    001/*
    002 * Licensed to the Apache Software Foundation (ASF) under one or more
    003 * contributor license agreements.  See the NOTICE file distributed with
    004 * this work for additional information regarding copyright ownership.
    005 * The ASF licenses this file to You under the Apache License, Version 2.0
    006 * (the "License"); you may not use this file except in compliance with
    007 * the License.  You may obtain a copy of the License at
    008 *
    009 *      https://www.apache.org/licenses/LICENSE-2.0
    010 *
    011 * Unless required by applicable law or agreed to in writing, software
    012 * distributed under the License is distributed on an "AS IS" BASIS,
    013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    014 * See the License for the specific language governing permissions and
    015 * limitations under the License.
    016 */
    017package org.apache.commons.collections4.bloomfilter;
    018
    019import java.util.Objects;
    020import java.util.function.IntPredicate;
    021
    022/**
    023 * A Hasher that implements combinatorial hashing as described by
    024 * <a href="https://www.eecs.harvard.edu/~michaelm/postscripts/tr-02-05.pdf">Krisch and Mitzenmacher</a> using the enhanced double hashing technique
    025 * described in the wikipedia article  <a href="https://en.wikipedia.org/wiki/Double_hashing#Enhanced_double_hashing">Double Hashing</a>.
    026 * <p>
    027 * Common use for this hasher is to generate bit indices from a byte array output of a hashing
    028 * or MessageDigest algorithm.</p>
    029 *
    030 * <h2>Thoughts on the hasher input</h2>
    031 *
    032 * <p>Note that it is worse to create smaller numbers for the {@code initial} and {@code increment}. If the {@code initial} is smaller than
    033 * the number of bits in a filter then hashing will start at the same point when the size increases; likewise the {@code increment} will be
    034 * the same if it remains smaller than the number of bits in the filter and so the first few indices will be the same if the number of bits
    035 * changes (but is still larger than the {@code increment}). In a worse case scenario with small {@code initial} and {@code increment} for
    036 * all items, hashing may not create indices that fill the full region within a much larger filter. Imagine hashers created with {@code initial}
    037 * and {@code increment} values less than 255 with a filter size of 30000 and number of hash functions as 5. Ignoring the
    038 * tetrahedral addition (a maximum of 20 for k=5) the max index is 255 * 4 + 255 = 1275, this covers 4.25% of the filter. This also
    039 * ignores the negative wrapping but the behavior is the same, some bits cannot be reached.
    040 * </p><p>
    041 * So this needs to be avoided as the filter probability assumptions will be void. If the {@code initial} and {@code increment} are larger
    042 * than the number of bits then the modulus will create a 'random' position and increment within the size.
    043 * </p>
    044 *
    045 * @since 4.5.0-M1
    046 */
    047public class EnhancedDoubleHasher implements Hasher {
    048
    049    /**
    050     * Convert bytes to big-endian long filling with zero bytes as necessary.
    051     *
    052     * @param byteArray The byte array to extract the values from.
    053     * @param offset The offset to start extraction from.
    054     * @param len The length of the extraction, may be longer than 8.
    055     * @return
    056     */
    057    private static long toLong(final byte[] byteArray, final int offset, final int len) {
    058        long val = 0;
    059        int shift = Long.SIZE;
    060        final int end = offset + Math.min(len, Long.BYTES);
    061        for (int i = offset; i < end; i++) {
    062            shift -= Byte.SIZE;
    063            val |= (long) (byteArray[i] & 0xFF) << shift;
    064        }
    065        return val;
    066    }
    067
    068    /**
    069     * The initial hash value.
    070     */
    071    private final long initial;
    072
    073    /**
    074     * The value to increment the hash value by.
    075     */
    076    private final long increment;
    077
    078    /**
    079     * Constructs the EnhancedDoubleHasher from a byte array.
    080     * <p>
    081     * This method simplifies the conversion from a Digest or hasher algorithm output
    082     * to the two values used by the EnhancedDoubleHasher.</p>
    083     * <p>The byte array is split in 2 and the first 8 bytes of each half are interpreted as a big-endian long value.
    084     * Excess bytes are ignored.
    085     * If there are fewer than 16 bytes the following conversions are made.
    086     * </p>
    087     * <ol>
    088     * <li>If there is an odd number of bytes the excess byte is assigned to the increment value</li>
    089     * <li>The bytes allotted are read in big-endian order any byte not populated is set to zero.</li>
    090     * </ol>
    091     * <p>
    092     * This ensures that small arrays generate the largest possible increment and initial values.
