What is the fastest hash function for pointers?
Solution 1
After letting this question lay for a while, I'll post my best hash function for pointers so far:
template<typename Tval>
struct MyTemplatePointerHash1 {
size_t operator()(const Tval* val) const {
static const size_t shift = (size_t)log2(1 + sizeof(Tval));
return (size_t)(val) >> shift;
}
};
It's high performing for various block sizes.
If someone has a better function, I'll change the accepted answer.
Solution 2
The correct answer from a theoretical point of view is: "Use std::hash which is likely specialized to be as good as it gets, and if that is not applicable, use a good hash function rather than a fast one. The speed of the hash function does not matter so much as its quality".
The practical answer is: "Use std::hash, which is piss-poor, but nevertheless performs surprisingly well."
TL;DR
After having become intrigued, I ran about 30 hours of benchmarks over the weekend. Among other things, I tried to get an average case vs. worst case and tried to coerce std::unordered_map into worst-case behavior by giving it deliberately bad hints on bucket counts in respect of the set size inserted.
I compared poor hashes (std::hash<T*>) to well-known general purpose hashes of overall good quality (djb2, sdbm) as well as variations of these that account for the very short input length, and to hashes which are explicitly thought to be used in hashtables (murmur2 and murmur3), and piss-poor hashes that are actually worse than not hashing at all since they throw away entropy.
Since the lowest 2-3 bits are always zero on pointers due to alignment, I deemed it worthwhile to test a simple right-shift as "hash", so only the non-zero information would be used, in case the hashtable e.g. used only the lowermost N bits. Turned out that for reasonable shifts (I also tried unreasonable shifts!) this actually performs quite well.
Findings
Some of my findings were well-known and unsurprising, others are very surprising:
- It is hard to predict what is a "good" hash. Writing good hash functions is hard. Not surprising, well-known fact, and once again proven.
- No single hash significantly outperforms all others in every scenario. No single hash even significantly outperforms all others 80% of the time. The first result was expected, the second is nevertheless surprising.
- It is really hard to press
std::unordered_mapinto behaving badly. Even when given deliberately bad hints to bucket counts which will force several re-hashes, the overall performance is not much worse. Only the very worst hash functions that throw away most of the entropy in an almost ridiculous way are able to significantly impact performance by more than 10-20% (such asright_shift_12, which practically results in only 12 distinct hash values for 50,000 inputs! It is not surprising that the hash map runs around 100 times slower in this case -- we're basically doing random access lookup on a linked list.). - Some "funny" results are surely due to implementation details. My implementation (GCC) uses a slighly-larger-than-2^N prime bucket count, and inserts values with indentical hashes head-first into linked lists.
- The specialization of
std::hash<T*>is outright pathetic for GCC (a simplereinterpret_cast). Funnily, a functor which does the identical thing consistently performs faster at insertions and slower at random access. The difference is small (a dozen milliseconds on a 8-10 second test run), but it is not noise, it's consistenly present -- probably related to instruction reordering or pipelining. It's stunning how the exact same code (which is also a no-op) consistenly performs differently in two different scenarios. - Pathetic hashes do not perform significantly worse than "good" hashes or hashes explicitly designed for hash tables. Indeed, half of the time, they are the best performers, or among the top 3.
- The "best" hash functions rarely if ever result in the best overall performance.
- The hashes posted as answers in this SO question are generally OK. They are good average, but not superior to
std::hash. Usually they'll land in the top 3-4. - Poor hashes are somewhat vulnerable to the order of insertion (performing worse on random insertion and random lookup following random insertion) whereas "good" hashes are more resilient to the impact of the order of insertion (little or no difference), but overall performance is still slightly slower.
Test Setup
Test were done not just any 4-byte or 8-byte (or whatever) aligned values, but for actual addresses obtained from allocating the complete set of elements on the heap, and storing the addresses as provided by the allocator in a std::vector (the objects were then deleted, they're not needed).
Addresses were inserted into a newly allocated std::unordered_map for every test in the order stored in the vector, once in the original order ("sequential") and once after applying a std::random_shuffle on the vector.
