-- CXG2003.A
|
-- CXG2003.A
|
--
|
--
|
-- Grant of Unlimited Rights
|
-- Grant of Unlimited Rights
|
--
|
--
|
-- Under contracts F33600-87-D-0337, F33600-84-D-0280, MDA903-79-C-0687,
|
-- 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
|
-- 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 in the software and documentation contained herein.
|
-- Unlimited rights are defined in DFAR 252.227-7013(a)(19). By making
|
-- Unlimited rights are defined in DFAR 252.227-7013(a)(19). By making
|
-- this public release, the Government intends to confer upon all
|
-- this public release, the Government intends to confer upon all
|
-- recipients unlimited rights equal to those held by the Government.
|
-- recipients unlimited rights equal to those held by the Government.
|
-- These rights include rights to use, duplicate, release or disclose the
|
-- These rights include rights to use, duplicate, release or disclose the
|
-- released technical data and computer software in whole or in part, in
|
-- 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
|
-- any manner and for any purpose whatsoever, and to have or permit others
|
-- to do so.
|
-- to do so.
|
--
|
--
|
-- DISCLAIMER
|
-- DISCLAIMER
|
--
|
--
|
-- ALL MATERIALS OR INFORMATION HEREIN RELEASED, MADE AVAILABLE OR
|
-- ALL MATERIALS OR INFORMATION HEREIN RELEASED, MADE AVAILABLE OR
|
-- DISCLOSED ARE AS IS. THE GOVERNMENT MAKES NO EXPRESS OR IMPLIED
|
-- DISCLOSED ARE AS IS. THE GOVERNMENT MAKES NO EXPRESS OR IMPLIED
|
-- WARRANTY AS TO ANY MATTER WHATSOEVER, INCLUDING THE CONDITIONS OF THE
|
-- WARRANTY AS TO ANY MATTER WHATSOEVER, INCLUDING THE CONDITIONS OF THE
|
-- SOFTWARE, DOCUMENTATION OR OTHER INFORMATION RELEASED, MADE AVAILABLE
|
-- SOFTWARE, DOCUMENTATION OR OTHER INFORMATION RELEASED, MADE AVAILABLE
|
-- OR DISCLOSED, OR THE OWNERSHIP, MERCHANTABILITY, OR FITNESS FOR A
|
-- OR DISCLOSED, OR THE OWNERSHIP, MERCHANTABILITY, OR FITNESS FOR A
|
-- PARTICULAR PURPOSE OF SAID MATERIAL.
|
-- PARTICULAR PURPOSE OF SAID MATERIAL.
|
--*
|
--*
|
--
|
--
|
-- OBJECTIVE:
|
-- OBJECTIVE:
|
-- Check that the sqrt function returns
|
-- Check that the sqrt function returns
|
-- results that are within the error bound allowed.
|
-- results that are within the error bound allowed.
|
--
|
--
|
-- TEST DESCRIPTION:
|
-- TEST DESCRIPTION:
|
-- This test contains three test packages that are almost
|
-- This test contains three test packages that are almost
|
-- identical. The first two packages differ only in the
|
-- identical. The first two packages differ only in the
|
-- floating point type that is being tested. The first
|
-- floating point type that is being tested. The first
|
-- and third package differ only in whether the generic
|
-- and third package differ only in whether the generic
|
-- elementary functions package or the pre-instantiated
|
-- elementary functions package or the pre-instantiated
|
-- package is used.
|
-- package is used.
|
-- The test package is not generic so that the arguments
|
-- The test package is not generic so that the arguments
|
-- and expected results for some of the test values
|
-- and expected results for some of the test values
|
-- can be expressed as universal real instead of being
|
-- can be expressed as universal real instead of being
|
-- computed at runtime.
|
-- computed at runtime.
|
--
|
--
|
-- SPECIAL REQUIREMENTS
|
-- SPECIAL REQUIREMENTS
|
-- The Strict Mode for the numerical accuracy must be
|
-- The Strict Mode for the numerical accuracy must be
|
-- selected. The method by which this mode is selected
|
-- selected. The method by which this mode is selected
|
-- is implementation dependent.
|
-- is implementation dependent.
|
--
|
--
|
-- APPLICABILITY CRITERIA:
|
-- APPLICABILITY CRITERIA:
|
-- This test applies only to implementations supporting the
|
-- This test applies only to implementations supporting the
|
-- Numerics Annex.
|
-- Numerics Annex.
|
-- This test only applies to the Strict Mode for numerical
|
-- This test only applies to the Strict Mode for numerical
|
-- accuracy.
|
-- accuracy.
|
--
|
--
|
--
|
--
|
-- CHANGE HISTORY:
|
-- CHANGE HISTORY:
|
-- 2 FEB 96 SAIC Initial release for 2.1
|
-- 2 FEB 96 SAIC Initial release for 2.1
|
-- 18 AUG 96 SAIC Made Check consistent with other tests.
|
-- 18 AUG 96 SAIC Made Check consistent with other tests.
|
--
|
--
|
--!
|
--!
