### Are we reaching the maximum of CPU performance ?

 1 Nicolaas Vroom Are we reaching the maximum of CPU performance ? zondag 7 november 2010 18:18 2 Dirk Bruere at NeoPax Re: Are we reaching the maximum of CPU performance ? maandag 8 november 2010 4:09 3 Giorgio Pastore Re: Are we reaching the maximum of CPU performance ? maandag 8 november 2010 4:17 4 Lester Welch Re: Are we reaching the maximum of CPU performance ? maandag 8 november 2010 11:52 5 Nicolaas Vroom Re: Are we reaching the maximum of CPU performance ? maandag 8 november 2010 22:01 6 Nicolaas Vroom Re: Are we reaching the maximum of CPU performance ? maandag 8 november 2010 22:28 7 Dirk Bruere at NeoPax Re: Are we reaching the maximum of CPU performance ? maandag 8 november 2010 22:28 8 Arnold Neumaier Re: Are we reaching the maximum of CPU performance ? maandag 8 november 2010 22:28 9 Nicolaas Vroom Re: Are we reaching the maximum of CPU performance ? dinsdag 9 november 2010 4:05 10 Hans Aberg Re: Are we reaching the maximum of CPU performance ? dinsdag 9 november 2010 4:13 11 Juan R. González-Álvarez Re: Are we reaching the maximum of CPU performance ? woensdag 10 november 2010 5:02 12 Hans Aberg Re: Are we reaching the maximum of CPU performance ? woensdag 10 november 2010 18:45 13 Hans Aberg Re: Are we reaching the maximum of CPU performance ? donderdag 11 november 2010 9:11 14 Hans Aberg Re: Are we reaching the maximum of CPU performance ? donderdag 11 november 2010 9:11 15 Arnold Neumaier Re: Are we reaching the maximum of CPU performance ? donderdag 11 november 2010 17:13 16 Juan R. González-Álvarez Re: Are we reaching the maximum of CPU performance ? vrijdag 12 november 2010 10:14 17 JohnF Re: Are we reaching the maximum of CPU performance ? vrijdag 12 november 2010 10:14 18 Arnold Neumaier Re: Are we reaching the maximum of CPU performance ? vrijdag 12 november 2010 16:50 19 Surfer Re: Are we reaching the maximum of CPU performance ? vrijdag 12 november 2010 22:32 20 Dirk Bruere at NeoPax Re: Are we reaching the maximum of CPU performance ? zaterdag 13 november 2010 9:04 21 Juan R. González-Álvarez Re: Are we reaching the maximum of CPU performance ? maandag 15 november 2010 18:39 22 Hans Aberg Re: Are we reaching the maximum of CPU performance ? maandag 15 november 2010 18:44 23 Arnold Neumaier Re: Are we reaching the maximum of CPU performance ? maandag 15 november 2010 18:46 24 Nicolaas Vroom Re: Are we reaching the maximum of CPU performance ? maandag 15 november 2010 18:46 25 Dirk Bruere at NeoPax Re: Are we reaching the maximum of CPU performance ? dinsdag 16 november 2010 22:15 26 BW Re: Are we reaching the maximum of CPU performance ? donderdag 18 november 2010 7:55 27 Dirk Bruere at NeoPax Re: Are we reaching the maximum of CPU performance ? donderdag 18 november 2010 9:47 28 Nicolaas Vroom Re: Are we reaching the maximum of CPU performance ? donderdag 18 november 2010 9:47 29 Joseph Warner Re: Are we reaching the maximum of CPU performance ? donderdag 18 november 2010 9:48 30 JohnF Re: Are we reaching the maximum of CPU performance ? vrijdag 19 november 2010 10:36 31 Dirk Bruere at NeoPax Re: Are we reaching the maximum of CPU performance ? zaterdag 20 november 2010 4:10 32 Juan R. Gonzàlez-Àlvarez Re: Are we reaching the maximum of CPU performance ? zaterdag 20 november 2010 19:56 33 Nicolaas Vroom Re: Are we reaching the maximum of CPU performance ? Donderdag 2 december 2010 22.49

### 1 Are we reaching the maximum of CPU performance ?

Van: Nicolaas Vroom
Onderwerp: Are we reaching the maximum of CPU performance ?
Datum: zondag 7 november 2010 18:18

I could also have raised the following question:

Which is currently the best performing CPU ?
This question is important for all people who try to simulate physical systems. In my case this is the movement of 7 planets around the Sun using Newton's Law
I have tested 4 different types of CPU's. In order to compare I use the same VB program. In order to test performance the program calculates the number of years in 1 minute.
a) In the case of a Intel Pentium R II processor I get 0.825 years
b) Genuineltel X86 Family 6 Model 8 I get 1.542 years
c) Intel Pentium R 4 CPU 2.8 GHZ I get 6 years This one is roughly 8 years old. Load 100%
d) Intel Quad Core i5 M460 I get 3.9 years. Load 27%

In the last case I can also load the program 4 times. On average I get 2.6 years. Load 100%

Does this mean that we have reached the top of CPU performance ?
Ofcourse I can rewrite my program in a different language. Maybe than my program runs faster but that does not solve the issue. I did not test a Dual Core, may be those are faster. Of my Pentium R 4 CPU there apparently exists a 3.3 GHZ version. Is that the solution?

Any suggestion what to do ?

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### 2 Are we reaching the maximum of CPU performance ?

Van: Dirk Bruere at NeoPax
Onderwerp: Are we reaching the maximum of CPU performance ?
Datum: maandag 8 november 2010 4:09

On 07/11/2010 17:18, Nicolaas Vroom wrote: posting Mesg1
 > I could also have raised the following question: Which is currently the best performing CPU ? This question is important for all people who try to simulate physical systems. In my case this is the movement of 7 planets around the Sun using Newton's Law I have tested 4 different types of CPU's. In order to compare I use the same VB program. In order to test performance the program calculates the number of years in 1 minute. a) In the case of a Intel Pentium R II processor I get 0.825 years b) Genuineltel X86 Family 6 Model 8 I get 1.542 years c) Intel Pentium R 4 CPU 2.8 GHZ I get 6 years This one is roughly 8 years old. Load 100% d) Intel Quad Core i5 M460 I get 3.9 years. Load 27% In the last case I can also load the program 4 times. On average I get 2.6 years. Load 100% Does this mean that we have reached the top of CPU performance ? Ofcourse I can rewrite my program in a different language. Maybe than my program runs faster but that does not solve the issue. I did not test a Dual Core, may be those are faster. Of my Pentium R 4 CPU there apparently exists a 3.3 GHZ version. Is that the solution? Any suggestion what to do ?

