1Host        = ee.ece.utah.edu
2Command     = ./talldp >>talldp.lst-intel-ia32-freebsd-c89-g 2>&1
3uname -a    = FreeBSD ee.ece.utah.edu 4.4-RELEASE FreeBSD 4.4-RELEASE #0: Tue Oct i386 unknown unknown FreeBSD
4Make flags  = -i NAME=intel-ia32-freebsd-c89-g CC=c89 CFLAGS=-g
5Date        = Tue May 28 14:59:26 MDT 2002
6----------------------------------------
7
8ibeta............       2
9it...............      53
10irnd.............       5
11ngrd.............       0
12machep...........     -52
13negep............     -53
14iexp.............      11
15minexp...........   -1022
16maxexp...........    1024
17eps..............   2.22044604925031308e-16
18epsneg...........   1.11022302462515654e-16
19xmin.............  2.22507385850720138e-308
20xmax.............  1.79769313486231571e+308
211TEST OF ALOG(X) VS T.S. EXPANSION OF ALOG(1+Y)
22
23
24   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
25      (1-EPS,1+EPS), WHERE EPS =     7.6294e-06
26
27
28 ALOG(X) WAS LARGER     0 TIMES,
29             AGREED  2000 TIMES, AND
30        WAS SMALLER     0 TIMES.
31
32
33 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
34
35
36 THE MAXIMUM RELATIVE ERROR OF     0.0000e+00 =    2 **-999.00
37    OCCURRED FOR X =     0.000000e+00
38 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
39
40
41 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     0.0000e+00 =    2 **-999.00
42 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
43
44
451TEST OF ALOG(X) VS ALOG(17X/16)-ALOG(17/16)
46
47
48   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
49      (     7.0711e-01,     9.3750e-01)
50
51
52 ALOG(X) WAS LARGER     0 TIMES,
53             AGREED  1718 TIMES, AND
54        WAS SMALLER   282 TIMES.
55
56
57 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
58
59
60 THE MAXIMUM RELATIVE ERROR OF     2.2185e-16 =    2 ** -52.00
61    OCCURRED FOR X =     7.786299e-01
62 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00
63
64
65 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     6.8010e-17 =    2 ** -53.71
66 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
67
68
691TEST OF ALOG10(X) VS ALOG10(11X/10)-ALOG10(11/10)
70
71
72   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
73      (     3.1623e-01,     9.0000e-01)
74
75
76 ALOG10(X) WAS LARGER     0 TIMES,
77               AGREED  1002 TIMES, AND
78          WAS SMALLER   998 TIMES.
79
80
81 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
82
83
84 THE MAXIMUM RELATIVE ERROR OF     4.5325e-16 =    2 ** -50.97
85    OCCURRED FOR X =     8.996477e-01
86 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.03
87
88
89 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.3742e-16 =    2 ** -52.69
90 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.31
91
92
931TEST OF ALOG(X*X) VS 2 * LOG(X)
94
95
96   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
97      (     1.6000e+01,     2.4000e+02)
98
99
100 ALOG(X) WAS LARGER    63 TIMES,
101             AGREED  1937 TIMES, AND
102        WAS SMALLER     0 TIMES.
103
104
105 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
106
107
108 THE MAXIMUM RELATIVE ERROR OF     2.2042e-16 =    2 ** -52.01
109    OCCURRED FOR X =     5.622823e+01
110 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.99
111
112
113 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     2.9630e-17 =    2 ** -54.91
114 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
115
116
1171SPECIAL TESTS
118
119
120 THE IDENTITY  ALOG(X) = -ALOG(1/X)  WILL BE TESTED.
121
122        X         F(X) + F(1/X)
123
124  1.5983318e+01  3.2244173e-16
125
126  1.5339606e+01 -1.1839488e-16
127
128  1.5347572e+01  2.8731358e-16
129
130  1.5813231e+01 -6.7437375e-17
131
132  1.5740176e+01 -1.7390603e-16
133
134
135
136 TEST OF SPECIAL ARGUMENTS
137
138
139 ALOG(1.0) =   0.0000000e+00
140
141
142 ALOG(XMIN) = ALOG( 2.2250739e-308) =  -7.0839642e+02
143
144
145 ALOG(XMAX) = ALOG( 1.7976931e+308) =   7.0978271e+02
146
147
1481TEST OF ERROR RETURNS
149
150
151 ALOG WILL BE CALLED WITH THE ARGUMENT    -2.0000e+00
152 THIS SHOULD TRIGGER AN ERROR MESSAGE
153
154
155 ALOG RETURNED THE VALUE            NaN
156
157
158 ALOG WILL BE CALLED WITH THE ARGUMENT     0.0000e+00
159 THIS SHOULD TRIGGER AN ERROR MESSAGE
160
161
162 ALOG RETURNED THE VALUE           -Inf
163
164
165
166 THIS CONCLUDES THE TESTS
1671TEST OF ASIN(X) VS TAYLOR SERIES
168
169   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
170      (    -1.2500e-01,     1.2500e-01)
