ThreadBuffer&& thread_buffer_)
+{
+    return static_distributed_tensor<remove_cvref_t<DataType>,
+                                     remove_cvref_t<StaticTileDistribution>>{thread_buffer_};
+}
+
+// get X indices from tuple of tile_distributed_index<>
+template <typename StaticTileDistribution, typename DistributedIndices>
+CK_TILE_HOST_DEVICE constexpr auto
+get_x_indices_from_distributed_indices(StaticTileDistribution tile_distribution,
+                                       DistributedIndices distributed_indices)
+{
+    const auto partition_index = detail::get_partition_index(tile_distribution);
+    constexpr auto y_indices =
+        tile_distribution.get_y_indices_from_distributed_indices(distributed_indices);
+
+    const auto x_coord = make_tensor_adaptor_coordinate(
+        tile_distribution.get_ps_ys_to_xs_adaptor(),
+        container_concat(partition_index, to_array<ck_tile::index_t, y_indices.size()>(y_indices)));
+
+    return x_coord.get_bottom_index();
+}
+
+template <typename DataType, typename StaticTileDistribution, typename XIndicesPredicate>
+CK_TILE_HOST_DEVICE void
+set_tile_if(static_distributed_tensor<DataType, StaticTileDistribution>& out_tensor,
+            DataType value,
+            XIndicesPredicate predicate)
+{
+    constexpr auto out_spans =
+        static_distributed_tensor<DataType, StaticTileDistribution>::get_distributed_spans();
+    sweep_tile_span(out_spans[number<0>{}], [&](auto idx0) {
+        sweep_tile_span(out_spans[number<1>{}], [&](auto idx1) {
+            constexpr auto distributed_indices = make_tuple(idx0, idx1);
+            const auto x_indices = get_x_indices_from_distributed_indices(StaticTileDistribution{},
+                                                                          distributed_indices);
+
+            if(predicate(x_indices))
+            {
+                out_tensor(distributed_indices) = value;
+            }
+        });
+    });
+}
+
+} // namespace ck_tile

include/ck_tile/core/tensor/store_tile.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/algorithm/coordinate_transform.hpp"
+#include "ck_tile/core/container/container_helper.hpp"
+#include "ck_tile/core/numeric/math.hpp"
+#include "ck_tile/core/tensor/tile_window.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+
+namespace ck_tile {
+
+template <typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          typename DataType_>
+CK_TILE_DEVICE void
+store_tile(tile_window_with_static_lengths<BottomTensorView_, WindowLengths_>& tile_window_tmp,
+           const static_distributed_tensor<DataType_, TileDistribution_>& dstr_tensor)
+{
+    using DataType = remove_cvref_t<typename BottomTensorView_::DataType>;
+    using TileDstr = remove_cvref_t<TileDistribution_>;
+
+    static_assert(std::is_same_v<remove_cvref_t<DataType_>, DataType>, "wrong!");
+
+    constexpr auto tile_dstr = TileDstr{};
+
+    auto tile_window = make_tile_window(tile_window_tmp.get_bottom_tensor_view(),
+                                        tile_window_tmp.get_window_lengths(),
+                                        tile_window_tmp.get_window_origin(),
+                                        tile_dstr);
+
+    tile_window.store(dstr_tensor);
+}
+
+template <typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          typename DataType_>
+CK_TILE_DEVICE void
+store_tile_raw(tile_window_with_static_lengths<BottomTensorView_, WindowLengths_>& tile_window_tmp,
+               const static_distributed_tensor<DataType_, TileDistribution_>& dstr_tensor)
+{
+    using DataType = remove_cvref_t<typename BottomTensorView_::DataType>;
+    using TileDstr = remove_cvref_t<TileDistribution_>;
+
+    static_assert(std::is_same_v<remove_cvref_t<DataType_>, DataType>, "wrong!");
+
+    constexpr auto tile_dstr = TileDstr{};
+
+    auto tile_window = make_tile_window(tile_window_tmp.get_bottom_tensor_view(),
+                                        tile_window_tmp.get_window_lengths(),
+                                        tile_window_tmp.get_window_origin(),
+                                        tile_dstr);
+
+    tile_window.store_raw(dstr_tensor);
+}
+
+template <typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          index_t NumCoord,
+          typename DataType_>
+CK_TILE_DEVICE void
+store_tile(tile_window_with_static_distribution<BottomTensorView_,
+                                                WindowLengths_,
+                                                TileDistribution_,
+                                                NumCoord>& tile_window,
+           const static_distributed_tensor<DataType_, TileDistribution_>& dstr_tensor)
+{
+    tile_window.store(dstr_tensor);
+}
+
+template <typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          index_t NumCoord,
+          typename DataType_>
+CK_TILE_DEVICE void
+store_tile_raw(tile_window_with_static_distribution<BottomTensorView_,
+                                                    WindowLengths_,
+                                                    TileDistribution_,
+                                                    NumCoord>& tile_window,
+               const static_distributed_tensor<DataType_, TileDistribution_>& dstr_tensor)
+{
+    tile_window.store_raw(dstr_tensor);
+}
+
+} // namespace ck_tile

include/ck_tile/core/tensor/sweep_tile.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/tensor/tile_distribution.hpp"
+#include "ck_tile/core/utility/functional.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+
+namespace ck_tile {
+
+// sweep over a span of a distribted tile and apply lambda function F
+template <typename TileDistributedSpan_, // tile_distributed_span<...>
+          typename F                     // signature: F(tile_distributed_index<...>)
+          >
+CK_TILE_DEVICE void sweep_tile_span(TileDistributedSpan_, const F& f)
+{
+    using DstrSpan = remove_cvref_t<TileDistributedSpan_>;
+
+    static_ford<typename DstrSpan::Impl>{}([&](auto dstr_idx_impl) {
+        constexpr auto dstr_idx = detail::make_tile_distributed_index(dstr_idx_impl);
+
+        f(dstr_idx);
+    });
+}
+
+} // namespace ck_tile

include/ck_tile/core/tensor/tensor_adaptor.hpp

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

include/ck_tile/core/tensor/tensor_adaptor_coordinate.hpp

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

include/ck_tile/core/tensor/tensor_coordinate.hpp

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