Synthesis of arithmetic expressions for the fixed-point arithmetic: The Sardana approach

Sardana is a tool which optimizes the arithmetic expressions present in source codes. The optimization is done by synthesizing automatically new mathematically equal expressions, given ranges of values for the variables. In previous work, Sardana has been used to optimize the numerical accuracy of floating-point expressions, by minimizing the worst roundoff error on the result of the evaluation. In this article, we show how our tool can be used to synthesize arithmetic expressions optimized for the fixed-point arithmetic. In this context, Sardana minimizes the number of bits required to represent without overflow the integer parts of the fixed-point numbers possibly occurring at any stage of the evaluation of an expression. We present experimental results showing how our tool optimizes the implementation of digital filters commonly used in image processing.