A Bloom filter is a probabilistic data structure which provides an efficient way to verify that an entry is certainly not in a set. This makes it especially ideal when trying to search for items on expensive-to-access resources (such as over a network or disk): If I have a large on-disk database and I want to know if the key foo exists in it, I can query the Bloom filter first, which will tell me with a certainty whether it potentially exists (and then the disk lookup can continue) or whether it does not exist, and in this case I can forego the expensive disk lookup and simply send a negative reply up the stack.
While it’s possible to use other data structures (such as a hash table) to perform this, Bloom filters are also especially useful in that they occupy very little space per element, typically counted in the number of bits (not bytes!). There will exist a percentage of false positives (which is controllable), but for an initial test of whether a key exists in a set, they provide excellent speed and most importantly excellent space efficiency.
Bloom filters are used in a wide variety of applications such as ad serving – making sure a user doesn’t see an ad too often; likewise in content recommendation systems – ensuring recommendations don’t appear too often, in databases – quickly checking if an entry exists in a table before accessing it on disk, and so on.
How Bloom filters work
Most of the literature on Bloom filter uses highly symbolic and/or mathematical descriptions to describe it. If you’re mathematically challenged like yours truly, you might find my explanation more useful.
A Bloom filter is an array of many bits. When an element is ‘added’ to a bloom filter, the element is hashed. Then bit[hashval % nbits] is set to 1. This looks fairly similar to how buckets in a hash table are mapped. To check if an item is present or not, the hash is computed and the filter sees if the corresponding bit is set or not.
Of course, this is subject to collisions. If a collision occurs, the filter will return a false positive – indicating that the entry is indeed found (note that a bloom filter will never return a false negative, that is, claim that something does not exist when it fact it is present).
In order to reduce the risk of collisions, an entry may use more than one bit: the entry is hashed bits_per_element (bpe) times with a different seed for each iteration resulting in a different hash value, and for each hash value, the corresponding hash % nbits bit is set. To check if an entry exists, the candidate key is also hashed bpe times, and if any corresponding bit is unset, the it can be determined with certainty that the item does not exist.
The actual value of bpe is determined at the time the filter is created. Generally the more bits per element, the lower the likelihood of false positives.
In the example above, all three bits would need to be set in order for the filter to return a positive result.
Another value affecting the accuracy of a Bloom filter is its fill ratio, or how many bits in the filter are actually set. If a filter has a vast majority of bits set, the likelihood of any specific lookup returning false is decreased, and thus the possibility of the filter returning false positives is increased.
Scalable Bloom filters
Typically Bloom filters must be created with a foreknowledge of how many entries they will contain. The bpe number needs to be fixed, and likewise the width of the bit array is also fixed.
Unlike hash tables, Bloom filters cannot be “rebalanced” because there is no way to know which entries are part of the filter (the filter can only determine whether a given entry is not present, but does not actually store the entries which are present).
In order to allow Bloom filters to ‘scale’ and be able to accommodate more elements than they’ve been designed to, they may be stacked. Once a single Bloom filter reaches capacity, a new one is created atop it. Typically the new filter will have greater capacity than the previous one in order to reduce the likelihood of needing to stack yet another filter.
In a stackable (scalable) Bloom filter, checking for membership now involves inspecting each layer for presence. Adding new items now involves checking that it does not exist beforehand, and adding it to the current filter. Hashes still only need to be computed once however.
When creating a Bloom filter – even a scalable one, it’s important to have a good idea of how many items it is expected to contain. A filter whose initial layer can only contain a small number of elements will degrade performance significantly because it will take more layers to reach a larger capacity.
Using Bloom filters in Redis
Redis users have been asking for a bloom filter data type for years, and there exist plans to add it to Redis in the future; However, since Redis 4.0 supports extending redis with Modules – we decided at Redis Labs to go ahead and add this capability to Redis right now.
Redis Modules are written in high performance C, and are able to expose their own commands and data types, as well as define how those data types get persisted. This allowed us to simply create a very powerful Bloom filter module, and have it easily added to Redis.
Getting the module and using it is very straightforward:
Downloading and building
You should first download and compile the module:
$ git clone git://github.com/RedisLabsModules/rebloom $ cd rebloom $ make
You should now have a rebloom.so in the rebloom directory.
Loading Rebloom into Redis
Once you’ve built the filter module you, point your redis.conf or the redis command line to the module using loadmodule or –loadmodule respectively:
$ redis-server --loadmodule /path/to/rebloom.so
Trying It Out
You can play with it a bit using redis-cli:
127.0.0.1:6379> BF.ADD bloom mark 1) (integer) 1 127.0.0.1:6379> BF.ADD bloom redis 1) (integer) 1 127.0.0.1:6379> BF.EXISTS bloom mark (integer) 1 127.0.0.1:6379> BF.EXISTS bloom redis (integer) 1 127.0.0.1:6379> BF.EXISTS bloom nonexist (integer) 0 127.0.0.1:6379> BF.EXISTS bloom que? (integer) 0 127.0.0.1:6379> 127.0.0.1:6379> BF.MADD bloom elem1 elem2 elem3 1) (integer) 1 2) (integer) 1 3) (integer) 1 127.0.0.1:6379> BF.MEXISTS bloom elem1 elem2 elem3 1) (integer) 1 2) (integer) 1 3) (integer) 1
You can also create a custom Bloom filter. The BF.ADD command creates a new Bloom filter suitable for a small-ish number of items. This consumes less memory but may be less ideal for large filters:
127.0.0.1:6379> BF.RESERVE largebloom 0.0001 1000000 OK 127.0.0.1:6379> BF.ADD largebloom mark 1) (integer) 1
Benchmarks, Speed and Implementation
Rebloom uses a modified version of libloom, with some additional enhancements:
- I discovered that when testing for presence, libbloom would continue checking for each bit even when an unset bit was discovered. Making it so that it returned as soon as it found the first unset bit increased performance.
