[System] You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.

[User]
Explain what this code does and identify the inference stage it belongs to.

File: metal/flash_attn.metal

```metal
simdgroup_multiply_accumulate(mqk, mq, mk, mqk);
                        }
                    } else {
                        k8x8_t mk[2];
                        q8x8_t mq[2];

                        #pragma unroll (MIN(DK8/2, 4*NSG))
                        for (short i = 0; i < DK8/2; ++i) {
                            simdgroup_barrier(mem_flags::mem_none);

                            simdgroup_load(mq[0], pq + 0*8 + 16*i, DK);
                            simdgroup_load(mq[1], pq + 1*8 + 16*i, DK);

                            simdgroup_load(mk[0], pk + 0*8 + 16*i, NS10, 0, true);
                            simdgroup_load(mk[1], pk + 1*8 + 16*i, NS10, 0, true);

                            simdgroup_barrier(mem_flags::mem_none);

                            simdgroup_multiply_accumulate(mqk, mq[0], mk[0], mqk);
                            simdgroup_multiply_accumulate(mqk, mq[1], mk[1], mqk);
                        }
                    }

                    simdgroup_store(mqk, ps, SH, 0, false);

                    pk += 8*(NSG*NS10);
                    ps += 8*(NSG);
                }
            } else {
                for (short ccc = 0; ccc < (C/8)/NSG; ++ccc) {
                    const short cc = ccc*NSG + sgitg;

                    const short tx = tiisg%4;
                    const short ty = tiisg/4;

                    qk8x8_t mqk = make_filled_simdgroup_matrix<qk_t, 8>((qk_t) 0.0f);

                    for (short ii = 0; ii < DK16; ii += 4) {
                        device const kd4x4_t * pk4x4 = (device const kd4x4_t *) (k + ((ic + 8*cc + ty)*args.nb11));

                        if (DK16%4 == 0) {
                            {
                                k4x4_t tmp;
                                deq_k(pk4x4 + (ii + tx)/nl_k, (ii + tx)%nl_k, tmp);
                                sk4x4[4*ty + tx] = tmp;
                            }

                            simdgroup_barrier(mem_flags::mem_threadgroup);

                            FOR_UNROLL (short k = 0; k < 4; ++k) {
                                k8x8_t mk;
                                q8x8_t mq;

                                simdgroup_load(mk, sk + 16*k + 0*8, 4*16, 0, true);
                                simdgroup_load(mq, sq + (2*(ii + k) + 0)*8, DK);
                                simdgroup_multiply_accumulate(mqk, mq, mk, mqk);

                                simdgroup_load(mk, sk + 16*k + 1*8, 4*16, 0, true);
                                simdgroup_load(mq, sq + (2*(ii + k) + 1)*8, DK);
```

<｜begin▁of▁sentence｜>You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.<｜User｜>Explain what this code does and identify the inference stage it belongs to.

File: metal/flash_attn.metal

```metal
simdgroup_multiply_accumulate(mqk, mq, mk, mqk);
                        }
                    } else {
                        k8x8_t mk[2];
                        q8x8_t mq[2];

                        #pragma unroll (MIN(DK8/2, 4*NSG))
                        for (short i = 0; i < DK8/2; ++i) {
                            simdgroup_barrier(mem_flags::mem_none);

                            simdgroup_load(mq[0], pq + 0*8 + 16*i, DK);
                            simdgroup_load(mq[1], pq + 1*8 + 16*i, DK);

                            simdgroup_load(mk[0], pk + 0*8 + 16*i, NS10, 0, true);
                            simdgroup_load(mk[1], pk + 1*8 + 16*i, NS10, 0, true);

                            simdgroup_barrier(mem_flags::mem_none);

                            simdgroup_multiply_accumulate(mqk, mq[0], mk[0], mqk);
                            simdgroup_multiply_accumulate(mqk, mq[1], mk[1], mqk);
                        }
                    }

                    simdgroup_store(mqk, ps, SH, 0, false);

                    pk += 8*(NSG*NS10);
                    ps += 8*(NSG);
                }
            } else {
                for (short ccc = 0; ccc < (C/8)/NSG; ++ccc) {
                    const short cc = ccc*NSG + sgitg;

                    const short tx = tiisg%4;
                    const short ty = tiisg/4;

                    qk8x8_t mqk = make_filled_simdgroup_matrix<qk_t, 8>((qk_t) 0.0f);

                    for (short ii = 0; ii < DK16; ii += 4) {
                        device const kd4x4_t * pk4x4 = (device const kd4x4_t *) (k + ((ic + 8*cc + ty)*args.nb11));

                        if (DK16%4 == 0) {
                            {
                                k4x4_t tmp;
                                deq_k(pk4x4 + (ii + tx)/nl_k, (ii + tx)%nl_k, tmp);
                                sk4x4[4*ty + tx] = tmp;
                            }

                            simdgroup_barrier(mem_flags::mem_threadgroup);

                            FOR_UNROLL (short k = 0; k < 4; ++k) {
                                k8x8_t mk;
                                q8x8_t mq;

                                simdgroup_load(mk, sk + 16*k + 0*8, 4*16, 0, true);
                                simdgroup_load(mq, sq + (2*(ii + k) + 0)*8, DK);
                                simdgroup_multiply_accumulate(mqk, mq, mk, mqk);

                                simdgroup_load(mk, sk + 16*k + 1*8, 4*16, 0, true);
                                simdgroup_load(mq, sq + (2*(ii + k) + 1)*8, DK);
```<｜Assistant｜><think>


[System] You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.

[User]
Suggest a minimal correctness-preserving optimization for this excerpt.

File: metal/flash_attn.metal

```metal
mq, mk, mqk);

                                simdgroup_load(mk, sk + 16*k + 1*8, 4*16, 0, true);
                                simdgroup_load(mq, sq + (2*(ii + k) + 1)*8, DK);
                                simdgroup_multiply_accumulate(mqk, mq, mk, mqk);
                            }
                        } else {
                            if (ii + tx < DK16) {
                                k4x4_t tmp;
                                deq_k(pk4x4 + (ii + tx)/nl_k, (ii + tx)%nl_k, tmp);
                                sk4x4[4*ty + tx] = tmp;
                            }

                            simdgroup_barrier(mem_flags::mem_threadgroup);

                            for (short k = 0; k < 4 && ii + k < DK16; ++k) {
                                k8x8_t mk;
                                q8x8_t mq;

                                simdgroup_load(mk, sk + 16*k + 0*8, 4*16, 0, true);
                                simdgroup_load(mq, sq + (2*(ii + k) + 0)*8, DK);
                                simdgroup_multiply_accumulate(mqk, mq, mk, mqk);

                                simdgroup_load(mk, sk + 16*k + 1*8, 4*16, 0, true);
                                simdgroup_load(mq, sq + (2*(ii + k) + 1)*8, DK);
                                simdgroup_multiply_accumulate(mqk, mq, mk, mqk);
                            }
                        }
                    }

                    simdgroup_store(mqk, ss + 8*cc, SH, 0, false);
                }
            }

            threadgroup_barrier(mem_flags::mem_threadgroup);

            FOR_UNROLL (short jj = 0; jj < NQ; ++jj) {
                const short j = jj*NSG + sgitg;

                const float m = M[jj];

                float2 s2 = ss2[j*SH/2 + tiisg]*args.scale;

                if (FC_flash_attn_ext_has_scap) {
                    s2 = args.logit_softcap*precise::tanh(s2);
                }

                if (blk_cur != 2) {
                    if (FC_flash_attn_ext_has_bias) {
                        s2 += s2_t(sm2[j*SH + tiisg])*slope;
                    } else {
                        s2 += s2_t(sm2[j*SH + tiisg]);
                    }
                }

                M[jj] = simd_max(max(M[jj], max(s2[0], s2[1])));

                const float  ms  = exp(m  - M[jj]);
                const float2 vs2 = exp(s2 - M[jj]);

                S[jj] = S[jj]*ms + simd_sum(vs2[0] + vs2[1]);

                ss2[j*SH/2 + tiisg] = vs2;

                if (DV4 % NW == 0) {
                    FOR_UNROLL (short ii = 0; ii < DV4/NW; ++ii) {
```

<｜begin▁of▁sentence｜>You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.<｜User｜>Suggest a minimal correctness-preserving optimization for this excerpt.

File: metal/flash_attn.metal

```metal
mq, mk, mqk);

                                simdgroup_load(mk, sk + 16*k + 1*8, 4*16, 0, true);
                                simdgroup_load(mq, sq + (2*(ii + k) + 1)*8, DK);
                                simdgroup_multiply_accumulate(mqk, mq, mk, mqk);
                            }
                        } else {
                            if (ii + tx < DK16) {
                                k4x4_t tmp;
                                deq_k(pk4x4 + (ii + tx)/nl_k, (ii + tx)%nl_k, tmp);
                                sk4x4[4*ty + tx] = tmp;
                            }

                            simdgroup_barrier(mem_flags::mem_threadgroup);

                            for (short k = 0; k < 4 && ii + k < DK16; ++k) {
                                k8x8_t mk;
                                q8x8_t mq;

                                simdgroup_load(mk, sk + 16*k + 0*8, 4*16, 0, true);
                                simdgroup_load(mq, sq + (2*(ii + k) + 0)*8, DK);
                                simdgroup_multiply_accumulate(mqk, mq, mk, mqk);

                                simdgroup_load(mk, sk + 16*k + 1*8, 4*16, 0, true);
                                simdgroup_load(mq, sq + (2*(ii + k) + 1)*8, DK);
                                simdgroup_multiply_accumulate(mqk, mq, mk, mqk);
                            }
                        }
                    }

                    simdgroup_store(mqk, ss + 8*cc, SH, 0, false);
                }
            }

            threadgroup_barrier(mem_flags::mem_threadgroup);

            FOR_UNROLL (short jj = 0; jj < NQ; ++jj) {
                const short j = jj*NSG + sgitg;

                const float m = M[jj];

                float2 s2 = ss2[j*SH/2 + tiisg]*args.scale;

                if (FC_flash_attn_ext_has_scap) {
                    s2 = args.logit_softcap*precise::tanh(s2);
                }

                if (blk_cur != 2) {
                    if (FC_flash_attn_ext_has_bias) {
                        s2 += s2_t(sm2[j*SH + tiisg])*slope;
                    } else {
                        s2 += s2_t(sm2[j*SH + tiisg]);
                    }
                }

                M[jj] = simd_max(max(M[jj], max(s2[0], s2[1])));

                const float  ms  = exp(m  - M[jj]);
                const float2 vs2 = exp(s2 - M[jj]);

                S[jj] = S[jj]*ms + simd_sum(vs2[0] + vs2[1]);

                ss2[j*SH/2 + tiisg] = vs2;

                if (DV4 % NW == 0) {
                    FOR_UNROLL (short ii = 0; ii < DV4/NW; ++ii) {
```<｜Assistant｜></think>


[System] You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.

[User]
Suggest a minimal correctness-preserving optimization for this excerpt.

