greater than 100% scaling? really?

[BFG10K]

If I understand you correctly, you said although the actual time required to render a frame does not decrease regardless of the number of cards present, but with N cards, it is possible, and practical under some specific scenarios where it is possible to render frames in the future. Assume that it takes X ms to generate a frame, ideally, N cards can generate N frames in X ms.

Yes, AFR is like CPU pipelining. It still takes the same amount of time to render a single frame, but the throughput is increased because you get more frames coming out in a given time due to parallelism.

Also, since there are more than one card, it is possible for the CPU to prepare a new frame even though one card is busy due to the fact that there may be another card that is actually ready.

Actually, the ideal scenario for performance is the CPU preparing multiple frames in advance when all of the GPUs in the system are busy. If you’re only doing this when one card is busy then you won’t get optimal scaling. Of course the more you do this, the more input latency you get.

However, pre-render is not exclusive to SLI/CF, and has a default value of 3.

“Pre-render” is a generic term given to what is happening here. You can bet both ATi and nVidia have internal values only accessible to the driver, and they probably dynamically adjust the value as needed, maybe even on a per-game basis. They probably also adjust it based on the number of GPUs in the system.

Now, suppose there are 2 cards, and delay between alternate frame is 0, then 2 card can generate 2x the number of frames a single card can produce. But if that is the case, video card itself is the bottleneck at CPU must wait. The wait is, at best, halfed, therefore able to generate 2x frames for video cards to render. That means, at the end, it is at best 2x performance(FPS count).

I don’t think you understand what is happening, so here’s a simple example.

Let’s say it takes 10 ms for the CPU to render its part a frame, and 20 ms for the GPU to render its part of a frame.

• With one GPU and pre-render=0, every frame will take 10ms + 20ms = 30 ms to render, because the CPU must always wait for the graphics card to finish. This is serial execution.

• With one GPU and pre-render=1, all frames after the first one will take 20 ms to render. This is because the CPU’s 10 ms time for every current frame is run in parallel to the GPU’s 20 ms time for the previous frame.

• Now assuming perfect scaling and pre-render=2, two GPUs will give you two frames in 20 ms (after the first two frames) since the CPU generates two new frames while the cards render the previous two frames.

Two frames in 20 ms is more than twice as fast as one frame in 30 ms. Of course it’s a lot more complicated than that due to other timing issues and overheads, so you might only end up with two frames in 29.9 ms, for example; but that’s still better than 100% scaling.

Well, that is cheating. If user don't go into the driver and change settings, the pre-render of pre-render value reminds the same.

The purpose of SLI/CF is to provide the highest possible performance benefit over a single card without degrading IQ. It’s rather naïve to not expect both nVidia and AMD to go all-out in an attempt to do this. If that’s “cheating” to you then AFR clearly isn’t technology for you.

Unless new bottleneck arises with the introduction of SLI/CF, the number of actual pre-rendered frame should be smaller than, or equal to a single card.

Uh, no. Like I said, if you pre-render like you do on a single card you’ll get sub-optimal scaling. An AFR system has to render enough frames ahead to saturate all of the GPUs in the system.

Of all reasoning, I must admit that this is the most sounding reason, but I highly doubted this.

You doubt what, exactly? Driver bugs or benchmarking noise? Both can be objectively proven to exist, so what you doubt isn’t really relevant here.

 

[Larries]

Ok, so basically you are trying to fix the number to keep everything under 2*performance. Which is what most of the posters are trying to say.

Now it is hard to find a cf/sli vs single time vs performance chart out there, you just need to find it. I found one where there is 5770 vs 5770CF from
Hardocp.

There are several pages of data. This page is particularly interesting as on the second graph at time 166, you see a single 4770 running at 30 FPS where 2x4770 runs at 100FPS. There are many graphs where > 2*performance at some time t occurs. What is your explanation on that?

Clearly, I didn't make those graphs, and I don't think the purpose of those graphs has any relationship of this debate, so it can't be bias. Also note that 4xxx doesn't scale well compare to newer generations. If you can find more graphs like this where it shows time vs performance on sli/cf, please share.

I always wonder how is fps in the charts captured? Does the program count the number of frames generated within the data point (e.g. 10s for each data point), and average out the fps? Or does the program use smaller unit or higher unit of time?

