# Matrix Kernels

> NumKong for C

This is a separate native subsystem from the raw vector kernels.
It is the right tool when the right-hand side is reused many times.

```cpp
#include <numkong/numkong.hpp>

namespace nk = ashvardanian::numkong;

auto [a, a_status] = nk::tensor<nk::f32_t>::full({2, 4}, nk::f32_t {1});
auto [b, b_status] = nk::tensor<nk::f32_t>::full({3, 4}, nk::f32_t {2});
if (nk::failed(a_status) || nk::failed(b_status)) return nk::failed(a_status) ? a_status : b_status;
auto [packed, packed_status] = nk::packed_matrix<nk::f32_t>::make(b.as_matrix_view());
if (nk::failed(packed_status)) return packed_status;

// Dot products, angular distances, and Euclidean distances all reuse the same packed B
auto [dots, dots_status] = nk::dots_packed<nk::f32_t>(a.as_matrix_view(), packed); // nk::matrix<nk::f64_t>
auto [angulars, angulars_status] = nk::angulars_packed<nk::f32_t>(a.as_matrix_view(), packed);
auto [euclideans, euclideans_status] = nk::euclideans_packed<nk::f32_t>(a.as_matrix_view(), packed);
```

This is GEMM-like in the workload shape, not in the strict BLAS API.
The useful economics are:

- one-time packing of `B`
- one-time type preconversion where needed
- depth padding handled internally
- per-column norm reuse for `angulars_packed` and `euclideans_packed`
- repeated reuse of the same packed RHS across many `A` batches

Caller-side alignment is not required.
Owned `packed_matrix` storage uses its allocator.
The C ABI also exposes `nk_dots_pack_size_*_best`, which writes the byte count of the capability the mask picks, so you can `malloc` the exact external buffer yourself.
In C++, `nk::dots_pack_size<nk::f32_t>(rows, depth)` returns that count as an `nk::expected<std::size_t>`.
A packed buffer records the capability that packed it, and a packed kernel of another capability refuses it with `nk_pack_mismatch_k`, so pack and multiply under the same mask.

### Attention over Packed Key-Value Caches

Attention packs a ragged batch of keys and values once, then attends to it with any number of query batches.
`packed_attention` keeps the segment offsets it was packed with, so the view overloads run self-attention over `[tokens, heads, depth]` queries without restating the batch, with query heads shared across fewer key-value heads.

```cpp
#include <numkong/attention.hpp>

// Two sequences of 32 and 64 tokens, 8 query heads over 2 key-value heads of depth 64
auto [keys, keys_status] = nk::tensor<nk::bf16_t>::full({96, 2, 64}, nk::bf16_t::one());
auto [values, values_status] = nk::tensor<nk::bf16_t>::full({96, 2, 64}, nk::bf16_t::one());
auto [queries, queries_status] = nk::tensor<nk::bf16_t>::full({96, 8, 64}, nk::bf16_t::one());
auto [output, output_status] = nk::tensor<nk::f32_t>::zeros({96, 8, 64});
for (nk::status_t made : {keys_status, values_status, queries_status, output_status})
    if (nk::failed(made)) return made;
nk_u32_t const offsets[] = {0, 32, 96}, lengths[] = {32, 64};

auto [packed, packed_status] = nk::packed_attention<nk::bf16_t>::make(
    keys.view(), values.view(), nk::vector_view<nk_u32_t>(offsets, 3u), nk::vector_view<nk_u32_t>(lengths, 2u));
if (nk::failed(packed_status)) return packed_status;
std::size_t const all_keys = std::numeric_limits<std::size_t>::max(), causal = 0;
nk::status_t status = nk::attention_packed<nk::bf16_t>(queries.view(), packed, output.span(), 0.125f, all_keys, causal);
auto [fresh, fresh_status] = nk::attention_packed<nk::bf16_t>(queries.view(), packed, 0.125f); // nk::tensor<nk::f32_t>
```

Every overload takes the band of keys each query sees, `keys_before` and `keys_after` its position, every key by default.
Queries align to the end of each segment's keys, so `keys_after = 0` is causal for prefill and decode alike, and `keys_before = 4095` with it attends to at most 4096 keys per row.
The raw-pointer overloads take the query offsets separately, for cross-attention, and a window over the query tokens × heads task grid, for sharding one launch across workers.

`#include <numkong/capabilities.h>`

`#include <numkong/dots.h>`

`#include <numkong/sets.h>`

`#include <numkong/spatials.h>`

`#include <numkong/attention.h>`

`#include <numkong/types.h>`

## nk_dots_pack_size_punned_t

Pack sizes are host arithmetic, so they take no stream.

```c
typedef nk_status_t(*) nk_dots_pack_size_punned_t(nk_size_t columns, nk_size_t depth, nk_size_t *bytes);
```

## nk_sets_packed_punned_t

Bit vectors have no scaled form, so the set batches keep their unscaled shapes.

```c
typedef nk_status_t(*) nk_sets_packed_punned_t(void const *a, void const *b_packed, void *c, nk_size_t rows, nk_size_t columns, nk_size_t depth, nk_size_t a_stride, nk_size_t c_stride, void *workspace, nk_size_t workspace_bytes, nk_stream_t stream);
```

## nk_attention_pack_size_punned_t

Pack sizes are host arithmetic, so they take no stream.

```c
typedef nk_status_t(*) nk_attention_pack_size_punned_t(nk_size_t key_value_head_count, nk_size_t depth, nk_size_t token_count, nk_size_t segment_count, nk_size_t *bytes);
```

## nk_attention_packed_workspace_size_punned_t

Workspace sizes of attention and its gradients, host arithmetic like pack sizes.

```c
typedef nk_status_t(*) nk_attention_packed_workspace_size_punned_t(nk_size_t head_count, nk_size_t key_value_head_count, nk_size_t depth, nk_size_t query_token_count, nk_size_t keys_before, nk_size_t keys_after, nk_size_t *bytes);
```

## nk_diagonal_band_t

The cells of a rows × columns grid a kernel visits, by their distance from the diagonal: column c of row r is visible when r − subdiagonals ≤ c ≤ r + superdiagonals, each side unbounded at NUMKONG_SIZE_MAX, like LAPACK's kl and ku.

```c
struct nk_diagonal_band_t
```

The `symmetric` products visit the upper triangle (0, NUMKONG_SIZE_MAX), because A × Aᵀ mirrors it. Masked attention visits (keys_before, keys_after) around each query's position, because the other keys are forbidden rather than mirrored: causal attention, (NUMKONG_SIZE_MAX, 0), skips the same triangle of tiles for a different reason. So the band is a parameter of `packed` attention rather than a verb like `symmetric`, as its operands and outputs don't change.

- `subdiagonals` `nk_size_t`
- `superdiagonals` `nk_size_t`

## nk_diagonal_band_coverage_t

Where a banded grid's tile lies: no visible cell, every cell visible, or an edge across it.

```c
enum nk_diagonal_band_coverage_t
```

- `nk_diagonal_band_outside_k` = `0`
- `nk_diagonal_band_inside_k` = `1`
- `nk_diagonal_band_crossing_k` = `2`

## nk_dots_pack_size_*_best

Returns packed buffer size in bytes for second multiplier matrix (B).

```c
nk_status_t nk_dots_pack_size_bf16_best(
    nk_size_t columns,
    nk_size_t depth,
    nk_capability_t capabilities,
    nk_size_t *bytes);
```

- `nk_dots_pack_size_bf16_best`
- `nk_dots_pack_size_f16_best`
- `nk_dots_pack_size_e4m3_best`
- `nk_dots_pack_size_e5m2_best`
- `nk_dots_pack_size_e2m3_best`
- `nk_dots_pack_size_e2m1_best`
- `nk_dots_pack_size_nvfp4_best`
- `nk_dots_pack_size_mxfp4_best`
- `nk_dots_pack_size_mxfp6e2m3_best`
- `nk_dots_pack_size_mxfp6e3m2_best`
- `nk_dots_pack_size_mxfp8e4m3_best`
- `nk_dots_pack_size_mxfp8e5m2_best`
- `nk_dots_pack_size_e3m2_best`
- `nk_dots_pack_size_f32_best`
- `nk_dots_pack_size_f64_best`
- `nk_dots_pack_size_i8_best`
- `nk_dots_pack_size_u8_best`
- `nk_dots_pack_size_i4_best`
- `nk_dots_pack_size_u4_best`
- `nk_dots_pack_size_u1_best`

- `nk_dots_pack_size_bf16` backends: serial, genoa, sapphireamx, sme, haswell, skylake, v128relaxed, v128, neon, neonbfdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_pack_size_f16` backends: serial, graniteamx, sme, haswell, skylake, v128relaxed, neon, neonfhm, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_pack_size_e4m3` backends: serial, genoa, diamond, sapphireamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_pack_size_e5m2` backends: serial, genoa, diamond, sapphireamx, graniteamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_pack_size_e2m3` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_pack_size_e2m1` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_pack_size_nvfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_pack_size_mxfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_pack_size_mxfp6e2m3` backends: serial, sme, skylake, neon, neonsdot, metal, apple9, apple10
- `nk_dots_pack_size_mxfp6e3m2` backends: serial, sme, skylake, neon, metal, apple9, apple10
- `nk_dots_pack_size_mxfp8e4m3` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_pack_size_mxfp8e5m2` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_pack_size_e3m2` backends: serial, sapphireamx, sme, haswell, skylake, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_pack_size_f32` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_dots_pack_size_f64` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_dots_pack_size_i8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_pack_size_u8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_pack_size_i4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_pack_size_u4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_pack_size_u1` backends: serial, smebi32, haswell, icelake, v128, neon, powervsx, loongsonasx

- `columns` (in): The number of rows in B (output columns).
- `depth` (in): Columns in B, counting dimensions, a multiple of the values per byte.
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `bytes` (out): The size of the packed buffer.

Notes: The packed layout is backend-specific and must be produced by the matching pack function.

Statuses: - [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it.

## nk_dots_packed_shape_*_best

Reads a packed B matrix's shape from its header.

```c
nk_status_t nk_dots_packed_shape_bf16_best(
    void const *b_packed,
    nk_size_t *columns,
    nk_size_t *depth,
    nk_capability_t capabilities,
    nk_stream_t stream);
```

- `nk_dots_packed_shape_bf16_best`
- `nk_dots_packed_shape_f16_best`
- `nk_dots_packed_shape_e4m3_best`
- `nk_dots_packed_shape_e5m2_best`
- `nk_dots_packed_shape_e2m3_best`
- `nk_dots_packed_shape_e2m1_best`
- `nk_dots_packed_shape_nvfp4_best`
- `nk_dots_packed_shape_mxfp4_best`
- `nk_dots_packed_shape_mxfp6e2m3_best`
- `nk_dots_packed_shape_mxfp6e3m2_best`
- `nk_dots_packed_shape_mxfp8e4m3_best`
- `nk_dots_packed_shape_mxfp8e5m2_best`
- `nk_dots_packed_shape_e3m2_best`
- `nk_dots_packed_shape_f32_best`
- `nk_dots_packed_shape_f64_best`
- `nk_dots_packed_shape_i8_best`
- `nk_dots_packed_shape_u8_best`
- `nk_dots_packed_shape_i4_best`
- `nk_dots_packed_shape_u4_best`
- `nk_dots_packed_shape_u1_best`

- `nk_dots_packed_shape_bf16` backends: serial, genoa, sapphireamx, sme, haswell, skylake, v128relaxed, v128, neon, neonbfdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_packed_shape_f16` backends: serial, graniteamx, sme, haswell, skylake, v128relaxed, neon, neonfhm, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_packed_shape_e4m3` backends: serial, genoa, diamond, sapphireamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_packed_shape_e5m2` backends: serial, genoa, diamond, sapphireamx, graniteamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_packed_shape_e2m3` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_packed_shape_e2m1` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_packed_shape_nvfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_packed_shape_mxfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_packed_shape_mxfp6e2m3` backends: serial, sme, skylake, neon, neonsdot, metal, apple9, apple10
- `nk_dots_packed_shape_mxfp6e3m2` backends: serial, sme, skylake, neon, metal, apple9, apple10
- `nk_dots_packed_shape_mxfp8e4m3` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_packed_shape_mxfp8e5m2` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_packed_shape_e3m2` backends: serial, sapphireamx, sme, haswell, skylake, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_packed_shape_f32` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_dots_packed_shape_f64` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_dots_packed_shape_i8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_packed_shape_u8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_packed_shape_i4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_packed_shape_u4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_packed_shape_u1` backends: serial, smebi32, haswell, icelake, v128, neon, powervsx, loongsonasx

- `b_packed` (in): A buffer produced by the matching nk_dots_pack_bf16_best.
- `columns` (out): Receives the column count (B rows).
- `depth` (out): Receives the inner dimension.
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `stream` (in): Null on the CPU, or the GPU stream of that device to queue on.

Statuses: - [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it.
- [`nk_device_code_mismatch_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_device_code_mismatch_k) A GPU stream capturing a graph, which reading the header back would void.