|
|
|
with System;
|
with System;
|
with Report;
|
with Report;
|
with Ada.Numerics.Generic_Elementary_Functions;
|
with Ada.Numerics.Generic_Elementary_Functions;
|
with Ada.Numerics.Elementary_Functions;
|
with Ada.Numerics.Elementary_Functions;
|
procedure CXG2003 is
|
procedure CXG2003 is
|
Verbose : constant Boolean := False;
|
Verbose : constant Boolean := False;
|
|
|
package Float_Check is
|
package Float_Check is
|
subtype Real is Float;
|
subtype Real is Float;
|
procedure Do_Test;
|
procedure Do_Test;
|
end Float_Check;
|
end Float_Check;
|
|
|
package body Float_Check is
|
package body Float_Check is
|
package Elementary_Functions is new
|
package Elementary_Functions is new
|
Ada.Numerics.Generic_Elementary_Functions (Real);
|
Ada.Numerics.Generic_Elementary_Functions (Real);
|
function Sqrt (X : Real) return Real renames
|
function Sqrt (X : Real) return Real renames
|
Elementary_Functions.Sqrt;
|
Elementary_Functions.Sqrt;
|
function Log (X : Real) return Real renames
|
function Log (X : Real) return Real renames
|
Elementary_Functions.Log;
|
Elementary_Functions.Log;
|
function Exp (X : Real) return Real renames
|
function Exp (X : Real) return Real renames
|
Elementary_Functions.Exp;
|
Elementary_Functions.Exp;
|
|
|
-- The default Maximum Relative Error is the value specified
|
-- The default Maximum Relative Error is the value specified
|
-- in the LRM.
|
-- in the LRM.
|
Default_MRE : constant Real := 2.0;
|
Default_MRE : constant Real := 2.0;
|
|
|
procedure Check (Actual, Expected : Real;
|
procedure Check (Actual, Expected : Real;
|
Test_Name : String;
|
Test_Name : String;
|
MRE : Real := Default_MRE) is
|
MRE : Real := Default_MRE) is
|
Rel_Error : Real;
|
Rel_Error : Real;
|
Abs_Error : Real;
|
Abs_Error : Real;
|
Max_Error : Real;
|
Max_Error : Real;
|
begin
|
begin
|
-- In the case where the expected result is very small or 0
|
-- In the case where the expected result is very small or 0
|
-- we compute the maximum error as a multiple of Model_Epsilon instead
|
-- we compute the maximum error as a multiple of Model_Epsilon instead
|
-- of Model_Epsilon and Expected.
|
-- of Model_Epsilon and Expected.
|
Rel_Error := MRE * abs Expected * Real'Model_Epsilon;
|
Rel_Error := MRE * abs Expected * Real'Model_Epsilon;
|
Abs_Error := MRE * Real'Model_Epsilon;
|
Abs_Error := MRE * Real'Model_Epsilon;
|
if Rel_Error > Abs_Error then
|
if Rel_Error > Abs_Error then
|
Max_Error := Rel_Error;
|
Max_Error := Rel_Error;
|
else
|
else
|
Max_Error := Abs_Error;
|
Max_Error := Abs_Error;
|
end if;
|
end if;
|
|
|
if abs (Actual - Expected) > Max_Error then
|
if abs (Actual - Expected) > Max_Error then
|
Report.Failed (Test_Name &
|
Report.Failed (Test_Name &
|
" actual: " & Real'Image (Actual) &
|
" actual: " & Real'Image (Actual) &
|
" expected: " & Real'Image (Expected) &
|
" expected: " & Real'Image (Expected) &
|
" difference: " &
|
" difference: " &
|
Real'Image (Actual - Expected) &
|
Real'Image (Actual - Expected) &
|
" mre:" & Real'Image (Max_Error) );
|
" mre:" & Real'Image (Max_Error) );
|
elsif Verbose then
|
elsif Verbose then
|
if Actual = Expected then
|
if Actual = Expected then
|
Report.Comment (Test_Name & " exact result");
|
Report.Comment (Test_Name & " exact result");
|
else
|
else
|
Report.Comment (Test_Name & " passed");
|
Report.Comment (Test_Name & " passed");
|
end if;
|
end if;
|
end if;
|
end if;
|
end Check;
|
end Check;
|
|
|
|
|
procedure Argument_Range_Check (A, B : Real;
|
procedure Argument_Range_Check (A, B : Real;
|
Test : String) is
|
Test : String) is
|
-- test a logarithmically distributed selection of
|
-- test a logarithmically distributed selection of
|
-- arguments selected from the range A to B.
|
-- arguments selected from the range A to B.
|
X : Real;
|
X : Real;
|
Expected : Real;
|
Expected : Real;
|
Y : Real;
|
Y : Real;
|
C : Real := Log(B/A);
|
C : Real := Log(B/A);
|
Max_Samples : constant := 1000;
|
Max_Samples : constant := 1000;
|
|
|
begin
|
begin
|
for I in 1..Max_Samples loop
|
for I in 1..Max_Samples loop
|
Expected := A * Exp(C * Real (I) / Real (Max_Samples));
|
Expected := A * Exp(C * Real (I) / Real (Max_Samples));
|
X := Expected * Expected;
|
X := Expected * Expected;
|
Y := Sqrt (X);
|
Y := Sqrt (X);
|
|
|
-- note that since the expected value is computed, we
|
-- note that since the expected value is computed, we
|
-- must take the error in that computation into account.
|
-- must take the error in that computation into account.
