Search     or:     and:
 LINUX 
 Language 
 Kernel 
 Package 
 Book 
 Test 
 OS 
 Forum 
 iakovlev.org 
 Kernels
 Boot 
 Memory 
 File system
 0.01
 1.0 
 2.0 
 2.4 
 2.6 
 3.x 
 4.x 
 Интервью 
 Kernel
 HOW-TO 1
 Ptrace
 Kernel-Rebuild-HOWTO
 Runlevel
 Linux daemons
 FAQ
NEWS
Последние статьи :
  Rust 07.11   
  Go 25.12   
  EXT4 10.11   
  FS benchmark 15.09   
  Сетунь 23.07   
  Trees 25.06   
  Apache 03.02   
  SQL 30.07   
  JFS 10.06   
  B-trees 01.06   
 
TOP 20
 Trees...511 
 Go Web ...334 
 Python...166 
 2.0-> Linux IP Networking...139 
 Steve Pate 3...138 
 Стивенс 9...129 
 Rubni-Corbet -> Глав...128 
 Stein-MacEachern-> Час...119 
 Secure Programming for Li...119 
 Daniel Bovet 2...113 
 Mike Perry...113 
 Rubni-Corbet -> Глав...111 
 Advanced Bash Scripting G...111 
 Stevens-> Глава 4...110 
 Stewens -> IPC 7...108 
 Ethreal 4...105 
 Rubni-Corbet -> Глав...103 
 Stewens -> IPC 9...102 
 Stevens-> Глава 25...102 
 Stevens-> Глава 23...100 
 
  01.12.2017 : 2356398 посещений 

iakovlev.org

Что каждый программист должен знать о памяти , часть 1

Сентябрь 21, 2007

Автор - Ulrich Drepper

1 Введение

Раньше компьютеры были проще. Процессоры , память , устройства хранения были единым целым. Например , память и сетевые устройства были сопоставимы по скорости работы с процессором.

Но с какого-то момента разработчики начали оптимизировать отдельные компоненты. В результате некоторые из них резко упали в производительности. Это касается устройств хранения и памяти.

Операционные системы хранят основные данные в памяти,которая в свою очередь быстрее остальных устройств хранения . У последних появился кеш , который прозрачен для операционных систем.

В отличие от устройств хранения , оптимизация памяти - намного более сложный процесс , который подчас идет на уровне железа. Это имеет следующие формы:

  • RAM hardware design (speed and parallelism).

  • Memory controller designs.

  • CPU caches.

  • Direct memory access (DMA) for devices.

В этом документе будет идти речь о кеше процессора и DMA, будут рассмотрены различные типы RAM.

1.1 Структура документа

Документ предназначен для широкой массы разработчиков , и не все подробные детали описания железа будут расшифрованы.

Вторая часть описывает т.н. random-access memory (RAM), и ее полное понимание необязательно для остальных частей. Вы можете найти тут полезные ссылки.

Третья часть описывает CPU cache. Она является ключевой для понимания оставшегося документа. 4-я часть описывает реализацию виртуальной памяти и также важна.

5-я часть описывает т.н. Non Uniform Memory Access (NUMA).

6-я часть - центральная в этом документе. В ней подводятся предварительные итоги и даются советы программистам , как лучше писать в различных ситуациях. В принципе , чтение документа можно начать прямо с нее и потом возвращаться по мере необходимости.

7-я часть посвящена всяким тулзам

8-я дает обзор перспективным технологиям будущего.

2 Commodity Hardware Today

Understanding commodity hardware is important because specialized hardware is in retreat. Scaling these days is most often achieved horizontally instead of vertically, meaning today it is more cost-effective to use many smaller, connected commodity computers instead of a few really large and exceptionally fast (and expensive) systems. This is the case because fast and inexpensive network hardware is widely available. There are still situations where the large specialized systems have their place and these systems still provide a business opportunity, but the overall market is dwarfed by the commodity hardware market. Red Hat, as of 2007, expects that for future products, the “standard building blocks” for most data centers will be a computer with up to four sockets, each filled with a quad core CPU that, in the case of Intel CPUs, will be hyper-threaded. {Hyper-threading enables a single processor core to be used for two or more concurrent executions with just a little extra hardware.} This means the standard system in the data center will have up to 64 virtual processors. Bigger machines will be supported, but the quad socket, quad CPU core case is currently thought to be the sweet spot and most optimizations are targeted for such machines.

Large differences exist in the structure of commodity computers. That said, we will cover more than 90% of such hardware by concentrating on the most important differences. Note that these technical details tend to change rapidly, so the the reader is advised to take the date of this writing into account.

Over the years the personal computers and smaller servers standardized on a chipset with two parts: the Northbridge and Southbridge. Figure 2.1 shows this structure.

Figure 2.1: Structure with Northbridge and Southbridge

All CPUs (two in the previous example, but there can be more) are connected via a common bus (the Front Side Bus, FSB) to the Northbridge. The Northbridge contains, among other things, the memory controller, and its implementation determines the type of RAM chips used for the computer. Different types of RAM, such as DRAM, Rambus, and SDRAM, require different memory controllers.

To reach all other system devices, the Northbridge must communicate with the Southbridge. The Southbridge, often referred to as the I/O bridge, handles communication with devices through a variety of different buses. Today the PCI, PCI Express, SATA, and USB buses are of most importance, but PATA, IEEE 1394, serial, and parallel ports are also supported by the Southbridge. Older systems had AGP slots which were attached to the Northbridge. This was done for performance reasons related to insufficiently fast connections between the Northbridge and Southbridge. However, today the PCI-E slots are all connected to the Southbridge.

Such a system structure has a number of noteworthy consequences:

  • All data communication from one CPU to another must travel over the same bus used to communicate with the Northbridge.

  • All communication with RAM must pass through the Northbridge.

  • The RAM has only a single port. {We will not discuss multi-port RAM in this document as this type of RAM is not found in commodity hardware, at least not in places where the programmer has access to it. It can be found in specialized hardware such as network routers which depend on utmost speed.}

  • Communication between a CPU and a device attached to the Southbridge is routed through the Northbridge.

A couple of bottlenecks are immediately apparent in this design. One such bottleneck involves access to RAM for devices. In the earliest days of the PC, all communication with devices on either bridge had to pass through the CPU, negatively impacting overall system performance. To work around this problem some devices became capable of direct memory access (DMA). DMA allows devices, with the help of the Northbridge, to store and receive data in RAM directly without the intervention of the CPU (and its inherent performance cost). Today all high-performance devices attached to any of the buses can utilize DMA. While this greatly reduces the workload on the CPU, it also creates contention for the bandwidth of the Northbridge as DMA requests compete with RAM access from the CPUs. This problem, therefore, must to be taken into account.

A second bottleneck involves the bus from the Northbridge to the RAM. The exact details of the bus depend on the memory types deployed. On older systems there is only one bus to all the RAM chips, so parallel access is not possible. Recent RAM types require two separate buses (or channels as they are called for DDR2, see Figure 2.8) which doubles the available bandwidth. The Northbridge interleaves memory access across the channels. More recent memory technologies (FB-DRAM, for instance) add more channels.

With limited bandwidth available, it is important to schedule memory access in ways that minimize delays. As we will see, processors are much faster and must wait to access memory, despite the use of CPU caches. If multiple hyper-threads, cores, or processors access memory at the same time, the wait times for memory access are even longer. This is also true for DMA operations.

There is more to accessing memory than concurrency, however. Access patterns themselves also greatly influence the performance of the memory subsystem, especially with multiple memory channels. Refer to Section 2.2 for more details of RAM access patterns.

On some more expensive systems, the Northbridge does not actually contain the memory controller. Instead the Northbridge can be connected to a number of external memory controllers (in the following example, four of them).

Figure 2.2: Northbridge with External Controllers

The advantage of this architecture is that more than one memory bus exists and therefore total bandwidth increases. This design also supports more memory. Concurrent memory access patterns reduce delays by simultaneously accessing different memory banks. This is especially true when multiple processors are directly connected to the Northbridge, as in Figure 2.2. For such a design, the primary limitation is the internal bandwidth of the Northbridge, which is phenomenal for this architecture (from Intel). {For completeness it should be mentioned that such a memory controller arrangement can be used for other purposes such as “memory RAID” which is useful in combination with hotplug memory.}

Using multiple external memory controllers is not the only way to increase memory bandwidth. One other increasingly popular way is to integrate memory controllers into the CPUs and attach memory to each CPU. This architecture is made popular by SMP systems based on AMD's Opteron processor. Figure 2.3 shows such a system. Intel will have support for the Common System Interface (CSI) starting with the Nehalem processors; this is basically the same approach: an integrated memory controller with the possibility of local memory for each processor.

Figure 2.3: Integrated Memory Controller

With an architecture like this there are as many memory banks available as there are processors. On a quad-CPU machine the memory bandwidth is quadrupled without the need for a complicated Northbridge with enormous bandwidth. Having a memory controller integrated into the CPU has some additional advantages; we will not dig deeper into this technology here.

There are disadvantages to this architecture, too. First of all, because the machine still has to make all the memory of the system accessible to all processors, the memory is not uniform anymore (hence the name NUMA - Non-Uniform Memory Architecture - for such an architecture). Local memory (memory attached to a processor) can be accessed with the usual speed. The situation is different when memory attached to another processor is accessed. In this case the interconnects between the processors have to be used. To access memory attached to CPU2 from CPU1 requires communication across one interconnect. When the same CPU accesses memory attached to CPU4 two interconnects have to be crossed.

Each such communication has an associated cost. We talk about “NUMA factors” when we describe the extra time needed to access remote memory. The example architecture in Figure 2.3 has two levels for each CPU: immediately adjacent CPUs and one CPU which is two interconnects away. With more complicated machines the number of levels can grow significantly. There are also machine architectures (for instance IBM's x445 and SGI's Altix series) where there is more than one type of connection. CPUs are organized into nodes; within a node the time to access the memory might be uniform or have only small NUMA factors. The connection between nodes can be very expensive, though, and the NUMA factor can be quite high.

Commodity NUMA machines exist today and will likely play an even greater role in the future. It is expected that, from late 2008 on, every SMP machine will use NUMA. The costs associated with NUMA make it important to recognize when a program is running on a NUMA machine. In Section 5 we will discuss more machine architectures and some technologies the Linux kernel provides for these programs.

Beyond the technical details described in the remainder of this section, there are several additional factors which influence the performance of RAM. They are not controllable by software, which is why they are not covered in this section. The interested reader can learn about some of these factors in Section 2.1. They are really only needed to get a more complete picture of RAM technology and possibly to make better decisions when purchasing computers.

The following two sections discuss hardware details at the gate level and the access protocol between the memory controller and the DRAM chips. Programmers will likely find this information enlightening since these details explain why RAM access works the way it does. It is optional knowledge, though, and the reader anxious to get to topics with more immediate relevance for everyday life can jump ahead to Section 2.2.5.

2.1 RAM Types

There have been many types of RAM over the years and each type varies, sometimes significantly, from the other. The older types are today really only interesting to the historians. We will not explore the details of those. Instead we will concentrate on modern RAM types; we will only scrape the surface, exploring some details which are visible to the kernel or application developer through their performance characteristics.

The first interesting details are centered around the question why there are different types of RAM in the same machine. More specifically, why there are both static RAM (SRAM {In other contexts SRAM might mean “synchronous RAM”.}) and dynamic RAM (DRAM). The former is much faster and provides the same functionality. Why is not all RAM in a machine SRAM? The answer is, as one might expect, cost. SRAM is much more expensive to produce and to use than DRAM. Both these cost factors are important, the second one increasing in importance more and more. To understand these difference we look at the implementation of a bit of storage for both SRAM and DRAM.

In the remainder of this section we will discuss some low-level details of the implementation of RAM. We will keep the level of detail as low as possible. To that end, we will discuss the signals at a “logic level” and not at a level a hardware designer would have to use. That level of detail is unnecessary for our purpose here.

2.1.1 Static RAM

Figure 2.4: 6-T Static RAM

Figure 2.4 shows the structure of a 6 transistor SRAM cell. The core of this cell is formed by the four transistors M1 to M4 which form two cross-coupled inverters. They have two stable states, representing 0 and 1 respectively. The state is stable as long as power on Vdd is available.

If access to the state of the cell is needed the word access line WL is raised. This makes the state of the cell immediately available for reading on BL and BL. If the cell state must be overwritten the BL and BL lines are first set to the desired values and then WL is raised. Since the outside drivers are stronger than the four transistors (M1 through M4) this allows the old state to be overwritten.

See [sramwiki] for a more detailed on the way the cell works. For the following discussion it is important to note that

  • one cell requires six transistors. There are variants with four transistors but they have disadvantages.

  • maintaining the state of the cell requires constant power.

  • the cell state is available for reading almost immediately once the word access line WL is raised. The signal is as rectangular (changing quickly between the two binary states) as other transistor-controlled signals.

  • the cell state is stable, no refresh cycles are needed.

There are other slow and less power-hungry SRAM forms available, but those are not of interest here since we are looking at fast RAM. These slow variants are mainly interesting because they can be more easily be used in a system than a dynamic RAM chip because of their simpler interface.

2.1.2 Dynamic RAM

Dynamic RAM is, in its structure, much simpler than static RAM. Figure 2.5 shows the structure of a usual DRAM cell design. All it consists of is one transistor and one capacitor. This huge difference in complexity of course means that it functions very differently than static RAM.

Figure 2.5: 1-T Dynamic RAM

A dynamic RAM cell keeps its state in the capacitor C. The transistor M is used to guard the access to the state. To read the state of the cell the access line AL is raised; this either causes a current to flow on the data line DL or not, depending on the charge in the capacitor. To write to the cell the data line DL is appropriately set and then AL is raised for a time long enough to charge or drain the capacitor.

There are a number of complications with the design of dynamic RAM. The use of a capacitor means that reading the cell discharges the capacitor. The procedure cannot be repeated indefinitely, the capacitor must be recharged at some point. Even worse, to accommodate the huge number of cells (chips with 109 or more cells are now common) the capacity to the capacitor must be low (in the femto-farad range or lower). A fully charged capacitor holds a few 10's of thousands of electrons. Even though the resistance of the capacitor is high (a couple of tera-ohms) it only takes a short time for the capacity to dissipate. This problem is called “leakage”.

This leakage is why a DRAM cell must be constantly refreshed. For most DRAM chips these days this refresh must happen every 64ms. During the refresh cycle no access to the memory is possible. For some workloads this overhead might stall up to 50% of the memory accesses (see [highperfdram]).

A second problem resulting from the tiny charge is that the information read from the cell is not directly usable. The data line must be connected to a sense amplifier which can distinguish between a stored 0 or 1 over the whole range of charges which still have to count as 1.