## nk_dots_pack_*_best

Packs the second multiplier (B) matrix into a backend-specific layout.

```c
nk_status_t nk_dots_pack_bf16_best(
    nk_bf16_t const *b,
    nk_size_t columns,
    nk_size_t depth,
    nk_size_t b_stride,
    void *b_packed,
    nk_size_t columns_begin,
    nk_size_t columns_end,
    nk_capability_t capabilities,
    nk_stream_t stream);
```

- `nk_dots_pack_bf16_best`: b `nk_bf16_t`
- `nk_dots_pack_f16_best`: b `nk_f16_t`
- `nk_dots_pack_e4m3_best`: b `nk_e4m3_t`
- `nk_dots_pack_e5m2_best`: b `nk_e5m2_t`
- `nk_dots_pack_e2m3_best`: b `nk_e2m3_t`
- `nk_dots_pack_e2m1_best`: b `nk_e2m1x2_t`
- `nk_dots_pack_nvfp4_best`: b `nk_nvfp4_cref_t`
- `nk_dots_pack_mxfp4_best`: b `nk_mxfp4_cref_t`
- `nk_dots_pack_mxfp6e2m3_best`: b `nk_mxfp6e2m3_cref_t`
- `nk_dots_pack_mxfp6e3m2_best`: b `nk_mxfp6e3m2_cref_t`
- `nk_dots_pack_mxfp8e4m3_best`: b `nk_mxfp8e4m3_cref_t`
- `nk_dots_pack_mxfp8e5m2_best`: b `nk_mxfp8e5m2_cref_t`
- `nk_dots_pack_e3m2_best`: b `nk_e3m2_t`
- `nk_dots_pack_f32_best`: b `nk_f32_t`
- `nk_dots_pack_f64_best`: b `nk_f64_t`
- `nk_dots_pack_i8_best`: b `nk_i8_t`
- `nk_dots_pack_u8_best`: b `nk_u8_t`
- `nk_dots_pack_i4_best`: b `nk_i4x2_t`
- `nk_dots_pack_u4_best`: b `nk_u4x2_t`
- `nk_dots_pack_u1_best`: b `nk_u1x8_t`

- `nk_dots_pack_bf16` backends: serial, genoa, sapphireamx, sme, haswell, skylake, v128relaxed, v128, neon, neonbfdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_pack_f16` backends: serial, graniteamx, sme, haswell, skylake, v128relaxed, neon, neonfhm, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_pack_e4m3` backends: serial, genoa, diamond, sapphireamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_pack_e5m2` backends: serial, genoa, diamond, sapphireamx, graniteamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_pack_e2m3` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_pack_e2m1` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_pack_nvfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_pack_mxfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_pack_mxfp6e2m3` backends: serial, sme, skylake, neon, neonsdot, metal, apple9, apple10
- `nk_dots_pack_mxfp6e3m2` backends: serial, sme, skylake, neon, metal, apple9, apple10
- `nk_dots_pack_mxfp8e4m3` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_pack_mxfp8e5m2` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_pack_e3m2` backends: serial, sapphireamx, sme, haswell, skylake, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_pack_f32` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_dots_pack_f64` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_dots_pack_i8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_pack_u8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_pack_i4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_pack_u4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_pack_u1` backends: serial, smebi32, haswell, icelake, v128, neon, powervsx, loongsonasx

- `b` (in): The input B matrix in row-major order. Packing fuses no transposition, so a transposed B is transposed in a separate pass first.
- `columns` (in): The number of rows in B (output columns).
- `depth` (in): Columns in B, counting dimensions, a multiple of the values per byte.
- `b_stride` (in): The row stride in bytes for B.
- `b_packed` (out): The output packed buffer from nk_dots_pack_size_bf16_best.
- `columns_begin` (in): First output column to pack; 0 for a full pack.
- `columns_end` (in): One past the last output column to pack; `columns` for a full pack.
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `stream` (in): Null on the CPU, or the GPU stream of that device to queue on.

Statuses: - [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it.

Notes: Block-scaled B arrives as a reference to its first codes and scales. `b_stride` counts bytes of codes and whole blocks, and rows of scales sit `b_stride / block_bytes` apart, as `[nk_block_scaled_format_t](https://www.unum.cloud/docs/numkong/c/scalar-types.md#nk_block_scaled_format_t)` says. The pack keeps B's tensor scale and every product applies it. `depth` must be a multiple of the block size: the CPU backends assert it, and the GPU backends return [`nk_unexpected_dimensions_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_unexpected_dimensions_k).

## nk_dots_packed_workspace_size_*_best

Returns the scratch bytes that [`nk_dots_packed_bf16_best`](#nk_dots_packed_bf16_best) can use for these shapes.

```c
nk_status_t nk_dots_packed_workspace_size_bf16_best(
    nk_size_t rows,
    nk_size_t columns,
    nk_size_t depth,
    nk_capability_t capabilities,
    nk_size_t *bytes);
```

- `nk_dots_packed_workspace_size_bf16_best`
- `nk_dots_packed_workspace_size_f16_best`
- `nk_dots_packed_workspace_size_e4m3_best`
- `nk_dots_packed_workspace_size_e5m2_best`
- `nk_dots_packed_workspace_size_e2m3_best`
- `nk_dots_packed_workspace_size_e2m1_best`
- `nk_dots_packed_workspace_size_nvfp4_best`
- `nk_dots_packed_workspace_size_mxfp4_best`
- `nk_dots_packed_workspace_size_mxfp6e2m3_best`
- `nk_dots_packed_workspace_size_mxfp6e3m2_best`
- `nk_dots_packed_workspace_size_mxfp8e4m3_best`
- `nk_dots_packed_workspace_size_mxfp8e5m2_best`
- `nk_dots_packed_workspace_size_e3m2_best`
- `nk_dots_packed_workspace_size_f32_best`
- `nk_dots_packed_workspace_size_f64_best`
- `nk_dots_packed_workspace_size_i8_best`
- `nk_dots_packed_workspace_size_u8_best`
- `nk_dots_packed_workspace_size_i4_best`
- `nk_dots_packed_workspace_size_u4_best`
- `nk_dots_packed_workspace_size_u1_best`

- `nk_dots_packed_workspace_size_bf16` backends: serial, genoa, sapphireamx, sme, haswell, skylake, v128relaxed, v128, neon, neonbfdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_packed_workspace_size_f16` backends: serial, graniteamx, sme, haswell, skylake, v128relaxed, neon, neonfhm, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_packed_workspace_size_e4m3` backends: serial, genoa, diamond, sapphireamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_packed_workspace_size_e5m2` backends: serial, genoa, diamond, sapphireamx, graniteamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_packed_workspace_size_e2m3` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_packed_workspace_size_e2m1` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_packed_workspace_size_nvfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_packed_workspace_size_mxfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_packed_workspace_size_mxfp6e2m3` backends: serial, sme, skylake, neon, neonsdot, metal, apple9, apple10
- `nk_dots_packed_workspace_size_mxfp6e3m2` backends: serial, sme, skylake, neon, metal, apple9, apple10
- `nk_dots_packed_workspace_size_mxfp8e4m3` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_packed_workspace_size_mxfp8e5m2` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_packed_workspace_size_e3m2` backends: serial, sapphireamx, sme, haswell, skylake, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_packed_workspace_size_f32` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_dots_packed_workspace_size_f64` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_dots_packed_workspace_size_i8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_packed_workspace_size_u8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_packed_workspace_size_i4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_packed_workspace_size_u4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_packed_workspace_size_u1` backends: serial, smebi32, haswell, icelake, v128, neon, powervsx, loongsonasx

- `rows` (in): The number of rows in A.
- `columns` (in): The number of rows in B (output columns).
- `depth` (in): Columns in A and B, counting dimensions.
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `bytes` (out): The workspace size, zero when no scratch is needed.

Statuses: - [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it.

## nk_dots_packed_*_best

Computes C = A × Bᵀ using packed second multiplier matrix (B), accumulating into C.

```c
nk_status_t nk_dots_packed_bf16_best(
    nk_bf16_t const *a,
    void const *b_packed,
    nk_f32_t *c,
    nk_size_t rows,
    nk_size_t columns,
    nk_size_t depth,
    nk_size_t a_stride,
    nk_size_t c_stride,
    void *workspace,
    nk_size_t workspace_bytes,
    nk_capability_t capabilities,
    nk_stream_t stream);
```

- `nk_dots_packed_bf16_best`: a `nk_bf16_t`, c `nk_f32_t`
- `nk_dots_packed_f16_best`: a `nk_f16_t`, c `nk_f32_t`
- `nk_dots_packed_e4m3_best`: a `nk_e4m3_t`, c `nk_f32_t`
- `nk_dots_packed_e5m2_best`: a `nk_e5m2_t`, c `nk_f32_t`
- `nk_dots_packed_e2m3_best`: a `nk_e2m3_t`, c `nk_f32_t`
- `nk_dots_packed_e2m1_best`: a `nk_e2m1x2_t`, c `nk_f32_t`
- `nk_dots_packed_nvfp4_best`: a `nk_nvfp4_cref_t`, c `nk_f32_t`
- `nk_dots_packed_mxfp4_best`: a `nk_mxfp4_cref_t`, c `nk_f32_t`
- `nk_dots_packed_mxfp6e2m3_best`: a `nk_mxfp6e2m3_cref_t`, c `nk_f32_t`
- `nk_dots_packed_mxfp6e3m2_best`: a `nk_mxfp6e3m2_cref_t`, c `nk_f32_t`
- `nk_dots_packed_mxfp8e4m3_best`: a `nk_mxfp8e4m3_cref_t`, c `nk_f32_t`
- `nk_dots_packed_mxfp8e5m2_best`: a `nk_mxfp8e5m2_cref_t`, c `nk_f32_t`
- `nk_dots_packed_e3m2_best`: a `nk_e3m2_t`, c `nk_f32_t`
- `nk_dots_packed_f32_best`: a `nk_f32_t`, c `nk_f64_t`
- `nk_dots_packed_f64_best`: a `nk_f64_t`, c `nk_f64_t`
- `nk_dots_packed_i8_best`: a `nk_i8_t`, c `nk_i32_t`
- `nk_dots_packed_u8_best`: a `nk_u8_t`, c `nk_u32_t`
- `nk_dots_packed_i4_best`: a `nk_i4x2_t`, c `nk_i32_t`
- `nk_dots_packed_u4_best`: a `nk_u4x2_t`, c `nk_u32_t`
- `nk_dots_packed_u1_best`: a `nk_u1x8_t`, c `nk_u32_t`

- `nk_dots_packed_bf16` backends: serial, genoa, sapphireamx, sme, haswell, skylake, v128relaxed, v128, neon, neonbfdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_packed_f16` backends: serial, graniteamx, sme, haswell, skylake, v128relaxed, neon, neonfhm, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_packed_e4m3` backends: serial, genoa, diamond, sapphireamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_packed_e5m2` backends: serial, genoa, diamond, sapphireamx, graniteamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_packed_e2m3` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_packed_e2m1` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_packed_nvfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_packed_mxfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_packed_mxfp6e2m3` backends: serial, sme, skylake, neon, neonsdot, metal, apple9, apple10
- `nk_dots_packed_mxfp6e3m2` backends: serial, sme, skylake, neon, metal, apple9, apple10
- `nk_dots_packed_mxfp8e4m3` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_packed_mxfp8e5m2` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_packed_e3m2` backends: serial, sapphireamx, sme, haswell, skylake, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_packed_f32` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_dots_packed_f64` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_dots_packed_i8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_packed_u8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_packed_i4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_packed_u4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_packed_u1` backends: serial, smebi32, haswell, icelake, v128, neon, powervsx, loongsonasx

- `a` (in): The input A matrix in row-major order.
- `b_packed` (in): The packed B matrix produced.
- `c` (out): The output C matrix in row-major order.
- `rows` (in): The number of rows in A.
- `columns` (in): The number of rows in B (output columns).
- `depth` (in): Columns in A and B, counting dimensions, a multiple of the values per byte.
- `a_stride` (in): The row stride in bytes for A.
- `c_stride` (in): The row stride in bytes for C.
- `workspace` (in): Scratch memory aligned to `nk_default_alignment_k`, device memory ordered by `stream` for GPU capabilities. Null with zero bytes selects the scratch-free path.
- `workspace_bytes` (in): At least what [`nk_dots_packed_workspace_size_bf16_best`](#nk_dots_packed_workspace_size_bf16_best) reports, or zero. Anything between zero and that size returns [`nk_unexpected_dimensions_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_unexpected_dimensions_k).
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `stream` (in): Null on the CPU, or the GPU stream of that device to queue on.

Statuses: - [`nk_misaligned_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_misaligned_k) A misaligned `workspace`.
- [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it.

Notes: Block-scaled A arrives as a reference, laid out as [`nk_dots_pack_nvfp4_best`](#nk_dots_pack_nvfp4_best) describes for B, and C holds true values, so every product takes the block scales and the tensor scales of both operands.

## nk_dots_symmetric_workspace_size_*_best

Returns the scratch bytes that [`nk_dots_symmetric_bf16_best`](#nk_dots_symmetric_bf16_best) can use for these shapes.

```c
nk_status_t nk_dots_symmetric_workspace_size_bf16_best(
    nk_size_t vector_count,
    nk_size_t depth,
    nk_size_t rows_begin,
    nk_size_t rows_end,
    nk_capability_t capabilities,
    nk_size_t *bytes);
```

- `nk_dots_symmetric_workspace_size_bf16_best`
- `nk_dots_symmetric_workspace_size_f16_best`
- `nk_dots_symmetric_workspace_size_e4m3_best`
- `nk_dots_symmetric_workspace_size_e5m2_best`
- `nk_dots_symmetric_workspace_size_e2m3_best`
- `nk_dots_symmetric_workspace_size_e2m1_best`
- `nk_dots_symmetric_workspace_size_nvfp4_best`
- `nk_dots_symmetric_workspace_size_mxfp4_best`
- `nk_dots_symmetric_workspace_size_mxfp6e2m3_best`
- `nk_dots_symmetric_workspace_size_mxfp6e3m2_best`
- `nk_dots_symmetric_workspace_size_mxfp8e4m3_best`
- `nk_dots_symmetric_workspace_size_mxfp8e5m2_best`
- `nk_dots_symmetric_workspace_size_e3m2_best`
- `nk_dots_symmetric_workspace_size_f32_best`
- `nk_dots_symmetric_workspace_size_f64_best`
- `nk_dots_symmetric_workspace_size_i8_best`
- `nk_dots_symmetric_workspace_size_u8_best`
- `nk_dots_symmetric_workspace_size_i4_best`
- `nk_dots_symmetric_workspace_size_u4_best`
- `nk_dots_symmetric_workspace_size_u1_best`

- `nk_dots_symmetric_workspace_size_bf16` backends: serial, genoa, sapphireamx, sme, haswell, skylake, v128relaxed, v128, neon, neonbfdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_symmetric_workspace_size_f16` backends: serial, graniteamx, sme, haswell, skylake, v128relaxed, neon, neonfhm, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_symmetric_workspace_size_e4m3` backends: serial, genoa, diamond, sapphireamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_symmetric_workspace_size_e5m2` backends: serial, genoa, diamond, sapphireamx, graniteamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_symmetric_workspace_size_e2m3` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_symmetric_workspace_size_e2m1` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_symmetric_workspace_size_nvfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_symmetric_workspace_size_mxfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_symmetric_workspace_size_mxfp6e2m3` backends: serial, sme, skylake, neon, neonsdot, metal, apple9, apple10
- `nk_dots_symmetric_workspace_size_mxfp6e3m2` backends: serial, sme, skylake, neon, metal, apple9, apple10
- `nk_dots_symmetric_workspace_size_mxfp8e4m3` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_symmetric_workspace_size_mxfp8e5m2` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_symmetric_workspace_size_e3m2` backends: serial, sapphireamx, sme, haswell, skylake, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_symmetric_workspace_size_f32` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_dots_symmetric_workspace_size_f64` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_dots_symmetric_workspace_size_i8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_symmetric_workspace_size_u8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_symmetric_workspace_size_i4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_symmetric_workspace_size_u4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_symmetric_workspace_size_u1` backends: serial, smebi32, haswell, icelake, v128, neon, powervsx, loongsonasx

- `vector_count` (in): Number of vectors (rows) in the input matrix.
- `depth` (in): Counts dimensions.
- `rows_begin` (in): First result row to compute.
- `rows_end` (in): Result row after the last to compute, clamped to `vector_count`.
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `bytes` (out): The workspace size, zero when no scratch is needed.