Use a top end graphics card and something like CUDA by nVidia. That will give you up to a 100x increase in computing power to around 1TFLOPS

Apart from that, processing power is still increasing by around 2 orders of magnitude per decade. If that's not enough the DARPA exascale computer is due around 2018 (10^18 FLOPS).

-- Dirk

http://www.transcendence.me.uk/ - Transcendence UK

[[Mod. note -- Sequential (single-thread) CPU speed has indeed roughly plateaued since 2005 or so, at roughly 3 GHz and 4 instructions-per-cycle out-of-order. More recent progress has been:
* bigger and bigger caches [transparent to the programmer]
* some small increases in memory bandwidth [transparent to the progrrammer]
* lots of parallelism [NOT transparent to the programmer]

Parallelism today comes in many flavors [almost all of which must be explicitly managed by the programmer]:
* lots of CPU chips are "multicore" and/or "multithreaded"
* lots of computer systems incorporate multiple CPUs [this includes the graphics-card processors mentioned in this posting]

*If* your application is such that it can be (re)programmed to use many individual processors working in parallel, then parallelism can be very useful. Alas, small-N N-body simulations of the type discussed by the original poster are notoriously hard to parallelize. :(

I'd also like to point out the existence of the newsgroup comp.arch (unmoderated), devoted to discussions of computer architecture. -- jt]]

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### 3 Are we reaching the maximum of CPU performance ?

Van: Giorgio Pastore
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: maandag 8 november 2010 4:17

On 11/7/10 6:18 PM, Nicolaas Vroom wrote in: posting Mesg1
 > ... In my case this is the movement of 7 planets around the Sun using Newton's Law ... In order to compare I use the same VB program. ... Any suggestion what to do ?

You said nothing about the algorithm you implemented in VB. If you chose the wrong algorithm you may may waist a lot of CPU time.

Giorgio

[[Mod. note -- If your goal is actually to study physics via N-body simulations of this sort, there's a considerable literature on clever numerical methods/codes which are very accurate and efficient. A good starting point to learn more might be http://www.amara.com/papers/nbody.html which has lots of references. It discusses both the small-N and large-N cases (which require vastly different sorts of numerical methods, and have very different accuracy/cost/fidelity tradeoffs).

A recent paper of interest (describing a set of simulations of Sun + 8 planets + Pluto + time-averaged Moon + approximate general relativistic effects) is

"Esistence of collisional trajectories of Mercury, Mars, and Venus with the Earth"
Nature volume 459, 11 June 2009, pages 817--819 http://dx.doi.org/10.1038/nature08096
-- jt]]

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### 4 Are we reaching the maximum of CPU performance ?

Van: Lester Welch
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: maandag 8 november 2010 11:52

On Nov 7, 10:17 pm, Giorgio Pastore wrote:posting Mesg3
 > On 11/7/10 6:18 PM, Nicolaas Vroom wrote:posting Mesg1
 > > ... In my case this is the movement of 7 planets around the Sun using Newton's Law ... In order to compare I use the same VB program. ... Any suggestion what to do ?
 > You said nothing about the algorithm you implemented in VB. If you chose the wrong algorithm you may may waist a lot of CPU time. Giorgio [[Mod. note -- If your goal is actually to study physics via N-body simulations of this sort, there's a considerable literature on clever numerical methods/codes which are very accurate and efficient. A good starting point to learn more might be http://www.amara.com/papers/nbody.html which has lots of references. It discusses both the small-N and large-N cases (which require vastly different sorts of numerical methods, and have very different accuracy/cost/fidelity tradeoffs). A recent paper of interest (describing a set of simulations of Sun + 8 planets + Pluto + time-averaged Moon + approximate general relativistic effects) is J. Laskar & M. Gastineau "Esistence of collisional trajectories of Mercury, Mars, and Venus with the Earth" Nature volume 459, 11 June 2009, pages 817--819 http://dx.doi.org/10.1038/nature08096 -- jt]]

Isn't the OP comparing CPU's - not algorithms? An inefficient algorithm run on a multitude of CPUs is a fair test of the CPUs is it not?

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### 5 Are we reaching the maximum of CPU performance ?

Van: Nicolaas Vroom
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: maandag 8 november 2010 22:01

"Dirk Bruere at NeoPax" schreef in bericht posting Mesg2
 > On 07/11/2010 17:18, Nicolaas Vroom wrote in: posting Mesg1
 >> a) In the case of a Intel Pentium R II processor I get 0.825 years b) Genuineltel X86 Family 6 Model 8 I get 1.542 years c) Intel Pentium R 4 CPU 2.8 GHZ I get 6 years This one is roughly 8 years old. Load 100% d) Intel Quad Core i5 M460 I get 3.9 years. Load 27% Does this mean that we have reached the top of CPU performance ? Ofcourse I can rewrite my program in a different language. Maybe than my program runs faster but that does not solve the issue. I did not test a Dual Core, may be those are faster. Of my Pentium R 4 CPU there apparently exists a 3.3 GHZ version. Is that the solution? Any suggestion what to do ?
 > Use a top end graphics card and something like CUDA by nVidia. That will give you up to a 100x increase in computing power to around 1TFLOPS

That is the same suggestion as my CPU vendor told me. But this solution requires reprogramming and that is not what I want. I also do not want to reprogram in C++

 > http://en.wikipedia.org/wiki/CUDA -- Dirk [[Mod. note -- Sequential (single-thread) CPU speed has indeed roughly plateaued since 2005 or so, at roughly 3 GHz and 4 instructions-per-cycle out-of-order. More recent progress has been

I did not know this. I was truelly amased by the results of my tests. You buy something expensive and almost for 60% you get the best results.

 > * bigger and bigger caches [transparent to the programmer] * some small increases in memory bandwidth [transparent to the progrrammer] * lots of parallelism [NOT transparent to the programmer] Parallelism today comes in many flavors [almost all of which must be explicitly managed by the programmer]: * lots of CPU chips are "multicore" and/or "multithreaded" * lots of computer systems incorporate multiple CPUs [this includes the graphics-card processors mentioned in this posting] *If* your application is such that it can be (re)programmed to use many individual processors working in parallel, then parallelism can be very useful.
I agree This is for example true for a game like chess. SETI falls in this category.

 > Alas, small-N N-body simulations of the type discussed by the original poster are notoriously hard to parallelize. :(
That is correct. But there is an inpact for all simulations of allmost physical systems where dependency is an issue.