Asking because these graphs show very erratic fps, it can be 100fps in one data point, and then 30fps the next data point.

 

[Ben90]

SSDs on the other hand scales really well, but can it exceed 200% scaling? No, but it is really close to 200%. That means, those little controllers are really good at doing its job, as if it takes no time at all.

No the theoretical scaling of two SSDs in RAID0 is 8x. /sarcasm

The total SSD power does not exceed 2, but the processing time may decrease more than half. The theoretical maximium of 2 SSDs in RAID0 is double I/O * double cache * double processing power = 8 times.

I would call you a complete dumbass because you cannot make a coherent argument, but that would get me an infraction so I won't.


Not clever enough. Personal attacks are not acceptable.

Moderator Idontcare

 

[taltamir]

To me, perfect scaling is a myth.

Did we not just spend about 2 pages arguing over this where you were saying you can get 700% performance increase by adding one more card?

than it is possible to have > 200% performance, while each factor is not where close to perfect scaling. The factors I chose may be wrong, but the existence of those factors and very high. Think about it.

Didn't you just say that was a myth? right there in the quote at the top of my post.

SSDs on the other hand scales really well, but can it exceed 200% scaling? No, but it is really close to 200%. That means, those little controllers are really good at doing its job, as if it takes no time at all.

SSD do not scale well in RAID0, not with only 2 drives. you lose out on trim, which costs performance (not as much as you gain, but enough) and random access doesn't improve, SSDs are very expensive right now and its hard to justify the performance increase of a second one.

Going from 1HDD to 1SSD about doubles sequential performance and increases random performance ~100x (this is what all the fuss is about). Going from 1SSD to 2SSD in raid0 increases sequential performance by about 50% while having no effect on random performance.

And because regular HDD ~50$ and SSD about 200$ each, you are looking at 150$ for first upgrade and 200$ for second... so you pay more, you pay another 200$, and you barely get anything back out of it.

 

[Seero]

I don’t think you understand what is happening, so here’s a simple example.

...
[/LIST]Two frames in 20 ms is more than twice as fast as one frame in 30 ms. Of course it’s a lot more complicated than that due to other timing issues and overheads, so you might only end up with two frames in 29.9 ms, for example; but that’s still better than 100% scaling.

First, pre-render is actually very simple in theory. It is a FIFO stack for data to GPU, to minimize delays.

Well, you are mixing 2 things together. You are saying that under single card configuration, there is no pre-render, and when there is SLI/CF, there are.

You can make it more complicated than necessary, but if CPU is not a bottleneck on SLI/CF, then it is (shouldn't be) a bottleneck on single. If 2x scaling is the best possible outcome, then this scenario can only be acquire when GPU is indeed the only bottleneck within the system.

The purpose of SLI/CF is to provide the highest possible performance benefit over a single card without degrading IQ. It’s rather naïve to not expect both nVidia and AMD to go all-out in an attempt to do this. If that’s “cheating” to you then AFR clearly isn’t technology for you.

Are you saying all reviewers use a different pre-render value on SLI/CF compare to single card for benchmarking? I will say this action of changing the driver during benchmarking is cheating, especially when the pre-render value hurts performance on a single card but not on SLI/CF.

Again, the default pre-render value is not 0 when there is a single card and has nothing to do with AFR or SFR. pre-render is used to minimize wait. AFR and SFR are implementation of load splitting. One is to generate multiple frames at the same time, the other is have the cards generate portion of the screen. SFR, in theory, is perfect. The implementation is not.

So far, you brought 1 example on how AFR may exceed 2xperformance, but you have given many more examples and explanation of AFR.

Uh, no. Like I said, if you pre-render like you do on a single card you’ll get sub-optimal scaling. An AFR system has to render enough frames ahead to saturate all of the GPUs in the system.

Are you saying that everyone with a single card should set pre-render value to 0 because both Nvidia and AMD made a mistake to have 3 as a default there?

You doubt what, exactly? Driver bugs or benchmarking noise? Both can be objectively proven to exist, so what you doubt isn’t really relevant here.

I am not doubting the exists of noise and bugs, I am doubting that those noise and bugs are the reason to SLI/CF > 2x performance.

