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-- CXG2008.A

--

--                             Grant of Unlimited Rights

--

--     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 multiplication and division

--      operations return results that are within the allowed

--      error bound.

--      Check that all the required pure Numerics packages are pure.

--

-- TEST DESCRIPTION:

--      This test contains three test packages that are almost

--      identical.  The first two packages differ only in the

--      floating point type that is being tested.  The first

--      and third package differ only in whether the generic

--      complex types package or the pre-instantiated

--      package is used.

--      The test package is not generic so that the arguments

--      and expected results for some of the test values

--      can be expressed as universal real instead of being

--      computed at runtime.

--

-- 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 FEB 96   SAIC    Initial release for 2.1

--      03 JUN 98   EDS     Correct the test program's incorrect assumption

--                          that Constraint_Error must be raised by complex

--                          division by zero, which is contrary to the

--                          allowance given by the Ada 95 standard G.1.1(40).

--      13 MAR 01   RLB     Replaced commented out Pure check on non-generic

--                          packages, as required by Defect Report

--                          8652/0020 and as reflected in Technical

--                          Corrigendum 1.

--!

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

-- Check that the required pure packages are pure by withing them from a

-- pure package. The non-generic versions of those packages are required to

-- be pure by Defect Report 8652/0020, Technical Corrigendum 1 [A.5.1(9/1) and

-- G.1.1(25/1)].

with Ada.Numerics.Generic_Elementary_Functions;

with Ada.Numerics.Elementary_Functions;

with Ada.Numerics.Generic_Complex_Types;

with Ada.Numerics.Complex_Types;

with Ada.Numerics.Generic_Complex_Elementary_Functions;

with Ada.Numerics.Complex_Elementary_Functions;

package CXG2008_0 is

  pragma Pure;

   -- 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;

end CXG2008_0;

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

with System;

with Report;

with Ada.Numerics.Generic_Complex_Types;

with Ada.Numerics.Complex_Types;

with CXG2008_0;  use CXG2008_0;

procedure CXG2008 is

   Verbose : constant Boolean := False;

   package Float_Check is

      subtype Real is Float;

      procedure Do_Test;

   end Float_Check;

   package body Float_Check is

      package Complex_Types is new

           Ada.Numerics.Generic_Complex_Types (Real);

      use Complex_Types;

      -- keep track if an accuracy failure has occurred so the test

      -- can be short-circuited to avoid thousands of error messages.

      Failure_Detected : Boolean := False;

      Mult_MBE : constant Real := 5.0;

      Divide_MBE : constant Real := 13.0;

      procedure Check (Actual, Expected : Complex;

                       Test_Name : String;

                       MBE : 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 := MBE * abs Expected.Re * Real'Model_Epsilon;

         Abs_Error := MBE * Real'Model_Epsilon;

         if Rel_Error > Abs_Error then

            Max_Error := Rel_Error;

         else

            Max_Error := Abs_Error;

         end if;

         if abs (Actual.Re - Expected.Re) > Max_Error then

            Failure_Detected := True;

            Report.Failed (Test_Name &

                           " actual.re: " & Real'Image (Actual.Re) &

                           " expected.re: " & Real'Image (Expected.Re) &

                           " difference.re " &

                           Real'Image (Actual.Re - Expected.Re) &

                           " mre:" & Real'Image (Max_Error) );

         elsif Verbose then

            if Actual = Expected then

               Report.Comment (Test_Name & " exact result for real part");

            else

               Report.Comment (Test_Name & " passed for real part");

            end if;

         end if;

         Rel_Error := MBE * abs Expected.Im * Real'Model_Epsilon;

         if Rel_Error > Abs_Error then

            Max_Error := Rel_Error;

         else

            Max_Error := Abs_Error;

         end if;

         if abs (Actual.Im - Expected.Im) > Max_Error then

            Failure_Detected := True;

            Report.Failed (Test_Name &

                           " actual.im: " & Real'Image (Actual.Im) &

                           " expected.im: " & Real'Image (Expected.Im) &

                           " difference.im " &

                           Real'Image (Actual.Im - Expected.Im) &

                           " mre:" & Real'Image (Max_Error) );

         elsif Verbose then

            if Actual = Expected then

               Report.Comment (Test_Name & " exact result for imaginary part");

            else

               Report.Comment (Test_Name & " passed for imaginary part");

            end if;

         end if;

      end Check;

      procedure Special_Values is

      begin

         --- test 1 ---

         declare

            T : constant := (Real'Machine_EMax - 1) / 2;

