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 // Copyright (c) Advanced Micro Devices, Inc., or its affiliates.
 // SPDX-License-Identifier: MIT
  
 #pragma once
  
 #include "ck_tile/core.hpp"
 #include "ck_tile/ops/common.hpp"
 #include "ck_tile/ops/fmha/block/block_attention_bias_enum.hpp"
 #include "ck_tile/ops/fmha/block/variants.hpp"
  
 #include <string>
 #include <type_traits>
 #include <utility>
 #include <variant>
  
 // S[seqlen_q, seqlen_k] = Q[seqlen_q, hdim_q] @ K[seqlen_k, hdim_q]
 // S'[seqlen_q, seqlen_k] = S[seqlen_q, seqlen_k] * Scale[1]
 // S''[seqlen_q, seqlen_k] = S'[seqlen_q, seqlen_k] + Bias[seqlen_q, seqlen_k]
 // P[seqlen_q, seqlen_k] = Softmax(S''[seqlen_q, seqlen_k])
 // O[seqlen_q, hdim_v] = P[seqlen_q, seqlen_k] @ V^T[hdim_v, seqlen_k]
  
 namespace ck_tile {
  
 // TODO: This class is a variant of the existing FmhaFwdSplitKVKernel pipeline.
 //       Refactoring to extract shared logic is recommended as future work.
 template <typename FmhaPipeline_, typename EpiloguePipeline_>
 struct FmhaFwdPagedKVKernel
 {
     using FmhaPipeline                            = ck_tile::remove_cvref_t<FmhaPipeline_>;
     using EpiloguePipeline                        = ck_tile::remove_cvref_t<EpiloguePipeline_>;
     static constexpr ck_tile::index_t kBlockSize  = FmhaPipeline::kBlockSize;
     static constexpr ck_tile::index_t kBlockPerCu = FmhaPipeline::kBlockPerCu;
  
     static_assert(kBlockPerCu > 0);
     static constexpr ck_tile::index_t kBlockPerCuInput = FmhaPipeline::Problem::kBlockPerCu;
  
     using QDataType    = ck_tile::remove_cvref_t<typename FmhaPipeline::QDataType>;
     using KDataType    = ck_tile::remove_cvref_t<typename FmhaPipeline::KDataType>;
     using VDataType    = ck_tile::remove_cvref_t<typename FmhaPipeline::VDataType>;
     using BiasDataType = ck_tile::remove_cvref_t<typename FmhaPipeline::BiasDataType>;
     using LSEDataType  = ck_tile::remove_cvref_t<typename FmhaPipeline::LSEDataType>;
     using ODataType    = ck_tile::remove_cvref_t<typename FmhaPipeline::ODataType>;
     using SaccDataType = ck_tile::remove_cvref_t<typename FmhaPipeline::SaccDataType>;
  
     using VLayout = ck_tile::remove_cvref_t<typename FmhaPipeline::VLayout>;
  
     static constexpr bool kIsGroupMode      = FmhaPipeline::kIsGroupMode;
     static constexpr bool kPadSeqLenQ       = FmhaPipeline::kPadSeqLenQ;
     static constexpr bool kPadSeqLenK       = FmhaPipeline::kPadSeqLenK;
     static constexpr bool kPadHeadDimQ      = FmhaPipeline::kPadHeadDimQ;
     static constexpr bool kPadHeadDimV      = FmhaPipeline::kPadHeadDimV;
     static constexpr bool kHasLogitsSoftCap = FmhaPipeline::kHasLogitsSoftCap;
     static constexpr auto BiasEnum          = FmhaPipeline::BiasEnum;
     static constexpr bool kStoreLSE         = FmhaPipeline::kStoreLSE;
     static constexpr bool kDoFp8StaticQuant = FmhaPipeline::Problem::kDoFp8StaticQuant;
     static constexpr bool kSkipMinSeqlenQ   = FmhaPipeline::Problem::kSkipMinSeqlenQ;
     static constexpr bool kIsPagedKV        = FmhaPipeline::Problem::kIsPagedKV;
     static constexpr bool kHasSink          = FmhaPipeline::kHasSink;
  
     using AttentionVariant = ck_tile::remove_cvref_t<typename FmhaPipeline::AttentionVariant>;
     using FmhaMask         = ck_tile::remove_cvref_t<typename FmhaPipeline::FmhaMask>;
     static constexpr bool kHasMask = FmhaMask::IsMasking;
  
     static constexpr bool kUseAsyncCopy = FmhaPipeline::Policy::AsyncCopy;
  
     // clang-format off
     template <typename T> struct t2s;
     template <> struct t2s<float> { static constexpr const char * name = "fp32"; };
     template <> struct t2s<ck_tile::fp16_t> { static constexpr const char * name = "fp16"; };
     template <> struct t2s<ck_tile::bf16_t> { static constexpr const char * name = "bf16"; };
     template <> struct t2s<ck_tile::fp8_t> { static constexpr const char * name = "fp8"; };
     template <> struct t2s<ck_tile::bf8_t> { static constexpr const char * name = "bf8"; };
     // clang-format on
  
     CK_TILE_HOST static std::string GetName()
     {
         // sync with generate.py
         // clang-format off
         using bfs = typename FmhaPipeline::BlockFmhaShape;
         using g0br = typename bfs::Gemm0BlockWarps;
         using g1br = typename bfs::Gemm1BlockWarps;
         using g0wt = typename bfs::Gemm0WarpTile;
         using g1wt = typename bfs::Gemm1WarpTile;
         #define _SS_  std::string
         #define _TS_  std::to_string
         auto pn = [&] () {
             std::string n;
             if (kPadSeqLenQ) n += "s";
             if (kPadSeqLenK) n += "sk";
             if (kPadHeadDimQ) n += "d";
             if (kPadHeadDimV) n += "dv";
             return n.empty() ? n : std::string("p") + n; }();
         return
             _SS_("fmha_fwd_pagedkv_d") + _TS_(bfs::kQKHeaddim) + "_" + _SS_(t2s<QDataType>::name) +
             "_" + (kIsGroupMode ? "group" : "batch") + "_"
             "b" + _TS_(bfs::kM0) + "x" + _TS_(bfs::kN0) + "x" + _TS_(bfs::kK0) + "x" +
                     _TS_(bfs::kN1) + "x" + _TS_(bfs::kK1) + "x" + _TS_(bfs::kQKHeaddim) + "_" +
             "r" + _TS_(g0br::at(ck_tile::number<0>{})) + "x" + _TS_(g0br::at(ck_tile::number<1>{})) + "x" + _TS_(g0br::at(ck_tile::number<2>{})) + "_" +
             "r" + _TS_(g1br::at(ck_tile::number<0>{})) + "x" + _TS_(g1br::at(ck_tile::number<1>{})) + "x" + _TS_(g1br::at(ck_tile::number<2>{})) + "_" +
             "w" + _TS_(g0wt::at(ck_tile::number<0>{})) + "x" + _TS_(g0wt::at(ck_tile::number<1>{})) + "x" + _TS_(g0wt::at(ck_tile::number<2>{})) + "_" +
             "w" + _TS_(g1wt::at(ck_tile::number<0>{})) + "x" + _TS_(g1wt::at(ck_tile::number<1>{})) + "x" + _TS_(g1wt::at(ck_tile::number<2>{})) + "_" +
             (kBlockPerCuInput == -1 ? "" : ("o" + _TS_(kBlockPerCu) + "_")) + _SS_(FmhaPipeline::name) + "_" +
             "v" + (std::is_same_v<VLayout, ck_tile::tensor_layout::gemm::RowMajor> ? "r" : "c") + (pn.empty() ? "_npad" : "_" + pn) +
             (kHasLogitsSoftCap ? "_logits" : "_nlogits" ) + (BiasEnum == BlockAttentionBiasEnum::NO_BIAS ? _SS_("_nbias") : (_SS_("_") + BlockAttentionBiasEnumToStr<BiasEnum>::name)) +
             (kHasMask ? "_" + _SS_(FmhaMask::name) : "_nmask") + (kStoreLSE ? "_lse" : "_nlse" )  + (kSkipMinSeqlenQ ? "_skip" : "_nskip" )  + (kDoFp8StaticQuant ? "_squant" : "_nsquant" ) + (kIsPagedKV ? "_pagedkv" : "_npagedkv" ) + (kHasSink ? "_sink" : "_nsink" );
         #undef _SS_
         #undef _TS_
         // clang-format on
     }
  