Right now, 580 > 570 in benchmarks, is that due to noise and bugs? What is the margin of errors from noise? Or are you saying that benchmarks are inaccurate in general? It isn't like I run a single test and jump up and down about it, but like I said, is a repeated phenomenon but different setup and different people. The noise bug can not be a factor of that magnitude. Bugs can, but you are suggesting a bug that hurts performance on single card but not SLI/CF from 2 different companies.

 

[Seero]

No the theoretical scaling of two SSDs in RAID0 is 8x. /sarcasm

I would call you a complete dumbass because you cannot make a coherent argument, but that would get me an infraction so I won't.

Am I being sensitive, or Ben90 continuously attacking me?

Anyways. Back to your question. You must not have known what is famous about Anandtech. IMO it got famous due to its comments of first generation SSDs where people experience shuttering after installing SSDs while benchmarks indicate that SSD is far faster than HDD. Of course at the time people claim it is a user setup and no indication of a hardware problem until Anandtech came up with the 4k I/O write.

Now before SSD got better, some users realize that by using it on raid0, the problem is not as bad due to the fact that cache is doubled. It is not like shutter reduced to half, but completely gone.

If you don't think the argument holds, then look at this performance graph SSD raid write performance.
Read out loud about the min write speed of a single drive, then read out loud about the min write speed of a 4D@raid0. You can still buy first-generation SSDs and raid0 them yourself and see for yourself.

This is a known problem back then, which is a clear case where people IGNORE statistics and CLAIMS THEY ARE ERRORS!

 

[yottabit]

Umm. I'm just going to take a laid back stance and say that sometimes the sum of the parts is not equal to the whole.

 

[Seero]

Did we not just spend about 2 pages arguing over this where you were saying you can get 700% performance increase by adding one more card?

There is a big different between what we say. Performance can increase > 2, while the processing power can not. Again, if you read the first post clearly, may be you don't need to spend those time.

Didn't you just say that was a myth? right there in the quote at the top of my post.

Scaling can be linear, or exponential in theory. Just because you see something that appears to be scaling linearly doesn't mean it is perfect linear scaling or a linear scaling at all, but rather an exponential scaling that isn't perfect in practice.

SSD do not scale well in RAID0, not with only 2 drives. you lose out on trim, which costs performance (not as much as you gain, but enough) and random access doesn't improve, SSDs are very expensive right now and its hard to justify the performance increase of a second one.

Going from 1HDD to 1SSD about doubles sequential performance and increases random performance ~100x (this is what all the fuss is about). Going from 1SSD to 2SSD in raid0 increases sequential performance by about 50% while having no effect on random performance.

And because regular HDD ~50$ and SSD about 200$ each, you are looking at 150$ for first upgrade and 200$ for second... so you pay more, you pay another 200$, and you barely get anything back out of it.

I won't comment on your understanding on SSD. If you want to debate about this, make another post on another part of the forum.

 

[Seero]

I always wonder how is fps in the charts captured? Does the program count the number of frames generated within the data point (e.g. 10s for each data point), and average out the fps? Or does the program use smaller unit or higher unit of time?

Asking because these graphs show very erratic fps, it can be 100fps in one data point, and then 30fps the next data point.

I don't know for sure how FPS is captured. I believe it is done by taking the average running time of a draw command. So say the running time of a draw command is say 26ms, then the FPS is 1000/26 = 38.46. Due to the complexity of the scene, and bottlenecks left and right, it can fluctuate wildly.

Again, I don't know this for sure, just a guess.

 

[BFG10K]

You are saying that under single card configuration, there is no pre-render, and when there is SLI/CF, there are.

No I’m not. I’m using a simple example to illustrate how a different pre-render value can impact performance over and above the expected impact by adding more GPUs to a system.

I’m also stating that an AFR system will typically render ahead further than a single card system, which means the CPU can keep working in situations where it might’ve stopped on a single GPU system.

I’m also stating this is done at the driver level and extends beyond the simple pre-render value that is available to users.

You can make it more complicated than necessary, but if CPU is not a bottleneck on SLI/CF, then it is (shouldn't be) a bottleneck on single. If 2x scaling is the best possible outcome, then this scenario can only be acquire when GPU is indeed the only bottleneck within the system.

Nobody is saying the CPU is a bottleneck; in fact, pre-render achieves nothing if the CPU is the bottleneck. I’d suggest you re-read my example because I’m not going to repeat it.

