Commit 71b1be50 authored by zhuwenwen's avatar zhuwenwen
Browse files

back to pa and rn

parent c628c6ec
...@@ -81,11 +81,13 @@ inline __device__ float block_sum(float* red_smem, float sum) { ...@@ -81,11 +81,13 @@ inline __device__ float block_sum(float* red_smem, float sum) {
return VLLM_SHFL_SYNC(sum, 0); return VLLM_SHFL_SYNC(sum, 0);
} }
// TODO(woosuk): Merge the last two dimensions of the grid.
// Grid: (num_heads, num_seqs, max_num_partitions).
template <typename scalar_t, typename cache_t, int HEAD_SIZE, int BLOCK_SIZE, template <typename scalar_t, typename cache_t, int HEAD_SIZE, int BLOCK_SIZE,
int NUM_THREADS, vllm::Fp8KVCacheDataType KV_DTYPE, int NUM_THREADS, vllm::Fp8KVCacheDataType KV_DTYPE,
bool IS_BLOCK_SPARSE, bool IS_BLOCK_SPARSE,
int PARTITION_SIZE = 0> // Zero means no partitioning. int PARTITION_SIZE = 0> // Zero means no partitioning.
__device__ void paged_attention_kernel_v1( __device__ void paged_attention_kernel(
float* __restrict__ exp_sums, // [num_seqs, num_heads, max_num_partitions] float* __restrict__ exp_sums, // [num_seqs, num_heads, max_num_partitions]
float* __restrict__ max_logits, // [num_seqs, num_heads, float* __restrict__ max_logits, // [num_seqs, num_heads,
// max_num_partitions] // max_num_partitions]
...@@ -266,448 +268,6 @@ __device__ void paged_attention_kernel_v1( ...@@ -266,448 +268,6 @@ __device__ void paged_attention_kernel_v1(
const int token_idx = block_idx * BLOCK_SIZE + physical_block_offset; const int token_idx = block_idx * BLOCK_SIZE + physical_block_offset;
K_vec k_vecs[NUM_VECS_PER_THREAD]; K_vec k_vecs[NUM_VECS_PER_THREAD];
#pragma unroll
for (int j = 0; j < NUM_VECS_PER_THREAD; j++) {
const cache_t* k_ptr =
k_cache + physical_block_number * kv_block_stride +
kv_head_idx * kv_head_stride + physical_block_offset * x;
const int vec_idx = thread_group_offset + j * THREAD_GROUP_SIZE;
const int offset1 = (vec_idx * VEC_SIZE) / x;
const int offset2 = (vec_idx * VEC_SIZE) % x;
if constexpr (KV_DTYPE == Fp8KVCacheDataType::kAuto) {
k_vecs[j] = *reinterpret_cast<const K_vec*>(
k_ptr + offset1 * BLOCK_SIZE * x + offset2);
} else {
// Vector conversion from Quant_vec to K_vec.
Quant_vec k_vec_quant = *reinterpret_cast<const Quant_vec*>(
k_ptr + offset1 * BLOCK_SIZE * x + offset2);
k_vecs[j] = fp8::scaled_convert<K_vec, Quant_vec, KV_DTYPE>(
k_vec_quant, kv_scale);
}
}
// Compute dot product.
// This includes a reduction across the threads in the same thread group.
float qk = scale * Qk_dot<scalar_t, THREAD_GROUP_SIZE>::dot_v1(
q_vecs[thread_group_offset], k_vecs);
// Add the ALiBi bias if slopes are given.
qk += (alibi_slope != 0) ? alibi_slope * (token_idx - seq_len + 1) : 0;
if (thread_group_offset == 0) {
// Store the partial reductions to shared memory.
// NOTE(woosuk): It is required to zero out the masked logits.
const bool mask = token_idx >= seq_len;
logits[token_idx - start_token_idx] = mask ? 0.f : qk;
// Update the max value.
qk_max = mask ? qk_max : fmaxf(qk_max, qk);
}
}
}
// Perform reduction across the threads in the same warp to get the
// max qk value for each "warp" (not across the thread block yet).
// The 0-th thread of each thread group already has its max qk value.
#pragma unroll
for (int mask = WARP_SIZE / 2; mask >= THREAD_GROUP_SIZE; mask /= 2) {
qk_max = fmaxf(qk_max, VLLM_SHFL_XOR_SYNC(qk_max, mask));
}
if (lane == 0) {
red_smem[warp_idx] = qk_max;
}
__syncthreads();
// TODO(woosuk): Refactor this part.
// Get the max qk value for the sequence.
qk_max = lane < NUM_WARPS ? red_smem[lane] : -FLT_MAX;
#pragma unroll
for (int mask = NUM_WARPS / 2; mask >= 1; mask /= 2) {
qk_max = fmaxf(qk_max, VLLM_SHFL_XOR_SYNC(qk_max, mask));
}
// Broadcast the max qk value to all threads.
qk_max = VLLM_SHFL_SYNC(qk_max, 0);
// Get the sum of the exp values.
float exp_sum = 0.f;
for (int i = thread_idx; i < num_tokens; i += NUM_THREADS) {
float val = __expf(logits[i] - qk_max);
logits[i] = val;
exp_sum += val;
}
exp_sum = block_sum<NUM_WARPS>(&red_smem[NUM_WARPS], exp_sum);
// Compute softmax.
const float inv_sum = __fdividef(1.f, exp_sum + 1e-6f);
for (int i = thread_idx; i < num_tokens; i += NUM_THREADS) {
logits[i] *= inv_sum;
}
__syncthreads();
// If partitioning is enabled, store the max logit and exp_sum.
if (USE_PARTITIONING && thread_idx == 0) {
float* max_logits_ptr = max_logits +
seq_idx * num_heads * max_num_partitions +
head_idx * max_num_partitions + partition_idx;
*max_logits_ptr = qk_max;
float* exp_sums_ptr = exp_sums + seq_idx * num_heads * max_num_partitions +
head_idx * max_num_partitions + partition_idx;
*exp_sums_ptr = exp_sum;
}
// Each thread will fetch 16 bytes from the value cache at a time.
