fork pipeline

include/ck_tile/ops/flex_fmha.hpp

@@ -12,8 +12,8 @@
 #include "ck_tile/ops/fmha/kernel/fmha_fwd_kernel.hpp"
 #include "ck_tile/ops/fmha/pipeline/block_fmha_pipeline_enum.hpp"
 #include "ck_tile/ops/fmha/pipeline/block_fmha_pipeline_problem.hpp"
-#include "ck_tile/ops/fmha/pipeline/block_fmha_pipeline_qr_ks_vs.hpp"
-#include "ck_tile/ops/fmha/pipeline/block_fmha_pipeline_qr_ks_vs_async.hpp"
+#include "ck_tile/ops/fmha/pipeline/block_fmha_pipeline_flex_qr_ks_vs.hpp"
+#include "ck_tile/ops/fmha/pipeline/block_fmha_pipeline_flex_qr_ks_vs_async.hpp"
 #include "ck_tile/ops/fmha/pipeline/block_fmha_pipeline_qr_ks_vs_async_default_policy.hpp"
 #include "ck_tile/ops/fmha/pipeline/block_fmha_pipeline_qr_ks_vs_default_policy.hpp"
 #include "ck_tile/ops/fmha/pipeline/tile_fmha_shape.hpp"

include/ck_tile/ops/fmha/pipeline/block_fmha_pipeline_flex_qr_ks_vs.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core.hpp"
+#include "ck_tile/ops/fmha/block/block_attention_bias_enum.hpp"
+#include "ck_tile/ops/fmha/pipeline/block_fmha_pipeline_qr_ks_vs_default_policy.hpp"
+#include "ck_tile/ops/fmha/block/block_dropout.hpp"
+#include "ck_tile/ops/reduce/block/block_reduce.hpp"
+
+namespace ck_tile {
+
+// This pipeline is qkv all located in LDS
+template <typename Problem_, typename Policy_ = BlockFmhaPipelineQRKSVSDefaultPolicy>
+struct BlockFmhaPipelineQRKSVS
+{
+    using Problem               = remove_cvref_t<Problem_>;
+    using Policy                = remove_cvref_t<Policy_>;
+    using QDataType             = remove_cvref_t<typename Problem::QDataType>;
+    using KDataType             = remove_cvref_t<typename Problem::KDataType>;
+    using VDataType             = remove_cvref_t<typename Problem::VDataType>;
+    using SaccDataType          = remove_cvref_t<typename Problem::SaccDataType>;
+    using SMPLComputeDataType   = remove_cvref_t<typename Problem::SMPLComputeDataType>;
+    using BiasDataType          = remove_cvref_t<typename Problem::BiasDataType>;
+    using RandValOutputDataType = remove_cvref_t<typename Problem::RandValOutputDataType>;
+    using LSEDataType           = remove_cvref_t<typename Problem::LSEDataType>;
+    using PDataType             = remove_cvref_t<typename Problem::PDataType>;
+    using OaccDataType          = remove_cvref_t<typename Problem::OaccDataType>;
+    using ODataType             = remove_cvref_t<typename Problem::ODataType>;
+    using FmhaMask              = remove_cvref_t<typename Problem::FmhaMask>;
+
+    using BlockFmhaShape             = remove_cvref_t<typename Problem::BlockFmhaShape>;
+    using VLayout                    = remove_cvref_t<typename BlockFmhaShape::VLayout>;
+    static constexpr bool kQLoadOnce = true; // if q_tile load whole block length (hdim) at once
+    static_assert(kQLoadOnce == Policy::QLoadOnce);
+
+    static constexpr index_t kBlockSize = Problem::kBlockSize;
+
+    static constexpr index_t kM0           = BlockFmhaShape::kM0;
+    static constexpr index_t kN0           = BlockFmhaShape::kN0;
+    static constexpr index_t kK0           = BlockFmhaShape::kK0;
+    static constexpr index_t kN1           = BlockFmhaShape::kN1;
+    static constexpr index_t kK1           = BlockFmhaShape::kK1;
+    static constexpr index_t kQKHeaddim    = BlockFmhaShape::kQKHeaddim;
+    static constexpr index_t kSubQKHeaddim = BlockFmhaShape::kSubQKHeaddim;
+
+    static constexpr bool kIsGroupMode = Problem::kIsGroupMode;
+    static constexpr bool kPadSeqLenQ  = Problem::kPadSeqLenQ;
+    static constexpr bool kPadSeqLenK  = Problem::kPadSeqLenK;
+    static constexpr bool kPadHeadDimQ = Problem::kPadHeadDimQ;
+    static constexpr bool kPadHeadDimV = Problem::kPadHeadDimV;
+    static constexpr auto BiasEnum     = Problem::BiasEnum;
+    static constexpr bool kStoreLSE    = Problem::kStoreLSE;
+    static constexpr bool kHasDropout  = Problem::kHasDropout;
+
+    // last dimension vector length used to create tensor view(and decide buffer_load vector length)
+    // ... together with tensor distribution. tensor dist should able to overwrite this
+    static constexpr index_t kAlignmentQ =
+        kPadHeadDimQ ? 1 : Policy::template GetAlignmentQ<Problem>();
+    static constexpr index_t kAlignmentK =
+        kPadHeadDimQ ? 1 : Policy::template GetAlignmentK<Problem>();
+    static constexpr index_t kAlignmentV = []() {
+        if constexpr(std::is_same_v<VLayout, ck_tile::tensor_layout::gemm::RowMajor>)
+            return kPadHeadDimV ? 1 : Policy::template GetAlignmentV<Problem>();
+        else
+            return kPadSeqLenK ? 1 : Policy::template GetAlignmentV<Problem>();
+    }();
+
+    static constexpr index_t kAlignmentO =
+        kPadHeadDimV ? 1 : Policy::template GetAlignmentO<Problem>();
+    static constexpr index_t kAlignmentBias =
+        kPadSeqLenK ? 1 : Policy::template GetAlignmentBias<Problem>();
+
+    static constexpr index_t kBlockPerCu = []() {
+        if constexpr(Problem::kBlockPerCu != -1)
+            return Problem::kBlockPerCu;
+        else
+        {
+            if constexpr(kQKHeaddim <= 32)
+            {
+                return 2;
+            }
+            else if constexpr(kQKHeaddim <= 64)
+            {
+                return 3;
+            }
+            else if constexpr(kQKHeaddim <= 128)
+            {
+                if constexpr(BiasEnum == BlockAttentionBiasEnum::ELEMENTWISE_BIAS)
+                    return 1;
+                else
+                    return 2;
+            }
+            else if constexpr(kQKHeaddim <= 256)
+            {
+                return 1;
+            }
+        }
+    }();
+
+    static constexpr const char* name = "qr";
+
+    using DropoutType = std::conditional_t<kHasDropout, BlockDropout, NullBlockDropout>;
+
+    CK_TILE_HOST_DEVICE static constexpr ck_tile::index_t GetSmemSize()
+    {
+        return Policy::template GetSmemSize<Problem>();
+    }
+
+    template <typename QDramBlockWindowTmp,
+              typename KDramBlockWindowTmp,
+              typename VDramBlockWindowTmp,
+              typename BiasDramBlockWindowTmp,
+              typename RandValDramBlockWindowTmp,
+              typename LSEDramBlockWindowTmp,
+              typename QElementFunction,
+              typename KElementFunction,
+              typename VElementFunction,
+              typename BiasElementFunction,
+              typename LSEElementFunction,
+              typename SAccElementFunction,
+              typename PComputeElementFunction,
+              typename OAccElementFunction,
+              typename PositionEncoding>
+    CK_TILE_HOST_DEVICE auto
+    operator()(const QDramBlockWindowTmp& q_dram_block_window_tmp, // M0*K0 tile
+               const QElementFunction& q_element_func,
+               const KDramBlockWindowTmp& k_dram_block_window_tmp, // N0*K0 tile
+               const KElementFunction& k_element_func,
+               const VDramBlockWindowTmp& v_dram_block_window_tmp, // N1*K1 tile
+               const VElementFunction& v_element_func,
+               const BiasDramBlockWindowTmp& bias_dram_block_window_tmp, // M0*N0 tile
+               const BiasElementFunction& bias_element_func,
+               RandValDramBlockWindowTmp& randval_dram_block_window_tmp,
+               LSEDramBlockWindowTmp& lse_dram_window_tmp, // M0*1 tile
+               const LSEElementFunction& lse_element_func,
+               const SAccElementFunction& s_acc_element_func,
+               const PComputeElementFunction& p_compute_element_func,
+               const OAccElementFunction& o_acc_element_func,
+               FmhaMask mask,
+               PositionEncoding position_encoding,
+               float scale_s,
+               void* smem_ptr,
+               DropoutType& dropout) const
+    {
+        static_assert(
+            std::is_same_v<QDataType, remove_cvref_t<typename QDramBlockWindowTmp::DataType>> &&
+                std::is_same_v<KDataType, remove_cvref_t<typename KDramBlockWindowTmp::DataType>> &&
