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26 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
27 <a name="math_toolkit.comp_compilers"></a><a class="link" href="comp_compilers.html" title="Comparing Different Compilers">Comparing Different Compilers</a>
28 </h2></div></div></div>
29 <p>
30 By running our performance test suite multiple times, we can compare the effect
31 of different compilers: as might be expected, the differences are generally
32 small compared to say disabling internal use of <code class="computeroutput"><span class="keyword">long</span>
33 <span class="keyword">double</span></code>. However, there are still gains
34 to be main, particularly from some of the commercial offerings:
35 </p>
36 <div class="table">
37 <a name="math_toolkit.comp_compilers.table_Compiler_Comparison_on_Windows_x64"></a><p class="title"><b>Table&#160;16.5.&#160;Compiler Comparison on Windows x64</b></p>
38 <div class="table-contents"><table class="table" summary="Compiler Comparison on Windows x64">
39 <colgroup>
40 <col>
41 <col>
42 <col>
43 <col>
44 <col>
45 </colgroup>
46 <thead><tr>
47 <th>
48 <p>
49 Function
50 </p>
51 </th>
52 <th>
53 <p>
54 Microsoft Visual C++ version 14.0<br> boost 1.61
55 </p>
56 </th>
57 <th>
58 <p>
59 GNU C++ version 5.3.0<br> boost 1.61
60 </p>
61 </th>
62 <th>
63 <p>
64 GNU C++ version 5.3.0<br> boost 1.61<br> promote_double&lt;false&gt;
65 </p>
66 </th>
67 <th>
68 <p>
69 Intel C++ C++0x mode version 1600<br> boost 1.61
70 </p>
71 </th>
72 </tr></thead>
73 <tbody>
74 <tr>
75 <td>
76 <p>
77 assoc_laguerre
78 </p>
79 </td>
80 <td>
81 <p>
82 <span class="green">1.16<br> (208ns)</span>
83 </p>
84 </td>
85 <td>
86 <p>
87 <span class="blue">1.21<br> (217ns)</span>
88 </p>
89 </td>
90 <td>
91 <p>
92 <span class="green">1.06<br> (190ns)</span>
93 </p>
94 </td>
95 <td>
96 <p>
97 <span class="green">1.00<br> (180ns)</span>
98 </p>
99 </td>
100 </tr>
101 <tr>
102 <td>
103 <p>
104 assoc_legendre
105 </p>
106 </td>
107 <td>
108 <p>
109 <span class="blue">1.57<br> (151ns)</span>
110 </p>
111 </td>
112 <td>
113 <p>
114 <span class="blue">1.80<br> (173ns)</span>
115 </p>
116 </td>
117 <td>
118 <p>
119 <span class="green">1.16<br> (111ns)</span>
120 </p>
121 </td>
122 <td>
123 <p>
124 <span class="green">1.00<br> (96ns)</span>
125 </p>
126 </td>
127 </tr>
128 <tr>
129 <td>
130 <p>
131 beta
132 </p>
133 </td>
134 <td>
135 <p>
136 <span class="blue">1.74<br> (176ns)</span>
137 </p>
138 </td>
139 <td>
140 <p>
141 <span class="red">3.78<br> (382ns)</span>
142 </p>
143 </td>
144 <td>
145 <p>
146 <span class="red">2.17<br> (219ns)</span>
147 </p>
148 </td>
149 <td>
150 <p>
151 <span class="green">1.00<br> (101ns)</span>
152 </p>
153 </td>
154 </tr>
155 <tr>
156 <td>
157 <p>
158 beta (incomplete)
159 </p>
160 </td>
161 <td>
162 <p>
163 <span class="blue">1.44<br> (520ns)</span>
164 </p>
165 </td>
166 <td>
167 <p>
168 <span class="red">3.03<br> (1096ns)</span>
169 </p>
170 </td>
171 <td>
172 <p>
173 <span class="blue">1.84<br> (666ns)</span>
174 </p>
175 </td>
176 <td>
177 <p>
178 <span class="green">1.00<br> (362ns)</span>
179 </p>
180 </td>
181 </tr>
182 <tr>
183 <td>
184 <p>
185 cbrt
186 </p>
187 </td>
188 <td>
189 <p>
190 <span class="red">3.21<br> (45ns)</span>
191 </p>
192 </td>
193 <td>
194 <p>
195 <span class="red">3.43<br> (48ns)</span>
196 </p>
197 </td>
198 <td>
199 <p>
200 <span class="red">3.07<br> (43ns)</span>
201 </p>
202 </td>
203 <td>
204 <p>
205 <span class="green">1.00<br> (14ns)</span>
206 </p>
207 </td>
208 </tr>
209 <tr>
210 <td>
211 <p>
212 cyl_bessel_i
213 </p>
214 </td>
215 <td>
216 <p>
217 <span class="green">1.11<br> (404ns)</span>
218 </p>
219 </td>
220 <td>
221 <p>
222 <span class="red">2.78<br> (1016ns)</span>
223 </p>
224 </td>
225 <td>
226 <p>
227 <span class="blue">1.21<br> (442ns)</span>
228 </p>
229 </td>
230 <td>
231 <p>
232 <span class="green">1.00<br> (365ns)</span>
233 </p>
234 </td>
235 </tr>
236 <tr>
237 <td>
238 <p>
239 cyl_bessel_i (integer order)
240 </p>
241 </td>
242 <td>
243 <p>
244 <span class="blue">1.29<br> (261ns)</span>
245 </p>
246 </td>
247 <td>
248 <p>
249 <span class="red">3.16<br> (638ns)</span>
250 </p>
251 </td>
252 <td>
253 <p>
254 <span class="blue">1.22<br> (247ns)</span>
255 </p>
256 </td>
257 <td>
258 <p>
259 <span class="green">1.00<br> (202ns)</span>
260 </p>
261 </td>
262 </tr>
263 <tr>
264 <td>
265 <p>
266 cyl_bessel_j
267 </p>
268 </td>
269 <td>
270 <p>
271 <span class="green">1.19<br> (488ns)</span>
272 </p>
273 </td>
274 <td>
275 <p>
276 <span class="red">2.06<br> (841ns)</span>
277 </p>
278 </td>
279 <td>
280 <p>
281 <span class="blue">1.25<br> (513ns)</span>
282 </p>
283 </td>
284 <td>
285 <p>