I decoupled the hash calculation API from the lookup API. This meant I only needed to compute the hash, and then feed it into the filter code.
- Here’s a summary of performance benchmarks. The table below shows a benchmark of setting a single Bloom filter with an initial capacity of 10,000, an error rate of 0.01, and a scaling factor of 2. Tests were done using a single client thread, and with pipelining to avoid network/scheduling interference as much as possible:
Once all was done, I benchmarked it and compared it to some other implementations. I wrote this filter initially because a previous filter implementation was too slow. Compared to a Lua implementation which yielded 30k/sec, redablooms was slower with 20k/sec.
Running the equivalent command with rebloom:
mnunberg@mbp15III ~/Source/rebloom $ redis-benchmark -e -r 100000000 -n 1000000 -c 20 bf.add test __rand_int__ ====== bf.add test __rand_int__ ====== 1000000 requests completed in 8.92 seconds 20 parallel clients 3 bytes payload keep alive: 1 99.99% <= 1 milliseconds 100.00% <= 2 milliseconds 100.00% <= 3 milliseconds 100.00% <= 3 milliseconds 112082.49 requests per second
With pipelining and perhaps modifying the thread count, it would have been possible to get even nicer numbers, but a fair benchmark is an apples-to-apples comparison.
I compared bloomd’s own benchmark to an equivalent rebloom commandset. Bloomd by default uses an initial capacity of 100k and an error ratio of 1/10k, or 0.0001. Its benchmark program simply sets 1,000,000 items and then reads them. It uses fire-and-forget semantics when setting items so network latency doesn’t become a factor when sending the commands:
mnunberg@mbp15III ~/Source/bloomd $ ./bench Thread started.Using filter: foobar1464749818 Connect: 0 msec Create: 1 msec Set: 4090 msec. Num: 999987 Check: 6130 msec. Num: 1000000
So we get 1M sets in 4 seconds, or 250K op/s, and 1M reads in 6 seconds, or 166K ops/sec.
The equivalent with rebloom:
mnunberg@mbp15III ~/Source/rebloom $ redis-cli del test; redis-cli bf.reserve test 0.0001 100000; redis-benchmark -e -r 1000000 -l -n 1000000 -P 100 -c 1 bf.add test __rand_int__ (integer) 1 OK ====== bf.add test __rand_int__ ====== 1000000 requests completed in 2.65 seconds 1 parallel clients 3 bytes payload keep alive: 1 100.00% <= 0 milliseconds 376931.75 requests per second
I let this loop for a while because unlike the bloomd benchmark which uses sequential keys, redis-bench uses random IDs. this means that there would be a greater chance for collision.
Rebloom performs at 370k/s, or about 50% faster than bloomd.
mnunberg@mbp15III ~/Source/rebloom $ redis-benchmark -e -r 1000000 -n 1000000 -l -P 100 -c 1 bf.exists test __rand_int__ ====== bf.exists test __rand_int__ ====== 1000000 requests completed in 2.65 seconds 1 parallel clients 3 bytes payload keep alive: 1 99.99% <= 1 milliseconds 100.00% <= 1 milliseconds 377073.91 requests per second
Which is about 150% faster than bloomd!
Debugging Bloom filters
Finally, I added a BF.DEBUG command, to see exactly how the filter is being utilized:
127.0.0.1:6379> BF.DEBUG test 1) "size:987949" 2) "bytes:239627 bits:1917011 hashes:14 capacity:100000 size:100000 ratio:0.0001" 3) "bytes:551388 bits:4411101 hashes:16 capacity:200000 size:200000 ratio:2.5e-05" 4) "bytes:1319180 bits:10553436 hashes:19 capacity:400000 size:400000 ratio:3.125e-06" 5) "bytes:3215438 bits:25723497 hashes:23 capacity:800000 size:287949 ratio:1.95313e-07"
This outputs the total number of elements as the first result, and then a list of details for each filter in the chain. As you can see, whenever a new filter is added, its capacity grows exponentially and the strictness for errors increases.
Note that this filter chain also uses a total of 5MB. This is still much more space efficient than alternative solutions, since we’re still at about 5 bytes per element, and the uppermost filter is only at about 12% utilization. Had the initial capacity been greater, more space would have been saved and lookups would have been quicker.
You can download rebloom yourself at https://github.com/RedisLabsModules/rebloom. If you’re using Redis Enterprise, it will be bundled with version 5.0.
Let me know if you think you can make it even faster, or file a github issue if you are having problems.