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-- CXG2017.A

--

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--     F08630-91-C-0015, and DCA100-97-D-0025, the U.S. Government obtained

--     unlimited rights in the software and documentation contained herein.

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--     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

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--                                    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 TANH function returns

--      a result that is 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.

--

-- 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:

--      20 Mar 96   SAIC    Initial release for 2.1

--      17 Aug 96   SAIC    Incorporated reviewer comments.

--      03 Jun 98   EDS     Add parens to remove the potential for overflow.

--                          Remove the invocation of Identity_Test that checks

--                          Tanh values that are too close to zero for the

--                          test's error bounds.

--!

--

-- 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 CXG2017 is

   Verbose : constant Boolean := False;

   Max_Samples : constant := 1000;

   E  : constant := Ada.Numerics.E;

   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 Tanh (X : Real) return Real renames

           Elementary_Functions.Tanh;

      function Log (X : 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_Small instead

         -- of Model_Epsilon and Expected.

         Rel_Error := MRE * abs Expected * Real'Model_Epsilon;

         Abs_Error := MRE * Real'Model_Small;

         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.

         Minimum_Error : constant := 8.0;

         E2 : constant := E * E;

      begin

         Check (Tanh (1.0),

                (E - 1.0 / E) / (E + 1.0 / E),

                "tanh(1)",

                Minimum_Error);

         Check (Tanh (2.0),

                (E2 - 1.0 / E2) / (E2 + 1.0 / E2),

                "tanh(2)",

                Minimum_Error);

      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 Exact_Result_Test is

         No_Error : constant := 0.0;

      begin

         -- A.5.1(38);6.0

         Check (Tanh (0.0),  0.0, "tanh(0)", No_Error);

      exception

         when Constraint_Error =>

            Report.Failed ("Constraint_Error raised in Exact_Result Test");

         when others =>

            Report.Failed ("exception in Exact_Result Test");

      end Exact_Result_Test;

      procedure Identity_Test (A, B : Real) is

      -- For this test we use the identity

      --    TANH(u+v) = [TANH(u) + TANH(v)] / [1 + TANH(u)*TANH(v)]

      -- which is transformed to

      --    TANH(x) = [TANH(y)+C] / [1 + TANH(y) * C]

      -- where C = TANH(1/8) and y = x - 1/8

      --

      -- see Cody pg 248-249 for details on the error analysis.

      -- The net result is a relative error bound of 16 * Model_Epsilon.

      --

      -- The second part of this test checks the identity

      --    TANH(-x) = -TANH(X)

         X, Y : Real;

         Actual1, Actual2 : Real;

         C : constant := 1.2435300177159620805e-1;

      begin

         if Real'Digits > 20 then

            -- constant C is accurate to 20 digits.  Set the low bound

            -- on the error to 16*10**-20

            Error_Low_Bound := 0.00000_00000_00000_00016;

            Report.Comment ("tanh accuracy checked to 20 digits");

         end if;

         Accuracy_Error_Reported := False;  -- reset

         for I in 1..Max_Samples loop

            X :=  (B - A) * (Real (I) / Real (Max_Samples)) + A;

            Actual1 := Tanh(X);

            -- TANH(x) = [TANH(y)+C] / [1 + TANH(y) * C]

            Y := X - (1.0 / 8.0);

            Actual2 := (Tanh (Y) + C) / (1.0 + Tanh(Y) * C);

            Check (Actual1, Actual2,

                   "Identity_1_Test " & Integer'Image (I) & ": tanh(" &

                   Real'Image (X) & ") ",

                   16.0);

            -- TANH(-x) = -TANH(X)

            Actual2 := Tanh(-X);

            Check (-Actual1, Actual2,

                   "Identity_2_Test " & Integer'Image (I) & ": tanh(" &

                   Real'Image (X) & ") ",

                   16.0);

            if Accuracy_Error_Reported then

              -- only report the first error in this test in order to keep

              -- lots of failures from producing a huge error log

              return;

            end if;

         end loop;

         Error_Low_Bound := 0.0;   -- reset

      exception

         when Constraint_Error =>

            Report.Failed

               ("Constraint_Error raised in Identity_Test" &

                " for X=" & Real'Image (X));

         when others =>

            Report.Failed ("exception in Identity_Test" &

                " for X=" & Real'Image (X));

      end Identity_Test;

      procedure Do_Test is

      begin

         Special_Value_Test;

         Exact_Result_Test;

            -- cover a large range

         Identity_Test (1.0, Real'Safe_Last);

      end Do_Test;

   end Generic_Check;

   -----------------------------------------------------------------------

   -----------------------------------------------------------------------

   package Float_Check is new Generic_Check (Float);

   -- check the floating point type with the most digits

   type A_Long_Float is digits System.Max_Digits;

   package A_Long_Float_Check is new Generic_Check (A_Long_Float);

   -----------------------------------------------------------------------

   -----------------------------------------------------------------------

begin

   Report.Test ("CXG2017",

                "Check the accuracy of the TANH function");

   if Verbose then

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

   end if;

   Float_Check.Do_Test;

   if Verbose then

      Report.Comment ("checking a digits" &

                      Integer'Image (System.Max_Digits) &

                      " floating point type");

   end if;

   A_Long_Float_Check.Do_Test;

   Report.Result;

end CXG2017;