            Big : constant := (1.0 * Real'Machine_Radix) ** (2 * T);

            Expected : Complex := (0.0, 0.0);

            X : Complex := (0.0, 0.0);

            Y : Complex := (Big, Big);

            Z : Complex;

         begin

            Z := X * Y;

            Check (Z, Expected, "test 1a -- (0+0i) * (big+big*i)",

                   Mult_MBE);

            Z := Y * X;

            Check (Z, Expected, "test 1b -- (big+big*i) * (0+0i)",

                   Mult_MBE);

         exception

            when Constraint_Error =>

               Report.Failed ("Constraint_Error raised in test 1");

            when others =>

               Report.Failed ("exception in test 1");

         end;

         --- test 2 ---

         declare

            T : constant := Real'Model_EMin + 1;

            Tiny : constant := (1.0 * Real'Machine_Radix) ** T;

            U : Complex := (Tiny, Tiny);

            X : Complex := (0.0, 0.0);

            Expected : Complex := (0.0, 0.0);

            Z : Complex;

         begin

            Z := U * X;

            Check (Z, Expected, "test 2 -- (tiny,tiny) * (0,0)",

                   Mult_MBE);

         exception

            when Constraint_Error =>

               Report.Failed ("Constraint_Error raised in test 2");

            when others =>

               Report.Failed ("exception in test 2");

         end;

         --- test 3 ---

         declare

            T : constant := (Real'Machine_EMax - 1) / 2;

            Big : constant := (1.0 * Real'Machine_Radix) ** (2 * T);

            B : Complex := (Big, Big);

            X : Complex := (0.0, 0.0);

            Z : Complex;

         begin

            if Real'Machine_Overflows then

               Z := B / X;

               Report.Failed ("test 3 - Constraint_Error not raised");

               Check (Z, Z, "not executed - optimizer thwarting", 0.0);

            end if;

         exception

            when Constraint_Error => null;  -- expected

            when others =>

               Report.Failed ("exception in test 3");

         end;

         --- test 4 ---

         declare

            T : constant := Real'Model_EMin + 1;

            Tiny : constant := (1.0 * Real'Machine_Radix) ** T;

            U : Complex := (Tiny, Tiny);

            X : Complex := (0.0, 0.0);

            Z : Complex;

         begin

            if Real'Machine_Overflows then

               Z := U / X;

               Report.Failed ("test 4 - Constraint_Error not raised");

               Check (Z, Z, "not executed - optimizer thwarting", 0.0);

            end if;

         exception

            when Constraint_Error => null;  -- expected

            when others =>

               Report.Failed ("exception in test 4");

         end;

         --- test 5 ---

         declare

            X : Complex := (Sqrt2, Sqrt2);

            Z : Complex;

            Expected : constant Complex := (0.0, 4.0);

         begin

            Z := X * X;

            Check (Z, Expected, "test 5 -- (sqrt2,sqrt2) * (sqrt2,sqrt2)",

                   Mult_MBE);

         exception

            when Constraint_Error =>

               Report.Failed ("Constraint_Error raised in test 5");

            when others =>

               Report.Failed ("exception in test 5");

         end;

         --- test 6 ---

         declare

            X : Complex := Sqrt3 - Sqrt3 * i;

            Z : Complex;

            Expected : constant Complex := (0.0, -6.0);

         begin

            Z := X * X;

            Check (Z, Expected, "test 6 -- (sqrt3,-sqrt3) * (sqrt3,-sqrt3)",

                   Mult_MBE);

         exception

            when Constraint_Error =>

               Report.Failed ("Constraint_Error raised in test 6");

            when others =>

               Report.Failed ("exception in test 6");

         end;

         --- test 7 ---

         declare

            X : Complex := Sqrt2 + Sqrt2 * i;

            Y : Complex := Sqrt2 - Sqrt2 * i;

            Z : Complex;

            Expected : constant Complex := 0.0 + i;

         begin

            Z := X / Y;

