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gemma.cpp/gemma/flash_attention.cc

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// Copyright 2025 Google LLC
// SPDX-License-Identifier: Apache-2.0
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// https://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include <stddef.h>
#include <stdint.h>
#include <algorithm>
#include <array>
#include <cmath>
#include <cstdlib>
#include <limits>
#include "compression/types.h" // GEMMA_DISABLED_TARGETS
#include "gemma/flash_structs.h"
#include "util/threading_context.h"
#include "util/zones.h"
#ifndef HWY_DISABLED_TARGETS
#define HWY_DISABLED_TARGETS GEMMA_DISABLED_TARGETS
#endif // HWY_DISABLED_TARGETS
#include "gemma/activations.h"
#include "gemma/configs.h" // kMaxQKVDim
#include "gemma/gemma.h"
#include "util/threading.h"
#include "hwy/profiler.h"
// Compiles this file for multiple architectures via "foreach_target.h", to
// which we pass the filename via macro 'argument'.
// clang-format off
#undef HWY_TARGET_INCLUDE
#define HWY_TARGET_INCLUDE "gemma/flash_attention.cc" // NOLINT
// clang-format on
#include "hwy/foreach_target.h" // IWYU pragma: keep
#include "hwy/highway.h"
// After highway.h
#include "compression/compress-inl.h"
#include "gemma/attention.h"
#include "ops/matmul-inl.h"
#include "ops/ops-inl.h"
HWY_BEFORE_NAMESPACE();
namespace gcpp {
namespace HWY_NAMESPACE {
static constexpr size_t kNFx8HTileSize = 8;
// Transposes q into q_t.
// Both are 4D tensors stuffed into a 2-D MatPtrT.
// q has shape [batch, qbatch][head, qkv_dim].
// q_t has shape [qkv_dim][qbatch, head, batch] in order to make the maximum
// possible consecutive elements have the same KV.
static void TransposeQ(const MatPtrT<float>& q, MatPtrT<BF16>& q_t,
const size_t qbatch_size, ThreadingContext& ctx) {
// Group floats by the number of floats in a cache line.
const size_t kNF = ctx.cache_info.LineBytes() / sizeof(float);
const size_t num_heads = q.Cols() / q_t.Rows();
const size_t batch_size = q.Rows() / qbatch_size;
const auto func = [&](const size_t task, size_t worker) HWY_ATTR {
GCPP_ZONE(ctx, worker, Zones::kFlashAttentionTransposeQ);
for (size_t lane = 0; lane < kNF; ++lane) {
size_t q_row = task * kNF + lane;
if (q_row >= q_t.Rows()) break;
BF16* HWY_RESTRICT qt_row = q_t.Row(q_row);
for (size_t qi = 0; qi < qbatch_size; ++qi) {
for (size_t h = 0; h < num_heads; ++h) {
for (size_t b = 0; b < batch_size; ++b) {
qt_row[(qi * num_heads + h) * batch_size + b] =
hwy::ConvertScalarTo<BF16>(
q.Row(b * qbatch_size + qi)[h * q_t.Rows() + q_row]);
}
}
}
}
};
{
const size_t num_tasks = hwy::DivCeil(q_t.Rows(), kNF);
// Better than kFlat.
ParallelFor(Parallelism::kHierarchical, num_tasks, ctx,
/*cluster_idx=*/0, Callers::kFlashTransposeQ, func);
}
}
// Updates q in place for RMSNorm and positional encoding.
void RMSNormAndPositionalEncoding(const size_t num_tokens, const QBatch& qbatch,
MatPtrT<float>& q,
const MatPtr& query_norm_scale,
const size_t layer_idx,
const AttentionActivationsPtrs& activations,
ThreadingContext& ctx) {
const LayerConfig& layer_config = activations.config.layer_configs[layer_idx];
const float query_scale = activations.query_scale;
const hwy::Divisor div_qbatch(qbatch.Size());
const auto func = [&](const size_t task, size_t worker) HWY_ATTR {
GCPP_ZONE(ctx, worker, Zones::kFlashAttentionRmsNormAndPositionalEncoding);
size_t qi = div_qbatch.Remainder(task);
size_t batch_idx = div_qbatch.Divide(task);
for (size_t h = 0; h < layer_config.heads; ++h) {
const size_t tq_idx = qbatch.Size() * batch_idx + qi;
// Find the token position in the query and calculate
// the range of cache positions to attend to.
const size_t pos = qbatch.Pos(qi) + batch_idx;
float* HWY_RESTRICT q_row = q.Row(tq_idx) + h * layer_config.qkv_dim;
// Apply rope and scaling to Q.
if (query_norm_scale.HasPtr()) {
CallUpcasted(&query_norm_scale, [&](const auto* weights_t) {
RMSNormInplace(weights_t->PackedScale1(), /*w_ofs=*/0, q_row,
layer_config.qkv_dim, ctx, worker);
});
}
PositionalEncodingQK(q_row, layer_idx, activations, ctx, worker, pos,
query_scale);
}
};
{
// kHierarchical is not worth the extra sync overhead because the tasks are
// very lightweight.
