]>
Commit | Line | Data |
---|---|---|
1 | <html> | |
2 | <head> | |
3 | <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> | |
4 | <title>Tables of Error Rates for all Functions</title> | |
5 | <link rel="stylesheet" href="../../math.css" type="text/css"> | |
6 | <meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> | |
7 | <link rel="home" href="../../index.html" title="Math Toolkit 2.5.1"> | |
8 | <link rel="up" href="../logs_and_tables.html" title="Error logs and tables"> | |
9 | <link rel="prev" href="../logs_and_tables.html" title="Error logs and tables"> | |
10 | <link rel="next" href="logs.html" title="Error Logs For Error Rate Tables"> | |
11 | </head> | |
12 | <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> | |
13 | <table cellpadding="2" width="100%"><tr> | |
14 | <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> | |
15 | <td align="center"><a href="../../../../../../index.html">Home</a></td> | |
16 | <td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> | |
17 | <td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> | |
18 | <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> | |
19 | <td align="center"><a href="../../../../../../more/index.htm">More</a></td> | |
20 | </tr></table> | |
21 | <hr> | |
22 | <div class="spirit-nav"> | |
23 | <a accesskey="p" href="../logs_and_tables.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../logs_and_tables.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="logs.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> | |
24 | </div> | |
25 | <div class="section"> | |
26 | <div class="titlepage"><div><div><h3 class="title"> | |
27 | <a name="math_toolkit.logs_and_tables.all_table"></a><a class="link" href="all_table.html" title="Tables of Error Rates for all Functions">Tables of Error | |
28 | Rates for all Functions</a> | |
29 | </h3></div></div></div> | |
30 | <div class="table"> | |
31 | <a name="math_toolkit.logs_and_tables.all_table.table_beta"></a><p class="title"><b>Table 17.3. Error rates for beta</b></p> | |
32 | <div class="table-contents"><table class="table" summary="Error rates for beta"> | |
33 | <colgroup> | |
34 | <col> | |
35 | <col> | |
36 | <col> | |
37 | <col> | |
38 | <col> | |
39 | </colgroup> | |
40 | <thead><tr> | |
41 | <th> | |
42 | </th> | |
43 | <th> | |
44 | <p> | |
45 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
46 | </p> | |
47 | </th> | |
48 | <th> | |
49 | <p> | |
50 | GNU C++ version 5.1.0<br> linux<br> long double | |
51 | </p> | |
52 | </th> | |
53 | <th> | |
54 | <p> | |
55 | GNU C++ version 5.1.0<br> linux<br> double | |
56 | </p> | |
57 | </th> | |
58 | <th> | |
59 | <p> | |
60 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
61 | </p> | |
62 | </th> | |
63 | </tr></thead> | |
64 | <tbody> | |
65 | <tr> | |
66 | <td> | |
67 | <p> | |
68 | Beta Function: Small Values | |
69 | </p> | |
70 | </td> | |
71 | <td> | |
72 | <p> | |
73 | <span class="blue">Max = 1.75ε (Mean = 0.828ε)</span> | |
74 | </p> | |
75 | </td> | |
76 | <td> | |
77 | <p> | |
78 | <span class="blue">Max = 2.65ε (Mean = 1.22ε)</span><br> <br> | |
79 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 11.9ε (Mean = 7.03ε)) | |
80 | </p> | |
81 | </td> | |
82 | <td> | |
83 | <p> | |
84 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
85 | 1.16:</em></span> Max = 3.94ε (Mean = 1.44ε))<br> (<span class="emphasis"><em>Rmath | |
86 | 3.0.2:</em></span> Max = 1.14ε (Mean = 0.601ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
87 | Max = 1.97ε (Mean = 0.934ε)) | |
88 | </p> | |
89 | </td> | |
90 | <td> | |
91 | <p> | |
92 | <span class="blue">Max = 2.86ε (Mean = 1.31ε)</span> | |
93 | </p> | |
94 | </td> | |
95 | </tr> | |
96 | <tr> | |
97 | <td> | |
98 | <p> | |
99 | Beta Function: Medium Values | |
100 | </p> | |
101 | </td> | |
102 | <td> | |
103 | <p> | |
104 | <span class="blue">Max = 99.1ε (Mean = 22.4ε)</span> | |
105 | </p> | |
106 | </td> | |
107 | <td> | |
108 | <p> | |
109 | <span class="blue">Max = 60.4ε (Mean = 19.4ε)</span><br> <br> | |
110 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.07e+03ε (Mean = | |
111 | 264ε)) | |
112 | </p> | |
113 | </td> | |
114 | <td> | |
115 | <p> | |
116 | <span class="blue">Max = 0.978ε (Mean = 0.0578ε)</span><br> | |
117 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.18e+03ε (Mean = 238ε))<br> | |
118 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 1.09e+03ε (Mean = 265ε))<br> | |
119 | (<span class="emphasis"><em>Cephes:</em></span> Max = 1.5e+03ε (Mean = 329ε)) | |
120 | </p> | |
121 | </td> | |
122 | <td> | |
123 | <p> | |
124 | <span class="blue">Max = 107ε (Mean = 24.5ε)</span> | |
125 | </p> | |
126 | </td> | |
127 | </tr> | |
128 | <tr> | |
129 | <td> | |
130 | <p> | |
131 | Beta Function: Divergent Values | |
132 | </p> | |
133 | </td> | |
134 | <td> | |
135 | <p> | |
136 | <span class="blue">Max = 10.7ε (Mean = 2.22ε)</span> | |
137 | </p> | |
138 | </td> | |
139 | <td> | |
140 | <p> | |
141 | <span class="blue">Max = 10.3ε (Mean = 2.41ε)</span><br> <br> | |
142 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 128ε (Mean = 23.8ε)) | |
143 | </p> | |
144 | </td> | |
145 | <td> | |
146 | <p> | |
147 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
148 | 1.16:</em></span> Max = 12.1ε (Mean = 1.99ε))<br> (<span class="emphasis"><em>Rmath | |
149 | 3.0.2:</em></span> Max = 176ε (Mean = 28ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
150 | Max = 175ε (Mean = 22ε)) | |
151 | </p> | |
152 | </td> | |
153 | <td> | |
154 | <p> | |
155 | <span class="blue">Max = 19.7ε (Mean = 2.75ε)</span> | |
156 | </p> | |
157 | </td> | |
158 | </tr> | |
159 | </tbody> | |
160 | </table></div> | |
161 | </div> | |
162 | <br class="table-break"><div class="table"> | |
163 | <a name="math_toolkit.logs_and_tables.all_table.table_beta_incomplete_"></a><p class="title"><b>Table 17.4. Error rates for beta (incomplete)</b></p> | |
164 | <div class="table-contents"><table class="table" summary="Error rates for beta (incomplete)"> | |
165 | <colgroup> | |
166 | <col> | |
167 | <col> | |
168 | <col> | |
169 | <col> | |
170 | <col> | |
171 | </colgroup> | |
172 | <thead><tr> | |
173 | <th> | |
174 | </th> | |
175 | <th> | |
176 | <p> | |
177 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
178 | </p> | |
179 | </th> | |
180 | <th> | |
181 | <p> | |
182 | GNU C++ version 5.1.0<br> linux<br> double | |
183 | </p> | |
184 | </th> | |
185 | <th> | |
186 | <p> | |
187 | GNU C++ version 5.1.0<br> linux<br> long double | |
188 | </p> | |
189 | </th> | |
190 | <th> | |
191 | <p> | |
192 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
193 | </p> | |
194 | </th> | |
195 | </tr></thead> | |
196 | <tbody> | |
197 | <tr> | |
198 | <td> | |
199 | <p> | |
200 | Incomplete Beta Function: Small Values | |
201 | </p> | |
202 | </td> | |
203 | <td> | |
204 | <p> | |
205 | <span class="blue">Max = 11.1ε (Mean = 2.28ε)</span> | |
206 | </p> | |
207 | </td> | |
208 | <td> | |
209 | <p> | |
210 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
211 | </p> | |
212 | </td> | |
213 | <td> | |
214 | <p> | |
215 | <span class="blue">Max = 12.5ε (Mean = 2.01ε)</span> | |
216 | </p> | |
217 | </td> | |
218 | <td> | |
219 | <p> | |
220 | <span class="blue">Max = 18.7ε (Mean = 3.19ε)</span> | |
221 | </p> | |
222 | </td> | |
223 | </tr> | |
224 | <tr> | |
225 | <td> | |
226 | <p> | |
227 | Incomplete Beta Function: Medium Values | |
228 | </p> | |
229 | </td> | |
230 | <td> | |
231 | <p> | |
232 | <span class="blue">Max = 91.1ε (Mean = 12.7ε)</span> | |
233 | </p> | |
234 | </td> | |
235 | <td> | |
236 | <p> | |
237 | <span class="blue">Max = 0.568ε (Mean = 0.0342ε)</span> | |
238 | </p> | |
239 | </td> | |
240 | <td> | |
241 | <p> | |
242 | <span class="blue">Max = 67.1ε (Mean = 13.3ε)</span> | |
243 | </p> | |
244 | </td> | |
245 | <td> | |
246 | <p> | |
247 | <span class="blue">Max = 174ε (Mean = 25ε)</span> | |
248 | </p> | |
249 | </td> | |
250 | </tr> | |
251 | <tr> | |
252 | <td> | |
253 | <p> | |
254 | Incomplete Beta Function: Large and Diverse Values | |
255 | </p> | |
256 | </td> | |
257 | <td> | |
258 | <p> | |
259 | <span class="blue">Max = 635ε (Mean = 29.5ε)</span> | |
260 | </p> | |
261 | </td> | |
262 | <td> | |
263 | <p> | |
264 | <span class="blue">Max = 0.999ε (Mean = 0.0399ε)</span> | |
265 | </p> | |
266 | </td> | |
267 | <td> | |
268 | <p> | |
269 | <span class="blue">Max = 6.84e+04ε (Mean = 2.76e+03ε)</span> | |
270 | </p> | |
271 | </td> | |
272 | <td> | |
273 | <p> | |
274 | <span class="blue">Max = 6.86e+04ε (Mean = 2.79e+03ε)</span> | |
275 | </p> | |
276 | </td> | |
277 | </tr> | |
278 | <tr> | |
279 | <td> | |
280 | <p> | |
281 | Incomplete Beta Function: Small Integer Values | |
282 | </p> | |
283 | </td> | |
284 | <td> | |
285 | <p> | |
286 | <span class="blue">Max = 26.8ε (Mean = 6.61ε)</span> | |
287 | </p> | |
288 | </td> | |
289 | <td> | |
290 | <p> | |
291 | <span class="blue">Max = 0.786ε (Mean = 0.0248ε)</span> | |
292 | </p> | |
293 | </td> | |
294 | <td> | |
295 | <p> | |
296 | <span class="blue">Max = 10.2ε (Mean = 3.49ε)</span> | |
297 | </p> | |
298 | </td> | |
299 | <td> | |
300 | <p> | |
301 | <span class="blue">Max = 51.8ε (Mean = 11ε)</span> | |
302 | </p> | |
303 | </td> | |
304 | </tr> | |
305 | </tbody> | |
306 | </table></div> | |
307 | </div> | |
308 | <br class="table-break"><div class="table"> | |
309 | <a name="math_toolkit.logs_and_tables.all_table.table_betac"></a><p class="title"><b>Table 17.5. Error rates for betac</b></p> | |
310 | <div class="table-contents"><table class="table" summary="Error rates for betac"> | |
311 | <colgroup> | |
312 | <col> | |
313 | <col> | |
314 | <col> | |
315 | <col> | |
316 | <col> | |
317 | </colgroup> | |
318 | <thead><tr> | |
319 | <th> | |
320 | </th> | |
321 | <th> | |
322 | <p> | |
323 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
324 | </p> | |
325 | </th> | |
326 | <th> | |
327 | <p> | |
328 | GNU C++ version 5.1.0<br> linux<br> double | |
329 | </p> | |
330 | </th> | |
331 | <th> | |
332 | <p> | |
333 | GNU C++ version 5.1.0<br> linux<br> long double | |
334 | </p> | |
335 | </th> | |
336 | <th> | |
337 | <p> | |
338 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
339 | </p> | |
340 | </th> | |
341 | </tr></thead> | |
342 | <tbody> | |
343 | <tr> | |
344 | <td> | |
345 | <p> | |
346 | Incomplete Beta Function: Small Values | |
347 | </p> | |
348 | </td> | |
349 | <td> | |
350 | <p> | |
351 | <span class="blue">Max = 12ε (Mean = 2.43ε)</span> | |
352 | </p> | |
353 | </td> | |
354 | <td> | |
355 | <p> | |
356 | <span class="blue">Max = 0.676ε (Mean = 0.0302ε)</span> | |
357 | </p> | |
358 | </td> | |
359 | <td> | |
360 | <p> | |
361 | <span class="blue">Max = 7.75ε (Mean = 1.91ε)</span> | |
362 | </p> | |
363 | </td> | |
364 | <td> | |
365 | <p> | |
366 | <span class="blue">Max = 12.6ε (Mean = 3.02ε)</span> | |
367 | </p> | |
368 | </td> | |
369 | </tr> | |
370 | <tr> | |
371 | <td> | |
372 | <p> | |
373 | Incomplete Beta Function: Medium Values | |
374 | </p> | |
375 | </td> | |
376 | <td> | |
377 | <p> | |
378 | <span class="blue">Max = 91.3ε (Mean = 14.8ε)</span> | |
379 | </p> | |
380 | </td> | |
381 | <td> | |
382 | <p> | |
383 | <span class="blue">Max = 0.949ε (Mean = 0.0944ε)</span> | |
384 | </p> | |
385 | </td> | |
386 | <td> | |
387 | <p> | |
388 | <span class="blue">Max = 63.5ε (Mean = 13.4ε)</span> | |
389 | </p> | |
390 | </td> | |
391 | <td> | |
392 | <p> | |
393 | <span class="blue">Max = 97.6ε (Mean = 24.3ε)</span> | |
394 | </p> | |
395 | </td> | |
396 | </tr> | |
397 | <tr> | |
398 | <td> | |
399 | <p> | |
400 | Incomplete Beta Function: Large and Diverse Values | |
401 | </p> | |
402 | </td> | |
403 | <td> | |
404 | <p> | |
405 | <span class="blue">Max = 3.72e+003ε (Mean = 113ε)</span> | |
406 | </p> | |
407 | </td> | |
408 | <td> | |
409 | <p> | |
410 | <span class="blue">Max = 1.12ε (Mean = 0.0458ε)</span> | |
411 | </p> | |
412 | </td> | |
413 | <td> | |
414 | <p> | |
415 | <span class="blue">Max = 1.05e+05ε (Mean = 5.45e+03ε)</span> | |
416 | </p> | |
417 | </td> | |
418 | <td> | |
419 | <p> | |
420 | <span class="blue">Max = 1.04e+05ε (Mean = 5.46e+03ε)</span> | |
421 | </p> | |
422 | </td> | |
423 | </tr> | |
424 | <tr> | |
425 | <td> | |
426 | <p> | |
427 | Incomplete Beta Function: Small Integer Values | |
428 | </p> | |
429 | </td> | |
430 | <td> | |
431 | <p> | |
432 | <span class="blue">Max = 26.7ε (Mean = 6.67ε)</span> | |
433 | </p> | |
434 | </td> | |
435 | <td> | |
436 | <p> | |
437 | <span class="blue">Max = 0.586ε (Mean = 0.0314ε)</span> | |
438 | </p> | |
439 | </td> | |
440 | <td> | |
441 | <p> | |
442 | <span class="blue">Max = 10.4ε (Mean = 3.54ε)</span> | |
443 | </p> | |
444 | </td> | |
445 | <td> | |
446 | <p> | |
447 | <span class="blue">Max = 103ε (Mean = 17.4ε)</span> | |
448 | </p> | |
449 | </td> | |
450 | </tr> | |
451 | </tbody> | |
452 | </table></div> | |
453 | </div> | |
454 | <br class="table-break"><div class="table"> | |
455 | <a name="math_toolkit.logs_and_tables.all_table.table_binomial_coefficient"></a><p class="title"><b>Table 17.6. Error rates for binomial_coefficient</b></p> | |
456 | <div class="table-contents"><table class="table" summary="Error rates for binomial_coefficient"> | |
457 | <colgroup> | |
458 | <col> | |
459 | <col> | |
460 | <col> | |
461 | <col> | |
462 | <col> | |
463 | </colgroup> | |
464 | <thead><tr> | |
465 | <th> | |
466 | </th> | |
467 | <th> | |
468 | <p> | |
469 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
470 | </p> | |
471 | </th> | |
472 | <th> | |
473 | <p> | |
474 | GNU C++ version 5.1.0<br> linux<br> double | |
475 | </p> | |
476 | </th> | |
477 | <th> | |
478 | <p> | |
479 | GNU C++ version 5.1.0<br> linux<br> long double | |
480 | </p> | |
481 | </th> | |
482 | <th> | |
483 | <p> | |
484 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
485 | </p> | |
486 | </th> | |
487 | </tr></thead> | |
488 | <tbody> | |
489 | <tr> | |
490 | <td> | |
491 | <p> | |
492 | Binomials: small arguments | |
493 | </p> | |
494 | </td> | |
495 | <td> | |
496 | <p> | |
497 | <span class="blue">Max = 1ε (Mean = 0.369ε)</span> | |
498 | </p> | |
499 | </td> | |
500 | <td> | |
501 | <p> | |
502 | <span class="blue">Max = 1ε (Mean = 0.369ε)</span> | |
503 | </p> | |
504 | </td> | |
505 | <td> | |
506 | <p> | |
507 | <span class="blue">Max = 1.5ε (Mean = 0.339ε)</span> | |
508 | </p> | |
509 | </td> | |
510 | <td> | |
511 | <p> | |
512 | <span class="blue">Max = 1.5ε (Mean = 0.339ε)</span> | |
513 | </p> | |
514 | </td> | |
515 | </tr> | |
516 | <tr> | |
517 | <td> | |
518 | <p> | |
519 | Binomials: large arguments | |
520 | </p> | |
521 | </td> | |
522 | <td> | |
523 | <p> | |
524 | <span class="blue">Max = 24.3ε (Mean = 6.3ε)</span> | |
525 | </p> | |
526 | </td> | |
527 | <td> | |
528 | <p> | |
529 | <span class="blue">Max = 0.939ε (Mean = 0.314ε)</span> | |
530 | </p> | |
531 | </td> | |
532 | <td> | |
533 | <p> | |
534 | <span class="blue">Max = 26ε (Mean = 6.09ε)</span> | |
535 | </p> | |
536 | </td> | |
537 | <td> | |
538 | <p> | |
539 | <span class="blue">Max = 54.1ε (Mean = 10.9ε)</span> | |
540 | </p> | |
541 | </td> | |
542 | </tr> | |
543 | </tbody> | |
544 | </table></div> | |
545 | </div> | |
546 | <br class="table-break"><div class="table"> | |
547 | <a name="math_toolkit.logs_and_tables.all_table.table_cbrt"></a><p class="title"><b>Table 17.7. Error rates for cbrt</b></p> | |
548 | <div class="table-contents"><table class="table" summary="Error rates for cbrt"> | |
549 | <colgroup> | |
550 | <col> | |
551 | <col> | |
552 | <col> | |
553 | <col> | |
554 | <col> | |
555 | </colgroup> | |
556 | <thead><tr> | |
557 | <th> | |
558 | </th> | |
559 | <th> | |
560 | <p> | |
561 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
562 | </p> | |
563 | </th> | |
564 | <th> | |
565 | <p> | |
566 | GNU C++ version 5.1.0<br> linux<br> double | |
567 | </p> | |
568 | </th> | |
569 | <th> | |
570 | <p> | |
571 | GNU C++ version 5.1.0<br> linux<br> long double | |
572 | </p> | |
573 | </th> | |
574 | <th> | |
575 | <p> | |
576 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
577 | </p> | |
578 | </th> | |
579 | </tr></thead> | |
580 | <tbody><tr> | |
581 | <td> | |
582 | <p> | |
583 | cbrt Function | |
584 | </p> | |
585 | </td> | |
586 | <td> | |
587 | <p> | |
588 | <span class="blue">Max = 1.7ε (Mean = 0.565ε)</span><br> <br> | |
589 | (<span class="emphasis"><em><math.h>:</em></span> Max = 1.7ε (Mean = 0.565ε)) | |
590 | </p> | |
591 | </td> | |
592 | <td> | |
593 | <p> | |
594 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Cephes:</em></span> | |
595 | Max = 0ε (Mean = 0ε)) | |
596 | </p> | |
597 | </td> | |
598 | <td> | |
599 | <p> | |
600 | <span class="blue">Max = 1.34ε (Mean = 0.471ε)</span><br> <br> | |
601 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.34ε (Mean = 0.471ε))<br> | |
602 | (<span class="emphasis"><em><math.h>:</em></span> Max = 1.34ε (Mean = 0.471ε)) | |
603 | </p> | |
604 | </td> | |
605 | <td> | |
606 | <p> | |
607 | <span class="blue">Max = 1.11ε (Mean = 0.424ε)</span><br> <br> | |
608 | (<span class="emphasis"><em><math.h>:</em></span> Max = 1.11ε (Mean = 0.424ε)) | |
609 | </p> | |
610 | </td> | |
611 | </tr></tbody> | |
612 | </table></div> | |
613 | </div> | |
614 | <br class="table-break"><div class="table"> | |
615 | <a name="math_toolkit.logs_and_tables.all_table.table_cos_pi"></a><p class="title"><b>Table 17.8. Error rates for cos_pi</b></p> | |
616 | <div class="table-contents"><table class="table" summary="Error rates for cos_pi"> | |
617 | <colgroup> | |
618 | <col> | |
619 | <col> | |
620 | <col> | |
621 | <col> | |
622 | <col> | |
623 | </colgroup> | |
624 | <thead><tr> | |
625 | <th> | |
626 | </th> | |
627 | <th> | |
628 | <p> | |
629 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
630 | </p> | |
631 | </th> | |
632 | <th> | |
633 | <p> | |
634 | GNU C++ version 5.1.0<br> linux<br> double | |
635 | </p> | |
636 | </th> | |
637 | <th> | |
638 | <p> | |
639 | GNU C++ version 5.1.0<br> linux<br> long double | |
640 | </p> | |
641 | </th> | |
642 | <th> | |
643 | <p> | |
644 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
645 | </p> | |
646 | </th> | |
647 | </tr></thead> | |
648 | <tbody> | |
649 | <tr> | |
650 | <td> | |
651 | <p> | |
652 | sin_pi and cos_pi | |
653 | </p> | |
654 | </td> | |
655 | <td> | |
656 | <p> | |
657 | <span class="blue">Max = 0.996ε (Mean = 0.281ε)</span> | |
658 | </p> | |
659 | </td> | |
660 | <td> | |
661 | <p> | |
662 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
663 | </p> | |
664 | </td> | |
665 | <td> | |
666 | <p> | |
667 | <span class="blue">Max = 0.991ε (Mean = 0.302ε)</span> | |
668 | </p> | |
669 | </td> | |
670 | <td> | |
671 | <p> | |
672 | <span class="blue">Max = 0.991ε (Mean = 0.302ε)</span> | |
673 | </p> | |
674 | </td> | |
675 | </tr> | |
676 | <tr> | |
677 | <td> | |
678 | <p> | |
679 | sin_pi and cos_pi near integers and half integers | |
680 | </p> | |
681 | </td> | |
682 | <td> | |
683 | <p> | |
684 | <span class="blue">Max = 0.996ε (Mean = 0.298ε)</span> | |
685 | </p> | |
686 | </td> | |
687 | <td> | |
688 | <p> | |
689 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
690 | </p> | |
691 | </td> | |
692 | <td> | |
693 | <p> | |
694 | <span class="blue">Max = 0.976ε (Mean = 0.28ε)</span> | |
695 | </p> | |
696 | </td> | |
697 | <td> | |
698 | <p> | |
699 | <span class="blue">Max = 0.976ε (Mean = 0.28ε)</span> | |
700 | </p> | |
701 | </td> | |
702 | </tr> | |
703 | </tbody> | |
704 | </table></div> | |
705 | </div> | |
706 | <br class="table-break"><div class="table"> | |
707 | <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i"></a><p class="title"><b>Table 17.9. Error rates for cyl_bessel_i</b></p> | |
708 | <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i"> | |
709 | <colgroup> | |
710 | <col> | |
711 | <col> | |
712 | <col> | |
713 | <col> | |
714 | <col> | |
715 | </colgroup> | |
716 | <thead><tr> | |
717 | <th> | |
718 | </th> | |
719 | <th> | |
720 | <p> | |
721 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
722 | </p> | |
723 | </th> | |
724 | <th> | |
725 | <p> | |
726 | GNU C++ version 5.1.0<br> linux<br> long double | |
727 | </p> | |
728 | </th> | |
729 | <th> | |
730 | <p> | |
731 | GNU C++ version 5.1.0<br> linux<br> double | |
732 | </p> | |
733 | </th> | |
734 | <th> | |
735 | <p> | |
736 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
737 | </p> | |
738 | </th> | |
739 | </tr></thead> | |
740 | <tbody> | |
741 | <tr> | |
742 | <td> | |
743 | <p> | |
744 | Bessel I0: Mathworld Data | |
745 | </p> | |
746 | </td> | |
747 | <td> | |
748 | <p> | |
749 | <span class="blue">Max = 0.877ε (Mean = 0.549ε)</span> | |
750 | </p> | |
751 | </td> | |
752 | <td> | |
753 | <p> | |
754 | <span class="blue">Max = 4.57ε (Mean = 2.1ε)</span><br> <br> | |
755 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 8.49ε (Mean = 3.46ε) | |
756 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i__tr1_cmath__Bessel_I0_Mathworld_Data">And | |
757 | other failures.</a>) | |
758 | </p> | |
759 | </td> | |
760 | <td> | |
761 | <p> | |
762 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
763 | 1.16:</em></span> Max = 270ε (Mean = 91.6ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_I0_Mathworld_Data">And | |
764 | other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> | |
765 | <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Rmath_3_0_2_Bessel_I0_Mathworld_Data">And | |
766 | other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span> | |
767 | <span class="red">Max = 2.55e+43ε (Mean = 8.06e+42ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Cephes_Bessel_I0_Mathworld_Data">And | |
768 | other failures.</a>)</span> | |
769 | </p> | |
770 | </td> | |
771 | <td> | |
772 | <p> | |
773 | <span class="blue">Max = 4.54ε (Mean = 2.11ε)</span> | |
774 | </p> | |
775 | </td> | |
776 | </tr> | |
777 | <tr> | |
778 | <td> | |
779 | <p> | |
780 | Bessel I1: Mathworld Data | |
781 | </p> | |
782 | </td> | |
783 | <td> | |
784 | <p> | |
785 | <span class="blue">Max = 0.885ε (Mean = 0.55ε)</span> | |
786 | </p> | |
787 | </td> | |
788 | <td> | |
789 | <p> | |
790 | <span class="blue">Max = 7.83ε (Mean = 2.79ε)</span><br> <br> | |
791 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 5ε (Mean = 2.15ε) | |
792 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i__tr1_cmath__Bessel_I1_Mathworld_Data">And | |
793 | other failures.</a>) | |
794 | </p> | |
795 | </td> | |
796 | <td> | |
797 | <p> | |
798 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
799 | 1.16:</em></span> Max = 128ε (Mean = 41ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_I1_Mathworld_Data">And | |
800 | other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> | |
801 | <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Rmath_3_0_2_Bessel_I1_Mathworld_Data">And | |
802 | other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span> | |
803 | <span class="red">Max = 1.28e+43ε (Mean = 4.05e+42ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Cephes_Bessel_I1_Mathworld_Data">And | |
804 | other failures.</a>)</span> | |
805 | </p> | |
806 | </td> | |
807 | <td> | |
808 | <p> | |
809 | <span class="blue">Max = 6.52ε (Mean = 2.25ε)</span> | |
810 | </p> | |
811 | </td> | |
812 | </tr> | |
813 | <tr> | |
814 | <td> | |
815 | <p> | |
816 | Bessel In: Mathworld Data | |
817 | </p> | |
818 | </td> | |
819 | <td> | |
820 | <p> | |
821 | <span class="blue">Max = 3.46ε (Mean = 1.32ε)</span> | |
822 | </p> | |
823 | </td> | |
824 | <td> | |
825 | <p> | |
826 | <span class="blue">Max = 1.8ε (Mean = 1.33ε)</span><br> <br> | |
827 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 430ε (Mean = 163ε) | |
828 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i__tr1_cmath__Bessel_In_Mathworld_Data">And | |
829 | other failures.</a>) | |
830 | </p> | |
831 | </td> | |
832 | <td> | |
833 | <p> | |
834 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
835 | 1.16:</em></span> Max = 2.31ε (Mean = 0.838ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_In_Mathworld_Data">And | |
836 | other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> | |
837 | <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Rmath_3_0_2_Bessel_In_Mathworld_Data">And | |
838 | other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span> | |
839 | <span class="red">Max = 3.67e+177ε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Cephes_Bessel_In_Mathworld_Data">And | |
840 | other failures.</a>)</span> | |
841 | </p> | |
842 | </td> | |
843 | <td> | |
844 | <p> | |
845 | <span class="blue">Max = 463ε (Mean = 140ε)</span> | |
846 | </p> | |
847 | </td> | |
848 | </tr> | |
849 | <tr> | |
850 | <td> | |
851 | <p> | |
852 | Bessel Iv: Mathworld Data | |
853 | </p> | |
854 | </td> | |
855 | <td> | |
856 | <p> | |
857 | <span class="blue">Max = 2.97ε (Mean = 1.33ε)</span> | |
858 | </p> | |
859 | </td> | |
860 | <td> | |
861 | <p> | |
862 | <span class="blue">Max = 4.12ε (Mean = 1.85ε)</span><br> <br> | |
863 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 616ε (Mean = 221ε) | |
864 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i__tr1_cmath__Bessel_Iv_Mathworld_Data">And | |
865 | other failures.</a>) | |
866 | </p> | |
867 | </td> | |
868 | <td> | |
869 | <p> | |
870 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
871 | 1.16:</em></span> Max = 5.95ε (Mean = 2.08ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_Iv_Mathworld_Data">And | |
872 | other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> | |
873 | Max = 1e+04ε (Mean = 3.18e+03ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
874 | <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Cephes_Bessel_Iv_Mathworld_Data">And | |
875 | other failures.</a>)</span> | |
876 | </p> | |
877 | </td> | |
878 | <td> | |
879 | <p> | |
880 | <span class="blue">Max = 4.12ε (Mean = 1.95ε)</span> | |
881 | </p> | |
882 | </td> | |
883 | </tr> | |
884 | <tr> | |
885 | <td> | |
886 | <p> | |
887 | Bessel In: Random Data | |
888 | </p> | |
889 | </td> | |
890 | <td> | |
891 | <p> | |
892 | <span class="blue">Max = 9.67ε (Mean = 1.89ε)</span> | |
893 | </p> | |
894 | </td> | |
895 | <td> | |
896 | <p> | |
897 | <span class="blue">Max = 6.79ε (Mean = 1.15ε)</span><br> <br> | |
898 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 645ε (Mean = 132ε)) | |
899 | </p> | |
900 | </td> | |
901 | <td> | |
902 | <p> | |
903 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
904 | 1.16:</em></span> Max = 261ε (Mean = 53.2ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_In_Random_Data">And | |
905 | other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> | |
906 | Max = 7.37ε (Mean = 2.4ε))<br> (<span class="emphasis"><em>Cephes:</em></span> Max | |
907 | = 4.22e+06ε (Mean = 2.26e+05ε)) | |
908 | </p> | |
909 | </td> | |
910 | <td> | |
911 | <p> | |
912 | <span class="blue">Max = 176ε (Mean = 39.2ε)</span> | |
913 | </p> | |
914 | </td> | |
915 | </tr> | |
916 | <tr> | |
917 | <td> | |
918 | <p> | |
919 | Bessel Iv: Random Data | |
920 | </p> | |
921 | </td> | |
922 | <td> | |
923 | <p> | |
924 | <span class="blue">Max = 7.46ε (Mean = 1.54ε)</span> | |
925 | </p> | |
926 | </td> | |
927 | <td> | |
928 | <p> | |
929 | <span class="blue">Max = 8.35ε (Mean = 1.49ε)</span><br> <br> | |
930 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.05e+03ε (Mean = | |
931 | 224ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i__tr1_cmath__Bessel_Iv_Random_Data">And | |
932 | other failures.</a>) | |
933 | </p> | |
934 | </td> | |
935 | <td> | |
936 | <p> | |
937 | <span class="blue">Max = 0.661ε (Mean = 0.0441ε)</span><br> | |
938 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 6.18e+03ε (Mean = 1.55e+03ε) | |
939 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_Iv_Random_Data">And | |
940 | other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> | |
941 | <span class="red">Max = 4.28e+08ε (Mean = 2.85e+07ε))</span><br> | |
942 | (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = 6e+30ε (Mean | |
943 | = 4e+29ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Cephes_Bessel_Iv_Random_Data">And | |
944 | other failures.</a>)</span> | |
945 | </p> | |
946 | </td> | |
947 | <td> | |
948 | <p> | |
949 | <span class="blue">Max = 283ε (Mean = 88.4ε)</span> | |
950 | </p> | |
951 | </td> | |
952 | </tr> | |
953 | <tr> | |
954 | <td> | |
955 | <p> | |
956 | Bessel Iv: Mathworld Data (large values) | |
957 | </p> | |
958 | </td> | |
959 | <td> | |
960 | <p> | |
961 | <span class="blue">Max = 3.67ε (Mean = 1.64ε)</span> | |
962 | </p> | |
963 | </td> | |
964 | <td> | |
965 | <p> | |
966 | <span class="blue">Max = 14.7ε (Mean = 6.57ε)</span><br> <br> | |
967 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 118ε (Mean = 57.2ε) | |
968 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i__tr1_cmath__Bessel_Iv_Mathworld_Data_large_values_">And | |
969 | other failures.</a>) | |
970 | </p> | |
971 | </td> | |
972 | <td> | |
973 | <p> | |
974 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
975 | 1.16:</em></span> Max = 37ε (Mean = 18ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_Iv_Mathworld_Data_large_values_">And | |
976 | other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> | |
977 | <span class="red">Max = 3.77e+168ε (Mean = 2.39e+168ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Rmath_3_0_2_Bessel_Iv_Mathworld_Data_large_values_">And | |
978 | other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span> | |
979 | Max = 73.7ε (Mean = 58.5ε)) | |
980 | </p> | |
981 | </td> | |
982 | <td> | |
983 | <p> | |
984 | <span class="blue">Max = 14.7ε (Mean = 6.59ε)</span> | |
985 | </p> | |
986 | </td> | |
987 | </tr> | |
988 | </tbody> | |
989 | </table></div> | |
990 | </div> | |
991 | <br class="table-break"><div class="table"> | |
992 | <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i_integer_orders_"></a><p class="title"><b>Table 17.10. Error rates for cyl_bessel_i (integer orders)</b></p> | |
993 | <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i (integer orders)"> | |
994 | <colgroup> | |
995 | <col> | |
996 | <col> | |
997 | <col> | |
998 | <col> | |
999 | <col> | |
1000 | </colgroup> | |
1001 | <thead><tr> | |
1002 | <th> | |
1003 | </th> | |
1004 | <th> | |
1005 | <p> | |
1006 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
1007 | </p> | |
1008 | </th> | |
1009 | <th> | |
1010 | <p> | |
1011 | GNU C++ version 5.1.0<br> linux<br> long double | |
1012 | </p> | |
1013 | </th> | |
1014 | <th> | |
1015 | <p> | |
1016 | GNU C++ version 5.1.0<br> linux<br> double | |
1017 | </p> | |
1018 | </th> | |
1019 | <th> | |
1020 | <p> | |
1021 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
1022 | </p> | |
1023 | </th> | |
1024 | </tr></thead> | |
1025 | <tbody> | |
1026 | <tr> | |
1027 | <td> | |
1028 | <p> | |
1029 | Bessel I0: Mathworld Data (Integer Version) | |
1030 | </p> | |
1031 | </td> | |
1032 | <td> | |
1033 | <p> | |
1034 | <span class="blue">Max = 0.877ε (Mean = 0.549ε)</span> | |
1035 | </p> | |
1036 | </td> | |
1037 | <td> | |
1038 | <p> | |
1039 | <span class="blue">Max = 4.57ε (Mean = 2.1ε)</span><br> <br> | |
1040 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 8.49ε (Mean = 3.46ε) | |
1041 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i_integer_orders___tr1_cmath__Bessel_I0_Mathworld_Data_Integer_Version_">And | |
1042 | other failures.</a>) | |
1043 | </p> | |
1044 | </td> | |
1045 | <td> | |
1046 | <p> | |
1047 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
1048 | 1.16:</em></span> Max = 0.79ε (Mean = 0.482ε))<br> (<span class="emphasis"><em>Rmath | |
1049 | 3.0.2:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_0_2_Bessel_I0_Mathworld_Data_Integer_Version_">And | |
1050 | other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span> | |
1051 | <span class="red">Max = 2.55e+43ε (Mean = 8.06e+42ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__Cephes_Bessel_I0_Mathworld_Data_Integer_Version_">And | |
1052 | other failures.</a>)</span> | |
1053 | </p> | |
1054 | </td> | |
1055 | <td> | |
1056 | <p> | |
1057 | <span class="blue">Max = 4.54ε (Mean = 2.11ε)</span> | |
1058 | </p> | |
1059 | </td> | |
1060 | </tr> | |
1061 | <tr> | |
1062 | <td> | |
1063 | <p> | |
1064 | Bessel I1: Mathworld Data (Integer Version) | |
1065 | </p> | |
1066 | </td> | |
1067 | <td> | |
1068 | <p> | |
1069 | <span class="blue">Max = 0.885ε (Mean = 0.55ε)</span> | |
1070 | </p> | |
1071 | </td> | |
1072 | <td> | |
1073 | <p> | |
1074 | <span class="blue">Max = 7.83ε (Mean = 2.79ε)</span><br> <br> | |
1075 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 5ε (Mean = 2.15ε) | |
1076 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i_integer_orders___tr1_cmath__Bessel_I1_Mathworld_Data_Integer_Version_">And | |
1077 | other failures.</a>) | |
1078 | </p> | |
1079 | </td> | |
1080 | <td> | |
1081 | <p> | |
1082 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
1083 | 1.16:</em></span> Max = 0.82ε (Mean = 0.456ε))<br> (<span class="emphasis"><em>Rmath | |
1084 | 3.0.2:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_0_2_Bessel_I1_Mathworld_Data_Integer_Version_">And | |
1085 | other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span> | |
1086 | <span class="red">Max = 1.28e+43ε (Mean = 4.05e+42ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__Cephes_Bessel_I1_Mathworld_Data_Integer_Version_">And | |
1087 | other failures.</a>)</span> | |
1088 | </p> | |
1089 | </td> | |
1090 | <td> | |
1091 | <p> | |
1092 | <span class="blue">Max = 6.52ε (Mean = 2.25ε)</span> | |
1093 | </p> | |
1094 | </td> | |
1095 | </tr> | |
1096 | <tr> | |
1097 | <td> | |
1098 | <p> | |
1099 | Bessel In: Mathworld Data (Integer Version) | |
1100 | </p> | |
1101 | </td> | |
1102 | <td> | |
1103 | <p> | |
1104 | <span class="blue">Max = 3.46ε (Mean = 1.32ε)</span> | |
1105 | </p> | |
1106 | </td> | |
1107 | <td> | |
1108 | <p> | |
1109 | <span class="blue">Max = 1.8ε (Mean = 1.33ε)</span><br> <br> | |
1110 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 430ε (Mean = 163ε) | |
1111 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i_integer_orders___tr1_cmath__Bessel_In_Mathworld_Data_Integer_Version_">And | |
1112 | other failures.</a>) | |
1113 | </p> | |
1114 | </td> | |
1115 | <td> | |
1116 | <p> | |
1117 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
1118 | 1.16:</em></span> Max = 5.15ε (Mean = 2.13ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__GSL_1_16_Bessel_In_Mathworld_Data_Integer_Version_">And | |
1119 | other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> | |
1120 | <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_0_2_Bessel_In_Mathworld_Data_Integer_Version_">And | |
1121 | other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span> | |
1122 | <span class="red">Max = 3.67e+177ε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__Cephes_Bessel_In_Mathworld_Data_Integer_Version_">And | |
1123 | other failures.</a>)</span> | |
1124 | </p> | |
1125 | </td> | |
1126 | <td> | |
1127 | <p> | |
1128 | <span class="blue">Max = 463ε (Mean = 140ε)</span> | |
1129 | </p> | |
1130 | </td> | |
1131 | </tr> | |
1132 | </tbody> | |
1133 | </table></div> | |
1134 | </div> | |
1135 | <br class="table-break"><div class="table"> | |
1136 | <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i_prime"></a><p class="title"><b>Table 17.11. Error rates for cyl_bessel_i_prime</b></p> | |
1137 | <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime"> | |
1138 | <colgroup> | |
1139 | <col> | |
1140 | <col> | |
1141 | <col> | |
1142 | <col> | |
1143 | <col> | |
1144 | </colgroup> | |
1145 | <thead><tr> | |
1146 | <th> | |
1147 | </th> | |
1148 | <th> | |
1149 | <p> | |
1150 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
1151 | </p> | |
1152 | </th> | |
1153 | <th> | |
1154 | <p> | |
1155 | GNU C++ version 5.1.0<br> linux<br> double | |
1156 | </p> | |
1157 | </th> | |
1158 | <th> | |
1159 | <p> | |
1160 | GNU C++ version 5.1.0<br> linux<br> long double | |
1161 | </p> | |
1162 | </th> | |
1163 | <th> | |
1164 | <p> | |
1165 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
1166 | </p> | |
1167 | </th> | |
1168 | </tr></thead> | |
1169 | <tbody> | |
1170 | <tr> | |
1171 | <td> | |
1172 | <p> | |
1173 | Bessel I'0: Mathworld Data | |
1174 | </p> | |
1175 | </td> | |
1176 | <td> | |
1177 | <p> | |
1178 | <span class="blue">Max = 0.885ε (Mean = 0.567ε)</span> | |
1179 | </p> | |
1180 | </td> | |
1181 | <td> | |
1182 | <p> | |
1183 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
1184 | </p> | |
1185 | </td> | |
1186 | <td> | |
1187 | <p> | |
1188 | <span class="blue">Max = 7.83ε (Mean = 2.84ε)</span> | |
1189 | </p> | |
1190 | </td> | |
1191 | <td> | |
1192 | <p> | |
1193 | <span class="blue">Max = 6.52ε (Mean = 2.26ε)</span> | |
1194 | </p> | |
1195 | </td> | |
1196 | </tr> | |
1197 | <tr> | |
1198 | <td> | |
1199 | <p> | |
1200 | Bessel I'1: Mathworld Data | |
1201 | </p> | |
1202 | </td> | |
1203 | <td> | |
1204 | <p> | |
1205 | <span class="blue">Max = 1.61ε (Mean = 0.786ε)</span> | |
1206 | </p> | |
1207 | </td> | |
1208 | <td> | |
1209 | <p> | |
1210 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
1211 | </p> | |
1212 | </td> | |
1213 | <td> | |
1214 | <p> | |
1215 | <span class="blue">Max = 2.3ε (Mean = 1.28ε)</span> | |
1216 | </p> | |
1217 | </td> | |
1218 | <td> | |
1219 | <p> | |
1220 | <span class="blue">Max = 2.3ε (Mean = 1.29ε)</span> | |
1221 | </p> | |
1222 | </td> | |
1223 | </tr> | |
1224 | <tr> | |
1225 | <td> | |
1226 | <p> | |
1227 | Bessel I'n: Mathworld Data | |
1228 | </p> | |
1229 | </td> | |
1230 | <td> | |
1231 | <p> | |
1232 | <span class="blue">Max = 3.61ε (Mean = 1.22ε)</span> | |
1233 | </p> | |
1234 | </td> | |
1235 | <td> | |
1236 | <p> | |
1237 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
1238 | </p> | |
1239 | </td> | |
1240 | <td> | |
1241 | <p> | |
1242 | <span class="blue">Max = 2.31ε (Mean = 1.41ε)</span> | |
1243 | </p> | |
1244 | </td> | |
1245 | <td> | |
1246 | <p> | |
1247 | <span class="blue">Max = 701ε (Mean = 212ε)</span> | |
1248 | </p> | |
1249 | </td> | |
1250 | </tr> | |
1251 | <tr> | |
1252 | <td> | |
1253 | <p> | |
1254 | Bessel I'v: Mathworld Data | |
1255 | </p> | |
1256 | </td> | |
1257 | <td> | |
1258 | <p> | |
1259 | <span class="blue">Max = 3.76e+003ε (Mean = 1.19e+003ε)</span> | |
1260 | </p> | |
1261 | </td> | |
1262 | <td> | |
1263 | <p> | |
1264 | <span class="blue">Max = 1.62ε (Mean = 0.512ε)</span> | |
1265 | </p> | |
1266 | </td> | |
1267 | <td> | |
1268 | <p> | |
1269 | <span class="blue">Max = 2.89e+03ε (Mean = 914ε)</span> | |
1270 | </p> | |
1271 | </td> | |
1272 | <td> | |
1273 | <p> | |
1274 | <span class="blue">Max = 2.89e+03ε (Mean = 914ε)</span> | |
1275 | </p> | |
1276 | </td> | |
1277 | </tr> | |
1278 | <tr> | |
1279 | <td> | |
1280 | <p> | |
1281 | Bessel I'n: Random Data | |
1282 | </p> | |
1283 | </td> | |
1284 | <td> | |
1285 | <p> | |
1286 | <span class="blue">Max = 9.85ε (Mean = 1.83ε)</span> | |
1287 | </p> | |
1288 | </td> | |
1289 | <td> | |
1290 | <p> | |
1291 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
1292 | </p> | |
1293 | </td> | |
1294 | <td> | |
1295 | <p> | |
1296 | <span class="blue">Max = 6.79ε (Mean = 1.13ε)</span> | |
1297 | </p> | |
1298 | </td> | |
1299 | <td> | |
1300 | <p> | |
1301 | <span class="blue">Max = 195ε (Mean = 37.1ε)</span> | |
1302 | </p> | |
1303 | </td> | |
1304 | </tr> | |
1305 | <tr> | |
1306 | <td> | |
1307 | <p> | |
1308 | Bessel I'v: Random Data | |
1309 | </p> | |
1310 | </td> | |
1311 | <td> | |
1312 | <p> | |
1313 | <span class="blue">Max = 14ε (Mean = 2.46ε)</span> | |
1314 | </p> | |
1315 | </td> | |
1316 | <td> | |
1317 | <p> | |
1318 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
1319 | </p> | |
1320 | </td> | |
1321 | <td> | |
1322 | <p> | |
1323 | <span class="blue">Max = 14.1ε (Mean = 2.93ε)</span> | |
1324 | </p> | |
1325 | </td> | |
1326 | <td> | |
1327 | <p> | |
1328 | <span class="blue">Max = 336ε (Mean = 68.5ε)</span> | |
1329 | </p> | |
1330 | </td> | |
1331 | </tr> | |
1332 | <tr> | |
1333 | <td> | |
1334 | <p> | |
1335 | Bessel I'v: Mathworld Data (large values) | |
1336 | </p> | |
1337 | </td> | |
1338 | <td> | |
1339 | <p> | |
1340 | <span class="blue">Max = 59.5ε (Mean = 26.8ε)</span> | |
1341 | </p> | |
1342 | </td> | |
1343 | <td> | |
1344 | <p> | |
1345 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
1346 | </p> | |
1347 | </td> | |
1348 | <td> | |
1349 | <p> | |
1350 | <span class="blue">Max = 42.6ε (Mean = 20.2ε)</span> | |
1351 | </p> | |
1352 | </td> | |
1353 | <td> | |
1354 | <p> | |
1355 | <span class="blue">Max = 43.9ε (Mean = 20.7ε)</span> | |
1356 | </p> | |
1357 | </td> | |
1358 | </tr> | |
1359 | </tbody> | |
1360 | </table></div> | |
1361 | </div> | |
1362 | <br class="table-break"><div class="table"> | |
1363 | <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i_prime_integer_orders_"></a><p class="title"><b>Table 17.12. Error rates for cyl_bessel_i_prime (integer orders)</b></p> | |
1364 | <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime (integer orders)"> | |
1365 | <colgroup> | |
1366 | <col> | |
1367 | <col> | |
1368 | <col> | |
1369 | <col> | |
1370 | <col> | |
1371 | </colgroup> | |
1372 | <thead><tr> | |
1373 | <th> | |
1374 | </th> | |
1375 | <th> | |
1376 | <p> | |
1377 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
1378 | </p> | |
1379 | </th> | |
1380 | <th> | |
1381 | <p> | |
1382 | GNU C++ version 5.1.0<br> linux<br> double | |
1383 | </p> | |
1384 | </th> | |
1385 | <th> | |
1386 | <p> | |
1387 | GNU C++ version 5.1.0<br> linux<br> long double | |
1388 | </p> | |
1389 | </th> | |
1390 | <th> | |
1391 | <p> | |
1392 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
1393 | </p> | |
1394 | </th> | |
1395 | </tr></thead> | |
1396 | <tbody> | |
1397 | <tr> | |
1398 | <td> | |
1399 | <p> | |
1400 | Bessel I'0: Mathworld Data (Integer Version) | |
1401 | </p> | |
1402 | </td> | |
1403 | <td> | |
1404 | <p> | |
1405 | <span class="blue">Max = 0.885ε (Mean = 0.567ε)</span> | |
1406 | </p> | |
1407 | </td> | |
1408 | <td> | |
1409 | <p> | |
1410 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
1411 | </p> | |
1412 | </td> | |
1413 | <td> | |
1414 | <p> | |
1415 | <span class="blue">Max = 7.83ε (Mean = 2.84ε)</span> | |
1416 | </p> | |
1417 | </td> | |
1418 | <td> | |
1419 | <p> | |
1420 | <span class="blue">Max = 6.52ε (Mean = 2.26ε)</span> | |
1421 | </p> | |
1422 | </td> | |
1423 | </tr> | |
1424 | <tr> | |
1425 | <td> | |
1426 | <p> | |
1427 | Bessel I'1: Mathworld Data (Integer Version) | |
1428 | </p> | |
1429 | </td> | |
1430 | <td> | |
1431 | <p> | |
1432 | <span class="blue">Max = 1.61ε (Mean = 0.786ε)</span> | |
1433 | </p> | |
1434 | </td> | |
1435 | <td> | |
1436 | <p> | |
1437 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
1438 | </p> | |
1439 | </td> | |
1440 | <td> | |
1441 | <p> | |
1442 | <span class="blue">Max = 2.3ε (Mean = 1.28ε)</span> | |
1443 | </p> | |
1444 | </td> | |
1445 | <td> | |
1446 | <p> | |
1447 | <span class="blue">Max = 2.3ε (Mean = 1.29ε)</span> | |
1448 | </p> | |
1449 | </td> | |
1450 | </tr> | |
1451 | <tr> | |
1452 | <td> | |
1453 | <p> | |
1454 | Bessel I'n: Mathworld Data (Integer Version) | |
1455 | </p> | |
1456 | </td> | |
1457 | <td> | |
1458 | <p> | |
1459 | <span class="blue">Max = 3.61ε (Mean = 1.22ε)</span> | |
1460 | </p> | |
1461 | </td> | |
1462 | <td> | |
1463 | <p> | |
1464 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
1465 | </p> | |
1466 | </td> | |
1467 | <td> | |
1468 | <p> | |
1469 | <span class="blue">Max = 2.31ε (Mean = 1.41ε)</span> | |
1470 | </p> | |
1471 | </td> | |
1472 | <td> | |
1473 | <p> | |
1474 | <span class="blue">Max = 701ε (Mean = 212ε)</span> | |
1475 | </p> | |
1476 | </td> | |
1477 | </tr> | |
1478 | </tbody> | |
1479 | </table></div> | |
1480 | </div> | |
1481 | <br class="table-break"><div class="table"> | |
1482 | <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j"></a><p class="title"><b>Table 17.13. Error rates for cyl_bessel_j</b></p> | |
1483 | <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j"> | |
1484 | <colgroup> | |
1485 | <col> | |
1486 | <col> | |
1487 | <col> | |
1488 | <col> | |
1489 | <col> | |
1490 | </colgroup> | |
1491 | <thead><tr> | |
1492 | <th> | |
1493 | </th> | |
1494 | <th> | |
1495 | <p> | |
1496 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
1497 | </p> | |
1498 | </th> | |
1499 | <th> | |
1500 | <p> | |
1501 | GNU C++ version 5.1.0<br> linux<br> long double | |
1502 | </p> | |
1503 | </th> | |
1504 | <th> | |
1505 | <p> | |
1506 | GNU C++ version 5.1.0<br> linux<br> double | |
1507 | </p> | |
1508 | </th> | |
1509 | <th> | |
1510 | <p> | |
1511 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
1512 | </p> | |
1513 | </th> | |
1514 | </tr></thead> | |
1515 | <tbody> | |
1516 | <tr> | |
1517 | <td> | |
1518 | <p> | |
1519 | Bessel J0: Mathworld Data | |
1520 | </p> | |
1521 | </td> | |
1522 | <td> | |
1523 | <p> | |
1524 | <span class="blue">Max = 2.52ε (Mean = 1.2ε)</span> | |
1525 | </p> | |
1526 | </td> | |
1527 | <td> | |
1528 | <p> | |
