1-- CXA5A08.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 Arccot provides correct results.
28--
29-- TEST DESCRIPTION:
30--      This test examines both the version of Arccot resulting from the
31--      instantiation of the Ada.Numerics.Generic_Elementary_Functions
32--      with 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--         CXA5A08.A
45--
46--
47-- CHANGE HISTORY:
48--      06 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--      18 Apr 96   SAIC    Incorporated reviewer comments for ACVC 2.1.
53--      28 Feb 97   CTA.PWB Removed checks with explicit Cycle => 2.0*Pi
54--
55-- CHANGE NOTE:
56--      According to Ken Dritz, author of the Numerics Annex of the RM,
57--      one should never specify the cycle 2.0*Pi for the trigonometric
58--      functions.  In particular, if the machine number for the first
59--      argument is not an exact multiple of the machine number for the
60--      explicit cycle, then the specified exact results cannot be
61--      reasonably expected.  The affected checks in this test have been
62--      marked as comments, with the additional notation "pwb-math".
63--      Phil Brashear
64--!
65
66with Ada.Exceptions;
67with Ada.Numerics.Elementary_Functions;
68with Ada.Numerics.Generic_Elementary_Functions;
69with FXA5A00;
70with Report;
71
72procedure CXA5A08 is
73begin
74
75   Report.Test ("CXA5A08", "Check that the Arccot function provides " &
76                           "correct results");
77
78   Test_Block:
79   declare
80
81      use Ada.Exceptions;
82      use Ada.Numerics;
83      use FXA5A00;
84
85      package GEF is new Ada.Numerics.Generic_Elementary_Functions(New_Float);
86      package  EF renames Ada.Numerics.Elementary_Functions;
87
88      Float_Result      : Float;
89      Angle             : Float;
90      New_Float_Result  : New_Float;
91      New_Float_Angle   : New_Float;
92      Incorrect_Inverse : Boolean := False;
93
94      procedure Dont_Optimize_Float     is new Dont_Optimize(Float);
95      procedure Dont_Optimize_New_Float is new Dont_Optimize(New_Float);
96
97   begin
98
99      -- Testing of Arccot Function, both instantiated and pre-instantiated
100      -- version.
101
102      -- Check that Argument_Error is raised by the Arccot function when
103      -- provided parameter values of 0.0, 0.0.
104
105      begin
106         New_Float_Result := GEF.Arccot(X => 0.0, Y => 0.0);
107         Report.Failed("Argument_Error not raised when the Arccot " &
108                       "function is provided input of 0.0, 0.0");
109         Dont_Optimize_New_Float(New_Float_Result, 1);
110      exception
111         when Argument_Error => null;  -- OK, expected exception.
112         when others         =>
113            Report.Failed("Incorrect exception raised by the Arccot " &
114                          "function when provided 0.0, 0.0 input parameters");
115      end;
116
117
118      -- Check that no exception is raised by the Arccot function when
119      -- provided a large positive or negative X parameter value, when
120      -- using the default value for parameter Y.
121
122      begin
123         Float_Result := EF.Arccot(X => FXA5A00.Large);
124         Dont_Optimize_Float(Float_Result, 2);
125      exception
126         when others =>
127            Report.Failed("Exception raised when the Arccot function is " &
128                          "provided a large positive X parameter value");
129      end;
130
131      begin
132         New_Float_Result := GEF.Arccot(X => New_Float(-FXA5A00.Large));
133         Dont_Optimize_New_Float(New_Float_Result, 3);
134      exception
135         when others =>
136            Report.Failed("Exception raised when the Arccot function is " &
137                          "provided a large negative X parameter value");
138      end;
139
140
141      -- Check that no exception is raised by the Arccot function when
142      -- provided a small positive or negative X parameter value, when
143      -- using the default value for parameter Y.
144
145      begin
146         Float_Result := EF.Arccot(X => FXA5A00.Small);
147         Dont_Optimize_Float(Float_Result, 4);
148      exception
149         when others =>
150            Report.Failed("Exception raised when the Arccot function is " &
151                          "provided a small positive X parameter value");
152      end;
153
154      begin
155         New_Float_Result := GEF.Arccot(X => New_Float(-FXA5A00.Small));
156         Dont_Optimize_New_Float(New_Float_Result, 5);
157      exception
158         when others =>
159            Report.Failed("Exception raised when the Arccot function is " &
160                          "provided a small negative X parameter value");
161      end;
162
163
164      -- Check that no exception is raised by the Arccot function when
165      -- provided combinations of large and small positive or negative
166      -- parameter values for both X and Y input parameters.
