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halton.c
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1
19/*****************************************************************************/
20#include "tpcclibConfig.h"
21/*****************************************************************************/
22#include <stdio.h>
23#include <stdlib.h>
24#include <stdbool.h>
25#include <math.h>
26#include <time.h>
27#include <string.h>
28/*****************************************************************************/
29#include "tpcextensions.h"
30/*****************************************************************************/
31#include "tpcrand.h"
32/*****************************************************************************/
33
34/*****************************************************************************/
38int haltonElement(
40 const int i,
42 const int dim,
44 double *r
45) {
46 if(i<0 || dim<1 || r==NULL) return(1);
47
48 int t[dim];
49 for(int j=0; j<dim; j++) t[j]=1+i; // Plus one by VO, because otherwise results are set to zero for i=0
50
51 double prime_inv[dim];
52 for(int j=0; j<dim; j++) prime_inv[j] = 1.0 / (double)haltonPrime(1+j);
53
54 for(int j=0; j<dim; j++) r[j]=0.0;
55 while(1) {
56 for(int j=0; j<dim; j++) {
57 int d = (t[j] % haltonPrime(1+j));
58 r[j] += (double)d * prime_inv[j];
59 prime_inv[j] /= (double)haltonPrime(1+j);
60 t[j] /= haltonPrime(1+j);
61 }
62 int tmax=t[0];
63 for(int j=1; j<dim; j++) if(t[j]>tmax) tmax=t[j];
64 if(tmax<1) break;
65 }
66 return(0);
67}
68/*****************************************************************************/
69
70/*****************************************************************************/
75int haltonPrime(
80 const int N
81) {
83
84#define iMAX 1600
85
86 if(N<0) return(iMAX);
87 if(N==0) return(1);
88 if(N>iMAX) return(0);
89 const int npvec[iMAX] = {
90 2, 3, 5, 7, 11, 13, 17, 19, 23, 29,
91 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
92 73, 79, 83, 89, 97, 101, 103, 107, 109, 113,
93 127, 131, 137, 139, 149, 151, 157, 163, 167, 173,
94 179, 181, 191, 193, 197, 199, 211, 223, 227, 229,
95 233, 239, 241, 251, 257, 263, 269, 271, 277, 281,
96 283, 293, 307, 311, 313, 317, 331, 337, 347, 349,
97 353, 359, 367, 373, 379, 383, 389, 397, 401, 409,
98 419, 421, 431, 433, 439, 443, 449, 457, 461, 463,
99 467, 479, 487, 491, 499, 503, 509, 521, 523, 541,
100 547, 557, 563, 569, 571, 577, 587, 593, 599, 601,
101 607, 613, 617, 619, 631, 641, 643, 647, 653, 659,
102 661, 673, 677, 683, 691, 701, 709, 719, 727, 733,
103 739, 743, 751, 757, 761, 769, 773, 787, 797, 809,
104 811, 821, 823, 827, 829, 839, 853, 857, 859, 863,
105 877, 881, 883, 887, 907, 911, 919, 929, 937, 941,
106 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013,
107 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069,
108 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151,
109 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223,
110 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291,
111 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373,
112 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451,
113 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511,
114 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583,
115 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657,
116 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733,
117 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811,
118 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889,
119 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987,
120 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053,
121 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129,
122 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213,
123 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287,
124 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357,
125 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423,
126 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531,
127 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617,
128 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687,
129 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741,
130 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819,
131 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903,
132 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999,
133 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079,
134 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181,
135 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257,
136 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331,
137 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413,
138 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511,
139 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571,
140 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643,
141 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727,
142 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821,
143 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907,
144 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989,
145 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057,
146 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139,
147 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231,
148 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297,
149 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409,
150 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493,
151 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583,
152 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657,
153 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751,
154 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831,
155 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937,
156 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003,
157 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087,
158 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179,
159 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279,
160 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387,
161 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443,
162 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521,
