> For the complete documentation index, see [llms.txt](https://docs.algenta.ai/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.algenta.ai/benchmarks/compute-kernels.md).

# Compute kernels

Quantized matrix-vector results — the fused NF4 path measured against expand-then-multiply, with correctness asserted against the reference kernel.

{% hint style="info" %}
**Baseline:** expand-then-multiply — the cost of the same computation without the fused path. Correctness is asserted against the reference kernel before any timing is reported.
{% endhint %}

## Hardware

| Property           | Value                            |
| ------------------ | -------------------------------- |
| Chip               | Apple silicon, 16 physical cores |
| Precision measured | 64-bit floating point            |

## Fused NF4 matrix-vector

A 4-bit weight is dequantized before it multiplies anything. The unfused path expands the whole matrix and then calls a dense kernel. The fused path dequantizes inside the k-loop, so the expanded matrix is never allocated.

| Path                  | Time    | Peak intermediate allocation |
| --------------------- | ------- | ---------------------------- |
| Fused NF4 GEMV        | 0.42 ms | none                         |
| Expand, then multiply | 1.47 ms | 2 MB                         |

The fused path is 3.5x faster and does not allocate the expanded matrix. Expansion converts a 4-bit weight to a 64-bit value, so the intermediate is sixteen times the size of the weights it is derived from.

**Correctness:** maximum elementwise difference against the reference kernel is 2.8e-14.

## Reproduce

```
mojo run benchmarks/mojo_benchmarks/bench_tensorx_and_gemm.mojo
```

The benchmark prints its own gate results. Gates check properties, not absolute times, which vary by machine and load.

## See also

* [Benchmarks](/benchmarks/overview.md)
* [Code retrieval quality](/benchmarks/code-retrieval.md)
* [Runtime library catalog](/engine-runtime/runtime-library-catalog.md)


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