So, in this case it wasn't correct to do so, but there is actually a current algorithm which uses floating point: Falcon (aka FN-DSA).
https://keymaterial.net/2026/05/13/so-you-want-to-deploy-fn-... talks about FN-DSA and has a section about how it's require to hand-implement floats to get constant-time operations.
> how it's require to hand-implement floats to get constant-time operations.
That and not be at the mercy of someone changing the current rounding mode behind your back.
Also hand-implement floats ... not likely to be particularly efficient, no ?
I took a quick glance at the section "About those floating points". Whomever designed that algorithm used the biggest footgun ever. I mean floating point numbers? For crypto?
Even if he can mathematically prove is algorithm is solid, he's going to lose 99% of his intended audience the moment he's going to use the words crypto and floating point in the same sentence.
It really should have been defined in terms of fixed point like HAWK was. Supposedly you'd need a large number of bits for it, but I'm not sure I find that argument particularly convincing given that floats are a kind of fixed point in log space, with a bunch of asterisks that don't help falcon much.