Re: Making Lemonade (Floating-point format changes)

On Tue, 21 May 2024 05:49:55 -0000 (UTC)
Thomas Koenig <tkoenig@netcologne.de> wrote:

BGB <cr88192@gmail.com> schrieb:
 

Granted, they are not necessarily the option one would go if they
wanted "cheapest possible FPU that is still good enough to be
usable".
>
Though, the point at which an FPU manages to suck badly enough that
one needs to resort to software emulation to make software work, is
probably a lower limit.
>
>
Luckily, "uses 754 formats, but with aggressive cost cutting" can
be "good enough", and so long as they more-or-less deliver a full
width mantissa, and can exactly compute exact-value calculations,
most software is generally going to work. 

 
This will require extensive testing and possibly modification for
a lot of software ported to such a system.  This will drive up
the total cost, presumably far more than any hardware savings.
 

But OTOH, if 1.0+2.0 gives 2.999999, that is, not good enough, so
there is a lower limit here. 

 
An example of a more interesting question is
 
  if (a >= 0.) {
    if (b >= 0) {
      if (a + b < a) {
        printf("We should never get here!\n);
abort();
      }
    }
  }

If I am not mistaken, that should hold on VAX, which has floating-point
very close to BGB ideal. It looks like it would hold even on less
robust formats, like IBM's hex float. I wonder where it is not true?

The biggest difference between IEEE and VAX is that on IEEE when (a > b)
then (a - b > 0) while on VAX (a - b >= 0).

Of course, IEEE has non-intuitive cases as well.
if (!(a < 0)) {
  if (!(b < 0)) {
    if (!(a + b >= a)) {
      printf("It's IEEE 754, baby!\n);
    }
  }
}