     template <ck_tile::index_t I> // to avoid duplicated base class prblem, introduce an template
                                   // arg
     struct FmhaFwdEmptyKargs
     {
     };
  
     // kargs use aggregate initializer, so no constructor will provided
     // use inheritance to minimize karg size
     // user need to use MakeKargs() function to create kargs.
     struct FmhaFwdCommonKargs
     {
         const void* q_ptr;
         const void* k_ptr;
         const void* v_ptr;
         void* o_ptr;
         const void* sink_ptr;
  
         ck_tile::index_t seqlen_q;
         ck_tile::index_t seqlen_k;
         ck_tile::index_t hdim_q;
         ck_tile::index_t hdim_v;
  
         ck_tile::index_t num_head_q;
         // for MQA/GQA, nhead could be different. This parameter is nhead_q / nhead_k
         // if this param is larger than 1, indicate MQA/GQA case
         ck_tile::index_t nhead_ratio_qk;
         float scale_s;
  
         ck_tile::index_t stride_q;
         ck_tile::index_t stride_k;
         ck_tile::index_t stride_v;
         ck_tile::index_t stride_o;
  
         ck_tile::index_t nhead_stride_q;
         ck_tile::index_t nhead_stride_k;
         ck_tile::index_t nhead_stride_v;
         ck_tile::index_t nhead_stride_o;
     };
  
     struct FmhaFwdLogitsSoftCapKargs
     {
         FmhaFwdLogitsSoftCapKargs() = default;
  
         void init_logits_soft_cap(float logits_soft_cap_)
         {
             if(0 < logits_soft_cap_)
             {
                 logits_soft_cap     = logits_soft_cap_;
                 logits_soft_cap_rcp = 1.f / logits_soft_cap;
             }
             else
             {
                 logits_soft_cap     = 0.f;
                 logits_soft_cap_rcp = 0.f;
             }
         }
  
         float logits_soft_cap;
         float logits_soft_cap_rcp;
     };
  
     struct FmhaFwdCommonBiasKargs
     {
         const void* bias_ptr               = nullptr;
         ck_tile::index_t stride_bias       = 0;
         ck_tile::index_t nhead_stride_bias = 0;
     };
  
     struct FmhaFwdBatchModeBiasKargs : FmhaFwdCommonBiasKargs
     {
         ck_tile::index_t batch_stride_bias = 0;
     };
  
     struct FmhaFwdAlibiKargs
     {
         // alibi is batch*nhead*1, no matter in batch/group mode, they are the same
         const void* alibi_slope_ptr;
         ck_tile::index_t alibi_slope_stride; // stride in batch, or 0 for all batch share same slope
     };
  
     struct FmhaFwdMaskKargs
     {
         // ck_tile::index_t window_size_left, window_size_right;
         ck_tile::index_t window_size_left, window_size_right, sink_size;
         ck_tile::GenericAttentionMaskEnum mask_type;
     };
  
     struct FmhaFwdFp8StaticQuantKargs
     {
         float scale_p;
         float scale_o;
     };
  
     struct FmhaFwdCommonLSEKargs
     {
         void* lse_ptr                     = nullptr;
         ck_tile::index_t nhead_stride_lse = 0;
         ck_tile::index_t batch_stride_lse = 0;
     };
  
     struct FmhaFwdSkipMinSeqlenQKargs
     {
         ck_tile::index_t min_seqlen_q = 0;
     };
  
     struct CommonPageBlockTableKargs
     {
         const int32_t* block_table_ptr;
         ck_tile::index_t batch_stride_block_table;
         ck_tile::index_t page_block_size;
     };
  
     struct GroupModePageBlockTableKargs : CommonPageBlockTableKargs
     {
         bool is_gappy = false;
     };
  
     struct CacheBatchIdxKargs
     {
         const int32_t* cache_batch_idx;
     };
  
     struct FmhaFwdBatchModeKargs
         : FmhaFwdCommonKargs,
           std::conditional_t<BiasEnum == BlockAttentionBiasEnum::ELEMENTWISE_BIAS,
                              FmhaFwdBatchModeBiasKargs,
                              std::conditional_t<BiasEnum == BlockAttentionBiasEnum::ALIBI,
                                                 FmhaFwdAlibiKargs,
                                                 FmhaFwdEmptyKargs<0>>>,
           std::conditional_t<kHasMask, FmhaFwdMaskKargs, FmhaFwdEmptyKargs<1>>,
           std::conditional_t<kStoreLSE, FmhaFwdCommonLSEKargs, FmhaFwdEmptyKargs<2>>,
           std::conditional_t<kDoFp8StaticQuant, FmhaFwdFp8StaticQuantKargs, FmhaFwdEmptyKargs<3>>,
           std::conditional_t<kIsPagedKV, CommonPageBlockTableKargs, CacheBatchIdxKargs>,
           std::conditional_t<kHasLogitsSoftCap, FmhaFwdLogitsSoftCapKargs, FmhaFwdEmptyKargs<4>>
     {
         const int32_t* seqlen_k_ptr;
  
         ck_tile::index_t batch_stride_q;
         ck_tile::index_t batch_stride_k; // when using paged-kvcache, this will be stride/size for
                                          // single kcache page-block
         ck_tile::index_t batch_stride_v; // when using paged-kvcache, this will be stride/size for
                                          // single vcache page-block
         ck_tile::index_t batch_stride_o;
     };
  
     struct FmhaFwdGroupModeKargs
         : FmhaFwdCommonKargs,
           std::conditional_t<BiasEnum == BlockAttentionBiasEnum::ELEMENTWISE_BIAS,
                              FmhaFwdCommonBiasKargs,
                              std::conditional_t<BiasEnum == BlockAttentionBiasEnum::ALIBI,
                                                 FmhaFwdAlibiKargs,
                                                 FmhaFwdEmptyKargs<0>>>,
           std::conditional_t<kHasMask, FmhaFwdMaskKargs, FmhaFwdEmptyKargs<1>>,
           std::conditional_t<kStoreLSE, FmhaFwdCommonLSEKargs, FmhaFwdEmptyKargs<2>>,
           std::conditional_t<kDoFp8StaticQuant, FmhaFwdFp8StaticQuantKargs, FmhaFwdEmptyKargs<3>>,
           std::conditional_t<kHasLogitsSoftCap, FmhaFwdLogitsSoftCapKargs, FmhaFwdEmptyKargs<4>>,
           std::conditional_t<kIsPagedKV, GroupModePageBlockTableKargs, FmhaFwdEmptyKargs<5>>,
           std::conditional_t<kSkipMinSeqlenQ, FmhaFwdSkipMinSeqlenQKargs, FmhaFwdEmptyKargs<6>>
     {
         const int32_t* seqstart_q_ptr;
         const int32_t* seqstart_k_ptr;
         const int32_t* seqlen_k_ptr;
  
