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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 22.12. 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</colgroup>
45<thead><tr>
46<th>
47              <p>
48                Function
49              </p>
50            </th>
51<th>
52              <p>
53                Microsoft Visual C++ version 14.2<br> boost 1.73
54              </p>
55            </th>
56<th>
57              <p>
58                GNU C++ version 9.2.0<br> boost 1.73
59              </p>
60            </th>
61<th>
62              <p>
63                GNU C++ version 9.2.0<br> boost 1.73<br> promote_double&lt;false&gt;
64              </p>
65            </th>
66</tr></thead>
67<tbody>
68<tr>
69<td>
70              <p>
71                assoc_laguerre
72              </p>
73            </td>
74<td>
75              <p>
76                <span class="blue">1.41<br> (179ns)</span>
77              </p>
78            </td>
79<td>
80              <p>
81                <span class="green">1.08<br> (137ns)</span>
82              </p>
83            </td>
84<td>
85              <p>
86                <span class="green">1.00<br> (127ns)</span>
87              </p>
88            </td>
89</tr>
90<tr>
91<td>
92              <p>
93                assoc_legendre
94              </p>
95            </td>
96<td>
97              <p>
98                <span class="blue">1.76<br> (248ns)</span>
99              </p>
100            </td>
101<td>
102              <p>
103                <span class="blue">1.36<br> (192ns)</span>
104              </p>
105            </td>
106<td>
107              <p>
108                <span class="green">1.00<br> (141ns)</span>
109              </p>
110            </td>
111</tr>
112<tr>
113<td>
114              <p>
115                beta
116              </p>
117            </td>
118<td>
119              <p>
120                <span class="green">1.00<br> (123ns)</span>
121              </p>
122            </td>
123<td>
124              <p>
125                <span class="red">2.62<br> (322ns)</span>
126              </p>
127            </td>
128<td>
129              <p>
130                <span class="blue">1.93<br> (237ns)</span>
131              </p>
132            </td>
133</tr>
134<tr>
135<td>
136              <p>
137                beta (incomplete)
138              </p>
139            </td>
140<td>
141              <p>
142                <span class="green">1.00<br> (470ns)</span>
143              </p>
144            </td>
145<td>
146              <p>
147                <span class="red">2.95<br> (1385ns)</span>
148              </p>
149            </td>
150<td>
151              <p>
152                <span class="blue">1.58<br> (741ns)</span>
153              </p>
154            </td>
155</tr>
156<tr>
157<td>
158              <p>
159                cbrt
160              </p>
161            </td>
162<td>
163              <p>
164                <span class="red">3.40<br> (51ns)</span>
165              </p>
166            </td>
167<td>
168              <p>
169                <span class="red">4.67<br> (70ns)</span>
170              </p>
171            </td>
172<td>
173              <p>
174                <span class="green">1.00<br> (15ns)</span>
175              </p>
176            </td>
177</tr>
178<tr>
179<td>
180              <p>
181                cyl_bessel_i
182              </p>
183            </td>
184<td>
185              <p>
186                <span class="green">1.00<br> (281ns)</span>
187              </p>
188            </td>
189<td>
190              <p>
191                <span class="red">3.38<br> (949ns)</span>
192              </p>
193            </td>
194<td>
195              <p>
196                <span class="blue">1.38<br> (387ns)</span>
197              </p>
198            </td>
199</tr>
200<tr>
201<td>
202              <p>
203                cyl_bessel_i (integer order)
204              </p>
205            </td>
206<td>
207              <p>
208                <span class="green">1.00<br> (195ns)</span>
209              </p>
210            </td>
211<td>
212              <p>
213                <span class="red">3.06<br> (597ns)</span>
214              </p>
215            </td>
216<td>
217              <p>
218                <span class="green">1.00<br> (195ns)</span>
219              </p>
220            </td>
221</tr>
222<tr>
223<td>
224              <p>
225                cyl_bessel_j
226              </p>
227            </td>
228<td>
229              <p>
230                <span class="green">1.00<br> (371ns)</span>
231              </p>
232            </td>
233<td>
234              <p>
235                <span class="red">2.39<br> (886ns)</span>
236              </p>
237            </td>
238<td>
239              <p>
240                <span class="blue">1.35<br> (499ns)</span>
241              </p>
242            </td>
243</tr>
244<tr>
245<td>
246              <p>
247                cyl_bessel_j (integer order)
248              </p>
249            </td>
250<td>
251              <p>
252                <span class="blue">1.28<br> (123ns)</span>
253              </p>
254            </td>
255<td>
256              <p>
257                <span class="blue">1.92<br> (184ns)</span>
258              </p>
259            </td>
260<td>
261              <p>
262                <span class="green">1.00<br> (96ns)</span>
263              </p>
264            </td>
265</tr>
266<tr>
267<td>
268              <p>
269                cyl_bessel_k
270              </p>
271            </td>
272<td>
273              <p>
274                <span class="green">1.11<br> (385ns)</span>
275              </p>
276            </td>
277<td>
278              <p>
279                <span class="red">19.68<br> (6847ns)</span>
280              </p>
281            </td>
282<td>
283              <p>
284                <span class="green">1.00<br> (348ns)</span>
285              </p>
286            </td>
287</tr>
288<tr>
289<td>
290              <p>
291                cyl_bessel_k (integer order)
292              </p>
293            </td>
294<td>
295              <p>
296                <span class="green">1.06<br> (217ns)</span>
297              </p>
298            </td>
299<td>
300              <p>
301                <span class="red">18.17<br> (3724ns)</span>
302              </p>
303            </td>
304<td>
305              <p>
306                <span class="green">1.00<br> (205ns)</span>
307              </p>
308            </td>
309</tr>
310<tr>
311<td>
312              <p>
313                cyl_neumann
314              </p>
315            </td>
316<td>
317              <p>
318                <span class="green">1.17<br> (6696ns)</span>
319              </p>
320            </td>
321<td>
322              <p>
323                <span class="blue">1.76<br> (10032ns)</span>
324              </p>
325            </td>
326<td>
327              <p>
328                <span class="green">1.00<br> (5715ns)</span>
329              </p>
330            </td>
331</tr>
332<tr>
333<td>
334              <p>
335                cyl_neumann (integer order)
336              </p>
337            </td>
338<td>
339              <p>
340                <span class="green">1.00<br> (158ns)</span>
341              </p>
342            </td>
343<td>
344              <p>
345                <span class="red">2.20<br> (348ns)</span>
346              </p>
347            </td>
348<td>
349              <p>
350                <span class="blue">1.59<br> (252ns)</span>
351              </p>
352            </td>
353</tr>
354<tr>
355<td>
356              <p>
357                digamma
358              </p>
359            </td>
360<td>
361              <p>
362                <span class="green">1.00<br> (20ns)</span>
363              </p>
364            </td>
365<td>
366              <p>
367                <span class="red">3.45<br> (69ns)</span>
368              </p>
369            </td>
370<td>
371              <p>
372                <span class="red">2.30<br> (46ns)</span>
373              </p>
374            </td>
375</tr>
376<tr>
377<td>
378              <p>
379                ellint_1
380              </p>
381            </td>
382<td>
383              <p>
384                <span class="blue">1.57<br> (390ns)</span>
385              </p>
386            </td>
387<td>
388              <p>
389                <span class="blue">1.41<br> (349ns)</span>
390              </p>
391            </td>
392<td>
393              <p>
394                <span class="green">1.00<br> (248ns)</span>
395              </p>
396            </td>
397</tr>
398<tr>
399<td>
400              <p>
401                ellint_1 (complete)
402              </p>
403            </td>
404<td>
405              <p>
406                <span class="blue">1.64<br> (77ns)</span>
407              </p>
408            </td>
409<td>
410              <p>
411                <span class="blue">1.64<br> (77ns)</span>
412              </p>
413            </td>
414<td>
415              <p>
416                <span class="green">1.00<br> (47ns)</span>
417              </p>
418            </td>
419</tr>
420<tr>
421<td>
422              <p>
423                ellint_2
424              </p>
425            </td>
426<td>
427              <p>
428                <span class="blue">1.81<br> (702ns)</span>
429              </p>
430            </td>
431<td>
432              <p>
433                <span class="blue">1.50<br> (583ns)</span>
434              </p>
435            </td>
436<td>
437              <p>
438                <span class="green">1.00<br> (388ns)</span>
439              </p>
440            </td>
441</tr>
442<tr>
443<td>
444              <p>
445                ellint_2 (complete)
446              </p>
447            </td>
448<td>
449              <p>
450                <span class="red">3.11<br> (84ns)</span>
451              </p>
452            </td>
453<td>
454              <p>
455                <span class="red">2.11<br> (57ns)</span>
456              </p>
457            </td>
458<td>
