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Apple Inc. is an American multinational technology company headquartered in Cupertino, California. , Apple is the world's biggest company by market capitalization, and with the largest technology company by 2022 revenue. , Apple is the fourth-largest personal computer vendor by unit sales; the largest manufacturing company by revenue; and the second-largest mobile phone manufacturer in the world. It is considered one of the Big Five American information technology companies, alongside Alphabet (parent company of Google), Amazon, Meta Platforms, and Microsoft. Apple was founded as Apple Computer Company on April 1, 1976, by Steve Wozniak, Steve Jobs and Ronald Wayne to develop and sell Wozniak's Apple I personal computer. It was incorporated by Jobs and Wozniak as Apple Computer, Inc. in 1977. The company's second computer, the Apple II, became a best seller and one of the first mass-produced microcomputers. Apple went public in 1980 to instant financial success. The company developed computers featuring innovative graphical user interfaces, including the 1984 original Macintosh, announced that year in a critically acclaimed advertisement called "1984". By 1985, the high cost of its products, and power struggles between executives, caused problems. Wozniak stepped back from Apple and pursued other ventures, while Jobs resigned and founded NeXT, taking some Apple employees with him. As the market for personal computers expanded and evolved throughout the 1990s, Apple lost considerable market share to the lower-priced duopoly of the Microsoft Windows operating system on Intel-powered PC clones (also known as "Wintel"). In 1997, weeks away from bankruptcy, the company bought NeXT to resolve Apple's unsuccessful operating system strategy and entice Jobs back to the company. Over the next decade, Jobs guided Apple back to profitability through a number of tactics including introducing the iMac, iPod, iPhone and iPad to critical acclaim, launching the "Think different" campaign and other memorable advertising campaigns, opening the Apple Store retail chain, and acquiring numerous companies to broaden the company's product portfolio. When Jobs resigned in 2011 for health reasons, and died two months later, he was succeeded as CEO by Tim Cook. Apple became the first publicly traded U.S. company to be valued at over $1 trillion in August 2018, then at $2 trillion in August 2020, and at $3 trillion in January 2022. In June 2023, it was valued at just over $3 trillion. The company receives criticism regarding the labor practices of its contractors, its environmental practices, and its business ethics, including anti-competitive practices and materials sourcing. Nevertheless, the company has a large following and enjoys a high level of brand loyalty. It has also been consistently ranked as one of the world's most valuable brands. History 1976–1980: Founding and incorporation Apple Computer Company was founded on April 1, 1976, by Steve Jobs, Steve Wozniak, and Ronald Wayne as a partnership. The company's first product was the Apple I, a computer designed and hand-built entirely by Wozniak. To finance its creation, Jobs sold his Volkswagen Bus, and Wozniak sold his HP-65 calculator. Wozniak debuted the first prototype Apple I at the Homebrew Computer Club in July 1976. The Apple I was sold as a motherboard with CPU, RAM, and basic textual-video chips—a base kit concept which would not yet be marketed as a complete personal computer. It went on sale soon after debut for . Wozniak later said he was unaware of the coincidental mark of the beast in the number 666, and that he came up with the price because he liked "repeating digits". Apple Computer, Inc. was incorporated on January 3, 1977, without Wayne, who had left and sold his share of the company back to Jobs and Wozniak for $800 only twelve days after having co-founded Apple. Multimillionaire Mike Markkula provided essential business expertise and funding of to Jobs and Wozniak during the incorporation of Apple. During the first five years of operations, revenues grew exponentially, doubling about every four months. Between September 1977 and September 1980, yearly sales grew from $775,000 to $118 million, an average annual growth rate of 533%. The Apple II, also invented by Wozniak, was introduced on April 16, 1977, at the first West Coast Computer Faire. It differed from its major rivals, the TRS-80 and Commodore PET, because of its character cell-based color graphics and open architecture. While the Apple I and early Apple II models used ordinary audio cassette tapes as storage devices, they were superseded by the introduction of a -inch floppy disk drive and interface called the Disk II in 1978. The Apple II was chosen to be the desktop platform for the first "killer application" of the business world: VisiCalc, a spreadsheet program released in 1979. VisiCalc created a business market for the Apple II and gave home users an additional reason to buy an Apple II: compatibility with the office, but Apple II market share remained behind home computers made by competitors such as Atari, Commodore, and Tandy. On December 12, 1980, Apple (ticker symbol "AAPL") went public selling 4.6 million shares at $22 per share ($.10 per share when adjusting for stock splits ), generating over $100 million, which was more capital than any IPO since Ford Motor Company in 1956. By the end of the day, 300 millionaires were created, from a stock price of $29 per share and a market cap of $1.778 billion. 1980–1990: Success with Macintosh A critical moment in the company's history came in December 1979 when Jobs and several Apple employees, including human–computer interface expert Jef Raskin, visited Xerox PARC in to see a demonstration of the Xerox Alto, a computer using a graphical user interface. Xerox granted Apple engineers three days of access to the PARC facilities in return for the option to buy 100,000 shares (22.4 million split-adjusted shares ) of Apple at the pre-IPO price of $10 a share. After the demonstration, Jobs was immediately convinced that all future computers would use a graphical user interface, and development of a GUI began for the Apple Lisa, named after Jobs's daughter. The Lisa division would be plagued by infighting, and in 1982 Jobs was pushed off the project. The Lisa launched in 1983 and became the first personal computer sold to the public with a GUI, but was a commercial failure due to its high price and limited software titles. Jobs, angered by being pushed off the Lisa team, took over the company's Macintosh division. Wozniak and Raskin had envisioned the Macintosh as a low-cost computer with a text-based interface like the Apple II, but a plane crash in 1981 forced Wozniak to step back from the project. Jobs quickly redefined the Macintosh as a graphical system that would be cheaper than the Lisa, undercutting his former division. Jobs was also hostile to the Apple II division, which at the time, generated most of the company's revenue. In 1984, Apple launched the Macintosh, the first personal computer to be sold without a programming language. Its debut was signified by "1984", a $1.5 million television advertisement directed by Ridley Scott that aired during the third quarter of Super Bowl XVIII on January 22, 1984. This is now hailed as a watershed event for Apple's success and was called a "masterpiece" by CNN and one of the greatest TV advertisements of all time by TV Guide. The advertisement created great interest in the original Macintosh, and sales were initially good, but began to taper off dramatically after the first three months as reviews started to come in. Jobs had made the decision to equip the original Macintosh with 128 kilobytes of RAM, attempting to reach a price point, which limited its speed and the software that could be used. The Macintosh would eventually ship for , a price panned by critics in light of its slow performance. In early 1985, this sales slump triggered a power struggle between Steve Jobs and CEO John Sculley, who had been hired away from Pepsi two years earlier by Jobs saying, "Do you want to sell sugar water for the rest of your life or come with me and change the world?" Sculley decided to remove Jobs as the head of the Macintosh division, with unanimous support from the Apple board of directors. The board of directors instructed Sculley to contain Jobs and his ability to launch expensive forays into untested products. Rather than submit to Sculley's direction, Jobs attempted to oust him from his leadership role at Apple. Informed by Jean-Louis Gassée, Sculley found out that Jobs had been attempting to organize a boardroom coup and called an emergency meeting at which Apple's executive staff sided with Sculley and stripped Jobs of all operational duties. Jobs resigned from Apple in September 1985 and took a number of Apple employees with him to found NeXT. Wozniak had also quit his active employment at Apple earlier in 1985 to pursue other ventures, expressing his frustration with Apple's treatment of the Apple II division and stating that the company had "been going in the wrong direction for the last five years." Despite Wozniak's grievances, he officially remained employed by Apple, and to this day continues to work for the company as a representative, receiving a stipend estimated to be $120,000 per year for this role. Both Jobs and Wozniak remained Apple shareholders after their departures. After the departures of Jobs and Wozniak, Sculley worked to improve the Macintosh in 1985 by quadrupling the RAM and introducing the LaserWriter, the first reasonably priced PostScript laser printer. PageMaker, an early desktop publishing application taking advantage of the PostScript language, was also released by Aldus Corporation in July 1985. It has been suggested that the combination of Macintosh, LaserWriter and PageMaker was responsible for the creation of the desktop publishing market. This dominant position in the desktop publishing market allowed the company to focus on higher price points, the so-called "high-right policy" named for the position on a chart of price vs. profits. Newer models selling at higher price points offered higher profit margin, and appeared to have no effect on total sales as power users snapped up every increase in speed. Although some worried about pricing themselves out of the market, the high-right policy was in full force by the mid-1980s, notably due to Jean-Louis Gassée's mantra of "fifty-five or die", referring to the 55% profit margins of the Macintosh II. This policy began to backfire in the last years of the decade as desktop publishing programs appeared on PC clones that offered some or much of the same functionality of the Macintosh, but at far lower price points. The company lost its dominant position in the desktop publishing market and estranged many of its original consumer customer base who could no longer afford their high-priced products. The Christmas season of 1989 was the first in the company's history to have declining sales, which led to a 20% drop in Apple's stock price. During this period, the relationship between Sculley and Gassée deteriorated, leading Sculley to effectively demote Gassée in January 1990 by appointing Michael Spindler as the chief operating officer. Gassée left the company later that year. 1990–1997: Decline and restructuring The company pivoted strategy and in October 1990 introduced three lower-cost models, the Macintosh Classic, the Macintosh LC, and the Macintosh IIsi, all of which saw significant sales due to pent-up demand. In 1991, Apple introduced the hugely successful PowerBook with a design that set the current shape for almost all modern laptops. The same year, Apple introduced System 7, a major upgrade to the Macintosh operating system, adding color to the interface and introducing new networking capabilities. The success of the lower-cost Macs and PowerBook brought increasing revenue. For some time, Apple was doing incredibly well, introducing fresh new products and generating increasing profits in the process. The magazine MacAddict named the period between 1989 and 1991 as the "first golden age" of the Macintosh. The success of Apple's lower-cost consumer models, especially the LC, also led to the cannibalization of their higher-priced machines. To address this, management introduced several new brands, selling largely identical machines at different price points, aimed at different markets: the high-end Quadra models, the mid-range Centris line, and the consumer-marketed Performa series. This led to significant market confusion, as customers did not understand the difference between models. The early 1990s also saw the discontinuation of the Apple II series, which was expensive to produce, and the company felt was still taking sales away from lower-cost Macintosh models. After the launch of the LC, Apple began encouraging developers to create applications for Macintosh rather than Apple II, and authorized salespersons to direct consumers towards Macintosh and away from Apple II. The Apple IIe was discontinued in 1993. Throughout this period, Microsoft continued to gain market share with its Windows graphical user interface that it sold to manufacturers of generally less expensive PC clones. While the Macintosh was more expensive, it offered a more tightly integrated user experience, but the company struggled to make the case to consumers. Apple also experimented with a number of other unsuccessful consumer targeted products during the 1990s, including digital cameras, portable CD audio players, speakers, video game consoles, the eWorld online service, and TV appliances. Most notably, enormous resources were invested in the problem-plagued Newton tablet division, based on John Sculley's unrealistic market forecasts. Throughout this period, Microsoft continued to gain market share with Windows by focusing on delivering software to inexpensive personal computers, while Apple was delivering a richly engineered but expensive experience. Apple relied on high profit margins and never developed a clear response; instead, they sued Microsoft for using a GUI similar to the Apple Lisa in Apple Computer, Inc. v. Microsoft Corp. The lawsuit dragged on for years before it was finally dismissed. The major product flops and the rapid loss of market share to Windows sullied Apple's reputation, and in 1993 Sculley was replaced as CEO by Michael Spindler. With Spindler at the helm, Apple, IBM, and Motorola formed the AIM alliance in 1994 with the goal of creating a new computing platform (the PowerPC Reference Platform; PReP), which would use IBM and Motorola hardware coupled with Apple software. The AIM alliance hoped that PReP's performance and Apple's software would leave the PC far behind and thus counter the dominance of Windows. The same year, Apple introduced the Power Macintosh, the first of many Apple computers to use Motorola's PowerPC processor. In the wake of the alliance, Apple opened up to the idea of allowing Motorola and other companies to build Macintosh clones. Over the next two years, 75 distinct Macintosh clone models were introduced. However, by 1996, Apple executives were worried that the clones were cannibalizing sales of their own high-end computers, where profit margins were highest. In 1996, Spindler was replaced by Gil Amelio as CEO. Hired for his reputation as a corporate rehabilitator, Amelio made deep changes, including extensive layoffs and cost-cutting. This period was also marked by numerous failed attempts to modernize the Macintosh operating system (MacOS). The original Macintosh operating system (System 1) was not built for multitasking (running several applications at once). The company attempted to correct this with by introducing cooperative multitasking in System 5, but the company still felt it needed a more modern approach. This led to the Pink project in 1988, A/UX that same year, Copland in 1994, and the attempted purchase of BeOS in 1996. Talks with Be stalled when the CEO, former Apple executive Jean-Louis Gassée, demanded $300 million instead of the $125 million Apple wanted to pay. Only weeks away from bankruptcy, Apple's board decided NeXTSTEP was a better choice for its next operating system and purchased NeXT in late 1996 for $400 million, bringing back Apple co-founder Steve Jobs. 1997–2007: Return to profitability The NeXT acquisition was finalized on February 9, 1997, and the board brought Jobs back to Apple as an advisor. On July 9, 1997, Jobs staged a boardroom coup