Double-double: 31 digits of precision without leaving the FPU

AI has rediscovered https://www.davidhbailey.com/dhbsoftware/ and similar? Or are there algorithmic improvements? Without referencing established double-double work it's hard to know.

Fun fact - Google Maps does something similar to this in WebGL in order to keep accurate coordinates across a planet-sized map using only 32-bit floats.

I have a Go library implementing double-double arithmetic (and also exponentials, logarithms, trigonometry...): https://github.com/ncruces/dbldbl

Mostly useless, but was quite fun to write.

Such trick looks interesting. But I think for many cases it would be better to use fixed-width arithmetic based on 128-bit integers. Operations for them are much cheaper if done right (and assuming compilers are smart enough to optimize them). For the Mandelbrot set one don't need huge range, maybe 4 bits of range or so, the remaining 124 bits of precision can increase quality significantly.

Could be a neat post, but it was too obviously LLM-generated for me to care about reading it deeply. I’m really fine with people using LLMs to write code and understand stuff, but at least drop a disclaimer when you’re blogging straight Claude text.

If you need that precision, especially for position and not values, why use floats at all?

This feels like a lot of words to say "a decimal point between two integers".

Could call it... 'a Hamburglar'

At least Dekker is referenced.

Reads like AI slop. It circles around the point, uses C# examples while talking about FPU, duplicates examples and so on.