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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;
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