cheby

Why it exists

cheby provides a complete Chebyshev interpolation pipeline suitable for numerical kernels and ephemeris-style piecewise approximations. Its segment-table API offers O(1) lookup for high-accuracy function approximation over arbitrary intervals.

Key Features

• Node generation on [-1, 1] and mapped intervals
• DCT-based coefficient fitting
• Stable Clenshaw evaluation (value + derivative)
• Uniform piecewise segment tables with O(1) lookup
• Generic over ChebyScalar (works with qtty quantities)

Getting Started

# Add to your Cargo.toml
[dependencies]
cheby = "0.1"

# Interpolate sin(x) with Chebyshev polynomials
use cheby::{evaluate, fit_coeffs, nodes};

const N: usize = 9;
let xi: [f64; N] = nodes();
let values: [f64; N] = std::array::from_fn(|k| xi[k].sin());
let coeffs = fit_coeffs(&values);

let tau = 0.42;
let approx = evaluate(&coeffs, tau);
println!("sin({tau}) ~= {approx}");

Contributing

We welcome contributions! Here's how you can help:

• 1 Fork the repository and create your branch from main
• 2 Make your changes and add tests if applicable
• 3 Ensure all tests pass with cargo test
• 4 Submit a pull request with a clear description

License

This project is licensed under the AGPL-3.0 license. See the LICENSE file for details.