1529 | <span class="blue">Max = 6.55ε (Mean = 2.89ε)</span><br> <br> | |
1530 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 5.04ε (Mean = 1.78ε) | |
1531 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j__tr1_cmath__Bessel_J0_Mathworld_Data">And | |
1532 | other failures.</a>) | |
1533 | </p> | |
1534 | </td> | |
1535 | <td> | |
1536 | <p> | |
1537 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
1538 | 1.16:</em></span> Max = 0.629ε (Mean = 0.223ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_GSL_1_16_Bessel_J0_Mathworld_Data">And | |
1539 | other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> | |
1540 | <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_Rmath_3_0_2_Bessel_J0_Mathworld_Data">And | |
1541 | other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span> | |
1542 | Max = 1.12ε (Mean = 0.568ε)) | |
1543 | </p> | |
1544 | </td> | |
1545 | <td> | |
1546 | <p> | |
1547 | <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span> | |
1548 | </p> | |
1549 | </td> | |
1550 | </tr> | |
1551 | <tr> | |
1552 | <td> | |
1553 | <p> | |
1554 | Bessel J0: Mathworld Data (Tricky cases) | |
1555 | </p> | |
1556 | </td> | |
1557 | <td> | |
1558 | <p> | |
1559 | <span class="blue">Max = 1e+007ε (Mean = 4.09e+006ε)</span> | |
1560 | </p> | |
1561 | </td> | |
1562 | <td> | |
1563 | <p> | |
1564 | <span class="blue">Max = 1.63e+08ε (Mean = 6.67e+07ε)</span><br> | |
1565 | <br> (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 4.79e+08ε (Mean | |
1566 | = 1.96e+08ε)) | |
1567 | </p> | |
1568 | </td> | |
1569 | <td> | |
1570 | <p> | |
1571 | <span class="blue">Max = 7.98e+04ε (Mean = 3.26e+04ε)</span><br> | |
1572 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 6.5e+07ε (Mean = 2.66e+07ε))<br> | |
1573 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 1.04e+07ε (Mean = 4.29e+06ε))<br> | |
1574 | (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = 2.54e+08ε (Mean | |
1575 | = 1.04e+08ε))</span> | |
1576 | </p> | |
1577 | </td> | |
1578 | <td> | |
1579 | <p> | |
1580 | <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span> | |
1581 | </p> | |
1582 | </td> | |
1583 | </tr> | |
1584 | <tr> | |
1585 | <td> | |
1586 | <p> | |
1587 | Bessel J1: Mathworld Data | |
1588 | </p> | |
1589 | </td> | |
1590 | <td> | |
1591 | <p> | |
1592 | <span class="blue">Max = 1.73ε (Mean = 0.976ε)</span> | |
1593 | </p> | |
1594 | </td> | |
1595 | <td> | |
1596 | <p> | |
1597 | <span class="blue">Max = 2.66ε (Mean = 1.38ε)</span><br> <br> | |
1598 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 6.1ε (Mean = 2.95ε) | |
1599 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j__tr1_cmath__Bessel_J1_Mathworld_Data">And | |
1600 | other failures.</a>) | |
1601 | </p> | |
1602 | </td> | |
1603 | <td> | |
1604 | <p> | |
1605 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
1606 | 1.16:</em></span> Max = 6.62ε (Mean = 2.35ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_GSL_1_16_Bessel_J1_Mathworld_Data">And | |
1607 | other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> | |
1608 | <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_Rmath_3_0_2_Bessel_J1_Mathworld_Data">And | |
1609 | other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span> | |
1610 | Max = 2.88ε (Mean = 1.12ε)) | |
1611 | </p> | |
1612 | </td> | |
1613 | <td> | |
1614 | <p> | |
1615 | <span class="blue">Max = 1.44ε (Mean = 0.637ε)</span> | |
1616 | </p> | |
1617 | </td> | |
1618 | </tr> | |
1619 | <tr> | |
1620 | <td> | |
1621 | <p> | |
1622 | Bessel J1: Mathworld Data (tricky cases) | |
1623 | </p> | |
1624 | </td> | |
1625 | <td> | |
1626 | <p> | |
1627 | <span class="blue">Max = 3.23e+004ε (Mean = 1.45e+004ε)</span> | |
1628 | </p> | |
1629 | </td> | |
1630 | <td> | |
1631 | <p> | |
1632 | <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span><br> | |
1633 | <br> (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.15e+06ε (Mean | |
1634 | = 1.58e+06ε)) | |
1635 | </p> | |
1636 | </td> | |
1637 | <td> | |
1638 | <p> | |
1639 | <span class="blue">Max = 106ε (Mean = 47.5ε)</span><br> <br> | |
1640 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 8.75e+05ε (Mean = 5.32e+05ε))<br> | |
1641 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 2.93e+06ε (Mean = 1.7e+06ε))<br> | |
1642 | (<span class="emphasis"><em>Cephes:</em></span> Max = 9.56e+05ε (Mean = 4.99e+05ε)) | |
1643 | </p> | |
1644 | </td> | |
1645 | <td> | |
1646 | <p> | |
1647 | <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span> | |
1648 | </p> | |
1649 | </td> | |
1650 | </tr> | |
1651 | <tr> | |
1652 | <td> | |
1653 | <p> | |
1654 | Bessel JN: Mathworld Data | |
1655 | </p> | |
1656 | </td> | |
1657 | <td> | |
1658 | <p> | |
1659 | <span class="blue">Max = 14.7ε (Mean = 5.4ε)</span> | |
1660 | </p> | |
1661 | </td> | |
1662 | <td> | |
1663 | <p> | |
1664 | <span class="blue">Max = 6.85ε (Mean = 3.41ε)</span><br> <br> | |
1665 | (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max | |
1666 | = 2.13e+19ε (Mean = 5.16e+18ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j__tr1_cmath__Bessel_JN_Mathworld_Data">And | |
1667 | other failures.</a>)</span> | |
1668 | </p> | |
1669 | </td> | |
1670 | <td> | |
1671 | <p> | |
1672 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
1673 | 1.16:</em></span> Max = 6.9e+05ε (Mean = 2.15e+05ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_GSL_1_16_Bessel_JN_Mathworld_Data">And | |
1674 | other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> | |
1675 | <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_Rmath_3_0_2_Bessel_JN_Mathworld_Data">And | |
1676 | other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span> | |
1677 | Max = 5.53e+05ε (Mean = 1.9e+05ε)) | |
1678 | </p> | |
1679 | </td> | |
1680 | <td> | |
1681 | <p> | |
1682 | <span class="blue">Max = 463ε (Mean = 112ε)</span> | |
1683 | </p> | |
1684 | </td> | |
1685 | </tr> | |
1686 | <tr> | |
1687 | <td> | |
1688 | <p> | |
1689 | Bessel J: Mathworld Data | |
1690 | </p> | |
1691 | </td> | |
1692 | <td> | |
1693 | <p> | |
1694 | <span class="blue">Max = 14.9ε (Mean = 3.82ε)</span> | |
1695 | </p> | |
1696 | </td> | |
1697 | <td> | |
1698 | <p> | |
1699 | <span class="blue">Max = 14.7ε (Mean = 4.05ε)</span><br> <br> | |
1700 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 3.49e+05ε (Mean = | |
1701 | 7.89e+04ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j__tr1_cmath__Bessel_J_Mathworld_Data">And | |
1702 | other failures.</a>) | |
1703 | </p> | |
1704 | </td> | |
1705 | <td> | |
1706 | <p> | |
1707 | <span class="blue">Max = 10ε (Mean = 2.19ε)</span><br> <br> | |
1708 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.39e+05ε (Mean = 5.24e+04ε) | |
1709 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_GSL_1_16_Bessel_J_Mathworld_Data">And | |
1710 | other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> | |
1711 | <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_Rmath_3_0_2_Bessel_J_Mathworld_Data">And | |
1712 | other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span> | |
1713 | Max = 5.47e+05ε (Mean = 1.3e+05ε)) | |
1714 | </p> | |
1715 | </td> | |
1716 | <td> | |
1717 | <p> | |
1718 | <span class="blue">Max = 14.7ε (Mean = 4.12ε)</span> | |
1719 | </p> | |
1720 | </td> | |
1721 | </tr> | |
1722 | <tr> | |
1723 | <td> | |
1724 | <p> | |
1725 | Bessel J: Mathworld Data (large values) | |
1726 | </p> | |
1727 | </td> | |
1728 | <td> | |
1729 | <p> | |
1730 | <span class="blue">Max = 9.31ε (Mean = 5.52ε)</span> | |
1731 | </p> | |
1732 | </td> | |
1733 | <td> | |
1734 | <p> | |
1735 | <span class="blue">Max = 607ε (Mean = 305ε)</span><br> <br> | |
1736 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 34.9ε (Mean = 17.4ε) | |
1737 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j__tr1_cmath__Bessel_J_Mathworld_Data_large_values_">And | |
1738 | other failures.</a>) | |
1739 | </p> | |
1740 | </td> | |
1741 | <td> | |
1742 | <p> | |
1743 | <span class="blue">Max = 0.536ε (Mean = 0.268ε)</span><br> <br> | |
1744 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 4.91e+03ε (Mean = 2.46e+03ε) | |
1745 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_GSL_1_16_Bessel_J_Mathworld_Data_large_values_">And | |
1746 | other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> | |
1747 | Max = 35.9ε (Mean = 18.1ε))<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_Cephes_Bessel_J_Mathworld_Data_large_values_">And | |
1748 | other failures.</a>)</span> | |
1749 | </p> | |
1750 | </td> | |
1751 | <td> | |
1752 | <p> | |
1753 | <span class="blue">Max = 607ε (Mean = 305ε)</span> | |
1754 | </p> | |
1755 | </td> | |
1756 | </tr> | |
1757 | <tr> | |
1758 | <td> | |
1759 | <p> | |
1760 | Bessel JN: Random Data | |
1761 | </p> | |
1762 | </td> | |
1763 | <td> | |
1764 | <p> | |
1765 | <span class="blue">Max = 17.5ε (Mean = 1.46ε)</span> | |
1766 | </p> | |
1767 | </td> | |
1768 | <td> | |
1769 | <p> | |
1770 | <span class="blue">Max = 50.8ε (Mean = 4.15ε)</span><br> <br> | |
1771 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.12e+03ε (Mean = | |
1772 | 88.7ε)) | |
1773 | </p> | |
1774 | </td> | |
1775 | <td> | |
1776 | <p> | |
1777 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
1778 | 1.16:</em></span> Max = 75.7ε (Mean = 5.36ε))<br> (<span class="emphasis"><em>Rmath | |
1779 | 3.0.2:</em></span> Max = 3.93ε (Mean = 1.22ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
1780 | Max = 91.4ε (Mean = 6.47ε)) | |
1781 | </p> | |
1782 | </td> | |
1783 | <td> | |
1784 | <p> | |
1785 | <span class="blue">Max = 99.6ε (Mean = 22ε)</span> | |
1786 | </p> | |
1787 | </td> | |
1788 | </tr> | |
1789 | <tr> | |
1790 | <td> | |
1791 | <p> | |
1792 | Bessel J: Random Data | |
1793 | </p> | |
1794 | </td> | |
1795 | <td> | |
1796 | <p> | |
1797 | <span class="blue">Max = 9.24ε (Mean = 1.36ε)</span> | |
1798 | </p> | |
1799 | </td> | |
1800 | <td> | |
1801 | <p> | |
1802 | <span class="blue">Max = 9.81ε (Mean = 1.59ε)</span><br> <br> | |
1803 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 501ε (Mean = 52.3ε)) | |
1804 | </p> | |
1805 | </td> | |
1806 | <td> | |
1807 | <p> | |
1808 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
1809 | 1.16:</em></span> Max = 15.5ε (Mean = 3.33ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_GSL_1_16_Bessel_J_Random_Data">And | |
1810 | other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> | |
1811 | Max = 6.74ε (Mean = 1.3ε))<br> (<span class="emphasis"><em>Cephes:</em></span> Max | |
1812 | = 16.7ε (Mean = 2.5ε)) | |
1813 | </p> | |
1814 | </td> | |
1815 | <td> | |
1816 | <p> | |
1817 | <span class="blue">Max = 260ε (Mean = 34ε)</span> | |
1818 | </p> | |
1819 | </td> | |
1820 | </tr> | |
1821 | <tr> | |
1822 | <td> | |
1823 | <p> | |
1824 | Bessel J: Random Data (Tricky large values) | |
1825 | </p> | |
1826 | </td> | |
1827 | <td> | |
1828 | <p> | |
1829 | <span class="blue">Max = 59.2ε (Mean = 8.67ε)</span> | |
1830 | </p> | |
1831 | </td> | |
1832 | <td> | |
1833 | <p> | |
1834 | <span class="blue">Max = 785ε (Mean = 94.2ε)</span><br> <br> | |
1835 | (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max | |
1836 | = 5.01e+17ε (Mean = 6.23e+16ε))</span> | |
1837 | </p> | |
1838 | </td> | |
1839 | <td> | |
1840 | <p> | |
1841 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
1842 | 1.16:</em></span> Max = 2.48e+05ε (Mean = 5.11e+04ε))<br> (<span class="emphasis"><em>Rmath | |
1843 | 3.0.2:</em></span> Max = 71.6ε (Mean = 11.7ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
1844 | Max = 2.48e+05ε (Mean = 3.02e+04ε)) | |
1845 | </p> | |
1846 | </td> | |
1847 | <td> | |
1848 | <p> | |
1849 | <span class="blue">Max = 785ε (Mean = 97.4ε)</span> | |
1850 | </p> | |
1851 | </td> | |
1852 | </tr> | |
1853 | </tbody> | |
1854 | </table></div> | |
1855 | </div> | |
1856 | <br class="table-break"><div class="table"> | |
1857 | <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j_integer_orders_"></a><p class="title"><b>Table 17.14. Error rates for cyl_bessel_j (integer orders)</b></p> | |
1858 | <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j (integer orders)"> | |
1859 | <colgroup> | |
1860 | <col> | |
1861 | <col> | |
1862 | <col> | |
1863 | <col> | |
1864 | <col> | |
1865 | </colgroup> | |
1866 | <thead><tr> | |
1867 | <th> | |
1868 | </th> | |
1869 | <th> | |
1870 | <p> | |
1871 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
1872 | </p> | |
1873 | </th> | |
1874 | <th> | |
1875 | <p> | |
1876 | GNU C++ version 5.1.0<br> linux<br> long double | |
1877 | </p> | |
1878 | </th> | |
1879 | <th> | |
1880 | <p> | |
1881 | GNU C++ version 5.1.0<br> linux<br> double | |
1882 | </p> | |
1883 | </th> | |
1884 | <th> | |
1885 | <p> | |
1886 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
1887 | </p> | |
1888 | </th> | |
1889 | </tr></thead> | |
1890 | <tbody> | |
1891 | <tr> | |
1892 | <td> | |
1893 | <p> | |
1894 | Bessel J0: Mathworld Data (Integer Version) | |
1895 | </p> | |
1896 | </td> | |
1897 | <td> | |
1898 | <p> | |
1899 | <span class="blue">Max = 2.52ε (Mean = 1.2ε)</span><br> <br> | |
1900 | (<span class="emphasis"><em><math.h>:</em></span> Max = 1.89ε (Mean = 0.988ε)) | |
1901 | </p> | |
1902 | </td> | |
1903 | <td> | |
1904 | <p> | |
1905 | <span class="blue">Max = 6.55ε (Mean = 2.89ε)</span><br> <br> | |
1906 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 5.04ε (Mean = 1.78ε) | |
1907 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j_integer_orders___tr1_cmath__Bessel_J0_Mathworld_Data_Integer_Version_">And | |
1908 | other failures.</a>) | |
1909 | </p> | |
1910 | </td> | |
1911 | <td> | |
1912 | <p> | |
1913 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
1914 | 1.16:</em></span> Max = 1.12ε (Mean = 0.488ε))<br> (<span class="emphasis"><em>Rmath | |
1915 | 3.0.2:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_0_2_Bessel_J0_Mathworld_Data_Integer_Version_">And | |
1916 | other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span> | |
1917 | Max = 1.12ε (Mean = 0.568ε)) | |
1918 | </p> | |
1919 | </td> | |
1920 | <td> | |
1921 | <p> | |
1922 | <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span> | |
1923 | </p> | |
1924 | </td> | |
1925 | </tr> | |
1926 | <tr> | |
1927 | <td> | |
1928 | <p> | |
1929 | Bessel J0: Mathworld Data (Tricky cases) (Integer Version) | |
1930 | </p> | |
1931 | </td> | |
1932 | <td> | |
1933 | <p> | |
1934 | <span class="blue">Max = 1e+007ε (Mean = 4.09e+006ε)</span><br> | |
1935 | <br> (<span class="emphasis"><em><math.h>:</em></span> <span class="red">Max | |
1936 | = 2.54e+008ε (Mean = 1.04e+008ε))</span> | |
1937 | </p> | |
1938 | </td> | |
1939 | <td> | |
1940 | <p> | |
1941 | <span class="blue">Max = 1.63e+08ε (Mean = 6.67e+07ε)</span><br> | |
1942 | <br> (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 4.79e+08ε (Mean | |
1943 | = 1.96e+08ε)) | |
1944 | </p> | |
1945 | </td> | |
1946 | <td> | |
1947 | <p> | |
1948 | <span class="blue">Max = 7.98e+04ε (Mean = 3.26e+04ε)</span><br> | |
1949 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1e+07ε (Mean = 4.11e+06ε))<br> | |
1950 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 1.04e+07ε (Mean = 4.29e+06ε))<br> | |
1951 | (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = 2.54e+08ε (Mean | |
1952 | = 1.04e+08ε))</span> | |
1953 | </p> | |
1954 | </td> | |
1955 | <td> | |
1956 | <p> | |
1957 | <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span> | |
1958 | </p> | |
1959 | </td> | |
1960 | </tr> | |
1961 | <tr> | |
1962 | <td> | |
1963 | <p> | |
1964 | Bessel J1: Mathworld Data (Integer Version) | |
1965 | </p> | |
1966 | </td> | |
1967 | <td> | |
1968 | <p> | |
1969 | <span class="blue">Max = 1.73ε (Mean = 0.976ε)</span><br> <br> | |
1970 | (<span class="emphasis"><em><math.h>:</em></span> Max = 11.4ε (Mean = 4.15ε)) | |
1971 | </p> | |
1972 | </td> | |
1973 | <td> | |
1974 | <p> | |
1975 | <span class="blue">Max = 2.66ε (Mean = 1.38ε)</span><br> <br> | |
1976 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 6.1ε (Mean = 2.95ε) | |
1977 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j_integer_orders___tr1_cmath__Bessel_J1_Mathworld_Data_Integer_Version_">And | |
1978 | other failures.</a>) | |
1979 | </p> | |
1980 | </td> | |
1981 | <td> | |
1982 | <p> | |
1983 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
1984 | 1.16:</em></span> Max = 1.89ε (Mean = 0.721ε))<br> (<span class="emphasis"><em>Rmath | |
1985 | 3.0.2:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_0_2_Bessel_J1_Mathworld_Data_Integer_Version_">And | |
1986 | other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span> | |
1987 | Max = 2.88ε (Mean = 1.12ε)) | |
1988 | </p> | |
1989 | </td> | |
1990 | <td> | |
1991 | <p> | |
1992 | <span class="blue">Max = 1.44ε (Mean = 0.637ε)</span> | |
1993 | </p> | |
1994 | </td> | |
1995 | </tr> | |
1996 | <tr> | |
1997 | <td> | |
1998 | <p> | |
1999 | Bessel J1: Mathworld Data (tricky cases) (Integer Version) | |
2000 | </p> | |
2001 | </td> | |
2002 | <td> | |
2003 | <p> | |
2004 | <span class="blue">Max = 3.23e+004ε (Mean = 1.45e+004ε)</span><br> | |
2005 | <br> (<span class="emphasis"><em><math.h>:</em></span> Max = 1.44e+007ε (Mean | |
2006 | = 6.5e+006ε)) | |
2007 | </p> | |
2008 | </td> | |
2009 | <td> | |
2010 | <p> | |
2011 | <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span><br> | |
2012 | <br> (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.15e+06ε (Mean | |
2013 | = 1.58e+06ε)) | |
2014 | </p> | |
2015 | </td> | |
2016 | <td> | |
2017 | <p> | |
2018 | <span class="blue">Max = 106ε (Mean = 47.5ε)</span><br> <br> | |
2019 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.26e+06ε (Mean = 6.28e+05ε))<br> | |
2020 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 2.93e+06ε (Mean = 1.7e+06ε))<br> | |
2021 | (<span class="emphasis"><em>Cephes:</em></span> Max = 9.56e+05ε (Mean = 4.99e+05ε)) | |
2022 | </p> | |
2023 | </td> | |
2024 | <td> | |
2025 | <p> | |
2026 | <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span> | |
2027 | </p> | |
2028 | </td> | |
2029 | </tr> | |
2030 | <tr> | |
2031 | <td> | |
2032 | <p> | |
2033 | Bessel JN: Mathworld Data (Integer Version) | |
2034 | </p> | |
2035 | </td> | |
2036 | <td> | |
2037 | <p> | |
2038 | <span class="blue">Max = 14.7ε (Mean = 5.4ε)</span><br> <br> | |
2039 | (<span class="emphasis"><em><math.h>:</em></span> <span class="red">Max = | |
2040 | +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_">And | |
2041 | other failures.</a>)</span> | |
2042 | </p> | |
2043 | </td> | |
2044 | <td> | |
2045 | <p> | |
2046 | <span class="blue">Max = 6.85ε (Mean = 3.41ε)</span><br> <br> | |
2047 | (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max | |
2048 | = 2.13e+19ε (Mean = 5.16e+18ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j_integer_orders___tr1_cmath__Bessel_JN_Mathworld_Data_Integer_Version_">And | |
2049 | other failures.</a>)</span> | |
2050 | </p> | |
2051 | </td> | |
2052 | <td> | |
2053 | <p> | |
2054 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
2055 | 1.16:</em></span> Max = 6.9e+05ε (Mean = 2.53e+05ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_integer_orders__GSL_1_16_Bessel_JN_Mathworld_Data_Integer_Version_">And | |
2056 | other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> | |
2057 | <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_0_2_Bessel_JN_Mathworld_Data_Integer_Version_">And | |
2058 | other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span> | |
2059 | <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_integer_orders__Cephes_Bessel_JN_Mathworld_Data_Integer_Version_">And | |
2060 | other failures.</a>)</span> | |
2061 | </p> | |
2062 | </td> | |
2063 | <td> | |
2064 | <p> | |
2065 | <span class="blue">Max = 463ε (Mean = 112ε)</span> | |
2066 | </p> | |
2067 | </td> | |
2068 | </tr> | |
2069 | </tbody> | |
2070 | </table></div> | |
2071 | </div> | |
2072 | <br class="table-break"><div class="table"> | |
2073 | <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j_prime"></a><p class="title"><b>Table 17.15. Error rates for cyl_bessel_j_prime</b></p> | |
2074 | <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime"> | |
2075 | <colgroup> | |
2076 | <col> | |
2077 | <col> | |
2078 | <col> | |
2079 | <col> | |
2080 | <col> | |
2081 | </colgroup> | |
2082 | <thead><tr> | |
2083 | <th> | |
2084 | </th> | |
2085 | <th> | |
2086 | <p> | |
2087 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
2088 | </p> | |
2089 | </th> | |
2090 | <th> | |
2091 | <p> | |
2092 | GNU C++ version 5.1.0<br> linux<br> double | |
2093 | </p> | |
2094 | </th> | |
2095 | <th> | |
2096 | <p> | |
2097 | GNU C++ version 5.1.0<br> linux<br> long double | |
2098 | </p> | |
2099 | </th> | |
2100 | <th> | |
2101 | <p> | |
2102 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
2103 | </p> | |
2104 | </th> | |
2105 | </tr></thead> | |
2106 | <tbody> | |
2107 | <tr> | |
2108 | <td> | |
2109 | <p> | |
2110 | Bessel J0': Mathworld Data | |
2111 | </p> | |
2112 | </td> | |
2113 | <td> | |
2114 | <p> | |
2115 | <span class="blue">Max = 6.62ε (Mean = 2.55ε)</span> | |
2116 | </p> | |
2117 | </td> | |
2118 | <td> | |
2119 | <p> | |
2120 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
2121 | </p> | |
2122 | </td> | |
2123 | <td> | |
2124 | <p> | |
2125 | <span class="blue">Max = 18.9ε (Mean = 6.81ε)</span> | |
2126 | </p> | |
2127 | </td> | |
2128 | <td> | |
2129 | <p> | |
2130 | <span class="blue">Max = 18.9ε (Mean = 6.72ε)</span> | |
2131 | </p> | |
2132 | </td> | |
2133 | </tr> | |
2134 | <tr> | |
2135 | <td> | |
2136 | <p> | |
2137 | Bessel J0': Mathworld Data (Tricky cases) | |
2138 | </p> | |
2139 | </td> | |
2140 | <td> | |
2141 | <p> | |
2142 | <span class="blue">Max = 3.67ε (Mean = 1.74ε)</span> | |
2143 | </p> | |
2144 | </td> | |
2145 | <td> | |
2146 | <p> | |
2147 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
2148 | </p> | |
2149 | </td> | |
2150 | <td> | |
2151 | <p> | |
2152 | <span class="blue">Max = 8.08ε (Mean = 4.57ε)</span> | |
2153 | </p> | |
2154 | </td> | |
2155 | <td> | |
2156 | <p> | |
2157 | <span class="blue">Max = 7.44ε (Mean = 3.31ε)</span> | |
2158 | </p> | |
2159 | </td> | |
2160 | </tr> | |
2161 | <tr> | |
2162 | <td> | |
2163 | <p> | |
2164 | Bessel J1': Mathworld Data | |
2165 | </p> | |
2166 | </td> | |
2167 | <td> | |
2168 | <p> | |
2169 | <span class="blue">Max = 0.999ε (Mean = 0.627ε)</span> | |
2170 | </p> | |
2171 | </td> | |
2172 | <td> | |
2173 | <p> | |
2174 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
2175 | </p> | |
2176 | </td> | |
2177 | <td> | |
2178 | <p> | |
2179 | <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span> | |
2180 | </p> | |
2181 | </td> | |
2182 | <td> | |
2183 | <p> | |
2184 | <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span> | |
2185 | </p> | |
2186 | </td> | |
2187 | </tr> | |
2188 | <tr> | |
2189 | <td> | |
2190 | <p> | |
2191 | Bessel J1': Mathworld Data (tricky cases) | |
2192 | </p> | |
2193 | </td> | |
2194 | <td> | |
2195 | <p> | |
2196 | <span class="blue">Max = 288ε (Mean = 129ε)</span> | |
2197 | </p> | |
2198 | </td> | |
2199 | <td> | |
2200 | <p> | |
2201 | <span class="blue">Max = 287ε (Mean = 129ε)</span> | |
2202 | </p> | |
2203 | </td> | |
2204 | <td> | |
2205 | <p> | |
2206 | <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span> | |
2207 | </p> | |
2208 | </td> | |
2209 | <td> | |
2210 | <p> | |
2211 | <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span> | |
2212 | </p> | |
2213 | </td> | |
2214 | </tr> | |
2215 | <tr> | |
2216 | <td> | |
2217 | <p> | |
2218 | Bessel JN': Mathworld Data | |
2219 | </p> | |
2220 | </td> | |
2221 | <td> | |
2222 | <p> | |
2223 | <span class="blue">Max = 14ε (Mean = 6.13ε)</span> | |
2224 | </p> | |
2225 | </td> | |
2226 | <td> | |
2227 | <p> | |
2228 | <span class="blue">Max = 0.527ε (Mean = 0.128ε)</span> | |
2229 | </p> | |
2230 | </td> | |
2231 | <td> | |
2232 | <p> | |
2233 | <span class="blue">Max = 1.29e+03ε (Mean = 312ε)</span> | |
2234 | </p> | |
2235 | </td> | |
2236 | <td> | |
2237 | <p> | |
2238 | <span class="blue">Max = 1.29e+03ε (Mean = 355ε)</span> | |
2239 | </p> | |
2240 | </td> | |
2241 | </tr> | |
2242 | <tr> | |
2243 | <td> | |
2244 | <p> | |
2245 | Bessel J': Mathworld Data | |
2246 | </p> | |
2247 | </td> | |
2248 | <td> | |
2249 | <p> | |
2250 | <span class="blue">Max = 23.7ε (Mean = 8.01ε)</span> | |
2251 | </p> | |
2252 | </td> | |
2253 | <td> | |
2254 | <p> | |
2255 | <span class="blue">Max = 21.5ε (Mean = 4.7ε)</span> | |
2256 | </p> | |
2257 | </td> | |
2258 | <td> | |
2259 | <p> | |
2260 | <span class="blue">Max = 42.5ε (Mean = 9.31ε)</span> | |
2261 | </p> | |
2262 | </td> | |
2263 | <td> | |
2264 | <p> | |
2265 | <span class="blue">Max = 42.5ε (Mean = 9.32ε)</span> | |
2266 | </p> | |
2267 | </td> | |
2268 | </tr> | |
2269 | <tr> | |
2270 | <td> | |
2271 | <p> | |
2272 | Bessel J': Mathworld Data (large values) | |
2273 | </p> | |
2274 | </td> | |
2275 | <td> | |
2276 | <p> | |
2277 | <span class="blue">Max = 2.9ε (Mean = 1.61ε)</span> | |
2278 | </p> | |
2279 | </td> | |
2280 | <td> | |
2281 | <p> | |
2282 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
2283 | </p> | |
2284 | </td> | |
2285 | <td> | |
2286 | <p> | |
2287 | <span class="blue">Max = 989ε (Mean = 495ε)</span> | |
2288 | </p> | |
2289 | </td> | |
2290 | <td> | |
2291 | <p> | |
2292 | <span class="blue">Max = 989ε (Mean = 495ε)</span> | |
2293 | </p> | |
2294 | </td> | |
2295 | </tr> | |
2296 | <tr> | |
2297 | <td> | |
2298 | <p> | |
2299 | Bessel JN': Random Data | |
2300 | </p> | |
2301 | </td> | |
2302 | <td> | |
2303 | <p> | |
2304 | <span class="blue">Max = 6.34ε (Mean = 0.997ε)</span> | |
2305 | </p> | |
2306 | </td> | |
2307 | <td> | |
2308 | <p> | |
2309 | <span class="blue">Max = 0.593ε (Mean = 0.0396ε)</span> | |
2310 | </p> | |
2311 | </td> | |
2312 | <td> | |
2313 | <p> | |
2314 | <span class="blue">Max = 17.3ε (Mean = 2.47ε)</span> | |
2315 | </p> | |
2316 | </td> | |
2317 | <td> | |
2318 | <p> | |
2319 | <span class="blue">Max = 79.4ε (Mean = 16.2ε)</span> | |
2320 | </p> | |
2321 | </td> | |
2322 | </tr> | |
2323 | <tr> | |
2324 | <td> | |
2325 | <p> | |
2326 | Bessel J': Random Data | |
2327 | </p> | |
2328 | </td> | |
2329 | <td> | |
2330 | <p> | |
2331 | <span class="blue">Max = 176ε (Mean = 9.76ε)</span> | |
2332 | </p> | |
2333 | </td> | |
2334 | <td> | |
2335 | <p> | |
2336 | <span class="blue">Max = 0.885ε (Mean = 0.0457ε)</span> | |
2337 | </p> | |
2338 | </td> | |
2339 | <td> | |
2340 | <p> | |
2341 | <span class="blue">Max = 139ε (Mean = 6.47ε)</span> | |
2342 | </p> | |
2343 | </td> | |
2344 | <td> | |
2345 | <p> | |
2346 | <span class="blue">Max = 279ε (Mean = 27.2ε)</span> | |
2347 | </p> | |
2348 | </td> | |
2349 | </tr> | |
2350 | <tr> | |
2351 | <td> | |
2352 | <p> | |
2353 | Bessel J': Random Data (Tricky large values) | |
2354 | </p> | |
2355 | </td> | |
2356 | <td> | |
2357 | <p> | |
2358 | <span class="blue">Max = 379ε (Mean = 45.4ε)</span> | |
2359 | </p> | |
2360 | </td> | |
2361 | <td> | |
2362 | <p> | |
2363 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
2364 | </p> | |
2365 | </td> | |
2366 | <td> | |
2367 | <p> | |
2368 | <span class="blue">Max = 474ε (Mean = 62.2ε)</span> | |
2369 | </p> | |
2370 | </td> | |
2371 | <td> | |
2372 | <p> | |
2373 | <span class="blue">Max = 474ε (Mean = 64.5ε)</span> | |
2374 | </p> | |
2375 | </td> | |
2376 | </tr> | |
2377 | </tbody> | |
2378 | </table></div> | |
2379 | </div> | |
2380 | <br class="table-break"><div class="table"> | |
2381 | <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j_prime_integer_orders_"></a><p class="title"><b>Table 17.16. Error rates for cyl_bessel_j_prime (integer orders)</b></p> | |
2382 | <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime (integer orders)"> | |
2383 | <colgroup> | |
2384 | <col> | |
2385 | <col> | |
2386 | <col> | |
2387 | <col> | |
2388 | <col> | |
2389 | </colgroup> | |
2390 | <thead><tr> | |
2391 | <th> | |
2392 | </th> | |
2393 | <th> | |
2394 | <p> | |
2395 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
2396 | </p> | |
2397 | </th> | |
2398 | <th> | |
2399 | <p> | |
2400 | GNU C++ version 5.1.0<br> linux<br> double | |
2401 | </p> | |
2402 | </th> | |
2403 | <th> | |
2404 | <p> | |
2405 | GNU C++ version 5.1.0<br> linux<br> long double | |
2406 | </p> | |
2407 | </th> | |
2408 | <th> | |
2409 | <p> | |
2410 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
2411 | </p> | |
2412 | </th> | |
2413 | </tr></thead> | |
2414 | <tbody> | |
2415 | <tr> | |
2416 | <td> | |
2417 | <p> | |
2418 | Bessel J0': Mathworld Data (Integer Version) | |
2419 | </p> | |
2420 | </td> | |
2421 | <td> | |
2422 | <p> | |
2423 | <span class="blue">Max = 6.62ε (Mean = 2.55ε)</span> | |
2424 | </p> | |
2425 | </td> | |
2426 | <td> | |
2427 | <p> | |
2428 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
2429 | </p> | |
2430 | </td> | |
2431 | <td> | |
2432 | <p> | |
2433 | <span class="blue">Max = 18.9ε (Mean = 6.81ε)</span> | |
2434 | </p> | |
2435 | </td> | |
2436 | <td> | |
2437 | <p> | |
2438 | <span class="blue">Max = 18.9ε (Mean = 6.72ε)</span> | |
2439 | </p> | |
2440 | </td> | |
2441 | </tr> | |
2442 | <tr> | |
2443 | <td> | |
2444 | <p> | |
2445 | Bessel J0': Mathworld Data (Tricky cases) (Integer Version) | |
2446 | </p> | |
2447 | </td> | |
2448 | <td> | |
2449 | <p> | |
2450 | <span class="blue">Max = 3.67ε (Mean = 1.74ε)</span> | |
2451 | </p> | |
2452 | </td> | |
2453 | <td> | |
2454 | <p> | |
2455 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
2456 | </p> | |
2457 | </td> | |
2458 | <td> | |
2459 | <p> | |
2460 | <span class="blue">Max = 8.08ε (Mean = 4.57ε)</span> | |
2461 | </p> | |
2462 | </td> | |
2463 | <td> | |
2464 | <p> | |
2465 | <span class="blue">Max = 7.44ε (Mean = 3.31ε)</span> | |
2466 | </p> | |
2467 | </td> | |
2468 | </tr> | |
2469 | <tr> | |
2470 | <td> | |
2471 | <p> | |
2472 | Bessel J1': Mathworld Data (Integer Version) | |
2473 | </p> | |
2474 | </td> | |
2475 | <td> | |
2476 | <p> | |
2477 | <span class="blue">Max = 0.999ε (Mean = 0.627ε)</span> | |
2478 | </p> | |
2479 | </td> | |
2480 | <td> | |
2481 | <p> | |
2482 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
2483 | </p> | |
2484 | </td> | |
2485 | <td> | |
2486 | <p> | |
2487 | <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span> | |
2488 | </p> | |
2489 | </td> | |
2490 | <td> | |
2491 | <p> | |
2492 | <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span> | |
2493 | </p> | |
2494 | </td> | |
2495 | </tr> | |
2496 | <tr> | |
2497 | <td> | |
2498 | <p> | |
2499 | Bessel J1': Mathworld Data (tricky cases) (Integer Version) | |
2500 | </p> | |
2501 | </td> | |
2502 | <td> | |
2503 | <p> | |
2504 | <span class="blue">Max = 288ε (Mean = 129ε)</span> | |
2505 | </p> | |
2506 | </td> | |
2507 | <td> | |
2508 | <p> | |
2509 | <span class="blue">Max = 287ε (Mean = 129ε)</span> | |
2510 | </p> | |
2511 | </td> | |
2512 | <td> | |
2513 | <p> | |
2514 | <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span> | |
2515 | </p> | |
2516 | </td> | |
2517 | <td> | |
2518 | <p> | |
2519 | <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span> | |
2520 | </p> | |
2521 | </td> | |
2522 | </tr> | |
2523 | <tr> | |
2524 | <td> | |
2525 | <p> | |
2526 | Bessel JN': Mathworld Data (Integer Version) | |
2527 | </p> | |
2528 | </td> | |
2529 | <td> | |
2530 | <p> | |
2531 | <span class="blue">Max = 14ε (Mean = 6.13ε)</span> | |
2532 | </p> | |
2533 | </td> | |
2534 | <td> | |
2535 | <p> | |
2536 | <span class="blue">Max = 0.527ε (Mean = 0.128ε)</span> | |
2537 | </p> | |
2538 | </td> | |
2539 | <td> | |
2540 | <p> | |
2541 | <span class="blue">Max = 1.29e+03ε (Mean = 312ε)</span> | |
2542 | </p> | |
2543 | </td> | |
2544 | <td> | |
2545 | <p> | |
2546 | <span class="blue">Max = 1.29e+03ε (Mean = 355ε)</span> | |
2547 | </p> | |
2548 | </td> | |
2549 | </tr> | |
2550 | </tbody> | |
2551 | </table></div> | |
2552 | </div> | |
2553 | <br class="table-break"><div class="table"> | |
2554 | <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k"></a><p class="title"><b>Table 17.17. Error rates for cyl_bessel_k</b></p> | |
2555 | <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k"> | |
2556 | <colgroup> | |
2557 | <col> | |
2558 | <col> | |
2559 | <col> | |
2560 | <col> | |
2561 | <col> | |
2562 | </colgroup> | |
2563 | <thead><tr> | |
2564 | <th> | |
2565 | </th> | |
2566 | <th> | |
2567 | <p> | |
2568 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
2569 | </p> | |
2570 | </th> | |
2571 | <th> | |
2572 | <p> | |
2573 | GNU C++ version 5.1.0<br> linux<br> long double | |
2574 | </p> | |
2575 | </th> | |
2576 | <th> | |
2577 | <p> | |
2578 | GNU C++ version 5.1.0<br> linux<br> double | |
2579 | </p> | |
2580 | </th> | |
2581 | <th> | |
2582 | <p> | |
2583 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
2584 | </p> | |
2585 | </th> | |
2586 | </tr></thead> | |
2587 | <tbody> | |
2588 | <tr> | |
2589 | <td> | |
2590 | <p> | |
2591 | Bessel K0: Mathworld Data | |
2592 | </p> | |
2593 | </td> | |
2594 | <td> | |
2595 | <p> | |
2596 | <span class="blue">Max = 1.55ε (Mean = 0.837ε)</span> | |
2597 | </p> | |
2598 | </td> | |
2599 | <td> | |
2600 | <p> | |
2601 | <span class="blue">Max = 4.16ε (Mean = 1.46ε)</span><br> <br> | |
2602 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 9.33ε (Mean = 3.25ε)) | |
2603 | </p> | |
2604 | </td> | |
2605 | <td> | |
2606 | <p> | |
2607 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
2608 | 1.16:</em></span> Max = 6.04ε (Mean = 2.16ε))<br> (<span class="emphasis"><em>Rmath | |
2609 | 3.0.2:</em></span> Max = 0.833ε (Mean = 0.601ε)) | |
2610 | </p> | |
2611 | </td> | |
2612 | <td> | |
2613 | <p> | |
2614 | <span class="blue">Max = 4.16ε (Mean = 1.49ε)</span> | |
2615 | </p> | |
2616 | </td> | |
2617 | </tr> | |
2618 | <tr> | |
2619 | <td> | |
2620 | <p> | |
2621 | Bessel K1: Mathworld Data | |
2622 | </p> | |
2623 | </td> | |
2624 | <td> | |
2625 | <p> | |
2626 | <span class="blue">Max = 1ε (Mean = 0.573ε)</span> | |
2627 | </p> | |
2628 | </td> | |
2629 | <td> | |
2630 | <p> | |
2631 | <span class="blue">Max = 1.8ε (Mean = 1.02ε)</span><br> <br> | |
2632 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 8.94ε (Mean = 3.19ε)) | |
2633 | </p> | |
2634 | </td> | |
2635 | <td> | |
2636 | <p> | |
2637 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
2638 | 1.16:</em></span> Max = 6.26ε (Mean = 2.21ε))<br> (<span class="emphasis"><em>Rmath | |
2639 | 3.0.2:</em></span> Max = 0.894ε (Mean = 0.516ε)) | |
2640 | </p> | |
2641 | </td> | |
2642 | <td> | |
2643 | <p> | |
2644 | <span class="blue">Max = 1.8ε (Mean = 1.02ε)</span> | |
2645 | </p> | |
2646 | </td> | |
2647 | </tr> | |
2648 | <tr> | |
2649 | <td> | |
2650 | <p> | |
2651 | Bessel Kn: Mathworld Data | |
2652 | </p> | |
2653 | </td> | |
2654 | <td> | |
2655 | <p> | |
2656 | <span class="blue">Max = 3.63ε (Mean = 1.46ε)</span> | |
2657 | </p> | |
2658 | </td> | |
2659 | <td> | |
2660 | <p> | |
2661 | <span class="blue">Max = 4.48ε (Mean = 2.14ε)</span><br> <br> | |
2662 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 12.9ε (Mean = 4.91ε) | |
2663 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_k__tr1_cmath__Bessel_Kn_Mathworld_Data">And | |
2664 | other failures.</a>) | |
2665 | </p> | |
2666 | </td> | |
2667 | <td> | |
2668 | <p> | |
2669 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
2670 | 1.16:</em></span> Max = 3.36ε (Mean = 1.43ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_k_GSL_1_16_Bessel_Kn_Mathworld_Data">And | |
2671 | other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> | |
2672 | Max = 8.48ε (Mean = 2.98ε)) | |
2673 | </p> | |
2674 | </td> | |
2675 | <td> | |
2676 | <p> | |
2677 | <span class="blue">Max = 4.48ε (Mean = 1.98ε)</span> | |
2678 | </p> | |
2679 | </td> | |
2680 | </tr> | |
2681 | <tr> | |
2682 | <td> | |
2683 | <p> | |
2684 | Bessel Kv: Mathworld Data | |
2685 | </p> | |
2686 | </td> | |
2687 | <td> | |
2688 | <p> | |
2689 | <span class="blue">Max = 4.78ε (Mean = 2.2ε)</span> | |
2690 | </p> | |
2691 | </td> | |
2692 | <td> | |
2693 | <p> | |
2694 | <span class="blue">Max = 3.58ε (Mean = 2.44ε)</span><br> <br> | |
2695 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 13ε (Mean = 4.81ε) | |
2696 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_k__tr1_cmath__Bessel_Kv_Mathworld_Data">And | |
2697 | other failures.</a>) | |
2698 | </p> | |
2699 | </td> | |
2700 | <td> | |
2701 | <p> | |
2702 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
2703 | 1.16:</em></span> Max = 5.47ε (Mean = 2.04ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_k_GSL_1_16_Bessel_Kv_Mathworld_Data">And | |
2704 | other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> | |
2705 | Max = 3.15ε (Mean = 1.35ε)) | |
2706 | </p> | |
2707 | </td> | |
2708 | <td> | |
2709 | <p> | |
2710 | <span class="blue">Max = 3.58ε (Mean = 2.29ε)</span> | |
2711 | </p> | |
2712 | </td> | |
2713 | </tr> | |
2714 | <tr> | |
2715 | <td> | |
2716 | <p> | |
2717 | Bessel Kv: Mathworld Data (large values) | |
2718 | </p> | |
2719 | </td> | |
2720 | <td> | |
2721 | <p> | |
2722 | <span class="blue">Max = 59.8ε (Mean = 26.9ε)</span> | |
2723 | </p> | |
2724 | </td> | |
2725 | <td> | |
2726 | <p> | |
2727 | <span class="blue">Max = 42.3ε (Mean = 21ε)</span><br> <br> | |
2728 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 42.3ε (Mean = 19.8ε) | |
2729 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_k__tr1_cmath__Bessel_Kv_Mathworld_Data_large_values_">And | |
2730 | other failures.</a>) | |
2731 | </p> | |
2732 | </td> | |
2733 | <td> | |
2734 | <p> | |
2735 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
2736 | 1.16:</em></span> Max = 308ε (Mean = 142ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_k_GSL_1_16_Bessel_Kv_Mathworld_Data_large_values_">And | |
2737 | other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> | |
2738 | Max = 84.6ε (Mean = 37.8ε)) | |
2739 | </p> | |
2740 | </td> | |
2741 | <td> | |
2742 | <p> | |
2743 | <span class="blue">Max = 43.1ε (Mean = 21.3ε)</span> | |
2744 | </p> | |
2745 | </td> | |
2746 | </tr> | |
2747 | <tr> | |
2748 | <td> | |
2749 | <p> | |
2750 | Bessel Kn: Random Data | |
2751 | </p> | |
2752 | </td> | |
2753 | <td> | |
2754 | <p> | |
2755 | <span class="blue">Max = 7.47ε (Mean = 1.4ε)</span> | |
2756 | </p> | |
2757 | </td> | |
2758 | <td> | |
2759 | <p> | |
2760 | <span class="blue">Max = 4.55ε (Mean = 1.09ε)</span><br> <br> | |
2761 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 13.9ε (Mean = 2.91ε)) | |
2762 | </p> | |
2763 | </td> | |
2764 | <td> | |
2765 | <p> | |
2766 | <span class="blue">Max = 0.764ε (Mean = 0.0348ε)</span><br> | |
2767 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 8.71ε (Mean = 1.76ε) | |
2768 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_k_GSL_1_16_Bessel_Kn_Random_Data">And | |
2769 | other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> | |
2770 | Max = 7.47ε (Mean = 1.34ε)) | |
2771 | </p> | |
2772 | </td> | |
2773 | <td> | |
2774 | <p> | |
2775 | <span class="blue">Max = 4.55ε (Mean = 1.21ε)</span> | |
2776 | </p> | |
2777 | </td> | |
2778 | </tr> | |
2779 | <tr> | |
2780 | <td> | |
2781 | <p> | |
2782 | Bessel Kv: Random Data | |
2783 | </p> | |
2784 | </td> | |
2785 | <td> | |
2786 | <p> | |
2787 | <span class="blue">Max = 8.33ε (Mean = 1.62ε)</span> | |
2788 | </p> | |
2789 | </td> | |
2790 | <td> | |
2791 | <p> | |
2792 | <span class="blue">Max = 7.88ε (Mean = 1.48ε)</span><br> <br> | |
2793 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 13.6ε (Mean = 2.68ε) | |
2794 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_k__tr1_cmath__Bessel_Kv_Random_Data">And | |
2795 | other failures.</a>) | |
2796 | </p> | |
2797 | </td> | |
2798 | <td> | |
2799 | <p> | |
2800 | <span class="blue">Max = 0.507ε (Mean = 0.0313ε)</span><br> | |
2801 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 9.71ε (Mean = 1.47ε) | |
2802 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_k_GSL_1_16_Bessel_Kv_Random_Data">And | |
2803 | other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> | |
2804 | Max = 7.37ε (Mean = 1.49ε)) | |
2805 | </p> | |
2806 | </td> | |
2807 | <td> | |
2808 | <p> | |
2809 | <span class="blue">Max = 7.88ε (Mean = 1.49ε)</span> | |
2810 | </p> | |
2811 | </td> | |
2812 | </tr> | |
2813 | </tbody> | |
2814 | </table></div> | |
2815 | </div> | |
2816 | <br class="table-break"><div class="table"> | |
2817 | <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k_integer_orders_"></a><p class="title"><b>Table 17.18. Error rates for cyl_bessel_k (integer orders)</b></p> | |
2818 | <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k (integer orders)"> | |
2819 | <colgroup> | |
2820 | <col> | |
2821 | <col> | |
2822 | <col> | |
2823 | <col> | |
2824 | <col> | |
2825 | </colgroup> | |
2826 | <thead><tr> | |
2827 | <th> | |
2828 | </th> | |
2829 | <th> | |
2830 | <p> | |
2831 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
2832 | </p> | |
2833 | </th> | |
2834 | <th> | |
2835 | <p> | |
2836 | GNU C++ version 5.1.0<br> linux<br> long double | |
2837 | </p> | |
2838 | </th> | |
2839 | <th> | |
2840 | <p> | |
2841 | GNU C++ version 5.1.0<br> linux<br> double | |
2842 | </p> | |
2843 | </th> | |
2844 | <th> | |
2845 | <p> | |
2846 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
2847 | </p> | |
2848 | </th> | |
2849 | </tr></thead> | |
2850 | <tbody> | |
2851 | <tr> | |
2852 | <td> | |
2853 | <p> | |
2854 | Bessel K0: Mathworld Data (Integer Version) | |
2855 | </p> | |
2856 | </td> | |
2857 | <td> | |
2858 | <p> | |
2859 | <span class="blue">Max = 1.55ε (Mean = 0.837ε)</span> | |
2860 | </p> | |
2861 | </td> | |
2862 | <td> | |
2863 | <p> | |
2864 | <span class="blue">Max = 4.16ε (Mean = 1.46ε)</span><br> <br> | |
2865 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 9.33ε (Mean = 3.25ε)) | |
2866 | </p> | |
2867 | </td> | |
2868 | <td> | |
2869 | <p> | |
2870 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
2871 | 1.16:</em></span> Max = 1.2ε (Mean = 0.733ε))<br> (<span class="emphasis"><em>Rmath | |
2872 | 3.0.2:</em></span> Max = 0.833ε (Mean = 0.601ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
2873 | Max = 1.1e+06ε (Mean = 3.68e+05ε)) | |
2874 | </p> | |
2875 | </td> | |
2876 | <td> | |
2877 | <p> | |
2878 | <span class="blue">Max = 4.16ε (Mean = 1.49ε)</span> | |
2879 | </p> | |
2880 | </td> | |
2881 | </tr> | |
2882 | <tr> | |
2883 | <td> | |
2884 | <p> | |
2885 | Bessel K1: Mathworld Data (Integer Version) | |
2886 | </p> | |
2887 | </td> | |
2888 | <td> | |
2889 | <p> | |
2890 | <span class="blue">Max = 1ε (Mean = 0.573ε)</span> | |
2891 | </p> | |
2892 | </td> | |
2893 | <td> | |
2894 | <p> | |
2895 | <span class="blue">Max = 1.8ε (Mean = 1.02ε)</span><br> <br> | |
2896 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 8.94ε (Mean = 3.19ε)) | |
2897 | </p> | |
2898 | </td> | |
2899 | <td> | |
2900 | <p> | |
2901 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
2902 | 1.16:</em></span> Max = 0.626ε (Mean = 0.333ε))<br> (<span class="emphasis"><em>Rmath | |
2903 | 3.0.2:</em></span> Max = 0.894ε (Mean = 0.516ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
2904 | Max = 5.38e+05ε (Mean = 1.79e+05ε)) | |
2905 | </p> | |
2906 | </td> | |
2907 | <td> | |
2908 | <p> | |
2909 | <span class="blue">Max = 1.8ε (Mean = 1.02ε)</span> | |
2910 | </p> | |
2911 | </td> | |
2912 | </tr> | |
2913 | <tr> | |
2914 | <td> | |
2915 | <p> | |
2916 | Bessel Kn: Mathworld Data (Integer Version) | |
2917 | </p> | |
2918 | </td> | |
2919 | <td> | |
2920 | <p> | |
2921 | <span class="blue">Max = 3.63ε (Mean = 1.46ε)</span> | |
2922 | </p> | |
2923 | </td> | |
2924 | <td> | |
2925 | <p> | |
2926 | <span class="blue">Max = 4.48ε (Mean = 2.14ε)</span><br> <br> | |
2927 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 12.9ε (Mean = 4.91ε) | |
2928 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_k_integer_orders___tr1_cmath__Bessel_Kn_Mathworld_Data_Integer_Version_">And | |
2929 | other failures.</a>) | |
2930 | </p> | |
2931 | </td> | |
2932 | <td> | |
2933 | <p> | |
2934 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
2935 | 1.16:</em></span> Max = 168ε (Mean = 59.5ε))<br> (<span class="emphasis"><em>Rmath | |
2936 | 3.0.2:</em></span> Max = 8.48ε (Mean = 2.98ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
2937 | <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_k_integer_orders__Cephes_Bessel_Kn_Mathworld_Data_Integer_Version_">And | |
2938 | other failures.</a>)</span> | |
2939 | </p> | |
2940 | </td> | |
2941 | <td> | |
2942 | <p> | |
2943 | <span class="blue">Max = 4.48ε (Mean = 1.98ε)</span> | |
2944 | </p> | |
2945 | </td> | |
2946 | </tr> | |
2947 | </tbody> | |
2948 | </table></div> | |
2949 | </div> | |
2950 | <br class="table-break"><div class="table"> | |
2951 | <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k_prime"></a><p class="title"><b>Table 17.19. Error rates for cyl_bessel_k_prime</b></p> | |
2952 | <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime"> | |
2953 | <colgroup> | |
2954 | <col> | |
2955 | <col> | |
2956 | <col> | |
2957 | <col> | |
2958 | <col> | |
2959 | </colgroup> | |
