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1 294 jeremybenn
-- CXG2006.A
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--
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--                             Grant of Unlimited Rights
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--
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--     Under contracts F33600-87-D-0337, F33600-84-D-0280, MDA903-79-C-0687,
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--     F08630-91-C-0015, and DCA100-97-D-0025, the U.S. Government obtained
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--     unlimited rights in the software and documentation contained herein.
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--     Unlimited rights are defined in DFAR 252.227-7013(a)(19).  By making
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--     this public release, the Government intends to confer upon all
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--     recipients unlimited rights  equal to those held by the Government.
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--     These rights include rights to use, duplicate, release or disclose the
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--     released technical data and computer software in whole or in part, in
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--     any manner and for any purpose whatsoever, and to have or permit others
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--     to do so.
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--
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--                                    DISCLAIMER
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--
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--     ALL MATERIALS OR INFORMATION HEREIN RELEASED, MADE AVAILABLE OR
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--     DISCLOSED ARE AS IS.  THE GOVERNMENT MAKES NO EXPRESS OR IMPLIED
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--     WARRANTY AS TO ANY MATTER WHATSOEVER, INCLUDING THE CONDITIONS OF THE
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--     SOFTWARE, DOCUMENTATION OR OTHER INFORMATION RELEASED, MADE AVAILABLE
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--     OR DISCLOSED, OR THE OWNERSHIP, MERCHANTABILITY, OR FITNESS FOR A
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--     PARTICULAR PURPOSE OF SAID MATERIAL.
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--*
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--
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-- OBJECTIVE:
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--      Check that the complex Argument function returns
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--      results that are within the error bound allowed.
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--      Check that Argument_Error is raised if the Cycle parameter
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--      is less than or equal to zero.
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--
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-- TEST DESCRIPTION:
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--      This test uses a generic package to compute and check the
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--      values of the Argument function.
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--      Of special interest is the case where either the real or
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--      the imaginary part of the parameter is very large while the
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--      other part is very small or 0.
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--
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-- SPECIAL REQUIREMENTS
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--      The Strict Mode for the numerical accuracy must be
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--      selected.  The method by which this mode is selected
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--      is implementation dependent.
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--
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-- APPLICABILITY CRITERIA:
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--      This test applies only to implementations supporting the
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--      Numerics Annex.
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--      This test only applies to the Strict Mode for numerical
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--      accuracy.
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--
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--
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-- CHANGE HISTORY:
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--      15 FEB 96   SAIC    Initial release for 2.1
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--      03 MAR 97   PWB.CTA Removed checks involving explicit cycle => 2.0*Pi
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--
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-- CHANGE NOTE:
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--      According to Ken Dritz, author of the Numerics Annex of the RM,
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--      one should never specify the cycle 2.0*Pi for the trigonometric
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--      functions.  In particular, if the machine number for the first
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--      argument is not an exact multiple of the machine number for the
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--      explicit cycle, then the specified exact results cannot be
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--      reasonably expected.  The affected checks in this test have been
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--      marked as comments, with the additional notation "pwb-math".
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--      Phil Brashear
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--!
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--
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-- Reference:
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-- Problems and Methodologies in Mathematical Software Production;
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-- editors: P. C. Messina and A Murli;
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-- Lecture Notes in Computer Science
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-- Volume 142
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-- Springer Verlag 1982
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--
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75
with System;
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with Report;
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with ImpDef.Annex_G;
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with Ada.Numerics;
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with Ada.Numerics.Generic_Complex_Types;
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with Ada.Numerics.Complex_Types;
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procedure CXG2006 is
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   Verbose : constant Boolean := False;
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84
 
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   -- CRC Standard Mathematical Tables;  23rd Edition; pg 738
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   Sqrt2 : constant :=
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        1.41421_35623_73095_04880_16887_24209_69807_85696_71875_37695;
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   Sqrt3 : constant :=
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        1.73205_08075_68877_29352_74463_41505_87236_69428_05253_81039;
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91
   Pi : constant := Ada.Numerics.Pi;
92
 
