Fun with Unbounded Rational Numbers

["Jeffrey R. Carter" <spam.jrcarter.not@spam.not.acm.org>]

I decided to see what happens when you calculate square roots using Newton's 
method and the unbounded rational numbers in PragmARC.Rational_Numbers. Some 
interesting things happen.

For example, trying to calculate sqrt(2) to a small enough accuracy (0.000001 
will do it) results in the calculation of the next estimate

          M := Two * X;
          X := X - Y / M;

taking a Long Time (it does conclude eventually).

More alarming, though, is that for some values, even a fairly large accuracy 
will quickly result in Storage_Error. For example, sqrt(1.28) to an accuracy of 
0.01 will do it.

I realize that square roots are often irrational, but the accuracies seem so 
large that I didn't anticipate consuming GB of memory. Just naive, I guess.

-- 
Jeff Carter
"C++ is vast and dangerous, a sort of Mordor of
programming languages."
Jason R. Fruit
120