> trick

Normally fp numbers have an "invisible leading one bit", so an ieee fp is (1+0.nnnn) x 2^E where nnn is the mantissa and E is the exponent.

as posits are always two's complement, you can model negative posits as having an "invisible leading two bit", aka (2-0.nnnn) x 2^E-1. this greatly simplifies circuitry for addition and multiplication.

> the addition operation takes up quite a bit more floorspace,

I miswrote, it's multiplication. This is simple: since the math requires floorspace of size n^2 where n is the maximum resolution of the mantissa, and posits have more resolution around unity.

we did floorspace estimates for fp32 versus p32 and it looked like the extra space required for the mantissa did not overtake the savings from the crazy logic required for sign flipping, nans, and denormals that IEEE requires that posits don't.

> I was hoping the current AI hype wave would bring some custom silicon for alternative float formats, Posits included

i was hoping for this too!

I really want a standards body to standardize a positized version of floating point numbers. Everything about the encoding of posits (i.e. NaR, no -0.0, exponent encoding) is so much nicer. The tapered precision part of posits is IMO the least interesting part.

the twos complement thing is really elegant (-p == (posit -(int p))) in c notation

relatedly, having the same ordering as signed ints just makes everything so much easier. You can just use your integer radix sort to sort your floats without having to deal with sign and nans first!

So do floats if you don't care about NaN

They do not; if you sort as unsigned ints then negative floats sort above positive ones, and if you sort as signed ints then the negative range is reversed. IEEE floats are sign-magnitude, not twos-complement.

Add "simple and consistent rounding" to that list!

There's a tentative standard btw: https://posithub.org/docs/posit_standard-2.pdf

> as posits are always two's complement, you can model negative posits as having an "invisible leading two bit", aka (2-0.nnnn) x 2^E-1. this greatly simplifies circuitry for addition and multiplication.

Ahh indeed! I'm working on a software posit implementation (for fun, I'll eventually post it as a rust crate) so I already make use of this trick :) decoding a p64 into an exponent and twos complement signed mantissa can be done in 9 instructions on x86!