Small Vectors Proposal

[Bill Baxter]

Don Clugston wrote:
> Mikola Lysenko wrote:
>> Benji Smith wrote:
>>> Right now, I'm working on a statistical prediction algorithm that 
>>> uses *sparse* 300,000-dimensional feature vectors. There's no reason 
>>> to limit SSE optimizations to small-dimensionality vectors.
>>>
>>
>> I can understand your desire to create a universal solution, and for a 
>> long time I too was convinced this was the way to go.  However I have 
>> come to understand that there are many practical differences between 
>> low and high dimension vectors.  Think about it this way: would you 
>> try to use a sparse matrix/vector library for doing operations on 4-d 
>> vectors and matrices?  It should be clear that these are two different 
>> very different types of problems.
> 
> I completely agree. For large vectors and matrices, you're going to have 
> to use a loop, and the loop startup costs are amortised; you can use the 
> same BLAS code for a 3159 element vector as for a 3158 element one, and 
> it makes negligible difference to the speed. But for 3 and 4 element 
> vectors it makes an enormous difference.
> 
> And the applications are completely different. I imagine games 
> programmers don't use much above 4x4 matrices.

I'd say that's not necessarily true with games using more and more 
realistic physics, and even with run of the mill skeletal animation 
techniques.  But in those cases you're talking arbitrary N-vectors, so 
in any event the most common dimensions for data are:
     2 (screen/texture space),
     3 (3D world space, homogeneous 2D space, color space),
     4 (homogeneous 3D world space),
and N (physics and everything else).

--bb