-- CXG2006.A
|
-- CXG2006.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 complex Argument function returns
|
-- Check that the complex Argument function returns
|
-- results that are within the error bound allowed.
|
-- results that are within the error bound allowed.
|
-- Check that Argument_Error is raised if the Cycle parameter
|
-- Check that Argument_Error is raised if the Cycle parameter
|
-- is less than or equal to zero.
|
-- is less than or equal to zero.
|
--
|
--
|
-- TEST DESCRIPTION:
|
-- TEST DESCRIPTION:
|
-- This test uses a generic package to compute and check the
|
-- This test uses a generic package to compute and check the
|
-- values of the Argument function.
|
-- values of the Argument function.
|
-- Of special interest is the case where either the real or
|
-- Of special interest is the case where either the real or
|
-- the imaginary part of the parameter is very large while the
|
-- the imaginary part of the parameter is very large while the
|
-- other part is very small or 0.
|
-- other part is very small or 0.
|
--
|
--
|
-- 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:
|
-- 15 FEB 96 SAIC Initial release for 2.1
|
-- 15 FEB 96 SAIC Initial release for 2.1
|
-- 03 MAR 97 PWB.CTA Removed checks involving explicit cycle => 2.0*Pi
|
-- 03 MAR 97 PWB.CTA Removed checks involving explicit cycle => 2.0*Pi
|
--
|
--
|
-- CHANGE NOTE:
|
-- CHANGE NOTE:
|
-- According to Ken Dritz, author of the Numerics Annex of the RM,
|
-- According to Ken Dritz, author of the Numerics Annex of the RM,
|
-- one should never specify the cycle 2.0*Pi for the trigonometric
|
-- one should never specify the cycle 2.0*Pi for the trigonometric
|
-- functions. In particular, if the machine number for the first
|
-- functions. In particular, if the machine number for the first
|
-- argument is not an exact multiple of the machine number for the
|
-- argument is not an exact multiple of the machine number for the
|
-- explicit cycle, then the specified exact results cannot be
|
-- explicit cycle, then the specified exact results cannot be
|
-- reasonably expected. The affected checks in this test have been
|
-- reasonably expected. The affected checks in this test have been
|
-- marked as comments, with the additional notation "pwb-math".
|
-- marked as comments, with the additional notation "pwb-math".
|
-- Phil Brashear
|
-- Phil Brashear
|
--!
|
--!
|
|
|
--
|
--
|
-- Reference:
|
-- Reference:
|
-- Problems and Methodologies in Mathematical Software Production;
|
-- Problems and Methodologies in Mathematical Software Production;
|
-- editors: P. C. Messina and A Murli;
|
-- editors: P. C. Messina and A Murli;
|
-- Lecture Notes in Computer Science
|
-- Lecture Notes in Computer Science
|
-- Volume 142
|
-- Volume 142
|
-- Springer Verlag 1982
|
-- Springer Verlag 1982
|
--
|
--
|
|
|
with System;
|
with System;
|
with Report;
|
with Report;
|
with ImpDef.Annex_G;
|
with ImpDef.Annex_G;
|
with Ada.Numerics;
|
with Ada.Numerics;
|
with Ada.Numerics.Generic_Complex_Types;
|
with Ada.Numerics.Generic_Complex_Types;
|
with Ada.Numerics.Complex_Types;
|
with Ada.Numerics.Complex_Types;
|
procedure CXG2006 is
|
procedure CXG2006 is
|
Verbose : constant Boolean := False;
|
Verbose : constant Boolean := False;
|
|
|
|
|
-- CRC Standard Mathematical Tables; 23rd Edition; pg 738
|
-- CRC Standard Mathematical Tables; 23rd Edition; pg 738
|
Sqrt2 : constant :=
|
Sqrt2 : constant :=
|
1.41421_35623_73095_04880_16887_24209_69807_85696_71875_37695;
|
1.41421_35623_73095_04880_16887_24209_69807_85696_71875_37695;
|
Sqrt3 : constant :=
|
Sqrt3 : constant :=
|
1.73205_08075_68877_29352_74463_41505_87236_69428_05253_81039;
|
1.73205_08075_68877_29352_74463_41505_87236_69428_05253_81039;
|
|
|
Pi : constant := Ada.Numerics.Pi;
|
Pi : constant := Ada.Numerics.Pi;
|
|
|
generic
|
generic
|
type Real is digits <>;
|
type Real is digits <>;
|
package Generic_Check is
|
package Generic_Check is
|
procedure Do_Test;
|
procedure Do_Test;
|
end Generic_Check;
|
end Generic_Check;
|
|
|
package body Generic_Check is
|
package body Generic_Check is
|
package Complex_Types is new
|
package Complex_Types is new
|
Ada.Numerics.Generic_Complex_Types (Real);
|
Ada.Numerics.Generic_Complex_Types (Real);
|
use Complex_Types;
|
use Complex_Types;
|
|
|
|
|
procedure Check (Actual, Expected : Real;
|
procedure Check (Actual, Expected : Real;
|
Test_Name : String;
|
Test_Name : String;
|
MRE : Real) is
|
MRE : Real) 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 Special_Cases is
|
procedure Special_Cases is
|
type Data_Point is
|
type Data_Point is
|
record
|
record
|
Re,
|
Re,
|
Im,
|
Im,
|
Radians,
|
Radians,
|
Degrees,
|
Degrees,
|
Error_Bound : Real;
|
Error_Bound : Real;
|
end record;
|
end record;
|
|
|
type Test_Data_Type is array (Positive range <>) of Data_Point;
|
type Test_Data_Type is array (Positive range <>) of Data_Point;
|
|
|
-- the values in the following table only involve static
|
-- the values in the following table only involve static
|
-- expressions to minimize errors in precision introduced by the
|
-- expressions to minimize errors in precision introduced by the
|
-- test. For cases where Pi is used in the argument we must
|
-- 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
|
-- allow an extra 1.0*MRE to account for roundoff error in the
|
-- argument. Where the result involves a square root we allow
|
-- argument. Where the result involves a square root we allow
|
-- an extra 0.5*MRE to allow for roundoff error.
