replit/replit-code-v1_5-3b

1"""2Copied from https://github.com/HazyResearch/flash-attention/blob/eff9fe6b8076df59d64d7a3f464696738a3c7c24/flash_attn/flash_attn_triton.py3update imports to use 'triton_pre_mlir'4 5*Experimental* implementation of FlashAttention in Triton.6Tested with triton==2.0.0.dev20221202.7Triton 2.0 has a new backend (MLIR) but seems like it doesn't yet work for head dimensions8other than 64:9https://github.com/openai/triton/blob/d376020f90002757eea3ea9475d4f7cfc2ec5ead/python/triton/ops/flash_attention.py#L20710We'll update this implementation with the new Triton backend once this is fixed.11 12We use the FlashAttention implementation from Phil Tillet a starting point.13https://github.com/openai/triton/blob/master/python/tutorials/06-fused-attention.py14 15Changes:16- Implement both causal and non-causal attention.17- Implement both self-attention and cross-attention.18- Support arbitrary seqlens (not just multiples of 128), for both forward and backward.19- Support all head dimensions up to 128 (not just 16, 32, 64, 128), for both forward and backward.20- Support attention bias.21- Speed up the forward pass a bit, and only store the LSE instead of m and l.22- Make the backward for d=128 much faster by reducing register spilling.23- Optionally parallelize the backward pass across seqlen_k, to deal with the case of24small batch size * nheads.25 26Caution:27- This is an *experimental* implementation. The forward pass should be quite robust but28I'm not 100% sure that the backward pass doesn't have race conditions (due to the Triton compiler).29- This implementation has only been tested on A100.30- If you plan to use headdim other than 64 and 128, you should test for race conditions31(due to the Triton compiler), as done in tests/test_flash_attn.py32"test_flash_attn_triton_race_condition". I've tested and fixed many race conditions33for different head dimensions (40, 48, 64, 128, 80, 88, 96), but I'm still not 100% confident34that there are none left for other head dimensions.35 36Differences between this Triton version and the CUDA version:37- Triton version doesn't support dropout.38- Triton forward is generally faster than CUDA forward, while Triton backward is39generally slower than CUDA backward. Overall Triton forward + backward is slightly slower40than CUDA forward + backward.41- Triton version doesn't support different sequence lengths in a batch (i.e., RaggedTensor/NestedTensor).42- Triton version supports attention bias, while CUDA version doesn't.43"""44import math45import torch46import triton_pre_mlir as triton47import triton_pre_mlir.language as tl48 49@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']})50@triton.jit51def _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):52    start_m = tl.program_id(0)53    off_hb = tl.program_id(1)54    off_b = off_hb // nheads55    off_h = off_hb % nheads56    offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M)57    offs_n = tl.arange(0, BLOCK_N)58    offs_d = tl.arange(0, BLOCK_HEADDIM)59    q_ptrs = Q + off_b * stride_qb + off_h * stride_qh + (offs_m[:, None] * stride_qm + offs_d[None, :])60    k_ptrs = K + off_b * stride_kb + off_h * stride_kh + (offs_n[:, None] * stride_kn + offs_d[None, :])61    v_ptrs = V + off_b * stride_vb + off_h * stride_vh + (offs_n[:, None] * stride_vn + offs_d[None, :])62    if BIAS_TYPE == 'vector':63        b_ptrs = Bias + off_b * stride_bb + off_h * stride_bh + offs_n64    elif BIAS_TYPE == 'matrix':65        