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qp tries and crit-bit tries

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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:

  • HAVE_SLOW_POPCOUNT compiles the code to use a hand-coded 16 bit popcount() instead of __builtin_popcount(). No need for this with recent clang/llvm; useful with older gcc.

  • HAVE_NARROW_CPU uses a 2 x 16 bit SIMD-within-a-register popcount instead of two separate 16 bit popcounts; might be useful on small CPUs but makes little difference on 64 bit Intel.

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...


  • 2015-10-04 - qp tries: smaller and faster than crit-bit tries

    A blog article / announcement.

  • 2015-10-07 - crit-bit tries without allocation

    An unimplemented sketch of a neat way to use crit-bit tries.

  • 2015-10-11 - prefetching tries

  • 2015-10-13 - Devon O'Dell benchmarks qp tries against some alternatives

  • 2015-10-19 - never mind the quadbits, feel the width!

    Benchmarking wider-fanout versions of qp tries.

  • 2016-20-23 - How does a qp trie compare to a network routing trie?

    Reading some vaguely-related academic literature.

  • 2016-03-06 - TinyToCS vol. 4 includes a paper on QP tries!

    Nicest comment from a reviewer:

    The body of this paper is a masterpiece of economy: results are presented very clearly and understandably. The result here is simple, compact, and unambiguous, which makes it perfect for TinyToCS.

  • 2016-11-21 - https://gitlab.labs.nic.cz/knot/knot-dns/-/merge_requests/574

    A greatly enhanced and properly engineered implementation of a qp trie is being incorporated into CZ.NIC Knot DNS, for better memory efficiency.

  • 2016-12-20 - https://github.com/jedisct1/rust-qptrie

    Frank Denis's Rust version of qp tries

  • 2017-01-09 - qp trie news roundup

  • 2020-07-05 - A compelling idea: the genesis of my DNS-trie

  • 2020-07-20 - https://github.com/fanf2/nsd

    A fork of NSD that uses my DNS-trie code. It is significantly faster and much smaller than NSD's default radix tree.

    https://twitter.com/fanf/status/1285181266850205696 - a thread about how to optimize a qp-trie for the DNS

  • 2021-06-23 - Page-based GC for qp-trie RCU

    Memory management to support multithreaded readers

  • 2022-05-23 qp guts + 2022-05-23 qp api

    A couple of qp-trie presentations I gave at the 2022 isc.org all-hands meeting; the PDFs have the slides with speaker notes

  • 2022-06-22 - Compacting a qp-trie

    notes on several experiments


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:


  • Tbl.h Tbl.c

    Abstract programming interface for tables with string keys and associated void* values. Intended to be shareable by multiple different implementations.

  • qp.h qp.c

    My original qp trie implementation. See qp.h for a longer description of where the data structure comes from.

  • fp.h fp.c

    5-bit clone-and-hack variant of qp tries.

  • fn.h fn.c

    Newer version of 5-bit qp trie, which should be more portable.

    This is the version that I recommend - faster and less memory overhead

  • dns.h dns.c

    A qp-trie variant optimized for domain names. As well as the comments in dns.h there are some design notes. The DNS-trie implementation in this repository is heavily bodged to fit into my test / benchmark harness so it can be directly compared with the other qp-trie versions.

  • wp.h wp.c

    6-bit clone-and-hack variant of qp tries.

  • cb.h cb.c

    My crit-bit trie implementation. See cb.h for a description of how it differs from DJB's crit-bit code.

  • qp-debug.c fp-debug.c fn-debug.c wp-debug.c cb-debug.c

    Debug support code.

  • bench.c bench-multi.pl bench-more.pl bench-cross.pl

    Generic benchmark for Tbl.h implementations, and benchmark drivers for comparing different implementations.

  • test.c test.pl

    Generic test harness for the Tbl.h API, and a perl reference implementation for verifying correctness.

  • test-gen.pl test-once.sh

    Driver scripts for the test harness.


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

Open Source Agenda is not affiliated with "Qp" Project. README Source: fanf2/qp
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