Multiprocessor Operating Systems
A shared-memory multiprocessor (or just multiprocessor henceforth) is a computer system in which two or more CPUs share full access to a common RAM. A program running on any of the CPUs sees a normal (usually paged) virtual address space. The only unusual property this system has is that the CPU can write some value into a memory word and then read the word back and get a different value (because another CPU has changed it). When organized correctly, this property forms the basis of interprocessor communication: one CPU writes some data into memory and another one reads the data out.
Below we will first take a brief look at multiprocessor hardware and then move on to the unique issues facing multiprocessor operating systems.
8.1.1 Multiprocessor Hardware
Although all multiprocessors have the property that every CPU can address all of memory, some multiprocessors have the additional property that every memory word can be read as fast as every other memory word. These machines are called UMA (Uniform Memory Access) multiprocessors. In contrast, NUMA (Nonuniform Memory Access) multiprocessors do not have this property. Why this difference exists will become clear later. We will first examine UMA multiprocessors and then move on to NUMA multiprocessors.
UMA Bus-Based SMP Architectures
The simplest multiprocessors are based on a single bus, as illustrated in Fig. 8-1(a). Two or more CPUs and one or more memory modules all use the same bus for communication. When a CPU wants to read a memory word, it first checks to see if the bus is busy. If the bus is idle, the CPU puts the address of the word it wants on the bus, asserts a few control signals, and waits until the memory puts the desired word on the bus.
If the bus is busy when a CPU wants to read or write memory, the CPU just waits until the bus becomes idle. Herein lies the problem with this design. With two or three CPUs, contention for the bus will be manageable; with 32 or 64 it will be unbearable. The system will be totally limited by the bandwidth of the bus, and most of the CPUs will be idle most of the time.
The solution to this problem is to add a cache to each CPU, as depicted in Fig. 8-1(b). The cache can be inside the CPU chip, next to the CPU chip, on the processor board, or some combination of all three. Since many reads can now be satisfied out of the local cache, there will be much less bus traffic, and the system can support more CPUs. In general, caching is not done on an individual word basis but on the basis of 32- or 64-byte blocks. When a word is referenced, its entire block is fetched into the cache of the CPU touching it.
Figure 8-1 Three bus-based multiprocessors. (a) Without caching. (b) With caching. (c) With caching and private memories.
Each cache block is marked as being either read-only (in which case it can be present in multiple caches at the same time), or as read-write (in which case it may not be present in any other caches). If a CPU attempts to write a word that is in one or more remote caches, the bus hardware detects the write and puts a signal on the bus informing all other caches of the write. If other caches have a ''clean'' copy, that is, an exact copy of what is in memory, they can just discard their copies and let the writer fetch the cache block from memory before modifying it. If some other cache has a ''dirty'' (i.e., modified) copy, it must either write it back to memory before the write can proceed or transfer it directly to the writer over the bus. Many cache transfer protocols exist.
Yet another possibility is the design of Fig. 8-1(c), in which each CPU has not only a cache, but also a local, private memory which it accesses over a dedicated (private) bus. To use this configuration optimally, the compiler should place all the program text, strings, constants and other read-only data, stacks, and local variables in the private memories. The shared memory is then only used for writable shared variables. In most cases, this careful placement will greatly reduce bus traffic, but it does require active cooperation from the compiler.
UMA Multiprocessors Using Crossbar Switches
Even with the best caching, the use of a single bus limits the size of a UMA multiprocessor to about 16 or 32 CPUs. To go beyond that, a different kind of interconnection network is needed. The simplest circuit for connecting n CPUs to k memories is the crossbar switch, shown in Fig. 8-2. Crossbar switches have been used for decades within telephone switching exchanges to connect a group of incoming lines to a set of outgoing lines in an arbitrary way.
At each intersection of a horizontal (incoming) and vertical (outgoing) line is a crosspoint. A crosspoint is a small switch that can be electrically opened or closed, depending on whether the horizontal and vertical lines are to be connected or not. In Fig. 8-2(a) we see three crosspoints closed simultaneously, allowing connections between the (CPU, memory) pairs (001, 000), (101, 101), and (110, 010) at the same time. Many other combinations are also possible. In fact, the number of combinations is equal to the number of different ways eight rooks can be safely placed on a chess board.
