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-- CXG2019.A

--

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--*

--

-- OBJECTIVE:

--      Check that the complex LOG function returns

--      a result that is within the error bound allowed.

--

-- TEST DESCRIPTION:

--      This test consists of a generic package that is

--      instantiated to check complex numbers based upon

--      both Float and a long float type.

--      The test for each floating point type is divided into

--      several parts:

--         Special value checks where the result is a known constant.

--         Checks that use an identity for determining the result.

--         Exception conditions.

--

-- 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:

--      22 Mar 96   SAIC    Initial release for 2.1

--

--!

--

-- References:

--

-- W. J. Cody

-- CELEFUNT: A Portable Test Package for Complex Elementary Functions

-- Algorithm 714, Collected Algorithms from ACM.

-- Published in Transactions On Mathematical Software,

-- Vol. 19, No. 1, March, 1993, pp. 1-21.

--

-- CRC Standard Mathematical Tables

-- 23rd Edition

--

with System;

with Report;

with Ada.Numerics.Generic_Complex_Types;

with Ada.Numerics.Generic_Complex_Elementary_Functions;

procedure CXG2019 is

   Verbose : constant Boolean := False;

   -- Note that Max_Samples is the number of samples taken in

   -- both the real and imaginary directions.  Thus, for Max_Samples

   -- of 100 the number of values checked is 10000.

   Max_Samples : constant := 100;

   E  : constant := Ada.Numerics.E;

   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_Type is new

           Ada.Numerics.Generic_Complex_Types (Real);

      use Complex_Type;

      package CEF is new

           Ada.Numerics.Generic_Complex_Elementary_Functions (Complex_Type);

      function Log (X : Complex) return Complex renames CEF.Log;

      -- flag used to terminate some tests early

      Accuracy_Error_Reported : Boolean := False;

      procedure Check (Actual, Expected : Real;

                       Test_Name : String;

                       MRE : Real) is

         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;

         if abs (Actual - Expected) > Max_Error then

            Accuracy_Error_Reported := True;

            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) is

      begin

         Check (Actual.Re, Expected.Re, Test_Name & " real part", MRE);

         Check (Actual.Im, Expected.Im, Test_Name & " imaginary part", MRE);

      end Check;

      procedure Special_Value_Test is

         -- In the following tests the expected result is accurate

         -- to the machine precision so the minimum guaranteed error

         -- bound can be used if the argument is exact.

         --

         -- When using pi there is an extra error of 1.0ME.

         -- Although the real component has an error bound of 13.0,

         -- the complex component must take into account this error

         -- in the value for Pi.

         --

         -- One or i is added to the actual and expected results in

         -- order to prevent the expected result from having a

         -- real or imaginary part of 0.  This is to allow a reasonable

         -- relative error for that component.

         Minimum_Error : constant := 13.0;

      begin

         Check (1.0 + Log (0.0 + i),

                1.0 + Pi / 2.0 * i,

                "1+log(0+i)",

                Minimum_Error + 1.0);

         Check (1.0 + Log ((-1.0, 0.0)),

                1.0 + (Pi * i),

                "log(-1+0i)+1 ",

                Minimum_Error + 1.0);

      exception

         when Constraint_Error =>

            Report.Failed ("Constraint_Error raised in special value test");

         when others =>

            Report.Failed ("exception in special value test");

      end Special_Value_Test;

      procedure Exact_Result_Test is

         No_Error : constant := 0.0;

      begin

         -- G.1.2(37);6.0

         Check (Log(1.0 + 0.0*i),  0.0 + 0.0 * i, "log(1+0i)", No_Error);

      exception

         when Constraint_Error =>

            Report.Failed ("Constraint_Error raised in Exact_Result Test");

         when others =>

            Report.Failed ("exception in Exact_Result Test");

      end Exact_Result_Test;

      procedure Identity_Test (RA, RB, IA, IB : Real) is

      -- Tests an identity over a range of values specified

      -- by the 4 parameters.  RA and RB denote the range for the

      -- real part while IA and IB denote the range for the

      -- imaginary part.

