Programmatically detect Heroku dyno size at run time?

Say I have a Heroku app that is deployed to various different sizes of dynos over time or by different users. How can I reliably determine what size dyno the app is running in? I know that $DYNO will tell me what the process name is (e.g. web.123 or worker.456), but none of the Heroku environment vars indicate whether that's a 256MB 1X, 1024MB 2X, or a 6GB PX dyno.

Heroku support provided this answer, which they refused to document because it's a hack, and they intend to provide a reasonable solution in the future.

The only way to do this would be to shell out and call ulimit -u to get the max number of tasks. 256 for 1X dynos, 512 for 2X and MAX_SUPPORTED_BY_LINUX for PX.

Bash example:

function dyno_size() {
  case $(ulimit -u) in
    256)
      echo "1X"
      ;;
    512)
      echo "2X"
      ;;
    32768)
      echo "PX"
      ;;
    *)
      echo "unknown"
      ;;
  esac
}