| -- CXG2002.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 complex "abs" or modulus function returns |
| -- results that are within the error bound allowed. |
| -- |
| -- TEST DESCRIPTION: |
| -- This test uses a generic package to compute and check the |
| -- values of the modulus function. In addition, a non-generic |
| -- copy of this package is used to check the non-generic package |
| -- Ada.Numerics.Complex_Types. |
| -- Of special interest is the case where either the real or |
| -- the imaginary part of the argument is very large while the |
| -- other part is very small or 0. |
| -- We want to check that the value is computed such that |
| -- an overflow does not occur. If computed directly from the |
| -- definition |
| -- abs (x+yi) = sqrt(x**2 + y**2) |
| -- then overflow or underflow is much more likely than if the |
| -- argument is normalized first. |
| -- |
| -- 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: |
| -- 31 JAN 96 SAIC Initial release for 2.1 |
| -- 02 JUN 98 EDS Add parens to intermediate calculations. |
| --! |
| |
| -- |
| -- Reference: |
| -- Problems and Methodologies in Mathematical Software Production; |
| -- editors: P. C. Messina and A Murli; |
| -- Lecture Notes in Computer Science |
| -- Volume 142 |
| -- Springer Verlag 1982 |
| -- |
| |
| with System; |
| with Report; |
| with Ada.Numerics.Generic_Complex_Types; |
| with Ada.Numerics.Complex_Types; |
| procedure CXG2002 is |
| Verbose : constant Boolean := False; |
| Maximum_Relative_Error : constant := 3.0; |
| |
| generic |
| type Real is digits <>; |
| package Generic_Check is |
| procedure Do_Test; |
| end Generic_Check; |
| |
| package body Generic_Check is |
| package Complex_Types is new |
| Ada.Numerics.Generic_Complex_Types (Real); |
| use Complex_Types; |
| |
| procedure Check (Actual, Expected : Real; |
| Test_Name : String; |
| MRE : Real := Maximum_Relative_Error) is |
| Rel_Error, |
| Abs_Error, |
| 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 (Expected - Actual) & |
| " 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 Do_Test is |
| Z : Complex; |
| X : Real; |
| T : Real; |
| begin |
| |
| --- test 1 --- |
| begin |
| T := Real'Safe_Last; |
| Z := T + 0.0*i; |
| X := abs Z; |
| Check (X, T, "test 1 -- abs(bigreal + 0i)"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 1"); |
| when others => |
| Report.Failed ("exception in test 1"); |
| end; |
| |
| --- test 2 --- |
| begin |
| T := Real'Safe_Last; |
| Z := 0.0 + T*i; |
| X := Modulus (Z); |
| Check (X, T, "test 2 -- abs(0 + bigreal*i)"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 2"); |
| when others => |
| Report.Failed ("exception in test 2"); |
| end; |
| |
| --- test 3 --- |
| begin |
| Z := 3.0 + 4.0*i; |
| X := abs Z; |
| Check (X, 5.0 , "test 3 -- abs(3 + 4*i)"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 3"); |
| when others => |
| Report.Failed ("exception in test 3"); |
| end; |
| |
| --- test 4 --- |
| declare |
| S : Real; |
| begin |
| S := Real(Real'Machine_Radix) ** (Real'Machine_EMax - 3); |
| Z := 3.0 * S + 4.0*S*i; |
| X := abs Z; |
| Check (X, 5.0*S, "test 4 -- abs(3S + 4S*i) for large S", |
| 5.0*Real'Model_Epsilon); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 4"); |
| when others => |
| Report.Failed ("exception in test 4"); |
| end; |
| |
| --- test 5 --- |
| begin |
| T := Real'Model_Small; |
| Z := T + 0.0*i; |
| X := abs Z; |
| Check (X, T , "test 5 -- abs(small + 0*i)"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 5"); |
| when others => |
| Report.Failed ("exception in test 5"); |
| end; |
| |
| --- test 6 --- |
| begin |
| T := Real'Model_Small; |
| Z := 0.0 + T*i; |
| X := abs Z; |
| Check (X, T , "test 6 -- abs(0 + small*i)"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 6"); |
| when others => |
| Report.Failed ("exception in test 6"); |
| end; |
| |
| --- test 7 --- |
| declare |
| S : Real; |
| begin |
| S := Real(Real'Machine_Radix) ** (Real'Model_EMin + 3); |
| Z := 3.0 * S + 4.0*S*i; |
| X := abs Z; |
| Check (X, 5.0*S, "test 7 -- abs(3S + 4S*i) for small S", |
| 5.0*Real'Model_Epsilon); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 7"); |
| when others => |
| Report.Failed ("exception in test 7"); |
| end; |
| |
| --- test 8 --- |
| declare |
| -- CRC Standard Mathematical Tables; 23rd Edition; pg 738 |
| Sqrt2 : constant := |
| 1.41421_35623_73095_04880_16887_24209_69807_85696_71875_37695; |
| begin |
| Z := 1.0 + 1.0*i; |
| X := abs Z; |
| Check (X, Sqrt2 , "test 8 -- abs(1 + 1*i)"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 8"); |
| when others => |
| Report.Failed ("exception in test 8"); |
| end; |
| |
| --- test 9 --- |
| begin |
| T := 0.0; |
| Z := T + 0.0*i; |
| X := abs Z; |