            Check (Z, Expected, "test 7 -- (sqrt2,sqrt2) / (sqrt2,-sqrt2)",

                   Divide_MBE);

         exception

            when Constraint_Error =>

               Report.Failed ("Constraint_Error raised in test 7");

            when others =>

               Report.Failed ("exception in test 7");

         end;

      end Special_Values;

      procedure Do_Mult_Div (X, Y : Complex) is

         Z : Complex;

         Args : constant String :=

           "X=(" & Real'Image (X.Re) & "," & Real'Image (X.Im) & ") " &

           "Y=(" & Real'Image (Y.Re) & "," & Real'Image (Y.Im) & ") " ;

      begin

         Z := (X * X) / X;

         Check (Z, X, "X*X/X " & Args, Mult_MBE + Divide_MBE);

         Z := (X * Y) / X;

         Check (Z, Y, "X*Y/X " & Args, Mult_MBE + Divide_MBE);

         Z := (X * Y) / Y;

         Check (Z, X, "X*Y/Y " & Args, Mult_MBE + Divide_MBE);

      exception

         when Constraint_Error =>

            Report.Failed ("Constraint_Error in Do_Mult_Div for " & Args);

         when others =>

            Report.Failed ("exception in Do_Mult_Div for " & Args);

      end Do_Mult_Div;

      -- select complex values X and Y where the real and imaginary

      -- parts are selected from the ranges (1/radix..1) and

      -- (1..radix).  This translates into quite a few combinations.

      procedure Mult_Div_Check is

         Samples : constant := 17;

         Radix : constant Real := Real(Real'Machine_Radix);

         Inv_Radix : constant Real := 1.0 / Real(Real'Machine_Radix);

         Low_Sample : Real;  -- (1/radix .. 1)

         High_Sample : Real; -- (1 .. radix)

         Sample : array (1..2) of Real;

         X, Y : Complex;

      begin

         for I in 1 .. Samples loop

            Low_Sample := (1.0 - Inv_Radix) / Real (Samples) * Real (I) +

                          Inv_Radix;

            Sample (1) := Low_Sample;

            for J in 1 .. Samples loop

               High_Sample := (Radix - 1.0) / Real (Samples) * Real (I) +

                              Radix;

               Sample (2) := High_Sample;

               for K in 1 .. 2 loop

                  for L in 1 .. 2 loop

                     X := Complex'(Sample (K), Sample (L));

                     Y := Complex'(Sample (L), Sample (K));

                     Do_Mult_Div (X, Y);

                     if Failure_Detected then

                        return;   -- minimize flood of error messages

                     end if;

                  end loop;

               end loop;

            end loop;  -- J

         end loop;  -- I

      end Mult_Div_Check;

      procedure Do_Test is

      begin

         Special_Values;

         Mult_Div_Check;

      end Do_Test;

   end Float_Check;

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

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

   -- check the floating point type with the most digits

   package A_Long_Float_Check is

      type A_Long_Float is digits System.Max_Digits;

      subtype Real is A_Long_Float;

      procedure Do_Test;

   end A_Long_Float_Check;

   package body A_Long_Float_Check is

      package Complex_Types is new

           Ada.Numerics.Generic_Complex_Types (Real);

      use Complex_Types;

      -- keep track if an accuracy failure has occurred so the test

      -- can be short-circuited to avoid thousands of error messages.

      Failure_Detected : Boolean := False;

      Mult_MBE : constant Real := 5.0;

      Divide_MBE : constant Real := 13.0;

      procedure Check (Actual, Expected : Complex;

                       Test_Name : String;

                       MBE : 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 := MBE * abs Expected.Re * Real'Model_Epsilon;

         Abs_Error := MBE * Real'Model_Epsilon;

         if Rel_Error > Abs_Error then

            Max_Error := Rel_Error;

         else

            Max_Error := Abs_Error;

         end if;

         if abs (Actual.Re - Expected.Re) > Max_Error then

            Failure_Detected := True;

            Report.Failed (Test_Name &

                           " actual.re: " & Real'Image (Actual.Re) &

                           " expected.re: " & Real'Image (Expected.Re) &

                           " difference.re " &

                           Real'Image (Actual.Re - Expected.Re) &

                           " mre:" & Real'Image (Max_Error) );

         elsif Verbose then

            if Actual = Expected then

               Report.Comment (Test_Name & " exact result for real part");

            else

               Report.Comment (Test_Name & " passed for real part");

            end if;

         end if;

