Circuits, systems, and methods implementing approximations for logarithm, inverse logrithm,and reciprocal

摘要

A digital signal system (30) for determining an approximate logarithm of a value of x having a base b. The system comprises circuitry (32) for storing x as a digital representation and circuitry for identifying a most significant digit (MSD) of the digital representation. Adjacent the most significant digit is located a set of bits in respective lesser significant bit locations. The system further comprises a table (36) for storing a set of predetermined logarithms having the base b, wherein each of the predetermined logarithms corresponds to a number in a set of numbers. The system further comprises circuitry for addressing the table in response to a first bit group (t) of the set of bits in respective lesser significant bit locations, and in response the table is for outputting a one of the predetermined logarithms corresponding to a first number (I_a) in the set of numbers. Lastly, the system comprises circuitry (38) for outputting the approximate logarithm of the value of x in response to the one of the predetermined logarithms and further in response to a function estimation between logarithms at a first and second endpoint. The first endpoint corresponds to the first number in the set of numbers times a power of b and the second endpoint corresponds to a second number in the set of numbers times the power of b. Further, the function estimation estimates a logarithm at a number located at distance from one of the first and second endpoints, wherein the distance is responsive to a second bit group of the set of bits.