A third problem is that charging and draining a capacitor is not instantaneous. The signals received by the sense amplifier are not rectangular, so a conservative estimate as to when the output of the cell is usable has to be used. The formulas for charging and discharging a capacitor are

[Formulas]

This means it takes some time (determined by the capacity C and resistance R) for the capacitor to be charged and discharged. It also means that the current which can be detected by the sense amplifiers is not immediately available. Figure 2.6 shows the charge and discharge curves. The X—axis is measured in units of RC (resistance multiplied by capacitance) which is a unit of time.

Figure 2.6: Capacitor Charge and Discharge Timing

Unlike the static RAM case where the output is immediately available when the word access line is raised, it will always take a bit of time until the capacitor discharges sufficiently. This delay severely limits how fast DRAM can be.

The simple approach has its advantages, too. The main advantage is size. The chip real estate needed for one DRAM cell is many times smaller than that of an SRAM cell. The SRAM cells also need individual power for the transistors maintaining the state. The structure of the DRAM cell is also simpler and more regular which means packing many of them close together on a die is simpler.

Overall, the (quite dramatic) difference in cost wins. Except in specialized hardware — network routers, for example — we have to live with main memory which is based on DRAM. This has huge implications on the programmer which we will discuss in the remainder of this paper. But first we need to look into a few more details of the actual use of DRAM cells.

2.1.3 DRAM Access

A program selects a memory location using a virtual address. The processor translates this into a physical address and finally the memory controller selects the RAM chip corresponding to that address. To select the individual memory cell on the RAM chip, parts of the physical address are passed on in the form of a number of address lines.

It would be completely impractical to address memory locations individually from the memory controller: 4GB of RAM would require 232 address lines. Instead the address is passed encoded as a binary number using a smaller set of address lines. The address passed to the DRAM chip this way must be demultiplexed first. A demultiplexer with N address lines will have 2N output lines. These output lines can be used to select the memory cell. Using this direct approach is no big problem for chips with small capacities.

But if the number of cells grows this approach is not suitable anymore. A chip with 1Gbit {I hate those SI prefixes. For me a giga-bit will always be 230 and not 109 bits.} capacity would need 30 address lines and 230 select lines. The size of a demultiplexer increases exponentially with the number of input lines when speed is not to be sacrificed. A demultiplexer for 30 address lines needs a whole lot of chip real estate in addition to the complexity (size and time) of the demultiplexer. Even more importantly, transmitting 30 impulses on the address lines synchronously is much harder than transmitting “only” 15 impulses. Fewer lines have to be laid out at exactly the same length or timed appropriately. {Modern DRAM types like DDR3 can automatically adjust the timing but there is a limit as to what can be tolerated.}

Figure 2.7: Dynamic RAM Schematic

Figure 2.7 shows a DRAM chip at a very high level. The DRAM cells are organized in rows and columns. They could all be aligned in one row but then the DRAM chip would need a huge demultiplexer. With the array approach the design can get by with one demultiplexer and one multiplexer of half the size. {Multiplexers and demultiplexers are equivalent and the multiplexer here needs to work as a demultiplexer when writing. So we will drop the differentiation from now on.} This is a huge saving on all fronts. In the example the address lines a0 and a1 through the row address selection (RAS) demultiplexer select the address lines of a whole row of cells. When reading, the content of all cells is thusly made available to the column address selection (CAS) {The line over the name indicates that the signal is negated} multiplexer. Based on the address lines a2 and a3 the content of one column is then made available to the data pin of the DRAM chip. This happens many times in parallel on a number of DRAM chips to produce a total number of bits corresponding to the width of the data bus.

For writing, the new cell value is put on the data bus and, when the cell is selected using the RAS and CAS, it is stored in the cell. A pretty straightforward design. There are in reality — obviously — many more complications. There need to be specifications how much delay there is after the signal before the data will be available on the data bus for reading. The capacitors do not unload instantaneously, as described in the previous section. The signal from the cells is so weak that it needs to be amplified. For writing it must be specified how long the data must be available on the bus after the RAS and CAS is done to successfully store the new value in the cell (again, capacitor do not fill or drain instantaneously). These timing constants are crucial for the performance of the DRAM chip. We will talk about this in the next section.

A secondary scalability problem is that having 30 address lines connected to every RAM chip is not feasible either. Pins of a chip are a precious resources. It is “bad” enough that the data must be transferred as much as possible in parallel (e.g., in 64 bit batches). The memory controller must be able to address each RAM module (collection of RAM chips). If parallel access to multiple RAM modules is required for performance reasons and each RAM module requires its own set of 30 or more address lines, then the memory controller needs to have, for 8 RAM modules, a whopping 240+ pins only for the address handling.

To counter these secondary scalability problems DRAM chips have, for a long time, multiplexed the address itself. That means the address is transferred in two parts. The first part consisting of address bits a0 and a1 in the example in Figure 2.7) select the row. This selection remains active until revoked. Then the second part, address bits a2 and a3, select the column. The crucial difference is that only two external address lines are needed. A few more lines are needed to indicate when the RAS and CAS signals are available but this is a small price to pay for cutting the number of address lines in half. This address multiplexing brings its own set of problems, though. We will discuss them in Section 2.2.

2.1.4 Conclusions

Do not worry if the details in this section are a bit overwhelming. The important things to take away from this section are:

  • there are reasons why not all memory is SRAM

  • memory cells need to be individually selected to be used

  • the number of address lines is directly responsible for the cost of the memory controller, motherboards, DRAM module, and DRAM chip

  • it takes a while before the results of the read or write operation are available

The following section will go into more details about the actual process of accessing DRAM memory. We are not going into more details of accessing SRAM, which is usually directly addressed. This happens for speed and because the SRAM memory is limited in size. SRAM is currently used in CPU caches and on-die where the connections are small and fully under control of the CPU designer. CPU caches are a topic which we discuss later but all we need to know is that SRAM cells have a certain maximum speed which depends on the effort spent on the SRAM. The speed can vary from only slightly slower than the CPU core to one or two orders of magnitude slower.

2.2 DRAM Access Technical Details

In the section introducing DRAM we saw that DRAM chips multiplex the addresses in order to save resources. We also saw that accessing DRAM cells takes time since the capacitors in those cells do not discharge instantaneously to produce a stable signal; we also saw that DRAM cells must be refreshed. Now it is time to put this all together and see how all these factors determine how the DRAM access has to happen.

We will concentrate on current technology; we will not discuss asynchronous DRAM and its variants as they are simply not relevant anymore. Readers interested in this topic are referred to [highperfdram] and [arstechtwo]. We will also not talk about Rambus DRAM (RDRAM) even though the technology is not obsolete. It is just not widely used for system memory. We will concentrate exclusively on Synchronous DRAM (SDRAM) and its successors Double Data Rate DRAM (DDR).

Synchronous DRAM, as the name suggests, works relative to a time source. The memory controller provides a clock, the frequency of which determines the speed of the Front Side Bus (FSB) — the memory controller interface used by the DRAM chips. As of this writing, frequencies of 800MHz, 1,066MHz, or even 1,333MHz are available with higher frequencies (1,600MHz) being announced for the next generation. This does not mean the frequency used on the bus is actually this high. Instead, today's buses are double- or quad-pumped, meaning that data is transported two or four times per cycle. Higher numbers sell so the manufacturers like to advertise a quad-pumped 200MHz bus as an “effective” 800MHz bus.

For SDRAM today each data transfer consists of 64 bits — 8 bytes. The transfer rate of the FSB is therefore 8 bytes multiplied by the effective bus frequency (6.4GB/s for the quad-pumped 200MHz bus). That sounds a lot but it is the burst speed, the maximum speed which will never be surpassed. As we will see now the protocol for talking to the RAM modules has a lot of downtime when no data can be transmitted. It is exactly this downtime which we must understand and minimize to achieve the best performance.

2.2.1 Read Access Protocol

Figure 2.8: SDRAM Read Access Timing

Figure 2.8 shows the activity on some of the connectors of a DRAM module which happens in three differently colored phases. As usual, time flows from left to right. A lot of details are left out. Here we only talk about the bus clock, RAS and CAS signals, and the address and data buses. A read cycle begins with the memory controller making the row address available on the address bus and lowering the RAS signal. All signals are read on the rising edge of the clock (CLK) so it does not matter if the signal is not completely square as long as it is stable at the time it is read. Setting the row address causes the RAM chip to start latching the addressed row.

The CAS signal can be sent after tRCD (RAS-to-CAS Delay) clock cycles. The column address is then transmitted by making it available on the address bus and lowering the CAS line. Here we can see how the two parts of the address (more or less halves, nothing else makes sense) can be transmitted over the same address bus.

Now the addressing is complete and the data can be transmitted. The RAM chip needs some time to prepare for this. The delay is usually called CAS Latency (CL). In Figure 2.8 the CAS latency is 2. It can be higher or lower, depending on the quality of the memory controller, motherboard, and DRAM module. The latency can also have half values. With CL=2.5 the first data would be available at the first falling flank in the blue area.

With all this preparation to get to the data it would be wasteful to only transfer one data word. This is why DRAM modules allow the memory controller to specify how much data is to be transmitted. Often the choice is between 2, 4, or 8 words. This allows filling entire lines in the caches without a new RAS/CAS sequence. It is also possible for the memory controller to send a new CAS signal without resetting the row selection. In this way, consecutive memory addresses can be read from or written to significantly faster because the RAS signal does not have to be sent and the row does not have to be deactivated (see below). Keeping the row “open” is something the memory controller has to decide. Speculatively leaving it open all the time has disadvantages with real-world applications (see [highperfdram]). Sending new CAS signals is only subject to the Command Rate of the RAM module (usually specified as Tx, where x is a value like 1 or 2; it will be 1 for high-performance DRAM modules which accept new commands every cycle).

In this example the SDRAM spits out one word per cycle. This is what the first generation does. DDR is able to transmit two words per cycle. This cuts down on the transfer time but does not change the latency. In principle, DDR2 works the same although in practice it looks different. There is no need to go into the details here. It is sufficient to note that DDR2 can be made faster, cheaper, more reliable, and is more energy efficient (see [ddrtwo] for more information).

2.2.2 Precharge and Activation

Figure 2.8 does not cover the whole cycle. It only shows parts of the full cycle of accessing DRAM. Before a new RAS signal can be sent the currently latched row must be deactivated and the new row must be precharged. We can concentrate here on the case where this is done with an explicit command. There are improvements to the protocol which, in some situations, allows this extra step to be avoided. The delays introduced by precharging still affect the operation, though.

Figure 2.9: SDRAM Precharge and Activation

Figure 2.9 shows the activity starting from one CAS signal to the CAS signal for another row. The data requested with the first CAS signal is available as before, after CL cycles. In the example two words are requested which, on a simple SDRAM, takes two cycles to transmit. Alternatively, imagine four words on a DDR chip.

Even on DRAM modules with a command rate of one the precharge command cannot be issued right away. It is necessary to wait as long as it takes to transmit the data. In this case it takes two cycles. This happens to be the same as CL but that is just a coincidence. The precharge signal has no dedicated line; instead, some implementations issue it by lowering the Write Enable (WE) and RAS line simultaneously. This combination has no useful meaning by itself (see [micronddr] for encoding details).

Once the precharge command is issued it takes tRP (Row Precharge time) cycles until the row can be selected. In Figure 2.9 much of the time (indicated by the purplish color) overlaps with the memory transfer (light blue). This is good! But tRP is larger than the transfer time and so the next RAS signal is stalled for one cycle.

If we were to continue the timeline in the diagram we would find that the next data transfer happens 5 cycles after the previous one stops. This means the data bus is only in use two cycles out of seven. Multiply this with the FSB speed and the theoretical 6.4GB/s for a 800MHz bus become 1.8GB/s. That is bad and must be avoided. The techniques described in Section 6 help to raise this number. But the programmer usually has to do her share.

There is one more timing value for a SDRAM module which we have not discussed. In Figure 2.9 the precharge command was only limited by the data transfer time. Another constraint is that an SDRAM module needs time after a RAS signal before it can precharge another row (denoted as tRAS). This number is usually pretty high, in the order of two or three times the tRP value. This is a problem if, after a RAS signal, only one CAS signal follows and the data transfer is finished in a few cycles. Assume that in Figure 2.9 the initial CAS signal was preceded directly by a RAS signal and that tRAS is 8 cycles. Then the precharge command would have to be delayed by one additional cycle since the sum of tRCD, CL, and tRP (since it is larger than the data transfer time) is only 7 cycles.

DDR modules are often described using a special notation: w-x-y-z-T. For instance: 2-3-2-8-T1. This means:

w 2 CAS Latency (CL)
x 3 RAS-to-CAS delay (tRCD)
y 2 RAS Precharge (tRP)
z 8 Active to Precharge delay (tRAS)
T T1 Command Rate

There are numerous other timing constants which affect the way commands can be issued and are handled. Those five constants are in practice sufficient to determine the performance of the module, though.

It is sometimes useful to know this information for the computers in use to be able to interpret certain measurements. It is definitely useful to know these details when buying computers since they, along with the FSB and SDRAM module speed, are among the most important factors determining a computer's speed.

The very adventurous reader could also try to tweak a system. Sometimes the BIOS allows changing some or all these values. SDRAM modules have programmable registers where these values can be set. Usually the BIOS picks the best default value. If the quality of the RAM module is high it might be possible to reduce the one or the other latency without affecting the stability of the computer. Numerous overclocking websites all around the Internet provide ample of documentation for doing this. Do it at your own risk, though and do not say you have not been warned.

2.2.3 Recharging

A mostly-overlooked topic when it comes to DRAM access is recharging. As explained in Section 2.1.2, DRAM cells must constantly be refreshed. This does not happen completely transparently for the rest of the system. At times when a row {Rows are the granularity this happens with despite what [highperfdram] and other literature says (see [micronddr]).} is recharged no access is possible. The study in [highperfdram] found that “[s]urprisingly, DRAM refresh organization can affect performance dramatically”.

Each DRAM cell must be refreshed every 64ms according to the JEDEC specification. If a DRAM array has 8,192 rows this means the memory controller has to issue a refresh command on average every 7.8125µs (refresh commands can be queued so in practice the maximum interval between two requests can be higher). It is the memory controller's responsibility to schedule the refresh commands. The DRAM module keeps track of the address of the last refreshed row and automatically increases the address counter for each new request.

There is really not much the programmer can do about the refresh and the points in time when the commands are issued. But it is important to keep this part to the DRAM life cycle in mind when interpreting measurements. If a critical word has to be retrieved from a row which currently is being refreshed the processor could be stalled for quite a long time. How long each refresh takes depends on the DRAM module.

2.2.4 Memory Types

It is worth spending some time on the current and soon-to-be current memory types in use. We will start with SDR (Single Data Rate) SDRAMs since they are the basis of the DDR (Double Data Rate) SDRAMs. SDRs were pretty simple. The memory cells and the data transfer rate were identical.

