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A new function-evaluation algorithm is presented using a two-level approximation scheme. In the first level, piecewise degree-one polynomial is used for initial approximation to obtain the so-called normalized difference functions that are similar in shape. Then, a shared normalized difference function is computed to achieve the target precision in the second level of refined approximation. We also perform the error analysis and bit-width optimization with two different design goals: area optimization and ROM optimization. Experimental results show that the proposed ROM-optimized architecture, when used in the multifunction evaluator for computing several elementary arithmetic functions on the same hardware, has significant area saving compared to previous approaches.