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1 -- CXA5A07.A
2 --
3 -- Grant of Unlimited Rights
4 --
5 -- Under contracts F33600-87-D-0337, F33600-84-D-0280, MDA903-79-C-0687,
6 -- F08630-91-C-0015, and DCA100-97-D-0025, the U.S. Government obtained
7 -- unlimited rights in the software and documentation contained herein.
8 -- Unlimited rights are defined in DFAR 252.227-7013(a)(19). By making
9 -- this public release, the Government intends to confer upon all
10 -- recipients unlimited rights equal to those held by the Government.
11 -- These rights include rights to use, duplicate, release or disclose the
12 -- released technical data and computer software in whole or in part, in
13 -- any manner and for any purpose whatsoever, and to have or permit others
14 -- to do so.
15 --
16 -- DISCLAIMER
17 --
18 -- ALL MATERIALS OR INFORMATION HEREIN RELEASED, MADE AVAILABLE OR
19 -- DISCLOSED ARE AS IS. THE GOVERNMENT MAKES NO EXPRESS OR IMPLIED
20 -- WARRANTY AS TO ANY MATTER WHATSOEVER, INCLUDING THE CONDITIONS OF THE
21 -- SOFTWARE, DOCUMENTATION OR OTHER INFORMATION RELEASED, MADE AVAILABLE
22 -- OR DISCLOSED, OR THE OWNERSHIP, MERCHANTABILITY, OR FITNESS FOR A
23 -- PARTICULAR PURPOSE OF SAID MATERIAL.
24 --*
25 --
26 -- OBJECTIVE:
27 -- Check that the function Arctan provides correct results.
28 --
29 -- TEST DESCRIPTION:
30 -- This test examines both the version of Arctan resulting from the
31 -- instantiation of the Ada.Numerics.Generic_Elementary_Functions with
32 -- a type derived from type Float, as well as the preinstantiated
33 -- version of this package for type Float.
34 -- Prescribed results, including instances prescribed to raise
35 -- exceptions, are examined in the test cases. In addition,
36 -- certain evaluations are performed where the actual function result
37 -- is compared with the expected result (within an epsilon range of
38 -- accuracy).
39 --
40 -- TEST FILES:
41 -- The following files comprise this test:
42 --
43 -- FXA5A00.A (foundation code)
44 -- CXA5A07.A
45 --
46 --
47 -- CHANGE HISTORY:
48 -- 04 Apr 95 SAIC Initial prerelease version.
49 -- 13 Jun 95 SAIC Incorporated use of Dont_Optimize procedure, and
50 -- use of Result_Within_Range function overloaded for
51 -- FXA5A00.New_Float_Type.
52 -- 28 Feb 97 PWB.CTA Removed checks with explicit Cycle => 2.0*Pi
53 --
54 -- CHANGE NOTE:
55 -- According to Ken Dritz, author of the Numerics Annex of the RM,
56 -- one should never specify the cycle 2.0*Pi for the trigonometric
57 -- functions. In particular, if the machine number for the first
58 -- argument is not an exact multiple of the machine number for the
59 -- explicit cycle, then the specified exact results cannot be
60 -- reasonably expected. The affected checks in this test have been
61 -- marked as comments, with the additional notation "pwb-math".
62 -- Phil Brashear
63 --!
64
65 with Ada.Numerics.Elementary_Functions;
66 with Ada.Numerics.Generic_Elementary_Functions;
67 with FXA5A00;
68 with Report;
69
70 procedure CXA5A07 is
71 begin
72
73 Report.Test ("CXA5A07", "Check that the Arctan function provides " &
74 "correct results");
75
76 Test_Block:
77 declare
78
79 use Ada.Numerics;
80 use FXA5A00;
81
82 package GEF is new Ada.Numerics.Generic_Elementary_Functions(New_Float);
83 package EF renames Ada.Numerics.Elementary_Functions;
84
85 Float_Result : Float;
86 New_Float_Result : New_Float;
87
88 procedure Dont_Optimize_Float is new Dont_Optimize(Float);
89 procedure Dont_Optimize_New_Float is new Dont_Optimize(New_Float);
90
91 begin
92
93 -- Testing of Arctan Function, both instantiated and pre-instantiated
94 -- version.
95
96 -- Check that Argument_Error is raised by the Arctan function when
97 -- provided parameter values of 0.0, 0.0.
