| 00:00 | Okay, so a couple points before start. So first point about the |
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| 00:10 | measurements. So if you notice the run time off a code, |
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| 00:16 | less than a millisecond, which as professor just mentioned, is the |
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| 00:21 | for rappel sampling. Then try Wrap the computation part off your code |
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| 00:30 | a loop and run it multiple earned multiple iterations. So the total time |
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| 00:36 | at least larger than tents or 10 20 milliseconds so that you don't get |
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| 00:44 | issues with our measurements. Otherwise, you're run time off, the code |
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| 00:51 | smaller than does sampling resolution off rappel you. Your measurements could may not |
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| 00:57 | much sense when you try to analyze . So wrap it into a loop |
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| 01:03 | then take the average to get the off. Power consumption for one |
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| 01:09 | The second point is about problem, . Thea End body called. So |
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| 01:15 | you, uh, compile it using Dow's C compiler rapper and when you |
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| 01:22 | it in case you encounter is segmentation , then try to copy that instrumented |
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| 01:31 | to your home directory. That usually the problem with that code. |
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| 01:37 | if you still find any trouble with . Just reach out to me and |
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| 01:41 | can try toe, get it working and I follow up questions. Air |
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| 01:50 | Thio Cash points. Okay, then start to talk about today's lecture. |
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| 02:04 | this is, I would say, for quite some time, the last |
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| 02:09 | there. Let's kind of the hardware tools so as we continual movement of |
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| 02:18 | programming aspects in terms of programming lycopene, MP and FBI and talk |
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| 02:25 | about software and algorithms. But these the topic for today. Focus on |
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| 02:31 | power and try to understand what goes on, why things are the way |
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| 02:36 | are in terms off architecture, er computers. So the first thing why |
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| 02:45 | an important aspect, as it has a design constraint for over a |
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| 02:51 | Prior to that kind off, people used more slow to get more compute |
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| 02:58 | on things works kind of wonderfully. didn't work so well, Um, |
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| 03:04 | this so called them out, scaling working, and I'll talk a little |
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| 03:07 | about that today on then. The part is, of course, as |
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| 03:13 | showed, I think in the first or maybe last lecture? Is that |
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| 03:18 | total cost of ownership for computer system , or PC or whatever you have |
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| 03:25 | cost off electricity and if it's a center? Also, the calling on |
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| 03:31 | cast is actually exceeds the cost of system itself. And that clearly a |
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| 03:36 | concern from any companies a T East the other part is because off electricity |
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| 03:47 | not necessarily generated by so called Resource is so a lot of it |
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| 03:55 | based on trust and fuels, so even though depending on where you are |
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| 04:01 | the globe, companies may have an thio explicitly by clean energy. But |
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| 04:07 | average, at least about two thirds the energy comes from combustion. Herbal |
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| 04:16 | is supposed to wind and solar and thermal that are inherent thickly so. |
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| 04:22 | a big concern for companies off the sizes, like Google and Amazon. |
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| 04:27 | they take various steps as I mentioned to death, clean energy and the |
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| 04:33 | neutral before too long and away a bit justice to explain the cost. |
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| 04:40 | cost is important. The cost of is increasing, but that doesn't explain |
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| 04:44 | whole thing So I'm trying to focus the other parts in of the electricity |
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| 04:50 | for the reason. And here is the I guess, another part off |
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| 04:56 | parent energy is a new, important , and that is that computing is |
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| 05:04 | an increasing portion on the total electricity globally. So it has what used |
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| 05:13 | be kind of even only 10 years , a very small portion on the |
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| 05:17 | energy consumption, electric energy consumption. it's now about a third of 40% |
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| 05:24 | the best scenario in about 10 this or so. It's not necessarily a |
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| 05:29 | thing because computing tends to replace more energy consuming activities or in |
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| 05:37 | It's not the bad thing. On other hand, um, it's something |
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| 05:41 | needs to pay attention to. To Thio both reduce the cost and |
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| 05:47 | environmental impact off, uh, computing information technologies in general. That's and |
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| 05:57 | didn't want to move so on. is just a reminder, a little |
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| 06:01 | curiosity thing work just the PC, it may consume over its lifetime. |
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| 06:09 | , as the power is a limiting in terms of design, and this |
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| 06:16 | kind of a old graft by as you can see at the bottom |
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| 06:19 | the years, and this covers the up to about 15 years ago. |
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| 06:26 | during the time covered by the you can see that the heat density |
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| 06:35 | computing chips approach basically the same intensity you have in a nuclear reactor, |
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| 06:41 | that probably give you some idea That's not sustainable. This type of |
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| 06:47 | that was exhibited until about 15 years ago on this side about us cute |
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| 06:55 | it also relates what the heat density on the processor chip compared to your |
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| 07:03 | place where you used for, you , making the tea, coffee or |
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| 07:07 | X or, uh, similar So the cooking plate is considerably |
