/home/docs/checkouts/readthedocs.org/user_builds/advanced-micro-devices-composable-kernel/checkouts/docs-6.4.3/include/ck_tile/core/tensor/tile_distribution_encoding.hpp Source File

/home/docs/checkouts/readthedocs.org/user_builds/advanced-micro-devices-composable-kernel/checkouts/docs-6.4.3/include/ck_tile/core/tensor/tile_distribution_encoding.hpp Source File#

Composable Kernel: /home/docs/checkouts/readthedocs.org/user_builds/advanced-micro-devices-composable-kernel/checkouts/docs-6.4.3/include/ck_tile/core/tensor/tile_distribution_encoding.hpp Source File
Go to the documentation of this file.
 // SPDX-License-Identifier: MIT
 // Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
  
 #pragma once
  
 #include "ck_tile/core/config.hpp"
 #include "ck_tile/core/numeric/integer.hpp"
 #include "ck_tile/core/numeric/integral_constant.hpp"
 #include "ck_tile/core/algorithm/coordinate_transform.hpp"
 #include "ck_tile/core/tensor/tensor_adaptor.hpp"
 #include "ck_tile/core/tensor/tensor_adaptor_coordinate.hpp"
 #include "ck_tile/core/container/container_helper.hpp"
 #include "ck_tile/core/container/multi_index.hpp"
 #include "ck_tile/core/numeric/math.hpp"
 #include "ck_tile/core/utility/type_traits.hpp"
  
 namespace ck_tile {
  
 template <typename RsLengths_,    // sequence<...>
           typename HsLengthss_,   // tuple<sequence<...>, ...>
           typename Ps2RHssMajor_, // tuple<sequence<...>, ...>
           typename Ps2RHssMinor_, // tuple<sequence<...>, ...>
           typename Ys2RHsMajor_,  // sequence<...>
           typename Ys2RHsMinor_>  // sequence<...>
 struct tile_distribution_encoding
 {
     using RsLengths    = remove_cvref_t<RsLengths_>;
     using HsLengthss   = remove_cvref_t<HsLengthss_>;
     using Ps2RHssMajor = remove_cvref_t<Ps2RHssMajor_>;
     using Ps2RHssMinor = remove_cvref_t<Ps2RHssMinor_>;
     using Ys2RHsMajor  = remove_cvref_t<Ys2RHsMajor_>;
     using Ys2RHsMinor  = remove_cvref_t<Ys2RHsMinor_>;
  
     static_assert(Ps2RHssMajor::size() == Ps2RHssMinor::size(), "wrong!");
     static_assert(Ys2RHsMajor::size() == Ys2RHsMinor::size(), "wrong!");
  
     static constexpr index_t NDimX = HsLengthss::size();
     static constexpr index_t NDimP = Ps2RHssMajor::size();
     static constexpr index_t NDimY = Ys2RHsMajor::size();
     static constexpr index_t NDimR = RsLengths::size();
  
     // FIXME: move into detail
     static constexpr auto rs_lengths_       = RsLengths{};
     static constexpr auto hs_lengthss_      = HsLengthss{};
     static constexpr auto ps_to_rhss_major_ = Ps2RHssMajor{};
     static constexpr auto ps_to_rhss_minor_ = Ps2RHssMinor{};
     static constexpr auto ys_to_rhs_major_  = Ys2RHsMajor{};
     static constexpr auto ys_to_rhs_minor_  = Ys2RHsMinor{};
  
     // redundant but useful info
     // TODO: really bad code, should be over-hauled
     struct detail
     {
         // ndim_rh_major_, ndim_span_mainor_
         static constexpr index_t ndim_rh_major_   = NDimX + 1;
         static constexpr index_t ndim_span_major_ = NDimX;
  
         // ndims_rhs_minor_[ndim_rh_major_]
         static constexpr auto ndims_rhs_minor_ = generate_array(
             [](auto i) {
                 if constexpr(i.value == 0)
                 {
                     return rs_lengths_.size();
                 }
                 else
                 {
                     return hs_lengthss_[i - number<1>{}].size();
                 }
             },
             number<ndim_rh_major_>{});
  