93
   generic
94
      type Real is digits <>;
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   package Generic_Check is
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      procedure Do_Test;
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   end Generic_Check;
98
 
99
   package body Generic_Check is
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      package Complex_Types is new
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           Ada.Numerics.Generic_Complex_Types (Real);
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      use Complex_Types;
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104
 
105
      procedure Check (Actual, Expected : Real;
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                       Test_Name : String;
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                       MRE : Real) is
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         Rel_Error : Real;
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         Abs_Error : Real;
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         Max_Error : Real;
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      begin
112
         -- In the case where the expected result is very small or 0
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         -- we compute the maximum error as a multiple of Model_Epsilon instead
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         -- of Model_Epsilon and Expected.
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         Rel_Error := MRE * abs Expected * Real'Model_Epsilon;
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         Abs_Error := MRE * Real'Model_Epsilon;
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         if Rel_Error > Abs_Error then
118
            Max_Error := Rel_Error;
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         else
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            Max_Error := Abs_Error;
121
         end if;
122
 
123
         if abs (Actual - Expected) > Max_Error then
124
            Report.Failed (Test_Name &
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                           " actual: " & Real'Image (Actual) &
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                           " expected: " & Real'Image (Expected) &
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                           " difference: " &
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                           Real'Image (Actual - Expected) &
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                           " mre:" & Real'Image (Max_Error) );
130
         elsif Verbose then
131
            if Actual = Expected then
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               Report.Comment (Test_Name & "  exact result");
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            else
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               Report.Comment (Test_Name & "  passed");
135
            end if;
136
         end if;
137
      end Check;
138
 
139
 
140
      procedure Special_Cases is
141
         type Data_Point is
142
            record
143
               Re,
144
               Im,
145
               Radians,
146
               Degrees,
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               Error_Bound   : Real;
148
            end record;
149
 
150
         type Test_Data_Type is array (Positive range <>) of Data_Point;
151
 
152
         -- the values in the following table only involve static
153
         -- expressions to minimize errors in precision introduced by the
154
         -- test.  For cases where Pi is used in the argument we must
155
         -- allow an extra 1.0*MRE to account for roundoff error in the
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         -- argument.  Where the result involves a square root we allow
157
         -- an extra 0.5*MRE to allow for roundoff error.
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         Test_Data : constant Test_Data_Type := (
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--    Re               Im                     Radians  Degrees  Err    Test #
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    (0.0,               0.0,                       0.0,   0.0,  4.0 ),  -- 1
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    (1.0,               0.0,                       0.0,   0.0,  4.0 ),  -- 2
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    (Real'Safe_Last,    0.0,                       0.0,   0.0,  4.0 ),  -- 3
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    (Real'Model_Small,  0.0,                       0.0,   0.0,  4.0 ),  -- 4
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    (1.0,               1.0,                    Pi/4.0,  45.0,  5.0 ),  -- 5
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    (1.0,              -1.0,                   -Pi/4.0, -45.0,  5.0 ),  -- 6
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    (-1.0,             -1.0,               -3.0*Pi/4.0,-135.0,  5.0 ),  -- 7
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    (-1.0,              1.0,                3.0*Pi/4.0, 135.0,  5.0 ),  -- 8
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    (Sqrt3,             1.0,                    Pi/6.0,  30.0,  5.5 ),  -- 9
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    (-Sqrt3,            1.0,                5.0*Pi/6.0, 150.0,  5.5 ),  -- 10
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    (Sqrt3,            -1.0,                   -Pi/6.0, -30.0,  5.5 ),  -- 11
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    (-Sqrt3,           -1.0,               -5.0*Pi/6.0,-150.0,  5.5 ),  -- 12
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    (Real'Model_Small,  Real'Model_Small,       Pi/4.0,  45.0,  5.0 ),  -- 13
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    (-Real'Safe_Last,   0.0,                        Pi, 180.0,  5.0 ),  -- 14
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    (-Real'Safe_Last,  -Real'Model_Small,          -Pi,-180.0,  5.0 ),  -- 15
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    (100000.0,          100000.0,               Pi/4.0,  45.0,  5.0 )); -- 16
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177
         X : Real;
178
         Z : Complex;
179
      begin
180
         for I in Test_Data'Range loop
181
            begin
182
               Z := (Test_Data(I).Re, Test_Data(I).Im);
183
               X := Argument (Z);
184
               Check (X, Test_Data(I).Radians,
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                   "test" & Integer'Image (I) & " argument(z)",
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                   Test_Data (I).Error_Bound);
187
--pwb-math               X := Argument (Z, 2.0*Pi);
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--pwb-math             Check (X, Test_Data(I).Radians,
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--pwb-math                   "test" & Integer'Image (I) & " argument(z, 2pi)",
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--pwb-math                   Test_Data (I).Error_Bound);
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               X := Argument (Z, 360.0);
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               Check (X, Test_Data(I).Degrees,
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                   "test" & Integer'Image (I) & " argument(z, 360)",
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                   Test_Data (I).Error_Bound);
195
 