    093     * </p>
    094     *
    095     * @param buffer The buffer to extract the longs from.
    096     * @throws IllegalArgumentException is buffer length is zero.
    097     */
    098    public EnhancedDoubleHasher(final byte[] buffer) {
    099        if (buffer.length == 0) {
    100            throw new IllegalArgumentException("buffer length must be greater than 0");
    101        }
    102        // divide by 2
    103        final int segment = buffer.length / 2;
    104        this.initial = toLong(buffer, 0, segment);
    105        this.increment = toLong(buffer, segment, buffer.length - segment);
    106    }
    107
    108    /**
    109     * Constructs the EnhancedDoubleHasher from 2 longs. The long values will be interpreted as unsigned values.
    110     *
    111     * @param initial The initial value for the hasher.
    112     * @param increment The value to increment the hash by on each iteration.
    113     */
    114    public EnhancedDoubleHasher(final long initial, final long increment) {
    115        this.initial = initial;
    116        this.increment = increment;
    117    }
    118
    119    /**
    120     * Gets the increment value for the hash calculation.
    121     *
    122     * @return The increment value for the hash calculation.
    123     */
    124    long getIncrement() {
    125        return increment;
    126    }
    127
    128    /**
    129     * Gets the initial value for the hash calculation.
    130     *
    131     * @return The initial value for the hash calculation.
    132     */
    133    long getInitial() {
    134        return initial;
    135    }
    136
    137    @Override
    138    public IndexExtractor indices(final Shape shape) {
    139        Objects.requireNonNull(shape, "shape");
    140
    141        return new IndexExtractor() {
    142
    143            @Override
    144            public int[] asIndexArray() {
    145                final int[] result = new int[shape.getNumberOfHashFunctions()];
    146                final int[] idx = new int[1];
    147
    148                // This method needs to return duplicate indices
    149
    150                processIndices(i -> {
    151                    result[idx[0]++] = i;
    152                    return true;
    153                });
    154                return result;
    155            }
    156
    157            @Override
    158            public boolean processIndices(final IntPredicate consumer) {
    159                Objects.requireNonNull(consumer, "consumer");
    160                final int bits = shape.getNumberOfBits();
    161                // Enhanced double hashing:
    162                // hash[i] = ( h1(x) + i*h2(x) + (i*i*i - i)/6 ) mod bits
    163                // See: https://en.wikipedia.org/wiki/Double_hashing#Enhanced_double_hashing
    164                //
    165                // Essentially this is computing a wrapped modulus from a start point and an
    166                // increment and an additional term as a tetrahedral number.
    167                // You only need two modulus operations before the loop. Within the loop
    168                // the modulus is handled using the sign bit to detect wrapping to ensure:
    169                // 0 <= index < bits
    170                // 0 <= inc < bits
    171                // The final hash is:
    172                // hash[i] = ( h1(x) - i*h2(x) - (i*i*i - i)/6 ) wrapped in [0, bits)
    173
    174                int index = BitMaps.mod(initial, bits);
    175                if (!consumer.test(index)) {
    176                    return false;
    177                }
    178                int inc = BitMaps.mod(increment, bits);
    179
    180                final int k = shape.getNumberOfHashFunctions();
    181
    182                if (k >= bits) {
    183                    // the tetraheadral incrementer.  We need to ensure that this
    184                    // number does not exceed bits-1 or we may end up with an index > bits.
    185                    int tet = 1;
    186                    for (int i = 1; i < k; i++) {
    187                        // Update index and handle wrapping
    188                        index -= inc;
    189                        index = index < 0 ? index + bits : index;
    190                        if (!consumer.test(index)) {
    191                            return false;
    192                        }
    193
    194                        // Incorporate the counter into the increment to create a
    195                        // tetrahedral number additional term, and handle wrapping.
    196                        inc -= tet;
    197                        inc = inc < 0 ? inc + bits : inc;
    198                        if (++tet == bits) {
    199                            tet = 0;
    200                        }
    201                    }
    202                } else {
    203                    for (int i = 1; i < k; i++) {
    204                        // Update index and handle wrapping
    205                        index -= inc;
    206                        index = index < 0 ? index + bits : index;
    207                        if (!consumer.test(index)) {
    208                            return false;
    209                        }
    210
    211                        // Incorporate the counter into the increment to create a
    212                        // tetrahedral number additional term, and handle wrapping.
    213                        inc -= i;
    214                        inc = inc < 0 ? inc + bits : inc;
    215                    }
    216
    217                }
    218                return true;
    219            }
    220        };
    221    }
    222}