Note: This has been adapted from Swift NumberKit by Matthias Zenger.

The goal with this modification was to make simplification an "opt in" operation. By default, Rational values will not simpify when created, and will generally keep the numerator unchanged unless combining rational values with different numberators.

Swift NumberKit

Overview

This is a framework implementing advanced numeric data types for the Swift programming language on macOS and iOS. Currently, the framework provides three new numeric types, each represented as a struct:

BigInt: arbitrary-precision signed integers
Rational: signed rational numbers
Complex: complex floating-point numbers

Note: So far, with every major version of Swift, Apple decided to change the foundational APIs of the numeric types in Swift significantly and consistently in a backward incompatible way. In order to be more isolated from such changes in future, with Swift 3, I decided to introduce a distinct integer type used in NumberKit based on a new protocol IntegerNumber. All standard numeric integer types implement this protocol. This is now consistent with the usage of protocol FloatingPointNumber for floating point numbers, where there was, so far, never a real, generic enough foundation (and still isn't).

BigInt

BigInt objects are immutable, signed, arbitrary-precision integers that can be used as a drop-in replacement for the existing binary integer types of Swift 5. Struct BigInt defines all the standard arithmetic integer operations and implements the corresponding protocols defined in the standard library.

Rational

Struct Rational<T> defines immutable, rational numbers based on an existing signed integer type T, like Int32, Int64, or BigInt. A rational number is a signed number that can be expressed as the quotient of two integers a and b: a / b.

Complex

Struct Complex<T> defines complex numbers based on an existing floating point type T, like Float or Double. A complex number consists of two components, a real part re and an imaginary part im and is typically written as: re + im * i where i is the imaginary unit.

Requirements

The following technologies are needed to build the components of the Swift NumberKit framework: