PrimeFinder


1   //   Copyright (c) 1999 CERN - European Organization for Nuclear Research.
2   
3   //   Permission to use, copy, modify, distribute and sell this software
4   //   and its documentation for any purpose is hereby granted without fee,
5   //   provided that the above copyright notice appear in all copies and
6   //   that both that copyright notice and this permission notice appear in
7   //   supporting documentation. CERN makes no representations about the
8   //   suitability of this software for any purpose. It is provided "as is"
9   //   without expressed or implied warranty.
10  package gnu.trove;
11  
12  import java.util.Arrays  ;
13  
14  /*
15   * Modified for Trove to use the java.util.Arrays sort/search
16   * algorithms instead of those provided with colt.
17   */
18  
19  /**
20   * Used to keep hash table capacities prime numbers.
21   * Not of interest for users; only for implementors of hashtables.
22   *
23   * <p>Choosing prime numbers as hash table capacities is a good idea
24   * to keep them working fast, particularly under hash table
25   * expansions.
26   *
27   * <p>However, JDK 1.2, JGL 3.1 and many other toolkits do nothing to
28   * keep capacities prime.  This class provides efficient means to
29   * choose prime capacities.
30   *
31   * <p>Choosing a prime is <tt>O(log 300)</tt> (binary search in a list
32   * of 300 ints).  Memory requirements: 1 KB static memory.
33   *
34   * @author wolfgang.hoschek@cern.ch
35   * @version 1.0, 09/24/99
36   */
37  public final class PrimeFinder {
38      /**
39       * The largest prime this class can generate; currently equal to
40       * <tt>Integer.MAX_VALUE</tt>.
41       */
42      public static final int largestPrime = Integer.MAX_VALUE; //yes, it is prime.
43  
44      /**
45       * The prime number list consists of 11 chunks.
46       *
47       * Each chunk contains prime numbers.
48       *
49       * A chunk starts with a prime P1. The next element is a prime
50       * P2. P2 is the smallest prime for which holds: P2 >= 2*P1.
51       *
52       * The next element is P3, for which the same holds with respect
53       * to P2, and so on.
54       *
55       * Chunks are chosen such that for any desired capacity >= 1000
56       * the list includes a prime number <= desired capacity * 1.11.
57       *
58       * Therefore, primes can be retrieved which are quite close to any
59       * desired capacity, which in turn avoids wasting memory.
60       *
61       * For example, the list includes
62       * 1039,1117,1201,1277,1361,1439,1523,1597,1759,1907,2081.
63       *
64       * So if you need a prime >= 1040, you will find a prime <=
65       * 1040*1.11=1154.
66       *    
67       * Chunks are chosen such that they are optimized for a hashtable
68       * growthfactor of 2.0;
69       *
70       * If your hashtable has such a growthfactor then, after initially
71       * "rounding to a prime" upon hashtable construction, it will
72       * later expand to prime capacities such that there exist no
73       * better primes.
74       *
75       * In total these are about 32*10=320 numbers -> 1 KB of static
76       * memory needed.
77       *
78       * If you are stingy, then delete every second or fourth chunk.
79       */
80      
81      private static final int[] primeCapacities = {
82          //chunk #0
83          largestPrime,
84          
85          //chunk #1
86          5,11,23,47,97,197,397,797,1597,3203,6421,12853,25717,51437,102877,205759,
87          411527,823117,1646237,3292489,6584983,13169977,26339969,52679969,105359939,
88          210719881,421439783,842879579,1685759167,
89            
90          //chunk #2
91          433,877,1759,3527,7057,14143,28289,56591,113189,226379,452759,905551,1811107,
92          3622219,7244441,14488931,28977863,57955739,115911563,231823147,463646329,927292699,
93          1854585413,
94            
95          //chunk #3
96          953,1907,3821,7643,15287,30577,61169,122347,244703,489407,978821,1957651,3915341,
97          7830701,15661423,31322867,62645741,125291483,250582987,501165979,1002331963,
98          2004663929,
99            
100         //chunk #4
101         1039,2081,4177,8363,16729,33461,66923,133853,267713,535481,1070981,2141977,4283963,
102         8567929,17135863,34271747,68543509,137087021,274174111,548348231,1096696463,
103           
104         //chunk #5
105         31,67,137,277,557,1117,2237,4481,8963,17929,35863,71741,143483,286973,573953,
106         1147921,2295859,4591721,9183457,18366923,36733847,73467739,146935499,293871013,
107         587742049,1175484103,
108           
109         //chunk #6
110         599,1201,2411,4831,9677,19373,38747,77509,155027,310081,620171,1240361,2480729,
111         4961459,9922933,19845871,39691759,79383533,158767069,317534141,635068283,1270136683,
112           
113         //chunk #7
114         311,631,1277,2557,5119,10243,20507,41017,82037,164089,328213,656429,1312867,
115         2625761,5251529,10503061,21006137,42012281,84024581,168049163,336098327,672196673,
116         1344393353,
117           
118         //chunk #8
119         3,7,17,37,79,163,331,673,1361,2729,5471,10949,21911,43853,87719,175447,350899,
120         701819,1403641,2807303,5614657,11229331,22458671,44917381,89834777,179669557,
121         359339171,718678369,1437356741,
122           
123         //chunk #9
124         43,89,179,359,719,1439,2879,5779,11579,23159,46327,92657,185323,370661,741337,
125         1482707,2965421,5930887,11861791,23723597,47447201,94894427,189788857,379577741,
126         759155483,1518310967,
127           
128         //chunk #10
129         379,761,1523,3049,6101,12203,24407,48817,97649,195311,390647,781301,1562611,
130         3125257,6250537,12501169,25002389,50004791,100009607,200019221,400038451,800076929,
131         1600153859
132     };
133 
134     static { //initializer
135         // The above prime numbers are formatted for human readability.
136         // To find numbers fast, we sort them once and for all.
137         
138         Arrays.sort(primeCapacities);
139     }
140     
141     /**
142      * Returns a prime number which is <code>&gt;= desiredCapacity</code>
143      * and very close to <code>desiredCapacity</code> (within 11% if
144      * <code>desiredCapacity &gt;= 1000</code>).
145      *
146      * @param desiredCapacity the capacity desired by the user.
147      * @return the capacity which should be used for a hashtable.
148      */
149     public static final int nextPrime(int desiredCapacity) {
150         int i = Arrays.binarySearch(primeCapacities, desiredCapacity);
151         if (i<0) {
152             // desired capacity not found, choose next prime greater
153             // than desired capacity
154             i = -i -1; // remember the semantics of binarySearch...
155         }
156         return primeCapacities[i];
157     }
158 }
159
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