-- CXA5A10.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 functions Exp and Sqrt, and the exponentiation -- operator "**" provide correct results. -- -- TEST DESCRIPTION: -- This test examines both the versions of Exp, Sqrt, and "**" -- 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 (stated as such in the reference manual), -- including instances prescribed to raise exceptions, are examined -- in the test cases. In addition, certain evaluations are performed -- for the preinstantiated package 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) -- CXA5A10.A -- -- -- CHANGE HISTORY: -- 17 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. -- 01 Oct 01 RLB Protected Constraint_Error exception tests by -- first testing for 'Machine_Overflows. -- --! with Ada.Exceptions; with Ada.Numerics.Elementary_Functions; with Ada.Numerics.Generic_Elementary_Functions; with FXA5A00; with Report; procedure CXA5A10 is begin Report.Test ("CXA5A10", "Check that Exp, Sqrt, and the ""**"" operator " & "provide correct results"); Test_Block: declare use FXA5A00, Ada.Numerics; use Ada.Exceptions; package GEF is new Ada.Numerics.Generic_Elementary_Functions(New_Float); package EF renames Ada.Numerics.Elementary_Functions; use GEF, EF; Arg, Float_Result : Float; New_Float_Result : New_Float; Flag_1, Flag_2, Flag_3, Flag_4, Incorrect_Inverse_Base_e, Incorrect_Inverse_Base_2, Incorrect_Inverse_Base_8, Incorrect_Inverse_Base_10, Incorrect_Inverse_Base_16 : 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 the "**" operator, both instantiated and pre-instantiated -- version. -- Check that Argument_Error is raised by the exponentiation operator -- when the value of the Left parameter (operand) is negative. begin New_Float_Result := GEF."**"(Left => -10.0, Right => 2.0); Report.Failed("Argument_Error not raised by the instantiated " & "version of the exponentiation operator when the " & "value of the Left parameter is negative"); Dont_Optimize_New_Float(New_Float_Result, 1); exception when Argument_Error => null; -- OK, expected exception. when others => Report.Failed("Unexpected exception raised by the " & "instantiated version of the exponentiation " & "operator when the value of the Left parameter " & "is negative"); end; begin Float_Result := (-FXA5A00.Small) ** 4.0; Report.Failed("Argument_Error not raised by the preinstantiated " & "version of the exponentiation operator when the " & "value of the Left parameter is negative"); Dont_Optimize_Float(Float_Result, 2); exception when Argument_Error => null; -- OK, expected exception. when others => Report.Failed("Unexpected exception raised by the " & "preinstantiated version of the exponentiation " & "operator when the value of the Left parameter " & "is negative"); end; -- Check that Argument_Error is raised by the exponentiation operator -- when both parameters (operands) have the value 0.0. begin New_Float_Result := GEF."**"(0.0, Right => 0.0); Report.Failed("Argument_Error not raised by the instantiated " & "version of the exponentiation operator when " & "both operands are zero"); Dont_Optimize_New_Float(New_Float_Result, 3); exception when Argument_Error => null; -- OK, expected exception. when others => Report.Failed("Unexpected exception raised by the " & "instantiated version of the exponentiation " & "operator when both operands are zero"); end; begin Float_Result := 0.0**0.0; Report.Failed("Argument_Error not raised by the preinstantiated " & "version of the exponentiation operator when both " & "operands are zero"); Dont_Optimize_Float(Float_Result, 4); exception when Argument_Error => null; -- OK, expected exception. when others => Report.Failed("Unexpected exception raised by the " & "preinstantiated version of the exponentiation " & "operator when both operands are zero"); end; -- Check that Constraint_Error is raised by the exponentiation -- operator when the value of the left parameter (operand) is zero, -- and the value of the right parameter (exponent) is negative. -- This check applies only if Machine_Overflows is true [A.5.1(28, 30)]. if New_Float'Machine_Overflows = True then begin New_Float_Result := GEF."