that resulted in Amelio's resignation after overseeing a three-year record-low stock price and crippling financial losses. The board named Jobs as interim CEO and he immediately began a review of the company's products. Jobs would order 70% of the company's products to be cancelled, resulting in the loss of 3,000 jobs, and taking Apple back to the core of its computer offerings. The next month, in August 1997, Steve Jobs convinced Microsoft to make a $150 million investment in Apple and a commitment to continue developing software for the Mac. The investment was seen as an "antitrust insurance policy" for Microsoft who had recently settled with the Department of Justice over anti-competitive practices. Jobs also ended the Mac clone deals and in September 1997, purchased the largest clone maker, Power Computing. On November 10, 1997, Apple introduced the Apple Store website, which was tied to a new build-to-order manufacturing that had been successfully used by PC manufacturer Dell. The moves paid off for Jobs; at the end of his first year as CEO, the company turned a $309 million profit. On May 6, 1998, Apple introduced a new all-in-one computer reminiscent of the original Macintosh: the iMac. The iMac was a huge success for Apple selling 800,000 units in its first five months and ushered in major shifts in the industry by abandoning legacy technologies like the -inch diskette, being an early adopter of the USB connector, and coming pre-installed with internet connectivity (the "i" in iMac) via Ethernet and a dial-up modem. The device also had a striking teardrop shape and translucent materials, designed by Jonathan Ive, who although hired by Amelio, would go on to work collaboratively with Jobs for the next decade to chart a new course the design of Apple's products. A little more than a year later on July 21, 1999, Apple introduced the iBook, a laptop for consumers. It was the culmination of a strategy established by Jobs to produce only four products: refined versions of the Power Macintosh G3 desktop and PowerBook G3 laptop for professionals, along with the iMac desktop and iBook laptop for consumers. Jobs felt the small product line allowed for a greater focus on quality and innovation. At around the same time, Apple also completed numerous acquisitions to create a portfolio of digital media production software for both professionals and consumers. Apple acquired of Macromedia's Key Grip digital video editing software project which was renamed Final Cut Pro when it was launched on the retail market in April 1999. The development of Key Grip also led to Apple's release of the consumer video-editing product iMovie in October 1999. Next, Apple successfully acquired the German company Astarte in April 2000, which had developed the DVD authoring software DVDirector, which Apple would sell as the professional-oriented DVD Studio Pro software product, and used the same technology to create iDVD for the consumer market. In 2000, Apple purchased the SoundJam MP audio player software from Casady & Greene. Apple renamed the program iTunes, while simplifying the user interface and adding the ability to burn CDs. 2001 would be a pivotal year for the Apple with the company making three announcements that would change the course of the company. The first announcement came on March 24, 2001, that Apple was nearly ready to release a new modern operating system, Mac OS X. The announcement came after numerous failed attempts in the early 1990s, and several years of development. Mac OS X was based on NeXTSTEP, OPENSTEP, and BSD Unix, with Apple aiming to combine the stability, reliability, and security of Unix with the ease of use afforded by an overhauled user interface, heavily influenced by NeXTSTEP. To aid users in migrating from Mac OS 9, the new operating system allowed the use of OS 9 applications within Mac OS X via the Classic Environment. In May 2001, the company opened its first two Apple Store retail locations in Virginia and California, offering an improved presentation of the company's products. At the time, many speculated that the stores would fail, but they went on to become highly successful, and the first of more than 500 stores around the world. On October 23, 2001, Apple debuted the iPod portable digital audio player. The product, which was first sold on November 10, 2001, was phenomenally successful with over 100 million units sold within six years. In 2003, Apple's iTunes Store was introduced. The service offered music downloads for 99¢ a song and integration with the iPod. The iTunes Store quickly became the market leader in online music services, with over five billion downloads by June 19, 2008. Two years later, the iTunes Store was the world's largest music retailer. In 2002, Apple purchased Nothing Real for their advanced digital compositing application Shake, as well as Emagic for the music productivity application Logic. The purchase of Emagic made Apple the first computer manufacturer to own a music software company. The acquisition was followed by the development of Apple's consumer-level GarageBand application. The release of iPhoto in the same year completed the iLife suite. At the Worldwide Developers Conference keynote address on June 6, 2005, Jobs announced that Apple would move away from PowerPC processors, and the Mac would transition to Intel processors in 2006. On January 10, 2006, the new MacBook Pro and iMac became the first Apple computers to use Intel's Core Duo CPU. By August 7, 2006, Apple made the transition to Intel chips for the entire Mac product line—over one year sooner than announced. The Power Mac, iBook, and PowerBook brands were retired during the transition; the Mac Pro, MacBook, and MacBook Pro became their respective successors. On April 29, 2009, The Wall Street Journal reported that Apple was building its own team of engineers to design microchips. Apple also introduced Boot Camp in 2006 to help users install Windows XP or Windows Vista on their Intel Macs alongside Mac OS X. Apple's success during this period was evident in its stock price. Between early 2003 and 2006, the price of Apple's stock increased more than tenfold, from around $6 per share (split-adjusted) to over $80. When Apple surpassed Dell's market cap in January 2006, Jobs sent an email to Apple employees saying Dell's CEO Michael Dell should eat his words. Nine years prior, Dell had said that if he ran Apple he would "shut it down and give the money back to the shareholders". 2007–2011: Success with mobile devices During his keynote speech at the Macworld Expo on January 9, 2007, Jobs announced that Apple Computer, Inc. would thereafter be known as "Apple Inc.", because the company had shifted its emphasis from computers to consumer electronics. This event also saw the announcement of the iPhone and the Apple TV. The company sold 270,000 iPhone units during the first 30 hours of sales, and the device was called "a game changer for the industry". In an article posted on Apple's website on February 6, 2007, Jobs wrote that Apple would be willing to sell music on the iTunes Store without digital rights management (DRM), thereby allowing tracks to be played on third-party players if record labels would agree to drop the technology. On April 2, 2007, Apple and EMI jointly announced the removal of DRM technology from EMI's catalog in the iTunes Store, effective in May 2007. Other record labels eventually followed suit and Apple published a press release in January 2009 to announce that all songs on the iTunes Store are available without their FairPlay DRM. In July 2008, Apple launched the App Store to sell third-party applications for the iPhone and iPod Touch. Within a month, the store sold 60 million applications and registered an average daily revenue of $1 million, with Jobs speculating in August 2008 that the App Store could become a billion-dollar business for Apple. By October 2008, Apple was the third-largest mobile handset supplier in the world due to the popularity of the iPhone. On January 14, 2009, Jobs announced in an internal memo that he would be taking a six-month medical leave of absence from Apple until the end of June 2009 and would spend the time focusing on his health. In the email, Jobs stated that "the curiosity over my personal health continues to be a distraction not only for me and my family, but everyone else at Apple as well", and explained that the break would allow the company "to focus on delivering extraordinary products". Though Jobs was absent, Apple recorded its best non-holiday quarter (Q1 FY 2009) during the recession with revenue of $8.16 billion and profit of $1.21 billion. After years of speculation and multiple rumored "leaks", Apple unveiled a large screen, tablet-like media device known as the iPad on January 27, 2010. The iPad ran the same touch-based operating system as the iPhone, and all iPhone apps were compatible with the iPad. This gave the iPad a large app catalog on launch, though having very little development time before the release. Later that year on April 3, 2010, the iPad was launched in the U.S. It sold more than 300,000 units on its first day, and 500,000 by the end of the first week. In May of the same year, Apple's market cap exceeded that of competitor Microsoft for the first time since 1989. In June 2010, Apple released the iPhone 4, which introduced video calling using FaceTime, multitasking, and a new uninsulated stainless steel design that acted as the phone's antenna. Later that year, Apple again refreshed its iPod line of MP3 players by introducing a multi-touch iPod Nano, an iPod Touch with FaceTime, and an iPod Shuffle that brought back the clickwheel buttons of earlier generations. It also introduced the smaller, cheaper second generation Apple TV which allowed renting of movies and shows. On January 17, 2011, Jobs announced in an internal Apple memo that he would take another medical leave of absence for an indefinite period to allow him to focus on his health. Chief operating officer Tim Cook assumed Jobs's day-to-day operations at Apple, although Jobs would still remain "involved in major strategic decisions". Apple became the most valuable consumer-facing brand in the world. In June 2011, Jobs surprisingly took the stage and unveiled iCloud, an online storage and syncing service for music, photos, files, and software which replaced MobileMe, Apple's previous attempt at content syncing. This would be the last product launch Jobs would attend before his death. On August 24, 2011, Jobs resigned his position as CEO of Apple. He was replaced by Cook and Jobs became Apple's chairman. Apple did not have a chairman at the time and instead had two co-lead directors, Andrea Jung and Arthur D. Levinson, who continued with those titles until Levinson replaced Jobs as chairman of the board in November after Jobs' death. 2011–present: Post-Jobs era, Cook's leadership On October 5, 2011, Steve Jobs died, marking the end of an era for Apple. The first major product announcement by Apple following Jobs's passing occurred on January 19, 2012, when Apple's Phil Schiller introduced iBook's Textbooks for iOS and iBook Author for Mac OS X in New York City. Jobs stated in the biography "Steve Jobs" that he wanted to reinvent the textbook industry and education. From 2011 to 2012, Apple released the iPhone 4S and iPhone 5, which featured improved cameras, an intelligent software assistant named Siri, and cloud-synced data with iCloud; the third- and fourth-generation iPads, which featured Retina displays; and the iPad Mini, which featured a 7.9-inch screen in contrast to the iPad's 9.7-inch screen. These launches were successful, with the iPhone 5 (released September 21, 2012) becoming Apple's biggest iPhone launch with over two million pre-orders and sales of three million iPads in three days following the launch of the iPad Mini and fourth-generation iPad (released November 3, 2012). Apple also released a third-generation 13-inch MacBook Pro with a Retina display and new iMac and Mac Mini computers. On August 20, 2012, Apple's rising stock price increased the company's market capitalization to a then-record $624 billion. This beat the non-inflation-adjusted record for market capitalization previously set by Microsoft in 1999. On August 24, 2012, a US jury ruled that Samsung should pay Apple $1.05 billion (£665m) in damages in an intellectual property lawsuit. Samsung appealed the damages award, which was reduced by $450 million and further granted Samsung's request for a new trial. On November 10, 2012, Apple confirmed a global settlement that dismissed all existing lawsuits between Apple and HTC up to that date, in favor of a ten-year license agreement for current and future patents between the two companies. It is predicted that Apple will make $280 million a year from this deal with HTC. In May 2014, the company confirmed its intent to acquire Dr. Dre and Jimmy Iovine's audio company Beats Electronics—producer of the "Beats by Dr. Dre" line of headphones and speaker products, and operator of the music streaming service Beats Music—for $3 billion, and to sell their products through Apple's retail outlets and resellers. Iovine believed that Beats had always "belonged" with Apple, as the company modeled itself after Apple's "unmatched ability to marry culture and technology." The acquisition was the largest purchase in Apple's history. During a press event on September 9, 2014, Apple introduced a smartwatch, the Apple Watch. Initially, Apple marketed the device as a fashion accessory and a complement to the iPhone, that would allow people to look at their smartphones less. Over time, the company has focused on developing health and fitness-oriented features on the watch, in an effort to compete with dedicated activity trackers. In January 2016, it was announced that one billion Apple devices were in active use worldwide. On June 6, 2016, Fortune released Fortune 500, their list of companies ranked on revenue generation. In the trailing fiscal year (2015), Apple appeared on the list as the top tech company. It ranked third, overall, with $233 billion in revenue. This represents a movement upward of two spots from the previous year's list. In June 2017, Apple announced the HomePod, its smart speaker aimed to compete against Sonos, Google Home, and Amazon Echo. Towards the end of the year, TechCrunch reported that Apple was acquiring Shazam, a company that introduced its products at WWDC and specializing in music, TV, film and advertising recognition. The acquisition was confirmed a few days later, reportedly costing Apple $400 million, with media reports noting that the purchase looked like a move to acquire data and tools bolstering the Apple Music streaming service. The purchase was approved by the European Union in September 2018. Also in June 2017, Apple appointed Jamie Erlicht and Zack Van Amburg to head the newly formed worldwide video unit. In November 2017, Apple announced it was branching out into original scripted programming: a drama series starring Jennifer Aniston and Reese Witherspoon, and a reboot of the anthology series Amazing Stories with Steven Spielberg. In June 2018, Apple signed the Writers Guild of America's minimum basic agreement and Oprah Winfrey to a multi-year content partnership. Additional partnerships for original series include Sesame Workshop and DHX Media and its subsidiary Peanuts Worldwide, as well as a partnership with A24 to create original films. During the Apple Special Event in September 2017, the AirPower wireless charger was announced alongside the iPhone X, 8 and Watch Series 3. The AirPower was intended to wirelessly charge multiple devices, simultaneously. Though initially set to release in early 2018, the AirPower would be canceled in March 2019, marking the first cancellation of a device under Cook's leadership. On August 19, 2020, Apple's share price briefly topped $467.77, making Apple the first US company with a market capitalization of $2 trillion. During its annual WWDC keynote speech on June 22, 2020, Apple announced it would move away from Intel processors, and the Mac would transition to processors developed in-house. The announcement was expected by industry analysts, and it has been noted that Macs featuring Apple's processors would allow for big increases in performance over current Intel-based models. On November 10, 2020, the MacBook Air, MacBook Pro, and the Mac Mini became the first Mac devices powered by an Apple-designed processor, the Apple M1. In April 2022, it was reported that Samsung Electro-Mechanics would