| Check (X, T , "test 5 -- abs(0 + 0*i)"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 9"); |
| when others => |
| Report.Failed ("exception in test 9"); |
| end; |
| end Do_Test; |
| end Generic_Check; |
| |
| ----------------------------------------------------------------------- |
| --- non generic copy of the above generic package |
| ----------------------------------------------------------------------- |
| |
| package Non_Generic_Check is |
| subtype Real is Float; |
| procedure Do_Test; |
| end Non_Generic_Check; |
| |
| package body Non_Generic_Check is |
| use Ada.Numerics.Complex_Types; |
| |
| procedure Check (Actual, Expected : Real; |
| Test_Name : String; |
| MRE : Real := Maximum_Relative_Error) is |
| Rel_Error, |
| Abs_Error, |
| 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 (Expected - Actual) & |
| " 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 Do_Test is |
| Z : Complex; |
| X : Real; |
| T : Real; |
| begin |
| |
| --- test 1 --- |
| begin |
| T := Real'Safe_Last; |
| Z := T + 0.0*i; |
| X := abs Z; |
| Check (X, T, "test 1 -- abs(bigreal + 0i)"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 1"); |
| when others => |
| Report.Failed ("exception in test 1"); |
| end; |
| |
| --- test 2 --- |
| begin |
| T := Real'Safe_Last; |
| Z := 0.0 + T*i; |
| X := Modulus (Z); |
| Check (X, T, "test 2 -- abs(0 + bigreal*i)"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 2"); |
| when others => |
| Report.Failed ("exception in test 2"); |
| end; |
| |
| --- test 3 --- |
| begin |
| Z := 3.0 + 4.0*i; |
| X := abs Z; |
| Check (X, 5.0 , "test 3 -- abs(3 + 4*i)"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 3"); |
| when others => |
| Report.Failed ("exception in test 3"); |
| end; |
| |
| --- test 4 --- |
| declare |
| S : Real; |
| begin |
| S := Real(Real'Machine_Radix) ** (Real'Machine_EMax - 3); |
| Z := 3.0 * S + 4.0*S*i; |
| X := abs Z; |
| Check (X, 5.0*S, "test 4 -- abs(3S + 4S*i) for large S", |
| 5.0*Real'Model_Epsilon); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 4"); |
| when others => |
| Report.Failed ("exception in test 4"); |
| end; |
| |
| --- test 5 --- |
| begin |
| T := Real'Model_Small; |
| Z := T + 0.0*i; |
| X := abs Z; |
| Check (X, T , "test 5 -- abs(small + 0*i)"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 5"); |
| when others => |
| Report.Failed ("exception in test 5"); |
| end; |
| |
| --- test 6 --- |
| begin |
| T := Real'Model_Small; |
| Z := 0.0 + T*i; |
| X := abs Z; |
| Check (X, T , "test 6 -- abs(0 + small*i)"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 6"); |
| when others => |
| Report.Failed ("exception in test 6"); |
| end; |
| |
| --- test 7 --- |
| declare |
| S : Real; |
| begin |
| S := Real(Real'Machine_Radix) ** (Real'Model_EMin + 3); |
| Z := 3.0 * S + 4.0*S*i; |
| X := abs Z; |
| Check (X, 5.0*S, "test 7 -- abs(3S + 4S*i) for small S", |
| 5.0*Real'Model_Epsilon); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 7"); |
| when others => |
| Report.Failed ("exception in test 7"); |
| end; |
| |
| --- test 8 --- |
| declare |
| -- CRC Standard Mathematical Tables; 23rd Edition; pg 738 |
| Sqrt2 : constant := |
| 1.41421_35623_73095_04880_16887_24209_69807_85696_71875_37695; |
| begin |
| Z := 1.0 + 1.0*i; |
| X := abs Z; |
| Check (X, Sqrt2 , "test 8 -- abs(1 + 1*i)"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 8"); |
| when others => |
| Report.Failed ("exception in test 8"); |
| end; |
| |
| --- test 9 --- |
| begin |
| T := 0.0; |
| Z := T + 0.0*i; |
| X := abs Z; |
| Check (X, T , "test 5 -- abs(0 + 0*i)"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 9"); |
| when others => |
| Report.Failed ("exception in test 9"); |
| end; |
| end Do_Test; |
| end Non_Generic_Check; |
| |
| ----------------------------------------------------------------------- |
| --- end of "manual instantiation" |
| ----------------------------------------------------------------------- |
| package Chk_Float is new Generic_Check (Float); |
| |
| -- check the floating point type with the most digits |
| type A_Long_Float is digits System.Max_Digits; |
| package Chk_A_Long_Float is new Generic_Check (A_Long_Float); |
| begin |
| Report.Test ("CXG2002", |
| "Check the accuracy of the complex modulus" & |
| " function"); |
| |
| if Verbose then |
| Report.Comment ("checking Standard.Float"); |
| end if; |
| Chk_Float.Do_Test; |
| |
| if Verbose then |
| Report.Comment ("checking a digits" & |
| Integer'Image (System.Max_Digits) & |
| " floating point type"); |
| end if; |
| Chk_A_Long_Float.Do_Test; |
| |
| if Verbose then |
| Report.Comment ("checking non-generic package"); |
| end if; |
| Non_Generic_Check.Do_Test; |
| Report.Result; |
| end CXG2002; |
