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—A table-based method for high-speed function approximation in single-precision floating-point format is presented in this paper. Our focus is the approximation of reciprocal, square root, square root reciprocal, exponentials, logarithms, trigonometric functions, powering (with a fixed exponent p), or special functions. The algorithm presented here combines(More)
—A new method for the high-speed computation of double-precision floating-point reciprocal, division, square root, and inverse square root operations is presented in this paper. This method employs a second-degree minimax polynomial approximation to obtain an accurate initial estimate of the reciprocal and the inverse square root values, and then performs a(More)
A high-radix digit-recurrence algorithm for the computation of the logarithm, and an analysis of the tradeoffs between area and speed for its implementation, are presented in this paper. Selection by rounding is used in iterations j ≥ 2, and by table look-up in the first iteration. A sequential architecture is proposed, and estimates of the execution time(More)
—An architecture for the computation of logarithm, exponential, and powering operations is presented in this paper, based on a high-radix composite algorithm for the computation of the powering function (X Y). The algorithm consists of a sequence of overlapped operations: 1) digit-recurrence logarithm, 2) left-to-right carry-free (LRCF) multiplication, and(More)
The Mahler measure formula expresses the height of an algebraic number as the integral of the log of the absolute value of its minimal polynomial on the unit circle. The height is in fact the canonical height associated to the monomial maps x n. We show in this work that for any rational map ϕ(x) the canonical height of an algebraic number with respect to ϕ(More)