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fla / build /torch-cuda /ops /nsa /parallel.py

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	# Copyright (c) 2023-2026, Songlin Yang, Yu Zhang, Zhiyuan Li
	#
	# This source code is licensed under the MIT license found in the
	# LICENSE file in the root directory of this source tree.
	# For a list of all contributors, visit:
	# https://github.com/fla-org/flash-linear-attention/graphs/contributors

	import warnings

	import torch
	import triton
	import triton.language as tl

	from ...ops.attn.parallel import parallel_attn_bwd_preprocess
	from ...ops.nsa.compression import parallel_nsa_compression
	from ...ops.nsa.utils import _bitonic_merge
	from ...ops.utils import prepare_block_csr, prepare_chunk_indices, prepare_chunk_offsets, prepare_lens, prepare_token_indices
	from ...ops.utils.op import exp, log
	from ...ops.utils.pooling import mean_pooling
	from ...utils import autocast_custom_bwd, autocast_custom_fwd, autotune_cache_kwargs, check_shared_mem, contiguous

	try:
	from flash_attn import flash_attn_func, flash_attn_varlen_func
	except ImportError:
	warnings.warn(
	"Flash Attention is not installed. Please install it via `pip install flash-attn --no-build-isolation`",
	category=ImportWarning,
	)
	flash_attn_func = flash_attn_varlen_func = None


	@triton.heuristics({
	'IS_VARLEN': lambda args: args['cu_seqlens_q'] is not None,
	})
	@triton.autotune(
	configs=[
	triton.Config({}, num_warps=num_warps)
	for num_warps in [1, 2, 4]
	],
	key=['BS', 'BK'],
	**autotune_cache_kwargs,
	)
	@triton.jit
	def parallel_nsa_kernel_topk(
	q,
	k,
	lse,
	scale,
	block_indices,
	cu_seqlens_q,
	cu_seqlens_k,
	token_indices_q,
	chunk_offsets,
	TQ,
	TK,
	H: tl.constexpr,
	HQ: tl.constexpr,
	G: tl.constexpr,
	K: tl.constexpr,
	S: tl.constexpr,
	BC: tl.constexpr,
	BS: tl.constexpr,
	BK: tl.constexpr,
	IS_VARLEN: tl.constexpr,
	):
	i_t, i_bh = tl.program_id(0), tl.program_id(1)
	i_b, i_h = i_bh // H, i_bh % H

	if IS_VARLEN:
	i_n, i_t = tl.load(token_indices_q + i_t * 2).to(tl.int32), tl.load(token_indices_q + i_t * 2 + 1).to(tl.int32)
	bos_q, eos_q = tl.load(cu_seqlens_q + i_n).to(tl.int64), tl.load(cu_seqlens_q + i_n + 1).to(tl.int64)
	bos_k, eos_k = tl.load(cu_seqlens_k + i_n).to(tl.int64), tl.load(cu_seqlens_k + i_n + 1).to(tl.int64)
	TQ = (eos_q - bos_q).to(tl.int32)
	TK = (eos_k - bos_k).to(tl.int32)
	TC = tl.cdiv(TK, BS)
	boc = tl.load(chunk_offsets + i_n).to(tl.int32)
	else:
	bos_q, eos_q = (i_b * TQ).to(tl.int64), (i_b * TQ + TQ).to(tl.int64)
	TC = tl.cdiv(TK, BS)
	boc = i_b * TC
	# boc is the start of the current sequence at [B, TC] dimensions
	p_q = tl.make_block_ptr(q + (bos_q + i_t) * HQ * K, (HQ, K), (K, 1), (i_h * G, 0), (G, BK), (1, 0))
	Q_OFFSET = TK - TQ

	# the Q block is kept in the shared memory throughout the whole kernel
	# [G, BK]
	b_q = tl.load(p_q, boundary_check=(0, 1))
	b_q = (b_q * scale).to(b_q.dtype)

	# number of complete compression blocks visible to the query (q tokens are the last TQ of the sequence)
	NC = (i_t + Q_OFFSET + 1) // BS
	################################
	# 1. lse computation
	################################
	if lse is not None:
	b_lse = tl.load(lse + (bos_q + i_t) * HQ + i_h * G + tl.arange(0, G))
	else:
	# max scores for the current block
	b_m = tl.full([G], float('-inf'), dtype=tl.float32)
	# lse = log(acc) + m
	b_acc = tl.zeros([G], dtype=tl.float32)
	for i_c in range(0, NC, BC):
	o_c = i_c + tl.arange(0, BC)

	p_k = tl.make_block_ptr(k + (boc * H + i_h) * K, (K, TC), (1, H*K), (0, i_c), (BK, BC), (0, 1))
	# [BK, BC]
	b_k = tl.load(p_k, boundary_check=(0, 1))

