The Spiral Search: A Linear Complexity Algorithm for the Generation of Convex MIMO Instruction-Set Extensions

The instruction-set extension problem has been one of the major topics in the last decade and it consists of the addition of a set of new complex instructions to a given instruction-set. This problem in its general formulation requires an exhaustive search of the design space to identify the candidate instructions. A tradeoff between complexity and quality of the solution can be achieved limiting this search to implementable instructions. In this paper we propose a linear complexity algorithm for the generation of convex multiple input multiple output (MIMO) instructions of variable size based on the notion of spiral. Convex implementable MIMO clusters of instructions are identified by means of a spiral search through the levels of a graph. These new instructions can be directly selected or combined for more complex instruction-set extensions. An important feature of our algorithm is that it is neither restricted to basic-block level nor it imposes any limitation on the number of the newly instructions nor on the number of the inputs/outputs of these instructions.