2960 | <thead><tr> | |
2961 | <th> | |
2962 | </th> | |
2963 | <th> | |
2964 | <p> | |
2965 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
2966 | </p> | |
2967 | </th> | |
2968 | <th> | |
2969 | <p> | |
2970 | GNU C++ version 5.1.0<br> linux<br> double | |
2971 | </p> | |
2972 | </th> | |
2973 | <th> | |
2974 | <p> | |
2975 | GNU C++ version 5.1.0<br> linux<br> long double | |
2976 | </p> | |
2977 | </th> | |
2978 | <th> | |
2979 | <p> | |
2980 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
2981 | </p> | |
2982 | </th> | |
2983 | </tr></thead> | |
2984 | <tbody> | |
2985 | <tr> | |
2986 | <td> | |
2987 | <p> | |
2988 | Bessel K'0: Mathworld Data | |
2989 | </p> | |
2990 | </td> | |
2991 | <td> | |
2992 | <p> | |
2993 | <span class="blue">Max = 1ε (Mean = 0.573ε)</span> | |
2994 | </p> | |
2995 | </td> | |
2996 | <td> | |
2997 | <p> | |
2998 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
2999 | </p> | |
3000 | </td> | |
3001 | <td> | |
3002 | <p> | |
3003 | <span class="blue">Max = 1.8ε (Mean = 1.02ε)</span> | |
3004 | </p> | |
3005 | </td> | |
3006 | <td> | |
3007 | <p> | |
3008 | <span class="blue">Max = 1.8ε (Mean = 1.02ε)</span> | |
3009 | </p> | |
3010 | </td> | |
3011 | </tr> | |
3012 | <tr> | |
3013 | <td> | |
3014 | <p> | |
3015 | Bessel K'1: Mathworld Data | |
3016 | </p> | |
3017 | </td> | |
3018 | <td> | |
3019 | <p> | |
3020 | <span class="blue">Max = 1.09ε (Mean = 0.607ε)</span> | |
3021 | </p> | |
3022 | </td> | |
3023 | <td> | |
3024 | <p> | |
3025 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
3026 | </p> | |
3027 | </td> | |
3028 | <td> | |
3029 | <p> | |
3030 | <span class="blue">Max = 1.96ε (Mean = 1ε)</span> | |
3031 | </p> | |
3032 | </td> | |
3033 | <td> | |
3034 | <p> | |
3035 | <span class="blue">Max = 1.96ε (Mean = 1.04ε)</span> | |
3036 | </p> | |
3037 | </td> | |
3038 | </tr> | |
3039 | <tr> | |
3040 | <td> | |
3041 | <p> | |
3042 | Bessel K'n: Mathworld Data | |
3043 | </p> | |
3044 | </td> | |
3045 | <td> | |
3046 | <p> | |
3047 | <span class="blue">Max = 4.17ε (Mean = 1.74ε)</span> | |
3048 | </p> | |
3049 | </td> | |
3050 | <td> | |
3051 | <p> | |
3052 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
3053 | </p> | |
3054 | </td> | |
3055 | <td> | |
3056 | <p> | |
3057 | <span class="blue">Max = 4.47ε (Mean = 2.05ε)</span> | |
3058 | </p> | |
3059 | </td> | |
3060 | <td> | |
3061 | <p> | |
3062 | <span class="blue">Max = 4.47ε (Mean = 1.93ε)</span> | |
3063 | </p> | |
3064 | </td> | |
3065 | </tr> | |
3066 | <tr> | |
3067 | <td> | |
3068 | <p> | |
3069 | Bessel K'v: Mathworld Data | |
3070 | </p> | |
3071 | </td> | |
3072 | <td> | |
3073 | <p> | |
3074 | <span class="blue">Max = 3.94ε (Mean = 1.43ε)</span> | |
3075 | </p> | |
3076 | </td> | |
3077 | <td> | |
3078 | <p> | |
3079 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
3080 | </p> | |
3081 | </td> | |
3082 | <td> | |
3083 | <p> | |
3084 | <span class="blue">Max = 3.94ε (Mean = 2.49ε)</span> | |
3085 | </p> | |
3086 | </td> | |
3087 | <td> | |
3088 | <p> | |
3089 | <span class="blue">Max = 3.94ε (Mean = 2.35ε)</span> | |
3090 | </p> | |
3091 | </td> | |
3092 | </tr> | |
3093 | <tr> | |
3094 | <td> | |
3095 | <p> | |
3096 | Bessel K'v: Mathworld Data (large values) | |
3097 | </p> | |
3098 | </td> | |
3099 | <td> | |
3100 | <p> | |
3101 | <span class="blue">Max = 18.6ε (Mean = 12.1ε)</span> | |
3102 | </p> | |
3103 | </td> | |
3104 | <td> | |
3105 | <p> | |
3106 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
3107 | </p> | |
3108 | </td> | |
3109 | <td> | |
3110 | <p> | |
3111 | <span class="blue">Max = 59.2ε (Mean = 42.9ε)</span> | |
3112 | </p> | |
3113 | </td> | |
3114 | <td> | |
3115 | <p> | |
3116 | <span class="blue">Max = 59.8ε (Mean = 43.4ε)</span> | |
3117 | </p> | |
3118 | </td> | |
3119 | </tr> | |
3120 | <tr> | |
3121 | <td> | |
3122 | <p> | |
3123 | Bessel K'n: Random Data | |
3124 | </p> | |
3125 | </td> | |
3126 | <td> | |
3127 | <p> | |
3128 | <span class="blue">Max = 8.18ε (Mean = 1.45ε)</span> | |
3129 | </p> | |
3130 | </td> | |
3131 | <td> | |
3132 | <p> | |
3133 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
3134 | </p> | |
3135 | </td> | |
3136 | <td> | |
3137 | <p> | |
3138 | <span class="blue">Max = 4.53ε (Mean = 1.12ε)</span> | |
3139 | </p> | |
3140 | </td> | |
3141 | <td> | |
3142 | <p> | |
3143 | <span class="blue">Max = 4.45ε (Mean = 1.23ε)</span> | |
3144 | </p> | |
3145 | </td> | |
3146 | </tr> | |
3147 | <tr> | |
3148 | <td> | |
3149 | <p> | |
3150 | Bessel K'v: Random Data | |
3151 | </p> | |
3152 | </td> | |
3153 | <td> | |
3154 | <p> | |
3155 | <span class="blue">Max = 8.32ε (Mean = 1.65ε)</span> | |
3156 | </p> | |
3157 | </td> | |
3158 | <td> | |
3159 | <p> | |
3160 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
3161 | </p> | |
3162 | </td> | |
3163 | <td> | |
3164 | <p> | |
3165 | <span class="blue">Max = 7.95ε (Mean = 1.53ε)</span> | |
3166 | </p> | |
3167 | </td> | |
3168 | <td> | |
3169 | <p> | |
3170 | <span class="blue">Max = 7.95ε (Mean = 1.55ε)</span> | |
3171 | </p> | |
3172 | </td> | |
3173 | </tr> | |
3174 | </tbody> | |
3175 | </table></div> | |
3176 | </div> | |
3177 | <br class="table-break"><div class="table"> | |
3178 | <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k_prime_integer_orders_"></a><p class="title"><b>Table 17.20. Error rates for cyl_bessel_k_prime (integer orders)</b></p> | |
3179 | <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime (integer orders)"> | |
3180 | <colgroup> | |
3181 | <col> | |
3182 | <col> | |
3183 | <col> | |
3184 | <col> | |
3185 | <col> | |
3186 | </colgroup> | |
3187 | <thead><tr> | |
3188 | <th> | |
3189 | </th> | |
3190 | <th> | |
3191 | <p> | |
3192 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
3193 | </p> | |
3194 | </th> | |
3195 | <th> | |
3196 | <p> | |
3197 | GNU C++ version 5.1.0<br> linux<br> double | |
3198 | </p> | |
3199 | </th> | |
3200 | <th> | |
3201 | <p> | |
3202 | GNU C++ version 5.1.0<br> linux<br> long double | |
3203 | </p> | |
3204 | </th> | |
3205 | <th> | |
3206 | <p> | |
3207 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
3208 | </p> | |
3209 | </th> | |
3210 | </tr></thead> | |
3211 | <tbody> | |
3212 | <tr> | |
3213 | <td> | |
3214 | <p> | |
3215 | Bessel K'0: Mathworld Data (Integer Version) | |
3216 | </p> | |
3217 | </td> | |
3218 | <td> | |
3219 | <p> | |
3220 | <span class="blue">Max = 1ε (Mean = 0.573ε)</span> | |
3221 | </p> | |
3222 | </td> | |
3223 | <td> | |
3224 | <p> | |
3225 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
3226 | </p> | |
3227 | </td> | |
3228 | <td> | |
3229 | <p> | |
3230 | <span class="blue">Max = 1.8ε (Mean = 1.02ε)</span> | |
3231 | </p> | |
3232 | </td> | |
3233 | <td> | |
3234 | <p> | |
3235 | <span class="blue">Max = 1.8ε (Mean = 1.02ε)</span> | |
3236 | </p> | |
3237 | </td> | |
3238 | </tr> | |
3239 | <tr> | |
3240 | <td> | |
3241 | <p> | |
3242 | Bessel K'1: Mathworld Data (Integer Version) | |
3243 | </p> | |
3244 | </td> | |
3245 | <td> | |
3246 | <p> | |
3247 | <span class="blue">Max = 1.09ε (Mean = 0.607ε)</span> | |
3248 | </p> | |
3249 | </td> | |
3250 | <td> | |
3251 | <p> | |
3252 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
3253 | </p> | |
3254 | </td> | |
3255 | <td> | |
3256 | <p> | |
3257 | <span class="blue">Max = 1.96ε (Mean = 1ε)</span> | |
3258 | </p> | |
3259 | </td> | |
3260 | <td> | |
3261 | <p> | |
3262 | <span class="blue">Max = 1.96ε (Mean = 1.04ε)</span> | |
3263 | </p> | |
3264 | </td> | |
3265 | </tr> | |
3266 | <tr> | |
3267 | <td> | |
3268 | <p> | |
3269 | Bessel K'n: Mathworld Data (Integer Version) | |
3270 | </p> | |
3271 | </td> | |
3272 | <td> | |
3273 | <p> | |
3274 | <span class="blue">Max = 4.17ε (Mean = 1.74ε)</span> | |
3275 | </p> | |
3276 | </td> | |
3277 | <td> | |
3278 | <p> | |
3279 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
3280 | </p> | |
3281 | </td> | |
3282 | <td> | |
3283 | <p> | |
3284 | <span class="blue">Max = 4.47ε (Mean = 2.05ε)</span> | |
3285 | </p> | |
3286 | </td> | |
3287 | <td> | |
3288 | <p> | |
3289 | <span class="blue">Max = 4.47ε (Mean = 1.93ε)</span> | |
3290 | </p> | |
3291 | </td> | |
3292 | </tr> | |
3293 | </tbody> | |
3294 | </table></div> | |
3295 | </div> | |
3296 | <br class="table-break"><div class="table"> | |
3297 | <a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann"></a><p class="title"><b>Table 17.21. Error rates for cyl_neumann</b></p> | |
3298 | <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann"> | |
3299 | <colgroup> | |
3300 | <col> | |
3301 | <col> | |
3302 | <col> | |
3303 | <col> | |
3304 | <col> | |
3305 | </colgroup> | |
3306 | <thead><tr> | |
3307 | <th> | |
3308 | </th> | |
3309 | <th> | |
3310 | <p> | |
3311 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
3312 | </p> | |
3313 | </th> | |
3314 | <th> | |
3315 | <p> | |
3316 | GNU C++ version 5.1.0<br> linux<br> double | |
3317 | </p> | |
3318 | </th> | |
3319 | <th> | |
3320 | <p> | |
3321 | GNU C++ version 5.1.0<br> linux<br> long double | |
3322 | </p> | |
3323 | </th> | |
3324 | <th> | |
3325 | <p> | |
3326 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
3327 | </p> | |
3328 | </th> | |
3329 | </tr></thead> | |
3330 | <tbody> | |
3331 | <tr> | |
3332 | <td> | |
3333 | <p> | |
3334 | Y0: Mathworld Data | |
3335 | </p> | |
3336 | </td> | |
3337 | <td> | |
3338 | <p> | |
3339 | <span class="blue">Max = 4.61ε (Mean = 2.29ε)</span> | |
3340 | </p> | |
3341 | </td> | |
3342 | <td> | |
3343 | <p> | |
3344 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
3345 | 1.16:</em></span> Max = 60.9ε (Mean = 20.4ε))<br> (<span class="emphasis"><em>Rmath | |
3346 | 3.0.2:</em></span> Max = 167ε (Mean = 56.5ε)) | |
3347 | </p> | |
3348 | </td> | |
3349 | <td> | |
3350 | <p> | |
3351 | <span class="blue">Max = 5.59ε (Mean = 2.54ε)</span><br> <br> | |
3352 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.05e+05ε (Mean = | |
3353 | 6.87e+04ε)) | |
3354 | </p> | |
3355 | </td> | |
3356 | <td> | |
3357 | <p> | |
3358 | <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span> | |
3359 | </p> | |
3360 | </td> | |
3361 | </tr> | |
3362 | <tr> | |
3363 | <td> | |
3364 | <p> | |
3365 | Y1: Mathworld Data | |
3366 | </p> | |
3367 | </td> | |
3368 | <td> | |
3369 | <p> | |
3370 | <span class="blue">Max = 4.75ε (Mean = 1.72ε)</span> | |
3371 | </p> | |
3372 | </td> | |
3373 | <td> | |
3374 | <p> | |
3375 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
3376 | 1.16:</em></span> Max = 23.4ε (Mean = 8.1ε))<br> (<span class="emphasis"><em>Rmath | |
3377 | 3.0.2:</em></span> Max = 193ε (Mean = 64.4ε)) | |
3378 | </p> | |
3379 | </td> | |
3380 | <td> | |
3381 | <p> | |
3382 | <span class="blue">Max = 12.7ε (Mean = 4.34ε)</span><br> <br> | |
3383 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 9.71e+03ε (Mean = | |
3384 | 4.08e+03ε)) | |
3385 | </p> | |
3386 | </td> | |
3387 | <td> | |
3388 | <p> | |
3389 | <span class="blue">Max = 6.33ε (Mean = 2.29ε)</span> | |
3390 | </p> | |
3391 | </td> | |
3392 | </tr> | |
3393 | <tr> | |
3394 | <td> | |
3395 | <p> | |
3396 | Yn: Mathworld Data | |
3397 | </p> | |
3398 | </td> | |
3399 | <td> | |
3400 | <p> | |
3401 | <span class="blue">Max = 35ε (Mean = 11.8ε)</span> | |
3402 | </p> | |
3403 | </td> | |
3404 | <td> | |
3405 | <p> | |
3406 | <span class="blue">Max = 0.993ε (Mean = 0.314ε)</span><br> <br> | |
3407 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.41e+05ε (Mean = 7.62e+04ε) | |
3408 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_neumann_GSL_1_16_Yn_Mathworld_Data">And | |
3409 | other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> | |
3410 | Max = 1.24e+04ε (Mean = 4e+03ε)) | |
3411 | </p> | |
3412 | </td> | |
3413 | <td> | |
3414 | <p> | |
3415 | <span class="blue">Max = 55.2ε (Mean = 17.7ε)</span><br> <br> | |
3416 | (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max | |
3417 | = 2.2e+20ε (Mean = 6.97e+19ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_neumann__tr1_cmath__Yn_Mathworld_Data">And | |
3418 | other failures.</a>)</span> | |
3419 | </p> | |
3420 | </td> | |
3421 | <td> | |
3422 | <p> | |
3423 | <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span> | |
3424 | </p> | |
3425 | </td> | |
3426 | </tr> | |
3427 | <tr> | |
3428 | <td> | |
3429 | <p> | |
3430 | Yv: Mathworld Data | |
3431 | </p> | |
3432 | </td> | |
3433 | <td> | |
3434 | <p> | |
3435 | <span class="blue">Max = 7.89ε (Mean = 3.27ε)</span> | |
3436 | </p> | |
3437 | </td> | |
3438 | <td> | |
3439 | <p> | |
3440 | <span class="blue">Max = 10ε (Mean = 3.02ε)</span><br> <br> | |
3441 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.07e+05ε (Mean = 3.22e+04ε) | |
3442 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_neumann_GSL_1_16_Yv_Mathworld_Data">And | |
3443 | other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> | |
3444 | Max = 1.05e+03ε (Mean = 326ε)) | |
3445 | </p> | |
3446 | </td> | |
3447 | <td> | |
3448 | <p> | |
3449 | <span class="blue">Max = 10.7ε (Mean = 4.92ε)</span><br> <br> | |
3450 | (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max | |
3451 | = 3.49e+15ε (Mean = 1.05e+15ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_neumann__tr1_cmath__Yv_Mathworld_Data">And | |
3452 | other failures.</a>)</span> | |
3453 | </p> | |
3454 | </td> | |
3455 | <td> | |
3456 | <p> | |
3457 | <span class="blue">Max = 10.7ε (Mean = 5.1ε)</span> | |
3458 | </p> | |
3459 | </td> | |
3460 | </tr> | |
3461 | <tr> | |
3462 | <td> | |
3463 | <p> | |
3464 | Yv: Mathworld Data (large values) | |
3465 | </p> | |
3466 | </td> | |
3467 | <td> | |
3468 | <p> | |
3469 | <span class="blue">Max = 0.682ε (Mean = 0.35ε)</span> | |
3470 | </p> | |
3471 | </td> | |
3472 | <td> | |
3473 | <p> | |
3474 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
3475 | 1.16:</em></span> Max = 60.8ε (Mean = 23ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_neumann_GSL_1_16_Yv_Mathworld_Data_large_values_">And | |
3476 | other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> | |
3477 | <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_neumann_Rmath_3_0_2_Yv_Mathworld_Data_large_values_">And | |
3478 | other failures.</a>)</span> | |
3479 | </p> | |
3480 | </td> | |
3481 | <td> | |
3482 | <p> | |
3483 | <span class="blue">Max = 1.57ε (Mean = 1.17ε)</span><br> <br> | |
3484 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 43.2ε (Mean = 16.3ε) | |
3485 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_neumann__tr1_cmath__Yv_Mathworld_Data_large_values_">And | |
3486 | other failures.</a>) | |
3487 | </p> | |
3488 | </td> | |
3489 | <td> | |
3490 | <p> | |
3491 | <span class="blue">Max = 1.57ε (Mean = 1.24ε)</span> | |
3492 | </p> | |
3493 | </td> | |
3494 | </tr> | |
3495 | <tr> | |
3496 | <td> | |
3497 | <p> | |
3498 | Y0 and Y1: Random Data | |
3499 | </p> | |
3500 | </td> | |
3501 | <td> | |
3502 | <p> | |
3503 | <span class="blue">Max = 4.17ε (Mean = 1.24ε)</span> | |
3504 | </p> | |
3505 | </td> | |
3506 | <td> | |
3507 | <p> | |
3508 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
3509 | 1.16:</em></span> Max = 34.4ε (Mean = 8.9ε))<br> (<span class="emphasis"><em>Rmath | |
3510 | 3.0.2:</em></span> Max = 83ε (Mean = 14.2ε)) | |
3511 | </p> | |
3512 | </td> | |
3513 | <td> | |
3514 | <p> | |
3515 | <span class="blue">Max = 11.8ε (Mean = 3.28ε)</span><br> <br> | |
3516 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.59e+03ε (Mean = | |
3517 | 500ε)) | |
3518 | </p> | |
3519 | </td> | |
3520 | <td> | |
3521 | <p> | |
3522 | <span class="blue">Max = 10.8ε (Mean = 3.04ε)</span> | |
3523 | </p> | |
3524 | </td> | |
3525 | </tr> | |
3526 | <tr> | |
3527 | <td> | |
3528 | <p> | |
3529 | Yn: Random Data | |
3530 | </p> | |
3531 | </td> | |
3532 | <td> | |
3533 | <p> | |
3534 | <span class="blue">Max = 117ε (Mean = 10.2ε)</span> | |
3535 | </p> | |
3536 | </td> | |
3537 | <td> | |
3538 | <p> | |
3539 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
3540 | 1.16:</em></span> Max = 500ε (Mean = 47.8ε))<br> (<span class="emphasis"><em>Rmath | |
3541 | 3.0.2:</em></span> Max = 691ε (Mean = 67.9ε)) | |
3542 | </p> | |
3543 | </td> | |
3544 | <td> | |
3545 | <p> | |
3546 | <span class="blue">Max = 338ε (Mean = 28.2ε)</span><br> <br> | |
3547 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 4.01e+03ε (Mean = | |
3548 | 348ε)) | |
3549 | </p> | |
3550 | </td> | |
3551 | <td> | |
3552 | <p> | |
3553 | <span class="blue">Max = 338ε (Mean = 27.5ε)</span> | |
3554 | </p> | |
3555 | </td> | |
3556 | </tr> | |
3557 | <tr> | |
3558 | <td> | |
3559 | <p> | |
3560 | Yv: Random Data | |
3561 | </p> | |
3562 | </td> | |
3563 | <td> | |
3564 | <p> | |
3565 | <span class="blue">Max = 1.23e+003ε (Mean = 69.9ε)</span> | |
3566 | </p> | |
3567 | </td> | |
3568 | <td> | |
3569 | <p> | |
3570 | <span class="blue">Max = 1.53ε (Mean = 0.102ε)</span><br> <br> | |
3571 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.41e+06ε (Mean = 7.67e+04ε))<br> | |
3572 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 1.79e+05ε (Mean = 9.64e+03ε)) | |
3573 | </p> | |
3574 | </td> | |
3575 | <td> | |
3576 | <p> | |
3577 | <span class="blue">Max = 2.08e+03ε (Mean = 149ε)</span><br> | |
3578 | <br> (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max | |
3579 | = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_neumann__tr1_cmath__Yv_Random_Data">And | |
3580 | other failures.</a>)</span> | |
3581 | </p> | |
3582 | </td> | |
3583 | <td> | |
3584 | <p> | |
3585 | <span class="blue">Max = 2.08e+03ε (Mean = 149ε)</span> | |
3586 | </p> | |
3587 | </td> | |
3588 | </tr> | |
3589 | </tbody> | |
3590 | </table></div> | |
3591 | </div> | |
3592 | <br class="table-break"><div class="table"> | |
3593 | <a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann_integer_orders_"></a><p class="title"><b>Table 17.22. Error rates for cyl_neumann (integer orders)</b></p> | |
3594 | <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann (integer orders)"> | |
3595 | <colgroup> | |
3596 | <col> | |
3597 | <col> | |
3598 | <col> | |
3599 | <col> | |
3600 | <col> | |
3601 | </colgroup> | |
3602 | <thead><tr> | |
3603 | <th> | |
3604 | </th> | |
3605 | <th> | |
3606 | <p> | |
3607 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
3608 | </p> | |
3609 | </th> | |
3610 | <th> | |
3611 | <p> | |
3612 | GNU C++ version 5.1.0<br> linux<br> double | |
3613 | </p> | |
3614 | </th> | |
3615 | <th> | |
3616 | <p> | |
3617 | GNU C++ version 5.1.0<br> linux<br> long double | |
3618 | </p> | |
3619 | </th> | |
3620 | <th> | |
3621 | <p> | |
3622 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
3623 | </p> | |
3624 | </th> | |
3625 | </tr></thead> | |
3626 | <tbody> | |
3627 | <tr> | |
3628 | <td> | |
3629 | <p> | |
3630 | Y0: Mathworld Data (Integer Version) | |
3631 | </p> | |
3632 | </td> | |
3633 | <td> | |
3634 | <p> | |
3635 | <span class="blue">Max = 4.61ε (Mean = 2.29ε)</span><br> <br> | |
3636 | (<span class="emphasis"><em><math.h>:</em></span> Max = 5.37e+003ε (Mean = 1.81e+003ε)) | |
3637 | </p> | |
3638 | </td> | |
3639 | <td> | |
3640 | <p> | |
3641 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
3642 | 1.16:</em></span> Max = 6.46ε (Mean = 2.38ε))<br> (<span class="emphasis"><em>Rmath | |
3643 | 3.0.2:</em></span> Max = 167ε (Mean = 56.5ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
3644 | Max = 5.37e+03ε (Mean = 1.81e+03ε)) | |
3645 | </p> | |
3646 | </td> | |
3647 | <td> | |
3648 | <p> | |
3649 | <span class="blue">Max = 5.59ε (Mean = 2.54ε)</span><br> <br> | |
3650 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.05e+05ε (Mean = | |
3651 | 6.87e+04ε)) | |
3652 | </p> | |
3653 | </td> | |
3654 | <td> | |
3655 | <p> | |
3656 | <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span> | |
3657 | </p> | |
3658 | </td> | |
3659 | </tr> | |
3660 | <tr> | |
3661 | <td> | |
3662 | <p> | |
3663 | Y1: Mathworld Data (Integer Version) | |
3664 | </p> | |
3665 | </td> | |
3666 | <td> | |
3667 | <p> | |
3668 | <span class="blue">Max = 4.75ε (Mean = 1.72ε)</span><br> <br> | |
3669 | (<span class="emphasis"><em><math.h>:</em></span> Max = 1.86e+004ε (Mean = 6.2e+003ε)) | |
3670 | </p> | |
3671 | </td> | |
3672 | <td> | |
3673 | <p> | |
3674 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
3675 | 1.16:</em></span> Max = 1.51ε (Mean = 0.839ε))<br> (<span class="emphasis"><em>Rmath | |
3676 | 3.0.2:</em></span> Max = 193ε (Mean = 64.4ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
3677 | Max = 1.86e+04ε (Mean = 6.2e+03ε)) | |
3678 | </p> | |
3679 | </td> | |
3680 | <td> | |
3681 | <p> | |
3682 | <span class="blue">Max = 12.7ε (Mean = 4.34ε)</span><br> <br> | |
3683 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 9.71e+03ε (Mean = | |
3684 | 4.08e+03ε)) | |
3685 | </p> | |
3686 | </td> | |
3687 | <td> | |
3688 | <p> | |
3689 | <span class="blue">Max = 6.33ε (Mean = 2.29ε)</span> | |
3690 | </p> | |
3691 | </td> | |
3692 | </tr> | |
3693 | <tr> | |
3694 | <td> | |
3695 | <p> | |
3696 | Yn: Mathworld Data (Integer Version) | |
3697 | </p> | |
3698 | </td> | |
3699 | <td> | |
3700 | <p> | |
3701 | <span class="blue">Max = 35ε (Mean = 11.8ε)</span><br> <br> | |
3702 | (<span class="emphasis"><em><math.h>:</em></span> Max = 2.49e+005ε (Mean = 8.14e+004ε)) | |
3703 | </p> | |
3704 | </td> | |
3705 | <td> | |
3706 | <p> | |
3707 | <span class="blue">Max = 0.993ε (Mean = 0.314ε)</span><br> <br> | |
3708 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.41e+05ε (Mean = 7.62e+04ε))<br> | |
3709 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 1.24e+04ε (Mean = 4e+03ε))<br> | |
3710 | (<span class="emphasis"><em>Cephes:</em></span> Max = 2.49e+05ε (Mean = 8.14e+04ε)) | |
3711 | </p> | |
3712 | </td> | |
3713 | <td> | |
3714 | <p> | |
3715 | <span class="blue">Max = 55.2ε (Mean = 17.7ε)</span><br> <br> | |
3716 | (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max | |
3717 | = 2.2e+20ε (Mean = 6.97e+19ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_neumann_integer_orders___tr1_cmath__Yn_Mathworld_Data_Integer_Version_">And | |
3718 | other failures.</a>)</span> | |
3719 | </p> | |
3720 | </td> | |
3721 | <td> | |
3722 | <p> | |
3723 | <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span> | |
3724 | </p> | |
3725 | </td> | |
3726 | </tr> | |
3727 | </tbody> | |
3728 | </table></div> | |
3729 | </div> | |
3730 | <br class="table-break"><div class="table"> | |
3731 | <a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann_prime"></a><p class="title"><b>Table 17.23. Error rates for cyl_neumann_prime</b></p> | |
3732 | <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime"> | |
3733 | <colgroup> | |
3734 | <col> | |
3735 | <col> | |
3736 | <col> | |
3737 | <col> | |
3738 | <col> | |
3739 | </colgroup> | |
3740 | <thead><tr> | |
3741 | <th> | |
3742 | </th> | |
3743 | <th> | |
3744 | <p> | |
3745 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
3746 | </p> | |
3747 | </th> | |
3748 | <th> | |
3749 | <p> | |
3750 | GNU C++ version 5.1.0<br> linux<br> double | |
3751 | </p> | |
3752 | </th> | |
3753 | <th> | |
3754 | <p> | |
3755 | GNU C++ version 5.1.0<br> linux<br> long double | |
3756 | </p> | |
3757 | </th> | |
3758 | <th> | |
3759 | <p> | |
3760 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
3761 | </p> | |
3762 | </th> | |
3763 | </tr></thead> | |
3764 | <tbody> | |
3765 | <tr> | |
3766 | <td> | |
3767 | <p> | |
3768 | Y'0: Mathworld Data | |
3769 | </p> | |
3770 | </td> | |
3771 | <td> | |
3772 | <p> | |
3773 | <span class="blue">Max = 4.75ε (Mean = 1.75ε)</span> | |
3774 | </p> | |
3775 | </td> | |
3776 | <td> | |
3777 | <p> | |
3778 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
3779 | </p> | |
3780 | </td> | |
3781 | <td> | |
3782 | <p> | |
3783 | <span class="blue">Max = 12.7ε (Mean = 4.85ε)</span> | |
3784 | </p> | |
3785 | </td> | |
3786 | <td> | |
3787 | <p> | |
3788 | <span class="blue">Max = 6.33ε (Mean = 3.14ε)</span> | |
3789 | </p> | |
3790 | </td> | |
3791 | </tr> | |
3792 | <tr> | |
3793 | <td> | |
3794 | <p> | |
3795 | Y'1: Mathworld Data | |
3796 | </p> | |
3797 | </td> | |
3798 | <td> | |
3799 | <p> | |
3800 | <span class="blue">Max = 3.08ε (Mean = 1.2ε)</span> | |
3801 | </p> | |
3802 | </td> | |
3803 | <td> | |
3804 | <p> | |
3805 | <span class="blue">Max = 0.58ε (Mean = 0.193ε)</span> | |
3806 | </p> | |
3807 | </td> | |
3808 | <td> | |
3809 | <p> | |
3810 | <span class="blue">Max = 36.6ε (Mean = 12.7ε)</span> | |
3811 | </p> | |
3812 | </td> | |
3813 | <td> | |
3814 | <p> | |
3815 | <span class="blue">Max = 34ε (Mean = 11.8ε)</span> | |
3816 | </p> | |
3817 | </td> | |
3818 | </tr> | |
3819 | <tr> | |
3820 | <td> | |
3821 | <p> | |
3822 | Y'n: Mathworld Data | |
3823 | </p> | |
3824 | </td> | |
3825 | <td> | |
3826 | <p> | |
3827 | <span class="blue">Max = 563ε (Mean = 178ε)</span> | |
3828 | </p> | |
3829 | </td> | |
3830 | <td> | |
3831 | <p> | |
3832 | <span class="blue">Max = 2.05ε (Mean = 0.677ε)</span> | |
3833 | </p> | |
3834 | </td> | |
3835 | <td> | |
3836 | <p> | |
3837 | <span class="blue">Max = 56ε (Mean = 18.2ε)</span> | |
3838 | </p> | |
3839 | </td> | |
3840 | <td> | |
3841 | <p> | |
3842 | <span class="blue">Max = 56ε (Mean = 18.2ε)</span> | |
3843 | </p> | |
3844 | </td> | |
3845 | </tr> | |
3846 | <tr> | |
3847 | <td> | |
3848 | <p> | |
3849 | Y'v: Mathworld Data | |
3850 | </p> | |
3851 | </td> | |
3852 | <td> | |
3853 | <p> | |
3854 | <span class="blue">Max = 23.7ε (Mean = 10.1ε)</span> | |
3855 | </p> | |
3856 | </td> | |
3857 | <td> | |
3858 | <p> | |
3859 | <span class="blue">Max = 21.5ε (Mean = 6.49ε)</span> | |
3860 | </p> | |
3861 | </td> | |
3862 | <td> | |
3863 | <p> | |
3864 | <span class="blue">Max = 42.5ε (Mean = 13.4ε)</span> | |
3865 | </p> | |
3866 | </td> | |
3867 | <td> | |
3868 | <p> | |
3869 | <span class="blue">Max = 42.5ε (Mean = 13.6ε)</span> | |
3870 | </p> | |
3871 | </td> | |
3872 | </tr> | |
3873 | <tr> | |
3874 | <td> | |
3875 | <p> | |
3876 | Y'v: Mathworld Data (large values) | |
3877 | </p> | |
3878 | </td> | |
3879 | <td> | |
3880 | <p> | |
3881 | <span class="blue">Max = 0.627ε (Mean = 0.237ε)</span> | |
3882 | </p> | |
3883 | </td> | |
3884 | <td> | |
3885 | <p> | |
3886 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
3887 | </p> | |
3888 | </td> | |
3889 | <td> | |
3890 | <p> | |
3891 | <span class="blue">Max = 1.57ε (Mean = 1.24ε)</span> | |
3892 | </p> | |
3893 | </td> | |
3894 | <td> | |
3895 | <p> | |
3896 | <span class="blue">Max = 1.57ε (Mean = 1.24ε)</span> | |
3897 | </p> | |
3898 | </td> | |
3899 | </tr> | |
3900 | <tr> | |
3901 | <td> | |
3902 | <p> | |
3903 | Y'0 and Y'1: Random Data | |
3904 | </p> | |
3905 | </td> | |
3906 | <td> | |
3907 | <p> | |
3908 | <span class="blue">Max = 5.95ε (Mean = 1.36ε)</span> | |
3909 | </p> | |
3910 | </td> | |
3911 | <td> | |
3912 | <p> | |
3913 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
3914 | </p> | |
3915 | </td> | |
3916 | <td> | |
3917 | <p> | |
3918 | <span class="blue">Max = 23.8ε (Mean = 3.84ε)</span> | |
3919 | </p> | |
3920 | </td> | |
3921 | <td> | |
3922 | <p> | |
3923 | <span class="blue">Max = 23.8ε (Mean = 3.69ε)</span> | |
3924 | </p> | |
3925 | </td> | |
3926 | </tr> | |
3927 | <tr> | |
3928 | <td> | |
3929 | <p> | |
3930 | Y'n: Random Data | |
3931 | </p> | |
3932 | </td> | |
3933 | <td> | |
3934 | <p> | |
3935 | <span class="blue">Max = 621ε (Mean = 36ε)</span> | |
3936 | </p> | |
3937 | </td> | |
3938 | <td> | |
3939 | <p> | |
3940 | <span class="blue">Max = 1.53ε (Mean = 0.0885ε)</span> | |
3941 | </p> | |
3942 | </td> | |
3943 | <td> | |
3944 | <p> | |
3945 | <span class="blue">Max = 2.35e+03ε (Mean = 136ε)</span> | |
3946 | </p> | |
3947 | </td> | |
3948 | <td> | |
3949 | <p> | |
3950 | <span class="blue">Max = 2.35e+03ε (Mean = 136ε)</span> | |
3951 | </p> | |
3952 | </td> | |
3953 | </tr> | |
3954 | <tr> | |
3955 | <td> | |
3956 | <p> | |
3957 | Y'v: Random Data | |
3958 | </p> | |
3959 | </td> | |
3960 | <td> | |
3961 | <p> | |
3962 | <span class="blue">Max = 3.23e+004ε (Mean = 1.13e+003ε)</span> | |
3963 | </p> | |
3964 | </td> | |
3965 | <td> | |
3966 | <p> | |
3967 | <span class="blue">Max = 56.8ε (Mean = 2.59ε)</span> | |
3968 | </p> | |
3969 | </td> | |
3970 | <td> | |
3971 | <p> | |
3972 | <span class="blue">Max = 1.16e+05ε (Mean = 5.28e+03ε)</span> | |
3973 | </p> | |
3974 | </td> | |
3975 | <td> | |
3976 | <p> | |
3977 | <span class="blue">Max = 1.16e+05ε (Mean = 5.28e+03ε)</span> | |
3978 | </p> | |
3979 | </td> | |
3980 | </tr> | |
3981 | </tbody> | |
3982 | </table></div> | |
3983 | </div> | |
3984 | <br class="table-break"><div class="table"> | |
3985 | <a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann_prime_integer_orders_"></a><p class="title"><b>Table 17.24. Error rates for cyl_neumann_prime (integer orders)</b></p> | |
3986 | <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime (integer orders)"> | |
3987 | <colgroup> | |
3988 | <col> | |
3989 | <col> | |
3990 | <col> | |
3991 | <col> | |
3992 | <col> | |
3993 | </colgroup> | |
3994 | <thead><tr> | |
3995 | <th> | |
3996 | </th> | |
3997 | <th> | |
3998 | <p> | |
3999 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
4000 | </p> | |
4001 | </th> | |
4002 | <th> | |
4003 | <p> | |
4004 | GNU C++ version 5.1.0<br> linux<br> double | |
4005 | </p> | |
4006 | </th> | |
4007 | <th> | |
4008 | <p> | |
4009 | GNU C++ version 5.1.0<br> linux<br> long double | |
4010 | </p> | |
4011 | </th> | |
4012 | <th> | |
4013 | <p> | |
4014 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
4015 | </p> | |
4016 | </th> | |
4017 | </tr></thead> | |
4018 | <tbody> | |
4019 | <tr> | |
4020 | <td> | |
4021 | <p> | |
4022 | Y'0: Mathworld Data (Integer Version) | |
4023 | </p> | |
4024 | </td> | |
4025 | <td> | |
4026 | <p> | |
4027 | <span class="blue">Max = 4.75ε (Mean = 1.75ε)</span> | |
4028 | </p> | |
4029 | </td> | |
4030 | <td> | |
4031 | <p> | |
4032 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
4033 | </p> | |
4034 | </td> | |
4035 | <td> | |
4036 | <p> | |
4037 | <span class="blue">Max = 12.7ε (Mean = 4.85ε)</span> | |
4038 | </p> | |
4039 | </td> | |
4040 | <td> | |
4041 | <p> | |
4042 | <span class="blue">Max = 6.33ε (Mean = 3.14ε)</span> | |
4043 | </p> | |
4044 | </td> | |
4045 | </tr> | |
4046 | <tr> | |
4047 | <td> | |
4048 | <p> | |
4049 | Y'1: Mathworld Data (Integer Version) | |
4050 | </p> | |
4051 | </td> | |
4052 | <td> | |
4053 | <p> | |
4054 | <span class="blue">Max = 3.08ε (Mean = 1.2ε)</span> | |
4055 | </p> | |
4056 | </td> | |
4057 | <td> | |
4058 | <p> | |
4059 | <span class="blue">Max = 0.58ε (Mean = 0.193ε)</span> | |
4060 | </p> | |
4061 | </td> | |
4062 | <td> | |
4063 | <p> | |
4064 | <span class="blue">Max = 36.6ε (Mean = 12.7ε)</span> | |
4065 | </p> | |
4066 | </td> | |
4067 | <td> | |
4068 | <p> | |
4069 | <span class="blue">Max = 34ε (Mean = 11.8ε)</span> | |
4070 | </p> | |
4071 | </td> | |
4072 | </tr> | |
4073 | <tr> | |
4074 | <td> | |
4075 | <p> | |
4076 | Y'n: Mathworld Data (Integer Version) | |
4077 | </p> | |
4078 | </td> | |
4079 | <td> | |
4080 | <p> | |
4081 | <span class="blue">Max = 563ε (Mean = 178ε)</span> | |
4082 | </p> | |
4083 | </td> | |
4084 | <td> | |
4085 | <p> | |
4086 | <span class="blue">Max = 2.05ε (Mean = 0.677ε)</span> | |
4087 | </p> | |
4088 | </td> | |
4089 | <td> | |
4090 | <p> | |
4091 | <span class="blue">Max = 56ε (Mean = 18.2ε)</span> | |
4092 | </p> | |
4093 | </td> | |
4094 | <td> | |
4095 | <p> | |
4096 | <span class="blue">Max = 56ε (Mean = 18.2ε)</span> | |
4097 | </p> | |
4098 | </td> | |
4099 | </tr> | |
4100 | </tbody> | |
4101 | </table></div> | |
4102 | </div> | |
4103 | <br class="table-break"><div class="table"> | |
4104 | <a name="math_toolkit.logs_and_tables.all_table.table_digamma"></a><p class="title"><b>Table 17.25. Error rates for digamma</b></p> | |
4105 | <div class="table-contents"><table class="table" summary="Error rates for digamma"> | |
4106 | <colgroup> | |
4107 | <col> | |
4108 | <col> | |
4109 | <col> | |
4110 | <col> | |
4111 | <col> | |
4112 | </colgroup> | |
4113 | <thead><tr> | |
4114 | <th> | |
4115 | </th> | |
4116 | <th> | |
4117 | <p> | |
4118 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
4119 | </p> | |
4120 | </th> | |
4121 | <th> | |
4122 | <p> | |
4123 | GNU C++ version 5.1.0<br> linux<br> double | |
4124 | </p> | |
4125 | </th> | |
4126 | <th> | |
4127 | <p> | |
4128 | GNU C++ version 5.1.0<br> linux<br> long double | |
4129 | </p> | |
4130 | </th> | |
4131 | <th> | |
4132 | <p> | |
4133 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
4134 | </p> | |
4135 | </th> | |
4136 | </tr></thead> | |
4137 | <tbody> | |
4138 | <tr> | |
4139 | <td> | |
4140 | <p> | |
4141 | Digamma Function: Large Values | |
4142 | </p> | |
4143 | </td> | |
4144 | <td> | |
4145 | <p> | |
4146 | <span class="blue">Max = 0.98ε (Mean = 0.369ε)</span> | |
4147 | </p> | |
4148 | </td> | |
4149 | <td> | |
4150 | <p> | |
4151 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
4152 | 1.16:</em></span> Max = 1.84ε (Mean = 0.71ε))<br> (<span class="emphasis"><em>Rmath | |
4153 | 3.0.2:</em></span> Max = 1.18ε (Mean = 0.331ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
4154 | Max = 0.919ε (Mean = 0.394ε)) | |
4155 | </p> | |
4156 | </td> | |
4157 | <td> | |
4158 | <p> | |
4159 | <span class="blue">Max = 1.39ε (Mean = 0.413ε)</span> | |
4160 | </p> | |
4161 | </td> | |
4162 | <td> | |
4163 | <p> | |
4164 | <span class="blue">Max = 1.39ε (Mean = 0.413ε)</span> | |
4165 | </p> | |
4166 | </td> | |
4167 | </tr> | |
4168 | <tr> | |
4169 | <td> | |
4170 | <p> | |
4171 | Digamma Function: Near the Positive Root | |
4172 | </p> | |
4173 | </td> | |
4174 | <td> | |
4175 | <p> | |
4176 | <span class="blue">Max = 0.997ε (Mean = 0.527ε)</span> | |
4177 | </p> | |
4178 | </td> | |
4179 | <td> | |
4180 | <p> | |
4181 | <span class="blue">Max = 0.891ε (Mean = 0.0995ε)</span><br> | |
4182 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 135ε (Mean = 11.9ε))<br> | |
4183 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 2.02e+03ε (Mean = 256ε))<br> | |
4184 | (<span class="emphasis"><em>Cephes:</em></span> Max = 1.42e+04ε (Mean = 1.14e+03ε)) | |
4185 | </p> | |
4186 | </td> | |
4187 | <td> | |
4188 | <p> | |
4189 | <span class="blue">Max = 1.37ε (Mean = 0.477ε)</span> | |
4190 | </p> | |
4191 | </td> | |
4192 | <td> | |
4193 | <p> | |
4194 | <span class="blue">Max = 1.31ε (Mean = 0.451ε)</span> | |
4195 | </p> | |
4196 | </td> | |
4197 | </tr> | |
4198 | <tr> | |
4199 | <td> | |
4200 | <p> | |
4201 | Digamma Function: Near Zero | |
4202 | </p> | |
4203 | </td> | |
4204 | <td> | |
4205 | <p> | |
4206 | <span class="blue">Max = 0.953ε (Mean = 0.337ε)</span> | |
4207 | </p> | |
4208 | </td> | |
4209 | <td> | |
4210 | <p> | |
4211 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
4212 | 1.16:</em></span> Max = 0.953ε (Mean = 0.348ε))<br> (<span class="emphasis"><em>Rmath | |
4213 | 3.0.2:</em></span> Max = 1.17ε (Mean = 0.564ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
4214 | Max = 3.5ε (Mean = 1.04ε)) | |
4215 | </p> | |
4216 | </td> | |
4217 | <td> | |
4218 | <p> | |
4219 | <span class="blue">Max = 0.984ε (Mean = 0.361ε)</span> | |
4220 | </p> | |
4221 | </td> | |
4222 | <td> | |
4223 | <p> | |
4224 | <span class="blue">Max = 0.984ε (Mean = 0.361ε)</span> | |
4225 | </p> | |
4226 | </td> | |
4227 | </tr> | |
4228 | <tr> | |
4229 | <td> | |
4230 | <p> | |
4231 | Digamma Function: Negative Values | |
4232 | </p> | |
4233 | </td> | |
4234 | <td> | |
4235 | <p> | |
4236 | <span class="blue">Max = 214ε (Mean = 16.1ε)</span> | |
4237 | </p> | |
4238 | </td> | |
4239 | <td> | |
4240 | <p> | |
4241 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
4242 | 1.16:</em></span> Max = 4.56e+04ε (Mean = 3.91e+03ε))<br> (<span class="emphasis"><em>Rmath | |
4243 | 3.0.2:</em></span> Max = 4.6e+04ε (Mean = 3.94e+03ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
4244 | Max = 214ε (Mean = 16.4ε)) | |
4245 | </p> | |
4246 | </td> | |
4247 | <td> | |
4248 | <p> | |
4249 | <span class="blue">Max = 180ε (Mean = 13ε)</span> | |
4250 | </p> | |
4251 | </td> | |
4252 | <td> | |
4253 | <p> | |
4254 | <span class="blue">Max = 180ε (Mean = 13ε)</span> | |
4255 | </p> | |
4256 | </td> | |
4257 | </tr> | |
4258 | <tr> | |
4259 | <td> | |
4260 | <p> | |
4261 | Digamma Function: Values near 0 | |
4262 | </p> | |
4263 | </td> | |
4264 | <td> | |
4265 | <p> | |
4266 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
4267 | </p> | |
4268 | </td> | |
4269 | <td> | |
4270 | <p> | |
4271 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
4272 | 1.16:</em></span> Max = 0.866ε (Mean = 0.387ε))<br> (<span class="emphasis"><em>Rmath | |
4273 | 3.0.2:</em></span> Max = 3.58e+05ε (Mean = 1.6e+05ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
4274 | Max = 0.5ε (Mean = 0.224ε)) | |
4275 | </p> | |
4276 | </td> | |
4277 | <td> | |
4278 | <p> | |
4279 | <span class="blue">Max = 1ε (Mean = 0.592ε)</span> | |
4280 | </p> | |
4281 | </td> | |
4282 | <td> | |
4283 | <p> | |
4284 | <span class="blue">Max = 1ε (Mean = 0.592ε)</span> | |
4285 | </p> | |
4286 | </td> | |
4287 | </tr> | |
4288 | <tr> | |
4289 | <td> | |
4290 | <p> | |
4291 | Digamma Function: Integer arguments | |
4292 | </p> | |
4293 | </td> | |
4294 | <td> | |
4295 | <p> | |
4296 | <span class="blue">Max = 0.992ε (Mean = 0.452ε)</span> | |
4297 | </p> | |
4298 | </td> | |
4299 | <td> | |
4300 | <p> | |
4301 | <span class="blue">Max = 0.992ε (Mean = 0.215ε)</span><br> <br> | |
4302 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.18ε (Mean = 0.607ε))<br> | |
4303 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 4.33ε (Mean = 0.982ε))<br> | |
4304 | (<span class="emphasis"><em>Cephes:</em></span> Max = 0.992ε (Mean = 0.383ε)) | |
4305 | </p> | |
4306 | </td> | |
4307 | <td> | |
4308 | <p> | |
4309 | <span class="blue">Max = 0.888ε (Mean = 0.403ε)</span> | |
4310 | </p> | |
4311 | </td> | |
4312 | <td> | |
4313 | <p> | |
4314 | <span class="blue">Max = 0.888ε (Mean = 0.403ε)</span> | |
4315 | </p> | |
4316 | </td> | |
4317 | </tr> | |
4318 | <tr> | |
4319 | <td> | |
4320 | <p> | |
4321 | Digamma Function: Half integer arguments | |
4322 | </p> | |
4323 | </td> | |
4324 | <td> | |
4325 | <p> | |
4326 | <span class="blue">Max = 0.78ε (Mean = 0.314ε)</span> | |
4327 | </p> | |
4328 | </td> | |
4329 | <td> | |
4330 | <p> | |
4331 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
4332 | 1.16:</em></span> Max = 1.09ε (Mean = 0.531ε))<br> (<span class="emphasis"><em>Rmath | |
4333 | 3.0.2:</em></span> Max = 46.2ε (Mean = 7.24ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
4334 | Max = 8.56ε (Mean = 1.44ε)) | |
4335 | </p> | |
4336 | </td> | |
4337 | <td> | |
4338 | <p> | |
4339 | <span class="blue">Max = 0.906ε (Mean = 0.409ε)</span> | |
4340 | </p> | |
4341 | </td> | |
4342 | <td> | |
4343 | <p> | |
4344 | <span class="blue">Max = 0.906ε (Mean = 0.409ε)</span> | |
4345 | </p> | |
4346 | </td> | |
4347 | </tr> | |
4348 | </tbody> | |
4349 | </table></div> | |
4350 | </div> | |
4351 | <br class="table-break"><div class="table"> | |
4352 | <a name="math_toolkit.logs_and_tables.all_table.table_ellint_1"></a><p class="title"><b>Table 17.26. Error rates for ellint_1</b></p> | |
4353 | <div class="table-contents"><table class="table" summary="Error rates for ellint_1"> | |
4354 | <colgroup> | |
4355 | <col> | |
4356 | <col> | |
4357 | <col> | |
4358 | <col> | |
4359 | <col> | |
4360 | </colgroup> | |
4361 | <thead><tr> | |
4362 | <th> | |
4363 | </th> | |
4364 | <th> | |
4365 | <p> | |
4366 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
4367 | </p> | |
4368 | </th> | |
4369 | <th> | |
4370 | <p> | |
4371 | GNU C++ version 5.1.0<br> linux<br> long double | |
4372 | </p> | |
4373 | </th> | |
4374 | <th> | |
4375 | <p> | |
4376 | GNU C++ version 5.1.0<br> linux<br> double | |
4377 | </p> | |
4378 | </th> | |
4379 | <th> | |
4380 | <p> | |
4381 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
4382 | </p> | |
4383 | </th> | |
4384 | </tr></thead> | |
4385 | <tbody> | |
4386 | <tr> | |
4387 | <td> | |
4388 | <p> | |
4389 | Elliptic Integral F: Mathworld Data | |
4390 | </p> | |
4391 | </td> | |
4392 | <td> | |
4393 | <p> | |
4394 | <span class="blue">Max = 0.919ε (Mean = 0.542ε)</span> | |
4395 | </p> | |
4396 | </td> | |
4397 | <td> | |
4398 | <p> | |
4399 | <span class="blue">Max = 0.94ε (Mean = 0.509ε)</span><br> <br> | |
4400 | (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max | |
4401 | = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_1__tr1_cmath__Elliptic_Integral_F_Mathworld_Data">And | |
4402 | other failures.</a>)</span> | |
4403 | </p> | |
4404 | </td> | |
4405 | <td> | |
4406 | <p> | |
4407 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
4408 | 1.16:</em></span> Max = 0.919ε (Mean = 0.544ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
4409 | <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ellint_1_Cephes_Elliptic_Integral_F_Mathworld_Data">And | |
4410 | other failures.</a>)</span> | |
4411 | </p> | |
4412 | </td> | |
4413 | <td> | |
4414 | <p> | |
4415 | <span class="blue">Max = 0.94ε (Mean = 0.509ε)</span> | |
4416 | </p> | |
4417 | </td> | |
4418 | </tr> | |
4419 | <tr> | |
4420 | <td> | |
4421 | <p> | |
4422 | Elliptic Integral F: Random Data | |
4423 | </p> | |
4424 | </td> | |
4425 | <td> | |
4426 | <p> | |
4427 | <span class="blue">Max = 2.26ε (Mean = 0.631ε)</span> | |
4428 | </p> | |
4429 | </td> | |
4430 | <td> | |
4431 | <p> | |
4432 | <span class="blue">Max = 1.57ε (Mean = 0.56ε)</span><br> <br> | |
4433 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.56ε (Mean = 0.816ε)) | |
4434 | </p> | |
4435 | </td> | |
4436 | <td> | |
4437 | <p> | |
4438 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
4439 | 1.16:</em></span> Max = 2.99ε (Mean = 0.797ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
4440 | Max = 2.18ε (Mean = 0.535ε)) | |
4441 | </p> | |
4442 | </td> | |
4443 | <td> | |
4444 | <p> | |
4445 | <span class="blue">Max = 1.57ε (Mean = 0.561ε)</span> | |
4446 | </p> | |
4447 | </td> | |
4448 | </tr> | |
4449 | </tbody> | |
4450 | </table></div> | |
4451 | </div> | |
4452 | <br class="table-break"><div class="table"> | |
4453 | <a name="math_toolkit.logs_and_tables.all_table.table_ellint_1_complete_"></a><p class="title"><b>Table 17.27. Error rates for ellint_1 (complete)</b></p> | |
4454 | <div class="table-contents"><table class="table" summary="Error rates for ellint_1 (complete)"> | |
4455 | <colgroup> | |
4456 | <col> | |
4457 | <col> | |
4458 | <col> | |
4459 | <col> | |
4460 | <col> | |
4461 | </colgroup> | |
4462 | <thead><tr> | |
4463 | <th> | |
4464 | </th> | |
4465 | <th> | |
4466 | <p> | |
4467 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
4468 | </p> | |
4469 | </th> | |
4470 | <th> | |
4471 | <p> | |
4472 | GNU C++ version 5.1.0<br> linux<br> long double | |
4473 | </p> | |
4474 | </th> | |
4475 | <th> | |
4476 | <p> | |
4477 | GNU C++ version 5.1.0<br> linux<br> double | |
4478 | </p> | |
4479 | </th> | |
4480 | <th> | |
4481 | <p> | |
4482 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
4483 | </p> | |
4484 | </th> | |
4485 | </tr></thead> | |
4486 | <tbody> | |
4487 | <tr> | |
4488 | <td> | |
4489 | <p> | |
4490 | Elliptic Integral K: Mathworld Data | |
4491 | </p> | |
4492 | </td> | |
4493 | <td> | |
4494 | <p> | |
4495 | <span class="blue">Max = 0.915ε (Mean = 0.547ε)</span> | |
4496 | </p> | |
4497 | </td> | |
4498 | <td> | |
4499 | <p> | |
4500 | <span class="blue">Max = 0.887ε (Mean = 0.296ε)</span><br> <br> | |
4501 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.19ε (Mean = 0.765ε)) | |
4502 | </p> | |
4503 | </td> | |
4504 | <td> | |
4505 | <p> | |
4506 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
4507 | 1.16:</em></span> Max = 0.623ε (Mean = 0.393ε)) | |
4508 | </p> | |
4509 | </td> | |
4510 | <td> | |
4511 | <p> | |
4512 | <span class="blue">Max = 0.887ε (Mean = 0.296ε)</span> | |
4513 | </p> | |
4514 | </td> | |
4515 | </tr> | |
4516 | <tr> | |
4517 | <td> | |
4518 | <p> | |
4519 | Elliptic Integral K: Random Data | |
4520 | </p> | |
4521 | </td> | |
4522 | <td> | |
4523 | <p> | |
4524 | <span class="blue">Max = 0.958ε (Mean = 0.408ε)</span> | |
4525 | </p> | |
4526 | </td> | |
4527 | <td> | |
4528 | <p> | |
4529 | <span class="blue">Max = 1.27ε (Mean = 0.473ε)</span><br> <br> | |
4530 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.19ε (Mean = 0.694ε)) | |
4531 | </p> | |
4532 | </td> | |
4533 | <td> | |
4534 | <p> | |
4535 | <span class="blue">Max = 0.851ε (Mean = 0.0851ε)</span><br> | |
4536 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.32ε (Mean = 0.688ε)) | |
4537 | </p> | |
4538 | </td> | |
4539 | <td> | |
4540 | <p> | |
4541 | <span class="blue">Max = 1.27ε (Mean = 0.473ε)</span> | |
4542 | </p> | |
4543 | </td> | |
4544 | </tr> | |
4545 | </tbody> | |
4546 | </table></div> | |
4547 | </div> | |
4548 | <br class="table-break"><div class="table"> | |
4549 | <a name="math_toolkit.logs_and_tables.all_table.table_ellint_2"></a><p class="title"><b>Table 17.28. Error rates for ellint_2</b></p> | |
4550 | <div class="table-contents"><table class="table" summary="Error rates for ellint_2"> | |
4551 | <colgroup> | |
4552 | <col> | |
