t1ha

Fast Positive Hash, aka "Позитивный Хэш" by Positive Technologies. Included in the Awesome C list of open source C software.

The Future will (be) Positive. Всё будет хорошо.

Briefly, it is a portable non-cryptographic 64-bit hash function:

1. Intended for 64-bit little-endian platforms, predominantly for Elbrus and x86_64, but portable and without penalties it can run on any 64-bit CPU.

2. In most cases up to 15% faster than xxHash, StadtX, MUM and others portable hash-functions (which do not use specific hardware tricks).

   Currently wyhash outperforms t1ha on x86_64. However next version t1ha3_atonce() will be even faster on all platforms, especially on E2K, architectures with SIMD and most RISC-V implementations. In addition, it should be noted that wyhash have a "blinding multiplication" flaw and can lose entropy (similarly as described below). For instance, when data could be correlated with the seed ^ _wypN values or equal to it. Another case is where one of _wymum() multipliers becomes zero. In result of such blinding all previous data will not be influence to the hash value.

3. Licensed under zlib License.

Also pay attention to Rust, Erlang and Golang implementations.

FAQ: Why t1ha don't follow NH-approach like FARSH, XXH3, HighwayHash and so on?

Okay, just for clarity, we should distinguish functions families: MMH (Multilinear-Modular-Hashing), NMH (Non-linear Modular-Hashing) and the next simplification step UMAC's NH.

Now take a look to NH hash-function family definition:

It is very SIMD-friendly, since SSE2's _mm_add_epi32() and _mm_mul_epu32() is enough for . On the other hand, the result of the inner multiplication becomes zero when (m[2i] + k[2i]) mod 2^32 == 0 or (m[2i+1] + k[2i+1]) mod 2^32 == 0, in which case the opposite multiplier will not affect the result of hashing, i.e. NH function just ignores part of the input data. I called this an "blinding multiplication". That's all. More useful related information can be googled by "UMAC NH key recovery attack".

The right NMH/NH code without entropy loss should be looking like this:

    uint64_t proper_NH_block(const uint32_t *M /* message data */,
                             const uint64_t *K /* 64-bit primes */,
                             size_t N_even, uint64_t optional_weak_seed) {
      uint64_t H = optional_weak_seed;
      for (size_t i = 0; i < N_even / 2; ++i)
        H += (uint64_t(M[i*2]) + K[i*2]) * (uint64_t(M[i*2+1]) + K[i*2+1]);
      return H;
    }

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Usage

The t1ha library provides several terraced hash functions with the dissimilar properties and for a different cases. These functions briefly described below, see t1ha.h for more API details.

To use in your own project you may link with the t1ha-library, or just add to your project corresponding source files from /src directory.

Please, feel free to fill an issue or make pull request.

t1ha0 = 64 bits, "Just Only Faster"

Provides fast-as-possible hashing for current CPU, including 32-bit systems and engaging the available hardware acceleration. You can rest assured that t1ha0 faster than all other fast hashes (with comparable quality) so, otherwise we will extend and refine it time-to-time.

On the other hand, without warranty that the hash result will be same for particular key on another machine or another version. Moreover, is deliberately known that the result will be different for systems with different bitness or endianness. Briefly, such hash-results and their derivatives, should be used only in runtime, but should not be persist or transferred over a network.

Also should be noted, the quality of t1ha0() hashing is a subject for tradeoffs with performance. Therefore the quality and strength of t1ha0() may be lower than t1ha1() and t1ha2(), especially on 32-bit targets, but then much faster. However, guaranteed that it passes all SMHasher tests.

Internally t1ha0() selects most faster implementation for current CPU, for now these are includes:

Implementation	Platform/CPU
t1ha0_ia32aes_avx()	x86 with AES-NI and AVX extensions
t1ha0_ia32aes_avx2()	x86 with AES-NI and AVX2 extensions
t1ha0_ia32aes_noavx()	x86 with AES-NI without AVX extensions
t1ha0_32le()	32-bit little-endian
t1h0a_32be()	32-bit big-endian
t1ha1_le()	64-bit little-endian
t1ha1_be()	64-bit big-endian
t1ha2_atonce()	64-bit little-endian

t1ha1 = 64 bits, baseline fast portable hash

The first version of "Fast Positive Hash" with reasonable quality for checksum, hash tables and thin fingerprinting. It is stable, e.g. returns same result on all architectures and CPUs.

