default random object?

[Don]

Bill Baxter wrote:
> On Mon, Feb 16, 2009 at 2:33 AM, Don Clugston <nospam at nospam.com> wrote:
>> Andrei Alexandrescu wrote:
>>> Don wrote:
>>>> Andrei Alexandrescu wrote:
>>>>> auto rng = Random(unpredictableSeed);
>>>>> auto a = 0.0, b = 1.0;
>>>>> auto x1 = uniform!("[]")(rng, a, b);
>>>>> auto x2 = uniform!("[)")(rng, a, b);
>>>>> auto x3 = uniform!("(]")(rng, a, b);
>>>>> auto x4 = uniform!("()")(rng, a, b);
>>>> This is a general issue applying to any numeric range. I've been giving
>>>> the issue of numeric ranges some thought, and I have begun an implementation
>>>> of a general abstraction.
>>>> Any open range can be converted into a closed range, but the converse
>>>> does not apply. So any implementation will be using "[]" internally.
>>>>
>>>> -range("[)", a, b) == range("(]", -b, -a)
>>>> range("[)", a, b) == range("[]", a, predecessor(b))
>>>> range("()", a, b) == range("[]", successor(a), predecessor(b))
>>>>
>>>>
>>>> There's a couple of difficult situations involving floating-point
>>>> numbers.
>>>> *  "[)" has the uncomfortable property that (-2,-1, rng) includes -2 but
>>>> not -1, whereas (1, 2, rng) includes 1 but not 2.
>>>>
>>>> * any floating point range which includes 0 is difficult, because there
>>>> are so many numbers which are almost zero. The probability of getting a zero
>>>> for an 80-bit real is so small that you probably wouldn't encounter it in
>>>> your lifetime. I think this weakens arguments based on analogy with the
>>>> integer case.
>>>>
>>>> However, it is much easier to make an unbiased rng for [1,2) than for
>>>> [1,2] or (1,2) (since the number of members in the range is even).
>>> So what would you recommend? [a, b) for floats and [a, b] for ints, or [a,
>>> b) for everything?
>>>
>>> Andrei
>> I'm leaning towards [a,b) for everything (consistency with arrays), but I'd
>> want to know what the reasoning of the boost/c++0x guys was.
> 
> How do you create a random uint that can take on any of uint's values
> with [a,b)?  That's the main reason I can think of to go with [a,b]
> for integral types.  With floats it's never useful to use the entire
> value range.
> 
> --bb

I think that is the primary argument. BUT:
* You _can_ still use "[]" in that case.
* I also think it'd be worth having a "create a random n-byte number", 
as well, which would be the main use for a full uint random number.
* If you're creating a number in the range 0..uint.max+1, you're going 
to have to be careful in lots of places. You can't get that number from 
an array length, for example.
* I think that hard-core scientific/mathematical users are the main 
users of the more esoteric cases, and can be expected to get it right 
(and have no problem with the "[]","()","(]"... notation. I think that 
what's important for the default is that be correct and obvious for as 
many cases as possible.

The strength of "[)" is that if we can say "ALL ranges in D are [) 
unless otherwise stated by the user", it's hard to ever justify breaking 
that convention.