June 9 2007 11:57:13.854 AM FAURE_PRB FORTRAN90 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_I4: logarith of I4 base J4, I4 J4 I4_LOG_I4 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 prime base QS = 2 Seed Seed Faure In Out -1 16 0.937500 0.562500 16 17 0.031250 0.531250 17 18 0.531250 0.531250 18 19 0.281250 0.281250 19 20 0.781250 0.281250 20 21 0.156250 0.156250 21 22 0.656250 0.156250 22 23 0.406250 0.906250 23 24 0.906250 0.906250 24 25 0.093750 0.468750 Using dimension DIM_NUM = 3 The prime base QS = 3 Seed Seed Faure In Out -1 81 0.987654 0.098765 0.543210 81 82 0.004115 0.460905 0.251029 82 83 0.337449 0.460905 0.251029 83 84 0.670782 0.460905 0.251029 84 85 0.115226 0.905350 0.362140 85 86 0.448560 0.905350 0.362140 86 87 0.781893 0.905350 0.362140 87 88 0.226337 0.016461 0.806584 88 89 0.559671 0.016461 0.806584 89 90 0.893004 0.016461 0.806584 Using dimension DIM_NUM = 4 The prime base QS = 5 Seed Seed Faure In Out -1 625 0.998400 0.574400 0.950400 0.046400 625 626 0.000320 0.374720 0.117120 0.155520 626 627 0.200320 0.374720 0.117120 0.155520 627 628 0.400320 0.374720 0.117120 0.155520 628 629 0.600320 0.374720 0.117120 0.155520 629 630 0.800320 0.374720 0.117120 0.155520 630 631 0.040320 0.414720 0.357120 0.395520 631 632 0.240320 0.414720 0.357120 0.395520 632 633 0.440320 0.414720 0.357120 0.395520 633 634 0.640320 0.414720 0.357120 0.395520 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 prime base 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 0.098765 0.543210 81 82 0.004115 0.460905 0.251029 82 83 0.337449 0.460905 0.251029 83 84 0.670782 0.460905 0.251029 84 85 0.115226 0.905350 0.362140 However, if the input value of SEED is 0, then no initial skipping is done. Seed Seed Faure In Out 0 1 0.000000 0.000000 0.000000 1 2 0.333333 0.000000 0.000000 2 3 0.666667 0.000000 0.000000 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 0.189300 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 0.592593 0.148148 10 11 0.370370 0.592593 0.148148 11 12 0.703704 0.592593 0.148148 12 13 0.148148 0.703704 0.592593 TEST03 FAURE computes the next element of a Faure sequence. In this test, we try some large dimensions. Using dimension DIM_NUM = 10 The prime base QS = 11 Seed in = -1 Seed out = 14641 R(1:10) = 0.999932 0.774537 0.045011 0.811352 0.990916 0.567174 0.639301 0.207295 0.188512 0.657332 Seed in = 14641 Seed out = 14642 R(1:10) = 0.000006 0.128754 0.448336 0.991059 0.940243 0.592657 0.054989 0.527088 0.115640 0.100887 Using dimension DIM_NUM = 20 The prime base QS = 23 Seed in = -1 Seed out = 279841 R(1:20) = 0.999996 0.903342 0.534475 0.936875 0.067063 0.925040 0.554283 0.911314 0.998024 0.810632 0.351028 0.662691 0.702142 0.512859 0.007887 0.274181 0.270153 0.035502 0.485161 0.706087 Seed in = 279841 Seed out = 279842 R(1:20) = 0.000000 0.051547 0.669298 0.857033 0.614753 0.076672 0.199231 0.073331 0.698890 0.208233 0.561662 0.804546 0.023760 0.221358 0.487995 0.869040 0.321015 0.976244 0.838426 0.994683 Using dimension DIM_NUM = 30 The prime base QS = 31 Seed in = -1 Seed out = 923521 R(1:30) = 0.999999 0.930179 0.660568 0.223422 0.554227 0.717497 0.680976 0.476921 0.040817 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 