Statuses: - [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it.

## nk_dots_symmetric_*_best

Computes C = A × Aᵀ symmetric Gram matrix.

```c
nk_status_t nk_dots_symmetric_bf16_best(
    nk_bf16_t const *vectors,
    nk_size_t vector_count,
    nk_size_t depth,
    nk_size_t stride,
    nk_f32_t *result,
    nk_size_t result_stride,
    nk_size_t rows_begin,
    nk_size_t rows_end,
    void *workspace,
    nk_size_t workspace_bytes,
    nk_capability_t capabilities,
    nk_stream_t stream);
```

- `nk_dots_symmetric_bf16_best`: vectors `nk_bf16_t`, result `nk_f32_t`
- `nk_dots_symmetric_f16_best`: vectors `nk_f16_t`, result `nk_f32_t`
- `nk_dots_symmetric_e4m3_best`: vectors `nk_e4m3_t`, result `nk_f32_t`
- `nk_dots_symmetric_e5m2_best`: vectors `nk_e5m2_t`, result `nk_f32_t`
- `nk_dots_symmetric_e2m3_best`: vectors `nk_e2m3_t`, result `nk_f32_t`
- `nk_dots_symmetric_e2m1_best`: vectors `nk_e2m1x2_t`, result `nk_f32_t`
- `nk_dots_symmetric_nvfp4_best`: vectors `nk_nvfp4_cref_t`, result `nk_f32_t`
- `nk_dots_symmetric_mxfp4_best`: vectors `nk_mxfp4_cref_t`, result `nk_f32_t`
- `nk_dots_symmetric_mxfp6e2m3_best`: vectors `nk_mxfp6e2m3_cref_t`, result `nk_f32_t`
- `nk_dots_symmetric_mxfp6e3m2_best`: vectors `nk_mxfp6e3m2_cref_t`, result `nk_f32_t`
- `nk_dots_symmetric_mxfp8e4m3_best`: vectors `nk_mxfp8e4m3_cref_t`, result `nk_f32_t`
- `nk_dots_symmetric_mxfp8e5m2_best`: vectors `nk_mxfp8e5m2_cref_t`, result `nk_f32_t`
- `nk_dots_symmetric_e3m2_best`: vectors `nk_e3m2_t`, result `nk_f32_t`
- `nk_dots_symmetric_f32_best`: vectors `nk_f32_t`, result `nk_f64_t`
- `nk_dots_symmetric_f64_best`: vectors `nk_f64_t`, result `nk_f64_t`
- `nk_dots_symmetric_i8_best`: vectors `nk_i8_t`, result `nk_i32_t`
- `nk_dots_symmetric_u8_best`: vectors `nk_u8_t`, result `nk_u32_t`
- `nk_dots_symmetric_i4_best`: vectors `nk_i4x2_t`, result `nk_i32_t`
- `nk_dots_symmetric_u4_best`: vectors `nk_u4x2_t`, result `nk_u32_t`
- `nk_dots_symmetric_u1_best`: vectors `nk_u1x8_t`, result `nk_u32_t`

- `nk_dots_symmetric_bf16` backends: serial, genoa, sapphireamx, sme, haswell, skylake, v128relaxed, v128, neon, neonbfdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_symmetric_f16` backends: serial, graniteamx, sme, haswell, skylake, v128relaxed, neon, neonfhm, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_symmetric_e4m3` backends: serial, genoa, diamond, sapphireamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_symmetric_e5m2` backends: serial, genoa, diamond, sapphireamx, graniteamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_symmetric_e2m3` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_symmetric_e2m1` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_symmetric_nvfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_symmetric_mxfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_symmetric_mxfp6e2m3` backends: serial, sme, skylake, neon, neonsdot, metal, apple9, apple10
- `nk_dots_symmetric_mxfp6e3m2` backends: serial, sme, skylake, neon, metal, apple9, apple10
- `nk_dots_symmetric_mxfp8e4m3` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_symmetric_mxfp8e5m2` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, ampere, hopper, blackwell, metal, apple9, apple10
- `nk_dots_symmetric_e3m2` backends: serial, sapphireamx, sme, haswell, skylake, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_dots_symmetric_f32` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_dots_symmetric_f64` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_dots_symmetric_i8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_symmetric_u8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_symmetric_i4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_symmetric_u4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_dots_symmetric_u1` backends: serial, smebi32, haswell, icelake, v128, neon, powervsx, loongsonasx

Visits the upper triangle, the band (0, NUMKONG_SIZE_MAX) of `[nk_diagonal_band_t](#nk_diagonal_band_t)`.

- `vectors` (in): Input matrix of row vectors in row-major order.
- `vector_count` (in): Number of vectors (rows) in the input matrix.
- `depth` (in): Counts dimensions, a multiple of the values per byte.
- `stride` (in): Row stride in bytes for the input matrix.
- `result` (out): Output symmetric matrix of `vector_count` × `vector_count`.
- `result_stride` (in): Row stride in bytes for the result matrix.
- `rows_begin` (in): First result row to compute, so threads split the work by rows.
- `rows_end` (in): Result row after the last to compute, clamped to `vector_count`.
- `workspace` (in): Scratch memory aligned to `nk_default_alignment_k`, device memory ordered by `stream` for GPU capabilities. Null with zero bytes selects the scratch-free path.
- `workspace_bytes` (in): At least what [`nk_dots_symmetric_workspace_size_bf16_best`](#nk_dots_symmetric_workspace_size_bf16_best) reports, or zero. Anything between zero and that size returns [`nk_unexpected_dimensions_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_unexpected_dimensions_k).
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `stream` (in): Null on the CPU, or the GPU stream of that device to queue on.

Statuses: - [`nk_misaligned_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_misaligned_k) A misaligned `workspace`.
- [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it.

## nk_*_find_kernel

Finds the dots kernel of `kind` for `dtype`, from the best of `capabilities`.

```c
nk_status_t nk_dots_find_kernel(
    nk_kernel_kind_t kind,
    nk_dtype_t dtype,
    nk_capability_t capabilities,
    nk_kernel_punned_t *kernel,
    nk_capability_t *capability);
```

- `nk_dots_find_kernel`
- `nk_sets_find_kernel`
- `nk_spatials_find_kernel`
- `nk_attention_find_kernel`

- `kind` (in): The verb whose kernel to find.
- `dtype` (in): The input type the kernel reads.
- `capabilities` (in): The mask to pick the best capability from.
- `kernel` (out): The kernel, or null when none of `capabilities` has it.
- `capability` (out): The capability the kernel belongs to, or zero.

Statuses: - [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k)
- [`nk_missing_library_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_library_k) Header-only.

## nk_hammings_packed_u1_best

Compute Hamming distances between V rows and packed Q rows.

```c
nk_status_t nk_hammings_packed_u1_best(
    nk_u1x8_t const *v,
    void const *query_packed,
    nk_u32_t *result,
    nk_size_t rows,
    nk_size_t columns,
    nk_size_t d,
    nk_size_t v_stride,
    nk_size_t r_stride,
    void *workspace,
    nk_size_t workspace_bytes,
    nk_capability_t capabilities,
    nk_stream_t stream);
```

- `nk_hammings_packed_u1` backends: serial, smebi32, haswell, icelake, neon, v128, powervsx, loongsonasx

- `v` (in): Input values matrix
- `query_packed` (in): Packed queries matrix
- `result` (out): Row-major results matrix
- `rows` (in): Number of rows in the results matrix
- `columns` (in): Number of columns in the results matrix
- `d` (in): Counts dimensions, a multiple of the values per byte.
- `v_stride` (in): Byte stride between rows of A
- `r_stride` (in): Byte stride between rows of C
- `workspace` (in): Scratch aligned to `nk_default_alignment_k`, or null with zero bytes.
- `workspace_bytes` (in): At least what the matching workspace-size query reports, or zero.
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `stream` (in): Null on the CPU, or the GPU stream of that device to queue on.

Statuses: - [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it.

## nk_hammings_symmetric_u1_best

Computes C = A × Aᵀ symmetric Gram matrix of Hamming distances.

```c
nk_status_t nk_hammings_symmetric_u1_best(
    nk_u1x8_t const *vectors,
    nk_size_t vector_count,
    nk_size_t d,
    nk_size_t stride,
    nk_u32_t *result,
    nk_size_t result_stride,
    nk_size_t rows_begin,
    nk_size_t rows_end,
    void *workspace,
    nk_size_t workspace_bytes,
    nk_capability_t capabilities,
    nk_stream_t stream);
```

- `nk_hammings_symmetric_u1` backends: serial, smebi32, haswell, icelake, neon, v128, powervsx, loongsonasx

- `vectors` (in): Input matrix of row vectors in row-major order.
- `vector_count` (in): Number of vectors (rows) in the input matrix.
- `d` (in): Counts dimensions, a multiple of the values per byte.
- `stride` (in): Row stride in bytes for the input matrix.
- `result` (out): Output symmetric matrix of `vector_count` × `vector_count`.
- `result_stride` (in): Row stride in bytes for the result matrix.
- `rows_begin` (in): First result row to compute, so threads split the work by rows.
- `rows_end` (in): Result row after the last to compute, clamped to `vector_count`.
- `workspace` (in): Scratch aligned to `nk_default_alignment_k`, or null with zero bytes.
- `workspace_bytes` (in): At least what the matching workspace-size query reports, or zero.
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `stream` (in): Null on the CPU, or the GPU stream of that device to queue on.

Statuses: - [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it.

## nk_jaccards_packed_u1_best

Compute Jaccard distances between V rows and packed Q rows.

```c
nk_status_t nk_jaccards_packed_u1_best(
    nk_u1x8_t const *v,
    void const *query_packed,
    nk_f32_t *result,
    nk_size_t rows,
    nk_size_t columns,
    nk_size_t d,
    nk_size_t v_stride,
    nk_size_t r_stride,
    void *workspace,
    nk_size_t workspace_bytes,
    nk_capability_t capabilities,
    nk_stream_t stream);
```

- `nk_jaccards_packed_u1` backends: serial, smebi32, haswell, icelake, neon, v128, powervsx, loongsonasx

- `v` (in): Input values matrix
- `query_packed` (in): Packed queries matrix (with norms)
- `result` (out): Row-major f32 results matrix
- `rows` (in): Number of rows in the results matrix
- `columns` (in): Number of columns in the results matrix
- `d` (in): Counts dimensions, a multiple of the values per byte.
- `v_stride` (in): Byte stride between rows of A
- `r_stride` (in): Byte stride between rows of C
- `workspace` (in): Scratch aligned to `nk_default_alignment_k`, or null with zero bytes.
- `workspace_bytes` (in): At least what the matching workspace-size query reports, or zero.
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `stream` (in): Null on the CPU, or the GPU stream of that device to queue on.

Statuses: - [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it.

## nk_jaccards_symmetric_u1_best

Computes C = f(A, Aᵀ) symmetric Gram matrix of Jaccard distances.

```c
nk_status_t nk_jaccards_symmetric_u1_best(
    nk_u1x8_t const *vectors,
    nk_size_t vector_count,
    nk_size_t d,
    nk_size_t stride,
    nk_f32_t *result,
    nk_size_t result_stride,
    nk_size_t rows_begin,
    nk_size_t rows_end,
    void *workspace,
    nk_size_t workspace_bytes,
    nk_capability_t capabilities,
    nk_stream_t stream);
```

- `nk_jaccards_symmetric_u1` backends: serial, smebi32, haswell, icelake, neon, v128, powervsx, loongsonasx

- `vectors` (in): Input matrix of row vectors in row-major order.
- `vector_count` (in): Number of vectors (rows).
- `d` (in): Counts dimensions, a multiple of the values per byte.
- `stride` (in): Row stride in bytes.
- `result` (out): Output symmetric f32 matrix of `vector_count` × `vector_count`.
- `result_stride` (in): Row stride in bytes for the result matrix.
- `rows_begin` (in): First result row to compute, so threads split the work by rows.
- `rows_end` (in): Result row after the last to compute, clamped to `vector_count`.
- `workspace` (in): Scratch aligned to `nk_default_alignment_k`, or null with zero bytes.
- `workspace_bytes` (in): At least what the matching workspace-size query reports, or zero.
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `stream` (in): Null on the CPU, or the GPU stream of that device to queue on.

Statuses: - [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it.

## nk_*_packed_workspace_size_u1_best

Returns the workspace bytes of [`nk_hammings_packed_u1_best`](#nk_hammings_packed_u1_best) for these shapes.

```c
nk_status_t nk_hammings_packed_workspace_size_u1_best(
    nk_size_t rows,
    nk_size_t columns,
    nk_size_t d,
    nk_capability_t capabilities,
    nk_size_t *bytes);
```

- `nk_hammings_packed_workspace_size_u1_best`
- `nk_jaccards_packed_workspace_size_u1_best`

- `nk_hammings_packed_workspace_size_u1` backends: serial, smebi32, haswell, icelake, neon, v128, powervsx, loongsonasx
- `nk_jaccards_packed_workspace_size_u1` backends: serial, smebi32, haswell, icelake, neon, v128, powervsx, loongsonasx

- `rows` (in): Number of rows in the results matrix
- `columns` (in): Number of columns in the results matrix
- `d` (in): Counts dimensions, a multiple of the values per byte.
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `bytes` (out): The scratch the fast path takes, zero when the kernel needs none.

