flash-attention/hopper/softmax.h

/******************************************************************************
 * Copyright (c) 2024, Jay Shah, Ganesh Bikshandi, Ying Zhang, Vijay Thakkar, Pradeep Ramani, Tri Dao.
 ******************************************************************************/

#pragma once

#include <cmath>

#include <cute/tensor.hpp>

#include <cutlass/numeric_types.h>

#include "utils.h"

#include "cutlass/fast_math.h"

namespace flash {

using namespace cute;

////////////////////////////////////////////////////////////////////////////////////////////////////

template<bool zero_init=true, typename Engine0, typename Layout0, typename Engine1, typename Layout1, typename Operator>
__device__ __forceinline__ void thread_reduce_(Tensor<Engine0, Layout0> const &tensor, Tensor<Engine1, Layout1> &summary, Operator &op) {
    static_assert(Layout0::rank == 2, "Only support 2D Tensor");
    static_assert(Layout1::rank == 1, "Only support 1D Tensor");
    CUTE_STATIC_ASSERT_V(size<0>(summary) == size<0>(tensor));
    #pragma unroll
    for (int mi = 0; mi < size<0>(tensor); mi++) {
        summary(mi) = zero_init ? tensor(mi, 0) : op(summary(mi), tensor(mi, 0));
        #pragma unroll
        for (int ni = 1; ni < size<1>(tensor); ni++) {
            summary(mi) = op(summary(mi), tensor(mi, ni));
        }
    }
}

template<typename Engine0, typename Layout0, typename Engine1, typename Layout1, typename Operator>
__device__ __forceinline__ void quad_allreduce_(Tensor<Engine0, Layout0> &dst, Tensor<Engine1, Layout1> &src, Operator &op) {
    CUTE_STATIC_ASSERT_V(size(dst) == size(src));
    #pragma unroll
    for (int i = 0; i < size(dst); i++){
        dst(i) = Allreduce<4>::run(src(i), op);
    }
}

template<bool zero_init=true, typename Engine0, typename Layout0, typename Engine1, typename Layout1, typename Operator>
__device__ __forceinline__ void reduce_(Tensor<Engine0, Layout0> const& tensor, Tensor<Engine1, Layout1> &summary, Operator &op) {
    thread_reduce_<zero_init>(tensor, summary, op);
    quad_allreduce_(summary, summary, op);
}

template<bool zero_init=true, typename Engine0, typename Layout0, typename Engine1, typename Layout1>
__device__ __forceinline__ void reduce_max(Tensor<Engine0, Layout0> const& tensor, Tensor<Engine1, Layout1> &max){
    MaxOp<float> max_op;
    reduce_<zero_init>(tensor, max, max_op);
}

template<bool zero_init=true, bool warp_reduce=true, typename Engine0, typename Layout0, typename Engine1, typename Layout1>
__device__ __forceinline__ void reduce_sum(Tensor<Engine0, Layout0> const& tensor, Tensor<Engine1, Layout1> &sum){
    SumOp<float> sum_op;
    thread_reduce_<zero_init>(tensor, sum, sum_op);
    if constexpr (warp_reduce) { quad_allreduce_(sum, sum, sum_op); }
}

__forceinline__ __device__ __half2 half_exp(__half2 x) {
    uint32_t tmp_out, tmp_in;
    tmp_in = reinterpret_cast<uint32_t&>(x);
    asm ("ex2.approx.f16x2 %0, %1;\n"
      : "=r"(tmp_out)
      : "r"(tmp_in));
    __half2 out = reinterpret_cast<__half2&>(tmp_out);
    return out;
}

// Apply the exp to all the elements.
template <bool zero_init=false, typename Engine0, typename Layout0, typename Engine1, typename Layout1>
__forceinline__ __device__ void max_scale_exp2_sum(Tensor<Engine0, Layout0> &tensor, Tensor<Engine1, Layout1> &max, Tensor<Engine1, Layout1> &sum, const float scale) {
    static_assert(Layout0::rank == 2, "Only support 2D Tensor"); static_assert(Layout1::rank == 1, "Only support 1D Tensor"); CUTE_STATIC_ASSERT_V(size<0>(max) == size<0>(tensor));
    #pragma unroll
    for (int mi = 0; mi < size<0>(tensor); ++mi) {
        MaxOp<float> max_op;
        max(mi) = zero_init ? tensor(mi, 0) : max_op(max(mi), tensor(mi, 0));
        #pragma unroll
        for (int ni = 1; ni < size<1>(tensor); ni++) {
            max(mi) = max_op(max(mi), tensor(mi, ni));
        }
        max(mi) = Allreduce<4>::run(max(mi), max_op);
        // If max is -inf, then all elements must have been -inf (possibly due to masking).
        // We don't want (-inf - (-inf)) since that would give NaN.
        const float max_scaled = max(mi) == -INFINITY ? 0.f : max(mi) * scale;
        sum(mi) = 0;
        #pragma unroll
        for (int ni = 0; ni < size<1>(tensor); ++ni)  {
            // Instead of computing exp(x - max), we compute exp2(x * log_2(e) -
            // max * log_2(e)) This allows the compiler to use the ffma
            // instruction instead of fadd and fmul separately.
            tensor(mi, ni) = exp2f(tensor(mi, ni) * scale - max_scaled);
            sum(mi) += tensor(mi, ni);
        }
    }
}

