Simplify and optimize Hilbert tile ID <-> XYZ conversion

[ciscorn]

I found that we can simplify and optimize the conversion between XYZ tile coordinates and the Hilbert tile IDs.

This optimization is primarily based on the fact that the tile IDs for (zi, 0, 0) are given by the sum of a geometric series with a common ratio of 4.

Related PR: protomaps/go-pmtiles#208

[bdon]

Same with #470 - please provide some evidence or benchmark this is faster across different JavaScript engines, otherwise we will just have other PRs optimizing it in different ways (iterative, lookup table, etc)

[ciscorn]

Sorry for unintentionally creating a duplicate PR. I’ll take some time later to run benchmarks.

[ciscorn]

@bdon

I have now benchmarked the JavaScript implementation across multiple runtimes and browsers.

Benchmarking script: https://gist.github.com/ciscorn/e84d41fe5c7ac7c1857d8f64fc1df069

Results on my M1 Apple Silicon:

Chrome 133

zxyToTileId: Original=2665.60(ms), Modified=42.50(ms) (62.72x faster)
tileIdToZxy: Original=548.10(ms), Modified=381.60(ms) (1.44x faster)

Firefox 125

zxyToTileId: Original=2677.00(ms), Modified=47.00(ms) (56.96x faster)
tileIdToZxy: Original=942.00(ms), Modified=555.00(ms) (1.70x faster)

NodeJS 22.12

zxyToTileId: Original=2760.29(ms), Modified=40.69(ms) (67.83x faster)
tileIdToZxy: Original=625.26(ms), Modified=384.92(ms) (1.62x faster)

Bun 1.2.2

zxyToTileId: Original=1483.75(ms), Modified=80.07(ms) (18.53x faster)
tileIdToZxy: Original=1003.57(ms), Modified=702.73(ms) (1.43x faster)

Deno 2.1.10

zxyToTileId: Original=2730.63(ms), Modified=40.57(ms) (67.30x faster)
tileIdToZxy: Original=646.00(ms), Modified=380.45(ms) (1.70x faster)

[bdon]

Released in https://www.npmjs.com/package/pmtiles 4.3.0, thanks!