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From: da Silva, Joe
Subject: Complex_SqRt bug
Date: 14 Jan 2002, 09:58:19

Well, I haven't seen the computations, but if you are happy that
they are "sound" and that they will be more accurate than the
existing algorithm, then I agree that you should use them.

The advantage of the Clipped_SqRt solution was simplicity and
clarity (and certainty;-). However, it does not change the accuracy.

Joe.

> -----Original Message-----
> From:	Frank Heckenbach [SMTP:frank@g-n-u.de]
> Sent:	Friday, January 11, 2002 12:43 PM
> To:	gpc@gnu.de
> Subject:	Re: Complex_SqRt bug
> 
> da Silva, Joe wrote:
> 
> > OK, if you're happy that the code is correct ... I guess I just don't
> > understand what the "a := Abs(Im(z)) / (2 * b)" statement does ...
> 
> I could write down the computations if you like (unless Emil has
> them readily available already) ...
> 
> > Anyway, although you might say the Clipped_SqRt solution is a
> > kludge, it is certainly not second-guessing. It would only be applied
> > where the minimum theoretical argument was zero, in which case
> > it would avoid (and eliminate) rounding errors which produced a
> > slightly negative "zero".
> 
> As I said, I'm no expert on numeric algorithms, but I think if an
> algorithm can produce such wrong results, it might also be
> inaccurate for other values and should be improved (such as
> Complex_Sqrt). After all, normal rounding doesn't easily make a
> positive value (even very close to 0) negative. So it might be
> better if the programmer sees the problem clearly with an error
> message. If it really turns out that an algorithm is as good as
> possible (numerically) and still prone to this kind of problem,
> something like Clipped_SqRt might be in order. But I guess this is
> rather an exceptional situation, so Clipped_SqRt does not seem a
> good candidate for a general library routine.
> 
> But perhaps Emil can comment better on these matters ...
> 
> Frank
> 
> -- 
> Frank Heckenbach, frank@g-n-u.de, http://fjf.gnu.de/, 7977168E
> GPC To-Do list, latest features, fixed bugs:
> http://agnes.dida.physik.uni-essen.de/~gnu-pascal/todo.html

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