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""" |
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Copied from https://github.com/HazyResearch/flash-attention/blob/eff9fe6b8076df59d64d7a3f464696738a3c7c24/flash_attn/flash_attn_triton.py |
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update imports to use 'triton_pre_mlir' |
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|
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*Experimental* implementation of FlashAttention in Triton. |
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Tested with triton==2.0.0.dev20221202. |
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Triton 2.0 has a new backend (MLIR) but seems like it doesn't yet work for head dimensions |
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other than 64: |
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https://github.com/openai/triton/blob/d376020f90002757eea3ea9475d4f7cfc2ec5ead/python/triton/ops/flash_attention.py#L207 |
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We'll update this implementation with the new Triton backend once this is fixed. |
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|
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We use the FlashAttention implementation from Phil Tillet a starting point. |
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https://github.com/openai/triton/blob/master/python/tutorials/06-fused-attention.py |
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|
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Changes: |
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- Implement both causal and non-causal attention. |
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- Implement both self-attention and cross-attention. |
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- Support arbitrary seqlens (not just multiples of 128), for both forward and backward. |
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- Support all head dimensions up to 128 (not just 16, 32, 64, 128), for both forward and backward. |
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- Support attention bias. |
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- Speed up the forward pass a bit, and only store the LSE instead of m and l. |
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- Make the backward for d=128 much faster by reducing register spilling. |
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- Optionally parallelize the backward pass across seqlen_k, to deal with the case of |
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small batch size * nheads. |
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|
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Caution: |
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- This is an *experimental* implementation. The forward pass should be quite robust but |
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I'm not 100% sure that the backward pass doesn't have race conditions (due to the Triton compiler). |
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- This implementation has only been tested on A100. |
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- If you plan to use headdim other than 64 and 128, you should test for race conditions |
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(due to the Triton compiler), as done in tests/test_flash_attn.py |
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"test_flash_attn_triton_race_condition". I've tested and fixed many race conditions |
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for different head dimensions (40, 48, 64, 128, 80, 88, 96), but I'm still not 100% confident |
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that there are none left for other head dimensions. |
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|
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Differences between this Triton version and the CUDA version: |
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- Triton version doesn't support dropout. |
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- Triton forward is generally faster than CUDA forward, while Triton backward is |
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generally slower than CUDA backward. Overall Triton forward + backward is slightly slower |
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than CUDA forward + backward. |
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- Triton version doesn't support different sequence lengths in a batch (i.e., RaggedTensor/NestedTensor). |
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- Triton version supports attention bias, while CUDA version doesn't. |
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""" |
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import math |
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import torch |
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import triton_pre_mlir as triton |
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import triton_pre_mlir.language as tl |
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|
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@triton.heuristics({'EVEN_M': lambda args: args['seqlen_q'] % args['BLOCK_M'] == 0, 'EVEN_N': lambda args: args['seqlen_k'] % args['BLOCK_N'] == 0, 'EVEN_HEADDIM': lambda args: args['headdim'] == args['BLOCK_HEADDIM']}) |
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@triton.jit |
