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|
-- CXG2002.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 complex "abs" or modulus function returns
-- results that are within the error bound allowed.
--
-- TEST DESCRIPTION:
-- This test uses a generic package to compute and check the
-- values of the modulus function. In addition, a non-generic
-- copy of this package is used to check the non-generic package
-- Ada.Numerics.Complex_Types.
-- Of special interest is the case where either the real or
-- the imaginary part of the argument is very large while the
-- other part is very small or 0.
-- We want to check that the value is computed such that
-- an overflow does not occur. If computed directly from the
-- definition
-- abs (x+yi) = sqrt(x**2 + y**2)
-- then overflow or underflow is much more likely than if the
-- argument is normalized first.
--
-- 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:
-- 31 JAN 96 SAIC Initial release for 2.1
-- 02 JUN 98 EDS Add parens to intermediate calculations.
--!
--
-- Reference:
-- 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_Complex_Types;
with Ada.Numerics.Complex_Types;
procedure CXG2002 is
Verbose : constant Boolean := False;
Maximum_Relative_Error : constant := 3.0;
generic
type Real is digits <>;
package Generic_Check is
procedure Do_Test;
end Generic_Check;
package body Generic_Check is
package Complex_Types is new
Ada.Numerics.Generic_Complex_Types (Real);
use Complex_Types;
procedure Check (Actual, Expected : Real;
Test_Name : String;
MRE : Real := Maximum_Relative_Error) is
Rel_Error,
Abs_Error,
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 (Expected - Actual) &
" 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;
procedure Do_Test is
Z : Complex;
X : Real;
T : Real;
begin
--- test 1 ---
begin
T := Real'Safe_Last;
Z := T + 0.0*i;
X := abs Z;
Check (X, T, "test 1 -- abs(bigreal + 0i)");
exception
when Constraint_Error =>
Report.Failed ("Constraint_Error raised in test 1");
when others =>
Report.Failed ("exception in test 1");
end;
--- test 2 ---
begin
T := Real'Safe_Last;
Z := 0.0 + T*i;
X := Modulus (Z);
Check (X, T, "test 2 -- abs(0 + bigreal*i)");
exception
when Constraint_Error =>
Report.Failed ("Constraint_Error raised in test 2");
when others =>
Report.Failed ("exception in test 2");
end;
--- test 3 ---
begin
Z := 3.0 + 4.0*i;
X := abs Z;
Check (X, 5.0 , "test 3 -- abs(3 + 4*i)");
exception
when Constraint_Error =>
Report.Failed ("Constraint_Error raised in test 3");
when others =>
Report.Failed ("exception in test 3");
end;
--- test 4 ---
declare
S : Real;
begin
S := Real(Real'Machine_Radix) ** (Real'Machine_EMax - 3);
Z := 3.0 * S + 4.0*S*i;
X := abs Z;
Check (X, 5.0*S, "test 4 -- abs(3S + 4S*i) for large S",
5.0*Real'Model_Epsilon);
exception
when Constraint_Error =>
Report.Failed ("Constraint_Error raised in test 4");
when others =>
Report.Failed ("exception in test 4");
end;
--- test 5 ---
begin
T := Real'Model_Small;
Z := T + 0.0*i;
X := abs Z;
Check (X, T , "test 5 -- abs(small + 0*i)");
exception
when Constraint_Error =>
Report.Failed ("Constraint_Error raised in test 5");
when others =>
Report.Failed ("exception in test 5");
end;
--- test 6 ---
begin
T := Real'Model_Small;
Z := 0.0 + T*i;
X := abs Z;
Check (X, T , "test 6 -- abs(0 + small*i)");
exception
when Constraint_Error =>
Report.Failed ("Constraint_Error raised in test 6");
when others =>
Report.Failed ("exception in test 6");
end;
--- test 7 ---
declare
S : Real;
begin
S := Real(Real'Machine_Radix) ** (Real'Model_EMin + 3);
Z := 3.0 * S + 4.0*S*i;
X := abs Z;
Check (X, 5.0*S, "test 7 -- abs(3S + 4S*i) for small S",
5.0*Real'Model_Epsilon);
exception
when Constraint_Error =>
Report.Failed ("Constraint_Error raised in test 7");
when others =>
Report.Failed ("exception in test 7");
end;
--- test 8 ---
declare
-- CRC Standard Mathematical Tables; 23rd Edition; pg 738
Sqrt2 : constant :=
1.41421_35623_73095_04880_16887_24209_69807_85696_71875_37695;
begin
Z := 1.0 + 1.0*i;
X := abs Z;
Check (X, Sqrt2 , "test 8 -- abs(1 + 1*i)");
exception
when Constraint_Error =>
Report.Failed ("Constraint_Error raised in test 8");
when others =>
Report.Failed ("exception in test 8");
end;
--- test 9 ---
begin
T := 0.0;
Z := T + 0.0*i;
X := abs Z;
Check (X, T , "test 5 -- abs(0 + 0*i)");
exception
when Constraint_Error =>
