prefix_prefill.py

# The kernels in this file are adapted from LightLLM's context_attention_fwd:
# https://github.com/ModelTC/lightllm/blob/main/lightllm/models/llama/triton_kernel/context_flashattention_nopad.py

import torch
import triton
import triton.language as tl

if triton.__version__ >= "2.1.0":

    @triton.jit
    def _fwd_kernel(
        Q,
        K,
        V,
        K_cache,
        V_cache,
        B_Loc,
        sm_scale,
        B_Start_Loc,
        B_Seqlen,
        B_Ctxlen,
        block_size,
        x,
        Out,
        stride_b_loc_b,
        stride_b_loc_s,
        stride_qbs,
        stride_qh,
        stride_qd,
        stride_kbs,
        stride_kh,
        stride_kd,
        stride_vbs,
        stride_vh,
        stride_vd,
        stride_obs,
        stride_oh,
        stride_od,
        stride_k_cache_bs,
        stride_k_cache_h,
        stride_k_cache_d,
        stride_k_cache_bl,
        stride_k_cache_x,
        stride_v_cache_bs,
        stride_v_cache_h,
        stride_v_cache_d,
        stride_v_cache_bl,
        num_queries_per_kv: int,
        BLOCK_M: tl.constexpr,
        BLOCK_DMODEL: tl.constexpr,
        BLOCK_N: tl.constexpr,
    ):
        cur_batch = tl.program_id(0)
        cur_head = tl.program_id(1)
        start_m = tl.program_id(2)

        cur_kv_head = cur_head // num_queries_per_kv

        cur_batch_ctx_len = tl.load(B_Ctxlen + cur_batch)
        cur_batch_seq_len = tl.load(B_Seqlen + cur_batch)
        cur_batch_in_all_start_index = tl.load(B_Start_Loc + cur_batch)

        block_start_loc = BLOCK_M * start_m

        # initialize offsets
        offs_n = tl.arange(0, BLOCK_N)
        offs_d = tl.arange(0, BLOCK_DMODEL)
        offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M)
        off_q = (
            (cur_batch_in_all_start_index + offs_m[:, None]) * stride_qbs +
            cur_head * stride_qh + offs_d[None, :] * stride_qd)

        q = tl.load(
            Q + off_q,
            mask=offs_m[:, None] < cur_batch_seq_len - cur_batch_ctx_len,
            other=0.0)

        # # initialize pointer to m and l
        m_i = tl.zeros([BLOCK_M], dtype=tl.float32) - float("inf")
        l_i = tl.zeros([BLOCK_M], dtype=tl.float32)
        acc = tl.zeros([BLOCK_M, BLOCK_DMODEL], dtype=tl.float32)

        for start_n in range(0, cur_batch_ctx_len, BLOCK_N):
            start_n = tl.multiple_of(start_n, BLOCK_N)
            # -- compute qk ----
            bn = tl.load(B_Loc + cur_batch * stride_b_loc_b +
                         ((start_n + offs_n) // block_size) * stride_b_loc_s,
                         mask=(start_n + offs_n) < cur_batch_ctx_len,
                         other=0)
            off_k = (bn[None, :] * stride_k_cache_bs +
                     cur_kv_head * stride_k_cache_h +
                     (offs_d[:, None] // x) * stride_k_cache_d +
                     ((start_n + offs_n[None, :]) % block_size) *
                     stride_k_cache_bl +
                     (offs_d[:, None] % x) * stride_k_cache_x)
            off_v = (
                bn[:, None] * stride_v_cache_bs +
                cur_kv_head * stride_v_cache_h +
                offs_d[None, :] * stride_v_cache_d +
                (start_n + offs_n[:, None]) % block_size * stride_v_cache_bl)
            k = tl.load(K_cache + off_k,
                        mask=(start_n + offs_n[None, :]) < cur_batch_ctx_len,
                        other=0.0)

            qk = tl.zeros([BLOCK_M, BLOCK_N], dtype=tl.float32)
            qk += tl.dot(q, k)
            qk = tl.where((start_n + offs_n[None, :]) < cur_batch_ctx_len, qk,
                          float("-inf"))
            qk *= sm_scale