Are you saying all reviewers use a different pre-render value on SLI/CF compare to single card for benchmarking?

No. Where did I say that? I said the driver more aggressively renders ahead in an AFR system because ATi & nVidia want to get the best possible scaling.

I will say this action of changing the driver during benchmarking is cheating, especially when the pre-render value hurts performance on a single card but not on SLI/CF.

You asked how it’s possible to get greater than 100% scaling, and I explained the theory of how it’s possible. Your opinion of whether this is cheating is not relevant to this discussion.

Are you saying that everyone with a single card should set pre-render value to 0 because both Nvidia and AMD made a mistake to have 3 as a default there?

Please, stop with the strawmans. I never said that all. It’s obvious you’re just in this thread to argue despite being proven wrong multiple times by multiple people.

I am not doubting the exists of noise and bugs, I am doubting that those noise and bugs are the reason to SLI/CF > 2x performance.

How so? If there’s a bug that reduces a single card to 80% of its performance but is not manifested in a multi-GPU setup for whatever reason, you’ll potentially get more than 100% scaling when two cards are running at full capacity.

Right now, 580 > 570 in benchmarks, is that due to noise and bugs?

No, why would it be? The 580’s specs explain such a performance gain.

 

[Seero]

No I’m not. I’m using a simple example to illustrate how a different pre-render value can impact performance over and above the expected impact by adding more GPUs to a system.

I’m also stating that an AFR system will typically render ahead further than a single card system, which means the CPU can keep working in situations where it might’ve stopped on a single GPU system.

I’m also stating this is done at the driver level and extends beyond the simple pre-render value that is available to users.

Nobody is saying the CPU is a bottleneck; in fact, pre-render achieves nothing if the CPU is the bottleneck. I’d suggest you re-read my example because I’m not going to repeat it.

No. Where did I say that? I said the driver more aggressively renders ahead in an AFR system because ATi & nVidia want to get the best possible scaling.

You asked how it’s possible to get greater than 100% scaling, and I explained the theory of how it’s possible. Your opinion of whether this is cheating is not relevant to this discussion.

Please, stop with the strawmans. I never said that all. It’s obvious you’re just in this thread to argue despite being proven wrong multiple times by multiple people.

Excuse me, but when was I proven wrong? Some said > 200% is impossible, you (and I) said it is. You said that the reason of superscaling is not presented here and after my request, you shared your opinion.

I read you definition of AFR and pre-render and posted my understanding about the subject twice with my own words. If my understanding is wrong, then state it. I, on the other hand, am trying to state what I failed to understand from your post. You believe that it changes based on multi card setup, but then what is the point of having those settings on the driver?

Those are tech talks, and I have no problem with it as I will always learn something new from it. I, however, have a problem where you suddenly said I am no arguing without providing support to your claim. In fact, you further said that I have been proven wrong out of the sudden, and multiple times, and by multiple people. Are you referring to my understanding to AFR and/or SFR? Or the fact that scaling does exceeded 200%? Or the theoretical maximum?

I am not the one who put a default pre-render value on the video card drivers, I simply see them on video card drivers. You said

...if you pre-render like you do on a single card you’ll get sub-optimal scaling...

That means, it is a bug in 2 ways. First, it ignores user setting. Second, it actually reduce the performance of a single card.

Maybe that isn't what you are trying to say. What you really mean is they are using the optimal value so that both single and multi cards plays are best. Well, then we are back to square one. I still don't see how can it be the reasoning of the > 200% scaling.

How so? If there’s a bug that reduces a single card to 80% of its performance but is not manifested in a multi-GPU setup for whatever reason, you’ll potentially get more than 100% scaling when two cards are running at full capacity.

Come on now, you asked me about my doubt, so I share my opinion with you. Again, I doubt that both AMD and Nvidia has a bug like you described. I didn't say it is impossible, I said it is very interesting. Was there a confusion here?

No, why would it be? The 580’s specs explain such a performance gain.

You see, if something is reliable, then it is. If it is not reliable, then it is not. If there exists benchmarking noise which makes it unreliable, then it is unreliable. If there exists noises, but still reliable, than it is reliable. When it shows 580 > 570, you said reliable. When it shows SLI/CF > 2x single, you said it is not reliable. So what exactly are you trying to say?