## nk_*_symmetric_workspace_size_u1_best

Returns the workspace bytes of [`nk_hammings_symmetric_u1_best`](#nk_hammings_symmetric_u1_best) for these shapes.

```c
nk_status_t nk_hammings_symmetric_workspace_size_u1_best(
    nk_size_t vector_count,
    nk_size_t d,
    nk_size_t rows_begin,
    nk_size_t rows_end,
    nk_capability_t capabilities,
    nk_size_t *bytes);
```

- `nk_hammings_symmetric_workspace_size_u1_best`
- `nk_jaccards_symmetric_workspace_size_u1_best`

- `nk_hammings_symmetric_workspace_size_u1` backends: serial, smebi32, haswell, icelake, neon, v128, powervsx, loongsonasx
- `nk_jaccards_symmetric_workspace_size_u1` backends: serial, smebi32, haswell, icelake, neon, v128, powervsx, loongsonasx

- `vector_count` (in): Number of vectors (rows) in the input matrix.
- `d` (in): Counts dimensions, a multiple of the values per byte.
- `rows_begin` (in): First result row to compute.
- `rows_end` (in): Result row after the last to compute.
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `bytes` (out): The scratch the fast path takes, zero when the kernel needs none.

## nk_angulars_packed_workspace_size_*_best

Returns the workspace bytes of [`nk_angulars_packed_f32_best`](#nk_angulars_packed_f32_best) for one shape.

```c
nk_status_t nk_angulars_packed_workspace_size_f32_best(
    nk_size_t rows,
    nk_size_t columns,
    nk_size_t depth,
    nk_capability_t capabilities,
    nk_size_t *bytes);
```

- `nk_angulars_packed_workspace_size_f32_best`
- `nk_angulars_packed_workspace_size_f64_best`
- `nk_angulars_packed_workspace_size_f16_best`
- `nk_angulars_packed_workspace_size_bf16_best`
- `nk_angulars_packed_workspace_size_e4m3_best`
- `nk_angulars_packed_workspace_size_e5m2_best`
- `nk_angulars_packed_workspace_size_e2m3_best`
- `nk_angulars_packed_workspace_size_e2m1_best`
- `nk_angulars_packed_workspace_size_nvfp4_best`
- `nk_angulars_packed_workspace_size_mxfp4_best`
- `nk_angulars_packed_workspace_size_mxfp6e2m3_best`
- `nk_angulars_packed_workspace_size_mxfp6e3m2_best`
- `nk_angulars_packed_workspace_size_mxfp8e4m3_best`
- `nk_angulars_packed_workspace_size_mxfp8e5m2_best`
- `nk_angulars_packed_workspace_size_e3m2_best`
- `nk_angulars_packed_workspace_size_i8_best`
- `nk_angulars_packed_workspace_size_u8_best`
- `nk_angulars_packed_workspace_size_i4_best`
- `nk_angulars_packed_workspace_size_u4_best`

- `nk_angulars_packed_workspace_size_f32` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_angulars_packed_workspace_size_f64` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_angulars_packed_workspace_size_f16` backends: serial, graniteamx, sme, haswell, skylake, v128relaxed, neon, neonfhm, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_packed_workspace_size_bf16` backends: serial, genoa, sapphireamx, sme, haswell, skylake, v128relaxed, v128, neon, neonbfdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_packed_workspace_size_e4m3` backends: serial, genoa, diamond, sapphireamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_packed_workspace_size_e5m2` backends: serial, genoa, diamond, sapphireamx, graniteamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_packed_workspace_size_e2m3` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_packed_workspace_size_e2m1` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_packed_workspace_size_nvfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, blackwell, metal, apple9, apple10
- `nk_angulars_packed_workspace_size_mxfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, blackwell, metal, apple9, apple10
- `nk_angulars_packed_workspace_size_mxfp6e2m3` backends: serial, sme, skylake, neon, neonsdot, metal, apple9, apple10
- `nk_angulars_packed_workspace_size_mxfp6e3m2` backends: serial, sme, skylake, neon, metal, apple9, apple10
- `nk_angulars_packed_workspace_size_mxfp8e4m3` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, blackwell, metal, apple9, apple10
- `nk_angulars_packed_workspace_size_mxfp8e5m2` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, blackwell, metal, apple9, apple10
- `nk_angulars_packed_workspace_size_e3m2` backends: serial, sapphireamx, sme, haswell, skylake, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_packed_workspace_size_i8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_angulars_packed_workspace_size_u8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_angulars_packed_workspace_size_i4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_angulars_packed_workspace_size_u4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10

- `rows` (in): Number of rows in A.
- `columns` (in): Number of columns in B (packed).
- `depth` (in): Shared inner dimension in dimensions.
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `bytes` (out): The scratch size, 0 when the capability needs none.

Statuses: - [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it.

## nk_angulars_symmetric_workspace_size_*_best

Returns the workspace bytes of [`nk_angulars_symmetric_f32_best`](#nk_angulars_symmetric_f32_best) for one shape.

```c
nk_status_t nk_angulars_symmetric_workspace_size_f32_best(
    nk_size_t vector_count,
    nk_size_t depth,
    nk_size_t rows_begin,
    nk_size_t rows_end,
    nk_capability_t capabilities,
    nk_size_t *bytes);
```

- `nk_angulars_symmetric_workspace_size_f32_best`
- `nk_angulars_symmetric_workspace_size_f64_best`
- `nk_angulars_symmetric_workspace_size_f16_best`
- `nk_angulars_symmetric_workspace_size_bf16_best`
- `nk_angulars_symmetric_workspace_size_e4m3_best`
- `nk_angulars_symmetric_workspace_size_e5m2_best`
- `nk_angulars_symmetric_workspace_size_e2m3_best`
- `nk_angulars_symmetric_workspace_size_e2m1_best`
- `nk_angulars_symmetric_workspace_size_nvfp4_best`
- `nk_angulars_symmetric_workspace_size_mxfp4_best`
- `nk_angulars_symmetric_workspace_size_mxfp6e2m3_best`
- `nk_angulars_symmetric_workspace_size_mxfp6e3m2_best`
- `nk_angulars_symmetric_workspace_size_mxfp8e4m3_best`
- `nk_angulars_symmetric_workspace_size_mxfp8e5m2_best`
- `nk_angulars_symmetric_workspace_size_e3m2_best`
- `nk_angulars_symmetric_workspace_size_i8_best`
- `nk_angulars_symmetric_workspace_size_u8_best`
- `nk_angulars_symmetric_workspace_size_i4_best`
- `nk_angulars_symmetric_workspace_size_u4_best`

- `nk_angulars_symmetric_workspace_size_f32` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_angulars_symmetric_workspace_size_f64` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_angulars_symmetric_workspace_size_f16` backends: serial, graniteamx, sme, haswell, skylake, v128relaxed, neon, neonfhm, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_symmetric_workspace_size_bf16` backends: serial, genoa, sapphireamx, sme, haswell, skylake, v128relaxed, v128, neon, neonbfdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_symmetric_workspace_size_e4m3` backends: serial, genoa, diamond, sapphireamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_symmetric_workspace_size_e5m2` backends: serial, genoa, diamond, sapphireamx, graniteamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_symmetric_workspace_size_e2m3` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_symmetric_workspace_size_e2m1` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_symmetric_workspace_size_nvfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, blackwell, metal, apple9, apple10
- `nk_angulars_symmetric_workspace_size_mxfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, blackwell, metal, apple9, apple10
- `nk_angulars_symmetric_workspace_size_mxfp6e2m3` backends: serial, sme, skylake, neon, neonsdot, metal, apple9, apple10
- `nk_angulars_symmetric_workspace_size_mxfp6e3m2` backends: serial, sme, skylake, neon, metal, apple9, apple10
- `nk_angulars_symmetric_workspace_size_mxfp8e4m3` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, blackwell, metal, apple9, apple10
- `nk_angulars_symmetric_workspace_size_mxfp8e5m2` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, blackwell, metal, apple9, apple10
- `nk_angulars_symmetric_workspace_size_e3m2` backends: serial, sapphireamx, sme, haswell, skylake, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_symmetric_workspace_size_i8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_angulars_symmetric_workspace_size_u8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_angulars_symmetric_workspace_size_i4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_angulars_symmetric_workspace_size_u4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10

- `vector_count` (in): Number of vectors (rows) in the input matrix.
- `depth` (in): Counts dimensions.
- `rows_begin` (in): First row of results to compute.
- `rows_end` (in): One past the last row of results to compute.
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `bytes` (out): The scratch size, 0 when the capability needs none.

Statuses: - [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it.

## nk_euclideans_packed_workspace_size_*_best

Returns the workspace bytes of [`nk_euclideans_packed_f32_best`](#nk_euclideans_packed_f32_best) for one shape.

```c
nk_status_t nk_euclideans_packed_workspace_size_f32_best(
    nk_size_t rows,
    nk_size_t columns,
    nk_size_t depth,
    nk_capability_t capabilities,
    nk_size_t *bytes);
```

- `nk_euclideans_packed_workspace_size_f32_best`
- `nk_euclideans_packed_workspace_size_f64_best`
- `nk_euclideans_packed_workspace_size_f16_best`
- `nk_euclideans_packed_workspace_size_bf16_best`
- `nk_euclideans_packed_workspace_size_e4m3_best`
- `nk_euclideans_packed_workspace_size_e5m2_best`
- `nk_euclideans_packed_workspace_size_e2m3_best`
- `nk_euclideans_packed_workspace_size_e2m1_best`
- `nk_euclideans_packed_workspace_size_nvfp4_best`
- `nk_euclideans_packed_workspace_size_mxfp4_best`
- `nk_euclideans_packed_workspace_size_mxfp6e2m3_best`
- `nk_euclideans_packed_workspace_size_mxfp6e3m2_best`
- `nk_euclideans_packed_workspace_size_mxfp8e4m3_best`
- `nk_euclideans_packed_workspace_size_mxfp8e5m2_best`
- `nk_euclideans_packed_workspace_size_e3m2_best`
- `nk_euclideans_packed_workspace_size_i8_best`
- `nk_euclideans_packed_workspace_size_u8_best`
- `nk_euclideans_packed_workspace_size_i4_best`
- `nk_euclideans_packed_workspace_size_u4_best`

- `nk_euclideans_packed_workspace_size_f32` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_euclideans_packed_workspace_size_f64` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_euclideans_packed_workspace_size_f16` backends: serial, graniteamx, sme, haswell, skylake, v128relaxed, neon, neonfhm, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_packed_workspace_size_bf16` backends: serial, genoa, sapphireamx, sme, haswell, skylake, v128relaxed, v128, neon, neonbfdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_packed_workspace_size_e4m3` backends: serial, genoa, diamond, sapphireamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_packed_workspace_size_e5m2` backends: serial, genoa, diamond, sapphireamx, graniteamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_packed_workspace_size_e2m3` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_packed_workspace_size_e2m1` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_packed_workspace_size_nvfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, blackwell, metal, apple9, apple10
- `nk_euclideans_packed_workspace_size_mxfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, blackwell, metal, apple9, apple10
- `nk_euclideans_packed_workspace_size_mxfp6e2m3` backends: serial, sme, skylake, neon, neonsdot, metal, apple9, apple10
- `nk_euclideans_packed_workspace_size_mxfp6e3m2` backends: serial, sme, skylake, neon, metal, apple9, apple10
- `nk_euclideans_packed_workspace_size_mxfp8e4m3` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, blackwell, metal, apple9, apple10
- `nk_euclideans_packed_workspace_size_mxfp8e5m2` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, blackwell, metal, apple9, apple10
- `nk_euclideans_packed_workspace_size_e3m2` backends: serial, sapphireamx, sme, haswell, skylake, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_packed_workspace_size_i8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_euclideans_packed_workspace_size_u8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_euclideans_packed_workspace_size_i4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_euclideans_packed_workspace_size_u4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10

- `rows` (in): Number of rows in A.
- `columns` (in): Number of columns in B (packed).
- `depth` (in): Shared inner dimension in dimensions.
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `bytes` (out): The scratch size, 0 when the capability needs none.

Statuses: - [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it.

## nk_euclideans_symmetric_workspace_size_*_best

Returns the workspace bytes of [`nk_euclideans_symmetric_f32_best`](#nk_euclideans_symmetric_f32_best) for one shape.

```c
nk_status_t nk_euclideans_symmetric_workspace_size_f32_best(
    nk_size_t vector_count,
    nk_size_t depth,
    nk_size_t rows_begin,
    nk_size_t rows_end,
    nk_capability_t capabilities,
    nk_size_t *bytes);
```

- `nk_euclideans_symmetric_workspace_size_f32_best`
- `nk_euclideans_symmetric_workspace_size_f64_best`
- `nk_euclideans_symmetric_workspace_size_f16_best`
- `nk_euclideans_symmetric_workspace_size_bf16_best`
- `nk_euclideans_symmetric_workspace_size_e4m3_best`
- `nk_euclideans_symmetric_workspace_size_e5m2_best`
- `nk_euclideans_symmetric_workspace_size_e2m3_best`
- `nk_euclideans_symmetric_workspace_size_e2m1_best`
- `nk_euclideans_symmetric_workspace_size_nvfp4_best`
- `nk_euclideans_symmetric_workspace_size_mxfp4_best`
- `nk_euclideans_symmetric_workspace_size_mxfp6e2m3_best`
- `nk_euclideans_symmetric_workspace_size_mxfp6e3m2_best`
- `nk_euclideans_symmetric_workspace_size_mxfp8e4m3_best`
- `nk_euclideans_symmetric_workspace_size_mxfp8e5m2_best`
- `nk_euclideans_symmetric_workspace_size_e3m2_best`
- `nk_euclideans_symmetric_workspace_size_i8_best`
- `nk_euclideans_symmetric_workspace_size_u8_best`
- `nk_euclideans_symmetric_workspace_size_i4_best`
- `nk_euclideans_symmetric_workspace_size_u4_best`

- `nk_euclideans_symmetric_workspace_size_f32` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_euclideans_symmetric_workspace_size_f64` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_euclideans_symmetric_workspace_size_f16` backends: serial, graniteamx, sme, haswell, skylake, v128relaxed, neon, neonfhm, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_symmetric_workspace_size_bf16` backends: serial, genoa, sapphireamx, sme, haswell, skylake, v128relaxed, v128, neon, neonbfdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_symmetric_workspace_size_e4m3` backends: serial, genoa, diamond, sapphireamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_symmetric_workspace_size_e5m2` backends: serial, genoa, diamond, sapphireamx, graniteamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_symmetric_workspace_size_e2m3` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_symmetric_workspace_size_e2m1` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_symmetric_workspace_size_nvfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, blackwell, metal, apple9, apple10
- `nk_euclideans_symmetric_workspace_size_mxfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, blackwell, metal, apple9, apple10
- `nk_euclideans_symmetric_workspace_size_mxfp6e2m3` backends: serial, sme, skylake, neon, neonsdot, metal, apple9, apple10
- `nk_euclideans_symmetric_workspace_size_mxfp6e3m2` backends: serial, sme, skylake, neon, metal, apple9, apple10
- `nk_euclideans_symmetric_workspace_size_mxfp8e4m3` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, blackwell, metal, apple9, apple10
- `nk_euclideans_symmetric_workspace_size_mxfp8e5m2` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, blackwell, metal, apple9, apple10
- `nk_euclideans_symmetric_workspace_size_e3m2` backends: serial, sapphireamx, sme, haswell, skylake, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_symmetric_workspace_size_i8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_euclideans_symmetric_workspace_size_u8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_euclideans_symmetric_workspace_size_i4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_euclideans_symmetric_workspace_size_u4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10

- `vector_count` (in): Number of vectors (rows) in the input matrix.
- `depth` (in): Counts dimensions.
- `rows_begin` (in): First row of results to compute.
- `rows_end` (in): One past the last row of results to compute.
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `bytes` (out): The scratch size, 0 when the capability needs none.

