fix(web): Uniform random distribution during shuffle

[Pascal-So]

Description

In the slide show settings, the user can select if a slide show should run in forward, reverse, or shuffle order. This PR modifies the shuffle algorithm to improve the randomness, while not changing anything else.

Previously, the algorithm to determine the next photo was to: uniformly at random select a month from all the months with photos in them, then uniformly at random select a day within this month, then a random photo within that day. This has the issue that the algorithm does not result in a uniform distribution over all photos.

Assume that a user has 10 photos in their library, one in January and the other ones in February. Then the January photo will on average be shown on 50% of the slides in the slide show, even though we would only expect that to be 10%.

This PR achieves a uniform distribution by first select a month, weighted by the number of photos in that month, followed by a weighted selection of the day within that month, and then a uniform distribution over the photos within that day.

This change was discussed yesterday in the "contributing" channel on discord.

Note: I set up a quick benchmark here to compare the performance of a linear scan vs. binary search to find the matching element in the prefix sum. The runtime complexity is O(n) either way due to the assembly of the prefix sum. We could theoretically cache the prefix sum over the asset counts of the months, but since n is so small I'd argue that it's not worth it. Overall I prefer the linear scan version due to the shorter and simpler code.

How Has This Been Tested?

Testing was done manually. Without this change I always start to notice duplicates after a short while in the slide show. This has not been the case with this change added.

Note that I also added some basic tests for the sampling utility function.

Checklist:

• I have performed a self-review of my own code
• I have made corresponding changes to the documentation if applicable
• I have no unrelated changes in the PR.
• I have confirmed that any new dependencies are strictly necessary.
• I have written tests for new code (if applicable)
• I have followed naming conventions/patterns in the surrounding code
• All code in src/services/ uses repositories implementations for database calls, filesystem operations, etc.
• All code in src/repositories/ is pretty basic/simple and does not have any immich specific logic (that belongs in src/services/)

[github-actions]

Label error. Requires exactly 1 of: changelog:.*. Found: 🖥️web. A maintainer will add the required label.

[Pascal-So]

hmm, I intuitively set the title of the PR to "feat(web)".. now that I think about it a bit more, would you consider this more of a fix than a feat? I'm not sure, open to your opinion.

Edit: changed it to "fix(web)" since I now think that this is more appropriate.

[Pascal-So]

About testing: I was thinking about splitting the code up into two methods on the timeline manager: getNthAsset which we could test, and then make getRandomAsset just a thin untested wrapper.

The downside that I could see with that is that getNthAsset might not have a clear semantic meaning, since from looking at DayGroup.sortAssets I saw that there is the concept of AssetOrder which opens up the question if such a getNthAsset method should change behaviour depending on the order. For the shuffle we don't actually care about the order so in a test I'd just ensure that every asset gets visited if we call getNthAsset with every index so that test would not break either way.

Do you think it would be sufficient if we just add a comment to the getNthAsset method warning any possible future users that the behaviour is dependent on the current AssetOrder?

[Pascal-So]

To have at least some test I now decided to add an optional index argument, which, if present, replaces the floor(rand() * assetCount) index. I'm not that happy with the fact that this is now an argument to the method that is only there to enable testing and should not be used by actual callers, but it's the least bad option that I can come up with.

Let me know if there's anything else that I can do to help get this merged :)