|
Check (Y, Expected,
|
Check (Y, Expected,
|
"test " & Test & " -" &
|
"test " & Test & " -" &
|
Integer'Image (I) &
|
Integer'Image (I) &
|
" of argument range",
|
" of argument range",
|
3.0);
|
3.0);
|
end loop;
|
end loop;
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed
|
Report.Failed
|
("Constraint_Error raised in argument range check");
|
("Constraint_Error raised in argument range check");
|
when others =>
|
when others =>
|
Report.Failed ("exception in argument range check");
|
Report.Failed ("exception in argument range check");
|
end Argument_Range_Check;
|
end Argument_Range_Check;
|
|
|
procedure Do_Test is
|
procedure Do_Test is
|
begin
|
begin
|
|
|
--- test 1 ---
|
--- test 1 ---
|
declare
|
declare
|
T : constant := (Real'Machine_EMax - 1) / 2;
|
T : constant := (Real'Machine_EMax - 1) / 2;
|
X : constant := (1.0 * Real'Machine_Radix) ** (2 * T);
|
X : constant := (1.0 * Real'Machine_Radix) ** (2 * T);
|
Expected : constant := (1.0 * Real'Machine_Radix) ** T;
|
Expected : constant := (1.0 * Real'Machine_Radix) ** T;
|
Y : Real;
|
Y : Real;
|
begin
|
begin
|
Y := Sqrt (X);
|
Y := Sqrt (X);
|
Check (Y, Expected, "test 1 -- sqrt(radix**((emax-1)/2))");
|
Check (Y, Expected, "test 1 -- sqrt(radix**((emax-1)/2))");
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 1");
|
Report.Failed ("Constraint_Error raised in test 1");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 1");
|
Report.Failed ("exception in test 1");
|
end;
|
end;
|
|
|
--- test 2 ---
|
--- test 2 ---
|
declare
|
declare
|
T : constant := (Real'Model_EMin + 1) / 2;
|
T : constant := (Real'Model_EMin + 1) / 2;
|
X : constant := (1.0 * Real'Machine_Radix) ** (2 * T);
|
X : constant := (1.0 * Real'Machine_Radix) ** (2 * T);
|
Expected : constant := (1.0 * Real'Machine_Radix) ** T;
|
Expected : constant := (1.0 * Real'Machine_Radix) ** T;
|
Y : Real;
|
Y : Real;
|
begin
|
begin
|
Y := Sqrt (X);
|
Y := Sqrt (X);
|
Check (Y, Expected, "test 2 -- sqrt(radix**((emin+1)/2))");
|
Check (Y, Expected, "test 2 -- sqrt(radix**((emin+1)/2))");
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 2");
|
Report.Failed ("Constraint_Error raised in test 2");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 2");
|
Report.Failed ("exception in test 2");
|
end;
|
end;
|
|
|
--- test 3 ---
|
--- test 3 ---
|
declare
|
declare
|
X : constant := 1.0;
|
X : constant := 1.0;
|
Expected : constant := 1.0;
|
Expected : constant := 1.0;
|
Y : Real;
|
Y : Real;
|
begin
|
begin
|
Y := Sqrt(X);
|
Y := Sqrt(X);
|
Check (Y, Expected, "test 3 -- sqrt(1.0)",
|
Check (Y, Expected, "test 3 -- sqrt(1.0)",
|
0.0); -- no error allowed
|
0.0); -- no error allowed
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 3");
|
Report.Failed ("Constraint_Error raised in test 3");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 3");
|
Report.Failed ("exception in test 3");
|
end;
|
end;
|
|
|
--- test 4 ---
|
--- test 4 ---
|
declare
|
declare
|
X : constant := 0.0;
|
X : constant := 0.0;
|
Expected : constant := 0.0;
|
Expected : constant := 0.0;
|
Y : Real;
|
Y : Real;
|
begin
|
begin
|
Y := Sqrt(X);
|
Y := Sqrt(X);
|
Check (Y, Expected, "test 4 -- sqrt(0.0)",
|
Check (Y, Expected, "test 4 -- sqrt(0.0)",
|
0.0); -- no error allowed
|
0.0); -- no error allowed
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 4");
|
Report.Failed ("Constraint_Error raised in test 4");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 4");
|
Report.Failed ("exception in test 4");
|
end;
|
end;
|
|
|
--- test 5 ---
|
--- test 5 ---
|
declare
|
declare
|
X : constant := -1.0;
|
X : constant := -1.0;
|
Y : Real;
|
Y : Real;
|
begin
|
begin
|
Y := Sqrt(X);
|
Y := Sqrt(X);
|
-- the following code should not be executed.
|
-- the following code should not be executed.
|
-- The call to Check is to keep the call to Sqrt from
|
-- The call to Check is to keep the call to Sqrt from
|
-- appearing to be dead code.
|
-- appearing to be dead code.
