# SimSIMD 📏
Computing dot-products, similarity measures, and distances between low- and high-dimensional vectors is ubiquitous in Machine Learning, Scientific Computing, Geo-Spatial Analysis, and Information Retrieval.
These algorithms generally have linear complexity in time, constant complexity in space, and are data-parallel.
In other words, it is easily parallelizable and vectorizable and often available in packages like BLAS and LAPACK, as well as higher-level `numpy` and `scipy` Python libraries.
Ironically, even with decades of evolution in compilers and numerical computing, [most libraries can be 3-200x slower than hardware potential][benchmarks] even on the most popular hardware, like 64-bit x86 and Arm CPUs.
SimSIMD attempts to fill that gap.
1️⃣ SimSIMD functions are practically as fast as `memcpy`.
2️⃣ SimSIMD [compiles to more platforms than NumPy (105 vs 35)][compatibility] and has more backends than most BLAS implementations.
[benchmarks]: https://ashvardanian.com/posts/simsimd-faster-scipy
[compatibility]: https://pypi.org/project/simsimd/#files
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## Features
SimSIMD provides over 100 SIMD-optimized kernels for various distance and similarity measures, accelerating search in [USearch](https://github.com/unum-cloud/usearch) and several DBMS products.
Implemented distance functions include:
- Euclidean (L2) and Cosine (Angular) spatial distances for Vector Search.
- Dot-Products for real & complex vectors for DSP & Quantum computing.
- Hamming (~ Manhattan) and Jaccard (~ Tanimoto) bit-level distances.
- Kullback-Leibler and Jensen–Shannon divergences for probability distributions.
- Haversine and Vincenty's formulae for Geospatial Analysis.
- For Levenshtein, Needleman–Wunsch and other text metrics, check [StringZilla][stringzilla].
[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
[stringzilla]: https://github.com/ashvardanian/stringzilla
Moreover, SimSIMD...
- handles `f64`, `f32`, and `f16` real & complex vectors.
- handles `i8` integral and `b8` binary vectors.
- is a zero-dependency [header-only C 99](#using-simsimd-in-c) library.
- has bindings for [Python](#using-simsimd-in-python), [Rust](#using-simsimd-in-rust) and [JavaScript](#using-simsimd-in-javascript).
- has Arm backends for NEON and Scalable Vector Extensions (SVE).
- has x86 backends for Haswell, Skylake, Ice Lake, and Sapphire Rapids.
Due to the high-level of fragmentation of SIMD support in different x86 CPUs, SimSIMD uses the names of select Intel CPU generations for its backends.
They, however, also work on AMD CPUs.
Inel Haswell is compatible with AMD Zen 1/2/3, while AMD Genoa Zen 4 covers AVX-512 instructions added to Intel Skylake and Ice Lake.
You can learn more about the technical implementation details in the following blogposts:
- [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 bit-hacks 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
### Against NumPy and SciPy
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 |
| :------------------------ | ----------------: | ----------------: | ---------------: | :------------------------------------- | :-------------- |
| Inner Product | __2 x__ | __9 x__ | __18 x__ | `numpy.inner` | `inner` |
| Cosine Distance | __32 x__ | __79 x__ | __133 x__ | `scipy.spatial.distance.cosine` | `cosine` |
| Euclidean Distance ² | __5 x__ | __26 x__ | __17 x__ | `scipy.spatial.distance.sqeuclidean` | `sqeuclidean` |
| Jensen-Shannon Divergence | __31 x__ | __53 x__ | | `scipy.spatial.distance.jensenshannon` | `jensenshannon` |
### Against GCC Auto-Vectorization
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 have been part of the C language since 2011.
| Kind | GCC 12 `f32` | GCC 12 `f16` | SimSIMD `f16` | `f16` improvement |
| :------------------------ | -----------: | -----------: | ------------: | ----------------: |
| Inner Product | 3,810 K/s | 192 K/s | 5,990 K/s | __31 x__ |
| Cosine Distance | 3,280 K/s | 336 K/s | 6,880 K/s | __20 x__ |
| Euclidean Distance ² | 4,620 K/s | 147 K/s | 5,320 K/s | __36 x__ |
| Jensen-Shannon Divergence | 1,180 K/s | 18 K/s | 2,140 K/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
The package is intended to replace the usage of `numpy.inner`, `numpy.dot`, and `scipy.spatial.distance`.
Aside from drastic performance improvements, SimSIMD significantly improves accuracy in mixed precision setups.
NumPy and SciPy, processing `i8` or `f16` vectors, will use the same types for accumulators, while SimSIMD can combine `i8` enumeration, `i16` multiplication, and `i32` accumulation to avoid overflows entirely.
The same applies to processing `f16` values with `f32` precision.
### Installation
Use the following snippet to install SimSIMD and list available hardware acceleration options available on your machine:
```sh
pip install simsimd
python -c "import simsimd; print(simsimd.get_capabilities())"
```
### One-to-One Distance
```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`.
Dot products are supported for both real and complex numbers:
```py
vec1 = np.random.randn(768).astype(np.float64) + 1j * np.random.randn(768).astype(np.float64)
vec2 = np.random.randn(768).astype(np.float64) + 1j * np.random.randn(768).astype(np.float64)
dist = simsimd.dot(vec1.astype(np.complex128), vec2.astype(np.complex128))
dist = simsimd.dot(vec1.astype(np.complex64), vec2.astype(np.complex64))
dist = simsimd.vdot(vec1.astype(np.complex64), vec2.astype(np.complex64)) # conjugate, same as `np.vdot`
```
Unlike SciPy, SimSIMD allows explicitly stating the precision of the input vectors, which is especially useful for mixed-precision setups.
```py
dist = simsimd.cosine(vec1, vec2, "i8")
dist = simsimd.cosine(vec1, vec2, "f16")
dist = simsimd.cosine(vec1, vec2, "f32")
dist = simsimd.cosine(vec1, vec2, "f64")
```
It also allows using SimSIMD for half-precision complex numbers, which NumPy does not support.
For that, view data as continuous even-length `np.float16` vectors and override type-resolution with `complex32` string.
```py
vec1 = np.random.randn(1536).astype(np.float16)
vec2 = np.random.randn(1536).astype(np.float16)
simd.dot(vec1, vec2, "complex32")
simd.vdot(vec1, vec2, "complex32")
```
### One-to-Many Distances
Every distance function can be used not only for one-to-one but also one-to-many and many-to-many distance calculations.
For one-to-many:
```py
vec1 = np.random.randn(1536).astype(np.float32) # rank 1 tensor
batch1 = np.random.randn(1, 1536).astype(np.float32) # rank 2 tensor
batch2 = np.random.randn(100, 1536).astype(np.float32)
dist_rank1 = simsimd.cosine(vec1, batch2)
dist_rank2 = simsimd.cosine(batch1, batch2)
```
### Many-to-Many Distances
All distance functions in SimSIMD can be used to compute many-to-many distances.
For two batches of 100 vectors to compute 100 distances, one would call it like this:
```py
batch1 = np.random.randn(100, 1536).astype(np.float32)
batch2 = np.random.randn(100, 1536).astype(np.float32)
dist = simsimd.cosine(batch1, batch2)
```
Input matrices must have identical shapes.
This functionality isn't natively present in NumPy or SciPy, and generally requires creating intermediate arrays, which is inefficient and memory-consuming.
### Many-to-Many All-Pairs Distances
One can use SimSIMD to compute 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)).
