cxg2001.a

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-- CXG2001.A
--
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--     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 floating point attributes Model_Mantissa,
--      Machine_Mantissa, Machine_Radix, and Machine_Rounds
--      are properly reported.
--
-- TEST DESCRIPTION:
--      This test uses a generic package to compute and check the
--      values of the Machine_  attributes listed above.  The
--      generic package is instantiated with the standard FLOAT 
--      type and a floating point type for the maximum number
--      of digits of precision.
--
-- APPLICABILITY CRITERIA:
--      This test applies only to implementations supporting the
--      Numerics Annex.
--
--
-- CHANGE HISTORY:
--      26 JAN 96   SAIC    Initial Release for 2.1
--
--!

-- References:
--
--    "Algorithms To Reveal Properties of Floating-Point Arithmetic"
--    Michael A. Malcolm;  CACM November 1972;  pgs 949-951.
--
--    Software Manual for Elementary Functions; W. J. Cody and W. Waite;
--    Prentice-Hall; 1980
-----------------------------------------------------------------------
-- 
-- This test relies upon the fact that
-- (A+2.0)-A is not necessarily 2.0.  If A is large enough then adding 
-- a small value to A does not change the value of A.  Consider the case
-- where we have a decimal based floating point representation with 4
-- digits of precision.  A floating point number would logically be 
-- represented as "DDDD * 10 ** exp" where D is a value in the range 0..9.
-- The first loop of the test starts A at 2.0 and doubles it until
-- ((A+1.0)-A)-1.0 is no longer zero.  For our decimal floating point
-- number this will be 1638 * 10**1  (the value 16384 rounded or truncated
-- to fit in 4 digits).
-- The second loop starts B at 2.0 and keeps doubling B until (A+B)-A is
-- no longer 0.  This will keep looping until B is 8.0 because that is
-- the first value where rounding (assuming our machine rounds and addition
-- employs a guard digit) will change the upper 4 digits of the result:
--       1638_
--     +     8
--      -------
--       1639_
-- Without rounding the second loop will continue until
-- B is 16:
--       1638_
--     +    16
--      -------
--       1639_
-- 
-- The radix is then determined by (A+B)-A which will give 10.
-- 
-- The use of Tmp and ITmp in the test is to force values to be 
-- stored into memory in the event that register precision is greater
-- than the stored precision of the floating point values.
--      
-- 
-- The test for rounding is (ignoring the temporary variables used to 
-- get the stored precision) is 
--       Rounds := A + Radix/2.0 - A /= 0.0 ;
-- where A is the value determined in the first step that is the smallest
-- power of 2 such that A + 1.0 = A.  This means that the true value of
-- A has one more digit in its value than 'Machine_Mantissa.
-- This check will detect the case where a value is always rounded.
-- There is an additional case where values are rounded to the nearest
-- even value.  That is referred to as IEEE style rounding in the test.
-- 
-----------------------------------------------------------------------

with System;
with Report;
with Ada.Numerics.Generic_Elementary_Functions;
procedure CXG2001 is
   Verbose : constant Boolean := False;

   -- if one of the attribute computation loops exceeds Max_Iterations
   -- it is most likely due to the compiler reordering an expression
   -- that should not be reordered.
   Illegal_Optimization : exception;
   Max_Iterations : constant := 10_000;

   generic
      type Real is digits <>;
   package Chk_Attrs is
      procedure Do_Test;
   end Chk_Attrs;

   package body Chk_Attrs is
      package EF is new Ada.Numerics.Generic_Elementary_Functions (Real);
      function Log (X : Real) return Real renames EF.Log;


                                   -- names used in paper
      Radix : Integer;             -- Beta
      Mantissa_Digits : Integer;   -- t
      Rounds : Boolean;            -- RND

      -- made global to Determine_Attributes to help thwart optimization
      A, B : Real := 2.0;
      Tmp, Tmpa, Tmp1 : Real;
      ITmp : Integer;
      Half_Radix : Real;

      -- special constants - not declared as constants so that 
      -- the "stored" precision will be used instead of a "register"
      -- precision.
      Zero : Real := 0.0;
      One  : Real := 1.0;
      Two  : Real := 2.0;


      procedure Thwart_Optimization is
      -- the purpose of this procedure is to reference the
      -- global variables used by Determine_Attributes so
      -- that the compiler is not likely to keep them in
      -- a higher precision register for their entire lifetime.
      begin
	 if Report.Ident_Bool (False) then
	    -- never executed
	    A := A + 5.0;
	    B := B + 6.0;
	    Tmp := Tmp + 1.0;
	    Tmp1 := Tmp1 + 2.0;
	    Tmpa := Tmpa + 2.0;
            One := 12.34;   Two := 56.78;  Zero := 90.12;
	 end if;
      end Thwart_Optimization;


      -- determines values for Radix, Mantissa_Digits, and Rounds
      -- This is mostly a straight translation of the C code.
      -- The only significant addition is the iteration count
      -- to prevent endless looping if things are really screwed up.
      procedure Determine_Attributes is
         Iterations : Integer;
      begin
         Rounds := True;

