Re: efficient vector/matrix operations in Ada

["Russ P." <18k11tm001@sneakemail.com>]

tmoran@acm.org wrote:
> 
> >tacky, ambiguous expressions like
> >   PlusEquals(A,B);
> but is
>     Inc(A, B);
> so bad or non-obvious?  Fortran programmers, no slouch at fast matrix
> operations, seem to have figured out a satisfactory approach.  If you
> are really pressed for speed, you are going to be calling an optimized
> library anyway.

I'm not looking for high-level optimization, I'm just looking for
something that is reasonably efficient.

> 
> >    A = A + B; // inefficient
> >
> >is much less efficient than
> >
> >    A += B; // efficient
> >
> >The former requires the dynamic construction of a temporary matrix to
> >hold the sum (A + B), which must then be passed by value and copied into
> >A.
>   Is A = A+B, an O(n**2) operation, going to be limiting the speed of
> your matrix arithmetic, which probably involves some O(n**3) operations
> if it does anything substantial?
>   Just because one way of doing it is slow doesn't mean there isn't a
> fast way.  For instance why does a temporary need to be dynamic?
> Register oriented CPUs don't dynamically create a new register
> every time they need one.  One could easily imagine a machine with
> vector instructions that can do A+B->C very fast, but has no special
> instruction for A+B->A.  In the case of a temporary matrix, of
> course, "dynamic construction" could mean something as simple as
> "move the stack pointer".  Or your aithmetic operations could create
> expressions, moving just pointers and op-codes, and the assignment
> operator could analyze the expression and decide the fastest way
> to actually calculate the result.  Think outside of the box. ;)

No, you really need the dynamically instantiated temporary matrix, I
believe. I've been through this little lesson years ago. Don't forget
that you also need to be able to handle expressions such as "A = B + C +
D;". You can play complicated games with static arrays of "work"
matrices, but you are asking for trouble and the resulting code is
likely to not be re-entrant.

-- 
Russ P.
http://RussP.org