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From: robert_dewar@my-dejanews.com
Subject: Re: Calculating SQRT in ADA
Date: 1999/03/25
Message-ID: <7dbv6t$4u5$1@nnrp1.dejanews.com>#1/1
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 <19990324125518.01416.00000432@ngol08.aol.com>
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Date: 1999-03-25T00:00:00+00:00
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In article <19990324125518.01416.00000432@ngol08.aol.com>,
  johnherro@aol.com (John Herro) wrote:
> Here's a generic square root routine in Ada 83, taken
from my AdaTutor program:
>
> generic
>   type Dummy is digits <>;
> function Sqrt(X :in Dummy) return Dummy;
> function Sqrt(X :in Dummy) return Dummy is
>   Guess : Dummy := X;
> begin
>   if X < 0.0 then
>     raise Constraint_Error;
>   end if;
>   while X /= 0.0 and then
>        abs(Guess*Guess/X - 1.0) > 3.0*Dummy'Epsilon loop
>     Guess := (X/Guess + Guess) * 0.5;
>   end loop;
>   return Guess;
> end Sqrt;

Why the epsilon test, this iteration will terminate to
exact equality in any reasonable floating-point model,
and you cannot guarantee the 3*epsilon convergence if
the floating-point model is silly anyway.

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