RE: [f-cpu] Re: Floating-Point?

[Juergen Goeritz <goeritz@oekomm.de>]

Hi guys,

don't fight about it :-)

All fast implementations have a problem on precision.
Usually you shrink down the window where the system
will work correctly to achieve maximum speed. I read
a lot about filtering lately - my head still aches.

Was talking to Yann lately if it won't be possible
to design fast 32 bit floating point instructions
that keep the computed value as one part of a 64 bit
value pair, the other being the imprecise error of
this value due to the limitations of precision.

I am just getting into floating point methods though
and therefore can't tell today if this is possible
or not. But imagine you add/subtract/multiply/divide
a number and take care of the number unsharpness the
same instance. Forget about rounding problems, just
track them with the computation values.

What's your opinion?

JG

On Fri, 17 Aug 2001, Hans Summers wrote:
> 
> > 
> > > Ah, I have the same opinion about this theme. You don't really
> > > need a higher precision than 64 bit. Maybe that will change for
> > > galaxy navigation in the future but until now 32 bit are good
> > > (and fast) for most cases.
> > 
> > Actually, floating-point is too imprecise for ANY precision 
> > calculation. There are lots of numbers that can't be encoded 
> > into floating-point values.
> > 
> > The bits in the mantissa are encoded as follows, for example:
> > - bit 0: 1/2: 0.5
> > - bit 1: 1/4: 0.25
> > - bit 2: 1/8: 0.125
> > - bit 3: 1/16: 0.0625
> > 
> > and so on. By setting the bits, you're adding up the fractions.
> > 
> > So, for example with financial computing, floating-point is a 
> > big no-no, otherwise you end up with respresentation and rounding 
> > errors.
> 
> I've spent the last 7 years writing financial applications, and have NEVER
> seen or heard of BCD arithmetic being used. I always use 64-bit
> representation mostly because it is most standard. Yes, you will get
> rounding errors but you need a heck of a lot of calculations for the
> rounding errors in the 16'th decimal place to add up to anything of any
> significance.
> 
> Hans
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