Wednesday, March 1, 2023

Geo Timezones

Brad Fitzpatrick wrote a Go package called latlong which efficiently maps a latitude/longitude to a timezone. The original post describing it was on Google+ and is likely lost forever — unless it made it into the Google+ archive before Google+ joined the Google Graveyard.

It tries to have a small binary size (~360 KB), low memory footprint (~1 MB), and incredibly fast lookups (~0.5 microseconds). It does not try to be perfectly accurate when very close to borders.

It’s available in other languages, too!

Huon Wilson ported the library to the Rust Programming Language, making the code available on GitHub and installable via Cargo. There is even a wrapper made for NodeJs that is installable via NPM that uses a command-line executable written in Go.

When it was announced in 2015, I had ported the library to Factor, but missed the opportunity to blog about it. Below we discuss some details about the implementation, starting with its use of a shapefile of the TZ timezones of the world to divide the world into zones that are assigned timezone values — looking something like this:

The world is divided into 6 zoom levels of tiles (represented by a key and an index value) that allow us to search from a very large area first, then down to the more specific geographic area. Note: we represent the struct as a big endian struct with structure packing to minimize wasted space in the files.

The zoom levels are then cached using literal syntax into a zoom-levels constant.

    { key uint }
    { idx ushort } ;


CONSTANT: zoom-levels $[
    6 <iota> [
        "vocab:geo-tz/zoom" ".dat" surround
        binary file-contents tile cast-array
    ] map

Each of the zoom levels reference indexes into a leaves data structure that contains 14,110 items — each represented by one of three data types:

  1. Type S is a string.
  2. Type 2 is a one bit tile.
  3. Type P is a pixmap thats 128 bytes long.

These we load and cache into a unique-leaves constant.

CONSTANT: #leaves 14110

BE-PACKED-STRUCT: one-bit-tile
    { idx0 ushort }
    { idx1 ushort }
    { bits ulonglong } ;

CONSTANT: unique-leaves $[
    "vocab:geo-tz/leaves.dat" binary [
        #leaves [
            read1 {
                { CHAR: S [ { 0 } read-until drop utf8 decode ] }
                { CHAR: 2 [ one-bit-tile read-struct ] }
                { CHAR: P [ 128 read ] }
            } case
        ] replicate
    ] with-file-reader

The core logic involves looking up a leaf (which is one of three types, loaded above), given an (x, y) coordinate. If it is a string type, we are done. If it is a one-bit-tile, we defer to the appropriate leaf specified by idx0 or idx1. And if it is pixmap, we have a smidge more logic to detect oceans or defer again to a different leaf.

CONSTANT: ocean-index 0xffff

GENERIC#: lookup-leaf 2 ( leaf x y -- zone/f )

M: string lookup-leaf 2drop ;

M:: one-bit-tile lookup-leaf ( leaf x y -- zone/f )
    leaf bits>> y 3 bits 3 shift x 3 bits bitor bit?
    [ leaf idx1>> ] [ leaf idx0>> ] if
    unique-leaves nth x y lookup-leaf ;

M:: byte-array lookup-leaf ( leaf x y -- zone/f )
    y 3 bits 3 shift x 3 bits bitor 2 * :> i
    i leaf nth 8 shift i 1 + leaf nth +
    dup ocean-index = [ drop f ] [
        unique-leaves nth x y lookup-leaf
    ] if ;

We’re almost done! Given a zoom level, a tile-key helps us find a specific tile that we then can lookup the leaf for, hopefully finding the timezone associated with the coordinate.

:: lookup-zoom-level ( zoom-level x y tile-key -- zone/f )
    zoom-level [ key>> tile-key >=< ] search swap [
        dup key>> tile-key = [
            idx>> unique-leaves nth x y lookup-leaf
        ] [ drop f ] if
    ] [ drop f ] if ;

Each coordinate is effectively a pixel in the image, so our logic searches from the outermost zoom level to the innermost, trying to lookup a timezone in each one using the coordinate and level as a tile-key.

:: tile-key ( x y level -- tile-key )
    level dup 3 + neg :> n
    y x [ n shift 14 bits ] bi@
    { 0 14 28 } bitfield ;

:: lookup-pixel ( x y -- zone )
    6 <iota> [| level |
        level zoom-levels nth
        x y 2dup level tile-key
    ] map-find-last drop ;

Finally, we have enough to implement our public API, converting a given latitude/longitude coordinate to a pixel value, deferring to the word we just defined above.

CONSTANT: deg-pixels 32

:: lookup-zone ( lat lon -- zone )
    lon 180 + deg-pixels * 0 360 deg-pixels * 1 - clamp
    90 lat - deg-pixels * 0 180 deg-pixels * 1 - clamp
    [ >integer ] bi@ lookup-pixel ;

And then a couple of test cases to show it’s working:

{ "America/Los_Angeles" } [ 37.7833 -122.4167 lookup-zone ] unit-test

{ "Australia/Sydney" } [ -33.8885 151.1908 lookup-zone ] unit-test

Performance is pretty good, we can generate over 3 million lookups per second, putting our cost per lookup around 0.33 microseconds. And all of that in less than 70 lines of code.

This is available on my GitHub.

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