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| 07:14 | um, it dense than computing And so they got to the point |
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| 07:20 | one could not necessarily find cooling technology , actually prevent them from melting or |
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| 07:29 | . And there's kind of another. on the horizontal axis Now instead of |
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| 07:35 | clock frequency on the chips, whereas previous slide had the years and the |
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| 07:44 | technology being used, that being smaller smaller feature sizes by the years on |
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| 07:52 | vertical axis is still the heat and the various processor names is |
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| 07:57 | The slide is something you may but 4000 and 411 of the first |
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| 08:04 | microprocessors. And as she go up the right, there's more and more |
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| 08:09 | processors, even though even on this it covers up until about 78 years |
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| 08:16 | , maybe 10 years ago. um, and part of the reason |
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| 08:25 | obviously chip designers want Thio get more more uses out of the silicon and |
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| 08:34 | of it that most increase the clock and increased clock frequencies. Contributed |
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| 08:41 | The exponential improvement in performance that, , uses industry got used to on |
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| 08:49 | of expect on That's actually has Bean critical basis for the entire industry. |
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| 08:57 | if performance on chip doesn't improve, the point of buying a new |
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| 09:03 | It is also interesting it in there left corner. You can see what |
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| 09:07 | brain does. Your brain is in off computational rating, um, in |
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| 09:14 | of neurons incredibly slow compared to current . But it's also incredibly much more |
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| 09:21 | efficient than anything we build today. . Here is a little bit of |
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| 09:26 | picture again in terms of clock Now, over time instead of related |
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| 09:33 | the power consumption as you can see frequencies five adore off at about 2005 |
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| 09:42 | again, the reason for that was intensity was not sustainable, and there's |
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| 09:48 | reason as well. Which is this North scaling that I will mention? |
|
| 09:54 | in the beginning off, this is of, you know, As you |
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| 10:00 | see, the first few years Thio show or start, the multi |
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| 10:05 | area with IBM was one of the one of the first company. |
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| 10:09 | that came up with them off to processor, and then Andy came a |
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| 10:15 | of years later on. Then another years later in tow, joined also |
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| 10:21 | the club producing multi core chips. the point was essentially to try to |
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| 10:29 | , yeah, the exponential improvement in performance of a chip when the Cooperates |
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| 10:36 | not go up. And the reason clock rights has could not go up |
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| 10:44 | the way the sea most technology So this is the famous square law |
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| 10:51 | I would say anyone that does computer should that you will be familiar with |
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| 10:55 | at least know off because it's fundamental rule anything being done with sea moss |
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| 11:02 | terms of computing. So the square is this thing where P is the |
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| 11:09 | consumed bye some any form of circuit switching device transistors in particular. In |
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| 11:16 | case, which is proportionate to the used square by square of the voltage |
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| 11:24 | proportions of the frequency four was known the dynamic of the switching power. |
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| 11:30 | is the thing that actually changes And that means does the actual computing |
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| 11:36 | is in dynamic piece. Then there a leakage inboard power that is the |
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| 11:43 | to points. Transistors and capacitors are of leaky. The Loew's charges I |
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| 11:50 | when we talked about the Iran and then there's three cooling part of |
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| 11:57 | can be a model as being proportional their both is to the fourth |
|
| 12:03 | Well, that's a separate issue. then there's a couple of diagrams |
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| 12:07 | and one is the left hand Three different to curves by three different |
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| 12:14 | of symbols. The cars for three frequencies where the the world one is |
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| 12:20 | the lower clock, three points or gigahertz. And how you run with |
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| 12:25 | marks is I have to 0.60 60 and what's on the left. Access |
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| 12:34 | the participation for running. Gaussian Elimination holding a system of dense equations, |
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| 12:42 | it basically shows that the higher the of the higher participation and has predicted |
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| 12:52 | square bill on the top of the . And on the right hand |
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| 12:57 | it shows the fact that the clock has a relationship with the voltage as |
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| 13:04 | . So and in that case has different chips, um, being illustrated |
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| 13:12 | how the clock frequency can be controlled the both the channel ships. But |
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| 13:18 | point is, from Texas altogether in . In a way, the power |
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| 13:25 | is more than proportionate to the clock because you also have to work with |
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| 13:31 | voltages. So in the end, power grows quite quickly in principle. |
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| 13:38 | the left side, you have kind separated them to some degree. One |
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| 13:43 | do that control the both things separately the clock Rico in city, but |
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| 13:50 | general, from a design principle, are tied. So this is just |
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| 13:58 | quotes because into levels kind of caught surprise, and it shows how serious |
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| 14:04 | was. And that's what we Multiple chips. And in fact, |
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| 14:09 | had the backtracks. They had everything ship the product, and it turned |
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| 14:15 | it was so hot that they couldn't cool it, and it became |
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| 14:19 | So they decided not to ship that and had to go back to the |
