Continued fractions for high-speed and high-accuracy computer arithmetic

Continued fraction representation has many advantages for fast and high-accuracy computation when compared with positional notation. A continued fraction is a number of the form p1 + q1/(p2 + q2/(p3 + …)), where pi and qi are integers. Some of the benefits of continued fraction representation for computer arithmetic are: faster multiply and divide than with positional notation, fast evaluation of trigonometric, logarithmic, and other unary functions, easy extension to infinite-precision arithmetic, infinite-precision representation of many transcendental numbers, no roundoff or truncation errors, and improved software transportability because accuracy is not hardware dependent. A unified system for continued fraction arithmetic is given, along with an outline of a hardware architecture for evaluating these functions.