File: metal/flash_attn.metal

```metal
mq, mk, mqk);

                                simdgroup_load(mk, sk + 16*k + 1*8, 4*16, 0, true);
                                simdgroup_load(mq, sq + (2*(ii + k) + 1)*8, DK);
                                simdgroup_multiply_accumulate(mqk, mq, mk, mqk);
                            }
                        } else {
                            if (ii + tx < DK16) {
                                k4x4_t tmp;
                                deq_k(pk4x4 + (ii + tx)/nl_k, (ii + tx)%nl_k, tmp);
                                sk4x4[4*ty + tx] = tmp;
                            }

                            simdgroup_barrier(mem_flags::mem_threadgroup);

                            for (short k = 0; k < 4 && ii + k < DK16; ++k) {
                                k8x8_t mk;
                                q8x8_t mq;

                                simdgroup_load(mk, sk + 16*k + 0*8, 4*16, 0, true);
                                simdgroup_load(mq, sq + (2*(ii + k) + 0)*8, DK);
                                simdgroup_multiply_accumulate(mqk, mq, mk, mqk);

                                simdgroup_load(mk, sk + 16*k + 1*8, 4*16, 0, true);
                                simdgroup_load(mq, sq + (2*(ii + k) + 1)*8, DK);
                                simdgroup_multiply_accumulate(mqk, mq, mk, mqk);
                            }
                        }
                    }

                    simdgroup_store(mqk, ss + 8*cc, SH, 0, false);
                }
            }

            threadgroup_barrier(mem_flags::mem_threadgroup);

            FOR_UNROLL (short jj = 0; jj < NQ; ++jj) {
                const short j = jj*NSG + sgitg;

                const float m = M[jj];

                float2 s2 = ss2[j*SH/2 + tiisg]*args.scale;

                if (FC_flash_attn_ext_has_scap) {
                    s2 = args.logit_softcap*precise::tanh(s2);
                }

                if (blk_cur != 2) {
                    if (FC_flash_attn_ext_has_bias) {
                        s2 += s2_t(sm2[j*SH + tiisg])*slope;
                    } else {
                        s2 += s2_t(sm2[j*SH + tiisg]);
                    }
                }

                M[jj] = simd_max(max(M[jj], max(s2[0], s2[1])));

                const float  ms  = exp(m  - M[jj]);
                const float2 vs2 = exp(s2 - M[jj]);

                S[jj] = S[jj]*ms + simd_sum(vs2[0] + vs2[1]);

                ss2[j*SH/2 + tiisg] = vs2;

                if (DV4 % NW == 0) {
                    FOR_UNROLL (short ii = 0; ii < DV4/NW; ++ii) {
```

<｜begin▁of▁sentence｜>You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.<｜User｜>Suggest a minimal correctness-preserving optimization for this excerpt.

File: metal/flash_attn.metal

```metal
mq, mk, mqk);

                                simdgroup_load(mk, sk + 16*k + 1*8, 4*16, 0, true);
                                simdgroup_load(mq, sq + (2*(ii + k) + 1)*8, DK);
                                simdgroup_multiply_accumulate(mqk, mq, mk, mqk);
                            }
                        } else {
                            if (ii + tx < DK16) {
                                k4x4_t tmp;
                                deq_k(pk4x4 + (ii + tx)/nl_k, (ii + tx)%nl_k, tmp);
                                sk4x4[4*ty + tx] = tmp;
                            }

                            simdgroup_barrier(mem_flags::mem_threadgroup);

                            for (short k = 0; k < 4 && ii + k < DK16; ++k) {
                                k8x8_t mk;
                                q8x8_t mq;

                                simdgroup_load(mk, sk + 16*k + 0*8, 4*16, 0, true);
                                simdgroup_load(mq, sq + (2*(ii + k) + 0)*8, DK);
                                simdgroup_multiply_accumulate(mqk, mq, mk, mqk);

                                simdgroup_load(mk, sk + 16*k + 1*8, 4*16, 0, true);
                                simdgroup_load(mq, sq + (2*(ii + k) + 1)*8, DK);
                                simdgroup_multiply_accumulate(mqk, mq, mk, mqk);
                            }
                        }
                    }

                    simdgroup_store(mqk, ss + 8*cc, SH, 0, false);
                }
            }

            threadgroup_barrier(mem_flags::mem_threadgroup);

            FOR_UNROLL (short jj = 0; jj < NQ; ++jj) {
                const short j = jj*NSG + sgitg;

                const float m = M[jj];

                float2 s2 = ss2[j*SH/2 + tiisg]*args.scale;

                if (FC_flash_attn_ext_has_scap) {
                    s2 = args.logit_softcap*precise::tanh(s2);
                }

                if (blk_cur != 2) {
                    if (FC_flash_attn_ext_has_bias) {
                        s2 += s2_t(sm2[j*SH + tiisg])*slope;
                    } else {
                        s2 += s2_t(sm2[j*SH + tiisg]);
                    }
                }

                M[jj] = simd_max(max(M[jj], max(s2[0], s2[1])));

                const float  ms  = exp(m  - M[jj]);
                const float2 vs2 = exp(s2 - M[jj]);

                S[jj] = S[jj]*ms + simd_sum(vs2[0] + vs2[1]);

                ss2[j*SH/2 + tiisg] = vs2;

                if (DV4 % NW == 0) {
                    FOR_UNROLL (short ii = 0; ii < DV4/NW; ++ii) {
```<｜Assistant｜><think>


[System] You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.

[User]
Trova bug sottili e spiega quali invarianti dell'inferenza possono rompersi.

File: metal/flash_attn.metal

```metal
ms + simd_sum(vs2[0] + vs2[1]);

                ss2[j*SH/2 + tiisg] = vs2;

                if (DV4 % NW == 0) {
                    FOR_UNROLL (short ii = 0; ii < DV4/NW; ++ii) {
                        const short i = ii*NW + tiisg;

                        so4[j*PV4 + i] *= ms;
                    }
                } else {
                    for (short i = tiisg; i < DV4; i += NW) {
                        so4[j*PV4 + i] *= ms;
                    }
                }
            }

            threadgroup_barrier(mem_flags::mem_threadgroup);

            {
                if (is_same<vd4x4_t, v4x4_t>::value) {
                    static_assert(PV8 % NSG == 0, "");

                    constexpr short NO = PV8/NSG;

                    o8x8_t lo[NO];

                    {
                        auto sot = so + 8*sgitg;

                        FOR_UNROLL (short ii = 0; ii < NO; ++ii) {
                            simdgroup_load(lo[ii], sot, PV, 0, false);

                            sot += 8*NSG;
                        }
                    }

                    {
                        device const v_t * pv = (device const v_t *) (v + ic*args.nb21);

                        pv += 8*sgitg;

                        if (DV <= 64) {
                            FOR_UNROLL (short cc = 0; cc < C/8; ++cc) {
                                s8x8_t vs;
                                simdgroup_load(vs, ss + 8*cc, SH, 0, false);

                                FOR_UNROLL (short ii = 0; ii < NO/2; ++ii) {
                                    v8x8_t mv[2];

                                    simdgroup_load(mv[0], pv + 0*NSG + 16*ii*NSG, NS20, 0, false);
                                    simdgroup_load(mv[1], pv + 8*NSG + 16*ii*NSG, NS20, 0, false);

                                    simdgroup_multiply_accumulate(lo[2*ii + 0], vs, mv[0], lo[2*ii + 0]);
                                    simdgroup_multiply_accumulate(lo[2*ii + 1], vs, mv[1], lo[2*ii + 1]);
                                }

                                pv  += 8*NS20;
                            }
                        } else {
                            constexpr short NC = (C/8)/2;

                            FOR_UNROLL (short cc = 0; cc < NC; ++cc) {
                                s8x8_t vs[2];

                                simdgroup_load(vs[0], ss + 16*cc + 0, SH, 0, false);
                                simdgroup_load(vs[1], ss + 16*cc + 8, SH, 0, false);

                                FOR_UNROLL (short ii = 0; ii < NO/2; ++ii) {
```

<｜begin▁of▁sentence｜>You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.<｜User｜>Trova bug sottili e spiega quali invarianti dell'inferenza possono rompersi.

File: metal/flash_attn.metal

```metal
ms + simd_sum(vs2[0] + vs2[1]);

                ss2[j*SH/2 + tiisg] = vs2;

                if (DV4 % NW == 0) {
                    FOR_UNROLL (short ii = 0; ii < DV4/NW; ++ii) {
                        const short i = ii*NW + tiisg;

                        so4[j*PV4 + i] *= ms;
                    }
                } else {
                    for (short i = tiisg; i < DV4; i += NW) {
                        so4[j*PV4 + i] *= ms;
                    }
                }
            }

            threadgroup_barrier(mem_flags::mem_threadgroup);

            {
                if (is_same<vd4x4_t, v4x4_t>::value) {
                    static_assert(PV8 % NSG == 0, "");

                    constexpr short NO = PV8/NSG;

                    o8x8_t lo[NO];

                    {
                        auto sot = so + 8*sgitg;

                        FOR_UNROLL (short ii = 0; ii < NO; ++ii) {
                            simdgroup_load(lo[ii], sot, PV, 0, false);

                            sot += 8*NSG;
                        }
                    }

                    {
                        device const v_t * pv = (device const v_t *) (v + ic*args.nb21);

                        pv += 8*sgitg;

                        if (DV <= 64) {
                            FOR_UNROLL (short cc = 0; cc < C/8; ++cc) {
                                s8x8_t vs;
                                simdgroup_load(vs, ss + 8*cc, SH, 0, false);

                                FOR_UNROLL (short ii = 0; ii < NO/2; ++ii) {
                                    v8x8_t mv[2];

                                    simdgroup_load(mv[0], pv + 0*NSG + 16*ii*NSG, NS20, 0, false);
                                    simdgroup_load(mv[1], pv + 8*NSG + 16*ii*NSG, NS20, 0, false);

                                    simdgroup_multiply_accumulate(lo[2*ii + 0], vs, mv[0], lo[2*ii + 0]);
                                    simdgroup_multiply_accumulate(lo[2*ii + 1], vs, mv[1], lo[2*ii + 1]);
                                }

                                pv  += 8*NS20;
                            }
                        } else {
                            constexpr short NC = (C/8)/2;

                            FOR_UNROLL (short cc = 0; cc < NC; ++cc) {
                                s8x8_t vs[2];

                                simdgroup_load(vs[0], ss + 16*cc + 0, SH, 0, false);
                                simdgroup_load(vs[1], ss + 16*cc + 8, SH, 0, false);

                                FOR_UNROLL (short ii = 0; ii < NO/2; ++ii) {
```<｜Assistant｜></think>


[System] You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.

[User]
Trova bug sottili e spiega quali invarianti dell'inferenza possono rompersi.

File: metal/flash_attn.metal

```metal
ms + simd_sum(vs2[0] + vs2[1]);

                ss2[j*SH/2 + tiisg] = vs2;

                if (DV4 % NW == 0) {
                    FOR_UNROLL (short ii = 0; ii < DV4/NW; ++ii) {
                        const short i = ii*NW + tiisg;

                        so4[j*PV4 + i] *= ms;
                    }
                } else {
                    for (short i = tiisg; i < DV4; i += NW) {
                        so4[j*PV4 + i] *= ms;
                    }
                }
            }

            threadgroup_barrier(mem_flags::mem_threadgroup);

            {
                if (is_same<vd4x4_t, v4x4_t>::value) {
                    static_assert(PV8 % NSG == 0, "");

                    constexpr short NO = PV8/NSG;

                    o8x8_t lo[NO];

                    {
                        auto sot = so + 8*sgitg;

                        FOR_UNROLL (short ii = 0; ii < NO; ++ii) {
                            simdgroup_load(lo[ii], sot, PV, 0, false);

                            sot += 8*NSG;
                        }
                    }

                    {
                        device const v_t * pv = (device const v_t *) (v + ic*args.nb21);

                        pv += 8*sgitg;

                        if (DV <= 64) {
                            FOR_UNROLL (short cc = 0; cc < C/8; ++cc) {
                                s8x8_t vs;
                                simdgroup_load(vs, ss + 8*cc, SH, 0, false);

                                FOR_UNROLL (short ii = 0; ii < NO/2; ++ii) {
                                    v8x8_t mv[2];

                                    simdgroup_load(mv[0], pv + 0*NSG + 16*ii*NSG, NS20, 0, false);
                                    simdgroup_load(mv[1], pv + 8*NSG + 16*ii*NSG, NS20, 0, false);

                                    simdgroup_multiply_accumulate(lo[2*ii + 0], vs, mv[0], lo[2*ii + 0]);
                                    simdgroup_multiply_accumulate(lo[2*ii + 1], vs, mv[1], lo[2*ii + 1]);
                                }

                                pv  += 8*NS20;
                            }
                        } else {
                            constexpr short NC = (C/8)/2;

                            FOR_UNROLL (short cc = 0; cc < NC; ++cc) {
                                s8x8_t vs[2];

                                simdgroup_load(vs[0], ss + 16*cc + 0, SH, 0, false);
                                simdgroup_load(vs[1], ss + 16*cc + 8, SH, 0, false);

                                FOR_UNROLL (short ii = 0; ii < NO/2; ++ii) {
```

<｜begin▁of▁sentence｜>You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.<｜User｜>Trova bug sottili e spiega quali invarianti dell'inferenza possono rompersi.