Now BFG10K, educate me please. Am I wrong in believing that forum is a place where people share their opinions? Am I wrong in asking questions? Not a single word I used in my post is directed to you in person. I didn't say you were arguing when you have a different opinion. Did I?

 

[zebrax2]

Excuse me, but when was I proven wrong? Some said > 200% is impossible, you (and I) said it is. You said that the reason of superscaling is not presented here and after my request, you shared your opinion.

I read you definition of AFR and pre-render and posted my understanding about the subject twice with my own words. If my understanding is wrong, then state it. I, on the other hand, am trying to state what I failed to understand from your post. You believe that it changes based on multi card setup, but then what is the point of having those settings on the driver?

Those are tech talks, and I have no problem with it as I will always learn something new from it. I, however, have a problem where you suddenly said I am no arguing without providing support to your claim. In fact, you further said that I have been proven wrong out of the sudden, and multiple times, and by multiple people. Are you referring to my understanding to AFR and/or SFR? Or the fact that scaling does exceeded 200%? Or the theoretical maximum?

I am not the one who put a default pre-render value on the video card drivers, I simply see them on video card drivers. You said

That means, it is a bug in 2 ways. First, it ignores user setting. Second, it actually reduce the performance of a single card.

Maybe that isn't what you are trying to say. What you really mean is they are using the optimal value so that both single and multi cards plays are best. Well, then we are back to square one. I still don't see how can it be the reasoning of the > 200% scaling.

I think the what many are disagreeing with aside from the over 1
200% scalling issue is your belief that the maximum is 800%.

As for the pre-render maybe the pre-render value settings is not a global value but rather a global fallback value when there is no hard set value for a game.

Come on now, you asked me about my doubt, so I share my opinion with you. Again, I doubt that both AMD and Nvidia has a bug like you described. I didn't say it is impossible, I said it is very interesting. Was there a confusion here?

You say you believe there are noises and bugs but doubt that it could be the possible reason as to why greater than 200% scalling happens is just rather stange.

 

[Seero]

I think the what many are disagreeing with aside from the over 1
200% scalling issue is your belief that the maximum is 800%.

I can take disagreement. It isn't like I tried to say something complicated with terms and techs that no one understand, I simply say 3 factors that many people know, each increase performance, independent to each other, and stated that it is indeed possible since each of them has increased, and each of them has a possitive impact to performance. I never said is it possible to have a perfect scaling so that you can actually get 800%(Which is why i said theoretical maximum). I said, in practice, may be none of them scaled perfectly even though they are doubled, but together, make > 200% possible.

Again, It was not a claim that performance goes beyond 200%, but statistics shows it does. If something should, in theory scale twice at best, in practice, you can't possible see close to 2x performance, so let alone > 200% because it is not even possible in theory.

So is the explanation of AFR made scaling > 200% something reasonable and mine is off the norm? Hey both of us is trying to explain the same thing with different theories. Or am I understanding? Is AFR make scaling > 200% a fact and not a theory?

As for the pre-render maybe the pre-render value settings is not a global value but rather a global fallback value when there is no hard set value for a game.

I open my Nvidia control panel and see "Maximum pre-render frames" setting, and I can choose a different value on different games due to its gaming profile. This setting won't change regardless of how many video cards on board. BFG10K suggested that this value will change when adding a card, I said that if you change that number so that it hurts single card configuration to acquire > 200% performance, then it is cheating.

OP's question is clear, is it possible to have > 200% scaling and was reviewers wrong? Many got upset when I say it is in fact possible and the statistics showed that it is possible. Because of that I got people saying that I have been proven wrong to personal attacks.

You say you believe there are noises and bugs but doubt that it could be the possible reason as to why greater than 200% scalling happens is just rather stange.

As to noise, all benchmark is accurate to a degree. When it state 60FPS, it doesn't mean it drew 1 frame .016666666666666666666667 second. In fact, it may not even drew exactly 60 frames per second. In short, there is a margin of errors. Now what is the chance of having all odds against single card setup and all odds favoring SLI/CF? Given that it isn't due to noise that 580 > 570. It is like telling you that when measuring white papers, ruler is accurate, but if you measuring yellow papers, it is not. If benchmarking is reliable, than it is. If it is not reliable, than it is not. You can't say the benchmark is accurate on 580 vs 570 and not accurate on 6870 vs 6870x2, or any single vs multi. Either it is reliable, or it is not.