171
172
173 ASIN(X) WAS LARGER   416 TIMES,
174             AGREED  1185 TIMES, AND
175        WAS SMALLER   399 TIMES.
176
177 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
178
179 THE MAXIMUM RELATIVE ERROR OF     2.5819e-16 =    2 ** -51.78
180    OCCURRED FOR X =    -1.072935e-01
181 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.22
182
183
184 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.0032e-16 =    2 ** -53.15
185 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
186
187
1881TEST OF ACOS(X) VS TAYLOR SERIES
189
190   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
191      (    -1.2500e-01,     1.2500e-01)
192
193
194 ACOS(X) WAS LARGER   494 TIMES,
195             AGREED  1054 TIMES, AND
196        WAS SMALLER   452 TIMES.
197
198 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
199
200 THE MAXIMUM RELATIVE ERROR OF     1.5360e-16 =    2 ** -52.53
201    OCCURRED FOR X =     1.248467e-01
202 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.47
203
204
205 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     9.7674e-17 =    2 ** -53.18
206 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
207
208
2091TEST OF ASIN(X) VS TAYLOR SERIES
210
211   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
212      (     7.5000e-01,     1.0000e+00)
213
214
215 ASIN(X) WAS LARGER   365 TIMES,
216             AGREED  1277 TIMES, AND
217        WAS SMALLER   358 TIMES.
218
219 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
220
221 THE MAXIMUM RELATIVE ERROR OF     2.2191e-16 =    2 ** -52.00
222    OCCURRED FOR X =     8.418029e-01
223 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00
224
225
226 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.0044e-16 =    2 ** -53.14
227 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
228
229
2301TEST OF ACOS(X) VS TAYLOR SERIES
231
232   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
233      (     7.5000e-01,     1.0000e+00)
234
235
236 ACOS(X) WAS LARGER   429 TIMES,
237             AGREED  1116 TIMES, AND
238        WAS SMALLER   455 TIMES.
239
240 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
241
242 THE MAXIMUM RELATIVE ERROR OF     4.2522e-16 =    2 ** -51.06
243    OCCURRED FOR X =     8.667282e-01
244 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.94
245
246
247 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.1398e-16 =    2 ** -52.96
248 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.04
249
250
2511TEST OF ACOS(X) VS TAYLOR SERIES
252
253   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
254      (    -1.0000e+00,    -7.5000e-01)
255
256
257 ACOS(X) WAS LARGER   409 TIMES,
258             AGREED  1163 TIMES, AND
259        WAS SMALLER   428 TIMES.
260
261 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
262
263 THE MAXIMUM RELATIVE ERROR OF     1.8358e-16 =    2 ** -52.27
264    OCCURRED FOR X =    -7.501318e-01
265 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.73
266
267
268 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.0794e-16 =    2 ** -53.04
269 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
270
271
2721SPECIAL TESTS
273
274 THE IDENTITY  ASIN(-X) = -ASIN(X)  WILL BE TESTED.
275
276        X         F(X) + F(-X)
277 -5.0384110e-01  3.7784446e-17
278
279 -5.1721352e-01  4.0115480e-18
280
281 -4.6127087e-01 -2.3418767e-17
282
283 -3.5739680e-01 -2.5939537e-17
284
285 -3.2497569e-01 -1.8973538e-19
286
287 THE IDENTITY ASIN(X) = X , X SMALL, WILL BE TESTED.
288
289        X         X - F(X)
290  8.2729394e-17 -9.1842784e-33
291
292  4.1364697e-17  0.0000000e+00
293
294  2.0682348e-17  0.0000000e+00
295
296  1.0341174e-17  0.0000000e+00
297
298  5.1705871e-18  0.0000000e+00
299
300 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.
301
302       ASIN(1.821832e-231) =1.821832e-231
303
3041TEST OF ERROR RETURNS
305
306
307 ASIN WILL BE CALLED WITH THE ARGUMENT     1.2000e+00
308 THIS SHOULD TRIGGER AN ERROR MESSAGE
309
310
311 ASIN RETURNED THE VALUE            NaN
312
313
314 THIS CONCLUDES THE TESTS
3151TEST OF ATAN(X) VS TRUNCATED TAYLOR SERIES
316
317   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
318      (    -6.2500e-02,     6.2500e-02)
319
320
321 ATAN(X) WAS LARGER     0 TIMES,
322             AGREED  1999 TIMES, AND
323        WAS SMALLER     1 TIMES.
324
325 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
326
327 THE MAXIMUM RELATIVE ERROR OF     1.1856e-16 =    2 ** -52.91
328    OCCURRED FOR X =    -5.859376e-02
329 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.09
330
331
332 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     2.6511e-18 =    2 ** -58.39
333 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
334
335
3361TEST OF ATAN(X) VS ATAN(1/16) + ATAN((X-1/16)/(1+X/16))
337
338   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
339      (     6.2500e-02,     2.6795e-01)
340
341
342 ATAN(X) WAS LARGER   265 TIMES,
343             AGREED  1509 TIMES, AND
344        WAS SMALLER   226 TIMES.
345
346 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
347
348 THE MAXIMUM RELATIVE ERROR OF     2.2199e-16 =    2 ** -52.00
349    OCCURRED FOR X =     1.256840e-01
350 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00
351
352
353 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     7.9412e-17 =    2 ** -53.48
354 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
355
356
3571TEST OF 2*ATAN(X) VS ATAN(2X/(1-X*X))
358
359   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
360      (     2.6795e-01,     4.1421e-01)
