1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Known Issues, and TODO List</title> 5<link rel="stylesheet" href="../math.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="../index.html" title="Math Toolkit 2.12.0"> 8<link rel="up" href="../status.html" title="Chapter 24. Library Status"> 9<link rel="prev" href="history2.html" title="History and What's New"> 10<link rel="next" href="credits.html" title="Credits and Acknowledgements"> 11</head> 12<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 13<table cellpadding="2" width="100%"><tr> 14<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td> 15<td align="center"><a href="../../../../../index.html">Home</a></td> 16<td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td> 17<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> 18<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> 19<td align="center"><a href="../../../../../more/index.htm">More</a></td> 20</tr></table> 21<hr> 22<div class="spirit-nav"> 23<a accesskey="p" href="history2.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../status.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="credits.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> 24</div> 25<div class="section"> 26<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 27<a name="math_toolkit.issues"></a><a class="link" href="issues.html" title="Known Issues, and TODO List">Known Issues, and TODO List</a> 28</h2></div></div></div> 29<p> 30 Predominantly this is a TODO list, or a list of possible future enhancements. 31 Items labeled "High Priority" effect the proper functioning of the 32 component, and should be fixed as soon as possible. Items labeled "Medium 33 Priority" are desirable enhancements, often pertaining to the performance 34 of the component, but do not effect it's accuracy or functionality. Items labeled 35 "Low Priority" should probably be investigated at some point. Such 36 classifications are obviously highly subjective. 37 </p> 38<p> 39 If you don't see a component listed here, then we don't have any known issues 40 with it. 41 </p> 42<h5> 43<a name="math_toolkit.issues.h0"></a> 44 <span class="phrase"><a name="math_toolkit.issues.tgamma"></a></span><a class="link" href="issues.html#math_toolkit.issues.tgamma">tgamma</a> 45 </h5> 46<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem"> 47 Can the <a class="link" href="lanczos.html" title="The Lanczos Approximation">Lanczos approximation</a> 48 be optimized any further? (low priority) 49 </li></ul></div> 50<h5> 51<a name="math_toolkit.issues.h1"></a> 52 <span class="phrase"><a name="math_toolkit.issues.incomplete_beta"></a></span><a class="link" href="issues.html#math_toolkit.issues.incomplete_beta">Incomplete 53 Beta</a> 54 </h5> 55<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem"> 56 Investigate Didonato and Morris' asymptotic expansion for large a and b 57 (medium priority). 58 </li></ul></div> 59<h5> 60<a name="math_toolkit.issues.h2"></a> 61 <span class="phrase"><a name="math_toolkit.issues.inverse_gamma"></a></span><a class="link" href="issues.html#math_toolkit.issues.inverse_gamma">Inverse 62 Gamma</a> 63 </h5> 64<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem"> 65 Investigate whether we can skip iteration altogether if the first approximation 66 is good enough (Medium Priority). 