Re: erroneous claim at sources.redhat.com/gsl/ref/gsl-ref_4.html#SEC3 2

[Achim Gädke <Achim dot Gaedke at physik dot tu-darmstadt dot de>]

Yes, this is quite true, that I do not really know, what's the optimal way.

1) In order to fix a documentation bug, we should correct the manual.

2) Here we multiply numbers (plain floating point numbers), so the 
effort to do the optimum should be not to large: approx. O(2*log_2(n)) 
is not bad in contrast to O(n).

3) If it is cheap to find a better way or if we deal with matrices (e.g. 
in characteristic polynoms), we may want to find out a better way to 
split this multiplication. Finding prime factors is quite expensive. For 
21 I avoid one multiplication, but what about the costs?

4) I like this problem, because it's simple to explain and becomes 
difficult when solving it. :-)

Achim

jimmy mcguire wrote:

> Breaking my usual rule against speaking proir to knowing for sure, how 
> about use the powers of two approach if the destination exponent is a 
> power of two or if it is prime, otherwise the break the destination 
> exponent into prime addends and construct multiplicative factors 
> corresponding to the prime additive exponents. Repeat (recurse) as 
> necessary.
>
> Achim Gädke wrote:
>
> > so, is there anyone outside, knowing similar problems?
> >
> > I agree, repeated squaring is likely to be the best solution, because 
> > the binary representation can be obtained easily on a computer.
> > So the manual should state, that this algorithm is efficient and in 
> > most cases the fastest.
> >
> > Achim
> >
> > keith.briggs@bt.com wrote: