Struct ComputableReal 

pub struct ComputableReal { /* private fields */ }

A computable real number (Level 3 of the tower).

Implementations

impl ComputableReal

pub fn evaluate(&self, precision: u64) -> RnsRational

Approximate to precision decimal places, memoizing the result.

The cache is keyed by precision but a cached entry with key ≥ request satisfies the ask (a 50-digit enclosure answers a 10-digit query), so we reuse the tightest already-computed result instead of recomputing.

pub fn enclose(&self, precision: u64) -> Ball

A rigorous Ball of width < 2·10^(-precision) containing this number.

This is the Archimedean (Level-3) face of the value: ordering, sign, and magnitude on computable reals all flow through the returned Ball, the same type the algebraic layer uses for sign-of-a-root. Because the oracle contract guarantees |value - evaluate(p)| < 10^(-p), padding the rational midpoint by that radius yields a certified enclosure that composes rigorously under Ball interval arithmetic.

pub fn evaluate_f64(&self) -> f64

Convenience: evaluate at roughly f64 precision.

pub fn channels(&self) -> Basis

The RNS channels this value computes over.

pub fn from_rational(r: RnsRational) -> Self

A constant rational.

pub fn from_algebraic(a: AlgebraicNumber) -> Self

Drop a Level-2 algebraic number down to Level 3 for digit production.

pub fn pi(channels: Basis) -> Self

π via Machin’s formula π = 16·atan(1/5) - 4·atan(1/239).

pub fn e(channels: Basis) -> Self

Euler’s number e via the factorial series Σ 1/k!.

pub fn sqrt(r: RnsRational) -> Self

√r by Newton’s method on rationals (quadratic convergence).

pub fn exp(r: RnsRational) -> Self

exp(r) via the Taylor series Σ rᵏ/k!.

pub fn ln(r: RnsRational) -> Self

ln(r) for r > 0 via 2·atanh((r-1)/(r+1)).

pub fn add(&self, other: &Self) -> Self

Sum (lazy).

pub fn sub(&self, other: &Self) -> Self

Difference (lazy).

pub fn mul(&self, other: &Self) -> Self

Product (lazy).

pub fn neg(&self) -> Self

Negation (lazy).

pub fn recip(&self) -> Self

Reciprocal (lazy). Undefined behaviour if the value is zero.

Trait Implementations

impl Clone for ComputableReal

fn clone(&self) -> ComputableReal

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.