**"(0.0, Right => -2.0); Report.Failed("Constraint_Error not raised by the instantiated " & "version of the exponentiation operator when " & "the left parameter is 0.0, and the right " & "parameter is negative"); Dont_Optimize_New_Float(New_Float_Result, 5); exception when Constraint_Error => null; -- OK, expected exception. when others => Report.Failed("Unexpected exception raised by the " & "instantiated version of the exponentiation " & "operator when the left parameter is 0.0, " & "and the right parameter is negative"); end; end if; if Float'Machine_Overflows = True then begin Float_Result := 0.0 ** (-FXA5A00.Small); Report.Failed("Constraint_Error not raised by the " & "preinstantiated version of the exponentiation " & "operator when the left parameter is 0.0, and the " & "right parameter is negative"); Dont_Optimize_Float(Float_Result, 6); exception when Constraint_Error => null; -- OK, expected exception. when others => Report.Failed("Unexpected exception raised by the " & "preinstantiated version of the exponentiation " & "operator when the left parameter is 0.0, and " & "the right parameter is negative"); end; end if; -- Prescribed results. -- Check that exponentiation by a 0.0 exponent yields the value one. if GEF."**"(Left => 10.0, Right => 0.0) /= 1.0 or EF."**"(FXA5A00.Large, Right => 0.0) /= 1.0 or GEF."**"(3.0, 0.0) /= 1.0 or FXA5A00.Small ** 0.0 /= 1.0 then Report.Failed("Incorrect results returned from the ""**"" " & "operator when the value of the exponent is 0.0"); end if; -- Check that exponentiation by a unit exponent yields the value -- of the left operand. if GEF."**"(Left => 50.0, Right => 1.0) /= 50.0 or EF."**"(FXA5A00.Large, Right => 1.0) /= FXA5A00.Large or GEF."**"(6.0, 1.0) /= 6.0 or FXA5A00.Small ** 1.0 /= FXA5A00.Small then Report.Failed("Incorrect results returned from the ""**"" " & "operator when the value of the exponent is 1.0"); end if; -- Check that exponentiation of the value 1.0 yields the value 1.0. if GEF."**"(Left => 1.0, Right => 16.0) /= 1.0 or EF."**"(1.0, Right => FXA5A00.Large) /= 1.0 or GEF."**"(1.0, 3.0) /= 1.0 or 1.0 ** FXA5A00.Small /= 1.0 then Report.Failed("Incorrect results returned from the ""**"" " & "operator when the value of the operand is 1.0"); end if; -- Check that exponentiation of the value 0.0 yields the value 0.0. if GEF."**"(Left => 0.0, Right => 10.0) /= 0.0 or EF."**"(0.0, Right => FXA5A00.Large) /= 0.0 or GEF."**"(0.0, 4.0) /= 0.0 or 0.0 ** FXA5A00.Small /= 0.0 then Report.Failed("Incorrect results returned from the ""**"" " & "operator when the value of the operand is 0.0"); end if; -- Check that exponentiation of various operands with a variety of -- of exponent values yield correct results. if not Result_Within_Range(GEF."**"(5.0, 2.0), 25.0, 0.01) or not Result_Within_Range(GEF."**"(1.225, 1.5), 1.36, 0.01) or not Result_Within_Range(GEF."**"(0.26, 2.0), 0.068, 0.001) or not Result_Within_Range( EF."**"(e, 5.0), 148.4, 0.1) or not Result_Within_Range( EF."**"(10.0, e), 522.7, 0.1) or not Result_Within_Range( EF."**"(e, (-3.0)), 0.050, 0.001) or not Result_Within_Range(GEF."