# -*- coding: utf-8 -*- # Copyright (c) 2023-2025, Songlin Yang, Yu Zhang from typing import Optional, Tuple import torch import triton import triton.language as tl from fla.ops.utils.op import exp from fla.utils import check_shared_mem, use_cuda_graph BK_LIST = [32, 64, 128] if check_shared_mem() else [16, 32] @triton.heuristics({ 'USE_OFFSETS': lambda args: args['offsets'] is not None }) @triton.autotune( configs=[ triton.Config({}, num_warps=num_warps, num_stages=num_stages) for num_warps in [2, 4, 8, 16, 32] for num_stages in [2, 3, 4] ], key=['BV', 'BT'], use_cuda_graph=use_cuda_graph, ) @triton.jit(do_not_specialize=['T']) def chunk_dplr_bwd_kernel_dAu( v, do, v_new, A_qb, dA_qk, dA_qb, dv_new, offsets, indices, scale: tl.constexpr, T, H: tl.constexpr, V: tl.constexpr, BT: tl.constexpr, BV: tl.constexpr, USE_OFFSETS: tl.constexpr, HEAD_FIRST: 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 USE_OFFSETS: i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32) bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32) else: bos, eos = i_b * T, i_b * T + T T = eos - bos b_dA_qk = tl.zeros([BT, BT], dtype=tl.float32) b_dA_qb = tl.zeros([BT, BT], dtype=tl.float32) if HEAD_FIRST: p_A_qb = tl.make_block_ptr(A_qb + i_bh * T*BT, (T, BT), (BT, 1), (i_t * BT, 0), (BT, BT), (1, 0)) else: p_A_qb = tl.make_block_ptr(A_qb + (bos * H + i_h) * BT, (T, BT), (H*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0)) b_A_qb = tl.load(p_A_qb, boundary_check=(0, 1)) # causal mask b_A_qb = tl.where(tl.arange(0, BT)[:, None] >= tl.arange(0, BT)[None, :], b_A_qb, 0.).to(b_A_qb.dtype) for i_v in range(tl.cdiv(V, BV)): if HEAD_FIRST: p_do = tl.make_block_ptr(do + i_bh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) p_v = tl.make_block_ptr(v + i_bh * T*V, (V, T), (1, V), (i_v * BV, i_t * BT), (BV, BT), (0, 1)) p_v_new = tl.make_block_ptr(v_new + i_bh * T*V, (V, T), (1, V), (i_v * BV, i_t * BT), (BV, BT), (0, 1)) p_dv_new = tl.make_block_ptr(dv_new + i_bh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) else: p_do = tl.make_block_ptr(do + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) p_v = tl.make_block_ptr(v + (bos*H + i_h) * V, (V, T), (1, H*V), (i_v * BV, i_t * BT), (BV, BT), (0, 1)) p_v_new = tl.make_block_ptr(v_new + (bos*H + i_h) * V, (V, T), (1, H*V), (i_v * BV, i_t * BT), (BV, BT), (0, 1)) p_dv_new = tl.make_block_ptr(dv_new + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) b_v = tl.load(p_v, boundary_check=(0, 1)) b_do = tl.load(p_do, boundary_check=(0, 1)) b_v_new = tl.load(p_v_new, boundary_check=(0, 1)) b_dA_qk += tl.dot(b_do, b_v) b_dA_qb += tl.dot(b_do, b_v_new) b_dv_new = tl.dot(tl.trans(b_A_qb), b_do) # for recurrent tl.store(p_dv_new, b_dv_new.to(p_dv_new.dtype.element_ty), boundary_check=(0, 1)) if HEAD_FIRST: p_dA_qk = tl.make_block_ptr(dA_qk + i_bh * T*BT, (T, BT), (BT, 1), (i_t * BT, 0), (BT, BT), (1, 0)) p_dA_qb = tl.make_block_ptr(dA_qb + i_bh * T*BT, (T, BT), (BT, 1), (i_t * BT, 0), (BT, BT), (1, 0)) else: p_dA_qk = tl.make_block_ptr(dA_qk + (bos * H + i_h) * BT, (T, BT), (H*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0)) p_dA_qb = tl.make_block_ptr(dA_qb + (bos * H + i_h) * BT, (T, BT), (H*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0)) m_s = tl.arange(0, BT)[:, None] >= tl.arange(0, BT)[None, :] b_dA_qk = tl.where(m_s, b_dA_qk * scale, 0.) tl.store(p_dA_qk, b_dA_qk.to(p_dA_qk.dtype.element_ty), boundary_check=(0, 1)) b_dA_qb = tl.where(m_s, b_dA_qb * scale, 