dead programming languages...

[Phil Hobbs]

On 2023-03-02 10:36, Joe Gwinn wrote:

On Thu, 02 Mar 2023 11:17:08 +0200, upsidedown@downunder.com wrote:

On Wed, 01 Mar 2023 15:26:08 -0500, Joe Gwinn <joegwinn@comcast.net
wrote:


But the more fundamental limitation is Amdahl\'s Law, which applies to
all parallel computations:

.<https://en.wikipedia.org/wiki/Amdahl%27s_law

This is why it\'s hard to parallelize for instance a FFT.


If you have a lot of cores, why not use discrete FT instead of FFT,
especially if you do not need all points or the input size is
something different from some power of 2 ?

Actually, the problem is with all integral transforms, regardless of
the existence of a fast algorithm, because by definition an integral
transform uses the entire input to generate each point in the output.

Only if the kernel occupies the whole interval for all values of the
parameters. Wavelet transforms, for instance, are more or less well
localized in both time and frequency.

But there are problems where there are things that can be computed in
parallel independently. These are called \"embarrassingly parallel\"
problems.

Joe Gwinn

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

 

[Phil Hobbs]

On 2023-03-02 14:34, wmartin wrote:

On 2/22/23 11:05, John Larkin wrote:
https://en.wikipedia.org/wiki/Timeline_of_programming_languages


Now I\'m told that we should be coding hard embedded products in C++ or
Rust.

Usenet needs a \"dead horse language\", to speed up describing all the
dead horse beatings...

We\'re still waiting for the horse\'s morale to improve.

Cheers

Phil Hobbs

 

[Joe Gwinn]

On Thu, 2 Mar 2023 22:00:10 -0500, Phil Hobbs
<pcdhSpamMeSenseless@electrooptical.net> wrote:

On 2023-03-02 10:36, Joe Gwinn wrote:
On Thu, 02 Mar 2023 11:17:08 +0200, upsidedown@downunder.com wrote:

On Wed, 01 Mar 2023 15:26:08 -0500, Joe Gwinn <joegwinn@comcast.net
wrote:


But the more fundamental limitation is Amdahl\'s Law, which applies to
all parallel computations:

.<https://en.wikipedia.org/wiki/Amdahl%27s_law

This is why it\'s hard to parallelize for instance a FFT.


If you have a lot of cores, why not use discrete FT instead of FFT,
especially if you do not need all points or the input size is
something different from some power of 2 ?

Actually, the problem is with all integral transforms, regardless of
the existence of a fast algorithm, because by definition an integral
transform uses the entire input to generate each point in the output.

Only if the kernel occupies the whole interval for all values of the
parameters. Wavelet transforms, for instance, are more or less well
localized in both time and frequency.

Yes, and in practice we truncate infinite tails as well, and live with
the resulting errors.

In radar, the 2^20 point FFTs are often for pulse compression in chirp
radars, and at least half of the kernel cells are set to zero, because
we don\'t know in advance where the targets and thus echoes are in
advance.

Joe Gwinn

 

[Joe Gwinn]

On Thu, 2 Mar 2023 21:57:41 -0500, Phil Hobbs
<pcdhSpamMeSenseless@electrooptical.net> wrote:

On 2023-03-02 10:49, Joe Gwinn wrote:
On Thu, 2 Mar 2023 09:12:20 -0500, Phil Hobbs
pcdhSpamMeSenseless@electrooptical.net> wrote:

On 2023-03-02 04:17, upsidedown@downunder.com wrote:
On Wed, 01 Mar 2023 15:26:08 -0500, Joe Gwinn <joegwinn@comcast.net
wrote:


But the more fundamental limitation is Amdahl\'s Law, which applies to
all parallel computations:

.<https://en.wikipedia.org/wiki/Amdahl%27s_law

This is why it\'s hard to parallelize for instance a FFT.


If you have a lot of cores, why not use discrete FT instead of FFT,
especially if you do not need all points or the input size is
something different from some power of 2 ?


There are fast algorithms for all array lengths, including prime
numbers. See e.g. <https://www.fftw.org/>.

FFTs can be parallellized reasonably well. IIRC it\'s the bit-reversal
step that makes radix-2 transforms a bit slow on highly multicore SMPs.

http://www.fftw.org/parallel/parallel-fftw.html


Yes, all true. But in radar we often want million-point (2^20)
discrete Fourier transforms.

Well, for that job you ain\'t going to be using an N**2 algorithm
(straight DFT), multicore or no multicore.