Figure 2.10: SDR SDRAM Operation

In Figure 2.10 the DRAM cell array can output the memory content at the same rate it can be transported over the memory bus. If the DRAM cell array can operate at 100MHz, the data transfer rate of the bus is thus 100Mb/s. The frequency f for all components is the same. Increasing the throughput of the DRAM chip is expensive since the energy consumption rises with the frequency. With a huge number of array cells this is prohibitively expensive. {Power = Dynamic Capacity Ч Voltage2 Ч Frequency.} In reality it is even more of a problem since increasing the frequency usually also requires increasing the voltage to maintain stability of the system. DDR SDRAM (called DDR1 retroactively) manages to improve the throughput without increasing any of the involved frequencies.

Figure 2.11: DDR1 SDRAM Operation

The difference between SDR and DDR1 is, as can be seen in Figure 2.11 and guessed from the name, that twice the amount of data is transported per cycle. I.e., the DDR1 chip transports data on the rising and falling edge. This is sometimes called a “double-pumped” bus. To make this possible without increasing the frequency of the cell array a buffer has to be introduced. This buffer holds two bits per data line. This in turn requires that, in the cell array in Figure 2.7, the data bus consists of two lines. Implementing this is trivial: one only has the use the same column address for two DRAM cells and access them in parallel. The changes to the cell array to implement this are also minimal.

The SDR DRAMs were known simply by their frequency (e.g., PC100 for 100MHz SDR). To make DDR1 DRAM sound better the marketers had to come up with a new scheme since the frequency did not change. They came with a name which contains the transfer rate in bytes a DDR module (they have 64-bit busses) can sustain:

100MHz Ч 64bit Ч 2 = 1,600MB/s

Hence a DDR module with 100MHz frequency is called PC1600. With 1600 > 100 all marketing requirements are fulfilled; it sounds much better although the improvement is really only a factor of two. {I will take the factor of two but I do not have to like the inflated numbers.}

Figure 2.12: DDR2 SDRAM Operation

To get even more out of the memory technology DDR2 includes a bit more innovation. The most obvious change that can be seen in Figure 2.12 is the doubling of the frequency of the bus. Doubling the frequency means doubling the bandwidth. Since this doubling of the frequency is not economical for the cell array it is now required that the I/O buffer gets four bits in each clock cycle which it then can send on the bus. This means the changes to the DDR2 modules consist of making only the I/O buffer component of the DIMM capable of running at higher speeds. This is certainly possible and will not require measurably more energy, it is just one tiny component and not the whole module. The names the marketers came up with for DDR2 are similar to the DDR1 names only in the computation of the value the factor of two is replaced by four (we now have a quad-pumped bus). Figure 2.13 shows the names of the modules in use today.

Array
Freq.
Bus
Freq.
Data
Rate
Name
(Rate)
Name
(FSB)
133MHz 266MHz 4,256MB/s PC2-4200 DDR2-533
166MHz 333MHz 5,312MB/s PC2-5300 DDR2-667
200MHz 400MHz 6,400MB/s PC2-6400 DDR2-800
250MHz 500MHz 8,000MB/s PC2-8000 DDR2-1000
266MHz 533MHz 8,512MB/s PC2-8500 DDR2-1066

Figure 2.13: DDR2 Module Names

There is one more twist to the naming. The FSB speed used by CPU, motherboard, and DRAM module is specified by using the effective frequency. I.e., it factors in the transmission on both flanks of the clock cycle and thereby inflates the number. So, a 133MHz module with a 266MHz bus has an FSB “frequency” of 533MHz.

The specification for DDR3 (the real one, not the fake GDDR3 used in graphics cards) calls for more changes along the lines of the transition to DDR2. The voltage will be reduced from 1.8V for DDR2 to 1.5V for DDR3. Since the power consumption equation is calculated using the square of the voltage this alone brings a 30% improvement. Add to this a reduction in die size plus other electrical advances and DDR3 can manage, at the same frequency, to get by with half the power consumption. Alternatively, with higher frequencies, the same power envelope can be hit. Or with double the capacity the same heat emission can be achieved.

The cell array of DDR3 modules will run at a quarter of the speed of the external bus which requires an 8 bit I/O buffer, up from 4 bits for DDR2. See Figure 2.14 for the schematics.

Figure 2.14: DDR3 SDRAM Operation

Initially DDR3 modules will likely have slightly higher CAS latencies just because the DDR2 technology is more mature. This would cause DDR3 to be useful only at frequencies which are higher than those which can be achieved with DDR2, and, even then, mostly when bandwidth is more important than latency. There is already talk about 1.3V modules which can achieve the same CAS latency as DDR2. In any case, the possibility of achieving higher speeds because of faster buses will outweigh the increased latency.

One possible problem with DDR3 is that, for 1,600Mb/s transfer rate or higher, the number of modules per channel may be reduced to just one. In earlier versions this requirement held for all frequencies, so one can hope that the requirement will at some point be lifted for all frequencies. Otherwise the capacity of systems will be severely limited.

Figure 2.15 shows the names of the expected DDR3 modules. JEDEC agreed so far on the first four types. Given that Intel's 45nm processors have an FSB speed of 1,600Mb/s, the 1,866Mb/s is needed for the overclocking market. We will likely see more of this towards the end of the DDR3 lifecycle.

Array
Freq.
Bus
Freq.
Data
Rate
Name
(Rate)
Name
(FSB)
100MHz 400MHz 6,400MB/s PC3-6400 DDR3-800
133MHz 533MHz 8,512MB/s PC3-8500 DDR3-1066
166MHz 667MHz 10,667MB/s PC3-10667 DDR3-1333
200MHz 800MHz 12,800MB/s PC3-12800 DDR3-1600
233MHz 933MHz 14,933MB/s PC3-14900 DDR3-1866

Figure 2.15: DDR3 Module Names

All DDR memory has one problem: the increased bus frequency makes it hard to create parallel data busses. A DDR2 module has 240 pins. All connections to data and address pins must be routed so that they have approximately the same length. Even more of a problem is that, if more than one DDR module is to be daisy-chained on the same bus, the signals get more and more distorted for each additional module. The DDR2 specification allow only two modules per bus (aka channel), the DDR3 specification only one module for high frequencies. With 240 pins per channel a single Northbridge cannot reasonably drive more than two channels. The alternative is to have external memory controllers (as in Figure 2.2) but this is expensive.

What this means is that commodity motherboards are restricted to hold at most four DDR2 or DDR3 modules. This restriction severely limits the amount of memory a system can have. Even old 32-bit IA-32 processors can handle 64GB of RAM and memory demand even for home use is growing, so something has to be done.

One answer is to add memory controllers into each processor as explained in Section 2. AMD does it with the Opteron line and Intel will do it with their CSI technology. This will help as long as the reasonable amount of memory a processor is able to use can be connected to a single processor. In some situations this is not the case and this setup will introduce a NUMA architecture and its negative effects. For some situations another solution is needed.

Intel's answer to this problem for big server machines, at least for the next years, is called Fully Buffered DRAM (FB-DRAM). The FB-DRAM modules use the same components as today's DDR2 modules which makes them relatively cheap to produce. The difference is in the connection with the memory controller. Instead of a parallel data bus FB-DRAM utilizes a serial bus (Rambus DRAM had this back when, too, and SATA is the successor of PATA, as is PCI Express for PCI/AGP). The serial bus can be driven at a much higher frequency, reverting negative impact of the serialization and even increase the bandwidth. The main effects of using a serial bus are

  1. more modules per channel can be used.
  2. more channels per Northbridge/memory controller can be used.
  3. the serial bus is designed to be fully-duplex (two lines).

An FB-DRAM module has only 69 pins, compared with the 240 for DDR2. Daisy chaining FB-DRAM modules is much easier since the electrical effects of the bus can be handled much better. The FB-DRAM specification allows up to 8 DRAM modules per channel.

Compared with the connectivity requirements of a dual-channel Northbridge it is now possible to drive 6 channels of FB-DRAM with fewer pins: 2Ч240 pins versus 6Ч69 pins. The routing for each channel is much simpler which could also help reducing the cost of the motherboards.

Fully duplex parallel busses are prohibitively expensive for the traditional DRAM modules, duplicating all those lines is too costly. With serial lines (even if they are differential, as FB-DRAM requires) this is not the case and so the serial bus is designed to be fully duplexed, which means, in some situations, that the bandwidth is theoretically doubled alone by this. But it is not the only place where parallelism is used for bandwidth increase. Since an FB-DRAM controller can run up to six channels at the same time the bandwidth can be increased even for systems with smaller amounts of RAM by using FB-DRAM. Where a DDR2 system with four modules has two channels, the same capacity can handled via four channels using an ordinary FB-DRAM controller. The actual bandwidth of the serial bus depends on the type of DDR2 (or DDR3) chips used on the FB-DRAM module.

We can summarize the advantages like this:

DDR2 FB-DRAM

Pins 240 69
Channels 2 6
DIMMs/Channel 2 8
Max Memory 16GB 192GB
Throughput ~10GB/s ~40GB/s

There are a few drawbacks to FB-DRAMs if multiple DIMMs on one channel are used. The signal is delayed—albeit minimally—at each DIMM in the chain, which means the latency increases. But for the same amount of memory with the same frequency FB-DRAM can always be faster than DDR2 and DDR3 since only one DIMM per channel is needed; for large memory systems DDR simply has no answer using commodity components.

2.2.5 Conclusions

This section should have shown that accessing DRAM is not an arbitrarily fast process. At least not fast compared with the speed the processor is running and with which it can access registers and cache. It is important to keep in mind the differences between CPU and memory frequencies. An Intel Core 2 processor running at 2.933GHz and a 1.066GHz FSB have a clock ratio of 11:1 (note: the 1.066GHz bus is quad-pumped). Each stall of one cycle on the memory bus means a stall of 11 cycles for the processor. For most machines the actual DRAMs used are slower, thusly increasing the delay. Keep these numbers in mind when we are talking about stalls in the upcoming sections.

The timing charts for the read command have shown that DRAM modules are capable of high sustained data rates. Entire DRAM rows could be transported without a single stall. The data bus could be kept occupied 100%. For DDR modules this means two 64-bit words transferred each cycle. With DDR2-800 modules and two channels this means a rate of 12.8GB/s.

But, unless designed this way, DRAM access is not always sequential. Non-continuous memory regions are used which means precharging and new RAS signals are needed. This is when things slow down and when the DRAM modules need help. The sooner the precharging can happen and the RAS signal sent the smaller the penalty when the row is actually used.

Hardware and software prefetching (see Section 6.3) can be used to create more overlap in the timing and reduce the stall. Prefetching also helps shift memory operations in time so that there is less contention at later times, right before the data is actually needed. This is a frequent problem when the data produced in one round has to be stored and the data required for the next round has to be read. By shifting the read in time, the write and read operations do not have to be issued at basically the same time.

2.3 Other Main Memory Users

Beside the CPUs there are other system components which can access the main memory. High-performance cards such as network and mass-storage controllers cannot afford to pipe all the data they need or provide through the CPU. Instead, they read or write the data directly from/to the main memory (Direct Memory Access, DMA). In Figure 2.1 we can see that the cards can talk through the South- and Northbridge directly with the memory. Other buses, like USB, also require FSB bandwidth—even though they do not use DMA—since the Southbridge is connected to the Northbridge through the FSB, too.

While DMA is certainly beneficial, it means that there is more competition for the FSB bandwidth. In times with high DMA traffic the CPU might stall more than usual while waiting for data from the main memory. There are ways around this given the right hardware. With an architecture as in Figure 2.3 one can make sure the computation uses memory on nodes which are not affected by DMA. It is also possible to attach a Southbridge to each node, equally distributing the load on the FSB of all the nodes. There are a myriad of possibilities. In Section 6 we will introduce techniques and programming interfaces which help achieving the improvements which are possible in software.

Finally it should be mentioned that some cheap systems have graphics systems without separate, dedicated video RAM. Those systems use parts of the main memory as video RAM. Since access to the video RAM is frequent (for a 1024x768 display with 16 bpp at 60Hz we are talking 94MB/s) and system memory, unlike RAM on graphics cards, does not have two ports this can substantially influence the systems performance and especially the latency. It is best to ignore such systems when performance is a priority. They are more trouble than they are worth. People buying those machines know they will not get the best performance.

Memory part 2: CPU caches

[Editor's note: This is the second installment in Ulrich Drepper's "What every programmer should know about memory" document. Those who have not read the first part will likely want to start there. This is good stuff, and we once again thank Ulrich for allowing us to publish it.

One quick request: in a document of this length there are bound to be a few typographical errors remaining. If you find one, and wish to see it corrected, please let us know via mail to lwn@lwn.net rather than by posting a comment. That way we will be sure to incorporate the fix and get it back into Ulrich's copy of the document and other readers will not have to plow through uninteresting comments.]

CPUs are today much more sophisticated than they were only 25 years ago. In those days, the frequency of the CPU core was at a level equivalent to that of the memory bus. Memory access was only a bit slower than register access. But this changed dramatically in the early 90s, when CPU designers increased the frequency of the CPU core but the frequency of the memory bus and the performance of RAM chips did not increase proportionally. This is not due to the fact that faster RAM could not be built, as explained in the previous section. It is possible but it is not economical. RAM as fast as current CPU cores is orders of magnitude more expensive than any dynamic RAM.

If the choice is between a machine with very little, very fast RAM and a machine with a lot of relatively fast RAM, the second will always win given a working set size which exceeds the small RAM size and the cost of accessing secondary storage media such as hard drives. The problem here is the speed of secondary storage, usually hard disks, which must be used to hold the swapped out part of the working set. Accessing those disks is orders of magnitude slower than even DRAM access.

Fortunately it does not have to be an all-or-nothing decision. A computer can have a small amount of high-speed SRAM in addition to the large amount of DRAM. One possible implementation would be to dedicate a certain area of the address space of the processor as containing the SRAM and the rest the DRAM. The task of the operating system would then be to optimally distribute data to make use of the SRAM. Basically, the SRAM serves in this situation as an extension of the register set of the processor.

While this is a possible implementation it is not viable. Ignoring the problem of mapping the physical resources of such SRAM-backed memory to the virtual address spaces of the processes (which by itself is terribly hard) this approach would require each process to administer in software the allocation of this memory region. The size of the memory region can vary from processor to processor (i.e., processors have different amounts of the expensive SRAM-backed memory). Each module which makes up part of a program will claim its share of the fast memory, which introduces additional costs through synchronization requirements. In short, the gains of having fast memory would be eaten up completely by the overhead of administering the resources.

So, instead of putting the SRAM under the control of the OS or user, it becomes a resource which is transparently used and administered by the processors. In this mode, SRAM is used to make temporary copies of (to cache, in other words) data in main memory which is likely to be used soon by the processor. This is possible because program code and data has temporal and spatial locality. This means that, over short periods of time, there is a good chance that the same code or data gets reused. For code this means that there are most likely loops in the code so that the same code gets executed over and over again (the perfect case for spatial locality). Data accesses are also ideally limited to small regions. Even if the memory used over short time periods is not close together there is a high chance that the same data will be reused before long (temporal locality). For code this means, for instance, that in a loop a function call is made and that function is located elsewhere in the address space. The function may be distant in memory, but calls to that function will be close in time. For data it means that the total amount of memory used at one time (the working set size) is ideally limited but the memory used, as a result of the random access nature of RAM, is not close together. Realizing that locality exists is key to the concept of CPU caches as we use them today.