67 </li></ul></div> 68<h5> 69<a name="math_toolkit.issues.h3"></a> 70 <span class="phrase"><a name="math_toolkit.issues.polynomials"></a></span><a class="link" href="issues.html#math_toolkit.issues.polynomials">Polynomials</a> 71 </h5> 72<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem"> 73 The Legendre and Laguerre Polynomials have surprisingly different error 74 rates on different platforms, considering they are evaluated with only 75 basic arithmetic operations. Maybe this is telling us something, or maybe 76 not (Low Priority). 77 </li></ul></div> 78<h5> 79<a name="math_toolkit.issues.h4"></a> 80 <span class="phrase"><a name="math_toolkit.issues.elliptic_integrals"></a></span><a class="link" href="issues.html#math_toolkit.issues.elliptic_integrals">Elliptic 81 Integrals</a> 82 </h5> 83<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> 84<li class="listitem"> 85 [para Carlson's algorithms (mainly R<sub>J</sub>) are somewhat prone to internal overflow/underflow 86 when the arguments are very large or small. The homogeneity relations:] 87 [para R<sub>F</sub>(ka, kb, kc) = k<sup>-1/2</sup> R<sub>F</sub>(a, b, c)] [para and] [para R<sub>J</sub>(ka, kb, kc, 88 kr) = k<sup>-3/2</sup> R<sub>J</sub>(a, b, c, r)] [para could be used to sidestep trouble here: 89 provided the problem domains can be accurately identified. (Medium Priority).] 90 </li> 91<li class="listitem"> 92 There are a several other integrals: Bulirsch's <span class="emphasis"><em>el</em></span> 93 functions that could be implemented using Carlson's integrals (Low Priority). 94 </li> 95<li class="listitem"> 96 The integrals K(k) and E(k) could be implemented using rational approximations 97 (both for efficiency and accuracy), assuming we can find them. (Medium 98 Priority). 99 </li> 100</ul></div> 101<h5> 102<a name="math_toolkit.issues.h5"></a> 103 <span class="phrase"><a name="math_toolkit.issues.owen_s_t_function"></a></span><a class="link" href="issues.html#math_toolkit.issues.owen_s_t_function">Owen's 104 T Function</a> 105 </h5> 106<p> 107 There is a problem area at arbitrary precision when <span class="emphasis"><em>a</em></span> 108 is very close to 1. However, note that the value for <span class="emphasis"><em>T(h, 1)</em></span> 109 is well known and easy to compute, and if we replaced the <span class="emphasis"><em>a<sup>k</sup></em></span> 110 terms in series T1, T2 or T4 by <span class="emphasis"><em>(a<sup>k</sup> - 1)</em></span> then we would 111 have the difference between <span class="emphasis"><em>T(h, a)</em></span> and <span class="emphasis"><em>T(h, 112 1)</em></span>. Unfortunately this doesn't improve the convergence of those 113 series in that area. It certainly looks as though a new series in terms of 114 <span class="emphasis"><em>(1-a)<sup>k</sup></em></span> is both possible and desirable in this area, but 115 it remains elusive at present. 116 </p> 117<h5> 118<a name="math_toolkit.issues.h6"></a> 119 <span class="phrase"><a name="math_toolkit.issues.statistical_distributions"></a></span><a class="link" href="issues.html#math_toolkit.issues.statistical_distributions">Statistical 120 distributions</a> 121 </h5> 122<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem"> 123 Student's t Perhaps switch to normal distribution as a better approximation 124 for very large degrees of freedom? 