fastfilter: Binary fuse & xor filters for Zig

Binary fuse filters & xor filters are probabilistic data structures which allow for quickly checking whether an element is part of a set.

Both are faster and more concise than Bloom filters, and smaller than Cuckoo filters. Binary fuse filters are a bleeding-edge development and are competitive with Facebook's ribbon filters:

• Thomas Mueller Graf, Daniel Lemire, Binary Fuse Filters: Fast and Smaller Than Xor Filters (not yet published)
• Thomas Mueller Graf, Daniel Lemire, Xor Filters: Faster and Smaller Than Bloom and Cuckoo Filters, Journal of Experimental Algorithmics 25 (1), 2020. DOI: 10.1145/3376122

Benefits of Zig implementation

This is a Zig implementation, which provides many practical benefits:

1. Iterator-based: you can populate xor or binary fuse filters using an iterator, without keeping your entire key set in-memory and without it being a contiguous array of keys. This can reduce memory usage when populating filters substantially.
2. Distinct allocators: you can provide separate Zig std.mem.Allocator implementations for the filter itself and population, enabling interesting opportunities like mmap-backed population of filters with low physical memory usage.
3. Generic implementation: use Xor(u8), Xor(u16), BinaryFuse(u8), BinaryFuse(u16), or experiment with more exotic variants like Xor(u4) thanks to Zig's bit-width integers and generic type system.

Zig's safety-checking and checked overflows has also enabled us to improve the upstream C/Go implementations where overflow and undefined behavior went unnoticed.[1]

Usage

Decide if xor or binary fuse filters fit your use case better: should I use binary fuse filters or xor filters?

Get your keys into u64 values. If you have strings, structs, etc. then use something like Zig's std.hash_map.getAutoHashFn to convert your keys to u64 first. ("It is not important to have a good hash function, but collisions should be unlikely (~1/2^64).")

Create a build.zig.zon file in your project (replace $LATEST_COMMIT with the latest commit hash):

.{
    .name = "mypkg",
    .version = "0.1.0",
    .dependencies = .{
        .fastfilter = .{
            .url = "https://github.com/hexops/fastfilter/archive/$LATEST_COMMIT.tar.gz",
        },
    },
}

Run zig build in your project, and the compiler instruct you to add a .hash = "..." field next to .url.

Then use the dependency in your build.zig:

pub fn build(b: *std.Build) void {
    ...
    exe.addModule("fastfilter", b.dependency("fastfilter", .{
        .target = target,
        .optimize = optimize,
    }).module("fastfilter"));
}

In your main.zig, make use of the library:

const std = @import("std");
const testing = std.testing;
const fastfilter = @import("fastfilter");

test "mytest" {
    const allocator = std.heap.page_allocator;

    // Initialize the binary fuse filter with room for 1 million keys.
    const size = 1_000_000;
    var filter = try fastfilter.BinaryFuse8.init(allocator, size);
    defer filter.deinit(allocator);

    // Generate some consecutive keys.
    var keys = try allocator.alloc(u64, size);
    defer allocator.free(keys);
    for (keys, 0..) |key, i| {
        _ = key;
        keys[i] = i;
    }

    // Populate the filter with our keys. You can't update a xor / binary fuse filter after the
    // fact, instead you should build a new one.
    try filter.populate(allocator, keys[0..]);

    // Now we can quickly test for containment. So fast!
    try testing.expect(filter.contain(1) == true);
}

(you can just add this project as a Git submodule in yours for now, as Zig's official package manager is still under way.)

Binary fuse filters automatically deduplicate any keys during population. If you are using a different filter type (you probably shouldn't be!) then keys must be unique or else filter population will fail. You can use the fastfilter.AutoUnique(u64)(keys) helper to deduplicate (in typically O(N) time complexity), see the tests in src/unique.zig for usage examples.

Serialization

To serialize the filters, you only need to encode these struct fields:

pub fn BinaryFuse(comptime T: type) type {
    return struct {
        ...
        seed: u64,
        segment_length: u32,
        segment_length_mask: u32,
        segment_count: u32,
        segment_count_length: u32,
        fingerprints: []T,
        ...

