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| 1 | +package org.fastfilter.xor; |
| 2 | + |
| 3 | +import java.util.Arrays; |
| 4 | + |
| 5 | +import org.fastfilter.Filter; |
| 6 | +import org.fastfilter.utils.Hash; |
| 7 | + |
| 8 | +/** |
| 9 | + * The xor binary fuse filter, a new algorithm that can replace a Bloom filter. |
| 10 | + */ |
| 11 | +public class XorBinaryFuse32 implements Filter { |
| 12 | + |
| 13 | + private static final int ARITY = 3; |
| 14 | + |
| 15 | + private final int segmentCount; |
| 16 | + private final int segmentCountLength; |
| 17 | + private final int segmentLength; |
| 18 | + private final int segmentLengthMask; |
| 19 | + private final int arrayLength; |
| 20 | + private final int[] fingerprints; |
| 21 | + private long seed; |
| 22 | + |
| 23 | + public XorBinaryFuse32(int segmentCount, int segmentLength) { |
| 24 | + if (segmentLength < 0 || Integer.bitCount(segmentLength) != 1) { |
| 25 | + throw new IllegalArgumentException("Segment length needs to be a power of 2, is " + segmentLength); |
| 26 | + } |
| 27 | + if (segmentCount <= 0) { |
| 28 | + throw new IllegalArgumentException("Illegal segment count: " + segmentCount); |
| 29 | + } |
| 30 | + this.segmentLength = segmentLength; |
| 31 | + this.segmentCount = segmentCount; |
| 32 | + this.segmentLengthMask = segmentLength - 1; |
| 33 | + this.segmentCountLength = segmentCount * segmentLength; |
| 34 | + this.arrayLength = (segmentCount + ARITY - 1) * segmentLength; |
| 35 | + this.fingerprints = new int[arrayLength]; |
| 36 | + } |
| 37 | + |
| 38 | + public long getBitCount() { |
| 39 | + return ((long) (arrayLength)) * Integer.SIZE; |
| 40 | + } |
| 41 | + |
| 42 | + static int calculateSegmentLength(int arity, int size) { |
| 43 | + int segmentLength; |
| 44 | + if (arity == 3) { |
| 45 | + segmentLength = 1 << (int) Math.floor(Math.log(size) / Math.log(3.33) + 2.11); |
| 46 | + } else if (arity == 4) { |
| 47 | + segmentLength = 1 << (int) Math.floor(Math.log(size) / Math.log(2.91) - 0.5); |
| 48 | + } else { |
| 49 | + // not supported |
| 50 | + segmentLength = 65536; |
| 51 | + } |
| 52 | + return segmentLength; |
| 53 | + } |
| 54 | + |
| 55 | + static double calculateSizeFactor(int arity, int size) { |
| 56 | + double sizeFactor; |
| 57 | + if (arity == 3) { |
| 58 | + sizeFactor = Math.max(1.125, 0.875 + 0.25 * Math.log(1000000) / Math.log(size)); |
| 59 | + } else if (arity == 4) { |
| 60 | + sizeFactor = Math.max(1.075, 0.77 + 0.305 * Math.log(600000) / Math.log(size)); |
| 61 | + } else { |
| 62 | + // not supported |
| 63 | + sizeFactor = 2.0; |
| 64 | + } |
| 65 | + return sizeFactor; |
| 66 | + } |
| 67 | + |
| 68 | + private static int mod3(int x) { |
| 69 | + if (x > 2) { |
| 70 | + x -= 3; |
| 71 | + } |
| 72 | + return x; |
| 73 | + } |
| 74 | + |
| 75 | + public static XorBinaryFuse32 construct(long[] keys) { |
| 76 | + int size = keys.length; |
| 77 | + int segmentLength = calculateSegmentLength(ARITY, size); |
| 78 | + // the current implementation hardcodes a 18-bit limit to |
| 79 | + // to the segment length. |
| 80 | + if (segmentLength > (1 << 18)) { |
| 81 | + segmentLength = (1 << 18); |
| 82 | + } |
| 83 | + double sizeFactor = calculateSizeFactor(ARITY, size); |
| 84 | + int capacity = (int) (size * sizeFactor); |
| 85 | + int segmentCount = (capacity + segmentLength - 1) / segmentLength - (ARITY - 1); |