            # -- compute m_ij, p, l_ij
            m_ij = tl.max(qk, 1)
            p = tl.exp(qk - m_ij[:, None])
            l_ij = tl.sum(p, 1)
            # -- update m_i and l_i
            m_i_new = tl.maximum(m_i, m_ij)
            alpha = tl.exp(m_i - m_i_new)
            beta = tl.exp(m_ij - m_i_new)
            l_i_new = alpha * l_i + beta * l_ij
            # -- update output accumulator --
            # scale p
            p_scale = beta / l_i_new
            p = p * p_scale[:, None]
            # scale acc
            acc_scale = l_i / l_i_new * alpha
            acc = acc * acc_scale[:, None]
            # update acc
            v = tl.load(V_cache + off_v,
                        mask=(start_n + offs_n[:, None]) < cur_batch_ctx_len,
                        other=0.0)

            p = p.to(v.dtype)
            acc += tl.dot(p, v)
            # # update m_i and l_i
            l_i = l_i_new
            m_i = m_i_new

        off_k = (offs_n[None, :] * stride_kbs + cur_kv_head * stride_kh +
                 offs_d[:, None] * stride_kd)
        off_v = (offs_n[:, None] * stride_vbs + cur_kv_head * stride_vh +
                 offs_d[None, :] * stride_vd)
        k_ptrs = K + off_k
        v_ptrs = V + off_v

        block_mask = tl.where(
            block_start_loc < cur_batch_seq_len - cur_batch_ctx_len, 1, 0)

        for start_n in range(0, block_mask * (start_m + 1) * BLOCK_M, BLOCK_N):
            start_n = tl.multiple_of(start_n, BLOCK_N)
            # -- compute qk ----
            k = tl.load(k_ptrs +
                        (cur_batch_in_all_start_index + start_n) * stride_kbs,
                        mask=(start_n + offs_n[None, :]) <
                        cur_batch_seq_len - cur_batch_ctx_len,
                        other=0.0)

            qk = tl.zeros([BLOCK_M, BLOCK_N], dtype=tl.float32)
            qk += tl.dot(q, k)
            qk *= sm_scale
            qk = tl.where(offs_m[:, None] >= (start_n + offs_n[None, :]), qk,
                          float("-inf"))

            # -- compute m_ij, p, l_ij
            m_ij = tl.max(qk, 1)
            p = tl.exp(qk - m_ij[:, None])
            l_ij = tl.sum(p, 1)
            # -- update m_i and l_i
            m_i_new = tl.maximum(m_i, m_ij)
            alpha = tl.exp(m_i - m_i_new)
            beta = tl.exp(m_ij - m_i_new)
            l_i_new = alpha * l_i + beta * l_ij
            # -- update output accumulator --
            # scale p
            p_scale = beta / l_i_new
            p = p * p_scale[:, None]
            # scale acc
            acc_scale = l_i / l_i_new * alpha
            acc = acc * acc_scale[:, None]
            # update acc
            v = tl.load(v_ptrs +
                        (cur_batch_in_all_start_index + start_n) * stride_vbs,
                        mask=(start_n + offs_n[:, None]) <
                        cur_batch_seq_len - cur_batch_ctx_len,
                        other=0.0)

            p = p.to(v.dtype)
            acc += tl.dot(p, v)
            # update m_i and l_i
            l_i = l_i_new
            m_i = m_i_new
        # initialize pointers to output
        off_o = (
            (cur_batch_in_all_start_index + offs_m[:, None]) * stride_obs +
            cur_head * stride_oh + offs_d[None, :] * stride_od)
        out_ptrs = Out + off_o
        tl.store(out_ptrs,
                 acc,
                 mask=offs_m[:, None] < cur_batch_seq_len - cur_batch_ctx_len)
        return

