Calculate reciprocal with NewtonRaphson approximation method
HDL Coder / HDL Operations
The HDL Reciprocal block uses the NewtonRaphson iterative method to compute the reciprocal of the block input. The NewtonRaphson method uses linear approximation to successively find better approximations to the roots of a realvalued function.
The reciprocal of a real number $$a$$ is defined as a zero of the function:
$$f\left(x\right)=\frac{1}{x}a$$
HDL Coder™ chooses an initial estimate in the range $$0<{x}_{0}<\frac{2}{a}$$ as this is the domain of convergence for the function.
To successively compute the roots of the function, specify the Number of iterations parameter in the Block Parameters dialog box. The process is repeated as:
$${x}_{i+1}={x}_{i}\frac{f\left({x}_{i}\right)}{f\text{'}\left({x}_{i}\right)}={x}_{i}+({x}_{i}a{x}_{i}{}^{2})={x}_{i}.(2a{x}_{i})$$
$$f\text{'}(x)$$ is the derivative of the function $$f(x)$$.
Following table shows comparison of simulation behavior of HDL Reciprocal with Math Reciprocal block:
Math Reciprocal  HDL Reciprocal 

Computes the reciprocal as 1/N by using the HDL divide operator (/) to implement the division.  Uses the NewtonRaphson iterative method. The block computes an approximate value of reciprocal of the block input and can yield different simulation results compared to the Math Reciprocal block. To match the simulation results with the Math Reciprocal block, increase the number of iterations for the HDL Reciprocal block. 
Number of NewtonRaphson iterations. The default is 3.
The block has the following ports:
Supported data types: Fixedpoint, integer (signed or unsigned), double, single
Minimum bit width: 2
Maximum bit width: 128
Input data type  Output data type 

double  double 
single  single 
builtin integer  builtin integer 
builtin fixedpoint  builtin fixedpoint 