	# [G, BC]
	b_s = tl.dot(b_q, b_k)
	b_s = tl.where((o_c < NC)[None, :], b_s, float('-inf'))

	# [G]
	b_m, b_mp = tl.maximum(b_m, tl.max(b_s, 1)), b_m
	b_r = exp(b_mp - b_m)
	# [G, BC]
	b_p = exp(b_s - b_m[:, None])
	# [G]
	b_acc = b_acc * b_r + tl.sum(b_p, 1)

	b_mp = b_m
	if NC == 0:
	b_lse = tl.zeros([G], dtype=tl.float32)
	else:
	b_lse = b_m + log(b_acc)

	################################
	# 2. topk selection
	################################
	# [BC]
	b_i = tl.full([BC], -1, dtype=tl.float32)
	o_i = tl.zeros([BC], dtype=tl.int32)
	m_i = tl.arange(0, BC) < BC//2

	IC = (i_t + Q_OFFSET) // BS # Idx of the current query block
	for i_c in range(0, IC + 1, BC): # +1, because the current block might be also included
	o_c = i_c + tl.arange(0, BC)
	p_k = tl.make_block_ptr(k + (boc * H + i_h) * K, (K, TC), (1, H*K), (0, i_c), (BK, BC), (0, 1))
	# [BK, BC]
	b_k = tl.load(p_k, boundary_check=(0, 1))
	# [G, BC]
	b_s = tl.dot(b_q, b_k)
	b_s = tl.where(o_c < IC, b_s, float('-inf'))
	# the 1st and the last 2 blocks are always selected, with normalized score set to 1.0
	b_p = tl.where((o_c == 0) \| ((o_c == IC - 1) \| (o_c == IC)), 1., exp(b_s - b_lse[:, None]))
	# [BC] importance score = sum over the group's heads
	b_i, b_ip = tl.sum(b_p, 0), b_i
	# blocks with index < 0 will be skipped
	o_i, o_ip = tl.where(o_c <= IC, o_c, -1), o_i

	n_dims: tl.constexpr = tl.standard._log2(b_i.shape[0])
	for i in tl.static_range(1, n_dims):
	b_i, o_i = _bitonic_merge(b_i, o_i.to(tl.int32), i, 2, n_dims)

	if i_c != 0:
	b_i, o_i = _bitonic_merge(b_i, o_i.to(tl.int32), n_dims, False, n_dims)
	b_i_new = b_ip * m_i + b_i * (1 - m_i)
	o_i_new = o_ip * m_i + o_i * (1 - m_i)
	b_i, o_i = _bitonic_merge(b_i_new, o_i_new.to(tl.int32), n_dims, True, n_dims)
	else:
	b_i, o_i = _bitonic_merge(b_i, o_i.to(tl.int32), n_dims, True, n_dims)

	m_top = tl.arange(0, BC // S) == 0
	b_top = tl.sum(m_top[:, None] * tl.reshape(o_i, [BC // S, S]), 0)

	p_b = tl.make_block_ptr(block_indices + (bos_q + i_t) * HS, (HS,), (1,), (i_h * S,), (S,), (0,))
	tl.store(p_b, b_top.to(p_b.dtype.element_ty))


	@triton.heuristics({
	'IS_VARLEN': lambda args: args['cu_seqlens_q'] is not None,
	'USE_BLOCK_COUNTS': lambda args: isinstance(args['block_counts'], torch.Tensor),
	})
	@triton.autotune(
	configs=[
	triton.Config({}, num_warps=num_warps, num_stages=num_stages)
	for num_warps in [1, 2, 4, 8]
	for num_stages in [1, 2, 3]
	],
	key=['BS', 'BK', 'BV', 'G'],
	**autotune_cache_kwargs,
	)
	@triton.jit
	def parallel_nsa_fwd_kernel(
	q,
	k,
	v,
	o,
	lse,
	scale,
	block_indices,
	block_counts,
	cu_seqlens_q,
	cu_seqlens_k,
	token_indices_q,
	TQ,
	TK,
	H: tl.constexpr,
	HQ: tl.constexpr,
	G: tl.constexpr,
	K: tl.constexpr,
	V: tl.constexpr,
	S: tl.constexpr,
	BS: tl.constexpr,
	BK: tl.constexpr,
	BV: tl.constexpr,
	IS_VARLEN: tl.constexpr,
	USE_BLOCK_COUNTS: tl.constexpr,
	):
	i_t, i_v, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
	i_b, i_h = i_bh // H, i_bh % H
	# k/v: [B, TK, H, *], q: [B, TQ, HQ, K], block_indices: [B, TQ, H, S], lse: [B, TQ, HQ]; G = HQ // H

	if IS_VARLEN:
	# token_indices_q maps a flattened query to its (sequence index, in-sequence position)
	i_n, i_t = tl.load(token_indices_q + i_t * 2).to(tl.int32), tl.load(token_indices_q + i_t * 2 + 1).to(tl.int32)
	bos_q, eos_q = tl.load(cu_seqlens_q + i_n).to(tl.int64), tl.load(cu_seqlens_q + i_n + 1).to(tl.int64)
	bos_k, eos_k = tl.load(cu_seqlens_k + i_n).to(tl.int64), tl.load(cu_seqlens_k + i_n + 1).to(tl.int64)
	TQ = (eos_q - bos_q).to(tl.int32)
	TK = (eos_k - bos_k).to(tl.int32)
	else:
	bos_q, eos_q = (i_b * TQ).to(tl.int64), (i_b * TQ + TQ).to(tl.int64)
	bos_k, eos_k = (i_b * TK).to(tl.int64), (i_b * TK + TK).to(tl.int64)

