09 June 2007 12:08:08 PM FAURE_PRB C++ version Test the routines in the FAURE library. TEST005 BINOMIAL_TABLE computes a table of binomial. coefficients mod QS. Here, QS = 7 I/J 0 1 2 3 4 5 6 7 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 2 1 2 1 0 0 0 0 0 3 1 3 3 1 0 0 0 0 4 1 4 6 4 1 0 0 0 5 1 5 3 3 5 1 0 0 6 1 6 1 6 1 6 1 0 7 1 0 0 0 0 0 0 1 8 1 1 0 0 0 0 0 1 9 1 2 1 0 0 0 0 1 10 1 3 3 1 0 0 0 1 TEST006 I4_LOG_R8: whole part of log base B, I4 J4 I4_LOG_J4 0 2 0 1 2 0 2 2 1 3 2 1 4 2 2 5 2 2 6 2 2 7 2 2 8 2 3 9 2 3 10 2 3 0 3 0 1 3 0 2 3 0 3 3 1 4 3 1 5 3 1 6 3 1 7 3 1 8 3 1 9 3 2 10 3 2 0 4 0 1 4 0 2 4 0 3 4 0 4 4 1 5 4 1 6 4 1 7 4 1 8 4 1 9 4 1 10 4 1 0 5 0 1 5 0 2 5 0 3 5 0 4 5 0 5 5 1 6 5 1 7 5 1 8 5 1 9 5 1 10 5 1 TEST01 FAURE computes the next element of a Faure sequence. In this test, we call FAURE repeatedly. Using dimension DIM_NUM = 2 The underlying base is QS = 2 Seed Seed Faure In Out -1 16 0.9375 0.5625 16 17 0.03125 0.53125 17 18 0.53125 0.53125 18 19 0.28125 0.28125 19 20 0.78125 0.28125 20 21 0.15625 0.15625 21 22 0.65625 0.15625 22 23 0.40625 0.90625 23 24 0.90625 0.90625 24 25 0.09375 0.46875 Using dimension DIM_NUM = 3 The underlying base is QS = 3 Seed Seed Faure In Out -1 81 0.987654 0.0987654 0.54321 81 82 0.00411523 0.460905 0.251029 82 83 0.337449 0.460905 0.251029 83 84 0.670782 0.460905 0.251029 84 85 0.115226 0.90535 0.36214 85 86 0.44856 0.90535 0.36214 86 87 0.781893 0.90535 0.36214 87 88 0.226337 0.0164609 0.806584 88 89 0.559671 0.0164609 0.806584 89 90 0.893004 0.0164609 0.806584 Using dimension DIM_NUM = 4 The underlying base is QS = 5 Seed Seed Faure In Out -1 625 0.9984 0.5744 0.9504 0.0464 625 626 0.00032 0.37472 0.11712 0.15552 626 627 0.20032 0.37472 0.11712 0.15552 627 628 0.40032 0.37472 0.11712 0.15552 628 629 0.60032 0.37472 0.11712 0.15552 629 630 0.80032 0.37472 0.11712 0.15552 630 631 0.04032 0.41472 0.35712 0.39552 631 632 0.24032 0.41472 0.35712 0.39552 632 633 0.44032 0.41472 0.35712 0.39552 633 634 0.64032 0.41472 0.35712 0.39552 TEST02 FAURE computes the next element of a Faure sequence. In this test, we demonstrate how the SEED can be manipulated to skip ahead in the sequence, or to come back to any part of the sequence. Using dimension DIM_NUM = 3 The underlying base is QS = 3 Note that on the first call to FAURE, if SEED is negative, it is reset to a value that is the recommended starting point: Seed Seed Faure In Out -1 81 0.987654 0.0987654 0.54321 81 82 0.00411523 0.460905 0.251029 82 83 0.337449 0.460905 0.251029 83 84 0.670782 0.460905 0.251029 84 85 0.115226 0.90535 0.36214 However, if the input value of SEED is 0, then no initial skipping is done. Seed Seed Faure In Out 0 1 0 0 0 1 2 0.333333 