167
168      begin
169         Float_Result := EF.Arccot(X => FXA5A00.Large, Y => FXA5A00.Large);
170         Dont_Optimize_Float(Float_Result, 6);
171      exception
172         when others =>
173            Report.Failed("Exception raised when the Arccot function is " &
174                          "provided large positive X and Y parameter values");
175      end;
176
177      begin
178         New_Float_Result := GEF.Arccot(New_Float(-FXA5A00.Large),
179                                        Y => New_Float(FXA5A00.Small));
180         Dont_Optimize_New_Float(New_Float_Result, 7);
181      exception
182         when others =>
183            Report.Failed("Exception raised when the Arccot function is " &
184                          "provided a large negative X parameter value "  &
185                          "and a small positive Y parameter value");
186      end;
187
188
189      begin
190         Float_Result := EF.Arccot(X => FXA5A00.Small, Y => FXA5A00.Large);
191         Dont_Optimize_Float(Float_Result, 8);
192      exception
193         when others =>
194            Report.Failed("Exception raised when the Arccot function is " &
195                          "provided a small positive X parameter value "  &
196                          "and a large positive Y parameter value");
197      end;
198
199      begin
200         New_Float_Result := GEF.Arccot(New_Float(-FXA5A00.Small),
201                                        New_Float(-FXA5A00.Large));
202         Dont_Optimize_New_Float(New_Float_Result, 9);
203      exception
204         when others =>
205            Report.Failed("Exception raised when the Arccot function is " &
206                          "provided a small negative X parameter value "  &
207                          "and a large negative Y parameter value");
208      end;
209
210
211      -- Check that when the Arccot function is provided a Y parameter value
212      -- of 0.0 and a positive X parameter input value, the prescribed result
213      -- of zero is returned.
214
215      if  EF.Arccot(X => FXA5A00.Large, Y => 0.0)                 /= 0.0 or
216         GEF.Arccot(2.0*Pi, Y => 0.0)                             /= 0.0 or
217          EF.Arccot(FXA5A00.Small, 0.0)                           /= 0.0 or
218          EF.Arccot(X => FXA5A00.Large, Y => 0.0, Cycle => 360.0) /= 0.0 or
219         GEF.Arccot(2.0*Pi, Y => 0.0, Cycle => 360.0)             /= 0.0 or
220          EF.Arccot(FXA5A00.Small, 0.0, Cycle => 360.0)           /= 0.0
221      then
222         Report.Failed("Incorrect results from the Arccot function when " &
223                       "provided a Y parameter value of 0.0 and various " &
224                       "positive X parameter values");
225      end if;
226
227
228      -- Check that the Arccot function provides correct results when
229      -- provided a variety of X parameter values.
230
231      if not Result_Within_Range( EF.Arccot( 1.0), Pi/4.0, 0.001)     or
232         not Result_Within_Range(GEF.Arccot( 0.0), Pi/2.0, 0.001)     or
233         not Result_Within_Range( EF.Arccot(-1.0), 3.0*Pi/4.0, 0.001)
234      then
235         Report.Failed("Incorrect results from the Arccot function when " &
236                       "provided a variety of Y parameter values");
237      end if;
238
239
240      -- Check the results of the Arccot function with specified cycle
241      -- parameter.
242
243      -- Check that the Arccot function with specified Cycle parameter
244      -- raises Argument_Error when the value of the Cycle parameter is zero
245      -- or negative.
246
247      begin
248         Float_Result := EF.Arccot(X => Pi, Cycle => 0.0);  -- Default Y value
249         Report.Failed("Argument_Error not raised by the Arccot function " &
250                       "with default Y parameter value, when the Cycle "   &
251                       "parameter is 0.0");
252         Dont_Optimize_Float(Float_Result, 10);
253      exception
254         when Argument_Error => null;  -- OK, expected exception.