459              <p>
460                <span class="green">1.00<br> (27ns)</span>
461              </p>
462            </td>
463</tr>
464<tr>
465<td>
466              <p>
467                ellint_3
468              </p>
469            </td>
470<td>
471              <p>
472                <span class="red">3.47<br> (1381ns)</span>
473              </p>
474            </td>
475<td>
476              <p>
477                <span class="blue">1.68<br> (670ns)</span>
478              </p>
479            </td>
480<td>
481              <p>
482                <span class="green">1.00<br> (398ns)</span>
483              </p>
484            </td>
485</tr>
486<tr>
487<td>
488              <p>
489                ellint_3 (complete)
490              </p>
491            </td>
492<td>
493              <p>
494                <span class="red">inf<br> (802ns)</span>
495              </p>
496            </td>
497<td>
498              <p>
499                <span class="green">-nan(ind)<br> (0ns)</span>
500              </p>
501            </td>
502<td>
503              <p>
504                <span class="green">-nan(ind)<br> (0ns)</span>
505              </p>
506            </td>
507</tr>
508<tr>
509<td>
510              <p>
511                ellint_rc
512              </p>
513            </td>
514<td>
515              <p>
516                <span class="blue">1.55<br> (59ns)</span>
517              </p>
518            </td>
519<td>
520              <p>
521                <span class="red">2.21<br> (84ns)</span>
522              </p>
523            </td>
524<td>
525              <p>
526                <span class="green">1.00<br> (38ns)</span>
527              </p>
528            </td>
529</tr>
530<tr>
531<td>
532              <p>
533                ellint_rd
534              </p>
535            </td>
536<td>
537              <p>
538                <span class="blue">1.32<br> (271ns)</span>
539              </p>
540            </td>
541<td>
542              <p>
543                <span class="blue">1.26<br> (260ns)</span>
544              </p>
545            </td>
546<td>
547              <p>
548                <span class="green">1.00<br> (206ns)</span>
549              </p>
550            </td>
551</tr>
552<tr>
553<td>
554              <p>
555                ellint_rf
556              </p>
557            </td>
558<td>
559              <p>
560                <span class="blue">1.27<br> (62ns)</span>
561              </p>
562            </td>
563<td>
564              <p>
565                <span class="blue">1.94<br> (95ns)</span>
566              </p>
567            </td>
568<td>
569              <p>
570                <span class="green">1.00<br> (49ns)</span>
571              </p>
572            </td>
573</tr>
574<tr>
575<td>
576              <p>
577                ellint_rj
578              </p>
579            </td>
580<td>
581              <p>
582                <span class="blue">1.46<br> (264ns)</span>
583              </p>
584            </td>
585<td>
586              <p>
587                <span class="red">2.29<br> (414ns)</span>
588              </p>
589            </td>
590<td>
591              <p>
592                <span class="green">1.00<br> (181ns)</span>
593              </p>
594            </td>
595</tr>
596<tr>
597<td>
598              <p>
599                erf
600              </p>
601            </td>
602<td>
603              <p>
604                <span class="blue">1.30<br> (43ns)</span>
605              </p>
606            </td>
607<td>
608              <p>
609                <span class="blue">1.85<br> (61ns)</span>
610              </p>
611            </td>
612<td>
613              <p>
614                <span class="green">1.00<br> (33ns)</span>
615              </p>
616            </td>
617</tr>
618<tr>
619<td>
620              <p>
621                erfc
622              </p>
623            </td>
624<td>
625              <p>
626                <span class="green">1.06<br> (54ns)</span>
627              </p>
628            </td>
629<td>
630              <p>
631                <span class="blue">1.76<br> (90ns)</span>
632              </p>
633            </td>
634<td>
635              <p>
636                <span class="green">1.00<br> (51ns)</span>
637              </p>
638            </td>
639</tr>
640<tr>
641<td>
642              <p>
643                expint
644              </p>
645            </td>
646<td>
647              <p>
648                <span class="green">1.00<br> (27ns)</span>
649              </p>
650            </td>
651<td>
652              <p>
653                <span class="red">3.41<br> (92ns)</span>
654              </p>
655            </td>
656<td>
657              <p>
658                <span class="red">2.22<br> (60ns)</span>
659              </p>
660            </td>
661</tr>
662<tr>
663<td>
664              <p>
665                expint (En)
666              </p>
667            </td>
668<td>
669              <p>
670                <span class="green">1.00<br> (106ns)</span>
671              </p>
672            </td>
673<td>
674              <p>
675                <span class="blue">1.94<br> (206ns)</span>
676              </p>
677            </td>
678<td>
679              <p>
680                <span class="blue">1.29<br> (137ns)</span>
681              </p>
682            </td>
683</tr>
684<tr>
685<td>
686              <p>
687                expm1
688              </p>
689            </td>
690<td>
691              <p>
692                <span class="green">1.00<br> (11ns)</span>
693              </p>
694            </td>
695<td>
696              <p>
697                <span class="red">3.00<br> (33ns)</span>
698              </p>
699            </td>
700<td>
701              <p>
702                <span class="red">2.36<br> (26ns)</span>
703              </p>
704            </td>
705</tr>
706<tr>
707<td>
708              <p>
709                gamma_p
710              </p>
711            </td>
712<td>
713              <p>
714                <span class="green">1.00<br> (303ns)</span>
715              </p>
716            </td>
717<td>
718              <p>
719                <span class="blue">2.00<br> (605ns)</span>
720              </p>
721            </td>
722<td>
723              <p>
724                <span class="green">1.17<br> (355ns)</span>
725              </p>
726            </td>
727</tr>
728<tr>
729<td>
730              <p>
731                gamma_p_inv
732              </p>
733            </td>
734<td>
735              <p>
736                <span class="green">1.00<br> (1266ns)</span>
737              </p>
738            </td>
739<td>
740              <p>
741                <span class="blue">1.85<br> (2341ns)</span>
742              </p>
743            </td>
744<td>
745              <p>
746                <span class="green">1.15<br> (1460ns)</span>
747              </p>
748            </td>
749</tr>
750<tr>
751<td>
752              <p>
753                gamma_q
754              </p>
755            </td>
756<td>
757              <p>
758                <span class="green">1.00<br> (294ns)</span>
759              </p>
760            </td>
761<td>
762              <p>
763                <span class="red">2.10<br> (618ns)</span>
764              </p>
765            </td>
766<td>
767              <p>
768                <span class="blue">1.21<br> (356ns)</span>
769              </p>
770            </td>
771</tr>
772<tr>
773<td>
774              <p>
775                gamma_q_inv
776              </p>
777            </td>
778<td>
779              <p>
780                <span class="green">1.00<br> (1194ns)</span>
781              </p>
782            </td>
783<td>
784              <p>
785                <span class="blue">1.66<br> (1987ns)</span>
786              </p>
787            </td>
788<td>
789              <p>
790                <span class="green">1.14<br> (1357ns)</span>
791              </p>
792            </td>
793</tr>
794<tr>
795<td>
796              <p>
797                ibeta
798              </p>
799            </td>
800<td>
801              <p>
802                <span class="green">1.00<br> (512ns)</span>
803              </p>
804            </td>
805<td>
806              <p>
807                <span class="red">2.63<br> (1344ns)</span>
808              </p>
809            </td>
810<td>
811              <p>
812                <span class="blue">1.31<br> (673ns)</span>
813              </p>
814            </td>
815</tr>
816<tr>
817<td>
818              <p>
819                ibeta_inv
820              </p>
821            </td>
822<td>
823              <p>
824                <span class="green">1.00<br> (1910ns)</span>
825              </p>
826            </td>
827<td>
828              <p>
829                <span class="red">2.49<br> (4751ns)</span>
830              </p>
831            </td>
832<td>
833              <p>
834                <span class="blue">1.48<br> (2822ns)</span>
835              </p>
836            </td>
837</tr>
838<tr>
839<td>
840              <p>
841                ibetac
842              </p>
843            </td>
844<td>
845              <p>
846                <span class="green">1.00<br> (525ns)</span>
847              </p>
848            </td>
849<td>
850              <p>
851                <span class="red">2.60<br> (1365ns)</span>
852              </p>
853            </td>
854<td>
855              <p>
856                <span class="blue">1.27<br> (668ns)</span>
857              </p>
858            </td>
859</tr>
860<tr>
861<td>
862              <p>
863                ibetac_inv
864              </p>
865            </td>
866<td>
867              <p>
868                <span class="green">1.00<br> (1676ns)</span>
869              </p>
870            </td>
871<td>
872              <p>
873                <span class="red">2.85<br> (4778ns)</span>
874              </p>
875            </td>
876<td>
877              <p>
878                <span class="blue">1.74<br> (2910ns)</span>
879              </p>
880            </td>
881</tr>
882<tr>
883<td>
884              <p>
