Rationals Lib?

[Don]

dsimcha wrote:
> I've written a prototype lib that does arithmetic on rational numbers
> (fractions).  I got the idea from the Maxima computer algebra system.  (
> http://maxima.sourceforge.net ). It's templated to work on any integer type
> where operators are properly overloaded, though in practice you'd probably
> want to use something arbitrary precision, since adding/subtracting fractions
> can yield some really really big numbers for numerators and denominators, and
> if you don't care that much about accuracy, floats are faster anyhow.
> 
> I'm still cleaning things up, etc, but usage is something like this:
> 
> import std.bigint, fractions;
> 
> void main() {
>     auto f1 = fraction( BigInt("314159265"), BigInt("27182818"));
>     auto f2 = fraction( BigInt("8675309"), BigInt("362436"));
>     f1 += f2;
>     assert(f1 == fraction( BigInt("174840986505151"),
>         BigInt("4926015912324")));
> 
>     // Print result.  Prints:
>     // "174840986505151 / 4926015912324"
>     writeln(f1);
> 
>     // Print result in decimal form.  Prints:
>     // "35.4934"
>     writeln(cast(real) result);
> }
> 
> Some questions for the community:
> 
> 1.  Does this look useful to anyone?
> 2.  What might be some non-obvious key features for a lib like this?

> 3.  What is the status of arbitrary precision integer arithmetic in D2?  Will
> we be getting something better than std.bigint in the foreseeable future?
> This lib isn't very useful without a fast BigInt underneath it.

Yes, I will moving Tango BigInt to D2 Phobos. I've been delaying it for 
ages, hoping there would be a progress on the Phobos/Tango merger. But 
the Tango folks just don't seem interested in a merger, or even in 
closing the rift. :-(


> 4.  There is one small part (conversion to float) where I had to assume that
> the BigInt implementation was the one in std.bigint, to cast certain division
> results back to native types.  Will there eventually be a de facto standard
> way to cast BigInts to native types so I can get rid of this dependency?

Yes.

> 5.  Is there any use for approximate rational arithmetic built on
> machine-sized integers?  For example, if adding two fractions would generate
> an overflow, try to find the closest answer that wouldn't?  I would guess that
> if you want to do something like this, you're better off just using floats,
> but I could be wrong.

I can't think of a use for it.