topk_softmax (#1592)

* topk_softmax

* remove some file

* fix atomix linear_offset

* address various comment, and change sfc get_index api to static(tuple)

example/ck_tile/09_topk_softmax/CMakeLists.txt

+add_executable(tile_example_topk_softmax EXCLUDE_FROM_ALL topk_softmax.cpp topk_softmax_api.cpp)
+target_include_directories(tile_example_topk_softmax PRIVATE ${CMAKE_CURRENT_SOURCE_DIR}/)
+
+set(EXAMPLE_TOPK_SOFTMAX_COMPILE_OPTIONS)
+# NOTE: we turn off undefined-func-template to let source compile without explicit declare function specializations
+list(APPEND EXAMPLE_TOPK_SOFTMAX_COMPILE_OPTIONS -Wno-undefined-func-template -Wno-float-equal)
+# list(APPEND EXAMPLE_TOPK_SOFTMAX_COMPILE_OPTIONS -v --save-temps -Wno-gnu-line-marker)
+target_compile_options(tile_example_topk_softmax PRIVATE ${EXAMPLE_TOPK_SOFTMAX_COMPILE_OPTIONS})

example/ck_tile/09_topk_softmax/README.md

+# topk-softmax
+
+This folder contains example for topk-softmax kernel using ck_tile tile-programming implementation. This kernel is often used in Moe model, before launching the fused-moe-gemm block. The input is a `token*expert` 2d matrix. The op will do a softmax per row(`expert`), then find the `topk` value for each row. Output is a `token*topk`  weight(usually fp32) and index(int32) 2d tensor.
+
+## build
+```
+# in the root of ck_tile
+mkdir build && cd build
+sh ../script/cmake-ck-dev.sh  ../ <arch>  # you can replace this <arch> to gfx90a, gfx942...
+make tile_example_topk_softmax -j
+```
+This will result in an executable `build/bin/tile_example_topk_softmax`
+
+## example
+```
+args:
+          -v    weather do CPU validation or not (default:1)
+       -pr_i    input data type. fp16/fp32 (representing 8/16/32 bit data) (default:fp16)
+       -pr_w    output weight data type(currently only fp32 supported now) (default:fp32)
+          -t    number of input tokens (default:32)
+          -e    number of experts (default:8)
+          -k    topk (default:2)
+       -st_i    row stride of input, -1 means same as experts (default:-1)
+       -st_o    row stride of output/indices, -1 means same as topk (default:-1)
+       -seed    seed to be used, -1 means random every time (default:-1)
+      -kname    when set to 1 it will print kernel name (default:0)
+
+```

example/ck_tile/09_topk_softmax/script/smoke_test.sh

+#!/bin/sh
+
+EXE=./build/bin/tile_example_topk_softmax
+
+for pr_i in "fp16" "bf16" ; do
+$EXE -pr_i=$pr_i -t=80 -e=17
+$EXE -pr_i=$pr_i -t=111 -e=117
+$EXE -pr_i=$pr_i -t=1000 -e=55
+$EXE -pr_i=$pr_i -t=99 -e=180
+$EXE -pr_i=$pr_i -t=175 -e=64 -k=8
+$EXE -pr_i=$pr_i -t=65 -e=8 -k=2
+$EXE -pr_i=$pr_i -t=1 -e=25
+$EXE -pr_i=$pr_i -t=31 -e=19 -k=15
+$EXE -pr_i=$pr_i -t=81 -e=37 -k=7
+$EXE -pr_i=$pr_i -t=199 -e=128 -k=13
+$EXE -pr_i=$pr_i -t=23 -e=1 -k=1
+$EXE -pr_i=$pr_i -t=127 -e=99 -k=19 -st_i=233 -st_o=31
+$EXE -pr_i=$pr_i -t=71 -e=11 -k=11 -st_i=30 -st_o=12
+$EXE -pr_i=$pr_i -t=1 -e=1 -k=1
+$EXE -pr_i=$pr_i -t=99 -e=2 -k=1 -st_i=11 -st_o=5
+$EXE -pr_i=$pr_i -t=333 -e=99 -k=13 -st_i=191 -st_o=17
+done

example/ck_tile/09_topk_softmax/topk_softmax.cpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#include <vector>
+#include <iostream>
+#include <numeric>
+#include <cassert>
+#include <cstdlib>
+#include <iostream>
+#include <time.h>
+#include <unordered_set>
+
+#include "ck_tile/core.hpp"
+#include "ck_tile/ops/reduce.hpp"
+#include "topk_softmax_api.hpp"
+
+#if 0
+template <typename T>
+void dump_host_tensor_2d(const ck_tile::HostTensor<T>& x)
+{
+    auto len = x.get_lengths();
+    assert(len.size() == 2);
+    std::cout << "[";
+    for(size_t i = 0; i < len[0]; i++)
+    {
+        std::cout << i << ": [";
+        for(size_t j = 0; j < len[1]; j++)
+        {
+            if constexpr(std::is_same_v<T, ck_tile::fp16_t>)
+            {
+                auto v = ck_tile::type_convert<float>(x(i, j));
+
+                std::cout << v;
+                if(j != len[1] - 1)
+                    std::cout << ",";
+            }
+            else
+            {
+                std::cout << x(i, j) << " ";
+            }
+        }
+        std::cout << "]";
+        if(i != len[0] - 1)
+            std::cout << ",";
+        else
+            std::cout << "]";
+        std::cout << std::endl;
+    }
+    std::cout << "--------------------" << std::endl;
+}
+#endif
+
+// CPU reference
+template <typename InputType, typename WeightType, typename IndexType = ck_tile::index_t>
+auto reference_topk_softmax(const ck_tile::HostTensor<InputType>& x,
+                            ck_tile::index_t k,
+                            ck_tile::index_t dim = -1,
+                            bool largest         = true,
+                            bool sorted          = true)
+{
+    using namespace ck_tile;
+
+    auto y = reference_softmax<InputType, WeightType, WeightType>(x, dim);
+
+    auto [y_values, y_indices] = reference_topk(y, k, dim, largest, sorted);
+
+    return ck_tile::make_tuple(y_values, y_indices);
+}
+
+template <typename InputType, typename WeightType, typename IndexType = ck_tile::index_t>
+auto reference_topk_softmax(const ck_tile::HostTensor<InputType>& x,
+                            ck_tile::HostTensor<WeightType>& y_values,
+                            ck_tile::HostTensor<IndexType>& y_indices,
+                            ck_tile::index_t k,
+                            ck_tile::index_t dim = -1,
+                            bool largest         = true,
+                            bool sorted          = true)
+{
+    using namespace ck_tile;
+
+    auto y = reference_softmax<InputType, WeightType, WeightType>(x, dim);
+    reference_topk(y, y_values, y_indices, k, dim, largest, sorted);
+}
+
+// different threshold for different dtype
+template <typename DataType>
+auto get_elimit(std::string /*init_method*/)
+{
+    double rtol = 1e-3;
+    double atol = 1e-3;
+    return ck_tile::make_tuple(rtol, atol);
+}
+
+template <>
+auto get_elimit<ck_tile::bf16_t>(std::string /*init_method*/)
+{
+    double rtol = 1e-2;
+    double atol = 1e-2;
+    return ck_tile::make_tuple(rtol, atol);
+}
+
+template <>
+auto get_elimit<ck_tile::fp8_t>(std::string init_method)
+{
+    if(init_method == "ui" || init_method == "ni")
+    {
+        unsigned max_rounding_point_distance = 0;
+        double atol                          = 2e-3;
+        return ck_tile::make_tuple(max_rounding_point_distance, atol);
+    }
+    else
+    {
+        unsigned max_rounding_point_distance = 1;
+        double atol                          = 0.0625;
+        return ck_tile::make_tuple(max_rounding_point_distance, atol);
+    }
+}
+
+auto create_args(int argc, char* argv[])
+{
+    ck_tile::ArgParser arg_parser;
+    arg_parser.insert("v", "1", "weather do CPU validation or not")
+        .insert("pr_i", "fp16", "input data type. fp16/fp32 (representing 8/16/32 bit data)")
+        .insert("pr_w", "fp32", "output weight data type(currently only fp32 supported now)")
+        .insert("t", "32", "number of input tokens")
+        .insert("e", "8", "number of experts")
+        .insert("k", "2", "topk")
+        .insert("st_i", "-1", "row stride of input, -1 means same as experts")
+        .insert("st_o", "-1", "row stride of output/indices, -1 means same as topk")
+        .insert("seed", "-1", "seed to be used, -1 means random every time")
+        .insert("kname", "0", "when set to 1 it will print kernel name")
+        .insert("warmup", "5", "number of iterations before benchmark the kernel")
+        .insert("repeat", "20", "number of iterations to benchmark the kernel");
+
+    bool result = arg_parser.parse(argc, argv);
+    return std::make_tuple(result, arg_parser);
+}
+
+template <typename InputType, typename WeightType, typename IndexType = ck_tile::index_t>
+bool test_topk_softmax(ck_tile::ArgParser args)
+{
+    int validate            = args.get_int("v");
+    std::string input_prec  = args.get_str("pr_i");
+    std::string weight_prec = args.get_str("pr_w");
+    int tokens              = args.get_int("t");
+    int experts             = args.get_int("e");
+    int topk                = args.get_int("k");
+    int seed                = args.get_int("seed");
+    int stride_input        = args.get_int("st_i");
+    int stride_output       = args.get_int("st_o");
+    int kname               = args.get_int("kname");
+    int warmup              = args.get_int("warmup");
+    int repeat              = args.get_int("repeat");
+
+    if(stride_input < 0)
+    {
+        stride_input = experts;
+    }
+    if(stride_output < 0)
+    {
+        stride_output = topk;
+    }
+    assert(stride_input >= experts);
+    assert(stride_output >= topk);
+
+    if(seed < 0)
+    {
+        seed = std::time(nullptr);
+    }
+
+    if(topk > experts)
+    {
+        printf("topk:%d value should be smaller than, or equal to number of experts:%d\n",
+               topk,
+               experts);
+        return false;
+    }
+
+    // tokens already considered batch size
+    ck_tile::HostTensor<InputType> x_host({tokens, experts}, {stride_input, 1});
+    ck_tile::HostTensor<WeightType> value_host({tokens, topk}, {stride_output, 1});
+    ck_tile::HostTensor<IndexType> index_host({tokens, topk}, {stride_output, 1});
+
+    {
+        // random require per-row unique
+        auto rand_gen = ck_tile::FillUniformDistribution_Unique<InputType>{
+            -5.f, 5.f, static_cast<uint32_t>(seed)};
+
+        for(int i_t = 0; i_t < tokens; i_t++)
+        {
+            ck_tile::HostTensor<InputType> x_row({experts});
+            rand_gen(x_row);
+            std::copy(x_row.begin(), x_row.end(), x_host.begin() + i_t * stride_input);
+            rand_gen.clear();
+        }
+    }
+
+    ck_tile::DeviceMem x_dev(x_host.get_element_space_size_in_bytes());
+    ck_tile::DeviceMem value_dev(value_host.get_element_space_size_in_bytes());
+    ck_tile::DeviceMem index_dev(index_host.get_element_space_size_in_bytes());
+
+    x_dev.ToDevice(x_host.data());
+
+    topk_softmax_trait trait{input_prec, weight_prec, experts};
+
+    topk_softmax_kargs karg{x_dev.GetDeviceBuffer(),
+                            value_dev.GetDeviceBuffer(),
+                            index_dev.GetDeviceBuffer(),
+                            tokens,
+                            experts,
+                            topk,
+                            stride_input,
+                            stride_output};
+
+    ck_tile::stream_config sc{nullptr,
+                              true,
+                              /* log_level = */ (kname ? 1 : 0),
+                              warmup,
+                              repeat};
+    auto ms = topk_softmax(trait, karg, sc);
+    printf("[%s|%s]tokens:%d, experts:%d, topk:%d, st_i:%d, st_o:%d, ms:%f, ",
+           input_prec.c_str(),
+           weight_prec.c_str(),
+           tokens,
+           experts,
+           topk,
+           stride_input,
+           stride_output,
+           ms);
+    if(ms < 0)
+        printf("not supported\n");
+    fflush(stdout);
+    if(ms < 0)
+    {
+        return false;
+    }
+
+    value_dev.FromDevice(value_host.data());
+    index_dev.FromDevice(index_host.data());
+
+    bool rtn = true;
+    if(validate)
+    {
+        ck_tile::HostTensor<WeightType> value_ref({tokens, topk}, {stride_output, 1});
+        ck_tile::HostTensor<IndexType> index_ref({tokens, topk}, {stride_output, 1});
+
+        reference_topk_softmax<InputType, WeightType, IndexType>(
+            x_host, value_ref, index_ref, topk);
+
+        auto [rtol, atol] = get_elimit<InputType>("");
+        for(int i_t = 0; i_t < tokens; i_t++)
+        {
+            auto s_begin = std::vector<size_t>{static_cast<size_t>(i_t), static_cast<size_t>(0)};
+            auto s_end =
+                std::vector<size_t>{static_cast<size_t>(i_t + 1), static_cast<size_t>(topk)};
+            auto s_value_host = value_host.slice(s_begin, s_end);
+            auto s_value_ref  = value_ref.slice(s_begin, s_end);
+            rtn &= ck_tile::check_err(s_value_host,
+                                      s_value_ref,
+                                      std::string("[") + std::to_string(i_t) +
+                                          std::string("] Value Error:"),
+                                      rtol,
+                                      atol);
+            auto s_index_host = index_host.slice(s_begin, s_end);
+            auto s_index_ref  = index_ref.slice(s_begin, s_end);
+            rtn &= ck_tile::check_err(s_index_host,
+                                      s_index_ref,
+                                      std::string("[") + std::to_string(i_t) +
+                                          std::string("] Index Error:"),
+                                      rtol,
+                                      atol);
+        }
+    }
+
+    printf("valid:%s\n", rtn ? "y" : "n");
+    fflush(stdout);
+    return rtn;
+}
+
+int main(int argc, char** argv)
+{
+    auto [result, args] = create_args(argc, argv);
+    if(!result)
+        return -1;
+    std::string input_prec  = args.get_str("pr_i");
+    std::string weight_prec = args.get_str("pr_w");
+
+    bool r = true;
+    if(input_prec.compare("fp16") == 0 && weight_prec.compare("fp32") == 0)
+    {
+        r &= test_topk_softmax<ck_tile::fp16_t, float, ck_tile::index_t>(args);
+    }
+    else if(input_prec.compare("bf16") == 0 && weight_prec.compare("fp32") == 0)
+    {
+        r &= test_topk_softmax<ck_tile::bf16_t, float, ck_tile::index_t>(args);
+    }
+
+    return r ? 0 : -1;
+}

example/ck_tile/09_topk_softmax/topk_softmax_api.cpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#include "topk_softmax_api.hpp"
+
+#define TOPK_SOFTMAX_DISPATCH(experts_)                                                         \
+    constexpr ck_tile::index_t ts_experts = experts_;                                           \
+    using ts_problem                      = ck_tile::                                           \
+        TopkSoftmaxWarpPerRowProblem<ts_input_type, ts_weight_type, ts_index_type, ts_experts>; \
+    using ts_pipeline = ck_tile::TopkSoftmaxWarpPerRowPipeline<ts_problem>;                     \
+                                                                                                \
+    using kernel = ck_tile::TopkSoftmaxKernel<ts_pipeline>;                                     \
+                                                                                                \
+    auto kargs = kernel::MakeKargs(a);                                                          \
+                                                                                                \
+    const dim3 grids      = kernel::GridSize(a);                                                \
+    constexpr dim3 blocks = kernel::BlockSize();                                                \
+                                                                                                \
+    float ave_time = ck_tile::launch_kernel(                                                    \
+        s, ck_tile::make_kernel<blocks.x, 1>(kernel{}, grids, blocks, 0, kargs));               \
+                                                                                                \
+    return ave_time;
+
+float topk_softmax(topk_softmax_trait t, topk_softmax_kargs a, ck_tile::stream_config s)
+{
+    if(t.input_type == "fp16" && t.weight_type == "fp32")
+    {
+        using ts_input_type  = ck_tile::fp16_t;
+        using ts_weight_type = float;
+        using ts_index_type  = ck_tile::index_t;
+#if 1
+        if(t.experts <= 8)
+        {
+            TOPK_SOFTMAX_DISPATCH(8)
+        }
+        else if(t.experts <= 16)
+        {
+            TOPK_SOFTMAX_DISPATCH(16)
+        }
+        else if(t.experts <= 32)
+        {
+            TOPK_SOFTMAX_DISPATCH(32)
+        }
+        else if(t.experts <= 64)
+        {
+            TOPK_SOFTMAX_DISPATCH(64)
+        }
+        else if(t.experts <= 128)
+        {
+            TOPK_SOFTMAX_DISPATCH(128)
+        }
+        else if(t.experts <= 192)
+        {
+            TOPK_SOFTMAX_DISPATCH(192)
+        }
+#else
+        if(t.experts <= 128)
+        {
+            TOPK_SOFTMAX_DISPATCH(128)
+        }
+#endif
+    }
+    else if(t.input_type == "bf16" && t.weight_type == "fp32")
+    {
+#if 1
+        using ts_input_type  = ck_tile::bf16_t;
+        using ts_weight_type = float;
+        using ts_index_type  = ck_tile::index_t;
+        if(t.experts <= 8)
+        {
+            TOPK_SOFTMAX_DISPATCH(8)
+        }
+        else if(t.experts <= 16)
+        {
+            TOPK_SOFTMAX_DISPATCH(16)
+        }
+        else if(t.experts <= 32)
+        {
+            TOPK_SOFTMAX_DISPATCH(32)
+        }
+        else if(t.experts <= 64)
+        {
+            TOPK_SOFTMAX_DISPATCH(64)
+        }
+        else if(t.experts <= 128)
+        {
+            TOPK_SOFTMAX_DISPATCH(128)
+        }
+        else if(t.experts <= 192)
+        {
+            TOPK_SOFTMAX_DISPATCH(192)
+        }
+#endif
+    }
+    return -1;
+}

example/ck_tile/09_topk_softmax/topk_softmax_api.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+#include "ck_tile/core.hpp"
+#include "ck_tile/host.hpp"
+#include "ck_tile/ops/topk_softmax.hpp"
+#include <string>
+
+struct topk_softmax_trait
+{
+    std::string input_type;
+    std::string weight_type; // currently always float
+    int experts;
+};
+
+struct topk_softmax_kargs : public ck_tile::TopkSoftmaxHostArgs
+{
+};
+
+float topk_softmax(topk_softmax_trait t, topk_softmax_kargs a, ck_tile::stream_config s);

example/ck_tile/CMakeLists.txt

@@ -7,3 +7,5 @@ add_subdirectory(02_layernorm2d)
 add_subdirectory(03_gemm)
 add_subdirectory(04_img2col)
 add_subdirectory(05_reduce)
+add_subdirectory(09_topk_softmax)
+

include/ck_tile/core.hpp

@@ -49,6 +49,7 @@
 #include "ck_tile/core/tensor/tile_distribution_encoding.hpp"
 #include "ck_tile/core/tensor/tile_elementwise.hpp"
 #include "ck_tile/core/tensor/tile_window.hpp"
+#include "ck_tile/core/tensor/tile_window_linear.hpp"
 #include "ck_tile/core/tensor/update_tile.hpp"
 #include "ck_tile/core/utility/bit_cast.hpp"
 #include "ck_tile/core/utility/functional.hpp"

include/ck_tile/core/algorithm/space_filling_curve.hpp

 // SPDX-License-Identifier: MIT
-// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+// Copyright (c) 2024, Advanced Micro Devices, Inc. All rights reserved.
 