	# q tokens are assumed to be the last TQ tokens of the sequence (cached decoding)
	Q_OFFSET = TK - TQ

	k += (bos_k * H + i_h) * K
	v += (bos_k * H + i_h) * V
	block_indices += (bos_q + i_t) * H * S + i_h * S

	# block_counts: [B, TQ, H]
	if USE_BLOCK_COUNTS:
	NS = tl.load(block_counts + (bos_q + i_t) * H + i_h)
	else:
	NS = S

	p_q = tl.make_block_ptr(q + (bos_q + i_t) * HQ * K, (HQ, K), (K, 1), (i_h * G, 0), (G, BK), (1, 0))
	# the Q block is kept in shared memory throughout the kernel
	# [G, BK]
	b_q = tl.load(p_q, boundary_check=(0, 1))
	b_q = (b_q * scale).to(b_q.dtype)

	p_o = tl.make_block_ptr(o + (bos_q + i_t) * HQ * V, (HQ, V), (V, 1), (i_h * G, i_v * BV), (G, BV), (1, 0))
	p_lse = lse + (bos_q + i_t) * HQ + i_h * G + tl.arange(0, G)

	# [G, BV]
	b_o = tl.zeros([G, BV], dtype=tl.float32)

	b_m = tl.full([G], float('-inf'), dtype=tl.float32)
	b_acc = tl.zeros([G], dtype=tl.float32)
	for i in range(NS):
	i_s = tl.load(block_indices + i).to(tl.int32) * BS # start token index of the i-th selected KV block
	if i_s <= Q_OFFSET + i_t and i_s >= 0:
	p_k = tl.make_block_ptr(k, (K, TK), (1, H*K), (0, i_s), (BK, BS), (0, 1))
	p_v = tl.make_block_ptr(v, (TK, V), (HV, 1), (i_s, i_v BV), (BS, BV), (1, 0))
	# [BK, BS]
	b_k = tl.load(p_k, boundary_check=(0, 1))
	# [BS, BV]
	b_v = tl.load(p_v, boundary_check=(0, 1))
	# [G, BS]
	b_s = tl.dot(b_q, b_k)
	# causal mask against the absolute query position Q_OFFSET + i_t
	b_s = tl.where((Q_OFFSET + i_t >= (i_s + tl.arange(0, BS)))[None, :], b_s, float('-inf'))

	# [G]
	b_m, b_mp = tl.maximum(b_m, tl.max(b_s, 1)), b_m
	b_r = exp(b_mp - b_m)
	# [G, BS]
	b_p = exp(b_s - b_m[:, None])
	# [G]
	b_acc = b_acc * b_r + tl.sum(b_p, 1)
	# [G, BV]
	b_o = b_o * b_r[:, None] + tl.dot(b_p.to(b_q.dtype), b_v)

	b_o = b_o / b_acc[:, None]
	b_m += log(b_acc)
	tl.store(p_o, b_o.to(p_o.dtype.element_ty), boundary_check=(0, 1))
	tl.store(p_lse, b_m.to(p_lse.dtype.element_ty))


	@triton.heuristics({
	'IS_VARLEN': lambda args: args['cu_seqlens'] is not None,
	'USE_BLOCK_COUNTS': lambda args: isinstance(args['block_counts'], torch.Tensor),
	})
	@triton.autotune(
	configs=[
	triton.Config({}, num_warps=num_warps, num_stages=num_stages)
	for num_warps in [1, 2, 4, 8]
	for num_stages in [1, 2, 3]
	],
	key=['BS', 'BK', 'BV', 'G'],
	**autotune_cache_kwargs,
	)
	@triton.jit(do_not_specialize=['T'])
	def parallel_nsa_bwd_kernel_dq(
	q,
	k,
	v,
	lse,
	delta,
	do,
	dq,
	scale,
	block_indices,
	block_counts,
	cu_seqlens,
	token_indices,
	T,
	B: tl.constexpr,
	H: tl.constexpr,
	HQ: tl.constexpr,
	G: tl.constexpr,
	K: tl.constexpr,
	V: tl.constexpr,
	S: tl.constexpr,
	BS: tl.constexpr,
	BK: tl.constexpr,
	BV: tl.constexpr,
	IS_VARLEN: tl.constexpr,
	USE_BLOCK_COUNTS: tl.constexpr,
	):
	i_t, i_v, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
	i_b, i_h = i_bh // H, i_bh % H

	all = B * T
	if IS_VARLEN:
	i_n, i_t = tl.load(token_indices + i_t * 2).to(tl.int32), tl.load(token_indices + i_t * 2 + 1).to(tl.int32)
	bos, eos = tl.load(cu_seqlens + i_n).to(tl.int64), tl.load(cu_seqlens + i_n + 1).to(tl.int64)
	T = (eos - bos).to(tl.int32)
	else:
	bos, eos = (i_b * T).to(tl.int64), (i_b * T + T).to(tl.int64)

