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Contents

Course Introduction

Hello, and welcome to this review course, which is a prep for my graduate course on operating systems. When I teach graduate students on campus at Georgia Tech, I often find that there's a gap between the knowledge they have of operating systems at the start of the course and what they really should know in order to get the full benefit of my graduate class. This is not being judgmental. But it is just that, not all undergraduate operating systems courses are the same. And you may have taken a course on undergraduate operating systems a long time back. Or maybe you were not that enthusiastic about operating systems at the time that you took the course. This review course is not meant to be a substitute for an undergraduate education in systems. Rather, it cover the topics many students have expressed that they wished they had it before starting to take my class. Helping me with this review course is Charles Brubaker, a PhD graduate from Georgia Tech, now turned into a course developer for Udacity. Hi there. With this course, I'll try to give you concise explanations that will quickly put you into a better position. To fully understand the vectors and complete the projects of the advanced operating systems class. With these goals, let's get started.

Introduction

The most important resources in a computer are space and time. Space in memory for storage, and time on central processing unit for computation. We may tend to think about these things separately, but there are important interactions between the two. And just as understanding the relationship between space and time is important for any good physicist. Understanding the relationship between efficient use of memory and then the CPU, is important for any good program. This interaction will be the subject of this lesson, as we look at cache systems and that all important abstraction of virtual memory.

Naive Memory Model

In your first programming class, computer memory may have been explained to you with a picture that looks something like this. We have the CPU, where your instructions get executed, and these instructions may read or write to either main Memory, or to Disk. Main memory is Fast, and you can access any element in the same amount of time. That's what we mean by Random Access. And it is Temporary in the sense that when the program exits or if power is lost, all the information stored in it disappears. The hard disk, by contrast, is slow. It uses Sequential Access since you have to actually spin the disk to the right place. And what you write to the disk is permanent. It will still be there when the program exits or if power is lost. In this lecture, we're going to refine this picture in two ways. First, we'll look at Cache Systems, which allow the CPU to access the same information that is in main memory, only faster. Understanding how cache systems work will help you optimize your code when you need to. Second, we will explain the Virtual Memory system. As you write your application and compiler compiles it to generate addresses for all your variables and your code, you don't have to worry about other programs and what memory addresses they might be using. In fact there's often an illusion that having even more main memory then exists in the system, and that your application has them all to yourself. W'll see how the operating system maintains this abstraction to the virtual memory system. The details are essential to understanding operating systems optimizations. And how the need to share resources affects program performance.

Cache Motivation

To help us see the need for caches, we'll examine this little snippet of code. From an application programmer's perspective, a statement like this one, the sum plus equals a of i, would seem to happen in one step. Even in assembly, it would only take a few instructions. In terms of time on the clock, however, not all of these instructions are the same. Sum, being a local variable, is most likely stored in a register in the CPU, therefore there is almost no cost to retrieving its value. a of i, however, is in main memory, and retrieving its value can take 100 CPU cycles. And even then, the bus bandwidth might only be able to pass back two bytes a cycle or thereabouts, to get the data back. Trips to main memory are expensive, and this trend has only become worse over the past few decades with hardware advances. The solution to this problem has been to place a smaller, faster set of memory made with faster technology, closer to the CPU. We call this memory a cache. And here, we're looking at a latency of about ten cycles. So, when the CPU wants the contents of some memory address, it looks in the cache first. If it finds the data it needs, great, we've just achieved a factor of ten speedups. We call this a cache hit. If the data it wants is not in the cache then we have to go to main memory. We call this a cache miss. The key is keeping these cache meshes infrequent, so that on average, time spent accessing is more like the time it takes to access the cache, than it is like the time to access main memory.

Data Costs

To illustrate the power of the cache, as well as the importance of high hit rates. We'll do a few calculations in the form of a question. Suppose that retrieving data costs 4 cycles on a cache hit, but 100 cycles on a cache miss. Then how many cycles does it process with a 99% hit rate, spend on average? And then we want to compare that to one with only a 90% hit rate.

