kernel_traits.h

/******************************************************************************
 * Copyright (c) 2023, Tri Dao.
 ******************************************************************************/

#pragma once

#include "cute/algorithm/copy.hpp"

#include "cutlass/cutlass.h"
#include "cutlass/layout/layout.h"
#include <cutlass/numeric_types.h>

using namespace cute;

template<int kHeadDim_, int kBlockM_, int kBlockN_, int kNWarps_, typename elem_type=cutlass::half_t>
struct Flash_kernel_traits {

#if defined(__CUDA_ARCH__) &&  __CUDA_ARCH__ >= 800
    using Element = elem_type;
    static constexpr bool Has_cp_async = true;
#else
    using Element = cutlass::half_t;
    static constexpr bool Has_cp_async = false;
#endif

    using ElementAccum = float;
    using index_t = uint32_t;

#if defined(__CUDA_ARCH__) &&  __CUDA_ARCH__ >= 800
    using MMA_Atom_Arch = std::conditional_t<
        std::is_same_v<elem_type, cutlass::half_t>,
        MMA_Atom<SM80_16x8x16_F32F16F16F32_TN>,
        MMA_Atom<SM80_16x8x16_F32BF16BF16F32_TN>
    >;
    using ValLayoutMNK = Layout<Shape<_1, _2, _1>>;
#else
    using MMA_Atom_Arch = MMA_Atom<SM75_16x8x8_F32F16F16F32_TN>;
    using ValLayoutMNK = Layout<Shape<_1, _2, _2>>;
#endif

#if defined(__CUDA_ARCH__) &&  __CUDA_ARCH__ >= 750
    using SmemCopyAtom = Copy_Atom<SM75_U32x4_LDSM_N, elem_type>;
    using SmemCopyAtomTransposed = Copy_Atom<SM75_U16x8_LDSM_T, elem_type>;
#else
    using SmemCopyAtom = Copy_Atom<DefaultCopy, elem_type>;
    using SmemCopyAtomTransposed = Copy_Atom<DefaultCopy, elem_type>;
#endif
};

// If Share_Q_K_smem is true, that forces Is_Q_in_regs to be true
template<int kHeadDim_, int kBlockM_, int kBlockN_, int kNWarps_, bool Is_Q_in_regs_=false, bool Share_Q_K_smem_=false, typename elem_type=cutlass::half_t,
         typename Base=Flash_kernel_traits<kHeadDim_, kBlockM_, kBlockN_, kNWarps_, elem_type> >
struct Flash_fwd_kernel_traits : public Base {
    using Element = typename Base::Element;
    using ElementAccum = typename Base::ElementAccum;
    using index_t = typename Base::index_t;
    static constexpr bool Has_cp_async = Base::Has_cp_async;
    using SmemCopyAtom = typename Base::SmemCopyAtom;
    using SmemCopyAtomTransposed = typename Base::SmemCopyAtomTransposed;

    static constexpr bool Share_Q_K_smem = Share_Q_K_smem_;
    static constexpr bool Is_Q_in_regs = Is_Q_in_regs_ || Share_Q_K_smem;

    // The number of threads.
    static constexpr int kNWarps = kNWarps_;
    static constexpr int kNThreads = kNWarps * 32;

    static constexpr int kBlockM = kBlockM_;
    static constexpr int kBlockN = kBlockN_;
    static constexpr int kHeadDim = kHeadDim_;
    static_assert(kHeadDim % 32 == 0);
    static constexpr int kBlockKSmem = kHeadDim % 64 == 0 ? 64 : 32;
    static constexpr int kBlockKGmem = kHeadDim % 128 == 0 ? 128 : (kHeadDim % 64 == 0 ? 64 : 32);
    static constexpr int kSwizzle = kBlockKSmem == 32 ? 2 : 3;

    using TiledMma = TiledMMA<
        typename Base::MMA_Atom_Arch,
        Layout<Shape<Int<kNWarps>,_1,_1>>,  // 4x1x1 or 8x1x1 thread group
        typename Base::ValLayoutMNK>; // 1x2x1 or 1x2x2 value group for 16x16x16 MMA and LDSM