b_ptrs = Bias + off_b * stride_bb + off_h * stride_bh + (offs_m[:, None] * stride_bm + offs_n[None, :])66    t_ptrs = TMP + off_hb * seqlen_q_rounded + offs_m67    lse_i = tl.zeros([BLOCK_M], dtype=tl.float32) - float('inf')68    m_i = tl.zeros([BLOCK_M], dtype=tl.float32) - float('inf')69    acc_o = tl.zeros([BLOCK_M, BLOCK_HEADDIM], dtype=tl.float32)70    if EVEN_M & EVEN_N:71        if EVEN_HEADDIM:72            q = tl.load(q_ptrs)73        else:74            q = tl.load(q_ptrs, mask=offs_d[None, :] < headdim, other=0.0)75    elif EVEN_HEADDIM:76        q = tl.load(q_ptrs, mask=offs_m[:, None] < seqlen_q, other=0.0)77    else:78        q = tl.load(q_ptrs, mask=(offs_m[:, None] < seqlen_q) & (offs_d[None, :] < headdim), other=0.0)79    end_n = seqlen_k if not IS_CAUSAL else tl.minimum((start_m + 1) * BLOCK_M, seqlen_k)80    for start_n in range(0, end_n, BLOCK_N):81        start_n = tl.multiple_of(start_n, BLOCK_N)82        if EVEN_N & EVEN_M:83            if EVEN_HEADDIM:84                k = tl.load(k_ptrs + start_n * stride_kn)85            else:86                k = tl.load(k_ptrs + start_n * stride_kn, mask=offs_d[None, :] < headdim, other=0.0)87        elif EVEN_HEADDIM:88            k = tl.load(k_ptrs + start_n * stride_kn, mask=(start_n + offs_n)[:, None] < seqlen_k, other=0.0)89        else:90            k = tl.load(k_ptrs + start_n * stride_kn, mask=((start_n + offs_n)[:, None] < seqlen_k) & (offs_d[None, :] < headdim), other=0.0)91        qk = tl.zeros([BLOCK_M, BLOCK_N], dtype=tl.float32)92        qk += tl.dot(q, k, trans_b=True)93        if not EVEN_N:94            qk += tl.where((start_n + offs_n)[None, :] < seqlen_k, 0, float('-inf'))95        if IS_CAUSAL:96            qk += tl.where(offs_m[:, None] >= (start_n + offs_n)[None, :], 0, float('-inf'))97        if BIAS_TYPE != 'none':98            if BIAS_TYPE == 'vector':99                if EVEN_N:100                    bias = tl.load(b_ptrs + start_n).to(tl.float32)101                else:102                    bias = tl.load(b_ptrs + start_n, mask=start_n + offs_n < seqlen_k, other=0.0).to(tl.float32)103                bias = bias[None, :]104            elif BIAS_TYPE == 'matrix':105                if EVEN_M & EVEN_N:106                    bias = tl.load(b_ptrs + start_n).to(tl.float32)107                else:108                    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)109            qk = qk * softmax_scale + bias110            m_ij = tl.maximum(tl.max(qk, 1), lse_i)111            p = tl.exp(qk - m_ij[:, None])112        else:113            m_ij = tl.maximum(tl.max(qk, 1) * softmax_scale, lse_i)114            p = tl.exp(qk * softmax_scale - m_ij[:, None])115        l_ij = tl.sum(p, 1)116        acc_o_scale = tl.exp(m_i - m_ij)117        tl.store(t_ptrs, acc_o_scale)118        acc_o_scale = tl.load(t_ptrs)119        acc_o = acc_o * acc_o_scale[:, None]120        if EVEN_N & EVEN_M:121            if EVEN_HEADDIM:122                v = tl.load(v_ptrs + start_n * stride_vn)123            else:124                v = tl.load(v_ptrs + start_n * stride_vn, mask=offs_d[None, :] < headdim, other=0.0)125        elif EVEN_HEADDIM:126            v = tl.load(v_ptrs + start_n * stride_vn, mask=(start_n + offs_n)[:, None] < seqlen_k, other=0.0)127        else:128            v = tl.load(v_ptrs + start_n * stride_vn, mask=((start_n + offs_n)[:, None] < seqlen_k) & (offs_d[None, :] < headdim), other=0.0)129        p = p.to(v.dtype)130        acc_o += tl.dot(p, v)131        m_i = m_ij132        l_i_new = tl.exp(lse_i - m_ij) + l_ij133        lse_i = m_ij + tl.log(l_i_new)134    o_scale = tl.exp(m_i - lse_i)135    tl.store(t_ptrs, o_scale)136    o_scale = tl.load(t_ptrs)137    acc_o = acc_o * o_scale[:, None]138    start_m = tl.program_id(0)139    offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M)140    lse_ptrs = Lse + off_hb * seqlen_q_rounded + offs_m141    tl.store(lse_ptrs, lse_i)142    offs_d = tl.arange(0, BLOCK_HEADDIM)143    out_ptrs = Out + off_b * stride_ob + off_h * stride_oh + (offs_m[:, None] * stride_om + offs_d[None, :])144    if EVEN_M:145        if EVEN_HEADDIM:146            tl.store(out_ptrs, acc_o)147        else:148            tl.store(out_ptrs, acc_o, mask=offs_d[None, :] < headdim)149    elif EVEN_HEADDIM:150        tl.store(out_ptrs, acc_o, mask=offs_m[:, None] < seqlen_q)151    else:152        tl.store(out_ptrs, acc_o, mask=(offs_m[:, None] < seqlen_q) & (offs_d[None, :] < headdim))153 154@triton.jit155def _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):156    start_m = tl.program_id(0)157    off_hb = tl.program_id(1)158    off_b = off_hb // nheads159    off_h = off_hb % nheads160    offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M)161    offs_d = tl.arange(0, BLOCK_HEADDIM)162    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)163    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)164    delta = tl.sum(o * do, axis=1)165    tl.store(Delta + off_hb * seqlen_q_rounded + offs_m, delta)166 167@triton.jit168def _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):169    if EVEN_N & EVEN_M:170        if EVEN_HEADDIM:171            tl.store(dv_ptrs, dv)172            tl.store(dk_ptrs, dk)173        else:174            tl.store(dv_ptrs, dv, mask=offs_d[None, :] < headdim)175            tl.store(dk_ptrs, dk, mask=offs_d[None, :] < headdim)176    elif EVEN_HEADDIM:177        tl.store(dv_ptrs, dv, mask=offs_n[:, None] < seqlen_k)178        tl.store(dk_ptrs, dk, mask=offs_n[:, None] < seqlen_k)179    else:180        tl.store(dv_ptrs, dv, mask=(offs_n[:, None] < seqlen_k) & (offs_d[None, :] < headdim))181        tl.store(dk_ptrs, dk, mask=(offs_n[:, None] < seqlen_k) & (offs_d[None, :] < headdim))182 183@triton.jit184def _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):185    begin_m = 0 if not IS_CAUSAL else start_n * BLOCK_N // BLOCK_M * BLOCK_M186    offs_qm = begin_m + tl.arange(0, BLOCK_M)187    offs_n = start_n * BLOCK_N + tl.arange(0, BLOCK_N)188    offs_m = tl.arange(0, BLOCK_M)189    offs_d = tl.arange(0, BLOCK_HEADDIM)190    q_ptrs = Q + (offs_qm[:, None] * stride_qm + offs_d[None, :])191    k_ptrs = K + (offs_n[:, None] * stride_kn + offs_d[None, :])192    v_ptrs = V + (offs_n[:, None] * stride_vn + offs_d[None, :])193    do_ptrs = DO + (offs_qm[:, None] * stride_dom + offs_d[None, :])194    dq_ptrs = DQ + (offs_qm[:, None] * stride_dqm + offs_d[None, :])195    if BIAS_TYPE == 'vector':196        b_ptrs = Bias + offs_n197    elif BIAS_TYPE == 'matrix':198        b_ptrs = Bias + (offs_qm[:, None] * stride_bm + offs_n[None, :])199    dv = tl.zeros([BLOCK_N, BLOCK_HEADDIM], dtype=tl.float32)200    dk = tl.zeros([BLOCK_N, BLOCK_HEADDIM], dtype=tl.float32)201    if begin_m >= seqlen_q:202        dv_ptrs = DV + (offs_n[:, None] * stride_dvn + offs_d[None, :])203        dk_ptrs = DK + (offs_n[:, None] * stride_dkn + offs_d[None, :])204        _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)205        