ParallelFor(Parallelism::kFlat, num_tokens * qbatch.Size(), ctx,
/*cluster_idx=*/0, Callers::kFlashRMSNormAndPositionalEncoding,
func);
}
}
// Handles a single v row of flash attention for a single q.k dot product.
void HWY_INLINE SingleFlashAttentionStep(float x, float cap, float& old_max,
float& old_d,
const float* HWY_RESTRICT v,
const size_t v_cols,
float* HWY_RESTRICT att_out) {
if (cap > 0.0f) {
// Compute tanh(x / cap) * cap, being LogitsSoftCap on the scalar x.
x = cap * std::tanh(x / cap);
}
float m = std::max(x, old_max);
x = std::exp(x - m);
float scale = old_d * std::exp(old_max - m);
old_d = x + scale;
old_max = m;
float one_over_d = 1.0f / old_d;
scale *= one_over_d;
x *= one_over_d;
MulByConst(scale, att_out, v_cols);
MulByConstAndAdd(x, v, att_out, v_cols);
}
// Calculates the complete attention outputs for a single row of q.
void SingleFlashAttention(const size_t start_pos, const size_t last_pos,
const BF16* HWY_RESTRICT q, const MatPtrT<KV_t>& k,
const MatPtrT<KV_t>& v, const size_t layer_idx,
const AttentionActivationsPtrs& activations,
float* HWY_RESTRICT att_out, ThreadingContext& ctx,
const size_t worker) {
GCPP_ZONE(ctx, worker, Zones::kFlashAttentionSingleFlashAttention);
const hn::ScalableTag<BF16> dbf;
const size_t qkv_dim = k.Cols();
const size_t pos_mod = activations.div_seq_len.Remainder(start_pos);
// TODO: Mixed-mode can be further improved for Turin: we can demote right
// before we do the dot product instruction, rather than promote both to f32.
// But some potential accuracy loss there, needs evaluation first.
float m = Dot(dbf, MakeConstSpan(q, qkv_dim), 0, k.Row(pos_mod), qkv_dim);
if (float cap = activations.config.att_cap; cap > 0.0f) {
// Compute tanh(x / cap) * cap, being LogitsSoftCap on the scalar x.
m = cap * std::tanh(m / cap);
}
float d = 1.0f;
// This is just a copy of the first token.
MulByConstTo(d, v.Row(pos_mod), att_out, v.Cols(), ctx, worker);
for (size_t pos = start_pos + 1; pos <= last_pos; ++pos) {
const size_t pos_mod = activations.div_seq_len.Remainder(pos);
float x = Dot(dbf, MakeConstSpan(q, qkv_dim), 0, k.Row(pos_mod), qkv_dim);
SingleFlashAttentionStep(x, activations.config.att_cap, m, d,
v.Row(pos_mod), v.Cols(), att_out);
}
}
// Computes and returns a single vector of NF Q.K dot products, which represents
// the dot products of NF rows of Q for a single K timestep.
template <class DF, class VF = hn::Vec<DF>>
VF QDotKVector(DF df, const uint32_t* HWY_RESTRICT q_offsets,
const size_t k_pos, const MatPtrT<BF16>& q,
const MatPtrT<KV_t>& k) {
const hn::ScalableTag<BF16> dbf;
const size_t qkv_dim = k.Cols();
hn::TFromD<DF> results[hn::MaxLanes(df)];
for (size_t i = 0; i < hn::Lanes(df); ++i) {
results[i] = Dot(dbf, MakeConstSpan(q.Row(0) + q_offsets[i], qkv_dim), 0,
k.Row(k_pos), qkv_dim);
}
return hn::LoadU(df, results);
}
// Returns an NF Q rows by 8 K rows tile of Q.K dot products.
// This is the result of NF rows of Q against 8 K timesteps, with positions
// given by k_pos[0..7]. Q has been transposed so that the NF rows are read in
// consecutive elements, and other columns by adding q_stride.
template <class DF, class VF = hn::Vec<DF>>
void QDotKTile(DF df, const BF16* HWY_RESTRICT q, const size_t q_stride,
const MatPtrT<KV_t>& k, const size_t* k_pos, VF& sum0, VF& sum1,
VF& sum2, VF& sum3, VF& sum4, VF& sum5, VF& sum6, VF& sum7) {
constexpr size_t kHTileSize = kNFx8HTileSize;
sum0 = hn::Zero(df);
sum1 = hn::Zero(df);
sum2 = hn::Zero(df);
sum3 = hn::Zero(df);
sum4 = hn::Zero(df);
sum5 = hn::Zero(df);
sum6 = hn::Zero(df);
sum7 = hn::Zero(df);
const float* HWY_RESTRICT k_row[kHTileSize];
for (size_t i = 0; i < kHTileSize; ++i) {
k_row[i] = k.Row(k_pos[i]);
}
const hn::Rebind<BF16, DF> dbfh;
using VBF = hn::Vec<decltype(dbfh)>;
for (size_t i = 0; i < k.Cols(); ++i) {
const VBF q_vec_bf = hn::Load(dbfh, q);
const VF q_vec = hn::PromoteTo(df, q_vec_bf);
VF k_0 = hn::Set(df, k_row[0][i]);
sum0 = hn::MulAdd(q_vec, k_0, sum0);
VF k_1 = hn::Set(df, k_row[1][i]);
sum1 = hn::MulAdd(q_vec, k_1, sum1);
VF k_2 = hn::Set(df, k_row[2][i]);
sum2 = hn::MulAdd(q_vec, k_2, sum2);
VF k_3 = hn::Set(df, k_row[3][i]);
sum3 = hn::MulAdd(q_vec, k_3, sum3);
VF k_4 = hn::Set(df, k_row[4][i]);
sum4 = hn::MulAdd(q_vec, k_4, sum4);
VF k_5 = hn::Set(df, k_row[5][i]);
sum5 = hn::MulAdd(q_vec, k_5, sum5);
VF k_6 = hn::Set(df, k_row[6][i]);
sum6 = hn::MulAdd(q_vec, k_6, sum6);
VF k_7 = hn::Set(df, k_row[7][i]);
sum7 = hn::MulAdd(q_vec, k_7, sum7);
q += q_stride;
}
}
// Returns the element-wise maximum of 8 vectors, in a single vector.
