Breaking News
Blog

# Doing Math in FPGAs, Part 1

Part 1:
NO RATINGS
7 saves
View Comments: Newest First | Oldest First | Threaded View
Page 1 / 3   >   >>
User Rank
Author
its fixed point math
12/10/2013 4:45:31 AM
NO RATINGS
1 saves
here's why it works: x/10=x*0.1={2^16*x*0.1}/2^16={x*2^16*0.1}/2^16 =x*1999H/2^16

User Rank
Author
Re: Know the limitations of your tools
12/9/2013 2:37:47 PM
NO RATINGS
Very important point and one difficult to do in practice. How many tools actually document (in detail) what the tool will do or not do. I find I need to do small example designs and look over th output of the place and route tool to figure out what is going on. Widh the vendors did this for me!

Anyone else have tools with detailed enough docs that they can tell ahead of time what is being done?

User Rank
Author
Know the limitations of your tools
12/9/2013 2:20:02 PM
NO RATINGS
I remember the first time I synthesized an FPGA design for a real product.  The synthesizer automatically came up with a one-hot state machine coding.  Everything simulated fine.   Unfortunately, this particular design did not have a well-formed clock when connecting or disconnecting the input signal, which would cause it to lose the one-hot code occasionally when reconnecting.  Switching to a manual state coding that automatically recovered from bad states fixed the problem -- and saved logic cells in this case.

Lesson 1:  Don't trust automatic state assignment.  Some synthesizers make it hard to turn off automatic state assignment, but it's worth the effort.

Lesson 2:  Don't trust simulation.  It only simulates theoretical models, not the real world.

Lessons 1+2 combined and generalized:  Know the limitations of your tools.

User Rank
Author
12/9/2013 11:02:27 AM
NO RATINGS
Remember when we had to do many of the FPGA tricks by hand? Register retiming, one hot state machines, if then else to mux conversions? Now the synthesis tools do all this for us. Hopefully tricks like the multiply by a constant will get folded in too. Just depends on how common the need is for these tricks I guess.

Maybe there should be a 'list' of tricks that users suggest would be good to put into synthesis tools. Perhaps via a discussion thread on Programmable Logic Design Line?

User Rank
Author
12/9/2013 10:04:24 AM
NO RATINGS
@Kris: Pretty cool math...I wonder whether they teach something like that in vlsi classes...

I'd be interested to knwo that myself -- but I fear not. When I started out, everyone knew and "swapped" tips and tricks like this -- it was key to making programs run as fast as possible when you were limited in terms of memory size, clock frequency, and the fac tthat CPUs too multiple cycles to do anything.

Magazines like BYTE were always publishing stuff like this... I love this stuff

User Rank
Author
12/9/2013 10:01:11 AM
NO RATINGS
1 saves
@Brian: There's some nice material about constant division on the companion website for "Hacker's Delight"

I was going to mention that book Hacker's Delight -- it's a great book -- lots of useful tricks in it. I just now found there's a second edition (the link above) -- I have th efirst -- I'll have to add this second edition to my wish list :-)

User Rank
Author
How the divisor works
12/9/2013 4:04:30 AM
NO RATINGS
1 saves
The divider works because the 0x199A for a 16 bit number is the reciprocal of 10 which is 1/10 or 0.1

This is then scaled by integer(2**16 * 0.1) = 6554 or 0x199A doing the multiply then works out the same as doing the divide. This trick can be used for any number when the divisor is fixed.

User Rank
Author
Re: How FPGA do math
12/9/2013 3:47:20 AM
NO RATINGS
You are welcome I tried to make it as simple as possible to explain within the 2000 word limit how to do maths in FPGA's

The more complex things like filters and CORDICs etc are covered in other articles

I find a simple example often helps to demonstrate the principles

User Rank
Author
Re: How FPGA do math
12/8/2013 11:49:13 PM
NO RATINGS

Thanx for posting the link to your article. Very detailed and even had some code!

User Rank
Author
Re: How FPGA do math
12/8/2013 10:31:35 AM
NO RATINGS