From mboxrd@z Thu Jan  1 00:00:00 1970
X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on polar.synack.me
X-Spam-Level: 
X-Spam-Status: No, score=-1.9 required=5.0 tests=BAYES_00 autolearn=ham
	autolearn_force=no version=3.4.4
X-Google-Thread: 103376,b2993a94987e380e
X-Google-Attributes: gid103376,domainid0,public,usenet
X-Google-Language: ENGLISH,ASCII-7-bit
Path: 
 g2news1.google.com!news3.google.com!news4.google.com!out03a.usenetserver.com!news.usenetserver.com!in01.usenetserver.com!news.usenetserver.com!in03.usenetserver.com!news.usenetserver.com!pc02.usenetserver.com!news.flashnewsgroups.com-b7.4zTQh5tI3A!not-for-mail
Newsgroups: comp.lang.ada
Subject: Re: Epsilon
References: <CRYVj.2543$ah4.2038@flpi148.ffdc.sbc.com>
From: Stephen Leake <Stephe.Leake@nasa.gov>
Date: Tue, 13 May 2008 07:42:35 -0400
Message-ID: <umymuph04.fsf@nasa.gov>
User-Agent: Gnus/5.1008 (Gnus v5.10.8) Emacs/22.1 (windows-nt)
Cancel-Lock: sha1:oZSkCs6nAZ07BUXepN+BmgR1U0k=
MIME-Version: 1.0
Content-Type: text/plain; charset=us-ascii
X-Complaints-To: abuse@flashnewsgroups.com
Organization: FlashNewsgroups.com
X-Trace: e54b748297a38e05e48ed10922
Xref: g2news1.google.com comp.lang.ada:54
Date: 2008-05-13T07:42:35-04:00
List-Id: <comp.lang.ada>

<adaworks@sbcglobal.net> writes:

> I am looking for some short, practical examples of the Epsilon
> attribute.  If you do have some source code examples to post,
> please also send them to my academic email:  rdriehle@nps.edu

   --  These values guarantee Integer_16 (value) or Unsigned_16
   --  (value) won't raise Constraint_Error, and allow for maximum
   --  round-off error. Useful with Clip_Scale_Limit when result will
   --  be converted to Integer_16 or Unsigned_16.
   Integer_16_First_Real : constant Real_Type := Real_Type (Interfaces.Integer_16'First) - 0.5 +
     (Real_Type'Epsilon * Real_Type (Interfaces.Integer_16'Last));

   Integer_16_Last_Real  : constant Real_Type := Real_Type (Interfaces.Integer_16'Last) + 0.5 -
     (Real_Type'Epsilon * Real_Type (Interfaces.Integer_16'Last));

   Unsigned_16_First_Real : constant Real_Type := -0.5 + Real_Type'Epsilon;
   Unsigned_16_Last_Real  : constant Real_Type := Real_Type (Interfaces.Unsigned_16'Last) + 0.5 -
     (Real_Type'Epsilon * Real_Type (Interfaces.Unsigned_16'Last));


   function First_Order_Trig return Real_Type
   is begin
      return Elementary.Sqrt (Real_Type'Model_Epsilon);
   end First_Order_Trig;

   function Half_Trig (Trig : in Trig_Pair_Type) return Trig_Pair_Type
   is
      --  The result Trig.Cos is >= 0.0.
      --
      --  A linear approximation is used when Trig.Sin <
      --  First_Order_Trig. this is exact since cos x = 1 - x**2 for
      --  this range of x.
   begin
      if abs Trig.Sin < First_Order_Trig then
         --  angle near 0 or Pi.
         if Trig.Cos > 0.0 then
            --  angle near 0
            return (Trig.Sin / 2.0, 1.0);
         else    -- angle near Pi
            if Trig.Sin >= 0.0 then
               return (1.0 - Trig.Sin / 2.0, 0.0);
            else
               return (-1.0 + Trig.Sin / 2.0, 0.0);
            end if;
         end if;
      else    -- angle not near 0 or Pi
         if Trig.Sin >= 0.0 then
            return (Elementary.Sqrt ((1.0 - Trig.Cos) / 2.0), Elementary.Sqrt ((1.0 + Trig.Cos) / 2.0));
         else
            return (-Elementary.Sqrt ((1.0 - Trig.Cos) / 2.0), Elementary.Sqrt ((1.0 + Trig.Cos) / 2.0));
         end if;
      end if;
   end Half_Trig;

-- 
-- Stephe