This paper presents a unified algorithm for calculating elementary functions, including multiplication, division, trigonometric, hyperbolic, and logarithmic functions. The algorithm is based on coordinate rotation in linear, circular, or hyperbolic coordinate systems, using only shifting, adding, subtracting, and recalling pre-stored constants. The convergence domain of the algorithm is limited, and modifications are discussed to extend it for floating-point calculations. A hardware floating-point processor based on this algorithm was developed at Hewlett-Packard Laboratories, with a block diagram, microprogram control, and performance metrics provided. The algorithm's simplicity, accuracy, and high-speed execution via parallel processing make it suitable for applications such as desktop calculators, air navigation computers, and floating-point processors.This paper presents a unified algorithm for calculating elementary functions, including multiplication, division, trigonometric, hyperbolic, and logarithmic functions. The algorithm is based on coordinate rotation in linear, circular, or hyperbolic coordinate systems, using only shifting, adding, subtracting, and recalling pre-stored constants. The convergence domain of the algorithm is limited, and modifications are discussed to extend it for floating-point calculations. A hardware floating-point processor based on this algorithm was developed at Hewlett-Packard Laboratories, with a block diagram, microprogram control, and performance metrics provided. The algorithm's simplicity, accuracy, and high-speed execution via parallel processing make it suitable for applications such as desktop calculators, air navigation computers, and floating-point processors.