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From: "John B. Matthews" <nospam@nospam.invalid>
Newsgroups: comp.lang.ada
Subject: Re: Inferring array index type from array object
Date: Tue, 29 Jun 2010 17:47:58 -0400
Organization: The Wasteland
Message-ID: <nospam-807C34.17475829062010@news.aioe.org>
References: 
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 <Xns9DA07FC9F98B5WarrensBlatherings@81.169.183.62>
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 <Xns9DA563139F62CWarrensBlatherings@85.214.73.210>
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 <Xns9DA683A562C67WarrensBlatherings@81.169.183.62>
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Date: 2010-06-29T17:47:58-04:00
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In article <Xns9DA6ACEFDCF8BWarrensBlatherings@81.169.183.62>,
 Warren <ve3wwg@gmail.com> wrote:

> Warren expounded in news:Xns9DA6AC2A2C8BWarrensBlatherings@81.169.183.62:
> 
> > Adam Beneschan expounded in news:73a0af1d-7213-44af-90fa-ed6de4c64ce8
> > @b4g2000pra.googlegroups.com:
> > 
> >> On Jun 29, 12:31 pm, Warren <ve3...@gmail.com> wrote:
> >>>
> >>> > So, what is the "missing" function?
> >>>
> >>> > <http://www.adaic.com/standards/05rm/html/RM-G-1-2.html>
> >>>
> >>> 1) The "inverse" of a complex number.
> >> 
> >> Isn't that just 1.0 / X?  
> > 
> > Ok, it seems to be, as the GSL (Gnu Scientific Library)
> > defines it as:
> > 
> > gsl_complex
> > gsl_complex_inverse (gsl_complex a)
> > {                               /* z=1/a */
> >   double s = 1.0 / gsl_complex_abs (a);
> > 
> >   gsl_complex z;
> >   GSL_SET_COMPLEX (
> >     &z, (GSL_REAL (a) * s) * s, -(GSL_IMAG (a) * s) * s);
> >   return z;
> > }
> 
> Apologies for following up my own post, but
> looking at the GSL implementation of complex 
> division:
> [...]
> Given a=1.0, the inverse function is definitely
> higher performance.  It's simpler calculation 
> probably implies more accuracy as well.

The more comparable Ada implementation (from GNAT) would be

function "/" (Left : Real'Base; Right : Complex) return Complex is
    a : constant R := Left;
    c : constant R := Right.Re;
    d : constant R := Right.Im;
begin
    return Complex'(Re =>   (a * c) / (c ** 2 + d ** 2),
                    Im => -((a * d) / (c ** 2 + d ** 2)));
end "/";

-- 
John B. Matthews
trashgod at gmail dot com
<http://sites.google.com/site/drjohnbmatthews>