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-- CXG2007.A

--

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--     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 complex Compose_From_Polar function returns

--      results that are within the error bound allowed.

--      Check that Argument_Error is raised if the Cycle parameter

--      is less than or equal to zero.

--

-- TEST DESCRIPTION:

--      This test uses a generic package to compute and check the

--      values of the Compose_From_Polar function.

--

-- SPECIAL REQUIREMENTS

--      The Strict Mode for the numerical accuracy must be

--      selected.  The method by which this mode is selected

--      is implementation dependent.

--

-- APPLICABILITY CRITERIA:

--      This test applies only to implementations supporting the

--      Numerics Annex.

--      This test only applies to the Strict Mode for numerical

--      accuracy.

--

--

-- CHANGE HISTORY:

--      23 FEB 96   SAIC    Initial release for 2.1

--      23 APR 96   SAIC    Fixed error checking

--      03 MAR 97   PWB.CTA Deleted 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 System;

with Report;

with Ada.Numerics;

with Ada.Numerics.Generic_Complex_Types;

procedure CXG2007 is

   Verbose : constant Boolean := False;

   -- CRC Standard Mathematical Tables;  23rd Edition; pg 738

   Sqrt2 : constant :=

        1.41421_35623_73095_04880_16887_24209_69807_85696_71875_37695;

   Sqrt3 : constant :=

        1.73205_08075_68877_29352_74463_41505_87236_69428_05253_81039;

   Pi : constant := Ada.Numerics.Pi;

   generic

      type Real is digits <>;

   package Generic_Check is

      procedure Do_Test;

   end Generic_Check;

   package body Generic_Check is

      package Complex_Types is new

           Ada.Numerics.Generic_Complex_Types (Real);

      use Complex_Types;

      Maximum_Relative_Error : constant Real := 3.0;

      procedure Check (Actual, Expected : Real;

                       Test_Name : String;

                       MRE : Real;

                       Arg_Error : Real) is

         -- Arg_Error is additional absolute error that is allowed beyond

         -- the MRE to account for error in the result that can be

         -- attributed to error in the arguments.

         Max_Error : Real;

         Rel_Error : Real;

         Abs_Error : Real;

      begin

         -- In the case where the expected result is very small or 0

         -- we compute the maximum error as a multiple of Model_Small instead

         -- of Model_Epsilon and Expected.

         Rel_Error := MRE * abs Expected * Real'Model_Epsilon;

         Abs_Error := MRE * Real'Model_Epsilon;

         if Rel_Error > Abs_Error then

            Max_Error := Rel_Error;

         else

            Max_Error := Abs_Error;

         end if;

         Max_Error := Max_Error + Arg_Error;

         if abs (Actual - Expected) > Max_Error then

            Report.Failed (Test_Name &

                           " actual: " & Real'Image (Actual) &

                           " expected: " & Real'Image (Expected) &

                           " difference: " & Real'Image (Actual - Expected) &

                           " max err:" & Real'Image (Max_Error) );

         elsif Verbose then

            if Actual = Expected then

               Report.Comment (Test_Name & "  exact result");

            else

               Report.Comment (Test_Name & "  passed");

            end if;

         end if;

      end Check;

      procedure Check (Actual, Expected : Complex;

                       Test_Name : String;

                       MRE : Real;

                       Arg_Error : Real) is

         -- Arg_Error is additional absolute error that is allowed beyond

         -- the MRE to account for error in the result that can be

         -- attributed to error in the arguments.

      begin

         Check (Actual.Re, Expected.Re,

                Test_Name & " real part",

                MRE, Arg_Error);

         Check (Actual.Im, Expected.Im,

                Test_Name & " imaginary part",

                MRE, Arg_Error);

      end Check;

      procedure Special_Cases is

         type Data_Point is

            record

               Re,

               Im,

               Modulus,

               Radians,

               Degrees,

               Arg_Error : Real;

            end record;

         -- shorthand names for various constants

         P4 : constant := Pi/4.0;

         P6 : constant := Pi/6.0;

         MER2 : constant Real := Real'Model_Epsilon * Sqrt2;

         type Test_Data_Type is array (Positive range <>) of Data_Point;

         -- the values in the following table only involve static

         -- expressions so no loss of precision occurs.

         Test_Data : constant Test_Data_Type := (

         --Re          Im   Modulus     Radians  Degrees  Arg_Err

         ( 0.0,        0.0, 0.0,            0.0,   0.0,    0.0 ),    -- 1

         ( 0.0,        0.0, 0.0,             Pi, 180.0,    0.0 ),    -- 2

         ( 1.0,        0.0, 1.0,            0.0,   0.0,    0.0 ),    -- 3

         (-1.0,        0.0, -1.0,           0.0,   0.0,    0.0 ),    -- 4

         ( 1.0,        1.0,  Sqrt2,          P4,  45.0,    MER2),    -- 5

         (-1.0,        1.0, -Sqrt2,         -P4, -45.0,    MER2),    -- 6

         ( 1.0,       -1.0,  Sqrt2,         -P4, -45.0,    MER2),    -- 7

         (-1.0,       -1.0, -Sqrt2,          P4,  45.0,    MER2),    -- 8

         (-1.0,       -1.0,  Sqrt2,     -3.0*P4,-135.0,    MER2),    -- 9

         (-1.0,        1.0,  Sqrt2,      3.0*P4, 135.0,    MER2),    -- 10

         ( 1.0,       -1.0, -Sqrt2,      3.0*P4, 135.0,    MER2),    -- 11

         (-1.0,        0.0, 1.0,             Pi, 180.0,    0.0 ),    -- 12

         ( 1.0,        0.0, -1.0,            Pi, 180.0,    0.0 ) );  -- 13

         Z : Complex;

         Exp : Complex;

      begin

         for I in Test_Data'Range loop

            begin

               Exp := (Test_Data (I).Re, Test_Data (I).Im);

               Z := Compose_From_Polar (Test_Data (I).Modulus,

                                        Test_Data (I).Radians);

               Check (Z, Exp,

                 "test" & Integer'Image (I) & " compose_from_polar(m,r)",

                 Maximum_Relative_Error, Test_Data (I).Arg_Error);

--pwb-math               Z := Compose_From_Polar (Test_Data (I).Modulus,

--pwb-math                                      Test_Data (I).Radians,

--pwb-math                                      2.0*Pi);

--pwb-math             Check (Z, Exp,

--pwb-math                 "test" & Integer'Image (I) & " compose_from_polar(m,r,2pi)",

--pwb-math               Maximum_Relative_Error, Test_Data (I).Arg_Error);

               Z := Compose_From_Polar (Test_Data (I).Modulus,

                                        Test_Data (I).Degrees,

                                        360.0);

               Check (Z, Exp,

                 "test" & Integer'Image (I) & " compose_from_polar(m,d,360)",

                 Maximum_Relative_Error, Test_Data (I).Arg_Error);

            exception

               when Constraint_Error =>

                  Report.Failed ("Constraint_Error raised in test" &

                      Integer'Image (I));

               when others =>

                  Report.Failed ("exception in test" &

                      Integer'Image (I));

            end;

         end loop;

      end Special_Cases;

      procedure Exception_Cases is

      -- check that Argument_Error is raised if Cycle is <= 0

         Z : Complex;

         W : Complex;

      begin

         begin

           Z := Compose_From_Polar (3.0, 0.0, Cycle => 0.0);

           Report.Failed ("no exception for cycle = 0.0");

         exception

            when Ada.Numerics.Argument_Error => null;

            when others =>

               Report.Failed ("wrong exception for cycle = 0.0");

         end;

         begin

           W := Compose_From_Polar (6.0, 1.0, Cycle => -10.0);

           Report.Failed ("no exception for cycle < 0.0");

         exception

            when Ada.Numerics.Argument_Error => null;

            when others =>

               Report.Failed ("wrong exception for cycle < 0.0");

         end;

         if Report.Ident_Int (1) = 2 then

             -- not executed - used to make it appear that we use the

             -- results of the above computation

             Z := Z * W;

             Report.Failed(Real'Image (Z.Re + Z.Im));

         end if;

      end Exception_Cases;

      procedure Do_Test is

      begin

         Special_Cases;

         Exception_Cases;

      end Do_Test;

   end Generic_Check;

   package Chk_Float is new Generic_Check (Float);

   -- check the floating point type with the most digits

   type A_Long_Float is digits System.Max_Digits;

   package Chk_A_Long_Float is new Generic_Check (A_Long_Float);

begin

   Report.Test ("CXG2007",

                "Check the accuracy of the Compose_From_Polar" &

                " function");

   if Verbose then

      Report.Comment ("checking Standard.Float");

   end if;

   Chk_Float.Do_Test;

   if Verbose then

      Report.Comment ("checking a digits" &

                      Integer'Image (System.Max_Digits) &

                      " floating point type");

   end if;

   Chk_A_Long_Float.Do_Test;

   Report.Result;

end CXG2007;