T will be the chosen fingerprint size, e.g. u8 for BinaryFuse8 or Xor8.

Look at std.io.Writer and std.io.BitWriter for ideas on actual serialization.

Similarly, for xor filters you only need these struct fields:

pub fn Xor(comptime T: type) type {
    return struct {
        seed: u64,
        blockLength: u64,
        fingerprints: []T,
        ...

Should I use binary fuse filters or xor filters?

If you're not sure, start with BinaryFuse8 filters. They're fast, and have a false-positive probability rate of 1/256 (or 0.4%).

There are many tradeoffs, primarily between:

• Memory usage
• Containment check time
• Population / creation time & memory usage

See the benchmarks section for a comparison of the tradeoffs between binary fuse filters and xor filters, as well as how larger bit sizes (e.g. BinaryFuse(u16)) consume more memory in exchange for a lower false-positive probability rate.

Note that fuse filters are not to be confused with binary fuse filters, the former have issues with construction, often failing unless you have a large number of unique keys. Binary fuse filters do not suffer from this and are generally better than traditional ones in several ways. For this reason, we consider traditional fuse filters deprecated.

Note about extremely large datasets

This implementation supports key iterators, so you do not need to have all of your keys in-memory, see BinaryFuse8.populateIter and Xor8.populateIter.

If you intend to use a xor filter with datasets of 100m+ keys, there is a possible faster implementation for construction found in the C implementation xor8_buffered_populate which is not implemented here.

Changelog

The API is generally finalized, but we may make some adjustments as Zig changes or we learn of more idiomatic ways to express things. We will release v1.0 once Zig v1.0 is released.

v0.11.0

• fastfilter is now available via the Zig package manager.
• Updated to the latest version of Zig nightly 0.12.0-dev.706+62a0fbdae

v0.10.3

• Updated to the latest version of Zig 0.12.0-dev.706+62a0fbdae (build.zig .path -> .source change.)

v0.10.2

• Fixed a few correctness / integer overflow/underflow possibilities where we were inconsistent with the Go/C implementations of binary fuse filters.
• Added debug-mode checks for iterator correctness (wraparound behavior.)

v0.10.1

• Updated to the latest version of Zig 0.12.0-dev.706+62a0fbdae

v0.10.0

• All types are now unmanaged (allocator must be passed via parameters)
• Renamed util.sliceIterator to fastfilter.SliceIterator
• SliceIterator is now unmanaged / does not store an allocator.
• SliceIterator now stores []const T instead of []T internally.
• BinaryFuseFilter.max_iterations is now a constant.
• Added fastfilter.MeasuredAllocator for measuring allocations.
• Improved usage example.
• Properly free xorfilter/fusefilter fingerprints.
• Updated benchmark to latest Zig version.

v0.9.3

• Fixed potential integer overflow.

v0.9.2

• Handle duplicated keys automatically
• Added a std.build.Pkg definition
• Fixed an unlikely bug
• Updated usage instructions
• Updated to Zig v0.10.0-dev.1736

v0.9.1

• Updated to Zig v0.10.0-dev.36

v0.9.0

• Renamed repository github.com/hexops/xorfilter -> github.com/hexops/fastfilter to account for binary fuse filters.
• Implemented bleeding-edge (paper not yet published) "Binary Fuse Filters: Fast and Smaller Than Xor Filters" algorithm by Thomas Mueller Graf, Daniel Lemire
• BinaryFuse filters are now recommended by default, are generally better than Xor and Fuse filters.
• Deprecated traditional Fuse filters (BinaryFuse are much better.)
• Added much improved benchmarking suite with more details on memory consumption during filter population, etc.

v0.8.0

initial release with support for Xor and traditional Fuse filters of varying bit sizes, key iterators, serialization, and a slice de-duplication helper.

