tangara-fw/lib/komihash

KOMIHASH - Very Fast Hash Function (in C)

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, header-only inlineable C (C++).

This function features both a high large-block hashing performance (26 GB/s on Ryzen 3700X) and a high hashing throughput for small strings/messages (about 10 cycles/hash for 0-15-byte strings). Performance on 32-bit systems is, however, quite low. Also, large-block hashing performance on big-endian systems may be 20% lower due to the need of byte-swapping (can be switched off with a define).

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. However, when the default seed is used (0), this further reduces function's overhead by 1-2 cycles/hash (compiler-dependent).

This function passes all SMHasher tests.

An aspect worth noting, important to some users, is that komihash at its base uses a very simple mathematical construct, and uses no author-intended nor author-fabricated information. The base state of the function is equal to the first mantissa bits of PI, and can be changed to any uniformly-random values.

Discrete-Incremental Hashing

A correct way to hash an array of independent values, and which does not require pre-buffering, is to pass previous hash value as a seed value. This method may be as fast or faster than pre-buffering, especially if lengths of values in the array are not small. An additional 1-2 cycles/hash advantage is obtained if fixed-size values are being hashed incrementally (due to compiler's branching optimization). In most cases, incremental hashing of even a few 2-8-byte values may be faster than using pre-buffering if the overall input length is not known in advance.

	uint64_t HashVal = komihash( &val1, sizeof( val1 ), Seed );
	HashVal = komihash( &val2, sizeof( val2 ), HashVal );
	...
	HashVal = komihash( &valN, sizeof( valN ), HashVal );

Note that this approach is not the same as "streamed" hashing since this approach implicitly encodes the length of each independent value. Such kind of hashing can be beneficial when a database record is being hashed, when it is necessary to separate fields by means of encoding their lengths.

Discrete-incremental hashing of nested structures requires a "hash value stack" where the current hash value is pushed into it upon each nesting, the nested level starts at hash value 0, and the resulting value is hashed with a popped previous hash value upon exiting the nesting level.

Streamed Hashing

The komihash.h file also features a fast continuously streamed implementation of the komihash hash function. Streamed hashing expects any number of update calls inbetween the init and final calls:

	komihash_stream_t ctx;
	komihash_stream_init( &ctx, UseSeed );

	komihash_stream_update( &ctx, &val1, sizeof( val1 ));
	komihash_stream_update( &ctx, &val2, sizeof( val2 ));
	...
	komihash_stream_update( &ctx, &valN, sizeof( valN ));

	uint64_t Hash = komihash_stream_final( &ctx );

Since the final function is non-destructive for the context structure, the function can be used to obtain intermediate "incremental" hashes of the data stream being hashed, and the hashing can then be resumed.

The hash value produced via streamed hashing can be used in the discrete-incremental hashing outlined above (e.g., for files and blobs).

You may also consider using PRVHASH64S which provides 8.4 GB/s hashing throughput on Ryzen 3700X, and is able to produce a hash value of any required bit-size.

Ports

• Java, by Dynatrace
• LUA, by rangercyh
• .NET
• Rust

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.

Hash function	0-15b, cycles/h	8-28b, cycles/h	bulk, GB/s
komihash 4.5	11.0	12.7	26.2
komihash 4.3	11.2	13.0	26.0
komihash 3.6	11.1	16.9	27.5
komihash 2.8	11.3	17.4	27.7
wyhash_final3	13.4	17.8	29.7
XXH3_64 0.8.0	17.5	21.1	29.0
XXH64 0.8.0	12.7	17.3	17.3
prvhash64m 4.1	19.9	26.1	4.1

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

Hash function	0-15b, cycles/h	8-28b, cycles/h	bulk, GB/s
komihash 4.5	11.1	12.7	26.3
komihash 4.3	11.2	13.0	25.9
komihash 3.6	11.0	16.3	27.5
komihash 2.8	11.1	17.7	27.8
wyhash_final3	13.4	17.7	29.8
XXH3_64 0.8.0	17.7	21.3	61.0
XXH64 0.8.0	12.8	17.4	17.1
prvhash64m 4.1	20.0	26.2	4.1

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

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

Hash function	0-15b, cycles/h	8-28b, cycles/h	bulk, GB/s
komihash 4.5	18.1	21.9	16.4
komihash 4.3	17.9	21.6	16.3
komihash 3.6	20.1	24.0	16.3
komihash 2.8	21.3	25.6	16.2
wyhash_final3	24.1	32.0	12.6
XXH3_64 0.8.0	21.8	27.2	29.6
XXH64 0.8.0	24.3	36.6	8.9
prvhash64m 4.1	29.9	39.1	3.2

(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)

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.

