[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/argsort.metal

```metal
const int total = len0 + len1;

    device const int32_t * tmp0 = tmp + start
        + i01*args.ne0
        + i02*args.ne0*args.ne01
        + i03*args.ne0*args.ne01*args.ne02;

    device const int32_t * tmp1 = tmp0 + args.len;

    dst += start
        + i01*args.top_k
        + i02*args.top_k*args.ne01
        + i03*args.top_k*args.ne01*args.ne02;

    device const float * src0_row = (device const float *)(src0
        + args.nb01*i01
        + args.nb02*i02
        + args.nb03*i03);

    if (total == 0) {
        return;
    }

    const int chunk = (total + ntg.x - 1) / ntg.x;

    const int k0 = tpitg.x * chunk;
    const int k1 = MIN(MIN(k0 + chunk, total), args.top_k);

    if (k0 >= args.top_k) {
        return;
    }

    if (k0 >= total) {
        return;
    }

    int low  = k0 > len1 ? k0 - len1 : 0;
    int high = MIN(k0, len0);

    // binary-search partition (i, j) such that i + j = k
    while (low < high) {
        const int mid = (low + high) >> 1;

        const int32_t idx0 = tmp0[mid];
        const int32_t idx1 = tmp1[k0 - mid - 1];

        const float val0 = src0_row[idx0];
        const float val1 = src0_row[idx1];

        bool take_left;
        if (order == DS4_SORT_ORDER_ASC) {
            take_left = (val0 <= val1);
        } else {
            take_left = (val0 >= val1);
        }

        if (take_left) {
            low = mid + 1;
        } else {
            high = mid;
        }
    }

    int i = low;
    int j = k0 - i;

    // keep the merge fronts into registers
    int32_t idx0 = 0;
    float   val0 = 0.0f;
    if (i < len0) {
        idx0 = tmp0[i];
        val0 = src0_row[idx0];
    }

    int32_t idx1 = 0;
    float   val1 = 0.0f;
    if (j < len1) {
        idx1 = tmp1[j];
        val1 = src0_row[idx1];
    }

    for (int k = k0; k < k1; ++k) {
        int32_t out_idx;

        if (i >= len0) {
            while (k < k1) {
                dst[k++] = tmp1[j++];
            }
            break;
        } else if (j >= len1) {
            while (k < k1) {
                dst[k++] = tmp0[i++];
            }
            break;
        } else {
            bool take_left;

            if (order == DS4_SORT_ORDER_ASC) {
                take_left = (val0 <= val1);
            } else {
                take_left = (val0 >= val1);
            }

            if (take_left) {
                out_idx = idx0;
                ++i;
                if (i < len0) {
                    idx0 = tmp0[i];
                    val0 = src0_row[idx0];
                }
            } else {
                out_idx = idx1;
```

<｜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/argsort.metal

```metal
const int total = len0 + len1;

    device const int32_t * tmp0 = tmp + start
        + i01*args.ne0
        + i02*args.ne0*args.ne01
        + i03*args.ne0*args.ne01*args.ne02;

    device const int32_t * tmp1 = tmp0 + args.len;

    dst += start
        + i01*args.top_k
        + i02*args.top_k*args.ne01
        + i03*args.top_k*args.ne01*args.ne02;

    device const float * src0_row = (device const float *)(src0
        + args.nb01*i01
        + args.nb02*i02
        + args.nb03*i03);

    if (total == 0) {
        return;
    }

    const int chunk = (total + ntg.x - 1) / ntg.x;

    const int k0 = tpitg.x * chunk;
    const int k1 = MIN(MIN(k0 + chunk, total), args.top_k);

    if (k0 >= args.top_k) {
        return;
    }

    if (k0 >= total) {
        return;
    }

    int low  = k0 > len1 ? k0 - len1 : 0;
    int high = MIN(k0, len0);

    // binary-search partition (i, j) such that i + j = k
    while (low < high) {
        const int mid = (low + high) >> 1;

        const int32_t idx0 = tmp0[mid];
        const int32_t idx1 = tmp1[k0 - mid - 1];

        const float val0 = src0_row[idx0];
        const float val1 = src0_row[idx1];

        bool take_left;
        if (order == DS4_SORT_ORDER_ASC) {
            take_left = (val0 <= val1);
        } else {
            take_left = (val0 >= val1);
        }

        if (take_left) {
            low = mid + 1;
        } else {
            high = mid;
        }
    }

    int i = low;
    int j = k0 - i;

    // keep the merge fronts into registers
    int32_t idx0 = 0;
    float   val0 = 0.0f;
    if (i < len0) {
        idx0 = tmp0[i];
        val0 = src0_row[idx0];
    }

    int32_t idx1 = 0;
    float   val1 = 0.0f;
    if (j < len1) {
        idx1 = tmp1[j];
        val1 = src0_row[idx1];
    }

    for (int k = k0; k < k1; ++k) {
        int32_t out_idx;

        if (i >= len0) {
            while (k < k1) {
                dst[k++] = tmp1[j++];
            }
            break;
        } else if (j >= len1) {
            while (k < k1) {
                dst[k++] = tmp0[i++];
            }
            break;
        } else {
            bool take_left;

            if (order == DS4_SORT_ORDER_ASC) {
                take_left = (val0 <= val1);
            } else {
                take_left = (val0 >= val1);
            }

            if (take_left) {
                out_idx = idx0;
                ++i;
                if (i < len0) {
                    idx0 = tmp0[i];
                    val0 = src0_row[idx0];
                }
            } else {
                out_idx = idx1;
```<｜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/argsort.metal

```metal
const int total = len0 + len1;

    device const int32_t * tmp0 = tmp + start
        + i01*args.ne0
        + i02*args.ne0*args.ne01
        + i03*args.ne0*args.ne01*args.ne02;

    device const int32_t * tmp1 = tmp0 + args.len;

    dst += start
        + i01*args.top_k
        + i02*args.top_k*args.ne01
        + i03*args.top_k*args.ne01*args.ne02;

    device const float * src0_row = (device const float *)(src0
        + args.nb01*i01
        + args.nb02*i02
        + args.nb03*i03);

    if (total == 0) {
        return;
    }

    const int chunk = (total + ntg.x - 1) / ntg.x;

    const int k0 = tpitg.x * chunk;
    const int k1 = MIN(MIN(k0 + chunk, total), args.top_k);

    if (k0 >= args.top_k) {
        return;
    }

    if (k0 >= total) {
        return;
    }

    int low  = k0 > len1 ? k0 - len1 : 0;
    int high = MIN(k0, len0);

    // binary-search partition (i, j) such that i + j = k
    while (low < high) {
        const int mid = (low + high) >> 1;

        const int32_t idx0 = tmp0[mid];
        const int32_t idx1 = tmp1[k0 - mid - 1];

        const float val0 = src0_row[idx0];
        const float val1 = src0_row[idx1];

        bool take_left;
        if (order == DS4_SORT_ORDER_ASC) {
            take_left = (val0 <= val1);
        } else {
            take_left = (val0 >= val1);
        }

        if (take_left) {
            low = mid + 1;
        } else {
            high = mid;
        }
    }

    int i = low;
    int j = k0 - i;

    // keep the merge fronts into registers
    int32_t idx0 = 0;
    float   val0 = 0.0f;
    if (i < len0) {
        idx0 = tmp0[i];
        val0 = src0_row[idx0];
    }

    int32_t idx1 = 0;
    float   val1 = 0.0f;
    if (j < len1) {
        idx1 = tmp1[j];
        val1 = src0_row[idx1];
    }

    for (int k = k0; k < k1; ++k) {
        int32_t out_idx;

        if (i >= len0) {
            while (k < k1) {
                dst[k++] = tmp1[j++];
            }
            break;
        } else if (j >= len1) {
            while (k < k1) {
                dst[k++] = tmp0[i++];
            }
            break;
        } else {
            bool take_left;

            if (order == DS4_SORT_ORDER_ASC) {
                take_left = (val0 <= val1);
            } else {
                take_left = (val0 >= val1);
            }

            if (take_left) {
                out_idx = idx0;
                ++i;
                if (i < len0) {
                    idx0 = tmp0[i];
                    val0 = src0_row[idx0];
                }
            } else {
                out_idx = idx1;
```

<｜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/argsort.metal

```metal
const int total = len0 + len1;

    device const int32_t * tmp0 = tmp + start
        + i01*args.ne0
        + i02*args.ne0*args.ne01
        + i03*args.ne0*args.ne01*args.ne02;

    device const int32_t * tmp1 = tmp0 + args.len;

    dst += start
        + i01*args.top_k
        + i02*args.top_k*args.ne01
        + i03*args.top_k*args.ne01*args.ne02;

    device const float * src0_row = (device const float *)(src0
        + args.nb01*i01
        + args.nb02*i02
        + args.nb03*i03);

    if (total == 0) {
        return;
    }

    const int chunk = (total + ntg.x - 1) / ntg.x;

    const int k0 = tpitg.x * chunk;
    const int k1 = MIN(MIN(k0 + chunk, total), args.top_k);

    if (k0 >= args.top_k) {
        return;
    }

    if (k0 >= total) {
        return;
    }

    int low  = k0 > len1 ? k0 - len1 : 0;
    int high = MIN(k0, len0);

    // binary-search partition (i, j) such that i + j = k
    while (low < high) {
        const int mid = (low + high) >> 1;

        const int32_t idx0 = tmp0[mid];
        const int32_t idx1 = tmp1[k0 - mid - 1];

        const float val0 = src0_row[idx0];
        const float val1 = src0_row[idx1];

        bool take_left;
        if (order == DS4_SORT_ORDER_ASC) {
            take_left = (val0 <= val1);
        } else {
            take_left = (val0 >= val1);
        }

        if (take_left) {
            low = mid + 1;
        } else {
            high = mid;
        }
    }

    int i = low;
    int j = k0 - i;

    // keep the merge fronts into registers
    int32_t idx0 = 0;
    float   val0 = 0.0f;
    if (i < len0) {
        idx0 = tmp0[i];
        val0 = src0_row[idx0];
    }

    int32_t idx1 = 0;
    float   val1 = 0.0f;
    if (j < len1) {
        idx1 = tmp1[j];
        val1 = src0_row[idx1];
    }

    for (int k = k0; k < k1; ++k) {
        int32_t out_idx;

        if (i >= len0) {
            while (k < k1) {
                dst[k++] = tmp1[j++];
            }
            break;
        } else if (j >= len1) {
            while (k < k1) {
                dst[k++] = tmp0[i++];
            }
            break;
        } else {
            bool take_left;

            if (order == DS4_SORT_ORDER_ASC) {
                take_left = (val0 <= val1);
            } else {
                take_left = (val0 >= val1);
            }

            if (take_left) {
                out_idx = idx0;
                ++i;
                if (i < len0) {
                    idx0 = tmp0[i];
                    val0 = src0_row[idx0];
                }
            } else {
                out_idx = idx1;
```<｜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/argsort.metal

```metal
if (i < len0) {
                    idx0 = tmp0[i];
                    val0 = src0_row[idx0];
                }
            } else {
                out_idx = idx1;
                ++j;
                if (j < len1) {
                    idx1 = tmp1[j];
                    val1 = src0_row[idx1];
                }
            }
        }

        dst[k] = out_idx;
    }
}

// Host-visible merge variant used by DS4 top-k selection.
template [[host_name("kernel_argsort_merge_f32_i32_desc")]] kernel argsort_merge_t kernel_argsort_merge_f32_i32<DS4_SORT_ORDER_DESC>;
```

