Concerning hash algorithms, for me, it was cuckoo hashing that blew me away. The algorithm is so simple and yet has O(1) guaranteed lookup complexity, i.e., it is better on theoretical level than other open addressing. It is also versatile by having a configurable trade-off (the number of buckets) between time constant and fill ratio. Most impressive is its simplicity combined with that it was invented only so recently (2001).
I always find it interesting how often the simplest hash table layouts end up performing best in real workloads. Once you avoid pointer chasing and keep everything in a compact array, CPU caches do most of the heavy lifting.
It’s also a good reminder that clarity of layout often beats more “clever” designs, especially when the dataset fits comfortably in memory.
Until you get high memory contention from the rest of the code. Once eviction gets high you get some pretty counterintuitive improvements by fixing things that seem like they shouldn’t need to be fixed.
My best documented case was a 10x speed up from removing a double lookup that was killing caches.
My best improvment was just bit-interleaving both axes of a 2x32bit integer coordinate (aka z-curve). I obtained factor ~100x (yes factor not percent) throughput improvement over locality in only one dimension. All it took was ~10 lines of bit twiddling. The runtime went from a bit above 300ms to slightly less then 3ms.
End to end gets weird. I was asked to look at an admin page, nobody could figure out why it was 30s. Literally the first thing I tried got it under 4 and the second down to three. It was pulling the same list of rows twice, applying two filters and then looking at the intersection. I changed the signature to send the list as input instead of the query constraints. Then I changed them to avoid the intersect.
If you would have asked me to bet on which one would have had the bigger impact I would have split the difference.
My second favorite was similar. Two functions making a call instead of sharing the answer. Profiler said 10% cumulative. I removed half. Instead of 5% I got 20%. Which just demonstrates how much data a profiler cannot show you.
Profilers lie and some more than most. I’ve gotten 3x from code with a perfectly rectangular profile output.
Part of it comes down to a trick game devs steal from finance: give each task a budget and keep it to the budget even if it’s not the tall tent pole.
You should not spend 10% of your response time on telemetry and logging combined. Yet I pulled 10% TTFB out of just the logging and telemetry code on a project. It was a frog boiling situation. Every new epic used the new code and determining the cumulative cost wasn’t easy.
To me, these sorts of examples always seem contrived. To the first order, I've never had a real hash table problem that was on machine word keys.
I've nearly always had a variable length string or other complex structure that was being hashed, not their handles.
Back in my early career in C, this would be a generic API to hash and store void pointers, but the pointers were not being hashed. The domain-specific hash function needed to downcast and perform the appropriate remote memory access to fetch the variable-length material that was actually being hashed.
I'm a big fan of the basic power of two choices hash table design. It's simple to understand and implement, has reasonable constant factors, and hits high load factors on real world datasets.
You can use more elaborate probe and relocation schemes, but just choosing the less full bucket and resizing if both choices are full gets you surprisingly far.
This constraint allows making a linear array of all the 4 billion values, with the key as array index, which fits in 16 GiB. Another 500 MiB is enough to have a bit indicating present or not for each.
Perhaps text strings as keys and values would give a more interesting example...
That's not a constraint as much as the worst case size.
If you actually only have a handful of entries in the table, it is measurable in bytes.
A linear array of all 4 billion possible values will occupy 16 GiB (of virtual memory) upfront. We have then essentially replaced the hash table with a radix tree --- that made up of the page directories and tables of the VM system. If only the highest and lowest value are present in the table, then we only need the highest and lowest page (4 kB or whatever) to be mapped. It's not very compact for small sets; storing N numbers in random locations could require as many as N virtual memory pages to be committed.
This is a smart implementation of Robin Hood hashing I am not aware of. In my understanding, a standard implementation keeps the probe length of each entry. This one avoids that due to its extra constraints. I don't quite understand the following strategy, though
> To meet property (3) [if the key 0 is present, its value is not 0] ... "array index plus one" can be stored rather than "array index".
If hash code can take any value in [0,2^32), how to define a special value for empty buckets? The more common solution is to have a special key, not a special hash code, for empty slots, which is easier to achieve. In addition, as the author points out, supporting generic keys requires to store 32-bit hash values. With the extra 4 bytes per bucket, it is not clear if this implementation is better than plain linear probing (my favorite). The fastest hash table implementations like boost and abseil don't often use Robin Hood hashing.
Awesome blog! Looking at the code I feel like there’s a kindred soul behind that keyboard, but there’s no About page afaict. Who beeth this mysterious writer?
Since both members of the union are effectively the exact same type, there is no issue. C99: "If the member used to access the contents of a union is not the same as the member last used to store a value, the object representation of the value that was stored is reinterpreted as an object representation of the new type". Meaning, you can initialise keyvalue and that will initialise both key and value, so writing "union slot s{0}" initialises everything to 0. One issue is that the exact layout for bit fields is implementation defined, so if you absolutely need to know where key and value are in memory, you will have to read GCC's manual (or just experiment). Another is that you cannot take the address of key or value individually, but if your code was already using uint64_t, you probably don't need to.