 > I'd also like to point out the existence of the newsgroup comp.arch (unmoderated), devoted to discussions of computer architecture. -- jt]]

Nicolaas Vroom

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### 6 Are we reaching the maximum of CPU performance ?

Van: Nicolaas Vroom
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: maandag 8 november 2010 22:28

"Dirk Bruere at NeoPax" schreef in bericht posting Mesg2
 > On 07/11/2010 17:18, Nicolaas Vroom wrote:posting Mesg1
 >> I could also have raised the following question: Which is currently the best performing CPU ? This question is important for all people who try to simulate physical systems. In my case this is the movement of 7 planets around the Sun using Newton's Law I have tested 4 different types of CPU's. In order to compare I use the same VB program. In order to test performance the program calculates the number of years in 1 minute. a) In the case of a Intel Pentium R II processor I get 0.825 years b) Genuineltel X86 Family 6 Model 8 I get 1.542 years c) Intel Pentium R 4 CPU 2.8 GHZ I get 6 years This one is roughly 8 years old. Load 100% d) Intel Quad Core i5 M460 I get 3.9 years. Load 27% In the last case I can also load the program 4 times. On average I get 2.6 years. Load 100% Does this mean that we have reached the top of CPU performance ? Ofcourse I can rewrite my program in a different language. Maybe than my program runs faster but that does not solve the issue. I did not test a Dual Core, may be those are faster. Of my Pentium R 4 CPU there apparently exists a 3.3 GHZ version. Is that the solution? Any suggestion what to do ?
 > Use a top end graphics card and something like CUDA by nVidia. That will give you up to a 100x increase in computing power to around 1TFLOPS Apart from that, processing power is still increasing by around 2 orders of magnitude per decade. If that's not enough the DARPA exascale computer is due around 2018 (10^18 FLOPS). -- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.blogtalkradio.com/onetribe - Occult Talk Show [[Mod. note -- Sequential (single-thread) CPU speed has indeed roughly plateaued since 2005 or so, at roughly 3 GHz and 4 instructions-per-cycle out-of-order. More recent progress has been * bigger and bigger caches [transparent to the programmer] * some small increases in memory bandwidth [transparent to the progrrammer] * lots of parallelism [NOT transparent to the programmer] Parallelism today comes in many flavors [almost all of which must be explicitly managed by the programmer]: * lots of CPU chips are "multicore" and/or "multithreaded" * lots of computer systems incorporate multiple CPUs [this includes the graphics-card processors mentioned in this posting] *If* your application is such that it can be (re)programmed to use many individual processors working in parallel, then parallelism can be very useful. Alas, small-N N-body simulations of the type discussed by the original poster are notoriously hard to parallelize. :( I'd also like to point out the existence of the newsgroup comp.arch (unmoderated), devoted to discussions of computer architecture. -- jt]]

### 7 Are we reaching the maximum of CPU performance ?

Van: Dirk Bruere at NeoPax
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: maandag 8 november 2010 22:28

 > Isn't the OP comparing CPU's - not algorithms? An inefficient algorithm run on a multitude of CPUs is a fair test of the CPUs is it not?

Not necessarily if the algorithm is playing to a common weakness rather than the increasing strengths of modern CPUs. For example, if the algorithm requires significant HDD access, or overflows the onchip cache, or simply requires more memory than is placed in the motherboard and has to use a pagefile.

-- Dirk

http://www.transcendence.me.uk/ - Transcendence UK http://www.blogtalkradio.com/onetribe - Occult Talk Show

### 8 Are we reaching the maximum of CPU performance ?

Van: Arnold Neumaier
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: maandag 8 november 2010 22:28

Nicolaas Vroom wrote in:posting Mesg1
 > Does this mean that we have reached the top of CPU performance ?

We reached the top of CPU performance/core.

Performance is still increasing but by using slower multiple core architectures and balancing the load. This is the curent trend, and is likely to be so in the future.

 > Ofcourse I can rewrite my program in a different language. Maybe than my program runs faster but that does not solve the issue. I did not test a Dual Core, may be those are faster. Of my Pentium R 4 CPU there apparently exists a 3.3 GHZ version. Is that the solution? Any suggestion what to do ?

You need to use multiple cores. If you are purely sequential code, you are unlucky. Computers will become _slower_ for these.

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### 9 Are we reaching the maximum of CPU performance ?

Van: Nicolaas Vroom
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: dinsdag 9 november 2010 4:05

"Giorgio Pastore" schreef in bericht :posting Mesg3
 > On 11/7/10 6:18 PM, Nicolaas Vroom wrote:posting Mesg1
 >> ... In my case this is the movement of 7 planets around the Sun using Newton's Law ... In order to compare I use the same VB program. ... Any suggestion what to do ?
 > You said nothing about the algorithm you implemented in VB. If you chose the wrong algorithm you may may waist a lot of CPU time. Giorgio

My goal is not to find the cleverst algorithm. My goal is to find the best CPU using the same program. What my tests show is that single cores are the fastest. However there is a small chance that there are dual cores which are faster, but I do not know if that is actual true.

Nicolaas Vroom

 > [[Mod. note -- If your goal is actually to study physics via N-body simulations of this sort, there's a considerable literature on clever numerical methods/codes which are very accurate and efficient. A good starting point to learn more might be http://www.amara.com/papers/nbody.html which has lots of references. It discusses both the small-N and large-N cases (which require vastly different sorts of numerical methods, and have very different accuracy/cost/fidelity tradeoffs). A recent paper of interest (describing a set of simulations of Sun + 8 planets + Pluto + time-averaged Moon + approximate general relativistic effects) is J. Laskar & M. Gastineau "Esistence of collisional trajectories of Mercury, Mars, and Venus with the Earth" Nature volume 459, 11 June 2009, pages 817--819 http://dx.doi.org/10.1038/nature08096 -- jt]]

### 10 Are we reaching the maximum of CPU performance ?

Van: Hans Aberg
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: dinsdag 9 november 2010 4:13

On 2010/11/08 22:28, Arnold Neumaier wrote:posting Mesg8
 > Nicolaas Vroom wrote:posting Mesg1
 >> Does this mean that we have reached the top of CPU performance ?
 > We reached the top of CPU performance/core. Performance is still increasing but by using slower multiple core architectures and balancing the load. This is the curent trend, and is likely to be so in the future.

There is no technological limitation going into higher frequencies, but energy consumption is higher than linear. So using parallelism at lower frequencies requires less energy, and is easier to cool.

[[Mod. note -- Actually there are very difficult technological obstacles to increasing CPU clock rates. Historically, surmouting these obstacles has required lots of very clever electrical engineering and applied physics (and huge amounts of money).