be collaborating with Apple on its M2 chip instead of LG Innotek. Developer logs showed that at least nine Mac models with four different M2 chips were being tested. The Wall Street Journal reported that an effort to develop its own chips left Apple better prepared to deal with the semiconductor shortage that emerged during the pandemic era and led to increased profitability, with sales of Mac computers that included M1 chips rising sharply in 2020 and 2021. It also inspired other companies like Tesla, Amazon, and Meta Platforms to pursue a similar path. In April 2022, Apple opened an online store that allowed anyone in the US to view repair manuals and order replacement parts for specific recent iPhones, although the difference in cost between this method and official repair is anticipated to be minimal. In May 2022, a trademark was filed for RealityOS, an operating system reportedly intended for virtual and augmented reality headsets, first mentioned in 2017. According to Bloomberg, the headset may come out in 2023. Further insider reports state that the device uses iris scanning for payment confirmation and signing into accounts. On June 18, 2022, the Apple Store in Towson, Maryland became the first to unionize in the U.S., with the employees voting to join the International Association of Machinists and Aerospace Workers. On July 7, 2022, Apple added Lockdown Mode to macOS 13 and iOS 16, as a response to the earlier Pegasus revelations; the mode increases security protections for high-risk users against targeted zero-day malware. Apple launched a buy now, pay later service called 'Apple Pay Later' for its Apple Wallet users in March 2023. The program allows its users to apply for loans between $50 and $1,000 to make online or in-app purchases and then repaying them through four installments spread over six weeks without any interest or fees. Products Mac The Mac is Apple's family of personal computers. Macs are known for their ease of use and distinctive aluminium, minimalist designs. Macs have been popular among students, creative professionals, and software engineers. The current lineup consists of the MacBook Air and MacBook Pro laptops, and the iMac, Mac mini, Mac Studio and Mac Pro desktop computers. Often described as a walled garden, Macs use Apple silicon chips, run the macOS operating system, and include Apple software like the Safari web browser, iMovie for home movie editing, GarageBand for music creation, and the iWork productivity suite. Apple also sells pro apps: Final Cut Pro for video production, Logic Pro for musicians and producers, and Xcode for software developers. Apple also sells a variety of accessories for Macs, including the Pro Display XDR, Apple Studio Display, Magic Mouse, Magic Trackpad, and Magic Keyboard. iPhone The iPhone is Apple's line of smartphones, which run the iOS operating system. The first iPhone was unveiled by Steve Jobs on January 9, 2007. Since then, new models have been released annually. When it was introduced, its multi-touch screen was described as "revolutionary" and a "game-changer" for the mobile phone industry. The device has been credited with creating the app economy. , the iPhone has 15% market share, yet represents 50% of global smartphone revenues, with Android phones accounting for the rest. The iPhone has generated large profits for the company, and is credited with helping to make Apple one of the world's most valuable publicly traded companies. The most recent iPhones are the iPhone 15, iPhone 15 Plus, iPhone 15 Pro and iPhone 15 Pro Max. iPad The iPad is Apple's line of tablets which run iPadOS. The first-generation iPad was announced on January 27, 2010. The iPad is mainly marketed for consuming multimedia, creating art, working on documents, videoconferencing, and playing games. The iPad lineup consists of several base iPad models, and the smaller iPad Mini, upgraded iPad Air, and high-end iPad Pro. Apple has consistently improved the iPad's performance, with the iPad Pro adopting the same M1 and M2 chips as the Mac; but the iPad still receives criticism for its limited OS. Apple has sold more than 500 million iPads, though sales peaked in 2013. The iPad still remains the most popular tablet computer by sales , and accounted for nine percent of the company's revenue . Apple sells several iPad accessories, including the Apple Pencil, Smart Keyboard, Smart Keyboard Folio, Magic Keyboard, and several adapters. Other products Apple also makes several other products that it categorizes as "Wearables, Home and Accessories". These products include the AirPods line of wireless headphones, Apple TV digital media players, Apple Watch smartwatches, Beats headphones and HomePod Mini smart speakers. , this broad line of products comprises about 11% of the company's revenues. At WWDC 2023, Apple introduced its new VR headset, Vision Pro, along with visionOS. Apple announced that it will be partnering with Unity to bring existing 3D apps to Vision Pro using Unity's PolySpatial technology. Services Apple also offers a broad line of services that it earns revenue on, including advertising in the App Store and Apple News app, the AppleCare+ extended warranty plan, the iCloud+ cloud-based data storage service, payment services through the Apple Card credit card and the Apple Pay processing platform, a digital content services including Apple Books, Apple Fitness+, Apple Music, Apple News+, Apple TV+, and the iTunes Store. , services comprise about 19% of the company's revenue. Many of the services have been launched when Apple announced it would be making a concerted effort to expand its service revenues. Marketing Branding According to Steve Jobs, the company's name was inspired by his visit to an apple farm while he was on a fruitarian diet. Jobs thought the name "Apple" was "fun, spirited and not intimidating." Steve Jobs and Steve Wozniak were fans of the Beatles, but Apple Inc. had name and logo trademark issues with Apple Corps Ltd., a multimedia company started by the Beatles in 1968. This resulted in a series of lawsuits and tension between the two companies. These issues ended with the settling of their lawsuit in 2007. Apple's first logo, designed by Ron Wayne, depicts Sir Isaac Newton sitting under an apple tree. It was almost immediately replaced by Rob Janoff's "rainbow Apple", the now-familiar rainbow-colored silhouette of an apple with a bite taken out of it. On August 27, 1999, Apple officially dropped the rainbow scheme and began to use monochromatic logos nearly identical in shape to the previous rainbow incarnation. Apple evangelists were actively engaged by the company at one time, but this was after the phenomenon had already been firmly established. Apple evangelist Guy Kawasaki has called the brand fanaticism "something that was stumbled upon," while Ive claimed in 2014 that "people have an incredibly personal relationship" with Apple's products. Fortune magazine named Apple the most admired company in the United States in 2008, and in the world from 2008 to 2012. On September 30, 2013, Apple surpassed Coca-Cola to become the world's most valuable brand in the Omnicom Group's "Best Global Brands" report. Boston Consulting Group has ranked Apple as the world's most innovative brand every year . there were 1.65 billion Apple products in active use. In February 2023 that number exceeded 2 billion devices. Advertising Apple's first slogan, "Byte into an Apple", was coined in the late 1970s. From 1997 to 2002, the slogan "Think different" was used in advertising campaigns, and is still closely associated with Apple. Apple also has slogans for specific product lines—for example, "iThink, therefore iMac" was used in 1998 to promote the iMac, and "Say hello to iPhone" has been used in iPhone advertisements. "Hello" was also used to introduce the original Macintosh, Newton, iMac ("hello (again)"), and iPod. From the introduction of the Macintosh in 1984, with the 1984 Super Bowl advertisement to the more modern Get a Mac adverts, Apple has been recognized for its efforts towards effective advertising and marketing for its products. However, claims made by later campaigns were criticized, particularly the 2005 Power Mac ads. Apple's product advertisements gained significant attention as a result of their eye-popping graphics and catchy tunes. Musicians who benefited from an improved profile as a result of their songs being included on Apple advertisements include Canadian singer Feist with the song "1234" and Yael Naïm with the song "New Soul". Stores The first Apple Stores were originally opened as two locations in May 2001 by then-CEO Steve Jobs, after years of attempting but failing store-within-a-store concepts. Seeing a need for improved retail presentation of the company's products, he began an effort in 1997 to revamp the retail program to get an improved relationship to consumers, and hired Ron Johnson in 2000. Jobs relaunched Apple's online store in 1997, and opened the first two physical stores in 2001. The media initially speculated that Apple would fail, but its stores were highly successful, bypassing the sales numbers of competing nearby stores and within three years reached US$1 billion in annual sales, becoming the fastest retailer in history to do so. Over the years, Apple has expanded the number of retail locations and its geographical coverage, with 499 stores across 22 countries worldwide . Strong product sales have placed Apple among the top-tier retail stores, with sales over $16 billion globally in 2011. Apple Stores underwent a period of significant redesign, beginning in May 2016. This redesign included physical changes to the Apple Stores, such as open spaces and re-branded rooms, as well as changes in function to facilitate interaction between consumers and professionals. Many Apple Stores are located inside shopping malls, but Apple has built several stand-alone "flagship" stores in high-profile locations. It has been granted design patents and received architectural awards for its stores' designs and construction, specifically for its use of glass staircases and cubes. The success of Apple Stores have had significant influence over other consumer electronics retailers, who have lost traffic, control and profits due to a perceived higher quality of service and products at Apple Stores. Due to the popularity of the brand, Apple receives a large number of job applications, many of which come from young workers. Although Apple Store employees receive above-average pay, are offered money toward education and health care, and receive product discounts, there are limited or no paths of career advancement. Market power On March 16, 2020, France fined Apple €1.1 billion for colluding with two wholesalers to stifle competition and keep prices high by handicapping independent resellers. The arrangement created aligned prices for Apple products such as iPads and personal computers for about half the French retail market. According to the French regulators, the abuses occurred between 2005 and 2017 but were first discovered after a complaint by an independent reseller, eBizcuss, in 2012. On August 13, 2020, Epic Games, the maker of the popular game Fortnite, sued Apple and Google after its hugely popular video game was removed from Apple and Google's App Store. The suits come after both Apple and Google blocked the game after it introduced a direct payment system, effectively shutting out the tech titans from collecting fees. In September 2020 Epic Games founded the Coalition for App Fairness together with other thirteen companies, which aims for better conditions for the inclusion of apps in the app stores. Later in December 2020, Facebook agreed to assist Epic in their legal game against Apple, planning to support the company by providing materials and documents to Epic. Facebook had, however, stated that the company will not participate directly with the lawsuit, although did commit to helping with the discovery of evidence relating to the trial of 2021. In the months prior to their agreement, Facebook had been dealing with feuds against Apple relating to the prices of paid apps as well as privacy rule changes. Head of ad products for Facebook Dan Levy commented, saying that "this is not really about privacy for them, this is about an attack on personalized ads and the consequences it's going to have on small-business owners," commenting on the full-page ads placed by Facebook in various newspapers in December 2020. Customer privacy Apple has a notable pro-privacy stance, actively making privacy-conscious features and settings part of its conferences, promotional campaigns, and public image. With its iOS 8 mobile operating system in 2014, the company started encrypting all contents of iOS devices through users' passcodes, making it impossible at the time for the company to provide customer data to law enforcement requests seeking such information. With the popularity rise of cloud storage solutions, Apple began a technique in 2016 to do deep learning scans for facial data in photos on the user's local device and encrypting the content before uploading it to Apple's iCloud storage system. It also introduced "differential privacy", a way to collect crowdsourced data from many users, while keeping individual users anonymous, in a system that Wired described as "trying to learn as much as possible about a group while learning as little as possible about any individual in it". Users are explicitly asked if they want to participate, and can actively opt-in or opt-out. With Apple's release of an update to iOS 14, Apple required all developers of iPhone, iPad, and iPod Touch applications to directly ask iPhone users permission to track them. The feature, titled "App Tracking Transparency", received heavy criticism from Facebook, whose primary business model revolves around the tracking of users' data and sharing such data with advertisers so users can see more relevant ads, a technique commonly known as targeted advertising. Despite Facebook's measures, including purchasing full-page newspaper advertisements protesting App Tracking Transparency, Apple released the update in mid-spring 2021. A study by Verizon subsidiary Flurry Analytics reported only 4% of iOS users in the United States and 12% worldwide have opted into tracking. However, Apple aids law enforcement in criminal investigations by providing iCloud backups of users' devices, and the company's commitment to privacy has been questioned by its efforts to promote biometric authentication technology in its newer iPhone models, which do not have the same level of constitutional privacy as a passcode in the United States. Prior to the release of iOS 15, Apple announced new efforts at combating child sexual abuse material on iOS and Mac platforms. Parents of minor iMessage users can now be alerted if their child sends or receives nude photographs. Additionally, on-device hashing would take place on media destined for upload to iCloud, and hashes would be compared to a list of known abusive images provided by law enforcement; if enough matches were found, Apple would be alerted and authorities informed. The new features received praise from law enforcement and victims rights advocates, however privacy advocates, including the Electronic Frontier Foundation, condemned the new features as invasive and highly prone to abuse by authoritarian governments. Ireland's Data Protection Commission launched a privacy investigation to examine whether Apple complied with the EU's GDPR law following an investigation into how the company processes personal data with targeted ads on its platform. In December 2019, a report found that the iPhone 11 Pro continues tracking location and collecting user data even after users have disabled location services. In response, an Apple engineer said the Location Services icon "appears for system services that do not have a switch in settings." According to published reports by Bloomberg News on March 30, 2022, Apple turned over data such as phone numbers, physical addresses, and IP addresses to hackers posing as law enforcement officials using forged documents. The law enforcement requests sometimes included forged signatures of real or fictional officials. When asked about the allegations, an Apple representative referred the reporter to a section of the company policy for law enforcement guidelines, which stated, "We review every data request for legal sufficiency and use advanced systems and processes to validate law enforcement requests and detect abuse." Corporate affairs Leadership