 #pragma once
 
@@ -81,8 +81,10 @@ struct space_filling_curve
         return get_step_between(number<AccessIdx1d>{}, number<AccessIdx1d - 1>{});
     }
 
+    // Do not use this function directly!
+    // TODO: can refactor into generic lambda in the future
     template <index_t AccessIdx1d>
-    static CK_TILE_HOST_DEVICE constexpr Index get_index(number<AccessIdx1d>)
+    static CK_TILE_HOST_DEVICE constexpr Index _get_index(number<AccessIdx1d>)
     {
 #if 0
         /*
@@ -153,11 +155,11 @@ struct space_filling_curve
         return idx_md;
     }
 
-    // FIXME: rename this function
+    // FIXME: return tuple of number<>, which is compile time only variable
     template <index_t AccessIdx1d>
-    static CK_TILE_HOST_DEVICE constexpr auto get_index_tuple_of_number(number<AccessIdx1d>)
+    static CK_TILE_HOST_DEVICE constexpr auto get_index(number<AccessIdx1d>)
     {
-        constexpr auto idx = get_index(number<AccessIdx1d>{});
+        constexpr auto idx = _get_index(number<AccessIdx1d>{});
 
         return generate_tuple([&](auto i) { return number<idx[i]>{}; }, number<nDim>{});
     }

include/ck_tile/core/arch/amd_buffer_addressing.hpp

@@ -621,6 +621,99 @@ CK_TILE_DEVICE void buffer_load_fence(index_t cnt = 0)
     asm volatile("s_waitcnt vmcnt(%0)" : : "n"(cnt) : "memory");
 }
 
+namespace impl {
+// below type indicate the data type used for buffer load inline asm
+// clang-format off
+template<index_t N, typename T> struct smem_load_trait;
+
+template<typename T> struct smem_load_trait<16, T> { using payload_t = fp32x4_t; };
+template<typename T> struct smem_load_trait<8 , T> { using payload_t = fp32x2_t; };
+template<typename T> struct smem_load_trait<4 , T> { using payload_t = float; };
+template<typename T> struct smem_load_trait<2 , T> { using payload_t = float; };
+template<typename T> struct smem_load_trait<1 , T> { using payload_t = float; };
+
+// clang-format on
+} // namespace impl
+
+// NOTE: smem load/store no need pre_nop to make sure dependency by sw, happy :)
+template <index_t>
+struct smem_load;
+
+template <>
+struct smem_load<16>
+{
+    template <typename T>
+    CK_TILE_DEVICE void operator()(T& value, index_t v_offset, index_t i_offset)
+    {
+        static_assert(sizeof(T) == 16);
+        using mbuf_t = typename impl::smem_load_trait<16, T>::payload_t;
+        asm volatile("ds_read_b128 %0, %1 offset:%2"
+                     : "=v"(reinterpret_cast<mbuf_t&>(value)) // ! direct write
+                     : "v"(v_offset), "n"(i_offset)
+                     : "memory");
+    }
+};
+
+template <>
+struct smem_load<8>
+{
+    template <typename T>
+    CK_TILE_DEVICE void operator()(T& value, index_t v_offset, index_t i_offset)
+    {
+        static_assert(sizeof(T) == 8);
+        using mbuf_t = typename impl::smem_load_trait<8, T>::payload_t;
+        asm volatile("ds_read_b64 %0, %1 offset:%2"
+                     : "=v"(reinterpret_cast<mbuf_t&>(value)) // ! direct write
+                     : "v"(v_offset), "n"(i_offset)
+                     : "memory");
+    }
+};
+
+template <>
+struct smem_load<4>
+{
+    template <typename T>
+    CK_TILE_DEVICE void operator()(T& value, index_t v_offset, index_t i_offset)
+    {
+        static_assert(sizeof(T) == 4);
+        using mbuf_t = typename impl::smem_load_trait<4, T>::payload_t;
+        asm volatile("ds_read_b32 %0, %1 offset:%2"
+                     : "=v"(reinterpret_cast<mbuf_t&>(value)) // ! direct write
+                     : "v"(v_offset), "n"(i_offset)
+                     : "memory");
+    }
+};
+
+template <>
+struct smem_load<2>
+{
+    template <typename T>
+    CK_TILE_DEVICE void operator()(T& value, index_t v_offset, index_t i_offset)
+    {
+        static_assert(sizeof(T) == 4); // subdword is buggy, use dword buf and convert manually
+        using mbuf_t = typename impl::smem_load_trait<1, T>::payload_t;
+        asm volatile("ds_read_u16 %0, %1 offset:%2"
+                     : "=v"(reinterpret_cast<mbuf_t&>(value)) // ! direct write
+                     : "v"(v_offset), "n"(i_offset)
+                     : "memory");
+    }
+};
+
+template <>
+struct smem_load<1>
+{
+    template <typename T>
+    CK_TILE_DEVICE void operator()(T& value, index_t v_offset, index_t i_offset)
+    {
+        static_assert(sizeof(T) == 4);
+        using mbuf_t = typename impl::smem_load_trait<1, T>::payload_t;
+        asm volatile("ds_read_u8 %0, %1 offset:%2"
+                     : "=v"(reinterpret_cast<mbuf_t&>(value)) // ! direct write
+                     : "v"(v_offset), "n"(i_offset)
+                     : "memory");
+    }
+};
+
 // clang-format off
 namespace impl{
 
@@ -976,6 +1069,16 @@ llvm_amdgcn_raw_buffer_atomic_max_fp64(double vdata,
                                        int soffset,    // dst_wave_addr_offset
                                        int glc_slc) __asm("llvm.amdgcn.raw.buffer.atomic.fmax.f64");
 
+// Direct loads from global to LDS.
+CK_TILE_DEVICE_EXTERN void
+llvm_amdgcn_raw_buffer_load_lds(int32x4_t rsrc,
+                                __attribute__((address_space(3))) uint32_t* lds_ptr,
+                                index_t size,
+                                index_t voffset,
+                                index_t soffset,
+                                index_t offset,
+                                index_t aux) __asm("llvm.amdgcn.raw.buffer.load.lds");
+
 template <bool pre_nop = false>
 CK_TILE_DEVICE void async_buffer_load_dword_v(void* smem,
                                               int32x4_t rsrc,
@@ -1313,6 +1416,7 @@ CK_TILE_DEVICE void amd_buffer_load_raw_impl(thread_buffer<T, N>& dst,
                                              int32x4_t src_wave_buffer_resource,
                                              index_t src_thread_addr_offset,
                                              index_t src_wave_addr_offset,
+                                             index_t src_linear_addr_offset,
                                              index_t flag           = 0,
                                              bool_constant<pre_nop> = {})
 {
@@ -1327,7 +1431,7 @@ CK_TILE_DEVICE void amd_buffer_load_raw_impl(thread_buffer<T, N>& dst,
                                                 src_wave_buffer_resource,
                                                 src_thread_addr_offset,
                                                 src_wave_addr_offset,
-                                                0,
+                                                src_linear_addr_offset,
                                                 flag,
                                                 bool_constant<pre_nop>{});
     }
@@ -1337,7 +1441,7 @@ CK_TILE_DEVICE void amd_buffer_load_raw_impl(thread_buffer<T, N>& dst,
                                              src_wave_buffer_resource,
                                              src_thread_addr_offset,
                                              src_wave_addr_offset,
-                                             0,
+                                             src_linear_addr_offset,
                                              flag,
                                              bool_constant<pre_nop>{});
     }
@@ -1365,6 +1469,43 @@ CK_TILE_DEVICE void amd_async_buffer_load_impl(T* smem,
                               bool_constant<pre_nop>{});
 }
 
+template <typename T,
+          index_t N,
+          amd_buffer_coherence_enum coherence = amd_buffer_coherence_enum::coherence_default,
+          bool oob_conditional_check          = true>
+CK_TILE_DEVICE void amd_async_buffer_load(CK_TILE_LDS_ADDR T* smem,
+                                          int32x4_t src_wave_buffer_resource,
+                                          index_t src_thread_addr_offset,
+                                          index_t src_wave_addr_offset,
+                                          index_t src_immediate_addr_offset    = 0,
+                                          index_t flag                         = 0,
+                                          bool_constant<oob_conditional_check> = {})
+{
+    static_assert(sizeof(T) * N == 4, "wrong! not implemented vector size");
+
+    if constexpr(oob_conditional_check)
+    {
+        index_t v_offset = flag ? v_offset : src_wave_buffer_resource[2];
+        llvm_amdgcn_raw_buffer_load_lds(src_wave_buffer_resource,
+                                        smem,
+                                        sizeof(uint32_t),
+                                        v_offset,
+                                        src_wave_addr_offset,
+                                        src_immediate_addr_offset,
+                                        static_cast<index_t>(coherence));
+    }
+    else
+    {
+        llvm_amdgcn_raw_buffer_load_lds(src_wave_buffer_resource,
+                                        smem,
+                                        sizeof(uint32_t),
+                                        src_thread_addr_offset,
+                                        src_wave_addr_offset,
+                                        src_immediate_addr_offset,
+                                        static_cast<index_t>(coherence));
+    }
+}
+
 template <index_t N,
           amd_buffer_coherence_enum coherence = amd_buffer_coherence_enum::coherence_default>
 CK_TILE_DEVICE void amd_buffer_store_impl_with_bytes(const thread_buffer<int8_t, N> src_thread_data,
@@ -1685,6 +1826,7 @@ CK_TILE_DEVICE void amd_buffer_store_raw_impl(const thread_buffer<T, N>& dst_thr
                                               int32x4_t dst_wave_buffer_resource,
                                               index_t dst_thread_addr_offset,
                                               index_t dst_wave_addr_offset,
+                                              index_t dst_linear_addr_offset,
                                               index_t is_valid_element = 1)
 {
     constexpr index_t bytes = sizeof(T) * N;
@@ -1698,7 +1840,7 @@ CK_TILE_DEVICE void amd_buffer_store_raw_impl(const thread_buffer<T, N>& dst_thr
                                         dst_wave_buffer_resource,
                                         dst_thread_addr_offset,
                                         dst_wave_addr_offset,
-                                        0,
+                                        dst_linear_addr_offset,
                                         is_valid_element);
     }
     else
@@ -1707,7 +1849,7 @@ CK_TILE_DEVICE void amd_buffer_store_raw_impl(const thread_buffer<T, N>& dst_thr
                                      dst_wave_buffer_resource,
                                      dst_thread_addr_offset,
                                      dst_wave_addr_offset,
-                                     0);
+                                     dst_linear_addr_offset);
     }
 }
 
@@ -2014,6 +2156,7 @@ template <typename T,
 CK_TILE_DEVICE void amd_buffer_load_raw(thread_buffer<T, N>& dst,
                                         const T* p_src_wave,
                                         index_t src_thread_element_offset,
+                                        index_t src_linear_element_offset,
                                         index_t src_element_space_size,
                                         index_t is_valid_element = 0,
                                         bool_constant<pre_nop>   = {})
@@ -2022,12 +2165,14 @@ CK_TILE_DEVICE void amd_buffer_load_raw(thread_buffer<T, N>& dst,
         make_wave_buffer_resource(p_src_wave, src_element_space_size * sizeof(T));
 
     index_t src_thread_addr_offset = src_thread_element_offset * sizeof(T);
+    index_t src_linear_addr_offset = src_linear_element_offset * sizeof(T);
 
     amd_buffer_load_raw_impl<T, N, coherence, oob_conditional_check, pre_nop>(
         dst,
         src_wave_buffer_resource,
         src_thread_addr_offset,
         0,
+        src_linear_addr_offset,
         is_valid_element,
         bool_constant<pre_nop>{});
 }
@@ -2041,16 +2186,19 @@ template <typename T,
 CK_TILE_DEVICE void amd_buffer_load_raw(thread_buffer<T, N>& dst,
                                         const int32x4_t src_wave_buffer_resource,
                                         index_t src_thread_element_offset,
+                                        index_t src_linear_element_offset,
                                         index_t is_valid_element = 0,
                                         bool_constant<pre_nop>   = {})
 {
     index_t src_thread_addr_offset = src_thread_element_offset * sizeof(T);
+    index_t src_linear_addr_offset = src_linear_element_offset * sizeof(T);
 
     amd_buffer_load_raw_impl<T, N, coherence, oob_conditional_check, pre_nop>(
         dst,
         src_wave_buffer_resource,
         src_thread_addr_offset,
         0,
+        src_linear_addr_offset,
         is_valid_element,
         bool_constant<pre_nop>{});
 }
@@ -2066,6 +2214,7 @@ template <typename T,
 CK_TILE_DEVICE void amd_async_buffer_load_with_oob_raw(T* smem,
                                                        const T* p_src_wave,
                                                        index_t src_thread_element_offset,
+                                                       index_t src_linear_element_offset,
                                                        index_t src_element_space_size,
                                                        bool_constant<pre_nop> = {})
 {
@@ -2073,9 +2222,14 @@ CK_TILE_DEVICE void amd_async_buffer_load_with_oob_raw(T* smem,
         make_wave_buffer_resource(p_src_wave, src_element_space_size * sizeof(T));
 
     index_t src_thread_addr_offset = src_thread_element_offset * sizeof(T);
+    index_t src_linear_addr_offset = src_linear_element_offset * sizeof(T);
 
-    amd_async_buffer_load_impl<T, N, coherence>(
-        smem, src_wave_buffer_resource, src_thread_addr_offset, 0, 0, bool_constant<pre_nop>{});
+    amd_async_buffer_load_impl<T, N, coherence>(smem,
+                                                src_wave_buffer_resource,
+                                                src_thread_addr_offset,
+                                                0,
+                                                src_linear_addr_offset,
+                                                bool_constant<pre_nop>{});
 }
 
 // This version support buffer resource as input arg
@@ -2086,12 +2240,42 @@ template <typename T,
 CK_TILE_DEVICE void amd_async_buffer_load_with_oob_raw(T* smem,
                                                        const int32x4_t src_wave_buffer_resource,
                                                        index_t src_thread_element_offset,
+                                                       index_t src_linear_element_offset,
                                                        bool_constant<pre_nop> = {})
 {
     index_t src_thread_addr_offset = src_thread_element_offset * sizeof(T);
+    index_t src_linear_addr_offset = src_linear_element_offset * sizeof(T);
 
-    amd_async_buffer_load_impl<T, N, coherence>(
-        smem, src_wave_buffer_resource, src_thread_addr_offset, 0, 0, bool_constant<pre_nop>{});
+    amd_async_buffer_load_impl<T, N, coherence>(smem,
+                                                src_wave_buffer_resource,
+                                                src_thread_addr_offset,
+                                                0,
+                                                src_linear_addr_offset,
+                                                bool_constant<pre_nop>{});
+}
+
+// This version support buffer resource as input arg
+template <typename T,
+          index_t N,
+          amd_buffer_coherence_enum coherence = amd_buffer_coherence_enum::coherence_default,
+          bool oob_conditional_check          = false>
+CK_TILE_DEVICE void amd_async_buffer_load_with_oob(CK_TILE_LDS_ADDR T* smem,
+                                                   const int32x4_t src_wave_buffer_resource,
+                                                   index_t src_thread_element_offset,
+                                                   index_t src_linear_element_offset,
+                                                   bool is_valid_element,
+                                                   bool_constant<oob_conditional_check> = {})
+{
+    index_t src_thread_addr_offset = src_thread_element_offset * sizeof(T);
+    index_t src_linear_addr_offset = src_linear_element_offset * sizeof(T);
+
+    amd_async_buffer_load<T, N, coherence>(smem,
+                                           src_wave_buffer_resource,
+                                           src_thread_addr_offset,
+                                           0,
+                                           src_linear_addr_offset,
+                                           is_valid_element,
+                                           bool_constant<oob_conditional_check>{});
 }
 
 // buffer_store requires:
@@ -2146,6 +2330,7 @@ template <typename T,
 CK_TILE_DEVICE void amd_buffer_store_raw(const thread_buffer<T, N>& src_thread_data,
                                          T* p_dst_wave,
                                          const index_t dst_thread_element_offset,
+                                         const index_t dst_linear_element_offset,
                                          const bool dst_thread_element_valid,
                                          const index_t dst_element_space_size)
 {
@@ -2153,11 +2338,13 @@ CK_TILE_DEVICE void amd_buffer_store_raw(const thread_buffer<T, N>& src_thread_d
         make_wave_buffer_resource(p_dst_wave, dst_element_space_size * sizeof(T));
 
     index_t dst_thread_addr_offset = dst_thread_element_offset * sizeof(T);
+    index_t dst_linear_addr_offset = dst_linear_element_offset * sizeof(T);
 
     amd_buffer_store_raw_impl<T, N, coherence, oob_conditional_check>(src_thread_data,
                                                                       dst_wave_buffer_resource,
                                                                       dst_thread_addr_offset,
                                                                       0,
+                                                                      dst_linear_addr_offset,
                                                                       dst_thread_element_valid);
 }
 
@@ -2221,16 +2408,6 @@ CK_TILE_DEVICE void amd_buffer_atomic_max(const thread_buffer<T, N>& src_thread_
 #endif
 }
 
-// Direct loads from global to LDS.
-CK_TILE_DEVICE_EXTERN void
-llvm_amdgcn_raw_buffer_load_lds(int32x4_t rsrc,
-                                __attribute__((address_space(3))) uint32_t* lds_ptr,
-                                index_t size,
-                                index_t voffset,
-                                index_t soffset,
-                                index_t offset,
-                                index_t aux) __asm("llvm.amdgcn.raw.buffer.load.lds");
-
 template <typename T, index_t NumElemsPerThread>
 CK_TILE_DEVICE void amd_direct_load_global_to_lds(const T* global_base_ptr,
                                                   const index_t global_offset,

include/ck_tile/core/config.hpp

@@ -41,6 +41,19 @@
 #define CK_TILE_HOST_DEVICE_EXTERN
 #endif
 
+// implementing the "memory address space" attribute
+// https://llvm.org/docs/AMDGPUUsage.html#amdgpu-address-spaces-table
+#ifdef __HIPCC_
+#define CK_TILE_GENERIC_ADDR __attribute__((address_space(0)))
+#define CK_TILE_GLOBAL_ADDR __attribute__((address_space(1)))
+#define CK_TILE_LDS_ADDR __attribute__((address_space(3)))
+#define CK_TILE_BUF_RES_ADDR __attribute__((address_space(8)))
+#else
+#define CK_TILE_GENERIC_ADDR
+#define CK_TILE_GLOBAL_ADDR
+#define CK_TILE_LDS_ADDR
+#define CK_TILE_BUF_RES_ADDR
+#endif
 #ifndef CK_TILE_USE_CUSTOM_DATA_TYPE
 #define CK_TILE_USE_CUSTOM_DATA_TYPE 0 // custom data type will generate extra move/bfi code
 #endif
@@ -205,3 +218,8 @@
 #ifndef CK_TILE_BUFFER_LOAD_RAW_BF16_WA
 #define CK_TILE_BUFFER_LOAD_RAW_BF16_WA 1
 #endif
+
+// workaround: compiler not emiting reciprocal instruction frm __frcp_rn()
+#ifndef CK_TILE_WORKAROUND_SWDEV_383542
+#define CK_TILE_WORKAROUND_SWDEV_383542 1
+#endif

include/ck_tile/core/container/tuple.hpp

@@ -623,7 +623,7 @@ template <typename... Ys,
               false>
 CK_TILE_HOST_DEVICE constexpr auto operator+=(tuple<Ys...>& y, const X& x)
 {
-    static_assert(X::Size() == sizeof...(Ys), "wrong! size not the same");
+    static_assert(X::size() == sizeof...(Ys), "wrong! size not the same");
     constexpr index_t NSize = sizeof...(Ys);
     static_for<0, NSize, 1>{}([&](auto i) { y[i] += x[i]; });
     return y;
@@ -635,7 +635,7 @@ template <typename... Ys,
               false>
 CK_TILE_HOST_DEVICE constexpr auto operator-=(tuple<Ys...>& y, const X& x)
 {
-    static_assert(X::Size() == sizeof...(Ys), "wrong! size not the same");
+    static_assert(X::size() == sizeof...(Ys), "wrong! size not the same");
     constexpr index_t NSize = sizeof...(Ys);
     static_for<0, NSize, 1>{}([&](auto i) { y[i] -= x[i]; });
     return y;
@@ -647,7 +647,7 @@ template <typename... Xs,
               false>
 CK_TILE_HOST_DEVICE constexpr auto operator+(const tuple<Xs...>& x, const Y& y)
 {
-    static_assert(Y::Size() == sizeof...(Xs), "wrong! size not the same");
+    static_assert(Y::size() == sizeof...(Xs), "wrong! size not the same");
     constexpr index_t NSize = sizeof...(Xs);
 
     tuple<Xs...> r;
@@ -655,13 +655,21 @@ CK_TILE_HOST_DEVICE constexpr auto operator+(const tuple<Xs...>& x, const Y& y)
     return r;
 }
 
+template <typename... Xs, typename... Ys>
+CK_TILE_HOST_DEVICE constexpr auto operator+(const tuple<Xs...>& x, const tuple<Ys...>& y)
+{
+    static_assert(sizeof...(Xs) == sizeof...(Ys), "wrong!");
+    constexpr index_t NSize = sizeof...(Xs);
+    return generate_tuple([&](auto i) { return x[i] + y[i]; }, number<NSize>{});
+}
+
 template <typename... Xs,
           typename Y,
           std::enable_if_t<!std::is_integral<Y>::value && !std::is_floating_point<Y>::value, bool> =
               false>
 CK_TILE_HOST_DEVICE constexpr auto operator-(const tuple<Xs...>& x, const Y& y)
 {
-    static_assert(Y::Size() == sizeof...(Xs), "wrong! size not the same");
+    static_assert(Y::size() == sizeof...(Xs), "wrong! size not the same");
     constexpr index_t NSize = sizeof...(Xs);
 
     tuple<Xs...> r;
@@ -669,13 +677,21 @@ CK_TILE_HOST_DEVICE constexpr auto operator-(const tuple<Xs...>& x, const Y& y)
     return r;
 }
 
