SimSIMD 📏

Efficient Alternative to scipy.spatial.distance and numpy.inner

SimSIMD leverages SIMD intrinsics, capabilities that only select compilers effectively utilize. This framework supports conventional AVX2 instructions on x86, NEON on Arm, as well as rare AVX-512 FP16 instructions on x86 and Scalable Vector Extensions (SVE) on Arm. Designed specifically for Machine Learning contexts, it's optimized for handling high-dimensional vector embeddings.

• ✅ 3-200x faster than NumPy and SciPy distance functions.
• ✅ 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.
• ✅ Single-precision f32, half-precision f16, i8, and binary vectors.
• ✅ Compatible with GCC and Clang on MacOS and Linux, and MinGW on Windows.
• ✅ Compatible with NumPy, PyTorch, TensorFlow, and other tensors.
• ✅ Has no dependencies, not even LibC.
• ✅ JavaScript API.
• ✅ C API.

Technical Insights and related articles:

• Uses Horner's method for polynomial approximations, beating GCC 12 by 119x.
• Uses Arm SVE and x86 AVX-512's masked loads to eliminate tail for-loops.
• Uses AVX-512 FP16 for half-precision operations, that few compilers vectorize.
• Substitutes LibC's sqrt calls with bithacks using Jan Kadlec's constant.
• For Python avoids slow PyBind11, SWIG, and even PyArg_ParseTuple for speed.
• For JavaScript uses typed arrays and NAPI for zero-copy calls.

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.
• 4th Gen Intel Xeon Platinum.
• AWS Graviton 3.

Using in Python

Installation

pip install simsimd

Distance Between 2 Vectors

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

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 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):

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:

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

Hardware Backend Capabilities

To view a list of hardware backends that SimSIMD supports:

print(simsimd.get_capabilities())

Using Python API with USearch

Want to use it in Python with 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.

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

After you add simsimd as a dependency and npm install, you will be able to call SimSIMD function on various TypedArray variants:

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

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.

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

FetchContent_Declare(
    simsimd
    GIT_REPOSITORY https://github.com/ashvardanian/simsimd.git
    GIT_SHALLOW TRUE
)
FetchContent_MakeAvailable(simsimd)
include_directories(${simsimd_SOURCE_DIR}/include)

Stay updated with the latest advancements by always using the most recent compiler available for your platform. This ensures that you benefit from the newest intrinsics.

Should you wish to integrate SimSIMD within USearch, simply compile USearch with the flag USEARCH_USE_SIMSIMD=1. Notably, this is the default setting on the majority of platforms.

Benchmarking and Contributing

To rerun experiments utilize the following command:

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:

pip install -e .
pytest python/test.py -s -x 
python python/bench.py --n 1000 --ndim 1000000 # batch size and dimensions

To test and benchmark JavaScript bindings:

npm install --dev
npm test
npm run bench

To test and benchmark GoLang bindings:

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