+                std::is_same_v<VDataType, remove_cvref_t<typename VDramBlockWindowTmp::DataType>>,
+            "wrong!");
+
+        static_assert(kM0 == QDramBlockWindowTmp{}.get_window_lengths()[number<0>{}] &&
+                          kN0 == KDramBlockWindowTmp{}.get_window_lengths()[number<0>{}] &&
+                          kK0 == KDramBlockWindowTmp{}.get_window_lengths()[number<1>{}] &&
+                          kN1 == VDramBlockWindowTmp{}.get_window_lengths()[number<0>{}] &&
+                          kK1 == VDramBlockWindowTmp{}.get_window_lengths()[number<1>{}] &&
+                          kM0 == BiasDramBlockWindowTmp{}.get_window_lengths()[number<0>{}] &&
+                          kN0 == BiasDramBlockWindowTmp{}.get_window_lengths()[number<1>{}],
+                      "wrong!");
+
+        // K tile in LDS
+        KDataType* k_lds_ptr = static_cast<KDataType*>(static_cast<void*>(
+            static_cast<char*>(smem_ptr) + Policy::template GetSmemSizeQ<Problem>()));
+        auto k_lds           = make_tensor_view<address_space_enum::lds>(
+            k_lds_ptr, Policy::template MakeKLdsBlockDescriptor<Problem>());
+        auto k_lds_window =
+            make_tile_window(k_lds, make_tuple(number<kN0>{}, number<kK0>{}), {0, 0});
+
+        // V tile in LDS
+        auto v_lds = make_tensor_view<address_space_enum::lds>(
+            reinterpret_cast<VDataType*>(smem_ptr),
+            Policy::template MakeVLdsBlockDescriptor<Problem>());
+        auto v_lds_window = make_tile_window(
+            v_lds, Policy::template MakeVLdsBlockDescriptor<Problem>().get_lengths(), {0, 0});
+
+        // Block GEMM
+        constexpr auto gemm_0 = Policy::template GetQKBlockGemm<Problem>();
+        constexpr auto gemm_1 = Policy::template GetKVBlockGemm<Problem>();
+
+        auto q_dram_window = make_tile_window(
+            q_dram_block_window_tmp.get_bottom_tensor_view(),
+            q_dram_block_window_tmp.get_window_lengths(),
+            q_dram_block_window_tmp.get_window_origin(),
+            Policy::template MakeQDramTileDistribution<Problem, decltype(gemm_0)>());
+
+        auto q = load_tile(q_dram_window);
+
+        using SaccBlockTileType = decltype(gemm_0.MakeCBlockTile());
+        auto s_acc              = SaccBlockTileType{};
+
+        // reduction function for softmax
+        const auto f_max = [](auto e0, auto e1) { return max(e0, e1); };
+        const auto f_sum = [](auto e0, auto e1) { return e0 + e1; };
+
+        // infer Sacc, S, P, M, L, Oacc type
+        using SBlockTileType = decltype(cast_tile<SMPLComputeDataType>(s_acc));
+
+        using MLBlockTileType = decltype(block_tile_reduce<SMPLComputeDataType>(
+            SBlockTileType{}, sequence<1>{}, f_max, SMPLComputeDataType{0}));
+
+        using OaccBlockTileType = decltype(gemm_1.MakeCBlockTile());
+
+        // init Oacc, M, L
+        auto o_acc = OaccBlockTileType{};
+        auto m     = MLBlockTileType{};
+        auto l     = MLBlockTileType{};
+
+        clear_tile(o_acc);
+        set_tile(m, -numeric<SMPLComputeDataType>::infinity());
+        clear_tile(l);
+
+        const auto q_origin = q_dram_window.get_window_origin();
+        const auto [seqlen_k_start, seqlen_k_end] =
+            mask.GetTileRangeAlongX(q_origin.at(number<0>{}), number<kM0>{}, number<kN0>{});
+
+        const auto num_total_loop = integer_divide_ceil(seqlen_k_end - seqlen_k_start, kN0);
+
+        // check early exit if no work to do
+        if constexpr(FmhaMask::IsMasking || kPadSeqLenK)
+        {
+            if(num_total_loop <= 0)
+            {
+                if constexpr(kStoreLSE)
+                {
+                    auto lse =
+                        make_static_distributed_tensor<LSEDataType>(m.get_tile_distribution());
+
+                    set_tile(lse, -numeric<SMPLComputeDataType>::infinity());
+
+                    store_tile(lse_dram_window_tmp, tile_elementwise_in(lse_element_func, lse));
+                }
+
+                // Note: here occ are all cleard, return it
+                // Note: q loaded but no fence, ignore it.
+                return o_acc;
+            }
+        }
+
+        auto k_dram_block_window =
+            make_tile_window(k_dram_block_window_tmp.get_bottom_tensor_view(),
+                             k_dram_block_window_tmp.get_window_lengths(),
+                             {seqlen_k_start, 0});
+
+        const auto bias_origin = bias_dram_block_window_tmp.get_window_origin();
+        auto bias_dram_window =
+            make_tile_window(bias_dram_block_window_tmp.get_bottom_tensor_view(),
+                             bias_dram_block_window_tmp.get_window_lengths(),
+                             {bias_origin.at(number<0>{}), seqlen_k_start}, // M/N
+                             Policy::template MakeBiasDramTileDistribution<decltype(gemm_0)>());
+
+        auto randval_dram_window = dropout.template MakeRandvalDramWindow<decltype(gemm_0)>(
+            randval_dram_block_window_tmp, seqlen_k_start);
+
+        auto v_dram_window =
+            make_tile_window(v_dram_block_window_tmp.get_bottom_tensor_view(),
+                             v_dram_block_window_tmp.get_window_lengths(),
+                             {0, seqlen_k_start}, // TODO: hdim split?
+                             Policy::template MakeVDramTileDistribution<Problem>());
+
+        auto q_tile = tile_elementwise_in(q_element_func, q);
+
+        // prefetch K tile
+        index_t i_total_loops      = 0;
+        constexpr index_t k0_loops = kQKHeaddim / kK0;
+        constexpr index_t k1_loops = kN0 / kK1;
+
+        static_assert(2 <= k0_loops);
+        static_assert(1 <= k1_loops);
+        do
+        {
+            // STAGE 1, QK gemm
+            auto k_dram_window = make_tile_window(
+                k_dram_block_window.get_bottom_tensor_view(),
+                k_dram_block_window.get_window_lengths(),
+                k_dram_block_window.get_window_origin(),
+                Policy::template MakeKDramTileDistribution<Problem>()); // K DRAM tile window for
+                                                                        // load
+
+            auto k_block_tile = load_tile(k_dram_window);
+            {
+                move_tile_window(k_dram_window, {0, kK0});
+                clear_tile(s_acc); // initialize C
+                store_tile(k_lds_window, tile_elementwise_in(k_element_func, k_block_tile));
+                k_block_tile = load_tile(k_dram_window);
+            }
+
+            if constexpr(BiasEnum == BlockAttentionBiasEnum::ELEMENTWISE_BIAS)
+            {
+                __builtin_amdgcn_sched_barrier(
+                    0); // prevent from messing up the order of global loads
+            }
+            const auto bias_tile = load_tile(bias_dram_window); // load bias tile
+            if constexpr(BiasEnum == BlockAttentionBiasEnum::ELEMENTWISE_BIAS)
+            {
+                __builtin_amdgcn_sched_barrier(
+                    0); // prevent from messing up the order of global loads
+            }
+
+            if constexpr(k0_loops > 2)
+            {
+                static_for<0, k0_loops - 2, 1>{}([&](auto i_k0) {
+                    block_sync_lds();
+                    gemm_0(s_acc,
+                           get_slice_tile(q_tile,
+                                          sequence<0, i_k0 * kK0>{},
+                                          sequence<kM0, (i_k0 + 1) * kK0>{}),
+                           k_lds_window);
+                    block_sync_lds();
+                    move_tile_window(k_dram_window, {0, kK0});
+
+                    store_tile(
+                        k_lds_window,
+                        tile_elementwise_in(k_element_func, k_block_tile)); // LDS write i + 1
+                    k_block_tile = load_tile(k_dram_window);                // global read i + 2
+                });
+            }
+
+            const auto v_prefetch = load_tile(v_dram_window); // prefetch load v tile
+            {                                                 // tail