The resulting object will have a type `DistancesTensor`, zero-copy compatible with NumPy and other libraries.
For two arrays of 10 and 1,000 entries, the resulting tensor will have 10,000 cells:
```py
import numpy as np
from simsimd import cdist, DistancesTensor
matrix1 = np.random.randn(1000, 1536).astype(np.float32)
matrix2 = np.random.randn(10, 1536).astype(np.float32)
distances: DistancesTensor = simsimd.cdist(matrix1, matrix2, metric="cosine") # zero-copy
distances_array: np.ndarray = np.array(distances, copy=True) # now managed by NumPy
```
### 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)
```
### 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 Rust
To install, add the following to your `Cargo.toml`:
```toml
[dependencies]
simsimd = "..."
```
Before using the SimSIMD library, ensure you have imported the necessary traits and types into your Rust source file.
The library provides several traits for different distance/similarity kinds - `SpatialSimilarity`, `BinarySimilarity`, and `ProbabilitySimilarity`.
### Spatial Similarity: Cosine and Euclidean Distances
```rust
use simsimd::SpatialSimilarity;
fn main() {
let vector_a: Vec<f32> = vec![1.0, 2.0, 3.0];
let vector_b: Vec<f32> = vec![4.0, 5.0, 6.0];
// Compute the cosine similarity between vector_a and vector_b
let cosine_similarity = f32::cosine(&vector_a, &vector_b)
.expect("Vectors must be of the same length");
println!("Cosine Similarity: {}", cosine_similarity);
// Compute the squared Euclidean distance between vector_a and vector_b
let sq_euclidean_distance = f32::sqeuclidean(&vector_a, &vector_b)
.expect("Vectors must be of the same length");
println!("Squared Euclidean Distance: {}", sq_euclidean_distance);
}
```
Spatial similarity functions are available for `f64`, `f32`, `f16`, and `i8` types.
### Dot-Products: Inner and Complex Inner Products
```rust
use simsimd::SpatialSimilarity;
use simsimd::ComplexProducts;
fn main() {
let vector_a: Vec<f32> = vec![1.0, 2.0, 3.0, 4.0];
let vector_b: Vec<f32> = vec![5.0, 6.0, 7.0, 8.0];
// Compute the inner product between vector_a and vector_b
let inner_product = SpatialSimilarity::dot(&vector_a, &vector_b)
.expect("Vectors must be of the same length");
println!("Inner Product: {}", inner_product);
// Compute the complex inner product between complex_vector_a and complex_vector_b
let complex_inner_product = ComplexProducts::dot(&vector_a, &vector_b)
.expect("Vectors must be of the same length");
let complex_conjugate_inner_product = ComplexProducts::vdot(&vector_a, &vector_b)
.expect("Vectors must be of the same length");
println!("Complex Inner Product: {:?}", complex_inner_product); // -18, 69
println!("Complex C. Inner Product: {:?}", complex_conjugate_inner_product); // 70, -8
}
```
Complex inner products are available for `f64`, `f32`, and `f16` types.
### Probability Distributions: Jensen-Shannon and Kullback-Leibler Divergences
```rust
use simsimd::SpatialSimilarity;
fn main() {
let vector_a: Vec<f32> = vec![1.0, 2.0, 3.0];
let vector_b: Vec<f32> = vec![4.0, 5.0, 6.0];
let cosine_similarity = f32::jensenshannon(&vector_a, &vector_b)
.expect("Vectors must be of the same length");
println!("Cosine Similarity: {}", cosine_similarity);
let sq_euclidean_distance = f32::kullbackleibler(&vector_a, &vector_b)
.expect("Vectors must be of the same length");
println!("Squared Euclidean Distance: {}", sq_euclidean_distance);
}
```
Probability similarity functions are available for `f64`, `f32`, and `f16` types.
### Binary Similarity: Hamming and Jaccard Distances
Similar to spatial distances, one can compute bit-level distance functions between slices of unsigned integers:
```rust
use simsimd::BinarySimilarity;
fn main() {
let vector_a = &[0b11110000, 0b00001111, 0b10101010];
let vector_b = &[0b11110000, 0b00001111, 0b01010101];
// Compute the Hamming distance between vector_a and vector_b
let hamming_distance = u8::hamming(&vector_a, &vector_b)
.expect("Vectors must be of the same length");
println!("Hamming Distance: {}", hamming_distance);
// Compute the Jaccard distance between vector_a and vector_b
let jaccard_distance = u8::jaccard(&vector_a, &vector_b)
.expect("Vectors must be of the same length");
println!("Jaccard Distance: {}", jaccard_distance);
}
```
Binary similarity functions are available only for `u8` types.
### Half-Precision Floating-Point Numbers
Rust has no native support for half-precision floating-point numbers, but SimSIMD provides a `f16` type.
It has no functionality - it is a `transparent` wrapper around `u16` and can be used with `half` or any other half-precision library.
```rust
use simsimd::SpatialSimilarity;
use simsimd::f16 as SimF16;
use half::f16 as HalfF16;
fn main() {
let vector_a: Vec<HalfF16> = ...
let vector_b: Vec<HalfF16> = ...
let buffer_a: &[SimF16] = unsafe { std::slice::from_raw_parts(a_half.as_ptr() as *const SimF16, a_half.len()) };
let buffer_b: &[SimF16] = unsafe { std::slice::from_raw_parts(b_half.as_ptr() as *const SimF16, b_half.len()) };
// Compute the cosine similarity between vector_a and vector_b
let cosine_similarity = SimF16::cosine(&vector_a, &vector_b)
.expect("Vectors must be of the same length");
println!("Cosine Similarity: {}", cosine_similarity);
}
```
### Dynamic Dispatch
SimSIMD provides a dynamic dispatch mechanism to select the most advanced micro-kernel for the current CPU.
You can query supported backends and use the `SimSIMD::capabilities` function to select the best one.
```rust
println!("uses neon: {}", capabilties::uses_neon());
println!("uses sve: {}", capabilties::uses_sve());
println!("uses haswell: {}", capabilties::uses_haswell());
println!("uses skylake: {}", capabilties::uses_skylake());
println!("uses ice: {}", capabilties::uses_ice());
println!("uses sapphire: {}", capabilties::uses_sapphire());
```
## 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, but if your platform is not supported, you can build the package from the source via `npm run build`.
This will automatically happen unless you install the package with the `--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);
```
Other numeric types and precision levels are supported as well.
For double-precsion floating-point numbers, use `Float64Array`:
```js
const vectorA = new Float64Array([1.0, 2.0, 3.0]);
const vectorB = new Float64Array([4.0, 5.0, 6.0]);
const distance = cosine(vectorA, vectorB);
```
When doing machine learning and vector search with high-dimensional vectors you may want to quantize them to 8-bit integers.
You may want to project values from the $[-1, 1]$ range to the $[-100, 100]$ range and then cast them to `Uint8Array`:
```js
const quantizedVectorA = new Uint8Array(vectorA.map(v => (v * 100)));
const quantizedVectorB = new Uint8Array(vectorB.map(v => (v * 100)));
const distance = cosine(quantizedVectorA, quantizedVectorB);
```
A more extreme quantization case would be to use binary vectors.
You can map all positive values to `1` and all negative values and zero to `0`, packing eight values into a single byte.
After that, Hamming and Jaccard distances can be computed.
