FPGA Central

Hi,

I'm looking for good links to information on Fixed Point Arithmetic.

The only good resource I could find was -

Fixed Point Arithmetic: An Introduction - by Randy Yates
http://mel.interspace.dk/~sune/old-s...ixed-point.pdf

But, it is only an intro and does not deal with concepts like
overflow, saturation and scaling.

Are there any other good resources on the web related to Fixed Point
Arithmetic?


Thanks,
Ashwin
--
http://symonds.net/~ash/

[email protected] (Ashwin) wrote in message news:<[email protected] com>...
> Hi,
>
> I'm looking for good links to information on Fixed Point Arithmetic.
>
> The only good resource I could find was -
>
> Fixed Point Arithmetic: An Introduction - by Randy Yates
> http://mel.interspace.dk/~sune/old-s...ixed-point.pdf

Interesting link. You can get the "official" version from

http://home.earthlink.net/~yatescr/fp.pdf

> But, it is only an intro and does not deal with concepts like
> overflow, saturation and scaling.

Methinks you didn't really read the paper. The whole paper is
on scaling. That's the point (pun intended!). There is also
some information on overflow in the example at the end. There
is indeed no information on saturation, although I'm not sure
what information you would need on the matter. Do you not
understand what the operation of saturation actually does? Do
you not understand when you would saturate and when you would
not?

There is another paper called "Practical Considerations in
Fixed-Point FIR implementations" that deals with overflows
and coefficient scaling. Perhaps it may touch on some of
your questions.

I suspect you may have a specific problem in mind that the paper
didn't address. Why don't you present it here?

--Randy




>
> Are there any other good resources on the web related to Fixed Point
> Arithmetic?
>
>
> Thanks,
> Ashwin

"Randy Yates" <[email protected]> wrote in message
news:[email protected] om...
> [email protected] (Ashwin) wrote in message
news:<[email protected] com>...

<snipped>

Do you not understand when you would saturate and when you would not?

<snipped>

================================================== =======

Randy,

I suspect that a lot of people do not understand this seemingly "simple"
topic because there is not a clean generalized answer that is
processor/situation independent.

Some situations to consider (not exhaustive) assuming 2's complement math
for multiply-accumulates (MACs):

Do I want to saturate every time I overflow? If I know I overflowed at some
point in a calculation do I always want to saturate the final result? What
if intermediate calculations overflow but the final results are valid? Can I
tell if the final result is valid? What is the impact if the final result
overflows and is not saturated? If I avoid overflows by scaling my numbers
down, what does that do to my numerical resolution including underflows?
Does the range of my accumulator support the detection of the situation
where intermediate values in a MAC overflow but the final result does not?
How many MACs can I perform and not destroy this detection capability? ...

Not so simple.

Dirk

Dirk A. Bell
DSP Consultant

"Randy Yates" <[email protected]> wrote in message
news:[email protected]..
> Dirk Bell wrote:
> >
> > "Randy Yates" <[email protected]> wrote in message
> > news:[email protected] om...
> > > [email protected] (Ashwin) wrote in message
> > news:<[email protected] com>...
> >
> > <snipped>
> >
> > Do you not understand when you would saturate and when you would not?
> >
> > <snipped>
> >
> > ================================================== =======
> >
> > Randy,
> >
> > I suspect that a lot of people do not understand this seemingly "simple"
> > topic because there is not a clean generalized answer that is
> > processor/situation independent.
> >
> > Some situations to consider (not exhaustive) assuming 2's complement
math
> > for multiply-accumulates (MACs):
> >
> > Do I want to saturate every time I overflow? If I know I overflowed at
some
> > point in a calculation do I always want to saturate the final result?
What
> > if intermediate calculations overflow but the final results are valid?
Can I
> > tell if the final result is valid? What is the impact if the final
result
> > overflows and is not saturated? If I avoid overflows by scaling my
numbers
> > down, what does that do to my numerical resolution including underflows?
> > Does the range of my accumulator support the detection of the situation
> > where intermediate values in a MAC overflow but the final result does
not?
> > How many MACs can I perform and not destroy this detection capability?
....
> >
> > Not so simple.
>
> Did I say, "It is simple to understand when you would saturate and when
> you would not"???
> --
> % Randy Yates % "...the answer lies within your soul
> %% Fuquay-Varina, NC % 'cause no one knows which side
> %%% 919-577-9882 % the coin will fall."
> %%%% <[email protected]> % 'Big Wheels', *Out of the Blue*, ELO
> http://home.earthlink.net/~yatescr

Randy,

In the context of

"There is indeed no information on saturation, although I'm not sure what
information you would need on the matter. Do you not understand what the
operation of saturation actually does? Do you not understand when you would
saturate and when you would not? "

I would say you most definitely implied it.

