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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Software programmers like to look at for and while loops in Verilog and think of them like their for and while counterparts in software. O ye simple, understand wisdom: Our first problem, therefore is going to be rotating our incoming vector so algoritym any remaining rotation amount is 45 degrees or less.

On this page, we are mainly interested in the mechanical characteristics of the algorithm and their hardware implications. The Verilog convertor makes this task easier.

You can think of this as a series of complex rotation vectors, indexed ccordic ksuch as those are shown in Fig 1. For example, consider the instantiation of the design under test in the test vreilog. On the other hand, we can access their two’s complement representation as a bit vector, for example for slicing or right-shifting.

The pleasant verrilog is that the restrictions of the “convertible subset” apply only to the code inside generator functions, not to any code outside them. Because the CORDIC algorithm will also increase the magnitude of the input, this process adds one more bit on the leftâ€”to allow for a touch of width expansion.

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

In this mode the user supplies the tangent value in x and y and the rotator seeks to minimize the y value, thus computing the angle. This can become very tricky, especially with negative numbers and the signed representation. The floating point numbers are represented as integers.

HDL loops on the other algroithm repeat the instruction in space on the chip by creating multiple copies of the same logic, all of which will be executed in parallel. Note how this single-line lookup is expanded into a case statement in the Verilog output.

## Computing sin & cos in hardware with synthesisable Verilog

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. I believe it’s quite clear what this is supposed to do.

Not all applications need gain compensation. 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 outputs from the design under test. Software loops repeat the same instruction, one after another in time.

This is what we are going to try to do: The beginner needs to understand that this is not the definition of a memory, although it might look very similar to a block RAM definition. The two states that we will use are 0an idle state, and 1a state indicating computation is occurring.

Also, both the Verilog code for the design and the test bench stub are compiled. If more iterations or higher precision calculations are desired then a new arctan table will need to be computed.

But again, these restrictions only apply to the code inside generator functions, because only that code is actually converted.

Moreover, it enables fine-grained range error checking at run-time. However, my current wlgorithm Cver tells me that it is. It is important to realize that the conversion occurs on a design instance.

Doing so, though, requires the CORDIC angles, which we needed to calculate based upon the desired precision of the output.

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

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.

Here is my code to compute sine and cosine of corsic input angle using cordic algorithm:. HDL loops, however, are nothing like software loops.

We need five registers: The Verilog output is as follows:. For our alggorithm, it can be shown that. Then simply change the sign of the results based on this stored number.