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1 294 jeremybenn
-- CXG2007.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 Compose_From_Polar 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 Compose_From_Polar function.
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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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--      23 FEB 96   SAIC    Initial release for 2.1
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--      23 APR 96   SAIC    Fixed error checking
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--      03 MAR 97   PWB.CTA Deleted checks with 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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64
with System;
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with Report;
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with Ada.Numerics;
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with Ada.Numerics.Generic_Complex_Types;
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procedure CXG2007 is
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   Verbose : constant Boolean := False;
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71
 
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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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   Pi : constant := Ada.Numerics.Pi;
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80
   generic
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      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;
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86
   package body Generic_Check is
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      package Complex_Types is new
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           Ada.Numerics.Generic_Complex_Types (Real);
89
      use Complex_Types;
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91
      Maximum_Relative_Error : constant Real := 3.0;
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93
      procedure Check (Actual, Expected : Real;
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                       Test_Name : String;
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                       MRE : Real;
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                       Arg_Error : Real) is
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         -- Arg_Error is additional absolute error that is allowed beyond
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         -- the MRE to account for error in the result that can be
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         -- attributed to error in the arguments.
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         Max_Error : Real;
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         Rel_Error : Real;
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         Abs_Error : Real;
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      begin
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         -- 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_Small 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
110
            Max_Error := Rel_Error;
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         else
112
            Max_Error := Abs_Error;
113
         end if;
114
         Max_Error := Max_Error + Arg_Error;
115
 
116
         if abs (Actual - Expected) > Max_Error then
117
            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: " & Real'Image (Actual - Expected) &
121
                           " max err:" & Real'Image (Max_Error) );
122
         elsif Verbose then
123
            if Actual = Expected then
124
               Report.Comment (Test_Name & "  exact result");
125
            else
126
               Report.Comment (Test_Name & "  passed");
127
            end if;
128
         end if;
129
      end Check;
130
 
131
 
132
      procedure Check (Actual, Expected : Complex;
133
                       Test_Name : String;
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                       MRE : Real;
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                       Arg_Error : Real) is
136
         -- Arg_Error is additional absolute error that is allowed beyond
137
         -- the MRE to account for error in the result that can be
138
         -- attributed to error in the arguments.
139
      begin
140
         Check (Actual.Re, Expected.Re,
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                Test_Name & " real part",
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                MRE, Arg_Error);
143
         Check (Actual.Im, Expected.Im,
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                Test_Name & " imaginary part",
145
                MRE, Arg_Error);
146
      end Check;
147
 
148
 
149
      procedure Special_Cases is
150
         type Data_Point is
151
            record
152
               Re,
153
               Im,
154
               Modulus,
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               Radians,
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               Degrees,
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               Arg_Error : Real;
158
            end record;
159
 
160
         -- shorthand names for various constants
161
         P4 : constant := Pi/4.0;
162
         P6 : constant := Pi/6.0;
163
 
164
         MER2 : constant Real := Real'Model_Epsilon * Sqrt2;
165
 
166
         type Test_Data_Type is array (Positive range <>) of Data_Point;
167
 
168
         -- the values in the following table only involve static
169
         -- expressions so no loss of precision occurs.
170
         Test_Data : constant Test_Data_Type := (
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         --Re          Im   Modulus     Radians  Degrees  Arg_Err
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         ( 0.0,        0.0, 0.0,            0.0,   0.0,    0.0 ),    -- 1
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         ( 0.0,        0.0, 0.0,             Pi, 180.0,    0.0 ),    -- 2
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175
         ( 1.0,        0.0, 1.0,            0.0,   0.0,    0.0 ),    -- 3
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         (-1.0,        0.0, -1.0,           0.0,   0.0,    0.0 ),    -- 4
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178
         ( 1.0,        1.0,  Sqrt2,          P4,  45.0,    MER2),    -- 5
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         (-1.0,        1.0, -Sqrt2,         -P4, -45.0,    MER2),    -- 6
180
         ( 1.0,       -1.0,  Sqrt2,         -P4, -45.0,    MER2),    -- 7
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         (-1.0,       -1.0, -Sqrt2,          P4,  45.0,    MER2),    -- 8
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         (-1.0,       -1.0,  Sqrt2,     -3.0*P4,-135.0,    MER2),    -- 9
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         (-1.0,        1.0,  Sqrt2,      3.0*P4, 135.0,    MER2),    -- 10
184
         ( 1.0,       -1.0, -Sqrt2,      3.0*P4, 135.0,    MER2),    -- 11
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186
         (-1.0,        0.0, 1.0,             Pi, 180.0,    0.0 ),    -- 12
187
         ( 1.0,        0.0, -1.0,            Pi, 180.0,    0.0 ) );  -- 13
188
 