885                jacobi_cn
886              </p>
887            </td>
888<td>
889              <p>
890                <span class="green">1.00<br> (181ns)</span>
891              </p>
892            </td>
893<td>
894              <p>
895                <span class="red">3.10<br> (561ns)</span>
896              </p>
897            </td>
898<td>
899              <p>
900                <span class="blue">2.00<br> (362ns)</span>
901              </p>
902            </td>
903</tr>
904<tr>
905<td>
906              <p>
907                jacobi_dn
908              </p>
909            </td>
910<td>
911              <p>
912                <span class="green">1.00<br> (203ns)</span>
913              </p>
914            </td>
915<td>
916              <p>
917                <span class="red">3.03<br> (616ns)</span>
918              </p>
919            </td>
920<td>
921              <p>
922                <span class="blue">1.93<br> (392ns)</span>
923              </p>
924            </td>
925</tr>
926<tr>
927<td>
928              <p>
929                jacobi_sn
930              </p>
931            </td>
932<td>
933              <p>
934                <span class="green">1.00<br> (202ns)</span>
935              </p>
936            </td>
937<td>
938              <p>
939                <span class="red">2.81<br> (568ns)</span>
940              </p>
941            </td>
942<td>
943              <p>
944                <span class="blue">1.73<br> (350ns)</span>
945              </p>
946            </td>
947</tr>
948<tr>
949<td>
950              <p>
951                laguerre
952              </p>
953            </td>
954<td>
955              <p>
956                <span class="green">1.02<br> (107ns)</span>
957              </p>
958            </td>
959<td>
960              <p>
961                <span class="green">1.07<br> (112ns)</span>
962              </p>
963            </td>
964<td>
965              <p>
966                <span class="green">1.00<br> (105ns)</span>
967              </p>
968            </td>
969</tr>
970<tr>
971<td>
972              <p>
973                legendre
974              </p>
975            </td>
976<td>
977              <p>
978                <span class="green">1.11<br> (283ns)</span>
979              </p>
980            </td>
981<td>
982              <p>
983                <span class="blue">1.25<br> (320ns)</span>
984              </p>
985            </td>
986<td>
987              <p>
988                <span class="green">1.00<br> (255ns)</span>
989              </p>
990            </td>
991</tr>
992<tr>
993<td>
994              <p>
995                legendre Q
996              </p>
997            </td>
998<td>
999              <p>
1000                <span class="green">1.00<br> (309ns)</span>
1001              </p>
1002            </td>
1003<td>
1004              <p>
1005                <span class="blue">1.51<br> (466ns)</span>
1006              </p>
1007            </td>
1008<td>
1009              <p>
1010                <span class="green">1.15<br> (354ns)</span>
1011              </p>
1012            </td>
1013</tr>
1014<tr>
1015<td>
1016              <p>
1017                lgamma
1018              </p>
1019            </td>
1020<td>
1021              <p>
1022                <span class="green">1.00<br> (80ns)</span>
1023              </p>
1024            </td>
1025<td>
1026              <p>
1027                <span class="red">2.67<br> (214ns)</span>
1028              </p>
1029            </td>
1030<td>
1031              <p>
1032                <span class="blue">2.00<br> (160ns)</span>
1033              </p>
1034            </td>
1035</tr>
1036<tr>
1037<td>
1038              <p>
1039                log1p
1040              </p>
1041            </td>
1042<td>
1043              <p>
1044                <span class="green">1.00<br> (14ns)</span>
1045              </p>
1046            </td>
1047<td>
1048              <p>
1049                <span class="red">2.07<br> (29ns)</span>
1050              </p>
1051            </td>
1052<td>
1053              <p>
1054                <span class="blue">1.21<br> (17ns)</span>
1055              </p>
1056            </td>
1057</tr>
1058<tr>
1059<td>
1060              <p>
1061                polygamma
1062              </p>
1063            </td>
1064<td>
1065              <p>
1066                <span class="green">1.00<br> (4193ns)</span>
1067              </p>
1068            </td>
1069<td>
1070              <p>
1071                <span class="blue">1.85<br> (7743ns)</span>
1072              </p>
1073            </td>
1074<td>
1075              <p>
1076                <span class="blue">1.91<br> (8018ns)</span>
1077              </p>
1078            </td>
1079</tr>
1080<tr>
1081<td>
1082              <p>
1083                sph_bessel
1084              </p>
1085            </td>
1086<td>
1087              <p>
1088                <span class="green">1.01<br> (668ns)</span>
1089              </p>
1090            </td>
1091<td>
1092              <p>
1093                <span class="blue">1.48<br> (975ns)</span>
1094              </p>
1095            </td>
1096<td>
1097              <p>
1098                <span class="green">1.00<br> (661ns)</span>
1099              </p>
1100            </td>
1101</tr>
1102<tr>
1103<td>
1104              <p>
1105                sph_neumann
1106              </p>
1107            </td>
1108<td>
1109              <p>
1110                <span class="green">1.07<br> (1138ns)</span>
1111              </p>
1112            </td>
1113<td>
1114              <p>
1115                <span class="red">2.96<br> (3153ns)</span>
1116              </p>
1117            </td>
1118<td>
1119              <p>
1120                <span class="green">1.00<br> (1064ns)</span>
1121              </p>
1122            </td>
1123</tr>
1124<tr>
1125<td>
1126              <p>
1127                tgamma
1128              </p>
1129            </td>
1130<td>
1131              <p>
1132                <span class="green">1.00<br> (74ns)</span>
1133              </p>
1134            </td>
1135<td>
1136              <p>
1137                <span class="red">3.50<br> (259ns)</span>
1138              </p>
1139            </td>
1140<td>
1141              <p>
1142                <span class="red">2.14<br> (158ns)</span>
1143              </p>
1144            </td>
1145</tr>
1146<tr>
1147<td>
1148              <p>
1149                tgamma (incomplete)
1150              </p>
1151            </td>
1152<td>
1153              <p>
1154                <span class="green">1.00<br> (208ns)</span>
1155              </p>
1156            </td>
1157<td>
1158              <p>
1159                <span class="red">2.30<br> (478ns)</span>
1160              </p>
1161            </td>
1162<td>
1163              <p>
1164                <span class="blue">1.64<br> (342ns)</span>
1165              </p>
1166            </td>
1167</tr>
1168<tr>
1169<td>
1170              <p>
1171                trigamma
1172              </p>
1173            </td>
1174<td>
1175              <p>
1176                <span class="green">1.00<br> (12ns)</span>
1177              </p>
1178            </td>
1179<td>
1180              <p>
1181                <span class="red">2.83<br> (34ns)</span>
1182              </p>
1183            </td>
1184<td>
1185              <p>
1186                <span class="green">1.17<br> (14ns)</span>
1187              </p>
1188            </td>
1189</tr>
1190<tr>
1191<td>
1192              <p>
1193                zeta
1194              </p>
1195            </td>
1196<td>
1197              <p>
1198                <span class="green">1.00<br> (117ns)</span>
1199              </p>
1200            </td>
1201<td>
1202              <p>
1203                <span class="red">2.65<br> (310ns)</span>
1204              </p>
1205            </td>
1206<td>
1207              <p>
1208                <span class="blue">1.89<br> (221ns)</span>
1209              </p>
1210            </td>
1211</tr>
1212</tbody>
1213</table></div>
1214</div>
1215<br class="table-break"><div class="table">
1216<a name="math_toolkit.comp_compilers.table_Compiler_Comparison_on_linux"></a><p class="title"><b>Table 22.13. Compiler Comparison on linux</b></p>
1217<div class="table-contents"><table class="table" summary="Compiler Comparison on linux">
1218<colgroup>
1219<col>
1220<col>
1221<col>
1222<col>
1223<col>
1224<col>
1225<col>
1226</colgroup>
1227<thead><tr>
1228<th>
1229              <p>
1230                Function
1231              </p>
1232            </th>
1233<th>
1234              <p>
1235                GNU C++ version 9.2.1 20191008<br> boost 1.73
1236              </p>
1237            </th>
1238<th>
1239              <p>
1240                GNU C++ version 9.2.1 20191008<br> boost 1.73<br> promote_double&lt;false&gt;
1241              </p>
1242            </th>
1243<th>
1244              <p>
1245                Clang version 9.0.0 (tags/RELEASE_900/final)<br> boost 1.73
1246              </p>
1247            </th>
1248<th>
1249              <p>
1250                Clang version 9.0.0 (tags/RELEASE_900/final)<br> boost 1.73<br>
1251                promote_double&lt;false&gt;
1252              </p>
1253            </th>
1254<th>
1255              <p>
1256                Intel C++ C++0x mode version 1910<br> boost 1.73
1257              </p>
1258            </th>
1259<th>
1260              <p>
1261                Intel C++ C++0x mode version 1910<br> boost 1.73<br> promote_double&lt;false&gt;
1262              </p>
1263            </th>
1264</tr></thead>
1265<tbody>
1266<tr>
1267<td>
1268              <p>
1269                assoc_laguerre
1270              </p>
1271            </td>
1272<td>
1273              <p>
1274                <span class="green">1.17<br> (156ns)</span>
1275              </p>
1276            </td>
1277<td>
1278              <p>
1279                <span class="green">1.08<br> (143ns)</span>
1280              </p>
1281            </td>
1282<td>
1283              <p>
1284                <span class="blue">1.72<br> (229ns)</span>