Edit: Note also that you can cast a pointer to slot to a pointer to uint64_t and that does not break strict aliasing rules.
Maybe trying to avoid struct padding? Although having done a quick test on {arm64, amd64} {gcc, clang}, they all give the same `sizeof` for a struct with 2x`uint32_t`, a struct with a single `uint64_t`, or a bare `uint64_t`.
In any struct where all fields have the same size (and no field type requires higher alignment than its size), it is guaranteed on every (relevant) ABI that there is no padding bytes.
> If the Zba extension is present, sh3add.uw is a single instruction for zero-extending idx from 32 bits to 64, multiplying it by sizeof(uint64_t), and adding it to slots.
Yay, we've got an equivalent of SIB byte but as three (six?) separate opcodes. Well, sub-opcodes.
It's a shame though that Zcmp extension didn't get into RVA23 even as an optional extension.
I don't understand the part about key removal. Is it correct to shift values to the left? Can't it break lookups for keys inserted into their natural positions?
I am dipping my toes in programming. But I can't follow this without graphical representations of the tables as the author (brilliantly) walks through it.
This hash table is pretty good. It has at best one memory read if there’s no collision. Randomized key might introduce any level of key collision though.
Concerning hash algorithms, for me, it was cuckoo hashing that blew me away. The algorithm is so simple and yet has O(1) guaranteed lookup complexity, i.e., it is better on theoretical level than other open addressing. It is also versatile by having a configurable trade-off (the number of buckets) between time constant and fill ratio. Most impressive is its simplicity combined with that it was invented only so recently (2001).
https://en.wikipedia.org/wiki/Cuckoo_hashing
I always find it interesting how often the simplest hash table layouts end up performing best in real workloads. Once you avoid pointer chasing and keep everything in a compact array, CPU caches do most of the heavy lifting.
It’s also a good reminder that clarity of layout often beats more “clever” designs, especially when the dataset fits comfortably in memory.
Until you get high memory contention from the rest of the code. Once eviction gets high you get some pretty counterintuitive improvements by fixing things that seem like they shouldn’t need to be fixed.
My best documented case was a 10x speed up from removing a double lookup that was killing caches.
My best improvment was just bit-interleaving both axes of a 2x32bit integer coordinate (aka z-curve). I obtained factor ~100x (yes factor not percent) throughput improvement over locality in only one dimension. All it took was ~10 lines of bit twiddling. The runtime went from a bit above 300ms to slightly less then 3ms.
End to end gets weird. I was asked to look at an admin page, nobody could figure out why it was 30s. Literally the first thing I tried got it under 4 and the second down to three. It was pulling the same list of rows twice, applying two filters and then looking at the intersection. I changed the signature to send the list as input instead of the query constraints. Then I changed them to avoid the intersect.
If you would have asked me to bet on which one would have had the bigger impact I would have split the difference.
My second favorite was similar. Two functions making a call instead of sharing the answer. Profiler said 10% cumulative. I removed half. Instead of 5% I got 20%. Which just demonstrates how much data a profiler cannot show you.
I'm wondering how do you folk even come up with this kind of optimisations.
Sheer stubbornness.
Profilers lie and some more than most. I’ve gotten 3x from code with a perfectly rectangular profile output.
Part of it comes down to a trick game devs steal from finance: give each task a budget and keep it to the budget even if it’s not the tall tent pole.
You should not spend 10% of your response time on telemetry and logging combined. Yet I pulled 10% TTFB out of just the logging and telemetry code on a project. It was a frog boiling situation. Every new epic used the new code and determining the cumulative cost wasn’t easy.
To me, these sorts of examples always seem contrived. To the first order, I've never had a real hash table problem that was on machine word keys.
I've nearly always had a variable length string or other complex structure that was being hashed, not their handles.
Back in my early career in C, this would be a generic API to hash and store void pointers, but the pointers were not being hashed. The domain-specific hash function needed to downcast and perform the appropriate remote memory access to fetch the variable-length material that was actually being hashed.
I'm a big fan of the basic power of two choices hash table design. It's simple to understand and implement, has reasonable constant factors, and hits high load factors on real world datasets.
You can use more elaborate probe and relocation schemes, but just choosing the less full bucket and resizing if both choices are full gets you surprisingly far.
Power-of-two length is also the natural choice for a growable linear array where the designer has no idea how many elements there will be.
> The table occupies at most 32 GiB of memory.
This constraint allows making a linear array of all the 4 billion values, with the key as array index, which fits in 16 GiB. Another 500 MiB is enough to have a bit indicating present or not for each.
Perhaps text strings as keys and values would give a more interesting example...