         Rel_Error := MBE * abs Expected.Im * Real'Model_Epsilon;

         if Rel_Error > Abs_Error then

            Max_Error := Rel_Error;

         else

            Max_Error := Abs_Error;

         end if;

         if abs (Actual.Im - Expected.Im) > Max_Error then

            Failure_Detected := True;

            Report.Failed (Test_Name &

                           " actual.im: " & Real'Image (Actual.Im) &

                           " expected.im: " & Real'Image (Expected.Im) &

                           " difference.im " &

                           Real'Image (Actual.Im - Expected.Im) &

                           " mre:" & Real'Image (Max_Error) );

         elsif Verbose then

            if Actual = Expected then

               Report.Comment (Test_Name & " exact result for imaginary part");

            else

               Report.Comment (Test_Name & " passed for imaginary part");

            end if;

         end if;

      end Check;

      procedure Special_Values is

      begin

         --- test 1 ---

         declare

            T : constant := (Real'Machine_EMax - 1) / 2;

            Big : constant := (1.0 * Real'Machine_Radix) ** (2 * T);

            Expected : Complex := (0.0, 0.0);

            X : Complex := (0.0, 0.0);

            Y : Complex := (Big, Big);

            Z : Complex;

         begin

            Z := X * Y;

            Check (Z, Expected, "test 1a -- (0+0i) * (big+big*i)",

                   Mult_MBE);

            Z := Y * X;

            Check (Z, Expected, "test 1b -- (big+big*i) * (0+0i)",

                   Mult_MBE);

         exception

            when Constraint_Error =>

               Report.Failed ("Constraint_Error raised in test 1");

            when others =>

               Report.Failed ("exception in test 1");

         end;

         --- test 2 ---

         declare

            T : constant := Real'Model_EMin + 1;

            Tiny : constant := (1.0 * Real'Machine_Radix) ** T;

            U : Complex := (Tiny, Tiny);

            X : Complex := (0.0, 0.0);

            Expected : Complex := (0.0, 0.0);

            Z : Complex;

         begin

            Z := U * X;

            Check (Z, Expected, "test 2 -- (tiny,tiny) * (0,0)",

                   Mult_MBE);

         exception

            when Constraint_Error =>

               Report.Failed ("Constraint_Error raised in test 2");

            when others =>

               Report.Failed ("exception in test 2");

         end;

         --- test 3 ---

         declare

            T : constant := (Real'Machine_EMax - 1) / 2;

            Big : constant := (1.0 * Real'Machine_Radix) ** (2 * T);

            B : Complex := (Big, Big);

            X : Complex := (0.0, 0.0);

            Z : Complex;

         begin

            if Real'Machine_Overflows then

               Z := B / X;

               Report.Failed ("test 3 - Constraint_Error not raised");

               Check (Z, Z, "not executed - optimizer thwarting", 0.0);

            end if;

         exception

            when Constraint_Error => null;  -- expected

            when others =>

               Report.Failed ("exception in test 3");

         end;

         --- test 4 ---

         declare

            T : constant := Real'Model_EMin + 1;

            Tiny : constant := (1.0 * Real'Machine_Radix) ** T;

            U : Complex := (Tiny, Tiny);

            X : Complex := (0.0, 0.0);

            Z : Complex;

         begin

            if Real'Machine_Overflows then

               Z := U / X;

               Report.Failed ("test 4 - Constraint_Error not raised");

               Check (Z, Z, "not executed - optimizer thwarting", 0.0);

            end if;

         exception

            when Constraint_Error => null;  -- expected

            when others =>

               Report.Failed ("exception in test 4");

         end;

         --- test 5 ---

         declare

            X : Complex := (Sqrt2, Sqrt2);

            Z : Complex;

            Expected : constant Complex := (0.0, 4.0);

         begin

            Z := X * X;

            Check (Z, Expected, "test 5 -- (sqrt2,sqrt2) * (sqrt2,sqrt2)",

                   Mult_MBE);

         exception

            when Constraint_Error =>

               Report.Failed ("Constraint_Error raised in test 5");

            when others =>

               Report.Failed ("exception in test 5");

         end;

         --- test 6 ---

         declare

            X : Complex := Sqrt3 - Sqrt3 * i;

            Z : Complex;

