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| author | kono |
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| date | Fri, 27 Oct 2017 22:46:09 +0900 |
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-- CXG2010.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 exp function returns -- results that are within the error bound allowed. -- -- TEST DESCRIPTION: -- This test contains three test packages that are almost -- identical. The first two packages differ only in the -- floating point type that is being tested. The first -- and third package differ only in whether the generic -- elementary functions package or the pre-instantiated -- package is used. -- The test package is not generic so that the arguments -- and expected results for some of the test values -- can be expressed as universal real instead of being -- computed at runtime. -- -- 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 and where the Machine_Radix is 2, 4, 8, or 16. -- This test only applies to the Strict Mode for numerical -- accuracy. -- -- -- CHANGE HISTORY: -- 1 Mar 96 SAIC Initial release for 2.1 -- 2 Sep 96 SAIC Improved check routine -- --! -- -- 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 -- -- -- Notes on derivation of error bound for exp(p)*exp(-p) -- -- Let a = true value of exp(p) and ac be the computed value. -- Then a = ac(1+e1), where |e1| <= 4*Model_Epsilon. -- Similarly, let b = true value of exp(-p) and bc be the computed value. -- Then b = bc(1+e2), where |e2| <= 4*ME. -- -- The product of x and y is (x*y)(1+e3), where |e3| <= 1.0ME -- -- Hence, the computed ab is [ac(1+e1)*bc(1+e2)](1+e3) = -- (ac*bc)[1 + e1 + e2 + e3 + e1e2 + e1e3 + e2e3 + e1e2e3). -- -- Throwing away the last four tiny terms, we have (ac*bc)(1 + eta), -- -- where |eta| <= (4+4+1)ME = 9.0Model_Epsilon. with System; with Report; with Ada.Numerics.Generic_Elementary_Functions; with Ada.Numerics.Elementary_Functions; procedure CXG2010 is Verbose : constant Boolean := False; Max_Samples : constant := 1000; Accuracy_Error_Reported : Boolean := False; package Float_Check is subtype Real is Float; procedure Do_Test; end Float_Check; package body Float_Check is package Elementary_Functions is new Ada.Numerics.Generic_Elementary_Functions (Real); function Sqrt (X : Real) return Real renames Elementary_Functions.Sqrt; function Exp (X : Real) return Real renames Elementary_Functions.Exp; -- 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 Argument_Range_Check_1 (A, B : Real; Test : String) is -- test a evenly distributed selection of -- arguments selected from the range A to B. -- Test using identity: EXP(X-V) = EXP(X) * EXP (-V) -- The parameter One_Minus_Exp_Minus_V is the value -- 1.0 - Exp (-V) -- accurate to machine precision. -- This procedure is a translation of part of Cody's test X : Real; Y : Real; ZX, ZY : Real; V : constant := 1.0 / 16.0; One_Minus_Exp_Minus_V : constant := 6.058693718652421388E-2; begin Accuracy_Error_Reported := False; for I in 1..Max_Samples loop X := (B - A) * Real (I) / Real (Max_Samples) + A; Y := X - V; if Y < 0.0 then X := Y + V; end if; ZX := Exp (X); ZY := Exp (Y); -- ZX := Exp(X) - Exp(X) * (1 - Exp(-V); -- which simplifies to ZX := Exp (X-V); ZX := ZX - ZX * One_Minus_Exp_Minus_V; -- note that since the expected value is computed, we -- must take the error in that computation into account. Check (ZY, ZX, "test " & Test & " -" & Integer'Image (I) & " exp (" & Real'Image (X) & ")", 9.0); exit when Accuracy_Error_Reported; end loop; exception when Constraint_Error => Report.Failed ("Constraint_Error raised in argument range check 1"); when others => Report.Failed ("exception in argument range check 1"); end Argument_Range_Check_1; procedure Argument_Range_Check_2 (A, B : Real; Test : String) is -- test a evenly distributed selection of -- arguments selected from the range A to B. -- Test using identity: EXP(X-V) = EXP(X) * EXP (-V) -- The parameter One_Minus_Exp_Minus_V is the value -- 1.0 - Exp (-V) -- accurate to machine precision. -- This procedure is a translation of part of Cody's test X : Real; Y : Real; ZX, ZY : Real; V : constant := 45.0 / 16.0; -- 1/16 - Exp(45/16) Coeff : constant := 2.4453321046920570389E-3; begin Accuracy_Error_Reported := False; for I in 1..Max_Samples loop X := (B - A) * Real (I) / Real (Max_Samples) + A; Y := X - V; if Y < 0.0 then X := Y + V; end if; ZX := Exp (X); ZY := Exp (Y); -- ZX := Exp(X) * 1/16 - Exp(X) * Coeff; -- where Coeff is 1/16 - Exp(45/16) -- which simplifies to ZX := Exp (X-V); ZX := ZX * 0.0625 - ZX * Coeff; -- note that since the expected value is computed, we -- must take the error in that computation into account. Check (ZY, ZX, "test " & Test & " -" & Integer'Image (I) & " exp (" & Real'Image (X) & ")", 9.0); exit when Accuracy_Error_Reported; end loop; exception when Constraint_Error => Report.Failed ("Constraint_Error raised in argument range check 2"); when others => Report.Failed ("exception in argument range check 2"); end Argument_Range_Check_2; procedure Do_Test is begin --- test 1 --- declare Y : Real; begin Y := Exp(1.0); -- normal accuracy requirements Check (Y, Ada.Numerics.e, "test 1 -- exp(1)", 4.0); exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 1"); when others => Report.Failed ("exception in test 1"); end; --- test 2 --- declare Y : Real; begin Y := Exp(16.0) * Exp(-16.0); Check (Y, 1.0, "test 2 -- exp(16)*exp(-16)", 9.0); exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 2"); when others => Report.Failed ("exception in test 2"); end; --- test 3 --- declare Y : Real; begin Y := Exp (Ada.Numerics.Pi) * Exp (-Ada.Numerics.Pi); Check (Y, 1.0, "test 3 -- exp(pi)*exp(-pi)", 9.0); exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 3"); when others => Report.Failed ("exception in test 3"); end; --- test 4 --- declare Y : Real; begin Y := Exp(0.0); Check (Y, 1.0, "test 4 -- exp(0.0)", 0.0); -- no error allowed exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 4"); when others => Report.Failed ("exception in test 4"); end; --- test 5 --- -- constants used here only have 19 digits of precision if Real'Digits > 19 then Error_Low_Bound := 0.00000_00000_00000_0001; Report.Comment ("exp accuracy checked to 19 digits"); end if; Argument_Range_Check_1 ( 1.0/Sqrt(Real(Real'Machine_Radix)), 1.0, "5"); Error_Low_Bound := 0.0; -- reset --- test 6 --- -- constants used here only have 19 digits of precision if Real'Digits > 19 then Error_Low_Bound := 0.00000_00000_00000_0001; Report.Comment ("exp accuracy checked to 19 digits"); end if; Argument_Range_Check_2 (1.0, Sqrt(Real(Real'Machine_Radix)), "6"); Error_Low_Bound := 0.0; -- reset end Do_Test; end Float_Check; ----------------------------------------------------------------------- ----------------------------------------------------------------------- -- check the floating point type with the most digits type A_Long_Float is digits System.Max_Digits; package A_Long_Float_Check is subtype Real is A_Long_Float; procedure Do_Test; end A_Long_Float_Check; package body A_Long_Float_Check is package Elementary_Functions is new Ada.Numerics.Generic_Elementary_Functions (Real); function Sqrt (X : Real) return Real renames Elementary_Functions.Sqrt; function Exp (X : Real) return Real renames Elementary_Functions.Exp; -- 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 Argument_Range_Check_1 (A, B : Real; Test : String) is -- test a evenly distributed selection of -- arguments selected from the range A to B. -- Test using identity: EXP(X-V) = EXP(X) * EXP (-V) -- The parameter One_Minus_Exp_Minus_V is the value -- 1.0 - Exp (-V) -- accurate to machine precision. -- This procedure is a translation of part of Cody's test X : Real; Y : Real; ZX, ZY : Real; V : constant := 1.0 / 16.0; One_Minus_Exp_Minus_V : constant := 6.058693718652421388E-2; begin Accuracy_Error_Reported := False; for I in 1..Max_Samples loop X := (B - A) * Real (I) / Real (Max_Samples) + A; Y := X - V; if Y < 0.0 then X := Y + V; end if; ZX := Exp (X); ZY := Exp (Y); -- ZX := Exp(X) - Exp(X) * (1 - Exp(-V); -- which simplifies to ZX := Exp (X-V); ZX := ZX - ZX * One_Minus_Exp_Minus_V; -- note that since the expected value is computed, we -- must take the error in that computation into account. Check (ZY, ZX, "test " & Test & " -" & Integer'Image (I) & " exp (" & Real'Image (X) & ")", 9.0); exit when Accuracy_Error_Reported; end loop; exception when Constraint_Error => Report.Failed ("Constraint_Error raised in