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-- CXG2022.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 multiplication and division of binary fixed point

--      numbers with compatible 'small values produce exact results.

--

-- TEST DESCRIPTION:

--      Signed, unsigned, and a mixture of signed and unsigned

--      binary fixed point values are multiplied and divided.

--      The result is checked against the expected "perfect result set"

--

-- 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:

--       1 Apr 96   SAIC    Initial release for 2.1

--      29 Jan 1998 EDS     Repaired fixed point errors ("**" and

--                          assumptions about 'Small)

--!

with System;

with Report;

procedure CXG2022 is

   Verbose : constant Boolean := False;

procedure Check_Signed is

   type Pairs is delta 2.0 range -2.0 ** (System.Max_Mantissa) ..

                                  2.0 ** (System.Max_Mantissa) - 1.0;

   type Halves is delta 0.5 range -2.0 ** (System.Max_Mantissa-2) ..

                                   2.0 ** (System.Max_Mantissa-2) - 1.0;

   P1, P2, P3, P4 : Pairs;

   H1, H2, H3, H4 : Halves;

   procedure Dont_Opt is

   -- keep optimizer from knowing the constant value of expressions

   begin

      if Report.Ident_Bool (False) then

         P1 :=  2.0;  P2 := 4.0;  P3 := 6.0;

         H1 := -2.0;  H2 := 9.0;  H3 := 3.0;

      end if;

   end Dont_Opt;

begin

   H1 := -0.5;

   H2 := Halves'First;

   H3 := 1.0;

   P1 := 12.0;

   P2 := Pairs'First;

   P3 := Pairs'Last;

   Dont_Opt;

   P4 := Pairs (P1 * H1);     -- 12.0 * -0.5

   if P4 /= -6.0 then

      Report.Failed ("12.0 * -0.5 = " & Pairs'Image (P4));

   end if;

   H4 := Halves (P1 / H1);     -- 12.0 / -0.5

   if H4 /= -24.0 then

      Report.Failed ("12.0 / -0.5 = " & Halves'Image (H4));

   end if;

   P4 := P3 * H3;     -- Pairs'Last * 1.0

   if P4 /= Pairs'Last then

      Report.Failed ("Pairs'Last * 1.0 = " & Pairs'Image (P4));

   end if;

   P4 := P3 / H3;     -- Pairs'Last / 1.0

   if P4 /= Pairs'Last then

      Report.Failed ("Pairs'Last / 1.0 = " & Pairs'Image (P4));

   end if;

   P4 := P2 * 0.25;     -- Pairs'First * 0.25

   if P4 /= Pairs (-2.0 ** (System.Max_Mantissa - 2)) then

      Report.Failed ("Pairs'First * 0.25 = " & Pairs'Image (P4));

   end if;

   P4 := 100.5 / H1;   -- 100.5 / -0.5

   if P4 = -201.0 then

      null;   -- Perfect result

   elsif Pairs'Small = 2.0 and ( P4 = -200.0 or P4 = -202.0 ) then

      null;   -- Allowed variation

   else

      Report.Failed ("Pairs'Small =" & Pairs'Image (Pairs'Small) &

                     " and 100.5/-0.5 = " & Pairs'Image (P4) );

   end if;

   H4 := H1 * H2;   --  -0.5 * Halves'First

   if H4 /= Halves (2.0 ** (System.Max_Mantissa-3)) then

      Report.Failed ("-0.5 * Halves'First =" & Halves'Image (H4) &

                     " instead of " &

                     Halves'Image( Halves(2.0 ** (System.Max_Mantissa-3))));

   end if;

exception

   when others =>

      Report.Failed ("unexpected exception in Check_Signed");

end Check_Signed;

procedure Check_Unsigned is

   type Pairs is delta 2.0 range 0.0 .. 2.0 ** (System.Max_Mantissa+1) - 1.0;

   type Halves is delta 0.5 range 0.0 .. 2.0 ** (System.Max_Mantissa-1) - 1.0;

   P1, P2, P3, P4 : Pairs;

   H1, H2, H3, H4 : Halves;

   procedure Dont_Opt is

   -- keep optimizer from knowing the constant value of expressions

   begin

      if Report.Ident_Bool (False) then

         P1 :=  2.0;  P2 := 4.0;  P3 := 6.0;

         H1 :=  2.0;  H2 := 9.0;  H3 := 3.0;

      end if;

   end Dont_Opt;

begin

   H1 := 10.5;

   H2 := Halves(2.0 ** (System.Max_Mantissa - 6));

   H3 := 1.0;

   P1 := 12.0;

   P2 := Pairs'Last / 2;

   P3 := Pairs'Last;

   Dont_Opt;

   P4 := Pairs (P1 * H1);     -- 12.0 * 10.5

   if P4 /= 126.0 then

      Report.Failed ("12.0 * 10.5 = " & Pairs'Image (P4));

   end if;

   H4 := Halves (P1 / H1);     -- 12.0 / 10.5

   if H4 /= 1.0 and H4 /= 1.5 then

      Report.Failed ("12.0 / 10.5 = " & Halves'Image (H4));

   end if;

   P4 := P3 * H3;     -- Pairs'Last * 1.0

   if P4 /= Pairs'Last then

      Report.Failed ("Pairs'Last * 1.0 = " & Pairs'Image (P4));

   end if;

