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1 294 jeremybenn
-- CXG2019.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 LOG function returns
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--      a result that is within the error bound allowed.
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--
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-- TEST DESCRIPTION:
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--      This test consists of a generic package that is
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--      instantiated to check complex numbers based upon
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--      both Float and a long float type.
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--      The test for each floating point type is divided into
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--      several parts:
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--         Special value checks where the result is a known constant.
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--         Checks that use an identity for determining the result.
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--         Exception conditions.
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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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--      22 Mar 96   SAIC    Initial release for 2.1
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--
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--!
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57
--
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-- References:
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--
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-- W. J. Cody
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-- CELEFUNT: A Portable Test Package for Complex Elementary Functions
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-- Algorithm 714, Collected Algorithms from ACM.
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-- Published in Transactions On Mathematical Software,
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-- Vol. 19, No. 1, March, 1993, pp. 1-21.
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--
66
-- CRC Standard Mathematical Tables
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-- 23rd Edition
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--
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70
with System;
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with Report;
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with Ada.Numerics.Generic_Complex_Types;
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with Ada.Numerics.Generic_Complex_Elementary_Functions;
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procedure CXG2019 is
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   Verbose : constant Boolean := False;
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   -- Note that Max_Samples is the number of samples taken in
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   -- both the real and imaginary directions.  Thus, for Max_Samples
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   -- of 100 the number of values checked is 10000.
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   Max_Samples : constant := 100;
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81
   E  : constant := Ada.Numerics.E;
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   Pi : constant := Ada.Numerics.Pi;
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84
   generic
85
      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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90
   package body Generic_Check is
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      package Complex_Type is new
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           Ada.Numerics.Generic_Complex_Types (Real);
93
      use Complex_Type;
94
 
95
      package CEF is new
96
           Ada.Numerics.Generic_Complex_Elementary_Functions (Complex_Type);
97
 
98
      function Log (X : Complex) return Complex renames CEF.Log;
99
 
100
      -- flag used to terminate some tests early
101
      Accuracy_Error_Reported : Boolean := False;
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103
 
104
      procedure Check (Actual, Expected : Real;
105
                       Test_Name : String;
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                       MRE : Real) is
107
         Max_Error : Real;
108
         Rel_Error : Real;
109
         Abs_Error : Real;
110
      begin
111
         -- 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
113
         -- of Model_Epsilon and Expected.
114
         Rel_Error := MRE * abs Expected * Real'Model_Epsilon;
115
         Abs_Error := MRE * Real'Model_Epsilon;
116
         if Rel_Error > Abs_Error then
117
            Max_Error := Rel_Error;
118
         else
119
            Max_Error := Abs_Error;
120
         end if;
121
 
122
         if abs (Actual - Expected) > Max_Error then
123
            Accuracy_Error_Reported := True;
124
            Report.Failed (Test_Name &
125
                           " actual: " & Real'Image (Actual) &
126
                           " expected: " & Real'Image (Expected) &
127
                           " difference: " & Real'Image (Actual - Expected) &
128
                           " max err:" & Real'Image (Max_Error) );
129
         elsif Verbose then
130
            if Actual = Expected then
131
               Report.Comment (Test_Name & "  exact result");
132
            else
133
               Report.Comment (Test_Name & "  passed");
134
            end if;
135
         end if;
136
      end Check;
137
 
138
 
139
      procedure Check (Actual, Expected : Complex;
140
                       Test_Name : String;
141
                       MRE : Real) is
142
      begin
143
         Check (Actual.Re, Expected.Re, Test_Name & " real part", MRE);
144
         Check (Actual.Im, Expected.Im, Test_Name & " imaginary part", MRE);
145
      end Check;
146
 
147
 
148
      procedure Special_Value_Test is
149
         -- In the following tests the expected result is accurate
150
         -- to the machine precision so the minimum guaranteed error
151
         -- bound can be used if the argument is exact.
152
         --
153
         -- When using pi there is an extra error of 1.0ME.
154
         -- Although the real component has an error bound of 13.0,
155
         -- the complex component must take into account this error
156
         -- in the value for Pi.
157
         --
158
         -- One or i is added to the actual and expected results in
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         -- order to prevent the expected result from having a
160
         -- real or imaginary part of 0.  This is to allow a reasonable
161
         -- relative error for that component.
162
         Minimum_Error : constant := 13.0;
163
      begin
164
         Check (1.0 + Log (0.0 + i),
165
                1.0 + Pi / 2.0 * i,
166
                "1+log(0+i)",
167
                Minimum_Error + 1.0);
168
         Check (1.0 + Log ((-1.0, 0.0)),
169
                1.0 + (Pi * i),
170
                "log(-1+0i)+1 ",
171
                Minimum_Error + 1.0);
172
      exception
173
         when Constraint_Error =>
174
            Report.Failed ("Constraint_Error raised in special value test");
175
         when others =>
176
            Report.Failed ("exception in special value test");
177
      end Special_Value_Test;
178
 
179
 
180
 
181
      procedure Exact_Result_Test is
182
         No_Error : constant := 0.0;
183
      begin
184
         -- G.1.2(37);6.0
185
         Check (Log(1.0 + 0.0*i),  0.0 + 0.0 * i, "log(1+0i)", No_Error);
186
      exception
187
         when Constraint_Error =>
188
            Report.Failed ("Constraint_Error raised in Exact_Result Test");
189
         when others =>
190
            Report.Failed ("exception in Exact_Result Test");
191
      end Exact_Result_Test;
192
 
