dankogai/swift-interval

Synopsis

import Interval
let about1 = 1.0 ± 0.1  // 0.9...1.1
about1+about1           // 1.8...2.2
about1-about1           // -0.2...0.2
about1*about1           // 0.81...1.21
about1/about1           // 0.818181818181818...1.22222222222222

Prerequisite

Swift 6.0 or better, macOS or Linux. This package depends on nothing: Double conforms to IntervalElement out of the box, via libm. Other element types are one empty extension away — see the example subpackages below.

Usage

build

git clone https://github.com/dankogai/swift-interval.git
cd swift-interval
swift build

REPL

swift run --repl

import Interval
let about1 = 1.0 ± 0.1

in your project

Add the following to the dependencies of your Package.swift:

.package(url: "https://github.com/dankogai/swift-interval.git", from: "6.0.0")

and add "Interval" to the dependencies of your target.

with playground

Have fun with [macOS.playground] that is a part of this git repo: open the package folder in Xcode, let it resolve, and the playground pages can import Interval. Four pages: a synopsis of the API, the quadratic formula with its cancellation made visible, error propagation without the calculus, and a scratch pad.

[macOS.playground]: ./macOS.playground

with swift-numerics

IntervalElement's function requirements deliberately share their names and signatures with [apple/swift-numerics]' Real, so any Real type is one empty extension away from being an element. SwiftNumericsExample conforms Float that way — and goes the other direction too, making Interval itself a RealModule.Real, so intervals flow through code written generically for scalars:

extension Float: @retroactive IntervalElement {}

func rms<T: Real>(_ x: T, _ y: T) -> T { T.sqrt((x*x + y*y)/2) }
rms(3.0 ± 0.1, 4.0 ± 0.1)   // 3.5355622…±0.0989941…

[apple/swift-numerics]: https://github.com/apple/swift-numerics

with swift-bignum

The same one-liner works for [dankogai/swift-bignum]. SwiftBigNumExample shows Interval<BigRat> and Interval<BigFloat>, where interval arithmetic becomes exact:

let about1 = BigRat(1) ± BigRat(1, 10)   // [9/10, 11/10]
about1 / about1                          // [9/11, 11/9] — the fractions, exactly

[dankogai/swift-bignum]: https://github.com/dankogai/swift-bignum

Test

swift test

Package Metadata

Repository: dankogai/swift-interval

Default branch: main

README: README.md