4553 | <col> | |
4554 | <col> | |
4555 | <col> | |
4556 | <col> | |
4557 | </colgroup> | |
4558 | <thead><tr> | |
4559 | <th> | |
4560 | </th> | |
4561 | <th> | |
4562 | <p> | |
4563 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
4564 | </p> | |
4565 | </th> | |
4566 | <th> | |
4567 | <p> | |
4568 | GNU C++ version 5.1.0<br> linux<br> long double | |
4569 | </p> | |
4570 | </th> | |
4571 | <th> | |
4572 | <p> | |
4573 | GNU C++ version 5.1.0<br> linux<br> double | |
4574 | </p> | |
4575 | </th> | |
4576 | <th> | |
4577 | <p> | |
4578 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
4579 | </p> | |
4580 | </th> | |
4581 | </tr></thead> | |
4582 | <tbody> | |
4583 | <tr> | |
4584 | <td> | |
4585 | <p> | |
4586 | Elliptic Integral E: Mathworld Data | |
4587 | </p> | |
4588 | </td> | |
4589 | <td> | |
4590 | <p> | |
4591 | <span class="blue">Max = 1.31ε (Mean = 0.727ε)</span> | |
4592 | </p> | |
4593 | </td> | |
4594 | <td> | |
4595 | <p> | |
4596 | <span class="blue">Max = 0.656ε (Mean = 0.317ε)</span><br> <br> | |
4597 | (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max | |
4598 | = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_2__tr1_cmath__Elliptic_Integral_E_Mathworld_Data">And | |
4599 | other failures.</a>)</span> | |
4600 | </p> | |
4601 | </td> | |
4602 | <td> | |
4603 | <p> | |
4604 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
4605 | 1.16:</em></span> Max = 0.63ε (Mean = 0.325ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
4606 | <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ellint_2_Cephes_Elliptic_Integral_E_Mathworld_Data">And | |
4607 | other failures.</a>)</span> | |
4608 | </p> | |
4609 | </td> | |
4610 | <td> | |
4611 | <p> | |
4612 | <span class="blue">Max = 0.656ε (Mean = 0.317ε)</span> | |
4613 | </p> | |
4614 | </td> | |
4615 | </tr> | |
4616 | <tr> | |
4617 | <td> | |
4618 | <p> | |
4619 | Elliptic Integral E: Random Data | |
4620 | </p> | |
4621 | </td> | |
4622 | <td> | |
4623 | <p> | |
4624 | <span class="blue">Max = 2.23ε (Mean = 0.639ε)</span> | |
4625 | </p> | |
4626 | </td> | |
4627 | <td> | |
4628 | <p> | |
4629 | <span class="blue">Max = 2.05ε (Mean = 0.632ε)</span><br> <br> | |
4630 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 3.08e+04ε (Mean = | |
4631 | 3.84e+03ε)) | |
4632 | </p> | |
4633 | </td> | |
4634 | <td> | |
4635 | <p> | |
4636 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
4637 | 1.16:</em></span> Max = 4.4ε (Mean = 1.16ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
4638 | Max = 8.92ε (Mean = 1.48ε)) | |
4639 | </p> | |
4640 | </td> | |
4641 | <td> | |
4642 | <p> | |
4643 | <span class="blue">Max = 2.05ε (Mean = 0.632ε)</span> | |
4644 | </p> | |
4645 | </td> | |
4646 | </tr> | |
4647 | </tbody> | |
4648 | </table></div> | |
4649 | </div> | |
4650 | <br class="table-break"><div class="table"> | |
4651 | <a name="math_toolkit.logs_and_tables.all_table.table_ellint_2_complete_"></a><p class="title"><b>Table 17.29. Error rates for ellint_2 (complete)</b></p> | |
4652 | <div class="table-contents"><table class="table" summary="Error rates for ellint_2 (complete)"> | |
4653 | <colgroup> | |
4654 | <col> | |
4655 | <col> | |
4656 | <col> | |
4657 | <col> | |
4658 | <col> | |
4659 | </colgroup> | |
4660 | <thead><tr> | |
4661 | <th> | |
4662 | </th> | |
4663 | <th> | |
4664 | <p> | |
4665 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
4666 | </p> | |
4667 | </th> | |
4668 | <th> | |
4669 | <p> | |
4670 | GNU C++ version 5.1.0<br> linux<br> long double | |
4671 | </p> | |
4672 | </th> | |
4673 | <th> | |
4674 | <p> | |
4675 | GNU C++ version 5.1.0<br> linux<br> double | |
4676 | </p> | |
4677 | </th> | |
4678 | <th> | |
4679 | <p> | |
4680 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
4681 | </p> | |
4682 | </th> | |
4683 | </tr></thead> | |
4684 | <tbody> | |
4685 | <tr> | |
4686 | <td> | |
4687 | <p> | |
4688 | Elliptic Integral E: Mathworld Data | |
4689 | </p> | |
4690 | </td> | |
4691 | <td> | |
4692 | <p> | |
4693 | <span class="blue">Max = 1.3ε (Mean = 0.615ε)</span> | |
4694 | </p> | |
4695 | </td> | |
4696 | <td> | |
4697 | <p> | |
4698 | <span class="blue">Max = 0.836ε (Mean = 0.469ε)</span><br> <br> | |
4699 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 170ε (Mean = 55.1ε)) | |
4700 | </p> | |
4701 | </td> | |
4702 | <td> | |
4703 | <p> | |
4704 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
4705 | 1.16:</em></span> Max = 3.09ε (Mean = 1.04ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ellint_2_complete__GSL_1_16_Elliptic_Integral_E_Mathworld_Data">And | |
4706 | other failures.</a>) | |
4707 | </p> | |
4708 | </td> | |
4709 | <td> | |
4710 | <p> | |
4711 | <span class="blue">Max = 0.836ε (Mean = 0.469ε)</span> | |
4712 | </p> | |
4713 | </td> | |
4714 | </tr> | |
4715 | <tr> | |
4716 | <td> | |
4717 | <p> | |
4718 | Elliptic Integral E: Random Data | |
4719 | </p> | |
4720 | </td> | |
4721 | <td> | |
4722 | <p> | |
4723 | <span class="blue">Max = 1.71ε (Mean = 0.553ε)</span> | |
4724 | </p> | |
4725 | </td> | |
4726 | <td> | |
4727 | <p> | |
4728 | <span class="blue">Max = 1.97ε (Mean = 0.629ε)</span><br> <br> | |
4729 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.49e+04ε (Mean = | |
4730 | 3.39e+03ε)) | |
4731 | </p> | |
4732 | </td> | |
4733 | <td> | |
4734 | <p> | |
4735 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
4736 | 1.16:</em></span> Max = 4.34ε (Mean = 1.18ε)) | |
4737 | </p> | |
4738 | </td> | |
4739 | <td> | |
4740 | <p> | |
4741 | <span class="blue">Max = 1.97ε (Mean = 0.629ε)</span> | |
4742 | </p> | |
4743 | </td> | |
4744 | </tr> | |
4745 | </tbody> | |
4746 | </table></div> | |
4747 | </div> | |
4748 | <br class="table-break"><div class="table"> | |
4749 | <a name="math_toolkit.logs_and_tables.all_table.table_ellint_3"></a><p class="title"><b>Table 17.30. Error rates for ellint_3</b></p> | |
4750 | <div class="table-contents"><table class="table" summary="Error rates for ellint_3"> | |
4751 | <colgroup> | |
4752 | <col> | |
4753 | <col> | |
4754 | <col> | |
4755 | <col> | |
4756 | <col> | |
4757 | </colgroup> | |
4758 | <thead><tr> | |
4759 | <th> | |
4760 | </th> | |
4761 | <th> | |
4762 | <p> | |
4763 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
4764 | </p> | |
4765 | </th> | |
4766 | <th> | |
4767 | <p> | |
4768 | GNU C++ version 5.1.0<br> linux<br> long double | |
4769 | </p> | |
4770 | </th> | |
4771 | <th> | |
4772 | <p> | |
4773 | GNU C++ version 5.1.0<br> linux<br> double | |
4774 | </p> | |
4775 | </th> | |
4776 | <th> | |
4777 | <p> | |
4778 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
4779 | </p> | |
4780 | </th> | |
4781 | </tr></thead> | |
4782 | <tbody> | |
4783 | <tr> | |
4784 | <td> | |
4785 | <p> | |
4786 | Elliptic Integral PI: Mathworld Data | |
4787 | </p> | |
4788 | </td> | |
4789 | <td> | |
4790 | <p> | |
4791 | <span class="blue">Max = 565ε (Mean = 102ε)</span> | |
4792 | </p> | |
4793 | </td> | |
4794 | <td> | |
4795 | <p> | |
4796 | <span class="blue">Max = 475ε (Mean = 86.3ε)</span><br> <br> | |
4797 | (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max | |
4798 | = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_3__tr1_cmath__Elliptic_Integral_PI_Mathworld_Data">And | |
4799 | other failures.</a>)</span> | |
4800 | </p> | |
4801 | </td> | |
4802 | <td> | |
4803 | <p> | |
4804 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
4805 | 1.16:</em></span> Max = 1.48e+05ε (Mean = 2.54e+04ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ellint_3_GSL_1_16_Elliptic_Integral_PI_Mathworld_Data">And | |
4806 | other failures.</a>) | |
4807 | </p> | |
4808 | </td> | |
4809 | <td> | |
4810 | <p> | |
4811 | <span class="blue">Max = 475ε (Mean = 86.3ε)</span> | |
4812 | </p> | |
4813 | </td> | |
4814 | </tr> | |
4815 | <tr> | |
4816 | <td> | |
4817 | <p> | |
4818 | Elliptic Integral PI: Random Data | |
4819 | </p> | |
4820 | </td> | |
4821 | <td> | |
4822 | <p> | |
4823 | <span class="blue">Max = 9.08ε (Mean = 0.99ε)</span> | |
4824 | </p> | |
4825 | </td> | |
4826 | <td> | |
4827 | <p> | |
4828 | <span class="blue">Max = 4.54ε (Mean = 0.895ε)</span><br> <br> | |
4829 | (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max | |
4830 | = 3.37e+20ε (Mean = 3.47e+19ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_3__tr1_cmath__Elliptic_Integral_PI_Random_Data">And | |
4831 | other failures.</a>)</span> | |
4832 | </p> | |
4833 | </td> | |
4834 | <td> | |
4835 | <p> | |
4836 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
4837 | 1.16:</em></span> Max = 633ε (Mean = 50.1ε)) | |
4838 | </p> | |
4839 | </td> | |
4840 | <td> | |
4841 | <p> | |
4842 | <span class="blue">Max = 4.49ε (Mean = 0.891ε)</span> | |
4843 | </p> | |
4844 | </td> | |
4845 | </tr> | |
4846 | <tr> | |
4847 | <td> | |
4848 | <p> | |
4849 | Elliptic Integral PI: Large Random Data | |
4850 | </p> | |
4851 | </td> | |
4852 | <td> | |
4853 | <p> | |
4854 | <span class="blue">Max = 2.86ε (Mean = 0.944ε)</span> | |
4855 | </p> | |
4856 | </td> | |
4857 | <td> | |
4858 | <p> | |
4859 | <span class="blue">Max = 3.7ε (Mean = 0.893ε)</span><br> <br> | |
4860 | (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max | |
4861 | = 2.52e+18ε (Mean = 4.83e+17ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_3__tr1_cmath__Elliptic_Integral_PI_Large_Random_Data">And | |
4862 | other failures.</a>)</span> | |
4863 | </p> | |
4864 | </td> | |
4865 | <td> | |
4866 | <p> | |
4867 | <span class="blue">Max = 0.557ε (Mean = 0.0389ε)</span><br> | |
4868 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 40.1ε (Mean = 7.77ε)) | |
4869 | </p> | |
4870 | </td> | |
4871 | <td> | |
4872 | <p> | |
4873 | <span class="blue">Max = 3.7ε (Mean = 0.892ε)</span> | |
4874 | </p> | |
4875 | </td> | |
4876 | </tr> | |
4877 | </tbody> | |
4878 | </table></div> | |
4879 | </div> | |
4880 | <br class="table-break"><div class="table"> | |
4881 | <a name="math_toolkit.logs_and_tables.all_table.table_ellint_3_complete_"></a><p class="title"><b>Table 17.31. Error rates for ellint_3 (complete)</b></p> | |
4882 | <div class="table-contents"><table class="table" summary="Error rates for ellint_3 (complete)"> | |
4883 | <colgroup> | |
4884 | <col> | |
4885 | <col> | |
4886 | <col> | |
4887 | <col> | |
4888 | <col> | |
4889 | </colgroup> | |
4890 | <thead><tr> | |
4891 | <th> | |
4892 | </th> | |
4893 | <th> | |
4894 | <p> | |
4895 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
4896 | </p> | |
4897 | </th> | |
4898 | <th> | |
4899 | <p> | |
4900 | GNU C++ version 5.1.0<br> linux<br> long double | |
4901 | </p> | |
4902 | </th> | |
4903 | <th> | |
4904 | <p> | |
4905 | GNU C++ version 5.1.0<br> linux<br> double | |
4906 | </p> | |
4907 | </th> | |
4908 | <th> | |
4909 | <p> | |
4910 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
4911 | </p> | |
4912 | </th> | |
4913 | </tr></thead> | |
4914 | <tbody> | |
4915 | <tr> | |
4916 | <td> | |
4917 | <p> | |
4918 | Complete Elliptic Integral PI: Mathworld Data | |
4919 | </p> | |
4920 | </td> | |
4921 | <td> | |
4922 | <p> | |
4923 | <span class="blue">Max = 0.971ε (Mean = 0.464ε)</span> | |
4924 | </p> | |
4925 | </td> | |
4926 | <td> | |
4927 | <p> | |
4928 | <span class="blue">Max = 1.4ε (Mean = 0.575ε)</span><br> <br> | |
4929 | (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max | |
4930 | = 6.31e+20ε (Mean = 1.53e+20ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_3_complete___tr1_cmath__Complete_Elliptic_Integral_PI_Mathworld_Data">And | |
4931 | other failures.</a>)</span> | |
4932 | </p> | |
4933 | </td> | |
4934 | <td> | |
4935 | <p> | |
4936 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
4937 | 1.16:</em></span> Max = 6.33e+04ε (Mean = 1.54e+04ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ellint_3_complete__GSL_1_16_Complete_Elliptic_Integral_PI_Mathworld_Data">And | |
4938 | other failures.</a>) | |
4939 | </p> | |
4940 | </td> | |
4941 | <td> | |
4942 | <p> | |
4943 | <span class="blue">Max = 1.4ε (Mean = 0.575ε)</span> | |
4944 | </p> | |
4945 | </td> | |
4946 | </tr> | |
4947 | <tr> | |
4948 | <td> | |
4949 | <p> | |
4950 | Complete Elliptic Integral PI: Random Data | |
4951 | </p> | |
4952 | </td> | |
4953 | <td> | |
4954 | <p> | |
4955 | <span class="blue">Max = 2.46ε (Mean = 0.654ε)</span> | |
4956 | </p> | |
4957 | </td> | |
4958 | <td> | |
4959 | <p> | |
4960 | <span class="blue">Max = 2.45ε (Mean = 0.696ε)</span><br> <br> | |
4961 | (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max | |
4962 | = 8.78e+20ε (Mean = 1.02e+20ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_3_complete___tr1_cmath__Complete_Elliptic_Integral_PI_Random_Data">And | |
4963 | other failures.</a>)</span> | |
4964 | </p> | |
4965 | </td> | |
4966 | <td> | |
4967 | <p> | |
4968 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
4969 | 1.16:</em></span> Max = 24ε (Mean = 2.99ε)) | |
4970 | </p> | |
4971 | </td> | |
4972 | <td> | |
4973 | <p> | |
4974 | <span class="blue">Max = 2.4ε (Mean = 0.681ε)</span> | |
4975 | </p> | |
4976 | </td> | |
4977 | </tr> | |
4978 | </tbody> | |
4979 | </table></div> | |
4980 | </div> | |
4981 | <br class="table-break"><div class="table"> | |
4982 | <a name="math_toolkit.logs_and_tables.all_table.table_ellint_d"></a><p class="title"><b>Table 17.32. Error rates for ellint_d</b></p> | |
4983 | <div class="table-contents"><table class="table" summary="Error rates for ellint_d"> | |
4984 | <colgroup> | |
4985 | <col> | |
4986 | <col> | |
4987 | <col> | |
4988 | <col> | |
4989 | <col> | |
4990 | </colgroup> | |
4991 | <thead><tr> | |
4992 | <th> | |
4993 | </th> | |
4994 | <th> | |
4995 | <p> | |
4996 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
4997 | </p> | |
4998 | </th> | |
4999 | <th> | |
5000 | <p> | |
5001 | GNU C++ version 5.1.0<br> linux<br> double | |
5002 | </p> | |
5003 | </th> | |
5004 | <th> | |
5005 | <p> | |
5006 | GNU C++ version 5.1.0<br> linux<br> long double | |
5007 | </p> | |
5008 | </th> | |
5009 | <th> | |
5010 | <p> | |
5011 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
5012 | </p> | |
5013 | </th> | |
5014 | </tr></thead> | |
5015 | <tbody> | |
5016 | <tr> | |
5017 | <td> | |
5018 | <p> | |
5019 | Elliptic Integral E: Mathworld Data | |
5020 | </p> | |
5021 | </td> | |
5022 | <td> | |
5023 | <p> | |
5024 | <span class="blue">Max = 0.862ε (Mean = 0.457ε)</span> | |
5025 | </p> | |
5026 | </td> | |
5027 | <td> | |
5028 | <p> | |
5029 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
5030 | 1.16:</em></span> Max = 0.862ε (Mean = 0.568ε)) | |
5031 | </p> | |
5032 | </td> | |
5033 | <td> | |
5034 | <p> | |
5035 | <span class="blue">Max = 1.3ε (Mean = 0.813ε)</span> | |
5036 | </p> | |
5037 | </td> | |
5038 | <td> | |
5039 | <p> | |
5040 | <span class="blue">Max = 1.3ε (Mean = 0.813ε)</span> | |
5041 | </p> | |
5042 | </td> | |
5043 | </tr> | |
5044 | <tr> | |
5045 | <td> | |
5046 | <p> | |
5047 | Elliptic Integral D: Random Data | |
5048 | </p> | |
5049 | </td> | |
5050 | <td> | |
5051 | <p> | |
5052 | <span class="blue">Max = 2.87ε (Mean = 0.805ε)</span> | |
5053 | </p> | |
5054 | </td> | |
5055 | <td> | |
5056 | <p> | |
5057 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
5058 | 1.16:</em></span> Max = 3.01ε (Mean = 0.928ε)) | |
5059 | </p> | |
5060 | </td> | |
5061 | <td> | |
5062 | <p> | |
5063 | <span class="blue">Max = 2.51ε (Mean = 0.883ε)</span> | |
5064 | </p> | |
5065 | </td> | |
5066 | <td> | |
5067 | <p> | |
5068 | <span class="blue">Max = 2.51ε (Mean = 0.883ε)</span> | |
5069 | </p> | |
5070 | </td> | |
5071 | </tr> | |
5072 | </tbody> | |
5073 | </table></div> | |
5074 | </div> | |
5075 | <br class="table-break"><div class="table"> | |
5076 | <a name="math_toolkit.logs_and_tables.all_table.table_ellint_d_complete_"></a><p class="title"><b>Table 17.33. Error rates for ellint_d (complete)</b></p> | |
5077 | <div class="table-contents"><table class="table" summary="Error rates for ellint_d (complete)"> | |
5078 | <colgroup> | |
5079 | <col> | |
5080 | <col> | |
5081 | <col> | |
5082 | <col> | |
5083 | <col> | |
5084 | </colgroup> | |
5085 | <thead><tr> | |
5086 | <th> | |
5087 | </th> | |
5088 | <th> | |
5089 | <p> | |
5090 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
5091 | </p> | |
5092 | </th> | |
5093 | <th> | |
5094 | <p> | |
5095 | GNU C++ version 5.1.0<br> linux<br> double | |
5096 | </p> | |
5097 | </th> | |
5098 | <th> | |
5099 | <p> | |
5100 | GNU C++ version 5.1.0<br> linux<br> long double | |
5101 | </p> | |
5102 | </th> | |
5103 | <th> | |
5104 | <p> | |
5105 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
5106 | </p> | |
5107 | </th> | |
5108 | </tr></thead> | |
5109 | <tbody> | |
5110 | <tr> | |
5111 | <td> | |
5112 | <p> | |
5113 | Elliptic Integral E: Mathworld Data | |
5114 | </p> | |
5115 | </td> | |
5116 | <td> | |
5117 | <p> | |
5118 | <span class="blue">Max = 0.637ε (Mean = 0.368ε)</span> | |
5119 | </p> | |
5120 | </td> | |
5121 | <td> | |
5122 | <p> | |
5123 | <span class="blue">Max = 0.637ε (Mean = 0.368ε)</span> | |
5124 | </p> | |
5125 | </td> | |
5126 | <td> | |
5127 | <p> | |
5128 | <span class="blue">Max = 1.27ε (Mean = 0.735ε)</span> | |
5129 | </p> | |
5130 | </td> | |
5131 | <td> | |
5132 | <p> | |
5133 | <span class="blue">Max = 1.27ε (Mean = 0.735ε)</span> | |
5134 | </p> | |
5135 | </td> | |
5136 | </tr> | |
5137 | <tr> | |
5138 | <td> | |
5139 | <p> | |
5140 | Elliptic Integral D: Random Data | |
5141 | </p> | |
5142 | </td> | |
5143 | <td> | |
5144 | <p> | |
5145 | <span class="blue">Max = 1.27ε (Mean = 0.355ε)</span> | |
5146 | </p> | |
5147 | </td> | |
5148 | <td> | |
5149 | <p> | |
5150 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
5151 | </p> | |
5152 | </td> | |
5153 | <td> | |
5154 | <p> | |
5155 | <span class="blue">Max = 1.27ε (Mean = 0.334ε)</span> | |
5156 | </p> | |
5157 | </td> | |
5158 | <td> | |
5159 | <p> | |
5160 | <span class="blue">Max = 1.27ε (Mean = 0.334ε)</span> | |
5161 | </p> | |
5162 | </td> | |
5163 | </tr> | |
5164 | </tbody> | |
5165 | </table></div> | |
5166 | </div> | |
5167 | <br class="table-break"><div class="table"> | |
5168 | <a name="math_toolkit.logs_and_tables.all_table.table_ellint_rc"></a><p class="title"><b>Table 17.34. Error rates for ellint_rc</b></p> | |
5169 | <div class="table-contents"><table class="table" summary="Error rates for ellint_rc"> | |
5170 | <colgroup> | |
5171 | <col> | |
5172 | <col> | |
5173 | <col> | |
5174 | <col> | |
5175 | <col> | |
5176 | </colgroup> | |
5177 | <thead><tr> | |
5178 | <th> | |
5179 | </th> | |
5180 | <th> | |
5181 | <p> | |
5182 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
5183 | </p> | |
5184 | </th> | |
5185 | <th> | |
5186 | <p> | |
5187 | GNU C++ version 5.1.0<br> linux<br> double | |
5188 | </p> | |
5189 | </th> | |
5190 | <th> | |
5191 | <p> | |
5192 | GNU C++ version 5.1.0<br> linux<br> long double | |
5193 | </p> | |
5194 | </th> | |
5195 | <th> | |
5196 | <p> | |
5197 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
5198 | </p> | |
5199 | </th> | |
5200 | </tr></thead> | |
5201 | <tbody><tr> | |
5202 | <td> | |
5203 | <p> | |
5204 | RC: Random data | |
5205 | </p> | |
5206 | </td> | |
5207 | <td> | |
5208 | <p> | |
5209 | <span class="blue">Max = 0.962ε (Mean = 0.407ε)</span> | |
5210 | </p> | |
5211 | </td> | |
5212 | <td> | |
5213 | <p> | |
5214 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
5215 | 1.16:</em></span> Max = 2.4ε (Mean = 0.624ε)) | |
5216 | </p> | |
5217 | </td> | |
5218 | <td> | |
5219 | <p> | |
5220 | <span class="blue">Max = 0.995ε (Mean = 0.433ε)</span> | |
5221 | </p> | |
5222 | </td> | |
5223 | <td> | |
5224 | <p> | |
5225 | <span class="blue">Max = 0.995ε (Mean = 0.438ε)</span> | |
5226 | </p> | |
5227 | </td> | |
5228 | </tr></tbody> | |
5229 | </table></div> | |
5230 | </div> | |
5231 | <br class="table-break"><div class="table"> | |
5232 | <a name="math_toolkit.logs_and_tables.all_table.table_ellint_rd"></a><p class="title"><b>Table 17.35. Error rates for ellint_rd</b></p> | |
5233 | <div class="table-contents"><table class="table" summary="Error rates for ellint_rd"> | |
5234 | <colgroup> | |
5235 | <col> | |
5236 | <col> | |
5237 | <col> | |
5238 | <col> | |
5239 | <col> | |
5240 | </colgroup> | |
5241 | <thead><tr> | |
5242 | <th> | |
5243 | </th> | |
5244 | <th> | |
5245 | <p> | |
5246 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
5247 | </p> | |
5248 | </th> | |
5249 | <th> | |
5250 | <p> | |
5251 | GNU C++ version 5.1.0<br> linux<br> double | |
5252 | </p> | |
5253 | </th> | |
5254 | <th> | |
5255 | <p> | |
5256 | GNU C++ version 5.1.0<br> linux<br> long double | |
5257 | </p> | |
5258 | </th> | |
5259 | <th> | |
5260 | <p> | |
5261 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
5262 | </p> | |
5263 | </th> | |
5264 | </tr></thead> | |
5265 | <tbody> | |
5266 | <tr> | |
5267 | <td> | |
5268 | <p> | |
5269 | RD: Random data | |
5270 | </p> | |
5271 | </td> | |
5272 | <td> | |
5273 | <p> | |
5274 | <span class="blue">Max = 2.16ε (Mean = 0.803ε)</span> | |
5275 | </p> | |
5276 | </td> | |
5277 | <td> | |
5278 | <p> | |
5279 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
5280 | 1.16:</em></span> Max = 2.59ε (Mean = 0.878ε)) | |
5281 | </p> | |
5282 | </td> | |
5283 | <td> | |
5284 | <p> | |
5285 | <span class="blue">Max = 2.73ε (Mean = 0.831ε)</span> | |
5286 | </p> | |
5287 | </td> | |
5288 | <td> | |
5289 | <p> | |
5290 | <span class="blue">Max = 2.73ε (Mean = 0.829ε)</span> | |
5291 | </p> | |
5292 | </td> | |
5293 | </tr> | |
5294 | <tr> | |
5295 | <td> | |
5296 | <p> | |
5297 | RD: y = z | |
5298 | </p> | |
5299 | </td> | |
5300 | <td> | |
5301 | <p> | |
5302 | <span class="blue">Max = 16.5ε (Mean = 0.843ε)</span> | |
5303 | </p> | |
5304 | </td> | |
5305 | <td> | |
5306 | <p> | |
5307 | <span class="blue">Max = 0.896ε (Mean = 0.022ε)</span><br> <br> | |
5308 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.88ε (Mean = 0.839ε)) | |
5309 | </p> | |
5310 | </td> | |
5311 | <td> | |
5312 | <p> | |
5313 | <span class="blue">Max = 2.65ε (Mean = 0.82ε)</span> | |
5314 | </p> | |
5315 | </td> | |
5316 | <td> | |
5317 | <p> | |
5318 | <span class="blue">Max = 2.65ε (Mean = 0.819ε)</span> | |
5319 | </p> | |
5320 | </td> | |
5321 | </tr> | |
5322 | <tr> | |
5323 | <td> | |
5324 | <p> | |
5325 | RD: x = y | |
5326 | </p> | |
5327 | </td> | |
5328 | <td> | |
5329 | <p> | |
5330 | <span class="blue">Max = 3.51ε (Mean = 0.816ε)</span> | |
5331 | </p> | |
5332 | </td> | |
5333 | <td> | |
5334 | <p> | |
5335 | <span class="blue">Max = 0.824ε (Mean = 0.0272ε)</span><br> | |
5336 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 3.74ε (Mean = 0.84ε)) | |
5337 | </p> | |
5338 | </td> | |
5339 | <td> | |
5340 | <p> | |
5341 | <span class="blue">Max = 2.85ε (Mean = 0.865ε)</span> | |
5342 | </p> | |
5343 | </td> | |
5344 | <td> | |
5345 | <p> | |
5346 | <span class="blue">Max = 2.85ε (Mean = 0.865ε)</span> | |
5347 | </p> | |
5348 | </td> | |
5349 | </tr> | |
5350 | <tr> | |
5351 | <td> | |
5352 | <p> | |
5353 | RD: x = 0, y = z | |
5354 | </p> | |
5355 | </td> | |
5356 | <td> | |
5357 | <p> | |
5358 | <span class="blue">Max = 1.16ε (Mean = 0.493ε)</span> | |
5359 | </p> | |
5360 | </td> | |
5361 | <td> | |
5362 | <p> | |
5363 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
5364 | 1.16:</em></span> Max = 2ε (Mean = 0.656ε)) | |
5365 | </p> | |
5366 | </td> | |
5367 | <td> | |
5368 | <p> | |
5369 | <span class="blue">Max = 1.19ε (Mean = 0.522ε)</span> | |
5370 | </p> | |
5371 | </td> | |
5372 | <td> | |
5373 | <p> | |
5374 | <span class="blue">Max = 1.19ε (Mean = 0.522ε)</span> | |
5375 | </p> | |
5376 | </td> | |
5377 | </tr> | |
5378 | <tr> | |
5379 | <td> | |
5380 | <p> | |
5381 | RD: x = y = z | |
5382 | </p> | |
5383 | </td> | |
5384 | <td> | |
5385 | <p> | |
5386 | <span class="blue">Max = 1.03ε (Mean = 0.418ε)</span> | |
5387 | </p> | |
5388 | </td> | |
5389 | <td> | |
5390 | <p> | |
5391 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
5392 | 1.16:</em></span> Max = 1.03ε (Mean = 0.418ε)) | |
5393 | </p> | |
5394 | </td> | |
5395 | <td> | |
5396 | <p> | |
5397 | <span class="blue">Max = 0.998ε (Mean = 0.387ε)</span> | |
5398 | </p> | |
5399 | </td> | |
5400 | <td> | |
5401 | <p> | |
5402 | <span class="blue">Max = 0.998ε (Mean = 0.387ε)</span> | |
5403 | </p> | |
5404 | </td> | |
5405 | </tr> | |
5406 | <tr> | |
5407 | <td> | |
5408 | <p> | |
5409 | RD: x = 0 | |
5410 | </p> | |
5411 | </td> | |
5412 | <td> | |
5413 | <p> | |
5414 | <span class="blue">Max = 2.64ε (Mean = 0.894ε)</span> | |
5415 | </p> | |
5416 | </td> | |
5417 | <td> | |
5418 | <p> | |
5419 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
5420 | 1.16:</em></span> Max = 2.85ε (Mean = 0.781ε)) | |
5421 | </p> | |
5422 | </td> | |
5423 | <td> | |
5424 | <p> | |
5425 | <span class="blue">Max = 2.79ε (Mean = 0.883ε)</span> | |
5426 | </p> | |
5427 | </td> | |
5428 | <td> | |
5429 | <p> | |
5430 | <span class="blue">Max = 2.79ε (Mean = 0.883ε)</span> | |
5431 | </p> | |
5432 | </td> | |
5433 | </tr> | |
5434 | </tbody> | |
5435 | </table></div> | |
5436 | </div> | |
5437 | <br class="table-break"><div class="table"> | |
5438 | <a name="math_toolkit.logs_and_tables.all_table.table_ellint_rf"></a><p class="title"><b>Table 17.36. Error rates for ellint_rf</b></p> | |
5439 | <div class="table-contents"><table class="table" summary="Error rates for ellint_rf"> | |
5440 | <colgroup> | |
5441 | <col> | |
5442 | <col> | |
5443 | <col> | |
5444 | <col> | |
5445 | <col> | |
5446 | </colgroup> | |
5447 | <thead><tr> | |
5448 | <th> | |
5449 | </th> | |
5450 | <th> | |
5451 | <p> | |
5452 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
5453 | </p> | |
5454 | </th> | |
5455 | <th> | |
5456 | <p> | |
5457 | GNU C++ version 5.1.0<br> linux<br> double | |
5458 | </p> | |
5459 | </th> | |
5460 | <th> | |
5461 | <p> | |
5462 | GNU C++ version 5.1.0<br> linux<br> long double | |
5463 | </p> | |
5464 | </th> | |
5465 | <th> | |
5466 | <p> | |
5467 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
5468 | </p> | |
5469 | </th> | |
5470 | </tr></thead> | |
5471 | <tbody> | |
5472 | <tr> | |
5473 | <td> | |
5474 | <p> | |
5475 | RF: Random data | |
5476 | </p> | |
5477 | </td> | |
5478 | <td> | |
5479 | <p> | |
5480 | <span class="blue">Max = 2.02ε (Mean = 0.677ε)</span> | |
5481 | </p> | |
5482 | </td> | |
5483 | <td> | |
5484 | <p> | |
5485 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
5486 | 1.16:</em></span> Max = 2.73ε (Mean = 0.804ε)) | |
5487 | </p> | |
5488 | </td> | |
5489 | <td> | |
5490 | <p> | |
5491 | <span class="blue">Max = 2.54ε (Mean = 0.674ε)</span> | |
5492 | </p> | |
5493 | </td> | |
5494 | <td> | |
5495 | <p> | |
5496 | <span class="blue">Max = 2.54ε (Mean = 0.674ε)</span> | |
5497 | </p> | |
5498 | </td> | |
5499 | </tr> | |
5500 | <tr> | |
5501 | <td> | |
5502 | <p> | |
5503 | RF: x = y = z | |
5504 | </p> | |
5505 | </td> | |
5506 | <td> | |
5507 | <p> | |
5508 | <span class="blue">Max = 0.999ε (Mean = 0.335ε)</span> | |
5509 | </p> | |
5510 | </td> | |
5511 | <td> | |
5512 | <p> | |
5513 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
5514 | 1.16:</em></span> Max = 0.999ε (Mean = 0.34ε)) | |
5515 | </p> | |
5516 | </td> | |
5517 | <td> | |
5518 | <p> | |
5519 | <span class="blue">Max = 0.991ε (Mean = 0.345ε)</span> | |
5520 | </p> | |
5521 | </td> | |
5522 | <td> | |
5523 | <p> | |
5524 | <span class="blue">Max = 0.991ε (Mean = 0.345ε)</span> | |
5525 | </p> | |
5526 | </td> | |
5527 | </tr> | |
5528 | <tr> | |
5529 | <td> | |
5530 | <p> | |
5531 | RF: x = y or y = z or x = z | |
5532 | </p> | |
5533 | </td> | |
5534 | <td> | |
5535 | <p> | |
5536 | <span class="blue">Max = 1.21ε (Mean = 0.394ε)</span> | |
5537 | </p> | |
5538 | </td> | |
5539 | <td> | |
5540 | <p> | |
5541 | <span class="blue">Max = 0.536ε (Mean = 0.00658ε)</span><br> | |
5542 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.89ε (Mean = 0.749ε)) | |
5543 | </p> | |
5544 | </td> | |
5545 | <td> | |
5546 | <p> | |
5547 | <span class="blue">Max = 1.95ε (Mean = 0.418ε)</span> | |
5548 | </p> | |
5549 | </td> | |
5550 | <td> | |
5551 | <p> | |
5552 | <span class="blue">Max = 1.57ε (Mean = 0.418ε)</span> | |
5553 | </p> | |
5554 | </td> | |
5555 | </tr> | |
5556 | <tr> | |
5557 | <td> | |
5558 | <p> | |
5559 | RF: x = 0, y = z | |
5560 | </p> | |
5561 | </td> | |
5562 | <td> | |
5563 | <p> | |
5564 | <span class="blue">Max = 0.999ε (Mean = 0.407ε)</span> | |
5565 | </p> | |
5566 | </td> | |
5567 | <td> | |
5568 | <p> | |
5569 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
5570 | 1.16:</em></span> Max = 1.29ε (Mean = 0.527ε)) | |
5571 | </p> | |
5572 | </td> | |
5573 | <td> | |
5574 | <p> | |
5575 | <span class="blue">Max = 0.894ε (Mean = 0.338ε)</span> | |
5576 | </p> | |
5577 | </td> | |
5578 | <td> | |
5579 | <p> | |
5580 | <span class="blue">Max = 0.894ε (Mean = 0.338ε)</span> | |
5581 | </p> | |
5582 | </td> | |
5583 | </tr> | |
5584 | <tr> | |
5585 | <td> | |
5586 | <p> | |
5587 | RF: z = 0 | |
5588 | </p> | |
5589 | </td> | |
5590 | <td> | |
5591 | <p> | |
5592 | <span class="blue">Max = 1.89ε (Mean = 0.587ε)</span> | |
5593 | </p> | |
5594 | </td> | |
5595 | <td> | |
5596 | <p> | |
5597 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
5598 | 1.16:</em></span> Max = 2.54ε (Mean = 0.781ε)) | |
5599 | </p> | |
5600 | </td> | |
5601 | <td> | |
5602 | <p> | |
5603 | <span class="blue">Max = 1.7ε (Mean = 0.539ε)</span> | |
5604 | </p> | |
5605 | </td> | |
5606 | <td> | |
5607 | <p> | |
5608 | <span class="blue">Max = 1.7ε (Mean = 0.539ε)</span> | |
5609 | </p> | |
5610 | </td> | |
5611 | </tr> | |
5612 | </tbody> | |
5613 | </table></div> | |
5614 | </div> | |
5615 | <br class="table-break"><div class="table"> | |
5616 | <a name="math_toolkit.logs_and_tables.all_table.table_ellint_rg"></a><p class="title"><b>Table 17.37. Error rates for ellint_rg</b></p> | |
5617 | <div class="table-contents"><table class="table" summary="Error rates for ellint_rg"> | |
5618 | <colgroup> | |
5619 | <col> | |
5620 | <col> | |
5621 | <col> | |
5622 | <col> | |
5623 | <col> | |
5624 | </colgroup> | |
5625 | <thead><tr> | |
5626 | <th> | |
5627 | </th> | |
5628 | <th> | |
5629 | <p> | |
5630 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
5631 | </p> | |
5632 | </th> | |
5633 | <th> | |
5634 | <p> | |
5635 | GNU C++ version 5.1.0<br> linux<br> double | |
5636 | </p> | |
5637 | </th> | |
5638 | <th> | |
5639 | <p> | |
5640 | GNU C++ version 5.1.0<br> linux<br> long double | |
5641 | </p> | |
5642 | </th> | |
5643 | <th> | |
5644 | <p> | |
5645 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
5646 | </p> | |
5647 | </th> | |
5648 | </tr></thead> | |
5649 | <tbody> | |
5650 | <tr> | |
5651 | <td> | |
5652 | <p> | |
5653 | RG: Random Data | |
5654 | </p> | |
5655 | </td> | |
5656 | <td> | |
5657 | <p> | |
5658 | <span class="blue">Max = 3.65ε (Mean = 0.929ε)</span> | |
5659 | </p> | |
5660 | </td> | |
5661 | <td> | |
5662 | <p> | |
5663 | <span class="blue">Max = 0.983ε (Mean = 0.0172ε)</span><br> | |
5664 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0.983ε (Mean = 0.0172ε)) | |
5665 | </p> | |
5666 | </td> | |
5667 | <td> | |
5668 | <p> | |
5669 | <span class="blue">Max = 3.95ε (Mean = 0.951ε)</span> | |
5670 | </p> | |
5671 | </td> | |
5672 | <td> | |
5673 | <p> | |
5674 | <span class="blue">Max = 3.95ε (Mean = 0.951ε)</span> | |
5675 | </p> | |
5676 | </td> | |
5677 | </tr> | |
5678 | <tr> | |
5679 | <td> | |
5680 | <p> | |
5681 | RG: two values 0 | |
5682 | </p> | |
5683 | </td> | |
5684 | <td> | |
5685 | <p> | |
5686 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
5687 | </p> | |
5688 | </td> | |
5689 | <td> | |
5690 | <p> | |
5691 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
5692 | 1.16:</em></span> Max = 0ε (Mean = 0ε)) | |
5693 | </p> | |
5694 | </td> | |
5695 | <td> | |
5696 | <p> | |
5697 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
5698 | </p> | |
5699 | </td> | |
5700 | <td> | |
5701 | <p> | |
5702 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
5703 | </p> | |
5704 | </td> | |
5705 | </tr> | |
5706 | <tr> | |
5707 | <td> | |
5708 | <p> | |
5709 | RG: All values the same or zero | |
5710 | </p> | |
5711 | </td> | |
5712 | <td> | |
5713 | <p> | |
5714 | <span class="blue">Max = 1.06ε (Mean = 0.348ε)</span> | |
5715 | </p> | |
5716 | </td> | |
5717 | <td> | |
5718 | <p> | |
5719 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
5720 | 1.16:</em></span> Max = 0ε (Mean = 0ε)) | |
5721 | </p> | |
5722 | </td> | |
5723 | <td> | |
5724 | <p> | |
5725 | <span class="blue">Max = 0.992ε (Mean = 0.288ε)</span> | |
5726 | </p> | |
5727 | </td> | |
5728 | <td> | |
5729 | <p> | |
5730 | <span class="blue">Max = 0.992ε (Mean = 0.288ε)</span> | |
5731 | </p> | |
5732 | </td> | |
5733 | </tr> | |
5734 | <tr> | |
5735 | <td> | |
5736 | <p> | |
5737 | RG: two values the same | |
5738 | </p> | |
5739 | </td> | |
5740 | <td> | |
5741 | <p> | |
5742 | <span class="blue">Max = 1.96ε (Mean = 0.374ε)</span> | |
5743 | </p> | |
5744 | </td> | |
5745 | <td> | |
5746 | <p> | |
5747 | <span class="blue">Max = 0.594ε (Mean = 0.0103ε)</span><br> | |
5748 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0.594ε (Mean = 0.0103ε)) | |
5749 | </p> | |
5750 | </td> | |
5751 | <td> | |
5752 | <p> | |
5753 | <span class="blue">Max = 1.51ε (Mean = 0.404ε)</span> | |
5754 | </p> | |
5755 | </td> | |
5756 | <td> | |
5757 | <p> | |
5758 | <span class="blue">Max = 1.51ε (Mean = 0.404ε)</span> | |
5759 | </p> | |
5760 | </td> | |
5761 | </tr> | |
5762 | <tr> | |
5763 | <td> | |
5764 | <p> | |
5765 | RG: one value zero | |
5766 | </p> | |
5767 | </td> | |
5768 | <td> | |
5769 | <p> | |
5770 | <span class="blue">Max = 1.96ε (Mean = 0.674ε)</span> | |
5771 | </p> | |
5772 | </td> | |
5773 | <td> | |
5774 | <p> | |
5775 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
5776 | 1.16:</em></span> Max = 0ε (Mean = 0ε)) | |
5777 | </p> | |
5778 | </td> | |
5779 | <td> | |
5780 | <p> | |
5781 | <span class="blue">Max = 2.14ε (Mean = 0.722ε)</span> | |
5782 | </p> | |
5783 | </td> | |
5784 | <td> | |
5785 | <p> | |
5786 | <span class="blue">Max = 2.14ε (Mean = 0.722ε)</span> | |
5787 | </p> | |
5788 | </td> | |
5789 | </tr> | |
5790 | </tbody> | |
5791 | </table></div> | |
5792 | </div> | |
5793 | <br class="table-break"><div class="table"> | |
5794 | <a name="math_toolkit.logs_and_tables.all_table.table_ellint_rj"></a><p class="title"><b>Table 17.38. Error rates for ellint_rj</b></p> | |
5795 | <div class="table-contents"><table class="table" summary="Error rates for ellint_rj"> | |
5796 | <colgroup> | |
5797 | <col> | |
5798 | <col> | |
5799 | <col> | |
5800 | <col> | |
5801 | <col> | |
5802 | </colgroup> | |
5803 | <thead><tr> | |
5804 | <th> | |
5805 | </th> | |
5806 | <th> | |
5807 | <p> | |
5808 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
5809 | </p> | |
5810 | </th> | |
5811 | <th> | |
5812 | <p> | |
5813 | GNU C++ version 5.1.0<br> linux<br> double | |
5814 | </p> | |
5815 | </th> | |
5816 | <th> | |
5817 | <p> | |
5818 | GNU C++ version 5.1.0<br> linux<br> long double | |
5819 | </p> | |
5820 | </th> | |
5821 | <th> | |
5822 | <p> | |
5823 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
5824 | </p> | |
5825 | </th> | |
5826 | </tr></thead> | |
5827 | <tbody> | |
5828 | <tr> | |
5829 | <td> | |
5830 | <p> | |
5831 | RJ: Random data | |
5832 | </p> | |
5833 | </td> | |
5834 | <td> | |
5835 | <p> | |
5836 | <span class="blue">Max = 119ε (Mean = 4.32ε)</span> | |
5837 | </p> | |
5838 | </td> | |
5839 | <td> | |
5840 | <p> | |
5841 | <span class="blue">Max = 0.52ε (Mean = 0.0184ε)</span><br> <br> | |
5842 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 3.57ε (Mean = 0.704ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ellint_rj_GSL_1_16_RJ_Random_data">And | |
5843 | other failures.</a>) | |
5844 | </p> | |
5845 | </td> | |
5846 | <td> | |
5847 | <p> | |
5848 | <span class="blue">Max = 186ε (Mean = 6.67ε)</span> | |
5849 | </p> | |
5850 | </td> | |
5851 | <td> | |
5852 | <p> | |
5853 | <span class="blue">Max = 186ε (Mean = 6.7ε)</span> | |
5854 | </p> | |
5855 | </td> | |
5856 | </tr> | |
5857 | <tr> | |
5858 | <td> | |
5859 | <p> | |
5860 | RJ: 4 Equal Values | |
5861 | </p> | |
5862 | </td> | |
5863 | <td> | |
5864 | <p> | |
5865 | <span class="blue">Max = 1.03ε (Mean = 0.418ε)</span> | |
5866 | </p> | |
5867 | </td> | |
5868 | <td> | |
5869 | <p> | |
5870 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
5871 | 1.16:</em></span> Max = 1.03ε (Mean = 0.418ε)) | |
5872 | </p> | |
5873 | </td> | |
5874 | <td> | |
5875 | <p> | |
5876 | <span class="blue">Max = 0.998ε (Mean = 0.387ε)</span> | |
5877 | </p> | |
5878 | </td> | |
5879 | <td> | |
5880 | <p> | |
5881 | <span class="blue">Max = 0.998ε (Mean = 0.387ε)</span> | |
5882 | </p> | |
5883 | </td> | |
5884 | </tr> | |
5885 | <tr> | |
5886 | <td> | |
5887 | <p> | |
5888 | RJ: 3 Equal Values | |
5889 | </p> | |
5890 | </td> | |
5891 | <td> | |
5892 | <p> | |
5893 | <span class="blue">Max = 39.9ε (Mean = 1.12ε)</span> | |
5894 | </p> | |
5895 | </td> | |
5896 | <td> | |
5897 | <p> | |
5898 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
5899 | 1.16:</em></span> Max = 3.96ε (Mean = 1.06ε)) | |
5900 | </p> | |
5901 | </td> | |
5902 | <td> | |
5903 | <p> | |
5904 | <span class="blue">Max = 20.8ε (Mean = 0.986ε)</span> | |
5905 | </p> | |
5906 | </td> | |
5907 | <td> | |
5908 | <p> | |
5909 | <span class="blue">Max = 18.2ε (Mean = 0.917ε)</span> | |
5910 | </p> | |
5911 | </td> | |
5912 | </tr> | |
5913 | <tr> | |
5914 | <td> | |
5915 | <p> | |
5916 | RJ: 2 Equal Values | |
5917 | </p> | |
5918 | </td> | |
5919 | <td> | |
5920 | <p> | |
5921 | <span class="blue">Max = 214ε (Mean = 5.05ε)</span> | |
5922 | </p> | |
5923 | </td> | |
5924 | <td> | |
5925 | <p> | |
5926 | <span class="blue">Max = 0.6ε (Mean = 0.0228ε)</span><br> <br> | |
5927 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.57ε (Mean = 0.754ε)) | |
5928 | </p> | |
5929 | </td> | |
5930 | <td> | |
5931 | <p> | |
5932 | <span class="blue">Max = 220ε (Mean = 6.64ε)</span> | |
5933 | </p> | |
5934 | </td> | |
5935 | <td> | |
5936 | <p> | |
5937 | <span class="blue">Max = 135ε (Mean = 5.3ε)</span> | |
5938 | </p> | |
5939 | </td> | |
5940 | </tr> | |
5941 | <tr> | |
5942 | <td> | |
5943 | <p> | |
5944 | RJ: Equal z and p | |
5945 | </p> | |
5946 | </td> | |
5947 | <td> | |
5948 | <p> | |
5949 | <span class="blue">Max = 15.4ε (Mean = 1.05ε)</span> | |
5950 | </p> | |
5951 | </td> | |
5952 | <td> | |
5953 | <p> | |
5954 | <span class="blue">Max = 0.742ε (Mean = 0.0166ε)</span><br> | |
5955 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.62ε (Mean = 0.699ε)) | |
5956 | </p> | |
5957 | </td> | |
5958 | <td> | |
5959 | <p> | |
5960 | <span class="blue">Max = 17.2ε (Mean = 1.16ε)</span> | |
5961 | </p> | |
5962 | </td> | |
5963 | <td> | |
5964 | <p> | |
5965 | <span class="blue">Max = 16.6ε (Mean = 1.15ε)</span> | |
5966 | </p> | |
5967 | </td> | |
5968 | </tr> | |
5969 | </tbody> | |
5970 | </table></div> | |
5971 | </div> | |
5972 | <br class="table-break"><div class="table"> | |
5973 | <a name="math_toolkit.logs_and_tables.all_table.table_erf"></a><p class="title"><b>Table 17.39. Error rates for erf</b></p> | |
5974 | <div class="table-contents"><table class="table" summary="Error rates for erf"> | |
5975 | <colgroup> | |
5976 | <col> | |
5977 | <col> | |
5978 | <col> | |
5979 | <col> | |
5980 | <col> | |
5981 | </colgroup> | |
5982 | <thead><tr> | |
5983 | <th> | |
5984 | </th> | |
5985 | <th> | |
5986 | <p> | |
5987 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
5988 | </p> | |
5989 | </th> | |
5990 | <th> | |
5991 | <p> | |
5992 | GNU C++ version 5.1.0<br> linux<br> long double | |
5993 | </p> | |
5994 | </th> | |
5995 | <th> | |
5996 | <p> | |
5997 | GNU C++ version 5.1.0<br> linux<br> double | |
5998 | </p> | |
5999 | </th> | |
6000 | <th> | |
6001 | <p> | |
6002 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
6003 | </p> | |
6004 | </th> | |
6005 | </tr></thead> | |
6006 | <tbody> | |
6007 | <tr> | |
6008 | <td> | |
6009 | <p> | |
6010 | Erf Function: Small Values | |
6011 | </p> | |
6012 | </td> | |
6013 | <td> | |
6014 | <p> | |
6015 | <span class="blue">Max = 0.996ε (Mean = 0.182ε)</span><br> <br> | |
6016 | (<span class="emphasis"><em><math.h>:</em></span> Max = 1.57ε (Mean = 0.317ε)) | |
6017 | </p> | |
6018 | </td> | |
6019 | <td> | |
6020 | <p> | |
6021 | <span class="blue">Max = 0.925ε (Mean = 0.193ε)</span><br> <br> | |
6022 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 0.944ε (Mean = 0.191ε))<br> | |
6023 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0.944ε (Mean = 0.191ε)) | |
6024 | </p> | |
6025 | </td> | |
6026 | <td> | |
6027 | <p> | |
6028 | <span class="blue">Max = 0.841ε (Mean = 0.0687ε)</span><br> | |
6029 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.06ε (Mean = 0.319ε))<br> | |
6030 | (<span class="emphasis"><em>Cephes:</em></span> Max = 1.13ε (Mean = 0.442ε)) | |
6031 | </p> | |
6032 | </td> | |
6033 | <td> | |
6034 | <p> | |
6035 | <span class="blue">Max = 0.925ε (Mean = 0.193ε)</span><br> <br> | |
6036 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0.944ε (Mean = 0.194ε)) | |
6037 | </p> | |
6038 | </td> | |
6039 | </tr> | |
6040 | <tr> | |
6041 | <td> | |
6042 | <p> | |
6043 | Erf Function: Medium Values | |
6044 | </p> | |
6045 | </td> | |
6046 | <td> | |
6047 | <p> | |
6048 | <span class="blue">Max = 1ε (Mean = 0.169ε)</span><br> <br> | |
6049 | (<span class="emphasis"><em><math.h>:</em></span> Max = 1.19ε (Mean = 0.244ε)) | |
6050 | </p> | |
6051 | </td> | |
6052 | <td> | |
6053 | <p> | |
6054 | <span class="blue">Max = 1.5ε (Mean = 0.193ε)</span><br> <br> | |
6055 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 0.921ε (Mean = 0.0723ε))<br> | |
6056 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0.921ε (Mean = 0.0723ε)) | |
6057 | </p> | |
6058 | </td> | |
6059 | <td> | |
6060 | <p> | |
6061 | <span class="blue">Max = 1ε (Mean = 0.119ε)</span><br> <br> | |
6062 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.31ε (Mean = 0.368ε))<br> | |
6063 | (<span class="emphasis"><em>Cephes:</em></span> Max = 1.34ε (Mean = 0.279ε)) | |
6064 | </p> | |
6065 | </td> | |
6066 | <td> | |
6067 | <p> | |
6068 | <span class="blue">Max = 1.5ε (Mean = 0.202ε)</span><br> <br> | |
6069 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0.921ε (Mean = 0.071ε)) | |
6070 | </p> | |
6071 | </td> | |
6072 | </tr> | |
6073 | <tr> | |
6074 | <td> | |
6075 | <p> | |
6076 | Erf Function: Large Values | |
6077 | </p> | |
6078 | </td> | |
6079 | <td> | |
6080 | <p> | |
6081 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> | |
6082 | Max = 0ε (Mean = 0ε)) | |
6083 | </p> | |
6084 | </td> | |
6085 | <td> | |
6086 | <p> | |
6087 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><tr1/cmath>:</em></span> | |
6088 | Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em><math.h>:</em></span> | |
6089 | Max = 0ε (Mean = 0ε)) | |
6090 | </p> | |
6091 | </td> | |
6092 | <td> | |
6093 | <p> | |
6094 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
6095 | 1.16:</em></span> Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
6096 | Max = 0ε (Mean = 0ε)) | |
6097 | </p> | |
6098 | </td> | |
6099 | <td> | |
6100 | <p> | |
6101 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> | |
6102 | Max = 0ε (Mean = 0ε)) | |
6103 | </p> | |
6104 | </td> | |
6105 | </tr> | |
6106 | </tbody> | |
6107 | </table></div> | |
6108 | </div> | |
6109 | <br class="table-break"><div class="table"> | |
6110 | <a name="math_toolkit.logs_and_tables.all_table.table_erf_inv"></a><p class="title"><b>Table 17.40. Error rates for erf_inv</b></p> | |
6111 | <div class="table-contents"><table class="table" summary="Error rates for erf_inv"> | |
6112 | <colgroup> | |
6113 | <col> | |
6114 | <col> | |
6115 | <col> | |
6116 | <col> | |
6117 | <col> | |
6118 | </colgroup> | |
6119 | <thead><tr> | |
6120 | <th> | |
6121 | </th> | |
6122 | <th> | |
6123 | <p> | |
6124 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
6125 | </p> | |
6126 | </th> | |
6127 | <th> | |
6128 | <p> | |
6129 | GNU C++ version 5.1.0<br> linux<br> double | |
6130 | </p> | |
6131 | </th> | |
6132 | <th> | |
6133 | <p> | |
6134 | GNU C++ version 5.1.0<br> linux<br> long double | |
6135 | </p> | |
6136 | </th> | |
6137 | <th> | |
6138 | <p> | |
6139 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
6140 | </p> | |
6141 | </th> | |
6142 | </tr></thead> | |
6143 | <tbody><tr> | |
6144 | <td> | |
6145 | <p> | |
6146 | Inverse Erf Function | |
6147 | </p> | |
6148 | </td> | |
6149 | <td> | |
6150 | <p> | |
6151 | <span class="blue">Max = 1.09ε (Mean = 0.502ε)</span> | |
6152 | </p> | |
6153 | </td> | |
6154 | <td> | |
6155 | <p> | |
6156 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
6157 | </p> | |
6158 | </td> | |
6159 | <td> | |
6160 | <p> | |
6161 | <span class="blue">Max = 0.996ε (Mean = 0.389ε)</span> | |
6162 | </p> | |
6163 | </td> | |
6164 | <td> | |
6165 | <p> | |
6166 | <span class="blue">Max = 0.996ε (Mean = 0.385ε)</span> | |
6167 | </p> | |
6168 | </td> | |
6169 | </tr></tbody> | |
6170 | </table></div> | |
6171 | </div> | |
6172 | <br class="table-break"><div class="table"> | |