+                block_sync_lds();
+                gemm_0(s_acc,
+                       get_slice_tile(q_tile,
+                                      sequence<0, (k0_loops - 2) * kK0>{},
+                                      sequence<kM0, (k0_loops - 1) * kK0>{}),
+                       k_lds_window);
+                block_sync_lds();
+
+                store_tile(k_lds_window, tile_elementwise_in(k_element_func, k_block_tile));
+                block_sync_lds();
+
+                gemm_0(s_acc,
+                       get_slice_tile(q_tile,
+                                      sequence<0, (k0_loops - 1) * kK0>{},
+                                      sequence<kM0, k0_loops * kK0>{}),
+                       k_lds_window);
+            }
+
+            // STAGE 2, scale_s, add bias, mask, softmax
+            if constexpr(BiasEnum == BlockAttentionBiasEnum::ELEMENTWISE_BIAS)
+            {
+                s_acc = tile_elementwise_in(s_acc_element_func, s_acc);
+                tile_elementwise_inout([&scale_s](auto& x) { x = x * scale_s; }, s_acc);
+                tile_elementwise_inout(
+                    [&](auto& x, const auto& y) {
+#if !CK_TILE_FMHA_FWD_FAST_EXP2
+                        x += type_convert<SaccDataType>(bias_element_func(y));
+#else
+                        x += log2e_v<SaccDataType> *
+                             type_convert<SaccDataType>(bias_element_func(y));
+#endif
+                    },
+                    s_acc,
+                    bias_tile);
+            }
+            else if constexpr(BiasEnum == BlockAttentionBiasEnum::ALIBI)
+            {
+                const auto k_origin    = k_dram_block_window.get_window_origin();
+                constexpr auto s_spans = decltype(s_acc)::get_distributed_spans();
+                s_acc                  = tile_elementwise_in(s_acc_element_func, s_acc);
+                sweep_tile_span(s_spans[number<0>{}], [&](auto idx0) {
+                    sweep_tile_span(s_spans[number<1>{}], [&](auto idx1) {
+                        const auto tile_idx = get_x_indices_from_distributed_indices(
+                            s_acc.get_tile_distribution(), make_tuple(idx0, idx1));
+
+                        const auto row = q_origin.at(number<0>{}) + tile_idx.at(number<0>{});
+                        const auto col = k_origin.at(number<0>{}) + tile_idx.at(number<1>{});
+                        constexpr auto i_j_idx = make_tuple(idx0, idx1);
+
+                        s_acc(i_j_idx) *= scale_s;
+                        position_encoding.update(s_acc(i_j_idx), row, col);
+                    });
+                });
+            }
+            else
+            {
+                s_acc = tile_elementwise_in(s_acc_element_func, s_acc);
+#if !CK_TILE_FMHA_FWD_FAST_EXP2
+                tile_elementwise_inout([&scale_s](auto& x) { x = x * scale_s; }, s_acc);
+#endif
+            }
+            move_tile_window(bias_dram_window, {0, kN0});
+            if constexpr(kPadSeqLenK || FmhaMask::IsMasking)
+            {
+                const auto k_origin      = k_dram_block_window.get_window_origin();
+                bool need_perpixel_check = mask.IsEdgeTile(q_origin.at(number<0>{}),
+                                                           k_origin.at(number<0>{}),
+                                                           number<kM0>{},
+                                                           number<kN0>{});
+                if(need_perpixel_check)
+                {
+                    set_tile_if(
+                        s_acc, -numeric<SMPLComputeDataType>::infinity(), [&](auto tile_idx) {
+                            const auto row = q_origin.at(number<0>{}) + tile_idx.at(number<0>{});
+                            const auto col = k_origin.at(number<0>{}) + tile_idx.at(number<1>{});
+                            return mask.IsOutOfBound(row, col);
+                        });
+                }
+            }
+
+            const auto s = cast_tile<SMPLComputeDataType>(s_acc); // S{j}
+            auto m_local = block_tile_reduce<SMPLComputeDataType>(
+                s,
+                sequence<1>{},
+                f_max,
+                -numeric<SMPLComputeDataType>::infinity()); // m_local = rowmax(S{j})
+            block_tile_reduce_sync(m_local, f_max, bool_constant<false>{});
+
+            const auto m_old = m; // m{j-1}
+            tile_elementwise_inout(
+                [](auto& e0, auto e1, auto e2) { e0 = max(e1, e2); }, m, m_old, m_local); // m{j}
+
+            auto p_compute = make_static_distributed_tensor<SMPLComputeDataType>(
+                s.get_tile_distribution()); // Pcompute{j}
+
+            static const auto get_validated_m = [](SMPLComputeDataType raw_m) {
+                /// NOTICE: bias might be materialized mask including -inf values, need
+                /// consideration
+                if constexpr(BiasEnum == BlockAttentionBiasEnum::ELEMENTWISE_BIAS ||
+                             FmhaMask::IsMasking)
+                {
+                    return raw_m == -numeric<SMPLComputeDataType>::infinity()
+                               ? type_convert<SMPLComputeDataType>(0.f)
+                               : raw_m;
+                }
+                else
+                {
+                    return raw_m;
+                }
+            };
+
+            constexpr auto p_spans = decltype(p_compute)::get_distributed_spans();
+            sweep_tile_span(p_spans[number<0>{}], [&](auto idx0) {
+                constexpr auto i_idx = make_tuple(idx0);
+#if CK_TILE_FMHA_FWD_FAST_EXP2
+                auto row_max = scale_s * get_validated_m(m[i_idx]);
+#endif
+                sweep_tile_span(p_spans[number<1>{}], [&](auto idx1) {
+                    constexpr auto i_j_idx = make_tuple(idx0, idx1);
+#if CK_TILE_FMHA_FWD_FAST_EXP2
+                    if constexpr(BiasEnum == BlockAttentionBiasEnum::ELEMENTWISE_BIAS ||
+                                 BiasEnum == BlockAttentionBiasEnum::ALIBI)
+                    {
+                        p_compute(i_j_idx) = exp2(s[i_j_idx] - get_validated_m(m[i_idx]));
+                    }
+                    else
+                    {
+                        p_compute(i_j_idx) = exp2(scale_s * s[i_j_idx] - row_max);
+                    }
+#else
+                    p_compute(i_j_idx)     = exp(s[i_j_idx] - get_validated_m(m[i_idx]));
+#endif
+                });
+            });
+
+            auto rowsum_p = block_tile_reduce<SMPLComputeDataType>(
+                p_compute, sequence<1>{}, f_sum, SMPLComputeDataType{0}); // rowsum(Pcompute{j})
+
+            block_tile_reduce_sync(rowsum_p, f_sum, bool_constant<false>{});
+            // l{j}, Oacc{j}
+            constexpr auto o_spans = decltype(o_acc)::get_distributed_spans();
+            sweep_tile_span(o_spans[number<0>{}], [&](auto idx0) {
+                constexpr auto i_idx = make_tuple(idx0);
+#if CK_TILE_FMHA_FWD_FAST_EXP2
+                const auto tmp = [&]() {
+                    if constexpr(BiasEnum == BlockAttentionBiasEnum::ELEMENTWISE_BIAS ||
+                                 BiasEnum == BlockAttentionBiasEnum::ALIBI)
+                    {
+                        return exp2(m_old[i_idx] - get_validated_m(m[i_idx]));
+                    }
+                    else
+                    {
+                        auto row_max = scale_s * get_validated_m(m[i_idx]);
+                        return exp2(scale_s * m_old[i_idx] - row_max);
+                    }
+                }();
+#else
+                const auto tmp       = exp(m_old[i_idx] - get_validated_m(m[i_idx]));
+#endif
+                l(i_idx) = tmp * l[i_idx] + rowsum_p[i_idx];
+                sweep_tile_span(o_spans[number<1>{}], [&](auto idx1) {
+                    constexpr auto i_j_idx = make_tuple(idx0, idx1);
+                    // FIXME: this use different equation from FA v2 paper,
+                    // but produce correc result.
+                    // Is the equation wrong?