         ck_tile::index_t batch_stride_k; // only used for paged-kvcache, this will be stride/size
                                          // for single kcache page-block
         ck_tile::index_t batch_stride_v; // only used for paged-kvcache, this will be stride/size
                                          // for single vcache page-block
     };
  
     using Kargs = std::conditional_t<kIsGroupMode, FmhaFwdGroupModeKargs, FmhaFwdBatchModeKargs>;
  
     struct BlockIndices
     {
         ck_tile::index_t batch_idx;
         ck_tile::index_t qo_head_idx;
         ck_tile::index_t kv_head_idx;
     };
  
     template <bool Cond = !kIsGroupMode>
     CK_TILE_HOST static constexpr std::enable_if_t<Cond, Kargs>
     MakeKargsImpl(const void* q_ptr,
                   const void* k_ptr,
                   const void* v_ptr,
                   const void* bias_ptr,
                   void* lse_ptr,
                   void* o_ptr,
                   ck_tile::index_t seqlen_q,
                   ck_tile::index_t seqlen_k,
                   const void* seqlen_k_ptr, // only used for (paged-) kvcache
                   ck_tile::index_t hdim_q,
                   ck_tile::index_t hdim_v,
                   ck_tile::index_t num_head_q,
                   ck_tile::index_t nhead_ratio_qk,
                   const void* block_table_ptr,
                   ck_tile::index_t batch_stride_block_table,
                   ck_tile::index_t page_block_size,
                   const void* cache_batch_idx,
                   float scale_s,
                   float scale_p,
                   float scale_o,
                   float logits_soft_cap,
                   ck_tile::index_t stride_q,
                   ck_tile::index_t stride_k,
                   ck_tile::index_t stride_v,
                   ck_tile::index_t stride_bias,
                   ck_tile::index_t stride_o,
                   ck_tile::index_t nhead_stride_q,
                   ck_tile::index_t nhead_stride_k,
                   ck_tile::index_t nhead_stride_v,
                   ck_tile::index_t nhead_stride_bias,
                   ck_tile::index_t nhead_stride_lse,
                   ck_tile::index_t nhead_stride_o,
                   ck_tile::index_t batch_stride_q,
                   ck_tile::index_t batch_stride_k,
                   ck_tile::index_t batch_stride_v,
                   ck_tile::index_t batch_stride_bias,
                   ck_tile::index_t batch_stride_lse,
                   ck_tile::index_t batch_stride_o,
                   ck_tile::index_t window_size_left,
                   ck_tile::index_t window_size_right,
                   ck_tile::index_t sink_size,
                   ck_tile::index_t mask_type,
                   const void* sink_ptr = nullptr)
     {
         Kargs kargs{{q_ptr,
                      k_ptr,
                      v_ptr,
                      o_ptr,
                      sink_ptr,
                      seqlen_q,
                      seqlen_k,
                      hdim_q,
                      hdim_v,
                      num_head_q,
                      nhead_ratio_qk,
 #if CK_TILE_FMHA_FWD_FAST_EXP2
                      static_cast<float>(scale_s * ck_tile::log2e_v<>),
 #else
                      scale_s,
 #endif
                      stride_q,
                      stride_k,
                      stride_v,
                      stride_o,
                      nhead_stride_q,
                      nhead_stride_k,
                      nhead_stride_v,
                      nhead_stride_o}, // args for common karg
                     {},               // placeholder for bias
                     {},               // placeholder for mask
                     {},               // placeholder for lse
                     {},               // placeholder for fp8_static_quant args
                     {},               // placeholder for pagedkv
                     {},               // placeholder for logits_soft_cap
                     reinterpret_cast<const int32_t*>(seqlen_k_ptr),
                     batch_stride_q,
                     batch_stride_k,
                     batch_stride_v,
                     batch_stride_o};
  
         if constexpr(BiasEnum == BlockAttentionBiasEnum::ELEMENTWISE_BIAS)
         {
             kargs.bias_ptr          = bias_ptr;
             kargs.stride_bias       = stride_bias;
             kargs.nhead_stride_bias = nhead_stride_bias;
             kargs.batch_stride_bias = batch_stride_bias;
         }
         else if constexpr(BiasEnum == BlockAttentionBiasEnum::ALIBI)
         {
             kargs.alibi_slope_ptr    = bias_ptr;
             kargs.alibi_slope_stride = stride_bias;
         }
         if constexpr(kHasMask)
         {
             kargs.window_size_left  = window_size_left;
             kargs.window_size_right = window_size_right;
             kargs.sink_size         = sink_size;
             kargs.mask_type         = static_cast<ck_tile::GenericAttentionMaskEnum>(mask_type);
         }
         if constexpr(kStoreLSE)
         {
             kargs.lse_ptr          = lse_ptr;
             kargs.nhead_stride_lse = nhead_stride_lse;
             kargs.batch_stride_lse = batch_stride_lse;
         }
         if constexpr(kDoFp8StaticQuant)
         {
             kargs.scale_p = scale_p;
             kargs.scale_o = scale_o;
         }
         if constexpr(kIsPagedKV)
         {
             kargs.block_table_ptr          = reinterpret_cast<const int32_t*>(block_table_ptr);
             kargs.batch_stride_block_table = batch_stride_block_table;
             kargs.page_block_size          = page_block_size;
         }
         else
         {
             kargs.cache_batch_idx = reinterpret_cast<const int32_t*>(cache_batch_idx);
         }
         if constexpr(kHasLogitsSoftCap)
         {
             kargs.init_logits_soft_cap(logits_soft_cap);
         }
  