| 86 | + int arrayLength = (segmentCount + ARITY - 1) * segmentLength; |
| 87 | + segmentCount = (arrayLength + segmentLength - 1) / segmentLength; |
| 88 | + segmentCount = segmentCount <= ARITY - 1 ? 1 : segmentCount - (ARITY - 1); |
| 89 | + XorBinaryFuse32 filter = new XorBinaryFuse32(segmentCount, segmentLength); |
| 90 | + filter.addAll(keys); |
| 91 | + return filter; |
| 92 | + } |
| 93 | + |
| 94 | + private void addAll(long[] keys) { |
| 95 | + int size = keys.length; |
| 96 | + long[] reverseOrder = new long[size + 1]; |
| 97 | + int[] reverseH = new int[size]; |
| 98 | + int reverseOrderPos = 0; |
| 99 | + |
| 100 | + // the lowest 2 bits are the h index (0, 1, or 2) |
| 101 | + // so we only have 6 bits for counting; |
| 102 | + // but that's sufficient |
| 103 | + int[] t2count = new int[arrayLength]; |
| 104 | + long[] t2hash = new long[arrayLength]; |
| 105 | + int[] alone = new int[arrayLength]; |
| 106 | + int hashIndex = 0; |
| 107 | + // the array h0, h1, h2, h0, h1, h2 |
| 108 | + int[] h012 = new int[5]; |
| 109 | + int blockBits = 1; |
| 110 | + while ((1 << blockBits) < segmentCount) { |
| 111 | + blockBits++; |
| 112 | + } |
| 113 | + int block = 1 << blockBits; |
| 114 | + mainloop: |
| 115 | + while (true) { |
| 116 | + reverseOrder[size] = 1; |
| 117 | + int[] startPos = new int[block]; |
| 118 | + for (int i = 0; i < 1 << blockBits; i++) { |
| 119 | + startPos[i] = (int) ((long) i * size / block); |
| 120 | + } |
| 121 | + // counting sort |
| 122 | + |
| 123 | + for (long key : keys) { |
| 124 | + long hash = Hash.hash64(key, seed); |
| 125 | + int segmentIndex = (int) (hash >>> (64 - blockBits)); |
| 126 | + // We only overwrite when the hash was zero. Zero hash values |
| 127 | + // may be misplaced (unlikely). |
| 128 | + while (reverseOrder[startPos[segmentIndex]] != 0) { |
| 129 | + segmentIndex++; |
| 130 | + segmentIndex &= (1 << blockBits) - 1; |
| 131 | + } |
| 132 | + reverseOrder[startPos[segmentIndex]] = hash; |
| 133 | + startPos[segmentIndex]++; |
| 134 | + } |
| 135 | + int countMask = 0; |
| 136 | + for (int i = 0; i < size; i++) { |
| 137 | + long hash = reverseOrder[i]; |
| 138 | + for (int hi = 0; hi < 3; hi++) { |
| 139 | + int index = getHashFromHash(hash, hi); |
| 140 | + t2count[index] += 4; |
| 141 | + t2count[index] ^= hi; |
| 142 | + t2hash[index] ^= hash; |
| 143 | + countMask |= t2count[index]; |
| 144 | + } |
| 145 | + } |
| 146 | + startPos = null; |
| 147 | + if (countMask < 0) { |
| 148 | + // we have a possible counter overflow |
| 149 | + continue mainloop; |
| 150 | + } |
| 151 | + |
| 152 | + reverseOrderPos = 0; |
| 153 | + int alonePos = 0; |
| 154 | + for (int i = 0; i < arrayLength; i++) { |
| 155 | + alone[alonePos] = i; |
| 156 | + int inc = (t2count[i] >> 2) == 1 ? 1 : 0; |
| 157 | + alonePos += inc; |
| 158 | + } |
| 159 | + |
| 160 | + while (alonePos > 0) { |
| 161 | + alonePos--; |
| 162 | + int index = alone[alonePos]; |
| 163 | + if ((t2count[index] >> 2) == 1) { |
| 164 | + // It is still there! |
| 165 | + long hash = t2hash[index]; |
| 166 | + int found = t2count[index] & 3; |
| 167 | + |
| 168 | + reverseH[reverseOrderPos] = found; |
| 169 | + reverseOrder[reverseOrderPos] = hash; |
| 170 | + |
| 171 | + h012[0] = getHashFromHash(hash, 0); |
| 172 | + h012[1] = getHashFromHash(hash, 1); |
| 173 | + h012[2] = getHashFromHash(hash, 2); |
| 174 | + |
