# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang import torch import triton import triton.language as tl from fla.ops.utils import chunk_local_cumsum, prepare_chunk_indices, solve_tril from fla.ops.utils.op import exp from fla.utils import autotune_cache_kwargs @triton.heuristics({ 'IS_VARLEN': lambda args: args['cu_seqlens'] is not None, }) @triton.autotune( configs=[ triton.Config({'BK': BK}, num_warps=num_warps, num_stages=num_stages) for BK in [32, 64] for num_warps in [1, 2, 4, 8] for num_stages in [2, 3, 4] ], key=["BC"], **autotune_cache_kwargs, ) @triton.jit(do_not_specialize=['T']) def chunk_kda_fwd_kernel_intra_sub_inter( q, k, g, beta, Aqk, Akk, scale, cu_seqlens, chunk_indices, T, H: tl.constexpr, K: tl.constexpr, BT: tl.constexpr, BC: tl.constexpr, BK: tl.constexpr, NC: tl.constexpr, IS_VARLEN: tl.constexpr, ): i_t, i_c, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2) i_b, i_h = i_bh // H, i_bh % H i_i, i_j = i_c // NC, i_c % NC if IS_VARLEN: i_n, i_t = tl.load(chunk_indices + i_t * 2).to(tl.int32), tl.load(chunk_indices + i_t * 2 + 1).to(tl.int32) bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(cu_seqlens + i_n + 1).to(tl.int32) T = eos - bos else: bos, eos = i_b * T, i_b * T + T if i_t * BT + i_i * BC >= T: return if i_i <= i_j: return q += (bos * H + i_h) * K k += (bos * H + i_h) * K g += (bos * H + i_h) * K Aqk += (bos * H + i_h) * BT Akk += (bos * H + i_h) * BT p_b = tl.make_block_ptr(beta + bos * H + i_h, (T,), (H,), (i_t * BT + i_i * BC,), (BC,), (0,)) b_b = tl.load(p_b, boundary_check=(0,)) b_Aqk = tl.zeros([BC, BC], dtype=tl.float32) b_Akk = tl.zeros([BC, BC], dtype=tl.float32) for i_k in range(tl.cdiv(K, BK)): p_q = tl.make_block_ptr(q, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_k = tl.make_block_ptr(k, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_g = tl.make_block_ptr(g, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) b_kt = tl.make_block_ptr(k, (K, T), (1, H*K), (i_k * BK, i_t * BT + i_j * BC), (BK, BC), (0, 1)) p_gk = tl.make_block_ptr(g, (K, T), (1, H*K), (i_k * BK, i_t * BT + i_j * BC), (BK, BC), (0, 1)) o_k = i_k * BK + tl.arange(0, BK) m_k = o_k < K # [BK,] b_gn = tl.load(g + (i_t * BT + i_i * BC) * H*K + o_k, mask=m_k, other=0) # [BC, BK] b_g = tl.load(p_g, boundary_check=(0, 1)) b_k = tl.load(p_k, boundary_check=(0, 1)) * exp(b_g - b_gn[None, :]) # [BK, BC] b_gk = tl.load(p_gk, boundary_check=(0, 1)) b_kt = tl.load(b_kt, boundary_check=(0, 1)) # [BC, BC] b_ktg = b_kt * exp(b_gn[:, None] - b_gk) b_Akk += tl.dot(b_k, b_ktg) b_q = tl.load(p_q, boundary_check=(0, 1)) b_qg = b_q * exp(b_g - b_gn[None, :]) * scale b_Aqk += tl.dot(b_qg, b_ktg) b_Akk *= b_b[:, None] p_Akk = tl.make_block_ptr(Akk, (T, BT), (H*BT, 1), (i_t * BT + i_i * BC, i_j * BC), (BC, BC), (1, 0)) tl.store(p_Akk, b_Akk.to(Akk.dtype.element_ty), boundary_check=(0, 1)) p_Aqk = tl.make_block_ptr(Aqk, (T, BT), (H*BT, 1), (i_t * BT + i_i * BC, i_j * BC), (BC, BC), (1, 0)) tl.store(p_Aqk, b_Aqk.to(Aqk.dtype.element_ty), boundary_check=(0, 1)) @triton.heuristics({ 'IS_VARLEN': lambda