         Iterations := 0;
         Tmp := Real'Machine (((A + One) - A) - One);
         while Tmp = Zero loop
            A := Real'Machine(A + A);
            Tmp := Real'Machine(A + One);
            Tmp1 := Real'Machine(Tmp - A);
	    Tmp := Real'Machine(Tmp1 - One);

            Iterations := Iterations + 1;
            if Iterations > Max_Iterations then
               raise Illegal_Optimization;
            end if;
         end loop;

         Iterations := 0;
	 Tmp := Real'Machine(A + B);
	 ITmp := Integer (Tmp - A);
         while ITmp = 0 loop
            B := Real'Machine(B + B);
	    Tmp := Real'Machine(A + B);
	    ITmp := Integer (Tmp - A);

            Iterations := Iterations + 1;
            if Iterations > Max_Iterations then
               raise Illegal_Optimization;
            end if;
         end loop;

         Radix := ITmp;

         Mantissa_Digits := 0;
         B := 1.0;
	 Tmp := Real'Machine(((B + One) - B) - One);
         Iterations := 0;
         while (Tmp = Zero) loop
            Mantissa_Digits := Mantissa_Digits + 1;
            B := B * Real (Radix);
	    Tmp := Real'Machine(B + One);
	    Tmp1 := Real'Machine(Tmp - B);
	    Tmp := Real'Machine(Tmp1 - One);

            Iterations := Iterations + 1;
            if Iterations > Max_Iterations then
               raise Illegal_Optimization;
            end if;
         end loop;

	 Rounds := False;
	 Half_Radix := Real (Radix) / Two;
	 Tmp := Real'Machine(A + Half_Radix);
	 Tmp1 := Real'Machine(Tmp - A);
	 if (Tmp1 /= Zero) then
	    Rounds := True;
	 end if;
	 Tmpa := Real'Machine(A + Real (Radix));
	 Tmp := Real'Machine(Tmpa + Half_Radix);
	 if not Rounds and (Tmp - TmpA /= Zero) then
	    Rounds := True;
            if Verbose then
	       Report.Comment ("IEEE style rounding");
            end if;
	 end if;

      exception
	 when others =>
	    Thwart_Optimization;
	    raise;
      end Determine_Attributes;


      procedure Do_Test is
         Show_Results : Boolean := Verbose;
         Min_Mantissa_Digits : Integer;
      begin
         -- compute the actual Machine_* attribute values
         Determine_Attributes;

         if Real'Machine_Radix /= Radix then
            Report.Failed ("'Machine_Radix incorrectly reports" &
                           Integer'Image (Real'Machine_Radix));
            Show_Results := True;
         end if;

         if Real'Machine_Mantissa /= Mantissa_Digits then
            Report.Failed ("'Machine_Mantissa incorrectly reports" &
                           Integer'Image (Real'Machine_Mantissa));
            Show_Results := True;
         end if;

         if Real'Machine_Rounds /= Rounds then
            Report.Failed ("'Machine_Rounds incorrectly reports " &
                           Boolean'Image (Real'Machine_Rounds));
            Show_Results := True;
         end if;

         if Show_Results then
            Report.Comment ("computed Machine_Mantissa is" & 
                            Integer'Image (Mantissa_Digits));
            Report.Comment ("computed Radix is" &
                            Integer'Image (Radix));
            Report.Comment ("computed Rounds is " &
                            Boolean'Image (Rounds));
         end if;

         -- check the model attributes against the machine attributes
	 -- G.2.2(3)/3;6.0
         if Real'Model_Mantissa > Real'Machine_Mantissa then
	    Report.Failed ("model mantissa > machine mantissa");
	 end if;

         -- G.2.2(3)/2;6.0
         --  'Model_Mantissa >= ceiling(d*log(10)/log(radix))+1
         Min_Mantissa_Digits := 
           Integer (
              Real'Ceiling (
                 Real(Real'Digits) * Log(10.0) / Log(Real(Real'Machine_Radix))
                   )       ) + 1;
         if Real'Model_Mantissa < Min_Mantissa_Digits then
            Report.Failed ("Model_Mantissa [" &
                           Integer'Image (Real'Model_Mantissa) &
                           "] < minimum mantissa digits [" &
                           Integer'Image (Min_Mantissa_Digits) &
                           "]");
         end if;

      exception
         when Illegal_Optimization =>
             Report.Failed ("illegal optimization of" &
                            " floating point expression");
      end Do_Test;
   end Chk_Attrs;

   package Chk_Float is new Chk_Attrs (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 Chk_Attrs (A_Long_Float);
begin
   Report.Test ("CXG2001",
                "Check the attributes Model_Mantissa," &
                " Machine_Mantissa, Machine_Radix," &
                " and Machine_Rounds");

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

   Report.Comment ("checking a digits" & 
                   Integer'Image (System.Max_Digits) &
                   " floating point type");
   Chk_A_Long_Float.Do_Test;

   Report.Result;
end CXG2001;