|
Check (Y, -1.0, "test 5 -- sqrt(-1)" );
|
Check (Y, -1.0, "test 5 -- sqrt(-1)" );
|
Report.Failed ("test 5 - argument_error expected");
|
Report.Failed ("test 5 - argument_error expected");
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 5");
|
Report.Failed ("Constraint_Error raised in test 5");
|
when Ada.Numerics.Argument_Error =>
|
when Ada.Numerics.Argument_Error =>
|
if Verbose then
|
if Verbose then
|
Report.Comment ("test 5 correctly got argument_error");
|
Report.Comment ("test 5 correctly got argument_error");
|
end if;
|
end if;
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 5");
|
Report.Failed ("exception in test 5");
|
end;
|
end;
|
|
|
--- test 6 ---
|
--- test 6 ---
|
declare
|
declare
|
X : constant := Ada.Numerics.Pi ** 2;
|
X : constant := Ada.Numerics.Pi ** 2;
|
Expected : constant := Ada.Numerics.Pi;
|
Expected : constant := Ada.Numerics.Pi;
|
Y : Real;
|
Y : Real;
|
begin
|
begin
|
Y := Sqrt (X);
|
Y := Sqrt (X);
|
Check (Y, Expected, "test 6 -- sqrt(pi**2)");
|
Check (Y, Expected, "test 6 -- sqrt(pi**2)");
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 6");
|
Report.Failed ("Constraint_Error raised in test 6");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 6");
|
Report.Failed ("exception in test 6");
|
end;
|
end;
|
|
|
--- test 7 & 8 ---
|
--- test 7 & 8 ---
|
Argument_Range_Check (1.0/Sqrt(Real(Real'Machine_Radix)),
|
Argument_Range_Check (1.0/Sqrt(Real(Real'Machine_Radix)),
|
1.0,
|
1.0,
|
"7");
|
"7");
|
Argument_Range_Check (1.0,
|
Argument_Range_Check (1.0,
|
Sqrt(Real(Real'Machine_Radix)),
|
Sqrt(Real(Real'Machine_Radix)),
|
"8");
|
"8");
|
end Do_Test;
|
end Do_Test;
|
end Float_Check;
|
end Float_Check;
|
|
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
-- check the floating point type with the most digits
|
-- check the floating point type with the most digits
|
type A_Long_Float is digits System.Max_Digits;
|
type A_Long_Float is digits System.Max_Digits;
|
|
|
|
|
package A_Long_Float_Check is
|
package A_Long_Float_Check is
|
subtype Real is A_Long_Float;
|
subtype Real is A_Long_Float;
|
procedure Do_Test;
|
procedure Do_Test;
|
end A_Long_Float_Check;
|
end A_Long_Float_Check;
|
|
|
package body A_Long_Float_Check is
|
package body A_Long_Float_Check is
|
package Elementary_Functions is new
|
package Elementary_Functions is new
|
Ada.Numerics.Generic_Elementary_Functions (Real);
|
Ada.Numerics.Generic_Elementary_Functions (Real);
|
function Sqrt (X : Real) return Real renames
|
function Sqrt (X : Real) return Real renames
|
Elementary_Functions.Sqrt;
|
Elementary_Functions.Sqrt;
|
function Log (X : Real) return Real renames
|
function Log (X : Real) return Real renames
|
Elementary_Functions.Log;
|
Elementary_Functions.Log;
|
function Exp (X : Real) return Real renames
|
function Exp (X : Real) return Real renames
|
Elementary_Functions.Exp;
|
Elementary_Functions.Exp;
|
|
|
-- The default Maximum Relative Error is the value specified
|
-- The default Maximum Relative Error is the value specified
|
-- in the LRM.
|
-- in the LRM.
|
Default_MRE : constant Real := 2.0;
|
Default_MRE : constant Real := 2.0;
|
|
|
procedure Check (Actual, Expected : Real;
|
procedure Check (Actual, Expected : Real;
|
Test_Name : String;
|
Test_Name : String;
|
MRE : Real := Default_MRE) is
|
MRE : Real := Default_MRE) is
|
Rel_Error : Real;
|
Rel_Error : Real;
|
Abs_Error : Real;
|
Abs_Error : Real;
|
Max_Error : Real;
|
Max_Error : Real;
|
begin
|
begin
|
-- In the case where the expected result is very small or 0
|
-- In the case where the expected result is very small or 0
|
-- we compute the maximum error as a multiple of Model_Epsilon instead
|
-- we compute the maximum error as a multiple of Model_Epsilon instead
|
-- of Model_Epsilon and Expected.
|
-- of Model_Epsilon and Expected.
|
Rel_Error := MRE * abs Expected * Real'Model_Epsilon;
|
Rel_Error := MRE * abs Expected * Real'Model_Epsilon;
|
Abs_Error := MRE * Real'Model_Epsilon;
|
Abs_Error := MRE * Real'Model_Epsilon;
|
if Rel_Error > Abs_Error then
|
if Rel_Error > Abs_Error then
|
Max_Error := Rel_Error;
|
Max_Error := Rel_Error;
|
else
|
else
|
Max_Error := Abs_Error;
|
Max_Error := Abs_Error;
|
end if;
|
end if;
|
|
|
if abs (Actual - Expected) > Max_Error then
|
if abs (Actual - Expected) > Max_Error then
|
Report.Failed (Test_Name &
|
Report.Failed (Test_Name &
|
" actual: " & Real'Image (Actual) &
|
" actual: " & Real'Image (Actual) &
|
" expected: " & Real'Image (Expected) &
|
" expected: " & Real'Image (Expected) &
|
" difference: " &
|
" difference: " &
|
Real'Image (Actual - Expected) &
|
Real'Image (Actual - Expected) &
|
" mre:" & Real'Image (Max_Error) );
|
" mre:" & Real'Image (Max_Error) );
|
elsif Verbose then
|
elsif Verbose then
|
if Actual = Expected then
|
if Actual = Expected then
|
Report.Comment (Test_Name & " exact result");
|
Report.Comment (Test_Name & " exact result");
|
else
|
else
|
Report.Comment (Test_Name & " passed");
|
Report.Comment (Test_Name & " passed");
|
end if;
|
end if;
|
end if;
|
end if;
|
end Check;
|
end Check;
|
|
|
|
|
procedure Argument_Range_Check (A, B : Real;
|
procedure Argument_Range_Check (A, B : Real;
|
Test : String) is
|
Test : String) is
|
-- test a logarithmically distributed selection of
|
-- test a logarithmically distributed selection of
|
-- arguments selected from the range A to B.
