Floats Don't Agree with Themselves (opens in new tab)

> It was IEEE 754 working as advertised. The standard pins down the storage format. It does not pin down behavior.

IEEE 754 absolutely does pin down behavior.

Not sure if this was written with AI assistance of not, but I've become allergic to linguistic triples as LLMs use them so much, reading "Same code. Same input. Different answer" makes me not want to read the rest.

I wish the blog would reveal the values of the 3 floats that make their

    cross_sign(A, B, C)

to give different results in different platforms.

If the original code was written in Rust, then I don't think the Rust compiler is allowed to do any of these "optimizations" of rewriting floating point expressions.

> -ffast-math default, often on without intent

Ah yes -ffast-math, also known as -fincorrect-math

I love seeing a Shewchuk citation other than my ML background of learning conjugate gradient! He is truly a great educator!

That's why they always teach: "never compare floats for equality."

Or maybe they don't teach that anymore, I dunno.

See link for the Fundamental Axiom of Floating Point Arithmetic: All floating point arithmetic operations are exact up to a relative error of epsilon_machine.

https://www.johnbcoughlin.com/posts/floating-point-axiom/

Makes you wish everyone agreed on extended precision!