```js
const { toBinary, hamming } = require('simsimd');
const binaryVectorA = toBinary(vectorA);
const binaryVectorB = toBinary(vectorB);
const distance = hamming(binaryVectorA, binaryVectorB);
```
## 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)
```
After that, you can use the SimSIMD library in your C code in several ways.
Simplest of all, you can include the headers, and the compiler will automatically select the most recent CPU extensions that SimSIMD will use.
```c
#include <simsimd/simsimd.h>
int main() {
simsimd_f32_t vector_a[1536];
simsimd_f32_t vector_b[1536];
simsimd_metric_punned_t distance_function = simsimd_metric_punned(
simsimd_metric_cos_k, // Metric kind, like the angular cosine distance
simsimd_datatype_f32_k, // Data type, like: f16, f32, f64, i8, b8, and complex variants
simsimd_cap_any_k); // Which CPU capabilities are we allowed to use
simsimd_distance_t distance;
distance_function(vector_a, vector_b, 1536, &distance);
return 0;
}
```
### Dynamic Dispatch
To avoid hard-coding the backend, you can rely on `c/lib.c` to prepackage all possible backends in one binary, and select the most recent CPU features at runtime.
That feature of the C library is called dynamic dispatch and is extensively used in the Python, JavaScript, and Rust bindings.
To test which CPU features are available on the machine at runtime, use the following APIs:
```c
int uses_neon = simsimd_uses_neon();
int uses_sve = simsimd_uses_sve();
int uses_haswell = simsimd_uses_haswell();
int uses_skylake = simsimd_uses_skylake();
int uses_ice = simsimd_uses_ice();
int uses_sapphire = simsimd_uses_sapphire();
simsimd_capability_t capabilities = simsimd_capabilities();
```
To differentiate between runtime and compile-time dispatch, define the following macro:
```c
#define SIMSIMD_DYNAMIC_DISPATCH 1 // or 0
```
### Spatial Distances: Cosine and Euclidean Distances
```c
#include <simsimd/simsimd.h>
int main() {
simsimd_f64_t f64s[1536];
simsimd_f32_t f32s[1536];
simsimd_f16_t f16s[1536];
simsimd_i8_t i8[1536];
simsimd_distance_t distance;
// Cosine distance between two vectors
simsimd_cos_i8(i8s, i8s, 1536, &distance);
simsimd_cos_f16(f16s, f16s, 1536, &distance);
simsimd_cos_f32(f32s, f32s, 1536, &distance);
simsimd_cos_f64(f64s, f64s, 1536, &distance);
// Euclidean distance between two vectors
simsimd_l2sq_i8(i8s, i8s, 1536, &distance);
simsimd_l2sq_f16(f16s, f16s, 1536, &distance);
simsimd_l2sq_f32(f32s, f32s, 1536, &distance);
simsimd_l2sq_f64(f64s, f64s, 1536, &distance);
return 0;
}
```
### Dot-Products: Inner and Complex Inner Products
```c
#include <simsimd/simsimd.h>
int main() {
simsimd_f64_t f64s[1536];
simsimd_f32_t f32s[1536];
simsimd_f16_t f16s[1536];
simsimd_distance_t distance;
// Inner product between two vectors
simsimd_dot_f16(f16s, f16s, 1536, &distance);
simsimd_dot_f32(f32s, f32s, 1536, &distance);
simsimd_dot_f64(f64s, f64s, 1536, &distance);
// Complex inner product between two vectors
simsimd_dot_f16c(f16s, f16s, 1536, &distance);
simsimd_dot_f32c(f32s, f32s, 1536, &distance);
simsimd_dot_f64c(f64s, f64s, 1536, &distance);
// Complex conjugate inner product between two vectors
simsimd_vdot_f16c(f16s, f16s, 1536, &distance);
simsimd_vdot_f32c(f32s, f32s, 1536, &distance);
simsimd_vdot_f64c(f64s, f64s, 1536, &distance);
return 0;
}
```
### Binary Distances: Hamming and Jaccard Distances
```c
#include <simsimd/simsimd.h>
int main() {
simsimd_b8_t b8s[1536 / 8]; // 8 bits per word
simsimd_distance_t distance;
// Hamming distance between two vectors
simsimd_hamming_b8(b8s, b8s, 1536 / 8, &distance);
// Jaccard distance between two vectors
simsimd_jaccard_b8(b8s, b8s, 1536 / 8, &distance);
return 0;
}
```
### Probability Distributions: Jensen-Shannon and Kullback-Leibler Divergences
```c
#include <simsimd/simsimd.h>
int main() {
simsimd_f64_t f64s[1536];
simsimd_f32_t f32s[1536];
simsimd_f16_t f16s[1536];
simsimd_distance_t distance;
// Jensen-Shannon divergence between two vectors
simsimd_js_f16(f16s, f16s, 1536, &distance);
simsimd_js_f32(f32s, f32s, 1536, &distance);
simsimd_js_f64(f64s, f64s, 1536, &distance);
// Kullback-Leibler divergence between two vectors
simsimd_kl_f16(f16s, f16s, 1536, &distance);
simsimd_kl_f32(f32s, f32s, 1536, &distance);
simsimd_kl_f64(f64s, f64s, 1536, &distance);
return 0;
}
```
### Half-Precision Floating-Point Numbers
If you aim to utilize the `_Float16` functionality with SimSIMD, ensure your development environment is compatible with C 11.
For other SimSIMD functionalities, C 99 compatibility will suffice.
To explicitly disable half-precision support, define the following macro before imports:
```c
#define SIMSIMD_NATIVE_F16 0 // or 1
#include <simsimd/simsimd.h>
```
### Target Specific Backends
SimSIMD exposes all kernels for all backends, and you can select the most advanced one for the current CPU without relying on built-in dispatch mechanisms.
All of the function names follow the same pattern: `simsimd_{function}_{type}_{backend}`.
- The backend can be `serial`, `haswell`, `skylake`, `ice`, `sapphire`, `neon`, or `sve`.
- The type can be `f64`, `f32`, `f16`, `f64c`, `f32c`, `f16c`, `i8`, or `b8`.
- The function can be `dot`, `vdot`, `cos`, `l2sq`, `hamming`, `jaccard`, `kl`, or `js`.
To avoid hard-coding the backend, you can use the `simsimd_metric_punned_t` to pun the function pointer and the `simsimd_capabilities` function to get the available backends at runtime.
