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authorupstream source tree <ports@midipix.org>2015-03-15 20:14:05 -0400
committerupstream source tree <ports@midipix.org>2015-03-15 20:14:05 -0400
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+-- CXG2001.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 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;