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1 149 jeremybenn
-- CXG2013.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 TAN and COT functions return
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--      results that are 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
32
--      instantiated to check 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 checks.
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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
--      11 Mar 96   SAIC    Initial release for 2.1
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--      17 Aug 96   SAIC    Commentary fixes.
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--      03 Feb 97   PWB.CTA Removed checks with explicit Cycle => 2.0*Pi
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--      02 DEC 97   EDS     Change Max_Samples constant to 1001.
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--      29 JUN 98   EDS     Deleted Special_Angle_Test as fatally flawed.
57
 
58
--!
59
 
60
--
61
-- References:
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--
63
-- Software Manual for the Elementary Functions
64
-- William J. Cody, Jr. and William Waite
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-- Prentice-Hall, 1980
66
--
67
-- CRC Standard Mathematical Tables
68
-- 23rd Edition
69
--
70
-- Implementation and Testing of Function Software
71
-- W. J. Cody
72
-- Problems and Methodologies in Mathematical Software Production
73
-- editors P. C. Messina and A. Murli
74
-- Lecture Notes in Computer Science   Volume 142
75
-- Springer Verlag, 1982
76
--
77
 
78
with System;
79
with Report;
80
with Ada.Numerics.Generic_Elementary_Functions;
81
procedure CXG2013 is
82
   Verbose : constant Boolean := False;
83
   Max_Samples : constant := 1001;
84
 
85
   -- CRC Standard Mathematical Tables;  23rd Edition; pg 738
86
   Sqrt2 : constant :=
87
        1.41421_35623_73095_04880_16887_24209_69807_85696_71875_37695;
88
   Sqrt3 : constant :=
89
        1.73205_08075_68877_29352_74463_41505_87236_69428_05253_81039;
90
 
91
   Pi : constant := Ada.Numerics.Pi;
92
 
93
   generic
94
      type Real is digits <>;
95
   package Generic_Check is
96
      procedure Do_Test;
97
   end Generic_Check;
98
 
99
   package body Generic_Check is
100
      package Elementary_Functions is new
101
           Ada.Numerics.Generic_Elementary_Functions (Real);
102
      function Sqrt (X : Real) return Real renames
103
           Elementary_Functions.Sqrt;
104
      function Tan (X : Real) return Real renames
105
           Elementary_Functions.Tan;
106
      function Cot (X : Real) return Real renames
107
           Elementary_Functions.Cot;
108
      function Tan (X, Cycle : Real) return Real renames
109
           Elementary_Functions.Tan;
110
      function Cot (X, Cycle : Real) return Real renames
111
           Elementary_Functions.Cot;
112
 
113
      -- flag used to terminate some tests early
114
      Accuracy_Error_Reported : Boolean := False;
115
 
116
      -- factor to be applied in computing MRE
117
      Maximum_Relative_Error : constant Real := 4.0;
118
 
119
      procedure Check (Actual, Expected : Real;
120
                       Test_Name : String;
121
                       MRE : Real) is
122
         Max_Error : Real;
123
         Rel_Error : Real;
124
         Abs_Error : Real;
125
      begin
126
         -- In the case where the expected result is very small or 0
127
         -- we compute the maximum error as a multiple of Model_Epsilon instead
128
         -- of Model_Epsilon and Expected.
129
         Rel_Error := MRE * abs Expected * Real'Model_Epsilon;
130
         Abs_Error := MRE * Real'Model_Epsilon;
131
         if Rel_Error > Abs_Error then
132
            Max_Error := Rel_Error;
133
         else
134
            Max_Error := Abs_Error;
135
         end if;
136
 
137
         if abs (Actual - Expected) > Max_Error then
138
            Accuracy_Error_Reported := True;
139
            Report.Failed (Test_Name &
140
                           " actual: " & Real'Image (Actual) &
141
                           " expected: " & Real'Image (Expected) &
142
                           " difference: " & Real'Image (Actual - Expected) &
143
                           " max err:" & Real'Image (Max_Error) );
144
         elsif Verbose then
145
            if Actual = Expected then
146
               Report.Comment (Test_Name & "  exact result");
147
            else
148
               Report.Comment (Test_Name & "  passed");
149
            end if;
150
         end if;
151
      end Check;
152
 