```c
simsimd_dot_f64_sve
simsimd_cos_f64_sve
simsimd_l2sq_f64_sve
simsimd_dot_f64_skylake
simsimd_cos_f64_skylake
simsimd_l2sq_f64_skylake
simsimd_dot_f64_serial
simsimd_cos_f64_serial
simsimd_l2sq_f64_serial
simsimd_js_f64_serial
simsimd_kl_f64_serial
simsimd_dot_f32_sve
simsimd_cos_f32_sve
simsimd_l2sq_f32_sve
simsimd_dot_f32_neon
simsimd_cos_f32_neon
simsimd_l2sq_f32_neon
simsimd_js_f32_neon
simsimd_kl_f32_neon
simsimd_dot_f32_skylake
simsimd_cos_f32_skylake
simsimd_l2sq_f32_skylake
simsimd_js_f32_skylake
simsimd_kl_f32_skylake
simsimd_dot_f32_serial
simsimd_cos_f32_serial
simsimd_l2sq_f32_serial
simsimd_js_f32_serial
simsimd_kl_f32_serial
simsimd_dot_f16_sve
simsimd_cos_f16_sve
simsimd_l2sq_f16_sve
simsimd_dot_f16_neon
simsimd_cos_f16_neon
simsimd_l2sq_f16_neon
simsimd_js_f16_neon
simsimd_kl_f16_neon
simsimd_dot_f16_sapphire
simsimd_cos_f16_sapphire
simsimd_l2sq_f16_sapphire
simsimd_js_f16_sapphire
simsimd_kl_f16_sapphire
simsimd_dot_f16_haswell
simsimd_cos_f16_haswell
simsimd_l2sq_f16_haswell
simsimd_js_f16_haswell
simsimd_kl_f16_haswell
simsimd_dot_f16_serial
simsimd_cos_f16_serial
simsimd_l2sq_f16_serial
simsimd_js_f16_serial
simsimd_kl_f16_serial
simsimd_cos_i8_neon
simsimd_cos_i8_neon
simsimd_l2sq_i8_neon
simsimd_cos_i8_ice
simsimd_cos_i8_ice
simsimd_l2sq_i8_ice
simsimd_cos_i8_haswell
simsimd_cos_i8_haswell
simsimd_l2sq_i8_haswell
simsimd_cos_i8_serial
simsimd_cos_i8_serial
simsimd_l2sq_i8_serial
simsimd_hamming_b8_sve
simsimd_jaccard_b8_sve
simsimd_hamming_b8_neon
simsimd_jaccard_b8_neon
simsimd_hamming_b8_ice
simsimd_jaccard_b8_ice
simsimd_hamming_b8_haswell
simsimd_jaccard_b8_haswell
simsimd_hamming_b8_serial
simsimd_jaccard_b8_serial
simsimd_dot_f32c_sve
simsimd_vdot_f32c_sve
simsimd_dot_f32c_neon
simsimd_vdot_f32c_neon
simsimd_dot_f32c_haswell
simsimd_vdot_f32c_haswell
simsimd_dot_f32c_skylake
simsimd_vdot_f32c_skylake
simsimd_dot_f32c_serial
simsimd_vdot_f32c_serial
simsimd_dot_f64c_sve
simsimd_vdot_f64c_sve
simsimd_dot_f64c_skylake
simsimd_vdot_f64c_skylake
simsimd_dot_f64c_serial
simsimd_vdot_f64c_serial
simsimd_dot_f16c_sve
simsimd_vdot_f16c_sve
simsimd_dot_f16c_neon
simsimd_vdot_f16c_neon
simsimd_dot_f16c_haswell
simsimd_vdot_f16c_haswell
simsimd_dot_f16c_sapphire
simsimd_vdot_f16c_sapphire
simsimd_dot_f16c_serial
simsimd_vdot_f16c_serial
```
Raw data
{
"_id": null,
"home_page": "https://github.com/ashvardanian/simsimd",
"name": "simsimd",
"maintainer": null,
"docs_url": null,
"requires_python": null,
"maintainer_email": null,
"keywords": null,
"author": "Ash Vardanian",
"author_email": "1983160+ashvardanian@users.noreply.github.com",
"download_url": null,
"platform": null,
"description": "# SimSIMD \ud83d\udccf\n\n\n\nComputing dot-products, similarity measures, and distances between low- and high-dimensional vectors is ubiquitous in Machine Learning, Scientific Computing, Geo-Spatial Analysis, and Information Retrieval.\nThese algorithms generally have linear complexity in time, constant complexity in space, and are data-parallel.\nIn other words, it is easily parallelizable and vectorizable and often available in packages like BLAS and LAPACK, as well as higher-level `numpy` and `scipy` Python libraries.\nIronically, even with decades of evolution in compilers and numerical computing, [most libraries can be 3-200x slower than hardware potential][benchmarks] even on the most popular hardware, like 64-bit x86 and Arm CPUs.\nSimSIMD attempts to fill that gap.\n1\ufe0f\u20e3 SimSIMD functions are practically as fast as `memcpy`.\n2\ufe0f\u20e3 SimSIMD [compiles to more platforms than NumPy (105 vs 35)][compatibility] and has more backends than most BLAS implementations.\n\n[benchmarks]: https://ashvardanian.com/posts/simsimd-faster-scipy\n[compatibility]: https://pypi.org/project/simsimd/#files\n\n<div>\n<a href=\"https://pepy.tech/project/simsimd\">\n <img alt=\"PyPI\" src=\"https://static.pepy.tech/personalized-badge/simsimd?period=total&units=abbreviation&left_color=black&right_color=blue&left_text=SimSIMD%20Python%20installs\" />\n</a>\n<a href=\"https://www.npmjs.com/package/simsimd\">\n <img alt=\"npm\" src=\"https://img.shields.io/npm/dy/simsimd?label=JavaScript%20NPM%20installs\" />\n</a>\n<a href=\"https://crates.io/crates/simsimd\">\n <img alt=\"rust\" src=\"https://img.shields.io/crates/d/simsimd?label=Rust%20Crate%20installs\" />\n</a>\n<img alt=\"GitHub code size in bytes\" src=\"https://img.shields.io/github/languages/code-size/ashvardanian/simsimd\">\n<a href=\"https://github.com/ashvardanian/SimSIMD/actions/workflows/release.yml\">\n <img alt=\"GitHub Actions Ubuntu\" src=\"https://img.shields.io/github/actions/workflow/status/ashvardanian/SimSIMD/release.yml?branch=main&label=Ubuntu&logo=github&color=blue\">\n</a>\n<a href=\"https://github.com/ashvardanian/SimSIMD/actions/workflows/release.yml\">\n <img alt=\"GitHub Actions Windows\" src=\"https://img.shields.io/github/actions/workflow/status/ashvardanian/SimSIMD/release.yml?branch=main&label=Windows&logo=windows&color=blue\">\n</a>\n<a href=\"https://github.com/ashvardanian/SimSIMD/actions/workflows/release.yml\">\n <img alt=\"GitHub Actions MacOS\" src=\"https://img.shields.io/github/actions/workflow/status/ashvardanian/SimSIMD/release.yml?branch=main&label=MacOS&logo=apple&color=blue\">\n</a>\n<a href=\"https://github.com/ashvardanian/SimSIMD/actions/workflows/release.yml\">\n <img alt=\"GitHub Actions CentOS Linux\" src=\"https://img.shields.io/github/actions/workflow/status/ashvardanian/SimSIMD/release.yml?branch=main&label=CentOS&logo=centos&color=blue\">\n</a>\n\n</div>\n\n## Features\n\nSimSIMD provides over 100 SIMD-optimized kernels for various distance and similarity measures, accelerating search in [USearch](https://github.com/unum-cloud/usearch) and several DBMS products.\nImplemented distance functions include:\n\n- Euclidean (L2) and Cosine (Angular) spatial distances for Vector Search.\n- Dot-Products for real & complex vectors for DSP & Quantum computing.\n- Hamming (~ Manhattan) and Jaccard (~ Tanimoto) bit-level distances.\n- Kullback-Leibler and Jensen\u2013Shannon divergences for probability distributions.\n- Haversine and Vincenty's formulae for Geospatial Analysis.