""" 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) """ import pytest import torch import triton import triton.language as tl @triton.jit def _fwd_kernel( Q, K, V, sm_scale, TMP, L, M, # NOTE: TMP is a scratchpad buffer to work around 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 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, tl.trans(k)) 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 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, tl.trans(k)) 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(tl.trans(p.to(tl.float16)), do) # 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, tl.trans(v)) # compute ds = p * (dp - delta[:, None]) ds = p * dp * sm_scale # compute dk = dot(ds.T, q) dk += tl.dot(tl.trans(ds.to(tl.float16)), q) # compute dq dq = tl.load(dq_ptrs) dq += tl.dot(ds.to(tl.float16), k) tl.store(dq_ptrs, dq) # 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) empty = torch.empty(128, device="cuda") class _attention(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], 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 attention = _attention.apply @pytest.mark.parametrize('Z, H, N_CTX, D_HEAD', [(4, 48, 1024, 64)]) def test_op(Z, H, N_CTX, D_HEAD, dtype=torch.float16): torch.manual_seed(20) q = torch.empty((Z, H, N_CTX, D_HEAD), dtype=dtype, device="cuda").normal_(mean=0.1, std=0.2).requires_grad_() k = torch.empty((Z, H, N_CTX, D_HEAD), dtype=dtype, device="cuda").normal_(mean=0.4, std=0.2).requires_grad_() v = torch.empty((Z, H, N_CTX, D_HEAD), dtype=dtype, device="cuda").normal_(mean=0.3, std=0.2).requires_grad_() sm_scale = 0.2 dout = torch.randn_like(q) # reference implementation M = torch.tril(torch.ones((N_CTX, N_CTX), device="cuda")) p = torch.matmul(q, k.transpose(2, 3)) * sm_scale for z in range(Z): for h in range(H): p[:, :, M == 0] = float("-inf") p = torch.softmax(p.float(), dim=-1).half() # p = torch.exp(p) ref_out = torch.matmul(p, v) ref_out.backward(dout) ref_dv, v.grad = v.grad.clone(), None ref_dk, k.grad = k.grad.clone(), None ref_dq, q.grad = q.grad.clone(), None # # triton implementation tri_out = attention(q, k, v, sm_scale) # print(ref_out) # print(tri_out) tri_out.backward(dout) tri_dv, v.grad = v.grad.clone(), None tri_dk, k.grad = k.grad.clone(), None tri_dq, q.grad = q.grad.clone(), None # compare triton.testing.assert_almost_equal(ref_out, tri_out) triton.testing.assert_almost_equal(ref_dv, tri_dv) triton.testing.assert_almost_equal(ref_dk, tri_dk) triton.testing.assert_almost_equal(ref_dq, tri_dq) try: from flash_attn.flash_attn_interface import flash_attn_func HAS_FLASH = True except BaseException: HAS_FLASH = False BATCH, N_HEADS, N_CTX, D_HEAD = 4, 48, 4096, 64 # vary seq length for fixed head and batch=4 configs = [triton.testing.Benchmark( x_names=['N_CTX'], x_vals=[2**i for i in range(10, 16)], line_arg='provider', line_vals=['triton'] + (['flash'] if HAS_FLASH else []), line_names=['Triton'] + (['Flash'] if HAS_FLASH else []), styles=[('red', '-'), ('blue', '-')], ylabel='ms', plot_name=f'fused-attention-batch{BATCH}-head{N_HEADS}-d{D_HEAD}-{mode}', args={'H': N_HEADS, 'BATCH': BATCH, 'D_HEAD': D_HEAD, 'dtype': torch.float16, 'mode': mode} ) for mode in ['fwd']] @triton.testing.perf_report(configs) def bench_flash_attention(BATCH, H, N_CTX, D_HEAD, mode, provider, dtype=torch.float16, device="cuda"): assert mode in ['fwd', 'bwd'] warmup = 25 rep = 100 if provider == "triton": q = torch.randn((BATCH, H, N_CTX, D_HEAD), dtype=dtype, device="cuda", requires_grad=True) k = torch.randn((BATCH, H, N_CTX, D_HEAD), dtype=dtype, device="cuda", requires_grad=True) v = torch.randn((BATCH, H, N_CTX, D_HEAD), dtype=dtype, device="cuda", requires_grad=True) sm_scale = 1.3 fn = lambda: attention(q, k, v, sm_scale) if mode == 'bwd': o = fn() do = torch.randn_like(o) fn = lambda: o.backward(do, retain_graph=True) ms = triton.testing.do_bench(fn, percentiles=None, warmup=warmup, rep=rep) return ms if provider == "flash": lengths = torch.full((BATCH,), fill_value=N_CTX, device=device) cu_seqlens = torch.zeros((BATCH + 1,), device=device, dtype=torch.int32) cu_seqlens[1:] = lengths.cumsum(0) qkv = torch.randn((BATCH * N_CTX, 3, H, D_HEAD), dtype=dtype, device=device, requires_grad=True) fn = lambda: flash_attn_func(qkv, cu_seqlens, 0., N_CTX, causal=True) if mode == 'bwd': o = fn() do = torch.randn_like(o) fn = lambda: o.backward(do, retain_graph=True) ms = triton.testing.do_bench(fn, percentiles=None, warmup=warmup, rep=rep) return ms # bench_flash_attention.run(save_path='.', print_data=True)