@triton.jit
def kernel_paged_attention_2d(
output_ptr, # [num_tokens, num_query_heads, head_size]
query_ptr, # [num_tokens, num_query_heads, head_size]
key_cache_ptr, # [num_blks, num_kv_heads, head_size // x, blk_size, x]
value_cache_ptr, # [num_blks, num_kv_heads, head_size, blk_size]
block_tables_ptr, # [num_seqs, max_num_blocks_per_seq]
seq_lens_ptr, # [num_seqs]
alibi_slopes_ptr, # [num_query_heads]
scale, # float32
k_scale, # float32
v_scale, # float32
num_query_heads: tl.constexpr, # int
num_queries_per_kv: tl.constexpr, # int
num_queries_per_kv_padded: tl.constexpr, # int
block_table_stride: tl.int64, # int
query_stride_0: tl.int64, # int
query_stride_1: tl.int64, # int, should be equal to head_size
output_stride_0: tl.int64, # int
output_stride_1: tl.int64, # int, should be equal to head_size
BLOCK_SIZE: tl.constexpr, # int
HEAD_SIZE: tl.constexpr, # int
HEAD_SIZE_PADDED: tl.constexpr, # int, must be power of 2
USE_ALIBI_SLOPES: tl.constexpr, # bool
SLIDING_WINDOW: tl.constexpr, # int
x: tl.constexpr, # int
stride_k_cache_0: tl.int64, # int
stride_k_cache_1: tl.int64, # int
stride_k_cache_2: tl.int64, # int
stride_k_cache_3: tl.int64, # int
stride_k_cache_4: tl.int64, # int
stride_v_cache_0: tl.int64, # int
stride_v_cache_1: tl.int64, # int
stride_v_cache_2: tl.int64, # int
stride_v_cache_3: tl.int64, # int
filter_by_query_len: tl.constexpr, # bool
query_start_len_ptr, # [num_seqs+1]
):
seq_idx = tl.program_id(0)
kv_head_idx = tl.program_id(1)
if filter_by_query_len:
cur_batch_in_all_start_index = tl.load(query_start_len_ptr + seq_idx)
cur_batch_in_all_stop_index = tl.load(query_start_len_ptr + seq_idx +
1)
cur_batch_query_len = cur_batch_in_all_stop_index \
- cur_batch_in_all_start_index
if cur_batch_query_len > 1:
return
else:
cur_batch_in_all_start_index = seq_idx
query_head_idx = kv_head_idx * num_queries_per_kv + tl.arange(
0, num_queries_per_kv_padded)
query_offset = (cur_batch_in_all_start_index * query_stride_0 +
query_head_idx[:, None] * query_stride_1)
head_mask = query_head_idx < (kv_head_idx + 1) * num_queries_per_kv
head_mask = head_mask & (query_head_idx < num_query_heads)
dim_mask = tl.where(tl.arange(0, HEAD_SIZE_PADDED) < HEAD_SIZE, 1,
0).to(tl.int1)
# Q : (num_queries_per_kv, HEAD_SIZE,)
Q = tl.load(
query_ptr + query_offset + tl.arange(0, HEAD_SIZE_PADDED)[None, :],
mask=dim_mask[None, :] & head_mask[:, None],
other=0.0,
)
block_table_offset = seq_idx * block_table_stride
M = tl.full([num_queries_per_kv_padded], float("-inf"), dtype=tl.float32)
L = tl.full([num_queries_per_kv_padded], 1.0, dtype=tl.float32)
acc = tl.zeros([num_queries_per_kv_padded, HEAD_SIZE_PADDED],
dtype=tl.float32)
# sequence len for this particular sequence
seq_len = tl.load(seq_lens_ptr + seq_idx)
# alibi slope for this head
if USE_ALIBI_SLOPES:
alibi_slope = tl.load(alibi_slopes_ptr + query_head_idx,
mask=head_mask,
other=0.0)
num_blocks = cdiv_fn(seq_len, BLOCK_SIZE)
# iterate through tiles
for j in range(0, num_blocks):
physical_block_idx = tl.load(block_tables_ptr + block_table_offset + j)
offs_n = tl.arange(0, BLOCK_SIZE)
offs_d = tl.arange(0, HEAD_SIZE_PADDED)
v_offset = (physical_block_idx * stride_v_cache_0 +
kv_head_idx * stride_v_cache_1 +
offs_d[None, :] * stride_v_cache_2 +
offs_n[:, None] * stride_v_cache_3)
k_offset = (physical_block_idx * stride_k_cache_0 +
kv_head_idx * stride_k_cache_1 +
(offs_d[:, None] // x) * stride_k_cache_2 +
offs_n[None, :] * stride_k_cache_3 +
(offs_d[:, None] % x) * stride_k_cache_4)
# K : (HEAD_SIZE, BLOCK_SIZE)
K_load = tl.load(key_cache_ptr + k_offset,
mask=dim_mask[:, None],
other=0.0)
if K_load.dtype.is_fp8():
K = (K_load.to(tl.float32) * tl.load(k_scale)).to(Q.dtype)
else:
K = K_load
# V : (BLOCK_SIZE, HEAD_SIZE)
V_load = tl.load(value_cache_ptr + v_offset,
mask=dim_mask[None, :],
other=0.0)
if V_load.dtype.is_fp8():
V = (V_load.to(tl.float32) * tl.load(v_scale)).to(Q.dtype)
else:
V = V_load
seq_offset = j * BLOCK_SIZE + tl.arange(0, BLOCK_SIZE)
boundary = tl.full([BLOCK_SIZE], seq_len, dtype=tl.int32)
seq_mask = seq_offset[None, :] < boundary
# S : (num_queries_per_kv, BLOCK_SIZE,)
S = tl.where(head_mask[:, None] & seq_mask, 0.0,
float("-inf")).to(tl.float32)
S += scale * tl.dot(Q, K)
context_len = seq_len - 1
if SLIDING_WINDOW > 0:
S = tl.where((context_len - seq_offset) < SLIDING_WINDOW, S,
-10000)
if USE_ALIBI_SLOPES:
S += alibi_slope[:, None] * (seq_offset - context_len)
# compute running maximum
# m_j : (num_queries_per_kv,)
m_j = tl.maximum(M, tl.max(S, axis=1))
# P : (num_queries_per_kv, BLOCK_SIZE,)
P = tl.exp(S - m_j[:, None])
# l_j : (num_queries_per_kv,)
l_j = tl.sum(P, axis=1)
# alpha : (num_queries_per_kv, )
alpha = tl.exp(M - m_j)
# acc : (num_queries_per_kv, BLOCK_SIZE,)
acc = acc * alpha[:, None]
# update constants
L = L * alpha + l_j
M = m_j
# acc : (num_queries_per_kv, BLOCK_SIZE,)
acc += tl.dot(P.to(V.dtype), V)
# epilogue
acc = acc / L[:, None]
output_offset = (cur_batch_in_all_start_index * output_stride_0 +
query_head_idx * output_stride_1)
tl.store(
output_ptr + output_offset[:, None] +
tl.arange(0, HEAD_SIZE_PADDED)[None, :],
acc,
mask=dim_mask[None, :] & head_mask[:, None],
)