/**
* 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 com.facebook.infrastructure.utils;
/**
* The following calculations are taken from:
* http://www.cs.wisc.edu/~cao/papers/summary-cache/node8.html
* "Bloom Filters - the math"
*
* This class's static methods are meant to facilitate the use of the Bloom
* Filter class by helping to choose correct values of 'buckets per element' and
* 'number of hash functions, k'.
* Author : Avinash Lakshman ( alakshman@facebook.com) & Prashant Malik ( pmalik@facebook.com )
*/
public class BloomCalculations {
private static final int maxBuckets = 15;
private static final int minBuckets = 2;
private static final int minK = 1;
private static final int maxK = 8;
private static final int[] optKPerBuckets =
new int[]{1, // dummy K for 0 buckets per element
1, // dummy K for 1 buckets per element
1, 2, 3, 3, 4, 5, 5, 6, 7, 8, 8, 8, 8, 8};
/**
* In the following table, the row 'i' shows false positive rates if i buckets
* per element are used. Column 'j' shows false positive rates if j hash
* functions are used. The first row is 'i=0', the first column is 'j=0'.
* Each cell (i,j) the false positive rate determined by using i buckets per
* element and j hash functions.
*/
private static final double[][] probs = new double[][]{
{1.0}, // dummy row representing 0 buckets per element
{1.0, 1.0}, // dummy row representing 1 buckets per element
{1.0, 0.393, 0.400},
{1.0, 0.283, 0.237, 0.253},
{1.0, 0.221, 0.155, 0.147, 0.160},
{1.0, 0.181, 0.109, 0.092, 0.092, 0.101}, // 5
{1.0, 0.154, 0.0804, 0.0609, 0.0561, 0.0578, 0.0638},
{1.0, 0.133, 0.0618, 0.0423, 0.0359, 0.0347, 0.0364},
{1.0, 0.118, 0.0489, 0.0306, 0.024, 0.0217, 0.0216, 0.0229},
{1.0, 0.105, 0.0397, 0.0228, 0.0166, 0.0141, 0.0133, 0.0135, 0.0145}, // 9
{1.0, 0.0952, 0.0329, 0.0174, 0.0118, 0.00943, 0.00844, 0.00819, 0.00846},
{1.0, 0.0869, 0.0276, 0.0136, 0.00864, 0.0065, 0.00552, 0.00513, 0.00509},
{1.0, 0.08, 0.0236, 0.0108, 0.00646, 0.00459, 0.00371, 0.00329, 0.00314},
{1.0, 0.074, 0.0203, 0.00875, 0.00492, 0.00332, 0.00255, 0.00217, 0.00199},
{1.0, 0.0689, 0.0177, 0.00718, 0.00381, 0.00244, 0.00179, 0.00146, 0.00129},
{1.0, 0.0645, 0.0156, 0.00596, 0.003, 0.00183, 0.00128, 0.001, 0.000852} // 15
}; // the first column is a dummy column representing K=0.
/**
* Given the number of buckets that can be used per element, return the optimal
* number of hash functions in order to minimize the false positive rate.
*
* @param bucketsPerElement
* @return The number of hash functions that minimize the false positive rate.
*/
public static int computeBestK(int bucketsPerElement){
assert bucketsPerElement >= 0;
if(bucketsPerElement >= optKPerBuckets.length)
return optKPerBuckets[optKPerBuckets.length-1];
return optKPerBuckets[bucketsPerElement];
}
/**
* A wrapper class that holds two key parameters for a Bloom Filter: the
* number of hash functions used, and the number of buckets per element used.
*/
public static final class BloomSpecification {
final int K; // number of hash functions.
final int bucketsPerElement;
public BloomSpecification(int k, int bucketsPerElement) {
K = k;
this.bucketsPerElement = bucketsPerElement;
}
}
/**
* Given a maximum tolerable false positive probability, compute a Bloom
* specification which will give less than the specified false positive rate,
* but minimize the number of buckets per element and the number of hash
* functions used. Because bandwidth (and therefore total bitvector size)
* is considered more expensive than computing power, preference is given
* to minimizing buckets per element rather than number of hash funtions.
*
* @param maxFalsePosProb The maximum tolerable false positive rate.
* @return A Bloom Specification which would result in a false positive rate
* less than specified by the function call.
*/
public static BloomSpecification computeBucketsAndK(double maxFalsePosProb){
// Handle the trivial cases
if(maxFalsePosProb >= probs[minBuckets][minK]) {
return new BloomSpecification(2, optKPerBuckets[2]);
}
if(maxFalsePosProb < probs[maxBuckets][maxK]) {
return new BloomSpecification(maxK, maxBuckets);
}
// First find the minimal required number of buckets:
int bucketsPerElement = 2;
int K = optKPerBuckets[2];
while(probs[bucketsPerElement][K] > maxFalsePosProb){
bucketsPerElement++;
K = optKPerBuckets[bucketsPerElement];
}
// Now that the number of buckets is sufficient, see if we can relax K
// without losing too much precision.
while(probs[bucketsPerElement][K - 1] <= maxFalsePosProb){
K--;
}
return new BloomSpecification(K, bucketsPerElement);
}
}