return206    if EVEN_N & EVEN_M:207        if EVEN_HEADDIM:208            k = tl.load(k_ptrs)209            v = tl.load(v_ptrs)210        else:211            k = tl.load(k_ptrs, mask=offs_d[None, :] < headdim, other=0.0)212            v = tl.load(v_ptrs, mask=offs_d[None, :] < headdim, other=0.0)213    elif EVEN_HEADDIM:214        k = tl.load(k_ptrs, mask=offs_n[:, None] < seqlen_k, other=0.0)215        v = tl.load(v_ptrs, mask=offs_n[:, None] < seqlen_k, other=0.0)216    else:217        k = tl.load(k_ptrs, mask=(offs_n[:, None] < seqlen_k) & (offs_d[None, :] < headdim), other=0.0)218        v = tl.load(v_ptrs, mask=(offs_n[:, None] < seqlen_k) & (offs_d[None, :] < headdim), other=0.0)219    num_block_m = tl.cdiv(seqlen_q, BLOCK_M)220    for start_m in range(begin_m, num_block_m * BLOCK_M, BLOCK_M):221        start_m = tl.multiple_of(start_m, BLOCK_M)222        offs_m_curr = start_m + offs_m223        if EVEN_M & EVEN_HEADDIM:224            q = tl.load(q_ptrs)225        elif EVEN_HEADDIM:226            q = tl.load(q_ptrs, mask=offs_m_curr[:, None] < seqlen_q, other=0.0)227        else:228            q = tl.load(q_ptrs, mask=(offs_m_curr[:, None] < seqlen_q) & (offs_d[None, :] < headdim), other=0.0)229        qk = tl.dot(q, k, trans_b=True)230        if not EVEN_N:231            qk = tl.where(offs_n[None, :] < seqlen_k, qk, float('-inf'))232        if IS_CAUSAL:233            qk = tl.where(offs_m_curr[:, None] >= offs_n[None, :], qk, float('-inf'))234        if BIAS_TYPE != 'none':235            tl.debug_barrier()236            if BIAS_TYPE == 'vector':237                if EVEN_N:238                    bias = tl.load(b_ptrs).to(tl.float32)239                else:240                    bias = tl.load(b_ptrs, mask=offs_n < seqlen_k, other=0.0).to(tl.float32)241                bias = bias[None, :]242            elif BIAS_TYPE == 'matrix':243                if EVEN_M & EVEN_N:244                    bias = tl.load(b_ptrs).to(tl.float32)245                else:246                    bias = tl.load(b_ptrs, mask=(offs_m_curr[:, None] < seqlen_q) & (offs_n[None, :] < seqlen_k), other=0.0).to(tl.float32)247            qk = qk * softmax_scale + bias248        if not EVEN_M & EVEN_HEADDIM:249            tl.debug_barrier()250        lse_i = tl.load(LSE + offs_m_curr)251        if BIAS_TYPE == 'none':252            p = tl.exp(qk * softmax_scale - lse_i[:, None])253        else:254            p = tl.exp(qk - lse_i[:, None])255        if EVEN_M & EVEN_HEADDIM:256            do = tl.load(do_ptrs)257        else:258            do = tl.load(do_ptrs, mask=(offs_m_curr[:, None] < seqlen_q) & (offs_d[None, :] < headdim), other=0.0)259        dv += tl.dot(p.to(do.dtype), do, trans_a=True)260        if not EVEN_M & EVEN_HEADDIM:261            tl.debug_barrier()262        dp = tl.dot(do, v, trans_b=True)263        if not EVEN_HEADDIM:264            tl.debug_barrier()265        Di = tl.load(D + offs_m_curr)266        ds = (p * (dp - Di[:, None]) * softmax_scale).to(q.dtype)267        dk += tl.dot(ds, q, trans_a=True)268        if not EVEN_M & EVEN_HEADDIM:269            tl.debug_barrier()270        if not ATOMIC_ADD:271            if EVEN_M & EVEN_HEADDIM:272                dq = tl.load(dq_ptrs, eviction_policy='evict_last')273                dq += tl.dot(ds, k)274                tl.store(dq_ptrs, dq, eviction_policy='evict_last')275            elif EVEN_HEADDIM:276                dq = tl.load(dq_ptrs, mask=offs_m_curr[:, None] < seqlen_q, other=0.0, eviction_policy='evict_last')277                