complex.h math functions

[Steve Kargl]

On Wed, Oct 12, 2005 at 05:23:28PM +1000, Bruce Evans wrote:
> On Mon, 10 Oct 2005, Steve Kargl wrote:
> 
> >I've attached the latest version.  Hopefully, I caught the
> >rest of the style(9) problems.  The cosh.3 man page has been
> 
> No :-).

Hopefully, this new version is closer to KNF.

> >updated.  I did not hook s_ccosh.c up to the Makefile
> >because I wasn't sure were to put it in msun/src.  If you have
> >no further comments, can you commit this version (or your
> >simplified version)?  I'll look at the other trigometric and
> >hyperbolic functions when we converge on s_ccosh.c.
> 
> use it.  Listing all the special cases also serves as documentation.
> I think the current order of special cases is not quite the best,
> however.

I don't follow why you think the special cases need to be re-order.
Without knowing how the user base will abuse ccosh, there should
be no prefered order.

> Patch relative to your last version:

This version incorporates your changes, fixes
a few more whitespace problems, and expands the
comments on the exceptional cases.

> % diff -ruN /usr/src/lib/msun/man/cosh.3 freebsd/src/lib/msun/man/cosh.3
> % --- /usr/src/lib/msun/man/cosh.3	Fri Jan 14 15:28:28 2005
> % +++ freebsd/src/lib/msun/man/cosh.3	Sat Oct  8 11:46:29 2005
> % ...
> 
> OK; could be more detailed.

Do you want a section that describes the range of inputs that
return a non-infinite results?  Do you want a section that
describes the return value and the exceptional cases?  I'll
have to do this later because I'll need to learning some
additional mdoc features.

> Still has lots of strange indents -- corrupt tab above, 4-chars only for
> most second indents.

I'm not sure how these crept into the last version.  I re-indented
the file, so hopefully this is fixed.

> % +	 *  cosh(x + I Inf) = NaN + I NaN, finite x != 0, invalid exception.
> % +	 *  cosh(x + I NaN) = NaN + I NaN, finite x != 0, opt. inval. except.
> % +	 */
> 
> Not quite enough space to describe it all on 1 line; the inputs and outputs
> get mixed cryptically; might use more formal abbreviations.

I've expanded all comments to essentially the language in n1124.pdf.

> % +	 *  cosh(+Inf + I y)   = +Inf [cos(y) + I sin(y)], y != 0 and finite.
> 
> Still have the strange brackets here.

It's a mathematical expression; not a KNF-ized C language construct.
However, I changed the comment to n1124.pdf's use of cis(y) and then
define cis(y) = cos(y) + I sin(y). 

> % +float complex
> % +ccoshf(float complex z)
> % +{
> % +	return ((float complex) ccosh((double complex) z));
> % +}
> 
> I prefer to use implicit conversions.

I've updated this also.  Note, the forward declaration of
ccosh() is not needed because complex.h should contain a
prototype for it.

> % diff -ruN /usr/src/lib/msun/src/math_private.h 
> freebsd/src/lib/msun/src/math_private.h
> % --- /usr/src/lib/msun/src/math_private.h	Fri Feb  4 12:05:39 2005
> % +++ freebsd/src/lib/msun/src/math_private.h	Fri Oct  7 17:30:40 2005
> % @@ -155,6 +155,36 @@
> %  } while (0)
> % 
> 
> I needed a namespace hack to make this compile.  Clients that don't use
> this shouldn't need to include <complex.h>, and this file shouldn't
> include it.  I used "#ifdef I".

A single letter #ifdef makes me nervous, and it isn't very descriptive.
I would suggest using #ifdef _COMPLEX_H.  OTOH, math_private.h isn't
an installed header file, so only the person or persons writing the
complex math functions need to be bothered by this.

> I think the underscores shouldn't be used here (not even for __inline).
> This is not a public interface so we don't need to be very careful with
> the namespace.

I removed the underscores in my local tree.  There, of course, were no problems.

> Otherwise good.  These interfaces seem to work well.

You did not provide a patch to your local math_private.h.

> Here is my current "simpler" version.  I plan to merge it into the
> other version when the other version's indentationis fixed.

See the new version.

BTW, the exceptional cases for ccos(z) are defined in n1124.pdf
in terms of ccos(z) = ccosh(I z).  We can do

double complex
ccos(double complex z)
{
   return (ccosh(-cimag(z),creal(z));
}

or if you prefer we can copy s_ccosh.c and change

   x = creal(z);
   y = cimag(z);
to
   x = -cimag(z);
   y = creal(x); 

-- 
Steve