A combined interval and floating-point reciprocal unit

Abstract

Interval arithmetic is one technique for accurate and reliable computing. Among interval arithmetic operations, division is the most time consuming operation. This paper presents the design and implementation of a combined interval and floating-point reciprocal unit. To compute the reciprocal of an operand, an initial approximation is computed first and then iterated twice by Newton-Raphson iteration. The combined interval and floating-point reciprocal unit computes the reciprocal of a double precision floating-point number in eleven clock cycles and the reciprocal of an interval in twenty-one clock cycles. The unit is implemented in VHDL and synthesized to estimate the area and the worst case delay. Simulation results showed that the least significant bit of the floating-point result cannot be guaranteed to be same for all cases compared to the result based on an infinite precision. For interval reciprocal, however, the true result is contained in the result interval.