0.022556 0.319021 0.415695 0.312577 0.009666 0.539222 Seed in = 923521 Seed out = 923522 R(1:30) = 0.000000 0.036626 0.485726 0.113168 0.653604 0.908283 0.674290 0.654020 0.679904 0.518921 0.936903 0.734061 0.645045 0.435725 0.906308 0.854920 0.017222 0.192447 0.114173 0.582607 0.395877 0.321933 0.095426 0.514483 0.347021 0.360016 0.383819 0.120825 0.372281 0.935274 Using dimension DIM_NUM = 40 The prime base QS = 41 Seed in = -1 Seed out = 2825761 R(1:40) = 1.000000 0.948201 0.746492 0.394872 0.917732 0.290680 0.489328 0.562455 0.510062 0.283368 0.906762 0.404637 0.752600 0.950653 0.999390 0.897622 0.645942 0.244352 0.717241 0.040220 0.213287 0.236444 0.109690 0.833026 0.430841 0.854355 0.152348 0.300431 0.299197 0.147458 0.870199 0.418638 0.841557 0.114566 0.237663 0.210850 0.034126 0.707491 0.255335 0.653269 Seed in = 2825761 Seed out = 2825762 R(1:40) = 0.000000 0.026858 0.385241 0.601026 0.274450 0.005158 0.367806 0.962634 0.364893 0.125446 0.892123 0.216365 0.672860 0.862426 0.383517 0.787590 0.698083 0.666454 0.316736 0.175402 0.890279 0.012812 0.142673 0.830113 0.724153 0.351264 0.335479 0.227066 0.650654 0.156510 0.345467 0.815964 0.143877 0.879459 0.671730 0.071552 0.654177 0.018653 0.740829 0.420348 Using dimension DIM_NUM = 50 The prime base QS = 53 Seed in = -1 Seed out = 7890481 R(1:50) = 1.000000 0.960464 0.805584 0.535361 0.168663 0.667752 0.070367 0.357637 0.510697 0.567280 0.527388 0.353285 0.063838 0.677915 0.157781 0.541171 0.809218 0.961921 0.999637 0.921653 0.728326 0.419655 0.014508 0.475151 0.839317 0.088140 0.221619 0.239755 0.142547 0.929996 0.620969 0.177730 0.638016 0.964091 0.193690 0.307945 0.307213 0.190782 0.977874 0.630755 0.187161 0.609355 0.935074 0.145449 0.240480 0.220168 0.084513 0.833513 0.486039 0.004352 Seed in = 7890481 Seed out = 7890482 R(1:50) = 0.000000 0.020333 0.294573 0.227135 0.317842 0.970750 0.666103 0.865987 0.993327 0.509855 0.895812 0.574836 0.007946 0.656871 0.945244 0.372187 0.342465 0.354832 0.814413 0.220319 0.995832 0.603039 0.483733 0.099644 0.911792 0.363393 0.915111 0.009800 0.108849 0.654401 0.108541 0.913065 0.529702 0.419470 0.025589 0.808719 0.192855 0.677108 0.665891 0.658671 0.060211 0.369635 0.010574 0.444046 0.131782 0.497420 0.021202 0.164146 0.350602 0.041233 Using dimension DIM_NUM = 60 The prime base QS = 61 Seed in = -1 Seed out = 13845841 R(1:60) = 1.000000 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 0.178640 0.577982 0.893744 0.109533 0.225349 0.241192 0.157062 0.972958 0.688881 0.321225 0.837202 0.269600 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 Seed in = 13845841 Seed out = 13845842 R(1:60) = 0.000000 0.017495 0.254608 0.078444 0.872233 0.052530 0.002835 0.123039 0.796373 0.423267 0.386683 0.086781 0.923186 0.279935 0.572774 0.152687 0.452346 0.838868 0.728533 0.504572 0.550752 0.266967 0.053108 0.308799 0.401684 0.747510 0.730047 0.749185 0.188156 0.447389 0.926240 0.008472 0.093986 0.566008 0.824969 0.270222 0.285537 0.270804 0.609256 0.717715 0.962749 0.744519 0.462919 0.517840 0.292513 0.170706 0.568700 0.853609 0.458109 0.732644 0.094036 0.925246 0.626437 0.597233 0.221669 0.899100 0.013295 0.964146 0.135151 0.942329 FAURE_PRB Normal end of execution. June 9 2007 11:57:13.859 AM