Calculate reciprocal with Newton-Raphson approximation method (HDL Coder)
The HDL Reciprocal block is available with Simulink®.
For information about the simulation behavior and block parameters, see HDL Reciprocal block in the Simulink documentation.
The HDL Reciprocal block 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 is defined as a zero of the function:
HDL Coder™ chooses an initial estimate in the range 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:
is the derivative of the function .
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 Newton-Rapshon iterative method to compute an approximate value of reciprocal of the block input. This approximation 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. However, increasing the number of iterations increases the number of hardware resources that your design uses. |
This block has multi-cycle implementations that introduce additional latency in the generated code. To see the added latency, view the generated model or validation model. See Generated Model and Validation Model.
| Architecture | Additional cycles of latency | Description |
|---|---|---|
ReciprocalNewton (default) | Iterations + 1 | Use the multirate implementation of the iterative Newton method. Select this option to optimize area. The default
value for The recommended
value for |
ReciprocalNewtonSingleRate | (Iterations * 2) + 1 | Use the single rate pipelined Newton method. Select this option to optimize speed, or if you want a single rate implementation. The
default value for The
recommended value for |
Number of registers to place at the outputs by moving existing delays within your design. Distributed pipelining does not redistribute these registers. The default is 0. See also ConstrainedOutputPipeline.
Number of input pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is 0. See also InputPipeline.
Number of output pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is 0. See also OutputPipeline.