npm package: @sroussey/simsimd
Description: Fastest SIMD-Accelerated Vector Similarity Functions for x86 and Arm
Author: Ash Vardanian
Latest version: 3.6.25

# SimSIMD 📏

<div>
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## Hardware-Accelerated Similarity Metrics and Distance Functions

- Zero-dependency [header-only C 99](#using-simsimd-in-c) library with bindings for [Python](#using-simsimd-in-python) and [JavaScript](#using-simsimd-in-javascript).
- Targets ARM NEON, SVE, x86 AVX2, AVX-512 (VNNI, FP16) hardware backends.
- Zero-copy compatible with NumPy, PyTorch, TensorFlow, and other tensors.
- Handles `f64` double-, `f32` single-, and `f16` half-precision, `i8` integral, and binary vectors.
- __Up to 200x faster__ than [`scipy.spatial.distance`][scipy] and [`numpy.inner`][numpy].
- Used in [USearch](https://github.com/unum-cloud/usearch) and several DBMS products.

__Implemented distance functions__ include:

- Euclidean (L2), Inner Product, and Cosine (Angular) spatial distances.
- Hamming (~ Manhattan) and Jaccard (~ Tanimoto) binary distances.
- Kullback-Leibler and Jensen–Shannon divergences for probability distributions.

[scipy]: https://docs.scipy.org/doc/scipy/reference/spatial.distance.html#module-scipy.spatial.distance
[numpy]: https://numpy.org/doc/stable/reference/generated/numpy.inner.html

__Technical Insights__ and related articles:

- [Uses Horner's method for polynomial approximations, beating GCC 12 by 119x](https://ashvardanian.com/posts/gcc-12-vs-avx512fp16/).
- [Uses Arm SVE and x86 AVX-512's masked loads to eliminate tail `for`-loops](https://ashvardanian.com/posts/simsimd-faster-scipy/#tails-of-the-past-the-significance-of-masked-loads).
- [Uses AVX-512 FP16 for half-precision operations, that few compilers vectorize](https://ashvardanian.com/posts/simsimd-faster-scipy/#the-challenge-of-f16).
- [Substitutes LibC's `sqrt` calls with bithacks using Jan Kadlec's constant](https://ashvardanian.com/posts/simsimd-faster-scipy/#bonus-section-bypassing-sqrt-and-libc-dependencies).
- [For Python avoids slow PyBind11, SWIG, and even `PyArg_ParseTuple` for speed](https://ashvardanian.com/posts/pybind11-cpython-tutorial/).
- [For JavaScript uses typed arrays and NAPI for zero-copy calls](https://ashvardanian.com/posts/javascript-ai-vector-search/).

## Benchmarks

### Apple M2 Pro

Given 1000 embeddings from OpenAI Ada API with 1536 dimensions, running on the Apple M2 Pro Arm CPU with NEON support, here's how SimSIMD performs against conventional methods:

| Kind           | `f32` improvement | `f16` improvement | `i8` improvement | Conventional method                    | SimSIMD         |
| :------------- | ----------------: | ----------------: | ---------------: | :------------------------------------- | :-------------- |
| Cosine         |          __32 x__ |          __79 x__ |        __133 x__ | `scipy.spatial.distance.cosine`        | `cosine`        |
| Euclidean ²    |           __5 x__ |          __26 x__ |         __17 x__ | `scipy.spatial.distance.sqeuclidean`   | `sqeuclidean`   |
| Inner Product  |           __2 x__ |           __9 x__ |         __18 x__ | `numpy.inner`                          | `inner`         |
| Jensen Shannon |          __31 x__ |          __53 x__ |                  | `scipy.spatial.distance.jensenshannon` | `jensenshannon` |

### Intel Sapphire Rapids

On the Intel Sapphire Rapids platform, SimSIMD was benchmarked against auto-vectorized code using GCC 12. GCC handles single-precision `float` but might not be the best choice for `int8` and `_Float16` arrays, which has been part of the C language since 2011.

| Kind           | GCC 12 `f32` | GCC 12 `f16` | SimSIMD `f16` | `f16` improvement |
| :------------- | -----------: | -----------: | ------------: | ----------------: |
| Cosine         |     3.28 M/s | _336.29 k/s_ |    _6.88 M/s_ |          __20 x__ |
| Euclidean ²    |     4.62 M/s | _147.25 k/s_ |    _5.32 M/s_ |          __36 x__ |
| Inner Product  |     3.81 M/s | _192.02 k/s_ |    _5.99 M/s_ |          __31 x__ |
| Jensen Shannon |     1.18 M/s |  _18.13 k/s_ |    _2.14 M/s_ |         __118 x__ |

__Broader Benchmarking Results__:

- [Apple M2 Pro](https://ashvardanian.com/posts/simsimd-faster-scipy/#appendix-1-performance-on-apple-m2-pro).
- [4th Gen Intel Xeon Platinum](https://ashvardanian.com/posts/simsimd-faster-scipy/#appendix-2-performance-on-4th-gen-intel-xeon-platinum-8480).
- [AWS Graviton 3](https://ashvardanian.com/posts/simsimd-faster-scipy/#appendix-3-performance-on-aws-graviton-3).

