1. A method, comprising the steps of: providing a plurality of virtual register addresses; providing a plurality of physical register addresses; providing a map that maintains a mapping between each of the plurality of virtual register addresses and a corresponding one of a subset of the plurality of physical register addresses; dispatching a sequence of instructions; generating a sequence of mapped instructions in response to receiving the sequence of instructions, wherein the step of generating a sequence of mapped instructions comprises: generating a new mapping for a particular virtual register address whenever that virtual register address is specified as a destination register address by one of the sequence of instructions; and generating a mapped instruction using the new mapping, the mapped instruction including the new mapping and a previous mapping of the particular virtual register address; executing the sequence of mapped instructions such that younger mapped instructions occurring later in a program order are allowed to complete execution before older mapped instructions occurring earlier in the program order complete; and storing a result for each mapped instruction that successfully completes execution, the result being stored at the physical register address indicated by the new mapping of that mapped instruction.