         return kargs;
     }
  
     // std::variant<> can't take in a list initializer, overload for backward compatibility
     template <bool Cond = !kIsGroupMode>
     CK_TILE_HOST static constexpr std::enable_if_t<Cond, Kargs>
     MakeKargs(const void* q_ptr,
               const void* k_ptr,
               const void* v_ptr,
               const void* bias_ptr,
               void* lse_ptr,
               void* o_ptr,
               ck_tile::index_t seqlen_q,
               ck_tile::index_t seqlen_k,
               const void* seqlen_k_ptr, // only used for (paged-) kvcache
               ck_tile::index_t hdim_q,
               ck_tile::index_t hdim_v,
               ck_tile::index_t num_head_q,
               ck_tile::index_t nhead_ratio_qk,
               const void* block_table_ptr,
               ck_tile::index_t batch_stride_block_table,
               ck_tile::index_t page_block_size,
               const void* cache_batch_idx,
               float scale_s,
               float scale_p,
               float scale_o,
               float logits_soft_cap,
               ck_tile::index_t stride_q,
               ck_tile::index_t stride_k,
               ck_tile::index_t stride_v,
               ck_tile::index_t stride_bias,
               ck_tile::index_t stride_o,
               ck_tile::index_t nhead_stride_q,
               ck_tile::index_t nhead_stride_k,
               ck_tile::index_t nhead_stride_v,
               ck_tile::index_t nhead_stride_bias,
               ck_tile::index_t nhead_stride_lse,
               ck_tile::index_t nhead_stride_o,
               ck_tile::index_t batch_stride_q,
               ck_tile::index_t batch_stride_k,
               ck_tile::index_t batch_stride_v,
               ck_tile::index_t batch_stride_bias,
               ck_tile::index_t batch_stride_lse,
               ck_tile::index_t batch_stride_o,
               ck_tile::index_t window_size_left,
               ck_tile::index_t window_size_right,
               ck_tile::index_t sink_size,
               ck_tile::index_t mask_type,
               const void* sink_ptr = nullptr)
     {
         return MakeKargsImpl(q_ptr,
                              k_ptr,
                              v_ptr,
                              bias_ptr,
                              lse_ptr,
                              o_ptr,
                              seqlen_q,
                              seqlen_k,
                              seqlen_k_ptr,
                              hdim_q,
                              hdim_v,
                              num_head_q,
                              nhead_ratio_qk,
                              block_table_ptr,
                              batch_stride_block_table,
                              page_block_size,
                              cache_batch_idx,
                              scale_s,
                              scale_p,
                              scale_o,
                              logits_soft_cap,
                              stride_q,
                              stride_k,
                              stride_v,
                              stride_bias,
                              stride_o,
                              nhead_stride_q,
                              nhead_stride_k,
                              nhead_stride_v,
                              nhead_stride_bias,
                              nhead_stride_lse,
                              nhead_stride_o,
                              batch_stride_q,
                              batch_stride_k,
                              batch_stride_v,
                              batch_stride_bias,
                              batch_stride_lse,
                              batch_stride_o,
                              window_size_left,
                              window_size_right,
                              sink_size,
                              mask_type,
                              sink_ptr);
     }
  
     template <bool Cond = kIsGroupMode>
     CK_TILE_HOST static constexpr std::enable_if_t<Cond, Kargs>
     MakeKargsImpl(const void* q_ptr,
                   const void* k_ptr,
                   const void* v_ptr,
                   const void* bias_ptr,
                   void* lse_ptr,
                   void* o_ptr,
                   const void* seqstart_q_ptr,
                   const void* seqstart_k_ptr,
                   const void* seqlen_k_ptr,
                   ck_tile::index_t hdim_q,
                   ck_tile::index_t hdim_v,
                   ck_tile::index_t num_head_q,
                   ck_tile::index_t nhead_ratio_qk,
                   const void* block_table_ptr,
                   ck_tile::index_t batch_stride_block_table,
                   ck_tile::index_t page_block_size,
                   bool is_gappy,
                   float scale_s,
                   float scale_p,
                   float scale_o,
                   float logits_soft_cap,
                   ck_tile::index_t stride_q,
                   ck_tile::index_t stride_k,
                   ck_tile::index_t stride_v,
                   ck_tile::index_t stride_bias,
                   ck_tile::index_t stride_o,
                   ck_tile::index_t nhead_stride_q,
                   ck_tile::index_t nhead_stride_k,
                   ck_tile::index_t nhead_stride_v,
                   ck_tile::index_t nhead_stride_bias,
                   ck_tile::index_t nhead_stride_lse,
                   ck_tile::index_t nhead_stride_o,
                   ck_tile::index_t batch_stride_k, // only used for paged-kvcache
                   ck_tile::index_t batch_stride_v, // only used for paged-kvcache
                   ck_tile::index_t window_size_left,
                   ck_tile::index_t window_size_right,
                   ck_tile::index_t sink_size,
                   ck_tile::index_t mask_type,
                   ck_tile::index_t min_seqlen_q,
                   const void* sink_ptr = nullptr)
     {
         Kargs kargs{{q_ptr,
                      k_ptr,
                      v_ptr,
                      o_ptr,
                      sink_ptr,
                      -1, // seqlen will be updated by another pointer
                      -1, //
                      hdim_q,
                      hdim_v,
                      num_head_q,
                      nhead_ratio_qk,
 #if CK_TILE_FMHA_FWD_FAST_EXP2
                      static_cast<float>(scale_s * ck_tile::log2e_v<>),
 #else
                      scale_s,
 #endif
                      stride_q,
                      stride_k,
                      stride_v,
                      stride_o,
                      nhead_stride_q,
                      nhead_stride_k,
                      nhead_stride_v,
                      nhead_stride_o}, // args for common karg
                     {},               // placeholder for bias
                     {},               // placeholder for mask
                     {},               // placeholder for lse
                     {},               // placeholder for fp8_static_quant args
                     {},               // placeholder for logits_soft_cap
                     {},               // placeholder for pagdkv
                     {},               // placeholder for min_seqlen_q
                     reinterpret_cast<const int32_t*>(seqstart_q_ptr),
                     reinterpret_cast<const int32_t*>(seqstart_k_ptr),
                     reinterpret_cast<const int32_t*>(seqlen_k_ptr),
                     batch_stride_k,
                     batch_stride_v};
  
         if constexpr(BiasEnum == BlockAttentionBiasEnum::ELEMENTWISE_BIAS)
         {
             kargs.bias_ptr          = bias_ptr;
             kargs.stride_bias       = stride_bias;
             kargs.nhead_stride_bias = nhead_stride_bias;
         }
         else if constexpr(BiasEnum == BlockAttentionBiasEnum::ALIBI)
         {
             kargs.alibi_slope_ptr    = bias_ptr;
             kargs.alibi_slope_stride = stride_bias;
         }
         if constexpr(kHasMask)
         {
             kargs.window_size_left  = window_size_left;
             kargs.window_size_right = window_size_right;
             kargs.sink_size         = sink_size;
             kargs.mask_type         = static_cast<ck_tile::GenericAttentionMaskEnum>(mask_type);
         }
         if constexpr(kStoreLSE)
         {
             kargs.lse_ptr          = lse_ptr;
             kargs.nhead_stride_lse = nhead_stride_lse;
         }
         if constexpr(kDoFp8StaticQuant)
         {
             kargs.scale_p = scale_p;
             kargs.scale_o = scale_o;
         }
         if constexpr(kHasLogitsSoftCap)
         {
             kargs.init_logits_soft_cap(logits_soft_cap);
         }
         if constexpr(kIsPagedKV)
         {
             kargs.block_table_ptr          = reinterpret_cast<const int32_t*>(block_table_ptr);
             kargs.batch_stride_block_table = batch_stride_block_table;
             kargs.page_block_size          = page_block_size;
             kargs.is_gappy                 = is_gappy;
         }
         if constexpr(kSkipMinSeqlenQ)
         {
             kargs.min_seqlen_q = min_seqlen_q;
         }
  
