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1 720 jeremybenn
-- CXG2018.A
2
--
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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
10
--     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 EXP function returns
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--      a result that is within the error bound allowed.
29
--
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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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--
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-- SPECIAL REQUIREMENTS
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--      The Strict Mode for the numerical accuracy must be
41
--      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.
49
--
50
--
51
-- CHANGE HISTORY:
52
--      21 Mar 96   SAIC    Initial release for 2.1
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--      17 Aug 96   SAIC    Incorporated reviewer comments.
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--      27 Aug 99   RLB     Repair on the error result of checks.
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--      02 Apr 03   RLB     Added code to discard excess precision in the
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--                          construction of the test value for the
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--                          Identity_Test.
58
--
59
--!
60
 
61
--
62
-- References:
63
--
64
-- W. J. Cody
65
-- 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,
68
-- Vol. 19, No. 1, March, 1993, pp. 1-21.
69
--
70
-- CRC Standard Mathematical Tables
71
-- 23rd Edition
72
--
73
 
74
with System;
75
with Report;
76
with Ada.Numerics.Generic_Complex_Types;
77
with Ada.Numerics.Generic_Complex_Elementary_Functions;
78
procedure CXG2018 is
79
   Verbose : constant Boolean := False;
80
   -- Note that Max_Samples is the number of samples taken in
81
   -- both the real and imaginary directions.  Thus, for Max_Samples
82
   -- of 100 the number of values checked is 10000.
83
   Max_Samples : constant := 100;
84
 
85
   E  : constant := Ada.Numerics.E;
86
   Pi : constant := Ada.Numerics.Pi;
87
 
88
   generic
89
      type Real is digits <>;
90
   package Generic_Check is
91
      procedure Do_Test;
92
   end Generic_Check;
93
 
94
   package body Generic_Check is
95
      package Complex_Type is new
96
           Ada.Numerics.Generic_Complex_Types (Real);
97
      use Complex_Type;
98
 
99
      package CEF is new
100
           Ada.Numerics.Generic_Complex_Elementary_Functions (Complex_Type);
101
 
102
      function Exp (X : Complex) return Complex renames CEF.Exp;
103
      function Exp (X : Imaginary) return Complex renames CEF.Exp;
104
 
105
      -- flag used to terminate some tests early
106
      Accuracy_Error_Reported : Boolean := False;
107
 
108
 
109
      -- The following value is a lower bound on the accuracy
110
      -- required.  It is normally 0.0 so that the lower bound
111
      -- is computed from Model_Epsilon.  However, for tests
112
      -- where the expected result is only known to a certain
113
      -- amount of precision this bound takes on a non-zero
114
      -- value to account for that level of precision.
115
      Error_Low_Bound : Real := 0.0;
116
 
117
      procedure Check (Actual, Expected : Real;
118
                       Test_Name : String;
119
                       MRE : Real) is
120
         Max_Error : Real;
121
         Rel_Error : Real;
122
         Abs_Error : Real;
123
      begin
124
         -- In the case where the expected result is very small or 0
125
         -- we compute the maximum error as a multiple of Model_Small instead
126
         -- of Model_Epsilon and Expected.
127
         Rel_Error := MRE * abs Expected * Real'Model_Epsilon;
128
         Abs_Error := MRE * Real'Model_Small;
129
         if Rel_Error > Abs_Error then
130
            Max_Error := Rel_Error;
131
         else
132
            Max_Error := Abs_Error;
133
         end if;
134
 
135
         -- take into account the low bound on the error
136
         if Max_Error < Error_Low_Bound then
137
            Max_Error := Error_Low_Bound;
138
         end if;
139
 
140
         if abs (Actual - Expected) > Max_Error then
141
            Accuracy_Error_Reported := True;
142
            Report.Failed (Test_Name &
143
                           " actual: " & Real'Image (Actual) &
144
                           " expected: " & Real'Image (Expected) &
145
                           " difference: " & Real'Image (Actual - Expected) &
146
                           " max err:" & Real'Image (Max_Error) );
147
         elsif Verbose then
148
            if Actual = Expected then
149
               Report.Comment (Test_Name & "  exact result");
150
            else
151
               Report.Comment (Test_Name & "  passed");
152
            end if;
153
         end if;
154
      end Check;
155
 