    @triton.jit
    def _fwd_kernel_flash_attn_v2(
        Q,
        K,
        V,
        K_cache,
        V_cache,
        B_Loc,
        sm_scale,
        B_Start_Loc,
        B_Seqlen,
        B_Ctxlen,
        block_size,
        x,
        Out,
        stride_b_loc_b,
        stride_b_loc_s,
        stride_qbs,
        stride_qh,
        stride_qd,
        stride_kbs,
        stride_kh,
        stride_kd,
        stride_vbs,
        stride_vh,
        stride_vd,
        stride_obs,
        stride_oh,
        stride_od,
        stride_k_cache_bs,
        stride_k_cache_h,
        stride_k_cache_d,
        stride_k_cache_bl,
        stride_k_cache_x,
        stride_v_cache_bs,
        stride_v_cache_h,
        stride_v_cache_d,
        stride_v_cache_bl,
        num_queries_per_kv: int,
        BLOCK_M: tl.constexpr,
        BLOCK_DMODEL: tl.constexpr,
        BLOCK_N: tl.constexpr,
    ):
        cur_batch = tl.program_id(0)
        cur_head = tl.program_id(1)
        start_m = tl.program_id(2)

        cur_kv_head = cur_head // num_queries_per_kv

        cur_batch_ctx_len = tl.load(B_Ctxlen + cur_batch)
        cur_batch_seq_len = tl.load(B_Seqlen + cur_batch)
        cur_batch_in_all_start_index = tl.load(B_Start_Loc + cur_batch)

        block_start_loc = BLOCK_M * start_m

        # initialize offsets
        offs_n = tl.arange(0, BLOCK_N)
        offs_d = tl.arange(0, BLOCK_DMODEL)
        offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M)
        off_q = (
            (cur_batch_in_all_start_index + offs_m[:, None]) * stride_qbs +
            cur_head * stride_qh + offs_d[None, :] * stride_qd)

        q = tl.load(
            Q + off_q,
            mask=offs_m[:, None] < cur_batch_seq_len - cur_batch_ctx_len,
            other=0.0)

        # # initialize pointer to m and l
        m_i = tl.zeros([BLOCK_M], dtype=tl.float32) - float("inf")
        l_i = tl.zeros([BLOCK_M], dtype=tl.float32)
        acc = tl.zeros([BLOCK_M, BLOCK_DMODEL], dtype=tl.float32)

        for start_n in range(0, cur_batch_ctx_len, BLOCK_N):
            start_n = tl.multiple_of(start_n, BLOCK_N)
            # -- compute qk ----
            bn = tl.load(B_Loc + cur_batch * stride_b_loc_b +
                         ((start_n + offs_n) // block_size) * stride_b_loc_s,
                         mask=(start_n + offs_n) < cur_batch_ctx_len,
                         other=0)
            off_k = (bn[None, :] * stride_k_cache_bs +
                     cur_kv_head * stride_k_cache_h +
                     (offs_d[:, None] // x) * stride_k_cache_d +
                     ((start_n + offs_n[None, :]) % block_size) *
                     stride_k_cache_bl +
                     (offs_d[:, None] % x) * stride_k_cache_x)
            off_v = (
                bn[:, None] * stride_v_cache_bs +
                cur_kv_head * stride_v_cache_h +
                offs_d[None, :] * stride_v_cache_d +
                (start_n + offs_n[:, None]) % block_size * stride_v_cache_bl)
            k = tl.load(K_cache + off_k,
                        mask=(start_n + offs_n[None, :]) < cur_batch_ctx_len,
                        other=0.0)

            qk = tl.zeros([BLOCK_M, BLOCK_N], dtype=tl.float32)
            qk += tl.dot(q, k)
            qk = tl.where((start_n + offs_n[None, :]) < cur_batch_ctx_len, qk,
                          float("-inf"))
            qk *= sm_scale

