Entropy Coders for Research and Production

The constriction library provides a set of composable entropy coding algorithms with a focus on correctness, versatility, ease of use, compression performance, and computational efficiency. The goals of constriction are three-fold:

1. to facilitate research on novel lossless and lossy compression methods by providing a composable set of primitives (e.g., you can can easily switch out a Range Coder for an ANS coder without having to find a new library or change how you represent exactly invertible entropy models);
2. to simplify the transition from research code to deployed software by providing similar APIs and binary compatible entropy coders for both Python (for rapid prototyping on research code) and Rust (for turning successful prototypes into standalone binaries, libraries, or WebAssembly modules); and
3. to serve as a teaching resource by providing a variety of entropy coding primitives within a single consistent framework. Check out our additional teaching material from a university course on data compression, which contains some problem sets where you use constriction (with solutions).

More Information: project website

Live demo: here's a web app that started out as a machine-learning research project in Python and was later turned into a web app by using constriction in a WebAssembly module.

Project Status

We currently provide implementations of the following entropy coding algorithms (see also benchmarks below):

• Asymmetric Numeral Systems (ANS): a fast modern entropy coder with near-optimal compression effectiveness that supports advanced use cases like bits-back coding.
• Range Coding: a computationally efficient variant of Arithmetic Coding that has essentially the same compression effectiveness as ANS Coding but operates as a queue ("first in first out"), which makes it preferable for autoregressive models.
• Chain Coding: an experimental new entropy coder that combines the (net) effectiveness of stream codes with the locality of symbol codes (for details, see Section 4.3 in this paper); it admits experimental new compression techniques that perform joint inference, quantization, and bits-back coding in an end-to-end optimization. This experimental coder is mainly provided to prove to ourselves that the API for encoding and decoding, which is shared across all stream coders, is flexible enough to express complex novel tasks.
• Huffman Coding: a well-known symbol code, mainly provided here for teaching purpose; you'll usually want to use a stream code like ANS or Range Coding instead since symbol codes can have a considerable overhead on the bit rate, especially in the regime of low entropy per symbol, which is common in machine-learning based compression methods.

Further, constriction provides implementations of common probability distributions in fixed-point arithmetic, which can be used as entropy models in either of the above stream codes. The library also provides adapters for turning custom probability distributions into exactly invertible fixed-point arithmetic.

The provided implementations of entropy coding algorithms and probability distributions are continuously and extensively tested. We consider updates that can affect the encoder or decoder output in existing code as breaking changes that necessitate a bump in the leading nonzero number of the version string (this is a stronger guarantee than SemVer in that we apply it even to 0.y.z versions). Please file an issue if you find a bug, are missing a particular feature, or run into a scenario where the current APIs are confusing or unnecessarily limit what you can achieve with constriction.

Quick Start Guides And Examples in Python and Rust

Python

Install constriction for Python:

pip install constriction~=0.4.1

Then go ahead and encode and decode some data:

import constriction
import numpy as np

message = np.array([6, 10, -4, 2, 5, 2, 1, 0, 2], dtype=np.int32)

# Define an i.i.d. entropy model (see links below for more complex models):
entropy_model = constriction.stream.model.QuantizedGaussian(-50, 50, 3.2, 9.6)

# Let's use an ANS coder in this example (see links below for Range Coding examples).
encoder = constriction.stream.stack.AnsCoder()
encoder.encode_reverse(message, entropy_model)

compressed = encoder.get_compressed()
print(f"compressed representation: {compressed}")
print(f"(in binary: {[bin(word) for word in compressed]})")

decoder = constriction.stream.stack.AnsCoder(compressed)
decoded = decoder.decode(entropy_model, 9) # (decodes 9 symbols)
assert np.all(decoded == message) # (verifies correctness)

There's a lot more you can do with constriction's Python API. Please check out the Python API Documentation or our example jupyter notebooks.

Rust

Add this line to your Cargo.toml:

[dependencies]
constriction = "0.4.1"
probability = "0.20" # Not strictly required but used in many code examples.

