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-- CXG2012.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 the exponentiation operator returns

--      results that are within the error bound allowed.

--

-- TEST DESCRIPTION:

--      This test consists of a generic package that is

--      instantiated to check both Float and a long float type.

--      The test for each floating point type is divided into

--      several parts:

--         Special value checks where the result is a known constant.

--         Checks that use an identity for determining the result.

--         Exception checks.

--      While this test concentrates on the "**" operator

--      defined in Generic_Elementary_Functions, a check is also

--      performed on the standard "**" operator.

--

-- SPECIAL REQUIREMENTS

--      The Strict Mode for the numerical accuracy must be

--      selected.  The method by which this mode is selected

--      is implementation dependent.

--

-- APPLICABILITY CRITERIA:

--      This test applies only to implementations supporting the

--      Numerics Annex.

--      This test only applies to the Strict Mode for numerical

--      accuracy.

--

--

-- CHANGE HISTORY:

--       7 Mar 96   SAIC    Initial release for 2.1

--       2 Sep 96   SAIC    Improvements as suggested by reviewers

--       3 Jun 98   EDS     Add parens to ensure that the expression is not

--                          evaluated by multiplying its two large terms

--                          together and overflowing.

--       3 Dec 01   RLB     Added 'Machine to insure that equality tests

--                          are certain to work.

--

--!

--

-- References:

--

-- Software Manual for the Elementary Functions

-- William J. Cody, Jr. and William Waite

-- Prentice-Hall, 1980

--

-- CRC Standard Mathematical Tables

-- 23rd Edition

--

-- Implementation and Testing of Function Software

-- W. J. Cody

-- Problems and Methodologies in Mathematical Software Production

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

-- Lecture Notes in Computer Science   Volume 142

-- Springer Verlag, 1982

--

with System;

with Report;

with Ada.Numerics.Generic_Elementary_Functions;

procedure CXG2012 is

   Verbose : constant Boolean := False;

   Max_Samples : constant := 1000;

   -- CRC Standard Mathematical Tables;  23rd Edition; pg 738

   Sqrt2 : constant :=

        1.41421_35623_73095_04880_16887_24209_69807_85696_71875_37695;

   Sqrt3 : constant :=

        1.73205_08075_68877_29352_74463_41505_87236_69428_05253_81039;

   generic

      type Real is digits <>;

   package Generic_Check is

      procedure Do_Test;

   end Generic_Check;

   package body Generic_Check is

      package Elementary_Functions is new

           Ada.Numerics.Generic_Elementary_Functions (Real);

      function Sqrt (X : Real) return Real renames

           Elementary_Functions.Sqrt;

      function Exp (X : Real) return Real renames

           Elementary_Functions.Exp;

      function Log (X : Real) return Real renames

           Elementary_Functions.Log;

      function "**" (L, R : Real) return Real renames

           Elementary_Functions."**";

      -- flag used to terminate some tests early

      Accuracy_Error_Reported : Boolean := False;

      procedure Check (Actual, Expected : Real;

                       Test_Name : String;

                       MRE : Real) is

         Max_Error : Real;

         Rel_Error : Real;

         Abs_Error : Real;

      begin

         -- In the case where the expected result is very small or 0

         -- we compute the maximum error as a multiple of Model_Epsilon

         -- instead of Model_Epsilon and Expected.

         Rel_Error := MRE * (abs Expected * Real'Model_Epsilon);

         Abs_Error := MRE * Real'Model_Epsilon;

         if Rel_Error > Abs_Error then

            Max_Error := Rel_Error;

         else

            Max_Error := Abs_Error;

         end if;

         if abs (Actual - Expected) > Max_Error then

            Accuracy_Error_Reported := True;

            Report.Failed (Test_Name &

                           " actual: " & Real'Image (Actual) &

                           " expected: " & Real'Image (Expected) &

                           " difference: " & Real'Image (Actual - Expected) &

                           " max err:" & Real'Image (Max_Error) );

         elsif Verbose then

            if Actual = Expected then

               Report.Comment (Test_Name & "  exact result");

            else

               Report.Comment (Test_Name & "  passed");

            end if;

         end if;

      end Check;

      -- the following version of Check computes the allowed error bound

      -- using the operands

      procedure Check (Actual, Expected : Real;

                       Left, Right : Real;

                       Test_Name : String;

                       MRE_Factor : Real := 1.0) is

         MRE : Real;

      begin

         MRE := MRE_Factor * (4.0 + abs (Right * Log(Left)) / 32.0);

         Check (Actual, Expected, Test_Name, MRE);

      end Check;

      procedure Real_To_Integer_Test is

         type Int_Check is

            record

               Left : Real;

               Right : Integer;

               Expected : Real;

            end record;

         type Int_Checks is array (Positive range <>) of Int_Check;

         -- the following tests use only model numbers so the result

         -- is expected to be exact.

