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1 294 jeremybenn
-- CXG2005.A
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--
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--                             Grant of Unlimited Rights
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--
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--     Under contracts F33600-87-D-0337, F33600-84-D-0280, MDA903-79-C-0687,
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--     F08630-91-C-0015, and DCA100-97-D-0025, the U.S. Government obtained
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--     unlimited rights in the software and documentation contained herein.
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--     Unlimited rights are defined in DFAR 252.227-7013(a)(19).  By making
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--     this public release, the Government intends to confer upon all
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--     recipients unlimited rights  equal to those held by the Government.
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--     These rights include rights to use, duplicate, release or disclose the
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--     released technical data and computer software in whole or in part, in
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--     any manner and for any purpose whatsoever, and to have or permit others
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--     to do so.
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--
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--                                    DISCLAIMER
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--
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--     ALL MATERIALS OR INFORMATION HEREIN RELEASED, MADE AVAILABLE OR
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--     DISCLOSED ARE AS IS.  THE GOVERNMENT MAKES NO EXPRESS OR IMPLIED
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--     WARRANTY AS TO ANY MATTER WHATSOEVER, INCLUDING THE CONDITIONS OF THE
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--     SOFTWARE, DOCUMENTATION OR OTHER INFORMATION RELEASED, MADE AVAILABLE
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--     OR DISCLOSED, OR THE OWNERSHIP, MERCHANTABILITY, OR FITNESS FOR A
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--     PARTICULAR PURPOSE OF SAID MATERIAL.
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--*
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--
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-- OBJECTIVE:
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--      Check that floating point addition and multiplication
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--      have the required accuracy.
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--
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-- TEST DESCRIPTION:
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--      The check for the required precision is essentially a
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--      check that a guard digit is used for the operations.
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--      This test uses a generic package to check the addition
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--      and multiplication results.  The
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--      generic package is instantiated with the standard FLOAT
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--      type and a floating point type for the maximum number
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--      of digits of precision.
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--
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-- APPLICABILITY CRITERIA:
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--      This test applies only to implementations supporting the
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--      Numerics Annex.
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--
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--
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-- CHANGE HISTORY:
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--      14 FEB 96   SAIC    Initial Release for 2.1
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--      16 SEP 99   RLB     Repaired to avoid printing thousands of (almost)
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--                          identical failure messages.
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--!
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-- References:
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--
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--    Basic Concepts for Computational Software
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--    W. J. Cody
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--    Problems and Methodologies in Mathematical Software Production
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--    editors P. C. Messina and A. Murli
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--    Lecture Notes in Computer Science   Vol 142
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--    Springer Verlag,  1982
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--
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--    Software Manual for the Elementary Functions
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--    William J. Cody and William Waite
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--    Prentice-Hall, 1980
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--
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with System;
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with Report;
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procedure CXG2005 is
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   Verbose : constant Boolean := False;
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   generic
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      type Real is digits <>;
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   package Guard_Digit_Check is
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      procedure Do_Test;
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   end Guard_Digit_Check;
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   package body Guard_Digit_Check is
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      -- made global so that the compiler will be more likely
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      -- to keep the values in memory instead of in higher
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      -- precision registers.
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      X, Y, Z : Real;
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      OneX : Real;
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      Eps, BN : Real;
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      -- special constants - not declared as constants so that
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      -- the "stored" precision will be used instead of a "register"
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      -- precision.
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      Zero : Real := 0.0;
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      One  : Real := 1.0;
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      Two  : Real := 2.0;
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      Failure_Count : Natural := 0;
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      procedure Thwart_Optimization is
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      -- the purpose of this procedure is to reference the
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      -- global variables used by the test so
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      -- that the compiler is not likely to keep them in
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      -- a higher precision register for their entire lifetime.
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      begin
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         if Report.Ident_Bool (False) then
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            -- never executed
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            X := X + 5.0;
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            Y := Y + 6.0;
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            Z := Z + 1.0;
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            Eps := Eps + 2.0;
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            BN := BN + 2.0;
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            OneX := X + Y;
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            One := 12.34;   Two := 56.78;  Zero := 90.12;
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         end if;
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      end Thwart_Optimization;
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      procedure Addition_Test is
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      begin
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         for K in 1..10 loop
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            Eps := Real (K) * Real'Model_Epsilon;
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            for N in 1.. Real'Machine_EMax - 1 loop
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               BN := Real(Real'Machine_Radix) ** N;
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               X := (One + Eps) * BN;
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               Y := (One - Eps) * BN;
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               Z := X - Y; -- true value for Z is 2*Eps*BN
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               if Z /= Eps*BN + Eps*BN then
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                  Report.Failed ("addition check failed.  K=" &
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                     Integer'Image (K) &
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                     "  N=" & Integer'Image (N) &
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                     "  difference=" & Real'Image (Z - 2.0*Eps*BN) &
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                     "  Eps*BN=" & Real'Image (Eps*BN) );
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                  Failure_Count := Failure_Count + 1;
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                  exit when Failure_Count > K*4; -- Avoid displaying dozens of messages.
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               end if;
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            end loop;
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         end loop;
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      exception
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         when others =>
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            Thwart_Optimization;
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            Report.Failed ("unexpected exception in addition test");
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      end Addition_Test;
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      procedure Multiplication_Test is
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      begin
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          X := Real (Real'Machine_Radix) ** (Real'Machine_EMax - 1);
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          OneX := One * X;
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          Thwart_Optimization;
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          if OneX /= X then
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             Report.Failed ("multiplication for large values");
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          end if;
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          X := Real (Real'Machine_Radix) ** (Real'Model_EMin + 1);
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          OneX := One * X;
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          Thwart_Optimization;
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          if OneX /= X then
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             Report.Failed ("multiplication for small values");
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          end if;
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          -- selection of "random" values between 1/radix and radix
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          Y := One / Real (Real'Machine_Radix);
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          Z := Real(Real'Machine_Radix) - One/Real(Real'Machine_Radix);
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          for I in 0..100 loop
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             X := Y + Real (I) / 100.0 * Z;
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             OneX := One * X;
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             Thwart_Optimization;
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             if OneX /= X then
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                Report.Failed ("multiplication for case" & Integer'Image (I));
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                exit when Failure_Count > 40+8; -- Avoid displaying dozens of messages.
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             end if;
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          end loop;
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      exception
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         when others =>
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            Thwart_Optimization;
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            Report.Failed ("unexpected exception in multiplication test");
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      end Multiplication_Test;
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      procedure Do_Test is
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      begin
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         Addition_Test;
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         Multiplication_Test;
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      end Do_Test;
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   end Guard_Digit_Check;
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   package Chk_Float is new Guard_Digit_Check (Float);
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   -- check the floating point type with the most digits
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   type A_Long_Float is digits System.Max_Digits;
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   package Chk_A_Long_Float is new Guard_Digit_Check (A_Long_Float);
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begin
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   Report.Test ("CXG2005",
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                "Check the accuracy of floating point" &
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                " addition and multiplication");
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   if Verbose then
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      Report.Comment ("checking Standard.Float");
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   end if;
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   Chk_Float.Do_Test;
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   if Verbose then
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      Report.Comment ("checking a digits" &
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                      Integer'Image (System.Max_Digits) &
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                      " floating point type");
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   end if;
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   Chk_A_Long_Float.Do_Test;
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   Report.Result;
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end CXG2005;

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