dq += tl.dot(ds, k)278                tl.store(dq_ptrs, dq, mask=offs_m_curr[:, None] < seqlen_q, eviction_policy='evict_last')279            else:280                dq = tl.load(dq_ptrs, mask=(offs_m_curr[:, None] < seqlen_q) & (offs_d[None, :] < headdim), other=0.0, eviction_policy='evict_last')281                dq += tl.dot(ds, k)282                tl.store(dq_ptrs, dq, mask=(offs_m_curr[:, None] < seqlen_q) & (offs_d[None, :] < headdim), eviction_policy='evict_last')283        else:284            dq = tl.dot(ds, k)285            if EVEN_M & EVEN_HEADDIM:286                tl.atomic_add(dq_ptrs, dq)287            elif EVEN_HEADDIM:288                tl.atomic_add(dq_ptrs, dq, mask=offs_m_curr[:, None] < seqlen_q)289            else:290                tl.atomic_add(dq_ptrs, dq, mask=(offs_m_curr[:, None] < seqlen_q) & (offs_d[None, :] < headdim))291        dq_ptrs += BLOCK_M * stride_dqm292        q_ptrs += BLOCK_M * stride_qm293        do_ptrs += BLOCK_M * stride_dom294        if BIAS_TYPE == 'matrix':295            b_ptrs += BLOCK_M * stride_bm296    dv_ptrs = DV + (offs_n[:, None] * stride_dvn + offs_d[None, :])297    dk_ptrs = DK + (offs_n[:, None] * stride_dkn + offs_d[None, :])298    _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)299 300def init_to_zero(name):301    return lambda nargs: nargs[name].zero_()302 303@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'])304@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']})305@triton.jit306def _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):307    off_hb = tl.program_id(1)308    off_b = off_hb // nheads309    off_h = off_hb % nheads310    Q += off_b * stride_qb + off_h * stride_qh311    K += off_b * stride_kb + off_h * stride_kh312    V += off_b * stride_vb + off_h * stride_vh313    DO += off_b * stride_dob + off_h * stride_doh314    DQ += off_b * stride_dqb + off_h * stride_dqh315    DK += off_b * stride_dkb + off_h * stride_dkh316    DV += off_b * stride_dvb + off_h * stride_dvh317    if BIAS_TYPE != 'none':318        Bias += off_b * stride_bb + off_h * stride_bh319    D += off_hb * seqlen_q_rounded320    LSE += off_hb * seqlen_q_rounded321    if not SEQUENCE_PARALLEL:322        num_block_n = tl.cdiv(seqlen_k, BLOCK_N)323        for start_n in range(0, num_block_n):324            _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)325    else:326        start_n = tl.program_id(0)327        _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)328 329def _flash_attn_forward(q, k, v, bias=None, causal=False, softmax_scale=None):330    (batch, seqlen_q, nheads, d) = q.shape331    (_, seqlen_k, _, _) = k.shape332    assert k.shape == (batch, seqlen_k, nheads, d)333    assert v.shape == (batch, seqlen_k, nheads, d)334    assert d <= 128, 'FlashAttention only support head dimensions up to 128'335    assert q.dtype == k.dtype == v.dtype, 'All tensors must have the same type'336    assert q.dtype in [torch.float16, torch.bfloat16], 'Only support fp16 and bf16'337    assert q.is_cuda and k.is_cuda and v.is_cuda338    softmax_scale = softmax_scale or 1.0 / math.sqrt(d)339    has_bias = bias is not None340    bias_type = 'none'341    if has_bias:342        assert bias.dtype in [q.dtype, torch.float]343        assert bias.is_cuda344        assert bias.dim() == 4345        if bias.stride(-1) != 1:346            bias = bias.contiguous()347        if bias.shape[2:] == (1, seqlen_k):348            