HDL Coder: Replace the exp Function with a Lookup Table

Hello,

I want to use an exponential function with complex input values on an FPGA.

I followed the following guide to convert a not supported fixed point function into a lookup table: https://de.mathworks.com/help/hdlcoder/ug/replace-the-exp-function-with-a-lookup-table.html

If I run the example with complex input values then the replacing of the exp function with a lookup table fails. Using the same example with non complex input values succeeds. When looking at the fixpt function it can be seen that it still uses exp:

...
function y = custom_fcn(x)
  fm = get_fimath();

    y = fi(exp(x), 1, 14, 12, fm);
  end
  ...

Which results in the error: ??? Function 'exp' is not defined for values of class 'embedded.fi'.

Which leaves me at the question how can an exponential function with complex inputs be implemented on an FPGA using the HDL coder?

I attached my files here. Testbench:

close all

nbrIterations = 10000;
LUT_result = zeros(nbrIterations,1);
diff = zeros(nbrIterations,1);
%Random values betwen -1.5705 and 1.5705
random_in = (3.141.*rand(nbrIterations,1) -1.5705)*1j;

for i=1:nbrIterations
    LUT_result(i) = call_custom_fcn( random_in(i));
    diff(i)       = abs( LUT_result(i) - exp(random_in(i)) );
end

figure(1); plot(diff);

custom_fcn.m:

function y = custom_fcn(x)
  y = exp(x);
end

call_custom_fcn.m:

function y = call_custom_fcn(x)
  y = custom_fcn(x);
end

Answer 1

[Bharath Venkataraman]

You can try using a lookup table to implement exponent for a given input range. Another option is to try the CORDIC implementation .

[Fabig]

Thanks that was an easy fix. Using cordiccexp(real(x)) worked very well. How would I create a lookup table with a complex input range? Would I use two lookup tabels one with the complex and one with the real value?

[Bharath Venkataraman]

In MATLAB, you can have one lookup table with complex values and HDL Coder will do the right thing in generating code for the complex numbers. You may also split it up if that is more readable.