   P4 := P3 / H3;     -- Pairs'Last / 1.0

   if P4 /= Pairs'Last then

      Report.Failed ("Pairs'Last / 1.0 = " & Pairs'Image (P4));

   end if;

   P4 := P1 * 0.25;     -- 12.0 * 0.25

   if P4 /= 2.0 and P4 /= 4.0 then

      Report.Failed ("12.0 * 0.25 = " & Pairs'Image (P4));

   end if;

   P4 := 100.5 / H1;   -- 100.5 / 10.5    = 9.571...

   if P4 /= 8.0 and P4 /= 10.0 then

      Report.Failed ("100.5/10.5 = " & Pairs'Image (P4));

   end if;

   H4 := H2 * 2;   --  2**(max_mantissa-6) * 2

   if H4 /= Halves(2.0 ** (System.Max_Mantissa-5)) then

      Report.Failed ("2**(System.Max_Mantissa-6) * 2=" & Halves'Image (H4) &

                     " instead of " &

                     Halves'Image( Halves(2.0 ** (System.Max_Mantissa-5))));

   end if;

exception

   when others =>

      Report.Failed ("unexpected exception in Check_Unsigned");

end Check_Unsigned;

procedure Check_Mixed is

   type Pairs is delta 2.0 range -2.0 ** (System.Max_Mantissa) ..

                                  2.0 ** (System.Max_Mantissa) - 1.0;

   type Halves is delta 0.5 range 0.0 .. 2.0 ** (System.Max_Mantissa-1) - 1.0;

   P1, P2, P3, P4 : Pairs;

   H1, H2, H3, H4 : Halves;

   procedure Dont_Opt is

   -- keep optimizer from knowing the constant value of expressions

   begin

      if Report.Ident_Bool (False) then

         P1 :=  2.0;  P2 := 4.0;  P3 := 6.0;

         H1 :=  2.0;  H2 := 9.0;  H3 := 3.0;

      end if;

   end Dont_Opt;

begin

   H1 := 10.5;

   H2 := Halves(2.0 ** (System.Max_Mantissa - 6));

   H3 := 1.0;

   P1 := 12.0;

   P2 := -4.0;

   P3 := Pairs'Last;

   Dont_Opt;

   P4 := Pairs (P1 * H1);     -- 12.0 * 10.5

   if P4 /= 126.0 then

      Report.Failed ("12.0 * 10.5 = " & Pairs'Image (P4));

   end if;

   H4 := Halves (P1 / H1);     -- 12.0 / 10.5

   if H4 /= 1.0 and H4 /= 1.5 then

      Report.Failed ("12.0 / 10.5 = " & Halves'Image (H4));

   end if;

   P4 := P3 * H3;     -- Pairs'Last * 1.0

   if P4 /= Pairs'Last then

      Report.Failed ("Pairs'Last * 1.0 = " & Pairs'Image (P4));

   end if;

   P4 := P3 / H3;     -- Pairs'Last / 1.0

   if P4 /= Pairs'Last then

      Report.Failed ("Pairs'Last / 1.0 = " & Pairs'Image (P4));

   end if;

   P4 := P1 * 0.25;   -- 12.0 * 0.25

   if P4 = 3.0 then

      null;    -- Perfect result

   elsif Pairs'Small = 2.0 and then ( P4 = 2.0 or P4 = 4.0 ) then

      null;    -- Allowed deviation

   else

      Report.Failed ("Pairs'Small =" & Pairs'Image (Pairs'Small) &

                     "and 12.0 * 0.25 = " & Pairs'Image (P4) );

   end if;

   P4 := 100.5 / H1;   -- 100.5 / 10.5    = 9.571...

   if P4 = 9.0 then

      null;    -- Perfect result

   elsif Pairs'Small = 2.0 and then ( P4 = 8.0 or P4 = 10.0 ) then

      null;    -- Allowed values

   else

     Report.Failed ("Pairs'Small =" & Pairs'Image (Pairs'Small) &

                    "and 100.5/10.5 = " & Pairs'Image (P4) );

   end if;

   H4 := H2 * 2;   --  2**(max_mantissa-6) * 2

   if H4 /= Halves(2.0 ** (System.Max_Mantissa-5)) then

      Report.Failed ("2**(System.Max_Mantissa-6) * 2=" & Halves'Image (H4) &

                     " instead of " &

                     Halves'Image( Halves(2.0 ** (System.Max_Mantissa-5))));

   end if;

   P4 := Pairs(P1 * 6) / P2;    -- 12 * 6 / -4

   if (P4 /= -18.0)  then

      Report.Failed ("12*6/-4 = " & Pairs'Image(P4));

   end if;

   P4 := Halves(P1 * 6.0) / P2;    -- 12 * 6 / -4

   if (P4 /= -18.0)  then

      Report.Failed ("Halves(12*6)/-4 = " & Pairs'Image(P4));

   end if;

exception

   when others =>

      Report.Failed ("unexpected exception in Check_Mixed");

end Check_Mixed;

begin  -- main

   Report.Test ("CXG2022",

                "Check the accuracy of multiplication and division" &

                " of binary fixed point numbers");

   if Verbose then

      Report.Comment ("starting signed test");

   end if;

   Check_Signed;

   if Verbose then

      Report.Comment ("starting unsigned test");

   end if;

   Check_Unsigned;

   if Verbose then

      Report.Comment ("starting mixed sign test");

   end if;

   Check_Mixed;

   Report.Result;

end CXG2022;