args: args['cu_seqlens'] is not None, }) @triton.autotune( configs=[ triton.Config({}, num_warps=num_warps) for num_warps in [1, 2, 4, 8] ], key=["BK", "BT"], **autotune_cache_kwargs, ) @triton.jit(do_not_specialize=['T']) def chunk_kda_fwd_kernel_intra_sub_intra( q, k, g, beta, Aqk, Akk, scale, cu_seqlens, chunk_indices, T, H: tl.constexpr, K: tl.constexpr, BT: tl.constexpr, BC: tl.constexpr, BK: tl.constexpr, IS_VARLEN: tl.constexpr, ): i_t, i_i, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2) i_b, i_h = i_bh // H, i_bh % H if IS_VARLEN: i_n, i_t = tl.load(chunk_indices + i_t * 2).to(tl.int32), tl.load(chunk_indices + i_t * 2 + 1).to(tl.int32) bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(cu_seqlens + i_n + 1).to(tl.int32) T = eos - bos else: bos, eos = i_b * T, i_b * T + T if i_t * BT + i_i * BC >= T: return o_i = tl.arange(0, BC) o_k = tl.arange(0, BK) m_k = o_k < K m_A = (i_t * BT + i_i * BC + o_i) < T o_A = (bos + i_t * BT + i_i * BC + o_i) * H*BT + i_h * BT + i_i * BC p_q = tl.make_block_ptr(q + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT + i_i * BC, 0), (BC, BK), (1, 0)) p_k = tl.make_block_ptr(k + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT + i_i * BC, 0), (BC, BK), (1, 0)) p_g = tl.make_block_ptr(g + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT + i_i * BC, 0), (BC, BK), (1, 0)) b_q = tl.load(p_q, boundary_check=(0, 1)) b_k = tl.load(p_k, boundary_check=(0, 1)) b_g = tl.load(p_g, boundary_check=(0, 1)) p_b = beta + (bos + i_t * BT + i_i * BC + o_i) * H + i_h b_k = b_k * tl.load(p_b, mask=m_A, other=0)[:, None] p_kt = k + (bos + i_t * BT + i_i * BC) * H*K + i_h * K + o_k p_gk = g + (bos + i_t * BT + i_i * BC) * H*K + i_h * K + o_k for j in range(0, min(BC, T - i_t * BT - i_i * BC)): b_kt = tl.load(p_kt, mask=m_k, other=0).to(tl.float32) b_gk = tl.load(p_gk, mask=m_k, other=0).to(tl.float32) b_ktg = b_kt[None, :] * exp(b_g - b_gk[None, :]) b_Aqk = tl.sum(b_q * b_ktg, 1) b_Aqk = tl.where(o_i >= j, b_Aqk * scale, 0.) b_Akk = tl.sum(b_k * b_ktg, 1) b_Akk = tl.where(o_i > j, b_Akk, 0.) tl.store(Aqk + o_A + j, b_Aqk, mask=m_A) tl.store(Akk + o_A + j, b_Akk, mask=m_A) p_kt += H*K p_gk += H*K @triton.heuristics({ 'IS_VARLEN': lambda args: args['cu_seqlens'] is not None, }) @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 [2, 3, 4] ], key=['BK', 'NC', 'BT'], **autotune_cache_kwargs, ) @triton.jit(do_not_specialize=['B', 'T']) def chunk_kda_bwd_kernel_intra( q, k, g, beta, dAqk, dAkk, dq, dq2, dk, dk2, dg, db, cu_seqlens, chunk_indices, B, T, H: tl.constexpr, K: tl.constexpr, BT: tl.constexpr, BC: tl.constexpr, BK: tl.constexpr, NC: tl.constexpr, IS_VARLEN: tl.constexpr, ): i_kc, i_t, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2) i_b, i_h = i_bh // H, i_bh % H i_k, i_i = i_kc // NC, i_kc % NC all = B * T if IS_VARLEN: i_n, i_t = tl.load(chunk_indices + i_t * 2).to(tl.int32), tl.load(chunk_indices + i_t * 2 + 1).to(tl.int32) bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(cu_seqlens + i_n + 1).to(tl.int32) else: bos, eos = i_b * T, i_b * T + T T = eos - bos if i_t * BT + i_i * BC >= T: return o_k = i_k * BK + tl.arange(0, BK) m_k = o_k < K q += (bos * H + i_h) * K k += (bos * H + i_h) * K g += (bos * H + i_h) * K beta += bos * H + i_h dAqk += (bos * H + i_h) * BT dAkk += (bos * H + i_h) * BT dq += (bos * H + i_h) * K dq2 += (bos * H + i_h) * K dk += (bos * H + i_h) * K dk2 += (bos * H + i_h) * K dg += (bos * H + i_h) * K db += (i_k * all + bos) * H + i_h p_g = tl.make_block_ptr(g, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) b_g = tl.load(p_g, boundary_check=(0, 1)) p_b = tl.make_block_ptr(beta, (T,), (H,), (i_t * BT + i_i * BC,), (BC,), (0,)) b_b = tl.load(p_b, boundary_check=(0,)) b_dq2 = tl.zeros([BC, BK], dtype=tl.float32) b_dk2 = tl.zeros([BC, BK], dtype=tl.float32) if i_i > 0: p_gn = g + (i_t * BT + i_i * BC) * H*K + o_k # [BK,] b_gn = tl.load(p_gn, mask=m_k, other=0) for i_j in range(0, i_i): p_k = tl.make_block_ptr(k, (T, K), (H*K, 1), (i_t * BT + i_j * BC, i_k * BK), (BC, BK), (1, 0)) p_gk = tl.make_block_ptr(g, (T, K), (H*K, 1), (i_t * BT + i_j * BC, i_k * BK), (BC, BK), (1, 0)) p_dAqk = tl.make_block_ptr(dAqk, (T, BT), (H*BT, 1), (i_t * BT + i_i * BC, i_j * BC), (BC, BC), (1, 0)) p_dAkk = tl.make_block_ptr(dAkk, (T, BT), (H*BT, 1), (i_t * BT + i_i * BC, i_j * BC), (BC, BC), (1, 0)) # [BC, BK] b_k = tl.load(p_k, boundary_check=(0, 1)) b_gk = tl.load(p_gk, boundary_check=(0, 1)) b_kg = b_k * exp(b_gn[None, :] - b_gk) # [BC, BC] b_dAqk = tl.load(p_dAqk, boundary_check=(0, 1)) b_dAkk = tl.load(p_dAkk, boundary_check=(0, 1)) # [BC, BK] b_dq2 += tl.dot(b_dAqk, b_kg) b_dk2 += tl.dot(b_dAkk, b_kg) b_dq2 *= exp(b_g - b_gn[None, :]) b_dk2 *= exp(b_g - b_gn[None, :]) o_i = tl.arange(0, BC) m_dA = (i_t * BT + i_i * BC + o_i) < T o_dA = (i_t * BT + i_i * BC + o_i) * H*BT + i_i * BC p_kj = k + (i_t * BT + i_i * BC) * H*K + o_k p_gkj = g + (i_t * BT + i_i * BC) * H*K + o_k p_q = tl.make_block_ptr(q, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_k = tl.make_block_ptr(k, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) b_q = tl.load(p_q, boundary_check=(0, 1)) b_k = tl.load(p_k, boundary_check=(0, 1)) for j in range(0, min(BC, T - i_t * BT - i_i * BC)): # [BC] b_dAqk = tl.load(dAqk + o_dA + j, mask=m_dA, other=0) b_dAkk = tl.load(dAkk + o_dA + j, mask=m_dA, other=0) # [BK] b_kj = tl.load(p_kj, mask=m_k, other=0).to(tl.float32) b_gkj = tl.load(p_gkj, mask=m_k, other=0).to(tl.float32) # [BC, BK] m_i = o_i[:, None] >= j # [BC, BK] b_dq2 += tl.where(m_i, b_dAqk[:, None] * b_kj[None, :] * exp(b_g - b_gkj[None, :]), 0.) b_dk2 += tl.where(m_i, b_dAkk[:, None] * b_kj[None, :] * exp(b_g - b_gkj[None, :]), 0.) p_kj += H*K p_gkj += H*K b_db = tl.sum(b_dk2 * b_k, 1) b_dk2 *= b_b[:, None] p_dq = tl.make_block_ptr(dq, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_dq2 = tl.make_block_ptr(dq2, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_db = tl.make_block_ptr(db, (T,), (H,), (i_t * BT + i_i * BC,), (BC,), (0,)) b_dg = b_q * b_dq2 b_dq2 = b_dq2 + tl.load(p_dq, boundary_check=(0, 1)) tl.store(p_dq2, b_dq2.to(p_dq2.dtype.element_ty), boundary_check=(0, 