1. Speed with the reasonable quality of hashing.
2. Efficiency on modern 64-bit CPUs, but not in a hardware.
3. Strong as possible, until no penalties on performance.

Unfortunatelly, Yves Orton discovered that t1ha1() family fails the strict avalanche criteria in some cases. This flaw is insignificant for the t1ha1() purposes and imperceptible from a practical point of view. However, nowadays this issue has resolved in the next t1ha2() function, that was initially planned to providing a bit more quality.

The basic version of t1ha1() intends for little-endian systems and will run slowly on big-endian. Therefore a dedicated big-endian version is also provided, but returns the different result than the basic version.

t1ha2 = 64 and 128 bits, slightly more attention for quality and strength

The recommended version of "Fast Positive Hash" with good quality for checksum, hash tables and fingerprinting. It is stable, e.g. returns same result on all architectures and CPUs.

1. Portable and extremely efficiency on modern 64-bit CPUs.
2. Great quality of hashing and still faster than other non-t1ha hashes.
3. Provides streaming mode and 128-bit result.

The t1ha2() is intended for little-endian systems and will run slightly slowly on big-endian systems.

t1ha3 = 128 and 256 bits, fast non-cryptographic fingerprinting

The next-step version of "Fast Positive Hash", but not yet finished and therefore not available.

Planned: t1ha4 = 128 and 256 bits, fast insecure fingerprinting

Planned: t1ha5 = 256 bits, fast Cryptographic, but with some limitations

Planned: t1ha6 = 256 and 512 bits, Cryptographic with reasonable resistance to acceleration on GPU and FPGA.

Planned: t1ha7 = 256, 512 and 1024 bits, Cryptographic, Strong Post-Quantum

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Requirements and Portability:

1. t1ha designed for modern 64-bit architectures. But on the other hand, t1ha doesn't require instructions specific to a particular architecture:
   • therefore t1ha could be used on any CPU for which compiler provides support 64-bit arithmetic.
   • but unfortunately t1ha could be dramatically slowly on architectures without native 64-bit operations.
2. This implementation of t1ha requires modern GNU C compatible compiler, including Clang/LLVM, or Visual Studio 2013/2015/2017. For proper performance please use one of: GNU C 5.5 or later, CLANG 5.0 or later, Microsoft Visual Studio 2017 15.6 or later.

Acknowledgement:

The t1ha was originally developed by Leonid Yuriev (Леонид Юрьев) for The 1Hippeus project - zerocopy messaging in the spirit of Sparta!

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Benchmarking and Testing

Current version of t1ha library includes tool for basic testing and benchmarking. Just try make check from t1ha directory.

To comparison benchmark also includes wyhash, xxHash, StadtX and HighwayHash functions. For example actual results for Intel(R) Core(TM) i7-4600U CPU:

$ make all && sudo make check
Build by GNU C/C++ compiler 9.3 (self-check passed)
Testing t1ha2_atonce... Ok
Testing t1ha2_atonce128... Ok
Testing t1ha2_stream... Ok
Testing t1ha2_stream128... Ok
Testing t1ha1_64le... Ok
Testing t1ha1_64be... Ok
Testing t1ha0_32le... Ok
Testing t1ha0_32be... Ok
Testing t1ha0_ia32aes_noavx... Ok
Testing t1ha0_ia32aes_avx... Ok
Testing t1ha0_ia32aes_avx2... Ok
Testing HighwayHash64_pure_c... Ok
Testing HighwayHash64_portable_cxx... Ok
Testing HighwayHash64_sse41... Ok
Testing HighwayHash64_avx2... Ok
Testing StadtX... Ok
Testing wyhash_v7... Ok

Preparing to benchmarking...
 - running on CPU#0
 - use RDPMC_40000001 as clock source for benchmarking
 - assume it cheap and stable
 - measure granularity and overhead: 54 cycles, 0.0185185 iteration/cycle

