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package it.unimi.dsi.fastutil;
/*
* Copyright (C) 2002-2016 Sebastiano Vigna
*
* Licensed 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.
*/
/** Basic data for all hash-based classes.
*
* Historical note
*
* Warning: the following comments are here for historical reasons,
* and apply just to the double hash classes that can be optionally generated.
* The standard fastutil distribution since 6.1.0 uses linear-probing hash
* tables, and tables are always sized as powers of two.
*
*
The classes in fastutil are built around open-addressing hashing
* implemented via double hashing. Following Knuth's suggestions in the third volume of The Art of Computer
* Programming, we use for the table size a prime p such that
* p-2 is also prime. In this way hashing is implemented with modulo p,
* and secondary hashing with modulo p-2.
*
*
Entries in a table can be in three states: {@link #FREE}, {@link #OCCUPIED} or {@link #REMOVED}.
* The naive handling of removed entries requires that you search for a free entry as if they were occupied. However,
* fastutil implements two useful optimizations, based on the following invariant:
*
* Let i0, i1, …, ip-1 be
* the permutation of the table indices induced by the key k, that is, i0 is the hash
* of k and the following indices are obtained by adding (modulo p) the secondary hash plus one.
* If there is a {@link #OCCUPIED} entry with key k, its index in the sequence above comes before
* the indices of any {@link #REMOVED} entries with key k.
*
*
* When we search for the key k we scan the entries in the
* sequence i0, i1, …,
* ip-1 and stop when k is found,
* when we finished the sequence or when we find a {@link #FREE} entry. Note
* that the correctness of this procedure it is not completely trivial. Indeed,
* when we stop at a {@link #REMOVED} entry with key k we must rely
* on the invariant to be sure that no {@link #OCCUPIED} entry with the same
* key can appear later. If we insert and remove frequently the same entries,
* this optimization can be very effective (note, however, that when using
* objects as keys or values deleted entries are set to a special fixed value to
* optimize garbage collection).
*
*
Moreover, during the probe we keep the index of the first {@link #REMOVED} entry we meet.
* If we actually have to insert a new element, we use that
* entry if we can, thus avoiding to pollute another {@link #FREE} entry. Since this position comes
* a fortiori before any {@link #REMOVED} entries with the same key, we are also keeping the invariant true.
*/
public interface Hash {
/** The initial default size of a hash table. */
final public int DEFAULT_INITIAL_SIZE = 16;
/** The default load factor of a hash table. */
final public float DEFAULT_LOAD_FACTOR = .75f;
/** The load factor for a (usually small) table that is meant to be particularly fast. */
final public float FAST_LOAD_FACTOR = .5f;
/** The load factor for a (usually very small) table that is meant to be extremely fast. */
final public float VERY_FAST_LOAD_FACTOR = .25f;
/** A generic hash strategy.
*
* using arbitrary functions, a typical example being that of {@linkplain
* it.unimi.dsi.fastutil.ints.IntArrays#HASH_STRATEGY arrays}. Of course,
* one has to compare objects for equality consistently with the chosen
* function. A hash strategy, thus, specifies an {@linkplain
* #equals(Object,Object) equality method} and a {@linkplain
* #hashCode(Object) hash function}, with the obvious property that
* equal objects must have the same hash code.
*
*
Note that the {@link #equals(Object,Object) equals()} method of a strategy must
* be able to handle null, too.
*/
public interface Strategy {
/** Returns the hash code of the specified object with respect to this hash strategy.
*
* @param o an object (or null).
* @return the hash code of the given object with respect to this hash strategy.
*/
public int hashCode(K o);
/** Returns true if the given objects are equal with respect to this hash strategy.
*
* @param a an object (or null).
* @param b another object (or null).
* @return true if the two specified objects are equal with respect to this hash strategy.
