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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The next step is to rotate the xv and yv values through the remaining phase angle, ph. Also, both the Verilog code for the design and the test bench stub are compiled. Were we to get rid of the reset, then all of this logic could fit within one shift register logic block on a 7-Series Xilinx FPGA. Software programmers like to look at for and while loops in Verilog and think of them like their for and while counterparts in software.
Angles beyond 45 degrees just get smaller. Further, as you may have guessed from Fig 1 above, we can apply a similar rotation going in the opposite direction: The fundamental problem is that Verilog uses an unsigned interpretation by default, which is the opposite from what you should do to get the naturally expected results.
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. But as wlgorithm code is alggorithm a generator function, it doesn’t matter. The convertor has to deal with several potential pitfalls. For our purposes, it can be shown that.
In MyHDL, a single type does it all – the intbv class. The dual nature of this class comes in very handy. For more information and background on the algorithm itself, please consult other sources, such as this paper by Ray Andraka. On this page, we will implement a parallel, algoithm processor, cordif is a fairly straightforward mapping of the equations into a bit-parallel data path and a state machine.
This can become very tricky, especially with negative numbers and the signed representation.
This line uses things like a list comprehension and a call to the trigonometric function atan from the math library, At this point, this is beyond the scope of ccordic convertible subset, and it may stay like that forever. The precision is specified in terms of the number of bits after the point, using the parameter fractionSize.
To see this, first calculate the angles of the vectors in Fig 1 above: Clearly we will want to verify that the Verilog output from the convertor is correct. You clear the angle during a reset just like cos, sin, count etc.
Using a CORDIC to calculate sines and cosines in an FPGA
First of all, note in the Verilog output that veriloy convertor infers which variables have to be declared as signed. The Cordic equations can be used for a variety of computations.
It basically calculates the product of all of the gains of the various stages in our algorithm. These rotation matrices can be strung together to accomplish many digital logic purposes.
The Verilog convertor makes this task easier. On this page, we are mainly interested in the mechanical characteristics of the algorithm and their hardware implications.
Cordic-based Sine Computer
The first three are 32 bits wide, since they are storing fixed-point numbers as described above. Both the sine and the cosine of the input angle will be computed. For now, remember that the global CE strategy requires that nothing changes unless a CE line is true. This means that only the source code of generator functions is converted. The Cosimulation object is then constructed with the command as its first parameter, followed by a number of keyword arguments.
Sign up using Email and Password. Such a core generator will be our approach here. This mode seeks to reduce the Y values and is used to compute an angle given a point.
Going to a higher number of bits would allow more iterations thus improving accuracy. Here is my code to compute sine and cosine of the input angle using cordic algorithm:. cordiic
You need to rotate the original vector by some multiple of ninety degree angles until the remaining rotation angle is less than forty five degrees.
The floating point numbers are represented as integers by scaling them up with a factor corresponding to the number of bits after the point. Hence we are rotating xv and yv in a counter-clockwise direction, while the remaining phase angle will decrease in what will look like a clock-wise direction.
It may be redundant in this case. 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. The first step in building this rotation, though, is to massage the problem so that the rotation desired is less than 45 degrees.
With the reset, this will require 1-FF per stage. Otherwise, Verilog will interprete all operands in a mixed expression as unsigned. The two states that we will use are 0an idle state, and 1a state indicating computation is occurring.