125 </li></ul></div> 126<h5> 127<a name="math_toolkit.issues.h7"></a> 128 <span class="phrase"><a name="math_toolkit.issues.feature_requests"></a></span><a class="link" href="issues.html#math_toolkit.issues.feature_requests">Feature 129 Requests</a> 130 </h5> 131<p> 132 The following table lists distributions that are found in other packages but 133 which are not yet present here, the more frequently the distribution is found, 134 the higher the priority for implementing it: 135 </p> 136<div class="informaltable"><table class="table"> 137<colgroup> 138<col> 139<col> 140<col> 141<col> 142<col> 143<col> 144</colgroup> 145<thead><tr> 146<th> 147 <p> 148 Distribution 149 </p> 150 </th> 151<th> 152 <p> 153 R 154 </p> 155 </th> 156<th> 157 <p> 158 Mathematica 6 159 </p> 160 </th> 161<th> 162 <p> 163 NIST 164 </p> 165 </th> 166<th> 167 <p> 168 Regress+ 169 </p> 170 </th> 171<th> 172 <p> 173 Matlab 174 </p> 175 </th> 176</tr></thead> 177<tbody> 178<tr> 179<td> 180 <p> 181 Geometric 182 </p> 183 </td> 184<td> 185 <p> 186 X 187 </p> 188 </td> 189<td> 190 <p> 191 X 192 </p> 193 </td> 194<td> 195 <p> 196 - 197 </p> 198 </td> 199<td> 200 <p> 201 - 202 </p> 203 </td> 204<td> 205 <p> 206 X 207 </p> 208 </td> 209</tr> 210<tr> 211<td> 212 <p> 213 Multinomial 214 </p> 215 </td> 216<td> 217 <p> 218 X 219 </p> 220 </td> 221<td> 222 <p> 223 - 224 </p> 225 </td> 226<td> 227 <p> 228 - 229 </p> 230 </td> 231<td> 232 <p> 233 - 234 </p> 235 </td> 236<td> 237 <p> 238 X 239 </p> 240 </td> 241</tr> 242<tr> 243<td> 244 <p> 245 Tukey Lambda 246 </p> 247 </td> 248<td> 249 <p> 250 X 251 </p> 252 </td> 253<td> 254 <p> 255 - 256 </p> 257 </td> 258<td> 259 <p> 260 X 261 </p> 262 </td> 263<td> 264 <p> 265 - 266 </p> 267 </td> 268<td> 269 <p> 270 - 271 </p> 272 </td> 273</tr> 274<tr> 275<td> 276 <p> 277 Half Normal / Folded Normal 278 </p> 279 </td> 280<td> 281 <p> 282 - 283 </p> 284 </td> 285<td> 286 <p> 287 X 288 </p> 289 </td> 290<td> 291 <p> 292 - 293 </p> 294 </td> 295<td> 296 <p> 297 X 298 </p> 299 </td> 300<td> 301 <p> 302 - 303 </p> 304 </td> 305</tr> 306<tr> 307<td> 308 <p> 309 Chi 310 </p> 311 </td> 312<td> 313 <p> 314 - 315 </p> 316 </td> 317<td> 318 <p> 319 X 320 </p> 321 </td> 322<td> 323 <p> 324 - 325 </p> 326 </td> 327<td> 328 <p> 329 X 330 </p> 331 </td> 332<td> 333 <p> 334 - 335 </p> 336 </td> 337</tr> 338<tr> 339<td> 340 <p> 341 Gumbel 342 </p> 343 </td> 344<td> 345 <p> 346 - 347 </p> 348 </td> 349<td> 350 <p> 351 X 352 </p> 353 </td> 354<td> 355 <p> 356 - 357 </p> 358 </td> 359<td> 360 <p> 361 X 362 </p> 363 </td> 364<td> 365 <p> 366 - 367 </p> 368 </td> 369</tr> 370<tr> 371<td> 372 <p> 373 Discrete Uniform 374 </p> 375 </td> 376<td> 377 <p> 378 - 379 </p> 380 </td> 381<td> 382 <p> 383 X 384 </p> 385 </td> 386<td> 387 <p> 388 - 389 </p> 390 </td> 391<td> 392 <p> 393 - 394 </p> 395 </td> 396<td> 397 <p> 398 X 399 </p> 400 </td> 401</tr> 402<tr> 403<td> 404 <p> 405 Log Series 406 </p> 407 </td> 408<td> 409 <p> 410 - 411 </p> 412 </td> 413<td> 414 <p> 415 X 416 </p> 417 </td> 418<td> 419 <p> 420 - 421 </p> 422 </td> 423<td> 424 <p> 425 X 426 </p> 427 </td> 428<td> 429 <p> 430 - 431 </p> 432 </td> 433</tr> 434<tr> 435<td> 436 <p> 437 Nakagami (generalised Chi) 438 </p> 439 </td> 440<td> 441 <p> 442 - 443 </p> 444 </td> 445<td> 446 <p> 447 - 448 </p> 449 </td> 450<td> 451 <p> 452 - 453 </p> 454 </td> 455<td> 456 <p> 457 X 458 </p> 459 </td> 460<td> 461 <p> 462 X 463 </p> 464 </td> 465</tr> 466<tr> 467<td> 468 <p> 469 Log Logistic 470 </p> 471 </td> 472<td> 473 <p> 474 - 475 </p> 476 </td> 477<td> 478 <p> 479 - 480 </p> 481 </td> 482<td> 483 <p> 484 - 485 </p> 486 </td> 487<td> 488 <p> 489 - 490 </p> 491 </td> 492<td> 493 <p> 494 X 495 </p> 496 </td> 497</tr> 498<tr> 499<td> 500 <p> 501 Tukey (Studentized range) 502 </p> 503 </td> 504<td> 505 <p> 506 X 507 </p> 508 </td> 509<td> 510 <p> 511 - 512 </p> 513 </td> 514<td> 515 <p> 516 - 517 </p> 518 </td> 519<td> 520 <p> 521 - 522 </p> 523 </td> 524<td> 525 <p> 526 - 527 </p> 528 </td> 529</tr> 530<tr> 531<td> 532 <p> 533 Wilcoxon rank sum 534 </p> 535 </td> 536<td> 537 <p> 538 X 539 </p> 540 </td> 541<td> 542 <p> 543 - 544 </p> 545 </td> 546<td> 547 <p> 548 - 549 </p> 550 </td> 551<td> 552 <p> 553 - 554 </p> 555 </td> 556<td> 557 <p> 558 - 559 </p> 560 </td> 561</tr> 562<tr> 563<td> 564 <p> 565 Wincoxon signed rank 566 </p> 567 </td> 568<td> 569 <p> 570 X 571 </p> 572 </td> 573<td> 574 <p> 575 - 576 </p> 577 </td> 578<td> 579 <p> 580 - 581 </p> 582 </td> 583<td> 584 <p> 585 - 586 </p> 587 </td> 588<td> 589 <p> 590 - 591 </p> 592 </td> 593</tr> 594<tr> 595<td> 596 <p> 597 Non-central Beta 598 </p> 599 </td> 600<td> 601 <p> 602 X 603 </p> 604 </td> 605<td> 606 <p> 607 - 608 </p> 609 </td> 610<td> 611 <p> 612 - 613 </p> 614 </td> 615<td> 616 <p> 617 - 618 </p> 619 </td> 620<td> 621 <p> 622 - 623 </p> 624 </td> 625</tr> 626<tr> 627<td> 628 <p> 629 Maxwell 630 </p> 631 </td> 632<td> 633 <p> 634 - 635 </p> 636 </td> 637<td> 638 <p> 639 X 640 </p> 641 </td> 642<td> 643 <p> 644 - 645 </p> 646 </td> 647<td> 648 <p> 649 - 650 </p> 651 </td> 652<td> 653 <p> 654 - 655 </p> 656 </td> 657</tr> 658<tr> 659<td> 660 <p> 661 Beta-Binomial 662 </p> 663 </td> 664<td> 665 <p> 666 - 667 </p> 668 </td> 669<td> 670 <p> 671 X 672 </p> 673 </td> 674<td> 675 <p> 676 - 677 </p> 678 </td> 679<td> 680 <p> 681 - 682 </p> 683 </td> 684<td> 685 <p> 686 - 687 </p> 688 </td> 689</tr> 690<tr> 691<td> 692 <p> 693 Beta-negative Binomial 694 </p> 695 </td> 696<td> 697 <p> 698 - 699 </p> 700 </td> 701<td> 702 <p> 703 X 704 </p> 705 </td> 706<td> 707 <p> 708 - 709 </p> 710 </td> 711<td> 712 <p> 713 - 714 </p> 715 </td> 716<td> 717 <p> 718 - 719 </p> 720 </td> 721</tr> 722<tr> 723<td> 724 <p> 725 Zipf 726 </p> 727 </td> 728<td> 729 <p> 730 - 731 </p> 732 </td> 733<td> 734 <p> 735 X 736 </p> 737 </td> 738<td> 739 <p> 740 - 741 </p> 742 </td> 743<td> 744 <p> 745 - 746 </p> 747 </td> 748<td> 749 <p> 750 - 751 </p> 752 </td> 753</tr> 754<tr> 755<td> 756 <p> 757 Birnbaum-Saunders / Fatigue Life 758 </p> 759 </td> 760<td> 761 <p> 762 - 763 </p> 764 </td> 765<td> 766 <p> 767 - 768 </p> 769 </td> 770<td> 771 <p> 772 X 773 </p> 774 </td> 775<td> 776 <p> 777 - 778 </p> 779 </td> 780<td> 781 <p> 782 - 783 </p> 784 </td> 785</tr> 786<tr> 787<td> 788 <p> 789 Double Exponential 790 </p> 791 </td> 792<td> 793 <p> 794 - 795 </p> 796 </td> 797<td> 798 <p> 799 - 800 </p> 801 </td> 802<td> 803 <p> 804 X 805 </p> 806 </td> 807<td> 808 <p> 809 - 810 </p> 811 </td> 812<td> 813 <p> 814 - 815 </p> 816 </td> 817</tr> 818<tr> 819<td> 820 <p> 821 Power Normal 822 </p> 823 </td> 824<td> 825 <p> 826 - 827 </p> 828 </td> 829<td> 830 <p> 831 - 832 </p> 833 </td> 834<td> 835 <p> 836 X 837 </p> 838 </td> 839<td> 840 <p> 841 - 842 </p> 843 </td> 844<td> 845 <p> 846 - 847 </p> 848 </td> 849</tr> 850<tr> 851<td> 852 <p> 853 Power Lognormal 854 </p> 855 </td> 856<td> 857 <p> 858 - 859 </p> 860 </td> 861<td> 862 <p> 863 - 864 </p> 865 </td> 866<td> 867 <p> 868 X 869 </p> 870 </td> 871<td> 872 <p> 873 - 874 </p> 875 </td> 876<td> 877 <p> 878 - 879 </p> 880 </td> 881</tr> 882<tr> 883<td> 884 <p> 885 Cosine 886 </p> 887 </td> 888<td> 889 <p> 890 - 891 </p> 892 </td> 893<td> 894 <p> 895 - 896 </p> 897 </td> 898<td> 899 <p> 900 - 901 </p> 902 </td> 903<td> 904 <p> 905 X 906 </p> 907 </td> 908<td> 909 <p> 910 - 911 </p> 912 </td> 913</tr> 914<tr> 915<td> 916 <p> 917 Double Gamma 918 </p> 919 </td> 920<td> 921 <p> 922 - 923 </p> 924 </td> 925<td> 926 <p> 927 - 928 </p> 929 </td> 930<td> 931 <p> 932 - 933 </p> 934 </td> 935<td> 936 <p> 937 X 938 </p> 939 </td> 940<td> 941 <p> 942 - 943 </p> 944 </td> 945</tr> 946<tr> 947<td> 948 <p> 949 Double Weibul 950 </p> 951 </td> 952<td> 