CORDIC Architectures: A Survey : Table 1

Table 1: Realization of some functions using CORDIC Algorithm.


$m$	Mode	Initialization	Output

1 (Circular)	Rotation	$x_{0} = x_{in}$	$x_{n} = K_{m} \cdot (x_{in} \cos θ - y_{in} \sin θ)$
		$y_{0} = y_{in}$	$y_{n} = K_{m} \cdot (y_{in} \cos θ + x_{in} \sin θ)$
		$z_{0} = θ$	$z_{n} = 0$

		$x_{0} = 1 / K_{m}$	$x_{n} = \cos θ$
		$y_{0} = 0$	$y_{n} = \sin θ$
		$z_{0} = θ$	$z_{n} = 0$

		$x_{0} = 1$	$x_{n} = \sqrt{1 + a^{2}}$
		$y_{0} = a$	$y_{n} = \sin θ$
		$z_{0} = π / 2$	$z_{n} = 0$

1 (Circular)	Vectoring	$x_{0} = x_{in}$	$x_{n} = K_{m} \cdot sign (x_{0}) \cdot (x_{in}^{2} + y_{in}^{2})^{1 / 2}$
		$y_{0} = y_{in}$	$y_{n} = 0$
		$z_{0} = 0$	$z_{n} = \tan^{- 1} (y_{in} / x_{in})$

0 (Linear)	Rotation	$x_{0} = x_{in}$	$x_{n} = x_{in}$
		$y_{0} = y_{in}$	$y_{n} = y_{in} + x_{in} \cdot z$
		$z_{0} = z$	$z_{n} = 0$

0 (Linear)	Vectoring	$x_{0} = x_{in}$	$x_{n} = x_{in}$
		$y_{0} = y_{in}$	$y_{n} = 0$
		$z_{0} = z$	$z_{n} = z + y_{in} / x_{in}$

$- 1$ (Hyperbolic)	Rotation	$x_{0} = x_{in}$	$x_{n} = K_{m} \cdot (x_{in} \cosh θ + y_{in} \sinh θ)$
		$y_{0} = y_{in}$	$y_{n} = K_{m} \cdot (y_{in} \cosh θ + x_{in} \sinh θ)$
		$z_{0} = θ$	$z_{n} = 0$

		$x_{0} = 1 / K_{m}$	$x_{n} = \cosh θ$
		$y_{0} = 0, z_{0} = θ$	$z_{n} = 0, y_{n} = \sinh θ$

		$x_{0} = a$	$x_{n} = a e^{θ}$
		$y_{0} = a, z_{0} = θ$	$z_{n} = 0, y_{n} = a e^{θ}$

$- 1$ (Hyperbolic)	Vectoring	$x_{0} = x_{in}$	$x_{n} = K_{m} \cdot sign (x_{0}) \cdot (x_{in}^{2} - y_{in}^{2})^{1 / 2}$
$- 1$ (Hyperbolic)	Vectoring	$y_{0} = y_{in}$	$y_{n} = 0, z_{n} = θ + {tanh}^{- 1} (y_{in} / x_{in})$

		$x_{0} = a$	$x_{n} = \sqrt{a^{2} - 1}$
		$y_{0} = 0$	$y_{n} = 0, z_{n} = \coth^{- 1} a$

		$x_{0} = a + 1$	$x_{n} = 2 \sqrt{a}$
		$y_{0} = a - 1$	$y_{n} = 0, z_{n} = 0.5 \ln (a)$

		$x_{0} = a + b$	$x_{n} = 2 \sqrt{a b}$
		$y_{0} = a - b$	$y_{n} = 0, z_{n} = 0.5 \ln (a / b)$