Figure 8-2 (a) An 8 X 8 crossbar switch. (b) An open crosspoint. (c) A closed crosspoint.
One of the nicest properties of the crossbar switch is that it is a nonblocking network, meaning that no CPU is ever denied the connection it needs because some crosspoint or line is already occupied (assuming the memory module itself is available). Furthermore, no advance planning is needed. Even if seven arbitrary connections are already set up, it is always possible to connect the remaining CPU to the remaining memory.
One of the worst properties of the crossbar switch is the fact that the number of crosspoints grows as n2. With 1000 CPUs and 1000 memory modules we need a million crosspoints. Such a large crossbar switch is not feasible. Nevertheless, for medium-sized systems, a crossbar design is workable.
UMA Multiprocessors Using Multistage Switching Networks
A completely different multiprocessor design is based on the humble 2 X 2 switch shown in Fig. 8-3(a). This switch has two inputs and two outputs. Messages arriving on either input line can be switched to either output line. For our purposes, messages will contain up to four parts, as shown in Fig. 8-3(b). The Module field tells which memory to use. The Address specifies an address within a module. The Opcode gives the operation, such as READ or WRITE. Finally, the optional Value field may contain an operand, such as a 32-bit word to be written on a WRITE. The switch inspects the Module field and uses it to determine if the message should be sent on X or on Y.
Figure 8-3 (a) A 2 X 2 switch. (b) A message format.
Our 2 X 2 switches can be arranged in many ways to build larger multistage switching networks (Adams et al., 1987; Bhuyan et al., 1989; and Kumar and Reddy, 1987). One possibility is the no-frills, economy class omega network, illustrated in Fig. 8-4. Here we have connected eight CPUs to eight memories using 12 switches. More generally, for n CPUs and n memories we would need log2n stages, with n/2 switches per stage, for a total of (n/2)log2n switches, which is a lot better than n 2 crosspoints, especially for large values of n.
Figure 8-4 An omega switching network.
The wiring pattern of the omega network is often called the perfect shuffle, since the mixing of the signals at each stage resembles a deck of cards being cut in half and then mixed card-for-card. To see how the omega network works, suppose that CPU 011 wants to read a word from memory module 110. The CPU sends a READ message to switch 1D containing 110 in the Module field. The switch takes the first (i.e., leftmost) bit of 110 and uses it for routing. A 0 routes to the upper output and a 1 routes to the lower one. Since this bit is a 1, the message is routed via the lower output to 2D.
All the second-stage switches, including 2D, use the second bit for routing. This, too, is a 1, so the message is now forwarded via the lower output to 3D. Here the third bit is tested and found to be a 0. Consequently, the message goes out on the upper output and arrives at memory 110, as desired. The path followed by this message is marked in Fig. 8-4 by the letter a.
As the message moves through the switching network, the bits at the left-hand end of the module number are no longer needed. They can be put to good use by recording the incoming line number there, so the reply can find its way back. For path a, the incoming lines are 0 (upper input to 1D), 1 (lower input to 2D), and 1 (lower input to 3D), respectively. The reply is routed back using 011, only reading it from right to left this time.
At the same time all this is going on, CPU 001 wants to write a word to memory module 001. An analogous process happens here, with the message routed via the upper, upper, and lower outputs, respectively, marked by the letter b. When it arrives, its Module field reads 001, representing the path it took. Since these two requests do not use any of the same switches, lines, or memory modules, they can proceed in parallel.
Now consider what would happen if CPU 000 simultaneously wanted to access memory module 000. Its request would come into conflict with CPU 001's request at switch 3A. One of them would have to wait. Unlike the crossbar switch, the omega network is a blocking network. Not every set of requests can be processed simultaneously. Conflicts can occur over the use of a wire or a switch, as well as between requests to memory and replies from memory.
It is clearly desirable to spread the memory references uniformly across the modules. One common technique is to use the low-order bits as the module number. Consider, for example, a byte-oriented address space for a computer that mostly accesses 32-bit words. The 2 low-order bits will usually be 00, but the next 3 bits will be uniformly distributed. By using these 3 bits as the module number, consecutively addressed words will be in consecutive modules. A memory system in which consecutive words are in different modules is said to be interleaved. Interleaved memories maximize parallelism because most memory references are to consecutive addresses. It is also possible to design switching networks that are nonblocking and which offer multiple paths from each CPU to each memory module, to spread the traffic better.