156
 
157
      procedure Check (Actual, Expected : Complex;
158
                       Test_Name : String;
159
                       MRE : Real) is
160
      begin
161
         Check (Actual.Re, Expected.Re, Test_Name & " real part", MRE);
162
         Check (Actual.Im, Expected.Im, Test_Name & " imaginary part", MRE);
163
      end Check;
164
 
165
 
166
      procedure Special_Value_Test is
167
         -- In the following tests the expected result is accurate
168
         -- to the machine precision so the minimum guaranteed error
169
         -- bound can be used.
170
         --
171
         -- The error bounds given assumed z is  exact.  When using
172
         -- pi there is an extra error of 1.0ME.
173
         -- The pi inside the exp call requires that the complex
174
         -- component have an extra error allowance of 1.0*angle*ME.
175
         -- Thus for pi/2,the Minimum_Error_I is
176
         -- (2.0 + 1.0(pi/2))ME <= 3.6ME.
177
         -- For pi, it is (2.0 + 1.0*pi)ME <= 5.2ME,
178
         -- and for 2pi, it is (2.0 + 1.0(2pi))ME <= 8.3ME.
179
 
180
         -- The addition of 1 or i to a result is so that neither of
181
         -- the components of an expected result is 0.  This is so
182
         -- that a reasonable relative error is allowed.
183
         Minimum_Error_C : constant := 7.0;   -- for exp(Complex)
184
         Minimum_Error_I : constant := 2.0;   -- for exp(Imaginary)
185
      begin
186
         Check (Exp (1.0 + 0.0*i) + i,
187
                E + i,
188
                "exp(1+0i)",
189
                Minimum_Error_C);
190
         Check (Exp ((Pi / 2.0) * i) + 1.0,
191
                1.0 + 1.0*i,
192
                "exp(pi/2*i)",
193
                3.6);
194
         Check (Exp (Pi * i) + i,
195
                -1.0 + 1.0*i,
196
                "exp(pi*i)",
197
                5.2);
198
         Check (Exp (Pi * 2.0 * i) + i,
199
                1.0 + i,
200
                "exp(2pi*i)",
201
                8.3);
202
      exception
203
         when Constraint_Error =>
204
            Report.Failed ("Constraint_Error raised in special value test");
205
         when others =>
206
            Report.Failed ("exception in special value test");
207
      end Special_Value_Test;
208
 
209
 
210
 
211
      procedure Exact_Result_Test is
212
         No_Error : constant := 0.0;
213
      begin
214
         -- G.1.2(36);6.0
215
         Check (Exp(0.0 + 0.0*i),  1.0 + 0.0 * i, "exp(0+0i)", No_Error);
216
         Check (Exp(      0.0*i),  1.0 + 0.0 * i, "exp(0i)", No_Error);
217
      exception
218
         when Constraint_Error =>
219
            Report.Failed ("Constraint_Error raised in Exact_Result Test");
220
         when others =>
221
            Report.Failed ("exception in Exact_Result Test");
222
      end Exact_Result_Test;
223
 
224
 
225
      procedure Identity_Test (A, B : Real) is
226
      -- For this test we use the identity
227
      --    Exp(Z) = Exp(Z-W) * Exp (W)
228
      -- where W = (1+i)/16
229
      --
230
      -- The second part of this test checks the identity
231
      --    Exp(Z) * Exp(-Z)  = 1
232
      --
233
 
234
         X, Y : Complex;
235
         Actual1, Actual2 : Complex;
236
         W : constant Complex := (0.0625, 0.0625);
237
         -- the following constant was taken from the CELEFUNC EXP test.
238
         -- This is the value EXP(W) - 1
239
         C : constant Complex := (6.2416044877018563681e-2,
240
                                  6.6487597751003112768e-2);
241
      begin
242
         if Real'Digits > 20 then
243
            -- constant ExpW is accurate to 20 digits.
244
            -- The low bound is 19 * 10**-20
245
            Error_Low_Bound := 0.00000_00000_00019;
246
            Report.Comment ("complex exp accuracy checked to 20 digits");
247
         end if;
248
 
