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-- CXG2013.A

--

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--     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

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--     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 TAN and COT functions return

--      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.

--

-- 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:

--      11 Mar 96   SAIC    Initial release for 2.1

--      17 Aug 96   SAIC    Commentary fixes.

--      03 Feb 97   PWB.CTA Removed checks with explicit Cycle => 2.0*Pi

--      02 DEC 97   EDS     Change Max_Samples constant to 1001.

--      29 JUN 98   EDS     Deleted Special_Angle_Test as fatally flawed.

--!

--

-- 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 CXG2013 is

   Verbose : constant Boolean := False;

   Max_Samples : constant := 1001;

   -- 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;

   Pi : constant := Ada.Numerics.Pi;

   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 Tan (X : Real) return Real renames

           Elementary_Functions.Tan;

      function Cot (X : Real) return Real renames

           Elementary_Functions.Cot;

      function Tan (X, Cycle : Real) return Real renames

           Elementary_Functions.Tan;

      function Cot (X, Cycle : Real) return Real renames

           Elementary_Functions.Cot;

      -- flag used to terminate some tests early

      Accuracy_Error_Reported : Boolean := False;

      -- factor to be applied in computing MRE

      Maximum_Relative_Error : constant Real := 4.0;

      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;

      procedure Exact_Result_Test is

         No_Error : constant := 0.0;

      begin

         -- A.5.1(38);6.0

         Check (Tan (0.0),  0.0, "tan(0)", No_Error);

         -- A.5.1(41);6.0

         Check (Tan (180.0, 360.0), 0.0, "tan(180,360)", No_Error);

         Check (Tan (360.0, 360.0), 0.0, "tan(360,360)", No_Error);

         Check (Tan (720.0, 360.0), 0.0, "tan(720,360)", No_Error);

         -- A.5.1(41);6.0

         Check (Cot ( 90.0, 360.0), 0.0, "cot( 90,360)", No_Error);

         Check (Cot (270.0, 360.0), 0.0, "cot(270,360)", No_Error);

         Check (Cot (810.0, 360.0), 0.0, "cot(810,360)", No_Error);

      exception

         when Constraint_Error =>

            Report.Failed ("Constraint_Error raised in Exact_Result Test");

         when others =>

            Report.Failed ("exception in Exact_Result Test");

      end Exact_Result_Test;

      procedure Tan_Test (A, B : Real) is

      -- Use identity Tan(X) = [2*Tan(x/2)]/[1-Tan(x/2) ** 2]

      -- checks over the range -pi/4 .. pi/4 require no argument reduction

      -- checks over the range 7pi/8 .. 9pi/8 require argument reduction

         X, Y : Real;

         Actual1, Actual2 : Real;

      begin

         Accuracy_Error_Reported := False;  -- reset

         for I in 1..Max_Samples loop

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

            -- argument purification to insure x and x/2 are exact

            -- See Cody page 170.

            Y := Real'Machine (X*0.5);

            X := Real'Machine (Y + Y);

            Actual1 := Tan(X);

            Actual2 := (2.0 * Tan (Y)) / (1.0 - Tan (Y) ** 2);

            if abs (X - Pi) > ( (B-A)/Real(2*Max_Samples) ) then

              Check (Actual1, Actual2,

                     "Tan_Test " & Integer'Image (I) & ": tan(" &

                     Real'Image (X) & ") ",

                     (1.0 + Sqrt2) * Maximum_Relative_Error);

                     -- see Cody pg 165 for error bound info

            end if;

            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 Tan_Test");

         when others =>

            Report.Failed ("exception in Tan_Test");

      end Tan_Test;

      procedure Cot_Test is

      -- Use identity Cot(X) = [Cot(X/2)**2 - 1]/[2*Cot(X/2)]

         A : constant := 6.0 * Pi;

         B : constant := 25.0 / 4.0 * Pi;

         X, Y : Real;

         Actual1, Actual2 : Real;

      begin

         Accuracy_Error_Reported := False;  -- reset

         for I in 1..Max_Samples loop

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

            -- argument purification to insure x and x/2 are exact.

            -- See Cody page 170.

            Y := Real'Machine (X*0.5);

            X := Real'Machine (Y + Y);

            Actual1 := Cot(X);

            Actual2 := (Cot (Y) ** 2 - 1.0) / (2.0 * Cot (Y));

            Check (Actual1, Actual2,

                   "Cot_Test " & Integer'Image (I) & ": cot(" &

                   Real'Image (X) & ") ",

                   (1.0 + Sqrt2) * Maximum_Relative_Error);

                   -- see Cody pg 165 for error bound info

            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 Cot_Test");

         when others =>

            Report.Failed ("exception in Cot_Test");

      end Cot_Test;

      procedure Exception_Test is

         X1, X2, X3, X4, X5 : Real := 0.0;

      begin

         begin  -- A.5.1(20);6.0

           X1 := Tan (0.0, Cycle => 0.0);

           Report.Failed ("no exception for cycle = 0.0");

         exception

            when Ada.Numerics.Argument_Error => null;

            when others =>

               Report.Failed ("wrong exception for cycle = 0.0");

         end;

         begin  -- A.5.1(20);6.0

           X2 := Cot (1.0, Cycle => -3.0);

           Report.Failed ("no exception for cycle < 0.0");

         exception

            when Ada.Numerics.Argument_Error => null;

            when others =>

               Report.Failed ("wrong exception for cycle < 0.0");

         end;

         -- the remaining tests only apply to machines that overflow

         if Real'Machine_Overflows then    -- A.5.1(28);6.0

            begin   -- A.5.1(29);6.0

               X3 := Cot (0.0);

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

            exception

               when Constraint_Error => null;   -- ok

               when others =>

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

            end;

            begin   -- A.5.1(31);6.0

               X4 := Tan (90.0, 360.0);

               Report.Failed ("exception not raised for tan(90,360)");

            exception

               when Constraint_Error => null;  -- ok

               when others =>

                  Report.Failed ("wrong exception raised for tan(90,360)");

            end;

            begin   -- A.5.1(32);6.0

               X5 := Cot (180.0, 360.0);

               Report.Failed ("exception not raised for cot(180,360)");

            exception

               when Constraint_Error => null;  -- ok

               when others =>

                  Report.Failed ("wrong exception raised for cot(180,360)");

            end;

         end if;

         -- optimizer thwarting

         if Report.Ident_Bool (False) then

            Report.Comment (Real'Image (X1+X2+X3+X4+X5));

         end if;

      end Exception_Test;

      procedure Do_Test is

      begin

         Exact_Result_Test;

         Tan_Test (-Pi/4.0, Pi/4.0);

         Tan_Test (7.0*Pi/8.0, 9.0*Pi/8.0);

         Cot_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 ("CXG2013",

                "Check the accuracy of the TAN and COT functions");

   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 CXG2013;