Statuses: - [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it.

## nk_angulars_packed_*_best

Computes batched angular distances using a packed second matrix.

```c
nk_status_t nk_angulars_packed_f32_best(
    nk_f32_t const *a,
    void const *b_packed,
    nk_f64_t *result,
    nk_size_t rows,
    nk_size_t columns,
    nk_size_t depth,
    nk_size_t a_stride,
    nk_size_t r_stride,
    void *workspace,
    nk_size_t workspace_bytes,
    nk_capability_t capabilities,
    nk_stream_t stream);
```

- `nk_angulars_packed_f32_best`: a `nk_f32_t`, result `nk_f64_t`
- `nk_angulars_packed_f64_best`: a `nk_f64_t`, result `nk_f64_t`
- `nk_angulars_packed_f16_best`: a `nk_f16_t`, result `nk_f32_t`
- `nk_angulars_packed_bf16_best`: a `nk_bf16_t`, result `nk_f32_t`
- `nk_angulars_packed_e4m3_best`: a `nk_e4m3_t`, result `nk_f32_t`
- `nk_angulars_packed_e5m2_best`: a `nk_e5m2_t`, result `nk_f32_t`
- `nk_angulars_packed_e2m3_best`: a `nk_e2m3_t`, result `nk_f32_t`
- `nk_angulars_packed_e2m1_best`: a `nk_e2m1x2_t`, result `nk_f32_t`
- `nk_angulars_packed_nvfp4_best`: a `nk_nvfp4_cref_t`, result `nk_f32_t`
- `nk_angulars_packed_mxfp4_best`: a `nk_mxfp4_cref_t`, result `nk_f32_t`
- `nk_angulars_packed_mxfp6e2m3_best`: a `nk_mxfp6e2m3_cref_t`, result `nk_f32_t`
- `nk_angulars_packed_mxfp6e3m2_best`: a `nk_mxfp6e3m2_cref_t`, result `nk_f32_t`
- `nk_angulars_packed_mxfp8e4m3_best`: a `nk_mxfp8e4m3_cref_t`, result `nk_f32_t`
- `nk_angulars_packed_mxfp8e5m2_best`: a `nk_mxfp8e5m2_cref_t`, result `nk_f32_t`
- `nk_angulars_packed_e3m2_best`: a `nk_e3m2_t`, result `nk_f32_t`
- `nk_angulars_packed_i8_best`: a `nk_i8_t`, result `nk_f32_t`
- `nk_angulars_packed_u8_best`: a `nk_u8_t`, result `nk_f32_t`
- `nk_angulars_packed_i4_best`: a `nk_i4x2_t`, result `nk_f32_t`
- `nk_angulars_packed_u4_best`: a `nk_u4x2_t`, result `nk_f32_t`

- `nk_angulars_packed_f32` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_angulars_packed_f64` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_angulars_packed_f16` backends: serial, graniteamx, sme, haswell, skylake, v128relaxed, neon, neonfhm, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_packed_bf16` backends: serial, genoa, sapphireamx, sme, haswell, skylake, v128relaxed, v128, neon, neonbfdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_packed_e4m3` backends: serial, genoa, diamond, sapphireamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_packed_e5m2` backends: serial, genoa, diamond, sapphireamx, graniteamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_packed_e2m3` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_packed_e2m1` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_packed_nvfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, blackwell, metal, apple9, apple10
- `nk_angulars_packed_mxfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, blackwell, metal, apple9, apple10
- `nk_angulars_packed_mxfp6e2m3` backends: serial, sme, skylake, neon, neonsdot, metal, apple9, apple10
- `nk_angulars_packed_mxfp6e3m2` backends: serial, sme, skylake, neon, metal, apple9, apple10
- `nk_angulars_packed_mxfp8e4m3` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, blackwell, metal, apple9, apple10
- `nk_angulars_packed_mxfp8e5m2` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, blackwell, metal, apple9, apple10
- `nk_angulars_packed_e3m2` backends: serial, sapphireamx, sme, haswell, skylake, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_packed_i8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_angulars_packed_u8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_angulars_packed_i4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_angulars_packed_u4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10

- `a` (in): Input A matrix in row-major order.
- `b_packed` (in): Packed B with norms from `nk_dots_pack_*_best` on the same `capabilities`.
- `result` (out): Output matrix (rows x columns) of angular distances.
- `rows` (in): Number of rows in A.
- `columns` (in): Number of columns in B (packed).
- `depth` (in): Shared inner dimension in dimensions, a multiple of the values per byte.
- `a_stride` (in): Row stride in bytes for A.
- `r_stride` (in): Row stride in bytes for the result matrix.
- `workspace` (in): Scratch memory aligned to `nk_default_alignment_k`, in device memory ordered by `stream` on GPU capabilities. May be null with `workspace_bytes` of 0.
- `workspace_bytes` (in): At least what the matching workspace-size query reports for the fast path, or 0 for the scratch-free path. Anything in between is [`nk_unexpected_dimensions_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_unexpected_dimensions_k).
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `stream` (in): Null on the CPU, or the GPU stream of that device to queue on.

Statuses: - [`nk_misaligned_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_misaligned_k) A misaligned `workspace`.
- [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it.

## nk_angulars_symmetric_*_best

Computes symmetric angular distance matrix (Gram-style) for a set of vectors.

```c
nk_status_t nk_angulars_symmetric_f32_best(
    nk_f32_t const *vectors,
    nk_size_t vector_count,
    nk_size_t depth,
    nk_size_t stride,
    nk_f64_t *result,
    nk_size_t result_stride,
    nk_size_t rows_begin,
    nk_size_t rows_end,
    void *workspace,
    nk_size_t workspace_bytes,
    nk_capability_t capabilities,
    nk_stream_t stream);
```

- `nk_angulars_symmetric_f32_best`: vectors `nk_f32_t`, result `nk_f64_t`
- `nk_angulars_symmetric_f64_best`: vectors `nk_f64_t`, result `nk_f64_t`
- `nk_angulars_symmetric_f16_best`: vectors `nk_f16_t`, result `nk_f32_t`
- `nk_angulars_symmetric_bf16_best`: vectors `nk_bf16_t`, result `nk_f32_t`
- `nk_angulars_symmetric_e4m3_best`: vectors `nk_e4m3_t`, result `nk_f32_t`
- `nk_angulars_symmetric_e5m2_best`: vectors `nk_e5m2_t`, result `nk_f32_t`
- `nk_angulars_symmetric_e2m3_best`: vectors `nk_e2m3_t`, result `nk_f32_t`
- `nk_angulars_symmetric_e2m1_best`: vectors `nk_e2m1x2_t`, result `nk_f32_t`
- `nk_angulars_symmetric_nvfp4_best`: vectors `nk_nvfp4_cref_t`, result `nk_f32_t`
- `nk_angulars_symmetric_mxfp4_best`: vectors `nk_mxfp4_cref_t`, result `nk_f32_t`
- `nk_angulars_symmetric_mxfp6e2m3_best`: vectors `nk_mxfp6e2m3_cref_t`, result `nk_f32_t`
- `nk_angulars_symmetric_mxfp6e3m2_best`: vectors `nk_mxfp6e3m2_cref_t`, result `nk_f32_t`
- `nk_angulars_symmetric_mxfp8e4m3_best`: vectors `nk_mxfp8e4m3_cref_t`, result `nk_f32_t`
- `nk_angulars_symmetric_mxfp8e5m2_best`: vectors `nk_mxfp8e5m2_cref_t`, result `nk_f32_t`
- `nk_angulars_symmetric_e3m2_best`: vectors `nk_e3m2_t`, result `nk_f32_t`
- `nk_angulars_symmetric_i8_best`: vectors `nk_i8_t`, result `nk_f32_t`
- `nk_angulars_symmetric_u8_best`: vectors `nk_u8_t`, result `nk_f32_t`
- `nk_angulars_symmetric_i4_best`: vectors `nk_i4x2_t`, result `nk_f32_t`
- `nk_angulars_symmetric_u4_best`: vectors `nk_u4x2_t`, result `nk_f32_t`

- `nk_angulars_symmetric_f32` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_angulars_symmetric_f64` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_angulars_symmetric_f16` backends: serial, graniteamx, sme, haswell, skylake, v128relaxed, neon, neonfhm, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_symmetric_bf16` backends: serial, genoa, sapphireamx, sme, haswell, skylake, v128relaxed, v128, neon, neonbfdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_symmetric_e4m3` backends: serial, genoa, diamond, sapphireamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_symmetric_e5m2` backends: serial, genoa, diamond, sapphireamx, graniteamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_symmetric_e2m3` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_symmetric_e2m1` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_symmetric_nvfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, blackwell, metal, apple9, apple10
- `nk_angulars_symmetric_mxfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, blackwell, metal, apple9, apple10
- `nk_angulars_symmetric_mxfp6e2m3` backends: serial, sme, skylake, neon, neonsdot, metal, apple9, apple10
- `nk_angulars_symmetric_mxfp6e3m2` backends: serial, sme, skylake, neon, metal, apple9, apple10
- `nk_angulars_symmetric_mxfp8e4m3` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, blackwell, metal, apple9, apple10
- `nk_angulars_symmetric_mxfp8e5m2` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, blackwell, metal, apple9, apple10
- `nk_angulars_symmetric_e3m2` backends: serial, sapphireamx, sme, haswell, skylake, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_angulars_symmetric_i8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_angulars_symmetric_u8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_angulars_symmetric_i4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_angulars_symmetric_u4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10

- `vectors` (in): Input matrix of row vectors in row-major order.
- `vector_count` (in): Number of vectors (rows) in the input matrix.
- `depth` (in): Counts dimensions, a multiple of the values per byte.
- `stride` (in): Row stride in bytes for the input matrix.
- `result` (out): Output symmetric matrix of `vector_count` × `vector_count`.
- `result_stride` (in): Row stride in bytes for the result matrix.
- `rows_begin` (in): First row of results to compute (for parallelism).
- `rows_end` (in): One past the last row of results to compute, clamped to `vector_count`.
- `workspace` (in): Scratch memory aligned to `nk_default_alignment_k`, in device memory ordered by `stream` on GPU capabilities. May be null with `workspace_bytes` of 0.
- `workspace_bytes` (in): At least what the matching workspace-size query reports for the fast path, or 0 for the scratch-free path. Anything in between is [`nk_unexpected_dimensions_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_unexpected_dimensions_k).
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `stream` (in): Null on the CPU, or the GPU stream of that device to queue on.

Statuses: - [`nk_misaligned_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_misaligned_k) A misaligned `workspace`.
- [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it.

## nk_euclideans_packed_*_best

Computes batched euclidean distances using a packed second matrix.

```c
nk_status_t nk_euclideans_packed_f32_best(
    nk_f32_t const *a,
    void const *b_packed,
    nk_f64_t *result,
    nk_size_t rows,
    nk_size_t columns,
    nk_size_t depth,
    nk_size_t a_stride,
    nk_size_t r_stride,
    void *workspace,
    nk_size_t workspace_bytes,
    nk_capability_t capabilities,
    nk_stream_t stream);
```

- `nk_euclideans_packed_f32_best`: a `nk_f32_t`, result `nk_f64_t`
- `nk_euclideans_packed_f64_best`: a `nk_f64_t`, result `nk_f64_t`
- `nk_euclideans_packed_f16_best`: a `nk_f16_t`, result `nk_f32_t`
- `nk_euclideans_packed_bf16_best`: a `nk_bf16_t`, result `nk_f32_t`
- `nk_euclideans_packed_e4m3_best`: a `nk_e4m3_t`, result `nk_f32_t`
- `nk_euclideans_packed_e5m2_best`: a `nk_e5m2_t`, result `nk_f32_t`
- `nk_euclideans_packed_e2m3_best`: a `nk_e2m3_t`, result `nk_f32_t`
- `nk_euclideans_packed_e2m1_best`: a `nk_e2m1x2_t`, result `nk_f32_t`
- `nk_euclideans_packed_nvfp4_best`: a `nk_nvfp4_cref_t`, result `nk_f32_t`
- `nk_euclideans_packed_mxfp4_best`: a `nk_mxfp4_cref_t`, result `nk_f32_t`
- `nk_euclideans_packed_mxfp6e2m3_best`: a `nk_mxfp6e2m3_cref_t`, result `nk_f32_t`
- `nk_euclideans_packed_mxfp6e3m2_best`: a `nk_mxfp6e3m2_cref_t`, result `nk_f32_t`
- `nk_euclideans_packed_mxfp8e4m3_best`: a `nk_mxfp8e4m3_cref_t`, result `nk_f32_t`
- `nk_euclideans_packed_mxfp8e5m2_best`: a `nk_mxfp8e5m2_cref_t`, result `nk_f32_t`
- `nk_euclideans_packed_e3m2_best`: a `nk_e3m2_t`, result `nk_f32_t`
- `nk_euclideans_packed_i8_best`: a `nk_i8_t`, result `nk_f32_t`
- `nk_euclideans_packed_u8_best`: a `nk_u8_t`, result `nk_f32_t`
- `nk_euclideans_packed_i4_best`: a `nk_i4x2_t`, result `nk_f32_t`
- `nk_euclideans_packed_u4_best`: a `nk_u4x2_t`, result `nk_f32_t`