## Using SimSIMD in Python

### Installation

```sh
pip install simsimd
```

### Distance Between 2 Vectors

```py
import simsimd
import numpy as np

vec1 = np.random.randn(1536).astype(np.float32)
vec2 = np.random.randn(1536).astype(np.float32)
dist = simsimd.cosine(vec1, vec2)
```

Supported functions include `cosine`, `inner`, `sqeuclidean`, `hamming`, and `jaccard`.

### Distance Between 2 Batches

```py
batch1 = np.random.randn(100, 1536).astype(np.float32)
batch2 = np.random.randn(100, 1536).astype(np.float32)
dist = simsimd.cosine(batch1, batch2)
```

If either batch has more than one vector, the other batch must have one or the same number of vectors.
If it contains just one, the value is broadcasted.

### All Pairwise Distances

For calculating distances between all possible pairs of rows across two matrices (akin to [`scipy.spatial.distance.cdist`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.distance.cdist.html)):

```py
matrix1 = np.random.randn(1000, 1536).astype(np.float32)
matrix2 = np.random.randn(10, 1536).astype(np.float32)
distances = simsimd.cdist(matrix1, matrix2, metric="cosine")
```

### Multithreading

By default, computations use a single CPU core. To optimize and utilize all CPU cores on Linux systems, add the `threads=0` argument. Alternatively, specify a custom number of threads:

```py
distances = simsimd.cdist(matrix1, matrix2, metric="cosine", threads=0)
```

### Hardware Backend Capabilities

To view a list of hardware backends that SimSIMD supports:

```py
print(simsimd.get_capabilities())
```

### Using Python API with USearch

Want to use it in Python with [USearch](https://github.com/unum-cloud/usearch)?
You can wrap the raw C function pointers SimSIMD backends into a `CompiledMetric` and pass it to USearch, similar to how it handles Numba's JIT-compiled code.

```py
from usearch.index import Index, CompiledMetric, MetricKind, MetricSignature
from simsimd import pointer_to_sqeuclidean, pointer_to_cosine, pointer_to_inner

metric = CompiledMetric(
    pointer=pointer_to_cosine("f16"),
    kind=MetricKind.Cos,
    signature=MetricSignature.ArrayArraySize,
)

index = Index(256, metric=metric)
```

## Using SimSIMD in JavaScript

To install, choose one of the following options depending on your environment:

- `npm install --save simsimd`
- `yarn add simsimd`
- `pnpm add simsimd`
- `bun install simsimd`

The package is distributed with prebuilt binaries for Node.js v10 and above for Linux (x86_64, arm64), macOS (x86_64, arm64), and Windows (i386,x86_64).

If your platform is not supported, you can build the package from source via `npm run build`. This will automatically happen unless you install the package with `--ignore-scripts` flag or use Bun.

After you install it, you will be able to call the SimSIMD functions on various `TypedArray` variants:

```js
const { sqeuclidean, cosine, inner, hamming, jaccard } = require('simsimd');

const vectorA = new Float32Array([1.0, 2.0, 3.0]);
const vectorB = new Float32Array([4.0, 5.0, 6.0]);

const distance = sqeuclidean(vectorA, vectorB);
console.log('Squared Euclidean Distance:', distance);
```

## Using SimSIMD in C

For integration within a CMake-based project, add the following segment to your `CMakeLists.txt`:

```cmake
FetchContent_Declare(
    simsimd
    GIT_REPOSITORY https://github.com/ashvardanian/simsimd.git
    GIT_SHALLOW TRUE
)
FetchContent_MakeAvailable(simsimd)
```

If you're aiming to utilize the `_Float16` functionality with SimSIMD, ensure your development environment is compatible with C 11.
For other functionalities of SimSIMD, C 99 compatibility will suffice.
A minimal usage example would be:

```c
#include <simsimd/simsimd.h>

int main() {
    simsimd_f32_t vector_a[1536];
    simsimd_f32_t vector_b[1536];
    simsimd_f32_t distance = simsimd_avx512_f32_cos(vector_a, vector_b, 1536);
    return 0;
}
```

All of the functions names follow the same pattern: `simsimd_{backend}_{type}_{metric}`.

- The backend can be `avx512`, `avx2`, `neon`, or `sve`.
- The type can be `f64`, `f32`, `f16`, `i8`, or `b8`.
- The metric can be `cos`, `ip`, `l2sq`, `hamming`, `jaccard`, `kl`, or `js`.

In case you want to avoid hard-coding the backend, you can use the `simsimd_metric_punned_t` to pun the function pointer, and `simsimd_capabilities` function to get the available backends at runtime.

## Benchmarking and Contributing

__To rerun experiments__ utilize the following command:

```sh
cmake -DCMAKE_BUILD_TYPE=Release -DSIMSIMD_BUILD_BENCHMARKS=1 -B ./build_release
cmake --build build_release --config Release
./build_release/simsimd_bench
./build_release/simsimd_bench --benchmark_filter=js
```

__To test and benchmark with Python bindings__:

```sh
pip install -e .
pytest python/test.py -s -x 

pip install numpy scipy scikit-learn # for comparison baselines
python python/bench.py # to run default benchmarks
python python/bench.py --n 1000 --ndim 1000000 # batch size and dimensions
```

__To test and benchmark JavaScript bindings__:

```sh
npm install --dev
npm test
npm run bench
```

__To test and benchmark GoLang bindings__:

```sh
cd golang
go test # To test
go test -run=^$ -bench=. -benchmem # To benchmark
```