constexpr int V_VEC_SIZE = MIN(16 / sizeof(scalar_t), BLOCK_SIZE);
using V_vec = typename Vec<scalar_t, V_VEC_SIZE>::Type;
using L_vec = typename Vec<scalar_t, V_VEC_SIZE>::Type;
using V_quant_vec = typename Vec<cache_t, V_VEC_SIZE>::Type;
using Float_L_vec = typename FloatVec<L_vec>::Type;
constexpr int NUM_V_VECS_PER_ROW = BLOCK_SIZE / V_VEC_SIZE;
constexpr int NUM_ROWS_PER_ITER = WARP_SIZE / NUM_V_VECS_PER_ROW;
constexpr int NUM_ROWS_PER_THREAD =
DIVIDE_ROUND_UP(HEAD_SIZE, NUM_ROWS_PER_ITER);
// NOTE(woosuk): We use FP32 for the accumulator for better accuracy.
float accs[NUM_ROWS_PER_THREAD];
#pragma unroll
for (int i = 0; i < NUM_ROWS_PER_THREAD; i++) {
accs[i] = 0.f;
}
scalar_t zero_value;
zero(zero_value);
for (int block_idx = start_block_idx + warp_idx; block_idx < end_block_idx;
block_idx += NUM_WARPS) {
// NOTE(woosuk): The block number is stored in int32. However, we cast it to
// int64 because int32 can lead to overflow when this variable is multiplied
// by large numbers (e.g., kv_block_stride).
// For blocksparse attention: skip computation on blocks that are not
// attended
if constexpr (IS_BLOCK_SPARSE) {
int v_bs_block_id = block_idx * BLOCK_SIZE / blocksparse_block_size;
if (!((v_bs_block_id + bs_block_offset) % blocksparse_vert_stride == 0) &&
!((v_bs_block_id > q_bs_block_id - blocksparse_local_blocks))) {
continue;
}
}
const int64_t physical_block_number =
static_cast<int64_t>(block_table[block_idx]);
const int physical_block_offset = (lane % NUM_V_VECS_PER_ROW) * V_VEC_SIZE;
const int token_idx = block_idx * BLOCK_SIZE + physical_block_offset;
L_vec logits_vec;
from_float(logits_vec, *reinterpret_cast<Float_L_vec*>(logits + token_idx -
start_token_idx));
const cache_t* v_ptr = v_cache + physical_block_number * kv_block_stride +
kv_head_idx * kv_head_stride;
#pragma unroll
for (int i = 0; i < NUM_ROWS_PER_THREAD; i++) {
const int row_idx = lane / NUM_V_VECS_PER_ROW + i * NUM_ROWS_PER_ITER;
if (row_idx < HEAD_SIZE) {
const int offset = row_idx * BLOCK_SIZE + physical_block_offset;
V_vec v_vec;
if constexpr (KV_DTYPE == Fp8KVCacheDataType::kAuto) {
v_vec = *reinterpret_cast<const V_vec*>(v_ptr + offset);
} else {
V_quant_vec v_quant_vec =
*reinterpret_cast<const V_quant_vec*>(v_ptr + offset);
// Vector conversion from V_quant_vec to V_vec.
v_vec = fp8::scaled_convert<V_vec, V_quant_vec, KV_DTYPE>(v_quant_vec,
kv_scale);
}
if (block_idx == num_seq_blocks - 1) {
// NOTE(woosuk): When v_vec contains the tokens that are out of the
// context, we should explicitly zero out the values since they may
// contain NaNs. See
// https://github.com/vllm-project/vllm/issues/641#issuecomment-1682544472
scalar_t* v_vec_ptr = reinterpret_cast<scalar_t*>(&v_vec);
#pragma unroll
for (int j = 0; j < V_VEC_SIZE; j++) {
v_vec_ptr[j] = token_idx + j < seq_len ? v_vec_ptr[j] : zero_value;
}
}
accs[i] += dot(logits_vec, v_vec);
}
}
}
// Perform reduction within each warp.
#pragma unroll
for (int i = 0; i < NUM_ROWS_PER_THREAD; i++) {
float acc = accs[i];
#pragma unroll
for (int mask = NUM_V_VECS_PER_ROW / 2; mask >= 1; mask /= 2) {
acc += VLLM_SHFL_XOR_SYNC(acc, mask);
}
accs[i] = acc;
}
// NOTE(woosuk): A barrier is required because the shared memory space for
// logits is reused for the output.
__syncthreads();
// Perform reduction across warps.
float* out_smem = reinterpret_cast<float*>(shared_mem);
#pragma unroll
for (int i = NUM_WARPS; i > 1; i /= 2) {
int mid = i / 2;
// Upper warps write to shared memory.
if (warp_idx >= mid && warp_idx < i) {
float* dst = &out_smem[(warp_idx - mid) * HEAD_SIZE];
#pragma unroll
for (int i = 0; i < NUM_ROWS_PER_THREAD; i++) {
const int row_idx = lane / NUM_V_VECS_PER_ROW + i * NUM_ROWS_PER_ITER;
if (row_idx < HEAD_SIZE && lane % NUM_V_VECS_PER_ROW == 0) {
dst[row_idx] = accs[i];
}
}
}
__syncthreads();
// Lower warps update the output.
if (warp_idx < mid) {
const float* src = &out_smem[warp_idx * HEAD_SIZE];
#pragma unroll
for (int i = 0; i < NUM_ROWS_PER_THREAD; i++) {
const int row_idx = lane / NUM_V_VECS_PER_ROW + i * NUM_ROWS_PER_ITER;
if (row_idx < HEAD_SIZE && lane % NUM_V_VECS_PER_ROW == 0) {
accs[i] += src[row_idx];
}
}
}
__syncthreads();
}
// Write the final output.
if (warp_idx == 0) {
scalar_t* out_ptr =
out + seq_idx * num_heads * max_num_partitions * HEAD_SIZE +
head_idx * max_num_partitions * HEAD_SIZE + partition_idx * HEAD_SIZE;
#pragma unroll
for (int i = 0; i < NUM_ROWS_PER_THREAD; i++) {
const int row_idx = lane / NUM_V_VECS_PER_ROW + i * NUM_ROWS_PER_ITER;
if (row_idx < HEAD_SIZE && lane % NUM_V_VECS_PER_ROW == 0) {
from_float(*(out_ptr + row_idx), accs[i]);
}
}
}
}
// remove bf16 surport,because bf16 has bad performance on dcu.
template <typename scalar_t, typename cache_t, int HEAD_SIZE, int BLOCK_SIZE,
int NUM_THREADS, vllm::Fp8KVCacheDataType KV_DTYPE,
bool IS_BLOCK_SPARSE,int PARTITION_SIZE = 0,bool big_seq=false,
std::enable_if_t<!std::is_same<scalar_t, uint16_t>::value, int> = 0> // Zero means no partitioning.