template <class DF, class VF = hn::Vec<DF>>
VF HWY_INLINE ElementwiseMaxOf8(DF df, const VF& x0, const VF& x1, const VF& x2,
const VF& x3, const VF& x4, const VF& x5,
const VF& x6, const VF& x7) {
VF m0 = hn::Max(x0, x1);
VF m1 = hn::Max(x2, x3);
VF m2 = hn::Max(x4, x5);
VF m3 = hn::Max(x6, x7);
m0 = hn::Max(m0, m1);
m2 = hn::Max(m2, m3);
return hn::Max(m0, m2);
}
// Returns the element-wise sum of 8 vectors, in a single vector.
template <class DF, class VF = hn::Vec<DF>>
VF HWY_INLINE ElementwiseSumOf8(DF df, const VF& x0, const VF& x1, const VF& x2,
const VF& x3, const VF& x4, const VF& x5,
const VF& x6, const VF& x7) {
VF sum0 = hn::Add(x0, x1);
VF sum1 = hn::Add(x2, x3);
VF sum2 = hn::Add(x4, x5);
VF sum3 = hn::Add(x6, x7);
sum0 = hn::Add(sum0, sum1);
sum2 = hn::Add(sum2, sum3);
return hn::Add(sum0, sum2);
}
// Sweeps a tile of NF Q rows by 8 K timesteps accumulators from start_pos to
// min_last_pos, then sweeps the remaining timesteps in the range (min_last_pos,
// max_last_pos].
void TileFlashAttention(
const MatPtrT<BF16>& q, const uint32_t* HWY_RESTRICT q_offsets,
const StridedView<BF16>& qT, const MatPtrT<KV_t>& k, const size_t start_pos,
const uint32_t* HWY_RESTRICT last_pos, const size_t min_last_pos,
const size_t max_last_pos, const MatPtrT<KV_t>& v, const size_t layer_idx,
const AttentionActivationsPtrs& activations, MatPtrT<float>& att_out,
const uint32_t* HWY_RESTRICT out_offsets, ThreadingContext& ctx,
const size_t worker) {
GCPP_ZONE(ctx, worker, Zones::kFlashAttentionTileFlashAttention);
constexpr size_t kHTileSize = kNFx8HTileSize;
using DF = hn::ScalableTag<float>;
const DF df;
using VF = hn::Vec<DF>;
using DI = hn::ScalableTag<uint32_t>;
const DI di;
using VI = hn::Vec<DI>;
const size_t kVTileSize = hn::Lanes(df);
for (size_t i = 0; i < kVTileSize; ++i) {
hwy::ZeroBytes(att_out.Row(0) + out_offsets[i],
v.Cols() * sizeof(att_out.Row(0)[0]));
}
VI lasts = hn::LoadU(di, last_pos);
VF old_m = hn::Set(df, -std::numeric_limits<float>::max() / 2.0f);
VF old_d = hn::Zero(df);
const BF16* HWY_RESTRICT qT_row = qT.Row(0);
const size_t qT_stride = qT.Stride();
size_t position = start_pos;
while (position + kHTileSize - 1 <= min_last_pos) {
size_t k_pos[kHTileSize];
for (size_t i = 0; i < kHTileSize; ++i) {
k_pos[i] = activations.div_seq_len.Remainder(position + i);
}
VF x0, x1, x2, x3, x4, x5, x6, x7;
QDotKTile(df, qT_row, qT_stride, k, k_pos, x0, x1, x2, x3, x4, x5, x6, x7);
if (activations.config.att_cap > 0.0f) {
// Compute tanh(x / cap) * cap, being LogitsSoftCap on the tile.