+                    o_acc(i_j_idx) *= tmp;
+                });
+            });
+
+            if constexpr(kHasDropout)
+            {
+                dropout.template Run<decltype(gemm_0), SMPLComputeDataType, RandValOutputDataType>(
+                    smem_ptr, seqlen_k_start + i_total_loops * kN0, p_compute, randval_dram_window);
+            }
+
+            block_sync_lds();
+            if constexpr(std::is_same_v<VLayout, ck_tile::tensor_layout::gemm::RowMajor>)
+            {
+                auto v_shuffle_tmp = make_static_distributed_tensor<VDataType>(
+                    Policy::template MakeShuffledVRegBlockDescriptor<Problem>());
+                shuffle_tile(v_shuffle_tmp, v_prefetch);
+                store_tile(
+                    v_lds_window,
+                    tile_elementwise_in(v_element_func, v_shuffle_tmp)); // store the prefetch
+            }
+            else
+            {
+                store_tile(v_lds_window,
+                           tile_elementwise_in(v_element_func, v_prefetch)); // store the prefetch
+            }
+            move_tile_window(v_dram_window, {0, kK1});
+
+            const auto p =
+                cast_tile<PDataType>(tile_elementwise_in(p_compute_element_func, p_compute));
+
+            // STAGE 3, KV gemm
+            if constexpr(k1_loops > 1)
+            {
+                static_for<0, k1_loops - 1, 1>{}([&](auto i_k1) {
+                    const auto v = load_tile(v_dram_window); // load next v
+                    block_sync_lds();
+                    gemm_1(o_acc,
+                           get_slice_tile(
+                               p, sequence<0, i_k1 * kK1>{}, sequence<kM0, (i_k1 + 1) * kK1>{}),
+                           v_lds_window);
+                    block_sync_lds();
+                    if constexpr(std::is_same_v<VLayout, ck_tile::tensor_layout::gemm::RowMajor>)
+                    {
+                        auto v_shuffle_tmp = make_static_distributed_tensor<VDataType>(
+                            Policy::template MakeShuffledVRegBlockDescriptor<Problem>());
+                        shuffle_tile(v_shuffle_tmp, v);
+                        store_tile(v_lds_window,
+                                   tile_elementwise_in(v_element_func,
+                                                       v_shuffle_tmp)); // store the prefetch
+                    }
+                    else
+                    {
+                        store_tile(v_lds_window,
+                                   tile_elementwise_in(v_element_func, v)); // store next v
+                    }
+                    move_tile_window(v_dram_window, {0, kK1});
+                });
+            }
+            // move K tile windows
+            move_tile_window(k_dram_block_window, {kN0, 0});
+            // tail
+            {
+                block_sync_lds();
+                gemm_1(o_acc,
+                       get_slice_tile(p, sequence<0, (k1_loops - 1) * kK1>{}, sequence<kM0, kN0>{}),
+                       v_lds_window);
+                block_sync_lds();
+            }
+        } while(++i_total_loops < num_total_loop);
+
+        // store lse
+        if constexpr(kStoreLSE)
+        {
+            auto lse = make_static_distributed_tensor<LSEDataType>(m.get_tile_distribution());
+
+            constexpr auto lse_spans = decltype(lse)::get_distributed_spans();
+            sweep_tile_span(lse_spans[number<0>{}], [&, m_ = m, l_ = l](auto idx0) {
+                constexpr auto i_idx = make_tuple(idx0);
+#if CK_TILE_FMHA_FWD_FAST_EXP2
+                if constexpr(BiasEnum == BlockAttentionBiasEnum::ELEMENTWISE_BIAS ||
+                             BiasEnum == BlockAttentionBiasEnum::ALIBI)
+                {
+                    lse(i_idx) = m_[i_idx] / C_LOG2E + log(l_[i_idx]);
+                }
+                else
+                {
+                    lse(i_idx) = m_[i_idx] * scale_s / C_LOG2E + log(l_[i_idx]);
+                }
+#else
+                lse(i_idx) = m_[i_idx] + log(l_[i_idx]);
+#endif
+            });
+
+            store_tile(lse_dram_window_tmp, tile_elementwise_in(lse_element_func, lse));
+        }
+
+        // finally, O
+        constexpr auto o_spans = decltype(o_acc)::get_distributed_spans();
+
+        sweep_tile_span(o_spans[number<0>{}], [&](auto idx0) {
+            constexpr auto i_idx = make_tuple(idx0);
+            const auto tmp       = [&]() {
+                if constexpr(FmhaMask::IsMasking)
+                {
+                    return l[i_idx] == 0.f ? 0.f : 1 / l[i_idx];
+                }
+                else
+                    return 1 / l[i_idx];
+            }();
+            sweep_tile_span(o_spans[number<1>{}], [&](auto idx1) {
+                constexpr auto i_j_idx = make_tuple(idx0, idx1);
+                o_acc(i_j_idx) *= tmp;
+            });
+        });
+
+        o_acc = tile_elementwise_in(o_acc_element_func, o_acc);
+
+        return o_acc;
+    }
+
+    template <typename QDramBlockWindowTmp,
+              typename KDramBlockWindowTmp,
+              typename VDramBlockWindowTmp,
+              typename BiasDramBlockWindowTmp,
+              typename RandValDramBlockWindowTmp,
+              typename LSEDramBlockWindowTmp,
+              typename PositionEncoding>
+    CK_TILE_HOST_DEVICE auto
+    operator()(const QDramBlockWindowTmp& q_dram_block_window_tmp,       // M0*K0 tile
+               const KDramBlockWindowTmp& k_dram_block_window_tmp,       // N0*K0 tile
+               const VDramBlockWindowTmp& v_dram_block_window_tmp,       // N1*K1 tile
+               const BiasDramBlockWindowTmp& bias_dram_block_window_tmp, // M0*N0 tile
+               RandValDramBlockWindowTmp& randval_dram_block_window_tmp, // M0*N0 tile
+               LSEDramBlockWindowTmp& lse_dram_block_window_tmp,         // M0*1 tile
+               FmhaMask mask,
+               PositionEncoding position_encoding,
+               float scale_s,
+               void* smem_ptr,
+               DropoutType& dropout) const
+    {
+        return operator()(q_dram_block_window_tmp,
+                          identity{},
+                          k_dram_block_window_tmp,
+                          identity{},
+                          v_dram_block_window_tmp,
+                          identity{},
+                          bias_dram_block_window_tmp,
+                          identity{},
+                          randval_dram_block_window_tmp,
+                          lse_dram_block_window_tmp,
+                          identity{},
+                          identity{},
+                          identity{},
+                          identity{},
+                          mask,
+                          position_encoding,
+                          scale_s,
+                          smem_ptr,
+                          dropout);
+    }
+};
+
+} // namespace ck_tile

include/ck_tile/ops/fmha/pipeline/block_fmha_pipeline_flex_qr_ks_vs_async.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core.hpp"
+#include "ck_tile/ops/common/tensor_layout.hpp"
+#include "ck_tile/ops/fmha/block/block_attention_bias_enum.hpp"
+#include "ck_tile/ops/fmha/pipeline/block_fmha_pipeline_qr_ks_vs_async_default_policy.hpp"
+#include "ck_tile/ops/fmha/block/block_dropout.hpp"
+#include "ck_tile/ops/reduce/block/block_reduce.hpp"
+
+namespace ck_tile {
+
+// a variation of qr/ks/vs, where we use async copy to load k (potentially v in the future)
+template <typename Problem_, typename Policy_ = BlockFmhaPipelineQRKSVSAsyncDefaultPolicy>
+struct BlockFmhaPipelineQRKSVSAsync
+{
+    using Problem               = remove_cvref_t<Problem_>;
+    using Policy                = remove_cvref_t<Policy_>;
+    using QDataType             = remove_cvref_t<typename Problem::QDataType>;
+    using KDataType             = remove_cvref_t<typename Problem::KDataType>;
+    using VDataType             = remove_cvref_t<typename Problem::VDataType>;
+    using SaccDataType          = remove_cvref_t<typename Problem::SaccDataType>;
+    using SMPLComputeDataType   = remove_cvref_t<typename Problem::SMPLComputeDataType>;
+    using BiasDataType          = remove_cvref_t<typename Problem::BiasDataType>;
+    using RandValOutputDataType = remove_cvref_t<typename Problem::RandValOutputDataType>;
+    using LSEDataType           = remove_cvref_t<typename Problem::LSEDataType>;
+    using PDataType             = remove_cvref_t<typename Problem::PDataType>;
+    using OaccDataType          = remove_cvref_t<typename Problem::OaccDataType>;
+    using ODataType             = remove_cvref_t<typename Problem::ODataType>;
+    using FmhaMask              = remove_cvref_t<typename Problem::FmhaMask>;
+
+    using BlockFmhaShape             = remove_cvref_t<typename Problem::BlockFmhaShape>;
+    using VLayout                    = remove_cvref_t<typename BlockFmhaShape::VLayout>;
+    static constexpr bool kQLoadOnce = true; // if q_tile load whole block length (hdim) at once
+    static_assert(kQLoadOnce == Policy::QLoadOnce);
+
+    static constexpr index_t kBlockSize = Problem::kBlockSize;
+
+    static constexpr index_t kM0           = BlockFmhaShape::kM0;
+    static constexpr index_t kN0           = BlockFmhaShape::kN0;
+    static constexpr index_t kK0           = BlockFmhaShape::kK0;