249
         Accuracy_Error_Reported := False;  -- reset
250
         for II in 1..Max_Samples loop
251
            X.Re :=  Real'Machine ((B - A) * Real (II) / Real (Max_Samples)
252
                        + A);
253
            for J in 1..Max_Samples loop
254
               X.Im :=  Real'Machine ((B - A) * Real (J) / Real (Max_Samples)
255
                           + A);
256
 
257
               Actual1 := Exp(X);
258
 
259
               -- Exp(X) = Exp(X-W) * Exp (W)
260
               --        = Exp(X-W) * (1 - (1-Exp(W))
261
               --        = Exp(X-W) * (1 + (Exp(W) - 1))
262
               --        = Exp(X-W) * (1 + C)
263
               Y := X - W;
264
               Actual2 := Exp(Y);
265
               Actual2 := Actual2 + Actual2 * C;
266
 
267
               Check (Actual1, Actual2,
268
                      "Identity_1_Test " & Integer'Image (II) &
269
                         Integer'Image (J) & ": Exp((" &
270
                         Real'Image (X.Re) & ", " &
271
                         Real'Image (X.Im) & ")) ",
272
                      20.0);   -- 2 exp and 1 multiply and 1 add = 2*7+1*5+1
273
                    -- Note: The above is not strictly correct, as multiply
274
                    -- has a box error, rather than a relative error.
275
                    -- Supposedly, the interval is chosen to avoid the need
276
                    -- to worry about this.
277
 
278
               -- Exp(X) * Exp(-X) + i  = 1 + i
279
               -- The addition of i is to allow a reasonable relative
280
               -- error in the imaginary part
281
               Actual2 := (Actual1 * Exp(-X)) + i;
282
               Check (Actual2, (1.0, 1.0),
283
                      "Identity_2_Test " & Integer'Image (II) &
284
                         Integer'Image (J) & ": Exp((" &
285
                         Real'Image (X.Re) & ", " &
286
                         Real'Image (X.Im) & ")) ",
287
                      20.0);   -- 2 exp and 1 multiply and one add = 2*7+1*5+1
288
 
289
               if Accuracy_Error_Reported then
290
                 -- only report the first error in this test in order to keep
291
                 -- lots of failures from producing a huge error log
292
                 return;
293
               end if;
294
            end loop;
295
         end loop;
296
         Error_Low_Bound := 0.0;
297
      exception
298
         when Constraint_Error =>
299
            Report.Failed
300
               ("Constraint_Error raised in Identity_Test" &
301
                " for X=(" & Real'Image (X.Re) &
302
                ", " & Real'Image (X.Im) & ")");
303
         when others =>
304
            Report.Failed ("exception in Identity_Test" &
305
                " for X=(" & Real'Image (X.Re) &
306
                ", " & Real'Image (X.Im) & ")");
307
      end Identity_Test;
308
 
309
 
310
 
311
      procedure Do_Test is
312
      begin
313
         Special_Value_Test;
314
         Exact_Result_Test;
315
            -- test regions where we can avoid cancellation error problems
316
            -- See Cody page 10.
317
         Identity_Test (0.0625, 1.0);
318
         Identity_Test (15.0, 17.0);
319
         Identity_Test (1.625, 3.0);
320
      end Do_Test;
321
   end Generic_Check;
322
 
323
   -----------------------------------------------------------------------
324
   -----------------------------------------------------------------------
325
   package Float_Check is new Generic_Check (Float);
326
 
327
   -- check the floating point type with the most digits
328
   type A_Long_Float is digits System.Max_Digits;
329
   package A_Long_Float_Check is new Generic_Check (A_Long_Float);
330
 
331
   -----------------------------------------------------------------------
332
   -----------------------------------------------------------------------
333
 
334
 
335
begin
336
   Report.Test ("CXG2018",
337
                "Check the accuracy of the complex EXP function");
338
 
339
   if Verbose then
340
      Report.Comment ("checking Standard.Float");
341
   end if;
342
 
343
   Float_Check.Do_Test;
344
 
345
   if Verbose then
346
      Report.Comment ("checking a digits" &
347
                      Integer'Image (System.Max_Digits) &
348
                      " floating point type");
349
   end if;
350
 
351
   A_Long_Float_Check.Do_Test;
352
 
353
 
354
   Report.Result;
355
end CXG2018;

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