         // max_ndim_rh_minor_
         static constexpr index_t max_ndim_rh_minor_ =
             container_reduce(ndims_rhs_minor_, maximize<index_t>{}, 0);
  
         // rhs_lengthss_[ndim_rh_major_][max_ndim_rh_minor_]
         static constexpr auto rhs_lengthss_ =
             to_array_of_array(container_concat(make_tuple(rs_lengths_), hs_lengthss_));
  
         // ys_lengths_
         static constexpr auto ys_lengths_ = [] {
             array<index_t, NDimY> ys_lengths_tmp{-1};
  
             for(index_t i = 0; i < NDimY; i++)
             {
                 index_t rh_major = ys_to_rhs_major_[i];
                 index_t rh_minor = ys_to_rhs_minor_[i];
  
                 ys_lengths_tmp(i) = rhs_lengthss_[rh_major][rh_minor];
             }
  
             return ys_lengths_tmp;
         }();
  
         // rhs_major_minor_to_ys_[ndim_rh_majpr_][max_ndim_rh_minor_]
         static constexpr auto rhs_major_minor_to_ys_ = [] {
             array<array<index_t, max_ndim_rh_minor_>, NDimX + 1> rhs_major_minor_to_ys_tmp{{-1}};
  
             static_for<0, NDimY, 1>{}([&](auto i) {
                 constexpr index_t rh_major = ys_to_rhs_major_[i];
                 constexpr index_t rh_minor = ys_to_rhs_minor_[i];
  
                 rhs_major_minor_to_ys_tmp(rh_major)(rh_minor) = i;
             });
  
             return rhs_major_minor_to_ys_tmp;
         }();
  
         // ndims_span_minor_[NDimY]
         static constexpr auto ndims_span_minor_ = [] {
             array<index_t, NDimX> ndims_span_minor{0};
  
             for(index_t i = 0; i < NDimY; i++)
             {
                 const index_t span_major = ys_to_rhs_major_[i] - 1;
  
                 ndims_span_minor(span_major)++;
             }
  
             return ndims_span_minor;
         }();
  
         // max_ndim_span_minor_
         static constexpr index_t max_ndim_span_minor_ =
             container_reduce(ndims_span_minor_, maximize<index_t>{}, 0);
  
         // rhs_major_minor_to_span_minor_ [ndim_rh_major_][max_ndim_rh_minor_]
         static constexpr auto rhs_major_minor_to_span_minor_ = [] {
             array<array<index_t, max_ndim_rh_minor_>, ndim_rh_major_> rhs_major_minor_to_span_minor{
                 {-1}};
  
             static_for<0, ndim_rh_major_, 1>{}([&](auto rh_major) {
                 constexpr index_t ndim_rh_minor = ndims_rhs_minor_[rh_major];
  
                 index_t cnt_ndim_span_minor = 0;
  
                 static_for<0, ndim_rh_minor, 1>{}([&](auto rh_minor) {
                     constexpr index_t idim_y = rhs_major_minor_to_ys_[rh_major][rh_minor];
  
                     if(idim_y >= 0)
                     {
                         rhs_major_minor_to_span_minor(rh_major)(rh_minor) = cnt_ndim_span_minor;
  
                         cnt_ndim_span_minor++;
                     }
                 });
             });
  
             return rhs_major_minor_to_span_minor;
         }();
  
         // ys_to_span_major_[NDimY]
         static constexpr auto ys_to_span_major_ =
             generate_array([](auto i) { return ys_to_rhs_major_[i] - 1; }, number<NDimY>{});
  
         // ys_to_span_minor_[NDimY]
         static constexpr auto ys_to_span_minor_ = generate_array(
             [](auto i) {
                 return rhs_major_minor_to_span_minor_[ys_to_rhs_major_[i]][ys_to_rhs_minor_[i]];
             },
             number<NDimY>{});
  