+template <typename... Xs, typename... Ys>
+CK_TILE_HOST_DEVICE constexpr auto operator-(const tuple<Xs...>& x, const tuple<Ys...>& y)
+{
+    static_assert(sizeof...(Xs) == sizeof...(Ys), "wrong!");
+    constexpr index_t NSize = sizeof...(Xs);
+    return generate_tuple([&](auto i) { return x[i] - y[i]; }, number<NSize>{});
+}
+
 template <typename... Xs,
           typename Y,
           std::enable_if_t<!std::is_integral<Y>::value && !std::is_floating_point<Y>::value, bool> =
               false>
 CK_TILE_HOST_DEVICE constexpr auto operator*(const tuple<Xs...>& x, const Y& y)
 {
-    static_assert(Y::Size() == sizeof...(Xs), "wrong! size not the same");
+    static_assert(Y::size() == sizeof...(Xs), "wrong! size not the same");
     constexpr index_t NSize = sizeof...(Xs);
 
     tuple<Xs...> r;
@@ -706,6 +722,14 @@ CK_TILE_HOST_DEVICE constexpr auto operator*(const tuple<Xs...>& x, Y a)
     return a * x;
 }
 
+template <typename... Xs, typename... Ys>
+CK_TILE_HOST_DEVICE constexpr auto operator*(const tuple<Xs...>& x, const tuple<Ys...>& y)
+{
+    static_assert(sizeof...(Xs) == sizeof...(Ys), "wrong!");
+    constexpr index_t NSize = sizeof...(Xs);
+    return generate_tuple([&](auto i) { return x[i] * y[i]; }, number<NSize>{});
+}
+
 template <typename... Xs, typename... Ys>
 CK_TILE_HOST_DEVICE constexpr auto operator/(const tuple<Xs...>& x, const tuple<Ys...>& y)
 {

include/ck_tile/core/numeric/math.hpp

@@ -487,55 +487,12 @@ struct log2e<float>
 template <typename T = double>
 constexpr T log2e_v = log2e<T>::value;
 
-// math
-CK_TILE_HOST_DEVICE
-float abs(const float& x)
-{
-    union
-    {
-        float f32;
-        uint32_t u32;
-    } y;
-    y.f32 = x;
-    y.u32 = y.u32 & 0x7fffffff;
-    return y.f32;
-}
-
-CK_TILE_HOST_DEVICE
-bool isnan(const float& x)
-{
-    uint32_t xx = bit_cast<uint32_t>(x);
-    return (xx & 0x7fffffff) > 0x7F800000;
-}
-
-CK_TILE_HOST float sqrt(float x) { return std::sqrt(x); };
-
-CK_TILE_HOST double sqrt(double x) { return std::sqrt(x); };
-
-CK_TILE_DEVICE
-float sqrt(float x) { return __builtin_amdgcn_sqrtf(x); };
-
-CK_TILE_DEVICE
-double sqrt(double x) { return __builtin_amdgcn_sqrt(x); };
-
-CK_TILE_DEVICE
-float exp(float x) { return __ocml_exp_f32(x); };
-
-CK_TILE_HOST
-float exp(float x) { return std::expf(x); }
-
 CK_TILE_DEVICE
 float exp2(float x) { return exp2f(x); };
 
 CK_TILE_HOST
 float exp2(float x) { return std::exp2f(x); };
 
-CK_TILE_DEVICE
-float log(float x) { return __logf(x); };
-
-CK_TILE_HOST
-float log(float x) { return std::logf(x); };
-
 CK_TILE_DEVICE uint16_t sad_u16(uint16_t x, uint16_t y, uint16_t acc)
 {
     return __builtin_amdgcn_sad_u16(x, y, acc);
@@ -554,4 +511,933 @@ CK_TILE_HOST uint32_t sad_u32(uint32_t x, uint32_t y, uint32_t acc)
     return (x > y ? (x - y) : (y - x)) + acc;
 }
 
+///////////////////////////////////////////////////////////////
+
+} // namespace ck_tile
+// blow function need data type pre-defined
+#include "ck_tile/core/numeric/half.hpp"
+#include "ck_tile/core/numeric/bfloat16.hpp"
+#include "ck_tile/core/numeric/float8.hpp"
+#include "ck_tile/core/numeric/type_convert.hpp"
+#ifndef __HIP_DEVICE_COMPILE__
+#include <cmath>
+#endif
+
+namespace ck_tile {
+#if CK_TILE_WORKAROUND_SWDEV_383542
+extern "C" CK_TILE_DEVICE float __ocml_native_recip_f32(float);
+#endif
+
+// math functions for the host,  some are implemented by calling C++ std functions
+
+CK_TILE_HOST float abs(float x) { return std::abs(x); };
+
+CK_TILE_HOST double abs(double x) { return std::abs(x); };
+
+CK_TILE_HOST int8_t abs(int8_t x)
+{
+    int8_t sgn = x >> (8 - 1);
+
+    return (x ^ sgn) - sgn;
+};
+
+CK_TILE_HOST int32_t abs(int32_t x)
+{
+    int32_t sgn = x >> (32 - 1);
+
+    return (x ^ sgn) - sgn;
+};
+
+CK_TILE_HOST fp16_t abs(fp16_t x)
+{
+    uint16_t xx = bit_cast<uint16_t>(x);
+
+    uint16_t abs_xx = xx & 0x7fff;
+
+    fp16_t abs_x = bit_cast<fp16_t>(abs_xx);
+
+    return abs_x;
+};
+
+#ifdef CK_TILE_EXPERIMENTAL_BIT_INT_EXTENSION_INT4
+CK_TILE_HOST int4_t abs(int4_t x)
+{
+    int4_t sgn = x >> (4 - 1);
+    return (x ^ sgn) - sgn;
+}
+#endif
+
+CK_TILE_HOST bool isnan(float x) { return std::isnan(x); };
+
+CK_TILE_HOST bool isnan(double x) { return std::isnan(x); };
+
+CK_TILE_HOST bool isnan(int8_t x)
+{
+    (void)x;
+    return false;
+};
+
+CK_TILE_HOST bool isnan(int32_t x)
+{
+    (void)x;
+    return false;
+};
+
+CK_TILE_HOST bool isnan(fp16_t x)
+{
+    uint16_t xx = bit_cast<uint16_t>(x);
+
+    return (xx & 0x7FFF) > 0x7C00;
+};
+
+#ifdef CK_TILE_EXPERIMENTAL_BIT_INT_EXTENSION_INT4
+CK_TILE_HOST bool isnan(int4_t x)
+{
+    (void)x;
+    return false;
+};
+#endif
+
+CK_TILE_HOST fp16_t sqrt(fp16_t x)
+{
+    return static_cast<fp16_t>(std::sqrt(static_cast<float>(x)));
+};
+
+CK_TILE_HOST float sqrt(float x) { return std::sqrt(x); };
+
+CK_TILE_HOST double sqrt(double x) { return std::sqrt(x); };
+
+template <typename T>
+CK_TILE_HOST T tanh(T x)
+{
+    return type_convert<T>(std::tanhf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_HOST float tanh<float>(float x)
+{
+    return std::tanhf(x);
+};
+
+template <>
+CK_TILE_HOST double tanh<double>(double x)
+{
+    return std::tanh(x);
+};
+
+template <typename T>
+CK_TILE_HOST T acos(T x)
+{
+    return type_convert<T>(std::acosf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_HOST float acos<float>(float x)
+{
+    return std::acosf(x);
+};
+
+template <>
+CK_TILE_HOST double acos<double>(double x)
+{
+    return std::acos(x);
+};
+
+template <typename T>
+CK_TILE_HOST T neg(T x)
+{
+    return type_convert<T>(-(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_HOST float neg<float>(float x)
+{
+    return -x;
+};
+
+template <>
+CK_TILE_HOST double neg<double>(double x)
+{
+    return -x;
+};
+
+template <>
+CK_TILE_HOST int32_t neg<int32_t>(int32_t x)
+{
+    return -x;
+};
+
+template <>
+CK_TILE_HOST int8_t neg<int8_t>(int8_t x)
+{
+    return -x;
+};
+
+template <typename T>
+CK_TILE_HOST T atan(T x)
+{
+    return type_convert<T>(std::atanf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_HOST float atan<float>(float x)
+{
+    return std::atanf(x);
+};
+
+template <>
+CK_TILE_HOST double atan<double>(double x)
+{
+    return std::atan(x);
+};
+
+template <typename T>
+CK_TILE_HOST T sin(T x)
+{
+    return type_convert<T>(std::sinf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_HOST float sin<float>(float x)
+{
+    return std::sinf(x);
+};
+
+template <>
+CK_TILE_HOST double sin<double>(double x)
+{
+    return std::sin(x);
+};
+
+template <typename T>
+CK_TILE_HOST T asin(T x)
+{
+    return type_convert<T>(std::asinf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_HOST float asin<float>(float x)
+{
+    return std::asinf(x);
+};
+
+template <>
+CK_TILE_HOST double asin<double>(double x)
+{
+    return std::asin(x);
+};
+
+template <typename T>
+CK_TILE_HOST T asinh(T x)
+{
+    return type_convert<T>(std::asinhf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_HOST float asinh<float>(float x)
+{
+    return std::asinhf(x);
+};
+
+template <>
+CK_TILE_HOST double asinh<double>(double x)
+{
+    return std::asinh(x);
+};
+
+template <typename T>
+CK_TILE_HOST T cos(T x)
+{
+    return type_convert<T>(std::cosf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_HOST float cos<float>(float x)
+{
+    return std::cosf(x);
+};
+
+template <>
+CK_TILE_HOST double cos<double>(double x)
+{
+    return std::cos(x);
+};
+
+template <typename T>
+CK_TILE_HOST T acosh(T x)
+{
+    return type_convert<T>(std::acoshf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_HOST float acosh<float>(float x)
+{
+    return std::acoshf(x);
+};
+
+template <>
+CK_TILE_HOST double acosh<double>(double x)
+{
+    return std::acosh(x);
+};
+
+template <typename T>
+CK_TILE_HOST T tan(T x)
+{
+    return type_convert<T>(std::tanf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_HOST float tan<float>(float x)
+{
+    return std::tanf(x);
+};
+
+template <>
+CK_TILE_HOST double tan<double>(double x)
+{
+    return std::tan(x);
+};
+
+template <typename T>
+CK_TILE_HOST T atanh(T x)
+{
+    return type_convert<T>(std::atanhf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_HOST float atanh<float>(float x)
+{
+    return std::atanhf(x);
+};
+
+template <>
+CK_TILE_HOST double atanh<double>(double x)
+{
+    return std::atanh(x);
+};
+
+template <typename T>
+CK_TILE_HOST T sinh(T x)
+{
+    return type_convert<T>(std::sinhf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_HOST float sinh<float>(float x)
+{
+    return std::sinhf(x);
+};
+
+template <>
+CK_TILE_HOST double sinh<double>(double x)
+{
+    return std::sinh(x);
+};
+
+template <typename T>
+CK_TILE_HOST T ceil(T x)
+{
+    return type_convert<T>(std::ceilf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_HOST float ceil<float>(float x)
+{
+    return std::ceilf(x);
+};
+
+template <>
+CK_TILE_HOST double ceil<double>(double x)
+{
+    return std::ceil(x);
+};
+
+template <typename T>
+CK_TILE_HOST T cosh(T x)
+{
+    return type_convert<T>(std::coshf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_HOST float cosh<float>(float x)
+{
+    return std::coshf(x);
+};
+
+template <>
+CK_TILE_HOST double cosh<double>(double x)
+{
+    return std::cosh(x);
+};
+
+template <typename T>
+CK_TILE_HOST T floor(T x)
+{
+    return type_convert<T>(std::floorf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_HOST float floor<float>(float x)
+{
+    return std::floorf(x);
+};
+
+template <>
+CK_TILE_HOST double floor<double>(double x)
+{
+    return std::floor(x);
+};
+
+template <typename T>
+CK_TILE_HOST T rcp(T x)
+{
+    return type_convert<T>(1.f / type_convert<float>(x));
+};
+
+template <typename T>
+CK_TILE_HOST T exp(T x)
+{
+    return type_convert<T>(std::expf(type_convert<float>(x)));
+}
+
+template <>
+CK_TILE_HOST float exp<float>(float x)
+{
+    return std::expf(x);
+}
+
+template <>
+CK_TILE_HOST double exp<double>(double x)
+{
+    return std::exp(x);
+}
+
+template <typename T>
+CK_TILE_HOST T log(T x)
+{
+    return type_convert<T>(std::logf(type_convert<float>(x)));
+}
+
+template <>
+CK_TILE_HOST float log<float>(float x)
+{
+    return std::logf(x);
+}
+
+template <>
+CK_TILE_HOST double log<double>(double x)
+{
+    return std::log(x);
+}
+
+template <typename T>
+CK_TILE_HOST T pow(T x, T gamma)
+{
+    return type_convert<T>(std::powf(type_convert<float>(x), type_convert<float>(gamma)));
+}
+
+template <>
+CK_TILE_HOST float pow<float>(float x, float gamma)
+{
+    return std::powf(x, gamma);
+}
+
+template <>
+CK_TILE_HOST double pow<double>(double x, double gamma)
+{
+    return std::pow(x, gamma);
+}
+
+template <typename T>
+CK_TILE_HOST T expm1(T x)
+{
+    return type_convert<T>(std::expm1f(type_convert<float>(x)));
+}
+
+template <>
+CK_TILE_HOST float expm1<float>(float x)
+{
+    return std::expm1f(x);
+}
+
+template <>
+CK_TILE_HOST double expm1<double>(double x)
+{
+    return std::expm1(x);
+}
+
+// math functions for the HIP kernel,  some are implemented by calling hip builtin functions
+
+CK_TILE_DEVICE float abs(float x)
+{
+    union
+    {
+        float f32;
+        uint32_t u32;
+    } y;
+    y.f32 = x;
+    y.u32 = y.u32 & 0x7fffffff;
+    return y.f32;
+};
+
+CK_TILE_DEVICE double abs(double x) { return ::abs(x); };
+
+CK_TILE_DEVICE int8_t abs(int8_t x)
+{
+    int8_t sgn = x >> (8 - 1);
+
+    return (x ^ sgn) - sgn;
+};
+
+CK_TILE_DEVICE int32_t abs(int32_t x)
+{
+    int32_t sgn = x >> (32 - 1);
+
+    return (x ^ sgn) - sgn;
+};
+
+#ifdef CK_TILE_EXPERIMENTAL_BIT_INT_EXTENSION_INT4
+CK_TILE_DEVICE int4_t abs(int4_t x)
+{
+    int4_t sgn = x >> (4 - 1);
+
+    return (x ^ sgn) - sgn;
+};
+#endif
+
+CK_TILE_DEVICE fp16_t abs(fp16_t x)
+{
+    uint16_t xx = bit_cast<uint16_t>(x);
+
+    uint16_t abs_xx = xx & 0x7fff;
+
+    fp16_t abs_x = bit_cast<fp16_t>(abs_xx);
+
+    return abs_x;
+};
+
+CK_TILE_DEVICE bool isnan(float x) { return ::isnan(x); };
+
+CK_TILE_DEVICE bool isnan(double x) { return ::isnan(x); };
+
+CK_TILE_DEVICE bool isnan(int8_t x)
+{
+    (void)x;
+    return false;
+};
+
+CK_TILE_DEVICE bool isnan(int32_t x)
+{
+    (void)x;
+    return false;
+};
+
+#ifdef CK_TILE_EXPERIMENTAL_BIT_INT_EXTENSION_INT4
+CK_TILE_DEVICE bool isnan(int4_t x)
+{
+    (void)x;
+    return false;
+};
+#endif
+
+CK_TILE_DEVICE bool isnan(fp16_t x)
+{
+    uint16_t xx = bit_cast<uint16_t>(x);
+
+    return (xx & 0x7FFF) > 0x7C00;
+};
+
+CK_TILE_DEVICE fp16_t sqrt(fp16_t x)
+{
+    return static_cast<fp16_t>(__builtin_amdgcn_sqrtf(static_cast<float>(x)));
+};
+
+CK_TILE_DEVICE float sqrt(float x) { return __builtin_amdgcn_sqrtf(x); };
+
+CK_TILE_DEVICE double sqrt(double x) { return __builtin_amdgcn_sqrt(x); };
+
+template <typename T>
+CK_TILE_DEVICE T tanh(T x)
+{
+    return type_convert<T>(::tanhf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_DEVICE float tanh<float>(float x)
+{
+    return ::tanhf(x);
+};
+
+template <>
+CK_TILE_DEVICE double tanh<double>(double x)
+{
+    return ::tanh(x);
+};
+
+template <typename T>
+CK_TILE_DEVICE T acos(T x)
+{
+    return type_convert<T>(::acosf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_DEVICE float acos<float>(float x)
+{
+    return ::acosf(x);
+};
+
+template <>
+CK_TILE_DEVICE double acos<double>(double x)
+{
+    return ::acos(x);
+};
+
+template <typename T>
+CK_TILE_DEVICE T neg(T x)
+{
+    return type_convert<T>(-(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_DEVICE float neg<float>(float x)
+{
+    return -x;
+};
+
+template <>
+CK_TILE_DEVICE double neg<double>(double x)
+{
+    return -x;
+};
+
+template <>
+CK_TILE_DEVICE int32_t neg<int32_t>(int32_t x)
+{
+    return -x;
+};
+
+template <>
+CK_TILE_DEVICE int8_t neg<int8_t>(int8_t x)
+{
+    return -x;
+};
+
+template <>
+CK_TILE_DEVICE fp16_t neg<fp16_t>(fp16_t x)
+{
+    return __hneg(x);
+};
+
+template <typename T>
+CK_TILE_DEVICE T atan(T x)
+{
+    return type_convert<T>(::atanf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_DEVICE float atan<float>(float x)
+{
+    return ::atanf(x);
+};
+
+template <>
+CK_TILE_DEVICE double atan<double>(double x)
+{
+    return ::atan(x);
+};
+
+template <typename T>
+CK_TILE_DEVICE T sin(T x)
+{
+    return type_convert<T>(::sinf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_DEVICE float sin<float>(float x)
+{
+    return ::sinf(x);
+};
+
+template <>
+CK_TILE_DEVICE double sin<double>(double x)
+{
+    return ::sin(x);
+};
+
+template <>
+CK_TILE_DEVICE fp16_t sin<fp16_t>(fp16_t x)
+{
+    return ::hsin(x);
+};
+
+template <typename T>
+CK_TILE_DEVICE T asin(T x)
+{
+    return type_convert<T>(::asinf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_DEVICE float asin<float>(float x)
+{
+    return ::asinf(x);
+};
+
+template <>
+CK_TILE_DEVICE double asin<double>(double x)
+{
+    return ::asin(x);
+};
+
+template <typename T>
+CK_TILE_DEVICE T asinh(T x)
+{
+    return type_convert<T>(::asinhf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_DEVICE float asinh<float>(float x)
+{
+    return ::asinhf(x);
+};
+
+template <>
+CK_TILE_DEVICE double asinh<double>(double x)
+{
+    return ::asinh(x);
+};
+
+template <typename T>
+CK_TILE_DEVICE T acosh(T x)
+{
+    return type_convert<T>(::acoshf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_DEVICE float acosh<float>(float x)
+{
+    return ::acoshf(x);
+};
+
+template <>
+CK_TILE_DEVICE double acosh<double>(double x)
+{
+    return ::acosh(x);
+};
+
+template <typename T>
+CK_TILE_DEVICE T tan(T x)
+{
+    return type_convert<T>(::tanf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_DEVICE float tan<float>(float x)
+{
+    return ::tanf(x);
+};
+
+template <>
+CK_TILE_DEVICE double tan<double>(double x)
+{
+    return ::tan(x);
+};
+
+template <typename T>
+CK_TILE_DEVICE T atanh(T x)
+{
+    return type_convert<T>(::atanhf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_DEVICE float atanh<float>(float x)
+{
+    return ::atanhf(x);
+};
+
+template <>
+CK_TILE_DEVICE double atanh<double>(double x)
+{
+    return ::atanh(x);
+};
+
+template <typename T>
+CK_TILE_DEVICE T sinh(T x)
+{
+    return type_convert<T>(::sinhf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_DEVICE float sinh<float>(float x)
+{
+    return ::sinhf(x);
+};
+
+template <>
+CK_TILE_DEVICE double sinh<double>(double x)
+{
+    return ::sinh(x);
+};
+
+template <typename T>
+CK_TILE_DEVICE T ceil(T x)
+{
+    return type_convert<T>(::ceilf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_DEVICE float ceil<float>(float x)
+{
+    return ::ceilf(x);
+};
+
+template <>
+CK_TILE_DEVICE double ceil<double>(double x)
+{
+    return ::ceil(x);
+};
+
+template <>
+CK_TILE_DEVICE fp16_t ceil<fp16_t>(fp16_t x)
+{
+    return ::hceil(x);
+};
+
+template <typename T>
+CK_TILE_DEVICE T cosh(T x)
+{
+    return type_convert<T>(::coshf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_DEVICE float cosh<float>(float x)
+{
+    return ::coshf(x);
+};
+
+template <>
+CK_TILE_DEVICE double cosh<double>(double x)
+{
+    return ::cosh(x);
+};
+
+template <typename T>
+CK_TILE_DEVICE T floor(T x)
+{
+    return type_convert<T>(::floorf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_DEVICE float floor<float>(float x)
+{
+    return ::floorf(x);
+};
+
+template <>
+CK_TILE_DEVICE double floor<double>(double x)
+{
+    return ::floor(x);
+};
+
+template <>
+CK_TILE_DEVICE fp16_t floor<fp16_t>(fp16_t x)
+{
+    return ::hfloor(x);
+};
+
+template <typename T>
+CK_TILE_DEVICE T rcp(T x)
+{
+#if !CK_TILE_WORKAROUND_SWDEV_383542
+    return __frcp_rn(x);
+#else
+    // return __ocml_native_recip_f32(x);
+    return __builtin_amdgcn_rcpf(x);
+#endif
+};
+
+template <typename T>
+CK_TILE_DEVICE T exp(T x)
+{
+    return type_convert<T>(__ocml_exp_f32(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_DEVICE fp16_t exp<fp16_t>(fp16_t x)
+{
+    return hexp(x);
+};
+
+template <>
+CK_TILE_DEVICE float exp<float>(float x)
+{
+    return __ocml_exp_f32(x);
+};
+
+template <>
+CK_TILE_DEVICE double exp<double>(double x)
+{
+    return exp(x);
+};
+
+template <typename T>
+CK_TILE_DEVICE T log(T x)
+{
+    return type_convert<T>(__logf(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_DEVICE fp16_t log<fp16_t>(fp16_t x)
+{
+    return hlog(x);
+};
+
+template <>
+CK_TILE_DEVICE float log<float>(float x)
+{
+    return __logf(x);
+};
+
+template <>
+CK_TILE_DEVICE double log<double>(double x)
+{
+    return log(x);
+};
+
+template <typename T>
+CK_TILE_DEVICE T pow(T x, T gamma)
+{
+    return type_convert<T>(powf(type_convert<float>(x), type_convert<float>(gamma)));
+};
+
+template <>
+CK_TILE_DEVICE float pow<float>(float x, float gamma)
+{
+    return powf(x, gamma);
+};
+
+template <>
+CK_TILE_DEVICE double pow<double>(double x, double gamma)
+{
+    return pow(x, gamma);
+};
+
+template <typename T>
+CK_TILE_DEVICE T expm1(T x)
+{
+    return type_convert<T>(expm1f(type_convert<float>(x)));
+};
+
+template <>
+CK_TILE_DEVICE float expm1<float>(float x)
+{
+    return expm1f(x);
+};
+
+template <>
+CK_TILE_DEVICE double expm1<double>(double x)
+{
+    return expm1(x);
+};
+
 } // namespace ck_tile