If you compile in no_std mode then you have to deactivate constriction's default features (and you can't use the probability crate):

[dependencies]
constriction = {version = "0.4.1", default-features = false} # for `no_std` mode

Then go ahead and encode and decode some data:

use constriction::stream::{model::DefaultLeakyQuantizer, stack::DefaultAnsCoder, Decode};

// Let's use an ANS Coder in this example. Constriction also provides a Range
// Coder, a Huffman Coder, and an experimental new "Chain Coder".
let mut coder = DefaultAnsCoder::new();
 
// Define some data and a sequence of entropy models. We use quantized Gaussians here,
// but `constriction` also provides other models and allows you to implement your own.
let symbols = [23i32, -15, 78, 43, -69];
let quantizer = DefaultLeakyQuantizer::new(-100..=100);
let means = [35.2f64, -1.7, 30.1, 71.2, -75.1];
let stds = [10.1f64, 25.3, 23.8, 35.4, 3.9];
let models = means.iter().zip(&stds).map(
    |(&mean, &std)| quantizer.quantize(probability::distribution::Gaussian::new(mean, std))
);

// Encode symbols (in *reverse* order, because ANS Coding operates as a stack).
coder.encode_symbols_reverse(symbols.iter().zip(models.clone())).unwrap();

// Obtain temporary shared access to the compressed bit string. If you want ownership of the
// compressed bit string, call `.into_compressed()` instead of `.get_compressed()`.
println!("Encoded into {} bits: {:?}", coder.num_bits(), &*coder.get_compressed().unwrap());

// Decode the symbols and verify correctness.
let reconstructed = coder.decode_symbols(models).collect::<Result<Vec<_>, _>>().unwrap();
assert_eq!(reconstructed, symbols);

There's a lot more you can do with constriction's Rust API. Please check out the Rust API Documentation.

Benchmarks

The following table and diagrams show empirical bit rates and run-time performances of the two main entropy coders provided by constriction: Range Coding (RC) and Asymmetric Numeral Systems (ANS). We compare both to Arithmetic Coding (AC), as implemented in the arcode crate. The reported results are from experiments with data that came up in a real-world application. In each experiment, we compressed a message that consists of 3 million symbols, which we modeled as i.i.d. within each message. The messages span a wide range of entropy from about 0.001 to 10 bits per symbol. Reported run times for encoding and decoding were observed on an Intel Core i7-7500U CPU (2.70 GHz) using constrictions Rust API (runtimes of constriction's Python bindings in any real-world scenario will almost certainly be dwarfed by any additionally necessary python operations). More experimental details are explained in Section 5.2 of this paper, and in the benchmarking code.

Aggregated Benchmark Results

The table below shows bit rates and run times for each tested entropy coder, aggregated over all tested messages. For RC and ANS, the numbers in brackets after the entropy coder name denote advanced coder settings that are only exposed in constriction's Rust API (see documentation). The most relevant settings are the ones labeled as "default" (bold). These settings are the only ones exposed by constriction's Python API, and they are generally recommended for prototyping. The table reports bit rates as relative overhead over the information content. Thus, e.g., the 0.02 % overhead reported for Range Coding (RC) means that constriction's range coder compresses the entire benchmark data to a bit string that is 1.0002 times as long as the bit rate that a hypothetical optimal lossless compression code would achieve.

