Home > Articles > Programming

  • Print
  • + Share This
Like this article? We recommend

Like this article? We recommend

Cache Organization and Replacement Policies

Caches have a certain organization and a replacement policy. The organization describes in what way the lines are organized within the cache. The replacement policy dictates which line will be removed (evicted) from the cache in case an incoming line must be placed in the cache.

Direct Mapped

Direct mapped is a simple and efficient organization. The (virtual or physical) memory address of the incoming cache line controls which cache location is going to be used.

Implementing this organization is straightforward and is relatively easy to make it scale with the processor clock.

In a direct mapped organization, the replacement policy is built-in because cache line replacement is controlled by the (virtual or physical) memory address.

In many cases this design works well, but, because the candidate location is controlled by the memory address and not the usage, this policy has the potential downside of replacing a cache line that still contains information needed shortly afterwards.

Any line with the same address modulo the cache size, will map onto the same cache location. As long as the program accesses one single stream of data consecutively (unit stride) all is well. If the program skips elements or accesses multiple data streams simultaneously, additional cache refills may be generated.

Consider a simple example—a 4-kilobyte cache with a line size of 32 bytes direct-mapped on virtual addresses. Thus each load/store to cache moves 32 bytes. If one variable of type float takes 4 bytes on our system, each cache line will hold eight (32/4=8) such variables.

The following loop calculates the inner product of these two arrays. Each array element is assumed to be 4 bytes long; the data has not been cached yet.

float a[1024], b[1024];

for (i=0; i<1024; i++)
 sum += a[i]*b[i];

The generic system executes this loop as follows:

i	Operation	 Status	 In cache	 Comment

0	load a[0]	 miss	 a[0..7]     assume a[] was not cached yet
	load b[0]	 miss	 b[0..7]	 assume b[] was not cached yet
	t=a[0]*b[0]
	sum += t
1	load a[1]	 hit	 a[0..7]	 previous load brought it in
	load b[1]	 hit	 b[0..7]	 previous load brought it in
	t=a[1]*b[1]
	sum += t
	..... etc .....
7	load a[7]	 hit	 a[0..7]	 previous load brought it in
	load b[7]	 hit	 b[0..7]	 previous load brought it in
	t=a[7]*b[7]
	sum += t
8	load a[8]	 miss	 a[8..15]	 this line was not cached yet
	load b[8]	 miss	 b[8..15]	 this line was not cached yet
	t=a[8]*b[8]
	sum += t
9	load a[9]	 hit	 a[8..15]  previous load brought it in
	load b[9]	 hit	 b[8..15]	 previous load brought it in
	t=a[9]*b[9]
	sum += t
	.......

In this example a[0...7] denotes elements a[0],..,a[7] ; a similar notation is used for vector b and other array squences of elements.

The cache hit rate is 7/8, which equals 87.5 percent. However, this is the best case scenario.

Assume that the two arrays a[1024] and b[1024] are stored consecutively in memory. That is, a[i+1] follows a[i] (i=0.,,,.n-2) in memory and b[0] follows a[n-1], b[1] again follows b[0], and so forth. This loop will no longer perform as nicely as indicated previously.

In this case, the following occurs:

i	Operation	 Status	 In cache 	Comment

0	load a[0]	 miss	 a[0..7]	assume a[] was not cached yet
	load b[0]	 miss	 b[0..7]	b[0] is 4 KByte away from a[0] in 
				                    memory and will wipe out
                                    a[0..7] from the cache 
	t=a[0]*b[0]
	sum += t
1	load a[1]	 miss	a[0..7]	    previous load wiped out a[0..7]
    load b[1]	 miss  	b[0..7] 	previous load wiped out b[0..7]
	t=a[1]*b[1]
	sum += t
2	load a[2]	 miss	a[0..7]	    previous load wiped out a[0..7]
	load b[2]	 miss  	b[0..7]	    previous load wiped out b[0..7]
	.......

Because of the direct-mapped architecture of the cache and the way the data is organized, every array reference results in a cache miss. This degrades performance noticeably. More specifically, you get seven times as many cache misses as in the favorable scenario. This is called cache thrashing.

Several software-based solutions to this thrashing problem are available. At the source code level, you might consider unrolling the loop. In the following example this has been done to a depth of two.

for (i=0; i<1024; i+=2){
 ta0 = a[i];
 ta1 = a[i+1];
 tb0 = b[i];
 tb1 = b[i+1];
 sum += ta0*tb0+ta1*tb1;
}

The advantage of this approach is that now a[i+1] and b[i+1] are used before the cache line they are part of is evicted from the cache. Note that the optimal unroll depth is eight so all elements brought in are used immediately, before they are evicted by a next load.

The downside of loop unrolling is the need for more registers. For example, the original loop needs three floating point registers to store a[i], b[i] and sum. The unrolled version needs five floating point registers.

On Sun systems with direct mapped caches, several solutions are available. At a higher level, you might get help from the Solaris OE and/or compiler.