__device__ void paged_attention_kernel_v2(
float* __restrict__ exp_sums, // [num_seqs, num_heads, max_num_partitions]
float* __restrict__ max_logits, // [num_seqs, num_heads,
// max_num_partitions]
scalar_t* __restrict__ out, // [num_seqs, num_heads, max_num_partitions,
// head_size]
const scalar_t* __restrict__ q, // [num_seqs, num_heads, head_size]
const cache_t* __restrict__ k_cache, // [num_blocks, num_kv_heads,
// head_size/x, block_size, x]
const cache_t* __restrict__ v_cache, // [num_blocks, num_kv_heads,
// head_size, block_size]
const int num_kv_heads, // [num_heads]
const float scale,
const int* __restrict__ block_tables, // [num_seqs, max_num_blocks_per_seq]
const int* __restrict__ seq_lens, // [num_seqs]
const int max_num_blocks_per_seq,
const float* __restrict__ alibi_slopes, // [num_heads]
const int q_stride, const int kv_block_stride, const int kv_head_stride,
const float kv_scale, const int tp_rank, const int blocksparse_local_blocks,
const int blocksparse_vert_stride, const int blocksparse_block_size,
const int blocksparse_head_sliding_step) {}
// TODO(woosuk): Merge the last two dimensions of the grid.
// Grid: (num_heads, num_seqs, max_num_partitions).
template <typename scalar_t, typename cache_t, int HEAD_SIZE, int BLOCK_SIZE,
int NUM_THREADS, vllm::Fp8KVCacheDataType KV_DTYPE,
bool IS_BLOCK_SPARSE,int PARTITION_SIZE = 0,bool big_seq=false,
std::enable_if_t<std::is_same<scalar_t, uint16_t>::value, int> = 0> // Zero means no partitioning.
__device__ void paged_attention_kernel_v2(
float* __restrict__ exp_sums, // [num_seqs, num_heads, max_num_partitions]
float* __restrict__ max_logits, // [num_seqs, num_heads,
// max_num_partitions]
scalar_t* __restrict__ out, // [num_seqs, num_heads, max_num_partitions,
// head_size]
const scalar_t* __restrict__ q, // [num_seqs, num_heads, head_size]
const cache_t* __restrict__ k_cache, // [num_blocks, num_kv_heads,
// head_size/x, block_size, x]
const cache_t* __restrict__ v_cache, // [num_blocks, num_kv_heads,
// head_size, block_size]
const int num_kv_heads, // [num_heads]
const float scale,
const int* __restrict__ block_tables, // [num_seqs, max_num_blocks_per_seq]
const int* __restrict__ seq_lens, // [num_seqs]
const int max_num_blocks_per_seq,
const float* __restrict__ alibi_slopes, // [num_heads]
const int q_stride, const int kv_block_stride, const int kv_head_stride,
const float kv_scale, const int tp_rank, const int blocksparse_local_blocks,
const int blocksparse_vert_stride, const int blocksparse_block_size,
const int blocksparse_head_sliding_step) {
const int seq_idx = blockIdx.y;
const int partition_idx = blockIdx.z;
const int max_num_partitions = gridDim.z;
constexpr bool USE_PARTITIONING = PARTITION_SIZE > 0;
const int seq_len = seq_lens[seq_idx];
if (USE_PARTITIONING && partition_idx * PARTITION_SIZE >= seq_len) {
// No work to do. Terminate the thread block.
return;
}
const int num_seq_blocks = DIVIDE_ROUND_UP(seq_len, BLOCK_SIZE);
const int num_blocks_per_partition =
USE_PARTITIONING ? PARTITION_SIZE / BLOCK_SIZE : num_seq_blocks;
// [start_block_idx, end_block_idx) is the range of blocks to process.
const int start_block_idx =
USE_PARTITIONING ? partition_idx * num_blocks_per_partition : 0;
const int end_block_idx =
MIN(start_block_idx + num_blocks_per_partition, num_seq_blocks);
const int num_blocks = end_block_idx - start_block_idx;
// [start_token_idx, end_token_idx) is the range of tokens to process.
const int start_token_idx = start_block_idx * BLOCK_SIZE;
const int end_token_idx =
MIN(start_token_idx + num_blocks * BLOCK_SIZE, seq_len);
const int num_tokens = end_token_idx - start_token_idx;
constexpr int THREAD_GROUP_SIZE = MAX(WARP_SIZE / BLOCK_SIZE, 1);
constexpr int NUM_THREAD_GROUPS =
NUM_THREADS / THREAD_GROUP_SIZE; // Note: This assumes THREAD_GROUP_SIZE
// divides NUM_THREADS
static_assert(NUM_THREADS % THREAD_GROUP_SIZE == 0);
constexpr int NUM_TOKENS_PER_THREAD_GROUP =
DIVIDE_ROUND_UP(BLOCK_SIZE, WARP_SIZE);
constexpr int NUM_WARPS = NUM_THREADS / WARP_SIZE;
const int thread_idx = threadIdx.x;
const int warp_idx = thread_idx / WARP_SIZE;
const int lane = thread_idx % WARP_SIZE;
const int head_idx = blockIdx.x;
const int num_heads = gridDim.x;
const int num_queries_per_kv = num_heads / num_kv_heads;
const int kv_head_idx = head_idx / num_queries_per_kv;
const float alibi_slope =
alibi_slopes == nullptr ? 0.f : alibi_slopes[head_idx];
// A vector type to store a part of a key or a query.
// The vector size is configured in such a way that the threads in a thread
// group fetch or compute 16 bytes at a time. For example, if the size of a
// thread group is 4 and the data type is half, then the vector size is 16 /
// (4 * sizeof(half)) == 2.
constexpr int VEC_SIZE = MAX(16 / (THREAD_GROUP_SIZE * sizeof(scalar_t)), 1);
using K_vec = typename Vec<scalar_t, VEC_SIZE>::Type;
using Q_vec = typename Vec<scalar_t, VEC_SIZE>::Type;
using Quant_vec = typename Vec<cache_t, VEC_SIZE>::Type;
constexpr int NUM_ELEMS_PER_THREAD = HEAD_SIZE / THREAD_GROUP_SIZE;
constexpr int NUM_VECS_PER_THREAD = NUM_ELEMS_PER_THREAD / VEC_SIZE;
const int thread_group_idx = thread_idx / THREAD_GROUP_SIZE;
const int thread_group_offset = thread_idx % THREAD_GROUP_SIZE;
// Load the query to registers.
