| -- CXG2003.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 sqrt 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. |
| -- This test only applies to the Strict Mode for numerical |
| -- accuracy. |
| -- |
| -- |
| -- CHANGE HISTORY: |
| -- 2 FEB 96 SAIC Initial release for 2.1 |
| -- 18 AUG 96 SAIC Made Check consistent with other tests. |
| -- |
| --! |
| |
| with System; |
| with Report; |
| with Ada.Numerics.Generic_Elementary_Functions; |
| with Ada.Numerics.Elementary_Functions; |
| procedure CXG2003 is |
| Verbose : constant 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 Log (X : Real) return Real renames |
| Elementary_Functions.Log; |
| function Exp (X : Real) return Real renames |
| Elementary_Functions.Exp; |
| |
| -- The default Maximum Relative Error is the value specified |
| -- in the LRM. |
| Default_MRE : constant Real := 2.0; |
| |
| procedure Check (Actual, Expected : Real; |
| Test_Name : String; |
| MRE : Real := Default_MRE) is |
| Rel_Error : Real; |
| Abs_Error : Real; |
| Max_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; |
| |
| if abs (Actual - Expected) > Max_Error then |
| Report.Failed (Test_Name & |
| " actual: " & Real'Image (Actual) & |
| " expected: " & Real'Image (Expected) & |
| " difference: " & |
| Real'Image (Actual - Expected) & |
| " mre:" & 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 (A, B : Real; |
| Test : String) is |
| -- test a logarithmically distributed selection of |
| -- arguments selected from the range A to B. |
| X : Real; |
| Expected : Real; |
| Y : Real; |
| C : Real := Log(B/A); |
| Max_Samples : constant := 1000; |
| |
| begin |
| for I in 1..Max_Samples loop |
| Expected := A * Exp(C * Real (I) / Real (Max_Samples)); |
| X := Expected * Expected; |
| Y := Sqrt (X); |
| |
| -- note that since the expected value is computed, we |
| -- must take the error in that computation into account. |
| Check (Y, Expected, |
| "test " & Test & " -" & |
| Integer'Image (I) & |
| " of argument range", |
| 3.0); |
| end loop; |
| exception |
| when Constraint_Error => |
| Report.Failed |
| ("Constraint_Error raised in argument range check"); |
| when others => |
| Report.Failed ("exception in argument range check"); |
| end Argument_Range_Check; |
| |
| procedure Do_Test is |
| begin |
| |
| --- test 1 --- |
| declare |
| T : constant := (Real'Machine_EMax - 1) / 2; |
| X : constant := (1.0 * Real'Machine_Radix) ** (2 * T); |
| Expected : constant := (1.0 * Real'Machine_Radix) ** T; |
| Y : Real; |
| begin |
| Y := Sqrt (X); |
| Check (Y, Expected, "test 1 -- sqrt(radix**((emax-1)/2))"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 1"); |
| when others => |
| Report.Failed ("exception in test 1"); |
| end; |
| |
| --- test 2 --- |
| declare |
| T : constant := (Real'Model_EMin + 1) / 2; |
| X : constant := (1.0 * Real'Machine_Radix) ** (2 * T); |
| Expected : constant := (1.0 * Real'Machine_Radix) ** T; |
| Y : Real; |
| begin |
| Y := Sqrt (X); |
| Check (Y, Expected, "test 2 -- sqrt(radix**((emin+1)/2))"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 2"); |
| when others => |
| Report.Failed ("exception in test 2"); |
| end; |
| |
| --- test 3 --- |
| declare |
| X : constant := 1.0; |
| Expected : constant := 1.0; |
| Y : Real; |
| begin |
| Y := Sqrt(X); |
| Check (Y, Expected, "test 3 -- sqrt(1.0)", |
| 0.0); -- no error allowed |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 3"); |
| when others => |
| Report.Failed ("exception in test 3"); |
| end; |
| |
| --- test 4 --- |
| declare |
