Calculate reciprocal with Newton-Raphson approximation method - Simulink - 万博1manbetx,s manbetx 845,万博尤文图斯

Description

TheHDL Reciprocalblock uses the Newton-Raphson iterative method to compute the reciprocal of the block input. The Newton-Raphson method uses linear approximation to successively find better approximations to the roots of a real-valued function.

The reciprocal of a real number $a$ is defined as a zero of the function:

$f (x) = \frac{1}{x} - a$

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 theNumber of iterationsparameter in the Block Parameters dialog box. The process is repeated as:

$x_{i + 1} = x_{i} - \frac{f (x_{i})}{f' (x_{i})} = x_{i} + (x_{i} - a x_{i}^{2}) = x_{i} . (2 - a x_{i})$

$f' (x)$ is the derivative of the function $f (x)$ .

Following table shows comparison of simulation behavior ofHDL ReciprocalwithMath Reciprocalblock:

Math Reciprocal	HDL Reciprocal
Computes the reciprocal as 1/N by using the HDL divide operator (/) to implement the division.	Uses the Newton-Rapshon 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 theMath Reciprocalblock, increase the number of iterations for theHDL Reciprocalblock.

Math Reciprocal

HDL Reciprocal

Computes the reciprocal as 1/N by using the HDL divide operator (/) to implement the division.

Uses the Newton-Rapshon 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 theMath Reciprocalblock, increase the number of iterations for theHDL Reciprocalblock.

Parameters

Number of iterations: Number of Newton-Raphson iterations. The default is 3.

Ports

The block has the following ports:

Input

Supported data types: Fixed-point, integer (signed or unsigned), double, single
Minimum bit width: 2
Maximum bit width: 128

Output

Input data type	Output data type
double	double
single	single
built-in integer	built-in integer
built-in fixed-point	built-in fixed-point
`fi`(value, 0,word_length,fraction_length)	`fi`(value, 0,word_length,word_length–fraction_length–1)
`fi`(value, 1,word_length,fraction_length)	`fi`(value, 1,word_length,word_length–fraction_length–2)

Documentation

HDL Reciprocal

Library

Description

Parameters

Ports

See Also

Introduced in R2014b

Simulink Documentation

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