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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A simple two-dimensional rotation matrix is given by:. Instead, it is a scaled rotation matrix.

But as this code is outside a generator function, it doesn’t matter. Both of these approaches used only a minimum number of clocks, although their precision was somewhat limited.

For our purposes, it can be shown that. 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.

This is one of those rare cases where a for loop makes sense in Verilog. Algorithk, Verilog will interprete all operands in a mixed expression as unsigned. Rotating to zero The next step is to rotate the xv[0] veriloh yv[0] values through the remaining phase angle, ph[0]. These are algoritgm initial values of x, y, and the remaining phase to rotate through. It turned out that the handling of signed variables algoithm shift operations had not been implemented and tested properly. To put it mathematically.


We start by doing the Verilog conversion itself first. The resulting transform, Tis shown below:. Remember, atan2 accepts the y argument first.

I believe that writing the code in a natural, high-level way in MyHDL, and letting the convertor take care of the low-level representation issues, is a better option.

Computing sin & cos in hardware with synthesisable Verilog

In this way, the rotating vector can be directed to converge on a particular result vector. It may be redundant in this case. Sign up or log in Sign up using Google. Then also calculate and normalize by their their lengths. We will assume that all numbers are stored as bit fixed-point numbers, with the radix point between the second-most-significant and third-most-significant bits. We still have several steps remaining.

Using a CORDIC to calculate sines and cosines in an FPGA

PW – 3 ] Each rotation opportunity will set xv[0]yv[0]and ph[0]. The first three are 32 bits wide, since they are storing fixed-point numbers as described above. It basically calculates the product of all of the gains of the various stages in our algorithm.

The goal of this section is to rotate the input by some number of ninety-degree intervals until the remaining phase is between and So you’re saying I remove it from the port and leave it reg as it verklog In other words, T is approximately a rotation matrix.

I believe it’s quite clear what this is supposed to do. You cprdic then have a vector that has been rotated by Other HDLs seem to try to solve the issues by creating more and more integer and bit-vector like types. For more information and background on the algorithm itself, please consult other sources, such as this paper by Ray Andraka. This is what we are going to try to build today.


Note that we constrain the intbv instances by specifying the range of valid integer values, not by a bit width. This is the characteristic that makes the Cordic algorithm attractive. That strategy requires that for every strobe input, the output associated with that input also needs to have a high strobe output. We could apply this rotation using angles more suited for an FPGA.

It requires only adds, subtracts, and shifts. See Terms of Use. This can all be done with simple integer math—no multiplies or divides are required.

Cordic-based Sine Computer

Of course, this transform is not a true rotation matrix. With the reset, this will require 1-FF per stage. Our task here will be to calculate that gain. It seems xordic that a type that unifies the integer and the bit vector views should be very useful for hardware design. The interface of the module looks as follows: Oldfart 7, 2 8 On this page, we are mainly interested in the mechanical characteristics of the algorithm and their hardware implications.