The result of this effort is that historically each successive generation of semiconductor-fabrication process has been very roughly ~1/3 faster than the previous generation (i.e., all other things being equal, each successive generation allows roughly a 50% increase in clock frequency), and uses roughly 1/2 to 2/3 the power at a given clock frequency. Alas, power generally increases at least quadratically with clock frequency. -- jt]]

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### 11 Are we reaching the maximum of CPU performance ?

Van: Juan R. González-Álvarez
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: woensdag 10 november 2010 5:02

 > On 2010/11/08 22:28, Arnold Neumaier wrote:posting Mesg8
 >> Nicolaas Vroom wrote::posting Mesg1
 >>> Does this mean that we have reached the top of CPU performance ?
 >> We reached the top of CPU performance/core. Performance is still increasing but by using slower multiple core architectures and balancing the load. This is the curent trend, and is likely to be so in the future.
 > There is no technological limitation going into higher frequencies, but energy consumption is higher than linear. So using parallelism at lower frequencies requires less energy, and is easier to cool.

Currently there is stronger technological limitations (reflected in the current frequency limits for the CPUs that you can buy). And we are close to the physical limits for the current technology (that is why optical or quantum computers are an active research topic).

You are right that energy consumption is not linear for increasing frecuencies, but neither is for *algorithmic* parallelism. Duplicating the number of cores roughly increase energetic consumption by a factor of 2, but not the algorithmic power. There is many variables to consider here but you would get about a 10-30% gain over a single Intel core.

For obtaining double algorithmic power you would maybe need 8x cores, doing the real power consumption non-linear again. And I doubt that VB software of the original poster can use all the cores in any decent way.

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### 12 Are we reaching the maximum of CPU performance ?

Van: Hans Aberg
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: woensdag 10 november 2010 18:45

On 2010/11/10 05:02, Juan R. González-Álvarez wrote:posting Mesg11
 >>>> Does this mean that we have reached the top of CPU performance ?
 >>> We reached the top of CPU performance/core. Performance is still increasing but by using slower multiple core architectures and balancing the load. This is the curent trend, and is likely to be so in the future.
 >> There is no technological limitation going into higher frequencies, but energy consumption is higher than linear. So using parallelism at lower frequencies requires less energy, and is easier to cool.
 > Currently there is stronger technological limitations (reflected in the current frequency limits for the CPUs that you can buy).

The fastest you can buy is over 5 Ghz, which sits i a mainframe (see WP "Clock rate" article). So if energy consumption and and heat dissipation wasn't a problem, you could have it in your laptop.

 > And we are close to the physical limits for the current technology (that is why optical or quantum computers are an active research topic).

Don't hold your breath for the latter.

 > You are right that energy consumption is not linear for increasing frecuencies, but neither is for *algorithmic* parallelism. Duplicating the number of cores roughly increase energetic consumption by a factor of 2, but not the algorithmic power. There is many variables to consider here but you would get about a 10-30% gain over a single Intel core.

That's why much parallel capacity currently moves into the GPU, where it is needed and is fairly easy to parallelize algorithms.

 > For obtaining double algorithmic power you would maybe need 8x cores, doing the real power consumption non-linear again. And I doubt that VB software of the original poster can use all the cores in any decent way.

Classical computer languages are made for single threading, so making full parallelization isn't easy.

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### 13 Are we reaching the maximum of CPU performance ?

Van: Hans Aberg
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: donderdag 11 november 2010 9:11

 >> Use a top end graphics card and something like CUDA by nVidia. That will give you up to a 100x increase in computing power to around 1TFLOPS
 > That is the same suggestion as my CPU vendor told me. But this solution requires reprogramming and that is not what I want. I also do not want to reprogram in C++

I pointed out OpenCL in post that has not yet appeared. See WP article, which has an example.

### 14 Are we reaching the maximum of CPU performance ?

Van: Hans Aberg
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: donderdag 11 november 2010 9:11

On 2010/11/07 18:18, Nicolaas Vroom wrote:posting Mesg1
 > d) Intel Quad Core i5 M460 I get 3.9 years. Load 27% In the last case I can also load the program 4 times. On average I get 2.6 years. Load 100%

If you only get about a quarter of full load on a quad core, perhaps you haven't threaded it. Here is an OpenCL example implementing a FFT, which using a rather old GPU gets 144 Gflops (see reference 27): http://en.wikipedia.org/wiki/OpenCL

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### 15 Are we reaching the maximum of CPU performance ?

Van: Arnold Neumaier
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: donderdag 11 november 2010 17:13

Juan R. González-Álvarez wrote::posting Mesg11
 > Hans Aberg wrote on Mon, 08 Nov 2010 22:13:14 -0500:posting Mesg10
 >> On 2010/11/08 22:28, Arnold Neumaier wrote:posting Mesg8
 >>> Nicolaas Vroom wrote:posting Mesg1
 >>>> Does this mean that we have reached the top of CPU performance ?
 >>> We reached the top of CPU performance/core. Performance is still increasing but by using slower multiple core architectures and balancing the load. This is the curent trend, and is likely to be so in the future.
 >> There is no technological limitation going into higher frequencies, but energy consumption is higher than linear. So using parallelism at lower frequencies requires less energy, and is easier to cool.
 > Currently there is stronger technological limitations (reflected in the current frequency limits for the CPUs that you can buy). And we are close to the physical limits for the current technology (that is why optical or quantum computers are an active research topic). You are right that energy consumption is not linear for increasing frecuencies, but neither is for *algorithmic* parallelism. Duplicating the number of cores roughly increase energetic consumption by a factor of 2, but not the algorithmic power. There is many variables to consider here but you would get about a 10-30% gain over a single Intel core. For obtaining double algorithmic power you would maybe need 8x cores,

This depends very much on the algorithm.

Some algorithms (e.g., Monte Carlo simulation) can be trivially parallelized, so the factor is only 2x. For many othe cases, n times the alg. speed needs a number of cores that grows slowly with n. And there are algorithms that one can hardly spped up no matter how many cores one uses.

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### 16 Are we reaching the maximum of CPU performance ?

Van: Juan R. González-Álvarez
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: vrijdag 12 november 2010 10:14

Hans Aberg wrote on Wed, 10 Nov 2010 18:45:50 +0100:posting Mesg12
 > On 2010/11/10 05:02, Juan R. González-Álvarez wrote:posting Mesg11
 >>>>> Does this mean that we have reached the top of CPU performance ?
 >>>> We reached the top of CPU performance/core. Performance is still increasing but by using slower multiple core architectures and balancing the load. This is the curent trend, and is likely to be so in the future.
 >>> There is no technological limitation going into higher frequencies, but energy consumption is higher than linear. So using parallelism at lower frequencies requires less energy, and is easier to cool.
 >> Currently there is stronger technological limitations (reflected in the current frequency limits for the CPUs that you can buy).
 > The fastest you can buy is over 5 Ghz, which sits i a mainframe (see WP "Clock rate" article). So if energy consumption and and heat dissipation wasn't a problem, you could have it in your laptop.

