@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, 128] for BV in [32,
    64, 128] for num_warps in [2, 4, 8] for num_stages in [2, 3, 4]], key=[
    'BT'])
@triton.jit
def chunk_retention_bwd_kernel_dh(q, do, dh, dh0, dht, offsets,
    chunk_offsets, scale, T: tl.constexpr, H: tl.constexpr, K: tl.constexpr,
    V: tl.constexpr, BT: tl.constexpr, BK: tl.constexpr, BV: 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_n, i_h = i_nh // H, i_nh % H
    b_b = tl.math.log2(1 - tl.math.exp2(-5 - i_h * 1.0))
    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
    o_i = tl.arange(0, BT)
    d_i = tl.math.exp2((o_i + 1) * b_b)
    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_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))
            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_q = tl.make_block_ptr(q + (bos * H + i_h) * K, (K, T), (1, H *
                K), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
            p_do = tl.make_block_ptr(do + (bos * H + i_h) * V, (T, V), (H *
                V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
            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))
        d_b = tl.math.exp2(min(BT, T - i_t * BT) * b_b)
        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))
        b_dh = d_b * b_dh + tl.dot(b_q, (b_do * d_i[:, None]).to(b_q.dtype),
            allow_tf32=False)
    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))