196
            exception
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               when Constraint_Error =>
198
                  Report.Failed ("Constraint_Error raised in test" &
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                      Integer'Image (I));
200
               when others =>
201
                  Report.Failed ("exception in test" &
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                      Integer'Image (I));
203
            end;
204
         end loop;
205
 
206
         if Real'Signed_Zeros then
207
            begin
208
              X := Argument ((-1.0, Real(ImpDef.Annex_G.Negative_Zero)));
209
              Check (X, -Pi, "test of arg((-1,-0)", 4.0);
210
            exception
211
               when others =>
212
                  Report.Failed ("exception in signed zero test");
213
            end;
214
         end if;
215
      end Special_Cases;
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218
      procedure Exception_Cases is
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      -- check that Argument_Error is raised if Cycle is <= 0
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         Z : Complex := (1.0, 1.0);
221
         X : Real;
222
         Y : Real;
223
      begin
224
         begin
225
           X := Argument (Z, Cycle => 0.0);
226
           Report.Failed ("no exception for cycle = 0.0");
227
         exception
228
            when Ada.Numerics.Argument_Error => null;
229
            when others =>
230
               Report.Failed ("wrong exception for cycle = 0.0");
231
         end;
232
 
233
         begin
234
           Y := Argument (Z, Cycle => -3.0);
235
           Report.Failed ("no exception for cycle < 0.0");
236
         exception
237
            when Ada.Numerics.Argument_Error => null;
238
            when others =>
239
               Report.Failed ("wrong exception for cycle < 0.0");
240
         end;
241
 
242
         if Report.Ident_Int (2) = 1 then
243
            -- optimization thwarting code - never executed
244
            Report.Failed("2=1" & Real'Image (X+Y));
245
         end if;
246
      end Exception_Cases;
247
 
248
 
249
      procedure Do_Test is
250
      begin
251
         Special_Cases;
252
         Exception_Cases;
253
      end Do_Test;
254
   end Generic_Check;
255
 
256
   package Chk_Float is new Generic_Check (Float);
257
 
258
   -- check the floating point type with the most digits
259
   type A_Long_Float is digits System.Max_Digits;
260
   package Chk_A_Long_Float is new Generic_Check (A_Long_Float);
261
begin
262
   Report.Test ("CXG2006",
263
                "Check the accuracy of the complex argument" &
264
                " function");
265
 
266
   if Verbose then
267
      Report.Comment ("checking Standard.Float");
268
   end if;
269
 
270
   Chk_Float.Do_Test;
271
 
272
   if Verbose then
273
      Report.Comment ("checking a digits" &
274
                      Integer'Image (System.Max_Digits) &
275
                      " floating point type");
276
   end if;
277
 
278
   Chk_A_Long_Float.Do_Test;
279
 
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   Report.Result;
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end CXG2006;

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