286 <span class="green">1.00<br> (409ns)</span>
287 </p>
288 </td>
289 </tr>
290 <tr>
291 <td>
292 <p>
293 cyl_bessel_j (integer order)
294 </p>
295 </td>
296 <td>
297 <p>
298 <span class="blue">1.36<br> (103ns)</span>
299 </p>
300 </td>
301 <td>
302 <p>
303 <span class="red">2.39<br> (182ns)</span>
304 </p>
305 </td>
306 <td>
307 <p>
308 <span class="blue">1.47<br> (112ns)</span>
309 </p>
310 </td>
311 <td>
312 <p>
313 <span class="green">1.00<br> (76ns)</span>
314 </p>
315 </td>
316 </tr>
317 <tr>
318 <td>
319 <p>
320 cyl_bessel_k
321 </p>
322 </td>
323 <td>
324 <p>
325 <span class="green">1.04<br> (747ns)</span>
326 </p>
327 </td>
328 <td>
329 <p>
330 <span class="red">9.43<br> (6743ns)</span>
331 </p>
332 </td>
333 <td>
334 <p>
335 <span class="green">1.03<br> (734ns)</span>
336 </p>
337 </td>
338 <td>
339 <p>
340 <span class="green">1.00<br> (715ns)</span>
341 </p>
342 </td>
343 </tr>
344 <tr>
345 <td>
346 <p>
347 cyl_bessel_k (integer order)
348 </p>
349 </td>
350 <td>
351 <p>
352 <span class="blue">1.26<br> (419ns)</span>
353 </p>
354 </td>
355 <td>
356 <p>
357 <span class="red">10.49<br> (3494ns)</span>
358 </p>
359 </td>
360 <td>
361 <p>
362 <span class="green">1.10<br> (367ns)</span>
363 </p>
364 </td>
365 <td>
366 <p>
367 <span class="green">1.00<br> (333ns)</span>
368 </p>
369 </td>
370 </tr>
371 <tr>
372 <td>
373 <p>
374 cyl_neumann
375 </p>
376 </td>
377 <td>
378 <p>
379 <span class="red">16.76<br> (11212ns)</span>
380 </p>
381 </td>
382 <td>
383 <p>
384 <span class="red">2.01<br> (1346ns)</span>
385 </p>
386 </td>
387 <td>
388 <p>
389 <span class="green">1.00<br> (669ns)</span>
390 </p>
391 </td>
392 <td>
393 <p>
394 <span class="red">15.35<br> (10266ns)</span>
395 </p>
396 </td>
397 </tr>
398 <tr>
399 <td>
400 <p>
401 cyl_neumann (integer order)
402 </p>
403 </td>
404 <td>
405 <p>
406 <span class="green">1.00<br> (225ns)</span>
407 </p>
408 </td>
409 <td>
410 <p>
411 <span class="blue">1.79<br> (403ns)</span>
412 </p>
413 </td>
414 <td>
415 <p>
416 <span class="blue">1.24<br> (279ns)</span>
417 </p>
418 </td>
419 <td>
420 <p>
421 <span class="green">1.02<br> (229ns)</span>
422 </p>
423 </td>
424 </tr>
425 <tr>
426 <td>
427 <p>
428 digamma
429 </p>
430 </td>
431 <td>
432 <p>
433 <span class="green">1.20<br> (24ns)</span>
434 </p>
435 </td>
436 <td>
437 <p>
438 <span class="red">3.75<br> (75ns)</span>
439 </p>
440 </td>
441 <td>
442 <p>
443 <span class="red">2.15<br> (43ns)</span>
444 </p>
445 </td>
446 <td>
447 <p>
448 <span class="green">1.00<br> (20ns)</span>
449 </p>
450 </td>
451 </tr>
452 <tr>
453 <td>
454 <p>
455 ellint_1
456 </p>
457 </td>
458 <td>
459 <p>
460 <span class="blue">1.87<br> (329ns)</span>
461 </p>
462 </td>
463 <td>
464 <p>
465 <span class="blue">1.99<br> (350ns)</span>
466 </p>
467 </td>
468 <td>
469 <p>
470 <span class="blue">1.32<br> (232ns)</span>
471 </p>
472 </td>
473 <td>
474 <p>
475 <span class="green">1.00<br> (176ns)</span>
476 </p>
477 </td>
478 </tr>
479 <tr>
480 <td>
481 <p>
482 ellint_1 (complete)
483 </p>
484 </td>
485 <td>
486 <p>
487 <span class="red">2.18<br> (61ns)</span>
488 </p>
489 </td>
490 <td>
491 <p>
492 <span class="red">2.57<br> (72ns)</span>
493 </p>
494 </td>
495 <td>
496 <p>
497 <span class="blue">1.57<br> (44ns)</span>
498 </p>
499 </td>
500 <td>
501 <p>
502 <span class="green">1.00<br> (28ns)</span>
503 </p>
504 </td>
505 </tr>
506 <tr>
507 <td>
508 <p>
509 ellint_2
510 </p>
511 </td>
512 <td>
513 <p>
514 <span class="blue">1.78<br> (525ns)</span>
515 </p>
516 </td>
517 <td>
518 <p>
519 <span class="red">2.17<br> (640ns)</span>
520 </p>
521 </td>
522 <td>
523 <p>
524 <span class="blue">1.52<br> (449ns)</span>
525 </p>
526 </td>
527 <td>
528 <p>
529 <span class="green">1.00<br> (295ns)</span>
530 </p>
531 </td>
532 </tr>
533 <tr>
534 <td>
535 <p>
536 ellint_2 (complete)
537 </p>
538 </td>
539 <td>
540 <p>
541 <span class="red">2.14<br> (62ns)</span>
542 </p>
543 </td>
544 <td>
545 <p>
546 <span class="red">2.07<br> (60ns)</span>
547 </p>
548 </td>
549 <td>
550 <p>
551 <span class="blue">1.24<br> (36ns)</span>
552 </p>
553 </td>
554 <td>
555 <p>
556 <span class="green">1.00<br> (29ns)</span>
557 </p>
558 </td>
559 </tr>
560 <tr>
561 <td>
562 <p>
563 ellint_3
564 </p>
565 </td>
566 <td>
567 <p>
568 <span class="blue">1.94<br> (1155ns)</span>
569 </p>
570 </td>
571 <td>
572 <p>
573 <span class="red">2.91<br> (1733ns)</span>
574 </p>
575 </td>
576 <td>
577 <p>
578 <span class="blue">1.65<br> (986ns)</span>
579 </p>
580 </td>
581 <td>
582 <p>
583 <span class="green">1.00<br> (596ns)</span>
584 </p>
585 </td>
586 </tr>
587 <tr>
588 <td>
589 <p>
590 ellint_3 (complete)
591 </p>
592 </td>
593 <td>
594 <p>
595 <span class="red">2.05<br> (721ns)</span>