|
-- arguments selected from the range A to B.
|
X : Real;
|
X : Real;
|
Expected : Real;
|
Expected : Real;
|
Y : Real;
|
Y : Real;
|
C : Real := Log(B/A);
|
C : Real := Log(B/A);
|
Max_Samples : constant := 1000;
|
Max_Samples : constant := 1000;
|
|
|
begin
|
begin
|
for I in 1..Max_Samples loop
|
for I in 1..Max_Samples loop
|
Expected := A * Exp(C * Real (I) / Real (Max_Samples));
|
Expected := A * Exp(C * Real (I) / Real (Max_Samples));
|
X := Expected * Expected;
|
X := Expected * Expected;
|
Y := Sqrt (X);
|
Y := Sqrt (X);
|
|
|
-- note that since the expected value is computed, we
|
-- note that since the expected value is computed, we
|
-- must take the error in that computation into account.
|
-- must take the error in that computation into account.
|
Check (Y, Expected,
|
Check (Y, Expected,
|
"test " & Test & " -" &
|
"test " & Test & " -" &
|
Integer'Image (I) &
|
Integer'Image (I) &
|
" of argument range",
|
" of argument range",
|
3.0);
|
3.0);
|
end loop;
|
end loop;
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed
|
Report.Failed
|
("Constraint_Error raised in argument range check");
|
("Constraint_Error raised in argument range check");
|
when others =>
|
when others =>
|
Report.Failed ("exception in argument range check");
|
Report.Failed ("exception in argument range check");
|
end Argument_Range_Check;
|
end Argument_Range_Check;
|
|
|
|
|
procedure Do_Test is
|
procedure Do_Test is
|
begin
|
begin
|
|
|
--- test 1 ---
|
--- test 1 ---
|
declare
|
declare
|
T : constant := (Real'Machine_EMax - 1) / 2;
|
T : constant := (Real'Machine_EMax - 1) / 2;
|
X : constant := (1.0 * Real'Machine_Radix) ** (2 * T);
|
X : constant := (1.0 * Real'Machine_Radix) ** (2 * T);
|
Expected : constant := (1.0 * Real'Machine_Radix) ** T;
|
Expected : constant := (1.0 * Real'Machine_Radix) ** T;
|
Y : Real;
|
Y : Real;
|
begin
|
begin
|
Y := Sqrt (X);
|
Y := Sqrt (X);
|
Check (Y, Expected, "test 1 -- sqrt(radix**((emax-1)/2))");
|
Check (Y, Expected, "test 1 -- sqrt(radix**((emax-1)/2))");
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 1");
|
Report.Failed ("Constraint_Error raised in test 1");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 1");
|
Report.Failed ("exception in test 1");
|
end;
|
end;
|
|
|
--- test 2 ---
|
--- test 2 ---
|
declare
|
declare
|
T : constant := (Real'Model_EMin + 1) / 2;
|
T : constant := (Real'Model_EMin + 1) / 2;
|
X : constant := (1.0 * Real'Machine_Radix) ** (2 * T);
|
X : constant := (1.0 * Real'Machine_Radix) ** (2 * T);
|
Expected : constant := (1.0 * Real'Machine_Radix) ** T;
|
Expected : constant := (1.0 * Real'Machine_Radix) ** T;
|
Y : Real;
|
Y : Real;
|
begin
|
begin
|
Y := Sqrt (X);
|
Y := Sqrt (X);
|
Check (Y, Expected, "test 2 -- sqrt(radix**((emin+1)/2))");
|
Check (Y, Expected, "test 2 -- sqrt(radix**((emin+1)/2))");
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 2");
|
Report.Failed ("Constraint_Error raised in test 2");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 2");
|
Report.Failed ("exception in test 2");
|
end;
|
end;
|
|
|
--- test 3 ---
|
--- test 3 ---
|
declare
|
declare
|
X : constant := 1.0;
|
X : constant := 1.0;
|
Expected : constant := 1.0;
|
Expected : constant := 1.0;
|
Y : Real;
|
Y : Real;
|
begin
|
begin
|
Y := Sqrt(X);
|
Y := Sqrt(X);
|
Check (Y, Expected, "test 3 -- sqrt(1.0)",
|
Check (Y, Expected, "test 3 -- sqrt(1.0)",
|
0.0); -- no error allowed
|
0.0); -- no error allowed
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 3");
|
Report.Failed ("Constraint_Error raised in test 3");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 3");
|
Report.Failed ("exception in test 3");
|
end;
|
end;
|
|
|
--- test 4 ---
|
--- test 4 ---
|
declare
|
declare
|
X : constant := 0.0;
|
X : constant := 0.0;
|
Expected : constant := 0.0;
|
Expected : constant := 0.0;
|
Y : Real;
|
Y : Real;
|
begin
|
begin
|
Y := Sqrt(X);
|
Y := Sqrt(X);
|
Check (Y, Expected, "test 4 -- sqrt(0.0)",
|
Check (Y, Expected, "test 4 -- sqrt(0.0)",
|
0.0); -- no error allowed
|
0.0); -- no error allowed
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 4");
|
Report.Failed ("Constraint_Error raised in test 4");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 4");
|
Report.Failed ("exception in test 4");
|
end;
|
end;
|
|
|
--- test 5 ---
|
--- test 5 ---
|
declare
|
declare
|
X : constant := -1.0;
|
X : constant := -1.0;
|
Y : Real;
|
Y : Real;
|
begin
|
begin
|
Y := Sqrt(X);
|
Y := Sqrt(X);
|
-- the following code should not be executed.
