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-- CXA5A04.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.

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

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

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--

--                                    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 functions Cot, Coth, and Arccoth provide correct

--      results.

--

-- TEST DESCRIPTION:

--      This test examines both the version of Cot, Coth, and Arccoth

--      the instantiation of the Ada.Numerics.Generic_Elementary_Functions

--      with a type derived from type Float, as well as the preinstantiated

--      version of this package for type Float.

--      Prescribed results, including instances prescribed to raise

--      exceptions, are examined in the test cases.  In addition,

--      certain evaluations are performed where the actual function result

--      is compared with the expected result (within an epsilon range of

--      accuracy).

--

-- TEST FILES:

--      The following files comprise this test:

--

--         FXA5A00.A   (foundation code)

--         CXA5A04.A

--

--

-- CHANGE HISTORY:

--      15 Mar 95   SAIC    Initial prerelease version.

--      07 Apr 95   SAIC    Corrected errors in context clause reference,

--                          added trigonometric relationship checks.

--      13 Jun 95   SAIC    Incorporated use of Dont_Optimize procedure, and

--                          use of Result_Within_Range function overloaded for

--                          FXA5A00.New_Float_Type.

--      18 Apr 96   SAIC    Incorporated reviewer comments for ACVC 2.1.

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

--      29 Jun 98   EDS     Protected exception tests by first testing

--                          for 'Machine_Overflows

--

-- CHANGE NOTE:

--      According to Ken Dritz, author of the Numerics Annex of the RM,

--      one should never specify the cycle 2.0*Pi for the trigonometric

--      functions.  In particular, if the machine number for the first

--      argument is not an exact multiple of the machine number for the

--      explicit cycle, then the specified exact results cannot be

--      reasonably expected.  The affected checks in this test have been

--      marked as comments, with the additional notation "pwb-math".

--      Phil Brashear

--!

with Ada.Exceptions;

with Ada.Numerics.Elementary_Functions;

with Ada.Numerics.Generic_Elementary_Functions;

with FXA5A00;

with Report;

procedure CXA5A04 is

begin

   Report.Test ("CXA5A04", "Check that the functions Cot, Coth, and " &

                           "Arccoth provide correct results");

   Test_Block:

   declare

      use Ada.Exceptions;

      use Ada.Numerics;

      use FXA5A00;

      package GEF is new Ada.Numerics.Generic_Elementary_Functions(New_Float);

      package  EF renames Ada.Numerics.Elementary_Functions;

      The_Result       : Float;

      New_Float_Result : New_Float;

      procedure Dont_Optimize_Float     is new Dont_Optimize(Float);

      procedure Dont_Optimize_New_Float is new Dont_Optimize(New_Float);

   begin

      -- Testing of Cot Function, both instantiated and pre-instantiated

      -- version.

      -- Check that Constraint_Error is raised with the Cot function is

      -- given a parameter input value of 0.0.

      if New_Float'Machine_Overflows = True then

         begin

            New_Float_Result := GEF.Cot (0.0);

            Report.Failed("Constraint_Error not raised by Function Cot " &

                          "when provided a zero input parameter value");

            Dont_Optimize_New_Float(New_Float_Result, 1);

         exception

            when Constraint_Error => null;  -- OK, expected exception.

            when others           =>

            Report.Failed("Unexpected exception raised by Function Cot " &

                          "when provided a zero input parameter value");

         end;

      end if;

      -- Check that no exception occurs on computing the Cot with very

      -- large (positive and negative) input values.

      begin

         New_Float_Result := GEF.Cot (New_Float(FXA5A00.Large));

         Dont_Optimize_New_Float(New_Float_Result, 2);

      exception

         when others =>

           Report.Failed("Unexpected exception on GEF.Cot with large " &

                         "positive value");

      end;

      begin

         The_Result := EF.Cot (FXA5A00.Minus_Large);