Bench for tiny keys (7 bytes):
t1ha2_atonce          :     17.250 cycle/hash,  2.464 cycle/byte,  0.406 byte/cycle,  1.217 GiB/s @3GHz
t1ha2_atonce128*      :     33.281 cycle/hash,  4.754 cycle/byte,  0.210 byte/cycle,  0.631 GiB/s @3GHz
t1ha2_stream*         :     77.500 cycle/hash, 11.071 cycle/byte,  0.090 byte/cycle,  0.271 GiB/s @3GHz
t1ha2_stream128*      :     99.125 cycle/hash, 14.161 cycle/byte,  0.071 byte/cycle,  0.212 GiB/s @3GHz
t1ha1_64le            :     18.219 cycle/hash,  2.603 cycle/byte,  0.384 byte/cycle,  1.153 GiB/s @3GHz
t1ha0                 :     15.102 cycle/hash,  2.157 cycle/byte,  0.464 byte/cycle,  1.391 GiB/s @3GHz
xxhash32              :     16.545 cycle/hash,  2.364 cycle/byte,  0.423 byte/cycle,  1.269 GiB/s @3GHz
xxhash64              :     27.203 cycle/hash,  3.886 cycle/byte,  0.257 byte/cycle,  0.772 GiB/s @3GHz
xxh3_64               :     15.102 cycle/hash,  2.157 cycle/byte,  0.464 byte/cycle,  1.391 GiB/s @3GHz
xxh3_128              :     18.219 cycle/hash,  2.603 cycle/byte,  0.384 byte/cycle,  1.153 GiB/s @3GHz
StadtX                :     20.203 cycle/hash,  2.886 cycle/byte,  0.346 byte/cycle,  1.039 GiB/s @3GHz
HighwayHash64_pure_c  :    607.000 cycle/hash, 86.714 cycle/byte,  0.012 byte/cycle,  0.035 GiB/s @3GHz
HighwayHash64_portable:    513.000 cycle/hash, 73.286 cycle/byte,  0.014 byte/cycle,  0.041 GiB/s @3GHz
HighwayHash64_sse41   :     69.438 cycle/hash,  9.920 cycle/byte,  0.101 byte/cycle,  0.302 GiB/s @3GHz
HighwayHash64_avx2    :     54.875 cycle/hash,  7.839 cycle/byte,  0.128 byte/cycle,  0.383 GiB/s @3GHz
wyhash_v7             :     14.102 cycle/hash,  2.015 cycle/byte,  0.496 byte/cycle,  1.489 GiB/s @3GHz

Bench for large keys (16384 bytes):
t1ha2_atonce          :   3493.000 cycle/hash,  0.213 cycle/byte,  4.691 byte/cycle, 14.072 GiB/s @3GHz
t1ha2_atonce128*      :   3664.000 cycle/hash,  0.224 cycle/byte,  4.472 byte/cycle, 13.415 GiB/s @3GHz
t1ha2_stream*         :   3684.000 cycle/hash,  0.225 cycle/byte,  4.447 byte/cycle, 13.342 GiB/s @3GHz
t1ha2_stream128*      :   3709.239 cycle/hash,  0.226 cycle/byte,  4.417 byte/cycle, 13.251 GiB/s @3GHz
t1ha1_64le            :   3644.000 cycle/hash,  0.222 cycle/byte,  4.496 byte/cycle, 13.488 GiB/s @3GHz
t1ha0                 :   1289.000 cycle/hash,  0.079 cycle/byte, 12.711 byte/cycle, 38.132 GiB/s @3GHz
xxhash32              :   8198.000 cycle/hash,  0.500 cycle/byte,  1.999 byte/cycle,  5.996 GiB/s @3GHz
xxhash64              :   4126.750 cycle/hash,  0.252 cycle/byte,  3.970 byte/cycle, 11.911 GiB/s @3GHz
xxh3_64               :   4929.000 cycle/hash,  0.301 cycle/byte,  3.324 byte/cycle,  9.972 GiB/s @3GHz
xxh3_128              :   4887.536 cycle/hash,  0.298 cycle/byte,  3.352 byte/cycle, 10.057 GiB/s @3GHz
StadtX                :   3667.000 cycle/hash,  0.224 cycle/byte,  4.468 byte/cycle, 13.404 GiB/s @3GHz
HighwayHash64_pure_c  :  55294.000 cycle/hash,  3.375 cycle/byte,  0.296 byte/cycle,  0.889 GiB/s @3GHz
HighwayHash64_portable:  44982.321 cycle/hash,  2.746 cycle/byte,  0.364 byte/cycle,  1.093 GiB/s @3GHz
HighwayHash64_sse41   :   7041.000 cycle/hash,  0.430 cycle/byte,  2.327 byte/cycle,  6.981 GiB/s @3GHz
HighwayHash64_avx2    :   4542.000 cycle/hash,  0.277 cycle/byte,  3.607 byte/cycle, 10.822 GiB/s @3GHz
wyhash_v7             :   3383.000 cycle/hash,  0.206 cycle/byte,  4.843 byte/cycle, 14.529 GiB/s @3GHz

