""" Fused Attention =============== This is a Triton implementation of the Flash Attention algorithm (see: Dao et al., https://arxiv.org/pdf/2205.14135v2.pdf; Rabe and Staats https://arxiv.org/pdf/2112.05682v2.pdf; Triton https://github.com/openai/triton) """ import os import subprocess import torch def triton_check(): cuda_home = os.getenv("CUDA_HOME", default="/usr/local/cuda") cuda_version = subprocess.check_output([os.path.join(cuda_home, "bin/nvcc"), "--version"]).decode().strip() cuda_version = cuda_version.split('release ')[1] cuda_version = cuda_version.split(',')[0] cuda_version = cuda_version.split('.') if len(cuda_version) == 2 and \ (int(cuda_version[0]) == 11 and int(cuda_version[1]) >= 4) or \ int(cuda_version[0]) > 11: return True return False try: import triton import triton.language as tl if triton_check(): HAS_TRITON = True else: print("triton requires cuda >= 11.4") HAS_TRITON = False except ImportError: print('please install triton from https://github.com/openai/triton') HAS_TRITON = False try: from flash_attn.flash_attn_interface import flash_attn_unpadded_func HAS_FLASH_ATTN = True except ImportError: HAS_FLASH_ATTN = False print('please install flash_attn from https://github.com/HazyResearch/flash-attention') if HAS_TRITON: @triton.jit def _fwd_kernel( Q, K, V, sm_scale, TMP, L, M, # NOTE: TMP is a scratchpad buffer to workaround a compiler bug Out, stride_qz, stride_qh, stride_qm, stride_qk, stride_kz, stride_kh, stride_kn, stride_kk, stride_vz, stride_vh, stride_vk, stride_vn, stride_oz, stride_oh, stride_om, stride_on, Z, H, N_CTX, BLOCK_M: tl.constexpr, BLOCK_DMODEL: tl.constexpr, BLOCK_N: tl.constexpr, ): start_m = tl.program_id(0) off_hz = tl.program_id(1) # initialize offsets offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M) offs_n = tl.arange(0, BLOCK_N) offs_d = tl.arange(0, BLOCK_DMODEL) off_q = off_hz * stride_qh + offs_m[:, None] * stride_qm + offs_d[None, :] * stride_qk off_k = off_hz * stride_qh + offs_n[:, None] * stride_kn + offs_d[None, :] * stride_kk off_v = off_hz * stride_qh + offs_n[:, None] * stride_qm + offs_d[None, :] * stride_qk # Initialize pointers to Q, K, V q_ptrs = Q + off_q k_ptrs = K + off_k v_ptrs = V + off_v # initialize pointer to m and l t_ptrs = TMP + off_hz * N_CTX + offs_m m_i = tl.zeros([BLOCK_M], dtype=tl.float32) - float("inf") l_i = tl.zeros([BLOCK_M], dtype=tl.float32) acc = tl.zeros([BLOCK_M, BLOCK_DMODEL], dtype=tl.float32) # load q: it will stay in SRAM throughout q = tl.load(q_ptrs) # loop over k, v and update accumulator for start_n in range(0, (start_m + 1) * BLOCK_M, BLOCK_N): start_n = tl.multiple_of(start_n, BLOCK_N) # -- compute qk ---- k = tl.load(k_ptrs + start_n * stride_kn) qk = tl.zeros([BLOCK_M, BLOCK_N], dtype=tl.float32) qk += tl.dot(q, k, trans_b=True) qk *= sm_scale qk += tl.where(offs_m[:, None] >= (start_n + offs_n[None, :]), 0, float("-inf")) # -- compute m_ij, p, l_ij m_ij = tl.max(qk, 1) p = tl.exp(qk - m_ij[:, None]) l_ij = tl.sum(p, 1) # -- update m_i and l_i m_i_new = tl.maximum(m_i, m_ij) alpha = tl.exp(m_i - m_i_new) beta = tl.exp(m_ij - m_i_new) l_i_new = alpha * l_i + beta * l_ij # -- update output accumulator -- # scale p p_scale = beta / l_i_new p = p * p_scale[:, None] # scale acc acc_scale = l_i / l_i_new * alpha tl.store(t_ptrs, acc_scale) acc_scale = tl.load(t_ptrs) # BUG: have to store and immediately load acc = acc * acc_scale[:, None] # update acc v = tl.load(v_ptrs + start_n * stride_vk) p = p.to(tl.float16) acc += tl.dot(p, v) # update m_i and l_i l_i = l_i_new m_i = m_i_new # rematerialize offsets to save registers start_m = tl.program_id(0) offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M) # write