Re: binary128 implementation

Anton Ertl wrote:

Michael S <already5chosen@yahoo.com> writes:

On Sun, 19 May 2024 18:37:51 +0200
Terje Mathisen <terje.mathisen@tmsw.no> wrote:

The FMA normalizer has to handle a maximally bad cancellation, so it
needs to be around 350 bits wide. Mitch knows of course but I'm
guessing that this could at least be close to needing an extra cycle
on its own and/or heroic hardware?
>
Terje
>

>
Why so wide?
Assuming that subnormal multiplier inputs are normalized before
multiplication, the product of multiplication is 226 bits

 The product of the mantissa multiplication is at most 226 bits even if
you don't normalize subnormal numbers.  For cancellation to play a
role the addend has to be close in absolute value and have the
opposite sign as the product, so at most one additional bit comes into
play for that case (for something like the product being
0111111... and the addend being -10000000...).

This is the part of Mitch's explanation that I have never been able to totally grok, I do think you could get away with less bits, but only if you can collapse the extra mantissa bits into sticky while aligning the product with the addend. If that takes too long or it turns out to be easier/faster in hardware to simply work with a much wider mantissa, then I'll accept that.
I don't think I've ever seen Mitch make a mistake on anything like this!
Terje
--
- <Terje.Mathisen at tmsw.no>
"almost all programming can be viewed as an exercise in caching"