Re: [Caml-list] Complex stuff

[Xavier Leroy <xavier.leroy@inria.fr>]

> I know that the Ocaml team might be implementing complex numbers in 
> Ocaml.

I've just completed a first implementation.  You can see what it looks
like from our anonymous CVS repository camlcvs.inria.fr.

> However, I need complex support now and I was wondering what the best 
> way to proceed would be, if I want to port the code over to the native 
> complex support as and when it becomes available?
> 
> I need the basic arithmetic and trignometric operations and bigarray 
> (complex32, complex64 and fortran layout) support.

Done in the working sources.

> I could borrow the basic arithmetic and trignometric stuff from Psilab 
> or even Clean libraries. Should I represent complex numbers as tuples or 
> record (tuples I guess, since that is what Psilab does)?

I chose to use a record type {re:float; im:float} because this leads
to a more efficient memory layout than a pair of float.

> What about the bigarray support? The basic stuff I can roll on my own, 
> unless somebody else has already done it and can provide me with code. 
> How about the bracket notation? Do I need to use camlp4 to get a.{i,j} 
> to return a complex number and a.{i,j} <- to store a complex number in 
> (i,j)th position (etc..)?

The a.{i,j} notation is supported for complex types.

By the way, if there are numerically competent folks on this list,
please have a look at
     http://camlcvs.inria.fr/cgi-bin/cvsweb.cgi/ocaml/stdlib/complex.ml
and let me know if the implementation of complex arithmetic is (1)
mathematically correct, and (2) numerically reasonable.  I tried to
guard against overflows and underflows in intermediate results, but
could use some help here.  Please reply to me directly -- no need to
split machine epsilons and count ulp's on this list.

- Xavier Leroy
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