Hazy

A dependency-free Python toolkit for fast, mergeable probabilistic data structures, implemented in Rust.

Why Hazy?

When working with massive datasets, exact answers become expensive. Counting unique visitors across billions of events? A precise solution needs gigabytes of memory. Checking if a URL exists in a blocklist of millions? Exact lookups are slow.

Probabilistic data structures solve this by trading perfect accuracy for dramatic improvements in speed and memory. A HyperLogLog can count 1 billion unique items using just 16KB of memory (with ~1% error). A Bloom filter can check membership in a set of 10 million items using 12MB instead of hundreds of megabytes.

Hazy provides compact implementations with one consistent Python API, batch operations, deterministic hashing, and a Rust core. Use it when you need to:

Count unique items in streams too large to fit in memory
Check set membership without storing every element
Estimate frequencies of items in high-throughput streams
Find similar documents without comparing every pair
Track top-K items in real-time leaderboards

Features

Bloom Filter: Space-efficient set membership testing
Counting Bloom Filter: Bloom filter with deletion support
Scalable Bloom Filter: Auto-scaling Bloom filter for unknown cardinality
Cuckoo Filter: Fixed-capacity membership filter with deletion
HyperLogLog: Cardinality estimation with ~2% error using minimal memory
Count-Min Sketch: Frequency estimation for streaming data
MinHash: Set similarity estimation using Jaccard index
Top-K (Space-Saving): Find the most frequent items in a stream

Engineering features

Rust backend with GIL-free batch operations
xxHash3 for fast, high-quality hashing
Pre-hashed input for interoperable high-throughput pipelines
Goal-oriented planning from accuracy and memory requirements
Byte and JSON serialization for storage and transport
File I/O with save()/load() for persistence

Installation

pip install hazy

Building from source

Requires a current stable Rust toolchain and Python 3.9+:

# Install Rust if needed
curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh

# Build and install
pip install maturin
maturin develop --release

Quick Start

from hazy import BloomFilter, HyperLogLog, CountMinSketch

# Bloom Filter - set membership
bf = BloomFilter(expected_items=10000, false_positive_rate=0.01)
bf.add("hello")
print("hello" in bf)  # True
print("world" in bf)  # False (probably)

# HyperLogLog - count unique items
hll = HyperLogLog(precision=14)
hll.update_many(f"user_{i}" for i in range(1_000_000))
print(f"Unique users: {hll.cardinality():.0f}")  # ~1,000,000

# Count-Min Sketch - frequency estimation
cms = CountMinSketch(width=10000, depth=5)
cms.add("apple")
cms.add("apple")
cms.add("banana")
print(f"Apple count: {cms['apple']}")  # >= 2

Plan from a goal

You do not need to start with the sketch mathematics:

from hazy import plan

recommendation = plan(
    "count_unique",
    expected_items=100_000_000,
    error_rate=0.01,
    max_memory="16 MiB",
)
counter = recommendation.create()
print(recommendation.explain())

Direct parameter selection

Use the estimation helpers to choose optimal parameters:

from hazy import estimate_bloom_params, estimate_hll_params

# Bloom filter for 1M items at 1% FPR
params = estimate_bloom_params(expected_items=1_000_000, false_positive_rate=0.01)
print(f"Memory needed: {params.memory_mb:.1f} MB")
print(f"Hash functions: {params.num_hashes}")

# HyperLogLog for 1% error
params = estimate_hll_params(expected_cardinality=1_000_000, error_rate=0.01)
print(f"Precision: {params.precision}")
print(f"Memory: {params.memory_bytes} bytes")

API Overview

All structures share a consistent API:

# Add items
structure.add(item)           # Add single item
structure.update(items)       # Add multiple items
structure.update_many(items)  # Explicit optimized batch path

# Query
structure.query(item)         # Query (meaning varies by structure)
structure.query_many(items)   # Batch query where applicable
item in structure             # Membership test (where applicable)

# Combine
structure.merge(other)        # Combine two structures
result = structure | other    # Union operator (where applicable)

# Serialize
data = structure.to_bytes()   # Binary serialization
structure = Type.from_bytes(data)

json_str = structure.to_json()
structure = Type.from_json(json_str)

# Introspection
len(structure)                # Approximate count
structure.size_in_bytes       # Memory footprint

# File I/O
structure.save("filter.hazy")
structure = Type.load("filter.hazy")

Data Structures

BloomFilter

from hazy import BloomFilter

bf = BloomFilter(expected_items=10000)
bf.add("hello")
assert "hello" in bf
assert bf.false_positive_rate < 0.02

CountingBloomFilter

from hazy import CountingBloomFilter

cbf = CountingBloomFilter(expected_items=10000)
cbf.add("hello")
cbf.add("hello")
cbf.remove("hello")  # Still contains "hello"
cbf.remove("hello")  # Now removed

Only remove items known to have been inserted. Like other probabilistic filters, a positive membership check can be a false positive; removing an item that was never added can decrement counters shared with real items.