98
99 begin
100 New_Float_Result := GEF.Arctan(Y => 0.0, X => 0.0);
101 Report.Failed("Argument_Error not raised when the Arctan " &
102 "function is provided input of 0.0, 0.0");
103 Dont_Optimize_New_Float(New_Float_Result, 1);
104 exception
105 when Argument_Error => null; -- OK, expected exception.
106 when others =>
107 Report.Failed("Incorrect exception raised by the Arctan " &
108 "function when provided 0.0, 0.0 input parameters");
109 end;
110
111
112 -- Check that no exception is raised by the Arctan function when
113 -- provided a large positive or negative Y parameter value, when
114 -- using the default value for parameter X.
115
116 begin
117 Float_Result := EF.Arctan(Y => FXA5A00.Large);
118 Dont_Optimize_Float(Float_Result, 2);
119 exception
120 when others =>
121 Report.Failed("Exception raised when the Arctan function is " &
122 "provided a large positive Y parameter value");
123 end;
124
125 begin
126 New_Float_Result := GEF.Arctan(Y => New_Float(-FXA5A00.Large));
127 Dont_Optimize_New_Float(New_Float_Result, 3);
128 exception
129 when others =>
130 Report.Failed("Exception raised when the Arctan function is " &
131 "provided a large negative Y parameter value");
132 end;
133
134
135 -- Check that no exception is raised by the Arctan function when
136 -- provided a small positive or negative Y parameter value, when
137 -- using the default value for parameter X.
138
139 begin
140 Float_Result := EF.Arctan(Y => FXA5A00.Small);
141 Dont_Optimize_Float(Float_Result, 4);
142 exception
143 when others =>
144 Report.Failed("Exception raised when the Arctan function is " &
145 "provided a small positive Y parameter value");
146 end;
147
148 begin
149 New_Float_Result := GEF.Arctan(Y => New_Float(-FXA5A00.Small));
150 Dont_Optimize_New_Float(New_Float_Result, 5);
151 exception
152 when others =>
153 Report.Failed("Exception raised when the Arctan function is " &
154 "provided a small negative Y parameter value");
155 end;
156
157
158 -- Check that no exception is raised by the Arctan function when
159 -- provided combinations of large and small positive or negative
160 -- parameter values for both Y and X input parameters.
161
162 begin
163 Float_Result := EF.Arctan(Y => FXA5A00.Large, X => FXA5A00.Large);
164 Dont_Optimize_Float(Float_Result, 6);
165 exception
166 when others =>
167 Report.Failed("Exception raised when the Arctan function is " &
168 "provided large positive X and Y parameter values");
169 end;
170
171 begin
172 New_Float_Result := GEF.Arctan(New_Float(-FXA5A00.Large),
173 X => New_Float(FXA5A00.Small));
174 Dont_Optimize_New_Float(New_Float_Result, 7);
175 exception
176 when others =>
177 Report.Failed("Exception raised when the Arctan function is " &
178 "provided a large negative Y parameter value " &
179 "and a small positive X parameter value");
180 end;
181
182
183 begin
184 Float_Result := EF.Arctan(Y => FXA5A00.Small, X => FXA5A00.Large);
185 Dont_Optimize_Float(Float_Result, 8);
186 exception
187 when others =>
188 Report.Failed("Exception raised when the Arctan function is " &
189 "provided a small positive Y parameter value " &
190 "and a large positive X parameter value");
191 end;
192
193 begin
194 New_Float_Result := GEF.Arctan(New_Float(-FXA5A00.Small),
195 New_Float(-FXA5A00.Large));
196 Dont_Optimize_New_Float(New_Float_Result, 9);
197 exception
198 when others =>
199 Report.Failed("Exception raised when the Arctan function is " &
200 "provided a small negative Y parameter value " &
201 "and a large negative parameter value");
202 end;
203
204
205 -- Check that when the Arctan function is provided a Y parameter value
206 -- of 0.0 and a positive X parameter input value, the prescribed result
207 -- of zero is returned.
