Re: [musl] Re: cacosh.c - Comment needs correction

[Szabolcs Nagy <nsz@port70.net>]

* Damian McGuckin <damianm@esi.com.au> [2024-03-08 15:44:32 +1100]:

> On Fri, 8 Mar 2024, Damian McGuckin wrote:
> 
> > 
> > The routine produces the correct answer.
> > 
> > However, currently, the comment at the top says
> > 
> > 	/* acosh(z) = i acos(z) */
> > 
> > I believe this is technically wrong;
> > 
> > To reflect the code, it should be changed to something like:
> > 
> > 	/* cacosh(z) = acosh(x +/- i y) = +/- i acos(x + i y) */
> 
> Sorry (fat fingers or worse):
> 
>  	/* cacosh(z) = acosh(x +/- i y) = +/- i acos(x +/- i y) */
> 

according to section 6.2 of

https://cs.uwaterloo.ca/~smwatt/pub/reprints/2000-sigsam-according.pdf

  acosh(z) = +-i acos(z)

with + when Im(z)>0 or Im(z)==0 && Re(z)<=1

i guess the Im(z)==+0 && Re(z)>1 case is tricky with ieee -0.0 as it
depends on if sqrt(-z) is i or -i for z=1, which depends on if pure
reals are treated specially sqrt(-1)==i or as sqrt(-1-0i)==-i, in the
latter case the current code looks right to me, just the comment wrong.


> Thanks - Damian
> 
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