<｜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/argsort.metal

```metal
if (i < len0) {
                    idx0 = tmp0[i];
                    val0 = src0_row[idx0];
                }
            } else {
                out_idx = idx1;
                ++j;
                if (j < len1) {
                    idx1 = tmp1[j];
                    val1 = src0_row[idx1];
                }
            }
        }

        dst[k] = out_idx;
    }
}

// Host-visible merge variant used by DS4 top-k selection.
template [[host_name("kernel_argsort_merge_f32_i32_desc")]] kernel argsort_merge_t kernel_argsort_merge_f32_i32<DS4_SORT_ORDER_DESC>;
```<｜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/argsort.metal

```metal
if (i < len0) {
                    idx0 = tmp0[i];
                    val0 = src0_row[idx0];
                }
            } else {
                out_idx = idx1;
                ++j;
                if (j < len1) {
                    idx1 = tmp1[j];
                    val1 = src0_row[idx1];
                }
            }
        }

        dst[k] = out_idx;
    }
}

// Host-visible merge variant used by DS4 top-k selection.
template [[host_name("kernel_argsort_merge_f32_i32_desc")]] kernel argsort_merge_t kernel_argsort_merge_f32_i32<DS4_SORT_ORDER_DESC>;
```

<｜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/argsort.metal

```metal
if (i < len0) {
                    idx0 = tmp0[i];
                    val0 = src0_row[idx0];
                }
            } else {
                out_idx = idx1;
                ++j;
                if (j < len1) {
                    idx1 = tmp1[j];
                    val1 = src0_row[idx1];
                }
            }
        }

        dst[k] = out_idx;
    }
}

// Host-visible merge variant used by DS4 top-k selection.
template [[host_name("kernel_argsort_merge_f32_i32_desc")]] kernel argsort_merge_t kernel_argsort_merge_f32_i32<DS4_SORT_ORDER_DESC>;
```<｜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/bin.metal

```metal
struct ds4_metal_args_bin {
    int32_t  ne00;
    int32_t  ne01;
    int32_t  ne02;
    int32_t  ne03;
    uint64_t nb00;
    uint64_t nb01;
    uint64_t nb02;
    uint64_t nb03;
    int32_t  ne10;
    int32_t  ne11;
    int32_t  ne12;
    int32_t  ne13;
    uint64_t nb10;
    uint64_t nb11;
    uint64_t nb12;
    uint64_t nb13;
    int32_t  ne0;
    int32_t  ne1;
    int32_t  ne2;
    int32_t  ne3;
    uint64_t nb0;
    uint64_t nb1;
    uint64_t nb2;
    uint64_t nb3;
    uint64_t offs;
    uint64_t o1[8];
};

constant short FC_bin_op [[function_constant(FC_BIN + 0)]];
constant short FC_bin_f  [[function_constant(FC_BIN + 1)]];
constant bool  FC_bin_rb [[function_constant(FC_BIN + 2)]];
constant bool  FC_bin_cb [[function_constant(FC_BIN + 3)]];

// Generic binary elementwise op with compile-time operation and broadcast
// modes. DS4 currently instantiates this as add, multiply, scalar multiply, and
// row division in the static graph.
template <typename T0, typename T1, typename T>
kernel void kernel_bin_fuse_impl(
        constant ds4_metal_args_bin & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
#define FC_OP FC_bin_op
#define FC_F  FC_bin_f
#define FC_RB FC_bin_rb
#define FC_CB FC_bin_cb

    if (FC_RB) {
        const uint i0 = tgpig.y*args.ne00 + tgpig.x;
        const uint i1 = FC_CB ? tgpig.x%args.ne10 : tgpig.x;

        device const T0 * src0_row = (device const T0 *) (src0);
        device       T  * dst_row  = (device       T  *) (dst);

        if (FC_F == 1) {
            device const T1 * src1_row = (device const T1 *) (src1 + args.o1[0]);

            if (FC_OP == 0) {
                dst_row[i0] = src0_row[i0] + src1_row[i1];
            }

            if (FC_OP == 1) {
                dst_row[i0] = src0_row[i0] - src1_row[i1];
            }

            if (FC_OP == 2) {
                dst_row[i0] = src0_row[i0] * src1_row[i1];
            }

            if (FC_OP == 3) {
                dst_row[i0] = src0_row[i0] / src1_row[i1];
            }
        } else {
            T0 res = src0_row[i0];

            if (FC_OP == 0) {
                FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                    res += ((device const T1 *) (src1 + args.o1[j]))[i1];
                }
            }

            if (FC_OP == 1) {
                FOR_UNROLL (short j = 0; j < FC_F; ++j) {
```

<｜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/bin.metal

```metal
struct ds4_metal_args_bin {
    int32_t  ne00;
    int32_t  ne01;
    int32_t  ne02;
    int32_t  ne03;
    uint64_t nb00;
    uint64_t nb01;
    uint64_t nb02;
    uint64_t nb03;
    int32_t  ne10;
    int32_t  ne11;
    int32_t  ne12;
    int32_t  ne13;
    uint64_t nb10;
    uint64_t nb11;
    uint64_t nb12;
    uint64_t nb13;
    int32_t  ne0;
    int32_t  ne1;
    int32_t  ne2;
    int32_t  ne3;
    uint64_t nb0;
    uint64_t nb1;
    uint64_t nb2;
    uint64_t nb3;
    uint64_t offs;
    uint64_t o1[8];
};

constant short FC_bin_op [[function_constant(FC_BIN + 0)]];
constant short FC_bin_f  [[function_constant(FC_BIN + 1)]];
constant bool  FC_bin_rb [[function_constant(FC_BIN + 2)]];
constant bool  FC_bin_cb [[function_constant(FC_BIN + 3)]];

// Generic binary elementwise op with compile-time operation and broadcast
// modes. DS4 currently instantiates this as add, multiply, scalar multiply, and
// row division in the static graph.
template <typename T0, typename T1, typename T>
kernel void kernel_bin_fuse_impl(
        constant ds4_metal_args_bin & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
#define FC_OP FC_bin_op
#define FC_F  FC_bin_f
#define FC_RB FC_bin_rb
#define FC_CB FC_bin_cb

    if (FC_RB) {
        const uint i0 = tgpig.y*args.ne00 + tgpig.x;
        const uint i1 = FC_CB ? tgpig.x%args.ne10 : tgpig.x;

        device const T0 * src0_row = (device const T0 *) (src0);
        device       T  * dst_row  = (device       T  *) (dst);

        if (FC_F == 1) {
            device const T1 * src1_row = (device const T1 *) (src1 + args.o1[0]);

            if (FC_OP == 0) {
                dst_row[i0] = src0_row[i0] + src1_row[i1];
            }

            if (FC_OP == 1) {
                dst_row[i0] = src0_row[i0] - src1_row[i1];
            }

            if (FC_OP == 2) {
                dst_row[i0] = src0_row[i0] * src1_row[i1];
            }

            if (FC_OP == 3) {
                dst_row[i0] = src0_row[i0] / src1_row[i1];
            }
        } else {
            T0 res = src0_row[i0];

            if (FC_OP == 0) {
                FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                    res += ((device const T1 *) (src1 + args.o1[j]))[i1];
                }
            }

            if (FC_OP == 1) {
                FOR_UNROLL (short j = 0; j < FC_F; ++j) {
```<｜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/bin.metal

```metal
struct ds4_metal_args_bin {
    int32_t  ne00;
    int32_t  ne01;
    int32_t  ne02;
    int32_t  ne03;
    uint64_t nb00;
    uint64_t nb01;
    uint64_t nb02;
    uint64_t nb03;
    int32_t  ne10;
    int32_t  ne11;
    int32_t  ne12;
    int32_t  ne13;
    uint64_t nb10;
    uint64_t nb11;
    uint64_t nb12;
    uint64_t nb13;
    int32_t  ne0;
    int32_t  ne1;
    int32_t  ne2;
    int32_t  ne3;
    uint64_t nb0;
    uint64_t nb1;
    uint64_t nb2;
    uint64_t nb3;
    uint64_t offs;
    uint64_t o1[8];
};

constant short FC_bin_op [[function_constant(FC_BIN + 0)]];
constant short FC_bin_f  [[function_constant(FC_BIN + 1)]];
constant bool  FC_bin_rb [[function_constant(FC_BIN + 2)]];
constant bool  FC_bin_cb [[function_constant(FC_BIN + 3)]];

// Generic binary elementwise op with compile-time operation and broadcast
// modes. DS4 currently instantiates this as add, multiply, scalar multiply, and
// row division in the static graph.
template <typename T0, typename T1, typename T>
kernel void kernel_bin_fuse_impl(
        constant ds4_metal_args_bin & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
#define FC_OP FC_bin_op
#define FC_F  FC_bin_f
#define FC_RB FC_bin_rb
#define FC_CB FC_bin_cb

    if (FC_RB) {
        const uint i0 = tgpig.y*args.ne00 + tgpig.x;
        const uint i1 = FC_CB ? tgpig.x%args.ne10 : tgpig.x;

        device const T0 * src0_row = (device const T0 *) (src0);
        device       T  * dst_row  = (device       T  *) (dst);

        if (FC_F == 1) {
            device const T1 * src1_row = (device const T1 *) (src1 + args.o1[0]);

            if (FC_OP == 0) {
                dst_row[i0] = src0_row[i0] + src1_row[i1];
            }

            if (FC_OP == 1) {
                dst_row[i0] = src0_row[i0] - src1_row[i1];
            }

            if (FC_OP == 2) {
                dst_row[i0] = src0_row[i0] * src1_row[i1];
            }

            if (FC_OP == 3) {
                dst_row[i0] = src0_row[i0] / src1_row[i1];
            }
        } else {
            T0 res = src0_row[i0];

            if (FC_OP == 0) {
                FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                    res += ((device const T1 *) (src1 + args.o1[j]))[i1];
                }
            }

            if (FC_OP == 1) {
                FOR_UNROLL (short j = 0; j < FC_F; ++j) {
```