- `nk_euclideans_packed_f32` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_euclideans_packed_f64` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_euclideans_packed_f16` backends: serial, graniteamx, sme, haswell, skylake, v128relaxed, neon, neonfhm, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_packed_bf16` backends: serial, genoa, sapphireamx, sme, haswell, skylake, v128relaxed, v128, neon, neonbfdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_packed_e4m3` backends: serial, genoa, diamond, sapphireamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_packed_e5m2` backends: serial, genoa, diamond, sapphireamx, graniteamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_packed_e2m3` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_packed_e2m1` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_packed_nvfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, blackwell, metal, apple9, apple10
- `nk_euclideans_packed_mxfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, blackwell, metal, apple9, apple10
- `nk_euclideans_packed_mxfp6e2m3` backends: serial, sme, skylake, neon, neonsdot, metal, apple9, apple10
- `nk_euclideans_packed_mxfp6e3m2` backends: serial, sme, skylake, neon, metal, apple9, apple10
- `nk_euclideans_packed_mxfp8e4m3` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, blackwell, metal, apple9, apple10
- `nk_euclideans_packed_mxfp8e5m2` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, blackwell, metal, apple9, apple10
- `nk_euclideans_packed_e3m2` backends: serial, sapphireamx, sme, haswell, skylake, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_packed_i8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_euclideans_packed_u8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_euclideans_packed_i4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_euclideans_packed_u4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10

- `a` (in): Input A matrix in row-major order.
- `b_packed` (in): Packed B with norms from `nk_dots_pack_*_best` on the same `capabilities`.
- `result` (out): Output matrix (rows x columns) of euclidean distances.
- `rows` (in): Number of rows in A.
- `columns` (in): Number of columns in B (packed).
- `depth` (in): Shared inner dimension in dimensions, a multiple of the values per byte.
- `a_stride` (in): Row stride in bytes for A.
- `r_stride` (in): Row stride in bytes for the result matrix.
- `workspace` (in): Scratch memory aligned to `nk_default_alignment_k`, in device memory ordered by `stream` on GPU capabilities. May be null with `workspace_bytes` of 0.
- `workspace_bytes` (in): At least what the matching workspace-size query reports for the fast path, or 0 for the scratch-free path. Anything in between is [`nk_unexpected_dimensions_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_unexpected_dimensions_k).
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `stream` (in): Null on the CPU, or the GPU stream of that device to queue on.

Statuses: - [`nk_misaligned_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_misaligned_k) A misaligned `workspace`.
- [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it.

## nk_euclideans_symmetric_*_best

Computes symmetric euclidean distance matrix (Gram-style) for a set of vectors.

```c
nk_status_t nk_euclideans_symmetric_f32_best(
    nk_f32_t const *vectors,
    nk_size_t vector_count,
    nk_size_t depth,
    nk_size_t stride,
    nk_f64_t *result,
    nk_size_t result_stride,
    nk_size_t rows_begin,
    nk_size_t rows_end,
    void *workspace,
    nk_size_t workspace_bytes,
    nk_capability_t capabilities,
    nk_stream_t stream);
```

- `nk_euclideans_symmetric_f32_best`: vectors `nk_f32_t`, result `nk_f64_t`
- `nk_euclideans_symmetric_f64_best`: vectors `nk_f64_t`, result `nk_f64_t`
- `nk_euclideans_symmetric_f16_best`: vectors `nk_f16_t`, result `nk_f32_t`
- `nk_euclideans_symmetric_bf16_best`: vectors `nk_bf16_t`, result `nk_f32_t`
- `nk_euclideans_symmetric_e4m3_best`: vectors `nk_e4m3_t`, result `nk_f32_t`
- `nk_euclideans_symmetric_e5m2_best`: vectors `nk_e5m2_t`, result `nk_f32_t`
- `nk_euclideans_symmetric_e2m3_best`: vectors `nk_e2m3_t`, result `nk_f32_t`
- `nk_euclideans_symmetric_e2m1_best`: vectors `nk_e2m1x2_t`, result `nk_f32_t`
- `nk_euclideans_symmetric_nvfp4_best`: vectors `nk_nvfp4_cref_t`, result `nk_f32_t`
- `nk_euclideans_symmetric_mxfp4_best`: vectors `nk_mxfp4_cref_t`, result `nk_f32_t`
- `nk_euclideans_symmetric_mxfp6e2m3_best`: vectors `nk_mxfp6e2m3_cref_t`, result `nk_f32_t`
- `nk_euclideans_symmetric_mxfp6e3m2_best`: vectors `nk_mxfp6e3m2_cref_t`, result `nk_f32_t`
- `nk_euclideans_symmetric_mxfp8e4m3_best`: vectors `nk_mxfp8e4m3_cref_t`, result `nk_f32_t`
- `nk_euclideans_symmetric_mxfp8e5m2_best`: vectors `nk_mxfp8e5m2_cref_t`, result `nk_f32_t`
- `nk_euclideans_symmetric_e3m2_best`: vectors `nk_e3m2_t`, result `nk_f32_t`
- `nk_euclideans_symmetric_i8_best`: vectors `nk_i8_t`, result `nk_f32_t`
- `nk_euclideans_symmetric_u8_best`: vectors `nk_u8_t`, result `nk_f32_t`
- `nk_euclideans_symmetric_i4_best`: vectors `nk_i4x2_t`, result `nk_f32_t`
- `nk_euclideans_symmetric_u4_best`: vectors `nk_u4x2_t`, result `nk_f32_t`

- `nk_euclideans_symmetric_f32` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_euclideans_symmetric_f64` backends: serial, smef64, haswell, skylake, v128relaxed, neon, rvv, powervsx, loongsonasx, cuda, ampere, rocm
- `nk_euclideans_symmetric_f16` backends: serial, graniteamx, sme, haswell, skylake, v128relaxed, neon, neonfhm, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_symmetric_bf16` backends: serial, genoa, sapphireamx, sme, haswell, skylake, v128relaxed, v128, neon, neonbfdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_symmetric_e4m3` backends: serial, genoa, diamond, sapphireamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_symmetric_e5m2` backends: serial, genoa, diamond, sapphireamx, graniteamx, sme, haswell, skylake, v128relaxed, neonfhm, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_symmetric_e2m3` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_symmetric_e2m1` backends: serial, sapphireamx, sme, haswell, skylake, icelake, alder, sierra, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, hopper, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_symmetric_nvfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, blackwell, metal, apple9, apple10
- `nk_euclideans_symmetric_mxfp4` backends: serial, sapphireamx, sme, skylake, neon, neonsdot, cuda, blackwell, metal, apple9, apple10
- `nk_euclideans_symmetric_mxfp6e2m3` backends: serial, sme, skylake, neon, neonsdot, metal, apple9, apple10
- `nk_euclideans_symmetric_mxfp6e3m2` backends: serial, sme, skylake, neon, metal, apple9, apple10
- `nk_euclideans_symmetric_mxfp8e4m3` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, blackwell, metal, apple9, apple10
- `nk_euclideans_symmetric_mxfp8e5m2` backends: serial, sapphireamx, sme, skylake, neon, neonfhm, cuda, blackwell, metal, apple9, apple10
- `nk_euclideans_symmetric_e3m2` backends: serial, sapphireamx, sme, haswell, skylake, v128relaxed, neonsdot, neonfp8, rvv, cuda, ampere, blackwell, blackwellrtx, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_euclideans_symmetric_i8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_euclideans_symmetric_u8` backends: serial, sapphireamx, sme, haswell, icelake, alder, sierra, v128relaxed, v128, neonsdot, rvv, powervsx, loongsonasx, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_euclideans_symmetric_i4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_euclideans_symmetric_u4` backends: serial, sme, haswell, icelake, v128relaxed, neonsdot, cuda, ampere, hopper, blackwell, rocm, cdna3, cdna4, cdna5, metal, apple10

- `vectors` (in): Input matrix of row vectors in row-major order.
- `vector_count` (in): Number of vectors (rows) in the input matrix.
- `depth` (in): Counts dimensions, a multiple of the values per byte.
- `stride` (in): Row stride in bytes for the input matrix.
- `result` (out): Output symmetric matrix of `vector_count` × `vector_count`.
- `result_stride` (in): Row stride in bytes for the result matrix.
- `rows_begin` (in): First row of results to compute (for parallelism).
- `rows_end` (in): One past the last row of results to compute, clamped to `vector_count`.
- `workspace` (in): Scratch memory aligned to `nk_default_alignment_k`, in device memory ordered by `stream` on GPU capabilities. May be null with `workspace_bytes` of 0.
- `workspace_bytes` (in): At least what the matching workspace-size query reports for the fast path, or 0 for the scratch-free path. Anything in between is [`nk_unexpected_dimensions_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_unexpected_dimensions_k).
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `stream` (in): Null on the CPU, or the GPU stream of that device to queue on.

Statuses: - [`nk_misaligned_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_misaligned_k) A misaligned `workspace`.
- [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it.

## nk_attention_pack_size_*_best

Returns bytes enough to pack a ragged batch of segments however its tokens split.

```c
nk_status_t nk_attention_pack_size_bf16_best(
    nk_size_t key_value_head_count,
    nk_size_t depth,
    nk_size_t token_count,
    nk_size_t segment_count,
    nk_capability_t capabilities,
    nk_size_t *bytes);
```

- `nk_attention_pack_size_bf16_best`
- `nk_attention_pack_size_f16_best`
- `nk_attention_pack_size_e4m3_best`
- `nk_attention_pack_size_i8_best`
- `nk_attention_pack_size_nvfp4_best`
- `nk_attention_pack_size_mxfp4_best`
- `nk_attention_pack_size_mxfp6e2m3_best`
- `nk_attention_pack_size_mxfp6e3m2_best`
- `nk_attention_pack_size_mxfp8e4m3_best`
- `nk_attention_pack_size_mxfp8e5m2_best`

- `nk_attention_pack_size_bf16` backends: serial, haswell, skylake, genoa, sapphireamx, sme, neon, neonbfdot, rvv, v128relaxed, cuda, ampere, hopper, blackwell, blackwellultra, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_attention_pack_size_f16` backends: serial, sme, neon, neonfhm, cuda, ampere, blackwell, blackwellultra, metal, apple9, apple10
- `nk_attention_pack_size_e4m3` backends: serial, haswell, skylake, genoa, sapphireamx, diamondamx, sme, neon, neonfhm, rvv, v128relaxed, cuda, ampere, hopper, blackwell, blackwellrtx, blackwellultra, rocm, cdna4, cdna5, metal, apple9, apple10
- `nk_attention_pack_size_i8` backends: serial, haswell, icelake, sapphireamx, sme, neon, neonsdot, rvv, v128relaxed, cuda, ampere, hopper, blackwell, blackwellultra, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_attention_pack_size_nvfp4` backends: serial, sme, neon, neonfhm, metal, apple9, apple10
- `nk_attention_pack_size_mxfp4` backends: serial, sme, neon, neonbfdot, metal, apple9, apple10
- `nk_attention_pack_size_mxfp6e2m3` backends: serial, sme, neon, neonbfdot, metal, apple9, apple10
- `nk_attention_pack_size_mxfp6e3m2` backends: serial, sme, neon, neonbfdot, metal, apple9, apple10
- `nk_attention_pack_size_mxfp8e4m3` backends: serial, sme, neon, neonbfdot, metal, apple9, apple10
- `nk_attention_pack_size_mxfp8e5m2` backends: serial, sme, neon, neonbfdot, metal, apple9, apple10

- `key_value_head_count` (in): Number of K/V heads, a nonzero divisor of the query head count; attention must take it and `depth` as packed, and only debug builds assert these rules.
- `depth` (in): Head dimension; any value ≥ 1.
- `token_count` (in): Tokens across all segments, the sum of the pack's key counts.
- `segment_count` (in): Number of segments packed together.
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `bytes` (out): The size of the packed buffer.

Notes: The packed layout is backend-specific and must be produced by the matching pack function.

Statuses: - [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it.

## nk_attention_packed_shape_*_best

Reads a packed KV cache's shape from its header.

```c
nk_status_t nk_attention_packed_shape_bf16_best(
    void const *key_value_packed,
    nk_size_t *key_value_head_count,
    nk_size_t *depth,
    nk_size_t *segments,
    nk_capability_t capabilities,
    nk_stream_t stream);
```

- `nk_attention_packed_shape_bf16_best`
- `nk_attention_packed_shape_f16_best`
- `nk_attention_packed_shape_e4m3_best`
- `nk_attention_packed_shape_i8_best`
- `nk_attention_packed_shape_nvfp4_best`
- `nk_attention_packed_shape_mxfp4_best`
- `nk_attention_packed_shape_mxfp6e2m3_best`
- `nk_attention_packed_shape_mxfp6e3m2_best`
- `nk_attention_packed_shape_mxfp8e4m3_best`
- `nk_attention_packed_shape_mxfp8e5m2_best`

- `nk_attention_packed_shape_bf16` backends: serial, haswell, skylake, genoa, sapphireamx, sme, neon, neonbfdot, rvv, v128relaxed, cuda, ampere, hopper, blackwell, blackwellultra, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_attention_packed_shape_f16` backends: serial, sme, neon, neonfhm, cuda, ampere, blackwell, blackwellultra, metal, apple9, apple10
- `nk_attention_packed_shape_e4m3` backends: serial, haswell, skylake, genoa, sapphireamx, diamondamx, sme, neon, neonfhm, rvv, v128relaxed, cuda, ampere, hopper, blackwell, blackwellrtx, blackwellultra, rocm, cdna4, cdna5, metal, apple9, apple10
- `nk_attention_packed_shape_i8` backends: serial, haswell, icelake, sapphireamx, sme, neon, neonsdot, rvv, v128relaxed, cuda, ampere, hopper, blackwell, blackwellultra, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_attention_packed_shape_nvfp4` backends: serial, sme, neon, neonfhm, metal, apple9, apple10
- `nk_attention_packed_shape_mxfp4` backends: serial, sme, neon, neonbfdot, metal, apple9, apple10
- `nk_attention_packed_shape_mxfp6e2m3` backends: serial, sme, neon, neonbfdot, metal, apple9, apple10
- `nk_attention_packed_shape_mxfp6e3m2` backends: serial, sme, neon, neonbfdot, metal, apple9, apple10
- `nk_attention_packed_shape_mxfp8e4m3` backends: serial, sme, neon, neonbfdot, metal, apple9, apple10
- `nk_attention_packed_shape_mxfp8e5m2` backends: serial, sme, neon, neonbfdot, metal, apple9, apple10

- `key_value_packed` (in): A buffer produced by the matching [`nk_attention_pack_bf16_best`](#nk_attention_pack_bf16_best).
- `key_value_head_count` (out): Receives the K/V head count.
- `depth` (out): Receives the head dimension.
- `segments` (out): Receives the segment count.
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `stream` (in): Null on the CPU, or the GPU stream of that device to queue on.