Senior management As of March 16, 2021, the management of Apple Inc. includes: Tim Cook (chief executive officer) Jeff Williams (chief operating officer) Luca Maestri (senior vice president and chief financial officer) Katherine L. Adams (senior vice president and general counsel) Eddy Cue (senior vice president – Internet Software and Services) Craig Federighi (senior vice president – Software Engineering) John Giannandrea (senior vice president – Machine Learning and AI Strategy) Deirdre O'Brien (senior vice president – Retail + People) John Ternus (senior vice president – Hardware Engineering) Greg Josiwak (senior vice president – Worldwide Marketing) Johny Srouji (senior vice president – Hardware Technologies) Sabih Khan (senior vice president – Operations) Board of directors As of January 20, 2023, the board of directors of Apple Inc. includes: Arthur D. Levinson (chairman) Tim Cook (executive director and CEO) James A. Bell Al Gore Alex Gorsky Andrea Jung Monica Lozano Ronald Sugar Susan Wagner Previous CEOs Michael Scott (1977–1981) Mike Markkula (1981–1983) John Sculley (1983–1993) Michael Spindler (1993–1996) Gil Amelio (1996–1997) Steve Jobs (1997–2011) Corporate culture Apple is one of several highly successful companies founded in the 1970s that bucked the traditional notions of corporate culture. Jobs often walked around the office barefoot even after Apple became a Fortune 500 company. By the time of the "1984" television advertisement, Apple's informal culture had become a key trait that differentiated it from its competitors. According to a 2011 report in Fortune, this has resulted in a corporate culture more akin to a startup rather than a multinational corporation. In a 2017 interview, Wozniak credited watching Star Trek and attending Star Trek conventions while in his youth as a source of inspiration for his co-founding Apple. As the company has grown and been led by a series of differently opinionated chief executives, it has arguably lost some of its original character. Nonetheless, it has maintained a reputation for fostering individuality and excellence that reliably attracts talented workers, particularly after Jobs returned to the company. Numerous Apple employees have stated that projects without Jobs's involvement often took longer than projects with it. To recognize the best of its employees, Apple created the Apple Fellows program which awards individuals who make extraordinary technical or leadership contributions to personal computing while at the company. The Apple Fellowship has so far been awarded to individuals including Bill Atkinson, Steve Capps, Rod Holt, Alan Kay, Guy Kawasaki, Al Alcorn, Don Norman, Rich Page, Steve Wozniak, and Phil Schiller. At Apple, employees are intended to be specialists who are not exposed to functions outside their area of expertise. Jobs saw this as a means of having "best-in-class" employees in every role. For instance, Ron Johnson—Senior Vice President of Retail Operations until November 1, 2011—was responsible for site selection, in-store service, and store layout, yet had no control of the inventory in his stores. This was done by Tim Cook, who had a background in supply-chain management. Apple is known for strictly enforcing accountability. Each project has a "directly responsible individual" or "DRI" in Apple jargon. As an example, when iOS senior vice president Scott Forstall refused to sign Apple's official apology for numerous errors in the redesigned Maps app, he was forced to resign. Unlike other major U.S. companies, Apple provides a relatively simple compensation policy for executives that does not include perks enjoyed by other CEOs like country club fees or private use of company aircraft. The company typically grants stock options to executives every other year. In 2015, Apple had 110,000 full-time employees. This increased to 116,000 full-time employees the next year, a notable hiring decrease, largely due to its first revenue decline. Apple does not specify how many of its employees work in retail, though its 2014 SEC filing put the number at approximately half of its employee base. In September 2017, Apple announced that it had over 123,000 full-time employees. Apple has a strong culture of corporate secrecy, and has an anti-leak Global Security team that recruits from the National Security Agency, the Federal Bureau of Investigation, and the United States Secret Service. In December 2017, Glassdoor said Apple was the 48th best place to work, having originally entered at rank 19 in 2009, peaking at rank 10 in 2012, and falling down the ranks in subsequent years. In 2023, Bloomberg Mark Gurman revealed the existence of Apple's Exploratory Design Group (XDG), which was working to add glucose monitoring to the Apple Watch. Gurman compared XDG to Alphabet's X "moonshot factory". Offices Apple Inc.'s world corporate headquarters are located in Cupertino, in the middle of California's Silicon Valley, at Apple Park, a massive circular groundscraper building with a circumference of . The building opened in April 2017 and houses more than 12,000 employees. Apple co-founder Steve Jobs wanted Apple Park to look less like a business park and more like a nature refuge, and personally appeared before the Cupertino City Council in June 2011 to make the proposal, in his final public appearance before his death. Apple also operates from the Apple Campus (also known by its address, 1 Infinite Loop), a grouping of six buildings in Cupertino that total located about to the west of Apple Park. The Apple Campus was the company's headquarters from its opening in 1993, until the opening of Apple Park in 2017. The buildings, located at 1–6 Infinite Loop, are arranged in a circular pattern around a central green space, in a design that has been compared to that of a university. In addition to Apple Park and the Apple Campus, Apple occupies an additional thirty office buildings scattered throughout the city of Cupertino, including three buildings that also served as prior headquarters: "Stephens Creek Three" (1977–1978), Bandley One" (1978–1982), and "Mariani One" (1982–1993). In total, Apple occupies almost 40% of the available office space in the city. Apple's headquarters for Europe, the Middle East and Africa (EMEA) are located in Cork in the south of Ireland, called the Hollyhill campus. The facility, which opened in 1980, houses 5,500 people and was Apple's first location outside of the United States. Apple's international sales and distribution arms operate out of the campus in Cork. Apple has two campuses near Austin, Texas: a campus opened in 2014 houses 500 engineers who work on Apple silicon and a campus opened in 2021 where 6,000 people work in technical support, supply chain management, online store curation, and Apple Maps data management. The company also has several other locations in Boulder, Colorado, Culver City, California, Herzliya (Israel), London, New York, Pittsburgh, San Diego, and Seattle that each employ hundreds of people. Litigation Apple has been a participant in various legal proceedings and claims since it began operation. In particular, Apple is known for and promotes itself as actively and aggressively enforcing its intellectual property interests. Some litigation examples include Apple v. Samsung, Apple v. Microsoft, Motorola Mobility v. Apple Inc., and Apple Corps v. Apple Computer. Apple has also had to defend itself against charges on numerous occasions of violating intellectual property rights. Most have been dismissed in the courts as shell companies known as patent trolls, with no evidence of actual use of patents in question. On December 21, 2016, Nokia announced that in the U.S. and Germany, it has filed a suit against Apple, claiming that the latter's products infringe on Nokia's patents. Most recently, in November 2017, the United States International Trade Commission announced an investigation into allegations of patent infringement in regards to Apple's remote desktop technology; Aqua Connect, a company that builds remote desktop software, has claimed that Apple infringed on two of its patents. In January 2022, Ericsson sued Apple over payment of royalty of 5G technology. Finances Apple is the world's largest technology company by revenue, the world's largest technology company by total assets, and the world's second-largest mobile phone manufacturer after Samsung. In its fiscal year ending in September 2011, Apple Inc. reported a total of $108 billion in annual revenues—a significant increase from its 2010 revenues of $65 billion—and nearly $82 billion in cash reserves. On March 19, 2012, Apple announced plans for a $2.65-per-share dividend beginning in fourth quarter of 2012, per approval by their board of directors. The company's worldwide annual revenue in 2013 totaled $170 billion. In May 2013, Apple entered the top ten of the Fortune 500 list of companies for the first time, rising 11 places above its 2012 ranking to take the sixth position. , Apple has around US$234 billion of cash and marketable securities, of which 90% is located outside the United States for tax purposes. Apple amassed 65% of all profits made by the eight largest worldwide smartphone manufacturers in quarter one of 2014, according to a report by Canaccord Genuity. In the first quarter of 2015, the company garnered 92% of all earnings. On April 30, 2017, The Wall Street Journal reported that Apple had cash reserves of $250 billion, officially confirmed by Apple as specifically $256.8 billion a few days later. , Apple was the largest publicly traded corporation in the world by market capitalization. On August 2, 2018, Apple became the first publicly traded U.S. company to reach a $1 trillion market value. Apple was ranked No. 4 on the 2018 Fortune 500 rankings of the largest United States corporations by total revenue. In July 2022, Apple reported an 11% decline in Q3 profits compared to 2021. Its revenue in the same period rose 2% year-on-year to $83 billion, though this figure was also lower than in 2021, where the increase was at 36%. The general downturn is reportedly caused by the slowing global economy and supply chain disruptions in China. In May 2023, Apple reported a decline in its sales for the first quarter of 2023. Compared to that of 2022, revenue for 2023 fell by 3%. This is Apple's second consecutive quarter of sales decline. This fall is attributed to the slowing economy and consumers putting off purchases of iPads and computers due to increased pricing. However, iPhone sales held up with a year-on-year increase of 1.5%. According to Apple, demands for such devices were strong, particularly in Latin America and South Asia. Taxes Apple has created subsidiaries in low-tax places such as Ireland, the Netherlands, Luxembourg, and the British Virgin Islands to cut the taxes it pays around the world. According to The New York Times, in the 1980s Apple was among the first tech companies to designate overseas salespeople in high-tax countries in a manner that allowed the company to sell on behalf of low-tax subsidiaries on other continents, sidestepping income taxes. In the late 1980s, Apple was a pioneer of an accounting technique known as the "Double Irish with a Dutch sandwich", which reduces taxes by routing profits through Irish subsidiaries and the Netherlands and then to the Caribbean. British Conservative Party Member of Parliament Charlie Elphicke published research on October 30, 2012, which showed that some multinational companies, including Apple Inc., were making billions of pounds of profit in the UK, but were paying an effective tax rate to the UK Treasury of only 3 percent, well below standard corporate tax rates. He followed this research by calling on the Chancellor of the Exchequer George Osborne to force these multinationals, which also included Google and The Coca-Cola Company, to state the effective rate of tax they pay on their UK revenues. Elphicke also said that government contracts should be withheld from multinationals who do not pay their fair share of UK tax. According to a US Senate report on the company's offshore tax structure concluded in May 2013, Apple has held billions of dollars in profits in Irish subsidiaries to pay little or no taxes to any government by using an unusual global tax structure. The main subsidiary, a holding company that includes Apple's retail stores throughout Europe, has not paid any corporate income tax in the last five years. "Apple has exploited a difference between Irish and U.S. tax residency rules", the report said. On May 21, 2013, Apple CEO Tim Cook defended his company's tax tactics at a Senate hearing. Apple says that it is the single largest taxpayer in the U.S., with an effective tax rate of approximately of 26% as of Q2 FY2016. In an interview with the German newspaper FAZ in October 2017, Tim Cook stated that Apple was the biggest taxpayer worldwide. In 2016, after a two-year investigation, the European Commission claimed that Apple's use of a hybrid Double Irish tax arrangement constituted "illegal state aid" from Ireland, and ordered Apple to pay 13 billion euros ($14.5 billion) in unpaid taxes, the largest corporate tax fine in history. This was later annulled, after the European General Court ruled that the Commission had provided insufficient evidence. In 2018, Apple repatriated $285 billion to America, resulting in a $38 billion tax payment spread over the following 8 years. Charity Apple is a partner of (PRODUCT)RED, a fundraising campaign for AIDS charity. In November 2014, Apple arranged for all App Store revenue in a two-week period to go to the fundraiser, generating more than US$20 million, and in March 2017, it released an iPhone 7 with a red color finish. Apple contributes financially to fundraisers in times of natural disasters. In November 2012, it donated $2.5 million to the American Red Cross to aid relief efforts after Hurricane Sandy, and in 2017 it donated $5 million to relief efforts for both Hurricane Irma and Hurricane Harvey, as well as for the 2017 Central Mexico earthquake. The company has also used its iTunes platform to encourage donations in the wake of environmental disasters and humanitarian crises, such as the 2010 Haiti earthquake, the 2011 Japan earthquake, Typhoon Haiyan in the Philippines in November 2013, and the 2015 European migrant crisis. Apple emphasizes that it does not incur any processing or other fees for iTunes donations, sending 100% of the payments directly to relief efforts, though it also acknowledges that the Red Cross does not receive any personal information on the users donating and that the payments may not be tax deductible. On April 14, 2016, Apple and the World Wide Fund for Nature (WWF) announced that they have engaged in a partnership to, "help protect life on our planet." Apple released a special page in the iTunes App Store, Apps for Earth. In the arrangement, Apple has committed that through April 24, WWF will receive 100% of the proceeds from the applications participating in the App Store via both the purchases of any paid apps and the In-App Purchases. Apple and WWF's Apps for Earth campaign raised more than $8 million in total proceeds to support WWF's conservation work. WWF announced the results at WWDC 2016 in San Francisco. During the COVID-19 pandemic, Apple's CEO Cook announced that the company will be donating "millions" of masks to health workers in the United States and Europe. On January 13, 2021, Apple announced a $100 million "Racial Equity and Justice Initiative" to help combat institutional racism worldwide. Environment Apple Energy Apple Energy, LLC is a wholly-owned subsidiary of Apple Inc. that sells solar energy. , Apple's solar farms in California and Nevada have been declared to provide 217.9 megawatts of solar generation capacity. In addition to the company's solar energy production, Apple has received regulatory approval to construct a landfill gas energy plant in North Carolina. Apple will use the methane emissions to generate electricity. Apple's North Carolina data center is already powered entirely with energy from renewable sources. Energy and resources In 2010, Climate Counts, a nonprofit organization dedicated to directing consumers toward the greenest companies, gave Apple a score of 52 points out of a possible 100, which puts Apple in their top category "Striding". This was an increase from May 2008, when Climate Counts only gave Apple 11 points out of 100, which placed the company last among electronics companies, at which time Climate Counts also labeled Apple with a "stuck