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| 14:24 | board. And that's why they ended coming a bit later than the other |
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| 14:29 | processor vendors with multi core chips. here is a little bit as one |
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| 14:36 | the info fellows, literally fellow very exceptional scientists within infill. |
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| 14:48 | um, benefits are in position, as fellows, so it's kind of |
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| 14:54 | very it's the Inquisition within in This is one of them. |
|
| 15:00 | and what I want you to focus . This particular slide is to look |
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| 15:05 | the right column and says energy for of FBI. And then each role |
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| 15:12 | the stable is different generations or off for different at that time, what |
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| 15:20 | known as inter processor by the name pendulums on pension problem for etcetera. |
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| 15:27 | in the right column, you can that the energy per instruction grow from |
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| 15:33 | the first I the 40 86 for nanograms per instruction, Thio almost 59 |
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| 15:42 | for instructions that grow fivefold over a generation are into the processors. And |
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| 15:51 | , they realized this is not And they had to go back to |
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| 15:55 | drawing board and start to do designs in order to still get the exponential |
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| 16:02 | in performance. Um, here's another from inter processors again, more or |
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| 16:09 | showing the same thing. And I this because it had sort of one |
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| 16:16 | that is the kind of orangey colored the has the dashed, um, |
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| 16:25 | of initially declining writers line as I to the right and then uh |
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| 16:32 | to the very far right on the diagram and up words error and when |
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| 16:39 | chose the performance provoked that has now one of the guiding principal for judging |
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| 16:48 | quality of designs so you can see a number of generations off see most |
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| 16:56 | . The energy efficiency actually went down again it got to the point where |
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| 17:01 | was not sustainable to do business that . And then a number of the |
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| 17:06 | that was used to make programming like counter order, execution and a |
|
| 17:14 | off other features ended up being taking in order to get improve performance for |
|
| 17:26 | ? And that's what's happened in terms the month score a high court |
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| 17:30 | Things in fill in this particular case back to, uh, much earlier |
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| 17:36 | that has less feature in it in to put surf, of course, |
|
| 17:41 | the same guy and Gap exponential improvements for code that had parallelism by using |
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| 17:48 | course instead of trying to push the . So this is kind of what |
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| 17:55 | is the fact that they had the law. That's a lot more transistors |
|
| 18:00 | each generation of the most technology that used to introduced all kinds of nice |
|
| 18:07 | from a programming point of view. it waas and also from reliability and |
|
| 18:16 | kinds of respect. But it did the energy efficiency and again, uh |
|
| 18:22 | , the same principle had to So any I guess I can stop |
|
| 18:30 | talking a little bit. Why these happened in terms of the energy consumption |
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| 18:37 | how things are. Actually, what rules are today is supposed to. |
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| 18:43 | the first 30 or so years off law, I had a question or |
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| 18:53 | clarification to make sure that I understand . Okay, so you said we |
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| 18:58 | in the course of history. We steadily, you know, following Morse |
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| 19:02 | up until we reached a wall, which point we solved by introducing multi |
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| 19:09 | which decrease the efficiency overall, no. It didn't decrease the efficiency |
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| 19:17 | the way until about 2000 fire and will talk about in the next several |
|
| 19:24 | . In addition to Maura's long, was something else that worked that this |
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| 19:29 | called Denard scaling. So that May that in addition, Thio getting more |
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| 19:38 | on the diet, you could also the clock frequency. So at constant |
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| 19:46 | on the chip now, when this start scaling, stopped working that was |
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| 19:55 | longer true. And then the chip started to increase beyond what was sustainable |
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| 20:05 | before, when they are computer added features that consume power, the |
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| 20:14 | efficiency for doing, say arithmetic in went out, and I can come |
|
| 20:24 | to these questions once I talked about next several slides on we can see |
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| 20:31 | I have answered the questions at that . Okay. Thank you, Dr |
|
| 20:36 | . Sure, now you're welcome is good question. So So I'll come |
|
| 20:41 | to a little bit when I talked when I talked about the the Iran |
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| 20:46 | with Iran is slow. So the thing is again all the computing, |
|
| 20:51 | just storing information and basically the captured this little simple R C circuit. |
|
| 21:01 | what did they not scaling? Kind implied is what is on the left |
|
| 21:08 | side with the text here that basically that the switching energy. If you |
|
| 21:17 | out there, uh, electrical our equations as that the energy per switching |
|
| 21:24 | proportional to the volte square and the . If it's second and in |
|
| 21:30 | the transistors that are the switching agents computing. In fact, our acting |
|
| 21:39 | capacitance is as well. They're more it because they switch on and |
|
| 21:43 | But it's basically charging the plates off transistors. That makes changes the |
|
| 21:49 | so it's proportional to the wealthy square capacitance. And, of course, |
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| 21:55 | the energy part, the power than the consequence of how frequented you charge |
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| 22:03 | discharge is capacitor. So the power becomes proportion to the frequency so that |
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| 22:09 | have the dynamic energy part that is both the square times, the |
|
| 22:17 | Now the typical thing that waas and sea more scaling technology in every generation |
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| 22:29 | sizes got the butt down to about of 700.7 or the previous generation. |
|
| 22:37 | if you take it as a square of chip, that means you get |
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| 22:44 | square. So that means of roughly factor tomb or transistors in the |
|
| 22:49 | area. So that's the double the of transistors. But that also means |
|
| 22:56 | a capacitor parked a little plate. also gets basically half area, so |
|
| 23:03 | means first, the power or energy transistor gets down by half. But |