Yep.

The bottom line for attempts to do just that were that time (latency)
to done ceased decreasing and began increasing somewhere around 4 to 6
parallel processors.

That seems pessimistic.

This was the measured result of a direct test of a 2^20-point FFT of
random data, on the chosen platform. The benchmark is slightly
pessimistic in that in actual use, because less than half of the
points are non-zero, but still ...

My EM simulator code scales nearly linearly up
to 40 processors, which is as far as I\'ve tested it.

At the time, it was all in main memory of a big \"massively parallel\"
(maybe 128 processors?) enterprise server, and part of the test was if
this particular make and model of machine could do the job, and it was
shown that it was not even close. (It was really intended to be a web
server handling web inquiries, a massively parallel application.)

I think EM simulators are structurally similar to finite-element
stress analysis analyzers in that all communications is with the
abutting finite elements, and if so the linear scaling you observed is
plausible.

Of course you
folks probably didn\'t have Infiniband or GbE connections. The biggest
killer is handshake latency, IME.

We do now. And yes, handshake latency (needed for command and control
to forge all those moving parts into a functional whole) still
dominates.

This is Amdahl territory - I rejected signal-processing\'s estimate of
performance because it omitted this very thing, the control plane.

Also missing was how to coordinate actions that must be atomic across
the whole processing fabric.

And because they were using throughput estimates, versus latency
estimates - in realtime, one usually runs out of timeline first, often
long before saturating the CPUs.

In the old days, the poster child was a spinning-metal disk - all
latency, no CPU.

Now days, the poster child is a processor core - these are limited by
how fast random data can get to the processor, and how fast it can be
put where it must go - in short, the memory system is the bottleneck,
and it is shared by many processors. And so on.

This was a big problem because (marketing?) people assumed that if you
used 10^4 processors, time to done would be reduced by 10^4. Oops.
Even after people decided that 256K (2^18) points would suffice, still
no go. They also believed the marketing MIPS of the computer
platform, but that\'s another story. All these fables were killed by a
direct FFT benchmark.

The eventual solution was to use specialized array-processing
hardware.

That, I believe. One reason FPGAs don\'t get used for ordinary computing
workloads is the gigantic task switching overhead that would impose.
But when you don\'t need to switch tasks, a big array is very very powerful.

Yes. We now use FPGAs in place of those array processors. FPGAs are
much faster and much more flexible.

Joe Gwinn

 

[Martin Brown]

On 03/03/2023 19:31, Joe Gwinn wrote:

On Thu, 2 Mar 2023 22:00:10 -0500, Phil Hobbs
pcdhSpamMeSenseless@electrooptical.net> wrote:

On 2023-03-02 10:36, Joe Gwinn wrote:
On Thu, 02 Mar 2023 11:17:08 +0200, upsidedown@downunder.com wrote:

On Wed, 01 Mar 2023 15:26:08 -0500, Joe Gwinn <joegwinn@comcast.net
wrote:


But the more fundamental limitation is Amdahl\'s Law, which applies to
all parallel computations:

.<https://en.wikipedia.org/wiki/Amdahl%27s_law

This is why it\'s hard to parallelize for instance a FFT.


If you have a lot of cores, why not use discrete FT instead of FFT,
especially if you do not need all points or the input size is
something different from some power of 2 ?

Actually, the problem is with all integral transforms, regardless of
the existence of a fast algorithm, because by definition an integral
transform uses the entire input to generate each point in the output.

Only if the kernel occupies the whole interval for all values of the
parameters. Wavelet transforms, for instance, are more or less well
localized in both time and frequency.

Yes, and in practice we truncate infinite tails as well, and live with
the resulting errors.

In radar, the 2^20 point FFTs are often for pulse compression in chirp
radars, and at least half of the kernel cells are set to zero, because
we don\'t know in advance where the targets and thus echoes are in
advance.

Out of curiosity do you do it the same way as in radio astronomy to kill
off edge effects or just rely on uniform temporal sampling?
(which you generally have in a radar system - and we don\'t)

The radio astronomy trick is to preconvolve the raw data with a gridding
function on a compact support of 5 or 7 cells centred on the data point
so that when the FFT is done the resulting transform is a very close
approximation to the DFT apart from very close to the edges where the
results are haywire so you discard a narrow guard band. Schwab at the
VLA first catalogued the most interesting functions for this trick.

https://library.nrao.edu/public/memos/vla/sci/VLAS_132.pdf

This is a later version by Sze Tan that formalises the guard band and
generalises the functions beyond prolate spheroidal Bessel functions.

https://arxiv.org/pdf/1906.07102.pdf

Failure to use the right functions on an irregularly sampled dataset
seriously compromises signal to noise in the resulting transform.