         return kargs;
     }
  
     // std::variant<> can't take in a list initializer, overload for backward compatibility
     template <bool Cond = kIsGroupMode>
     CK_TILE_HOST static constexpr std::enable_if_t<Cond, Kargs>
     MakeKargs(const void* q_ptr,
               const void* k_ptr,
               const void* v_ptr,
               const void* bias_ptr,
               void* lse_ptr,
               void* o_ptr,
               const void* seqstart_q_ptr,
               const void* seqstart_k_ptr,
               const void* seqlen_k_ptr,
               ck_tile::index_t hdim_q,
               ck_tile::index_t hdim_v,
               ck_tile::index_t num_head_q,
               ck_tile::index_t nhead_ratio_qk,
               const void* block_table_ptr,
               ck_tile::index_t batch_stride_block_table,
               ck_tile::index_t page_block_size,
               bool is_gappy,
               float scale_s,
               float scale_p,
               float scale_o,
               float logits_soft_cap,
               ck_tile::index_t stride_q,
               ck_tile::index_t stride_k,
               ck_tile::index_t stride_v,
               ck_tile::index_t stride_bias,
               ck_tile::index_t stride_o,
               ck_tile::index_t nhead_stride_q,
               ck_tile::index_t nhead_stride_k,
               ck_tile::index_t nhead_stride_v,
               ck_tile::index_t nhead_stride_bias,
               ck_tile::index_t nhead_stride_lse,
               ck_tile::index_t nhead_stride_o,
               ck_tile::index_t batch_stride_k, // only used for paged-kvcache
               ck_tile::index_t batch_stride_v, // only used for paged-kvcache
               ck_tile::index_t window_size_left,
               ck_tile::index_t window_size_right,
               ck_tile::index_t sink_size,
               ck_tile::index_t mask_type,
               ck_tile::index_t min_seqlen_q,
               const void* sink_ptr = nullptr)
     {
         return MakeKargsImpl(q_ptr,
                              k_ptr,
                              v_ptr,
                              bias_ptr,
                              lse_ptr,
                              o_ptr,
                              seqstart_q_ptr,
                              seqstart_k_ptr,
                              seqlen_k_ptr,
                              hdim_q,
                              hdim_v,
                              num_head_q,
                              nhead_ratio_qk,
                              block_table_ptr,
                              batch_stride_block_table,
                              page_block_size,
                              is_gappy,
                              scale_s,
                              scale_p,
                              scale_o,
                              logits_soft_cap,
                              stride_q,
                              stride_k,
                              stride_v,
                              stride_bias,
                              stride_o,
                              nhead_stride_q,
                              nhead_stride_k,
                              nhead_stride_v,
                              nhead_stride_bias,
                              nhead_stride_lse,
                              nhead_stride_o,
                              batch_stride_k,
                              batch_stride_v,
                              window_size_left,
                              window_size_right,
                              sink_size,
                              mask_type,
                              min_seqlen_q,
                              sink_ptr);
     }
  
     CK_TILE_HOST static void PrintParameters(const Kargs& kargs, int num_batches)
     {
         static bool dummy = [&]() {
             std::cout << std::endl;
  
             std::cout << " q_ptr: " << kargs.q_ptr << " k_ptr:" << kargs.k_ptr
                       << " v_ptr: " << kargs.v_ptr << " o_ptr:" << kargs.o_ptr
                       << " hdim_q: " << kargs.hdim_q << " hdim_v: " << kargs.hdim_v
                       << " num_head_q:" << kargs.num_head_q
                       << " nhead_ratio_qk: " << kargs.nhead_ratio_qk << " scale_s:" << kargs.scale_s
                       << " stride_q:" << kargs.stride_q << " stride_k:" << kargs.stride_k
                       << " stride_v:" << kargs.stride_v << " stride_o:" << kargs.stride_o
                       << " nhead_stride_q: " << kargs.nhead_stride_q
                       << " nhead_stride_k: " << kargs.nhead_stride_k
                       << " nhead_stride_v:" << kargs.nhead_stride_v
                       << " nhead_stride_o: " << kargs.nhead_stride_o;
             if constexpr(!kIsGroupMode)
             {
                 std::cout << " batch_stride_q:" << kargs.batch_stride_q;
             }
             std::cout << " batch_stride_k:" << kargs.batch_stride_k
                       << " batch_stride_v:" << kargs.batch_stride_v;
  
             if constexpr(kIsGroupMode)
             {
                 if constexpr(kSkipMinSeqlenQ)
                 {
                     std::cout << " min_seqlen_q: " << kargs.min_seqlen_q;
                 }
  
                 std::cout << " seqstart_q_ptr:" << kargs.seqstart_q_ptr
                           << " seqstart_k_ptr: " << kargs.seqstart_k_ptr
                           << " seqlen_k_ptr:" << kargs.seqlen_k_ptr;
                 if(kargs.seqlen_k_ptr != nullptr)
                 {
                     std::cout << "{";
                     for(int i_batch = 0; i_batch < num_batches; i_batch++)
                         std::cout << kargs.seqlen_k_ptr[i_batch] << ",";
                     std::cout << "}";
                 }
             }
             if constexpr(kHasMask)
             {
                 std::cout << " window_size_left: " << kargs.window_size_left
                           << " window_size_right:" << kargs.window_size_right
                           << " mask_type: " << static_cast<int>(kargs.mask_type);
             }
  
             if constexpr(kIsPagedKV)
             {
                 std::cout << " block_table_ptr: " << kargs.block_table_ptr
                           << " batch_stride_block_table:" << kargs.batch_stride_block_table
                           << " page_block_size: " << kargs.page_block_size;
  
                 std::cout << "table value: [";
                 for(int b = 0; b < num_batches; b++)
                 {
                     std::cout << "[ ";
                     for(int i = 0; i < kargs.batch_stride_block_table; i++)
                     {
                         std::cout << kargs.block_table_ptr[b * kargs.batch_stride_block_table + i]
                                   << ",";
                     }
                     std::cout << " ]";
                 }
                 std::cout << " ]";
             }
             std::cout << std::endl;
             return true;
         }();
         (void)dummy;
     }
     CK_TILE_HOST static constexpr auto GridSize(ck_tile::index_t batch_size_,
                                                 ck_tile::index_t nhead_,
                                                 ck_tile::index_t seqlen_q_,
                                                 ck_tile::index_t hdim_v_,
                                                 bool has_padded_seqlen_k)
     {
         // has_padded_seqlen_k is determined by checking (seqlen_k_ptr != nullptr)
         if(has_padded_seqlen_k)
         {
             // TODO: this may need tuning
             return dim3(nhead_,
                         batch_size_,
                         ck_tile::integer_divide_ceil(seqlen_q_, FmhaPipeline::kM0) *
                             ck_tile::integer_divide_ceil(hdim_v_, FmhaPipeline::kN1));
         }
         else
         {
             // TODO: this may need tuning
             return dim3(ck_tile::integer_divide_ceil(seqlen_q_, FmhaPipeline::kM0) *
                             ck_tile::integer_divide_ceil(hdim_v_, FmhaPipeline::kN1),
                         nhead_,
                         batch_size_);
         }
     }
  
