Abstract: Loops with internal data dependencies (e.g., in a Mersenne Twister pseudorandom number generator) are implemented by exploiting arrays of cooperating threads that can be executed concurrently using a suitably configured processor. In one implementation, each thread is assigned to update a different element of a data array where updating of later elements depends on updates to earlier elements. Thread synchronization techniques are advantageously used to control the order in which different threads update their assigned elements such that the data dependencies are correctly handled. To the extent that threads assigned to different data elements do not have data dependencies on each other, those threads can be executed in parallel.