596 </p>
597 </td>
598 <td>
599 <p>
600 <span class="red">3.07<br> (1079ns)</span>
601 </p>
602 </td>
603 <td>
604 <p>
605 <span class="blue">1.46<br> (514ns)</span>
606 </p>
607 </td>
608 <td>
609 <p>
610 <span class="green">1.00<br> (352ns)</span>
611 </p>
612 </td>
613 </tr>
614 <tr>
615 <td>
616 <p>
617 ellint_rc
618 </p>
619 </td>
620 <td>
621 <p>
622 <span class="blue">1.58<br> (49ns)</span>
623 </p>
624 </td>
625 <td>
626 <p>
627 <span class="red">2.68<br> (83ns)</span>
628 </p>
629 </td>
630 <td>
631 <p>
632 <span class="blue">1.55<br> (48ns)</span>
633 </p>
634 </td>
635 <td>
636 <p>
637 <span class="green">1.00<br> (31ns)</span>
638 </p>
639 </td>
640 </tr>
641 <tr>
642 <td>
643 <p>
644 ellint_rd
645 </p>
646 </td>
647 <td>
648 <p>
649 <span class="blue">1.75<br> (332ns)</span>
650 </p>
651 </td>
652 <td>
653 <p>
654 <span class="blue">1.83<br> (348ns)</span>
655 </p>
656 </td>
657 <td>
658 <p>
659 <span class="blue">1.40<br> (266ns)</span>
660 </p>
661 </td>
662 <td>
663 <p>
664 <span class="green">1.00<br> (190ns)</span>
665 </p>
666 </td>
667 </tr>
668 <tr>
669 <td>
670 <p>
671 ellint_rf
672 </p>
673 </td>
674 <td>
675 <p>
676 <span class="blue">1.69<br> (71ns)</span>
677 </p>
678 </td>
679 <td>
680 <p>
681 <span class="red">2.40<br> (101ns)</span>
682 </p>
683 </td>
684 <td>
685 <p>
686 <span class="blue">1.57<br> (66ns)</span>
687 </p>
688 </td>
689 <td>
690 <p>
691 <span class="green">1.00<br> (42ns)</span>
692 </p>
693 </td>
694 </tr>
695 <tr>
696 <td>
697 <p>
698 ellint_rj
699 </p>
700 </td>
701 <td>
702 <p>
703 <span class="blue">1.91<br> (344ns)</span>
704 </p>
705 </td>
706 <td>
707 <p>
708 <span class="red">2.96<br> (532ns)</span>
709 </p>
710 </td>
711 <td>
712 <p>
713 <span class="blue">1.43<br> (257ns)</span>
714 </p>
715 </td>
716 <td>
717 <p>
718 <span class="green">1.00<br> (180ns)</span>
719 </p>
720 </td>
721 </tr>
722 <tr>
723 <td>
724 <p>
725 erf
726 </p>
727 </td>
728 <td>
729 <p>
730 <span class="blue">1.77<br> (23ns)</span>
731 </p>
732 </td>
733 <td>
734 <p>
735 <span class="red">2.92<br> (38ns)</span>
736 </p>
737 </td>
738 <td>
739 <p>
740 <span class="blue">1.92<br> (25ns)</span>
741 </p>
742 </td>
743 <td>
744 <p>
745 <span class="green">1.00<br> (13ns)</span>
746 </p>
747 </td>
748 </tr>
749 <tr>
750 <td>
751 <p>
752 erfc
753 </p>
754 </td>
755 <td>
756 <p>
757 <span class="blue">1.29<br> (22ns)</span>
758 </p>
759 </td>
760 <td>
761 <p>
762 <span class="red">3.41<br> (58ns)</span>
763 </p>
764 </td>
765 <td>
766 <p>
767 <span class="red">2.06<br> (35ns)</span>
768 </p>
769 </td>
770 <td>
771 <p>
772 <span class="green">1.00<br> (17ns)</span>
773 </p>
774 </td>
775 </tr>
776 <tr>
777 <td>
778 <p>
779 expint
780 </p>
781 </td>
782 <td>
783 <p>
784 <span class="blue">1.39<br> (39ns)</span>
785 </p>
786 </td>
787 <td>
788 <p>
789 <span class="red">3.07<br> (86ns)</span>
790 </p>
791 </td>
792 <td>
793 <p>
794 <span class="red">2.14<br> (60ns)</span>
795 </p>
796 </td>
797 <td>
798 <p>
799 <span class="green">1.00<br> (28ns)</span>
800 </p>
801 </td>
802 </tr>
803 <tr>
804 <td>
805 <p>
806 expint (En)
807 </p>
808 </td>
809 <td>
810 <p>
811 <span class="green">1.10<br> (117ns)</span>
812 </p>
813 </td>
814 <td>
815 <p>
816 <span class="red">2.19<br> (232ns)</span>
817 </p>
818 </td>
819 <td>
820 <p>
821 <span class="blue">1.38<br> (146ns)</span>
822 </p>
823 </td>
824 <td>
825 <p>
826 <span class="green">1.00<br> (106ns)</span>
827 </p>
828 </td>
829 </tr>
830 <tr>
831 <td>
832 <p>
833 expm1
834 </p>
835 </td>
836 <td>
837 <p>
838 <span class="green">1.00<br> (10ns)</span>
839 </p>
840 </td>
841 <td>
842 <p>
843 <span class="red">3.10<br> (31ns)</span>
844 </p>
845 </td>
846 <td>
847 <p>
848 <span class="red">2.40<br> (24ns)</span>
849 </p>
850 </td>
851 <td>
852 <p>
853 <span class="green">1.10<br> (11ns)</span>
854 </p>
855 </td>
856 </tr>
857 <tr>
858 <td>
859 <p>
860 gamma_p
861 </p>
862 </td>
863 <td>
864 <p>
865 <span class="blue">1.29<br> (192ns)</span>
866 </p>
867 </td>
868 <td>
869 <p>
870 <span class="red">2.64<br> (393ns)</span>
871 </p>
872 </td>
873 <td>
874 <p>
875 <span class="blue">1.71<br> (255ns)</span>
876 </p>
877 </td>
878 <td>
879 <p>
880 <span class="green">1.00<br> (149ns)</span>
881 </p>
882 </td>
883 </tr>
884 <tr>
885 <td>
886 <p>
887 gamma_p_inv
888 </p>
889 </td>
890 <td>
891 <p>
892 <span class="blue">1.36<br> (706ns)</span>
893 </p>
894 </td>
895 <td>
896 <p>
897 <span class="red">2.47<br> (1288ns)</span>
898 </p>
899 </td>
900 <td>
901 <p>
902 <span class="blue">1.91<br> (997ns)</span>
903 </p>
904 </td>
905 <td>
906 <p>
907 <span class="green">1.00<br> (521ns)</span>
908 </p>
909 </td>
910 </tr>
911 <tr>
