Enum TowerValue 

pub enum TowerValue {
    Integer(RnsInt),
    Rational(RnsRational),
    Algebraic(AlgebraicNumber),
    Computable(ComputableReal),
    Symbolic(SymbolicExpr),
}

A value somewhere in the number tower.

Variants

Integer(RnsInt)

Rational(RnsRational)

Algebraic(AlgebraicNumber)

Computable(ComputableReal)

Symbolic(SymbolicExpr)

Implementations

impl TowerValue

pub fn level(&self) -> TowerLevel

The level this value currently sits at.

pub fn channels(&self) -> Channels

Best-effort channels for this value (symbolic falls back to the standard set).

pub fn reduce(&self) -> TowerValue

Reduce to the lowest valid level (applied to a fixed point).

pub fn elevate_to(&self, target: TowerLevel) -> TowerValue

Elevate to at least target (for mixed-level operations). Symbolic is the top; numeric levels rise one step at a time.

pub fn to_f64(&self) -> Option<f64>

Decimal approximation (levels 0–3; symbolic is simplified/evaluated first).

Examples found in repository

examples/float_comparison.rs (line 44)

fn main() {
    let ch = Channels::standard(32);
    println!("== adele-ring :: exact vs f64 ==\n");
    println!(
        "{:<16} | {:<10} | {:<22} | {:<12} | ULPs",
        "expression", "exact", "f64 result", "abs error"
    );
    println!("{}", "-".repeat(78));

    // 0.1 + 0.2 = 3/10
    let exact = RnsRational::from_fraction(1, 10, ch.clone())
        .add(&RnsRational::from_fraction(1, 5, ch.clone()));
    row("0.1 + 0.2", &exact.display(), 0.1 + 0.2, exact.to_f64());

    // 1/3 * 3 = 1
    let one = RnsRational::from_fraction(1, 3, ch.clone()).mul(&RnsRational::from_int(3, ch.clone()));
    row("1/3 * 3", &one.display(), (1.0 / 3.0) * 3.0, one.to_f64());

    // sqrt(2) * sqrt(2) = 2  (drops to Integer through the tower)
    let s2 = TowerValue::Algebraic(AlgebraicNumber::sqrt(2, ch.clone()));
    let two = s2.mul(&s2);
    let naive = 2f64.sqrt() * 2f64.sqrt();
    row("sqrt2 * sqrt2", "2", naive, two.to_f64().unwrap());

    // sin(pi) = 0  (exact identity; f64 gives ~1.2e-16)
    let sin_pi = TowerValue::Symbolic(SymbolicExpr::Pi).sin();
    row("sin(pi)", "0", std::f64::consts::PI.sin(), sin_pi.to_f64().unwrap());

    // 1/7 * 7 = 1
    let one7 = RnsRational::from_fraction(1, 7, ch.clone()).mul(&RnsRational::from_int(7, ch));
    row("1/7 * 7", &one7.display(), (1.0 / 7.0) * 7.0, one7.to_f64());

    println!("\nEvery `exact` column is bit-for-bit correct; the f64 column drifts.");
}

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

Produce exact digits to precision decimal places, as a rational.

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

Addition, dropping the result to its lowest valid level.

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

Multiplication, dropping the result to its lowest valid level.

Examples found in repository

examples/float_comparison.rs (line 42)

fn main() {
    let ch = Channels::standard(32);
    println!("== adele-ring :: exact vs f64 ==\n");
    println!(
        "{:<16} | {:<10} | {:<22} | {:<12} | ULPs",
        "expression", "exact", "f64 result", "abs error"
    );
    println!("{}", "-".repeat(78));

    // 0.1 + 0.2 = 3/10
    let exact = RnsRational::from_fraction(1, 10, ch.clone())
        .add(&RnsRational::from_fraction(1, 5, ch.clone()));
    row("0.1 + 0.2", &exact.display(), 0.1 + 0.2, exact.to_f64());

    // 1/3 * 3 = 1
    let one = RnsRational::from_fraction(1, 3, ch.clone()).mul(&RnsRational::from_int(3, ch.clone()));
    row("1/3 * 3", &one.display(), (1.0 / 3.0) * 3.0, one.to_f64());

    // sqrt(2) * sqrt(2) = 2  (drops to Integer through the tower)
    let s2 = TowerValue::Algebraic(AlgebraicNumber::sqrt(2, ch.clone()));
    let two = s2.mul(&s2);
    let naive = 2f64.sqrt() * 2f64.sqrt();
    row("sqrt2 * sqrt2", "2", naive, two.to_f64().unwrap());

    // sin(pi) = 0  (exact identity; f64 gives ~1.2e-16)
    let sin_pi = TowerValue::Symbolic(SymbolicExpr::Pi).sin();
    row("sin(pi)", "0", std::f64::consts::PI.sin(), sin_pi.to_f64().unwrap());

    // 1/7 * 7 = 1
    let one7 = RnsRational::from_fraction(1, 7, ch.clone()).mul(&RnsRational::from_int(7, ch));
    row("1/7 * 7", &one7.display(), (1.0 / 7.0) * 7.0, one7.to_f64());

    println!("\nEvery `exact` column is bit-for-bit correct; the f64 column drifts.");
}

pub fn sqrt(&self) -> TowerValue

Square root: a perfect square drops to Integer, otherwise rises to Algebraic.

pub fn sin(&self) -> TowerValue

sin: checks the symbolic identity graph; otherwise stays symbolic.

Examples found in repository

examples/float_comparison.rs (line 47)

fn main() {
    let ch = Channels::standard(32);
    println!("== adele-ring :: exact vs f64 ==\n");
    println!(
        "{:<16} | {:<10} | {:<22} | {:<12} | ULPs",
        "expression", "exact", "f64 result", "abs error"
    );
    println!("{}", "-".repeat(78));

    // 0.1 + 0.2 = 3/10
    let exact = RnsRational::from_fraction(1, 10, ch.clone())
        .add(&RnsRational::from_fraction(1, 5, ch.clone()));
    row("0.1 + 0.2", &exact.display(), 0.1 + 0.2, exact.to_f64());

    // 1/3 * 3 = 1
    let one = RnsRational::from_fraction(1, 3, ch.clone()).mul(&RnsRational::from_int(3, ch.clone()));
    row("1/3 * 3", &one.display(), (1.0 / 3.0) * 3.0, one.to_f64());

    // sqrt(2) * sqrt(2) = 2  (drops to Integer through the tower)
    let s2 = TowerValue::Algebraic(AlgebraicNumber::sqrt(2, ch.clone()));
    let two = s2.mul(&s2);
    let naive = 2f64.sqrt() * 2f64.sqrt();
    row("sqrt2 * sqrt2", "2", naive, two.to_f64().unwrap());

    // sin(pi) = 0  (exact identity; f64 gives ~1.2e-16)
    let sin_pi = TowerValue::Symbolic(SymbolicExpr::Pi).sin();
    row("sin(pi)", "0", std::f64::consts::PI.sin(), sin_pi.to_f64().unwrap());

    // 1/7 * 7 = 1
    let one7 = RnsRational::from_fraction(1, 7, ch.clone()).mul(&RnsRational::from_int(7, ch));
    row("1/7 * 7", &one7.display(), (1.0 / 7.0) * 7.0, one7.to_f64());

    println!("\nEvery `exact` column is bit-for-bit correct; the f64 column drifts.");
}

Trait Implementations

impl Clone for TowerValue

fn clone(&self) -> TowerValue

Returns a duplicate of the value.

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

Performs copy-assignment from source.