      --

      -- For this test we use the identity

      --    Log(Z*Z) = 2 * Log(Z)

      --

         Scale : Real := Real (Real'Machine_Radix) ** (Real'Mantissa / 2 + 4);

         W, X, Y, Z : Real;

         CX, CY : Complex;

         Actual1, Actual2 : Complex;

      begin

         Accuracy_Error_Reported := False;  -- reset

         for II in 1..Max_Samples loop

            X :=  (RB - RA) * Real (II) / Real (Max_Samples) + RA;

            for J in 1..Max_Samples loop

               Y :=  (IB - IA) * Real (J) / Real (Max_Samples) + IA;

               -- purify the arguments to minimize roundoff error.

               -- We construct the values so that the products X*X,

               -- Y*Y, and X*Y are all exact machine numbers.

               -- See Cody page 7 and CELEFUNT code.

               Z := X * Scale;

               W := Z + X;

               X := W - Z;

               Z := Y * Scale;

               W := Z + Y;

               Y := W - Z;

               CX := Compose_From_Cartesian(X,Y);

               Z := X*X - Y*Y;

               W := X*Y;

               CY := Compose_From_Cartesian(Z,W+W);

               -- The arguments are now ready so on with the

               -- identity computation.

               Actual1 := Log(CX);

               Actual2 := Log(CY) * 0.5;

               Check (Actual1, Actual2,

                      "Identity_1_Test " & Integer'Image (II) &

                         Integer'Image (J) & ": Log((" &

                         Real'Image (CX.Re) & ", " &

                         Real'Image (CX.Im) & ")) ",

                      26.0);   -- 2 logs = 2*13.  no error from this multiply

               if Accuracy_Error_Reported then

                 -- only report the first error in this test in order to keep

                 -- lots of failures from producing a huge error log

                 return;

               end if;

            end loop;

         end loop;

      exception

         when Constraint_Error =>

            Report.Failed

               ("Constraint_Error raised in Identity_Test" &

                " for X=(" & Real'Image (X) &

                ", " & Real'Image (X) & ")");

         when others =>

            Report.Failed ("exception in Identity_Test" &

                " for X=(" & Real'Image (X) &

                ", " & Real'Image (X) & ")");

      end Identity_Test;

      procedure Exception_Test is

      -- Check that log((0,0)) causes constraint_error.

      -- G.1.2(29);

         X : Complex := (0.0, 0.0);

      begin

         if not Real'Machine_Overflows then

            -- not applicable:   G.1.2(28);6.0

            return;

         end if;

         begin

            X := Log ((0.0, 0.0));

            Report.Failed ("exception not raised for log(0,0)");

         exception

            when Constraint_Error => null;  -- ok

            when others =>

               Report.Failed ("wrong exception raised for log(0,0)");

         end;

         -- optimizer thwarting

         if Report.Ident_Bool(False) then

            Report.Comment (Real'Image (X.Re + X.Im));

         end if;

      end Exception_Test;

      procedure Do_Test is

      begin

         Special_Value_Test;

         Exact_Result_Test;

            -- test regions that do not include the unit circle so that

            -- the real part of LOG(Z) does not vanish

            -- See Cody page 9.

         Identity_Test (   2.0,   10.0,       0.0,    10.0);

         Identity_Test (1000.0, 2000.0,   -4000.0, -1000.0);

         Identity_Test (Real'Model_Epsilon, 0.25,

                        -0.25,              -Real'Model_Epsilon);

         Exception_Test;

      end Do_Test;

   end Generic_Check;

   -----------------------------------------------------------------------

   -----------------------------------------------------------------------

   package Float_Check is new Generic_Check (Float);

   -- check the floating point type with the most digits

   type A_Long_Float is digits System.Max_Digits;

   package A_Long_Float_Check is new Generic_Check (A_Long_Float);

   -----------------------------------------------------------------------

   -----------------------------------------------------------------------

begin

   Report.Test ("CXG2019",

                "Check the accuracy of the complex LOG function");

   if Verbose then

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

   end if;

   Float_Check.Do_Test;

   if Verbose then

      Report.Comment ("checking a digits" &

                      Integer'Image (System.Max_Digits) &

                      " floating point type");

   end if;

   A_Long_Float_Check.Do_Test;

   Report.Result;

end CXG2019;