            Expected : constant Complex := (0.0, -6.0);

         begin

            Z := X * X;

            Check (Z, Expected, "test 6 -- (sqrt3,-sqrt3) * (sqrt3,-sqrt3)",

                   Mult_MBE);

         exception

            when Constraint_Error =>

               Report.Failed ("Constraint_Error raised in test 6");

            when others =>

               Report.Failed ("exception in test 6");

         end;

         --- test 7 ---

         declare

            X : Complex := Sqrt2 + Sqrt2 * i;

            Y : Complex := Sqrt2 - Sqrt2 * i;

            Z : Complex;

            Expected : constant Complex := 0.0 + i;

         begin

            Z := X / Y;

            Check (Z, Expected, "test 7 -- (sqrt2,sqrt2) / (sqrt2,-sqrt2)",

                   Divide_MBE);

         exception

            when Constraint_Error =>

               Report.Failed ("Constraint_Error raised in test 7");

            when others =>

               Report.Failed ("exception in test 7");

         end;

      end Special_Values;

      procedure Do_Mult_Div (X, Y : Complex) is

         Z : Complex;

         Args : constant String :=

           "X=(" & Real'Image (X.Re) & "," & Real'Image (X.Im) & ") " &

           "Y=(" & Real'Image (Y.Re) & "," & Real'Image (Y.Im) & ") " ;

      begin

         Z := (X * X) / X;

         Check (Z, X, "X*X/X " & Args, Mult_MBE + Divide_MBE);

         Z := (X * Y) / X;

         Check (Z, Y, "X*Y/X " & Args, Mult_MBE + Divide_MBE);

         Z := (X * Y) / Y;

         Check (Z, X, "X*Y/Y " & Args, Mult_MBE + Divide_MBE);

      exception

         when Constraint_Error =>

            Report.Failed ("Constraint_Error in Do_Mult_Div for " & Args);

         when others =>

            Report.Failed ("exception in Do_Mult_Div for " & Args);

      end Do_Mult_Div;

      -- select complex values X and Y where the real and imaginary

      -- parts are selected from the ranges (1/radix..1) and

      -- (1..radix).  This translates into quite a few combinations.

      procedure Mult_Div_Check is

         Samples : constant := 17;

         Radix : constant Real := Real(Real'Machine_Radix);

         Inv_Radix : constant Real := 1.0 / Real(Real'Machine_Radix);

         Low_Sample : Real;  -- (1/radix .. 1)

         High_Sample : Real; -- (1 .. radix)

         Sample : array (1..2) of Real;

         X, Y : Complex;

      begin

         for I in 1 .. Samples loop

            Low_Sample := (1.0 - Inv_Radix) / Real (Samples) * Real (I) +

                          Inv_Radix;

            Sample (1) := Low_Sample;

            for J in 1 .. Samples loop

               High_Sample := (Radix - 1.0) / Real (Samples) * Real (I) +

                              Radix;

               Sample (2) := High_Sample;

               for K in 1 .. 2 loop

                  for L in 1 .. 2 loop

                     X := Complex'(Sample (K), Sample (L));

                     Y := Complex'(Sample (L), Sample (K));

                     Do_Mult_Div (X, Y);

                     if Failure_Detected then

                        return;   -- minimize flood of error messages

                     end if;

                  end loop;

               end loop;

            end loop;  -- J

         end loop;  -- I

      end Mult_Div_Check;

      procedure Do_Test is

      begin

         Special_Values;

         Mult_Div_Check;

      end Do_Test;

   end A_Long_Float_Check;

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

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

   package Non_Generic_Check is

      subtype Real is Float;

      procedure Do_Test;

   end Non_Generic_Check;

   package body Non_Generic_Check is

      use Ada.Numerics.Complex_Types;

      -- keep track if an accuracy failure has occurred so the test

      -- can be short-circuited to avoid thousands of error messages.