// Each thread in a thread group has a different part of the query.
// For example, if the the thread group size is 4, then the first thread in
// the group has 0, 4, 8, ... th vectors of the query, and the second thread
// has 1, 5, 9, ... th vectors of the query, and so on. NOTE(woosuk): Because
// q is split from a qkv tensor, it may not be contiguous.
const scalar_t* q_ptr = q + seq_idx * q_stride + head_idx * HEAD_SIZE;
__shared__ Q_vec q_vecs[THREAD_GROUP_SIZE][NUM_VECS_PER_THREAD];
#pragma unroll
for (int i = thread_group_idx; i < NUM_VECS_PER_THREAD;
i += NUM_THREAD_GROUPS) {
const int vec_idx = thread_group_offset + i * THREAD_GROUP_SIZE;
q_vecs[thread_group_offset][i] =
*reinterpret_cast<const Q_vec*>(q_ptr + vec_idx * VEC_SIZE);
}
__syncthreads(); // TODO(naed90): possible speedup if this is replaced with a
// memory wall right before we use q_vecs
// Memory planning.
extern __shared__ char shared_mem[];
// NOTE(woosuk): We use FP32 for the softmax logits for better accuracy.
float* logits = reinterpret_cast<float*>(shared_mem);
// Workspace for reduction.
__shared__ float red_smem[2 * NUM_WARPS];
// x == THREAD_GROUP_SIZE * VEC_SIZE
// Each thread group fetches x elements from the key at a time.
constexpr int x = 16 / sizeof(cache_t);
float qk_max = -FLT_MAX;
// Iterate over the key blocks.
// Each warp fetches a block of keys for each iteration.
// Each thread group in a warp fetches a key from the block, and computes
// dot product with the query.
const int* block_table = block_tables + seq_idx * max_num_blocks_per_seq;
// blocksparse specific vars
int bs_block_offset;
int q_bs_block_id;
if constexpr (IS_BLOCK_SPARSE) {
// const int num_blocksparse_blocks = DIVIDE_ROUND_UP(seq_len,
// blocksparse_block_size);
q_bs_block_id = (seq_len - 1) / blocksparse_block_size;
if (blocksparse_head_sliding_step >= 0)
// sliding on q heads
bs_block_offset =
(tp_rank * num_heads + head_idx) * blocksparse_head_sliding_step + 1;
else
// sliding on kv heads
bs_block_offset = (tp_rank * num_kv_heads + kv_head_idx) *
(-blocksparse_head_sliding_step) +
1;
}
for (int block_idx = start_block_idx + warp_idx; block_idx < end_block_idx;
block_idx += NUM_WARPS) {
// NOTE(woosuk): The block number is stored in int32. However, we cast it to
// int64 because int32 can lead to overflow when this variable is multiplied
// by large numbers (e.g., kv_block_stride).
// For blocksparse attention: skip computation on blocks that are not
// attended
if constexpr (IS_BLOCK_SPARSE) {
const int k_bs_block_id = block_idx * BLOCK_SIZE / blocksparse_block_size;
const bool is_remote =
((k_bs_block_id + bs_block_offset) % blocksparse_vert_stride == 0);
const bool is_local =
(k_bs_block_id > q_bs_block_id - blocksparse_local_blocks);
if (!is_remote && !is_local) {
for (int i = 0; i < NUM_TOKENS_PER_THREAD_GROUP; i++) {
const int physical_block_offset =
(thread_group_idx + i * WARP_SIZE) % BLOCK_SIZE;
const int token_idx = block_idx * BLOCK_SIZE + physical_block_offset;
if (thread_group_offset == 0) {
// NOTE(linxihui): assign very large number to skipped tokens to
// avoid contribution to the sumexp softmax normalizer. This will
// not be used at computing sum(softmax*v) as the blocks will be
// skipped.
logits[token_idx - start_token_idx] = -FLT_MAX;
}
}
continue;
}
}
const int64_t physical_block_number =
static_cast<int64_t>(block_table[block_idx]);
// Load a key to registers.
// Each thread in a thread group has a different part of the key.
// For example, if the the thread group size is 4, then the first thread in
// the group has 0, 4, 8, ... th vectors of the key, and the second thread
// has 1, 5, 9, ... th vectors of the key, and so on.
for (int i = 0; i < NUM_TOKENS_PER_THREAD_GROUP; i++) {
const int physical_block_offset =
(thread_group_idx + i * WARP_SIZE) % BLOCK_SIZE;
const int token_idx = block_idx * BLOCK_SIZE + physical_block_offset;
K_vec k_vecs[NUM_VECS_PER_THREAD];
#pragma unroll #pragma unroll
for (int j = 0; j < NUM_VECS_PER_THREAD; j++) { for (int j = 0; j < NUM_VECS_PER_THREAD; j++) {
const cache_t* k_ptr = const cache_t* k_ptr =
...@@ -868,15 +428,10 @@ __device__ void paged_attention_kernel_v2( ...@@ -868,15 +428,10 @@ __device__ void paged_attention_kernel_v2(
v_vec_ptr[j] = token_idx + j < seq_len ? v_vec_ptr[j] : zero_value; v_vec_ptr[j] = token_idx + j < seq_len ? v_vec_ptr[j] : zero_value;
} }
} }
if constexpr(big_seq){
v_pk_fma_f16x8(accs[i],logits_vec,v_vec);
}
else{
accs[i] += dot(logits_vec, v_vec); accs[i] += dot(logits_vec, v_vec);
} }
} }
} }
}
// Perform reduction within each warp. // Perform reduction within each warp.
