| -- CXG2007.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 Compose_From_Polar function returns |
| -- results that are within the error bound allowed. |
| -- Check that Argument_Error is raised if the Cycle parameter |
| -- is less than or equal to zero. |
| -- |
| -- TEST DESCRIPTION: |
| -- This test uses a generic package to compute and check the |
| -- values of the Compose_From_Polar function. |
| -- |
| -- 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: |
| -- 23 FEB 96 SAIC Initial release for 2.1 |
| -- 23 APR 96 SAIC Fixed error checking |
| -- 03 MAR 97 PWB.CTA Deleted checks with explicit Cycle => 2.0*Pi |
| -- |
| -- 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 |
| --! |
| |
| with System; |
| with Report; |
| with Ada.Numerics; |
| with Ada.Numerics.Generic_Complex_Types; |
| procedure CXG2007 is |
| Verbose : constant Boolean := False; |
| |
| |
| -- 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; |
| |
| 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; |
| |
| Maximum_Relative_Error : constant Real := 3.0; |
| |
| procedure Check (Actual, Expected : Real; |
| Test_Name : String; |
| MRE : Real; |
| Arg_Error : Real) is |
| -- Arg_Error is additional absolute error that is allowed beyond |
| -- the MRE to account for error in the result that can be |
| -- attributed to error in the arguments. |
| 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_Small 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; |
| Max_Error := Max_Error + Arg_Error; |
| |
| if abs (Actual - Expected) > Max_Error then |
| 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 Check (Actual, Expected : Complex; |
| Test_Name : String; |
| MRE : Real; |
| Arg_Error : Real) is |
| -- Arg_Error is additional absolute error that is allowed beyond |
| -- the MRE to account for error in the result that can be |
| -- attributed to error in the arguments. |
| begin |
| Check (Actual.Re, Expected.Re, |
| Test_Name & " real part", |
| MRE, Arg_Error); |
| Check (Actual.Im, Expected.Im, |
| Test_Name & " imaginary part", |
| MRE, Arg_Error); |
| end Check; |
| |
| |
| procedure Special_Cases is |
| type Data_Point is |
| record |
| Re, |
| Im, |
| Modulus, |
| Radians, |
| Degrees, |
| Arg_Error : Real; |
| end record; |
| |
| -- shorthand names for various constants |
| P4 : constant := Pi/4.0; |
| P6 : constant := Pi/6.0; |
| |
| MER2 : constant Real := Real'Model_Epsilon * Sqrt2; |
| |
| type Test_Data_Type is array (Positive range <>) of Data_Point; |
| |
| -- the values in the following table only involve static |
| -- expressions so no loss of precision occurs. |
| Test_Data : constant Test_Data_Type := ( |
| --Re Im Modulus Radians Degrees Arg_Err |
| ( 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ), -- 1 |
| ( 0.0, 0.0, 0.0, Pi, 180.0, 0.0 ), -- 2 |
| |
| ( 1.0, 0.0, 1.0, 0.0, 0.0, 0.0 ), -- 3 |
| (-1.0, 0.0, -1.0, 0.0, 0.0, 0.0 ), -- 4 |
| |
| ( 1.0, 1.0, Sqrt2, P4, 45.0, MER2), -- 5 |
| (-1.0, 1.0, -Sqrt2, -P4, -45.0, MER2), -- 6 |
| ( 1.0, -1.0, Sqrt2, -P4, -45.0, MER2), -- 7 |
| (-1.0, -1.0, -Sqrt2, P4, 45.0, MER2), -- 8 |
| (-1.0, -1.0, Sqrt2, -3.0*P4,-135.0, MER2), -- 9 |
| (-1.0, 1.0, Sqrt2, 3.0*P4, 135.0, MER2), -- 10 |
| ( 1.0, -1.0, -Sqrt2, 3.0*P4, 135.0, MER2), -- 11 |
| |
| (-1.0, 0.0, 1.0, Pi, 180.0, 0.0 ), -- 12 |
| ( 1.0, 0.0, -1.0, Pi, 180.0, 0.0 ) ); -- 13 |
| |
| |
| Z : Complex; |
| Exp : Complex; |
| begin |
| for I in Test_Data'Range loop |
| begin |
| Exp := (Test_Data (I).Re, Test_Data (I).Im); |
| |
| Z := Compose_From_Polar (Test_Data (I).Modulus, |
| Test_Data (I).Radians); |
| Check (Z, Exp, |
| "test" & Integer'Image (I) & " compose_from_polar(m,r)", |
| Maximum_Relative_Error, Test_Data (I).Arg_Error); |
| |
| --pwb-math Z := Compose_From_Polar (Test_Data (I).Modulus, |
| --pwb-math Test_Data (I).Radians, |
| --pwb-math 2.0*Pi); |
| --pwb-math Check (Z, Exp, |
| --pwb-math "test" & Integer'Image (I) & " compose_from_polar(m,r,2pi)", |
| --pwb-math Maximum_Relative_Error, Test_Data (I).Arg_Error); |
| |
| Z := Compose_From_Polar (Test_Data (I).Modulus, |
| Test_Data (I).Degrees, |
| 360.0); |
| Check (Z, Exp, |
| "test" & Integer'Image (I) & " compose_from_polar(m,d,360)", |
| Maximum_Relative_Error, Test_Data (I).Arg_Error); |
| |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test" & |
| Integer'Image (I)); |
| when others => |
| Report.Failed ("exception in test" & |
| Integer'Image (I)); |
| end; |
| end loop; |
| end Special_Cases; |
| |
| |
| procedure Exception_Cases is |
| -- check that Argument_Error is raised if Cycle is <= 0 |
| Z : Complex; |
| W : Complex; |
| begin |
| begin |
| Z := Compose_From_Polar (3.0, 0.0, Cycle => 0.0); |
| Report.Failed ("no exception for cycle = 0.0"); |
| exception |
| when Ada.Numerics.Argument_Error => null; |
| when others => |
| Report.Failed ("wrong exception for cycle = 0.0"); |
| end; |
| |
| begin |
| W := Compose_From_Polar (6.0, 1.0, Cycle => -10.0); |
| Report.Failed ("no exception for cycle < 0.0"); |
| exception |
| when Ada.Numerics.Argument_Error => null; |
| when others => |
| Report.Failed ("wrong exception for cycle < 0.0"); |
| end; |
| |
| if Report.Ident_Int (1) = 2 then |
| -- not executed - used to make it appear that we use the |
| -- results of the above computation |
| Z := Z * W; |
| Report.Failed(Real'Image (Z.Re + Z.Im)); |
| end if; |
| end Exception_Cases; |
| |
| |
| procedure Do_Test is |
| begin |
| Special_Cases; |
| Exception_Cases; |
| end Do_Test; |
| end Generic_Check; |
| |
| 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 ("CXG2007", |
| "Check the accuracy of the Compose_From_Polar" & |
| " 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; |
| |
| Report.Result; |
| end CXG2007; |
