Is There A Megafunction For Arctan ?

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The arctan() function in the library expects a real as input where Angela specified 18 bits...

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Yes, you have a point. Maybe we can do some conversion to real first?

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Second, if the compiler will synthesize the library function, we end up with combinatorial implementation which may be too slow. But the library function can do double duty: first serve as a guidance into Cordic and second to use in the testbench.

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I think Quartus should be able to synthesise the library function, since I looked the arctan() function up in the math_real.vhd IEEE package inside the Quartus distribution. But not too sure on how fast this algorithm is going to be. Probably, we can study the CORDIC() function inside the same file to see if it will be fast enough?