#pragma unroll #pragma unroll
...@@ -961,7 +516,7 @@ __global__ void paged_attention_v1_kernel( ...@@ -961,7 +516,7 @@ __global__ void paged_attention_v1_kernel(
const float kv_scale, const int tp_rank, const int blocksparse_local_blocks, const float kv_scale, const int tp_rank, const int blocksparse_local_blocks,
const int blocksparse_vert_stride, const int blocksparse_block_size, const int blocksparse_vert_stride, const int blocksparse_block_size,
const int blocksparse_head_sliding_step) { const int blocksparse_head_sliding_step) {
paged_attention_kernel_v1<scalar_t, cache_t, HEAD_SIZE, BLOCK_SIZE, NUM_THREADS, paged_attention_kernel<scalar_t, cache_t, HEAD_SIZE, BLOCK_SIZE, NUM_THREADS,
KV_DTYPE, IS_BLOCK_SPARSE>( KV_DTYPE, IS_BLOCK_SPARSE>(
/* exp_sums */ nullptr, /* max_logits */ nullptr, out, q, k_cache, /* exp_sums */ nullptr, /* max_logits */ nullptr, out, q, k_cache,
v_cache, num_kv_heads, scale, block_tables, seq_lens, v_cache, num_kv_heads, scale, block_tables, seq_lens,
...@@ -975,7 +530,7 @@ __global__ void paged_attention_v1_kernel( ...@@ -975,7 +530,7 @@ __global__ void paged_attention_v1_kernel(
template <typename scalar_t, typename cache_t, int HEAD_SIZE, int BLOCK_SIZE, template <typename scalar_t, typename cache_t, int HEAD_SIZE, int BLOCK_SIZE,
int NUM_THREADS, vllm::Fp8KVCacheDataType KV_DTYPE, int NUM_THREADS, vllm::Fp8KVCacheDataType KV_DTYPE,
bool IS_BLOCK_SPARSE, bool IS_BLOCK_SPARSE,
int PARTITION_SIZE,bool big_seq=false> int PARTITION_SIZE>
__global__ void paged_attention_v2_kernel( __global__ void paged_attention_v2_kernel(
float* __restrict__ exp_sums, // [num_seqs, num_heads, max_num_partitions] float* __restrict__ exp_sums, // [num_seqs, num_heads, max_num_partitions]
float* __restrict__ max_logits, // [num_seqs, num_heads, float* __restrict__ max_logits, // [num_seqs, num_heads,
...@@ -997,8 +552,8 @@ __global__ void paged_attention_v2_kernel( ...@@ -997,8 +552,8 @@ __global__ void paged_attention_v2_kernel(
const float kv_scale, const int tp_rank, const int blocksparse_local_blocks, const float kv_scale, const int tp_rank, const int blocksparse_local_blocks,
const int blocksparse_vert_stride, const int blocksparse_block_size, const int blocksparse_vert_stride, const int blocksparse_block_size,
const int blocksparse_head_sliding_step) { const int blocksparse_head_sliding_step) {
paged_attention_kernel_v2<scalar_t, cache_t, HEAD_SIZE, BLOCK_SIZE, NUM_THREADS, paged_attention_kernel<scalar_t, cache_t, HEAD_SIZE, BLOCK_SIZE, NUM_THREADS,
KV_DTYPE, IS_BLOCK_SPARSE, PARTITION_SIZE, big_seq>( KV_DTYPE, IS_BLOCK_SPARSE, PARTITION_SIZE>(
exp_sums, max_logits, tmp_out, q, k_cache, v_cache, num_kv_heads, scale, exp_sums, max_logits, tmp_out, q, k_cache, v_cache, num_kv_heads, scale,
block_tables, seq_lens, max_num_blocks_per_seq, alibi_slopes, q_stride, block_tables, seq_lens, max_num_blocks_per_seq, alibi_slopes, q_stride,
kv_block_stride, kv_head_stride, kv_scale, tp_rank, kv_block_stride, kv_head_stride, kv_scale, tp_rank,
...@@ -1273,7 +828,7 @@ void paged_attention_v1( ...@@ -1273,7 +828,7 @@ void paged_attention_v1(
#define LAUNCH_PAGED_ATTENTION_V2(HEAD_SIZE) \ #define LAUNCH_PAGED_ATTENTION_V2(HEAD_SIZE) \
vllm::paged_attention_v2_kernel<T, CACHE_T, HEAD_SIZE, BLOCK_SIZE, \ vllm::paged_attention_v2_kernel<T, CACHE_T, HEAD_SIZE, BLOCK_SIZE, \
NUM_THREADS, KV_DTYPE, IS_BLOCK_SPARSE, \ NUM_THREADS, KV_DTYPE, IS_BLOCK_SPARSE, \
PARTITION_SIZE,big_seq> \ PARTITION_SIZE> \
<<<grid, block, shared_mem_size, stream>>>( \ <<<grid, block, shared_mem_size, stream>>>( \
exp_sums_ptr, max_logits_ptr, tmp_out_ptr, query_ptr, key_cache_ptr, \ exp_sums_ptr, max_logits_ptr, tmp_out_ptr, query_ptr, key_cache_ptr, \
value_cache_ptr, num_kv_heads, scale, block_tables_ptr, \ value_cache_ptr, num_kv_heads, scale, block_tables_ptr, \
...@@ -1287,17 +842,6 @@ void paged_attention_v1( ...@@ -1287,17 +842,6 @@ void paged_attention_v1(
out_ptr, exp_sums_ptr, max_logits_ptr, tmp_out_ptr, seq_lens_ptr, \ out_ptr, exp_sums_ptr, max_logits_ptr, tmp_out_ptr, seq_lens_ptr, \
max_num_partitions); max_num_partitions);
#define BOOL_SWITCH(COND, CONST_NAME, ...) \
[&] { \
if (COND) { \
constexpr static bool CONST_NAME = true; \
return __VA_ARGS__(); \
} else { \
constexpr static bool CONST_NAME = false; \
return __VA_ARGS__(); \
} \
}()
template <typename T, typename CACHE_T, int BLOCK_SIZE, template <typename T, typename CACHE_T, int BLOCK_SIZE,
vllm::Fp8KVCacheDataType KV_DTYPE, bool IS_BLOCK_SPARSE, vllm::Fp8KVCacheDataType KV_DTYPE, bool IS_BLOCK_SPARSE,
int NUM_THREADS = 256, int PARTITION_SIZE = 512> int NUM_THREADS = 256, int PARTITION_SIZE = 512>
...@@ -1352,7 +896,6 @@ void paged_attention_v2_launcher( ...@@ -1352,7 +896,6 @@ void paged_attention_v2_launcher(
dim3 block(NUM_THREADS); dim3 block(NUM_THREADS);
const at::cuda::OptionalCUDAGuard device_guard(device_of(query)); const at::cuda::OptionalCUDAGuard device_guard(device_of(query));
const cudaStream_t stream = at::cuda::getCurrentCUDAStream(); const cudaStream_t stream = at::cuda::getCurrentCUDAStream();
BOOL_SWITCH(num_seqs>=16,big_seq,[&]{
switch (head_size) { switch (head_size) {
// NOTE(woosuk): To reduce the compilation time, we only compile for the // NOTE(woosuk): To reduce the compilation time, we only compile for the
// head sizes that we use in the model. However, we can easily extend this // head sizes that we use in the model. However, we can easily extend this
...@@ -1382,7 +925,6 @@ void paged_attention_v2_launcher( ...@@ -1382,7 +925,6 @@ void paged_attention_v2_launcher(
TORCH_CHECK(false, "Unsupported head size: ", head_size); TORCH_CHECK(false, "Unsupported head size: ", head_size);
break; break;
} }
});
} }
#define CALL_V2_LAUNCHER(T, CACHE_T, BLOCK_SIZE, KV_DTYPE, IS_BLOCK_SPARSE) \ #define CALL_V2_LAUNCHER(T, CACHE_T, BLOCK_SIZE, KV_DTYPE, IS_BLOCK_SPARSE) \
......
