Re: Math Libraries (was Re: Ada2005)

[FGD <presbeis@look.ca>]

I'm not completely for extending Ada to include new math types. As I 
stressed earlier such extensions would generally be useless for most 
people. The only possible exception I can see is linear algebra...

Marin David Condic wrote:

> "FGD" <presbeis@look.ca> wrote in message news:3C236F94.7020101@look.ca...
> 
>>I agree that linear algebra types such as vector and matrix would be a
>>nice language extension. These would benefit the most from hardware
>>
> 
> I don't know that it needs to be a language extension. That starts asking
> for something that is harder to do than simply providing a package and I
> don't see an enormous amount of utility to it. Most Ada programmers would
> probably easily comprehend and work with a package that defined "+" and so
> on for a vector or matrix type so I think you could get the features (albeit
> maybe not quite as cleanly) without forcing the compiler writers to make the
> language itself more complex.


The reason why I mentionned it as a language extension is that the 
"matrix type" is simply not efficient when represented as an array of 
coefficients. Having a language defined matrix type acting on vector 
types leaved the compiler writers free to use whatever internal 
representation they like.

>>extensions such as SIMD, and having them within the language would
>>ensure that all target machines are exploited to their full potential.
>>
>>
> Obviously, it would be advantageous for a compiler writer to take advantage
> of any underlying hardware rather than rely strictly on Ada syntax to
> implement the type. The nice thing about implementing it as a package is
> that the body could be implementation dependent, but the spec could be
> portable. If you've got the hardware, implement it in assembler.


Of course, that's what we currently do---in Ada and all other 
general-purpose languages. But one of the main advantages of Ada is low 
maintenace cost. I, for one, write and maintain a lot of such packages 
but almost all of my maintenance work goes into code that looks like:

    procedure Whatever ...
    begin
        case Machine is
        when Alpha_EV4 =>
             Asm(....
        when X86_Pentium_3 =>
             Asm(....
        when others =>
             ....
        end case;
    end Whatever;

For example, when Intel released the Pentum 4, I spent weeks rewrite and 
test asm code for relatively basic little things. I still have months to 
go writing and testing new code for the Itanium chip... and then the 
AMD-64... Sigh! :-(

For such code, Ada doesn't present any more advantages than any other 
language. Of course, that only leaves the burden of asm maintenance to 
compiler writers. Still having a few non-elementary types such as matrix 
and vector would make my life a lot simpler sometimes.

>>I'm not too sure about stats. Basic stats can be handled with linear
>>algebra and elementary math. The problem is that it's not clear where to
>>stop. It's something to think about...
>>
>>
> I'm thinking that some packages to get you things like mean, variance,
> standard deviation, etc., from arrays of various numeric types would be
> enough - for now. :-) (I've got some packages that do this already - it
> really isn't that hard to implement.) Sure, you could imagine all kinds of
> wonerful sophistication that one might get from a true statistical package,
> but why push our luck? Settle for some nice, basic statistics that let
> people throw some analysis into their run-of-the-mill apps rather than shoot
> for something that would satisfy the full-blown statisticians. It would
> still be ahead of most other languages I'm aware of and wouldn't require
> some major revision to the language syntax or semantics.


There are already lots of stuff out there to satisfy "full-blown" 
statisticians and mathematicians. Ada has no business there. We should 
focus on stuff that is useful to a great deal of people. As far as I can 
tell, linear algebra with all of its applications is the only branch of 
math which is useful to a great deal of people. BTW mean, variance and 
standard deviation are all linear algebra except maybe for a few square 
roots here and there.

-- Frank