6173 | <a name="math_toolkit.logs_and_tables.all_table.table_erfc"></a><p class="title"><b>Table 17.41. Error rates for erfc</b></p> | |
6174 | <div class="table-contents"><table class="table" summary="Error rates for erfc"> | |
6175 | <colgroup> | |
6176 | <col> | |
6177 | <col> | |
6178 | <col> | |
6179 | <col> | |
6180 | <col> | |
6181 | </colgroup> | |
6182 | <thead><tr> | |
6183 | <th> | |
6184 | </th> | |
6185 | <th> | |
6186 | <p> | |
6187 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
6188 | </p> | |
6189 | </th> | |
6190 | <th> | |
6191 | <p> | |
6192 | GNU C++ version 5.1.0<br> linux<br> long double | |
6193 | </p> | |
6194 | </th> | |
6195 | <th> | |
6196 | <p> | |
6197 | GNU C++ version 5.1.0<br> linux<br> double | |
6198 | </p> | |
6199 | </th> | |
6200 | <th> | |
6201 | <p> | |
6202 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
6203 | </p> | |
6204 | </th> | |
6205 | </tr></thead> | |
6206 | <tbody> | |
6207 | <tr> | |
6208 | <td> | |
6209 | <p> | |
6210 | Erf Function: Small Values | |
6211 | </p> | |
6212 | </td> | |
6213 | <td> | |
6214 | <p> | |
6215 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> | |
6216 | Max = 0ε (Mean = 0ε)) | |
6217 | </p> | |
6218 | </td> | |
6219 | <td> | |
6220 | <p> | |
6221 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><tr1/cmath>:</em></span> | |
6222 | Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em><math.h>:</em></span> | |
6223 | Max = 0ε (Mean = 0ε)) | |
6224 | </p> | |
6225 | </td> | |
6226 | <td> | |
6227 | <p> | |
6228 | <span class="blue">Max = 0.658ε (Mean = 0.0537ε)</span><br> | |
6229 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.01ε (Mean = 0.485ε))<br> | |
6230 | (<span class="emphasis"><em>Cephes:</em></span> Max = 0.786ε (Mean = 0.0642ε)) | |
6231 | </p> | |
6232 | </td> | |
6233 | <td> | |
6234 | <p> | |
6235 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> | |
6236 | Max = 0ε (Mean = 0ε)) | |
6237 | </p> | |
6238 | </td> | |
6239 | </tr> | |
6240 | <tr> | |
6241 | <td> | |
6242 | <p> | |
6243 | Erf Function: Medium Values | |
6244 | </p> | |
6245 | </td> | |
6246 | <td> | |
6247 | <p> | |
6248 | <span class="blue">Max = 1.65ε (Mean = 0.373ε)</span><br> <br> | |
6249 | (<span class="emphasis"><em><math.h>:</em></span> Max = 2.36ε (Mean = 0.539ε)) | |
6250 | </p> | |
6251 | </td> | |
6252 | <td> | |
6253 | <p> | |
6254 | <span class="blue">Max = 1.76ε (Mean = 0.365ε)</span><br> <br> | |
6255 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.35ε (Mean = 0.307ε))<br> | |
6256 | (<span class="emphasis"><em><math.h>:</em></span> Max = 1.35ε (Mean = 0.307ε)) | |
6257 | </p> | |
6258 | </td> | |
6259 | <td> | |
6260 | <p> | |
6261 | <span class="blue">Max = 0.983ε (Mean = 0.213ε)</span><br> <br> | |
6262 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.64ε (Mean = 0.662ε))<br> | |
6263 | (<span class="emphasis"><em>Cephes:</em></span> Max = 3.59ε (Mean = 0.779ε)) | |
6264 | </p> | |
6265 | </td> | |
6266 | <td> | |
6267 | <p> | |
6268 | <span class="blue">Max = 1.76ε (Mean = 0.383ε)</span><br> <br> | |
6269 | (<span class="emphasis"><em><math.h>:</em></span> Max = 2.81ε (Mean = 0.739ε)) | |
6270 | </p> | |
6271 | </td> | |
6272 | </tr> | |
6273 | <tr> | |
6274 | <td> | |
6275 | <p> | |
6276 | Erf Function: Large Values | |
6277 | </p> | |
6278 | </td> | |
6279 | <td> | |
6280 | <p> | |
6281 | <span class="blue">Max = 1.14ε (Mean = 0.248ε)</span><br> <br> | |
6282 | (<span class="emphasis"><em><math.h>:</em></span> Max = 1.84ε (Mean = 0.331ε)) | |
6283 | </p> | |
6284 | </td> | |
6285 | <td> | |
6286 | <p> | |
6287 | <span class="blue">Max = 1.57ε (Mean = 0.542ε)</span><br> <br> | |
6288 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.26ε (Mean = 0.441ε))<br> | |
6289 | (<span class="emphasis"><em><math.h>:</em></span> Max = 1.26ε (Mean = 0.441ε)) | |
6290 | </p> | |
6291 | </td> | |
6292 | <td> | |
6293 | <p> | |
6294 | <span class="blue">Max = 0.868ε (Mean = 0.147ε)</span><br> <br> | |
6295 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 3.9ε (Mean = 0.472ε))<br> | |
6296 | (<span class="emphasis"><em>Cephes:</em></span> Max = 2.74ε (Mean = 0.413ε)) | |
6297 | </p> | |
6298 | </td> | |
6299 | <td> | |
6300 | <p> | |
6301 | <span class="blue">Max = 1.57ε (Mean = 0.564ε)</span><br> <br> | |
6302 | (<span class="emphasis"><em><math.h>:</em></span> Max = 4.91ε (Mean = 1.54ε)) | |
6303 | </p> | |
6304 | </td> | |
6305 | </tr> | |
6306 | </tbody> | |
6307 | </table></div> | |
6308 | </div> | |
6309 | <br class="table-break"><div class="table"> | |
6310 | <a name="math_toolkit.logs_and_tables.all_table.table_erfc_inv"></a><p class="title"><b>Table 17.42. Error rates for erfc_inv</b></p> | |
6311 | <div class="table-contents"><table class="table" summary="Error rates for erfc_inv"> | |
6312 | <colgroup> | |
6313 | <col> | |
6314 | <col> | |
6315 | <col> | |
6316 | <col> | |
6317 | <col> | |
6318 | </colgroup> | |
6319 | <thead><tr> | |
6320 | <th> | |
6321 | </th> | |
6322 | <th> | |
6323 | <p> | |
6324 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
6325 | </p> | |
6326 | </th> | |
6327 | <th> | |
6328 | <p> | |
6329 | GNU C++ version 5.1.0<br> linux<br> double | |
6330 | </p> | |
6331 | </th> | |
6332 | <th> | |
6333 | <p> | |
6334 | GNU C++ version 5.1.0<br> linux<br> long double | |
6335 | </p> | |
6336 | </th> | |
6337 | <th> | |
6338 | <p> | |
6339 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
6340 | </p> | |
6341 | </th> | |
6342 | </tr></thead> | |
6343 | <tbody> | |
6344 | <tr> | |
6345 | <td> | |
6346 | <p> | |
6347 | Inverse Erfc Function | |
6348 | </p> | |
6349 | </td> | |
6350 | <td> | |
6351 | <p> | |
6352 | <span class="blue">Max = 1ε (Mean = 0.491ε)</span> | |
6353 | </p> | |
6354 | </td> | |
6355 | <td> | |
6356 | <p> | |
6357 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
6358 | </p> | |
6359 | </td> | |
6360 | <td> | |
6361 | <p> | |
6362 | <span class="blue">Max = 0.996ε (Mean = 0.397ε)</span> | |
6363 | </p> | |
6364 | </td> | |
6365 | <td> | |
6366 | <p> | |
6367 | <span class="blue">Max = 0.996ε (Mean = 0.397ε)</span> | |
6368 | </p> | |
6369 | </td> | |
6370 | </tr> | |
6371 | <tr> | |
6372 | <td> | |
6373 | <p> | |
6374 | Inverse Erfc Function: extreme values | |
6375 | </p> | |
6376 | </td> | |
6377 | <td> | |
6378 | </td> | |
6379 | <td> | |
6380 | </td> | |
6381 | <td> | |
6382 | <p> | |
6383 | <span class="blue">Max = 1.62ε (Mean = 0.383ε)</span> | |
6384 | </p> | |
6385 | </td> | |
6386 | <td> | |
6387 | <p> | |
6388 | <span class="blue">Max = 1.62ε (Mean = 0.385ε)</span> | |
6389 | </p> | |
6390 | </td> | |
6391 | </tr> | |
6392 | </tbody> | |
6393 | </table></div> | |
6394 | </div> | |
6395 | <br class="table-break"><div class="table"> | |
6396 | <a name="math_toolkit.logs_and_tables.all_table.table_expint_Ei_"></a><p class="title"><b>Table 17.43. Error rates for expint (Ei)</b></p> | |
6397 | <div class="table-contents"><table class="table" summary="Error rates for expint (Ei)"> | |
6398 | <colgroup> | |
6399 | <col> | |
6400 | <col> | |
6401 | <col> | |
6402 | <col> | |
6403 | <col> | |
6404 | </colgroup> | |
6405 | <thead><tr> | |
6406 | <th> | |
6407 | </th> | |
6408 | <th> | |
6409 | <p> | |
6410 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
6411 | </p> | |
6412 | </th> | |
6413 | <th> | |
6414 | <p> | |
6415 | GNU C++ version 5.1.0<br> linux<br> long double | |
6416 | </p> | |
6417 | </th> | |
6418 | <th> | |
6419 | <p> | |
6420 | GNU C++ version 5.1.0<br> linux<br> double | |
6421 | </p> | |
6422 | </th> | |
6423 | <th> | |
6424 | <p> | |
6425 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
6426 | </p> | |
6427 | </th> | |
6428 | </tr></thead> | |
6429 | <tbody> | |
6430 | <tr> | |
6431 | <td> | |
6432 | <p> | |
6433 | Exponential Integral Ei | |
6434 | </p> | |
6435 | </td> | |
6436 | <td> | |
6437 | <p> | |
6438 | <span class="blue">Max = 1.43ε (Mean = 0.541ε)</span> | |
6439 | </p> | |
6440 | </td> | |
6441 | <td> | |
6442 | <p> | |
6443 | <span class="blue">Max = 5.05ε (Mean = 0.821ε)</span><br> <br> | |
6444 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 14.1ε (Mean = 2.43ε) | |
6445 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_expint_Ei___tr1_cmath__Exponential_Integral_Ei">And | |
6446 | other failures.</a>) | |
6447 | </p> | |
6448 | </td> | |
6449 | <td> | |
6450 | <p> | |
6451 | <span class="blue">Max = 0.994ε (Mean = 0.142ε)</span><br> <br> | |
6452 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 8.96ε (Mean = 0.703ε))<br> | |
6453 | (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean | |
6454 | = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_expint_Ei__Cephes_Exponential_Integral_Ei">And | |
6455 | other failures.</a>)</span> | |
6456 | </p> | |
6457 | </td> | |
6458 | <td> | |
6459 | <p> | |
6460 | <span class="blue">Max = 3.34ε (Mean = 0.631ε)</span> | |
6461 | </p> | |
6462 | </td> | |
6463 | </tr> | |
6464 | <tr> | |
6465 | <td> | |
6466 | <p> | |
6467 | Exponential Integral Ei: double exponent range | |
6468 | </p> | |
6469 | </td> | |
6470 | <td> | |
6471 | <p> | |
6472 | <span class="blue">Max = 1.7ε (Mean = 0.66ε)</span> | |
6473 | </p> | |
6474 | </td> | |
6475 | <td> | |
6476 | <p> | |
6477 | <span class="blue">Max = 1.72ε (Mean = 0.593ε)</span><br> <br> | |
6478 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 3.11ε (Mean = 1.13ε)) | |
6479 | </p> | |
6480 | </td> | |
6481 | <td> | |
6482 | <p> | |
6483 | <span class="blue">Max = 0.998ε (Mean = 0.156ε)</span><br> <br> | |
6484 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.5ε (Mean = 0.612ε))<br> | |
6485 | (<span class="emphasis"><em>Cephes:</em></span> Max = 1.77ε (Mean = 0.644ε)) | |
6486 | </p> | |
6487 | </td> | |
6488 | <td> | |
6489 | <p> | |
6490 | <span class="blue">Max = 1.72ε (Mean = 0.618ε)</span> | |
6491 | </p> | |
6492 | </td> | |
6493 | </tr> | |
6494 | <tr> | |
6495 | <td> | |
6496 | <p> | |
6497 | Exponential Integral Ei: long exponent range | |
6498 | </p> | |
6499 | </td> | |
6500 | <td> | |
6501 | </td> | |
6502 | <td> | |
6503 | <p> | |
6504 | <span class="blue">Max = 1.98ε (Mean = 0.595ε)</span><br> <br> | |
6505 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.93ε (Mean = 0.855ε)) | |
6506 | </p> | |
6507 | </td> | |
6508 | <td> | |
6509 | </td> | |
6510 | <td> | |
6511 | <p> | |
6512 | <span class="blue">Max = 1.98ε (Mean = 0.575ε)</span> | |
6513 | </p> | |
6514 | </td> | |
6515 | </tr> | |
6516 | </tbody> | |
6517 | </table></div> | |
6518 | </div> | |
6519 | <br class="table-break"><div class="table"> | |
6520 | <a name="math_toolkit.logs_and_tables.all_table.table_expint_En_"></a><p class="title"><b>Table 17.44. Error rates for expint (En)</b></p> | |
6521 | <div class="table-contents"><table class="table" summary="Error rates for expint (En)"> | |
6522 | <colgroup> | |
6523 | <col> | |
6524 | <col> | |
6525 | <col> | |
6526 | <col> | |
6527 | <col> | |
6528 | </colgroup> | |
6529 | <thead><tr> | |
6530 | <th> | |
6531 | </th> | |
6532 | <th> | |
6533 | <p> | |
6534 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
6535 | </p> | |
6536 | </th> | |
6537 | <th> | |
6538 | <p> | |
6539 | GNU C++ version 5.1.0<br> linux<br> double | |
6540 | </p> | |
6541 | </th> | |
6542 | <th> | |
6543 | <p> | |
6544 | GNU C++ version 5.1.0<br> linux<br> long double | |
6545 | </p> | |
6546 | </th> | |
6547 | <th> | |
6548 | <p> | |
6549 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
6550 | </p> | |
6551 | </th> | |
6552 | </tr></thead> | |
6553 | <tbody> | |
6554 | <tr> | |
6555 | <td> | |
6556 | <p> | |
6557 | Exponential Integral En | |
6558 | </p> | |
6559 | </td> | |
6560 | <td> | |
6561 | <p> | |
6562 | <span class="blue">Max = 7.16ε (Mean = 1.85ε)</span> | |
6563 | </p> | |
6564 | </td> | |
6565 | <td> | |
6566 | <p> | |
6567 | <span class="blue">Max = 0.589ε (Mean = 0.0331ε)</span><br> | |
6568 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 58.5ε (Mean = 17.1ε)) | |
6569 | </p> | |
6570 | </td> | |
6571 | <td> | |
6572 | <p> | |
6573 | <span class="blue">Max = 9.97ε (Mean = 2.13ε)</span> | |
6574 | </p> | |
6575 | </td> | |
6576 | <td> | |
6577 | <p> | |
6578 | <span class="blue">Max = 9.97ε (Mean = 2.13ε)</span> | |
6579 | </p> | |
6580 | </td> | |
6581 | </tr> | |
6582 | <tr> | |
6583 | <td> | |
6584 | <p> | |
6585 | Exponential Integral En: small z values | |
6586 | </p> | |
6587 | </td> | |
6588 | <td> | |
6589 | <p> | |
6590 | <span class="blue">Max = 2.62ε (Mean = 0.531ε)</span> | |
6591 | </p> | |
6592 | </td> | |
6593 | <td> | |
6594 | <p> | |
6595 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
6596 | 1.16:</em></span> Max = 115ε (Mean = 23.6ε)) | |
6597 | </p> | |
6598 | </td> | |
6599 | <td> | |
6600 | <p> | |
6601 | <span class="blue">Max = 1.99ε (Mean = 0.559ε)</span> | |
6602 | </p> | |
6603 | </td> | |
6604 | <td> | |
6605 | <p> | |
6606 | <span class="blue">Max = 1.99ε (Mean = 0.559ε)</span> | |
6607 | </p> | |
6608 | </td> | |
6609 | </tr> | |
6610 | <tr> | |
6611 | <td> | |
6612 | <p> | |
6613 | Exponential Integral E1 | |
6614 | </p> | |
6615 | </td> | |
6616 | <td> | |
6617 | <p> | |
6618 | <span class="blue">Max = 0.988ε (Mean = 0.486ε)</span> | |
6619 | </p> | |
6620 | </td> | |
6621 | <td> | |
6622 | <p> | |
6623 | <span class="blue">Max = 0.556ε (Mean = 0.0625ε)</span><br> | |
6624 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0.988ε (Mean = 0.469ε)) | |
6625 | </p> | |
6626 | </td> | |
6627 | <td> | |
6628 | <p> | |
6629 | <span class="blue">Max = 0.965ε (Mean = 0.414ε)</span> | |
6630 | </p> | |
6631 | </td> | |
6632 | <td> | |
6633 | <p> | |
6634 | <span class="blue">Max = 0.965ε (Mean = 0.409ε)</span> | |
6635 | </p> | |
6636 | </td> | |
6637 | </tr> | |
6638 | </tbody> | |
6639 | </table></div> | |
6640 | </div> | |
6641 | <br class="table-break"><div class="table"> | |
6642 | <a name="math_toolkit.logs_and_tables.all_table.table_expm1"></a><p class="title"><b>Table 17.45. Error rates for expm1</b></p> | |
6643 | <div class="table-contents"><table class="table" summary="Error rates for expm1"> | |
6644 | <colgroup> | |
6645 | <col> | |
6646 | <col> | |
6647 | <col> | |
6648 | <col> | |
6649 | <col> | |
6650 | </colgroup> | |
6651 | <thead><tr> | |
6652 | <th> | |
6653 | </th> | |
6654 | <th> | |
6655 | <p> | |
6656 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
6657 | </p> | |
6658 | </th> | |
6659 | <th> | |
6660 | <p> | |
6661 | GNU C++ version 5.1.0<br> linux<br> double | |
6662 | </p> | |
6663 | </th> | |
6664 | <th> | |
6665 | <p> | |
6666 | GNU C++ version 5.1.0<br> linux<br> long double | |
6667 | </p> | |
6668 | </th> | |
6669 | <th> | |
6670 | <p> | |
6671 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
6672 | </p> | |
6673 | </th> | |
6674 | </tr></thead> | |
6675 | <tbody><tr> | |
6676 | <td> | |
6677 | <p> | |
6678 | Random test data | |
6679 | </p> | |
6680 | </td> | |
6681 | <td> | |
6682 | <p> | |
6683 | <span class="blue">Max = 0.996ε (Mean = 0.283ε)</span><br> <br> | |
6684 | (<span class="emphasis"><em><math.h>:</em></span> Max = 1.31ε (Mean = 0.496ε)) | |
6685 | </p> | |
6686 | </td> | |
6687 | <td> | |
6688 | <p> | |
6689 | <span class="blue">Max = 0.793ε (Mean = 0.126ε)</span><br> <br> | |
6690 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 0.793ε (Mean = 0.126ε))<br> | |
6691 | (<span class="emphasis"><em>Cephes:</em></span> Max = 1.53ε (Mean = 0.535ε)) | |
6692 | </p> | |
6693 | </td> | |
6694 | <td> | |
6695 | <p> | |
6696 | <span class="blue">Max = 0.992ε (Mean = 0.402ε)</span><br> <br> | |
6697 | (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max | |
6698 | = 1.26e+19ε (Mean = 4.89e+18ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_expm1__tr1_cmath__Random_test_data">And | |
6699 | other failures.</a>)</span><br> (<span class="emphasis"><em><math.h>:</em></span> | |
6700 | Max = 0.992ε (Mean = 0.402ε)) | |
6701 | </p> | |
6702 | </td> | |
6703 | <td> | |
6704 | <p> | |
6705 | <span class="blue">Max = 1.31ε (Mean = 0.406ε)</span><br> <br> | |
6706 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0.996ε (Mean = 0.426ε)) | |
6707 | </p> | |
6708 | </td> | |
6709 | </tr></tbody> | |
6710 | </table></div> | |
6711 | </div> | |
6712 | <br class="table-break"><div class="table"> | |
6713 | <a name="math_toolkit.logs_and_tables.all_table.table_gamma_p"></a><p class="title"><b>Table 17.46. Error rates for gamma_p</b></p> | |
6714 | <div class="table-contents"><table class="table" summary="Error rates for gamma_p"> | |
6715 | <colgroup> | |
6716 | <col> | |
6717 | <col> | |
6718 | <col> | |
6719 | <col> | |
6720 | <col> | |
6721 | </colgroup> | |
6722 | <thead><tr> | |
6723 | <th> | |
6724 | </th> | |
6725 | <th> | |
6726 | <p> | |
6727 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
6728 | </p> | |
6729 | </th> | |
6730 | <th> | |
6731 | <p> | |
6732 | GNU C++ version 5.1.0<br> linux<br> double | |
6733 | </p> | |
6734 | </th> | |
6735 | <th> | |
6736 | <p> | |
6737 | GNU C++ version 5.1.0<br> linux<br> long double | |
6738 | </p> | |
6739 | </th> | |
6740 | <th> | |
6741 | <p> | |
6742 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
6743 | </p> | |
6744 | </th> | |
6745 | </tr></thead> | |
6746 | <tbody> | |
6747 | <tr> | |
6748 | <td> | |
6749 | <p> | |
6750 | tgamma(a, z) medium values | |
6751 | </p> | |
6752 | </td> | |
6753 | <td> | |
6754 | <p> | |
6755 | <span class="blue">Max = 35.1ε (Mean = 6.97ε)</span> | |
6756 | </p> | |
6757 | </td> | |
6758 | <td> | |
6759 | <p> | |
6760 | <span class="blue">Max = 0.955ε (Mean = 0.05ε)</span><br> <br> | |
6761 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 342ε (Mean = 45.8ε))<br> (<span class="emphasis"><em>Rmath | |
6762 | 3.0.2:</em></span> Max = 389ε (Mean = 44ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
6763 | Max = 492ε (Mean = 101ε)) | |
6764 | </p> | |
6765 | </td> | |
6766 | <td> | |
6767 | <p> | |
6768 | <span class="blue">Max = 41ε (Mean = 8.09ε)</span> | |
6769 | </p> | |
6770 | </td> | |
6771 | <td> | |
6772 | <p> | |
6773 | <span class="blue">Max = 239ε (Mean = 30.2ε)</span> | |
6774 | </p> | |
6775 | </td> | |
6776 | </tr> | |
6777 | <tr> | |
6778 | <td> | |
6779 | <p> | |
6780 | tgamma(a, z) small values | |
6781 | </p> | |
6782 | </td> | |
6783 | <td> | |
6784 | <p> | |
6785 | <span class="blue">Max = 1.54ε (Mean = 0.439ε)</span> | |
6786 | </p> | |
6787 | </td> | |
6788 | <td> | |
6789 | <p> | |
6790 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
6791 | 1.16:</em></span> Max = 4.82ε (Mean = 0.758ε))<br> (<span class="emphasis"><em>Rmath | |
6792 | 3.0.2:</em></span> Max = 1.01ε (Mean = 0.306ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
6793 | Max = 21ε (Mean = 5.65ε)) | |
6794 | </p> | |
6795 | </td> | |
6796 | <td> | |
6797 | <p> | |
6798 | <span class="blue">Max = 2ε (Mean = 0.461ε)</span> | |
6799 | </p> | |
6800 | </td> | |
6801 | <td> | |
6802 | <p> | |
6803 | <span class="blue">Max = 2ε (Mean = 0.472ε)</span> | |
6804 | </p> | |
6805 | </td> | |
6806 | </tr> | |
6807 | <tr> | |
6808 | <td> | |
6809 | <p> | |
6810 | tgamma(a, z) large values | |
6811 | </p> | |
6812 | </td> | |
6813 | <td> | |
6814 | <p> | |
6815 | <span class="blue">Max = 244ε (Mean = 20.2ε)</span> | |
6816 | </p> | |
6817 | </td> | |
6818 | <td> | |
6819 | <p> | |
6820 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
6821 | 1.16:</em></span> Max = 1.02e+03ε (Mean = 105ε))<br> (<span class="emphasis"><em>Rmath | |
6822 | 3.0.2:</em></span> Max = 1.11e+03ε (Mean = 67.5ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
6823 | Max = 8.18e+06ε (Mean = 7.69e+05ε)) | |
6824 | </p> | |
6825 | </td> | |
6826 | <td> | |
6827 | <p> | |
6828 | <span class="blue">Max = 3.08e+04ε (Mean = 1.86e+03ε)</span> | |
6829 | </p> | |
6830 | </td> | |
6831 | <td> | |
6832 | <p> | |
6833 | <span class="blue">Max = 3.02e+04ε (Mean = 1.91e+03ε)</span> | |
6834 | </p> | |
6835 | </td> | |
6836 | </tr> | |
6837 | <tr> | |
6838 | <td> | |
6839 | <p> | |
6840 | tgamma(a, z) integer and half integer values | |
6841 | </p> | |
6842 | </td> | |
6843 | <td> | |
6844 | <p> | |
6845 | <span class="blue">Max = 13ε (Mean = 2.93ε)</span> | |
6846 | </p> | |
6847 | </td> | |
6848 | <td> | |
6849 | <p> | |
6850 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
6851 | 1.16:</em></span> Max = 128ε (Mean = 22.6ε))<br> (<span class="emphasis"><em>Rmath | |
6852 | 3.0.2:</em></span> Max = 66.2ε (Mean = 12.2ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
6853 | Max = 83.6ε (Mean = 22.2ε)) | |
6854 | </p> | |
6855 | </td> | |
6856 | <td> | |
6857 | <p> | |
6858 | <span class="blue">Max = 11.8ε (Mean = 2.65ε)</span> | |
6859 | </p> | |
6860 | </td> | |
6861 | <td> | |
6862 | <p> | |
6863 | <span class="blue">Max = 71.6ε (Mean = 9.47ε)</span> | |
6864 | </p> | |
6865 | </td> | |
6866 | </tr> | |
6867 | </tbody> | |
6868 | </table></div> | |
6869 | </div> | |
6870 | <br class="table-break"><div class="table"> | |
6871 | <a name="math_toolkit.logs_and_tables.all_table.table_gamma_p_inv"></a><p class="title"><b>Table 17.47. Error rates for gamma_p_inv</b></p> | |
6872 | <div class="table-contents"><table class="table" summary="Error rates for gamma_p_inv"> | |
6873 | <colgroup> | |
6874 | <col> | |
6875 | <col> | |
6876 | <col> | |
6877 | <col> | |
6878 | <col> | |
6879 | </colgroup> | |
6880 | <thead><tr> | |
6881 | <th> | |
6882 | </th> | |
6883 | <th> | |
6884 | <p> | |
6885 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
6886 | </p> | |
6887 | </th> | |
6888 | <th> | |
6889 | <p> | |
6890 | GNU C++ version 5.1.0<br> linux<br> double | |
6891 | </p> | |
6892 | </th> | |
6893 | <th> | |
6894 | <p> | |
6895 | GNU C++ version 5.1.0<br> linux<br> long double | |
6896 | </p> | |
6897 | </th> | |
6898 | <th> | |
6899 | <p> | |
6900 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
6901 | </p> | |
6902 | </th> | |
6903 | </tr></thead> | |
6904 | <tbody> | |
6905 | <tr> | |
6906 | <td> | |
6907 | <p> | |
6908 | incomplete gamma inverse(a, z) medium values | |
6909 | </p> | |
6910 | </td> | |
6911 | <td> | |
6912 | <p> | |
6913 | <span class="blue">Max = 1.01ε (Mean = 0.307ε)</span> | |
6914 | </p> | |
6915 | </td> | |
6916 | <td> | |
6917 | <p> | |
6918 | <span class="blue">Max = 0.993ε (Mean = 0.15ε)</span><br> <br> | |
6919 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 4.88ε (Mean = 0.868ε)) | |
6920 | </p> | |
6921 | </td> | |
6922 | <td> | |
6923 | <p> | |
6924 | <span class="blue">Max = 1.62ε (Mean = 0.365ε)</span> | |
6925 | </p> | |
6926 | </td> | |
6927 | <td> | |
6928 | <p> | |
6929 | <span class="blue">Max = 1.86ε (Mean = 0.405ε)</span> | |
6930 | </p> | |
6931 | </td> | |
6932 | </tr> | |
6933 | <tr> | |
6934 | <td> | |
6935 | <p> | |
6936 | incomplete gamma inverse(a, z) large values | |
6937 | </p> | |
6938 | </td> | |
6939 | <td> | |
6940 | <p> | |
6941 | <span class="blue">Max = 0.924ε (Mean = 0.118ε)</span> | |
6942 | </p> | |
6943 | </td> | |
6944 | <td> | |
6945 | <p> | |
6946 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath | |
6947 | 3.0.2:</em></span> Max = 0.816ε (Mean = 0.0874ε)) | |
6948 | </p> | |
6949 | </td> | |
6950 | <td> | |
6951 | <p> | |
6952 | <span class="blue">Max = 0.509ε (Mean = 0.0447ε)</span> | |
6953 | </p> | |
6954 | </td> | |
6955 | <td> | |
6956 | <p> | |
6957 | <span class="blue">Max = 0.509ε (Mean = 0.0447ε)</span> | |
6958 | </p> | |
6959 | </td> | |
6960 | </tr> | |
6961 | <tr> | |
6962 | <td> | |
6963 | <p> | |
6964 | incomplete gamma inverse(a, z) small values | |
6965 | </p> | |
6966 | </td> | |
6967 | <td> | |
6968 | <p> | |
6969 | <span class="blue">Max = 1.1e+003ε (Mean = 108ε)</span> | |
6970 | </p> | |
6971 | </td> | |
6972 | <td> | |
6973 | <p> | |
6974 | <span class="blue">Max = 441ε (Mean = 53.9ε)</span><br> <br> | |
6975 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 547ε (Mean = 61.6ε)) | |
6976 | </p> | |
6977 | </td> | |
6978 | <td> | |
6979 | <p> | |
6980 | <span class="blue">Max = 9.17e+03ε (Mean = 1.32e+03ε)</span> | |
6981 | </p> | |
6982 | </td> | |
6983 | <td> | |
6984 | <p> | |
6985 | <span class="blue">Max = 1.09e+04ε (Mean = 1.46e+03ε)</span> | |
6986 | </p> | |
6987 | </td> | |
6988 | </tr> | |
6989 | </tbody> | |
6990 | </table></div> | |
6991 | </div> | |
6992 | <br class="table-break"><div class="table"> | |
6993 | <a name="math_toolkit.logs_and_tables.all_table.table_gamma_p_inva"></a><p class="title"><b>Table 17.48. Error rates for gamma_p_inva</b></p> | |
6994 | <div class="table-contents"><table class="table" summary="Error rates for gamma_p_inva"> | |
6995 | <colgroup> | |
6996 | <col> | |
6997 | <col> | |
6998 | <col> | |
6999 | <col> | |
7000 | <col> | |
7001 | </colgroup> | |
7002 | <thead><tr> | |
7003 | <th> | |
7004 | </th> | |
7005 | <th> | |
7006 | <p> | |
7007 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
7008 | </p> | |
7009 | </th> | |
7010 | <th> | |
7011 | <p> | |
7012 | GNU C++ version 5.1.0<br> linux<br> double | |
7013 | </p> | |
7014 | </th> | |
7015 | <th> | |
7016 | <p> | |
7017 | GNU C++ version 5.1.0<br> linux<br> long double | |
7018 | </p> | |
7019 | </th> | |
7020 | <th> | |
7021 | <p> | |
7022 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
7023 | </p> | |
7024 | </th> | |
7025 | </tr></thead> | |
7026 | <tbody><tr> | |
7027 | <td> | |
7028 | <p> | |
7029 | Incomplete gamma inverses. | |
7030 | </p> | |
7031 | </td> | |
7032 | <td> | |
7033 | <p> | |
7034 | <span class="blue">Max = 3.52ε (Mean = 0.997ε)</span> | |
7035 | </p> | |
7036 | </td> | |
7037 | <td> | |
7038 | <p> | |
7039 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
7040 | </p> | |
7041 | </td> | |
7042 | <td> | |
7043 | <p> | |
7044 | <span class="blue">Max = 6.44ε (Mean = 1.1ε)</span> | |
7045 | </p> | |
7046 | </td> | |
7047 | <td> | |
7048 | <p> | |
7049 | <span class="blue">Max = 4.08ε (Mean = 1.12ε)</span> | |
7050 | </p> | |
7051 | </td> | |
7052 | </tr></tbody> | |
7053 | </table></div> | |
7054 | </div> | |
7055 | <br class="table-break"><div class="table"> | |
7056 | <a name="math_toolkit.logs_and_tables.all_table.table_gamma_q"></a><p class="title"><b>Table 17.49. Error rates for gamma_q</b></p> | |
7057 | <div class="table-contents"><table class="table" summary="Error rates for gamma_q"> | |
7058 | <colgroup> | |
7059 | <col> | |
7060 | <col> | |
7061 | <col> | |
7062 | <col> | |
7063 | <col> | |
7064 | </colgroup> | |
7065 | <thead><tr> | |
7066 | <th> | |
7067 | </th> | |
7068 | <th> | |
7069 | <p> | |
7070 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
7071 | </p> | |
7072 | </th> | |
7073 | <th> | |
7074 | <p> | |
7075 | GNU C++ version 5.1.0<br> linux<br> double | |
7076 | </p> | |
7077 | </th> | |
7078 | <th> | |
7079 | <p> | |
7080 | GNU C++ version 5.1.0<br> linux<br> long double | |
7081 | </p> | |
7082 | </th> | |
7083 | <th> | |
7084 | <p> | |
7085 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
7086 | </p> | |
7087 | </th> | |
7088 | </tr></thead> | |
7089 | <tbody> | |
7090 | <tr> | |
7091 | <td> | |
7092 | <p> | |
7093 | tgamma(a, z) medium values | |
7094 | </p> | |
7095 | </td> | |
7096 | <td> | |
7097 | <p> | |
7098 | <span class="blue">Max = 23.7ε (Mean = 4.03ε)</span> | |
7099 | </p> | |
7100 | </td> | |
7101 | <td> | |
7102 | <p> | |
7103 | <span class="blue">Max = 0.927ε (Mean = 0.035ε)</span><br> <br> | |
7104 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 201ε (Mean = 13.5ε))<br> (<span class="emphasis"><em>Rmath | |
7105 | 3.0.2:</em></span> Max = 131ε (Mean = 12.7ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
7106 | Max = 388ε (Mean = 93.8ε)) | |
7107 | </p> | |
7108 | </td> | |
7109 | <td> | |
7110 | <p> | |
7111 | <span class="blue">Max = 31.3ε (Mean = 6.56ε)</span> | |
7112 | </p> | |
7113 | </td> | |
7114 | <td> | |
7115 | <p> | |
7116 | <span class="blue">Max = 199ε (Mean = 26.6ε)</span> | |
7117 | </p> | |
7118 | </td> | |
7119 | </tr> | |
7120 | <tr> | |
7121 | <td> | |
7122 | <p> | |
7123 | tgamma(a, z) small values | |
7124 | </p> | |
7125 | </td> | |
7126 | <td> | |
7127 | <p> | |
7128 | <span class="blue">Max = 2.26ε (Mean = 0.732ε)</span> | |
7129 | </p> | |
7130 | </td> | |
7131 | <td> | |
7132 | <p> | |
7133 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
7134 | 1.16:</em></span> <span class="red">Max = 1.38e+10ε (Mean = 1.05e+09ε))</span><br> | |
7135 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 65.6ε (Mean = 11ε))<br> | |
7136 | (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = 3.42e+11ε (Mean | |
7137 | = 4.1e+10ε))</span> | |
7138 | </p> | |
7139 | </td> | |
7140 | <td> | |
7141 | <p> | |
7142 | <span class="blue">Max = 2.45ε (Mean = 0.832ε)</span> | |
7143 | </p> | |
7144 | </td> | |
7145 | <td> | |
7146 | <p> | |
7147 | <span class="blue">Max = 2.25ε (Mean = 0.81ε)</span> | |
7148 | </p> | |
7149 | </td> | |
7150 | </tr> | |
7151 | <tr> | |
7152 | <td> | |
7153 | <p> | |
7154 | tgamma(a, z) large values | |
7155 | </p> | |
7156 | </td> | |
7157 | <td> | |
7158 | <p> | |
7159 | <span class="blue">Max = 470ε (Mean = 31.5ε)</span> | |
7160 | </p> | |
7161 | </td> | |
7162 | <td> | |
7163 | <p> | |
7164 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
7165 | 1.16:</em></span> Max = 2.71e+04ε (Mean = 2.16e+03ε))<br> (<span class="emphasis"><em>Rmath | |
7166 | 3.0.2:</em></span> Max = 1.02e+03ε (Mean = 62.7ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
7167 | Max = 8.17e+06ε (Mean = 7.7e+05ε)) | |
7168 | </p> | |
7169 | </td> | |
7170 | <td> | |
7171 | <p> | |
7172 | <span class="blue">Max = 6.82e+03ε (Mean = 414ε)</span> | |
7173 | </p> | |
7174 | </td> | |
7175 | <td> | |
7176 | <p> | |
7177 | <span class="blue">Max = 1.15e+04ε (Mean = 733ε)</span> | |
7178 | </p> | |
7179 | </td> | |
7180 | </tr> | |
7181 | <tr> | |
7182 | <td> | |
7183 | <p> | |
7184 | tgamma(a, z) integer and half integer values | |
7185 | </p> | |
7186 | </td> | |
7187 | <td> | |
7188 | <p> | |
7189 | <span class="blue">Max = 8.48ε (Mean = 1.42ε)</span> | |
7190 | </p> | |
7191 | </td> | |
7192 | <td> | |
7193 | <p> | |
7194 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
7195 | 1.16:</em></span> Max = 118ε (Mean = 12.5ε))<br> (<span class="emphasis"><em>Rmath | |
7196 | 3.0.2:</em></span> Max = 138ε (Mean = 16.9ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
7197 | Max = 129ε (Mean = 26.5ε)) | |
7198 | </p> | |
7199 | </td> | |
7200 | <td> | |
7201 | <p> | |
7202 | <span class="blue">Max = 11.1ε (Mean = 2.09ε)</span> | |
7203 | </p> | |
7204 | </td> | |
7205 | <td> | |
7206 | <p> | |
7207 | <span class="blue">Max = 54.7ε (Mean = 6.16ε)</span> | |
7208 | </p> | |
7209 | </td> | |
7210 | </tr> | |
7211 | </tbody> | |
7212 | </table></div> | |
7213 | </div> | |
7214 | <br class="table-break"><div class="table"> | |
7215 | <a name="math_toolkit.logs_and_tables.all_table.table_gamma_q_inv"></a><p class="title"><b>Table 17.50. Error rates for gamma_q_inv</b></p> | |
7216 | <div class="table-contents"><table class="table" summary="Error rates for gamma_q_inv"> | |
7217 | <colgroup> | |
7218 | <col> | |
7219 | <col> | |
7220 | <col> | |
7221 | <col> | |
7222 | <col> | |
7223 | </colgroup> | |
7224 | <thead><tr> | |
7225 | <th> | |
7226 | </th> | |
7227 | <th> | |
7228 | <p> | |
7229 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
7230 | </p> | |
7231 | </th> | |
7232 | <th> | |
7233 | <p> | |
7234 | GNU C++ version 5.1.0<br> linux<br> double | |
7235 | </p> | |
7236 | </th> | |
7237 | <th> | |
7238 | <p> | |
7239 | GNU C++ version 5.1.0<br> linux<br> long double | |
7240 | </p> | |
7241 | </th> | |
7242 | <th> | |
7243 | <p> | |
7244 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
7245 | </p> | |
7246 | </th> | |
7247 | </tr></thead> | |
7248 | <tbody> | |
7249 | <tr> | |
7250 | <td> | |
7251 | <p> | |
7252 | incomplete gamma inverse(a, z) medium values | |
7253 | </p> | |
7254 | </td> | |
7255 | <td> | |
7256 | <p> | |
7257 | <span class="blue">Max = 3.46ε (Mean = 0.475ε)</span> | |
7258 | </p> | |
7259 | </td> | |
7260 | <td> | |
7261 | <p> | |
7262 | <span class="blue">Max = 0.912ε (Mean = 0.154ε)</span><br> <br> | |
7263 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 4.66ε (Mean = 0.792ε)) | |
7264 | </p> | |
7265 | </td> | |
7266 | <td> | |
7267 | <p> | |
7268 | <span class="blue">Max = 6.2ε (Mean = 0.659ε)</span> | |
7269 | </p> | |
7270 | </td> | |
7271 | <td> | |
7272 | <p> | |
7273 | <span class="blue">Max = 6.2ε (Mean = 0.661ε)</span> | |
7274 | </p> | |
7275 | </td> | |
7276 | </tr> | |
7277 | <tr> | |
7278 | <td> | |
7279 | <p> | |
7280 | incomplete gamma inverse(a, z) large values | |
7281 | </p> | |
7282 | </td> | |
7283 | <td> | |
7284 | <p> | |
7285 | <span class="blue">Max = 0.814ε (Mean = 0.0856ε)</span> | |
7286 | </p> | |
7287 | </td> | |
7288 | <td> | |
7289 | <p> | |
7290 | <span class="blue">Max = 0.894ε (Mean = 0.0915ε)</span><br> | |
7291 | <br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 0.894ε (Mean = 0.106ε)) | |
7292 | </p> | |
7293 | </td> | |
7294 | <td> | |
7295 | <p> | |
7296 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
7297 | </p> | |
7298 | </td> | |
7299 | <td> | |
7300 | <p> | |
7301 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
7302 | </p> | |
7303 | </td> | |
7304 | </tr> | |
7305 | <tr> | |
7306 | <td> | |
7307 | <p> | |
7308 | incomplete gamma inverse(a, z) small values | |
7309 | </p> | |
7310 | </td> | |
7311 | <td> | |
7312 | <p> | |
7313 | <span class="blue">Max = 451ε (Mean = 65ε)</span> | |
7314 | </p> | |
7315 | </td> | |
7316 | <td> | |
7317 | <p> | |
7318 | <span class="blue">Max = 292ε (Mean = 36.4ε)</span><br> <br> | |
7319 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 415ε (Mean = 48.7ε)) | |
7320 | </p> | |
7321 | </td> | |
7322 | <td> | |
7323 | <p> | |
7324 | <span class="blue">Max = 8.28e+03ε (Mean = 963ε)</span> | |
7325 | </p> | |
7326 | </td> | |
7327 | <td> | |
7328 | <p> | |
7329 | <span class="blue">Max = 8.98e+03ε (Mean = 877ε)</span> | |
7330 | </p> | |
7331 | </td> | |
7332 | </tr> | |
7333 | </tbody> | |
7334 | </table></div> | |
7335 | </div> | |
7336 | <br class="table-break"><div class="table"> | |
7337 | <a name="math_toolkit.logs_and_tables.all_table.table_gamma_q_inva"></a><p class="title"><b>Table 17.51. Error rates for gamma_q_inva</b></p> | |
7338 | <div class="table-contents"><table class="table" summary="Error rates for gamma_q_inva"> | |
7339 | <colgroup> | |
7340 | <col> | |
7341 | <col> | |
7342 | <col> | |
7343 | <col> | |
7344 | <col> | |
7345 | </colgroup> | |
7346 | <thead><tr> | |
7347 | <th> | |
7348 | </th> | |
7349 | <th> | |
7350 | <p> | |
7351 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
7352 | </p> | |
7353 | </th> | |
7354 | <th> | |
7355 | <p> | |
7356 | GNU C++ version 5.1.0<br> linux<br> double | |
7357 | </p> | |
7358 | </th> | |
7359 | <th> | |
7360 | <p> | |
7361 | GNU C++ version 5.1.0<br> linux<br> long double | |
7362 | </p> | |
7363 | </th> | |
7364 | <th> | |
7365 | <p> | |
7366 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
7367 | </p> | |
7368 | </th> | |
7369 | </tr></thead> | |
7370 | <tbody><tr> | |
7371 | <td> | |
7372 | <p> | |
7373 | Incomplete gamma inverses. | |
7374 | </p> | |
7375 | </td> | |
7376 | <td> | |
7377 | <p> | |
7378 | <span class="blue">Max = 5.64ε (Mean = 1.09ε)</span> | |
7379 | </p> | |
7380 | </td> | |
7381 | <td> | |
7382 | <p> | |
7383 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
7384 | </p> | |
7385 | </td> | |
7386 | <td> | |
7387 | <p> | |
7388 | <span class="blue">Max = 6.91ε (Mean = 1.17ε)</span> | |
7389 | </p> | |
7390 | </td> | |
7391 | <td> | |
7392 | <p> | |
7393 | <span class="blue">Max = 7.86ε (Mean = 1.25ε)</span> | |
7394 | </p> | |
7395 | </td> | |
7396 | </tr></tbody> | |
7397 | </table></div> | |
7398 | </div> | |
7399 | <br class="table-break"><div class="table"> | |
7400 | <a name="math_toolkit.logs_and_tables.all_table.table_hermite"></a><p class="title"><b>Table 17.52. Error rates for hermite</b></p> | |
7401 | <div class="table-contents"><table class="table" summary="Error rates for hermite"> | |
7402 | <colgroup> | |
7403 | <col> | |
7404 | <col> | |
7405 | <col> | |
7406 | <col> | |
7407 | <col> | |
7408 | </colgroup> | |
7409 | <thead><tr> | |
7410 | <th> | |
7411 | </th> | |
7412 | <th> | |
7413 | <p> | |
7414 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
7415 | </p> | |
7416 | </th> | |
7417 | <th> | |
7418 | <p> | |
7419 | GNU C++ version 5.1.0<br> linux<br> double | |
7420 | </p> | |
7421 | </th> | |
7422 | <th> | |
7423 | <p> | |
7424 | GNU C++ version 5.1.0<br> linux<br> long double | |
7425 | </p> | |
7426 | </th> | |
7427 | <th> | |
7428 | <p> | |
7429 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
7430 | </p> | |
7431 | </th> | |
7432 | </tr></thead> | |
7433 | <tbody><tr> | |
7434 | <td> | |
7435 | <p> | |
7436 | Hermite Polynomials | |
7437 | </p> | |
7438 | </td> | |
7439 | <td> | |
7440 | <p> | |
7441 | <span class="blue">Max = 4.46ε (Mean = 1.41ε)</span> | |
7442 | </p> | |
7443 | </td> | |
7444 | <td> | |
7445 | <p> | |
7446 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
7447 | </p> | |
7448 | </td> | |
7449 | <td> | |
7450 | <p> | |
7451 | <span class="blue">Max = 6.24ε (Mean = 2.07ε)</span> | |
7452 | </p> | |
7453 | </td> | |
7454 | <td> | |
7455 | <p> | |
7456 | <span class="blue">Max = 6.24ε (Mean = 2.07ε)</span> | |
7457 | </p> | |
7458 | </td> | |
7459 | </tr></tbody> | |
7460 | </table></div> | |
7461 | </div> | |
7462 | <br class="table-break"><div class="table"> | |
7463 | <a name="math_toolkit.logs_and_tables.all_table.table_heuman_lambda"></a><p class="title"><b>Table 17.53. Error rates for heuman_lambda</b></p> | |
7464 | <div class="table-contents"><table class="table" summary="Error rates for heuman_lambda"> | |
7465 | <colgroup> | |
7466 | <col> | |
7467 | <col> | |
7468 | <col> | |
7469 | <col> | |
7470 | <col> | |
7471 | </colgroup> | |
7472 | <thead><tr> | |
7473 | <th> | |
7474 | </th> | |
7475 | <th> | |
7476 | <p> | |
7477 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
7478 | </p> | |
7479 | </th> | |
7480 | <th> | |
7481 | <p> | |
7482 | GNU C++ version 5.1.0<br> linux<br> double | |
7483 | </p> | |
7484 | </th> | |
7485 | <th> | |
7486 | <p> | |
7487 | GNU C++ version 5.1.0<br> linux<br> long double | |
7488 | </p> | |
7489 | </th> | |
7490 | <th> | |
7491 | <p> | |
7492 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
7493 | </p> | |
7494 | </th> | |
7495 | </tr></thead> | |
7496 | <tbody> | |
7497 | <tr> | |
7498 | <td> | |
7499 | <p> | |
7500 | Elliptic Integral Jacobi Zeta: Mathworld Data | |
7501 | </p> | |
7502 | </td> | |
7503 | <td> | |
7504 | <p> | |
7505 | <span class="blue">Max = 1.08ε (Mean = 0.734ε)</span> | |
7506 | </p> | |
7507 | </td> | |
7508 | <td> | |
7509 | <p> | |
7510 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
7511 | </p> | |
7512 | </td> | |
7513 | <td> | |
7514 | <p> | |
7515 | <span class="blue">Max = 1.89ε (Mean = 0.887ε)</span> | |
7516 | </p> | |
7517 | </td> | |
7518 | <td> | |
7519 | <p> | |
7520 | <span class="blue">Max = 1.89ε (Mean = 0.887ε)</span> | |
7521 | </p> | |
7522 | </td> | |
7523 | </tr> | |
7524 | <tr> | |
7525 | <td> | |
7526 | <p> | |
7527 | Elliptic Integral Heuman Lambda: Random Data | |
7528 | </p> | |
7529 | </td> | |
7530 | <td> | |
7531 | <p> | |
7532 | <span class="blue">Max = 2.12ε (Mean = 0.59ε)</span> | |
7533 | </p> | |
7534 | </td> | |
7535 | <td> | |
7536 | <p> | |
7537 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
7538 | </p> | |
7539 | </td> | |
7540 | <td> | |
7541 | <p> | |
7542 | <span class="blue">Max = 3.82ε (Mean = 0.609ε)</span> | |
7543 | </p> | |
7544 | </td> | |
7545 | <td> | |
7546 | <p> | |
7547 | <span class="blue">Max = 3.82ε (Mean = 0.608ε)</span> | |
7548 | </p> | |
7549 | </td> | |
7550 | </tr> | |
7551 | </tbody> | |
7552 | </table></div> | |
7553 | </div> | |
7554 | <br class="table-break"><div class="table"> | |
7555 | <a name="math_toolkit.logs_and_tables.all_table.table_ibeta"></a><p class="title"><b>Table 17.54. Error rates for ibeta</b></p> | |
7556 | <div class="table-contents"><table class="table" summary="Error rates for ibeta"> | |
7557 | <colgroup> | |
7558 | <col> | |
7559 | <col> | |
7560 | <col> | |
7561 | <col> | |
7562 | <col> | |
7563 | </colgroup> | |
7564 | <thead><tr> | |
7565 | <th> | |
7566 | </th> | |
7567 | <th> | |
7568 | <p> | |
7569 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
7570 | </p> | |
7571 | </th> | |
7572 | <th> | |
7573 | <p> | |
7574 | GNU C++ version 5.1.0<br> linux<br> double | |
7575 | </p> | |
7576 | </th> | |
7577 | <th> | |
7578 | <p> | |
7579 | GNU C++ version 5.1.0<br> linux<br> long double | |
7580 | </p> | |
7581 | </th> | |
7582 | <th> | |
7583 | <p> | |
7584 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
7585 | </p> | |
7586 | </th> | |
7587 | </tr></thead> | |
7588 | <tbody> | |
7589 | <tr> | |
7590 | <td> | |
7591 | <p> | |
7592 | Incomplete Beta Function: Small Values | |
7593 | </p> | |
7594 | </td> | |
7595 | <td> | |
7596 | <p> | |
7597 | <span class="blue">Max = 9.42ε (Mean = 2.24ε)</span> | |
7598 | </p> | |
7599 | </td> | |
7600 | <td> | |
7601 | <p> | |
7602 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
7603 | 1.16:</em></span> Max = 682ε (Mean = 32.6ε))<br> (<span class="emphasis"><em>Rmath | |
7604 | 3.0.2:</em></span> Max = 22.9ε (Mean = 3.35ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
7605 | Max = 22.7ε (Mean = 1.69ε)) | |
7606 | </p> | |
7607 | </td> | |
7608 | <td> | |
7609 | <p> | |
7610 | <span class="blue">Max = 6.27ε (Mean = 1.7ε)</span> | |
7611 | </p> | |
7612 | </td> | |
7613 | <td> | |
7614 | <p> | |
7615 | <span class="blue">Max = 21.3ε (Mean = 2.74ε)</span> | |
7616 | </p> | |
7617 | </td> | |
7618 | </tr> | |
7619 | <tr> | |
7620 | <td> | |
7621 | <p> | |
7622 | Incomplete Beta Function: Medium Values | |
7623 | </p> | |
7624 | </td> | |
7625 | <td> | |
7626 | <p> | |
7627 | <span class="blue">Max = 108ε (Mean = 16.3ε)</span> | |
7628 | </p> | |
7629 | </td> | |
7630 | <td> | |
7631 | <p> | |
7632 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
7633 | 1.16:</em></span> Max = 690ε (Mean = 151ε))<br> (<span class="emphasis"><em>Rmath | |
7634 | 3.0.2:</em></span> Max = 232ε (Mean = 27.9ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
7635 | Max = 1.55e+03ε (Mean = 121ε)) | |
7636 | </p> | |
7637 | </td> | |
7638 | <td> | |
7639 | <p> | |
7640 | <span class="blue">Max = 51.4ε (Mean = 12ε)</span> | |
7641 | </p> | |
7642 | </td> | |
7643 | <td> | |
7644 | <p> | |
7645 | <span class="blue">Max = 124ε (Mean = 18.4ε)</span> | |
7646 | </p> | |
7647 | </td> | |
7648 | </tr> | |
7649 | <tr> | |
7650 | <td> | |
7651 | <p> | |
7652 | Incomplete Beta Function: Large and Diverse Values | |
7653 | </p> | |
7654 | </td> | |
7655 | <td> | |
7656 | <p> | |
7657 | <span class="blue">Max = 1.19e+003ε (Mean = 59.5ε)</span> | |
7658 | </p> | |
7659 | </td> | |
7660 | <td> | |
7661 | <p> | |
7662 | <span class="blue">Max = 1.26ε (Mean = 0.063ε)</span><br> <br> | |
7663 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 3.9e+05ε (Mean = 1.82e+04ε) | |
7664 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ibeta_GSL_1_16_Incomplete_Beta_Function_Large_and_Diverse_Values">And | |
7665 | other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> | |
7666 | Max = 574ε (Mean = 49.4ε))<br> (<span class="emphasis"><em>Cephes:</em></span> Max | |
7667 | = 5.92e+05ε (Mean = 2.17e+04ε)) | |
7668 | </p> | |
7669 | </td> | |
7670 | <td> | |
7671 | <p> | |
7672 | <span class="blue">Max = 1.96e+04ε (Mean = 997ε)</span> | |
7673 | </p> | |
7674 | </td> | |
7675 | <td> | |
7676 | <p> | |
7677 | <span class="blue">Max = 4.98e+04ε (Mean = 2.07e+03ε)</span> | |
7678 | </p> | |
7679 | </td> | |
7680 | </tr> | |
7681 | <tr> | |
7682 | <td> | |
7683 | <p> | |
7684 | Incomplete Beta Function: Small Integer Values | |
7685 | </p> | |
7686 | </td> | |
7687 | <td> | |
7688 | <p> | |
7689 | <span class="blue">Max = 3.69ε (Mean = 0.765ε)</span> | |
7690 | </p> | |
7691 | </td> | |
7692 | <td> | |
7693 | <p> | |
7694 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
7695 | 1.16:</em></span> Max = 254ε (Mean = 50.9ε))<br> (<span class="emphasis"><em>Rmath | |
7696 | 3.0.2:</em></span> Max = 62.2ε (Mean = 8.95ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
7697 | Max = 7.96ε (Mean = 1.3ε)) | |
7698 | </p> | |
7699 | </td> | |
7700 | <td> | |
7701 | <p> | |
7702 | <span class="blue">Max = 4.45ε (Mean = 0.814ε)</span> | |
7703 | </p> | |
7704 | </td> | |
7705 | <td> | |
7706 | <p> | |
7707 | <span class="blue">Max = 44.5ε (Mean = 10.1ε)</span> | |
7708 | </p> | |
7709 | </td> | |
7710 | </tr> | |
7711 | </tbody> | |
7712 | </table></div> | |
7713 | </div> | |
7714 | <br class="table-break"><div class="table"> | |
7715 | <a name="math_toolkit.logs_and_tables.all_table.table_ibeta_inv"></a><p class="title"><b>Table 17.55. Error rates for ibeta_inv</b></p> | |
7716 | <div class="table-contents"><table class="table" summary="Error rates for ibeta_inv"> | |
7717 | <colgroup> | |
7718 | <col> | |
7719 | <col> | |
7720 | <col> | |
7721 | <col> | |
7722 | <col> | |
7723 | </colgroup> | |
7724 | <thead><tr> | |
7725 | <th> | |
7726 | </th> | |
7727 | <th> | |
7728 | <p> | |