The test tool support a set of command line options to selecting functions and size of keys for benchmarking. For more info please run ./test --help.

The --hash-stdin-strings option

One noteable option is --hash-stdin-strings, it intended to estimate hash collisions on your custom data. With this option test tool will hash each line from standard input and print its hash to standard output.

For instance, you could count collisions for lines from some words.list file by bash's command:

  ./t1ha/test --hash-stdin-strings < words.list | sort | uniq -c -d | wc -l

More complex example - count xxhash() collisions for lines from words.list and 0...10000 numbers, with distinction only in 32 bit of hash values:

  (cat words.list && seq 0 10000) | \
     ./t1ha/test --xxhash --hash-stdin-strings | \
     cut --bytes=-8 | sort | uniq -c -d | wc -l

SMHasher

SMHasher is a wellknown test suite designed to test the distribution, collision, and performance properties of non-cryptographic hash functions.

Reini Urban provides extended version/fork of SMHasher which integrates a lot of modern hash functions, including t1ha.

So, the quality and speed of t1ha can be easily checked with the following scenario:

git clone https://github.com/rurban/smhasher
cd smhasher
cmake .
make
./SMHasher City64
./SMHasher metrohash64_1
./SMHasher xxHash64
...
./SMHasher t1ha

For properly performance please use at least GCC 5.5, Clang 6.0 or Visual Studio 2017.

Scores

Please take in account that the results is significantly depend on actual CPU, compiler version and CFLAGS. The results below were obtained in 2016 with:

• CPU: Intel(R) Core(TM) i7-6700K CPU;
• Compiler: gcc version 5.4.0 20160609 (Ubuntu 5.4.0-6ubuntu1~16.04.4);
• CFLAGS: -march=native -O3 -fPIC;

The SMALL KEYS case

Order by average Cycles per Hash for 1..31 bytes (less is better).

