CORDIC Totally Explained

Everything about Cordic totally explained

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 (for example, 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's similar to techniques published by Henry Briggs as early as 1624. John Stephen Walther at Hewlett-Packard further generalized the algorithm, allowing to calculate hyperbolic and exponential functions, logarithm, multiplication, division, and square root.
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 (for example, 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.

Application

CORDIC is generally faster than other approaches when a hardware multiplier is unavailable (for example in a microcontroller), or when the number of gates required to implement one needs to be minimized (for example in an FPGA). On the other hand, when a hardware multiplier is available (for example in a DSP microprocessor), table-lookup methods and power series are generally faster than CORDIC.

Mode of operation

CORDIC can be used to calculate a number of different functions. This explanation shows how to use CORDIC in rotation mode to calculate sin and cos of an angle, and assumes the wanted angle is given in radians and represented in a fixed point format. To determine the sine or cosine for an angle

eta

, the y or x coordinate of a point on the unit circle corresponding to the wanted angle needs to be found. Using CORDIC, we'd start with the vector

v_0

:
ť

v_o = egin

, the Intel 80x87 coprocessor series until Intel 80486, and Motorola 68881.
Decimal CORDIC was first suggested by Hermann Schmid and Anthony Bogacki

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