         Dont_Optimize_Float(The_Result, 3);

      exception

         when others =>

           Report.Failed("Unexpected exception on EF.Cot with large " &

                         "negative value");

      end;

      -- Check the results of the Cot function with various input parameters.

      if not (FXA5A00.Result_Within_Range(GEF.Cot(Pi/4.0),     1.0, 0.001) and

              FXA5A00.Result_Within_Range( EF.Cot(Pi/2.0),     0.0, 0.001) and

              FXA5A00.Result_Within_Range(GEF.Cot(3.0*Pi/4.0),-1.0, 0.001) and

              FXA5A00.Result_Within_Range( EF.Cot(3.0*Pi/2.0), 0.0, 0.001))

      then

         Report.Failed("Incorrect result from Cot function with various " &

                       "input parameters");

      end if;

      -- Check the results of the Cot function against the results of

      -- various trigonometric relationships.

      if not FXA5A00.Result_Within_Range(GEF.Cot(New_Float(Pi/4.0)),

                                         1.0/EF.Tan(Pi/4.0),

                                         0.001)           or

         not FXA5A00.Result_Within_Range(EF.Cot(Pi/4.0),

                                         EF.Cos(Pi/4.0)/EF.Sin(Pi/4.0),

                                         0.001) or

         not FXA5A00.Result_Within_Range(EF.Cot(EF.Arccot(Pi/4.0)),

                                         Pi/4.0,

                                         0.001)

      then

         Report.Failed("Incorrect result from Cot function with respect " &

                       "to various trigonometric relationship expected "  &

                       "results");

      end if;

      -- Testing of Cot with Cycle parameter.

      -- Check that Argument_Error is raised by the Cot function when the

      -- value of the Cycle parameter is zero or negative.

      begin

         New_Float_Result := GEF.Cot (1.0, Cycle => 0.0);

         Report.Failed("Argument_Error not raised by the Cot Function " &

                       "with a specified cycle value of 0.0");

         Dont_Optimize_New_Float(New_Float_Result, 4);

      exception

         when Argument_Error => null;  -- OK, expected exception.

         when others         =>

            Report.Failed

              ("Unexpected exception raised by the Cot Function with " &

               "a specified cycle value of 0.0");

      end;

      begin

         The_Result := EF.Cot (X => 1.0, Cycle => -360.0);

         Report.Failed("Argument_Error not raised by the Cot Function " &

                       "with a specified cycle value of -360.0");

         Dont_Optimize_Float(The_Result, 5);

      exception

         when Argument_Error => null;  -- OK, expected exception.

         when others         =>

            Report.Failed

              ("Unexpected exception raised by the Cot Function with " &

               "a specified cycle value of -360.0");

      end;

      -- Check that Constraint_Error is raised by the Cot Function with

      -- specified cycle, when the value of the parameter X is 0.0.

      if New_Float'Machine_Overflows = True then

         begin

            New_Float_Result := GEF.Cot (0.0, 360.0);

            Report.Failed("Constraint_Error not raised by Function Cot "   &

                          "with specified cycle, when value of parameter " &

                          "X is 0.0");

            Dont_Optimize_New_Float(New_Float_Result, 6);

         exception

            when Constraint_Error => null;  -- OK, expected exception.

            when others           =>

               Report.Failed("Unexpected exception raised by Function Cot "   &

                             "with specified cycle, when value of parameter " &

                             "X is 0.0");

         end;

      end if;

      -- Check that Constraint_Error is raised by the Cot Function with

      -- specified cycle, when the value of the parameter X is a multiple

      -- of the half cycle.

      if New_Float'Machine_Overflows = True then

         begin

            New_Float_Result := GEF.Cot (180.0, 360.0);

            Report.Failed("Constraint_Error not raised by Function Cot "   &

                          "with specified cycle, when value of parameter " &

                          "X is a multiple of the half cycle (180.0, 360.0)");