VF cap = hn::Set(df, activations.config.att_cap);
VF one_over_cap = hn::Div(hn::Set(df, 1.0f), cap);
x0 = hn::Mul(cap, hn::Tanh(df, hn::Mul(x0, one_over_cap)));
x1 = hn::Mul(cap, hn::Tanh(df, hn::Mul(x1, one_over_cap)));
x2 = hn::Mul(cap, hn::Tanh(df, hn::Mul(x2, one_over_cap)));
x3 = hn::Mul(cap, hn::Tanh(df, hn::Mul(x3, one_over_cap)));
x4 = hn::Mul(cap, hn::Tanh(df, hn::Mul(x4, one_over_cap)));
x5 = hn::Mul(cap, hn::Tanh(df, hn::Mul(x5, one_over_cap)));
x6 = hn::Mul(cap, hn::Tanh(df, hn::Mul(x6, one_over_cap)));
x7 = hn::Mul(cap, hn::Tanh(df, hn::Mul(x7, one_over_cap)));
}
VF m = ElementwiseMaxOf8(df, x0, x1, x2, x3, x4, x5, x6, x7);
m = hn::Max(old_m, m);
x0 = hn::Exp(df, x0 - m);
x1 = hn::Exp(df, x1 - m);
x2 = hn::Exp(df, x2 - m);
x3 = hn::Exp(df, x3 - m);
x4 = hn::Exp(df, x4 - m);
x5 = hn::Exp(df, x5 - m);
x6 = hn::Exp(df, x6 - m);
x7 = hn::Exp(df, x7 - m);
VF scale = hn::Mul(old_d, hn::Exp(df, old_m - m));
old_d = ElementwiseSumOf8(df, x0, x1, x2, x3, x4, x5, x6, x7);
old_d = hn::Add(scale, old_d);
old_m = m;
VF one_over_d = hn::Div(hn::Set(df, 1.0f), old_d);
scale = hn::Mul(scale, one_over_d);
x0 = hn::Mul(x0, one_over_d);
x1 = hn::Mul(x1, one_over_d);
x2 = hn::Mul(x2, one_over_d);
x3 = hn::Mul(x3, one_over_d);
x4 = hn::Mul(x4, one_over_d);
x5 = hn::Mul(x5, one_over_d);
x6 = hn::Mul(x6, one_over_d);
x7 = hn::Mul(x7, one_over_d);
MulByConstAndAddTile(df, scale, x0, x1, x2, x3, x4, x5, x6, x7, v, k_pos,
att_out.Row(0), out_offsets, v.Cols());
position += kHTileSize;
}
while (position <= max_last_pos) {
size_t k_pos = activations.div_seq_len.Remainder(position);
VF x0 = QDotKVector(df, q_offsets, k_pos, q, k);
if (activations.config.att_cap > 0.0f) {
// Compute tanh(x / cap) * cap, being LogitsSoftCap on the vector.
VF cap = hn::Set(df, activations.config.att_cap);
VF one_over_cap = hn::Div(hn::Set(df, 1.0f), cap);
x0 = hn::Mul(cap, hn::Tanh(df, hn::Mul(x0, one_over_cap)));
}
// Past the last position, x0 doesn't count.
auto mask = hn::Gt(hn::Set(di, position), lasts);
VF causal_offset = hn::MaskedSet(df, RebindMask(df, mask),
std::numeric_limits<float>::max() / 2.0f);
x0 = hn::Sub(x0, causal_offset);
VF m = hn::Max(old_m, x0);
x0 = hn::Exp(df, x0 - m);
VF scale = hn::Mul(old_d, hn::Exp(df, old_m - m));
old_m = m;
old_d = hn::Add(scale, x0);
VF one_over_d = hn::Div(hn::Set(df, 1.0f), old_d);
x0 = hn::Mul(x0, one_over_d);
scale = hn::Mul(scale, one_over_d);
MulByConstAndAddVector(df, scale, x0, v, k_pos, att_out.Row(0), out_offsets,
v.Cols());
++position;
}
}
// Returns an 4 Q rows by NF K tile of Q.K dot products, in single precision.
// This is the result of 4 rows of Q against NF K timesteps, with positions
// given by k_offsets[0..NF].
template <class DF, class VF = hn::Vec<DF>>
void QDotKTilex4(DF df, const BF16* HWY_RESTRICT q,
const uint32_t* HWY_RESTRICT q_offsets, const MatPtrT<KV_t>& k,
const int32_t* HWY_RESTRICT k_offsets, VF& sum0, VF& sum1,
VF& sum2, VF& sum3) {
sum0 = hn::Zero(df);
sum1 = hn::Zero(df);
sum2 = hn::Zero(df);
sum3 = hn::Zero(df);
const float* HWY_RESTRICT k_base = k.Row(0);
using DI = hn::ScalableTag<int32_t>;
const DI di;
using VI = hn::Vec<DI>;
VI k_offsets_vec = hn::LoadU(di, k_offsets);
for (size_t i = 0; i < k.Cols(); ++i) {
VF k_vec = hn::GatherIndex(df, k_base + i, k_offsets_vec);
VF q_0 = hn::Set(df, hwy::ConvertScalarTo<float>(q[q_offsets[0] + i]));
sum0 = hn::MulAdd(q_0, k_vec, sum0);
VF q_1 = hn::Set(df, hwy::ConvertScalarTo<float>(q[q_offsets[1] + i]));
sum1 = hn::MulAdd(q_1, k_vec, sum1);
VF q_2 = hn::Set(df, hwy::ConvertScalarTo<float>(q[q_offsets[2] + i]));
sum2 = hn::MulAdd(q_2, k_vec, sum2);
VF q_3 = hn::Set(df, hwy::ConvertScalarTo<float>(q[q_offsets[3] + i]));
sum3 = hn::MulAdd(q_3, k_vec, sum3);
}
}
// Handles NF v rows of flash attention for NF q.k dot products from one q row.
template <class DF, class VF = hn::Vec<DF>>
float HWY_INLINE SingleFlashAttentionRowVector(DF df, VF& x, float& old_max,
float& old_d) {
float m = hn::ReduceMax(df, x);
m = std::max(m, old_max);
x = hn::Exp(df, x - hn::Set(df, m));
float scale = old_d * std::exp(old_max - m);
old_d = hn::ReduceSum(df, x) + scale;
old_max = m;
float one_over_d = 1.0f / old_d;
scale *= one_over_d;
x = hn::Mul(x, hn::Set(df, one_over_d));
return scale;
}
// Implements flash attention for a strip of 4 query vectors.