<｜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/bin.metal

```metal
struct ds4_metal_args_bin {
    int32_t  ne00;
    int32_t  ne01;
    int32_t  ne02;
    int32_t  ne03;
    uint64_t nb00;
    uint64_t nb01;
    uint64_t nb02;
    uint64_t nb03;
    int32_t  ne10;
    int32_t  ne11;
    int32_t  ne12;
    int32_t  ne13;
    uint64_t nb10;
    uint64_t nb11;
    uint64_t nb12;
    uint64_t nb13;
    int32_t  ne0;
    int32_t  ne1;
    int32_t  ne2;
    int32_t  ne3;
    uint64_t nb0;
    uint64_t nb1;
    uint64_t nb2;
    uint64_t nb3;
    uint64_t offs;
    uint64_t o1[8];
};

constant short FC_bin_op [[function_constant(FC_BIN + 0)]];
constant short FC_bin_f  [[function_constant(FC_BIN + 1)]];
constant bool  FC_bin_rb [[function_constant(FC_BIN + 2)]];
constant bool  FC_bin_cb [[function_constant(FC_BIN + 3)]];

// Generic binary elementwise op with compile-time operation and broadcast
// modes. DS4 currently instantiates this as add, multiply, scalar multiply, and
// row division in the static graph.
template <typename T0, typename T1, typename T>
kernel void kernel_bin_fuse_impl(
        constant ds4_metal_args_bin & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
#define FC_OP FC_bin_op
#define FC_F  FC_bin_f
#define FC_RB FC_bin_rb
#define FC_CB FC_bin_cb

    if (FC_RB) {
        const uint i0 = tgpig.y*args.ne00 + tgpig.x;
        const uint i1 = FC_CB ? tgpig.x%args.ne10 : tgpig.x;

        device const T0 * src0_row = (device const T0 *) (src0);
        device       T  * dst_row  = (device       T  *) (dst);

        if (FC_F == 1) {
            device const T1 * src1_row = (device const T1 *) (src1 + args.o1[0]);

            if (FC_OP == 0) {
                dst_row[i0] = src0_row[i0] + src1_row[i1];
            }

            if (FC_OP == 1) {
                dst_row[i0] = src0_row[i0] - src1_row[i1];
            }

            if (FC_OP == 2) {
                dst_row[i0] = src0_row[i0] * src1_row[i1];
            }

            if (FC_OP == 3) {
                dst_row[i0] = src0_row[i0] / src1_row[i1];
            }
        } else {
            T0 res = src0_row[i0];

            if (FC_OP == 0) {
                FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                    res += ((device const T1 *) (src1 + args.o1[j]))[i1];
                }
            }

            if (FC_OP == 1) {
                FOR_UNROLL (short j = 0; j < FC_F; ++j) {
```<｜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/bin.metal

```metal
res += ((device const T1 *) (src1 + args.o1[j]))[i1];
                }
            }

            if (FC_OP == 1) {
                FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                    res -= ((device const T1 *) (src1 + args.o1[j]))[i1];
                }
            }

            if (FC_OP == 2) {
                FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                    res *= ((device const T1 *) (src1 + args.o1[j]))[i1];
                }
            }

            if (FC_OP == 3) {
                FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                    res /= ((device const T1 *) (src1 + args.o1[j]))[i1];
                }
            }

            dst_row[i0] = res;
        }
    } else {
        const int i03 = tgpig.z;
        const int i02 = tgpig.y;
        const int i01 = tgpig.x;

        if (i01 >= args.ne01) {
            return;
        }

        const int i13 = i03%args.ne13;
        const int i12 = i02%args.ne12;
        const int i11 = i01%args.ne11;

        device const T0 * src0_ptr = (device const T0 *) (src0 + i03*args.nb03 + i02*args.nb02 + i01*args.nb01 + args.offs);
        device       T  * dst_ptr  = (device       T  *) (dst  + i03*args.nb3  + i02*args.nb2  + i01*args.nb1  + args.offs);

        if (FC_F == 1) {
            device const T1 * src1_ptr = (device const T1 *) (src1 + args.o1[0] + i13*args.nb13 + i12*args.nb12 + i11*args.nb11);

            for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
                const int i10 = FC_CB ? i0%args.ne10 : i0;

                if (FC_OP == 0) {
                    dst_ptr[i0] = src0_ptr[i0] + src1_ptr[i10];
                }

                if (FC_OP == 1) {
                    dst_ptr[i0] = src0_ptr[i0] - src1_ptr[i10];
                }

                if (FC_OP == 2) {
                    dst_ptr[i0] = src0_ptr[i0] * src1_ptr[i10];
                }

                if (FC_OP == 3) {
                    dst_ptr[i0] = src0_ptr[i0] / src1_ptr[i10];
                }
            }
        } else {
            device const T1 * src1_ptr[8];
            FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                src1_ptr[j] = (device const T1 *) (src1 + args.o1[j] + i13*args.nb13 + i12*args.nb12 + i11*args.nb11);
            }

            for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
                const int i10 = FC_CB ? i0%args.ne10 : i0;

                T res = src0_ptr[i0];

                if (FC_OP == 0) {
                    FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                        res += src1_ptr[j][i10];
```

<｜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/bin.metal

```metal
res += ((device const T1 *) (src1 + args.o1[j]))[i1];
                }
            }

            if (FC_OP == 1) {
                FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                    res -= ((device const T1 *) (src1 + args.o1[j]))[i1];
                }
            }

            if (FC_OP == 2) {
                FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                    res *= ((device const T1 *) (src1 + args.o1[j]))[i1];
                }
            }

            if (FC_OP == 3) {
                FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                    res /= ((device const T1 *) (src1 + args.o1[j]))[i1];
                }
            }

            dst_row[i0] = res;
        }
    } else {
        const int i03 = tgpig.z;
        const int i02 = tgpig.y;
        const int i01 = tgpig.x;

        if (i01 >= args.ne01) {
            return;
        }

        const int i13 = i03%args.ne13;
        const int i12 = i02%args.ne12;
        const int i11 = i01%args.ne11;

        device const T0 * src0_ptr = (device const T0 *) (src0 + i03*args.nb03 + i02*args.nb02 + i01*args.nb01 + args.offs);
        device       T  * dst_ptr  = (device       T  *) (dst  + i03*args.nb3  + i02*args.nb2  + i01*args.nb1  + args.offs);

        if (FC_F == 1) {
            device const T1 * src1_ptr = (device const T1 *) (src1 + args.o1[0] + i13*args.nb13 + i12*args.nb12 + i11*args.nb11);

            for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
                const int i10 = FC_CB ? i0%args.ne10 : i0;

                if (FC_OP == 0) {
                    dst_ptr[i0] = src0_ptr[i0] + src1_ptr[i10];
                }

                if (FC_OP == 1) {
                    dst_ptr[i0] = src0_ptr[i0] - src1_ptr[i10];
                }

                if (FC_OP == 2) {
                    dst_ptr[i0] = src0_ptr[i0] * src1_ptr[i10];
                }

                if (FC_OP == 3) {
                    dst_ptr[i0] = src0_ptr[i0] / src1_ptr[i10];
                }
            }
        } else {
            device const T1 * src1_ptr[8];
            FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                src1_ptr[j] = (device const T1 *) (src1 + args.o1[j] + i13*args.nb13 + i12*args.nb12 + i11*args.nb11);
            }

            for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
                const int i10 = FC_CB ? i0%args.ne10 : i0;

                T res = src0_ptr[i0];

                if (FC_OP == 0) {
                    FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                        res += src1_ptr[j][i10];
```<｜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/bin.metal

```metal
res += ((device const T1 *) (src1 + args.o1[j]))[i1];
                }
            }

            if (FC_OP == 1) {
                FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                    res -= ((device const T1 *) (src1 + args.o1[j]))[i1];
                }
            }

            if (FC_OP == 2) {
                FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                    res *= ((device const T1 *) (src1 + args.o1[j]))[i1];
                }
            }

            if (FC_OP == 3) {
                FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                    res /= ((device const T1 *) (src1 + args.o1[j]))[i1];
                }
            }

            dst_row[i0] = res;
        }
    } else {
        const int i03 = tgpig.z;
        const int i02 = tgpig.y;
        const int i01 = tgpig.x;

        if (i01 >= args.ne01) {
            return;
        }

        const int i13 = i03%args.ne13;
        const int i12 = i02%args.ne12;
        const int i11 = i01%args.ne11;

        device const T0 * src0_ptr = (device const T0 *) (src0 + i03*args.nb03 + i02*args.nb02 + i01*args.nb01 + args.offs);
        device       T  * dst_ptr  = (device       T  *) (dst  + i03*args.nb3  + i02*args.nb2  + i01*args.nb1  + args.offs);

        if (FC_F == 1) {
            device const T1 * src1_ptr = (device const T1 *) (src1 + args.o1[0] + i13*args.nb13 + i12*args.nb12 + i11*args.nb11);

            for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
                const int i10 = FC_CB ? i0%args.ne10 : i0;

                if (FC_OP == 0) {
                    dst_ptr[i0] = src0_ptr[i0] + src1_ptr[i10];
                }

                if (FC_OP == 1) {
                    dst_ptr[i0] = src0_ptr[i0] - src1_ptr[i10];
                }

                if (FC_OP == 2) {
                    dst_ptr[i0] = src0_ptr[i0] * src1_ptr[i10];
                }

                if (FC_OP == 3) {
                    dst_ptr[i0] = src0_ptr[i0] / src1_ptr[i10];
                }
            }
        } else {
            device const T1 * src1_ptr[8];
            FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                src1_ptr[j] = (device const T1 *) (src1 + args.o1[j] + i13*args.nb13 + i12*args.nb12 + i11*args.nb11);
            }

            for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
                const int i10 = FC_CB ? i0%args.ne10 : i0;

                T res = src0_ptr[i0];

                if (FC_OP == 0) {
                    FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                        res += src1_ptr[j][i10];
```

<｜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/bin.metal

```metal
res += ((device const T1 *) (src1 + args.o1[j]))[i1];
                }
            }

            if (FC_OP == 1) {
                FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                    res -= ((device const T1 *) (src1 + args.o1[j]))[i1];
                }
            }

            if (FC_OP == 2) {
                FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                    res *= ((device const T1 *) (src1 + args.o1[j]))[i1];
                }
            }

            if (FC_OP == 3) {
                FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                    res /= ((device const T1 *) (src1 + args.o1[j]))[i1];
                }
            }

            dst_row[i0] = res;
        }
    } else {
        const int i03 = tgpig.z;
        const int i02 = tgpig.y;
        const int i01 = tgpig.x;

        if (i01 >= args.ne01) {
            return;
        }

        const int i13 = i03%args.ne13;
        const int i12 = i02%args.ne12;
        const int i11 = i01%args.ne11;

        device const T0 * src0_ptr = (device const T0 *) (src0 + i03*args.nb03 + i02*args.nb02 + i01*args.nb01 + args.offs);
        device       T  * dst_ptr  = (device       T  *) (dst  + i03*args.nb3  + i02*args.nb2  + i01*args.nb1  + args.offs);

        if (FC_F == 1) {
            device const T1 * src1_ptr = (device const T1 *) (src1 + args.o1[0] + i13*args.nb13 + i12*args.nb12 + i11*args.nb11);

            for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
                const int i10 = FC_CB ? i0%args.ne10 : i0;

                if (FC_OP == 0) {
                    dst_ptr[i0] = src0_ptr[i0] + src1_ptr[i10];
                }

                if (FC_OP == 1) {
                    dst_ptr[i0] = src0_ptr[i0] - src1_ptr[i10];
                }

                if (FC_OP == 2) {
                    dst_ptr[i0] = src0_ptr[i0] * src1_ptr[i10];
                }

                if (FC_OP == 3) {
                    dst_ptr[i0] = src0_ptr[i0] / src1_ptr[i10];
                }
            }
        } else {
            device const T1 * src1_ptr[8];
            FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                src1_ptr[j] = (device const T1 *) (src1 + args.o1[j] + i13*args.nb13 + i12*args.nb12 + i11*args.nb11);
            }

            for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
                const int i10 = FC_CB ? i0%args.ne10 : i0;

                T res = src0_ptr[i0];

                if (FC_OP == 0) {
                    FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                        res += src1_ptr[j][i10];
```<｜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/bin.metal

```metal
T res = src0_ptr[i0];

                if (FC_OP == 0) {
                    FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                        res += src1_ptr[j][i10];
                    }
                }

                if (FC_OP == 1) {
                    FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                        res -= src1_ptr[j][i10];
                    }
                }

                if (FC_OP == 2) {
                    FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                        res *= src1_ptr[j][i10];
                    }
                }

                if (FC_OP == 3) {
                    FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                        res /= src1_ptr[j][i10];
                    }
                }

                dst_ptr[i0] = res;
            }
        }
    }

#undef FC_OP
#undef FC_F
#undef FC_RB
#undef FC_CB
}

typedef decltype(kernel_bin_fuse_impl<float, float, float>) kernel_bin_fuse_t;
// Host-visible F32 binary op; function constants specialize it per use site.
template [[host_name("kernel_bin_fuse_f32_f32_f32")]] kernel kernel_bin_fuse_t kernel_bin_fuse_impl<float, float, float>;
```