            # -- compute m_ij, p, l_ij
            m_ij = tl.max(qk, 1)
            m_i_new = tl.maximum(m_i, m_ij)
            p = tl.math.exp(qk - m_i_new[:, None])
            l_ij = tl.sum(p, 1)
            # -- update m_i and l_i

            alpha = tl.math.exp(m_i - m_i_new)
            l_i_new = alpha * l_i + l_ij
            # -- update output accumulator --
            # scale p
            # scale acc
            acc_scale = alpha
            # acc_scale = l_i / l_i_new * alpha
            acc = acc * acc_scale[:, None]
            # update acc
            v = tl.load(V_cache + off_v,
                        mask=(start_n + offs_n[:, None]) < cur_batch_ctx_len,
                        other=0.0)

            p = p.to(v.dtype)
            acc += tl.dot(p, v)
            # update m_i and l_i
            l_i = l_i_new
            m_i = m_i_new

        off_k = (offs_n[None, :] * stride_kbs + cur_kv_head * stride_kh +
                 offs_d[:, None] * stride_kd)
        off_v = (offs_n[:, None] * stride_vbs + cur_kv_head * stride_vh +
                 offs_d[None, :] * stride_vd)
        k_ptrs = K + off_k
        v_ptrs = V + off_v

        block_mask = tl.where(
            block_start_loc < cur_batch_seq_len - cur_batch_ctx_len, 1, 0)

        for start_n in range(0, block_mask * (start_m + 1) * BLOCK_M, BLOCK_N):
            start_n = tl.multiple_of(start_n, BLOCK_N)
            # -- compute qk ----
            k = tl.load(k_ptrs +
                        (cur_batch_in_all_start_index + start_n) * stride_kbs,
                        mask=(start_n + offs_n[None, :]) <
                        cur_batch_seq_len - cur_batch_ctx_len,
                        other=0.0)

            qk = tl.zeros([BLOCK_M, BLOCK_N], dtype=tl.float32)
            qk += tl.dot(q, k)
            qk *= sm_scale
            qk = tl.where(offs_m[:, None] >= (start_n + offs_n[None, :]), qk,
                          float("-inf"))

            # -- compute m_ij, p, l_ij
            m_ij = tl.max(qk, 1)
            m_i_new = tl.maximum(m_i, m_ij)
            p = tl.math.exp(qk - m_i_new[:, None])
            l_ij = tl.sum(p, 1)
            # -- update m_i and l_i

            alpha = tl.math.exp(m_i - m_i_new)
            l_i_new = alpha * l_i + l_ij
            # -- update output accumulator --
            # scale p
            # scale acc
            acc_scale = alpha
            # acc_scale = l_i / l_i_new * alpha
            acc = acc * acc_scale[:, None]
            # update acc
            v = tl.load(v_ptrs +
                        (cur_batch_in_all_start_index + start_n) * stride_vbs,
                        mask=(start_n + offs_n[:, None]) <
                        cur_batch_seq_len - cur_batch_ctx_len,
                        other=0.0)

            p = p.to(v.dtype)
            acc += tl.dot(p, v)
            # update m_i and l_i
            l_i = l_i_new
            m_i = m_i_new

        # acc /= l_i[:, None]
        # initialize pointers to output
        off_o = (
            (cur_batch_in_all_start_index + offs_m[:, None]) * stride_obs +
            cur_head * stride_oh + offs_d[None, :] * stride_od)
        out_ptrs = Out + off_o
        tl.store(out_ptrs,
                 acc,
                 mask=offs_m[:, None] < cur_batch_seq_len - cur_batch_ctx_len)
        return

    @triton.jit
    def _fwd_kernel_alibi(
        Q,
        K,
        V,
        K_cache,
        V_cache,
        B_Loc,
        sm_scale,
        B_Start_Loc,
        B_Seqlen,
        B_Ctxlen,
        Alibi_slopes,
        block_size,
        x,
        Out,
        stride_b_loc_b,
        stride_b_loc_s,
        stride_qbs,
        stride_qh,
        stride_qd,
        stride_kbs,
        stride_kh,
        stride_kd,
        stride_vbs,
        stride_vh,
        stride_vd,
        stride_obs,
        stride_oh,
        stride_od,
        stride_k_cache_bs,
        stride_k_cache_h,
        stride_k_cache_d,
        stride_k_cache_bl,
        stride_k_cache_x,
        stride_v_cache_bs,
        stride_v_cache_h,
        stride_v_cache_d,
        stride_v_cache_bl,
        num_queries_per_kv: int,
        BLOCK_M: tl.constexpr,
        BLOCK_DMODEL: tl.constexpr,
        BLOCK_N: tl.constexpr,
    ):
        # attn_bias[]
        cur_batch = tl.program_id(0)
        cur_head = tl.program_id(1)
        start_m = tl.program_id(2)