	q += (bos + i_t) * HQ*K
	do += (bos + i_t) * HQ*V
	lse += (bos + i_t) * HQ
	delta += (bos + i_t) * HQ
	dq += (i_v * all + bos + i_t) * HQ*K
	block_indices += (bos + i_t) * HS + i_h S

	if USE_BLOCK_COUNTS:
	NS = tl.load(block_counts + (bos + i_t) * H + i_h)
	else:
	NS = S

	k += (bos * H + i_h) * K
	v += (bos * H + i_h) * V

	p_q = tl.make_block_ptr(q, (HQ, K), (K, 1), (i_h * G, 0), (G, BK), (1, 0))
	p_dq = tl.make_block_ptr(dq, (HQ, K), (K, 1), (i_h * G, 0), (G, BK), (1, 0))

	# [G, BK]
	b_q = tl.load(p_q, boundary_check=(0, 1))
	b_q = (b_q * scale).to(b_q.dtype)

	p_do = tl.make_block_ptr(do, (HQ, V), (V, 1), (i_h * G, i_v * BV), (G, BV), (1, 0))
	p_lse = lse + i_h * G + tl.arange(0, G)
	p_delta = delta + i_h * G + tl.arange(0, G)

	# [G, BV]
	b_do = tl.load(p_do, boundary_check=(0, 1))
	# [G]
	b_lse = tl.load(p_lse)
	b_delta = tl.load(p_delta)

	# [G, BK]
	b_dq = tl.zeros([G, BK], dtype=tl.float32)
	for i in range(NS):
	i_s = tl.load(block_indices + i).to(tl.int32) * BS
	if i_s <= i_t and i_s >= 0:
	p_k = tl.make_block_ptr(k, (K, T), (1, H*K), (0, i_s), (BK, BS), (0, 1))
	p_v = tl.make_block_ptr(v, (V, T), (1, HV), (i_v BV, i_s), (BV, BS), (0, 1))
	# [BK, BS]
	b_k = tl.load(p_k, boundary_check=(0, 1))
	# [BV, BS]
	b_v = tl.load(p_v, boundary_check=(0, 1))

	# [G, BS]
	b_s = tl.dot(b_q, b_k)
	b_p = exp(b_s - b_lse[:, None])
	b_p = tl.where((i_t >= (i_s + tl.arange(0, BS)))[None, :], b_p, 0)

	# [G, BV] @ [BV, BS] -> [G, BS]
	b_dp = tl.dot(b_do, b_v)
	b_ds = b_p * (b_dp.to(tl.float32) - b_delta[:, None])
	# [G, BS] @ [BS, BK] -> [G, BK]
	b_dq += tl.dot(b_ds.to(b_k.dtype), tl.trans(b_k))
	b_dq *= scale

	tl.store(p_dq, b_dq.to(p_dq.dtype.element_ty), boundary_check=(0, 1))


	def _prune_dkv_bq(configs, nargs, **kwargs):
	# the gather stacks BQ queries x G group heads into a [BQ*G]-wide tile; past ~1024 columns the
	# Triton compiler fails outright (which autotune cannot catch), so cap BQ*G here. Shared-memory
	# fit is left to autotune, which prunes configs that don't fit the device. Always keep BQ=1.
	G = {(nargs or {}), kwargs}.get('G', 1)
	return [c for c in configs if c.kwargs['BQ'] == 1 or c.kwargs['BQ'] * G <= 256]


	@triton.heuristics({
	'IS_VARLEN': lambda args: args['cu_seqlens'] is not None,
	})
	@triton.autotune(
	configs=[
	triton.Config({'BQ': BQ}, num_warps=num_warps, num_stages=num_stages)
	for BQ in [1, 2, 4, 8]
	for num_warps in [4, 8]
	for num_stages in [1, 2]
	],
	key=['BS', 'BK', 'BV', 'G'],
	prune_configs_by={'early_config_prune': _prune_dkv_bq},
	**autotune_cache_kwargs,
	)
	@triton.jit(do_not_specialize=['T'])
	def parallel_nsa_bwd_kernel_dkv(
	q,
	k,
	v,
	lse,
	delta,
	do,
	dk,
	dv,
	scale,
	csr_indices,
	csr_offsets,
	cu_seqlens,
	chunk_indices,
	T,
	B: tl.constexpr,
	H: tl.constexpr,
	HQ: tl.constexpr,
	G: tl.constexpr,
	K: tl.constexpr,
	V: tl.constexpr,
	TC: tl.constexpr,
	BS: tl.constexpr,
	BK: tl.constexpr,
	BV: tl.constexpr,
	BQ: tl.constexpr,
	IS_VARLEN: tl.constexpr,
	):
	i_v, i_blk = tl.program_id(0), tl.program_id(1)
	all = B * T
	if IS_VARLEN:
	i_c, i_h = i_blk // H, i_blk % H
	i_n = tl.load(chunk_indices + i_c * 2).to(tl.int32)
	i_s = tl.load(chunk_indices + i_c * 2 + 1).to(tl.int32)
	bos = tl.load(cu_seqlens + i_n).to(tl.int64)
	eos = tl.load(cu_seqlens + i_n + 1).to(tl.int64)
	else:
	i_s = i_blk % TC
	i_b, i_h = (i_blk // TC) // H, (i_blk // TC) % H
	bos = (i_b * T).to(tl.int64)
	eos = bos + T
	o_t = bos + i_s * BS + tl.arange(0, BS)
	o_d = tl.arange(0, BK)
	o_v = i_v * BV + tl.arange(0, BV)
	o_h = tl.arange(0, BQ * G) % G
	m_t, m_d, m_v = o_t < eos, o_d < K, o_v < V