912 <td>
913 <p>
914 gamma_q
915 </p>
916 </td>
917 <td>
918 <p>
919 <span class="green">1.16<br> (179ns)</span>
920 </p>
921 </td>
922 <td>
923 <p>
924 <span class="red">2.79<br> (429ns)</span>
925 </p>
926 </td>
927 <td>
928 <p>
929 <span class="blue">1.61<br> (248ns)</span>
930 </p>
931 </td>
932 <td>
933 <p>
934 <span class="green">1.00<br> (154ns)</span>
935 </p>
936 </td>
937 </tr>
938 <tr>
939 <td>
940 <p>
941 gamma_q_inv
942 </p>
943 </td>
944 <td>
945 <p>
946 <span class="blue">1.37<br> (703ns)</span>
947 </p>
948 </td>
949 <td>
950 <p>
951 <span class="red">2.38<br> (1225ns)</span>
952 </p>
953 </td>
954 <td>
955 <p>
956 <span class="blue">1.89<br> (971ns)</span>
957 </p>
958 </td>
959 <td>
960 <p>
961 <span class="green">1.00<br> (515ns)</span>
962 </p>
963 </td>
964 </tr>
965 <tr>
966 <td>
967 <p>
968 ibeta
969 </p>
970 </td>
971 <td>
972 <p>
973 <span class="blue">1.34<br> (520ns)</span>
974 </p>
975 </td>
976 <td>
977 <p>
978 <span class="red">3.13<br> (1218ns)</span>
979 </p>
980 </td>
981 <td>
982 <p>
983 <span class="blue">1.83<br> (711ns)</span>
984 </p>
985 </td>
986 <td>
987 <p>
988 <span class="green">1.00<br> (389ns)</span>
989 </p>
990 </td>
991 </tr>
992 <tr>
993 <td>
994 <p>
995 ibeta_inv
996 </p>
997 </td>
998 <td>
999 <p>
1000 <span class="blue">1.51<br> (2193ns)</span>
1001 </p>
1002 </td>
1003 <td>
1004 <p>
1005 <span class="red">2.81<br> (4085ns)</span>
1006 </p>
1007 </td>
1008 <td>
1009 <p>
1010 <span class="red">2.27<br> (3303ns)</span>
1011 </p>
1012 </td>
1013 <td>
1014 <p>
1015 <span class="green">1.00<br> (1452ns)</span>
1016 </p>
1017 </td>
1018 </tr>
1019 <tr>
1020 <td>
1021 <p>
1022 ibetac
1023 </p>
1024 </td>
1025 <td>
1026 <p>
1027 <span class="blue">1.29<br> (518ns)</span>
1028 </p>
1029 </td>
1030 <td>
1031 <p>
1032 <span class="red">2.94<br> (1179ns)</span>
1033 </p>
1034 </td>
1035 <td>
1036 <p>
1037 <span class="blue">1.73<br> (694ns)</span>
1038 </p>
1039 </td>
1040 <td>
1041 <p>
1042 <span class="green">1.00<br> (401ns)</span>
1043 </p>
1044 </td>
1045 </tr>
1046 <tr>
1047 <td>
1048 <p>
1049 ibetac_inv
1050 </p>
1051 </td>
1052 <td>
1053 <p>
1054 <span class="blue">1.41<br> (2045ns)</span>
1055 </p>
1056 </td>
1057 <td>
1058 <p>
1059 <span class="red">2.80<br> (4058ns)</span>
1060 </p>
1061 </td>
1062 <td>
1063 <p>
1064 <span class="blue">1.78<br> (2572ns)</span>
1065 </p>
1066 </td>
1067 <td>
1068 <p>
1069 <span class="green">1.00<br> (1447ns)</span>
1070 </p>
1071 </td>
1072 </tr>
1073 <tr>
1074 <td>
1075 <p>
1076 jacobi_cn
1077 </p>
1078 </td>
1079 <td>
1080 <p>
1081 <span class="blue">1.36<br> (182ns)</span>
1082 </p>
1083 </td>
1084 <td>
1085 <p>
1086 <span class="red">3.72<br> (499ns)</span>
1087 </p>
1088 </td>
1089 <td>
1090 <p>
1091 <span class="red">2.28<br> (306ns)</span>
1092 </p>
1093 </td>
1094 <td>
1095 <p>
1096 <span class="green">1.00<br> (134ns)</span>
1097 </p>
1098 </td>
1099 </tr>
1100 <tr>
1101 <td>
1102 <p>
1103 jacobi_dn
1104 </p>
1105 </td>
1106 <td>
1107 <p>
1108 <span class="blue">1.82<br> (262ns)</span>
1109 </p>
1110 </td>
1111 <td>
1112 <p>
1113 <span class="red">3.68<br> (530ns)</span>
1114 </p>
1115 </td>
1116 <td>
1117 <p>
1118 <span class="red">2.27<br> (327ns)</span>
1119 </p>
1120 </td>
1121 <td>
1122 <p>
1123 <span class="green">1.00<br> (144ns)</span>
1124 </p>
1125 </td>
1126 </tr>
1127 <tr>
1128 <td>
1129 <p>
1130 jacobi_sn
1131 </p>
1132 </td>
1133 <td>
1134 <p>
1135 <span class="blue">1.31<br> (179ns)</span>
1136 </p>
1137 </td>
1138 <td>
1139 <p>
1140 <span class="red">3.73<br> (511ns)</span>
1141 </p>
1142 </td>
1143 <td>
1144 <p>
1145 <span class="red">2.43<br> (333ns)</span>
1146 </p>
1147 </td>
1148 <td>
1149 <p>
1150 <span class="green">1.00<br> (137ns)</span>
1151 </p>
1152 </td>
1153 </tr>
1154 <tr>
1155 <td>
1156 <p>
1157 laguerre
1158 </p>
1159 </td>
1160 <td>
1161 <p>
1162 <span class="green">1.00<br> (121ns)</span>
1163 </p>
1164 </td>
1165 <td>
1166 <p>
1167 <span class="green">1.15<br> (139ns)</span>
1168 </p>
1169 </td>
1170 <td>
1171 <p>
1172 <span class="green">1.04<br> (126ns)</span>
1173 </p>
1174 </td>
1175 <td>
1176 <p>
1177 <span class="green">1.10<br> (133ns)</span>
1178 </p>
1179 </td>
1180 </tr>
1181 <tr>
1182 <td>
1183 <p>
1184 legendre
1185 </p>
1186 </td>
1187 <td>
1188 <p>
1189 <span class="green">1.07<br> (364ns)</span>
1190 </p>
1191 </td>
1192 <td>
1193 <p>
1194 <span class="green">1.16<br> (396ns)</span>
1195 </p>
1196 </td>
1197 <td>
1198 <p>
1199 <span class="green">1.00<br> (340ns)</span>
1200 </p>
1201 </td>
1202 <td>
1203 <p>
1204 <span class="green">1.13<br> (383ns)</span>
1205 </p>
1206 </td>
1207 </tr>
1208 <tr>
1209 <td>
1210 <p>
1211 legendre Q
1212 </p>