208
209 if GEF.Arctan(Y => 0.0) /= 0.0 or -- Default X value
210 EF.Arctan(Y => 0.0, X => FXA5A00.Large) /= 0.0 or
211 --pwb-math: Next line: changed 2.0*Pi to 360.0
212 GEF.Arctan(0.0, 360.0) /= 0.0 or
213 EF.Arctan(0.0, FXA5A00.Small) /= 0.0
214 then
215 Report.Failed("Incorrect results from the Arctan function when " &
216 "provided a Y parameter value of 0.0 and various " &
217 "positive X parameter values");
218 end if;
219
220
221 -- Check that the Arctan function provides correct results when provided
222 -- a variety of Y parameter values.
223
224 if not FXA5A00.Result_Within_Range(EF.Arctan(Pi), 1.26, 0.01) or
225 not FXA5A00.Result_Within_Range(EF.Arctan(-Pi), -1.26, 0.01) or
226 not FXA5A00.Result_Within_Range(GEF.Arctan(1.0), 0.785, 0.001) or
227 not FXA5A00.Result_Within_Range(EF.Arctan(-1.0), -0.785, 0.001) or
228 not FXA5A00.Result_Within_Range(GEF.Arctan(0.25), 0.245, 0.001) or
229 not FXA5A00.Result_Within_Range(EF.Arctan(0.92), 0.744, 0.001)
230 then
231 Report.Failed("Incorrect results from the Arctan function when " &
232 "provided a variety of Y parameter values");
233 end if;
234
235
236
237 -- Check the results of the Arctan function with specified cycle
238 -- parameter.
239
240 -- Check that the Arctan function with specified Cycle parameter
241 -- raises Argument_Error when the value of the Cycle parameter is zero
242 -- or negative.
243
244 begin
245 Float_Result := EF.Arctan(Y => Pi, Cycle => 0.0); -- Default X value
246 Report.Failed("Argument_Error not raised by the Arctan function " &
247 "with default X parameter value, when the Cycle " &
248 "parameter is 0.0");
249 Dont_Optimize_Float(Float_Result, 10);
250 exception
251 when Argument_Error => null; -- OK, expected exception.
252 when others =>
253 Report.Failed("Incorrect exception raised by the Arctan " &
254 "function with default X parameter value, when " &
255 "provided a 0.0 cycle parameter value");
256 end;
257
258 begin
259 New_Float_Result := GEF.Arctan(Y => Pi, X => 1.0, Cycle => 0.0);
260 Report.Failed("Argument_Error not raised by the Arctan function " &
261 "when the Cycle parameter is 0.0");
262 Dont_Optimize_New_Float(New_Float_Result, 11);
263 exception
264 when Argument_Error => null; -- OK, expected exception.
265 when others =>
266 Report.Failed("Incorrect exception raised by the Arctan " &
267 "function when provided a 0.0 cycle parameter " &
268 "value");
269 end;
270
271 begin
272 Float_Result := EF.Arctan(Y => Pi, Cycle => -360.0);
273 Report.Failed("Argument_Error not raised by the Arctan function " &
274 "with a default X parameter value, when the Cycle " &
275 "parameter is -360.0");
276 Dont_Optimize_Float(Float_Result, 12);
277 exception
278 when Argument_Error => null; -- OK, expected exception.
279 when others =>
280 Report.Failed("Incorrect exception raised by the Arctan " &
281 "function with a default X parameter value, when " &
282 "provided a -360.0 cycle parameter value");
283 end;
284
285 begin
286 New_Float_Result := GEF.Arctan(Y => Pi, X => 1.0, Cycle => -Pi);
287 Report.Failed("Argument_Error not raised by the Arctan function " &
288 "when the Cycle parameter is -Pi");
289 Dont_Optimize_New_Float(New_Float_Result, 13);
290 exception
291 when Argument_Error => null; -- OK, expected exception.
292 when others =>
293 Report.Failed("Incorrect exception raised by the Arctan " &
294 "function when provided a -Pi cycle parameter " &
295 "value");
296 end;
297
298
299 -- Check that no exception is raised by the Arctan function with
300 -- specified Cycle parameter, when provided large and small positive
301 -- or negative parameter values for both Y and X input parameters.