// Apply the exp to all the elements.
template <bool Scale_max=true, bool Check_inf=true, bool Use_max_offset=false,
          typename Engine0, typename Layout0, typename Engine1, typename Layout1>
__forceinline__ __device__ void scale_apply_exp2(Tensor<Engine0, Layout0> &tensor, Tensor<Engine1, Layout1> const &max, const float scale) {
    constexpr static float max_offset = Use_max_offset ? 8.0f : 0.0f;
    static_assert(Layout0::rank == 2, "Only support 2D Tensor");
    static_assert(Layout1::rank == 1, "Only support 1D Tensor");
    CUTE_STATIC_ASSERT_V(size<0>(max) == size<0>(tensor));
    #pragma unroll
    for (int mi = 0; mi < size<0>(tensor); ++mi) {
        // If max is -inf, then all elements must have been -inf (possibly due to masking).
        // We don't want (-inf - (-inf)) since that would give NaN.
        // If we don't have float around M_LOG2E the multiplication is done in fp64.
        const float max_scaled = Check_inf
            ? (max(mi) == -INFINITY ? 0.f : (!Scale_max ? max(mi) : max(mi) * scale) - max_offset)
            : (!Scale_max ? max(mi) : max(mi) * scale) - max_offset;
        #pragma unroll
        for (int ni = 0; ni < size<1>(tensor); ++ni)  {
            // Instead of computing exp(x - max), we compute exp2(x * log_2(e) -
            // max * log_2(e)) This allows the compiler to use the ffma
            // instruction instead of fadd and fmul separately.
            tensor(mi, ni) = exp2f(tensor(mi, ni) * scale - max_scaled);
        }
    }
}

////////////////////////////////////////////////////////////////////////////////////////////////////

template <int kNRows, bool Use_max_offset_ = false>
struct Softmax { 
    constexpr static bool Use_max_offset = Use_max_offset_; 
    // constexpr static float max_offset = Use_max_offset ? 8.0f : 0.0f;
    // constexpr static float max_offset_E = max_offset * float(M_LN2);

    using TensorT = decltype(make_tensor<float>(Shape<Int<kNRows>>{}));
    TensorT row_max, row_sum;
    const float softmax_scale_log2;

    CUTLASS_DEVICE Softmax(float scale_ = 1.f) : softmax_scale_log2(scale_) {};

    template<bool Is_first, bool Check_inf=false, typename Tensor0>
    __forceinline__ __device__ TensorT max(Tensor0 &acc_s) {
        // Reshape acc_s from ((2, 2, V), MMA_M, MMA_N) to (nrow=(2, MMA_M), ncol=(2, V, MMA_N))
        Tensor scores = make_tensor(acc_s.data(), flash::convert_layout_acc_rowcol(acc_s.layout()));
        static_assert(decltype(size<0>(scores))::value == kNRows);
        TensorT scores_scale;
        if constexpr (Is_first) {
            flash::template reduce_max</*zero_init=*/true>(scores, row_max);
            cute::fill(scores_scale, 1.f);
        } else {
            Tensor scores_max_prev = make_fragment_like(row_max);
            cute::copy(row_max, scores_max_prev);
            flash::template reduce_max</*zero_init=*/false>(scores, row_max);
            #pragma unroll
            for (int mi = 0; mi < size(row_max); ++mi) {
                float scores_max_cur = !Check_inf
                    ? row_max(mi)
                    : (row_max(mi) == -INFINITY ? 0.0f : row_max(mi));
                scores_scale(mi) = exp2f((scores_max_prev(mi) - scores_max_cur) * softmax_scale_log2);
                row_sum(mi) *= scores_scale(mi);
            }
        }
        return scores_scale;
    };

