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Review Article

# CORDIC Architectures: A Survey

## Table 1

Realization of some functions using CORDIC Algorithm.
 $m$ Mode Initialization Output 1 (Circular) Rotation ${x}_{0}={x}_{\text{in}}$ ${x}_{n}={K}_{m}·\left({x}_{\text{in}}\mathrm{cos} \theta -{y}_{\text{in}}\mathrm{sin}\theta \right)$ ${y}_{0}={y}_{\text{in}}$ ${y}_{n}={K}_{m}·\left({y}_{\text{in}}\mathrm{cos} \theta +{x}_{\text{in}}\mathrm{sin}\theta \right)$ ${z}_{0}=\theta$ ${z}_{n}=0$ ${x}_{0}=1/{K}_{m}$ ${x}_{n}=\mathrm{cos} \theta$ ${y}_{0}=0$ ${y}_{n}=\mathrm{sin}\theta$ ${z}_{0}=\theta$ ${z}_{n}=0$ ${x}_{0}=1$ ${x}_{n}=\sqrt{1+{a}^{2}}$ ${y}_{0}=a$ ${y}_{n}=\mathrm{sin}\theta$ ${z}_{0}=\pi /2$ ${z}_{n}=0$ 1 (Circular) Vectoring ${x}_{0}={x}_{\text{in}}$ ${x}_{n}={K}_{m}·\mathrm{sign} \left({x}_{0}\right)·\left({x}_{\text{in}}^{2}+{y}_{\text{in}}^{2}{\right)}^{1/2}$ ${y}_{0}={y}_{\text{in}}$ ${y}_{n}=0$ ${z}_{0}=0$ ${z}_{n}={\mathrm{tan}}^{-1}\left({y}_{\text{in}}/{x}_{\text{in}}\right)$ 0 (Linear) Rotation ${x}_{0}={x}_{\text{in}}$ ${x}_{n}={x}_{\text{in}}$ ${y}_{0}={y}_{\text{in}}$ ${y}_{n}={y}_{\text{in}}+{x}_{\text{in}}·z$ ${z}_{0}=z$ ${z}_{n}=0$ 0 (Linear) Vectoring ${x}_{0}={x}_{\text{in}}$ ${x}_{n}={x}_{\text{in}}$ ${y}_{0}={y}_{\text{in}}$ ${y}_{n}=0$ ${z}_{0}=z$ ${z}_{n}=z+{y}_{\text{in}}/{x}_{\text{in}}$ $-1\mathrm{ }$(Hyperbolic) Rotation ${x}_{0}={x}_{\text{in}}$ ${x}_{n}={K}_{m}·\left({x}_{\text{in}}\mathrm{cosh} \theta +{y}_{\text{in}}\mathrm{sinh} \theta \right)$ ${y}_{0}={y}_{\text{in}}$ ${y}_{n}={K}_{m}·\left({y}_{\text{in}}\mathrm{cosh} \theta +{x}_{\text{in}}\mathrm{sinh} \theta \right)$ ${z}_{0}=\theta$ ${z}_{n}=0$ ${x}_{0}=1/{K}_{m}$ ${x}_{n}=\mathrm{cosh} \theta$ ${y}_{0}=0,\mathrm{ }{z}_{0}=\theta$ ${z}_{n}=0,\mathrm{ }{y}_{n}=\mathrm{sinh} \theta$ ${x}_{0}=a$ ${x}_{n}=a{e}^{\theta }$ ${y}_{0}=a,\mathrm{ }{z}_{0}=\theta$ ${z}_{n}=0,\mathrm{ }{y}_{n}=a{e}^{\theta }$ $-1\mathrm{ }$(Hyperbolic) Vectoring ${x}_{0}={x}_{\text{in}}$ ${x}_{n}={K}_{m}·\mathrm{sign} \left({x}_{0}\right)·\left({x}_{\text{in}}^{2}-{y}_{\text{in}}^{2}{\right)}^{1/2}$ ${y}_{0}={y}_{\text{in}}$ ${y}_{n}=0,\mathrm{ }{z}_{n}=\theta +{\text{tanh}}^{-1}\left({y}_{\text{in}}/{x}_{\text{in}}\right)$ ${x}_{0}=a$ ${x}_{n}=\sqrt{{a}^{2}-1}$ ${y}_{0}=0$ ${y}_{n}=0,\mathrm{ }{z}_{n}={\mathrm{coth} }^{-1}a$ ${x}_{0}=a+1$ ${x}_{n}=2\sqrt{a}$ ${y}_{0}=a-1$ ${y}_{n}=0,\mathrm{ }{z}_{n}=0.5\mathrm{ln} \left(a\right)$ ${x}_{0}=a+b$ ${x}_{n}=2\sqrt{ab}$ ${y}_{0}=a-b$ ${y}_{n}=0,\mathrm{ }{z}_{n}=0.5\mathrm{ln} \left(a/b\right)$

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