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Cache Memory

If you look at a typical program (as many researchers have), you'll discover that it tends to access the same memory locations repeatedly. Furthermore, you also discover that a program often accesses adjacent memory locations. The technical names given to this phenomenon are temporal locality of reference  and spatial locality of reference. When exhibiting spatial locality, a program accesses neighboring memory locations. When displaying temporal locality of reference a program repeatedly accesses the same memory location during a short time period. Both forms of locality occur in the following Pascal code segment:

for i := 0 to 10 do
A [i] := 0;

There are two occurrences each of spatial and temporal locality of reference within this loop. Let's consider the obvious ones first.

In the Pascal code above, the program references the variable i several times. The for loop compares i against 10 to see if the loop is complete. It also increments i by one at the bottom of the loop. The assignment statement also uses i as an array index. This shows temporal locality of reference in action since the CPU accesses i at three points in a short time period.

This program also exhibits spatial locality of reference. The loop itself zeros out the elements of array A by writing a zero to the first location in A, then to the second location in A, and so on. Assuming that Pascal stores the elements of A into consecutive memory locations, each loop iteration accesses adjacent memory locations.

There is an additional example of temporal and spatial locality of reference in the Pascal example above, although it is not so obvious. Computer instructions that tell the system to do the specified task also reside in memory. These instructions appear sequentially in memory - the spatial locality part. The computer also executes these instructions repeatedly, once for each loop iteration - the temporal locality part.

If you look at the execution profile of a typical program, you'd discover that the program typically executes less than half the statements. Generally, a typical program might only use 10-20% of the memory allotted to it. At any one given time, a one megabyte program might only access four to eight kilobytes of data and code. So if you paid an outrageous sum of money for expensive zero wait state RAM, you wouldn't be using most of it at any one given time! Wouldn't it be nice if you could buy a small amount of fast RAM and dynamically reassign its address(es) as the program executes?

This is exactly what cache memory does for you. Cache memory sits between the CPU and main memory. It is a small amount of very fast (zero wait state) memory. Unlike normal memory, the bytes appearing within a cache do not have fixed addresses. Instead, cache memory can reassign the address of a data object. This allows the system to keep recently accessed values in the cache. Addresses that the CPU has never accessed or hasn't accessed in some time remain in main (slow) memory. Since most memory accesses are to recently accessed variables (or to locations near a recently accessed location), the data generally appears in cache memory.

Cache memory is not perfect. Although a program may spend considerable time executing code in one place, eventually it will call a procedure or wander off to some section of code outside cache memory. In such an event the CPU has to go to main memory to fetch the data. Since main memory is slow, this will require the insertion of wait states.

A cache hit occurs whenever the CPU accesses memory and finds the data in the cache. In such a case the CPU can usually access data with zero wait states. A cache miss occurs if the CPU accesses memory and the data is not present in cache. Then the CPU has to read the data from main memory, incurring a performance loss. To take advantage of locality of reference, the CPU copies data into the cache whenever it accesses an address not present in the cache. Since it is likely the system will access that same location shortly, the system will save wait states by having that data in the cache.

As described above, cache memory handles the temporal aspects of memory access, but not the spatial aspects. Caching memory locations when you access them won't speed up the program if you constantly access consecutive locations (spatial locality of reference). To solve this problem, most caching systems read several consecutive bytes from memory when a cache miss occurs1. 80x86 CPUs, for example, read beween 16 and 64 bytes at a shot (depending upon the CPU) upon a cache miss. If you read 16 bytes, why read them in blocks rather than as you need them? As it turns out, most memory chips available today have special modes which let you quickly access several consecutive memory locations on the chip. The cache exploits this capability to reduce the average number of wait states needed to access memory.

If you write a program that randomly accesses memory, using a cache might actually slow you down. Reading 16 bytes on each cache miss is expensive if you only access a few bytes in the corresponding cache line. Nonetheless, cache memory systems work quite well in the average case.

It should come as no surprise that the ratio of cache hits to misses increases with the size (in bytes) of the cache memory subsystem. The 80486 chip, for example, has 8,192 bytes of on-chip cache. Intel claims to get an 80-95% hit rate with this cache (meaning 80-95% of the time the CPU finds the data in the cache). This sounds very impressive. However, if you play around with the numbers a little bit, you'll discover it's not all that impressive. Suppose we pick the 80% figure. Then one out of every five memory accesses, on the average, will not be in the cache. If you have a 50 MHz processor and a 90 ns memory access time, four out of five memory accesses require only one clock cycle (since they are in the cache) and the fifth will require about 10 wait states2.  Altogether, the system will require 15 clock cycles to access five memory locations, or three clock cycles per access, on the average. That's equivalent to two wait states added to every memory access. Doesn't sound as impressive, does it?