|
| 23:12 | you double the number off transistors. then you're back and having the same |
|
| 23:18 | by, uh, making things smaller the same time as you double them |
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| 23:23 | the same area. But when this North scaling worked, you could also |
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| 23:30 | the clock frequency by about 40% for chip generation. So in that, |
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| 23:37 | total, for any given ship we've got almost three times the performance |
|
| 23:44 | these scaling laws. And again, was used to introducing more and more |
|
| 23:50 | features on the chip at constant power put on the right hand side of |
|
| 23:59 | side. First on the Moore's That again is not about performance, |
|
| 24:05 | it's about transistor density. But that's of the doubling every 18 20 |
|
| 24:12 | That used to be the case. no longer quite true, because it's |
|
| 24:17 | significantly harder to do things. And fact that things are significantly harder is |
|
| 24:24 | of reflected on the bottom right level Graham that shows that the cost of |
|
| 24:30 | transistor went down significantly. So that's the chip cost to sort of the |
|
| 24:36 | . Consumer ended up being pretty much over the years because the cost per |
|
| 24:42 | went down and when the transistor count up. But that hasn't quite been |
|
| 24:49 | anymore, so that's why sometimes, , chips now gets more expensive because |
|
| 24:55 | cost of a transistor is no longer justice of curiosity part maybe, but |
|
| 25:01 | a good thing to know on what expect. So this is just a |
|
| 25:07 | bit graph to illustrate the same thing in terms of chip power meaning capability |
|
| 25:14 | the left hand side you got twice number of transistors, and then they |
|
| 25:18 | faster as you got almost three times performance, um, for hardship |
|
| 25:28 | And that worked as long as these prediction how the see most technology work |
|
| 25:40 | to reduce the electric field between these place in the capacitor kind of |
|
| 25:48 | So that meant as long as you the electric field so it remained |
|
| 25:54 | then you can get this benefit are both increased, cooperate and, |
|
| 26:02 | constant power for the silicon area or chip. The problem. Waas. |
|
| 26:10 | is what's known as the leakage power as the what's called the gate accent |
|
| 26:16 | best that the thing between the two so they capacitor got thinner and |
|
| 26:25 | It also meant that the leakage parent higher and higher and when, so |
|
| 26:33 | you look at the upper left hand of the true crossing line or upper |
|
| 26:39 | that this reasonably flat, not increasing rapidly as you move to the |
|
| 26:46 | which is reduced feature sizes or time to the left on the upper left |
|
| 26:52 | graph. The dynamic part did not all that much, but the leakage |
|
| 27:00 | increased significantly, so it became a factor. And that's why, |
|
| 27:08 | scaling the way it used to work about 2005 and leakage car became a |
|
| 27:16 | , uh, kind of stopped. that's sort of the end over this |
|
| 27:20 | called the North Scaling because of leakage . And as you can see at |
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| 27:25 | point, um, it waas the between the plates off the capacitor. |
|
| 27:33 | no more than about five atomic so it wasn't practical, even with |
|
| 27:41 | technology to make it all that much . So, in fact, so |
|
| 27:48 | kind of the choice that happened after scaling stopped working, that either you |
|
| 27:56 | basically the double the capability. But the park consumption went up with the |
|
| 28:03 | of otherwise Prior to that, you gain in terms of clock frequency, |
|
| 28:08 | now it actually would increase the or the other option is to keep |
|
| 28:16 | power and then then the basically the capability is limited to maybe increase about |
|
| 28:28 | per generation instead of the factor of . And as build already pointed |
|
| 28:35 | reality isn't quite as good even at . So that's why basically sets at |
|
| 28:43 | , you can expect to get about more capability out of a piece of |
|
| 28:49 | after the end of the North So that's why, because cooling limits |
|
| 28:57 | cooling technologies are really at its limit , or waas about 2005 and not |
|
| 29:03 | much has happened since things the hot and so there. So this big |
|
| 29:12 | , in fact, today require literally off some flavor or another. Air |
|
| 29:17 | is no longer good enough, so the participation isn't really an option. |
|
| 29:24 | one pretty much are limited by constant and as well as as it was |
|
| 29:30 | in previously the car creates stopped going up for chips. Uh, after |
|
| 29:38 | 2005 when this all technology scaling stop anyway, more slower still has kind |
|
| 29:46 | been working, but more slower is about transistor density, not about |
|
| 29:53 | but even that just now getting and here is kind of a little |
|
| 29:58 | of the slides showing how things have the So it's the power limitation. |
|
| 30:08 | , calling capability limited the participation and was kind of reached peak or and |
|
| 30:16 | been pretty much being flat in terms power density and the power density and |
|
| 30:23 | lack of the North. Scaling then forced the clock frequencies to pretty much |
|
| 30:27 | level on that in itself. That core performance pretty much also leveled |
|
| 30:34 | um, at around the same but again, more slow. It's |
|
| 30:40 | of still working, so you can get a lot more transistors on the |
|
| 30:45 | . And the way that tells them used is, as it shows on |
|
| 30:49 | bottom to get more and more cores the guy. And this is basically |
|
| 30:55 | for the industry, too. give people exponential improvement in terms off |
|
| 31:03 | and make it justified. Thio, know, buy new computers or new |
|
| 31:12 | with new technology and generations, and has also caused this notion because off |
|
| 31:22 | the cooling capabilities. So what it out to be is you can't really |
|
| 31:29 | all the transistors on the chips to working and doing stuff at the same |
|
| 31:34 | , because then the chips would overheat you can call them. So now |
|
| 31:41 | there's this concept off dark silicon that just trying to signify that it's not |
|
| 31:51 | to actively use all of the transistors a chip at any given moment. |
|
| 32:00 | here is kind of another slide showing with technology and generations Ah, the |
|
| 32:08 | of chip that can effectively be actively in computing at any given time. |
|
| 32:18 | today technology are and the depending upon and others. But 14 is what |
|
| 32:30 | with introduces. They also use 10 trying to move to seven and other |
|
| 32:38 | , um, or foundries. They Nargis what's known as seven nanometer design |
|
| 32:45 | , but it's basically shows you that much today on about the quarter of |
|
| 32:52 | transistors on a chip is coming, maximum that can be used in a |
|
| 32:56 | time. Um, so um, a bit this has a consequences that |
|
| 33:08 | was trying to say here that part the reason why there are the size |
|
| 33:19 | cash is on chips have gone up particular the last level cash is that |
|
| 33:25 | are largely idle most of the so that is a helpful thing in |
|
| 33:31 | to keep the power consumption down. , of course, it also helps |
|
| 33:36 | improving the performance. So going forward one chemist certainly expect that, |
|
| 33:45 | cash is will keep growing as a count keeps increasing on the tips. |
|
| 33:52 | course, there needs to be a of one. Also sees the number |
|
| 33:55 | course growing, but course are relatively compared to the total ship area. |
|
| 34:02 | a large more than half of the area today tends to be cash. |
|
| 34:10 | this is just another thing off Anyone interested in this topic. I |
|
| 34:15 | you to kind of go on Look something called the international technology roadmap for |
|
| 34:21 | , and they issue new road I think nowadays, about every other |
|
| 34:29 | and my demon back more than five ago, they made the point that |
|
| 34:35 | and power consumption is the key part moving forward and designing chips. And |
|
| 34:46 | think this is a good stopping point come back and see if there are |
|
| 34:53 | . Central air. So the one I wanted to remember is in addition |
|
| 34:58 | more stolen that I'm sure all of have heard about. There is also |
|
| 35:01 | scaling that you may not have heard . But that was a big |