bias_type = 'vector'349        elif bias.shape[2:] == (seqlen_q, seqlen_k):350            bias_type = 'matrix'351        else:352            raise RuntimeError('Last 2 dimensions of bias must be (1, seqlen_k) or (seqlen_q, seqlen_k)')353        bias = bias.expand(batch, nheads, seqlen_q, seqlen_k)354    bias_strides = (bias.stride(0), bias.stride(1), bias.stride(2)) if has_bias else (0, 0, 0)355    seqlen_q_rounded = math.ceil(seqlen_q / 128) * 128356    lse = torch.empty((batch, nheads, seqlen_q_rounded), device=q.device, dtype=torch.float32)357    tmp = torch.empty((batch, nheads, seqlen_q_rounded), device=q.device, dtype=torch.float32)358    o = torch.empty_like(q)359    BLOCK_HEADDIM = max(triton.next_power_of_2(d), 16)360    BLOCK = 128361    num_warps = 4 if d <= 64 else 8362    grid = lambda META: (triton.cdiv(seqlen_q, META['BLOCK_M']), batch * nheads)363    _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)364    return (o, lse, softmax_scale)365 366def _flash_attn_backward(do, q, k, v, o, lse, dq, dk, dv, bias=None, causal=False, softmax_scale=None):367    if do.stride(-1) != 1:368        do = do.contiguous()369    (batch, seqlen_q, nheads, d) = q.shape370    (_, seqlen_k, _, _) = k.shape371    assert d <= 128372    seqlen_q_rounded = math.ceil(seqlen_q / 128) * 128373    assert lse.shape == (batch, nheads, seqlen_q_rounded)374    assert q.stride(-1) == k.stride(-1) == v.stride(-1) == o.stride(-1) == 1375    assert dq.stride(-1) == dk.stride(-1) == dv.stride(-1) == 1376    softmax_scale = softmax_scale or 1.0 / math.sqrt(d)377    dq_accum = torch.empty_like(q, dtype=torch.float32)378    delta = torch.empty_like(lse)379    BLOCK_HEADDIM = max(triton.next_power_of_2(d), 16)380    grid = lambda META: (triton.cdiv(seqlen_q, META['BLOCK_M']), batch * nheads)381    _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)382    has_bias = bias is not None383    bias_type = 'none'384    if has_bias:385        assert bias.dtype in [q.dtype, torch.float]386        assert bias.is_cuda387        assert bias.dim() == 4388        assert bias.stride(-1) == 1389        if bias.shape[2:] == (1, seqlen_k):390            bias_type = 'vector'391        elif bias.shape[2:] == (seqlen_q, seqlen_k):392            bias_type = 'matrix'393        else:394            raise RuntimeError('Last 2 dimensions of bias must be (1, seqlen_k) or (seqlen_q, seqlen_k)')395        bias = bias.expand(batch, nheads, seqlen_q, seqlen_k)396    bias_strides = (bias.stride(0), bias.stride(1), bias.stride(2)) if has_bias else (0, 0, 0)397    grid = lambda META: (triton.cdiv(seqlen_k, META['BLOCK_N']) if META['SEQUENCE_PARALLEL'] else 1, batch * nheads)398    _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)399    dq.copy_(dq_accum)400 401class FlashAttnQKVPackedFunc(torch.autograd.Function):402 403    @staticmethod404    def forward(ctx, qkv, bias=None, causal=False, softmax_scale=None):405        """406            qkv: (batch, seqlen, 3, nheads, headdim)407            bias: optional, shape broadcastible to (batch, nheads, seqlen, seqlen).408                For example, ALiBi mask for causal would have shape (1, nheads, 1, seqlen).409                ALiBi mask for non-causal would have shape (1, nheads, seqlen, seqlen)410        """411        if qkv.stride(-1) != 1:412            qkv = qkv.contiguous()413        (o, lse, ctx.softmax_scale) = _flash_attn_forward(qkv[:, :, 0], qkv[:, :, 1], qkv[:, :, 2], bias=bias, causal=causal, softmax_scale=softmax_scale)414        