      Failure_Detected : Boolean := False;

      Mult_MBE : constant Real := 5.0;

      Divide_MBE : constant Real := 13.0;

      procedure Check (Actual, Expected : Complex;

                       Test_Name : String;

                       MBE : 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 := MBE * abs Expected.Re * Real'Model_Epsilon;

         Abs_Error := MBE * Real'Model_Epsilon;

         if Rel_Error > Abs_Error then

            Max_Error := Rel_Error;

         else

            Max_Error := Abs_Error;

         end if;

         if abs (Actual.Re - Expected.Re) > Max_Error then

            Failure_Detected := True;

            Report.Failed (Test_Name &

                           " actual.re: " & Real'Image (Actual.Re) &

                           " expected.re: " & Real'Image (Expected.Re) &

                           " difference.re " &

                           Real'Image (Actual.Re - Expected.Re) &

                           " mre:" & Real'Image (Max_Error) );

         elsif Verbose then

            if Actual = Expected then

               Report.Comment (Test_Name & " exact result for real part");

            else

               Report.Comment (Test_Name & " passed for real part");

            end if;

         end if;

         Rel_Error := MBE * abs Expected.Im * Real'Model_Epsilon;

         if Rel_Error > Abs_Error then

            Max_Error := Rel_Error;

         else

            Max_Error := Abs_Error;

         end if;

         if abs (Actual.Im - Expected.Im) > Max_Error then

            Failure_Detected := True;

            Report.Failed (Test_Name &

                           " actual.im: " & Real'Image (Actual.Im) &

                           " expected.im: " & Real'Image (Expected.Im) &

                           " difference.im " &

                           Real'Image (Actual.Im - Expected.Im) &

                           " mre:" & Real'Image (Max_Error) );

         elsif Verbose then

            if Actual = Expected then

               Report.Comment (Test_Name & " exact result for imaginary part");

            else

               Report.Comment (Test_Name & " passed for imaginary part");

            end if;

         end if;

      end Check;

      procedure Special_Values is

      begin

         --- test 1 ---

         declare

            T : constant := (Real'Machine_EMax - 1) / 2;

            Big : constant := (1.0 * Real'Machine_Radix) ** (2 * T);

            Expected : Complex := (0.0, 0.0);

            X : Complex := (0.0, 0.0);

            Y : Complex := (Big, Big);

            Z : Complex;

         begin

            Z := X * Y;

            Check (Z, Expected, "test 1a -- (0+0i) * (big+big*i)",

                   Mult_MBE);

            Z := Y * X;

            Check (Z, Expected, "test 1b -- (big+big*i) * (0+0i)",

                   Mult_MBE);

         exception

            when Constraint_Error =>

               Report.Failed ("Constraint_Error raised in test 1");

            when others =>

               Report.Failed ("exception in test 1");

         end;

         --- test 2 ---

         declare

            T : constant := Real'Model_EMin + 1;

            Tiny : constant := (1.0 * Real'Machine_Radix) ** T;

            U : Complex := (Tiny, Tiny);

            X : Complex := (0.0, 0.0);

            Expected : Complex := (0.0, 0.0);

            Z : Complex;

         begin

            Z := U * X;

            Check (Z, Expected, "test 2 -- (tiny,tiny) * (0,0)",

                   Mult_MBE);

         exception

            when Constraint_Error =>

               Report.Failed ("Constraint_Error raised in test 2");

            when others =>

               Report.Failed ("exception in test 2");

         end;

         --- test 3 ---

         declare

            T : constant := (Real'Machine_EMax - 1) / 2;

            Big : constant := (1.0 * Real'Machine_Radix) ** (2 * T);

            B : Complex := (Big, Big);

            X : Complex := (0.0, 0.0);

            Z : Complex;

         begin

            if Real'Machine_Overflows then

               Z := B / X;

               Report.Failed ("test 3 - Constraint_Error not raised");

               Check (Z, Z, "not executed - optimizer thwarting", 0.0);

            end if;

         exception

            when Constraint_Error => null;  -- expected

            when others =>

               Report.Failed ("exception in test 3");

         end;

         --- test 4 ---

         declare

            T : constant := Real'Model_EMin + 1;

            Tiny : constant := (1.0 * Real'Machine_Radix) ** T;

            U : Complex := (Tiny, Tiny);

            X : Complex := (0.0, 0.0);

            Z : Complex;

         begin

            if Real'Machine_Overflows then

               Z := U / X;

               Report.Failed ("test 4 - Constraint_Error not raised");

               Check (Z, Z, "not executed - optimizer thwarting", 0.0);

            end if;

         exception

            when Constraint_Error => null;  -- expected

            when others =>

               Report.Failed ("exception in test 4");

         end;