include/ck_tile/core/tensor/buffer_view.hpp

@@ -91,8 +91,10 @@ struct buffer_view<address_space_enum::generic,
                   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
+    CK_TILE_DEVICE constexpr auto get(index_t i,
+                                      index_t linear_offset,
+                                      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;
@@ -107,11 +109,11 @@ struct buffer_view<address_space_enum::generic,
 #if CK_TILE_EXPERIMENTAL_USE_MEMCPY_FOR_VECTOR_ACCESS
             X tmp;
 
-            __builtin_memcpy(&tmp, &(p_data_[i]), sizeof(X));
+            __builtin_memcpy(&tmp, &(p_data_[i + linear_offset]), sizeof(X));
 
             return tmp;
 #else
-            return *c_style_pointer_cast<const X*>(&p_data_[i]);
+            return *c_style_pointer_cast<const X*>(&p_data_[i + linear_offset]);
 #endif
         }
         else
@@ -134,17 +136,17 @@ struct buffer_view<address_space_enum::generic,
                   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)
+    CK_TILE_DEVICE void update(index_t i, index_t linear_offset, bool is_valid_element, const X& x)
     {
         if constexpr(Op == memory_operation_enum::set)
         {
-            this->template set<X>(i, is_valid_element, x);
+            this->template set<X>(i, linear_offset, 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);
+            auto tmp = this->template get<X>(i, linear_offset, is_valid_element);
+            this->template set<X>(i, linear_offset, is_valid_element, x + tmp);
         }
     }
 
@@ -154,7 +156,7 @@ struct buffer_view<address_space_enum::generic,
                   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)
+    CK_TILE_DEVICE void set(index_t i, index_t linear_offset, 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;
@@ -169,9 +171,9 @@ struct buffer_view<address_space_enum::generic,
 #if CK_TILE_EXPERIMENTAL_USE_MEMCPY_FOR_VECTOR_ACCESS
             X tmp = x;
 
-            __builtin_memcpy(&(p_data_[i]), &tmp, sizeof(X));
+            __builtin_memcpy(&(p_data_[i + linear_offset]), &tmp, sizeof(X));
 #else
-            *c_style_pointer_cast<X*>(&p_data_[i]) = x;
+            *c_style_pointer_cast<X*>(&p_data_[i + linear_offset]) = x;
 #endif
         }
     }
@@ -276,8 +278,10 @@ struct buffer_view<address_space_enum::global,
                   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
+    CK_TILE_DEVICE constexpr auto get(index_t i,
+                                      index_t linear_offset,
+                                      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;
@@ -303,7 +307,7 @@ struct buffer_view<address_space_enum::global,
                                                                    t_per_x,
                                                                    Coherence,
                                                                    oob_conditional_check>(
-                    p_data_, i, is_valid_element, buffer_size_);
+                    p_data_, i + linear_offset, is_valid_element, buffer_size_);
             }
             else
             {
@@ -311,8 +315,11 @@ struct buffer_view<address_space_enum::global,
                     remove_cvref_t<T>,
                     t_per_x,
                     Coherence,
-                    oob_conditional_check>(
-                    p_data_, i, is_valid_element, buffer_size_, invalid_element_value_);
+                    oob_conditional_check>(p_data_,
+                                           i + linear_offset,
+                                           is_valid_element,
+                                           buffer_size_,
+                                           invalid_element_value_);
             }
         }
         else
@@ -322,11 +329,11 @@ struct buffer_view<address_space_enum::global,
 #if CK_TILE_EXPERIMENTAL_USE_MEMCPY_FOR_VECTOR_ACCESS
                 X tmp;
 
-                __builtin_memcpy(&tmp, &(p_data_[i]), sizeof(X));
+                __builtin_memcpy(&tmp, &(p_data_[i + linear_offset]), sizeof(X));
 
                 return tmp;
 #else
-                return *c_style_pointer_cast<const X*>(&p_data_[i]);
+                return *c_style_pointer_cast<const X*>(&p_data_[i + linear_offset]);
 #endif
             }
             else
@@ -352,7 +359,8 @@ struct buffer_view<address_space_enum::global,
                                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,
+                                          index_t v_offset,
+                                          index_t i_offset,
                                           bool is_valid_element,
                                           bool_constant<pre_nop> = {}) const
     {
@@ -366,7 +374,38 @@ struct buffer_view<address_space_enum::global,
         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, pre_nop>(
-            dst, cached_buf_res_, i, is_valid_element, bool_constant<pre_nop>{});
+            dst, cached_buf_res_, v_offset, i_offset, is_valid_element, bool_constant<pre_nop>{});
+    }
+
+    // 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 async_get(CK_TILE_LDS_ADDR remove_cvref_t<T>* smem,
+                                            index_t i,
+                                            index_t linear_offset,
+                                            bool is_valid_element,
+                                            bool_constant<oob_conditional_check> = {}) 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,
+            cached_buf_res_,
+            i,
+            linear_offset,
+            is_valid_element,
+            bool_constant<oob_conditional_check>{});
     }
 
     // i is offset of T, not X. i should be aligned to X
@@ -378,6 +417,7 @@ struct buffer_view<address_space_enum::global,
                   bool>::type = false>
     CK_TILE_DEVICE constexpr auto async_get_raw(remove_cvref_t<T>* smem,
                                                 index_t i,
+                                                index_t linear_offset,
                                                 bool /*is_valid_element*/,
                                                 bool_constant<pre_nop> = {}) const
     {
@@ -391,7 +431,7 @@ struct buffer_view<address_space_enum::global,
         constexpr index_t t_per_x = scalar_per_x_vector / scalar_per_t_vector;
 
         amd_async_buffer_load_with_oob_raw<remove_cvref_t<T>, t_per_x, Coherence>(
-            smem, cached_buf_res_, i, bool_constant<pre_nop>{});
+            smem, cached_buf_res_, i, linear_offset, bool_constant<pre_nop>{});
     }
 
     // i is offset of T, not X. i should be aligned to X
@@ -401,25 +441,25 @@ struct buffer_view<address_space_enum::global,
                   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)
+    CK_TILE_DEVICE void update(index_t i, index_t linear_offset, bool is_valid_element, const X& x)
     {
         if constexpr(Op == memory_operation_enum::set)
         {
-            this->template set<X>(i, is_valid_element, x);
+            this->template set<X>(i, linear_offset, is_valid_element, x);
         }
         else if constexpr(Op == memory_operation_enum::atomic_add)
         {
-            this->template atomic_add<X>(i, is_valid_element, x);
+            this->template atomic_add<X>(i, linear_offset, is_valid_element, x);
         }
         else if constexpr(Op == memory_operation_enum::atomic_max)
         {
-            this->template atomic_max<X>(i, is_valid_element, x);
+            this->template atomic_max<X>(i, linear_offset, 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);
+            auto tmp = this->template get<X>(i, linear_offset, is_valid_element);
+            this->template set<X>(i, linear_offset, is_valid_element, x + tmp);
             // tmp += x;
             // this->template set<X>(i, is_valid_element, tmp);
         }
@@ -432,7 +472,7 @@ struct buffer_view<address_space_enum::global,
                   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)
+    CK_TILE_DEVICE void set(index_t i, index_t linear_offset, 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;
@@ -453,7 +493,7 @@ struct buffer_view<address_space_enum::global,
             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_);
+                x, p_data_, i + linear_offset, is_valid_element, buffer_size_);
         }
         else
         {
@@ -462,9 +502,9 @@ struct buffer_view<address_space_enum::global,
 #if CK_TILE_EXPERIMENTAL_USE_MEMCPY_FOR_VECTOR_ACCESS
                 X tmp = x;
 
-                __builtin_memcpy(&(p_data_[i]), &tmp, sizeof(X));
+                __builtin_memcpy(&(p_data_[i + linear_offset]), &tmp, sizeof(X));
 #else
-                *c_style_pointer_cast<X*>(&p_data_[i]) = x;
+                *c_style_pointer_cast<X*>(&p_data_[i + linear_offset]) = x;
 #endif
             }
         }
@@ -477,7 +517,7 @@ struct buffer_view<address_space_enum::global,
                   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)
+    CK_TILE_DEVICE void set_raw(index_t i, index_t linear_offset, 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;
@@ -489,7 +529,7 @@ struct buffer_view<address_space_enum::global,
 
         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_);
+            x, p_data_, i, linear_offset, is_valid_element, buffer_size_);
     }
 
     template <typename X,
@@ -497,7 +537,8 @@ struct buffer_view<address_space_enum::global,
                   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)
+    CK_TILE_DEVICE void
+    atomic_add(index_t i, index_t linear_offset, bool is_valid_element, const X& x)
     {
         using scalar_t = typename vector_traits<remove_cvref_t<T>>::scalar_type;
 
@@ -532,13 +573,13 @@ struct buffer_view<address_space_enum::global,
         if constexpr(use_amd_buffer_addressing)
         {
             amd_buffer_atomic_add<remove_cvref_t<T>, t_per_x>(
-                x, p_data_, i, is_valid_element, buffer_size_);
+                x, p_data_, i + linear_offset, is_valid_element, buffer_size_);
         }
         else
         {
             if(is_valid_element)
             {
-                atomic_add_g<remove_cvref_t<T>, t_per_x>(&p_data_[i], x);
+                atomic_add_g<remove_cvref_t<T>, t_per_x>(&p_data_[i + linear_offset], x);
             }
         }
     }
@@ -548,7 +589,8 @@ struct buffer_view<address_space_enum::global,
                   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)
+    CK_TILE_DEVICE void
+    atomic_max(index_t i, index_t linear_offset, 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;
@@ -572,11 +614,11 @@ struct buffer_view<address_space_enum::global,
         if constexpr(use_amd_buffer_addressing)
         {
             amd_buffer_atomic_max<remove_cvref_t<T>, t_per_x>(
-                x, p_data_, i, is_valid_element, buffer_size_);
+                x, p_data_, i + linear_offset, is_valid_element, buffer_size_);
         }
         else if(is_valid_element)
         {
-            atomic_max_g<remove_cvref_t<T>, t_per_x>(&p_data_[i], x);
+            atomic_max_g<remove_cvref_t<T>, t_per_x>(&p_data_[i + linear_offset], x);
         }
     }
 
@@ -668,8 +710,10 @@ struct buffer_view<address_space_enum::lds,
                   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
+    CK_TILE_DEVICE constexpr auto get(index_t i,
+                                      index_t linear_offset,
+                                      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;
@@ -684,14 +728,14 @@ struct buffer_view<address_space_enum::lds,
 #if CK_TILE_EXPERIMENTAL_USE_MEMCPY_FOR_VECTOR_ACCESS
             X tmp;
 
-            __builtin_memcpy(&tmp, &(p_data_[i]), sizeof(X));
+            __builtin_memcpy(&tmp, &(p_data_[i + linear_offset]), 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]);
+            auto rtn = *c_style_pointer_cast<const buf_t*>(&p_data_[i + linear_offset]);
             return bit_cast<X>(rtn);
 #endif
         }
@@ -708,6 +752,23 @@ struct buffer_view<address_space_enum::lds,
         }
     }
 
+    // i is offset of T, not X. i should be aligned to X
+    template <typename X,
+              bool oob_conditional_check = true,
+              bool pre_nop               = false,
+              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 v_offset,
+                                          index_t i_offset,
+                                          bool /*is_valid_element*/,
+                                          bool_constant<pre_nop> = {}) const
+    {
+        smem_load<sizeof(X)>{}(dst, v_offset * sizeof(T), i_offset * sizeof(T));
+    }
+
     // i is offset of T, not X. i should be aligned to X
     template <memory_operation_enum Op,
               typename X,
@@ -715,17 +776,17 @@ struct buffer_view<address_space_enum::lds,
                   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)
+    CK_TILE_DEVICE void update(index_t i, index_t linear_offset, bool is_valid_element, const X& x)
     {
         if constexpr(Op == memory_operation_enum::set)
         {
-            this->template set<X>(i, is_valid_element, x);
+            this->template set<X>(i, linear_offset, 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);
+            auto tmp = this->template get<X>(i, linear_offset, is_valid_element);
+            this->template set<X>(i, linear_offset, is_valid_element, x + tmp);
         }
     }
 
@@ -735,7 +796,7 @@ struct buffer_view<address_space_enum::lds,
                   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)
+    CK_TILE_DEVICE void set(index_t i, index_t linear_offset, 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;
@@ -751,6 +812,7 @@ struct buffer_view<address_space_enum::lds,
         bool constexpr workaround_int8_ds_write_issue = false;
 #endif
 
+        i += linear_offset; // simplicity
         if constexpr(std::is_same<typename vector_traits<remove_cvref_t<T>>::scalar_type,
                                   int8_t>::value &&
                      workaround_int8_ds_write_issue)
@@ -952,8 +1014,10 @@ struct buffer_view<address_space_enum::vgpr,
                   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
+    CK_TILE_DEVICE constexpr auto get(index_t i,
+                                      index_t /*linear_offset*/,
+                                      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;
@@ -995,17 +1059,17 @@ struct buffer_view<address_space_enum::vgpr,
                   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)
+    CK_TILE_DEVICE void update(index_t i, index_t linear_offset, bool is_valid_element, const X& x)
     {
         if constexpr(Op == memory_operation_enum::set)
         {
-            this->template set<X>(i, is_valid_element, x);
+            this->template set<X>(i, linear_offset, 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);
+            auto tmp = this->template get<X>(i, linear_offset, is_valid_element);
+            this->template set<X>(i, linear_offset, is_valid_element, x + tmp);
         }
     }
 
@@ -1015,7 +1079,7 @@ struct buffer_view<address_space_enum::vgpr,
                   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)
+    CK_TILE_DEVICE void set(index_t i, index_t linear_offset, 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;
@@ -1030,9 +1094,9 @@ struct buffer_view<address_space_enum::vgpr,
 #if CK_TILE_EXPERIMENTAL_USE_MEMCPY_FOR_VECTOR_ACCESS
             X tmp = x;
 
-            __builtin_memcpy(&(p_data_[i]), &tmp, sizeof(X));
+            __builtin_memcpy(&(p_data_[i + linear_offset]), &tmp, sizeof(X));
 #else
-            *c_style_pointer_cast<X*>(&p_data_[i]) = x;
+            *c_style_pointer_cast<X*>(&p_data_[i + linear_offset]) = x;
 #endif
         }
     }

include/ck_tile/core/tensor/load_tile.hpp

@@ -12,6 +12,7 @@
 #include "ck_tile/core/tensor/tile_window.hpp"
 #include "ck_tile/core/utility/type_traits.hpp"
 #include "ck_tile/core/tensor/tile_window.hpp"
+#include "ck_tile/core/tensor/tile_window_linear.hpp"
 #include "ck_tile/core/tensor/null_tile_window.hpp"
 #include "ck_tile/core/tensor/null_tensor.hpp"
 
@@ -28,7 +29,21 @@ CK_TILE_DEVICE auto load_tile(const tile_window_with_static_distribution<BottomT
                                                                          NumCoord>& tile_window,
                               bool_constant<oob_conditional_check> = {})
 {
-    return tile_window.load(bool_constant<oob_conditional_check>{});
+    return tile_window.load(number<-1>{}, bool_constant<oob_conditional_check>{});
+}
+
+template <typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          typename LinearBottomDims_,
+          bool oob_conditional_check = true>
+CK_TILE_DEVICE auto load_tile(const tile_window_linear<BottomTensorView_,
+                                                       WindowLengths_,
+                                                       TileDistribution_,
+                                                       LinearBottomDims_>& tile_window,
+                              bool_constant<oob_conditional_check> = {})
+{
+    return tile_window.load(number<-1>{}, bool_constant<oob_conditional_check>{});
 }
 
 template <typename T,
@@ -46,7 +61,27 @@ CK_TILE_DEVICE auto load_tile_raw(T& tile,
                                   bool_constant<oob_conditional_check> = {},
                                   bool_constant<pre_nop>               = {})
 {
-    tile_window.load_raw(tile, bool_constant<oob_conditional_check>{}, bool_constant<pre_nop>{});
+    tile_window.load_raw(
+        tile, number<-1>{}, bool_constant<oob_conditional_check>{}, bool_constant<pre_nop>{});
+}
+
+template <typename T,
+          typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          typename LinearBottomDims_,
+          bool oob_conditional_check = true,
+          bool pre_nop               = false>
+CK_TILE_DEVICE auto load_tile_raw(T& tile,
+                                  const tile_window_linear<BottomTensorView_,
+                                                           WindowLengths_,
+                                                           TileDistribution_,
+                                                           LinearBottomDims_>& tile_window,
+                                  bool_constant<oob_conditional_check> = {},
+                                  bool_constant<pre_nop>               = {})
+{
+    tile_window.load_raw(
+        tile, number<-1>{}, bool_constant<oob_conditional_check>{}, bool_constant<pre_nop>{});
 }
 
 template <typename LdsTileWindow_,
@@ -66,7 +101,26 @@ async_load_tile_raw(LdsTileWindow_&& lds_tile,
                     bool_constant<pre_nop>               = {})
 {
     return tile_window.async_load_raw(
-        lds_tile, bool_constant<oob_conditional_check>{}, bool_constant<pre_nop>{});
+        lds_tile, number<-1>{}, bool_constant<oob_conditional_check>{}, bool_constant<pre_nop>{});
+}
+
+template <typename LdsTileWindow_,
+          typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          typename LinearBottomDims_,
+          bool oob_conditional_check = true,
+          bool pre_nop               = false>
+CK_TILE_DEVICE auto async_load_tile_raw(LdsTileWindow_&& lds_tile,
+                                        const tile_window_linear<BottomTensorView_,
+                                                                 WindowLengths_,
+                                                                 TileDistribution_,
+                                                                 LinearBottomDims_>& tile_window,
+                                        bool_constant<oob_conditional_check> = {},
+                                        bool_constant<pre_nop>               = {})
+{
+    return tile_window.async_load_raw(
+        lds_tile, number<-1>{}, bool_constant<oob_conditional_check>{}, bool_constant<pre_nop>{});
 }
 
 CK_TILE_DEVICE auto async_load_fence(index_t cnt = 0)

include/ck_tile/core/tensor/shuffle_tile.hpp

@@ -109,7 +109,7 @@ CK_TILE_DEVICE void shuffle_tile_impl_in_thread(OutTensor& out_tensor, const InT
 