A simple computation can show how effective caches can theoretically be. Assume access to main memory takes 200 cycles and access to the cache memory take 15 cycles. Then code using 100 data elements 100 times each will spend 2,000,000 cycles on memory operations if there is no cache and only 168,500 cycles if all data can be cached. That is an improvement of 91.5%.

The size of the SRAM used for caches is many times smaller than the main memory. In the author's experience with workstations with CPU caches the cache size has always been around 1/1000th of the size of the main memory (today: 4MB cache and 4GB main memory). This alone does not constitute a problem. If the size of the working set (the set of data currently worked on) is smaller than the cache size it does not matter. But computers do not have large main memories for no reason. The working set is bound to be larger than the cache. This is especially true for systems running multiple processes where the size of the working set is the sum of the sizes of all the individual processes and the kernel.

What is needed to deal with the limited size of the cache is a set of good strategies to determine what should be cached at any given time. Since not all data of the working set is used at exactly the same time we can use techniques to temporarily replace some data in the cache with other data. And maybe this can be done before the data is actually needed. This prefetching would remove some of the costs of accessing main memory since it happens asynchronously with respect to the execution of the program. All these techniques and more can be used to make the cache appear bigger than it actually is. We will discuss them in Section 3.3. Once all these techniques are exploited it is up to the programmer to help the processor. How this can be done will be discussed in Section 6.

3.1 CPU Caches in the Big Picture

Before diving into technical details of the implementation of CPU caches some readers might find it useful to first see in some more details how caches fit into the “big picture” of a modern computer system.

Figure 3.1: Minimum Cache Configuration

Figure 3.1 shows the minimum cache configuration. It corresponds to the architecture which could be found in early systems which deployed CPU caches. The CPU core is no longer directly connected to the main memory. {In even earlier systems the cache was attached to the system bus just like the CPU and the main memory. This was more a hack than a real solution.} All loads and stores have to go through the cache. The connection between the CPU core and the cache is a special, fast connection. In a simplified representation, the main memory and the cache are connected to the system bus which can also be used for communication with other components of the system. We introduced the system bus as “FSB” which is the name in use today; see Section 2.2. In this section we ignore the Northbridge; it is assumed to be present to facilitate the communication of the CPU(s) with the main memory.

Even though computers for the last several decades have used the von Neumann architecture, experience has shown that it is of advantage to separate the caches used for code and for data. Intel has used separate code and data caches since 1993 and never looked back. The memory regions needed for code and data are pretty much independent of each other, which is why independent caches work better. In recent years another advantage emerged: the instruction decoding step for the most common processors is slow; caching decoded instructions can speed up the execution, especially when the pipeline is empty due to incorrectly predicted or impossible-to-predict branches.

Soon after the introduction of the cache the system got more complicated. The speed difference between the cache and the main memory increased again, to a point that another level of cache was added, bigger and slower than the first-level cache. Only increasing the size of the first-level cache was not an option for economical reasons. Today, there are even machines with three levels of cache in regular use. A system with such a processor looks like Figure 3.2. With the increase on the number of cores in a single CPU the number of cache levels might increase in future even more.

Figure 3.2: Processor with Level 3 Cache

Figure 3.2 shows three levels of cache and introduces the nomenclature we will use in the remainder of the document. L1d is the level 1 data cache, L1i the level 1 instruction cache, etc. Note that this is a schematic; the data flow in reality need not pass through any of the higher-level caches on the way from the core to the main memory. CPU designers have a lot of freedom designing the interfaces of the caches. For programmers these design choices are invisible.

In addition we have processors which have multiple cores and each core can have multiple “threads”. The difference between a core and a thread is that separate cores have separate copies of (almost {Early multi-core processors even had separate 2nd level caches and no 3rd level cache.}) all the hardware resources. The cores can run completely independently unless they are using the same resources—e.g., the connections to the outside—at the same time. Threads, on the other hand, share almost all of the processor's resources. Intel's implementation of threads has only separate registers for the threads and even that is limited, some registers are shared. The complete picture for a modern CPU therefore looks like Figure 3.3.

Figure 3.3: Multi processor, multi-core, multi-thread

In this figure we have two processors, each with two cores, each of which has two threads. The threads share the Level 1 caches. The cores (shaded in the darker gray) have individual Level 1 caches. All cores of the CPU share the higher-level caches. The two processors (the two big boxes shaded in the lighter gray) of course do not share any caches. All this will be important, especially when we are discussing the cache effects on multi-process and multi-thread applications.

3.2 Cache Operation at High Level

To understand the costs and savings of using a cache we have to combine the knowledge about the machine architecture and RAM technology from Section 2 with the structure of caches described in the previous section.

By default all data read or written by the CPU cores is stored in the cache. There are memory regions which cannot be cached but this is something only the OS implementers have to be concerned about; it is not visible to the application programmer. There are also instructions which allow the programmer to deliberately bypass certain caches. This will be discussed in Section 6.

If the CPU needs a data word the caches are searched first. Obviously, the cache cannot contain the content of the entire main memory (otherwise we would need no cache), but since all memory addresses are cacheable, each cache entry is tagged using the address of the data word in the main memory. This way a request to read or write to an address can search the caches for a matching tag. The address in this context can be either the virtual or physical address, varying based on the cache implementation.

Since the tag requires space in addition to the actual memory, it is inefficient to chose a word as the granularity of the cache. For a 32-bit word on an x86 machine the tag itself might need 32 bits or more. Furthermore, since spatial locality is one of the principles on which caches are based, it would be bad to not take this into account. Since neighboring memory is likely to be used together it should also be loaded into the cache together. Remember also what we learned in Section 2.2.1: RAM modules are much more effective if they can transport many data words in a row without a new CAS or even RAS signal. So the entries stored in the caches are not single words but, instead, “lines” of several contiguous words. In early caches these lines were 32 bytes long; now the norm is 64 bytes. If the memory bus is 64 bits wide this means 8 transfers per cache line. DDR supports this transport mode efficiently.

When memory content is needed by the processor the entire cache line is loaded into the L1d. The memory address for each cache line is computed by masking the address value according to the cache line size. For a 64 byte cache line this means the low 6 bits are zeroed. The discarded bits are used as the offset into the cache line. The remaining bits are in some cases used to locate the line in the cache and as the tag. In practice an address value is split into three parts. For a 32-bit address it might look as follows:

With a cache line size of 2O the low O bits are used as the offset into the cache line. The next S bits select the “cache set”. We will go into more detail soon on why sets, and not single slots, are used for cache lines. For now it is sufficient to understand there are 2S sets of cache lines. This leaves the top 32 - S - O = T bits which form the tag. These T bits are the value associated with each cache line to distinguish all the aliases {All cache lines with the same S part of the address are known by the same alias.} which are cached in the same cache set. The S bits used to address the cache set do not have to be stored since they are the same for all cache lines in the same set.

When an instruction modifies memory the processor still has to load a cache line first because no instruction modifies an entire cache line at once (exception to the rule: write-combining as explained in Section 6.1). The content of the cache line before the write operation therefore has to be loaded. It is not possible for a cache to hold partial cache lines. A cache line which has been written to and which has not been written back to main memory is said to be “dirty”. Once it is written the dirty flag is cleared.

To be able to load new data in a cache it is almost always first necessary to make room in the cache. An eviction from L1d pushes the cache line down into L2 (which uses the same cache line size). This of course means room has to be made in L2. This in turn might push the content into L3 and ultimately into main memory. Each eviction is progressively more expensive. What is described here is the model for an exclusive cache as is preferred by modern AMD and VIA processors. Intel implements inclusive caches {This generalization is not completely correct. A few caches are exclusive and some inclusive caches have exclusive cache properties.} where each cache line in L1d is also present in L2. Therefore evicting from L1d is much faster. With enough L2 cache the disadvantage of wasting memory for content held in two places is minimal and it pays off when evicting. A possible advantage of an exclusive cache is that loading a new cache line only has to touch the L1d and not the L2, which could be faster.

The CPUs are allowed to manage the caches as they like as long as the memory model defined for the processor architecture is not changed. It is, for instance, perfectly fine for a processor to take advantage of little or no memory bus activity and proactively write dirty cache lines back to main memory. The wide variety of cache architectures among the processors for the x86 and x86-64, between manufacturers and even within the models of the same manufacturer, are testament to the power of the memory model abstraction.

In symmetric multi-processor (SMP) systems the caches of the CPUs cannot work independently from each other. All processors are supposed to see the same memory content at all times. The maintenance of this uniform view of memory is called “cache coherency”. If a processor were to look simply at its own caches and main memory it would not see the content of dirty cache lines in other processors. Providing direct access to the caches of one processor from another processor would be terribly expensive and a huge bottleneck. Instead, processors detect when another processor wants to read or write to a certain cache line.

If a write access is detected and the processor has a clean copy of the cache line in its cache, this cache line is marked invalid. Future references will require the cache line to be reloaded. Note that a read access on another CPU does not necessitate an invalidation, multiple clean copies can very well be kept around.

More sophisticated cache implementations allow another possibility to happen. If the cache line which another processor wants to read from or write to is currently marked dirty in the first processor's cache a different course of action is needed. In this case the main memory is out-of-date and the requesting processor must, instead, get the cache line content from the first processor. Through snooping, the first processor notices this situation and automatically sends the requesting processor the data. This action bypasses main memory, though in some implementations the memory controller is supposed to notice this direct transfer and store the updated cache line content in main memory. If the access is for writing the first processor then invalidates its copy of the local cache line.

Over time a number of cache coherency protocols have been developed. The most important is MESI, which we will introduce in Section 3.3.4. The outcome of all this can be summarized in a few simple rules:

  • A dirty cache line is not present in any other processor's cache.

  • Clean copies of the same cache line can reside in arbitrarily many caches.

If these rules can be maintained, processors can use their caches efficiently even in multi-processor systems. All the processors need to do is to monitor each others' write accesses and compare the addresses with those in their local caches. In the next section we will go into a few more details about the implementation and especially the costs.

Finally, we should at least give an impression of the costs associated with cache hits and misses. These are the numbers Intel lists for a Pentium M:

To WhereCycles
Register <= 1
L1d ~3
L2 ~14
Main Memory ~240

These are the actual access times measured in CPU cycles. It is interesting to note that for the on-die L2 cache a large part (probably even the majority) of the access time is caused by wire delays. This is a physical limitation which can only get worse with increasing cache sizes. Only process shrinking (for instance, going from 60nm for Merom to 45nm for Penryn in Intel's lineup) can improve those numbers.

The numbers in the table look high but, fortunately, the entire cost does not have to be paid for each occurrence of the cache load and miss. Some parts of the cost can be hidden. Today's processors all use internal pipelines of different lengths where the instructions are decoded and prepared for execution. Part of the preparation is loading values from memory (or cache) if they are transferred to a register. If the memory load operation can be started early enough in the pipeline, it may happen in parallel with other operations and the entire cost of the load might be hidden. This is often possible for L1d; for some processors with long pipelines for L2 as well.

There are many obstacles to starting the memory read early. It might be as simple as not having sufficient resources for the memory access or it might be that the final address of the load becomes available late as the result of another instruction. In these cases the load costs cannot be hidden (completely).

For write operations the CPU does not necessarily have to wait until the value is safely stored in memory. As long as the execution of the following instructions appears to have the same effect as if the value were stored in memory there is nothing which prevents the CPU from taking shortcuts. It can start executing the next instruction early. With the help of shadow registers which can hold values no longer available in a regular register it is even possible to change the value which is to be stored in the incomplete write operation.

Figure 3.4: Access Times for Random Writes

For an illustration of the effects of cache behavior see Figure 3.4. We will talk about the program which generated the data later; it is a simple simulation of a program which accesses a configurable amount of memory repeatedly in a random fashion. Each data item has a fixed size. The number of elements depends on the selected working set size. The Y–axis shows the average number of CPU cycles it takes to process one element; note that the scale for the Y–axis is logarithmic. The same applies in all the diagrams of this kind to the X–axis. The size of the working set is always shown in powers of two.

The graph shows three distinct plateaus. This is not surprising: the specific processor has L1d and L2 caches, but no L3. With some experience we can deduce that the L1d is 213 bytes in size and that the L2 is 220 bytes in size. If the entire working set fits into the L1d the cycles per operation on each element is below 10. Once the L1d size is exceeded the processor has to load data from L2 and the average time springs up to around 28. Once the L2 is not sufficient anymore the times jump to 480 cycles and more. This is when many or most operations have to load data from main memory. And worse: since data is being modified dirty cache lines have to be written back, too.

This graph should give sufficient motivation to look into coding improvements which help improve cache usage. We are not talking about a few measly percent here; we are talking about orders-of-magnitude improvements which are sometimes possible. In Section 6 we will discuss techniques which allow writing more efficient code. The next section goes into more details of CPU cache designs. The knowledge is good to have but not necessary for the rest of the paper. So this section could be skipped.

3.3 CPU Cache Implementation Details

Cache implementers have the problem that each cell in the huge main memory potentially has to be cached. If the working set of a program is large enough this means there are many main memory locations which fight for each place in the cache. Previously it was noted that a ratio of 1-to-1000 for cache versus main memory size is not uncommon.

3.3.1 Associativity

It would be possible to implement a cache where each cache line can hold a copy of any memory location. This is called a fully associative cache. To access a cache line the processor core would have to compare the tags of each and every cache line with the tag for the requested address. The tag would be comprised of the entire part of the address which is not the offset into the cache line (that means, S in the figure on Section 3.2 is zero).

There are caches which are implemented like this but, by looking at the numbers for an L2 in use today, will show that this is impractical. Given a 4MB cache with 64B cache lines the cache would have 65,536 entries. To achieve adequate performance the cache logic would have to be able to pick from all these entries the one matching a given tag in just a few cycles. The effort to implement this would be enormous.

Figure 3.5: Fully Associative Cache Schematics

For each cache line a comparator is needed to compare the large tag (note, S is zero). The letter next to each connection indicates the width in bits. If none is given it is a single bit line. Each comparator has to compare two T-bit-wide values. Then, based on the result, the appropriate cache line content is selected and made available. This requires merging as many sets of O data lines as there are cache buckets. The number of transistors needed to implement a single comparator is large especially since it must work very fast. No iterative comparator is usable. The only way to save on the number of comparators is to reduce the number of them by iteratively comparing the tags. This is not suitable for the same reason that iterative comparators are not: it takes too long.

Fully associative caches are practical for small caches (for instance, the TLB caches on some Intel processors are fully associative) but those caches are small, really small. We are talking about a few dozen entries at most.

For L1i, L1d, and higher level caches a different approach is needed. What can be done is to restrict the search. In the most extreme restriction each tag maps to exactly one cache entry. The computation is simple: given the 4MB/64B cache with 65,536 entries we can directly address each entry by using bits 5 to 21 of the address (16 bits). The low 6 bits are the index into the cache line.