1285              </p>
1286            </td>
1287<td>
1288              <p>
1289                <span class="blue">1.31<br> (174ns)</span>
1290              </p>
1291            </td>
1292<td>
1293              <p>
1294                <span class="green">1.15<br> (153ns)</span>
1295              </p>
1296            </td>
1297<td>
1298              <p>
1299                <span class="green">1.00<br> (133ns)</span>
1300              </p>
1301            </td>
1302</tr>
1303<tr>
1304<td>
1305              <p>
1306                assoc_legendre
1307              </p>
1308            </td>
1309<td>
1310              <p>
1311                <span class="red">2.91<br> (279ns)</span>
1312              </p>
1313            </td>
1314<td>
1315              <p>
1316                <span class="blue">1.78<br> (171ns)</span>
1317              </p>
1318            </td>
1319<td>
1320              <p>
1321                <span class="red">2.86<br> (275ns)</span>
1322              </p>
1323            </td>
1324<td>
1325              <p>
1326                <span class="green">1.00<br> (96ns)</span>
1327              </p>
1328            </td>
1329<td>
1330              <p>
1331                <span class="red">2.79<br> (268ns)</span>
1332              </p>
1333            </td>
1334<td>
1335              <p>
1336                <span class="red">2.16<br> (207ns)</span>
1337              </p>
1338            </td>
1339</tr>
1340<tr>
1341<td>
1342              <p>
1343                beta
1344              </p>
1345            </td>
1346<td>
1347              <p>
1348                <span class="red">10.52<br> (789ns)</span>
1349              </p>
1350            </td>
1351<td>
1352              <p>
1353                <span class="blue">1.40<br> (105ns)</span>
1354              </p>
1355            </td>
1356<td>
1357              <p>
1358                <span class="red">10.56<br> (792ns)</span>
1359              </p>
1360            </td>
1361<td>
1362              <p>
1363                <span class="blue">1.73<br> (130ns)</span>
1364              </p>
1365            </td>
1366<td>
1367              <p>
1368                <span class="red">6.07<br> (455ns)</span>
1369              </p>
1370            </td>
1371<td>
1372              <p>
1373                <span class="green">1.00<br> (75ns)</span>
1374              </p>
1375            </td>
1376</tr>
1377<tr>
1378<td>
1379              <p>
1380                beta (incomplete)
1381              </p>
1382            </td>
1383<td>
1384              <p>
1385                <span class="red">4.98<br> (2076ns)</span>
1386              </p>
1387            </td>
1388<td>
1389              <p>
1390                <span class="blue">1.26<br> (524ns)</span>
1391              </p>
1392            </td>
1393<td>
1394              <p>
1395                <span class="red">5.44<br> (2267ns)</span>
1396              </p>
1397            </td>
1398<td>
1399              <p>
1400                <span class="green">1.00<br> (417ns)</span>
1401              </p>
1402            </td>
1403<td>
1404              <p>
1405                <span class="red">3.15<br> (1315ns)</span>
1406              </p>
1407            </td>
1408<td>
1409              <p>
1410                <span class="green">1.16<br> (484ns)</span>
1411              </p>
1412            </td>
1413</tr>
1414<tr>
1415<td>
1416              <p>
1417                cbrt
1418              </p>
1419            </td>
1420<td>
1421              <p>
1422                <span class="red">2.52<br> (58ns)</span>
1423              </p>
1424            </td>
1425<td>
1426              <p>
1427                <span class="green">1.09<br> (25ns)</span>
1428              </p>
1429            </td>
1430<td>
1431              <p>
1432                <span class="red">2.35<br> (54ns)</span>
1433              </p>
1434            </td>
1435<td>
1436              <p>
1437                <span class="blue">1.22<br> (28ns)</span>
1438              </p>
1439            </td>
1440<td>
1441              <p>
1442                <span class="blue">1.91<br> (44ns)</span>
1443              </p>
1444            </td>
1445<td>
1446              <p>
1447                <span class="green">1.00<br> (23ns)</span>
1448              </p>
1449            </td>
1450</tr>
1451<tr>
1452<td>
1453              <p>
1454                cyl_bessel_i
1455              </p>
1456            </td>
1457<td>
1458              <p>
1459                <span class="red">5.05<br> (1182ns)</span>
1460              </p>
1461            </td>
1462<td>
1463              <p>
1464                <span class="green">1.02<br> (239ns)</span>
1465              </p>
1466            </td>
1467<td>
1468              <p>
1469                <span class="red">10.73<br> (2511ns)</span>
1470              </p>
1471            </td>
1472<td>
1473              <p>
1474                <span class="blue">1.74<br> (406ns)</span>
1475              </p>
1476            </td>
1477<td>
1478              <p>
1479                <span class="red">3.99<br> (933ns)</span>
1480              </p>
1481            </td>
1482<td>
1483              <p>
1484                <span class="green">1.00<br> (234ns)</span>
1485              </p>
1486            </td>
1487</tr>
1488<tr>
1489<td>
1490              <p>
1491                cyl_bessel_i (integer order)
1492              </p>
1493            </td>
1494<td>
1495              <p>
1496                <span class="red">4.41<br> (767ns)</span>
1497              </p>
1498            </td>
1499<td>
1500              <p>
1501                <span class="green">1.00<br> (174ns)</span>
1502              </p>
1503            </td>
1504<td>
1505              <p>
1506                <span class="red">5.09<br> (886ns)</span>
1507              </p>
1508            </td>
1509<td>
1510              <p>
1511                <span class="green">1.03<br> (179ns)</span>
1512              </p>
1513            </td>
1514<td>
1515              <p>
1516                <span class="red">3.63<br> (631ns)</span>
1517              </p>
1518            </td>
1519<td>
1520              <p>
1521                <span class="green">1.12<br> (195ns)</span>
1522              </p>
1523            </td>
1524</tr>
1525<tr>
1526<td>
1527              <p>
1528                cyl_bessel_j
1529              </p>
1530            </td>
1531<td>
1532              <p>
1533                <span class="red">3.80<br> (1067ns)</span>
1534              </p>
1535            </td>
1536<td>
1537              <p>
1538                <span class="blue">1.28<br> (359ns)</span>
1539              </p>
1540            </td>
1541<td>
1542              <p>
1543                <span class="red">4.72<br> (1327ns)</span>
1544              </p>
1545            </td>
1546<td>
1547              <p>
1548                <span class="blue">1.55<br> (436ns)</span>
1549              </p>
1550            </td>
1551<td>
1552              <p>
1553                <span class="red">3.05<br> (857ns)</span>
1554              </p>
1555            </td>
1556<td>
1557              <p>
1558                <span class="green">1.00<br> (281ns)</span>
1559              </p>
1560            </td>
1561</tr>
1562<tr>
1563<td>
1564              <p>
1565                cyl_bessel_j (integer order)
1566              </p>
1567            </td>
1568<td>
1569              <p>
1570                <span class="red">3.10<br> (319ns)</span>
1571              </p>
1572            </td>
1573<td>
1574              <p>
1575                <span class="green">1.05<br> (108ns)</span>
1576              </p>
1577            </td>
1578<td>
1579              <p>
1580                <span class="red">4.73<br> (487ns)</span>
1581              </p>
1582            </td>
1583<td>
1584              <p>
1585                <span class="green">1.00<br> (103ns)</span>
1586              </p>
1587            </td>
1588<td>
1589              <p>
1590                <span class="red">2.30<br> (237ns)</span>
1591              </p>
1592            </td>
1593<td>
1594              <p>
1595                <span class="green">1.12<br> (115ns)</span>
1596              </p>
1597            </td>
1598</tr>
1599<tr>
1600<td>
1601              <p>
1602                cyl_bessel_k
1603              </p>
1604            </td>
1605<td>
1606              <p>
1607                <span class="red">10.37<br> (3962ns)</span>
1608              </p>
1609            </td>
1610<td>
1611              <p>
1612                <span class="green">1.00<br> (382ns)</span>
1613              </p>
1614            </td>
1615<td>
1616              <p>
1617                <span class="red">11.55<br> (4414ns)</span>
1618              </p>
1619            </td>
1620<td>
1621              <p>
1622                <span class="blue">1.52<br> (582ns)</span>
1623              </p>
1624            </td>
1625<td>
1626              <p>
1627                <span class="red">12.41<br> (4739ns)</span>
1628              </p>
1629            </td>
1630<td>
1631              <p>
1632                <span class="green">1.09<br> (416ns)</span>
1633              </p>
1634            </td>
1635</tr>
1636<tr>
1637<td>
1638              <p>
1639                cyl_bessel_k (integer order)
1640              </p>
1641            </td>
1642<td>
1643              <p>
1644                <span class="red">19.23<br> (3289ns)</span>
1645              </p>
1646            </td>
1647<td>
1648              <p>
1649                <span class="green">1.06<br> (181ns)</span>
1650              </p>
1651            </td>
1652<td>
1653              <p>
1654                <span class="red">19.78<br> (3382ns)</span>
1655              </p>
1656            </td>
1657<td>
1658              <p>
1659                <span class="blue">1.27<br> (217ns)</span>
1660              </p>
1661            </td>
1662<td>
1663              <p>
1664                <span class="red">20.02<br> (3423ns)</span>
1665              </p>
1666            </td>
1667<td>
1668              <p>
