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-- CXA5A08.A

--

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

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--*

--

-- OBJECTIVE:

--      Check that the function Arccot provides correct results.

--

-- TEST DESCRIPTION:

--      This test examines both the version of Arccot resulting from 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)

--         CXA5A08.A

--

--

-- CHANGE HISTORY:

--      06 Apr 95   SAIC    Initial prerelease version.

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

--

-- 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 CXA5A08 is

begin

   Report.Test ("CXA5A08", "Check that the Arccot function provides " &

                           "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;

      Float_Result      : Float;

      Angle             : Float;

      New_Float_Result  : New_Float;

      New_Float_Angle   : New_Float;

      Incorrect_Inverse : Boolean := False;

      procedure Dont_Optimize_Float     is new Dont_Optimize(Float);

      procedure Dont_Optimize_New_Float is new Dont_Optimize(New_Float);

   begin

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

      -- version.

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

      -- provided parameter values of 0.0, 0.0.

      begin

         New_Float_Result := GEF.Arccot(X => 0.0, Y => 0.0);

         Report.Failed("Argument_Error not raised when the Arccot " &

                       "function is provided input of 0.0, 0.0");

         Dont_Optimize_New_Float(New_Float_Result, 1);

      exception

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

         when others         =>

            Report.Failed("Incorrect exception raised by the Arccot " &

                          "function when provided 0.0, 0.0 input parameters");

      end;

      -- Check that no exception is raised by the Arccot function when

      -- provided a large positive or negative X parameter value, when

      -- using the default value for parameter Y.

      begin

         Float_Result := EF.Arccot(X => FXA5A00.Large);

         Dont_Optimize_Float(Float_Result, 2);

      exception

         when others =>

            Report.Failed("Exception raised when the Arccot function is " &

                          "provided a large positive X parameter value");

      end;

      begin

         New_Float_Result := GEF.Arccot(X => New_Float(-FXA5A00.Large));

         Dont_Optimize_New_Float(New_Float_Result, 3);

      exception

         when others =>

            Report.Failed("Exception raised when the Arccot function is " &

                          "provided a large negative X parameter value");

      end;

      -- Check that no exception is raised by the Arccot function when

      -- provided a small positive or negative X parameter value, when

      -- using the default value for parameter Y.

      begin

         Float_Result := EF.Arccot(X => FXA5A00.Small);

         Dont_Optimize_Float(Float_Result, 4);

      exception

         when others =>

            Report.Failed("Exception raised when the Arccot function is " &

                          "provided a small positive X parameter value");

      end;

      begin

         New_Float_Result := GEF.Arccot(X => New_Float(-FXA5A00.Small));

         Dont_Optimize_New_Float(New_Float_Result, 5);

      exception

         when others =>

            Report.Failed("Exception raised when the Arccot function is " &

                          "provided a small negative X parameter value");

      end;

      -- Check that no exception is raised by the Arccot function when

      -- provided combinations of large and small positive or negative

      -- parameter values for both X and Y input parameters.

      begin

         Float_Result := EF.Arccot(X => FXA5A00.Large, Y => FXA5A00.Large);

         Dont_Optimize_Float(Float_Result, 6);

      exception

         when others =>

            Report.Failed("Exception raised when the Arccot function is " &

                          "provided large positive X and Y parameter values");

      end;

      begin

         New_Float_Result := GEF.Arccot(New_Float(-FXA5A00.Large),

                                        Y => New_Float(FXA5A00.Small));

         Dont_Optimize_New_Float(New_Float_Result, 7);

      exception

         when others =>

            Report.Failed("Exception raised when the Arccot function is " &

                          "provided a large negative X parameter value "  &

                          "and a small positive Y parameter value");

      end;

      begin

         Float_Result := EF.Arccot(X => FXA5A00.Small, Y => FXA5A00.Large);

         Dont_Optimize_Float(Float_Result, 8);

      exception

         when others =>

            Report.Failed("Exception raised when the Arccot function is " &

                          "provided a small positive X parameter value "  &

                          "and a large positive Y parameter value");

      end;

      begin

         New_Float_Result := GEF.Arccot(New_Float(-FXA5A00.Small),

                                        New_Float(-FXA5A00.Large));

         Dont_Optimize_New_Float(New_Float_Result, 9);

      exception

         when others =>

            Report.Failed("Exception raised when the Arccot function is " &

                          "provided a small negative X parameter value "  &

                          "and a large negative Y parameter value");

      end;

      -- Check that when the Arccot function is provided a Y parameter value

      -- of 0.0 and a positive X parameter input value, the prescribed result

      -- of zero is returned.

