| -- CXG2012.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 exponentiation operator returns |
| -- 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. |
| -- While this test concentrates on the "**" operator |
| -- defined in Generic_Elementary_Functions, a check is also |
| -- performed on the standard "**" operator. |
| -- |
| -- 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: |
| -- 7 Mar 96 SAIC Initial release for 2.1 |
| -- 2 Sep 96 SAIC Improvements as suggested by reviewers |
| -- 3 Jun 98 EDS Add parens to ensure that the expression is not |
| -- evaluated by multiplying its two large terms |
| -- together and overflowing. |
| -- 3 Dec 01 RLB Added 'Machine to insure that equality tests |
| -- are certain to work. |
| -- |
| --! |
| |
| -- |
| -- 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 CXG2012 is |
| Verbose : constant Boolean := False; |
| Max_Samples : constant := 1000; |
| |
| -- 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; |
| |
| |
| 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 Exp (X : Real) return Real renames |
| Elementary_Functions.Exp; |
| function Log (X : Real) return Real renames |
| Elementary_Functions.Log; |
| function "**" (L, R : Real) return Real renames |
| Elementary_Functions."**"; |
| |
| -- 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_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; |
| |
| |
| -- the following version of Check computes the allowed error bound |
| -- using the operands |
| procedure Check (Actual, Expected : Real; |
| Left, Right : Real; |
| Test_Name : String; |
| MRE_Factor : Real := 1.0) is |
| MRE : Real; |
| begin |
| MRE := MRE_Factor * (4.0 + abs (Right * Log(Left)) / 32.0); |
| Check (Actual, Expected, Test_Name, MRE); |
| end Check; |
| |
| |
| procedure Real_To_Integer_Test is |
| type Int_Check is |
| record |
| Left : Real; |
| Right : Integer; |
| Expected : Real; |
| end record; |
| type Int_Checks is array (Positive range <>) of Int_Check; |
| |
| -- the following tests use only model numbers so the result |
| -- is expected to be exact. |
| IC : constant Int_Checks := |
| ( ( 2.0, 5, 32.0), |
| ( -2.0, 5, -32.0), |
| ( 0.5, -5, 32.0), |
| ( 2.0, 0, 1.0), |
| ( 0.0, 0, 1.0) ); |
| begin |
| for I in IC'Range loop |
| declare |
| Y : Real; |
| begin |
| Y := IC (I).Left ** IC (I).Right; |
| Check (Y, IC (I).Expected, |
| "real to integer test" & |
| Real'Image (IC (I).Left) & " ** " & |
| Integer'Image (IC (I).Right), |
| 0.0); -- no error allowed |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in rtoi test " & |
| Integer'Image (I)); |
| when others => |
| Report.Failed ("exception in rtoi test " & |
| Integer'Image (I)); |
| end; |
| end loop; |
| end Real_To_Integer_Test; |
| |
| |
| procedure Special_Value_Test is |
| No_Error : constant := 0.0; |
| begin |
| Check (0.0 ** 1.0, 0.0, "0**1", No_Error); |
| Check (1.0 ** 0.0, 1.0, "1**0", No_Error); |
| |
| Check ( 2.0 ** 5.0, 32.0, 2.0, 5.0, "2**5"); |
| Check ( 0.5**(-5.0), 32.0, 0.5, -5.0, "0.5**-5"); |
| |
| Check (Sqrt2 ** 4.0, 4.0, Sqrt2, 4.0, "Sqrt2**4"); |
| Check (Sqrt3 ** 6.0, 27.0, Sqrt3, 6.0, "Sqrt3**6"); |
| |
| Check (2.0 ** 0.5, Sqrt2, 2.0, 0.5, "2.0**0.5"); |
| |
| 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 Small_Range_Test is |
| -- Several checks over the range 1/radix .. 1 |
| A : constant Real := 1.0 / Real (Real'Machine_Radix); |
| B : constant Real := 1.0; |
| X : Real; |
| -- In the cases below where the expected result is |
| -- inexact we allow an additional error amount of |
| -- 1.0 * Model_Epsilon to account for that error. |
| -- This is accomplished by the factor of 1.25 times |
| -- the computed error bound (which is > 4.0) thus |
| -- increasing the error bound by at least |
| -- 1.0 * Model_Epsilon |
| begin |
| Accuracy_Error_Reported := False; -- reset |
| for I in 0..Max_Samples loop |
| X := Real'Machine((B - A) * Real (I) / Real (Max_Samples) + A); |
| |
| Check (X ** 1.0, X, -- exact result required |
| "Small range" & Integer'Image (I) & ": " & |
