Extending arithmetic

[Thomas Lindgren]

--- Peter-Henry Mander
<erlang@REDACTED> wrote:
> 
>  From what I've been hearing on this discussion, I
> don't think tuples 
> are the proper vehicle for multidimentional math,
> they're just too abstract.
> 
> Why not introduce new *numeric* types instead of
> contriving tuples to 
> act like numbers? Then there will be less scope for
> surprises and 
> exceptions occuring. 

That sounds good to me. (Not that I'm sure building in
matrices is worth the effort ...) Besides the nicer
semantics, you can also have a far more efficient
representation: a flat (aligned) memory region holding
double-precision floats, rather than tuples pointing
to tuples (rows or columns?) pointing to boxed
doubles.

Making operations on matrices efficient (= avoiding
copying the matrix when you update an element)
requires one of:

- an APL- or FP-like sublanguage that builds the final
matrix in one operation, or

- fast-update vectors (as were discarded from erts in
a more general incarnation for various technical
reasons), or

- losing referential transparency (huge mistake)

- ... or perhaps something else?

Those who want to clean up Erlang numerically might
also take a look at how Common Lisp does things (for
scalars, principally). That's the best proposal I'm
aware of. (Though numeric computing isn't my day job
by any means.)

Best,
Thomas


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