	# this block's CSR slice: the queries that selected it
	i_q0, i_q1 = tl.load(csr_offsets + i_blk).to(tl.int64), tl.load(csr_offsets + i_blk + 1).to(tl.int64)
	NQ = i_q1 - i_q0

	q += i_h * G*K
	k += i_h * K
	v += i_h * V
	lse += i_h * G
	delta += i_h * G
	do += i_h * G*V
	dk += i_h * K
	dv += i_h * V

	# [BS, BK] / [BS, BV] k/v tile for this kv block
	b_k = tl.load(k + o_t[:, None] * H*K + o_d[None, :], mask=m_t[:, None] & m_d[None, :], other=0.)
	b_v = tl.load(v + o_t[:, None] * H*V + o_v[None, :], mask=m_t[:, None] & m_v[None, :], other=0.)
	b_dk = tl.zeros([BS, BK], dtype=tl.float32)
	b_dv = tl.zeros([BS, BV], dtype=tl.float32)

	for i in range(tl.cdiv(NQ, BQ)):
	# BQ queries x G group heads flattened to [BQG] columns; row r -> query slot iBQ + r//G, head o_h[r]
	o_q = i * BQ + tl.arange(0, BQ * G) // G
	m_q = o_q < NQ
	o_q = tl.load(csr_indices + i_q0 + o_q, mask=m_q, other=0).to(tl.int64)

	# gather q/do/lse/delta for the [BQ*G] (query, group-head) columns
	# [BQ*G, BK]
	b_q = tl.load(q + o_q[:, None] * HQK + o_h[:, None] K + o_d[None, :], mask=m_q[:, None] & m_d[None, :], other=0.)
	b_q = (b_q * scale).to(b_k.dtype)
	# [BQ*G, BV]
	b_do = tl.load(do + o_q[:, None] * HQV + o_h[:, None] V + o_v[None, :], mask=m_q[:, None] & m_v[None, :], other=0.)
	# [BQ*G]
	b_lse = tl.load(lse + o_q * HQ + o_h, mask=m_q, other=0.)
	b_delta = tl.load(delta + o_q * HQ + o_h, mask=m_q, other=0.)

	# [BS, BK] @ [BK, BQG] -> [BS, BQG]
	b_s = tl.dot(b_k, tl.trans(b_q))
	b_p = exp(b_s - b_lse[None, :])
	# causal: a key contributes only to queries at or after its position
	b_p = tl.where((o_q[None, :] >= o_t[:, None]) & m_q[None, :], b_p, 0.)

	# [BS, BQG] @ [BQG, BV] -> [BS, BV]
	b_dv += tl.dot(b_p.to(b_do.dtype), b_do)
	# [BS, BV] @ [BV, BQG] -> [BS, BQG]
	b_dp = tl.dot(b_v, tl.trans(b_do))
	b_ds = b_p * (b_dp.to(tl.float32) - b_delta[None, :])
	# [BS, BQG] @ [BQG, BK] -> [BS, BK]
	b_dk += tl.dot(b_ds.to(b_q.dtype), b_q)

	o_dk = (i_v * all + o_t)[:, None] * H*K + o_d[None, :]
	o_dv = o_t[:, None] * H*V + o_v[None, :]
	tl.store(dk + o_dk, b_dk.to(dk.dtype.element_ty), mask=m_t[:, None] & m_d[None, :])
	tl.store(dv + o_dv, b_dv.to(dv.dtype.element_ty), mask=m_t[:, None] & m_v[None, :])


	@contiguous
	def parallel_nsa_topk(
	q: torch.Tensor,
	k: torch.Tensor,
	TK: int,
	lse: torch.Tensor \| None,
	block_counts: torch.LongTensor \| int,
	block_size: int = 64,
	scale: float = None,
	cu_seqlens: torch.LongTensor \| tuple[torch.LongTensor, torch.LongTensor] \| None = None,
	) -> torch.LongTensor:
	B, TQ, HQ, K, H = *q.shape, k.shape[2]

	assert k.shape[0] == q.shape[0] and k.shape[-1] == q.shape[-1], "The last dimension of k and q must match"
	assert lse is None or lse.shape == (B, TQ, HQ), "The shape of lse must be (B, TQ, HQ)"

	if cu_seqlens is not None:
	if isinstance(cu_seqlens, tuple):
	cu_seqlens_q, cu_seqlens_k = cu_seqlens
	else:
	cu_seqlens_q = cu_seqlens_k = cu_seqlens
	token_indices_q = prepare_token_indices(cu_seqlens_q)
	else:
	cu_seqlens_q = cu_seqlens_k = token_indices_q = None

	G = HQ // H
	# the number of selected blocks for each token
	S = block_counts if isinstance(block_counts, int) else block_counts.max().item()
	S = triton.next_power_of_2(S)
	# here we set BC = BS, but beware that they can be chosen separately if required
	BC = BS = block_size
	BK = max(triton.next_power_of_2(K), 16)
	assert BC >= 2 * S, f"BC ({BC}) must be greater than or equal to 2 * S ({S})"

	block_indices = torch.zeros(B, TQ, H, S, dtype=torch.int32, device=q.device)
	chunk_offsets = prepare_chunk_offsets(cu_seqlens_k, BS) if cu_seqlens_k is not None else None
	grid = (TQ, B * H)
	# the 1st and the last 2 blocks are always selected
	parallel_nsa_kernel_topk[grid](
	q=q,
	k=k,
	lse=lse,
	scale=scale,
	block_indices=block_indices,
	cu_seqlens_q=cu_seqlens_q,
	cu_seqlens_k=cu_seqlens_k,
	token_indices_q=token_indices_q,
	chunk_offsets=chunk_offsets,
	TQ=TQ,
	TK=TK,
	H=H,
	HQ=HQ,
	G=G,
	K=K,
	S=S,
	BC=BC,
	BS=BS,
	BK=BK,
	)
	return block_indices


	@contiguous
	def parallel_nsa_fwd(
	q: torch.Tensor,
	k: torch.Tensor,
	v: torch.Tensor,
	block_indices: torch.LongTensor,
	block_counts: torch.LongTensor \| int,
	block_size: int,
	scale: float,
	cu_seqlens_q: torch.LongTensor \| None = None,
	cu_seqlens_k: torch.LongTensor \| None = None,
	token_indices_q: torch.LongTensor \| None = None,
	):
	B, TK, H, K, V, S = *k.shape, v.shape[-1], block_indices.shape[-1]
	_, TQ, HQ, _ = q.shape
	G = HQ // H
	BS = block_size
	if check_shared_mem('hopper', q.device.index):
	BK = min(256, triton.next_power_of_2(K))
	BV = min(256, triton.next_power_of_2(V))
	else:
	BK = min(128, triton.next_power_of_2(K))
	BV = min(128, triton.next_power_of_2(V))
	NK = triton.cdiv(K, BK)
	NV = triton.cdiv(V, BV)
	assert NK == 1, "The key dimension can not be larger than 256"

	grid = (TQ, NV, B * H)
	o = torch.empty(B, TQ, HQ, V, dtype=v.dtype, device=q.device)
	lse = torch.empty(B, TQ, HQ, dtype=torch.float, device=q.device)

	parallel_nsa_fwd_kernel[grid](
	q=q,
	k=k,
	v=v,
	o=o,
	lse=lse,
	scale=scale,
	block_indices=block_indices,
	block_counts=block_counts,
	cu_seqlens_q=cu_seqlens_q,
	cu_seqlens_k=cu_seqlens_k,
	token_indices_q=token_indices_q,
	TQ=TQ,
	TK=TK,
	H=H,
	HQ=HQ,
	G=G,
	K=K,
	V=V,
	S=S,
	BS=BS,
	BK=BK,
	BV=BV,
	)
	return o, lse


	def parallel_nsa_bwd(
	q: torch.Tensor,
	k: torch.Tensor,
	v: torch.Tensor,
	o: torch.Tensor,
	lse: torch.Tensor,
	do: torch.Tensor,
	block_indices: torch.Tensor,
	block_counts: torch.LongTensor \| int,
	block_size: int = 64,
	scale: float = None,
	cu_seqlens: torch.LongTensor \| None = None,
	token_indices: torch.LongTensor \| None = None,
	chunk_indices: torch.LongTensor \| None = None,
	):
	B, T, H, K, V, S = *k.shape, v.shape[-1], block_indices.shape[-1]
	HQ = q.shape[2]
	G = HQ // H
	BS = block_size
	BK = max(triton.next_power_of_2(K), 16)
	BV = min(128, max(triton.next_power_of_2(v.shape[-1]), 16))
	NV = triton.cdiv(V, BV)

	delta = parallel_attn_bwd_preprocess(o, do)

	dq = torch.empty(NV, *q.shape, dtype=q.dtype if NV == 1 else torch.float, device=q.device)
	grid = (T, NV, B * H)
	parallel_nsa_bwd_kernel_dq[grid](
	q=q,
	k=k,
	v=v,
	lse=lse,
	delta=delta,
	do=do,
	dq=dq,
	block_indices=block_indices,
	block_counts=block_counts,
	cu_seqlens=cu_seqlens,
	token_indices=token_indices,
	scale=scale,
	T=T,
	B=B,
	H=H,
	HQ=HQ,
	G=G,
	K=K,
	V=V,
	S=S,
	BS=BS,
	BK=BK,
	BV=BV,
	)
	dq = dq.sum(0)

	if cu_seqlens is not None and chunk_indices is None:
	chunk_indices = prepare_chunk_indices(cu_seqlens, BS)

