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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;