--
Martin Brown

 

[Joe Gwinn]

On Sat, 4 Mar 2023 09:26:39 +0000, Martin Brown
<\'\'\'newspam\'\'\'@nonad.co.uk> wrote:

On 03/03/2023 19:31, Joe Gwinn wrote:
On Thu, 2 Mar 2023 22:00:10 -0500, Phil Hobbs
pcdhSpamMeSenseless@electrooptical.net> wrote:

On 2023-03-02 10:36, Joe Gwinn wrote:
On Thu, 02 Mar 2023 11:17:08 +0200, upsidedown@downunder.com wrote:

On Wed, 01 Mar 2023 15:26:08 -0500, Joe Gwinn <joegwinn@comcast.net
wrote:


But the more fundamental limitation is Amdahl\'s Law, which applies to
all parallel computations:

.<https://en.wikipedia.org/wiki/Amdahl%27s_law

This is why it\'s hard to parallelize for instance a FFT.


If you have a lot of cores, why not use discrete FT instead of FFT,
especially if you do not need all points or the input size is
something different from some power of 2 ?

Actually, the problem is with all integral transforms, regardless of
the existence of a fast algorithm, because by definition an integral
transform uses the entire input to generate each point in the output.

Only if the kernel occupies the whole interval for all values of the
parameters. Wavelet transforms, for instance, are more or less well
localized in both time and frequency.

Yes, and in practice we truncate infinite tails as well, and live with
the resulting errors.

In radar, the 2^20 point FFTs are often for pulse compression in chirp
radars, and at least half of the kernel cells are set to zero, because
we don\'t know in advance where the targets and thus echoes are in
advance.

Out of curiosity do you do it the same way as in radio astronomy to kill
off edge effects or just rely on uniform temporal sampling?
(which you generally have in a radar system - and we don\'t)

The data is always taken with uniform temporal sampling, but usually
with missing samples (often due to blanking of impulse noise or CW
tones in the frequency domain). At low SNR levels, the result can be
pretty ragged, so the gaps are generally repaired by complex
interpolating of flanking stretches of samples into the gap. The
detailed algorithms are tightly held.

Another approach, sometimes combined with interpolating across the
gap, is resample and decimate in a combined algorithm, where the
original sample rate and reduced sample rate are not an integer
multiple of one another.

The radio astronomy trick is to preconvolve the raw data with a gridding
function on a compact support of 5 or 7 cells centred on the data point
so that when the FFT is done the resulting transform is a very close
approximation to the DFT apart from very close to the edges where the
results are haywire so you discard a narrow guard band. Schwab at the
VLA first catalogued the most interesting functions for this trick.

.<https://library.nrao.edu/public/memos/vla/sci/VLAS_132.pdf

This sounds similar to the above combined decimate and resample scheme
described above.

This is a later version by Sze Tan that formalises the guard band and
generalises the functions beyond prolate spheroidal Bessel functions.

.<https://arxiv.org/pdf/1906.07102.pdf

Failure to use the right functions on an irregularly sampled dataset
seriously compromises signal to noise in the resulting transform.

Yes. The signal-processing folk perform massive trade studies of
algorithms and the best order in which to apply them.

I\'ll read the above memos. Some of the s-p folk follow the radio
astronomy literature, so I\'d guess that they already know of these
algorithms.

Joe Gwinn

 

[Martin Brown]

On 04/03/2023 19:37, Joe Gwinn wrote:

On Sat, 4 Mar 2023 09:26:39 +0000, Martin Brown
\'\'\'newspam\'\'\'@nonad.co.uk> wrote:

This is a later version by Sze Tan that formalises the guard band and
generalises the functions beyond prolate spheroidal Bessel functions.

.<https://arxiv.org/pdf/1906.07102.pdf

Failure to use the right functions on an irregularly sampled dataset
seriously compromises signal to noise in the resulting transform.

Yes. The signal-processing folk perform massive trade studies of
algorithms and the best order in which to apply them.

I\'ll read the above memos. Some of the s-p folk follow the radio
astronomy literature, so I\'d guess that they already know of these
algorithms.

That figures - some of our graduates would go on to work for RSRE.