The last worldwide record that I know was 8.20 Ghz overclocked.

 >> And we are close to the physical limits for the current technology (that is why optical or quantum computers are an active research topic).
 > Don't hold your breath for the latter.

Why?

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### 17 Are we reaching the maximum of CPU performance ?

Van: JohnF
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: vrijdag 12 november 2010 10:14

Arnold Neumaier wrote:posting Mesg15
 > Juan R. González-Álvarez wrote:posting Mesg11
 >>>
 >> For obtaining double algorithmic power you would maybe need 8x cores,
 > This depends very much on the algorithm. Some algorithms (e.g., Monte Carlo simulation) can be trivially parallelized, so the factor is only 2x. For many othe cases, n times the alg. speed needs a number of cores that grows slowly with n. And there are algorithms that one can hardly spped up no matter how many cores one uses.

That's typically true, but just for completeness, you can google "super-linear speedup" for examples of parallelized calculations that speed up faster than linearly with the number of cores. There are several short instructional examples that make it intuitively clear why this should be possible, but, sorry, I can't find links offhand.
--
John Forkosh ( mailto: j@f.com where j=john and f=forkosh )

### 18 Are we reaching the maximum of CPU performance ?

Van: Arnold Neumaier
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: vrijdag 12 november 2010 16:50

JohnF wrote:
 > Arnold Neumaier wrote:posting Mesg15
 >> Juan R. González-Álvarez wrote:posting Mesg11
 >>>>
 >>> For obtaining double algorithmic power you would maybe need 8x cores,
 >> This depends very much on the algorithm. Some algorithms (e.g., Monte Carlo simulation) can be trivially parallelized, so the factor is only 2x. For many othe cases, n times the alg. speed needs a number of cores that grows slowly with n. And there are algorithms that one can hardly spped up no matter how many cores one uses.
 > That's typically true, but just for completeness, you can google "super-linear speedup" for examples of parallelized calculations that speed up faster than linearly with the number of cores. There are several short instructional examples that make it intuitively clear why this should be possible, but, sorry, I can't find links offhand.

Yes, it means that one has an inefficient serial algorithm.

Any serial algorithm with superlinear speedup can be rewritten into a faster serial algorithm where the speedup is only linear.

### 19 Are we reaching the maximum of CPU performance ?

Van: Surfer
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: vrijdag 12 november 2010 22:32

 > The fastest you can buy is over 5 Ghz, which sits i a mainframe (see WP "Clock rate" article). So if energy consumption and and heat dissipation wasn't a problem, you could have it in your laptop.

By coincidence, I just saw a TV program about uses of diamond, including for semi-conductors. That prompted me to search for articles. I found the following.

This paper dated June 2010 (in Japanese) discusses diamond field effect transistors http://www.ntt.co.jp/journal/1006/files/jn201006014.pdf

Fig 1 suggests that gallium arsenide and diamond FETs could be made to operate up to 100s of GHz.

The above and the high thermal conductivity of diamond implies that it could be used to build much faster CPUs.

next posting Mesg20

### 20 Are we reaching the maximum of CPU performance ?

Van: Dirk Bruere at NeoPax
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: zaterdag 13 november 2010 9:04

On 12/11/2010 21:32, Surfer wrote in: posting Mesg19
 > On Wed, 10 Nov 2010 18:45:50 +0100 (CET), Hans Aberg wrote in:posting Mesg12
 >> The fastest you can buy is over 5 Ghz, which sits i a mainframe (see WP "Clock rate" article). So if energy consumption and and heat dissipation wasn't a problem, you could have it in your laptop.
 > By coincidence, I just saw a TV program about uses of diamond, including for semi-conductors. That prompted me to search for articles. I found the following. This paper dated June 2010 (in Japanese) discusses diamond field effect transistors http://www.ntt.co.jp/journal/1006/files/jn201006014.pdf Fig 1 suggests that gallium arsenide and diamond FETs could be made to operate up to 100s of GHz. This article describes successful manufacture of inch size diamond wafers http://www.nanowerk.com/news/newsid=15514.php The above and the high thermal conductivity of diamond implies that it could be used to build much faster CPUs.

I think almost all of the progress over the next 10 years is going to be Systems on Chip, multiple cores, power efficiency and parallel programming (esp at the OS level). After that fairly radical new tech will start to appear (memristors, graphene etc) and the clock rates will climb again.

One interesting question is how much of a need is there for high clock speed serial processing? Most realworld apps can benefit from the parallel approach and do not really need a serial speedup, except to make the programming easier.

Can anyone name any major serial-only applications?

-- Dirk

http://www.transcendence.me.uk/ - Transcendence UK

next posting Mesg23

### 21 Are we reaching the maximum of CPU performance ?

Van: Juan R. González-Álvarez
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: maandag 15 november 2010 18:39

 > Juan R. González-Álvarez wrote in:posting Mesg11
 >> Hans Aberg wrote on Mon, 08 Nov 2010 22:13:14 -0500 in:posting Mesg10
 >>> On 2010/11/08 22:28, Arnold Neumaier wrote in:posting Mesg8
 >>>> Nicolaas Vroom wrote in:posting Mesg1

(...)

 >> You are right that energy consumption is not linear for increasing frecuencies, but neither is for *algorithmic* parallelism. Duplicating the number of cores roughly increase energetic consumption by a factor of 2, but not the algorithmic power. There is many variables to consider here but you would get about a 10-30% gain over a single Intel core. For obtaining double algorithmic power you would maybe need 8x cores,
 > This depends very much on the algorithm. Some algorithms (e.g., Monte Carlo simulation) can be trivially parallelized, so the factor is only 2x. For many othe cases, n times the alg. speed needs a number of cores that grows slowly with n. And there are algorithms that one can hardly spped up no matter how many cores one uses.

As said "There is many variables to consider": algorithms, Operative System, CPU design (including node topology, size and speed of caches), motherboard...

Correct me if wrong but the OP is not looking for a Monte Carlo in C++ of Fortran but for celestial dynamics using VB. I maintain my estimation that he would need many cores to get a 2x speed.