+    static constexpr index_t kN1           = BlockFmhaShape::kN1;
+    static constexpr index_t kK1           = BlockFmhaShape::kK1;
+    static constexpr index_t kQKHeaddim    = BlockFmhaShape::kQKHeaddim;
+    static constexpr index_t kSubQKHeaddim = BlockFmhaShape::kSubQKHeaddim;
+
+    static constexpr bool kIsGroupMode = Problem::kIsGroupMode;
+    // TODO: seq_q always support padding, hdim_q/v support multiple of vector(like 8x)
+    //       only need special care about seq_k padding (oob need set -INF of p instead of zero)
+    static_assert(Problem::kPadSeqLenQ == true && Problem::kPadHeadDimQ == true &&
+                  Problem::kPadHeadDimV == true);
+    static constexpr bool kPadSeqLenQ  = true;
+    static constexpr bool kPadSeqLenK  = Problem::kPadSeqLenK;
+    static constexpr bool kPadHeadDimQ = true; // support multiple of vector(like 8x)
+    static constexpr bool kPadHeadDimV = true; // support multiple of vector(like 8x)
+    static constexpr auto BiasEnum     = Problem::BiasEnum;
+    static constexpr bool kStoreLSE    = Problem::kStoreLSE;
+    static constexpr bool kHasDropout  = Problem::kHasDropout;
+
+    // last dimension vector length used to create tensor view(and decide buffer_load vector length)
+    // ... together with tensor distribution. tensor dist should able to overwrite this
+    static constexpr index_t kAlignmentQ = Policy::template GetAlignmentQ<Problem>();
+    static constexpr index_t kAlignmentK = Policy::template GetAlignmentK<Problem>();
+    static constexpr index_t kAlignmentV = []() {
+        if constexpr(std::is_same_v<VLayout, ck_tile::tensor_layout::gemm::RowMajor>)
+            return Policy::template GetAlignmentV<Problem>();
+        else
+            return kPadSeqLenK ? 1 : Policy::template GetAlignmentV<Problem>();
+    }();
+    static constexpr index_t kAlignmentO = Policy::template GetAlignmentO<Problem>();
+    static constexpr index_t kAlignmentBias =
+        kPadSeqLenK ? 1 : Policy::template GetAlignmentBias<Problem>();
+
+#if CK_TILE_FMHA_FWD_FAST_EXP2
+    static constexpr auto R_LOG2E = 1.0 / log2e_v<SaccDataType>;
+#endif
+
+    static constexpr index_t kBlockPerCu = []() {
+        if constexpr(Problem::kBlockPerCu != -1)
+            return Problem::kBlockPerCu;
+        else
+        {
+            // minimize occupancy
+            if constexpr(BiasEnum != BlockAttentionBiasEnum::NO_BIAS && kHasDropout)
+            {
+                return 1;
+            }
+
+            if constexpr(kQKHeaddim <= 32)
+            {
+                if constexpr(kPadSeqLenK && BiasEnum == BlockAttentionBiasEnum::ELEMENTWISE_BIAS &&
+                             FmhaMask::IsMasking)
+                    return 1;
+                else
+                    return 2;
+            }
+            else if constexpr(kQKHeaddim <= 64)
+            {
+                if constexpr(kPadSeqLenK && BiasEnum == BlockAttentionBiasEnum::ELEMENTWISE_BIAS)
+                    return 2;
+                else
+                    return 3;
+            }
+            else if constexpr(kQKHeaddim <= 128)
+            {
+                if constexpr(kPadSeqLenK && BiasEnum == BlockAttentionBiasEnum::ELEMENTWISE_BIAS)
+                    return 1;
+                else
+                    return 2;
+            }
+            else if constexpr(kQKHeaddim <= 256)
+            {
+                return 1;
+            }
+        }
+    }();
+
+    static constexpr const char* name = "qr_async";
+
+    using DropoutType = std::conditional_t<kHasDropout, BlockDropout, NullBlockDropout>;
+
+    CK_TILE_HOST_DEVICE static constexpr ck_tile::index_t GetSmemSize()
+    {
+        return Policy::template GetSmemSize<Problem>();
+    }
+
+    template <typename QDramBlockWindowTmp,
+              typename KDramBlockWindowTmp,
+              typename VDramBlockWindowTmp,
+              typename BiasDramBlockWindowTmp,
+              typename RandValDramBlockWindowTmp,
+              typename LSEDramBlockWindowTmp,
+              typename QElementFunction,
+              typename KElementFunction,
+              typename VElementFunction,
+              typename BiasElementFunction,
+              typename LSEElementFunction,
+              typename SAccElementFunction,
+              typename PComputeElementFunction,
+              typename OAccElementFunction,
+              typename PositionEncoding>
+    CK_TILE_HOST_DEVICE auto
+    operator()(const QDramBlockWindowTmp& q_dram_block_window_tmp, // M0*K0 tile
+               const QElementFunction& q_element_func,
+               const KDramBlockWindowTmp& k_dram_block_window_tmp, // N0*K0 tile
+               const KElementFunction& /*k_element_func*/,
+               const VDramBlockWindowTmp& v_dram_block_window_tmp, // N1*K1 tile
+               const VElementFunction& v_element_func,
+               const BiasDramBlockWindowTmp& bias_dram_block_window_tmp, // M0*N0 tile
+               const BiasElementFunction& bias_element_func,
+               RandValDramBlockWindowTmp& randval_dram_block_window_tmp,
+               LSEDramBlockWindowTmp& lse_dram_window_tmp, // M0*1 tile
+               const LSEElementFunction& lse_element_func,
+               const SAccElementFunction& s_acc_element_func,
+               const PComputeElementFunction& p_compute_element_func,
+               const OAccElementFunction& o_acc_element_func,
+               FmhaMask mask,
+               PositionEncoding position_encoding,
+               float scale_s,
+               void* smem_ptr,
+               DropoutType& dropout) const
+    {
+        static_assert(
+            std::is_same_v<QDataType, remove_cvref_t<typename QDramBlockWindowTmp::DataType>> &&
+                std::is_same_v<KDataType, remove_cvref_t<typename KDramBlockWindowTmp::DataType>> &&
+                std::is_same_v<VDataType, remove_cvref_t<typename VDramBlockWindowTmp::DataType>>,
+            "wrong!");
+
+        static_assert(kM0 == QDramBlockWindowTmp{}.get_window_lengths()[number<0>{}] &&
+                          kN0 == KDramBlockWindowTmp{}.get_window_lengths()[number<0>{}] &&
+                          kK0 == KDramBlockWindowTmp{}.get_window_lengths()[number<1>{}] &&
+                          kN1 == VDramBlockWindowTmp{}.get_window_lengths()[number<0>{}] &&
+                          kK1 == VDramBlockWindowTmp{}.get_window_lengths()[number<1>{}] &&
+                          kM0 == BiasDramBlockWindowTmp{}.get_window_lengths()[number<0>{}] &&
+                          kN0 == BiasDramBlockWindowTmp{}.get_window_lengths()[number<1>{}],
+                      "wrong!");
+
+        constexpr auto LdsSeq = Policy::template GetLdsBufferSequence<Problem>();
+
+        // K tile in LDS
+        auto k_lds_ptr   = reinterpret_cast<KDataType*>(smem_ptr);
+        auto k_lds_store = generate_tuple(
+            [&](auto i_buf) {
+                return make_tile_window(
+                    make_tensor_view<address_space_enum::lds>(
+                        k_lds_ptr, Policy::template MakeKLdsStoreBlockDescriptor<Problem>(i_buf)),
+                    Policy::template MakeKLdsStoreBlockDescriptor<Problem>(i_buf).get_lengths(),
+                    {0, 0, 0});
+            },
+            number<Policy::NumPrefetchK>{});
+
+#if K_LDS_LOAD_USE_OFFSET_TRANSFORM
+        auto k_lds_load = generate_tuple(
+            [&](auto i_buf) {
+                return make_tile_window(
+                    make_tensor_view<address_space_enum::lds>(
+                        k_lds_ptr, Policy::template MakeKLdsLoadBlockDescriptor<Problem>(i_buf)),
+                    Policy::template MakeKLdsLoadBlockDescriptor<Problem>(i_buf).get_lengths(),
+                    {0, 0});
+            },
+            number<Policy::NumPrefetchK>{});
+#else
+        auto k_lds_Load_view = make_tensor_view<address_space_enum::lds>(
+            k_lds_ptr, Policy::template MakeKLdsLoadBlockDescriptor<Problem>());
+
+        auto k_lds_load =
+            make_tile_window(k_lds_Load_view,
+                             Policy::template MakeKLdsLoadBlockDescriptor<Problem>().get_lengths(),
+                             {0, 0});
+#endif
+
+        // V tile in LDS
+        auto v_lds = make_tensor_view<address_space_enum::lds>(
+            reinterpret_cast<VDataType*>(smem_ptr),
+            Policy::template MakeVLdsBlockDescriptor<Problem>());
+        auto v_lds_window = make_tile_window(
+            v_lds, Policy::template MakeVLdsBlockDescriptor<Problem>().get_lengths(), {0, 0});
+
+        // Block GEMM
+        constexpr auto gemm_0 = Policy::template GetQKBlockGemm<Problem>();
+        constexpr auto gemm_1 = Policy::template GetKVBlockGemm<Problem>();
+
+        auto q_dram_window = make_tile_window(
+            q_dram_block_window_tmp.get_bottom_tensor_view(),
+            q_dram_block_window_tmp.get_window_lengths(),
+            q_dram_block_window_tmp.get_window_origin(),
+            Policy::template MakeQDramTileDistribution<Problem, decltype(gemm_0)>());
+        q_dram_window.init_raw();
+
+        // TODO: we use async Copy for K, which is inline asm
+        // a side effect is we have to use inline asm for q as well
+        auto q = decltype(load_tile(q_dram_window)){};
+        // TODO: start from rocm-6.2, compiler will have problem if manually set clear of q.