Data Costs

For the first calculation, we have that 99% of the time it only costs four cycles, and 1% of the time it costs 100 cycles. For a total of 4.96. And for the second, we have that of 13.6. This may be a little bit counterintuitive to see that a relatively small change in the percentage can have such a dramatic change in the speed. And the key is to think about the fact that it's actually really the miss rate that matters here. We're improving it by a factor of ten, with having a 99% hit rate.

Memory Hierarchy

Probably the most important consideration in cache design is the trade off between speed and capacity. To help understand the impact of this trade off, I'd like to visualize requests from the CPU to Main Memory like this, where the orange lines represent the requests to the CPU. We would like the cache hit rate to be high and the speed to be fast. These goals, however, are somewhat contradictory. We can have a small but fast cache and just accept that this would have a low hit rate, being only able to intercept quickly a few of the requests from the CPU. Or we could have a large cache, but this would be slow there. Either because the physical limitations like the speed of light, or because of the high cost of fast hardware. So we intercept more requests from the CPU. But, we aren't able to return them as quickly. What is the right trade off? Well, it's hard to say. But, fortunately we don't have to make just one choice. We can trade off side versus speed multiple times at various levels within something called the cache hierarchy. What is not in the CPU registers, we look for in an L1 cache. What's not in an L1 cache, we look in the L2 cache. A multicore processors, there might be even a third level of cache. What's not there, finally we look for in main memory. Even main memory, however, we can think of as a cache for what is on disk. Or we can also think about maybe main memory as a cache for what's on the file system. Notice here that the top is smaller, faster and costlier per byte. And as we go down the hierarchy, we get things that are bigger, slower and cheaper per byte. And if we do a good job of keeping the data that we're going to access next in the higher levels of the hierarchy. That is, if we can keep our hit rates high, then making at the speed of the top part of the pyramid that has the capacity in the overall cost per byte of the lower end of the pyramid.

Locality and Cache Blocks

As we've seen, in order for a cache to be effective the hit rate must be high. That is, we need to be able to anticipate what data the process will need next. Ideally, we would be able to look ahead in the code and plan ahead, but so far this has proved impractical. Instead ,we used the heuristic of locality. That is ,we assume that if an application accesses one memory address, then it will need nearby addresses soon. Sort of like, how a psychologist says that the best predictor of future behavior is past behavior. Experts like to distinguish ,two types of locality. Temporal and spacial. Temporal refers to the tendency to refer to the same memory close and time. The spacial, refers to the tendency to access memory that is close together in terms of address. Typical cache policies exploit both kinds. It exploits temporal locality by putting the data in the cache right after you use it, thinking that you're likely to use it again soon. It exploits spatial by putting not just the memory address that you access, but putting the whole block into the cache. Blocks, I should explain, are a division of memory by relatively small amounts, often 64 bytes. This one block is from zero to 64. Another from 64 to 128, etcetera. If we access the memory location, 87. Then we reason that we are likely to use addresses close to this one. And so ,we put the whole block, from 64 to 128, in the cache. Now, you may ask yourself, why do we put the block of memory into the cache instead of something more consistent? Say, maybe, the previous 32 bytes, and the next 31 bytes, or something like that. After all with blocks, sometimes most of the data we pull in will be higher in the address space, and sometimes most of it will be lower. Well the answer is that, it makes it much easier to figure out what is in the cache and where. The size of the cache block is always a power of two, so we can read which cache block we belong to just by looking at the higher-order bits. The lower-order bits are called the offset And tell us where within a given cache block the data we want is.