argument range check 1"); when others => Report.Failed ("exception in argument range check 1"); end Argument_Range_Check_1; procedure Argument_Range_Check_2 (A, B : Real; Test : String) is -- test a evenly distributed selection of -- arguments selected from the range A to B. -- Test using identity: EXP(X-V) = EXP(X) * EXP (-V) -- The parameter One_Minus_Exp_Minus_V is the value -- 1.0 - Exp (-V) -- accurate to machine precision. -- This procedure is a translation of part of Cody's test X : Real; Y : Real; ZX, ZY : Real; V : constant := 45.0 / 16.0; -- 1/16 - Exp(45/16) Coeff : constant := 2.4453321046920570389E-3; begin Accuracy_Error_Reported := False; for I in 1..Max_Samples loop X := (B - A) * Real (I) / Real (Max_Samples) + A; Y := X - V; if Y < 0.0 then X := Y + V; end if; ZX := Exp (X); ZY := Exp (Y); -- ZX := Exp(X) * 1/16 - Exp(X) * Coeff; -- where Coeff is 1/16 - Exp(45/16) -- which simplifies to ZX := Exp (X-V); ZX := ZX * 0.0625 - ZX * Coeff; -- note that since the expected value is computed, we -- must take the error in that computation into account. Check (ZY, ZX, "test " & Test & " -" & Integer'Image (I) & " exp (" & Real'Image (X) & ")", 9.0); exit when Accuracy_Error_Reported; end loop; exception when Constraint_Error => Report.Failed ("Constraint_Error raised in argument range check 2"); when others => Report.Failed ("exception in argument range check 2"); end Argument_Range_Check_2; procedure Do_Test is begin --- test 1 --- declare Y : Real; begin Y := Exp(1.0); -- normal accuracy requirements Check (Y, Ada.Numerics.e, "test 1 -- exp(1)", 4.0); exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 1"); when others => Report.Failed ("exception in test 1"); end; --- test 2 --- declare Y : Real; begin Y := Exp(16.0) * Exp(-16.0); Check (Y, 1.0, "test 2 -- exp(16)*exp(-16)", 9.0); exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 2"); when others => Report.Failed ("exception in test 2"); end; --- test 3 --- declare Y : Real; begin Y := Exp (Ada.Numerics.Pi) * Exp (-Ada.Numerics.Pi); Check (Y, 1.0, "test 3 -- exp(pi)*exp(-pi)", 9.0); exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 3"); when others => Report.Failed ("exception in test 3"); end; --- test 4 --- declare Y : Real; begin Y := Exp(0.0); Check (Y, 1.0, "test 4 -- exp(0.0)", 0.0); -- no error allowed exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 4"); when others => Report.Failed ("exception in test 4"); end; --- test 5 --- -- constants used here only have 19 digits of precision if Real'Digits > 19 then Error_Low_Bound := 0.00000_00000_00000_0001; Report.Comment ("exp accuracy checked to 19 digits"); end if; Argument_Range_Check_1 ( 1.0/Sqrt(Real(Real'Machine_Radix)), 1.0, "5"); Error_Low_Bound := 0.0; -- reset --- test 6 --- -- constants used here only have 19 digits of precision if Real'Digits > 19 then Error_Low_Bound := 0.00000_00000_00000_0001; Report.Comment ("exp accuracy checked to 19 digits"); end if; Argument_Range_Check_2 (1.0, Sqrt(Real(Real'Machine_Radix)), "6"); Error_Low_Bound := 0.0; -- reset end Do_Test; end A_Long_Float_Check; ----------------------------------------------------------------------- ----------------------------------------------------------------------- package Non_Generic_Check is procedure Do_Test; subtype Real is Float; end Non_Generic_Check; package body Non_Generic_Check is package Elementary_Functions renames Ada.Numerics.Elementary_Functions; function Sqrt (X : Real) return Real renames Elementary_Functions.Sqrt; function Exp (X : Real) return Real renames Elementary_Functions.Exp; -- 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 Argument_Range_Check_1 (A, B : Real; Test : String) is -- test a evenly distributed selection of -- arguments selected from the range A to B. -- Test using identity: EXP(X-V) = EXP(X) * EXP (-V) -- The parameter One_Minus_Exp_Minus_V is the value -- 1.0 - Exp (-V) -- accurate to machine precision. -- This procedure is a translation of part of Cody's test X : Real; Y : Real; ZX, ZY : Real; V : constant := 1.0 / 16.0; One_Minus_Exp_Minus_V : constant := 6.058693718652421388E-2; begin Accuracy_Error_Reported := False; for I in 1..Max_Samples loop X := (B - A) * Real (I) / Real (Max_Samples) + A; Y := X - V; if Y < 0.0 then X := Y + V; end if; ZX := Exp (X); ZY := Exp (Y); -- ZX := Exp(X) - Exp(X) * (1 - Exp(-V); -- which simplifies to ZX := Exp (X-V); ZX := ZX - ZX * One_Minus_Exp_Minus_V; -- note that since the expected value is computed, we -- must take the error in that computation into account. Check (ZY, ZX, "test " & Test & " -" & Integer'Image (I) & " exp (" & Real'Image (X) & ")", 9.0); exit when Accuracy_Error_Reported; end loop; exception when Constraint_Error => Report.Failed ("Constraint_Error raised in argument range check 1"); when others => Report.Failed ("exception in argument range check 1"); end Argument_Range_Check_1; procedure Argument_Range_Check_2 (A, B : Real; Test : String) is -- test a evenly distributed selection of -- arguments selected from the range A to B. -- Test using identity: EXP(X-V) = EXP(X) * EXP (-V) -- The parameter One_Minus_Exp_Minus_V is the value -- 1.0 - Exp (-V) -- accurate to machine precision. -- This procedure is a translation of part of Cody's test X : Real; Y : Real; ZX, ZY : Real; V : constant := 45.0 / 16.0; -- 1/16 - Exp(45/16) Coeff : constant := 2.4453321046920570389E-3; begin Accuracy_Error_Reported := False; for I in 1..Max_Samples loop X := (B - A) * Real (I) / Real (Max_Samples) + A; Y := X - V; if Y < 0.0 then X := Y + V; end if; ZX := Exp (X); ZY := Exp (Y); -- ZX := Exp(X) * 1/16 - Exp(X) * Coeff; -- where Coeff is 1/16 - Exp(45/16) -- which simplifies to ZX := Exp (X-V); ZX := ZX * 0.0625 - ZX * Coeff; -- note that since the expected value is computed, we -- must take the error in that computation into account. Check (ZY, ZX, "test " & Test & " -" & Integer'Image (I) & " exp (" & Real'Image (X) & ")", 9.0); exit when Accuracy_Error_Reported; end loop; exception when Constraint_Error => Report.Failed ("Constraint_Error raised in argument range check 2"); when others => Report.Failed ("exception in argument range check 2"); end Argument_Range_Check_2; procedure Do_Test is begin --- test 1 --- declare Y : Real; begin Y := Exp(1.0); -- normal accuracy requirements Check (Y, Ada.Numerics.e, "test 1 -- exp(1)", 4.0); exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 1"); when others => Report.Failed ("exception in test 1"); end; --- test 2 --- declare Y : Real; begin Y := Exp(16.0) * Exp(-16.0); Check (Y, 1.0, "test 2 -- exp(16)*exp(-16)", 9.0); exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 2"); when others => Report.Failed ("exception in test 2"); end; --- test 3 --- declare Y : Real; begin Y := Exp (Ada.Numerics.Pi) * Exp (-Ada.Numerics.Pi); Check (Y, 1.0, "test 3 -- exp(pi)*exp(-pi)", 9.0); exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 3"); when others => Report.Failed ("exception in test 3"); end; --- test 4 --- declare Y : Real; begin Y := Exp(0.0); Check (Y, 1.0, "test 4 -- exp(0.0)", 0.0); -- no error allowed exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 4"); when others => Report.Failed ("exception in test 4"); end; --- test 5 --- -- constants used here only have 19 digits of precision if Real'Digits > 19 then Error_Low_Bound := 0.00000_00000_00000_0001; Report.Comment ("exp accuracy checked to 19 digits"); end if; Argument_Range_Check_1 ( 1.0/Sqrt(Real(Real'Machine_Radix)), 1.0, "5"); Error_Low_Bound := 0.0; -- reset --- test 6 --- -- constants used here only have 19 digits of precision if Real'Digits > 19 then Error_Low_Bound := 0.00000_00000_00000_0001; Report.Comment ("exp accuracy checked to 19 digits"); end if; Argument_Range_Check_2 (1.0, Sqrt(Real(Real'Machine_Radix)), "6"); Error_Low_Bound := 0.0; -- reset end Do_Test; end Non_Generic_Check; ----------------------------------------------------------------------- ----------------------------------------------------------------------- begin Report.Test ("CXG2010", "Check the accuracy of the exp function"); -- the test only applies to machines with a radix of 2,4,8, or 16 case Float'Machine_Radix is when 2 | 4 | 8 | 16 => null; when others => Report.Not_Applicable ("only applicable to binary radix"); Report.Result; return; end case; 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; if Verbose then Report.Comment ("checking non-generic package"); end if; Non_Generic_Check.Do_Test; Report.Result; end CXG2010;