| Real'Image (X) & " ** 1.0", |
| 0.0); |
| |
| Check ((X*X) ** 1.5, X**3, X*X, 1.5, |
| "Small range" & Integer'Image (I) & ": " & |
| Real'Image (X*X) & " ** 1.5", |
| 1.25); |
| |
| Check (X ** 13.5, 1.0 / (X ** (-13.5)), X, 13.5, |
| "Small range" & Integer'Image (I) & ": " & |
| Real'Image (X) & " ** 13.5", |
| 2.0); -- 2 ** computations |
| |
| Check ((X*X) ** 1.25, X**(2.5), X*X, 1.25, |
| "Small range" & Integer'Image (I) & ": " & |
| Real'Image (X*X) & " ** 1.25", |
| 2.0); -- 2 ** computations |
| |
| 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 Small Range Test"); |
| when others => |
| Report.Failed ("exception in Small Range Test"); |
| end Small_Range_Test; |
| |
| |
| procedure Large_Range_Test is |
| -- Check over the range A to B where A is 1.0 and |
| -- B is a large value. |
| A : constant Real := 1.0; |
| B : Real; |
| X : Real; |
| Iteration : Integer := 0; |
| Subtest : Character := 'X'; |
| begin |
| -- upper bound of range should be as large as possible where |
| -- B**3 is still valid. |
| B := Real'Safe_Last ** 0.333; |
| Accuracy_Error_Reported := False; -- reset |
| for I in 0..Max_Samples loop |
| Iteration := I; |
| Subtest := 'X'; |
| X := Real'Machine((B - A) * (Real (I) / Real (Max_Samples)) + A); |
| |
| Subtest := 'A'; |
| Check (X ** 1.0, X, -- exact result required |
| "Large range" & Integer'Image (I) & ": " & |
| Real'Image (X) & " ** 1.0", |
| 0.0); |
| |
| Subtest := 'B'; |
| Check ((X*X) ** 1.5, X**3, X*X, 1.5, |
| "Large range" & Integer'Image (I) & ": " & |
| Real'Image (X*X) & " ** 1.5", |
| 1.25); -- inexact expected result |
| |
| Subtest := 'C'; |
| Check ((X*X) ** 1.25, X**(2.5), X*X, 1.25, |
| "Large range" & Integer'Image (I) & ": " & |
| Real'Image (X*X) & " ** 1.25", |
| 2.0); -- two ** operators |
| |
| 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 Large Range Test" & |
| Integer'Image (Iteration) & Subtest); |
| when others => |
| Report.Failed ("exception in Large Range Test" & |
| Integer'Image (Iteration) & Subtest); |
| end Large_Range_Test; |
| |
| |
| procedure Exception_Test is |
| X1, X2, X3, X4 : Real; |
| begin |
| begin |
| X1 := 0.0 ** (-1.0); |
| Report.Failed ("exception not raised for 0**-1"); |
| exception |
| when Ada.Numerics.Argument_Error => |
| Report.Failed ("argument_error raised instead of" & |
| " constraint_error for 0**-1"); |
| when Constraint_Error => null; -- ok |
| when others => |
| Report.Failed ("wrong exception raised for 0**-1"); |
| end; |
| |
| begin |
| X2 := 0.0 ** 0.0; |
| Report.Failed ("exception not raised for 0**0"); |
| exception |
| when Ada.Numerics.Argument_Error => null; -- ok |
| when Constraint_Error => |
| Report.Failed ("constraint_error raised instead of" & |
| " argument_error for 0**0"); |
| when others => |
| Report.Failed ("wrong exception raised for 0**0"); |
| end; |
| |
| begin |
| X3 := (-1.0) ** 1.0; |
| Report.Failed ("exception not raised for -1**1"); |
| exception |
| when Ada.Numerics.Argument_Error => null; -- ok |
| when Constraint_Error => |
| Report.Failed ("constraint_error raised instead of" & |
| " argument_error for -1**1"); |
| when others => |
| Report.Failed ("wrong exception raised for -1**1"); |
| end; |
| |
| begin |
| X4 := (-2.0) ** 2.0; |
| Report.Failed ("exception not raised for -2**2"); |
| exception |
| when Ada.Numerics.Argument_Error => null; -- ok |
| when Constraint_Error => |
| Report.Failed ("constraint_error raised instead of" & |
| " argument_error for -2**2"); |
| when others => |
| Report.Failed ("wrong exception raised for -2**2"); |
| end; |
| |
| -- optimizer thwarting |
| if Report.Ident_Bool (False) then |
| Report.Comment (Real'Image (X1+X2+X3+X4)); |
| end if; |
| end Exception_Test; |
| |
| |
| procedure Do_Test is |
| begin |
| Real_To_Integer_Test; |
| Special_Value_Test; |
| Small_Range_Test; |
| Large_Range_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 ("CXG2012", |
| "Check the accuracy of the ** operator"); |
| |
| 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 CXG2012; |