Hash function	0-15b, cycles/h	8-28b, cycles/h	bulk, GB/s
komihash 4.5	12.8	14.4	22.4
komihash 4.3	15.3	16.3	22.8
komihash 3.6	16.0	19.0	22.3
komihash 2.8	18.1	22.3	23.5
wyhash_final3	14.0	18.7	28.4
XXH3_64 0.8.0	18.0	29.3	51.0
XXH64 0.8.0	12.5	16.4	18.2
prvhash64m 4.1	27.0	29.9	4.3

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

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

Hash function	0-15b, cycles/h	8-28b, cycles/h	bulk, GB/s
komihash 4.5	13.2	15.1	24.7
komihash 4.3	15.4	16.2	24.4
komihash 3.6	16.4	20.3	24.7
komihash 2.8	18.5	22.4	24.7
wyhash_final3	14.9	19.5	29.8
XXH3_64 0.8.0	16.9	22.3	26.6
XXH64 0.8.0	13.7	17.7	18.0
prvhash64m 4.1	23.2	27.8	4.3

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

Hash function	0-15b, cycles/h	8-28b, cycles/h	bulk, GB/s
komihash 4.5	13.8	15.2	24.7
komihash 4.3	15.3	16.4	24.4
komihash 3.6	15.8	20.1	24.7
komihash 2.8	16.6	21.2	24.7
wyhash_final3	15.4	19.0	30.1
XXH3_64 0.8.0	18.8	23.4	38.0
XXH64 0.8.0	15.3	17.9	18.1
prvhash64m 4.1	21.7	27.1	4.4

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.

Hash function	0-15b, cycles/h	8-28b, cycles/h	bulk, GB/s
komihash 4.5	12.6	14.5	22.2
komihash 4.3	14.1	16.0	22.0
komihash 3.6	14.0	22.0	22.9
komihash 2.8	13.4	22.7	23.7
wyhash_final3	14.5	20.1	30.0
XXH3_64 0.8.0	18.4	23.0	48.3
XXH64 0.8.0	13.2	17.3	17.7
prvhash64m 4.1	23.2	29.6	4.1

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

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

Hash function	0-15b, cycles/h	8-28b, cycles/h	bulk, GB/s
komihash 4.5	18.1	21.1	17.2
komihash 4.3	18.7	21.5	18.5
komihash 3.6	19.5	23.1	18.1
komihash 2.8	20.1	23.6	18.4
wyhash_final3	19.2	24.5	20.0
XXH3_64 0.8.0	19.9	25.8	28.0
XXH64 0.8.0	18.8	24.7	16.0
prvhash64m 4.1	25.5	32.4	3.2

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

Compiler options: -O3; overhead: unestimatable.

Hash function	0-15b, cycles/h	8-28b, cycles/h	bulk, GB/s
komihash 4.5	8.3	8.7	23.6
komihash 4.3	8.6	9.0	23.6
komihash 3.6	8.5	10.7	23.6
komihash 2.8	10.1	11.4	23.5
wyhash_final3	7.9	8.0	26.1
XXH3_64 0.8.0	8.2	8.2	30.5
XXH64 0.8.0	8.8	10.4	14.5
prvhash64m 4.1	12.9	16.8	3.5

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)

Hash function	0-15b, cycles/h	8-28b, cycles/h
komihash 4.5	9.5	11.4
komihash 4.3	10.4	12.1
komihash 3.6	10.9	15.4
komihash 2.8	11.8	16.7
wyhash_final3	11.4	15.9
XXH3_64 0.8.0	13.7	18.6
XXH64 0.8.0	10.9	15.8
prvhash64m 4.1	18.8	24.6

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 strings (messages) 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.

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.

Test Vectors

Test vectors for the current version of komihash, string-hash pairs (note that the parentheses are not included in the calculation). The bulk is a buffer with increasing 8-bit values; bulk hashes are calculated from this buffer using various lengths. See the testvec.c file for details.

