> When the Hand finds a victim we just replace the Hand slot with the new item, and mark it visited
That would cause newly inserted items to take at least N (size of the cache) rounds to be evicted. Evicting cache entries early is extremely important for performance. Their algorithm means new items will have a higher chance of being evicted, and that is by design, not random chance.
Here's the paper: https://yazhuozhang.com/assets/pdf/nsdi24-sieve.pdf
Recent work [94] shows that “lazy promotion” and “quick demotion” are two important properties of efficient cache eviction algorithms.
[...]
Quick demotion removes most objects quickly after they are inserted. Many previous works have discussed this idea in the context of evicting pages from a scan [16,60,67,70,75,77]. Recent work also shows that not only storage workloads but web cache workloads also benefit from quick demotion [94] because object popularity follows a power-law distribution, and many objects are unpopular.
[...]
[94] Juncheng Yang, Ziyue Qiu, Yazhuo Zhang, Yao Yue, and K. V. Rashmi. FIFO can be better than LRU: the power of lazy promotion and quick demotion. In The 19th Workshop on Hot Topics in Operating Systems (HotOS 23), 2023.
Caching is predicated on locality. We put things into a cache based on the idea that something accessed once is likely to be used again, due to locality.
Lazy promotion is useful in a situation in which we don't trust that the access pattern exhibits locality, nor not fully. Perhaps it exhibits locality for some data, but is widely scattered for others.
For instance, an algorithm is working with numerous local variables in a loop (good locality) but the loop is also stepping through a very large set of data in memory, much larger than the cache. Moreover, items in this set are visited only once (poor/nonexistent locality).
If we regard accesses with a bit of suspicion ("this might not have good locality") we can avoid those latter items from overstaying in the cache. Items in the cache that are not going to be touched again effectively shrink the cache. Like if at any given time about half our cache has such items, the cache is effectively halved.
With a deterministic, fixed distance between the Hand pointer and the Insert point, which we can tune, we could empirically adjust for this. For instance we could have it so that, consistently, every new item that is not visited within 4 subsequent cache misses will be evicted.
If we had a magic oracle, we would not use LRU or any of these other approaches. We would ask the oracle questions "Great Oracle, given these items in the cache, and this new one which is not in the cache, which one(s) will not be seen again, or else which one(s) will be seen again farthest into the future?" That's really what we want to know, but since oracles don't exist, we use heuristics, like the idea that the longer an item goes without being accessed, the more likely it is that it's a never-again-accessed item.
Without my proposal, there is no control over the parameter: the distance is an average, and so about half the cache size. When Hand is on the far right, a new item inserted at that time will stay in the cache long. When the Hand is far left, it may get evicted almost immediately.
The only thing important for performance is a good hit ratio, however it is achieved. An evicted item is one that cannot be hit. Early eviction is not ipso facto good for performance; only with regard to some access patterns where early eviction of the right items improves retention of other items that yield good hits.
You really need to measure, because this will depend on your workload, how fast your implementation is relative to the cost of a miss, what the ratio of "likely to never be requested again" to potentially long-lived objects are, etc.
[ ][ ][I][ ][ ][H][ ][ ]
^^^^^^^^
`these items move right
[ ][ ][H][ ][I][ ][ ][ ]
^^^^ ^^^^^^^ ^- this item moves to the top (left most slot)
| `--- these items move right
` these items move right
> If we think about doing it in hardware, like for each set of a set-associative L1 or L2 cache, it's a hindrance.
I don't see why I would think about doing it in hardware.
https://gist.github.com/vidarh/b72615c16673cb38630cab5148190...
You'll note it avoids a bunch of conditionals in add_to_head, remove_node and evict because the wraparound happens automatically and the next/prev pointers are never nil/None
I've not verified it matches the behaviour of yours exactly other than adding a handful of extra access calls and comparing the state.