Figure 3.6: Direct-Mapped Cache Schematics

Such a direct-mapped cache is fast and relatively easy to implement as can be seen in Figure 3.6. It requires exactly one comparator, one multiplexer (two in this diagram where tag and data are separated, but this is not a hard requirement on the design), and some logic to select only valid cache line content. The comparator is complex due to the speed requirements but there is only one of them now; as a result more effort can be spent on making it fast. The real complexity in this approach lies in the multiplexers. The number of transistors in a simple multiplexer grows with O(log N), where N is the number of cache lines. This is tolerable but might get slow, in which case speed can be increased by spending more real estate on transistors in the multiplexers to parallelize some of the work and to increase the speed. The total number of transistors can grow slowly with a growing cache size which makes this solution very attractive. But it has a drawback: it only works well if the addresses used by the program are evenly distributed with respect to the bits used for the direct mapping. If they are not, and this is usually the case, some cache entries are heavily used and therefore repeated evicted while others are hardly used at all or remain empty.

Figure 3.7: Set-Associative Cache Schematics

This problem can be solved by making the cache set associative. A set-associative cache combines the features of the full associative and direct-mapped caches to largely avoid the weaknesses of those designs. Figure 3.7 shows the design of a set-associative cache. The tag and data storage are divided into sets which are selected by the address. This is similar to the direct-mapped cache. But instead of only having one element for each set value in the cache a small number of values is cached for the same set value. The tags for all the set members is compared in parallel, which is similar to the functioning of the fully associative cache.

The result is a cache which is not easily defeated by unfortunate or deliberate selection of addresses with the same set numbers and at the same time the size of the cache is not limited by the number of comparators which can be implemented in parallel. If the cache grows it is (in this figure) only the number of columns which increases, not the number of rows. The number of rows only increases if the associativity of the cache is increased. Today processors are using associativity levels of up to 16 for L2 caches or higher. L1 caches usually get by with 8.

L2
Cache
Size
Associativity
Direct 2 4 8
CL=32CL=64 CL=32CL=64 CL=32CL=64 CL=32CL=64
512k 27,794,595 20,422,527 25,222,611 18,303,581 24,096,510 17,356,121 23,666,929 17,029,334
1M 19,007,315 13,903,854 16,566,738 12,127,174 15,537,500 11,436,705 15,162,895 11,233,896
2M 12,230,962 8,801,403 9,081,881 6,491,011 7,878,601 5,675,181 7,391,389 5,382,064
4M 7,749,986 5,427,836 4,736,187 3,159,507 3,788,122 2,418,898 3,430,713 2,125,103
8M 4,731,904 3,209,693 2,690,498 1,602,957 2,207,655 1,228,190 2,111,075 1,155,847
16M 2,620,587 1,528,592 1,958,293 1,089,580 1,704,878 883,530 1,671,541 862,324

Table 3.1: Effects of Cache Size, Associativity, and Line Size

Given our 4MB/64B cache and 8-way set associativity the cache we are left with has 8,192 sets and only 13 bits of the tag are used in addressing the cache set. To determine which (if any) of the entries in the cache set contains the addressed cache line 8 tags have to be compared. That is feasible to do in very short time. With an experiment we can see that this makes sense.

Table 3.1 shows the number of L2 cache misses for a program (gcc in this case, the most important benchmark of them all, according to the Linux kernel people) for changing cache size, cache line size, and associativity set size. In Section 7.2 we will introduce the tool to simulate the caches as required for this test.

Just in case this is not yet obvious, the relationship of all these values is that the cache size is

cache line size Ч associativity Ч number of sets

The addresses are mapped into the cache by using

O = log2 cache line size
S = log2 number of sets

in the way the figure in Section 3.2 shows.

Figure 3.8: Cache Size vs Associativity (CL=32)

Figure 3.8 makes the data of the table more comprehensible. It shows the data for a fixed cache line size of 32 bytes. Looking at the numbers for a given cache size we can see that associativity can indeed help to reduce the number of cache misses significantly. For an 8MB cache going from direct mapping to 2-way set associative cache saves almost 44% of the cache misses. The processor can keep more of the working set in the cache with a set associative cache compared with a direct mapped cache.

In the literature one can occasionally read that introducing associativity has the same effect as doubling cache size. This is true in some extreme cases as can be seen in the jump from the 4MB to the 8MB cache. But it certainly is not true for further doubling of the associativity. As we can see in the data, the successive gains are much smaller. We should not completely discount the effects, though. In the example program the peak memory use is 5.6M. So with a 8MB cache there are unlikely to be many (more than two) uses for the same cache set. With a larger working set the savings can be higher as we can see from the larger benefits of associativity for the smaller cache sizes.

In general, increasing the associativity of a cache above 8 seems to have little effects for a single-thread workload. With the introduction of multi-core processors which use a shared L2 the situation changes. Now you basically have two programs hitting on the same cache which causes the associativity in practice to be halved (or quartered for quad-core processors). So it can be expected that, with increasing numbers of cores, the associativity of the shared caches should grow. Once this is not possible anymore (16-way set associativity is already hard) processor designers have to start using shared L3 caches and beyond, while L2 caches are potentially shared by a subset of the cores.

Another effect we can study in Figure 3.8 is how the increase in cache size helps with performance. This data cannot be interpreted without knowing about the working set size. Obviously, a cache as large as the main memory would lead to better results than a smaller cache, so there is in general no limit to the largest cache size with measurable benefits.

As already mentioned above, the size of the working set at its peak is 5.6M. This does not give us any absolute number of the maximum beneficial cache size but it allows us to estimate the number. The problem is that not all the memory used is contiguous and, therefore, we have, even with a 16M cache and a 5.6M working set, conflicts (see the benefit of the 1-way set associative 16MB cache over the direct mapped version). But it is a safe bet that with the same workload the benefits of a 32MB cache would be negligible. But who says the working set has to stay the same? Workloads are growing over time and so should the cache size. When buying machines, and one has to choose the cache size one is willing to pay for, it is worthwhile to measure the working set size. Why this is important can be seen in the figures on Figure 3.10.

Figure 3.9: Test Memory Layouts

Two types of tests are run. In the first test the elements are processed sequentially. The test program follows the pointer n but the array elements are chained so that they are traversed in the order in which they are found in memory. This can be seen in the lower part of Figure 3.9. There is one back reference from the last element. In the second test (upper part of the figure) the array elements are traversed in a random order. In both cases the array elements form a circular single-linked list.

3.3.2 Measurements of Cache Effects

All the figures are created by measuring a program which can simulate working sets of arbitrary size, read and write access, and sequential or random access. We have already seen some results in Figure 3.4. The program creates an array corresponding to the working set size of elements of this type:

  struct l {
     struct l *n;
     long int pad[NPAD];
   };
 

All entries are chained in a circular list using the n element, either in sequential or random order. Advancing from one entry to the next always uses the pointer, even if the elements are laid out sequentially. The pad element is the payload and it can grow arbitrarily large. In some tests the data is modified, in others the program only performs read operations.

In the performance measurements we are talking about working set sizes. The working set is made up of an array of struct l elements. A working set of 2N bytes contains

2N/sizeof(struct l)

elements. Obviously sizeof(struct l) depends on the value of NPAD. For 32-bit systems, NPAD=7 means the size of each array element is 32 bytes, for 64-bit systems the size is 64 bytes.

Single Threaded Sequential Access

The simplest case is a simple walk over all the entries in the list. The list elements are laid out sequentially, densely packed. Whether the order of processing is forward or backward does not matter, the processor can deal with both directions equally well. What we measure here—and in all the following tests—is how long it takes to handle a single list element. The time unit is a processor cycle. Figure 3.10 shows the result. Unless otherwise specified, all measurements are made on a Pentium 4 machine in 64-bit mode which means the structure l with NPAD=0 is eight bytes in size.

Figure 3.10: Sequential Read Access, NPAD=0

Figure 3.11: Sequential Read for Several Sizes

The first two measurements are polluted by noise. The measured workload is simply too small to filter the effects of the rest of the system out. We can safely assume that the values are all at the 4 cycles level. With this in mind we can see three distinct levels:

  • Up to a working set size of 214 bytes.

  • From 215 bytes to 220 bytes.

  • From 221 bytes and up.

These steps can be easily explained: the processor has a 16kB L1d and 1MB L2. We do not see sharp edges in the transition from one level to the other because the caches are used by other parts of the system as well and so the cache is not exclusively available for the program data. Specifically the L2 cache is a unified cache and also used for the instructions (NB: Intel uses inclusive caches).

What is perhaps not quite expected are the actual times for the different working set sizes. The times for the L1d hits are expected: load times after an L1d hit are around 4 cycles on the P4. But what about the L2 accesses? Once the L1d is not sufficient to hold the data one might expect it would take 14 cycles or more per element since this is the access time for the L2. But the results show that only about 9 cycles are required. This discrepancy can be explained by the advanced logic in the processors. In anticipation of using consecutive memory regions, the processor prefetches the next cache line. This means that when the next line is actually used it is already halfway loaded. The delay required to wait for the next cache line to be loaded is therefore much less than the L2 access time.

The effect of prefetching is even more visible once the working set size grows beyond the L2 size. Before we said that a main memory access takes 200+ cycles. Only with effective prefetching is it possible for the processor to keep the access times as low as 9 cycles. As we can see from the difference between 200 and 9, this works out nicely.

We can observe the processor while prefetching, at least indirectly. In Figure 3.11 we see the times for the same working set sizes but this time we see the graphs for different sizes of the structure l. This means we have fewer but larger elements in the list. The different sizes have the effect that the distance between the n elements in the (still consecutive) list grows. In the four cases of the graph the distance is 0, 56, 120, and 248 bytes respectively.

At the bottom we can see the line from the previous graph, but this time it appears more or less as a flat line. The times for the other cases are simply so much worse. We can see in this graph, too, the three different levels and we see the large errors in the tests with the small working set sizes (ignore them again). The lines more or less all match each other as long as only the L1d is involved. There is no prefetching necessary so all element sizes just hit the L1d for each access.

For the L2 cache hits we see that the three new lines all pretty much match each other but that they are at a higher level (about 28). This is the level of the access time for the L2. This means prefetching from L2 into L1d is basically disabled. Even with NPAD=7 we need a new cache line for each iteration of the loop; for NPAD=0, instead, the loop has to iterate eight times before the next cache line is needed. The prefetch logic cannot load a new cache line every cycle. Therefore we see a stall to load from L2 in every iteration.

It gets even more interesting once the working set size exceeds the L2 capacity. Now all four lines vary widely. The different element sizes play obviously a big role in the difference in performance. The processor should recognize the size of the strides and not fetch unnecessary cache lines for NPAD=15 and 31 since the element size is smaller than the prefetch window (see Section 6.3.1). Where the element size is hampering the prefetching efforts is a result of a limitation of hardware prefetching: it cannot cross page boundaries. We are reducing the effectiveness of the hardware scheduler by 50% for each size increase. If the hardware prefetcher were allowed to cross page boundaries and the next page is not resident or valid the OS would have to get involved in locating the page. That means the program would experience a page fault it did not initiate itself. This is completely unacceptable since the processor does not know whether a page is not present or does not exist. In the latter case the OS would have to abort the process. In any case, given that, for NPAD=7 and higher, we need one cache line per list element the hardware prefetcher cannot do much. There simply is no time to load the data from memory since all the processor does is read one word and then load the next element.

Another big reason for the slowdown are the misses of the TLB cache. This is a cache where the results of the translation of a virtual address to a physical address are stored, as is explained in more detail in Section 4. The TLB cache is quite small since it has to be extremely fast. If more pages are accessed repeatedly than the TLB cache has entries for the translation from virtual to physical address has to be constantly repeated. This is a very costly operation. With larger element sizes the cost of a TLB lookup is amortized over fewer elements. That means the total number of TLB entries which have to be computed per list element is higher.

To observe the TLB effects we can run a different test. For one measurement we lay out the elements sequentially as usual. We use NPAD=7 for elements which occupy one entire cache line. For the second measurement we place each list element on a separate page. The rest of each page is left untouched and we do not count it in the total for the working set size. {Yes, this is a bit inconsistent because in the other tests we count the unused part of the struct in the element size and we could define NPAD so that each element fills a page. In that case the working set sizes would be very different. This is not the point of this test, though, and since prefetching is ineffective anyway this makes little difference.} The consequence is that, for the first measurement, each list iteration requires a new cache line and, for every 64 elements, a new page. For the second measurement each iteration requires loading a new cache line which is on a new page.

Figure 3.12: TLB Influence for Sequential Read

The result can be seen in Figure 3.12. The measurements were performed on the same machine as Figure 3.11. Due to limitations of the available RAM the working set size had to be restricted to 224 bytes which requires 1GB to place the objects on separate pages. The lower, red curve corresponds exactly to the NPAD=7 curve in Figure 3.11. We see the distinct steps showing the sizes of the L1d and L2 caches. The second curve looks radically different. The important feature is the huge spike starting when the working set size reaches 213 bytes. This is when the TLB cache overflows. With an element size of 64 bytes we can compute that the TLB cache has 64 entries. There are no page faults affecting the cost since the program locks the memory to prevent it from being swapped out.

As can be seen the number of cycles it takes to compute the physical address and store it in the TLB is very high. The graph in Figure 3.12 shows the extreme case, but it should now be clear that a significant factor in the slowdown for larger NPAD values is the reduced efficiency of the TLB cache. Since the physical address has to be computed before a cache line can be read for either L2 or main memory the address translation penalties are additive to the memory access times. This in part explains why the total cost per list element for NPAD=31 is higher than the theoretical access time for the RAM.

Figure 3.13: Sequential Read and Write, NPAD=1

We can glimpse a few more details of the prefetch implementation by looking at the data of test runs where the list elements are modified. Figure 3.13 shows three lines. The element width is in all cases 16 bytes. The first line is the now familiar list walk which serves as a baseline. The second line, labeled “Inc”, simply increments the pad[0] member of the current element before going on to the next. The third line, labeled “Addnext0”, takes the pad[0] list element of the next element and adds it to the pad[0] member of the current list element.

The naпve assumption would be that the “Addnext0” test runs slower because it has more work to do. Before advancing to the next list element a value from that element has to be loaded. This is why it is surprising to see that this test actually runs, for some working set sizes, faster than the “Inc” test. The explanation for this is that the load from the next list element is basically a forced prefetch. Whenever the program advances to the next list element we know for sure that element is already in the L1d cache. As a result we see that the “Addnext0” performs as well as the simple “Follow” test as long as the working set size fits into the L2 cache.

The “Addnext0” test runs out of L2 faster than the “Inc” test, though. It needs more data loaded from main memory. This is why the “Addnext0” test reaches the 28 cycles level for a working set size of 221 bytes. The 28 cycles level is twice as high as the 14 cycles level the “Follow” test reaches. This is easy to explain, too. Since the other two tests modify memory an L2 cache eviction to make room for new cache lines cannot simply discard the data. Instead it has to be written to memory. This means the available bandwidth on the FSB is cut in half, hence doubling the time it takes to transfer the data from main memory to L2.