| 175 | + int index3 = h012[mod3(found + 1)]; |
| 176 | + alone[alonePos] = index3; |
| 177 | + alonePos += ((t2count[index3] >> 2) == 2 ? 1 : 0); |
| 178 | + t2count[index3] -= 4; |
| 179 | + t2count[index3] ^= mod3(found + 1); |
| 180 | + t2hash[index3] ^= hash; |
| 181 | + |
| 182 | + index3 = h012[mod3(found + 2)]; |
| 183 | + alone[alonePos] = index3; |
| 184 | + alonePos += ((t2count[index3] >> 2) == 2 ? 1 : 0); |
| 185 | + t2count[index3] -= 4; |
| 186 | + t2count[index3] ^= mod3(found + 2); |
| 187 | + t2hash[index3] ^= hash; |
| 188 | + |
| 189 | + reverseOrderPos++; |
| 190 | + } |
| 191 | + } |
| 192 | + |
| 193 | + if (reverseOrderPos == size) { |
| 194 | + break; |
| 195 | + } |
| 196 | + hashIndex++; |
| 197 | + Arrays.fill(t2count, 0); |
| 198 | + Arrays.fill(t2hash, 0); |
| 199 | + Arrays.fill(reverseOrder, 0); |
| 200 | + |
| 201 | + if (hashIndex > 100) { |
| 202 | + // if construction doesn't succeed eventually, |
| 203 | + // then there is likely a problem with the hash function |
| 204 | + // let us not crash the system: |
| 205 | + for (int i = 0; i < fingerprints.length; i++) { |
| 206 | + fingerprints[i] = (int) 0xFFFFFFFF; |
| 207 | + } |
| 208 | + return; |
| 209 | + } |
| 210 | + // use a new random numbers |
| 211 | + seed = Hash.randomSeed(); |
| 212 | + } |
| 213 | + alone = null; |
| 214 | + t2count = null; |
| 215 | + t2hash = null; |
| 216 | + |
| 217 | + for (int i = reverseOrderPos - 1; i >= 0; i--) { |
| 218 | + long hash = reverseOrder[i]; |
| 219 | + int found = reverseH[i]; |
| 220 | + int xor2 = fingerprint(hash); |
| 221 | + h012[0] = getHashFromHash(hash, 0); |
| 222 | + h012[1] = getHashFromHash(hash, 1); |
| 223 | + h012[2] = getHashFromHash(hash, 2); |
| 224 | + h012[3] = h012[0]; |
| 225 | + h012[4] = h012[1]; |
| 226 | + fingerprints[h012[found]] = (xor2 ^ fingerprints[h012[found + 1]] ^ fingerprints[h012[found + 2]]); |
| 227 | + } |
| 228 | + } |
| 229 | + |
| 230 | + @Override |
| 231 | + public boolean mayContain(long key) { |
| 232 | + long hash = Hash.hash64(key, seed); |
| 233 | + int f = fingerprint(hash); |
| 234 | + int h0 = Hash.reduce((int) (hash >>> 32), segmentCountLength); |
| 235 | + int h1 = h0 + segmentLength; |
| 236 | + int h2 = h1 + segmentLength; |
| 237 | + long hh = hash; |
| 238 | + h1 ^= (int) ((hh >> 18) & segmentLengthMask); |
| 239 | + h2 ^= (int) ((hh) & segmentLengthMask); |
| 240 | + f ^= fingerprints[h0] ^ fingerprints[h1] ^ fingerprints[h2]; |
| 241 | + return (f & 0xff) == 0; |
| 242 | + } |
| 243 | + |
| 244 | + @Override |
| 245 | + public String toString() { |
| 246 | + return "segmentLength " + segmentLength + " segmentCount " + segmentCount; |
| 247 | + } |
| 248 | + |
| 249 | + int getHashFromHash(long hash, int index) { |
| 250 | + long h = Hash.reduce((int) (hash >>> 32), segmentCountLength); |
| 251 | + // long h = Hash.multiplyHighUnsigned(hash, segmentCountLength); |
| 252 | + h += index * segmentLength; |
| 253 | + // keep the lower 36 bits |
| 254 | + long hh = hash & ((1L << 36) - 1); |
| 255 | + // index 0: right shift by 36; index 1: right shift by 18; index 2: no shift |
| 256 | + h ^= (int) ((hh >>> (36 - 18 * index)) & segmentLengthMask); |
| 257 | + return (int) h; |
| 258 | + } |
| 259 | + |
| 260 | + private int fingerprint(long hash) { |
| 261 | + return (int) hash; |
| 262 | + } |
| 263 | + |
| 264 | +} |
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