cxg2004.a

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-- CXG2004.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 sin and cos functions return
--      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
--      the following parts:
--         Special value checks where the result is a known constant.
--         Checks using an identity relationship.
--
-- 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:
--      13 FEB 96   SAIC    Initial release for 2.1
--      22 APR 96   SAIC    Changed to generic implementation.
--      18 AUG 96   SAIC    Improvements to commentary.
--      23 OCT 96   SAIC    Exact results are not required unless the
--                          cycle is specified.  
--      28 FEB 97   PWB.CTA Removed checks where cycle 2.0*Pi is specified
--      02 JUN 98   EDS     Revised calculations to ensure that X is exactly
--                          three times Y per advice of numerics experts.
--
-- CHANGE NOTE:
--      According to Ken Dritz, author of the Numerics Annex of the RM,
--      one should never specify the cycle 2.0*Pi for the trigonometric
--      functions.  In particular, if the machine number for the first
--      argument is not an exact multiple of the machine number for the
--      explicit cycle, then the specified exact results cannot be
--      reasonably expected.  The affected checks in this test have been
--      marked as comments, with the additional notation "pwb-math".
--      Phil Brashear
--!

--
-- 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
--
-- The sin and cos checks are translated directly from 
-- the netlib FORTRAN code that was written by W. Cody.
--

with System;
with Report;
with Ada.Numerics.Generic_Elementary_Functions;
with Ada.Numerics.Elementary_Functions;
procedure CXG2004 is
   Verbose : constant Boolean := False;
   Number_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;

   Pi : constant := Ada.Numerics.Pi;

   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 Sin (X : Real) return Real renames
           Elementary_Functions.Sin;
      function Cos (X : Real) return Real renames
           Elementary_Functions.Cos;
      function Sin (X, Cycle : Real) return Real renames
           Elementary_Functions.Sin;
      function Cos (X, Cycle : Real) return Real renames
           Elementary_Functions.Cos;

      Accuracy_Error_Reported : Boolean := False;

      procedure Check (Actual, Expected : Real;
                       Test_Name : String;
                       MRE : Real) is
         Rel_Error,
         Abs_Error,
         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 := 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; 


         -- in addition to the relative error checks we apply the
         -- criteria of G.2.4(16)
         if abs (Actual) > 1.0 then
            Accuracy_Error_Reported := True;
            Report.Failed (Test_Name & " result > 1.0");
         elsif 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) &
                           " mre:" & 
                           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;


      procedure Sin_Check (A, B : Real;
                           Arg_Range : String) is
         -- test a selection of 
         -- arguments selected from the range A to B. 
         --
         -- This test uses the identity
	 --   sin(x) = sin(x/3)*(3 - 4 * sin(x/3)**2)
	 --
         -- Note that in this test we must take into account the
         -- error in the calculation of the expected result so
         -- the maximum relative error is larger than the
         -- accuracy required by the ARM.

         X, Y, ZZ : Real;
	 Actual, Expected : Real;
	 MRE : Real;
	 Ran : Real;
      begin
         Accuracy_Error_Reported := False;  -- reset
         for I in 1 .. Number_Samples loop
	    -- Evenly distributed selection of arguments
	    Ran := Real (I) / Real (Number_Samples);

	    -- make sure x and x/3 are both exactly representable
	    -- on the machine.  See "Implementation and Testing of
            -- Function Software" page 44.
            X := (B - A) * Ran + A;
            Y := Real'Leading_Part 
                      ( X/3.0, 
                        Real'Machine_Mantissa - Real'Exponent (3.0) );
            X := Y * 3.0;

	    Actual := Sin (X);

	    ZZ := Sin(Y);
	    Expected := ZZ * (3.0 - 4.0 * ZZ * ZZ);

            -- note that since the expected value is computed, we
            -- must take the error in that computation into account.
            -- See Cody pp 139-141.
	    MRE := 4.0;

            Check (Actual, Expected,
                   "sin test of range" & Arg_Range &
                      Integer'Image (I),
                   MRE);
            exit when Accuracy_Error_Reported;
         end loop;
      exception
         when Constraint_Error => 
            Report.Failed 
               ("Constraint_Error raised in sin check");
         when others =>
            Report.Failed ("exception in sin check");
      end Sin_Check;



      procedure Cos_Check (A, B : Real;
                                  Arg_Range : String) is
         -- test a selection of 
         -- arguments selected from the range A to B. 
         --
         -- This test uses the identity
	 --   cos(x) = cos(x/3)*(4 * cos(x/3)**2 - 3)
	 --
         -- Note that in this test we must take into account the
         -- error in the calculation of the expected result so
         -- the maximum relative error is larger than the
         -- accuracy required by the ARM.

         X, Y, ZZ : Real;
	 Actual, Expected : Real;
	 MRE : Real;
	 Ran : Real;
      begin
         Accuracy_Error_Reported := False;  -- reset
         for I in 1 .. Number_Samples loop