    using SmemLayoutAtomQ = decltype(
        composition(Swizzle<kSwizzle, 3, 3>{},
                    // This has to be kBlockKSmem, using kHeadDim gives wrong results for d=128
                    Layout<Shape<_8, Int<kBlockKSmem>>,
                           Stride<Int<kBlockKSmem>, _1>>{}));
    using SmemLayoutQ = decltype(tile_to_shape(
        SmemLayoutAtomQ{},
        Shape<Int<kBlockM>, Int<kHeadDim>>{}));

    using SmemLayoutKV = decltype(tile_to_shape(
        SmemLayoutAtomQ{},
        Shape<Int<kBlockN>, Int<kHeadDim>>{}));

    // This has to be kBlockN and not 8, otherwise we get wrong results for d=128
    using SmemLayoutAtomVtransposedNoSwizzle = Layout<Shape<Int<kBlockKSmem>, Int<kBlockN>>,
                                                      Stride<_1, Int<kBlockKSmem>>>;
    using SmemLayoutAtomVtransposed = decltype(
        composition(Swizzle<kSwizzle, 3, 3>{}, SmemLayoutAtomVtransposedNoSwizzle{}));
    using SmemLayoutVtransposed = decltype(tile_to_shape(
        SmemLayoutAtomVtransposed{},
        Shape<Int<kHeadDim>, Int<kBlockN>>{}));
    // Maybe the VtransposeNoSwizzle just needs to have the right shape
    // And the strides don't matter?
    using SmemLayoutVtransposedNoSwizzle = decltype(tile_to_shape(
        SmemLayoutAtomVtransposedNoSwizzle{},
        Shape<Int<kHeadDim>, Int<kBlockN>>{}));
    // using SmemLayoutVtransposedNoSwizzle = decltype(SmemLayoutVtransposed{}.layout_fn());

    using SmemLayoutAtomO = decltype(
        composition(Swizzle<kSwizzle, 3, 3>{},
                    Layout<Shape<Int<8>, Int<kBlockKSmem>>,
                           Stride<Int<kBlockKSmem>, _1>>{}));
    using SmemLayoutO = decltype(tile_to_shape(
        SmemLayoutAtomO{},
        Shape<Int<kBlockM>, Int<kHeadDim>>{}));
    using SmemCopyAtomO = Copy_Atom<DefaultCopy, Element>;
    using SmemCopyAtomOaccum = Copy_Atom<DefaultCopy, ElementAccum>;

    static constexpr int kSmemQCount = size(SmemLayoutQ{});
    static constexpr int kSmemKVCount = size(SmemLayoutKV{}) * 2;
    static constexpr int kSmemQSize = kSmemQCount * sizeof(Element);
    static constexpr int kSmemKVSize = kSmemKVCount * sizeof(Element);
    static constexpr int kSmemSize = Share_Q_K_smem ? std::max(kSmemQSize, kSmemKVSize) : kSmemQSize + kSmemKVSize;

    static constexpr int kGmemElemsPerLoad = sizeof(cute::uint128_t) / sizeof(Element);
    static_assert(kHeadDim % kGmemElemsPerLoad == 0, "kHeadDim must be a multiple of kGmemElemsPerLoad");
    // Using kBlockKSmem here is 6-10% faster than kBlockKGmem for d=128 because of bank conflicts.
    // For example, for d=128, smem is split into 2 "pages", each page takes care of columns
    // 0-63 and 64-127. If we have 16 threads per row for gmem read, when we write to smem,
    // thread 0 - 7 will write to the first page and thread 8 - 15 will write to the second page,
    // to the same banks.
    static constexpr int kGmemThreadsPerRow = kBlockKSmem / kGmemElemsPerLoad;
    static_assert(kNThreads % kGmemThreadsPerRow == 0, "kNThreads must be a multiple of kGmemThreadsPerRow");
    using GmemLayoutAtom = Layout<Shape <Int<kNThreads / kGmemThreadsPerRow>, Int<kGmemThreadsPerRow>>,
                                  Stride<Int<kGmemThreadsPerRow>, _1>>;

