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Tim Wescott
Guest

Fri Oct 14, 2016 12:46 am   



Now that FPGAs have built-in DSP blocks, how commonly is CORDIC used? Is
it still a necessary go-to for anyone contemplating doing DSP in an FPGA,
or is it starting to ease onto the off-ramp of history?

And, putting FPGA use aside -- how common is it is ASICs?

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

I'm looking for work -- see my website!

Rob Gaddi
Guest

Fri Oct 14, 2016 12:46 am   



Tim Wescott wrote:

Quote:
On Thu, 13 Oct 2016 13:46:18 -0500, Tim Wescott wrote:

Now that FPGAs have built-in DSP blocks, how commonly is CORDIC used?
Is it still a necessary go-to for anyone contemplating doing DSP in an
FPGA,
or is it starting to ease onto the off-ramp of history?

And, putting FPGA use aside -- how common is it is ASICs?

Being bad because I'm cross-posting. Being bad because I'm cross-posting
a reply to _my own post_.

Oh well -- I'm thinking that maybe some of the folks on comp.dsp who
aren't also on comp.arch.fpga will have some thoughts.


I've considered it many times, but never used it. Then again it's not
like I use the DSP blocks for CORDIC sorts of things anyhow; I just
throw a RAM lookup table at the problem.

--
Rob Gaddi, Highland Technology -- www.highlandtechnology.com
Email address domain is currently out of order. See above to fix.

Tim Wescott
Guest

Fri Oct 14, 2016 1:03 am   



On Thu, 13 Oct 2016 13:46:18 -0500, Tim Wescott wrote:

Quote:
Now that FPGAs have built-in DSP blocks, how commonly is CORDIC used?
Is it still a necessary go-to for anyone contemplating doing DSP in an
FPGA,
or is it starting to ease onto the off-ramp of history?

And, putting FPGA use aside -- how common is it is ASICs?


Being bad because I'm cross-posting. Being bad because I'm cross-posting
a reply to _my own post_.

Oh well -- I'm thinking that maybe some of the folks on comp.dsp who
aren't also on comp.arch.fpga will have some thoughts.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

I'm looking for work -- see my website!

Tim Wescott
Guest

Fri Oct 14, 2016 3:10 am   



On Thu, 13 Oct 2016 20:59:49 +0000, Rob Gaddi wrote:

Quote:
Tim Wescott wrote:

On Thu, 13 Oct 2016 13:46:18 -0500, Tim Wescott wrote:

Now that FPGAs have built-in DSP blocks, how commonly is CORDIC used?
Is it still a necessary go-to for anyone contemplating doing DSP in an
FPGA,
or is it starting to ease onto the off-ramp of history?

And, putting FPGA use aside -- how common is it is ASICs?

Being bad because I'm cross-posting. Being bad because I'm
cross-posting a reply to _my own post_.

Oh well -- I'm thinking that maybe some of the folks on comp.dsp who
aren't also on comp.arch.fpga will have some thoughts.


I've considered it many times, but never used it. Then again it's not
like I use the DSP blocks for CORDIC sorts of things anyhow; I just
throw a RAM lookup table at the problem.


That was the other thing that I should have mentioned.

I've heard a lot of talk about CORDIC, but it seems to be one of those
things that was Really Critically Important back when an Intel 4004 cost
(reputedly) $5 in then-dollars, but maybe isn't so important now, when it
seems like the package costs more than the silicon inside it.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

I'm looking for work -- see my website!

rickman
Guest

Fri Oct 14, 2016 4:14 am   



On 10/13/2016 5:10 PM, Tim Wescott wrote:
Quote:
On Thu, 13 Oct 2016 20:59:49 +0000, Rob Gaddi wrote:

Tim Wescott wrote:

On Thu, 13 Oct 2016 13:46:18 -0500, Tim Wescott wrote:

Now that FPGAs have built-in DSP blocks, how commonly is CORDIC used?
Is it still a necessary go-to for anyone contemplating doing DSP in an
FPGA,
or is it starting to ease onto the off-ramp of history?

And, putting FPGA use aside -- how common is it is ASICs?