|
| 35:06 | Thio the exponential growth and performance per generation up until about 15 years |
|
| 35:15 | and that's no longer works. And , um, the rules of designing |
|
| 35:21 | have quite changed on. That's why see increased caches. And, of |
|
| 35:28 | , there is a balance with increased council exponential improvement and performances. |
|
| 35:36 | uh, Onley possible for applications that apparently in because single core, the |
|
| 35:45 | third performance is not like 60 Eso now, I guess, to |
|
| 35:58 | get more of background information, I'll a little bit. So where does |
|
| 36:02 | go? And of course, there the simple again most technology, which |
|
| 36:10 | George transfer technology, just moving electrons between transistors and if it's storage just |
|
| 36:18 | time. So here's a little bit the slide, and this is something |
|
| 36:25 | think even at one should be aware , not only for understanding the technology |
|
| 36:31 | the rules for how things might change forward and what computer architects are trying |
|
| 36:36 | do, but it also tells you that is relevant for applications relative to |
|
| 36:45 | consumption in power. So there is the left upper left hand side. |
|
| 36:52 | is kind of a table in the graph that illustrates the table and what |
|
| 36:57 | shows there. Energy for certain types operations. So it, as you |
|
| 37:05 | see for arithmetic like addition, it's much linear in the size of the |
|
| 37:15 | type. So if you have and kids, uh, and Versus is |
|
| 37:22 | and they it, it takes about the energy. 16 bit floating point |
|
| 37:30 | a little bit more expensive, but more complicated because in the floating point |
|
| 37:38 | have Manti PSAs and you have exponents you need toe line the operations in |
|
| 37:46 | to be able thio, add or things so it does become more |
|
| 37:54 | Then, uh, so it's a about the factor of what Uh huh |
|
| 38:02 | 30 to be done in 5 32 . Rolling point out. That's a |
|
| 38:05 | of 10 ish. More or Um, multiplication is definitely more expensive |
|
| 38:11 | the ad, as you can because it's the 32 bits mouth |
|
| 38:20 | but fire for yeah, 3.5 times something. The multiplication is kind of |
|
| 38:27 | squared type operation compared to add, you know they expect the multiplication czar |
|
| 38:33 | expensive than additions, whether it's integral point now the big point and then |
|
| 38:42 | back to my stressing off memory and last lecture or two is that accessing |
|
| 38:56 | even S Thomas has said here, means cash practically is more expensive than |
|
| 39:04 | operations. It's even more expensive than 32 bit floating point multiplication. And |
|
| 39:13 | you need to go to the that means you need to go off |
|
| 39:19 | . It's more than two orders of more expensive. So that's why having |
|
| 39:30 | cold or algorithms being, um, using cash is effectively is incredibly important |
|
| 39:40 | terms of total energy consumption. yes, could you remind us is |
|
| 39:48 | what I'm used for all the levels cash or just the lower ones. |
|
| 39:52 | levels of cash? Yes, they even even there were three caches and |
|
| 39:59 | ones that I have to start to a level four whatever for that may |
|
| 40:05 | use s tram. They may use Embedded the ram? A. So |
|
| 40:12 | mentioned it depends on whether they need fourth level or level beyond three. |
|
| 40:22 | retain information or not So extreme is for cashes in order. Thio for |
|
| 40:29 | to be retained and speed so That's the basis. Why Ekstrom is |
|
| 40:38 | for cash is be the attention, question. And this might be out |
|
| 40:45 | the scope of what we're discussing. typically, when we discuss, |
|
| 40:50 | data structures and algorithms, we assume memory, right, which is a |
|
| 40:56 | pitfall that that being said, can design data structures that are aware of |
|
| 41:01 | different levels of cash and maybe even type of ram that's being used to |
|
| 41:06 | for that as opposed to, you , just saying that a binary search |
|
| 41:10 | is long gone. Um, that a good question. I'm not sure |
|
| 41:17 | have a good answer. So there two elements to it. Uh, |
|
| 41:25 | first, this the size. if the sizes of the data structures |
|
| 41:34 | relatively small, and then it doesn't too much, because then hopefully it |
|
| 41:42 | 15 cash. But the other part the Traverse ALS scheme. So how |
|
| 41:48 | access the data structure It, even design, has lots of cash is |
|
| 41:57 | important because that quote a bad Elin, terms of higher step through |
|
| 42:05 | and then the two excessive access is river off chip memory. So I |
|
| 42:14 | say it's a large fraction of how access to data structure. Okay, |
|
| 42:23 | , someone shouldn't. It's not just static structure. It's a traverse ALS |
|
| 42:31 | is important. Unfortunately, programming the standard ones don't have control mechanisms |
|
| 42:40 | deciding how data gets advocated. And is, you know, it comes |
|
| 42:49 | every now and then, uh, discussions about programming language to sign. |
|
| 42:57 | of course, calls against making source highly portable because then they come dependent |
|
| 43:10 | Sisters of the target platform. So lower left hand corner graph trying to |
|
| 43:26 | also a little bit, uh, the energy consumption for accessing data. |
|
| 43:39 | it basically points to the fact that distance and the wire energy is effectively |
|
| 43:48 | in Esther himself, consume the same of energy regardless of where on the |
|
| 43:54 | it is. But it, um from where the functions units are is |
|
| 44:03 | culprit. That's where a lot of energy goals of the wire energy is |
|
| 44:11 | very important aspect. So again, very, um, cash efficient algorithms |
|
| 44:21 | , thio get this much usage out level one cash is that you |
|
| 44:27 | once you have the data in etcetera is an important aspect, and |
|
| 44:32 | is, we'll talk a little bit about that. Target can help computers |
|
| 44:39 | out how to allocate things, or Thio do. The sequence of access |
|
| 44:45 | we'll talk about and some structure I want to talk about how to |
|
| 44:51 | and basically organized the source code so amenable or takes less transformation for a |
|
| 44:58 | to do the right thing. so I think that's what I wanted |
|
| 45:06 | say. So not a little bit what both computer architects and can |
|
| 45:13 | and then very high level software comments and then that will be future lectures |
|
| 45:21 | well as the algorithms for. And I'll talk a little bit more of |
|
| 45:26 | management that is related to rappel and current assignment that you have so now |
|
| 45:35 | architectures. So again, big data as well, Azaz chipped in and |
|
| 45:45 | like Intel Andy, but also the , in this case slowly. Berkeley |
|
| 45:51 | . It'll be element. So may one of the Department of Energy's national |
|
| 45:58 | . They spent also, like Internet , a lot of money on utility |
|
| 46:04 | infrastructure. And, of course, want to spend your money on the |
|
| 46:10 | part and knocked on infrastructure. So did investigate their codes and that all |
|
| 46:18 | their codes after within MX code and mechanics codes on but increasing also chemistry |
|
| 46:28 | . So what they did, as said on this slide here on this |
|
| 46:33 | a few years back at that time X 36 or instructions that used by |
|
| 46:40 | of interest computer as well as saying , um at the time, about |
|
| 46:47 | instructions. And today it's over 500 , but they discovered, but their |
|
| 46:55 | they would do just fine with 80 them, of course, support for |
|
| 47:00 | other 200 plus instructions it requires Iligan the silicon parked on requires foreign |
|
| 47:09 | So they're basically they thing is to energy efficiency is to avoid waste |
|
| 47:20 | That was, in fact, the that was used by one of the |
|
| 47:24 | famous computer architects and the HPC Seymour Cray, in the sign of |
|
| 47:30 | computers. Wave. Don't introduce anything don't need on this is the |
|
| 47:38 | and I think I may have shown the first lecture that in regards to |
|
| 47:45 | waste on the purplish dragging kervin and , depending on the degree of specialization |
|
| 47:55 | tailoring they were designed thio. The you'll find most important issue can get |
|
| 48:03 | three orders of magnitude more operations per millimeter out of your silicon or being |
|
| 48:12 | it application conscious in the way and terms off energy efficiency and operations for |
|
