December 11 2009 9:29:53.121 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 1 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 0.062500 16 17 0.031250 0.531250 17 18 0.531250 0.031250 18 19 0.281250 0.281250 19 20 0.781250 0.781250 20 21 0.156250 0.156250 21 22 0.656250 0.656250 22 23 0.406250 0.906250 23 24 0.906250 0.406250 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 0.765432 0.209877 81 82 0.004115 0.460905 0.584362 82 83 0.337449 0.794239 0.917695 83 84 0.670782 0.127572 0.251029 84 85 0.115226 0.905350 0.028807 85 86 0.448560 0.238683 0.362140 86 87 0.781893 0.572016 0.695473 87 88 0.226337 0.016461 0.806584 88 89 0.559671 0.349794 0.139918 89 90 0.893004 0.683128 0.473251 Using dimension DIM_NUM = 4 The prime base QS = 5 Seed Seed Faure In Out -1 625 0.998400 0.374400 0.150400 0.046400 625 626 0.000320 0.374720 0.317120 0.355520 626 627 0.200320 0.574720 0.517120 0.555520 627 628 0.400320 0.774720 0.717120 0.755520 628 629 0.600320 0.974720 0.917120 0.955520 629 630 0.800320 0.174720 0.117120 0.155520 630 631 0.040320 0.414720 0.757120 0.995520 631 632 0.240320 0.614720 0.957120 0.195520 632 633 0.440320 0.814720 0.157120 0.395520 633 634 0.640320 0.014720 0.357120 0.595520 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 0.765432 0.209877 81 82 0.004115 0.460905 0.584362 82 83 0.337449 0.794239 0.917695 83 84 0.670782 0.127572 0.251029 84 85 0.115226 0.905350 0.028807 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 0.333333 0.333333 2 3 0.666667 0.666667 0.666667 3 4 0.111111 0.444444 0.777778 4 5 0.444444 0.777778 0.111111 5 6 0.777778 0.111111 0.444444 6 7 0.222222 0.888889 0.555556 7 8 0.555556 0.222222 0.888889 8 9 0.888889 0.555556 0.222222 9 10 0.037037 0.592593 0.481481 Jump ahead by increasing SEED: Seed Seed Faure In Out 100 101 0.411523 0.646091 0.547325 101 102 0.744856 0.979424 0.880658 102 103 0.189300 0.423868 0.991770 103 104 0.522634 0.757202 0.325103 104 105 0.855967 0.090535 0.658436 Jump back by decreasing SEED: Seed Seed Faure In Out 3 4 0.111111 0.444444 0.777778 4 5 0.444444 0.777778 0.111111 5 6 0.777778 0.111111 0.444444 6 7 0.222222 0.888889 0.555556 7 8 0.555556 0.222222 0.888889 8 9 0.888889 0.555556 0.222222 9 10 0.037037 0.592593 0.481481 10 11 0.370370 0.925926 0.814815 11 12 0.703704 0.259259 0.148148 12 13 0.148148 0.703704 0.259259 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 0.683628 0.681374 0.447715 0.354552 0.839902 0.457482 0.661840 0.824875 0.475514 Seed in = 14641 Seed out = 14642 R(1:10) = 0.000006 0.128754 0.539245 0.445604 0.303879 0.865384 0.873171 0.345270 0.388368 0.464524 Using dimension DIM_NUM = 20 The prime base QS = 23 Seed in = -1 Seed out = 279841 R(1:20) = 0.999996 0.859863 0.360562 0.284701 0.327933 0.229387 0.771674 0.650444 0.606720 0.375849 0.698854 0.358343 0.049968 0.556337 0.529626 0.795920 0.052762 0.078981 0.528639 0.227826 Seed in = 279841 Seed out = 279842 R(1:20) = 0.000000 0.051547 0.712776 0.552685 0.136492 0.207107 0.373144 0.421157 0.090194 0.295189 0.822532 0.587155 0.588977 0.786575 0.270604 0.129910 0.407971 0.367548 0.186252 0.168596 Using dimension DIM_NUM = 30 The prime base QS = 31 Seed in = -1 Seed out = 923521 R(1:30) = 0.999999 0.897921 0.531535 0.739551 0.263904 0.975562 0.648718 0.122083 0.137591 0.566210 0.182134 0.792856 0.202745 0.251551 0.681211 0.362692 0.070188 0.642408 0.821287 0.477794 0.386122 0.353763 0.185088 0.687589 0.699975 0.996441 0.383437 0.667415 0.654828 0.184383 Seed in = 923521 