icon", adding that Apple at the time was "a choice to avoid for the climate-conscious consumer". Following a Greenpeace protest, Apple released a statement on April 17, 2012, committing to ending its use of coal and shifting to 100% renewable clean energy. By 2013, Apple was using 100% renewable energy to power their data centers. Overall, 75% of the company's power came from clean renewable sources. In May 2015, Greenpeace evaluated the state of the Green Internet and commended Apple on their environmental practices saying, "Apple's commitment to renewable energy has helped set a new bar for the industry, illustrating in very concrete terms that a 100% renewable Internet is within its reach, and providing several models of intervention for other companies that want to build a sustainable Internet." , Apple states that 100% of its U.S. operations run on renewable energy, 100% of Apple's data centers run on renewable energy and 93% of Apple's global operations run on renewable energy. However, the facilities are connected to the local grid which usually contains a mix of fossil and renewable sources, so Apple carbon offsets its electricity use. The Electronic Product Environmental Assessment Tool (EPEAT) allows consumers to see the effect a product has on the environment. Each product receives a Gold, Silver, or Bronze rank depending on its efficiency and sustainability. Every Apple tablet, notebook, desktop computer, and display that EPEAT ranks achieves a Gold rating, the highest possible. Although Apple's data centers recycle water 35 times, the increased activity in retail, corporate and data centers also increase the amount of water use to in 2015. During an event on March 21, 2016, Apple provided a status update on its environmental initiative to be 100% renewable in all of its worldwide operations. Lisa P. Jackson, Apple's vice president of Environment, Policy and Social Initiatives who reports directly to CEO, Tim Cook, announced that , 93% of Apple's worldwide operations are powered with renewable energy. Also featured was the company's efforts to use sustainable paper in their product packaging; 99% of all paper used by Apple in the product packaging comes from post-consumer recycled paper or sustainably managed forests, as the company continues its move to all paper packaging for all of its products. Apple working in partnership with Conservation Fund, have preserved 36,000 acres of working forests in Maine and North Carolina. Another partnership announced is with the World Wildlife Fund to preserve up to of forests in China. Featured was the company's installation of a 40 MW solar power plant in the Sichuan province of China that was tailor-made to coexist with the indigenous yaks that eat hay produced on the land, by raising the panels to be several feet off of the ground so the yaks and their feed would be unharmed grazing beneath the array. This installation alone compensates for more than all of the energy used in Apple's Stores and Offices in the whole of China, negating the company's energy carbon footprint in the country. In Singapore, Apple has worked with the Singaporean government to cover the rooftops of 800 buildings in the city-state with solar panels allowing Apple's Singapore operations to be run on 100% renewable energy. Liam was introduced to the world, an advanced robotic disassembler and sorter designed by Apple Engineers in California specifically for recycling outdated or broken iPhones. Reuses and recycles parts from traded in products. Apple announced on August 16, 2016, that Lens Technology, one of its major suppliers in China, has committed to power all its glass production for Apple with 100 percent renewable energy by 2018. The commitment is a large step in Apple's efforts to help manufacturers lower their carbon footprint in China. Apple also announced that all 14 of its final assembly sites in China are now compliant with UL's Zero Waste to Landfill validation. The standard, which started in January 2015, certifies that all manufacturing waste is reused, recycled, composted, or converted into energy (when necessary). Since the program began, nearly 140,000 metric tons of waste have been diverted from landfills. On July 21, 2020, Apple announced its plan to become carbon neutral across its entire business, manufacturing supply chain, and product life cycle by 2030. In the next 10 years, Apple will try to lower emissions with a series of innovative actions, including: low carbon product design, expanding energy efficiency, renewable energy, process and material innovations, and carbon removal. In April 2021, Apple said that it had started a $200 million fund in order to combat climate change by removing 1 million metric tons of carbon dioxide from the atmosphere each year. In February 2022, the NewClimate Institute, a German environmental policy think tank, published a survey evaluating the transparency and progress of the climate strategies and carbon neutrality pledges announced by 25 major companies in the United States that found that Apple's carbon neutrality pledge and climate strategy was unsubstantiated and misleading. Toxins Following further campaigns by Greenpeace, in 2008, Apple became the first electronics manufacturer to eliminate all polyvinyl chloride (PVC) and brominated flame retardants (BFRs) in its complete product line. In June 2007, Apple began replacing the cold cathode fluorescent lamp (CCFL) backlit LCD displays in its computers with mercury-free LED-backlit LCD displays and arsenic-free glass, starting with the upgraded MacBook Pro. Apple offers comprehensive and transparent information about the CO2e, emissions, materials, and electrical usage concerning every product they currently produce or have sold in the past (and which they have enough data needed to produce the report), in their portfolio on their homepage. Allowing consumers to make informed purchasing decisions on the products they offer for sale. In June 2009, Apple's iPhone 3GS was free of PVC, arsenic, and BFRs. All Apple products now have mercury-free LED-backlit LCD displays, arsenic-free glass, and non-PVC cables. All Apple products have EPEAT Gold status and beat the latest Energy Star guidelines in each product's respective regulatory category. In November 2011, Apple was featured in Greenpeace's Guide to Greener Electronics, which ranks electronics manufacturers on sustainability, climate and energy policy, and how "green" their products are. The company ranked fourth of fifteen electronics companies (moving up five places from the previous year) with a score of 4.6/10. Greenpeace praised Apple's sustainability, noting that the company exceeded its 70% global recycling goal in 2010. Apple continues to score well on product ratings, with all of their products now being free of PVC plastic and BFRs. However, the guide criticized Apple on the Energy criteria for not seeking external verification of its greenhouse gas emissions data, and for not setting any targets to reduce emissions. In January 2012, Apple requested that its cable maker, Volex, begin producing halogen-free USB and power cables. Green bonds In February 2016, Apple issued a US$1.5 billion green bond (climate bond), the first ever of its kind by a U.S. tech company. The green bond proceeds are dedicated to the financing of environmental projects. Supply chain Apple products were made in America in Apple-owned factories until the late 1990s; however, as a result of outsourcing initiatives in the 2000s, almost all of its manufacturing is now handled abroad. According to a report by The New York Times, Apple insiders "believe the vast scale of overseas factories, as well as the flexibility, diligence and industrial skills of foreign workers, have so outpaced their American counterparts that "Made in the USA" is no longer a viable option for most Apple products". The company's manufacturing, procurement, and logistics enable it to execute massive product launches without having to maintain large, profit-sapping inventories. In 2011, Apple's profit margins were 40 percent, compared with between 10 and 20 percent for most other hardware companies. Cook's catchphrase to describe his focus on the company's operational arm is: "Nobody wants to buy sour milk." In May 2017, the company announced a $1 billion funding project for "advanced manufacturing" in the United States, and subsequently invested $200 million in Corning Inc., a manufacturer of toughened Gorilla Glass technology used in its iPhone devices. The following December, Apple's chief operating officer, Jeff Williams, told CNBC that the "$1 billion" amount was "absolutely not" the final limit on its spending, elaborating that "We're not thinking in terms of a fund limit... We're thinking about, where are the opportunities across the U.S. to help nurture companies that are making the advanced technology— and the advanced manufacturing that goes with that— that quite frankly is essential to our innovation." , Apple uses components from 43 countries. The majority of assembling is done by Taiwanese original design manufacturer firms Foxconn, Pegatron, Wistron and Compal Electronics with factories mostly located inside China, but also Brazil, and India. Taiwan Semiconductor Manufacturing Co., (TSMC) is a pure-play semiconductor manufacturing company. They make the majority of Apple's smartphone SoCs, with Samsung Semiconductor, playing a minority role. Apple, alone accounted for over 25% of TSMC's total income in 2021. Apple's Bionic lineup of smartphone SoCs, are currently made exclusively by TSMC from the A7 bionic onwards, previously manufacturing was shared with Samsung. The M series of Apple SoC for consumer computers and tablets is made by TSMC as well. During the Mac's early history Apple generally refused to adopt prevailing industry standards for hardware, instead creating their own. This trend was largely reversed in the late 1990s, beginning with Apple's adoption of the PCI bus in the 7500/8500/9500 Power Macs. Apple has since joined the industry standards groups to influence the future direction of technology standards such as USB, AGP, HyperTransport, Wi-Fi, NVMe, PCIe and others in its products. FireWire is an Apple-originated standard that was widely adopted across the industry after it was standardized as IEEE 1394 and is a legally mandated port in all Cable TV boxes in the United States. Apple has gradually expanded its efforts in getting its products into the Indian market. In July 2012, during a conference call with investors, CEO Tim Cook said that he "[loves] India", but that Apple saw larger opportunities outside the region. India's requirement that 30% of products sold be manufactured in the country was described as "really adds cost to getting product to market". In May 2016, Apple opened an iOS app development center in Bangalore and a maps development office for 4,000 staff in Hyderabad. In March, The Wall Street Journal reported that Apple would begin manufacturing iPhone models in India "over the next two months", and in May, the Journal wrote that an Apple manufacturer had begun production of iPhone SE in the country, while Apple told CNBC that the manufacturing was for a "small number" of units. In April 2019, Apple initiated manufacturing of iPhone 7 at its Bengaluru facility, keeping in mind demand from local customers even as they seek more incentives from the government of India. At the beginning of 2020, Tim Cook announced that Apple schedules the opening of its first physical outlet in India for 2021, while an online store is to be launched by the end of the year. During the 2022 COVID-19 protests in China, Chinese state-owned company Wingtech was reported by The Wall Street Journal to gain an additional foothold in Apple's supply chain following protests at a Foxconn factory in the Zhengzhou Airport Economy Zone. Worker organizations In 2006, one complex of factories in Shenzhen, China that assembled the iPod and other items had over 200,000 workers living and working within it. Employees regularly worked more than 60 hours per week and made around $100 per month. A little over half of the workers' earnings was required to pay for rent and food from the company. Apple immediately launched an investigation after the 2006 media report, and worked with their manufacturers to ensure acceptable working conditions. In 2007, Apple started yearly audits of all its suppliers regarding worker's rights, slowly raising standards and pruning suppliers that did not comply. Yearly progress reports have been published . In 2011, Apple admitted that its suppliers' child labor practices in China had worsened. The Foxconn suicides occurred between January and November 2010, when 18 Foxconn () employees attempted suicide, resulting in 14 deaths—the company was the world's largest contract electronics manufacturer, for clients including Apple, at the time. The suicides drew media attention, and employment practices at Foxconn were investigated by Apple. Apple issued a public statement about the suicides, and company spokesperson Steven Dowling said: The statement was released after the results from the company's probe into its suppliers' labor practices were published in early 2010. Foxconn was not specifically named in the report, but Apple identified a series of serious labor violations of labor laws, including Apple's own rules, and some child labor existed in a number of factories. Apple committed to the implementation of changes following the suicides. Also in 2010, workers in China planned to sue iPhone contractors over poisoning by a cleaner used to clean LCD screens. One worker claimed that he and his coworkers had not been informed of possible occupational illnesses. After a high suicide rate in a Foxconn facility in China making iPads and iPhones, albeit a lower rate than that of China as a whole, workers were forced to sign a legally binding document guaranteeing that they would not kill themselves. Workers in factories producing Apple products have also been exposed to hexane, a neurotoxin that is a cheaper alternative than alcohol for cleaning the products. A 2014 BBC investigation found excessive hours and other problems persisted, despite Apple's promise to reform factory practice after the 2010 Foxconn suicides. The Pegatron factory was once again the subject of review, as reporters gained access to the working conditions inside through recruitment as employees. While the BBC maintained that the experiences of its reporters showed that labor violations were continuing , Apple publicly disagreed with the BBC and stated: "We are aware of no other company doing as much as Apple to ensure fair and safe working conditions". In December 2014, the Institute for Global Labour and Human Rights published a report which documented inhumane conditions for the 15,000 workers at a Zhen Ding Technology factory in Shenzhen, China, which serves as a major supplier of circuit boards for Apple's iPhone and iPad. According to the report, workers are pressured into 65-hour work weeks which leaves them so exhausted that they often sleep during lunch breaks. They are also made to reside in "primitive, dark and filthy dorms" where they sleep "on plywood, with six to ten workers in each crowded room." Omnipresent security personnel also routinely harass and beat the workers. In 2019, there were reports stating that some of Foxconn's managers had used rejected parts to build iPhones and that Apple was investigating the issue. See also List of Apple Inc. media events Pixar Notes References Bibliography Further reading External links 1976 establishments in California 1980s initial public offerings American brands Companies based in Cupertino, California Companies in the Dow Jones Industrial Average Companies in the PRISM network Companies listed on the Nasdaq Computer companies established in 1976 Computer companies of the United States Display technology companies Electronics companies of the United States Home computer hardware companies Mobile phone manufacturers Multinational companies headquartered in the United States Networking hardware companies Portable audio player manufacturers Retail companies of the United States Software companies based in the San Francisco Bay Area Software companies established in 1976 Steve Jobs Technology companies based in the San Francisco Bay Area Technology companies established in 1976 Technology companies of the United States