|
-- the following code should not be executed.
|
-- The call to Check is to keep the call to Sqrt from
|
-- The call to Check is to keep the call to Sqrt from
|
-- appearing to be dead code.
|
-- appearing to be dead code.
|
Check (Y, -1.0, "test 5 -- sqrt(-1)" );
|
Check (Y, -1.0, "test 5 -- sqrt(-1)" );
|
Report.Failed ("test 5 - argument_error expected");
|
Report.Failed ("test 5 - argument_error expected");
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 5");
|
Report.Failed ("Constraint_Error raised in test 5");
|
when Ada.Numerics.Argument_Error =>
|
when Ada.Numerics.Argument_Error =>
|
if Verbose then
|
if Verbose then
|
Report.Comment ("test 5 correctly got argument_error");
|
Report.Comment ("test 5 correctly got argument_error");
|
end if;
|
end if;
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 5");
|
Report.Failed ("exception in test 5");
|
end;
|
end;
|
|
|
--- test 6 ---
|
--- test 6 ---
|
declare
|
declare
|
X : constant := Ada.Numerics.Pi ** 2;
|
X : constant := Ada.Numerics.Pi ** 2;
|
Expected : constant := Ada.Numerics.Pi;
|
Expected : constant := Ada.Numerics.Pi;
|
Y : Real;
|
Y : Real;
|
begin
|
begin
|
Y := Sqrt (X);
|
Y := Sqrt (X);
|
Check (Y, Expected, "test 6 -- sqrt(pi**2)");
|
Check (Y, Expected, "test 6 -- sqrt(pi**2)");
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 6");
|
Report.Failed ("Constraint_Error raised in test 6");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 6");
|
Report.Failed ("exception in test 6");
|
end;
|
end;
|
|
|
--- test 7 & 8 ---
|
--- test 7 & 8 ---
|
Argument_Range_Check (1.0/Sqrt(Real(Real'Machine_Radix)),
|
Argument_Range_Check (1.0/Sqrt(Real(Real'Machine_Radix)),
|
1.0,
|
1.0,
|
"7");
|
"7");
|
Argument_Range_Check (1.0,
|
Argument_Range_Check (1.0,
|
Sqrt(Real(Real'Machine_Radix)),
|
Sqrt(Real(Real'Machine_Radix)),
|
"8");
|
"8");
|
end Do_Test;
|
end Do_Test;
|
end A_Long_Float_Check;
|
end A_Long_Float_Check;
|
|
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
|
|
package Non_Generic_Check is
|
package Non_Generic_Check is
|
procedure Do_Test;
|
procedure Do_Test;
|
end Non_Generic_Check;
|
end Non_Generic_Check;
|
|
|
package body Non_Generic_Check is
|
package body Non_Generic_Check is
|
package EF renames
|
package EF renames
|
Ada.Numerics.Elementary_Functions;
|
Ada.Numerics.Elementary_Functions;
|
subtype Real is Float;
|
subtype Real is Float;
|
|
|
-- The default Maximum Relative Error is the value specified
|
-- The default Maximum Relative Error is the value specified
|
-- in the LRM.
|
-- in the LRM.
|
Default_MRE : constant Real := 2.0;
|
Default_MRE : constant Real := 2.0;
|
|
|
procedure Check (Actual, Expected : Real;
|
procedure Check (Actual, Expected : Real;
|
Test_Name : String;
|
Test_Name : String;
|
MRE : Real := Default_MRE) is
|
MRE : Real := Default_MRE) is
|
Rel_Error : Real;
|
Rel_Error : Real;
|
Abs_Error : Real;
|
Abs_Error : Real;
|
Max_Error : Real;
|
Max_Error : Real;
|
begin
|
begin
|
-- In the case where the expected result is very small or 0
|
-- In the case where the expected result is very small or 0
|
-- we compute the maximum error as a multiple of Model_Epsilon instead
|
-- we compute the maximum error as a multiple of Model_Epsilon instead
|
-- of Model_Epsilon and Expected.
|
-- of Model_Epsilon and Expected.