| 48:21 | there is actually one more order of . So you can in fact it |
|
| 48:29 | four order magnitude or 10,000 times more or operations for what part of the |
|
| 48:36 | design. So this is there's lots potential by specialize in and not using |
|
| 48:45 | general purpose type design, and that's what has been happening. And it |
|
| 48:51 | is happening at the moment some of that are interested in AI in particular |
|
| 48:59 | A I N is driving a lot innovation and computer architecture or chip design |
|
| 49:09 | the level to support. Uh machine learning or deep learning networks. |
|
| 49:16 | part of the things coming back to that showed a couple of slides back |
|
| 49:21 | if you can reduce the data So there's some things with reduce |
|
| 49:26 | safe a lot of energy as well increasing performance. So that's what's goes |
|
| 49:31 | in terms off chip designs for a Dr Jumping. Yes. So I |
|
| 49:37 | there's a very rigorous pro con cost analysis of the degree of specialization that |
|
| 49:44 | like to do, right? So is the role of a I |
|
| 49:49 | to identify what we should and what shouldn't specialize. Or what kind of |
|
| 49:54 | kind of patterns are we trying to when we like, For example, |
|
| 49:57 | know Apple introduce a machine learning and into their hardware as well? |
|
| 50:05 | so so see if I can give the reasonable answer So there is in |
|
| 50:18 | off the computer architecture or the silicon . So first, I think the |
|
| 50:30 | learning community, um, now for number of applications that it has been |
|
| 50:39 | , that which is image understanding or and also, um, speech recognition |
|
| 50:51 | translation has been quite successful application for learning. And in those they have |
|
| 51:00 | that for many parts off the both and in France part, you don't |
|
| 51:12 | very high position. So a lot things can. It's good enough to |
|
| 51:18 | eight or four bit vintages or people even played around one or two |
|
| 51:25 | So in order to support those algorithms applications that use the algorithms that |
|
| 51:35 | um, cost, you know, and Intel and M D now mostly |
|
| 51:46 | off dp used being the ones that was used Because the machine learning algorithms |
|
| 51:55 | highly structured, they use many of are based on convolutions that are not |
|
| 52:01 | dependent. So you can get kind streaming processors on the GP use being |
|
| 52:07 | good, um, vehicle for doing learning. So the wise the companies |
|
| 52:16 | video named Ian Predictor that were, , dominating the DP use for the |
|
| 52:24 | type processors. They introduced, hardware, direct or circles. The |
|
| 52:34 | support 8 16 bits position and I remember. I think they even now |
|
| 52:43 | forbid position, so that allowed them get a lot mawr application performance out |
|
| 52:50 | the same piece of silicon for the power. So that has kind of |
|
| 52:56 | and mhm, um, the industry again and has been a good |
|
| 53:05 | And until also not having deep use for, um, chips for basically |
|
| 53:22 | and laptops that has integrated on the Die GP use. So, in |
|
| 53:29 | , in terms of the total number GP use Intel, it's the largest |
|
| 53:34 | GPU. So even though it doesn't them separately, it all comes on |
|
| 53:40 | of silicon where it's embedded but now tow towards the end of this year |
|
| 53:46 | start to compete with envy and into name D in terms of discreet dp |
|
| 53:53 | . And but it was a long was saying because they were late in |
|
| 53:58 | that, they started also to introduce reduce position. Uh, special circuits |
|
| 54:06 | there kind of serve erred on focused . So I don't know if that |
|
| 54:14 | answer the question. Yeah, I . Okay. Thanks for asking. |
|
| 54:21 | good to help me elaborate on So So this is just the same |
|
| 54:27 | the specialization and where power and energy been prime concern concern that is mostly |
|
| 54:36 | the mobile market. Specialization has always there that they don't use the standard |
|
| 54:45 | CPU to do everything. There is users. They did not sing the |
|
| 54:49 | . There are encryption engines, their engines. So it's the diversity off |
|
| 54:56 | pieces on the same piece of um, now to sort of bigger |
|
| 55:06 | of the concern for energy consumption. I said, the big users like |
|
| 55:16 | Internet companies Google, Facebook and Microsoft Amazon they Goudelock and were the first |
|
| 55:25 | were a bit earlier in terms off things, then Microsoft and more focused |
|
| 55:34 | software for peace is something they started to do cloud computing. But Google |
|
| 55:39 | Randall data centers. The first thing did was to design their own servers |
|
| 55:44 | they didn't think the server they could from IBM, HP, Dell, |
|
| 55:50 | company where. Na enough off energy power conscious. So they started to |
|
| 55:58 | their own servers, and a few later, Facebook got to the same |
|
| 56:05 | . They also started to design their servers, and Facebook came and started |
|
| 56:12 | consortium, known as Open Compute where published our designs that are more energy |
|
| 56:19 | than what platform and is used to . Of course, Google and Facebook |
|
| 56:24 | are sufficiently large customers. They don't to go to a karaoke shop to |
|
| 56:30 | their stuff built to just tell HP Dell and IBM what they want, |
|
| 56:34 | they get it good for them. it's just to point out that these |
|
| 56:40 | that run very large data centers and giant electricity bill that I mentioned before |
|
| 56:47 | took things in their own hands. they started by this during the signs |
|
| 56:54 | this survey level. Okay, And , after having done that for a |
|
| 57:01 | years, they got more ambitious because , the silicon wasn't really up thio |
|
| 57:09 | power and energy standards that they So Google, as some of you |
|
| 57:16 | , that they're interested in machine learning no over there tensor processing unit that |
|
| 57:21 | went off to design and they're now the third generation on. They're tp |
|
| 57:28 | . They don't sell them something, they use them in their data centers |
|
| 57:34 | they part of their motivation for doing and concrete terms us that I remember |
|
| 57:46 | was they needed to more than double size of their data centers if they |
|
| 57:52 | continue as the distance as usual. it's a substantial element in, |
|
| 58:02 | their strategy, and I'm sure they continue to an asset. And then |
|
| 58:10 | wasn't quite as ambitious in the sense they did not quite designed their own |
|
| 58:16 | . But they use this field programmable arrays to, uh, implements support |
|
| 58:22 | some other search engines in and also terms of some other image and is |
|
| 58:30 | that they support on their cloud. they went after again, standard processes |
|
| 58:36 | measure up in terms of performance and and power. So they took |
|
| 58:41 | the situation in their own hands. this was just another example that I |
|
| 58:48 | before in terms of this vision processing that also ended up being used for |
|
| 58:54 | learning and, um, movie. was an independent company bought by |
|
| 59:00 | And then they put this in this Compute Sticks that you can now buy |
|
| 59:06 | about 100 bucks and has a used attachment. And, um, I |
|
| 59:15 | ended. Yet another design that is necessary are being too, knows that |
|
| 59:22 | is smaller than in a row more computing time to make it these air |
|
| 59:28 | example. To show that the big with sufficient resources, they said business |
|
| 59:35 | usual doesn't work. And a lot the driving part is the power and |
|
| 59:41 | consumption where the standardized design and I I should answer. There was another |
|
| 59:48 | of the question that comes back to now is that because of the design |
|
| 59:53 | has improved, it also means that volume or chips that you need to |
|
| 60:05 | in order to obey, make some these Mawr application specific designs. Payoff |
|
| 60:12 | smaller than it used to be, with two or three orders of magnitude |
|
| 60:19 | performance and are gain. The business is kind of there for doing, |
|
| 60:28 | , some more specialized design. So why there is kind of now the |
|
| 60:34 | of proliferation. Off chip designs are feasible. Where is from about 19 |
|
| 60:44 | to 90? Until a few years or 10 years ago, the sort |
|
| 60:52 | convergence happen because again the cost off business, you needed a high |
|
| 60:58 | and that's why you know into, others introduced more and more features on |
|
