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24</div>
25<div class="section">
26<div class="titlepage"><div><div><h2 class="title" style="clear: both">
27<a name="math_toolkit.issues"></a><a class="link" href="issues.html" title="Known Issues, and TODO List">Known Issues, and TODO List</a>
28</h2></div></div></div>
29<p>
30 Predominantly this is a TODO list, or a list of possible future enhancements.
31 Items labled "High Priority" effect the proper functioning of the
32 component, and should be fixed as soon as possible. Items labled "Medium
33 Priority" are desirable enhancements, often pertaining to the performance
34 of the component, but do not effect it's accuracy or functionality. Items labled
35 "Low Priority" should probably be investigated at some point. Such
36 classifications are obviously highly subjective.
37 </p>
38<p>
39 If you don't see a component listed here, then we don't have any known issues
40 with it.
41 </p>
42<h5>
43<a name="math_toolkit.issues.h0"></a>
44 <span class="phrase"><a name="math_toolkit.issues.derivatives_of_bessel_functions_"></a></span><a class="link" href="issues.html#math_toolkit.issues.derivatives_of_bessel_functions_">Derivatives
45 of Bessel functions (and their zeros)</a>
46 </h5>
47<p>
48 Potentially, there could be native support for <code class="computeroutput"><span class="identifier">cyl_bessel_j_prime</span><span class="special">()</span></code> and <code class="computeroutput"><span class="identifier">cyl_neumann_prime</span><span class="special">()</span></code>. One could also imagine supporting the zeros
49 thereof, but they might be slower to calculate since root bracketing might
50 be needed instead of Newton iteration (for the lack of 2nd derivatives).
51 </p>
52<p>
53 Since Boost.Math's Bessel functions are so excellent, the quick way to <code class="computeroutput"><span class="identifier">cyl_bessel_j_prime</span><span class="special">()</span></code>
54 and <code class="computeroutput"><span class="identifier">cyl_neumann_prime</span><span class="special">()</span></code>
55 would be via relationship with <code class="computeroutput"><span class="identifier">cyl_bessel_j</span><span class="special">()</span></code> and <code class="computeroutput"><span class="identifier">cyl_neumann</span><span class="special">()</span></code>.
56 </p>
57<h5>
58<a name="math_toolkit.issues.h1"></a>
59 <span class="phrase"><a name="math_toolkit.issues.tgamma"></a></span><a class="link" href="issues.html#math_toolkit.issues.tgamma">tgamma</a>
60 </h5>
61<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
62 Can the <a class="link" href="lanczos.html" title="The Lanczos Approximation">Lanczos approximation</a>
63 be optimized any further? (low priority)
64 </li></ul></div>
65<h5>
66<a name="math_toolkit.issues.h2"></a>
67 <span class="phrase"><a name="math_toolkit.issues.incomplete_beta"></a></span><a class="link" href="issues.html#math_toolkit.issues.incomplete_beta">Incomplete
68 Beta</a>
69 </h5>
70<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
71 Investigate Didonato and Morris' asymptotic expansion for large a and b
72 (medium priority).
73 </li></ul></div>
74<h5>
75<a name="math_toolkit.issues.h3"></a>
76 <span class="phrase"><a name="math_toolkit.issues.inverse_gamma"></a></span><a class="link" href="issues.html#math_toolkit.issues.inverse_gamma">Inverse
77 Gamma</a>
78 </h5>
79<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
80 Investigate whether we can skip iteration altogether if the first approximation
81 is good enough (Medium Priority).
82 </li></ul></div>
83<h5>
84<a name="math_toolkit.issues.h4"></a>
85 <span class="phrase"><a name="math_toolkit.issues.polynomials"></a></span><a class="link" href="issues.html#math_toolkit.issues.polynomials">Polynomials</a>
86 </h5>
87<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
88 The Legendre and Laguerre Polynomials have surprisingly different error
89 rates on different platforms, considering they are evaluated with only
90 basic arithmetic operations. Maybe this is telling us something, or maybe
91 not (Low Priority).