There are a couple of ways to improve the situation. First, you can add more cache memory. This improves the cache hit ratio, reducing the number of wait states. For example, increasing the hit ratio from 80% to 90% lets you access 10 memory locations in 20 cycles. This reduces the average number of wait states per memory access to one wait state in our 80486 example - a substantial improvement. Alas, you can't pull an 80486 chip apart and solder more cache onto the chip. However, modern Pentium CPUs have a significantly larger cache than the 80486 and operates with fewer average wait states.

Another way to improve performance is to build a two-level caching system. The first level is the on-chip Level 1 cache. The next level, between the L1 cache and main memory, is a secondary cache (the Level 2 cache) also built on chip.

Figure 1.15 A Two Level Caching System

A typical secondary cache contains anywhere from 32,768 bytes to several megabytes of memory. Common sizes on PC subsystems are 256K, 512K, and 1024 Kbytes (1 MB) of cache.

You might ask, 'Why bother with a two-level cache? Why not use a 262,144 byte cache to begin with?' Well, the secondary cache generally does not operate at zero wait states. The circuitry to support 262,144 bytes fast memory would be very expensive. So most system designers use slower memory which requires one or two wait states. This is still much faster than main memory. Combined with the Level 1 cache, you can get better performance from the system.

Consider the previous example with an 80% hit ratio. If the secondary cache requires two cycles for each memory access and three cycles for the first access, then a cache miss on the on-chip cache will require a total of six clock cycles. All told, the average system performance will be two clocks per memory access. Quite a bit faster than the three required by the system without the secondary cache. Furthermore, the secondary cache can update its values in parallel with the CPU. So the number of cache misses (which affect CPU performance) goes way down.

Cache Architecture

Up to this point, cache has been this magical place that automatically stores data when we need it, perhaps fetching new data as the CPU requires it. However, a good question is 'how exactly does the cache do this?' Another might be 'what happens when the cache is full and the CPU is requesting additional data not in the cache?' In this section, we'll take a look at the internal cache organization and try to answer these questions along with a few others.

The basic idea behind a cache is that a program only access a small amount of data at a given time. If the cache is the same size as the typical amount of data the program access at any one given time, then we can put that data into the cache and access most of the data at a very high speed. Unfortunately, the data rarely sits in contiguous memory locations; usually, there's a few bytes here, a few bytes there, and some bytes somewhere else. In general, the data is spread out all over the address space. Therefore, the cache design has got to accommodate the fact that it must map data objects at widely varying addresses in memory.

As noted in the previous section, cache memory is not organized as a group of bytes. Instead, cache organization is usually in blocks of cache lines with each line containing some number of bytes (typically a small number that is a power of two like 16, 32, or 64), see Figure 6.2.

Figure 6.2 Possible Organization of an 8 Kilobyte Cache

The idea of a cache system is that we can attach a different (non-contiguous) address to each of the cache lines. So cache line #0 might correspond to addresses $10000..$1000F and cache line #1 might correspond to addresses $21400..$2140F. Generally, if a cache line is n bytes long (n is usually some power of two) then that cache line will hold n bytes from main memory that fall on an n-byte boundary. In this example, the cache lines are 16 bytes long, so a cache line holds blocks of 16 bytes whose addresses fall on 16-byte boundaries in main memory (i.e., the L.O. four bits of the address of the first byte in the cache line are always zero).

When the cache controller reads a cache line from a lower level in the memory hierarchy, a good question is 'where does the data go in the cache?' The most flexible cache system is the fully associative cache. In a fully associative cache subsystem, the caching controller can place a block of bytes in any one of the cache lines present in the cache memory. While this is a very flexible system, the flexibility is not without cost. The extra circuitry to achieve full associativity is expensive and, worse, can slow down the memory subsystem. Most L1 and L2 caches are not fully associative for this reason.

At the other extreme is the direct mapped cache (also known as the one-way set associative cache). In a direct mapped cache, a block of main memory is always loaded into the same cache line in the cache. Generally, some number of bits in the main memory address select the cache line. For example, Figure 6.3 shows how the cache controller could select a cache line for an 8 Kilobyte cache with 16-byte cache lines and a 32-bit main memory address. Since there are 512 cache lines, this example uses bits four through twelve to select one of the cache lines (bits zero through three select a particular byte within the 16-byte cache line). The direct-mapped cache scheme is very easy to implement. Extracting nine (or some other number of) bits from the address and using this as an index into the array of cache lines is trivial and fast. However, direct-mapped caches to suffer from some other problems.