| 61:03 | tips to be able to support a and bigger market and get more sort |
|
| 61:10 | revenue in money to support to chip . So but at the time when |
|
| 61:17 | scaling work that work. But once this the North scaling stopped working, |
|
| 61:24 | economic rules changed as well as the change improve. And this was the |
|
| 61:31 | thing I talked about this in terms the memory park today. That's also |
|
| 61:36 | energy by the tighter integration of memory , um, the processing part. |
|
| 61:42 | now, through comments about software, comments, and we'll talk much more |
|
| 61:48 | issues about software and remaining part of course. But this is, I |
|
| 61:56 | , the preamble to the next few , more so than the rest of |
|
| 62:01 | that, um, shows the huge and performance in this case. That |
|
| 62:17 | the time for doing it, so doesn't reflect the energy. But energy |
|
| 62:22 | not proportional to the computing part. will talk about, I guess, |
|
| 62:26 | the end of the lecture, I , but that's basically shows that by |
|
| 62:31 | is a good thing. In terms programmer productivity. I think most people |
|
| 62:37 | on that. But if not everybody on the efficiency in terms of performance |
|
| 62:48 | energy. When it comes to product , though some advocates things, it's |
|
| 62:51 | that bad. But as you can here, there's kind of four orders |
|
| 62:58 | magnitude and mawr between and a fairly , piped in cold and highly optimized |
|
| 63:05 | . When it comes to this particular , that is something that benefits high |
|
| 63:12 | of optimization, and it's not too to do the optimization for that. |
|
| 63:17 | you write your program and what languages um, in itself is a big |
|
| 63:24 | . So if one is interested in , one need to think twice or |
|
| 63:31 | times if they don't want to move fighting. But we'll talk about the |
|
| 63:38 | techniques, starting with kind of vanilla code and the addressing higher improve that |
|
| 63:45 | coming lectures. Now a little bit about the power part, I |
|
| 63:53 | First I show a couple of just thio, make everybody ever the |
|
| 63:58 | off sort of the big picture and talking a bit about measurement, but |
|
| 64:04 | talked about how you can control the and energy consumption. Um, from |
|
| 64:12 | hardware and software, not algorithmic point view that that will talk about |
|
| 64:16 | So here is kind of a typical in a day doesn't and not necessary |
|
| 64:22 | your own personal computer. But it , um, So this picture is |
|
| 64:27 | from a Facebook presentation, and in case, it's serious power coming into |
|
| 64:35 | data centers of this is a fairly one words 30 megawatts, and that's |
|
| 64:44 | to several 1000 households. Tens of of households in your small town. |
|
| 64:50 | , that's the big data center is to in terms of power. But |
|
| 64:55 | , so this is at the various in this part distribution getting in from |
|
| 65:01 | power grade down to the service at bottom. There are several points where |
|
| 65:06 | gets quote unquote transformed from high voltage the power grids. Teoh sort of |
|
| 65:15 | nish molds, uh, the chip and it is each of these |
|
| 65:23 | There tends to be both control points certainly measurement points for, um, |
|
| 65:30 | our energy. Um, consumption here kind of dropping down to once you |
|
| 65:37 | onto the circuit board and then onto chip. So and I'll talk more |
|
| 65:41 | that is just to give you the and rappel. As you know, |
|
| 65:47 | no. But mention it is at chip level soul. We don't quite |
|
| 65:54 | access Thio the other levels, our measurements unfortunately, systems that miss don't |
|
| 66:01 | Thio make those accessible for, I , security reasons. But maybe someday |
|
| 66:08 | will figure it out. I need face where Lincoln also get interesting parks |
|
| 66:15 | both survey level of board level and control application level power consumption. So |
|
| 66:26 | is a little bit off said there devices where levels of position, |
|
| 66:35 | the I was Iraq role level that called Khar distribution units. There are |
|
| 66:44 | taking something that is so, 400 goals are up or maybe sometimes |
|
| 66:55 | on down to something that individual service handle. That is, sometimes it's |
|
| 67:01 | volts. Sometimes it is 27 in US and you can see the sampling |
|
| 67:09 | is not all that time for a seconds. And the accuracy is not |
|
| 67:15 | in terms of absolute what but on other hand, is quite if you |
|
| 67:20 | going through Iraq tends to be. track may be in the order of |
|
| 67:25 | to 100 kilowatts today. So one is not an unreasonable relative set to |
|
| 67:33 | accuracy. Then, of course, have water, meters and other |
|
| 67:38 | And as I mentioned at the board , there are something called the intelligent |
|
| 67:43 | management interface that is in every And if you have your own |
|
| 67:48 | you should be able to get access it. Then if you're interested, |
|
| 67:52 | , information about fan power and board and a bunch of other things that |
|
| 67:59 | outside the chip. Um, then are things even power strips that they |
|
| 68:05 | use have. Sometimes some of them better ones. If you like their |
|
| 68:13 | to also report, uh, current both the tragedies and power values at |
|
| 68:22 | chip level, there is rappel in are using for your current assignment. |
|
| 68:30 | as I mentioned, the sampling rate about one hurt. Yes, one |
|
| 68:37 | . Not so sorry. I was , one millisecond 1000 samples per |
|
| 68:46 | So it was actually until was head A and E. And introducing |
|
| 68:54 | And as Josh mentioned last time and talked briefly or limited as it was |
|
| 69:00 | too manage part consumption in the data . So the L is limits, |
|
| 69:07 | it basically has political running average power . So it has a window of |
|
| 69:13 | for which, and determines the average of consumption. And then it has |
|
| 69:19 | to figure out whether you have room dissipate, more power or if it |
|
| 69:30 | does forecasting and for what's going to in the next window, since there's |
|
| 69:35 | inertia in the system. So it's sophisticated control, but it can be |
|
| 69:43 | in America. Is Thio get some what the power consumption is? It's |
|
| 69:49 | a little bit of helping getting insights but by now, and they also |
|
| 69:56 | the same kind of features for their . And indeed, A has also |
|
| 70:01 | correspondent things for their GPS. And side is I think I'm pretty much |
|
| 70:10 | yes. So update frequency. And one point is also the resolution. |
|
| 70:16 | terms of power on there has been time we did the confusion. It |
|
| 70:21 | still be, but most sources The resolution is about 15 micro channels |
|
| 70:29 | terms off the descriptive station that happens wrap up. It's unfortunately very hard |
|
| 70:38 | find exactly where this is well So it's a victim, an |
|
| 70:46 | but it's others don't claim all that numbers. So it's, uh it's |
|
| 70:54 | good, uh, things to keep mind both the time resolution and the |
|
| 70:59 | optimization in terms off resolution and Then it can Onley monitor limited |
|
| 71:13 | And that's what's known as the which is the whole CPU packages kind |
|
| 71:22 | . Um, sensible thing is kind want the thing that you plug into |
|
| 71:26 | on the circuit courts. It's kind the whole thing, the whole |
|
| 71:30 | And then there's a couple of different off power domains and one ISS, |
|
| 71:38 | PP. Zero. That is of course, and then it's the |
|
| 71:44 | of what is on the diet that Inter calls Encore, but it depends |
|
| 71:52 | what they intended. Use of the is whether that is the feature you |
|
| 71:59 | get or if it's used for something . So it's basically three things you |
|
| 72:07 | get up. You can get the , you can get all the course |
|
| 72:11 | , not individual course, and then can get another thing either the memory |
|
| 72:17 | the encore and the next slide just . They tried to point out, |
|
| 72:22 | know, packages the whole thing pp is just the core and associating |
|
| 72:29 | And then the third option is either and you cannot choose it comes be |
|
| 72:36 | by the chip. You're actually using now? How do you control |
|
| 72:44 | I guess. Any questions on Okay, so next is how do |
|
| 72:55 | actually control and manage the power? we'll cover that until the time is |
|
| 73:02 | on dso way back Google again. I said, this were the first |
|
| 73:08 | the start to design their own They were not happy with what they |
|