7729 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
7730 | </p> | |
7731 | </th> | |
7732 | <th> | |
7733 | <p> | |
7734 | GNU C++ version 5.1.0<br> linux<br> double | |
7735 | </p> | |
7736 | </th> | |
7737 | <th> | |
7738 | <p> | |
7739 | GNU C++ version 5.1.0<br> linux<br> long double | |
7740 | </p> | |
7741 | </th> | |
7742 | <th> | |
7743 | <p> | |
7744 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
7745 | </p> | |
7746 | </th> | |
7747 | </tr></thead> | |
7748 | <tbody><tr> | |
7749 | <td> | |
7750 | <p> | |
7751 | Inverse incomplete beta | |
7752 | </p> | |
7753 | </td> | |
7754 | <td> | |
7755 | <p> | |
7756 | <span class="blue">Max = 7.08e+003ε (Mean = 244ε)</span> | |
7757 | </p> | |
7758 | </td> | |
7759 | <td> | |
7760 | <p> | |
7761 | <span class="blue">Max = 3.21ε (Mean = 0.158ε)</span><br> <br> | |
7762 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = +INFε (Mean | |
7763 | = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ibeta_inv_Rmath_3_0_2_Inverse_incomplete_beta">And | |
7764 | other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span> | |
7765 | <span class="red">Max = 1.28e+10ε (Mean = 5.17e+08ε))</span> | |
7766 | </p> | |
7767 | </td> | |
7768 | <td> | |
7769 | <p> | |
7770 | <span class="blue">Max = 4.53e+04ε (Mean = 2.93e+03ε)</span> | |
7771 | </p> | |
7772 | </td> | |
7773 | <td> | |
7774 | <p> | |
7775 | <span class="blue">Max = 4.22e+04ε (Mean = 2.8e+03ε)</span> | |
7776 | </p> | |
7777 | </td> | |
7778 | </tr></tbody> | |
7779 | </table></div> | |
7780 | </div> | |
7781 | <br class="table-break"><div class="table"> | |
7782 | <a name="math_toolkit.logs_and_tables.all_table.table_ibeta_inva"></a><p class="title"><b>Table 17.56. Error rates for ibeta_inva</b></p> | |
7783 | <div class="table-contents"><table class="table" summary="Error rates for ibeta_inva"> | |
7784 | <colgroup> | |
7785 | <col> | |
7786 | <col> | |
7787 | <col> | |
7788 | <col> | |
7789 | <col> | |
7790 | </colgroup> | |
7791 | <thead><tr> | |
7792 | <th> | |
7793 | </th> | |
7794 | <th> | |
7795 | <p> | |
7796 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
7797 | </p> | |
7798 | </th> | |
7799 | <th> | |
7800 | <p> | |
7801 | GNU C++ version 5.1.0<br> linux<br> double | |
7802 | </p> | |
7803 | </th> | |
7804 | <th> | |
7805 | <p> | |
7806 | GNU C++ version 5.1.0<br> linux<br> long double | |
7807 | </p> | |
7808 | </th> | |
7809 | <th> | |
7810 | <p> | |
7811 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
7812 | </p> | |
7813 | </th> | |
7814 | </tr></thead> | |
7815 | <tbody><tr> | |
7816 | <td> | |
7817 | <p> | |
7818 | Inverse incomplete beta | |
7819 | </p> | |
7820 | </td> | |
7821 | <td> | |
7822 | <p> | |
7823 | <span class="blue">Max = 395ε (Mean = 24.7ε)</span> | |
7824 | </p> | |
7825 | </td> | |
7826 | <td> | |
7827 | <p> | |
7828 | <span class="blue">Max = 0.602ε (Mean = 0.0239ε)</span> | |
7829 | </p> | |
7830 | </td> | |
7831 | <td> | |
7832 | <p> | |
7833 | <span class="blue">Max = 377ε (Mean = 25.1ε)</span> | |
7834 | </p> | |
7835 | </td> | |
7836 | <td> | |
7837 | <p> | |
7838 | <span class="blue">Max = 438ε (Mean = 31.6ε)</span> | |
7839 | </p> | |
7840 | </td> | |
7841 | </tr></tbody> | |
7842 | </table></div> | |
7843 | </div> | |
7844 | <br class="table-break"><div class="table"> | |
7845 | <a name="math_toolkit.logs_and_tables.all_table.table_ibeta_invb"></a><p class="title"><b>Table 17.57. Error rates for ibeta_invb</b></p> | |
7846 | <div class="table-contents"><table class="table" summary="Error rates for ibeta_invb"> | |
7847 | <colgroup> | |
7848 | <col> | |
7849 | <col> | |
7850 | <col> | |
7851 | <col> | |
7852 | <col> | |
7853 | </colgroup> | |
7854 | <thead><tr> | |
7855 | <th> | |
7856 | </th> | |
7857 | <th> | |
7858 | <p> | |
7859 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
7860 | </p> | |
7861 | </th> | |
7862 | <th> | |
7863 | <p> | |
7864 | GNU C++ version 5.1.0<br> linux<br> double | |
7865 | </p> | |
7866 | </th> | |
7867 | <th> | |
7868 | <p> | |
7869 | GNU C++ version 5.1.0<br> linux<br> long double | |
7870 | </p> | |
7871 | </th> | |
7872 | <th> | |
7873 | <p> | |
7874 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
7875 | </p> | |
7876 | </th> | |
7877 | </tr></thead> | |
7878 | <tbody><tr> | |
7879 | <td> | |
7880 | <p> | |
7881 | Inverse incomplete beta | |
7882 | </p> | |
7883 | </td> | |
7884 | <td> | |
7885 | <p> | |
7886 | <span class="blue">Max = 409ε (Mean = 17.9ε)</span> | |
7887 | </p> | |
7888 | </td> | |
7889 | <td> | |
7890 | <p> | |
7891 | <span class="blue">Max = 0.836ε (Mean = 0.0491ε)</span> | |
7892 | </p> | |
7893 | </td> | |
7894 | <td> | |
7895 | <p> | |
7896 | <span class="blue">Max = 407ε (Mean = 27.2ε)</span> | |
7897 | </p> | |
7898 | </td> | |
7899 | <td> | |
7900 | <p> | |
7901 | <span class="blue">Max = 407ε (Mean = 24.4ε)</span> | |
7902 | </p> | |
7903 | </td> | |
7904 | </tr></tbody> | |
7905 | </table></div> | |
7906 | </div> | |
7907 | <br class="table-break"><div class="table"> | |
7908 | <a name="math_toolkit.logs_and_tables.all_table.table_ibetac"></a><p class="title"><b>Table 17.58. Error rates for ibetac</b></p> | |
7909 | <div class="table-contents"><table class="table" summary="Error rates for ibetac"> | |
7910 | <colgroup> | |
7911 | <col> | |
7912 | <col> | |
7913 | <col> | |
7914 | <col> | |
7915 | <col> | |
7916 | </colgroup> | |
7917 | <thead><tr> | |
7918 | <th> | |
7919 | </th> | |
7920 | <th> | |
7921 | <p> | |
7922 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
7923 | </p> | |
7924 | </th> | |
7925 | <th> | |
7926 | <p> | |
7927 | GNU C++ version 5.1.0<br> linux<br> double | |
7928 | </p> | |
7929 | </th> | |
7930 | <th> | |
7931 | <p> | |
7932 | GNU C++ version 5.1.0<br> linux<br> long double | |
7933 | </p> | |
7934 | </th> | |
7935 | <th> | |
7936 | <p> | |
7937 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
7938 | </p> | |
7939 | </th> | |
7940 | </tr></thead> | |
7941 | <tbody> | |
7942 | <tr> | |
7943 | <td> | |
7944 | <p> | |
7945 | Incomplete Beta Function: Small Values | |
7946 | </p> | |
7947 | </td> | |
7948 | <td> | |
7949 | <p> | |
7950 | <span class="blue">Max = 6.56ε (Mean = 1.88ε)</span> | |
7951 | </p> | |
7952 | </td> | |
7953 | <td> | |
7954 | <p> | |
7955 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath | |
7956 | 3.0.2:</em></span> Max = 22.4ε (Mean = 3.67ε)) | |
7957 | </p> | |
7958 | </td> | |
7959 | <td> | |
7960 | <p> | |
7961 | <span class="blue">Max = 8.47ε (Mean = 1.68ε)</span> | |
7962 | </p> | |
7963 | </td> | |
7964 | <td> | |
7965 | <p> | |
7966 | <span class="blue">Max = 13.8ε (Mean = 2.69ε)</span> | |
7967 | </p> | |
7968 | </td> | |
7969 | </tr> | |
7970 | <tr> | |
7971 | <td> | |
7972 | <p> | |
7973 | Incomplete Beta Function: Medium Values | |
7974 | </p> | |
7975 | </td> | |
7976 | <td> | |
7977 | <p> | |
7978 | <span class="blue">Max = 56.2ε (Mean = 14.1ε)</span> | |
7979 | </p> | |
7980 | </td> | |
7981 | <td> | |
7982 | <p> | |
7983 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath | |
7984 | 3.0.2:</em></span> Max = 204ε (Mean = 25.8ε)) | |
7985 | </p> | |
7986 | </td> | |
7987 | <td> | |
7988 | <p> | |
7989 | <span class="blue">Max = 75.3ε (Mean = 11.3ε)</span> | |
7990 | </p> | |
7991 | </td> | |
7992 | <td> | |
7993 | <p> | |
7994 | <span class="blue">Max = 132ε (Mean = 19.8ε)</span> | |
7995 | </p> | |
7996 | </td> | |
7997 | </tr> | |
7998 | <tr> | |
7999 | <td> | |
8000 | <p> | |
8001 | Incomplete Beta Function: Large and Diverse Values | |
8002 | </p> | |
8003 | </td> | |
8004 | <td> | |
8005 | <p> | |
8006 | <span class="blue">Max = 1.87e+003ε (Mean = 93.8ε)</span> | |
8007 | </p> | |
8008 | </td> | |
8009 | <td> | |
8010 | <p> | |
8011 | <span class="blue">Max = 0.981ε (Mean = 0.0638ε)</span><br> | |
8012 | <br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 889ε (Mean = 68.4ε)) | |
8013 | </p> | |
8014 | </td> | |
8015 | <td> | |
8016 | <p> | |
8017 | <span class="blue">Max = 3.45e+04ε (Mean = 1.32e+03ε)</span> | |
8018 | </p> | |
8019 | </td> | |
8020 | <td> | |
8021 | <p> | |
8022 | <span class="blue">Max = 4.26e+04ε (Mean = 1.54e+03ε)</span> | |
8023 | </p> | |
8024 | </td> | |
8025 | </tr> | |
8026 | <tr> | |
8027 | <td> | |
8028 | <p> | |
8029 | Incomplete Beta Function: Small Integer Values | |
8030 | </p> | |
8031 | </td> | |
8032 | <td> | |
8033 | <p> | |
8034 | <span class="blue">Max = 6.37ε (Mean = 1.03ε)</span> | |
8035 | </p> | |
8036 | </td> | |
8037 | <td> | |
8038 | <p> | |
8039 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath | |
8040 | 3.0.2:</em></span> Max = 84.6ε (Mean = 18ε)) | |
8041 | </p> | |
8042 | </td> | |
8043 | <td> | |
8044 | <p> | |
8045 | <span class="blue">Max = 5.34ε (Mean = 1.11ε)</span> | |
8046 | </p> | |
8047 | </td> | |
8048 | <td> | |
8049 | <p> | |
8050 | <span class="blue">Max = 107ε (Mean = 17.1ε)</span> | |
8051 | </p> | |
8052 | </td> | |
8053 | </tr> | |
8054 | </tbody> | |
8055 | </table></div> | |
8056 | </div> | |
8057 | <br class="table-break"><div class="table"> | |
8058 | <a name="math_toolkit.logs_and_tables.all_table.table_ibetac_inv"></a><p class="title"><b>Table 17.59. Error rates for ibetac_inv</b></p> | |
8059 | <div class="table-contents"><table class="table" summary="Error rates for ibetac_inv"> | |
8060 | <colgroup> | |
8061 | <col> | |
8062 | <col> | |
8063 | <col> | |
8064 | <col> | |
8065 | <col> | |
8066 | </colgroup> | |
8067 | <thead><tr> | |
8068 | <th> | |
8069 | </th> | |
8070 | <th> | |
8071 | <p> | |
8072 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
8073 | </p> | |
8074 | </th> | |
8075 | <th> | |
8076 | <p> | |
8077 | GNU C++ version 5.1.0<br> linux<br> double | |
8078 | </p> | |
8079 | </th> | |
8080 | <th> | |
8081 | <p> | |
8082 | GNU C++ version 5.1.0<br> linux<br> long double | |
8083 | </p> | |
8084 | </th> | |
8085 | <th> | |
8086 | <p> | |
8087 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
8088 | </p> | |
8089 | </th> | |
8090 | </tr></thead> | |
8091 | <tbody><tr> | |
8092 | <td> | |
8093 | <p> | |
8094 | Inverse incomplete beta | |
8095 | </p> | |
8096 | </td> | |
8097 | <td> | |
8098 | <p> | |
8099 | <span class="blue">Max = 5.53e+003ε (Mean = 220ε)</span> | |
8100 | </p> | |
8101 | </td> | |
8102 | <td> | |
8103 | <p> | |
8104 | <span class="blue">Max = 1.71ε (Mean = 0.108ε)</span><br> <br> | |
8105 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = +INFε (Mean | |
8106 | = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ibetac_inv_Rmath_3_0_2_Inverse_incomplete_beta">And | |
8107 | other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span> | |
8108 | Max = 1.71ε (Mean = 0.108ε)) | |
8109 | </p> | |
8110 | </td> | |
8111 | <td> | |
8112 | <p> | |
8113 | <span class="blue">Max = 6.17e+04ε (Mean = 3.77e+03ε)</span> | |
8114 | </p> | |
8115 | </td> | |
8116 | <td> | |
8117 | <p> | |
8118 | <span class="blue">Max = 5.15e+04ε (Mean = 3.51e+03ε)</span> | |
8119 | </p> | |
8120 | </td> | |
8121 | </tr></tbody> | |
8122 | </table></div> | |
8123 | </div> | |
8124 | <br class="table-break"><div class="table"> | |
8125 | <a name="math_toolkit.logs_and_tables.all_table.table_ibetac_inva"></a><p class="title"><b>Table 17.60. Error rates for ibetac_inva</b></p> | |
8126 | <div class="table-contents"><table class="table" summary="Error rates for ibetac_inva"> | |
8127 | <colgroup> | |
8128 | <col> | |
8129 | <col> | |
8130 | <col> | |
8131 | <col> | |
8132 | <col> | |
8133 | </colgroup> | |
8134 | <thead><tr> | |
8135 | <th> | |
8136 | </th> | |
8137 | <th> | |
8138 | <p> | |
8139 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
8140 | </p> | |
8141 | </th> | |
8142 | <th> | |
8143 | <p> | |
8144 | GNU C++ version 5.1.0<br> linux<br> double | |
8145 | </p> | |
8146 | </th> | |
8147 | <th> | |
8148 | <p> | |
8149 | GNU C++ version 5.1.0<br> linux<br> long double | |
8150 | </p> | |
8151 | </th> | |
8152 | <th> | |
8153 | <p> | |
8154 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
8155 | </p> | |
8156 | </th> | |
8157 | </tr></thead> | |
8158 | <tbody><tr> | |
8159 | <td> | |
8160 | <p> | |
8161 | Inverse incomplete beta | |
8162 | </p> | |
8163 | </td> | |
8164 | <td> | |
8165 | <p> | |
8166 | <span class="blue">Max = 408ε (Mean = 27.8ε)</span> | |
8167 | </p> | |
8168 | </td> | |
8169 | <td> | |
8170 | <p> | |
8171 | <span class="blue">Max = 0.683ε (Mean = 0.0271ε)</span> | |
8172 | </p> | |
8173 | </td> | |
8174 | <td> | |
8175 | <p> | |
8176 | <span class="blue">Max = 382ε (Mean = 22.2ε)</span> | |
8177 | </p> | |
8178 | </td> | |
8179 | <td> | |
8180 | <p> | |
8181 | <span class="blue">Max = 315ε (Mean = 23.7ε)</span> | |
8182 | </p> | |
8183 | </td> | |
8184 | </tr></tbody> | |
8185 | </table></div> | |
8186 | </div> | |
8187 | <br class="table-break"><div class="table"> | |
8188 | <a name="math_toolkit.logs_and_tables.all_table.table_ibetac_invb"></a><p class="title"><b>Table 17.61. Error rates for ibetac_invb</b></p> | |
8189 | <div class="table-contents"><table class="table" summary="Error rates for ibetac_invb"> | |
8190 | <colgroup> | |
8191 | <col> | |
8192 | <col> | |
8193 | <col> | |
8194 | <col> | |
8195 | <col> | |
8196 | </colgroup> | |
8197 | <thead><tr> | |
8198 | <th> | |
8199 | </th> | |
8200 | <th> | |
8201 | <p> | |
8202 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
8203 | </p> | |
8204 | </th> | |
8205 | <th> | |
8206 | <p> | |
8207 | GNU C++ version 5.1.0<br> linux<br> double | |
8208 | </p> | |
8209 | </th> | |
8210 | <th> | |
8211 | <p> | |
8212 | GNU C++ version 5.1.0<br> linux<br> long double | |
8213 | </p> | |
8214 | </th> | |
8215 | <th> | |
8216 | <p> | |
8217 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
8218 | </p> | |
8219 | </th> | |
8220 | </tr></thead> | |
8221 | <tbody><tr> | |
8222 | <td> | |
8223 | <p> | |
8224 | Inverse incomplete beta | |
8225 | </p> | |
8226 | </td> | |
8227 | <td> | |
8228 | <p> | |
8229 | <span class="blue">Max = 329ε (Mean = 18.2ε)</span> | |
8230 | </p> | |
8231 | </td> | |
8232 | <td> | |
8233 | <p> | |
8234 | <span class="blue">Max = 0.724ε (Mean = 0.0303ε)</span> | |
8235 | </p> | |
8236 | </td> | |
8237 | <td> | |
8238 | <p> | |
8239 | <span class="blue">Max = 317ε (Mean = 19.7ε)</span> | |
8240 | </p> | |
8241 | </td> | |
8242 | <td> | |
8243 | <p> | |
8244 | <span class="blue">Max = 369ε (Mean = 21.7ε)</span> | |
8245 | </p> | |
8246 | </td> | |
8247 | </tr></tbody> | |
8248 | </table></div> | |
8249 | </div> | |
8250 | <br class="table-break"><div class="table"> | |
8251 | <a name="math_toolkit.logs_and_tables.all_table.table_jacobi_cn"></a><p class="title"><b>Table 17.62. Error rates for jacobi_cn</b></p> | |
8252 | <div class="table-contents"><table class="table" summary="Error rates for jacobi_cn"> | |
8253 | <colgroup> | |
8254 | <col> | |
8255 | <col> | |
8256 | <col> | |
8257 | <col> | |
8258 | <col> | |
8259 | </colgroup> | |
8260 | <thead><tr> | |
8261 | <th> | |
8262 | </th> | |
8263 | <th> | |
8264 | <p> | |
8265 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
8266 | </p> | |
8267 | </th> | |
8268 | <th> | |
8269 | <p> | |
8270 | GNU C++ version 5.1.0<br> linux<br> double | |
8271 | </p> | |
8272 | </th> | |
8273 | <th> | |
8274 | <p> | |
8275 | GNU C++ version 5.1.0<br> linux<br> long double | |
8276 | </p> | |
8277 | </th> | |
8278 | <th> | |
8279 | <p> | |
8280 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
8281 | </p> | |
8282 | </th> | |
8283 | </tr></thead> | |
8284 | <tbody> | |
8285 | <tr> | |
8286 | <td> | |
8287 | <p> | |
8288 | Jacobi Elliptic: Mathworld Data | |
8289 | </p> | |
8290 | </td> | |
8291 | <td> | |
8292 | <p> | |
8293 | <span class="blue">Max = 45.8ε (Mean = 11.4ε)</span> | |
8294 | </p> | |
8295 | </td> | |
8296 | <td> | |
8297 | <p> | |
8298 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
8299 | 1.16:</em></span> Max = 17.3ε (Mean = 4.29ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_GSL_1_16_Jacobi_Elliptic_Mathworld_Data">And | |
8300 | other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_Cephes_Jacobi_Elliptic_Mathworld_Data">And | |
8301 | other failures.</a>)</span> | |
8302 | </p> | |
8303 | </td> | |
8304 | <td> | |
8305 | <p> | |
8306 | <span class="blue">Max = 71.6ε (Mean = 19.3ε)</span> | |
8307 | </p> | |
8308 | </td> | |
8309 | <td> | |
8310 | <p> | |
8311 | <span class="blue">Max = 71.6ε (Mean = 19.4ε)</span> | |
8312 | </p> | |
8313 | </td> | |
8314 | </tr> | |
8315 | <tr> | |
8316 | <td> | |
8317 | <p> | |
8318 | Jacobi Elliptic: Random Data | |
8319 | </p> | |
8320 | </td> | |
8321 | <td> | |
8322 | <p> | |
8323 | <span class="blue">Max = 1.83ε (Mean = 0.455ε)</span> | |
8324 | </p> | |
8325 | </td> | |
8326 | <td> | |
8327 | <p> | |
8328 | <span class="blue">Max = 0.816ε (Mean = 0.0563ε)</span><br> | |
8329 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.43ε (Mean = 0.803ε))<br> | |
8330 | (<span class="emphasis"><em>Cephes:</em></span> Max = 1.83ε (Mean = 0.437ε)) | |
8331 | </p> | |
8332 | </td> | |
8333 | <td> | |
8334 | <p> | |
8335 | <span class="blue">Max = 1.68ε (Mean = 0.443ε)</span> | |
8336 | </p> | |
8337 | </td> | |
8338 | <td> | |
8339 | <p> | |
8340 | <span class="blue">Max = 1.68ε (Mean = 0.454ε)</span> | |
8341 | </p> | |
8342 | </td> | |
8343 | </tr> | |
8344 | <tr> | |
8345 | <td> | |
8346 | <p> | |
8347 | Jacobi Elliptic: Random Small Values | |
8348 | </p> | |
8349 | </td> | |
8350 | <td> | |
8351 | <p> | |
8352 | <span class="blue">Max = 26.2ε (Mean = 1.17ε)</span> | |
8353 | </p> | |
8354 | </td> | |
8355 | <td> | |
8356 | <p> | |
8357 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
8358 | 1.16:</em></span> Max = 55.2ε (Mean = 1.64ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_GSL_1_16_Jacobi_Elliptic_Random_Small_Values">And | |
8359 | other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_Cephes_Jacobi_Elliptic_Random_Small_Values">And | |
8360 | other failures.</a>)</span> | |
8361 | </p> | |
8362 | </td> | |
8363 | <td> | |
8364 | <p> | |
8365 | <span class="blue">Max = 10.4ε (Mean = 0.594ε)</span> | |
8366 | </p> | |
8367 | </td> | |
8368 | <td> | |
8369 | <p> | |
8370 | <span class="blue">Max = 10.4ε (Mean = 0.602ε)</span> | |
8371 | </p> | |
8372 | </td> | |
8373 | </tr> | |
8374 | <tr> | |
8375 | <td> | |
8376 | <p> | |
8377 | Jacobi Elliptic: Modulus near 1 | |
8378 | </p> | |
8379 | </td> | |
8380 | <td> | |
8381 | <p> | |
8382 | <span class="blue">Max = 513ε (Mean = 126ε)</span> | |
8383 | </p> | |
8384 | </td> | |
8385 | <td> | |
8386 | <p> | |
8387 | <span class="blue">Max = 0.919ε (Mean = 0.127ε)</span><br> <br> | |
8388 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_GSL_1_16_Jacobi_Elliptic_Modulus_near_1">And | |
8389 | other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_Cephes_Jacobi_Elliptic_Modulus_near_1">And | |
8390 | other failures.</a>)</span> | |
8391 | </p> | |
8392 | </td> | |
8393 | <td> | |
8394 | <p> | |
8395 | <span class="blue">Max = 675ε (Mean = 87.1ε)</span> | |
8396 | </p> | |
8397 | </td> | |
8398 | <td> | |
8399 | <p> | |
8400 | <span class="blue">Max = 675ε (Mean = 86.8ε)</span> | |
8401 | </p> | |
8402 | </td> | |
8403 | </tr> | |
8404 | <tr> | |
8405 | <td> | |
8406 | <p> | |
8407 | Jacobi Elliptic: Large Phi | |
8408 | </p> | |
8409 | </td> | |
8410 | <td> | |
8411 | <p> | |
8412 | <span class="blue">Max = 3.27e+004ε (Mean = 1.93e+003ε)</span> | |
8413 | </p> | |
8414 | </td> | |
8415 | <td> | |
8416 | <p> | |
8417 | <span class="blue">Max = 14.2ε (Mean = 0.927ε)</span><br> <br> | |
8418 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 5.92e+03ε (Mean = 477ε))<br> | |
8419 | (<span class="emphasis"><em>Cephes:</em></span> Max = 3.27e+04ε (Mean = 1.93e+03ε)) | |
8420 | </p> | |
8421 | </td> | |
8422 | <td> | |
8423 | <p> | |
8424 | <span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</span> | |
8425 | </p> | |
8426 | </td> | |
8427 | <td> | |
8428 | <p> | |
8429 | <span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</span> | |
8430 | </p> | |
8431 | </td> | |
8432 | </tr> | |
8433 | </tbody> | |
8434 | </table></div> | |
8435 | </div> | |
8436 | <br class="table-break"><div class="table"> | |
8437 | <a name="math_toolkit.logs_and_tables.all_table.table_jacobi_dn"></a><p class="title"><b>Table 17.63. Error rates for jacobi_dn</b></p> | |
8438 | <div class="table-contents"><table class="table" summary="Error rates for jacobi_dn"> | |
8439 | <colgroup> | |
8440 | <col> | |
8441 | <col> | |
8442 | <col> | |
8443 | <col> | |
8444 | <col> | |
8445 | </colgroup> | |
8446 | <thead><tr> | |
8447 | <th> | |
8448 | </th> | |
8449 | <th> | |
8450 | <p> | |
8451 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
8452 | </p> | |
8453 | </th> | |
8454 | <th> | |
8455 | <p> | |
8456 | GNU C++ version 5.1.0<br> linux<br> double | |
8457 | </p> | |
8458 | </th> | |
8459 | <th> | |
8460 | <p> | |
8461 | GNU C++ version 5.1.0<br> linux<br> long double | |
8462 | </p> | |
8463 | </th> | |
8464 | <th> | |
8465 | <p> | |
8466 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
8467 | </p> | |
8468 | </th> | |
8469 | </tr></thead> | |
8470 | <tbody> | |
8471 | <tr> | |
8472 | <td> | |
8473 | <p> | |
8474 | Jacobi Elliptic: Mathworld Data | |
8475 | </p> | |
8476 | </td> | |
8477 | <td> | |
8478 | <p> | |
8479 | <span class="blue">Max = 34.3ε (Mean = 8.71ε)</span> | |
8480 | </p> | |
8481 | </td> | |
8482 | <td> | |
8483 | <p> | |
8484 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
8485 | 1.16:</em></span> Max = 2.82ε (Mean = 1.18ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_GSL_1_16_Jacobi_Elliptic_Mathworld_Data">And | |
8486 | other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_Cephes_Jacobi_Elliptic_Mathworld_Data">And | |
8487 | other failures.</a>)</span> | |
8488 | </p> | |
8489 | </td> | |
8490 | <td> | |
8491 | <p> | |
8492 | <span class="blue">Max = 49ε (Mean = 14ε)</span> | |
8493 | </p> | |
8494 | </td> | |
8495 | <td> | |
8496 | <p> | |
8497 | <span class="blue">Max = 49ε (Mean = 14ε)</span> | |
8498 | </p> | |
8499 | </td> | |
8500 | </tr> | |
8501 | <tr> | |
8502 | <td> | |
8503 | <p> | |
8504 | Jacobi Elliptic: Random Data | |
8505 | </p> | |
8506 | </td> | |
8507 | <td> | |
8508 | <p> | |
8509 | <span class="blue">Max = 1.52ε (Mean = 0.466ε)</span> | |
8510 | </p> | |
8511 | </td> | |
8512 | <td> | |
8513 | <p> | |
8514 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
8515 | 1.16:</em></span> Max = 3ε (Mean = 0.61ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
8516 | Max = 1.49ε (Mean = 0.321ε)) | |
8517 | </p> | |
8518 | </td> | |
8519 | <td> | |
8520 | <p> | |
8521 | <span class="blue">Max = 1.53ε (Mean = 0.473ε)</span> | |
8522 | </p> | |
8523 | </td> | |
8524 | <td> | |
8525 | <p> | |
8526 | <span class="blue">Max = 1.53ε (Mean = 0.481ε)</span> | |
8527 | </p> | |
8528 | </td> | |
8529 | </tr> | |
8530 | <tr> | |
8531 | <td> | |
8532 | <p> | |
8533 | Jacobi Elliptic: Random Small Values | |
8534 | </p> | |
8535 | </td> | |
8536 | <td> | |
8537 | <p> | |
8538 | <span class="blue">Max = 16.1ε (Mean = 0.685ε)</span> | |
8539 | </p> | |
8540 | </td> | |
8541 | <td> | |
8542 | <p> | |
8543 | <span class="blue">Max = 0.5ε (Mean = 0.0122ε)</span><br> <br> | |
8544 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.5ε (Mean = 0.391ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_GSL_1_16_Jacobi_Elliptic_Random_Small_Values">And | |
8545 | other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_Cephes_Jacobi_Elliptic_Random_Small_Values">And | |
8546 | other failures.</a>)</span> | |
8547 | </p> | |
8548 | </td> | |
8549 | <td> | |
8550 | <p> | |
8551 | <span class="blue">Max = 22.4ε (Mean = 0.777ε)</span> | |
8552 | </p> | |
8553 | </td> | |
8554 | <td> | |
8555 | <p> | |
8556 | <span class="blue">Max = 22.4ε (Mean = 0.763ε)</span> | |
8557 | </p> | |
8558 | </td> | |
8559 | </tr> | |
8560 | <tr> | |
8561 | <td> | |
8562 | <p> | |
8563 | Jacobi Elliptic: Modulus near 1 | |
8564 | </p> | |
8565 | </td> | |
8566 | <td> | |
8567 | <p> | |
8568 | <span class="blue">Max = 6.24e+003ε (Mean = 482ε)</span> | |
8569 | </p> | |
8570 | </td> | |
8571 | <td> | |
8572 | <p> | |
8573 | <span class="blue">Max = 2.28ε (Mean = 0.194ε)</span><br> <br> | |
8574 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_GSL_1_16_Jacobi_Elliptic_Modulus_near_1">And | |
8575 | other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_Cephes_Jacobi_Elliptic_Modulus_near_1">And | |
8576 | other failures.</a>)</span> | |
8577 | </p> | |
8578 | </td> | |
8579 | <td> | |
8580 | <p> | |
8581 | <span class="blue">Max = 3.75e+03ε (Mean = 293ε)</span> | |
8582 | </p> | |
8583 | </td> | |
8584 | <td> | |
8585 | <p> | |
8586 | <span class="blue">Max = 3.75e+03ε (Mean = 293ε)</span> | |
8587 | </p> | |
8588 | </td> | |
8589 | </tr> | |
8590 | <tr> | |
8591 | <td> | |
8592 | <p> | |
8593 | Jacobi Elliptic: Large Phi | |
8594 | </p> | |
8595 | </td> | |
8596 | <td> | |
8597 | <p> | |
8598 | <span class="blue">Max = 1.67e+004ε (Mean = 1e+003ε)</span> | |
8599 | </p> | |
8600 | </td> | |
8601 | <td> | |
8602 | <p> | |
8603 | <span class="blue">Max = 14.1ε (Mean = 0.897ε)</span><br> <br> | |
8604 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 121ε (Mean = 22ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
8605 | Max = 196ε (Mean = 30.2ε)) | |
8606 | </p> | |
8607 | </td> | |
8608 | <td> | |
8609 | <p> | |
8610 | <span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</span> | |
8611 | </p> | |
8612 | </td> | |
8613 | <td> | |
8614 | <p> | |
8615 | <span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</span> | |
8616 | </p> | |
8617 | </td> | |
8618 | </tr> | |
8619 | </tbody> | |
8620 | </table></div> | |
8621 | </div> | |
8622 | <br class="table-break"><div class="table"> | |
8623 | <a name="math_toolkit.logs_and_tables.all_table.table_jacobi_sn"></a><p class="title"><b>Table 17.64. Error rates for jacobi_sn</b></p> | |
8624 | <div class="table-contents"><table class="table" summary="Error rates for jacobi_sn"> | |
8625 | <colgroup> | |
8626 | <col> | |
8627 | <col> | |
8628 | <col> | |
8629 | <col> | |
8630 | <col> | |
8631 | </colgroup> | |
8632 | <thead><tr> | |
8633 | <th> | |
8634 | </th> | |
8635 | <th> | |
8636 | <p> | |
8637 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
8638 | </p> | |
8639 | </th> | |
8640 | <th> | |
8641 | <p> | |
8642 | GNU C++ version 5.1.0<br> linux<br> double | |
8643 | </p> | |
8644 | </th> | |
8645 | <th> | |
8646 | <p> | |
8647 | GNU C++ version 5.1.0<br> linux<br> long double | |
8648 | </p> | |
8649 | </th> | |
8650 | <th> | |
8651 | <p> | |
8652 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
8653 | </p> | |
8654 | </th> | |
8655 | </tr></thead> | |
8656 | <tbody> | |
8657 | <tr> | |
8658 | <td> | |
8659 | <p> | |
8660 | Jacobi Elliptic: Mathworld Data | |
8661 | </p> | |
8662 | </td> | |
8663 | <td> | |
8664 | <p> | |
8665 | <span class="blue">Max = 481ε (Mean = 113ε)</span> | |
8666 | </p> | |
8667 | </td> | |
8668 | <td> | |
8669 | <p> | |
8670 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
8671 | 1.16:</em></span> Max = 588ε (Mean = 146ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_GSL_1_16_Jacobi_Elliptic_Mathworld_Data">And | |
8672 | other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_Cephes_Jacobi_Elliptic_Mathworld_Data">And | |
8673 | other failures.</a>)</span> | |
8674 | </p> | |
8675 | </td> | |
8676 | <td> | |
8677 | <p> | |
8678 | <span class="blue">Max = 341ε (Mean = 80.7ε)</span> | |
8679 | </p> | |
8680 | </td> | |
8681 | <td> | |
8682 | <p> | |
8683 | <span class="blue">Max = 341ε (Mean = 80.7ε)</span> | |
8684 | </p> | |
8685 | </td> | |
8686 | </tr> | |
8687 | <tr> | |
8688 | <td> | |
8689 | <p> | |
8690 | Jacobi Elliptic: Random Data | |
8691 | </p> | |
8692 | </td> | |
8693 | <td> | |
8694 | <p> | |
8695 | <span class="blue">Max = 1.92ε (Mean = 0.567ε)</span> | |
8696 | </p> | |
8697 | </td> | |
8698 | <td> | |
8699 | <p> | |
8700 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
8701 | 1.16:</em></span> Max = 4.02ε (Mean = 1.07ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
8702 | Max = 1.92ε (Mean = 0.567ε)) | |
8703 | </p> | |
8704 | </td> | |
8705 | <td> | |
8706 | <p> | |
8707 | <span class="blue">Max = 2.01ε (Mean = 0.584ε)</span> | |
8708 | </p> | |
8709 | </td> | |
8710 | <td> | |
8711 | <p> | |
8712 | <span class="blue">Max = 2.01ε (Mean = 0.593ε)</span> | |
8713 | </p> | |
8714 | </td> | |
8715 | </tr> | |
8716 | <tr> | |
8717 | <td> | |
8718 | <p> | |
8719 | Jacobi Elliptic: Random Small Values | |
8720 | </p> | |
8721 | </td> | |
8722 | <td> | |
8723 | <p> | |
8724 | <span class="blue">Max = 2.11ε (Mean = 0.385ε)</span> | |
8725 | </p> | |
8726 | </td> | |
8727 | <td> | |
8728 | <p> | |
8729 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
8730 | 1.16:</em></span> Max = 11.7ε (Mean = 1.65ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_GSL_1_16_Jacobi_Elliptic_Random_Small_Values">And | |
8731 | other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_Cephes_Jacobi_Elliptic_Random_Small_Values">And | |
8732 | other failures.</a>)</span> | |
8733 | </p> | |
8734 | </td> | |
8735 | <td> | |
8736 | <p> | |
8737 | <span class="blue">Max = 1.99ε (Mean = 0.347ε)</span> | |
8738 | </p> | |
8739 | </td> | |
8740 | <td> | |
8741 | <p> | |
8742 | <span class="blue">Max = 1.99ε (Mean = 0.347ε)</span> | |
8743 | </p> | |
8744 | </td> | |
8745 | </tr> | |
8746 | <tr> | |
8747 | <td> | |
8748 | <p> | |
8749 | Jacobi Elliptic: Modulus near 1 | |
8750 | </p> | |
8751 | </td> | |
8752 | <td> | |
8753 | <p> | |
8754 | <span class="blue">Max = 23.2ε (Mean = 1.85ε)</span> | |
8755 | </p> | |
8756 | </td> | |
8757 | <td> | |
8758 | <p> | |
8759 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
8760 | 1.16:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_GSL_1_16_Jacobi_Elliptic_Modulus_near_1">And | |
8761 | other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_Cephes_Jacobi_Elliptic_Modulus_near_1">And | |
8762 | other failures.</a>)</span> | |
8763 | </p> | |
8764 | </td> | |
8765 | <td> | |
8766 | <p> | |
8767 | <span class="blue">Max = 109ε (Mean = 7.35ε)</span> | |
8768 | </p> | |
8769 | </td> | |
8770 | <td> | |
8771 | <p> | |
8772 | <span class="blue">Max = 109ε (Mean = 7.38ε)</span> | |
8773 | </p> | |
8774 | </td> | |
8775 | </tr> | |
8776 | <tr> | |
8777 | <td> | |
8778 | <p> | |
8779 | Jacobi Elliptic: Large Phi | |
8780 | </p> | |
8781 | </td> | |
8782 | <td> | |
8783 | <p> | |
8784 | <span class="blue">Max = 4.36e+004ε (Mean = 2.54e+003ε)</span> | |
8785 | </p> | |
8786 | </td> | |
8787 | <td> | |
8788 | <p> | |
8789 | <span class="blue">Max = 12ε (Mean = 0.771ε)</span><br> <br> | |
8790 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 4.54e+04ε (Mean = 2.63e+03ε))<br> | |
8791 | (<span class="emphasis"><em>Cephes:</em></span> Max = 4.36e+04ε (Mean = 2.54e+03ε)) | |
8792 | </p> | |
8793 | </td> | |
8794 | <td> | |
8795 | <p> | |
8796 | <span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</span> | |
8797 | </p> | |
8798 | </td> | |
8799 | <td> | |
8800 | <p> | |
8801 | <span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</span> | |
8802 | </p> | |
8803 | </td> | |
8804 | </tr> | |
8805 | </tbody> | |
8806 | </table></div> | |
8807 | </div> | |
8808 | <br class="table-break"><div class="table"> | |
8809 | <a name="math_toolkit.logs_and_tables.all_table.table_jacobi_zeta"></a><p class="title"><b>Table 17.65. Error rates for jacobi_zeta</b></p> | |
8810 | <div class="table-contents"><table class="table" summary="Error rates for jacobi_zeta"> | |
8811 | <colgroup> | |
8812 | <col> | |
8813 | <col> | |
8814 | <col> | |
8815 | <col> | |
8816 | <col> | |
8817 | </colgroup> | |
8818 | <thead><tr> | |
8819 | <th> | |
8820 | </th> | |
8821 | <th> | |
8822 | <p> | |
8823 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
8824 | </p> | |
8825 | </th> | |
8826 | <th> | |
8827 | <p> | |
8828 | GNU C++ version 5.1.0<br> linux<br> double | |
8829 | </p> | |
8830 | </th> | |
8831 | <th> | |
8832 | <p> | |
8833 | GNU C++ version 5.1.0<br> linux<br> long double | |
8834 | </p> | |
8835 | </th> | |
8836 | <th> | |
8837 | <p> | |
8838 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
8839 | </p> | |
8840 | </th> | |
8841 | </tr></thead> | |
8842 | <tbody> | |
8843 | <tr> | |
8844 | <td> | |
8845 | <p> | |
8846 | Elliptic Integral Jacobi Zeta: Mathworld Data | |
8847 | </p> | |
8848 | </td> | |
8849 | <td> | |
8850 | <p> | |
8851 | <span class="blue">Max = 0.505ε (Mean = 0.119ε)</span> | |
8852 | </p> | |
8853 | </td> | |
8854 | <td> | |
8855 | <p> | |
8856 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
8857 | </p> | |
8858 | </td> | |
8859 | <td> | |
8860 | <p> | |
8861 | <span class="blue">Max = 1.66ε (Mean = 0.48ε)</span> | |
8862 | </p> | |
8863 | </td> | |
8864 | <td> | |
8865 | <p> | |
8866 | <span class="blue">Max = 1.66ε (Mean = 0.48ε)</span> | |
8867 | </p> | |
8868 | </td> | |
8869 | </tr> | |
8870 | <tr> | |
8871 | <td> | |
8872 | <p> | |
8873 | Elliptic Integral Jacobi Zeta: Random Data | |
8874 | </p> | |
8875 | </td> | |
8876 | <td> | |
8877 | <p> | |
8878 | <span class="blue">Max = 3.89ε (Mean = 0.818ε)</span> | |
8879 | </p> | |
8880 | </td> | |
8881 | <td> | |
8882 | <p> | |
8883 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
8884 | </p> | |
8885 | </td> | |
8886 | <td> | |
8887 | <p> | |
8888 | <span class="blue">Max = 2.99ε (Mean = 0.824ε)</span> | |
8889 | </p> | |
8890 | </td> | |
8891 | <td> | |
8892 | <p> | |
8893 | <span class="blue">Max = 3.96ε (Mean = 1.06ε)</span> | |
8894 | </p> | |
8895 | </td> | |
8896 | </tr> | |
8897 | <tr> | |
8898 | <td> | |
8899 | <p> | |
8900 | Elliptic Integral Jacobi Zeta: Large Phi Values | |
8901 | </p> | |
8902 | </td> | |
8903 | <td> | |
8904 | <p> | |
8905 | <span class="blue">Max = 2.92ε (Mean = 0.964ε)</span> | |
8906 | </p> | |
8907 | </td> | |
8908 | <td> | |
8909 | <p> | |
8910 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
8911 | </p> | |
8912 | </td> | |
8913 | <td> | |
8914 | <p> | |
8915 | <span class="blue">Max = 2.92ε (Mean = 0.951ε)</span> | |
8916 | </p> | |
8917 | </td> | |
8918 | <td> | |
8919 | <p> | |
8920 | <span class="blue">Max = 3.05ε (Mean = 1.13ε)</span> | |
8921 | </p> | |
8922 | </td> | |
8923 | </tr> | |
8924 | </tbody> | |
8925 | </table></div> | |
8926 | </div> | |
8927 | <br class="table-break"><div class="table"> | |
8928 | <a name="math_toolkit.logs_and_tables.all_table.table_laguerre_n_m_x_"></a><p class="title"><b>Table 17.66. Error rates for laguerre(n, m, x)</b></p> | |
8929 | <div class="table-contents"><table class="table" summary="Error rates for laguerre(n, m, x)"> | |
8930 | <colgroup> | |
8931 | <col> | |
8932 | <col> | |
8933 | <col> | |
8934 | <col> | |
8935 | <col> | |
8936 | </colgroup> | |
8937 | <thead><tr> | |
8938 | <th> | |
8939 | </th> | |
8940 | <th> | |
8941 | <p> | |
8942 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
8943 | </p> | |
8944 | </th> | |
8945 | <th> | |
8946 | <p> | |
8947 | GNU C++ version 5.1.0<br> linux<br> double | |
8948 | </p> | |
8949 | </th> | |
8950 | <th> | |
8951 | <p> | |
8952 | GNU C++ version 5.1.0<br> linux<br> long double | |
8953 | </p> | |
8954 | </th> | |
8955 | <th> | |
8956 | <p> | |
8957 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
8958 | </p> | |
8959 | </th> | |
8960 | </tr></thead> | |
8961 | <tbody><tr> | |
8962 | <td> | |
8963 | <p> | |
8964 | Associated Laguerre Polynomials | |
8965 | </p> | |
8966 | </td> | |
8967 | <td> | |
8968 | <p> | |
8969 | <span class="blue">Max = 434ε (Mean = 11.1ε)</span> | |
8970 | </p> | |
8971 | </td> | |
8972 | <td> | |
8973 | <p> | |
8974 | <span class="blue">Max = 0.84ε (Mean = 0.0358ε)</span><br> <br> | |
8975 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 434ε (Mean = 10.7ε)) | |
8976 | </p> | |
8977 | </td> | |
8978 | <td> | |
8979 | <p> | |
8980 | <span class="blue">Max = 167ε (Mean = 6.38ε)</span><br> <br> | |
8981 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 206ε (Mean = 6.86ε)) | |
8982 | </p> | |
8983 | </td> | |
8984 | <td> | |
8985 | <p> | |
8986 | <span class="blue">Max = 167ε (Mean = 6.38ε)</span> | |
8987 | </p> | |
8988 | </td> | |
8989 | </tr></tbody> | |
8990 | </table></div> | |
8991 | </div> | |
8992 | <br class="table-break"><div class="table"> | |
8993 | <a name="math_toolkit.logs_and_tables.all_table.table_laguerre_n_x_"></a><p class="title"><b>Table 17.67. Error rates for laguerre(n, x)</b></p> | |
8994 | <div class="table-contents"><table class="table" summary="Error rates for laguerre(n, x)"> | |
8995 | <colgroup> | |
8996 | <col> | |
8997 | <col> | |
8998 | <col> | |
8999 | <col> | |
9000 | <col> | |
9001 | </colgroup> | |
9002 | <thead><tr> | |
9003 | <th> | |
9004 | </th> | |
9005 | <th> | |
9006 | <p> | |
9007 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
9008 | </p> | |
9009 | </th> | |
9010 | <th> | |
9011 | <p> | |
9012 | GNU C++ version 5.1.0<br> linux<br> double | |
9013 | </p> | |
9014 | </th> | |
9015 | <th> | |
9016 | <p> | |
9017 | GNU C++ version 5.1.0<br> linux<br> long double | |
9018 | </p> | |
9019 | </th> | |
9020 | <th> | |
9021 | <p> | |
9022 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
9023 | </p> | |
9024 | </th> | |
9025 | </tr></thead> | |
9026 | <tbody><tr> | |
9027 | <td> | |
9028 | <p> | |
9029 | Laguerre Polynomials | |
9030 | </p> | |
9031 | </td> | |
9032 | <td> | |
9033 | <p> | |
9034 | <span class="blue">Max = 3.1e+003ε (Mean = 185ε)</span> | |
9035 | </p> | |
9036 | </td> | |
9037 | <td> | |
9038 | <p> | |
9039 | <span class="blue">Max = 6.82ε (Mean = 0.408ε)</span><br> <br> | |
9040 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 3.1e+03ε (Mean = 185ε)) | |
9041 | </p> | |
9042 | </td> | |
9043 | <td> | |
9044 | <p> | |
9045 | <span class="blue">Max = 1.39e+04ε (Mean = 828ε)</span><br> | |
9046 | <br> (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 4.2e+03ε (Mean | |
9047 | = 251ε)) | |
9048 | </p> | |
9049 | </td> | |
9050 | <td> | |
9051 | <p> | |
9052 | <span class="blue">Max = 1.39e+04ε (Mean = 828ε)</span> | |
9053 | </p> | |
9054 | </td> | |
9055 | </tr></tbody> | |
9056 | </table></div> | |
9057 | </div> | |
9058 | <br class="table-break"><div class="table"> | |
9059 | <a name="math_toolkit.logs_and_tables.all_table.table_legendre_p"></a><p class="title"><b>Table 17.68. Error rates for legendre_p</b></p> | |
9060 | <div class="table-contents"><table class="table" summary="Error rates for legendre_p"> | |
9061 | <colgroup> | |
9062 | <col> | |
9063 | <col> | |
9064 | <col> | |
9065 | <col> | |
9066 | <col> | |
9067 | </colgroup> | |
9068 | <thead><tr> | |
9069 | <th> | |
9070 | </th> | |
9071 | <th> | |
9072 | <p> | |
9073 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
9074 | </p> | |
9075 | </th> | |
9076 | <th> | |
9077 | <p> | |
9078 | GNU C++ version 5.1.0<br> linux<br> double | |
9079 | </p> | |
9080 | </th> | |
9081 | <th> | |
9082 | <p> | |
9083 | GNU C++ version 5.1.0<br> linux<br> long double | |
9084 | </p> | |
9085 | </th> | |
9086 | <th> | |
9087 | <p> | |
9088 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
9089 | </p> | |
9090 | </th> | |
9091 | </tr></thead> | |
9092 | <tbody> | |
9093 | <tr> | |
9094 | <td> | |
9095 | <p> | |
9096 | Legendre Polynomials: Small Values | |
9097 | </p> | |
9098 | </td> | |
9099 | <td> | |
9100 | <p> | |
9101 | <span class="blue">Max = 211ε (Mean = 20.4ε)</span> | |
9102 | </p> | |
9103 | </td> | |
9104 | <td> | |
9105 | <p> | |
9106 | <span class="blue">Max = 0.732ε (Mean = 0.0619ε)</span><br> | |
9107 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 211ε (Mean = 20.4ε)) | |
9108 | </p> | |
9109 | </td> | |
9110 | <td> | |
9111 | <p> | |
9112 | <span class="blue">Max = 69.2ε (Mean = 9.58ε)</span><br> <br> | |
9113 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 124ε (Mean = 13.2ε)) | |
9114 | </p> | |
9115 | </td> | |
9116 | <td> | |
9117 | <p> | |
9118 | <span class="blue">Max = 69.2ε (Mean = 9.58ε)</span> | |
9119 | </p> | |
9120 | </td> | |
9121 | </tr> | |
9122 | <tr> | |
9123 | <td> | |
9124 | <p> | |
9125 | Legendre Polynomials: Large Values | |
9126 | </p> | |
9127 | </td> | |
9128 | <td> | |
9129 | <p> | |
9130 | <span class="blue">Max = 300ε (Mean = 33.2ε)</span> | |
9131 | </p> | |
9132 | </td> | |
9133 | <td> | |
9134 | <p> | |
9135 | <span class="blue">Max = 0.632ε (Mean = 0.0693ε)</span><br> | |
9136 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 300ε (Mean = 33.2ε)) | |
9137 | </p> | |
9138 | </td> | |
9139 | <td> | |
9140 | <p> | |
9141 | <span class="blue">Max = 699ε (Mean = 59.6ε)</span><br> <br> | |
9142 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 343ε (Mean = 32.1ε)) | |
9143 | </p> | |
9144 | </td> | |
9145 | <td> | |
9146 | <p> | |
9147 | <span class="blue">Max = 699ε (Mean = 59.6ε)</span> | |
9148 | </p> | |
9149 | </td> | |
9150 | </tr> | |
9151 | </tbody> | |
9152 | </table></div> | |
9153 | </div> | |
9154 | <br class="table-break"><div class="table"> | |
9155 | <a name="math_toolkit.logs_and_tables.all_table.table_legendre_p_associated_"></a><p class="title"><b>Table 17.69. Error rates for legendre_p (associated)</b></p> | |
9156 | <div class="table-contents"><table class="table" summary="Error rates for legendre_p (associated)"> | |
9157 | <colgroup> | |
9158 | <col> | |
9159 | <col> | |
9160 | <col> | |
9161 | <col> | |
9162 | <col> | |
9163 | </colgroup> | |
9164 | <thead><tr> | |
9165 | <th> | |
9166 | </th> | |
9167 | <th> | |
9168 | <p> | |
9169 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
9170 | </p> | |
9171 | </th> | |
9172 | <th> | |
9173 | <p> | |
9174 | GNU C++ version 5.1.0<br> linux<br> double | |
9175 | </p> | |
9176 | </th> | |
9177 | <th> | |
9178 | <p> | |
9179 | GNU C++ version 5.1.0<br> linux<br> long double | |
9180 | </p> | |
9181 | </th> | |
9182 | <th> | |
9183 | <p> | |
9184 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
9185 | </p> | |
9186 | </th> | |
9187 | </tr></thead> | |
9188 | <tbody><tr> | |
9189 | <td> | |
9190 | <p> | |
9191 | Associated Legendre Polynomials: Small Values | |
9192 | </p> | |
9193 | </td> | |
9194 | <td> | |
9195 | <p> | |
9196 | <span class="blue">Max = 121ε (Mean = 7.14ε)</span> | |
9197 | </p> | |
9198 | </td> | |
9199 | <td> | |
9200 | <p> | |
9201 | <span class="blue">Max = 0.999ε (Mean = 0.05ε)</span><br> <br> | |
9202 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 121ε (Mean = 6.75ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_legendre_p_associated__GSL_1_16_Associated_Legendre_Polynomials_Small_Values">And | |
9203 | other failures.</a>) | |
9204 | </p> | |
9205 | </td> | |
9206 | <td> | |
9207 | <p> | |
9208 | <span class="blue">Max = 175ε (Mean = 9.88ε)</span><br> <br> | |
9209 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 175ε (Mean = 9.36ε) | |
9210 | <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_legendre_p_associated___tr1_cmath__Associated_Legendre_Polynomials_Small_Values">And | |
9211 | other failures.</a>) | |
9212 | </p> | |
9213 | </td> | |
9214 | <td> | |
9215 | <p> | |
9216 | <span class="blue">Max = 77.7ε (Mean = 5.59ε)</span> | |
9217 | </p> | |
9218 | </td> | |
9219 | </tr></tbody> | |
9220 | </table></div> | |
9221 | </div> | |
9222 | <br class="table-break"><div class="table"> | |
9223 | <a name="math_toolkit.logs_and_tables.all_table.table_legendre_q"></a><p class="title"><b>Table 17.70. Error rates for legendre_q</b></p> | |
9224 | <div class="table-contents"><table class="table" summary="Error rates for legendre_q"> | |
9225 | <colgroup> | |
9226 | <col> | |
9227 | <col> | |
9228 | <col> | |
9229 | <col> | |
9230 | <col> | |
9231 | </colgroup> | |
9232 | <thead><tr> | |
9233 | <th> | |
9234 | </th> | |
9235 | <th> | |
9236 | <p> | |
9237 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
9238 | </p> | |
9239 | </th> | |
9240 | <th> | |
9241 | <p> | |
9242 | GNU C++ version 5.1.0<br> linux<br> double | |
9243 | </p> | |
9244 | </th> | |
9245 | <th> | |
9246 | <p> | |
9247 | GNU C++ version 5.1.0<br> linux<br> long double | |
9248 | </p> | |
9249 | </th> | |
9250 | <th> | |
9251 | <p> | |
9252 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
9253 | </p> | |
9254 | </th> | |
9255 | </tr></thead> | |
9256 | <tbody> | |
9257 | <tr> | |
9258 | <td> | |
9259 | <p> | |
9260 | Legendre Polynomials: Small Values | |
9261 | </p> | |
9262 | </td> | |
9263 | <td> | |
9264 | <p> | |
9265 | <span class="blue">Max = 46.4ε (Mean = 7.32ε)</span> | |
9266 | </p> | |
9267 | </td> | |
9268 | <td> | |
9269 | <p> | |
9270 | <span class="blue">Max = 0.612ε (Mean = 0.0517ε)</span><br> | |
9271 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 46.4ε (Mean = 7.46ε)) | |
9272 | </p> | |
9273 | </td> | |
9274 | <td> | |
9275 | <p> | |
9276 | <span class="blue">Max = 50.9ε (Mean = 9ε)</span> | |
9277 | </p> | |
9278 | </td> | |
9279 | <td> | |
9280 | <p> | |
9281 | <span class="blue">Max = 50.9ε (Mean = 8.98ε)</span> | |
9282 | </p> | |
9283 | </td> | |
9284 | </tr> | |
9285 | <tr> | |
9286 | <td> | |
9287 | <p> | |
9288 | Legendre Polynomials: Large Values | |
9289 | </p> | |
9290 | </td> | |
9291 | <td> | |
9292 | <p> | |
9293 | <span class="blue">Max = 4.6e+003ε (Mean = 366ε)</span> | |
9294 | </p> | |
9295 | </td> | |
9296 | <td> | |
