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-- CXG2020.A

--

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

--     unlimited rights in the software and documentation contained herein.

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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 SQRT 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.

--

-- 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:

--      24 Mar 96   SAIC    Initial release for 2.1

--      17 Aug 96   SAIC    Incorporated reviewer comments.

--      03 Jun 98   EDS     Added parens to ensure that the expression is not

--                          evaluated by multiplying its two large terms

--                          together and overflowing.

--!

--

-- 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 CXG2020 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;

   -- 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;

   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 Sqrt (X : Complex) return Complex renames CEF.Sqrt;

      -- 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_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

            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.

         --

         -- 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 := 6.0;

         Z1, Z2 : Complex;

      begin

         Check (Sqrt(9.0+0.0*i) + i,

                3.0+1.0*i,

                "sqrt(9+0i)+i",

                Minimum_Error);

         Check (Sqrt (-2.0 + 0.0 * i) + 1.0,

                1.0 + Sqrt2 * i,

                "sqrt(-2)+1 ",

                Minimum_Error);

         -- make sure no exception occurs when taking the sqrt of

         -- very large and very small values.

         Z1 := (Real'Safe_Last * 0.9, Real'Safe_Last * 0.9);

         Z2 := Sqrt (Z1);

         begin

            Check (Z2 * Z2,

                   Z1,

                   "sqrt((big,big))",

                   Minimum_Error + 5.0);  -- +5 for multiply

         exception

            when others =>

                Report.Failed ("unexpected exception in sqrt((big,big))");

         end;

         Z1 := (Real'Model_Epsilon * 10.0, Real'Model_Epsilon * 10.0);

         Z2 := Sqrt (Z1);

         begin

            Check (Z2 * Z2,

                   Z1,

                   "sqrt((little,little))",

                   Minimum_Error + 5.0);  -- +5 for multiply

         exception

            when others =>

                Report.Failed ("unexpected exception in " &

                    "sqrt((little,little))");

         end;

      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(36);6.0

         Check (Sqrt(0.0 + 0.0*i),  0.0 + 0.0 * i, "sqrt(0+0i)", No_Error);

         -- G.1.2(37);6.0

         Check (Sqrt(1.0 + 0.0*i),  1.0 + 0.0 * i, "sqrt(1+0i)", No_Error);

         -- G.1.2(38-39);6.0

         Check (Sqrt(-1.0 + 0.0*i),  0.0 + 1.0 * i, "sqrt(-1+0i)", No_Error);

         -- G.1.2(40);6.0

         if Real'Signed_Zeros then

            Check (Sqrt(-1.0-0.0*i), 0.0 - 1.0 * i, "sqrt(-1-0i)", No_Error);

         end if;

      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 of the result.

      --

      -- For this test we use the identity

      --    Sqrt(Z*Z) = Z

      --

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

         W, X, Y, Z : Real;

         CX : Complex;

         Actual, Expected : 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;

                 -- G.1.2(21);6.0 - real part of result is non-negative

               Expected := Compose_From_Cartesian( abs X,Y);

               Z := X*X - Y*Y;

               W := X*Y;

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

               -- The arguments are now ready so on with the

               -- identity computation.

               Actual := Sqrt(CX);

               Check (Actual, Expected,

                      "Identity_1_Test " & Integer'Image (II) &

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

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

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

                      8.5);   -- 6.0 from sqrt, 2.5 from argument.

               -- See Cody pg 7-8 for analysis of additional error amount.

               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 Do_Test is

      begin

         Special_Value_Test;

         Exact_Result_Test;

         -- ranges where the sign is the same and where it

         -- differs.

         Identity_Test (   0.0,   10.0,       0.0,    10.0);

         Identity_Test (   0.0,  100.0,    -100.0,     0.0);

      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 ("CXG2020",

                "Check the accuracy of the complex SQRT 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 CXG2020;