Function	MiB/Second	Cycles/Hash	Notes (quality, portability)
donothing	15747227.36	6.00	not a hash (just for reference)
sumhash32	43317.86	16.69	not a hash (just for reference)
FNV1a_YoshimitsuTRIAD	13000.49	24.96	poor (100% bias, collisions, distrib)
crc64_hw	7308.06	28.37	poor (insecure, 100% bias, collisions, distrib), non-portable (SSE4.2)
crc32_hw	5577.64	29.10	poor (insecure, 100% bias, collisions, distrib), non-portable (SSE4.2)
NOP_OAAT_read64	1991.31	30.46	poor (100% bias, 2.17x collisions)
Crap8	2743.80	32.50	poor (2.42% bias, collisions, 2% distrib)
t1ha_aes	34636.42	33.03	non-portable (AES-NI)
t1ha	12228.80	35.55
MUM	10246.20	37.25	non-portable (different result, machine specific)
Murmur2	2789.89	38.37	poor (1.7% bias, 81x coll, 1.7% distrib)
t1ha_32le	5958.54	38.54	alien (designed for 32-bit CPU)
t1ha_64be	9321.23	38.29	alien (designed for big-endian CPU)
lookup3	1817.11	39.30	poor (28% bias, collisions, 30% distrib)
t1ha_32be	5873.45	39.81	alien (designed for 32-bit big-endian CPU)
Murmur2C	3655.60	42.68	poor (91% bias, collisions, distrib)
fasthash64	5578.06	43.42
Murmur2A	2789.85	43.38	poor (12.7% bias)
xxHash32	5513.55	43.72
Murmur2B	5578.21	44.13	weak (1.8% bias, collisions, distrib)
fasthash32	5381.46	45.50
cmetrohash64_1_optshort	11808.92	46.33	seems weak (likely cyclic collisions)
metrohash64_2	12113.12	46.88	seems weak (likely cyclic collisions)
cmetrohash64_1	12081.32	47.28	seems weak (likely cyclic collisions)
metrohash64_1	12024.68	47.21	seems weak (likely cyclic collisions)
Murmur3F	5473.62	47.37
superfast	1860.25	47.45	poor (91% bias, 5273.01x collisions, 37% distrib)
cmetrohash64_2	12052.58	48.66
Murmur3A	2232.00	48.16
City32	5014.33	51.13	far to perfect (2 minor collisions)
City64	11041.72	51.77
metrohash64crc_2	20582.76	51.39	seems weak (likely cyclic collisions), non-portable (SSE4.2)
sumhash	9668.13	51.31	not a hash (just for reference)
metrohash64crc_1	21319.23	52.36	weak (cyclic collisions), non-portable (SSE4.2)
PMurHash32	2232.26	53.18
Murmur3C	3719.22	54.05
bernstein	921.43	55.17	poor (100% bias, collisions, distrib)
xxHash64	11123.15	56.17
Spooky32	11464.20	59.45
City128	12551.54	60.93
FarmHash64	12145.36	60.12	non-portable (SSE4.2)
Spooky128	11735.99	60.45	weak (collisions with 4bit diff)
Spooky64	11820.20	60.39
CityCrc128	14821.82	62.38	non-portable (SSE4.2)
MicroOAAT	826.32	62.06	poor (100% bias, distrib)
metrohash128_1	11063.78	66.58	seems weak (likely cyclic collisions)
metrohash128_2	11465.18	66.72	weak (cyclic collisions)
GoodOAAT	930.18	68.24
metrohash128crc_1	21322.80	70.33	seems weak (likely cyclic collisions), non-portable (SSE4.2)
metrohash128crc_2	20990.70	70.40	seems weak (likely cyclic collisions), non-portable (SSE4.2)
farmhash64_c	12033.13	71.30	non-portable (SSE4.2)
sdbm	695.29	71.76	poor (100% bias, collisions, distrib)
FNV1a	684.17	72.75	poor (zeros, 100% bias, collisions, distrib)
FNV64	697.67	72.70	poor (100% bias, collisions, distrib)
FarmHash128	12515.98	77.43	non-portable (SSE4.2)
hasshe2	2587.39	81.23	poor (insecure, 100% bias, collisions, distrib), non-portable (SSE2)
BadHash	558.14	87.87	not a hash (just for reference)
x17	551.99	89.24	poor (99.98% bias, collisions, distrib)
JenkinsOOAT_perl	558.14	95.26	poor (1.5-11.5% bias, 7.2x collisions)
farmhash128_c	12709.06	96.42	non-portable (SSE4.1)
MurmurOAAT	465.12	107.61	poor (collisions, 99.99% distrib)
JenkinsOOAT	558.13	116.75	poor (53.5% bias, collisions, distrib)
falkhash	8909.54	124.48	non-portable (AES-NI)
crc32	342.27	142.06	poor (insecure, 8589.93x collisions, distrib)
SipHash	962.35	147.36
md5_32a	433.03	508.98
sha1_32a	531.44	1222.44

The LARGE KEYS case

Order by hashing speed in Mi-bytes (2^20 = 1048576) per second for 262144-byte block (more is better).