     CK_TILE_DEVICE static constexpr auto GetTileIndex(const Kargs& kargs)
     {
         bool has_padded_seqlen_k = false;
  
         if constexpr(kIsGroupMode)
             has_padded_seqlen_k = (kargs.seqlen_k_ptr != nullptr);
  
         if(has_padded_seqlen_k)
         {
             // const index_t num_tile_m0 = seqlen_q / kM0;
             const index_t num_tile_n1 =
                 ck_tile::integer_divide_ceil(kargs.hdim_v, FmhaPipeline::kN1);
  
             const index_t i_block = blockIdx.z;
             const index_t i_nhead = blockIdx.x;
             const index_t i_batch = blockIdx.y;
  
             const auto f = [](index_t dividend, index_t divisor) {
                 index_t quotient = dividend / divisor;
                 index_t modulus  = dividend - quotient * divisor;
                 return ck_tile::make_tuple(quotient, modulus);
             };
  
             const auto [i_tile_m, i_tile_n] = f(i_block, num_tile_n1);
  
             if constexpr(kHasMask)
             {
                 // assume that num_tile_n1 is always 1
                 return ck_tile::make_tuple(gridDim.z - 1 - i_tile_m, i_tile_n, i_nhead, i_batch);
             }
             else
             {
                 return ck_tile::make_tuple(i_tile_m, i_tile_n, i_nhead, i_batch);
             }
         }
         else
         {
             // const index_t num_tile_m0 = seqlen_q / kM0;
             const index_t num_tile_n1 =
                 ck_tile::integer_divide_ceil(kargs.hdim_v, FmhaPipeline::kN1);
  
             const index_t i_block = blockIdx.x;
             const index_t i_nhead = blockIdx.y;
             const index_t i_batch = blockIdx.z;
  
             const auto f = [](index_t dividend, index_t divisor) {
                 index_t quotient = dividend / divisor;
                 index_t modulus  = dividend - quotient * divisor;
                 return ck_tile::make_tuple(quotient, modulus);
             };
  
             const auto [i_tile_m, i_tile_n] = f(i_block, num_tile_n1);
  
             if constexpr(kHasMask)
             {
                 // assume that num_tile_n1 is always 1
                 return ck_tile::make_tuple(gridDim.x - 1 - i_tile_m, i_tile_n, i_nhead, i_batch);
             }
             else
             {
                 return ck_tile::make_tuple(i_tile_m, i_tile_n, i_nhead, i_batch);
             }
         }
     }
  
     CK_TILE_HOST static dim3 BlockSize()
     {
         if(is_wave32())
         {
             return dim3(kBlockSize / 2);
         }
         else
         {
             return dim3(kBlockSize);
         }
     }
  
     CK_TILE_HOST_DEVICE static constexpr ck_tile::index_t GetSmemSize()
     {
         return ck_tile::max(FmhaPipeline::GetSmemSize(), EpiloguePipeline::GetSmemSize());
     }
  
     CK_TILE_DEVICE void operator()(Kargs kargs) const
     {
         // allocate LDS
         __shared__ char smem_ptr[GetSmemSize()];
  
         // divide problem
         const auto [i_tile_m, i_tile_n, i_nhead, i_batch] = GetTileIndex(kargs);
         const index_t i_m0 = amd_wave_read_first_lane(i_tile_m * FmhaPipeline::kM0);
         const index_t i_n1 = amd_wave_read_first_lane(i_tile_n * FmhaPipeline::kN1);
  
         long_index_t batch_offset_q    = 0;
         long_index_t batch_offset_k    = 0;
         long_index_t batch_offset_v    = 0;
         long_index_t batch_offset_bias = 0;
         long_index_t batch_offset_lse  = 0;
         long_index_t batch_offset_o    = 0;
         index_t kv_l2p_offset          = 0;
         const float sink_value =
             kargs.sink_ptr != nullptr
                 ? (*(static_cast<const float*>(kargs.sink_ptr) + i_nhead)) / kargs.scale_s
                 : -numeric<float>::infinity();
  
         if constexpr(kIsGroupMode)
         {
             // get starting offset for each batch
             const long_index_t query_start = kargs.seqstart_q_ptr[i_batch];
             const long_index_t key_start   = kargs.seqstart_k_ptr[i_batch];
  
             batch_offset_q = query_start * kargs.stride_q;
             batch_offset_k = key_start * kargs.stride_k;
             if constexpr(std::is_same_v<VLayout, ck_tile::tensor_layout::gemm::RowMajor>)
             {
                 batch_offset_v = key_start * kargs.stride_v;
             }
             else
             {
                 batch_offset_v = key_start;
             }
             if constexpr(BiasEnum == BlockAttentionBiasEnum::ELEMENTWISE_BIAS)
             {
                 batch_offset_bias = query_start * kargs.stride_bias;
             }
             if constexpr(kStoreLSE)
             {
                 batch_offset_lse = query_start;
             }
  
             batch_offset_o = query_start * kargs.stride_o;
  
             // get real # queries & # keys under group mode
             const auto adjusted_seqstart_q_ptr = kargs.seqstart_q_ptr + i_batch;
             kargs.seqlen_q = adjusted_seqstart_q_ptr[1] - adjusted_seqstart_q_ptr[0];
  
             if constexpr(kSkipMinSeqlenQ)
             {
                 if(kargs.seqlen_q <= kargs.min_seqlen_q)
                 {
                     return;
                 }
             }
  
             // # of required blocks is different in each groups, terminate unnecessary blocks
             // earlier
             if(kargs.seqlen_q <= i_m0)
             {
                 return;
             }
  
             if(kargs.seqlen_k_ptr != nullptr)
             {
                 kargs.seqlen_k = kargs.seqlen_k_ptr[i_batch];
             }
             else
             {
                 const auto adjusted_seqstart_k_ptr = kargs.seqstart_k_ptr + i_batch;
                 kargs.seqlen_k = adjusted_seqstart_k_ptr[1] - adjusted_seqstart_k_ptr[0];
             }
  
             if constexpr(kIsPagedKV)
             {
                 if(kargs.is_gappy)
                 {
                     // seqstart_k_ptr has different meaning in this case
                     kv_l2p_offset = kargs.seqstart_k_ptr[i_batch];
                 }
             }
         }
         else
         {
             const index_t i_cache_batch = [&, i_batch_ = i_batch] {
                 if constexpr(kIsPagedKV)
                 {
                     return i_batch_;
                 }
                 else
                 {
                     return (kargs.cache_batch_idx != nullptr ? kargs.cache_batch_idx[i_batch_]
                                                              : i_batch_);
                 }
             }();
  
             batch_offset_q = static_cast<long_index_t>(i_batch) * kargs.batch_stride_q;
             batch_offset_k = static_cast<long_index_t>(i_cache_batch) * kargs.batch_stride_k;
             batch_offset_v = static_cast<long_index_t>(i_cache_batch) * kargs.batch_stride_v;
             if constexpr(BiasEnum == BlockAttentionBiasEnum::ELEMENTWISE_BIAS)
             {
                 batch_offset_bias = static_cast<long_index_t>(i_batch) * kargs.batch_stride_bias;
             }
             if constexpr(kStoreLSE)
             {
                 batch_offset_lse = static_cast<long_index_t>(i_batch) * kargs.batch_stride_lse;
             }
  
             batch_offset_o = static_cast<long_index_t>(i_batch) * kargs.batch_stride_o;
  
             if(kargs.seqlen_k_ptr != nullptr)
             {
                 kargs.seqlen_k = kargs.seqlen_k_ptr[i_batch];
             }
         }
  
         // for simplicity, batch stride we just modify the pointer
         const QDataType* q_ptr = reinterpret_cast<const QDataType*>(kargs.q_ptr) +
                                  static_cast<long_index_t>(i_nhead) * kargs.nhead_stride_q +
                                  batch_offset_q;
         const KDataType* k_ptr =
             reinterpret_cast<const KDataType*>(kargs.k_ptr) +
             static_cast<long_index_t>(i_nhead / kargs.nhead_ratio_qk) * kargs.nhead_stride_k +
             batch_offset_k;
         const VDataType* v_ptr =
             reinterpret_cast<const VDataType*>(kargs.v_ptr) +
             static_cast<long_index_t>(i_nhead / kargs.nhead_ratio_qk) * kargs.nhead_stride_v +
             batch_offset_v;
         ODataType* o_ptr = reinterpret_cast<ODataType*>(kargs.o_ptr) +
                            static_cast<long_index_t>(i_nhead) * kargs.nhead_stride_o +
                            batch_offset_o;
  
