Efficient arithmetic expression optimization with weighted adjoint matrix

Polynomial arithmetic expressions are frequently used in encryption, decryption, digital signal processing and many other embedded applications. Compiler optimization for polynomial expressions can improve the performance of the embedded applications. This article presents an improved compiler optimization method for multiple arithmetic polynomial expressions. Considering the semantic and timing information of arithmetic instructions, the algorithm uses a canonical representation for all expressions, taking consideration of times of execution, architecture feature and control-flow information. It calculates sub-expressions’ weights based on the target architecture description and heuristically choose the sub-expressions. It achieves better instruction level parallelism from the consideration of sub-expressions’ weights, which contains architecture information. Experiment results show that compared to traditional optimization methods, this algorithm further improves the code density and the performance of the generated binary codes.