import torch import torch.nn.functional as F import tilelang from tilelang.autotuner import * import tilelang.language as T import argparse @tilelang.jit(out_idx=[3, 4]) def flashattn_fwd(batch, heads, seq_len, dim, is_causal, block_M, block_N): scale = (1.0 / dim)**0.5 * 1.44269504 # log2(e) shape = [batch, seq_len, heads, dim] dtype = "float16" accum_dtype = "float" @T.prim_func def flash_fwd( Q: T.Tensor(shape, dtype), # type: ignore K: T.Tensor(shape, dtype), # type: ignore V: T.Tensor(shape, dtype), # type: ignore Output: T.Tensor(shape, dtype), # type: ignore lse: T.Tensor([batch, heads, seq_len], accum_dtype), # type: ignore ): with T.Kernel(T.ceildiv(seq_len, block_M), heads, batch, threads=128) as (bx, by, bz): Q_shared = T.alloc_shared([block_M, dim], dtype) # Q_local = T.alloc_fragment([block_M, dim], dtype) K_shared = T.alloc_shared([block_N, dim], dtype) V_shared = T.alloc_shared([block_N, dim], dtype) acc_s = T.alloc_fragment([block_M, block_N], accum_dtype) acc_s_cast = T.alloc_fragment([block_M, block_N], dtype) acc_o = T.alloc_fragment([block_M, dim], accum_dtype) scores_max = T.alloc_fragment([block_M], accum_dtype) scores_max_prev = T.alloc_fragment([block_M], accum_dtype) scores_scale = T.alloc_fragment([block_M], accum_dtype) scores_sum = T.alloc_fragment([block_M], accum_dtype) logsum = T.alloc_fragment([block_M], accum_dtype) T.annotate_layout({Q_shared: tilelang.layout.make_swizzled_layout(Q_shared)}) T.copy(Q[bz, bx * block_M:(bx + 1) * block_M, by, :], Q_shared) T.fill(acc_o, 0) T.fill(logsum, 0) T.fill(scores_max, -T.infinity(accum_dtype)) # T.copy(Q_shared, Q_local) # for i, j in T.Parallel(block_M, dim): # Q_local[i, j] *= scale loop_range = ( T.ceildiv( (bx + 1) * block_M, block_N) if is_causal else T.ceildiv(seq_len, block_N)) for k in T.Pipelined(loop_range, num_stages=1): T.copy(K[bz, k * block_N:(k + 1) * block_N, by, :], K_shared) if is_causal: for i, j in T.Parallel(block_M, block_N): acc_s[i, j] = T.if_then_else(bx * block_M + i >= k * block_N + j, 0, -T.infinity(acc_s.dtype)) else: T.clear(acc_s) T.gemm(Q_shared, K_shared, acc_s, transpose_B=True, policy=T.GemmWarpPolicy.FullRow) T.copy(V[bz, k * block_N:(k + 1) * block_N, by, :], V_shared) T.copy(scores_max, scores_max_prev) T.reduce_max(acc_s, scores_max, dim=1, clear=False) for i in T.Parallel(block_M): scores_scale[i] = T.exp2(scores_max_prev[i] * scale - scores_max[i] * scale) for i, j in T.Parallel(block_M, dim): acc_o[i, j] *= scores_scale[i] for i, j in T.Parallel(block_M, block_N): acc_s[i, j] = T.exp2(acc_s[i, j] * scale - scores_max[i] * scale) T.copy(acc_s, acc_s_cast) T.gemm(acc_s_cast, V_shared, acc_o, policy=T.GemmWarpPolicy.FullRow) T.reduce_sum(acc_s, scores_sum, dim=1) for i in T.Parallel(block_M): logsum[i] = logsum[i] * scores_scale[i] + scores_sum[i] for i, j in T.Parallel(block_M, dim): acc_o[i, j] /= logsum[i] T.copy(acc_o, Output[bz, bx * block_M:(bx + 1) * block_M, by, :]) for i in T.Parallel(block_M): logsum[i] = T.log2(logsum[i]) + scores_max[i] * scale T.copy(logsum, lse[bz, by, bx * block_M:(bx + 1) * block_M]) return flash_fwd @tilelang.jit(out_idx=[2]) def flashattn_bwd_preprocess(batch, heads, seq_len, dim): dtype = "float16" accum_dtype = "float" shape = [batch, seq_len, heads, dim] blk = 32 @T.prim_func def flash_bwd_prep( O: T.Tensor(shape, dtype), # type: ignore dO: T.Tensor(shape, dtype), # type: ignore Delta: T.Tensor([batch, heads, seq_len], accum_dtype), # type: ignore ): with T.Kernel(heads, T.ceildiv(seq_len, blk), batch) as (bx, by, bz): o = T.alloc_fragment([blk, blk], dtype) do = T.alloc_fragment([blk, blk], dtype) acc = T.alloc_fragment([blk, blk], accum_dtype) delta = T.alloc_fragment([blk], accum_dtype) T.clear(acc) for k in range(T.ceildiv(dim, blk)): T.copy(O[bz, by * blk:(by + 1) * blk, bx, k * blk:(k + 1) * blk], o) T.copy(dO[bz, by * blk:(by + 1) * blk, bx, k * blk:(k + 1) * blk], do) for i, j in T.Parallel(blk, blk): acc[i, j] += o[i, j] * do[i, j] T.reduce_sum(acc, delta, 1) T.copy(delta, Delta[bz, bx, by * blk:(by + 1) * blk]) return flash_bwd_prep def make_dq_layout(dQ): # atomicAdd can not be vectorized, so we need to reorder dq to match the 8x8 gemm fragment return T.Layout(dQ.shape, lambda b, l, h, d: [b, l // 8, h, d // 8, (d % 2), 4 * (l % 8) + (d % 8) // 2]) @tilelang.jit(out_idx=[1]) def flashattn_bwd_postprocess(batch, heads, seq_len, dim): dtype = "float16" accum_dtype = "float" shape = [batch, seq_len, heads, dim] blk = 64 @T.prim_func def flash_bwd_post( dQ: T.Tensor(shape, accum_dtype), # type: ignore dQ_out: T.Tensor(shape, dtype), # type: ignore ): with T.Kernel(T.ceildiv(seq_len, blk), heads, batch, threads=128) as (bx, by, bz): T.annotate_layout({dQ: make_dq_layout(dQ)}) T.copy( dQ[bz, bx * blk:(bx + 1) * blk, by, :], dQ_out[bz, bx * blk:(bx + 1) * blk, by, :], ) return flash_bwd_post @tilelang.jit def flashattn_bwd(batch, heads, seq_len, dim, is_causal, block_M, block_N): sm_scale = (1.0 / dim)**0.5 scale = (1.0 / dim)**0.5 * 1.44269504 # log2(e) shape = [batch, seq_len, heads, dim] dtype = "float16" accum_dtype = "float" @T.prim_func def flash_bwd( Q: T.Tensor(shape, dtype), # type: ignore K: T.Tensor(shape, dtype), # type: ignore V: T.Tensor(shape, dtype), # type: ignore dO: T.Tensor(shape, dtype), # type: ignore lse: T.Tensor([batch, heads, seq_len], accum_dtype), # type: ignore Delta: T.Tensor([batch, heads, seq_len], accum_dtype), # type: ignore dQ: T.Tensor(shape, accum_dtype), # type: ignore dK: T.Tensor(shape, dtype), # type: ignore dV: T.Tensor(shape, dtype), # type: ignore ): with T.Kernel(heads, T.ceildiv(seq_len, block_M), batch, threads=128) as (bx, by, bz): K_shared = T.alloc_shared([block_M, dim], dtype) dsT_shared = T.alloc_shared([block_M, block_N], dtype) # should not store K to local if dim is large # K_local = T.alloc_fragment([block_M, dim], dtype) # K_local_T = T.alloc_fragment([block_M, dim], dtype) # V_local = T.alloc_fragment([block_M, dim], dtype) q = T.alloc_shared([block_N, dim], dtype) V_shared = T.alloc_shared([block_M, dim], dtype) qkT = T.alloc_fragment([block_M, block_N], accum_dtype) dsT = T.alloc_fragment([block_M, block_N], accum_dtype) qkT_cast = T.alloc_fragment([block_M, block_N], dtype) dsT_cast = T.alloc_fragment([block_M, block_N], dtype) lse_shared = T.alloc_shared([block_N], accum_dtype) delta = T.alloc_shared([block_N], accum_dtype) do = T.alloc_shared([block_N, dim], dtype) dv = T.alloc_fragment([block_M, dim], accum_dtype) dk = T.alloc_fragment([block_M, dim], accum_dtype) dq = T.alloc_fragment([block_N, dim], accum_dtype) dv_shared = T.alloc_shared([block_N, dim], dtype) dk_shared = T.alloc_shared([block_N, dim], dtype) T.annotate_layout({ dQ: make_dq_layout(dQ), K_shared: tilelang.layout.make_swizzled_layout(K_shared), dv_shared: tilelang.layout.make_swizzled_layout(dv_shared), dk_shared: tilelang.layout.make_swizzled_layout(dk_shared), }) T.copy(K[bz, by * block_M:(by + 1) * block_M, bx, :], K_shared) T.copy(V[bz, by * block_M:(by + 1) * block_M, bx, :], V_shared) T.clear(dv) T.clear(dk) loop_st = T.floordiv(by * block_M, block_N) if is_causal else 0 loop_ed = T.ceildiv(seq_len, block_N) for k in T.Pipelined(loop_st, loop_ed, num_stages=2): T.copy(Q[bz, k * block_N:(k + 1) * block_N, bx, :], q) T.clear(qkT) T.gemm(K_shared, q, qkT, transpose_B=True, policy=T.GemmWarpPolicy.FullRow) T.copy(lse[bz, bx, k * block_N:(k + 1) * block_N], lse_shared) for i, j in T.Parallel(block_M, block_N): qkT[i, j] = T.exp2(qkT[i, j] * scale - lse_shared[j]) if is_causal: for i, j in T.Parallel(block_M, block_N): qkT[i, j] = T.if_then_else(by * block_M + i <= k * block_N + j, qkT[i, j], 0) T.copy(dO[bz, k * block_N:(k + 1) * block_N, bx, :], do) T.clear(dsT) T.gemm(V_shared, do, dsT, transpose_B=True, policy=T.GemmWarpPolicy.FullRow) T.copy(qkT, qkT_cast) T.gemm(qkT_cast, do, dv, policy=T.GemmWarpPolicy.FullRow) T.copy(Delta[bz, bx, k * block_N:(k + 1) * block_N], delta) for i, j in T.Parallel(block_M, block_N): dsT_cast[i, j] = qkT[i, j] * (dsT[i, j] - delta[j]) * sm_scale T.gemm(dsT_cast, q, dk, policy=T.GemmWarpPolicy.FullRow) T.copy(dsT_cast, dsT_shared) T.clear(dq) T.gemm(dsT_shared, K_shared, dq, transpose_A=True) for i, j in T.Parallel(block_N, dim): if k * block_N + i < seq_len: T.atomic_add(dQ[bz, k * block_N + i, bx, j], dq[i, j]) T.copy(dv, dv_shared) T.copy(dk, dk_shared) T.copy(dv_shared, dV[bz, by * block_M:(by + 1) * block_M, bx, :]) T.copy(dk_shared, dK[bz, by * block_M:(by + 1) * block_M, bx, :]) return flash_bwd class _attention(torch.autograd.Function): @staticmethod def forward(ctx, q, k, v, causal): BATCH, N_CTX, H, D_HEAD = q.shape block_M = 64 block_N = 64 if D_HEAD <= 128 else 32 o, lse = flashattn_fwd(BATCH, H, N_CTX, D_HEAD, causal, block_M, block_N)(q, k, v) ctx.save_for_backward(q, k, v, o, lse) ctx.causal = causal return o @staticmethod def backward(ctx, do): q, k, v, o, lse = ctx.saved_tensors BATCH, N_CTX, H, D_HEAD = q.shape def maybe_contiguous(x): if x.stride(-1) != 1: return x.contiguous() return x do, q, k, v, o = [maybe_contiguous(x) for x in (do, q, k, v, o)] block_M = 64 block_N = 64 if D_HEAD <= 64 else 32 kernel_prep = flashattn_bwd_preprocess(BATCH, H, N_CTX, D_HEAD) kernel_post = flashattn_bwd_postprocess(BATCH, H, N_CTX, D_HEAD) delta = kernel_prep(o, do) kernel = flashattn_bwd(BATCH, H, N_CTX, D_HEAD, ctx.causal, block_M, block_N) shape = [BATCH, N_CTX, H, D_HEAD] dq = torch.zeros(shape, dtype=torch.float32, device=q.device) dk = torch.empty(shape, dtype=torch.float16, device=q.device) dv = torch.empty(shape, dtype=torch.float16, device=q.device) kernel(q, k, v, do, lse, delta, dq, dk, dv) dq = kernel_post(dq) return dq, dk, dv, None attention = _attention.apply def ref_program(Q, K, V, is_causal): dim = Q.size(-1) scores = torch.einsum('bqhd,bkhd->bhqk', Q, K) scores = scores / torch.sqrt(torch.tensor(dim, dtype=scores.dtype)) if is_causal: seq_len = Q.size(1) mask = torch.tril(torch.ones(seq_len, seq_len, device=scores.device)) mask = mask.unsqueeze(0).unsqueeze(0) scores = scores.masked_fill(mask == 0, float('-inf')) attention_weights = F.softmax(scores, dim=-1) output = torch.einsum('bhqk,bkhd->bqhd', attention_weights, V) return output def main( BATCH: int = 8, H: int = 32, N_CTX: int = 1024, D_HEAD: int = 64, causal: bool = False, ): flops_per_matmul = 2.0 * BATCH * H * N_CTX * N_CTX * D_HEAD total_flops = 5 * flops_per_matmul if causal: total_flops *= 0.5 Q = ( torch.empty(BATCH, N_CTX, H, D_HEAD, dtype=torch.half, device="cuda").normal_().requires_grad_()) K = torch.empty_like(Q).normal_().requires_grad_() V = torch.empty_like(Q).normal_().requires_grad_() dO = torch.randn_like(Q) O = attention(Q, K, V, causal) O.backward(dO, retain_graph=True) dQ, Q.grad = Q.grad.clone(), None dK, K.grad = K.grad.clone(), None dV, V.grad = V.grad.clone(), None O_ref = ref_program(Q, K, V, causal) O_ref.backward(dO, retain_graph=True) dQ_ref, Q.grad = Q.grad.clone(), None dK_ref, K.grad = K.grad.clone(), None dV_ref, V.grad = V.grad.clone(), None assert torch.allclose(O, O_ref, rtol=1e-2, atol=1e-2) assert torch.allclose(dV, dV_ref, rtol=1e-2, atol=1e-2) assert torch.allclose(dK, dK_ref, rtol=1e-2, atol=1e-2) assert torch.allclose(dQ, dQ_ref, rtol=1e-2, atol=1e-2) def run(): O_ref.backward(dO, retain_graph=True) def run1(): O.backward(dO, retain_graph=True) from tilelang.profiler import do_bench latency = do_bench(run, warmup=500) print("torch: {:.2f} ms".format(latency)) print("torch: {:.2f} TFlops".format(total_flops / latency * 1e-9)) latency = do_bench(run1, warmup=500) print("tilelang: {:.2f} ms".format(latency)) print("tilelang: {:.2f} TFlops".format(total_flops / latency * 1e-9)) if __name__ == "__main__": parser = argparse.ArgumentParser() parser.add_argument('--batch', type=int, default=8, help='Batch size') parser.add_argument('--h', type=int, default=32, help='Number of heads') parser.add_argument('--n_ctx', type=int, default=1024, help='Context size') parser.add_argument('--d_head', type=int, default=64, help='Head dimension') parser.add_argument('--causal', type=bool, default=False, help='Causal flag') args = parser.parse_args() main(args.batch, args.h, args.n_ctx, args.d_head, args.causal)