USearch

Smaller & Faster Single-File
Vector Search Engine

Euclidean • Angular • Jaccard • Hamming • Haversine • User-Defined Metrics
C++11 • Python • JavaScript • Java • Rust • Objective-C • Swift • GoLang • Wolfram
Linux • MacOS • Windows • Docker • WebAssembly 🔜

[x] Industry-leading performance.
[x] Easily-extendible single C++11 header implementation.
[x] SIMD-accelerated and User-defined metrics with JIT-compilation.
[x] Variable dimensionality vectors - for obscure use-cases, like GIS and Chess.
[x] Bitwise Tanimoto and Sorensen coefficients for Genomics and Chemistry.
[x] [Half-precision f16 and Quarter-precision f8](#quantize-on-the-fly) support on any hardware.
[x] [View from disk](#view-larger-indexes-from-disk), without loading into RAM.
[x] [4B+](#go-beyond-4b-entries) sized space efficient point-clouds with uint40_t.
[x] [Bring your threads](#bring-your-threads), like OpenMP or C++23 executors.
[x] Multiple vectors per label.
[ ] Thread-safe reserve.
[ ] On-the-fly deletions.
[x] USearch + UForm Transformers = Semantic Search.
[x] USearch + RDKit = Molecule Search.

FAISS is the industry standard for a high-performance batteries-included vector search engine. Both USearch and FAISS implement the same HNSW algorithm. But they differ in a lot of design decisions. USearch is designed to be compact and broadly compatible without sacrificing performance.

| | FAISS, f32 | USearch, f32 | USearch, f16 | USearch, f8 | | :----------- | -----------: | -------------: | -------------: | ------------: | | Batch Insert | 16 K/s | 73 K/s | 100 K/s | 104 K/s | | Batch Search | 82 K/s | 103 K/s | 113 K/s | 134 K/s | | Bulk Insert | 76 K/s | 105 K/s | 115 K/s | 202 K/s | | Bulk Search | 118 K/s | 174 K/s | 173 K/s | 304 K/s | | Recall @1 | 99% | 99.2% | 99.1% | 99.2% |

Dataset: 1M vectors sample of the Deep1B dataset. Hardware: c7g.metal AWS instance with 64 cores and DDR5 memory. HNSW was configured with identical hyper-parameters: connectivity M=16, expansion @ construction efConstruction=128, and expansion @ search ef=64. Batch size is 256. Both libraries were compiled for the target architecture. Jump to the Performance Tuning section to read about the effects of those hyper-parameters.

User-Defined Functions

Most vector-search packages focus on just 2 metrics - "Inner Product distance" and "Euclidean distance". That only partially exhausts the list of possible metrics. A good example would be the rare Haversine distance, used to compute the distance between geo-spatial coordinates, extending Vector Search into the GIS domain. Another example would be designing a custom metric for composite embeddings concatenated from multiple AI models in real-world applications. USearch supports that: Python and C++ examples.

USearch: Vector Search Approaches

Unlike older approaches indexing high-dimensional spaces, like KD-Trees and Locality Sensitive Hashing, HNSW doesn't require vectors to be identical in length. They only have to be comparable. So you can apply it in obscure applications, like searching for similar sets or fuzzy text matching.

Memory Efficiency, Downcasting, and Quantization

Training a quantization model and dimension-reduction is a common approach to accelerate vector search. Those, however, are only sometimes reliable, can significantly affect the statistical properties of your data, and require regular adjustments if your distribution shifts.

USearch uint40_t support

Instead, we have focused on high-precision arithmetic over low-precision downcasted vectors. The same index, and add and search operations will automatically down-cast or up-cast between f32_t, f16_t, f64_t, and f8_t representations, even if the hardware doesn't natively support it. Continuing the topic of memory-efficiency, we provide a uint40_t to allow collection with over 4B+ vectors without allocating 8 bytes for every neighbor reference in the proximity graph.

