std.rational?

[ilya-stromberg]

On Tuesday, 1 October 2013 at 08:02:12 UTC, Joseph Rushton 
Wakeling wrote:
> On 01/10/13 08:26, ilya-stromberg wrote:
>> Note that denumerator must be allways positive (> 0).
>> But numerator can be positive, zero or negative, and can be 
>> bigger than
>> denumerator.
>> It means that we can use different types for numerator and 
>> denumerator:
>
> Seems an overcomplication for me, and it doesn't save you from 
> denominator == 0, so it doesn't get you out of any checks.

It's from a mathematics:
http://ru.wikipedia.org/wiki/%D0%94%D1%80%D0%BE%D0%B1%D1%8C_%28%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%29
Numerator must be integer (..., -2, -1, 0, 1, 2, ...):
http://en.wikipedia.org/wiki/Integer
Denumerator must be natural number (1, 2, 3, ...):
http://en.wikipedia.org/wiki/Natural_number

Note that english wikipedia says that denumerator is integer not 
equal to zero:
http://en.wikipedia.org/wiki/Rational_number
It's interesting: have we got 2 different mathematics, or it's 
just mistake in wikipedia? I didn't read any english mathematics 
books, but the GMP library agree with me:
"All rational arithmetic functions assume operands have a 
canonical form, and canonicalize their result. The canonical from 
means that the denominator and the numerator have no common 
factors, and that the denominator is positive. Zero has the 
unique representation 0/1."
http://gmplib.org/manual/Rational-Number-Functions.html#Rational-Number-Functions

May be you are rigth and store numerator and denumerator type is 
too complex, but it have some benefits. For example, we can save 
some memory with BigUint type because it doesn't store 
unnecessary sign.

>
>> We have BigUint in Phobos, but it's private.
>
> Interesting.  Any particular reason?  (I suppose the nature of 
> BigInt is that you don't need to worry about signed/unsigned 
> distinction because there is no range limit.)

I don't know, I just found it in source code:
https://github.com/D-Programming-Language/phobos/blob/master/std/bigint.d

module std.bigint;

private import std.internal.math.biguintcore;

struct BigInt
{
private:
         BigUint data; // BigInt adds signed arithmetic to BigUint.
         bool sign = false;
//...
}

>
>> Also, if we need only positive rationals, we can use unsigned 
>> types for numerator:
>
> Yes, but you can already get that as is by 
> Rational!(UnsignedTypeOfChoice) :-)