ScalableBloomFilter

from hazy import ScalableBloomFilter

# Automatically grows as you add items
sbf = ScalableBloomFilter(initial_capacity=1000)
for i in range(1_000_000):  # Way more than initial capacity
    sbf.add(f"item_{i}")

print(f"Slices: {sbf.num_slices}")  # Multiple slices created
print("item_500" in sbf)  # True

CuckooFilter

from hazy import CuckooFilter

cf = CuckooFilter(capacity=10000)
cf.add("hello")
cf.remove("hello")
assert "hello" not in cf

For the same reason, only remove keys known to have been inserted: an absent key can share a fingerprint with a stored key.

HyperLogLog

from hazy import HyperLogLog

hll = HyperLogLog(precision=14)  # 16KB memory, ~0.8% error
hll.update([f"item_{i}" for i in range(1000000)])
print(f"Cardinality: {hll.cardinality():.0f}")

CountMinSketch

from hazy import CountMinSketch

cms = CountMinSketch(width=10000, depth=5)
# Or: cms = CountMinSketch(error_rate=0.001, confidence=0.99)
cms.add("apple", count=10)
print(f"Apple frequency: {cms['apple']}")

MinHash

from hazy import MinHash

mh1 = MinHash(num_hashes=128)
mh1.update(["a", "b", "c", "d"])

mh2 = MinHash(num_hashes=128)
mh2.update(["c", "d", "e", "f"])

print(f"Jaccard similarity: {mh1.jaccard(mh2):.2f}")  # ~0.33

TopK

from hazy import TopK

tk = TopK(k=10)
for word in ["apple"] * 100 + ["banana"] * 50 + ["cherry"] * 25:
    tk.add(word)

for item, count in tk.top(3):
    print(f"{item}: {count}")

Visualization

Install with visualization support:

pip install hazy[viz]

Plotting

from hazy import BloomFilter, HyperLogLog, CountMinSketch, TopK
from hazy.viz import plot_bloom, plot_hll, plot_cms, plot_topk, show

# Bloom filter bit array heatmap
bf = BloomFilter(expected_items=10000)
bf.update([f"item_{i}" for i in range(5000)])
plot_bloom(bf)

# HyperLogLog register histogram
hll = HyperLogLog(precision=12)
hll.update([f"user_{i}" for i in range(100000)])
plot_hll(hll)

# Count-Min Sketch heatmap
cms = CountMinSketch(width=100, depth=5)
for word in ["apple"] * 50 + ["banana"] * 30 + ["cherry"] * 10:
    cms.add(word)
plot_cms(cms)

# Top-K bar chart
tk = TopK(k=10)
tk.update(["apple"] * 100 + ["banana"] * 50 + ["cherry"] * 25)
plot_topk(tk)

show()  # Display all figures

Jupyter Notebooks

Enable rich HTML display in Jupyter:

import hazy
hazy.enable_notebook_display()

bf = hazy.BloomFilter(expected_items=1000)
bf.add("hello")
bf  # Displays rich HTML with stats and progress bar

Development

# Install dev dependencies
pip install -e ".[dev]"

# Run tests
pytest

# Build release wheel
maturin build --release

License

MIT

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Dec 7, 2025 2 files

hazy 0.3.0

Hazy

Why Hazy?

Features

Engineering features

Installation

Building from source

Quick Start

Plan from a goal

Direct parameter selection

API Overview

Data Structures

BloomFilter

CountingBloomFilter

ScalableBloomFilter

CuckooFilter

HyperLogLog

CountMinSketch

MinHash

TopK

Visualization

Plotting

Jupyter Notebooks

Development

License

Project links

Key dates

1 maintainer

Credits

GitHub Statistics

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Provides Extra

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