         // distributed_spans_lengthss_[ndim_span_major_][max_ndim_span_minor_]
         static constexpr auto distributed_spans_lengthss_ = [] {
             array<array<index_t, max_ndim_span_minor_>, ndim_span_major_>
                 distributed_spans_lengthss{{-1}};
  
             static_for<0, NDimY, 1>{}([&](auto i) {
                 const index_t rh_major = ys_to_rhs_major_[i];
                 const index_t rh_minor = ys_to_rhs_minor_[i];
  
                 const index_t h_length = hs_lengthss_[number<rh_major - 1>{}][rh_minor];
  
                 const index_t span_major = rh_major - 1;
                 const index_t span_minor = rhs_major_minor_to_span_minor_[rh_major][rh_minor];
  
                 distributed_spans_lengthss(span_major)(span_minor) = h_length;
             });
  
             return distributed_spans_lengthss;
         }();
  
         // ndims_distributed_spans_minor_[ndim_span_major_]
         static constexpr auto ndims_distributed_spans_minor_ = [] {
             array<index_t, ndim_span_major_> ndims_distributed_spans_minor{0};
  
             static_for<0, NDimY, 1>{}([&](auto i) {
                 const index_t span_major = ys_to_rhs_major_[i] - 1;
  
                 ndims_distributed_spans_minor(span_major)++;
             });
  
             return ndims_distributed_spans_minor;
         }();
  
         // does_p_own_r_[NDimP][NDimR]
         static constexpr auto does_p_own_r_ = [] {
             if constexpr(NDimR > 0)
             {
                 array<array<bool, NDimR>, NDimP> does_p_own_r{{false}};
  
                 static_for<0, NDimP, 1>{}([&](auto idim_p) {
                     constexpr index_t ndim_low = ps_to_rhss_major_[idim_p].size();
  
                     static_for<0, ndim_low, 1>{}([&](auto idim_low) {
                         constexpr index_t rh_major = ps_to_rhss_major_[idim_p][idim_low];
                         constexpr index_t rh_minor = ps_to_rhss_minor_[idim_p][idim_low];
  
                         if constexpr(rh_major == 0)
                         {
                             does_p_own_r(idim_p)(rh_minor) = true;
                         }
                     });
                 });
  
                 return does_p_own_r;
             }
             else
             {
                 return array<array<bool, NDimR>, NDimP>{};
             }
         }();
  
         // ps_over_rs_derivative_[NDimP][NDimR]
         static constexpr auto ps_over_rs_derivative_ = [] {
             if constexpr(NDimR > 0)
             {
                 array<array<index_t, NDimR>, NDimP> ps_over_rs_derivative{{0}};
  
                 static_for<0, NDimP, 1>{}([&](auto idim_p) {
                     constexpr index_t ndim_low = ps_to_rhss_major_[idim_p].size();
  
                     index_t p_over_rh_derivative = 1;
  
                     static_for<ndim_low - 1, -1, -1>{}([&](auto idim_low) {
                         constexpr index_t rh_major = ps_to_rhss_major_[idim_p][idim_low];
                         constexpr index_t rh_minor = ps_to_rhss_minor_[idim_p][idim_low];
  
                         constexpr index_t rh_length = rhs_lengthss_[rh_major][rh_minor];
  
                         if constexpr(rh_major == 0)
                         {
                             ps_over_rs_derivative(idim_p)(rh_minor) = p_over_rh_derivative;
                         }
  
                         p_over_rh_derivative *= rh_length;
                     });
                 });
  
                 return ps_over_rs_derivative;
             }
             else
             {
                 return array<array<index_t, NDimR>, NDimP>{};
             }
         }();
  
         // e.g. tuple<seq<1, 4, 32>, seq<4, 1, 4, 2, 4>> --> seq<3, 5> --> seq<0, 3, 8>
         CK_TILE_HOST_DEVICE static constexpr auto get_h_dim_lengths_prefix_sum()
         {
             // <len_d0, len_d1, ...>
             // e.g. tuple<seq<1, 4, 32>, seq<4, 1, 4, 2, 4>> --> seq<3, 5>
             constexpr auto uniformed_h_dim_lengths = generate_sequence_v2(
                 [&](auto i) {
                     constexpr index_t size = HsLengthss{}[i].size();
                     return number<size>{};
                 },
                 number<NDimX>{});
  
