Zeckendorf Compression

A Rust library for compressing and decompressing data using the Zeckendorf representation algorithm.

Overview

The Zeckendorf algorithm represents numbers as a sum of non-consecutive Fibonacci numbers. This library interprets input data as a big integer (either big-endian or little-endian), converts it to its Zeckendorf representation, and sometimes achieves compression. However, compression is not guaranteed; the algorithm may result in a larger representation depending on the input data. The library can automatically try both endian interpretations and select the one that produces the best compression.

⚠️ Warning: Compressing or decompressing files larger than 10KB (10,000 bytes) is unstable due to time and memory pressure. The library may experience performance issues, excessive memory usage, or failures when processing files exceeding this size.

Command-line tools (zeck-compress and zeck-decompress) are available and can be installed via cargo install zeck. See the Binaries section for usage details.

Features

Compression & Decompression: Convert data to/from Zeckendorf representation
Multiple Endian Interpretations: Support for both big-endian and little-endian input interpretations
Automatic Best Compression: Try both endian interpretations and automatically select the best result
Multiple Fibonacci Algorithms:
- Slow recursive (memoized, for small numbers)
- Slow iterative (memoized, for large numbers)
- Fast Doubling (optimized, ~160x faster for large indices)
BigInt Support: Handle arbitrarily large numbers using num-bigint
Memoization: Thread-safe caching for improved performance
Statistics & Visualization: Generate compression statistics and plots
Benchmarking: Comprehensive performance benchmarks
WebAssembly Support: Available as a WebAssembly module for use in web browsers

WebAssembly

This library is also available as a WebAssembly module for use in web browsers. Available functions are marked with the #[wasm_bindgen] attribute. The WebAssembly module can be built using the convenience script at scripts/build_wasm_bundle.sh that builds the WebAssembly module with the wasm-pack tool.

You can see a live demo of the WebAssembly module in action at https://prizz.github.io/zeckendorf-webapp/. The source code for the demo is available at https://github.com/pRizz/zeckendorf-webapp.

Installation

Install from crates.io

Run:

cargo add zeck

Or add this to your Cargo.toml:

[dependencies]
zeck = "0.1.0"

For plotting features:

[dependencies]
zeck = { version = "0.1.0", features = ["plotting"] }

Install from GitHub (development version)

Run:

cargo add zeck --git https://github.com/pRizz/zeckendorf

Or add this to your Cargo.toml:

[dependencies]
zeck = { git = "https://github.com/pRizz/zeckendorf" }

For plotting features:

[dependencies]
zeck = { git = "https://github.com/pRizz/zeckendorf", features = ["plotting"] }

Install from npm

Run:

npm install zeck

Or add this to your package.json:

{
  "dependencies": {
    "zeck": "^0.1.0"
  }
}

Usage

Basic Compression/Decompression

Big-Endian Interpretation

use zeck::{zeckendorf_compress_be, zeckendorf_decompress_be};

// Compress data (interpreted as big-endian integer)
let data = vec![12u8];
let compressed = zeckendorf_compress_be(&data);

// Decompress data
let decompressed = zeckendorf_decompress_be(&compressed);
assert_eq!(data, decompressed);

Little-Endian Interpretation

use zeck::{zeckendorf_compress_le, zeckendorf_decompress_le};

// Compress data (interpreted as little-endian integer)
let data = vec![12u8];
let compressed = zeckendorf_compress_le(&data);

// Decompress data
let decompressed = zeckendorf_decompress_le(&compressed);
assert_eq!(data, decompressed);

Automatic Best Compression

use zeck::{zeckendorf_compress_best, zeckendorf_decompress_be, zeckendorf_decompress_le, CompressionResult};