1213 </td>
1214 <td>
1215 <p>
1216 <span class="green">1.00<br> (427ns)</span>
1217 </p>
1218 </td>
1219 <td>
1220 <p>
1221 <span class="green">1.20<br> (512ns)</span>
1222 </p>
1223 </td>
1224 <td>
1225 <p>
1226 <span class="green">1.01<br> (430ns)</span>
1227 </p>
1228 </td>
1229 <td>
1230 <p>
1231 <span class="green">1.07<br> (455ns)</span>
1232 </p>
1233 </td>
1234 </tr>
1235 <tr>
1236 <td>
1237 <p>
1238 lgamma
1239 </p>
1240 </td>
1241 <td>
1242 <p>
1243 <span class="green">1.00<br> (73ns)</span>
1244 </p>
1245 </td>
1246 <td>
1247 <p>
1248 <span class="red">3.07<br> (224ns)</span>
1249 </p>
1250 </td>
1251 <td>
1252 <p>
1253 <span class="blue">1.82<br> (133ns)</span>
1254 </p>
1255 </td>
1256 <td>
1257 <p>
1258 <span class="green">1.05<br> (77ns)</span>
1259 </p>
1260 </td>
1261 </tr>
1262 <tr>
1263 <td>
1264 <p>
1265 log1p
1266 </p>
1267 </td>
1268 <td>
1269 <p>
1270 <span class="green">1.00<br> (14ns)</span>
1271 </p>
1272 </td>
1273 <td>
1274 <p>
1275 <span class="blue">2.00<br> (28ns)</span>
1276 </p>
1277 </td>
1278 <td>
1279 <p>
1280 <span class="green">1.14<br> (16ns)</span>
1281 </p>
1282 </td>
1283 <td>
1284 <p>
1285 <span class="green">1.00<br> (14ns)</span>
1286 </p>
1287 </td>
1288 </tr>
1289 <tr>
1290 <td>
1291 <p>
1292 polygamma
1293 </p>
1294 </td>
1295 <td>
1296 <p>
1297 <span class="green">1.16<br> (3773ns)</span>
1298 </p>
1299 </td>
1300 <td>
1301 <p>
1302 <span class="green">1.02<br> (3320ns)</span>
1303 </p>
1304 </td>
1305 <td>
1306 <p>
1307 <span class="red">2.24<br> (7270ns)</span>
1308 </p>
1309 </td>
1310 <td>
1311 <p>
1312 <span class="green">1.00<br> (3246ns)</span>
1313 </p>
1314 </td>
1315 </tr>
1316 <tr>
1317 <td>
1318 <p>
1319 sph_bessel
1320 </p>
1321 </td>
1322 <td>
1323 <p>
1324 <span class="green">1.17<br> (1005ns)</span>
1325 </p>
1326 </td>
1327 <td>
1328 <p>
1329 <span class="blue">1.55<br> (1325ns)</span>
1330 </p>
1331 </td>
1332 <td>
1333 <p>
1334 <span class="green">1.09<br> (931ns)</span>
1335 </p>
1336 </td>
1337 <td>
1338 <p>
1339 <span class="green">1.00<br> (857ns)</span>
1340 </p>
1341 </td>
1342 </tr>
1343 <tr>
1344 <td>
1345 <p>
1346 sph_neumann
1347 </p>
1348 </td>
1349 <td>
1350 <p>
1351 <span class="green">1.08<br> (1827ns)</span>
1352 </p>
1353 </td>
1354 <td>
1355 <p>
1356 <span class="red">2.07<br> (3483ns)</span>
1357 </p>
1358 </td>
1359 <td>
1360 <p>
1361 <span class="green">1.00<br> (1685ns)</span>
1362 </p>
1363 </td>
1364 <td>
1365 <p>
1366 <span class="green">1.01<br> (1702ns)</span>
1367 </p>
1368 </td>
1369 </tr>
1370 <tr>
1371 <td>
1372 <p>
1373 tgamma
1374 </p>
1375 </td>
1376 <td>
1377 <p>
1378 <span class="blue">1.31<br> (77ns)</span>
1379 </p>
1380 </td>
1381 <td>
1382 <p>
1383 <span class="red">4.03<br> (238ns)</span>
1384 </p>
1385 </td>
1386 <td>
1387 <p>
1388 <span class="red">2.49<br> (147ns)</span>
1389 </p>
1390 </td>
1391 <td>
1392 <p>
1393 <span class="green">1.00<br> (59ns)</span>
1394 </p>
1395 </td>
1396 </tr>
1397 <tr>
1398 <td>
1399 <p>
1400 tgamma (incomplete)
1401 </p>
1402 </td>
1403 <td>
1404 <p>
1405 <span class="blue">1.26<br> (276ns)</span>
1406 </p>
1407 </td>
1408 <td>
1409 <p>
1410 <span class="red">2.52<br> (552ns)</span>
1411 </p>
1412 </td>
1413 <td>
1414 <p>
1415 <span class="blue">1.73<br> (379ns)</span>
1416 </p>
1417 </td>
1418 <td>
1419 <p>
1420 <span class="green">1.00<br> (219ns)</span>
1421 </p>
1422 </td>
1423 </tr>
1424 <tr>
1425 <td>
1426 <p>
1427 trigamma
1428 </p>
1429 </td>
1430 <td>
1431 <p>
1432 <span class="blue">1.35<br> (23ns)</span>
1433 </p>
1434 </td>
1435 <td>
1436 <p>
1437 <span class="red">2.88<br> (49ns)</span>
1438 </p>
1439 </td>
1440 <td>
1441 <p>
1442 <span class="blue">1.41<br> (24ns)</span>
1443 </p>
1444 </td>
1445 <td>
1446 <p>
1447 <span class="green">1.00<br> (17ns)</span>
1448 </p>
1449 </td>
1450 </tr>
1451 <tr>
1452 <td>
1453 <p>
1454 zeta
1455 </p>
1456 </td>
1457 <td>
1458 <p>
1459 <span class="blue">1.34<br> (121ns)</span>
1460 </p>
1461 </td>
1462 <td>
1463 <p>
1464 <span class="red">3.83<br> (345ns)</span>
1465 </p>
1466 </td>
1467 <td>
1468 <p>
1469 <span class="red">2.52<br> (227ns)</span>
1470 </p>
1471 </td>
1472 <td>
1473 <p>
1474 <span class="green">1.00<br> (90ns)</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.comp_compilers.table_Compiler_Comparison_on_linux"></a><p class="title"><b>Table&#160;16.6.&#160;Compiler Comparison on linux</b></p>
1483 <div class="table-contents"><table class="table" summary="Compiler Comparison on linux">
1484 <colgroup>
1485 <col>
1486 <col>
1487 <col>
1488 </colgroup>
1489 <thead><tr>
1490 <th>
1491 <p>
1492 Function
1493 </p>
1494 </th>
1495 <th>
1496 <p>
1497 GNU C++ version 5.3.0<br> boost 1.61