File: metal/flash_attn.metal

```metal
ms + simd_sum(vs2[0] + vs2[1]);

                ss2[j*SH/2 + tiisg] = vs2;

                if (DV4 % NW == 0) {
                    FOR_UNROLL (short ii = 0; ii < DV4/NW; ++ii) {
                        const short i = ii*NW + tiisg;

                        so4[j*PV4 + i] *= ms;
                    }
                } else {
                    for (short i = tiisg; i < DV4; i += NW) {
                        so4[j*PV4 + i] *= ms;
                    }
                }
            }

            threadgroup_barrier(mem_flags::mem_threadgroup);

            {
                if (is_same<vd4x4_t, v4x4_t>::value) {
                    static_assert(PV8 % NSG == 0, "");

                    constexpr short NO = PV8/NSG;

                    o8x8_t lo[NO];

                    {
                        auto sot = so + 8*sgitg;

                        FOR_UNROLL (short ii = 0; ii < NO; ++ii) {
                            simdgroup_load(lo[ii], sot, PV, 0, false);

                            sot += 8*NSG;
                        }
                    }

                    {
                        device const v_t * pv = (device const v_t *) (v + ic*args.nb21);

                        pv += 8*sgitg;

                        if (DV <= 64) {
                            FOR_UNROLL (short cc = 0; cc < C/8; ++cc) {
                                s8x8_t vs;
                                simdgroup_load(vs, ss + 8*cc, SH, 0, false);

                                FOR_UNROLL (short ii = 0; ii < NO/2; ++ii) {
                                    v8x8_t mv[2];

                                    simdgroup_load(mv[0], pv + 0*NSG + 16*ii*NSG, NS20, 0, false);
                                    simdgroup_load(mv[1], pv + 8*NSG + 16*ii*NSG, NS20, 0, false);

                                    simdgroup_multiply_accumulate(lo[2*ii + 0], vs, mv[0], lo[2*ii + 0]);
                                    simdgroup_multiply_accumulate(lo[2*ii + 1], vs, mv[1], lo[2*ii + 1]);
                                }

                                pv  += 8*NS20;
                            }
                        } else {
                            constexpr short NC = (C/8)/2;

                            FOR_UNROLL (short cc = 0; cc < NC; ++cc) {
                                s8x8_t vs[2];

                                simdgroup_load(vs[0], ss + 16*cc + 0, SH, 0, false);
                                simdgroup_load(vs[1], ss + 16*cc + 8, SH, 0, false);

                                FOR_UNROLL (short ii = 0; ii < NO/2; ++ii) {
```<｜Assistant｜><think>


[System] You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.

[User]
Review this excerpt for correctness risks, memory lifetime issues, and performance bottlenecks.

File: metal/get_rows.metal

```metal
// DS4 Metal get-rows kernel.

struct ds4_metal_args_get_rows {
    int32_t  ne00t;
    int32_t  ne00;
    uint64_t nb01;
    uint64_t nb02;
    uint64_t nb03;
    int32_t  ne10;
    uint64_t nb10;
    uint64_t nb11;
    uint64_t nb12;
    uint64_t nb1;
    uint64_t nb2;
    uint64_t nb3;
};

// Gathers embedding/table rows by integer ids. DS4 uses this for token
// embeddings and small indexed tables such as router/hash lookup outputs.
template<typename T0, typename T>
kernel void kernel_get_rows_f(
        constant ds4_metal_args_get_rows & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3               tgpig[[threadgroup_position_in_grid]],
        ushort              tiitg[[thread_index_in_threadgroup]],
        ushort3             ntg [[threads_per_threadgroup]]) {
    const int32_t iw0 = tgpig.x/args.ne10;
    const int32_t i10 = tgpig.x%args.ne10;
    const int32_t i11 = tgpig.y;
    const int32_t i12 = tgpig.z;

    const int32_t r = ((const device int32_t *) (src1 + i12*args.nb12 + i11*args.nb11 + i10*args.nb10))[0];

    const int32_t i02 = i11;
    const int32_t i03 = i12;

    auto psrc = (const device T0 *) (src0 + i03*args.nb03 + i02*args.nb02 + r*args.nb01);
    auto pdst = (      device T  *) (dst  + i12*args.nb3  + i11*args.nb2  + i10*args.nb1);

    for (int ind = iw0*ntg.x + tiitg; ind < args.ne00t;) {
        pdst[ind] = psrc[ind];

        break;
    }
}

typedef decltype(kernel_get_rows_f<float, float>) get_rows_f_t;

// Host-visible gather variants for F32, F16, and I32 tables.
template [[host_name("kernel_get_rows_f32")]] kernel get_rows_f_t kernel_get_rows_f<float, float>;
template [[host_name("kernel_get_rows_f16")]] kernel get_rows_f_t kernel_get_rows_f<half, float>;
template [[host_name("kernel_get_rows_i32")]] kernel get_rows_f_t kernel_get_rows_f<int32_t, int32_t>;
```

<｜begin▁of▁sentence｜>You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.<｜User｜>Review this excerpt for correctness risks, memory lifetime issues, and performance bottlenecks.

File: metal/get_rows.metal

```metal
// DS4 Metal get-rows kernel.

struct ds4_metal_args_get_rows {
    int32_t  ne00t;
    int32_t  ne00;
    uint64_t nb01;
    uint64_t nb02;
    uint64_t nb03;
    int32_t  ne10;
    uint64_t nb10;
    uint64_t nb11;
    uint64_t nb12;
    uint64_t nb1;
    uint64_t nb2;
    uint64_t nb3;
};

// Gathers embedding/table rows by integer ids. DS4 uses this for token
// embeddings and small indexed tables such as router/hash lookup outputs.
template<typename T0, typename T>
kernel void kernel_get_rows_f(
        constant ds4_metal_args_get_rows & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3               tgpig[[threadgroup_position_in_grid]],
        ushort              tiitg[[thread_index_in_threadgroup]],
        ushort3             ntg [[threads_per_threadgroup]]) {
    const int32_t iw0 = tgpig.x/args.ne10;
    const int32_t i10 = tgpig.x%args.ne10;
    const int32_t i11 = tgpig.y;
    const int32_t i12 = tgpig.z;

    const int32_t r = ((const device int32_t *) (src1 + i12*args.nb12 + i11*args.nb11 + i10*args.nb10))[0];

    const int32_t i02 = i11;
    const int32_t i03 = i12;

    auto psrc = (const device T0 *) (src0 + i03*args.nb03 + i02*args.nb02 + r*args.nb01);
    auto pdst = (      device T  *) (dst  + i12*args.nb3  + i11*args.nb2  + i10*args.nb1);

    for (int ind = iw0*ntg.x + tiitg; ind < args.ne00t;) {
        pdst[ind] = psrc[ind];

        break;
    }
}

typedef decltype(kernel_get_rows_f<float, float>) get_rows_f_t;

// Host-visible gather variants for F32, F16, and I32 tables.
template [[host_name("kernel_get_rows_f32")]] kernel get_rows_f_t kernel_get_rows_f<float, float>;
template [[host_name("kernel_get_rows_f16")]] kernel get_rows_f_t kernel_get_rows_f<half, float>;
template [[host_name("kernel_get_rows_i32")]] kernel get_rows_f_t kernel_get_rows_f<int32_t, int32_t>;
```<｜Assistant｜></think>


[System] You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.

[User]
Review this excerpt for correctness risks, memory lifetime issues, and performance bottlenecks.

File: metal/get_rows.metal

```metal
// DS4 Metal get-rows kernel.

struct ds4_metal_args_get_rows {
    int32_t  ne00t;
    int32_t  ne00;
    uint64_t nb01;
    uint64_t nb02;
    uint64_t nb03;
    int32_t  ne10;
    uint64_t nb10;
    uint64_t nb11;
    uint64_t nb12;
    uint64_t nb1;
    uint64_t nb2;
    uint64_t nb3;
};

// Gathers embedding/table rows by integer ids. DS4 uses this for token
// embeddings and small indexed tables such as router/hash lookup outputs.
template<typename T0, typename T>
kernel void kernel_get_rows_f(
        constant ds4_metal_args_get_rows & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3               tgpig[[threadgroup_position_in_grid]],
        ushort              tiitg[[thread_index_in_threadgroup]],
        ushort3             ntg [[threads_per_threadgroup]]) {
    const int32_t iw0 = tgpig.x/args.ne10;
    const int32_t i10 = tgpig.x%args.ne10;
    const int32_t i11 = tgpig.y;
    const int32_t i12 = tgpig.z;

    const int32_t r = ((const device int32_t *) (src1 + i12*args.nb12 + i11*args.nb11 + i10*args.nb10))[0];

    const int32_t i02 = i11;
    const int32_t i03 = i12;

    auto psrc = (const device T0 *) (src0 + i03*args.nb03 + i02*args.nb02 + r*args.nb01);
    auto pdst = (      device T  *) (dst  + i12*args.nb3  + i11*args.nb2  + i10*args.nb1);

    for (int ind = iw0*ntg.x + tiitg; ind < args.ne00t;) {
        pdst[ind] = psrc[ind];

        break;
    }
}

typedef decltype(kernel_get_rows_f<float, float>) get_rows_f_t;

// Host-visible gather variants for F32, F16, and I32 tables.
template [[host_name("kernel_get_rows_f32")]] kernel get_rows_f_t kernel_get_rows_f<float, float>;
template [[host_name("kernel_get_rows_f16")]] kernel get_rows_f_t kernel_get_rows_f<half, float>;
template [[host_name("kernel_get_rows_i32")]] kernel get_rows_f_t kernel_get_rows_f<int32_t, int32_t>;
```

<｜begin▁of▁sentence｜>You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.<｜User｜>Review this excerpt for correctness risks, memory lifetime issues, and performance bottlenecks.

File: metal/get_rows.metal

```metal
// DS4 Metal get-rows kernel.

struct ds4_metal_args_get_rows {
    int32_t  ne00t;
    int32_t  ne00;
    uint64_t nb01;
    uint64_t nb02;
    uint64_t nb03;
    int32_t  ne10;
    uint64_t nb10;
    uint64_t nb11;
    uint64_t nb12;
    uint64_t nb1;
    uint64_t nb2;
    uint64_t nb3;
};

// Gathers embedding/table rows by integer ids. DS4 uses this for token
// embeddings and small indexed tables such as router/hash lookup outputs.
template<typename T0, typename T>
kernel void kernel_get_rows_f(
        constant ds4_metal_args_get_rows & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3               tgpig[[threadgroup_position_in_grid]],
        ushort              tiitg[[thread_index_in_threadgroup]],
        ushort3             ntg [[threads_per_threadgroup]]) {
    const int32_t iw0 = tgpig.x/args.ne10;
    const int32_t i10 = tgpig.x%args.ne10;
    const int32_t i11 = tgpig.y;
    const int32_t i12 = tgpig.z;

    const int32_t r = ((const device int32_t *) (src1 + i12*args.nb12 + i11*args.nb11 + i10*args.nb10))[0];

    const int32_t i02 = i11;
    const int32_t i03 = i12;

    auto psrc = (const device T0 *) (src0 + i03*args.nb03 + i02*args.nb02 + r*args.nb01);
    auto pdst = (      device T  *) (dst  + i12*args.nb3  + i11*args.nb2  + i10*args.nb1);

    for (int ind = iw0*ntg.x + tiitg; ind < args.ne00t;) {
        pdst[ind] = psrc[ind];

        break;
    }
}

typedef decltype(kernel_get_rows_f<float, float>) get_rows_f_t;

// Host-visible gather variants for F32, F16, and I32 tables.
template [[host_name("kernel_get_rows_f32")]] kernel get_rows_f_t kernel_get_rows_f<float, float>;
template [[host_name("kernel_get_rows_f16")]] kernel get_rows_f_t kernel_get_rows_f<half, float>;
template [[host_name("kernel_get_rows_i32")]] kernel get_rows_f_t kernel_get_rows_f<int32_t, int32_t>;
```<｜Assistant｜><think>


[System] You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.