361
362
363 ATAN(X) WAS LARGER   269 TIMES,
364             AGREED  1416 TIMES, AND
365        WAS SMALLER   315 TIMES.
366
367 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
368
369 THE MAXIMUM RELATIVE ERROR OF     2.1197e-16 =    2 ** -52.07
370    OCCURRED FOR X =     2.680413e-01
371 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.93
372
373
374 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     9.3466e-17 =    2 ** -53.25
375 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
376
377
3781TEST OF 2*ATAN(X) VS ATAN(2X/(1-X*X))
379
380   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
381      (     4.1421e-01,     1.0000e+00)
382
383
384 ATAN(X) WAS LARGER   137 TIMES,
385             AGREED  1717 TIMES, AND
386        WAS SMALLER   146 TIMES.
387
388 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
389
390 THE MAXIMUM RELATIVE ERROR OF     2.2064e-16 =    2 ** -52.01
391    OCCURRED FOR X =     5.504280e-01
392 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.99
393
394
395 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.7452e-17 =    2 ** -53.95
396 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
397
398
3991SPECIAL TESTS
400
401 THE IDENTITY   ATAN(-X) = -ATAN(X)   WILL BE TESTED.
402
403
404        X         F(X) + F(-X)
405
406  2.4582943e+00 -3.9356539e-17
407
408  8.4901561e-01 -3.4694470e-18
409
410  8.6893012e-01  3.3285007e-17
411
412  2.0330784e+00  9.0856142e-17
413
414  1.8504397e+00 -2.9490299e-17
415
416 THE IDENTITY ATAN(X) = X , X SMALL, WILL BE TESTED.
417
418
419        X         X - F(X)
420
421  6.9279836e-17  0.0000000e+00
422
423  3.4639918e-17  0.0000000e+00
424
425  1.7319959e-17  0.0000000e+00
426
427  8.6599794e-18  0.0000000e+00
428
429  4.3299897e-18  0.0000000e+00
430
431 THE IDENTITY ATAN(X/Y) = ATAN2(X,Y) WILL BE TESTED
432 THE FIRST COLUMN OF RESULTS SHOULD BE 0, THE SECOND +-PI
433
434        X             Y     F1(X/Y)-F2(X,Y)F1(X/Y)-F2(X/(-Y))
435 -9.1978515e-01  5.8925193e-01 -2.2442985e-17  3.1415927e+00
436
437 -1.7546973e+00  2.1346841e-01 -2.9923980e-17  3.1415927e+00
438
439 -2.2456381e-01  2.9761609e-01  6.0173221e-18  3.1415927e+00
440
441 -9.9445784e-01  8.9905633e-01 -1.6263033e-18  3.1415927e+00
442
443  1.0204660e+00  6.9518594e-01 -1.8377227e-17 -3.1415927e+00
444
445 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.
446
447       ATAN(1.821832e-231) =1.821832e-231
4481TEST OF ERROR RETURNS
449
450
451 ATAN WILL BE CALLED WITH THE ARGUMENT 1.7976931e+308
452 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE
453
454
455       ATAN(1.797693e+308) = 1.570796e+00
456 ATAN2 WILL BE CALLED WITH THE ARGUMENTS
457  1.0000000e+00  0.0000000e+00
458
459 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE
460
461
462       ATAN2( 1.000000e+00 0.000000e+00) = 1.570796e+00
463 ATAN2 WILL BE CALLED WITH THE ARGUMENTS
464 2.2250739e-308 1.7976931e+308
465
466 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE
467
468
469       ATAN2(2.225074e-3081.797693e+308) = 0.000000e+00
470 ATAN2 WILL BE CALLED WITH THE ARGUMENTS
471 1.7976931e+308 2.2250739e-308
472
473 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE
474
475
476       ATAN2(1.797693e+3082.225074e-308) = 1.570796e+00
477 ATAN2 WILL BE CALLED WITH THE ARGUMENTS
478  0.0000000e+00  0.0000000e+00
479
480 THIS SHOULD TRIGGER AN ERROR MESSAGE
481
482
483       ATAN2( 0.000000e+00 0.000000e+00) = 0.000000e+00
484 THIS CONCLUDES THE TESTS
4851TEST OF EXP(X- 0.0625) VS EXP(X)/EXP( 0.0625)
486
487
488   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
489      (    -2.8407e-01,     3.4657e-01)
490
491
492 EXP(X-V) WAS LARGER   258 TIMES,
493              AGREED  1484 TIMES, AND
494         WAS SMALLER   258 TIMES.
495
496
497 THERE ARE   53 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
498
499
500 THE MAXIMUM RELATIVE ERROR OF     2.2196e-16 =    2 ** -52.00
501    OCCURRED FOR X =     6.288667e-02
502 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00
503
504
505 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     8.0711e-17 =    2 ** -53.46
506 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
507
508
5091TEST OF EXP(X- 2.8125) VS EXP(X)/EXP( 2.8125)
510
511
512   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
513      (    -3.4657e+00,    -6.7027e+02)
