-- 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;