A high-speed processor utilizes combinational logic and range limitation for a modified input value to increase efficiency in convergence factor determination for convergent division and square root computation. An input value is modified to a value in a limited range, which is then partitioned into two subdivisions. By utilizing these two groupings, the processing platform minimizes time consumption in conversion factor determination by inverting selected binary bits to form a modified factor and utilizes that modified factor to facilitate high-speed convergence factor computation.