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

The Future will Positive. Всё будет хорошо.

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 StadtX hash, xxHash, mum-hash, metro-hash, etc. and all others portable hash-functions (which do not use specific hardware tricks).

Currently wyhash outperforms t1ha. Nevertheless I think the next version of t1ha will be even faster.

At the same time, I do not recommend using wyhash, since in some cases this function can fatally lose entropy. For example, completely loses the dependence of the result on the input data (performs a multiplying by zero) when the internal state coincides with 0xa0761d6478bd642f and so on.

3. Provides a set of terraced hash functions.
4. Currently not suitable for cryptography.
5. Licensed under zlib License.

Also pay attention to Rust, Erlang and Golang implementations.

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. That's all. For more related info please google for "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;
    }

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.

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:

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.

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.

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

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.

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

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

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

$ CC=gcc-8 CXX=g++-8 make all && sudo make check
...
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

Preparing to benchmarking...
 - suggest enable rdpmc for usermode (echo 2 | sudo tee /sys/devices/cpu/rdpmc)
 - running on CPU#3
 - use RDPMC_perf as clock source for benchmarking
 - assume it cheap and stable
 - measure granularity and overhead: 53 cycle, 0.0188679 iteration/cycle

Bench for tiny keys (7 bytes):
t1ha2_atonce            :     18.188 cycle/hash,  2.598 cycle/byte,  0.385 byte/cycle,  1.155 Gb/s @3GHz
t1ha2_atonce128*        :     36.969 cycle/hash,  5.281 cycle/byte,  0.189 byte/cycle,  0.568 Gb/s @3GHz
t1ha2_stream*           :     84.237 cycle/hash, 12.034 cycle/byte,  0.083 byte/cycle,  0.249 Gb/s @3GHz
t1ha2_stream128*        :    101.812 cycle/hash, 14.545 cycle/byte,  0.069 byte/cycle,  0.206 Gb/s @3GHz
t1ha1_64le              :     19.188 cycle/hash,  2.741 cycle/byte,  0.365 byte/cycle,  1.094 Gb/s @3GHz
t1ha0                   :     14.102 cycle/hash,  2.015 cycle/byte,  0.496 byte/cycle,  1.489 Gb/s @3GHz
xxhash32                :     18.859 cycle/hash,  2.694 cycle/byte,  0.371 byte/cycle,  1.114 Gb/s @3GHz
xxhash64                :     27.188 cycle/hash,  3.884 cycle/byte,  0.257 byte/cycle,  0.772 Gb/s @3GHz
StadtX                  :     19.188 cycle/hash,  2.741 cycle/byte,  0.365 byte/cycle,  1.094 Gb/s @3GHz
HighwayHash64_pure_c    :    630.000 cycle/hash, 90.000 cycle/byte,  0.011 byte/cycle,  0.033 Gb/s @3GHz
HighwayHash64_portable  :    507.500 cycle/hash, 72.500 cycle/byte,  0.014 byte/cycle,  0.041 Gb/s @3GHz
HighwayHash64_sse41     :     69.625 cycle/hash,  9.946 cycle/byte,  0.101 byte/cycle,  0.302 Gb/s @3GHz
HighwayHash64_avx2      :     57.500 cycle/hash,  8.214 cycle/byte,  0.122 byte/cycle,  0.365 Gb/s @3GHz

Bench for large keys (16384 bytes):
t1ha2_atonce            :   3544.000 cycle/hash,  0.216 cycle/byte,  4.623 byte/cycle, 13.869 Gb/s @3GHz
t1ha2_atonce128*        :   3590.000 cycle/hash,  0.219 cycle/byte,  4.564 byte/cycle, 13.691 Gb/s @3GHz
t1ha2_stream*           :   3600.000 cycle/hash,  0.220 cycle/byte,  4.551 byte/cycle, 13.653 Gb/s @3GHz
t1ha2_stream128*        :   3618.000 cycle/hash,  0.221 cycle/byte,  4.528 byte/cycle, 13.585 Gb/s @3GHz
t1ha1_64le              :   3562.818 cycle/hash,  0.217 cycle/byte,  4.599 byte/cycle, 13.796 Gb/s @3GHz
t1ha0                   :   1281.203 cycle/hash,  0.078 cycle/byte, 12.788 byte/cycle, 38.364 Gb/s @3GHz
xxhash32                :   8203.360 cycle/hash,  0.501 cycle/byte,  1.997 byte/cycle,  5.992 Gb/s @3GHz
xxhash64                :   4128.240 cycle/hash,  0.252 cycle/byte,  3.969 byte/cycle, 11.906 Gb/s @3GHz
StadtX                  :   3631.000 cycle/hash,  0.222 cycle/byte,  4.512 byte/cycle, 13.537 Gb/s @3GHz
HighwayHash64_pure_c    :  55309.000 cycle/hash,  3.376 cycle/byte,  0.296 byte/cycle,  0.889 Gb/s @3GHz
HighwayHash64_portable  :  44433.000 cycle/hash,  2.712 cycle/byte,  0.369 byte/cycle,  1.106 Gb/s @3GHz
HighwayHash64_sse41     :   6567.000 cycle/hash,  0.401 cycle/byte,  2.495 byte/cycle,  7.485 Gb/s @3GHz
HighwayHash64_avx2      :   4528.996 cycle/hash,  0.276 cycle/byte,  3.618 byte/cycle, 10.853 Gb/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.

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 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.

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;

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

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