Distributed multi-writer atomic registers are at the heart of a large number of distributed algorithms. While enjoying the benefits of atomicity, researchers further explore fast implementations of atomic reigsters which are optimal in terms of data access latency. Though it is proved that multi-writer atomic register implementations are impossible when both read and write are required to be fast, it is still open whether implementations are impossible when only write or read is required to be fast. This work proves the impossibility of fast write implementations based on a series of chain arguments among indistiguishable executions. We also show the necessary and sufficient condition for fast read implementations by extending the results in the single-writer case. This work concludes a series of studies on fast implementations of distributed atomic registers.