Of course I could be wrong. At least that's what my wife says.

Dirk

Dirk A. Bell
DSP Consultant

In article bdck9p$bku$[email protected], Dirk Bell at [email protected]
wrote on 06/25/2003 12:56:

> "Randy Yates" <[email protected]> wrote in message
> news:[email protected] om...
>> [email protected] (Ashwin) wrote in message
> news:<[email protected] com>...
>
> <snipped>
>
> Do you not understand when you would saturate and when you would not?
>
> <snipped>
>
> ================================================== =======
>
> Randy,
>
> I suspect that a lot of people do not understand this seemingly "simple"
> topic because there is not a clean generalized answer that is
> processor/situation independent.
>
> Some situations to consider (not exhaustive) assuming 2's complement math
> for multiply-accumulates (MACs):
>
> Do I want to saturate every time I overflow? If I know I overflowed at some
> point in a calculation do I always want to saturate the final result? What
> if intermediate calculations overflow but the final results are valid? Can I
> tell if the final result is valid? What is the impact if the final result
> overflows and is not saturated? If I avoid overflows by scaling my numbers
> down, what does that do to my numerical resolution including underflows?
> Does the range of my accumulator support the detection of the situation
> where intermediate values in a MAC overflow but the final result does not?
> How many MACs can I perform and not destroy this detection capability? ...

depends on how many guard bits on the lefta and how many on the righta.

> Not so simple.

it's not so bad on a 56K. that is one reason i was such a proponent of the
56K over TI or even the SHArC until a couple of years ago.

r b-j

[email protected] (Randy Yates) wrote in message news:<[email protected] com>...

> > I'm looking for good links to information on Fixed Point Arithmetic.
> >
> > The only good resource I could find was -
> >
> > Fixed Point Arithmetic: An Introduction - by Randy Yates
> > http://mel.interspace.dk/~sune/old-s...ixed-point.pdf
>
> Interesting link. You can get the "official" version from
>
> http://home.earthlink.net/~yatescr/fp.pdf

Interestingly, Google lists the other one as more popular than your
home link :-)

> There is another paper called "Practical Considerations in
> Fixed-Point FIR implementations" that deals with overflows
> and coefficient scaling. Perhaps it may touch on some of
> your questions.

I got that one here -
http://home.earthlink.net/~yatescr/fir.pdf

I will look into it.

> I suspect you may have a specific problem in mind that the paper
> didn't address. Why don't you present it here?

No specific problem. I was just looking around for information on FP
math and was surprised to see so very less of it on the net.


Ashwin
--
http://symonds.net/~ash/

[email protected] (Nithin) wrote in message news:<[email protected] om>...

> > I'm looking for good links to information on Fixed Point Arithmetic.
> >
> > The only good resource I could find was -
> >
> > Fixed Point Arithmetic: An Introduction - by Randy Yates
> > http://mel.interspace.dk/~sune/old-s...ixed-point.pdf

[...]

> The effect of scaling, overflow and saturation is application specific
> ans so are ways of handling them. For general filter applications in
> fixed point point arithmetic u might want to refer the book - Advanced
> DSP (sorry i dont remember the title exactly) by Sanjit K Mitra or any
> other classical DSP book. The book has interesting references as well.
>
> u might also want search in ieee online library (free for all)
> http://ieeexplore.ieee.org. i got some useful stuff from this site for
> my research.

Here are some general resources on FPA I was able to dig out in these weeks -

----------

Fixed Point Arithmetic
http://cnx.rice.edu/content/m11054/latest/

Fixed point numbers and fixed point arithmetic
http://andercheran.aiind.upv.es/~ams.../fixedpnt.html

A Calculated Look at Fixed-Point Arithmetic
by Robert Gordon
http://www.embedded.com/98/9804fe2.htm

Fixed-point Arithmetic
http://www.accu.org/acornsig/public/...ixedpoint.html

Fixed Point Math For Speed Freaks
http://www.mactech.com/articles/mact...ath/index.html

Getting a Speed Boost with Fixed-Point Math
http://www.mactech.com/articles/mact...ointMathSpeed/

Comp.dsp FAQ: Algorithm implementation: floating-point versus fixed-point
http://www.bdti.com/faq/2.htm#211

----------

Thanks for all your help on this thread guys! :-)
(Thumba sahaya aythu ;-)


ashwin
--
Ashwin N
http://symonds.net/~ash/