CORDIC
CORDIC (digit-by-digit method, Volder’s algorithm) (for COordinate Rotation DIgital Computer) is a simple and efficient algorithm to calculate hyperbolic and trigonometric functions. It is commonly used when no hardware multiplier is available (e.g., simple microcontrollers and FPGAs) as the only operations it requires are addition, subtraction, bitshift and table lookup.
The modern CORDIC algorithm was first described in 1959 by Jack E. Volder. It was developed at the aeroelectronics department of Convair to replace the analog resolver in the B-58 bomber’s navigation computer, although it is similar to techniques published by Henry Briggs as early as 1624. John Stephen Walther at Hewlett-Packard further generalized the algorithm, allowing it to calculate hyperbolic and exponential functions, logarithms, multiplications, divisions, and square roots.
Originally, CORDIC was implemented using the binary numeral system. In the 1970s, decimal CORDIC became widely used in pocket calculators, most of which operate in binary-coded-decimal BCD rather than binary. CORDIC is particularly well-suited for handheld calculators, an application for which cost (eg, chip gate count has to be minimised) is much more important than is speed. Also the CORDIC subroutines for trigonometric and hyperbolic functions can share most of their code.
CORDIC is generally faster than other approaches when a hardware multiplier is unavailable (e.g., in a microcontroller based system), or when the number of gates required to implement the functions it supports should be minimized (e.g., in an FPGA). On the other hand, when a hardware multiplier is available (e.g., in a DSP microprocessor), table-lookup methods and power series are generally faster than CORDIC. These days, CORDIC algorithm is used extensively for various biomedical applications, especially in the FPGA domain.