Benchmarks

Benchmarks were ran on both a 2019 Macbook Pro and Windows 10 desktop machine using e.g.:

zig run -O ReleaseFast src/benchmark.zig -- --xor 8 --num-keys 1000000

Benchmarks: 2019 Macbook Pro, Intel i9 (1M - 100M keys)

• CPU: 2.3 GHz 8-Core Intel Core i9
• Memory: 16 GB 2667 MHz DDR4
• Zig version: 0.12.0-dev.706+62a0fbdae

Algorithm	# of keys	populate	contains(k)	false+ prob.	bits per entry	peak populate	filter total
binaryfuse8	1000000	37.5ms	24.0ns	0.00391115	9.04	22 MiB	1 MiB
binaryfuse16	1000000	45.5ms	24.0ns	0.00001524	18.09	24 MiB	2 MiB
binaryfuse32	1000000	56.0ms	24.0ns	0	36.18	28 MiB	4 MiB
xor2	1000000	108.0ms	25.0ns	0.2500479	9.84	52 MiB	1 MiB
xor4	1000000	99.0ms	25.0ns	0.06253865	9.84	52 MiB	1 MiB
xor8	1000000	103.4ms	25.0ns	0.0039055	9.84	52 MiB	1 MiB
xor16	1000000	104.7ms	26.0ns	0.00001509	19.68	52 MiB	2 MiB
xor32	1000000	102.2ms	25.0ns	0	39.36	52 MiB	4 MiB
binaryfuse8	10000000	621.2ms	36.0ns	0.0039169	9.02	225 MiB	10 MiB
binaryfuse16	10000000	666.6ms	102.0ns	0.0000147	18.04	245 MiB	21 MiB
binaryfuse32	10000000	769.0ms	135.0ns	0	36.07	286 MiB	43 MiB
xor2	10000000	1.9s	43.0ns	0.2500703	9.84	527 MiB	11 MiB
xor4	10000000	2.0s	41.0ns	0.0626137	9.84	527 MiB	11 MiB
xor8	10000000	1.9s	42.0ns	0.0039369	9.84	527 MiB	11 MiB
xor16	10000000	2.2s	106.0ns	0.0000173	19.68	527 MiB	23 MiB
xor32	10000000	2.2s	140.0ns	0	39.36	527 MiB	46 MiB
binaryfuse8	100000000	7.4s	145.0ns	0.003989	9.01	2 GiB	107 MiB
binaryfuse16	100000000	8.4s	169.0ns	0.000016	18.01	2 GiB	214 MiB
binaryfuse32	100000000	10.2s	173.0ns	0	36.03	2 GiB	429 MiB
xor2	100000000	28.5s	144.0ns	0.249843	9.84	5 GiB	117 MiB
xor4	100000000	27.4s	154.0ns	0.062338	9.84	5 GiB	117 MiB
xor8	100000000	28.0s	153.0ns	0.004016	9.84	5 GiB	117 MiB
xor16	100000000	29.5s	161.0ns	0.000012	19.68	5 GiB	234 MiB
xor32	100000000	29.4s	157.0ns	0	39.36	5 GiB	469 MiB

Legend:

• contains(k): The time taken to check if a key is in the filter
• false+ prob.: False positive probability, the probability that a containment check will erroneously return true for a key that has not actually been added to the filter.
• bits per entry: The amount of memory in bits the filter uses to store a single entry.
• peak populate: Amount of memory consumed during filter population, excluding keys themselves (8 bytes * num_keys.)
• filter total: Amount of memory consumed for filter itself in total (bits per entry * entries.)

Benchmarks: Windows 10, AMD Ryzen 9 3900X (1M - 100M keys)

• CPU: 3.79Ghz AMD Ryzen 9 3900X
• Memory: 32 GB 2133 MHz DDR4
• Zig version: 0.12.0-dev.706+62a0fbdae