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def _fwd_kernel(Q, K, V, Bias, Out, Lse, TMP, softmax_scale, stride_qb, stride_qh, stride_qm, stride_kb, stride_kh, stride_kn, stride_vb, stride_vh, stride_vn, stride_bb, stride_bh, stride_bm, stride_ob, stride_oh, stride_om, nheads, seqlen_q, seqlen_k, seqlen_q_rounded, headdim, CACHE_KEY_SEQLEN_Q, CACHE_KEY_SEQLEN_K, BIAS_TYPE: tl.constexpr, IS_CAUSAL: tl.constexpr, BLOCK_HEADDIM: tl.constexpr, EVEN_M: tl.constexpr, EVEN_N: tl.constexpr, EVEN_HEADDIM: tl.constexpr, BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr): |
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start_m = tl.program_id(0) |
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off_hb = tl.program_id(1) |
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off_b = off_hb // nheads |
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off_h = off_hb % nheads |
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offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M) |
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offs_n = tl.arange(0, BLOCK_N) |
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offs_d = tl.arange(0, BLOCK_HEADDIM) |
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q_ptrs = Q + off_b * stride_qb + off_h * stride_qh + (offs_m[:, None] * stride_qm + offs_d[None, :]) |
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k_ptrs = K + off_b * stride_kb + off_h * stride_kh + (offs_n[:, None] * stride_kn + offs_d[None, :]) |
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v_ptrs = V + off_b * stride_vb + off_h * stride_vh + (offs_n[:, None] * stride_vn + offs_d[None, :]) |
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if BIAS_TYPE == 'vector': |
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b_ptrs = Bias + off_b * stride_bb + off_h * stride_bh + offs_n |
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elif BIAS_TYPE == 'matrix': |
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b_ptrs = Bias + off_b * stride_bb + off_h * stride_bh + (offs_m[:, None] * stride_bm + offs_n[None, :]) |
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t_ptrs = TMP + off_hb * seqlen_q_rounded + offs_m |
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lse_i = tl.zeros([BLOCK_M], dtype=tl.float32) - float('inf') |
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m_i = tl.zeros([BLOCK_M], dtype=tl.float32) - float('inf') |
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acc_o = tl.zeros([BLOCK_M, BLOCK_HEADDIM], dtype=tl.float32) |
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if EVEN_M & EVEN_N: |
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if EVEN_HEADDIM: |
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q = tl.load(q_ptrs) |
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else: |
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q = tl.load(q_ptrs, mask=offs_d[None, :] < headdim, other=0.0) |
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elif EVEN_HEADDIM: |
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q = tl.load(q_ptrs, mask=offs_m[:, None] < seqlen_q, other=0.0) |
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else: |
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q = tl.load(q_ptrs, mask=(offs_m[:, None] < seqlen_q) & (offs_d[None, :] < headdim), other=0.0) |
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end_n = seqlen_k if not IS_CAUSAL else tl.minimum((start_m + 1) * BLOCK_M, seqlen_k) |
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for start_n in range(0, end_n, BLOCK_N): |
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start_n = tl.multiple_of(start_n, BLOCK_N) |
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if EVEN_N & EVEN_M: |
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if EVEN_HEADDIM: |
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k = tl.load(k_ptrs + start_n * stride_kn) |
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else: |
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k = tl.load(k_ptrs + start_n * stride_kn, mask=offs_d[None, :] < headdim, other=0.0) |
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elif EVEN_HEADDIM: |
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k = tl.load(k_ptrs + start_n * stride_kn, mask=(start_n + offs_n)[:, None] < seqlen_k, other=0.0) |
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else: |
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k = tl.load(k_ptrs + start_n * stride_kn, mask=((start_n + offs_n)[:, None] < seqlen_k) & (offs_d[None, :] < headdim), other=0.0) |
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qk = tl.zeros([BLOCK_M, BLOCK_N], dtype=tl.float32) |
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qk += tl.dot(q, k, trans_b=True) |
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if not EVEN_N: |
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qk += tl.where((start_n + offs_n)[None, :] < seqlen_k, 0, float('-inf')) |
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if IS_CAUSAL: |
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qk += tl.where(offs_m[:, None] >= (start_n + offs_n)[None, :], 0, float('-inf')) |
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if BIAS_TYPE != 'none': |
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if BIAS_TYPE == 'vector': |
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if EVEN_N: |
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bias = tl.load(b_ptrs + start_n).to(tl.float32) |
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else: |
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bias = tl.load(b_ptrs + start_n, mask=start_n + offs_n < seqlen_k, other=0.0).to(tl.float32) |
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bias = bias[None, :] |
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elif BIAS_TYPE == 'matrix': |
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if EVEN_M & EVEN_N: |
