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Date: Tue, 29 Jun 2010 23:52:07 +0200
From: Damien Carbonne <damien.carbonne@free.fr>
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Subject: Re: Inferring array index type from array object
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Date: 2010-06-29T23:52:13+02:00
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Le 29/06/2010 23:00, Warren a �crit :
> Warren expounded in news:Xns9DA6AC2A2C8BWarrensBlatherings@81.169.183.62:
>>>>
>>>> 1) The "inverse" of a complex number.
>>>
>>> Isn't that just 1.0 / X?
>>
<snip>
>
> Given a=1.0, the inverse function is definitely
> higher performance.  It's simpler calculation
> probably implies more accuracy as well.
>
> Warren

Ada has several overloaded versions of "/".
GNAT seems to implement "/" (Real, Complex) using a simplified version 
of "/" (Complex, Complex).
It looks (almost) like the example you gave.

    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 "/";

There are differences that may have an impact on speed.
But the above version is simpler than this one:

    function "/" (Left, Right : Complex) return Complex is
       a : constant R := Left.Re;
       b : constant R := Left.Im;
       c : constant R := Right.Re;
       d : constant R := Right.Im;

    begin
       if c = 0.0 and then d = 0.0 then
          raise Constraint_Error;
       else
          return Complex'(Re => ((a * c) + (b * d)) / (c ** 2 + d ** 2),
                          Im => ((b * c) - (a * d)) / (c ** 2 + d ** 2));
       end if;
    end "/";

Damien