Disclosed herein are a processing unit and a multi-processing unit system that implement a cache-coherency method. Such a multi-processing unit system includes a main memory, a first processing unit, and a second processing unit. The first processing unit and the second processing unit are coupled to the main memory. The first processing unit includes a cache and logic. The cache is configured to store data from the main memory. The logic is configured to maintain an entry in a directory of the cache. The entry indicates whether either of the first processing unit and the second processing unit accesses a data object of a cache line for which the first processing unit is a home node.