### 22 Are we reaching the maximum of CPU performance ?

Van: Hans Aberg
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: maandag 15 november 2010 18:44

On 2010/11/12 10:14, Juan R. González-Álvarez wrote in:posting Mesg16
 >>>> There is no technological limitation going into higher frequencies, but energy consumption is higher than linear. So using parallelism at lower frequencies requires less energy, and is easier to cool.
 >>> Currently there is stronger technological limitations (reflected in the current frequency limits for the CPUs that you can buy).
 >> The fastest you can buy is over 5 Ghz, which sits i a mainframe (see WP "Clock rate" article). So if energy consumption and and heat dissipation wasn't a problem, you could have it in your laptop.
 > The last worldwide record that I know was 8.20 Ghz overclocked.

At the end of of the manufacturing process, one puts the CPU through tests, and it gets marked at a frequency passing those. When overclocking, one expects certain misses, which may not be reliable.

[[Mod. note -- Testing often covers a 2-D matrix of frequency and power supply voltage. A plot of test results (often color-coded for ok/bad) against these variables is often called a "Shmoo plot". See http://www.computer.org/portal/web/csdl/doi/10.1109/TEST.1996.557162 for a nice discussion. -- jt]]

I computed Moore's law for frequency data from a personal computer manufacture (Apple), and it was a doubling every three years since the first Mac, whereas for RAM it is every second year (for hard disks every year).

So if one can combine those, it gives five doublings every 6 years in overall capacity, or nearly one every year.

But anyway, there was a Apple Developer video a few years ago describing the energy gains when clocking down and adding cores, important in these consumer devices.

 >>> And we are close to the physical limits for the current technology (that is why optical or quantum computers are an active research topic).
 >> Don't hold your breath for the latter.
 > Why?

Because they haven't been made yet, except possibly in rudimentary form. Here is a video: http://vimeo.com/14711919

### 23 Are we reaching the maximum of CPU performance ?

Van: Arnold Neumaier
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: maandag 15 november 2010 18:46

 > One interesting question is how much of a need is there for high clock speed serial processing? Most realworld apps can benefit from the parallel approach and do not really need a serial speedup, except to make the programming easier. Can anyone name any major serial-only applications?

Large-scale eigenvalue computations for multiparticle Hamiltonians are difficult to parallelize.

next posting Mesg25

### 24 Are we reaching the maximum of CPU performance ?

Van: Nicolaas Vroom
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: maandag 15 november 2010 18:46

"Hans Aberg" schreef in bericht posting Mesg14
 > On 2010/11/07 18:18, Nicolaas Vroom wrote:posting Mesg1
 >> d) Intel Quad Core i5 M460 I get 3.9 years. Load 27% In the last case I can also load the program 4 times. On average I get 2.6 years. Load 100%

That is correct. What I need are threads which run in different processors. The question is is all the work (assuming the program runs correct) worthwhile the effort i.e. will the final program run faster The biggest problem is the communication between the treads. This should be some common type of memory, which all the processors should be able to address. I do not know if that is possible using Visual Basic.

 > Here is an OpenCL example implementing a FFT, which using a rather old GPU gets 144 Gflops (see reference 27): http://en.wikipedia.org/wiki/OpenCL

When you look to that example it is terrible complex.

You also get the message if you study this: http://www.openmp.org/presentations/miguel/F95_OpenMPv1_v2.pdf

In my case the program looks like:

Do
Synchronise 0                  ' Communication
For i = 1 to 5                  ' Activate task 1
*     a = 0
*     For j = 1 to 5
*        d = x(i) - x(j)             ' Calculate distance
*        a = a + 1/(d*d)          ' Calculate acceleration
*    Next j
*    v(i) = a  * dt                   ' Calculate speed
next  i
Synchronise  1                  ' Wait all threads finished
For i = 1 to 5                    ' Activate task 2
$x(i) = x(i) + v(i) * dt ' Calculate positions Next i Synchronise 2 ' Wait all threads finished Loop  There are two parts you can do in parallel i.e. in threads. This is the starting with * and with$.
Each thread requires three parameters: i, task number(1 or 2) and a communication parameter (start active finished)
To make communication easier you should dedicate each thread to to specific i values. Thread 1 to i = 1 and 5 etc. Again the biggest problem are the data base variables x, v and dt

Nicolaas Vroom

[[Mod. note -- The newsgroup comp.parallel might also be of interest here. -- jt]]

next posting Mesg26
next posting Mesg27
next posting Mesg28

### 25 Are we reaching the maximum of CPU performance ?

Van: Dirk Bruere at NeoPax
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: dinsdag 16 november 2010 22:15

On 15/11/2010 17:46, Arnold Neumaier wrote in: posting Mesg23
 > Dirk Bruere at NeoPax wrote in: posting Mesg20
 >> One interesting question is how much of a need is there for high clock speed serial processing? Most realworld apps can benefit from the parallel approach and do not really need a serial speedup, except to make the programming easier. Can anyone name any major serial-only applications?
 > Large-scale eigenvalue computations for multiparticle Hamiltonians are difficult to parallelize.

Well, I don't think Wintel is going to lose much sleep over not being able to grab that market niche :-)

I was thinking more about possible mass market (future?) apps that could force up clock speeds again. Graphics and gaming physics engines are clearly *very* capable of being parallelized.

[Moderator's note: Note that some high-performance scientific computing is done with graphics cards, since that is where the most number-crunching ability is these days. Further posts should make sure there is enough physics content as this thread is rapidly becoming off- topic for the group. -P.H.]

-- Dirk

http://www.transcendence.me.uk/ - Transcendence UK

next posting Mesg29
next posting Mesg32

### 26 Are we reaching the maximum of CPU performance ?

Van: BW
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: donderdag 18 november 2010 7:55

On Nov 16, 10:15 pm, Dirk Bruere at NeoPax wrote in: posting Mesg25
 > I was thinking more about possible mass market (future?) apps that could force up clock speeds again. Graphics and gaming physics engines are clearly *very* capable of being parallelized. [Moderator's note: Note that some high-performance scientific computing is done with graphics cards, since that is where the most number-crunching ability is these days. Further posts should make sure there is enough physics content as this thread is rapidly becoming off- topic for the group. -P.H.]

Actually, there is a very interesting parallel (haha..) between the ability to parallelize physics simulation code and the locality of real-world physics.

Parallelizing computer algorithms, either on GPUs or especially when using supercomputer clusters, *very heavily* relies on either very fast inter-core communications or algorithms where the individual threads don't have to communicate very much. Making chips and boards that compute in teraflops is no problem - communicating the data is.