[User]
Trova bug sottili e spiega quali invarianti dell'inferenza possono rompersi.

File: metal/glu.metal

```metal
struct ds4_metal_args_glu {
    int32_t  ne00;
    uint64_t nb01;
    int32_t  ne10;
    uint64_t nb11;
    int32_t  ne0;
    uint64_t nb1;
    int32_t  i00;
    int32_t  i10;
    float    alpha;
    float    limit;
};

// SwiGLU activation for the FFN inner state: silu(gate) * up. The DS4 graph
// uses it between the gate/up expert matmuls and the down projection.
kernel void kernel_swiglu_f32(
        constant ds4_metal_args_glu & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint tgpig[[threadgroup_position_in_grid]],
        uint tpitg[[thread_position_in_threadgroup]],
        uint   ntg[[threads_per_threadgroup]]) {
    device const float * src0_row = (device const float *) ((device const char *) src0 + tgpig*args.nb01) + args.i00;
    device const float * src1_row = (device const float *) ((device const char *) src1 + tgpig*args.nb11) + args.i10;
    device       float * dst_row  = (device       float *) ((device       char *) dst  + tgpig*args.nb1);

    for (int i0 = tpitg; i0 < args.ne0; i0 += ntg) {
        const float x0 = src0_row[i0];
        const float x1 = src1_row[i0];

        const float silu = x0 / (1.0f + exp(-x0));

        dst_row[i0] = silu*x1;
    }
}
```

<｜begin▁of▁sentence｜>You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.<｜User｜>Trova bug sottili e spiega quali invarianti dell'inferenza possono rompersi.

File: metal/glu.metal

```metal
struct ds4_metal_args_glu {
    int32_t  ne00;
    uint64_t nb01;
    int32_t  ne10;
    uint64_t nb11;
    int32_t  ne0;
    uint64_t nb1;
    int32_t  i00;
    int32_t  i10;
    float    alpha;
    float    limit;
};

// SwiGLU activation for the FFN inner state: silu(gate) * up. The DS4 graph
// uses it between the gate/up expert matmuls and the down projection.
kernel void kernel_swiglu_f32(
        constant ds4_metal_args_glu & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint tgpig[[threadgroup_position_in_grid]],
        uint tpitg[[thread_position_in_threadgroup]],
        uint   ntg[[threads_per_threadgroup]]) {
    device const float * src0_row = (device const float *) ((device const char *) src0 + tgpig*args.nb01) + args.i00;
    device const float * src1_row = (device const float *) ((device const char *) src1 + tgpig*args.nb11) + args.i10;
    device       float * dst_row  = (device       float *) ((device       char *) dst  + tgpig*args.nb1);

    for (int i0 = tpitg; i0 < args.ne0; i0 += ntg) {
        const float x0 = src0_row[i0];
        const float x1 = src1_row[i0];

        const float silu = x0 / (1.0f + exp(-x0));

        dst_row[i0] = silu*x1;
    }
}
```<｜Assistant｜></think>


[System] You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.

[User]
Trova bug sottili e spiega quali invarianti dell'inferenza possono rompersi.

File: metal/glu.metal

```metal
struct ds4_metal_args_glu {
    int32_t  ne00;
    uint64_t nb01;
    int32_t  ne10;
    uint64_t nb11;
    int32_t  ne0;
    uint64_t nb1;
    int32_t  i00;
    int32_t  i10;
    float    alpha;
    float    limit;
};

// SwiGLU activation for the FFN inner state: silu(gate) * up. The DS4 graph
// uses it between the gate/up expert matmuls and the down projection.
kernel void kernel_swiglu_f32(
        constant ds4_metal_args_glu & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint tgpig[[threadgroup_position_in_grid]],
        uint tpitg[[thread_position_in_threadgroup]],
        uint   ntg[[threads_per_threadgroup]]) {
    device const float * src0_row = (device const float *) ((device const char *) src0 + tgpig*args.nb01) + args.i00;
    device const float * src1_row = (device const float *) ((device const char *) src1 + tgpig*args.nb11) + args.i10;
    device       float * dst_row  = (device       float *) ((device       char *) dst  + tgpig*args.nb1);

    for (int i0 = tpitg; i0 < args.ne0; i0 += ntg) {
        const float x0 = src0_row[i0];
        const float x1 = src1_row[i0];

        const float silu = x0 / (1.0f + exp(-x0));

        dst_row[i0] = silu*x1;
    }
}
```

<｜begin▁of▁sentence｜>You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.<｜User｜>Trova bug sottili e spiega quali invarianti dell'inferenza possono rompersi.

File: metal/glu.metal

```metal
struct ds4_metal_args_glu {
    int32_t  ne00;
    uint64_t nb01;
    int32_t  ne10;
    uint64_t nb11;
    int32_t  ne0;
    uint64_t nb1;
    int32_t  i00;
    int32_t  i10;
    float    alpha;
    float    limit;
};

// SwiGLU activation for the FFN inner state: silu(gate) * up. The DS4 graph
// uses it between the gate/up expert matmuls and the down projection.
kernel void kernel_swiglu_f32(
        constant ds4_metal_args_glu & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint tgpig[[threadgroup_position_in_grid]],
        uint tpitg[[thread_position_in_threadgroup]],
        uint   ntg[[threads_per_threadgroup]]) {
    device const float * src0_row = (device const float *) ((device const char *) src0 + tgpig*args.nb01) + args.i00;
    device const float * src1_row = (device const float *) ((device const char *) src1 + tgpig*args.nb11) + args.i10;
    device       float * dst_row  = (device       float *) ((device       char *) dst  + tgpig*args.nb1);

    for (int i0 = tpitg; i0 < args.ne0; i0 += ntg) {
        const float x0 = src0_row[i0];
        const float x1 = src1_row[i0];

        const float silu = x0 / (1.0f + exp(-x0));

        dst_row[i0] = silu*x1;
    }
}
```<｜Assistant｜><think>


[System] You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.

[User]
Trova bug sottili e spiega quali invarianti dell'inferenza possono rompersi.

File: metal/moe.metal

```metal
// DS4 Metal routed-MoE matvec kernels.

#define QK_K 256
#define N_R0_Q2_K 4
#define N_R0_Q4_K 2
#define N_R0_IQ2_XXS 4

static constant uchar ds4_metal_kmask_iq2xs[8] = {
    1, 2, 4, 8, 16, 32, 64, 128
};

static constant uchar ds4_metal_ksigns_iq2xs[128] = {
      0, 129, 130,   3, 132,   5,   6, 135, 136,   9,  10, 139,  12, 141, 142,  15,
    144,  17,  18, 147,  20, 149, 150,  23,  24, 153, 154,  27, 156,  29,  30, 159,
    160,  33,  34, 163,  36, 165, 166,  39,  40, 169, 170,  43, 172,  45,  46, 175,
     48, 177, 178,  51, 180,  53,  54, 183, 184,  57,  58, 187,  60, 189, 190,  63,
    192,  65,  66, 195,  68, 197, 198,  71,  72, 201, 202,  75, 204,  77,  78, 207,
     80, 209, 210,  83, 212,  85,  86, 215, 216,  89,  90, 219,  92, 221, 222,  95,
     96, 225, 226,  99, 228, 101, 102, 231, 232, 105, 106, 235, 108, 237, 238, 111,
    240, 113, 114, 243, 116, 245, 246, 119, 120, 249, 250, 123, 252, 125, 126, 255,
};

static constant ulong ds4_metal_iq2xxs_grid[256] = {
    0x0808080808080808, 0x080808080808082b, 0x0808080808081919, 0x0808080808082b08,
    0x0808080808082b2b, 0x0808080808190819, 0x0808080808191908, 0x08080808082b0808,
    0x08080808082b082b, 0x08080808082b2b08, 0x08080808082b2b2b, 0x0808080819080819,
    0x0808080819081908, 0x0808080819190808, 0x0808080819192b08, 0x08080808192b0819,
    0x08080808192b1908, 0x080808082b080808, 0x080808082b08082b, 0x080808082b082b2b,
    0x080808082b2b082b, 0x0808081908080819, 0x0808081908081908, 0x0808081908190808,
    0x0808081908191919, 0x0808081919080808, 0x080808192b081908, 0x080808192b192b08,
    0x0808082b08080808, 0x0808082b0808082b, 0x0808082b082b082b, 0x0808082b2b08082b,
    0x0808190808080819, 0x0808190808081908, 0x0808190808190808, 0x08081908082b0819,
    0x08081908082b1908, 0x0808190819080808, 0x080819081908082b, 0x0808190819082b08,
    0x08081908192b0808, 0x080819082b080819, 0x080819082b081908, 0x080819082b190808,
    0x080819082b2b1908, 0x0808191908080808, 0x080819190808082b, 0x0808191908082b08,
    0x08081919082b0808, 0x080819191908192b, 0x08081919192b2b19, 0x080819192b080808,
    0x080819192b190819, 0x0808192b08082b19, 0x0808192b08190808, 0x0808192b19080808,
    0x0808192b2b081908, 0x0808192b2b2b1908, 0x08082b0808080808, 0x08082b0808081919,
    0x08082b0808082b08, 0x08082b0808191908, 0x08082b08082b2b08, 0x08082b0819080819,
    0x08082b0819081908, 0x08082b0819190808, 0x08082b081919082b, 0x08082b082b082b08,
    0x08082b1908081908, 0x08082b1919080808, 0x08082b2b0808082b, 0x08082b2b08191908,
    0x0819080808080819, 0x0819080808081908, 0x0819080808190808, 0x08190808082b0819,
```


[System] You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.

[User]
Trova bug sottili e spiega quali invarianti dell'inferenza possono rompersi.

File: metal/moe.metal

```metal
// DS4 Metal routed-MoE matvec kernels.

#define QK_K 256
#define N_R0_Q2_K 4
#define N_R0_Q4_K 2
#define N_R0_IQ2_XXS 4

static constant uchar ds4_metal_kmask_iq2xs[8] = {
    1, 2, 4, 8, 16, 32, 64, 128
};

static constant uchar ds4_metal_ksigns_iq2xs[128] = {
      0, 129, 130,   3, 132,   5,   6, 135, 136,   9,  10, 139,  12, 141, 142,  15,
    144,  17,  18, 147,  20, 149, 150,  23,  24, 153, 154,  27, 156,  29,  30, 159,
    160,  33,  34, 163,  36, 165, 166,  39,  40, 169, 170,  43, 172,  45,  46, 175,
     48, 177, 178,  51, 180,  53,  54, 183, 184,  57,  58, 187,  60, 189, 190,  63,
    192,  65,  66, 195,  68, 197, 198,  71,  72, 201, 202,  75, 204,  77,  78, 207,
     80, 209, 210,  83, 212,  85,  86, 215, 216,  89,  90, 219,  92, 221, 222,  95,
     96, 225, 226,  99, 228, 101, 102, 231, 232, 105, 106, 235, 108, 237, 238, 111,
    240, 113, 114, 243, 116, 245, 246, 119, 120, 249, 250, 123, 252, 125, 126, 255,
};

static constant ulong ds4_metal_iq2xxs_grid[256] = {
    0x0808080808080808, 0x080808080808082b, 0x0808080808081919, 0x0808080808082b08,
    0x0808080808082b2b, 0x0808080808190819, 0x0808080808191908, 0x08080808082b0808,
    0x08080808082b082b, 0x08080808082b2b08, 0x08080808082b2b2b, 0x0808080819080819,
    0x0808080819081908, 0x0808080819190808, 0x0808080819192b08, 0x08080808192b0819,
    0x08080808192b1908, 0x080808082b080808, 0x080808082b08082b, 0x080808082b082b2b,
    0x080808082b2b082b, 0x0808081908080819, 0x0808081908081908, 0x0808081908190808,
    0x0808081908191919, 0x0808081919080808, 0x080808192b081908, 0x080808192b192b08,
    0x0808082b08080808, 0x0808082b0808082b, 0x0808082b082b082b, 0x0808082b2b08082b,
    0x0808190808080819, 0x0808190808081908, 0x0808190808190808, 0x08081908082b0819,
    0x08081908082b1908, 0x0808190819080808, 0x080819081908082b, 0x0808190819082b08,
    0x08081908192b0808, 0x080819082b080819, 0x080819082b081908, 0x080819082b190808,
    0x080819082b2b1908, 0x0808191908080808, 0x080819190808082b, 0x0808191908082b08,
    0x08081919082b0808, 0x080819191908192b, 0x08081919192b2b19, 0x080819192b080808,
    0x080819192b190819, 0x0808192b08082b19, 0x0808192b08190808, 0x0808192b19080808,
    0x0808192b2b081908, 0x0808192b2b2b1908, 0x08082b0808080808, 0x08082b0808081919,
    0x08082b0808082b08, 0x08082b0808191908, 0x08082b08082b2b08, 0x08082b0819080819,
    0x08082b0819081908, 0x08082b0819190808, 0x08082b081919082b, 0x08082b082b082b08,
    0x08082b1908081908, 0x08082b1919080808, 0x08082b2b0808082b, 0x08082b2b08191908,
    0x0819080808080819, 0x0819080808081908, 0x0819080808190808, 0x08190808082b0819,
```


[System] You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.