// It iterates through timesteps in K from `start_pos` up to `max_last_pos`.
// Timesteps up to `min_last_pos` (*) are processed in tiles of shape 4 Q rows
// by NF timesteps in K for efficiency while timesteps between `min_last_pos +
// 1` and `max_last_pos` are processed one-by-one to handle differing `last_pos`
// values within the strip.
// (*) Actually, it only iterates through
// `min_last_pos - (min_last_pos + 1 - start_pos) % NF` in tiles, as the tiled
// computation can, for obvious reasons, only process an integer number of
// tiles.
//
// @param q The query matrix [batch_size * q_heads, qkv_dim] in BF16 format.
// @param q_offsets Offsets from `q.Row(0)` to the start of the 4 query
// vectors to be processed in this tile.
// @param k Key matrix [seq_len, qkv_dim] from KV cache.
// @param start_pos The first token position in the KV cache to attend to.
// @param last_pos An array of 4 indices giving the last token position
// (inclusive) that each of the 4 queries may attend to.
// @param min_last_pos The minimum value in `last_pos`. Timesteps up to this
// position can be processed efficiently in batches.
// @param max_last_pos The maximum value in `last_pos`. Timesteps between
// `min_last_pos + 1` and this position are processed individually to
// respect each query's `last_pos` limit.
// @param v Value matrix [seq_len, qkv_dim] from KV cache.
// @param layer_idx The index of the current transformer layer.
// @param activations Attention configurations and buffers.
// @param att_out Output buffer for attention results.
// @param out_offsets Offsets from `att_out.Row(0)` to store the 4 output
// vectors.
// @param ctx Threading context.
// @param worker Worker thread index.
Tile4FlashState TileFlashAttention4(
const MatPtrT<BF16>& q, const uint32_t* HWY_RESTRICT q_offsets,
const MatPtrT<KV_t>& k, const size_t start_pos,
const uint32_t* HWY_RESTRICT last_pos, const size_t min_last_pos,
const size_t max_last_pos, const MatPtrT<KV_t>& v, const size_t layer_idx,
const AttentionActivationsPtrs& activations, MatPtrT<float>& att_out,
const uint32_t* HWY_RESTRICT out_offsets, ThreadingContext& ctx,
const size_t worker) {
GCPP_ZONE(ctx, worker, Zones::kFlashAttentionTileFlashAttention4);
using DF = hn::ScalableTag<float>;
const DF df;
using VF = hn::Vec<DF>;
constexpr size_t kMaxNF = hn::MaxLanes(df);
const size_t kHTileSize = hn::Lanes(df);
HWY_DASSERT(kHTileSize <= kMaxNF);
constexpr size_t kVTileSize = 4;
float scales[kVTileSize];
for (size_t i = 0; i < kVTileSize; ++i) {
hwy::ZeroBytes(att_out.Row(0) + out_offsets[i],
v.Cols() * sizeof(att_out.Row(0)[0]));
}
Tile4FlashState state;
size_t position = start_pos;
while (position + kHTileSize - 1 <= min_last_pos) {
int32_t k_offsets[kMaxNF];
size_t v_pos[kMaxNF];
for (size_t i = 0; i < kHTileSize; ++i) {
v_pos[i] = activations.div_seq_len.Remainder(position + i);
k_offsets[i] = k.Row(v_pos[i]) - k.Row(0);
}
VF x0, x1, x2, x3;
QDotKTilex4(df, q.Row(0), q_offsets, k, k_offsets, x0, x1, x2, x3);
if (activations.config.att_cap > 0.0f) {
// Compute tanh(x / cap) * cap, being LogitsSoftCap on the tile.
VF cap = hn::Set(df, activations.config.att_cap);
VF one_over_cap = hn::Div(hn::Set(df, 1.0f), cap);
x0 = hn::Mul(cap, hn::Tanh(df, hn::Mul(x0, one_over_cap)));
x1 = hn::Mul(cap, hn::Tanh(df, hn::Mul(x1, one_over_cap)));
x2 = hn::Mul(cap, hn::Tanh(df, hn::Mul(x2, one_over_cap)));
x3 = hn::Mul(cap, hn::Tanh(df, hn::Mul(x3, one_over_cap)));
}
scales[0] = SingleFlashAttentionRowVector(df, x0, state.row_states[0].max,
state.row_states[0].d);
scales[1] = SingleFlashAttentionRowVector(df, x1, state.row_states[1].max,
state.row_states[1].d);
scales[2] = SingleFlashAttentionRowVector(df, x2, state.row_states[2].max,
state.row_states[2].d);
scales[3] = SingleFlashAttentionRowVector(df, x3, state.row_states[3].max,
state.row_states[3].d);
MulByConstAndAddTile4(df, scales, x0, x1, x2, x3, v, v_pos, att_out.Row(0),
out_offsets, v.Cols());
position += kHTileSize;
}
const hn::ScalableTag<BF16> dbf;
const size_t qkv_dim = k.Cols();
while (position <= max_last_pos) {
size_t k_pos = activations.div_seq_len.Remainder(position);
if (position <= last_pos[0]) {
// Past the last position, x0 doesn't count.