Function	MiB/Second	Cycles/Hash	Notes (quality, portability)
donothing	15747227.36	6.00	not a hash (just for reference)
sumhash32	43317.86	16.69	not a hash (just for reference)
t1ha_aes	34636.42	33.03	non-portable (AES-NI)
metrohash128crc_1	21322.80	70.33	seems weak (likely cyclic collisions), non-portable (SSE4.2)
metrohash64crc_1	21319.23	52.36	seems weak (cyclic collisions), non-portable (SSE4.2)
metrohash128crc_2	20990.70	70.40	seems weak (likely cyclic collisions), non-portable (SSE4.2)
metrohash64crc_2	20582.76	51.39	seems weak (likely cyclic collisions), non-portable (SSE4.2)
CityCrc128	14821.82	62.38	non-portable (SSE4.2)
FNV1a_YoshimitsuTRIAD	13000.49	24.96	poor (100% bias, collisions, distrib)
farmhash128_c	12709.06	96.42	non-portable (SSE4.1)
City128	12551.54	60.93
FarmHash128	12515.98	77.43	non-portable (SSE4.2)
t1ha	12228.80	35.55
FarmHash64	12145.36	60.12	non-portable (SSE4.2)
metrohash64_2	12113.12	46.88	seems weak (likely cyclic collisions)
cmetrohash64_1	12081.32	47.28	seems weak (likely cyclic collisions)
cmetrohash64_2	12052.58	48.66	seems weak (likely cyclic collisions)
farmhash64_c	12033.13	71.30	non-portable (SSE4.2)
metrohash64_1	12024.68	47.21	seems weak (likely cyclic collisions)
Spooky64	11820.20	60.39
cmetrohash64_1_optshort	11808.92	46.33	seems weak (likely cyclic collisions)
Spooky128	11735.99	60.45	weak (collisions with 4-bit diff)
metrohash128_2	11465.18	66.72	weak (cyclic collisions)
Spooky32	11464.20	59.45
xxHash64	11123.15	56.17
metrohash128_1	11063.78	66.58	seems weak (likely cyclic collisions)
City64	11041.72	51.77
MUM	10246.20	37.25	non-portable (different result, machine specific)
sumhash	9668.13	51.31	not a hash (just for reference)
t1ha_64be	9321.23	38.29	alien (designed for big-endian CPU)
falkhash	8909.54	124.48	non-portable (AES-NI)
crc64_hw	7308.06	28.37	poor (insecure, 100% bias, collisions, distrib), non-portable (SSE4.2)
t1ha_32le	5958.54	38.54	alien (designed for 32-bit CPU)
t1ha_32be	5873.45	39.81	alien (designed for 32-bit big-endian CPU)
fasthash64	5578.06	43.42
Murmur2B	5578.21	44.13	weak (1.8% bias, collisions, distrib)
crc32_hw	5577.64	29.10	poor (insecure, 100% bias, collisions, distrib), non-portable (SSE4.2)
xxHash32	5513.55	43.72
Murmur3F	5473.62	47.37
fasthash32	5381.46	45.50
City32	5014.33	51.13	far to perfect (2 minor collisions)
Murmur3C	3719.22	54.05
Murmur2C	3655.60	42.68	poor (91% bias, collisions, distrib)
Murmur2	2789.89	38.37	poor (1.7% bias, 81x coll, 1.7% distrib)
Murmur2A	2789.85	43.38	poor (12.7% bias)
Crap8	2743.80	32.50	poor (2.42% bias, collisions, 2% distrib)
hasshe2	2587.39	81.23	poor (insecure, 100% bias, collisions, distrib), non-portable (SSE2)
Murmur3A	2232.00	48.16
PMurHash32	2232.26	53.18
NOP_OAAT_read64	1991.31	30.46	poor (100% bias, 2.17x collisions)
superfast	1860.25	47.45	poor (91% bias, 5273.01x collisions, 37% distrib)
lookup3	1817.11	39.30	poor (28% bias, collisions, 30% distrib)
SipHash	962.35	147.36
GoodOAAT	930.18	68.24
bernstein	921.43	55.17	poor (100% bias, collisions, distrib)
MicroOAAT	826.32	62.06	poor (100% bias, distrib)
FNV64	697.67	72.70	poor (100% bias, collisions, distrib)
sdbm	695.29	71.76	poor (100% bias, collisions, distrib)
FNV1a	684.17	72.75	poor (zeros, 100% bias, collisions, distrib)
BadHash	558.14	87.87	not a hash (just for reference)
JenkinsOOAT	558.13	116.75	poor (53.5% bias, collisions, distrib)
JenkinsOOAT_perl	558.14	95.26	poor (1.5-11.5% bias, 7.2x collisions)
x17	551.99	89.24	poor (99.98% bias, collisions, distrib)
sha1_32a	531.44	1222.44
MurmurOAAT	465.12	107.61	poor (collisions, 99.99% distrib)
md5_32a	433.03	508.98
crc32	342.27	142.06	poor (insecure, 8589.93x collisions, distrib)

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This is a mirror of the origin repository that was moved to abf.io because of discriminatory restrictions for Russian Crimea.