Doing complex math in C

[Bennett E. Todd III]

In net.math someone asked how you go about clobbering a cubic. Turns out
there is a nice closed-form solution. So I looked it up and wrote a
trivial little program to solve the cubic. I like C, so I wrote it in C.
C doesn't have a complex data type, and doesn't seem inclined to
encourage me to write a support library -- in particular, without
operator overloading the resulting syntax is vaguely reminiscent of
publication LISP syntax, and makes for excessively verbose expressions.
Oh well said I, that can be lived with.

Turns out I dislike structure passing and return, and think it shouldn't
have been added to the language in the first place. (I consider structs
to be aggragates just like arrays; references to the name of a struct
should be resolved into pointers to that struct). So I didn't use struct
passing and return. My complex library routines take as arguments one or
more pointers to complex structs, and return a pointer to a complex
struct containing the result. Unfortunately, something like

	C_plus(Complex(1.0, 0.0), Complex(0.0, 1.0))

	(Complex() returns a pointer to a struct initialized to the values
	specified, C_plus() returns a pointer to a struct containing the sum
	of the two structs passed in.)

will drop the two intermediate structs containing the two "constants" on
the floor -- they will not be pointed to by anything. Rather than
implement a garbage collector, or force all computations to go through
temporary variables which can then be freed, I decided to make all the
complex routines free any complex args they are passed. Thus if you want
to pass a program variable to a complex routine, you must make a copy --
the utility routine C_copy() returns a copy of its arg (which it doesn't
free).

Well, the end result is that there is a hefty amount of overhead, though
not intolerable for light work, and largely optimizable by a
sufficiently good compiler. The code ends up being reasonably clear,
except for the sort-of-prefix functional notation for expressions.
The semantics of these routines is as far as I know unique. Comments?

The program (and the complex support library I created) can be found in
net.sources.

-Bennett
-- 

"Hypocrisy is the vaseline of social intercourse." (Who said that?)

Bennett Todd -- Duke Computation Center, Durham, NC 27706-7756; (919) 684-3695
UUCP: ...{decvax,seismo,philabs,ihnp4,akgua}!mcnc!ecsvax!duccpc!bet