Toward the synthesis of fixed-point code for matrix inversion based on Cholesky decomposition

Matrix inversion is a computationally intensive basic block of many digital signal processing algorithms. To decrease the cost of their implementations, programmers often prefer the fixed-point arithmetic. This arithmetic requires less resources and runs faster than the floating-point arithmetic, but all the arithmetical details must be handled by the programmer. In this article, we overcome this drawback by presenting an automated approach to synthesize fixed-point code for matrix inversion based on Cholesky decomposition. First we rigorously define the square root and division operators especially in terms of rounding error, and we implement them in the CGPE library. This allows us to provide accuracy certificates for the generated code. Second we propose a workflow based on Cholesky decomposition that carefully uses these operators to produce accurate code for the basic blocks of matrix inversion. Finally we illustrate the efficiency of our approach on some benchmarks, and show how it allows us to synthesize accurate code in a few seconds and thus to reduce the development time of fixed-point matrix inversion.