Because the mapping is a function of the memory address, the Solaris OE might change the addresses such that different lines no longer map onto the same cache location. This technique is often referred to as page coloring or cache coloring (MauMcDl).

The compiler typically unrolls loops and supports padding of data5 to avoid collisions.

Fully Associative

The fully associative cache design solves the potential problem of thrashing with a direct-mapped cache. The replacement policy is no longer a function of the memory address, but considers usage instead.

With this design, typically the oldest cache line is evicted from the cache. This policy is called least recently used (LRU)6.

In the previous example, LRU prevents the cache lines of a and b from being moved out prematurely.

The downside of a fully associative design is cost. Additional logic is required to track usage of lines. The larger the cache, the higher the cost. Therefore, it is difficult to scale this technology to very large (data) caches. Luckily, a good alternative exists.

Set Associative

A set-associative cache design uses several direct-mapped caches. Each cache is often referred to as a set. On an incoming request, the cache controller decides which set the line will go into. Within the set, a direct-mapped scheme is used to allocate a slot in the cache.

The name reflects the number of direct-mapped caches. For example, in a 2-way set associative design two direct mapped caches are used.

Another design parameter is the algorithm that selects the set. This could be random, LRU, or any other selection scheme.

FIGURE 5 shows a four-way set associative cache.

Figure 5FIGURE 5 Four-Way Set Associative Design.

Note that a set-associative cache tends to reduce the amount of thrashing. Thrashing can still occur, however, not only within one set but also between sets.

Thrashing between sets is a function of the algorithm that selects the set; whereas thrashing within one set is related to the (virtual) memory address of the data.

Usually, the size of a set is 2n kilobytes (n=1, 2,...). If (virtual) addresses of incoming lines in the same set are 2m apart (m > n), thrashing occurs.

For example, in a two-way set associative design, an update of this type might cause thrashing:

float x[4096][4096];

for (i=1; i<n-1; i++)
  for (j=1; j<n-1; j++)
   x[i][j] = x[i][j-1]+x[i][j+1]+x[i][j]+x[i-1][j]+x[i+1][j];

FIGURE 6 shows the computational grid on which these computations are performed. Array element x[i][j] is located at the intersection of the vertical line at i and the horizontal line at j.

Figure 6FIGURE 6 Computational Grid

For a fixed value of i, this loop updates one cache line (containing x[i][j]) and references two other lines (containing x[i-1][j] and x[i+1][j]).

Assume that the two lines containing x[i][j] and x[i-1][j] are in a different set (to avoid collisions). The question is where the line with x[i+1][j] will go.

As there are only two sets, the cache controller has no other choice than to select a set that already has one of the other two cache lines. In virtual memory, these three lines are 4 * 4096 =16 kilobytes apart. Therefore, cache thrashing within one of the sets will occur if one set is 16 kilobytes or less in size.

  • + Share This
  • 🔖 Save To Your Account

InformIT Promotional Mailings & Special Offers

I would like to receive exclusive offers and hear about products from InformIT and its family of brands. I can unsubscribe at any time.

Overview


Pearson Education, Inc., 221 River Street, Hoboken, New Jersey 07030, (Pearson) presents this site to provide information about products and services that can be purchased through this site.

This privacy notice provides an overview of our commitment to privacy and describes how we collect, protect, use and share personal information collected through this site. Please note that other Pearson websites and online products and services have their own separate privacy policies.

Collection and Use of Information


To conduct business and deliver products and services, Pearson collects and uses personal information in several ways in connection with this site, including:

Questions and Inquiries

For inquiries and questions, we collect the inquiry or question, together with name, contact details (email address, phone number and mailing address) and any other additional information voluntarily submitted to us through a Contact Us form or an email. We use this information to address the inquiry and respond to the question.

Online Store

For orders and purchases placed through our online store on this site, we collect order details, name, institution name and address (if applicable), email address, phone number, shipping and billing addresses, credit/debit card information, shipping options and any instructions. We use this information to complete transactions, fulfill orders, communicate with individuals placing orders or visiting the online store, and for related purposes.

Surveys

Pearson may offer opportunities to provide feedback or participate in surveys, including surveys evaluating Pearson products, services or sites. Participation is voluntary. Pearson collects information requested in the survey questions and uses the information to evaluate, support, maintain and improve products, services or sites, develop new products and services, conduct educational research and for other purposes specified in the survey.

Contests and Drawings

Occasionally, we may sponsor a contest or drawing. Participation is optional. Pearson collects name, contact information and other information specified on the entry form for the contest or drawing to conduct the contest or drawing. Pearson may collect additional personal information from the winners of a contest or drawing in order to award the prize and for tax reporting purposes, as required by law.

Newsletters

If you have elected to receive email newsletters or promotional mailings and special offers but want to unsubscribe, simply email information@informit.com.

Service Announcements

On rare occasions it is necessary to send out a strictly service related announcement. For instance, if our service is temporarily suspended for maintenance we might send users an email. Generally, users may not opt-out of these communications, though they can deactivate their account information. However, these communications are not promotional in nature.