153
 
154
 
155
      procedure Exact_Result_Test is
156
         No_Error : constant := 0.0;
157
      begin
158
         -- A.5.1(38);6.0
159
         Check (Tan (0.0),  0.0, "tan(0)", No_Error);
160
 
161
         -- A.5.1(41);6.0
162
         Check (Tan (180.0, 360.0), 0.0, "tan(180,360)", No_Error);
163
         Check (Tan (360.0, 360.0), 0.0, "tan(360,360)", No_Error);
164
         Check (Tan (720.0, 360.0), 0.0, "tan(720,360)", No_Error);
165
 
166
         -- A.5.1(41);6.0
167
         Check (Cot ( 90.0, 360.0), 0.0, "cot( 90,360)", No_Error);
168
         Check (Cot (270.0, 360.0), 0.0, "cot(270,360)", No_Error);
169
         Check (Cot (810.0, 360.0), 0.0, "cot(810,360)", No_Error);
170
 
171
      exception
172
         when Constraint_Error =>
173
            Report.Failed ("Constraint_Error raised in Exact_Result Test");
174
         when others =>
175
            Report.Failed ("exception in Exact_Result Test");
176
      end Exact_Result_Test;
177
 
178
 
179
      procedure Tan_Test (A, B : Real) is
180
      -- Use identity Tan(X) = [2*Tan(x/2)]/[1-Tan(x/2) ** 2]
181
      -- checks over the range -pi/4 .. pi/4 require no argument reduction
182
      -- checks over the range 7pi/8 .. 9pi/8 require argument reduction
183
         X, Y : Real;
184
         Actual1, Actual2 : Real;
185
      begin
186
         Accuracy_Error_Reported := False;  -- reset
187
         for I in 1..Max_Samples loop
188
            X :=  (B - A) * Real (I) / Real (Max_Samples) + A;
189
            -- argument purification to insure x and x/2 are exact
190
            -- See Cody page 170.
191
            Y := Real'Machine (X*0.5);
192
            X := Real'Machine (Y + Y);
193
 
194
            Actual1 := Tan(X);
195
            Actual2 := (2.0 * Tan (Y)) / (1.0 - Tan (Y) ** 2);
196
 
197
            if abs (X - Pi) > ( (B-A)/Real(2*Max_Samples) ) then
198
              Check (Actual1, Actual2,
199
                     "Tan_Test " & Integer'Image (I) & ": tan(" &
200
                     Real'Image (X) & ") ",
201
                     (1.0 + Sqrt2) * Maximum_Relative_Error);
202
                     -- see Cody pg 165 for error bound info
203
            end if;
204
 
205
            if Accuracy_Error_Reported then
206
              -- only report the first error in this test in order to keep
207
              -- lots of failures from producing a huge error log
208
              return;
209
            end if;
210
 
211
         end loop;
212
 
213
      exception
214
         when Constraint_Error =>
215
            Report.Failed
216
               ("Constraint_Error raised in Tan_Test");
217
         when others =>
218
            Report.Failed ("exception in Tan_Test");
219
      end Tan_Test;
220
 
221
 
222
 
223
      procedure Cot_Test is
224
      -- Use identity Cot(X) = [Cot(X/2)**2 - 1]/[2*Cot(X/2)]
225
         A : constant := 6.0 * Pi;
226
         B : constant := 25.0 / 4.0 * Pi;
227
         X, Y : Real;
228
         Actual1, Actual2 : Real;
229
      begin
230
         Accuracy_Error_Reported := False;  -- reset
231
         for I in 1..Max_Samples loop
232
            X :=  (B - A) * Real (I) / Real (Max_Samples) + A;
233
            -- argument purification to insure x and x/2 are exact.
234
            -- See Cody page 170.
235
            Y := Real'Machine (X*0.5);
236
            X := Real'Machine (Y + Y);
237
 
238
            Actual1 := Cot(X);
239
            Actual2 := (Cot (Y) ** 2 - 1.0) / (2.0 * Cot (Y));
240
 
241
            Check (Actual1, Actual2,
242
                   "Cot_Test " & Integer'Image (I) & ": cot(" &
243
                   Real'Image (X) & ") ",
244
                   (1.0 + Sqrt2) * Maximum_Relative_Error);
245
                   -- see Cody pg 165 for error bound info
246
 
