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From: Thomas Koenig <tkoenig@netcologne.de>
Newsgroups: comp.arch
Subject: Re: Making Lemonade (Floating-point format changes)
Date: Tue, 21 May 2024 17:53:47 -0000 (UTC)
Organization: A noiseless patient Spider
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Michael S <already5chosen@yahoo.com> schrieb:
> 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?

IIRC, something like that was possible when mixing 80-bit and 64-bit
quantities on x387.

But the code I posted probably does not qualify for this.