0 0 2 3 0.666667 0 0 3 4 0.111111 0.444444 0.444444 4 5 0.444444 0.444444 0.444444 5 6 0.777778 0.444444 0.444444 6 7 0.222222 0.888889 0.888889 7 8 0.555556 0.888889 0.888889 8 9 0.888889 0.888889 0.888889 9 10 0.037037 0.592593 0.148148 Jump ahead by increasing SEED: Seed Seed Faure In Out 100 101 0.411523 0.312757 0.213992 101 102 0.744856 0.312757 0.213992 102 103 0.1893 0.423868 0.658436 103 104 0.522634 0.423868 0.658436 104 105 0.855967 0.423868 0.658436 Jump back by decreasing SEED: Seed Seed Faure In Out 3 4 0.111111 0.444444 0.444444 4 5 0.444444 0.444444 0.444444 5 6 0.777778 0.444444 0.444444 6 7 0.222222 0.888889 0.888889 7 8 0.555556 0.888889 0.888889 8 9 0.888889 0.888889 0.888889 9 10 0.037037 0.333333 0 10 11 0.37037 0.333333 0 11 12 0.703704 0.333333 0 12 13 0.148148 0.777778 0.444444 TEST03 FAURE computes the next element of a Faure sequence. In this test, we try some large dimensions. Using dimension DIM_NUM = 10 The underlying base is QS = 11 Seed Seed Faure In Out -1 14641 0.999932 0.774537 0.0450106 0.811352 0.990916 0.567174 0.639301 0.207295 0.188512 0.657332 14641 14642 6.20921e-06 0.128754 0.448336 0.991059 0.940243 0.592657 0.0549888 0.527088 0.11564 0.100887 Using dimension DIM_NUM = 20 The underlying base is QS = 23 Seed Seed Faure In Out -1 279841 0.999996 0.903342 0.534475 0.936875 0.0670631 0.92504 0.554283 0.911314 0.998024 0.810632 0.351028 0.662691 0.702142 0.512859 0.00788662 0.274181 0.270153 0.0355023 0.485161 0.706087 279841 279842 1.55368e-07 0.0515473 0.669298 0.857033 0.614753 0.0766723 0.199231 0.0733311 0.69889 0.208233 0.561662 0.804546 0.0237601 0.221358 0.487995 0.86904 0.321015 0.976244 0.838426 0.994683 Using dimension DIM_NUM = 30 The underlying base is QS = 31 Seed Seed Faure In Out -1 923521 0.999999 0.930179 0.660568 0.223422 0.554227 0.717497 0.680976 0.476921 0.0408166 0.437178 0.633747 0.631565 0.428551 0.058003 0.455405 0.685273 0.715349 0.577892 0.208384 0.671343 0.934509 0.998925 0.862508 0.526299 0.0225561 0.319021 0.415695 0.312577 0.00966627 0.539222 923521 923522 3.49294e-08 0.0366262 0.485726 0.113168 0.653604 0.908283 0.67429 0.65402 0.679904 0.518921 0.936903 0.734061 0.645045 0.435725 0.906308 0.85492 0.0172222 0.192447 0.114173 0.582607 0.395877 0.321933 0.0954261 0.514483 0.347021 0.360016 0.383819 0.120825 0.372281 0.935274 Using dimension DIM_NUM = 40 The underlying base is QS = 41 Seed Seed Faure In Out -1 2825761 1 0.948201 0.746492 0.394872 0.917732 0.29068 0.489328 0.562455 0.510062 0.283368 0.906762 0.404637 0.7526 0.950653 0.99939 0.897622 0.645942 0.244352 0.717241 0.0402196 0.213287 0.236444 0.10969 0.833026 0.430841 0.854355 0.152348 0.300431 0.299197 0.147458 0.870199 0.418638 0.841557 