    // We use CACHEGLOBAL instead of CACHEALWAYS for both Q and K/V, since we won't be reading
    // from the same address by the same threadblock. This is slightly faster.
    using Gmem_copy_struct = std::conditional_t<
        Has_cp_async,
        SM80_CP_ASYNC_CACHEGLOBAL<cute::uint128_t>,
        DefaultCopy
    >;
    using GmemTiledCopyQKV = decltype(
        make_tiled_copy(Copy_Atom<Gmem_copy_struct, elem_type>{},
                        GmemLayoutAtom{},
                        Layout<Shape<_1, _8>>{}));  // Val layout, 8 vals per read
    using GmemTiledCopyO = decltype(
        make_tiled_copy(Copy_Atom<DefaultCopy, elem_type>{},
                        GmemLayoutAtom{},
                        Layout<Shape<_1, _8>>{}));  // Val layout, 8 vals per store
    static constexpr int kGmemThreadsPerRowP = kBlockN / kGmemElemsPerLoad;
    static_assert(kNThreads % kGmemThreadsPerRowP == 0, "kNThreads must be a multiple of kGmemThreadsPerRowP");
    using GmemLayoutAtomP = Layout<Shape <Int<kNThreads / kGmemThreadsPerRowP>, Int<kGmemThreadsPerRowP>>,
                                   Stride<Int<kGmemThreadsPerRowP>, _1>>;

    using GmemTiledCopyP = decltype(
        make_tiled_copy(Copy_Atom<DefaultCopy, elem_type>{},
                        GmemLayoutAtomP{},
                        Layout<Shape<_1, _8>>{}));  // Val layout, 8 vals per store

    using GmemLayoutAtomOaccum = std::conditional_t<
        kBlockKSmem == 32,
        Layout<Shape <_16, _8>,  // Thread layout, 8 threads per row
               Stride< _8, _1>>,
        Layout<Shape <_8, _16>,  // Thread layout, 16 threads per row
               Stride< _16, _1>>
    >;
    using GmemTiledCopyOaccum = decltype(
        make_tiled_copy(Copy_Atom<DefaultCopy, ElementAccum>{},
                        GmemLayoutAtomOaccum{},
                        Layout<Shape < _1, _4>>{}));  // Val layout, 4 vals per store
};

// Is_V_in_regs is an option to reduce smem usage, but will increase register pressue.
// No_double_buffer is another option to reduce smem usage, but will slow things down.
template<int kHeadDim_, int kBlockM_, int kBlockN_, int kNWarps_,
         int AtomLayoutMSdP_=1, int AtomLayoutNdKV=2, int AtomLayoutMdQ=2,
         bool Is_V_in_regs_=false, bool No_double_buffer_=false, typename elem_type=cutlass::half_t,
         typename Base=Flash_kernel_traits<kHeadDim_, kBlockM_, kBlockN_, kNWarps_, elem_type> >
struct Flash_bwd_kernel_traits : public Base {
    using Element = typename Base::Element;
    using ElementAccum = typename Base::ElementAccum;
    using index_t = typename Base::index_t;
    static constexpr bool Has_cp_async = Base::Has_cp_async;
    using SmemCopyAtom = typename Base::SmemCopyAtom;
    using SmemCopyAtomTransposed = typename Base::SmemCopyAtomTransposed;

    static constexpr bool Is_V_in_regs = Is_V_in_regs_;
    static constexpr bool No_double_buffer = No_double_buffer_;

    // The number of threads.
    static constexpr int kNWarps = kNWarps_;
    static constexpr int kNThreads = kNWarps * 32;

    static constexpr int kBlockM = kBlockM_;
    static constexpr int kBlockN = kBlockN_;
    static constexpr int kHeadDim = kHeadDim_;
    static_assert(kHeadDim % 32 == 0);
    static constexpr int kBlockKSmem = kHeadDim % 64 == 0 ? 64 : 32;
    static constexpr int kBlockKGmem = kHeadDim % 128 == 0 ? 128 : (kHeadDim % 64 == 0 ? 64 : 32);
    static constexpr int kSwizzle = kBlockKSmem == 32 ? 2 : 3;

    static constexpr int AtomLayoutMSdP = AtomLayoutMSdP_;
    static_assert(kNWarps % AtomLayoutMSdP == 0);
    static_assert(kNWarps % AtomLayoutNdKV == 0);
    static_assert(kNWarps % AtomLayoutMdQ == 0);

