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-- 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 isVerbose : constant Boolean := False;package Float_Check issubtype Real is Float;procedure Do_Test;end Float_Check;package body Float_Check ispackage Elementary_Functions is newAda.Numerics.Generic_Elementary_Functions (Real);function Sqrt (X : Real) return Real renamesElementary_Functions.Sqrt;function Log (X : Real) return Real renamesElementary_Functions.Log;function Exp (X : Real) return Real renamesElementary_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) isRel_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 thenMax_Error := Rel_Error;elseMax_Error := Abs_Error;end if;if abs (Actual - Expected) > Max_Error thenReport.Failed (Test_Name &" actual: " & Real'Image (Actual) &" expected: " & Real'Image (Expected) &" difference: " &Real'Image (Actual - Expected) &" mre:" & Real'Image (Max_Error) );elsif Verbose thenif Actual = Expected thenReport.Comment (Test_Name & " exact result");elseReport.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;beginfor I in 1..Max_Samples loopExpected := 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;exceptionwhen 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 isbegin--- test 1 ---declareT : 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;beginY := Sqrt (X);Check (Y, Expected, "test 1 -- sqrt(radix**((emax-1)/2))");exceptionwhen Constraint_Error =>Report.Failed ("Constraint_Error raised in test 1");when others =>Report.Failed ("exception in test 1");end;--- test 2 ---declareT : 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;beginY := Sqrt (X);Check (Y, Expected, "test 2 -- sqrt(radix**((emin+1)/2))");exceptionwhen Constraint_Error =>Report.Failed ("Constraint_Error raised in test 2");when others =>Report.Failed ("exception in test 2");end;--- test 3 ---declareX : constant := 1.0;Expected : constant := 1.0;Y : Real;beginY := Sqrt(X);Check (Y, Expected, "test 3 -- sqrt(1.0)",0.0); -- no error allowedexceptionwhen Constraint_Error =>Report.Failed ("Constraint_Error raised in test 3");when others =>Report.Failed ("exception in test 3");end;--- test 4 ---declareX : constant := 0.0;Expected : constant := 0.0;Y : Real;beginY := Sqrt(X);Check (Y, Expected, "test 4 -- sqrt(0.0)",0.0); -- no error allowedexceptionwhen Constraint_Error =>Report.Failed ("Constraint_Error raised in test 4");when others =>Report.Failed ("exception in test 4");end;--- test 5 ---declareX : constant := -1.0;Y : Real;beginY := 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");exceptionwhen Constraint_Error =>Report.Failed ("Constraint_Error raised in test 5");when Ada.Numerics.Argument_Error =>if Verbose thenReport.Comment ("test 5 correctly got argument_error");end if;when others =>Report.Failed ("exception in test 5");end;--- test 6 ---declareX : constant := Ada.Numerics.Pi ** 2;Expected : constant := Ada.Numerics.Pi;Y : Real;beginY := Sqrt (X);Check (Y, Expected, "test 6 -- sqrt(pi**2)");exceptionwhen 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 digitstype A_Long_Float is digits System.Max_Digits;package A_Long_Float_Check issubtype Real is A_Long_Float;procedure Do_Test;end A_Long_Float_Check;package body A_Long_Float_Check ispackage Elementary_Functions is newAda.Numerics.Generic_Elementary_Functions (Real);function Sqrt (X : Real) return Real renamesElementary_Functions.Sqrt;function Log (X : Real) return Real renamesElementary_Functions.Log;function Exp (X : Real) return Real renamesElementary_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) isRel_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 thenMax_Error := Rel_Error;elseMax_Error := Abs_Error;end if;if abs (Actual - Expected) > Max_Error thenReport.Failed (Test_Name &" actual: " & Real'Image (Actual) &" expected: " & Real'Image (Expected) &" difference: " &Real'Image (Actual - Expected) &" mre:" & Real'Image (Max_Error) );elsif Verbose thenif Actual = Expected thenReport.Comment (Test_Name & " exact result");elseReport.