|
Rel_Error := MRE * abs Expected * Real'Model_Epsilon;
|
Rel_Error := MRE * abs Expected * Real'Model_Epsilon;
|
Abs_Error := MRE * Real'Model_Epsilon;
|
Abs_Error := MRE * Real'Model_Epsilon;
|
if Rel_Error > Abs_Error then
|
if Rel_Error > Abs_Error then
|
Max_Error := Rel_Error;
|
Max_Error := Rel_Error;
|
else
|
else
|
Max_Error := Abs_Error;
|
Max_Error := Abs_Error;
|
end if;
|
end if;
|
|
|
if abs (Actual - Expected) > Max_Error then
|
if abs (Actual - Expected) > Max_Error then
|
Report.Failed (Test_Name &
|
Report.Failed (Test_Name &
|
" actual: " & Real'Image (Actual) &
|
" actual: " & Real'Image (Actual) &
|
" expected: " & Real'Image (Expected) &
|
" expected: " & Real'Image (Expected) &
|
" difference: " &
|
" difference: " &
|
Real'Image (Actual - Expected) &
|
Real'Image (Actual - Expected) &
|
" mre:" & Real'Image (Max_Error) );
|
" mre:" & Real'Image (Max_Error) );
|
elsif Verbose then
|
elsif Verbose then
|
if Actual = Expected then
|
if Actual = Expected then
|
Report.Comment (Test_Name & " exact result");
|
Report.Comment (Test_Name & " exact result");
|
else
|
else
|
Report.Comment (Test_Name & " passed");
|
Report.Comment (Test_Name & " passed");
|
end if;
|
end if;
|
end if;
|
end if;
|
end Check;
|
end Check;
|
|
|
|
|
|
|
procedure Argument_Range_Check (A, B : Float;
|
procedure Argument_Range_Check (A, B : Float;
|
Test : String) is
|
Test : String) is
|
-- test a logarithmically distributed selection of
|
-- test a logarithmically distributed selection of
|
-- arguments selected from the range A to B.
|
-- arguments selected from the range A to B.
|
X : Float;
|
X : Float;
|
Expected : Float;
|
Expected : Float;
|
Y : Float;
|
Y : Float;
|
C : Float := EF.Log(B/A);
|
C : Float := EF.Log(B/A);
|
Max_Samples : constant := 1000;
|
Max_Samples : constant := 1000;
|
|
|
begin
|
begin
|
for I in 1..Max_Samples loop
|
for I in 1..Max_Samples loop
|
Expected := A * EF.Exp(C * Float (I) / Float (Max_Samples));
|
Expected := A * EF.Exp(C * Float (I) / Float (Max_Samples));
|
X := Expected * Expected;
|
X := Expected * Expected;
|
Y := EF.Sqrt (X);
|
Y := EF.Sqrt (X);
|
|
|
-- note that since the expected value is computed, we
|
-- note that since the expected value is computed, we
|
-- must take the error in that computation into account.
|
-- must take the error in that computation into account.
|
Check (Y, Expected,
|
Check (Y, Expected,
|
"test " & Test & " -" &
|
"test " & Test & " -" &
|
Integer'Image (I) &
|
Integer'Image (I) &
|
" of argument range",
|
" of argument range",
|
3.0);
|
3.0);
|
end loop;
|
end loop;
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed
|
Report.Failed
|
("Constraint_Error raised in argument range check");
|
("Constraint_Error raised in argument range check");
|
when others =>
|
when others =>
|
Report.Failed ("exception in argument range check");
|
Report.Failed ("exception in argument range check");
|
end Argument_Range_Check;
|
end Argument_Range_Check;
|
|
|
|
|
procedure Do_Test is
|
procedure Do_Test is
|
begin
|
begin
|
|
|
--- test 1 ---
|
--- test 1 ---
|
declare
|
declare
|
T : constant := (Float'Machine_EMax - 1) / 2;
|
T : constant := (Float'Machine_EMax - 1) / 2;
|
X : constant := (1.0 * Float'Machine_Radix) ** (2 * T);
|
X : constant := (1.0 * Float'Machine_Radix) ** (2 * T);
|
Expected : constant := (1.0 * Float'Machine_Radix) ** T;
|
Expected : constant := (1.0 * Float'Machine_Radix) ** T;
|
Y : Float;
|
Y : Float;
|
begin
|
begin
|
Y := EF.Sqrt (X);
|
Y := EF.Sqrt (X);
|
Check (Y, Expected, "test 1 -- sqrt(radix**((emax-1)/2))");
|
Check (Y, Expected, "test 1 -- sqrt(radix**((emax-1)/2))");
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 1");
|
Report.Failed ("Constraint_Error raised in test 1");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 1");
|
Report.Failed ("exception in test 1");
|
end;
|
end;
|
|
|
--- test 2 ---
|
--- test 2 ---
|
declare
|
declare
|
T : constant := (Float'Model_EMin + 1) / 2;
|
T : constant := (Float'Model_EMin + 1) / 2;
|
X : constant := (1.0 * Float'Machine_Radix) ** (2 * T);
|
X : constant := (1.0 * Float'Machine_Radix) ** (2 * T);
|
Expected : constant := (1.0 * Float'Machine_Radix) ** T;
|
Expected : constant := (1.0 * Float'Machine_Radix) ** T;
|
Y : Float;
|
Y : Float;
|
begin
|
begin
|
Y := EF.Sqrt (X);
|
Y := EF.Sqrt (X);
|
Check (Y, Expected, "test 2 -- sqrt(radix**((emin+1)/2))");
|
Check (Y, Expected, "test 2 -- sqrt(radix**((emin+1)/2))");
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 2");
|
Report.Failed ("Constraint_Error raised in test 2");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 2");
|
Report.Failed ("exception in test 2");
|
end;
|
end;
|
|
|
--- test 3 ---
|
--- test 3 ---
|
declare
|
declare
|
X : constant := 1.0;
|
X : constant := 1.0;
|
Expected : constant := 1.0;
|
Expected : constant := 1.0;
|
Y : Float;
|
Y : Float;
|
begin
|
begin
|
Y := EF.Sqrt(X);
|
Y := EF.Sqrt(X);
|
Check (Y, Expected, "test 3 -- sqrt(1.0)",
|
Check (Y, Expected, "test 3 -- sqrt(1.0)",
|
0.0); -- no error allowed
|
0.0); -- no error allowed
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 3");
|
Report.Failed ("Constraint_Error raised in test 3");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 3");
|
Report.Failed ("exception in test 3");
|
end;
|
end;
|
|
|
--- test 4 ---
|
--- test 4 ---
|
declare
|
declare
|
X : constant := 0.0;
|
X : constant := 0.0;
|
Expected : constant := 0.0;
|
Expected : constant := 0.0;
|
Y : Float;
|
Y : Float;
|
begin
|
begin
|
Y := EF.Sqrt(X);
|
Y := EF.Sqrt(X);
|
Check (Y, Expected, "test 4 -- sqrt(0.0)",
|
Check (Y, Expected, "test 4 -- sqrt(0.0)",
|
0.0); -- no error allowed
|
0.0); -- no error allowed
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 4");
|
Report.Failed ("Constraint_Error raised in test 4");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 4");
|
Report.Failed ("exception in test 4");
|
end;
|
end;
|
|
|
--- test 5 ---
|
--- test 5 ---
|
declare
|
declare
|
X : constant := -1.0;
|
X : constant := -1.0;
|
Y : Float;
|
Y : Float;
|
begin
|
begin
|
Y := EF.Sqrt(X);
|
Y := EF.Sqrt(X);
|
-- the following code should not be executed.