    using TiledMmaSdP = TiledMMA<
        typename Base::MMA_Atom_Arch,
        Layout<Shape<Int<AtomLayoutMSdP>, Int<kNWarps / AtomLayoutMSdP>, _1>>,
        typename Base::ValLayoutMNK>; // 1x2x1 or 1x2x2 value group for 16x16x16 MMA and LDSM

    using TiledMmadKV = TiledMMA<
        typename Base::MMA_Atom_Arch,
        Layout<Shape<Int<AtomLayoutNdKV>, Int<kNWarps / AtomLayoutNdKV>, _1>>,
        typename Base::ValLayoutMNK>; // 1x2x1 or 1x2x2 value group for 16x16x16 MMA and LDSM

    using TiledMmadQ = TiledMMA<
        typename Base::MMA_Atom_Arch,
        Layout<Shape<Int<AtomLayoutMdQ>, Int<kNWarps / AtomLayoutMdQ>, _1>>,  // 2x4x1 or 4x2x1 thread group
        typename Base::ValLayoutMNK>; // 1x2x1 or 1x2x2 value group for 16x16x16 MMA and LDSM

    using SmemLayoutAtomQdO = decltype(
        composition(Swizzle<kSwizzle, 3, 3>{},
                    Layout<Shape<_8, Int<kBlockKSmem>>,
                           Stride<Int<kBlockKSmem>, _1>>{}));
    using SmemLayoutQdO = decltype(tile_to_shape(
        SmemLayoutAtomQdO{},
        make_shape(Int<kBlockM>{}, Int<kHeadDim>{})));

    using SmemLayoutAtomKV = decltype(
        composition(Swizzle<kSwizzle, 3, 3>{},
                    Layout<Shape<Int<kBlockM / kNWarps>, Int<kBlockKSmem>>,
                           Stride<Int<kBlockKSmem>, _1>>{}));
    using SmemLayoutKV = decltype(tile_to_shape(
        // SmemLayoutAtomQdO{},
        SmemLayoutAtomKV{},
        make_shape(Int<kBlockN>{}, Int<kHeadDim>{})));

    using SmemLayoutAtomKtransposedNoSwizzle = Layout<Shape<Int<kBlockKSmem>, Int<kBlockN>>,
                                                      Stride<_1, Int<kBlockKSmem>>>;
    using SmemLayoutAtomKtransposed = decltype(
        composition(Swizzle<kSwizzle, 3, 3>{}, SmemLayoutAtomKtransposedNoSwizzle{}));
    using SmemLayoutKtransposed = decltype(tile_to_shape(
        SmemLayoutAtomKtransposed{},
        make_shape(Int<kHeadDim>{}, Int<kBlockN>{})));
    // Maybe the KtransposeNoSwizzle just needs to have the right shape
    // And the strides don't matter?
    using SmemLayoutKtransposedNoSwizzle = decltype(tile_to_shape(
        SmemLayoutAtomKtransposedNoSwizzle{},
        make_shape(Int<kHeadDim>{}, Int<kBlockN>{})));
    // using SmemLayoutKtransposedNoSwizzle = decltype(SmemLayoutKtransposed{}.layout_fn());

