README

A PHP library for working with mathematical intervals. It provides an elegant way to create, compare, and work with intervals using standard mathematical notation.

Installation

Install the package via Composer:

composer require superscript/interval

Requirements

• PHP 8.3 or higher

Usage

Creating Intervals

You can create intervals from string notation:

use Superscript\Interval\Interval;

// Create from string notation
$interval = Interval::fromString('[1,5]');  // Closed interval
$interval = Interval::fromString('(1,5)');  // Open interval 
$interval = Interval::fromString('[1,5)');  // Right-open interval
$interval = Interval::fromString('(1,5]');  // Left-open interval
$interval = Interval::fromString('[1,)');  // Left-bounded interval (infinite upper bound)
$interval = Interval::fromString('(,1]');  // Right-bounded interval (infinite lower bound)

Interval Notation

The library supports four types of interval notation:

• [a,b] - Closed interval: includes both endpoints a and b. Example: [1,5] includes all numbers from 1 to 5, including 1 and 5.
• (a,b) - Open interval: excludes both endpoints a and b. Example: (1,5) includes all numbers greater than 1 and less than 5, but not 1 or 5 themselves.
• [a,b) - Right-open interval: includes a but not b. Example: [1,5) includes 1 and all values up to (but not including) 5.
• (a,b] - Left-open interval: excludes a but includes b. Example: (1,5] includes all values greater than 1 up to and including 5.

The inclusion or exclusion of the endpoints determines how comparisons behave. For example, if an interval is (1,5), calling $interval->isGreaterThan(1) will return true because 1 is not part of the interval. However, if the interval is [1,5], then $interval->isGreaterThanOrEqualTo(1) will return true since 1 is included.

Understanding this notation is crucial for interpreting comparison behavior correctly.

The library also supports unbounded intervals using empty endpoints. These are interpreted as extending to infinity:

• [a,) - Left-bounded interval: includes a and extends infinitely to the right.
• (,b] - Right-bounded interval: includes b and extends infinitely to the left.
• (,) - Fully unbounded interval: represents all real numbers.

Internally, unbounded sides are represented using PHP_INT_MIN or PHP_INT_MAX.

Interval Comparisons

$interval = Interval::fromString('[2,5]');

$interval->isGreaterThan(1);      // true
$interval->isGreaterThanOrEqualTo(2);  // true
$interval->isLessThan(6);         // true
$interval->isLessThanOrEqualTo(5);     // true

Comparisons such as $interval->isGreaterThan($value) evaluate whether all values within the interval are greater than the given value. So [2,5] is greater than 1 (because every number from 2 to 5 is greater than 1), but not greater than 2 unless the interval is open on the left side (e.g., (2,5)).

Similarly, $interval->isLessThan($value) checks whether all values in the interval are less than the given value. (1,5) is less than 6, but not less than 5 unless the interval excludes 5 (e.g., (1,5) or [1,5).

This logic allows for precise control over numeric comparisons, especially when you want to reason about bounds inclusivity.

Testing

Run the test suite:

composer test

This includes:

• Static analysis (composer test:types)
• Unit tests with coverage (composer test:unit)
• Mutation testing (composer test:infection)

License

MIT

About

This package is developed and maintained by Superscript.