Being bad because I'm cross-posting. Being bad because I'm
cross-posting a reply to _my own post_.

Oh well -- I'm thinking that maybe some of the folks on comp.dsp who
aren't also on comp.arch.fpga will have some thoughts.


I've considered it many times, but never used it. Then again it's not
like I use the DSP blocks for CORDIC sorts of things anyhow; I just
throw a RAM lookup table at the problem.

That was the other thing that I should have mentioned.

I've heard a lot of talk about CORDIC, but it seems to be one of those
things that was Really Critically Important back when an Intel 4004 cost
(reputedly) $5 in then-dollars, but maybe isn't so important now, when it
seems like the package costs more than the silicon inside it.


There are still FPGAs at the lower end that don't include multipliers.
I have an older design in a small FPGA I am still shipping that does the
iterative adding thing. It has been a while since I considered using
the CORDIC algorithm. What exactly is the advantage of the CORDIC
algorithm again?

--

Rick C

Tim Wescott
Guest

Fri Oct 14, 2016 4:16 am   



On Thu, 13 Oct 2016 18:14:58 -0400, rickman wrote:

Quote:
On 10/13/2016 5:10 PM, Tim Wescott wrote:
On Thu, 13 Oct 2016 20:59:49 +0000, Rob Gaddi wrote:

Tim Wescott wrote:

On Thu, 13 Oct 2016 13:46:18 -0500, Tim Wescott wrote:

Now that FPGAs have built-in DSP blocks, how commonly is CORDIC
used? Is it still a necessary go-to for anyone contemplating doing
DSP in an FPGA,
or is it starting to ease onto the off-ramp of history?

And, putting FPGA use aside -- how common is it is ASICs?

Being bad because I'm cross-posting. Being bad because I'm
cross-posting a reply to _my own post_.

Oh well -- I'm thinking that maybe some of the folks on comp.dsp who
aren't also on comp.arch.fpga will have some thoughts.


I've considered it many times, but never used it. Then again it's not
like I use the DSP blocks for CORDIC sorts of things anyhow; I just
throw a RAM lookup table at the problem.

That was the other thing that I should have mentioned.

I've heard a lot of talk about CORDIC, but it seems to be one of those
things that was Really Critically Important back when an Intel 4004
cost (reputedly) $5 in then-dollars, but maybe isn't so important now,
when it seems like the package costs more than the silicon inside it.

There are still FPGAs at the lower end that don't include multipliers. I
have an older design in a small FPGA I am still shipping that does the
iterative adding thing. It has been a while since I considered using
the CORDIC algorithm. What exactly is the advantage of the CORDIC
algorithm again?


It uses less gates. Which is why I'm asking my question -- gates seem to
be a lot cheaper these days, so do people still use CORDIC?

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

I'm looking for work -- see my website!

BobH
Guest

Fri Oct 14, 2016 7:30 am   



On 10/13/2016 03:16 PM, Tim Wescott wrote:
Quote:
On Thu, 13 Oct 2016 18:14:58 -0400, rickman wrote:

On 10/13/2016 5:10 PM, Tim Wescott wrote:
On Thu, 13 Oct 2016 20:59:49 +0000, Rob Gaddi wrote:

Tim Wescott wrote:

On Thu, 13 Oct 2016 13:46:18 -0500, Tim Wescott wrote:

Now that FPGAs have built-in DSP blocks, how commonly is CORDIC
used? Is it still a necessary go-to for anyone contemplating doing
DSP in an FPGA,
or is it starting to ease onto the off-ramp of history?

And, putting FPGA use aside -- how common is it is ASICs?

Being bad because I'm cross-posting. Being bad because I'm
cross-posting a reply to _my own post_.

Oh well -- I'm thinking that maybe some of the folks on comp.dsp who
aren't also on comp.arch.fpga will have some thoughts.


I've considered it many times, but never used it. Then again it's not
like I use the DSP blocks for CORDIC sorts of things anyhow; I just
throw a RAM lookup table at the problem.

That was the other thing that I should have mentioned.

I've heard a lot of talk about CORDIC, but it seems to be one of those
things that was Really Critically Important back when an Intel 4004
cost (reputedly) $5 in then-dollars, but maybe isn't so important now,
when it seems like the package costs more than the silicon inside it.

