-- 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;