Figure 3.14: Advantage of Larger L2/L3 Caches

One last aspect of the sequential, efficient cache handling is the size of the cache. This should be obvious but it still should be pointed out. Figure 3.14 shows the timing for the Increment benchmark with 128-byte elements (NPAD=15 on 64-bit machines). This time we see the measurement from three different machines. The first two machines are P4s, the last one a Core2 processor. The first two differentiate themselves by having different cache sizes. The first processor has a 32k L1d and an 1M L2. The second one has 16k L1d, 512k L2, and 2M L3. The Core2 processor has 32k L1d and 4M L2.

The interesting part of the graph is not necessarily how well the Core2 processor performs relative to the other two (although it is impressive). The main point of interest here is the region where the working set size is too large for the respective last level cache and the main memory gets heavily involved.

Set
Size
Sequential Random
L2 Hit L2 Miss #Iter Ratio Miss/Hit L2 Accesses Per Iter L2 Hit L2 Miss #Iter Ratio Miss/Hit L2 Accesses Per Iter
22088,63684316,3840.94%5.530,46247211,02413.42%34.4
22188,1051,5848,1921.77%10.921,81715,15151240.98%72.2
22288,1061,6004,0961.78%21.922,25822,28525650.03% 174.0
22388,1041,6142,0481.80%43.827,52126,27412848.84% 420.3
22488,1141,6551,0241.84%87.733,16629,1156446.75%973.1
22588,1121,7305121.93%175.539,85832,3603244.81%2,256.8
22688,1121,9062562.12%351.648,53938,1511644.01%5,418.1
22788,1142,2441282.48%705.962,42352,049845.47%14,309.0
22888,1202,939643.23%1,422.881,90687,1674 51.56%42,268.3
22988,1374,318324.67%2,889.2119,079163,398257.84% 141,238.5

Table 3.2: L2 Hits and Misses for Sequential and Random Walks, NPAD=0

As expected, the larger the last level cache is the longer the curve stays at the low level corresponding to the L2 access costs. The important part to notice is the performance advantage this provides. The second processor (which is slightly older) can perform the work on the working set of 220 bytes twice as fast as the first processor. All thanks to the increased last level cache size. The Core2 processor with its 4M L2 performs even better.

For a random workload this might not mean that much. But if the workload can be tailored to the size of the last level cache the program performance can be increased quite dramatically. This is why it sometimes is worthwhile to spend the extra money for a processor with a larger cache.

Single Threaded Random Access Measurements

We have seen that the processor is able to hide most of the main memory and even L2 access latency by prefetching cache lines into L2 and L1d. This can work well only when the memory access is predictable, though.

Figure 3.15: Sequential vs Random Read, NPAD=0

If the access is unpredictable or random the situation is quite different. Figure 3.15 compares the per-list-element times for the sequential access (same as in Figure 3.10) with the times when the list elements are randomly distributed in the working set. The order is determined by the linked list which is randomized. There is no way for the processor to reliably prefetch data. This can only work by chance if elements which are used shortly after one another are also close to each other in memory.

There are two important points to note in Figure 3.15. First, the large number is cycles needed for growing working set sizes. The machine makes it possible to access the main memory in 200-300 cycles but here we reach 450 cycles and more. We have seen this phenomenon before (compare Figure 3.11). The automatic prefetching is actually working to a disadvantage here.

The second interesting point is that the curve is not flattening at various plateaus as it has been for the sequential access cases. The curve keeps on rising. To explain this we can measure the L2 access of the program for the various working set sizes. The result can be seen in Figure 3.16 and Table 3.2.

The figure shows the when the working set size is larger than the L2 size the cache miss ratio (L2 misses / L2 access) starts to grow. The curve has a similar form to the one in Figure 3.15: it rises quickly, declines slightly, and starts to rise again. There is a strong correlation with the cycles per list element graph. The L2 miss rate will grow until it eventually reaches close to 100%. Given a large enough working set (and RAM) the probability that any of the randomly picked cache lines is in L2 or is in the process of being loaded can be reduced arbitrarily.

The increasing cache miss rate alone explains some of the costs. But there is another factor. Looking at Table 3.2 we can see in the L2/#Iter columns that the total number of L2 uses per iteration of the program is growing. Each working set is twice as large as the one before. So, without caching we would expect double the main memory accesses. With caches and (almost) perfect predictability we see the modest increase in the L2 use shown in the data for sequential access. The increase is due to the increase of the workspace set size and nothing else.

Figure 3.16: L2d Miss Ratio

Figure 3.17: Page-Wise Randomization, NPAD=7

For random access the per-element time increases by more than 100% for each doubling of the working set size. This means the average access time per list element increases since the working set size only doubles. The reason behind this is a rising rate of TLB misses. In Figure 3.17 we see the cost for random accesses for NPAD=7. Only this time the randomization is modified. While in the normal case the entire list of randomized as one block (indicated by the label ∞) the other 11 curves show randomizations which are performed in smaller blocks. For the curve labeled '60' each set of 60 pages (245.760 bytes) is randomized individually. That means all list elements in block are traversed before going over to an element in the next block. This has the effect that number of TLB entries which are used at any one time is limited.

The element size for NPAD=7 is 64 bytes, which corresponds to the cache line size. Due to the randomized order of the list elements it is unlikely that the hardware prefetcher has any effect, most certainly not for more than a handful of elements. This means the L2 cache miss rate does not differ significantly from the randomization of the entire list in one block. The performance of the test with increasing block size approaches asymptotically the curve for the one-block randomization. This means the performance of this latter test case is significantly influenced by the TLB misses. If the TLB misses can be lowered the performance increases significantly (in one test we will see later up to 38%).

3.3.3 Write Behavior

Before we start looking at the cache behavior when multiple execution contexts (threads or processes) use the same memory we have to explore a detail of cache implementations. Caches are supposed to be coherent and this coherency is supposed to be completely transparent for the userlevel code. Kernel code is a different story; it occasionally requires cache flushes.

This specifically means that, if a cache line is modified, the result for the system after this point in time is the same as if there were no cache at all and the main memory location itself had been modified. This can be implemented in two ways or policies:

  • write-through cache implementation;
  • write-back cache implementation.

The write-through cache is the simplest way to implement cache coherency. If the cache line is written to, the processor immediately also writes the cache line into main memory. This ensures that, at all times, the main memory and cache are in sync. The cache content could simply be discarded whenever a cache line is replaced. This cache policy is simple but not very fast. A program which, for instance, modifies a local variable over and over again would create a lot of traffic on the FSB even though the data is likely not used anywhere else and might be short-lived.

The write-back policy is more sophisticated. Here the processor does not immediately write the modified cache line back to main memory. Instead, the cache line is only marked as dirty. When the cache line is dropped from the cache at some point in the future the dirty bit will instruct the processor to write the data back at that time instead of just discarding the content.

Write-back caches have the chance to be significantly better performing, which is why most memory in a system with a decent processor is cached this way. The processor can even take advantage of free capacity on the FSB to store the content of a cache line before the line has to be evacuated. This allows the dirty bit to be cleared and the processor can just drop the cache line when the room in the cache is needed.

But there is a significant problem with the write-back implementation. When more than one processor (or core or hyper-thread) is available and accessing the same memory it must still be assured that both processors see the same memory content at all times. If a cache line is dirty on one processor (i.e., it has not been written back yet) and a second processor tries to read the same memory location, the read operation cannot just go out to the main memory. Instead the content of the first processor's cache line is needed. In the next section we will see how this is currently implemented.

Before we get to this there are two more cache policies to mention:

  • write-combining; and
  • uncacheable.

Both these policies are used for special regions of the address space which are not backed by real RAM. The kernel sets up these policies for the address ranges (on x86 processors using the Memory Type Range Registers, MTRRs) and the rest happens automatically. The MTRRs are also usable to select between write-through and write-back policies.

Write-combining is a limited caching optimization more often used for RAM on devices such as graphics cards. Since the transfer costs to the devices are much higher than the local RAM access it is even more important to avoid doing too many transfers. Transferring an entire cache line just because a word in the line has been written is wasteful if the next operation modifies the next word. One can easily imagine that this is a common occurrence, the memory for horizontal neighboring pixels on a screen are in most cases neighbors, too. As the name suggests, write-combining combines multiple write accesses before the cache line is written out. In ideal cases the entire cache line is modified word by word and, only after the last word is written, the cache line is written to the device. This can speed up access to RAM on devices significantly.

Finally there is uncacheable memory. This usually means the memory location is not backed by RAM at all. It might be a special address which is hardcoded to have some functionality outside the CPU. For commodity hardware this most often is the case for memory mapped address ranges which translate to accesses to cards and devices attached to a bus (PCIe etc). On embedded boards one sometimes finds such a memory address which can be used to turn an LED on and off. Caching such an address would obviously be a bad idea. LEDs in this context are used for debugging or status reports and one wants to see this as soon as possible. The memory on PCIe cards can change without the CPU's interaction, so this memory should not be cached.

3.3.4 Multi-Processor Support

In the previous section we have already pointed out the problem we have when multiple processors come into play. Even multi-core processors have the problem for those cache levels which are not shared (at least the L1d).

It is completely impractical to provide direct access from one processor to the cache of another processor. The connection is simply not fast enough, for a start. The practical alternative is to transfer the cache content over to the other processor in case it is needed. Note that this also applies to caches which are not shared on the same processor.

The question now is when does this cache line transfer have to happen? This question is pretty easy to answer: when one processor needs a cache line which is dirty in another processor's cache for reading or writing. But how can a processor determine whether a cache line is dirty in another processor's cache? Assuming it is just because a cache line is loaded by another processor would be suboptimal (at best). Usually the majority of memory accesses are read accesses and the resulting cache lines are not dirty. Processor operations on cache lines are frequent (of course, why else would we have this paper?) which means broadcasting information about changed cache lines after each write access would be impractical.

What developed over the years is the MESI cache coherency protocol (Modified, Exclusive, Shared, Invalid). The protocol is named after the four states a cache line can be in when using the MESI protocol:

  • Modified: The local processor has modified the cache line. This also implies it is the only copy in any cache.

  • Exclusive: The cache line is not modified but known to not be loaded into any other processor's cache.

  • Shared: The cache line is not modified and might exist in another processor's cache.

  • Invalid: The cache line is invalid, i.e., unused.

This protocol developed over the years from simpler versions which were less complicated but also less efficient. With these four states it is possible to efficiently implement write-back caches while also supporting concurrent use of read-only data on different processors.

Figure 3.18: MESI Protocol Transitions

The state changes are accomplished without too much effort by the processors listening, or snooping, on the other processors' work. Certain operations a processor performs are announced on external pins and thus make the processor's cache handling visible to the outside. The address of the cache line in question is visible on the address bus. In the following description of the states and their transitions (shown in Figure 3.18) we will point out when the bus is involved.

Initially all cache lines are empty and hence also Invalid. If data is loaded into the cache for writing the cache changes to Modified. If the data is loaded for reading the new state depends on whether another processor has the cache line loaded as well. If this is the case then the new state is Shared, otherwise Exclusive.

If a Modified cache line is read from or written to on the local processor, the instruction can use the current cache content and the state does not change. If a second processor wants to read from the cache line the first processor has to send the content of its cache to the second processor and then it can change the state to Shared. The data sent to the second processor is also received and processed by the memory controller which stores the content in memory. If this did not happen the cache line could not be marked as Shared. If the second processor wants to write to the cache line the first processor sends the cache line content and marks the cache line locally as Invalid. This is the infamous “Request For Ownership” (RFO) operation. Performing this operation in the last level cache, just like the I→M transition is comparatively expensive. For write-through caches we also have to add the time it takes to write the new cache line content to the next higher-level cache or the main memory, further increasing the cost.

If a cache line is in the Shared state and the local processor reads from it no state change is necessary and the read request can be fulfilled from the cache. If the cache line is locally written to the cache line can be used as well but the state changes to Modified. It also requires that all other possible copies of the cache line in other processors are marked as Invalid. Therefore the write operation has to be announced to the other processors via an RFO message. If the cache line is requested for reading by a second processor nothing has to happen. The main memory contains the current data and the local state is already Shared. In case a second processor wants to write to the cache line (RFO) the cache line is simply marked Invalid. No bus operation is needed.

The Exclusive state is mostly identical to the Shared state with one crucial difference: a local write operation does not have to be announced on the bus. The local cache copy is known to be the only one. This can be a huge advantage so the processor will try to keep as many cache lines as possible in the Exclusive state instead of the Shared state. The latter is the fallback in case the information is not available at that moment. The Exclusive state can also be left out completely without causing functional problems. It is only the performance that will suffer since the E→M transition is much faster than the S→M transition.

From this description of the state transitions it should be clear where the costs specific to multi-processor operations are. Yes, filling caches is still expensive but now we also have to look out for RFO messages. Whenever such a message has to be sent things are going to be slow.

There are two situations when RFO messages are necessary:

  • A thread is migrated from one processor to another and all the cache lines have to be moved over to the new processor once.

  • A cache line is truly needed in two different processors. {At a smaller level the same is true for two cores on the same processor. The costs are just a bit smaller. The RFO message is likely to be sent many times.}

In multi-thread or multi-process programs there is always some need for synchronization; this synchronization is implemented using memory. So there are some valid RFO messages. They still have to be kept as infrequent as possible. There are other sources of RFO messages, though. In Section 6 we will explain these scenarios. The Cache coherency protocol messages must be distributed among the processors of the system. A MESI transition cannot happen until it is clear that all the processors in the system have had a chance to reply to the message. That means that the longest possible time a reply can take determines the speed of the coherency protocol. {Which is why we see nowadays, for instance, AMD Opteron systems with three sockets. Each processor is exactly one hop away given that the processors only have three hyperlinks and one is needed for the Southbridge connection.} Collisions on the bus are possible, latency can be high in NUMA systems, and of course sheer traffic volume can slow things down. All good reasons to focus on avoiding unnecessary traffic.

There is one more problem related to having more than one processor in play. The effects are highly machine specific but in principle the problem always exists: the FSB is a shared resource. In most machines all processors are connected via one single bus to the memory controller (see Figure 2.1). If a single processor can saturate the bus (as is usually the case) then two or four processors sharing the same bus will restrict the bandwidth available to each processor even more.

Even if each processor has its own bus to the memory controller as in Figure 2.2 there is still the bus to the memory modules. Usually this is one bus but, even in the extended model in Figure 2.2, concurrent accesses to the same memory module will limit the bandwidth.

The same is true with the AMD model where each processor can have local memory. Yes, all processors can concurrently access their local memory quickly. But multi-thread and multi-process programs--at least from time to time--have to access the same memory regions to synchronize.

Concurrency is severely limited by the finite bandwidth available for the implementation of the necessary synchronization. Programs need to be carefully designed to minimize accesses from different processors and cores to the same memory locations. The following measurements will show this and the other cache effects related to multi-threaded code.