92 </li></ul></div>
93<h5>
94<a name="math_toolkit.issues.h5"></a>
95 <span class="phrase"><a name="math_toolkit.issues.elliptic_integrals"></a></span><a class="link" href="issues.html#math_toolkit.issues.elliptic_integrals">Elliptic
96 Integrals</a>
97 </h5>
98<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
99<li class="listitem">
100 [para Carlson's algorithms (mainly R<sub>J</sub>) are somewhat prone to internal overflow/underflow
101 when the arguments are very large or small. The homogeneity relations:]
102 [para R<sub>F</sub>(ka, kb, kc) = k<sup>-1/2</sup> R<sub>F</sub>(a, b, c)] [para and] [para R<sub>J</sub>(ka, kb, kc,
103 kr) = k<sup>-3/2</sup> R<sub>J</sub>(a, b, c, r)] [para could be used to sidestep trouble here:
104 provided the problem domains can be accurately identified. (Medium Priority).]
105 </li>
106<li class="listitem">
107 There are a several other integrals: Bulirsch's <span class="emphasis"><em>el</em></span>
108 functions that could be implemented using Carlson's integrals (Low Priority).
109 </li>
110<li class="listitem">
111 The integrals K(k) and E(k) could be implemented using rational approximations
112 (both for efficiency and accuracy), assuming we can find them. (Medium
113 Priority).
114 </li>
115</ul></div>
116<h5>
117<a name="math_toolkit.issues.h6"></a>
118 <span class="phrase"><a name="math_toolkit.issues.owen_s_t_function"></a></span><a class="link" href="issues.html#math_toolkit.issues.owen_s_t_function">Owen's
119 T Function</a>
120 </h5>
121<p>
122 There is a problem area at arbitrary precision when <span class="emphasis"><em>a</em></span>
123 is very close to 1. However, note that the value for <span class="emphasis"><em>T(h, 1)</em></span>
124 is well known and easy to compute, and if we replaced the <span class="emphasis"><em>a<sup>k</sup></em></span>
125 terms in series T1, T2 or T4 by <span class="emphasis"><em>(a<sup>k</sup> - 1)</em></span> then we would
126 have the difference between <span class="emphasis"><em>T(h, a)</em></span> and <span class="emphasis"><em>T(h,
127 1)</em></span>. Unfortunately this doesn't improve the convergence of those
128 series in that area. It certainly looks as though a new series in terms of
129 <span class="emphasis"><em>(1-a)<sup>k</sup></em></span> is both possible and desirable in this area, but
130 it remains elusive at present.
131 </p>
132<h5>
133<a name="math_toolkit.issues.h7"></a>
134 <span class="phrase"><a name="math_toolkit.issues.jocobi_elliptic_functions"></a></span><a class="link" href="issues.html#math_toolkit.issues.jocobi_elliptic_functions">Jocobi
135 elliptic functions</a>
136 </h5>
137<p>
138 These are useful in engineering applications - we have had a request to add
139 these.
140 </p>
141<h5>
142<a name="math_toolkit.issues.h8"></a>
143 <span class="phrase"><a name="math_toolkit.issues.statistical_distributions"></a></span><a class="link" href="issues.html#math_toolkit.issues.statistical_distributions">Statistical
144 distributions</a>
145 </h5>
146<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
147 Student's t Perhaps switch to normal distribution as a better approximation
148 for very large degrees of freedom?
149 </li></ul></div>
150<h5>
151<a name="math_toolkit.issues.h9"></a>
152 <span class="phrase"><a name="math_toolkit.issues.feature_requests"></a></span><a class="link" href="issues.html#math_toolkit.issues.feature_requests">Feature
153 Requests</a>
154 </h5>
155<p>
156 We have a request for the Lambert W function, see <a href="https://svn.boost.org/trac/boost/ticket/11027" target="_top">#11027</a>.