9297 | <p> | |
9298 | <span class="blue">Max = 2.49ε (Mean = 0.202ε)</span><br> <br> | |
9299 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 4.6e+03ε (Mean = 366ε)) | |
9300 | </p> | |
9301 | </td> | |
9302 | <td> | |
9303 | <p> | |
9304 | <span class="blue">Max = 5.98e+03ε (Mean = 478ε)</span> | |
9305 | </p> | |
9306 | </td> | |
9307 | <td> | |
9308 | <p> | |
9309 | <span class="blue">Max = 5.98e+03ε (Mean = 478ε)</span> | |
9310 | </p> | |
9311 | </td> | |
9312 | </tr> | |
9313 | </tbody> | |
9314 | </table></div> | |
9315 | </div> | |
9316 | <br class="table-break"><div class="table"> | |
9317 | <a name="math_toolkit.logs_and_tables.all_table.table_lgamma"></a><p class="title"><b>Table 17.71. Error rates for lgamma</b></p> | |
9318 | <div class="table-contents"><table class="table" summary="Error rates for lgamma"> | |
9319 | <colgroup> | |
9320 | <col> | |
9321 | <col> | |
9322 | <col> | |
9323 | <col> | |
9324 | <col> | |
9325 | </colgroup> | |
9326 | <thead><tr> | |
9327 | <th> | |
9328 | </th> | |
9329 | <th> | |
9330 | <p> | |
9331 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
9332 | </p> | |
9333 | </th> | |
9334 | <th> | |
9335 | <p> | |
9336 | GNU C++ version 5.1.0<br> linux<br> double | |
9337 | </p> | |
9338 | </th> | |
9339 | <th> | |
9340 | <p> | |
9341 | GNU C++ version 5.1.0<br> linux<br> long double | |
9342 | </p> | |
9343 | </th> | |
9344 | <th> | |
9345 | <p> | |
9346 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
9347 | </p> | |
9348 | </th> | |
9349 | </tr></thead> | |
9350 | <tbody> | |
9351 | <tr> | |
9352 | <td> | |
9353 | <p> | |
9354 | factorials | |
9355 | </p> | |
9356 | </td> | |
9357 | <td> | |
9358 | <p> | |
9359 | <span class="blue">Max = 0.914ε (Mean = 0.167ε)</span><br> <br> | |
9360 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0.958ε (Mean = 0.38ε)) | |
9361 | </p> | |
9362 | </td> | |
9363 | <td> | |
9364 | <p> | |
9365 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
9366 | 1.16:</em></span> Max = 33.6ε (Mean = 2.78ε))<br> (<span class="emphasis"><em>Rmath | |
9367 | 3.0.2:</em></span> Max = 1.55ε (Mean = 0.592ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
9368 | Max = 1.55ε (Mean = 0.512ε)) | |
9369 | </p> | |
9370 | </td> | |
9371 | <td> | |
9372 | <p> | |
9373 | <span class="blue">Max = 0.991ε (Mean = 0.311ε)</span><br> <br> | |
9374 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.67ε (Mean = 0.487ε))<br> | |
9375 | (<span class="emphasis"><em><math.h>:</em></span> Max = 1.67ε (Mean = 0.487ε)) | |
9376 | </p> | |
9377 | </td> | |
9378 | <td> | |
9379 | <p> | |
9380 | <span class="blue">Max = 0.991ε (Mean = 0.383ε)</span><br> <br> | |
9381 | (<span class="emphasis"><em><math.h>:</em></span> Max = 1.36ε (Mean = 0.476ε)) | |
9382 | </p> | |
9383 | </td> | |
9384 | </tr> | |
9385 | <tr> | |
9386 | <td> | |
9387 | <p> | |
9388 | near 0 | |
9389 | </p> | |
9390 | </td> | |
9391 | <td> | |
9392 | <p> | |
9393 | <span class="blue">Max = 0.964ε (Mean = 0.462ε)</span><br> <br> | |
9394 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0.962ε (Mean = 0.372ε)) | |
9395 | </p> | |
9396 | </td> | |
9397 | <td> | |
9398 | <p> | |
9399 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
9400 | 1.16:</em></span> Max = 5.21ε (Mean = 1.57ε))<br> (<span class="emphasis"><em>Rmath | |
9401 | 3.0.2:</em></span> Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
9402 | Max = 1.16ε (Mean = 0.341ε)) | |
9403 | </p> | |
9404 | </td> | |
9405 | <td> | |
9406 | <p> | |
9407 | <span class="blue">Max = 1.42ε (Mean = 0.566ε)</span><br> <br> | |
9408 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 0.964ε (Mean = 0.543ε))<br> | |
9409 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0.964ε (Mean = 0.543ε)) | |
9410 | </p> | |
9411 | </td> | |
9412 | <td> | |
9413 | <p> | |
9414 | <span class="blue">Max = 1.42ε (Mean = 0.566ε)</span><br> <br> | |
9415 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0.964ε (Mean = 0.543ε)) | |
9416 | </p> | |
9417 | </td> | |
9418 | </tr> | |
9419 | <tr> | |
9420 | <td> | |
9421 | <p> | |
9422 | near 1 | |
9423 | </p> | |
9424 | </td> | |
9425 | <td> | |
9426 | <p> | |
9427 | <span class="blue">Max = 0.867ε (Mean = 0.468ε)</span><br> <br> | |
9428 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0.906ε (Mean = 0.565ε)) | |
9429 | </p> | |
9430 | </td> | |
9431 | <td> | |
9432 | <p> | |
9433 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
9434 | 1.16:</em></span> Max = 442ε (Mean = 88.8ε))<br> (<span class="emphasis"><em>Rmath | |
9435 | 3.0.2:</em></span> Max = 7.99e+04ε (Mean = 1.68e+04ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
9436 | Max = 1.14e+05ε (Mean = 2.64e+04ε)) | |
9437 | </p> | |
9438 | </td> | |
9439 | <td> | |
9440 | <p> | |
9441 | <span class="blue">Max = 0.948ε (Mean = 0.36ε)</span><br> <br> | |
9442 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 0.615ε (Mean = 0.096ε))<br> | |
9443 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0.615ε (Mean = 0.096ε)) | |
9444 | </p> | |
9445 | </td> | |
9446 | <td> | |
9447 | <p> | |
9448 | <span class="blue">Max = 0.866ε (Mean = 0.355ε)</span><br> <br> | |
9449 | (<span class="emphasis"><em><math.h>:</em></span> Max = 1.71ε (Mean = 0.581ε)) | |
9450 | </p> | |
9451 | </td> | |
9452 | </tr> | |
9453 | <tr> | |
9454 | <td> | |
9455 | <p> | |
9456 | near 2 | |
9457 | </p> | |
9458 | </td> | |
9459 | <td> | |
9460 | <p> | |
9461 | <span class="blue">Max = 0.591ε (Mean = 0.159ε)</span><br> <br> | |
9462 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0.741ε (Mean = 0.473ε)) | |
9463 | </p> | |
9464 | </td> | |
9465 | <td> | |
9466 | <p> | |
9467 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
9468 | 1.16:</em></span> Max = 1.17e+03ε (Mean = 274ε))<br> (<span class="emphasis"><em>Rmath | |
9469 | 3.0.2:</em></span> Max = 2.63e+05ε (Mean = 5.84e+04ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
9470 | Max = 5.08e+05ε (Mean = 9.04e+04ε)) | |
9471 | </p> | |
9472 | </td> | |
9473 | <td> | |
9474 | <p> | |
9475 | <span class="blue">Max = 0.878ε (Mean = 0.242ε)</span><br> <br> | |
9476 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 0.741ε (Mean = 0.263ε))<br> | |
9477 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0.741ε (Mean = 0.263ε)) | |
9478 | </p> | |
9479 | </td> | |
9480 | <td> | |
9481 | <p> | |
9482 | <span class="blue">Max = 0.878ε (Mean = 0.241ε)</span><br> <br> | |
9483 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0.598ε (Mean = 0.235ε)) | |
9484 | </p> | |
9485 | </td> | |
9486 | </tr> | |
9487 | <tr> | |
9488 | <td> | |
9489 | <p> | |
9490 | near -10 | |
9491 | </p> | |
9492 | </td> | |
9493 | <td> | |
9494 | <p> | |
9495 | <span class="blue">Max = 4.22ε (Mean = 1.33ε)</span><br> <br> | |
9496 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0.997ε (Mean = 0.444ε)) | |
9497 | </p> | |
9498 | </td> | |
9499 | <td> | |
9500 | <p> | |
9501 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
9502 | 1.16:</em></span> Max = 24.9ε (Mean = 4.6ε))<br> (<span class="emphasis"><em>Rmath | |
9503 | 3.0.2:</em></span> Max = 2.41e+05ε (Mean = 4.29e+04ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
9504 | Max = 0.997ε (Mean = 0.429ε)) | |
9505 | </p> | |
9506 | </td> | |
9507 | <td> | |
9508 | <p> | |
9509 | <span class="blue">Max = 3.81ε (Mean = 1.01ε)</span><br> <br> | |
9510 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 3.01ε (Mean = 0.86ε))<br> | |
9511 | (<span class="emphasis"><em><math.h>:</em></span> Max = 3.01ε (Mean = 0.86ε)) | |
9512 | </p> | |
9513 | </td> | |
9514 | <td> | |
9515 | <p> | |
9516 | <span class="blue">Max = 3.81ε (Mean = 1.01ε)</span><br> <br> | |
9517 | (<span class="emphasis"><em><math.h>:</em></span> Max = 3.04ε (Mean = 1.01ε)) | |
9518 | </p> | |
9519 | </td> | |
9520 | </tr> | |
9521 | <tr> | |
9522 | <td> | |
9523 | <p> | |
9524 | near -55 | |
9525 | </p> | |
9526 | </td> | |
9527 | <td> | |
9528 | <p> | |
9529 | <span class="blue">Max = 0.821ε (Mean = 0.419ε)</span><br> <br> | |
9530 | (<span class="emphasis"><em><math.h>:</em></span> Max = 249ε (Mean = 43.1ε)) | |
9531 | </p> | |
9532 | </td> | |
9533 | <td> | |
9534 | <p> | |
9535 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
9536 | 1.16:</em></span> Max = 7.02ε (Mean = 1.47ε))<br> (<span class="emphasis"><em>Rmath | |
9537 | 3.0.2:</em></span> Max = 4.08e+04ε (Mean = 7.26e+03ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
9538 | Max = 1.64ε (Mean = 0.693ε)) | |
9539 | </p> | |
9540 | </td> | |
9541 | <td> | |
9542 | <p> | |
9543 | <span class="blue">Max = 0.821ε (Mean = 0.513ε)</span><br> <br> | |
9544 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.58ε (Mean = 0.672ε))<br> | |
9545 | (<span class="emphasis"><em><math.h>:</em></span> Max = 1.58ε (Mean = 0.672ε)) | |
9546 | </p> | |
9547 | </td> | |
9548 | <td> | |
9549 | <p> | |
9550 | <span class="blue">Max = 1.59ε (Mean = 0.587ε)</span><br> <br> | |
9551 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0.821ε (Mean = 0.674ε)) | |
9552 | </p> | |
9553 | </td> | |
9554 | </tr> | |
9555 | </tbody> | |
9556 | </table></div> | |
9557 | </div> | |
9558 | <br class="table-break"><div class="table"> | |
9559 | <a name="math_toolkit.logs_and_tables.all_table.table_log1p"></a><p class="title"><b>Table 17.72. Error rates for log1p</b></p> | |
9560 | <div class="table-contents"><table class="table" summary="Error rates for log1p"> | |
9561 | <colgroup> | |
9562 | <col> | |
9563 | <col> | |
9564 | <col> | |
9565 | <col> | |
9566 | <col> | |
9567 | </colgroup> | |
9568 | <thead><tr> | |
9569 | <th> | |
9570 | </th> | |
9571 | <th> | |
9572 | <p> | |
9573 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
9574 | </p> | |
9575 | </th> | |
9576 | <th> | |
9577 | <p> | |
9578 | GNU C++ version 5.1.0<br> linux<br> double | |
9579 | </p> | |
9580 | </th> | |
9581 | <th> | |
9582 | <p> | |
9583 | GNU C++ version 5.1.0<br> linux<br> long double | |
9584 | </p> | |
9585 | </th> | |
9586 | <th> | |
9587 | <p> | |
9588 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
9589 | </p> | |
9590 | </th> | |
9591 | </tr></thead> | |
9592 | <tbody><tr> | |
9593 | <td> | |
9594 | <p> | |
9595 | Random test data | |
9596 | </p> | |
9597 | </td> | |
9598 | <td> | |
9599 | <p> | |
9600 | <span class="blue">Max = 0.509ε (Mean = 0.057ε)</span><br> <br> | |
9601 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0.509ε (Mean = 0.057ε)) | |
9602 | </p> | |
9603 | </td> | |
9604 | <td> | |
9605 | <p> | |
9606 | <span class="blue">Max = 0.846ε (Mean = 0.153ε)</span><br> <br> | |
9607 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 0.846ε (Mean = 0.153ε))<br> | |
9608 | (<span class="emphasis"><em>Cephes:</em></span> Max = 0.799ε (Mean = 0.122ε)) | |
9609 | </p> | |
9610 | </td> | |
9611 | <td> | |
9612 | <p> | |
9613 | <span class="blue">Max = 0.818ε (Mean = 0.227ε)</span><br> <br> | |
9614 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 0.818ε (Mean = 0.227ε))<br> | |
9615 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0.818ε (Mean = 0.227ε)) | |
9616 | </p> | |
9617 | </td> | |
9618 | <td> | |
9619 | <p> | |
9620 | <span class="blue">Max = 1.53ε (Mean = 0.627ε)</span><br> <br> | |
9621 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0.818ε (Mean = 0.249ε)) | |
9622 | </p> | |
9623 | </td> | |
9624 | </tr></tbody> | |
9625 | </table></div> | |
9626 | </div> | |
9627 | <br class="table-break"><div class="table"> | |
9628 | <a name="math_toolkit.logs_and_tables.all_table.table_non_central_beta_CDF"></a><p class="title"><b>Table 17.73. Error rates for non central beta CDF</b></p> | |
9629 | <div class="table-contents"><table class="table" summary="Error rates for non central beta CDF"> | |
9630 | <colgroup> | |
9631 | <col> | |
9632 | <col> | |
9633 | <col> | |
9634 | <col> | |
9635 | <col> | |
9636 | </colgroup> | |
9637 | <thead><tr> | |
9638 | <th> | |
9639 | </th> | |
9640 | <th> | |
9641 | <p> | |
9642 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
9643 | </p> | |
9644 | </th> | |
9645 | <th> | |
9646 | <p> | |
9647 | GNU C++ version 5.1.0<br> linux<br> double | |
9648 | </p> | |
9649 | </th> | |
9650 | <th> | |
9651 | <p> | |
9652 | GNU C++ version 5.1.0<br> linux<br> long double | |
9653 | </p> | |
9654 | </th> | |
9655 | <th> | |
9656 | <p> | |
9657 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
9658 | </p> | |
9659 | </th> | |
9660 | </tr></thead> | |
9661 | <tbody> | |
9662 | <tr> | |
9663 | <td> | |
9664 | <p> | |
9665 | Non Central Beta, medium parameters | |
9666 | </p> | |
9667 | </td> | |
9668 | <td> | |
9669 | <p> | |
9670 | <span class="blue">Max = 240ε (Mean = 31ε)</span> | |
9671 | </p> | |
9672 | </td> | |
9673 | <td> | |
9674 | <p> | |
9675 | <span class="blue">Max = 0.998ε (Mean = 0.0659ε)</span><br> | |
9676 | <br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max | |
9677 | = 1.46e+26ε (Mean = 3.5e+24ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_beta_CDF_Rmath_3_0_2_Non_Central_Beta_medium_parameters">And | |
9678 | other failures.</a>)</span> | |
9679 | </p> | |
9680 | </td> | |
9681 | <td> | |
9682 | <p> | |
9683 | <span class="blue">Max = 825ε (Mean = 27.4ε)</span> | |
9684 | </p> | |
9685 | </td> | |
9686 | <td> | |
9687 | <p> | |
9688 | <span class="blue">Max = 832ε (Mean = 38.1ε)</span> | |
9689 | </p> | |
9690 | </td> | |
9691 | </tr> | |
9692 | <tr> | |
9693 | <td> | |
9694 | <p> | |
9695 | Non Central Beta, large parameters | |
9696 | </p> | |
9697 | </td> | |
9698 | <td> | |
9699 | <p> | |
9700 | <span class="blue">Max = 3.41e+003ε (Mean = 475ε)</span> | |
9701 | </p> | |
9702 | </td> | |
9703 | <td> | |
9704 | <p> | |
9705 | <span class="blue">Max = 1.18ε (Mean = 0.175ε)</span><br> <br> | |
9706 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = 1.01e+36ε (Mean | |
9707 | = 1.19e+35ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_beta_CDF_Rmath_3_0_2_Non_Central_Beta_large_parameters">And | |
9708 | other failures.</a>)</span> | |
9709 | </p> | |
9710 | </td> | |
9711 | <td> | |
9712 | <p> | |
9713 | <span class="blue">Max = 2.5e+04ε (Mean = 3.78e+03ε)</span> | |
9714 | </p> | |
9715 | </td> | |
9716 | <td> | |
9717 | <p> | |
9718 | <span class="blue">Max = 2.57e+04ε (Mean = 4.43e+03ε)</span> | |
9719 | </p> | |
9720 | </td> | |
9721 | </tr> | |
9722 | </tbody> | |
9723 | </table></div> | |
9724 | </div> | |
9725 | <br class="table-break"><div class="table"> | |
9726 | <a name="math_toolkit.logs_and_tables.all_table.table_non_central_beta_CDF_complement"></a><p class="title"><b>Table 17.74. Error rates for non central beta CDF complement</b></p> | |
9727 | <div class="table-contents"><table class="table" summary="Error rates for non central beta CDF complement"> | |
9728 | <colgroup> | |
9729 | <col> | |
9730 | <col> | |
9731 | <col> | |
9732 | <col> | |
9733 | <col> | |
9734 | </colgroup> | |
9735 | <thead><tr> | |
9736 | <th> | |
9737 | </th> | |
9738 | <th> | |
9739 | <p> | |
9740 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
9741 | </p> | |
9742 | </th> | |
9743 | <th> | |
9744 | <p> | |
9745 | GNU C++ version 5.1.0<br> linux<br> double | |
9746 | </p> | |
9747 | </th> | |
9748 | <th> | |
9749 | <p> | |
9750 | GNU C++ version 5.1.0<br> linux<br> long double | |
9751 | </p> | |
9752 | </th> | |
9753 | <th> | |
9754 | <p> | |
9755 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
9756 | </p> | |
9757 | </th> | |
9758 | </tr></thead> | |
9759 | <tbody> | |
9760 | <tr> | |
9761 | <td> | |
9762 | <p> | |
9763 | Non Central Beta, medium parameters | |
9764 | </p> | |
9765 | </td> | |
9766 | <td> | |
9767 | <p> | |
9768 | <span class="blue">Max = 619ε (Mean = 62.7ε)</span> | |
9769 | </p> | |
9770 | </td> | |
9771 | <td> | |
9772 | <p> | |
9773 | <span class="blue">Max = 0.998ε (Mean = 0.0957ε)</span><br> | |
9774 | <br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max | |
9775 | = 7.5e+97ε (Mean = 1.37e+96ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_0_2_Non_Central_Beta_medium_parameters">And | |
9776 | other failures.</a>)</span> | |
9777 | </p> | |
9778 | </td> | |
9779 | <td> | |
9780 | <p> | |
9781 | <span class="blue">Max = 396ε (Mean = 50.7ε)</span> | |
9782 | </p> | |
9783 | </td> | |
9784 | <td> | |
9785 | <p> | |
9786 | <span class="blue">Max = 554ε (Mean = 57.3ε)</span> | |
9787 | </p> | |
9788 | </td> | |
9789 | </tr> | |
9790 | <tr> | |
9791 | <td> | |
9792 | <p> | |
9793 | Non Central Beta, large parameters | |
9794 | </p> | |
9795 | </td> | |
9796 | <td> | |
9797 | <p> | |
9798 | <span class="blue">Max = 8.67e+003ε (Mean = 1.04e+003ε)</span> | |
9799 | </p> | |
9800 | </td> | |
9801 | <td> | |
9802 | <p> | |
9803 | <span class="blue">Max = 0.986ε (Mean = 0.188ε)</span><br> <br> | |
9804 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = +INFε (Mean | |
9805 | = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_0_2_Non_Central_Beta_large_parameters">And | |
9806 | other failures.</a>)</span> | |
9807 | </p> | |
9808 | </td> | |
9809 | <td> | |
9810 | <p> | |
9811 | <span class="blue">Max = 6.83e+03ε (Mean = 993ε)</span> | |
9812 | </p> | |
9813 | </td> | |
9814 | <td> | |
9815 | <p> | |
9816 | <span class="blue">Max = 3.56e+03ε (Mean = 704ε)</span> | |
9817 | </p> | |
9818 | </td> | |
9819 | </tr> | |
9820 | </tbody> | |
9821 | </table></div> | |
9822 | </div> | |
9823 | <br class="table-break"><div class="table"> | |
9824 | <a name="math_toolkit.logs_and_tables.all_table.table_non_central_chi_squared_CDF"></a><p class="title"><b>Table 17.75. Error rates for non central chi squared CDF</b></p> | |
9825 | <div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF"> | |
9826 | <colgroup> | |
9827 | <col> | |
9828 | <col> | |
9829 | <col> | |
9830 | <col> | |
9831 | <col> | |
9832 | </colgroup> | |
9833 | <thead><tr> | |
9834 | <th> | |
9835 | </th> | |
9836 | <th> | |
9837 | <p> | |
9838 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
9839 | </p> | |
9840 | </th> | |
9841 | <th> | |
9842 | <p> | |
9843 | GNU C++ version 5.1.0<br> linux<br> double | |
9844 | </p> | |
9845 | </th> | |
9846 | <th> | |
9847 | <p> | |
9848 | GNU C++ version 5.1.0<br> linux<br> long double | |
9849 | </p> | |
9850 | </th> | |
9851 | <th> | |
9852 | <p> | |
9853 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
9854 | </p> | |
9855 | </th> | |
9856 | </tr></thead> | |
9857 | <tbody> | |
9858 | <tr> | |
9859 | <td> | |
9860 | <p> | |
9861 | Non Central Chi Squared, medium parameters | |
9862 | </p> | |
9863 | </td> | |
9864 | <td> | |
9865 | <p> | |
9866 | <span class="blue">Max = 48.9ε (Mean = 10ε)</span> | |
9867 | </p> | |
9868 | </td> | |
9869 | <td> | |
9870 | <p> | |
9871 | <span class="blue">Max = 0.99ε (Mean = 0.0529ε)</span><br> <br> | |
9872 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 727ε (Mean = 121ε)) | |
9873 | </p> | |
9874 | </td> | |
9875 | <td> | |
9876 | <p> | |
9877 | <span class="blue">Max = 46.5ε (Mean = 10.3ε)</span> | |
9878 | </p> | |
9879 | </td> | |
9880 | <td> | |
9881 | <p> | |
9882 | <span class="blue">Max = 115ε (Mean = 13.9ε)</span> | |
9883 | </p> | |
9884 | </td> | |
9885 | </tr> | |
9886 | <tr> | |
9887 | <td> | |
9888 | <p> | |
9889 | Non Central Chi Squared, large parameters | |
9890 | </p> | |
9891 | </td> | |
9892 | <td> | |
9893 | <p> | |
9894 | <span class="blue">Max = 9.79e+003ε (Mean = 723ε)</span> | |
9895 | </p> | |
9896 | </td> | |
9897 | <td> | |
9898 | <p> | |
9899 | <span class="blue">Max = 1.07ε (Mean = 0.102ε)</span><br> <br> | |
9900 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = 3.27e+08ε (Mean | |
9901 | = 2.23e+07ε))</span> | |
9902 | </p> | |
9903 | </td> | |
9904 | <td> | |
9905 | <p> | |
9906 | <span class="blue">Max = 3.07e+03ε (Mean = 336ε)</span> | |
9907 | </p> | |
9908 | </td> | |
9909 | <td> | |
9910 | <p> | |
9911 | <span class="blue">Max = 6.17e+03ε (Mean = 677ε)</span> | |
9912 | </p> | |
9913 | </td> | |
9914 | </tr> | |
9915 | </tbody> | |
9916 | </table></div> | |
9917 | </div> | |
9918 | <br class="table-break"><div class="table"> | |
9919 | <a name="math_toolkit.logs_and_tables.all_table.table_non_central_chi_squared_CDF_complement"></a><p class="title"><b>Table 17.76. Error rates for non central chi squared CDF complement</b></p> | |
9920 | <div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF complement"> | |
9921 | <colgroup> | |
9922 | <col> | |
9923 | <col> | |
9924 | <col> | |
9925 | <col> | |
9926 | <col> | |
9927 | </colgroup> | |
9928 | <thead><tr> | |
9929 | <th> | |
9930 | </th> | |
9931 | <th> | |
9932 | <p> | |
9933 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
9934 | </p> | |
9935 | </th> | |
9936 | <th> | |
9937 | <p> | |
9938 | GNU C++ version 5.1.0<br> linux<br> double | |
9939 | </p> | |
9940 | </th> | |
9941 | <th> | |
9942 | <p> | |
9943 | GNU C++ version 5.1.0<br> linux<br> long double | |
9944 | </p> | |
9945 | </th> | |
9946 | <th> | |
9947 | <p> | |
9948 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
9949 | </p> | |
9950 | </th> | |
9951 | </tr></thead> | |
9952 | <tbody> | |
9953 | <tr> | |
9954 | <td> | |
9955 | <p> | |
9956 | Non Central Chi Squared, medium parameters | |
9957 | </p> | |
9958 | </td> | |
9959 | <td> | |
9960 | <p> | |
9961 | <span class="blue">Max = 98.6ε (Mean = 15.8ε)</span> | |
9962 | </p> | |
9963 | </td> | |
9964 | <td> | |
9965 | <p> | |
9966 | <span class="blue">Max = 0.96ε (Mean = 0.0635ε)</span><br> <br> | |
9967 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = +INFε (Mean | |
9968 | = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_0_2_Non_Central_Chi_Squared_medium_parameters">And | |
9969 | other failures.</a>)</span> | |
9970 | </p> | |
9971 | </td> | |
9972 | <td> | |
9973 | <p> | |
9974 | <span class="blue">Max = 107ε (Mean = 17.1ε)</span> | |
9975 | </p> | |
9976 | </td> | |
9977 | <td> | |
9978 | <p> | |
9979 | <span class="blue">Max = 171ε (Mean = 22.8ε)</span> | |
9980 | </p> | |
9981 | </td> | |
9982 | </tr> | |
9983 | <tr> | |
9984 | <td> | |
9985 | <p> | |
9986 | Non Central Chi Squared, large parameters | |
9987 | </p> | |
9988 | </td> | |
9989 | <td> | |
9990 | <p> | |
9991 | <span class="blue">Max = 5.43e+003ε (Mean = 705ε)</span> | |
9992 | </p> | |
9993 | </td> | |
9994 | <td> | |
9995 | <p> | |
9996 | <span class="blue">Max = 2.11ε (Mean = 0.278ε)</span><br> <br> | |
9997 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = +INFε (Mean | |
9998 | = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_0_2_Non_Central_Chi_Squared_large_parameters">And | |
9999 | other failures.</a>)</span> | |
10000 | </p> | |
10001 | </td> | |
10002 | <td> | |
10003 | <p> | |
10004 | <span class="blue">Max = 5.02e+03ε (Mean = 630ε)</span> | |
10005 | </p> | |
10006 | </td> | |
10007 | <td> | |
10008 | <p> | |
10009 | <span class="blue">Max = 5.1e+03ε (Mean = 577ε)</span> | |
10010 | </p> | |
10011 | </td> | |
10012 | </tr> | |
10013 | </tbody> | |
10014 | </table></div> | |
10015 | </div> | |
10016 | <br class="table-break"><div class="table"> | |
10017 | <a name="math_toolkit.logs_and_tables.all_table.table_non_central_t_CDF"></a><p class="title"><b>Table 17.77. Error rates for non central t CDF</b></p> | |
10018 | <div class="table-contents"><table class="table" summary="Error rates for non central t CDF"> | |
10019 | <colgroup> | |
10020 | <col> | |
10021 | <col> | |
10022 | <col> | |
10023 | <col> | |
10024 | <col> | |
10025 | </colgroup> | |
10026 | <thead><tr> | |
10027 | <th> | |
10028 | </th> | |
10029 | <th> | |
10030 | <p> | |
10031 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
10032 | </p> | |
10033 | </th> | |
10034 | <th> | |
10035 | <p> | |
10036 | GNU C++ version 5.1.0<br> linux<br> double | |
10037 | </p> | |
10038 | </th> | |
10039 | <th> | |
10040 | <p> | |
10041 | GNU C++ version 5.1.0<br> linux<br> long double | |
10042 | </p> | |
10043 | </th> | |
10044 | <th> | |
10045 | <p> | |
10046 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
10047 | </p> | |
10048 | </th> | |
10049 | </tr></thead> | |
10050 | <tbody> | |
10051 | <tr> | |
10052 | <td> | |
10053 | <p> | |
10054 | Non Central T | |
10055 | </p> | |
10056 | </td> | |
10057 | <td> | |
10058 | <p> | |
10059 | <span class="blue">Max = 138ε (Mean = 31.5ε)</span> | |
10060 | </p> | |
10061 | </td> | |
10062 | <td> | |
10063 | <p> | |
10064 | <span class="blue">Max = 0.796ε (Mean = 0.0691ε)</span><br> | |
10065 | <br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max | |
10066 | = 5.28e+15ε (Mean = 8.49e+14ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_t_CDF_Rmath_3_0_2_Non_Central_T">And | |
10067 | other failures.</a>)</span> | |
10068 | </p> | |
10069 | </td> | |
10070 | <td> | |
10071 | <p> | |
10072 | <span class="blue">Max = 141ε (Mean = 31.1ε)</span> | |
10073 | </p> | |
10074 | </td> | |
10075 | <td> | |
10076 | <p> | |
10077 | <span class="blue">Max = 145ε (Mean = 30.2ε)</span> | |
10078 | </p> | |
10079 | </td> | |
10080 | </tr> | |
10081 | <tr> | |
10082 | <td> | |
10083 | <p> | |
10084 | Non Central T (small non-centrality) | |
10085 | </p> | |
10086 | </td> | |
10087 | <td> | |
10088 | <p> | |
10089 | <span class="blue">Max = 3.61ε (Mean = 1.03ε)</span> | |
10090 | </p> | |
10091 | </td> | |
10092 | <td> | |
10093 | <p> | |
10094 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath | |
10095 | 3.0.2:</em></span> Max = 2.09e+03ε (Mean = 244ε)) | |
10096 | </p> | |
10097 | </td> | |
10098 | <td> | |
10099 | <p> | |
10100 | <span class="blue">Max = 7.86ε (Mean = 1.69ε)</span> | |
10101 | </p> | |
10102 | </td> | |
10103 | <td> | |
10104 | <p> | |
10105 | <span class="blue">Max = 9.15ε (Mean = 2.25ε)</span> | |
10106 | </p> | |
10107 | </td> | |
10108 | </tr> | |
10109 | <tr> | |
10110 | <td> | |
10111 | <p> | |
10112 | Non Central T (large parameters) | |
10113 | </p> | |
10114 | </td> | |
10115 | <td> | |
10116 | <p> | |
10117 | <span class="blue">Max = 286ε (Mean = 62.8ε)</span> | |
10118 | </p> | |
10119 | </td> | |
10120 | <td> | |
10121 | <p> | |
10122 | <span class="blue">Max = 257ε (Mean = 72.1ε)</span><br> <br> | |
10123 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 2.46ε (Mean = 0.657ε)) | |
10124 | </p> | |
10125 | </td> | |
10126 | <td> | |
10127 | <p> | |
10128 | <span class="blue">Max = 5.26e+05ε (Mean = 1.48e+05ε)</span> | |
10129 | </p> | |
10130 | </td> | |
10131 | <td> | |
10132 | <p> | |
10133 | <span class="blue">Max = 5.24e+05ε (Mean = 1.47e+05ε)</span> | |
10134 | </p> | |
10135 | </td> | |
10136 | </tr> | |
10137 | </tbody> | |
10138 | </table></div> | |
10139 | </div> | |
10140 | <br class="table-break"><div class="table"> | |
10141 | <a name="math_toolkit.logs_and_tables.all_table.table_non_central_t_CDF_complement"></a><p class="title"><b>Table 17.78. Error rates for non central t CDF complement</b></p> | |
10142 | <div class="table-contents"><table class="table" summary="Error rates for non central t CDF complement"> | |
10143 | <colgroup> | |
10144 | <col> | |
10145 | <col> | |
10146 | <col> | |
10147 | <col> | |
10148 | <col> | |
10149 | </colgroup> | |
10150 | <thead><tr> | |
10151 | <th> | |
10152 | </th> | |
10153 | <th> | |
10154 | <p> | |
10155 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
10156 | </p> | |
10157 | </th> | |
10158 | <th> | |
10159 | <p> | |
10160 | GNU C++ version 5.1.0<br> linux<br> double | |
10161 | </p> | |
10162 | </th> | |
10163 | <th> | |
10164 | <p> | |
10165 | GNU C++ version 5.1.0<br> linux<br> long double | |
10166 | </p> | |
10167 | </th> | |
10168 | <th> | |
10169 | <p> | |
10170 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
10171 | </p> | |
10172 | </th> | |
10173 | </tr></thead> | |
10174 | <tbody> | |
10175 | <tr> | |
10176 | <td> | |
10177 | <p> | |
10178 | Non Central T | |
10179 | </p> | |
10180 | </td> | |
10181 | <td> | |
10182 | <p> | |
10183 | <span class="blue">Max = 150ε (Mean = 32.3ε)</span> | |
10184 | </p> | |
10185 | </td> | |
10186 | <td> | |
10187 | <p> | |
10188 | <span class="blue">Max = 0.707ε (Mean = 0.0497ε)</span><br> | |
10189 | <br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max | |
10190 | = 6.19e+15ε (Mean = 6.72e+14ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_t_CDF_complement_Rmath_3_0_2_Non_Central_T">And | |
10191 | other failures.</a>)</span> | |
10192 | </p> | |
10193 | </td> | |
10194 | <td> | |
10195 | <p> | |
10196 | <span class="blue">Max = 203ε (Mean = 31.8ε)</span> | |
10197 | </p> | |
10198 | </td> | |
10199 | <td> | |
10200 | <p> | |
10201 | <span class="blue">Max = 340ε (Mean = 43.6ε)</span> | |
10202 | </p> | |
10203 | </td> | |
10204 | </tr> | |
10205 | <tr> | |
10206 | <td> | |
10207 | <p> | |
10208 | Non Central T (small non-centrality) | |
10209 | </p> | |
10210 | </td> | |
10211 | <td> | |
10212 | <p> | |
10213 | <span class="blue">Max = 5.21ε (Mean = 1.43ε)</span> | |
10214 | </p> | |
10215 | </td> | |
10216 | <td> | |
10217 | <p> | |
10218 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath | |
10219 | 3.0.2:</em></span> Max = 1.87e+03ε (Mean = 263ε)) | |
10220 | </p> | |
10221 | </td> | |
10222 | <td> | |
10223 | <p> | |
10224 | <span class="blue">Max = 7.48ε (Mean = 1.86ε)</span> | |
10225 | </p> | |
10226 | </td> | |
10227 | <td> | |
10228 | <p> | |
10229 | <span class="blue">Max = 10.9ε (Mean = 2.43ε)</span> | |
10230 | </p> | |
10231 | </td> | |
10232 | </tr> | |
10233 | <tr> | |
10234 | <td> | |
10235 | <p> | |
10236 | Non Central T (large parameters) | |
10237 | </p> | |
10238 | </td> | |
10239 | <td> | |
10240 | <p> | |
10241 | <span class="blue">Max = 227ε (Mean = 50.4ε)</span> | |
10242 | </p> | |
10243 | </td> | |
10244 | <td> | |
10245 | <p> | |
10246 | <span class="blue">Max = 478ε (Mean = 96.3ε)</span><br> <br> | |
10247 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 2.24ε (Mean = 0.945ε)) | |
10248 | </p> | |
10249 | </td> | |
10250 | <td> | |
10251 | <p> | |
10252 | <span class="blue">Max = 9.79e+05ε (Mean = 1.97e+05ε)</span> | |
10253 | </p> | |
10254 | </td> | |
10255 | <td> | |
10256 | <p> | |
10257 | <span class="blue">Max = 9.79e+05ε (Mean = 1.97e+05ε)</span> | |
10258 | </p> | |
10259 | </td> | |
10260 | </tr> | |
10261 | </tbody> | |
10262 | </table></div> | |
10263 | </div> | |
10264 | <br class="table-break"><div class="table"> | |
10265 | <a name="math_toolkit.logs_and_tables.all_table.table_owens_t"></a><p class="title"><b>Table 17.79. Error rates for owens_t</b></p> | |
10266 | <div class="table-contents"><table class="table" summary="Error rates for owens_t"> | |
10267 | <colgroup> | |
10268 | <col> | |
10269 | <col> | |
10270 | <col> | |
10271 | <col> | |
10272 | <col> | |
10273 | </colgroup> | |
10274 | <thead><tr> | |
10275 | <th> | |
10276 | </th> | |
10277 | <th> | |
10278 | <p> | |
10279 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
10280 | </p> | |
10281 | </th> | |
10282 | <th> | |
10283 | <p> | |
10284 | GNU C++ version 5.1.0<br> linux<br> double | |
10285 | </p> | |
10286 | </th> | |
10287 | <th> | |
10288 | <p> | |
10289 | GNU C++ version 5.1.0<br> linux<br> long double | |
10290 | </p> | |
10291 | </th> | |
10292 | <th> | |
10293 | <p> | |
10294 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
10295 | </p> | |
10296 | </th> | |
10297 | </tr></thead> | |
10298 | <tbody> | |
10299 | <tr> | |
10300 | <td> | |
10301 | <p> | |
10302 | Owens T (medium small values) | |
10303 | </p> | |
10304 | </td> | |
10305 | <td> | |
10306 | <p> | |
10307 | <span class="blue">Max = 4.37ε (Mean = 0.973ε)</span> | |
10308 | </p> | |
10309 | </td> | |
10310 | <td> | |
10311 | <p> | |
10312 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
10313 | </p> | |
10314 | </td> | |
10315 | <td> | |
10316 | <p> | |
10317 | <span class="blue">Max = 3.34ε (Mean = 0.942ε)</span> | |
10318 | </p> | |
10319 | </td> | |
10320 | <td> | |
10321 | <p> | |
10322 | <span class="blue">Max = 3.34ε (Mean = 0.91ε)</span> | |
10323 | </p> | |
10324 | </td> | |
10325 | </tr> | |
10326 | <tr> | |
10327 | <td> | |
10328 | <p> | |
10329 | Owens T (large and diverse values) | |
10330 | </p> | |
10331 | </td> | |
10332 | <td> | |
10333 | <p> | |
10334 | <span class="blue">Max = 3.78ε (Mean = 0.621ε)</span> | |
10335 | </p> | |
10336 | </td> | |
10337 | <td> | |
10338 | <p> | |
10339 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
10340 | </p> | |
10341 | </td> | |
10342 | <td> | |
10343 | <p> | |
10344 | <span class="blue">Max = 49ε (Mean = 2.16ε)</span> | |
10345 | </p> | |
10346 | </td> | |
10347 | <td> | |
10348 | <p> | |
10349 | <span class="blue">Max = 24.5ε (Mean = 1.38ε)</span> | |
10350 | </p> | |
10351 | </td> | |
10352 | </tr> | |
10353 | </tbody> | |
10354 | </table></div> | |
10355 | </div> | |
10356 | <br class="table-break"><div class="table"> | |
10357 | <a name="math_toolkit.logs_and_tables.all_table.table_polygamma"></a><p class="title"><b>Table 17.80. Error rates for polygamma</b></p> | |
10358 | <div class="table-contents"><table class="table" summary="Error rates for polygamma"> | |
10359 | <colgroup> | |
10360 | <col> | |
10361 | <col> | |
10362 | <col> | |
10363 | <col> | |
10364 | <col> | |
10365 | </colgroup> | |
10366 | <thead><tr> | |
10367 | <th> | |
10368 | </th> | |
10369 | <th> | |
10370 | <p> | |
10371 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
10372 | </p> | |
10373 | </th> | |
10374 | <th> | |
10375 | <p> | |
10376 | GNU C++ version 5.1.0<br> linux<br> double | |
10377 | </p> | |
10378 | </th> | |
10379 | <th> | |
10380 | <p> | |
10381 | GNU C++ version 5.1.0<br> linux<br> long double | |
10382 | </p> | |
10383 | </th> | |
10384 | <th> | |
10385 | <p> | |
10386 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
10387 | </p> | |
10388 | </th> | |
10389 | </tr></thead> | |
10390 | <tbody> | |
10391 | <tr> | |
10392 | <td> | |
10393 | <p> | |
10394 | Mathematica Data | |
10395 | </p> | |
10396 | </td> | |
10397 | <td> | |
10398 | <p> | |
10399 | <span class="blue">Max = 6.34ε (Mean = 1.53ε)</span> | |
10400 | </p> | |
10401 | </td> | |
10402 | <td> | |
10403 | <p> | |
10404 | <span class="blue">Max = 0.824ε (Mean = 0.0574ε)</span><br> | |
10405 | <br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 108ε (Mean = 15.2ε))<br> | |
10406 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 62.9ε (Mean = 12.8ε)) | |
10407 | </p> | |
10408 | </td> | |
10409 | <td> | |
10410 | <p> | |
10411 | <span class="blue">Max = 7.38ε (Mean = 1.84ε)</span> | |
10412 | </p> | |
10413 | </td> | |
10414 | <td> | |
10415 | <p> | |
10416 | <span class="blue">Max = 18.3ε (Mean = 4.16ε)</span> | |
10417 | </p> | |
10418 | </td> | |
10419 | </tr> | |
10420 | <tr> | |
10421 | <td> | |
10422 | <p> | |
10423 | Mathematica Data - large arguments | |
10424 | </p> | |
10425 | </td> | |
10426 | <td> | |
10427 | <p> | |
10428 | <span class="blue">Max = 150ε (Mean = 15.1ε)</span> | |
10429 | </p> | |
10430 | </td> | |
10431 | <td> | |
10432 | <p> | |
10433 | <span class="blue">Max = 0.998ε (Mean = 0.0592ε)</span><br> | |
10434 | <br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max | |
10435 | = 1.71e+56ε (Mean = 1.01e+55ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_Rmath_3_0_2_Mathematica_Data_large_arguments">And | |
10436 | other failures.</a>)</span><br> (<span class="emphasis"><em>GSL 1.16:</em></span> | |
10437 | Max = 244ε (Mean = 32.8ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_GSL_1_16_Mathematica_Data_large_arguments">And | |
10438 | other failures.</a>) | |
10439 | </p> | |
10440 | </td> | |
10441 | <td> | |
10442 | <p> | |
10443 | <span class="blue">Max = 2.23ε (Mean = 0.323ε)</span> | |
10444 | </p> | |
10445 | </td> | |
10446 | <td> | |
10447 | <p> | |
10448 | <span class="blue">Max = 2.35ε (Mean = 0.34ε)</span> | |
10449 | </p> | |
10450 | </td> | |
10451 | </tr> | |
10452 | <tr> | |
10453 | <td> | |
10454 | <p> | |
10455 | Mathematica Data - negative arguments | |
10456 | </p> | |
10457 | </td> | |
10458 | <td> | |
10459 | <p> | |
10460 | <span class="blue">Max = 497ε (Mean = 129ε)</span> | |
10461 | </p> | |
10462 | </td> | |
10463 | <td> | |
10464 | <p> | |
10465 | <span class="blue">Max = 0.516ε (Mean = 0.022ε)</span><br> <br> | |
10466 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = +INFε (Mean | |
10467 | = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_Rmath_3_0_2_Mathematica_Data_negative_arguments">And | |
10468 | other failures.</a>)</span><br> (<span class="emphasis"><em>GSL 1.16:</em></span> | |
10469 | Max = 36.6ε (Mean = 3.04ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_GSL_1_16_Mathematica_Data_negative_arguments">And | |
10470 | other failures.</a>) | |
10471 | </p> | |
10472 | </td> | |
10473 | <td> | |
10474 | <p> | |
10475 | <span class="blue">Max = 269ε (Mean = 87.7ε)</span> | |
10476 | </p> | |
10477 | </td> | |
10478 | <td> | |
10479 | <p> | |
10480 | <span class="blue">Max = 269ε (Mean = 87.9ε)</span> | |
10481 | </p> | |
10482 | </td> | |
10483 | </tr> | |
10484 | <tr> | |
10485 | <td> | |
10486 | <p> | |
10487 | Mathematica Data - large negative arguments | |
10488 | </p> | |
10489 | </td> | |
10490 | <td> | |
10491 | <p> | |
10492 | <span class="blue">Max = 162ε (Mean = 101ε)</span> | |
10493 | </p> | |
10494 | </td> | |
10495 | <td> | |
10496 | <p> | |
10497 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath | |
10498 | 3.0.2:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_Rmath_3_0_2_Mathematica_Data_large_negative_arguments">And | |
10499 | other failures.</a>)</span><br> (<span class="emphasis"><em>GSL 1.16:</em></span> | |
10500 | Max = 1.79ε (Mean = 0.197ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_GSL_1_16_Mathematica_Data_large_negative_arguments">And | |
10501 | other failures.</a>) | |
10502 | </p> | |
10503 | </td> | |
10504 | <td> | |
10505 | <p> | |
10506 | <span class="blue">Max = 155ε (Mean = 96.4ε)</span> | |
10507 | </p> | |
10508 | </td> | |
10509 | <td> | |
10510 | <p> | |
10511 | <span class="blue">Max = 155ε (Mean = 96.4ε)</span> | |
10512 | </p> | |
10513 | </td> | |
10514 | </tr> | |
10515 | <tr> | |
10516 | <td> | |
10517 | <p> | |
10518 | Mathematica Data - small arguments | |
10519 | </p> | |
10520 | </td> | |
10521 | <td> | |
10522 | <p> | |
10523 | <span class="blue">Max = 3ε (Mean = 0.496ε)</span> | |
10524 | </p> | |
10525 | </td> | |
10526 | <td> | |
10527 | <p> | |
10528 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath | |
10529 | 3.0.2:</em></span> Max = 106ε (Mean = 20ε))<br> (<span class="emphasis"><em>GSL 1.16:</em></span> | |
10530 | Max = 15.2ε (Mean = 5.03ε)) | |
10531 | </p> | |
10532 | </td> | |
10533 | <td> | |
10534 | <p> | |
10535 | <span class="blue">Max = 3.33ε (Mean = 0.75ε)</span> | |
10536 | </p> | |
10537 | </td> | |
10538 | <td> | |
10539 | <p> | |
10540 | <span class="blue">Max = 3.33ε (Mean = 0.75ε)</span> | |
10541 | </p> | |
10542 | </td> | |
10543 | </tr> | |
10544 | <tr> | |
10545 | <td> | |
10546 | <p> | |
10547 | Mathematica Data - Large orders and other bug cases | |
10548 | </p> | |
10549 | </td> | |
10550 | <td> | |
10551 | <p> | |
10552 | <span class="blue">Max = 200ε (Mean = 57.2ε)</span> | |
10553 | </p> | |
10554 | </td> | |
10555 | <td> | |
10556 | <p> | |
10557 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath | |
10558 | 3.0.2:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_Rmath_3_0_2_Mathematica_Data_Large_orders_and_other_bug_cases">And | |
10559 | other failures.</a>)</span><br> (<span class="emphasis"><em>GSL 1.16:</em></span> | |
10560 | Max = 151ε (Mean = 39.3ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_GSL_1_16_Mathematica_Data_Large_orders_and_other_bug_cases">And | |
10561 | other failures.</a>) | |
10562 | </p> | |
10563 | </td> | |
10564 | <td> | |
10565 | <p> | |
10566 | <span class="blue">Max = 54.5ε (Mean = 13.3ε)</span> | |
10567 | </p> | |
10568 | </td> | |
10569 | <td> | |
10570 | <p> | |
10571 | <span class="blue">Max = 90.1ε (Mean = 30.6ε)</span> | |
10572 | </p> | |
10573 | </td> | |
10574 | </tr> | |
10575 | </tbody> | |
10576 | </table></div> | |
10577 | </div> | |
10578 | <br class="table-break"><div class="table"> | |
10579 | <a name="math_toolkit.logs_and_tables.all_table.table_powm1"></a><p class="title"><b>Table 17.81. Error rates for powm1</b></p> | |
10580 | <div class="table-contents"><table class="table" summary="Error rates for powm1"> | |
10581 | <colgroup> | |
10582 | <col> | |
10583 | <col> | |
10584 | <col> | |
10585 | <col> | |
10586 | <col> | |
10587 | </colgroup> | |
10588 | <thead><tr> | |
10589 | <th> | |
10590 | </th> | |
10591 | <th> | |
10592 | <p> | |
10593 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
10594 | </p> | |
10595 | </th> | |
10596 | <th> | |
10597 | <p> | |
10598 | GNU C++ version 5.1.0<br> linux<br> double | |
10599 | </p> | |
10600 | </th> | |
10601 | <th> | |
10602 | <p> | |
10603 | GNU C++ version 5.1.0<br> linux<br> long double | |
10604 | </p> | |
10605 | </th> | |
10606 | <th> | |
10607 | <p> | |
10608 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
10609 | </p> | |
10610 | </th> | |
10611 | </tr></thead> | |
10612 | <tbody><tr> | |
10613 | <td> | |
10614 | <p> | |
10615 | powm1 | |
10616 | </p> | |
10617 | </td> | |
10618 | <td> | |
10619 | <p> | |
10620 | <span class="blue">Max = 1.99ε (Mean = 0.461ε)</span> | |
10621 | </p> | |
10622 | </td> | |
10623 | <td> | |
10624 | <p> | |
10625 | <span class="blue">Max = 1.26ε (Mean = 0.428ε)</span> | |
10626 | </p> | |
10627 | </td> | |
10628 | <td> | |
10629 | <p> | |
10630 | <span class="blue">Max = 2.04ε (Mean = 0.521ε)</span> | |
10631 | </p> | |
10632 | </td> | |
10633 | <td> | |
10634 | <p> | |
10635 | <span class="blue">Max = 2.14ε (Mean = 0.498ε)</span> | |
10636 | </p> | |
10637 | </td> | |
10638 | </tr></tbody> | |
10639 | </table></div> | |
10640 | </div> | |
10641 | <br class="table-break"><div class="table"> | |
10642 | <a name="math_toolkit.logs_and_tables.all_table.table_sin_pi"></a><p class="title"><b>Table 17.82. Error rates for sin_pi</b></p> | |
10643 | <div class="table-contents"><table class="table" summary="Error rates for sin_pi"> | |
10644 | <colgroup> | |
10645 | <col> | |
10646 | <col> | |
10647 | <col> | |
10648 | <col> | |
10649 | <col> | |
10650 | </colgroup> | |
10651 | <thead><tr> | |
10652 | <th> | |
10653 | </th> | |
10654 | <th> | |
10655 | <p> | |
10656 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
10657 | </p> | |
10658 | </th> | |
10659 | <th> | |
10660 | <p> | |
10661 | GNU C++ version 5.1.0<br> linux<br> double | |
10662 | </p> | |
10663 | </th> | |
10664 | <th> | |
10665 | <p> | |
10666 | GNU C++ version 5.1.0<br> linux<br> long double | |
10667 | </p> | |
10668 | </th> | |
10669 | <th> | |
10670 | <p> | |
10671 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
10672 | </p> | |
10673 | </th> | |
10674 | </tr></thead> | |
10675 | <tbody> | |
10676 | <tr> | |
10677 | <td> | |
10678 | <p> | |
10679 | sin_pi and cos_pi | |
10680 | </p> | |
10681 | </td> | |
10682 | <td> | |
10683 | <p> | |
10684 | <span class="blue">Max = 0.99ε (Mean = 0.328ε)</span> | |
10685 | </p> | |
10686 | </td> | |
10687 | <td> | |
10688 | <p> | |
10689 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
10690 | </p> | |
10691 | </td> | |
10692 | <td> | |
10693 | <p> | |
10694 | <span class="blue">Max = 0.996ε (Mean = 0.335ε)</span> | |
10695 | </p> | |
10696 | </td> | |
10697 | <td> | |
10698 | <p> | |
10699 | <span class="blue">Max = 0.996ε (Mean = 0.336ε)</span> | |
10700 | </p> | |
10701 | </td> | |
10702 | </tr> | |
10703 | <tr> | |
10704 | <td> | |
10705 | <p> | |
10706 | sin_pi and cos_pi near integers and half integers | |
10707 | </p> | |
10708 | </td> | |
10709 | <td> | |
10710 | <p> | |
10711 | <span class="blue">Max = 0.996ε (Mean = 0.343ε)</span> | |
10712 | </p> | |
10713 | </td> | |
10714 | <td> | |
10715 | <p> | |
10716 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
10717 | </p> | |
10718 | </td> | |
10719 | <td> | |
10720 | <p> | |
10721 | <span class="blue">Max = 0.976ε (Mean = 0.293ε)</span> | |
10722 | </p> | |
10723 | </td> | |
10724 | <td> | |
10725 | <p> | |
10726 | <span class="blue">Max = 0.976ε (Mean = 0.293ε)</span> | |
10727 | </p> | |
10728 | </td> | |
10729 | </tr> | |
10730 | </tbody> | |
10731 | </table></div> | |
10732 | </div> | |
10733 | <br class="table-break"><div class="table"> | |
10734 | <a name="math_toolkit.logs_and_tables.all_table.table_sph_bessel"></a><p class="title"><b>Table 17.83. Error rates for sph_bessel</b></p> | |
10735 | <div class="table-contents"><table class="table" summary="Error rates for sph_bessel"> | |
10736 | <colgroup> | |
10737 | <col> | |
10738 | <col> | |
10739 | <col> | |
10740 | <col> | |
10741 | <col> | |
10742 | </colgroup> | |
10743 | <thead><tr> | |
10744 | <th> | |
10745 | </th> | |
10746 | <th> | |
10747 | <p> | |
10748 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
10749 | </p> | |
10750 | </th> | |
10751 | <th> | |
10752 | <p> | |
10753 | GNU C++ version 5.1.0<br> linux<br> long double | |
10754 | </p> | |
10755 | </th> | |
10756 | <th> | |
10757 | <p> | |
10758 | GNU C++ version 5.1.0<br> linux<br> double | |
10759 | </p> | |
10760 | </th> | |
10761 | <th> | |
10762 | <p> | |
10763 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
10764 | </p> | |
10765 | </th> | |
10766 | </tr></thead> | |
10767 | <tbody><tr> | |
10768 | <td> | |
10769 | <p> | |
10770 | Bessel j: Random Data | |