back l and m l_ptrs = L + off_hz * N_CTX + offs_m m_ptrs = M + off_hz * N_CTX + offs_m tl.store(l_ptrs, l_i) tl.store(m_ptrs, m_i) # initialize pointers to output offs_n = tl.arange(0, BLOCK_DMODEL) off_o = off_hz * stride_oh + offs_m[:, None] * stride_om + offs_n[None, :] * stride_on out_ptrs = Out + off_o tl.store(out_ptrs, acc) @triton.jit def _bwd_preprocess( Out, DO, L, NewDO, Delta, BLOCK_M: tl.constexpr, D_HEAD: tl.constexpr, ): off_m = tl.program_id(0) * BLOCK_M + tl.arange(0, BLOCK_M) off_n = tl.arange(0, D_HEAD) # load o = tl.load(Out + off_m[:, None] * D_HEAD + off_n[None, :]).to(tl.float32) do = tl.load(DO + off_m[:, None] * D_HEAD + off_n[None, :]).to(tl.float32) denom = tl.load(L + off_m).to(tl.float32) # compute do = do / denom[:, None] delta = tl.sum(o * do, axis=1) # write-back tl.store(NewDO + off_m[:, None] * D_HEAD + off_n[None, :], do) tl.store(Delta + off_m, delta) @triton.jit def _bwd_kernel( Q, K, V, sm_scale, Out, DO, DQ, DK, DV, L, M, D, stride_qz, stride_qh, stride_qm, stride_qk, stride_kz, stride_kh, stride_kn, stride_kk, stride_vz, stride_vh, stride_vk, stride_vn, Z, H, N_CTX, num_block, BLOCK_M: tl.constexpr, BLOCK_DMODEL: tl.constexpr, BLOCK_N: tl.constexpr, ): off_hz = tl.program_id(0) off_z = off_hz // H off_h = off_hz % H # offset pointers for batch/head Q += off_z * stride_qz + off_h * stride_qh K += off_z * stride_qz + off_h * stride_qh V += off_z * stride_qz + off_h * stride_qh DO += off_z * stride_qz + off_h * stride_qh DQ += off_z * stride_qz + off_h * stride_qh DK += off_z * stride_qz + off_h * stride_qh DV += off_z * stride_qz + off_h * stride_qh for start_n in range(0, num_block): lo = start_n * BLOCK_M # initialize row/col offsets offs_qm = lo + tl.arange(0, BLOCK_M) offs_n = start_n * BLOCK_M + tl.arange(0, BLOCK_M) offs_m = tl.arange(0, BLOCK_N) offs_k = tl.arange(0, BLOCK_DMODEL) # initialize pointers to value-like data q_ptrs = Q + (offs_qm[:, None] * stride_qm + offs_k[None, :] * stride_qk) k_ptrs = K + (offs_n[:, None] * stride_kn + offs_k[None, :] * stride_kk) v_ptrs = V + (offs_n[:, None] * stride_qm + offs_k[None, :] * stride_qk) do_ptrs = DO + (offs_qm[:, None] * stride_qm + offs_k[None, :] * stride_qk) dq_ptrs = DQ + (offs_qm[:, None] * stride_qm + offs_k[None, :] * stride_qk) # pointer to row-wise quantities in value-like data D_ptrs = D + off_hz * N_CTX m_ptrs = M + off_hz * N_CTX # initialize dv amd dk dv = tl.zeros([BLOCK_M, BLOCK_DMODEL], dtype=tl.float32) dk = tl.zeros([BLOCK_M, BLOCK_DMODEL], dtype=tl.float32) # k and v stay in SRAM throughout k = tl.load(k_ptrs) v = tl.load(v_ptrs) # loop over rows for start_m in range(lo, num_block * BLOCK_M, BLOCK_M): offs_m_curr = start_m + offs_m # load q, k, v, do on-chip q = tl.load(q_ptrs) # recompute p = softmax(qk, dim=-1).T # NOTE: `do` is pre-divided by `l`; no normalization here qk = tl.dot(q, k, trans_b=True) qk = tl.where(offs_m_curr[:, None] >= (offs_n[None, :]), qk, float("-inf")) m = tl.load(m_ptrs + offs_m_curr) p = tl.exp(qk * sm_scale - m[:, None]) # compute dv do = tl.load(do_ptrs) dv += tl.dot(p.to(tl.float16), do, trans_a=True) # compute dp = dot(v, do) Di = tl.load(D_ptrs + offs_m_curr) dp = tl.zeros([BLOCK_M, BLOCK_N], dtype=tl.float32) - Di[:, None] dp += tl.dot(do, v, trans_b=True) # compute ds = p * (dp - delta[:, None]) ds = p * dp * sm_scale # compute dk = dot(ds.T, q) dk += tl.dot(ds.to(tl.float16), q, trans_a=True) # # compute dq dq = tl.load(dq_ptrs, eviction_policy="evict_last") dq += tl.dot(ds.to(tl.float16), k) tl.store(dq_ptrs, dq, eviction_policy="evict_last") # # increment pointers dq_ptrs += BLOCK_M * stride_qm q_ptrs += BLOCK_M * stride_qm do_ptrs += BLOCK_M * stride_qm # write-back dv_ptrs = DV + (offs_n[:, None] * stride_qm + offs_k[None, :] * stride_qk) dk_ptrs = DK + (offs_n[:, None] * stride_kn + offs_k[None, :] * stride_kk) tl.store(dv_ptrs, dv) tl.store(dk_ptrs, dk) class _TritonFlashAttention(torch.autograd.Function): @staticmethod def forward(ctx, q, k, v, sm_scale): BLOCK = 128 # shape constraints Lq, Lk, Lv = q.shape[-1], k.shape[-1], v.shape[-1] assert Lq == Lk and Lk == Lv assert Lk in {16, 32, 64, 128} o = torch.empty_like(q) grid = (triton.cdiv(q.shape[2], BLOCK), q.shape[0] * q.shape[1]) tmp = torch.empty((q.shape[0] * q.shape[1], q.shape[2]), device=q.device, dtype=torch.float32) L = torch.empty((q.shape[0] * q.shape[1], q.shape[2]), device=q.device, dtype=torch.float32) m = torch.empty((q.shape[0] * q.shape[1], q.shape[2]), device=q.device, dtype=torch.float32) num_warps = 4 if Lk <= 64 else 8 _fwd_kernel[grid]( q, k, v, sm_scale, tmp, L, m, o, q.stride(0), q.stride(1), q.stride(2), q.stride(3), k.stride(0), k.stride(1), k.stride(2), k.stride(3), v.stride(0), v.stride(1), v.stride(2), v.stride(3), o.stride(0), o.stride(1), o.stride(2), o.stride(3), q.shape[0], q.shape[1], q.shape[2], BLOCK_M=BLOCK, BLOCK_N=BLOCK, BLOCK_DMODEL=Lk, num_warps=num_warps, num_stages=1, ) ctx.save_for_backward(q, k, v, o, L, m) ctx.BLOCK = BLOCK ctx.grid = grid ctx.sm_scale = sm_scale ctx.BLOCK_DMODEL = Lk return o @staticmethod def backward(ctx, do): q, k, v, o, l, m = ctx.saved_tensors do = do.contiguous() dq = torch.zeros_like(q, dtype=torch.float32) dk = torch.empty_like(k) dv = torch.empty_like(v) do_scaled = torch.empty_like(do) delta = torch.empty_like(l) _bwd_preprocess[(ctx.grid[0] * ctx.grid[1],)]( o, do, l, do_scaled, delta, BLOCK_M=ctx.BLOCK, D_HEAD=ctx.BLOCK_DMODEL, ) # NOTE: kernel currently buggy for other values of `num_warps` num_warps = 8 _bwd_kernel[(ctx.grid[1],)]( q, k, v, ctx.sm_scale, o, do_scaled, dq, dk, dv, l, m, delta, q.stride(0), q.stride(1), q.stride(2), q.stride(3), k.stride(0), k.stride(1), k.stride(2), k.stride(3), v.stride(0), v.stride(1), v.stride(2), v.stride(3), q.shape[0], q.shape[1], q.shape[2], ctx.grid[0], BLOCK_M=ctx.BLOCK, BLOCK_N=ctx.BLOCK, BLOCK_DMODEL=ctx.BLOCK_DMODEL, num_warps=num_warps, num_stages=1, ) return dq, dk, dv, None def triton_flash_attention(q, k, v, sm_scale): """ Arguments: q: (batch, nheads, seq, headdim) k: (batch, nheads, seq, headdim) v: (batch, nheads, seq, headdim) sm_scale: float. The scaling of QK^T before applying softmax. Return: out: (batch, nheads, seq, headdim) """ if HAS_TRITON: return _TritonFlashAttention.apply(q, k, v, sm_scale) else: raise RuntimeError("Triton kernel requires CUDA 11.4+!") if HAS_FLASH_ATTN: def flash_attention(q, k, v, sm_scale, batch_size, seq_len, dropout_p=0., causal=True): """ Arguments: q: (total_q, nheads, headdim), where total_q = total number of query tokens in the batch. k: (total_k, nheads, headdim), where total_k = total number of key tokens in the batch. v: (total_k, nheads, headdim), where total_k = total number of key tokens in the batch. batch_size: int. seq_len: int. dropout_p: float. Dropout probability. sm_scale: float. The scaling of QK^T before applying softmax. Default to 1 / sqrt(headdim). causal: bool. Whether to apply causal attention mask (e.g., for auto-regressive modeling). Return: out: (total, nheads, headdim). """ lengths = torch.full((batch_size,), fill_value=seq_len, device=q.device) cu_seqlens = torch.zeros((batch_size + 1,), device=q.device, dtype=torch.int32) cu_seqlens[1:] = lengths.cumsum(0) return flash_attn_unpadded_func(q, k, v, cu_seqlens_q=cu_seqlens, cu_seqlens_k=cu_seqlens, max_seqlen_q=seq_len, max_seqlen_k=seq_len, dropout_p=dropout_p, softmax_scale=sm_scale, causal=causal)