|
-- an extra 0.5*MRE to allow for roundoff error.
|
Test_Data : constant Test_Data_Type := (
|
Test_Data : constant Test_Data_Type := (
|
-- Re Im Radians Degrees Err Test #
|
-- Re Im Radians Degrees Err Test #
|
(0.0, 0.0, 0.0, 0.0, 4.0 ), -- 1
|
(0.0, 0.0, 0.0, 0.0, 4.0 ), -- 1
|
(1.0, 0.0, 0.0, 0.0, 4.0 ), -- 2
|
(1.0, 0.0, 0.0, 0.0, 4.0 ), -- 2
|
(Real'Safe_Last, 0.0, 0.0, 0.0, 4.0 ), -- 3
|
(Real'Safe_Last, 0.0, 0.0, 0.0, 4.0 ), -- 3
|
(Real'Model_Small, 0.0, 0.0, 0.0, 4.0 ), -- 4
|
(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 ), -- 5
|
(1.0, -1.0, -Pi/4.0, -45.0, 5.0 ), -- 6
|
(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 ), -- 7
|
(-1.0, 1.0, 3.0*Pi/4.0, 135.0, 5.0 ), -- 8
|
(-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, Pi/6.0, 30.0, 5.5 ), -- 9
|
(-Sqrt3, 1.0, 5.0*Pi/6.0, 150.0, 5.5 ), -- 10
|
(-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, -Pi/6.0, -30.0, 5.5 ), -- 11
|
(-Sqrt3, -1.0, -5.0*Pi/6.0,-150.0, 5.5 ), -- 12
|
(-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'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, 0.0, Pi, 180.0, 5.0 ), -- 14
|
(-Real'Safe_Last, -Real'Model_Small, -Pi,-180.0, 5.0 ), -- 15
|
(-Real'Safe_Last, -Real'Model_Small, -Pi,-180.0, 5.0 ), -- 15
|
(100000.0, 100000.0, Pi/4.0, 45.0, 5.0 )); -- 16
|
(100000.0, 100000.0, Pi/4.0, 45.0, 5.0 )); -- 16
|
|
|
X : Real;
|
X : Real;
|
Z : Complex;
|
Z : Complex;
|
begin
|
begin
|
for I in Test_Data'Range loop
|
for I in Test_Data'Range loop
|
begin
|
begin
|
Z := (Test_Data(I).Re, Test_Data(I).Im);
|
Z := (Test_Data(I).Re, Test_Data(I).Im);
|
X := Argument (Z);
|
X := Argument (Z);
|
Check (X, Test_Data(I).Radians,
|
Check (X, Test_Data(I).Radians,
|
"test" & Integer'Image (I) & " argument(z)",
|
"test" & Integer'Image (I) & " argument(z)",
|
Test_Data (I).Error_Bound);
|
Test_Data (I).Error_Bound);
|
--pwb-math X := Argument (Z, 2.0*Pi);
|
--pwb-math X := Argument (Z, 2.0*Pi);
|
--pwb-math Check (X, Test_Data(I).Radians,
|
--pwb-math Check (X, Test_Data(I).Radians,
|
--pwb-math "test" & Integer'Image (I) & " argument(z, 2pi)",
|
--pwb-math "test" & Integer'Image (I) & " argument(z, 2pi)",
|
--pwb-math Test_Data (I).Error_Bound);
|
--pwb-math Test_Data (I).Error_Bound);
|
X := Argument (Z, 360.0);
|
X := Argument (Z, 360.0);
|
Check (X, Test_Data(I).Degrees,
|
Check (X, Test_Data(I).Degrees,
|
"test" & Integer'Image (I) & " argument(z, 360)",
|
"test" & Integer'Image (I) & " argument(z, 360)",
|
Test_Data (I).Error_Bound);
|
Test_Data (I).Error_Bound);
|
|
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test" &
|
Report.Failed ("Constraint_Error raised in test" &
|
Integer'Image (I));
|
Integer'Image (I));
|
when others =>
|
when others =>
|
Report.Failed ("exception in test" &
|
Report.Failed ("exception in test" &
|
Integer'Image (I));
|
Integer'Image (I));
|
end;
|
end;
|
end loop;
|
end loop;
|
|
|
if Real'Signed_Zeros then
|
if Real'Signed_Zeros then
|
begin
|
begin
|
X := Argument ((-1.0, Real(ImpDef.Annex_G.Negative_Zero)));
