Struct RatInterval 

pub struct RatInterval { /* private fields */ }

A closed interval of exact rationals, lo <= hi (Appendix H.3).

Because the endpoints are exact rationals, +, - and x on intervals are themselves exact — there is nothing to round outward. Outward rounding enters at exactly two places, and both are explicit:

• RatInterval::sqrt_enclosure, which uses the directed integer roots;
• fixed-point scaling, where the scale is declared and recorded.

That is a stronger position than a float interval library can take, and it is what lets Rule X promise a certified enclosure rather than a tolerance.

Implementations

impl RatInterval

pub fn new(lo: Ratio, hi: Ratio) -> Result<RatInterval>

Construct, rejecting inversion with UCAL-E0022.

pub fn exact(v: Ratio) -> RatInterval

The degenerate interval at an exact value.

pub fn lo(&self) -> &Ratio

Lower bound.

pub fn hi(&self) -> &Ratio

Upper bound.

pub fn is_exact(&self) -> bool

Whether the interval is a single point.

pub fn width(&self) -> Result<Ratio>

hi - lo.

pub fn contains(&self, v: &Ratio) -> bool

Whether the interval contains a value.

pub fn contains_zero(&self) -> bool

Whether zero is inside the interval. Division requires this to be false (Appendix H.3).

pub fn add(&self, other: &RatInterval) -> Result<RatInterval>

Interval addition. Exact: lo with lo, hi with hi.

pub fn sub(&self, other: &RatInterval) -> Result<RatInterval>

Interval subtraction, [lo - other.hi, hi - other.lo].

pub fn mul(&self, other: &RatInterval) -> Result<RatInterval>

Interval multiplication: the min and max of the four endpoint products.

With non-negative endpoints this reduces to lo*lo and hi*hi, but the general form is computed anyway so the method stays correct if the endpoint domain is ever widened.

pub fn div(&self, other: &RatInterval) -> Result<RatInterval>

Interval division. UCAL-E0070 if the divisor interval contains zero.

pub fn sqrt_enclosure(&self, scale_digits: u32) -> Result<(RatInterval, u32)>

A certified enclosure of the square root, at a declared fixed-point scale (Appendix H.2).

Computes [isqrt_floor(lo x S^2) / S, isqrt_ceil(hi x S^2) / S], which provably contains the true root of every value in the interval. The scale is a parameter rather than a constant because different queries need different precision (D-6), and it is returned alongside the result so it can be recorded — CosmoResult carries it as scale.

Widening the interval is always sound; narrowing it would not be. Every rounding here goes outward.

pub fn hull(&self, other: &RatInterval) -> RatInterval

The smallest interval containing both.

Trait Implementations

impl Clone for RatInterval

fn clone(&self) -> RatInterval

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for RatInterval

impl Debug for RatInterval

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Eq for RatInterval

impl PartialEq for RatInterval

fn eq(&self, other: &RatInterval) -> bool

Equality operator ==.

fn ne(&self, other: &Rhs) -> bool

Inequality operator !=.

impl StructuralPartialEq for RatInterval