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Overview

The HyperLogLog algorithm [1] is a space efficient method to estimate the cardinality of extraordinarily large datasets. This module is written in C for Python >= 3.6 and Python 2.7.x. It implements a 64 bit version of HyperLogLog [2] using a Murmur64A hash.

Quick start

Install Python development libraries. This step will depend on your OS. On Ubuntu 24.0.4 LTS:

sudo apt install python-dev-is-python3

Install HLL:

pip install HLL

Example usage:

from HLL import HyperLogLog

hll = HyperLogLog(10) # use 2^10 registers
hll.add('some data')

estimate = hll.cardinality()
print(estimate)

2.3 Changelog

  • Fix bug causing cardinalities on the order of $2^{45}$ to be under-estimated.

2.2 Changelog

  • Remove support for Python 2.7.

2.1 Changelog

Deprecation notice: this is the last supported version for Python 2.7.x.

  • Fixed bug where HyperLogLogs of unequal sizes could be merged.
  • Fixed bug causing cardinality estimates to be off when repeatedly merging sparse HyperLogLogs loaded from a pickle dump.

2.0 Changelog

  • Algorithm has been updated to a 64 bit version [2]. This fixes the spike in relative error when switching from linear counting in the original HyperLogLog algorithm.
  • Hash function has been updated to the 64 bit Murmur64A function.
  • More efficiently store registers using a combination of sparse and dense representations.
  • Improved method for counting the number of leading zeroes.
  • Changed the return type of cardinality() from float to integer.
  • Changed the return logic of add(). This method no longer always indicates if a register was updated using its return value. This behavior is only preserved in dense representation. In sparse representation, add() always returns False.
  • HyperLogLog objects pickled in 1.x and 2.x are not compatible.
  • Added get_register()
  • Added hash()
  • Added _get_meta()
  • Deprecated murmur2_hash()
  • Deprecated registers()
  • Deprecated set_register()

Documentation

HyperLogLog objects

HyperLogLog objects implement a 64 bit HyperLogLog algorithm [2]. They can be used to estimate the cardinality of very large datasets. The estimation accuracy is proportional to the number of registers. Using more registers increases the accuracy and using less registers decreases the accuracy. The number of registers is set in powers of 2 using the parameter p and defaults to p=12 or $2^{12}$ registers.

>>> from hll import HyperLogLog
>>> hll = HyperLogLog() # Default to 2^12 registers
>>> hll.size()
4096
>>> hll = HyperLogLog(3) # Use 2^3 registers
>>> hll.size()
8
>>> for data in ['one', 'two', 'three', 'four',]:
...     hll.add(data)
>>> hll.cardinality()
4

HyperLogLogs use a Murmur64A hash. This function is fast and has a good uniform distribution of bits which is necessary for accurate estimations. The seed to this hash function can be set in the HyperLogLog constructor:

>>> hll = HyperLogLog(p=2, seed=123456789)
>>> hll.seed()
123456789

The hash function can also be called directly:

>>> hll.hash('something')
393810339

Individual registers can be printed:

>>> for i in range(2**4):
...     print(hll.get_register(i))
0
0
3
0
4

HyperLogLog objects can be merged. This is done by taking the maximum value of their respective registers:

>>> A = HyperLogLog(p=4)
>>> A.add('hello')
>>> B = HyperLogLog(p=4)
>>> B.add('world')
>>> A.merge(B)
>>> A.cardinality()
2

Register representation

Registers are stored using both sparse and dense representation. Originally all registers are initialized to zero. However storing all these zeroes individually is wasteful. Instead a sorted linked list [3] is used to store only registers that have been set (e.g. have a non-zero value). When this list reaches sufficient size the HyperLogLog object will switch to using dense representation where registers are stored invidiaully using 6 bits.

Sparse representation can be disabled using the sparse flag:

>>> HyperLogLog(p=2, sparse=False)

The maximum list size for the sparse register list determines when the HyperLogLog object switches to dense representation. This can be set using max_list_size:

>>> HyperLogLog(p=15, max_list_size=10**6)

Traversing the sparse register list every time an item is added to the HyperLogLog to update a register is expensive. A temporary buffer is instead used to defer this operation. Items added to the HyperLogLog are first added to the temporary buffer. When the buffer is full the items are sorted and then any register updates occur. These updates can be done in one pass since both the temproary buffer and sparse register list are sorted.

The buffer size can be set using max_buffer_size:

>>> HyperLogLog(p=15, max_buffer_size=10**5)

License

This software is released under the MIT License.

References

[1] P. Flajolet, E. Fusy, O. Gandouet, F. Meunier. "HyperLogLog: the analysis of a near-optimal cardinality estimation algorithm," Conference on the Analysis of Algorithms 2007.

[2] O. Ertl, "New Cardinality Estimation Methods for HyperLogLog Sketches," arXiv:1706.07290 [cs], June 2017.

[3] S. Heule, M. Nunkesser, A. Hall. "HyperLogLog in Practice: Algorithimic Engineering of a State of the Art Cardinality Estimation Algorithm," Proceedings of the EDBT 2013 Conference, ACM, Genoa March 2013.