\n- For Levenshtein, Needleman\u2013Wunsch and other text metrics, check [StringZilla][stringzilla].\n\n[scipy]: https://docs.scipy.org/doc/scipy/reference/spatial.distance.html#module-scipy.spatial.distance\n[numpy]: https://numpy.org/doc/stable/reference/generated/numpy.inner.html\n[stringzilla]: https://github.com/ashvardanian/stringzilla\n\nMoreover, SimSIMD...\n\n- handles `f64`, `f32`, and `f16` real & complex vectors.\n- handles `i8` integral and `b8` binary vectors.\n- is a zero-dependency [header-only C 99](#using-simsimd-in-c) library.\n- has bindings for [Python](#using-simsimd-in-python), [Rust](#using-simsimd-in-rust) and [JavaScript](#using-simsimd-in-javascript).\n- has Arm backends for NEON and Scalable Vector Extensions (SVE).\n- has x86 backends for Haswell, Skylake, Ice Lake, and Sapphire Rapids.\n\nDue to the high-level of fragmentation of SIMD support in different x86 CPUs, SimSIMD uses the names of select Intel CPU generations for its backends.\nThey, however, also work on AMD CPUs.\nInel Haswell is compatible with AMD Zen 1/2/3, while AMD Genoa Zen 4 covers AVX-512 instructions added to Intel Skylake and Ice Lake.\nYou can learn more about the technical implementation details in the following blogposts:\n\n- [Uses Horner's method for polynomial approximations, beating GCC 12 by 119x](https://ashvardanian.com/posts/gcc-12-vs-avx512fp16/).\n- [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).\n- [Uses AVX-512 FP16 for half-precision operations, that few compilers vectorize](https://ashvardanian.com/posts/simsimd-faster-scipy/#the-challenge-of-f16).\n- [Substitutes LibC's `sqrt` calls with bit-hacks using Jan Kadlec's constant](https://ashvardanian.com/posts/simsimd-faster-scipy/#bonus-section-bypassing-sqrt-and-libc-dependencies).\n- [For Python avoids slow PyBind11, SWIG, and even `PyArg_ParseTuple` for speed](https://ashvardanian.com/posts/pybind11-cpython-tutorial/).\n- [For JavaScript uses typed arrays and NAPI for zero-copy calls](https://ashvardanian.com/posts/javascript-ai-vector-search/).\n\n## Benchmarks\n\n### Against NumPy and SciPy\n\nGiven 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:\n\n| Kind | `f32` improvement | `f16` improvement | `i8` improvement | Conventional method | SimSIMD |\n| :------------------------ | ----------------: | ----------------: | ---------------: | :------------------------------------- | :-------------- |\n| Inner Product | __2 x__ | __9 x__ | __18 x__ | `numpy.inner` | `inner` |\n| Cosine Distance | __32 x__ | __79 x__ | __133 x__ | `scipy.spatial.distance.cosine` | `cosine` |\n| Euclidean Distance \u00b2 | __5 x__ | __26 x__ | __17 x__ | `scipy.spatial.distance.sqeuclidean` | `sqeuclidean` |\n| Jensen-Shannon Divergence | __31 x__ | __53 x__ | | `scipy.spatial.distance.jensenshannon` | `jensenshannon` |\n\n### Against GCC Auto-Vectorization\n\nOn the Intel Sapphire Rapids platform, SimSIMD was benchmarked against auto-vectorized code using GCC 12.\nGCC handles single-precision `float` but might not be the best choice for `int8` and `_Float16` arrays, which have been part of the C language since 2011.\n\n| Kind | GCC 12 `f32` | GCC 12 `f16` | SimSIMD `f16` | `f16` improvement |\n| :------------------------ | -----------: | -----------: | ------------: | ----------------: |\n| Inner Product | 3,810 K/s | 192 K/s | 5,990 K/s | __31 x__ |\n| Cosine Distance | 3,280 K/s | 336 K/s | 6,880 K/s | __20 x__ |\n| Euclidean Distance \u00b2 | 4,620 K/s | 147 K/s | 5,320 K/s | __36 x__ |\n| Jensen-Shannon Divergence | 1,180 K/s | 18 K/s | 2,140 K/s | __118 x__ |\n\n__Broader Benchmarking Results__:\n\n- [Apple M2 Pro](https://ashvardanian.com/posts/simsimd-faster-scipy/#appendix-1-performance-on-apple-m2-pro).\n- [4th Gen Intel Xeon Platinum](https://ashvardanian.com/posts/simsimd-faster-scipy/#appendix-2-performance-on-4th-gen-intel-xeon-platinum-8480).\n- [AWS Graviton 3](https://ashvardanian.com/posts/simsimd-faster-scipy/#appendix-3-performance-on-aws-graviton-3).\n\n## Using SimSIMD in Python\n\nThe package is intended to replace the usage of `numpy.inner`, `numpy.dot`, and `scipy.spatial.distance`.\nAside from drastic performance improvements, SimSIMD significantly improves accuracy in mixed precision setups.\nNumPy and SciPy, processing `i8` or `f16` vectors, will use the same types for accumulators, while SimSIMD can combine `i8` enumeration, `i16` multiplication, and `i32` accumulation to avoid overflows entirely.\nThe same applies to processing `f16` values with `f32` precision.\n\n### Installation\n\nUse the following snippet to install SimSIMD and list available hardware acceleration options available on your machine:\n\n```sh\npip install simsimd\npython -c \"import simsimd; print(simsimd.get_capabilities())\"\n```\n\n### One-to-One Distance\n\n```py\nimport simsimd\nimport numpy as np\n\nvec1 = np.random.randn(1536).astype(np.float32)\nvec2 = np.random.randn(1536).astype(np.float32)\ndist = simsimd.cosine(vec1, vec2)\n```\n\nSupported functions include `cosine`, `inner`, `sqeuclidean`, `hamming`, and `jaccard`.\nDot products are supported for both real and complex numbers:\n\n```py\nvec1 = np.random.randn(768).astype(np.float64) + 1j * np.random.randn(768).astype(np.float64)\nvec2 = np.random.randn(768).astype(np.float64) + 1j * np.random.randn(768).astype(np.float64)\n\ndist = simsimd.dot(vec1.astype(np.complex128), vec2.astype(np.complex128))\ndist = simsimd.dot(vec1.astype(np.complex64), vec2.astype(np.complex64))\ndist = simsimd.vdot(vec1.astype(np.complex64), vec2.astype(np.complex64)) # conjugate, same as `np.vdot`\n```\n\nUnlike SciPy, SimSIMD allows explicitly stating the precision of the input vectors, which is especially useful for mixed-precision setups.\n\n```py\ndist = simsimd.cosine(vec1, vec2, \"i8\")\ndist = simsimd.cosine(vec1, vec2, \"f16\")\ndist = simsimd.cosine(vec1, vec2, \"f32\")\ndist = simsimd.cosine(vec1, vec2, \"f64\")\n```\n\nIt also allows using SimSIMD for half-precision complex numbers, which NumPy does not support.\nFor that, view data as continuous even-length `np.float16` vectors and override type-resolution with `complex32` string.