      if  EF.Arccot(X => FXA5A00.Large, Y => 0.0)                 /= 0.0 or

         GEF.Arccot(2.0*Pi, Y => 0.0)                             /= 0.0 or

          EF.Arccot(FXA5A00.Small, 0.0)                           /= 0.0 or

          EF.Arccot(X => FXA5A00.Large, Y => 0.0, Cycle => 360.0) /= 0.0 or

         GEF.Arccot(2.0*Pi, Y => 0.0, Cycle => 360.0)             /= 0.0 or

          EF.Arccot(FXA5A00.Small, 0.0, Cycle => 360.0)           /= 0.0

      then

         Report.Failed("Incorrect results from the Arccot function when " &

                       "provided a Y parameter value of 0.0 and various " &

                       "positive X parameter values");

      end if;

      -- Check that the Arccot function provides correct results when

      -- provided a variety of X parameter values.

      if not Result_Within_Range( EF.Arccot( 1.0), Pi/4.0, 0.001)     or

         not Result_Within_Range(GEF.Arccot( 0.0), Pi/2.0, 0.001)     or

         not Result_Within_Range( EF.Arccot(-1.0), 3.0*Pi/4.0, 0.001)

      then

         Report.Failed("Incorrect results from the Arccot function when " &

                       "provided a variety of Y parameter values");

      end if;

      -- Check the results of the Arccot function with specified cycle

      -- parameter.

      -- Check that the Arccot function with specified Cycle parameter

      -- raises Argument_Error when the value of the Cycle parameter is zero

      -- or negative.

      begin

         Float_Result := EF.Arccot(X => Pi, Cycle => 0.0);  -- Default Y value

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

                       "with default Y parameter value, when the Cycle "   &

                       "parameter is 0.0");

         Dont_Optimize_Float(Float_Result, 10);

      exception

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

         when others         =>

            Report.Failed("Incorrect exception raised by the Arccot "      &

                          "function with default Y parameter value, when " &

                          "provided a 0.0 cycle parameter value");

      end;

      begin

         New_Float_Result := GEF.Arccot(X => Pi, Y => 1.0, Cycle => 0.0);

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

                       "when the Cycle parameter is 0.0");

         Dont_Optimize_New_Float(New_Float_Result, 11);

      exception

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

         when others         =>

            Report.Failed("Incorrect exception raised by the Arccot "     &

                          "function when provided a 0.0 cycle parameter " &

                          "value");

      end;

      begin

         Float_Result := EF.Arccot(X => Pi, Cycle => -360.0);

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

                       "with a default Y parameter value, when the Cycle " &

                       "parameter is -360.0");

         Dont_Optimize_Float(Float_Result, 12);

      exception

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

         when others         =>

            Report.Failed("Incorrect exception raised by the Arccot "        &

                          "function with a default Y parameter value, when " &

                          "provided a -360.0 cycle parameter value");

      end;

      begin

         New_Float_Result := GEF.Arccot(X => Pi, Y => 1.0, Cycle => -Pi);

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

                       "when the Cycle parameter is -Pi");

         Dont_Optimize_New_Float(New_Float_Result, 13);

      exception

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

         when others         =>

            Report.Failed("Incorrect exception raised by the Arccot "     &

                          "function when provided a -Pi cycle parameter " &

                          "value");

      end;

      -- Check that no exception is raised by the Arccot function with

      -- specified Cycle parameter, when provided large and small positive

      -- or negative parameter values for both X and Y input parameters.

      begin

         Float_Result := EF.Arccot(X     => -FXA5A00.Large,

                                   Y     => -FXA5A00.Large,

--pwb-math  Next line: changed 2.0*Pi to 360.0

                                   Cycle => 360.0);

         Dont_Optimize_Float(Float_Result, 14);

      exception

         when others =>

            Report.Failed("Exception raised when the Arccot function with " &

                          "specified Cycle parameter, when provided large " &

                          "negative X and Y parameter values");

      end;

      begin

         New_Float_Result := GEF.Arccot(New_Float(FXA5A00.Large),

                                        Y     => New_Float(-FXA5A00.Small),

--pwb-math  Next line: changed 2.0*Pi to 360.0

                                        Cycle => 360.0);

         Dont_Optimize_New_Float(New_Float_Result, 15);

      exception

         when others =>

            Report.Failed("Exception raised when the Arccot function with "  &

                          "specified Cycle parameter, when provided large "  &

                          "positive X parameter value and a small negative " &

                          "Y parameter value");

      end;

      begin

         Float_Result := EF.Arccot(X     => -FXA5A00.Small,

                                   Y     => -FXA5A00.Large,

--pwb-math  Next line: changed 2.0*Pi to 360.0

                                   Cycle => 360.0);