302
303 begin
304 Float_Result := EF.Arctan(Y => -FXA5A00.Large,
305 X => -FXA5A00.Large,
306 --pwb-math: Next line: changed 2.0*Pi to 360.0
307 Cycle => 360.0);
308 Dont_Optimize_Float(Float_Result, 14);
309 exception
310 when others =>
311 Report.Failed("Exception raised when the Arctan function with " &
312 "specified Cycle parameter, when provided large " &
313 "negative X and Y parameter values");
314 end;
315
316
317 begin
318 New_Float_Result := GEF.Arctan(New_Float(FXA5A00.Large),
319 X => New_Float(-FXA5A00.Small),
320 --pwb-math: Next line: changed 2.0*Pi to 360.0
321 Cycle => 360.0);
322 Dont_Optimize_New_Float(New_Float_Result, 15);
323 exception
324 when others =>
325 Report.Failed("Exception raised when the Arctan function with " &
326 "specified Cycle parameter, when provided large " &
327 "positive Y parameter value and a small negative " &
328 "X parameter value");
329 end;
330
331
332 begin
333 Float_Result := EF.Arctan(Y => -FXA5A00.Small,
334 X => -FXA5A00.Large,
335 --pwb-math: Next line: changed 2.0*Pi to 360.0
336 Cycle => 360.0);
337 Dont_Optimize_Float(Float_Result, 16);
338 exception
339 when others =>
340 Report.Failed("Exception raised when the Arctan function with " &
341 "specified Cycle parameter, when provided large " &
342 "negative Y parameter value and a large negative " &
343 "X parameter value");
344 end;
345
346 begin
347 New_Float_Result := GEF.Arctan(New_Float(FXA5A00.Small),
348 New_Float(FXA5A00.Large),
349 --pwb-math: Next line: changed 2.0*Pi to 360.0
350 360.0);
351 Dont_Optimize_New_Float(New_Float_Result, 17);
352 exception
353 when others =>
354 Report.Failed("Exception raised when the Arctan function with " &
355 "specified Cycle parameter, when provided a " &
356 "small negative Y parameter value and a large " &
357 "positive X parameter value");
358 end;
359
360
361 -- Check that the Arctan function with specified Cycle parameter
362 -- provides correct results when provided a variety of Y parameter
363 -- input values.
364
365 --pwb-math if not FXA5A00.Result_Within_Range(EF.Arctan(Pi, Cycle => 2.0*Pi),
366 --pwb-math 1.26,
367 --pwb-math 0.01) or
368 --pwb-math not FXA5A00.Result_Within_Range(EF.Arctan(-Pi, Cycle => 2.0*Pi),
369 --pwb-math -1.26,
370 --pwb-math 0.01) or
371 --pwb-math not FXA5A00.Result_Within_Range(GEF.Arctan(1.0, Cycle => 2.0*Pi),
372 --pwb-math 0.785,
373 --pwb-math 0.001) or
374 --pwb-math not FXA5A00.Result_Within_Range(EF.Arctan(-1.0, Cycle => 2.0*Pi),
375 --pwb-math -0.785,
376 --pwb-math 0.001) or
377 --pwb-math not FXA5A00.Result_Within_Range(GEF.Arctan(0.16, Cycle => 2.0*Pi),
378 --pwb-math 0.159,
379 --pwb-math 0.001) or
380 --pwb-math not FXA5A00.Result_Within_Range(EF.Arctan(1.0, Cycle => 360.0),
381 --pwb-math 45.0,
382 --pwb-math 0.1) or
383 --pwb-math not FXA5A00.Result_Within_Range(GEF.Arctan(1.0, Cycle => 100.0),
384 --pwb-math 12.5,
385 --pwb-math 0.1)
386
387 --pwb-math Next 12 lines are replacements for 21 commented lines above
388 if not FXA5A00.Result_Within_Range(GEF.Arctan(1.0, Cycle => 2.0*180.0),
389 45.0,
390 0.001) or
391 not FXA5A00.Result_Within_Range(EF.Arctan(-1.0, Cycle => 2.0*180.0),
392 -45.0,
393 0.001) or
394 not FXA5A00.Result_Within_Range(EF.Arctan(1.0, Cycle => 360.0),
395 45.0,
396 0.1) or
397 not FXA5A00.Result_Within_Range(GEF.Arctan(1.0, Cycle => 100.0),
398 12.5,
399 0.1)
400 then
401 Report.Failed("Incorrect results from the Arctan function with " &
402 "specified Cycle parameter when provided a variety " &
403 "of Y parameter values");
404 end if;
405
406
407 exception
408 when others => Report.Failed ("Exception raised in Test_Block");
409 end Test_Block;
410
411 Report.Result;
412
413 end CXA5A07;