// Try both endian interpretations and get the best result
let data = vec![1, 0];
let result = zeckendorf_compress_best(&data);

match result {
    CompressionResult::BigEndianBest { compressed_data, le_size } => {
        // Big-endian produced the best compression
        let decompressed = zeckendorf_decompress_be(&compressed_data);
        assert_eq!(data, decompressed);
    }
    CompressionResult::LittleEndianBest { compressed_data, be_size } => {
        // Little-endian produced the best compression
        let decompressed = zeckendorf_decompress_le(&compressed_data);
        assert_eq!(data, decompressed);
    }
    CompressionResult::Neither { be_size, le_size } => {
        // Neither method compressed the data (both were larger than original)
        println!("Neither method compressed: BE size = {}, LE size = {}", be_size, le_size);
    }
}

Fibonacci Numbers

use zeck::memoized_slow_fibonacci_recursive;

// Calculate Fibonacci numbers (for indices up to 93)
let fib_10 = memoized_slow_fibonacci_recursive(10); // Returns 55

// For larger numbers, use BigInt versions
use zeck::fast_doubling_fibonacci_bigint;
let fib_100 = fast_doubling_fibonacci_bigint(100);

Zeckendorf Representation

use zeck::memoized_zeckendorf_list_descending_for_integer;

// Get Zeckendorf representation as a list of Fibonacci indices
let zld = memoized_zeckendorf_list_descending_for_integer(12);
// Returns [6, 4, 2] meaning F(6) + F(4) + F(2) = 8 + 3 + 1 = 12

Binaries

The project includes several utility binaries. The command-line compression tools (zeck-compress and zeck-decompress) can be installed globally via:

Install from crates.io

cargo install zeck

Install from GitHub (development version)

cargo install --git https://github.com/pRizz/zeckendorf zeck

After installation, you can use zeck-compress and zeck-decompress directly from your command line.

Compression/Decompression Tools

zeck-compress

Compresses data using the Zeckendorf representation algorithm. Automatically adds .zbe extension for big-endian compression and .zle extension for little-endian compression.

zeck-compress [INPUT] [-o OUTPUT] [--endian ENDIAN] [-v]

Options:

INPUT: Input file path (optional, reads from stdin if not specified)
- Shows a warning if reading from stdin and no data was piped in
-o, --output FILE: Output file path (optional)
- If not specified and input is a file, uses the input filename with the appropriate extension (.zbe or .zle) appended
- If not specified and reading from stdin, writes to stdout
- The appropriate extension (.zbe for big-endian, .zle for little-endian) is automatically added unless the file already ends with .zbe or .zle
--endian ENDIAN: Endianness to use (big, little, or best). Default: best
- big: Use big-endian interpretation (output will have .zbe extension)
- little: Use little-endian interpretation (output will have .zle extension)
- best: Try both and use the best result (default, extension added based on which was used)
- Note: When using best, if neither method produces compression (both result in larger or equal output), the tool will exit with an error showing compression statistics
-v, --verbose: Show compression statistics (default: true, use --no-verbose to disable)

Examples:

# Compress a file (output filename automatically created from input with extension)
zeck-compress input.bin
# Creates input.bin.zbe or input.bin.zle depending on which endianness was used

# Compress with best endianness (statistics shown by default)
zeck-compress input.bin --endian best

# Compress with specific endianness (creates input.bin.zbe)
zeck-compress input.bin --endian big

# Compress to a specific output file
zeck-compress input.bin -o output
# Creates output.zbe or output.zle depending on which endianness was used

# Compress from stdin to stdout
cat input.bin | zeck-compress

Note: When writing to a file, the output filename is printed to stdout (e.g., "Compressed to: input.bin.zbe"). Verbose statistics are shown by default and include descriptive messages about compression ratios (e.g., "File was compressed by X.XX% (Y bytes -> Z bytes)"). A warning is shown when reading from stdin if no data was piped in.

zeck-decompress

Decompresses data that was compressed using the Zeckendorf representation algorithm. Automatically detects endianness from file extension (.zbe for big-endian, .zle for little-endian).

zeck-decompress [INPUT] [-o OUTPUT] [--endian ENDIAN] [-v]

Options:

