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-- CXA5A10.A

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--                                    DISCLAIMER

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--     ALL MATERIALS OR INFORMATION HEREIN RELEASED, MADE AVAILABLE OR

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

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--     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;