If you're not familiar with Ruby, the one particularly dirty trick I'm using is that in Ruby you can define methods directly on a specific object, so by defining the method "@head.visited" to always return true, the eviction will just try to set it to false and move straight over it every run, cutting a conditional. You could do a ring without a dummy @head to but it makes the insertion/deletion logic more annoying.
It simplifies a lot of algorithms to be able to guarantee no null pointers. It's a very old trick. You trade a lot of conditionals and a risk of null pointers dereference for a smaller risk of non-termination (failure to check for a null pointer is always bad; failure to check for the end is only a problem if the end of the list is actually your termination condition).
You could do a ring with an array and modulus too, but then you end up copying the whole thing to open up slots to insert to maintain the property of your insertion point being separate from the hand.
That may or may not do worse, but likely to depend on cache size and implementation language.
What you'd almost certainly want in a production implementation anyway would in any case be to do away with constantly allocating nodes and just move them to a free list and reuse to avoid dynamic allocation overhead and garbage collection.
That could possibly reveal interesting security-related properties, i.e. maybe future vulnerabilities.
There is a good reason. And that reason is that many recently accessed items survived. Then it's only prudent to devote more of the cache for surviving items than for fresh ones in such circumstances.
This continues until the cache is completely filled with recent survivors which moves the hand back to tail and oldest previous survivors get reevaluated for eviction. This, I imagine happens periodically in practice and often enough for the algorithm to perform well.
There doesn't seem to be any good reason for this over putting the newly inserted items at a consistent distance away from the Hand, so they are a predictable, controllable number of steps away from the threat of eviction, and so that the Hand movement is just a cyclic treadmill with no spot of the circular buffer being arbitrarily special.
If randomization of the distance is beneficial, let that be explicit! Feed a stream of pseudo-random integers to the cache which is used to select the distance between the Hand and the Insert point. That could be still be nicely controlled as a jitter within a minimum and maximum range.
That's a good thing because newly inserted items didn't prove yet that they are worth keeping.
They have less time to proove themselves but if they prove themselves they can have a long lifetime because they will remain when the hand loops back to tail.
End of cache is filled with items of proven utility. New ones are unproven. Shrinking distance between head and hand reflect accumulation of proven items which leaves less space for unproven ones. Which is good. Eventually (when the space for fresh ones ends) you want to reconsider the proven ones again and this is achieved by moving hand back from head to tail.
It might be unfair to new items comming in at the times when there are a lot of proven ones accumulated but it is a good strategy from the point of view of the whole process. Good solutions are not necessarily fair.
> If randomization of the distance is beneficial, let that be explicit!
But it's better than random. It's adaptive to how many of the items already stored were visited recently.
It isn't good that the probation is random, depending on how far left the Hand is at the time the item is inserted. Or else if it is good for that distance to be randomized, it would be good to make that random choice explicit.
> It's adaptive to how many of the items already stored were visited recently.
It's not adaptive whatsoever. The Hand moves left when there are cache misses, in order to find items to evict, and then wraps back to the rightmost slot. The current position of the Hand bears no relation to a newly observed cache miss, yet affects its retention.
Yes, SIEVE does not adapt to miss ratio, but it adapts to the inherent popularity in the workloads. You can see the evidence in the results.
It moves only if there were cache hits. If there are only cache misses it stays at the tail so the whole cache is dedicated for new unproven entries. Once there are some cache hits then they are retained and the area shrinks. It's not random. It reacts to whether it managed to catch something valuable or not.
> The current position of the Hand bears no relation to a newly observed cache miss, yet affects its retention.
Yes, but it is related to recent cache hits. It sacrifices chances of new items getting retained in exchange for retaining items that were recently proven to be worth keeping.
The Hand moves when it has to scan over visited items in search of an unvisited item to evict, when there is a cache miss. The scanned items are flipped to unvisited.
Once some visited items arrive they are retained and the fraction of cache dedicated to new ones shrinks, so they have less time to get visited again and avoid eviction. But this happens for the benefit of retained items. If they were already seen second time there's a chance they'll occur for the third time and more. They are worth more than fresh ones. It's unfair to new items but beneficial for the cache as a whole.
