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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Computing sin & cos in hardware with synthesisable Verilog
We discussed some time ago how to go about this via rounding. The only way to prevent this bit-width problem associated with a one-size fits all solution is to use a software program, sometimes called a core generator or coregento tailor the CORDIC to a specifically requested precision.
Also, both the Verilog code for the design and the test bench stub are compiled. The floating point numbers are represented as integers.
With the underlying two’s complement representation, it works for positive and negative values of y. These rotation matrices can be strung together to accomplish many digital logic purposes.
The combinatorial implementation runs at about 10 mhz while the iterative ones run at about in a Lattice ECP2 device.
For more information and background on the algorithm itself, please consult other sources, such as this paper by Ray Andraka. Hate it when I get this sort of incomplete error message.
The user can change the number of bits that represent the x,y, and theta values. As before, the dut object is a simulatable design instance, but as a side effect of the instantiation, an equivalent Verilog module file will be generated.
But as this code is outside a generator function, it doesn’t matter.
First off, we declare the constants that we will use: We will first write a unit test for the design. Introduction On this page we will present the design of a sine and cosine computer.
Angles beyond 45 degrees just get smaller. This means that only the source code of generator functions is converted. What we now have is an algorithm that is possible to implement in hardware, but is still equivalent to the original algorithm.
Cordic-based Sine Computer
cordi When writing synthesizable code, a MyHDL designer can use a high-level view for integer operations by using the intbv type, and rely on the underlying two’s complement representation to do the right thing automatically. Moreover, it enables fine-grained range error checking at run-time. Of course, this transform is not a true rotation matrix.
The dual nature of this class comes in very handy. In this mode the user supplies the tangent value in veerilog and y and the rotator seeks to minimize the y value, thus computing the angle. That allows you to pick the number of most-significant bits that you need, for the precision you want.
On the one hand, we can constrain the instances as integer subtypes by specifying the valid integer range at construction time. To implement the design, we will use the Cordic algorithm, a very popular algorithm to compute trigonometric functions in hardware.
Here, we follow the convergent rounding approach to drop any excess bits. Rotating into range The first step in building this rotation, though, is to massage the problem so that the rotation desired is less than 45 degrees.
That strategy requires that for every strobe input, the output associated with that input also needs to have a high strobe output. The Verilog convertor makes this task easier. Oldfart 7, 2 8 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.
Such a core generator will be our approach here. Other HDLs seem to try to solve the issues by creating more and more integer and bit-vector like types.
Note that we first check the sign of the remaining phase to know which direction to rotate, but otherwise the operations you see here should match the transform we discussed earlier.
HDL loops, however, are nothing like software loops.
Cordic-based Sine Computer
From here you can see that this is most definitely a rotation matrix with an amplitude increase associated with it. In other words, T veriolg approximately a rotation matrix. Further, as you may have guessed from Fig 1 above, verilov can apply a similar rotation going in the opposite direction:.
This can become very tricky, especially with negative numbers and the signed representation. The first three are 32 bits wide, since they are storing fixed-point numbers as described above.