--
Martin Brown

 

[John Walliker]

On Sunday, 5 March 2023 at 09:36:35 UTC, Martin Brown wrote:

On 04/03/2023 19:37, Joe Gwinn wrote:
On Sat, 4 Mar 2023 09:26:39 +0000, Martin Brown
\'\'\'newspam\'\'\'@nonad.co.uk> wrote:

This is a later version by Sze Tan that formalises the guard band and
generalises the functions beyond prolate spheroidal Bessel functions.

.<https://arxiv.org/pdf/1906.07102.pdf

Failure to use the right functions on an irregularly sampled dataset
seriously compromises signal to noise in the resulting transform.

Yes. The signal-processing folk perform massive trade studies of
algorithms and the best order in which to apply them.

I\'ll read the above memos. Some of the s-p folk follow the radio
astronomy literature, so I\'d guess that they already know of these
algorithms.
That figures - some of our graduates would go on to work for RSRE.

It hasn\'t been called that for a long time...
John

--
Martin Brown

 

[Joe Gwinn]

On Sun, 5 Mar 2023 09:36:08 +0000, Martin Brown
<\'\'\'newspam\'\'\'@nonad.co.uk> wrote:

On 04/03/2023 19:37, Joe Gwinn wrote:
On Sat, 4 Mar 2023 09:26:39 +0000, Martin Brown
\'\'\'newspam\'\'\'@nonad.co.uk> wrote:

This is a later version by Sze Tan that formalises the guard band and
generalises the functions beyond prolate spheroidal Bessel functions.

.<https://arxiv.org/pdf/1906.07102.pdf

Failure to use the right functions on an irregularly sampled dataset
seriously compromises signal to noise in the resulting transform.

Yes. The signal-processing folk perform massive trade studies of
algorithms and the best order in which to apply them.

I\'ll read the above memos. Some of the s-p folk follow the radio
astronomy literature, so I\'d guess that they already know of these
algorithms.

That figures - some of our graduates would go on to work for RSRE.

Same story here. We have lots of wayward astronomers, actually. The
screen saver is often the tell.

While I\'m no astronomer, the rule isn\'t absolute - my screen saver is
a hot Neptune (Kepler 36b):

..<https://www.nsf.gov/news/mmg/mmg_disp.jsp?med_id=133282>


I\'ve read both articles. The radar s-p folk do things resembling what
Sze Tan describes, but optimized for processing speed (short latency)
and for seeing small objects close to large objects at almost the same
range. The window and kernel functions are similar to Gaussian, to
reduce sidelobes appearing as false targets. Taylor, Bessel, and the
like being common. No prolate spheroids.

Joe Gwinn

 

[Martin Brown]

On 05/03/2023 19:19, Joe Gwinn wrote:

On Sun, 5 Mar 2023 09:36:08 +0000, Martin Brown
\'\'\'newspam\'\'\'@nonad.co.uk> wrote:

On 04/03/2023 19:37, Joe Gwinn wrote:
On Sat, 4 Mar 2023 09:26:39 +0000, Martin Brown
\'\'\'newspam\'\'\'@nonad.co.uk> wrote:

This is a later version by Sze Tan that formalises the guard band and
generalises the functions beyond prolate spheroidal Bessel functions.

.<https://arxiv.org/pdf/1906.07102.pdf

Failure to use the right functions on an irregularly sampled dataset
seriously compromises signal to noise in the resulting transform.

Yes. The signal-processing folk perform massive trade studies of
algorithms and the best order in which to apply them.

I\'ll read the above memos. Some of the s-p folk follow the radio
astronomy literature, so I\'d guess that they already know of these
algorithms.

That figures - some of our graduates would go on to work for RSRE.

Same story here. We have lots of wayward astronomers, actually. The
screen saver is often the tell.

While I\'m no astronomer, the rule isn\'t absolute - my screen saver is
a hot Neptune (Kepler 36b):

.<https://www.nsf.gov/news/mmg/mmg_disp.jsp?med_id=133282


I\'ve read both articles. The radar s-p folk do things resembling what
Sze Tan describes, but optimized for processing speed (short latency)
and for seeing small objects close to large objects at almost the same
range. The window and kernel functions are similar to Gaussian, to
reduce sidelobes appearing as false targets. Taylor, Bessel, and the
like being common. No prolate spheroids.

Prolate spheroids will beat truncated Gaussian hands down. The reason we
moved from simpler kernels was precisely to maximise the dynamic range
in images made from Fourier data. In our case the measurements taken on
ellipses as the Earth rotates so must be resampled prior to transform.