[User]
Review this excerpt for correctness risks, memory lifetime issues, and performance bottlenecks.

File: metal/moe.metal

```metal
b082b082b08,
    0x08082b1908081908, 0x08082b1919080808, 0x08082b2b0808082b, 0x08082b2b08191908,
    0x0819080808080819, 0x0819080808081908, 0x0819080808190808, 0x08190808082b0819,
    0x0819080819080808, 0x08190808192b0808, 0x081908082b081908, 0x081908082b190808,
    0x081908082b191919, 0x0819081908080808, 0x0819081908082b08, 0x08190819082b0808,
    0x0819081919190808, 0x0819081919192b2b, 0x081908192b080808, 0x0819082b082b1908,
    0x0819082b19081919, 0x0819190808080808, 0x0819190808082b08, 0x08191908082b0808,
    0x08191908082b1919, 0x0819190819082b19, 0x081919082b080808, 0x0819191908192b08,
    0x08191919192b082b, 0x0819192b08080808, 0x0819192b0819192b, 0x08192b0808080819,
    0x08192b0808081908, 0x08192b0808190808, 0x08192b0819080808, 0x08192b082b080819,
    0x08192b1908080808, 0x08192b1908081919, 0x08192b192b2b0808, 0x08192b2b19190819,
    0x082b080808080808, 0x082b08080808082b, 0x082b080808082b2b, 0x082b080819081908,
    0x082b0808192b0819, 0x082b08082b080808, 0x082b08082b08082b, 0x082b0819082b2b19,
    0x082b081919082b08, 0x082b082b08080808, 0x082b082b0808082b, 0x082b190808080819,
    0x082b190808081908, 0x082b190808190808, 0x082b190819080808, 0x082b19081919192b,
    0x082b191908080808, 0x082b191919080819, 0x082b1919192b1908, 0x082b192b2b190808,
    0x082b2b0808082b08, 0x082b2b08082b0808, 0x082b2b082b191908, 0x082b2b2b19081908,
    0x1908080808080819, 0x1908080808081908, 0x1908080808190808, 0x1908080808192b08,
    0x19080808082b0819, 0x19080808082b1908, 0x1908080819080808, 0x1908080819082b08,
    0x190808081919192b, 0x19080808192b0808, 0x190808082b080819, 0x190808082b081908,
    0x190808082b190808, 0x1908081908080808, 0x19080819082b0808, 0x19080819192b0819,
    0x190808192b080808, 0x190808192b081919, 0x1908082b08080819, 0x1908082b08190808,
    0x1908082b19082b08, 0x1908082b1919192b, 0x1908082b192b2b08, 0x1908190808080808,
    0x1908190808082b08, 0x19081908082b0808, 0x190819082b080808, 0x190819082b192b19,
    0x190819190819082b, 0x19081919082b1908, 0x1908192b08080808, 0x19082b0808080819,
    0x19082b0808081908, 0x19082b0808190808, 0x19082b0819080808, 0x19082b0819081919,
    0x19082b1908080808, 0x19082b1919192b08, 0x19082b19192b0819, 0x19082b192b08082b,
    0x19082b2b19081919, 0x19082b2b2b190808, 0x1919080808080808, 0x1919080808082b08,
    0x1919080808190819, 0x1919080808192b19, 0x19190808082b0808, 0x191908082b080808,
    0x191908082b082b08, 0x1919081908081908, 0x191908191908082b, 0x191908192b2b1908,
    0x1919082b2b190819, 0x191919082b190808, 0x191919082b19082b, 0x1919191908082b2b,
```


[System] You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.

[User]
Review this excerpt for correctness risks, memory lifetime issues, and performance bottlenecks.

File: metal/moe.metal

```metal
b082b082b08,
    0x08082b1908081908, 0x08082b1919080808, 0x08082b2b0808082b, 0x08082b2b08191908,
    0x0819080808080819, 0x0819080808081908, 0x0819080808190808, 0x08190808082b0819,
    0x0819080819080808, 0x08190808192b0808, 0x081908082b081908, 0x081908082b190808,
    0x081908082b191919, 0x0819081908080808, 0x0819081908082b08, 0x08190819082b0808,
    0x0819081919190808, 0x0819081919192b2b, 0x081908192b080808, 0x0819082b082b1908,
    0x0819082b19081919, 0x0819190808080808, 0x0819190808082b08, 0x08191908082b0808,
    0x08191908082b1919, 0x0819190819082b19, 0x081919082b080808, 0x0819191908192b08,
    0x08191919192b082b, 0x0819192b08080808, 0x0819192b0819192b, 0x08192b0808080819,
    0x08192b0808081908, 0x08192b0808190808, 0x08192b0819080808, 0x08192b082b080819,
    0x08192b1908080808, 0x08192b1908081919, 0x08192b192b2b0808, 0x08192b2b19190819,
    0x082b080808080808, 0x082b08080808082b, 0x082b080808082b2b, 0x082b080819081908,
    0x082b0808192b0819, 0x082b08082b080808, 0x082b08082b08082b, 0x082b0819082b2b19,
    0x082b081919082b08, 0x082b082b08080808, 0x082b082b0808082b, 0x082b190808080819,
    0x082b190808081908, 0x082b190808190808, 0x082b190819080808, 0x082b19081919192b,
    0x082b191908080808, 0x082b191919080819, 0x082b1919192b1908, 0x082b192b2b190808,
    0x082b2b0808082b08, 0x082b2b08082b0808, 0x082b2b082b191908, 0x082b2b2b19081908,
    0x1908080808080819, 0x1908080808081908, 0x1908080808190808, 0x1908080808192b08,
    0x19080808082b0819, 0x19080808082b1908, 0x1908080819080808, 0x1908080819082b08,
    0x190808081919192b, 0x19080808192b0808, 0x190808082b080819, 0x190808082b081908,
    0x190808082b190808, 0x1908081908080808, 0x19080819082b0808, 0x19080819192b0819,
    0x190808192b080808, 0x190808192b081919, 0x1908082b08080819, 0x1908082b08190808,
    0x1908082b19082b08, 0x1908082b1919192b, 0x1908082b192b2b08, 0x1908190808080808,
    0x1908190808082b08, 0x19081908082b0808, 0x190819082b080808, 0x190819082b192b19,
    0x190819190819082b, 0x19081919082b1908, 0x1908192b08080808, 0x19082b0808080819,
    0x19082b0808081908, 0x19082b0808190808, 0x19082b0819080808, 0x19082b0819081919,
    0x19082b1908080808, 0x19082b1919192b08, 0x19082b19192b0819, 0x19082b192b08082b,
    0x19082b2b19081919, 0x19082b2b2b190808, 0x1919080808080808, 0x1919080808082b08,
    0x1919080808190819, 0x1919080808192b19, 0x19190808082b0808, 0x191908082b080808,
    0x191908082b082b08, 0x1919081908081908, 0x191908191908082b, 0x191908192b2b1908,
    0x1919082b2b190819, 0x191919082b190808, 0x191919082b19082b, 0x1919191908082b2b,
```


[System] You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.

[User]
Explain what this code does and identify the inference stage it belongs to.

File: metal/moe.metal

```metal
q2 += args.nb01/2;
        }

        y4 += 32 * 32;
    }

    device float * dst_f32 = (device float *) dst + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;

    for (int row = 0; row < nr0 && first_row + row < args.ne0; ++row) {
        float sum_all = simd_sum(sumf[row]);
        if (tiisg == 0) {
            dst_f32[first_row + row] = sum_all * 0.25f;
        }
    }
}

template<int nr0>
void kernel_mul_mv_iq2_xxs_pair_f32_impl(
        ds4_metal_args_mul_mv args,
        device const char * src0_gate,
        device const char * src0_up,
        device const char * src1,
        device       char * dst_gate,
        device       char * dst_up,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    const int nb = args.ne00/QK_K;

    const int r0 = tgpig.x;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

    const int first_row = (r0 * NSG + sgitg) * nr0;

    const uint i12 = im%args.ne12;
    const uint i13 = im/args.ne12;

    const uint64_t offset0 = first_row*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const uint64_t offset1 =        r1*args.nb11 + (i12        )*args.nb12 + (i13        )*args.nb13;

    device const block_iq2_xxs * xg = (device const block_iq2_xxs *) (src0_gate + offset0);
    device const block_iq2_xxs * xu = (device const block_iq2_xxs *) (src0_up   + offset0);
    device const float         * y  = (device const float         *) (src1      + offset1);

    float yl[32];
    float sumg[nr0]={0.f};
    float sumu[nr0]={0.f};

    const int nb32 = nb * (QK_K / 32);

    threadgroup uint64_t * svalues = (threadgroup uint64_t *)(shmem);
    threadgroup uint8_t  * ssigns  = (threadgroup uint8_t  *)(svalues + 256);
    {
        int nval = 4;
        int pos  = (32*sgitg + tiisg)*nval;
        for (int i = 0; i < nval; ++i) svalues[pos + i] = ds4_metal_iq2xxs_grid[pos + i];
        nval = 2;
        pos  = (32*sgitg + tiisg)*nval;
        for (int i = 0; i < nval; ++i) ssigns[pos+i] = ds4_metal_ksigns_iq2xs[pos+i];
        threadgroup_barrier(mem_flags::mem_threadgroup);
    }

    const int ix = tiisg;
    device const float * y4 = y + 32 * ix;

    for (int ib32 = ix; ib32 < nb32; ib32 += 32) {
        for (short i = 0; i < 32; ++i) {
            yl[i] = y4[i];
        }

        const int ibl = ib32 / (QK_K / 32);
        const int ib  = ib32 % (QK_K / 32);

        device const block_iq2_xxs * xgr = xg + ibl;
        device const block_iq2_xxs * xur = xu + ibl;
```

<｜begin▁of▁sentence｜>You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.<｜User｜>Explain what this code does and identify the inference stage it belongs to.