1669                <span class="green">1.00<br> (171ns)</span>
1670              </p>
1671            </td>
1672</tr>
1673<tr>
1674<td>
1675              <p>
1676                cyl_neumann
1677              </p>
1678            </td>
1679<td>
1680              <p>
1681                <span class="red">2.18<br> (8826ns)</span>
1682              </p>
1683            </td>
1684<td>
1685              <p>
1686                <span class="green">1.19<br> (4814ns)</span>
1687              </p>
1688            </td>
1689<td>
1690              <p>
1691                <span class="red">3.23<br> (13059ns)</span>
1692              </p>
1693            </td>
1694<td>
1695              <p>
1696                <span class="blue">1.31<br> (5275ns)</span>
1697              </p>
1698            </td>
1699<td>
1700              <p>
1701                <span class="red">2.35<br> (9503ns)</span>
1702              </p>
1703            </td>
1704<td>
1705              <p>
1706                <span class="green">1.00<br> (4041ns)</span>
1707              </p>
1708            </td>
1709</tr>
1710<tr>
1711<td>
1712              <p>
1713                cyl_neumann (integer order)
1714              </p>
1715            </td>
1716<td>
1717              <p>
1718                <span class="red">3.67<br> (466ns)</span>
1719              </p>
1720            </td>
1721<td>
1722              <p>
1723                <span class="blue">1.35<br> (172ns)</span>
1724              </p>
1725            </td>
1726<td>
1727              <p>
1728                <span class="red">4.49<br> (570ns)</span>
1729              </p>
1730            </td>
1731<td>
1732              <p>
1733                <span class="green">1.15<br> (146ns)</span>
1734              </p>
1735            </td>
1736<td>
1737              <p>
1738                <span class="red">2.87<br> (364ns)</span>
1739              </p>
1740            </td>
1741<td>
1742              <p>
1743                <span class="green">1.00<br> (127ns)</span>
1744              </p>
1745            </td>
1746</tr>
1747<tr>
1748<td>
1749              <p>
1750                digamma
1751              </p>
1752            </td>
1753<td>
1754              <p>
1755                <span class="red">2.30<br> (62ns)</span>
1756              </p>
1757            </td>
1758<td>
1759              <p>
1760                <span class="blue">1.30<br> (35ns)</span>
1761              </p>
1762            </td>
1763<td>
1764              <p>
1765                <span class="red">3.11<br> (84ns)</span>
1766              </p>
1767            </td>
1768<td>
1769              <p>
1770                <span class="blue">1.33<br> (36ns)</span>
1771              </p>
1772            </td>
1773<td>
1774              <p>
1775                <span class="blue">1.85<br> (50ns)</span>
1776              </p>
1777            </td>
1778<td>
1779              <p>
1780                <span class="green">1.00<br> (27ns)</span>
1781              </p>
1782            </td>
1783</tr>
1784<tr>
1785<td>
1786              <p>
1787                ellint_1
1788              </p>
1789            </td>
1790<td>
1791              <p>
1792                <span class="red">2.26<br> (310ns)</span>
1793              </p>
1794            </td>
1795<td>
1796              <p>
1797                <span class="green">1.12<br> (154ns)</span>
1798              </p>
1799            </td>
1800<td>
1801              <p>
1802                <span class="red">6.96<br> (954ns)</span>
1803              </p>
1804            </td>
1805<td>
1806              <p>
1807                <span class="blue">1.25<br> (171ns)</span>
1808              </p>
1809            </td>
1810<td>
1811              <p>
1812                <span class="red">3.22<br> (441ns)</span>
1813              </p>
1814            </td>
1815<td>
1816              <p>
1817                <span class="green">1.00<br> (137ns)</span>
1818              </p>
1819            </td>
1820</tr>
1821<tr>
1822<td>
1823              <p>
1824                ellint_1 (complete)
1825              </p>
1826            </td>
1827<td>
1828              <p>
1829                <span class="red">4.65<br> (93ns)</span>
1830              </p>
1831            </td>
1832<td>
1833              <p>
1834                <span class="red">3.15<br> (63ns)</span>
1835              </p>
1836            </td>
1837<td>
1838              <p>
1839                <span class="red">6.00<br> (120ns)</span>
1840              </p>
1841            </td>
1842<td>
1843              <p>
1844                <span class="green">1.15<br> (23ns)</span>
1845              </p>
1846            </td>
1847<td>
1848              <p>
1849                <span class="blue">1.90<br> (38ns)</span>
1850              </p>
1851            </td>
1852<td>
1853              <p>
1854                <span class="green">1.00<br> (20ns)</span>
1855              </p>
1856            </td>
1857</tr>
1858<tr>
1859<td>
1860              <p>
1861                ellint_2
1862              </p>
1863            </td>
1864<td>
1865              <p>
1866                <span class="red">3.81<br> (704ns)</span>
1867              </p>
1868            </td>
1869<td>
1870              <p>
1871                <span class="blue">1.28<br> (236ns)</span>
1872              </p>
1873            </td>
1874<td>
1875              <p>
1876                <span class="red">8.95<br> (1655ns)</span>
1877              </p>
1878            </td>
1879<td>
1880              <p>
1881                <span class="blue">1.36<br> (251ns)</span>
1882              </p>
1883            </td>
1884<td>
1885              <p>
1886                <span class="red">4.36<br> (807ns)</span>
1887              </p>
1888            </td>
1889<td>
1890              <p>
1891                <span class="green">1.00<br> (185ns)</span>
1892              </p>
1893            </td>
1894</tr>
1895<tr>
1896<td>
1897              <p>
1898                ellint_2 (complete)
1899              </p>
1900            </td>
1901<td>
1902              <p>
1903                <span class="blue">1.83<br> (44ns)</span>
1904              </p>
1905            </td>
1906<td>
1907              <p>
1908                <span class="green">1.04<br> (25ns)</span>
1909              </p>
1910            </td>
1911<td>
1912              <p>
1913                <span class="red">6.25<br> (150ns)</span>
1914              </p>
1915            </td>
1916<td>
1917              <p>
1918                <span class="blue">1.25<br> (30ns)</span>
1919              </p>
1920            </td>
1921<td>
1922              <p>
1923                <span class="blue">2.00<br> (48ns)</span>
1924              </p>
1925            </td>
1926<td>
1927              <p>
1928                <span class="green">1.00<br> (24ns)</span>
1929              </p>
1930            </td>
1931</tr>
1932<tr>
1933<td>
1934              <p>
1935                ellint_3
1936              </p>
1937            </td>
1938<td>
1939              <p>
1940                <span class="red">3.27<br> (609ns)</span>
1941              </p>
1942            </td>
1943<td>
1944              <p>
1945                <span class="green">1.17<br> (217ns)</span>
1946              </p>
1947            </td>
1948<td>
1949              <p>
1950                <span class="red">5.37<br> (998ns)</span>
1951              </p>
1952            </td>
1953<td>
1954              <p>
1955                <span class="blue">1.32<br> (245ns)</span>
1956              </p>
1957            </td>
1958<td>
1959              <p>
1960                <span class="red">2.84<br> (528ns)</span>
1961              </p>
1962            </td>
1963<td>
1964              <p>
1965                <span class="green">1.00<br> (186ns)</span>
1966              </p>
1967            </td>
1968</tr>
1969<tr>
1970<td>
1971              <p>
1972                ellint_3 (complete)
1973              </p>
1974            </td>
1975<td>
1976              <p>
1977                <span class="green">-nan<br> (0ns)</span>
1978              </p>
1979            </td>
1980<td>
1981              <p>
1982                <span class="green">-nan<br> (0ns)</span>
1983              </p>
1984            </td>
1985<td>
1986              <p>
1987                <span class="green">-nan<br> (0ns)</span>
1988              </p>
1989            </td>
1990<td>
1991              <p>
1992                <span class="green">-nan<br> (0ns)</span>
1993              </p>
1994            </td>
1995<td>
1996              <p>
1997                <span class="green">-nan<br> (0ns)</span>
1998              </p>
1999            </td>
2000<td>
2001              <p>
2002                <span class="green">-nan<br> (0ns)</span>
2003              </p>
2004            </td>
2005</tr>
2006<tr>
2007<td>
2008              <p>
2009                ellint_rc
2010              </p>
2011            </td>
2012<td>
2013              <p>
2014                <span class="red">2.75<br> (66ns)</span>
2015              </p>
2016            </td>
2017<td>
2018              <p>
2019                <span class="blue">1.29<br> (31ns)</span>
2020              </p>
2021            </td>
2022<td>
2023              <p>
2024                <span class="red">4.71<br> (113ns)</span>
2025              </p>
2026            </td>
2027<td>
2028              <p>
2029                <span class="blue">1.42<br> (34ns)</span>
2030              </p>
2031            </td>
2032<td>
2033              <p>
2034                <span class="blue">1.83<br> (44ns)</span>
2035              </p>
2036            </td>
2037<td>
2038              <p>
2039                <span class="green">1.00<br> (24ns)</span>
2040              </p>
2041            </td>
2042</tr>
2043<tr>
2044<td>
2045              <p>
2046                ellint_rd
2047              </p>
2048            </td>
2049<td>
2050              <p>
2051                <span class="red">4.37<br> (428ns)</span>
2052              </p>
2053            </td>
2054<td>
2055              <p>