Statuses: - [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it.
- [`nk_device_code_mismatch_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_device_code_mismatch_k) A GPU stream capturing a graph, which reading the header back would void.

## nk_attention_packed_segments

Locates a pack's key slot boundaries and key counts.

```c
nk_status_t nk_attention_packed_segments(
    void const *key_value_packed,
    nk_size_t segment_count,
    nk_u32_t const **key_offsets,
    nk_u32_t const **key_lengths);
```

- `key_value_packed` (in): A buffer produced by the matching [`nk_attention_pack_bf16_best`](#nk_attention_pack_bf16_best).
- `segment_count` (in): The pack's segment count, from [`nk_attention_packed_shape_bf16_best`](#nk_attention_packed_shape_bf16_best).
- `key_offsets` (out): Points at the pack's `segment_count` + 1 slot boundaries.
- `key_lengths` (out): Points at the pack's `segment_count` key counts.

Notes: Pure address arithmetic that never dereferences the pack, so it works on device packs too.

## nk_attention_pack_*_best

Packs a ragged batch of K and V segments into a backend-opaque layout.

```c
nk_status_t nk_attention_pack_bf16_best(
    nk_size_t key_value_head_count,
    nk_size_t depth,
    nk_u32_t const *key_offsets,
    nk_u32_t const *key_lengths,
    nk_size_t segment_count,
    nk_bf16_t const *keys,
    nk_size_t key_stride,
    nk_bf16_t const *values,
    nk_size_t value_stride,
    void *key_value_packed,
    nk_size_t tasks_begin,
    nk_size_t tasks_end,
    nk_capability_t capabilities,
    nk_stream_t stream);
```

- `nk_attention_pack_bf16_best`: keys, values `nk_bf16_t`
- `nk_attention_pack_f16_best`: keys, values `nk_f16_t`
- `nk_attention_pack_e4m3_best`: keys, values `nk_e4m3_t`
- `nk_attention_pack_i8_best`: keys, values `nk_i8_t`

- `nk_attention_pack_bf16` backends: serial, haswell, skylake, genoa, sapphireamx, sme, neon, neonbfdot, rvv, v128relaxed, cuda, ampere, hopper, blackwell, blackwellultra, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_attention_pack_f16` backends: serial, sme, neon, neonfhm, cuda, ampere, blackwell, blackwellultra, metal, apple9, apple10
- `nk_attention_pack_e4m3` backends: serial, haswell, skylake, genoa, sapphireamx, diamondamx, sme, neon, neonfhm, rvv, v128relaxed, cuda, ampere, hopper, blackwell, blackwellrtx, blackwellultra, rocm, cdna4, cdna5, metal, apple9, apple10
- `nk_attention_pack_i8` backends: serial, haswell, icelake, sapphireamx, sme, neon, neonsdot, rvv, v128relaxed, cuda, ampere, hopper, blackwell, blackwellultra, rocm, cdna3, cdna4, cdna5, metal, apple10

GPU packs read the arrays on the device, so only their counts are checked. Windows let callers pack in parallel and in any order: tasks write disjoint ranges, the window starting at task 0 also writes the header and directory, and no window reads them.

- `key_value_head_count` (in): K/V heads, at most the query head count.
- `depth` (in): Head dimension.
- `key_offsets` (in): The `segment_count` + 1 slot boundaries: segment `s` keeps its keys in rows `key_offsets[s]` onward, and may leave spare capacity before `key_offsets[s + 1]`. Must not decrease.
- `key_lengths` (in): Keys each segment holds, at most its slot's width; zeros mark padding slots. Null means every slot is full: the difference of consecutive `key_offsets`.
- `segment_count` (in): Number of segments in the batch.
- `keys` (in): Token-major matrix, one row of `key_value_head_count` × `depth` contiguous elements per token, with strided rows. Packing fuses no transposition, so depth-major K is transposed in a separate pass first.
- `key_stride` (in): Row (token) stride of `keys` in bytes.
- `values` (in): Token-major matrix shaped like `keys`. Depth-major V is likewise transposed in a separate pass first.
- `value_stride` (in): Row (token) stride of `values` in bytes.
- `key_value_packed` (out): 64-byte-aligned buffer of `nk_attention_pack_size_*` bytes.
- `tasks_begin` (in): First task of a window over the segments × K/V heads grid.
- `tasks_end` (in): End of that half-open window, clipped to the grid.
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `stream` (in): Null on the CPU, or the GPU stream of that device to queue on.

Statuses: - [`nk_unexpected_dimensions_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_unexpected_dimensions_k) A count over `UINT32_MAX` or slots that decrease or overflow.
- [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it.

## nk_attention_pack_*_best

Packs block-scaled K and V as [`nk_attention_pack_bf16_best`](#nk_attention_pack_bf16_best) does, from references to their codes, block scales and NVFP4 tensor scale; `depth` is a whole number of blocks, and the strides count bytes of codes.

```c
nk_status_t nk_attention_pack_nvfp4_best(
    nk_size_t key_value_head_count,
    nk_size_t depth,
    nk_u32_t const *key_offsets,
    nk_u32_t const *key_lengths,
    nk_size_t segment_count,
    nk_nvfp4_cref_t const *keys,
    nk_size_t key_stride,
    nk_nvfp4_cref_t const *values,
    nk_size_t value_stride,
    void *key_value_packed,
    nk_size_t tasks_begin,
    nk_size_t tasks_end,
    nk_capability_t capabilities,
    nk_stream_t stream);
```

- `nk_attention_pack_nvfp4_best`: keys, values `nk_nvfp4_cref_t`
- `nk_attention_pack_mxfp4_best`: keys, values `nk_mxfp4_cref_t`
- `nk_attention_pack_mxfp6e2m3_best`: keys, values `nk_mxfp6e2m3_cref_t`
- `nk_attention_pack_mxfp6e3m2_best`: keys, values `nk_mxfp6e3m2_cref_t`
- `nk_attention_pack_mxfp8e4m3_best`: keys, values `nk_mxfp8e4m3_cref_t`
- `nk_attention_pack_mxfp8e5m2_best`: keys, values `nk_mxfp8e5m2_cref_t`

- `nk_attention_pack_nvfp4` backends: serial, sme, neon, neonfhm, metal, apple9, apple10
- `nk_attention_pack_mxfp4` backends: serial, sme, neon, neonbfdot, metal, apple9, apple10
- `nk_attention_pack_mxfp6e2m3` backends: serial, sme, neon, neonbfdot, metal, apple9, apple10
- `nk_attention_pack_mxfp6e3m2` backends: serial, sme, neon, neonbfdot, metal, apple9, apple10
- `nk_attention_pack_mxfp8e4m3` backends: serial, sme, neon, neonbfdot, metal, apple9, apple10
- `nk_attention_pack_mxfp8e5m2` backends: serial, sme, neon, neonbfdot, metal, apple9, apple10

## nk_attention_packed_*_best

Ragged scaled-dot-product attention under a band of visible keys.

```c
nk_status_t nk_attention_packed_bf16_best(
    nk_size_t head_count,
    nk_size_t key_value_head_count,
    nk_size_t depth,
    nk_u32_t const *query_offsets,
    nk_size_t query_token_count,
    nk_f32_t scale,
    nk_size_t keys_before,
    nk_size_t keys_after,
    nk_bf16_t const *queries,
    nk_size_t query_stride,
    void const *key_value_packed,
    nk_f32_t *output,
    nk_size_t output_stride,
    nk_f32_t *log_sum_exp,
    nk_size_t tasks_begin,
    nk_size_t tasks_end,
    void *workspace,
    nk_size_t workspace_bytes,
    nk_capability_t capabilities,
    nk_stream_t stream);
```

- `nk_attention_packed_bf16_best`: queries `nk_bf16_t`
- `nk_attention_packed_f16_best`: queries `nk_f16_t`
- `nk_attention_packed_e4m3_best`: queries `nk_e4m3_t`
- `nk_attention_packed_i8_best`: queries `nk_i8_t`
- `nk_attention_packed_nvfp4_best`: queries `nk_nvfp4_cref_t`
- `nk_attention_packed_mxfp4_best`: queries `nk_mxfp4_cref_t`
- `nk_attention_packed_mxfp6e2m3_best`: queries `nk_mxfp6e2m3_cref_t`
- `nk_attention_packed_mxfp6e3m2_best`: queries `nk_mxfp6e3m2_cref_t`
- `nk_attention_packed_mxfp8e4m3_best`: queries `nk_mxfp8e4m3_cref_t`
- `nk_attention_packed_mxfp8e5m2_best`: queries `nk_mxfp8e5m2_cref_t`

- `nk_attention_packed_bf16` backends: serial, haswell, skylake, genoa, sapphireamx, sme, neon, neonbfdot, rvv, v128relaxed, cuda, ampere, hopper, blackwell, blackwellultra, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_attention_packed_f16` backends: serial, sme, neon, neonfhm, cuda, ampere, blackwell, blackwellultra, metal, apple9, apple10
- `nk_attention_packed_e4m3` backends: serial, haswell, skylake, genoa, sapphireamx, diamondamx, sme, neon, neonfhm, rvv, v128relaxed, cuda, ampere, hopper, blackwell, blackwellrtx, blackwellultra, rocm, cdna4, cdna5, metal, apple9, apple10
- `nk_attention_packed_i8` backends: serial, haswell, icelake, sapphireamx, sme, neon, neonsdot, rvv, v128relaxed, cuda, ampere, hopper, blackwell, blackwellultra, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_attention_packed_nvfp4` backends: serial, sme, neon, neonfhm, metal, apple9, apple10
- `nk_attention_packed_mxfp4` backends: serial, sme, neon, neonbfdot, metal, apple9, apple10
- `nk_attention_packed_mxfp6e2m3` backends: serial, sme, neon, neonbfdot, metal, apple9, apple10
- `nk_attention_packed_mxfp6e3m2` backends: serial, sme, neon, neonbfdot, metal, apple9, apple10
- `nk_attention_packed_mxfp8e4m3` backends: serial, sme, neon, neonbfdot, metal, apple9, apple10
- `nk_attention_packed_mxfp8e5m2` backends: serial, sme, neon, neonbfdot, metal, apple9, apple10

Computes O[s] = softmax(Q[s] × K[s]ᵀ × scale) × V[s] for every segment s over the keys each query row sees, as Causal, Sliding-Window and Bidirectional Masks defines. Covers self-attention, where `query_offsets` equal the pack-time `key_offsets`, cross-attention, and pooling, where `query_offsets = {0, 1, 2, …}` holds one query per segment, plus GQA/MQA via `key_value_head_count` < `head_count`. Pack `key_value_packed` with the same `capabilities:` CPU kernels return [`nk_pack_mismatch_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_pack_mismatch_k) for buffers another capability packed, while GPU kernels trust it, as reading its device header would wait on the stream.

- `head_count` (in): Query heads.
- `key_value_head_count` (in): K/V heads, at most `head_count`.
- `depth` (in): Head dimension.
- `query_offsets` (in): First query row of each segment, as segment count + 1 prefix sums.
- `query_token_count` (in): Query rows the call addresses, `query_offsets[segments]`; GPU kernels size tensor maps and workspaces from it without reading the offsets.
- `scale` (in): Score multiplier, typically 1 / √depth.
- `keys_before` (in): Keys visible before each query's position: `NUMKONG_SIZE_MAX` for causal and bidirectional attention, `w − 1` for a sliding window of `w` keys.
- `keys_after` (in): Keys visible after each query's position: `0` for causal attention, `NUMKONG_SIZE_MAX` for bidirectional.
- `queries` (in): Token-major matrix, one row of `head_count` × `depth` elements per query token, with `query_stride` bytes between rows.
- `query_stride` (in): Row (token) stride of `queries` in bytes.
- `key_value_packed` (in): Buffer produced by the matching `nk_attention_pack_*` backend.
- `output` (out): Token-major F32 matrix, one row of `head_count` × `depth` elements per query token, with `output_stride` bytes between rows.
- `output_stride` (in): Row (token) stride of `output` in bytes.
- `log_sum_exp` (out): Optional natural log of Σ exp(score multiplier × q · k) over each row's keys, one per query token and head, ____[query_tokens,heads] with no padding, −∞ for a row without keys: what the backward pass recomputes the weights from. Null skips it.
- `tasks_begin` (in): First task of a window over the query tokens × heads grid, task t × `head_count` + h being head `h` of query token `t`, as in `log_sum_exp`.
- `tasks_end` (in): End of that half-open window, clipped to the grid's live rows from `query_offsets`[0] × `head_count`. A window partitions the rows of `output` and `log_sum_exp` the call writes, per query token × head, so callers parallelize freely; a window may split a segment or a head group.
- `workspace` (in): Scratch memory on `nk_default_alignment_k`, on the device of `stream`, used in its order, so the caller frees it only once the stream passes the call.
- `workspace_bytes` (in): At least what [`nk_attention_packed_workspace_size_bf16_best`](#nk_attention_packed_workspace_size_bf16_best) reports for the fast path, or 0 for the path without scratch.
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `stream` (in): Null on the CPU, or the GPU stream of that device to queue on.

Statuses: - [`nk_misaligned_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_misaligned_k) A misaligned `workspace`.
- [`nk_unexpected_dimensions_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_unexpected_dimensions_k) `workspace_bytes` between 0 and the reported size.
- [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it.

