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Date:      Sun, 12 Aug 2012 22:57:45 -0000
From:      Steve Kargl <sgk@troutmask.apl.washington.edu>
To:        Peter Jeremy <peter@rulingia.com>
Cc:        Diane Bruce <db@db.net>, John Baldwin <jhb@freebsd.org>, David Chisnall <theraven@freebsd.org>, Stephen Montgomery-Smith <stephen@missouri.edu>, Bruce Evans <bde@freebsd.org>, Bruce Evans <brde@optusnet.com.au>, David Schultz <das@freebsd.org>, Warner Losh <imp@bsdimp.com>
Subject:   Re: Use of C99 extra long double math functions after r236148
Message-ID:  <20120717232740.GA95026@troutmask.apl.washington.edu>
Resent-Message-ID: <20120812225738.GH20453@server.rulingia.com>
In-Reply-To: <20120717225328.GA86902@server.rulingia.com>
References:  <C527B388-3537-406F-BA6D-2FA45B9EAA3B@FreeBSD.org> <20120713155805.GC81965@zim.MIT.EDU> <20120714120432.GA70706@server.rulingia.com> <20120717084457.U3890@besplex.bde.org> <5004A5C7.1040405@missouri.edu> <5004DEA9.1050001@missouri.edu> <20120717040118.GA86840@troutmask.apl.washington.edu> <20120717042125.GF66913@server.rulingia.com> <20120717043848.GB87001@troutmask.apl.washington.edu> <20120717225328.GA86902@server.rulingia.com>

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On Wed, Jul 18, 2012 at 08:53:28AM +1000, Peter Jeremy wrote:
> On 2012-Jul-16 21:38:48 -0700, Steve Kargl <sgk@troutmask.apl.washington.edu> wrote:
> >On Tue, Jul 17, 2012 at 02:21:25PM +1000, Peter Jeremy wrote:
> >> Again, handling the special cases listed in G.6 is all just
> >> boilerplate code that we can take as assumed for pseudocode.  IMO, it
> >
> >As someone who spent 10+ years getting sqrtl(), cbrtl(), ccosh(), sinl(),
> >cosl(), tanl(), etc into FreeBSD, I respectfully disagree with your
> >take that it is just boilerplate.  Getting this stuff right is much harder
> >than I think some people understand.  Oh well, I'll back to lurking and
> >working on things I need.
> 
> OK.  I'll admit that I haven't tried this before but attached is my
> first try at catan[h]().  It should cover all the special casing
> according to WG14/N1256 and compiles if you add the relevant
> declarations to complex.h.  I'd appreciate feedback.
> 
> Notes on it:
> - The actual code at the end of catanh() is just one possible
>   algorithm.  It's not intended as final code and the final code is
>   likely to need additional special case handling to minimise
>   precision loss and prevent unwanted exceptions.
> - cpack(-cimag(r), -creal(r)) gives better code than
>   -cpack(cimag(r), creal(r)) on i386 and identical code on amd64.
> - The fpclassify() macros are bitmasks on FreeBSD.  Assuming this
>   would allow (ci == FP_ZERO || ci == FP_NAN) to be simplified but the
>   standard only requires that they have distinct values and (eg)
>   Solaris implements them as a series so the current code is more
>   portable.
> 

I won't have time to go over the code in detail until
this weekend, but a quick peek showed some issues.  The
first is style.  Although fdlibm has a rather interest
coding style, new code should use KNF.

/*
 * Calculate complex arc tangent using the identity:
 * catan(z) = -i catanh(iz)
 */
double complex
catan(double complex z)
{
	complex double r;
  
	r = catanh(cpack(cimag(z), creal(z)));

I think you're missing a sign.  Let z = x + i*y.
Then, i*z = i*x+i*i*y = -y + i*x, yielding

	r = catanh(cpack(-cimag(z), creal(z)));
	return (cpack(-cimag(r), -creal(r)));

Again, it seems a sign error has occurred.
Let catanh(i*z) = u + i*v.  Then, you have
-i*catanh(i*z) = -i*u-i*i*v = v-i*u, yielding

	return (cpack(cimag(r), -creal(r)));
}

Of coure, I could be wrong.

-- 
Steve



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