@triton.heuristics({'STORE_INITIAL_STATE_GRADIENT': lambda args: args['dh0'
    ] is not None, 'USE_FINAL_STATE_GRADIENT': lambda args: args['dht'] is not
    None, 'USE_OFFSETS': lambda args: args['offsets'] is not None})
@triton.autotune(configs=[triton.Config({'BK': BK, 'BV': BV}, num_warps=
    num_warps, num_stages=num_stages) for BK in [32, 64] for BV in [32, 64] for
    num_warps in [1, 2, 4, 8] for num_stages in [2, 3, 4]], key=['BT',
    'USE_G', 'USE_GK', 'USE_GV'])
@triton.jit
def chunk_bwd_kernel_dh(q, g, gk, gv, do, dh, dht, dh0, offsets,
    chunk_offsets, scale, T: tl.constexpr, HQ: tl.constexpr, H: tl.
    constexpr, K: tl.constexpr, V: tl.constexpr, BT: tl.constexpr, BK: tl.
    constexpr, BV: tl.constexpr, NG: tl.constexpr, USE_G: tl.constexpr,
    USE_GK: tl.constexpr, USE_GV: tl.constexpr,
    STORE_INITIAL_STATE_GRADIENT: tl.constexpr, USE_FINAL_STATE_GRADIENT:
    tl.constexpr, USE_OFFSETS: tl.constexpr, HEAD_FIRST: tl.constexpr):
    i_k, i_v, i_nh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
    i_bg = i_nh // NG
    i_n, i_hq = i_nh // HQ, i_nh % HQ
    i_h = i_hq // NG
    if USE_OFFSETS:
        bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets +
            i_n + 1).to(tl.int32)
        T = eos - bos
        NT = tl.cdiv(T, BT)
        boh = tl.load(chunk_offsets + i_n).to(tl.int32)
    else:
        bos, eos = i_n * T, i_n * T + T
        NT = tl.cdiv(T, BT)
        boh = i_n * NT
    b_dh = tl.zeros([BK, BV], dtype=tl.float32)
    if USE_FINAL_STATE_GRADIENT:
        p_dht = tl.make_block_ptr(dht + i_nh * K * V, (K, V), (V, 1), (i_k *
            BK, i_v * BV), (BK, BV), (1, 0))
        b_dh += tl.load(p_dht, boundary_check=(0, 1)).to(tl.float32)
    for i_t in range(NT - 1, -1, -1):
        if HEAD_FIRST:
            p_dh = tl.make_block_ptr(dh + (i_nh * NT + i_t) * K * V, (K, V),
                (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
        else:
            p_dh = tl.make_block_ptr(dh + ((boh + i_t) * H + i_h) * K * V,
                (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
        tl.store(p_dh, b_dh.to(p_dh.dtype.element_ty), boundary_check=(0, 1))
        last_idx = min(i_t * BT + BT, T) - 1
        if HEAD_FIRST:
            p_q = tl.make_block_ptr(q + i_nh * T * K, (K, T), (1, K), (i_k *
                BK, i_t * BT), (BK, BT), (0, 1))
            p_do = tl.make_block_ptr(do + i_nh * T * V, (T, V), (V, 1), (
                i_t * BT, i_v * BV), (BT, BV), (1, 0))
        else:
            p_q = tl.make_block_ptr(q + (bos * HQ + i_hq) * K, (K, T), (1, 
                HQ * K), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
            p_do = tl.make_block_ptr(do + (bos * HQ + i_hq) * V, (T, V), (
                HQ * V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
        b_q = tl.load(p_q, boundary_check=(0, 1))
        b_q = (b_q * scale).to(b_q.dtype)
        b_do = tl.load(p_do, boundary_check=(0, 1))
        if USE_G:
            if HEAD_FIRST:
                p_g = g + i_bg * T + i_t * BT + tl.arange(0, BT)
                p_g = tl.max_contiguous(tl.multiple_of(p_g, BT), BT)
                b_g_last = tl.load(g + i_bg * T + last_idx)
            else:
                p_g = g + (bos + i_t * BT + tl.arange(0, BT)) * H + i_h
                b_g_last = tl.load(g + (bos + last_idx) * H + i_h)
            b_g = tl.load(p_g, mask=i_t * BT + tl.arange(0, BT) < T, other=0.0)
            b_q = (b_q * tl.exp(b_g)[None, :]).to(b_q.dtype)
            b_dh *= tl.exp(b_g_last)
        if USE_GK:
            if HEAD_FIRST:
                p_gk = tl.make_block_ptr(gk + i_bg * T * K, (K, T), (1, K),
                    (i_k * BK, i_t * BT), (BK, BT), (0, 1))
                p_gk_last = gk + (i_bg * T + last_idx
                    ) * K + i_k * BK + tl.arange(0, BK)
            else:
                p_gk = tl.make_block_ptr(gk + (bos * H + i_h) * K, (K, T),
                    (1, H * K), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
                p_gk_last = gk + (bos + last_idx
                    ) * H * K + i_h * K + i_k * BK + tl.arange(0, BK)
            p_gk_last = tl.max_contiguous(tl.multiple_of(p_gk_last, BK), BK)
            b_gk = tl.load(p_gk, boundary_check=(0, 1))
            b_q = (b_q * tl.exp(b_gk)).to(b_q.dtype)
            b_gk_last = tl.load(p_gk_last, mask=i_k * BK + tl.arange(0, BK) <
                K, other=0.0)
            b_dh *= tl.exp(b_gk_last)[:, None]
        if USE_GV:
            if HEAD_FIRST:
                p_gv = tl.make_block_ptr(gv + i_bg * T * V, (T, V), (V, 1),
                    (i_t * BT, i_v * BV), (BT, BV), (1, 0))
                p_gv_last = gv + (i_bg * T + last_idx
                    ) * V + i_v * BV + tl.arange(0, BV)
            else:
                p_gv = tl.make_block_ptr(gv + (bos * H + i_h) * V, (T, V),
                    (H * V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
                p_gv_last = gv + (bos + last_idx
                    ) * H * V + i_h * V + i_v * BV + tl.arange(0, BV)
            p_gv_last = tl.max_contiguous(tl.multiple_of(p_gv_last, BV), BV)
            b_gv = tl.load(p_gv, boundary_check=(0, 1))
            b_do = (b_do * tl.exp(b_gv)).to(b_do.dtype)
            b_gv_last = tl.load(p_gv_last, mask=i_v * BV + tl.arange(0, BV) <
                V, other=0.0)
            b_dh *= tl.exp(b_gv_last)[None, :]
        b_dh += tl.dot(b_q, b_do)
    if STORE_INITIAL_STATE_GRADIENT:
        p_dh0 = tl.make_block_ptr(dh0 + i_nh * K * V, (K, V), (V, 1), (i_k *
            BK, i_v * BV), (BK, BV), (1, 0))
        tl.store(p_dh0, b_dh.to(p_dh0.dtype.element_ty), boundary_check=(0, 1))
