cxg2015.a

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-- CXG2015.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 ARCSIN and ARCCOS 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
--      several parts:
--         Special value checks where the result is a known constant.
--         Checks in a specific range where a Taylor series can be
--         used to compute an accurate result for comparison.
--         Exception checks.
--      The Taylor series tests are a direct translation of the
--      FORTRAN code found in the reference.
--
-- 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:
--      18 Mar 96   SAIC    Initial release for 2.1
--      24 Apr 96   SAIC    Fixed error bounds.
--      17 Aug 96   SAIC    Added reference information and improved
--                          checking for machines with more than 23
--                          digits of precision.
--      03 Feb 97   PWB.CTA Removed checks with explicit Cycle => 2.0*Pi
--      22 Dec 99   RLB     Added model range checking to "exact" results,
--                          in order to avoid too strictly requiring a specific
--                          result, and too weakly checking results.
--
-- 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
--
-- CELEFUNT: A Portable Test Package for Complex Elementary Functions
-- ACM Collected Algorithms number 714

with System;
with Report;
with Ada.Numerics.Generic_Elementary_Functions;
procedure CXG2015 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;

   Pi : constant := Ada.Numerics.Pi;

   -- relative error bound from G.2.4(7);6.0
   Minimum_Error : constant := 4.0;

   generic
      type Real is digits <>;
      Half_PI_Low : in Real; -- The machine number closest to, but not greater
                             -- than PI/2.0.
      Half_PI_High : in Real;-- The machine number closest to, but not less
                             -- than PI/2.0.
      PI_Low : in Real;      -- The machine number closest to, but not greater
                             -- than PI.
      PI_High : in Real;     -- The machine number closest to, but not less
                             -- than PI.
   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 Arcsin (X : Real) return Real renames
           Elementary_Functions.Arcsin;
      function Arcsin (X, Cycle : Real) return Real renames
           Elementary_Functions.Arcsin;
      function Arccos (X : Real) return Real renames
           Elementary_Functions.ArcCos;
      function Arccos (X, Cycle : Real) return Real renames
           Elementary_Functions.ArcCos;

      -- needed for support
      function Log (X, Base : Real) return Real renames
           Elementary_Functions.Log;

      -- flag used to terminate some tests early
      Accuracy_Error_Reported : Boolean := False;

      -- The following value is a lower bound on the accuracy
      -- required.  It is normally 0.0 so that the lower bound
      -- is computed from Model_Epsilon.  However, for tests
      -- where the expected result is only known to a certain
      -- amount of precision this bound takes on a non-zero
      -- value to account for that level of precision.
      Error_Low_Bound : Real := 0.0;


      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;

         -- take into account the low bound on the error
         if Max_Error < Error_Low_Bound then
            Max_Error := Error_Low_Bound;
         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;


      procedure Special_Value_Test is
         -- In the following tests the expected result is accurate
         -- to the machine precision so the minimum guaranteed error
         -- bound can be used.

         type Data_Point is
            record
               Degrees,
               Radians,
               Argument,
               Error_Bound : Real;
            end record;

         type Test_Data_Type is array (Positive range <>) of Data_Point;

         -- the values in the following tables only involve static
         -- expressions so no loss of precision occurs.  However,
         -- rounding can be an issue with expressions involving Pi
         -- and square roots.  The error bound specified in the
         -- table takes the sqrt error into account but not the
         -- error due to Pi.  The Pi error is added in in the
         -- radians test below.

         Arcsin_Test_Data : constant Test_Data_Type := (
         --  degrees      radians          sine  error_bound   test #
          --(  0.0,           0.0,          0.0,     0.0 ),    -- 1 - In Exact_Result_Test.
            ( 30.0,        Pi/6.0,          0.5,     4.0 ),    -- 2
            ( 60.0,        Pi/3.0,    Sqrt3/2.0,     5.0 ),    -- 3
          --( 90.0,        Pi/2.0,          1.0,     4.0 ),    -- 4 - In Exact_Result_Test.
          --(-90.0,       -Pi/2.0,         -1.0,     4.0 ),    -- 5 - In Exact_Result_Test.
            (-60.0,       -Pi/3.0,   -Sqrt3/2.0,     5.0 ),    -- 6
            (-30.0,       -Pi/6.0,         -0.5,     4.0 ),    -- 7
            ( 45.0,        Pi/4.0,    Sqrt2/2.0,     5.0 ),    -- 8
            (-45.0,       -Pi/4.0,   -Sqrt2/2.0,     5.0 ) );  -- 9