As to bugs, BFG10K stated himself. If there exists a bug that made single card performs only 80% where under SLI/CF, it performs 100%, then it may be used to explain the > 200% scaling. However, is the bug a software/hardware glitch? Or due to the fact that under multi-card setup, there is actually more resources, which allows performance to exceed 200% scaling in terms of performance? If that is the case, then what are those resoures? I/O? Memory?

 

[WelshBloke]

I can take disagreement. It isn't like I tried to say something complicated with terms and techs that no one understand, I simply say 3 factors that many people know, each increase performance, independent to each other, and stated that it is indeed possible since each of them has increased, and each of them has a possitive impact to performance. I never said is it possible to have a perfect scaling so that you can actually get 800%(Which is why i said theoretical maximum)...

Its not that we don't understand, its just that you're wrong about there being an 800% theoretical performance improvement.

You cant just pick a stupidly high number and say that thats the theoretical max, it has to be a number that you could actually get to if you removed all the little bugs/niggles and everything worked "just so". Otherwise why not say 1000% is the theoretical max, or over 9000%, or any other number?

I'm not sure why you're continuing to argue this point, sometimes its better to concede gracefully.

 

[GaiaHunter]

Seero you are saying it can scale to 800% because of doubling the memory, I/O, etc.

It doesn't happen due to that.

 

[Seero]

Its not that we don't understand, its just that you're wrong about there being an 800% theoretical performance improvement.

You cant just pick a stupidly high number and say that thats the theoretical max, it has to be a number that you could actually get to if you removed all the little bugs/niggles and everything worked "just so". Otherwise why not say 1000% is the theoretical max, or over 9000%, or any other number?

I'm not sure why you're continuing to argue this point, sometimes its better to concede gracefully.

You see, you said I am wrong. If I stop defending myself, then I am admitting it, so I am forced to continue. If you simply disagree, then I don't need to repost.

I am sorry to say this, depending on how you define "pick of numbers", all theoretical numbers can be simply a collection os stupidly high numbers. I repeated over and over and over and over again, and I will repeat the idea again. If performance is based upon 3 factors that are independent to each other, then if each of them has to potential of doubling performance, then the theory, it can go up to 800%. Bring this statement to any MATH teacher and see if it is wrong. There is a big difference between you fail to understand it vs I am wrong.

How hard is it to see the fact that data needs to be cloned towards multi card on SLI/CF in practice? Well that is increases the load. The need of synchronization also increases the load. If performance in fact did not exceed 200% scaling, how can it be possible for benchmark to show > 200%. Where is the loss factor? Latency? Overhead? If we are theory crafting, it can be left out, but we have a case where statistics shows performance scale > 200%. If you take your head out of the box and start to think instead of trying to prove someone wrong, you will probably wonder why too.

Make sure you got it right because saying someone is wrong.

 

[Gloomy]

I am sorry to say this, depending on how you define "pick of numbers", all theoretical numbers can be simply a collection os stupidly high numbers. I repeated over and over and over and over again, and I will repeat the idea again. If performance is based upon 3 factors that are independent to each other, then if each of them has to potential of doubling performance, then the theory, it can go up to 800%. Bring this statement to any MATH teacher and see if it is wrong. There is a big difference between you fail to understand it vs I am wrong.

It cannot happen because you cannot have more than one bottleneck.

 

[zebrax2]

I open my Nvidia control panel and see "Maximum pre-render frames" setting, and I can choose a different value on different games due to its gaming profile. This setting won't change regardless of how many video cards on board. BFG10K suggested that this value will change when adding a card, I said that if you change that number so that it hurts single card configuration to acquire > 200% performance, then it is cheating.

Maximum seems to be the magic word there meaning you are only setting the limit but it may actually go from 0 to say 3.

 

[taltamir]

If performance is based upon 3 factors that are independent to each other, then if each of them has to potential of doubling performance, then the theory, it can go up to 800%.