**"(10.0,(-2.0)), 0.010, 0.001) then Report.Failed("Incorrect results returned from the ""**"" " & "operator with a variety of operand and exponent " & "values"); end if; -- Use the following loops to check for internal consistency between -- inverse functions. declare -- Use the relative error value to account for non-exact -- computations. TC_Relative_Error: Float := 0.005; begin for i in 1..5 loop for j in 0..5 loop if not Incorrect_Inverse_Base_e and not FXA5A00.Result_Within_Range (Float(i)**Float(j), e**(Float(j)*EF.Log(Float(i))), TC_Relative_Error) then Incorrect_Inverse_Base_e := True; Report.Failed("Incorrect Log-** Inverse calc for Base e " & "with i= " & Integer'Image(i) & " and j= " & Integer'Image(j)); end if; if not Incorrect_Inverse_Base_2 and not FXA5A00.Result_Within_Range (Float(i)**Float(j), 2.0**(Float(j)*EF.Log(Float(i),2.0)), TC_Relative_Error) then Incorrect_Inverse_Base_2 := True; Report.Failed("Incorrect Log-** Inverse calc for Base 2 " & "with i= " & Integer'Image(i) & " and j= " & Integer'Image(j)); end if; if not Incorrect_Inverse_Base_8 and not FXA5A00.Result_Within_Range (Float(i)**Float(j), 8.0**(Float(j)*EF.Log(Float(i),8.0)), TC_Relative_Error) then Incorrect_Inverse_Base_8 := True; Report.Failed("Incorrect Log-** Inverse calc for Base 8 " & "with i= " & Integer'Image(i) & " and j= " & Integer'Image(j)); end if; if not Incorrect_Inverse_Base_10 and not FXA5A00.Result_Within_Range (Float(i)**Float(j), 10.0**(Float(j)*EF.Log(Float(i),10.0)), TC_Relative_Error) then Incorrect_Inverse_Base_10 := True; Report.Failed("Incorrect Log-** Inverse calc for Base 10 " & "with i= " & Integer'Image(i) & " and j= " & Integer'Image(j)); end if; if not Incorrect_Inverse_Base_16 and not FXA5A00.Result_Within_Range (Float(i)**Float(j), 16.0**(Float(j)*EF.Log(Float(i),16.0)), TC_Relative_Error) then Incorrect_Inverse_Base_16 := True; Report.Failed("Incorrect Log-** Inverse calc for Base 16 " & "with i= " & Integer'Image(i) & " and j= " & Integer'Image(j)); end if; end loop; end loop; end; -- Reset Flags. Incorrect_Inverse_Base_e := False; Incorrect_Inverse_Base_2 := False; Incorrect_Inverse_Base_8 := False; Incorrect_Inverse_Base_10 := False; Incorrect_Inverse_Base_16 := False; -- Testing of Exp Function, both instantiated and pre-instantiated -- version. -- Check that the result of the Exp Function, when provided an X -- parameter value of 0.0, is 1.0. if GEF.Exp(X => 0.0) /= 1.0 or EF.Exp(0.0) /= 1.0 then Report.Failed("Incorrect result returned by Function Exp when " & "given a parameter value of 0.0"); end if; -- Check that the Exp Function provides correct results when provided -- a variety of input parameter values. if not Result_Within_Range(GEF.Exp(0.001), 1.01, 0.01) or not Result_Within_Range( EF.Exp(0.1), 1.11, 0.01) or not Result_Within_Range(GEF.Exp(1.2697), 3.56, 0.01) or not Result_Within_Range( EF.Exp(3.2525), 25.9, 0.1) or not Result_Within_Range(GEF.Exp(-0.2198), 0.803, 0.001) or not Result_Within_Range( EF.Exp(-1.6621), 0.190, 0.001) or not Result_Within_Range(GEF.Exp(-2.3888), 0.092, 0.001) or not Result_Within_Range( EF.Exp(-5.4415), 0.004, 0.001) then Report.Failed("Incorrect result from Function Exp when provided " & "a variety of input parameter values"); end if; -- Use the following loops to check for internal consistency between -- inverse functions. Arg := 0.01; while Arg < 10.0 loop if not Incorrect_Inverse_Base_e and FXA5A00.Result_Within_Range(EF.Exp(Arg), e**(Arg*EF.Log(Arg)), 0.001) then Incorrect_Inverse_Base_e := True; Report.Failed("Incorrect Exp-** Inverse calc for Base e"); end if; if not Incorrect_Inverse_Base_2 and FXA5A00.Result_Within_Range(EF.Exp(Arg), 2.0**(Arg*EF.Log(Arg,2.0)), 0.001) then Incorrect_Inverse_Base_2 := True; Report.Failed("Incorrect Exp-** Inverse calc for Base 2"); end if; if not Incorrect_Inverse_Base_8 and FXA5A00.Result_Within_Range(EF.Exp(Arg), 8.0**(Arg*EF.Log(Arg,8.0)), 