<｜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/bin.metal

```metal
T res = src0_ptr[i0];

                if (FC_OP == 0) {
                    FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                        res += src1_ptr[j][i10];
                    }
                }

                if (FC_OP == 1) {
                    FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                        res -= src1_ptr[j][i10];
                    }
                }

                if (FC_OP == 2) {
                    FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                        res *= src1_ptr[j][i10];
                    }
                }

                if (FC_OP == 3) {
                    FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                        res /= src1_ptr[j][i10];
                    }
                }

                dst_ptr[i0] = res;
            }
        }
    }

#undef FC_OP
#undef FC_F
#undef FC_RB
#undef FC_CB
}

typedef decltype(kernel_bin_fuse_impl<float, float, float>) kernel_bin_fuse_t;
// Host-visible F32 binary op; function constants specialize it per use site.
template [[host_name("kernel_bin_fuse_f32_f32_f32")]] kernel kernel_bin_fuse_t kernel_bin_fuse_impl<float, float, float>;
```<｜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/bin.metal

```metal
T res = src0_ptr[i0];

                if (FC_OP == 0) {
                    FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                        res += src1_ptr[j][i10];
                    }
                }

                if (FC_OP == 1) {
                    FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                        res -= src1_ptr[j][i10];
                    }
                }

                if (FC_OP == 2) {
                    FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                        res *= src1_ptr[j][i10];
                    }
                }

                if (FC_OP == 3) {
                    FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                        res /= src1_ptr[j][i10];
                    }
                }

                dst_ptr[i0] = res;
            }
        }
    }

#undef FC_OP
#undef FC_F
#undef FC_RB
#undef FC_CB
}

typedef decltype(kernel_bin_fuse_impl<float, float, float>) kernel_bin_fuse_t;
// Host-visible F32 binary op; function constants specialize it per use site.
template [[host_name("kernel_bin_fuse_f32_f32_f32")]] kernel kernel_bin_fuse_t kernel_bin_fuse_impl<float, float, float>;
```

<｜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/bin.metal

```metal
T res = src0_ptr[i0];

                if (FC_OP == 0) {
                    FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                        res += src1_ptr[j][i10];
                    }
                }

                if (FC_OP == 1) {
                    FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                        res -= src1_ptr[j][i10];
                    }
                }

                if (FC_OP == 2) {
                    FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                        res *= src1_ptr[j][i10];
                    }
                }

                if (FC_OP == 3) {
                    FOR_UNROLL (short j = 0; j < FC_F; ++j) {
                        res /= src1_ptr[j][i10];
                    }
                }

                dst_ptr[i0] = res;
            }
        }
    }

#undef FC_OP
#undef FC_F
#undef FC_RB
#undef FC_CB
}

typedef decltype(kernel_bin_fuse_impl<float, float, float>) kernel_bin_fuse_t;
// Host-visible F32 binary op; function constants specialize it per use site.
template [[host_name("kernel_bin_fuse_f32_f32_f32")]] kernel kernel_bin_fuse_t kernel_bin_fuse_impl<float, float, float>;
```<｜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/concat.metal

```metal
// DS4 Metal concat kernel used by the graph.

struct ds4_metal_args_concat {
    int32_t  ne00;
    int32_t  ne01;
    int32_t  ne02;
    int32_t  ne03;
    uint64_t nb00;
    uint64_t nb01;
    uint64_t nb02;
    uint64_t nb03;
    int32_t  ne10;
    int32_t  ne11;
    int32_t  ne12;
    int32_t  ne13;
    uint64_t nb10;
    uint64_t nb11;
    uint64_t nb12;
    uint64_t nb13;
    int32_t  ne0;
    int32_t  ne1;
    int32_t  ne2;
    int32_t  ne3;
    uint64_t nb0;
    uint64_t nb1;
    uint64_t nb2;
    uint64_t nb3;
    int32_t  dim;
};

// Concatenates two float tensors along one dimension. In DS4 this is a graph
// utility for assembling attention inputs with exactly the same tensor layout
// expected by the downstream kernels.
kernel void kernel_concat(
        constant ds4_metal_args_concat & args,
        device  const char * src0,
        device  const char * src1,
        device        char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
    const int i3 = tgpig.z;
    const int i2 = tgpig.y;
    const int i1 = tgpig.x;

    int o[4] = {0, 0, 0, 0};
    o[args.dim] = args.dim == 0 ? args.ne00 : (args.dim == 1 ? args.ne01 : (args.dim == 2 ? args.ne02 : args.ne03));

    device const float * x;

    for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
        if (i0 < args.ne00 && i1 < args.ne01 && i2 < args.ne02 && i3 < args.ne03) {
            x = (device const float *)(src0 + (i3       )*args.nb03 + (i2       )*args.nb02 + (i1       )*args.nb01 + (i0       )*args.nb00);
        } else {
            x = (device const float *)(src1 + (i3 - o[3])*args.nb13 + (i2 - o[2])*args.nb12 + (i1 - o[1])*args.nb11 + (i0 - o[0])*args.nb10);
        }

        device float * y = (device float *)(dst + i3*args.nb3 + i2*args.nb2 + i1*args.nb1 + i0*args.nb0);

        *y = *x;
    }
}
```

<｜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/concat.metal

```metal
// DS4 Metal concat kernel used by the graph.

struct ds4_metal_args_concat {
    int32_t  ne00;
    int32_t  ne01;
    int32_t  ne02;
    int32_t  ne03;
    uint64_t nb00;
    uint64_t nb01;
    uint64_t nb02;
    uint64_t nb03;
    int32_t  ne10;
    int32_t  ne11;
    int32_t  ne12;
    int32_t  ne13;
    uint64_t nb10;
    uint64_t nb11;
    uint64_t nb12;
    uint64_t nb13;
    int32_t  ne0;
    int32_t  ne1;
    int32_t  ne2;
    int32_t  ne3;
    uint64_t nb0;
    uint64_t nb1;
    uint64_t nb2;
    uint64_t nb3;
    int32_t  dim;
};

// Concatenates two float tensors along one dimension. In DS4 this is a graph
// utility for assembling attention inputs with exactly the same tensor layout
// expected by the downstream kernels.
kernel void kernel_concat(
        constant ds4_metal_args_concat & args,
        device  const char * src0,
        device  const char * src1,
        device        char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
    const int i3 = tgpig.z;
    const int i2 = tgpig.y;
    const int i1 = tgpig.x;

    int o[4] = {0, 0, 0, 0};
    o[args.dim] = args.dim == 0 ? args.ne00 : (args.dim == 1 ? args.ne01 : (args.dim == 2 ? args.ne02 : args.ne03));

    device const float * x;

    for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
        if (i0 < args.ne00 && i1 < args.ne01 && i2 < args.ne02 && i3 < args.ne03) {
            x = (device const float *)(src0 + (i3       )*args.nb03 + (i2       )*args.nb02 + (i1       )*args.nb01 + (i0       )*args.nb00);
        } else {
            x = (device const float *)(src1 + (i3 - o[3])*args.nb13 + (i2 - o[2])*args.nb12 + (i1 - o[1])*args.nb11 + (i0 - o[0])*args.nb10);
        }

        device float * y = (device float *)(dst + i3*args.nb3 + i2*args.nb2 + i1*args.nb1 + i0*args.nb0);

        *y = *x;
    }
}
```<｜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/concat.metal

```metal
// DS4 Metal concat kernel used by the graph.

struct ds4_metal_args_concat {
    int32_t  ne00;
    int32_t  ne01;
    int32_t  ne02;
    int32_t  ne03;
    uint64_t nb00;
    uint64_t nb01;
    uint64_t nb02;
    uint64_t nb03;
    int32_t  ne10;
    int32_t  ne11;
    int32_t  ne12;
    int32_t  ne13;
    uint64_t nb10;
    uint64_t nb11;
    uint64_t nb12;
    uint64_t nb13;
    int32_t  ne0;
    int32_t  ne1;
    int32_t  ne2;
    int32_t  ne3;
    uint64_t nb0;
    uint64_t nb1;
    uint64_t nb2;
    uint64_t nb3;
    int32_t  dim;
};

// Concatenates two float tensors along one dimension. In DS4 this is a graph
// utility for assembling attention inputs with exactly the same tensor layout
// expected by the downstream kernels.
kernel void kernel_concat(
        constant ds4_metal_args_concat & args,
        device  const char * src0,
        device  const char * src1,
        device        char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
    const int i3 = tgpig.z;
    const int i2 = tgpig.y;
    const int i1 = tgpig.x;

    int o[4] = {0, 0, 0, 0};
    o[args.dim] = args.dim == 0 ? args.ne00 : (args.dim == 1 ? args.ne01 : (args.dim == 2 ? args.ne02 : args.ne03));

    device const float * x;

    for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
        if (i0 < args.ne00 && i1 < args.ne01 && i2 < args.ne02 && i3 < args.ne03) {
            x = (device const float *)(src0 + (i3       )*args.nb03 + (i2       )*args.nb02 + (i1       )*args.nb01 + (i0       )*args.nb00);
        } else {
            x = (device const float *)(src1 + (i3 - o[3])*args.nb13 + (i2 - o[2])*args.nb12 + (i1 - o[1])*args.nb11 + (i0 - o[0])*args.nb10);
        }

        device float * y = (device float *)(dst + i3*args.nb3 + i2*args.nb2 + i1*args.nb1 + i0*args.nb0);

        *y = *x;
    }
}
```