             // <0, len_d0, len_d0+len_d1, ...>
             // e.g. seq<3, 5> --> seq<0, 3, 8>
             constexpr auto h_dim_prefix_sum = prefix_sum_sequence(uniformed_h_dim_lengths);
  
             return h_dim_prefix_sum;
         }
  
         CK_TILE_HOST_DEVICE static constexpr auto get_uniformed_idx_y_to_h()
         {
             constexpr auto all_ys_2_rhss = transform_sequences(
                 [](auto major, auto minor) constexpr {
                     // <0, 0, len_d0, len_d0+len_d1, ...>
                     constexpr auto x_dim_prefix_sum = merge_sequences(
                         sequence<0>{} /*for R dims*/, get_h_dim_lengths_prefix_sum());
                     return x_dim_prefix_sum.at(major) + minor;
                 },
                 Ys2RHsMajor{},
                 Ys2RHsMinor{});
  
             return all_ys_2_rhss;
         }
  
         // return tuple<sorted_dims, sorted_maps, sorted_prefix_sum>
         template <typename IdxSeq, typename PrefixSumSeq>
         CK_TILE_HOST_DEVICE static constexpr auto get_sorted_info(IdxSeq, PrefixSumSeq)
         {
             using sorted_idx = sequence_unique_sort<IdxSeq, less<index_t>, equal<index_t>>;
  
             constexpr auto sorted_dims = typename sorted_idx::type{};
             constexpr auto sorted_maps = typename sorted_idx::sorted2unsorted_map{};
  
             constexpr auto sorted_histogram =
                 histogram_sorted_sequence(sorted_dims, PrefixSumSeq{});
             constexpr auto sorted_prefix_sum = prefix_sum_sequence(sorted_histogram);
  
             return make_tuple(sorted_dims, sorted_maps, sorted_prefix_sum);
         }
  
         CK_TILE_HOST_DEVICE static constexpr auto get_sorted_y_info()
         {
             return get_sorted_info(get_uniformed_idx_y_to_h(), get_h_dim_lengths_prefix_sum());
         }
  
         CK_TILE_HOST_DEVICE void print() const
         {
             printf("tile_distribution_encoding::detail{");
             //
             printf("ndim_rh_major_: ");
             print(ndim_rh_major_);
             printf(", ");
             //
             printf("ndim_span_major_: ");
             print(ndim_span_major_);
             printf(", ");
             //
             printf("ndims_rhs_minor_: ");
             print(ndims_rhs_minor_);
             printf(", ");
             //
             printf("ndim_rh_major_: ");
             print(ndim_rh_major_);
             printf(", ");
             //
             printf("max_ndim_rh_minor_: ");
             print(max_ndim_rh_minor_);
             printf(", ");
             //
             printf("rhs_lengthss_: ");
             print(rhs_lengthss_);
             printf(", ");
             //
             printf("ys_lengths_: ");
             print(ys_lengths_);
             printf(", ");
             //
             printf("rhs_major_minor_to_ys_: ");
             print(rhs_major_minor_to_ys_);
             printf(", ");
             //
             printf("ndims_span_minor_: ");
             print(ndims_span_minor_);
             printf(", ");
             //
             printf("max_ndim_span_minor_: ");
             print(max_ndim_span_minor_);
             printf(", ");
             //
             printf("ys_to_span_major_: ");
             print(ys_to_span_major_);
             printf(", ");
             //
             printf("ys_to_span_minor_: ");
             print(ys_to_span_minor_);
             printf(", ");
             //
             printf("distributed_spans_lengthss_: ");
             print(distributed_spans_lengthss_);
             printf(", ");
             //
             printf("ndims_distributed_spans_minor_: ");
             print(ndims_distributed_spans_minor_);
             printf(", ");
             //
             printf("ps_over_rs_derivative_: ");
             print(ps_over_rs_derivative_);
             //
             printf("}");
         }
     };
  
