Complex numbers in JavaScript | Hacker News Reader

Complex numbers in JavaScript

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Thinking for some time about refactoring Quantum Game (https://github.com/stared/quantum-game), including its complex tensor operation part (plus some "boring but important" like jspm.io -> webpack, actually using Vue or React vs the no-framework mess, etc). If anyone interested in collaboration, I am happy to talk!

You might as well use WebAssembly for the task. C and C++ have good native complex number support.

They don't really, they tried to glue IEEE semantics onto their complex numbers, so they're largely broken in the modern era of auto-vectorizing compilers.

Interesting. Under what circumstances are they broken?. Inf, NaN?

Here's an article on it that was posted awhile back: https://medium.com/@smcallis_71148/complex-arithmetic-is-com...

The gist is that you can get Nan+jNan for some operations where you wanted "infinity", so to do things their way, you have to insert a NaN check after multiplication for example. This isn't too bad by itself (it's just a bit mask), but it completely borks the vectorizer.

I like how you moved to Complex16Array for reduced memory overhead and improving CPU cache performance. I'd probably take a close look at your get method's "return new Complex16(...)" call and see if those object instantiations are consuming a lot of CPU time and memory churn on their own.

We use quite a bit of complex numbers in Javascript under the hood within CircuitLab for doing frequency-domain circuit analysis of electronic circuits like filters and amplifiers. In that mode, a circuit simulator is essentially solving a system of complex-valued equations using a sparse matrix solver that accepts complex numbers, so the complex arithmetic routines are some of the potential performance hot spots. You'd want to unroll a lot of the intermediate manipulation without creating a lot of new objects in the middle! I've written a short complex numbers tutorial here: https://www.circuitlab.com/textbook/complex-numbers/

Yes, I decided to add the instantiations for readability. It would be more efficient in a production setting to do the operations directly on the raw data.

Thank you for the link!

Cool!

I once wrote a much hackier version of complex arithmetic in JavaScript [0]. It was to support a visualization of the complex derivative [1].

I found it useful to think of a complex number as a point in R^2 that operates under some different rules. I used Mathematica's `ComplexExpand` to translate from traditional notation for complex numbers [2].

[0]: https://github.com/chnn/multivariable-derivative-viz/blob/ma...

[1]: http://people.reed.edu/~ormsbyk/projectproject/assets/posts/...

[2]: https://reference.wolfram.com/language/ref/ComplexExpand.htm...

Not much to say about the complex implementation itself; seems pretty good, and it's as 'bare-metal' as you can get in browser javascript. It's not a great abstraction, and very little error checking.

However, I really like this literate programming style. You've got live editing, and legible output, in the form of little TeX blocks. It's a really nice way to define, describe, and teach little libraries like this. Well done.

Why Complex16? What does 16 mean here?

16 bytes of memory for one complex number! I could've called it Complex128, but that’s a mouthful.

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