When many different items are revisited hand moves and eventually reaches the head. Then the cache is full. So it's moved back to tail to see if we can evict some of the old stuff because maybe they weren't re-visted since last time we considered them for eviction.
Can you see it's not random and that it's actually useful?
It's like being rude to customers whenever the day of year is divisible by five. Sure it's not mathematically even pseudo-random, but it's unrelated to the customers. It's effectively random to them.
It's unrelated to the new customers and in that sense unfair to them. But it's related to how successful is the restaurant at the moment.
Fairness is not the goal. Success of the restaurant is.
Objects near the tail are the people who occupy the table but keep ordering new dishes. Objects near the head are people who ordered just one thing and now they are politely asked to leave so new, potentially more generous customers can be accomodated.
If restaurant is more full, new customers have less time to justify their continued occupation of the table by ordering again, but it's fine because it allowes more of the older customers with repeated orders to be served again and again.
There is potential problem with the algorithm if there's very little space left for new items so they are never retained so hand never moves to head. Probaby you could refine the algorithm by moving hand to tail when it gets closer to head than some fixed value, finetuned to the production load. Or just occasionally move hand to tail every n inputs on average (also finetuned).
This is not so. The tail of the buffer is the Hand pointer, and it behaves like a circular buffer tail.
This is at odds with the fixed head.
Your full versus empty analysis is flawed, because once the cache warms up, which takes only one cycle, it stays permanently full. At each subsequent cache miss, one item is evicted and one item is inserted. One in, one out. There is no tide-like ebb and flow between empty and full. That is just rhetoric which is not anchored to anything that is real in the algorithm.
Items that are booted out are identified at the circular buffer tail. But, oddly, the new ones are inserted at the physical top of the circular buffer's linear implementation which bears no relation to the circularity.
In a circular buffer, the linear indices have no special meaning.
So it is like a code smell, but for algorithms.
Those two pointers split the circular buffer inti two parts. The part after insertion pointer but before eviction pointer you could call staging. It's a space where items that have not yet been considered for eviction are held. When an item gets evicted items in this staging space are moved one spot towards eviction pointer so that under insertion pointer a free space appears which is filled by the newly inserted item.
As items are considered for eviction and rejected (because they had visited status) eviction pointer moves closer and closer to insertion pointer shrinking the staging area. So the new items have less and less time to acquire visited status before the eviction pointer reaches them. This is what's unfair. That the chances of item getting visited and spared from eviction is lower for the items that arrive when staging is small.
This is somewhat alleviated by the fact that after eviction pointer in its motion reaches stationary insertion pointer it passes it so the staging area grows from almost nothing to the full size of the circular buffer. The items which had a bad luck to arrive when the staging is small, if they are repeated, have a later chance to arrive again when staging is large and then have a lot of time to earn visted status and avoid eviction the next time they are considered.
What you are advocating for is that insertion pointer should move too, either to keep fixed distance from the eviction pointer or to keep explicitly randomized distance. Those are of course valid choices when you design your cache algorithm. But the author(s) of this one went with another method. They reduce the distance between insertion and eviction pointer by one only after item is considered for eviction but rejected (because it got visited status since the time it was inserted or considered for eviction the previous time). Once the distance between insertion and eviction point reaches small enough value (for example zero) they increase the distance to be maximum possible (to the size of the circular buffer).
You don't see a reason for this choice and I'm telling you that the reason is that the second part of the buffer (the part starting at eviction point and ending at insertion point) is devoted exclusively to items that since their insertion acquired visited status at least once thus prooving they are worth keeping in cache.
So it might be a good strategy to dedicate larger part of the buffer to those items in times when they are abundant in the input rather than fixed part or random part as you propose.
To address your concern that new items are inserted at the physical top of circular buffer implementation ... It doesn't matter. Insertion pointer could be placed at any spot in the buffer. You can randomize its initial (and ultimate since its not moving) placement and it would change nothing in the performance of the algorithm (after the buffer is initially filled). This cache could be implemented as circular linked list with two pointers into it.