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bias = tl.load(b_ptrs + start_n).to(tl.float32) |
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else: |
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bias = tl.load(b_ptrs + start_n, mask=(offs_m[:, None] < seqlen_q) & ((start_n + offs_n)[None, :] < seqlen_k), other=0.0).to(tl.float32) |
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qk = qk * softmax_scale + bias |
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m_ij = tl.maximum(tl.max(qk, 1), lse_i) |
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p = tl.exp(qk - m_ij[:, None]) |
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else: |
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m_ij = tl.maximum(tl.max(qk, 1) * softmax_scale, lse_i) |
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p = tl.exp(qk * softmax_scale - m_ij[:, None]) |
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l_ij = tl.sum(p, 1) |
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acc_o_scale = tl.exp(m_i - m_ij) |
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tl.store(t_ptrs, acc_o_scale) |
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acc_o_scale = tl.load(t_ptrs) |
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acc_o = acc_o * acc_o_scale[:, None] |
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if EVEN_N & EVEN_M: |
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if EVEN_HEADDIM: |
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v = tl.load(v_ptrs + start_n * stride_vn) |
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else: |
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v = tl.load(v_ptrs + start_n * stride_vn, mask=offs_d[None, :] < headdim, other=0.0) |
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elif EVEN_HEADDIM: |
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v = tl.load(v_ptrs + start_n * stride_vn, mask=(start_n + offs_n)[:, None] < seqlen_k, other=0.0) |
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else: |
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v = tl.load(v_ptrs + start_n * stride_vn, mask=((start_n + offs_n)[:, None] < seqlen_k) & (offs_d[None, :] < headdim), other=0.0) |
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p = p.to(v.dtype) |
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acc_o += tl.dot(p, v) |
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m_i = m_ij |
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l_i_new = tl.exp(lse_i - m_ij) + l_ij |
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lse_i = m_ij + tl.log(l_i_new) |
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o_scale = tl.exp(m_i - lse_i) |
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tl.store(t_ptrs, o_scale) |
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o_scale = tl.load(t_ptrs) |
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acc_o = acc_o * o_scale[:, None] |
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start_m = tl.program_id(0) |
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offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M) |
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lse_ptrs = Lse + off_hb * seqlen_q_rounded + offs_m |
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tl.store(lse_ptrs, lse_i) |
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offs_d = tl.arange(0, BLOCK_HEADDIM) |
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out_ptrs = Out + off_b * stride_ob + off_h * stride_oh + (offs_m[:, None] * stride_om + offs_d[None, :]) |
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if EVEN_M: |
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if EVEN_HEADDIM: |
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tl.store(out_ptrs, acc_o) |
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else: |
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tl.store(out_ptrs, acc_o, mask=offs_d[None, :] < headdim) |
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elif EVEN_HEADDIM: |
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tl.store(out_ptrs, acc_o, mask=offs_m[:, None] < seqlen_q) |
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else: |
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tl.store(out_ptrs, acc_o, mask=(offs_m[:, None] < seqlen_q) & (offs_d[None, :] < headdim)) |
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|
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@triton.jit |
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def _bwd_preprocess_do_o_dot(Out, DO, Delta, stride_ob, stride_oh, stride_om, stride_dob, stride_doh, stride_dom, nheads, seqlen_q, seqlen_q_rounded, headdim, BLOCK_M: tl.constexpr, BLOCK_HEADDIM: tl.constexpr): |
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start_m = tl.program_id(0) |
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off_hb = tl.program_id(1) |
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off_b = off_hb // nheads |
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off_h = off_hb % nheads |
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offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M) |
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offs_d = tl.arange(0, BLOCK_HEADDIM) |
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o = tl.load(Out + off_b * stride_ob + off_h * stride_oh + offs_m[:, None] * stride_om + offs_d[None, :], mask=(offs_m[:, None] < seqlen_q) & (offs_d[None, :] < headdim), other=0.0).to(tl.float32) |
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do = tl.load(DO + off_b * stride_dob + off_h * stride_doh + offs_m[:, None] * stride_dom + offs_d[None, :], mask=(offs_m[:, None] < seqlen_q) & (offs_d[None, :] < headdim), other=0.0).to(tl.float32) |