ctx.save_for_backward(qkv, o, lse, bias)415        ctx.causal = causal416        return o417 418    @staticmethod419    def backward(ctx, do):420        (qkv, o, lse, bias) = ctx.saved_tensors421        assert not ctx.needs_input_grad[1], 'FlashAttention does not support bias gradient yet'422        with torch.inference_mode():423            dqkv = torch.empty_like(qkv)424            _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)425        return (dqkv, None, None, None)426flash_attn_qkvpacked_func = FlashAttnQKVPackedFunc.apply427 428class FlashAttnKVPackedFunc(torch.autograd.Function):429 430    @staticmethod431    def forward(ctx, q, kv, bias=None, causal=False, softmax_scale=None):432        """433            q: (batch, seqlen_q, nheads, headdim)434            kv: (batch, seqlen_k, 2, nheads, headdim)435            bias: optional, shape broadcastible to (batch, nheads, seqlen_q, seqlen_k).436                For example, ALiBi mask for causal would have shape (1, nheads, 1, seqlen_k).437                ALiBi mask for non-causal would have shape (1, nheads, seqlen_q, seqlen_k)438        """439        (q, kv) = [x if x.stride(-1) == 1 else x.contiguous() for x in [q, kv]]440        (o, lse, ctx.softmax_scale) = _flash_attn_forward(q, kv[:, :, 0], kv[:, :, 1], bias=bias, causal=causal, softmax_scale=softmax_scale)441        ctx.save_for_backward(q, kv, o, lse, bias)442        ctx.causal = causal443        return o444 445    @staticmethod446    def backward(ctx, do):447        (q, kv, o, lse, bias) = ctx.saved_tensors448        if len(ctx.needs_input_grad) >= 3:449            assert not ctx.needs_input_grad[2], 'FlashAttention does not support bias gradient yet'450        with torch.inference_mode():451            dq = torch.empty_like(q)452            dkv = torch.empty_like(kv)453            _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)454        return (dq, dkv, None, None, None)455flash_attn_kvpacked_func = FlashAttnKVPackedFunc.apply456 457class FlashAttnFunc(torch.autograd.Function):458 459    @staticmethod460    def forward(ctx, q, k, v, bias=None, causal=False, softmax_scale=None):461        """462            q: (batch_size, seqlen_q, nheads, headdim)463            k, v: (batch_size, seqlen_k, nheads, headdim)464            bias: optional, shape broadcastible to (batch, nheads, seqlen_q, seqlen_k).465                For example, ALiBi mask for causal would have shape (1, nheads, 1, seqlen_k).466                ALiBi mask for non-causal would have shape (1, nheads, seqlen_q, seqlen_k)467        """468        (q, k, v) = [x if x.stride(-1) == 1 else x.contiguous() for x in [q, k, v]]469        (o, lse, ctx.softmax_scale) = _flash_attn_forward(q, k, v, bias=bias, causal=causal, softmax_scale=softmax_scale)470        ctx.save_for_backward(q, k, v, o, lse, bias)471        ctx.causal = causal472        return o473 474    @staticmethod475    def backward(ctx, do):476        (q, k, v, o, lse, bias) = ctx.saved_tensors477        assert not ctx.needs_input_grad[3], 'FlashAttention does not support bias gradient yet'478        with torch.inference_mode():479            dq = torch.empty_like(q)480            dk = torch.empty_like(k)481            dv = torch.empty_like(v)482            _flash_attn_backward(do, q, k, v, o, lse, dq, dk, dv, bias=bias, causal=ctx.causal, softmax_scale=ctx.softmax_scale)483        return (dq, dk, dv, None, None, None)484flash_attn_func = FlashAttnFunc.apply