Figure 6.3 Selecting a Cache Line in a Direct-mapped Cache

Perhaps the biggest problem with a direct-mapped cache is that it may not make effective use of all the cache memory. For example, the cache scheme in Figure 6.3 maps address zero to cache line #0. It also maps address $2000 (8K), $4000 (16K), $6000 (24K), $8000 (32K), and, in fact, it maps every address that is an even multiple of eight kilobytes to cache line #0. This means that if a program is constantly accessing data at addresses that are even multiples of 8K and not accessing any other locations, the system will only use cache line #0, leaving all the other cache lines unused. Each time the CPU requests data at an address that is not at an address within cache line #0, the CPU will have to go down to a lower level in the memory hierarchy to access the data. In this pathological case, the cache is effectively limited to the size of one cache line. Had we used a fully associative cache organization, each access (up to 512 cache lines' worth) could have their own cache line, thus improving performance.

If a fully associative cache organization is too complex, expensive, and slow to implement, but a direct-mapped cache organization isn't as good as we'd like, one might ask if there is a compromise that gives us more capability that a direct-mapped approach without all the complexity of a fully associative cache. The answer is yes, we can create an n-way set associative cache which is a compromise between these two extremes. The idea here is to break up the cache into sets of cache lines. The CPU selects a particular set using some subset of the address bits, just as for direct-mapping. Within each set there are n cache lines. The caching controller uses a fully associative mapping algorithm to select one of the n cache lines within the set.

As an example, an 8 kilobyte two-way set associative cache subsystem with 16-byte cache lines organizes the cache as a set of 256 sets with each set containing two cache lines ('two-way' means each set contains two cache lines). Eight bits from the memory address select one of these 256 different sets. Then the cache controller can map the block of bytes to either cache line within the set (see Figure 6.4). The advantage of a two-way set associative cache over a direct mapped cache is that you can have two accesses on 8 Kilobyte boundaries (using the current example) and still get different cache lines for both accesses. However, once you attempt to access a third memory location at an address that is an even multiple of eight kilobytes you will have a conflict.

Figure 6.4 A Two-Way Set Associative Cache

A two-way set associative cache is much better than a direct-mapped cache and considerably less complex than a fully associative cache. However, if you're still getting too many conflicts, you might consider using a four-way set associative cache. A four-way set associative cache puts four associative cache lines in each block. In the current 8K cache example, a four-way set associative example would have 128 sets with each set containing four cache lines. This would allow up to four accesses to an address that is an even multiple of eight kilobytes before a conflict would occur.

Obviously, we can create an arbitrary m-way set associative cache (well, m does have to be a power of two). However, if m is equal to n, where n is the number of cache lines, then you've got a fully associative cache with all the attendant problems (complexity and speed). Most cache designs are direct-mapped, two-way set associative, or four-way set associative. The 80x86 family CPUs use all three (depending on the CPU and cache).

Although this section has made direct-mapped cache look bad, they are, in fact, very effective for many types of data. In particular, they are very good for data that you access in a sequential rather than random fashion. Since the CPU typically executes instructions in a sequential fashion, instructions are a good thing to put into a direct-mapped cache. Data access is probably a bit more random access, so a two-way or four-way set associative cache probably makes a better choice.

Because access to data and instructions is different, many CPU designers will use separate caches for instructions and data. For example, the CPU designer could choose to implement an 8K instruction cache and an 8K data cache rather than a 16K unified cache. The advantage is that the CPU designer could choose a more appropriate caching scheme for instructions versus data. The drawback is that the two caches are now each half the size of a unified cache and you may get fewer cache misses from a unified cache. The choice of an appropriate cache organization is a difficult one and can only be made after analyzing lots of running programs on the target processor. How to choose an appropriate cache format is beyond the scope of this text, just be aware that it's not an easy choice you can make by reading some textbook.

Thus far, we've answered the question 'where do we put a block of data when we read it into the cache?' An equally important question we ignored until now is 'what happens if a cache line isn't available when we need to read data from memory?' Clearly, if all the lines in a set of cache lines contain data, we're going to have to replace one of these lines with the new data. The question is, 'how do we choose the cache line to replace?'

For a direct-mapped (one-way set associative) cache architecture, the answer is trivial. We replace exactly the block that the memory data maps to in the cache. The cache controller replaces whatever data was formerly in the cache line with the new data. Any reference to the old data will result in a cache miss and the cache controller will have to bring that data into the cache replacing whatever data is in that block at that time.

