Add hilbertEncode and hilbertDecode functions

[Artemmm91]

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• New Feature

Changelog entry (a user-readable short description of the changes that goes to CHANGELOG.md):

Add Hilbert Curve encode and decode functions

https://en.wikipedia.org/wiki/Hilbert_curve
Closes #55520.

Documentation entry for user-facing changes

• Documentation is written (mandatory for new features)

Information about CI checks: https://clickhouse.com/docs/en/development/continuous-integration/

[CLAassistant]

All committers have signed the CLA.

[robot-clickhouse]

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[yariks5s]

Hello! Thanks for the pull request! Could you please sign the CLA?

[Artemmm91]

Hello! Thanks for the pull request! Could you please sign the CLA?

Sure, just signed it. And i'm still working on it, think that will finish in the end of this week

[Blargian]

@Artemmm91 the documentation team has a project to document all functions. mortonEncode and mortonDecode documentation were missing from the docs but will hopefully be added with 60868. It will be nice to also have it there for your functions as they are closely related :)

[Artemmm91]

@Artemmm91 the documentation team has a project to document all functions. mortonEncode and mortonDecode documentation were missing from the docs but will hopefully be added with 60868. It will be nice to also have it there for your functions as they are closely related :)

Okay, no problem)

[yariks5s]

For now, it will be good to have some stateless tests that check if we encode and decode values right (examples of tests can be found in /0_stateless/.. as .sql files).

[yariks5s]

any specific reason to use HilbertDetails namespace instead of anonymous namespace? (Also in hilbertEncode)

[Artemmm91]

AFAIC it is not recommended to make anonymous namespace in header files

[Artemmm91]

@yariks5s there are some problems with linking with gtest_hilbert_curve, so i'll make header in which i'll store implementations for 2D and lookup tables and will include it to test and to hilbertEncode.cpp file

[Artemmm91]

@yariks5s Hi! i think i'm ready with PR.

i see that there are some failed checks, but seems they are not correlated with my PR:

1. Stateful tests failed - 00159_parallel_formatting_json_and_friends_2
2. Stress test (asan) - DB::Exception: Unknown disk 03008_local_plain_rewritable - some problems with disks
3. Upgrade check - some problem with settings that i didn't add

[Artemmm91]

Also i'm currently working on index analysis of hilbert function - did this on my local branch, and will make other PR after merging this one

[yariks5s]

Generally, the Hilbert curve does not apply to a single argument (because it's generally used for coordinates). We can also mention here that the second argument is considered as zero (please correct me if I'm wrong)

[Artemmm91]

didn't quiet get you, but if you mean that we can state that hilbertEncode(N, 0) = hilbertEncode(N) that's not true

currently i'm adding the case with num_dimensions = 2, but i'm looking forward to also add the case of num_dimensions in [3, 8]. so for the completeness, i think it's good to also have the case num_dimemnsions = 1 (and mathematically speaking, it is a valid case)