View Larger Indexes from Disk

Modern search systems often suggest using different servers to maximize indexing speed and minimize serving costs. Memory-optimized for the first task, and storage-optimized for the second, if the index can be served from external memory, which USearch can.

There is a 50x difference between the cost of such instances for identical capacity. Of course, the latency of external memory access will be higher, but it is in part compensated with an excellent prefetching mechanism.

Usage

There are two usage patters:

Bare-bones with usearch/index.hpp, only available in C++.
Full-fat version with it's own threads, mutexes, type-punning, quantization, that is available both in C++ and is wrapped for higher-level bindings.

C++

Installation

To use in a C++ project simply copy the include/usearch/index.hpp header into your project. Alternatively fetch it with CMake:

cmake FetchContent_Declare(usearch GIT_REPOSITORY https://github.com/unum-cloud/usearch.git) FetchContent_MakeAvailable(usearch)

Quickstart

Once included, the low-level C++11 interface is as simple as it gets: reserve(), add(), search(), size(), capacity(), save(), load(), view(). This covers 90% of use-cases.

```c++ using namespace unum::usearch;

index_gt> index; float vec[3] = {0.1, 0.3, 0.2};

index.reserve(10); index.add(/* label: / 42, / vector: / {&vec[0], 3}); auto results = index.search(/ query: / {&vec[0], 3}, 5 / neighbors */);

for (std::size_t i = 0; i != results.size(); ++i) results[i].element.label, results[i].element.vector, results[i].distance; ```

The add is thread-safe for concurrent index construction.

Serialization

c++ index.save("index.usearch"); index.load("index.usearch"); // Copying from disk index.view("index.usearch"); // Memory-mapping from disk

User-Defined Metrics in C++

For advanced users, more compile-time abstractions are available.

cpp template <typename metric_at = ip_gt<float>, // typename label_at = std::size_t, // `uint32_t`, `uuid_t`... typename id_at = std::uint32_t, // `uint40_t`, `uint64_t`... typename scalar_at = float, // `double`, `half`, `char`... typename allocator_at = std::allocator<char>> // class index_gt;

You may want to use a custom memory allocator or a rare scalar type, but most often, you would start by defining a custom similarity measure. The function object should have the following signature to support different-length vectors.

cpp struct custom_metric_t { T operator()(T const* a, T const* b, std::size_t a_length, std::size_t b_length) const; };

The following distances are pre-packaged:

cos_gt<scalar_t> for "Cosine" or "Angular" distance.
ip_gt<scalar_t> for "Inner Product" or "Dot Product" distance.
l2sq_gt<scalar_t> for the squared "L2" or "Euclidean" distance.
jaccard_gt<scalar_t> for "Jaccard" distance between two ordered sets of unique elements.
hamming_gt<scalar_t> for "Hamming" distance, as the number of shared bits in hashes.
tanimoto_gt<scalar_t> for "Tanimoto" coefficient for bit-strings.
sorensen_gt<scalar_t> for "Dice-Sorensen" coefficient for bit-strings.
pearson_correlation_gt<scalar_t> for "Pearson" correlation between probability distributions.
haversine_gt<scalar_t> for "Haversine" or "Great Circle" distance between coordinates used in GIS applications.

Multi-Threading

Most AI, HPC, or Big Data packages use some form of a thread pool. Instead of spawning additional threads within USearch, we focus on the thread safety of add() function, simplifying resource management.