255         when others         =>
256            Report.Failed("Incorrect exception raised by the Arccot "      &
257                          "function with default Y parameter value, when " &
258                          "provided a 0.0 cycle parameter value");
259      end;
260
261      begin
262         New_Float_Result := GEF.Arccot(X => Pi, Y => 1.0, Cycle => 0.0);
263         Report.Failed("Argument_Error not raised by the Arccot function " &
264                       "when the Cycle parameter is 0.0");
265         Dont_Optimize_New_Float(New_Float_Result, 11);
266      exception
267         when Argument_Error => null;  -- OK, expected exception.
268         when others         =>
269            Report.Failed("Incorrect exception raised by the Arccot "     &
270                          "function when provided a 0.0 cycle parameter " &
271                          "value");
272      end;
273
274      begin
275         Float_Result := EF.Arccot(X => Pi, Cycle => -360.0);
276         Report.Failed("Argument_Error not raised by the Arccot function " &
277                       "with a default Y parameter value, when the Cycle " &
278                       "parameter is -360.0");
279         Dont_Optimize_Float(Float_Result, 12);
280      exception
281         when Argument_Error => null;  -- OK, expected exception.
282         when others         =>
283            Report.Failed("Incorrect exception raised by the Arccot "        &
284                          "function with a default Y parameter value, when " &
285                          "provided a -360.0 cycle parameter value");
286      end;
287
288      begin
289         New_Float_Result := GEF.Arccot(X => Pi, Y => 1.0, Cycle => -Pi);
290         Report.Failed("Argument_Error not raised by the Arccot function " &
291                       "when the Cycle parameter is -Pi");
292         Dont_Optimize_New_Float(New_Float_Result, 13);
293      exception
294         when Argument_Error => null;  -- OK, expected exception.
295         when others         =>
296            Report.Failed("Incorrect exception raised by the Arccot "     &
297                          "function when provided a -Pi cycle parameter " &
298                          "value");
299      end;
300
301
302      -- Check that no exception is raised by the Arccot function with
303      -- specified Cycle parameter, when provided large and small positive
304      -- or negative parameter values for both X and Y input parameters.
305
306      begin
307         Float_Result := EF.Arccot(X     => -FXA5A00.Large,
308                                   Y     => -FXA5A00.Large,
309--pwb-math  Next line: changed 2.0*Pi to 360.0
310                                   Cycle => 360.0);
311         Dont_Optimize_Float(Float_Result, 14);
312      exception
313         when others =>
314            Report.Failed("Exception raised when the Arccot function with " &
315                          "specified Cycle parameter, when provided large " &
316                          "negative X and Y parameter values");
317      end;
318
319
320      begin
321         New_Float_Result := GEF.Arccot(New_Float(FXA5A00.Large),
322                                        Y     => New_Float(-FXA5A00.Small),
323--pwb-math  Next line: changed 2.0*Pi to 360.0
324                                        Cycle => 360.0);
325         Dont_Optimize_New_Float(New_Float_Result, 15);
326      exception
327         when others =>
328            Report.Failed("Exception raised when the Arccot function with "  &
329                          "specified Cycle parameter, when provided large "  &
330                          "positive X parameter value and a small negative " &
331                          "Y parameter value");
332      end;
333
334
335      begin
336         Float_Result := EF.Arccot(X     => -FXA5A00.Small,
337                                   Y     => -FXA5A00.Large,
338--pwb-math  Next line: changed 2.0*Pi to 360.0
339                                   Cycle => 360.0);
340         Dont_Optimize_Float(Float_Result, 16);
341      exception
342         when others =>
343            Report.Failed("Exception raised when the Arccot function with "  &
344                          "specified Cycle parameter, when provided small "  &
345                          "negative X parameter value and a large negative " &
346                          "Y parameter value");
347      end;
348
349      begin
350         New_Float_Result := GEF.Arccot(New_Float(FXA5A00.Small),
351                                        New_Float(FXA5A00.Large),
352--pwb-math  Next line: changed 2.0*Pi to 360.0
353                                        360.0);
354         Dont_Optimize_New_Float(New_Float_Result, 17);
355      exception
356         when others =>
357            Report.Failed("Exception raised when the Arccot function with " &
358                          "specified Cycle parameter, when provided a "     &
359                          "small positive X parameter value and a large "   &
360                          "positive Y parameter value");
361      end;
362
363
364      -- Check that the Arccot function with specified Cycle parameter
365      -- provides correct results when provided a variety of X parameter
366      -- input values.