157 </p>
158<p>
159 The following table lists distributions that are found in other packages but
160 which are not yet present here, the more frequently the distribution is found,
161 the higher the priority for implementing it:
162 </p>
163<div class="informaltable"><table class="table">
164<colgroup>
165<col>
166<col>
167<col>
168<col>
169<col>
170<col>
171</colgroup>
172<thead><tr>
173<th>
174 <p>
175 Distribution
176 </p>
177 </th>
178<th>
179 <p>
180 R
181 </p>
182 </th>
183<th>
184 <p>
185 Mathematica 6
186 </p>
187 </th>
188<th>
189 <p>
190 NIST
191 </p>
192 </th>
193<th>
194 <p>
195 Regress+
196 </p>
197 </th>
198<th>
199 <p>
200 Matlab
201 </p>
202 </th>
203</tr></thead>
204<tbody>
205<tr>
206<td>
207 <p>
208 Geometric
209 </p>
210 </td>
211<td>
212 <p>
213 X
214 </p>
215 </td>
216<td>
217 <p>
218 X
219 </p>
220 </td>
221<td>
222 <p>
223 -
224 </p>
225 </td>
226<td>
227 <p>
228 -
229 </p>
230 </td>
231<td>
232 <p>
233 X
234 </p>
235 </td>
236</tr>
237<tr>
238<td>
239 <p>
240 Multinomial
241 </p>
242 </td>
243<td>
244 <p>
245 X
246 </p>
247 </td>
248<td>
249 <p>
250 -
251 </p>
252 </td>
253<td>
254 <p>
255 -
256 </p>
257 </td>
258<td>
259 <p>
260 -
261 </p>
262 </td>
263<td>
264 <p>
265 X
266 </p>
267 </td>
268</tr>
269<tr>
270<td>
271 <p>
272 Tukey Lambda
273 </p>
274 </td>
275<td>
276 <p>
277 X
278 </p>
279 </td>
280<td>
281 <p>
282 -
283 </p>
284 </td>
285<td>
286 <p>
287 X
288 </p>
289 </td>
290<td>
291 <p>
292 -
293 </p>
294 </td>
295<td>
296 <p>
297 -
298 </p>
299 </td>
300</tr>
301<tr>
302<td>
303 <p>
304 Half Normal / Folded Normal
305 </p>
306 </td>
307<td>
308 <p>
309 -
310 </p>
311 </td>
312<td>
313 <p>
314 X
315 </p>
316 </td>
317<td>
318 <p>
319 -
320 </p>
321 </td>
322<td>
323 <p>
324 X
325 </p>
326 </td>
327<td>
328 <p>
329 -
330 </p>
331 </td>
332</tr>
333<tr>
334<td>
335 <p>
336 Chi
337 </p>
338 </td>
339<td>
340 <p>
341 -
342 </p>
343 </td>
344<td>
345 <p>
346 X
347 </p>
348 </td>
349<td>
350 <p>
351 -
352 </p>
353 </td>
354<td>
355 <p>
356 X
357 </p>
358 </td>
359<td>
360 <p>
361 -
362 </p>
363 </td>
364</tr>
365<tr>
366<td>
367 <p>
368 Gumbel
369 </p>
370 </td>
371<td>
372 <p>
373 -
374 </p>
375 </td>
376<td>
377 <p>
378 X
379 </p>
380 </td>
381<td>
382 <p>
383 -
384 </p>
385 </td>
386<td>
387 <p>
388 X
389 </p>
390 </td>
391<td>
392 <p>
393 -
394 </p>
395 </td>
396</tr>
397<tr>
398<td>
399 <p>
400 Discrete Uniform
401 </p>
402 </td>
403<td>
404 <p>
405 -
406 </p>
407 </td>
408<td>
409 <p>
410 X
411 </p>
412 </td>
413<td>
414 <p>
415 -
416 </p>
417 </td>
418<td>
419 <p>
420 -
421 </p>
422 </td>
423<td>
424 <p>
425 X
426 </p>
427 </td>
428</tr>
429<tr>
430<td>
431 <p>
432 Log Series
433 </p>
434 </td>
435<td>