         // get input vectors
         static_for<0, num_vec_in, 1>{}([&](auto i) {
-            constexpr auto idx_y_in = generate_array(
+            constexpr auto idx_y_in = generate_tuple(
                 [&](auto ii) {
                     return ii == y_dim_vec_out ? idx_y_start[ii] + i : idx_y_start[ii];
                 },

include/ck_tile/core/tensor/store_tile.hpp

@@ -10,6 +10,7 @@
 #include "ck_tile/core/container/container_helper.hpp"
 #include "ck_tile/core/numeric/math.hpp"
 #include "ck_tile/core/tensor/tile_window.hpp"
+#include "ck_tile/core/tensor/tile_window_linear.hpp"
 #include "ck_tile/core/utility/type_traits.hpp"
 
 namespace ck_tile {
@@ -72,7 +73,7 @@ store_tile(tile_window_with_static_distribution<BottomTensorView_,
                                                 NumCoord>& tile_window,
            const static_distributed_tensor<DataType_, TileDistribution_>& dstr_tensor)
 {
-    tile_window.store(dstr_tensor);
+    tile_window.store(dstr_tensor, number<-1>{});
 }
 
 template <typename BottomTensorView_,
@@ -87,7 +88,33 @@ store_tile_raw(tile_window_with_static_distribution<BottomTensorView_,
                                                     NumCoord>& tile_window,
                const static_distributed_tensor<DataType_, TileDistribution_>& dstr_tensor)
 {
-    tile_window.store_raw(dstr_tensor);
+    tile_window.store_raw(dstr_tensor, number<-1>{});
+}
+
+template <typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          typename LinearBottomDims_,
+          typename DataType_>
+CK_TILE_DEVICE void store_tile(
+    tile_window_linear<BottomTensorView_, WindowLengths_, TileDistribution_, LinearBottomDims_>&
+        tile_window,
+    const static_distributed_tensor<DataType_, TileDistribution_>& dstr_tensor)
+{
+    tile_window.store(dstr_tensor, number<-1>{});
+}
+
+template <typename BottomTensorView_,
+          typename WindowLengths_,
+          typename TileDistribution_,
+          typename LinearBottomDims_,
+          typename DataType_>
+CK_TILE_DEVICE void store_tile_raw(
+    tile_window_linear<BottomTensorView_, WindowLengths_, TileDistribution_, LinearBottomDims_>&
+        tile_window,
+    const static_distributed_tensor<DataType_, TileDistribution_>& dstr_tensor)
+{
+    tile_window.store_raw(dstr_tensor, number<-1>{});
 }
 
 } // namespace ck_tile

include/ck_tile/core/tensor/tensor_view.hpp

@@ -16,6 +16,24 @@
 
 namespace ck_tile {
 
+/*
+ * tensor_view
+ * abstract the underneath memory buffer(global, LDS, etc...)
+ * and provide a unified get/set function for access
+ *
+ * For addressing into the buffer we use 2 variable to control:
+ * coord : ND tensor coordinate, will calculate the actual offset inside
+ * linear_offset : 1D offset, will be used in the immediate field of
+ *   the buffer instruction to help reduce register usage
+ *
+ * User can use either of the field, or both to indexing into the tensor
+ *
+ * We usually provide 2 set of API for buffer get/set, e.g.
+ * get_vectorized_elements()/get_vectorized_elements_raw()
+ * the former usually will call intrinsic or normal C function, the later
+ * usually will call inline-asm function
+ *
+ */
 template <typename BufferView_,
           typename TensorDesc_,
           memory_operation_enum DstInMemOp_ = memory_operation_enum::set>
@@ -49,22 +67,6 @@ struct tensor_view
 
     CK_TILE_HOST_DEVICE constexpr auto& get_buffer_view() { return buf_; }
 
-#if 0
-    CK_TILE_HOST_DEVICE constexpr DataType get_element(const TensorCoord& coord) const
-    {
-        return buf_.template get<DataType>(
-            coord.get_offset(),
-            coordinate_has_valid_offset_assuming_top_index_is_valid(desc_, coord));
-    }
-
-    CK_TILE_HOST_DEVICE constexpr void set_element(const TensorCoord& coord, const DataType& x)
-    {
-        buf_.template set<DataType>(
-            coord.get_offset(),
-            coordinate_has_valid_offset_assuming_top_index_is_valid(desc_, coord),
-            x);
-    }
-#endif
     // X is vector of DataType.
     // "coord" is coordinate of DataType, not X. "coord" should be aligned to X
     template <typename X,
@@ -75,14 +77,34 @@ struct tensor_view
                   bool>::type = false>
     CK_TILE_HOST_DEVICE constexpr remove_cvref_t<X>
     get_vectorized_elements(const TensorCoord& coord,
+                            index_t linear_offset,
                             bool_constant<oob_conditional_check> = {}) const
     {
         return buf_.template get<X>(
             coord.get_offset(),
+            linear_offset,
             coordinate_has_valid_offset_assuming_top_index_is_valid(desc_, coord),
             bool_constant<oob_conditional_check>{});
     }
 
+    template <typename X,
+              bool oob_conditional_check = true,
+              typename std::enable_if<
+                  std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                 typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
+                  bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr remove_cvref_t<X>
+    get_vectorized_elements(const TensorCoord& coord,
+                            index_t linear_offset,
+                            bool is_valid_element, // flag
+                            bool_constant<oob_conditional_check> = {}) const
+    {
+        return buf_.template get<X>(coord.get_offset(),
+                                    linear_offset,
+                                    is_valid_element,
+                                    bool_constant<oob_conditional_check>{});
+    }
+
     // X is vector of DataType.
     // "coord" is coordinate of DataType, not X. "coord" should be aligned to X
     template <typename X,
@@ -94,12 +116,90 @@ struct tensor_view
                   bool>::type = false>
     CK_TILE_HOST_DEVICE void get_vectorized_elements_raw(remove_cvref_t<X>& dst,
                                                          const TensorCoord& coord,
+                                                         index_t linear_offset,
                                                          bool_constant<oob_conditional_check> = {},
                                                          bool_constant<pre_nop> = {}) const
     {
         return buf_.template get_raw<X, oob_conditional_check, pre_nop>(
             dst,
             coord.get_offset(),
+            linear_offset,
+            coordinate_has_valid_offset_assuming_top_index_is_valid(desc_, coord),
+            bool_constant<pre_nop>{});
+    }
+
+    template <typename X,
+              bool oob_conditional_check = true,
+              bool pre_nop               = false,
+              typename std::enable_if<
+                  std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                 typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
+                  bool>::type = false>
+    CK_TILE_HOST_DEVICE void get_vectorized_elements_raw(remove_cvref_t<X>& dst,
+                                                         const TensorCoord& coord,
+                                                         index_t linear_offset,
+                                                         bool is_valid_element,
+                                                         bool_constant<oob_conditional_check> = {},
+                                                         bool_constant<pre_nop> = {}) const
+    {
+        return buf_.template get_raw<X, oob_conditional_check, pre_nop>(
+            dst, coord.get_offset(), linear_offset, is_valid_element, bool_constant<pre_nop>{});
+    }
+
+    template <typename X,
+              bool oob_conditional_check = true,
+              typename std::enable_if<
+                  std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                 typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
+                  bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr void
+    async_get_vectorized_elements(CK_TILE_LDS_ADDR remove_cvref_t<DataType>* smem,
+                                  const TensorCoord& coord,
+                                  index_t linear_offset) const
+    {
+        return buf_.template async_get<X>(
+            smem,
+            coord.get_offset(),
+            linear_offset,
+            coordinate_has_valid_offset_assuming_top_index_is_valid(desc_, coord),
+            bool_constant<oob_conditional_check>{});
+    }
+
+    template <typename X,
+              bool oob_conditional_check = true,
+              typename std::enable_if<
+                  std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                 typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
+                  bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr void
+    async_get_vectorized_elements(CK_TILE_LDS_ADDR remove_cvref_t<DataType>* smem,
+                                  const TensorCoord& coord,
+                                  index_t linear_offset,
+                                  bool is_valid_element) const
+    {
+        return buf_.template async_get<X>(smem,
+                                          coord.get_offset(),
+                                          linear_offset,
+                                          is_valid_element,
+                                          bool_constant<oob_conditional_check>{});
+    }
+
+    template <typename X,
+              bool pre_nop = false,
+              typename std::enable_if<
+                  std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                 typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
+                  bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr void
+    async_get_vectorized_elements_raw(remove_cvref_t<DataType>* smem,
+                                      const TensorCoord& coord,
+                                      index_t linear_offset,
+                                      bool_constant<pre_nop> = {}) const
+    {
+        return buf_.template async_get_raw<X>(
+            smem,
+            coord.get_offset(),
+            linear_offset,
             coordinate_has_valid_offset_assuming_top_index_is_valid(desc_, coord),
             bool_constant<pre_nop>{});
     }
@@ -110,11 +210,15 @@ struct tensor_view
                   std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
                                  typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
                   bool>::type = false>
-    CK_TILE_HOST_DEVICE constexpr void async_get_vectorized_elements_raw(
-        remove_cvref_t<DataType>* smem, const TensorCoord& coord, bool_constant<pre_nop> = {}) const
+    CK_TILE_HOST_DEVICE constexpr void
+    async_get_vectorized_elements_raw(remove_cvref_t<DataType>* smem,
+                                      const TensorCoord& coord,
+                                      index_t linear_offset,
+                                      bool is_valid_element,
+                                      bool_constant<pre_nop> = {}) const
     {
         return buf_.template async_get_raw<X>(
-            smem, coord.get_offset(), true /*not used*/, bool_constant<pre_nop>{});
+            smem, coord.get_offset(), linear_offset, is_valid_element, bool_constant<pre_nop>{});
     }
 
     // X is vector of DataType.
@@ -125,11 +229,15 @@ struct tensor_view
                   std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
                                  typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
                   bool>::type = false>
-    CK_TILE_HOST_DEVICE constexpr void set_vectorized_elements(
-        const TensorCoord& coord, const X& x, bool_constant<oob_conditional_check> = {})
+    CK_TILE_HOST_DEVICE constexpr void
+    set_vectorized_elements(const TensorCoord& coord,
+                            index_t linear_offset,
+                            const X& x,
+                            bool_constant<oob_conditional_check> = {})
     {
         buf_.template set<X, oob_conditional_check>(
             coord.get_offset(),
+            linear_offset,
             coordinate_has_valid_offset_assuming_top_index_is_valid(desc_, coord),
             x);
     }
@@ -140,15 +248,53 @@ struct tensor_view
                   std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
                                  typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
                   bool>::type = false>
-    CK_TILE_HOST_DEVICE constexpr void set_vectorized_elements_raw(
-        const TensorCoord& coord, const X& x, bool_constant<oob_conditional_check> = {})
+    CK_TILE_HOST_DEVICE constexpr void
+    set_vectorized_elements(const TensorCoord& coord,
+                            index_t linear_offset,
+                            bool is_valid_element,
+                            const X& x,
+                            bool_constant<oob_conditional_check> = {})
+    {
+        buf_.template set<X, oob_conditional_check>(
+            coord.get_offset(), linear_offset, is_valid_element, x);
+    }
+
+    template <typename X,
+              bool oob_conditional_check = true,
+              typename std::enable_if<
+                  std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                 typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
+                  bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr void
+    set_vectorized_elements_raw(const TensorCoord& coord,
+                                index_t linear_offset,
+                                const X& x,
+                                bool_constant<oob_conditional_check> = {})
     {
         buf_.template set_raw<X, oob_conditional_check>(
             coord.get_offset(),
+            linear_offset,
             coordinate_has_valid_offset_assuming_top_index_is_valid(desc_, coord),
             x);
     }
 
+    template <typename X,
+              bool oob_conditional_check = true,
+              typename std::enable_if<
+                  std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                 typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
+                  bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr void
+    set_vectorized_elements_raw(const TensorCoord& coord,
+                                index_t linear_offset,
+                                bool is_valid_element,
+                                const X& x,
+                                bool_constant<oob_conditional_check> = {})
+    {
+        buf_.template set_raw<X, oob_conditional_check>(
+            coord.get_offset(), linear_offset, is_valid_element, x);
+    }
+
     // X is vector of DataType.
     // "coord" is coordinate of DataType, not X. "coord" should be aligned to X
     template <typename X,
@@ -157,15 +303,36 @@ struct tensor_view
                   std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
                                  typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
                   bool>::type = false>
-    CK_TILE_HOST_DEVICE constexpr void update_vectorized_elements(
-        const TensorCoord& coord, const X& x, bool_constant<oob_conditional_check> = {})
+    CK_TILE_HOST_DEVICE constexpr void
+    update_vectorized_elements(const TensorCoord& coord,
+                               index_t linear_offset,
+                               const X& x,
+                               bool_constant<oob_conditional_check> = {})
     {
         buf_.template update<DstInMemOp, X, oob_conditional_check>(
             coord.get_offset(),
+            linear_offset,
             coordinate_has_valid_offset_assuming_top_index_is_valid(desc_, coord),
             x);
     }
 
+    template <typename X,
+              bool oob_conditional_check = true,
+              typename std::enable_if<
+                  std::is_same_v<typename vector_traits<remove_cvref_t<X>>::scalar_type,
+                                 typename vector_traits<remove_cvref_t<DataType>>::scalar_type>,
+                  bool>::type = false>
+    CK_TILE_HOST_DEVICE constexpr void
+    update_vectorized_elements(const TensorCoord& coord,
+                               index_t linear_offset,
+                               bool is_valid_element,
+                               const X& x,
+                               bool_constant<oob_conditional_check> = {})
+    {
+        buf_.template update<DstInMemOp, X, oob_conditional_check>(
+            coord.get_offset(), linear_offset, is_valid_element, x);
+    }
+
     CK_TILE_HOST_DEVICE void print() const
     {
         printf("tensor_view{");

include/ck_tile/core/tensor/tile_window.hpp

@@ -18,6 +18,8 @@
 
 namespace ck_tile {
 
+// Note: this tile window do not support single issue
+// you need to use tile_window_linear structure for this purpose
 template <typename BottomTensorView_,
           typename WindowLengths_,
           typename StaticTileDistribution_,
@@ -41,6 +43,7 @@ struct tile_window_with_static_distribution
 
     static constexpr auto I0 = number<0>{};
     static constexpr auto I1 = number<1>{};
+    static_assert(NumCoord == 1);
 
     // TODO: check WindowLengths and StaticTileDistribution are consistent
 
@@ -189,7 +192,8 @@ struct tile_window_with_static_distribution
             constexpr auto idx_diff_ys =
                 SFC_Ys::get_step_between(number<0>{}, number<iCoord * NumAccessPerCoord>{});
 
-            constexpr auto idx_diff_ps_ys = container_concat(array<index_t, NDimP>{0}, idx_diff_ys);
+            constexpr auto idx_diff_ps_ys = container_concat(
+                generate_tuple([&](auto) { return number<0>{}; }, number<NDimP>{}), idx_diff_ys);
 
             move_window_adaptor_and_bottom_tensor_thread_coordinate(
                 window_adaptor_thread_coord, bottom_tensor_thread_coord, idx_diff_ps_ys);
@@ -222,10 +226,11 @@ struct tile_window_with_static_distribution
 
     // move thread's window adaptor coordinate and bottom tensor coordinate
     // [p0, p1, ..., y0, y1, ...] ==> [x0, x1, ...] ==> [x0', x1', ...] ==> [offset]
+    template <typename ATopIndex>
     CK_TILE_DEVICE void move_window_adaptor_and_bottom_tensor_thread_coordinate(
         WindowAdaptorCoord& window_adaptor_thread_coord,
         BottomTensorCoord& bottom_tensor_thread_coord,
-        const AdaptorTopIndex& idx_diff_adaptor_top) const
+        const ATopIndex& idx_diff_adaptor_top) const
     {
         array<index_t, NDimBottomTensor> idx_diff_adaptor_bottom;
 
@@ -279,10 +284,11 @@ struct tile_window_with_static_distribution
                           get_container_subset(window_adaptor_ps_ys_vector_strides, y_dims));
     }
 
-    CK_TILE_DEVICE constexpr auto get_num_access() const { return load_store_traits::NumAccess; }
+    CK_TILE_DEVICE constexpr auto get_num_of_access() const { return load_store_traits::NumAccess; }
 
-    template <bool oob_conditional_check = true>
-    CK_TILE_DEVICE auto load(bool_constant<oob_conditional_check> = {}) const
+    template <index_t i_access_unsupport_ = -1, bool oob_conditional_check = true>
+    CK_TILE_DEVICE auto load(number<i_access_unsupport_>          = {},
+                             bool_constant<oob_conditional_check> = {}) const
     {
         using Traits = load_store_traits;
 
@@ -308,11 +314,11 @@ struct tile_window_with_static_distribution
                 // read from bottom tensor
                 const vector_t vec_value =
                     get_bottom_tensor_view().template get_vectorized_elements<vector_t>(
-                        bottom_tensor_thread_coord, bool_constant<oob_conditional_check>{});
+                        bottom_tensor_thread_coord, 0, bool_constant<oob_conditional_check>{});
 #if 1
                 // write into distributed tensor
                 static_for<0, Traits::ScalarPerVector, 1>{}([&](auto j) {
-                    constexpr auto idx_ys = generate_array(
+                    constexpr auto idx_ys = generate_tuple(
                         [&](auto jj) {
                             return jj == Traits::VectorDimY ? (idx_ys_start[jj] + j)
                                                             : idx_ys_start[jj];
@@ -338,8 +344,9 @@ struct tile_window_with_static_distribution
                 {
                     constexpr auto idx_diff_ys = SFC_Ys::get_forward_step(iAccess);
 
-                    constexpr auto idx_diff_ps_ys =
-                        container_concat(array<index_t, NDimP>{0}, idx_diff_ys);
+                    constexpr auto idx_diff_ps_ys = container_concat(
+                        generate_tuple([&](auto) { return number<0>{}; }, number<NDimP>{}),
+                        idx_diff_ys);
 
                     move_window_adaptor_and_bottom_tensor_thread_coordinate(
                         window_adaptor_thread_coord, bottom_tensor_thread_coord, idx_diff_ps_ys);
@@ -350,8 +357,12 @@ struct tile_window_with_static_distribution
         return dst_tensor;
     }
 
-    template <typename DstTile, bool oob_conditional_check = true, bool pre_nop = false>
+    template <typename DstTile,
+              index_t i_access_unsupport_ = -1,
+              bool oob_conditional_check  = true,
+              bool pre_nop                = false>
     CK_TILE_DEVICE void load_raw(DstTile& dst_tensor,
+                                 number<i_access_unsupport_>          = {},
                                  bool_constant<oob_conditional_check> = {},
                                  bool_constant<pre_nop>               = {}) const
     {
@@ -397,6 +408,7 @@ struct tile_window_with_static_distribution
                 get_bottom_tensor_view().template get_vectorized_elements_raw<vector_t>(
                     dst_vec_tbuf.template at<d / Traits::ScalarPerVector>(),
                     bottom_tensor_thread_coord,
+                    0 /**/,
                     bool_constant<oob_conditional_check>{},
                     pre_nop_);
 #if CK_TILE_WORKAROUND_ROCM_6_1_SCRATCH_MEMORY_ISSUE || \
@@ -409,23 +421,24 @@ struct tile_window_with_static_distribution
                 {
                     constexpr auto idx_diff_ys = SFC_Ys::get_forward_step(iAccess);
 
-                    constexpr auto idx_diff_ps_ys =
-                        container_concat(array<index_t, NDimP>{0}, idx_diff_ys);
+                    constexpr auto idx_diff_ps_ys = container_concat(
+                        generate_tuple([&](auto) { return number<0>{}; }, number<NDimP>{}),
+                        idx_diff_ys);
 
                     move_window_adaptor_and_bottom_tensor_thread_coordinate(
                         window_adaptor_thread_coord, bottom_tensor_thread_coord, idx_diff_ps_ys);
                 }
             });
         });
-#if CK_TILE_WORKAROUND_ROCM_6_1_SCRATCH_MEMORY_ISSUE
-        asm volatile("; this inline asm is workaround to prevent compiler from using too much "
-                     "scratch memory" ::);
-#endif
     }
 
     // TODO: currently async load only implemented in inline asm
-    template <typename LdsTileWindow_, bool oob_conditional_check = true, bool pre_nop = false>
+    template <typename LdsTileWindow_,
+              index_t i_access_unsupport_ = -1,
+              bool oob_conditional_check  = true,
+              bool pre_nop                = false>
     CK_TILE_DEVICE auto async_load_raw(LdsTileWindow_&& lds_tile,
+                                       number<i_access_unsupport_>          = {},
                                        bool_constant<oob_conditional_check> = {},
                                        bool_constant<pre_nop>               = {}) const
     {
@@ -467,7 +480,7 @@ struct tile_window_with_static_distribution
 
