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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 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;
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