A method of determining ranges for algorithmic variables for a processor that uses fixed point arithmetic is provided. The method comprises expressing overflow requirements of processor instructions as inequalities. The method also expresses precision requirements and expressiveness requirements as inequalities and merit functions. A global constraint and optimizer tool is used to find ranges for algorithmic variables based on the inequalities and the merit functions. The use of constraint equation solving and optimization finds optimal algorithmic ranges that provide overflow-free arithmetic as well as optimal expressiveness and precision.