There are still FPGAs at the lower end that don't include multipliers. I
have an older design in a small FPGA I am still shipping that does the
iterative adding thing. It has been a while since I considered using
the CORDIC algorithm. What exactly is the advantage of the CORDIC
algorithm again?

It uses less gates. Which is why I'm asking my question -- gates seem to
be a lot cheaper these days, so do people still use CORDIC?


My understanding (kind of limited) is that CORDIC is used for trig and
exponential calculations, more than just multiplication. I have never
used a CORDIC implementation in an FPGA or an ASIC. I tend to do more
control path and communications implementations than DSP/data path stuff
though.

BobH

rickman
Guest

Fri Oct 14, 2016 7:30 am   



On 10/13/2016 6:16 PM, Tim Wescott wrote:
Quote:
On Thu, 13 Oct 2016 18:14:58 -0400, rickman wrote:

On 10/13/2016 5:10 PM, Tim Wescott wrote:
On Thu, 13 Oct 2016 20:59:49 +0000, Rob Gaddi wrote:

Tim Wescott wrote:

On Thu, 13 Oct 2016 13:46:18 -0500, Tim Wescott wrote:

Now that FPGAs have built-in DSP blocks, how commonly is CORDIC
used? Is it still a necessary go-to for anyone contemplating doing
DSP in an FPGA,
or is it starting to ease onto the off-ramp of history?

And, putting FPGA use aside -- how common is it is ASICs?

Being bad because I'm cross-posting. Being bad because I'm
cross-posting a reply to _my own post_.

Oh well -- I'm thinking that maybe some of the folks on comp.dsp who
aren't also on comp.arch.fpga will have some thoughts.


I've considered it many times, but never used it. Then again it's not
like I use the DSP blocks for CORDIC sorts of things anyhow; I just
throw a RAM lookup table at the problem.

That was the other thing that I should have mentioned.

I've heard a lot of talk about CORDIC, but it seems to be one of those
things that was Really Critically Important back when an Intel 4004
cost (reputedly) $5 in then-dollars, but maybe isn't so important now,
when it seems like the package costs more than the silicon inside it.

There are still FPGAs at the lower end that don't include multipliers. I
have an older design in a small FPGA I am still shipping that does the
iterative adding thing. It has been a while since I considered using
the CORDIC algorithm. What exactly is the advantage of the CORDIC
algorithm again?

It uses less gates. Which is why I'm asking my question -- gates seem to
be a lot cheaper these days, so do people still use CORDIC?


Can you explain that briefly? Why is it less gates than an adder?
Adders are pretty durn simple. I thought the CORDIC algorithm used an
ADD.

--

Rick C

Cecil Bayona
Guest

Fri Oct 14, 2016 7:30 am   



On 10/13/2016 8:33 PM, rickman wrote:
Quote:
On 10/13/2016 6:16 PM, Tim Wescott wrote:
On Thu, 13 Oct 2016 18:14:58 -0400, rickman wrote:

On 10/13/2016 5:10 PM, Tim Wescott wrote:
On Thu, 13 Oct 2016 20:59:49 +0000, Rob Gaddi wrote:

Tim Wescott wrote:

On Thu, 13 Oct 2016 13:46:18 -0500, Tim Wescott wrote:

Now that FPGAs have built-in DSP blocks, how commonly is CORDIC
used? Is it still a necessary go-to for anyone contemplating doing
DSP in an FPGA,
or is it starting to ease onto the off-ramp of history?

And, putting FPGA use aside -- how common is it is ASICs?

Being bad because I'm cross-posting. Being bad because I'm
cross-posting a reply to _my own post_.

Oh well -- I'm thinking that maybe some of the folks on comp.dsp who
aren't also on comp.arch.fpga will have some thoughts.


I've considered it many times, but never used it. Then again it's not
like I use the DSP blocks for CORDIC sorts of things anyhow; I just
throw a RAM lookup table at the problem.

That was the other thing that I should have mentioned.

