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 processors, 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 on the cache memory 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, and the memory control apparatus performs a data transfer between the cache memory and the main storage device based on address information, state information, and directory information managed by the directory cache and accesses the main storage device to write-back the data on the main storage device in a case of receiving notification “Eviction” of a cache line in the state “Modify (M)”, wherein the directory cache includes, as the coherence state information, a state “Dirty formerly Invalid (DI)” and the state “Dirty formerly Invalid (DI)” is a state that is newly added as one piece of information which indicates a state of coherence between the directory information on the directory cache and the directory information on the cache memory and that indicates a state telling the directory information on the directory cache is different from the directory information on the cache memory and the directory information on the cache memory is in a state “Invalidate (I)”, wherein the notification “Eviction” is a signal to be transmitted to the memory control apparatus from the processor when the processor purges data in the cache memory in a case of purging the cache line because the cache line cannot be stored in the cache memory or becomes unnecessary, and includes information of whether or not the cached copy is modified and the memory control apparatus further includes a state managing unit that determines, in receiving the notification “Eviction”, a necessity of accessing the cache memory by referring to content of the received notification “Eviction”, determines whether or not the cached copy is modified and whether or not the state of an entry is “(Dirty formerly Invalid) DI”, when the cached copy is not modified and the state of the entry is “(Dirty formerly Invalid) DI”, and makes the directory information on the directory cache null without performing reading, modifying, and writing in the cache memory, wherein the state managing unit makes a state of an entry corresponding to data stored at an address X of the main storage device at an initial state “D” in a case where the directory information on the memory is not in the state “I” when the directory information on the directory cache is in the state “N” from the beginning.