hexhamming 2.4.0

Fast Hamming distance calculation for hexadecimal strings

What does it do?

This module performs a fast bitwise hamming distance of two hexadecimal strings.

This looks like:

DEADBEEF = 11011110101011011011111011101111
00000000 = 00000000000000000000000000000000
XOR      = 11011110101011011011111011101111
Hamming  = number of ones in DEADBEEF ^ 00000000 = 24

This essentially amounts to

>>> import gmpy
>>> gmpy.popcount(0xdeadbeef ^ 0x00000000)
24

except with Python strings, so

>>> import gmpy
>>> gmpy.popcount(int("deadbeef", 16) ^ int("00000000", 16))
24

A few assumptions are made and enforced:

• this is a valid hexadecimal string (i.e., [a-fA-F0-9]+)

• the strings are the same length

• the strings do not begin with "0x"

Why yet another Hamming distance library?

There are a lot of fantastic (python) libraries that offer methods to calculate various edit distances, including Hamming distances: Distance, textdistance, scipy, jellyfish, etc.

In this case, I needed a hamming distance library that worked on hexadecimal strings (i.e., a Python str) and performed blazingly fast. Furthermore, I often did not care about hex strings greater than 256 bits. That length constraint is different vs all the other libraries and enabled me to explore vectorization techniques via numba, numpy, and SSE/AVX intrinsics.

Lastly, I wanted to minimize dependencies, meaning you do not need to install numpy, gmpy, cython, pypy, pythran, etc.

Eventually, after playing around with gmpy.popcount, numba.jit, pythran.run, numpy, I decided to write what I wanted in essentially raw C. At this point, I’m using raw char* and int*, so exploring re-writing this in Fortran makes little sense.

Installation

To install, ensure you have Python 3.6+. Run

pip install hexhamming

or to install from source

git clone https://github.com/mrecachinas/hexhamming
cd hexhamming
python setup.py install # or pip install .

If you want to contribute to hexhamming, you should install the dev dependencies

pip install -r requirements-dev.txt

and make sure the tests pass with

python -m pytest -vls .

Example

Using hexhamming is as simple as

>>> from hexhamming import hamming_distance_string
>>> hamming_distance_string("deadbeef", "00000000")
24

New in v2.0.0 : hexhamming now supports byte``s via ``hamming_distance_bytes. You use it in the exact same way as before, except you pass in a byte string.

>>> from hexhamming import hamming_distance_bytes
>>> hamming_distance_bytes(b"\xde\xad\xbe\xef", b"\x00\x00\x00\x00")
24

We also provide a method for a quick boolean check of whether two hexadecimal strings are within a given Hamming distance.

>>> from hexhamming import check_hexstrings_within_dist
>>> check_hexstrings_within_dist("ffff", "fffe", 2)
True
>>> check_hexstrings_within_dist("ffff", "0000", 2)
False

Similarly, hexhamming supports a quick byte array check via check_bytes_within_dist, which has a similar API as check_hexstrings_within_dist, except it expects a bytes array.

The API described above is targeted at comparing two individual records and calculating their hamming distance quickly. For many applications the goal is to compare a given record to an array of other records and to find out if there are elements in the array that are within a given hamming distance of the search record. To support these application cases hexhamming has a set of array APIs. Given that these operations are often speed critical and require preparing data anyway, they are only available for bytes strings, not for hex strings.

They all have the same signature, they take two bytes arrays and the max_dist to consider. The difference is, that the first bytes string should be a concatenation of a number of records to compare to, i.e. the length needs to be a multiple of the length of the second bytes string.

There are three functions that return different results, depending on what is needed by the application.

check_bytes_arrays_first_within_dist returns the index of the first element that has a hamming distance less than max_dist.

>>> from hexhamming import check_bytes_arrays_first_within_dist
>>> check_bytes_arrays_first_within_dist(b"\xaa\xaa\xbb\xbb\xcc\xcc\xdd\xdd\xee\xee\xff\xff", b"\xff\xff", 4)
1

check_bytes_arrays_best_within_dist returns a tuple with the distance and the index of the element that has the lowest hamming distance less than max_dist, or (-1,-1) if none do.

>>> from hexhamming import check_bytes_arrays_best_within_dist
>>> check_bytes_arrays_best_within_dist(b"\xaa\xaa\xbb\xbb\xcc\xcc\xdd\xdd\xee\xee\xff\xff", b"\xff\xff", 4)
(0, 5)

>>> check_bytes_arrays_best_within_dist(b"\xaa\xaa\xbb\xbb\xcc\xcc\xdd\xdd\xee\xee\xff\xff", b"\xef\xfe", 4)
(2, 4)

check_bytes_arrays_all_within_dist returns a list of tuples with the distance and the index of the element that have a hamming distance less than max_dist, or [] if none do.

>>> from hexhamming import check_bytes_arrays_all_within_dist
>>> check_bytes_arrays_all_within_dist(b"\xaa\xaa\xbb\xbb\xcc\xcc\xdd\xdd\xee\xee\xff\xff", b"\xff\xff", 4)
[(4, 1), (4, 3), (4, 4), (0, 5)]

Tip: When you’re assembling the long array of records to compare against, don’t concatenate the different bytes together. As they’re immutable that is a very slow operation. Use a bytearray instead, and cast it to bytes at the end. See https://www.guyrutenberg.com/2020/04/04/fast-bytes-concatenation-in-python/ for more info and tests.

Benchmark

Below is a benchmark using pytest-benchmark with hexhamming==v1.3.2 my 2020 2.0 GHz quad-core Intel Core i5 16 GB 3733 MHz LPDDR4 macOS Catalina (10.15.5) with Python 3.7.3 and Apple clang version 11.0.3 (clang-1103.0.32.62).

Name	Mean (ns)	Std (ns)	Median (ns)	Rounds	Iterations
test_hamming_distance_bench_3	93.8	10.5	94.3	53268	200
test_hamming_distance_bench_3_same	94.2	15.2	94.9	102146	100
test_check_hexstrings_within_dist_bench	231.9	104.2	216.5	195122	22
test_hamming_distance_bench_256	97.5	34.1	94.0	195122	22
test_hamming_distance_bench_1000	489.8	159.4	477.5	94411	20
test_hamming_distance_bench_1000_same	497.8	87.8	496.6	18971	20
test_hamming_distance_bench_1024	509.9	299.5	506.7	18652	10
test_hamming_distance_bench_1024_same	467.4	205.9	450.4	181819	10