This more or less implies that the underlying data which a simulation algorithm trying to simulate the real world has to use, should be as local as possible to the interactions or transactions which the algorithm encodes at the lowest levels, to run quickly.

The fun thing is, this is what the last 100 years of physics exploration seem to have discovered too - that when interactions are executed they depend only on the absolute nearest region (in a pure QFT without external classic fields contaminating it).

You can speculate if nature did this to simplify simulation of itself, but it sure is a nice fact because you can perfectly well conceive of any number of working realities where interactions are not local - or in computer code, where calculations would require direct inputs from any number of non-neighboring compute nodes.

Note that I'm not talking about solving differential equations or finding eigenvalues in huge matrices here, but of how the world computes at the most basic level. I do understand that in practice this is not how you usually simulate physical systems. Also there is the little complication of the multiple-paths or worlds... but other than that, local interactions should be good in the long run for computational physics :)

Best regards, /Bjorn

next posting Mesg30

### 27 Are we reaching the maximum of CPU performance ?

Van: Dirk Bruere at NeoPax
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: donderdag 18 november 2010 9:47

On 16/11/2010 21:15, Dirk Bruere at NeoPax wrote in: posting Mesg25
 > On 15/11/2010 17:46, Arnold Neumaier wrote in: posting Mesg23
 >> Dirk Bruere at NeoPax wrote in: posting Mesg20
 >>> One interesting question is how much of a need is there for high clock speed serial processing? Most realworld apps can benefit from the parallel approach and do not really need a serial speedup, except to make the programming easier. Can anyone name any major serial-only applications?
 >> Large-scale eigenvalue computations for multiparticle Hamiltonians are difficult to parallelize.
 > Well, I don't think Wintel is going to lose much sleep over not being able to grab that market niche :-) I was thinking more about possible mass market (future?) apps that could force up clock speeds again. Graphics and gaming physics engines are clearly *very* capable of being parallelized. [Moderator's note: Note that some high-performance scientific computing is done with graphics cards, since that is where the most number-crunching ability is these days. Further posts should make sure there is enough physics content as this thread is rapidly becoming off- topic for the group. -P.H.]

To return it to being on-topic...
If physics is regarded as a computation, how is the parallelism synchronized?

-- Dirk

http://www.transcendence.me.uk/ - Transcendence UK

### 28 Are we reaching the maximum of CPU performance ?

Van: Nicolaas Vroom
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: donderdag 18 november 2010 9:47

"Arnold Neumaier" schreef in: posting Mesg23
 > Dirk Bruere at NeoPax wrote in: posting Mesg20
 >> One interesting question is how much of a need is there for high clock speed serial processing? Most realworld apps can benefit from the parallel approach and do not really need a serial speedup, except to make the programming easier. Can anyone name any major serial-only applications?
 > Large-scale eigenvalue computations for multiparticle Hamiltonians are difficult to parallelize.

The whole issue if systems can be simulated by a parallel approach depents if they can de divided in subsystems which are independent. Independent subsystems can de simulated (calculated) in parallel. The second parameter is time.

The impossible to parallize systems to parallelize are systems were quantum mechanism is involved i.e. superpositions and entanglement, because (i hope I describe this correct) the whole system is all its states (depending about the number of Qbits involved) at once.

The second most difficult system are analog computers depending about the time involved. The simplest is an oscillator (wave) which requires two integrators. The problem is the two are connected in a loop: the output of the first is input two the second and visa versa.
You can implement (simulate) each integrator in a separate processor but the communication between the two is such that such a solution using only one processor is much better. Better in the sense of the calculation time to find the solution of a certain system time.

This stil leaves me which the question: Are there dual processors in the market which outperform single processor systems, assuming that in the dual proccessor system my simulation solely runs in one processor and all the rest in the other one ? (outperform in the sense of # of revolutions per minute calulation time)

Nicolaas Vroom

### 29 Are we reaching the maximum of CPU performance ?

Van: Joseph Warner
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: donderdag 18 november 2010 9:48

"Dirk Bruere at NeoPax" wrote in message in: posting Mesg25
 > On 15/11/2010 17:46, Arnold Neumaier wrote in: posting Mesg23
 >> Dirk Bruere at NeoPax wrote in: posting Mesg20
 >>> One interesting question is how much of a need is there for high clock speed serial processing? Most realworld apps can benefit from the parallel approach and do not really need a serial speedup, except to make the programming easier.

To get on to the topic again.

Is there prospect of increasing the maximum of CPU performance. Yes there is. Intel had processes that had speeds above 4 GHz before they moved to the current circuit architecture and this using silicon. The line-width of the day was not small enough to advantage of ballistic electrons across the gate. Small line widths should be able to do that. One limiting factor in the processing speed is the speed of the electrons going through the gate. In standard terms the higher the mobility of the electron the faster the transistor can respond for a give gate length.

One way to increase the mobility of the electron or lower the transit time an electron spends in the gate area is to change material. That is easy said than done but if GaAs crystals had the same density of imperfections as Si then faster chips can be made. The mobility in GaAs is ~ 3 to 4 times that of Si. Even better yet is to use material structures such as GaAs/AlGaAs to form quantum wells where the electrons do not appreciable scatter when in the well for the material underneath the gate. Then mobility between 10,000 to 100,000 are achievable. For the material with the upper mobility though the current density is low and the mobility falls of rapidly with temperature; therefore keeping the transistors cooled through after cooling will help. But alas, this materials defect density doesn't allow one to have the scale of integration that Si presently has.

Other material systems that may be more practical is Si/SiGe. It can form shallow quantum wells but can increase the mobility of the electrons. In addition, devices made from them are more radiation hard than just pure Si. Presently, I think Intel and AMD do use Si/SiGe in there present day chips. To take better advantages of this material one needs to change the transistor from a FET transistor to a Bi-polar hetrojunction transistor.

On the horizon there is the graphene processor. People are still looking into computers using Josephson devices. In these it may be able to get speed approaching 100 GHz but the complexity of the system is large and the density of the junctions are still small.

next posting Mesg31

### 30 Are we reaching the maximum of CPU performance ?

Van: JohnF
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: vrijdag 19 november 2010 10:36

BW wrote in:posting Mesg26
 > You can speculate if nature did this to simplify simulation of itself, [...] Note that I'm not talking about solving differential equations, but of how the world computes at the most basic level. /Bjorn

The idea that "the world computes" (at any level) seems widespread and wrong to me. Math is just our way of organizing and describing observable behavior (which we call physics). But the world knows nothing of math, or of our organization of its behavior.