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;beginfor I in 1..Max_Samples loopExpected := 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;exceptionwhen 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 isbegin--- test 1 ---declareT : 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;beginY := Sqrt (X);Check (Y, Expected, "test 1 -- sqrt(radix**((emax-1)/2))");exceptionwhen Constraint_Error =>Report.Failed ("Constraint_Error raised in test 1");when others =>Report.Failed ("exception in test 1");end;--- test 2 ---declareT : 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;beginY := Sqrt (X);Check (Y, Expected, "test 2 -- sqrt(radix**((emin+1)/2))");exceptionwhen Constraint_Error =>Report.Failed ("Constraint_Error raised in test 2");when others =>Report.Failed ("exception in test 2");end;--- test 3 ---declareX : constant := 1.0;Expected : constant := 1.0;Y : Real;beginY := Sqrt(X);Check (Y, Expected, "test 3 -- sqrt(1.0)",0.0); -- no error allowedexceptionwhen Constraint_Error =>Report.Failed ("Constraint_Error raised in test 3");when others =>Report.Failed ("exception in test 3");end;--- test 4 ---declareX : constant := 0.0;Expected : constant := 0.0;Y : Real;beginY := Sqrt(X);Check (Y, Expected, "test 4 -- sqrt(0.0)",0.0); -- no error allowedexceptionwhen Constraint_Error =>Report.Failed ("Constraint_Error raised in test 4");when others =>Report.Failed ("exception in test 4");end;--- test 5 ---declareX : constant := -1.0;Y : Real;beginY := 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");exceptionwhen Constraint_Error =>Report.Failed ("Constraint_Error raised in test 5");when Ada.Numerics.Argument_Error =>if Verbose thenReport.Comment ("test 5 correctly got argument_error");end if;when others =>Report.Failed ("exception in test 5");end;--- test 6 ---declareX : constant := Ada.Numerics.Pi ** 2;Expected : constant := Ada.Numerics.Pi;Y : Real;beginY := Sqrt (X);Check (Y, Expected, "test 6 -- sqrt(pi**2)");exceptionwhen 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 isprocedure Do_Test;end Non_Generic_Check;package body Non_Generic_Check ispackage EF renamesAda.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) isRel_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 thenMax_Error := Rel_Error;elseMax_Error := Abs_Error;end if;if abs (Actual - Expected) > Max_Error thenReport.Failed (Test_Name &" actual: " & Real'Image (Actual) &" expected: " & Real'Image (Expected) &" difference: " &Real'Image (Actual - Expected) &" mre:" & Real'Image (Max_Error) );elsif Verbose thenif Actual = Expected thenReport.Comment (Test_Name & " exact result");elseReport.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;beginfor I in 1..Max_Samples loopExpected := 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;exceptionwhen 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 isbegin--- test 1 ---declareT : 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;beginY := EF.Sqrt (X);Check (Y, Expected, "test 1 -- sqrt(radix**((emax-1)/2))");exceptionwhen Constraint_Error =>Report.Failed ("Constraint_Error raised in test 1");when others =>Report.Failed ("exception in test 1");end;--- test 2 ---declareT : 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;beginY := EF.Sqrt (X);Check (Y, Expected, "test 2 -- sqrt(radix**((emin+1)/2))");exceptionwhen Constraint_Error =>Report.Failed ("Constraint_Error raised in test 2");when others =>Report.Failed ("exception in test 2");end;--- test 3 ---declareX : constant := 1.0;Expected : constant := 1.0;Y : Float;beginY := EF.Sqrt(X);Check (Y, Expected, "test 3 -- sqrt(1.0)",0.0); -- no error allowedexceptionwhen Constraint_Error =>Report.Failed ("Constraint_Error raised in test 3");when others =>Report.Failed ("exception in test 3");end;--- test 4 ---declareX : constant := 0.0;Expected : constant := 0.0;Y : Float;beginY := EF.Sqrt(X);Check (Y, Expected, "test 4 -- sqrt(0.0)",0.0); -- no error allowedexceptionwhen Constraint_Error =>Report.Failed ("Constraint_Error raised in test 4");when others =>Report.Failed ("exception in test 4");end;--- test 5 ---declareX : constant := -1.0;Y : Float;beginY := 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");exceptionwhen Constraint_Error =>Report.Failed ("Constraint_Error raised in test 5");when Ada.Numerics.Argument_Error =>if Verbose thenReport.Comment ("test 5 correctly got argument_error");end if;when others =>Report.Failed ("exception in test 5");end;--- test 6 ---declareX : constant := Ada.Numerics.Pi ** 2;Expected : constant := Ada.Numerics.Pi;Y : Float;beginY := EF.Sqrt (X);Check (Y, Expected, "test 6 -- sqrt(pi**2)");exceptionwhen 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;----------------------------------------------------------------------------------------------------------------------------------------------beginReport.Test ("CXG2003","Check the accuracy of the sqrt function");if Verbose thenReport.Comment ("checking Standard.Float");end if;Float_Check.Do_Test;if Verbose thenReport.Comment ("checking a digits" &Integer'Image (System.Max_Digits) &" floating point type");end if;A_Long_Float_Check.Do_Test;if Verbose thenReport.Comment ("checking non-generic package");end if;Non_Generic_Check.Do_Test;Report.Result;end CXG2003;