| -- CXG2018.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 EXP function returns |
| -- a result that is within the error bound allowed. |
| -- |
| -- TEST DESCRIPTION: |
| -- This test consists of a generic package that is |
| -- instantiated to check complex numbers based upon |
| -- 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. |
| -- |
| -- 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: |
| -- 21 Mar 96 SAIC Initial release for 2.1 |
| -- 17 Aug 96 SAIC Incorporated reviewer comments. |
| -- 27 Aug 99 RLB Repair on the error result of checks. |
| -- 02 Apr 03 RLB Added code to discard excess precision in the |
| -- construction of the test value for the |
| -- Identity_Test. |
| -- |
| --! |
| |
| -- |
| -- References: |
| -- |
| -- W. J. Cody |
| -- CELEFUNT: A Portable Test Package for Complex Elementary Functions |
| -- Algorithm 714, Collected Algorithms from ACM. |
| -- Published in Transactions On Mathematical Software, |
| -- Vol. 19, No. 1, March, 1993, pp. 1-21. |
| -- |
| -- CRC Standard Mathematical Tables |
| -- 23rd Edition |
| -- |
| |
| with System; |
| with Report; |
| with Ada.Numerics.Generic_Complex_Types; |
| with Ada.Numerics.Generic_Complex_Elementary_Functions; |
| procedure CXG2018 is |
| Verbose : constant Boolean := False; |
| -- Note that Max_Samples is the number of samples taken in |
| -- both the real and imaginary directions. Thus, for Max_Samples |
| -- of 100 the number of values checked is 10000. |
| Max_Samples : constant := 100; |
| |
| E : constant := Ada.Numerics.E; |
| 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_Type is new |
| Ada.Numerics.Generic_Complex_Types (Real); |
| use Complex_Type; |
| |
| package CEF is new |
| Ada.Numerics.Generic_Complex_Elementary_Functions (Complex_Type); |
| |
| function Exp (X : Complex) return Complex renames CEF.Exp; |
| function Exp (X : Imaginary) return Complex renames CEF.Exp; |
| |
| -- flag used to terminate some tests early |
| Accuracy_Error_Reported : Boolean := False; |
| |
| |
| -- The following value is a lower bound on the accuracy |
| -- required. It is normally 0.0 so that the lower bound |
| -- is computed from Model_Epsilon. However, for tests |
| -- where the expected result is only known to a certain |
| -- amount of precision this bound takes on a non-zero |
| -- value to account for that level of precision. |
| Error_Low_Bound : Real := 0.0; |
| |
| 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_Small instead |
| -- of Model_Epsilon and Expected. |
| Rel_Error := MRE * abs Expected * Real'Model_Epsilon; |
| Abs_Error := MRE * Real'Model_Small; |
| if Rel_Error > Abs_Error then |
| Max_Error := Rel_Error; |
| else |
| Max_Error := Abs_Error; |
| end if; |
| |
| -- take into account the low bound on the error |
| if Max_Error < Error_Low_Bound then |
| Max_Error := Error_Low_Bound; |
| 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 Check (Actual, Expected : Complex; |
| Test_Name : String; |
| MRE : Real) is |
| begin |
| Check (Actual.Re, Expected.Re, Test_Name & " real part", MRE); |
| Check (Actual.Im, Expected.Im, Test_Name & " imaginary part", MRE); |
| end Check; |
| |
| |
| procedure Special_Value_Test is |
| -- In the following tests the expected result is accurate |
| -- to the machine precision so the minimum guaranteed error |
| -- bound can be used. |
| -- |
| -- The error bounds given assumed z is exact. When using |
| -- pi there is an extra error of 1.0ME. |
| -- The pi inside the exp call requires that the complex |
| -- component have an extra error allowance of 1.0*angle*ME. |
| -- Thus for pi/2,the Minimum_Error_I is |
| -- (2.0 + 1.0(pi/2))ME <= 3.6ME. |
| -- For pi, it is (2.0 + 1.0*pi)ME <= 5.2ME, |
| -- and for 2pi, it is (2.0 + 1.0(2pi))ME <= 8.3ME. |
| |
| -- The addition of 1 or i to a result is so that neither of |
| -- the components of an expected result is 0. This is so |
| -- that a reasonable relative error is allowed. |