+        // however, q would be cleared in the constructor of static distributed tensor
+        // set_tile(q, number<0>{}); // use per-dword clear to avoid scratch
+        load_tile_raw(q, q_dram_window);
+        __builtin_amdgcn_sched_barrier(0);
+
+        using SaccBlockTileType = decltype(gemm_0.MakeCBlockTile());
+        auto s_acc              = SaccBlockTileType{};
+
+        // reduction function for softmax
+        const auto f_max = [](auto e0, auto e1) { return max(e0, e1); };
+        const auto f_sum = [](auto e0, auto e1) { return e0 + e1; };
+
+        // infer Sacc, S, P, M, L, Oacc type
+        using SBlockTileType = decltype(cast_tile<SMPLComputeDataType>(s_acc));
+
+        using MLBlockTileType = decltype(block_tile_reduce<SMPLComputeDataType>(
+            SBlockTileType{}, sequence<1>{}, f_max, SMPLComputeDataType{0}));
+
+        using OaccBlockTileType = decltype(gemm_1.MakeCBlockTile());
+
+        // init Oacc, M, L
+        auto o_acc = OaccBlockTileType{};
+        auto m     = MLBlockTileType{};
+        auto l     = MLBlockTileType{};
+
+        clear_tile(o_acc);
+        set_tile(m, -numeric<SMPLComputeDataType>::infinity());
+        clear_tile(l);
+
+        __builtin_amdgcn_sched_barrier(0);
+        const auto q_origin = q_dram_window.get_window_origin();
+        const auto [seqlen_k_start, seqlen_k_end] =
+            mask.GetTileRangeAlongX(q_origin.at(number<0>{}), number<kM0>{}, number<kN0>{});
+
+        const auto num_total_loop = integer_divide_ceil(seqlen_k_end - seqlen_k_start, kN0);
+
+        // check early exit if no work to do
+        if constexpr(FmhaMask::IsMasking || kPadSeqLenK)
+        {
+            if(num_total_loop <= 0)
+            {
+                if constexpr(kStoreLSE)
+                {
+                    auto lse =
+                        make_static_distributed_tensor<LSEDataType>(m.get_tile_distribution());
+
+                    set_tile(lse, -numeric<SMPLComputeDataType>::infinity());
+
+                    store_tile(lse_dram_window_tmp, tile_elementwise_in(lse_element_func, lse));
+                }
+                buffer_load_fence(0); // rocm-6.1, if whole tile is masked out, need to fence(0)
+                                      // otherwise will have compute error(maybe compiler bug?)
+
+                // Note: here occ are all cleard, return it
+                return o_acc;
+            }
+            __builtin_amdgcn_sched_barrier(0); // make sure sched_barrier(0) for this check
+        }
+
+        auto k_dram_block_window =
+            make_tile_window(k_dram_block_window_tmp.get_bottom_tensor_view(),
+                             k_dram_block_window_tmp.get_window_lengths(),
+                             {seqlen_k_start, 0});
+
+        auto k_dram_window = make_tile_window(
+            k_dram_block_window.get_bottom_tensor_view(),
+            k_dram_block_window.get_window_lengths(),
+            k_dram_block_window.get_window_origin(),
+            Policy::template MakeKDramTileDistribution<Problem>()); // K DRAM tile window for
+                                                                    // load
+        k_dram_window.init_raw();
+        constexpr auto k_oob_ck = bool_constant<true>{};
+        constexpr auto k_pre_np = [&]() {
+            if constexpr(kPadSeqLenK &&
+                         (BiasEnum == BlockAttentionBiasEnum::ELEMENTWISE_BIAS ||
+                          (BiasEnum != BlockAttentionBiasEnum::NO_BIAS && kHasDropout)))
+                return bool_constant<true>{};
+            else
+                return bool_constant<false>{};
+        }();
+
+        const auto bias_origin = bias_dram_block_window_tmp.get_window_origin();
+        auto bias_dram_window =
+            make_tile_window(bias_dram_block_window_tmp.get_bottom_tensor_view(),
+                             bias_dram_block_window_tmp.get_window_lengths(),
+                             {bias_origin.at(number<0>{}), seqlen_k_start}, // M/N
+                             Policy::template MakeBiasDramTileDistribution<decltype(gemm_0)>());
+
+        auto randval_dram_window = dropout.template MakeRandvalDramWindow<decltype(gemm_0)>(
+            randval_dram_block_window_tmp, seqlen_k_start);
+
+        auto v_dram_window =
+            make_tile_window(v_dram_block_window_tmp.get_bottom_tensor_view(),
+                             v_dram_block_window_tmp.get_window_lengths(),
+                             {0, seqlen_k_start}, // TODO: hdim split?
+                             Policy::template MakeVDramTileDistribution<Problem>());
+
+        // prefetch K tile
+        async_load_tile_raw(
+            k_lds_store(LdsSeq.at(number<0>{})), k_dram_window, number<-1>{}, k_oob_ck, k_pre_np);
+        move_tile_window(k_dram_window, {0, kK0});
+        __builtin_amdgcn_sched_barrier(0);
+
+        buffer_load_fence(k_dram_window.get_num_of_access(), q.get_thread_buffer());
+        (void)q_element_func; // ??? rocm-6.x if use q element func will have scratch on hdim=64/32
+        // auto q_tile = q;      // tile_elementwise_in(q_element_func, q);
+
+        index_t i_total_loops      = 0;
+        constexpr index_t k0_loops = kQKHeaddim / kK0;
+        constexpr index_t k1_loops = kN0 / kK1;
+
+        static_assert(1 <= k0_loops);
+        static_assert(1 <= k1_loops);
+        // main loop
+        do
+        {
+            // STAGE 1, QK gemm
+            clear_tile(s_acc); // initialize C
+            if constexpr(k0_loops > 1)
+            {
+                static_for<0, k0_loops - 1, 1>{}([&](auto i_k0) {
+                    async_load_tile_raw(k_lds_store(number<LdsSeq.at(number<i_k0 + 1>{})>{}),
+                                        k_dram_window,
+                                        number<-1>{},
+                                        k_oob_ck,
+                                        k_pre_np);
+                    if constexpr(i_k0 < k0_loops - 1)
+                        move_tile_window(k_dram_window, {0, kK0});
+
+                    async_load_fence(k_dram_window.get_num_of_access());
+                    __builtin_amdgcn_s_barrier();
+                    __builtin_amdgcn_sched_barrier(0);
+                    gemm_0(s_acc,
+                           get_slice_tile(
+                               q, sequence<0, i_k0 * kK0>{}, sequence<kM0, (i_k0 + 1) * kK0>{}),
+#if K_LDS_LOAD_USE_OFFSET_TRANSFORM
+                           k_lds_load[number<LdsSeq.at(number<i_k0>{})>{}]);
+
+#else
+                           get_slice_tile(k_lds_load,
+                                          sequence<(LdsSeq.at(number<i_k0>{})) * kN0, 0>{},
+                                          sequence<(LdsSeq.at(number<i_k0>{}) + 1) * kN0, kK0>{}));
+#endif
+                });
+            }
+
+            // TODO: this to fix a bug when loop smaller than 2,
+            // the following fence/barrier will be scheduled inside 1st loop
+            if constexpr(k0_loops <= 2)
+                __builtin_amdgcn_sched_barrier(0);
+
+            async_load_fence();
+            __builtin_amdgcn_s_barrier();
+
+            const auto bias_tile = load_tile(bias_dram_window); // load bias tile
+            auto v_buf           = load_tile(v_dram_window, number<-1>{}, bool_constant<false>{});
+            __builtin_amdgcn_sched_barrier(0);
+            { // tail
+                gemm_0(s_acc,
+                       get_slice_tile(
+                           q, sequence<0, (k0_loops - 1) * kK0>{}, sequence<kM0, k0_loops * kK0>{}),
+#if K_LDS_LOAD_USE_OFFSET_TRANSFORM
+                       k_lds_load[number<LdsSeq.at(number<k0_loops - 1>{})>{}]);
+
+#else
+                       get_slice_tile(
+                           k_lds_load,
+                           sequence<(LdsSeq.at(number<k0_loops - 1>{})) * kN0, 0>{},
+                           sequence<(LdsSeq.at(number<k0_loops - 1>{}) + 1) * kN0, kK0>{}));
+#endif
+            }
+            __builtin_amdgcn_sched_barrier(1);
+
+            // STAGE 2, scale_s, add bias, mask, softmax
+            if constexpr(BiasEnum == BlockAttentionBiasEnum::ELEMENTWISE_BIAS)
+            {
+                s_acc = tile_elementwise_in(s_acc_element_func, s_acc);
+                tile_elementwise_inout([&scale_s](auto& x) { x = x * scale_s; }, s_acc);
+                tile_elementwise_inout(
+                    [&](auto& x, const auto& y) {
+#if !CK_TILE_FMHA_FWD_FAST_EXP2
+                        x += type_convert<SaccDataType>(bias_element_func(y));
