In a typical computer system, is it possible to manually change the CPU cycle counter to a specific value? The most obvious method would be to check the counter value and then run NOP or other redundant instructions until the value is as desired, but if the required value is a long distance from the current one this may take an infeasible amount of time - I am looking for something more realistic.
I doubt most architectures would contain an instruction for doing this, but (perhaps because the answer is obvious) I can't find a clear answer elsewhere.
Related
I want my RL agent to reach the goal as quickly as possible and at the same time to minimize the number of times it uses a specific resource T (which sometimes though is necessary).
I thought of setting up the immediate rewards as -1 per step, an additional -1 if the agent uses T and 0 if it reaches the goal.
But the additional -1 is completely arbitrary, how do I decide how much punishment should the agent get for using T?
You should use a reward function which mimics your own values. If the resource is expensive (valuable to you), then the punishment for consuming it should be harsh. The same thing goes for time (which is also a resource if you think about it).
If the ratio between the two punishments (the one for time consumption and the one for resource consumption) is in accordance to how you value these resources, then the agent will act precisely in your interest. If you get it wrong (because maybe you don't know the precise cost of the resource nor the precise cost of slow learning), then it will strive for a pseudo optimal solution rather than an optimal one, which in a lot of cases is okay.
The question is obvious like specified in the title. I wonder this. Any expert can help?
OK, this is was going to be a long answer, so long that I may write an article about it instead. Strangely enough, I've been working on experiments that are closely related to your question -- determining performance per watt for a modern processor. As Paul and Sneftel indicated, it's not really possible with any real architecture today. You can probably compute this if you are looking at only the execution of that instruction given a certain silicon technology and a certain ALU design through calculating gate leakage and switching currents, voltages, etc. But that isn't a useful value because there is something always going on (from a HW perspective) in any processor newer than an 8086, and instructions haven't been executed in isolation since a pipeline first came into being.
Today, we have multi-function ALUs, out-of-order execution, multiple pipelines, hyperthreading, branch prediction, memory hierarchies, etc. What does this have to do with the execution of one ADD command? The energy used to execute one ADD command is different from the execution of multiple ADD commands. And if you wrap a program around it, then it gets really complicated.
SORT-OF-AN-ANSWER:
So let's look at what you can do.
Statistically measure running a given add over and over again. Remember that there are many different types of adds such as integer adds, floating-point, double precision, adds with carries, and even simultaneous adds (SIMD) to name a few. Limits: OSs and other apps are always there, though you may be able to run on bare metal if you know how; varies with different hardware, silicon technologies, architecture, etc; probably not useful because it is so far from reality that it means little; limits of measurement equipment (using interprocessor PMUs, from the wall meters, interposer socket, etc); memory hierarchy; and more
Statistically measuring an integer/floating-point/double -based workload kernel. This is beginning to have some meaning because it means something to the community. Limits: Still not real; still varies with architecture, silicon technology, hardware, etc; measuring equipment limits; etc
Statistically measuring a real application. Limits: same as above but it at least means something to the community; power states come into play during periods of idle; potentially cluster issues come into play.
When I say "Limits", that just means you need to well define the constraints of your answer / experiment, not that it isn't useful.
SUMMARY: it is possible to come up with a value for one add but it doesn't really mean anything anymore. A value that means anything is way more complicated but is useful and requires a lot of work to find.
By the way, I do think it is a good and important question -- in part because it is so deceptively simple.
I'm currently studying dynamic programming solutions to Markov Decision Processes. I feel like I've got a decent grip on VI and PI and the motivation for PI is pretty clear to me (converging on the correct state utilities seems like unnecessary work when all we need is the correct policy). However, none of my experiments show PI in a favourable light in terms of runtime. It seems to consistently take longer regardless of the size of the state space and discount factor.
This could be due the implementation (I'm using the BURLAP library), or poor experimentation on my part. However, even the trends don't seem to show a benefit. It should be noted that the BURLAP implementation of PI is actually "modified policy iteration" which runs a limited VI variant at each iteration. My question to you is do you know of any situations, theoretical or practical, in which (modified) PI should outperform VI?
