Re: How to use GNU MP in octave?

[Shai Ayal]

Javier Arantegui wrote:
> Hello,
>
> El Martes, 24 de Mayo de 2005 05:28, Keith Goodman escribió:
>
> > Here's a quote from google
>
> [...]
>
> > Let x = lg(8600!). Since lg(xy)=lg(x)+lg(y) you have
> >
> > x = sum(lg(k),k=1..86000)
> >
> > Define floor(x) as the integer part of x. Then
> >
> > 86000! = 10^(x-floor(x))*10^floor(x).
> >
> > You can evaluate x to the degree of accuracy you want, for example,
> > using Maple I got:
> >
> > 86000! = 7.91222558*10^372239
>
>
> Unfortunately, Octave doesn't buy the trick :-(:-(
>
> octave:4> k=1:1:86000;
> octave:5> x=sum(log10(k))
> x =  3.8702e+05
> octave:6> 10^(x-floor(x))*10^floor(x)
> ans = Inf

Octave doesn't buy this trick since the maximum double value is ~ 10^300. I 
think Keith meant to say:

use octave to calc 10^(x-floor(x)) which is hard to do by hand, and 
multiply by 10^floor(x) in your head which is easy, (at least to me ...)


octave:8>  k=1:1:86000;
octave:9>  x=sum(log10(k));
octave:10> format long
octave:11> x
x = 387020.407702849
octave:12> floor(x)
ans = 387020
octave:13> 10^(x-floor(x))
ans = 2.55683586378090

so your answer is approximately 2.55683586378090*10^387020, (or 
2.55683586378090e+387020 in octaves output format). 16 decimal digits is 
the limit of double precision floting point used in octave. If you need 
more precision, than other programing tools, as suggested in previous 
emails in this thread are appropriate.

Note that this result is different from the maple result given above, 
probably due to roundoff errors in the sum. I suppose this could be 
improved with some more perusing, although the double precision output of 
maple leads me to suspect that tin his case a a similar algorithm, or some 
approximation was used, not real arbitrary precision arithmetic.



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