Tests were performed for sets of 50,000 and 1,000,000 objects of size 4, 16, 64, 256, and 1024 (results for 64 omitted here for brevity, they're as you'd expect somewhere in the middle between 16 and 256 -- StackOverflow only allows 30k characters being posted).
Test suite was performed 3 times, results varying by 3 or 4 milliseconds here and there, but overall identical. The results posted here are the last run.
The order of insertions in the "random" test as well as the access pattern (in every test) is pseudorandom, but exactly identical for every hash function in a test run.
The timings under hash benchmarks are for summing up 4,000,000,000 hash values in an integer variable.
The column insert is the time in milliseconds for 50 iterations of creating a std::unordered_map, inserting 50,000 and 1,000,000 elements respectively, and destroying the map.
The column access is the time in milliseconds to do 100,000,000 lookups of a pseudorandom element in the 'vector' followed by looking up that address in the unordered_map.
This timing includes on the average one cache misse for accessing a random element in the vector, at least for the large dataset (small dataset fits completely into L2).
All timings on a 2.66GHz Intel Core2, Windows 7, gcc 4.8.1/MinGW-w64_32. Timer granularity @ 1ms.
Source Code
Source code is available on Ideone, again because of Stackoverflow's 30k character limit.
Note: Running the complete test suite takes well over 2 hours on a desktop PC, so be prepared to take a walk if you want to reproduce the results.
Test Results
Benchmarking hash funcs...
std::hash 2576
reinterpret_cast 2561
djb2 13970
djb2_mod 13969
sdbm 10246
yet_another_lc 13966
murmur2 11373
murmur3 15129
simple_xorshift 7829
double_xorshift 13567
right_shift_2 5806
right_shift_3 5866
right_shift_4 5705
right_shift_5 5691
right_shift_8 5795
right_shift_12 5728
MyTemplatePointerHash1 5652
BasileStarynkevitch 4315
--------------------------------
sizeof(T) = 4
sizeof(T*) = 4
insertion order = sequential
dataset size = 50000 elements
name insert access
std::hash 421 6988
reinterpret_cast 408 7083
djb2 451 8875
djb2_mod 450 8815
sdbm 455 8673
yet_another_lc 443 8292
murmur2 478 9006
murmur3 490 9213
simple_xorshift 460 8591
double_xorshift 477 8839
right_shift_2 416 7144
right_shift_3 422 7145
right_shift_4 414 6811
right_shift_5 425 8006
right_shift_8 540 11787
right_shift_12 1501 49604
MyTemplatePointerHash1 410 7138
BasileStarynkevitch 445 8014
--------------------------------
sizeof(T) = 4
sizeof(T*) = 4
insertion order = random
dataset size = 50000 elements
name insert access
std::hash 443 7570
reinterpret_cast 436 7658
djb2 473 8791
djb2_mod 472 8766
sdbm 472 8817
yet_another_lc 458 8419
murmur2 479 9005
murmur3 491 9205
simple_xorshift 464 8591
double_xorshift 476 8821
right_shift_2 441 7724
right_shift_3 440 7716
right_shift_4 450 8061
right_shift_5 463 8653
right_shift_8 649 16320
right_shift_12 3052 114185
MyTemplatePointerHash1 438 7718
BasileStarynkevitch 453 8140
--------------------------------
sizeof(T) = 4
sizeof(T*) = 4
insertion order = sequential
dataset size = 1000000 elements
name insert access
std::hash 8945 32801
reinterpret_cast 8796 33251
djb2 11139 54855
djb2_mod 11041 54831
sdbm 11459 36849
yet_another_lc 14258 57350
murmur2 16300 39024
murmur3 16572 39221
simple_xorshift 14930 38509
double_xorshift 16192 38762
right_shift_2 8843 33325
right_shift_3 8791 32979