            Dont_Optimize_New_Float(New_Float_Result, 7);

         exception

            when Constraint_Error => null;  -- OK, expected exception.

            when others           =>

               Report.Failed("Unexpected exception raised by Function Cot "   &

                             "with specified cycle, when value of parameter " &

                             "X is a multiple of the half cycle" &

                             " (180.0, 360.0)");

         end;

      end if;

      if Float'Machine_Overflows = True then

         begin

            The_Result := EF.Cot (540.0, 360.0);

            Report.Failed("Constraint_Error not raised by Function Cot "   &

                          "with specified cycle, when value of parameter " &

                          "X is a multiple of the half cycle (540.0, 360.0)");

            Dont_Optimize_Float(The_Result, 8);

         exception

            when Constraint_Error => null;  -- OK, expected exception.

            when others           =>

               Report.Failed("Unexpected exception raised by Function Cot "   &

                             "with specified cycle, when value of parameter " &

                             "X is a multiple of the half cycle (540.0, 360.0)");

         end;

      end if;

--pwb-math      -- Check that no exception occurs on computing the Cot with very

--pwb-math      -- large (positive and negative) input values.

--pwb-math

--pwb-math      begin

--pwb-math         New_Float_Result := GEF.Cot (New_Float(FXA5A00.Large), 2.0*Pi);

--pwb-math         Dont_Optimize_New_Float(New_Float_Result, 9);

--pwb-math      exception

--pwb-math         when others =>

--pwb-math           Report.Failed("Unexpected exception on GEF.Cot with large " &

--pwb-math                         "positive value");

--pwb-math      end;

--pwb-math

--pwb-math      begin

--pwb-math         The_Result := EF.Cot (FXA5A00.Minus_Large, Cycle => 2.0*Pi);

--pwb-math         Dont_Optimize_Float(The_Result, 10);

--pwb-math      exception

--pwb-math         when others =>

--pwb-math           Report.Failed("Unexpected exception on EF.Cot with large " &

--pwb-math                         "negative value");

--pwb-math      end;

--pwb-math

--pwb-math

--pwb-math      -- Check prescribed result from Cot function with Cycle parameter.

--pwb-math

--pwb-math      if not FXA5A00.Result_Within_Range

--pwb-math               (GEF.Cot(New_Float(FXA5A00.Half_Pi), 2.0*Pi), 0.0, 0.001) or

--pwb-math         not FXA5A00.Result_Within_Range

--pwb-math               (EF.Cot(3.0*Pi/2.0, Cycle => 2.0*Pi), 0.0, 0.001)

--pwb-math      then

--pwb-math         Report.Failed("Incorrect result from Cot function with cycle " &

--pwb-math                       "parameter, using a multiple of Pi/2 as the "    &

--pwb-math                       "input parameter");

--pwb-math      end if;

      -- Testing of Coth Function, both instantiated and pre-instantiated

      -- version.

      -- Check that no exception occurs on computing the Coth with very

      -- large (positive and negative) input values.

      begin

         The_Result := EF.Coth (FXA5A00.Large);

         if The_Result > 1.0 then

            Report.Failed("Result of Coth function with large positive " &

                          "value greater than 1.0");

         end if;

      exception

         when others =>

           Report.Failed("Unexpected exception on EF.Coth with large " &

                         "positive value");

      end;

      begin

         The_Result := EF.Coth (FXA5A00.Minus_Large);

         if The_Result < -1.0 then

            Report.Failed("Result of Coth function with large negative " &

                          "value less than -1.0");

         end if;

      exception

         when others =>

           Report.Failed("Unexpected exception on EF.Coth with large " &

                         "negative value");

      end;

      -- Check that Constraint_Error is raised by the Coth function, when

      -- the value of the parameter X is 0.0.

      if New_Float'Machine_Overflows = True then

         begin

            New_Float_Result := GEF.Coth (X => 0.0);

            Report.Failed("Constraint_Error not raised by the Coth function " &

                          "when the value of parameter X is 0.0");

            Dont_Optimize_New_Float(New_Float_Result, 11);

         exception

            when Constraint_Error => null;  -- OK, expected exception.

            when others           =>

               Report.Failed("Unexpected exception raised by the Coth " &

                             "function when the value of parameter X is 0.0");

         end;

      end if;

      -- Testing of Arccoth Function, both instantiated and pre-instantiated

      -- version.