<｜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/concat.metal

```metal
// DS4 Metal concat kernel used by the graph.

struct ds4_metal_args_concat {
    int32_t  ne00;
    int32_t  ne01;
    int32_t  ne02;
    int32_t  ne03;
    uint64_t nb00;
    uint64_t nb01;
    uint64_t nb02;
    uint64_t nb03;
    int32_t  ne10;
    int32_t  ne11;
    int32_t  ne12;
    int32_t  ne13;
    uint64_t nb10;
    uint64_t nb11;
    uint64_t nb12;
    uint64_t nb13;
    int32_t  ne0;
    int32_t  ne1;
    int32_t  ne2;
    int32_t  ne3;
    uint64_t nb0;
    uint64_t nb1;
    uint64_t nb2;
    uint64_t nb3;
    int32_t  dim;
};

// Concatenates two float tensors along one dimension. In DS4 this is a graph
// utility for assembling attention inputs with exactly the same tensor layout
// expected by the downstream kernels.
kernel void kernel_concat(
        constant ds4_metal_args_concat & args,
        device  const char * src0,
        device  const char * src1,
        device        char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
    const int i3 = tgpig.z;
    const int i2 = tgpig.y;
    const int i1 = tgpig.x;

    int o[4] = {0, 0, 0, 0};
    o[args.dim] = args.dim == 0 ? args.ne00 : (args.dim == 1 ? args.ne01 : (args.dim == 2 ? args.ne02 : args.ne03));

    device const float * x;

    for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
        if (i0 < args.ne00 && i1 < args.ne01 && i2 < args.ne02 && i3 < args.ne03) {
            x = (device const float *)(src0 + (i3       )*args.nb03 + (i2       )*args.nb02 + (i1       )*args.nb01 + (i0       )*args.nb00);
        } else {
            x = (device const float *)(src1 + (i3 - o[3])*args.nb13 + (i2 - o[2])*args.nb12 + (i1 - o[1])*args.nb11 + (i0 - o[0])*args.nb10);
        }

        device float * y = (device float *)(dst + i3*args.nb3 + i2*args.nb2 + i1*args.nb1 + i0*args.nb0);

        *y = *x;
    }
}
```<｜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/cpy.metal

```metal
struct ds4_metal_args_cpy {
    int64_t  nk0;
    int64_t  ne00;
    int64_t  ne01;
    int64_t  ne02;
    int64_t  ne03;
    uint64_t nb00;
    uint64_t nb01;
    uint64_t nb02;
    uint64_t nb03;
    int64_t  ne0;
    int64_t  ne1;
    int64_t  ne2;
    int64_t  ne3;
    uint64_t nb0;
    uint64_t nb1;
    uint64_t nb2;
    uint64_t nb3;
};

// Typed copy/conversion between graph tensors. DS4 uses this for layout
// materialization and F32/F16 conversions at graph boundaries such as KV/cache
// packing and compressor pooling.
template<typename T0, typename T1>
kernel void kernel_cpy_t_t(
        constant ds4_metal_args_cpy & args,
        device  const char * src0,
        device        char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort  tiitg[[thread_index_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
    const int i03 = tgpig[2];
    const int i02 = tgpig[1];
    const int i01 = ntg[1] == 1 ? tgpig[0]%args.ne01 : tgpig[0]*ntg[1] + tiitg/ntg[0];
    const int iw0 = ntg[1] == 1 ? tgpig[0]/args.ne01 : 0;

    const int64_t n = i03*args.ne02*args.ne01*args.ne00 + i02*args.ne01*args.ne00 + i01*args.ne00;

    const int64_t i3 = n/(args.ne2*args.ne1*args.ne0);
    const int64_t i2 = (n - i3*args.ne2*args.ne1*args.ne0)/(args.ne1*args.ne0);
    const int64_t i1 = (n - i3*args.ne2*args.ne1*args.ne0 - i2*args.ne1*args.ne0)/args.ne0;
    const int64_t i0 = (n - i3*args.ne2*args.ne1*args.ne0 - i2*args.ne1*args.ne0 - i1*args.ne0);

    device T1 * dst_data = (device T1 *) (dst + i3*args.nb3 + i2*args.nb2 + i1*args.nb1 + i0*args.nb0);

    for (int64_t i00 = iw0*ntg[0] + tiitg%ntg[0]; i00 < args.ne00; ) {
        device const T0 * src = (device T0 *)(src0 + i03*args.nb03 + i02*args.nb02 + i01*args.nb01 + i00*args.nb00);
        dst_data[i00] = (T1) src[0];
        break;
    }
}

typedef decltype(kernel_cpy_t_t<float, float>) kernel_cpy_t;
// Host-visible copy/conversion variants used by the DS4 graph.
template [[host_name("kernel_cpy_f32_f32")]] kernel kernel_cpy_t kernel_cpy_t_t<float, float>;
template [[host_name("kernel_cpy_f32_f16")]] kernel kernel_cpy_t kernel_cpy_t_t<float, half>;
template [[host_name("kernel_cpy_f16_f32")]] kernel kernel_cpy_t kernel_cpy_t_t<half, float>;
```

<｜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/cpy.metal

```metal
struct ds4_metal_args_cpy {
    int64_t  nk0;
    int64_t  ne00;
    int64_t  ne01;
    int64_t  ne02;
    int64_t  ne03;
    uint64_t nb00;
    uint64_t nb01;
    uint64_t nb02;
    uint64_t nb03;
    int64_t  ne0;
    int64_t  ne1;
    int64_t  ne2;
    int64_t  ne3;
    uint64_t nb0;
    uint64_t nb1;
    uint64_t nb2;
    uint64_t nb3;
};

// Typed copy/conversion between graph tensors. DS4 uses this for layout
// materialization and F32/F16 conversions at graph boundaries such as KV/cache
// packing and compressor pooling.
template<typename T0, typename T1>
kernel void kernel_cpy_t_t(
        constant ds4_metal_args_cpy & args,
        device  const char * src0,
        device        char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort  tiitg[[thread_index_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
    const int i03 = tgpig[2];
    const int i02 = tgpig[1];
    const int i01 = ntg[1] == 1 ? tgpig[0]%args.ne01 : tgpig[0]*ntg[1] + tiitg/ntg[0];
    const int iw0 = ntg[1] == 1 ? tgpig[0]/args.ne01 : 0;

    const int64_t n = i03*args.ne02*args.ne01*args.ne00 + i02*args.ne01*args.ne00 + i01*args.ne00;

    const int64_t i3 = n/(args.ne2*args.ne1*args.ne0);
    const int64_t i2 = (n - i3*args.ne2*args.ne1*args.ne0)/(args.ne1*args.ne0);
    const int64_t i1 = (n - i3*args.ne2*args.ne1*args.ne0 - i2*args.ne1*args.ne0)/args.ne0;
    const int64_t i0 = (n - i3*args.ne2*args.ne1*args.ne0 - i2*args.ne1*args.ne0 - i1*args.ne0);

    device T1 * dst_data = (device T1 *) (dst + i3*args.nb3 + i2*args.nb2 + i1*args.nb1 + i0*args.nb0);

    for (int64_t i00 = iw0*ntg[0] + tiitg%ntg[0]; i00 < args.ne00; ) {
        device const T0 * src = (device T0 *)(src0 + i03*args.nb03 + i02*args.nb02 + i01*args.nb01 + i00*args.nb00);
        dst_data[i00] = (T1) src[0];
        break;
    }
}

typedef decltype(kernel_cpy_t_t<float, float>) kernel_cpy_t;
// Host-visible copy/conversion variants used by the DS4 graph.
template [[host_name("kernel_cpy_f32_f32")]] kernel kernel_cpy_t kernel_cpy_t_t<float, float>;
template [[host_name("kernel_cpy_f32_f16")]] kernel kernel_cpy_t kernel_cpy_t_t<float, half>;
template [[host_name("kernel_cpy_f16_f32")]] kernel kernel_cpy_t kernel_cpy_t_t<half, float>;
```<｜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/cpy.metal

```metal
struct ds4_metal_args_cpy {
    int64_t  nk0;
    int64_t  ne00;
    int64_t  ne01;
    int64_t  ne02;
    int64_t  ne03;
    uint64_t nb00;
    uint64_t nb01;
    uint64_t nb02;
    uint64_t nb03;
    int64_t  ne0;
    int64_t  ne1;
    int64_t  ne2;
    int64_t  ne3;
    uint64_t nb0;
    uint64_t nb1;
    uint64_t nb2;
    uint64_t nb3;
};

// Typed copy/conversion between graph tensors. DS4 uses this for layout
// materialization and F32/F16 conversions at graph boundaries such as KV/cache
// packing and compressor pooling.
template<typename T0, typename T1>
kernel void kernel_cpy_t_t(
        constant ds4_metal_args_cpy & args,
        device  const char * src0,
        device        char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort  tiitg[[thread_index_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
    const int i03 = tgpig[2];
    const int i02 = tgpig[1];
    const int i01 = ntg[1] == 1 ? tgpig[0]%args.ne01 : tgpig[0]*ntg[1] + tiitg/ntg[0];
    const int iw0 = ntg[1] == 1 ? tgpig[0]/args.ne01 : 0;

    const int64_t n = i03*args.ne02*args.ne01*args.ne00 + i02*args.ne01*args.ne00 + i01*args.ne00;

    const int64_t i3 = n/(args.ne2*args.ne1*args.ne0);
    const int64_t i2 = (n - i3*args.ne2*args.ne1*args.ne0)/(args.ne1*args.ne0);
    const int64_t i1 = (n - i3*args.ne2*args.ne1*args.ne0 - i2*args.ne1*args.ne0)/args.ne0;
    const int64_t i0 = (n - i3*args.ne2*args.ne1*args.ne0 - i2*args.ne1*args.ne0 - i1*args.ne0);

    device T1 * dst_data = (device T1 *) (dst + i3*args.nb3 + i2*args.nb2 + i1*args.nb1 + i0*args.nb0);

    for (int64_t i00 = iw0*ntg[0] + tiitg%ntg[0]; i00 < args.ne00; ) {
        device const T0 * src = (device T0 *)(src0 + i03*args.nb03 + i02*args.nb02 + i01*args.nb01 + i00*args.nb00);
        dst_data[i00] = (T1) src[0];
        break;
    }
}

typedef decltype(kernel_cpy_t_t<float, float>) kernel_cpy_t;
// Host-visible copy/conversion variants used by the DS4 graph.
template [[host_name("kernel_cpy_f32_f32")]] kernel kernel_cpy_t kernel_cpy_t_t<float, float>;
template [[host_name("kernel_cpy_f32_f16")]] kernel kernel_cpy_t kernel_cpy_t_t<float, half>;
template [[host_name("kernel_cpy_f16_f32")]] kernel kernel_cpy_t kernel_cpy_t_t<half, float>;
```

