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Date: Fri, 14 Sep 2012 02:41:14 +1000 (EST)
From: Bruce Evans <brde@optusnet.com.au>
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Cc: freebsd-numerics@FreeBSD.org
Subject: Re: Complex arg-trig functions
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On Thu, 13 Sep 2012, Stephen Montgomery-Smith wrote:

> On 09/13/2012 07:55 AM, Bruce Evans wrote:
>
>> % -        /* casinh(NaN + I*inf) = inf + I*NaN */
>> % +        /* casinh(NaN + I*+-Inf) = +-Inf + I*NaN (sign optional) */
>
> How much do you want the "sign optional" put into the comments.  This will 
> have to be done in lots of places.

Eventually, always, but I'd like to have a convention to keep the comment
short.  Possible conventions:
- use inf for the simple case where signs interact unsurprisingly.  inf
   for an input operand combined with inf for an output operand means that
   the input operand is copied unchanged; add '-' to the output operand
   to indicate a sign change.
- use +-Inf particular signs and/or surprising sign rules
- combinations with 2 input infinities probably need to spell them as
   inf1 and inf2 or +-Inf1 and +-Inf2 so as to express combinations of
   them in output
- write options using something like opt(<option taken>) where the
   presense of opt() indicates that an option exists.

In casinh() this gives:

My previous version:
 		/* casinh(+-Inf + I*NaN) = +-Inf + I*NaN */
 		/* casinh(NaN + I*+-Inf) = +-Inf + I*NaN (sign optional) */
With the above, and also with (null) NaN annotation:
 		/* casinh(inf + I*NaN) = inf + I*NaN */
 		/* casinh(NaN + I*inf) = opt(inf) + I*NaN */

Here inf ... = ... opt(inf) says that:
- the input infinity can be +-Inf
- the ouptut infinity can by optionally either +Inf or -Inf
- but we choose to make it the same inf as the input infinity.

I first wrote the NaN annotation as d(NaN) but then saw that a convention
works for NaNs too -- the usual case where a single NaN is replaced by
the default conversion of the same NaN doesn't need special description.
We try not to change the signs for NaNs, but when we change them
intentionally, this needs special description.  It is always an option
to clobber the sign or other bits of NaNs, so the opt() markup is
not needed for NaNs to document that there is an option, but it could be
used to indicate that we make a choice.

Bruce