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authorupstream source tree <ports@midipix.org>2015-03-15 20:14:05 -0400
committerupstream source tree <ports@midipix.org>2015-03-15 20:14:05 -0400
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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;