/**
* Licensed to the Apache Software Foundation (ASF) under one
* or more contributor license agreements. See the NOTICE file
* distributed with this work for additional information
* regarding copyright ownership. The ASF licenses this file
* to you under the Apache License, Version 2.0 (the
* "License"); you may not use this file except in compliance
* with the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing,
* software distributed under the License is distributed on an
* "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
* KIND, either express or implied. See the License for the
* specific language governing permissions and limitations
* under the License.
*/
package org.apache.mahout.math.map;
import java.util.Arrays;
/**
* Not of interest for users; only for implementors of hashtables.
* Used to keep hash table capacities prime numbers.
*
* <p>Choosing prime numbers as hash table capacities is a good idea to keep them working fast,
* particularly under hash table expansions.
*
* <p>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.
*
* <p>Choosing a prime is <tt>O(log 300)</tt> (binary search in a list of 300 int's).
* Memory requirements: 1 KB static memory.
*
*/
public final class PrimeFinder {
/** The largest prime this class can generate; currently equal to <tt>Integer.MAX_VALUE</tt>. */
public static final int LARGEST_PRIME = 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[] PRIME_CAPACITIES = {
//chunk #0
LARGEST_PRIME,
//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(PRIME_CAPACITIES);
}
/** Makes this class non instantiable, but still let's others inherit from it. */
private PrimeFinder() {
}
/**
* Returns a prime number which is {@code <= desiredCapacity} and very close to {@code desiredCapacity}
* (within 11% if {@code 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(PRIME_CAPACITIES, desiredCapacity);
if (i < 0) {
// desired capacity not found, choose next prime greater than desired capacity
i = -i - 1; // remember the semantics of binarySearch...
}
return PRIME_CAPACITIES[i];
}
}