Crate axiolid_exact

Filtered exact arithmetic (ADR 0068).

Exact constructions – where two segments cross, where a line meets a circle – produce numbers f64 cannot hold. This crate answers each sign question in at most two passes over the same expression:

1. Interval arithmetic: f64 with every operation rounded outward, so the true value is provably inside [lo, hi]. If zero is outside, the sign is proven. This decides almost every real input.
2. Otherwise Dyadic arithmetic: a big-integer mantissa (num-bigint) times a power of two. Every finite f64 is one, and + - * stay exact, so the sign is exact.

There is no division, by design: constructions clear denominators, and a quotient’s sign is sign(numerator) * sign(denominator). Square roots appear only inside Root2, the value (a + b*sqrt(c)) / d, whose sign and order are decided by squaring with case analysis, never by evaluating the root.

Values no finite arithmetic holds – sin and cos of a dyadic angle – are enclosed in FixedIntervals whose precision the caller raises until a nonzero sign shows.

Expressions are written once against the Arith trait and run in both tiers, so the fast path and the exact path cannot compute different polynomials.

Re-exports

pub use arith::Arith;

pub use certify::certify;

pub use certify::filter;

pub use certify::require_finite;

pub use certify::ExactError;

pub use certify::SignExpr;

pub use conic::conic_intersections;

pub use conic::line_conic_hits;

pub use conic::Conic;

pub use conic::ConicIntersection;

pub use conic::ConicLineHit;

pub use conic::ConicLineHits;

pub use conic::ConicPoint;

pub use construct::compare_along;

pub use construct::crossing_orientation;

pub use construct::crossing_orientation_filter;

pub use construct::line_circle_hits;

pub use construct::Branch;

pub use construct::Circle;

pub use construct::HitCount;

pub use construct::Line;

pub use construct::LineHit;

pub use dyadic::Dyadic;

pub use fixed::FixedInterval;

pub use interval::Interval;

pub use poly::IntPoly;

pub use poly::RealRoot;

pub use root::sign_root;

pub use root::sign_two_roots;

pub use root::Root2;

pub use tower::Nested;

pub use tower::Tower;

Modules

arith

The arithmetic both evaluation tiers share.

certify

The two-tier driver: interval filter first, exact fallback second.

conic

Conics: exact line/conic and conic/conic intersection.

construct

Exact constructions over f64 inputs, decided without division.

dyadic

Dyadic rationals: the exact tier.

fixed

Fixed-point intervals at a chosen precision, with certified sin and cos: the tier for values no finite arithmetic holds exactly.

interval

Outward-rounded interval arithmetic: the fast tier.

poly

Integer polynomials and exact real-root isolation.

root

Numbers of the form (a + b*sqrt(c)) / d.

tower

Nested square roots: values in a tower of adjoined radicals.