The aspect ratio of a geometric shape is the ratio of its sizes in different dimensions. For example, the aspect ratio of a rectangle is the ratio of its longer side to its shorter side—the ratio of width to height, when the rectangle is oriented as a "landscape". The aspect ratio is most often expressed as two integer numbers separated by a colon (x:y), less commonly as a simple or decimal fraction. The values x and y do not represent actual widths and heights but, rather, the proportion between width and height. As an example, 8:5, 16:10, 1.6:1, and 1.6 are all ways of representing the same aspect ratio. In objects of more than two dimensions, such as hyperrectangles, the aspect ratio can still be defined as the ratio of the longest side to the shortest side. Applications and uses The term is most commonly used with reference to: Graphic / image Image aspect ratio Display aspect ratio Paper size Standard photographic print sizes Motion picture film formats Standard ad size Pixel aspect ratio Photolithography: the aspect ratio of an etched, or deposited structure is the ratio of the height of its vertical side wall to its width. HARMST High Aspect Ratios allow the construction of tall microstructures without slant Tire code Tire sizing Turbocharger impeller sizing Wing aspect ratio of an aircraft or bird Astigmatism of an optical lens Nanorod dimensions Shape factor (image analysis and microscopy) Finite Element Analysis Aspect ratios of simple shapes Rectangles For a rectangle, the aspect ratio denotes the ratio of the width to the height of the rectangle. A square has the smallest possible aspect ratio of 1:1. Examples: 4:3 = 1.: Some (not all) 20th century computer monitors (VGA, XGA, etc.), standard-definition television : international paper sizes (ISO 216) 3:2 = 1.5: 35mm still camera film, iPhone (until iPhone 5) displays 16:10 = 1.6: commonly used widescreen computer displays (WXGA) Φ:1 = 1.618...: golden ratio, close to 16:10 5:3 = 1.: super 16 mm, a standard film gauge in many European countries 16:9 = 1.: widescreen TV and most laptops 2:1 = 2: dominoes 64:27 = 2.: ultra-widescreen, 21:9 32:9 = 3.: super ultra-widescreen Ellipses For an ellipse, the aspect ratio denotes the ratio of the major axis to the minor axis. An ellipse with an aspect ratio of 1:1 is a circle. Aspect ratios of general shapes In geometry, there are several alternative definitions to aspect ratios of general compact sets in a d-dimensional space: The diameter-width aspect ratio (DWAR) of a compact set is the ratio of its diameter to its width. A circle has the minimal DWAR which is 1. A square has a DWAR of . The cube-volume aspect ratio (CVAR) of a compact set is the d-th root of the ratio of the d-volume of the smallest enclosing axes-parallel d-cube, to the set's own d-volume. A square has the minimal CVAR which is 1. A circle has a CVAR of . An axis-parallel rectangle of width W and height H, where W>H, has a CVAR of . If the dimension d is fixed, then all reasonable definitions of aspect ratio are equivalent to within constant factors. Notations Aspect ratios are mathematically expressed as x:y (pronounced "x-to-y"). Cinematographic aspect ratios are usually denoted as a (rounded) decimal multiple of width vs unit height, while photographic and videographic aspect ratios are usually defined and denoted by whole number ratios of width to height. In digital images there is a subtle distinction between the display aspect ratio (the image as displayed) and the storage aspect ratio (the ratio of pixel dimensions); see Distinctions. See also Axial ratio Ratio Equidimensional ratios in 3D List of film formats Squeeze mapping Scale (ratio) Vertical orientation References Ratios
Advanced Micro Devices, Inc., commonly abbreviated as AMD, is an American multinational semiconductor company based in Santa Clara, California, that develops computer processors and related technologies for business and consumer markets. The company was founded in 1969 by Jerry Sanders and a group of other technology professionals. AMD's early products were primarily memory chips and other components for computers. The company later expanded into the microprocessor market, competing with Intel, its main rival in the industry. In the early 2000s, AMD experienced significant growth and success, thanks in part to its strong position in the PC market and the success of its Athlon and Opteron processors. However, the company faced challenges in the late 2000s and early 2010s, as it struggled to keep up with Intel in the race to produce faster and more powerful processors. In the late 2010s, AMD regained some of its market share thanks to the success of its Ryzen processors which are now widely regarded as superior to Intel products in business applications including cloud applications. AMD's processors are used in a wide range of computing devices, including personal computers, servers, laptops, and gaming consoles. While it initially manufactured its own processors, the company later outsourced its manufacturing, a practice known as going fabless, after GlobalFoundries was spun off in 2009. AMD's main products include microprocessors, motherboard chipsets, embedded processors, graphics processors, and FPGAs for servers, workstations, personal computers, and embedded system applications. The company has also expanded into new markets, such as the data center and gaming markets, and has announced plans to enter the high-performance computing market. History First twelve years Advanced Micro Devices was formally incorporated by Jerry Sanders, along with seven of his colleagues from Fairchild Semiconductor, on May 1, 1969. Sanders, an electrical engineer who was the director of marketing at Fairchild, had, like many Fairchild executives, grown frustrated with the increasing lack of support, opportunity, and flexibility within the company. He later decided to leave to start his own semiconductor company, following the footsteps of Robert Noyce (developer of the first silicon integrated circuit at Fairchild in 1959) and Gordon Moore, who together founded the semiconductor company Intel in July 1968. In September 1969, AMD moved from its temporary location in Santa Clara to Sunnyvale, California. To immediately secure a customer base, AMD initially became a second source supplier of microchips designed by Fairchild and National Semiconductor. AMD first focused on producing logic chips. The company guaranteed quality control to United States Military Standard, an advantage in the early computer industry since unreliability in microchips was a distinct problem that customers – including computer manufacturers, the telecommunications industry, and instrument manufacturers – wanted to avoid. In November 1969, the company manufactured its first product: the Am9300, a 4-bit MSI shift register, which began selling in 1970. Also in 1970, AMD produced its first proprietary product, the Am2501 logic counter, which was highly successful. Its bestselling product in 1971 was the Am2505, the fastest multiplier available. In 1971, AMD entered the RAM chip market, beginning with the Am3101, a 64-bit bipolar RAM. That year AMD also greatly increased the sales volume of its linear integrated circuits, and by year-end the company's total annual sales reached US$4.6 million. AMD went public in September 1972. The company was a second source for Intel MOS/LSI circuits by 1973, with products such as Am14/1506 and Am14/1507, dual 100-bit dynamic shift registers. By 1975, AMD was producing 212 products – of which 49 were proprietary, including the Am9102 (a static N-channel 1024-bit RAM) and three low-power Schottky MSI circuits: Am25LS07, Am25LS08, and Am25LS09. Intel had created the first microprocessor, its 4-bit 4004, in 1971. By 1975, AMD entered the microprocessor market with the Am9080, a reverse-engineered clone of the Intel 8080, and the Am2900 bit-slice microprocessor family. When Intel began installing microcode in its microprocessors in 1976, it entered into a cross-licensing agreement with AMD, which was granted a copyright license to the microcode in its microprocessors and peripherals, effective October 1976. In 1977, AMD entered into a joint venture with Siemens, a German engineering conglomerate wishing to enhance its technology expertise and enter the American market. Siemens purchased 20% of AMD's stock, giving the company an infusion of cash to increase its product lines. The two companies also jointly established Advanced Micro Computers (AMC), located in Silicon Valley and in Germany, allowing AMD to enter the microcomputer development and manufacturing field, in particular based on AMD's second-source Zilog Z8000 microprocessors. When the two companies' vision for Advanced Micro Computers diverged, AMD bought out Siemens' stake in the American division in 1979. AMD closed Advanced Micro Computers in late 1981 after switching focus to manufacturing second-source Intel x86 microprocessors. Total sales in fiscal year 1978 topped $100 million, and in 1979, AMD debuted on the New York Stock Exchange. In 1979, production also began on AMD's new semiconductor fabrication plant in Austin, Texas; the company already had overseas assembly facilities in Penang and Manila, and began construction on a fabrication plant in San Antonio in 1981. In 1980, AMD began supplying semiconductor products for telecommunications, an industry undergoing rapid expansion and innovation. Technology exchange agreement with Intel Intel had introduced the first x86 microprocessors in 1978. In 1981, IBM created its PC, and wanted Intel's x86 processors, but only under the condition that Intel also provide a second-source manufacturer for its patented x86 microprocessors. Intel and AMD entered into a 10-year technology exchange agreement, first signed in October 1981 and formally executed in February 1982. The terms of the agreement were that each company could acquire the right to become a second-source manufacturer of semiconductor products developed by the other; that is, each party could "earn" the right to manufacture and sell a product developed by the other, if agreed to, by exchanging the manufacturing rights to a product of equivalent technical complexity. The technical information and licenses needed to make and sell a part would be exchanged for a royalty to the developing company. The 1982 agreement also extended the 1976 AMD–Intel cross-licensing agreement through 1995. The agreement included the right to invoke arbitration of disagreements, and after five years the right of either party to end the agreement with one year's notice. The main result of the 1982 agreement was that AMD became a second-source manufacturer of Intel's x86 microprocessors and related chips, and Intel provided AMD with database tapes for its 8086, 80186, and 80286 chips. However, in the event of a bankruptcy or takeover of AMD, the cross-licensing agreement would be effectively canceled. Beginning in 1982, AMD began volume-producing second-source Intel-licensed 8086, 8088, 80186, and 80188 processors, and by 1984, its own Am286 clone of Intel's 80286 processor, for the rapidly growing market of IBM PCs and IBM clones. It also continued its successful concentration on proprietary bipolar chips. The company continued to spend greatly on research and development, and created the world's first 512K EPROM in 1984. That year, AMD was listed in the book The 100 Best Companies to Work for in America, and later made the Fortune 500 list for the first time in 1985. By mid-1985, the microchip market experienced a severe downturn, mainly due to long-term aggressive trade practices (dumping) from Japan, but also due to a crowded and non-innovative chip market in the United States. AMD rode out the mid-1980s crisis by aggressively innovating and modernizing, devising the Liberty Chip program of designing and manufacturing one new chip or chipset per week for 52 weeks in fiscal year 1986, and by heavily lobbying the U.S. government until sanctions and restrictions were put in place to prevent predatory Japanese pricing. During this time, AMD withdrew from the DRAM market, and made some headway into the CMOS market, which it had lagged in entering, having focused instead on bipolar chips. AMD had some success in the mid-1980s with the AMD7910 and AMD7911 "World Chip" FSK modem, one of the first multi-standard devices that covered both Bell and CCITT tones at up to 1200 baud half duplex or 300/300 full duplex. Beginning in 1986, AMD embraced the perceived shift toward RISC with their own AMD Am29000 (29k) processor; the 29k survived as an embedded processor. The company also increased its EPROM memory market share in the late 1980s. Throughout the 1980s, AMD was a second-source supplier of Intel x86 processors. In 1991, it introduced its own 386-compatible Am386, an AMD-designed chip. Creating its own chips, AMD began to compete directly with Intel. AMD had a large, successful flash memory business, even during the dotcom bust. In 2003, to divest some manufacturing and aid its overall cash flow, which was under duress from aggressive microprocessor competition from Intel, AMD spun off its flash memory business and manufacturing into Spansion, a joint venture with Fujitsu, which had been co-manufacturing flash memory with AMD since 1993. In December 2005, AMD divested itself of Spansion to focus on the microprocessor market, and Spansion went public in an IPO. Acquisition of ATI, spin-off of GlobalFoundries, and acquisition of Xilinx On July 24, 2006, AMD announced its acquisition of the Canadian 3D graphics card company ATI Technologies. AMD paid $4.3 billion and 58 million shares of its capital stock, for a total of approximately $5.4 billion. The transaction was completed on October 25, 2006. On August 30, 2010, AMD announced that it would retire the ATI brand name for its graphics chipsets in favor of the AMD brand name. In October 2008, AMD announced plans to spin off manufacturing operations in the form of GlobalFoundries Inc., a multibillion-dollar joint venture with Advanced Technology Investment Co., an investment company formed by the government of Abu Dhabi. The partnership and spin-off gave AMD an infusion of cash and allowed it to focus solely on chip design. To assure the Abu Dhabi investors of the new venture's success, AMD's CEO Hector Ruiz stepped down in July 2008, while remaining executive chairman, in preparation for becoming chairman of GlobalFoundries in March 2009. President and COO Dirk Meyer became AMD's CEO. Recessionary losses necessitated AMD cutting 1,100 jobs in 2009. In August 2011, AMD announced that former Lenovo executive Rory Read would be joining the company as CEO, replacing Meyer. In November 2011, AMD announced plans to lay off more than 10% (1,400) of its employees from across all divisions worldwide. In October 2012, it announced plans to lay off an additional 15% of its workforce to reduce costs in the face of declining sales revenue. AMD acquired the low-power server manufacturer SeaMicro in early 2012, with an eye to bringing out an Arm64 server chip. On October 8, 2014, AMD announced that Rory Read had stepped down after three years as president and chief executive officer. He was succeeded by Lisa Su, a key lieutenant who had been serving as chief operating officer since June. On October 16, 2014, AMD announced a new restructuring plan along with its Q3 results. Effective July 1, 2014, AMD reorganized into two business groups: Computing and Graphics, which primarily includes desktop and notebook processors and chipsets, discrete GPUs, and professional graphics; and Enterprise, Embedded, and Semi-Custom, which primarily includes server and embedded processors, dense servers, semi-custom SoC products (including solutions for gaming consoles), engineering services, and royalties. As part of this restructuring, AMD announced that 7% of its global workforce would be laid off by the end of 2014. After the GlobalFoundries spin-off and subsequent layoffs, AMD was left with significant vacant space at 1 AMD Place, its aging Sunnyvale headquarters office complex. In August 2016, AMD's 47 years in Sunnyvale came to a close when it signed a lease with the Irvine Company for a new 220,000 sq. ft. headquarters building in Santa Clara. AMD's new location at Santa Clara Square faces the headquarters of archrival Intel across the Bayshore Freeway and San Tomas Aquino Creek. Around the same time, AMD also agreed to sell 1 AMD Place to the Irvine Company. In April 2019, the Irvine Company secured approval from the Sunnyvale City Council of its plans to demolish 1 AMD Place and redevelop the entire 32-acre site into townhomes and apartments. In October 2020, AMD