|
-- the following code should not be executed.
|
-- The call to Check is to keep the call to Sqrt from
|
-- The call to Check is to keep the call to Sqrt from
|
-- appearing to be dead code.
|
-- appearing to be dead code.
|
Check (Y, -1.0, "test 5 -- sqrt(-1)" );
|
Check (Y, -1.0, "test 5 -- sqrt(-1)" );
|
Report.Failed ("test 5 - argument_error expected");
|
Report.Failed ("test 5 - argument_error expected");
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 5");
|
Report.Failed ("Constraint_Error raised in test 5");
|
when Ada.Numerics.Argument_Error =>
|
when Ada.Numerics.Argument_Error =>
|
if Verbose then
|
if Verbose then
|
Report.Comment ("test 5 correctly got argument_error");
|
Report.Comment ("test 5 correctly got argument_error");
|
end if;
|
end if;
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 5");
|
Report.Failed ("exception in test 5");
|
end;
|
end;
|
|
|
--- test 6 ---
|
--- test 6 ---
|
declare
|
declare
|
X : constant := Ada.Numerics.Pi ** 2;
|
X : constant := Ada.Numerics.Pi ** 2;
|
Expected : constant := Ada.Numerics.Pi;
|
Expected : constant := Ada.Numerics.Pi;
|
Y : Float;
|
Y : Float;
|
begin
|
begin
|
Y := EF.Sqrt (X);
|
Y := EF.Sqrt (X);
|
Check (Y, Expected, "test 6 -- sqrt(pi**2)");
|
Check (Y, Expected, "test 6 -- sqrt(pi**2)");
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 6");
|
Report.Failed ("Constraint_Error raised in test 6");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 6");
|
Report.Failed ("exception in test 6");
|
end;
|
end;
|
|
|
--- test 7 & 8 ---
|
--- test 7 & 8 ---
|
Argument_Range_Check (1.0/EF.Sqrt(Float(Float'Machine_Radix)),
|
Argument_Range_Check (1.0/EF.Sqrt(Float(Float'Machine_Radix)),
|
1.0,
|
1.0,
|
"7");
|
"7");
|
Argument_Range_Check (1.0,
|
Argument_Range_Check (1.0,
|
EF.Sqrt(Float(Float'Machine_Radix)),
|
EF.Sqrt(Float(Float'Machine_Radix)),
|
"8");
|
"8");
|
end Do_Test;
|
end Do_Test;
|
end Non_Generic_Check;
|
end Non_Generic_Check;
|
|
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
|
|
begin
|
begin
|
Report.Test ("CXG2003",
|
Report.Test ("CXG2003",
|
"Check the accuracy of the sqrt function");
|
"Check the accuracy of the sqrt function");
|
|
|
if Verbose then
|
if Verbose then
|
Report.Comment ("checking Standard.Float");
|
Report.Comment ("checking Standard.Float");
|
end if;
|
end if;
|
|
|
Float_Check.Do_Test;
|
Float_Check.Do_Test;
|
|
|
if Verbose then
|
if Verbose then
|
Report.Comment ("checking a digits" &
|
Report.Comment ("checking a digits" &
|
Integer'Image (System.Max_Digits) &
|
Integer'Image (System.Max_Digits) &
|
" floating point type");
|
" floating point type");
|
end if;
|
end if;
|
|
|
A_Long_Float_Check.Do_Test;
|
A_Long_Float_Check.Do_Test;
|
|
|
if Verbose then
|
if Verbose then
|
Report.Comment ("checking non-generic package");
|
Report.Comment ("checking non-generic package");
|
end if;
|
end if;
|
|
|
Non_Generic_Check.Do_Test;
|
Non_Generic_Check.Do_Test;
|
|
|
Report.Result;
|
Report.Result;
|
end CXG2003;
|
end CXG2003;
|
|
|