Anything in the review queue?

[dsimcha]

On 3/21/2011 3:59 AM, Don wrote:
> The original plan for BigInt was to have a BigRational type. Suppose
> that such a thing existed -- would it affect plans for this library?
>
> I'm not sure that it is realistic to have a single templated type that
> does both BigInt rationals, together with rationals based on built-in
> integral types. The algorithms are different in a few respects:
> (1) copying built-ins is practically zero cost;

Doesn't BigInt use COW rather than eager copying?

> (2) operations on BigInts depend on the size of the number (whereas for
> builtins, all operations are O(1));

I don't understand how this is relevant.

> (3) BigInts cannot overflow.
> In particular, gcd algorithms for arbitrary precision types are quite
> different to gcd for built-ins.

Ok, I don't know much about how BigInts work under the hood.  I used a 
fairly simple implementation of Euler's algorithm here.  Is there 
something much more efficient for BigInts?

>
> I guess the primary question is:
> If there were a BigRational type, would you still want rational?
> Ie, are there use cases for rational over built-in types (rather than it
> just being a workaround for a lack of a BigRational type)?

My thoughts were that Rational would be **primarily** used with BigInt, 
but occasionally, if you really know what you're doing with regard to 
overflow, you could used fixed width as an optimization.

> If the answer to this question is yes, then I suspect that the semantics
> for rational over built-ins are so different to the semantics for
> BigRational, that the two could be relatively independent.