Patent ID: 8639737

Claim:
A method adapted to binary operations on a digital computer for balancing speed, simplicity and accuracy in computing an approximation of a reciprocal square root, reciprocal fourth root or square root of a binary floating point number, comprising steps of extracting by the digital computer an index comprising selected bits of said binary floating point number considered as a binary integer, accessing by the digital computer a binary integer and a binary floating point number from a table in a memory of the digital computer in accordance with said index, said indexed binary floating point number from said table being such as to yield an approximation of said reciprocal square root, reciprocal fourth root or square root, respectively, for said index when multiplied by a binary integer derived from said indexed binary integer, performing by the digital computer a shift operation on said binary floating point number considered as a binary integer to form a shifted binary integer, subtracting by the digital computer using said binary operations said shifted binary integer from said indexed binary integer obtained from said table in said accessing step, and multiplying by the digital computer using said binary operations said indexed binary floating point number by said binary integer derived in said subtracting step to provide said approximation, wherein the indexed binary integer from the table is chosen so that a ratio of end points of an interval of the table where the binary floating point number is located is not changed after the subtracting step.