-- CXG2003.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 sqrt function returns -- results that are within the error bound allowed. -- -- TEST DESCRIPTION: -- This test contains three test packages that are almost -- identical. The first two packages differ only in the -- floating point type that is being tested. The first -- and third package differ only in whether the generic -- elementary functions package or the pre-instantiated -- package is used. -- The test package is not generic so that the arguments -- and expected results for some of the test values -- can be expressed as universal real instead of being -- computed at runtime. -- -- 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: -- 2 FEB 96 SAIC Initial release for 2.1 -- 18 AUG 96 SAIC Made Check consistent with other tests. -- --! with System; with Report; with Ada.Numerics.Generic_Elementary_Functions; with Ada.Numerics.Elementary_Functions; procedure CXG2003 is Verbose : constant Boolean := False; package Float_Check is subtype Real is Float; procedure Do_Test; end Float_Check; package body Float_Check is package Elementary_Functions is new Ada.Numerics.Generic_Elementary_Functions (Real); function Sqrt (X : Real) return Real renames Elementary_Functions.Sqrt; function Log (X : Real) return Real renames Elementary_Functions.Log; function Exp (X : Real) return Real renames Elementary_Functions.Exp; -- The default Maximum Relative Error is the value specified -- in the LRM. Default_MRE : constant Real := 2.0; procedure Check (Actual, Expected : Real; Test_Name : String; MRE : Real := Default_MRE) is Rel_Error : Real; Abs_Error : Real; Max_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 Report.Failed (Test_Name & " actual: " & Real'Image (Actual) & " expected: " & Real'Image (Expected) & " difference: " & Real'Image (Actual - Expected) & " mre:" & 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 Argument_Range_Check (A, B : Real; Test : String) is -- test a logarithmically distributed selection of -- arguments selected from the range A to B. X : Real; Expected : Real; Y : Real; C : Real := Log(B/A); Max_Samples : constant := 1000; begin for I in 1..Max_Samples loop Expected := A * Exp(C * Real (I) / Real (Max_Samples)); X := Expected * Expected; Y := Sqrt (X); -- note that since the expected value is computed, we -- must take the error in that computation into account. Check (Y, Expected, "test " & Test & " -" & Integer'Image (I) & " of argument range", 3.0); end loop; exception when Constraint_Error => Report.Failed ("Constraint_Error raised in argument range check"); when others => Report.Failed ("exception in argument range check"); end Argument_Range_Check; procedure Do_Test is begin --- test 1 --- declare T : constant := (Real'Machine_EMax - 1) / 2; X : constant := (1.0 * Real'Machine_Radix) ** (2 * T); Expected : constant := (1.0 * Real'Machine_Radix) ** T; Y : Real; begin Y := Sqrt (X); Check (Y, Expected, "test 1 -- sqrt(radix**((emax-1)/2))"); exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 1"); when others => Report.Failed ("exception in test 1"); end; --- test 2 --- declare T : constant := (Real'Model_EMin + 1) / 2; X : constant := (1.0 * Real'Machine_Radix) ** (2 * T); Expected : constant := (1.0 * Real'Machine_Radix) ** T; Y : Real; begin Y := Sqrt (X); Check (Y, Expected, "test 2 -- sqrt(radix**((emin+1)/2))"); exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 2"); when others => Report.Failed ("exception in test 2"); end; --- test 3 --- declare X : constant := 1.0; Expected : constant := 1.0; Y : Real; begin Y := Sqrt(X); Check (Y, Expected, "test 3 -- sqrt(1.0)", 0.0); -- no error allowed exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 3"); when others => Report.Failed ("exception in test 3"); end; --- test 4 --- declare X : constant := 0.0; Expected : constant := 0.0; Y : Real; begin Y := Sqrt(X); Check (Y, Expected, "test 4 -- sqrt(0.0)", 0.0); -- no error allowed exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 4"); when others => Report.Failed ("exception in test 4"); end; --- test 5 --- declare X : constant := -1.0; Y : Real; begin Y := Sqrt(X); -- the following code should not be executed. -- The call to Check is to keep the call to Sqrt from -- appearing to be dead code. Check (Y, -1.0, "test 5 -- sqrt(-1)" ); Report.Failed ("test 5 - argument_error expected"); exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 5"); when Ada.Numerics.Argument_Error => if Verbose then Report.Comment ("test 5 correctly got argument_error"); end if; when others => Report.Failed ("exception in test 5"); end; --- test 6 --- declare X : constant := Ada.Numerics.Pi ** 2; Expected : constant := Ada.Numerics.Pi; Y : Real; begin Y := Sqrt (X); Check (Y, Expected, "test 6 -- sqrt(pi**2)"); exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 6"); when others => Report.Failed ("exception in test 6"); end; --- test 7 & 8 --- Argument_Range_Check (1.0/Sqrt(Real(Real'Machine_Radix)), 1.0, "7"); Argument_Range_Check (1.0, Sqrt(Real(Real'Machine_Radix)), "8"); end Do_Test; end Float_Check; ----------------------------------------------------------------------- ----------------------------------------------------------------------- -- check the floating point type with the most digits type A_Long_Float is digits System.Max_Digits; package A_Long_Float_Check is subtype Real is A_Long_Float; procedure Do_Test; end A_Long_Float_Check; package body A_Long_Float_Check is package Elementary_Functions is new Ada.Numerics.Generic_Elementary_Functions (Real); function Sqrt (X : Real) return Real renames Elementary_Functions.Sqrt; function Log (X : Real) return Real renames Elementary_Functions.Log; function Exp (X : Real) return Real renames Elementary_Functions.Exp; -- The default Maximum Relative Error is the value specified -- in the LRM. Default_MRE : constant Real := 2.0; procedure Check (Actual, Expected : Real; Test_Name : String; MRE : Real := Default_MRE) is Rel_Error : Real; Abs_Error : Real; Max_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 Report.Failed (Test_Name & " actual: " & Real'Image (Actual) & " expected: " & Real'Image (Expected) & " difference: " & Real'Image (Actual - Expected) & " mre:" & 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 Argument_Range_Check (A, B : Real; Test : String) is -- test a logarithmically distributed selection of -- arguments selected from the range A to B. X : Real; Expected : Real; Y : Real; C : Real := Log(B/A); Max_Samples : constant := 1000; begin for I in 1..Max_Samples loop Expected := A * Exp(C * Real (I) / Real (Max_Samples)); X := Expected * Expected; Y := Sqrt (X); -- note that since the expected value is computed, we -- must take the error in that computation into account. Check (Y, Expected, "test " & Test & " -" & Integer'Image (I) & " of argument range", 3.0); end loop; exception when Constraint_Error => Report.Failed ("Constraint_Error raised in argument range check"); when others => Report.Failed ("exception in argument range check"); end Argument_Range_Check; procedure Do_Test is begin --- test 1 --- declare T : constant := (Real'Machine_EMax - 1) / 2; X : constant := (1.0 * Real'Machine_Radix) ** (2 * T); Expected : constant := (1.0 * Real'Machine_Radix) ** T; Y : Real; begin Y := Sqrt (X); Check (Y, Expected, "test 1 -- sqrt(radix**((emax-1)/2))"); exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 1"); when others => Report.Failed ("exception in test 1"); end; --- test 2 --- declare T : constant := (Real'Model_EMin + 1) / 2; X : constant := (1.0 * Real'Machine_Radix) ** (2 * T); Expected : constant := (1.0 * Real'Machine_Radix) ** T; Y : Real; begin Y := Sqrt (X); Check (Y, Expected, "test 2 -- sqrt(radix**((emin+1)/2))"); exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 2"); when others => Report.Failed ("exception in test 2"); end; --- test 3 --- declare X : constant := 1.0; Expected : constant := 1.0; Y : Real; begin Y := Sqrt(X); Check (Y, Expected, "test 3 -- sqrt(1.0)", 0.0); -- no error allowed exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 3"); when others => Report.Failed ("exception in test 3"); end; --- test 4 --- declare X : constant := 0.0; Expected : constant := 0.0; Y : Real; begin Y := Sqrt(X); Check (Y, Expected, "test 4 -- sqrt(0.0)", 0.0); -- no error allowed exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 4"); when others => Report.Failed ("exception in test 4"); end; --- test 5 --- declare X : constant := -1.0; Y : Real; begin Y := Sqrt(X); -- the following code should not be executed. -- The call to Check is to keep the call to Sqrt from -- appearing to be dead code. Check (Y, -1.0, "test 5 -- sqrt(-1)" ); Report.Failed ("test 5 - argument_error expected"); exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 5"); when Ada.Numerics.Argument_Error => if Verbose then Report.Comment ("test 5 correctly got argument_error"); end if; when others => Report.Failed ("exception in test 5"); end; --- test 6 --- declare X : constant := Ada.Numerics.Pi ** 2; Expected : constant := Ada.Numerics.Pi; Y : Real; begin Y := Sqrt (X); Check (Y, Expected, "test 6 -- sqrt(pi**2)"); exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 6"); when others => Report.Failed ("exception in test 6"); end; --- test 7 & 8 --- Argument_Range_Check (1.0/Sqrt(Real(Real'Machine_Radix)), 1.0, "7"); Argument_Range_Check (1.0, Sqrt(Real(Real'Machine_Radix)), "8"); end Do_Test; end A_Long_Float_Check; ----------------------------------------------------------------------- ----------------------------------------------------------------------- package Non_Generic_Check is procedure Do_Test; end Non_Generic_Check; package body Non_Generic_Check is package EF renames Ada.Numerics.Elementary_Functions; subtype Real is Float; -- The default Maximum Relative Error is the value specified -- in the LRM. Default_MRE : constant Real := 2.0; procedure Check (Actual, Expected : Real; Test_Name : String; MRE : Real := Default_MRE) is Rel_Error : Real; Abs_Error : Real; Max_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 Report.Failed (Test_Name & " actual: " & Real'Image (Actual) & " expected: " & Real'Image (Expected) & " difference: " & Real'Image (Actual - Expected) & " mre:" & 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 Argument_Range_Check (A, B : Float; Test : String) is -- test a logarithmically distributed selection of -- arguments selected from the range A to B. X : Float; Expected : Float; Y : Float; C : Float := EF.Log(B/A); Max_Samples : constant := 1000; begin for I in 1..Max_Samples loop Expected := A * EF.Exp(C * Float (I) / Float (Max_Samples)); X := Expected * Expected; Y := EF.Sqrt (X); -- note that since the expected value is computed, we -- must take the error in that computation into account. Check (Y, Expected, "test " & Test & " -" & Integer'Image (I) & " of argument range", 3.0); end loop; exception when Constraint_Error => Report.Failed ("Constraint_Error raised in argument range check"); when others => Report.Failed ("exception in argument range check"); end Argument_Range_Check; procedure Do_Test is begin --- test 1 --- declare T : constant := (Float'Machine_EMax - 1) / 2; X : constant := (1.0 * Float'Machine_Radix) ** (2 * T); Expected : constant := (1.0 * Float'Machine_Radix) ** T; Y : Float; begin Y := EF.Sqrt (X); Check (Y, Expected, "test 1 -- sqrt(radix**((emax-1)/2))"); exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 1"); when others => Report.Failed ("exception in test 1"); end; --- test 2 --- declare T : constant := (Float'Model_EMin + 1) / 2; X : constant := (1.0 * Float'Machine_Radix) ** (2 * T); Expected : constant := (1.0 * Float'Machine_Radix) ** T; Y : Float; begin Y := EF.Sqrt (X); Check (Y, Expected, "test 2 -- sqrt(radix**((emin+1)/2))"); exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 2"); when others => Report.Failed ("exception in test 2"); end; --- test 3 --- declare X : constant := 1.0; Expected : constant := 1.0; Y : Float; begin Y := EF.Sqrt(X); Check (Y, Expected, "test 3 -- sqrt(1.0)", 0.0); -- no error allowed exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 3"); when others => Report.Failed ("exception in test 3"); end; --- test 4 --- declare X : constant := 0.0; Expected : constant := 0.0; Y : Float; begin Y := EF.Sqrt(X); Check (Y, Expected, "test 4 -- sqrt(0.0)", 0.0); -- no error allowed exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 4"); when others => Report.Failed ("exception in test 4"); end; --- test 5 --- declare X : constant := -1.0; Y : Float; begin Y := EF.Sqrt(X); -- the following code should not be executed. -- The call to Check is to keep the call to Sqrt from -- appearing to be dead code. Check (Y, -1.0, "test 5 -- sqrt(-1)" ); Report.Failed ("test 5 - argument_error expected"); exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 5"); when Ada.Numerics.Argument_Error => if Verbose then Report.Comment ("test 5 correctly got argument_error"); end if; when others => Report.Failed ("exception in test 5"); end; --- test 6 --- declare X : constant := Ada.Numerics.Pi ** 2; Expected : constant := Ada.Numerics.Pi; Y : Float; begin Y := EF.Sqrt (X); Check (Y, Expected, "test 6 -- sqrt(pi**2)"); exception when Constraint_Error => Report.Failed ("Constraint_Error raised in test 6"); when others => Report.Failed ("exception in test 6"); end; --- test 7 & 8 --- Argument_Range_Check (1.0/EF.Sqrt(Float(Float'Machine_Radix)), 1.0, "7"); Argument_Range_Check (1.0, EF.Sqrt(Float(Float'Machine_Radix)), "8"); end Do_Test; end Non_Generic_Check; ----------------------------------------------------------------------- ----------------------------------------------------------------------- begin Report.Test ("CXG2003", "Check the accuracy of the sqrt 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; if Verbose then Report.Comment ("checking non-generic package"); end if; Non_Generic_Check.Do_Test; Report.Result; end CXG2003;