Multi Threaded Measurements

To ensure that the gravity of the problems introduced by concurrently using the same cache lines on different processors is understood, we will look here at some more performance graphs for the same program we used before. This time, though, more than one thread is running at the same time. What is measured is the fastest runtime of any of the threads. This means the time for a complete run when all threads are done is even higher. The machine used has four processors; the tests use up to four threads. All processors share one bus to the memory controller and there is only one bus to the memory modules.

Figure 3.19: Sequential Read Access, Multiple Threads

Figure 3.19 shows the performance for sequential read-only access for 128 bytes entries (NPAD=15 on 64-bit machines). For the curve for one thread we can expect a curve similar to Figure 3.11. The measurements are for a different machine so the actual numbers vary.

The important part in this figure is of course the behavior when running multiple threads. Note that no memory is modified and no attempts are made to keep the threads in sync when walking the linked list. Even though no RFO messages are necessary and all the cache lines can be shared, we see up to an 18% performance decrease for the fastest thread when two threads are used and up to 34% when four threads are used. Since no cache lines have to be transported between the processors this slowdown is solely caused by one or both of the two bottlenecks: the shared bus from the processor to the memory controller and bus from the memory controller to the memory modules. Once the working set size is larger than the L3 cache in this machine all three threads will be prefetching new list elements. Even with two threads the available bandwidth is not sufficient to scale linearly (i.e., have no penalty from running multiple threads).

When we modify memory things get even uglier. Figure 3.20 shows the results for the sequential Increment test.

Figure 3.20: Sequential Increment, Multiple Threads

This graph is using a logarithmic scale for the Y axis. So, do not be fooled by the apparently small differences. We still have about a 18% penalty for running two threads and now an amazing 93% penalty for running four threads. This means the prefetch traffic together with the write-back traffic is pretty much saturating the bus when four threads are used.

We use the logarithmic scale to show the results for the L1d range. What can be seen is that, as soon as more than one thread is running, the L1d is basically ineffective. The single-thread access times exceed 20 cycles only when the L1d is not sufficient to hold the working set. When multiple threads are running, those access times are hit immediately, even with the smallest working set sizes.

One aspect of the problem is not shown here. It is hard to measure with this specific test program. Even though the test modifies memory and we therefore must expect RFO messages we do not see higher costs for the L2 range when more than one thread is used. The program would have to use a large amount of memory and all threads must access the same memory in parallel. This is hard to achieve without a lot of synchronization which would then dominate the execution time.

Figure 3.21: Random Addnextlast, Multiple Threads

Finally in Figure 3.21 we have the numbers for the Addnextlast test with random access of memory. This figure is provided mainly to show to the appallingly high numbers. It now take around 1,500 cycles to process a single list element in the extreme case. The use of more threads is even more questionable. We can summarize the efficiency of multiple thread use in a table.

#ThreadsSeq ReadSeq IncRand Add
2 1.69 1.69 1.54
4 2.98 2.07 1.65

Table 3.3: Efficiency for Multiple Threads

The table shows the efficiency for the multi-thread run with the largest working set size in the three figures on Figure 3.21. The number shows the best possible speed-up the test program incurs for the largest working set size by using two or four threads. For two threads the theoretical limits for the speed-up is 2 and, for four threads, 4. The numbers for two threads are not that bad. But for four threads the numbers for the last test show that it is almost not worth it to scale beyond two threads. The additional benefit is minuscule. We can see this more easily if we represent the data in Figure 3.21 a bit differently.

Figure 3.22: Speed-Up Through Parallelism

The curves in Figure 3.22 show the speed-up factors, i.e., relative performance compared to the code executed by a single thread. We have to ignore the smallest sizes, the measurements are not accurate enough. For the range of the L2 and L3 cache we can see that we indeed achieve almost linear acceleration. We almost reach factors of 2 and 4 respectively. But as soon as the L3 cache is not sufficient to hold the working set the numbers crash. They crash to the point that the speed-up of two and four threads is identical (see the fourth column in Table 3.3). This is one of the reasons why one can hardly find motherboard with sockets for more than four CPUs all using the same memory controller. Machines with more processors have to be built differently (see Section 5).

These numbers are not universal. In some cases even working sets which fit into the last level cache will not allow linear speed-ups. In fact, this is the norm since threads are usually not as decoupled as is the case in this test program. On the other hand it is possible to work with large working sets and still take advantage of more than two threads. Doing this requires thought, though. We will talk about some approaches in Section 6.

Special Case: Hyper-Threads

Hyper-Threads (sometimes called Symmetric Multi-Threading, SMT) are implemented by the CPU and are a special case since the individual threads cannot really run concurrently. They all share almost all the processing resources except for the register set. Individual cores and CPUs still work in parallel but the threads implemented on each core are limited by this restriction. In theory there can be many threads per core but, so far, Intel's CPUs at most have two threads per core. The CPU is responsible for time-multiplexing the threads. This alone would not make much sense, though. The real advantage is that the CPU can schedule another hyper-thread when the currently running hyper-thread is delayed. In most cases this is a delay caused by memory accesses.

If two threads are running on one hyper-threaded core the program is only more efficient than the single-threaded code if the combined runtime of both threads is lower than the runtime of the single-threaded code. This is possible by overlapping the wait times for different memory accesses which usually would happen sequentially. A simple calculation shows the minimum requirement on the cache hit rate to achieve a certain speed-up.

The execution time for a program can be approximated with a simple model with only one level of cache as follows (see [htimpact]):

Texe = N[(1-Fmem)Tproc + Fmem(GhitTcache + (1-Ghit)Tmem)]

The meaning of the variables is as follows:

N = Number of instructions.
Fmem = Fraction of N that access memory.
Ghit = Fraction of loads that hit the cache.
Tproc = Number of cycles per instruction.
Tcache = Number of cycles for cache hit.
Tmiss = Number of cycles for cache miss.
Texe = Execution time for program.

For it to make any sense to use two threads the execution time of each of the two threads must be at most half of that of the single-threaded code. The only variable on either side is the number of cache hits. If we solve the equation for the minimum cache hit rate required to not slow down the thread execution by 50% or more we get the graph in Figure 3.23.

Figure 3.23: Minimum Cache Hit Rate For Speed-Up

The X–axis represents the cache hit rate Ghit of the single-thread code. The Y–axis shows the required cache hit rate for the multi-threaded code. This value can never be higher than the single-threaded hit rate since, otherwise, the single-threaded code would use that improved code, too. For single-threaded hit rates below 55% the program can in all cases benefit from using threads. The CPU is more or less idle enough due to cache misses to enable running a second hyper-thread.

The green area is the target. If the slowdown for the thread is less than 50% and the workload of each thread is halved the combined runtime might be less than the single-thread runtime. For the modeled system here (numbers for a P4 with hyper-threads were used) a program with a hit rate of 60% for the single-threaded code requires a hit rate of at least 10% for the dual-threaded program. That is usually doable. But if the single-threaded code has a hit rate of 95% then the multi-threaded code needs a hit rate of at least 80%. That is harder. Especially, and this is the problem with hyper-threads, because now the effective cache size (L1d here, in practice also L2 and so on) available to each hyper-thread is cut in half. Both hyper-threads use the same cache to load their data. If the working set of the two threads is non-overlapping the original 95% hit rate could also be cut in half and is therefore much lower than the required 80%.

Hyper-Threads are therefore only useful in a limited range of situations. The cache hit rate of the single-threaded code must be low enough that given the equations above and reduced cache size the new hit rate still meets the goal. Then and only then can it make any sense at all to use hyper-threads. Whether the result is faster in practice depends on whether the processor is sufficiently able to overlap the wait times in one thread with execution times in the other threads. The overhead of parallelizing the code must be added to the new total runtime and this additional cost often cannot be neglected.

In Section 6.3.4 we will see a technique where threads collaborate closely and the tight coupling through the common cache is actually an advantage. This technique can be applicable to many situations if only the programmers are willing to put in the time and energy to extend their code.

What should be clear is that if the two hyper-threads execute completely different code (i.e., the two threads are treated like separate processors by the OS to execute separate processes) the cache size is indeed cut in half which means a significant increase in cache misses. Such OS scheduling practices are questionable unless the caches are sufficiently large. Unless the workload for the machine consists of processes which, through their design, can indeed benefit from hyper-threads it might be best to turn off hyper-threads in the computer's BIOS. {Another reason to keep hyper-threads enabled is debugging. SMT is astonishingly good at finding some sets of problems in parallel code.}

3.3.5 Other Details

So far we talked about the address as consisting of three parts, tag, set index, and cache line offset. But what address is actually used? All relevant processors today provide virtual address spaces to processes, which means that there are two different kinds of addresses: virtual and physical.

The problem with virtual addresses is that they are not unique. A virtual address over time can refer to different physical memory addresses. The same address in different process also likely refers to different physical addresses. So it is always better to use the physical memory address, right?

The problem here is that instructions use virtual addresses and these have to be translated with the help of the Memory Management Unit (MMU) into physical addresses. This is a non-trivial operation. In the pipeline to execute an instruction the physical address might only be available at a later stage. This means that the cache logic has to be very quick in determining whether the memory location is cached. If virtual addresses could be used the cache lookup can happen much earlier in the pipeline and in case of a cache hit the memory content can be made available. The result is that more of the memory access costs could be hidden by the pipeline.

Processor designers are currently using virtual address tagging for the first level caches. These caches are rather small and can be cleared without too much pain. At least partial clearing the cache is necessary if the page table tree of a process changes. It might be possible to avoid a complete flush if the processor has an instruction which specifies the virtual address range which has changed. Given the low latency of L1i and L1d caches (~3 cycles) using virtual addresses is almost mandatory.

For larger caches including L2, L3, ... caches physical address tagging is needed. These caches have a higher latency and the virtual→physical address translation can finish in time. Because these caches are larger (i.e., a lot of information is lost when they are flushed) and refilling them takes a long time due to the main memory access latency flushing them often would be costly.

It should, in general, not be necessary to know about the details of the address handling in those caches. They cannot be changed and all the factors which would influence the performance are normally something which should be avoided or is associated with high cost. Overflowing the cache capacity is bad and all caches run into problems early if the majority of the used cache lines fall into the same set. The latter can be avoided with virtually addressed caches but is impossible for user-level processes to avoid for caches addressed using physical addresses. The only detail one might want to keep in mind is to not map the same physical memory location to two or more virtual addresses in the same process, if at all possible.

Another detail of the caches which is rather uninteresting to programmers is the cache replacement strategy. Most caches evict the Least Recently Used (LRU) element first. This is always a good default strategy. With larger associativity (and associativity might indeed grow further in the coming years due to the addition of more cores) maintaining the LRU list becomes more and more expensive and we might see different strategies adopted.

As for the cache replacement there is not much a programmer can do. If the cache is using physical address tags there is no way to find out how the virtual addresses correlate with the cache sets. It might be that cache lines in all logical pages are mapped to the same cache sets, leaving much of the cache unused. If anything, it is the job of the OS to arrange that this does not happen too often.

With the advent of virtualization things get even more complicated. Now not even the OS has control over the assignment of physical memory. The Virtual Machine Monitor (VMM, aka hypervisor) is responsible for the physical memory assignment.

The best a programmer can do is to a) use logical memory pages completely and b) use page sizes as large as meaningful to diversify the physical addresses as much as possible. Larger page sizes have other benefits, too, but this is another topic (see Section 4).

3.4 Instruction Cache

Not just the data used by the processor is cached; the instructions executed by the processor are also cached. However, this cache is much less problematic than the data cache. There are several reasons:

  • The quantity of code which is executed depends on the size of the code that is needed. The size of the code in general depends on the complexity of the problem. The complexity of the problem is fixed.

  • While the program's data handling is designed by the programmer the program's instructions are usually generated by a compiler. The compiler writers know about the rules for good code generation.

  • Program flow is much more predictable than data access patterns. Today's CPUs are very good at detecting patterns. This helps with prefetching.

  • Code always has quite good spatial and temporal locality.

There are a few rules programmers should follow but these mainly consist of rules on how to use the tools. We will discuss them in Section 6. Here we talk only about the technical details of the instruction cache.

Ever since the core clock of CPUs increased dramatically and the difference in speed between cache (even first level cache) and core grew, CPUs have been pipelined. That means the execution of an instruction happens in stages. First an instruction is decoded, then the parameters are prepared, and finally it is executed. Such a pipeline can be quite long (> 20 stages for Intel's Netburst architecture). A long pipeline means that if the pipeline stalls (i.e., the instruction flow through it is interrupted) it takes a while to get up to speed again. Pipeline stalls happen, for instance, if the location of the next instruction cannot be correctly predicted or if it takes too long to load the next instruction (e.g., when it has to be read from memory).

As a result CPU designers spend a lot of time and chip real estate on branch prediction so that pipeline stalls happen as infrequently as possible.

On CISC processors the decoding stage can also take some time. The x86 and x86-64 processors are especially affected. In recent years these processors therefore do not cache the raw byte sequence of the instructions in L1i but instead they cache the decoded instructions. L1i in this case is called the “trace cache”. Trace caching allows the processor to skip over the first steps of the pipeline in case of a cache hit which is especially good if the pipeline stalled.

As said before, the caches from L2 on are unified caches which contain both code and data. Obviously here the code is cached in the byte sequence form and not decoded.

To achieve the best performance there are only a few rules related to the instruction cache:

  1. Generate code which is as small as possible. There are exceptions when software pipelining for the sake of using pipelines requires creating more code or where the overhead of using small code is too high.

  2. Whenever possible, help the processor to make good prefetching decisions. This can be done through code layout or with explicit prefetching.

These rules are usually enforced by the code generation of a compiler. There are a few things the programmer can do and we will talk about them in Section 6.

3.4.1 Self Modifying Code

In early computer days memory was a premium. People went to great lengths to reduce the size of the program to make more room for program data. One trick frequently deployed was to change the program itself over time. Such Self Modifying Code (SMC) is occasionally still found, these days mostly for performance reasons or in security exploits.

SMC should in general be avoided. Though it is generally executed correctly there are boundary cases in which it is not and it creates performance problems if not done correctly. Obviously, code which is changed cannot be kept in the trace cache which contains the decoded instructions. But even if the trace cache is not used because the code has not been executed at all (or for some time) the processor might have problems. If an upcoming instruction is changed while it already entered the pipeline the processor has to throw away a lot of work and start all over again. There are even situations where most of the state of the processor has to be tossed away.

Finally, since the processor assumes - for simplicity reasons and because it is true in 99.9999999% of all cases - that the code pages are immutable, the L1i implementation does not use the MESI protocol but instead a simplified SI protocol. This means if modifications are detected a lot of pessimistic assumptions have to be made.

It is highly advised to avoid SMC whenever possible. Memory is not such a scarce resource anymore. It is better to write separate functions instead of modifying one function according to specific needs. Maybe one day SMC support can be made optional and we can detect exploit code trying to modify code this way. If SMC absolutely has to be used, the write operations should bypass the cache as to not create problems with data in L1d needed in L1i. See Section 6.1 for more information on these instructions.