         --- test 5 ---

         declare

            X : Complex := (Sqrt2, Sqrt2);

            Z : Complex;

            Expected : constant Complex := (0.0, 4.0);

         begin

            Z := X * X;

            Check (Z, Expected, "test 5 -- (sqrt2,sqrt2) * (sqrt2,sqrt2)",

                   Mult_MBE);

         exception

            when Constraint_Error =>

               Report.Failed ("Constraint_Error raised in test 5");

            when others =>

               Report.Failed ("exception in test 5");

         end;

         --- test 6 ---

         declare

            X : Complex := Sqrt3 - Sqrt3 * i;

            Z : Complex;

            Expected : constant Complex := (0.0, -6.0);

         begin

            Z := X * X;

            Check (Z, Expected, "test 6 -- (sqrt3,-sqrt3) * (sqrt3,-sqrt3)",

                   Mult_MBE);

         exception

            when Constraint_Error =>

               Report.Failed ("Constraint_Error raised in test 6");

            when others =>

               Report.Failed ("exception in test 6");

         end;

         --- test 7 ---

         declare

            X : Complex := Sqrt2 + Sqrt2 * i;

            Y : Complex := Sqrt2 - Sqrt2 * i;

            Z : Complex;

            Expected : constant Complex := 0.0 + i;

         begin

            Z := X / Y;

            Check (Z, Expected, "test 7 -- (sqrt2,sqrt2) / (sqrt2,-sqrt2)",

                   Divide_MBE);

         exception

            when Constraint_Error =>

               Report.Failed ("Constraint_Error raised in test 7");

            when others =>

               Report.Failed ("exception in test 7");

         end;

      end Special_Values;

      procedure Do_Mult_Div (X, Y : Complex) is

         Z : Complex;

         Args : constant String :=

           "X=(" & Real'Image (X.Re) & "," & Real'Image (X.Im) & ") " &

           "Y=(" & Real'Image (Y.Re) & "," & Real'Image (Y.Im) & ") " ;

      begin

         Z := (X * X) / X;

         Check (Z, X, "X*X/X " & Args, Mult_MBE + Divide_MBE);

         Z := (X * Y) / X;

         Check (Z, Y, "X*Y/X " & Args, Mult_MBE + Divide_MBE);

         Z := (X * Y) / Y;

         Check (Z, X, "X*Y/Y " & Args, Mult_MBE + Divide_MBE);

      exception

         when Constraint_Error =>

            Report.Failed ("Constraint_Error in Do_Mult_Div for " & Args);

         when others =>

            Report.Failed ("exception in Do_Mult_Div for " & Args);

      end Do_Mult_Div;

      -- select complex values X and Y where the real and imaginary

      -- parts are selected from the ranges (1/radix..1) and

      -- (1..radix).  This translates into quite a few combinations.

      procedure Mult_Div_Check is

         Samples : constant := 17;

         Radix : constant Real := Real(Real'Machine_Radix);

         Inv_Radix : constant Real := 1.0 / Real(Real'Machine_Radix);

         Low_Sample : Real;  -- (1/radix .. 1)

         High_Sample : Real; -- (1 .. radix)

         Sample : array (1..2) of Real;

         X, Y : Complex;

      begin

         for I in 1 .. Samples loop

            Low_Sample := (1.0 - Inv_Radix) / Real (Samples) * Real (I) +

                          Inv_Radix;

            Sample (1) := Low_Sample;

            for J in 1 .. Samples loop

               High_Sample := (Radix - 1.0) / Real (Samples) * Real (I) +

                              Radix;

               Sample (2) := High_Sample;

               for K in 1 .. 2 loop

                  for L in 1 .. 2 loop

                     X := Complex'(Sample (K), Sample (L));

                     Y := Complex'(Sample (L), Sample (K));

                     Do_Mult_Div (X, Y);

                     if Failure_Detected then

                        return;   -- minimize flood of error messages

                     end if;

                  end loop;

               end loop;

            end loop;  -- J

         end loop;  -- I

      end Mult_Div_Check;

      procedure Do_Test is

      begin

         Special_Values;

         Mult_Div_Check;

      end Do_Test;

   end Non_Generic_Check;

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

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

begin

   Report.Test ("CXG2008",

                "Check the accuracy of the complex multiplication and" &

                " division operators");

   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;