1498 </p>
1499 </th>
1500 <th>
1501 <p>
1502 GNU C++ version 5.3.0<br> boost 1.61<br> promote_double&lt;false&gt;
1503 </p>
1504 </th>
1505 </tr></thead>
1506 <tbody>
1507 <tr>
1508 <td>
1509 <p>
1510 assoc_laguerre
1511 </p>
1512 </td>
1513 <td>
1514 <p>
1515 <span class="blue">1.36<br> (263ns)</span>
1516 </p>
1517 </td>
1518 <td>
1519 <p>
1520 <span class="green">1.00<br> (194ns)</span>
1521 </p>
1522 </td>
1523 </tr>
1524 <tr>
1525 <td>
1526 <p>
1527 assoc_legendre
1528 </p>
1529 </td>
1530 <td>
1531 <p>
1532 <span class="red">2.55<br> (258ns)</span>
1533 </p>
1534 </td>
1535 <td>
1536 <p>
1537 <span class="green">1.00<br> (101ns)</span>
1538 </p>
1539 </td>
1540 </tr>
1541 <tr>
1542 <td>
1543 <p>
1544 beta
1545 </p>
1546 </td>
1547 <td>
1548 <p>
1549 <span class="red">4.71<br> (734ns)</span>
1550 </p>
1551 </td>
1552 <td>
1553 <p>
1554 <span class="green">1.00<br> (156ns)</span>
1555 </p>
1556 </td>
1557 </tr>
1558 <tr>
1559 <td>
1560 <p>
1561 beta (incomplete)
1562 </p>
1563 </td>
1564 <td>
1565 <p>
1566 <span class="red">3.12<br> (1796ns)</span>
1567 </p>
1568 </td>
1569 <td>
1570 <p>
1571 <span class="green">1.00<br> (575ns)</span>
1572 </p>
1573 </td>
1574 </tr>
1575 <tr>
1576 <td>
1577 <p>
1578 cbrt
1579 </p>
1580 </td>
1581 <td>
1582 <p>
1583 <span class="red">2.53<br> (43ns)</span>
1584 </p>
1585 </td>
1586 <td>
1587 <p>
1588 <span class="green">1.00<br> (17ns)</span>
1589 </p>
1590 </td>
1591 </tr>
1592 <tr>
1593 <td>
1594 <p>
1595 cyl_bessel_i
1596 </p>
1597 </td>
1598 <td>
1599 <p>
1600 <span class="red">3.47<br> (1410ns)</span>
1601 </p>
1602 </td>
1603 <td>
1604 <p>
1605 <span class="green">1.00<br> (406ns)</span>
1606 </p>
1607 </td>
1608 </tr>
1609 <tr>
1610 <td>
1611 <p>
1612 cyl_bessel_i (integer order)
1613 </p>
1614 </td>
1615 <td>
1616 <p>
1617 <span class="red">3.38<br> (893ns)</span>
1618 </p>
1619 </td>
1620 <td>
1621 <p>
1622 <span class="green">1.00<br> (264ns)</span>
1623 </p>
1624 </td>
1625 </tr>
1626 <tr>
1627 <td>
1628 <p>
1629 cyl_bessel_j
1630 </p>
1631 </td>
1632 <td>
1633 <p>
1634 <span class="red">2.69<br> (1071ns)</span>
1635 </p>
1636 </td>
1637 <td>
1638 <p>
1639 <span class="green">1.00<br> (398ns)</span>
1640 </p>
1641 </td>
1642 </tr>
1643 <tr>
1644 <td>
1645 <p>
1646 cyl_bessel_j (integer order)
1647 </p>
1648 </td>
1649 <td>
1650 <p>
1651 <span class="red">2.59<br> (275ns)</span>
1652 </p>
1653 </td>
1654 <td>
1655 <p>
1656 <span class="green">1.00<br> (106ns)</span>
1657 </p>
1658 </td>
1659 </tr>
1660 <tr>
1661 <td>
1662 <p>
1663 cyl_bessel_k
1664 </p>
1665 </td>
1666 <td>
1667 <p>
1668 <span class="red">6.86<br> (4589ns)</span>
1669 </p>
1670 </td>
1671 <td>
1672 <p>
1673 <span class="green">1.00<br> (669ns)</span>
1674 </p>
1675 </td>
1676 </tr>
1677 <tr>
1678 <td>
1679 <p>
1680 cyl_bessel_k (integer order)
1681 </p>
1682 </td>
1683 <td>
1684 <p>
1685 <span class="red">10.17<br> (3673ns)</span>
1686 </p>
1687 </td>
1688 <td>
1689 <p>
1690 <span class="green">1.00<br> (361ns)</span>
1691 </p>
1692 </td>
1693 </tr>
1694 <tr>
1695 <td>
1696 <p>
1697 cyl_neumann
1698 </p>
1699 </td>
1700 <td>
1701 <p>
1702 <span class="red">2.48<br> (1478ns)</span>
1703 </p>
1704 </td>
1705 <td>
1706 <p>
1707 <span class="green">1.00<br> (597ns)</span>
1708 </p>
1709 </td>
1710 </tr>
1711 <tr>
1712 <td>
1713 <p>
1714 cyl_neumann (integer order)
1715 </p>
1716 </td>
1717 <td>
1718 <p>
1719 <span class="red">2.20<br> (484ns)</span>
1720 </p>
1721 </td>
1722 <td>
1723 <p>
1724 <span class="green">1.00<br> (220ns)</span>
1725 </p>
1726 </td>
1727 </tr>
1728 <tr>
1729 <td>
1730 <p>
1731 digamma
1732 </p>
1733 </td>
1734 <td>
1735 <p>
1736 <span class="blue">1.92<br> (75ns)</span>
1737 </p>
1738 </td>
1739 <td>
1740 <p>
1741 <span class="green">1.00<br> (39ns)</span>
1742 </p>
1743 </td>
1744 </tr>
1745 <tr>
1746 <td>
1747 <p>
1748 ellint_1
1749 </p>
1750 </td>
1751 <td>
1752 <p>
1753 <span class="blue">1.94<br> (358ns)</span>
1754 </p>
1755 </td>
1756 <td>
1757 <p>
1758 <span class="green">1.00<br> (185ns)</span>
1759 </p>
1760 </td>
1761 </tr>
1762 <tr>
1763 <td>
1764 <p>
1765 ellint_1 (complete)
1766 </p>
1767 </td>
1768 <td>
1769 <p>
1770 <span class="blue">1.86<br> (52ns)</span>
1771 </p>
1772 </td>
1773 <td>
1774 <p>
1775 <span class="green">1.00<br> (28ns)</span>
1776 </p>
1777 </td>
1778 </tr>
1779 <tr>
1780 <td>
1781 <p>
1782 ellint_2
1783 </p>
1784 </td>
1785 <td>
1786 <p>
1787 <span class="red">2.32<br> (805ns)</span>
1788 </p>
1789 </td>
1790 <td>
1791 <p>
1792 <span class="green">1.00<br> (347ns)</span>
1793 </p>
1794 </td>
1795 </tr>
1796 <tr>
1797 <td>
1798 <p>
1799 ellint_2 (complete)
1800 </p>
1801 </td>
1802 <td>
1803 <p>
1804 <span class="blue">1.71<br> (60ns)</span>