     CK_TILE_HOST_DEVICE void print() const
     {
         printf("tile_distribution_encoding{");
         //
         printf("NDimX: %d, NDimP: %d, NDimY: %d, ", NDimX, NDimP, NDimY);
         //
         printf("rs_lengths_: ");
         print(rs_lengths_);
         printf(", ");
         //
         printf("hs_lengthss_: ");
         print(hs_lengthss_);
         printf(", ");
         //
         printf("ps_to_rhss_major_: ");
         print(ps_to_rhss_major_);
         printf(", ");
         //
         printf("ps_to_rhss_minor_: ");
         print(ps_to_rhss_minor_);
         printf(", ");
         //
         printf("ys_to_rhs_major_: ");
         print(ys_to_rhs_major_);
         printf(", ");
         //
         printf("ys_to_rhs_minor_: ");
         print(ys_to_rhs_minor_);
         printf(", ");
         //
         printf("detail: ");
         print(detail{});
         //
         printf("}");
     }
 };
  
 namespace detail {
  
 template <typename OuterDstr, typename InnerDstr>
 CK_TILE_HOST_DEVICE constexpr auto make_embed_tile_distribution_encoding(OuterDstr, InnerDstr)
 {
     static_assert(OuterDstr::NDimX == InnerDstr::NDimX, "wrong!");
  
     constexpr index_t NDimHMajor = OuterDstr::NDimX;
  
     using RsLengths =
         sequence_merge_t<typename OuterDstr::RsLengths, typename InnerDstr::RsLengths>;
  
     constexpr auto hs_lengthss = generate_tuple(
         [&](auto i) {
             return merge_sequences(typename OuterDstr::HsLengthss{}[i],
                                    typename InnerDstr::HsLengthss{}[i]);
         },
         number<NDimHMajor>{});
  
     //
     constexpr auto rhs_major_2_ndim_outer_rhs_minor = [&]() {
         array<index_t, NDimHMajor + 1> rhs_major_2_ndim_outer_rhs_minor_;
  
         // R dimension
         rhs_major_2_ndim_outer_rhs_minor_(0) = OuterDstr::RsLengths::size();
  
         // Hs dimensions
         static_for<0, NDimHMajor, 1>{}([&](auto i) {
             rhs_major_2_ndim_outer_rhs_minor_(i + 1) = typename OuterDstr::HsLengthss{}[i].size();
         });
  
         return rhs_major_2_ndim_outer_rhs_minor_;
     }();
  
     // Ps2RHssMinor
     constexpr auto updated_inner_ps_2_rhss_minor = generate_tuple(
         [&](auto p) {
             constexpr auto inner_p_2_rhss_major = typename InnerDstr::Ps2RHssMajor{}[p];
             constexpr auto inner_p_2_rhss_minor = typename InnerDstr::Ps2RHssMinor{}[p];
  
             constexpr index_t ndim_tmp = inner_p_2_rhss_minor.size();
  
             constexpr auto updated_inner_p_2_rhss_minor = [&]() {
                 array<index_t, ndim_tmp> updated_inner_p_2_rhss_minor_;
  
                 for(index_t i = 0; i < ndim_tmp; i++)
                 {
                     index_t rh_major = inner_p_2_rhss_major[i];
  
                     index_t ndim_outer_h_minor = rhs_major_2_ndim_outer_rhs_minor[rh_major];
  
                     updated_inner_p_2_rhss_minor_(i) = inner_p_2_rhss_minor[i] + ndim_outer_h_minor;
                 }
  
                 return updated_inner_p_2_rhss_minor_;
             }();
  
             return TO_SEQUENCE(updated_inner_p_2_rhss_minor, ndim_tmp);
         },
         number<InnerDstr::NDimP>{});
  
     // Ys2RHsMinor
     constexpr auto updated_inner_ys_2_rhs_minor = [&]() {
         constexpr auto inner_ys_2_rhs_major = typename InnerDstr::Ys2RHsMajor{};
         constexpr auto inner_ys_2_rhs_minor = typename InnerDstr::Ys2RHsMinor{};
  
         constexpr index_t ndim_tmp = inner_ys_2_rhs_minor.size();
  
         constexpr auto updated_inner_ys_2_rhs_minor_ = [&]() {
             array<index_t, ndim_tmp> updated_inner_ys_2_rhs_minor__;
  
             for(index_t i = 0; i < ndim_tmp; i++)
             {
                 index_t rh_major = inner_ys_2_rhs_major[i];
  
                 index_t ndim_outer_h_minor = rhs_major_2_ndim_outer_rhs_minor[rh_major];
  
                 updated_inner_ys_2_rhs_minor__(i) = inner_ys_2_rhs_minor[i] + ndim_outer_h_minor;
             }
  
             return updated_inner_ys_2_rhs_minor__;
         }();
  
         return TO_SEQUENCE(updated_inner_ys_2_rhs_minor_, ndim_tmp);
     }();
  
