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-- CXG2006.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 Argument function returns
-- results that are within the error bound allowed.
-- Check that Argument_Error is raised if the Cycle parameter
-- is less than or equal to zero.
--
-- TEST DESCRIPTION:
-- This test uses a generic package to compute and check the
-- values of the Argument function.
-- Of special interest is the case where either the real or
-- the imaginary part of the parameter is very large while the
-- other part is very small or 0.
--
-- 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:
-- 15 FEB 96 SAIC Initial release for 2.1
-- 03 MAR 97 PWB.CTA Removed checks involving explicit cycle => 2.0*Pi
--
-- CHANGE NOTE:
-- According to Ken Dritz, author of the Numerics Annex of the RM,
-- one should never specify the cycle 2.0*Pi for the trigonometric
-- functions. In particular, if the machine number for the first
-- argument is not an exact multiple of the machine number for the
-- explicit cycle, then the specified exact results cannot be
-- reasonably expected. The affected checks in this test have been
-- marked as comments, with the additional notation "pwb-math".
-- Phil Brashear
--!
--
-- 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 ImpDef.Annex_G;
with Ada.Numerics;
with Ada.Numerics.Generic_Complex_Types;
with Ada.Numerics.Complex_Types;
procedure CXG2006 is
Verbose : constant Boolean := False;
-- CRC Standard Mathematical Tables; 23rd Edition; pg 738
Sqrt2 : constant :=
1.41421_35623_73095_04880_16887_24209_69807_85696_71875_37695;
Sqrt3 : constant :=
1.73205_08075_68877_29352_74463_41505_87236_69428_05253_81039;
Pi : constant := Ada.Numerics.Pi;
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) 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 Special_Cases is
type Data_Point is
record
Re,
Im,
Radians,
Degrees,
Error_Bound : Real;
end record;
type Test_Data_Type is array (Positive range <>) of Data_Point;
-- the values in the following table only involve static
-- expressions to minimize errors in precision introduced by the
-- test. For cases where Pi is used in the argument we must
-- allow an extra 1.0*MRE to account for roundoff error in the
-- argument. Where the result involves a square root we allow
-- an extra 0.5*MRE to allow for roundoff error.
Test_Data : constant Test_Data_Type := (
-- Re Im Radians Degrees Err Test #
(0.0, 0.0, 0.0, 0.0, 4.0 ), -- 1
(1.0, 0.0, 0.0, 0.0, 4.0 ), -- 2
(Real'Safe_Last, 0.0, 0.0, 0.0, 4.0 ), -- 3
(Real'Model_Small, 0.0, 0.0, 0.0, 4.0 ), -- 4
(1.0, 1.0, Pi/4.0, 45.0, 5.0 ), -- 5
(1.0, -1.0, -Pi/4.0, -45.0, 5.0 ), -- 6
(-1.0, -1.0, -3.0*Pi/4.0,-135.0, 5.0 ), -- 7
(-1.0, 1.0, 3.0*Pi/4.0, 135.0, 5.0 ), -- 8
(Sqrt3, 1.0, Pi/6.0, 30.0, 5.5 ), -- 9
(-Sqrt3, 1.0, 5.0*Pi/6.0, 150.0, 5.5 ), -- 10
(Sqrt3, -1.0, -Pi/6.0, -30.0, 5.5 ), -- 11
(-Sqrt3, -1.0, -5.0*Pi/6.0,-150.0, 5.5 ), -- 12
(Real'Model_Small, Real'Model_Small, Pi/4.0, 45.0, 5.0 ), -- 13
(-Real'Safe_Last, 0.0, Pi, 180.0, 5.0 ), -- 14
(-Real'Safe_Last, -Real'Model_Small, -Pi,-180.0, 5.0 ), -- 15
(100000.0, 100000.0, Pi/4.0, 45.0, 5.0 )); -- 16
X : Real;
Z : Complex;
begin
for I in Test_Data'Range loop
begin
Z := (Test_Data(I).Re, Test_Data(I).Im);
X := Argument (Z);
Check (X, Test_Data(I).Radians,
"test" & Integer'Image (I) & " argument(z)",
Test_Data (I).Error_Bound);
--pwb-math X := Argument (Z, 2.0*Pi);
--pwb-math Check (X, Test_Data(I).Radians,
--pwb-math "test" & Integer'Image (I) & " argument(z, 2pi)",
--pwb-math Test_Data (I).Error_Bound);
X := Argument (Z, 360.0);
Check (X, Test_Data(I).Degrees,
"test" & Integer'Image (I) & " argument(z, 360)",
Test_Data (I).Error_Bound);
exception
when Constraint_Error =>
Report.Failed ("Constraint_Error raised in test" &
Integer'Image (I));
when others =>
Report.Failed ("exception in test" &
Integer'Image (I));
end;
end loop;
if Real'Signed_Zeros then
begin
X := Argument ((-1.0, Real(ImpDef.Annex_G.Negative_Zero)));
Check (X, -Pi, "test of arg((-1,-0)", 4.0);
exception
when others =>
Report.Failed ("exception in signed zero test");
end;
end if;
end Special_Cases;
procedure Exception_Cases is
-- check that Argument_Error is raised if Cycle is <= 0
Z : Complex := (1.0, 1.0);
X : Real;
Y : Real;
begin
begin
X := Argument (Z, Cycle => 0.0);
Report.Failed ("no exception for cycle = 0.0");
exception
when Ada.Numerics.Argument_Error => null;
when others =>
Report.Failed ("wrong exception for cycle = 0.0");
end;
begin
Y := Argument (Z, Cycle => -3.0);
Report.Failed ("no exception for cycle < 0.0");
exception
when Ada.Numerics.Argument_Error => null;
when others =>
Report.Failed ("wrong exception for cycle < 0.0");
end;
if Report.Ident_Int (2) = 1 then
-- optimization thwarting code - never executed
Report.Failed("2=1" & Real'Image (X+Y));
end if;
end Exception_Cases;
procedure Do_Test is
begin
Special_Cases;
Exception_Cases;
end Do_Test;
end Generic_Check;
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 ("CXG2006",
"Check the accuracy of the complex argument" &
" 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;
Report.Result;
end CXG2006;
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