> a linear array of all the 4 billion values, with the key as array index, which fits in 16 GiB
The hash table has the significant advantage of having a much smaller minimum size.
> Perhaps text strings as keys and values would give a more interesting example
Keep reading to "If keys and values are larger than 32 bits"
That's not a constraint as much as the worst case size.
If you actually only have a handful of entries in the table, it is measurable in bytes.
A linear array of all 4 billion possible values will occupy 16 GiB (of virtual memory) upfront. We have then essentially replaced the hash table with a radix tree --- that made up of the page directories and tables of the VM system. If only the highest and lowest value are present in the table, then we only need the highest and lowest page (4 kB or whatever) to be mapped. It's not very compact for small sets; storing N numbers in random locations could require as many as N virtual memory pages to be committed.
This hashtable implements a multiset. Not (merely) a simple set.
This is a smart implementation of Robin Hood hashing I am not aware of. In my understanding, a standard implementation keeps the probe length of each entry. This one avoids that due to its extra constraints. I don't quite understand the following strategy, though
> To meet property (3) [if the key 0 is present, its value is not 0] ... "array index plus one" can be stored rather than "array index".
If hash code can take any value in [0,2^32), how to define a special value for empty buckets? The more common solution is to have a special key, not a special hash code, for empty slots, which is easier to achieve. In addition, as the author points out, supporting generic keys requires to store 32-bit hash values. With the extra 4 bytes per bucket, it is not clear if this implementation is better than plain linear probing (my favorite). The fastest hash table implementations like boost and abseil don't often use Robin Hood hashing.
Awesome blog! Looking at the code I feel like there’s a kindred soul behind that keyboard, but there’s no About page afaict. Who beeth this mysterious writer?
He’s done some interesting work with crc32 ~recently:
https://www.corsix.org/content/fast-crc32c-4k
https://github.com/corsix/fast-crc32/
https://github.com/corsix
Is there a specific reason to store the key + value as an `uint64_t` instead of just using a struct like this?
The alignment constraint is different, which they use to be able to load both as a 64-bit integer and compare to 0 (the empty slot).
You could work around that with a union or casts with explicit alignment constraints, but this is the shortest way to express that.
C has finally gained `alignas` so you can avoid the union hack or you could just rely on malloc to alway return the maximum alignment anyway.
In that case you can use bit fields in a union:
Since both members of the union are effectively the exact same type, there is no issue. C99: "If the member used to access the contents of a union is not the same as the member last used to store a value, the object representation of the value that was stored is reinterpreted as an object representation of the new type". Meaning, you can initialise keyvalue and that will initialise both key and value, so writing "union slot s{0}" initialises everything to 0. One issue is that the exact layout for bit fields is implementation defined, so if you absolutely need to know where key and value are in memory, you will have to read GCC's manual (or just experiment). Another is that you cannot take the address of key or value individually, but if your code was already using uint64_t, you probably don't need to.Edit: Note also that you can cast a pointer to slot to a pointer to uint64_t and that does not break strict aliasing rules.
You can probably get away with just a union between a 64 bit and 2 32 bit integers.
Maybe trying to avoid struct padding? Although having done a quick test on {arm64, amd64} {gcc, clang}, they all give the same `sizeof` for a struct with 2x`uint32_t`, a struct with a single `uint64_t`, or a bare `uint64_t`.
In any struct where all fields have the same size (and no field type requires higher alignment than its size), it is guaranteed on every (relevant) ABI that there is no padding bytes.
TIL! Thanks!
No real reason. Slightly terser to compare with zero to find an empty slot.
Or better, just store keys and values in separate arrays, so you can have compact cache lines of just keys when probing.
> If the Zba extension is present, sh3add.uw is a single instruction for zero-extending idx from 32 bits to 64, multiplying it by sizeof(uint64_t), and adding it to slots.
Yay, we've got an equivalent of SIB byte but as three (six?) separate opcodes. Well, sub-opcodes.
It's a shame though that Zcmp extension didn't get into RVA23 even as an optional extension.
> It's a shame though that Zcmp extension didn't get into RVA23 even as an optional extension
Zcmp is only for embedded applications without D support.
You wouldn't want an instruction with up to 13 destinations in high performance designs anyways.
If you want load/store pair, we already have that, you can just interpret two adjacent 16-bit load or stores as a single 32-bit instruction.
I don't understand the part about key removal. Is it correct to shift values to the left? Can't it break lookups for keys inserted into their natural positions?
I am dipping my toes in programming. But I can't follow this without graphical representations of the tables as the author (brilliantly) walks through it.
This hash table is pretty good. It has at best one memory read if there’s no collision. Randomized key might introduce any level of key collision though.
Used Gemini to explain this. Very interesting and I think Gemini did a good job explaining the Robin hood fairness mechanism
https://gemini.google.com/share/5add15a1c12f