    // TODO: generalize to other values of kBlockN
    // TODO: what should be the Swizzle here? 3 is faster than 1, and 1 is faster than 2
    // static constexpr int kPBlockN = kBlockN;
    static_assert(kBlockN >= 64);
    // TD [2023-03-19]: Idk why kPBlockN = 16 and kSwizzlePdS=3 is the fastest.
    static constexpr int kPBlockN = 64;
    static_assert(kPBlockN == 16 || kPBlockN == 32 || kPBlockN == 64);
    // static constexpr int kSwizzlePdS = kPBlockN == 16 ? 1 : (kPBlockN == 32 ? 2 : 3);
    static constexpr int kSwizzlePdS = 3;
    using SmemLayoutAtomPdS = decltype(
        composition(Swizzle<kSwizzlePdS, 3, 3>{},
                    Layout<Shape<Int<kBlockM>, Int<kPBlockN>>,
                           Stride<Int<kPBlockN>, _1>>{}));
    using SmemLayoutPdS = decltype(tile_to_shape(
        SmemLayoutAtomPdS{},
        make_shape(Int<kBlockM>{}, Int<kBlockN>{})));
    using SmemLayoutAtomPdStransposedNoSwizzle = Layout<Shape<Int<kPBlockN>, Int<kBlockM>>,
                                                        Stride<_1, Int<kPBlockN>>>;
    using SmemLayoutAtomPdStransposed = decltype(
        composition(Swizzle<kSwizzlePdS, 3, 3>{}, SmemLayoutAtomPdStransposedNoSwizzle{}));
    using SmemLayoutPdStransposed = decltype(tile_to_shape(
        SmemLayoutAtomPdStransposed{},
        make_shape(Int<kBlockN>{}, Int<kBlockM>{})));
    using SmemLayoutPdStransposedNoSwizzle = decltype(tile_to_shape(
        SmemLayoutAtomPdStransposedNoSwizzle{},
        make_shape(Int<kBlockN>{}, Int<kBlockM>{})));
    // using SmemLayoutPdStransposedNoSwizzle = decltype(SmemLayoutPdStransposed{}.layout_fn());
    using SmemCopyAtomPdS = Copy_Atom<DefaultCopy, elem_type>;

    using SmemLayoutAtomQdOtransposedNoSwizzle = Layout<Shape<Int<kBlockKSmem>, Int<kBlockM>>,
                                                        Stride<_1, Int<kBlockKSmem>>>;
    using SmemLayoutAtomQdOtransposed = decltype(
        composition(Swizzle<kSwizzle, 3, 3>{}, SmemLayoutAtomQdOtransposedNoSwizzle{}));
    using SmemLayoutQdOtransposed = decltype(tile_to_shape(
        SmemLayoutAtomQdOtransposed{},
        make_shape(Int<kHeadDim>{}, Int<kBlockM>{})));
    using SmemLayoutQdOtransposedNoSwizzle = decltype(tile_to_shape(
        SmemLayoutAtomQdOtransposedNoSwizzle{},
        make_shape(Int<kHeadDim>{}, Int<kBlockM>{})));
    // using SmemLayoutQdOtransposedNoSwizzle = decltype(SmemLayoutQdOtransposed{}.layout_fn());

    using SmemLayoutAtomdKV = decltype(
        composition(Swizzle<kSwizzle, 3, 3>{},
                    Layout<Shape<_8, Int<kBlockKSmem>>,
                           Stride<Int<kBlockKSmem>, _1>>{}));
    using SmemLayoutdKV = decltype(tile_to_shape(
        SmemLayoutAtomdKV{},
        make_shape(Int<kBlockN>{}, Int<kHeadDim>{})));
    using SmemCopyAtomdKV = Copy_Atom<DefaultCopy, elem_type>;

    using SmemLayoutAtomdQ = decltype(
        composition(Swizzle<kSwizzle, 3, 3>{},
                    Layout<Shape<_8, Int<kBlockKSmem>>,
                           Stride<Int<kBlockKSmem>, _1>>{}));
    using SmemLayoutdQ = decltype(tile_to_shape(
        SmemLayoutAtomdQ{},
        make_shape(Int<kBlockM>{}, Int<kHeadDim>{})));
    using SmemCopyAtomdQ = Copy_Atom<DefaultCopy, elem_type>;