right_shift_4 8818 32510
right_shift_5 8775 30436
right_shift_8 10505 35960
right_shift_12 30481 91350
MyTemplatePointerHash1 8800 33287
BasileStarynkevitch 12885 37829
--------------------------------
sizeof(T) = 4
sizeof(T*) = 4
insertion order = random
dataset size = 1000000 elements
name insert access
std::hash 12183 33424
reinterpret_cast 12125 34000
djb2 22693 51255
djb2_mod 22722 51266
sdbm 15160 37221
yet_another_lc 24125 51850
murmur2 16273 39020
murmur3 16587 39270
simple_xorshift 16031 38628
double_xorshift 16233 38757
right_shift_2 11181 33896
right_shift_3 10785 33660
right_shift_4 10615 33204
right_shift_5 10357 38216
right_shift_8 15445 100348
right_shift_12 73773 1044919
MyTemplatePointerHash1 11091 33883
BasileStarynkevitch 15701 38092
--------------------------------
sizeof(T) = 64
sizeof(T*) = 4
insertion order = sequential
dataset size = 50000 elements
name insert access
std::hash 415 8243
reinterpret_cast 422 8321
djb2 445 8730
djb2_mod 449 8696
sdbm 460 9439
yet_another_lc 455 9003
murmur2 475 9109
murmur3 482 9313
simple_xorshift 463 8694
double_xorshift 465 8900
right_shift_2 416 8402
right_shift_3 418 8405
right_shift_4 423 8366
right_shift_5 421 8347
right_shift_8 453 9195
right_shift_12 666 18008
MyTemplatePointerHash1 433 8191
BasileStarynkevitch 466 8443
--------------------------------
sizeof(T) = 64
sizeof(T*) = 4
insertion order = random
dataset size = 50000 elements
name insert access
std::hash 450 8135
reinterpret_cast 457 8208
djb2 470 8736
djb2_mod 476 8698
sdbm 483 9420
yet_another_lc 476 8953
murmur2 481 9089
murmur3 486 9283
simple_xorshift 466 8663
double_xorshift 468 8865
right_shift_2 456 8301
right_shift_3 456 8302
right_shift_4 453 8337
right_shift_5 457 8340
right_shift_8 505 10379
right_shift_12 1099 34923
MyTemplatePointerHash1 464 8226
BasileStarynkevitch 466 8372
--------------------------------
sizeof(T) = 64
sizeof(T*) = 4
insertion order = sequential
dataset size = 1000000 elements
name insert access
std::hash 9548 35362
reinterpret_cast 9635 35869
djb2 10668 37339
djb2_mod 10763 37311
sdbm 11126 37145
yet_another_lc 11597 39944
murmur2 16296 39029
murmur3 16432 39280
simple_xorshift 16066 38645
double_xorshift 16108 38778
right_shift_2 8966 35953
right_shift_3 8916 35949
right_shift_4 8973 35504
right_shift_5 8941 34997
right_shift_8 9356 31233
right_shift_12 13831 45799
MyTemplatePointerHash1 8839 31798
BasileStarynkevitch 15349 38223
--------------------------------
sizeof(T) = 64
sizeof(T*) = 4
insertion order = random
dataset size = 1000000 elements
name insert access
std::hash 14756 36237
reinterpret_cast 14763 36918
djb2 15406 38771
djb2_mod 15551 38765
sdbm 14886 37078
yet_another_lc 15700 40290
murmur2 16309 39024
murmur3 16432 39381
simple_xorshift 16177 38625
double_xorshift 16073 38750
right_shift_2 14732 36961
right_shift_3 14170 36965
right_shift_4 13687 37295
right_shift_5 11978 35135
right_shift_8 11498 46930
right_shift_12 25845 268052
MyTemplatePointerHash1 10150 32046
BasileStarynkevitch 15981 38143
--------------------------------
sizeof(T) = 256
sizeof(T*) = 4
insertion order = sequential
dataset size = 50000 elements
name insert access
std::hash 432 7957
reinterpret_cast 429 8036
djb2 462 8970
djb2_mod 453 8884
sdbm 460 9110
yet_another_lc 466 9015
murmur2 495 9147
murmur3 494 9300
simple_xorshift 479 8792
double_xorshift 477 8948
right_shift_2 430 8120
right_shift_3 429 8132
