default random object?

[Bill Baxter]

On Mon, Feb 16, 2009 at 3:33 AM, Don <nospam at nospam.com> wrote:
> 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.

I guess I'd find it more useful to have a function that gave a random
value of a given type, like random_value!(short).  That way you get
the signed/unsigned specification automatically.  But both could be
useful.

> * 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.

That sounds reasonable to me.  As long as there's an easy way to also
create a random number that covers an entire range of a given type
(perhaps limited to integral types).

--bb