1805 </p>
1806 </td>
1807 <td>
1808 <p>
1809 <span class="green">1.00<br> (35ns)</span>
1810 </p>
1811 </td>
1812 </tr>
1813 <tr>
1814 <td>
1815 <p>
1816 ellint_3
1817 </p>
1818 </td>
1819 <td>
1820 <p>
1821 <span class="red">2.75<br> (2154ns)</span>
1822 </p>
1823 </td>
1824 <td>
1825 <p>
1826 <span class="green">1.00<br> (783ns)</span>
1827 </p>
1828 </td>
1829 </tr>
1830 <tr>
1831 <td>
1832 <p>
1833 ellint_3 (complete)
1834 </p>
1835 </td>
1836 <td>
1837 <p>
1838 <span class="red">2.23<br> (1172ns)</span>
1839 </p>
1840 </td>
1841 <td>
1842 <p>
1843 <span class="green">1.00<br> (525ns)</span>
1844 </p>
1845 </td>
1846 </tr>
1847 <tr>
1848 <td>
1849 <p>
1850 ellint_rc
1851 </p>
1852 </td>
1853 <td>
1854 <p>
1855 <span class="blue">1.57<br> (77ns)</span>
1856 </p>
1857 </td>
1858 <td>
1859 <p>
1860 <span class="green">1.00<br> (49ns)</span>
1861 </p>
1862 </td>
1863 </tr>
1864 <tr>
1865 <td>
1866 <p>
1867 ellint_rd
1868 </p>
1869 </td>
1870 <td>
1871 <p>
1872 <span class="red">2.23<br> (520ns)</span>
1873 </p>
1874 </td>
1875 <td>
1876 <p>
1877 <span class="green">1.00<br> (233ns)</span>
1878 </p>
1879 </td>
1880 </tr>
1881 <tr>
1882 <td>
1883 <p>
1884 ellint_rf
1885 </p>
1886 </td>
1887 <td>
1888 <p>
1889 <span class="blue">1.51<br> (95ns)</span>
1890 </p>
1891 </td>
1892 <td>
1893 <p>
1894 <span class="green">1.00<br> (63ns)</span>
1895 </p>
1896 </td>
1897 </tr>
1898 <tr>
1899 <td>
1900 <p>
1901 ellint_rj
1902 </p>
1903 </td>
1904 <td>
1905 <p>
1906 <span class="red">2.33<br> (481ns)</span>
1907 </p>
1908 </td>
1909 <td>
1910 <p>
1911 <span class="green">1.00<br> (206ns)</span>
1912 </p>
1913 </td>
1914 </tr>
1915 <tr>
1916 <td>
1917 <p>
1918 erf
1919 </p>
1920 </td>
1921 <td>
1922 <p>
1923 <span class="red">2.60<br> (39ns)</span>
1924 </p>
1925 </td>
1926 <td>
1927 <p>
1928 <span class="green">1.00<br> (15ns)</span>
1929 </p>
1930 </td>
1931 </tr>
1932 <tr>
1933 <td>
1934 <p>
1935 erfc
1936 </p>
1937 </td>
1938 <td>
1939 <p>
1940 <span class="red">2.68<br> (59ns)</span>
1941 </p>
1942 </td>
1943 <td>
1944 <p>
1945 <span class="green">1.00<br> (22ns)</span>
1946 </p>
1947 </td>
1948 </tr>
1949 <tr>
1950 <td>
1951 <p>
1952 expint
1953 </p>
1954 </td>
1955 <td>
1956 <p>
1957 <span class="red">2.47<br> (94ns)</span>
1958 </p>
1959 </td>
1960 <td>
1961 <p>
1962 <span class="green">1.00<br> (38ns)</span>
1963 </p>
1964 </td>
1965 </tr>
1966 <tr>
1967 <td>
1968 <p>
1969 expint (En)
1970 </p>
1971 </td>
1972 <td>
1973 <p>
1974 <span class="blue">1.86<br> (273ns)</span>
1975 </p>
1976 </td>
1977 <td>
1978 <p>
1979 <span class="green">1.00<br> (147ns)</span>
1980 </p>
1981 </td>
1982 </tr>
1983 <tr>
1984 <td>
1985 <p>
1986 expm1
1987 </p>
1988 </td>
1989 <td>
1990 <p>
1991 <span class="green">1.00<br> (10ns)</span>
1992 </p>
1993 </td>
1994 <td>
1995 <p>
1996 <span class="green">1.10<br> (11ns)</span>
1997 </p>
1998 </td>
1999 </tr>
2000 <tr>
2001 <td>
2002 <p>
2003 gamma_p
2004 </p>
2005 </td>
2006 <td>
2007 <p>
2008 <span class="red">2.42<br> (492ns)</span>
2009 </p>
2010 </td>
2011 <td>
2012 <p>
2013 <span class="green">1.00<br> (203ns)</span>
2014 </p>
2015 </td>
2016 </tr>
2017 <tr>
2018 <td>
2019 <p>
2020 gamma_p_inv
2021 </p>
2022 </td>
2023 <td>
2024 <p>
2025 <span class="red">2.24<br> (1577ns)</span>
2026 </p>
2027 </td>
2028 <td>
2029 <p>
2030 <span class="green">1.00<br> (704ns)</span>
2031 </p>
2032 </td>
2033 </tr>
2034 <tr>
2035 <td>
2036 <p>
2037 gamma_q
2038 </p>
2039 </td>
2040 <td>
2041 <p>
2042 <span class="red">2.53<br> (508ns)</span>
2043 </p>
2044 </td>
2045 <td>
2046 <p>
2047 <span class="green">1.00<br> (201ns)</span>
2048 </p>
2049 </td>
2050 </tr>
2051 <tr>
2052 <td>
2053 <p>
2054 gamma_q_inv
2055 </p>
2056 </td>
2057 <td>
2058 <p>
2059 <span class="red">2.45<br> (1841ns)</span>
2060 </p>
2061 </td>
2062 <td>
2063 <p>
2064 <span class="green">1.00<br> (751ns)</span>
2065 </p>
2066 </td>
2067 </tr>
2068 <tr>
2069 <td>
2070 <p>
2071 ibeta
2072 </p>
2073 </td>
2074 <td>
2075 <p>
2076 <span class="red">2.71<br> (1715ns)</span>
2077 </p>
2078 </td>
2079 <td>
2080 <p>
2081 <span class="green">1.00<br> (634ns)</span>
2082 </p>
2083 </td>
2084 </tr>
2085 <tr>
2086 <td>
2087 <p>
2088 ibeta_inv
2089 </p>
2090 </td>
2091 <td>
2092 <p>
2093 <span class="red">2.58<br> (5742ns)</span>
2094 </p>
2095 </td>
2096 <td>
2097 <p>
2098 <span class="green">1.00<br> (2224ns)</span>
2099 </p>
2100 </td>
2101 </tr>
2102 <tr>
2103 <td>
2104 <p>
2105 ibetac
2106 </p>
2107 </td>
2108 <td>
2109 <p>
2110 <span class="red">2.66<br> (1736ns)</span>
2111 </p>
2112 </td>
2113 <td>
2114 <p>
2115 <span class="green">1.00<br> (653ns)</span>
2116 </p>
2117 </td>
2118 </tr>
2119 <tr>
2120 <td>
