1. An information processing apparatus, comprising: a main storage device that stores data and manages a state of the stored data as directory information; cache memories that retain a copy of the data stored in the main storage device; processors that perform a process by using the data retained in the cache memories; a directory cache that manages the directory information of the data stored in the main storage device separately from the main storage device, and manages coherence state information indicating a state of coherence between the directory information managed by the directory cache and the directory information managed by the main storage device; and a memory control apparatus that controls a data transfer between the cache memories and the main storage device based on the information managed by the directory cache, wherein when a single cache memory retains a copy of data stored in the main storage device and the memory control apparatus receives a notice that data retained in the cache memory is purged from any of the processor, the memory control apparatus updates the directory information on the directory cache and accesses the main storage device to perform a write-back of the directory information on the main storage device when the coherence state information indicates that the directory information on the directory cache and the directory information on the main storage device are different, and updates the directory information on the directory cache without accessing the main storage device when the data is not modified by the processor, the coherence state information indicates that the directory information on the directory cache and the directory information on the main storage device are different, and the directory information on the main storage device indicates that the copy of the data is not retained by any of the processors.