Another slightly fancier than the usual textbook approaches is cuckoo hashing. Has anyone done a comparison with cuckoo vs. robinhood?
If, however, both accesses are expected to incur TLB misses, you're very likely screwed: handling the misses takes a lot of resources and the vast majority of (commodity) CPUs can only handle one TLB miss at a time. After hashing, the time for lookups is now dominated by two TLB misses; compare to one TLB miss with linear probing. You can also play the odds and only do the second lookup conditionally; that's still ~1.5 random accesses on average (versus 1).
Cuckoo hashing can get you 95-99% occupancy versus 80-90% with simpler schemes. Unless you have specialised size or cost requirements, it seems to me the extra 10-20% space usage is a better choice than double the random accesses.
Separately, aren't TLB misses pretty fast compared to hitting RAM? I'd think they would only dominate if the TLB itself it too large for cache, which I don't think is common. And if you are using so much memory that this is happening, moving to GB Hugepages would solve it
The "sensitivity to a bad hash function" seems like an odd weakness. For a given quality of hash, wouldn't cuckoo tend to be less susceptible than any single hash approach?
I ask because I'm currently bullish on d-ary cuckoo hashes, and think they'd be a good fit for the fast gather on Skylake.
Why would TLB misses be small compared to RAM latency? A TLB miss must be serviced by reading more memory, and misses aren't handled in parallel, unlike random reads to RAM. Sure, you could use very large (1G) pages, but that's a pretty specialised setup that's not available on every platform and tends to require a reboot to enable/tweak. Not something we want to rely on in general.
Cuckoo is particularly sensitive to bad hash functions: if a few elements always hash to the same pair of values, you're screwed. That's particularly problematic with the usual interfaces that don't let the hash table specify a seed to the hash function and expect a machine word: we have to map values to hashes, and remix or split the hashes (in theory, that's defensible as long as the intermediate hash is strong and its codomain is at least (hash set size)^2), but there's nothing to remix away if we have too many values that map to the same intermediate hash. If the hash table specifies calls the hash function with two different seeds, that means double the time spent in hashing, and that overhead can cover for a lot of linear probing.
Simple deterministic probing technique just take a hit with a bigger cluster than expected; a performance degradation, but the table still work. You can also see theoretical analyses that'll lead you to similar conclusions if you look at the k-independence needed for each hashing technique.
Finally, I don't think gathers are faster than independent memory accesses unless everything is in the same cache line. You don't need SIMD instructions to expose memory level parallelism, you just need independent dependency graphs in your serial computation (until you're bottlenecked on an execution resource that's not duplicated and rarely pipelined, like the TLB miss logic).
Thanks, I was misreading.
Why would TLB misses be small compared to RAM latency?
Because for recent CPU's (post-P5 for Intel) the page walks to service a TLB miss use the standard data caching mechanisms, thus for a frequently used hash table that is reading only a couple cachelines per lookup, the page tables usually remain in cache: http://electronics.stackexchange.com/a/67985.
So while the TLB miss requires a lookup, this lookup frequently doesn't require hitting RAM. My recollection is that this means a TLB miss usually costs only the relevant cache miss plus ~10 cycles. But this does require certain assumptions about the access pattern, and I've been meaning to retest this on recent hardware to be sure.
misses aren't handled in parallel
Based on your earlier phrasing you probably realize, but in case others don't, since Broadwell Intel CPU's do handle two page walks in parallel: http://www.anandtech.com/show/8355/intel-broadwell-architect....
Cuckoo is particularly sensitive to bad hash functions: if a few elements always hash to the same pair of values, you're screwed.
Yes, although if you can choose a good hash function this should be rare. And there are variations of cuckoo hashes that are much less susceptible to this. The first either increases the number of hashes (d-ary), and the second adds multiple "bins" as described by 'cmurphycode' in another comment. Then you can add a "failsafe" by adding a "stash" of last resort: https://www.eecs.harvard.edu/~michaelm/postscripts/esa2008fu...
If the hash table specifies calls the hash function with two different seeds, that means double the time spent in hashing, and that overhead can cover for a lot of linear probing.
If you can choose your own hash function, the hashing cost should be minimal even for a "perfect" hash. And a SIMD approach usually means that you can create 2, 4, or 8 hashes using different seeds in exactly the same time that you can create a single hash: http://xoroshiro.di.unimi.it/xoroshiro128plus.c
Finally, I don't think gathers are faster than independent memory accesses unless everything is in the same cache line.