189
 
190
         Z : Complex;
191
         Exp : Complex;
192
      begin
193
         for I in Test_Data'Range loop
194
            begin
195
               Exp := (Test_Data (I).Re, Test_Data (I).Im);
196
 
197
               Z := Compose_From_Polar (Test_Data (I).Modulus,
198
                                        Test_Data (I).Radians);
199
               Check (Z, Exp,
200
                 "test" & Integer'Image (I) & " compose_from_polar(m,r)",
201
                 Maximum_Relative_Error, Test_Data (I).Arg_Error);
202
 
203
--pwb-math               Z := Compose_From_Polar (Test_Data (I).Modulus,
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--pwb-math                                      Test_Data (I).Radians,
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--pwb-math                                      2.0*Pi);
206
--pwb-math             Check (Z, Exp,
207
--pwb-math                 "test" & Integer'Image (I) & " compose_from_polar(m,r,2pi)",
208
--pwb-math               Maximum_Relative_Error, Test_Data (I).Arg_Error);
209
 
210
               Z := Compose_From_Polar (Test_Data (I).Modulus,
211
                                        Test_Data (I).Degrees,
212
                                        360.0);
213
               Check (Z, Exp,
214
                 "test" & Integer'Image (I) & " compose_from_polar(m,d,360)",
215
                 Maximum_Relative_Error, Test_Data (I).Arg_Error);
216
 
217
            exception
218
               when Constraint_Error =>
219
                  Report.Failed ("Constraint_Error raised in test" &
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                      Integer'Image (I));
221
               when others =>
222
                  Report.Failed ("exception in test" &
223
                      Integer'Image (I));
224
            end;
225
         end loop;
226
      end Special_Cases;
227
 
228
 
229
      procedure Exception_Cases is
230
      -- check that Argument_Error is raised if Cycle is <= 0
231
         Z : Complex;
232
         W : Complex;
233
      begin
234
         begin
235
           Z := Compose_From_Polar (3.0, 0.0, Cycle => 0.0);
236
           Report.Failed ("no exception for cycle = 0.0");
237
         exception
238
            when Ada.Numerics.Argument_Error => null;
239
            when others =>
240
               Report.Failed ("wrong exception for cycle = 0.0");
241
         end;
242
 
243
         begin
244
           W := Compose_From_Polar (6.0, 1.0, Cycle => -10.0);
245
           Report.Failed ("no exception for cycle < 0.0");
246
         exception
247
            when Ada.Numerics.Argument_Error => null;
248
            when others =>
249
               Report.Failed ("wrong exception for cycle < 0.0");
250
         end;
251
 
252
         if Report.Ident_Int (1) = 2 then
253
             -- not executed - used to make it appear that we use the
254
             -- results of the above computation
255
             Z := Z * W;
256
             Report.Failed(Real'Image (Z.Re + Z.Im));
257
         end if;
258
      end Exception_Cases;
259
 
260
 
261
      procedure Do_Test is
262
      begin
263
         Special_Cases;
264
         Exception_Cases;
265
      end Do_Test;
266
   end Generic_Check;
267
 
268
   package Chk_Float is new Generic_Check (Float);
269
 
270
   -- check the floating point type with the most digits
271
   type A_Long_Float is digits System.Max_Digits;
272
   package Chk_A_Long_Float is new Generic_Check (A_Long_Float);
273
begin
274
   Report.Test ("CXG2007",
275
                "Check the accuracy of the Compose_From_Polar" &
276
                " function");
277
 
278
   if Verbose then
279
      Report.Comment ("checking Standard.Float");
280
   end if;
281
   Chk_Float.Do_Test;
282
 
283
   if Verbose then
284
      Report.Comment ("checking a digits" &
285
                      Integer'Image (System.Max_Digits) &
286
                      " floating point type");
287
   end if;
288
   Chk_A_Long_Float.Do_Test;
289
 
290
   Report.Result;
291
end CXG2007;

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