```cpp

pragma omp parallel for

for (std::size_t i = 0; i < n; ++i)
    native.add(label, span_t{vector, dims}, add_config_t { .thread = omp_get_thread_num() });

```

During initialization, we allocate enough temporary memory for all the cores on the machine. On the call, the user can supply the identifier of the current thread, making this library easy to integrate with OpenMP and similar tools.

Python

Installation

sh pip install usearch

Quickstart

```python import numpy as np from usearch.index import Index

index = Index( ndim=3, # Define the number of dimensions in input vectors metric='cos', # Choose 'l2sq', 'haversine' or other metric, default = 'ip' dtype='f32', # Quantize to 'f16' or 'f8' if needed, default = 'f32' connectivity=16, # How frequent should the connections in the graph be, optional expansionadd=128, # Control the recall of indexing, optional expansionsearch=64, # Control the quality of search, optional )

vector = np.array([0.2, 0.6, 0.4]) index.add(42, vector) matches, distances, count = index.search(vector, 10)

assert len(index) == 1 assert count == 1 assert matches[0] == 42 assert distances[0] <= 0.001 assert np.allclose(index[42], vector) ```

Python bindings are implemented with pybind/pybind11. Assuming the presence of Global Interpreter Lock in Python, we spawn threads in the C++ layer on large insertions.

Serialization

py index.save('index.usearch') index.load('index.usearch') # Copy the whole index into memory index.view('index.usearch') # View from disk without loading in memory

If you don't know anything about the index except its path, there are two more endpoints to know:

py Index.metadata('index.usearch') -> IndexMetadata Index.restore('index.usearch', view=False) -> Index

Batch Operations

Adding or querying a batch of entries is identical to adding a single vector. The difference would be in the shape of the tensors.

```py n = 100 labels = np.arange(n) vectors = np.random.uniform(0, 0.3, (n, index.ndim)).astype(np.float32)

index.add(labels, vectors, threads=..., copy=...) matches, distances, counts = index.search(vectors, 10, threads=...)

assert matches.shape[0] == vectors.shape[0] assert counts[0] <= 10 ```

You can also override the default threads and copy arguments in bulk workloads. The first controls the number of threads spawned for the task. The second controls whether the vector itself will be persisted inside the index. If you can preserve the lifetime of the vector somewhere else, you can avoid the copy.

User-Defined Metrics and JIT in Python

Numba

Assuming the language boundary exists between Python user code and C++ implementation, there are more efficient solutions than passing a Python callable to the engine. Luckily, with the help of Numba, we can JIT compile a function with a matching signature and pass it down to the engine.

```py from numba import cfunc, types, carray

ndim = 256 signature = types.float32( types.CPointer(types.float32), types.CPointer(types.float32))

@cfunc(signature) def innerproduct(a, b): aarray = carray(a, ndim) barray = carray(b, ndim) c = 0.0 for i in range(ndim): c += aarray[i] * b_array[i] return 1 - c

index = Index(ndim=ndim, metric=CompiledMetric( pointer=inner_product.address, kind=MetricKind.IP, signature=MetricSignature.ArrayArray, )) ```

Alternatively, you can avoid pre-defining the number of dimensions, and pass it separately:

```py signature = types.float32( types.CPointer(types.float32), types.CPointer(types.float32), types.uint64)

@cfunc(signature) def innerproduct(a, b, ndim): aarray = carray(a, ndim) barray = carray(b, ndim) c = 0.0 for i in range(ndim): c += aarray[i] * b_array[i] return 1 - c

index = Index(ndim=ndim, metric=CompiledMetric( pointer=inner_product.address, kind=MetricKind.IP, signature=MetricSignature.ArrayArraySize, )) ```

sh pip install numba

Cppyy

Similarly, you can use Cppyy with Cling to JIT-compile native C or C++ code and pass it to USearch, which may be a good idea, if you want to explicitly request loop-unrolling or other low-level optimizations!