I've heard a lot of talk about CORDIC, but it seems to be one of those
things that was Really Critically Important back when an Intel 4004
cost (reputedly) $5 in then-dollars, but maybe isn't so important now,
when it seems like the package costs more than the silicon inside it.

There are still FPGAs at the lower end that don't include multipliers. I
have an older design in a small FPGA I am still shipping that does the
iterative adding thing. It has been a while since I considered using
the CORDIC algorithm. What exactly is the advantage of the CORDIC
algorithm again?

It uses less gates. Which is why I'm asking my question -- gates seem to
be a lot cheaper these days, so do people still use CORDIC?

Can you explain that briefly? Why is it less gates than an adder?
Adders are pretty durn simple. I thought the CORDIC algorithm used an ADD.

Cordic is used for items like sine, cosine, tangent, square root,etc
with involves multiplication and some division, but the Cordic
Algorithms eliminate multiply and divide so it simplifies the logic by
quite a bit. It's mainly used with devices that do not have multiply and
divide capability even then Cordic could be faster.

--
Cecil - k5nwa

Rafael Deliano
Guest

Fri Oct 14, 2016 7:30 am   



Quote:
I've heard a lot of talk about CORDIC, but it seems to be one of those
things that was Really Critically Important back when an Intel 4004 cost
(reputedly) $5 in then-dollars,


It was used in (HP-)pocket calculators then and got well known
that way.
Later on floating point coprocessors. 8087, probably up to MC68882.
Guess Cyrix were the first there to implement a big float multiplier
and do it differently.
In the 70ies and 80ies on (rad-hard) RCA1802 CPUs in AMSAT
satellites.
It calculates not only sin, cos, but also atan, atanh, sinh, cosh ...
For navigation, robotics on small memory it may be still usefull.

But who knows after all these years what it is and
how to implement it ?
Same for Logarithmic Number Systems ( LNS ).
There may be niche applications that benefit, but industry
will not offer it, because customers will not know & buy.

MfG JRD

rickman
Guest

Fri Oct 14, 2016 7:30 am   



On 10/13/2016 9:33 PM, rickman wrote:
Quote:
On 10/13/2016 6:16 PM, Tim Wescott wrote:
On Thu, 13 Oct 2016 18:14:58 -0400, rickman wrote:

On 10/13/2016 5:10 PM, Tim Wescott wrote:
On Thu, 13 Oct 2016 20:59:49 +0000, Rob Gaddi wrote:

Tim Wescott wrote:

On Thu, 13 Oct 2016 13:46:18 -0500, Tim Wescott wrote:

Now that FPGAs have built-in DSP blocks, how commonly is CORDIC
used? Is it still a necessary go-to for anyone contemplating doing
DSP in an FPGA,
or is it starting to ease onto the off-ramp of history?

And, putting FPGA use aside -- how common is it is ASICs?

Being bad because I'm cross-posting. Being bad because I'm
cross-posting a reply to _my own post_.

Oh well -- I'm thinking that maybe some of the folks on comp.dsp who
aren't also on comp.arch.fpga will have some thoughts.


I've considered it many times, but never used it. Then again it's not
like I use the DSP blocks for CORDIC sorts of things anyhow; I just
throw a RAM lookup table at the problem.

That was the other thing that I should have mentioned.

I've heard a lot of talk about CORDIC, but it seems to be one of those
things that was Really Critically Important back when an Intel 4004
cost (reputedly) $5 in then-dollars, but maybe isn't so important now,
when it seems like the package costs more than the silicon inside it.

There are still FPGAs at the lower end that don't include multipliers. I
have an older design in a small FPGA I am still shipping that does the
iterative adding thing. It has been a while since I considered using
the CORDIC algorithm. What exactly is the advantage of the CORDIC
algorithm again?

It uses less gates. Which is why I'm asking my question -- gates seem to
be a lot cheaper these days, so do people still use CORDIC?

Can you explain that briefly? Why is it less gates than an adder?
Adders are pretty durn simple. I thought the CORDIC algorithm used an ADD.


Opps, I see the CORDIC doesn't replace a multiplication... it replaces a
sine calculation. I told you it had been a while since I looked at it.

Yes, I recall now the CORDIC typically converges faster than a power
series and requires no multiplications. Do I have it now? Using fewer
gates is a bit of an understatement.

