> For the complete documentation index, see [llms.txt](https://docs.zama.org/tfhe-rs/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.zama.org/tfhe-rs/get-started/benchmarks/cpu/cpu-integer-operations.md).

# Integer

This document details the CPU performance benchmarks of homomorphic operations on integers using **TFHE-rs**.

By their nature, homomorphic operations run slower than their cleartext equivalents.

{% hint style="info" %}
All CPU benchmarks were launched on an `AWS hpc7a.96xlarge` instance equipped with two 96-core `AMD EPYC 9R14 CPU @ 2.60GHz` and 740GB of RAM.
{% endhint %}

The following tables benchmark the execution time of some operation sets using `FheUint` (unsigned integers). The `FheInt` (signed integers) performs similarly.

## Pfail: $$2^{-128}$$

The next tables show the operation timings on CPU when all inputs are encrypted:

### Encrypted/encrypted operations latency

![](/files/JHUAcSje30QnmXtla2ul)

### Encrypted/encrypted operations throughput

![](/files/vQ1E24DPeQdQXuUOO1MV)

The next tables show the operation timings on CPU when the left input is encrypted and the right is a clear scalar of the same size:

### Encrypted/clear operations latency

![](/files/FhMDqF8leK1TpBuxYCGs)

### Encrypted/clear operations throughput

![](/files/XTzGejFSNu15nLJq5rCF)

All timings are based on parallelized Radix-based integer operations where each block is encrypted using the default parameters `PARAM_MESSAGE_2_CARRY_2_KS32_PBS_TUNIFORM_2M128`. To ensure predictable timings, we perform operations in the `default` mode, which ensures that the input and output encoding are similar (i.e., the carries are always emptied).

You can minimize operational costs by selecting from 'unchecked', 'checked', or 'smart' modes from [the fine-grained APIs](/tfhe-rs/references/fine-grained-apis/quick-start.md), each balancing performance and correctness differently. For more details about parameters, see [here](/tfhe-rs/references/fine-grained-apis/shortint/parameters.md). You can find the benchmark results on GPU for all these operations on GPU [here](/tfhe-rs/get-started/benchmarks/gpu.md) and on HPU [here](/tfhe-rs/hardware-acceleration/run-on-hpu/benchmark.md).

## Reproducing TFHE-rs benchmarks

**TFHE-rs** benchmarks can be easily reproduced from the [source](https://github.com/zama-ai/tfhe-rs).

{% hint style="info" %}
AVX512 is now enabled by default for benchmarks when available
{% endhint %}

The following example shows how to reproduce **TFHE-rs** benchmarks:

```shell
#Integer benchmarks:
make bench_integer
```


---

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