File: metal/moe.metal

```metal
q2 += args.nb01/2;
        }

        y4 += 32 * 32;
    }

    device float * dst_f32 = (device float *) dst + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;

    for (int row = 0; row < nr0 && first_row + row < args.ne0; ++row) {
        float sum_all = simd_sum(sumf[row]);
        if (tiisg == 0) {
            dst_f32[first_row + row] = sum_all * 0.25f;
        }
    }
}

template<int nr0>
void kernel_mul_mv_iq2_xxs_pair_f32_impl(
        ds4_metal_args_mul_mv args,
        device const char * src0_gate,
        device const char * src0_up,
        device const char * src1,
        device       char * dst_gate,
        device       char * dst_up,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    const int nb = args.ne00/QK_K;

    const int r0 = tgpig.x;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

    const int first_row = (r0 * NSG + sgitg) * nr0;

    const uint i12 = im%args.ne12;
    const uint i13 = im/args.ne12;

    const uint64_t offset0 = first_row*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const uint64_t offset1 =        r1*args.nb11 + (i12        )*args.nb12 + (i13        )*args.nb13;

    device const block_iq2_xxs * xg = (device const block_iq2_xxs *) (src0_gate + offset0);
    device const block_iq2_xxs * xu = (device const block_iq2_xxs *) (src0_up   + offset0);
    device const float         * y  = (device const float         *) (src1      + offset1);

    float yl[32];
    float sumg[nr0]={0.f};
    float sumu[nr0]={0.f};

    const int nb32 = nb * (QK_K / 32);

    threadgroup uint64_t * svalues = (threadgroup uint64_t *)(shmem);
    threadgroup uint8_t  * ssigns  = (threadgroup uint8_t  *)(svalues + 256);
    {
        int nval = 4;
        int pos  = (32*sgitg + tiisg)*nval;
        for (int i = 0; i < nval; ++i) svalues[pos + i] = ds4_metal_iq2xxs_grid[pos + i];
        nval = 2;
        pos  = (32*sgitg + tiisg)*nval;
        for (int i = 0; i < nval; ++i) ssigns[pos+i] = ds4_metal_ksigns_iq2xs[pos+i];
        threadgroup_barrier(mem_flags::mem_threadgroup);
    }

    const int ix = tiisg;
    device const float * y4 = y + 32 * ix;

    for (int ib32 = ix; ib32 < nb32; ib32 += 32) {
        for (short i = 0; i < 32; ++i) {
            yl[i] = y4[i];
        }

        const int ibl = ib32 / (QK_K / 32);
        const int ib  = ib32 % (QK_K / 32);

        device const block_iq2_xxs * xgr = xg + ibl;
        device const block_iq2_xxs * xur = xu + ibl;
```<｜Assistant｜></think>


[System] You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.

[User]
Explain what this code does and identify the inference stage it belongs to.

File: metal/moe.metal

```metal
q2 += args.nb01/2;
        }

        y4 += 32 * 32;
    }

    device float * dst_f32 = (device float *) dst + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;

    for (int row = 0; row < nr0 && first_row + row < args.ne0; ++row) {
        float sum_all = simd_sum(sumf[row]);
        if (tiisg == 0) {
            dst_f32[first_row + row] = sum_all * 0.25f;
        }
    }
}

template<int nr0>
void kernel_mul_mv_iq2_xxs_pair_f32_impl(
        ds4_metal_args_mul_mv args,
        device const char * src0_gate,
        device const char * src0_up,
        device const char * src1,
        device       char * dst_gate,
        device       char * dst_up,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    const int nb = args.ne00/QK_K;

    const int r0 = tgpig.x;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

    const int first_row = (r0 * NSG + sgitg) * nr0;

    const uint i12 = im%args.ne12;
    const uint i13 = im/args.ne12;

    const uint64_t offset0 = first_row*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const uint64_t offset1 =        r1*args.nb11 + (i12        )*args.nb12 + (i13        )*args.nb13;

    device const block_iq2_xxs * xg = (device const block_iq2_xxs *) (src0_gate + offset0);
    device const block_iq2_xxs * xu = (device const block_iq2_xxs *) (src0_up   + offset0);
    device const float         * y  = (device const float         *) (src1      + offset1);

    float yl[32];
    float sumg[nr0]={0.f};
    float sumu[nr0]={0.f};

    const int nb32 = nb * (QK_K / 32);

    threadgroup uint64_t * svalues = (threadgroup uint64_t *)(shmem);
    threadgroup uint8_t  * ssigns  = (threadgroup uint8_t  *)(svalues + 256);
    {
        int nval = 4;
        int pos  = (32*sgitg + tiisg)*nval;
        for (int i = 0; i < nval; ++i) svalues[pos + i] = ds4_metal_iq2xxs_grid[pos + i];
        nval = 2;
        pos  = (32*sgitg + tiisg)*nval;
        for (int i = 0; i < nval; ++i) ssigns[pos+i] = ds4_metal_ksigns_iq2xs[pos+i];
        threadgroup_barrier(mem_flags::mem_threadgroup);
    }

    const int ix = tiisg;
    device const float * y4 = y + 32 * ix;

    for (int ib32 = ix; ib32 < nb32; ib32 += 32) {
        for (short i = 0; i < 32; ++i) {
            yl[i] = y4[i];
        }

        const int ibl = ib32 / (QK_K / 32);
        const int ib  = ib32 % (QK_K / 32);

        device const block_iq2_xxs * xgr = xg + ibl;
        device const block_iq2_xxs * xur = xu + ibl;
```

<｜begin▁of▁sentence｜>You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.<｜User｜>Explain what this code does and identify the inference stage it belongs to.

File: metal/moe.metal

```metal
q2 += args.nb01/2;
        }

        y4 += 32 * 32;
    }

    device float * dst_f32 = (device float *) dst + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;

    for (int row = 0; row < nr0 && first_row + row < args.ne0; ++row) {
        float sum_all = simd_sum(sumf[row]);
        if (tiisg == 0) {
            dst_f32[first_row + row] = sum_all * 0.25f;
        }
    }
}

template<int nr0>
void kernel_mul_mv_iq2_xxs_pair_f32_impl(
        ds4_metal_args_mul_mv args,
        device const char * src0_gate,
        device const char * src0_up,
        device const char * src1,
        device       char * dst_gate,
        device       char * dst_up,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    const int nb = args.ne00/QK_K;

    const int r0 = tgpig.x;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

    const int first_row = (r0 * NSG + sgitg) * nr0;

    const uint i12 = im%args.ne12;
    const uint i13 = im/args.ne12;

    const uint64_t offset0 = first_row*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const uint64_t offset1 =        r1*args.nb11 + (i12        )*args.nb12 + (i13        )*args.nb13;

    device const block_iq2_xxs * xg = (device const block_iq2_xxs *) (src0_gate + offset0);
    device const block_iq2_xxs * xu = (device const block_iq2_xxs *) (src0_up   + offset0);
    device const float         * y  = (device const float         *) (src1      + offset1);

    float yl[32];
    float sumg[nr0]={0.f};
    float sumu[nr0]={0.f};

    const int nb32 = nb * (QK_K / 32);

    threadgroup uint64_t * svalues = (threadgroup uint64_t *)(shmem);
    threadgroup uint8_t  * ssigns  = (threadgroup uint8_t  *)(svalues + 256);
    {
        int nval = 4;
        int pos  = (32*sgitg + tiisg)*nval;
        for (int i = 0; i < nval; ++i) svalues[pos + i] = ds4_metal_iq2xxs_grid[pos + i];
        nval = 2;
        pos  = (32*sgitg + tiisg)*nval;
        for (int i = 0; i < nval; ++i) ssigns[pos+i] = ds4_metal_ksigns_iq2xs[pos+i];
        threadgroup_barrier(mem_flags::mem_threadgroup);
    }

    const int ix = tiisg;
    device const float * y4 = y + 32 * ix;

    for (int ib32 = ix; ib32 < nb32; ib32 += 32) {
        for (short i = 0; i < 32; ++i) {
            yl[i] = y4[i];
        }

        const int ibl = ib32 / (QK_K / 32);
        const int ib  = ib32 % (QK_K / 32);

        device const block_iq2_xxs * xgr = xg + ibl;
        device const block_iq2_xxs * xur = xu + ibl;
```<｜Assistant｜><think>


[System] You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.

[User]
Suggest a minimal correctness-preserving optimization for this excerpt.

File: metal/moe.metal

```metal
int ibl = ib32 / (QK_K / 32);
        const int ib  = ib32 % (QK_K / 32);

        device const block_iq2_xxs * xgr = xg + ibl;
        device const block_iq2_xxs * xur = xu + ibl;
        device const uint16_t * qg = xgr->qs + 4 * ib;
        device const uint16_t * qu = xur->qs + 4 * ib;
        device const half * dhg = &xgr->d;
        device const half * dhu = &xur->d;

        for (short row = 0; row < nr0; row++) {
            device const uint8_t * aux8g = (device const uint8_t *)qg;
            device const uint8_t * aux8u = (device const uint8_t *)qu;
            const uint32_t aux32g = qg[2] | (qg[3] << 16);
            const uint32_t aux32u = qu[2] | (qu[3] << 16);
            const float dg = (float)dhg[0] * (0.5f + (aux32g >> 28));
            const float du = (float)dhu[0] * (0.5f + (aux32u >> 28));

            float sg = 0;
            float su = 0;
            for (short l = 0; l < 4; ++l) {
                const threadgroup uint8_t * gridg = (const threadgroup uint8_t *)(svalues + aux8g[l]);
                const threadgroup uint8_t * gridu = (const threadgroup uint8_t *)(svalues + aux8u[l]);
                const uint8_t signg = ssigns[(aux32g >> 7*l) & 127];
                const uint8_t signu = ssigns[(aux32u >> 7*l) & 127];
                for (short j = 0; j < 8; ++j) {
                    const float v = yl[8*l + j];
                    sg += v * gridg[j] * (signg & ds4_metal_kmask_iq2xs[j] ? -1.f : 1.f);
                    su += v * gridu[j] * (signu & ds4_metal_kmask_iq2xs[j] ? -1.f : 1.f);
                }
            }
            sumg[row] += dg * sg;
            sumu[row] += du * su;

            dhg += args.nb01/2;
            dhu += args.nb01/2;
            qg  += args.nb01/2;
            qu  += args.nb01/2;
        }

        y4 += 32 * 32;
    }

    device float * dst_gate_f32 = (device float *) dst_gate + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;
    device float * dst_up_f32   = (device float *) dst_up   + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;

    for (int row = 0; row < nr0 && first_row + row < args.ne0; ++row) {
        const float sum_gate = simd_sum(sumg[row]);
        const float sum_up   = simd_sum(sumu[row]);
        if (tiisg == 0) {
            dst_gate_f32[first_row + row] = sum_gate * 0.25f;
            dst_up_f32[first_row + row]   = sum_up   * 0.25f;
        }
    }
}

typedef void (kernel_mul_mv2_disp_t)(
        ds4_metal_args_mul_mv args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
```

<｜begin▁of▁sentence｜>You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.<｜User｜>Suggest a minimal correctness-preserving optimization for this excerpt.