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delta = tl.sum(o * do, axis=1) |
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tl.store(Delta + off_hb * seqlen_q_rounded + offs_m, delta) |
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|
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@triton.jit |
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def _bwd_store_dk_dv(dk_ptrs, dv_ptrs, dk, dv, offs_n, offs_d, seqlen_k, headdim, EVEN_M: tl.constexpr, EVEN_N: tl.constexpr, EVEN_HEADDIM: tl.constexpr): |
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if EVEN_N & EVEN_M: |
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if EVEN_HEADDIM: |
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tl.store(dv_ptrs, dv) |
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tl.store(dk_ptrs, dk) |
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else: |
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tl.store(dv_ptrs, dv, mask=offs_d[None, :] < headdim) |
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tl.store(dk_ptrs, dk, mask=offs_d[None, :] < headdim) |
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elif EVEN_HEADDIM: |
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tl.store(dv_ptrs, dv, mask=offs_n[:, None] < seqlen_k) |
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tl.store(dk_ptrs, dk, mask=offs_n[:, None] < seqlen_k) |
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else: |
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tl.store(dv_ptrs, dv, mask=(offs_n[:, None] < seqlen_k) & (offs_d[None, :] < headdim)) |
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tl.store(dk_ptrs, dk, mask=(offs_n[:, None] < seqlen_k) & (offs_d[None, :] < headdim)) |
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|
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@triton.jit |
|
def _bwd_kernel_one_col_block(start_n, Q, K, V, Bias, DO, DQ, DK, DV, LSE, D, softmax_scale, stride_qm, stride_kn, stride_vn, stride_bm, stride_dom, stride_dqm, stride_dkn, stride_dvn, seqlen_q, seqlen_k, headdim, ATOMIC_ADD: tl.constexpr, BIAS_TYPE: tl.constexpr, IS_CAUSAL: tl.constexpr, BLOCK_HEADDIM: tl.constexpr, EVEN_M: tl.constexpr, EVEN_N: tl.constexpr, EVEN_HEADDIM: tl.constexpr, BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr): |
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begin_m = 0 if not IS_CAUSAL else start_n * BLOCK_N // BLOCK_M * BLOCK_M |
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offs_qm = begin_m + tl.arange(0, BLOCK_M) |
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offs_n = start_n * BLOCK_N + tl.arange(0, BLOCK_N) |
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offs_m = tl.arange(0, BLOCK_M) |
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offs_d = tl.arange(0, BLOCK_HEADDIM) |
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q_ptrs = Q + (offs_qm[:, None] * stride_qm + offs_d[None, :]) |
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k_ptrs = K + (offs_n[:, None] * stride_kn + offs_d[None, :]) |
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v_ptrs = V + (offs_n[:, None] * stride_vn + offs_d[None, :]) |
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do_ptrs = DO + (offs_qm[:, None] * stride_dom + offs_d[None, :]) |
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dq_ptrs = DQ + (offs_qm[:, None] * stride_dqm + offs_d[None, :]) |
|
if BIAS_TYPE == 'vector': |
|
b_ptrs = Bias + offs_n |
|
elif BIAS_TYPE == 'matrix': |
|
b_ptrs = Bias + (offs_qm[:, None] * stride_bm + offs_n[None, :]) |
|
dv = tl.zeros([BLOCK_N, BLOCK_HEADDIM], dtype=tl.float32) |
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dk = tl.zeros([BLOCK_N, BLOCK_HEADDIM], dtype=tl.float32) |
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if begin_m >= seqlen_q: |
|
dv_ptrs = DV + (offs_n[:, None] * stride_dvn + offs_d[None, :]) |
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dk_ptrs = DK + (offs_n[:, None] * stride_dkn + offs_d[None, :]) |
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_bwd_store_dk_dv(dk_ptrs, dv_ptrs, dk, dv, offs_n, offs_d, seqlen_k, headdim, EVEN_M=EVEN_M, EVEN_N=EVEN_N, EVEN_HEADDIM=EVEN_HEADDIM) |
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return |
|
if EVEN_N & EVEN_M: |
|
if EVEN_HEADDIM: |
|
k = tl.load(k_ptrs) |
|
v = tl.load(v_ptrs) |
|
else: |
|
k = tl.load(k_ptrs, mask=offs_d[None, :] < headdim, other=0.0) |
|
v = tl.load(v_ptrs, mask=offs_d[None, :] < headdim, other=0.0) |
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elif EVEN_HEADDIM: |
|
k = tl.load(k_ptrs, mask=offs_n[:, None] < seqlen_k, other=0.0) |
|
v = tl.load(v_ptrs, mask=offs_n[:, None] < seqlen_k, other=0.0) |
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else: |
|
k = tl.load(k_ptrs, mask=(offs_n[:, None] < seqlen_k) & (offs_d[None, :] < headdim), other=0.0) |
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v = tl.load(v_ptrs, mask=(offs_n[:, None] < seqlen_k) & (offs_d[None, :] < headdim), other=0.0) |
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num_block_m = tl.cdiv(seqlen_q, BLOCK_M) |
|
for start_m in range(begin_m, num_block_m * BLOCK_M, BLOCK_M): |
|
start_m = tl.multiple_of(start_m, BLOCK_M) |
|
offs_m_curr = start_m + offs_m |
|
if EVEN_M & EVEN_HEADDIM: |
|
q = tl.load(q_ptrs) |
|
elif EVEN_HEADDIM: |
|
q = tl.load(q_ptrs, mask=offs_m_curr[:, None] < seqlen_q, other=0.0) |
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else: |
|
q = tl.load(q_ptrs, mask=(offs_m_curr[:, None] < seqlen_q) & (offs_d[None, :] < headdim), other=0.0) |
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qk = tl.dot(q, k, trans_b=True) |
