cheby

Chebyshev polynomial toolkit for scientific computing in Rust.

cheby provides a full interpolation pipeline suitable for numerical kernels
and ephemeris-style piecewise approximations:

1. Node generation on [-1, 1] and mapped intervals.
2. Coefficient fitting via DCT identities.
3. Stable Clenshaw evaluation (value, derivative, or both).
4. Uniform piecewise segment tables with O(1) segment lookup.

All core APIs are generic over ChebyScalar, so they work with f64 and with
typed quantities such as qtty::Quantity<Kilometer>.

Installation

[dependencies]
cheby = "0.1"

Quick start

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}");

Segment-table workflow

use cheby::ChebySegmentTable;

let table: ChebySegmentTable<f64, 15> =
    ChebySegmentTable::from_fn(f64::sin, 0.0, std::f64::consts::TAU, std::f64::consts::FRAC_PI_2);

let (value, derivative) = table.eval_both(1.0).unwrap();
println!("f(t)={value}, df/dt={derivative}");

Examples

Runnable examples are provided in examples/:

• basic_interpolation
• segment_table
• typed_quantities

Use:

cargo run --example basic_interpolation

See examples/README.md for details.

Tests and coverage

cheby includes:

• Unit tests inside modules.
• Functional integration tests in tests/functional_pipeline.rs.
• Doctests for public examples.

Run locally:

cargo test --all-targets
cargo test --doc
cargo +nightly llvm-cov --workspace --all-features --doctests --summary-only

Coverage is gated in CI at >= 90% line coverage.

CI

GitHub Actions workflow: /.github/workflows/ci.yml

Jobs:

• check
• fmt
• clippy (-D warnings)
• test (unit/integration + docs)
• coverage (cargo +nightly llvm-cov, PR summary, 90% gate)

License

AGPL-3.0-only