float x0 = Dot(dbf, MakeConstSpan(q.Row(0) + q_offsets[0], qkv_dim), 0,
k.Row(k_pos), qkv_dim);
SingleFlashAttentionStep(x0, activations.config.att_cap,
state.row_states[0].max, state.row_states[0].d,
v.Row(k_pos), v.Cols(),
att_out.Row(0) + out_offsets[0]);
}
if (position <= last_pos[1]) {
// Past the last position, x1 doesn't count.
float x1 = Dot(dbf, MakeConstSpan(q.Row(0) + q_offsets[1], qkv_dim), 0,
k.Row(k_pos), qkv_dim);
SingleFlashAttentionStep(x1, activations.config.att_cap,
state.row_states[1].max, state.row_states[1].d,
v.Row(k_pos), v.Cols(),
att_out.Row(0) + out_offsets[1]);
}
if (position <= last_pos[2]) {
// Past the last position, x2 doesn't count.
float x2 = Dot(dbf, MakeConstSpan(q.Row(0) + q_offsets[2], qkv_dim), 0,
k.Row(k_pos), qkv_dim);
SingleFlashAttentionStep(x2, activations.config.att_cap,
state.row_states[2].max, state.row_states[2].d,
v.Row(k_pos), v.Cols(),
att_out.Row(0) + out_offsets[2]);
}
if (position <= last_pos[3]) {
// Past the last position, x3 doesn't count.
float x3 = Dot(dbf, MakeConstSpan(q.Row(0) + q_offsets[3], qkv_dim), 0,
k.Row(k_pos), qkv_dim);
SingleFlashAttentionStep(x3, activations.config.att_cap,
state.row_states[3].max, state.row_states[3].d,
v.Row(k_pos), v.Cols(),
att_out.Row(0) + out_offsets[3]);
}
++position;
}
return state;
}
// Rounds n to a number that can be used as the number of Q rows in a tile
// of flash attention.
static size_t RoundToSuitablePowerOf2(size_t n) {
if (n < 4) return 1;
if (n < 8) return 4;
if (n < 16) return 8;
if (n < 32) return 16;
return 32;
}
// The vertical tile size is determined by the ability to use tiling and the
// target_parallelism. In practice the possible tile sizes in order of
// preference for efficiency are kNF, 4, 1, where kNF is likely to be 4 8 or
// 16. The final tile size is chosen to be the largest possible that allows
// for target_parallelism parallel tasks.
size_t GetVTileSize(size_t kNF, size_t num_head_groups, size_t num_tokens,
size_t total_tasks, size_t target_parallelism) {
const size_t kMaxEqualK =
RoundToSuitablePowerOf2(num_head_groups * num_tokens);
const size_t kMinTileSize = (total_tasks / 4 >= target_parallelism) ? 4 : 1;
return (kNF <= kMaxEqualK && total_tasks / kNF >= target_parallelism)
? kNF
: std::min(kMinTileSize, kMaxEqualK);
}
// The nominal aim of attention is to combine 3 inputs Q[L,D], K[L,D], V[L,D]
// into a single output O[L,D].
// Conventional attention first computes A[L,L] = Q . KT
// followed by A = softmax(A) (over invididual rows).
// Then A is multiplied by V to get O[L,D].
// For each row of O, this takes a read of one row of Q L times, all of K,
// 3 write/reads of one row of A, read all of V, and read/write the one row of O
// L times. Ignoring the computation for now, and focusing just on memory,
// the one row of O takes L(4D+3) reads and L(D+3) writes.
// For the whole of Q, this is L^2(4D+3) reads and L^2(D+3) writes.
//
// Flash attention fuses these operations together, and has 3 operating modes:
// 1. NF rows of the result computed using tiles of registers of shape NFx8.
// 2. 4 rows of the result computed using tiles of registers of shape 4xNF.
// 3. One row (of Q and the result) at a time.
// In all cases the intermediate result (Q.KT) is never stored to memory.
// NF is the number of float lanes in a register, being 16 for AVX3. The softmax
// is converted to streaming form using the algorithm from:
// https://courses.cs.washington.edu/courses/cse599m/23sp/notes/flashattn.pdf.
// Q is transposed to Q_T[D,L] to make the dot product computation efficient.
//
// In mode 1:
// QDotKTileFloat computes NF Q rows x 8 K timesteps of Q.K dot products in one
// go, reducing reads of Q by 8 and reads of K by NF. The streaming softmax is
// computed entirely in registers, and a further NF registers to accumulate the
// results of the product of the softmax and V, reduce the number of reads of V
// by NF, and the reads/writes of O by 8.
// The reads are thus reduced to 2DL^2(1/8+1/NF) and writes reduced to DL^2/8,
// which on AVX3 is an overall reduction by about a factor of 10.