436 <p>
437 -
438 </p>
439 </td>
440<td>
441 <p>
442 X
443 </p>
444 </td>
445<td>
446 <p>
447 -
448 </p>
449 </td>
450<td>
451 <p>
452 X
453 </p>
454 </td>
455<td>
456 <p>
457 -
458 </p>
459 </td>
460</tr>
461<tr>
462<td>
463 <p>
464 Nakagami (generalised Chi)
465 </p>
466 </td>
467<td>
468 <p>
469 -
470 </p>
471 </td>
472<td>
473 <p>
474 -
475 </p>
476 </td>
477<td>
478 <p>
479 -
480 </p>
481 </td>
482<td>
483 <p>
484 X
485 </p>
486 </td>
487<td>
488 <p>
489 X
490 </p>
491 </td>
492</tr>
493<tr>
494<td>
495 <p>
496 Log Logistic
497 </p>
498 </td>
499<td>
500 <p>
501 -
502 </p>
503 </td>
504<td>
505 <p>
506 -
507 </p>
508 </td>
509<td>
510 <p>
511 -
512 </p>
513 </td>
514<td>
515 <p>
516 -
517 </p>
518 </td>
519<td>
520 <p>
521 X
522 </p>
523 </td>
524</tr>
525<tr>
526<td>
527 <p>
528 Tukey (Studentized range)
529 </p>
530 </td>
531<td>
532 <p>
533 X
534 </p>
535 </td>
536<td>
537 <p>
538 -
539 </p>
540 </td>
541<td>
542 <p>
543 -
544 </p>
545 </td>
546<td>
547 <p>
548 -
549 </p>
550 </td>
551<td>
552 <p>
553 -
554 </p>
555 </td>
556</tr>
557<tr>
558<td>
559 <p>
560 Wilcoxon rank sum
561 </p>
562 </td>
563<td>
564 <p>
565 X
566 </p>
567 </td>
568<td>
569 <p>
570 -
571 </p>
572 </td>
573<td>
574 <p>
575 -
576 </p>
577 </td>
578<td>
579 <p>
580 -
581 </p>
582 </td>
583<td>
584 <p>
585 -
586 </p>
587 </td>
588</tr>
589<tr>
590<td>
591 <p>
592 Wincoxon signed rank
593 </p>
594 </td>
595<td>
596 <p>
597 X
598 </p>
599 </td>
600<td>
601 <p>
602 -
603 </p>
604 </td>
605<td>
606 <p>
607 -
608 </p>
609 </td>
610<td>
611 <p>
612 -
613 </p>
614 </td>
615<td>
616 <p>
617 -
618 </p>
619 </td>
620</tr>
621<tr>
622<td>
623 <p>
624 Non-central Beta
625 </p>
626 </td>
627<td>
628 <p>
629 X
630 </p>
631 </td>
632<td>
633 <p>
634 -
635 </p>
636 </td>
637<td>
638 <p>
639 -
640 </p>
641 </td>
642<td>
643 <p>
644 -
645 </p>
646 </td>
647<td>
648 <p>
649 -
650 </p>
651 </td>
652</tr>
653<tr>
654<td>
655 <p>
656 Maxwell
657 </p>
658 </td>
659<td>
660 <p>
661 -
662 </p>
663 </td>
664<td>
665 <p>
666 X
667 </p>
668 </td>
669<td>
670 <p>
671 -
672 </p>
673 </td>
674<td>
675 <p>
676 -
677 </p>
678 </td>
679<td>
680 <p>
681 -
682 </p>
683 </td>
684</tr>
685<tr>
686<td>
687 <p>
688 Beta-Binomial
689 </p>
690 </td>
691<td>
692 <p>
693 -
694 </p>
695 </td>
696<td>
697 <p>
698 X
699 </p>
700 </td>
701<td>
702 <p>
703 -
704 </p>
705 </td>
706<td>
707 <p>
708 -
709 </p>
710 </td>
711<td>
712 <p>
713 -
714 </p>
715 </td>
716</tr>
717<tr>
718<td>
719 <p>
720 Beta-negative Binomial
721 </p>
722 </td>
723<td>
724 <p>
725 -
726 </p>
727 </td>
728<td>
729 <p>
730 X
731 </p>
732 </td>
733<td>
734 <p>
735 -
736 </p>
737 </td>
738<td>
739 <p>
740 -
741 </p>
742 </td>
743<td>
744 <p>