\n\n```py\nvec1 = np.random.randn(1536).astype(np.float16)\nvec2 = np.random.randn(1536).astype(np.float16)\nsimd.dot(vec1, vec2, \"complex32\")\nsimd.vdot(vec1, vec2, \"complex32\")\n```\n\n### One-to-Many Distances\n\nEvery distance function can be used not only for one-to-one but also one-to-many and many-to-many distance calculations.\nFor one-to-many:\n\n```py\nvec1 = np.random.randn(1536).astype(np.float32) # rank 1 tensor\nbatch1 = np.random.randn(1, 1536).astype(np.float32) # rank 2 tensor\nbatch2 = np.random.randn(100, 1536).astype(np.float32)\n\ndist_rank1 = simsimd.cosine(vec1, batch2)\ndist_rank2 = simsimd.cosine(batch1, batch2)\n```\n\n### Many-to-Many Distances\n\nAll distance functions in SimSIMD can be used to compute many-to-many distances.\nFor two batches of 100 vectors to compute 100 distances, one would call it like this:\n\n```py\nbatch1 = np.random.randn(100, 1536).astype(np.float32)\nbatch2 = np.random.randn(100, 1536).astype(np.float32)\ndist = simsimd.cosine(batch1, batch2)\n```\n\nInput matrices must have identical shapes.\nThis functionality isn't natively present in NumPy or SciPy, and generally requires creating intermediate arrays, which is inefficient and memory-consuming.\n\n### Many-to-Many All-Pairs Distances\n\nOne can use SimSIMD to compute 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)).\nThe resulting object will have a type `DistancesTensor`, zero-copy compatible with NumPy and other libraries.\nFor two arrays of 10 and 1,000 entries, the resulting tensor will have 10,000 cells:\n\n```py\nimport numpy as np\nfrom simsimd import cdist, DistancesTensor\n\nmatrix1 = np.random.randn(1000, 1536).astype(np.float32)\nmatrix2 = np.random.randn(10, 1536).astype(np.float32)\ndistances: DistancesTensor = simsimd.cdist(matrix1, matrix2, metric=\"cosine\") # zero-copy\ndistances_array: np.ndarray = np.array(distances, copy=True) # now managed by NumPy\n```\n\n### Multithreading\n\nBy default, computations use a single CPU core.\nTo optimize and utilize all CPU cores on Linux systems, add the `threads=0` argument.\nAlternatively, specify a custom number of threads:\n\n```py\ndistances = simsimd.cdist(matrix1, matrix2, metric=\"cosine\", threads=0)\n```\n\n### Using Python API with USearch\n\nWant to use it in Python with [USearch](https://github.com/unum-cloud/usearch)?\nYou 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.\n\n```py\nfrom usearch.index import Index, CompiledMetric, MetricKind, MetricSignature\nfrom simsimd import pointer_to_sqeuclidean, pointer_to_cosine, pointer_to_inner\n\nmetric = CompiledMetric(\n pointer=pointer_to_cosine(\"f16\"),\n kind=MetricKind.Cos,\n signature=MetricSignature.ArrayArraySize,\n)\n\nindex = Index(256, metric=metric)\n```\n\n## Using SimSIMD in Rust\n\nTo install, add the following to your `Cargo.toml`:\n\n```toml\n[dependencies]\nsimsimd = \"...\"\n```\n\nBefore using the SimSIMD library, ensure you have imported the necessary traits and types into your Rust source file.\nThe library provides several traits for different distance/similarity kinds - `SpatialSimilarity`, `BinarySimilarity`, and `ProbabilitySimilarity`.\n\n### Spatial Similarity: Cosine and Euclidean Distances\n\n```rust\nuse simsimd::SpatialSimilarity;\n\nfn main() {\n let vector_a: Vec<f32> = vec![1.0, 2.0, 3.0];\n let vector_b: Vec<f32> = vec![4.0, 5.0, 6.0];\n\n // Compute the cosine similarity between vector_a and vector_b\n let cosine_similarity = f32::cosine(&vector_a, &vector_b)\n .expect(\"Vectors must be of the same length\");\n\n println!(\"Cosine Similarity: {}\", cosine_similarity);\n\n // Compute the squared Euclidean distance between vector_a and vector_b\n let sq_euclidean_distance = f32::sqeuclidean(&vector_a, &vector_b)\n .expect(\"Vectors must be of the same length\");\n\n println!(\"Squared Euclidean Distance: {}\", sq_euclidean_distance);\n}\n```\n\nSpatial similarity functions are available for `f64`, `f32`, `f16`, and `i8` types.\n\n### Dot-Products: Inner and Complex Inner Products\n\n```rust\nuse simsimd::SpatialSimilarity;\nuse simsimd::ComplexProducts;\n\nfn main() {\n let vector_a: Vec<f32> = vec![1.0, 2.0, 3.0, 4.0];\n let vector_b: Vec<f32> = vec![5.0, 6.0, 7.0, 8.0];\n\n // Compute the inner product between vector_a and vector_b\n let inner_product = SpatialSimilarity::dot(&vector_a, &vector_b)\n .expect(\"Vectors must be of the same length\");\n\n println!(\"Inner Product: {}\", inner_product);\n\n // Compute the complex inner product between complex_vector_a and complex_vector_b\n let complex_inner_product = ComplexProducts::dot(&vector_a, &vector_b)\n .expect(\"Vectors must be of the same length\");\n\n let complex_conjugate_inner_product = ComplexProducts::vdot(&vector_a, &vector_b)\n .expect(\"Vectors must be of the same length\");\n\n println!(\"Complex Inner Product: {:?}\", complex_inner_product); // -18, 69\n println!(\"Complex C. Inner Product: {:?}\", complex_conjugate_inner_product); // 70, -8\n}\n```\n\nComplex inner products are available for `f64`, `f32`, and `f16` types.\n\n### Probability Distributions: Jensen-Shannon and Kullback-Leibler Divergences\n\n```rust\nuse simsimd::SpatialSimilarity;\n\nfn main() {\n let vector_a: Vec<f32> = vec![1.0, 2.0, 3.0];\n let vector_b: Vec<f32> = vec![4.0, 5.0, 6.0];\n\n let cosine_similarity = f32::jensenshannon(&vector_a, &vector_b)\n .expect(\"Vectors must be of the same length\");\n\n println!(\"Cosine Similarity: {}\", cosine_similarity);\n\n let sq_euclidean_distance = f32::kullbackleibler(&vector_a, &vector_b)\n .expect(\"Vectors must be of the same length\");\n\n println!(\"Squared Euclidean Distance: {}\", sq_euclidean_distance);\n}\n```\n\nProbability similarity functions are available for `f64`, `f32`, and `f16` types.\n\n### Binary Similarity: Hamming and Jaccard Distances\n\nSimilar to spatial distances, one can compute bit-level distance functions between slices of unsigned integers:\n\n```rust\nuse simsimd::BinarySimilarity;\n\nfn main() {\n let vector_a = &[0b11110000, 0b00001111, 0b10101010];\n let vector_b = &[0b11110000, 0b00001111, 0b01010101];\n\n // Compute the Hamming distance between vector_a and vector_b\n let hamming_distance = u8::hamming(&vector_a, &vector_b)\n .expect(\"Vectors must be of the same length\");\n\n println!