Tile ranges are inclusive. When getting the tile range for an extent, the top-right corner of the extent should be considered with a different intersection policy than the bottom-left corner.
When the dom renderer included logic to stretch tiles so that gaps were properly filled for fractional zoom levels, we needed to take this into account when getting a tile coordinate for a given coordinate and resolution. This was never the proper logic for a renderer that wasn't stretching occassional tiles (e.g. the WebGL renderer, the Canvas renderer, or the new DOM renderer).
Previously, the TiledWMS source generated a resolutions array
derived from the world extent in meters, to match the default
Web Mercator resolutions of the map. This wouldn't work for
projections with distance units different than meters. It is
better to commit to a default resolutions array where zoom level
0 is the validity extent of the projection (not the Web Mercator
world extent!) at a 256 pixel tile size.
Tom Payne
Bruno Binet
Tim Schaub
ahocevar