| X : constant := 0.0; |
| Expected : constant := 0.0; |
| Y : Real; |
| begin |
| Y := Sqrt(X); |
| Check (Y, Expected, "test 4 -- sqrt(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 --- |
| declare |
| X : constant := -1.0; |
| Y : Real; |
| begin |
| Y := Sqrt(X); |
| -- the following code should not be executed. |
| -- The call to Check is to keep the call to Sqrt from |
| -- appearing to be dead code. |
| Check (Y, -1.0, "test 5 -- sqrt(-1)" ); |
| Report.Failed ("test 5 - argument_error expected"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 5"); |
| when Ada.Numerics.Argument_Error => |
| if Verbose then |
| Report.Comment ("test 5 correctly got argument_error"); |
| end if; |
| when others => |
| Report.Failed ("exception in test 5"); |
| end; |
| |
| --- test 6 --- |
| declare |
| X : constant := Ada.Numerics.Pi ** 2; |
| Expected : constant := Ada.Numerics.Pi; |
| Y : Real; |
| begin |
| Y := Sqrt (X); |
| Check (Y, Expected, "test 6 -- sqrt(pi**2)"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 6"); |
| when others => |
| Report.Failed ("exception in test 6"); |
| end; |
| |
| --- test 7 & 8 --- |
| Argument_Range_Check (1.0/Sqrt(Real(Real'Machine_Radix)), |
| 1.0, |
| "7"); |
| Argument_Range_Check (1.0, |
| Sqrt(Real(Real'Machine_Radix)), |
| "8"); |
| 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 Log (X : Real) return Real renames |
| Elementary_Functions.Log; |
| function Exp (X : Real) return Real renames |
| Elementary_Functions.Exp; |
| |
| -- The default Maximum Relative Error is the value specified |
| -- in the LRM. |
| Default_MRE : constant Real := 2.0; |
| |
| procedure Check (Actual, Expected : Real; |
| Test_Name : String; |
| MRE : Real := Default_MRE) is |
| Rel_Error : Real; |
| Abs_Error : Real; |
| Max_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; |
| |
| if abs (Actual - Expected) > Max_Error then |
| Report.Failed (Test_Name & |
| " actual: " & Real'Image (Actual) & |
| " expected: " & Real'Image (Expected) & |
| " difference: " & |
| Real'Image (Actual - Expected) & |
| " mre:" & 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 (A, B : Real; |
| Test : String) is |
| -- test a logarithmically distributed selection of |
| -- arguments selected from the range A to B. |
| X : Real; |
| Expected : Real; |
| Y : Real; |
| C : Real := Log(B/A); |
| Max_Samples : constant := 1000; |
| |
| begin |
| for I in 1..Max_Samples loop |
| Expected := A * Exp(C * Real (I) / Real (Max_Samples)); |
| X := Expected * Expected; |
| Y := Sqrt (X); |
| |
| -- note that since the expected value is computed, we |
| -- must take the error in that computation into account. |
| Check (Y, Expected, |
| "test " & Test & " -" & |
| Integer'Image (I) & |
| " of argument range", |
| 3.0); |
| end loop; |
| exception |
| when Constraint_Error => |
| Report.Failed |
| ("Constraint_Error raised in argument range check"); |
| when others => |
| Report.Failed ("exception in argument range check"); |
| end Argument_Range_Check; |
| |
| |
| procedure Do_Test is |
| begin |
| |
| --- test 1 --- |
| declare |
| T : constant := (Real'Machine_EMax - 1) / 2; |
| X : constant := (1.0 * Real'Machine_Radix) ** (2 * T); |
| Expected : constant := (1.0 * Real'Machine_Radix) ** T; |
| Y : Real; |
| begin |
| Y := Sqrt (X); |
| Check (Y, Expected, "test 1 -- sqrt(radix**((emax-1)/2))"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 1"); |
| when others => |
| Report.Failed ("exception in test 1"); |
| end; |
| |
| --- test 2 --- |
| declare |
| T : constant := (Real'Model_EMin + 1) / 2; |
