# CORDIC ALGORITHM VERILOG PDF

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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And if that code also obeys the constraints of the synthesizable subset, the result will be synthesizable Verilog. The resulting transform, Tis shown below: While the data width can ostensibly be adjusted, there are a fixed number of internal arc-tangent results, each created with a fixed width and a fixed value.

Note that we verilogg the intbv instances by specifying the range of valid integer values, not by a bit width.

These applications would nominally send 1,0 into the algorithm as an input. Instead, it is a scaled rotation matrix.

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

This is of course simulator-specific. To set up a co-simulation, we need to create a Cosimulation object for the Verilog design. Otherwise, Verilog will interprete all operands in a mixed expression as unsigned.

The internal number variables are represented by intbv instances. What we now have is an algorithm that is possible to implement in hardware, but is still equivalent to the original algorithm. Let me get this straight: For these applications, the way to compensate for the gain is to send a different number as an input.

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. But as this code is outside a generator function, it doesn’t matter.

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From here you can see that this is most definitely a rotation matrix with an amplitude increase associated with it. Then, we define the command to start up the Verilog simulator. Further, as you may have guessed from Fig 1 above, we can apply a similar rotation going in the opposite direction: Of course, this transform is not a true rotation matrix.

In rotation mode, it rotates a vector x 0y 0 in the Cartesian plane over an input angle z 0. Having said that, the Verilog literature seems to indicate that a shift operation is an exception to this rule. The page for rotation on Wikipedia tells us that it is equivalent to left-multiplying by a particular matrix:. Angles beyond 45 degrees just get smaller.

See Terms of Use. For high-level, algorithmic work, this is much easier. Each rotation opportunity will set xv[0]yv[0]and ph[0].

The core can operate in either radian or degree mode. Home Questions Tags Users Unanswered.

## Computing sin & cos in hardware with synthesisable Verilog

This code is for the first quadrant, but is easily extended to the full circle by first doing a coarse rotation. In contrast, a Ferilog designer is forced to deal with low-level representational issues explicitly. Obviously, MyHDL code intended for synthesis also has to take synthesis-related restrictions into account.

Therefore, this example has been the algirithm to fix these bugs and develop MyHDL 0. Further, as you may have guessed from Fig 1 above, we can apply a similar rotation going in the opposite direction:. With the reset, this will require 1-FF per stage. It may be wrong, I don’t know. The command shown is for the open-source Cver simulator.

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### Computing sin & cos in hardware with synthesisable Verilog

The first three are 32 bits wide, since they are storing fixed-point numbers as described above. The idea is to use the cos and sin functions from the math module to compute the expected results on a number of input angles, and to compare them with the verillog from the design under test. T is also something that is easy to calculate within an FPGA. As the design will perform its calculations in finite precision, there will be rounding errors.

We will use this as the basis of our algorithm:. We also discussed several different types of rounding at that same time. Hate it when I get this sort of incomplete error message. The resulting transform, Tis shown below:.

Clearly we will want to verify that the Verilog output from the convertor is correct. The reason is that the convertible subset is much less restrictive.

Here is my code to compute sine and cosine of the input angle using cordic algorithm: These rotation matrices can be strung together to accomplish many digital logic purposes. For more information and background on the algorithm itself, please consult other sources, such as this paper by Ray Andraka.

You need to rotate the original vector by some multiple of ninety degree angles until the remaining rotation angle is less verulog forty five degrees. This define determines the number of bits used to represent the angle.