         Arccos_Test_Data : constant Test_Data_Type := (
         --  degrees      radians       cosine   error_bound   test #
          --(  0.0,           0.0,         1.0,      0.0 ),    -- 1 - In Exact_Result_Test.
            ( 30.0,        Pi/6.0,   Sqrt3/2.0,      5.0 ),    -- 2
            ( 60.0,        Pi/3.0,         0.5,      4.0 ),    -- 3
          --( 90.0,        Pi/2.0,         0.0,      4.0 ),    -- 4 - In Exact_Result_Test.
            (120.0,    2.0*Pi/3.0,        -0.5,      4.0 ),    -- 5
            (150.0,    5.0*Pi/6.0,  -Sqrt3/2.0,      5.0 ),    -- 6
          --(180.0,            Pi,        -1.0,      4.0 ),    -- 7 - In Exact_Result_Test.
            ( 45.0,        Pi/4.0,   Sqrt2/2.0,      5.0 ),    -- 8
            (135.0,    3.0*Pi/4.0,  -Sqrt2/2.0,      5.0 ) );  -- 9

         Cycle_Error,
         Radian_Error : Real;
      begin
         for I in Arcsin_Test_Data'Range loop

            -- note exact result requirements  A.5.1(38);6.0 and
            -- G.2.4(12);6.0
            if Arcsin_Test_Data (I).Error_Bound = 0.0 then
               Cycle_Error := 0.0;
               Radian_Error := 0.0;
            else
               Cycle_Error := Arcsin_Test_Data (I).Error_Bound;
               -- allow for rounding error in the specification of Pi
               Radian_Error := Cycle_Error + 1.0;
            end if;

            Check (Arcsin (Arcsin_Test_Data (I).Argument),
                   Arcsin_Test_Data (I).Radians,
                   "test" & Integer'Image (I) &
                   " arcsin(" &
                   Real'Image (Arcsin_Test_Data (I).Argument) &
                   ")",
                   Radian_Error);
--pwb-math            Check (Arcsin (Arcsin_Test_Data (I).Argument, 2.0 * Pi),
--pwb-math                   Arcsin_Test_Data (I).Radians,
--pwb-math                   "test" & Integer'Image (I) &
--pwb-math                   " arcsin(" &
--pwb-math                   Real'Image (Arcsin_Test_Data (I).Argument) &
--pwb-math                   ", 2pi)",
--pwb-math                   Cycle_Error);
            Check (Arcsin (Arcsin_Test_Data (I).Argument, 360.0),
                   Arcsin_Test_Data (I).Degrees,
                   "test" & Integer'Image (I) &
                   " arcsin(" &
                   Real'Image (Arcsin_Test_Data (I).Argument) &
                   ", 360)",
                   Cycle_Error);
         end loop;


         for I in Arccos_Test_Data'Range loop

            -- note exact result requirements  A.5.1(39);6.0 and
            -- G.2.4(12);6.0
            if Arccos_Test_Data (I).Error_Bound = 0.0 then
               Cycle_Error := 0.0;
               Radian_Error := 0.0;
            else
               Cycle_Error := Arccos_Test_Data (I).Error_Bound;
               -- allow for rounding error in the specification of Pi
               Radian_Error := Cycle_Error + 1.0;
            end if;

            Check (Arccos (Arccos_Test_Data (I).Argument),
                   Arccos_Test_Data (I).Radians,
                   "test" & Integer'Image (I) &
                   " arccos(" &
                   Real'Image (Arccos_Test_Data (I).Argument) &
                   ")",
                   Radian_Error);
--pwb-math            Check (Arccos (Arccos_Test_Data (I).Argument, 2.0 * Pi),
--pwb-math                   Arccos_Test_Data (I).Radians,
--pwb-math                   "test" & Integer'Image (I) &
--pwb-math                   " arccos(" &
--pwb-math                   Real'Image (Arccos_Test_Data (I).Argument) &
--pwb-math                   ", 2pi)",
--pwb-math                   Cycle_Error);
            Check (Arccos (Arccos_Test_Data (I).Argument, 360.0),
                   Arccos_Test_Data (I).Degrees,
                   "test" & Integer'Image (I) &
                   " arccos(" &
                   Real'Image (Arccos_Test_Data (I).Argument) &
                   ", 360)",
                   Cycle_Error);
         end loop;

      exception
         when Constraint_Error =>
            Report.Failed ("Constraint_Error raised in special value test");
         when others =>
            Report.Failed ("exception in special value test");
      end Special_Value_Test;


      procedure Check_Exact (Actual, Expected_Low, Expected_High : Real;
	                     Test_Name : String) is
         -- If the expected result is not a model number, then Expected_Low is
         -- the first machine number less than the (exact) expected
         -- result, and Expected_High is the first machine number greater than
         -- the (exact) expected result. If the expected result is a model
         -- number, Expected_Low = Expected_High = the result.
         Model_Expected_Low  : Real := Expected_Low;
         Model_Expected_High : Real := Expected_High;
      begin
         -- Calculate the first model number nearest to, but below (or equal)
         -- to the expected result:
         while Real'Model (Model_Expected_Low) /= Model_Expected_Low loop
            -- Try the next machine number lower:
            Model_Expected_Low := Real'Adjacent(Model_Expected_Low, 0.0);
         end loop;