1. Performance is dependent on more than 3 factors.
2. the 3 factors you listed are NOT independent to each other.
3. They do NOT each have the potential to double performance.

as I said before, you solve the equation correctly, but you are setting it up wrong. 2x2x2=8, that is true, but the failure is in your myriad false assumptions that make you believe that 2x2x2 is the mathematical representation of what is going on there.

yet every time someone tells you that 2x2x2 is not a representation of what is going on because you set it up incorrectly, you react as if they are claiming that 2x2x2=8 is false.
The statement 2x2x2=8 is true, just as the statement I quoted in this post is true... but while being true it has absolutely nothing to do with GPUs. Your assertion that this statement is in any way shape or form indicative of GPUs is incorrect for reasons 1, 2 and 3 that I have listed above.

 

[sxr7171]

Let's see. So I run a Coca-Cola bottling plant. I want to increase production. So I will double the speed of the bottle conveyor belt. But my filling machines in the beginning will operate at the same rate. My production of filled bottles would be the same.

If I also doubled the rate of my filling machines I would then overall double my production.

I also have a capping machine that I could leave at the same speed or double as well.

If I double all 3 would I get 8x production?

I think that I would end up at a production rate limited by the speed of whichever machine runs the slowest. If all 3 are doubled I would get 2x production.

 

[ArchAngel777]

Let's see. So I run a Coca-Cola bottling plant. I want to increase production. So I will double the speed of the bottle conveyor belt. But my filling machines in the beginning will operate at the same rate. My production of filled bottles would be the same.

If I also doubled the rate of my filling machines I would then overall double my production.

I also have a capping machine that I could leave at the same speed or double as well.

If I double all 3 would I get 8x production?

I think that I would end up at a production rate limited by the speed of whichever machine runs the slowest. If all 3 are doubled I would get 2x production.

Good example. Hopefully Seero can just admit that he has no clue on how to apply mathematics. I laugh everytime I see this thread pop up on the main page. Others have more patience (and time) than I do...

 

[Seero]

Let's see. So I run a Coca-Cola bottling plant. I want to increase production. So I will double the speed of the bottle conveyor belt. But my filling machines in the beginning will operate at the same rate. My production of filled bottles would be the same.

If I also doubled the rate of my filling machines I would then overall double my production.

I also have a capping machine that I could leave at the same speed or double as well.

If I double all 3 would I get 8x production?

I think that I would end up at a production rate limited by the speed of whichever machine runs the slowest. If all 3 are doubled I would get 2x production.

It seems the traction of statistics is far less compare to my statment, that is fine, I know I am attractive.

First of all, video card doesn't work like a coca-cola battle factory. When you buy a coca-cola, you don't care if it is fresh or not. When it comes to gaming, you do care about it. Let me adjust your example a bit to make it more like a video card.

2nd, your plant takes questions and delivers answers.

3rd, you have cargo transport that comes to your docking station at a fix time interval, but transport may or may not carry questions.

4th, other than the throughput rate, the time it takes to proccess is critical, so change coca-cola battle to a bench of geniuses.

5th, you need a storage bay for 2 purpose, one is to storage questions that are to be processed/re-processed, and the other is to store answers.

6th, answers can go to 2 places, one is the cargo transport you get questions from, the other is all the retail trucks waiting for you to deliver. Retail trucks also comes at a fixed interval, and will only stay for a fixed duration. Those retail guys sometimes don't take partial shipments, either all or nothing.

7th, questions which may or may not come within one shipment, meaning that the time it take to make them varies from shipment.

Now, sometimes the questions is incomplete to be answered, sometimes answers are not fast enough to be delivered to the first available out-going retail truck, and sometimes there are no spaces for either answers, partial answers or questions.

You were told that in theory, in terms of raw power, your plant is capable of creating thousands of answers a day, while you have tested with simple simple questions and the plant does produce 500+ answers a day, but during live, it has difficulty producing 30 answers a day. You know that doubling storage area sometimes increase output, and in theory, can double production. You know what by doubling number of the incoming cargo transportations or doubling the factory line also increase productions, and in theory, each of them has the potential of doubling output.

And so you decided to make another plant with identical setup as the first one and thought "hey, this may double production."

After all this is done you realized that production didn't increase, but decreased because all orders are mixed up, so you added one more thing, an express cargo transit between the plants. After that, although production really don't increase by double, so you have been continuously optimizating the plants. One day, you discovered that sometimes the total production per day actually got better than twice as if you have one plant. You wonder "How the fuk is it possible?" and not that you don't like the result, you do like to find out why.

I believe I have covered all the bases, and now the talk can begin, again. Let me know if the above changes are bias to what I said or trying to demonstrate.