0.114566 0.237663 0.21085 0.0341257 0.707491 0.255335 0.653269 2825761 2825762 8.63139e-09 0.0268583 0.385241 0.601026 0.27445 0.00515791 0.367806 0.962634 0.364893 0.125446 0.892123 0.216365 0.67286 0.862426 0.383517 0.78759 0.698083 0.666454 0.316736 0.175402 0.890279 0.0128125 0.142673 0.830113 0.724153 0.351264 0.335479 0.227066 0.650654 0.15651 0.345467 0.815964 0.143877 0.879459 0.67173 0.0715517 0.654177 0.0186534 0.740829 0.420348 Using dimension DIM_NUM = 50 The underlying base is QS = 53 Seed Seed Faure In Out -1 7890481 1 0.960464 0.805584 0.535361 0.168663 0.667752 0.0703667 0.357637 0.510697 0.56728 0.527388 0.353285 0.0638378 0.677915 0.157781 0.541171 0.809218 0.961921 0.999637 0.921653 0.728326 0.419655 0.0145085 0.475151 0.839317 0.0881397 0.221619 0.239755 0.142547 0.929996 0.620969 0.17773 0.638016 0.964091 0.19369 0.307945 0.307213 0.190782 0.977874 0.630755 0.187161 0.609355 0.935074 0.145449 0.24048 0.220168 0.0845126 0.833513 0.486039 0.00435246 7890481 7890482 2.39123e-09 0.0203327 0.294573 0.227135 0.317842 0.97075 0.666103 0.865987 0.993327 0.509855 0.895812 0.574836 0.00794553 0.656871 0.945244 0.372187 0.342465 0.354832 0.814413 0.220319 0.995832 0.603039 0.483733 0.0996442 0.911792 0.363393 0.915111 0.00980029 0.108849 0.654401 0.108541 0.913065 0.529702 0.41947 0.0255887 0.808719 0.192855 0.677108 0.665891 0.658671 0.0602109 0.369635 0.0105736 0.444046 0.131782 0.49742 0.0212019 0.164146 0.350602 0.0412334 Using dimension DIM_NUM = 60 The underlying base is QS = 61 Seed Seed Faure In Out -1 13845841 1 0.965856 0.831739 0.597649 0.263586 0.845943 0.311934 0.694344 0.976782 0.159247 0.241738 0.224257 0.106802 0.889374 0.588366 0.170992 0.670038 0.052718 0.351818 0.550945 0.650098 0.649548 0.548755 0.347989 0.063644 0.662932 0.17864 0.577982 0.893744 0.109533 0.225349 0.241192 0.157062 0.972958 0.688881 0.321225 0.837202 0.2696 0.602024 0.834475 0.966953 0.999727 0.932259 0.764817 0.497403 0.146409 0.679048 0.128108 0.460801 0.709914 0.859054 0.908221 0.857415 0.706636 0.472277 0.121552 0.687247 0.136575 0.502324 0.768099 13845841 13845842 1.184e-09 0.0174951 0.254608 0.0784436 0.872233 0.0525301 0.00283457 0.123039 0.796373 0.423267 0.386683 0.0867814 0.923186 0.279935 0.572774 0.152687 0.452346 0.838868 0.728533 0.504572 0.550752 0.266967 0.0531077 0.308799 0.401684 0.74751 0.730047 0.749185 0.188156 0.447389 0.92624 0.00847222 0.0939863 0.566008 0.824969 0.270222 0.285537 0.270804 0.609256 0.717715 0.962749 0.744519 0.462919 0.51784 0.292513 0.170706 0.5687 0.853609 0.458109 0.732644 0.0940355 0.925246 0.626437 0.597233 0.221669 0.8991 0.0132948 0.964146 0.135151 0.942329 FAURE_PRB Normal end of execution. 09 June 2007 12:08:08 PM