Combining Height Reduction and Scheduling for VLIW Machines Enhanced with Three-Argument Arithmetic Operations

In here we consider a technique to automatically extract three-argument instructions from sequential arithmetic code. The instructions include: multiply and add, three argument additions and three argument multiplications (MUL3). The proposed solution combines a height reduction technique that generates three-argument instructions and a VLIW scheduling that can benefit from these instructions. The proposed height reduction technique is based on a known theoretical algorithm (MRK) that in some cases can evaluate an algebraic circuit faster than its depth. We modified the MRK algorithm to generate less instructions and emit VLIW instructions. The modified MRK algorithm was implemented in the LLVM compiler and the potential usefulness was measured. Our results show that for arithmetic benchmarks the proposed technique can improve the VLIW scheduling while emitting three-argument instructions. The contribution of this work includes: the modified MRK algorithm as a new technique for height reduction optimizations and the study of the potential usefulness of three-argument instructions. Though our results are for a non existing hardware they show the usefulness of adding such instructions to VLIW CPUs. Note that a previous research showed that MUL3 can be executed as fast as MUL2.