// Mode 1 can only be accessed if there is a large Qbatch size, or in multi-turn
// prefill, since in other cases, there is either a single K timestep (prefill)
// or a single num_heads set of Q rows (decode).
//
// In mode 2, the 4 rows of Q are computed against NF K timesteps in a tile,
// reducing the reads of Q by NF, and the reads of K by 4. The softmax and
// accumulation of the result is done in registers, cutting the reads of V by 4.
// The reads/writes of O are reduced by a factor of NF.
// The overall reduction is limited by the need to use gather to load K.
// Transposing K would be possible, but is complicated by the wraparound.
// Mode 2 can be used in all cases when there are at least 4 attention heads,
// but it may be prefereable to use mode 3 when the batch size is small to
// maximise parallelism.
//
// In mode 3, a single row of Q is computed against a single K timestep at a
// time, using SingleFlashAttention. In this case there is no reduction in the
// reads of Q or K, or V, or O, but the reads/writes of the intermediate A are
// still eliminated.
//
// A further complication is that real attention is not as simple as documented
// in the paper and above. There are multiple query heads, differing KV, and
// different sequence lengths, so a lot of the work in FlashAttention is making
// sure that a collection of q rows with the same KV and sequence length are
// grouped together so that mode 1 or 2 can be used, and choosing which of the
// 3 modes to use for best efficiency.
void FlashAttention(const size_t num_tokens, const size_t target_parallelism,
const size_t layer_idx, const MatPtr& query_norm_scale,
AttentionActivationsPtrs& activations, QBatch& qbatch,
ThreadingContext& ctx) {
GCPP_ZONE(ctx, 0, Zones::kFlashAttentionInclusive);
RMSNormAndPositionalEncoding(num_tokens, qbatch, activations.q,
query_norm_scale, layer_idx, activations, ctx);
const hwy::Divisor div_qbatch(qbatch.Size());
// Compress q to q_bf.
ParallelFor(
Parallelism::kWithinCluster, activations.q.Rows(), ctx,
/*cluster_idx=*/0, Callers::kFlashAttention,
[&](size_t row, size_t worker) {
CompressPerThread tls;
const hn::ScalableTag<float> df;
CompressTraits<BF16>::Compress(
df, activations.q.Row(row), activations.q.Cols(), tls,
MakeSpan(activations.q_bf.Row(row), activations.q_bf.Cols()), 0);
});
const LayerConfig& layer_config = activations.config.layer_configs[layer_idx];
const size_t qkv_dim = layer_config.qkv_dim;
// A "head group" in the context of GQA refers to a collection of query
// heads that share the same key and value heads.
const size_t kHeadGroups = layer_config.heads / layer_config.kv_heads;
const size_t cache_layer_size = layer_config.CacheLayerSize();
const size_t seq_len =
static_cast<size_t>(activations.div_seq_len.GetDivisor());
const size_t token_batch = num_tokens * div_qbatch.GetDivisor();
const size_t total_tasks = token_batch * layer_config.heads;
using DF = hn::ScalableTag<float>;
const DF df;
const size_t kNF = hn::Lanes(df);
constexpr size_t kMaxNF = hn::MaxLanes(df);
HWY_DASSERT(kNF <= kMaxNF);
const size_t kVTileSize = GetVTileSize(kNF, kHeadGroups, num_tokens,
total_tasks, target_parallelism);
// Only transpose Q if we are using tiling.
if (kVTileSize == kNF) {
size_t max_last = 0, min_start = std::numeric_limits<size_t>::max();
for (size_t qi = 0; qi < qbatch.Size(); ++qi) {
size_t pos = qbatch.Pos(qi);
const size_t start = StartPos(pos, activations.config, layer_idx);
pos += num_tokens - 1;
const size_t end = qbatch.PrefixEnd(qi);
if (end > 0 && end - 1 > pos) {
pos = end - 1;
}
max_last = std::max(max_last, pos);
min_start = std::min(min_start, start);
}
if (max_last - min_start + 1 >= kNFx8HTileSize) {
// q has shape [batch, qbatch][head, qkv_dim].
// We transpose it to [qkv_dim][qbatch, head, batch] in order to make the
// maximum possible number of consecutive columns have the same KV
// matrices. Each thread will process a tile of NF columns of QT so the
// starting column index of QT is just the task index * kVTileSize.
TransposeQ(activations.q, activations.q_T, qbatch.Size(), ctx);
}
}
const size_t num_thread_tasks = hwy::DivCeil(total_tasks, kVTileSize);
const hwy::Divisor div_tokens(num_tokens);
// All layers should have the same number of heads.