File: metal/moe.metal

```metal
int ibl = ib32 / (QK_K / 32);
        const int ib  = ib32 % (QK_K / 32);

        device const block_iq2_xxs * xgr = xg + ibl;
        device const block_iq2_xxs * xur = xu + ibl;
        device const uint16_t * qg = xgr->qs + 4 * ib;
        device const uint16_t * qu = xur->qs + 4 * ib;
        device const half * dhg = &xgr->d;
        device const half * dhu = &xur->d;

        for (short row = 0; row < nr0; row++) {
            device const uint8_t * aux8g = (device const uint8_t *)qg;
            device const uint8_t * aux8u = (device const uint8_t *)qu;
            const uint32_t aux32g = qg[2] | (qg[3] << 16);
            const uint32_t aux32u = qu[2] | (qu[3] << 16);
            const float dg = (float)dhg[0] * (0.5f + (aux32g >> 28));
            const float du = (float)dhu[0] * (0.5f + (aux32u >> 28));

            float sg = 0;
            float su = 0;
            for (short l = 0; l < 4; ++l) {
                const threadgroup uint8_t * gridg = (const threadgroup uint8_t *)(svalues + aux8g[l]);
                const threadgroup uint8_t * gridu = (const threadgroup uint8_t *)(svalues + aux8u[l]);
                const uint8_t signg = ssigns[(aux32g >> 7*l) & 127];
                const uint8_t signu = ssigns[(aux32u >> 7*l) & 127];
                for (short j = 0; j < 8; ++j) {
                    const float v = yl[8*l + j];
                    sg += v * gridg[j] * (signg & ds4_metal_kmask_iq2xs[j] ? -1.f : 1.f);
                    su += v * gridu[j] * (signu & ds4_metal_kmask_iq2xs[j] ? -1.f : 1.f);
                }
            }
            sumg[row] += dg * sg;
            sumu[row] += du * su;

            dhg += args.nb01/2;
            dhu += args.nb01/2;
            qg  += args.nb01/2;
            qu  += args.nb01/2;
        }

        y4 += 32 * 32;
    }

    device float * dst_gate_f32 = (device float *) dst_gate + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;
    device float * dst_up_f32   = (device float *) dst_up   + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;

    for (int row = 0; row < nr0 && first_row + row < args.ne0; ++row) {
        const float sum_gate = simd_sum(sumg[row]);
        const float sum_up   = simd_sum(sumu[row]);
        if (tiisg == 0) {
            dst_gate_f32[first_row + row] = sum_gate * 0.25f;
            dst_up_f32[first_row + row]   = sum_up   * 0.25f;
        }
    }
}

typedef void (kernel_mul_mv2_disp_t)(
        ds4_metal_args_mul_mv args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
```<｜Assistant｜></think>


[System] You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.

[User]
Suggest a minimal correctness-preserving optimization for this excerpt.

File: metal/moe.metal

```metal
int ibl = ib32 / (QK_K / 32);
        const int ib  = ib32 % (QK_K / 32);

        device const block_iq2_xxs * xgr = xg + ibl;
        device const block_iq2_xxs * xur = xu + ibl;
        device const uint16_t * qg = xgr->qs + 4 * ib;
        device const uint16_t * qu = xur->qs + 4 * ib;
        device const half * dhg = &xgr->d;
        device const half * dhu = &xur->d;

        for (short row = 0; row < nr0; row++) {
            device const uint8_t * aux8g = (device const uint8_t *)qg;
            device const uint8_t * aux8u = (device const uint8_t *)qu;
            const uint32_t aux32g = qg[2] | (qg[3] << 16);
            const uint32_t aux32u = qu[2] | (qu[3] << 16);
            const float dg = (float)dhg[0] * (0.5f + (aux32g >> 28));
            const float du = (float)dhu[0] * (0.5f + (aux32u >> 28));

            float sg = 0;
            float su = 0;
            for (short l = 0; l < 4; ++l) {
                const threadgroup uint8_t * gridg = (const threadgroup uint8_t *)(svalues + aux8g[l]);
                const threadgroup uint8_t * gridu = (const threadgroup uint8_t *)(svalues + aux8u[l]);
                const uint8_t signg = ssigns[(aux32g >> 7*l) & 127];
                const uint8_t signu = ssigns[(aux32u >> 7*l) & 127];
                for (short j = 0; j < 8; ++j) {
                    const float v = yl[8*l + j];
                    sg += v * gridg[j] * (signg & ds4_metal_kmask_iq2xs[j] ? -1.f : 1.f);
                    su += v * gridu[j] * (signu & ds4_metal_kmask_iq2xs[j] ? -1.f : 1.f);
                }
            }
            sumg[row] += dg * sg;
            sumu[row] += du * su;

            dhg += args.nb01/2;
            dhu += args.nb01/2;
            qg  += args.nb01/2;
            qu  += args.nb01/2;
        }

        y4 += 32 * 32;
    }

    device float * dst_gate_f32 = (device float *) dst_gate + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;
    device float * dst_up_f32   = (device float *) dst_up   + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;

    for (int row = 0; row < nr0 && first_row + row < args.ne0; ++row) {
        const float sum_gate = simd_sum(sumg[row]);
        const float sum_up   = simd_sum(sumu[row]);
        if (tiisg == 0) {
            dst_gate_f32[first_row + row] = sum_gate * 0.25f;
            dst_up_f32[first_row + row]   = sum_up   * 0.25f;
        }
    }
}

typedef void (kernel_mul_mv2_disp_t)(
        ds4_metal_args_mul_mv args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
```

<｜begin▁of▁sentence｜>You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.<｜User｜>Suggest a minimal correctness-preserving optimization for this excerpt.

File: metal/moe.metal

```metal
int ibl = ib32 / (QK_K / 32);
        const int ib  = ib32 % (QK_K / 32);

        device const block_iq2_xxs * xgr = xg + ibl;
        device const block_iq2_xxs * xur = xu + ibl;
        device const uint16_t * qg = xgr->qs + 4 * ib;
        device const uint16_t * qu = xur->qs + 4 * ib;
        device const half * dhg = &xgr->d;
        device const half * dhu = &xur->d;

        for (short row = 0; row < nr0; row++) {
            device const uint8_t * aux8g = (device const uint8_t *)qg;
            device const uint8_t * aux8u = (device const uint8_t *)qu;
            const uint32_t aux32g = qg[2] | (qg[3] << 16);
            const uint32_t aux32u = qu[2] | (qu[3] << 16);
            const float dg = (float)dhg[0] * (0.5f + (aux32g >> 28));
            const float du = (float)dhu[0] * (0.5f + (aux32u >> 28));

            float sg = 0;
            float su = 0;
            for (short l = 0; l < 4; ++l) {
                const threadgroup uint8_t * gridg = (const threadgroup uint8_t *)(svalues + aux8g[l]);
                const threadgroup uint8_t * gridu = (const threadgroup uint8_t *)(svalues + aux8u[l]);
                const uint8_t signg = ssigns[(aux32g >> 7*l) & 127];
                const uint8_t signu = ssigns[(aux32u >> 7*l) & 127];
                for (short j = 0; j < 8; ++j) {
                    const float v = yl[8*l + j];
                    sg += v * gridg[j] * (signg & ds4_metal_kmask_iq2xs[j] ? -1.f : 1.f);
                    su += v * gridu[j] * (signu & ds4_metal_kmask_iq2xs[j] ? -1.f : 1.f);
                }
            }
            sumg[row] += dg * sg;
            sumu[row] += du * su;

            dhg += args.nb01/2;
            dhu += args.nb01/2;
            qg  += args.nb01/2;
            qu  += args.nb01/2;
        }

        y4 += 32 * 32;
    }

    device float * dst_gate_f32 = (device float *) dst_gate + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;
    device float * dst_up_f32   = (device float *) dst_up   + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;

    for (int row = 0; row < nr0 && first_row + row < args.ne0; ++row) {
        const float sum_gate = simd_sum(sumg[row]);
        const float sum_up   = simd_sum(sumu[row]);
        if (tiisg == 0) {
            dst_gate_f32[first_row + row] = sum_gate * 0.25f;
            dst_up_f32[first_row + row]   = sum_up   * 0.25f;
        }
    }
}

typedef void (kernel_mul_mv2_disp_t)(
        ds4_metal_args_mul_mv args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
```<｜Assistant｜><think>


[System] You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.

[User]
Trova bug sottili e spiega quali invarianti dell'inferenza possono rompersi.

File: metal/moe.metal

```metal
}
}

typedef void (kernel_mul_mv2_disp_t)(
        ds4_metal_args_mul_mv args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg);

template<kernel_mul_mv2_disp_t disp_fn>
void mmv_fn(
        ds4_metal_args_mul_mv args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiitg,
        ushort tiisg,
        ushort sgitg) {
    disp_fn(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg);
}

typedef decltype(mmv_fn<kernel_mul_mv_q2_K_f32_impl<N_R0_Q2_K>>) mul_mv_id_disp_fn_t;

// Decode-time expert matvec. The ids tensor selects the routed expert for each
// slot, then this wrapper invokes the quantized row kernel for Q8_0, Q2_K, or
// IQ2_XXS weights without materializing per-expert dispatches on the CPU.
template<mul_mv_id_disp_fn_t disp_fn>
kernel void kernel_mul_mv_id(
        constant ds4_metal_args_mul_mv_id & args,
        device const char * src0s,
        device const char * src1,
        device       char * dst,
        device const char * ids,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiitg[[thread_index_in_threadgroup]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {
    (void)tiitg;

    const int iid1 = tgpig.z/args.nei0;
    const int idx  = tgpig.z%args.nei0;

    tgpig.z = 0;

    const int32_t i02 = ((device const int32_t *) (ids + iid1*args.nbi1))[idx];

    const int64_t i11 = idx % args.ne11;
    const int64_t i12 = iid1;

    const int64_t i1 = idx;
    const int64_t i2 = i12;

    device const char * src0_cur = src0s + i02*args.nb02;
    device const char * src1_cur = src1  + i11*args.nb11 + i12*args.nb12;

    device char * dst_cur = dst + (i1*args.ne0 + i2*args.ne1*args.ne0)*sizeof(float);

    ds4_metal_args_mul_mv args0 = {
        /*.ne00 =*/ args.ne00,
        /*.ne01 =*/ args.ne01,
        /*.ne02 =*/ 1,
        /*.nb00 =*/ args.nb00,
        /*.nb01 =*/ args.nb01,
        /*.nb02 =*/ args.nb02,
        /*.nb03 =*/ args.nb02,
        /*.ne10 =*/ args.ne10,
        /*.ne11 =*/ 1,
        /*.ne12 =*/ 1,
        /*.nb10 =*/ args.nb10,
        /*.nb11 =*/ args.nb11,
        /*.nb12 =*/ args.nb12,
        /*.nb13 =*/ args.nb12,
        /*.ne0  =*/ args.ne0,
        /*.ne1  =*/ 1,
        /*.nr0  =*/ args.nr0,
```

<｜begin▁of▁sentence｜>You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.<｜User｜>Trova bug sottili e spiega quali invarianti dell'inferenza possono rompersi.

File: metal/moe.metal

```metal
}
}

typedef void (kernel_mul_mv2_disp_t)(
        ds4_metal_args_mul_mv args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg);

template<kernel_mul_mv2_disp_t disp_fn>
void mmv_fn(
        ds4_metal_args_mul_mv args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiitg,
        ushort tiisg,
        ushort sgitg) {
    disp_fn(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg);
}

typedef decltype(mmv_fn<kernel_mul_mv_q2_K_f32_impl<N_R0_Q2_K>>) mul_mv_id_disp_fn_t;

// Decode-time expert matvec. The ids tensor selects the routed expert for each
// slot, then this wrapper invokes the quantized row kernel for Q8_0, Q2_K, or
// IQ2_XXS weights without materializing per-expert dispatches on the CPU.
template<mul_mv_id_disp_fn_t disp_fn>
kernel void kernel_mul_mv_id(
        constant ds4_metal_args_mul_mv_id & args,
        device const char * src0s,
        device const char * src1,
        device       char * dst,
        device const char * ids,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiitg[[thread_index_in_threadgroup]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {
    (void)tiitg;

    const int iid1 = tgpig.z/args.nei0;
    const int idx  = tgpig.z%args.nei0;

    tgpig.z = 0;

    const int32_t i02 = ((device const int32_t *) (ids + iid1*args.nbi1))[idx];

    const int64_t i11 = idx % args.ne11;
    const int64_t i12 = iid1;

    const int64_t i1 = idx;
    const int64_t i2 = i12;

    device const char * src0_cur = src0s + i02*args.nb02;
    device const char * src1_cur = src1  + i11*args.nb11 + i12*args.nb12;

    device char * dst_cur = dst + (i1*args.ne0 + i2*args.ne1*args.ne0)*sizeof(float);

    ds4_metal_args_mul_mv args0 = {
        /*.ne00 =*/ args.ne00,
        /*.ne01 =*/ args.ne01,
        /*.ne02 =*/ 1,
        /*.nb00 =*/ args.nb00,
        /*.nb01 =*/ args.nb01,
        /*.nb02 =*/ args.nb02,
        /*.nb03 =*/ args.nb02,
        /*.ne10 =*/ args.ne10,
        /*.ne11 =*/ 1,
        /*.ne12 =*/ 1,
        /*.nb10 =*/ args.nb10,
        /*.nb11 =*/ args.nb11,
        /*.nb12 =*/ args.nb12,
        /*.nb13 =*/ args.nb12,
        /*.ne0  =*/ args.ne0,
        /*.ne1  =*/ 1,
        /*.nr0  =*/ args.nr0,
```<｜Assistant｜></think>


[System] You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.