         // Q/K/V DRAM and DRAM window
         const auto q_dram = [&]() {
             const auto q_dram_naive = make_naive_tensor_view<address_space_enum::global>(
                 q_ptr,
                 make_tuple(kargs.seqlen_q, kargs.hdim_q),
                 make_tuple(kargs.stride_q, 1),
                 number<FmhaPipeline::kAlignmentQ>{},
                 number<1>{});
             if constexpr(FmhaPipeline::kQLoadOnce)
             {
                 return pad_tensor_view(
                     q_dram_naive,
                     make_tuple(number<FmhaPipeline::kM0>{}, number<FmhaPipeline::kSubQKHeaddim>{}),
                     sequence<kPadSeqLenQ, kPadHeadDimQ>{});
             }
             else
             {
                 return pad_tensor_view(
                     q_dram_naive,
                     make_tuple(number<FmhaPipeline::kM0>{}, number<FmhaPipeline::kK0>{}),
                     sequence<kPadSeqLenQ, kPadHeadDimQ>{});
             }
         }();
  
         const auto make_k_dram = [&](const KDataType* data, index_t height) {
             const auto k_dram_naive = make_naive_tensor_view<address_space_enum::global>(
                 data, // will update this pointer if using paged-kvcache
                 make_tuple(height, kargs.hdim_q),
                 make_tuple(kargs.stride_k, 1),
                 number<FmhaPipeline::kAlignmentK>{},
                 number<1>{});
  
             return pad_tensor_view(
                 k_dram_naive,
                 make_tuple(number<FmhaPipeline::kN0>{}, number<FmhaPipeline::kK0>{}),
                 sequence<false, kPadHeadDimQ>{});
         };
         const auto k_dram = [&]() {
             if constexpr(kIsPagedKV)
             {
                 return make_k_dram(nullptr, kargs.page_block_size);
             }
             else
             {
                 return make_k_dram(k_ptr, kargs.seqlen_k);
             }
         }();
  
         const auto make_v_dram = [&](const VDataType* data, index_t length) {
             if constexpr(std::is_same_v<VLayout, ck_tile::tensor_layout::gemm::RowMajor>)
             {
                 const auto v_dram_naive = make_naive_tensor_view<address_space_enum::global>(
                     data, // will update this pointer if using paged-kvcache
                     make_tuple(length, kargs.hdim_v),
                     make_tuple(kargs.stride_v, 1),
                     number<FmhaPipeline::kAlignmentV>{},
                     number<1>{});
  
                 const auto v_dram_transposed =
                     transform_tensor_view(v_dram_naive,
                                           make_tuple(make_pass_through_transform(kargs.hdim_v),
                                                      make_pass_through_transform(length)),
                                           make_tuple(sequence<1>{}, sequence<0>{}),
                                           make_tuple(sequence<0>{}, sequence<1>{}));
  
                 return pad_tensor_view(
                     v_dram_transposed,
                     make_tuple(number<FmhaPipeline::kN1>{}, number<FmhaPipeline::kK1>{}),
                     sequence<kPadHeadDimV, kPadSeqLenK>{});
             }
             else
             {
                 const auto v_dram_naive = make_naive_tensor_view<address_space_enum::global>(
                     data, // will update this pointer if using paged-kvcache
                     make_tuple(kargs.hdim_v, length),
                     make_tuple(kargs.stride_v, 1),
                     number<FmhaPipeline::kAlignmentV>{},
                     number<1>{});
  
                 return pad_tensor_view(
                     v_dram_naive,
                     make_tuple(number<FmhaPipeline::kN1>{}, number<FmhaPipeline::kK1>{}),
                     sequence<false, kPadSeqLenK>{});
             }
         };
         const auto v_dram = [&]() {
             if constexpr(kIsPagedKV)
             {
                 return make_v_dram(nullptr, kargs.page_block_size);
             }
             else
             {
                 return make_v_dram(v_ptr, kargs.seqlen_k);
             }
         }();
  
         auto q_dram_window = make_tile_window(
             q_dram,
             [&]() {
                 if constexpr(FmhaPipeline::kQLoadOnce)
                     return make_tuple(number<FmhaPipeline::kM0>{},
                                       number<FmhaPipeline::kSubQKHeaddim>{});
                 else
                     return make_tuple(number<FmhaPipeline::kM0>{}, number<FmhaPipeline::kK0>{});
             }(),
             {i_m0, 0});
  
         auto k_page_block_navigator =
             [&, i_batch_ = i_batch, i_nhead_ = i_nhead / kargs.nhead_ratio_qk]() {
                 if constexpr(kIsPagedKV)
                 {
                     const auto* block_indices =
                         reinterpret_cast<const int32_t*>(kargs.block_table_ptr) +
                         i_batch_ * kargs.batch_stride_block_table;
                     const index_t num_blocks =
                         integer_divide_ceil(kv_l2p_offset + kargs.seqlen_k, kargs.page_block_size);
  
                     const long_index_t fixed_offset =
                         static_cast<long_index_t>(i_nhead_) * kargs.nhead_stride_k;
  
                     return make_page_block_navigator<const KDataType, 0>(
                         kargs.k_ptr,
                         kargs.batch_stride_k, // kcache page-block stride/size
                         fixed_offset,
                         block_indices,
                         num_blocks,
                         kargs.page_block_size,
                         k_dram,
                         make_k_dram(nullptr,
                                     (kv_l2p_offset + kargs.seqlen_k) -
                                         (num_blocks - 1) * kargs.page_block_size));
                 }
                 else
                 {
                     return make_page_block_navigator(k_dram);
                 }
             }();
  
         auto v_page_block_navigator =
             [&, i_batch_ = i_batch, i_nhead_ = i_nhead / kargs.nhead_ratio_qk]() {
                 if constexpr(kIsPagedKV)
                 {
                     const auto* block_indices =
                         reinterpret_cast<const int32_t*>(kargs.block_table_ptr) +
                         i_batch_ * kargs.batch_stride_block_table;
                     const index_t num_blocks =
                         integer_divide_ceil(kv_l2p_offset + kargs.seqlen_k, kargs.page_block_size);
  
                     const long_index_t fixed_offset =
                         static_cast<long_index_t>(i_nhead_) * kargs.nhead_stride_v;
  
                     return make_page_block_navigator<const VDataType, 1>(
                         kargs.v_ptr,
                         kargs.batch_stride_v, // vcache page-block stride/size
                         fixed_offset,
                         block_indices,
                         num_blocks,
                         kargs.page_block_size,
                         v_dram,
                         make_v_dram(nullptr,
                                     (kv_l2p_offset + kargs.seqlen_k) -
                                         (num_blocks - 1) * kargs.page_block_size));
                 }
                 else
                 {
                     return make_page_block_navigator(v_dram);
                 }
             }();
  
         auto k_dram_window_lengths =
             make_tuple(number<FmhaPipeline::kN0>{}, number<FmhaPipeline::kK0>{});
         auto v_dram_window_lengths =
             make_tuple(number<FmhaPipeline::kN1>{}, number<FmhaPipeline::kK1>{});
  
         const auto bias_dram_window = [&, i_nhead_ = i_nhead]() {
             constexpr auto bias_dram_window_lengths =
                 make_tuple(number<FmhaPipeline::kM0>{}, number<FmhaPipeline::kN0>{});
             if constexpr(BiasEnum == BlockAttentionBiasEnum::ELEMENTWISE_BIAS)
             {
                 const BiasDataType* bias_ptr =
                     reinterpret_cast<const BiasDataType*>(kargs.bias_ptr) +
                     static_cast<long_index_t>(i_nhead_) * kargs.nhead_stride_bias +
                     batch_offset_bias;
  
                 const auto bias_dram = [&]() {
                     const auto bias_dram_naive = make_naive_tensor_view<address_space_enum::global>(
                         bias_ptr,
                         make_tuple(kargs.seqlen_q, kargs.seqlen_k),
                         make_tuple(kargs.stride_bias, 1),
                         number<FmhaPipeline::kAlignmentBias>{},
                         number<1>{});
  
                     return pad_tensor_view(bias_dram_naive,
                                            bias_dram_window_lengths,
                                            sequence<kPadSeqLenQ, kPadSeqLenK>{});
                 }();
  
                 return make_tile_window(bias_dram, bias_dram_window_lengths, {i_m0, 0});
             }
             else
             {
                 return make_null_tile_window(bias_dram_window_lengths);
             }
         }();
  
         // lse
         auto lse_dram_window = [&, i_nhead_ = i_nhead]() {
             constexpr auto lse_dram_window_lengths = make_tuple(number<FmhaPipeline::kM0>{});
             if constexpr(kStoreLSE)
             {
                 LSEDataType* lse_ptr =
                     reinterpret_cast<LSEDataType*>(kargs.lse_ptr) +
                     static_cast<long_index_t>(i_nhead_) * kargs.nhead_stride_lse + batch_offset_lse;
  
                 const auto lse_dram = [&]() {
                     const auto lse_dram_naive = make_naive_tensor_view<address_space_enum::global>(
                         lse_ptr,
                         make_tuple(kargs.seqlen_q),
                         make_tuple(1),
                         number<1>{},
                         number<1>{});
  
                     return pad_tensor_view(
                         lse_dram_naive, lse_dram_window_lengths, sequence<kPadSeqLenQ>{});
                 }();
  
                 return make_tile_window(lse_dram, lse_dram_window_lengths, {i_m0});
             }
             else
             {
                 return make_null_tile_window(lse_dram_window_lengths);
             }
         }();
  
         FmhaMask mask = [&]() {
             if constexpr(kHasMask)
                 return ck_tile::make_generic_attention_mask_from_lr_window<FmhaMask>(
                     kargs.window_size_left,
                     kargs.window_size_right,
                     kargs.sink_size,
                     kargs.seqlen_q,
                     kargs.seqlen_k,
                     kargs.mask_type == GenericAttentionMaskEnum::MASK_FROM_TOP_LEFT);
             else
                 return FmhaMask{kargs.seqlen_q, kargs.seqlen_k};
         }();
  
         // WA i_batch capture structure binding before c++20
         auto position_encoding = [&, i_batch_ = i_batch, i_nhead_ = i_nhead]() {
             if constexpr(BiasEnum == BlockAttentionBiasEnum::ALIBI)
             {
                 // data loading, shared by entire wg
                 // TODO: how to use s_read?
                 SaccDataType slope =
                     *(reinterpret_cast<const SaccDataType*>(kargs.alibi_slope_ptr) +
                       i_batch_ * kargs.alibi_slope_stride + i_nhead_);
 #if CK_TILE_FMHA_FWD_FAST_EXP2
                 slope *= ck_tile::log2e_v<>;
 #endif
                 if constexpr(kHasMask)
                 {
                     return make_alibi_from_lr_mask<SaccDataType, true>(slope,
                                                                        kargs.window_size_left,
                                                                        kargs.window_size_right,
                                                                        kargs.seqlen_q,
                                                                        kargs.seqlen_k,
                                                                        kargs.mask_type);
                 }
                 else
                 {
                     return Alibi<SaccDataType, true>{
                         slope, kargs.seqlen_q, kargs.seqlen_k, AlibiMode::FROM_BOTTOM_RIGHT};
                 }
             }
             else
             {
                 return EmptyPositionEncoding<SaccDataType>{};
             }
         }();
  
         AttentionVariant variant;
         const auto variant_params = [&] {
             if constexpr(kHasLogitsSoftCap)
             {
                 return ck_tile::LogitsSoftCapParams<FmhaMask, CK_TILE_FMHA_FWD_FAST_EXP2>{
                     mask, kargs.scale_s, kargs.logits_soft_cap, kargs.logits_soft_cap_rcp};
             }
             else
             {
                 return ck_tile::StandardAttentionParams<FmhaMask>{mask, kargs.scale_s};
             }
         }();
  
         BlockIndices block_indices{i_batch, i_nhead, i_nhead / kargs.nhead_ratio_qk};
  
         auto o_acc_tile = [&]() {
             if constexpr(kDoFp8StaticQuant)
             {
                 return FmhaPipeline{}(q_dram_window,
                                       identity{}, // q_element_func
                                       k_dram_window_lengths,
                                       k_page_block_navigator,
                                       identity{}, // k_element_func
                                       v_dram_window_lengths,
                                       v_page_block_navigator,
                                       identity{}, // v_element_func
                                       bias_dram_window,
                                       identity{}, // bias_element_func
                                       lse_dram_window,
                                       identity{}, // lse_element_func
                                       identity{}, // s_acc_element_func
                                       scales<remove_cvref_t<decltype(kargs.scale_p)>>{
                                           kargs.scale_p}, // p_compute_element_func
                                       make_composes(saturates<fp8_t>{},
                                                     scales<remove_cvref_t<decltype(kargs.scale_o)>>{
                                                         kargs.scale_o}), // o_acc_element_func
                                       mask,
                                       position_encoding,
                                       kargs.scale_s,
                                       variant,
                                       variant_params,
                                       block_indices,
                                       kv_l2p_offset,
                                       smem_ptr,
                                       sink_value);
             }
             else
             {
                 return FmhaPipeline{}(q_dram_window,
                                       k_dram_window_lengths,
                                       k_page_block_navigator,
                                       v_dram_window_lengths,
                                       v_page_block_navigator,
                                       bias_dram_window,
                                       lse_dram_window,
                                       mask,
                                       position_encoding,
                                       kargs.scale_s,
                                       variant,
                                       variant_params,
                                       block_indices,
                                       kv_l2p_offset,
                                       smem_ptr,
                                       sink_value);
             }
         }();
  
         // O DRAM and O DRAM window
         auto o_dram = [&]() {
             const auto o_dram_naive = make_naive_tensor_view<address_space_enum::global>(
                 o_ptr,
                 make_tuple(kargs.seqlen_q, kargs.hdim_v),
                 make_tuple(kargs.stride_o, 1),
                 number<FmhaPipeline::kAlignmentO>{},
                 number<1>{});
             return pad_tensor_view(
                 o_dram_naive,
                 make_tuple(number<FmhaPipeline::kM0>{}, number<FmhaPipeline::kN1>{}),
                 sequence<kPadSeqLenQ, kPadHeadDimV>{});
         }();
  
         auto o_dram_window =
             make_tile_window(o_dram,
                              make_tuple(number<FmhaPipeline::kM0>{}, number<FmhaPipeline::kN1>{}),
                              {i_m0, i_n1});
  
         EpiloguePipeline{}(o_dram_window, o_acc_tile, nullptr);
     }
 };
  
 } // namespace ck_tile