      -- Check that Constraint_Error is raised by the Arccoth function

      -- when the absolute value of the parameter X is 1.0.

      if New_Float'Machine_Overflows = True then

         begin

            New_Float_Result := GEF.Arccoth (X => 1.0);

            Report.Failed("Constraint_Error not raised by the Arccoth " &

                          "function when the value of parameter X is 1.0");

            Dont_Optimize_New_Float(New_Float_Result, 12);

         exception

            when Constraint_Error => null;  -- OK, expected exception.

            when others           =>

               Report.Failed("Unexpected exception raised by the Arccoth " &

                             "function when the value of parameter X is 1.0");

         end;

      end if;

      if Float'Machine_Overflows = True then

         begin

            The_Result := EF.Arccoth (-1.0);

            Report.Failed("Constraint_Error not raised by the Arccoth " &

                          "function when the value of parameter X is -1.0");

            Dont_Optimize_Float(The_Result, 13);

         exception

            when Constraint_Error => null;  -- OK, expected exception.

            when others           =>

               Report.Failed("Unexpected exception raised by the Arccoth " &

                             "function when the value of parameter X is -1.0");

         end;

      end if;

      -- Check that Argument_Error is raised by the Arccoth function when

      -- the absolute value of the parameter X is less than 1.0.

      begin

         New_Float_Result := GEF.Arccoth (X => New_Float(One_Minus_Delta));

         Report.Failed("Argument_Error not raised by the Arccoth " &

                       "function with parameter value less than 1.0");

         Dont_Optimize_New_Float(New_Float_Result, 14);

      exception

         when Argument_Error => null;  -- OK, expected exception.

         when others         =>

            Report.Failed("Unexpected exception raised by the Arccoth " &

                          "function with parameter value less than 1.0");

      end;

      begin

         The_Result := EF.Arccoth (X => FXA5A00.Minus_One_Plus_Delta);

         Report.Failed("Argument_Error not raised by the Arccoth function " &

                       "with parameter value between 0.0 and -1.0");

         Dont_Optimize_Float(The_Result, 15);

      exception

         when Argument_Error => null;  -- OK, expected exception.

         when others         =>

            Report.Failed("Unexpected exception raised by the Arccoth " &

                          "function with parameter value between 0.0 "  &

                          "and -1.0");

      end;

      -- Check the results of the Arccoth function with various input

      -- parameters.

      if not (Result_Within_Range(GEF.Arccoth(1.01), 2.652, 0.01)  and

              Result_Within_Range( EF.Arccoth(1.25), 1.099, 0.01)  and

              Result_Within_Range(GEF.Arccoth(1.56), 0.760, 0.001) and

              Result_Within_Range( EF.Arccoth(1.97), 0.560, 0.001) and

              Result_Within_Range(GEF.Arccoth(2.40), 0.444, 0.001) and

              Result_Within_Range( EF.Arccoth(4.30), 0.237, 0.001) and

              Result_Within_Range(GEF.Arccoth(5.80), 0.174, 0.001) and

              Result_Within_Range( EF.Arccoth(7.00), 0.144, 0.001))

      then

         Report.Failed("Incorrect result from Arccoth function with various " &

                       "input parameters");

      end if;

   exception

      when The_Error : others =>

         Report.Failed ("The following exception was raised in the " &

                        "Test_Block: " & Exception_Name(The_Error));

   end Test_Block;

   Report.Result;

end CXA5A04;