+#else
+                        x += log2e_v<SaccDataType> *
+                             type_convert<SaccDataType>(bias_element_func(y));
+#endif
+                    },
+                    s_acc,
+                    bias_tile);
+            }
+            else if constexpr(BiasEnum == BlockAttentionBiasEnum::ALIBI)
+            {
+                const auto k_origin    = k_dram_block_window.get_window_origin();
+                constexpr auto s_spans = decltype(s_acc)::get_distributed_spans();
+                s_acc                  = tile_elementwise_in(s_acc_element_func, s_acc);
+                sweep_tile_span(s_spans[number<0>{}], [&](auto idx0) {
+                    sweep_tile_span(s_spans[number<1>{}], [&](auto idx1) {
+                        const auto tile_idx = get_x_indices_from_distributed_indices(
+                            s_acc.get_tile_distribution(), make_tuple(idx0, idx1));
+
+                        const auto row = q_origin.at(number<0>{}) + tile_idx.at(number<0>{});
+                        const auto col = k_origin.at(number<0>{}) + tile_idx.at(number<1>{});
+                        constexpr auto i_j_idx = make_tuple(idx0, idx1);
+
+                        s_acc(i_j_idx) *= scale_s;
+                        position_encoding.update(s_acc(i_j_idx), row, col);
+                    });
+                });
+            }
+            else
+            {
+                s_acc = tile_elementwise_in(s_acc_element_func, s_acc);
+#if !CK_TILE_FMHA_FWD_FAST_EXP2
+                tile_elementwise_inout([&scale_s](auto& x) { x = x * scale_s; }, s_acc);
+#endif
+            }
+            move_tile_window(bias_dram_window, {0, kN0});
+            if constexpr(kPadSeqLenK || FmhaMask::IsMasking)
+            {
+                const auto k_origin      = k_dram_block_window.get_window_origin();
+                bool need_perpixel_check = mask.IsEdgeTile(q_origin.at(number<0>{}),
+                                                           k_origin.at(number<0>{}),
+                                                           number<kM0>{},
+                                                           number<kN0>{});
+
+                if(need_perpixel_check)
+                {
+                    set_tile_if(
+                        s_acc, -numeric<SMPLComputeDataType>::infinity(), [&](auto tile_idx) {
+                            const auto row = q_origin.at(number<0>{}) + tile_idx.at(number<0>{});
+                            const auto col = k_origin.at(number<0>{}) + tile_idx.at(number<1>{});
+                            return mask.IsOutOfBound(row, col);
+                        });
+                }
+            }
+
+            const auto s = cast_tile<SMPLComputeDataType>(s_acc); // S{j}
+            auto m_local = block_tile_reduce<SMPLComputeDataType>(
+                s,
+                sequence<1>{},
+                f_max,
+                -numeric<SMPLComputeDataType>::infinity()); // m_local = rowmax(S{j})
+            block_tile_reduce_sync(m_local, f_max, bool_constant<false>{});
+
+            const auto m_old = m; // m{j-1}
+            tile_elementwise_inout(
+                [](auto& e0, auto e1, auto e2) { e0 = max(e1, e2); }, m, m_old, m_local); // m{j}
+
+            auto p_compute = make_static_distributed_tensor<SMPLComputeDataType>(
+                s.get_tile_distribution()); // Pcompute{j}
+
+            __builtin_amdgcn_sched_barrier(0x7F);
+            // store & prefetch next v, after the max reduction
+            if constexpr(std::is_same_v<VLayout, ck_tile::tensor_layout::gemm::RowMajor>)
+            {
+                auto v_shuffle_tmp = make_static_distributed_tensor<VDataType>(
+                    Policy::template MakeShuffledVRegBlockDescriptor<Problem>());
+                shuffle_tile(v_shuffle_tmp, v_buf);
+
+                auto v_lds_window_tmp =
+                    get_slice_tile(v_lds_window,
+                                   sequence<(LdsSeq.at(number<k0_loops>{})) * kN1, 0>{},
+                                   sequence<(LdsSeq.at(number<k0_loops>{}) + 1) * kN1, kK1>{});
+
+                store_tile(
+                    v_lds_window_tmp,
+                    tile_elementwise_in(v_element_func, v_shuffle_tmp)); // store the prefetch
+            }
+            else
+            {
+                auto v_lds_window_tmp =
+                    get_slice_tile(v_lds_window,
+                                   sequence<(LdsSeq.at(number<k0_loops>{})) * kN1, 0>{},
+                                   sequence<(LdsSeq.at(number<k0_loops>{}) + 1) * kN1, kK1>{});
+                store_tile(v_lds_window_tmp,
+                           tile_elementwise_in(v_element_func, v_buf)); // store the prefetch
+            }
+
+            if constexpr(k1_loops > 1)
+            {
+                move_tile_window(
+                    v_dram_window,
+                    {0, kK1}); // will have scratch if move this right after load_tile(v_dram)...
+                v_buf = load_tile(
+                    v_dram_window, number<-1>{}, bool_constant<false>{}); // load next v_buf
+            }
+            __builtin_amdgcn_sched_barrier(0);
+
+            static const auto get_validated_m = [](SMPLComputeDataType raw_m) {
+                /// NOTICE: bias might be materialized mask including -inf values, need
+                /// consideration. alibi does not have this problem
+                if constexpr(BiasEnum == BlockAttentionBiasEnum::ELEMENTWISE_BIAS ||
+                             FmhaMask::IsMasking)
+                {
+                    return raw_m == -numeric<SMPLComputeDataType>::infinity()
+                               ? type_convert<SMPLComputeDataType>(0.f)
+                               : raw_m;
+                }
+                else
+                {
+                    return raw_m;
+                }
+            };
+
+            constexpr auto p_spans = decltype(p_compute)::get_distributed_spans();
+            sweep_tile_span(p_spans[number<0>{}], [&](auto idx0) {
+                constexpr auto i_idx = make_tuple(idx0);
+#if CK_TILE_FMHA_FWD_FAST_EXP2
+                auto row_max = scale_s * get_validated_m(m[i_idx]);
+#endif
+                sweep_tile_span(p_spans[number<1>{}], [&](auto idx1) {
+                    constexpr auto i_j_idx = make_tuple(idx0, idx1);
+#if CK_TILE_FMHA_FWD_FAST_EXP2
+                    if constexpr(BiasEnum == BlockAttentionBiasEnum::ELEMENTWISE_BIAS ||
+                                 BiasEnum == BlockAttentionBiasEnum::ALIBI)
+                    {
+                        p_compute(i_j_idx) = exp2(s[i_j_idx] - get_validated_m(m[i_idx]));
+                    }
+                    else
+                    {
+                        p_compute(i_j_idx) = exp2(scale_s * s[i_j_idx] - row_max);
+                    }
+#else
+                    p_compute(i_j_idx)     = exp(s[i_j_idx] - get_validated_m(m[i_idx]));
+#endif
+                });
+            });
+
+            auto rowsum_p = block_tile_reduce<SMPLComputeDataType>(
+                p_compute, sequence<1>{}, f_sum, SMPLComputeDataType{0}); // rowsum(Pcompute{j})
+
+            block_tile_reduce_sync(rowsum_p, f_sum, bool_constant<false>{});
+            // l{j}, Oacc{j}
+            constexpr auto o_spans = decltype(o_acc)::get_distributed_spans();
+            sweep_tile_span(o_spans[number<0>{}], [&](auto idx0) {
+                constexpr auto i_idx = make_tuple(idx0);
+#if CK_TILE_FMHA_FWD_FAST_EXP2
+                const auto tmp = [&]() {
+                    if constexpr(BiasEnum == BlockAttentionBiasEnum::ELEMENTWISE_BIAS ||
+                                 BiasEnum == BlockAttentionBiasEnum::ALIBI)
+                    {
+                        return exp2(m_old[i_idx] - get_validated_m(m[i_idx]));
+                    }
+                    else
+                    {
+                        auto row_max = scale_s * get_validated_m(m[i_idx]);
+                        return exp2(scale_s * m_old[i_idx] - row_max);
+                    }
+                }();
+#else
+                const auto tmp = exp(m_old[i_idx] - get_validated_m(m[i_idx]));
+#endif
+                l(i_idx) = tmp * l[i_idx] + rowsum_p[i_idx];
+                sweep_tile_span(o_spans[number<1>{}], [&](auto idx1) {
+                    constexpr auto i_j_idx = make_tuple(idx0, idx1);
+                    // FIXME: this use different equation from FA v2 paper,
+                    // but produce correc result.