For a two-way set associative cache, the replacement algorithm is a bit more complex. Whenever the CPU references a memory location, the cache controller uses some number of the address bits to select the set that should contain the cache line. Using some fancy circuity, the caching controller determines if the data is already present in one of the two cache lines in the set. If not, then the CPU has to bring the data in from memory. Since the main memory data can go into either cache line, somehow the controller has to pick one or the other. If either (or both) cache lines are currently unused, the selection is trivial: pick an unused cache line. If both cache lines are currently in use, then the cache controller must pick one of the cache lines and replace its data with the new data. Ideally, we'd like to keep the cache line that will be referenced first (that is, we want to replace the one whose next reference is later in time). Unfortunately, neither the cache controller nor the CPU is omniscient, they cannot predict which is the best one to replace. However, remember the principle of temporal locality (see 'Cache Memory'): if a memory location has been referenced recently, it is likely to be referenced again in the very near future. A corollary to this is 'if a memory location has not been accessed in a while, it is likely to be a long time before the CPU accesses it again.' Therefore, a good replacement policy that many caching controllers use is the 'least recently used' or LRU algorithm. The idea is to pick the cache line that was not most frequently accessed and replace that cache line with the new data. An LRU policy is fairly easy to implement in a two-way set associative cache system. All you need is a bit that is set to zero whenever the CPU accessing one cache line and set it to one when you access the other cache line. This bit will indicate which cache line to replace when a replacement is necessary. For four-way (and greater) set associative caches, maintaining the LRU information is a bit more difficult, which is one of the reasons the circuitry for such caches is more complex. Other possible replacement policies include First-in, First-out1 (FIFO) and random. These are easier to implement than LRU, but they have their own problems.

The replacement policies for four-way and n-way set associative caches are roughly the same as for two-way set associative caches. The major difference is in the complexity of the circuit needed to implement the replacement policy (see the comments on LRU in the previous paragraph).

Another problem we've overlooked in this discussion on caches is 'what happens when the CPU writes data to memory?' The simple answer is trivial, the CPU writes the data to the cache. However, what happens when the cache line containing this data is replaced by incoming data? If the contents of the cache line is not written back to main memory, then the data that was written will be lost. The next time the CPU reads that data, it will fetch the original data values from main memory and the value written is lost.

Clearly any data written to the cache must ultimately be written to main memory as well. There are two common write policies that caches use: write-back and write-through. Interestingly enough, it is sometimes possible to set the write policy under software control; these aren't hardwired into the cache controller like most of the rest of the cache design. However, don't get your hopes up. Generally the CPU only allows the BIOS or operating system to set the cache write policy, your applications don't get to mess with this. However, if you're the one writing the operating system

The write-through policy states that any time data is written to the cache, the cache immediately turns around and writes a copy of that cache line to main memory. Note that the CPU does not have to halt while the cache controller writes the data to memory. So unless the CPU needs to access main memory shortly after the write occurs, this writing takes place in parallel with the execution of the program. Still, writing a cache line to memory takes some time and it is likely that the CPU (or some CPU in a multiprocessor system) will want to access main memory during this time, so the write-through policy may not be a high performance solution to the problem. Worse, suppose the CPU reads and writes the value in a memory location several times in succession. With a write-through policy in place the CPU will saturate the bus with cache line writes and this will have a very negative impact on the program's performance. On the positive side, the write-through policy does update main memory with the new value as rapidly as possible. So if two different CPUs are communicating through the use of shared memory, the write-through policy is probably better because the second CPU will see the change to memory as rapidly as possible when using this policy.

The second common cache write policy is the write-back policy. In this mode, writes to the cache are not immediately written to main memory; instead, the cache controller updates memory at a later time. This scheme tends to be higher performance because several writes to the same variable (or cache line) only update the cache line, they do not generate multiple writes to main memory.

Of course, at some point the cache controller must write the data in cache to memory. To determine which cache lines must be written back to main memory, the cache controller usually maintains a dirty bit with each cache line. The cache system sets this bit whenever it writes data to the cache. At some later time the cache controller checks this dirty bit to determine if it must write the cache line to memory. Of course, whenever the cache controller replaces a cache line with other data from memory, it must first write that cache line to memory if the dirty bit is set. Note that this increases the latency time when replacing a cache line. If the cache controller were able to write dirty cache lines to main memory while no other bus access was occurring, the system could reduce this latency during cache line replacement.

A cache subsystem is not a panacea for slow memory access. In order for a cache system to be effective the software must exhibit locality of reference. If a program accesses memory in a random fashion (or in a fashion guaranteed to exploit the caching controller's weaknesses) then the caching subsystem will actually cause a big performance drop. Fortunately, real-world programs do exhibit locality of reference, so most programs will benefit from the presence of a cache in the memory subsystem.

1This policy does exhibit some anomalies. These problems are beyond the scope of this chapter, but a good text on architecture or operating systems will discuss the problems with the FIFO replacement policy.

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