514
515
516 EXP(X-V) WAS LARGER   295 TIMES,
517              AGREED  1487 TIMES, AND
518         WAS SMALLER   218 TIMES.
519
520
521 THERE ARE   53 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
522
523
524 THE MAXIMUM RELATIVE ERROR OF     2.3097e-16 =    2 ** -51.94
525    OCCURRED FOR X =    -4.505452e+02
526 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.06
527
528
529 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     8.2787e-17 =    2 ** -53.42
530 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
531
532
5331TEST OF EXP(X- 2.8125) VS EXP(X)/EXP( 2.8125)
534
535
536   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
537      (     6.9315e+00,     7.0968e+02)
538
539
540 EXP(X-V) WAS LARGER   304 TIMES,
541              AGREED  1456 TIMES, AND
542         WAS SMALLER   240 TIMES.
543
544
545 THERE ARE   53 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
546
547
548 THE MAXIMUM RELATIVE ERROR OF     2.2146e-16 =    2 ** -52.00
549    OCCURRED FOR X =     2.731425e+02
550 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00
551
552
553 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     8.3696e-17 =    2 ** -53.41
554 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
555
556
5571SPECIAL TESTS
558
559
560 THE IDENTITY EXP(X)*EXP(-X) = 1.0  WILL BE TESTED.
561
562       X        F(X)*F(-X) - 1
563
564  7.8325859e-01  0.0000000e+00
565
566  4.1536184e-01  0.0000000e+00
567
568  2.8620958e-02  0.0000000e+00
569
570  1.2024206e+00  0.0000000e+00
571
572  1.8213778e+00  0.0000000e+00
573
574
575
576 TEST OF SPECIAL ARGUMENTS
577
578
579 EXP(0.0) - 1.0E0 =   0.0000000e+00
580
581 EXP(-7.080000e+02) =3.307553e-308
582
583 EXP( 7.090000e+02) =8.218407e+307
584
585 IF EXP( 3.545000e+02) = 9.065543e+153 IS NOT ABOUT
586 EXP( 1.772500e+02)**2 =9.065543e+153 THERE IS AN ARG RED ERROR
5871TEST OF ERROR RETURNS
588
589
590 EXP WILL BE CALLED WITH THE ARGUMENT   -6.7039e+153
591 THIS SHOULD TRIGGER AN ERROR MESSAGE
592
593
594 EXP RETURNED THE VALUE     0.0000e+00
595
596
597
598 EXP WILL BE CALLED WITH THE ARGUMENT    6.7039e+153
599 THIS SHOULD TRIGGER AN ERROR MESSAGE
600
601
602 EXP RETURNED THE VALUE            Inf
603
604
605
606 THIS CONCLUDES THE TESTS
6071TEST OF X**1.0 VS X
608
609
610   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
611      (     5.0000e-01,     1.0000e+00)
612
613
614 X**1.0 WAS LARGER     0 TIMES,
615            AGREED     0 TIMES, AND
616       WAS SMALLER  2000 TIMES.
617
618
619 THERE ARE   53 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
620
621
622 THE MAXIMUM RELATIVE ERROR OF      0.0000e+00 =    2 ** -999.00
623    OCCURRED FOR X =     0.000000e+00
624 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
625
626
627 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      0.0000e+00 =    2 **-999.00
628 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
629
630
6311TEST OF XSQ**1.5 VS XSQ*X
632
633
634   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
635      (     5.0000e-01,     1.0000e+00)
636
637
638 X**1.5 WAS LARGER   141 TIMES,
639            AGREED     0 TIMES, AND
640       WAS SMALLER  1859 TIMES.
641
642
643 THERE ARE   53 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
644
645
646 THE MAXIMUM RELATIVE ERROR OF      2.2131e-16 =    2 **  -52.00
647    OCCURRED FOR X =     5.005552e-01
648 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00
649
650
651 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      6.2277e-17 =    2 ** -53.83
652 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
653
654
6551TEST OF XSQ**1.5 VS XSQ*X
656
657
658   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
659      (     1.0000e+00,    5.6438e+102)
660
661
662 X**1.5 WAS LARGER   158 TIMES,
663            AGREED     0 TIMES, AND
664       WAS SMALLER  1842 TIMES.
665
666
667 THERE ARE   53 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
668
669
670 THE MAXIMUM RELATIVE ERROR OF      2.2011e-16 =    2 **  -52.01
671    OCCURRED FOR X =    8.914343e+101
672 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.99
673
674
675 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      6.5334e-17 =    2 ** -53.76
676 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
677
678
6791TEST OF X**Y VS XSQ**(Y/2)
680
681
682   2000 RANDOM ARGUMENTS WERE TESTED FROM THE REGION
683      X IN (     1.0000e-02,     1.0000e+01), Y IN (    -1.5413e+02,     1.5413e+02)
684
685
686 X**Y  WAS LARGER   944 TIMES,
687           AGREED     0 TIMES, AND
688      WAS SMALLER  1056 TIMES.
689
690
691 THERE ARE   53 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
692
693
694 THE MAXIMUM RELATIVE ERROR OF      8.2124e-15 =    2 **  -46.79
695    OCCURRED FOR X =     5.686868e+00 Y =     1.504408e+02
696 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   6.21
697
698
699 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      2.0843e-15 =    2 ** -48.77
700 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   4.23
701
702
7031SPECIAL TESTS
704
705
706 THE IDENTITY  X ** Y = (1/X) ** (-Y)  WILL BE TESTED.
707
708        X              Y         (X**Y-(1/X)**(-Y)) / X**Y
709
710  6.0384110e+00  6.1721352e+00       -4.4054454e-16
711
712  5.6127087e+00  4.5739680e+00       -1.7024686e-16
713
714  4.2497569e+00  8.4516013e+00        0.0000000e+00
715
716  2.2708162e+00  7.5027289e+00       -2.4175382e-16
717
718  6.1387364e+00  3.7554795e+00       -2.4953170e-16
719
7201TEST OF ERROR RETURNS
721
722
723 ( 2.0000000e+00) ** (-1.0220000e+03) WILL BE COMPUTED.