INPUT: Input file path (optional, reads from stdin if not specified)
- When reading from a file, endianness is automatically detected from file extension (.zbe for big-endian, .zle for little-endian)
- If extension is not recognized, --endian is REQUIRED (exits with error if not specified)
- When reading from stdin, --endian is REQUIRED
- Shows a warning if reading from stdin and no data was piped in
-o, --output FILE: Output file path (optional)
- If not specified and input is a file, uses the input filename with .zbe or .zle extension removed
- If not specified and reading from stdin, writes to stdout
--endian ENDIAN: Endianness used during compression (big or little)
- big: Decompress as big-endian
- little: Decompress as little-endian
- REQUIRED when reading from stdin (no input file specified)
- When reading from a file, this option overrides automatic detection from file extension
-v, --verbose: Show decompression statistics (default: true, use --no-verbose to disable)

Examples:

# Decompress a file (endianness detected from .zbe extension, output filename automatically created)
zeck-decompress input.zbe
# Automatically uses big-endian decompression, creates output file "input"

# Decompress with little-endian file
zeck-decompress input.zle
# Automatically uses little-endian decompression, creates output file "input"

# Decompress to a specific output file
zeck-decompress input.zbe -o output.bin
# Automatically uses big-endian decompression

# Override automatic detection
zeck-decompress input.zbe --endian little -o output.bin
# Overrides the .zbe extension and uses little-endian

# Decompress from stdin to stdout (--endian is required)
cat input.zbe | zeck-decompress --endian big

Note: The endianness used for decompression must match the endianness used during compression. The file extension (.zbe or .zle) indicates which endianness was used, so decompression will automatically use the correct endianness when reading from a file. If the input file doesn't have a recognized extension, --endian must be explicitly specified (the tool will exit with an error if not provided). You can override automatic detection with the --endian flag if needed. When reading from stdin, --endian must be explicitly specified since there's no file extension to detect from.

Additional features:

When writing to a file, the output filename is printed to stdout (e.g., "Compressed to: input.bin.zbe" or "Decompressed to: output.bin")
Verbose statistics are shown by default (use --no-verbose to disable) and include descriptive messages about compression/decompression ratios
Compression will exit with an error if the data cannot be compressed (when using --endian best and neither method produces compression)
A warning is shown when reading from stdin if no data was piped in

Main Playground

cargo run --release --bin zeck

A playground/scratchpad for testing library functions.

Generate Test Data

cargo run --release --bin zeck-generate-data --features development_tools -- <size_in_bytes> [filename]

Generates random test data files in the generated_data/ directory.

Example:

cargo run --release --bin zeck-generate-data --features development_tools -- 1024 my_file.bin

Generate Statistics

cargo run --release --bin zeck-generate-statistics --features plotting,development_tools

Generates comprehensive compression statistics and plots:

Compression ratios across different input sizes
Chance of compression being favorable
Average and median compression ratios
Statistics saved to statistics_history/ directory
Plots saved to plots/ directory

Plot Compression Ratios

cargo run --release --bin zeck-plot --features plotting,development_tools

Generates visualization plots of:

Fibonacci numbers
Compression ratios for various input ranges

Benchmarks

Zeckendorf Compression Benchmarks

cargo bench --bench zeckendorf_bench

Benchmarks compression, decompression, and round-trip performance for various data sizes (4 bytes to 16KB).

Fibonacci Benchmarks

cargo bench --bench fibonacci_bench

Compares performance of different Fibonacci calculation algorithms:

Slow iterative method
Fast doubling method (~160x faster for large indices)

Working with Benchmark Baselines

Save a new baseline:

cargo bench --bench zeckendorf_bench -- --save-baseline <name>

Compare to an existing baseline:

cargo bench --bench zeckendorf_bench -- --baseline <name>

Performance Characteristics

Fast Doubling Fibonacci: ~160x faster than iterative method for the 100,000th Fibonacci number
Memoization: Thread-safe caching significantly improves repeated calculations. The trade-off is that the cache takes up memory.
Compression Effectiveness: Varies by input; compression ratios oscillate and become less favorable as input size increases