```py import cppyy import cppyy.ll

cppyy.cppdef(""" float inner_product(float *a, float *b) { float result = 0;

pragma unroll

for (size_t i = 0; i != ndim; ++i)
    result += a[i] * b[i];
return 1 - result;

} """.replace("ndim", str(ndim)))

function = cppyy.gbl.inner_product index = Index(ndim=ndim, metric=CompiledMetric( pointer=cppyy.ll.addressof(function), kind=MetricKind.IP, signature=MetricSignature.ArrayArraySize, )) ```

PeachPy

We have covered JIT-ing Python with Numba and C++ with Cppyy and Cling. How about writing Assembly directly? That is also possible. Below is an example of constructing the "Inner Product" distance for 8-dimensional f32 vectors for x86 using PeachPy.

```py from peachpy import ( Argument, ptr, float, constfloat, ) from peachpy.x8664 import ( abi, Function, uarch, isa, GeneralPurposeRegister64, LOAD, YMMRegister, VSUBPS, VADDPS, VHADDPS, VMOVUPS, VFMADD231PS, VPERM2F128, VXORPS, RETURN, )

a = Argument(ptr(constfloat), name="a") b = Argument(ptr(constfloat), name="b")

with Function( "innerproduct", (a, b), float, target=uarch.default + isa.avx2 ) as asm_function:

# Request two 64-bit general-purpose registers for addresses
reg_a, reg_b = GeneralPurposeRegister64(), GeneralPurposeRegister64()
LOAD.ARGUMENT(reg_a, a)
LOAD.ARGUMENT(reg_b, b)

# Load the vectors
ymm_a = YMMRegister()
ymm_b = YMMRegister()
VMOVUPS(ymm_a, [reg_a])
VMOVUPS(ymm_b, [reg_b])

# Prepare the accumulator
ymm_c = YMMRegister()
ymm_one = YMMRegister()
VXORPS(ymm_c, ymm_c, ymm_c)
VXORPS(ymm_one, ymm_one, ymm_one)

# Accumulate A and B product into C
VFMADD231PS(ymm_c, ymm_a, ymm_b)

# Reduce the contents of a YMM register
ymm_c_permuted = YMMRegister()
VPERM2F128(ymm_c_permuted, ymm_c, ymm_c, 1)
VADDPS(ymm_c, ymm_c, ymm_c_permuted)
VHADDPS(ymm_c, ymm_c, ymm_c)
VHADDPS(ymm_c, ymm_c, ymm_c)

# Negate the values, to go from "similarity" to "distance"
VSUBPS(ymm_c, ymm_one, ymm_c)

# A common convention is to return floats in XMM registers
RETURN(ymm_c.as_xmm)

pythonfunction = asmfunction.finalize(abi.detect()).encode().load() metric = CompiledMetric( pointer=pythonfunction.loader.codeaddress, kind=MetricKind.IP, signature=MetricSignature.ArrayArray, ) index = Index(ndim=ndim, metric=metric) ```

Tooling

To work with bbin, fbin, ibin, hbin matrix files USearch provides load_matrix and save_matrix. Such files are standard in k-ANN tasks and represent a binary object with all the scalars, prepended by two 32-bit integers - the number of rows and columns in the matrix.

```py from usearch.index import Index from usearch.io import loadmatrix, savematrix

vectors = load_matrix('deep1B.fbin') index = Index(ndim=vectors.shape[1]) index.add(labels, vectors) ```

One may often want to evaluate the quality of the constructed index before running in production. The trivial way is to measure recall@1 on the entries already present in the index.

```py from usearch.eval import recall_members

assert recallmembers(index, exact=True) == 1 print(recallmembers(index, exact=False)) ```

In case you have some ground-truth data for more than one entry, you compare search results against expected values:

```py from usearch.eval import relevance, dcg, ndcg, random_vectors

vectors = randomvectors(index=index) matchesapproximate = index.search(vectors) matchesexact = index.search(vectors, exact=True) relevancescores = relevance(matchesexact, matchesapproximate) print(dcg(relevancescores), ndcg(relevancescores)) ```

