cassandra/src/java/org/apache/cassandra/utils/PrimeFinder.java

/*
* 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.cassandra.utils;

import java.util.Arrays;

/**
 * Used to keep hash table capacities prime numbers. Not of interest for users;
 * only for implementors of hashtables.
 * 
 * <p>
 * Choosing prime numbers as hash table capacities is a good idea to keep them
 * working fast, particularly under hash table expansions.
 * 
 */
public final class PrimeFinder
{
    /**
     * The largest prime this class can generate; currently equal to
     * <tt>Integer.MAX_VALUE</tt>.
     */
    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.
     * 
     * 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 };

    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);
    }

    /**
     * Returns a prime number which is <code>&gt;= desiredCapacity</code> and
     * very close to <code>desiredCapacity</code> (within 11% if
     * <code>desiredCapacity &gt;= 1000</code>).
     * 
     * @param desiredCapacity
     *            the capacity desired by the user.
     * @return the capacity which should be used for a hashtable.
     */
    public static final int nextPrime(int desiredCapacity)
    {
        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];
    }
}