Direct Mapping

Next we turn to the problem of mapping. That is given an address, how do I find out whether the data is in the cache, and how do I retrieve it? We'll start with a direct mapped cache and a little notation. Let's suppose that we have two to the m addresses that our cache block or cache line is two to the n bytes. And that our cache has space for two decay entries. All of these are always the power of two. With these definitions, we'll call the lowest n bits the offset. They tell us where within a given cache block, the memory we want, is. And the rest of the bits, tell us the block number. But how do we know where to look for this block in the cache? We need some kind of hashing function. Well, the easiest hashing function just looks at the lower order bits and that is exactly what a direct mapping does. The next k bit's the address tells the right index to look for our data in, in the cache. Of course, this means that multiple addresses will get hashed to the same location within the cache. Given that our cache had to be small, this was inevitable. But we need a way to distinguish them. The solution is to use the tag, or the higher order bit, to the address as a kind of confirmation. Let's do a quick example. Suppose that we have an m bit address space. And our cache block is two bytes long, so we just have one bit for the offset, and that there are four entries in our cache. So we want two bits for our index. Then a direct mapping would look something like this, where all the blue addresses would get mapped to the blue block of the cache. The green addresses would get mapped to the green, and so forth. We can tell which of the color blocks is actually in the cache by consulting the tag associated with the data in the cache. In this example, the tag for the blue is zero, because it's the 0th blue block that's in the cache. Similarly, the tag for the green block is one. Because it's the oneth green block that's in the cache and the same principle holds for all the other colors, as well.

Fill in the Table

Okay. So let's do, quick exercise here. Suppose a 5 bit address space and the cache contents, given in this table here. Fill in this table, for each address, indicate whether it's a hit or miss in the cache, and if it's hit, provide the value, provided by the cache.

Fill in the Table

Okay, here are the answers that I came up with, let's go over this together. As in our example we have one bit for the offset, and then the next two are the index. So this here, I'm going to look at these two bits, see index 00, and then go over and look at the cache. I see there that the tag is 0 1, and oh that does not match my 1 0 tag of the part of this address here, so that's a miss. For the next one again I begin by consulting the index, that's 11, so I go over here, and I find that the tags part of my address and of the cache match. So that looks like a hit. Which of these two's values is it? Well, for that I'd look at the offset, and I'd see that it's the second one. So I write the value 99. For the third one, again, the index is here, 1 0. I go and look at that in my table. I see I have a tag,1 0, and oh, that matches the tag part of this address. So it's another hit. Which of these two values is it? Well I go look at the offset, that's zero, so it's this first one, 5 7. And lastly, again we'll start by looking at the index That's one one, and up, the tags do not match, so that's a miss.

How Many Bits

Okay, here's another question. Suppose a 22 bit address space, a 512 byte cache, and a cache block size of 64 bytes. And I want you to tell me how many bits are used for the index, and how many bits are used for the tag.

How Many Bits

Alright? Here are my calculations. I saw that we had So, how many entries could there be? Well, we just do the division. We find there are eight. So, that's three bits worth of index. And then to calculate how many bits are used for the tag. I start out with all 22 bits. I remember that three are used for the index, and since we have 64 byte cache lines, I say that there are six used for the offset, and that leaves me with 13 left over.

Set Associateive Mapping

It's possible to get unlucky using direct mapped caches, in that different blocks that are important to your application might get mapped to the same index in the cache. For instance, if an application happens to access two cache lines that have the same index, maybe this one and this one here, then they will constantly be evicting each other from the cache. And it, it will be essentially useless. This, of course, is rather silly given that there are all these other entries in the cache that aren't getting used at all. The fundamental problem is that the address, any one of these here, is only associated with one location in the cache. We can mitigate these effects by associating an address with more than one block in the cache. One strategy is to treat all the red lines as blue ones, and all of the orange lines as green ones. If we do this then we'll have twice as many places in the cache to store a blue line of memory. Actually, it's more convenient to think about the blue lines in the cache being together. And in this way, we can say that we have simply decided to ignore the most significant bit of our previous index, but to allow a cache block to now be stored in two possible places. Hence, this would be called a two way associative cache. The downside is that we have to check two tags now to see if we have a cache hit. But we are less likely run into a problem, where we are constantly evicting the memory we need from the cache. If we decide this isn't good enough, we can halve the number of indices again to create a four way associative cache. Returning to our general notation, we now say that we have two to the k minus j indices into our cache, and the index is really only k minus j bits long now. This greater associativity also gives the cache some choice about replacement. Whereas with the direct mount cache, there was only one block in the cache where the data could be stored. We now have a set of possible locations. Just two in our example but maybe more. Typically, we choose to evict the entry that was least recently used.