163 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639,
164 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693,
165 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791,
166 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857,
167 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939,
168 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053,
169 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133,
170 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221,
171 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301,
172 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367,
173 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473,
174 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571,
175 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673,
176 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761,
177 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833,
178 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917,
179 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997,
180 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103,
181 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207,
182 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297,
183 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411,
184 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499,
185 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561,
186 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643,
187 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723,
188 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829,
189 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919,
190 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017,
191 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111,
192 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219,
193 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291,
194 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387,
195 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501,
196 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597,
197 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677,
198 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741,
199 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831,
200 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929,
201 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011,
202 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109,
203 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199,
204 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283,
205 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377,
206 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439,
207 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533,
208 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631,
209 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733,
210 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811,
211 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887,
212 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973,10007,
213 10009,10037,10039,10061,10067,10069,10079,10091,10093,10099,
214 10103,10111,10133,10139,10141,10151,10159,10163,10169,10177,
215 10181,10193,10211,10223,10243,10247,10253,10259,10267,10271,
216 10273,10289,10301,10303,10313,10321,10331,10333,10337,10343,
217 10357,10369,10391,10399,10427,10429,10433,10453,10457,10459,
218 10463,10477,10487,10499,10501,10513,10529,10531,10559,10567,
219 10589,10597,10601,10607,10613,10627,10631,10639,10651,10657,
220 10663,10667,10687,10691,10709,10711,10723,10729,10733,10739,
221 10753,10771,10781,10789,10799,10831,10837,10847,10853,10859,
222 10861,10867,10883,10889,10891,10903,10909,10937,10939,10949,
223 10957,10973,10979,10987,10993,11003,11027,11047,11057,11059,
224 11069,11071,11083,11087,11093,11113,11117,11119,11131,11149,
225 11159,11161,11171,11173,11177,11197,11213,11239,11243,11251,
226 11257,11261,11273,11279,11287,11299,11311,11317,11321,11329,
227 11351,11353,11369,11383,11393,11399,11411,11423,11437,11443,
228 11447,11467,11471,11483,11489,11491,11497,11503,11519,11527,
229 11549,11551,11579,11587,11593,11597,11617,11621,11633,11657,
230 11677,11681,11689,11699,11701,11717,11719,11731,11743,11777,
231 11779,11783,11789,11801,11807,11813,11821,11827,11831,11833,
232 11839,11863,11867,11887,11897,11903,11909,11923,11927,11933,
233 11939,11941,11953,11959,11969,11971,11981,11987,12007,12011,
234 12037,12041,12043,12049,12071,12073,12097,12101,12107,12109,
235 12113,12119,12143,12149,12157,12161,12163,12197,12203,12211,
236 12227,12239,12241,12251,12253,12263,12269,12277,12281,12289,
237 12301,12323,12329,12343,12347,12373,12377,12379,12391,12401,
238 12409,12413,12421,12433,12437,12451,12457,12473,12479,12487,
239 12491,12497,12503,12511,12517,12527,12539,12541,12547,12553,
240 12569,12577,12583,12589,12601,12611,12613,12619,12637,12641,
241 12647,12653,12659,12671,12689,12697,12703,12713,12721,12739,
242 12743,12757,12763,12781,12791,12799,12809,12821,12823,12829,
243 12841,12853,12889,12893,12899,12907,12911,12917,12919,12923,
244 12941,12953,12959,12967,12973,12979,12983,13001,13003,13007,
245 13009,13033,13037,13043,13049,13063,13093,13099,13103,13109,
246 13121,13127,13147,13151,13159,13163,13171,13177,13183,13187,
247 13217,13219,13229,13241,13249,13259,13267,13291,13297,13309,
248 13313,13327,13331,13337,13339,13367,13381,13397,13399,13411,
249 13417,13421,13441,13451,13457,13463,13469,13477,13487,13499
250 };
251 return(npvec[N-1]);
252# undef iMAX
254}
255/*****************************************************************************/
256
257/*****************************************************************************/
haltonElement
int haltonElement(const int i, const int dim, double *r)
Calculation of an element of quasi-random low-discrepancy Halton sequence.
Definition halton.c:38
haltonPrime
int haltonPrime(const int N)
Subfunction for calculation of quasi-random Halton sequence.
Definition halton.c:75
tpcextensions.h
Header file for library libtpcextensions.
tpcrand.h
Header file for libtpcrand.
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