Re: efficient vector/matrix operations in Ada

[tmoran@acm.org]

>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.

>    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. ;)