	M = triton.cdiv(T, BS) if cu_seqlens is None else triton.cdiv(prepare_lens(cu_seqlens).max().item(), BS)
	dk = torch.empty(NV, *k.shape, dtype=k.dtype if NV == 1 else torch.float, device=q.device)
	dv = torch.empty(v.shape, dtype=v.dtype, device=q.device)

	# invert the selection into the per-block list of selecting queries (CSR), so the kernel
	# gathers and batches them into one MMA instead of scanning every query tile.
	csr_indices, csr_offsets = prepare_block_csr(
	block_indices=block_indices,
	block_counts=block_counts,
	cu_seqlens=cu_seqlens,
	chunk_indices=chunk_indices,
	num_blocks=M,
	block_size=block_size,
	)
	NB = chunk_indices.shape[0] * H if cu_seqlens is not None else B * H * M
	grid = (NV, NB)
	parallel_nsa_bwd_kernel_dkv[grid](
	q=q,
	k=k,
	v=v,
	lse=lse,
	delta=delta,
	do=do,
	dk=dk,
	dv=dv,
	scale=scale,
	csr_indices=csr_indices,
	csr_offsets=csr_offsets,
	cu_seqlens=cu_seqlens,
	chunk_indices=chunk_indices,
	T=T,
	B=B,
	H=H,
	HQ=HQ,
	G=G,
	K=K,
	V=V,
	TC=M,
	BS=BS,
	BK=BK,
	BV=BV,
	)
	dk = dk.sum(0)
	return dq, dk, dv


	@torch.compile
	class ParallelNSAFunction(torch.autograd.Function):

	@staticmethod
	@contiguous
	@autocast_custom_fwd
	def forward(ctx, q, k, v, block_indices, block_counts, block_size, scale, cu_seqlens):
	ctx.dtype = q.dtype

	# 2-d sequence indices denoting the cu_seqlens of tokens in each sequence
	# for example, if the passed `cu_seqlens` is [0, 2, 6],
	# then there are 2 and 4 tokens in the 1st and 2nd sequences respectively, and `token_indices` will be
	# [[0, 0], [0, 1], [1, 0], [1, 1], [1, 2], [1, 3]]
	if cu_seqlens is not None:
	if isinstance(cu_seqlens, tuple):
	cu_seqlens_q, cu_seqlens_k = cu_seqlens
	else:
	cu_seqlens_q = cu_seqlens_k = cu_seqlens
	token_indices_q = prepare_token_indices(cu_seqlens_q)
	else:
	cu_seqlens_q = cu_seqlens_k = token_indices_q = None

	o, lse = parallel_nsa_fwd(
	q=q,
	k=k,
	v=v,
	block_indices=block_indices,
	block_counts=block_counts,
	block_size=block_size,
	scale=scale,
	cu_seqlens_q=cu_seqlens_q,
	cu_seqlens_k=cu_seqlens_k,
	token_indices_q=token_indices_q
	)
	ctx.save_for_backward(q, k, v, o, lse)
	ctx.block_indices = block_indices
	ctx.block_counts = block_counts
	# Use cu_seqlens of q in backward, as cu_seqlens for q & k are different only for inference
	ctx.cu_seqlens = cu_seqlens_q
	ctx.token_indices = token_indices_q
	ctx.block_size = block_size
	ctx.scale = scale
	# q/k cu_seqlens differ only in cached inference (TQ != TK), where backward is not supported
	ctx.tq_ne_tk = isinstance(cu_seqlens, tuple)
	return o.to(q.dtype)

	@staticmethod
	@contiguous
	@autocast_custom_bwd
	def backward(ctx, do):
	if ctx.tq_ne_tk:
	raise NotImplementedError(
	"Backward is not supported when `cu_seqlens` differs for queries and keys (cached inference). "
	"Run the forward under `torch.no_grad()`."
	)
	q, k, v, o, lse = ctx.saved_tensors
	dq, dk, dv = parallel_nsa_bwd(
	q=q,
	k=k,
	v=v,
	o=o,
	lse=lse,
	do=do,
	block_indices=ctx.block_indices,
	block_counts=ctx.block_counts,
	block_size=ctx.block_size,
	scale=ctx.scale,
	cu_seqlens=ctx.cu_seqlens,
	token_indices=ctx.token_indices,
	)
	return dq.to(q), dk.to(k), dv.to(v), None, None, None, None, None, None, None, None