724 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE
725
726
727 THE VALUE RETURNED IS     2.2251e-308
728
729
730
731 ( 2.0000000e+00) ** ( 1.0230000e+03) WILL BE COMPUTED.
732 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE
733
734
735 THE VALUE RETURNED IS     8.9885e+307
736
737
738
739 ( 0.0000000e+00) ** ( 2.0000000e+00) WILL BE COMPUTED.
740 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE
741
742
743 THE VALUE RETURNED IS      0.0000e+00
744
745
746
747 (-2.0000000e+00) ** ( 0.0000000e+00) WILL BE COMPUTED.
748 THIS SHOULD TRIGGER AN ERROR MESSAGE
749
750
751 THE VALUE RETURNED IS      1.0000e+00
752
753
754
755 (-2.0000000e+00) ** ( 2.0000000e+00) WILL BE COMPUTED.
756 THIS SHOULD TRIGGER AN ERROR MESSAGE
757
758
759 THE VALUE RETURNED IS      4.0000e+00
760
761
762
763 ( 0.0000000e+00) ** ( 0.0000000e+00) WILL BE COMPUTED.
764 THIS SHOULD TRIGGER AN ERROR MESSAGE
765
766
767 THE VALUE RETURNED IS      1.0000e+00
768
769
770
771 THIS CONCLUDES THE TESTS
7721TEST OF SIN(X) VS 3*SIN(X/3)-4*SIN(X/3)**3
773
774   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
775      (     0.0000e+00,     1.5708e+00)
776
777
778 SIN(X) WAS LARGER   404 TIMES,
779            AGREED  1203 TIMES, AND
780       WAS SMALLER   393 TIMES.
781
782 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
783
784 THE MAXIMUM RELATIVE ERROR OF     2.4822e-16 =    2 ** -51.84
785    OCCURRED FOR X =     1.120528e-01
786 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.16
787
788
789 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     9.0431e-17 =    2 ** -53.30
790 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
791
792
7931TEST OF SIN(X) VS 3*SIN(X/3)-4*SIN(X/3)**3
794
795   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
796      (     1.8850e+01,     2.0420e+01)
797
798
799 SIN(X) WAS LARGER   384 TIMES,
800            AGREED  1266 TIMES, AND
801       WAS SMALLER   350 TIMES.
802
803 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
804
805 THE MAXIMUM RELATIVE ERROR OF     2.6086e-16 =    2 ** -51.77
806    OCCURRED FOR X =     1.886286e+01
807 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.23
808
809
810 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     8.5273e-17 =    2 ** -53.38
811 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
812
813
8141TEST OF COS(X) VS 4*COS(X/3)**3-3*COS(X/3)
815
816   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
817      (     2.1991e+01,     2.3562e+01)
818
819
820 COS(X) WAS LARGER   398 TIMES,
821            AGREED  1234 TIMES, AND
822       WAS SMALLER   368 TIMES.
823
824 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
825
826 THE MAXIMUM RELATIVE ERROR OF     2.8652e-16 =    2 ** -51.63
827    OCCURRED FOR X =     2.346492e+01
828 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.37
829
830
831 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     8.8469e-17 =    2 ** -53.33
832 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
833
834
8351SPECIAL TESTS
836
837 IF  1.000000e+00 IS NOT ALMOST 1.0E0,    SIN HAS THE WRONG PERIOD.
838
839 THE IDENTITY   SIN(-X) = -SIN(X)   WILL BE TESTED.
840     X        F(X) + F(-X)
841  7.3820383e+00 -1.1167282e-17
842
843  3.9146931e+00 -5.5077470e-17
844
845  2.6974617e-01  5.3668008e-18
846
847  1.1332547e+01  4.6024382e-17
848
849  1.7166081e+01 -3.8272337e-17
850
851 THE IDENTITY SIN(X) = X , X SMALL, WILL BE TESTED.
852    X         X - F(X)
853
854  5.7051156e-17  0.0000000e+00
855
856  2.8525578e-17  0.0000000e+00
857
858  1.4262789e-17  0.0000000e+00
859
860  7.1313945e-18  0.0000000e+00
861
862  3.5656973e-18  0.0000000e+00
863
864 THE IDENTITY   COS(-X) = COS(X)   WILL BE TESTED.
865        X         F(X) - F(-X)
866  4.4566459e+00  1.8919328e-17
867
868  4.8316547e+00 -5.7394953e-18
869
870  2.1326225e+00  1.5395671e-17
871
872  1.5061690e+01 -5.3668008e-18
873
874  2.2071794e+00  8.9446679e-18
875
876 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.