2 Associative Example

Now let's see a two-way set associative cache in action. We will assume a 5-bit address space with a 2 byte cache length. Notice that I've added a valid bit to our cache here, so that we can tell whether data has ever been loaded up to a line in the cache. Uninitialized caches are called coal. Let's say that 0 is the first address. In most systems that's not allowed, but it's fine for our example. The second bit here tells us the index for the cache. So we'll need to put this in the 0 set somewhere. We put it in here, flipping the recently used item to say 1, because that would be our preferred place to write the next cache line with index 0. Maybe after this, I have an address that looks like this one. The index here is 1, so we want to put it in this group, and again I'll put it in the first line, setting the valid bit, writing the data, and marking the least recently used bit. Our next address has index 0, so it gets written there. Notice that I chose this slot because the LRU had been one, and I flipped it back to zero because this is now the least recently used item in this part of the cache. Next we have an address with index 1. We checked the tag and we see that it's a hit. Oh my goodness. Notice that this address is a hit, even though we didn't read the exact same address before. But we did read an address belonging to the same cache block. Next, we have another address with index 0. So, he comes in here and evicting one of the previous entries. This one, because of the LRU bit.

2 Associative Question

Actually, let's make the next address a question. Is this address a hit or a miss?

2 Associative Question

The answer is that it's a miss. We find the index one, we're look in here and up, the tags don't match. It does match this tag up here, but that has the wrong index.

Fully Associative Mapping

Now we follow the idea of associativety to the extreme and let any cache block be put anywhere in the cache. Returning to our example, if this was a direct map cache, where every block has only one place to go. And this was a set associative cache, where there was a small set of places that a block can go. Then this is a fully associative cache where all cache blocks are treated alike and can be put anywhere in the cache. Looking at a more general notation, then we see that full associativity means we don't interpret any of the address as index anymore. It's all tag. This means that when we ask if a particular address is stored in the cache. The hardware has to check tags for every cache entry. Or at least, do it sequentially really, really fast. This fact, generally limits fully associative caches to sizes between 64 and 256 entries

Write Policy

So far we have focused mainly on reading data. But what happens when we want to write to memory? Here we'll consider a single core system. I'll refer you to an architecture class for a shared memory system where keeping a cache consistent becomes a challenge. We need to consider both what happens on a hit when the block we want to write to is already in the cache. And what happens on a miss, when it isn't. On a hit, the most obvious thing to do is to write-through to memory. That is, we'll write to the cache, and then also write to the main memory to copy the data, and keep the cache and main memory consistent. As long as I don't have to worry about some other entity needing an updated version from memory however, there's actually no need to write everything this instant. This is the insight behind the write-back policy which only writes to the cache. After all, that's where we'll look first if the same processor tries to read the data or write to it later. Only when the cache block gets evicted sometime later does the data really need to be written to main memory. And then it'll be the whole cache block. This lazy approach can be beneficial when the same cache block is written to many times before [INAUDIBLE]. For cache misses we also have two strategies. The first is write-allocate, which first reads the current value in memory into the cache. Then it behaves as though it were a hit, using either of the two hit strategies. Lastly we have the no-write allocate policy, where we just write the data to memory and don't bother with the cache at all. The interactions among these policies can be subtle, particularly when there are multiple cache levels. It is worth pointing out however, that some of these policies share certain assumptions, and are therefore often paired together. The write back policy is betting that there will be subsequent writes to the same cache block. That's why he is bundling up all the changes he is making for one trip to memory, when the block gets evicted. Write allocate is also betting on subsequent writes to the same block. That's why he loads the data up into the cache. On the other hand, write-through is betting on the cache block being evicted sooner rather than later. He does his writes to memory up front, so that he can quickly evict the cap block from the cache later if he has to, not having to worry about any writes to the disk. Similarly, the no-write allocate policy is also betting on that same cached block not being used again soon. It doesn't even bring the data into the cache.

