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From: Warren <ve3wwg@gmail.com>
Newsgroups: comp.lang.ada
Subject: Re: Inferring array index type from array object
Date: Tue, 29 Jun 2010 21:00:01 +0000 (UTC)
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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:

gsl_complex
gsl_complex_div (gsl_complex a, gsl_complex b)
{                               /* z=a/b */
  double ar = GSL_REAL (a), ai = GSL_IMAG (a);
  double br = GSL_REAL (b), bi = GSL_IMAG (b);
   
  double s = 1.0 / gsl_complex_abs (b);

  double sbr = s * br;
  double sbi = s * bi;
 
  double zr = (ar * sbr + ai * sbi) * s;
  double zi = (ai * sbr - ar * sbi) * s;

  gsl_complex z;
  GSL_SET_COMPLEX (&z, zr, zi);
  return z;
}

Given a=1.0, the inverse function is definitely
higher performance.  It's simpler calculation 
probably implies more accuracy as well.

Warren