| -- CXG2014.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 SINH and COSH 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: |
| -- 15 Mar 96 SAIC Initial release for 2.1 |
| -- 03 Jun 98 EDS In line 80, change 1000 to 1024, making it a model |
| -- number. Add Taylor Series terms in line 281. |
| -- 15 Feb 99 RLB Repaired Subtraction_Error_Test to avoid precision |
| -- problems. |
| --! |
| |
| -- |
| -- 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 CXG2014 is |
| Verbose : constant Boolean := False; |
| Max_Samples : constant := 1024; |
| |
| E : constant := Ada.Numerics.E; |
| Cosh1 : constant := (E + 1.0 / E) / 2.0; -- cosh(1.0) |
| |
| 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 Sinh (X : Real) return Real renames |
| Elementary_Functions.Sinh; |
| function Cosh (X : Real) return Real renames |
| Elementary_Functions.Cosh; |
| function Log (X : Real) return Real renames |
| Elementary_Functions.Log; |
| |
| -- flag used to terminate some tests early |
| Accuracy_Error_Reported : Boolean := False; |
| |
| |
| 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; |
| |
| 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; |
| begin |
| Check (Sinh (1.0), |
| (E - 1.0 / E) / 2.0, |
| "sinh(1)", |
| Minimum_Error); |
| Check (Cosh (1.0), |
| Cosh1, |
| "cosh(1)", |
| Minimum_Error); |
| Check (Sinh (2.0), |
| (E * E - (1.0 / (E * E))) / 2.0, |
| "sinh(2)", |
| Minimum_Error); |
| Check (Cosh (2.0), |
| (E * E + (1.0 / (E * E))) / 2.0, |
| "cosh(2)", |
| Minimum_Error); |
| Check (Sinh (-1.0), |
| (1.0 / E - E) / 2.0, |
| "sinh(-1)", |
| 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 (Sinh (0.0), 0.0, "sinh(0)", No_Error); |
| Check (Cosh (0.0), 1.0, "cosh(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_1_Test is |
| -- For the Sinh test use the identity |
| -- 2 * Sinh(x) * Cosh(1) = Sinh(x+1) + Sinh (x-1) |
| -- which is transformed to |
| -- Sinh(x) = ((Sinh(x+1) + Sinh(x-1)) * C |
| -- where C = 1/(2*Cosh(1)) |
| -- |
| -- For the Cosh test use the identity |
| -- 2 * Cosh(x) * Cosh(1) = Cosh(x+1) + Cosh(x-1) |
| -- which is transformed to |
| -- Cosh(x) = C * (Cosh(x+1) + Cosh(x-1)) |
| -- where C is the same as above |
| -- |
| -- see Cody pg 230-231 for details on the error analysis. |
| -- The net result is a relative error bound of 16 * Model_Epsilon. |
| |
| A : constant := 3.0; |
| -- large upper bound but not so large as to cause Cosh(B) |
| -- to overflow |
| B : constant Real := Log(Real'Safe_Last) - 2.0; |
| X_Minus_1, X, X_Plus_1 : Real; |
| Actual1, Actual2 : Real; |
| C : constant := 1.0 / (2.0 * Cosh1); |
| begin |
| Accuracy_Error_Reported := False; -- reset |
| for I in 1..Max_Samples loop |
| -- make sure there is no error in x-1, x, and x+1 |
| X_Plus_1 := (B - A) * Real (I) / Real (Max_Samples) + A; |
| X_Plus_1 := Real'Machine (X_Plus_1); |
| X := Real'Machine (X_Plus_1 - 1.0); |
| X_Minus_1 := Real'Machine (X - 1.0); |
| |
| -- Sinh(x) = ((Sinh(x+1) + Sinh(x-1)) * C |
| Actual1 := Sinh(X); |
| Actual2 := C * (Sinh(X_Plus_1) + Sinh(X_Minus_1)); |
| |
| Check (Actual1, Actual2, |
| "Identity_1_Test " & Integer'Image (I) & ": sinh(" & |
| Real'Image (X) & ") ", |
| 16.0); |
| |
| -- Cosh(x) = C * (Cosh(x+1) + Cosh(x-1)) |
| Actual1 := Cosh (X); |
| Actual2 := C * (Cosh(X_Plus_1) + Cosh (X_Minus_1)); |
| Check (Actual1, Actual2, |
