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1 149 jeremybenn
-- CXG2014.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
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--     to do so.
15
--
16
--                                    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
20
--     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.
24
--*
25
--
26
-- OBJECTIVE:
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--      Check that the SINH and COSH functions return
28
--      results that are within the error bound allowed.
29
--
30
-- TEST DESCRIPTION:
31
--      This test consists of a generic package that is
32
--      instantiated to check both Float and a long float type.
33
--      The test for each floating point type is divided into
34
--      several parts:
35
--         Special value checks where the result is a known constant.
36
--         Checks that use an identity for determining the result.
37
--         Exception checks.
38
--
39
-- SPECIAL REQUIREMENTS
40
--      The Strict Mode for the numerical accuracy must be
41
--      selected.  The method by which this mode is selected
42
--      is implementation dependent.
43
--
44
-- APPLICABILITY CRITERIA:
45
--      This test applies only to implementations supporting the
46
--      Numerics Annex.
47
--      This test only applies to the Strict Mode for numerical
48
--      accuracy.
49
--
50
--
51
-- CHANGE HISTORY:
52
--      15 Mar 96   SAIC    Initial release for 2.1
53
--      03 Jun 98   EDS     In line 80, change 1000 to 1024, making it a model
54
--                          number.  Add Taylor Series terms in line 281.
55
--      15 Feb 99   RLB     Repaired Subtraction_Error_Test to avoid precision
56
--                          problems.
57
--!
58
 
59
--
60
-- References:
61
--
62
-- Software Manual for the Elementary Functions
63
-- William J. Cody, Jr. and William Waite
64
-- Prentice-Hall, 1980
65
--
66
-- CRC Standard Mathematical Tables
67
-- 23rd Edition
68
--
69
-- Implementation and Testing of Function Software
70
-- W. J. Cody
71
-- Problems and Methodologies in Mathematical Software Production
72
-- editors P. C. Messina and A. Murli
73
-- Lecture Notes in Computer Science   Volume 142
74
-- Springer Verlag, 1982
75
--
76
 
77
with System;
78
with Report;
79
with Ada.Numerics.Generic_Elementary_Functions;
80
procedure CXG2014 is
81
   Verbose : constant Boolean := False;
82
   Max_Samples : constant := 1024;
83
 
84
   E  : constant := Ada.Numerics.E;
85
   Cosh1 : constant := (E + 1.0 / E) / 2.0;    -- cosh(1.0)
86
 
87
   generic
88
      type Real is digits <>;
89
   package Generic_Check is
90
      procedure Do_Test;
91
   end Generic_Check;
92
 
93
   package body Generic_Check is
94
      package Elementary_Functions is new
95
           Ada.Numerics.Generic_Elementary_Functions (Real);
96
      function Sinh (X : Real) return Real renames
97
           Elementary_Functions.Sinh;
98
      function Cosh (X : Real) return Real renames
99
           Elementary_Functions.Cosh;
100
      function Log (X : Real) return Real renames
101
           Elementary_Functions.Log;
102
 
103
      -- flag used to terminate some tests early
104
      Accuracy_Error_Reported : Boolean := False;
105
 
106
 
107
      procedure Check (Actual, Expected : Real;
108
                       Test_Name : String;
109
                       MRE : Real) is
110
         Max_Error : Real;
111
         Rel_Error : Real;
112
         Abs_Error : Real;
113
      begin
114
         -- In the case where the expected result is very small or 0
115
         -- we compute the maximum error as a multiple of Model_Small instead
116
         -- of Model_Epsilon and Expected.
117
         Rel_Error := MRE * abs Expected * Real'Model_Epsilon;
118
         Abs_Error := MRE * Real'Model_Small;
119
         if Rel_Error > Abs_Error then
120
            Max_Error := Rel_Error;
121
         else
122
            Max_Error := Abs_Error;
123
         end if;
124
 
125
         if abs (Actual - Expected) > Max_Error then
126
            Accuracy_Error_Reported := True;
127
            Report.Failed (Test_Name &
128
                           " actual: " & Real'Image (Actual) &
129
                           " expected: " & Real'Image (Expected) &
130
                           " difference: " & Real'Image (Actual - Expected) &
131
                           " max err:" & Real'Image (Max_Error) );
132
         elsif Verbose then
133
            if Actual = Expected then
134
               Report.Comment (Test_Name & "  exact result");
135
            else
136
               Report.Comment (Test_Name & "  passed");
137
            end if;
138
         end if;
139
      end Check;
140
 