	komihash UseSeed = 0x0000000000000000:
	"This is a 32-byte tester string." = 0x8e92e061278366d2
	"The cat is out of the bag" = 0xd15723521d3c37b1
	"A 16-byte string" = 0x467caa28ea3da7a6
	"The new string" = 0xf18e67bc90c43233
	"7 bytes" = 0xe72e558f5eaf2554
	bulk(6) = 0xa56469564c2ea0ff
	bulk(12) = 0x64c2ad96013f70fe
	bulk(20) = 0x7a3888bc95545364
	bulk(31) = 0xc77e02ed4b201b9a
	bulk(32) = 0x256d74350303a1ba
	bulk(40) = 0x59609c71697bb9df
	bulk(47) = 0x36eb9e6a4c2c5e4b
	bulk(48) = 0x8dd56c332850baa6
	bulk(56) = 0xcbb722192b353999
	bulk(64) = 0x5cf87bcba93e6a5b
	bulk(72) = 0x6c79a1d9474f003f
	bulk(80) = 0x88684fa67b351c33
	bulk(112) = 0xdc481a2af36a87dd
	bulk(132) = 0xe172275e13a1c938
	bulk(256) = 0xa9d9cde10342d965

	komihash UseSeed = 0x0123456789abcdef:
	"This is a 32-byte tester string." = 0x6455c9cfdd577ebd
	"The cat is out of the bag" = 0x5b1da0b43545d196
	"A 16-byte string" = 0x26af914213d0c915
	"The new string" = 0x62d9ca1b73250cb5
	"7 bytes" = 0x2bf17dbb71d92897
	bulk(6) = 0xaceebc32a3c0d9e4
	bulk(12) = 0xec8eb3ef4af380b4
	bulk(20) = 0x07045bd31abba34c
	bulk(31) = 0xd5f619fb2e62c4ae
	bulk(32) = 0x5a336fd2c4c39abe
	bulk(40) = 0x0e870b4623eea8ec
	bulk(47) = 0xe552edd6bf419d1d
	bulk(48) = 0x37d170ddcb1223e6
	bulk(56) = 0x1cd89e708e5098b6
	bulk(64) = 0x4da1005904c8d804
	bulk(72) = 0xc8b03f196b2551ee
	bulk(80) = 0x2d4d58743755344d
	bulk(112) = 0x0e77e5c92f929bdd
	bulk(132) = 0x0b3b216a1fc3234e
	bulk(256) = 0xeb726377f8d072e8

	komihash UseSeed = 0x0000000000000100:
	"This is a 32-byte tester string." = 0x60ed46218532462a
	"The cat is out of the bag" = 0xa761280322bb7698
	"A 16-byte string" = 0x11c31ccabaa524f1
	"The new string" = 0x3a43b7f58281c229
	"7 bytes" = 0x3c8a980831b70dc8
	bulk(6) = 0xea606e43d1976ccf
	bulk(12) = 0xacbec1886cd23275
	bulk(20) = 0x57c3affd1b71fcdb
	bulk(31) = 0x7ef6ba49a3b068c3
	bulk(32) = 0x49dbca62ed5a1ddf
	bulk(40) = 0x192848484481e8c0
	bulk(47) = 0x420b43a5edba1bd7
	bulk(48) = 0xd6e8400a9de24ce3
	bulk(56) = 0xbea291b225ff384d
	bulk(64) = 0xf237bc1d85f12b52
	bulk(72) = 0x577a4d993f26cd52
	bulk(80) = 0xace499103def982d
	bulk(112) = 0x200c46677408d850
	bulk(132) = 0x6b003f62eba47761
	bulk(256) = 0xa8a3bd0ecf908b92

	komirand Seed1/Seed2 = 0x0000000000000000:
	0xaaaaaaaaaaaaaaaa
	0xfffffffffffffffe
	0x4924924924924910
	0xbaebaebaebaeba00
	0x400c62cc4727496b
	0x35a969173e8f925b
	0xdb47f6bae9a247ad
	0x98e0f6cece6711fe
	0x97ffa2397fda534b
	0x11834262360df918
	0x34e53df5399f2252
	0xecaeb74a81d648ed

	komirand Seed1/Seed2 = 0x0123456789abcdef:
	0x776ad9718078ca64
	0x737aa5d5221633d0
	0x685046cca30f6f44
	0xfb725cb01b30c1ba
	0xc501cc999ede619f
	0x8427298e525db507
	0xd9baf3c54781f75e
	0x7f5a4e5b97b37c7b
	0xde8a0afe8e03b8c1
	0xb6ed3e72b69fc3d6
	0xa68727902f7628d0
	0x44162b63af484587

	komirand Seed1/Seed2 = 0x0000000000000100:
	0xaaaaaaaaaaababaa
	0xfffffffff8fcf8fe
	0xdb6dba1e4dbb1134
	0xf5b7d3aec37f4cb1
	0x66a571da7ded7051
	0x2d59ec9245bf03d9
	0x5c06a41bd510aed8
	0xea5e7ea9d2bd07a2
	0xe395015ddce7756f
	0xc07981aaeaae3b38
	0x2e120ebfee59a5a2
	0x9001eee495244dba