They weren't any faster until Skylake, but they are significantly faster now: https://github.com/lemire/dictionary
Don't people usually use buckets with cuckoo hashing, so that each location houses 2 or more values (one right after the other)? I guess I'm not seeing how that's fundamentally different from linear probing...
The cuckoo hashing is just a collision resolution technique used in open addressing hashing schemes. Having two possible hashes of a key always next to each other (that is what you suggest by using buckets if I understand correctly) would cause the cuckoo algorithm for kicking out the conflicting items to stop working.
If both possible locations for a key are always in the same bucket, the two keys with a colliding hash would also share the alternative hash (i.e. it would be the other place in the same bucket). And so, they would only be able to kick each other out. A loop of length 2. Always. If three keys hash into the same bucket, you will have to rehash the entire table.
You can have larger buckets, but the problem remains. Once a big enough number of keys hash into the same bucket, you will have to rehash the table. That would most probably mean low typical load factors.
Of course, what you will be getting in return is the locality of memory references. But is that a reasonable trade-off? I think there are better ways to achieve locality of memory references...
It works like this. A typical sizing is 4 slots in a bucket, with 2 bucket choices. So your first choice, you arrive at a bucket, and it is just a linear array of length 4. You can put your element anywhere! After a while, when you go to insert into your first choice and you find all 4 slots taken, then you can take ANY of those and try to put it in its alternate bucket. If that alternate bucket is full, you evict from that bucket, too! Thanks to the random nature of your hash functions, it works out very well. 2 bucket 4 slot gets you near 95% occupancy without many evictions on insert.
When you go to lookup, you check your first bucket, and you check all 4 elements until you find it. If you don't find it, you go to your alternate bucket and check all 4 elements. But that's it - only two random accesses (the 4 slots will easily fit in a cache line). It's not so bad to check all 4 elements because the cost is really dominated by loading the line to begin with.
I really recommend a read of some of the cuckoo papers, it's cool stuff.
I do not know what exactly the commenter meant by suggesting to use buckets. I assumed (as the conversation is predominantly about the locality of memory references) that they suggested to use buckets in order to avoid two (or more) cache misses. And I just pointed out that it would be a bad trade-off, because then the cuckoo algorithm would only operate within a bucket and the expected load factors would be low.
Like 'cmurphycode', I think you might be misinterpreting something about how the buckets would be used. The buckets are in addition to the multiple hashes (which I think some authors call 'ways'). A good number of buckets would those sufficient to fill 1 or 2 cachelines, since these are going to already be fetched from memory as a unit.
The idea is that you fetch the full buckets from 2 (or more) independent hashes, and then sift through them linearly without further memory accesses. The terminology for cuckoo hashes is poor, but I think "buckets", "bins", and "slots" are all synonyms depending on whose description you are using. By "using buckets", the idea is to have (at least) two regions in consecutive memory where the item will be if it exists.
I think this paper offers a reasonable terminology: http://www.cs.princeton.edu/~xl/Publications_files/cuckoo-eu.... They use a "num_hashes, num_buckets" pair to describe variations. The classic version is a "2,1-cuckoo": you create two hashes from the key, and look in one bucket in each location. Li et al. suggest that a "2,4-cuckoo" works allows much easier insertions at high density.
Maybe. How do you know what the commenter (erichocean) meant?
If they say that using "buckets" can mean the same locality of memory references as linear probing, their interpretation of what "buckets" mean must deal with that problem in some way.
Because "bucket" is a well-defined term-of-the-art with regard to cuckoo hashes, because Erich has demonstrated deep knowledge of similar algorithms in the past, because I've been thinking about improving the memory locality of cuckoo hashes for years, and because I would have used approximately the same phrasing as Erich did to describe the memory locality advantages of "buckets".
If they say that using "buckets" can mean the same locality of memory references as linear probing, their interpretation of what "buckets" mean must deal with that problem in some way.
Not only do buckets "deal" with locality, because of the granular nature of cachelines and parallel abilities of memory controllers, searching two compact small regions turns out to be just as searching one region of twice the size. Vectorized linear probing and SIMD cuckoo hashes are so similar that your question very likely indicates that you are not using the same terminology as others are.
Here's paper that offers a good comparison:
Rethinking SIMD Vectorization for In-Memory Databases
Polychroniou, Roghaven, and Ross (2015)
The difference between linear probing and buckets is a big one: buckets are linked lists. That means that hitting a bucket doesn't pull everything else inside the bucket into the CPU cache. So iterating through the bucket may incur a cache miss for every element. On the other hand, linear probing in open addressing does away with buckets and instead searches the neighbors of the collision. Because they're nearby in memory, it's a lot quicker to search.