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Interval API Reference

Complete API documentation for the interval<T> class template.

Class Template

template<Boundary T>
class interval;

Template Parameters

  • T: The value type for interval boundaries. Must satisfy the Boundary concept (totally ordered and regular).

Common Type Aliases

namespace dis {
    using real_interval = interval<double>;
    using integer_interval = interval<int>;
}

Named Constructors (Factory Methods)

Bounded Intervals

closed(T lower, T upper)

[[nodiscard]] static constexpr interval closed(T lower, T upper) noexcept;
Creates a closed interval \([a, b]\) that includes both endpoints.

Example: 

auto i = real_interval::closed(0, 10);  // [0, 10]
assert(i.contains(0));   // true
assert(i.contains(10));  // true

open(T lower, T upper)

[[nodiscard]] static constexpr interval open(T lower, T upper) noexcept;
Creates an open interval \((a, b)\) that excludes both endpoints.

Example: 

auto i = real_interval::open(0, 10);  // (0, 10)
assert(!i.contains(0));   // false
assert(!i.contains(10));  // false
assert(i.contains(5));    // true

left_open(T lower, T upper)

[[nodiscard]] static constexpr interval left_open(T lower, T upper) noexcept;
Creates a left-open interval \((a, b]\).

right_open(T lower, T upper)

[[nodiscard]] static constexpr interval right_open(T lower, T upper) noexcept;
Creates a right-open interval \([a, b)\).

Special Intervals

point(T value)

[[nodiscard]] static constexpr interval point(T value) noexcept;
Creates a singleton interval \(\{x\}\) containing exactly one point.

empty()

[[nodiscard]] static constexpr interval empty() noexcept;
Creates an empty interval \(\emptyset\).

Unbounded Intervals

Requires std::numeric_limits<T>::has_infinity.

unbounded()

[[nodiscard]] static constexpr interval unbounded() noexcept;
Creates \((-\infty, \infty)\).

at_least(T lower)

[[nodiscard]] static constexpr interval at_least(T lower) noexcept;
Creates \([a, \infty)\).

greater_than(T lower)

[[nodiscard]] static constexpr interval greater_than(T lower) noexcept;
Creates \((a, \infty)\).

at_most(T upper)

[[nodiscard]] static constexpr interval at_most(T upper) noexcept;
Creates \((-\infty, b]\).

less_than(T upper)

[[nodiscard]] static constexpr interval less_than(T upper) noexcept;
Creates \((-\infty, b)\).

Member Functions

Queries

is_empty()

constexpr bool is_empty() const noexcept;
Returns true if interval contains no points.

contains(T value)

constexpr bool contains(T value) const;
Tests if value is in interval.

overlaps(const interval& other)

constexpr bool overlaps(const interval& other) const;
Tests if intervals have non-empty intersection.

Accessors

lower_bound(), upper_bound()

constexpr std::optional<T> lower_bound() const noexcept;
constexpr std::optional<T> upper_bound() const noexcept;
Returns bounds, or std::nullopt for empty intervals.

Measures

(Requires std::is_arithmetic_v<T>)

length()

constexpr T length() const;
Returns \(b - a\).

midpoint()

constexpr T midpoint() const;
Returns \((a + b) / 2\).

Operations

intersect(const interval& other)

constexpr interval intersect(const interval& other) const;
Returns intersection.

hull(const interval& other)

constexpr std::optional<interval> hull(const interval& other) const;
Returns convex hull if intervals overlap or are adjacent, otherwise std::nullopt.

Operators

// Intersection
friend interval operator&(const interval& a, const interval& b);

// Comparison
friend auto operator<=>(const interval& a, const interval& b);
friend bool operator==(const interval& a, const interval& b);

// Stream output
friend std::ostream& operator<<(std::ostream& os, const interval& i);

Complete Example

See Getting Started and Examples for usage examples.