Exponential function in vhdl

For exponential, you will need to create a look up table filled with all the results.

The address input of the LUT is x and the output is your function.

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For exponential, you will need to create a look up table filled with all the results.

The address input of the LUT is x and the output is your function.

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Thank you Tricky for your reply. May be I can write this lookup table in a package and call it for places where I need exponential function. If you have any sample program then please share.

If not function then should I write any package for exp. Sorry I havent written any lookup table before so I dont know. And actually I want to design a Gaussian filter with variable window size & sigma value. For that I am using two 1D gaussian.

So the part I want to impliment is

Gauss= exp^(-(x^2)/2*(sigma)^2);

here sigma will vary from 0.1 to 5.

and x is a vector =[-2 -1 0 1 2] for length equal to 5. I want to vary length also. How to do it.please help me with this. If you know any book for these type of operation then please suggest.

I highly suggest you learn about digital design. What you are going to create is a ROM - a read only memory. This can be done in VHDL using a constant which can be initialised from a function, a specified constant or a .mif file. you can have matlab generate the values to go into the constant.

There are plenty of examples out on the web.

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If not function then should I write any package for exp. Sorry I havent written any lookup table before so I dont know. And actually I want to design a Gaussian filter with variable window size & sigma value. For that I am using two 1D gaussian.

So the part I want to impliment is

Gauss= exp^(-(x^2)/2*(sigma)^2);

here sigma will vary from 0.1 to 5.

and x is a vector =[-2 -1 0 1 2] for length equal to 5. I want to vary length also. How to do it.please help me with this. If you know any book for these type of operation then please suggest.

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Any equation can be implemented in fpga as LUT either fully or partially. In the partial case you do in fpga what is doable and then use LUT.

In your case I suggest:

get x^2 in fpga (x * x), one multiplier

get 2* sigma^2 in fpga, one multiplier and add one zero lsb

truncate above results to suitable bitwidth

divide -x2/(2*sigma^2) in fpga if you can afford a divider, else include this section within LUT

finally get LUT for your exp in software e.g. matlab and put it in a rom

To get LUT of exp:

you need to know range of your result. then just calculate exp of that range in suitable steps and rounded to your rom bitwidth

Then in fpga address LUT with actual fpga result.