         // loop over thread tensor space [y0, y1, ...]
         static_for<0, NumCoord, 1>{}([&](auto iCoord) {
-            // TODO: use structure binding (to be captured later) if compiled in C++20
+            /// TODO: use structure binding (to be captured later) if compiled in C++20
             auto window_adaptor_thread_coord = pre_computed_coords_[iCoord][I0];
             auto bottom_tensor_thread_coord  = pre_computed_coords_[iCoord][I1];
 
@@ -482,15 +495,16 @@ struct tile_window_with_static_distribution
 
                 // read from bottom tensor
                 get_bottom_tensor_view().template async_get_vectorized_elements_raw<vector_t>(
-                    smem, bottom_tensor_thread_coord, pre_nop_);
+                    smem, bottom_tensor_thread_coord, 0, pre_nop_);
 
                 // move thread coordinate
                 if constexpr(iCoordAccess != (NumAccessPerCoord - 1))
                 {
                     constexpr auto idx_diff_ys = SFC_Ys::get_forward_step(iAccess);
 
-                    constexpr auto idx_diff_ps_ys =
-                        container_concat(array<index_t, NDimP>{0}, idx_diff_ys);
+                    constexpr auto idx_diff_ps_ys = container_concat(
+                        generate_tuple([&](auto) { return number<0>{}; }, number<NDimP>{}),
+                        idx_diff_ys);
 
                     move_window_adaptor_and_bottom_tensor_thread_coordinate(
                         window_adaptor_thread_coord, bottom_tensor_thread_coord, idx_diff_ps_ys);
@@ -501,8 +515,81 @@ struct tile_window_with_static_distribution
         });
     }
 
-    template <bool oob_conditional_check = true>
+    template <typename LdsTileWindow_,
+              index_t i_access_unsupport_ = -1,
+              bool oob_conditional_check  = true>
+    CK_TILE_DEVICE auto async_load(LdsTileWindow_&& lds_tile,
+                                   number<i_access_unsupport_>          = {},
+                                   bool_constant<oob_conditional_check> = {}) const
+    {
+        using LdsTileWindow = remove_cvref_t<LdsTileWindow_>;
+        using LdsDataType   = typename LdsTileWindow::DataType;
+
+        // issues * warps * lanes
+        static_assert(LdsTileWindow::get_num_of_dimension() == 3); // TODO: hard coded
+
+        // TODO: LDS offset is not good for intrinsic based implementation(compiler can't figure out
+        // dependency) hence avoid use offset based solution. size_per_buf should be zero (how to
+        // check?)
+        constexpr index_t size_per_buf =
+            lds_tile.get_bottom_tensor_view().get_tensor_descriptor().calculate_offset(
+                make_tuple(number<0>{}, number<0>{}, number<0>{}));
+
+        constexpr index_t size_per_wave =
+            lds_tile.get_bottom_tensor_view().get_tensor_descriptor().calculate_offset(
+                make_tuple(number<0>{}, number<1>{}, number<0>{})) -
+            size_per_buf;
+
+        constexpr index_t size_per_issue =
+            lds_tile.get_bottom_tensor_view().get_tensor_descriptor().calculate_offset(
+                make_tuple(number<1>{}, number<0>{}, number<0>{})) -
+            size_per_buf;
+
+        const index_t m0_init_value = size_per_buf + size_per_wave * get_warp_id();
+
+        using Traits = load_store_traits;
+
+        using vector_t = typename Traits::vector_t;
+        using SFC_Ys   = typename Traits::SFC_Ys;
+
+        // TODO: we force CK_TILE_LDS_ADDR
+        CK_TILE_LDS_ADDR LdsDataType* smem =
+            lds_tile.get_bottom_tensor_view().get_buffer_view().p_data_ + m0_init_value;
+
+        // loop over thread tensor space [y0, y1, ...]
+        static_for<0, NumCoord, 1>{}([&](auto iCoord) {
+            /// TODO: use structure binding (to be captured later) if compiled in C++20
+            auto window_adaptor_thread_coord = pre_computed_coords_[iCoord][I0];
+            auto bottom_tensor_thread_coord  = pre_computed_coords_[iCoord][I1];
+
+            static_for<0, NumAccessPerCoord, 1>{}([&](auto iCoordAccess) {
+                constexpr auto iAccess = number<iCoord * NumAccessPerCoord + iCoordAccess>{};
+
+                // read from bottom tensor
+                get_bottom_tensor_view().template async_get_vectorized_elements<vector_t>(
+                    smem, bottom_tensor_thread_coord, 0, bool_constant<oob_conditional_check>{});
+
+                // move thread coordinate
+                if constexpr(iCoordAccess != (NumAccessPerCoord - 1))
+                {
+                    constexpr auto idx_diff_ys = SFC_Ys::get_forward_step(iAccess);
+
+                    constexpr auto idx_diff_ps_ys = container_concat(
+                        generate_tuple([&](auto) { return number<0>{}; }, number<NDimP>{}),
+                        idx_diff_ys);
+
+                    move_window_adaptor_and_bottom_tensor_thread_coordinate(
+                        window_adaptor_thread_coord, bottom_tensor_thread_coord, idx_diff_ps_ys);
+
+                    smem += size_per_issue; // Note we manually increase the per-issue offset
+                }
+            });
+        });
+    }
+
+    template <index_t i_access_unsupport_ = -1, bool oob_conditional_check = true>
     CK_TILE_DEVICE void store(const static_distributed_tensor<DataType, TileDstr>& dstr_tensor,
+                              number<i_access_unsupport_>          = {},
                               bool_constant<oob_conditional_check> = {}) const
     {
         using Traits = load_store_traits;
@@ -515,7 +602,6 @@ struct tile_window_with_static_distribution
 
         // loop over thread tensor space [y0, y1, ...]
         static_for<0, NumCoord, 1>{}([&](auto iCoord) {
-            /// TODO: use structure binding (to be captured later) if compiled in C++20
             auto window_adaptor_thread_coord = pre_computed_coords_[iCoord][I0];
             auto bottom_tensor_thread_coord  = pre_computed_coords_[iCoord][I1];
 
@@ -530,7 +616,7 @@ struct tile_window_with_static_distribution
                 vector_t vec_value;
 
                 static_for<0, Traits::ScalarPerVector, 1>{}([&](auto j) {
-                    constexpr auto idx_ys = generate_array(
+                    constexpr auto idx_ys = generate_tuple(
                         [&](auto jj) {
                             return jj == Traits::VectorDimY ? (idx_ys_start[jj] + j)
                                                             : idx_ys_start[jj];
@@ -548,15 +634,19 @@ struct tile_window_with_static_distribution
 
                 // write into bottom tensor
                 get_bottom_tensor_view().template set_vectorized_elements<vector_t>(
-                    bottom_tensor_thread_coord, vec_value, bool_constant<oob_conditional_check>{});
+                    bottom_tensor_thread_coord,
+                    0,
+                    vec_value,
+                    bool_constant<oob_conditional_check>{});
 
                 // move thread coordinate
                 if constexpr(iCoordAccess != (NumAccessPerCoord - 1))
                 {
                     constexpr auto idx_diff_ys = SFC_Ys::get_forward_step(iAccess);
 
-                    constexpr auto idx_diff_ps_ys =
-                        container_concat(array<index_t, NDimP>{0}, idx_diff_ys);
+                    constexpr auto idx_diff_ps_ys = container_concat(
+                        generate_tuple([&](auto) { return number<0>{}; }, number<NDimP>{}),
+                        idx_diff_ys);
 
                     move_window_adaptor_and_bottom_tensor_thread_coordinate(
                         window_adaptor_thread_coord, bottom_tensor_thread_coord, idx_diff_ps_ys);
@@ -565,8 +655,9 @@ struct tile_window_with_static_distribution
         });
     }
 
-    CK_TILE_DEVICE void
-    store_raw(const static_distributed_tensor<DataType, TileDstr>& dstr_tensor) const
+    template <index_t i_access_unsupport_ = -1>
+    CK_TILE_DEVICE void store_raw(const static_distributed_tensor<DataType, TileDstr>& dstr_tensor,
+                                  number<i_access_unsupport_> = {}) const
     {
         using Traits = load_store_traits;
 
@@ -591,7 +682,7 @@ struct tile_window_with_static_distribution
                 // read from distributed tensor
                 vector_t vec_value;
                 static_for<0, Traits::ScalarPerVector, 1>{}([&](auto j) {
-                    constexpr auto idx_ys = generate_array(
+                    constexpr auto idx_ys = generate_tuple(
                         [&](auto jj) {
                             return jj == Traits::VectorDimY ? (idx_ys_start[jj] + j)
                                                             : idx_ys_start[jj];
@@ -606,15 +697,16 @@ struct tile_window_with_static_distribution
                 // write into bottom tensor
                 get_bottom_tensor_view()
                     .template set_vectorized_elements_raw<vector_t, oob_conditional_check>(
-                        bottom_tensor_thread_coord, vec_value);
+                        bottom_tensor_thread_coord, 0, vec_value);
 
                 // move thread coordinate
                 if constexpr(iCoordAccess != (NumAccessPerCoord - 1))
                 {
                     constexpr auto idx_diff_ys = SFC_Ys::get_forward_step(iAccess);
 
-                    constexpr auto idx_diff_ps_ys =
-                        container_concat(array<index_t, NDimP>{0}, idx_diff_ys);
+                    constexpr auto idx_diff_ps_ys = container_concat(
+                        generate_tuple([&](auto) { return number<0>{}; }, number<NDimP>{}),
+                        idx_diff_ys);
 
                     move_window_adaptor_and_bottom_tensor_thread_coordinate(
                         window_adaptor_thread_coord, bottom_tensor_thread_coord, idx_diff_ps_ys);
@@ -623,8 +715,9 @@ struct tile_window_with_static_distribution
         });
     }
 
-    template <bool oob_conditional_check = true>
+    template <index_t i_access_unsupport_ = -1, bool oob_conditional_check = true>
     CK_TILE_DEVICE void update(const static_distributed_tensor<DataType, TileDstr>& dstr_tensor,
+                               number<i_access_unsupport_>          = {},
                                bool_constant<oob_conditional_check> = {}) const
     {
         using Traits = load_store_traits;
@@ -650,7 +743,7 @@ struct tile_window_with_static_distribution
                 vector_t vec_value;
 
                 static_for<0, Traits::ScalarPerVector, 1>{}([&](auto j) {
-                    constexpr auto idx_ys = generate_array(
+                    constexpr auto idx_ys = generate_tuple(
                         [&](auto jj) {
                             return jj == Traits::VectorDimY ? (idx_ys_start[jj] + j)
                                                             : idx_ys_start[jj];
@@ -666,15 +759,19 @@ struct tile_window_with_static_distribution
 
                 // write into bottom tensor
                 get_bottom_tensor_view().template update_vectorized_elements<vector_t>(
-                    bottom_tensor_thread_coord, vec_value, bool_constant<oob_conditional_check>{});
+                    bottom_tensor_thread_coord,
+                    0,
+                    vec_value,
+                    bool_constant<oob_conditional_check>{});
 
                 // move thread coordinate
                 if constexpr(iCoordAccess != (NumAccessPerCoord - 1))
                 {
                     constexpr auto idx_diff_ys = SFC_Ys::get_forward_step(iAccess);
 
-                    constexpr auto idx_diff_ps_ys =
-                        container_concat(array<index_t, NDimP>{0}, idx_diff_ys);
+                    constexpr auto idx_diff_ps_ys = container_concat(
+                        generate_tuple([&](auto) { return number<0>{}; }, number<NDimP>{}),
+                        idx_diff_ys);
 
                     move_window_adaptor_and_bottom_tensor_thread_coordinate(
                         window_adaptor_thread_coord, bottom_tensor_thread_coord, idx_diff_ps_ys);
@@ -746,7 +843,8 @@ struct tile_window_with_static_distribution
             constexpr auto idx_diff_ys =
                 SFC_Ys::get_step_between(number<0>{}, number<iCoord * NumAccessPerCoord>{});
 
-            constexpr auto idx_diff_ps_ys = container_concat(array<index_t, NDimP>{0}, idx_diff_ys);
+            constexpr auto idx_diff_ps_ys = container_concat(
+                generate_tuple([&](auto) { return number<0>{}; }, number<NDimP>{}), idx_diff_ys);
 
             move_window_adaptor_and_bottom_tensor_thread_coordinate(
                 window_adaptor_thread_coord, bottom_tensor_thread_coord, idx_diff_ps_ys);
@@ -798,6 +896,27 @@ make_tile_window(const TensorView_& tensor_view,
         tensor_view, window_lengths, origin, tile_distribution};
 }
 
+// this version can't be called in a constexpr context
+template <typename TensorView_,
+          typename WindowLengths_,
+          typename StaticTileDistribution_,
+          index_t NumCoord = 1>
+CK_TILE_DEVICE auto
+make_tile_window_raw(const TensorView_& tensor_view,
+                     const WindowLengths_& window_lengths,
+                     const multi_index<TensorView_::get_num_of_dimension()>& origin,
+                     const StaticTileDistribution_& tile_distribution,
+                     number<NumCoord> = {})
+{
+    auto w = tile_window_with_static_distribution<remove_cvref_t<TensorView_>,
+                                                  remove_cvref_t<WindowLengths_>,
+                                                  remove_cvref_t<StaticTileDistribution_>,
+                                                  NumCoord>{
+        tensor_view, window_lengths, origin, tile_distribution};
+    w.init_raw();
+    return w;
+}
+
 template <typename TensorView_,
           typename WindowLengths_,
           typename StaticTileDistribution_,
@@ -922,6 +1041,19 @@ make_tile_window(const tile_window_with_static_lengths<TensorView, WindowLengths
                             tile_distribution);
 }
 
+template <typename TensorView, typename WindowLengths, typename StaticTileDistribution>
+CK_TILE_DEVICE constexpr auto
+make_tile_window_raw(const tile_window_with_static_lengths<TensorView, WindowLengths>& tile_window,
+                     const StaticTileDistribution& tile_distribution)
+{
+    auto w = make_tile_window(tile_window.get_bottom_tensor_view(),
+                              tile_window.get_window_lengths(),
+                              tile_window.get_window_origin(),
+                              tile_distribution);
+    w.init_raw();
+    return w;
+}
+
 template <typename TensorView_, typename WindowLengths_>
 CK_TILE_DEVICE void move_tile_window(
     tile_window_with_static_lengths<TensorView_, WindowLengths_>& window,