    static constexpr int kSmemQdOCount = size(SmemLayoutQdO{}) * (No_double_buffer ? 2 : 3);  // Double buffer for sQ
    static constexpr int kSmemKVCount = size(SmemLayoutKV{}) * 2;
    static constexpr int kSmemdSCount = size(SmemLayoutPdS{});
    static constexpr int kSmemPCount = size(SmemLayoutPdS{});
    static constexpr int kSmemdQCount = size(SmemLayoutdQ{});
    static constexpr int kSmemQdOSize = kSmemQdOCount * sizeof(Element);
    static constexpr int kSmemKVSize = kSmemKVCount * sizeof(Element);
    static constexpr int kSmemdSSize = kSmemdSCount * sizeof(Element);
    static constexpr int kSmemPSize = kSmemPCount * sizeof(Element);
    static constexpr int kSmemdQSize = kSmemdQCount * sizeof(Element);
    static constexpr int kSmemSize = kSmemQdOSize
        + (!Is_V_in_regs
           ? kSmemKVSize + kSmemdSSize + std::max(kSmemPSize, kSmemdQSize)
           : std::max(kSmemKVSize, kSmemKVSize / 2 + kSmemdSSize + std::max(kSmemPSize, kSmemdQSize)));
    static constexpr int kSmemSize1colblock = kSmemQdOSize
        + (!Is_V_in_regs
           ? kSmemKVSize + kSmemdSSize + kSmemPSize
           : std::max(kSmemKVSize, kSmemKVSize / 2 + kSmemdSSize + kSmemPSize));
    static constexpr int kSmemSize1rowblock = kSmemQdOSize / 3 * 2 + kSmemKVSize / 2 * 3
        + kSmemdSSize + kSmemPSize;


    static constexpr int kGmemElemsPerLoad = sizeof(cute::uint128_t) / sizeof(Element);
    static_assert(kHeadDim % kGmemElemsPerLoad == 0, "kHeadDim must be a multiple of kGmemElemsPerLoad");
    // Using kBlockKSmem instead of kHeadDim here to avoid bank conflicts, but doesn't seem
    // to affect speed in practice.
    static constexpr int kGmemThreadsPerRow = kBlockKSmem / kGmemElemsPerLoad;
    static_assert(kNThreads % kGmemThreadsPerRow == 0, "kNThreads must be a multiple of kGmemThreadsPerRow");
    using GmemLayoutAtom = Layout<Shape <Int<kNThreads / kGmemThreadsPerRow>, Int<kGmemThreadsPerRow>>,
                                  Stride<Int<kGmemThreadsPerRow>, _1>>;

    // We use CACHEGLOBAL instead of CACHEALWAYS for both Q and K/V, since we won't be reading
    // from the same address by the same threadblock. This is slightly faster.
    using Gmem_copy_struct = std::conditional_t<
        Has_cp_async,
        SM80_CP_ASYNC_CACHEGLOBAL<cute::uint128_t>,
        DefaultCopy
    >;
    using GmemTiledCopyQKV = decltype(
        make_tiled_copy(Copy_Atom<Gmem_copy_struct, elem_type>{},
                        GmemLayoutAtom{},
                        Layout<Shape<_1, _8>>{}));  // Val layout, 8 vals per read
    using GmemTiledCopydO = decltype(
        make_tiled_copy(Copy_Atom<DefaultCopy, elem_type>{},
                        GmemLayoutAtom{},
                        Layout<Shape < _1, _8>>{}));  // Val layout, 8 vals per store
    using GmemTiledCopydKV = decltype(
        make_tiled_copy(Copy_Atom<DefaultCopy, elem_type>{},
                        GmemLayoutAtom{},
                        Layout<Shape < _1, _8>>{}));  // Val layout, 8 vals per store
    using GmemTiledCopydQ = decltype(
        make_tiled_copy(Copy_Atom<DefaultCopy, elem_type>{},
                        GmemLayoutAtom{},
                        Layout<Shape < _1, _8>>{}));  // Val layout, 8 vals per store
    using GmemLayoutAtomdQaccum = std::conditional_t<
        kBlockKSmem == 32,
        Layout<Shape <_32, _8>,  // Thread layout, 8 threads per row
               Stride< _8, _1>>,
        Layout<Shape <_16, _16>,  // Thread layout, 16 threads per row
               Stride< _16, _1>>
    >;
    using GmemTiledCopydQaccum = decltype(
        make_tiled_copy(Copy_Atom<DefaultCopy, ElementAccum>{},
                        GmemLayoutAtomdQaccum{},
                        Layout<Shape < _1, _4>>{}));  // Val layout, 4 vals per store

    using GmemTiledCopydQaccumAtomicAdd = decltype(
        make_tiled_copy(Copy_Atom<DefaultCopy, ElementAccum>{},
                        Layout<Shape <_8, _32>,  // Thread layout, 8 threads per row
                               Stride<_32, _1>>{},
                        Layout<Shape < _1, _1>>{}));  // Val layout, 1 val per store

};

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