877
878
879       SIN(1.821832e-231) = 1.821832e-231
880 THE FOLLOWING THREE LINES ILLUSTRATE THE LOSS IN SIGNIFICANCE
881 FOR LARGE ARGUMENTS.  THE ARGUMENTS ARE CONSECUTIVE.
882
883       SIN( 9.490627e+07) = 9.419571e-01
884
885       SIN( 9.490627e+07) = 9.419571e-01
886
887       SIN( 9.490627e+07) = 9.419570e-01
8881TEST OF ERROR RETURNS
889
890
891 SIN WILL BE CALLED WITH THE ARGUMENT     9.0072e+15
892 THIS SHOULD TRIGGER AN ERROR MESSAGE
893
894
895 SIN RETURNED THE VALUE    -8.4893e-01
896
897
898
899 THIS CONCLUDES THE TESTS
9001TEST OF SINH(X) VS T.S. EXPANSION OF SINH(X)
901
902   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
903      (     0.0000e+00,     5.0000e-01)
904
905
906 SINH(X) WAS LARGER   272 TIMES,
907             AGREED  1441 TIMES, AND
908        WAS SMALLER   287 TIMES.
909
910
911 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
912
913
914 THE MAXIMUM RELATIVE ERROR OF     2.2125e-16 =    2 ** -52.01
915    OCCURRED FOR X =     6.268396e-02
916 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.99
917
918
919 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     8.2273e-17 =    2 ** -53.43
920 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
921
922
9231TEST OF COSH(X) VS T.S. EXPANSION OF COSH(X)
924
925   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
926      (     0.0000e+00,     5.0000e-01)
927
928
929 COSH(X) WAS LARGER    40 TIMES,
930             AGREED  1908 TIMES, AND
931        WAS SMALLER    52 TIMES.
932
933
934 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
935
936
937 THE MAXIMUM RELATIVE ERROR OF     2.2036e-16 =    2 ** -52.01
938    OCCURRED FOR X =     1.236239e-01
939 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.99
940
941
942 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.3957e-17 =    2 ** -54.34
943 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
944
945
9461TEST OF SINH(X) VS C*(SINH(X+1)+SINH(X-1))
947
948   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
949      (     3.0000e+00,     7.0978e+02)
950
951
952 SINH(X) WAS LARGER   996 TIMES,
953             AGREED   954 TIMES, AND
954        WAS SMALLER    50 TIMES.
955
956
957 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
958
959
960 THE MAXIMUM RELATIVE ERROR OF     3.3802e-16 =    2 ** -51.39
961    OCCURRED FOR X =     6.234122e+02
962 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.61
963
964
965 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.2498e-16 =    2 ** -52.83
966 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.17
967
968
9691TEST OF COSH(X) VS C*(COSH(X+1)+COSH(X-1))
970
971   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
972      (     3.0000e+00,     7.0978e+02)
973
974
975 COSH(X) WAS LARGER   984 TIMES,
976             AGREED   967 TIMES, AND
977        WAS SMALLER    49 TIMES.
978
979
980 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
981
982
983 THE MAXIMUM RELATIVE ERROR OF     3.4980e-16 =    2 ** -51.34
984    OCCURRED FOR X =     1.146079e+02
985 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.66
986
987
988 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.2337e-16 =    2 ** -52.85
989 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.15
990
991
9921SPECIAL TESTS
993
994 THE IDENTITY  SINH(-X) = -SINH(X)  WILL BE TESTED.
995
996        X            F(X) + F(-X)
997
998  1.4749766e+00  0.0000000e+00
999
1000  5.0940937e-01  0.0000000e+00
1001
1002  5.2135807e-01  0.0000000e+00
1003
1004  1.2198471e+00  0.0000000e+00
1005
1006  1.1102638e+00  0.0000000e+00
1007
1008 THE IDENTITY SINH(X) = X , X SMALL, WILL BE TESTED.
1009
1010        X         X - F(X)
1011
1012  6.9279836e-17  0.0000000e+00
1013
1014  3.4639918e-17  0.0000000e+00
1015
1016  1.7319959e-17  0.0000000e+00
1017
1018  8.6599794e-18  0.0000000e+00
1019
1020  4.3299897e-18  0.0000000e+00
1021
1022 THE IDENTITY  COSH(-X) = COSH(X)  WILL BE TESTED.
1023
1024        X         F(X) - F(-X)
1025
1026  8.1016114e-01  0.0000000e+00
1027
1028  1.7677558e+00  0.0000000e+00
1029
1030  1.8397699e-01  0.0000000e+00
1031
1032  6.4040522e-01  0.0000000e+00
1033
1034  1.3315771e+00  0.0000000e+00
1035
1036 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.