| 73:11 | die. So and part of it they were pushing for what they call |
|
| 73:18 | proportion. Computing on the left dish here shows the typical work told pattern |
|
| 73:27 | gold. Oh, that Yes, . Hi. Ticks And those so |
|
| 73:35 | by no moans means uniforms. So that case, uh, having energy |
|
| 73:44 | computing could save them a lot of . So the upper right kind of |
|
| 73:49 | shows that the park consumption is very related thio the energy consumption it only |
|
| 73:56 | if they worked and went down to . You still have more half of |
|
| 74:00 | power. Morning. So what do do to control it? So there |
|
| 74:06 | two things that concept that you want to be familiar with, And that's |
|
| 74:10 | gating and complicating for kind of controlling first level or group force level kind |
|
| 74:20 | control. And I'll talk a little more about that. Then there is |
|
| 74:24 | bit more refined control that is known D. V S s for short |
|
| 74:28 | voltage and frequency scaling. And in to make some order in chaos, |
|
| 74:35 | is actually standard for doing this. is for short, known as a |
|
| 74:39 | P. I on Don't try to those in the last few minutes |
|
| 74:45 | So the thing is that in the of go down old days, all |
|
| 74:52 | conversions was done off chip and it just a single feet apart for all |
|
| 74:57 | pieces on the chip. However, 15 to 20 years ago, want |
|
| 75:05 | out how to also do part of on the chips and that enable to |
|
| 75:13 | separate part domains on the chip. today, as a minimum, each |
|
| 75:20 | has its own partner made. And there tend to be several own |
|
| 75:24 | for they caught up quote unquote encore chips also has. So those are |
|
| 75:33 | that can be individually control in terms voltage and on and off. And |
|
| 75:38 | is being used. Ah, and fact, that's built picture just |
|
| 75:45 | illustrated in order to do that's. , the chips have separate processors on |
|
| 75:50 | diet that actually does it power management the chip. And that's why, |
|
| 75:56 | instance, you can very well get performance when you do benchmarking because there |
|
| 76:02 | is independent controller that managers clock frequencies power to the chip in order to |
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| 76:11 | the chip safe. And it may be controlled with whatever power limits systems |
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| 76:17 | have set for maximum participation at the level. And I may not get |
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| 76:24 | it in this lecture. But at end of this slide deck, there |
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| 76:28 | a case study from Facebook that you find interesting in how they actually managing |
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| 76:34 | power consumption down to the chip There is just a picture of the |
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| 76:41 | off trying to manage part consumptions from of an old IBM processor on the |
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| 76:48 | side, things not using any form power management and things that kind of |
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| 76:53 | compared toa the dark things on the . I will skip this side at |
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| 77:01 | moment, running out of time. , I encourage you to look at |
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| 77:03 | . It's fairly self explanatory, showing the things that are constant, independent |
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| 77:11 | how Maney course are on and how and what power increases with the number |
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| 77:19 | ships. That is our course that on on the particular chip, and |
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| 77:23 | a couple of different benchmarks. Some them are compute intensive and somewhere |
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| 77:29 | But let me talk about this and it comes back to the square |
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| 77:33 | and again that the point is that can potentially reduce clock frequency without correspondingly |
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| 77:43 | the performance so you can gain energy without losing too much performance. Producing |
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| 77:53 | , uh, dynamic voltage and frequency and here is just an example for |
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| 78:01 | particular set of benchmarks known as the benchmarks. But there's an old processor |
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| 78:09 | now, but it shows a little in terms of the percentage gains and |
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| 78:14 | in terms of performance and energy, I encourage you to take a look |
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| 78:18 | it. But here's a little What actually happens under Iraq and like |
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| 78:25 | skylight processor, using stamping, it shows kind of two different scenarios |
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| 78:31 | how things are controlled by farmer in processors. Start is the red dotted |
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| 78:38 | that goes upwards toward the right, that basically shows the participation, |
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| 78:45 | a za function of the clock frequency the chip that you can control for |
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| 78:50 | firmware controls. There's a little bit trickery foreign uses to control it, |
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| 78:55 | it can be done but typically is by these control processor on the |
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| 79:03 | There are other tips that the dash line that goes down is that still |
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| 79:09 | , Thio says. For a an that is CPU limited. Um, |
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| 79:20 | means the faster you run it, less time it takes. And in |
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| 79:24 | case, you may actually save even though you've learned more power because |
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| 79:29 | time gets produced mawr than the power out. So that's known as the |
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| 79:35 | to the whole strategy, and that's way many of these controllers work, |
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| 79:41 | tried to maximize call frequency, to reduce time and minimize energy. |
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| 79:47 | the other hand, if it is , then with limited or then even |
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| 79:55 | you raised a buck frequent on the , you don't necessarily reduce the execution |
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| 80:02 | . And that means you burn a more power without gaining production in |
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| 80:07 | And then the energy consumption goes So what? This algorithm that is |
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| 80:13 | in the sky like processes does is to find the optimum point based on |
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| 80:19 | sampling off various registers in the process during around time, and find the |
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| 80:25 | spot in terms off car frequency off CPU. And I guess at this |
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| 80:33 | , my time is up, so I'll cover a few more slides at |
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| 80:37 | beginning of next lecture. But I stop since my time is up and |
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| 80:42 | if there's any questions on this Okay, so if not, I |
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| 81:02 | spend a little bit of time talk me about these Control works in terms |
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| 81:10 | frequency control. So we're probably talking 10 15 minutes in the beginning of |
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| 81:16 | lecture, and then I'll talking about empty next time |
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