JavaScript

Installation

sh npm install usearch

Quickstart

```js var index = new usearch.Index({ metric: 'cos', connectivity: 16, dimensions: 3 }) index.add(42, new Float32Array([0.2, 0.6, 0.4])) var results = index.search(new Float32Array([0.2, 0.6, 0.4]), 10)

assert.equal(index.size(), 1) assert.deepEqual(results.labels, new Uint32Array([42])) assert.deepEqual(results.distances, new Float32Array([0])) ```

Serialization

js index.save('index.usearch') index.load('index.usearch') index.view('index.usearch')

Rust

Installation

sh cargo add usearch

Quickstart

```rust

let options = IndexOptions { dimensions: 5, metric: MetricKind::IP, quantization: ScalarKind::F16, connectivity: 0, expansionadd: 0, expansionsearch: 0 };

let index = new_index(&options).unwrap();

assert!(index.reserve(10).isok()); assert!(index.capacity() >= 10); assert!(index.connectivity() != 0); asserteq!(index.dimensions(), 3); assert_eq!(index.size(), 0);

let first: [f32; 3] = [0.2, 0.1, 0.2]; let second: [f32; 3] = [0.2, 0.1, 0.2];

assert!(index.add(42, &first).isok()); assert!(index.add(43, &second).isok()); assert_eq!(index.size(), 2);

// Read back the tags let results = index.search(&first, 10).unwrap(); assert_eq!(results.count, 2); ```

Multi-Threading

rust assert!(index.add_in_thread(42, &first, 0).is_ok()); assert!(index.add_in_thread(43, &second, 0).is_ok()); let results = index.search_in_thread(&first, 10, 0).unwrap();

Being a systems-programming language, Rust has better control over memory management and concurrency but lacks function overloading. Aside from the add and search, USearch Rust binding also provides add_in_thread and search_in_thread, which let users identify the calling thread to use underlying temporary memory more efficiently.

Serialization

rust assert!(index.save("index.usearch").is_ok()); assert!(index.load("index.usearch").is_ok()); assert!(index.view("index.usearch").is_ok());

Metrics

rust assert!(new_l2sq(3, &quant, 0, 0, 0).is_ok()); assert!(new_cos(3, &quant, 0, 0, 0).is_ok()); assert!(new_haversine(&quant, 0, 0, 0).is_ok());

Java

Installation

xml <dependency> <groupId>cloud.unum</groupId> <artifactId>usearch</artifactId> <version>0.2.3</version> </dependency>

Add that snippet to your pom.xml and hit mvn install.

Quickstart

java Index index = new Index.Config().metric("cos").dimensions(2).build(); float vec[] = {10, 20}; index.add(42, vec); int[] labels = index.search(vec, 5);

Swift

Installation

txt https://github.com/unum-cloud/usearch

Quickstart

```swift let index = Index.l2sq(dimensions: 3, connectivity: 8) let vectorA: [Float32] = [0.3, 0.5, 1.2] let vectorB: [Float32] = [0.4, 0.2, 1.2] index.add(label: 42, vector: vectorA[...]) index.add(label: 43, vector: vectorB[...])

let results = index.search(vector: vectorA[...], count: 10) assert(results.0[0] == 42) ```

GoLang

Installation

golang import ( "github.com/unum-cloud/usearch/golang" )

Quickstart

```golang package main

import ( "fmt" "github.com/unum-cloud/usearch/golang" )

func main() { conf := usearch.DefaultConfig(128) index := usearch.NewIndex(conf) v := make([]float32, 128) index.Add(42, v) results := index.Search(v, 1) } ```

