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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;

         -- Calculate the first model number nearest to, but above (or equal)

         -- to the expected result:

         while Real'Model (Model_Expected_High) /= Model_Expected_High loop

            -- Try the next machine number higher:

            Model_Expected_High := Real'Adjacent(Model_Expected_High, 100.0);

         end loop;

         if Actual < Model_Expected_Low or Actual > Model_Expected_High then

            Accuracy_Error_Reported := True;

            if Actual < Model_Expected_Low then

               Report.Failed (Test_Name &

                              " actual: " & Real'Image (Actual) &

                              " expected low: " & Real'Image (Model_Expected_Low) &

                              " expected high: " & Real'Image (Model_Expected_High) &

                              " difference: " & Real'Image (Actual - Expected_Low));

            else

               Report.Failed (Test_Name &

                              " actual: " & Real'Image (Actual) &

                              " expected low: " & Real'Image (Model_Expected_Low) &

                              " expected high: " & Real'Image (Model_Expected_High) &

                              " difference: " & Real'Image (Expected_High - Actual));

            end if;

         elsif Verbose then

            Report.Comment (Test_Name & "  passed");

         end if;

      end Check_Exact;

      procedure Exact_Result_Test is

      begin

         --  A.5.1(38)

         Check_Exact (Arcsin (0.0),       0.0, 0.0, "arcsin(0)");

         Check_Exact (Arcsin (0.0, 45.0), 0.0, 0.0, "arcsin(0,45)");

         --  A.5.1(39)

         Check_Exact (Arccos (1.0),       0.0, 0.0, "arccos(1)");

         Check_Exact (Arccos (1.0, 75.0), 0.0, 0.0, "arccos(1,75)");

         --  G.2.4(11-13)

         Check_Exact (Arcsin (1.0), Half_PI_Low, Half_PI_High, "arcsin(1)");

         Check_Exact (Arcsin (1.0, 360.0), 90.0, 90.0, "arcsin(1,360)");

         Check_Exact (Arcsin (-1.0), -Half_PI_High, -Half_PI_Low, "arcsin(-1)");

         Check_Exact (Arcsin (-1.0, 360.0), -90.0, -90.0, "arcsin(-1,360)");

         Check_Exact (Arccos (0.0), Half_PI_Low, Half_PI_High, "arccos(0)");

         Check_Exact (Arccos (0.0, 360.0), 90.0, 90.0, "arccos(0,360)");

         Check_Exact (Arccos (-1.0), PI_Low, PI_High, "arccos(-1)");

         Check_Exact (Arccos (-1.0, 360.0), 180.0, 180.0, "arccos(-1,360)");

      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 Arcsin_Taylor_Series_Test is

         -- the following range is chosen so that the Taylor series

         -- used will produce a result accurate to machine precision.

         --

         -- The following formula is used for the Taylor series:

         --  TS(x) =  x { 1 + (xsq/2) [ (1/3) + (3/4)xsq { (1/5) +

         --                (5/6)xsq [ (1/7) + (7/8)xsq/9 ] } ] }

         --   where xsq = x * x

         --

         A : constant := -0.125;

         B : constant :=  0.125;

         X : Real;

         Y, Y_Sq : Real;

         Actual, Sum, Xm : Real;

         -- terms in Taylor series

         K : constant Integer := Integer (

                Log (

                  Real (Real'Machine_Radix) ** Real'Machine_Mantissa,

                  10.0)) + 1;

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

            Y := X;

            Y_Sq := Y * Y;

            Sum := 0.0;

            Xm := Real (K + K + 1);

            for M in 1 .. K loop

               Sum := Y_Sq * (Sum + 1.0/Xm);

               Xm := Xm - 2.0;

               Sum := Sum * (Xm /(Xm + 1.0));

            end loop;

            Sum := Sum * Y;

            Actual := Y + Sum;

            Sum := (Y - Actual) + Sum;

            if not Real'Machine_Rounds then

               Actual := Actual + (Sum + Sum);

            end if;

            Check (Actual, Arcsin (X),

                   "Taylor Series test" & Integer'Image (I) & ": arcsin(" &

                   Real'Image (X) & ") ",

                   Minimum_Error);

            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 Arcsin_Taylor_Series_Test" &

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

         when others =>

            Report.Failed ("exception in Arcsin_Taylor_Series_Test" &

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

      end Arcsin_Taylor_Series_Test;

      procedure Arccos_Taylor_Series_Test is

         -- the following range is chosen so that the Taylor series

         -- used will produce a result accurate to machine precision.

         --

         -- The following formula is used for the Taylor series:

         --  TS(x) =  x { 1 + (xsq/2) [ (1/3) + (3/4)xsq { (1/5) +

         --                (5/6)xsq [ (1/7) + (7/8)xsq/9 ] } ] }

         --  arccos(x) = pi/2 - TS(x)

         A : constant := -0.125;

         B : constant :=  0.125;

         C1, C2 : Real;

         X : Real;

         Y, Y_Sq : Real;

         Actual, Sum, Xm, S : Real;

         -- terms in Taylor series

         K : constant Integer := Integer (

                Log (

                  Real (Real'Machine_Radix) ** Real'Machine_Mantissa,

                  10.0)) + 1;

      begin

         if Real'Digits > 23 then

            -- constants in this section only accurate to 23 digits

            Error_Low_Bound := 0.00000_00000_00000_00000_001;

            Report.Comment ("arctan accuracy checked to 23 digits");

         end if;

         -- C1 + C2 equals Pi/2 accurate to 23 digits

         if Real'Machine_Radix = 10 then

            C1 := 1.57;

            C2 := 7.9632679489661923132E-4;

         else

            C1 := 201.0 / 128.0;

            C2 := 4.8382679489661923132E-4;

         end if;

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

            Y := X;

            Y_Sq := Y * Y;

            Sum := 0.0;

            Xm := Real (K + K + 1);

            for M in 1 .. K loop

               Sum := Y_Sq * (Sum + 1.0/Xm);

               Xm := Xm - 2.0;

               Sum := Sum * (Xm /(Xm + 1.0));

            end loop;

            Sum := Sum * Y;

            -- at this point we have arcsin(x).