Customer Service

We communicate with users on a regular basis to provide requested services and in regard to issues relating to their account we reply via email or phone in accordance with the users' wishes when a user submits their information through our Contact Us form.

Other Collection and Use of Information


Application and System Logs

Pearson automatically collects log data to help ensure the delivery, availability and security of this site. Log data may include technical information about how a user or visitor connected to this site, such as browser type, type of computer/device, operating system, internet service provider and IP address. We use this information for support purposes and to monitor the health of the site, identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents and appropriately scale computing resources.

Web Analytics

Pearson may use third party web trend analytical services, including Google Analytics, to collect visitor information, such as IP addresses, browser types, referring pages, pages visited and time spent on a particular site. While these analytical services collect and report information on an anonymous basis, they may use cookies to gather web trend information. The information gathered may enable Pearson (but not the third party web trend services) to link information with application and system log data. Pearson uses this information for system administration and to identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents, appropriately scale computing resources and otherwise support and deliver this site and its services.

Cookies and Related Technologies

This site uses cookies and similar technologies to personalize content, measure traffic patterns, control security, track use and access of information on this site, and provide interest-based messages and advertising. Users can manage and block the use of cookies through their browser. Disabling or blocking certain cookies may limit the functionality of this site.

Do Not Track

This site currently does not respond to Do Not Track signals.

Security


Pearson uses appropriate physical, administrative and technical security measures to protect personal information from unauthorized access, use and disclosure.

Children


This site is not directed to children under the age of 13.

Marketing


Pearson may send or direct marketing communications to users, provided that

  • Pearson will not use personal information collected or processed as a K-12 school service provider for the purpose of directed or targeted advertising.
  • Such marketing is consistent with applicable law and Pearson's legal obligations.
  • Pearson will not knowingly direct or send marketing communications to an individual who has expressed a preference not to receive marketing.
  • Where required by applicable law, express or implied consent to marketing exists and has not been withdrawn.

Pearson may provide personal information to a third party service provider on a restricted basis to provide marketing solely on behalf of Pearson or an affiliate or customer for whom Pearson is a service provider. Marketing preferences may be changed at any time.

Correcting/Updating Personal Information


If a user's personally identifiable information changes (such as your postal address or email address), we provide a way to correct or update that user's personal data provided to us. This can be done on the Account page. If a user no longer desires our service and desires to delete his or her account, please contact us at customer-service@informit.com and we will process the deletion of a user's account.

Choice/Opt-out


Users can always make an informed choice as to whether they should proceed with certain services offered by InformIT. If you choose to remove yourself from our mailing list(s) simply visit the following page and uncheck any communication you no longer want to receive: www.informit.com/u.aspx.

Sale of Personal Information


Pearson does not rent or sell personal information in exchange for any payment of money.

While Pearson does not sell personal information, as defined in Nevada law, Nevada residents may email a request for no sale of their personal information to NevadaDesignatedRequest@pearson.com.

Supplemental Privacy Statement for California Residents


California residents should read our Supplemental privacy statement for California residents in conjunction with this Privacy Notice. The Supplemental privacy statement for California residents explains Pearson's commitment to comply with California law and applies to personal information of California residents collected in connection with this site and the Services.

Sharing and Disclosure


Pearson may disclose personal information, as follows:

  • As required by law.
  • With the consent of the individual (or their parent, if the individual is a minor)
  • In response to a subpoena, court order or legal process, to the extent permitted or required by law
  • To protect the security and safety of individuals, data, assets and systems, consistent with applicable law
  • In connection the sale, joint venture or other transfer of some or all of its company or assets, subject to the provisions of this Privacy Notice
  • To investigate or address actual or suspected fraud or other illegal activities
  • To exercise its legal rights, including enforcement of the Terms of Use for this site or another contract
  • To affiliated Pearson companies and other companies and organizations who perform work for Pearson and are obligated to protect the privacy of personal information consistent with this Privacy Notice
  • To a school, organization, company or government agency, where Pearson collects or processes the personal information in a school setting or on behalf of such organization, company or government agency.

Links


This web site contains links to other sites. Please be aware that we are not responsible for the privacy practices of such other sites. We encourage our users to be aware when they leave our site and to read the privacy statements of each and every web site that collects Personal Information. This privacy statement applies solely to information collected by this web site.

Requests and Contact


Please contact us about this Privacy Notice or if you have any requests or questions relating to the privacy of your personal information.

Changes to this Privacy Notice


We may revise this Privacy Notice through an updated posting. We will identify the effective date of the revision in the posting. Often, updates are made to provide greater clarity or to comply with changes in regulatory requirements. If the updates involve material changes to the collection, protection, use or disclosure of Personal Information, Pearson will provide notice of the change through a conspicuous notice on this site or other appropriate way. Continued use of the site after the effective date of a posted revision evidences acceptance. Please contact us if you have questions or concerns about the Privacy Notice or any objection to any revisions.

Last Update: November 17, 2020