HWY_DASSERT(activations.div_heads.GetDivisor() == layer_config.heads);
// For each head/token/query, compute fused flash Q.K, softmax and weighted V.
const auto func = [&](const size_t task, size_t worker) HWY_ATTR {
GCPP_ZONE(ctx, worker, Zones::kFlashAttentionFlashAttention);
// Offsets into original Q for each row in the tile.
uint32_t q_offsets[kMaxNF];
// Offsets into att_out for each row in the tile.
uint32_t out_offsets[kMaxNF];
// Start positions for each row in the tile.
size_t start_positions[kMaxNF];
// Last positions for each row in the tile. Inclusive.
uint32_t last_pos[kMaxNF];
// min and max last positions across all rows in the tile determines when
// TileFlashAttention switches to single vector mode to handle the
// ragged sequence lengths.
size_t min_last_pos = std::numeric_limits<size_t>::max();
size_t max_last_pos = 0;
// Indices into the qbatch.KV for each row in the tile.
size_t qi_indices[kMaxNF];
// Indices into the kv_cache for each row in the tile.
size_t kv_offsets[kMaxNF];
// first_task is [qbatch, head, token].
const size_t first_task = task * kVTileSize;
const size_t last_task = first_task + kVTileSize - 1;
bool use_tile_attention = kVTileSize > 1 && last_task < total_tasks;
for (size_t offset = 0;
offset < kVTileSize && first_task + offset < total_tasks; ++offset) {
const size_t batch_idx = div_tokens.Remainder(first_task + offset);
const size_t qh = div_tokens.Divide(first_task + offset);
const size_t head = activations.div_heads.Remainder(qh);
const size_t qi = activations.div_heads.Divide(qh);
const size_t tq_idx = div_qbatch.GetDivisor() * batch_idx + qi;
qi_indices[offset] = qi;
// Find the token position in the query and calculate
// the range of cache positions to attend to.
const size_t pos = qbatch.Pos(qi) + batch_idx;
const size_t start_pos = StartPos(pos, activations.config, layer_idx);
start_positions[offset] = start_pos;
size_t last = pos;
const size_t prefix_end = qbatch.PrefixEnd(qi);
if (prefix_end > 0 && prefix_end - 1 > last) {
// last_pos in `TileFlashAttention` is inclusive.
last = prefix_end - 1;
}
last_pos[offset] = last;
min_last_pos = HWY_MIN(min_last_pos, last);
max_last_pos = HWY_MAX(max_last_pos, last);
q_offsets[offset] = activations.q_bf.Row(tq_idx) + head * qkv_dim -
activations.q_bf.Row(0);
out_offsets[offset] = activations.att_out.Row(tq_idx) + head * qkv_dim -
activations.att_out.Row(0);
const size_t kv_index = head / kHeadGroups;
const size_t head_offset = kv_index * qkv_dim * 2;
kv_offsets[offset] = layer_idx * cache_layer_size + head_offset;
// If any of the parameters in this if statement differ within this task,
// then we can't use TileFlashAttention. TileFlashAttention requires that
// all rows in the tile have the same K and V matrices, and Q starts at
// the same position. The end positions do not have to be the equal.
if (start_positions[offset] != start_positions[0] ||
qi_indices[offset] != qi_indices[0] ||
kv_offsets[offset] != kv_offsets[0]) {
use_tile_attention = false;
}
}
for (size_t offset = 0;
offset < kVTileSize && first_task + offset < total_tasks; ++offset) {
auto& kv_cache = qbatch.KV(qi_indices[offset]).kv_cache;
MatPtrT<KV_t> k("k_view", Extents2D(seq_len, qkv_dim));
k.SetPtr(kv_cache.Row(0) + kv_offsets[offset], kv_cache.Stride());
MatPtrT<KV_t> v("v_view", Extents2D(seq_len, qkv_dim));
v.SetPtr(kv_cache.Row(0) + kv_offsets[offset] + qkv_dim,
kv_cache.Stride());
if (use_tile_attention) {
// To avoid duplicating the code to setup K and V, the call to
// TileFlashAttention is inside the loop over tasks, even though it
// handles all rows in the task at once.
StridedView<BF16> qT =
StridedView<BF16>(activations.q_T.Row(0) + first_task, kVTileSize,
activations.q_T.Stride());
if (kVTileSize == kNF) {
// We can still use TileFlashAttention even if we didn't transpose Q
// above. The condition used for transposing Q above is more general
// and easier to compute than the condition used within
// TileFlashAttention that min_last_pos - start_positions[offset] <
// kNFx8HTileSize. In this case, qT is never used. Some tasks might
// use qT and some might not, which is why the more general condition
// is used above to catch all cases where qT will be used.
TileFlashAttention(activations.q_bf, q_offsets, qT, k,
start_positions[offset], last_pos, min_last_pos,
max_last_pos, v, layer_idx, activations,
activations.att_out, out_offsets, ctx, worker);
} else if (kVTileSize == 4) {
TileFlashAttention4(activations.q_bf, q_offsets, k,
start_positions[offset], last_pos, min_last_pos,
max_last_pos, v, layer_idx, activations,
activations.att_out, out_offsets, ctx, worker);
} else {
HWY_UNREACHABLE;
}
break;
} else {
SingleFlashAttention(start_positions[offset], last_pos[offset],
activations.q_bf.Row(0) + q_offsets[offset], k, v,
layer_idx, activations,
activations.att_out.Row(0) + out_offsets[offset],
ctx, worker);
}
}
};
{
PROFILER_ZONE("Gen.FlashAttention.ForkJoin");
// Full parallelism is helpful, SmallParallelFor is insufficient.
HierarchicalParallelFor(num_thread_tasks, ctx, Callers::kFlashAttention,
func);
}
}
// NOLINTNEXTLINE(google-readability-namespace-comments)
} // namespace HWY_NAMESPACE
} // namespace gcpp
HWY_AFTER_NAMESPACE();
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