The images tended to be very faint nebulosity flowing away from and in
close proximity to incredibly bright hotspots where relativistic
particle beams slam into the intergalactic medium. Think poached eggs!

https://skyandtelescope.org/astronomy-news/mystery-object-in-cygnus-a-galaxy-1301201623/

Seems it still holds surprises - new object resolved recently that
wasn\'t there back when I was involved in this sort of stuff.

The PSB functions main claim to fame it that like the Gaussian it is its
own Fourier transform when band limited to a particular length - but
without the restriction of remaining everywhere positive.

Superficially it looks a lot like a truncated sinc(x)exp(-ax^2) but the
zeroes are not precisely aligned with the sampling grid.

The big difference is that in all cases the multiplicative correction
factor in the transform domain corresponding to the convolution done in
sample regridding is exactly the same.

--
Martin Brown

 

[Joe Gwinn]

On Mon, 6 Mar 2023 08:51:55 +0000, Martin Brown
<\'\'\'newspam\'\'\'@nonad.co.uk> wrote:

On 05/03/2023 19:19, Joe Gwinn wrote:
On Sun, 5 Mar 2023 09:36:08 +0000, Martin Brown
\'\'\'newspam\'\'\'@nonad.co.uk> wrote:

On 04/03/2023 19:37, Joe Gwinn wrote:
On Sat, 4 Mar 2023 09:26:39 +0000, Martin Brown
\'\'\'newspam\'\'\'@nonad.co.uk> wrote:

This is a later version by Sze Tan that formalises the guard band and
generalises the functions beyond prolate spheroidal Bessel functions.

.<https://arxiv.org/pdf/1906.07102.pdf

Failure to use the right functions on an irregularly sampled dataset
seriously compromises signal to noise in the resulting transform.

Yes. The signal-processing folk perform massive trade studies of
algorithms and the best order in which to apply them.

I\'ll read the above memos. Some of the s-p folk follow the radio
astronomy literature, so I\'d guess that they already know of these
algorithms.

That figures - some of our graduates would go on to work for RSRE.

Same story here. We have lots of wayward astronomers, actually. The
screen saver is often the tell.

While I\'m no astronomer, the rule isn\'t absolute - my screen saver is
a hot Neptune (Kepler 36b):

.<https://www.nsf.gov/news/mmg/mmg_disp.jsp?med_id=133282


I\'ve read both articles. The radar s-p folk do things resembling what
Sze Tan describes, but optimized for processing speed (short latency)
and for seeing small objects close to large objects at almost the same
range. The window and kernel functions are similar to Gaussian, to
reduce sidelobes appearing as false targets. Taylor, Bessel, and the
like being common. No prolate spheroids.

Prolate spheroids will beat truncated Gaussian hands down. The reason we
moved from simpler kernels was precisely to maximise the dynamic range
in images made from Fourier data. In our case the measurements taken on
ellipses as the Earth rotates so must be resampled prior to transform.

I don\'t know the reason, but although prolate spheroids are mentioned
from time to time, I don\'t recall seeing them winning the tradeoffs in
radar. Now that I\'m sensitized, I\'ll probably begin to see them
everywhere. But see later herein.

The images tended to be very faint nebulosity flowing away from and in
close proximity to incredibly bright hotspots where relativistic
particle beams slam into the intergalactic medium. Think poached eggs!

.<https://skyandtelescope.org/astronomy-news/mystery-object-in-cygnus-a-galaxy-1301201623/

Seems it still holds surprises - new object resolved recently that
wasn\'t there back when I was involved in this sort of stuff.

That\'s interesting. My bet is on a black-hole merger in progress, as
a larger galaxy messily eats a smaller galaxy. I assume that LIGO
cannot see this yet.

The PSB functions main claim to fame it that like the Gaussian it is its
own Fourier transform when band limited to a particular length - but
without the restriction of remaining everywhere positive.

Superficially it looks a lot like a truncated sinc(x)exp(-ax^2) but the
zeroes are not precisely aligned with the sampling grid.

The big difference is that in all cases the multiplicative correction
factor in the transform domain corresponding to the convolution done in
sample regridding is exactly the same.

Hmm. This may be the key. In radar, we are looking for a finite
number of solid physical targets, versus an extended image containing
an unknown large number of physical objects that need not be solid.

And for speed, we zero as many array elements as possible.


Joe Gwinn

 

[sibolis jahanamnaburju]

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