Recent versions of Cloudera's Impala added NDV, a "number of distinct values" aggregate function that uses the HyperLogLog algorithm to estimate this number, in parallel, in a fixed amount of space.
This can make a really, really big difference: in a large table I tested this on, which had roughly 100M unique values of mycolumn, using NDV(mycolumn) got me an approximate answer in 27 seconds, whereas the exact answer using count(distinct mycolumn) took ... well, I don't know how long, because I got tired of waiting for it after 45 minutes.
It's fun to note, though, that because of another recent addition to Impala's dialect of SQL, the fnv_hash function, you don't actually need to use NDV; instead, you can build HyperLogLog yourself from mathematical primitives.
HyperLogLog hashes each value it sees, and then assigns them to a bucket based on the low order bits of the hash. It's common to use 1024 buckets, so we can get the bucket by using a bitwise & with 1023:
select