The Virtual Address Abstraction

The chief goal of a virtual memory system is to provide a process with the abstraction that it has an address space all to itself, typically organized like this. We have addresses for the program code. We have addresses for variables that are initialized, literals, constants, things like that. Space for uninitialized global variables that we expect to change over the course of the program. Space for the heap which is dynamically allocated and might grow or shrink over the course of the program and space for the user stack the procedures, local variables, all that sort of thing. There are also addresses reserved for the kernel, we'll see how this improves efficiency later in the lesson. The advantage of this abstration are best seen from the compiler's perspective. The compiler can choose an address for a local variable or code for the body of a procedure without having to worry about what other processes might be running on the computer at the same time as the application is compiling. And what physical memory those applications might be using. He gets to pretend that the application and the OS will have the computer entirely to themselves.

Address Translation

The key to maintaining the virtual memory abstraction is a layer of indirection. Without this layer of indirection, two processes couldn't use the same address for a variable, because then they would end up overwriting each other. This would make life very difficult for programmers and compilers. So, we play one of the classic computer science tricks and introduce a layer of indirection. Inside the operating system, each process has something called the page table that acts like a phone directory or a dictionary. Giving for each virtual address, the physical address that it corresponds to. Usually this will be a place in memory, but when space in main memory is low it might also be on part of the disk, called swap in many systems. And when a program is first starting up, you usually don't load the whole application into memory first thing but rather leave part of the program, that might not always be needed, on the disk. This indirection allows us to accomplish several things. First, it allows us to have an address space that is bigger than physical main memory. This is convenient when main memory itself isn't big enough and we need to use the disk, or when we want to map other storage devices and treat them like memory. Second, it provides protection between processes, as mentioned earlier, without indirection the applications might find themselves overwriting each other's data. With the operating system properly managing the page tables, however, these two virtual addresses can be pointed to different physical addresses. Thirdly, it can allow for sharing. Even different virtual addresses can be made to refer to the same physical address, again, just by properly maintaining the page tables. Lastly I should point out that because kernel addresses are the same for each process, they get their own page table that is shared among the processes. This is called the global page table.

Paging

Recall how for caches we divided memory into blocks, or cache lines. And this's the granularity at which caching operates. Similarly, for a paging system we divide up our physical address into pages, often 4k long. Pages, are the granularity at which we grant memory to processes. The higher order bytes determine the page number, also called the physical page frame. And the lower order bytes determine the offset into the page. Correspondingly, the virtual address space is similarly divided into pages. Again, lower order bytes determine the offset within a page. The higher ones determine the virtual page number. The number of bytes in the offset always match, that's because virtual page sizes and physical page sizes aren't necessarily the same. But, the number of bits involved in the virtual page number need not match the number of bits used to identify the physical frame number. That's because, as we said before, it's possible to have more virtual pages than physical pages. Since we're mapping page for page between virtual and physical addresses, the offsets stay the same. We do need to translate page numbers however. And for this, we use a data structure called the Page Table.

Virtual Page Numbers

Here's a quick question to make sure we're on the same page, so to speak. Consider a 16-bit virtual address space and a 512 byte page size. How many virtual page numbers are there? You can assume byte addressing.

Virtual Page Numbers

Here's how I write to my answer. The fact that we have a This leaves us with 7 bits for the virtual page number, and that gives us 128 possible pages since two to the seventh is equal to 128.

Page Table Implementation

Now we consider the implementation of the all-important page table data structure, which needs to translate virtual page numbers into physical page frames. Virtual page numbers start at zero, and then go up by one. So the most straightforward way to do this would be to create a giant array that is the number of pages long. Let's see how this strategy might work. Suppose that we have a 48-bit virtual address and 32-bit physical address and let's say pages of sizes 4K. We've used up 12 bits for the offset, leaving 2 to the 36 possible virtual page numbers. That means that we need an array 2 to the 36 long, each entry probably having 4 bytes to specify the physical address, which brings us to a total of about 256 gigs. Which is more memory than most machines have in RAM. And of course, almost all of it is wasted since most virtual addresses aren't used. Even with just 32 bit virtual addresses, we would still need a page table with 2 to the several megabytes. And of course we need one page table per process. So instead, page tables are done in a hierarchical way. In our 32-bit example, the highest order 10 bits are used as an index into a top level page table. The contents of this page table then give us the base address of another page table. We use the next 10 bits as the index into that lower level page table. And the contents of that page table then give us the physical page number. Why does this help us use less memory? Well recall our virtual address space. We use addresses at the bottom, and we use addresses at the top. But there's a vast empty region in the middle. Many of these unused addresses will have the same 10 higher order bits. And for these, we won't even have a secondary table. Thus, we end up using not too much more memory for the page table than we really need to. The particulars of the actual page implementation vary greatly. Some have three levels, others have four. But they all use this basic hierarchical strategy.