right_shift_4 432 8196
right_shift_5 437 8324
right_shift_8 425 8050
right_shift_12 519 11291
MyTemplatePointerHash1 425 8069
BasileStarynkevitch 468 8496
--------------------------------
sizeof(T) = 256
sizeof(T*) = 4
insertion order = random
dataset size = 50000 elements
name insert access
std::hash 462 7956
reinterpret_cast 456 8046
djb2 490 9002
djb2_mod 483 8905
sdbm 482 9116
yet_another_lc 492 8982
murmur2 492 9120
murmur3 492 9276
simple_xorshift 477 8761
double_xorshift 477 8903
right_shift_2 458 8116
right_shift_3 459 8124
right_shift_4 462 8281
right_shift_5 463 8370
right_shift_8 458 8069
right_shift_12 662 16244
MyTemplatePointerHash1 459 8091
BasileStarynkevitch 472 8476
--------------------------------
sizeof(T) = 256
sizeof(T*) = 4
insertion order = sequential
dataset size = 1000000 elements
name insert access
std::hash 9756 34368
reinterpret_cast 9718 34897
djb2 10935 36894
djb2_mod 10820 36788
sdbm 11084 37857
yet_another_lc 11125 37996
murmur2 16522 39078
murmur3 16461 39314
simple_xorshift 15982 38722
double_xorshift 16151 38868
right_shift_2 9611 34997
right_shift_3 9571 35006
right_shift_4 9135 34750
right_shift_5 8978 32878
right_shift_8 8688 30276
right_shift_12 10591 35827
MyTemplatePointerHash1 8721 30265
BasileStarynkevitch 15524 38315
--------------------------------
sizeof(T) = 256
sizeof(T*) = 4
insertion order = random
dataset size = 1000000 elements
name insert access
std::hash 14169 36078
reinterpret_cast 14096 36637
djb2 15373 37492
djb2_mod 15279 37438
sdbm 15531 38247
yet_another_lc 15924 38779
murmur2 16524 39109
murmur3 16422 39280
simple_xorshift 16119 38735
double_xorshift 16136 38875
right_shift_2 14319 36692
right_shift_3 14311 36776
right_shift_4 13932 35682
right_shift_5 12736 34530
right_shift_8 9221 30663
right_shift_12 15506 98465
MyTemplatePointerHash1 9268 30697
BasileStarynkevitch 15952 38349
--------------------------------
sizeof(T) = 1024
sizeof(T*) = 4
insertion order = sequential
dataset size = 50000 elements
name insert access
std::hash 421 7863
reinterpret_cast 419 7953
djb2 457 8983
djb2_mod 455 8927
sdbm 445 8609
yet_another_lc 446 8892
murmur2 492 9090
murmur3 507 9294
simple_xorshift 467 8687
double_xorshift 472 8872
right_shift_2 432 8009
right_shift_3 432 8014
right_shift_4 435 7998
right_shift_5 442 8099
right_shift_8 432 7914
right_shift_12 462 8911
MyTemplatePointerHash1 426 7744
BasileStarynkevitch 467 8417
--------------------------------
sizeof(T) = 1024
sizeof(T*) = 4
insertion order = random
dataset size = 50000 elements
name insert access
std::hash 452 7948
reinterpret_cast 456 8018
djb2 489 9037
djb2_mod 490 8992
sdbm 477 8795
yet_another_lc 491 9179
murmur2 502 9078
murmur3 507 9273
simple_xorshift 473 8671
double_xorshift 480 8873
right_shift_2 470 8105
right_shift_3 470 8100
right_shift_4 476 8333
right_shift_5 468 8065
right_shift_8 469 8094
right_shift_12 524 10216
MyTemplatePointerHash1 451 7826
BasileStarynkevitch 472 8419
--------------------------------
sizeof(T) = 1024
sizeof(T*) = 4
insertion order = sequential
dataset size = 1000000 elements
name insert access
std::hash 10910 38432
reinterpret_cast 10892 38994
djb2 10499 38985
djb2_mod 10507 38983
sdbm 11318 37450
yet_another_lc 11740 38260
murmur2 16960 39544
murmur3 16816 39647
simple_xorshift 16096 39021
double_xorshift 16419 39183
right_shift_2 10219 38909
right_shift_3 10012 39036
right_shift_4 10642 40284
right_shift_5 10116 38678