...@@ -26,75 +26,19 @@ ...@@ -26,75 +26,19 @@
namespace vllm { namespace vllm {
inline __device__ void v_dot2_f32_f16(float& a, const uint32_t & b,const uint32_t & c) { // Q*K^T operation.
asm volatile("v_dot2_f32_f16 %0, %1, %2, %0;": "=v"(a): "v"(b), "v"(c), "0"(a));
}
inline __device__ void v_pk_fma_f16(uint32_t& a, const uint32_t & b,const uint32_t & c){
asm volatile("v_pk_fma_f16 %0, %1, %2, %3;": "=v"(a) : "v"(b), "v"(c), "v"(a));
}
inline __device__ void v_dot2_f32_f16(float& a,const uint2 & b,const uint2 & c) {
v_dot2_f32_f16(a, b.x, c.x);
v_dot2_f32_f16(a, b.y, c.y);
}
inline __device__ void v_dot2_f32_f16(float& a,const uint4 & b,const uint4 & c) {
v_dot2_f32_f16(a, b.x, c.x);
v_dot2_f32_f16(a, b.y, c.y);
v_dot2_f32_f16(a, b.z, c.z);
v_dot2_f32_f16(a, b.w, c.w);
}
inline __device__ float add_half2(uint32_t a){
union {
uint32_t u32;
half u16[2];
} tmp;
tmp.u32=a;
return static_cast<float>(tmp.u16[0]+tmp.u16[1]);
}
inline __device__ void v_pk_fma_f16x8(float& a,const uint4 & b,const uint4 & c) {
uint32_t tmp = mul<uint32_t, uint32_t, uint32_t>(b.x,c.x);
v_pk_fma_f16(tmp,b.y,c.y);
v_pk_fma_f16(tmp,b.z,c.z);
v_pk_fma_f16(tmp,b.w,c.w);
a+=add_half2(tmp);
}
// Q*K^T operation. fp16
// template <int THREAD_GROUP_SIZE, typename Vec, int N, typename scalar_t, std::enable_if_t<std::is_same<scalar_t, uint16_t>::value, int> = 0>
template <int THREAD_GROUP_SIZE, typename Vec, int N> template <int THREAD_GROUP_SIZE, typename Vec, int N>
inline __device__ float qk_dot_(const Vec (&q)[N], const Vec (&k)[N]) { inline __device__ float qk_dot_(const Vec (&q)[N], const Vec (&k)[N]) {
float qk =0;
// Compute the parallel products for Q*K^T (treat vector lanes separately).
#pragma unroll
for (int ii = 0; ii < N; ++ii) {
v_dot2_f32_f16(qk,q[ii],k[ii]);
}
// Finalize the reduction across lanes.
#pragma unroll
for (int mask = THREAD_GROUP_SIZE / 2; mask >= 1; mask /= 2) {
qk += VLLM_SHFL_XOR_SYNC(qk, mask);
}
return qk;
}
// Q*K^T operation. //bf16
// template <int THREAD_GROUP_SIZE, typename Vec, int N, typename scalar_t, std::enable_if_t<!std::is_same<scalar_t, uint16_t>::value, int> = 0>
template <int THREAD_GROUP_SIZE, typename Vec, int N>
inline __device__ float qk_dot_v1(const Vec (&q)[N], const Vec (&k)[N]) {
using A_vec = typename FloatVec<Vec>::Type; using A_vec = typename FloatVec<Vec>::Type;
// Compute the parallel products for Q*K^T (treat vector lanes separately).
A_vec qk_vec = mul<A_vec, Vec, Vec>(q[0], k[0]); A_vec qk_vec = mul<A_vec, Vec, Vec>(q[0], k[0]);
#pragma unroll #pragma unroll
for (int ii = 1; ii < N; ++ii) { for (int ii = 1; ii < N; ++ii) {
qk_vec = fma(q[ii], k[ii], qk_vec); qk_vec = fma(q[ii], k[ii], qk_vec);
} }
float qk = sum(qk_vec);
// Finalize the reduction across lanes. // Finalize the reduction across lanes.