|
if not EVEN_N: |
|
qk = tl.where(offs_n[None, :] < seqlen_k, qk, float('-inf')) |
|
if IS_CAUSAL: |
|
qk = tl.where(offs_m_curr[:, None] >= offs_n[None, :], qk, float('-inf')) |
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if BIAS_TYPE != 'none': |
|
tl.debug_barrier() |
|
if BIAS_TYPE == 'vector': |
|
if EVEN_N: |
|
bias = tl.load(b_ptrs).to(tl.float32) |
|
else: |
|
bias = tl.load(b_ptrs, mask=offs_n < seqlen_k, other=0.0).to(tl.float32) |
|
bias = bias[None, :] |
|
elif BIAS_TYPE == 'matrix': |
|
if EVEN_M & EVEN_N: |
|
bias = tl.load(b_ptrs).to(tl.float32) |
|
else: |
|
bias = tl.load(b_ptrs, mask=(offs_m_curr[:, None] < seqlen_q) & (offs_n[None, :] < seqlen_k), other=0.0).to(tl.float32) |
|
qk = qk * softmax_scale + bias |
|
if not EVEN_M & EVEN_HEADDIM: |
|
tl.debug_barrier() |
|
lse_i = tl.load(LSE + offs_m_curr) |
|
if BIAS_TYPE == 'none': |
|
p = tl.exp(qk * softmax_scale - lse_i[:, None]) |
|
else: |
|
p = tl.exp(qk - lse_i[:, None]) |
|
if EVEN_M & EVEN_HEADDIM: |
|
do = tl.load(do_ptrs) |
|
else: |
|
do = tl.load(do_ptrs, mask=(offs_m_curr[:, None] < seqlen_q) & (offs_d[None, :] < headdim), other=0.0) |
|
dv += tl.dot(p.to(do.dtype), do, trans_a=True) |
|
if not EVEN_M & EVEN_HEADDIM: |
|
tl.debug_barrier() |
|
dp = tl.dot(do, v, trans_b=True) |
|
if not EVEN_HEADDIM: |
|
tl.debug_barrier() |
|
Di = tl.load(D + offs_m_curr) |
|
ds = (p * (dp - Di[:, None]) * softmax_scale).to(q.dtype) |
|
dk += tl.dot(ds, q, trans_a=True) |
|
if not EVEN_M & EVEN_HEADDIM: |
|
tl.debug_barrier() |
|
if not ATOMIC_ADD: |
|
if EVEN_M & EVEN_HEADDIM: |
|
dq = tl.load(dq_ptrs, eviction_policy='evict_last') |
|
dq += tl.dot(ds, k) |
|
tl.store(dq_ptrs, dq, eviction_policy='evict_last') |
|
elif EVEN_HEADDIM: |
|
dq = tl.load(dq_ptrs, mask=offs_m_curr[:, None] < seqlen_q, other=0.0, eviction_policy='evict_last') |
|
dq += tl.dot(ds, k) |
|
tl.store(dq_ptrs, dq, mask=offs_m_curr[:, None] < seqlen_q, eviction_policy='evict_last') |
|
else: |
|
dq = tl.load(dq_ptrs, mask=(offs_m_curr[:, None] < seqlen_q) & (offs_d[None, :] < headdim), other=0.0, eviction_policy='evict_last') |
|
dq += tl.dot(ds, k) |
|
tl.store(dq_ptrs, dq, mask=(offs_m_curr[:, None] < seqlen_q) & (offs_d[None, :] < headdim), eviction_policy='evict_last') |
|
else: |
|
dq = tl.dot(ds, k) |
|
if EVEN_M & EVEN_HEADDIM: |
|
tl.atomic_add(dq_ptrs, dq) |
|
elif EVEN_HEADDIM: |
|
tl.atomic_add(dq_ptrs, dq, mask=offs_m_curr[:, None] < seqlen_q) |
|
else: |
|
tl.atomic_add(dq_ptrs, dq, mask=(offs_m_curr[:, None] < seqlen_q) & (offs_d[None, :] < headdim)) |
|
dq_ptrs += BLOCK_M * stride_dqm |
|
q_ptrs += BLOCK_M * stride_qm |
|
do_ptrs += BLOCK_M * stride_dom |
|
if BIAS_TYPE == 'matrix': |
|
b_ptrs += BLOCK_M * stride_bm |
|
dv_ptrs = DV + (offs_n[:, None] * stride_dvn + offs_d[None, :]) |
|
dk_ptrs = DK + (offs_n[:, None] * stride_dkn + offs_d[None, :]) |
|
_bwd_store_dk_dv(dk_ptrs, dv_ptrs, dk, dv, offs_n, offs_d, seqlen_k, headdim, EVEN_M=EVEN_M, EVEN_N=EVEN_N, EVEN_HEADDIM=EVEN_HEADDIM) |
|
|
|
def init_to_zero(name): |
|
return lambda nargs: nargs[name].zero_() |
|
|
|
@triton.autotune(configs=[triton.Config({'BLOCK_M': 128, 'BLOCK_N': 128, 'SEQUENCE_PARALLEL': False}, num_warps=8, num_stages=1, pre_hook=init_to_zero('DQ')), triton.Config({'BLOCK_M': 128, 'BLOCK_N': 128, 'SEQUENCE_PARALLEL': True}, num_warps=8, num_stages=1, pre_hook=init_to_zero('DQ'))], key=['CACHE_KEY_SEQLEN_Q', 'CACHE_KEY_SEQLEN_K', 'BIAS_TYPE', 'IS_CAUSAL', 'BLOCK_HEADDIM']) |
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@triton.heuristics({'EVEN_M': lambda args: args['seqlen_q'] % args['BLOCK_M'] == 0, 'EVEN_N': lambda args: args['seqlen_k'] % args['BLOCK_N'] == 0, 'EVEN_HEADDIM': lambda args: args['headdim'] == args['BLOCK_HEADDIM']}) |
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@triton.jit |
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def _bwd_kernel(Q, K, V, Bias, DO, DQ, DK, DV, LSE, D, softmax_scale, stride_qb, stride_qh, stride_qm, stride_kb, stride_kh, stride_kn, stride_vb, stride_vh, stride_vn, stride_bb, stride_bh, stride_bm, stride_dob, stride_doh, stride_dom, stride_dqb, stride_dqh, stride_dqm, stride_dkb, stride_dkh, stride_dkn, stride_dvb, stride_dvh, stride_dvn, nheads, seqlen_q, seqlen_k, seqlen_q_rounded, headdim, CACHE_KEY_SEQLEN_Q, CACHE_KEY_SEQLEN_K, BIAS_TYPE: tl.constexpr, IS_CAUSAL: tl.constexpr, BLOCK_HEADDIM: tl.constexpr, SEQUENCE_PARALLEL: tl.constexpr, EVEN_M: tl.constexpr, EVEN_N: tl.constexpr, EVEN_HEADDIM: tl.constexpr, BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr): |
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off_hb = tl.program_id(1) |
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off_b = off_hb // nheads |
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off_h = off_hb % nheads |
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Q += off_b * stride_qb + off_h * stride_qh |
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K += off_b * stride_kb + off_h * stride_kh |
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V += off_b * stride_vb + off_h * stride_vh |
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DO += off_b * stride_dob + off_h * stride_doh |
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DQ += off_b * stride_dqb + off_h * stride_dqh |
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DK += off_b * stride_dkb + off_h * stride_dkh |
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DV += off_b * stride_dvb + off_h * stride_dvh |
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if BIAS_TYPE != 'none': |
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Bias += off_b * stride_bb + off_h * stride_bh |
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D += off_hb * seqlen_q_rounded |