745 -
746 </p>
747 </td>
748</tr>
749<tr>
750<td>
751 <p>
752 Zipf
753 </p>
754 </td>
755<td>
756 <p>
757 -
758 </p>
759 </td>
760<td>
761 <p>
762 X
763 </p>
764 </td>
765<td>
766 <p>
767 -
768 </p>
769 </td>
770<td>
771 <p>
772 -
773 </p>
774 </td>
775<td>
776 <p>
777 -
778 </p>
779 </td>
780</tr>
781<tr>
782<td>
783 <p>
784 Birnbaum-Saunders / Fatigue Life
785 </p>
786 </td>
787<td>
788 <p>
789 -
790 </p>
791 </td>
792<td>
793 <p>
794 -
795 </p>
796 </td>
797<td>
798 <p>
799 X
800 </p>
801 </td>
802<td>
803 <p>
804 -
805 </p>
806 </td>
807<td>
808 <p>
809 -
810 </p>
811 </td>
812</tr>
813<tr>
814<td>
815 <p>
816 Double Exponential
817 </p>
818 </td>
819<td>
820 <p>
821 -
822 </p>
823 </td>
824<td>
825 <p>
826 -
827 </p>
828 </td>
829<td>
830 <p>
831 X
832 </p>
833 </td>
834<td>
835 <p>
836 -
837 </p>
838 </td>
839<td>
840 <p>
841 -
842 </p>
843 </td>
844</tr>
845<tr>
846<td>
847 <p>
848 Power Normal
849 </p>
850 </td>
851<td>
852 <p>
853 -
854 </p>
855 </td>
856<td>
857 <p>
858 -
859 </p>
860 </td>
861<td>
862 <p>
863 X
864 </p>
865 </td>
866<td>
867 <p>
868 -
869 </p>
870 </td>
871<td>
872 <p>
873 -
874 </p>
875 </td>
876</tr>
877<tr>
878<td>
879 <p>
880 Power Lognormal
881 </p>
882 </td>
883<td>
884 <p>
885 -
886 </p>
887 </td>
888<td>
889 <p>
890 -
891 </p>
892 </td>
893<td>
894 <p>
895 X
896 </p>
897 </td>
898<td>
899 <p>
900 -
901 </p>
902 </td>
903<td>
904 <p>
905 -
906 </p>
907 </td>
908</tr>
909<tr>
910<td>
911 <p>
912 Cosine
913 </p>
914 </td>
915<td>
916 <p>
917 -
918 </p>
919 </td>
920<td>
921 <p>
922 -
923 </p>
924 </td>
925<td>
926 <p>
927 -
928 </p>
929 </td>
930<td>
931 <p>
932 X
933 </p>
934 </td>
935<td>
936 <p>
937 -
938 </p>
939 </td>
940</tr>
941<tr>
942<td>
943 <p>
944 Double Gamma
945 </p>
946 </td>
947<td>
948 <p>
949 -
950 </p>
951 </td>
952<td>
953 <p>
954 -
955 </p>
956 </td>
957<td>
958 <p>
959 -
960 </p>
961 </td>
962<td>
963 <p>
964 X
965 </p>
966 </td>
967<td>
968 <p>
969 -
970 </p>
971 </td>
972</tr>
973<tr>
974<td>
975 <p>
976 Double Weibul
977 </p>
978 </td>
979<td>
980 <p>
981 -
982 </p>
983 </td>
984<td>
985 <p>
986 -
987 </p>
988 </td>
989<td>
990 <p>
991 -
992 </p>
993 </td>
994<td>
995 <p>
996 X
997 </p>
998 </td>
999<td>
1000 <p>
1001 -
1002 </p>
1003 </td>
1004</tr>
1005<tr>
1006<td>
1007 <p>
1008 Hyperbolic Secant
1009 </p>
1010 </td>
1011<td>
1012 <p>
1013 -
1014 </p>
1015 </td>
1016<td>
1017 <p>
1018 -
1019 </p>
1020 </td>
1021<td>
1022 <p>
1023 -
1024 </p>
1025 </td>
1026<td>
1027 <p>
1028 X
1029 </p>
1030 </td>
1031<td>
1032 <p>
1033 -
1034 </p>
1035 </td>
1036</tr>
1037<tr>
1038<td>
1039 <p>
1040 Semicircular
1041 </p>
1042 </td>
1043<td>
1044 <p>
1045 -
1046 </p>
1047 </td>
1048<td>