Do you understand all that? Because I'm not sure if I can explain it any more clearly.
After that, you cannot "unsee" it any more.
> items that since their insertion acquired visited status at least once
> the second part of the buffer (the part starting at eviction point and ending at insertion point) is devoted exclusively to items that since their insertion acquired visited status at least once thus prooving they are worth keeping in cache.
Items can acquire visited status anywhere in the cache, to the left or right of the Hand pointer. There is no special area.
The "reaper" which ages visited items to unvisited, and which collects aged items, moves in a circle.
If an item is inserted while the Hand is in the leftmost position, it will be evicted immediately when another not-present item is accessed. If an item is inserted while the Hand is farthest away at the rightmost slot, and not visited again, it can stay in the cache for a number of miss cycles, until the Hand goes to the top again.
That variability, as such, may be useful and good.
One problem is that it's not actually random, and it's not even a good form of pseudo-random.
I posit that input sequences exist in which two items of equal importance, A and B, are consistently treated unequally, with B enjoying much longer retention in the cache than A.
Moreover, the algorithm doesn't allow for experimentation with randomly varying the trim distance between two arbitrary values. Like say random between 4 and 8 slots in a 64 slot cache. That's a disadvantage, because for some given patterns, it prevents the optimal parameters from being discoverable.
Algorithms like LRU don't have the above weird property. While their hit rate may be good or bad depending on the locality of patterns, you cannot construe a sequence of access patterns under LRU in which two items A and B appear equally frequently, yet enjoy significantly different retention times.
They can lose visited status only if they are between head and hand pointer. That's the special area. There's no way for item to loose their visited status if they are between hand and tail until the hand reaches head. In this sense area between hand and tail is privileged.
> If an item is inserted while the Hand is in the leftmost position, it will be evicted immediately when another not-present item is accessed.
You see the cost of small head-hand area but you don't see the benefit of large hand-tail area.
> Moreover, the algorithm doesn't allow for experimentation with randomly varying the trim distance between two arbitrary values.
In its basic form it doesn't. However I suggested that you might tweak how far from the head, the hand loops back to tail. It doesn't have to happen at exactly zero distance if you don't want to ever disadvantage new entries too much.
> .. construe a sequence of access patterns under LRU in which two items A and B appear equally frequently, yet enjoy significantly different retention times.
I see no cost of that. Cache doesn't need to be fair. It only needs to be successful. If it can serve item A from cache for 100% of the time and item B 0% of the time despite same patterns its still better than if it serves each of them 25% of time from cache.
* is not worse than
Sure, we can contrive access sequences where that is not random, because the whole thing is actually deterministic. That's not what I mean by random; I mean not expected to be related under realistic conditions where the inputs aren't contrived.
A good cache algorithm should be immune against contrived input sequences. With this one, we could devise a degenerate access sequence such that a particular item is always placed just ahead of the Hand, such that it is victimized in the next access cycle. Yet another particular item is given the maximum leeway. And that could be in spite of both items appearing equally often and deserving the same treatment.
If we consider LRU, no contrived pattern of access on LRU will cause it to evict some item Y if there is an item Z present which was less recently touched than Y.
If the algorithm is known and accepts user facing requests then it becomes a target. A client can use the network speed of a dialup modem to bring down a modern server simply by crafting a request pattern to exploit hash flooding. This is why you generally want some injected noise, adaptivity, and use an algorithm that offers robustly good hit rates. A specialized policy that is superior in a narrow set of workload is still very useful when targeted at an expensive problem, but that's a design assumption that few can reasonably make.
It is only these kinds of pseudo-randomized algorithms that have hidden degenerate cases that need to be randomized for protection.
More generally, software that has some hidden severe problems for certain inputs, such that the degenerate choice of inputs depends on incidental factors, benefits from having those incidental factors perturbed randomly (like a form of seeding) so that attackers cannot identify those inputs or use the same ones consistently.