            -- We compute arccos(x) = pi/2 - arcsin(x).

            -- The following code segment is translated directly from

            -- the CELEFUNT FORTRAN implementation

            S := C1 + C2;

            Sum := ((C1 - S) + C2) - Sum;

            Actual := S + Sum;

            Sum := ((S - Actual) + Sum) - Y;

            S := Actual;

            Actual := S + Sum;

            Sum := (S - Actual) + Sum;

            if not Real'Machine_Rounds then

               Actual := Actual + (Sum + Sum);

            end if;

            Check (Actual, Arccos (X),

                   "Taylor Series test" & Integer'Image (I) & ": arccos(" &

                   Real'Image (X) & ") ",

                   Minimum_Error);

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

              -- lots of failures from producing a huge error log

            exit when Accuracy_Error_Reported;

         end loop;

         Error_Low_Bound := 0.0;  -- reset

      exception

         when Constraint_Error =>

            Report.Failed

               ("Constraint_Error raised in Arccos_Taylor_Series_Test" &

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

         when others =>

            Report.Failed ("exception in Arccos_Taylor_Series_Test" &

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

      end Arccos_Taylor_Series_Test;

      procedure Identity_Test is

         -- test the identity arcsin(-x) = -arcsin(x)

         -- range chosen to be most of the valid range of the argument.

         A : constant := -0.999;

         B : constant :=  0.999;

         X : Real;

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

            Check (Arcsin(-X), -Arcsin (X),

                   "Identity test" & Integer'Image (I) & ": arcsin(" &

                   Real'Image (X) & ") ",

                   8.0);   -- 2 arcsin evaluations => twice the error bound

            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;

      end Identity_Test;

      procedure Exception_Test is

         X1, X2 : Real := 0.0;

      begin

            begin

              X1 := Arcsin (1.1);

              Report.Failed ("no exception for Arcsin (1.1)");

            exception

               when Constraint_Error =>

                  Report.Failed ("Constraint_Error instead of " &

                     "Argument_Error for Arcsin (1.1)");

               when Ada.Numerics.Argument_Error =>

                  null;    -- expected result

               when others =>

                  Report.Failed ("wrong exception for Arcsin(1.1)");

            end;

            begin

              X2 := Arccos (-1.1);

              Report.Failed ("no exception for Arccos (-1.1)");

            exception

               when Constraint_Error =>

                  Report.Failed ("Constraint_Error instead of " &

                     "Argument_Error for Arccos (-1.1)");

               when Ada.Numerics.Argument_Error =>

                  null;    -- expected result

               when others =>

                  Report.Failed ("wrong exception for Arccos(-1.1)");

            end;

         -- 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;

         Arcsin_Taylor_Series_Test;

         Arccos_Taylor_Series_Test;

         Identity_Test;

         Exception_Test;

      end Do_Test;

   end Generic_Check;

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

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

   -- These expressions must be truly static, which is why we have to do them

   -- outside of the generic, and we use the named numbers. Note that we know

   -- that PI is not a machine number (it is irrational), and it should be

   -- represented to more digits than supported by the target machine.

   Float_Half_PI_Low  : constant := Float'Adjacent(PI/2.0,  0.0);

   Float_Half_PI_High : constant := Float'Adjacent(PI/2.0, 10.0);

   Float_PI_Low       : constant := Float'Adjacent(PI,      0.0);

   Float_PI_High      : constant := Float'Adjacent(PI,     10.0);

   package Float_Check is new Generic_Check (Float,

        Half_PI_Low  => Float_Half_PI_Low,

        Half_PI_High => Float_Half_PI_High,

        PI_Low  => Float_PI_Low,

        PI_High => Float_PI_High);

   -- check the floating point type with the most digits

   type A_Long_Float is digits System.Max_Digits;

   A_Long_Float_Half_PI_Low  : constant := A_Long_Float'Adjacent(PI/2.0,  0.0);

   A_Long_Float_Half_PI_High : constant := A_Long_Float'Adjacent(PI/2.0, 10.0);

   A_Long_Float_PI_Low       : constant := A_Long_Float'Adjacent(PI,      0.0);

   A_Long_Float_PI_High      : constant := A_Long_Float'Adjacent(PI,     10.0);

   package A_Long_Float_Check is new Generic_Check (A_Long_Float,

        Half_PI_Low  => A_Long_Float_Half_PI_Low,

        Half_PI_High => A_Long_Float_Half_PI_High,

        PI_Low  => A_Long_Float_PI_Low,

        PI_High => A_Long_Float_PI_High);

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

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

begin

   Report.Test ("CXG2015",

                "Check the accuracy of the ARCSIN and ARCCOS 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 CXG2015;