Rapid computation of natural logarithms involves computing first order polynomial for mantissa range 1 to 2, computing log(x) for binary floating point representation using polynomial

摘要

The method involves dividing a mantissa range between 1 and 2 into N sub-ranges, pre-computing sub-range center points, computing a first order polynomial in m.log(m) for each m in the sub-range with a pre-selected accuracy, whereby m is a binary floating point representation of a binary mantissa number, and computing a log(x) value for a binary floating point representation of a special number x in a data processor memory using the polynomial. The method involves dividing a mantissa range between 1 and 2 into N sub-ranges, pre-computing center points of each sub-range, selecting N to be large enough that for each sub-range a first order polynomial in m.log(m) for each m in the sub-range is computed with a pre-selected degree of accuracy, whereby m is a binary floating point representation of a number of a binary mantissa, and computing a value of log(x) for a binary floating point representation of a special number x in a data processor memory using the first order polynomial in m. Independent claims are also included for the following: a data processor.