USING FRACTIONAL EXPONENTS TO REDUCE THE COMPUTATIONAL COMPLEXITY OF NUMERICAL OPERATIONS

摘要

Technologies are described herein for using efficient log-linear transformations to reduce the complexity of numerical computations. Efficient transforms can convert between linear fixed point values and log space values in about ten processor cycles per sample. A fractional exponent and an integer exponent may be combined together into a log domain variable representation. Log domain arithmetic operations may be performed on the combined variable as a whole. A fractional exponent representation of log domain numerical values can support automatic bit carries from the fractional exponent into the integer exponent. If an intermediate result of a calculation in the log domain causes the fractional portion of the exponent to exceed one, a bit carry can occur over to the integer component of the exponent. This carry can occur automatically due to the conjoined placement of the integer and fractional components of the exponent in the log domain combined variable.