float qk = sum(qk_vec);
#pragma unroll #pragma unroll
for (int mask = THREAD_GROUP_SIZE / 2; mask >= 1; mask /= 2) { for (int mask = THREAD_GROUP_SIZE / 2; mask >= 1; mask /= 2) {
qk += VLLM_SHFL_XOR_SYNC(qk, mask); qk += VLLM_SHFL_XOR_SYNC(qk, mask);
...@@ -102,17 +46,12 @@ inline __device__ float qk_dot_v1(const Vec (&q)[N], const Vec (&k)[N]) { ...@@ -102,17 +46,12 @@ inline __device__ float qk_dot_v1(const Vec (&q)[N], const Vec (&k)[N]) {
return qk; return qk;
} }
template <typename T, int THREAD_GROUP_SIZE> template <typename T, int THREAD_GROUP_SIZE>
struct Qk_dot { struct Qk_dot {
template <typename Vec, int N> template <typename Vec, int N>
static inline __device__ float dot(const Vec (&q)[N], const Vec (&k)[N]) { static inline __device__ float dot(const Vec (&q)[N], const Vec (&k)[N]) {
return qk_dot_<THREAD_GROUP_SIZE>(q, k); return qk_dot_<THREAD_GROUP_SIZE>(q, k);
} }
template <typename Vec, int N>
static inline __device__ float dot_v1(const Vec (&q)[N], const Vec (&k)[N]) {
return qk_dot_v1<THREAD_GROUP_SIZE>(q, k);
}
}; };
} // namespace vllm } // namespace vllm
\ No newline at end of file
#include <torch/all.h> #include <torch/all.h>
#include <ATen/cuda/CUDAContext.h> #include <ATen/cuda/CUDAContext.h>
#include <c10/cuda/CUDAGuard.h> #include <c10/cuda/CUDAGuard.h>
#include <ATen/native/cuda/MemoryAccess.cuh>
#include <c10/cuda/CUDAMathCompat.h>
#include <ATen/AccumulateType.h>
#include <THC/THCDeviceUtils.cuh>
#include "dispatch_utils.h" #include "dispatch_utils.h"
#include "reduction_utils.cuh" #include "reduction_utils.cuh"
#ifndef USE_ROCM #ifndef USE_ROCM
...@@ -291,149 +288,22 @@ fused_add_rms_norm_kernel( ...@@ -291,149 +288,22 @@ fused_add_rms_norm_kernel(
} // namespace vllm } // namespace vllm
template <typename T,int reducesize=C10_WARP_SIZE>
__inline__ __device__ T WarpReduceSum_NEW(T val) {
#pragma unroll
for (int offset = reducesize/2; offset > 0; offset >>= 1) {
val += WARP_SHFL_DOWN(val, offset);
}
return val;
}
template <typename T,int block_size=512>
__inline__ __device__ T BlockReduceSum_NEW(T val, T* shared) {
constexpr int share_size=block_size/C10_WARP_SIZE;
val = WarpReduceSum_NEW<T>(val);
if constexpr(block_size==C10_WARP_SIZE)
{
return val;
}
else{
const int lid = threadIdx.x % C10_WARP_SIZE;
const int wid = threadIdx.x / C10_WARP_SIZE;
__syncthreads();
if (lid == 0&&wid<share_size) {
shared[wid] = val;
}
__syncthreads();
if (wid == 0&&lid<share_size) {
val = WarpReduceSum_NEW<T,share_size>(shared[lid]);
}
return val;
}
}
template <typename scalar_t,typename T_ACC,int Vec=4,int block_size=512>
__global__ void fused_add_rms_kernel_eval(scalar_t* input,scalar_t* residual,scalar_t* gamma,int cols,T_ACC eps)
{
constexpr int share_size=block_size/C10_WARP_SIZE;
__shared__ T_ACC val_shared[share_size];
__shared__ T_ACC s_rstd;
T_ACC val=0;
int i=blockIdx.x;
int j=threadIdx.x;
int tcol=cols/Vec;
if(j>=tcol)return;
using LoadT = at::native::memory::aligned_vector<scalar_t, Vec>;
scalar_t intput_vec[Vec];
scalar_t residual_vec[Vec];
T_ACC trstd;
int idx = i * tcol + j;
idx*=Vec;
*(LoadT*)intput_vec = *(LoadT*)(input+idx);
*(LoadT*)residual_vec = *(LoadT*)(residual+idx);
#pragma unroll
for (int ii = 0; ii < Vec; ii++) {
residual_vec[ii]+=intput_vec[ii];
val += static_cast<T_ACC>(residual_vec[ii])*static_cast<T_ACC>(residual_vec[ii]);
}
val = BlockReduceSum_NEW<T_ACC,block_size>(val,val_shared);
if (j == 0) s_rstd=c10::cuda::compat::rsqrt(val/cols + eps);
__syncthreads();
trstd=s_rstd;
#pragma unroll
for(int ii=0;ii<Vec;ii++){
int jj=j*Vec+ii;
intput_vec[ii] = static_cast<T_ACC>(residual_vec[ii]) * trstd * static_cast<T_ACC>(gamma[jj]);
}
*(LoadT*)(residual+idx)=*(LoadT*)residual_vec;
*(LoadT*)(input+idx)=*(LoadT*)intput_vec;
}
template <typename scalar_t,typename T_ACC,int Vec=4,int block_size=512>
__global__ void fused_rms_kernel_eval(scalar_t* input,scalar_t* output,scalar_t* gamma,int cols,T_ACC eps)
{
constexpr int share_size=block_size/C10_WARP_SIZE;
__shared__ T_ACC val_shared[share_size];
__shared__ T_ACC s_rstd;
T_ACC val=0;
int i=blockIdx.x;
int j=threadIdx.x;
int tcol=cols/Vec;
if(j>=tcol)return;
using LoadT = at::native::memory::aligned_vector<scalar_t, Vec>;
scalar_t intput_vec[Vec];
T_ACC trstd;
int idx = i * tcol + j;
idx*=Vec;
*(LoadT*)intput_vec = *(LoadT*)(input+idx);
#pragma unroll
for (int ii = 0; ii < Vec; ii++) {
val += static_cast<T_ACC>(intput_vec[ii])*static_cast<T_ACC>(intput_vec[ii]);
}
val = BlockReduceSum_NEW<T_ACC,block_size>(val,val_shared);
if (j == 0) s_rstd=c10::cuda::compat::rsqrt(val/cols + eps);
__syncthreads();
trstd=s_rstd;
#pragma unroll
for(int ii=0;ii<Vec;ii++){
int jj=j*Vec+ii;
intput_vec[ii] = static_cast<T_ACC>(intput_vec[ii]) * trstd * static_cast<T_ACC>(gamma[jj]);
}
*(LoadT*)(output+idx)=*(LoadT*)intput_vec;
}
void rms_norm(torch::Tensor& out, // [..., hidden_size] void rms_norm(torch::Tensor& out, // [..., hidden_size]
torch::Tensor& input, // [..., hidden_size] torch::Tensor& input, // [..., hidden_size]
torch::Tensor& weight, // [hidden_size] torch::Tensor& weight, // [hidden_size]
double epsilon) { double epsilon) {
int hidden_size = input.size(-1); int hidden_size = input.size(-1);