        cur_kv_head = cur_head // num_queries_per_kv

        # cur_batch_seq_len: the length of prompts
        # cur_batch_ctx_len: the length of prefix
        # cur_batch_in_all_start_index: the start id of the dim=0
        cur_batch_ctx_len = tl.load(B_Ctxlen + cur_batch)
        cur_batch_seq_len = tl.load(B_Seqlen + cur_batch)
        cur_batch_in_all_start_index = tl.load(B_Start_Loc + cur_batch)

        block_start_loc = BLOCK_M * start_m

        # initialize offsets
        offs_n = tl.arange(0, BLOCK_N)
        offs_d = tl.arange(0, BLOCK_DMODEL)
        offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M)
        off_q = (
            (cur_batch_in_all_start_index + offs_m[:, None]) * stride_qbs +
            cur_head * stride_qh + offs_d[None, :] * stride_qd)

        q = tl.load(
            Q + off_q,
            mask=offs_m[:, None] < cur_batch_seq_len - cur_batch_ctx_len,
            other=0.0)

        # # initialize pointer to m and l
        m_i = tl.zeros([BLOCK_M], dtype=tl.float32) - float("inf")
        l_i = tl.zeros([BLOCK_M], dtype=tl.float32)
        acc = tl.zeros([BLOCK_M, BLOCK_DMODEL], dtype=tl.float32)

        alibi_slope = tl.load(Alibi_slopes + cur_head)
        alibi_start_q = tl.arange(
            0, BLOCK_M) + block_start_loc + cur_batch_ctx_len
        alibi_start_k = 0
        for start_n in range(0, cur_batch_ctx_len, BLOCK_N):
            start_n = tl.multiple_of(start_n, BLOCK_N)
            # -- compute qk ----
            bn = tl.load(B_Loc + cur_batch * stride_b_loc_b +
                         ((start_n + offs_n) // block_size) * stride_b_loc_s,
                         mask=(start_n + offs_n) < cur_batch_ctx_len,
                         other=0)
            off_k = (bn[None, :] * stride_k_cache_bs +
                     cur_kv_head * stride_k_cache_h +
                     (offs_d[:, None] // x) * stride_k_cache_d +
                     ((start_n + offs_n[None, :]) % block_size) *
                     stride_k_cache_bl +
                     (offs_d[:, None] % x) * stride_k_cache_x)
            off_v = (
                bn[:, None] * stride_v_cache_bs +
                cur_kv_head * stride_v_cache_h +
                offs_d[None, :] * stride_v_cache_d +
                (start_n + offs_n[:, None]) % block_size * stride_v_cache_bl)
            k = tl.load(K_cache + off_k,
                        mask=(start_n + offs_n[None, :]) < cur_batch_ctx_len,
                        other=0.0)

            qk = tl.zeros([BLOCK_M, BLOCK_N], dtype=tl.float32)
            qk += tl.dot(q, k)
            qk = tl.where((start_n + offs_n[None, :]) < cur_batch_ctx_len, qk,
                          float("-inf"))
            qk *= sm_scale

            # load alibi
            alibi = (tl.arange(0, BLOCK_N)[None, :] + alibi_start_k -
                     alibi_start_q[:, None]) * alibi_slope
            alibi = tl.where(
                (alibi <= 0) & (alibi_start_q[:, None] < cur_batch_seq_len),
                alibi, float("-inf"))
            qk += alibi
            alibi_start_k += BLOCK_N