--

Rick C

rickman
Guest

Fri Oct 14, 2016 1:32 pm   



On 10/13/2016 11:51 PM, Cecil Bayona wrote:
Quote:
On 10/13/2016 8:33 PM, rickman wrote:
On 10/13/2016 6:16 PM, Tim Wescott wrote:
On Thu, 13 Oct 2016 18:14:58 -0400, rickman wrote:

On 10/13/2016 5:10 PM, Tim Wescott wrote:
On Thu, 13 Oct 2016 20:59:49 +0000, Rob Gaddi wrote:

Tim Wescott wrote:

On Thu, 13 Oct 2016 13:46:18 -0500, Tim Wescott wrote:

Now that FPGAs have built-in DSP blocks, how commonly is CORDIC
used? Is it still a necessary go-to for anyone contemplating doing
DSP in an FPGA,
or is it starting to ease onto the off-ramp of history?

And, putting FPGA use aside -- how common is it is ASICs?

Being bad because I'm cross-posting. Being bad because I'm
cross-posting a reply to _my own post_.

Oh well -- I'm thinking that maybe some of the folks on comp.dsp who
aren't also on comp.arch.fpga will have some thoughts.


I've considered it many times, but never used it. Then again it's
not
like I use the DSP blocks for CORDIC sorts of things anyhow; I just
throw a RAM lookup table at the problem.

That was the other thing that I should have mentioned.

I've heard a lot of talk about CORDIC, but it seems to be one of those
things that was Really Critically Important back when an Intel 4004
cost (reputedly) $5 in then-dollars, but maybe isn't so important now,
when it seems like the package costs more than the silicon inside it.

There are still FPGAs at the lower end that don't include
multipliers. I
have an older design in a small FPGA I am still shipping that does the
iterative adding thing. It has been a while since I considered using
the CORDIC algorithm. What exactly is the advantage of the CORDIC
algorithm again?

It uses less gates. Which is why I'm asking my question -- gates
seem to
be a lot cheaper these days, so do people still use CORDIC?

Can you explain that briefly? Why is it less gates than an adder?
Adders are pretty durn simple. I thought the CORDIC algorithm used an
ADD.

Cordic is used for items like sine, cosine, tangent, square root,etc
with involves multiplication and some division, but the Cordic
Algorithms eliminate multiply and divide so it simplifies the logic by
quite a bit. It's mainly used with devices that do not have multiply and
divide capability even then Cordic could be faster.


It can be faster at trig functions than multiplying (assuming the
multiply was not with a parallel multiplier), but it is not faster than
a multiplier at multiplying, even a shift and add multiplier. The
CORDIC function converges at 1 bit per iteration. That's the same as a
sequential multiplier doing a shift and add which is very similar to the
CORDIC method.

The CORDIC function can always be pipelined to get higher throughput,
but it is not likely to outrun a dedicated multiplier in an FPGA.
Taylor series gets very high precisions very quickly.

--

Rick C


Guest

Fri Oct 14, 2016 3:04 pm   



On Friday, October 14, 2016 at 4:37:39 AM UTC+3, rickman wrote:
Quote:
On 10/13/2016 9:33 PM, rickman wrote:
On 10/13/2016 6:16 PM, Tim Wescott wrote:
On Thu, 13 Oct 2016 18:14:58 -0400, rickman wrote:

On 10/13/2016 5:10 PM, Tim Wescott wrote:
On Thu, 13 Oct 2016 20:59:49 +0000, Rob Gaddi wrote:

Tim Wescott wrote:

On Thu, 13 Oct 2016 13:46:18 -0500, Tim Wescott wrote:

Now that FPGAs have built-in DSP blocks, how commonly is CORDIC
used? Is it still a necessary go-to for anyone contemplating doing
DSP in an FPGA,
or is it starting to ease onto the off-ramp of history?

And, putting FPGA use aside -- how common is it is ASICs?

Being bad because I'm cross-posting. Being bad because I'm
cross-posting a reply to _my own post_.

Oh well -- I'm thinking that maybe some of the folks on comp.dsp who
aren't also on comp.arch.fpga will have some thoughts.