10771 | </p> | |
10772 | </td> | |
10773 | <td> | |
10774 | <p> | |
10775 | <span class="blue">Max = 245ε (Mean = 16.3ε)</span> | |
10776 | </p> | |
10777 | </td> | |
10778 | <td> | |
10779 | <p> | |
10780 | <span class="blue">Max = 243ε (Mean = 13.3ε)</span><br> <br> | |
10781 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.91e+06ε (Mean = | |
10782 | 1.09e+05ε)) | |
10783 | </p> | |
10784 | </td> | |
10785 | <td> | |
10786 | <p> | |
10787 | <span class="blue">Max = 0.978ε (Mean = 0.0539ε)</span><br> | |
10788 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.79e+03ε (Mean = 107ε)) | |
10789 | </p> | |
10790 | </td> | |
10791 | <td> | |
10792 | <p> | |
10793 | <span class="blue">Max = 243ε (Mean = 33.7ε)</span> | |
10794 | </p> | |
10795 | </td> | |
10796 | </tr></tbody> | |
10797 | </table></div> | |
10798 | </div> | |
10799 | <br class="table-break"><div class="table"> | |
10800 | <a name="math_toolkit.logs_and_tables.all_table.table_sph_bessel_prime"></a><p class="title"><b>Table 17.84. Error rates for sph_bessel_prime</b></p> | |
10801 | <div class="table-contents"><table class="table" summary="Error rates for sph_bessel_prime"> | |
10802 | <colgroup> | |
10803 | <col> | |
10804 | <col> | |
10805 | <col> | |
10806 | <col> | |
10807 | <col> | |
10808 | </colgroup> | |
10809 | <thead><tr> | |
10810 | <th> | |
10811 | </th> | |
10812 | <th> | |
10813 | <p> | |
10814 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
10815 | </p> | |
10816 | </th> | |
10817 | <th> | |
10818 | <p> | |
10819 | GNU C++ version 5.1.0<br> linux<br> double | |
10820 | </p> | |
10821 | </th> | |
10822 | <th> | |
10823 | <p> | |
10824 | GNU C++ version 5.1.0<br> linux<br> long double | |
10825 | </p> | |
10826 | </th> | |
10827 | <th> | |
10828 | <p> | |
10829 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
10830 | </p> | |
10831 | </th> | |
10832 | </tr></thead> | |
10833 | <tbody><tr> | |
10834 | <td> | |
10835 | <p> | |
10836 | Bessel j': Random Data | |
10837 | </p> | |
10838 | </td> | |
10839 | <td> | |
10840 | <p> | |
10841 | <span class="blue">Max = 307ε (Mean = 25.2ε)</span> | |
10842 | </p> | |
10843 | </td> | |
10844 | <td> | |
10845 | <p> | |
10846 | <span class="blue">Max = 0.753ε (Mean = 0.0343ε)</span> | |
10847 | </p> | |
10848 | </td> | |
10849 | <td> | |
10850 | <p> | |
10851 | <span class="blue">Max = 167ε (Mean = 12ε)</span> | |
10852 | </p> | |
10853 | </td> | |
10854 | <td> | |
10855 | <p> | |
10856 | <span class="blue">Max = 167ε (Mean = 33.2ε)</span> | |
10857 | </p> | |
10858 | </td> | |
10859 | </tr></tbody> | |
10860 | </table></div> | |
10861 | </div> | |
10862 | <br class="table-break"><div class="table"> | |
10863 | <a name="math_toolkit.logs_and_tables.all_table.table_sph_neumann"></a><p class="title"><b>Table 17.85. Error rates for sph_neumann</b></p> | |
10864 | <div class="table-contents"><table class="table" summary="Error rates for sph_neumann"> | |
10865 | <colgroup> | |
10866 | <col> | |
10867 | <col> | |
10868 | <col> | |
10869 | <col> | |
10870 | <col> | |
10871 | </colgroup> | |
10872 | <thead><tr> | |
10873 | <th> | |
10874 | </th> | |
10875 | <th> | |
10876 | <p> | |
10877 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
10878 | </p> | |
10879 | </th> | |
10880 | <th> | |
10881 | <p> | |
10882 | GNU C++ version 5.1.0<br> linux<br> double | |
10883 | </p> | |
10884 | </th> | |
10885 | <th> | |
10886 | <p> | |
10887 | GNU C++ version 5.1.0<br> linux<br> long double | |
10888 | </p> | |
10889 | </th> | |
10890 | <th> | |
10891 | <p> | |
10892 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
10893 | </p> | |
10894 | </th> | |
10895 | </tr></thead> | |
10896 | <tbody><tr> | |
10897 | <td> | |
10898 | <p> | |
10899 | y: Random Data | |
10900 | </p> | |
10901 | </td> | |
10902 | <td> | |
10903 | <p> | |
10904 | <span class="blue">Max = 281ε (Mean = 31.1ε)</span> | |
10905 | </p> | |
10906 | </td> | |
10907 | <td> | |
10908 | <p> | |
10909 | <span class="blue">Max = 0.995ε (Mean = 0.0665ε)</span><br> | |
10910 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 8.5e+04ε (Mean = 5.33e+03ε)) | |
10911 | </p> | |
10912 | </td> | |
10913 | <td> | |
10914 | <p> | |
10915 | <span class="blue">Max = 234ε (Mean = 19.5ε)</span><br> <br> | |
10916 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.6e+06ε (Mean = 1.4e+05ε)) | |
10917 | </p> | |
10918 | </td> | |
10919 | <td> | |
10920 | <p> | |
10921 | <span class="blue">Max = 234ε (Mean = 19.8ε)</span> | |
10922 | </p> | |
10923 | </td> | |
10924 | </tr></tbody> | |
10925 | </table></div> | |
10926 | </div> | |
10927 | <br class="table-break"><div class="table"> | |
10928 | <a name="math_toolkit.logs_and_tables.all_table.table_sph_neumann_prime"></a><p class="title"><b>Table 17.86. Error rates for sph_neumann_prime</b></p> | |
10929 | <div class="table-contents"><table class="table" summary="Error rates for sph_neumann_prime"> | |
10930 | <colgroup> | |
10931 | <col> | |
10932 | <col> | |
10933 | <col> | |
10934 | <col> | |
10935 | <col> | |
10936 | </colgroup> | |
10937 | <thead><tr> | |
10938 | <th> | |
10939 | </th> | |
10940 | <th> | |
10941 | <p> | |
10942 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
10943 | </p> | |
10944 | </th> | |
10945 | <th> | |
10946 | <p> | |
10947 | GNU C++ version 5.1.0<br> linux<br> double | |
10948 | </p> | |
10949 | </th> | |
10950 | <th> | |
10951 | <p> | |
10952 | GNU C++ version 5.1.0<br> linux<br> long double | |
10953 | </p> | |
10954 | </th> | |
10955 | <th> | |
10956 | <p> | |
10957 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
10958 | </p> | |
10959 | </th> | |
10960 | </tr></thead> | |
10961 | <tbody><tr> | |
10962 | <td> | |
10963 | <p> | |
10964 | y': Random Data | |
10965 | </p> | |
10966 | </td> | |
10967 | <td> | |
10968 | <p> | |
10969 | <span class="blue">Max = 296ε (Mean = 25.6ε)</span> | |
10970 | </p> | |
10971 | </td> | |
10972 | <td> | |
10973 | <p> | |
10974 | <span class="blue">Max = 0.752ε (Mean = 0.062ε)</span> | |
10975 | </p> | |
10976 | </td> | |
10977 | <td> | |
10978 | <p> | |
10979 | <span class="blue">Max = 158ε (Mean = 18.8ε)</span> | |
10980 | </p> | |
10981 | </td> | |
10982 | <td> | |
10983 | <p> | |
10984 | <span class="blue">Max = 158ε (Mean = 20.2ε)</span> | |
10985 | </p> | |
10986 | </td> | |
10987 | </tr></tbody> | |
10988 | </table></div> | |
10989 | </div> | |
10990 | <br class="table-break"><div class="table"> | |
10991 | <a name="math_toolkit.logs_and_tables.all_table.table_spherical_harmonic_i"></a><p class="title"><b>Table 17.87. Error rates for spherical_harmonic_i</b></p> | |
10992 | <div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_i"> | |
10993 | <colgroup> | |
10994 | <col> | |
10995 | <col> | |
10996 | <col> | |
10997 | <col> | |
10998 | <col> | |
10999 | </colgroup> | |
11000 | <thead><tr> | |
11001 | <th> | |
11002 | </th> | |
11003 | <th> | |
11004 | <p> | |
11005 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
11006 | </p> | |
11007 | </th> | |
11008 | <th> | |
11009 | <p> | |
11010 | GNU C++ version 5.1.0<br> linux<br> double | |
11011 | </p> | |
11012 | </th> | |
11013 | <th> | |
11014 | <p> | |
11015 | GNU C++ version 5.1.0<br> linux<br> long double | |
11016 | </p> | |
11017 | </th> | |
11018 | <th> | |
11019 | <p> | |
11020 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
11021 | </p> | |
11022 | </th> | |
11023 | </tr></thead> | |
11024 | <tbody><tr> | |
11025 | <td> | |
11026 | <p> | |
11027 | Spherical Harmonics | |
11028 | </p> | |
11029 | </td> | |
11030 | <td> | |
11031 | <p> | |
11032 | <span class="blue">Max = 2.27e+004ε (Mean = 725ε)</span> | |
11033 | </p> | |
11034 | </td> | |
11035 | <td> | |
11036 | <p> | |
11037 | <span class="blue">Max = 1.36ε (Mean = 0.0765ε)</span> | |
11038 | </p> | |
11039 | </td> | |
11040 | <td> | |
11041 | <p> | |
11042 | <span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span> | |
11043 | </p> | |
11044 | </td> | |
11045 | <td> | |
11046 | <p> | |
11047 | <span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span> | |
11048 | </p> | |
11049 | </td> | |
11050 | </tr></tbody> | |
11051 | </table></div> | |
11052 | </div> | |
11053 | <br class="table-break"><div class="table"> | |
11054 | <a name="math_toolkit.logs_and_tables.all_table.table_spherical_harmonic_r"></a><p class="title"><b>Table 17.88. Error rates for spherical_harmonic_r</b></p> | |
11055 | <div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_r"> | |
11056 | <colgroup> | |
11057 | <col> | |
11058 | <col> | |
11059 | <col> | |
11060 | <col> | |
11061 | <col> | |
11062 | </colgroup> | |
11063 | <thead><tr> | |
11064 | <th> | |
11065 | </th> | |
11066 | <th> | |
11067 | <p> | |
11068 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
11069 | </p> | |
11070 | </th> | |
11071 | <th> | |
11072 | <p> | |
11073 | GNU C++ version 5.1.0<br> linux<br> double | |
11074 | </p> | |
11075 | </th> | |
11076 | <th> | |
11077 | <p> | |
11078 | GNU C++ version 5.1.0<br> linux<br> long double | |
11079 | </p> | |
11080 | </th> | |
11081 | <th> | |
11082 | <p> | |
11083 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
11084 | </p> | |
11085 | </th> | |
11086 | </tr></thead> | |
11087 | <tbody><tr> | |
11088 | <td> | |
11089 | <p> | |
11090 | Spherical Harmonics | |
11091 | </p> | |
11092 | </td> | |
11093 | <td> | |
11094 | <p> | |
11095 | <span class="blue">Max = 2.27e+004ε (Mean = 725ε)</span> | |
11096 | </p> | |
11097 | </td> | |
11098 | <td> | |
11099 | <p> | |
11100 | <span class="blue">Max = 1.58ε (Mean = 0.0707ε)</span> | |
11101 | </p> | |
11102 | </td> | |
11103 | <td> | |
11104 | <p> | |
11105 | <span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span> | |
11106 | </p> | |
11107 | </td> | |
11108 | <td> | |
11109 | <p> | |
11110 | <span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span> | |
11111 | </p> | |
11112 | </td> | |
11113 | </tr></tbody> | |
11114 | </table></div> | |
11115 | </div> | |
11116 | <br class="table-break"><div class="table"> | |
11117 | <a name="math_toolkit.logs_and_tables.all_table.table_sqrt1pm1"></a><p class="title"><b>Table 17.89. Error rates for sqrt1pm1</b></p> | |
11118 | <div class="table-contents"><table class="table" summary="Error rates for sqrt1pm1"> | |
11119 | <colgroup> | |
11120 | <col> | |
11121 | <col> | |
11122 | <col> | |
11123 | <col> | |
11124 | <col> | |
11125 | </colgroup> | |
11126 | <thead><tr> | |
11127 | <th> | |
11128 | </th> | |
11129 | <th> | |
11130 | <p> | |
11131 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
11132 | </p> | |
11133 | </th> | |
11134 | <th> | |
11135 | <p> | |
11136 | GNU C++ version 5.1.0<br> linux<br> double | |
11137 | </p> | |
11138 | </th> | |
11139 | <th> | |
11140 | <p> | |
11141 | GNU C++ version 5.1.0<br> linux<br> long double | |
11142 | </p> | |
11143 | </th> | |
11144 | <th> | |
11145 | <p> | |
11146 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
11147 | </p> | |
11148 | </th> | |
11149 | </tr></thead> | |
11150 | <tbody><tr> | |
11151 | <td> | |
11152 | <p> | |
11153 | sqrt1pm1 | |
11154 | </p> | |
11155 | </td> | |
11156 | <td> | |
11157 | <p> | |
11158 | <span class="blue">Max = 1.36ε (Mean = 0.44ε)</span> | |
11159 | </p> | |
11160 | </td> | |
11161 | <td> | |
11162 | <p> | |
11163 | <span class="blue">Max = 1.3ε (Mean = 0.404ε)</span> | |
11164 | </p> | |
11165 | </td> | |
11166 | <td> | |
11167 | <p> | |
11168 | <span class="blue">Max = 1.33ε (Mean = 0.409ε)</span> | |
11169 | </p> | |
11170 | </td> | |
11171 | <td> | |
11172 | <p> | |
11173 | <span class="blue">Max = 1.54ε (Mean = 0.568ε)</span> | |
11174 | </p> | |
11175 | </td> | |
11176 | </tr></tbody> | |
11177 | </table></div> | |
11178 | </div> | |
11179 | <br class="table-break"><div class="table"> | |
11180 | <a name="math_toolkit.logs_and_tables.all_table.table_tgamma"></a><p class="title"><b>Table 17.90. Error rates for tgamma</b></p> | |
11181 | <div class="table-contents"><table class="table" summary="Error rates for tgamma"> | |
11182 | <colgroup> | |
11183 | <col> | |
11184 | <col> | |
11185 | <col> | |
11186 | <col> | |
11187 | <col> | |
11188 | </colgroup> | |
11189 | <thead><tr> | |
11190 | <th> | |
11191 | </th> | |
11192 | <th> | |
11193 | <p> | |
11194 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
11195 | </p> | |
11196 | </th> | |
11197 | <th> | |
11198 | <p> | |
11199 | GNU C++ version 5.1.0<br> linux<br> double | |
11200 | </p> | |
11201 | </th> | |
11202 | <th> | |
11203 | <p> | |
11204 | GNU C++ version 5.1.0<br> linux<br> long double | |
11205 | </p> | |
11206 | </th> | |
11207 | <th> | |
11208 | <p> | |
11209 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
11210 | </p> | |
11211 | </th> | |
11212 | </tr></thead> | |
11213 | <tbody> | |
11214 | <tr> | |
11215 | <td> | |
11216 | <p> | |
11217 | factorials | |
11218 | </p> | |
11219 | </td> | |
11220 | <td> | |
11221 | <p> | |
11222 | <span class="blue">Max = 1.85ε (Mean = 0.491ε)</span><br> <br> | |
11223 | (<span class="emphasis"><em><math.h>:</em></span> Max = 3.17ε (Mean = 0.928ε)) | |
11224 | </p> | |
11225 | </td> | |
11226 | <td> | |
11227 | <p> | |
11228 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
11229 | 1.16:</em></span> Max = 3.95ε (Mean = 0.783ε))<br> (<span class="emphasis"><em>Rmath | |
11230 | 3.0.2:</em></span> Max = 314ε (Mean = 93.4ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
11231 | Max = 3.19ε (Mean = 0.884ε)) | |
11232 | </p> | |
11233 | </td> | |
11234 | <td> | |
11235 | <p> | |
11236 | <span class="blue">Max = 1.96ε (Mean = 0.483ε)</span><br> <br> | |
11237 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.66ε (Mean = 0.584ε))<br> | |
11238 | (<span class="emphasis"><em><math.h>:</em></span> Max = 1.66ε (Mean = 0.584ε)) | |
11239 | </p> | |
11240 | </td> | |
11241 | <td> | |
11242 | <p> | |
11243 | <span class="blue">Max = 172ε (Mean = 41ε)</span><br> <br> | |
11244 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε)) | |
11245 | </p> | |
11246 | </td> | |
11247 | </tr> | |
11248 | <tr> | |
11249 | <td> | |
11250 | <p> | |
11251 | near 0 | |
11252 | </p> | |
11253 | </td> | |
11254 | <td> | |
11255 | <p> | |
11256 | <span class="blue">Max = 1.96ε (Mean = 0.684ε)</span><br> <br> | |
11257 | (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.405ε)) | |
11258 | </p> | |
11259 | </td> | |
11260 | <td> | |
11261 | <p> | |
11262 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
11263 | 1.16:</em></span> Max = 4.51ε (Mean = 1.92ε))<br> (<span class="emphasis"><em>Rmath | |
11264 | 3.0.2:</em></span> Max = 1ε (Mean = 0.335ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
11265 | Max = 1ε (Mean = 0.548ε)) | |
11266 | </p> | |
11267 | </td> | |
11268 | <td> | |
11269 | <p> | |
11270 | <span class="blue">Max = 2ε (Mean = 0.73ε)</span><br> <br> | |
11271 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1ε (Mean = 0.376ε))<br> | |
11272 | (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.376ε)) | |
11273 | </p> | |
11274 | </td> | |
11275 | <td> | |
11276 | <p> | |
11277 | <span class="blue">Max = 2ε (Mean = 0.647ε)</span><br> <br> | |
11278 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0.5ε (Mean = 0.0791ε)) | |
11279 | </p> | |
11280 | </td> | |
11281 | </tr> | |
11282 | <tr> | |
11283 | <td> | |
11284 | <p> | |
11285 | near 1 | |
11286 | </p> | |
11287 | </td> | |
11288 | <td> | |
11289 | <p> | |
11290 | <span class="blue">Max = 2ε (Mean = 0.865ε)</span><br> <br> | |
11291 | (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.4ε)) | |
11292 | </p> | |
11293 | </td> | |
11294 | <td> | |
11295 | <p> | |
11296 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
11297 | 1.16:</em></span> Max = 4.41ε (Mean = 1.81ε))<br> (<span class="emphasis"><em>Rmath | |
11298 | 3.0.2:</em></span> Max = 1ε (Mean = 0.32ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
11299 | Max = 1ε (Mean = 0.518ε)) | |
11300 | </p> | |
11301 | </td> | |
11302 | <td> | |
11303 | <p> | |
11304 | <span class="blue">Max = 2ε (Mean = 0.85ε)</span><br> <br> | |
11305 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 0.918ε (Mean = 0.203ε))<br> | |
11306 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0.918ε (Mean = 0.203ε)) | |
11307 | </p> | |
11308 | </td> | |
11309 | <td> | |
11310 | <p> | |
11311 | <span class="blue">Max = 3.01ε (Mean = 1.06ε)</span><br> <br> | |
11312 | (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.175ε)) | |
11313 | </p> | |
11314 | </td> | |
11315 | </tr> | |
11316 | <tr> | |
11317 | <td> | |
11318 | <p> | |
11319 | near 2 | |
11320 | </p> | |
11321 | </td> | |
11322 | <td> | |
11323 | <p> | |
11324 | <span class="blue">Max = 2ε (Mean = 0.995ε)</span><br> <br> | |
11325 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε)) | |
11326 | </p> | |
11327 | </td> | |
11328 | <td> | |
11329 | <p> | |
11330 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
11331 | 1.16:</em></span> Max = 7.95ε (Mean = 3.12ε))<br> (<span class="emphasis"><em>Rmath | |
11332 | 3.0.2:</em></span> Max = 1ε (Mean = 0.191ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
11333 | Max = 1.09ε (Mean = 0.502ε)) | |
11334 | </p> | |
11335 | </td> | |
11336 | <td> | |
11337 | <p> | |
11338 | <span class="blue">Max = 2ε (Mean = 0.913ε)</span><br> <br> | |
11339 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 0.558ε (Mean = 0.298ε))<br> | |
11340 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0.558ε (Mean = 0.298ε)) | |
11341 | </p> | |
11342 | </td> | |
11343 | <td> | |
11344 | <p> | |
11345 | <span class="blue">Max = 5.01ε (Mean = 1.89ε)</span><br> <br> | |
11346 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε)) | |
11347 | </p> | |
11348 | </td> | |
11349 | </tr> | |
11350 | <tr> | |
11351 | <td> | |
11352 | <p> | |
11353 | near -10 | |
11354 | </p> | |
11355 | </td> | |
11356 | <td> | |
11357 | <p> | |
11358 | <span class="blue">Max = 1.73ε (Mean = 0.729ε)</span><br> <br> | |
11359 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0.866ε (Mean = 0.445ε)) | |
11360 | </p> | |
11361 | </td> | |
11362 | <td> | |
11363 | <p> | |
11364 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
11365 | 1.16:</em></span> Max = 2.6ε (Mean = 1.05ε))<br> (<span class="emphasis"><em>Rmath | |
11366 | 3.0.2:</em></span> Max = 6.34e+05ε (Mean = 1.2e+05ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
11367 | Max = 2.6ε (Mean = 0.956ε)) | |
11368 | </p> | |
11369 | </td> | |
11370 | <td> | |
11371 | <p> | |
11372 | <span class="blue">Max = 2.6ε (Mean = 0.985ε)</span><br> <br> | |
11373 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.26ε (Mean = 1.08ε))<br> | |
11374 | (<span class="emphasis"><em><math.h>:</em></span> Max = 2.26ε (Mean = 1.08ε)) | |
11375 | </p> | |
11376 | </td> | |
11377 | <td> | |
11378 | <p> | |
11379 | <span class="blue">Max = 1.75ε (Mean = 0.819ε)</span><br> <br> | |
11380 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε)) | |
11381 | </p> | |
11382 | </td> | |
11383 | </tr> | |
11384 | <tr> | |
11385 | <td> | |
11386 | <p> | |
11387 | near -55 | |
11388 | </p> | |
11389 | </td> | |
11390 | <td> | |
11391 | <p> | |
11392 | <span class="blue">Max = 1.8ε (Mean = 0.817ε)</span><br> <br> | |
11393 | (<span class="emphasis"><em><math.h>:</em></span> Max = 3.87e+004ε (Mean = 6.71e+003ε)) | |
11394 | </p> | |
11395 | </td> | |
11396 | <td> | |
11397 | <p> | |
11398 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
11399 | 1.16:</em></span> Max = 1.8ε (Mean = 0.782ε))<br> (<span class="emphasis"><em>Rmath | |
11400 | 3.0.2:</em></span> Max = 6.36e+06ε (Mean = 1.13e+06ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
11401 | Max = 2.7ε (Mean = 0.988ε)) | |
11402 | </p> | |
11403 | </td> | |
11404 | <td> | |
11405 | <p> | |
11406 | <span class="blue">Max = 1.8ε (Mean = 0.847ε)</span><br> <br> | |
11407 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.79ε (Mean = 0.75ε))<br> | |
11408 | (<span class="emphasis"><em><math.h>:</em></span> Max = 1.79ε (Mean = 0.75ε)) | |
11409 | </p> | |
11410 | </td> | |
11411 | <td> | |
11412 | <p> | |
11413 | <span class="blue">Max = 98.5ε (Mean = 53.4ε)</span><br> <br> | |
11414 | (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε)) | |
11415 | </p> | |
11416 | </td> | |
11417 | </tr> | |
11418 | </tbody> | |
11419 | </table></div> | |
11420 | </div> | |
11421 | <br class="table-break"><div class="table"> | |
11422 | <a name="math_toolkit.logs_and_tables.all_table.table_tgamma1pm1"></a><p class="title"><b>Table 17.91. Error rates for tgamma1pm1</b></p> | |
11423 | <div class="table-contents"><table class="table" summary="Error rates for tgamma1pm1"> | |
11424 | <colgroup> | |
11425 | <col> | |
11426 | <col> | |
11427 | <col> | |
11428 | <col> | |
11429 | <col> | |
11430 | </colgroup> | |
11431 | <thead><tr> | |
11432 | <th> | |
11433 | </th> | |
11434 | <th> | |
11435 | <p> | |
11436 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
11437 | </p> | |
11438 | </th> | |
11439 | <th> | |
11440 | <p> | |
11441 | GNU C++ version 5.1.0<br> linux<br> double | |
11442 | </p> | |
11443 | </th> | |
11444 | <th> | |
11445 | <p> | |
11446 | GNU C++ version 5.1.0<br> linux<br> long double | |
11447 | </p> | |
11448 | </th> | |
11449 | <th> | |
11450 | <p> | |
11451 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
11452 | </p> | |
11453 | </th> | |
11454 | </tr></thead> | |
11455 | <tbody><tr> | |
11456 | <td> | |
11457 | <p> | |
11458 | tgamma1pm1(dz) | |
11459 | </p> | |
11460 | </td> | |
11461 | <td> | |
11462 | <p> | |
11463 | <span class="blue">Max = 0.982ε (Mean = 0.399ε)</span> | |
11464 | </p> | |
11465 | </td> | |
11466 | <td> | |
11467 | <p> | |
11468 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
11469 | </p> | |
11470 | </td> | |
11471 | <td> | |
11472 | <p> | |
11473 | <span class="blue">Max = 1.12ε (Mean = 0.49ε)</span> | |
11474 | </p> | |
11475 | </td> | |
11476 | <td> | |
11477 | <p> | |
11478 | <span class="blue">Max = 3.97ε (Mean = 0.713ε)</span> | |
11479 | </p> | |
11480 | </td> | |
11481 | </tr></tbody> | |
11482 | </table></div> | |
11483 | </div> | |
11484 | <br class="table-break"><div class="table"> | |
11485 | <a name="math_toolkit.logs_and_tables.all_table.table_tgamma_delta_ratio"></a><p class="title"><b>Table 17.92. Error rates for tgamma_delta_ratio</b></p> | |
11486 | <div class="table-contents"><table class="table" summary="Error rates for tgamma_delta_ratio"> | |
11487 | <colgroup> | |
11488 | <col> | |
11489 | <col> | |
11490 | <col> | |
11491 | <col> | |
11492 | <col> | |
11493 | </colgroup> | |
11494 | <thead><tr> | |
11495 | <th> | |
11496 | </th> | |
11497 | <th> | |
11498 | <p> | |
11499 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
11500 | </p> | |
11501 | </th> | |
11502 | <th> | |
11503 | <p> | |
11504 | GNU C++ version 5.1.0<br> linux<br> double | |
11505 | </p> | |
11506 | </th> | |
11507 | <th> | |
11508 | <p> | |
11509 | GNU C++ version 5.1.0<br> linux<br> long double | |
11510 | </p> | |
11511 | </th> | |
11512 | <th> | |
11513 | <p> | |
11514 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
11515 | </p> | |
11516 | </th> | |
11517 | </tr></thead> | |
11518 | <tbody> | |
11519 | <tr> | |
11520 | <td> | |
11521 | <p> | |
11522 | tgamma + small delta ratios | |
11523 | </p> | |
11524 | </td> | |
11525 | <td> | |
11526 | <p> | |
11527 | <span class="blue">Max = 10.1ε (Mean = 1.25ε)</span> | |
11528 | </p> | |
11529 | </td> | |
11530 | <td> | |
11531 | <p> | |
11532 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
11533 | </p> | |
11534 | </td> | |
11535 | <td> | |
11536 | <p> | |
11537 | <span class="blue">Max = 5.56ε (Mean = 0.969ε)</span> | |
11538 | </p> | |
11539 | </td> | |
11540 | <td> | |
11541 | <p> | |
11542 | <span class="blue">Max = 15.4ε (Mean = 2.09ε)</span> | |
11543 | </p> | |
11544 | </td> | |
11545 | </tr> | |
11546 | <tr> | |
11547 | <td> | |
11548 | <p> | |
11549 | tgamma + small delta ratios (negative delta) | |
11550 | </p> | |
11551 | </td> | |
11552 | <td> | |
11553 | <p> | |
11554 | <span class="blue">Max = 8.04ε (Mean = 1.31ε)</span> | |
11555 | </p> | |
11556 | </td> | |
11557 | <td> | |
11558 | <p> | |
11559 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
11560 | </p> | |
11561 | </td> | |
11562 | <td> | |
11563 | <p> | |
11564 | <span class="blue">Max = 8.67ε (Mean = 1.29ε)</span> | |
11565 | </p> | |
11566 | </td> | |
11567 | <td> | |
11568 | <p> | |
11569 | <span class="blue">Max = 18.3ε (Mean = 2.03ε)</span> | |
11570 | </p> | |
11571 | </td> | |
11572 | </tr> | |
11573 | <tr> | |
11574 | <td> | |
11575 | <p> | |
11576 | tgamma + small integer ratios | |
11577 | </p> | |
11578 | </td> | |
11579 | <td> | |
11580 | <p> | |
11581 | <span class="blue">Max = 2.74ε (Mean = 0.736ε)</span> | |
11582 | </p> | |
11583 | </td> | |
11584 | <td> | |
11585 | <p> | |
11586 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
11587 | </p> | |
11588 | </td> | |
11589 | <td> | |
11590 | <p> | |
11591 | <span class="blue">Max = 1.96ε (Mean = 0.677ε)</span> | |
11592 | </p> | |
11593 | </td> | |
11594 | <td> | |
11595 | <p> | |
11596 | <span class="blue">Max = 1.96ε (Mean = 0.677ε)</span> | |
11597 | </p> | |
11598 | </td> | |
11599 | </tr> | |
11600 | <tr> | |
11601 | <td> | |
11602 | <p> | |
11603 | tgamma + small integer ratios (negative delta) | |
11604 | </p> | |
11605 | </td> | |
11606 | <td> | |
11607 | <p> | |
11608 | <span class="blue">Max = 2.15ε (Mean = 0.685ε)</span> | |
11609 | </p> | |
11610 | </td> | |
11611 | <td> | |
11612 | <p> | |
11613 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
11614 | </p> | |
11615 | </td> | |
11616 | <td> | |
11617 | <p> | |
11618 | <span class="blue">Max = 1.62ε (Mean = 0.451ε)</span> | |
11619 | </p> | |
11620 | </td> | |
11621 | <td> | |
11622 | <p> | |
11623 | <span class="blue">Max = 1.62ε (Mean = 0.451ε)</span> | |
11624 | </p> | |
11625 | </td> | |
11626 | </tr> | |
11627 | <tr> | |
11628 | <td> | |
11629 | <p> | |
11630 | integer tgamma ratios | |
11631 | </p> | |
11632 | </td> | |
11633 | <td> | |
11634 | <p> | |
11635 | <span class="blue">Max = 0.968ε (Mean = 0.386ε)</span> | |
11636 | </p> | |
11637 | </td> | |
11638 | <td> | |
11639 | <p> | |
11640 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
11641 | </p> | |
11642 | </td> | |
11643 | <td> | |
11644 | <p> | |
11645 | <span class="blue">Max = 0.997ε (Mean = 0.4ε)</span> | |
11646 | </p> | |
11647 | </td> | |
11648 | <td> | |
11649 | <p> | |
11650 | <span class="blue">Max = 0.997ε (Mean = 0.4ε)</span> | |
11651 | </p> | |
11652 | </td> | |
11653 | </tr> | |
11654 | <tr> | |
11655 | <td> | |
11656 | <p> | |
11657 | integer tgamma ratios (negative delta) | |
11658 | </p> | |
11659 | </td> | |
11660 | <td> | |
11661 | <p> | |
11662 | <span class="blue">Max = 0.974ε (Mean = 0.184ε)</span> | |
11663 | </p> | |
11664 | </td> | |
11665 | <td> | |
11666 | <p> | |
11667 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
11668 | </p> | |
11669 | </td> | |
11670 | <td> | |
11671 | <p> | |
11672 | <span class="blue">Max = 0.853ε (Mean = 0.176ε)</span> | |
11673 | </p> | |
11674 | </td> | |
11675 | <td> | |
11676 | <p> | |
11677 | <span class="blue">Max = 0.853ε (Mean = 0.176ε)</span> | |
11678 | </p> | |
11679 | </td> | |
11680 | </tr> | |
11681 | </tbody> | |
11682 | </table></div> | |
11683 | </div> | |
11684 | <br class="table-break"><div class="table"> | |
11685 | <a name="math_toolkit.logs_and_tables.all_table.table_tgamma_incomplete_"></a><p class="title"><b>Table 17.93. Error rates for tgamma (incomplete)</b></p> | |
11686 | <div class="table-contents"><table class="table" summary="Error rates for tgamma (incomplete)"> | |
11687 | <colgroup> | |
11688 | <col> | |
11689 | <col> | |
11690 | <col> | |
11691 | <col> | |
11692 | <col> | |
11693 | </colgroup> | |
11694 | <thead><tr> | |
11695 | <th> | |
11696 | </th> | |
11697 | <th> | |
11698 | <p> | |
11699 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
11700 | </p> | |
11701 | </th> | |
11702 | <th> | |
11703 | <p> | |
11704 | GNU C++ version 5.1.0<br> linux<br> double | |
11705 | </p> | |
11706 | </th> | |
11707 | <th> | |
11708 | <p> | |
11709 | GNU C++ version 5.1.0<br> linux<br> long double | |
11710 | </p> | |
11711 | </th> | |
11712 | <th> | |
11713 | <p> | |
11714 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
11715 | </p> | |
11716 | </th> | |
11717 | </tr></thead> | |
11718 | <tbody> | |
11719 | <tr> | |
11720 | <td> | |
11721 | <p> | |
11722 | tgamma(a, z) medium values | |
11723 | </p> | |
11724 | </td> | |
11725 | <td> | |
11726 | <p> | |
11727 | <span class="blue">Max = 8.14ε (Mean = 1.71ε)</span> | |
11728 | </p> | |
11729 | </td> | |
11730 | <td> | |
11731 | <p> | |
11732 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
11733 | 1.16:</em></span> Max = 200ε (Mean = 13.3ε)) | |
11734 | </p> | |
11735 | </td> | |
11736 | <td> | |
11737 | <p> | |
11738 | <span class="blue">Max = 7.35ε (Mean = 1.69ε)</span> | |
11739 | </p> | |
11740 | </td> | |
11741 | <td> | |
11742 | <p> | |
11743 | <span class="blue">Max = 412ε (Mean = 95.5ε)</span> | |
11744 | </p> | |
11745 | </td> | |
11746 | </tr> | |
11747 | <tr> | |
11748 | <td> | |
11749 | <p> | |
11750 | tgamma(a, z) small values | |
11751 | </p> | |
11752 | </td> | |
11753 | <td> | |
11754 | <p> | |
11755 | <span class="blue">Max = 2.53ε (Mean = 0.66ε)</span> | |
11756 | </p> | |
11757 | </td> | |
11758 | <td> | |
11759 | <p> | |
11760 | <span class="blue">Max = 0.753ε (Mean = 0.0474ε)</span><br> | |
11761 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> <span class="red">Max = | |
11762 | 1.38e+10ε (Mean = 1.05e+09ε))</span> | |
11763 | </p> | |
11764 | </td> | |
11765 | <td> | |
11766 | <p> | |
11767 | <span class="blue">Max = 2.13ε (Mean = 0.717ε)</span> | |
11768 | </p> | |
11769 | </td> | |
11770 | <td> | |
11771 | <p> | |
11772 | <span class="blue">Max = 2.13ε (Mean = 0.712ε)</span> | |
11773 | </p> | |
11774 | </td> | |
11775 | </tr> | |
11776 | <tr> | |
11777 | <td> | |
11778 | <p> | |
11779 | tgamma(a, z) integer and half integer values | |
11780 | </p> | |
11781 | </td> | |
11782 | <td> | |
11783 | <p> | |
11784 | <span class="blue">Max = 5.16ε (Mean = 1.44ε)</span> | |
11785 | </p> | |
11786 | </td> | |
11787 | <td> | |
11788 | <p> | |
11789 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
11790 | 1.16:</em></span> Max = 117ε (Mean = 12.5ε)) | |
11791 | </p> | |
11792 | </td> | |
11793 | <td> | |
11794 | <p> | |
11795 | <span class="blue">Max = 5.52ε (Mean = 1.52ε)</span> | |
11796 | </p> | |
11797 | </td> | |
11798 | <td> | |
11799 | <p> | |
11800 | <span class="blue">Max = 79.6ε (Mean = 20.9ε)</span> | |
11801 | </p> | |
11802 | </td> | |
11803 | </tr> | |
11804 | </tbody> | |
11805 | </table></div> | |
11806 | </div> | |
11807 | <br class="table-break"><div class="table"> | |
11808 | <a name="math_toolkit.logs_and_tables.all_table.table_tgamma_lower"></a><p class="title"><b>Table 17.94. Error rates for tgamma_lower</b></p> | |
11809 | <div class="table-contents"><table class="table" summary="Error rates for tgamma_lower"> | |
11810 | <colgroup> | |
11811 | <col> | |
11812 | <col> | |
11813 | <col> | |
11814 | <col> | |
11815 | <col> | |
11816 | </colgroup> | |
11817 | <thead><tr> | |
11818 | <th> | |
11819 | </th> | |
11820 | <th> | |
11821 | <p> | |
11822 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
11823 | </p> | |
11824 | </th> | |
11825 | <th> | |
11826 | <p> | |
11827 | GNU C++ version 5.1.0<br> linux<br> double | |
11828 | </p> | |
11829 | </th> | |
11830 | <th> | |
11831 | <p> | |
11832 | GNU C++ version 5.1.0<br> linux<br> long double | |
11833 | </p> | |
11834 | </th> | |
11835 | <th> | |
11836 | <p> | |
11837 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
11838 | </p> | |
11839 | </th> | |
11840 | </tr></thead> | |
11841 | <tbody> | |
11842 | <tr> | |
11843 | <td> | |
11844 | <p> | |
11845 | tgamma(a, z) medium values | |
11846 | </p> | |
11847 | </td> | |
11848 | <td> | |
11849 | <p> | |
11850 | <span class="blue">Max = 5.62ε (Mean = 1.43ε)</span> | |
11851 | </p> | |
11852 | </td> | |
11853 | <td> | |
11854 | <p> | |
11855 | <span class="blue">Max = 0.833ε (Mean = 0.0315ε)</span><br> | |
11856 | <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0.833ε (Mean = 0.0315ε)) | |
11857 | </p> | |
11858 | </td> | |
11859 | <td> | |
11860 | <p> | |
11861 | <span class="blue">Max = 6.79ε (Mean = 1.38ε)</span> | |
11862 | </p> | |
11863 | </td> | |
11864 | <td> | |
11865 | <p> | |
11866 | <span class="blue">Max = 363ε (Mean = 63.8ε)</span> | |
11867 | </p> | |
11868 | </td> | |
11869 | </tr> | |
11870 | <tr> | |
11871 | <td> | |
11872 | <p> | |
11873 | tgamma(a, z) small values | |
11874 | </p> | |
11875 | </td> | |
11876 | <td> | |
11877 | <p> | |
11878 | <span class="blue">Max = 1.57ε (Mean = 0.527ε)</span> | |
11879 | </p> | |
11880 | </td> | |
11881 | <td> | |
11882 | <p> | |
11883 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
11884 | 1.16:</em></span> Max = 0ε (Mean = 0ε)) | |
11885 | </p> | |
11886 | </td> | |
11887 | <td> | |
11888 | <p> | |
11889 | <span class="blue">Max = 1.97ε (Mean = 0.552ε)</span> | |
11890 | </p> | |
11891 | </td> | |
11892 | <td> | |
11893 | <p> | |
11894 | <span class="blue">Max = 1.97ε (Mean = 0.567ε)</span> | |
11895 | </p> | |
11896 | </td> | |
11897 | </tr> | |
11898 | <tr> | |
11899 | <td> | |
11900 | <p> | |
11901 | tgamma(a, z) integer and half integer values | |
11902 | </p> | |
11903 | </td> | |
11904 | <td> | |
11905 | <p> | |
11906 | <span class="blue">Max = 2.69ε (Mean = 0.866ε)</span> | |
11907 | </p> | |
11908 | </td> | |
11909 | <td> | |
11910 | <p> | |
11911 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
11912 | 1.16:</em></span> Max = 0ε (Mean = 0ε)) | |
11913 | </p> | |
11914 | </td> | |
11915 | <td> | |
11916 | <p> | |
11917 | <span class="blue">Max = 4.83ε (Mean = 1.12ε)</span> | |
11918 | </p> | |
11919 | </td> | |
11920 | <td> | |
11921 | <p> | |
11922 | <span class="blue">Max = 84.7ε (Mean = 17.5ε)</span> | |
11923 | </p> | |
11924 | </td> | |
11925 | </tr> | |
11926 | </tbody> | |
11927 | </table></div> | |
11928 | </div> | |
11929 | <br class="table-break"><div class="table"> | |
11930 | <a name="math_toolkit.logs_and_tables.all_table.table_tgamma_ratio"></a><p class="title"><b>Table 17.95. Error rates for tgamma_ratio</b></p> | |
11931 | <div class="table-contents"><table class="table" summary="Error rates for tgamma_ratio"> | |
11932 | <colgroup> | |
11933 | <col> | |
11934 | <col> | |
11935 | <col> | |
11936 | <col> | |
11937 | <col> | |
11938 | </colgroup> | |
11939 | <thead><tr> | |
11940 | <th> | |
11941 | </th> | |
11942 | <th> | |
11943 | <p> | |
11944 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
11945 | </p> | |
11946 | </th> | |
11947 | <th> | |
11948 | <p> | |
11949 | GNU C++ version 5.1.0<br> linux<br> double | |
11950 | </p> | |
11951 | </th> | |
11952 | <th> | |
11953 | <p> | |
11954 | GNU C++ version 5.1.0<br> linux<br> long double | |
11955 | </p> | |
11956 | </th> | |
11957 | <th> | |
11958 | <p> | |
11959 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
11960 | </p> | |
11961 | </th> | |
11962 | </tr></thead> | |
11963 | <tbody><tr> | |
11964 | <td> | |
11965 | <p> | |
11966 | tgamma ratios | |
11967 | </p> | |
11968 | </td> | |
11969 | <td> | |
11970 | <p> | |
11971 | <span class="blue">Max = 3.66ε (Mean = 1.27ε)</span> | |
11972 | </p> | |
11973 | </td> | |
11974 | <td> | |
11975 | <p> | |
11976 | <span class="blue">Max = 0ε (Mean = 0ε)</span> | |
11977 | </p> | |
11978 | </td> | |
11979 | <td> | |
11980 | <p> | |
11981 | <span class="blue">Max = 3.09ε (Mean = 1.15ε)</span> | |
11982 | </p> | |
11983 | </td> | |
11984 | <td> | |
11985 | <p> | |
11986 | <span class="blue">Max = 174ε (Mean = 61.2ε)</span> | |
11987 | </p> | |
11988 | </td> | |
11989 | </tr></tbody> | |
11990 | </table></div> | |
11991 | </div> | |
11992 | <br class="table-break"><div class="table"> | |
11993 | <a name="math_toolkit.logs_and_tables.all_table.table_trigamma"></a><p class="title"><b>Table 17.96. Error rates for trigamma</b></p> | |
11994 | <div class="table-contents"><table class="table" summary="Error rates for trigamma"> | |
11995 | <colgroup> | |
11996 | <col> | |
11997 | <col> | |
11998 | <col> | |
11999 | <col> | |
12000 | <col> | |
12001 | </colgroup> | |
12002 | <thead><tr> | |
12003 | <th> | |
12004 | </th> | |
12005 | <th> | |
12006 | <p> | |
12007 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
12008 | </p> | |
12009 | </th> | |
12010 | <th> | |
12011 | <p> | |
12012 | GNU C++ version 5.1.0<br> linux<br> double | |
12013 | </p> | |
12014 | </th> | |
12015 | <th> | |
12016 | <p> | |
12017 | GNU C++ version 5.1.0<br> linux<br> long double | |
12018 | </p> | |
12019 | </th> | |
12020 | <th> | |
12021 | <p> | |
12022 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
12023 | </p> | |
12024 | </th> | |
12025 | </tr></thead> | |
12026 | <tbody><tr> | |
12027 | <td> | |
12028 | <p> | |
12029 | Mathematica Data | |
12030 | </p> | |
12031 | </td> | |
12032 | <td> | |
12033 | <p> | |
12034 | <span class="blue">Max = 1ε (Mean = 0.382ε)</span> | |
12035 | </p> | |
12036 | </td> | |
12037 | <td> | |
12038 | <p> | |
12039 | <span class="blue">Max = 0.998ε (Mean = 0.105ε)</span><br> <br> | |
12040 | (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 1.34e+04ε (Mean = 1.51e+03ε))<br> | |
12041 | (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.34e+04ε (Mean = 1.49e+03ε)) | |
12042 | </p> | |
12043 | </td> | |
12044 | <td> | |
12045 | <p> | |
12046 | <span class="blue">Max = 1.28ε (Mean = 0.449ε)</span> | |
12047 | </p> | |
12048 | </td> | |
12049 | <td> | |
12050 | <p> | |
12051 | <span class="blue">Max = 1.28ε (Mean = 0.447ε)</span> | |
12052 | </p> | |
12053 | </td> | |
12054 | </tr></tbody> | |
12055 | </table></div> | |
12056 | </div> | |
12057 | <br class="table-break"><div class="table"> | |
12058 | <a name="math_toolkit.logs_and_tables.all_table.table_zeta"></a><p class="title"><b>Table 17.97. Error rates for zeta</b></p> | |
12059 | <div class="table-contents"><table class="table" summary="Error rates for zeta"> | |
12060 | <colgroup> | |
12061 | <col> | |
12062 | <col> | |
12063 | <col> | |
12064 | <col> | |
12065 | <col> | |
12066 | </colgroup> | |
12067 | <thead><tr> | |
12068 | <th> | |
12069 | </th> | |
12070 | <th> | |
12071 | <p> | |
12072 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
12073 | </p> | |
12074 | </th> | |
12075 | <th> | |
12076 | <p> | |
12077 | GNU C++ version 5.1.0<br> linux<br> double | |
12078 | </p> | |
12079 | </th> | |
12080 | <th> | |
12081 | <p> | |
12082 | GNU C++ version 5.1.0<br> linux<br> long double | |
12083 | </p> | |
12084 | </th> | |
12085 | <th> | |
12086 | <p> | |
12087 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
12088 | </p> | |
12089 | </th> | |
12090 | </tr></thead> | |
12091 | <tbody> | |
12092 | <tr> | |
12093 | <td> | |
12094 | <p> | |
12095 | Zeta: Random values greater than 1 | |
12096 | </p> | |
12097 | </td> | |
12098 | <td> | |
12099 | <p> | |
12100 | <span class="blue">Max = 0.836ε (Mean = 0.093ε)</span> | |
12101 | </p> | |
12102 | </td> | |
12103 | <td> | |
12104 | <p> | |
12105 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
12106 | 1.16:</em></span> Max = 8.69ε (Mean = 1.03ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
12107 | <span class="red">Max = 4.49e+33ε (Mean = 6.85e+32ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_zeta_Cephes_Zeta_Random_values_greater_than_1">And | |
12108 | other failures.</a>)</span> | |
12109 | </p> | |
12110 | </td> | |
12111 | <td> | |
12112 | <p> | |
12113 | <span class="blue">Max = 0.846ε (Mean = 0.0833ε)</span><br> | |
12114 | <br> (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 5.45ε (Mean | |
12115 | = 1ε)) | |
12116 | </p> | |
12117 | </td> | |
12118 | <td> | |
12119 | <p> | |
12120 | <span class="blue">Max = 0.846ε (Mean = 0.0743ε)</span> | |
12121 | </p> | |
12122 | </td> | |
12123 | </tr> | |
12124 | <tr> | |
12125 | <td> | |
12126 | <p> | |
12127 | Zeta: Random values less than 1 | |
12128 | </p> | |
12129 | </td> | |
12130 | <td> | |
12131 | <p> | |
12132 | <span class="blue">Max = 7.03ε (Mean = 2.98ε)</span> | |
12133 | </p> | |
12134 | </td> | |
12135 | <td> | |
12136 | <p> | |
12137 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
12138 | 1.16:</em></span> Max = 137ε (Mean = 13.8ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
12139 | <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_zeta_Cephes_Zeta_Random_values_less_than_1">And | |
12140 | other failures.</a>)</span> | |
12141 | </p> | |
12142 | </td> | |
12143 | <td> | |
12144 | <p> | |
12145 | <span class="blue">Max = 7.03ε (Mean = 2.71ε)</span><br> <br> | |
12146 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 538ε (Mean = 59.3ε)) | |
12147 | </p> | |
12148 | </td> | |
12149 | <td> | |
12150 | <p> | |
12151 | <span class="blue">Max = 70.1ε (Mean = 17.1ε)</span> | |
12152 | </p> | |
12153 | </td> | |
12154 | </tr> | |
12155 | <tr> | |
12156 | <td> | |
12157 | <p> | |
12158 | Zeta: Values close to and greater than 1 | |
12159 | </p> | |
12160 | </td> | |
12161 | <td> | |
12162 | <p> | |
12163 | <span class="blue">Max = 0.994ε (Mean = 0.421ε)</span> | |
12164 | </p> | |
12165 | </td> | |
12166 | <td> | |
12167 | <p> | |
12168 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
12169 | 1.16:</em></span> Max = 7.73ε (Mean = 4.07ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
12170 | <span class="red">Max = 6.77e+15ε (Mean = 1.52e+15ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_zeta_Cephes_Zeta_Values_close_to_and_greater_than_1">And | |
12171 | other failures.</a>)</span> | |
12172 | </p> | |
12173 | </td> | |
12174 | <td> | |
12175 | <p> | |
12176 | <span class="blue">Max = 0.995ε (Mean = 0.5ε)</span><br> <br> | |
12177 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.9e+06ε (Mean = 5.11e+05ε)) | |
12178 | </p> | |
12179 | </td> | |
12180 | <td> | |
12181 | <p> | |
12182 | <span class="blue">Max = 0.995ε (Mean = 0.5ε)</span> | |
12183 | </p> | |
12184 | </td> | |
12185 | </tr> | |
12186 | <tr> | |
12187 | <td> | |
12188 | <p> | |
12189 | Zeta: Values close to and less than 1 | |
12190 | </p> | |
12191 | </td> | |
12192 | <td> | |
12193 | <p> | |
12194 | <span class="blue">Max = 0.991ε (Mean = 0.375ε)</span> | |
12195 | </p> | |
12196 | </td> | |
12197 | <td> | |
12198 | <p> | |
12199 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
12200 | 1.16:</em></span> Max = 0.991ε (Mean = 0.28ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
12201 | <span class="red">Max = 8.66e+15ε (Mean = 1.9e+15ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_zeta_Cephes_Zeta_Values_close_to_and_less_than_1">And | |
12202 | other failures.</a>)</span> | |
12203 | </p> | |
12204 | </td> | |
12205 | <td> | |
12206 | <p> | |
12207 | <span class="blue">Max = 0.998ε (Mean = 0.508ε)</span><br> <br> | |
12208 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 8.53e+06ε (Mean = | |
12209 | 1.87e+06ε)) | |
12210 | </p> | |
12211 | </td> | |
12212 | <td> | |
12213 | <p> | |
12214 | <span class="blue">Max = 0.998ε (Mean = 0.568ε)</span> | |
12215 | </p> | |
12216 | </td> | |
12217 | </tr> | |
12218 | <tr> | |
12219 | <td> | |
12220 | <p> | |
12221 | Zeta: Integer arguments | |
12222 | </p> | |
12223 | </td> | |
12224 | <td> | |
12225 | <p> | |
12226 | <span class="blue">Max = 6.5ε (Mean = 2.17ε)</span> | |
12227 | </p> | |
12228 | </td> | |
12229 | <td> | |
12230 | <p> | |
12231 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL | |
12232 | 1.16:</em></span> Max = 3.75ε (Mean = 1.1ε))<br> (<span class="emphasis"><em>Cephes:</em></span> | |
12233 | <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_zeta_Cephes_Zeta_Integer_arguments">And | |
12234 | other failures.</a>)</span> | |
12235 | </p> | |
12236 | </td> | |
12237 | <td> | |
12238 | <p> | |
12239 | <span class="blue">Max = 9ε (Mean = 3.06ε)</span><br> <br> | |
12240 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 70.3ε (Mean = 17.4ε)) | |
12241 | </p> | |
12242 | </td> | |
12243 | <td> | |
12244 | <p> | |
12245 | <span class="blue">Max = 21ε (Mean = 7.13ε)</span> | |
12246 | </p> | |
12247 | </td> | |
12248 | </tr> | |
12249 | </tbody> | |
12250 | </table></div> | |
12251 | </div> | |
12252 | <br class="table-break"> | |
12253 | </div> | |
12254 | <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> | |
12255 | <td align="left"></td> | |
12256 | <td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal, | |
12257 | Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert | |
12258 | Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani, | |
12259 | Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p> | |
12260 | Distributed under the Boost Software License, Version 1.0. (See accompanying | |
12261 | file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) | |
12262 | </p> | |
12263 | </div></td> | |
12264 | </tr></table> | |
12265 | <hr> | |
12266 | <div class="spirit-nav"> | |
12267 | <a accesskey="p" href="../logs_and_tables.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../logs_and_tables.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="logs.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> | |
12268 | </div> | |
12269 | </body> | |
12270 | </html> |