            # -- compute m_ij, p, l_ij
            m_ij = tl.max(qk, 1)
            m_i_new = tl.maximum(m_i, m_ij)
            p = tl.math.exp(qk - m_i_new[:, None])
            l_ij = tl.sum(p, 1)
            # -- update m_i and l_i

            alpha = tl.math.exp(m_i - m_i_new)
            l_i_new = alpha * l_i + l_ij
            # -- update output accumulator --
            # scale p
            # scale acc
            acc_scale = alpha
            # acc_scale = l_i / l_i_new * alpha
            acc = acc * acc_scale[:, None]
            # update acc
            v = tl.load(V_cache + off_v,
                        mask=(start_n + offs_n[:, None]) < cur_batch_ctx_len,
                        other=0.0)

            p = p.to(v.dtype)
            acc += tl.dot(p, v, allow_tf32=False)
            # update m_i and l_i
            l_i = l_i_new
            m_i = m_i_new

        off_k = (offs_n[None, :] * stride_kbs + cur_kv_head * stride_kh +
                 offs_d[:, None] * stride_kd)
        off_v = (offs_n[:, None] * stride_vbs + cur_kv_head * stride_vh +
                 offs_d[None, :] * stride_vd)
        k_ptrs = K + off_k
        v_ptrs = V + off_v

        block_mask = tl.where(
            block_start_loc < cur_batch_seq_len - cur_batch_ctx_len, 1, 0)

        # init alibi
        alibi_slope = tl.load(Alibi_slopes + cur_head)
        alibi_start_q = tl.arange(
            0, BLOCK_M) + block_start_loc + cur_batch_ctx_len
        alibi_start_k = cur_batch_ctx_len
        # # init debugger
        # offset_db_q = tl.arange(0, BLOCK_M) + block_start_loc
        # offset_db_k = tl.arange(0, BLOCK_N)
        # calc q[BLOCK_M, BLOCK_MODEL] mul k[prefix_len: , BLOCK_DMODEL]
        for start_n in range(0, block_mask * (start_m + 1) * BLOCK_M, BLOCK_N):
            start_n = tl.multiple_of(start_n, BLOCK_N)
            # -- compute qk ----
            k = tl.load(k_ptrs +
                        (cur_batch_in_all_start_index + start_n) * stride_kbs,
                        mask=(start_n + offs_n[None, :]) <
                        cur_batch_seq_len - cur_batch_ctx_len,
                        other=0.0)

            qk = tl.zeros([BLOCK_M, BLOCK_N], dtype=tl.float32)
            qk += tl.dot(q, k, allow_tf32=False)
            qk *= sm_scale
            qk = tl.where(offs_m[:, None] >= (start_n + offs_n[None, :]), qk,
                          float("-inf"))

            # load alibi
            alibi = (tl.arange(0, BLOCK_N)[None, :] + alibi_start_k -
                     alibi_start_q[:, None]) * alibi_slope
            alibi = tl.where(
                (alibi <= 0) & (alibi_start_q[:, None] < cur_batch_seq_len),
                alibi, float("-inf"))
            qk += alibi
            alibi_start_k += BLOCK_N

            # -- compute m_ij, p, l_ij
            m_ij = tl.max(qk, 1)
            m_i_new = tl.maximum(m_i, m_ij)
            p = tl.math.exp(qk - m_i_new[:, None])
            l_ij = tl.sum(p, 1)
            # -- update m_i and l_i

            alpha = tl.math.exp(m_i - m_i_new)
            l_i_new = alpha * l_i + l_ij
            # -- update output accumulator --
            # scale p
            # scale acc
            acc_scale = alpha
            # acc_scale = l_i / l_i_new * alpha
            acc = acc * acc_scale[:, None]
            # update acc
            v = tl.load(v_ptrs +
                        (cur_batch_in_all_start_index + start_n) * stride_vbs,
                        mask=(start_n + offs_n[:, None]) <
                        cur_batch_seq_len - cur_batch_ctx_len,
                        other=0.0)

            p = p.to(v.dtype)
            acc += tl.dot(p, v, allow_tf32=False)
            # update m_i and l_i
            l_i = l_i_new
            m_i = m_i_new

        acc = acc / l_i[:, None]