1037
1038      SINH(1.821832e-231) =1.821832e-231
1039
10401TEST OF ERROR RETURNS
1041
1042
1043 SINH WILL BE CALLED WITH THE ARGUMENT     7.0991e+02
1044 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE
1045
1046
1047 SINH RETURNED THE VALUE    1.0185e+308
1048
1049
1050
1051SINH WILL BE CALLED WITH THE ARGUMENT     9.0072e+15
1052 THIS SHOULD TRIGGER AN ERROR MESSAGE
1053
1054
1055 SINH RETURNED THE VALUE            Inf
1056
1057
1058
1059 THIS CONCLUDES THE TESTS
1060
10611TEST OF SQRT(X*X) - X
1062
1063
1064   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
1065       (     7.0711e-01,     1.0000e+00)
1066
1067
1068 SQRT(X) WAS LARGER     0 TIMES,
1069             AGREED  2000 TIMES, AND
1070        WAS SMALLER     0 TIMES.
1071
1072
1073 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
1074
1075
1076 THE MAXIMUM RELATIVE ERROR OF     0.0000e+00 =    2 **-999.00
1077    OCCURRED FOR X =     0.000000e+00
1078 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
1079
1080
1081 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     0.0000e+00 =    2 **-999.00
1082 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
1083
1084
10851TEST OF SQRT(X*X) - X
1086
1087
1088   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
1089       (     1.0000e+00,     1.4142e+00)
1090
1091
1092 SQRT(X) WAS LARGER     0 TIMES,
1093             AGREED  2000 TIMES, AND
1094        WAS SMALLER     0 TIMES.
1095
1096
1097 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
1098
1099
1100 THE MAXIMUM RELATIVE ERROR OF     0.0000e+00 =    2 **-999.00
1101    OCCURRED FOR X =     0.000000e+00
1102 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
1103
1104
1105 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     0.0000e+00 =    2 **-999.00
1106 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
1107
1108
11091TEST OF SPECIAL ARGUMENTS
1110
1111
1112 SQRT(XMIN) = SQRT( 2.2250739e-308) =  1.4916681e-154
1113
1114
1115 SQRT(1-EPSNEG) = SQRT(1-  1.1102230e-16) =   1.0000000e+00
1116
1117
1118 SQRT(1.0) = SQRT(  1.0000000e+00) =   1.0000000e+00
1119
1120
1121 SQRT(1+EPS) = SQRT(1+  2.2204460e-16) =   1.0000000e+00
1122
1123
1124 SQRT(XMAX) = SQRT( 1.7976931e+308) =  1.3407808e+154
1125
1126
11271TEST OF ERROR RETURNS
1128
1129
1130 SQRT WILL BE CALLED WITH THE ARGUMENT      0.0000e+00
1131 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE
1132
1133
1134 SQRT RETURNED THE VALUE      0.0000e+00
1135
1136
1137
1138SQRT WILL BE CALLED WITH THE ARGUMENT     -1.0000e+00
1139 THIS SHOULD TRIGGER AN ERROR MESSAGE
1140
1141
1142 SQRT RETURNED THE VALUE             NaN
1143
1144
1145
1146 THIS CONCLUDES THE TESTS
11471TEST OF TAN(X) VS 2*TAN(X/2)/(1-TAN(X/2)**2)
1148
1149
1150   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
1151    (     0.0000e+00,     7.8540e-01)
1152
1153
1154 TAN(X) WAS LARGER   467 TIMES,
1155            AGREED  1097 TIMES, AND
1156       WAS SMALLER   436 TIMES.
1157
1158 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
1159
1160
1161 THE MAXIMUM RELATIVE ERROR OF     3.9035e-16 =    2 ** -51.19
1162    OCCURRED FOR X =     2.771006e-01
1163 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.81
1164
1165
1166 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.0950e-16 =    2 ** -53.02
1167 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
1168
1169
11701TEST OF TAN(X) VS 2*TAN(X/2)/(1-TAN(X/2)**2)
1171
1172
1173   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
1174    (     2.7489e+00,     3.5343e+00)
1175
1176
1177 TAN(X) WAS LARGER   364 TIMES,
1178            AGREED  1293 TIMES, AND
1179       WAS SMALLER   343 TIMES.
1180
1181 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
1182
1183
1184 THE MAXIMUM RELATIVE ERROR OF     2.7828e-16 =    2 ** -51.67
1185    OCCURRED FOR X =     3.191421e+00
1186 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.33
1187
1188
1189 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     9.6273e-17 =    2 ** -53.21
1190 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
1191
1192
11931TEST OF TAN(X) VS 2*TAN(X/2)/(1-TAN(X/2)**2)
1194
1195
1196   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
1197    (     1.8850e+01,     1.9635e+01)
1198
1199
1200 TAN(X) WAS LARGER   445 TIMES,
1201            AGREED  1074 TIMES, AND
1202       WAS SMALLER   481 TIMES.
1203
1204 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
1205
1206
1207 THE MAXIMUM RELATIVE ERROR OF     4.3423e-16 =    2 ** -51.03
1208    OCCURRED FOR X =     1.903901e+01
1209 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.97
1210
1211
1212 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.1360e-16 =    2 ** -52.97
1213 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.03
1214
1215
12161TEST OF COT(X) VS (COT(X/2)**2-1)/(2*COT(X/2))
1217
1218
1219   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
1220    (     1.8850e+01,     1.9635e+01)