2121 <p>
2122 ibetac_inv
2123 </p>
2124 </td>
2125 <td>
2126 <p>
2127 <span class="red">2.44<br> (5451ns)</span>
2128 </p>
2129 </td>
2130 <td>
2131 <p>
2132 <span class="green">1.00<br> (2237ns)</span>
2133 </p>
2134 </td>
2135 </tr>
2136 <tr>
2137 <td>
2138 <p>
2139 jacobi_cn
2140 </p>
2141 </td>
2142 <td>
2143 <p>
2144 <span class="red">2.77<br> (476ns)</span>
2145 </p>
2146 </td>
2147 <td>
2148 <p>
2149 <span class="green">1.00<br> (172ns)</span>
2150 </p>
2151 </td>
2152 </tr>
2153 <tr>
2154 <td>
2155 <p>
2156 jacobi_dn
2157 </p>
2158 </td>
2159 <td>
2160 <p>
2161 <span class="red">2.80<br> (481ns)</span>
2162 </p>
2163 </td>
2164 <td>
2165 <p>
2166 <span class="green">1.00<br> (172ns)</span>
2167 </p>
2168 </td>
2169 </tr>
2170 <tr>
2171 <td>
2172 <p>
2173 jacobi_sn
2174 </p>
2175 </td>
2176 <td>
2177 <p>
2178 <span class="red">2.86<br> (492ns)</span>
2179 </p>
2180 </td>
2181 <td>
2182 <p>
2183 <span class="green">1.00<br> (172ns)</span>
2184 </p>
2185 </td>
2186 </tr>
2187 <tr>
2188 <td>
2189 <p>
2190 laguerre
2191 </p>
2192 </td>
2193 <td>
2194 <p>
2195 <span class="green">1.09<br> (139ns)</span>
2196 </p>
2197 </td>
2198 <td>
2199 <p>
2200 <span class="green">1.00<br> (128ns)</span>
2201 </p>
2202 </td>
2203 </tr>
2204 <tr>
2205 <td>
2206 <p>
2207 legendre
2208 </p>
2209 </td>
2210 <td>
2211 <p>
2212 <span class="green">1.16<br> (399ns)</span>
2213 </p>
2214 </td>
2215 <td>
2216 <p>
2217 <span class="green">1.00<br> (345ns)</span>
2218 </p>
2219 </td>
2220 </tr>
2221 <tr>
2222 <td>
2223 <p>
2224 legendre Q
2225 </p>
2226 </td>
2227 <td>
2228 <p>
2229 <span class="green">1.18<br> (496ns)</span>
2230 </p>
2231 </td>
2232 <td>
2233 <p>
2234 <span class="green">1.00<br> (422ns)</span>
2235 </p>
2236 </td>
2237 </tr>
2238 <tr>
2239 <td>
2240 <p>
2241 lgamma
2242 </p>
2243 </td>
2244 <td>
2245 <p>
2246 <span class="red">2.20<br> (257ns)</span>
2247 </p>
2248 </td>
2249 <td>
2250 <p>
2251 <span class="green">1.00<br> (117ns)</span>
2252 </p>
2253 </td>
2254 </tr>
2255 <tr>
2256 <td>
2257 <p>
2258 log1p
2259 </p>
2260 </td>
2261 <td>
2262 <p>
2263 <span class="green">1.00<br> (12ns)</span>
2264 </p>
2265 </td>
2266 <td>
2267 <p>
2268 <span class="green">1.00<br> (12ns)</span>
2269 </p>
2270 </td>
2271 </tr>
2272 <tr>
2273 <td>
2274 <p>
2275 polygamma
2276 </p>
2277 </td>
2278 <td>
2279 <p>
2280 <span class="red">3.93<br> (2885ns)</span>
2281 </p>
2282 </td>
2283 <td>
2284 <p>
2285 <span class="green">1.00<br> (734ns)</span>
2286 </p>
2287 </td>
2288 </tr>
2289 <tr>
2290 <td>
2291 <p>
2292 sph_bessel
2293 </p>
2294 </td>
2295 <td>
2296 <p>
2297 <span class="blue">1.71<br> (1563ns)</span>
2298 </p>
2299 </td>
2300 <td>
2301 <p>
2302 <span class="green">1.00<br> (915ns)</span>
2303 </p>
2304 </td>
2305 </tr>
2306 <tr>
2307 <td>
2308 <p>
2309 sph_neumann
2310 </p>
2311 </td>
2312 <td>
2313 <p>
2314 <span class="red">2.15<br> (3745ns)</span>
2315 </p>
2316 </td>
2317 <td>
2318 <p>
2319 <span class="green">1.00<br> (1744ns)</span>
2320 </p>
2321 </td>
2322 </tr>
2323 <tr>
2324 <td>
2325 <p>
2326 tgamma
2327 </p>
2328 </td>
2329 <td>
2330 <p>
2331 <span class="red">3.69<br> (354ns)</span>
2332 </p>
2333 </td>
2334 <td>
2335 <p>
2336 <span class="green">1.00<br> (96ns)</span>
2337 </p>
2338 </td>
2339 </tr>
2340 <tr>
2341 <td>
2342 <p>
2343 tgamma (incomplete)
2344 </p>
2345 </td>
2346 <td>
2347 <p>
2348 <span class="red">2.35<br> (744ns)</span>
2349 </p>
2350 </td>
2351 <td>
2352 <p>
2353 <span class="green">1.00<br> (316ns)</span>
2354 </p>
2355 </td>
2356 </tr>
2357 <tr>
2358 <td>
2359 <p>
2360 trigamma
2361 </p>
2362 </td>
2363 <td>
2364 <p>
2365 <span class="blue">1.64<br> (36ns)</span>
2366 </p>
2367 </td>
2368 <td>
2369 <p>
2370 <span class="green">1.00<br> (22ns)</span>
2371 </p>
2372 </td>
2373 </tr>
2374 <tr>
2375 <td>
2376 <p>
2377 zeta
2378 </p>
2379 </td>
2380 <td>
2381 <p>
2382 <span class="red">2.71<br> (509ns)</span>
2383 </p>
2384 </td>
2385 <td>
2386 <p>
2387 <span class="green">1.00<br> (188ns)</span>
2388 </p>
2389 </td>
2390 </tr>
2391 </tbody>
2392 </table></div>
2393 </div>
2394 <br class="table-break">
2395 </div>
2396 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
2397 <td align="left"></td>
2398 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
2399 Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
2400 Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
2401 Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
2402 Distributed under the Boost Software License, Version 1.0. (See accompanying
2403 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>)
2404 </p>
2405 </div></td>
2406 </tr></table>
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