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Chelis docs

Nautilus

Nautilus is the numerical computing library for the Chelis programming language. It provides the functions you need for scientific computing, statistics, and optimization, comparable to scipy and numpy in Python.

Everything in Nautilus is written in pure Chelis. There is no C FFI and no hand-written adjoints. Because all linear algebra is built from Chelis tensor primitives (matmul, permute, trace, einsum, and elementwise ops), automatic differentiation via grad flows through every function in the library.

What Nautilus provides

Section titled “What Nautilus provides”
  • Special functions: erf, erfc, erfinv, gamma, log_gamma, digamma, trigamma, beta, lbeta, Bessel, Airy, elliptic integrals
  • Probability distributions: 12 families (Normal, Gamma, Student-t, Poisson, Binomial, etc.) with PDF, CDF, inverse CDF, and sampling
  • Linear algebra: determinants, inverses, solves, eigenvalues (2x2/3x3), conjugate gradient (general-n)
  • Statistics: mean, variance, skewness, kurtosis, median, quantiles, covariance, correlation
  • Root finding: bisection, Newton, Brent-Dekker
  • ODE solvers: Euler, RK4, and adaptive RK45 endpoint solves
  • SDE solvers: Euler-Maruyama and Milstein with caller-supplied noise
  • Numerical integration: trapezoidal, Simpson, Gauss-Legendre, adaptive Simpson, Romberg, Gauss-Hermite, Gauss-Laguerre
  • Optimization: golden section, Brent minimize, gradient descent, Newton minimize (scalar 1D)
  • Interpolation: linear (uniform and sorted grids), cubic Hermite
  • Distance metrics: Euclidean, Manhattan, Chebyshev, cosine, Mahalanobis
  • Curve fitting: Levenberg-Marquardt (single parameter)
  • Hypothesis testing: z-tests, t-tests, chi-squared p-values, confidence intervals

Verification

Section titled “Verification”

Nautilus has two test gates. chelis test tests/ runs 438 native identity and structural tests across the library; parity/run_parity.py runs a scipy-oracle pass that compares Nautilus output to scipy/numpy at documented tolerances and currently passes 216/216 samples. Every non-stub exported function is runtime-verified on clean HEAD; Nautilus.Core.version is package metadata rather than part of the numerical harness.

Precision

Section titled “Precision”

All Nautilus functions operate in f32 (32-bit floating point). This gives approximately 6-7 significant digits of precision. If you need f64 precision, Nautilus is not the right choice today.