953 <p> 954 - 955 </p> 956 </td> 957<td> 958 <p> 959 - 960 </p> 961 </td> 962<td> 963 <p> 964 - 965 </p> 966 </td> 967<td> 968 <p> 969 X 970 </p> 971 </td> 972<td> 973 <p> 974 - 975 </p> 976 </td> 977</tr> 978<tr> 979<td> 980 <p> 981 Hyperbolic Secant 982 </p> 983 </td> 984<td> 985 <p> 986 - 987 </p> 988 </td> 989<td> 990 <p> 991 - 992 </p> 993 </td> 994<td> 995 <p> 996 - 997 </p> 998 </td> 999<td> 1000 <p> 1001 X 1002 </p> 1003 </td> 1004<td> 1005 <p> 1006 - 1007 </p> 1008 </td> 1009</tr> 1010<tr> 1011<td> 1012 <p> 1013 Semicircular 1014 </p> 1015 </td> 1016<td> 1017 <p> 1018 - 1019 </p> 1020 </td> 1021<td> 1022 <p> 1023 - 1024 </p> 1025 </td> 1026<td> 1027 <p> 1028 - 1029 </p> 1030 </td> 1031<td> 1032 <p> 1033 X 1034 </p> 1035 </td> 1036<td> 1037 <p> 1038 - 1039 </p> 1040 </td> 1041</tr> 1042<tr> 1043<td> 1044 <p> 1045 Bradford 1046 </p> 1047 </td> 1048<td> 1049 <p> 1050 - 1051 </p> 1052 </td> 1053<td> 1054 <p> 1055 - 1056 </p> 1057 </td> 1058<td> 1059 <p> 1060 - 1061 </p> 1062 </td> 1063<td> 1064 <p> 1065 X 1066 </p> 1067 </td> 1068<td> 1069 <p> 1070 - 1071 </p> 1072 </td> 1073</tr> 1074<tr> 1075<td> 1076 <p> 1077 Birr / Fisk 1078 </p> 1079 </td> 1080<td> 1081 <p> 1082 - 1083 </p> 1084 </td> 1085<td> 1086 <p> 1087 - 1088 </p> 1089 </td> 1090<td> 1091 <p> 1092 - 1093 </p> 1094 </td> 1095<td> 1096 <p> 1097 X 1098 </p> 1099 </td> 1100<td> 1101 <p> 1102 - 1103 </p> 1104 </td> 1105</tr> 1106<tr> 1107<td> 1108 <p> 1109 Reciprocal 1110 </p> 1111 </td> 1112<td> 1113 <p> 1114 - 1115 </p> 1116 </td> 1117<td> 1118 <p> 1119 - 1120 </p> 1121 </td> 1122<td> 1123 <p> 1124 - 1125 </p> 1126 </td> 1127<td> 1128 <p> 1129 X 1130 </p> 1131 </td> 1132<td> 1133 <p> 1134 - 1135 </p> 1136 </td> 1137</tr> 1138<tr> 1139<td> 1140 <p> 1141 Kolmogorov Distribution 1142 </p> 1143 </td> 1144<td> 1145 <p> 1146 - 1147 </p> 1148 </td> 1149<td> 1150 <p> 1151 - 1152 </p> 1153 </td> 1154<td> 1155 <p> 1156 - 1157 </p> 1158 </td> 1159<td> 1160 <p> 1161 - 1162 </p> 1163 </td> 1164<td> 1165 <p> 1166 - 1167 </p> 1168 </td> 1169</tr> 1170</tbody> 1171</table></div> 1172<p> 1173 Also asked for more than once: 1174 </p> 1175<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> 1176<li class="listitem"> 1177 Add support for interpolated distributions, possibly combine with numeric 1178 integration and differentiation. 1179 </li> 1180<li class="listitem"> 1181 Add support for bivariate and multivariate distributions: most especially 1182 the normal. 1183 </li> 1184<li class="listitem"> 1185 Add support for the log of the cdf and pdf: this is mainly a performance 1186 optimisation since we can avoid some special function calls for some distributions 1187 by returning the log of the result. 1188 </li> 1189</ul></div> 1190</div> 1191<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 1192<td align="left"></td> 1193<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar 1194 Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, 1195 Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan 1196 Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, 1197 Daryle Walker and Xiaogang Zhang<p> 1198 Distributed under the Boost Software License, Version 1.0. (See accompanying 1199 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>) 1200 </p> 1201</div></td> 1202</tr></table> 1203<hr> 1204<div class="spirit-nav"> 1205<a accesskey="p" href="history2.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../status.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="credits.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> 1206</div> 1207</body> 1208</html> 1209