| X : constant := (1.0 * Real'Machine_Radix) ** (2 * T); |
| Expected : constant := (1.0 * Real'Machine_Radix) ** T; |
| Y : Real; |
| begin |
| Y := Sqrt (X); |
| Check (Y, Expected, "test 2 -- sqrt(radix**((emin+1)/2))"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 2"); |
| when others => |
| Report.Failed ("exception in test 2"); |
| end; |
| |
| --- test 3 --- |
| declare |
| X : constant := 1.0; |
| Expected : constant := 1.0; |
| Y : Real; |
| begin |
| Y := Sqrt(X); |
| Check (Y, Expected, "test 3 -- sqrt(1.0)", |
| 0.0); -- no error allowed |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 3"); |
| when others => |
| Report.Failed ("exception in test 3"); |
| end; |
| |
| --- test 4 --- |
| declare |
| X : constant := 0.0; |
| Expected : constant := 0.0; |
| Y : Real; |
| begin |
| Y := Sqrt(X); |
| Check (Y, Expected, "test 4 -- sqrt(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 --- |
| declare |
| X : constant := -1.0; |
| Y : Real; |
| begin |
| Y := Sqrt(X); |
| -- the following code should not be executed. |
| -- The call to Check is to keep the call to Sqrt from |
| -- appearing to be dead code. |
| Check (Y, -1.0, "test 5 -- sqrt(-1)" ); |
| Report.Failed ("test 5 - argument_error expected"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 5"); |
| when Ada.Numerics.Argument_Error => |
| if Verbose then |
| Report.Comment ("test 5 correctly got argument_error"); |
| end if; |
| when others => |
| Report.Failed ("exception in test 5"); |
| end; |
| |
| --- test 6 --- |
| declare |
| X : constant := Ada.Numerics.Pi ** 2; |
| Expected : constant := Ada.Numerics.Pi; |
| Y : Real; |
| begin |
| Y := Sqrt (X); |
| Check (Y, Expected, "test 6 -- sqrt(pi**2)"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 6"); |
| when others => |
| Report.Failed ("exception in test 6"); |
| end; |
| |
| --- test 7 & 8 --- |
| Argument_Range_Check (1.0/Sqrt(Real(Real'Machine_Radix)), |
| 1.0, |
| "7"); |
| Argument_Range_Check (1.0, |
| Sqrt(Real(Real'Machine_Radix)), |
| "8"); |
| end Do_Test; |
| end A_Long_Float_Check; |
| |
| ----------------------------------------------------------------------- |
| ----------------------------------------------------------------------- |
| |
| package Non_Generic_Check is |
| procedure Do_Test; |
| end Non_Generic_Check; |
| |
| package body Non_Generic_Check is |
| package EF renames |
| Ada.Numerics.Elementary_Functions; |
| subtype Real is Float; |
| |
| -- The default Maximum Relative Error is the value specified |
| -- in the LRM. |
| Default_MRE : constant Real := 2.0; |
| |
| procedure Check (Actual, Expected : Real; |
| Test_Name : String; |
| MRE : Real := Default_MRE) is |
| Rel_Error : Real; |
| Abs_Error : Real; |
| Max_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; |
| |
| if abs (Actual - Expected) > Max_Error then |
| Report.Failed (Test_Name & |
| " actual: " & Real'Image (Actual) & |
| " expected: " & Real'Image (Expected) & |
| " difference: " & |
| Real'Image (Actual - Expected) & |
| " mre:" & 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 (A, B : Float; |
| Test : String) is |
| -- test a logarithmically distributed selection of |
| -- arguments selected from the range A to B. |
| X : Float; |
| Expected : Float; |
| Y : Float; |
| C : Float := EF.Log(B/A); |
| Max_Samples : constant := 1000; |
| |
| begin |
| for I in 1..Max_Samples loop |
| Expected := A * EF.Exp(C * Float (I) / Float (Max_Samples)); |
| X := Expected * Expected; |
| Y := EF.Sqrt (X); |
| |
| -- note that since the expected value is computed, we |