announced that it was acquiring Xilinx in an all-stock transaction. The acquisition was completed in February 2022, with an estimated acquisition price of $50 billion. In October 2023, AMD acquired an open-source AI software provider, Nod.ai, to bolster its AI software ecosystem. List of CEOs Products CPUs and APUs IBM PC and the x86 architecture In February 1982, AMD signed a contract with Intel, becoming a licensed second-source manufacturer of 8086 and 8088 processors. IBM wanted to use the Intel 8088 in its IBM PC, but its policy at the time was to require at least two sources for its chips. AMD later produced the Am286 under the same arrangement. In 1984, Intel internally decided to no longer cooperate with AMD in supplying product information to shore up its advantage in the marketplace, and delayed and eventually refused to convey the technical details of the Intel 80386. In 1987, AMD invoked arbitration over the issue, and Intel reacted by canceling the 1982 technological-exchange agreement altogether. After three years of testimony, AMD eventually won in arbitration in 1992, but Intel disputed this decision. Another long legal dispute followed, ending in 1994 when the Supreme Court of California sided with the arbitrator and AMD. In 1990, Intel countersued AMD, renegotiating AMD's right to use derivatives of Intel's microcode for its cloned processors. In the face of uncertainty during the legal dispute, AMD was forced to develop clean room designed versions of Intel code for its x386 and x486 processors, the former long after Intel had released its own x386 in 1985. In March 1991, AMD released the Am386, its clone of the Intel 386 processor. By October of the same year it had sold one million units. In 1993, AMD introduced the first of the Am486 family of processors, which proved popular with a large number of original equipment manufacturers, including Compaq, which signed an exclusive agreement using the Am486. The Am5x86, another Am486-based processor, was released in November 1995, and continued AMD's success as a fast, cost-effective processor. Finally, in an agreement effective 1996, AMD received the rights to the microcode in Intel's x386 and x486 processor families, but not the rights to the microcode in the following generations of processors. K5, K6, Athlon, Duron, and Sempron AMD's first in-house x86 processor was the K5, launched in 1996. The "K" in its name was a reference to Kryptonite, the only substance known to harm comic book character Superman. This itself was a reference to Intel's hegemony over the market, i.e., an anthropomorphization of them as Superman. The number "5" was a reference to the fifth generation of x86 processors; rival Intel had previously introduced its line of fifth-generation x86 processors as Pentium because the U.S. Trademark and Patent Office had ruled that mere numbers could not be trademarked. In 1996, AMD purchased NexGen, specifically for the rights to their Nx series of x86-compatible processors. AMD gave the NexGen design team their own building, left them alone, and gave them time and money to rework the Nx686. The result was the K6 processor, introduced in 1997. Although it was based on Socket 7, variants such as K6-III/450 were faster than Intel's Pentium II (sixth-generation processor). The K7 was AMD's seventh-generation x86 processor, making its debut under the brand name Athlon on June 23, 1999. Unlike previous AMD processors, it could not be used on the same motherboards as Intel's, due to licensing issues surrounding Intel's Slot 1 connector, and instead used a Slot A connector, referenced to the Alpha processor bus. The Duron was a lower-cost and limited version of the Athlon (64KB instead of 256KB L2 cache) in a 462-pin socketed PGA (socket A) or soldered directly onto the motherboard. Sempron was released as a lower-cost Athlon XP, replacing Duron in the socket A PGA era. It has since been migrated upward to all new sockets, up to AM3. On October 9, 2001, the Athlon XP was released. On February 10, 2003, the Athlon XP with 512KB L2 Cache was released. Athlon 64, Opteron and Phenom The K8 was a major revision of the K7 architecture, with the most notable features being the addition of a 64-bit extension to the x86 instruction set (called x86-64, AMD64, or x64), the incorporation of an on-chip memory controller, and the implementation of an extremely high-performance point-to-point interconnect called HyperTransport, as part of the Direct Connect Architecture. The technology was initially launched as the Opteron server-oriented processor on April 22, 2003. Shortly thereafter, it was incorporated into a product for desktop PCs, branded Athlon 64. On April 21, 2005, AMD released the first dual-core Opteron, an x86-based server CPU. A month later, it released the Athlon 64 X2, the first desktop-based dual-core processor family. In May 2007, AMD abandoned the string "64" in its dual-core desktop product branding, becoming Athlon X2, downplaying the significance of 64-bit computing in its processors. Further updates involved improvements to the microarchitecture, and a shift of the target market from mainstream desktop systems to value dual-core desktop systems. In 2008, AMD started to release dual-core Sempron processors exclusively in China, branded as the Sempron 2000 series, with lower HyperTransport speed and smaller L2 cache. AMD completed its dual-core product portfolio for each market segment. In September 2007, AMD released the first server Opteron K10 processors, followed in November by the Phenom processor for desktop. K10 processors came in dual-core, triple-core, and quad-core versions, with all cores on a single die. AMD released a new platform codenamed "Spider", which used the new Phenom processor, as well as an R770 GPU and a 790 GX/FX chipset from the AMD 700 chipset series. However, AMD built the Spider at 65nm, which was uncompetitive with Intel's smaller and more power-efficient 45nm. In January 2009, AMD released a new processor line dubbed Phenom II, a refresh of the original Phenom built using the 45 nm process. AMD's new platform, codenamed "Dragon", used the new Phenom II processor, and an ATI R770 GPU from the R700 GPU family, as well as a 790 GX/FX chipset from the AMD 700 chipset series. The Phenom II came in dual-core, triple-core and quad-core variants, all using the same die, with cores disabled for the triple-core and dual-core versions. The Phenom II resolved issues that the original Phenom had, including a low clock speed, a small L3 cache, and a Cool'n'Quiet bug that decreased performance. The Phenom II cost less but was not performance-competitive with Intel's mid-to-high-range Core 2 Quads. The Phenom II also enhanced its predecessor's memory controller, allowing it to use DDR3 in a new native socket AM3, while maintaining backward compatibility with AM2+, the socket used for the Phenom, and allowing the use of the DDR2 memory that was used with the platform. In April 2010, AMD released a new Phenom II Hexa-core (6-core) processor codenamed "Thuban". This was a totally new die based on the hexa-core "Istanbul" Opteron processor. It included AMD's "turbo core" technology, which allows the processor to automatically switch from 6 cores to 3 faster cores when more pure speed is needed. The Magny Cours and Lisbon server parts were released in 2010. The Magny Cours part came in 8 to 12 cores and the Lisbon part in 4 and 6 core parts. Magny Cours is focused on performance while the Lisbon part is focused on high performance per watt. Magny Cours is an MCM (multi-chip module) with two hexa-core "Istanbul" Opteron parts. This will use a new socket G34 for dual and quad-socket processors and thus will be marketed as Opteron 61xx series processors. Lisbon uses socket C32 certified for dual-socket use or single socket use only and thus will be marketed as Opteron 41xx processors. Both will be built on a 45 nm SOI process. Fusion becomes the AMD APU Following AMD's 2006 acquisition of Canadian graphics company ATI Technologies, an initiative codenamed Fusion was announced to integrate a CPU and GPU together on some of AMD's microprocessors, including a built in PCI Express link to accommodate separate PCI Express peripherals, eliminating the northbridge chip from the motherboard. The initiative intended to move some of the processing originally done on the CPU (e.g. floating-point unit operations) to the GPU, which is better optimized for some calculations. The Fusion was later renamed the AMD APU (Accelerated Processing Unit). Llano was AMD's first APU built for laptops. Llano was the second APU released, targeted at the mainstream market. It incorporated a CPU and GPU on the same die, as well as northbridge functions, and used "Socket FM1" with DDR3 memory. The CPU part of the processor was based on the Phenom II "Deneb" processor. AMD suffered an unexpected decrease in revenue based on production problems for the Llano. More AMD APUs for laptops running Windows 7 and Windows 8 OS are being used commonly. These include AMD's price-point APUs, the E1 and E2, and their mainstream competitors with Intel's Core i-series: The Vision A- series, the A standing for accelerated. These range from the lower-performance A4 chipset to the A6, A8, and A10. These all incorporate next-generation Radeon graphics cards, with the A4 utilizing the base Radeon HD chip and the rest using a Radeon R4 graphics card, with the exception of the highest-model A10 (A10-7300) which uses an R6 graphics card. New microarchitectures High-power, high-performance Bulldozer cores Bulldozer was AMD's microarchitecture codename for server and desktop AMD FX processors, first released on October 12, 2011. This family 15h microarchitecture is the successor to the family 10h (K10) microarchitecture design. Bulldozer was a clean-sheet design, not a development of earlier processors. The core was specifically aimed at 10–125 W TDP computing products. AMD claimed dramatic performance-per-watt efficiency improvements in high-performance computing (HPC) applications with Bulldozer cores. While hopes were high that Bulldozer would bring AMD to be performance-competitive with Intel once more, most benchmarks were disappointing. In some cases the new Bulldozer products were slower than the K10 models they were built to replace. The Piledriver microarchitecture was the 2012 successor to Bulldozer, increasing clock speeds and performance relative to its predecessor. Piledriver would be released in AMD FX, APU, and Opteron product lines. Piledriver was subsequently followed by the Steamroller microarchitecture in 2013. Used exclusively in AMD's APUs, Steamroller focused on greater parallelism. In 2015, the Excavator microarchitecture replaced Piledriver. Expected to be the last microarchitecture of the Bulldozer series, Excavator focused on improved power efficiency. Low-power Cat cores The Bobcat microarchitecture was revealed during a speech from AMD executive vice-president Henri Richard in Computex 2007 and was put into production during the first quarter of 2011. Based on the difficulty competing in the x86 market with a single core optimized for the 10–100 W range, AMD had developed a simpler core with a target range of 1–10 watts. In addition, it was believed that the core could migrate into the hand-held space if the power consumption can be reduced to less than 1 W. Jaguar is a microarchitecture codename for Bobcat's successor, released in 2013, that is used in various APUs from AMD aimed at the low-power/low-cost market. Jaguar and its derivates would go on to be used in the custom APUs of the PlayStation 4, Xbox One, PlayStation 4 Pro, Xbox One S, and Xbox One X. Jaguar would be later followed by the Puma microarchitecture in 2014. ARM architecture-based designs In 2012, AMD announced it was working on ARM products, both as a semi-custom product and server product. The initial server product was announced as the Opteron A1100 in 2014, an 8-core Cortex-A57 based ARMv8-A SoC, and was expected to be followed by an APU incorporating a Graphics Core Next GPU. However, the Opteron A1100 was not released until 2016, with the delay attributed to adding software support. The A1100 was also criticized for not having support from major vendors upon its release. In 2014, AMD also announced the K12 custom core for release in 2016. While being ARMv8-A instruction set architecture compliant, the K12 was expected to be entirely custom-designed, targeting the server, embedded, and semi-custom markets. While ARM architecture development continued, products based on K12 were subsequently delayed with no release planned. Development of AMD's x86-based Zen microarchitecture was preferred. Zen-based CPUs and APUs Zen is a new architecture for x86-64 based Ryzen series of CPUs and APUs, introduced in 2017 by AMD and built from the ground up by a team led by Jim Keller, beginning with his arrival in 2012, and taping out before his departure in September 2015. One of AMD's primary goals with Zen was an IPC increase of at least 40%, however in February 2017 AMD announced that they had actually achieved a 52% increase. Processors made on the Zen architecture are built on the 14 nm FinFET node and have a renewed focus on single-core performance and HSA compatibility. Previous processors from AMD were either built in the 32 nm process ("Bulldozer" and "Piledriver" CPUs) or the 28 nm process ("Steamroller" and "Excavator" APUs). Because of this, Zen is much more energy efficient. The Zen architecture is the first to encompass CPUs and APUs from AMD built for a single socket (Socket AM4). Also new for this architecture is the implementation of simultaneous multithreading (SMT) technology, something Intel has had for years on some of their processors with their proprietary hyper-threading implementation of SMT. This is a departure from the "Clustered MultiThreading" design introduced with the Bulldozer architecture. Zen also has support for DDR4 memory. AMD released the Zen-based high-end Ryzen 7 "Summit Ridge" series CPUs on March 2, 2017, mid-range Ryzen 5 series CPUs on April 11, 2017, and entry level Ryzen 3 series CPUs on July 27, 2017. AMD later released the Epyc line of Zen derived server processors for 1P and 2P systems. In October 2017, AMD released Zen-based APUs as Ryzen Mobile, incorporating Vega graphics cores. In January 2018 AMD has announced their new lineup plans, with Ryzen 2. AMD launched CPUs with the 12nm Zen+ microarchitecture in April 2018, following up with the 7nm Zen 2 microarchitecture in June 2019, including an update to the Epyc line with new processors using the Zen 2 microarchitecture in August 2019, and Zen 3 slated for release in Q3 2020. As of 2019, AMD's Ryzen processors were reported to outsell Intel's consumer desktop processors. At CES 2020 AMD announced their Ryzen Mobile 4000, as the first 7 nm x86 mobile processor, the first 7 nm 8-core (also 16-thread) high-performance mobile processor, and the first 8-core (also 16-thread) processor for ultrathin laptops. This generation is still based on the Zen 2 architecture. In October 2020, AMD announced new processors based on the Zen 3 architecture. On PassMark's Single thread performance test the Ryzen 5 5600x bested all other CPUs besides the Ryzen 9 5950X. In August 2022, AMD announced their initial lineup of CPUs based on the new Zen 4 architecture. The Steam Deck, PlayStation 5, Xbox Series X and Series S all use chips based on the Zen 2 microarchitecture, with proprietary tweaks and different configurations in each system's implementation than AMD sells in its own commercially available APUs. Graphics products and GPUs ATI prior to AMD acquisition Radeon within AMD In 2008, the ATI division of AMD released the TeraScale microarchitecture implementing a unified shader model. This design replaced the previous fixed-function hardware of previous graphics cards with multipurpose, programmable shaders. Initially released as part of the GPU for the Xbox 360, this technology would go on to be used in Radeon branded HD 2000 parts. Three generations of TeraScale would be designed and used in parts from 2008 to 2014. Combined GPU and CPU divisions In a 2009 restructuring, AMD merged the CPU and GPU divisions to support the company's APUs, which fused both graphics and general purpose processing. In 2011, AMD released the successor to TeraScale, Graphics Core Next (GCN). This new microarchitecture emphasized GPGPU compute capability in addition to graphics processing, with a particular aim of supporting heterogeneous computing on AMD's