*/
public boolean equals(K a, K b);
}
/** The default growth factor of a hash table. */
final public int DEFAULT_GROWTH_FACTOR = 16;
/** The state of a free hash table entry. */
final public byte FREE = 0;
/** The state of a occupied hash table entry. */
final public byte OCCUPIED = -1;
/** The state of a hash table entry freed by a deletion. */
final public byte REMOVED = 1;
/** A list of primes to be used as table sizes. The i-th element is
* the largest prime p smaller than 2(i+28)/16
* and such that p-2 is also prime (or 1, for the first few entries). */
final public int PRIMES[] = { 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 13, 13, 13, 13, 13, 13, 13, 13, 19, 19, 19, 19, 19,
19, 19, 19, 19, 19, 19, 19, 31, 31, 31, 31, 31, 31, 31, 43, 43, 43, 43, 43,
43, 43, 43, 61, 61, 61, 61, 61, 73, 73, 73, 73, 73, 73, 73, 103, 103, 109,
109, 109, 109, 109, 139, 139, 151, 151, 151, 151, 181, 181, 193, 199, 199,
199, 229, 241, 241, 241, 271, 283, 283, 313, 313, 313, 349, 349, 349, 349,
421, 433, 463, 463, 463, 523, 523, 571, 601, 619, 661, 661, 661, 661, 661,
823, 859, 883, 883, 883, 1021, 1063, 1093, 1153, 1153, 1231, 1321, 1321,
1429, 1489, 1489, 1621, 1699, 1789, 1873, 1951, 2029, 2131, 2143, 2311,
2383, 2383, 2593, 2731, 2803, 3001, 3121, 3259, 3391, 3583, 3673, 3919,
4093, 4273, 4423, 4651, 4801, 5023, 5281, 5521, 5743, 5881, 6301, 6571,
6871, 7129, 7489, 7759, 8089, 8539, 8863, 9283, 9721, 10141, 10531, 11071,
11551, 12073, 12613, 13009, 13759, 14323, 14869, 15649, 16363, 17029,
17839, 18541, 19471, 20233, 21193, 22159, 23059, 24181, 25171, 26263,
27541, 28753, 30013, 31321, 32719, 34213, 35731, 37309, 38923, 40639,
42463, 44281, 46309, 48313, 50461, 52711, 55051, 57529, 60091, 62299,
65521, 68281, 71413, 74611, 77713, 81373, 84979, 88663, 92671, 96739,
100801, 105529, 109849, 115021, 120079, 125509, 131011, 136861, 142873,
149251, 155863, 162751, 169891, 177433, 185071, 193381, 202129, 211063,
220021, 229981, 240349, 250969, 262111, 273643, 285841, 298411, 311713,
325543, 339841, 355009, 370663, 386989, 404269, 422113, 440809, 460081,
480463, 501829, 524221, 547399, 571603, 596929, 623353, 651019, 679909,
709741, 741343, 774133, 808441, 844201, 881539, 920743, 961531, 1004119,
1048573, 1094923, 1143283, 1193911, 1246963, 1302181, 1359733, 1420039,
1482853, 1548541, 1616899, 1688413, 1763431, 1841293, 1922773, 2008081,
2097133, 2189989, 2286883, 2388163, 2493853, 2604013, 2719669, 2840041,
2965603, 3097123, 3234241, 3377191, 3526933, 3682363, 3845983, 4016041,
4193803, 4379719, 4573873, 4776223, 4987891, 5208523, 5439223, 5680153,
5931313, 6194191, 6468463, 6754879, 7053331, 7366069, 7692343, 8032639,
8388451, 8759953, 9147661, 9552733, 9975193, 10417291, 10878619, 11360203,
11863153, 12387841, 12936529, 13509343, 14107801, 14732413, 15384673,
16065559, 16777141, 17519893, 18295633, 19105483, 19951231, 20834689,
21757291, 22720591, 23726449, 24776953, 25873963, 27018853, 28215619,
29464579, 30769093, 32131711, 33554011, 35039911, 36591211, 38211163,
39903121, 41669479, 43514521, 45441199, 47452879, 49553941, 51747991,
54039079, 56431513, 58930021, 61539091, 64263571, 67108669, 70079959,
73182409, 76422793, 79806229, 83339383, 87029053, 90881083, 94906249,
99108043, 103495879, 108077731, 112863013, 117860053, 123078019, 128526943,
134217439, 140159911, 146365159, 152845393, 159612601, 166679173,
174058849, 181765093, 189812341, 198216103, 206991601, 216156043,
225726379, 235720159, 246156271, 257054491, 268435009, 280319203,
292730833, 305691181, 319225021, 333358513, 348117151, 363529759,
379624279, 396432481, 413983771, 432312511, 451452613, 471440161,
492312523, 514109251, 536870839, 560640001, 585461743, 611382451,
638450569, 666717199, 696235363, 727060069, 759249643, 792864871,
827967631, 864625033, 902905501, 942880663, 984625531, 1028218189,
1073741719, 1121280091, 1170923713, 1222764841, 1276901371, 1333434301,
1392470281, 1454120779, 1518500173, 1585729993, 1655935399, 1729249999,
1805811253, 1885761133, 1969251079, 2056437379, 2147482951 };
}