cxg2012.a

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-- CXG2012.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 exponentiation operator returns
--      results that are within the error bound allowed.
--
-- TEST DESCRIPTION:
--      This test consists of a generic package that is
--      instantiated to check 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.
--         Exception checks.
--      While this test concentrates on the "**" operator
--      defined in Generic_Elementary_Functions, a check is also
--      performed on the standard "**" operator.
--
-- 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:
--       7 Mar 96   SAIC    Initial release for 2.1
--       2 Sep 96   SAIC    Improvements as suggested by reviewers
--	 3 Jun 98   EDS     Add parens to ensure that the expression is not
--                          evaluated by multiplying its two large terms
--                          together and overflowing.
--       3 Dec 01   RLB     Added 'Machine to insure that equality tests
--                          are certain to work.
--
--!

--
-- References:
--
-- Software Manual for the Elementary Functions
-- William J. Cody, Jr. and William Waite
-- Prentice-Hall, 1980
--
-- CRC Standard Mathematical Tables
-- 23rd Edition
--
-- Implementation and Testing of Function Software
-- W. J. Cody
-- Problems and Methodologies in Mathematical Software Production
-- editors P. C. Messina and A. Murli
-- Lecture Notes in Computer Science   Volume 142
-- Springer Verlag, 1982
--

with System;
with Report;
with Ada.Numerics.Generic_Elementary_Functions;
procedure CXG2012 is
   Verbose : constant Boolean := False;
   Max_Samples : constant := 1000;

   -- 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 Elementary_Functions is new
           Ada.Numerics.Generic_Elementary_Functions (Real);
      function Sqrt (X : Real) return Real renames
           Elementary_Functions.Sqrt;
      function Exp (X : Real) return Real renames
           Elementary_Functions.Exp;
      function Log (X : Real) return Real renames
           Elementary_Functions.Log;
      function "**" (L, R : Real) return Real renames
           Elementary_Functions."**";

      -- 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;


      -- the following version of Check computes the allowed error bound
      -- using the operands
      procedure Check (Actual, Expected : Real;
                       Left, Right : Real;
                       Test_Name : String;
                       MRE_Factor : Real := 1.0) is
         MRE : Real;
      begin
         MRE := MRE_Factor * (4.0 + abs (Right * Log(Left)) / 32.0);
         Check (Actual, Expected, Test_Name, MRE);
      end Check;


      procedure Real_To_Integer_Test is
         type Int_Check is
	    record
	       Left : Real;
	       Right : Integer;
	       Expected : Real;
	    end record;
	 type Int_Checks is array (Positive range <>) of Int_Check;

         -- the following tests use only model numbers so the result
         -- is expected to be exact.
	 IC : constant Int_Checks :=
         ( (  2.0,   5,       32.0),
           ( -2.0,   5,      -32.0),
           (  0.5,  -5,       32.0),
           (  2.0,   0,        1.0),
           (  0.0,   0,        1.0) );
      begin
	 for I in IC'Range loop
            declare
	       Y : Real;
            begin
               Y := IC (I).Left ** IC (I).Right;
               Check (Y, IC (I).Expected,
		      "real to integer test" &
		      Real'Image (IC (I).Left) & " ** " &
		      Integer'Image (IC (I).Right),
		      0.0);  -- no error allowed
            exception
               when Constraint_Error =>
                  Report.Failed ("Constraint_Error raised in rtoi test " &
		     Integer'Image (I));
               when others =>
                  Report.Failed ("exception in rtoi test " &
		     Integer'Image (I));
            end;
         end loop;
      end Real_To_Integer_Test;


      procedure Special_Value_Test is
         No_Error : constant := 0.0;
      begin
         Check (0.0 ** 1.0, 0.0, "0**1", No_Error);
         Check (1.0 ** 0.0, 1.0, "1**0", No_Error);

         Check ( 2.0 **  5.0,  32.0,  2.0,  5.0,  "2**5");
         Check ( 0.5**(-5.0),  32.0,  0.5, -5.0,  "0.5**-5");

         Check (Sqrt2 ** 4.0,   4.0,  Sqrt2, 4.0,  "Sqrt2**4");
         Check (Sqrt3 ** 6.0,  27.0,  Sqrt3, 6.0,  "Sqrt3**6");

         Check (2.0 ** 0.5,   Sqrt2,    2.0, 0.5,  "2.0**0.5");