1049 <p>
1050 -
1051 </p>
1052 </td>
1053<td>
1054 <p>
1055 -
1056 </p>
1057 </td>
1058<td>
1059 <p>
1060 X
1061 </p>
1062 </td>
1063<td>
1064 <p>
1065 -
1066 </p>
1067 </td>
1068</tr>
1069<tr>
1070<td>
1071 <p>
1072 Bradford
1073 </p>
1074 </td>
1075<td>
1076 <p>
1077 -
1078 </p>
1079 </td>
1080<td>
1081 <p>
1082 -
1083 </p>
1084 </td>
1085<td>
1086 <p>
1087 -
1088 </p>
1089 </td>
1090<td>
1091 <p>
1092 X
1093 </p>
1094 </td>
1095<td>
1096 <p>
1097 -
1098 </p>
1099 </td>
1100</tr>
1101<tr>
1102<td>
1103 <p>
1104 Birr / Fisk
1105 </p>
1106 </td>
1107<td>
1108 <p>
1109 -
1110 </p>
1111 </td>
1112<td>
1113 <p>
1114 -
1115 </p>
1116 </td>
1117<td>
1118 <p>
1119 -
1120 </p>
1121 </td>
1122<td>
1123 <p>
1124 X
1125 </p>
1126 </td>
1127<td>
1128 <p>
1129 -
1130 </p>
1131 </td>
1132</tr>
1133<tr>
1134<td>
1135 <p>
1136 Reciprocal
1137 </p>
1138 </td>
1139<td>
1140 <p>
1141 -
1142 </p>
1143 </td>
1144<td>
1145 <p>
1146 -
1147 </p>
1148 </td>
1149<td>
1150 <p>
1151 -
1152 </p>
1153 </td>
1154<td>
1155 <p>
1156 X
1157 </p>
1158 </td>
1159<td>
1160 <p>
1161 -
1162 </p>
1163 </td>
1164</tr>
1165<tr>
1166<td>
1167 <p>
1168 Kolmogorov Distribution
1169 </p>
1170 </td>
1171<td>
1172 <p>
1173 -
1174 </p>
1175 </td>
1176<td>
1177 <p>
1178 -
1179 </p>
1180 </td>
1181<td>
1182 <p>
1183 -
1184 </p>
1185 </td>
1186<td>
1187 <p>
1188 -
1189 </p>
1190 </td>
1191<td>
1192 <p>
1193 -
1194 </p>
1195 </td>
1196</tr>
1197</tbody>
1198</table></div>
1199<p>
1200 Also asked for more than once:
1201 </p>
1202<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1203<li class="listitem">
1204 Add support for interpolated distributions, possibly combine with numeric
1205 integration and differentiation.
1206 </li>
1207<li class="listitem">
1208 Add support for bivariate and multivariate distributions: most especially
1209 the normal.
1210 </li>
1211<li class="listitem">
1212 Add support for the log of the cdf and pdf: this is mainly a performance
1213 optimisation since we can avoid some special function calls for some distributions
1214 by returning the log of the result.
1215 </li>
1216</ul></div>
1217</div>
1218<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
1219<td align="left"></td>
1220<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
1221 Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
1222 Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
1223 Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
1224 Distributed under the Boost Software License, Version 1.0. (See accompanying
1225 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>)
1226 </p>
1227</div></td>
1228</tr></table>
1229<hr>
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