     //
     constexpr auto ps_2_rhss_major =
         container_concat(typename OuterDstr::Ps2RHssMajor{}, typename InnerDstr::Ps2RHssMajor{});
  
     constexpr auto ps_2_rhss_minor =
         container_concat(typename OuterDstr::Ps2RHssMinor{}, updated_inner_ps_2_rhss_minor);
  
     //
     constexpr auto ys_2_rhs_major =
         merge_sequences(typename OuterDstr::Ys2RHsMajor{}, typename InnerDstr::Ys2RHsMajor{});
  
     constexpr auto ys_2_rhs_minor =
         merge_sequences(typename OuterDstr::Ys2RHsMinor{}, updated_inner_ys_2_rhs_minor);
  
     return tile_distribution_encoding<RsLengths,
                                       remove_cvref_t<decltype(hs_lengthss)>,
                                       remove_cvref_t<decltype(ps_2_rhss_major)>,
                                       remove_cvref_t<decltype(ps_2_rhss_minor)>,
                                       remove_cvref_t<decltype(ys_2_rhs_major)>,
                                       remove_cvref_t<decltype(ys_2_rhs_minor)>>{};
 }
  
 template <typename InDstr, index_t... InReduceDimXs>
 CK_TILE_HOST_DEVICE constexpr auto
 make_reduce_tile_distribution_encoding_impl(InDstr, sequence<InReduceDimXs...> reduce_dim_xs_in)
 {
     constexpr auto I1 = number<1>{};
  
     // FIXME: increase if fail
     constexpr index_t max_ndim_r_out = 20;
     constexpr index_t max_ndim_y_out = 20;
  
     //
     constexpr index_t ndim_p               = InDstr::NDimP;
     constexpr index_t ndim_x_in            = InDstr::NDimX;
     constexpr index_t ndim_y_in            = InDstr::NDimY;
     constexpr index_t ndim_rh_major_in     = InDstr::NDimX + 1;
     constexpr index_t ndim_x_out           = ndim_x_in - sizeof...(InReduceDimXs);
     constexpr index_t max_ndim_rh_minor_in = InDstr::detail::max_ndim_rh_minor_;
  
     // ndims_ps_low
     constexpr auto ndims_ps_low = generate_array(
         [&](auto i) { return InDstr::ps_to_rhss_major_[i].size(); }, number<ndim_p>{});
  
     // is_rh_major_in_for_reduce
     array<bool, ndim_rh_major_in> is_rh_major_in_for_reduce{false};
  
     for(index_t i = 0; i < reduce_dim_xs_in.size(); i++)
     {
         index_t rh_major = reduce_dim_xs_in[i] + 1;
  
         is_rh_major_in_for_reduce(rh_major) = true;
     }
  
     // is_y_in_for_reduce
     array<bool, ndim_y_in> is_y_in_for_reduce{false};
  
     for(index_t i = 0; i < ndim_y_in; i++)
     {
         index_t rh_major = InDstr::ys_to_rhs_major_[i];
  
         if(is_rh_major_in_for_reduce[rh_major])
         {
             is_y_in_for_reduce(i) = true;
         }
     }
  
     // is_rh_minor_in_for_y_reduce
     array<array<bool, max_ndim_rh_minor_in>, ndim_rh_major_in> is_rh_minor_in_for_y_reduce{{false}};
  
     static_for<0, ndim_y_in, 1>{}([&](auto i) {
         index_t rh_major = InDstr::ys_to_rhs_major_[i];
         index_t rh_minor = InDstr::ys_to_rhs_minor_[i];
  
         if(is_y_in_for_reduce[i])
         {
             is_rh_minor_in_for_y_reduce(rh_major)(rh_minor) = true;
         }
     });
  