int num_tokens = input.numel() / hidden_size; int num_tokens = input.numel() / hidden_size;
const at::cuda::OptionalCUDAGuard device_guard(device_of(input));
const cudaStream_t stream = at::cuda::getCurrentCUDAStream();
if(hidden_size%16==0&&hidden_size>=2048&&hidden_size<=8192){
AT_DISPATCH_FLOATING_TYPES_AND2(
at::ScalarType::Half,
at::ScalarType::BFloat16,
input.scalar_type(),
"fused_add_rms_norm_kernel",
[&] {
using T_ACC = at::acc_type<scalar_t, true>;
T_ACC eps = epsilon;
scalar_t* self_data = input.data_ptr<scalar_t>();
scalar_t* out_data =out.data_ptr<scalar_t>();
scalar_t* weight_data=weight.data_ptr<scalar_t>();
if(hidden_size==2048){
fused_rms_kernel_eval<scalar_t,T_ACC,2,1024><<<num_tokens, 1024, 0, stream>>>(self_data,out_data,weight_data,hidden_size,eps);
}
else if(hidden_size<=4096){
fused_rms_kernel_eval<scalar_t,T_ACC,4,1024><<<num_tokens, 1024, 0, stream>>>(self_data,out_data,weight_data,hidden_size,eps);
}
else{
fused_rms_kernel_eval<scalar_t,T_ACC,8,1024><<<num_tokens, 1024, 0, stream>>>(self_data,out_data,weight_data,hidden_size,eps);
}
});
}
else{
dim3 grid(num_tokens); dim3 grid(num_tokens);
dim3 block(std::min(hidden_size, 1024)); dim3 block(std::min(hidden_size, 1024));
const at::cuda::OptionalCUDAGuard device_guard(device_of(input));
const cudaStream_t stream = at::cuda::getCurrentCUDAStream();
VLLM_DISPATCH_FLOATING_TYPES(input.scalar_type(), "rms_norm_kernel", [&] { VLLM_DISPATCH_FLOATING_TYPES(input.scalar_type(), "rms_norm_kernel", [&] {
vllm::rms_norm_kernel<scalar_t><<<grid, block, 0, stream>>>( vllm::rms_norm_kernel<scalar_t><<<grid, block, 0, stream>>>(
out.data_ptr<scalar_t>(), input.data_ptr<scalar_t>(), out.data_ptr<scalar_t>(), input.data_ptr<scalar_t>(),
weight.data_ptr<scalar_t>(), epsilon, num_tokens, hidden_size); weight.data_ptr<scalar_t>(), epsilon, num_tokens, hidden_size);
}); });
}
} }
#define LAUNCH_FUSED_ADD_RMS_NORM(width) \ #define LAUNCH_FUSED_ADD_RMS_NORM(width) \
...@@ -446,40 +316,13 @@ void rms_norm(torch::Tensor& out, // [..., hidden_size] ...@@ -446,40 +316,13 @@ void rms_norm(torch::Tensor& out, // [..., hidden_size]
num_tokens, hidden_size); \ num_tokens, hidden_size); \
}); });
void fused_add_rms_norm(torch::Tensor& input, // [..., hidden_size] void fused_add_rms_norm(torch::Tensor& input, // [..., hidden_size]
torch::Tensor& residual, // [..., hidden_size] torch::Tensor& residual, // [..., hidden_size]
torch::Tensor& weight, // [hidden_size] torch::Tensor& weight, // [hidden_size]
double epsilon) { double epsilon) {
int hidden_size = input.size(-1); int hidden_size = input.size(-1);
int num_tokens = input.numel() / hidden_size; int num_tokens = input.numel() / hidden_size;
const at::cuda::OptionalCUDAGuard device_guard(device_of(input));
const cudaStream_t stream = at::cuda::getCurrentCUDAStream();
if(hidden_size%16==0&&hidden_size>=2048&&hidden_size<=8192){
AT_DISPATCH_FLOATING_TYPES_AND2(
at::ScalarType::Half,
at::ScalarType::BFloat16,
input.scalar_type(),
"fused_add_rms_norm_kernel",
[&] {
using T_ACC = at::acc_type<scalar_t, true>;
T_ACC eps = epsilon;
scalar_t* self_data = input.data_ptr<scalar_t>();
scalar_t* other_data =residual.data_ptr<scalar_t>();
scalar_t* weight_data=weight.data_ptr<scalar_t>();
if(hidden_size==2048){
fused_add_rms_kernel_eval<scalar_t,T_ACC,2,1024><<<num_tokens, 1024, 0, stream>>>(self_data,other_data,weight_data,hidden_size,eps);
}
else if(hidden_size<=4096){
fused_add_rms_kernel_eval<scalar_t,T_ACC,4,1024><<<num_tokens, 1024, 0, stream>>>(self_data,other_data,weight_data,hidden_size,eps);
}
else{
fused_add_rms_kernel_eval<scalar_t,T_ACC,8,1024><<<num_tokens, 1024, 0, stream>>>(self_data,other_data,weight_data,hidden_size,eps);
}
});
}
else{
dim3 grid(num_tokens); dim3 grid(num_tokens);
/* This kernel is memory-latency bound in many scenarios. /* This kernel is memory-latency bound in many scenarios.
When num_tokens is large, a smaller block size allows When num_tokens is large, a smaller block size allows
...@@ -487,6 +330,8 @@ void fused_add_rms_norm(torch::Tensor& input, // [..., hidden_size] ...@@ -487,6 +330,8 @@ void fused_add_rms_norm(torch::Tensor& input, // [..., hidden_size]
hiding on global mem ops. */ hiding on global mem ops. */
const int max_block_size = (num_tokens < 256) ? 1024 : 256; const int max_block_size = (num_tokens < 256) ? 1024 : 256;
dim3 block(std::min(hidden_size, max_block_size)); dim3 block(std::min(hidden_size, max_block_size));
const at::cuda::OptionalCUDAGuard device_guard(device_of(input));
const cudaStream_t stream = at::cuda::getCurrentCUDAStream();
/*If the tensor types are FP16/BF16, try to use the optimized kernel /*If the tensor types are FP16/BF16, try to use the optimized kernel
with packed + vectorized ops. with packed + vectorized ops.
Max optimization is achieved with a width-8 vector of FP16/BF16s Max optimization is achieved with a width-8 vector of FP16/BF16s
...@@ -504,5 +349,4 @@ void fused_add_rms_norm(torch::Tensor& input, // [..., hidden_size] ...@@ -504,5 +349,4 @@ void fused_add_rms_norm(torch::Tensor& input, // [..., hidden_size]
} else { } else {
LAUNCH_FUSED_ADD_RMS_NORM(0); LAUNCH_FUSED_ADD_RMS_NORM(0);
} }
}
} }
\ No newline at end of file
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