Crate hyperreal 

Exact rational, symbolic real, and computable real arithmetic.

hyperreal represents values as a mix of exact rationals, recognized symbolic forms such as pi, e, logarithms, and trigonometric special forms, and lazily evaluated computable expressions. The public structural query APIs expose cheap conservative facts for callers that need to avoid forcing high-precision evaluation. The lazy approximation layer follows the exact-real arithmetic model described by Boehm et al., https://doi.org/10.1145/319838.319860.

Exactness here is a certified-data contract, not a promise that every value is eagerly reduced to one canonical scalar form. Following Yap’s exact geometric computation model, Real preserves rational, symbolic, structural, and refinement facts so higher layers can make exact decisions or return explicit uncertainty without hiding primitive-float fallbacks. See Yap, “Towards Exact Geometric Computation,” Computational Geometry, 1997, pp. 3-23.

Structs

Computable

Computable approximation of a Real number.

DomainFacts

Domain facts for common unary functions.

IdentityFacts

Exact identity facts that are cheap enough to compute from stored fields.

MagnitudeBits

A known most-significant binary digit for a nonzero value.

OrderingFacts

Cheap comparisons used by domain gates and filters.

PrimitiveFacts

Primitive range facts for named rendering, IO, diagnostics, or external solver export planning.

Rational

Ratio of two integers

RationalFacts

Exact-rational facts derived without approximation.

Real

(More) Real numbers

RealDetailedFacts

Opt-in detailed facts for callers that can use richer structural dispatch.

RealExactSetFacts

Exact-rational structure shared by a borrowed set of Real values.

RealStructuralFacts

Conservative public facts about a real value.

SymbolicDependencyMask

Opaque bit mask of symbolic dependencies visible in a Real.

SymbolicFacts

Coarse facts about the symbolic certificate.

Enums

CertifiedRealEquality

Result of asking whether two Real values are mathematically equal under a bounded exact-real policy.

CertifiedRealOrdering

Result of asking for a certified ordering under a bounded exact-real policy.

CertifiedRealSign

Result of asking a Real for a certified sign under a bounded policy.

DomainStatus

Conservative domain status for common real-valued functions.

ExpressionDegree

Coarse bounded expression degree for structural dispatch.

PrimitiveFloatStatus

Conservative primitive floating-point range classification.

Problem

Problems when either parsing or attempting Arithmetic with Real numbers or when trying to make or convert to a Rational.

RationalStorageClass

Coarse exact-rational storage cost bucket.

RealEqualityCertificate

Source of a certified equality or inequality decision between two Real values.

RealExactSetDenominatorKind

Coarse denominator class for an exact borrowed set with a shared scale.

RealExactSetDyadicExponentClass

Coarse class for the largest dyadic denominator exponent in a borrowed set.

RealExactSetSignPattern

Conservative sign pattern for a borrowed set of Real values.

RealOrderingCertificate

Source of a certified ordering decision between two Real values.

RealSign

Exact sign knowledge exposed by structural inspection.

RealSignCertificate

Source of a certified RealSign decision.

StructuralComparison

Known comparison result for cheap structural threshold tests.

StructuralKind

Coarse public category for the symbolic certificate carried by a Real.

ZeroKnowledge

Whether structural inspection can prove zero or nonzero status.

ZeroOneMinusOneStatus

Cheap exact classification for signed unit and zero values.

ZeroOneStatus

Cheap exact classification for values that are commonly special-cased.