CORDIC算法的理解和Verilog实现

0.引子

$x'=rcos(\theta+\alpha)=r(cos\theta cos\alpha-sin\theta sin\alpha) \\ y'=rsin(\theta+\alpha)=r(sin\theta cos\alpha+cos\theta sin\alpha)$

$sin\alpha=\frac{y}{r},~cos\alpha=\frac{x}{r}$

$x'=r(\frac{x}{r}cos\theta-\frac{y}{r}sin\theta)=xcos\theta-ysin\theta \\ y'=r(\frac{x}{r}sin\theta+\frac{y}{r}cos\theta) = xsin\theta+ycos\theta$

$\begin{bmatrix} x' \\ y' \\ \end{bmatrix} = \begin{bmatrix} cos\theta & -sin\theta \\ sin\theta & cos\theta \\ \end{bmatrix} \begin{bmatrix} x \\ y \\ \end{bmatrix}$

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