flash-attention/csrc/flash_attn/src/softmax.h

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

#pragma once

#include <cmath>

#include <cute/tensor.hpp>

#include <cutlass/numeric_types.h>

#include "philox.cuh"
#include "utils.h"

namespace flash {

using namespace cute;

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

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

template<typename Engine0, typename Layout0, typename Engine1, typename Layout1>
__device__ inline void reduce_sum(Tensor<Engine0, Layout0> const& tensor, Tensor<Engine1, Layout1> &sum){
    SumOp<float> sum_op;
    reduce_(tensor, sum, sum_op);
}

// Apply the exp to all the elements.
template <bool Scale_max=true, typename Engine0, typename Layout0, typename Engine1, typename Layout1>
inline __device__ void scale_apply_exp2(Tensor<Engine0, Layout0> &tensor, Tensor<Engine1, Layout1> const &max, 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) {
        // 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 = max(mi) == -INFINITY ? 0.f : max(mi) * (Scale_max ? scale : float(M_LOG2E));
        #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);
        }
    }
}

// Apply the exp to all the elements.
template <bool zero_init=true, typename Engine0, typename Layout0, typename Engine1, typename Layout1>
inline __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);
        }
        SumOp<float> sum_op;
        sum(mi) = Allreduce<4>::run(sum(mi), sum_op);
    }
}

}  // namespace flash