Algorithm and architecture for logarithm, exponential, and powering computation
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 (XY). The algorithm consists of a sequence of overlapped operations: 1) digit-recurrence logarithm, 2) left-to-right carry-free (LRCF) multiplication, and 3) online exponential. A redundant number system is used and the selection in 1) and 3) is done by rounding except from the first iteration, when selection by table look-up is necessary to guarantee the convergence of the recurrences. A sequential implementation of the algorithm, with a control unit which allows the independent computation of logarithm and exponential, is proposed and the execution times and hardware requirements are estimated for single and double-precision floating-point computations. These estimates are obtained for radices from r = 8 to r = 1,024, according to an approximate model for the delay and area of the main logic blocks and help determining the radix values which lead to the most efficient implementations: r = 32 and r = 128.
logarithm exponential powering high-radix computer arithmetic elementary function approximation digit-recurrence algorithms lrcf multiplication online arithmetic