Accelerating Address Translation

So far we've described the address translation process like this. The offset from the virtual address, simply gets copied to the physical address. And in order to translate the virtual page number, we do a look up in the page table, which is in memory, to find the physical page frame. Now you may be asking yourself, won't going to memory, for the page table every time we access a memory address be slow? In fact, we'll have to go multiple times for our hierarchical page table. Well indeed it would be. Thankfully the page tables themselves may end up in our cache, which can help considerably. But architects have also created a special purpose cache for storing page table entries, called the table lookaside buffer. Or TLB for short. Instead of going through these slower traditional memory mechanisms, we're taking a special shortcut. Whereas the caches we talked about earlier are usually indexed by physical address, the TLB is indexed by virtual address. After all, its job is to translate virtual page numbers to physical ones. This is extra tricky, because one virtual page number may be mapped to a physical address in one process, but it might be invalid in another or mapped to different location. There are two ways to handle this problem. Some systems simply flush the TLB, on every context switch. That is, every time the address space switches. This is a main reason that context switches are considered so costly. Alternatively, the TLB can use an address space identifier field in the table, to make sure that the translation in the table is meant for use in the current context. I should point out, too, that the kernel sometimes get's special treatment in the TLB. Because the kernel addresses our constant across processes, there is no need to flush them from the TLB on a context switch. Sometimes, too, part of the TLB is reserved for kernel addresses.

Page Table Entries

Now I want to consider the contents of the page table entries, at least the entries at the leaves of the hierarchy. In our example where we had a 32-bit physical address space, it would be typical to have a page table entries also of 32 bits. With 4k pages, only 20 bits would be needed for the physical page frame. What do we do with the other 12 bits? Well it turns out that there's lots of other information worth storing in the page table. Some of the more important are things like access control. Do we have read, write, or execute permissions on this memory? If we don't, then when we come to this page entry, an access violation or segmentation fault will occur. Another essential piece of information is whether the information associated with the virtual address is actually in memory at the moment. It may be the data that we need was not loaded on the application's start-up or it may have been swapped out to disk. In either of those cases, the valid or the present bit would be zero. When a process tries to access a page with a valid bit of zero, it creates a page fault and lets the OS try to bring the needed data into memory. We'll look at the page fault handler next. One of these bits also indicates whether the page is dirty. That is, has it been written to since it was loaded for disk? If not, then if it becomes necessary to evict this page from memory, there is no need to write it to disk if it's already there. A nice optimization. Sometimes a bit or two will also control how caching of this page is done. Page table entries corresponding to virtual addresses that were never mapped to a physical address by the OS usually have physical frame numbers of zero. The physical frame number of zero is rather like a null pointer. Everybody knows that that's an invalid physical frame number and a segment fault will be generated.

Page Fault

Next we turn to the page fault and ask the question: What happens when an application requests a virtual address that's not mapped to physical memory, but is somewhere on disk? I'll represent a user's process like so and at some point, he uses a virtual memory address that's not actually mapped to physical memory at the moment. Yikes! Actually it's not that big a deal. An exception is raised, which sets the running process back to be ready to repeat the instruction that created the, the fault. Meanwhile, the operating systems page fault handler takes over to address the problem. He checks to make sure the request is actually valid and sends, sends a segfault if it isn't. Then he loads the desired page into memory, gets everything ready and then tells the scheduler that the process is ready to resume. The process will execute its memory move or read or whatever it is again, and this time it will succeed because the page has been loaded into memory and it can continue running. That's the high-level picture. Let's talk a little bit more about what the page fault handler does. So assuming that the page we want really does reside on disk, the first thing the page handler does is to find a physical page frame in memory to load the data into. The best scenario is that one is free. The handler keeps a list of free pages. If this is not empty, then he can just pop one off. Okay? And that makes us very happy. If he doesn't have a free page, however, then he must choose a page for replacement. There are many possible page replacement algorithms. We won't go into them here. For our purposes, it suffices to say that a page handler will pick a page that it doesn't think is likely to be used soon. This page is saved to disk and then its physical memory can store the page that was created by the page fault. So, one way or another, we now have a free physical page in memory to which we can write the data we need from disk. Then we update the process's page table and any other data structures that are page fault handler needs to keep track of and then we're ready to restart the process and let it continue on to a