     // in2out_rh_major
     array<index_t, ndim_rh_major_in> in2out_rh_major{-1};
     index_t cnt_ndim_rh_major_out = 0;
  
     for(index_t i = 0; i < ndim_rh_major_in; i++)
     {
         if(is_rh_major_in_for_reduce[i])
         {
             in2out_rh_major(i) = 0;
         }
         else
         {
             in2out_rh_major(i) = cnt_ndim_rh_major_out;
  
             cnt_ndim_rh_major_out++;
         }
     }
  
     // rs_lengths_out, in2out_rh_minor
     array<index_t, max_ndim_r_out> rs_lengths_out{-1};
     array<array<index_t, max_ndim_rh_minor_in>, ndim_rh_major_in> in2out_rh_minor{{-1}};
  
     // loop over input R dim
     for(index_t i = 0; i < InDstr::rs_lengths_.size(); i++)
     {
         // rs_lengths_out
         rs_lengths_out(i) = InDstr::rs_lengths_[i];
  
         // in2out_rh_minor
         in2out_rh_minor(0)(i) = i;
     }
  
     // loop over input H Dim
     index_t cnt_ndim_r_out = InDstr::rs_lengths_.size();
  
     static_for<1, ndim_rh_major_in, 1>{}([&](auto rh_major_in) {
         constexpr auto h_major_in = rh_major_in - I1;
  
         constexpr index_t ndim_rh_minor_in = InDstr::hs_lengthss_[h_major_in].size();
  
         if(is_rh_major_in_for_reduce[rh_major_in])
         {
             for(index_t rh_minor_in = 0; rh_minor_in < ndim_rh_minor_in; rh_minor_in++)
             {
                 if(not is_rh_minor_in_for_y_reduce[rh_major_in][rh_minor_in])
                 {
                     // rs_lengths_out
                     rs_lengths_out(cnt_ndim_r_out) = InDstr::hs_lengthss_[h_major_in][rh_minor_in];
  
                     // in2out_rh_minor
                     in2out_rh_minor(rh_major_in)(rh_minor_in) = cnt_ndim_r_out;
  
                     cnt_ndim_r_out++;
                 }
             }
         }
         else
         {
             for(index_t rh_minor_in = 0; rh_minor_in < ndim_rh_minor_in; rh_minor_in++)
             {
                 // in2out_rh_minor
                 in2out_rh_minor(rh_major_in)(rh_minor_in) = rh_minor_in;
             }
         }
     });
  
     // ndim_r_out
     const index_t ndim_r_out = cnt_ndim_r_out;
  
     // ndims_hs_minor_out, hs_lengthss_out
     array<index_t, ndim_x_out> ndims_hs_minor_out{-1};
     array<array<index_t, max_ndim_rh_minor_in>, ndim_x_out> hs_lengthss_out{{-1}};
  
     index_t cnt_ndim_x_out = 0;
  
     static_for<0, ndim_x_in, 1>{}([&](auto i) {
         if(not is_rh_major_in_for_reduce[i + I1])
         {
             // ndims_hs_minor_out
             ndims_hs_minor_out(cnt_ndim_x_out) = InDstr::hs_lengthss_[i].size();
  
             // hs_lengthss_out
             static_for<0, InDstr::hs_lengthss_[i].size(), 1>{}(
                 [&](auto j) { hs_lengthss_out(cnt_ndim_x_out)(j) = InDstr::hs_lengthss_[i][j]; });
  
             cnt_ndim_x_out++;
         }
     });
  
     // ps_to_rhss_major_out, ps_to_rhss_minor_out
     array<array<index_t, max_ndim_rh_minor_in>, ndim_p> ps_to_rhss_major_out{{-1}};
     array<array<index_t, max_ndim_rh_minor_in>, ndim_p> ps_to_rhss_minor_out{{-1}};
  
     static_for<0, ndim_p, 1>{}([&](auto idim_p) {
         static_for<0, InDstr::ps_to_rhss_major_[idim_p].size(), 1>{}([&](auto idim_low) {
             index_t rh_major_in = InDstr::ps_to_rhss_major_[idim_p][idim_low];
             index_t rh_minor_in = InDstr::ps_to_rhss_minor_[idim_p][idim_low];
  
             ps_to_rhss_major_out(idim_p)(idim_low) = in2out_rh_major[rh_major_in];
             ps_to_rhss_minor_out(idim_p)(idim_low) = in2out_rh_minor[rh_major_in][rh_minor_in];
         });
     });
  
