Re: [Algorithms] Multi-precision math libraries

[Peter B. <be...@ge...>]

    Because errors accumulate! Crank something through an algo a few
trillion times, and even very small errors can become a problem. Double
precision numbers are NOT sufficient for a lot of things, like some
finite-element analysis methods, fractals with high zoom factors, certain
very-large matrix problems, etc...

----- Original Message -----
From: "Andy Ross" <an...@ne...>
To: <gda...@li...>
Sent: Saturday, March 10, 2001 6:01 AM
Subject: Re: [Algorithms] Multi-precision math libraries


> Robert Dibley wrote:
> >
> > > If anyone also has info on 128bit fixed-point math libraries
> > > that work exceedingly well, I may use that instead.
> >
> > No references for you, but if you do a little maths I think you'll find
128
> > bit integers would be plenty - it gives you something like the entire
> > universe down to micro-metre accuracy (ok, I'm exaggerating a little)
so
> > you won't need to worry about floating point.
>
> I beg to differ, you're actually UNDER estimating a bit:
>
> Speed of light:   3 x 10^8 m/s
> Length of year:   Pi x 10^7 seconds (within a few percent)
> Size of visible
>         universe: 1 x 10^10 light years (a rough age for the universe)
> um per meter:     1 x 10^6
>
> Multiply that all out, and you get:
>
> Size of universe in micrometers: 10^32
>
> Biggest value representable in 128 bits: 10^38
>
> Bingo.  So 128 bits actually represents the universe to within
> a picometer, not a micrometer.  Thbbt!
>
> More to the point: why on earth would anyone NEED this in a
> computer simulation?  This is precision to the point of absurdity;
> even double precision floating point is more than sufficient for
> pretty much anything someone would care to represent.
>
> Andy
>
> --
> Andrew J. Ross                NextBus Information Systems
> Senior Software Engineer      Emeryville, CA
> an...@ne...              http://www.nextbus.com
> (510)420-3126                 Why Wait?
>
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