Putting it all Together

At this point, we've covered all of the essential pieces of the memory system. Now, let's step back and put it all together. To help us do this, I've written some pseudocode that captures the strategy for loading data into the CPU. You can imagine that we're writing an emulator if you like. The first thing that needs to happen to a virtual address is for it to be converted to a physical address. We'll postpone that until later. Then, if the data is in the cache, we simply read from the cache otherwise, we read from memory. Note that whenever we read from memory, we also write to the cache evicting some block if necessary. This process is, is what we talked about in the first half of the lesson. The second half of the lesson was largely concerned with address translation. The first place we check is the tlb. If the physical page frame is there, then we're done. If not, then we need to consult the page table. Notice that none of these procedures that access the page table should use the load procedure as it's defined here. The top level page table cannot be in a paging system itself. Otherwise, load would call translation, which would then end up calling load again, which would end up calling translation and so forth. We can imagine a fixed page being assigned to store the top level of page table, another good reason for making this small. I've made the check for the access violation explicit here, because it's in the page table that this is most likely to happen. It's possible that we would get an access violation in the tlb if we try to read a kernel page. But for the most part, the page simply won't be there. If the present or valid bit isn't set in the page table entry, that means that the page we want isn't in memory. So, we raise a page_fault. This will then be caught by the page handler, up here, and then we can re-run the load procedure, and this time we will find that it's in memory. And so we won't raise the page fault again. Obviously this pseudocode has its limitations. By using just software, we can't capture the interaction between the OS and the hardware and we're abstracting away many of the details. Nevertheless, if this makes sense to you then you have a good high-level idea of how a memory system operates.

Virtually Indexed, Physically Tagged Caches

You can't resist talking about one final optimization. Looking at this load method, notice how the translation to the physical address and cache look-up happen in sequence. We could speed up our implementation if we could find a way to do this in parallel. At first this might seem impossible. After all, the cache is indexed by the physical address We don't know this until we've done the translation. Recall, however, that only the higher order bits are changed when we go from the virtual address to the physical address. The offsets within the page stays exactly the same. Which bits are important for extracting data from the cache? Well it's these middlest bits that come after the offset for the cache block. As long as the index bits for the cache don't extend beyond the offset for the page, this little red line here, then we can extract data from the cache. Before we know the full physical address. Conceptually, we're going to do something like this where the virtual page number goes to the TLB and the page offset goes to the cache. The tag, or tags in the said associative case, then gets compared with the page frame number from the TLB, and the correct data is returned.

Number of Entries in a Virtually Indexed, Physically Tagged Cache

Here's a question to test your understanding of the virtually indexed, physically tagged cache. Suppose 32-bit virtual and physical address spaces. Pages are four kilobytes, and cache blocks are 64 bytes. What is the maximum number of entries, in a virtually indexed, physically tagged cache?

Number of Entries in a Virtually Indexed, Physically Tagged Cache

Here's my answer. The 4k page size implies a 12 bit page offset. The the size of the virtual and physical address spaces don't matter at all.

Conclusion

This completes our lesson on memory systems and if you followed along, you now have an advanced understanding of how memory systems work. This should make you a better programmer and put you in a good position to think about some of the complex trade-offs involved in CPU scheduling and maintaining cache coherence, especailly in the context of shared memory machines where there are multiple CPU's. There is always plenty more to learn.