Report.Failed ("Constraint_Error raised in test 9");
when others =>
Report.Failed ("exception in test 9");
end;
end Do_Test;
end Generic_Check;
-----------------------------------------------------------------------
--- non generic copy of the above generic package
-----------------------------------------------------------------------
package Non_Generic_Check is
subtype Real is Float;
procedure Do_Test;
end Non_Generic_Check;
package body Non_Generic_Check is
use Ada.Numerics.Complex_Types;
procedure Check (Actual, Expected : Real;
Test_Name : String;
MRE : Real := Maximum_Relative_Error) is
Rel_Error,
Abs_Error,
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 (Expected - Actual) &
" 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;
procedure Do_Test is
Z : Complex;
X : Real;
T : Real;
begin
--- test 1 ---
begin
T := Real'Safe_Last;
Z := T + 0.0*i;
X := abs Z;
Check (X, T, "test 1 -- abs(bigreal + 0i)");
exception
when Constraint_Error =>
Report.Failed ("Constraint_Error raised in test 1");
when others =>
Report.Failed ("exception in test 1");
end;
--- test 2 ---
begin
T := Real'Safe_Last;
Z := 0.0 + T*i;
X := Modulus (Z);
Check (X, T, "test 2 -- abs(0 + bigreal*i)");
exception
when Constraint_Error =>
Report.Failed ("Constraint_Error raised in test 2");
when others =>
Report.Failed ("exception in test 2");
end;
--- test 3 ---
begin
Z := 3.0 + 4.0*i;
X := abs Z;
Check (X, 5.0 , "test 3 -- abs(3 + 4*i)");
exception
when Constraint_Error =>
Report.Failed ("Constraint_Error raised in test 3");
when others =>
Report.Failed ("exception in test 3");
end;
--- test 4 ---
declare
S : Real;
begin
S := Real(Real'Machine_Radix) ** (Real'Machine_EMax - 3);
Z := 3.0 * S + 4.0*S*i;
X := abs Z;
Check (X, 5.0*S, "test 4 -- abs(3S + 4S*i) for large S",
5.0*Real'Model_Epsilon);
exception
when Constraint_Error =>
Report.Failed ("Constraint_Error raised in test 4");
when others =>
Report.Failed ("exception in test 4");
end;
--- test 5 ---
begin
T := Real'Model_Small;
Z := T + 0.0*i;
X := abs Z;
Check (X, T , "test 5 -- abs(small + 0*i)");
exception
when Constraint_Error =>
Report.Failed ("Constraint_Error raised in test 5");
when others =>
Report.Failed ("exception in test 5");
end;
--- test 6 ---
begin
T := Real'Model_Small;
Z := 0.0 + T*i;
X := abs Z;
Check (X, T , "test 6 -- abs(0 + small*i)");
exception
when Constraint_Error =>
Report.Failed ("Constraint_Error raised in test 6");
when others =>
Report.Failed ("exception in test 6");
end;
--- test 7 ---
declare
S : Real;
begin
S := Real(Real'Machine_Radix) ** (Real'Model_EMin + 3);
Z := 3.0 * S + 4.0*S*i;
X := abs Z;
Check (X, 5.0*S, "test 7 -- abs(3S + 4S*i) for small S",
5.0*Real'Model_Epsilon);
exception
when Constraint_Error =>
Report.Failed ("Constraint_Error raised in test 7");
when others =>
Report.Failed ("exception in test 7");
end;
--- test 8 ---
declare
-- CRC Standard Mathematical Tables; 23rd Edition; pg 738
Sqrt2 : constant :=
1.41421_35623_73095_04880_16887_24209_69807_85696_71875_37695;
begin
Z := 1.0 + 1.0*i;
X := abs Z;
Check (X, Sqrt2 , "test 8 -- abs(1 + 1*i)");
exception
when Constraint_Error =>
Report.Failed ("Constraint_Error raised in test 8");
when others =>
Report.Failed ("exception in test 8");
end;
--- test 9 ---
begin
T := 0.0;
Z := T + 0.0*i;
X := abs Z;
Check (X, T , "test 5 -- abs(0 + 0*i)");
exception
when Constraint_Error =>
Report.Failed ("Constraint_Error raised in test 9");
when others =>
Report.Failed ("exception in test 9");
end;
end Do_Test;
end Non_Generic_Check;
-----------------------------------------------------------------------
--- end of "manual instantiation"
-----------------------------------------------------------------------
package Chk_Float is new Generic_Check (Float);
-- check the floating point type with the most digits
type A_Long_Float is digits System.Max_Digits;
package Chk_A_Long_Float is new Generic_Check (A_Long_Float);
begin
Report.Test ("CXG2002",
"Check the accuracy of the complex modulus" &
" function");
if Verbose then
Report.Comment ("checking Standard.Float");
end if;
Chk_Float.Do_Test;
if Verbose then
Report.Comment ("checking a digits" &
Integer'Image (System.Max_Digits) &
" floating point type");
end if;
Chk_A_Long_Float.Do_Test;
if Verbose then
Report.Comment ("checking non-generic package");
end if;
Non_Generic_Check.Do_Test;
Report.Result;
end CXG2002;
|