<｜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/cpy.metal

```metal
struct ds4_metal_args_cpy {
    int64_t  nk0;
    int64_t  ne00;
    int64_t  ne01;
    int64_t  ne02;
    int64_t  ne03;
    uint64_t nb00;
    uint64_t nb01;
    uint64_t nb02;
    uint64_t nb03;
    int64_t  ne0;
    int64_t  ne1;
    int64_t  ne2;
    int64_t  ne3;
    uint64_t nb0;
    uint64_t nb1;
    uint64_t nb2;
    uint64_t nb3;
};

// Typed copy/conversion between graph tensors. DS4 uses this for layout
// materialization and F32/F16 conversions at graph boundaries such as KV/cache
// packing and compressor pooling.
template<typename T0, typename T1>
kernel void kernel_cpy_t_t(
        constant ds4_metal_args_cpy & args,
        device  const char * src0,
        device        char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort  tiitg[[thread_index_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
    const int i03 = tgpig[2];
    const int i02 = tgpig[1];
    const int i01 = ntg[1] == 1 ? tgpig[0]%args.ne01 : tgpig[0]*ntg[1] + tiitg/ntg[0];
    const int iw0 = ntg[1] == 1 ? tgpig[0]/args.ne01 : 0;

    const int64_t n = i03*args.ne02*args.ne01*args.ne00 + i02*args.ne01*args.ne00 + i01*args.ne00;

    const int64_t i3 = n/(args.ne2*args.ne1*args.ne0);
    const int64_t i2 = (n - i3*args.ne2*args.ne1*args.ne0)/(args.ne1*args.ne0);
    const int64_t i1 = (n - i3*args.ne2*args.ne1*args.ne0 - i2*args.ne1*args.ne0)/args.ne0;
    const int64_t i0 = (n - i3*args.ne2*args.ne1*args.ne0 - i2*args.ne1*args.ne0 - i1*args.ne0);

    device T1 * dst_data = (device T1 *) (dst + i3*args.nb3 + i2*args.nb2 + i1*args.nb1 + i0*args.nb0);

    for (int64_t i00 = iw0*ntg[0] + tiitg%ntg[0]; i00 < args.ne00; ) {
        device const T0 * src = (device T0 *)(src0 + i03*args.nb03 + i02*args.nb02 + i01*args.nb01 + i00*args.nb00);
        dst_data[i00] = (T1) src[0];
        break;
    }
}

typedef decltype(kernel_cpy_t_t<float, float>) kernel_cpy_t;
// Host-visible copy/conversion variants used by the DS4 graph.
template [[host_name("kernel_cpy_f32_f32")]] kernel kernel_cpy_t kernel_cpy_t_t<float, float>;
template [[host_name("kernel_cpy_f32_f16")]] kernel kernel_cpy_t kernel_cpy_t_t<float, half>;
template [[host_name("kernel_cpy_f16_f32")]] kernel kernel_cpy_t kernel_cpy_t_t<half, float>;
```<｜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/dense.metal

```metal
// DS4 Metal matvec kernels used by generation.

constant short FC_mul_mv_nsg   [[function_constant(FC_MUL_MV + 0)]];
constant short FC_mul_mv_nxpsg [[function_constant(FC_MUL_MV + 1)]];

struct ds4_metal_args_mul_mv {
    int ne00;
    int ne01;
    int ne02;
    ulong nb00;
    ulong nb01;
    ulong nb02;
    ulong nb03;
    int ne10;
    int ne11;
    int ne12;
    ulong nb10;
    ulong nb11;
    ulong nb12;
    ulong nb13;
    int ne0;
    int ne1;
    int nr0;
    short r2;
    short r3;
};

struct ds4_metal_args_mul_mm {
    int32_t ne00;
    int32_t ne02;
    uint64_t nb01;
    uint64_t nb02;
    uint64_t nb03;
    int32_t ne12;
    uint64_t nb10;
    uint64_t nb11;
    uint64_t nb12;
    uint64_t nb13;
    int32_t ne0;
    int32_t ne1;
    int16_t r2;
    int16_t r3;
};

struct ds4_metal_args_mul_mv_ext {
    int32_t ne00;
    int32_t ne01;
    int32_t ne02;
    uint64_t nb00;
    uint64_t nb01;
    uint64_t nb02;
    uint64_t nb03;
    int32_t ne10;
    int32_t ne11;
    int32_t ne12;
    uint64_t nb10;
    uint64_t nb11;
    uint64_t nb12;
    uint64_t nb13;
    int32_t ne0;
    int32_t ne1;
    int16_t r2;
    int16_t r3;
};

template<short NR0>
static inline void helper_mv_reduce_and_write(
        device float * dst_f32,
        float sumf[NR0],
        const int r0,
        const int ne01,
        ushort tiisg,
        ushort sgitg,
        threadgroup char * shmem) {
    constexpr short NW = N_SIMDWIDTH;

    threadgroup float * shmem_f32[NR0];

    for (short row = 0; row < NR0; ++row) {
        shmem_f32[row] = (threadgroup float *) shmem + NW*row;

        if (sgitg == 0) {
            shmem_f32[row][tiisg] = 0.0f;
        }

        sumf[row] = simd_sum(sumf[row]);
    }

    threadgroup_barrier(mem_flags::mem_threadgroup);

    for (short row = 0; row < NR0; ++row) {
        if (tiisg == 0) {
            shmem_f32[row][sgitg] = sumf[row];
        }
    }

    threadgroup_barrier(mem_flags::mem_threadgroup);

    for (short row = 0; row < NR0 && r0 + row < ne01; ++row) {
        float tot = simd_sum(shmem_f32[row][tiisg]);

        if (tiisg == 0 && sgitg == 0) {
            dst_f32[r0 + row] = tot;
        }
    }
}

template<short NR0, typename args_t>
void kernel_mul_mv_q8_0_f32_impl(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    constexpr short NW = N_SIMDWIDTH;
    constexpr short NQ = 8;
```

<｜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/dense.metal

```metal
// DS4 Metal matvec kernels used by generation.

constant short FC_mul_mv_nsg   [[function_constant(FC_MUL_MV + 0)]];
constant short FC_mul_mv_nxpsg [[function_constant(FC_MUL_MV + 1)]];

struct ds4_metal_args_mul_mv {
    int ne00;
    int ne01;
    int ne02;
    ulong nb00;
    ulong nb01;
    ulong nb02;
    ulong nb03;
    int ne10;
    int ne11;
    int ne12;
    ulong nb10;
    ulong nb11;
    ulong nb12;
    ulong nb13;
    int ne0;
    int ne1;
    int nr0;
    short r2;
    short r3;
};

struct ds4_metal_args_mul_mm {
    int32_t ne00;
    int32_t ne02;
    uint64_t nb01;
    uint64_t nb02;
    uint64_t nb03;
    int32_t ne12;
    uint64_t nb10;
    uint64_t nb11;
    uint64_t nb12;
    uint64_t nb13;
    int32_t ne0;
    int32_t ne1;
    int16_t r2;
    int16_t r3;
};

struct ds4_metal_args_mul_mv_ext {
    int32_t ne00;
    int32_t ne01;
    int32_t ne02;
    uint64_t nb00;
    uint64_t nb01;
    uint64_t nb02;
    uint64_t nb03;
    int32_t ne10;
    int32_t ne11;
    int32_t ne12;
    uint64_t nb10;
    uint64_t nb11;
    uint64_t nb12;
    uint64_t nb13;
    int32_t ne0;
    int32_t ne1;
    int16_t r2;
    int16_t r3;
};

template<short NR0>
static inline void helper_mv_reduce_and_write(
        device float * dst_f32,
        float sumf[NR0],
        const int r0,
        const int ne01,
        ushort tiisg,
        ushort sgitg,
        threadgroup char * shmem) {
    constexpr short NW = N_SIMDWIDTH;

    threadgroup float * shmem_f32[NR0];

    for (short row = 0; row < NR0; ++row) {
        shmem_f32[row] = (threadgroup float *) shmem + NW*row;

        if (sgitg == 0) {
            shmem_f32[row][tiisg] = 0.0f;
        }

        sumf[row] = simd_sum(sumf[row]);
    }

    threadgroup_barrier(mem_flags::mem_threadgroup);

    for (short row = 0; row < NR0; ++row) {
        if (tiisg == 0) {
            shmem_f32[row][sgitg] = sumf[row];
        }
    }

    threadgroup_barrier(mem_flags::mem_threadgroup);

    for (short row = 0; row < NR0 && r0 + row < ne01; ++row) {
        float tot = simd_sum(shmem_f32[row][tiisg]);

        if (tiisg == 0 && sgitg == 0) {
            dst_f32[r0 + row] = tot;
        }
    }
}

template<short NR0, typename args_t>
void kernel_mul_mv_q8_0_f32_impl(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    constexpr short NW = N_SIMDWIDTH;
    constexpr short NQ = 8;
```<｜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/dense.metal

```metal
// DS4 Metal matvec kernels used by generation.

constant short FC_mul_mv_nsg   [[function_constant(FC_MUL_MV + 0)]];
constant short FC_mul_mv_nxpsg [[function_constant(FC_MUL_MV + 1)]];

struct ds4_metal_args_mul_mv {
    int ne00;
    int ne01;
    int ne02;
    ulong nb00;
    ulong nb01;
    ulong nb02;
    ulong nb03;
    int ne10;
    int ne11;
    int ne12;
    ulong nb10;
    ulong nb11;
    ulong nb12;
    ulong nb13;
    int ne0;
    int ne1;
    int nr0;
    short r2;
    short r3;
};

struct ds4_metal_args_mul_mm {
    int32_t ne00;
    int32_t ne02;
    uint64_t nb01;
    uint64_t nb02;
    uint64_t nb03;
    int32_t ne12;
    uint64_t nb10;
    uint64_t nb11;
    uint64_t nb12;
    uint64_t nb13;
    int32_t ne0;
    int32_t ne1;
    int16_t r2;
    int16_t r3;
};

struct ds4_metal_args_mul_mv_ext {
    int32_t ne00;
    int32_t ne01;
    int32_t ne02;
    uint64_t nb00;
    uint64_t nb01;
    uint64_t nb02;
    uint64_t nb03;
    int32_t ne10;
    int32_t ne11;
    int32_t ne12;
    uint64_t nb10;
    uint64_t nb11;
    uint64_t nb12;
    uint64_t nb13;
    int32_t ne0;
    int32_t ne1;
    int16_t r2;
    int16_t r3;
};

template<short NR0>
static inline void helper_mv_reduce_and_write(
        device float * dst_f32,
        float sumf[NR0],
        const int r0,
        const int ne01,
        ushort tiisg,
        ushort sgitg,
        threadgroup char * shmem) {
    constexpr short NW = N_SIMDWIDTH;

    threadgroup float * shmem_f32[NR0];

    for (short row = 0; row < NR0; ++row) {
        shmem_f32[row] = (threadgroup float *) shmem + NW*row;

        if (sgitg == 0) {
            shmem_f32[row][tiisg] = 0.0f;
        }

        sumf[row] = simd_sum(sumf[row]);
    }

    threadgroup_barrier(mem_flags::mem_threadgroup);

    for (short row = 0; row < NR0; ++row) {
        if (tiisg == 0) {
            shmem_f32[row][sgitg] = sumf[row];
        }
    }

    threadgroup_barrier(mem_flags::mem_threadgroup);

    for (short row = 0; row < NR0 && r0 + row < ne01; ++row) {
        float tot = simd_sum(shmem_f32[row][tiisg]);

        if (tiisg == 0 && sgitg == 0) {
            dst_f32[r0 + row] = tot;
        }
    }
}

template<short NR0, typename args_t>
void kernel_mul_mv_q8_0_f32_impl(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    constexpr short NW = N_SIMDWIDTH;
    constexpr short NQ = 8;
```

