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-- CXG2006.A

--

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--     F08630-91-C-0015, and DCA100-97-D-0025, the U.S. Government obtained

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--     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 Argument 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 Argument function.

--      Of special interest is the case where either the real or

--      the imaginary part of the parameter is very large while the

--      other part is very small or 0.

--

-- 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:

--      15 FEB 96   SAIC    Initial release for 2.1

--      03 MAR 97   PWB.CTA Removed checks involving 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

--!

--

-- Reference:

-- Problems and Methodologies in Mathematical Software Production;

-- editors: P. C. Messina and A Murli;

-- Lecture Notes in Computer Science

-- Volume 142

-- Springer Verlag 1982

--

with System;

with Report;

with ImpDef.Annex_G;

with Ada.Numerics;

with Ada.Numerics.Generic_Complex_Types;

with Ada.Numerics.Complex_Types;

procedure CXG2006 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;

      procedure Check (Actual, Expected : Real;

                       Test_Name : String;

                       MRE : Real) is

         Rel_Error : Real;

         Abs_Error : Real;

         Max_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_Epsilon 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;

         if abs (Actual - Expected) > Max_Error then

            Report.Failed (Test_Name &

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

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

                           " difference: " &

                           Real'Image (Actual - Expected) &

                           " mre:" & 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 Special_Cases is

         type Data_Point is

            record

               Re,

               Im,

               Radians,

               Degrees,

               Error_Bound   : Real;

            end record;

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

         -- the values in the following table only involve static

         -- expressions to minimize errors in precision introduced by the

         -- test.  For cases where Pi is used in the argument we must

         -- allow an extra 1.0*MRE to account for roundoff error in the

         -- argument.  Where the result involves a square root we allow

         -- an extra 0.5*MRE to allow for roundoff error.

         Test_Data : constant Test_Data_Type := (

--    Re               Im                     Radians  Degrees  Err    Test #

    (0.0,               0.0,                       0.0,   0.0,  4.0 ),  -- 1

    (1.0,               0.0,                       0.0,   0.0,  4.0 ),  -- 2

    (Real'Safe_Last,    0.0,                       0.0,   0.0,  4.0 ),  -- 3

    (Real'Model_Small,  0.0,                       0.0,   0.0,  4.0 ),  -- 4

    (1.0,               1.0,                    Pi/4.0,  45.0,  5.0 ),  -- 5

    (1.0,              -1.0,                   -Pi/4.0, -45.0,  5.0 ),  -- 6

    (-1.0,             -1.0,               -3.0*Pi/4.0,-135.0,  5.0 ),  -- 7

    (-1.0,              1.0,                3.0*Pi/4.0, 135.0,  5.0 ),  -- 8

    (Sqrt3,             1.0,                    Pi/6.0,  30.0,  5.5 ),  -- 9

    (-Sqrt3,            1.0,                5.0*Pi/6.0, 150.0,  5.5 ),  -- 10

    (Sqrt3,            -1.0,                   -Pi/6.0, -30.0,  5.5 ),  -- 11

    (-Sqrt3,           -1.0,               -5.0*Pi/6.0,-150.0,  5.5 ),  -- 12

    (Real'Model_Small,  Real'Model_Small,       Pi/4.0,  45.0,  5.0 ),  -- 13

    (-Real'Safe_Last,   0.0,                        Pi, 180.0,  5.0 ),  -- 14

    (-Real'Safe_Last,  -Real'Model_Small,          -Pi,-180.0,  5.0 ),  -- 15

    (100000.0,          100000.0,               Pi/4.0,  45.0,  5.0 )); -- 16

         X : Real;

         Z : Complex;

      begin

         for I in Test_Data'Range loop

            begin

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

               X := Argument (Z);

               Check (X, Test_Data(I).Radians,

                   "test" & Integer'Image (I) & " argument(z)",

                   Test_Data (I).Error_Bound);

--pwb-math               X := Argument (Z, 2.0*Pi);

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

--pwb-math                   "test" & Integer'Image (I) & " argument(z, 2pi)",

--pwb-math                   Test_Data (I).Error_Bound);

               X := Argument (Z, 360.0);

               Check (X, Test_Data(I).Degrees,

                   "test" & Integer'Image (I) & " argument(z, 360)",

                   Test_Data (I).Error_Bound);

            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;

         if Real'Signed_Zeros then

            begin

              X := Argument ((-1.0, Real(ImpDef.Annex_G.Negative_Zero)));

              Check (X, -Pi, "test of arg((-1,-0)", 4.0);

            exception

               when others =>

                  Report.Failed ("exception in signed zero test");

            end;

         end if;

      end Special_Cases;

      procedure Exception_Cases is

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

         Z : Complex := (1.0, 1.0);

         X : Real;

         Y : Real;

      begin

         begin

           X := Argument (Z, 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

           Y := Argument (Z, Cycle => -3.0);

           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 (2) = 1 then

            -- optimization thwarting code - never executed

            Report.Failed("2=1" & Real'Image (X+Y));

         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 ("CXG2006",

                "Check the accuracy of the complex argument" &

                " 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 CXG2006;