2056                <span class="blue">1.31<br> (128ns)</span>
2057              </p>
2058            </td>
2059<td>
2060              <p>
2061                <span class="red">9.24<br> (906ns)</span>
2062              </p>
2063            </td>
2064<td>
2065              <p>
2066                <span class="blue">1.31<br> (128ns)</span>
2067              </p>
2068            </td>
2069<td>
2070              <p>
2071                <span class="red">4.17<br> (409ns)</span>
2072              </p>
2073            </td>
2074<td>
2075              <p>
2076                <span class="green">1.00<br> (98ns)</span>
2077              </p>
2078            </td>
2079</tr>
2080<tr>
2081<td>
2082              <p>
2083                ellint_rf
2084              </p>
2085            </td>
2086<td>
2087              <p>
2088                <span class="red">2.47<br> (84ns)</span>
2089              </p>
2090            </td>
2091<td>
2092              <p>
2093                <span class="blue">1.44<br> (49ns)</span>
2094              </p>
2095            </td>
2096<td>
2097              <p>
2098                <span class="red">4.62<br> (157ns)</span>
2099              </p>
2100            </td>
2101<td>
2102              <p>
2103                <span class="blue">1.32<br> (45ns)</span>
2104              </p>
2105            </td>
2106<td>
2107              <p>
2108                <span class="blue">1.85<br> (63ns)</span>
2109              </p>
2110            </td>
2111<td>
2112              <p>
2113                <span class="green">1.00<br> (34ns)</span>
2114              </p>
2115            </td>
2116</tr>
2117<tr>
2118<td>
2119              <p>
2120                ellint_rj
2121              </p>
2122            </td>
2123<td>
2124              <p>
2125                <span class="red">4.14<br> (426ns)</span>
2126              </p>
2127            </td>
2128<td>
2129              <p>
2130                <span class="blue">1.36<br> (140ns)</span>
2131              </p>
2132            </td>
2133<td>
2134              <p>
2135                <span class="red">7.18<br> (740ns)</span>
2136              </p>
2137            </td>
2138<td>
2139              <p>
2140                <span class="blue">1.31<br> (135ns)</span>
2141              </p>
2142            </td>
2143<td>
2144              <p>
2145                <span class="red">3.33<br> (343ns)</span>
2146              </p>
2147            </td>
2148<td>
2149              <p>
2150                <span class="green">1.00<br> (103ns)</span>
2151              </p>
2152            </td>
2153</tr>
2154<tr>
2155<td>
2156              <p>
2157                erf
2158              </p>
2159            </td>
2160<td>
2161              <p>
2162                <span class="blue">1.69<br> (54ns)</span>
2163              </p>
2164            </td>
2165<td>
2166              <p>
2167                <span class="blue">1.28<br> (41ns)</span>
2168              </p>
2169            </td>
2170<td>
2171              <p>
2172                <span class="red">2.56<br> (82ns)</span>
2173              </p>
2174            </td>
2175<td>
2176              <p>
2177                <span class="blue">1.38<br> (44ns)</span>
2178              </p>
2179            </td>
2180<td>
2181              <p>
2182                <span class="blue">1.34<br> (43ns)</span>
2183              </p>
2184            </td>
2185<td>
2186              <p>
2187                <span class="green">1.00<br> (32ns)</span>
2188              </p>
2189            </td>
2190</tr>
2191<tr>
2192<td>
2193              <p>
2194                erfc
2195              </p>
2196            </td>
2197<td>
2198              <p>
2199                <span class="blue">1.65<br> (89ns)</span>
2200              </p>
2201            </td>
2202<td>
2203              <p>
2204                <span class="blue">1.20<br> (65ns)</span>
2205              </p>
2206            </td>
2207<td>
2208              <p>
2209                <span class="red">2.46<br> (133ns)</span>
2210              </p>
2211            </td>
2212<td>
2213              <p>
2214                <span class="blue">1.26<br> (68ns)</span>
2215              </p>
2216            </td>
2217<td>
2218              <p>
2219                <span class="blue">1.22<br> (66ns)</span>
2220              </p>
2221            </td>
2222<td>
2223              <p>
2224                <span class="green">1.00<br> (54ns)</span>
2225              </p>
2226            </td>
2227</tr>
2228<tr>
2229<td>
2230              <p>
2231                expint
2232              </p>
2233            </td>
2234<td>
2235              <p>
2236                <span class="red">2.93<br> (85ns)</span>
2237              </p>
2238            </td>
2239<td>
2240              <p>
2241                <span class="blue">1.45<br> (42ns)</span>
2242              </p>
2243            </td>
2244<td>
2245              <p>
2246                <span class="red">2.90<br> (84ns)</span>
2247              </p>
2248            </td>
2249<td>
2250              <p>
2251                <span class="blue">1.31<br> (38ns)</span>
2252              </p>
2253            </td>
2254<td>
2255              <p>
2256                <span class="red">2.21<br> (64ns)</span>
2257              </p>
2258            </td>
2259<td>
2260              <p>
2261                <span class="green">1.00<br> (29ns)</span>
2262              </p>
2263            </td>
2264</tr>
2265<tr>
2266<td>
2267              <p>
2268                expint (En)
2269              </p>
2270            </td>
2271<td>
2272              <p>
2273                <span class="red">2.42<br> (242ns)</span>
2274              </p>
2275            </td>
2276<td>
2277              <p>
2278                <span class="green">1.14<br> (114ns)</span>
2279              </p>
2280            </td>
2281<td>
2282              <p>
2283                <span class="red">2.76<br> (276ns)</span>
2284              </p>
2285            </td>
2286<td>
2287              <p>
2288                <span class="green">1.19<br> (119ns)</span>
2289              </p>
2290            </td>
2291<td>
2292              <p>
2293                <span class="blue">1.84<br> (184ns)</span>
2294              </p>
2295            </td>
2296<td>
2297              <p>
2298                <span class="green">1.00<br> (100ns)</span>
2299              </p>
2300            </td>
2301</tr>
2302<tr>
2303<td>
2304              <p>
2305                expm1
2306              </p>
2307            </td>
2308<td>
2309              <p>
2310                <span class="blue">1.90<br> (19ns)</span>
2311              </p>
2312            </td>
2313<td>
2314              <p>
2315                <span class="blue">1.60<br> (16ns)</span>
2316              </p>
2317            </td>
2318<td>
2319              <p>
2320                <span class="blue">1.50<br> (15ns)</span>
2321              </p>
2322            </td>
2323<td>
2324              <p>
2325                <span class="blue">1.40<br> (14ns)</span>
2326              </p>
2327            </td>
2328<td>
2329              <p>
2330                <span class="blue">1.80<br> (18ns)</span>
2331              </p>
2332            </td>
2333<td>
2334              <p>
2335                <span class="green">1.00<br> (10ns)</span>
2336              </p>
2337            </td>
2338</tr>
2339<tr>
2340<td>
2341              <p>
2342                gamma_p
2343              </p>
2344            </td>
2345<td>
2346              <p>
2347                <span class="red">2.43<br> (618ns)</span>
2348              </p>
2349            </td>
2350<td>
2351              <p>
2352                <span class="green">1.02<br> (260ns)</span>
2353              </p>
2354            </td>
2355<td>
2356              <p>
2357                <span class="red">2.95<br> (749ns)</span>
2358              </p>
2359            </td>
2360<td>
2361              <p>
2362                <span class="green">1.00<br> (254ns)</span>
2363              </p>
2364            </td>
2365<td>
2366              <p>
2367                <span class="red">2.15<br> (545ns)</span>
2368              </p>
2369            </td>
2370<td>
2371              <p>
2372                <span class="green">1.03<br> (262ns)</span>
2373              </p>
2374            </td>
2375</tr>
2376<tr>
2377<td>
2378              <p>
2379                gamma_p_inv
2380              </p>
2381            </td>
2382<td>
2383              <p>
2384                <span class="red">2.37<br> (2328ns)</span>
2385              </p>
2386            </td>
2387<td>
2388              <p>
2389                <span class="green">1.06<br> (1038ns)</span>
2390              </p>
2391            </td>
2392<td>
2393              <p>
2394                <span class="red">2.73<br> (2676ns)</span>
2395              </p>
2396            </td>
2397<td>
2398              <p>
2399                <span class="green">1.06<br> (1045ns)</span>
2400              </p>
2401            </td>
2402<td>
2403              <p>
2404                <span class="blue">1.92<br> (1883ns)</span>
2405              </p>
2406            </td>
2407<td>
2408              <p>
2409                <span class="green">1.00<br> (982ns)</span>
2410              </p>
2411            </td>
2412</tr>
2413<tr>
2414<td>
2415              <p>
2416                gamma_q
2417              </p>
2418            </td>
2419<td>
2420              <p>
2421                <span class="red">2.49<br> (629ns)</span>
2422              </p>
2423            </td>
2424<td>
2425              <p>
2426                <span class="green">1.00<br> (253ns)</span>
2427              </p>
2428            </td>
2429<td>
2430              <p>
2431                <span class="red">3.28<br> (831ns)</span>
2432              </p>
2433            </td>
2434<td>
2435              <p>
2436                <span class="green">1.11<br> (280ns)</span>
2437              </p>
2438            </td>
2439<td>
2440              <p>
2441                <span class="red">2.18<br> (551ns)</span>
2442              </p>
2443            </td>