For the simplest example, suppose you have a compass and straight edge. And suppose you draw a circle of radius R with the compass, using a pencil that draws lines of width w and thickness t. Does the world "compute" the volume of graphite laid down as 2piRwt? No. In the world, that's just what "happens". We're the only ones doing any computing here.

Next consider, say, a vibrating string. Does the world "compute" solutions to the one-dimensional wave equation, or even instantaneous forces and motions? Or does it just "happen" in a more complicated but analogous way to the drawn circle?

Likewise with, say, similarly simple and easily derived differential equations for radiative transfer, hydrostatic equilibrium, etc, etc. The world doesn't need to compute anything to produce these behaviors. It's we who need to compute, just to answer our own questions about why we see the world behave the way it does.

Is there some level below which the world's behavior becomes fundamentally computational (i.e., in other words, does math "exist")? As above, I'd guess not, and that math is just our way of grouping together ("organizing and describing" in the above words) phenomena that happen to have common explanatory models.

That is, the world produces a menagerie of behaviors, and then, from among them all, we pick and choose and group together those describable by one mathematical model. Then we group together others describable by some other model, etc. But that "partition of phenomena" is just our construction, built by mathematical methods that happen to make sense to us. The world knows nothing of it.

The one loophole seems to me to be reproducibility. Beyond just a "menagerie of behaviors", we can experimentally instigate, at will, behaviors describable by any of our mathematical models we like. So that must mean something. But jumping to the conclusion that it means "the world computes" (or that "math exists") seems way too broad a jump to me. -- John Forkosh ( mailto: j@f.com where j=john and f=forkosh )

### 31 Are we reaching the maximum of CPU performance ?

Van: Dirk Bruere at NeoPax
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: zaterdag 20 november 2010 4:10

On 19/11/2010 09:36, JohnF wrote in:posting Mesg30
 > BW wrote in:posting Mesg26
 >> You can speculate if nature did this to simplify simulation of itself, [...] Note that I'm not talking about solving differential equations, but of how the world computes at the most basic level. /Bjorn
 > The idea that "the world computes" (at any level) seems widespread and wrong to me. Math is just our way of organizing and describing observable behavior (which we call physics). But the world knows nothing of math, or of our organization of its behavior. For the simplest example, suppose you have a compass and straight edge. And suppose you draw a circle of radius R with the compass, using a pencil that draws lines of width w and thickness t. Does the world "compute" the volume of graphite laid down as 2piRwt? No. In the world, that's just what "happens". We're the only ones doing any computing here.

Yet there is a change in information as the circle is drawn. One can quite easily, and with good reason, claim that anything that changes information content is a computation.

-- Dirk

http://www.transcendence.me.uk/ - Transcendence UK

### 32 Are we reaching the maximum of CPU performance ?

Van: Juan R. Gonzàlez-Àlvarez
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: zaterdag 20 november 2010 19:56

(...)

 > The fun thing is, this is what the last 100 years of physics exploration seem to have discovered too - that when interactions are executed they depend only on the absolute nearest region (in a pure QFT without external classic fields contaminating it). You can speculate if nature did this to simplify simulation of itself, but it sure is a nice fact because you can perfectly well conceive of any number of working realities where interactions are not local - or in computer code, where calculations would require direct inputs from any number of non-neighboring compute nodes. Note that I'm not talking about solving differential equations or finding eigenvalues in huge matrices here, but of how the world computes at the most basic level. I do understand that in practice this is not how you usually simulate physical systems. Also there is the little complication of the multiple-paths or worlds... but other than that, local interactions should be good in the long run for computational physics :)

i)
Precisely, what science has showed in last 50 years or so, is that locality is only an approximation to how nature works. For instance, in the derivation of hidrodynamic equations authors invoke the so-called "local approximation". In very far from equilibrium regimes this approximation is very bad and, as a consequence, the hydrodynamic equations do not describe what one observes in the lab (more general nonlocal equations are then used).

ii)
Even if you consider only local potentials and near equilbrium regimes, this does not mean the no existence of nonlocal interactions. Nonlocal interactions can still appear due to a "curtain effect" [1,2].

iii)
It is ironic that you appeal to QFT to discuss locality of interactions, when precisely this theory is known for its defects in this topic. For instance, the five authors of [2] write:

"This demonstrates that localization in relativistic quantum field theory cannot be complete."

H. Bacry stated in a more sound form:

"Every physicist would easily convince himself that all quantum calculations are made in the energy-momentum space and that the Minkowski x^\mu are just dummy variables without physical meaning (although almost all textbooks insist on the fact that these variables are not related with position, they use them to express locality of interactions!)"

Yes indeed!

A more general and rigorous study of localization in both QFT and relativistic quantum mechanics and an elegant solution is given in the section "10 Solving the problems of relativistic localization" of [3].

References

### 33 Are we reaching the maximum of CPU performance ?

Van: Nicolaas Vroom
Onderwerp: Re: Are we reaching the maximum of CPU performance ?
Datum: Donderdag 2 december 2010 22.49

"Nicolaas Vroom" schreef in bericht posting Mesg1 .
 > I could also have raised the following question: Which is currently the best performing CPU ? This question is important for all people who try to simulate physical systems. Any suggestion what to do ? Nicolaas Vroom http://users.telenet.be/nicvroom/galaxy-mercury.htm

In order to answer this questioned I have installed Visual Studio 2010 which supports Visual Basic on my CPU. Visual Studio supports parallel programming and threading. In VB 2010 language each of those threads is called a backgroundworker. In the case of 4 processors you need 4 of those background workers to reach 100% load.
Using that concept and in order to test I have written 2 programs called: VStest1 and VStest2.
VStest1 creates 4 identical calculation loops in each Backgroundworker. Those loops or programs are idependant from each other. The performance factor of that program using only one processor is 97.
Next I loaded that program in my old pentium using the same parameters and the performance factor is 174
VStest2 uses the concept of parallel processing. The number of loops in one cycle is 10.
In VStest2 if you use one processor than all the 10 loops are executed in that one processor. If you use 2 processors than each performs 5 loops. (50 %) The performance factors are resp 75 and 110 with 1 and 2 processors. That means not better than my old pentium. When you use my old pentium than the performance factor is 135.
If you want all the details and a listing (+ .EXE) goto: http://users.telenet.be/nicvroom/performance.htm

In general what those numbers mean is that it does not make sense to rewrite a program and to use parallel programming. It only makes sense in a Quad core to load different programs in each core in order to reach 100% load, however the more programs you load the performance of the others already loaded will go down and the final performance of each one will be roughly 30% of my old pentium.

Nicolaas Vroom.

Created: 7 March 2011