193
 
194
      procedure Identity_Test (RA, RB, IA, IB : Real) is
195
      -- Tests an identity over a range of values specified
196
      -- by the 4 parameters.  RA and RB denote the range for the
197
      -- real part while IA and IB denote the range for the
198
      -- imaginary part.
199
      --
200
      -- For this test we use the identity
201
      --    Log(Z*Z) = 2 * Log(Z)
202
      --
203
 
204
         Scale : Real := Real (Real'Machine_Radix) ** (Real'Mantissa / 2 + 4);
205
         W, X, Y, Z : Real;
206
         CX, CY : Complex;
207
         Actual1, Actual2 : Complex;
208
      begin
209
         Accuracy_Error_Reported := False;  -- reset
210
         for II in 1..Max_Samples loop
211
            X :=  (RB - RA) * Real (II) / Real (Max_Samples) + RA;
212
            for J in 1..Max_Samples loop
213
               Y :=  (IB - IA) * Real (J) / Real (Max_Samples) + IA;
214
 
215
               -- purify the arguments to minimize roundoff error.
216
               -- We construct the values so that the products X*X,
217
               -- Y*Y, and X*Y are all exact machine numbers.
218
               -- See Cody page 7 and CELEFUNT code.
219
               Z := X * Scale;
220
               W := Z + X;
221
               X := W - Z;
222
               Z := Y * Scale;
223
               W := Z + Y;
224
               Y := W - Z;
225
               CX := Compose_From_Cartesian(X,Y);
226
               Z := X*X - Y*Y;
227
               W := X*Y;
228
               CY := Compose_From_Cartesian(Z,W+W);
229
 
230
               -- The arguments are now ready so on with the
231
               -- identity computation.
232
               Actual1 := Log(CX);
233
 
234
               Actual2 := Log(CY) * 0.5;
235
 
236
               Check (Actual1, Actual2,
237
                      "Identity_1_Test " & Integer'Image (II) &
238
                         Integer'Image (J) & ": Log((" &
239
                         Real'Image (CX.Re) & ", " &
240
                         Real'Image (CX.Im) & ")) ",
241
                      26.0);   -- 2 logs = 2*13.  no error from this multiply
242
 
243
               if Accuracy_Error_Reported then
244
                 -- only report the first error in this test in order to keep
245
                 -- lots of failures from producing a huge error log
246
                 return;
247
               end if;
248
            end loop;
249
         end loop;
250
 
251
      exception
252
         when Constraint_Error =>
253
            Report.Failed
254
               ("Constraint_Error raised in Identity_Test" &
255
                " for X=(" & Real'Image (X) &
256
                ", " & Real'Image (X) & ")");
257
         when others =>
258
            Report.Failed ("exception in Identity_Test" &
259
                " for X=(" & Real'Image (X) &
260
                ", " & Real'Image (X) & ")");
261
      end Identity_Test;
262
 
263
 
264
      procedure Exception_Test is
265
      -- Check that log((0,0)) causes constraint_error.
266
      -- G.1.2(29);
267
 
268
         X : Complex := (0.0, 0.0);
269
      begin
270
         if not Real'Machine_Overflows then
271
            -- not applicable:   G.1.2(28);6.0
272
            return;
273
         end if;
274
 
275
         begin
276
            X := Log ((0.0, 0.0));
277
            Report.Failed ("exception not raised for log(0,0)");
278
         exception
279
            when Constraint_Error => null;  -- ok
280
            when others =>
281
               Report.Failed ("wrong exception raised for log(0,0)");
282
         end;
283
 
284
         -- optimizer thwarting
285
         if Report.Ident_Bool(False) then
286
            Report.Comment (Real'Image (X.Re + X.Im));
287
         end if;
288
      end Exception_Test;
289
 
290
 
291
      procedure Do_Test is
292
      begin
293
         Special_Value_Test;
294
         Exact_Result_Test;
295
            -- test regions that do not include the unit circle so that
296
            -- the real part of LOG(Z) does not vanish
297
            -- See Cody page 9.
298
         Identity_Test (   2.0,   10.0,       0.0,    10.0);
299
         Identity_Test (1000.0, 2000.0,   -4000.0, -1000.0);
300
         Identity_Test (Real'Model_Epsilon, 0.25,
301
                        -0.25,              -Real'Model_Epsilon);
302
         Exception_Test;
303
      end Do_Test;
304
   end Generic_Check;
305
 
306
   -----------------------------------------------------------------------
307
   -----------------------------------------------------------------------
308
   package Float_Check is new Generic_Check (Float);
309
 
310
   -- check the floating point type with the most digits
311
   type A_Long_Float is digits System.Max_Digits;
312
   package A_Long_Float_Check is new Generic_Check (A_Long_Float);
313
 
314
   -----------------------------------------------------------------------
315
   -----------------------------------------------------------------------
316
 
317
 
318
begin
319
   Report.Test ("CXG2019",
320
                "Check the accuracy of the complex LOG function");
321
 
322
   if Verbose then
323
      Report.Comment ("checking Standard.Float");
324
   end if;
325
 
326
   Float_Check.Do_Test;
327
 
328
   if Verbose then
329
      Report.Comment ("checking a digits" &
330
                      Integer'Image (System.Max_Digits) &
331
                      " floating point type");
332
   end if;
333
 
334
   A_Long_Float_Check.Do_Test;
335
 
336
 
337
   Report.Result;
338
end CXG2019;

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