Wolfram

Application Examples

USearch + AI = Multi-Modal Semantic Search

AI has a growing number of applications, but one of the coolest classic ideas is to use it for Semantic Search. One can take an encoder model, like the multi-modal UForm, and a web-programming framework, like UCall, and build a text-to-image search platform in just 20 lines of Python.

```python import ucall import uform import usearch

import numpy as np import PIL as pil

server = ucall.Server() model = uform.get_model('unum-cloud/uform-vl-multilingual') index = usearch.index.Index(ndim=256)

@server def add(label: int, photo: pil.Image.Image): image = model.preprocessimage(photo) vector = model.encodeimage(image).detach().numpy() index.add(label, vector.flatten(), copy=True)

@server def search(query: str) -> np.ndarray: tokens = model.preprocesstext(query) vector = model.encodetext(tokens).detach().numpy() matches = index.search(vector.flatten(), 3) return matches.labels

server.run() ```

We have pre-processed some commonly used datasets, cleaning the images, producing the vectors, and pre-building the index.

| Dataset | Size | Images | Preprocessed | | :---------------------------------- | ---: | -----: | --------------------: | | Unsplash 25K | - | 25 K | HF | | Unsplash 2M | - | 2 M | HF | | LAION 400M | - | 400 M | HF | | LAION 5B | - | 5 B | HF |

USearch + RDKit = Molecular Search

Comparing molecule graphs and searching for similar structures is expensive and slow. It can be seen as a special case of the NP-Complete Subgraph Isomorphism problem. Luckily, domain-specific approximate methods exists. The one commonly used in Chemistry, is to generate structures from SMILES, and later hash them into binary fingerprints. The later are searchable with bitwise similarity metrics, like the Tanimoto coefficient. Below is na example using the RDKit package.

```python from usearch.index import Index, MetricKind from rdkit import Chem from rdkit.Chem import AllChem

import numpy as np

molecules = [Chem.MolFromSmiles('CCOC'), Chem.MolFromSmiles('CCO')] encoder = AllChem.GetRDKitFPGenerator()

fingerprints = np.vstack([encoder.GetFingerprint(x) for x in molecules]) fingerprints = np.packbits(fingerprints, axis=1)

index = Index(ndim=2048, metric=MetricKind.BitwiseTanimoto) labels = np.arange(len(molecules))

index.add(labels, fingerprints) matches = index.search(fingerprints, 10) ```

RDKit provides following fingerprinting techniques:

Atom-Pair,
Topological Torsion,
Morgan,
Layered Fingerprints.

We have preprocessed some of the most commonly used datasets, and made it available for free on the HuggingFace portal, together with visual interface.

| Dataset | Size | Molecules | Preprocessed | | :------------------------ | -------: | ----------: | ---------------: | | PubChem | 8 GB | 115'034'339 | HF | | GDB 13 | 2.3 GB | 977'468'301 | HF | | REAL | > 100 GB | 6 B | HF |

TODO

JavaScript: Allow calling from "worker threads".
Rust: Allow passing a custom thread ID.
C# .NET bindings.

Integrations

[x] GPT-Cache.
[ ] Langchain.
[ ] Microsoft Semantic Kernel.
[ ] PyTorch.

Citations

txt @software{Vardanian_USearch_2022, doi = {10.5281/zenodo.7949416}, author = {Vardanian, Ash}, title = {{USearch by Unum Cloud}}, url = {https://github.com/unum-cloud/usearch}, version = {0.13.0}, year = {2022} month = jun, }

Check that and other examples on our corporate GitHub 🤗

USearch

Smaller & Faster Single-File Vector Search Engine

User-Defined Functions

Memory Efficiency, Downcasting, and Quantization

View Larger Indexes from Disk

Usage

C++

Installation

Quickstart

Serialization

User-Defined Metrics in C++

Multi-Threading

pragma omp parallel for

Python

Installation

Quickstart

Serialization

Batch Operations

User-Defined Metrics and JIT in Python

Numba

Cppyy

pragma unroll

PeachPy

Tooling

JavaScript

Installation

Quickstart

Serialization

Rust

Installation

Quickstart

Multi-Threading

Serialization

Metrics

Java

Installation

Quickstart

Swift

Installation

Quickstart

GoLang

Installation

Quickstart

Wolfram

Application Examples

USearch + AI = Multi-Modal Semantic Search

USearch + RDKit = Molecular Search

TODO

Integrations

Citations

Smaller & Faster Single-File
Vector Search Engine