## nk_attention_packed_workspace_size_*_best

Returns the workspace bytes [`nk_attention_packed_bf16_best`](#nk_attention_packed_bf16_best) takes for its fast path on these shapes, by host arithmetic alone.

```c
nk_status_t nk_attention_packed_workspace_size_bf16_best(
    nk_size_t head_count,
    nk_size_t key_value_head_count,
    nk_size_t depth,
    nk_size_t query_token_count,
    nk_size_t keys_before,
    nk_size_t keys_after,
    nk_capability_t capabilities,
    nk_size_t *bytes);
```

- `nk_attention_packed_workspace_size_bf16_best`
- `nk_attention_packed_workspace_size_f16_best`
- `nk_attention_packed_workspace_size_e4m3_best`
- `nk_attention_packed_workspace_size_i8_best`
- `nk_attention_packed_workspace_size_nvfp4_best`
- `nk_attention_packed_workspace_size_mxfp4_best`
- `nk_attention_packed_workspace_size_mxfp6e2m3_best`
- `nk_attention_packed_workspace_size_mxfp6e3m2_best`
- `nk_attention_packed_workspace_size_mxfp8e4m3_best`
- `nk_attention_packed_workspace_size_mxfp8e5m2_best`

- `nk_attention_packed_workspace_size_bf16` backends: serial, haswell, skylake, genoa, sapphireamx, sme, neon, neonbfdot, rvv, v128relaxed, cuda, ampere, hopper, blackwell, blackwellultra, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_attention_packed_workspace_size_f16` backends: serial, sme, neon, neonfhm, cuda, ampere, blackwell, blackwellultra, metal, apple9, apple10
- `nk_attention_packed_workspace_size_e4m3` backends: serial, haswell, skylake, genoa, sapphireamx, diamondamx, sme, neon, neonfhm, rvv, v128relaxed, cuda, ampere, hopper, blackwell, blackwellrtx, blackwellultra, rocm, cdna4, cdna5, metal, apple9, apple10
- `nk_attention_packed_workspace_size_i8` backends: serial, haswell, icelake, sapphireamx, sme, neon, neonsdot, rvv, v128relaxed, cuda, ampere, hopper, blackwell, blackwellultra, rocm, cdna3, cdna4, cdna5, metal, apple10
- `nk_attention_packed_workspace_size_nvfp4` backends: serial, sme, neon, neonfhm, metal, apple9, apple10
- `nk_attention_packed_workspace_size_mxfp4` backends: serial, sme, neon, neonbfdot, metal, apple9, apple10
- `nk_attention_packed_workspace_size_mxfp6e2m3` backends: serial, sme, neon, neonbfdot, metal, apple9, apple10
- `nk_attention_packed_workspace_size_mxfp6e3m2` backends: serial, sme, neon, neonbfdot, metal, apple9, apple10
- `nk_attention_packed_workspace_size_mxfp8e4m3` backends: serial, sme, neon, neonbfdot, metal, apple9, apple10
- `nk_attention_packed_workspace_size_mxfp8e5m2` backends: serial, sme, neon, neonbfdot, metal, apple9, apple10

Only the Metal capabilities need one, for decoding at most four query rows against long keys, so every other capability reports 0. The bytes hold whenever the shapes allow the fast path, which may still decline it for the call's pointers or key count.

Every other parameter follows [`nk_attention_packed_bf16_best`](#nk_attention_packed_bf16_best).

- `head_count` (in): Query heads.
- `key_value_head_count` (in): K/V heads, at most `head_count`.
- `depth` (in): Head dimension.
- `query_token_count` (in): Query rows the call addresses.
- `keys_before` (in): Keys visible before each query's position.
- `keys_after` (in): Keys visible after each query's position.
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `bytes` (out): The workspace size, 0 when the capability needs none.

Statuses: - [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it.

## nk_attention_packed_gradients_*_best

Gradients of ragged attention with respect to its queries, keys and values.

```c
nk_status_t nk_attention_packed_gradients_bf16_best(
    nk_size_t head_count,
    nk_size_t key_value_head_count,
    nk_size_t depth,
    nk_u32_t const *query_offsets,
    nk_size_t query_token_count,
    nk_f32_t scale,
    nk_size_t keys_before,
    nk_size_t keys_after,
    nk_bf16_t const *queries,
    nk_size_t query_stride,
    void const *key_value_packed,
    nk_f32_t const *output,
    nk_f32_t const *output_gradient,
    nk_size_t output_stride,
    nk_f32_t const *log_sum_exp,
    nk_f32_t *query_gradient,
    nk_size_t query_gradient_stride,
    nk_f32_t *key_gradient,
    nk_f32_t *value_gradient,
    nk_size_t key_value_gradient_stride,
    nk_size_t tasks_begin,
    nk_size_t tasks_end,
    void *workspace,
    nk_size_t workspace_bytes,
    nk_capability_t capabilities,
    nk_stream_t stream);
```

- `nk_attention_packed_gradients_bf16_best`: queries `nk_bf16_t`
- `nk_attention_packed_gradients_nvfp4_best`: queries `nk_nvfp4_cref_t`
- `nk_attention_packed_gradients_mxfp4_best`: queries `nk_mxfp4_cref_t`
- `nk_attention_packed_gradients_mxfp6e2m3_best`: queries `nk_mxfp6e2m3_cref_t`
- `nk_attention_packed_gradients_mxfp6e3m2_best`: queries `nk_mxfp6e3m2_cref_t`
- `nk_attention_packed_gradients_mxfp8e4m3_best`: queries `nk_mxfp8e4m3_cref_t`
- `nk_attention_packed_gradients_mxfp8e5m2_best`: queries `nk_mxfp8e5m2_cref_t`

- `nk_attention_packed_gradients_bf16` backends: serial, cuda, ampere, hopper, blackwell, blackwellultra, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_attention_packed_gradients_nvfp4` backends: serial
- `nk_attention_packed_gradients_mxfp4` backends: serial
- `nk_attention_packed_gradients_mxfp6e2m3` backends: serial
- `nk_attention_packed_gradients_mxfp6e3m2` backends: serial
- `nk_attention_packed_gradients_mxfp8e4m3` backends: serial
- `nk_attention_packed_gradients_mxfp8e5m2` backends: serial

Recomputes every attention weight from `log_sum_exp`, so nothing of the forward but its output and that per-row statistic is kept. The gradients are F32 and overwritten: `query_gradient` holds one row of `head_count` × `depth` elements per query token, while `key_gradient` and `value_gradient` hold one row of `key_value_head_count` × `depth` elements per key token, token `t` of segment `s` at row `key_offsets[s] + t`, with the offsets the pack stored. Rows past a segment's key count, the gaps and tails before the next segment's first key, are never written, so callers zero them when they matter. Tasks cover the segments × key-value heads grid, each owning one KV head of one segment together with the query heads sharing it, so tasks write disjoint gradients and each sums in a fixed order. The Blackwell kernels run a single pass for BF16 heads of 64 or 128 dimensions with 16-byte aligned rows, given a workspace of `query_token_count` × `head_count` × (2 × `depth` + 4) bytes, as [`nk_attention_packed_gradients_workspace_size_bf16_best`](#nk_attention_packed_gradients_workspace_size_bf16_best) reports, and add the `query_gradient` partials of different key blocks in F32 in any order, so their low bits may vary run to run. Other calls, and calls without a workspace, take the two-pass path.

Every other parameter follows [`nk_attention_packed_bf16_best`](#nk_attention_packed_bf16_best).

- `head_count` (in): Query heads.
- `key_value_head_count` (in): K/V heads, at most `head_count`.
- `depth` (in): Head dimension.
- `query_offsets` (in): First query row of each segment, as in the forward pass.
- `query_token_count` (in): Query rows the call addresses, as in the forward pass.
- `scale` (in): Score multiplier of the forward pass.
- `keys_before` (in): Keys before each query that it saw in the forward pass.
- `keys_after` (in): Keys after each query that it saw in the forward pass.
- `queries` (in): The forward's queries, with `query_stride` bytes between token rows.
- `query_stride` (in): Row (token) stride of `queries` in bytes.
- `key_value_packed` (in): The pack the forward pass read.
- `output` (in): The forward's output for these queries and pack.
- `output_gradient` (in): Gradient of the loss with respect to `output`, laid out like it.
- `output_stride` (in): Row (token) stride of `output` and `output_gradient` in bytes.
- `log_sum_exp` (in): The forward's natural log of Σ exp(scale × score) over each row's keys, one per query token and head, ____[query_tokens,heads] with no padding.
- `query_gradient` (out): Gradient with respect to `queries`.
- `query_gradient_stride` (in): Bytes between the `query_gradient` rows of consecutive tokens.
- `key_gradient` (out): Gradient with respect to the packed keys.
- `value_gradient` (out): Gradient with respect to the packed values.
- `key_value_gradient_stride` (in): Bytes between the gradient rows of consecutive key tokens.
- `tasks_begin` (in): First task of a window over the segments × key-value heads grid.
- `tasks_end` (in): End of that half-open window, clipped to the grid. A window partitions the outputs the call writes: segments × K/V heads own their `key_gradient` and `value_gradient` rows and the `query_gradient` rows of their query heads.
- `workspace` (in): Scratch memory on `nk_default_alignment_k`, on the device of `stream`.
- `workspace_bytes` (in): At least what [`nk_attention_packed_gradients_workspace_size_bf16_best`](#nk_attention_packed_gradients_workspace_size_bf16_best) reports for the fast path, or 0 for the path without scratch.
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `stream` (in): Null on the CPU, or the GPU stream of that device to queue on.

## nk_attention_packed_gradients_workspace_size_*_best

Returns the workspace bytes [`nk_attention_packed_gradients_bf16_best`](#nk_attention_packed_gradients_bf16_best) takes for its fast path on these shapes, as [`nk_attention_packed_workspace_size_bf16_best`](#nk_attention_packed_workspace_size_bf16_best) does for attention: the Blackwell single pass for BF16 is the only one that needs any.

```c
nk_status_t nk_attention_packed_gradients_workspace_size_bf16_best(
    nk_size_t head_count,
    nk_size_t key_value_head_count,
    nk_size_t depth,
    nk_size_t query_token_count,
    nk_size_t keys_before,
    nk_size_t keys_after,
    nk_capability_t capabilities,
    nk_size_t *bytes);
```

- `nk_attention_packed_gradients_workspace_size_bf16_best`
- `nk_attention_packed_gradients_workspace_size_nvfp4_best`
- `nk_attention_packed_gradients_workspace_size_mxfp4_best`
- `nk_attention_packed_gradients_workspace_size_mxfp6e2m3_best`
- `nk_attention_packed_gradients_workspace_size_mxfp6e3m2_best`
- `nk_attention_packed_gradients_workspace_size_mxfp8e4m3_best`
- `nk_attention_packed_gradients_workspace_size_mxfp8e5m2_best`

- `nk_attention_packed_gradients_workspace_size_bf16` backends: serial, cuda, ampere, hopper, blackwell, blackwellultra, rocm, cdna3, cdna4, cdna5, metal, apple9, apple10
- `nk_attention_packed_gradients_workspace_size_nvfp4` backends: serial
- `nk_attention_packed_gradients_workspace_size_mxfp4` backends: serial
- `nk_attention_packed_gradients_workspace_size_mxfp6e2m3` backends: serial
- `nk_attention_packed_gradients_workspace_size_mxfp6e3m2` backends: serial
- `nk_attention_packed_gradients_workspace_size_mxfp8e4m3` backends: serial
- `nk_attention_packed_gradients_workspace_size_mxfp8e5m2` backends: serial

- `head_count` (in): Query heads.
- `key_value_head_count` (in): K/V heads, at most `head_count`.
- `depth` (in): Head dimension.
- `query_token_count` (in): Query rows the call addresses.
- `keys_before` (in): Keys before each query that it saw in the forward pass.
- `keys_after` (in): Keys after each query that it saw in the forward pass.
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `bytes` (out): The workspace size, 0 when the capability needs none.

## nk_attention_rope_*_best

NeoX split-half rotary position embedding (RoPE): rotates channel pairs by per-token angles.

```c
nk_status_t nk_attention_rope_f32_best(
    nk_f32_t const *x,
    nk_f32_t const *cos,
    nk_f32_t const *sin,
    nk_f32_t *y,
    nk_size_t rows,
    nk_size_t head_count,
    nk_size_t depth,
    nk_size_t x_stride,
    nk_size_t y_stride,
    nk_capability_t capabilities,
    nk_stream_t stream);
```

- `nk_attention_rope_f32_best`: x, y `nk_f32_t`
- `nk_attention_rope_bf16_best`: x, y `nk_bf16_t`
- `nk_attention_rope_e4m3_best`: x, y `nk_e4m3_t`

- `nk_attention_rope_f32` backends: serial, haswell, skylake, neon, cuda, metal
- `nk_attention_rope_bf16` backends: serial, haswell, skylake, neon, cuda, metal
- `nk_attention_rope_e4m3` backends: serial, haswell, skylake, neon, cuda, metal

Rotates the channel pair i and i + h of every head in every row, h being half the `depth:`

```
*  y[i]     = x[i] · cos - x[i + h] · sin
*  y[i + h] = x[i] · sin + x[i + h] · cos
*
```

The rotation is linear, so FP8 codes rotate at their own scale and need none passed.

- `x` (in): Input token matrix of shape `rows` by `head_count` × `depth`.
- `cos` (in): Per-token cosine angle grid of shape `rows` by `depth` / 2, shared by heads.
- `sin` (in): Per-token sine angle grid of shape `rows` by `depth` / 2, shared across heads.
- `y` (out): Output matrix, same shape and dtype as `x`; may alias `x` for in-place rotation.
- `rows` (in): The number of token rows.
- `head_count` (in): The number of heads per token.
- `depth` (in): The even number of channels per head.
- `x_stride` (in): Row stride of `x` in bytes.
- `y_stride` (in): Row stride of `y` in bytes.
- `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports.
- `stream` (in): Null on the CPU, or the GPU stream of that device to queue on.

Statuses: - [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it.

## nk_attention_output_dtype

Returns the output dtype for attention: accumulator-precision F32 for all inputs.

```c
nk_dtype_t nk_attention_output_dtype(nk_dtype_t dtype);
```

## nk_attention_rope_error_bound

Returns the error bound of RoPE outputs before they round into their type, relative to the two products each of them sums: 3 roundings in F32, which every input type rotates in, through the descale, the product and the sum.

```c
nk_f64_t nk_attention_rope_error_bound(nk_dtype_t dtype);
```