0.) tl.store(p_dA_qb, b_dA_qb.to(p_dA_qb.dtype.element_ty), boundary_check=(0, 1)) @triton.heuristics({ 'USE_OFFSETS': lambda args: args['offsets'] is not None, }) @triton.autotune( configs=[ triton.Config({}, num_warps=num_warps, num_stages=num_stages) for num_warps in [2, 4, 8, 16, 32] for num_stages in [2, 3, 4] ], key=['BT', 'BK', 'BV'], use_cuda_graph=use_cuda_graph, ) @triton.jit def chunk_dplr_bwd_o_kernel( v, v_new, h, do, dh, dk, db, w, dq, dv, dw, gk, dgk_last, k, b, offsets, indices, T, H: tl.constexpr, K: tl.constexpr, V: tl.constexpr, BT: tl.constexpr, BK: tl.constexpr, BV: tl.constexpr, USE_OFFSETS: tl.constexpr, HEAD_FIRST: tl.constexpr, ): i_k, 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 if USE_OFFSETS: i_tg = i_t i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32) bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32) T = eos - bos NT = tl.cdiv(T, BT) else: NT = tl.cdiv(T, BT) i_tg = i_b * NT + i_t bos, eos = i_b * T, i_b * T + T # offset calculation v += i_bh * T * V if HEAD_FIRST else (bos * H + i_h) * V v_new += i_bh * T * V if HEAD_FIRST else (bos * H + i_h) * V do += i_bh * T * V if HEAD_FIRST else (bos * H + i_h) * V h += (i_bh * NT + i_t) * K*V if HEAD_FIRST else (i_tg * H + i_h) * K * V dh += (i_bh * NT + i_t) * K*V if HEAD_FIRST else (i_tg * H + i_h) * K * V dk += i_bh * T * K if HEAD_FIRST else (bos * H + i_h) * K k += i_bh * T * K if HEAD_FIRST else (bos * H + i_h) * K db += i_bh * T * K if HEAD_FIRST else (bos * H + i_h) * K b += i_bh * T * K if HEAD_FIRST else (bos * H + i_h) * K dw += i_bh * T * K if HEAD_FIRST else (bos * H + i_h) * K dv += i_bh * T * V if HEAD_FIRST else (bos * H + i_h) * V dq += i_bh * T * K if HEAD_FIRST else (bos * H + i_h) * K w += i_bh * T * K if HEAD_FIRST else (bos * H + i_h) * K # CHECK HEAD_FIRST is FALSE dgk_last += (i_bh * NT + i_t) * K if HEAD_FIRST else (i_tg * H + i_h) * K gk += i_bh * T * K if HEAD_FIRST else (bos * H + i_h) * K stride_qk = K if HEAD_FIRST else H*K stride_vo = V if HEAD_FIRST else H*V b_dq = tl.zeros([BT, BK], dtype=tl.float32) b_dk = tl.zeros([BT, BK], dtype=tl.float32) b_dw = tl.zeros([BT, BK], dtype=tl.float32) b_db = tl.zeros([BT, BK], dtype=tl.float32) b_dgk_last = tl.zeros([BK], dtype=tl.float32) for i_v in range(tl.cdiv(V, BV)): p_v = tl.make_block_ptr(v, (T, V), (stride_vo, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) p_v_new = tl.make_block_ptr(v_new, (T, V), (stride_vo, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) p_do = tl.make_block_ptr(do, (T, V), (stride_vo, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) p_h = tl.make_block_ptr(h, (V, K), (1, V), (i_v * BV, i_k * BK), (BV, BK), (0, 1)) p_dh = tl.make_block_ptr(dh, (V, K), (1, V), (i_v * BV, i_k * BK), (BV, BK), (0, 1)) # [BT, BV] b_v = tl.load(p_v, boundary_check=(0, 1)) b_v_new = tl.load(p_v_new, boundary_check=(0, 1)) b_do = tl.load(p_do, boundary_check=(0, 1)) # [BV, BK] b_h = tl.load(p_h, boundary_check=(0, 1)) b_dh = tl.load(p_dh, boundary_check=(0, 1)) b_dgk_last += tl.sum((b_h * b_dh).to(tl.float32), axis=0) # [BT, BV] @ [BV, BK] -> [BT, BK] b_dq += tl.dot(b_do, b_h.to(b_do.dtype)) # [BT, BV] @ [BV, BK] -> [BT, BK] b_dk += tl.dot(b_v, b_dh.to(b_v.dtype)) b_db += tl.dot(b_v_new, b_dh.to(b_v_new.dtype)) p_dv = tl.make_block_ptr(dv, (T, V), (stride_vo, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) b_dv = tl.load(p_dv, boundary_check=(0, 1)) b_dw += tl.dot(b_dv.to(b_v.dtype), b_h.to(b_v.dtype)) m_k = (i_k*BK+tl.arange(0, BK)) < K last_idx = min(i_t * BT + BT, T) - 1 b_gk_last = tl.load(gk + last_idx * stride_qk + i_k*BK + tl.arange(0, BK), mask=m_k, other=float('-inf')) b_dgk_last *= exp(b_gk_last) p_k = tl.make_block_ptr(k, (T, K), (stride_qk, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_b = tl.make_block_ptr(b, (T, K), (stride_qk, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) b_k = tl.load(p_k, boundary_check=(0, 1)) b_b = tl.load(p_b, boundary_check=(0, 1)) b_dgk_last += tl.sum(b_k * b_dk, axis=0) b_dgk_last += tl.sum(b_b * b_db, axis=0) tl.store(dgk_last + tl.arange(0, BK) + i_k * BK, b_dgk_last, mask=m_k) p_dw = tl.make_block_ptr(dw, (T, K), (stride_qk, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_dk = tl.make_block_ptr(dk, (T, K), (stride_qk, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_db = tl.make_block_ptr(db, (T, K), (stride_qk, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_dq = tl.make_block_ptr(dq, (T, K), (stride_qk, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) tl.store(p_dw, b_dw.to(p_dw.dtype.element_ty), boundary_check=(0, 1)) tl.store(p_dk, b_dk.to(p_dk.dtype.element_ty), boundary_check=(0, 1)) tl.store(p_db, b_db.to(p_db.dtype.element_ty), boundary_check=(0, 1)) tl.store(p_dq, b_dq.to(p_dq.dtype.element_ty), boundary_check=(0, 1)) @triton.heuristics({ 'USE_OFFSETS': lambda args: args['offsets'] is not None, }) @triton.autotune( configs=[ triton.Config({'BK': BK, 'BV': BV}, num_warps=num_warps, num_stages=num_stages) for num_warps in [2, 4, 8, 16, 32] for num_stages in [2, 3, 4] for BK in BK_LIST for BV in BK_LIST ], key=['BT', 'BK', 'BV'], use_cuda_graph=use_cuda_graph, ) @triton.jit def chunk_dplr_bwd_kernel_dv( A_qk, kg, do, dv, dh, offsets, indices, T, H: tl.constexpr, K: tl.constexpr, V: tl.constexpr, BT: tl.constexpr, BK: tl.constexpr, BV: tl.constexpr, USE_OFFSETS: tl.constexpr, HEAD_FIRST: tl.constexpr, ): i_v, 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 if USE_OFFSETS: i_tg = i_t i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32) bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32) T = eos - bos NT = tl.cdiv(T, BT) else: NT = tl.cdiv(T, BT) i_tg = i_b * NT + i_t bos, eos = i_b * T, i_b * T + T b_dv = tl.zeros([BT, BV], dtype=tl.float32) # offset calculation A_qk += i_bh * T * BT if HEAD_FIRST else (bos * H + i_h) * BT do += i_bh * T * V if HEAD_FIRST else (bos * H + i_h) * V dv += i_bh * T * V if HEAD_FIRST else (bos * H + i_h) * V kg += i_bh * T * K if HEAD_FIRST else (bos * H + i_h) * K dh += (i_bh * NT + i_t) * K*V if HEAD_FIRST else (i_tg * H + i_h) * K*V stride_qk = K if HEAD_FIRST else H*K stride_vo = V if HEAD_FIRST else H*V stride_A = BT if HEAD_FIRST else H*BT for i_k in range(tl.cdiv(K, BK)): p_dh = tl.make_block_ptr(dh, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0)) p_kg = tl.make_block_ptr(kg, (T, K), (stride_qk, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) b_dh = tl.load(p_dh, boundary_check=(0, 1)) b_kg = tl.load(p_kg, boundary_check=(0, 1)) b_dv += tl.dot(b_kg, b_dh.to(b_kg.dtype)) p_Aqk = tl.make_block_ptr(A_qk, (BT, T), (1, stride_A), (0, i_t * BT), (BT, BT), (0, 1)) b_A = tl.where(tl.arange(0, BT)[:, None] <= tl.arange(0, BT)[None, :], tl.load(p_Aqk, boundary_check=(0, 1)), 0) p_do = tl.make_block_ptr(do, (T, V), (stride_vo, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) p_dv = tl.make_block_ptr(dv, (T, V), (stride_vo, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) b_do = tl.load(p_do, boundary_check=(0, 1)) b_dv += tl.dot(b_A.to(b_do.dtype), b_do) tl.store(p_dv, b_dv.to(p_dv.dtype.element_ty), boundary_check=(0, 1)) def chunk_dplr_bwd_dv( A_qk: torch.Tensor, kg: torch.Tensor, do: torch.Tensor, dh: torch.Tensor, offsets: Optional[torch.LongTensor] = None, indices: Optional[torch.LongTensor] = None, head_first: bool = True, chunk_size: int = 64 ) -> torch.Tensor: if head_first: B, H, T, K, V = *kg.shape, do.shape[-1] else: B, T, H, K, V = *kg.shape, do.shape[-1] BT = min(chunk_size, max(16, triton.next_power_of_2(T))) NT = triton.cdiv(T, BT) if offsets is None else len(indices) dv = torch.empty_like(do) def grid(meta): return ( triton.cdiv(V, meta['BV']), NT, B * H ) chunk_dplr_bwd_kernel_dv[grid]( A_qk=A_qk, kg=kg, do=do, dv=dv, dh=dh, offsets=offsets, indices=indices, T=T, H=H, K=K, V=V, BT=BT, HEAD_FIRST=head_first ) return dv def chunk_dplr_bwd_o( k: torch.Tensor, b: torch.Tensor, v: torch.Tensor, v_new: torch.Tensor, gk: torch.Tensor, do: torch.Tensor, h: torch.Tensor, dh: torch.Tensor, dv: torch.Tensor, w: torch.Tensor, offsets: Optional[torch.LongTensor] = None, indices: Optional[torch.LongTensor] = None, chunk_size: int = 64, scale: float = 1.0, head_first: bool = True, ) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor]: if head_first: B, H, T, K, V = *w.shape, v.shape[-1] else: B, T, H, K, V = *w.shape, v.shape[-1] BT = min(chunk_size, max(16, triton.next_power_of_2(T))) NT = triton.cdiv(T, BT) if offsets is None else len(indices) BK = min(triton.next_power_of_2(K), 64) if check_shared_mem() else min(triton.next_power_of_2(K), 32) BV = min(triton.next_power_of_2(V), 64) if check_shared_mem() else min(triton.next_power_of_2(K), 32) NK = triton.cdiv(K, BK) dq = torch.empty_like(k) dk = torch.empty_like(k) dw = torch.empty_like(w) db = torch.empty_like(b) grid = (NK, NT, B * H) dgk_last = torch.empty(B, H, NT, K, dtype=torch.float, device=w.device) if head_first \ else torch.empty(B, NT, H, K, dtype=torch.float, device=w.device) chunk_dplr_bwd_o_kernel[grid]( k=k, b=b, v=v, v_new=v_new, h=h, do=do, dh=dh, dq=dq, dk=dk, db=db, dgk_last=dgk_last, w=w, dv=dv, dw=dw, gk=gk, offsets=offsets, indices=indices, T=T, H=H, K=K, V=V, BT=BT, BK=BK, BV=BV, HEAD_FIRST=head_first, ) return dq, dk, dw, db, dgk_last def chunk_dplr_bwd_dAu( v: torch.Tensor, v_new: torch.Tensor, do: torch.Tensor, A_qb: torch.Tensor, scale: float, offsets: Optional[torch.LongTensor] = None, indices: Optional[torch.LongTensor] = None, head_first: bool = True, chunk_size: int = 64 ) -> torch.Tensor: if head_first: B, H, T, V = v.shape else: B, T, H, V = v.shape BT = min(chunk_size, max(16, triton.next_power_of_2(T))) NT = triton.cdiv(T, BT) if offsets is None else len(indices) if check_shared_mem('ampere'): # A100 BV = min(triton.next_power_of_2(V), 128) elif check_shared_mem('ada'): # 4090 BV = min(triton.next_power_of_2(V), 64) else: BV = min(triton.next_power_of_2(V), 32) grid = (NT, B * H) dA_qk = torch.empty(B, H, T, BT, dtype=torch.float, device=v.device) if head_first \ else torch.empty(B, T, H, BT, dtype=torch.float, device=v.device) dA_qb = torch.empty(B, H, T, BT, dtype=torch.float, device=v.device) if head_first \ else torch.empty(B, T, H, BT, dtype=torch.float, device=v.device) dv_new = torch.empty_like(v_new) chunk_dplr_bwd_kernel_dAu[grid]( v=v, do=do, v_new=v_new, A_qb=A_qb, dA_qk=dA_qk, dA_qb=dA_qb, dv_new=dv_new, offsets=offsets, indices=indices, scale=scale, T=T, H=H, V=V, BT=BT, BV=BV, HEAD_FIRST=head_first ) return dv_new, dA_qk, dA_qb