Known limitations

This page summarizes the functional limitations of Nautilus as documented in nautilus-status.md Section 6.1.

Precision

f32 precision throughout. All Nautilus functions operate in f32, providing approximately 6-7 significant digits. scipy runs f64. Acceptable for f32 workloads; f64 promotion would need upstream Chelis type support. See the Precision appendix for per-function details.

Missing builtins

No cos, tan, atan, abs, floor, ceil builtins in the Chelis language. Users must express these from primitives:

// cos(x) via sin
cos_x = sin(add(x, cast(1.5707963267948966, f32)))

// abs(x) via conditional
abs_x = if lt(x, cast(0.0, f32)) then neg(x) else x

This is a Chelis language limitation, not a Nautilus limitation. Upstream could add these as builtins.

Linear algebra

No general-n eigenvalue. lu_solve, qr_decompose, cholesky_n, and svd_n are now available at general n (alpha stability). Only 2x2 and 3x3 closed-form inverses, solves, and eigenvalues remain fixed-size. cg_solve provides iterative SPD linear solve at general n.

svd_n known limitations (alpha): (a) Uses fixed 30n Jacobi sweeps, so poorly separated singular values may not fully converge; use absolute-error tolerance

= 1e-3 for sigma. (b) U columns for null-space directions of rank-deficient A are zero vectors (not orthonormalized); U is orthogonal only when A has full rank. Reconstruction U S Vt approx A is correct regardless.

lu_solve has no partial pivoting. Requires all leading submatrices of A to be nonsingular. Well-conditioned matrices that need row swaps (e.g., [[0,1],[1,0]]) produce NaN instead of correct results. Use a row permutation on input to keep leading submatrices nonsingular.

Optimization

newton_minimize_1d strong-convexity heuristic. The Newton minimizer includes a curvature check that can false-positive on flat minima (e.g., f(x) = x^4 near x = 0). Use brent_minimize or golden_section_search for flat-Hessian targets.

Signal processing

Signal module is mostly stubs. The transform/filter helpers return NaN sentinels; fftfreq is a real-valued utility that ships today. The blocked pieces still depend on upstream complex-number support (Phase 5f). See the Signal chapter.

Airy function coverage

airy_ai large negative x. Power series only; no asymptotic branch for x < -5. The oscillatory regime works for moderate |x| but degrades at large negative x.

Test harness architecture

Bare-build path only. The test harness concatenates .ch sources, strips module directives, and builds a single C translation unit. It does not exercise the reef package import system at runtime, only at chelis reef build / chelis check time.

LTO flags are bench-only. The -flto -fvisibility=hidden -Wl,-Bsymbolic workaround for cross-TU inlining is applied only in the benchmark script, not in the test harness or any consumer build path.