<｜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/dense.metal

```metal
// DS4 Metal matvec kernels used by generation.

constant short FC_mul_mv_nsg   [[function_constant(FC_MUL_MV + 0)]];
constant short FC_mul_mv_nxpsg [[function_constant(FC_MUL_MV + 1)]];

struct ds4_metal_args_mul_mv {
    int ne00;
    int ne01;
    int ne02;
    ulong nb00;
    ulong nb01;
    ulong nb02;
    ulong nb03;
    int ne10;
    int ne11;
    int ne12;
    ulong nb10;
    ulong nb11;
    ulong nb12;
    ulong nb13;
    int ne0;
    int ne1;
    int nr0;
    short r2;
    short r3;
};

struct ds4_metal_args_mul_mm {
    int32_t ne00;
    int32_t ne02;
    uint64_t nb01;
    uint64_t nb02;
    uint64_t nb03;
    int32_t ne12;
    uint64_t nb10;
    uint64_t nb11;
    uint64_t nb12;
    uint64_t nb13;
    int32_t ne0;
    int32_t ne1;
    int16_t r2;
    int16_t r3;
};

struct ds4_metal_args_mul_mv_ext {
    int32_t ne00;
    int32_t ne01;
    int32_t ne02;
    uint64_t nb00;
    uint64_t nb01;
    uint64_t nb02;
    uint64_t nb03;
    int32_t ne10;
    int32_t ne11;
    int32_t ne12;
    uint64_t nb10;
    uint64_t nb11;
    uint64_t nb12;
    uint64_t nb13;
    int32_t ne0;
    int32_t ne1;
    int16_t r2;
    int16_t r3;
};

template<short NR0>
static inline void helper_mv_reduce_and_write(
        device float * dst_f32,
        float sumf[NR0],
        const int r0,
        const int ne01,
        ushort tiisg,
        ushort sgitg,
        threadgroup char * shmem) {
    constexpr short NW = N_SIMDWIDTH;

    threadgroup float * shmem_f32[NR0];

    for (short row = 0; row < NR0; ++row) {
        shmem_f32[row] = (threadgroup float *) shmem + NW*row;

        if (sgitg == 0) {
            shmem_f32[row][tiisg] = 0.0f;
        }

        sumf[row] = simd_sum(sumf[row]);
    }

    threadgroup_barrier(mem_flags::mem_threadgroup);

    for (short row = 0; row < NR0; ++row) {
        if (tiisg == 0) {
            shmem_f32[row][sgitg] = sumf[row];
        }
    }

    threadgroup_barrier(mem_flags::mem_threadgroup);

    for (short row = 0; row < NR0 && r0 + row < ne01; ++row) {
        float tot = simd_sum(shmem_f32[row][tiisg]);

        if (tiisg == 0 && sgitg == 0) {
            dst_f32[r0 + row] = tot;
        }
    }
}

template<short NR0, typename args_t>
void kernel_mul_mv_q8_0_f32_impl(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    constexpr short NW = N_SIMDWIDTH;
    constexpr short NQ = 8;
```<｜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/dense.metal

```metal
shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    constexpr short NW = N_SIMDWIDTH;
    constexpr short NQ = 8;

    const int nb = args.ne00/QK8_0;

    const int r0 = tgpig.x*NR0;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

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

    const uint64_t offset1 = r1*args.nb11 + (i12)*args.nb12 + (i13)*args.nb13;

    device const float * y = (device const float *) (src1 + offset1);

    device const block_q8_0 * ax[NR0];
    FOR_UNROLL (short row = 0; row < NR0; ++row) {
        const uint64_t offset0 = (r0 + row)*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;

        ax[row] = (device const block_q8_0 *) ((device char *) src0 + offset0);
    }

    float sumf[NR0] = { 0.f };

    const short ix = tiisg/(NW/NQ);
    const short il = tiisg%(NW/NQ);

    const int ib0 = sgitg*NQ + ix;

    float yl[NQ];

    device const float * yb = y + ib0*QK8_0 + il*NQ;

    for (int ib = ib0; ib < nb; ib += NSG*NQ) {
        for (short i = 0; i < NQ; ++i) {
            yl[i] = yb[i];
        }

        for (short row = 0; row < NR0; row++) {
            device const int8_t * qs = ax[row][ib].qs + il*NQ;

            float sumq = 0.f;
            FOR_UNROLL (short i = 0; i < NQ; ++i) {
                sumq += qs[i] * yl[i];
            }

            sumf[row] += sumq*ax[row][ib].d;
        }

        yb += NSG*NQ*QK8_0;
    }

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

    helper_mv_reduce_and_write<NR0>(dst_f32, sumf, r0, args.ne01, tiisg, sgitg, shmem);
}

// Decode-time Q8_0 matrix-vector multiply. DS4 uses this for Q8_0 dense
// projections such as shared experts and output-side small matvecs.
[[host_name("kernel_mul_mv_q8_0_f32")]]
kernel void kernel_mul_mv_q8_0_f32(
        constant ds4_metal_args_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {
    kernel_mul_mv_q8_0_f32_impl<N_R0_Q8_0, constant ds4_metal_args_mul_mv &>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg);
}

// Decode shared-expert gate/up projections followed by SwiGLU:
//
//     mid = silu(gate) * up
//
// DS4's shared expert uses two Q8_0 matrices with the same input row.  This
```

<｜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/dense.metal

```metal
shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    constexpr short NW = N_SIMDWIDTH;
    constexpr short NQ = 8;

    const int nb = args.ne00/QK8_0;

    const int r0 = tgpig.x*NR0;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

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

    const uint64_t offset1 = r1*args.nb11 + (i12)*args.nb12 + (i13)*args.nb13;

    device const float * y = (device const float *) (src1 + offset1);

    device const block_q8_0 * ax[NR0];
    FOR_UNROLL (short row = 0; row < NR0; ++row) {
        const uint64_t offset0 = (r0 + row)*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;

        ax[row] = (device const block_q8_0 *) ((device char *) src0 + offset0);
    }

    float sumf[NR0] = { 0.f };

    const short ix = tiisg/(NW/NQ);
    const short il = tiisg%(NW/NQ);

    const int ib0 = sgitg*NQ + ix;

    float yl[NQ];

    device const float * yb = y + ib0*QK8_0 + il*NQ;

    for (int ib = ib0; ib < nb; ib += NSG*NQ) {
        for (short i = 0; i < NQ; ++i) {
            yl[i] = yb[i];
        }

        for (short row = 0; row < NR0; row++) {
            device const int8_t * qs = ax[row][ib].qs + il*NQ;

            float sumq = 0.f;
            FOR_UNROLL (short i = 0; i < NQ; ++i) {
                sumq += qs[i] * yl[i];
            }

            sumf[row] += sumq*ax[row][ib].d;
        }

        yb += NSG*NQ*QK8_0;
    }

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

    helper_mv_reduce_and_write<NR0>(dst_f32, sumf, r0, args.ne01, tiisg, sgitg, shmem);
}

// Decode-time Q8_0 matrix-vector multiply. DS4 uses this for Q8_0 dense
// projections such as shared experts and output-side small matvecs.
[[host_name("kernel_mul_mv_q8_0_f32")]]
kernel void kernel_mul_mv_q8_0_f32(
        constant ds4_metal_args_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {
    kernel_mul_mv_q8_0_f32_impl<N_R0_Q8_0, constant ds4_metal_args_mul_mv &>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg);
}

// Decode shared-expert gate/up projections followed by SwiGLU:
//
//     mid = silu(gate) * up
//
// DS4's shared expert uses two Q8_0 matrices with the same input row.  This
```<｜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/dense.metal

```metal
shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    constexpr short NW = N_SIMDWIDTH;
    constexpr short NQ = 8;

    const int nb = args.ne00/QK8_0;

    const int r0 = tgpig.x*NR0;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

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

    const uint64_t offset1 = r1*args.nb11 + (i12)*args.nb12 + (i13)*args.nb13;

    device const float * y = (device const float *) (src1 + offset1);

    device const block_q8_0 * ax[NR0];
    FOR_UNROLL (short row = 0; row < NR0; ++row) {
        const uint64_t offset0 = (r0 + row)*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;

        ax[row] = (device const block_q8_0 *) ((device char *) src0 + offset0);
    }

    float sumf[NR0] = { 0.f };

    const short ix = tiisg/(NW/NQ);
    const short il = tiisg%(NW/NQ);

    const int ib0 = sgitg*NQ + ix;

    float yl[NQ];

    device const float * yb = y + ib0*QK8_0 + il*NQ;

    for (int ib = ib0; ib < nb; ib += NSG*NQ) {
        for (short i = 0; i < NQ; ++i) {
            yl[i] = yb[i];
        }

        for (short row = 0; row < NR0; row++) {
            device const int8_t * qs = ax[row][ib].qs + il*NQ;

            float sumq = 0.f;
            FOR_UNROLL (short i = 0; i < NQ; ++i) {
                sumq += qs[i] * yl[i];
            }

            sumf[row] += sumq*ax[row][ib].d;
        }

        yb += NSG*NQ*QK8_0;
    }

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

    helper_mv_reduce_and_write<NR0>(dst_f32, sumf, r0, args.ne01, tiisg, sgitg, shmem);
}

// Decode-time Q8_0 matrix-vector multiply. DS4 uses this for Q8_0 dense
// projections such as shared experts and output-side small matvecs.
[[host_name("kernel_mul_mv_q8_0_f32")]]
kernel void kernel_mul_mv_q8_0_f32(
        constant ds4_metal_args_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {
    kernel_mul_mv_q8_0_f32_impl<N_R0_Q8_0, constant ds4_metal_args_mul_mv &>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg);
}

// Decode shared-expert gate/up projections followed by SwiGLU:
//
//     mid = silu(gate) * up
//
// DS4's shared expert uses two Q8_0 matrices with the same input row.  This
```

