-- CXG2013.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 TAN and COT functions return -- results that are within the error bound allowed. -- -- TEST DESCRIPTION: -- This test consists of a generic package that is -- instantiated to check both Float and a long float type. -- The test for each floating point type is divided into -- several parts: -- Special value checks where the result is a known constant. -- Checks that use an identity for determining the result. -- Exception checks. -- -- 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: -- 11 Mar 96 SAIC Initial release for 2.1 -- 17 Aug 96 SAIC Commentary fixes. -- 03 Feb 97 PWB.CTA Removed checks with explicit Cycle => 2.0*Pi -- 02 DEC 97 EDS Change Max_Samples constant to 1001. -- 29 JUN 98 EDS Deleted Special_Angle_Test as fatally flawed. --! -- -- References: -- -- Software Manual for the Elementary Functions -- William J. Cody, Jr. and William Waite -- Prentice-Hall, 1980 -- -- CRC Standard Mathematical Tables -- 23rd Edition -- -- Implementation and Testing of Function Software -- W. J. Cody -- 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_Elementary_Functions; procedure CXG2013 is Verbose : constant Boolean := False; Max_Samples : constant := 1001; -- 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 Elementary_Functions is new Ada.Numerics.Generic_Elementary_Functions (Real); function Sqrt (X : Real) return Real renames Elementary_Functions.Sqrt; function Tan (X : Real) return Real renames Elementary_Functions.Tan; function Cot (X : Real) return Real renames Elementary_Functions.Cot; function Tan (X, Cycle : Real) return Real renames Elementary_Functions.Tan; function Cot (X, Cycle : Real) return Real renames Elementary_Functions.Cot; -- flag used to terminate some tests early Accuracy_Error_Reported : Boolean := False; -- factor to be applied in computing MRE Maximum_Relative_Error : constant Real := 4.0; procedure Check (Actual, Expected : Real; Test_Name : String; MRE : Real) is 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_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 Accuracy_Error_Reported := True; 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 Exact_Result_Test is No_Error : constant := 0.0; begin -- A.5.1(38);6.0 Check (Tan (0.0), 0.0, "tan(0)", No_Error); -- A.5.1(41);6.0 Check (Tan (180.0, 360.0), 0.0, "tan(180,360)", No_Error); Check (Tan (360.0, 360.0), 0.0, "tan(360,360)", No_Error); Check (Tan (720.0, 360.0), 0.0, "tan(720,360)", No_Error); -- A.5.1(41);6.0 Check (Cot ( 90.0, 360.0), 0.0, "cot( 90,360)", No_Error); Check (Cot (270.0, 360.0), 0.0, "cot(270,360)", No_Error); Check (Cot (810.0, 360.0), 0.0, "cot(810,360)", No_Error); exception when Constraint_Error => Report.Failed ("Constraint_Error raised in Exact_Result Test"); when others => Report.Failed ("exception in Exact_Result Test"); end Exact_Result_Test; procedure Tan_Test (A, B : Real) is -- Use identity Tan(X) = [2*Tan(x/2)]/[1-Tan(x/2) ** 2] -- checks over the range -pi/4 .. pi/4 require no argument reduction -- checks over the range 7pi/8 .. 9pi/8 require argument reduction X, Y : Real; Actual1, Actual2 : Real; begin Accuracy_Error_Reported := False; -- reset for I in 1..Max_Samples loop X := (B - A) * Real (I) / Real (Max_Samples) + A; -- argument purification to insure x and x/2 are exact -- See Cody page 170. Y := Real'Machine (X*0.5); X := Real'Machine (Y + Y); Actual1 := Tan(X); Actual2 := (2.0 * Tan (Y)) / (1.0 - Tan (Y) ** 2); if abs (X - Pi) > ( (B-A)/Real(2*Max_Samples) ) then Check (Actual1, Actual2, "Tan_Test " & Integer'Image (I) & ": tan(" & Real'Image (X) & ") ", (1.0 + Sqrt2) * Maximum_Relative_Error); -- see Cody pg 165 for error bound info end if; if Accuracy_Error_Reported then -- only report the first error in this test in order to keep -- lots of failures from producing a huge error log return; end if; end loop; exception when Constraint_Error => Report.Failed ("Constraint_Error raised in Tan_Test"); when others => Report.Failed ("exception in Tan_Test"); end Tan_Test; procedure Cot_Test is -- Use identity Cot(X) = [Cot(X/2)**2 - 1]/[2*Cot(X/2)] A : constant := 6.0 * Pi; B : constant := 25.0 / 4.0 * Pi; X, Y : Real; Actual1, Actual2 : Real; begin Accuracy_Error_Reported := False; -- reset for I in 1..Max_Samples loop X := (B - A) * Real (I) / Real (Max_Samples) + A; -- argument purification to insure x and x/2 are exact. -- See Cody page 170. Y := Real'Machine (X*0.5); X := Real'Machine (Y + Y); Actual1 := Cot(X); Actual2 := (Cot (Y) ** 2 - 1.0) / (2.0 * Cot (Y)); Check (Actual1, Actual2, "Cot_Test " & Integer'Image (I) & ": cot(" & Real'Image (X) & ") ", (1.0 + Sqrt2) * Maximum_Relative_Error); -- see Cody pg 165 for error bound info if Accuracy_Error_Reported then -- only report the first error in this test in order to keep -- lots of failures from producing a huge error log return; end if; end loop; exception when Constraint_Error => Report.Failed ("Constraint_Error raised in Cot_Test"); when others => Report.Failed ("exception in Cot_Test"); end Cot_Test; procedure Exception_Test is X1, X2, X3, X4, X5 : Real := 0.0; begin begin -- A.5.1(20);6.0 X1 := Tan (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 -- A.5.1(20);6.0 X2 := Cot (1.0, Cycle => -3.0); 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; -- the remaining tests only apply to machines that overflow if Real'Machine_Overflows then -- A.5.1(28);6.0 begin -- A.5.1(29);6.0 X3 := Cot (0.0); Report.Failed ("exception not raised for cot(0)"); exception when Constraint_Error => null; -- ok when others => Report.Failed ("wrong exception raised for cot(0)"); end; begin -- A.5.1(31);6.0 X4 := Tan (90.0, 360.0); Report.Failed ("exception not raised for tan(90,360)"); exception when Constraint_Error => null; -- ok when others => Report.Failed ("wrong exception raised for tan(90,360)"); end; begin -- A.5.1(32);6.0 X5 := Cot (180.0, 360.0); Report.Failed ("exception not raised for cot(180,360)"); exception when Constraint_Error => null; -- ok when others => Report.Failed ("wrong exception raised for cot(180,360)"); end; end if; -- optimizer thwarting if Report.Ident_Bool (False) then Report.Comment (Real'Image (X1+X2+X3+X4+X5)); end if; end Exception_Test; procedure Do_Test is begin Exact_Result_Test; Tan_Test (-Pi/4.0, Pi/4.0); Tan_Test (7.0*Pi/8.0, 9.0*Pi/8.0); Cot_Test; Exception_Test; end Do_Test; end Generic_Check; ----------------------------------------------------------------------- ----------------------------------------------------------------------- package Float_Check is new Generic_Check (Float); -- check the floating point type with the most digits type A_Long_Float is digits System.Max_Digits; package A_Long_Float_Check is new Generic_Check (A_Long_Float); ----------------------------------------------------------------------- ----------------------------------------------------------------------- begin Report.Test ("CXG2013", "Check the accuracy of the TAN and COT functions"); 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; Report.Result; end CXG2013;