| -- must take the error in that computation into account. |
| Check (Y, Expected, |
| "test " & Test & " -" & |
| Integer'Image (I) & |
| " of argument range", |
| 3.0); |
| end loop; |
| exception |
| when Constraint_Error => |
| Report.Failed |
| ("Constraint_Error raised in argument range check"); |
| when others => |
| Report.Failed ("exception in argument range check"); |
| end Argument_Range_Check; |
| |
| |
| procedure Do_Test is |
| begin |
| |
| --- test 1 --- |
| declare |
| T : constant := (Float'Machine_EMax - 1) / 2; |
| X : constant := (1.0 * Float'Machine_Radix) ** (2 * T); |
| Expected : constant := (1.0 * Float'Machine_Radix) ** T; |
| Y : Float; |
| begin |
| Y := EF.Sqrt (X); |
| Check (Y, Expected, "test 1 -- sqrt(radix**((emax-1)/2))"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 1"); |
| when others => |
| Report.Failed ("exception in test 1"); |
| end; |
| |
| --- test 2 --- |
| declare |
| T : constant := (Float'Model_EMin + 1) / 2; |
| X : constant := (1.0 * Float'Machine_Radix) ** (2 * T); |
| Expected : constant := (1.0 * Float'Machine_Radix) ** T; |
| Y : Float; |
| begin |
| Y := EF.Sqrt (X); |
| Check (Y, Expected, "test 2 -- sqrt(radix**((emin+1)/2))"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 2"); |
| when others => |
| Report.Failed ("exception in test 2"); |
| end; |
| |
| --- test 3 --- |
| declare |
| X : constant := 1.0; |
| Expected : constant := 1.0; |
| Y : Float; |
| begin |
| Y := EF.Sqrt(X); |
| Check (Y, Expected, "test 3 -- sqrt(1.0)", |
| 0.0); -- no error allowed |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 3"); |
| when others => |
| Report.Failed ("exception in test 3"); |
| end; |
| |
| --- test 4 --- |
| declare |
| X : constant := 0.0; |
| Expected : constant := 0.0; |
| Y : Float; |
| begin |
| Y := EF.Sqrt(X); |
| Check (Y, Expected, "test 4 -- sqrt(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 --- |
| declare |
| X : constant := -1.0; |
| Y : Float; |
| begin |
| Y := EF.Sqrt(X); |
| -- the following code should not be executed. |
| -- The call to Check is to keep the call to Sqrt from |
| -- appearing to be dead code. |
| Check (Y, -1.0, "test 5 -- sqrt(-1)" ); |
| Report.Failed ("test 5 - argument_error expected"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 5"); |
| when Ada.Numerics.Argument_Error => |
| if Verbose then |
| Report.Comment ("test 5 correctly got argument_error"); |
| end if; |
| when others => |
| Report.Failed ("exception in test 5"); |
| end; |
| |
| --- test 6 --- |
| declare |
| X : constant := Ada.Numerics.Pi ** 2; |
| Expected : constant := Ada.Numerics.Pi; |
| Y : Float; |
| begin |
| Y := EF.Sqrt (X); |
| Check (Y, Expected, "test 6 -- sqrt(pi**2)"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 6"); |
| when others => |
| Report.Failed ("exception in test 6"); |
| end; |
| |
| --- test 7 & 8 --- |
| Argument_Range_Check (1.0/EF.Sqrt(Float(Float'Machine_Radix)), |
| 1.0, |
| "7"); |
| Argument_Range_Check (1.0, |
| EF.Sqrt(Float(Float'Machine_Radix)), |
| "8"); |
| end Do_Test; |
| end Non_Generic_Check; |
| |
| ----------------------------------------------------------------------- |
| ----------------------------------------------------------------------- |
| |
| begin |
| Report.Test ("CXG2003", |
| "Check the accuracy of the sqrt 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; |
| |
| if Verbose then |
| Report.Comment ("checking non-generic package"); |
| end if; |
| |
| Non_Generic_Check.Do_Test; |
| |
| Report.Result; |
| end CXG2003; |