right_shift_8 9083 32914
right_shift_12 9376 31586
MyTemplatePointerHash1 8777 30129
BasileStarynkevitch 16036 38913
--------------------------------
sizeof(T) = 1024
sizeof(T*) = 4
insertion order = random
dataset size = 1000000 elements
name insert access
std::hash 16304 38695
reinterpret_cast 16241 39641
djb2 16377 39533
djb2_mod 16428 39526
sdbm 15402 37811
yet_another_lc 16180 38730
murmur2 16679 39355
murmur3 16792 39586
simple_xorshift 16196 38965
double_xorshift 16371 39127
right_shift_2 16445 39263
right_shift_3 16598 39421
right_shift_4 16378 39839
right_shift_5 15517 38442
right_shift_8 11589 33547
right_shift_12 11992 49041
MyTemplatePointerHash1 9052 30222
BasileStarynkevitch 16163 38829
Solution 3
The result returned by the hash function has type size_t, but it gets converted into a 'bucket index' by the container, identifying the correct bucket to locate the object.
I think this conversion is not specified in the standard : but I'd expect this is usually a Modulo N operation, where N is the number of buckets - and that N is typically a power of two, as doubling the bucket count is a good way of increasing the size when there's too many hits. The Modulo N operation would mean that - for pointers - the naive hash function only uses a fraction of the buckets.
The real problem is that a 'good' hash algorithm for containers has to be based on a knowledge of the bucket size, and the values you're hashing. For example, if the objects you were storing in the table were all of size 1024 bytes, it's possible that the low-order 10 bits of each pointer could be the same.
struct MyOneKStruct x[100]; //bottom 10 bits of &x[n] are always the same
So, a 'best' hash for any application is likely to require a lot of trial and error and measurement, and knowledge of the distribution of the values that you're hashing.
However, rather than simply shifting the pointer down N bits, I would try something like XORing the top 'word' into the bottom one. Much like @BasileStarynkevich's answer.
The proposal about adding hash tables makes interesting reading. My emphasis in the para below: http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2003/n1456.html
It is impossible to write a fully general hash function that's valid for all types. (You can't just convert an object to raw memory and hash the bytes; among other reasons, that idea fails because of padding.) Because of that, and also because a good hash function is only good in the context of a specific usage pattern, it's essential to allow users to provide their own hash functions.
Solution 4
Obviously the answer is system and processor dependent (in particular, because of the page size and of the word size). I am proposing
struct MyVoidPointerHash {
size_t operator()(const void* val) const {
uintptr_t ad = (uintptr_t) val;
return (size_t) ((13*ad) ^ (ad >> 15));
}
};
The insight is that on many systems the page size is often 4Kbytes (i.e. 212) so the right shift >>15 will put significant address parts in the lower bits. The 13* is mostly for fun (but 13 is prime) and to shuffle more the bits. The exclusive or ^ is mixing bits and is really fast. So the lower bits of the hash is a mixture of many bits (both high and low) of the pointer.
I don't claim having put a lot of "science" in such hash functions. But they happen to often work quite well. YMMV. I would guess that you should avoid deactivating ASLR !