     // ys_to_rhs_major_out, ys_to_rhs_minor_out
     array<index_t, max_ndim_y_out> ys_to_rhs_major_out{-1};
     array<index_t, max_ndim_y_out> ys_to_rhs_minor_out{-1};
  
     index_t cnt_ndim_y_out = 0;
  
     static_for<0, ndim_y_in, 1>{}([&](auto i) {
         if(not is_y_in_for_reduce[i])
         {
             index_t rh_major_in = InDstr::ys_to_rhs_major_[i];
             index_t rh_minor_in = InDstr::ys_to_rhs_minor_[i];
  
             ys_to_rhs_major_out(cnt_ndim_y_out) = in2out_rh_major[rh_major_in];
             ys_to_rhs_minor_out(cnt_ndim_y_out) = in2out_rh_minor[rh_major_in][rh_minor_in];
  
             cnt_ndim_y_out++;
         }
     });
  
     // ndim_y_out
     const index_t ndim_y_out = cnt_ndim_y_out;
  
     //
     return make_tuple(ndim_x_out,
                       ndim_p,
                       ndim_y_out,
                       ndim_r_out,
                       ndims_hs_minor_out,
                       ndims_ps_low,
                       rs_lengths_out,
                       hs_lengthss_out,
                       ps_to_rhss_major_out,
                       ps_to_rhss_minor_out,
                       ys_to_rhs_major_out,
                       ys_to_rhs_minor_out);
 }
  
 template <typename InDstr, index_t... InReduceDimXs>
 CK_TILE_HOST_DEVICE constexpr auto
 make_reduce_tile_distribution_encoding(InDstr, sequence<InReduceDimXs...> reduce_dim_xs_in)
 {
     constexpr auto impl = make_reduce_tile_distribution_encoding_impl(InDstr{}, reduce_dim_xs_in);
  
     constexpr index_t ndim_x             = impl.template at<0>();
     constexpr index_t ndim_p             = impl.template at<1>();
     constexpr index_t ndim_y             = impl.template at<2>();
     constexpr index_t ndim_r             = impl.template at<3>();
     constexpr auto ndims_hs_minor        = impl.template at<4>();
     constexpr auto ndims_ps_low          = impl.template at<5>();
     constexpr auto rs_lengths_impl       = impl.template at<6>();
     constexpr auto hs_lengthss_impl      = impl.template at<7>();
     constexpr auto ps_to_rhss_major_impl = impl.template at<8>();
     constexpr auto ps_to_rhss_minor_impl = impl.template at<9>();
     constexpr auto ys_to_rhs_major_impl  = impl.template at<10>();
     constexpr auto ys_to_rhs_minor_impl  = impl.template at<11>();
  
     constexpr auto rs_lengths  = TO_SEQUENCE(rs_lengths_impl, ndim_r);
     constexpr auto hs_lengthss = TO_TUPLE_OF_SEQUENCE(hs_lengthss_impl, ndim_x, ndims_hs_minor);
     constexpr auto ps_to_rhss_major =
         TO_TUPLE_OF_SEQUENCE(ps_to_rhss_major_impl, ndim_p, ndims_ps_low);
     constexpr auto ps_to_rhss_minor =
         TO_TUPLE_OF_SEQUENCE(ps_to_rhss_minor_impl, ndim_p, ndims_ps_low);
     constexpr auto ys_to_rhs_major = TO_SEQUENCE(ys_to_rhs_major_impl, ndim_y);
     constexpr auto ys_to_rhs_minor = TO_SEQUENCE(ys_to_rhs_minor_impl, ndim_y);
  
     return tile_distribution_encoding<remove_cvref_t<decltype(rs_lengths)>,
                                       remove_cvref_t<decltype(hs_lengthss)>,
                                       remove_cvref_t<decltype(ps_to_rhss_major)>,
                                       remove_cvref_t<decltype(ps_to_rhss_minor)>,
                                       remove_cvref_t<decltype(ys_to_rhs_major)>,
                                       remove_cvref_t<decltype(ys_to_rhs_minor)>>{};
 }
  
 } // namespace detail
 } // namespace ck_tile