Choosing prime numbers as hash table capacities is a good idea to keep them working fast, * particularly under hash table expansions. * *
However, JDK 1.2, JGL 3.1 and many other toolkits do nothing to keep capacities prime. * This class provides efficient means to choose prime capacities. * *
Choosing a prime is O(log 300) (binary search in a list of 300 int's).
* Memory requirements: 1 KB static memory.
*
* @author wolfgang.hoschek@cern.ch
* @version 1.0, 09/24/99
*/
public class PrimeFinder extends Object {
/**
* The largest prime this class can generate; currently equal to Integer.MAX_VALUE.
*/
public static final int largestPrime = Integer.MAX_VALUE; //yes, it is prime.
/**
* The prime number list consists of 11 chunks.
* Each chunk contains prime numbers.
* A chunk starts with a prime P1. The next element is a prime P2. P2 is the smallest prime for which holds: P2 >= 2*P1.
* The next element is P3, for which the same holds with respect to P2, and so on.
*
* Chunks are chosen such that for any desired capacity >= 1000
* the list includes a prime number <= desired capacity * 1.11 (11%).
* For any desired capacity >= 200
* the list includes a prime number <= desired capacity * 1.16 (16%).
* For any desired capacity >= 16
* the list includes a prime number <= desired capacity * 1.21 (21%).
*
* Therefore, primes can be retrieved which are quite close to any desired capacity,
* which in turn avoids wasting memory.
* For example, the list includes 1039,1117,1201,1277,1361,1439,1523,1597,1759,1907,2081.
* So if you need a prime >= 1040, you will find a prime <= 1040*1.11=1154.
*
* Chunks are chosen such that they are optimized for a hashtable growthfactor of 2.0;
* If your hashtable has such a growthfactor then,
* after initially "rounding to a prime" upon hashtable construction,
* it will later expand to prime capacities such that there exist no better primes.
*
* In total these are about 32*10=320 numbers -> 1 KB of static memory needed.
* If you are stingy, then delete every second or fourth chunk.
*/
private static final int[] primeCapacities = {
//chunk #0
largestPrime,
//chunk #1
5,11,23,47,97,197,397,797,1597,3203,6421,12853,25717,51437,102877,205759,
411527,823117,1646237,3292489,6584983,13169977,26339969,52679969,105359939,
210719881,421439783,842879579,1685759167,
//chunk #2
433,877,1759,3527,7057,14143,28289,56591,113189,226379,452759,905551,1811107,
3622219,7244441,14488931,28977863,57955739,115911563,231823147,463646329,927292699,
1854585413,
//chunk #3
953,1907,3821,7643,15287,30577,61169,122347,244703,489407,978821,1957651,3915341,
7830701,15661423,31322867,62645741,125291483,250582987,501165979,1002331963,
2004663929,
//chunk #4
1039,2081,4177,8363,16729,33461,66923,133853,267713,535481,1070981,2141977,4283963,
8567929,17135863,34271747,68543509,137087021,274174111,548348231,1096696463,
//chunk #5
31,67,137,277,557,1117,2237,4481,8963,17929,35863,71741,143483,286973,573953,
1147921,2295859,4591721,9183457,18366923,36733847,73467739,146935499,293871013,
587742049,1175484103,
//chunk #6
599,1201,2411,4831,9677,19373,38747,77509,155027,310081,620171,1240361,2480729,
4961459,9922933,19845871,39691759,79383533,158767069,317534141,635068283,1270136683,
//chunk #7
311,631,1277,2557,5119,10243,20507,41017,82037,164089,328213,656429,1312867,
2625761,5251529,10503061,21006137,42012281,84024581,168049163,336098327,672196673,
1344393353,
//chunk #8
3,7,17,37,79,163,331,673,1361,2729,5471,10949,21911,43853,87719,175447,350899,
701819,1403641,2807303,5614657,11229331,22458671,44917381,89834777,179669557,
359339171,718678369,1437356741,
//chunk #9
43,89,179,359,719,1439,2879,5779,11579,23159,46327,92657,185323,370661,741337,
1482707,2965421,5930887,11861791,23723597,47447201,94894427,189788857,379577741,
759155483,1518310967,
//chunk #10
379,761,1523,3049,6101,12203,24407,48817,97649,195311,390647,781301,1562611,
3125257,6250537,12501169,25002389,50004791,100009607,200019221,400038451,800076929,
1600153859
/*
// some more chunks for the low range [3..1000]
//chunk #11
13,29,59,127,257,521,1049,2099,4201,8419,16843,33703,67409,134837,269683,
539389,1078787,2157587,4315183,8630387,17260781,34521589,69043189,138086407,
276172823,552345671,1104691373,
//chunk #12
19,41,83,167,337,677,
//1361,2729,5471,10949,21911,43853,87719,175447,350899,
//701819,1403641,2807303,5614657,11229331,22458671,44917381,89834777,179669557,
//359339171,718678369,1437356741,
//chunk #13
53,107,223,449,907,1823,3659,7321,14653,29311,58631,117269,
234539,469099,938207,1876417,3752839,7505681,15011389,30022781,
60045577,120091177,240182359,480364727,960729461,1921458943
*/
};
static { //initializer
// The above prime numbers are formatted for human readability.
// To find numbers fast, we sort them once and for all.
java.util.Arrays.sort(primeCapacities);
//new cern.colt.list.IntArrayList(primeCapacities).mergeSort(); // for debug only, TODO
}
/**
* Makes this class non instantiable, but still let's others inherit from it.
*/
protected PrimeFinder() {}
/**
* Tests correctness. Try
* from=1000, to=10000
* from=200, to=1000
* from=16, to=1000
* from=1000, to=Integer.MAX_VALUE
*/
protected static void main(String args[]) {
int from = Integer.parseInt(args[0]);
int to = Integer.parseInt(args[1]);
statistics(from,to);
}
/**
* Returns a prime number which is >= desiredCapacity and very close to desiredCapacity (within 11% if desiredCapacity >= 1000).
* @param desiredCapacity the capacity desired by the user.
* @return the capacity which should be used for a hashtable.
*/
public static int nextPrime(int desiredCapacity) {
int i = java.util.Arrays.binarySearch(primeCapacities, desiredCapacity);
//int i = new cern.colt.list.IntArrayList(primeCapacities).binarySearch(desiredCapacity); // for debug only TODO
if (i<0) {
// desired capacity not found, choose next prime greater than desired capacity
i = -i -1; // remember the semantics of binarySearch...
}
return primeCapacities[i];
}
/**
* Tests correctness.
*/
protected static void statistics(int from, int to) {
// check that primes contain no accidental errors
for (int i=0; i