Complex numbers in Swift?

Question

Does Apple's Swift language support complex numbers out of the box?

I couldn't find any mention in the docs any equivalent for C++ std::complex nor could I find one when playing with it.

Misguided

can you bridge in complex.h? – Winfredwinfrey

Answer 1

I wrote the following:

https://github.com/dankogai/swift-complex

Just add complex.swift to your project and you can go like:

let z = 1-1.i

It has all functions and operators that of C++11 covers.

Unlike C++11 complex.swift is not generic -- z.real and z.imag are always Double.

But the necessity for complex integer is very moot and IMHO it should be treated in different type (GaussianInteger, maybe).

Granulite

Yes, very elegant syntax. I like the "1.i". However, for most realistic application, they may be used in a more computational intensive context. So performance may be a great concern. – Huddersfield

Answer 2

Apple's Swift Numerics package supports complex numbers. It was first released on November 7, 2019. The package became stable with a 1.0.0 release on August 31, 2021.

Here are some examples from the initial release announcement :

import Complex

let z: Complex<Double> = 2 + 3 * .i
print(z.real)      // 2.0
print(z.imaginary) // 3.0

let w = Complex<Double>(1, -2) // (1.0, -2.0)

let u: Complex<Double> = .i * .i // (-1.0, 0.0)

Landlocked

Answer 3

No. You may import the Accelerate module via import Accelerate and use the DSPComplex type. Refer to the documentation for more detail.

Organ

My experience with Accelerate is limited to a few line of testing and watching WWDC video. I took a dive to try to convert and i to a -i as a warm up and I find thats quite lot of boilerplate code working with this in Swift, such as code that convert/bridge from one "type" to another, in order to make it interoperate with C. Most of the APIs really work with vector. So if you don't have a vectorized problem at hand, I wonder if the overhead will be worth the trouble and dankogai's neat struct and integer extension could even be more performant. – Huddersfield

typo: "integer extension" is "Double extension" – Huddersfield