+                    // Is the equation wrong?
+                    o_acc(i_j_idx) *= tmp;
+                });
+            });
+
+            if constexpr(kHasDropout)
+            {
+                auto randval_ptr =
+                    reinterpret_cast<char*>(smem_ptr) + Policy::template GetSmemSizeKV<Problem>();
+                dropout.template Run<decltype(gemm_0), SMPLComputeDataType, RandValOutputDataType>(
+                    randval_ptr,
+                    seqlen_k_start + i_total_loops * kN0,
+                    p_compute,
+                    randval_dram_window);
+            }
+
+            const auto p = [&]() {
+                if constexpr(std::is_same_v<PDataType, fp16_t>)
+                    return impl::cast_tile_pk_fp16_fp32<PDataType>(
+                        tile_elementwise_in(p_compute_element_func, p_compute));
+                else
+                    return cast_tile<PDataType>(
+                        tile_elementwise_in(p_compute_element_func, p_compute));
+            }();
+
+            // STAGE 3, KV gemm
+            if constexpr(k1_loops > 1)
+            {
+                static_for<0, k1_loops - 1, 1>{}([&](auto i_k1) {
+                    if constexpr(i_k1 != 0 && i_k1 < k1_loops - 1)
+                    {
+                        v_buf = load_tile(
+                            v_dram_window, number<-1>{}, bool_constant<false>{}); // load next v_buf
+                    }
+                    block_sync_lds();
+                    gemm_1(o_acc,
+                           get_slice_tile(
+                               p, sequence<0, i_k1 * kK1>{}, sequence<kM0, (i_k1 + 1) * kK1>{}),
+                           get_slice_tile(
+                               v_lds_window,
+                               sequence<(LdsSeq.at(number<k0_loops + i_k1>{})) * kN1, 0>{},
+                               sequence<(LdsSeq.at(number<k0_loops + i_k1>{}) + 1) * kN1, kK1>{}));
+
+                    if constexpr(std::is_same_v<VLayout, ck_tile::tensor_layout::gemm::RowMajor>)
+                    {
+                        auto v_shuffle_tmp = make_static_distributed_tensor<VDataType>(
+                            Policy::template MakeShuffledVRegBlockDescriptor<Problem>());
+                        shuffle_tile(v_shuffle_tmp, v_buf);
+                        auto v_lds_window_tmp = get_slice_tile(
+                            v_lds_window,
+                            sequence<(LdsSeq.at(number<k0_loops + i_k1 + 1>{})) * kN1, 0>{},
+                            sequence<(LdsSeq.at(number<k0_loops + i_k1 + 1>{}) + 1) * kN1, kK1>{});
+                        store_tile(v_lds_window_tmp,
+                                   tile_elementwise_in(v_element_func,
+                                                       v_shuffle_tmp)); // store the prefetch
+                    }
+                    else
+                    {
+                        auto v_lds_window_tmp = get_slice_tile(
+                            v_lds_window,
+                            sequence<(LdsSeq.at(number<k0_loops + i_k1 + 1>{})) * kN1, 0>{},
+                            sequence<(LdsSeq.at(number<k0_loops + i_k1 + 1>{}) + 1) * kN1, kK1>{});
+                        store_tile(v_lds_window_tmp,
+                                   tile_elementwise_in(v_element_func, v_buf)); // store next v_buf
+                    }
+                    if constexpr(i_k1 < k1_loops - 1)
+                        move_tile_window(v_dram_window, {0, kK1});
+                });
+            }
+            i_total_loops++;
+            if(i_total_loops < num_total_loop)
+            {
+                // move K tile windows
+                move_tile_window(k_dram_block_window, {kN0, 0});
+                k_dram_window.set_window_origin(k_dram_block_window.get_window_origin());
+
+                if constexpr(k1_loops >= 2 &&
+                             LdsSeq.at(number<0>{}) == LdsSeq.at(number<k0_loops + k1_loops - 2>{}))
+                    __builtin_amdgcn_s_barrier();
+                async_load_tile_raw(k_lds_store(LdsSeq.at(number<0>{})),
+                                    k_dram_window,
+                                    number<-1>{},
+                                    k_oob_ck,
+                                    k_pre_np);
+                move_tile_window(k_dram_window, {0, kK0});
+            }
+            // tail
+            {
+                block_sync_lds();
+                gemm_1(
+                    o_acc,
+                    get_slice_tile(p, sequence<0, (k1_loops - 1) * kK1>{}, sequence<kM0, kN0>{}),
+                    get_slice_tile(
+                        v_lds_window,
+                        sequence<(LdsSeq.at(number<k0_loops + k1_loops - 1>{})) * kN1, 0>{},
+                        sequence<(LdsSeq.at(number<k0_loops + k1_loops - 1>{}) + 1) * kN1, kK1>{}));
+            }
+        } while(i_total_loops < num_total_loop);
+
+        // store lse
+        if constexpr(kStoreLSE)
+        {
+            auto lse = make_static_distributed_tensor<LSEDataType>(m.get_tile_distribution());
+
+            constexpr auto lse_spans = decltype(lse)::get_distributed_spans();
+            sweep_tile_span(lse_spans[number<0>{}], [&, m_ = m, l_ = l](auto idx0) {
+                constexpr auto i_idx = make_tuple(idx0);
+#if CK_TILE_FMHA_FWD_FAST_EXP2
+                if constexpr(BiasEnum == BlockAttentionBiasEnum::ELEMENTWISE_BIAS ||
+                             BiasEnum == BlockAttentionBiasEnum::ALIBI)
+                {
+                    lse(i_idx) = m_[i_idx] * R_LOG2E + log(l_[i_idx]);
+                }
+                else
+                {
+                    lse(i_idx) = m_[i_idx] * scale_s * R_LOG2E + log(l_[i_idx]);
+                }
+#else
+                lse(i_idx) = m_[i_idx] + log(l_[i_idx]);
+#endif
+            });
+
+            store_tile(lse_dram_window_tmp, tile_elementwise_in(lse_element_func, lse));
+        }
+
+        // finally, O
+        constexpr auto o_spans = decltype(o_acc)::get_distributed_spans();
+
+        sweep_tile_span(o_spans[number<0>{}], [&](auto idx0) {
+            constexpr auto i_idx = make_tuple(idx0);
+            const auto tmp       = [&]() {
+                if constexpr(FmhaMask::IsMasking)
+                {
+                    return l[i_idx] == 0.f ? 0.f : 1 / l[i_idx];
+                }
+                else
+                    return 1 / l[i_idx];
+            }();
+            sweep_tile_span(o_spans[number<1>{}], [&](auto idx1) {
+                constexpr auto i_j_idx = make_tuple(idx0, idx1);
+                o_acc(i_j_idx) *= tmp;
+            });
+        });
+
+        o_acc = tile_elementwise_in(o_acc_element_func, o_acc);
+
+        return o_acc;
+    }
+
+    template <typename QDramBlockWindowTmp,
+              typename KDramBlockWindowTmp,
+              typename VDramBlockWindowTmp,
+              typename BiasDramBlockWindowTmp,
+              typename RandValDramBlockWindowTmp,
+              typename LSEDramBlockWindowTmp,
+              typename PositionEncoding>
+    CK_TILE_HOST_DEVICE auto
+    operator()(const QDramBlockWindowTmp& q_dram_block_window_tmp,       // M0*K0 tile
+               const KDramBlockWindowTmp& k_dram_block_window_tmp,       // N0*K0 tile
+               const VDramBlockWindowTmp& v_dram_block_window_tmp,       // N1*K1 tile
+               const BiasDramBlockWindowTmp& bias_dram_block_window_tmp, // M0*N0 tile
+               RandValDramBlockWindowTmp& randval_dram_block_window_tmp, // M0*N0 tile
+               LSEDramBlockWindowTmp& lse_dram_block_window_tmp,         // M0*1 tile
+               FmhaMask mask,
+               PositionEncoding position_encoding,
+               float scale_s,
+               void* smem_ptr,
+               DropoutType& dropout) const
+    {
+        return operator()(q_dram_block_window_tmp,
+                          identity{},
+                          k_dram_block_window_tmp,
+                          identity{},
+                          v_dram_block_window_tmp,
+                          identity{},
+                          bias_dram_block_window_tmp,
+                          identity{},
+                          randval_dram_block_window_tmp,
+                          lse_dram_block_window_tmp,
+                          identity{},
+                          identity{},
+                          identity{},
+                          identity{},
+                          mask,
+                          position_encoding,
+                          scale_s,
+                          smem_ptr,
+                          dropout);
+    }
+};
+
+} // namespace ck_tile