141
 
142
      procedure Special_Value_Test is
143
         -- In the following tests the expected result is accurate
144
         -- to the machine precision so the minimum guaranteed error
145
         -- bound can be used.
146
         Minimum_Error : constant := 8.0;
147
      begin
148
         Check (Sinh (1.0),
149
                (E - 1.0 / E) / 2.0,
150
                "sinh(1)",
151
                Minimum_Error);
152
         Check (Cosh (1.0),
153
                Cosh1,
154
                "cosh(1)",
155
                Minimum_Error);
156
         Check (Sinh (2.0),
157
                (E * E - (1.0 / (E * E))) / 2.0,
158
                "sinh(2)",
159
                Minimum_Error);
160
         Check (Cosh (2.0),
161
                (E * E + (1.0 / (E * E))) / 2.0,
162
                "cosh(2)",
163
                Minimum_Error);
164
         Check (Sinh (-1.0),
165
                (1.0 / E - E) / 2.0,
166
                "sinh(-1)",
167
                Minimum_Error);
168
      exception
169
         when Constraint_Error =>
170
            Report.Failed ("Constraint_Error raised in special value test");
171
         when others =>
172
            Report.Failed ("exception in special value test");
173
      end Special_Value_Test;
174
 
175
 
176
 
177
      procedure Exact_Result_Test is
178
         No_Error : constant := 0.0;
179
      begin
180
         -- A.5.1(38);6.0
181
         Check (Sinh (0.0),  0.0, "sinh(0)", No_Error);
182
         Check (Cosh (0.0),  1.0, "cosh(0)", No_Error);
183
      exception
184
         when Constraint_Error =>
185
            Report.Failed ("Constraint_Error raised in Exact_Result Test");
186
         when others =>
187
            Report.Failed ("exception in Exact_Result Test");
188
      end Exact_Result_Test;
189
 
190
 
191
      procedure Identity_1_Test is
192
      -- For the Sinh test use the identity
193
      --    2 * Sinh(x) * Cosh(1) = Sinh(x+1) + Sinh (x-1)
194
      -- which is transformed to
195
      --    Sinh(x) = ((Sinh(x+1) + Sinh(x-1)) * C
196
      -- where C = 1/(2*Cosh(1))
197
      --
198
      -- For the Cosh test use the identity
199
      --    2 * Cosh(x) * Cosh(1) = Cosh(x+1) + Cosh(x-1)
200
      -- which is transformed to
201
      --    Cosh(x) = C * (Cosh(x+1) + Cosh(x-1))
202
      -- where C is the same as above
203
      --
204
      -- see Cody pg 230-231 for details on the error analysis.
205
      -- The net result is a relative error bound of 16 * Model_Epsilon.
206
 
207
         A : constant := 3.0;
208
            -- large upper bound but not so large as to cause Cosh(B)
209
            -- to overflow
210
         B : constant Real := Log(Real'Safe_Last) - 2.0;
211
         X_Minus_1, X, X_Plus_1 : Real;
212
         Actual1, Actual2 : Real;
213
         C : constant := 1.0 / (2.0 * Cosh1);
214
      begin
215
         Accuracy_Error_Reported := False;  -- reset
216
         for I in 1..Max_Samples loop
217
            -- make sure there is no error in x-1, x, and x+1
218
            X_Plus_1 :=  (B - A) * Real (I) / Real (Max_Samples) + A;
219
            X_Plus_1  := Real'Machine (X_Plus_1);
220
            X         := Real'Machine (X_Plus_1 - 1.0);
221
            X_Minus_1 := Real'Machine (X - 1.0);
222
 
223
            -- Sinh(x) = ((Sinh(x+1) + Sinh(x-1)) * C
224
            Actual1 := Sinh(X);
225
            Actual2 := C * (Sinh(X_Plus_1) + Sinh(X_Minus_1));
226
 
227
            Check (Actual1, Actual2,
228
                   "Identity_1_Test " & Integer'Image (I) & ": sinh(" &
229
                   Real'Image (X) & ") ",
230
                   16.0);
231
 
232
            -- Cosh(x) = C * (Cosh(x+1) + Cosh(x-1))
233
            Actual1 := Cosh (X);
234
            Actual2 := C * (Cosh(X_Plus_1) + Cosh (X_Minus_1));
235
            Check (Actual1, Actual2,
236
                   "Identity_1_Test " & Integer'Image (I) & ": cosh(" &
237
                   Real'Image (X) & ") ",
238
                   16.0);
239
 
240
            if Accuracy_Error_Reported then
241
              -- only report the first error in this test in order to keep
242
              -- lots of failures from producing a huge error log
243
              return;
244
            end if;
245
 
246
         end loop;
247
 
248
      exception
249
         when Constraint_Error =>
250
            Report.Failed
251
               ("Constraint_Error raised in Identity_1_Test" &
252
                " for X=" & Real'Image (X));
253
         when others =>
254
            Report.Failed ("exception in Identity_1_Test" &
255
                " for X=" & Real'Image (X));
256
      end Identity_1_Test;
257
 