include/ck_tile/core/tensor/tile_window_linear.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+#include "ck_tile/core/arch/arch.hpp"
+#include "ck_tile/core/arch/utility.hpp"
+#include "ck_tile/core/algorithm/space_filling_curve.hpp"
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/container/array.hpp"
+#include "ck_tile/core/container/sequence.hpp"
+#include "ck_tile/core/container/tuple.hpp"
+#include "ck_tile/core/container/container_helper.hpp"
+#include "ck_tile/core/tensor/static_distributed_tensor.hpp"
+#include "ck_tile/core/tensor/tensor_adaptor.hpp"
+#include "ck_tile/core/tensor/tile_distribution.hpp"
+#include "ck_tile/core/utility/functional.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+
+namespace ck_tile {
+
+#define WINDOW_DISPATCH_ISSUE()                                     \
+    if constexpr(i_access < 0)                                      \
+    {                                                               \
+        static_for<0, NumAccess, 1>{}([&](auto ia) { issue(ia); }); \
+    }                                                               \
+    else                                                            \
+    {                                                               \
+        static_assert(i_access < NumAccess);                        \
+        issue(number<i_access>{});                                  \
+    }
+
+//
+// This version of tile window will pre-cache offset/flags based on need
+//
+// LinearBottomDims_, e.g seq<0, 1> for 2d tensor, the last one is linear dim
+// so last dim can use immediate offset to indexing, can save register
+// TODO: if using this struct, better use load_raw()/store_raw(), can control
+//       the the immediate offset on the fly
+// space-filing-curve is non-snaked here!
+//
+template <typename BottomTensorView_,
+          typename WindowLengths_,
+          typename StaticTileDistribution_,
+          typename LinearBottomDims_>
+struct tile_window_linear
+{
+    using BottomTensorView = remove_reference_t<BottomTensorView_>;
+    using WindowLengths    = remove_cvref_t<WindowLengths_>;
+    using TileDstr         = remove_cvref_t<StaticTileDistribution_>;
+
+    using WindowAdaptor    = typename TileDstr::PsYs2XsAdaptor;
+    using BottomTensorDesc = typename BottomTensorView::TensorDesc;
+
+    using DataType         = remove_cvref_t<typename BottomTensorView::DataType>;
+    using LinearBottomDims = remove_cvref_t<LinearBottomDims_>;
+
+    static_assert(LinearBottomDims::size() == BottomTensorView::get_num_of_dimension());
+
+    static constexpr index_t NDimWindowAdaptorTop = WindowAdaptor::get_num_of_top_dimension();
+    static constexpr index_t NDimBottomTensor     = BottomTensorDesc::get_num_of_dimension();
+
+    static constexpr index_t NDimP = TileDstr::get_num_of_dimension_p();
+    static constexpr index_t NDimY = TileDstr::get_num_of_dimension_y();
+
+    static constexpr auto I0 = number<0>{};
+    static constexpr auto I1 = number<1>{};
+
+    // TODO: check WindowLengths and StaticTileDistribution are consistent
+
+    static_assert(ck_tile::is_known_at_compile_time<WindowLengths>::value,
+                  "wrong! lengths should be static");
+    static_assert(TileDstr::is_static(), "wrong!");
+
+    static_assert(NDimBottomTensor == WindowAdaptor::get_num_of_bottom_dimension(),
+                  "wrong! inconsistent # of diemsnions");
+
+    using AdaptorTopIndex   = array<index_t, NDimWindowAdaptorTop>;
+    using BottomTensorIndex = array<index_t, NDimBottomTensor>;
+
+    using WindowAdaptorCoord =
+        decltype(make_tensor_adaptor_coordinate(WindowAdaptor{}, AdaptorTopIndex{}));
+
+    using BottomTensorCoord =
+        decltype(make_tensor_coordinate(BottomTensorDesc{}, BottomTensorIndex{}));
+
+    struct traits
+    {
+        private:
+        // return vector dimension among [y0, y1, ...]
+        CK_TILE_DEVICE static constexpr auto get_window_adaptor_ys_safe_vector_length_strides()
+        {
+            // bottom tensor top dimension vector lengths and strides
+            const auto [bottom_tensor_top_dim_vector_lengths,
+                        bottom_tensor_top_dim_vector_strides] =
+                BottomTensorDesc::get_top_dimension_safe_vector_length_strides();
+
+            // window vector lengths/strides
+            const auto window_adaptor_bottom_dim_vector_lengths =
+                bottom_tensor_top_dim_vector_lengths;
+            const auto window_adaptor_bottom_dim_vector_strides =
+                bottom_tensor_top_dim_vector_strides;
+
+            // window adaptor [p0, p1, ..., y0, y1, ...]
+            array<index_t, WindowAdaptor::get_num_of_hidden_dimension()>
+                window_adaptor_vector_lengths{-1};
+            array<index_t, WindowAdaptor::get_num_of_hidden_dimension()>
+                window_adaptor_vector_strides{-1};
+
+            constexpr auto window_adaptor_bottom_dims =
+                WindowAdaptor::get_bottom_dimension_hidden_ids();
+
+            set_container_subset(window_adaptor_vector_lengths,
+                                 window_adaptor_bottom_dims,
+                                 window_adaptor_bottom_dim_vector_lengths);
+            set_container_subset(window_adaptor_vector_strides,
+                                 window_adaptor_bottom_dims,
+                                 window_adaptor_bottom_dim_vector_strides);
+
+            const auto [window_adaptor_ps_ys_vector_lengths, window_adaptor_ps_ys_vector_strides] =
+                WindowAdaptor{}.get_top_dimension_safe_vector_length_strides(
+                    window_adaptor_vector_lengths, window_adaptor_vector_strides);
+
+            // [y0, y1, ...]
+            constexpr auto y_dims =
+                typename arithmetic_sequence_gen<TileDstr::get_num_of_dimension_p(),
+                                                 NDimWindowAdaptorTop,
+                                                 1>::type{};
+
+            return make_tuple(get_container_subset(window_adaptor_ps_ys_vector_lengths, y_dims),
+                              get_container_subset(window_adaptor_ps_ys_vector_strides, y_dims));
+        }
+
+        static constexpr auto get_vector_dim_y_scalar_per_vector()
+        {
+            const auto [ys_vector_lengths, ys_vector_strides] =
+                get_window_adaptor_ys_safe_vector_length_strides();
+
+            index_t VectorDimY_      = 0;
+            index_t ScalarPerVector_ = 1;
+
+            for(index_t i = 0; i < NDimY; ++i)
+            {
+                if(ys_vector_strides[i] == 1 && ys_vector_lengths[i] > ScalarPerVector_)
+                {
+                    ScalarPerVector_ = ys_vector_lengths[i];
+                    VectorDimY_      = i;
+                }
+            }
+
+            return make_tuple(VectorDimY_, ScalarPerVector_);
+        }
+
+        public:
+        static constexpr index_t VectorDimY = get_vector_dim_y_scalar_per_vector().template at<0>();
+        static constexpr index_t ScalarPerVector =
+            get_vector_dim_y_scalar_per_vector().template at<1>();
+
+        using vector_t = thread_buffer<DataType, ScalarPerVector>;
+
+        private:
+        static constexpr auto scalars_per_access_ = [] {
+            constexpr auto scalars_per_access_arr = generate_array(
+                [&](auto i) { return (i == VectorDimY) ? ScalarPerVector : 1; }, number<NDimY>{});
+
+            /// TODO: add non-automatic storage argument support to macro TO_SEQUENCE()
+            constexpr auto NDimY_ = NDimY;
+
+            return TO_SEQUENCE(scalars_per_access_arr, NDimY_);
+        }();
+
+        static constexpr auto get_space_filling_curve()
+        {
+            constexpr auto thread_tensor_lengths_ys =
+                to_sequence(TileDstr{}.get_ys_to_d_descriptor().get_lengths());
+
+            // FIXME: need logic to judge dim access order
+            using DimAccessOrder = typename arithmetic_sequence_gen<0, NDimY, 1>::type;
+
+            return space_filling_curve<decltype(thread_tensor_lengths_ys),
+                                       DimAccessOrder,
+                                       decltype(scalars_per_access_),
+                                       false /*!!! no snaked curve! */>{};
+        }
+
+        public:
+        using SFC_Ys = decltype(get_space_filling_curve());
+
+        static constexpr index_t NumAccess = SFC_Ys::get_num_of_access();
+
+        static_assert(0 < NumAccess, "Wrong! NumAccess should be larger than 0");
+
+        private:
+        static constexpr auto get_num_non_linear_access()
+        {
+            constexpr auto sfc_access_lens = SFC_Ys::access_lengths;
+            using ys_to_rhs_major =
+                typename decltype(TileDstr{}.get_static_tile_distribution_encoding())::Ys2RHsMajor;
+
+            constexpr auto non_linear = [&]() {
+                index_t cnt = 1;
+                static_for<0, NDimY, 1>{}([&](auto i_dim_y) {
+                    constexpr auto rhs_major    = ys_to_rhs_major{}[i_dim_y];
+                    constexpr auto target_h_dim = number<rhs_major - 1>{}; // no r dim here!
+                    if constexpr(LinearBottomDims{}[target_h_dim] == 0)
+                    {
+                        cnt *= sfc_access_lens[i_dim_y];
+                    }
+                });
+                return cnt;
+            }();
+
+            return non_linear;
+        }
+
+        // example:
+        // non_linear_access_map: sequence<0, 0, 0, 0, 1, 1, 1, 1> for 8 access, totally 2 register
+        // used
+        //  -> histogram : sequence<4, 4>
+        //  -> prefixsum : seqneuce<0, 4, 8>
+        // non_linear_access_map: sequence<0, 1, 2, 3, 4, 5, 6, 7> for 8 access, totally 8 register
+        // used, will pre-cache 8
+        //  -> histogram : sequence<1, 1, 1, 1, 1, 1, 1, 1>
+        //  -> prefixsum : seqneuce<0, 1, 2, 3, 4, 5, 6, 7, 8>
+        // non_linear_access_map: sequence<0, 0, 1, 1, 2, 2, 3, 3> for 8 access, totally 4 register
+        // used, will pre-cache 4
+        //  -> histogram : sequence<2, 2, 2, 2>
+        //  -> prefixsum : seqneuce<0, 2, 4, 6, 8>
+        static constexpr auto get_non_linear_access_map()
+        {
+            constexpr auto sfc_access_lens = SFC_Ys::access_lengths;
+            using ys_to_rhs_major =
+                typename decltype(TileDstr{}.get_static_tile_distribution_encoding())::Ys2RHsMajor;
+            constexpr auto non_linear_map = [&]() {
+                array<index_t, NumAccess> m_{0};
+                index_t cumulative_len_            = 1;
+                index_t cumulative_non_linear_len_ = 1;
+                static_for<0, NDimY, 1>{}([&](auto i_y) {
+                    constexpr auto i_dim_y       = number<NDimY - i_y - 1>{}; // from right to left
+                    constexpr auto rhs_major     = ys_to_rhs_major{}[i_dim_y];
+                    constexpr auto target_h_dim  = number<rhs_major - 1>{}; // no r dim here!
+                    constexpr auto is_linear_dim = LinearBottomDims{}[target_h_dim];
+
+                    array<index_t, NumAccess> current_m_{0};
+                    constexpr auto current_len_ = sfc_access_lens[i_dim_y];
+
+                    // copy cumulative length as current pattern
+                    for(auto i_ = 0; i_ < cumulative_len_; i_++)
+                    {
+                        current_m_(i_) = m_[i_];
+                    }
+                    for(auto j_ = 0; j_ < current_len_; j_++)
+                    {
+                        auto j_offset_ = is_linear_dim ? 0 : j_ * cumulative_non_linear_len_;
+                        for(auto i_ = 0; i_ < cumulative_len_; i_++)
+                        {
+                            m_(j_ * cumulative_len_ + i_) = current_m_[i_] + j_offset_;
+                        }
+                    }
+                    cumulative_len_ *= current_len_;
+                    if(!is_linear_dim)
+                        cumulative_non_linear_len_ *= current_len_;
+                });
+                return m_;
+            }();
+
+            return TO_SEQUENCE(non_linear_map, NumAccess);
+        }
+
+        static constexpr auto get_non_linear_access_histogram()
+        {
+            constexpr auto m_ = get_non_linear_access_map();
+            // m_.foo();
+
+            constexpr auto r_ =
+                typename arithmetic_sequence_gen<0, get_num_non_linear_access() + 1, 1>::type{};
+
+            constexpr auto h_ = histogram_sorted_sequence(m_, r_);
+
+            return h_;
+        }
+
+        static constexpr auto get_non_linear_access_histogram_prefix_sum()
+        {
+            constexpr auto h_            = get_non_linear_access_histogram();
+            constexpr auto h_prefix_sum_ = prefix_sum_sequence(h_);
+            return h_prefix_sum_;
+        }
+
+        public:
+        static constexpr index_t NumAccess_NonLinear = get_num_non_linear_access();
+        using AccessMap_NonLinear       = decltype(get_non_linear_access_map()); // sequence
+        using AccessHistogram_NonLinear = decltype(get_non_linear_access_histogram());
+        using AccessPrefixSum_NonLinear = decltype(get_non_linear_access_histogram_prefix_sum());
+    };
+
+    static constexpr index_t NumAccess           = traits::NumAccess;
+    static constexpr index_t NumAccess_NonLinear = traits::NumAccess_NonLinear;
+    using AccessMap_NonLinear                    = typename traits::AccessMap_NonLinear;
+    using AccessHistogram_NonLinear              = typename traits::AccessHistogram_NonLinear;
+    using AccessPrefixSum_NonLinear              = typename traits::AccessPrefixSum_NonLinear;
+
+    CK_TILE_DEVICE constexpr tile_window_linear() = default;
+
+    CK_TILE_DEVICE constexpr tile_window_linear(const BottomTensorView& bottom_tensor_view,
+                                                const WindowLengths& window_lengths,
+                                                const BottomTensorIndex& window_origin,
+                                                const TileDstr& tile_distribution)
+        : bottom_tensor_view_{bottom_tensor_view},
+          window_lengths_{window_lengths},
+          window_origin_{window_origin},
+          tile_dstr_{tile_distribution},
+          cached_coords_{},
+          cached_flags_{}
+    {
+        auto window_adaptor_thread_coord_tmp = make_tensor_adaptor_coordinate(
+            tile_distribution.get_ps_ys_to_xs_adaptor(),
+            container_concat(make_tuple(get_warp_id(), get_lane_id()),
+                             generate_tuple([&](auto) { return number<0>{}; }, number<NDimY>{})));
+
+        BottomTensorIndex bottom_tensor_thread_origin_idx_tmp =
+            window_origin + window_adaptor_thread_coord_tmp.get_bottom_index();
+
+        auto bottom_tensor_thread_coord_tmp = make_tensor_coordinate(
+            bottom_tensor_view_.get_tensor_descriptor(), bottom_tensor_thread_origin_idx_tmp);
+
+        // future load/store() calls (might allocate more registers)
+        using SFC_Ys = typename traits::SFC_Ys;
+
+        static_for<0, NumAccess, 1>{}([&](auto i_access) {
+            constexpr auto non_linear_id = number<AccessMap_NonLinear{}[i_access]>{};
+            constexpr auto need_save_non_linear_coord =
+                bool_constant<AccessPrefixSum_NonLinear{}[non_linear_id] == i_access>{};
+
+            if constexpr(need_save_non_linear_coord)
+            {
+                cached_coords_(non_linear_id) = bottom_tensor_thread_coord_tmp;
+            }
+
+            // TODO: need pad_tensor_view to check which dim need use flag to check
+            //      cached flag is independent from non-linear-coord
+            //      but need be updated in move_tile, with proper dims
+            cached_flags_(i_access) = coordinate_has_valid_offset_assuming_top_index_is_valid(
+                bottom_tensor_view_.get_tensor_descriptor(), bottom_tensor_thread_coord_tmp);
+
+            if constexpr(i_access != (NumAccess - 1))
+            {
+                constexpr auto idx_diff_ys = SFC_Ys::get_forward_step(i_access); // tuple of number
+                constexpr auto idx_diff_ps_ys = container_concat(
+                    generate_tuple([&](auto) { return number<0>{}; }, number<NDimP>{}),
+                    idx_diff_ys);
+
+                move_window_adaptor_and_bottom_tensor_thread_coordinate(
+                    window_adaptor_thread_coord_tmp,
+                    bottom_tensor_thread_coord_tmp,
+                    idx_diff_ps_ys);
+            }
+        });
+    }
+
+    CK_TILE_DEVICE static constexpr index_t get_num_of_dimension() { return NDimBottomTensor; }
+
+    CK_TILE_DEVICE static constexpr bool has_static_tile_distribution()
+    {
+        return TileDstr::is_static();
+    }
+
+    CK_TILE_DEVICE constexpr auto get_window_lengths() const { return window_lengths_; }
+
+    CK_TILE_DEVICE constexpr auto get_tile_distribution() const { return tile_dstr_; }
+
+    CK_TILE_DEVICE constexpr auto get_bottom_tensor_view() const { return bottom_tensor_view_; }
+
+    CK_TILE_DEVICE constexpr auto get_window_origin() const { return window_origin_; }
+
+    CK_TILE_DEVICE constexpr void
+    set_bottom_tensor_view_data_ptr(typename BottomTensorView::DataType* data)
+    {
+        bottom_tensor_view_.buf_.p_data_ = data;
+    }
+
+    // move thread's window adaptor coordinate and bottom tensor coordinate
+    // [p0, p1, ..., y0, y1, ...] ==> [x0, x1, ...] ==> [x0', x1', ...] ==> [offset]
+    template <typename ATopIndex>
+    CK_TILE_DEVICE void move_window_adaptor_and_bottom_tensor_thread_coordinate(
+        WindowAdaptorCoord& window_adaptor_thread_coord,
+        BottomTensorCoord& bottom_tensor_thread_coord,
+        const ATopIndex& idx_diff_adaptor_top) const
+    {
+        array<index_t, NDimBottomTensor> idx_diff_adaptor_bottom;
+
+        move_tensor_adaptor_coordinate(tile_dstr_.get_ps_ys_to_xs_adaptor(),
+                                       window_adaptor_thread_coord,
+                                       idx_diff_adaptor_top,
+                                       idx_diff_adaptor_bottom);
+
+        move_tensor_coordinate(bottom_tensor_view_.get_tensor_descriptor(),
+                               bottom_tensor_thread_coord,
+                               idx_diff_adaptor_bottom);
+    }
+
+    template <index_t i_access>
+    CK_TILE_DEVICE static constexpr auto get_bottom_linear_coordinate(number<i_access>)
+    {
+        using SFC_Ys          = typename traits::SFC_Ys;
+        constexpr auto idx_ys = SFC_Ys::get_index(number<i_access>{});
+        using ys_to_rhs_major =
+            typename decltype(TileDstr{}.get_static_tile_distribution_encoding())::Ys2RHsMajor;
+
+        constexpr auto modified_idx_ys = generate_tuple(
+            [&](auto i_dim_y) {
+                constexpr auto rhs_major    = ys_to_rhs_major{}[i_dim_y];
+                constexpr auto target_h_dim = number<rhs_major - 1>{}; // no r dim here!
+                if constexpr(LinearBottomDims{}[target_h_dim] == 0)
+                {
+                    return number<0>{};
+                }
+                else
+                {
+                    return number<idx_ys[i_dim_y]>{};
+                }
+            },
+            number<NDimY>{});
+
+        constexpr auto adaptor_ = TileDstr{}.get_ps_ys_to_xs_adaptor();
+        constexpr auto idx_ =
+            container_concat(make_tuple(number<0>{}, number<0>{}), modified_idx_ys);
+
+        return adaptor_.calculate_bottom_index(idx_);
+    }
+
+    template <index_t i_access>
+    CK_TILE_DEVICE static constexpr index_t get_bottom_linear_offset(number<i_access>)
+    {
+        constexpr auto linear_coord = get_bottom_linear_coordinate(number<i_access>{});
+        // since this is linear offset, we assum bottom X tensor is always linear
+        constexpr index_t linear_offset = [&]() {
+            constexpr auto x_idx_ = linear_coord;
+            constexpr auto x_len_ = TileDstr{}.get_lengths();
+            static_assert(x_idx_.size() == x_len_.size());
+            constexpr index_t x_dims_ = x_idx_.size();
+            index_t cu_stride_        = 1;
+            index_t cu_offset_        = 0;
+            static_for<0, x_dims_, 1>{}([&](auto i_) {
+                auto r_i_ = number<x_dims_ - i_ - 1>{};
+                cu_offset_ += x_idx_[r_i_] * cu_stride_;
+                cu_stride_ *= x_len_[r_i_];
+            });
+            return cu_offset_;
+        }();
+
+        return linear_offset;
+    }
+
+    CK_TILE_DEVICE constexpr auto get_num_of_access() const { return traits::NumAccess; }
+
+    template <index_t i_access = -1, bool oob_conditional_check = true>
+    CK_TILE_DEVICE auto load(number<i_access> = {}, bool_constant<oob_conditional_check> = {}) const
+    {
+        using vector_t = typename traits::vector_t;
+        using SFC_Ys   = typename traits::SFC_Ys;
+
+        constexpr auto tile_dstr = TileDstr{};
+
+        auto dst_tensor = make_static_distributed_tensor<DataType>(tile_dstr);
+
+        auto issue = [&](auto i_access_) {
+            constexpr auto IAccess = number<i_access_>{};
+
+            constexpr auto non_linear_id    = number<AccessMap_NonLinear{}[IAccess]>{};
+            auto bottom_tensor_thread_coord = cached_coords_[non_linear_id];
+            auto bottom_tensor_flag         = cached_flags_[IAccess];
+
+            constexpr auto linear_offset = get_bottom_linear_offset(IAccess);
+
+            // read from bottom tensor
+            const vector_t vec_value =
+                get_bottom_tensor_view().template get_vectorized_elements<vector_t>(
+                    bottom_tensor_thread_coord,
+                    linear_offset,
+                    bottom_tensor_flag,
+                    bool_constant<oob_conditional_check>{});
+#if 1
+            // data index [y0, y1, ...]
+            constexpr auto idx_diff_ys = SFC_Ys::get_index(IAccess);
+            // write into distributed tensor
+            static_for<0, traits::ScalarPerVector, 1>{}([&](auto j) {
+                constexpr auto idx_ys = generate_tuple(
+                    [&](auto jj) {
+                        return jj == traits::VectorDimY ? (idx_diff_ys[jj] + j) : idx_diff_ys[jj];
+                    },
+                    number<NDimY>{});
+
+                constexpr index_t d = tile_dstr.get_ys_to_d_descriptor().calculate_offset(idx_ys);
+
+                dst_tensor.get_thread_buffer().template at<d>() =
+                    vec_value.template get_as<DataType>()[j];
+            });
+#else
+            constexpr index_t d = tile_dstr.get_ys_to_d_descriptor().calculate_offset(idx_ys_start);
+            static_assert(d % traits::ScalarPerVector == 0);
+
+            dst_tensor.get_thread_buffer().template get_as<vector_t>()(
+                number<d / traits::ScalarPerVector>{}) = bit_cast<vector_t>(vec_value);
+#endif
+        };
+
+        WINDOW_DISPATCH_ISSUE();
+
+        return dst_tensor;
+    }
+
+    template <typename DstTile,
+              index_t i_access           = -1,
+              bool oob_conditional_check = true,
+              bool pre_nop               = false>
+    CK_TILE_DEVICE void load_raw(DstTile& dst_tensor,
+                                 number<i_access> = {}, // negative means loop over all num_access
+                                 bool_constant<oob_conditional_check> = {},
+                                 bool_constant<pre_nop>               = {}) const
+    {
+        using vector_t = typename traits::vector_t;
+        using SFC_Ys   = typename traits::SFC_Ys;
+        static constexpr index_t YElementSize =
+            TileDstr{}.get_ys_to_d_descriptor().get_element_space_size();
+        static_assert(YElementSize % traits::ScalarPerVector == 0);
+        using vectorized_tbuf = array<vector_t, YElementSize / traits::ScalarPerVector>;
+
+        constexpr auto tile_dstr = TileDstr{};
+
+        auto& dst_vec_tbuf = reinterpret_cast<vectorized_tbuf&>(dst_tensor.get_thread_buffer());
+
+        auto issue = [&](auto i_access_) {
+            constexpr auto IAccess  = number<i_access_>{};
+            constexpr auto pre_nop_ = [&]() {
+                if constexpr(pre_nop && i_access_ == 0 &&
+                             BottomTensorView::buffer_view::get_address_space() ==