2444<td>
2445              <p>
2446                <span class="green">1.04<br> (263ns)</span>
2447              </p>
2448            </td>
2449</tr>
2450<tr>
2451<td>
2452              <p>
2453                gamma_q_inv
2454              </p>
2455            </td>
2456<td>
2457              <p>
2458                <span class="red">2.73<br> (2016ns)</span>
2459              </p>
2460            </td>
2461<td>
2462              <p>
2463                <span class="blue">1.30<br> (958ns)</span>
2464              </p>
2465            </td>
2466<td>
2467              <p>
2468                <span class="red">3.22<br> (2381ns)</span>
2469              </p>
2470            </td>
2471<td>
2472              <p>
2473                <span class="blue">1.30<br> (962ns)</span>
2474              </p>
2475            </td>
2476<td>
2477              <p>
2478                <span class="blue">1.73<br> (1275ns)</span>
2479              </p>
2480            </td>
2481<td>
2482              <p>
2483                <span class="green">1.00<br> (739ns)</span>
2484              </p>
2485            </td>
2486</tr>
2487<tr>
2488<td>
2489              <p>
2490                ibeta
2491              </p>
2492            </td>
2493<td>
2494              <p>
2495                <span class="red">4.56<br> (1979ns)</span>
2496              </p>
2497            </td>
2498<td>
2499              <p>
2500                <span class="blue">1.21<br> (524ns)</span>
2501              </p>
2502            </td>
2503<td>
2504              <p>
2505                <span class="red">4.60<br> (1996ns)</span>
2506              </p>
2507            </td>
2508<td>
2509              <p>
2510                <span class="green">1.00<br> (434ns)</span>
2511              </p>
2512            </td>
2513<td>
2514              <p>
2515                <span class="red">3.35<br> (1453ns)</span>
2516              </p>
2517            </td>
2518<td>
2519              <p>
2520                <span class="green">1.13<br> (491ns)</span>
2521              </p>
2522            </td>
2523</tr>
2524<tr>
2525<td>
2526              <p>
2527                ibeta_inv
2528              </p>
2529            </td>
2530<td>
2531              <p>
2532                <span class="red">3.22<br> (5552ns)</span>
2533              </p>
2534            </td>
2535<td>
2536              <p>
2537                <span class="green">1.10<br> (1902ns)</span>
2538              </p>
2539            </td>
2540<td>
2541              <p>
2542                <span class="red">3.49<br> (6013ns)</span>
2543              </p>
2544            </td>
2545<td>
2546              <p>
2547                <span class="green">1.03<br> (1781ns)</span>
2548              </p>
2549            </td>
2550<td>
2551              <p>
2552                <span class="red">2.58<br> (4437ns)</span>
2553              </p>
2554            </td>
2555<td>
2556              <p>
2557                <span class="green">1.00<br> (1722ns)</span>
2558              </p>
2559            </td>
2560</tr>
2561<tr>
2562<td>
2563              <p>
2564                ibetac
2565              </p>
2566            </td>
2567<td>
2568              <p>
2569                <span class="red">4.34<br> (2008ns)</span>
2570              </p>
2571            </td>
2572<td>
2573              <p>
2574                <span class="blue">1.27<br> (590ns)</span>
2575              </p>
2576            </td>
2577<td>
2578              <p>
2579                <span class="red">4.34<br> (2008ns)</span>
2580              </p>
2581            </td>
2582<td>
2583              <p>
2584                <span class="green">1.00<br> (463ns)</span>
2585              </p>
2586            </td>
2587<td>
2588              <p>
2589                <span class="red">3.11<br> (1438ns)</span>
2590              </p>
2591            </td>
2592<td>
2593              <p>
2594                <span class="green">1.17<br> (543ns)</span>
2595              </p>
2596            </td>
2597</tr>
2598<tr>
2599<td>
2600              <p>
2601                ibetac_inv
2602              </p>
2603            </td>
2604<td>
2605              <p>
2606                <span class="red">3.32<br> (5533ns)</span>
2607              </p>
2608            </td>
2609<td>
2610              <p>
2611                <span class="green">1.11<br> (1853ns)</span>
2612              </p>
2613            </td>
2614<td>
2615              <p>
2616                <span class="red">3.55<br> (5915ns)</span>
2617              </p>
2618            </td>
2619<td>
2620              <p>
2621                <span class="green">1.03<br> (1722ns)</span>
2622              </p>
2623            </td>
2624<td>
2625              <p>
2626                <span class="red">2.48<br> (4131ns)</span>
2627              </p>
2628            </td>
2629<td>
2630              <p>
2631                <span class="green">1.00<br> (1666ns)</span>
2632              </p>
2633            </td>
2634</tr>
2635<tr>
2636<td>
2637              <p>
2638                jacobi_cn
2639              </p>
2640            </td>
2641<td>
2642              <p>
2643                <span class="red">3.74<br> (483ns)</span>
2644              </p>
2645            </td>
2646<td>
2647              <p>
2648                <span class="blue">1.26<br> (163ns)</span>
2649              </p>
2650            </td>
2651<td>
2652              <p>
2653                <span class="red">4.98<br> (643ns)</span>
2654              </p>
2655            </td>
2656<td>
2657              <p>
2658                <span class="blue">1.61<br> (208ns)</span>
2659              </p>
2660            </td>
2661<td>
2662              <p>
2663                <span class="red">2.67<br> (345ns)</span>
2664              </p>
2665            </td>
2666<td>
2667              <p>
2668                <span class="green">1.00<br> (129ns)</span>
2669              </p>
2670            </td>
2671</tr>
2672<tr>
2673<td>
2674              <p>
2675                jacobi_dn
2676              </p>
2677            </td>
2678<td>
2679              <p>
2680                <span class="red">3.64<br> (503ns)</span>
2681              </p>
2682            </td>
2683<td>
2684              <p>
2685                <span class="blue">1.25<br> (173ns)</span>
2686              </p>
2687            </td>
2688<td>
2689              <p>
2690                <span class="red">4.70<br> (648ns)</span>
2691              </p>
2692            </td>
2693<td>
2694              <p>
2695                <span class="blue">1.49<br> (206ns)</span>
2696              </p>
2697            </td>
2698<td>
2699              <p>
2700                <span class="red">2.72<br> (375ns)</span>
2701              </p>
2702            </td>
2703<td>
2704              <p>
2705                <span class="green">1.00<br> (138ns)</span>
2706              </p>
2707            </td>
2708</tr>
2709<tr>
2710<td>
2711              <p>
2712                jacobi_sn
2713              </p>
2714            </td>
2715<td>
2716              <p>
2717                <span class="red">4.99<br> (614ns)</span>
2718              </p>
2719            </td>
2720<td>
2721              <p>
2722                <span class="blue">1.46<br> (180ns)</span>
2723              </p>
2724            </td>
2725<td>
2726              <p>
2727                <span class="red">5.20<br> (640ns)</span>
2728              </p>
2729            </td>
2730<td>
2731              <p>
2732                <span class="blue">1.72<br> (212ns)</span>
2733              </p>
2734            </td>
2735<td>
2736              <p>
2737                <span class="red">2.57<br> (316ns)</span>
2738              </p>
2739            </td>
2740<td>
2741              <p>
2742                <span class="green">1.00<br> (123ns)</span>
2743              </p>
2744            </td>
2745</tr>
2746<tr>
2747<td>
2748              <p>
2749                laguerre
2750              </p>
2751            </td>
2752<td>
2753              <p>
2754                <span class="green">1.11<br> (92ns)</span>
2755              </p>
2756            </td>
2757<td>
2758              <p>
2759                <span class="green">1.08<br> (90ns)</span>
2760              </p>
2761            </td>
2762<td>
2763              <p>
2764                <span class="blue">1.41<br> (117ns)</span>
2765              </p>
2766            </td>
2767<td>
2768              <p>
2769                <span class="green">1.11<br> (92ns)</span>
2770              </p>
2771            </td>
2772<td>
2773              <p>
2774                <span class="green">1.17<br> (97ns)</span>
2775              </p>
2776            </td>
2777<td>
2778              <p>
2779                <span class="green">1.00<br> (83ns)</span>
2780              </p>
2781            </td>
2782</tr>
2783<tr>
2784<td>
2785              <p>
2786                legendre
2787              </p>
2788            </td>
2789<td>
2790              <p>
2791                <span class="green">1.12<br> (282ns)</span>
2792              </p>
2793            </td>
2794<td>
2795              <p>
2796                <span class="green">1.00<br> (251ns)</span>
2797              </p>
2798            </td>
2799<td>
2800              <p>
2801                <span class="blue">1.21<br> (304ns)</span>
2802              </p>
2803            </td>
2804<td>
2805              <p>
2806                <span class="blue">1.30<br> (326ns)</span>
2807              </p>
2808            </td>
2809<td>
2810              <p>
2811                <span class="blue">1.39<br> (349ns)</span>
2812              </p>
2813            </td>
2814<td>
2815              <p>
2816                <span class="green">1.08<br> (270ns)</span>
2817              </p>
2818            </td>
2819</tr>
2820<tr>
2821<td>
2822              <p>
2823                legendre Q
2824              </p>
2825            </td>
2826<td>
2827              <p>
2828                <span class="blue">1.24<br> (390ns)</span>
2829              </p>
2830            </td>
2831<td>
2832              <p>
