A data prefetcher in a microprocessor having a cache memory receives memory accesses each to an address within a memory block. The access addresses are non-monotonically increasing or decreasing as a function of time. As the accesses are received, the prefetcher maintains a largest address and a smallest address of the accesses and counts of changes to the largest and smallest addresses and maintains a history of recently accessed cache lines implicated by the access addresses within the memory block. The prefetcher also determines a predominant access direction based on the counts and determines a predominant access pattern based on the history. The prefetcher also prefetches into the cache memory, in the predominant access direction according to the predominant access pattern, cache lines of the memory block which the history indicates have not been recently accessed.