T h e reciprocal and square-root reciprocal operations are in several applications. For these operations, we algorithms that combine a digitand one iteration of quadraticconvergence upproximation. T h e latter is implemented by a digit-recurrence, which uses the digits produced by the digit-by-digit part. In this way, both parts execute in a n overlapped manner, so that the total number of cycles is half of the that would be required by the digit-by-digit part alone. Because of the

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... , rounding of the result cannot be obtained directly all cases; we propose a variable-time that produces the correctly rounded result with a small average overhead. are described and have been synthesized. T h e y achieve the same cycle t i m e as the standard digit-bydigit implementation, resulting an a of about 2 and, because of the part, the factor is also about 2. W e also show a implernenf o r both operations that has essentially the same complexity as that for square-root alone.