Looking for HDL code for sin( a ) and x ** y Functions

You might have a look at the cordic algorithms.

Regards,

Norbert Stuhrmann

Elementary Functions, Algorithms and Implementation by Jean-Michel Muller. No HDL code but the algorithms are there.

Integer exponents are pretty straightforward. It is a similar algorithm to multiplication (multiply by 2 and optionally add), but with higher order operations (square and optionally multiply).

Integer roots are probably best done by something like Newton-Raphson.

Arbitrary powers probably require computing logarithms first. One issue with that is that you can't compute them for negative numbers. If you just want integer roots, computing arbitrary powers probably isn't the best way to do it.

It really depends on your precision and accuracy requirements. For arbitrarily high precision, CORDIC is the way to go for sin provided you can live with the latency. The other end of the spectrum is a look-up table. There are intermediate solutions which are generally a combination of angular reductions and interpolation that will get you a reasonably high resolution without a huge look-up table. Linear interpolation perhaps the easiest, and can be done with relatively little hardware. A parabolic fit interpolation will get you considerably smaller errors between table entries allowing a finer resolution, and can be done with relatively low hardware complexity.

For X**Y, it is easiest to work with normalized floating point as an input, and then using interpolated LUTs. Normalizing limits the range of the tables. For a general purpose trancendental function calculator, your best bet might be a CORDIC-like iterative engine, as CORDIC and CORDIC-like structures can handle trig, hyperbolic trig, logs and exponents, and multiply and divide.

So the point is, that there are many ways to skin this cat, and the "best" way depends heavily upon your particular requirements.

By the way, I have a paper on CORDIC on my web site that many have found ot be quite useful.

I also second the reference to Jean Muller's book elementary functions book for algorithms, although you may have difficulty translating it into hardware.

Ray,

In case your company uses Synopsys tools, there is a very simple solution available in their DesignWare library. They have both hardware as well as simulation models for both the above functions, which can be simply instantiated in the code. If you are not looking for any specific algorithm that implements the functions (and if you have access to the library) then this could be the right solution.

-Sourabh

Disclaimer: This is not push anyone's marketing agenda; just information about a solution for the given problem.

Hello,

Try this:

Mariusz

The port number fixed my problems with connecting.

Thanks, Derek

The cordic projects on OpenCores were hits I found searching for algorithms. Not that I'm able to connect, unless somebody recommends otherwise I'm going to focus my investigation and research on them.

Thanks, Derek

I found a couple of people have recommended this book and when I did a quick search on Amazon it came highly recommended. I'm looking into getting a copy.

Thanks, Derek

I can live with the latency because the math unit I'm designing is pipelined. As long as I organize the operations putting the ones with longest latency first and at the cost of a multiplier or adder I should keep a couple of parallel tracks busy.

I'm comparing the trade off for using a lookup table to using an iterative process. I have designed a general purpose rasterizer. I can feed it a canned list of triangles in screen coordinates and it can render them shaded. I'm working my way backwards up the pipeline to design the geometry engine stage. Given the parameters for viewing transformations I'm adding the functionality to build the viewing transforms, using the object space coordinates calculate the world space coordinates and from the worldspace coordinates calculate the screen coordinates for the rasterizer.

Right now I'm doing this with the attitude of a hobby but I would like to roll it over into something professional. Much of what I'm doing is iterative, it never amazes me when QuartusII finds a flaw in one of my state machines and decides to flatten it.

Thanks, Derek

Another book to consider is -

DIGITAL COMPUTER ARITHMETIC DATAPATH DESIGN USING VERILOG HDL by James Stine.

It has a 25 page chapter on Elementary Functions; the style of the book is to sketch the algorithm and then show the verilog code for typically a 16 bit implementation at the hierarchic gate level.