    template<bool Is_first, bool Check_inf=false, typename Tensor0>
    __forceinline__ __device__ TensorT online_softmax(Tensor0 &acc_s) {
        // Reshape acc_s from ((2, 2, V), MMA_M, MMA_N) to (nrow=(2, MMA_M), ncol=(2, V, MMA_N))
        Tensor scores = make_tensor(acc_s.data(), flash::convert_layout_acc_rowcol(acc_s.layout()));
        static_assert(decltype(size<0>(scores))::value == kNRows);
        TensorT scores_scale;
        if constexpr (Is_first) {
            flash::template reduce_max</*zero_init=*/true>(scores, row_max);
            flash::template scale_apply_exp2</*Scale_max=*/true, /*Check_inf=*/true, Use_max_offset>(scores, row_max, softmax_scale_log2);
            flash::reduce_sum</*zero_init=*/true, /*warp_reduce=*/false>(scores, row_sum);
            cute::fill(scores_scale, 1.f);
            // if (cute::thread0()) { print_tensor(scores); printf("\n scale = %f\n", softmax_scale_log2); print_tensor(row_sum); }
        } else {
            // Tensor scores_max_prev = make_fragment_like(row_max);
            // cute::copy(row_max, scores_max_prev);
            // flash::template reduce_max</*zero_init=*/false>(scores, row_max);
            // // if (cute::thread0()) { print_tensor(scores); printf("\n"); print_tensor(row_max); printf("\n"); }
            // #pragma unroll
            // for (int mi = 0; mi < size(row_max); ++mi) {
            //     float scores_max_cur = !Check_inf
            //         ? row_max(mi)
            //         : (row_max(mi) == -INFINITY ? 0.0f : row_max(mi));
            //     scores_scale(mi) = exp2f((scores_max_prev(mi) - scores_max_cur) * softmax_scale_log2);
            //     row_sum(mi) *= scores_scale(mi);
            // }
            flash::template scale_apply_exp2</*Scale_max=*/true, Check_inf, Use_max_offset>(scores, row_max, softmax_scale_log2);
            // We don't do the reduce across threads here since we don't need to use the row_sum.
            // We do that reduce at the end when we need to normalize the softmax.
            flash::reduce_sum</*zero_init=*/false, /*warp_reduce=*/false>(scores, row_sum);
        }
        return scores_scale;
    };

    template<bool Is_dropout=false, bool Split=false, typename Tensor0>
    __forceinline__ __device__ TensorT finalize(Tensor0 &acc_s, float descale_v = 1.f, float rp_dropout=1.f) {
        constexpr static float max_offset_E = Use_max_offset ? 8.f * float(M_LN2) : 0.f;
        // Reshape acc_s from ((2, 2, V), MMA_M, MMA_N) to (nrow=(2, MMA_M), ncol=(2, V, MMA_N))
        Tensor scores = make_tensor(acc_s.data(), flash::convert_layout_acc_rowcol(acc_s.layout()));
        static_assert(decltype(size<0>(scores))::value == kNRows);
        SumOp<float> sum_op;
        quad_allreduce_(row_sum, row_sum, sum_op);
        TensorT scores_scale;
        #pragma unroll
        for (int mi = 0; mi < size(row_max); ++mi) {
            float sum = row_sum(mi);
            float inv_sum = (sum == 0.f || sum != sum) ? 0.f : descale_v / sum;
            row_sum(mi) = (sum == 0.f || sum != sum) ? (Split ? -INFINITY : INFINITY) : (row_max(mi) * softmax_scale_log2) * float(M_LN2) - max_offset_E + __logf(sum);
            scores_scale(mi) = !Is_dropout ? inv_sum : inv_sum * rp_dropout;
        }
        return scores_scale;
    };

    template<typename Tensor1>
    __forceinline__ __device__ void rescale_o(Tensor1 &acc_o, TensorT const &scores_scale) {
        // Reshape acc_o from (MMA=4, MMA_M, MMA_K) to (nrow=(2, MMA_M), ncol=(2, MMA_K))
        Tensor acc_o_rowcol = make_tensor(acc_o.data(), flash::convert_layout_acc_rowcol(acc_o.layout()));
        static_assert(decltype(size<0>(acc_o_rowcol))::value == kNRows);
        #pragma unroll
        for (int mi = 0; mi < size(row_max); ++mi) {
            #pragma unroll
            for (int ni = 0; ni < size<1>(acc_o_rowcol); ++ni) { acc_o_rowcol(mi, ni) *= scores_scale(mi); }
        }
    };

};

} // namespace flash