1)) tl.store(p_db, b_db.to(p_db.dtype.element_ty), boundary_check=(0,)) tl.debug_barrier() b_dkt = tl.zeros([BC, BK], dtype=tl.float32) NC = min(NC, tl.cdiv(T - i_t * BT, BC)) if i_i < NC - 1: p_gn = g + (min(i_t * BT + i_i * BC + BC, T) - 1) * H*K + o_k # [BK,] b_gn = tl.load(p_gn, mask=m_k, other=0) for i_j in range(i_i + 1, NC): p_q = tl.make_block_ptr(q, (T, K), (H*K, 1), (i_t*BT+i_j*BC, i_k*BK), (BC, BK), (1, 0)) p_k = tl.make_block_ptr(k, (T, K), (H*K, 1), (i_t * BT + i_j * BC, i_k * BK), (BC, BK), (1, 0)) p_gk = tl.make_block_ptr(g, (T, K), (H*K, 1), (i_t * BT + i_j * BC, i_k*BK), (BC, BK), (1, 0)) p_b = tl.make_block_ptr(beta, (T,), (H,), (i_t * BT + i_j * BC,), (BC,), (0,)) p_dAqk = tl.make_block_ptr(dAqk, (BT, T), (1, H*BT), (i_i * BC, i_t * BT + i_j * BC), (BC, BC), (0, 1)) p_dAkk = tl.make_block_ptr(dAkk, (BT, T), (1, H*BT), (i_i * BC, i_t * BT + i_j * BC), (BC, BC), (0, 1)) # [BC] b_b = tl.load(p_b, boundary_check=(0,)) # [BC, BK] b_q = tl.load(p_q, boundary_check=(0, 1)) b_kb = tl.load(p_k, boundary_check=(0, 1)) * b_b[:, None] b_gk = tl.load(p_gk, boundary_check=(0, 1)) # [BC, BC] b_dAqk = tl.load(p_dAqk, boundary_check=(0, 1)) b_dAkk = tl.load(p_dAkk, boundary_check=(0, 1)) o_j = i_t * BT + i_j * BC + o_i m_j = o_j < T # [BC, BK] b_qg = b_q * tl.where(m_j[:, None], exp(b_gk - b_gn[None, :]), 0) b_kbg = b_kb * tl.where(m_j[:, None], exp(b_gk - b_gn[None, :]), 0) # [BC, BK] # (SY 09/17) important to not use bf16 here to have a good precision. b_dkt += tl.dot(b_dAqk, b_qg) b_dkt += tl.dot(b_dAkk, b_kbg) b_dkt *= exp(b_gn[None, :] - b_g) o_dA = (i_t * BT + i_i * BC) * H*BT + i_i * BC + o_i p_qj = q + (i_t * BT + i_i * BC) * H*K + o_k p_kj = k + (i_t * BT + i_i * BC) * H*K + o_k p_gkj = g + (i_t * BT + i_i * BC) * H*K + o_k p_bj = beta + (i_t * BT + i_i * BC) * H for j in range(0, min(BC, T - i_t * BT - i_i * BC)): # [BC,] b_dAqk = tl.load(dAqk + o_dA + j * H*BT) b_dAkk = tl.load(dAkk + o_dA + j * H*BT) # [BK,] b_qj = tl.load(p_qj, mask=m_k, other=0).to(tl.float32) b_kbj = tl.load(p_kj, mask=m_k, other=0).to(tl.float32) * tl.load(p_bj) b_gkj = tl.load(p_gkj, mask=m_k, other=0).to(tl.float32) # [BC, BK] m_i = o_i[:, None] <= j b_dkt += tl.where(m_i, b_dAqk[:, None] * b_qj[None, :] * exp(b_gkj[None, :] - b_g), 0.) b_dkt += tl.where(m_i, b_dAkk[:, None] * b_kbj[None, :] * exp(b_gkj[None, :] - b_g), 0.) p_qj += H*K p_kj += H*K p_gkj += H*K p_bj += H p_dk = tl.make_block_ptr(dk, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_dk2 = tl.make_block_ptr(dk2, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_dg = tl.make_block_ptr(dg, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) b_dg += (b_dk2 - b_dkt) * b_k b_dk2 += tl.load(p_dk, boundary_check=(0, 1)) b_dk2 += b_dkt tl.store(p_dk2, b_dk2.to(p_dk2.dtype.element_ty), boundary_check=(0, 1)) tl.store(p_dg, b_dg.to(p_dg.dtype.element_ty), boundary_check=(0, 1)) def chunk_kda_fwd_intra( q: torch.Tensor, k: torch.Tensor, gk: torch.Tensor | None = None, beta: torch.Tensor | None = None, scale: float | None = None, cu_seqlens: torch.LongTensor | None = None, chunk_size: int = 64, output_dtype: torch.dtype = torch.float32, ) -> tuple[torch.Tensor, torch.Tensor]: r""" Args: q (torch.Tensor): The query tensor of shape `[B, T, H, K]`. k (torch.Tensor): The key tensor of shape `[B, T, H, K]`. gk (torch.Tensor): The cumulative sum of the gate tensor of shape `[B, T, H, K]` applied to the key tensor. Default: `None`. beta (torch.Tensor): The beta tensor of shape `[B, T, H]`. Default: `None`. scale (Optional[float]): The scale factor. Default: `None`. cu_seqlens (torch.LongTensor): The cumulative sequence lengths of the input tensor. Default: None chunk_size (int): The chunk size. Default: 64. output_dtype (torch.dtype): The dtype of the output tensor. Default: `torch.float32` Returns: Aqk (torch.Tensor): The intra Aqk tensor of shape `[B, T, H, BT]` where `BT` is the chunk size. Akk (torch.Tensor): The intra Akk tensor of shape `[B, T, H, BT]` where `BT` is the chunk size. """ B, T, H, K = k.shape assert K <= 256 BT = chunk_size chunk_indices = prepare_chunk_indices(cu_seqlens, BT) if cu_seqlens is not None else None NT = triton.cdiv(T, BT) if cu_seqlens is None else len(chunk_indices) BC = min(16, BT) NC = triton.cdiv(BT, BC) BK = max(triton.next_power_of_2(K), 16) Aqk = torch.zeros(B, T, H, BT, device=k.device, dtype=output_dtype) Akk = torch.zeros(B, T, H, BT, device=k.device, dtype=output_dtype) grid = (NT, NC * NC, B * H) chunk_kda_fwd_kernel_intra_sub_inter[grid]( q=q, k=k, g=gk, beta=beta, Aqk=Aqk, Akk=Akk, scale=scale, cu_seqlens=cu_seqlens, chunk_indices=chunk_indices, T=T, H=H, K=K, BT=BT, BC=BC, NC=NC, ) grid = (NT, NC, B * H) chunk_kda_fwd_kernel_intra_sub_intra[grid]( q=q, k=k, g=gk, beta=beta, Aqk=Aqk, Akk=Akk, scale=scale, cu_seqlens=cu_seqlens, chunk_indices=chunk_indices, T=T, H=H, K=K, BT=BT, BC=BC, BK=BK, ) Akk = solve_tril( A=Akk, cu_seqlens=cu_seqlens, output_dtype=k.dtype, ) return Aqk, Akk def chunk_kda_bwd_intra( q: torch.Tensor, k: torch.Tensor, g: torch.Tensor, beta: torch.Tensor, dAqk: torch.Tensor, dAkk: torch.Tensor, dq: torch.Tensor, dk: torch.Tensor, db: torch.Tensor, dg: torch.Tensor, cu_seqlens: torch.LongTensor | None = None, chunk_size: int = 64, ): B, T, H, K = k.shape BT = chunk_size BC = min(16, BT) BK = min(64, triton.next_power_of_2(K)) chunk_indices = prepare_chunk_indices(cu_seqlens, chunk_size) if cu_seqlens is not None else None NT = triton.cdiv(T, BT) if cu_seqlens is None else len(chunk_indices) NC = triton.cdiv(BT, BC) NK = triton.cdiv(K, BK) dq2 = torch.empty_like(q) dk2 = torch.empty_like(k) db2 = beta.new_empty(NK, *beta.shape, dtype=torch.float) dg2 = torch.empty_like(dg, dtype=torch.float) grid = (NK * NC, NT, B * H) chunk_kda_bwd_kernel_intra[grid]( q=q, k=k, g=g, beta=beta, dAqk=dAqk, dAkk=dAkk, dq=dq, dq2=dq2, dk=dk, dk2=dk2, dg=dg2, db=db2, cu_seqlens=cu_seqlens, chunk_indices=chunk_indices, B=B, T=T, H=H, K=K, BT=BT, BC=BC, BK=BK, NC=NC, ) dq = dq2 dk = dk2 db = db2.sum(0).add_(db) dg = chunk_local_cumsum(dg2.add_(dg), chunk_size=chunk_size, reverse=True, cu_seqlens=cu_seqlens) return dq, dk2, db, dg