0.001) then Incorrect_Inverse_Base_8 := True; Report.Failed("Incorrect Exp-** Inverse calc for Base 8"); end if; if not Incorrect_Inverse_Base_10 and FXA5A00.Result_Within_Range(EF.Exp(Arg), 10.0**(Arg*EF.Log(Arg,10.0)), 0.001) then Incorrect_Inverse_Base_10 := True; Report.Failed("Incorrect Exp-** Inverse calc for Base 10"); end if; if not Incorrect_Inverse_Base_16 and FXA5A00.Result_Within_Range(EF.Exp(Arg), 16.0**(Arg*EF.Log(Arg,16.0)), 0.001) then Incorrect_Inverse_Base_16 := True; Report.Failed("Incorrect Exp-** Inverse calc for Base 16"); end if; Arg := Arg + 0.01; end loop; -- Testing of Sqrt Function, both instantiated and pre-instantiated -- version. -- Check that Argument_Error is raised by the Sqrt Function when -- the value of the input parameter X is negative. begin Float_Result := EF.Sqrt(X => -FXA5A00.Small); Report.Failed("Argument_Error not raised by Function Sqrt " & "when provided a small negative input parameter " & "value"); Dont_Optimize_Float(Float_Result, 7); exception when Argument_Error => null; -- OK, expected exception. when others => Report.Failed("Unexpected exception raised by Function Sqrt " & "when provided a small negative input parameter " & "value"); end; begin New_Float_Result := GEF.Sqrt(X => -64.0); Report.Failed("Argument_Error not raised by Function Sqrt " & "when provided a large negative input parameter " & "value"); Dont_Optimize_New_Float(New_Float_Result, 8); exception when Argument_Error => null; -- OK, expected exception. when others => Report.Failed("Unexpected exception raised by Function Sqrt " & "when provided a large negative input parameter " & "value"); end; -- Check that the Sqrt Function, when given an X parameter value of 0.0, -- returns a result of 0.0. if GEF.Sqrt(X => 0.0) /= 0.0 or EF.Sqrt(0.0) /= 0.0 then Report.Failed("Incorrect result from Function Sqrt when provided " & "an input parameter value of 0.0"); end if; -- Check that the Sqrt Function, when given an X parameter input value -- of 1.0, returns a result of 1.0. if GEF.Sqrt(X => 1.0) /= 1.0 or EF.Sqrt(1.0) /= 1.0 then Report.Failed("Incorrect result from Function Sqrt when provided " & "an input parameter value of 1.0"); end if; -- Check that the Sqrt Function provides correct results when provided -- a variety of input parameter values. if not FXA5A00.Result_Within_Range(GEF.Sqrt(0.0327), 0.181, 0.001) or not FXA5A00.Result_Within_Range( EF.Sqrt(0.1808), 0.425, 0.001) or not FXA5A00.Result_Within_Range(GEF.Sqrt(1.0556), 1.03, 0.01) or not FXA5A00.Result_Within_Range( EF.Sqrt(32.8208), 5.73, 0.01) or not FXA5A00.Result_Within_Range( EF.Sqrt(27851.0), 166.9, 0.1) or not FXA5A00.Result_Within_Range( EF.Sqrt(61203.4), 247.4, 0.1) or not FXA5A00.Result_Within_Range( EF.Sqrt(655891.0), 809.9, 0.1) then Report.Failed("Incorrect result from Function Sqrt when provided " & "a variety of input parameter values"); end if; -- Check internal consistency between functions. Arg := 0.01; while Arg < 10.0 loop if not Flag_1 and not FXA5A00.Result_Within_Range(Arg, EF.Sqrt(Arg)*EF.Sqrt(Arg), 0.01) then Report.Failed("Inconsistency found in Case 1"); Flag_1 := True; end if; if not Flag_2 and not FXA5A00.Result_Within_Range(Arg, EF.Sqrt(Arg)**2.0, 0.01) then Report.Failed("Inconsistency found in Case 2"); Flag_2 := True; end if; if not Flag_3 and not FXA5A00.Result_Within_Range(EF.Log(Arg), EF.Log(Sqrt(Arg)**2.0), 0.01) then Report.Failed("Inconsistency found in Case 3"); Flag_3 := True; end if; if not Flag_4 and not FXA5A00.Result_Within_Range(EF.Log(Arg), 2.00*EF.Log(EF.Sqrt(Arg)), 0.01) then Report.Failed("Inconsistency found in Case 4"); Flag_4 := True; end if; Arg := Arg + 1.0; end loop; 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 CXA5A10;