Entropy Coder (precision / word size / state size)	bit rate overhead	encoder / decoder runtime
ANS (24/32/64) ("default")	0.0015 %	24.2 / 6.1 ns/symbol
ANS (32/32/64)	0.0593 %	24.2 / 6.9 ns/symbol
ANS (16/16/32)	0.2402 %	19.8 / 6.4 ns/symbol
ANS (12/16/32) ("small")	3.9567 %	19.8 / 6.9 ns/symbol
RC (24/32/64) ("default")	0.0237 %	16.6 / 14.3 ns/symbol
RC (32/32/64)	1.6089 %	16.7 / 14.8 ns/symbol
RC (16/16/32)	3.4950 %	16.9 / 9.4 ns/symbol
RC (12/16/32) ("small")	4.5807 %	16.8 / 9.4 ns/symbol
Arithmetic Coding (AC; for comparison, using arcode crate)	0.0004 %	43.2 / 85.6 ns/symbol

We observe that the "default" ANS and RC coders, as well as the Arithmetic Coding baseline all essentially achieve the optimal bit rate (all with less than 0.1 % overhead). When choosing an entropy coder for a practical application, the decision should therefore typically not be based on the bit rate but rather on run time performance and ergonomics. Concerning run time, constriction's ANS and RC coders are both considerably faster than AC. When comparing ANS to RC, the main difference is in ergonomics: ANS operates as a stack ("last in first out"), which is good for bits-back coding with latent variable models, while RC operates as a queue ("first in first out"), which is good for autoregressive models.

Detailed Benchmark Results

The plots below break down each coder's performance as a function of the information content of the message that we compress. Each data point corresponds to a single message (consisting of 3 million symbols each), and the horizontal axis shows the information content of the message.

The most important results are again for entropy coders with the "default" settings (red plus signs), which are the ones that are also exposed in the Python API. Note the logarithmic scale on both axes.

Bit Rates

Run Times

Citing

I'd appreciate attribution if you use constriction in your scientific work. You can cite the following paper, which announces constriction (Section 5.1) and analyzes its compression performance and runtime efficiency (Section 5.2):

• R. Bamler, Understanding Entropy Coding With Asymmetric Numeral Systems (ANS): a Statistician's Perspective, arXiv preprint arXiv:2201.01741.

BibTex:

@article{bamler2022constriction,
  title   = {Understanding Entropy Coding With Asymmetric Numeral Systems (ANS): a Statistician's Perspective},
  author  = {Bamler, Robert},
  journal = {arXiv preprint arXiv:2201.01741},
  year    = {2022}
}

Compiling From Source

Users of constriction typically don't need to manually compile the library from source. Just install constriction via pip or cargo as described in the above quick start guides.

Contributors can compile constriction manually as follows:

1. Prepare your system:
   • If you don't have a Rust toolchain, install one as described on https://rustup.rs
   • If you already have a Rust toolchain, make sure it's on version 1.51 or later. Run rustc --version to find out and rustup update stable if you need to update.
2. git clone the repository and cd into it.
3. To compile the Rust library:
   • compile in development mode and execute all tests: cargo test
   • compile in release mode (i.e., with optimizations) and run the benchmarks: cargo bench
4. If you want to compile the Python module:
   • install poetry.
   • install Python dependencies: cd into the repository and run poetry install --no-root
   • build the Python module: poetry run maturin develop --features pybindings --release
   • run Python unit tests: poetry run pytest tests/python
   • start a Python REPL that sees the compiled Python module: poetry run ipython

Contributing

Pull requests and issue reports are welcome. Unless contributors explicitly state otherwise at the time of contributing, all contributions will be assumed to be licensed under either one of MIT license, Apache License Version 2.0, or Boost Software License Version 1.0, at the choice of each licensee.

There's no official guide for contributions since nobody reads those anyway. Just be nice to other people and act like a grown-up (i.e., it's OK to make mistakes as long as you strive for improvement and are open to consider respectfully phrased opinions of other people).

License

This work is licensed under the terms of the MIT license, Apache License Version 2.0, or Boost Software License Version 1.0. You can choose between these licenses if you use this work. See the files whose names start with LICENSE in this directory. The compiled python extension module is linked with a number of third party libraries. Binary distributions of the constriction python extension module contain a file LICENSE.html that includes all licenses of all dependencies (the file is also available online).

What's With the Name?

Constriction is a Rust library of compression primitives with bindings for Python. Pythons are a family of nonvenomous snakes that subdue their prey by "compressing" it, a method known as constriction.