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-- CXG2005.A

--

--                             Grant of Unlimited Rights

--

--     Under contracts F33600-87-D-0337, F33600-84-D-0280, MDA903-79-C-0687,

--     F08630-91-C-0015, and DCA100-97-D-0025, the U.S. Government obtained

--     unlimited rights in the software and documentation contained herein.

--     Unlimited rights are defined in DFAR 252.227-7013(a)(19).  By making

--     this public release, the Government intends to confer upon all

--     recipients unlimited rights  equal to those held by the Government.

--     These rights include rights to use, duplicate, release or disclose the

--     released technical data and computer software in whole or in part, in

--     any manner and for any purpose whatsoever, and to have or permit others

--     to do so.

--

--                                    DISCLAIMER

--

--     ALL MATERIALS OR INFORMATION HEREIN RELEASED, MADE AVAILABLE OR

--     DISCLOSED ARE AS IS.  THE GOVERNMENT MAKES NO EXPRESS OR IMPLIED

--     WARRANTY AS TO ANY MATTER WHATSOEVER, INCLUDING THE CONDITIONS OF THE

--     SOFTWARE, DOCUMENTATION OR OTHER INFORMATION RELEASED, MADE AVAILABLE

--     OR DISCLOSED, OR THE OWNERSHIP, MERCHANTABILITY, OR FITNESS FOR A

--     PARTICULAR PURPOSE OF SAID MATERIAL.

--*

--

-- OBJECTIVE:

--      Check that floating point addition and multiplication

--      have the required accuracy.

--

-- TEST DESCRIPTION:

--      The check for the required precision is essentially a

--      check that a guard digit is used for the operations.

--      This test uses a generic package to check the addition

--      and multiplication results.  The

--      generic package is instantiated with the standard FLOAT

--      type and a floating point type for the maximum number

--      of digits of precision.

--

-- APPLICABILITY CRITERIA:

--      This test applies only to implementations supporting the

--      Numerics Annex.

--

--

-- CHANGE HISTORY:

--      14 FEB 96   SAIC    Initial Release for 2.1

--      16 SEP 99   RLB     Repaired to avoid printing thousands of (almost)

--                          identical failure messages.

--!

-- References:

--

--    Basic Concepts for Computational Software

--    W. J. Cody

--    Problems and Methodologies in Mathematical Software Production

--    editors P. C. Messina and A. Murli

--    Lecture Notes in Computer Science   Vol 142

--    Springer Verlag,  1982

--

--    Software Manual for the Elementary Functions

--    William J. Cody and William Waite

--    Prentice-Hall, 1980

--

with System;

with Report;

procedure CXG2005 is

   Verbose : constant Boolean := False;

   generic

      type Real is digits <>;

   package Guard_Digit_Check is

      procedure Do_Test;

   end Guard_Digit_Check;

   package body Guard_Digit_Check is

      -- made global so that the compiler will be more likely

      -- to keep the values in memory instead of in higher

      -- precision registers.

      X, Y, Z : Real;

      OneX : Real;

      Eps, BN : Real;

      -- special constants - not declared as constants so that

      -- the "stored" precision will be used instead of a "register"

      -- precision.

      Zero : Real := 0.0;

      One  : Real := 1.0;

      Two  : Real := 2.0;

      Failure_Count : Natural := 0;

      procedure Thwart_Optimization is

      -- the purpose of this procedure is to reference the

      -- global variables used by the test so

      -- that the compiler is not likely to keep them in

      -- a higher precision register for their entire lifetime.

      begin

         if Report.Ident_Bool (False) then

            -- never executed

            X := X + 5.0;

            Y := Y + 6.0;

            Z := Z + 1.0;

            Eps := Eps + 2.0;

            BN := BN + 2.0;

            OneX := X + Y;

            One := 12.34;   Two := 56.78;  Zero := 90.12;

         end if;

      end Thwart_Optimization;

      procedure Addition_Test is

      begin

         for K in 1..10 loop

            Eps := Real (K) * Real'Model_Epsilon;

            for N in 1.. Real'Machine_EMax - 1 loop

               BN := Real(Real'Machine_Radix) ** N;

               X := (One + Eps) * BN;

               Y := (One - Eps) * BN;

               Z := X - Y; -- true value for Z is 2*Eps*BN

               if Z /= Eps*BN + Eps*BN then

                  Report.Failed ("addition check failed.  K=" &

                     Integer'Image (K) &

                     "  N=" & Integer'Image (N) &

                     "  difference=" & Real'Image (Z - 2.0*Eps*BN) &

                     "  Eps*BN=" & Real'Image (Eps*BN) );

                  Failure_Count := Failure_Count + 1;

                  exit when Failure_Count > K*4; -- Avoid displaying dozens of messages.

               end if;

            end loop;

         end loop;

      exception

         when others =>

            Thwart_Optimization;

            Report.Failed ("unexpected exception in addition test");

      end Addition_Test;

      procedure Multiplication_Test is

      begin

          X := Real (Real'Machine_Radix) ** (Real'Machine_EMax - 1);

          OneX := One * X;

          Thwart_Optimization;

          if OneX /= X then

             Report.Failed ("multiplication for large values");

          end if;

          X := Real (Real'Machine_Radix) ** (Real'Model_EMin + 1);

          OneX := One * X;

          Thwart_Optimization;

          if OneX /= X then

             Report.Failed ("multiplication for small values");

          end if;

          -- selection of "random" values between 1/radix and radix

          Y := One / Real (Real'Machine_Radix);

          Z := Real(Real'Machine_Radix) - One/Real(Real'Machine_Radix);

          for I in 0..100 loop

             X := Y + Real (I) / 100.0 * Z;

             OneX := One * X;

             Thwart_Optimization;

             if OneX /= X then

                Report.Failed ("multiplication for case" & Integer'Image (I));

                exit when Failure_Count > 40+8; -- Avoid displaying dozens of messages.

             end if;

          end loop;

      exception

         when others =>

            Thwart_Optimization;

            Report.Failed ("unexpected exception in multiplication test");

      end Multiplication_Test;

      procedure Do_Test is

      begin

         Addition_Test;

         Multiplication_Test;

      end Do_Test;

   end Guard_Digit_Check;

   package Chk_Float is new Guard_Digit_Check (Float);

   -- check the floating point type with the most digits

   type A_Long_Float is digits System.Max_Digits;

   package Chk_A_Long_Float is new Guard_Digit_Check (A_Long_Float);

begin

   Report.Test ("CXG2005",

                "Check the accuracy of floating point" &

                " addition and multiplication");

   if Verbose then

      Report.Comment ("checking Standard.Float");

   end if;

   Chk_Float.Do_Test;

   if Verbose then

      Report.Comment ("checking a digits" &

                      Integer'Image (System.Max_Digits) &

                      " floating point type");

   end if;

   Chk_A_Long_Float.Do_Test;

   Report.Result;

end CXG2005;