KOMIHASH - Very Fast Hash Function

Introduction

The komihash() function available in the komihash.h file implements a very fast 64-bit hash function, mainly designed for hash-table and hash-map uses; produces identical hashes on both big- and little-endian systems. Function's code is portable, scalar.

This function features both a high large-block hashing performance (26 GB/s on Ryzen 3700X) and a high hashing throughput for small messages (about 11 cycles/hash for 0-15-byte messages). Performance on 32-bit systems is, however, quite low. Also, large-block hashing performance on big-endian systems may be lower due to the need of byte-swapping.

Technically, komihash is close to the class of hash functions like wyhash and CircleHash, which are, in turn, close to the lehmer64 PRNG. However, komihash is structurally different to them in that it accumulates the full 128-bit multiplication result, without "compression" into a single 64-bit state variable. Thus komihash does not lose differentiation between consecutive states while others may. Another important difference in komihash is that it parses the input message without overlaps. While overlaps allow a function to have fewer code branches, they are considered "non-ideal", potentially causing collisions and seed value flaws. Beside that, komihash features superior seed value handling and Perlin Noise hashing.

Note that this function is not cryptographically-secure: in open systems it should only be used with a secret seed, to minimize the chance of a collision attack.

This function passes all SMHasher tests.

Ports

• LUA, by rangercyh
• Python/Cython, by x13a
• Java, by Dynatrace

Comparisons

These are the performance comparisons made and used by the author during the development of komihash.

LLVM clang-cl 8.0.1 64-bit, Windows 10, Ryzen 3700X (Zen2), 4.2 GHz

Compiler options: /Ox /arch:sse2; overhead: 1.8 cycles/h.

Compiler options: /Ox -mavx2; overhead: 1.8 cycles/h.

LLVM clang 12.0.1 64-bit, CentOS 8, Xeon E-2176G (CoffeeLake), 4.5 GHz

Compiler options: -O3 -mavx2; overhead: 5.3 cycles/h.

ICC 19.0 64-bit, Windows 10, Ryzen 3700X (Zen2), 4.2 GHz

Compiler options: /O3 /QxSSE2; overhead: 2.0 cycles/h.

(this is likely a worst-case scenario, when a compiler was not cross-tuned to a competing processor architecture; also, ICC for Windows does not support the __builtin_expect and __builtin_prefetch intrinsics)

GCC 8.5.0 64-bit, CentOS 8, Xeon E-2176G (CoffeeLake), 4.5 GHz

Compiler options: -O3 -msse2; overhead: 5.8 cycles/h.

Compiler options: -O3 -mavx2; overhead: 5.8 cycles/h.

ICC 19.0 64-bit, Windows 10, Core i7-7700K (KabyLake), 4.5 GHz

Compiler options: /O3 /QxSSE2; overhead: 5.9 cycles/h.

LLVM clang 8.0.0 64-bit, Windows 10, Core i7-7700K (KabyLake), 4.5 GHz

Compiler options: /Ox -mavx2; overhead: 5.5 cycles/h.

Apple clang 12.0.0 64-bit, macOS 12.0.1, Apple M1, 3.5 GHz

Compiler options: -O3; overhead: unestimatable.

Notes: XXH3_64 is unseeded (seeded variant is 1 cycle/h higher). bulk is 256000 bytes: this means it is mainly a cache-bound performance, not reflective of high-load situations. GB/s should not be misinterpreted as GiB/s. cycles/h means processor clock ticks per hash value, including overhead. Measurement error is approximately 3%.

Averages over all measurements (overhead excluded)

This is the throughput comparison of hash functions on Ryzen 3700X. The used measurement method actually measures hash function's "latencied throughput", or sequential hashing, due to the use of the "volatile" variable specifiers and result accumulation.

The following method was used to obtain the cycles/h values. Note that this method measures a "raw" throughput, when processor's branch predictor tunes to a specific message length and a specific memory address. Practical performance depends on actual statistics of messages (strings) being hashed, including memory access patterns. Note that particular hash functions may "over-favor" specific message lengths. In this respect, komihash does not "favor" any specific length, thus it may be more universal. Throughput aside, hashing quality is also an important factor as it drives a hash-map's creation and subsequent accesses. This, and many other synthetic hash function tests should be taken with a grain of salt. Only an actual use case can reveal which hash function is preferrable.

	const uint64_t rc = 1ULL << 26;
	const int minl = 8; const int maxl = 28;
	volatile uint64_t msg[ 8 ] = { 0 };
	uint64_t v = 0;

	const TClock t1( CSystem :: getClock() );

	for( int k = minl; k <= maxl; k++ )
	{
		volatile size_t msgl = k;
		volatile uint64_t sd = k + 1;

		for( uint64_t i = 0; i < rc; i++ )
		{
			v ^= komihash( (uint8_t*) &msg, msgl, sd );
//			v ^= wyhash( (uint8_t*) &msg, msgl, sd, _wyp );
//			v ^= XXH3_64bits( (uint8_t*) &msg, msgl );
//			v ^= msg[ 0 ]; // Used to estimate the overhead.
			msg[ 0 ]++;
		}
	}

	printf( "%016llx\n", v );
	printf( "%.1f\n", CSystem :: getClockDiffSec( t1 ) * 4.2e9 /
		( rc * ( maxl - minl + 1 ))); // 4.5 on Xeon, 4.5 on i7700K, 3.5 on M1

Discussion

You may wonder, why komihash does not include a quite common ^MsgLen XOR instruction at some place in the code? The main reason is that due to the way komihash parses the input message such instruction is not necessary. Another reason is that for a non-cryptographic hash function such instruction provides no additional security: while it may seem that such instruction protects from simple "state XORing" collision attacks, in practice it offers no protection, if one considers how powerful SAT solvers are: in less than a second they can "forge" a preimage which produces a required hash value. It is also important to note that in such "fast" hash functions like komihash the input message has complete control over the state variables.

Is 128-bit version of this hash function planned? Most probably, no, it is not. While such version may be reasonable for data structure compatibility reasons, there is no much practical sense to use 128-bit hashes at a local level: a reliable 64-bit hash allows one to have 2.1 billion diverse binary objects (e.g. files in a file system, or entries in a hash-map) without collisions, on average. On the other hand, on a worldwide scale, having 128-bit hashes is clearly not enough considering the number of existing digital devices and the number of diverse binary objects (e.g. files, records in databases) on each of them.

A similarly efficient streamed version of komihash is doable given a serious interest in one is expressed.

An opinion on the "bulk" performance of "fast" hash functions: in most practical situations, when processor's total memory bandwidth is limited to e.g. 41 GB/s, a "bulk" single-threaded hashing performance on the order of 30 GB/s is excessive considering memory bandwidth has to be spread over multiple cores. So, practically, such "fast" hash function, working on a high-load 8-core server, rarely receives more than 8 GB/s of bandwidth. Another factor worth mentioning is that a server rarely has more than 10 Gb/s network connectivity, thus further reducing practical hashing performance of incoming data. The same applies to disk system's throughput, if on-disk data is not yet in memory.

KOMIRAND

The komirand() function available in the komihash.h file implements a simple, but reliable, self-starting, and fast (0.62 cycles/byte) 64-bit pseudo-random number generator (PRNG) with 2^64 period. It is based on the same mathematical construct as the komihash hash function. komirand passes PractRand tests.

Other

This function is named the way it is named is to honor the Komi Republic (located in Russia), native to the author.