Algorithm	# of keys	populate	contains(k)	false+ prob.	bits per entry	peak populate	filter total
binaryfuse8	1000000	44.6ms	24.0ns	0.00390796	9.04	22 MiB	1 MiB
binaryfuse16	1000000	48.9ms	25.0ns	0.00001553	18.09	24 MiB	2 MiB
binaryfuse32	1000000	49.9ms	25.0ns	0.00000001	36.18	28 MiB	4 MiB
xor2	1000000	77.3ms	25.0ns	0.25000163	9.84	52 MiB	1 MiB
xor4	1000000	80.0ms	25.0ns	0.06250427	9.84	52 MiB	1 MiB
xor8	1000000	76.0ms	25.0ns	0.00391662	9.84	52 MiB	1 MiB
xor16	1000000	83.7ms	26.0ns	0.00001536	19.68	52 MiB	2 MiB
xor32	1000000	79.1ms	27.0ns	0	39.36	52 MiB	4 MiB
fuse8	1000000	69.4ms	25.0ns	0.00390663	9.10	49 MiB	1 MiB
fuse16	1000000	71.5ms	27.0ns	0.00001516	18.20	49 MiB	2 MiB
fuse32	1000000	71.1ms	27.0ns	0	36.40	49 MiB	4 MiB
binaryfuse8	10000000	572.3ms	33.0ns	0.0038867	9.02	225 MiB	10 MiB
binaryfuse16	10000000	610.6ms	108.0ns	0.0000127	18.04	245 MiB	21 MiB
binaryfuse32	10000000	658.2ms	144.0ns	0	36.07	286 MiB	43 MiB
xor2	10000000	1.2s	39.0ns	0.249876	9.84	527 MiB	11 MiB
xor4	10000000	1.2s	39.0ns	0.0625026	9.84	527 MiB	11 MiB
xor8	10000000	1.2s	41.0ns	0.0038881	9.84	527 MiB	11 MiB
xor16	10000000	1.3s	117.0ns	0.0000134	19.68	527 MiB	23 MiB
xor32	10000000	1.3s	147.0ns	0	39.36	527 MiB	46 MiB
fuse8	10000000	1.1s	36.0ns	0.0039089	9.10	499 MiB	10 MiB
fuse16	10000000	1.1s	112.0ns	0.0000172	18.20	499 MiB	21 MiB
fuse32	10000000	1.1s	145.0ns	0	36.40	499 MiB	43 MiB
binaryfuse8	100000000	6.9s	167.0ns	0.00381	9.01	2 GiB	107 MiB
binaryfuse16	100000000	7.2s	171.0ns	0.000009	18.01	2 GiB	214 MiB
binaryfuse32	100000000	8.5s	174.0ns	0	36.03	2 GiB	429 MiB
xor2	100000000	16.8s	166.0ns	0.249868	9.84	5 GiB	117 MiB
xor4	100000000	18.9s	183.0ns	0.062417	9.84	5 GiB	117 MiB
xor8	100000000	19.1s	168.0ns	0.003873	9.84	5 GiB	117 MiB
xor16	100000000	16.9s	171.0ns	0.000021	19.68	5 GiB	234 MiB
xor32	100000000	19.4s	189.0ns	0	39.36	5 GiB	469 MiB
fuse8	100000000	19.6s	167.0ns	0.003797	9.10	4 GiB	108 MiB
fuse16	100000000	20.8s	171.0ns	0.000015	18.20	4 GiB	216 MiB
fuse32	100000000	21.5s	176.0ns	0	36.40	4 GiB	433 MiB

Legend:

• contains(k): The time taken to check if a key is in the filter
• false+ prob.: False positive probability, the probability that a containment check will erroneously return true for a key that has not actually been added to the filter.
• bits per entry: The amount of memory in bits the filter uses to store a single entry.
• peak populate: Amount of memory consumed during filter population, excluding keys themselves (8 bytes * num_keys.)
• filter total: Amount of memory consumed for filter itself in total (bits per entry * entries.)

Related readings

• Blog post by Daniel Lemire: Xor Filters: Faster and Smaller Than Bloom Filters
• Fuse Filters (arxiv paper), as described by @jbapple (note these are not to be confused with binary fuse filters.)

Special thanks

• Thomas Mueller Graf and Daniel Lemire - for their excellent research into xor filters, xor+ filters, their C implementation, and more.
• Martin Dietzfelbinger and Stefan Walzer - for their excellent research into fuse filters.
• Jim Apple - for their C implementation[1] of fuse filters
• Andrew Gutekanst - for providing substantial help in debugging several issues in the Zig implementation.

If it was not for the above people, I (@slimsag) would not have been able to write this implementation and learn from the excellent C implementation. Please credit the above people if you use this library.