(\"Hamming Distance: {}\", hamming_distance);\n\n // Compute the Jaccard distance between vector_a and vector_b\n let jaccard_distance = u8::jaccard(&vector_a, &vector_b)\n .expect(\"Vectors must be of the same length\");\n\n println!(\"Jaccard Distance: {}\", jaccard_distance);\n}\n```\n\nBinary similarity functions are available only for `u8` types.\n\n### Half-Precision Floating-Point Numbers\n\nRust has no native support for half-precision floating-point numbers, but SimSIMD provides a `f16` type.\nIt has no functionality - it is a `transparent` wrapper around `u16` and can be used with `half` or any other half-precision library.\n\n```rust\nuse simsimd::SpatialSimilarity;\nuse simsimd::f16 as SimF16;\nuse half::f16 as HalfF16;\n\nfn main() {\n let vector_a: Vec<HalfF16> = ...\n let vector_b: Vec<HalfF16> = ...\n\n let buffer_a: &[SimF16] = unsafe { std::slice::from_raw_parts(a_half.as_ptr() as *const SimF16, a_half.len()) };\n let buffer_b: &[SimF16] = unsafe { std::slice::from_raw_parts(b_half.as_ptr() as *const SimF16, b_half.len()) };\n\n // Compute the cosine similarity between vector_a and vector_b\n let cosine_similarity = SimF16::cosine(&vector_a, &vector_b)\n .expect(\"Vectors must be of the same length\");\n\n println!(\"Cosine Similarity: {}\", cosine_similarity);\n}\n```\n\n### Dynamic Dispatch\n\nSimSIMD provides a dynamic dispatch mechanism to select the most advanced micro-kernel for the current CPU.\nYou can query supported backends and use the `SimSIMD::capabilities` function to select the best one.\n\n```rust\nprintln!(\"uses neon: {}\", capabilties::uses_neon());\nprintln!(\"uses sve: {}\", capabilties::uses_sve());\nprintln!(\"uses haswell: {}\", capabilties::uses_haswell());\nprintln!(\"uses skylake: {}\", capabilties::uses_skylake());\nprintln!(\"uses ice: {}\", capabilties::uses_ice());\nprintln!(\"uses sapphire: {}\", capabilties::uses_sapphire());\n```\n\n## Using SimSIMD in JavaScript\n\nTo install, choose one of the following options depending on your environment:\n\n- `npm install --save simsimd`\n- `yarn add simsimd`\n- `pnpm add simsimd`\n- `bun install simsimd`\n\nThe package is distributed with prebuilt binaries, but if your platform is not supported, you can build the package from the source via `npm run build`.\nThis will automatically happen unless you install the package with the `--ignore-scripts` flag or use Bun.\nAfter you install it, you will be able to call the SimSIMD functions on various `TypedArray` variants:\n\n```js\nconst { sqeuclidean, cosine, inner, hamming, jaccard } = require('simsimd');\n\nconst vectorA = new Float32Array([1.0, 2.0, 3.0]);\nconst vectorB = new Float32Array([4.0, 5.0, 6.0]);\n\nconst distance = sqeuclidean(vectorA, vectorB);\nconsole.log('Squared Euclidean Distance:', distance);\n```\n\nOther numeric types and precision levels are supported as well.\nFor double-precsion floating-point numbers, use `Float64Array`:\n\n```js\nconst vectorA = new Float64Array([1.0, 2.0, 3.0]);\nconst vectorB = new Float64Array([4.0, 5.0, 6.0]);\nconst distance = cosine(vectorA, vectorB);\n```\n\nWhen doing machine learning and vector search with high-dimensional vectors you may want to quantize them to 8-bit integers.\nYou may want to project values from the $[-1, 1]$ range to the $[-100, 100]$ range and then cast them to `Uint8Array`:\n\n```js\nconst quantizedVectorA = new Uint8Array(vectorA.map(v => (v * 100)));\nconst quantizedVectorB = new Uint8Array(vectorB.map(v => (v * 100)));\nconst distance = cosine(quantizedVectorA, quantizedVectorB);\n```\n\nA more extreme quantization case would be to use binary vectors.\nYou can map all positive values to `1` and all negative values and zero to `0`, packing eight values into a single byte.\nAfter that, Hamming and Jaccard distances can be computed.\n\n```js\nconst { toBinary, hamming } = require('simsimd');\n\nconst binaryVectorA = toBinary(vectorA);\nconst binaryVectorB = toBinary(vectorB);\nconst distance = hamming(binaryVectorA, binaryVectorB);\n```\n\n## Using SimSIMD in C\n\nFor integration within a CMake-based project, add the following segment to your `CMakeLists.txt`:\n\n```cmake\nFetchContent_Declare(\n simsimd\n GIT_REPOSITORY https://github.com/ashvardanian/simsimd.git\n GIT_SHALLOW TRUE\n)\nFetchContent_MakeAvailable(simsimd)\n```\n\nAfter that, you can use the SimSIMD library in your C code in several ways.\nSimplest of all, you can include the headers, and the compiler will automatically select the most recent CPU extensions that SimSIMD will use.\n\n```c\n#include <simsimd/simsimd.h>\n\nint main() {\n simsimd_f32_t vector_a[1536];\n simsimd_f32_t vector_b[1536];\n simsimd_metric_punned_t distance_function = simsimd_metric_punned(\n simsimd_metric_cos_k, // Metric kind, like the angular cosine distance\n simsimd_datatype_f32_k, // Data type, like: f16, f32, f64, i8, b8, and complex variants\n simsimd_cap_any_k); // Which CPU capabilities are we allowed to use\n simsimd_distance_t distance;\n distance_function(vector_a, vector_b, 1536, &distance);\n return 0;\n}\n```\n\n### Dynamic Dispatch\n\nTo avoid hard-coding the backend, you can rely on `c/lib.c` to prepackage all possible backends in one binary, and select the most recent CPU features at runtime.\nThat feature of the C library is called dynamic dispatch and is extensively used in the Python, JavaScript, and Rust bindings.