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--- CXA5A08.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 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;