Seed out = 923522 R(1:30) = 0.000000 0.036626 0.517984 0.629297 0.266507 0.166347 0.835580 0.460471 0.131517 0.647953 0.582065 0.314706 0.935368 0.338951 0.228888 0.080727 0.081738 0.256963 0.339979 0.905188 0.299103 0.612256 0.676071 0.159644 0.476053 0.811629 0.190271 0.282115 0.630345 0.548177 Using dimension DIM_NUM = 40 The prime base QS = 41 Seed in = -1 Seed out = 2825761 R(1:40) = 1.000000 0.923811 0.648931 0.029018 0.942122 0.217510 0.684450 0.245382 0.753964 0.015075 0.906762 0.307076 0.045283 0.975044 0.950610 0.824451 0.450820 0.683376 0.400168 0.430464 0.627921 0.846200 0.938959 0.759855 0.186938 0.025086 0.176738 0.471162 0.762612 0.903556 0.772638 0.174736 0.012289 0.114566 0.335224 0.527923 0.546321 0.244076 0.499238 0.141074 Seed in = 2825761 Seed out = 2825762 R(1:40) = 0.000000 0.026858 0.409631 0.991270 0.250060 0.249060 0.611709 0.572390 0.925868 0.027885 0.916513 0.118804 0.770421 0.618524 0.993273 0.763199 0.454180 0.105478 0.414297 0.565646 0.451255 0.451837 0.581697 0.391089 0.114397 0.448825 0.774503 0.983164 0.626264 0.766266 0.101565 0.913525 0.046316 0.903850 0.574169 0.632527 0.263933 0.262556 0.984732 0.395958 Using dimension DIM_NUM = 50 The prime base QS = 53 Seed in = -1 Seed out = 7890481 R(1:50) = 1.000000 0.941596 0.730113 0.252342 0.413946 0.063979 0.126970 0.470845 0.963527 0.529544 0.055690 0.391021 0.441196 0.111877 0.252121 0.786454 0.582803 0.527959 0.509071 0.412219 0.124552 0.532863 0.542810 0.003452 0.839317 0.918328 0.127279 0.352962 0.482170 0.401694 0.017195 0.177730 0.807828 0.756544 0.948407 0.251342 0.552496 0.737951 0.713723 0.328869 0.507916 0.099921 0.029413 0.164317 0.391424 0.597527 0.669418 0.493891 0.976605 0.966617 Seed in = 7890481 Seed out = 7890482 R(1:50) = 0.000000 0.020333 0.313441 0.529022 0.846143 0.800939 0.458556 0.318817 0.295214 0.792874 0.688265 0.254081 0.253229 0.902154 0.832036 0.202376 0.531145 0.883134 0.682337 0.899564 0.882625 0.470963 0.936563 0.024173 0.930660 0.287921 0.198130 0.198480 0.297528 0.937419 0.033069 0.931933 0.454230 0.872301 0.893513 0.695511 0.872101 0.545032 0.194193 0.847350 0.890400 0.256427 0.255857 0.689329 0.811027 0.289873 0.304221 0.466033 0.803433 0.833686 Using dimension DIM_NUM = 60 The prime base QS = 61 Seed in = -1 Seed out = 13845841 R(1:60) = 1.000000 0.949463 0.766165 0.351747 0.607848 0.452500 0.754556 0.448443 0.419405 0.569083 0.799115 0.011142 0.106802 0.987735 0.571973 0.728369 0.391350 0.429767 0.778047 0.321437 0.961574 0.600367 0.138919 0.479137 0.539054 0.187522 0.358968 0.922245 0.811777 0.912812 0.126989 0.355946 0.501324 0.464761 0.147898 0.468766 0.296219 0.564682 0.159401 0.982016 0.934166 0.917760 0.833898 0.584489 0.071173 0.211982 0.875769 0.996960 0.444407 0.152537 0.006595 0.908221 0.759055 0.460735 0.931294 0.039585 0.720034 0.841493 0.338389 0.095968 Seed in = 13845841 Seed out = 13845842 R(1:60) = 0.000000 0.017495 0.271001 0.340739 0.200102 0.249251 0.248736 0.368940 0.157029 0.570808 0.944060 0.021208 0.939580 0.214361 0.785889 0.923179 0.370379 0.199524 0.925254 0.422605 0.960588 0.217786 0.266222 0.571094 0.959061 0.698330 0.418571 0.159021 0.335697 0.775258 0.696732 0.696997 0.782511 0.336500 0.152838 0.417763 0.695373 0.959329 0.560075 0.275092 0.225044 0.957634 0.413738 0.927676 0.210546 0.367427 0.929355 0.771642 0.228601 0.945759 0.028462 0.941640 0.560864 0.154610 0.369209 0.259756 0.259196 0.210047 0.331873 0.270198 FAURE_PRB Normal end of execution. December 11 2009 9:29:53.129 AM