Normally on Linux it is easy to recognize programs which contain SMC. All program code is write-protected when built with the regular toolchain. The programmer has to perform significant magic at link time to create an executable where the code pages are writable. When this happens, modern Intel x86 and x86-64 processors have dedicated performance counters which count uses of self-modifying code. With the help of these counters it is quite easily possible to recognize programs with SMC even if the program will succeed due to relaxed permissions.

3.5 Cache Miss Factors

We have already seen that when memory accesses miss the caches the costs skyrocket. Sometimes this is not avoidable and it is important to understand the actual costs and what can be done to mitigate the problem.

3.5.1 Cache and Memory Bandwidth

To get a better understanding of the capabilities of the processors we measure the bandwidth available in optimal circumstances. This measurement is especially interesting since different processor versions vary widely. This is why this section is filled with the data of several different machines. The program to measure performance uses the SSE instructions of the x86 and x86-64 processors to load or store 16 bytes at once. The working set is increased from 1kB to 512MB just as in our other tests and it is measured how many bytes per cycle can be loaded or stored.

Figure 3.24: Pentium 4 Bandwidth

Figure 3.24 shows the performance on a 64-bit Intel Netburst processor. For working set sizes which fit into L1d the processor is able to read the full 16 bytes per cycle, i.e., one load instruction is performed per cycle (the movaps instruction moves 16 bytes at once). The test does not do anything with the read data, we test only the read instructions themselves. As soon as the L1d is not sufficient anymore the performance goes down dramatically to less than 6 bytes per cycle. The step at 218 bytes is due to the exhaustion of the DTLB cache which means additional work for each new page. Since the reading is sequential prefetching can predict the accesses perfectly and the FSB can stream the memory content at about 5.3 bytes per cycle for all sizes of the working set. The prefetched data is not propagated into L1d, though. These are of course numbers which will never be achievable in a real program. Think of them as practical limits.

What is more astonishing than the read performance is the write and copy performance. The write performance, even for small working set sizes, does not ever rise above 4 bytes per cycle. This indicates that, in these Netburst processors, Intel elected to use a Write-Through mode for L1d where the performance is obviously limited by the L2 speed. This also means that the performance of the copy test, which copies from one memory region into a second, non-overlapping memory region, is not significantly worse. The necessary read operations are so much faster and can partially overlap with the write operations. The most noteworthy detail of the write and copy measurements is the low performance once the L2 cache is not sufficient anymore. The performance drops to 0.5 bytes per cycle! That means write operations are by a factor of ten slower than the read operations. This means optimizing those operations is even more important for the performance of the program.

In Figure 3.25 we see the results on the same processor but with two threads running, one pinned to each of the two hyper-threads of the processor.

Figure 3.25: P4 Bandwidth with 2 Hyper-Threads

The graph is shown at the same scale as the previous one to illustrate the differences and the curves are a bit jittery simply because of the problem of measuring two concurrent threads. The results are as expected. Since the hyper-threads share all the resources except the registers each thread has only half the cache and bandwidth available. That means even though each thread has to wait a lot and could award the other thread with execution time this does not make any difference since the other thread also has to wait for the memory. This truly shows the worst possible use of hyper-threads.

Figure 3.26: Core 2 Bandwidth

Compared to Figures 3.24 and 3.25 the results in Figures 3.26 and 3.27 look quite different for an Intel Core 2 processor. This is a dual-core processor with shared L2 which is four times as big as the L2 on the P4 machine. This only explains the delayed drop-off of the write and copy performance, though.

There are much bigger differences. The read performance throughout the working set range hovers around the optimal 16 bytes per cycle. The drop-off in the read performance after 220 bytes is again due to the working set being too big for the DTLB. Achieving these high numbers means the processor is not only able to prefetch the data and transport the data in time. It also means the data is prefetched into L1d.

The write and copy performance is dramatically different, too. The processor does not have a Write-Through policy; written data is stored in L1d and only evicted when necessary. This allows for write speeds close to the optimal 16 bytes per cycle. Once L1d is not sufficient anymore the performance drops significantly. As with the Netburst processor, the write performance is significantly lower. Due to the high read performance the difference is even higher here. In fact, when even the L2 is not sufficient anymore the speed difference increases to a factor of 20! This does not mean the Core 2 processors perform poorly. To the contrary, their performance is always better than the Netburst core's.

Figure 3.27: Core 2 Bandwidth with 2 Threads

In Figure 3.27 the test runs two threads, one on each of the two cores of the Core 2 processor. Both threads access the same memory, not necessarily perfectly in sync, though. The results for the read performance are not different from the single-threaded case. A few more jitters are visible which is to be expected in any multi-threaded test case.

The interesting point is the write and copy performance for working set sizes which would fit into L1d. As can be seen in the figure, the performance is the same as if the data had to be read from the main memory. Both threads compete for the same memory location and RFO messages for the cache lines have to be sent. The problematic point is that these requests are not handled at the speed of the L2 cache, even though both cores share the cache. Once the L1d cache is not sufficient anymore modified entries are flushed from each core's L1d into the shared L2. At that point the performance increases significantly since now the L1d misses are satisfied by the L2 cache and RFO messages are only needed when the data has not yet been flushed. This is why we see a 50% reduction in speed for these sizes of the working set. The asymptotic behavior is as expected: since both cores share the same FSB each core gets half the FSB bandwidth which means for large working sets each thread's performance is about half that of the single threaded case.

Because there are significant differences between the processor versions of one vendor it is certainly worthwhile looking at the performance of other vendors' processors, too. Figure 3.28 shows the performance of an AMD family 10h Opteron processor. This processor has 64kB L1d, 512kB L2, and 2MB of L3. The L3 cache is shared between all cores of the processor. The results of the performance test can be seen in Figure 3.28.

Figure 3.28: AMD Family 10h Opteron Bandwidth

The first detail one notices about the numbers is that the processor is capable of handling two instructions per cycle if the L1d cache is sufficient. The read performance exceeds 32 bytes per cycle and even the write performance is, with 18.7 bytes per cycle, high. The read curve flattens quickly, though, and is, with 2.3 bytes per cycle, pretty low. The processor for this test does not prefetch any data, at least not efficiently.

The write curve on the other hand performs according to the sizes of the various caches. The peak performance is achieved for the full size of the L1d, going down to 6 bytes per cycle for L2, to 2.8 bytes per cycle for L3, and finally .5 bytes per cycle if not even L3 can hold all the data. The performance for the L1d cache exceeds that of the (older) Core 2 processor, the L2 access is equally fast (with the Core 2 having a larger cache), and the L3 and main memory access is slower.

The copy performance cannot be better than either the read or write performance. This is why we see the curve initially dominated by the read performance and later by the write performance.

The multi-thread performance of the Opteron processor is shown in Figure 3.29.

Figure 3.29: AMD Fam 10h Bandwidth with 2 Threads

The read performance is largely unaffected. Each thread's L1d and L2 works as before and the L3 cache is in this case not prefetched very well either. The two threads do not unduly stress the L3 for their purpose. The big problem in this test is the write performance. All data the threads share has to go through the L3 cache. This sharing seems to be quite inefficient since even if the L3 cache size is sufficient to hold the entire working set the cost is significantly higher than an L3 access. Comparing this graph with Figure 3.27 we see that the two threads of the Core 2 processor operate at the speed of the shared L2 cache for the appropriate range of working set sizes. This level of performance is achieved for the Opteron processor only for a very small range of the working set sizes and even here it approaches only the speed of the L3 which is slower than the Core 2's L2.

3.5.2 Critical Word Load

Memory is transferred from the main memory into the caches in blocks which are smaller than the cache line size. Today 64 bits are transferred at once and the cache line size is 64 or 128 bytes. This means 8 or 16 transfers per cache line are needed.

The DRAM chips can transfer those 64-bit blocks in burst mode. This can fill the cache line without any further commands from the memory controller and the possibly associated delays. If the processor prefetches cache lines this is probably the best way to operate.

If a program's cache access of the data or instruction caches misses (that means, it is a compulsory cache miss, because the data is used for the first time, or a capacity cache miss, because the limited cache size requires eviction of the cache line) the situation is different. The word inside the cache line which is required for the program to continue might not be the first word in the cache line. Even in burst mode and with double data rate transfer the individual 64-bit blocks arrive at noticeably different times. Each block arrives 4 CPU cycles or more later than the previous one. If the word the program needs to continue is the eighth of the cache line the program has to wait an additional 30 cycles or more after the first word arrives.

Things do not necessarily have to be like this. The memory controller is free to request the words of the cache line in a different order. The processor can communicate which word the program is waiting on, the critical word, and the memory controller can request this word first. Once the word arrives the program can continue while the rest of the cache line arrives and the cache is not yet in a consistent state. This technique is called Critical Word First & Early Restart.

Processors nowadays implement this technique but there are situations when that is not possible. If the processor prefetches data the critical word is not known. Should the processor request the cache line during the time the prefetch operation is in flight it will have to wait until the critical word arrives without being able to influence the order.

Figure 3.30: Critical Word at End of Cache Line

Even with these optimizations in place the position of the critical word on a cache line matters. Figure 3.30 shows the Follow test for sequential and random access. Shown is the slowdown of running the test with the pointer which is chased in the first word versus the case when the pointer is in the last word. The element size is 64 bytes, corresponding the cache line size. The numbers are quite noisy but it can be seen that, as soon as the L2 is not sufficient to hold the working set size, the performance of the case where the critical word is at the end is about 0.7% slower. The sequential access appears to be affected a bit more. This would be consistent with the aforementioned problem when prefetching the next cache line.

3.5.3 Cache Placement

Where the caches are placed in relationship to the hyper-threads, cores, and processors is not under control of the programmer. But programmers can determine where the threads are executed and then it becomes important how the caches relate to the used CPUs.

Here we will not go into details of when to select what cores to run the threads. We will only describe architecture details which the programmer has to take into account when setting the affinity of the threads.

Hyper-threads, by definition share everything but the register set. This includes the L1 caches. There is not much more to say here. The fun starts with the individual cores of a processor. Each core has at least its own L1 caches. Aside from this there are today not many details in common:

  • Early multi-core processors had separate L2 caches and no higher caches.

  • Later Intel models had shared L2 caches for dual-core processors. For quad-core processors we have to deal with separate L2 caches for each pair of two cores. There are no higher level caches.

  • AMD's family 10h processors have separate L2 caches and a unified L3 cache.

A lot has been written in the propaganda material of the processor vendors about the advantage of their respective models. Separate L2 caches have an advantage if the working sets handled by the cores do not overlap. This works well for single-threaded programs. Since this is still often the reality today this approach does not perform too badly. But there is always some overlap. The caches all contain the most actively used parts of the common runtime libraries which means some cache space is wasted.

Completely sharing all caches beside L1 as Intel's dual-core processors do can have a big advantage. If the working set of the threads working on the two cores overlaps significantly the total available cache memory is increased and working sets can be bigger without performance degradation. If the working sets do not overlap Intel's Advanced Smart Cache management is supposed to prevent any one core from monopolizing the entire cache.

If both cores use about half the cache for their respective working sets there is some friction, though. The cache constantly has to weigh the two cores' cache use and the evictions performed as part of this rebalancing might be chosen poorly. To see the problems we look at the results of yet another test program.

Figure 3.31: Bandwidth with two Processes

The test program has one process constantly reading or writing, using SSE instructions, a 2MB block of memory. 2MB was chosen because this is half the size of the L2 cache of this Core 2 processor. The process is pinned to one core while a second process is pinned to the other core. This second process reads and writes a memory region of variable size. The graph shows the number of bytes per cycle which are read or written. Four different graphs are shown, one for each combination of the processes reading and writing. The read/write graph is for the background process, which always uses a 2MB working set to write, and the measured process with variable working set to read.

The interesting part of the graph is the part between 220 and 223 bytes. If the L2 cache of the two cores were completely separate we could expect that the performance of all four tests would drop between 221 and 222 bytes, that means, once the L2 cache is exhausted. As we can see in Figure 3.31 this is not the case. For the cases where the background process is writing this is most visible. The performance starts to deteriorate before the working set size reaches 1MB. The two processes do not share memory and therefore the processes do not cause RFO messages to be generated. These are pure cache eviction problems. The smart cache handling has its problems with the effect that the experienced cache size per core is closer to 1MB than the 2MB per core which are available. One can only hope that, if caches shared between cores remain a feature of upcoming processors, the algorithm used for the smart cache handling will be fixed.

Having a quad-core processor with two L2 caches was just a stop-gap solution before higher-level caches could be introduced. This design provides no significant performance advantage over separate sockets and dual-core processors. The two cores communicate via the same bus which is, at the outside, visible as the FSB. There is no special fast-track data exchange.

The future of cache design for multi-core processors will lie in more layers. AMD's 10h family of processors make the start. Whether we will continue to see lower level caches be shared by a subset of the cores of a processor remains to be seen. The extra levels of cache are necessary since the high-speed and frequently used caches cannot be shared among many cores. The performance would be impacted. It would also require very large caches with high associativity. Both numbers, the cache size and the associativity, must scale with the number of cores sharing the cache. Using a large L3 cache and reasonably-sized L2 caches is a reasonable trade-off. The L3 cache is slower but it is ideally not as frequently used as the L2 cache.

For programmers all these different designs mean complexity when making scheduling decisions. One has to know the workloads and the details of the machine architecture to achieve the best performance. Fortunately we have support to determine the machine architecture. The interfaces will be introduced in later sections.

3.5.4 FSB Influence

The FSB plays a central role in the performance of the machine. Cache content can only be stored and loaded as quickly as the connection to the memory allows. We can show how much so by running a program on two machines which only differ in the speed of their memory modules. Figure 3.32 shows the results of the Addnext0 test (adding the content of the next elements pad[0] element to the own pad[0] element) for NPAD=7 on a 64-bit machine. Both machines have Intel Core 2 processors, the first uses 667MHz DDR2 modules, the second 800MHz modules (a 20% increase).

Figure 3.32: Influence of FSB Speed

The numbers show that, when the FSB is really stressed for large working set sizes, we indeed see a large benefit. The maximum performance increase measured in this test is 18.2%, close to the theoretical maximum. What this shows is that a faster FSB indeed can pay off big time. It is not critical when the working set fits into the caches (and these processors have a 4MB L2). It must be kept in mind that we are measuring one program here. The working set of a system comprises the memory needed by all concurrently running processes. This way it is easily possible to exceed 4MB memory or more with much smaller programs.

Today some of Intel's processors support FSB speeds up to 1,333MHz which would mean another 60% increase. The future is going to see even higher speeds. If speed is important and the working set sizes are larger, fast RAM and high FSB speeds are certainly worth the money. One has to be careful, though, since even though the processor might support higher FSB speeds the motherboard/Northbridge might not. It is critical to check the specifications.

Оставьте свой комментарий !

Ваше имя:
Комментарий:
Оба поля являются обязательными

 Автор  Комментарий к данной статье