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LSE += off_hb * seqlen_q_rounded |
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if not SEQUENCE_PARALLEL: |
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num_block_n = tl.cdiv(seqlen_k, BLOCK_N) |
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for start_n in range(0, num_block_n): |
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_bwd_kernel_one_col_block(start_n, Q, K, V, Bias, DO, DQ, DK, DV, LSE, D, softmax_scale, stride_qm, stride_kn, stride_vn, stride_bm, stride_dom, stride_dqm, stride_dkn, stride_dvn, seqlen_q, seqlen_k, headdim, ATOMIC_ADD=False, BIAS_TYPE=BIAS_TYPE, IS_CAUSAL=IS_CAUSAL, BLOCK_HEADDIM=BLOCK_HEADDIM, EVEN_M=EVEN_M, EVEN_N=EVEN_N, EVEN_HEADDIM=EVEN_HEADDIM, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N) |
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else: |
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start_n = tl.program_id(0) |
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_bwd_kernel_one_col_block(start_n, Q, K, V, Bias, DO, DQ, DK, DV, LSE, D, softmax_scale, stride_qm, stride_kn, stride_vn, stride_bm, stride_dom, stride_dqm, stride_dkn, stride_dvn, seqlen_q, seqlen_k, headdim, ATOMIC_ADD=True, BIAS_TYPE=BIAS_TYPE, IS_CAUSAL=IS_CAUSAL, BLOCK_HEADDIM=BLOCK_HEADDIM, EVEN_M=EVEN_M, EVEN_N=EVEN_N, EVEN_HEADDIM=EVEN_HEADDIM, BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N) |
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def _flash_attn_forward(q, k, v, bias=None, causal=False, softmax_scale=None): |
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(batch, seqlen_q, nheads, d) = q.shape |
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(_, seqlen_k, _, _) = k.shape |
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assert k.shape == (batch, seqlen_k, nheads, d) |
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assert v.shape == (batch, seqlen_k, nheads, d) |
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assert d <= 128, 'FlashAttention only support head dimensions up to 128' |
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assert q.dtype == k.dtype == v.dtype, 'All tensors must have the same type' |
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assert q.dtype in [torch.float16, torch.bfloat16], 'Only support fp16 and bf16' |
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assert q.is_cuda and k.is_cuda and v.is_cuda |
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softmax_scale = softmax_scale or 1.0 / math.sqrt(d) |
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has_bias = bias is not None |
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bias_type = 'none' |
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if has_bias: |
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assert bias.dtype in [q.dtype, torch.float] |
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assert bias.is_cuda |
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assert bias.dim() == 4 |
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if bias.stride(-1) != 1: |
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bias = bias.contiguous() |
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if bias.shape[2:] == (1, seqlen_k): |
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bias_type = 'vector' |
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elif bias.shape[2:] == (seqlen_q, seqlen_k): |
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bias_type = 'matrix' |
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else: |
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raise RuntimeError('Last 2 dimensions of bias must be (1, seqlen_k) or (seqlen_q, seqlen_k)') |
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bias = bias.expand(batch, nheads, seqlen_q, seqlen_k) |
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bias_strides = (bias.stride(0), bias.stride(1), bias.stride(2)) if has_bias else (0, 0, 0) |
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seqlen_q_rounded = math.ceil(seqlen_q / 128) * 128 |
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lse = torch.empty((batch, nheads, seqlen_q_rounded), device=q.device, dtype=torch.float32) |
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tmp = torch.empty((batch, nheads, seqlen_q_rounded), device=q.device, dtype=torch.float32) |
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o = torch.empty_like(q) |
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BLOCK_HEADDIM = max(triton.next_power_of_2(d), 16) |
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BLOCK = 128 |
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num_warps = 4 if d <= 64 else 8 |
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grid = lambda META: (triton.cdiv(seqlen_q, META['BLOCK_M']), batch * nheads) |
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_fwd_kernel[grid](q, k, v, bias, o, lse, tmp, softmax_scale, q.stride(0), q.stride(2), q.stride(1), k.stride(0), k.stride(2), k.stride(1), v.stride(0), v.stride(2), v.stride(1), *bias_strides, o.stride(0), o.stride(2), o.stride(1), nheads, seqlen_q, seqlen_k, seqlen_q_rounded, d, seqlen_q // 32, seqlen_k // 32, bias_type, causal, BLOCK_HEADDIM, BLOCK_M=BLOCK, BLOCK_N=BLOCK, num_warps=num_warps, num_stages=1) |
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return (o, lse, softmax_scale) |
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def _flash_attn_backward(do, q, k, v, o, lse, dq, dk, dv, bias=None, causal=False, softmax_scale=None): |
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if do.stride(-1) != 1: |
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do = do.contiguous() |
