Re: catan errors

[Rich Felker <dalias@libc.org>]

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On Wed, Apr 11, 2018 at 01:08:50AM +0200, Szabolcs Nagy wrote:
> * Rich Felker <dalias@libc.org> [2018-04-10 15:50:07 -0400]:
> > 
> > 3. Is only possible if y==1.0 and x==0.0, which is the only real
> >    exceptional case for atan: z==I.
> > 
> > I opted to replace the non-obvious (3) with an explicit check for z==I
> > but this isn't necessary.
> > 
> ....
> >  	t = y - 1.0;
> >  	a = x2 + (t * t);
> > -	if (a == 0.0)
> > -		goto ovrf;
> 
> why does a==0 imply x==0?

OK, at least by my reasoning it's only algebraically true not
necessarily as doubles.

> if |x| < sqrt(2)*0x1p-538, x2 underflows to 0 in nearest rounding mode.
> 
> to handle this correctly extra work would need to be done, so i think
> either way is fine (leaving the goto there or not are both wrong, but
> we dont guarantee correct complex functions yet)

I'm fine with just moving the check back here. But the special case
(maybe not near-special cases with internal over/underflow though)
works fine just replacing the *I with CMPLX. See attached.

Rich

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diff --git a/src/complex/catan.c b/src/complex/catan.c
index 39ce6cf..7dc2afe 100644
--- a/src/complex/catan.c
+++ b/src/complex/catan.c
@@ -91,29 +91,17 @@ double complex catan(double complex z)
 	x = creal(z);
 	y = cimag(z);
 
-	if (x == 0.0 && y > 1.0)
-		goto ovrf;
-
 	x2 = x * x;
 	a = 1.0 - x2 - (y * y);
-	if (a == 0.0)
-		goto ovrf;
 
 	t = 0.5 * atan2(2.0 * x, a);
 	w = _redupi(t);
 
 	t = y - 1.0;
 	a = x2 + (t * t);
-	if (a == 0.0)
-		goto ovrf;
 
 	t = y + 1.0;
 	a = (x2 + t * t)/a;
-	w = w + (0.25 * log(a)) * I;
-	return w;
-
-ovrf:
-	// FIXME
-	w = MAXNUM + MAXNUM * I;
+	w = CMPLX(w, 0.25 * log(a));
 	return w;
 }