t1ha

Fast Positive Hash, aka "Позитивный Хэш" by Positive Technologies.

The Future will Positive. Всё будет хорошо.

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

1. Intended for 64-bit little-endian platforms, predominantly for x86_64, but portable and without penalties could run on any 64-bit CPU.
2. In most cases up to 15% faster than City64, xxHash, mum-hash, metro-hash and all others portable hash-functions (which are not uses specific hardware tricks).
3. Currently not suitable for cryptography.

Also pay attention to Erlang and Golang implementations.

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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.

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 extending 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(), 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
t1ha_ia32aes_avx()	x86 with AES-NI and AVX extensions
t1ha_ia32aes_noavx()	x86 with AES-NI without AVX extensions
t1ha_32le()	32-bit little-endian
t1ha_32be()	32-bit big-endian
t1ha1_le()	64-bit little-endian
t1ha1_be()	32-bit big-endian

t1ha1 = 64 bits, fast portable hash

The main generic 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.

The main version is intended for little-endian systems and will runs slowly on big-endian. Therefore a dedicated big-endian version is also provided, but returns the different result than the main version.

t1ha2 = 64 bits, little more attention for quality and strength

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

t1ha3 = 128 bits, fast non-cryptographic fingerprinting

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

Planned: t1ha4 = 128 bits, fast alternative for SipHash

Planned: t1ha5 = 256 bits, fast insecure fingerprinting

Planned: t1ha6 = 256 bits, Cryptographic

Planned: t1ha7 = 256 bits, Cryptographic with reasonable resistance to acceleration on GPU and FPGA.

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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, includes Clang/LLVM, or Visual Studio 2015.

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

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 5.4 or Clang 3.8, at the worst Visual Studio 2015 (MSVC 19).

Scores

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

• 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)