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(batch, seqlen_q, nheads, d) = q.shape |
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(_, seqlen_k, _, _) = k.shape |
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assert d <= 128 |
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seqlen_q_rounded = math.ceil(seqlen_q / 128) * 128 |
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assert lse.shape == (batch, nheads, seqlen_q_rounded) |
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assert q.stride(-1) == k.stride(-1) == v.stride(-1) == o.stride(-1) == 1 |
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assert dq.stride(-1) == dk.stride(-1) == dv.stride(-1) == 1 |
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softmax_scale = softmax_scale or 1.0 / math.sqrt(d) |
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dq_accum = torch.empty_like(q, dtype=torch.float32) |
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delta = torch.empty_like(lse) |
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BLOCK_HEADDIM = max(triton.next_power_of_2(d), 16) |
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grid = lambda META: (triton.cdiv(seqlen_q, META['BLOCK_M']), batch * nheads) |
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_bwd_preprocess_do_o_dot[grid](o, do, delta, o.stride(0), o.stride(2), o.stride(1), do.stride(0), do.stride(2), do.stride(1), nheads, seqlen_q, seqlen_q_rounded, d, BLOCK_M=128, BLOCK_HEADDIM=BLOCK_HEADDIM) |
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has_bias = bias is not None |
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bias_type = 'none' |
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if has_bias: |
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assert bias.dtype in [q.dtype, torch.float] |
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assert bias.is_cuda |
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assert bias.dim() == 4 |
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assert bias.stride(-1) == 1 |
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if bias.shape[2:] == (1, seqlen_k): |
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bias_type = 'vector' |
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elif bias.shape[2:] == (seqlen_q, seqlen_k): |
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bias_type = 'matrix' |
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else: |
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raise RuntimeError('Last 2 dimensions of bias must be (1, seqlen_k) or (seqlen_q, seqlen_k)') |
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bias = bias.expand(batch, nheads, seqlen_q, seqlen_k) |
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bias_strides = (bias.stride(0), bias.stride(1), bias.stride(2)) if has_bias else (0, 0, 0) |
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grid = lambda META: (triton.cdiv(seqlen_k, META['BLOCK_N']) if META['SEQUENCE_PARALLEL'] else 1, batch * nheads) |
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_bwd_kernel[grid](q, k, v, bias, do, dq_accum, dk, dv, lse, delta, softmax_scale, q.stride(0), q.stride(2), q.stride(1), k.stride(0), k.stride(2), k.stride(1), v.stride(0), v.stride(2), v.stride(1), *bias_strides, do.stride(0), do.stride(2), do.stride(1), dq_accum.stride(0), dq_accum.stride(2), dq_accum.stride(1), dk.stride(0), dk.stride(2), dk.stride(1), dv.stride(0), dv.stride(2), dv.stride(1), nheads, seqlen_q, seqlen_k, seqlen_q_rounded, d, seqlen_q // 32, seqlen_k // 32, bias_type, causal, BLOCK_HEADDIM) |
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dq.copy_(dq_accum) |
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class FlashAttnQKVPackedFunc(torch.autograd.Function): |
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@staticmethod |
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def forward(ctx, qkv, bias=None, causal=False, softmax_scale=None): |
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""" |
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qkv: (batch, seqlen, 3, nheads, headdim) |
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bias: optional, shape broadcastible to (batch, nheads, seqlen, seqlen). |
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For example, ALiBi mask for causal would have shape (1, nheads, 1, seqlen). |
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ALiBi mask for non-causal would have shape (1, nheads, seqlen, seqlen) |
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""" |
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if qkv.stride(-1) != 1: |
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qkv = qkv.contiguous() |
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(o, lse, ctx.softmax_scale) = _flash_attn_forward(qkv[:, :, 0], qkv[:, :, 1], qkv[:, :, 2], bias=bias, causal=causal, softmax_scale=softmax_scale) |
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ctx.save_for_backward(qkv, o, lse, bias) |
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ctx.causal = causal |
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return o |
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@staticmethod |
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def backward(ctx, do): |
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(qkv, o, lse, bias) = ctx.saved_tensors |
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assert not ctx.needs_input_grad[1], 'FlashAttention does not support bias gradient yet' |
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with torch.inference_mode(): |
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dqkv = torch.empty_like(qkv) |