| "Identity_1_Test " & Integer'Image (I) & ": cosh(" & |
| 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; |
| |
| exception |
| when Constraint_Error => |
| Report.Failed |
| ("Constraint_Error raised in Identity_1_Test" & |
| " for X=" & Real'Image (X)); |
| when others => |
| Report.Failed ("exception in Identity_1_Test" & |
| " for X=" & Real'Image (X)); |
| end Identity_1_Test; |
| |
| |
| |
| procedure Subtraction_Error_Test is |
| -- This test detects the error resulting from subtraction if |
| -- the obvious algorithm was used for computing sinh. That is, |
| -- it it is computed as (e**x - e**-x)/2. |
| -- We check the result by using a Taylor series expansion that |
| -- will produce a result accurate to the machine precision for |
| -- the range under test. |
| -- |
| -- The maximum relative error bound for this test is |
| -- 8 for the sinh operation and 7 for the Taylor series |
| -- for a total of 15 * Model_Epsilon |
| A : constant := 0.0; |
| B : constant := 0.5; |
| X : Real; |
| X_Squared : Real; |
| Actual, Expected : Real; |
| begin |
| if Real'digits > 15 then |
| return; -- The approximation below is not accurate beyond |
| -- 15 digits. Adding more terms makes the error |
| -- larger, so it makes the test worse for more normal |
| -- values. Thus, we skip this subtest for larger than |
| -- 15 digits. |
| end if; |
| Accuracy_Error_Reported := False; -- reset |
| for I in 1..Max_Samples loop |
| X := (B - A) * Real (I) / Real (Max_Samples) + A; |
| X_Squared := X * X; |
| |
| Actual := Sinh(X); |
| |
| -- The Taylor series regrouped a bit |
| Expected := |
| X * (1.0 + (X_Squared / 6.0) * |
| (1.0 + (X_Squared/20.0) * |
| (1.0 + (X_Squared/42.0) * |
| (1.0 + (X_Squared/72.0) * |
| (1.0 + (X_Squared/110.0) * |
| (1.0 + (X_Squared/156.0) |
| )))))); |
| |
| Check (Actual, Expected, |
| "Subtraction_Error_Test " & Integer'Image (I) & ": sinh(" & |
| Real'Image (X) & ") ", |
| 15.0); |
| |
| 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; |
| |
| exception |
| when Constraint_Error => |
| Report.Failed |
| ("Constraint_Error raised in Subtraction_Error_Test"); |
| when others => |
| Report.Failed ("exception in Subtraction_Error_Test"); |
| end Subtraction_Error_Test; |
| |
| |
| procedure Exception_Test is |
| X1, X2 : Real := 0.0; |
| begin |
| -- this part of the test is only applicable if 'Machine_Overflows |
| -- is true. |
| if Real'Machine_Overflows then |
| |
| begin |
| X1 := Sinh (Real'Safe_Last / 2.0); |
| Report.Failed ("no exception for sinh overflow"); |
| exception |
| when Constraint_Error => null; |
| when others => |
| Report.Failed ("wrong exception sinh overflow"); |
| end; |
| |
| begin |
| X2 := Cosh (Real'Safe_Last / 2.0); |
| Report.Failed ("no exception for cosh overflow"); |
| exception |
| when Constraint_Error => null; |
| when others => |
| Report.Failed ("wrong exception cosh overflow"); |
| end; |
| |
| end if; |
| |
| -- optimizer thwarting |
| if Report.Ident_Bool (False) then |
| Report.Comment (Real'Image (X1 + X2)); |
| end if; |
| end Exception_Test; |
| |
| |
| procedure Do_Test is |
| begin |
| Special_Value_Test; |
| Exact_Result_Test; |
| Identity_1_Test; |
| Subtraction_Error_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 ("CXG2014", |
| "Check the accuracy of the SINH and COSH 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 CXG2014; |