Algorithm Details

Zeckendorf Representation

Every positive integer can be uniquely represented as a sum of non-consecutive Fibonacci numbers. For example:

12 = 8 + 3 + 1 = F(6) + F(4) + F(2)

Compression Process

Input data is interpreted as either a big-endian or little-endian integer (you can choose, or use zeckendorf_compress_best to try both)
The integer is converted to its Zeckendorf representation (list of Fibonacci indices)
The representation is encoded as bits (use/skip bits)
Bits are packed into bytes (little-endian output)

The library provides functions to compress with either interpretation, or you can use zeckendorf_compress_best to automatically try both and select the one that produces the smallest output.

Effective Fibonacci Indices

The library uses "Effective Fibonacci Indices" (EFI) starting from 0, where:

EFI 0 = Fibonacci Index 2 (value 1)
EFI 1 = Fibonacci Index 3 (value 2)
etc.

This avoids redundant Fibonacci numbers (F(0)=0 and F(1)=F(2)=1).

Limitations

Compression is not guaranteed—some inputs may result in larger output
Compression effectiveness decreases as input size increases
The library supports both big-endian and little-endian interpretations, but other byte orderings or word boundaries are not currently explored
⚠️ Warning: Compressing or decompressing files larger than 10KB (10,000 bytes) is unstable due to time and memory pressure. The library may experience performance issues, excessive memory usage, or failures when processing files exceeding this size.

NPM Versioning Quirk

For some reason, NPM was showing there were versions of zeck published between 1.0.0 and 1.0.6 from 2024, even though I never published them to npm. I don't know how this happened. So I bumped the version to 1.0.7 and was able to successfully publish it to npm. Maybe there was an old package with the same name that was deleted, and NPM is still showing the old versions.

Here is a snippet of the time object from the npm registry JSON (https://registry.npmjs.org/zeck):

  "time": {
    "created": "2026-01-02T20:19:14.018Z",
    "modified": "2026-01-03T17:25:15.940Z",
    "1.0.0": "2024-02-21T14:36:36.292Z",
    "1.0.1": "2024-02-21T15:26:38.621Z",
    "1.0.2": "2024-02-21T15:36:30.258Z",
    "1.0.3": "2024-02-21T15:48:07.853Z",
    "1.0.4": "2024-02-21T15:48:38.804Z",
    "1.0.5": "2024-02-21T16:02:36.339Z",
    "1.0.6": "2024-02-21T16:36:36.643Z",
    "0.1.0": "2026-01-02T20:19:14.175Z",
    "0.2.0": "2026-01-03T17:25:15.702Z"
  },

License

This project is licensed under the MIT License - see the LICENSE.txt file for details.

Contributing

Contributions are welcome! Please feel free to submit a Pull Request. For major changes, please open an issue first to discuss what you would like to change.

References

Fast Fibonacci Algorithms - Fast doubling algorithm reference
Zeckendorf's Theorem - Every positive integer has a unique representation as a sum of non-consecutive Fibonacci numbers

zeck 2.1.0

Zeckendorf Compression

Overview

Features

WebAssembly

Installation

Install from crates.io

Install from GitHub (development version)

Install from npm

Usage

Basic Compression/Decompression

Big-Endian Interpretation

Little-Endian Interpretation

Automatic Best Compression

Fibonacci Numbers

Zeckendorf Representation

Binaries

Install from crates.io

Install from GitHub (development version)

Compression/Decompression Tools

zeck-compress

zeck-decompress

Main Playground

Generate Test Data

Generate Statistics

Plot Compression Ratios

Benchmarks

Zeckendorf Compression Benchmarks

Fibonacci Benchmarks

Working with Benchmark Baselines

Performance Characteristics

Algorithm Details

Zeckendorf Representation

Compression Process

Effective Fibonacci Indices

Limitations

NPM Versioning Quirk

License

Contributing

References