+                                 address_space_enum::global)
+                    return bool_constant<true>{};
+                else
+                    return bool_constant<false>{};
+            }();
+
+            constexpr auto non_linear_id    = number<AccessMap_NonLinear{}[IAccess]>{};
+            auto bottom_tensor_thread_coord = cached_coords_[non_linear_id];
+            constexpr auto linear_offset    = get_bottom_linear_offset(IAccess);
+            auto bottom_tensor_flag         = cached_flags_[IAccess];
+
+            // data index [y0, y1, ...]
+            constexpr auto idx_ys_start = SFC_Ys::get_index(IAccess);
+            constexpr index_t d = tile_dstr.get_ys_to_d_descriptor().calculate_offset(idx_ys_start);
+            static_assert(d % traits::ScalarPerVector == 0);
+
+            get_bottom_tensor_view().template get_vectorized_elements_raw<vector_t>(
+                dst_vec_tbuf.template at<d / traits::ScalarPerVector>(),
+                bottom_tensor_thread_coord,
+                linear_offset /**/,
+                bottom_tensor_flag,
+                bool_constant<oob_conditional_check>{},
+                pre_nop_);
+#if CK_TILE_WORKAROUND_ROCM_6_1_SCRATCH_MEMORY_ISSUE || \
+    CK_TILE_WORKAROUND_ROCM_6_2_SCRATCH_MEMORY_ISSUE
+            asm volatile(""); // this is starting from rocm-6.2, but same sympton, reuse this flag
+#endif
+        };
+
+        WINDOW_DISPATCH_ISSUE();
+    }
+
+    // TODO: currently async load only implemented in inline asm
+    template <typename LdsTileWindow_,
+              index_t i_access           = -1,
+              bool oob_conditional_check = true,
+              bool pre_nop               = false>
+    CK_TILE_DEVICE auto async_load_raw(LdsTileWindow_&& lds_tile,
+                                       number<i_access>                     = {},
+                                       bool_constant<oob_conditional_check> = {},
+                                       bool_constant<pre_nop>               = {}) const
+    {
+        using LdsTileWindow = remove_cvref_t<LdsTileWindow_>;
+        using LdsDataType   = typename LdsTileWindow::DataType;
+
+        // currently we only support everything is non linear dim
+        // actually it's not performant if we have linear dim(e.g. fast changing)
+        static_assert(NumAccess_NonLinear == NumAccess);
+        static_assert(BottomTensorView::buffer_view::get_address_space() ==
+                      address_space_enum::global);
+
+        // issues * warps * lanes
+        static_assert(LdsTileWindow::get_num_of_dimension() == 3); // TODO: hard coded
+
+        const index_t size_per_buf =
+            lds_tile.get_bottom_tensor_view().get_tensor_descriptor().calculate_offset(
+                make_tuple(number<0>{}, number<0>{}, number<0>{})) *
+            sizeof(LdsDataType);
+
+        const index_t size_per_wave =
+            lds_tile.get_bottom_tensor_view().get_tensor_descriptor().calculate_offset(
+                make_tuple(number<0>{}, number<1>{}, number<0>{})) *
+                sizeof(LdsDataType) -
+            size_per_buf;
+
+        const index_t size_per_issue =
+            lds_tile.get_bottom_tensor_view().get_tensor_descriptor().calculate_offset(
+                make_tuple(number<1>{}, number<0>{}, number<0>{})) *
+                sizeof(LdsDataType) -
+            size_per_buf;
+
+        const index_t m0_init_value = size_per_buf + size_per_wave * get_warp_id();
+        m0_set_with_memory(m0_init_value); // This should be wave independent
+
+        using vector_t = typename traits::vector_t;
+
+        LdsDataType* smem = lds_tile.get_bottom_tensor_view().get_buffer_view().p_data_;
+
+        // loop over thread tensor space [y0, y1, ...]
+        auto issue = [&](auto i_access_) {
+            constexpr auto IAccess  = number<i_access_>{};
+            constexpr auto pre_nop_ = [&]() {
+                if constexpr(pre_nop && i_access_ == 0)
+                    return bool_constant<true>{};
+                else
+                    return bool_constant<false>{};
+            }();
+
+            constexpr auto non_linear_id    = number<AccessMap_NonLinear{}[IAccess]>{};
+            auto bottom_tensor_thread_coord = cached_coords_[non_linear_id];
+            auto bottom_tensor_flag         = cached_flags_[IAccess]; // get this flag anyway
+
+            // read from bottom tensor
+            get_bottom_tensor_view().template async_get_vectorized_elements_raw<vector_t>(
+                smem, bottom_tensor_thread_coord, 0, bottom_tensor_flag, pre_nop_);
+
+            // move thread coordinate
+            if constexpr(i_access_ != (NumAccess - 1))
+            {
+                m0_inc_with_memory(size_per_issue);
+            }
+        };
+
+        WINDOW_DISPATCH_ISSUE();
+    }
+
+    template <typename LdsTileWindow_, index_t i_access = -1, bool oob_conditional_check = true>
+    CK_TILE_DEVICE auto async_load(LdsTileWindow_&& lds_tile,
+                                   number<i_access>                     = {},
+                                   bool_constant<oob_conditional_check> = {}) const
+    {
+        using LdsTileWindow = remove_cvref_t<LdsTileWindow_>;
+        using LdsDataType   = typename LdsTileWindow::DataType;
+
+        // currently we only support everything is non linear dim
+        // actually it's not performant if we have linear dim(e.g. fast changing)
+        static_assert(NumAccess_NonLinear == NumAccess);
+        static_assert(BottomTensorView::buffer_view::get_address_space() ==
+                      address_space_enum::global);
+
+        // issues * warps * lanes
+        static_assert(LdsTileWindow::get_num_of_dimension() == 3); // TODO: hard coded
+
+        // TODO: LDS offset is not good for intrinsic based implementation(compiler can't figure out
+        // dependency) hence avoid use offset based solution. size_per_buf should be zero (how to
+        // check?)
+        constexpr index_t size_per_buf =
+            lds_tile.get_bottom_tensor_view().get_tensor_descriptor().calculate_offset(
+                make_tuple(number<0>{}, number<0>{}, number<0>{}));
+
+        constexpr index_t size_per_wave =
+            lds_tile.get_bottom_tensor_view().get_tensor_descriptor().calculate_offset(
+                make_tuple(number<0>{}, number<1>{}, number<0>{})) -
+            size_per_buf;
+
+        constexpr index_t size_per_issue =
+            lds_tile.get_bottom_tensor_view().get_tensor_descriptor().calculate_offset(
+                make_tuple(number<1>{}, number<0>{}, number<0>{})) -
+            size_per_buf;
+
+        const index_t m0_init_value = size_per_buf + size_per_wave * get_warp_id();
+
+        using vector_t = typename traits::vector_t;
+
+        // TODO: we force CK_TILE_LDS_ADDR
+        CK_TILE_LDS_ADDR LdsDataType* smem =
+            lds_tile.get_bottom_tensor_view().get_buffer_view().p_data_ + m0_init_value;
+
+        // loop over thread tensor space [y0, y1, ...]
+        auto issue = [&](auto i_access_) {
+            constexpr auto IAccess          = number<i_access_>{};
+            constexpr auto non_linear_id    = number<AccessMap_NonLinear{}[IAccess]>{};
+            auto bottom_tensor_thread_coord = cached_coords_[non_linear_id];
+            auto bottom_tensor_flag         = cached_flags_[IAccess];
+
+            // read from bottom tensor
+            get_bottom_tensor_view().template async_get_vectorized_elements<vector_t>(
+                smem,
+                bottom_tensor_thread_coord,
+                0,
+                bottom_tensor_flag,
+                bool_constant<oob_conditional_check>{});
+
+            // move thread coordinate
+            if constexpr(i_access_ != (NumAccess - 1))
+            {
+                smem += size_per_issue; // Note we manually increase the per-issue offset
+            }
+        };
+
+        WINDOW_DISPATCH_ISSUE();
+    }
+
+    template <index_t i_access = -1, bool oob_conditional_check = true>
+    CK_TILE_DEVICE void store(const static_distributed_tensor<DataType, TileDstr>& dstr_tensor,
+                              number<i_access>                     = {},
+                              bool_constant<oob_conditional_check> = {}) const
+    {
+
+        using vector_t = typename traits::vector_t;
+        using SFC_Ys   = typename traits::SFC_Ys;
+
+        constexpr auto tile_dstr = TileDstr{};
+
+        // loop over thread tensor space [y0, y1, ...]
+        auto issue = [&](auto i_access_) {
+            constexpr auto IAccess          = number<i_access_>{};
+            constexpr auto non_linear_id    = number<AccessMap_NonLinear{}[IAccess]>{};
+            auto bottom_tensor_thread_coord = cached_coords_[non_linear_id];
+            constexpr auto linear_offset    = get_bottom_linear_offset(IAccess);
+            auto bottom_tensor_flag         = cached_flags_[IAccess];
+            // data index [y0, y1, ...]
+            constexpr auto idx_ys_start = SFC_Ys::get_index(IAccess);
+
+            // read from distributed tensor
+            vector_t vec_value;
+
+            static_for<0, traits::ScalarPerVector, 1>{}([&](auto j) {
+                constexpr auto idx_ys = generate_tuple(
+                    [&](auto jj) {
+                        return jj == traits::VectorDimY ? (idx_ys_start[jj] + j) : idx_ys_start[jj];
+                    },
+                    number<NDimY>{});
+
+                constexpr index_t d = tile_dstr.get_ys_to_d_descriptor().calculate_offset(idx_ys);
+
+                vec_value.template get_as<DataType>()(j) =
+                    dstr_tensor.get_thread_buffer().template at<d>();
+            });
+
+            // write into bottom tensor
+            get_bottom_tensor_view().template set_vectorized_elements<vector_t>(
+                bottom_tensor_thread_coord,
+                linear_offset,
+                bottom_tensor_flag,
+                vec_value,
+                bool_constant<oob_conditional_check>{});
+        };
+
+        WINDOW_DISPATCH_ISSUE();
+    }
+
+    template <index_t i_access = -1>
+    CK_TILE_DEVICE void store_raw(const static_distributed_tensor<DataType, TileDstr>& dstr_tensor,
+                                  number<i_access> = {}) const
+    {
+        using vector_t = typename traits::vector_t;
+        using SFC_Ys   = typename traits::SFC_Ys;
+
+        constexpr auto tile_dstr                    = TileDstr{};
+        static constexpr bool oob_conditional_check = true;
+
+        // loop over thread tensor space [y0, y1, ...]
+        auto issue = [&](auto i_access_) {
+            constexpr auto IAccess          = number<i_access_>{};
+            constexpr auto non_linear_id    = number<AccessMap_NonLinear{}[IAccess]>{};
+            auto bottom_tensor_thread_coord = cached_coords_[non_linear_id];
+            constexpr auto linear_offset    = get_bottom_linear_offset(IAccess);
+            auto bottom_tensor_flag         = cached_flags_[IAccess];
+
+            // data index [y0, y1, ...]
+            constexpr auto idx_ys_start = SFC_Ys::get_index(IAccess);
+
+            // read from distributed tensor
+            vector_t vec_value;
+            static_for<0, traits::ScalarPerVector, 1>{}([&](auto j) {
+                constexpr auto idx_ys = generate_tuple(
+                    [&](auto jj) {
+                        return jj == traits::VectorDimY ? (idx_ys_start[jj] + j) : idx_ys_start[jj];
+                    },
+                    number<NDimY>{});
+                constexpr index_t d = tile_dstr.get_ys_to_d_descriptor().calculate_offset(idx_ys);
+                vec_value.template get_as<DataType>()(j) =
+                    dstr_tensor.get_thread_buffer().template at<d>();
+            });
+
+            // write into bottom tensor
+            get_bottom_tensor_view()
+                .template set_vectorized_elements_raw<vector_t, oob_conditional_check>(
+                    bottom_tensor_thread_coord, linear_offset, bottom_tensor_flag, vec_value);
+        };
+
+        WINDOW_DISPATCH_ISSUE();
+    }
+
+    template <index_t i_access = -1, bool oob_conditional_check = true>
+    CK_TILE_DEVICE void update(const static_distributed_tensor<DataType, TileDstr>& dstr_tensor,
+                               number<i_access>                     = {},
+                               bool_constant<oob_conditional_check> = {}) const
+    {
+
+        using vector_t = typename traits::vector_t;
+        using SFC_Ys   = typename traits::SFC_Ys;
+
+        constexpr auto tile_dstr = TileDstr{};
+
+        // loop over thread tensor space [y0, y1, ...]
+        auto issue = [&](auto i_access_) {
+            constexpr auto IAccess          = number<i_access_>{};
+            constexpr auto non_linear_id    = number<AccessMap_NonLinear{}[IAccess]>{};
+            auto bottom_tensor_thread_coord = cached_coords_[non_linear_id];
+            constexpr auto linear_offset    = get_bottom_linear_offset(IAccess);
+            auto bottom_tensor_flag         = cached_flags_[IAccess];
+
+            // data index [y0, y1, ...]
+            constexpr auto idx_ys_start = SFC_Ys::get_index(IAccess);
+
+            // read from distributed tensor
+            vector_t vec_value;
+
+            static_for<0, traits::ScalarPerVector, 1>{}([&](auto j) {
+                constexpr auto idx_ys = generate_tuple(
+                    [&](auto jj) {
+                        return jj == traits::VectorDimY ? (idx_ys_start[jj] + j) : idx_ys_start[jj];
+                    },
+                    number<NDimY>{});
+
+                constexpr index_t d = tile_dstr.get_ys_to_d_descriptor().calculate_offset(idx_ys);
+
+                vec_value.template get_as<DataType>()(j) =
+                    dstr_tensor.get_thread_buffer().template at<d>();
+            });
+
+            // write into bottom tensor
+            get_bottom_tensor_view().template update_vectorized_elements<vector_t>(
+                bottom_tensor_thread_coord,
+                linear_offset,
+                bottom_tensor_flag,
+                vec_value,
+                bool_constant<oob_conditional_check>{});
+        };
+
+        WINDOW_DISPATCH_ISSUE();
+    }
+
+    // move thread's botom tensor coordiante
+    // [x0', x1', ... ] ==> [offset]
+    // also move window-origin
+    CK_TILE_DEVICE void move(const BottomTensorIndex& step)
+    {
+        window_origin_ += step;
+
+        static_for<0, NumAccess, 1>{}([&](auto i_access) {
+            constexpr auto IAccess       = number<i_access>{};
+            constexpr auto non_linear_id = number<AccessMap_NonLinear{}[i_access]>{};
+            constexpr auto need_update_non_linear_coord =
+                bool_constant<AccessPrefixSum_NonLinear{}[non_linear_id] == i_access>{};
+
+            if constexpr(need_update_non_linear_coord)
+            {
+                move_tensor_coordinate(bottom_tensor_view_.get_tensor_descriptor(),
+                                       cached_coords_(non_linear_id),
+                                       step);
+            }
+
+            // move the current coord with linear_coords
+            auto tmp_coords             = cached_coords_[non_linear_id];
+            constexpr auto linear_coord = get_bottom_linear_coordinate(IAccess);
+            move_tensor_coordinate(
+                bottom_tensor_view_.get_tensor_descriptor(), tmp_coords, linear_coord);
+
+            cached_flags_(IAccess) = coordinate_has_valid_offset_assuming_top_index_is_valid(
+                bottom_tensor_view_.get_tensor_descriptor(), tmp_coords);
+        });
+    }
+
+    CK_TILE_DEVICE void set_window_origin(const BottomTensorIndex& new_window_origin)
+    {
+        window_origin_ = new_window_origin;
+
+        auto window_adaptor_thread_coord_tmp = make_tensor_adaptor_coordinate(
+            TileDstr{}.get_ps_ys_to_xs_adaptor(),
+            container_concat(make_tuple(get_warp_id(), get_lane_id()),
+                             generate_tuple([&](auto) { return number<0>{}; }, number<NDimY>{})));
+
+        BottomTensorIndex bottom_tensor_thread_origin_idx_tmp =
+            window_origin_ + window_adaptor_thread_coord_tmp.get_bottom_index();
+
+        auto bottom_tensor_thread_coord_tmp = make_tensor_coordinate(
+            bottom_tensor_view_.get_tensor_descriptor(), bottom_tensor_thread_origin_idx_tmp);
+
+        // future load/store() calls (might allocate more registers)
+        using SFC_Ys = typename traits::SFC_Ys;
+
+        static_for<0, NumAccess, 1>{}([&](auto i_access) {
+            constexpr auto non_linear_id = number<AccessMap_NonLinear{}[i_access]>{};
+            constexpr auto need_save_non_linear_coord =
+                bool_constant<AccessPrefixSum_NonLinear{}[non_linear_id] == i_access>{};
+
+            if constexpr(need_save_non_linear_coord)
+            {
+                cached_coords_(non_linear_id) = bottom_tensor_thread_coord_tmp;
+            }
+
+            if constexpr(i_access != (NumAccess - 1))
+            {
+                constexpr auto idx_diff_ys = SFC_Ys::get_forward_step(i_access); // tuple of number
+                constexpr auto idx_diff_ps_ys = container_concat(
+                    generate_tuple([&](auto) { return number<0>{}; }, number<NDimP>{}),
+                    idx_diff_ys);
+
+                move_window_adaptor_and_bottom_tensor_thread_coordinate(
+                    window_adaptor_thread_coord_tmp,
+                    bottom_tensor_thread_coord_tmp,
+                    idx_diff_ps_ys);
+            }
+        });
+    }
+
+    CK_TILE_HOST_DEVICE void init_raw() { bottom_tensor_view_.init_raw(); }
+
+    // this is the bottom tensor view
+    // [x0', x1', ...] ==> [offset]
+    BottomTensorView bottom_tensor_view_;
+
+    //
+    WindowLengths window_lengths_;
+
+    // origin ([x0', x1', ...]) of window on bottom tensor
+    BottomTensorIndex window_origin_;
+
+    // Tile tensor distribution, which contains:
+    //   1. adaptor for window: [p0, p1, ..., y0, y1, ...] ==> [x0, x1, ...]
+    //   2. thread descriptor for thread tensor in register: [y0, y1, ...] ==> [d]
+    TileDstr tile_dstr_;
+
+    // this contains:
+    array<BottomTensorCoord, traits::NumAccess_NonLinear> cached_coords_;
+    array<bool, traits::NumAccess> cached_flags_;
+};
+
+#undef WINDOW_DISPATCH_ISSUE
+
+namespace impl {
+template <address_space_enum, index_t len_>
+struct default_linear_bottom_dims_impl
+{
+    using type = typename uniform_sequence_gen<len_, 0>::type;
+};
+
+template <index_t len_>
+struct default_linear_bottom_dims_impl<address_space_enum::global, len_>
+{
+    // global default to seq<0,0,....1>
+    using type = typename sequence_merge<typename uniform_sequence_gen<len_ - 1, 0>::type,
+                                         sequence<1>>::type;
+};
+
+template <index_t len_>
+struct default_linear_bottom_dims_impl<address_space_enum::lds, len_>
+{
+    // lds default to seq<1,1.....1>
+    using type = typename uniform_sequence_gen<len_, 1>::type;
+};
+} // namespace impl
+
+template <typename TensorView_>
+using default_linear_bottom_dims =
+    typename impl::default_linear_bottom_dims_impl<TensorView_::buffer_view::get_address_space(),
+                                                   TensorView_::get_num_of_dimension()>::type;
+
+// if using this API, will create a tile_window_linear
+// this structure can have the chance to use immediate value, save register
+// need pass in LinearBottomDims_ properly to control which dim is linear
+// so to generate a constexpr offset as linear_offset for this dim
+// (and finally pass to the immediate offset of buffer/lds instruction)
+//
+// Note: there is no internal check for which dim is OK to use linear offset
+// user must make sure by themselves
+//
+// e.g.
+// 2d global matrix, set LinearBottomDims_=seq<0, 1>, the last dim will generate
+// immediate offset if each thread has multiple issue along last dim
+//
+// 2d LDS buffer, set LinearBottomDims_=seq<1, 1>, then only one vgpr used as offset
+// everything else is just using immediate offset.
+//
+template <typename TensorView_,
+          typename WindowLengths_,
+          typename StaticTileDistribution_,
+          typename LinearBottomDims_ = default_linear_bottom_dims<TensorView_>>
+CK_TILE_DEVICE constexpr auto
+make_tile_window_linear(const TensorView_& tensor_view,
+                        const WindowLengths_& window_lengths,
+                        const multi_index<TensorView_::get_num_of_dimension()>& origin,
+                        const StaticTileDistribution_& tile_distribution,
+                        LinearBottomDims_ = {})
+{
+    static_assert(LinearBottomDims_::size() == TensorView_::get_num_of_dimension());
+    return tile_window_linear<remove_cvref_t<TensorView_>,
+                              remove_cvref_t<WindowLengths_>,
+                              remove_cvref_t<StaticTileDistribution_>,
+                              remove_cvref_t<LinearBottomDims_>>{
+        tensor_view, window_lengths, origin, tile_distribution};
+}
+
+template <
+    typename TileWindow_,
+    typename StaticTileDistribution_,
+    typename LinearBottomDims_ = default_linear_bottom_dims<typename TileWindow_::BottomTensorView>>
+CK_TILE_DEVICE constexpr auto
+make_tile_window_linear(const TileWindow_& tile_window,
+                        const StaticTileDistribution_& tile_distribution,
+                        LinearBottomDims_ = {})
+{
+    return make_tile_window_linear(tile_window.get_bottom_tensor_view(),
+                                   tile_window.get_window_lengths(),
+                                   tile_window.get_window_origin(),
+                                   tile_distribution,
+                                   LinearBottomDims_{});
+}
+
+// this version must not be called under a constexpr context
+template <typename TensorView_,
+          typename WindowLengths_,
+          typename StaticTileDistribution_,
+          typename LinearBottomDims_ = default_linear_bottom_dims<TensorView_>>
+CK_TILE_DEVICE auto
+make_tile_window_linear_raw(const TensorView_& tensor_view,
+                            const WindowLengths_& window_lengths,
+                            const multi_index<TensorView_::get_num_of_dimension()>& origin,
+                            const StaticTileDistribution_& tile_distribution,
+                            LinearBottomDims_ = {})
+{
+    static_assert(LinearBottomDims_::size() == TensorView_::get_num_of_dimension());
+    auto w = tile_window_linear<remove_cvref_t<TensorView_>,
+                                remove_cvref_t<WindowLengths_>,
+                                remove_cvref_t<StaticTileDistribution_>,
+                                remove_cvref_t<LinearBottomDims_>>{
+        tensor_view, window_lengths, origin, tile_distribution};
+    w.init_raw();
+    return w;
+}
+
+template <
+    typename TileWindow_,
+    typename StaticTileDistribution_,
+    typename LinearBottomDims_ = default_linear_bottom_dims<typename TileWindow_::BottomTensorView>>
+CK_TILE_DEVICE constexpr auto
+make_tile_window_linear_raw(const TileWindow_& tile_window,
+                            const StaticTileDistribution_& tile_distribution,
+                            LinearBottomDims_ = {})
+{
+    return make_tile_window_linear_raw(tile_window.get_bottom_tensor_view(),
+                                       tile_window.get_window_lengths(),
+                                       tile_window.get_window_origin(),
+                                       tile_distribution,
+                                       LinearBottomDims_{});
+}
+
+template <typename TensorView_,
+          typename WindowLengths_,
+          typename StaticTileDistribution_,
+          typename LinearBottomDims_>
+CK_TILE_DEVICE void move_tile_window(
+    tile_window_linear<TensorView_, WindowLengths_, StaticTileDistribution_, LinearBottomDims_>&
+        window,
+    const typename tile_window_linear<TensorView_,
+                                      WindowLengths_,
+                                      StaticTileDistribution_,
+                                      LinearBottomDims_>::BottomTensorIndex& step)
+{
+    window.move(step);
+}
+
+} // namespace ck_tile