Improved non-recursive version of contFrac in contextFraction.pl.

[drgrice1]

This version uses a loop instead of a recursive function. Benchmarking shows it is at least twice as fast. It also should use less memory overhead as it does not store the steps in constructing the continued fraction in arrays. It only keeps what is needed to continue. That is the last two values of the convergent numerator and denominator.

A basic unit test is added to check that this does the right thing. Note that this unit test works with both this branch and the code in develop. Demonstrating that they both generate the same fractions.

I have had this sitting here since March. This is a good change, and I don't know why I didn't put it in sooner.

[pstaabp]

This looks good. Figured I would try in a problem. Here's a small problem that shows off a little bit:

DOCUMENT();
loadMacros("PGstandard.pl","PGML.pl",'contextFraction.pl');
Context('Fraction')->flags->set(contFracMaxDen => 1000);

$onethird = Fraction(0.33333333); 
$fracpi = Fraction(pi);

BEGIN_PGML
[$onethird]

[$fracpi]
END_PGML
ENDDOCUMENT();

Although the results are identical in both develop and this branch. I didn't benchmark them.

[Alex-Jordan]

I tested with the golden ratio, which I suspect makes a continued fraction algorithm loop/recurse the most relative to the max denominator, and I had about a 50% improvement in speed with 10,000 consecutive runs.

Something interesting though. When I timed runs individually, the first run takes 3 to 4 times as long as the runs that follow (whether it's thee old or new version). I guess something is loaded that first time that makes the remaining runs faster.