| Minimum_Error_C : constant := 7.0; -- for exp(Complex) |
| Minimum_Error_I : constant := 2.0; -- for exp(Imaginary) |
| begin |
| Check (Exp (1.0 + 0.0*i) + i, |
| E + i, |
| "exp(1+0i)", |
| Minimum_Error_C); |
| Check (Exp ((Pi / 2.0) * i) + 1.0, |
| 1.0 + 1.0*i, |
| "exp(pi/2*i)", |
| 3.6); |
| Check (Exp (Pi * i) + i, |
| -1.0 + 1.0*i, |
| "exp(pi*i)", |
| 5.2); |
| Check (Exp (Pi * 2.0 * i) + i, |
| 1.0 + i, |
| "exp(2pi*i)", |
| 8.3); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in special value test"); |
| when others => |
| Report.Failed ("exception in special value test"); |
| end Special_Value_Test; |
| |
| |
| |
| procedure Exact_Result_Test is |
| No_Error : constant := 0.0; |
| begin |
| -- G.1.2(36);6.0 |
| Check (Exp(0.0 + 0.0*i), 1.0 + 0.0 * i, "exp(0+0i)", No_Error); |
| Check (Exp( 0.0*i), 1.0 + 0.0 * i, "exp(0i)", 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 Identity_Test (A, B : Real) is |
| -- For this test we use the identity |
| -- Exp(Z) = Exp(Z-W) * Exp (W) |
| -- where W = (1+i)/16 |
| -- |
| -- The second part of this test checks the identity |
| -- Exp(Z) * Exp(-Z) = 1 |
| -- |
| |
| X, Y : Complex; |
| Actual1, Actual2 : Complex; |
| W : constant Complex := (0.0625, 0.0625); |
| -- the following constant was taken from the CELEFUNC EXP test. |
| -- This is the value EXP(W) - 1 |
| C : constant Complex := (6.2416044877018563681e-2, |
| 6.6487597751003112768e-2); |
| begin |
| if Real'Digits > 20 then |
| -- constant ExpW is accurate to 20 digits. |
| -- The low bound is 19 * 10**-20 |
| Error_Low_Bound := 0.00000_00000_00019; |
| Report.Comment ("complex exp accuracy checked to 20 digits"); |
| end if; |
| |
| Accuracy_Error_Reported := False; -- reset |
| for II in 1..Max_Samples loop |
| X.Re := Real'Machine ((B - A) * Real (II) / Real (Max_Samples) |
| + A); |
| for J in 1..Max_Samples loop |
| X.Im := Real'Machine ((B - A) * Real (J) / Real (Max_Samples) |
| + A); |
| |
| Actual1 := Exp(X); |
| |
| -- Exp(X) = Exp(X-W) * Exp (W) |
| -- = Exp(X-W) * (1 - (1-Exp(W)) |
| -- = Exp(X-W) * (1 + (Exp(W) - 1)) |
| -- = Exp(X-W) * (1 + C) |
| Y := X - W; |
| Actual2 := Exp(Y); |
| Actual2 := Actual2 + Actual2 * C; |
| |
| Check (Actual1, Actual2, |
| "Identity_1_Test " & Integer'Image (II) & |
| Integer'Image (J) & ": Exp((" & |
| Real'Image (X.Re) & ", " & |
| Real'Image (X.Im) & ")) ", |
| 20.0); -- 2 exp and 1 multiply and 1 add = 2*7+1*5+1 |
| -- Note: The above is not strictly correct, as multiply |
| -- has a box error, rather than a relative error. |
| -- Supposedly, the interval is chosen to avoid the need |
| -- to worry about this. |
| |
| -- Exp(X) * Exp(-X) + i = 1 + i |
| -- The addition of i is to allow a reasonable relative |
| -- error in the imaginary part |
| Actual2 := (Actual1 * Exp(-X)) + i; |
| Check (Actual2, (1.0, 1.0), |
| "Identity_2_Test " & Integer'Image (II) & |
| Integer'Image (J) & ": Exp((" & |
| Real'Image (X.Re) & ", " & |
| Real'Image (X.Im) & ")) ", |
| 20.0); -- 2 exp and 1 multiply and one add = 2*7+1*5+1 |
| |
| 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; |
| end loop; |
| Error_Low_Bound := 0.0; |
| exception |
| when Constraint_Error => |
| Report.Failed |
| ("Constraint_Error raised in Identity_Test" & |
| " for X=(" & Real'Image (X.Re) & |
| ", " & Real'Image (X.Im) & ")"); |
| when others => |
| Report.Failed ("exception in Identity_Test" & |
| " for X=(" & Real'Image (X.Re) & |
| ", " & Real'Image (X.Im) & ")"); |
| end Identity_Test; |
| |
| |
| |
| procedure Do_Test is |
| begin |
| Special_Value_Test; |
| Exact_Result_Test; |
| -- test regions where we can avoid cancellation error problems |
| -- See Cody page 10. |
| Identity_Test (0.0625, 1.0); |
| Identity_Test (15.0, 17.0); |
| Identity_Test (1.625, 3.0); |
| 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 ("CXG2018", |
| "Check the accuracy of the complex EXP function"); |
| |
| 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 CXG2018; |