ASLR is like this. A bug-free program (or at least one free of memory errors) does not benefit from address space layout randomization, only one that has bugs. The successful exploitation of those bugs for gaining unauthorized access depends on incidental pseudo-random factors like in what layout the misused objects are allocated.
I believe there's no need for a cache to have a behavior whereby a sequence of accesses that shows good locality its able to get a frequently accessed item to be given poor cache residency, while another item that is just as frequently accessed is given good residency. On the other hand kind of inputs that trigger poor hit rates in a cache are hardly random. To trigger a poor hit rate in almost any cache algorithm whatsoever, all you have to do is access a sequence of items in which nothing appears twice. Only an algorithm with prefetch that happens to predict that sequence will do well or at least somewhat well.
You're right that putting the insert in a fixed location will mean the time a new element has before it must either be visited or get evicted will vary quite a bit, but it's not obvious that it will always be better to "fix" that.
E.g. consider the typical "generation gap" where the set of objects are bimodal and either likely to be frequently used or be garbage right away. Depending on the odds that a new object falls in either category, it might be better for the insert to be closer to the hand than further away (or it might be opposite). That is, you might want the chance for a new entry to survive to be fairly low.
If the best bet is to have the new entry on average an inconvenient distance from the hand, it might well be the variability is better than either moving the insert to the hand or a more convoluted scheme to keep them at a fixed distance.
I agree it'd be more predictable and/or easier to reason about if it's a fixed distance, and if the fill size of the cache is the right distance then certainly inserting it at the hand works great.
But really, I think you should measure for your specific workflow. It'd be interesting to see this option and some other ways of separating them tested, though.
Another thing I think would be interesting to test is whether (it wasn't an accident that I hinted at generational garbage collection above) it'd be worth keeping a second pointer that you move past objects that have survived "long enough" in the cache, and most of the time move the hand back to that pointer instead of "all the way" so you don't spend as much time iterating over objects that won't get evicted anyway. If the number of cache entries is small, probably not worth it, but for a large cache with a decently large proportion of persistently hot objects, maybe (but then you could just also outright move objects to a second cache, and that might well be simpler; again something to measure on actual workloads).
I'm assuming this isn't anything new to people who follow the field more closely in any case.
Otherwise on that basis you shouldn't put a cache in at all as there will be workflows where the hit rate is so low the cache has a negative effect, however unlikely.
If you don't know e.g. the rough performance profile of your requests, and the typical distribution of them, you likely have far bigger things you should be worrying about.
This would help with the implementation with a circular buffer. But for now, let's decouple the algorithm from the implementation.
> we can make Insert and Hand be the same slot
This is just CLOCK algorithm. It is easy to implement with a circular buffer. But the change we made deliberately improves the miss ratio significantly.
But there is a bias in the algorithm. Arbitrarly, the circle is broken into a linear queue, and the not present items which are accessed are arbitrarily inserted into the head of the queue (leftmost slot).
This does not compute: a circular roving pointer sweeping through a queue? What?
The problem is that items that are inserted at the head of the queue during a moment when the Hand is in a low position (close to the head, toward the left) are closer to being doomed than items added when the Hand is in the rightmost position. This is for no good reason other than just luck.
How it should work is that new items should be added at a fixed distance from the Hand pointer. In other words, an Insert point moves around the circular buffer in lock step with the Hand. When the Hand obliterates an evicted item, items between that item and the Insert point will shuffle over, and the new item goes to the Insert point. Next time the Hand moves, the Insert point will move with it in the same direction.
And now here is an elegant thing: we can make Insert and Hand be the same slot! When the Hand finds a victim we just replace the Hand slot with the new item, and mark it visited. Don't move any items around. On the next miss, the Hand will hop away from that item and mark it unvisited, and that's it. That item can then live until the next visit of the Hand, if it isn't touched again. This is just a FIFO with protection for the visited, essentially.
The distance between Insert and Hand is a parameter; the algorithm can be measured at various values of that parameter.