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_flash_attn_backward(do, qkv[:, :, 0], qkv[:, :, 1], qkv[:, :, 2], o, lse, dqkv[:, :, 0], dqkv[:, :, 1], dqkv[:, :, 2], bias=bias, causal=ctx.causal, softmax_scale=ctx.softmax_scale) |
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return (dqkv, None, None, None) |
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flash_attn_qkvpacked_func = FlashAttnQKVPackedFunc.apply |
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class FlashAttnKVPackedFunc(torch.autograd.Function): |
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@staticmethod |
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def forward(ctx, q, kv, bias=None, causal=False, softmax_scale=None): |
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""" |
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q: (batch, seqlen_q, nheads, headdim) |
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kv: (batch, seqlen_k, 2, nheads, headdim) |
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bias: optional, shape broadcastible to (batch, nheads, seqlen_q, seqlen_k). |
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For example, ALiBi mask for causal would have shape (1, nheads, 1, seqlen_k). |
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ALiBi mask for non-causal would have shape (1, nheads, seqlen_q, seqlen_k) |
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""" |
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(q, kv) = [x if x.stride(-1) == 1 else x.contiguous() for x in [q, kv]] |
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(o, lse, ctx.softmax_scale) = _flash_attn_forward(q, kv[:, :, 0], kv[:, :, 1], bias=bias, causal=causal, softmax_scale=softmax_scale) |
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ctx.save_for_backward(q, kv, o, lse, bias) |
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ctx.causal = causal |
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return o |
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@staticmethod |
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def backward(ctx, do): |
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(q, kv, o, lse, bias) = ctx.saved_tensors |
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if len(ctx.needs_input_grad) >= 3: |
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assert not ctx.needs_input_grad[2], 'FlashAttention does not support bias gradient yet' |
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with torch.inference_mode(): |
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dq = torch.empty_like(q) |
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dkv = torch.empty_like(kv) |
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_flash_attn_backward(do, q, kv[:, :, 0], kv[:, :, 1], o, lse, dq, dkv[:, :, 0], dkv[:, :, 1], bias=bias, causal=ctx.causal, softmax_scale=ctx.softmax_scale) |
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return (dq, dkv, None, None, None) |
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flash_attn_kvpacked_func = FlashAttnKVPackedFunc.apply |
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class FlashAttnFunc(torch.autograd.Function): |
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@staticmethod |
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def forward(ctx, q, k, v, bias=None, causal=False, softmax_scale=None): |
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""" |
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q: (batch_size, seqlen_q, nheads, headdim) |
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k, v: (batch_size, seqlen_k, nheads, headdim) |
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bias: optional, shape broadcastible to (batch, nheads, seqlen_q, seqlen_k). |
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For example, ALiBi mask for causal would have shape (1, nheads, 1, seqlen_k). |
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ALiBi mask for non-causal would have shape (1, nheads, seqlen_q, seqlen_k) |
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""" |
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(q, k, v) = [x if x.stride(-1) == 1 else x.contiguous() for x in [q, k, v]] |
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(o, lse, ctx.softmax_scale) = _flash_attn_forward(q, k, v, bias=bias, causal=causal, softmax_scale=softmax_scale) |
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ctx.save_for_backward(q, k, v, o, lse, bias) |
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ctx.causal = causal |
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return o |
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@staticmethod |
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def backward(ctx, do): |
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(q, k, v, o, lse, bias) = ctx.saved_tensors |
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assert not ctx.needs_input_grad[3], 'FlashAttention does not support bias gradient yet' |
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with torch.inference_mode(): |
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dq = torch.empty_like(q) |
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dk = torch.empty_like(k) |
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dv = torch.empty_like(v) |
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_flash_attn_backward(do, q, k, v, o, lse, dq, dk, dv, bias=bias, causal=ctx.causal, softmax_scale=ctx.softmax_scale) |
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return (dq, dk, dv, None, None, None) |
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flash_attn_func = FlashAttnFunc.apply |