Single-bus UMA multiprocessors are generally limited to no more than a few dozen CPUs and crossbar or switched multiprocessors need a lot of (expensive) hardware and are not that much bigger. To get to more than 100 CPUs, something has to give. Usually, what gives is the idea that all memory modules have the same access time. This concession leads to the idea of NUMA multiprocessors, as mentioned above. Like their UMA cousins, they provide a single address space across all the CPUs, but unlike the UMA machines, access to local memory modules is faster than access to remote ones. Thus all UMA programs will run without change on NUMA machines, but the performance will be worse than on a UMA machine at the same clock speed.
NUMA machines have three key characteristics that all of them possess and which together distinguish them from other multiprocessors:
There is a single address space visible to all CPUs.
Access to remote memory is via LOAD and STORE instructions.
Access to remote memory is slower than access to local memory.
When the access time to remote memory is not hidden (because there is no caching), the system is called NC-NUMA. When coherent caches are present, the system is called CC-NUMA (Cache-Coherent NUMA).
The most popular approach for building large CC-NUMA multiprocessors currently is the directory-based multiprocessor. The idea is to maintain a database telling where each cache line is and what its status is. When a cache line is referenced, the database is queried to find out where it is and whether it is clean or dirty (modified). Since this database must be queried on every instruction that references memory, it must be kept in extremely-fast special-purpose hardware that can respond in a fraction of a bus cycle.
To make the idea of a directory-based multiprocessor somewhat more concrete, let us consider as a simple (hypothetical) example, a 256-node system, each node consisting of one CPU and 16 MB of RAM connected to the CPU via a local bus. The total memory is 232 bytes, divided up into 226 cache lines of 64 bytes each. The memory is statically allocated among the nodes, with 016M in node 0, 16M32M in node 1, and so on. The nodes are connected by an interconnection network, as shown in Fig. 8-5(a). Each node also holds the directory entries for the 218 64-byte cache lines comprising its 224 byte memory. For the moment, we will assume that a line can be held in at most one cache.
To see how the directory works, let us trace a LOAD instruction from CPU 20 that references a cached line. First the CPU issuing the instruction presents it to its MMU, which translates it to a physical address, say, 0x24000108. The MMU splits this address into the three parts shown in Fig. 8-5(b). In decimal, the three parts are node 36, line 4, and offset 8. The MMU sees that the memory word referenced is from node 36, not node 20, so it sends a request message through the interconnection network to the line's home node, 36, asking whether its line 4 is cached, and if so, where.
Figure 8-5 (a) A 256-node directory-based multiprocessor. (b) Division of a 32-bit memory address into fields. (c) The directory at node 36.
When the request arrives at node 36 over the interconnection network, it is routed to the directory hardware. The hardware indexes into its table of 218 entries, one for each of its cache lines and extracts entry 4. From Fig. 8-5(c) we see that the line is not cached, so the hardware fetches line 4 from the local RAM, sends it back to node 20, and updates directory entry 4 to indicate that the line is now cached at node 20.
Now let us consider a second request, this time asking about node 36's line 2. From Fig. 8-5(c) we see that this line is cached at node 82. At this point the hardware could update directory entry 2 to say that the line is now at node 20 and then send a message to node 82 instructing it to pass the line to node 20 and invalidate its cache. Note that even a so-called ''shared-memory multiprocessor'' has a lot of message passing going on under the hood.
As a quick aside, let us calculate how much memory is being taken up by the directories. Each node has 16 MB of RAM and 218 9-bit entries to keep track of that RAM. Thus the directory overhead is about 9 X 218 bits divided by 16 MB or about 1.76 percent, which is generally acceptable (although it has to be high-speed memory, which increases its cost). Even with 32-byte cache lines the overhead would only be 4 percent. With 128-byte cache lines, it would be under 1 percent.
An obvious limitation of this design is that a line can be cached at only one node. To allow lines to be cached at multiple nodes, we would need some way of locating all of them, for example, to invalidate or update them on a write. Various options are possible to allow caching at several nodes at the same time, but a discussion of these is beyond the scope of this book.