         IC : constant Int_Checks :=

         ( (  2.0,   5,       32.0),

           ( -2.0,   5,      -32.0),

           (  0.5,  -5,       32.0),

           (  2.0,   0,        1.0),

           (  0.0,   0,        1.0) );

      begin

         for I in IC'Range loop

            declare

               Y : Real;

            begin

               Y := IC (I).Left ** IC (I).Right;

               Check (Y, IC (I).Expected,

                      "real to integer test" &

                      Real'Image (IC (I).Left) & " ** " &

                      Integer'Image (IC (I).Right),

                      0.0);  -- no error allowed

            exception

               when Constraint_Error =>

                  Report.Failed ("Constraint_Error raised in rtoi test " &

                     Integer'Image (I));

               when others =>

                  Report.Failed ("exception in rtoi test " &

                     Integer'Image (I));

            end;

         end loop;

      end Real_To_Integer_Test;

      procedure Special_Value_Test is

         No_Error : constant := 0.0;

      begin

         Check (0.0 ** 1.0, 0.0, "0**1", No_Error);

         Check (1.0 ** 0.0, 1.0, "1**0", No_Error);

         Check ( 2.0 **  5.0,  32.0,  2.0,  5.0,  "2**5");

         Check ( 0.5**(-5.0),  32.0,  0.5, -5.0,  "0.5**-5");

         Check (Sqrt2 ** 4.0,   4.0,  Sqrt2, 4.0,  "Sqrt2**4");

         Check (Sqrt3 ** 6.0,  27.0,  Sqrt3, 6.0,  "Sqrt3**6");

         Check (2.0 ** 0.5,   Sqrt2,    2.0, 0.5,  "2.0**0.5");

      exception

         when Constraint_Error =>

            Report.Failed ("Constraint_Error raised in Special Value Test");

         when others =>

            Report.Failed ("exception in Special Value Test");

      end Special_Value_Test;

      procedure Small_Range_Test is

      -- Several checks over the range 1/radix .. 1

         A : constant Real := 1.0 / Real (Real'Machine_Radix);

         B : constant Real := 1.0;

         X : Real;

         -- In the cases below where the expected result is

         -- inexact we allow an additional error amount of

         -- 1.0 * Model_Epsilon to account for that error.

         -- This is accomplished by the factor of 1.25 times

         -- the computed error bound (which is > 4.0) thus

         -- increasing the error bound by at least

         -- 1.0 * Model_Epsilon

      begin

         Accuracy_Error_Reported := False;  -- reset

         for I in 0..Max_Samples loop

            X :=  Real'Machine((B - A) * Real (I) / Real (Max_Samples) + A);

            Check (X ** 1.0, X,  -- exact result required

                   "Small range" & Integer'Image (I) & ": " &

                   Real'Image (X) & " ** 1.0",

                   0.0);

            Check ((X*X) ** 1.5, X**3,  X*X, 1.5,

                   "Small range" & Integer'Image (I) & ": " &

                   Real'Image (X*X) & " ** 1.5",

                   1.25);

            Check (X ** 13.5, 1.0 / (X ** (-13.5)),  X, 13.5,

                   "Small range" & Integer'Image (I) & ": " &

                   Real'Image (X) & " ** 13.5",

                   2.0);   -- 2 ** computations

            Check ((X*X) ** 1.25, X**(2.5),  X*X, 1.25,

                   "Small range" & Integer'Image (I) & ": " &

                   Real'Image (X*X) & " ** 1.25",

                   2.0);   -- 2 ** computations

            if Accuracy_Error_Reported then

              -- only report the first error in this test in order to keep

              -- lots of failures from producing a huge error log

              return;

            end if;

         end loop;

      exception

         when Constraint_Error =>

            Report.Failed

               ("Constraint_Error raised in Small Range Test");

         when others =>

            Report.Failed ("exception in Small Range Test");

      end Small_Range_Test;

      procedure Large_Range_Test is

      -- Check over the range A to B where A is 1.0 and

      -- B is a large value.