Turns out that Policy Iteration, specifically Modified Policy Iteration, can outperform Value Iteration when the discount factor (gamma) is very high.
http://www.cs.cmu.edu/afs/cs/project/jair/pub/volume4/kaelbling96a.pdf
I have a project where I am asked to develop an application to simulate how different page replacement algorithms perform (with varying working set size and stability period). My results:
Vertical axis: page faults
Horizontal axis: working set size
Depth axis: stable period
Are my results reasonable? I expected LRU to have better results than FIFO. Here, they are approximately the same.
For random, stability period and working set size doesnt seem to affect the performance at all? I expected similar graphs as FIFO & LRU just worst performance? If the reference string is highly stable (little branches) and have a small working set size, it should still have less page faults that an application with many branches and big working set size?
More Info
My Python Code | The Project Question
Length of reference string (RS): 200,000
Size of virtual memory (P): 1000
Size of main memory (F): 100
number of time page referenced (m): 100
Size of working set (e): 2 - 100
Stability (t): 0 - 1
Working set size (e) & stable period (t) affects how reference string are generated.
|-----------|--------|------------------------------------|
0 p p+e P-1
So assume the above the the virtual memory of size P. To generate reference strings, the following algorithm is used:
Repeat until reference string generated
pick m numbers in [p, p+e]. m simulates or refers to number of times page is referenced
pick random number, 0 <= r < 1
if r < t
generate new p
else (++p)%P
UPDATE (In response to #MrGomez's answer)
However, recall how you seeded your input data: using random.random,
thus giving you a uniform distribution of data with your controllable
level of entropy. Because of this, all values are equally likely to
occur, and because you've constructed this in floating point space,
recurrences are highly improbable.
I am using random, but it is not totally random either, references are generated with some locality though the use of working set size and number page referenced parameters?
I tried increasing the numPageReferenced relative with numFrames in hope that it will reference a page currently in memory more, thus showing the performance benefit of LRU over FIFO, but that didn't give me a clear result tho. Just FYI, I tried the same app with the following parameters (Pages/Frames ratio is still kept the same, I reduced the size of data to make things faster).
--numReferences 1000 --numPages 100 --numFrames 10 --numPageReferenced 20
The result is
Still not such a big difference. Am I right to say if I increase numPageReferenced relative to numFrames, LRU should have a better performance as it is referencing pages in memory more? Or perhaps I am mis-understanding something?
For random, I am thinking along the lines of:
Suppose theres high stability and small working set. It means that the pages referenced are very likely to be in memory. So the need for the page replacement algorithm to run is lower?
Hmm maybe I got to think about this more :)
UPDATE: Trashing less obvious on lower stablity
Here, I am trying to show the trashing as working set size exceeds the number of frames (100) in memory. However, notice thrashing appears less obvious with lower stability (high t), why might that be? Is the explanation that as stability becomes low, page faults approaches maximum thus it does not matter as much what the working set size is?
These results are reasonable given your current implementation. The rationale behind that, however, bears some discussion.
When considering algorithms in general, it's most important to consider the properties of the algorithms currently under inspection. Specifically, note their corner cases and best and worst case conditions. You're probably already familiar with this terse method of evaluation, so this is mostly for the benefit of those reading here whom may not have an algorithmic background.
Let's break your question down by algorithm and explore their component properties in context:
FIFO shows an increase in page faults as the size of your working set (length axis) increases.
This is correct behavior, consistent with Bélády's anomaly for FIFO replacement. As the size of your working page set increases, the number of page faults should also increase.
FIFO shows an increase in page faults as system stability (1 - depth axis) decreases.
Noting your algorithm for seeding stability (if random.random() < stability), your results become less stable as stability (S) approaches 1. As you sharply increase the entropy in your data, the number of page faults, too, sharply increases and propagates the Bélády's anomaly.
So far, so good.
