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

Before I get spamed for this I have done a search and I see there are
references to what I'm looking for on www.opencores.org but for some
reason I'm unable to connect.

What I'm looking for is a resource like, if it existed, Numerical
Receipes in HDL (VHDL/Verilog). I have a need for the basic floating
point functions like sin( a ) and x ** y. For floating point numbers
that are only 12 to 18 bits I can use lookup tables but I was wondering
if there was another way of calculating these values. Most of the books
I have cover addition/subtraction, multiplication and division but
nothing more advance or even hints at how to go about it.

>From sin( a ) and x ** y I plan on deriving cos( a ), tan( a ), cot( a
), and yth root of x.

I'm looking for any helpful or constructive suggestions.

Thanks,
Derek

I had similar issues with opencores until now. It is working now.

Derek Simmons wrote:
> Before I get spamed for this I have done a search and I see there are
> references to what I'm looking for on www.opencores.org but for some
> reason I'm unable to connect.
>
> What I'm looking for is a resource like, if it existed, Numerical
> Receipes in HDL (VHDL/Verilog). I have a need for the basic floating
> point functions like sin( a ) and x ** y. For floating point numbers
> that are only 12 to 18 bits I can use lookup tables but I was wondering
> if there was another way of calculating these values. Most of the books
> I have cover addition/subtraction, multiplication and division but
> nothing more advance or even hints at how to go about it.
>
> >From sin( a ) and x ** y I plan on deriving cos( a ), tan( a ), cot( a
> ), and yth root of x.
>
> I'm looking for any helpful or constructive suggestions.
> 
> Thanks,
> Derek

for integer implementations the cordic algorithm covers most of the 
trigonometric functions
you need (no multipliers, but some latency)
Aurash

Derek Simmons wrote:

>Before I get spamed for this I have done a search and I see there are
>references to what I'm looking for on www.opencores.org but for some
>reason I'm unable to connect.
>
>What I'm looking for is a resource like, if it existed, Numerical
>Receipes in HDL (VHDL/Verilog). I have a need for the basic floating
>point functions like sin( a ) and x ** y. For floating point numbers
>that are only 12 to 18 bits I can use lookup tables but I was wondering
>if there was another way of calculating these values. Most of the books
>I have cover addition/subtraction, multiplication and division but
>nothing more advance or even hints at how to go about it.
>
>>From sin( a ) and x ** y I plan on deriving cos( a ), tan( a ), cot( a
>), and yth root of x.
>
>I'm looking for any helpful or constructive suggestions.
>
>Thanks,
>Derek
>
>  
>


-- 
 __
/ /\/\ Aurelian Lazarut
\ \  / System Verification Engineer
/ /  \ Xilinx Ireland
\_\/\/
 
phone:	353 01 4032639
fax:	353 01 4640324
    
     

If www.opencores.org link does not work, try
http://www.opencores.org:8080/

cbr_929rr wrote:
> I had similar issues with opencores until now. It is working now.
>
> Derek Simmons wrote:
> > Before I get spamed for this I have done a search and I see there are
> > references to what I'm looking for on www.opencores.org but for some
> > reason I'm unable to connect.
> >
> > What I'm looking for is a resource like, if it existed, Numerical
> > Receipes in HDL (VHDL/Verilog). I have a need for the basic floating
> > point functions like sin( a ) and x ** y. For floating point numbers
> > that are only 12 to 18 bits I can use lookup tables but I was wondering
> > if there was another way of calculating these values. Most of the books
> > I have cover addition/subtraction, multiplication and division but
> > nothing more advance or even hints at how to go about it.
> >
> > >From sin( a ) and x ** y I plan on deriving cos( a ), tan( a ), cot( a
> > ), and yth root of x.
> >
> > I'm looking for any helpful or constructive suggestions.
> > 
> > Thanks,
> > Derek

Hi Derek,

Derek Simmons wrote:
> I'm looking for any helpful or constructive suggestions.

You might have a look at the cordic algorithms.

Regards,

  Norbert Stuhrmann

> >What I'm looking for is a resource like, if it existed, Numerical
> >Receipes in HDL (VHDL/Verilog).

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

Derek Simmons wrote:
> >From sin( a ) and x ** y I plan on deriving cos( a ), tan( a ), cot( a
> ), and yth root of x.

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.

Derek Simmons wrote:
> Before I get spamed for this I have done a search and I see there are
> references to what I'm looking for on www.opencores.org but for some
> reason I'm unable to connect.
> 
> What I'm looking for is a resource like, if it existed, Numerical
> Receipes in HDL (VHDL/Verilog). I have a need for the basic floating
> point functions like sin( a ) and x ** y. For floating point numbers
> that are only 12 to 18 bits I can use lookup tables but I was wondering
> if there was another way of calculating these values. Most of the books
> I have cover addition/subtraction, multiplication and division but
> nothing more advance or even hints at how to go about it.
> 
>>From sin( a ) and x ** y I plan on deriving cos( a ), tan( a ), cot( a
> ), and yth root of x.
> 
> I'm looking for any helpful or constructive suggestions.
> 
> Thanks,
> Derek
> 


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.

Ray Andraka wrote:

By the way, I have a paper on CORDIC on my web site that many have found 
ot be quite useful.  Http://www.andraka.com/papers  see: A survey of 
CORDIC algorithms for FPGA based Computers.

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.