         A : constant Real := 1.0;

         B : Real;

         X : Real;

         Iteration : Integer := 0;

         Subtest : Character := 'X';

      begin

         -- upper bound of range should be as large as possible where

         -- B**3 is still valid.

         B := Real'Safe_Last ** 0.333;

         Accuracy_Error_Reported := False;  -- reset

         for I in 0..Max_Samples loop

            Iteration := I;

            Subtest := 'X';

            X :=  Real'Machine((B - A) * (Real (I) / Real (Max_Samples)) + A);

            Subtest := 'A';

            Check (X ** 1.0, X,  -- exact result required

                   "Large range" & Integer'Image (I) & ": " &

                   Real'Image (X) & " ** 1.0",

                   0.0);

            Subtest := 'B';

            Check ((X*X) ** 1.5, X**3,  X*X, 1.5,

                   "Large range" & Integer'Image (I) & ": " &

                   Real'Image (X*X) & " ** 1.5",

                   1.25);   -- inexact expected result

            Subtest := 'C';

            Check ((X*X) ** 1.25, X**(2.5),  X*X, 1.25,

                   "Large range" & Integer'Image (I) & ": " &

                   Real'Image (X*X) & " ** 1.25",

                   2.0);   -- two ** operators

            if Accuracy_Error_Reported then

              -- only report the first error in this test in order to keep

              -- lots of failures from producing a huge error log

              return;

            end if;

         end loop;

      exception

         when Constraint_Error =>

            Report.Failed

               ("Constraint_Error raised in Large Range Test" &

                Integer'Image (Iteration) & Subtest);

         when others =>

            Report.Failed ("exception in Large Range Test" &

                Integer'Image (Iteration) & Subtest);

      end Large_Range_Test;

      procedure Exception_Test is

         X1, X2, X3, X4 : Real;

      begin

         begin

            X1 := 0.0 ** (-1.0);

            Report.Failed ("exception not raised for 0**-1");

         exception

            when Ada.Numerics.Argument_Error =>

               Report.Failed ("argument_error raised instead of" &

                              " constraint_error for 0**-1");

            when Constraint_Error => null;   -- ok

            when others =>

               Report.Failed ("wrong exception raised for 0**-1");

         end;

         begin

            X2 := 0.0 ** 0.0;

            Report.Failed ("exception not raised for 0**0");

         exception

            when Ada.Numerics.Argument_Error =>  null;  -- ok

            when Constraint_Error =>

               Report.Failed ("constraint_error raised instead of" &

                              " argument_error for 0**0");

            when others =>

               Report.Failed ("wrong exception raised for 0**0");

         end;

         begin

            X3 := (-1.0) ** 1.0;

            Report.Failed ("exception not raised for -1**1");

         exception

            when Ada.Numerics.Argument_Error =>  null;  -- ok

            when Constraint_Error =>

               Report.Failed ("constraint_error raised instead of" &

                              " argument_error for -1**1");

            when others =>

               Report.Failed ("wrong exception raised for -1**1");

         end;

         begin

            X4 := (-2.0) ** 2.0;

            Report.Failed ("exception not raised for -2**2");

         exception

            when Ada.Numerics.Argument_Error =>  null;  -- ok

            when Constraint_Error =>

               Report.Failed ("constraint_error raised instead of" &

                              " argument_error for -2**2");

            when others =>

               Report.Failed ("wrong exception raised for -2**2");

         end;

         -- optimizer thwarting

         if Report.Ident_Bool (False) then

            Report.Comment (Real'Image (X1+X2+X3+X4));

         end if;

      end Exception_Test;

      procedure Do_Test is

      begin

         Real_To_Integer_Test;

         Special_Value_Test;

         Small_Range_Test;

         Large_Range_Test;

         Exception_Test;

      end Do_Test;

   end Generic_Check;

   -----------------------------------------------------------------------

   -----------------------------------------------------------------------

   package Float_Check is new Generic_Check (Float);

   -- check the floating point type with the most digits

   type A_Long_Float is digits System.Max_Digits;

   package A_Long_Float_Check is new Generic_Check (A_Long_Float);

   -----------------------------------------------------------------------

   -----------------------------------------------------------------------

begin

   Report.Test ("CXG2012",

                "Check the accuracy of the ** operator");

   if Verbose then

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

   end if;

   Float_Check.Do_Test;

   if Verbose then

      Report.Comment ("checking a digits" &

                      Integer'Image (System.Max_Digits) &

                      " floating point type");

   end if;

   A_Long_Float_Check.Do_Test;

   Report.Result;

end CXG2012;