Implementation of Cordic Algorithm for FPGA. Based Computers Using Verilog. pani1, ju, a3. If you’ve never worked with a CORDIC algorithm before, the .. Software programmers like to look at for and while loops in Verilog and think of. The CORDIC rotator seeks to reduce the angle to zero by rotating the vector. To compute . See the description of the CORDIC algorithm for details. */ module.

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Also, the arctangent values tan -i 2 -i can be precomputed and stored in a small look-up table.

Our task here will be to calculate that gain. For pipelined options, this is the number of stages. This is the characteristic that makes the Cordic algorithm attractive.

The command shown is for the open-source Cver simulator. That’s why I defined it as reg. These rotation matrices can be strung together to a,gorithm many digital logic purposes.

Note that we have been talking about the convertible subset, and not about the “synthesizable subset”.

Having said that, the Verilog literature seems to indicate that a shift operation is an exception to this rule. First off, we declare the constants that we will use: Other HDLs seem to try to solve the issues by creating more and more integer and bit-vector like types. You can think of this as a series of complex rotation vectors, indexed by ksuch as those are shown in Fig 1. Each rotation opportunity will set xv[0]yv[0]and ph[0]. Therefore, the convertor works on the simulatable data structure, which is a hierarchical list of generators.

For more information and background on the algorithm itself, please consult other sources, such as this paper by Ray Andraka. We will use this as the basis of our algorithm:. Clearly we will want to verify that the Verilog output from the convertor is correct. This is what we are going to try to build today.

## Using a CORDIC to calculate sines and cosines in an FPGA

Then, we define the command to start up the Cordif simulator. Therefore, the comparisons between expected and actual results are performed using an error margin.

Sign up using Facebook. The goal of this section is to rotate the input by some algorthm of ninety-degree intervals until the remaining phase is between and The resulting transform, Tis shown below: The number of stages and the number of bits in each stage can both be defined based upon arguments to the core generator program.

### Cordic Algorithm using Verilog – Electrical Engineering Stack Exchange

By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Further, the more of these rotation matrices you string together, the smaller the remaining rotation becomes, and hence the closer the result will come in angular distance to any desired rotation.

On this page, we will implement a parallel, iterative processor, which is a fairly straightforward mapping of the equations into a bit-parallel data path and a state machine. The Cordic equations for this mode are:. In contrast, a Verilog designer is forced to deal with low-level representational issues explicitly.

### Cordic-based Sine Computer

The Cosimulation object is then constructed with the command as its first parameter, followed by a number of keyword arguments. This module computes the sine and cosine of an input angle. In this way, the rotating vector can be directed to converge on a particular result vector. The only way to prevent this bit-width problem associated with a aalgorithm fits all solution is to use a software program, sometimes called a core generator or coregento tailor the CORDIC to a specifically requested precision.

We will use this as the basis of our algorithm: For example, consider how the look-up table of elementary arctangents is set up in the SineComputer design:. And if that code also obeys the constraints of algoirthm synthesizable subset, the result will be synthesizable Verilog. We may want to use the test bench for designs with different characteristics; therefore, the error margin is made a parameter.

Note that we constrain the intbv instances by specifying the range of valid integer values, not by a bit width. We verilof apply this rotation using angles more suited for an FPGA. Also, both the Verilog code for the design and the test bench stub are compiled. It uses the most amount of Algoritmh. Post Your Answer Discard By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies.

From here you can see that this is most definitely a rotation matrix with an amplitude increase associated with it. In rotation mode, it rotates a vector x 0y 0 in the Cartesian plane over an input angle z 0. That strategy requires that for every strobe input, the output associated with that input also needs to have a high strobe output. These are the initial values of x, y, and the remaining phase to rotate through.

The interface of the module looks as follows:. One important feature of the convertor is that it handles the details of signed and unsigned representations automatically.

Site powered by Hakyll. It may be wrong, I don’t know. The floating point numbers are represented as integers. Hate it when I get this sort of incomplete error message. This is one of those rare cases where a for loop makes sense in Verilog.