qp tries and crit-bit tries

I have been working on radix trees / patricia tries / crit-bit tries with a larger fan-out per branch to reduce lookup costs without wasting memory.

My best solution so far is the "qp trie", short for quelques-bits popcount patricia trie. (Nothing to do with cutie cupid dolls or Japanese mayonnaise!) A qp trie is like a crit-bit trie (aka patricia trie) except each branch is indexed by a few bits at a time instead of one bit. The array of sub-tries at a branch node is compressed using the popcount trick to omit unused branches, saving memory. When searching a qp trie, the child nodes are prefetched from memory while the CPU works out which child is next.

The original version of qp tries used 4 bits at a time, so it was a quadbit popcount patricia trie. There is a faster (but slightly more complicated) version that uses 5 bits at a time, a quintuple-bit popcount patricia trie. There is a faster, smaller, and simpler DNS-optimized version that uses a byte at a time for standard hostnames.

Based on a few benchmarks, qp tries have about 1/3 less memory overhead of crit-bit tries, 1.3 words vs 2 words of overhead per item; the average depth of a qp trie is about half that of a crit-bit trie; and the overall speed of qp tries is about 30% faster than crit-bit tries. The qp trie implementation is about 40% bigger.


Type make test or make bench. (You will need to use GNU make.) If you have a recent Intel CPU you might want to add -mpopcnt to the CFLAGS to get SSE4.2 POPCNT instructions. Other build options:

The makefile builds {test,bench}-{qs,qn} with these options; they are otherwise the same as test-qp and bench-qp.


Most of the code has only been tested on 64-bit little endian machines. It might work on 32-bit machines (provided the compiler supports 64 bit integers) and probably won't work on a big-endian machine. The "fn" (five-bit new) variation should be more portable since it avoids the mistakes of the earlier code.

Key strings can be byte-aligned but values must be word-aligned; you can swap this restriction (e.g. if you want to map from strings to integers) by tweaking the struct layout and adjusting the check in Tset().

Keys are '\0' terminated C strings, which guarantees one key is not a prefix of another, so leaves and branches cannot occur at the same point. It should be possible to support arbitrary binary keys by being more clever about handling string termination.


Newest at the bottom, scroll down...


Marek Vavrusa (CZ.NIC) and Devon O'Dell (Fastly) enthusiastically put this code to work and provided encouraging feedback.

Vladimír Čunát incorporated qp tries into CZ.NIC Knot DNS, at the suggestion of Jan Včelák.

Simon Tatham proved that parent pointers are not needed for embedded crit-bit tries.


You can clone or browse the repository from:



Written by Tony Finch dot@dotat.at https://dotat.at/; You may do anything with this. It has no warranty. https://creativecommons.org/publicdomain/zero/1.0/