[User]
Trova bug sottili e spiega quali invarianti dell'inferenza possono rompersi.

File: metal/moe.metal

```metal
}
}

typedef void (kernel_mul_mv2_disp_t)(
        ds4_metal_args_mul_mv args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg);

template<kernel_mul_mv2_disp_t disp_fn>
void mmv_fn(
        ds4_metal_args_mul_mv args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiitg,
        ushort tiisg,
        ushort sgitg) {
    disp_fn(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg);
}

typedef decltype(mmv_fn<kernel_mul_mv_q2_K_f32_impl<N_R0_Q2_K>>) mul_mv_id_disp_fn_t;

// Decode-time expert matvec. The ids tensor selects the routed expert for each
// slot, then this wrapper invokes the quantized row kernel for Q8_0, Q2_K, or
// IQ2_XXS weights without materializing per-expert dispatches on the CPU.
template<mul_mv_id_disp_fn_t disp_fn>
kernel void kernel_mul_mv_id(
        constant ds4_metal_args_mul_mv_id & args,
        device const char * src0s,
        device const char * src1,
        device       char * dst,
        device const char * ids,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiitg[[thread_index_in_threadgroup]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {
    (void)tiitg;

    const int iid1 = tgpig.z/args.nei0;
    const int idx  = tgpig.z%args.nei0;

    tgpig.z = 0;

    const int32_t i02 = ((device const int32_t *) (ids + iid1*args.nbi1))[idx];

    const int64_t i11 = idx % args.ne11;
    const int64_t i12 = iid1;

    const int64_t i1 = idx;
    const int64_t i2 = i12;

    device const char * src0_cur = src0s + i02*args.nb02;
    device const char * src1_cur = src1  + i11*args.nb11 + i12*args.nb12;

    device char * dst_cur = dst + (i1*args.ne0 + i2*args.ne1*args.ne0)*sizeof(float);

    ds4_metal_args_mul_mv args0 = {
        /*.ne00 =*/ args.ne00,
        /*.ne01 =*/ args.ne01,
        /*.ne02 =*/ 1,
        /*.nb00 =*/ args.nb00,
        /*.nb01 =*/ args.nb01,
        /*.nb02 =*/ args.nb02,
        /*.nb03 =*/ args.nb02,
        /*.ne10 =*/ args.ne10,
        /*.ne11 =*/ 1,
        /*.ne12 =*/ 1,
        /*.nb10 =*/ args.nb10,
        /*.nb11 =*/ args.nb11,
        /*.nb12 =*/ args.nb12,
        /*.nb13 =*/ args.nb12,
        /*.ne0  =*/ args.ne0,
        /*.ne1  =*/ 1,
        /*.nr0  =*/ args.nr0,
```

<｜begin▁of▁sentence｜>You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.<｜User｜>Trova bug sottili e spiega quali invarianti dell'inferenza possono rompersi.

File: metal/moe.metal

```metal
}
}

typedef void (kernel_mul_mv2_disp_t)(
        ds4_metal_args_mul_mv args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg);

template<kernel_mul_mv2_disp_t disp_fn>
void mmv_fn(
        ds4_metal_args_mul_mv args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiitg,
        ushort tiisg,
        ushort sgitg) {
    disp_fn(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg);
}

typedef decltype(mmv_fn<kernel_mul_mv_q2_K_f32_impl<N_R0_Q2_K>>) mul_mv_id_disp_fn_t;

// Decode-time expert matvec. The ids tensor selects the routed expert for each
// slot, then this wrapper invokes the quantized row kernel for Q8_0, Q2_K, or
// IQ2_XXS weights without materializing per-expert dispatches on the CPU.
template<mul_mv_id_disp_fn_t disp_fn>
kernel void kernel_mul_mv_id(
        constant ds4_metal_args_mul_mv_id & args,
        device const char * src0s,
        device const char * src1,
        device       char * dst,
        device const char * ids,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiitg[[thread_index_in_threadgroup]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {
    (void)tiitg;

    const int iid1 = tgpig.z/args.nei0;
    const int idx  = tgpig.z%args.nei0;

    tgpig.z = 0;

    const int32_t i02 = ((device const int32_t *) (ids + iid1*args.nbi1))[idx];

    const int64_t i11 = idx % args.ne11;
    const int64_t i12 = iid1;

    const int64_t i1 = idx;
    const int64_t i2 = i12;

    device const char * src0_cur = src0s + i02*args.nb02;
    device const char * src1_cur = src1  + i11*args.nb11 + i12*args.nb12;

    device char * dst_cur = dst + (i1*args.ne0 + i2*args.ne1*args.ne0)*sizeof(float);

    ds4_metal_args_mul_mv args0 = {
        /*.ne00 =*/ args.ne00,
        /*.ne01 =*/ args.ne01,
        /*.ne02 =*/ 1,
        /*.nb00 =*/ args.nb00,
        /*.nb01 =*/ args.nb01,
        /*.nb02 =*/ args.nb02,
        /*.nb03 =*/ args.nb02,
        /*.ne10 =*/ args.ne10,
        /*.ne11 =*/ 1,
        /*.ne12 =*/ 1,
        /*.nb10 =*/ args.nb10,
        /*.nb11 =*/ args.nb11,
        /*.nb12 =*/ args.nb12,
        /*.nb13 =*/ args.nb12,
        /*.ne0  =*/ args.ne0,
        /*.ne1  =*/ 1,
        /*.nr0  =*/ args.nr0,
```<｜Assistant｜><think>


[System] You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.

[User]
Review this excerpt for correctness risks, memory lifetime issues, and performance bottlenecks.

File: metal/moe.metal

```metal
b10,
        /*.nb11 =*/ args.nb11,
        /*.nb12 =*/ args.nb12,
        /*.nb13 =*/ args.nb12,
        /*.ne0  =*/ args.ne0,
        /*.ne1  =*/ 1,
        /*.nr0  =*/ args.nr0,
        /*.r2   =*/ 1,
        /*.r3   =*/ 1,
    };

    disp_fn(
        args0,
        /* src0 */ src0_cur,
        /* src1 */ src1_cur,
        /* dst  */ dst_cur,
        shmem,
        tgpig,
        tiitg,
        tiisg,
        sgitg);
}

typedef decltype(kernel_mul_mv_id<mmv_fn<kernel_mul_mv_q2_K_f32_impl<N_R0_Q2_K>>>) kernel_mul_mv_id_q_t;
typedef decltype(kernel_mul_mv_id<mmv_fn<kernel_mul_mv_q8_0_f32_impl<N_R0_Q8_0>>>) kernel_mul_mv_id_q8_0_t;

// Host-visible decode MoE matvec variants for the DS4 quant formats.
template [[host_name("kernel_mul_mv_id_q8_0_f32")]]    kernel kernel_mul_mv_id_q8_0_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_q8_0_f32_impl<N_R0_Q8_0>>>;
template [[host_name("kernel_mul_mv_id_q2_K_f32")]]    kernel kernel_mul_mv_id_q_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_q2_K_f32_impl<N_R0_Q2_K>>>;
template [[host_name("kernel_mul_mv_id_q4_K_f32")]]    kernel kernel_mul_mv_id_q_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_q4_K_f32_impl<N_R0_Q4_K>>>;
template [[host_name("kernel_mul_mv_id_iq2_xxs_f32")]] kernel kernel_mul_mv_id_q_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_iq2_xxs_f32_impl<N_R0_IQ2_XXS>>>;

// DS4 attention output low projection, specialized for the fixed block
// diagonal mapping used by the model:
//
//     low[token, group, rank] = heads[token, group, :] * Woa[group, rank, :]
//
// The generic GGML-style id matvec supports arbitrary routed expert ids.  Here
// the id is always equal to the group number, so this wrapper keeps the exact
// Q8_0 dot kernel but removes the id-buffer load and the CPU-side id table.
kernel void kernel_dsv4_attn_out_low_q8_0_f32(
        constant ds4_metal_args_mul_mv_id & args,
        device const char * src0s,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiitg[[thread_index_in_threadgroup]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {
    const int iid1 = tgpig.z/args.nei0;
    const int idx  = tgpig.z%args.nei0;

    tgpig.z = 0;

    const int64_t i11 = idx % args.ne11;
    const int64_t i12 = iid1;

    device const char * src0_cur = src0s + idx*args.nb02;
    device const char * src1_cur = src1  + i11*args.nb11 + i12*args.nb12;
```

<｜begin▁of▁sentence｜>You are DeepSeek V4 Flash running locally. Answer accurately, preserve technical details, and use tools only when the prompt asks for tool use.<｜User｜>Review this excerpt for correctness risks, memory lifetime issues, and performance bottlenecks.

File: metal/moe.metal

```metal
b10,
        /*.nb11 =*/ args.nb11,
        /*.nb12 =*/ args.nb12,
        /*.nb13 =*/ args.nb12,
        /*.ne0  =*/ args.ne0,
        /*.ne1  =*/ 1,
        /*.nr0  =*/ args.nr0,
        /*.r2   =*/ 1,
        /*.r3   =*/ 1,
    };

    disp_fn(
        args0,
        /* src0 */ src0_cur,
        /* src1 */ src1_cur,
        /* dst  */ dst_cur,
        shmem,
        tgpig,
        tiitg,
        tiisg,
        sgitg);
}

typedef decltype(kernel_mul_mv_id<mmv_fn<kernel_mul_mv_q2_K_f32_impl<N_R0_Q2_K>>>) kernel_mul_mv_id_q_t;
typedef decltype(kernel_mul_mv_id<mmv_fn<kernel_mul_mv_q8_0_f32_impl<N_R0_Q8_0>>>) kernel_mul_mv_id_q8_0_t;

// Host-visible decode MoE matvec variants for the DS4 quant formats.
template [[host_name("kernel_mul_mv_id_q8_0_f32")]]    kernel kernel_mul_mv_id_q8_0_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_q8_0_f32_impl<N_R0_Q8_0>>>;
template [[host_name("kernel_mul_mv_id_q2_K_f32")]]    kernel kernel_mul_mv_id_q_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_q2_K_f32_impl<N_R0_Q2_K>>>;
template [[host_name("kernel_mul_mv_id_q4_K_f32")]]    kernel kernel_mul_mv_id_q_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_q4_K_f32_impl<N_R0_Q4_K>>>;
template [[host_name("kernel_mul_mv_id_iq2_xxs_f32")]] kernel kernel_mul_mv_id_q_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_iq2_xxs_f32_impl<N_R0_IQ2_XXS>>>;

// DS4 attention output low projection, specialized for the fixed block
// diagonal mapping used by the model:
//
//     low[token, group, rank] = heads[token, group, :] * Woa[group, rank, :]
//
// The generic GGML-style id matvec supports arbitrary routed expert ids.  Here
// the id is always equal to the group number, so this wrapper keeps the exact
// Q8_0 dot kernel but removes the id-buffer load and the CPU-side id table.
kernel void kernel_dsv4_attn_out_low_q8_0_f32(
        constant ds4_metal_args_mul_mv_id & args,
        device const char * src0s,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiitg[[thread_index_in_threadgroup]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {
    const int iid1 = tgpig.z/args.nei0;
    const int idx  = tgpig.z%args.nei0;

    tgpig.z = 0;

    const int64_t i11 = idx % args.ne11;
    const int64_t i12 = iid1;

    device const char * src0_cur = src0s + idx*args.nb02;
    device const char * src1_cur = src1  + i11*args.nb11 + i12*args.nb12;
```<｜Assistant｜></think>