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-- CXG2014.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 SINH and COSH 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 that use an identity for determining the result.

--         Exception checks.

--

-- 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:

--      15 Mar 96   SAIC    Initial release for 2.1

--      03 Jun 98   EDS     In line 80, change 1000 to 1024, making it a model

--                          number.  Add Taylor Series terms in line 281.

--      15 Feb 99   RLB     Repaired Subtraction_Error_Test to avoid precision

--                          problems.

--!

--

-- 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 CXG2014 is

   Verbose : constant Boolean := False;

   Max_Samples : constant := 1024;

   E  : constant := Ada.Numerics.E;

   Cosh1 : constant := (E + 1.0 / E) / 2.0;    -- cosh(1.0)

   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 Sinh (X : Real) return Real renames

           Elementary_Functions.Sinh;

      function Cosh (X : Real) return Real renames

           Elementary_Functions.Cosh;

      function Log (X : Real) return Real renames

           Elementary_Functions.Log;

      -- 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_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;

         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;

      begin

         Check (Sinh (1.0),

                (E - 1.0 / E) / 2.0,

                "sinh(1)",

                Minimum_Error);

         Check (Cosh (1.0),

                Cosh1,

                "cosh(1)",

                Minimum_Error);

         Check (Sinh (2.0),

                (E * E - (1.0 / (E * E))) / 2.0,

                "sinh(2)",

                Minimum_Error);

         Check (Cosh (2.0),

                (E * E + (1.0 / (E * E))) / 2.0,

                "cosh(2)",

                Minimum_Error);

         Check (Sinh (-1.0),

                (1.0 / E - E) / 2.0,

                "sinh(-1)",

                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 (Sinh (0.0),  0.0, "sinh(0)", No_Error);

         Check (Cosh (0.0),  1.0, "cosh(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_1_Test is

      -- For the Sinh test use the identity

      --    2 * Sinh(x) * Cosh(1) = Sinh(x+1) + Sinh (x-1)

      -- which is transformed to

      --    Sinh(x) = ((Sinh(x+1) + Sinh(x-1)) * C

      -- where C = 1/(2*Cosh(1))

      --

      -- For the Cosh test use the identity

      --    2 * Cosh(x) * Cosh(1) = Cosh(x+1) + Cosh(x-1)

      -- which is transformed to

      --    Cosh(x) = C * (Cosh(x+1) + Cosh(x-1))

      -- where C is the same as above

      --

      -- see Cody pg 230-231 for details on the error analysis.

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

         A : constant := 3.0;

            -- large upper bound but not so large as to cause Cosh(B)

            -- to overflow

         B : constant Real := Log(Real'Safe_Last) - 2.0;

         X_Minus_1, X, X_Plus_1 : Real;

         Actual1, Actual2 : Real;

         C : constant := 1.0 / (2.0 * Cosh1);

      begin

         Accuracy_Error_Reported := False;  -- reset

         for I in 1..Max_Samples loop

            -- make sure there is no error in x-1, x, and x+1

            X_Plus_1 :=  (B - A) * Real (I) / Real (Max_Samples) + A;

            X_Plus_1  := Real'Machine (X_Plus_1);

            X         := Real'Machine (X_Plus_1 - 1.0);

            X_Minus_1 := Real'Machine (X - 1.0);

            -- Sinh(x) = ((Sinh(x+1) + Sinh(x-1)) * C

            Actual1 := Sinh(X);

            Actual2 := C * (Sinh(X_Plus_1) + Sinh(X_Minus_1));

            Check (Actual1, Actual2,

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

                   Real'Image (X) & ") ",

                   16.0);

            -- Cosh(x) = C * (Cosh(x+1) + Cosh(x-1))

            Actual1 := Cosh (X);

            Actual2 := C * (Cosh(X_Plus_1) + Cosh (X_Minus_1));

            Check (Actual1, Actual2,

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

                   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;

      exception

         when Constraint_Error =>

            Report.Failed

               ("Constraint_Error raised in Identity_1_Test" &

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

         when others =>

            Report.Failed ("exception in Identity_1_Test" &

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

      end Identity_1_Test;

      procedure Subtraction_Error_Test is

      -- This test detects the error resulting from subtraction if

      -- the obvious algorithm was used for computing sinh.  That is,

      -- it it is computed as (e**x - e**-x)/2.

      -- We check the result by using a Taylor series expansion that

      -- will produce a result accurate to the machine precision for

      -- the range under test.

      --

      -- The maximum relative error bound for this test is

      --  8 for the sinh operation and 7 for the Taylor series

      -- for a total of 15 * Model_Epsilon

         A : constant := 0.0;

         B : constant := 0.5;

         X : Real;

         X_Squared : Real;

         Actual, Expected : Real;

      begin

         if Real'digits > 15 then

             return; -- The approximation below is not accurate beyond

                     -- 15 digits. Adding more terms makes the error

                     -- larger, so it makes the test worse for more normal

                     -- values. Thus, we skip this subtest for larger than

                     -- 15 digits.

         end if;

         Accuracy_Error_Reported := False;  -- reset

         for I in 1..Max_Samples loop

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

            X_Squared := X * X;

            Actual := Sinh(X);

            -- The Taylor series regrouped a bit

            Expected :=

               X * (1.0 + (X_Squared / 6.0) *

                          (1.0 + (X_Squared/20.0) *

                                 (1.0 + (X_Squared/42.0) *

                                        (1.0 + (X_Squared/72.0) *

                                               (1.0 + (X_Squared/110.0) *

                                                      (1.0 + (X_Squared/156.0)

                   ))))));

            Check (Actual, Expected,

                   "Subtraction_Error_Test " & Integer'Image (I) & ": sinh(" &

                   Real'Image (X) & ") ",

                   15.0);

            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;

      exception

         when Constraint_Error =>

            Report.Failed

               ("Constraint_Error raised in Subtraction_Error_Test");

         when others =>

            Report.Failed ("exception in Subtraction_Error_Test");

      end Subtraction_Error_Test;

      procedure Exception_Test is

         X1, X2 : Real := 0.0;

      begin

         -- this part of the test is only applicable if 'Machine_Overflows

         -- is true.

         if Real'Machine_Overflows then

            begin

              X1 := Sinh (Real'Safe_Last / 2.0);

              Report.Failed ("no exception for sinh overflow");

            exception

               when Constraint_Error => null;

               when others =>

                  Report.Failed ("wrong exception sinh overflow");

            end;

            begin

              X2 := Cosh (Real'Safe_Last / 2.0);

              Report.Failed ("no exception for cosh overflow");

            exception

               when Constraint_Error => null;

               when others =>

                  Report.Failed ("wrong exception cosh overflow");

            end;

         end if;

         -- optimizer thwarting

         if Report.Ident_Bool (False) then

            Report.Comment (Real'Image (X1 + X2));

         end if;

      end Exception_Test;

      procedure Do_Test is

      begin

         Special_Value_Test;

         Exact_Result_Test;

         Identity_1_Test;

         Subtraction_Error_Test;

         Exception_Test;

      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 ("CXG2014",

                "Check the accuracy of the SINH and COSH functions");

   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 CXG2014;