-- CXG2017.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 TANH 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 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: -- 20 Mar 96 SAIC Initial release for 2.1 -- 17 Aug 96 SAIC Incorporated reviewer comments. -- --! -- -- 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 CXG2017 is Verbose : constant Boolean := False; Max_Samples : constant := 1000; E : constant := Ada.Numerics.E; 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 Tanh (X : Real) return Real renames Elementary_Functions.Tanh; function Log (X : Real) return Real renames Elementary_Functions.Log; -- 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 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. Minimum_Error : constant := 8.0; E2 : constant := E * E; begin Check (Tanh (1.0), (E - 1.0 / E) / (E + 1.0 / E), "tanh(1)", Minimum_Error); Check (Tanh (2.0), (E2 - 1.0 / E2) / (E2 + 1.0 / E2), "tanh(2)", Minimum_Error); 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 -- A.5.1(38);6.0 Check (Tanh (0.0), 0.0, "tanh(0)", 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 -- TANH(u+v) = [TANH(u) + TANH(v)] / [1 + TANH(u)*TANH(v)] -- which is transformed to -- TANH(x) = [TANH(y)+C] / [1 + TANH(y) * C] -- where C = TANH(1/8) and y = x - 1/8 -- -- see Cody pg 248-249 for details on the error analysis. -- The net result is a relative error bound of 16 * Model_Epsilon. -- -- The second part of this test checks the identity -- TANH(-x) = -TANH(X) X, Y : Real; Actual1, Actual2 : Real; C : constant := 1.2435300177159620805e-1; begin if Real'Digits > 20 then -- constant C is accurate to 20 digits. Set the low bound -- on the error to 16*10**-20 Error_Low_Bound := 0.00000_00000_00000_00016; Report.Comment ("tanh accuracy checked to 20 digits"); end if; Accuracy_Error_Reported := False; -- reset for I in 1..Max_Samples loop X := (B - A) * Real (I) / Real (Max_Samples) + A; Actual1 := Tanh(X); -- TANH(x) = [TANH(y)+C] / [1 + TANH(y) * C] Y := X - (1.0 / 8.0); Actual2 := (Tanh (Y) + C) / (1.0 + Tanh(Y) * C); Check (Actual1, Actual2, "Identity_1_Test " & Integer'Image (I) & ": tanh(" & Real'Image (X) & ") ", 16.0); -- TANH(-x) = -TANH(X) Actual2 := Tanh(-X); Check (-Actual1, Actual2, "Identity_2_Test " & Integer'Image (I) & ": tanh(" & Real'Image (X) & ") ", 16.0); 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; Error_Low_Bound := 0.0; -- reset exception when Constraint_Error => Report.Failed ("Constraint_Error raised in Identity_Test" & " for X=" & Real'Image (X)); when others => Report.Failed ("exception in Identity_Test" & " for X=" & Real'Image (X)); end Identity_Test; procedure Do_Test is begin Special_Value_Test; Exact_Result_Test; -- cover a small range Identity_Test (0.0, Log(3.0) / 2.0); -- cover a large range Identity_Test (1.0, Real'Safe_Last); 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 ("CXG2017", "Check the accuracy of the TANH 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 CXG2017;