and CURLOPT_CONNECTTIMEOUT_MS that, as their names should hint, do the
  timeouts with millisecond resolution instead. The only restriction to that
  is the alarm() (sometimes) used to abort name resolves as that uses full
  seconds. I fixed the FTP response timeout part of the patch.

  Internally we now count and keep the timeouts in milliseconds but it also
  means we multiply set timeouts with 1000. The effect of this is that no
  timeout can be set to more than 2^31 milliseconds (on 32 bit systems), which
  equals 24.86 days.  We probably couldn't before either since the code did
  *1000 on the timeout values on several places already.