\nTo test which CPU features are available on the machine at runtime, use the following APIs:\n\n```c\nint uses_neon = simsimd_uses_neon();\nint uses_sve = simsimd_uses_sve();\nint uses_haswell = simsimd_uses_haswell();\nint uses_skylake = simsimd_uses_skylake();\nint uses_ice = simsimd_uses_ice();\nint uses_sapphire = simsimd_uses_sapphire();\n\nsimsimd_capability_t capabilities = simsimd_capabilities();\n```\n\nTo differentiate between runtime and compile-time dispatch, define the following macro:\n\n```c\n#define SIMSIMD_DYNAMIC_DISPATCH 1 // or 0\n```\n\n### Spatial Distances: Cosine and Euclidean Distances\n\n```c\n#include <simsimd/simsimd.h>\n\nint main() {\n simsimd_f64_t f64s[1536];\n simsimd_f32_t f32s[1536];\n simsimd_f16_t f16s[1536];\n simsimd_i8_t i8[1536];\n simsimd_distance_t distance;\n\n // Cosine distance between two vectors\n simsimd_cos_i8(i8s, i8s, 1536, &distance);\n simsimd_cos_f16(f16s, f16s, 1536, &distance);\n simsimd_cos_f32(f32s, f32s, 1536, &distance);\n simsimd_cos_f64(f64s, f64s, 1536, &distance);\n \n // Euclidean distance between two vectors\n simsimd_l2sq_i8(i8s, i8s, 1536, &distance);\n simsimd_l2sq_f16(f16s, f16s, 1536, &distance);\n simsimd_l2sq_f32(f32s, f32s, 1536, &distance);\n simsimd_l2sq_f64(f64s, f64s, 1536, &distance);\n\n return 0;\n}\n```\n\n### Dot-Products: Inner and Complex Inner Products\n\n```c\n#include <simsimd/simsimd.h>\n\nint main() {\n simsimd_f64_t f64s[1536];\n simsimd_f32_t f32s[1536];\n simsimd_f16_t f16s[1536];\n simsimd_distance_t distance;\n\n // Inner product between two vectors\n simsimd_dot_f16(f16s, f16s, 1536, &distance);\n simsimd_dot_f32(f32s, f32s, 1536, &distance);\n simsimd_dot_f64(f64s, f64s, 1536, &distance);\n\n // Complex inner product between two vectors\n simsimd_dot_f16c(f16s, f16s, 1536, &distance);\n simsimd_dot_f32c(f32s, f32s, 1536, &distance);\n simsimd_dot_f64c(f64s, f64s, 1536, &distance);\n\n // Complex conjugate inner product between two vectors\n simsimd_vdot_f16c(f16s, f16s, 1536, &distance);\n simsimd_vdot_f32c(f32s, f32s, 1536, &distance);\n simsimd_vdot_f64c(f64s, f64s, 1536, &distance);\n\n return 0;\n}\n```\n\n### Binary Distances: Hamming and Jaccard Distances\n\n```c\n#include <simsimd/simsimd.h>\n\nint main() {\n simsimd_b8_t b8s[1536 / 8]; // 8 bits per word\n simsimd_distance_t distance;\n\n // Hamming distance between two vectors\n simsimd_hamming_b8(b8s, b8s, 1536 / 8, &distance);\n\n // Jaccard distance between two vectors\n simsimd_jaccard_b8(b8s, b8s, 1536 / 8, &distance);\n\n return 0;\n}\n```\n\n### Probability Distributions: Jensen-Shannon and Kullback-Leibler Divergences\n\n```c\n#include <simsimd/simsimd.h>\n\nint main() {\n simsimd_f64_t f64s[1536];\n simsimd_f32_t f32s[1536];\n simsimd_f16_t f16s[1536];\n simsimd_distance_t distance;\n\n // Jensen-Shannon divergence between two vectors\n simsimd_js_f16(f16s, f16s, 1536, &distance);\n simsimd_js_f32(f32s, f32s, 1536, &distance);\n simsimd_js_f64(f64s, f64s, 1536, &distance);\n\n // Kullback-Leibler divergence between two vectors\n simsimd_kl_f16(f16s, f16s, 1536, &distance);\n simsimd_kl_f32(f32s, f32s, 1536, &distance);\n simsimd_kl_f64(f64s, f64s, 1536, &distance);\n\n return 0;\n}\n```\n\n### Half-Precision Floating-Point Numbers\n\nIf you aim to utilize the `_Float16` functionality with SimSIMD, ensure your development environment is compatible with C 11.\nFor other SimSIMD functionalities, C 99 compatibility will suffice.\nTo explicitly disable half-precision support, define the following macro before imports:\n\n```c\n#define SIMSIMD_NATIVE_F16 0 // or 1\n#include <simsimd/simsimd.h>\n```\n\n### Target Specific Backends\n\nSimSIMD exposes all kernels for all backends, and you can select the most advanced one for the current CPU without relying on built-in dispatch mechanisms.\nAll of the function names follow the same pattern: `simsimd_{function}_{type}_{backend}`.\n\n- The backend can be `serial`, `haswell`, `skylake`, `ice`, `sapphire`, `neon`, or `sve`.\n- The type can be `f64`, `f32`, `f16`, `f64c`, `f32c`, `f16c`, `i8`, or `b8`.\n- The function can be `dot`, `vdot`, `cos`, `l2sq`, `hamming`, `jaccard`, `kl`, or `js`.\n\nTo avoid hard-coding the backend, you can use the `simsimd_metric_punned_t` to pun the function pointer and the `simsimd_capabilities` function to get the available backends at runtime.\n\n```c\nsimsimd_dot_f64_sve\nsimsimd_cos_f64_sve\nsimsimd_l2sq_f64_sve\nsimsimd_dot_f64_skylake\nsimsimd_cos_f64_skylake\nsimsimd_l2sq_f64_skylake\nsimsimd_dot_f64_serial\nsimsimd_cos_f64_serial\nsimsimd_l2sq_f64_serial\nsimsimd_js_f64_serial\nsimsimd_kl_f64_serial\nsimsimd_dot_f32_sve\nsimsimd_cos_f32_sve\nsimsimd_l2sq_f32_sve\nsimsimd_dot_f32_neon\nsimsimd_cos_f32_neon\nsimsimd_l2sq_f32_neon\nsimsimd_js_f32_neon\nsimsimd_kl_f32_neon\nsimsimd_dot_f32_skylake\nsimsimd_cos_f32_skylake\nsimsimd_l2sq_f32_skylake\nsimsimd_js_f32_skylake\nsimsimd_kl_f32_skylake\nsimsimd_dot_f32_serial\nsimsimd_cos_f32_serial\nsimsimd_l2sq_f32_serial\nsimsimd_js_f32_serial\nsimsimd_kl_f32_serial\nsimsimd_dot_f16_sve\nsimsimd_cos_f16_sve\nsimsimd_l2sq_f16_sve\nsimsimd_dot_f16_neon\nsimsimd_cos_f16_neon\nsimsimd_l2sq_f16_neon\nsimsimd_js_f16_neon\nsimsimd_kl_f16_neon\nsimsimd_dot_f16_sapphire\nsimsimd_cos_f16_sapphire\nsimsimd_l2sq_f16_sapphire\nsimsimd_js_f16_sapphire\nsimsimd_kl_f16_sapphire\nsimsimd_dot_f16_haswell\nsimsimd_cos_f16_haswell\nsimsimd_l2sq_f16_haswell\nsimsimd_js_f16_haswell\nsimsimd_kl_f16_haswell\nsimsimd_dot_f16_serial\nsimsimd_cos_f16_serial\nsimsimd_l2sq_f16_serial\nsimsimd_js_f16_serial\nsimsimd_kl_f16_serial\nsimsimd_cos_i8_neon\nsimsimd_cos_i8_neon\nsimsimd_l2sq_i8_neon\nsimsimd_cos_i8_ice\nsimsimd_cos_i8_ice\nsimsimd_l2sq_i8_ice\nsimsimd_cos_i8_haswell\nsimsimd_cos_i8_haswell\nsimsimd_l2sq_i8_haswell\nsimsimd_cos_i8_serial\nsimsimd_cos_i8_serial\nsimsimd_l2sq_i8_serial\nsimsimd_hamming_b8_sve\nsimsimd_jaccard_b8_sve\nsimsimd_hamming_b8_neon\nsimsimd_jaccard_b8_neon\nsimsimd_hamming_b8_ice\nsimsimd_jaccard_b8_ice\nsimsimd_hamming_b8_haswell\nsimsimd_jaccard_b8_haswell\nsimsimd_hamming_b8_serial\nsimsimd_jaccard_b8_serial\nsimsimd_dot_f32c_sve\nsimsimd_vdot_f32c_sve\nsimsimd_dot_f32c_neon\nsimsimd_vdot_f32c_neon\nsimsimd_dot_f32c_haswell\nsimsimd_vdot_f32c_haswell\nsimsimd_dot_f32c_skylake\nsimsimd_vdot_f32c_skylake\nsimsimd_dot_f32c_serial\nsimsimd_vdot_f32c_serial\nsimsimd_dot_f64c_sve\nsimsimd_vdot_f64c_sve\nsimsimd_dot_f64c_skylake\nsimsimd_vdot_f64c_skylake\nsimsimd_dot_f64c_serial\nsimsimd_vdot_f64c_serial\nsimsimd_dot_f16c_sve\nsimsimd_vdot_f16c_sve\nsimsimd_dot_f16c_neon\nsimsimd_vdot_f16c_neon\nsimsimd_dot_f16c_haswell\nsimsimd_vdot_f16c_haswell\nsimsimd_dot_f16c_sapphire\nsimsimd_vdot_f16c_sapphire\nsimsimd_dot_f16c_serial\nsimsimd_vdot_f16c_serial\n```\n",
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