<｜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/dense.metal

```metal
shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    constexpr short NW = N_SIMDWIDTH;
    constexpr short NQ = 8;

    const int nb = args.ne00/QK8_0;

    const int r0 = tgpig.x*NR0;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

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

    const uint64_t offset1 = r1*args.nb11 + (i12)*args.nb12 + (i13)*args.nb13;

    device const float * y = (device const float *) (src1 + offset1);

    device const block_q8_0 * ax[NR0];
    FOR_UNROLL (short row = 0; row < NR0; ++row) {
        const uint64_t offset0 = (r0 + row)*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;

        ax[row] = (device const block_q8_0 *) ((device char *) src0 + offset0);
    }

    float sumf[NR0] = { 0.f };

    const short ix = tiisg/(NW/NQ);
    const short il = tiisg%(NW/NQ);

    const int ib0 = sgitg*NQ + ix;

    float yl[NQ];

    device const float * yb = y + ib0*QK8_0 + il*NQ;

    for (int ib = ib0; ib < nb; ib += NSG*NQ) {
        for (short i = 0; i < NQ; ++i) {
            yl[i] = yb[i];
        }

        for (short row = 0; row < NR0; row++) {
            device const int8_t * qs = ax[row][ib].qs + il*NQ;

            float sumq = 0.f;
            FOR_UNROLL (short i = 0; i < NQ; ++i) {
                sumq += qs[i] * yl[i];
            }

            sumf[row] += sumq*ax[row][ib].d;
        }

        yb += NSG*NQ*QK8_0;
    }

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

    helper_mv_reduce_and_write<NR0>(dst_f32, sumf, r0, args.ne01, tiisg, sgitg, shmem);
}

// Decode-time Q8_0 matrix-vector multiply. DS4 uses this for Q8_0 dense
// projections such as shared experts and output-side small matvecs.
[[host_name("kernel_mul_mv_q8_0_f32")]]
kernel void kernel_mul_mv_q8_0_f32(
        constant ds4_metal_args_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {
    kernel_mul_mv_q8_0_f32_impl<N_R0_Q8_0, constant ds4_metal_args_mul_mv &>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg);
}

// Decode shared-expert gate/up projections followed by SwiGLU:
//
//     mid = silu(gate) * up
//
// DS4's shared expert uses two Q8_0 matrices with the same input row.  This
```<｜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/dense.metal

```metal
ushort tiisg[[thread_index_in_simdgroup]]) {
    kernel_mul_mv_t_t_short_impl<T0, T1, constant ds4_metal_args_mul_mv &>(
        args,
        src0,
        src1,
        dst,
        tgpig,
        tiisg);
}

typedef decltype(kernel_mul_mv_t_t_short<half, half>) mul_mv_t_t_short_t;

// Host-visible short-row dense matvec variants.
template [[host_name("kernel_mul_mv_f32_f32_short")]] kernel mul_mv_t_t_short_t kernel_mul_mv_t_t_short<float, float>;
template [[host_name("kernel_mul_mv_f16_f32_short")]] kernel mul_mv_t_t_short_t kernel_mul_mv_t_t_short<half,  float>;

template <typename type4x4>
void dequantize_f32(device const float4x4 * src, short il, thread type4x4 & reg) {
    reg = (type4x4)(*src);
}

template <typename type4x4>
void dequantize_f16(device const half4x4 * src, short il, thread type4x4 & reg) {
    reg = (type4x4)(*src);
}

template <typename type4x4>
void dequantize_q8_0(device const block_q8_0 *xb, short il, thread type4x4 & reg) {
    device const int8_t * qs = ((device const int8_t *)xb->qs);
    const float d = xb->d;

    float4x4 reg_f;

    for (int i = 0; i < 16; i++) {
        reg_f[i/4][i%4] = (qs[i + 16*il] * d);
    }

    reg = (type4x4) reg_f;
}

template <typename type4>
void dequantize_q8_0_t4(device const block_q8_0 *xb, short il, thread type4 & reg) {
    device const int8_t * qs = ((device const int8_t *)xb->qs);
    const float d = xb->d;

    for (int i = 0; i < 4; i++) {
        reg[i] = (qs[4*(il%4) + i + 16*(il/4)] * d);
    }
}

// DS4 small-batch mat-vec kernel used for 2..8 prompt tokens.
template<short r1ptg, typename q_t, short chpb, void (*deq_t4)(device const q_t *, short, thread float4 &) >
void kernel_mul_mv_ext_q4_f32_impl(
        constant ds4_metal_args_mul_mv_ext & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort  tiisg[[thread_index_in_simdgroup]],
        ushort  sgitg[[simdgroup_index_in_threadgroup]]) {
    const short NSG   = FC_mul_mv_nsg;
    const short nxpsg = FC_mul_mv_nxpsg;

    const short chpt = 4; // chunks per thread

    const short nypsg = (32/nxpsg);

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

    const int i01 = tgpig.x*(nypsg*NSG) + nypsg*sgitg + ty;
    const int i11 = tgpig.y*r1ptg;
    const int i1m = tgpig.z;

    const int i12 = i1m%args.ne12;
    const int i13 = i1m/args.ne12;

    const uint64_t offset0 = i01*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
```

<｜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/dense.metal

```metal
ushort tiisg[[thread_index_in_simdgroup]]) {
    kernel_mul_mv_t_t_short_impl<T0, T1, constant ds4_metal_args_mul_mv &>(
        args,
        src0,
        src1,
        dst,
        tgpig,
        tiisg);
}

typedef decltype(kernel_mul_mv_t_t_short<half, half>) mul_mv_t_t_short_t;

// Host-visible short-row dense matvec variants.
template [[host_name("kernel_mul_mv_f32_f32_short")]] kernel mul_mv_t_t_short_t kernel_mul_mv_t_t_short<float, float>;
template [[host_name("kernel_mul_mv_f16_f32_short")]] kernel mul_mv_t_t_short_t kernel_mul_mv_t_t_short<half,  float>;

template <typename type4x4>
void dequantize_f32(device const float4x4 * src, short il, thread type4x4 & reg) {
    reg = (type4x4)(*src);
}

template <typename type4x4>
void dequantize_f16(device const half4x4 * src, short il, thread type4x4 & reg) {
    reg = (type4x4)(*src);
}

template <typename type4x4>
void dequantize_q8_0(device const block_q8_0 *xb, short il, thread type4x4 & reg) {
    device const int8_t * qs = ((device const int8_t *)xb->qs);
    const float d = xb->d;

    float4x4 reg_f;

    for (int i = 0; i < 16; i++) {
        reg_f[i/4][i%4] = (qs[i + 16*il] * d);
    }

    reg = (type4x4) reg_f;
}

template <typename type4>
void dequantize_q8_0_t4(device const block_q8_0 *xb, short il, thread type4 & reg) {
    device const int8_t * qs = ((device const int8_t *)xb->qs);
    const float d = xb->d;

    for (int i = 0; i < 4; i++) {
        reg[i] = (qs[4*(il%4) + i + 16*(il/4)] * d);
    }
}

// DS4 small-batch mat-vec kernel used for 2..8 prompt tokens.
template<short r1ptg, typename q_t, short chpb, void (*deq_t4)(device const q_t *, short, thread float4 &) >
void kernel_mul_mv_ext_q4_f32_impl(
        constant ds4_metal_args_mul_mv_ext & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort  tiisg[[thread_index_in_simdgroup]],
        ushort  sgitg[[simdgroup_index_in_threadgroup]]) {
    const short NSG   = FC_mul_mv_nsg;
    const short nxpsg = FC_mul_mv_nxpsg;

    const short chpt = 4; // chunks per thread

    const short nypsg = (32/nxpsg);

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

    const int i01 = tgpig.x*(nypsg*NSG) + nypsg*sgitg + ty;
    const int i11 = tgpig.y*r1ptg;
    const int i1m = tgpig.z;

    const int i12 = i1m%args.ne12;
    const int i13 = i1m/args.ne12;

    const uint64_t offset0 = i01*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
```<｜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/dense.metal

```metal
ushort tiisg[[thread_index_in_simdgroup]]) {
    kernel_mul_mv_t_t_short_impl<T0, T1, constant ds4_metal_args_mul_mv &>(
        args,
        src0,
        src1,
        dst,
        tgpig,
        tiisg);
}

typedef decltype(kernel_mul_mv_t_t_short<half, half>) mul_mv_t_t_short_t;

// Host-visible short-row dense matvec variants.
template [[host_name("kernel_mul_mv_f32_f32_short")]] kernel mul_mv_t_t_short_t kernel_mul_mv_t_t_short<float, float>;
template [[host_name("kernel_mul_mv_f16_f32_short")]] kernel mul_mv_t_t_short_t kernel_mul_mv_t_t_short<half,  float>;

template <typename type4x4>
void dequantize_f32(device const float4x4 * src, short il, thread type4x4 & reg) {
    reg = (type4x4)(*src);
}

template <typename type4x4>
void dequantize_f16(device const half4x4 * src, short il, thread type4x4 & reg) {
    reg = (type4x4)(*src);
}

template <typename type4x4>
void dequantize_q8_0(device const block_q8_0 *xb, short il, thread type4x4 & reg) {
    device const int8_t * qs = ((device const int8_t *)xb->qs);
    const float d = xb->d;

    float4x4 reg_f;

    for (int i = 0; i < 16; i++) {
        reg_f[i/4][i%4] = (qs[i + 16*il] * d);
    }

    reg = (type4x4) reg_f;
}

template <typename type4>
void dequantize_q8_0_t4(device const block_q8_0 *xb, short il, thread type4 & reg) {
    device const int8_t * qs = ((device const int8_t *)xb->qs);
    const float d = xb->d;

    for (int i = 0; i < 4; i++) {
        reg[i] = (qs[4*(il%4) + i + 16*(il/4)] * d);
    }
}

// DS4 small-batch mat-vec kernel used for 2..8 prompt tokens.
template<short r1ptg, typename q_t, short chpb, void (*deq_t4)(device const q_t *, short, thread float4 &) >
void kernel_mul_mv_ext_q4_f32_impl(
        constant ds4_metal_args_mul_mv_ext & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort  tiisg[[thread_index_in_simdgroup]],
        ushort  sgitg[[simdgroup_index_in_threadgroup]]) {
    const short NSG   = FC_mul_mv_nsg;
    const short nxpsg = FC_mul_mv_nxpsg;

    const short chpt = 4; // chunks per thread

    const short nypsg = (32/nxpsg);

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

    const int i01 = tgpig.x*(nypsg*NSG) + nypsg*sgitg + ty;
    const int i11 = tgpig.y*r1ptg;
    const int i1m = tgpig.z;

    const int i12 = i1m%args.ne12;
    const int i13 = i1m/args.ne12;

    const uint64_t offset0 = i01*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
```

<｜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/dense.metal

```metal
ushort tiisg[[thread_index_in_simdgroup]]) {
    kernel_mul_mv_t_t_short_impl<T0, T1, constant ds4_metal_args_mul_mv &>(
        args,
        src0,
        src1,
        dst,
        tgpig,
        tiisg);
}

typedef decltype(kernel_mul_mv_t_t_short<half, half>) mul_mv_t_t_short_t;

// Host-visible short-row dense matvec variants.
template [[host_name("kernel_mul_mv_f32_f32_short")]] kernel mul_mv_t_t_short_t kernel_mul_mv_t_t_short<float, float>;
template [[host_name("kernel_mul_mv_f16_f32_short")]] kernel mul_mv_t_t_short_t kernel_mul_mv_t_t_short<half,  float>;

template <typename type4x4>
void dequantize_f32(device const float4x4 * src, short il, thread type4x4 & reg) {
    reg = (type4x4)(*src);
}

template <typename type4x4>
void dequantize_f16(device const half4x4 * src, short il, thread type4x4 & reg) {
    reg = (type4x4)(*src);
}

template <typename type4x4>
void dequantize_q8_0(device const block_q8_0 *xb, short il, thread type4x4 & reg) {
    device const int8_t * qs = ((device const int8_t *)xb->qs);
    const float d = xb->d;

    float4x4 reg_f;

    for (int i = 0; i < 16; i++) {
        reg_f[i/4][i%4] = (qs[i + 16*il] * d);
    }

    reg = (type4x4) reg_f;
}

template <typename type4>
void dequantize_q8_0_t4(device const block_q8_0 *xb, short il, thread type4 & reg) {
    device const int8_t * qs = ((device const int8_t *)xb->qs);
    const float d = xb->d;

    for (int i = 0; i < 4; i++) {
        reg[i] = (qs[4*(il%4) + i + 16*(il/4)] * d);
    }
}

// DS4 small-batch mat-vec kernel used for 2..8 prompt tokens.
template<short r1ptg, typename q_t, short chpb, void (*deq_t4)(device const q_t *, short, thread float4 &) >
void kernel_mul_mv_ext_q4_f32_impl(
        constant ds4_metal_args_mul_mv_ext & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort  tiisg[[thread_index_in_simdgroup]],
        ushort  sgitg[[simdgroup_index_in_threadgroup]]) {
    const short NSG   = FC_mul_mv_nsg;
    const short nxpsg = FC_mul_mv_nxpsg;

    const short chpt = 4; // chunks per thread

    const short nypsg = (32/nxpsg);

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

    const int i01 = tgpig.x*(nypsg*NSG) + nypsg*sgitg + ty;
    const int i11 = tgpig.y*r1ptg;
    const int i1m = tgpig.z;

    const int i12 = i1m%args.ne12;
    const int i13 = i1m/args.ne12;

    const uint64_t offset0 = i01*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
```<｜Assistant｜><think>