247
            if Accuracy_Error_Reported then
248
              -- only report the first error in this test in order to keep
249
              -- lots of failures from producing a huge error log
250
              return;
251
            end if;
252
 
253
         end loop;
254
 
255
      exception
256
         when Constraint_Error =>
257
            Report.Failed
258
               ("Constraint_Error raised in Cot_Test");
259
         when others =>
260
            Report.Failed ("exception in Cot_Test");
261
      end Cot_Test;
262
 
263
 
264
      procedure Exception_Test is
265
         X1, X2, X3, X4, X5 : Real := 0.0;
266
      begin
267
 
268
 
269
         begin  -- A.5.1(20);6.0
270
           X1 := Tan (0.0, Cycle => 0.0);
271
           Report.Failed ("no exception for cycle = 0.0");
272
         exception
273
            when Ada.Numerics.Argument_Error => null;
274
            when others =>
275
               Report.Failed ("wrong exception for cycle = 0.0");
276
         end;
277
 
278
         begin  -- A.5.1(20);6.0
279
           X2 := Cot (1.0, Cycle => -3.0);
280
           Report.Failed ("no exception for cycle < 0.0");
281
         exception
282
            when Ada.Numerics.Argument_Error => null;
283
            when others =>
284
               Report.Failed ("wrong exception for cycle < 0.0");
285
         end;
286
 
287
         -- the remaining tests only apply to machines that overflow
288
         if Real'Machine_Overflows then    -- A.5.1(28);6.0
289
 
290
            begin   -- A.5.1(29);6.0
291
               X3 := Cot (0.0);
292
               Report.Failed ("exception not raised for cot(0)");
293
            exception
294
               when Constraint_Error => null;   -- ok
295
               when others =>
296
                  Report.Failed ("wrong exception raised for cot(0)");
297
            end;
298
 
299
            begin   -- A.5.1(31);6.0
300
               X4 := Tan (90.0, 360.0);
301
               Report.Failed ("exception not raised for tan(90,360)");
302
            exception
303
               when Constraint_Error => null;  -- ok
304
               when others =>
305
                  Report.Failed ("wrong exception raised for tan(90,360)");
306
            end;
307
 
308
            begin   -- A.5.1(32);6.0
309
               X5 := Cot (180.0, 360.0);
310
               Report.Failed ("exception not raised for cot(180,360)");
311
            exception
312
               when Constraint_Error => null;  -- ok
313
               when others =>
314
                  Report.Failed ("wrong exception raised for cot(180,360)");
315
            end;
316
         end if;
317
 
318
         -- optimizer thwarting
319
         if Report.Ident_Bool (False) then
320
            Report.Comment (Real'Image (X1+X2+X3+X4+X5));
321
         end if;
322
      end Exception_Test;
323
 
324
 
325
      procedure Do_Test is
326
      begin
327
         Exact_Result_Test;
328
         Tan_Test (-Pi/4.0, Pi/4.0);
329
         Tan_Test (7.0*Pi/8.0, 9.0*Pi/8.0);
330
         Cot_Test;
331
         Exception_Test;
332
      end Do_Test;
333
   end Generic_Check;
334
 
335
   -----------------------------------------------------------------------
336
   -----------------------------------------------------------------------
337
   package Float_Check is new Generic_Check (Float);
338
 
339
   -- check the floating point type with the most digits
340
   type A_Long_Float is digits System.Max_Digits;
341
   package A_Long_Float_Check is new Generic_Check (A_Long_Float);
342
 
343
   -----------------------------------------------------------------------
344
   -----------------------------------------------------------------------
345
 
346
 
347
begin
348
   Report.Test ("CXG2013",
349
                "Check the accuracy of the TAN and COT functions");
350
 
351
   if Verbose then
352
      Report.Comment ("checking Standard.Float");
353
   end if;
354
 
355
   Float_Check.Do_Test;
356
 
357
   if Verbose then
358
      Report.Comment ("checking a digits" &
359
                      Integer'Image (System.Max_Digits) &
360
                      " floating point type");
361
   end if;
362
 
363
   A_Long_Float_Check.Do_Test;
364
 
365
 
366
   Report.Result;
367
end CXG2013;

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