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// Copyright (c) 1999 CERN - European Organization for Nuclear Research.
// Permission to use, copy, modify, distribute and sell this software
// and its documentation for any purpose is hereby granted without fee,
// provided that the above copyright notice appear in all copies and
// that both that copyright notice and this permission notice appear in
// supporting documentation. CERN makes no representations about the
// suitability of this software for any purpose. It is provided "as is"
// without expressed or implied warranty.
package com.alibaba.fastjson2.internal.trove.impl;
import java.util.Arrays;
/*
* Modified for Trove to use the java.util.Arrays sort/search
* algorithms instead of those provided with colt.
*/
/**
* Used to keep hash table capacities prime numbers.
* Not of interest for users; only for implementors of hashtables.
*
* 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 ints). Memory requirements: 1 KB static memory.
*
* @author [email protected]
* @version 1.0, 09/24/99
*/
public final class PrimeFinder {
/**
* The largest prime this class can generate; currently equal to
* 2,004,663,929.
*
* While Integer.MAX_VALUE is in fact the largest representable
* prime in the integer space, consumers of this class are
* intended to create arrays of size returned from
* {@link #nextPrime}. Since the VM needs to reserve a few bytes
* for internal overhead, new int[Integer.MAX_VALUE] fails with
* an "exceeds VM limits" exception. So, we pick the second-largest
* prime as the practical largest.
*/
public static final int largestPrime;
/**
* 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.
*
* 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 #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
};
static { //initializer
// The above prime numbers are formatted for human readability.
// To find numbers fast, we sort them once and for all.
Arrays.sort(primeCapacities);
largestPrime = primeCapacities[primeCapacities.length - 1];
}
/**
* 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) {
if (desiredCapacity >= largestPrime) {
return largestPrime;
}
int i = Arrays.binarySearch(primeCapacities, desiredCapacity);
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];
}
}