-- CXG2007.A -- -- Grant of Unlimited Rights -- -- Under contracts F33600-87-D-0337, F33600-84-D-0280, MDA903-79-C-0687 and -- F08630-91-C-0015, 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;