Patent ID: 7031993
Filing Date: 2006-04-18
Classification: G06F

Abstract:
1. A method for computing an approximation of a natural logarithm function comprising the steps of: partitioning an interval between 1 and 2 into N equally spaced sub-regions; precomputing a reference point a selecting N sufficiently large so that, for each sub-region, a first degree polynomial in m computes log(m) to within a preselected degree of accuracy for any m within the sub-region, where m is a binary mantissa of a binary floating point representation of a variable x; computing a value of log(x) for a binary floating point representation of x stored in a memory of a computing device utilizing the first degree polynomial in the binary mantissa m, wherein log(x) is a function of a distance between the reference point a generating an image by using the computed value of log(x), wherein x has a binary exponent e in addition to the binary mantissa m; and further wherein computing a value of log(x) for the binary floating point representation of x comprises the steps of: partitioning the binary mantissa m of a binary representation of x in a memory, the representation of x including a binary exponent e and the binary mantissa m, wherein a first, most significant part of the partition corresponds to a region i and a second, less significant part of the partition corresponds to a region Δx, where Δx is a distance from the binary mantissa m to the reference point computing an approximation to log(x), using the first degree polynomial in the binary mantissa m and a precomputed value of log(a for i=0, . . . ,N−1 where: precomputing a value for log(2); and for each i, precomputing each value of b