LRU shows consistency with FIFO. Why?
Note your seeding algorithm. Standard LRU is most optimal when you have paging requests that are structured to smaller operational frames. For ordered, predictable lookups, it improves upon FIFO by aging off results that no longer exist in the current execution frame, which is a very useful property for staged execution and encapsulated, modal operation. Again, so far, so good.
However, recall how you seeded your input data: using random.random, thus giving you a uniform distribution of data with your controllable level of entropy. Because of this, all values are equally likely to occur, and because you've constructed this in floating point space, recurrences are highly improbable.
As a result, your LRU is perceiving each element to occur a small number of times, then to be completely discarded when the next value was calculated. It thus correctly pages each value as it falls out of the window, giving you performance exactly comparable to FIFO. If your system properly accounted for recurrence or a compressed character space, you would see markedly different results.
For random, stability period and working set size doesn't seem to affect the performance at all. Why are we seeing this scribble all over the graph instead of giving us a relatively smooth manifold?
In the case of a random paging scheme, you age off each entry stochastically. Purportedly, this should give us some form of a manifold bound to the entropy and size of our working set... right?
Or should it? For each set of entries, you randomly assign a subset to page out as a function of time. This should give relatively even paging performance, regardless of stability and regardless of your working set, as long as your access profile is again uniformly random.
So, based on the conditions you are checking, this is entirely correct behavior consistent with what we'd expect. You get an even paging performance that doesn't degrade with other factors (but, conversely, isn't improved by them) that's suitable for high load, efficient operation. Not bad, just not what you might intuitively expect.
So, in a nutshell, that's the breakdown as your project is currently implemented.
As an exercise in further exploring the properties of these algorithms in the context of different dispositions and distributions of input data, I highly recommend digging into scipy.stats to see what, for example, a Gaussian or logistic distribution might do to each graph. Then, I would come back to the documented expectations of each algorithm and draft cases where each is uniquely most and least appropriate.
All in all, I think your teacher will be proud. :)
My question is specific to iPhone, iPod, and iPad, since I am assuming that the architecture makes a big difference. I'm hoping there is either a specification somewhere (for the various chips perhaps), or a reliable way to measure T for each specific instruction. I know I can use any number of tools to measure aggregate processor time used, memory used, etc. I want to quantify at a lower level.
So, I'm able to figure out how many times I go through the main part of the algorithm. For example, I iterate n * (n-1) times in a naive implementation, and between n (best case) and n + n * (n-1) (worst case) in another. I can also make a reasonable count of the total number of instructions (+ - = % * /, and logic statements), and I can compare those counts, but that's assuming the weight of each operation is the same. Also, I don't have any idea how to weight the actual time value of a logic statement (if, else, for, while) vs a mathematical operator... is "if" as much work as "+" each time I use it? I would love to know where to find this information.
So, for clarity, my goal is to discover how much processor time I am demanding of the CPU (or GPU or any U) so that I can design an optimal algorithm around processor time. Can someone give me an idea of where to start for iOS hardware?
Edit: This link to ClockServices.c and SIMD stuff in the developer portal might be a good start for people interested in this. A few more cups of coffee tonight and I might get through it ;)
On a modern platform, processor time isn't the only limiting factor. Often, memory access is.
Still, processor time:
Your basic approach at an estimation for the processor load is OK, though, and is sensible: Make a rough estimate of the cost based on your knowledge of typical platforms.
In this article, Table 1 shows the times for typical primitive operations in .NET. While your platform may vary, the relative time is usually very similar. Maybe you can find - or even make - one for iStuff.
(I haven't come across one so thorough for other platforms, except processor / instruction set manuals, but they deal with assembly instructions)
memory locality:
A cache miss can cost you hundreds of cycles, a disk access a thousand times as much. So controlling your memory access patterns (i.e. reducing the working set, restructuring and accessing data in a cache-friendly way) is an important part of evaluating an algorithm.
xCode has instruments to measure performance of each function/operation, you can simply use them.