2833                <span class="green">1.00<br> (314ns)</span>
2834              </p>
2835            </td>
2836<td>
2837              <p>
2838                <span class="blue">1.29<br> (404ns)</span>
2839              </p>
2840            </td>
2841<td>
2842              <p>
2843                <span class="green">1.14<br> (358ns)</span>
2844              </p>
2845            </td>
2846<td>
2847              <p>
2848                <span class="blue">1.42<br> (445ns)</span>
2849              </p>
2850            </td>
2851<td>
2852              <p>
2853                <span class="green">1.11<br> (347ns)</span>
2854              </p>
2855            </td>
2856</tr>
2857<tr>
2858<td>
2859              <p>
2860                lgamma
2861              </p>
2862            </td>
2863<td>
2864              <p>
2865                <span class="red">2.65<br> (265ns)</span>
2866              </p>
2867            </td>
2868<td>
2869              <p>
2870                <span class="green">1.17<br> (117ns)</span>
2871              </p>
2872            </td>
2873<td>
2874              <p>
2875                <span class="red">3.86<br> (386ns)</span>
2876              </p>
2877            </td>
2878<td>
2879              <p>
2880                <span class="blue">1.24<br> (124ns)</span>
2881              </p>
2882            </td>
2883<td>
2884              <p>
2885                <span class="blue">1.90<br> (190ns)</span>
2886              </p>
2887            </td>
2888<td>
2889              <p>
2890                <span class="green">1.00<br> (100ns)</span>
2891              </p>
2892            </td>
2893</tr>
2894<tr>
2895<td>
2896              <p>
2897                log1p
2898              </p>
2899            </td>
2900<td>
2901              <p>
2902                <span class="green">1.11<br> (20ns)</span>
2903              </p>
2904            </td>
2905<td>
2906              <p>
2907                <span class="blue">1.22<br> (22ns)</span>
2908              </p>
2909            </td>
2910<td>
2911              <p>
2912                <span class="green">1.06<br> (19ns)</span>
2913              </p>
2914            </td>
2915<td>
2916              <p>
2917                <span class="green">1.00<br> (18ns)</span>
2918              </p>
2919            </td>
2920<td>
2921              <p>
2922                <span class="green">1.06<br> (19ns)</span>
2923              </p>
2924            </td>
2925<td>
2926              <p>
2927                <span class="green">1.00<br> (18ns)</span>
2928              </p>
2929            </td>
2930</tr>
2931<tr>
2932<td>
2933              <p>
2934                polygamma
2935              </p>
2936            </td>
2937<td>
2938              <p>
2939                <span class="red">16.70<br> (8883ns)</span>
2940              </p>
2941            </td>
2942<td>
2943              <p>
2944                <span class="blue">1.42<br> (756ns)</span>
2945              </p>
2946            </td>
2947<td>
2948              <p>
2949                <span class="red">6.56<br> (3491ns)</span>
2950              </p>
2951            </td>
2952<td>
2953              <p>
2954                <span class="green">1.00<br> (532ns)</span>
2955              </p>
2956            </td>
2957<td>
2958              <p>
2959                <span class="red">7.49<br> (3985ns)</span>
2960              </p>
2961            </td>
2962<td>
2963              <p>
2964                <span class="green">1.05<br> (559ns)</span>
2965              </p>
2966            </td>
2967</tr>
2968<tr>
2969<td>
2970              <p>
2971                sph_bessel
2972              </p>
2973            </td>
2974<td>
2975              <p>
2976                <span class="red">2.36<br> (1122ns)</span>
2977              </p>
2978            </td>
2979<td>
2980              <p>
2981                <span class="blue">1.24<br> (588ns)</span>
2982              </p>
2983            </td>
2984<td>
2985              <p>
2986                <span class="red">3.31<br> (1574ns)</span>
2987              </p>
2988            </td>
2989<td>
2990              <p>
2991                <span class="blue">1.41<br> (673ns)</span>
2992              </p>
2993            </td>
2994<td>
2995              <p>
2996                <span class="red">2.12<br> (1010ns)</span>
2997              </p>
2998            </td>
2999<td>
3000              <p>
3001                <span class="green">1.00<br> (476ns)</span>
3002              </p>
3003            </td>
3004</tr>
3005<tr>
3006<td>
3007              <p>
3008                sph_neumann
3009              </p>
3010            </td>
3011<td>
3012              <p>
3013                <span class="red">3.40<br> (2842ns)</span>
3014              </p>
3015            </td>
3016<td>
3017              <p>
3018                <span class="blue">1.21<br> (1015ns)</span>
3019              </p>
3020            </td>
3021<td>
3022              <p>
3023                <span class="red">3.59<br> (3009ns)</span>
3024              </p>
3025            </td>
3026<td>
3027              <p>
3028                <span class="blue">1.21<br> (1012ns)</span>
3029              </p>
3030            </td>
3031<td>
3032              <p>
3033                <span class="red">3.14<br> (2627ns)</span>
3034              </p>
3035            </td>
3036<td>
3037              <p>
3038                <span class="green">1.00<br> (837ns)</span>
3039              </p>
3040            </td>
3041</tr>
3042<tr>
3043<td>
3044              <p>
3045                tgamma
3046              </p>
3047            </td>
3048<td>
3049              <p>
3050                <span class="red">4.72<br> (472ns)</span>
3051              </p>
3052            </td>
3053<td>
3054              <p>
3055                <span class="blue">1.44<br> (144ns)</span>
3056              </p>
3057            </td>
3058<td>
3059              <p>
3060                <span class="red">5.70<br> (570ns)</span>
3061              </p>
3062            </td>
3063<td>
3064              <p>
3065                <span class="green">1.05<br> (105ns)</span>
3066              </p>
3067            </td>
3068<td>
3069              <p>
3070                <span class="red">2.29<br> (229ns)</span>
3071              </p>
3072            </td>
3073<td>
3074              <p>
3075                <span class="green">1.00<br> (100ns)</span>
3076              </p>
3077            </td>
3078</tr>
3079<tr>
3080<td>
3081              <p>
3082                tgamma (incomplete)
3083              </p>
3084            </td>
3085<td>
3086              <p>
3087                <span class="red">3.28<br> (669ns)</span>
3088              </p>
3089            </td>
3090<td>
3091              <p>
3092                <span class="green">1.13<br> (231ns)</span>
3093              </p>
3094            </td>
3095<td>
3096              <p>
3097                <span class="red">3.88<br> (792ns)</span>
3098              </p>
3099            </td>
3100<td>
3101              <p>
3102                <span class="green">1.14<br> (232ns)</span>
3103              </p>
3104            </td>
3105<td>
3106              <p>
3107                <span class="red">2.21<br> (451ns)</span>
3108              </p>
3109            </td>
3110<td>
3111              <p>
3112                <span class="green">1.00<br> (204ns)</span>
3113              </p>
3114            </td>
3115</tr>
3116<tr>
3117<td>
3118              <p>
3119                trigamma
3120              </p>
3121            </td>
3122<td>
3123              <p>
3124                <span class="red">2.08<br> (25ns)</span>
3125              </p>
3126            </td>
3127<td>
3128              <p>
3129                <span class="green">1.00<br> (12ns)</span>
3130              </p>
3131            </td>
3132<td>
3133              <p>
3134                <span class="red">4.00<br> (48ns)</span>
3135              </p>
3136            </td>
3137<td>
3138              <p>
3139                <span class="blue">1.50<br> (18ns)</span>
3140              </p>
3141            </td>
3142<td>
3143              <p>
3144                <span class="blue">2.00<br> (24ns)</span>
3145              </p>
3146            </td>
3147<td>
3148              <p>
3149                <span class="green">1.08<br> (13ns)</span>
3150              </p>
3151            </td>
3152</tr>
3153<tr>
3154<td>
3155              <p>
3156                zeta
3157              </p>
3158            </td>
3159<td>
3160              <p>
3161                <span class="red">4.21<br> (455ns)</span>
3162              </p>
3163            </td>
3164<td>
3165              <p>
3166                <span class="green">1.00<br> (108ns)</span>
3167              </p>
3168            </td>
3169<td>
3170              <p>
3171                <span class="red">5.77<br> (623ns)</span>
3172              </p>
3173            </td>
3174<td>
3175              <p>
3176                <span class="blue">1.20<br> (130ns)</span>
3177              </p>
3178            </td>
3179<td>
3180              <p>
3181                <span class="red">2.98<br> (322ns)</span>
3182              </p>
3183            </td>
3184<td>
3185              <p>
3186                <span class="green">1.08<br> (117ns)</span>
3187              </p>
3188            </td>
3189</tr>
3190</tbody>
3191</table></div>
3192</div>
3193<br class="table-break">
3194</div>
3195<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
3196<td align="left"></td>
3197<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar
3198      Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
3199      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
3200      Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
3201      Daryle Walker and Xiaogang Zhang<p>
3202        Distributed under the Boost Software License, Version 1.0. (See accompanying
3203        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>)
3204      </p>
3205</div></td>
3206</tr></table>
3207<hr>
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