Optimal Polynomial-Time Interprocedural Register Allocation for High-Level Synthesis Using SSA Form

An optimal, polynomial-time algorithm for interprocedural register allocation in high-level synthesis and ASIP design is presented. The algorithm determines the minimum number of registers required to store all scalar variables in an application without spilling any to memory. Although an optimal polynomialtime algorithm has been presented in the past for individual procedures in Static Single Assignment (SSA) Form, this is the first such claim for the interprocedural analogue of the problem, which considers interferences across procedure calls. A new extension of SSA Form is introduced, and an example illustrates that this new representation can reduce the number of registers required for an optimal allocation. A secondary aspect of the optimal algorithm is that it is scalable: there is no need to build a complete interprocedural interference graph and each procedure can be colored individually. Our experiments show that the optimal algorithm runs more than 100× faster than a previously published scalable sub-optimal heuristic for the same problem.