        # initialize pointers to output
        off_o = (
            (cur_batch_in_all_start_index + offs_m[:, None]) * stride_obs +
            cur_head * stride_oh + offs_d[None, :] * stride_od)
        out_ptrs = Out + off_o
        tl.store(out_ptrs,
                 acc,
                 mask=offs_m[:, None] < cur_batch_seq_len - cur_batch_ctx_len)
        return

    @torch.inference_mode()
    def context_attention_fwd(q,
                              k,
                              v,
                              o,
                              k_cache,
                              v_cache,
                              b_loc,
                              b_start_loc,
                              b_seq_len,
                              b_ctx_len,
                              max_input_len,
                              alibi_slopes=None):

        cap = torch.cuda.get_device_capability()
        BLOCK = 128 if cap[0] >= 8 else 64
        # shape constraints
        Lq, Lk, Lv = q.shape[-1], k.shape[-1], v.shape[-1]
        assert Lq == Lk and Lk == Lv
        assert Lk in {16, 32, 64, 128}

        sm_scale = 1.0 / (Lq**0.5)
        batch, head = b_seq_len.shape[0], q.shape[1]
        num_queries_per_kv = q.shape[1] // k.shape[1]

        grid = (batch, head, triton.cdiv(max_input_len, BLOCK))  # batch, head,

        num_warps = 8 if Lk <= 64 else 8
        if alibi_slopes is not None:
            _fwd_kernel_alibi[grid](
                q,
                k,
                v,
                k_cache,
                v_cache,
                b_loc,
                sm_scale,
                b_start_loc,
                b_seq_len,
                b_ctx_len,
                alibi_slopes,
                v_cache.shape[3],
                8,
                o,
                b_loc.stride(0),
                b_loc.stride(1),
                q.stride(0),
                q.stride(1),
                q.stride(2),
                k.stride(0),
                k.stride(1),
                k.stride(2),
                v.stride(0),
                v.stride(1),
                v.stride(2),
                o.stride(0),
                o.stride(1),
                o.stride(2),
                k_cache.stride(0),
                k_cache.stride(1),
                k_cache.stride(2),
                k_cache.stride(3),
                k_cache.stride(
                    4
                ),  #[num_blocks, num_kv_heads, head_size/x, block_size, x]
                v_cache.stride(0),
                v_cache.stride(1),
                v_cache.stride(2),
                v_cache.stride(
                    3),  #[num_blocks, num_kv_heads, head_size, block_size]
                num_queries_per_kv=num_queries_per_kv,
                BLOCK_M=BLOCK,
                BLOCK_DMODEL=Lk,
                BLOCK_N=BLOCK,
                num_warps=num_warps,
                num_stages=1,
            )
            return

        _fwd_kernel[grid](
            q,
            k,
            v,
            k_cache,
            v_cache,
            b_loc,
            sm_scale,
            b_start_loc,
            b_seq_len,
            b_ctx_len,
            v_cache.shape[3],
            8,
            o,
            b_loc.stride(0),
            b_loc.stride(1),
            q.stride(0),
            q.stride(1),
            q.stride(2),
            k.stride(0),
            k.stride(1),
            k.stride(2),
            v.stride(0),
            v.stride(1),
            v.stride(2),
            o.stride(0),
            o.stride(1),
            o.stride(2),
            k_cache.stride(0),
            k_cache.stride(1),
            k_cache.stride(2),
            k_cache.stride(3),
            k_cache.stride(
                4),  #[num_blocks, num_kv_heads, head_size/x, block_size, x]
            v_cache.stride(0),
            v_cache.stride(1),
            v_cache.stride(2),
            v_cache.stride(
                3),  #[num_blocks, num_kv_heads, head_size, block_size]
            num_queries_per_kv=num_queries_per_kv,
            BLOCK_M=BLOCK,
            BLOCK_DMODEL=Lk,
            BLOCK_N=BLOCK,
            num_warps=num_warps,
            num_stages=1,
        )
        return