Struct Interval 

pub struct Interval {
    pub lo: Bound,
    pub hi: Bound,
    pub lo_open: bool,
    pub hi_open: bool,
}

An interval [lo, hi] with optional open/closed endpoints. Represents the set of values x such that lo ≤ x ≤ hi (closed) or lo < x < hi (open), depending on the flags.

Fields

lo: Bound

Lower bound.

hi: Bound

Upper bound.

lo_open: bool

True if lower bound is open (exclusive).

hi_open: bool

True if upper bound is open (exclusive).

Implementations

impl Interval

pub fn empty() -> Self

Create the empty interval.

pub fn reals() -> Self

Create the interval containing all reals (-∞, +∞).

pub fn point(a: BigRational) -> Self

Create a point interval [a, a].

pub fn closed(a: BigRational, b: BigRational) -> Self

Create a closed interval [a, b].

pub fn open(a: BigRational, b: BigRational) -> Self

Create an open interval (a, b).

pub fn half_open_right(a: BigRational, b: BigRational) -> Self

Create a half-open interval [a, b).

pub fn half_open_left(a: BigRational, b: BigRational) -> Self

Create a half-open interval (a, b].

pub fn at_most(b: BigRational) -> Self

Create an interval (-∞, b].

pub fn less_than(b: BigRational) -> Self

Create an interval (-∞, b).

pub fn at_least(a: BigRational) -> Self

Create an interval [a, +∞).

pub fn greater_than(a: BigRational) -> Self

Create an interval (a, +∞).

pub fn is_empty(&self) -> bool

Check if the interval is empty.

pub fn is_point(&self) -> bool

Check if the interval is a single point.

pub fn is_bounded(&self) -> bool

Check if the interval is bounded (both endpoints finite).

pub fn contains(&self, x: &BigRational) -> bool

Check if the interval contains a value.

pub fn contains_zero(&self) -> bool

Check if this interval contains zero.

pub fn is_positive(&self) -> bool

Check if all values in the interval are positive.

pub fn is_negative(&self) -> bool

Check if all values in the interval are negative.

pub fn is_non_negative(&self) -> bool

Check if all values are non-negative.

pub fn is_non_positive(&self) -> bool

Check if all values are non-positive.

pub fn sign(&self) -> Option<i8>

Get the sign of the interval. Returns Some(1) if all positive, Some(-1) if all negative, Some(0) if only zero. Returns None if the interval contains values of different signs.

pub fn negate(&self) -> Interval

Negate the interval.

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

Add two intervals.

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

Subtract two intervals.

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

Multiply two intervals.

pub fn div(&self, other: &Interval) -> Option<Interval>

Divide two intervals. Returns None if division by zero occurs (divisor contains zero).

pub fn intersect(&self, other: &Interval) -> Interval

Compute the intersection of two intervals.

pub fn union(&self, other: &Interval) -> Option<Interval>

Compute the union of two intervals (if contiguous). Returns None if the intervals are not contiguous.

pub fn pow(&self, n: u32) -> Interval

Compute the power of an interval.

pub fn midpoint(&self) -> Option<BigRational>

Get the midpoint of the interval (if bounded).

pub fn width(&self) -> Option<BigRational>

Get the width of the interval (if bounded).

pub fn split(&self, at: &BigRational) -> (Interval, Interval)

Split the interval at a point.

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

Convex hull of two intervals (always returns a single interval). This is the smallest interval containing both inputs.

pub fn tighten_lower(&self, new_lo: Bound, new_lo_open: bool) -> Interval

Tighten lower bound to be at least the given value. Returns a new interval with the tightened bound, or empty if inconsistent.

pub fn tighten_upper(&self, new_hi: Bound, new_hi_open: bool) -> Interval

Tighten upper bound to be at most the given value. Returns a new interval with the tightened bound, or empty if inconsistent.

pub fn propagate_add(x: &Interval, result: &Interval) -> Interval

Propagate bounds from constraint: x + y ∈ result_interval. Given x and result, tighten y’s bounds. Returns the tightened interval for y.

pub fn propagate_sub_left(x: &Interval, result: &Interval) -> Interval

Propagate bounds from constraint: x - y ∈ result_interval. Given x and result, tighten y’s bounds. Returns the tightened interval for y.

pub fn propagate_sub_right(y: &Interval, result: &Interval) -> Interval

Propagate bounds from constraint: x - y ∈ result_interval. Given y and result, tighten x’s bounds. Returns the tightened interval for x.

pub fn propagate_mul(x: &Interval, result: &Interval) -> Option<Interval>

Propagate bounds from constraint: x * y ∈ result_interval. Given x and result, tighten y’s bounds (if x doesn’t contain 0). Returns None if x contains 0, otherwise returns the tightened interval for y.

pub fn propagate_div_left(x: &Interval, result: &Interval) -> Option<Interval>

Propagate bounds from constraint: x / y ∈ result_interval. Given x and result, tighten y’s bounds (if result doesn’t contain 0). Returns None if propagation is impossible, otherwise returns the tightened interval for y.

pub fn propagate_div_right(y: &Interval, result: &Interval) -> Interval

Propagate bounds from constraint: x / y ∈ result_interval. Given y and result, tighten x’s bounds. Returns the tightened interval for x.

pub fn is_subset_of(&self, other: &Interval) -> bool

Check if this interval is a subset of another interval.

pub fn overlaps(&self, other: &Interval) -> bool

Check if two intervals overlap (have non-empty intersection).

pub fn widen(&self, amount: &BigRational) -> Interval

Widen the interval by a given amount on each side.

Trait Implementations

impl Add<&Interval> for &Interval

type Output = Interval

The resulting type after applying the + operator.

fn add(self, rhs: &Interval) -> Self::Output

Performs the + operation.

impl Add for Interval

type Output = Interval

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self::Output

Performs the + operation.

impl Clone for Interval

fn clone(&self) -> Interval

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Interval

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

Formats the value using the given formatter.

impl Default for Interval

fn default() -> Self

Returns the “default value” for a type.

impl Display for Interval

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

Formats the value using the given formatter.

impl Div<&Interval> for &Interval

type Output = Option<Interval>

The resulting type after applying the / operator.

fn div(self, rhs: &Interval) -> Self::Output

Performs the / operation.

impl Div for Interval

type Output = Option<Interval>

The resulting type after applying the / operator.

fn div(self, rhs: Self) -> Self::Output

Performs the / operation.

impl Mul<&Interval> for &Interval

type Output = Interval

The resulting type after applying the * operator.

fn mul(self, rhs: &Interval) -> Self::Output

Performs the * operation.

impl Mul for Interval

type Output = Interval

The resulting type after applying the * operator.

fn mul(self, rhs: Self) -> Self::Output

Performs the * operation.

impl Neg for &Interval

type Output = Interval

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl Neg for Interval

type Output = Interval

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl PartialEq for Interval

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

Tests for self and other values to be equal, and is used by ==.

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

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Sub<&Interval> for &Interval

type Output = Interval

The resulting type after applying the - operator.

fn sub(self, rhs: &Interval) -> Self::Output

Performs the - operation.

impl Sub for Interval

type Output = Interval

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self::Output

Performs the - operation.

impl Eq for Interval

impl StructuralPartialEq for Interval