|
X := Argument ((-1.0, Real(ImpDef.Annex_G.Negative_Zero)));
|
Check (X, -Pi, "test of arg((-1,-0)", 4.0);
|
Check (X, -Pi, "test of arg((-1,-0)", 4.0);
|
exception
|
exception
|
when others =>
|
when others =>
|
Report.Failed ("exception in signed zero test");
|
Report.Failed ("exception in signed zero test");
|
end;
|
end;
|
end if;
|
end if;
|
end Special_Cases;
|
end Special_Cases;
|
|
|
|
|
procedure Exception_Cases is
|
procedure Exception_Cases is
|
-- check that Argument_Error is raised if Cycle is <= 0
|
-- check that Argument_Error is raised if Cycle is <= 0
|
Z : Complex := (1.0, 1.0);
|
Z : Complex := (1.0, 1.0);
|
X : Real;
|
X : Real;
|
Y : Real;
|
Y : Real;
|
begin
|
begin
|
begin
|
begin
|
X := Argument (Z, Cycle => 0.0);
|
X := Argument (Z, Cycle => 0.0);
|
Report.Failed ("no exception for cycle = 0.0");
|
Report.Failed ("no exception for cycle = 0.0");
|
exception
|
exception
|
when Ada.Numerics.Argument_Error => null;
|
when Ada.Numerics.Argument_Error => null;
|
when others =>
|
when others =>
|
Report.Failed ("wrong exception for cycle = 0.0");
|
Report.Failed ("wrong exception for cycle = 0.0");
|
end;
|
end;
|
|
|
begin
|
begin
|
Y := Argument (Z, Cycle => -3.0);
|
Y := Argument (Z, Cycle => -3.0);
|
Report.Failed ("no exception for cycle < 0.0");
|
Report.Failed ("no exception for cycle < 0.0");
|
exception
|
exception
|
when Ada.Numerics.Argument_Error => null;
|
when Ada.Numerics.Argument_Error => null;
|
when others =>
|
when others =>
|
Report.Failed ("wrong exception for cycle < 0.0");
|
Report.Failed ("wrong exception for cycle < 0.0");
|
end;
|
end;
|
|
|
if Report.Ident_Int (2) = 1 then
|
if Report.Ident_Int (2) = 1 then
|
-- optimization thwarting code - never executed
|
-- optimization thwarting code - never executed
|
Report.Failed("2=1" & Real'Image (X+Y));
|
Report.Failed("2=1" & Real'Image (X+Y));
|
end if;
|
end if;
|
end Exception_Cases;
|
end Exception_Cases;
|
|
|
|
|
procedure Do_Test is
|
procedure Do_Test is
|
begin
|
begin
|
Special_Cases;
|
Special_Cases;
|
Exception_Cases;
|
Exception_Cases;
|
end Do_Test;
|
end Do_Test;
|
end Generic_Check;
|
end Generic_Check;
|
|
|
package Chk_Float is new Generic_Check (Float);
|
package Chk_Float is new Generic_Check (Float);
|
|
|
-- 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 Chk_A_Long_Float is new Generic_Check (A_Long_Float);
|
package Chk_A_Long_Float is new Generic_Check (A_Long_Float);
|
begin
|
begin
|
Report.Test ("CXG2006",
|
Report.Test ("CXG2006",
|
"Check the accuracy of the complex argument" &
|
"Check the accuracy of the complex argument" &
|
" function");
|
" function");
|
|
|
if Verbose then
|
if Verbose then
|
Report.Comment ("checking Standard.Float");
|
Report.Comment ("checking Standard.Float");
|
end if;
|
end if;
|
|
|
Chk_Float.Do_Test;
|
Chk_Float.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;
|
|
|
Chk_A_Long_Float.Do_Test;
|
Chk_A_Long_Float.Do_Test;
|
|
|
Report.Result;
|
Report.Result;
|
end CXG2006;
|
end CXG2006;
|
|
|