| -- 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; |