258
 
259
 
260
      procedure Subtraction_Error_Test is
261
      -- This test detects the error resulting from subtraction if
262
      -- the obvious algorithm was used for computing sinh.  That is,
263
      -- it it is computed as (e**x - e**-x)/2.
264
      -- We check the result by using a Taylor series expansion that
265
      -- will produce a result accurate to the machine precision for
266
      -- the range under test.
267
      --
268
      -- The maximum relative error bound for this test is
269
      --  8 for the sinh operation and 7 for the Taylor series
270
      -- for a total of 15 * Model_Epsilon
271
         A : constant := 0.0;
272
         B : constant := 0.5;
273
         X : Real;
274
         X_Squared : Real;
275
         Actual, Expected : Real;
276
      begin
277
         if Real'digits > 15 then
278
             return; -- The approximation below is not accurate beyond
279
                     -- 15 digits. Adding more terms makes the error
280
                     -- larger, so it makes the test worse for more normal
281
                     -- values. Thus, we skip this subtest for larger than
282
                     -- 15 digits.
283
         end if;
284
         Accuracy_Error_Reported := False;  -- reset
285
         for I in 1..Max_Samples loop
286
            X :=  (B - A) * Real (I) / Real (Max_Samples) + A;
287
            X_Squared := X * X;
288
 
289
            Actual := Sinh(X);
290
 
291
            -- The Taylor series regrouped a bit
292
            Expected :=
293
               X * (1.0 + (X_Squared / 6.0) *
294
                          (1.0 + (X_Squared/20.0) *
295
                                 (1.0 + (X_Squared/42.0) *
296
                                        (1.0 + (X_Squared/72.0) *
297
                                               (1.0 + (X_Squared/110.0) *
298
                                                      (1.0 + (X_Squared/156.0)
299
                   ))))));
300
 
301
            Check (Actual, Expected,
302
                   "Subtraction_Error_Test " & Integer'Image (I) & ": sinh(" &
303
                   Real'Image (X) & ") ",
304
                   15.0);
305
 
306
            if Accuracy_Error_Reported then
307
              -- only report the first error in this test in order to keep
308
              -- lots of failures from producing a huge error log
309
              return;
310
            end if;
311
 
312
         end loop;
313
 
314
      exception
315
         when Constraint_Error =>
316
            Report.Failed
317
               ("Constraint_Error raised in Subtraction_Error_Test");
318
         when others =>
319
            Report.Failed ("exception in Subtraction_Error_Test");
320
      end Subtraction_Error_Test;
321
 
322
 
323
      procedure Exception_Test is
324
         X1, X2 : Real := 0.0;
325
      begin
326
         -- this part of the test is only applicable if 'Machine_Overflows
327
         -- is true.
328
         if Real'Machine_Overflows then
329
 
330
            begin
331
              X1 := Sinh (Real'Safe_Last / 2.0);
332
              Report.Failed ("no exception for sinh overflow");
333
            exception
334
               when Constraint_Error => null;
335
               when others =>
336
                  Report.Failed ("wrong exception sinh overflow");
337
            end;
338
 
339
            begin
340
              X2 := Cosh (Real'Safe_Last / 2.0);
341
              Report.Failed ("no exception for cosh overflow");
342
            exception
343
               when Constraint_Error => null;
344
               when others =>
345
                  Report.Failed ("wrong exception cosh overflow");
346
            end;
347
 
348
         end if;
349
 
350
         -- optimizer thwarting
351
         if Report.Ident_Bool (False) then
352
            Report.Comment (Real'Image (X1 + X2));
353
         end if;
354
      end Exception_Test;
355
 
356
 
357
      procedure Do_Test is
358
      begin
359
         Special_Value_Test;
360
         Exact_Result_Test;
361
         Identity_1_Test;
362
         Subtraction_Error_Test;
363
         Exception_Test;
364
      end Do_Test;
365
   end Generic_Check;
366
 
367
   -----------------------------------------------------------------------
368
   -----------------------------------------------------------------------
369
   package Float_Check is new Generic_Check (Float);
370
 
371
   -- check the floating point type with the most digits
372
   type A_Long_Float is digits System.Max_Digits;
373
   package A_Long_Float_Check is new Generic_Check (A_Long_Float);
374
 
375
   -----------------------------------------------------------------------
376
   -----------------------------------------------------------------------
377
 
378
 
379
begin
380
   Report.Test ("CXG2014",
381
                "Check the accuracy of the SINH and COSH functions");
382
 
383
   if Verbose then
384
      Report.Comment ("checking Standard.Float");
385
   end if;
386
 
387
   Float_Check.Do_Test;
388
 
389
   if Verbose then
390
      Report.Comment ("checking a digits" &
391
                      Integer'Image (System.Max_Digits) &
392
                      " floating point type");
393
   end if;
394
 
395
   A_Long_Float_Check.Do_Test;
396
 
397
 
398
   Report.Result;
399
end CXG2014;

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