	@contiguous
	def parallel_nsa(
	q: torch.Tensor,
	k: torch.Tensor,
	v: torch.Tensor,
	g_cmp: torch.Tensor \| None = None,
	g_slc: torch.Tensor \| None = None,
	g_swa: torch.Tensor \| None = None,
	block_indices: torch.LongTensor \| None = None,
	block_counts: torch.LongTensor \| int = 16,
	block_size: int = 64,
	window_size: int = 0,
	scale: float \| None = None,
	cu_seqlens: torch.LongTensor \| tuple[torch.LongTensor, torch.LongTensor] \| None = None,
	) -> torch.Tensor:
	r"""
	Args:
	q (torch.Tensor):
	queries of shape `[B, TQ, HQ, K]`.
	k (torch.Tensor):
	keys of shape `[B, T, H, K]`.
	GQA is enforced here: the ratio of query heads (HQ) to key/value heads (H) must be a power of 2 and >= 16.
	This is a kernel tile dimension, which Triton requires to be a power-of-2 block shape.
	v (torch.Tensor):
	values of shape `[B, T, H, V]`.
	g_cmp (torch.Tensor):
	Gate score for compressed attention of shape `[B, TQ, HQ]`.
	g_slc (torch.Tensor):
	Gate score for selected attention of shape `[B, TQ, HQ]`.
	g_swa (torch.Tensor):
	Gate score for sliding attentionof shape `[B, TQ, HQ]`.
	block_indices (torch.LongTensor):
	Block indices of shape `[B, TQ, H, S]`.
	`S` is the number of selected blocks for each query token, which is set to 16 in the paper.
	Will override the computed block indices from compression if provided.
	block_counts (Optional[Union[torch.LongTensor, int]]):
	Number of selected blocks for each query.
	If a tensor is provided, with shape `[B, TQ, H]`,
	each query can select the same number of blocks.
	If not provided, it will default to 16.
	block_size (int):
	Selected block size. Default: 64.
	window_size (int):
	Sliding window size. Default: 0.
	scale (Optional[float]):
	Scale factor for attention scores.
	If not provided, it will default to `1 / sqrt(K)`. Default: `None`.
	cu_seqlens (torch.LongTensor, Tuple[torch.LongTensor, torch.LongTensor] or None):
	Cumulative sequence lengths of shape `[N+1]` used for variable-length training,
	consistent with the FlashAttention API.
	When a tuple is provided, it should contain two tensors: `(cu_seqlens_q, cu_seqlens_k)`.

	Returns:
	o (torch.Tensor):
	Outputs of shape `[B, T, HQ, V]`.
	"""
	assert block_counts is not None, "block counts must be provided for selection"
	if scale is None:
	scale = k.shape[-1] ** -0.5
	if cu_seqlens is not None and q.shape[0] != 1:
	raise ValueError(
	f"The batch size is expected to be 1 rather than {q.shape[0]} when using `cu_seqlens`. "
	f"Please flatten variable-length inputs before processing.",
	)
	G = q.shape[2] // k.shape[2]
	assert G >= 16 and (G & (G - 1)) == 0, "Group size (HQ/H) must be a power of 2 and >= 16 in NSA"

	if cu_seqlens is not None:
	if isinstance(cu_seqlens, tuple):
	cu_seqlens_q, cu_seqlens_k = cu_seqlens
	else:
	cu_seqlens_q = cu_seqlens_k = cu_seqlens
	else:
	cu_seqlens_q = cu_seqlens_k = None
	k_cmp, v_cmp = mean_pooling(k, block_size, cu_seqlens_k), mean_pooling(v, block_size, cu_seqlens_k)
	o_cmp, lse_cmp = None, None
	if g_cmp is not None:
	o_cmp, lse_cmp = parallel_nsa_compression(
	q=q,
	k=k_cmp,
	v=v_cmp,
	TK=k.shape[1],
	block_size=block_size,
	scale=scale,
	cu_seqlens=cu_seqlens,
	)
	if block_indices is None:
	block_indices = parallel_nsa_topk(
	q=q,
	k=k_cmp,
	lse=lse_cmp,
	TK=k.shape[1],
	block_counts=block_counts,
	block_size=block_size,
	scale=scale,
	cu_seqlens=cu_seqlens,
	)
	else:
	warnings.warn("`block_indices` is provided, overriding the selection computed from compression")
	o = o_slc = ParallelNSAFunction.apply(q, k, v, block_indices, block_counts, block_size, scale, cu_seqlens)
	if g_slc is not None:
	o = o_slc * g_slc.unsqueeze(-1)
	if o_cmp is not None:
	o = torch.addcmul(o, o_cmp, g_cmp.unsqueeze(-1))
	if window_size > 0:
	if cu_seqlens is not None:
	o_swa = flash_attn_varlen_func(
	q.squeeze(0), k.squeeze(0), v.squeeze(0),
	cu_seqlens_q=cu_seqlens_q,
	cu_seqlens_k=cu_seqlens_k,
	max_seqlen_q=q.shape[1],
	max_seqlen_k=k.shape[1],
	causal=True,
	window_size=(window_size-1, 0),
	).unsqueeze(0)
	else:
	o_swa = flash_attn_func(
	q, k, v,
	causal=True,
	window_size=(window_size-1, 0),
	)
	o = torch.addcmul(o, o_swa, g_swa.unsqueeze(-1))
	return o