I've considered it many times, but never used it. Then again it's not
like I use the DSP blocks for CORDIC sorts of things anyhow; I just
throw a RAM lookup table at the problem.

That was the other thing that I should have mentioned.

I've heard a lot of talk about CORDIC, but it seems to be one of those
things that was Really Critically Important back when an Intel 4004
cost (reputedly) $5 in then-dollars, but maybe isn't so important now,
when it seems like the package costs more than the silicon inside it..

There are still FPGAs at the lower end that don't include multipliers.. I
have an older design in a small FPGA I am still shipping that does the
iterative adding thing. It has been a while since I considered using
the CORDIC algorithm. What exactly is the advantage of the CORDIC
algorithm again?

It uses less gates. Which is why I'm asking my question -- gates seem to
be a lot cheaper these days, so do people still use CORDIC?

Can you explain that briefly? Why is it less gates than an adder?
Adders are pretty durn simple. I thought the CORDIC algorithm used an ADD.

Opps, I see the CORDIC doesn't replace a multiplication... it replaces a
sine calculation. I told you it had been a while since I looked at it.

Yes, I recall now the CORDIC typically converges faster than a power
series


If you properly chose your ranges then power series will converge many times faster than CORDIC.

For example, you want sin(x) for x in range [0..pi/2]. You don't apply power series to a full range.
Instead, you calculated it as sin(x_tab)*cos(x-x_tab)+cos(x)*sin(x-x_tab)
Where, sin(x_tab)/cos(x_tab) are taken from small table, e.g. 64 entries. Then, you only apply power series to x-x_tab, which is a small number. Such power series converges very quickly, in specific case of sin() and of 64-entry table, ~13 bits per iteration.

Please, don't take what is written above as an actual algorithm. It's just a guideline. An algorithm, that wants to produces a result with max. error of < 1 ULP, would have to be a little more careful about details.

Quote:
and requires no multiplications. Do I have it now? Using fewer
gates is a bit of an understatement.

--

Rick C



Guest

Fri Oct 14, 2016 3:17 pm   



On Friday, October 14, 2016 at 6:35:12 AM UTC+3, Rafael Deliano wrote:
Quote:
I've heard a lot of talk about CORDIC, but it seems to be one of those
things that was Really Critically Important back when an Intel 4004 cost
(reputedly) $5 in then-dollars,

It was used in (HP-)pocket calculators then and got well known
that way.
Later on floating point coprocessors. 8087,


Did 8087 use CORDIC for multiplication and division or only for trigonometric instructions, and, possibly, for BCD-binary conversions?
I googled for an answer several months ago, but found nothing.

Quote:
probably up to MC68882.
Guess Cyrix were the first there to implement a big float multiplier
and do it differently.
In the 70ies and 80ies on (rad-hard) RCA1802 CPUs in AMSAT
satellites.
It calculates not only sin, cos, but also atan, atanh, sinh, cosh ...
For navigation, robotics on small memory it may be still usefull.


Unlikely.
Nowadays, even small ARM Cortex-M4 has fast multiplier and is typically coupled with at least 128 KB of on-chip NOR flash. And robotics tend to use bigger CPUs than Cortex M4.

Quote:

But who knows after all these years what it is and
how to implement it ?
Same for Logarithmic Number Systems ( LNS ).
There may be niche applications that benefit, but industry
will not offer it, because customers will not know & buy.

MfG JRD


Steve Pope
Guest

Fri Oct 14, 2016 4:40 pm   



Cecil Bayona <cbayona_at_cbayona.com> wrote:

Quote:
Cordic is used for items like sine, cosine, tangent, square root,etc
with involves multiplication and some division, but the Cordic
Algorithms eliminate multiply and divide so it simplifies the logic by
quite a bit.


I've been designing DSP ASIC's since the 1980's and have never
chosen to use Cordic. I can envision where Cordic might make sense --
where the precision requirements are not really known or are
very high, Cordic will win over LUT-based designs but most typically
the LUT-based designs are a simpler way to meet the requirement.

It's also possible that in some PLD-based designs Cordic might
be the way to go.

Steve

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