         Dont_Optimize_Float(Float_Result, 16);

      exception

         when others =>

            Report.Failed("Exception raised when the Arccot function with "  &

                          "specified Cycle parameter, when provided small "  &

                          "negative X parameter value and a large negative " &

                          "Y parameter value");

      end;

      begin

         New_Float_Result := GEF.Arccot(New_Float(FXA5A00.Small),

                                        New_Float(FXA5A00.Large),

--pwb-math  Next line: changed 2.0*Pi to 360.0

                                        360.0);

         Dont_Optimize_New_Float(New_Float_Result, 17);

      exception

         when others =>

            Report.Failed("Exception raised when the Arccot function with " &

                          "specified Cycle parameter, when provided a "     &

                          "small positive X parameter value and a large "   &

                          "positive Y parameter value");

      end;

      -- Check that the Arccot function with specified Cycle parameter

      -- provides correct results when provided a variety of X parameter

      -- input values.

      if not FXA5A00.Result_Within_Range(GEF.Arccot( 0.0, Cycle => 360.0),

                                         90.0,

                                         0.001) or

         not FXA5A00.Result_Within_Range(EF.Arccot( 0.0, Cycle => 100.0),

                                         25.0,

                                         0.001) or

         not FXA5A00.Result_Within_Range(GEF.Arccot( 1.0, Cycle => 360.0),

                                         45.0,

                                         0.001) or

         not FXA5A00.Result_Within_Range(EF.Arccot( 1.0, Cycle => 100.0),

                                         12.5,

                                         0.001) or

         not FXA5A00.Result_Within_Range(GEF.Arccot(-1.0, Cycle => 360.0),

                                         135.0,

                                         0.001) or

         not FXA5A00.Result_Within_Range(EF.Arccot(-1.0, Cycle => 100.0),

                                         37.5,

                                         0.001)

      then

         Report.Failed("Incorrect results from the Arccot function with "   &

                       "specified Cycle parameter when provided a variety " &

                       "of X parameter values");

      end if;

      if not FXA5A00.Result_Within_Range(EF.Arccot(0.2425355, 0.9701420),

                                         EF.Arccot(0.25),

                                         0.01) or

         not FXA5A00.Result_Within_Range(EF.Arccot(0.3162277, 0.9486831),

                                         Ef.Arccot(0.33),

                                         0.01)

      then

         Report.Failed("Incorrect results from the Arccot function with " &

                       "comparison to other Arccot function results");

      end if;

      if not FXA5A00.Result_Within_Range(EF.Cot(EF.Arccot(0.4472135,

                                                          0.8944270)),

                                         0.5,

                                         0.01) or

         not FXA5A00.Result_Within_Range(EF.Cot(EF.Arccot(0.9987380,

                                                          0.0499369)),

                                         20.0,

                                         0.1)

      then

         Report.Failed("Incorrect results from the Arccot function when " &

                       "used as argument to Cot function");

      end if;

      -- Check that inverse function results are correct.

      -- Default Cycle test.

      Angle := 0.001;

      while Angle < Pi and not Incorrect_Inverse loop

         if not Result_Within_Range(EF.Arccot(EF.Cot(Angle)), Angle, 0.001)

         then

            Incorrect_Inverse := True;

         end if;

         Angle := Angle + 0.001;

      end loop;

      if Incorrect_Inverse then

         Report.Failed("Incorrect results returned from the Inverse "    &

                       "comparison of Cot and Arccot using the default " &

                       "cycle value");

         Incorrect_Inverse := False;

      end if;

      -- Non-Default Cycle test.

      New_Float_Angle := 0.01;

      while New_Float_Angle < 180.0 and not Incorrect_Inverse loop

         if not Result_Within_Range(EF.Arccot(EF.Cot(Float(New_Float_Angle),

                                                     Cycle => 360.0),

                                              Cycle => 360.0),

                                    Float(New_Float_Angle),

                                    0.01)  or

            not Result_Within_Range(GEF.Arccot(

                                       New_Float(GEF.Cot(New_Float_Angle,

                                                         Cycle => 360.0)),

                                       Cycle => 360.0),

                                    Float(New_Float_Angle),

                                    0.01)

         then

            Incorrect_Inverse := True;

         end if;

         New_Float_Angle := New_Float_Angle + 0.01;

      end loop;

      if Incorrect_Inverse then

         Report.Failed("Incorrect results returned from the Inverse "    &

                       "comparison of Cot and Arccot using non-default " &

                       "cycle value");

      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 CXA5A08;