367
368      if not FXA5A00.Result_Within_Range(GEF.Arccot( 0.0, Cycle => 360.0),
369                                         90.0,
370                                         0.001) or
371         not FXA5A00.Result_Within_Range(EF.Arccot( 0.0, Cycle => 100.0),
372                                         25.0,
373                                         0.001) or
374         not FXA5A00.Result_Within_Range(GEF.Arccot( 1.0, Cycle => 360.0),
375                                         45.0,
376                                         0.001) or
377         not FXA5A00.Result_Within_Range(EF.Arccot( 1.0, Cycle => 100.0),
378                                         12.5,
379                                         0.001) or
380         not FXA5A00.Result_Within_Range(GEF.Arccot(-1.0, Cycle => 360.0),
381                                         135.0,
382                                         0.001) or
383         not FXA5A00.Result_Within_Range(EF.Arccot(-1.0, Cycle => 100.0),
384                                         37.5,
385                                         0.001)
386      then
387         Report.Failed("Incorrect results from the Arccot function with "   &
388                       "specified Cycle parameter when provided a variety " &
389                       "of X parameter values");
390      end if;
391
392
393      if not FXA5A00.Result_Within_Range(EF.Arccot(0.2425355, 0.9701420),
394                                         EF.Arccot(0.25),
395                                         0.01) or
396         not FXA5A00.Result_Within_Range(EF.Arccot(0.3162277, 0.9486831),
397                                         Ef.Arccot(0.33),
398                                         0.01)
399      then
400         Report.Failed("Incorrect results from the Arccot function with " &
401                       "comparison to other Arccot function results");
402      end if;
403
404
405      if not FXA5A00.Result_Within_Range(EF.Cot(EF.Arccot(0.4472135,
406                                                          0.8944270)),
407                                         0.5,
408                                         0.01) or
409         not FXA5A00.Result_Within_Range(EF.Cot(EF.Arccot(0.9987380,
410                                                          0.0499369)),
411                                         20.0,
412                                         0.1)
413      then
414         Report.Failed("Incorrect results from the Arccot function when " &
415                       "used as argument to Cot function");
416      end if;
417
418
419      -- Check that inverse function results are correct.
420      -- Default Cycle test.
421
422      Angle := 0.001;
423      while Angle < Pi and not Incorrect_Inverse loop
424         if not Result_Within_Range(EF.Arccot(EF.Cot(Angle)), Angle, 0.001)
425         then
426            Incorrect_Inverse := True;
427         end if;
428         Angle := Angle + 0.001;
429      end loop;
430
431      if Incorrect_Inverse then
432         Report.Failed("Incorrect results returned from the Inverse "    &
433                       "comparison of Cot and Arccot using the default " &
434                       "cycle value");
435         Incorrect_Inverse := False;
436      end if;
437
438      -- Non-Default Cycle test.
439
440      New_Float_Angle := 0.01;
441      while New_Float_Angle < 180.0 and not Incorrect_Inverse loop
442         if not Result_Within_Range(EF.Arccot(EF.Cot(Float(New_Float_Angle),
443                                                     Cycle => 360.0),
444                                              Cycle => 360.0),
445                                    Float(New_Float_Angle),
446                                    0.01)  or
447            not Result_Within_Range(GEF.Arccot(
448                                       New_Float(GEF.Cot(New_Float_Angle,
449                                                         Cycle => 360.0)),
450                                       Cycle => 360.0),
451                                    Float(New_Float_Angle),
452                                    0.01)
453         then
454            Incorrect_Inverse := True;
455         end if;
456         New_Float_Angle := New_Float_Angle + 0.01;
457      end loop;
458
459      if Incorrect_Inverse then
460         Report.Failed("Incorrect results returned from the Inverse "    &
461                       "comparison of Cot and Arccot using non-default " &
462                       "cycle value");
463      end if;
464
465
466   exception
467      when The_Error : others =>
468         Report.Failed ("The following exception was raised in the " &
469                        "Test_Block: " & Exception_Name(The_Error));
470   end Test_Block;
471
472   Report.Result;
473
474end CXA5A08;
475