[thechao]

I'm mixed on Gustafson's posit stuff. For me, the only thing I'd change for fp would be:

1. -0 now encodes NAN.

2. +inf/-inf are all Fs with sign: 0x7FFFFFFF, 0xFFFFFFFF.

3. 0 is the only denorm.

Which does four good things:

1. Gets rid of the utter insanity which is -0.

2. Gets rid of all the redundant NANs.

3. Makes INF "look like" INF.

4. Gets rid of "hard" mixed denorm/norm math.

And one seriously bad thing:

1. Lose a bunch of underflow values in the denorm range.

However, as to the latter: who the fuck cares! Getting down to that range using anything other than divide-by-two completely trashes the error rate anyways, so why bother?

The rest of Gustafson's stuff always sounds like crazy-people talk, to me.

[piadodjanho]

He also propose the use of an opaque register to accumulate (quire), in contrast to the transparent float register (its a mess, each compiler does what it think is best).

When working with numbers that exceed the posit representation you use the quire to accumulate. At the end of the computation you convert again to posit to store in memory, or store the quire in memory.

In C, it would look like something like:

    posit32_r a, b;
    quire_t q;
    
    q = a; // load posit into quire
    
    q = q + b; // accumulate in quire
    
    a = q; // load quire into posit

> The rest of Gustafson's stuff always sounds like crazy-people talk, to me.

I've read all his papers on posit and agree. But I do believe the idea of encoding exponent with golomb-rice is actually very good and suit most users. The normalization hardware (used in the subtraction operation) can be easily repurposed to decode the exponent and shift the exponent.

But the quire logic (fixed point arithmetic) might use more area than a larger float-point. But maybe in power usage it pays of.

[thechao]

I come from GPU-land, and a quire always brings a chuckle from the fp HW folk. They like the rest of Gustafson’s stuff, though.

[piadodjanho]

Yeah. Gustafons is like, memory is cheap, just use a few hundreds of kb to store the quire. To be fair, he is not HW guy.

[cokernel_hacker]

Interesting. One issue is treatment of 1 / -inf. This would be -0 in traditional IEEE 754 but would now be +0 IIUC.

This would imply that 1 / (1 / -inf) would now be +inf instead of -inf.

[thechao]

0 is unsigned. I would reject 1/inf — it would be NAN. If the user wants to play silly games with derivatives, computer algebra systems are that way: —>.

[piadodjanho]

NaN is NaR (not a real) in posit notation.