1221
1222
1223 COT(X) WAS LARGER   381 TIMES,
1224            AGREED  1223 TIMES, AND
1225       WAS SMALLER   396 TIMES.
1226
1227
1228 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
1229
1230
1231 THE MAXIMUM RELATIVE ERROR OF     3.2058e-16 =    2 ** -51.47
1232    OCCURRED FOR X =     1.947482e+01
1233 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.53
1234
1235
1236 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.0360e-16 =    2 ** -53.10
1237 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
1238
1239
12401SPECIAL TESTS
1241
1242
1243 THE IDENTITY  TAN(-X) = -TAN(X)  WILL BE TESTED.
1244
1245        X         F(X) + F(-X)
1246
1247  9.2675513e+00  2.6834004e-18
1248
1249  3.2007135e+00 -9.1479558e-19
1250
1251  3.2757894e+00 -8.5380921e-19
1252
1253  7.6645251e+00 -1.2836954e-16
1254
1255  6.9759933e+00 -8.7278275e-18
1256
1257 THE IDENTITY TAN(X) = X , X SMALL, WILL BE TESTED.
1258
1259        X         X - F(X)
1260
1261  6.9279836e-17  0.0000000e+00
1262
1263  3.4639918e-17  0.0000000e+00
1264
1265  1.7319959e-17  0.0000000e+00
1266
1267  8.6599794e-18  0.0000000e+00
1268
1269  4.3299897e-18  0.0000000e+00
1270
1271 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.
1272
1273       TAN(1.821832e-231) =1.821832e-231
1274
1275 THE RELATIVE ERROR IN TAN(11) IS  5.4049159e-17 =    2 ** -54.04 WHERE
1276
1277      TAN( 1.100000e+01) =-2.259508e+02
1278
1279 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
1280
1281
12821TEST OF ERROR RETURNS
1283
1284
1285 TAN WILL BE CALLED WITH THE ARGUMENT     6.7109e+07
1286 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE
1287
1288
1289 TAN RETURNED THE VALUE    -4.6381e-01
1290
1291
1292
1293
1294TAN WILL BE CALLED WITH THE ARGUMENT     9.0072e+15
1295 THIS SHOULD TRIGGER AN ERROR MESSAGE
1296
1297
1298 TAN RETURNED THE VALUE     1.6063e+00
1299
1300
1301
1302 THIS CONCLUDES THE TESTS
13031TEST OF TANH(X) VS (TANH(X-1/8)+TANH(1/8))/(1+TANH(X-1/8)TANH(1/8))
1304
1305   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
1306      (     1.2500e-01,     5.4931e-01)
1307
1308
1309 TANH(X) WAS LARGER   620 TIMES,
1310             AGREED   863 TIMES, AND
1311        WAS SMALLER   517 TIMES.
1312
1313 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
1314
1315 THE MAXIMUM RELATIVE ERROR OF     4.4440e-16 =    2 ** -51.00
1316    OCCURRED FOR X =     5.488338e-01
1317 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.00
1318
1319
1320 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.4005e-16 =    2 ** -52.66
1321 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.34
1322
1323
13241TEST OF TANH(X) VS (TANH(X-1/8)+TANH(1/8))/(1+TANH(X-1/8)TANH(1/8))
1325
1326   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
1327      (     6.7431e-01,     1.9408e+01)
1328
1329
1330 TANH(X) WAS LARGER   579 TIMES,
1331             AGREED   941 TIMES, AND
1332        WAS SMALLER   480 TIMES.
1333
1334 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER
1335
1336 THE MAXIMUM RELATIVE ERROR OF     3.6158e-16 =    2 ** -51.30
1337    OCCURRED FOR X =     7.154747e-01
1338 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.70
1339
1340
1341 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     9.2767e-17 =    2 ** -53.26
1342 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00
1343
1344
13451SPECIAL TESTS
1346
1347 THE IDENTITY   TANH(-X) = -TANH(X)   WILL BE TESTED.
1348
1349
1350        X         F(X) + F(-X)
1351
1352  5.5568571e-02  0.0000000e+00
1353
1354  2.5889429e-01  0.0000000e+00
1355
1356  2.2333500e-01  0.0000000e+00
1357
1358  6.0939174e-01  0.0000000e+00
1359
1360  7.4587289e-01  0.0000000e+00
1361
1362 THE IDENTITY TANH(X) = X , X SMALL, WILL BE TESTED.
1363
1364
1365        X         X - F(X)
1366
1367  2.9291640e-17  0.0000000e+00
1368
1369  1.4645820e-17  0.0000000e+00
1370
1371  7.3229100e-18  0.0000000e+00
1372
1373  3.6614550e-18  0.0000000e+00
1374
1375  1.8307275e-18  0.0000000e+00
1376
1377 THE IDENTITY TANH(X) = 1 , X LARGE, WILL BE TESTED.
1378
1379
1380        X         1 - F(X)
1381
1382  1.9408121e+01  0.0000000e+00
1383
1384  2.3408121e+01  0.0000000e+00
1385
1386  2.7408121e+01  0.0000000e+00
1387
1388  3.1408121e+01  0.0000000e+00
1389
1390  3.5408121e+01  0.0000000e+00
1391
1392 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.
1393
1394       TANH(1.821832e-231) =1.821832e-231
1395 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT 1.7976931e+308
1396       TANH(1.797693e+308) = 1.000000e+00
1397 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT 2.2250739e-308
1398       TANH(2.225074e-308) =2.225074e-308
1399 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT  0.0000000e+00
1400       TANH( 0.000000e+00) = 0.000000e+00
1401 THIS CONCLUDES THE TESTS
1402