Solution 5
Can't beat your solution on performance racetrack (neither for char, nor for 1024-sized struct), but in sense of correctness there are some improvements:
#include <iostream>
#include <new>
#include <algorithm>
#include <unordered_set>
#include <chrono>
#include <cstdlib>
#include <cstdint>
#include <cstddef>
#include <cmath>
namespace
{
template< std::size_t argument, std::size_t base = 2, bool = (argument < base) >
constexpr std::size_t log = 1 + log< argument / base, base >;
template< std::size_t argument, std::size_t base >
constexpr std::size_t log< argument, base, true > = 0;
}
struct pointer_hash
{
template< typename type >
constexpr
std::size_t
operator () (type * p) const noexcept
{
return static_cast< std::size_t >(reinterpret_cast< std::uintptr_t >(p) >> log< std::max(sizeof(type), alignof(type)) >);
}
};
template< typename type = std::max_align_t, std::size_t i = 0 >
struct alignas(alignof(type) << i) S
{
};
int
main()
{
constexpr std::size_t _16M = (1 << 24);
S<> * p = new S<>[_16M]{};
auto latch = std::chrono::high_resolution_clock::now();
{
std::unordered_set< S<> *, pointer_hash > s;
for (auto * pp = p; pp < p + _16M; ++pp) {
s.insert(pp);
}
}
std::cout << std::chrono::duration_cast< std::chrono::milliseconds >(std::chrono::high_resolution_clock::now() - latch).count() << "ms" << std::endl;
delete [] p;
return EXIT_SUCCESS;
}
egur
Author of Intel QuickSync Decoder. Skills: Intel processor expert Expert overclocker Veteran C++ developer SW architect Video processing algorithm inventor Employed by Intel Corp. Currently enabling & supporting OEMs that use Intel processors. Tech lead in Overclocking and own Intel Software Guard Extensions (Intel® SGX) OEM enabling.
Updated on April 21, 2020Comments
-
egur about 4 years
Hash table based containers are very fast associative array (e.g.
unordered_map,unordered_set).Their performance is highly dependent on that hash function used to create an index for each entry. As hash tables grow, elements are rehashed again and again.
Pointers are simple type, basically a 4/8 byte value that uniquely identify an object. The problem is that using an address as a result of the hash function is not efficient due to several LSB being zero.
Example:
struct MyVoidPointerHash { size_t operator()(const void* val) const { return (size_t)val; } };A faster implementation is to lose a few bits:
struct MyVoidPointerHash2 { size_t operator()(const void* val) const { return ((size_t)val) >> 3; // 3 on 64 bit, 1 on 32 bit } };The latter produced 10-20% performance increase on a large application that uses hash sets and maps with tens of thousands of elements that are frequently built and cleared.
Can someone offer a better scheme for hashing pointers?
The function needs to be:
- Fast! and must inline well.
- Offer a reasonable distribution, rare collisions are allowed.
Update - benchmark results
I ran two sets of tests, one for
int*and for a class pointer that has a size of 4KB. The results are very interesting.I used
std::unordered_setfor all test with data size being 16MB that was allocated in a singlenewcall. The first algorithm ran twice to make sure sure caches are as hot as possible and the CPU is running at full speed.Setup: VS2013 (x64), i7-2600, Windows 8.1 x64.
- VS2013 default hash function
- Hash1:
return (size_t)(val); - Hash2:
return '(size_t)(val) >> 3; - Hash3(@BasileStarynkevitch):
uintptr_t ad = (uintptr_t)val; return (size_t)((13 * ad) ^ (ad >> 15)); - Hash4(@Roddy):
uintptr_t ad = (uintptr_t)val; return (size_t)(ad ^ (ad >> 16)); - Hash5(@egur):
Code:
template<typename Tval> struct MyTemplatePointerHash1 { size_t operator()(const Tval* val) const { static const size_t shift = (size_t)log2(1 + sizeof(Tval)); return (size_t)(val) >> shift; } };Test 1 -
int*:- VS2013 default took 1292ms
- Hash1 took 742ms
- Hash2 took 343ms
- Hash3 took 1008ms
- Hash4 took 629ms
- Hash5 took 350ms
Test 1 -
4K_class*:- VS2013 default took 0.423ms
- Hash1 took 23.889ms
- Hash2 took 6.331ms
- Hash3 took 0.366ms
- Hash4 took 0.390ms
- Hash5 took 0.290ms
Update2:
Winner so far is the templated hash (Hash5) function. Best level of performance for speed for various block sizes.
Update 3: Added default hash function for baseline. Turns out it's far from optimal.