APUs. GCN's reduced instruction set ISA allowed for significantly increased compute capability over TeraScale's very long instruction word ISA. Since GCN's introduction with the HD 7970, five generations of the GCN architecture have been produced from 2008 through at least 2017. Radeon Technologies Group In September 2015, AMD separated the graphics technology division of the company into an independent internal unit called the Radeon Technologies Group (RTG) headed by Raja Koduri. This gave the graphics division of AMD autonomy in product design and marketing. The RTG then went on to create and release the Polaris and Vega microarchitectures released in 2016 and 2017, respectively. In particular the Vega, or fifth generation GCN, microarchitecture includes a number of major revisions to improve performance and compute capabilities. In November 2017, Raja Koduri left RTG and CEO and President Lisa Su took his position. In January 2018, it was reported that two industry veterans joined RTG, namely Mike Rayfield as senior vice president and general manager of RTG, and David Wang as senior vice president of engineering for RTG. In January 2020, AMD announced that its second generation RDNA graphics architecture was in development, with the aim of competing with the Nvidia RTX graphics products for performance leadership. In October 2020, AMD announced their new RX 6000 series series GPUs, their first high-end product based on RDNA2 and capable of handling ray-tracing natively, aiming to challenge Nvidia's RTX 3000 GPUs. Semi-custom and game console products In 2012, AMD's then CEO Rory Read began a program to offer semi-custom designs. Rather than AMD simply designing and offering a single product, potential customers could work with AMD to design a custom chip based on AMD's intellectual property. Customers pay a non-recurring engineering fee for design and development, and a purchase price for the resulting semi-custom products. In particular, AMD noted their unique position of offering both x86 and graphics intellectual property. These semi-custom designs would have design wins as the APUs in the PlayStation 4 and Xbox One and the subsequent PlayStation 4 Pro, Xbox One S, Xbox One X, Xbox Series X/S, and PlayStation 5. Financially, these semi-custom products would represent a majority of the company's revenue in 2016. In November 2017, AMD and Intel announced that Intel would market a product combining in a single package an Intel Core CPU, a semi-custom AMD Radeon GPU, and HBM2 memory. Other hardware AMD motherboard chipsets Before the launch of Athlon 64 processors in 2003, AMD designed chipsets for their processors spanning the K6 and K7 processor generations. The chipsets include the AMD-640, AMD-751, and the AMD-761 chipsets. The situation changed in 2003 with the release of Athlon 64 processors, and AMD chose not to further design its own chipsets for its desktop processors while opening the desktop platform to allow other firms to design chipsets. This was the "Open Platform Management Architecture" with ATI, VIA and SiS developing their own chipset for Athlon 64 processors and later Athlon 64 X2 and Athlon 64 FX processors, including the Quad FX platform chipset from Nvidia. The initiative went further with the release of Opteron server processors as AMD stopped the design of server chipsets in 2004 after releasing the AMD-8111 chipset, and again opened the server platform for firms to develop chipsets for Opteron processors. As of today, Nvidia and Broadcom are the sole designing firms of server chipsets for Opteron processors. As the company completed the acquisition of ATI Technologies in 2006, the firm gained the ATI design team for chipsets which previously designed the Radeon Xpress 200 and the Radeon Xpress 3200 chipsets. AMD then renamed the chipsets for AMD processors under AMD branding (for instance, the CrossFire Xpress 3200 chipset was renamed as AMD 580X CrossFire chipset). In February 2007, AMD announced the first AMD-branded chipset since 2004 with the release of the AMD 690G chipset (previously under the development codename RS690), targeted at mainstream IGP computing. It was the industry's first to implement a HDMI 1.2 port on motherboards, shipping for more than a million units. While ATI had aimed at releasing an Intel IGP chipset, the plan was scrapped and the inventories of Radeon Xpress 1250 (codenamed RS600, sold under ATI brand) was sold to two OEMs, Abit and ASRock. Although AMD stated the firm would still produce Intel chipsets, Intel had not granted the license of FSB to ATI. On November 15, 2007, AMD announced a new chipset series portfolio, the AMD 7-Series chipsets, covering from the enthusiast multi-graphics segment to the value IGP segment, to replace the AMD 480/570/580 chipsets and AMD 690 series chipsets, marking AMD's first enthusiast multi-graphics chipset. Discrete graphics chipsets were launched on November 15, 2007, as part of the codenamed Spider desktop platform, and IGP chipsets were launched at a later time in spring 2008 as part of the codenamed Cartwheel platform. AMD returned to the server chipsets market with the AMD 800S series server chipsets. It includes support for up to six SATA 6.0 Gbit/s ports, the C6 power state, which is featured in Fusion processors and AHCI 1.2 with SATA FIS–based switching support. This is a chipset family supporting Phenom processors and Quad FX enthusiast platform (890FX), IGP (890GX). With the advent of AMD's APUs in 2011, traditional northbridge features such as the connection to graphics and the PCI Express controller were incorporated into the APU die. Accordingly, APUs were connected to a single chip chipset, renamed the Fusion Controller Hub (FCH), which primarily provided southbridge functionality. AMD released new chipsets in 2017 to support the release of their new Ryzen products. As the Zen microarchitecture already includes much of the northbridge connectivity, the AM4-based chipsets primarily varied in the number of additional PCI Express lanes, USB connections, and SATA connections available. These AM4 chipsets were designed in conjunction with ASMedia. Embedded products Embedded CPUs In the early 1990s, AMD began marketing a series of embedded System-on-a-chip (SoC) called AMD Élan, starting with the SC300 and SC310. Both combines a 32-Bit, Am386SX, low-voltage 25 MHz or 33 MHz CPU with memory controller, PC/AT peripheral controllers, real-time clock, PLL clock generators and ISA bus interface. The SC300 integrates in addition two PC card slots and a CGA-compatible LCD controller. They were followed in 1996 by the SC4xx types. Now supporting VESA Local Bus and using the Am486 with up to 100 MHz clock speed. A SC450 with 33 MHze.g. was used in the Nokia 9000 Communicator. In 1999 the SC520 was announced. Using an Am586 with 100 MHz or 133 MHz and supporting SDRAM and PCI it was the latest member of the series. In February 2002, AMD acquired Alchemy Semiconductor for its Alchemy line of MIPS processors for the hand-held and portable media player markets. On June 13, 2006, AMD officially announced that the line was to be transferred to Raza Microelectronics, Inc., a designer of MIPS processors for embedded applications. In August 2003, AMD also purchased the Geode business which was originally the Cyrix MediaGX from National Semiconductor to augment its existing line of embedded x86 processor products. During the second quarter of 2004, it launched new low-power Geode NX processors based on the K7 Thoroughbred architecture with speeds of fanless processors and , and processor with fan, of TDP 25 W. This technology is used in a variety of embedded systems (Casino slot machines and customer kiosks for instance), several UMPC designs in Asia markets, as well as the OLPC XO-1 computer, an inexpensive laptop computer intended to be distributed to children in developing countries around the world. The Geode LX processor was announced in 2005 and is said will continue to be available through 2015. AMD has also introduced 64-bit processors into its embedded product line starting with the AMD Opteron processor. Leveraging the high throughput enabled through HyperTransport and the Direct Connect Architecture these server-class processors have been targeted at high-end telecom and storage applications. In 2007, AMD added the AMD Athlon, AMD Turion, and Mobile AMD Sempron processors to its embedded product line. Leveraging the same 64-bit instruction set and Direct Connect Architecture as the AMD Opteron but at lower power levels, these processors were well suited to a variety of traditional embedded applications. Throughout 2007 and into 2008, AMD has continued to add both single-core Mobile AMD Sempron and AMD Athlon processors and dual-core AMD Athlon X2 and AMD Turion processors to its embedded product line and now offers embedded 64-bit solutions starting with 8 W TDP Mobile AMD Sempron and AMD Athlon processors for fan-less designs up to multi-processor systems leveraging multi-core AMD Opteron processors all supporting longer than standard availability. The ATI acquisition in 2006 included the Imageon and Xilleon product lines. In late 2008, the entire handheld division was sold off to Qualcomm, who have since produced the Adreno series. Also in 2008, the Xilleon division was sold to Broadcom. In April 2007, AMD announced the release of the M690T integrated graphics chipset for embedded designs. This enabled AMD to offer complete processor and chipset solutions targeted at embedded applications requiring high-performance 3D and video such as emerging digital signage, kiosk, and Point of Sale applications. The M690T was followed by the M690E specifically for embedded applications which removed the TV output, which required Macrovision licensing for OEMs, and enabled native support for dual TMDS outputs, enabling dual independent DVI interfaces. In January 2011, AMD announced the AMD Embedded G-Series Accelerated Processing Unit. This was the first APU for embedded applications. These were followed by updates in 2013 and 2016. In May 2012, AMD Announced the AMD Embedded R-Series Accelerated Processing Unit. This family of products incorporates the Bulldozer CPU architecture, and Discrete-class Radeon HD 7000G Series graphics. This was followed by a system on a chip (SoC) version in 2015 which offered a faster CPU and faster graphics, with support for DDR4 SDRAM memory. Embedded graphics AMD builds graphic processors for use in embedded systems. They can be found in anything from casinos to healthcare, with a large portion of products being used in industrial machines. These products include a complete graphics processing device in a compact multi-chip module including RAM and the GPU. ATI began offering embedded GPUs with the E2400 in 2008. Since that time AMD has released regular updates to their embedded GPU lineup in 2009, 2011, 2015, and 2016; reflecting improvements in their GPU technology. Current product lines CPU and APU products AMD's portfolio of CPUs and APUs Athlon – brand of entry level CPUs (Excavator) and APUs (Ryzen) A-series – Excavator-class consumer desktop and laptop APUs G-series – Excavator- and Jaguar-class low-power embedded APUs Ryzen – brand of consumer CPUs and APUs Ryzen Threadripper – brand of prosumer/professional CPUs R-series – Excavator class high-performance embedded APUs Epyc – brand of server CPUs Opteron – brand of microserver APUs Graphics products AMD's portfolio of dedicated graphics processors Radeon – brand for consumer line of graphics cards; the brand name originated with ATI. Mobility Radeon offers power-optimized versions of Radeon graphics chips for use in laptops. Radeon Pro – Workstation graphics card brand. Successor to the FirePro brand. Radeon Instinct – brand of server and workstation targeted machine learning and GPGPU products Radeon-branded products RAM In 2011, AMD began selling Radeon branded DDR3 SDRAM to support the higher bandwidth needs of AMD's APUs. While the RAM is sold by AMD, it was manufactured by Patriot Memory and VisionTek. This was later followed by higher speeds of gaming oriented DDR3 memory in 2013. Radeon branded DDR4 SDRAM memory was released in 2015, despite no AMD CPUs or APUs supporting DDR4 at the time. AMD noted in 2017 that these products are "mostly distributed in Eastern Europe" and that it continues to be active in the business. Solid-state drives AMD announced in 2014 it would sell Radeon branded solid-state drives manufactured by OCZ with capacities up to 480 GB and using the SATA interface. Technologies CPU hardware technologies found in AMD CPU/APU and other products include: HyperTransport – a high-bandwidth, low-latency system bus used in AMD's CPU and APU products Infinity Fabric – a derivative of HyperTransport used as the communication bus in AMD's Zen microarchitecture Graphics hardware technologies found in AMD GPU products include: AMD Eyefinity – facilitates multi-monitor setup of up to 6 monitors per graphics card AMD FreeSync – display synchronization based on the VESA Adaptive Sync standard AMD TrueAudio – acceleration of audio calculations AMD XConnect – allows the use of External GPU enclosures through Thunderbolt 3 AMD CrossFire – multi-GPU technology allowing the simultaneous use of multiple GPUs Unified Video Decoder (UVD) – acceleration of video decompression (decoding) Video Coding Engine (VCE) – acceleration of video compression (encoding) Software AMD has made considerable efforts towards opening its software tools above the firmware level in the past decade. For the following mentions, software not expressely stated free can be assumed to be proprietary. Distribution AMD Radeon Software is the default channel for official software distribution from AMD. It includes both free and proprietary software components, and supports both Microsoft Windows and Linux. Software by type CPU AOCC is AMD's optimizing proprietary C/C++ compiler based on LLVM and available for Linux. AMDuProf is AMD's CPU performance and Power profiling tool suite, available for Linux and Windows. AMD has also taken an active part in developing coreboot, an open-source project aimed at replacing the proprietary BIOS firmware. This cooperation ceased in 2013, but AMD has indicated recently that it is considering releasing source code so that Ryzen can be compatible with coreboot in the future. GPU Most notable public AMD software is on the GPU side. AMD has opened both its graphic and compute stacks: GPUOpen is AMD's graphics stack, which includes for example FidelityFX Super Resolution. ROCm (Radeon Open Compute platform) is AMD's compute stack for machine learning and high-performance computing, based on the LLVM compiler technologies. Under the ROCm project, AMDgpu is AMD's open source device driver supporting the GCN and following architectures, available for Linux. This latter driver component is used both by the graphics and compute stacks. Misc AMD conducts open research on heterogeneous computing. Other AMD software includes the AMD Core Math Library, and open-source software including the AMD Performance Library. AMD contributes to open source projects, including working with Sun Microsystems to enhance OpenSolaris and Sun xVM on the AMD platform. AMD also maintains its own Open64 compiler distribution and contributes its changes back to the community. In 2008, AMD released the low-level programming specifications for its GPUs, and works with the X.Org Foundation to develop drivers for AMD graphics cards. Extensions for software parallelism (xSP), aimed at speeding up programs to enable multi-threaded and multi-core processing, announced in Technology Analyst Day 2007. One of the initiatives being discussed since August 2007 is the Light Weight Profiling (LWP), providing internal hardware monitor with runtimes, to observe information about executing process and help the re-design of software to be optimized with multi-core and even multi-threaded programs. Another one is the extension of Streaming SIMD Extension (SSE) instruction set, the SSE5. Codenamed SIMFIRE – interoperability testing tool for the Desktop and mobile Architecture for System Hardware (DASH) open architecture. Production and fabrication Previously, AMD produced its chips at company-owned semiconductor foundries. AMD pursued a strategy of collaboration with other semiconductor manufacturers IBM and Motorola to co-develop production technologies. AMD's founder Jerry Sanders termed this the "Virtual Gorilla" strategy to compete with Intel's significantly greater investments in fabrication. In 2008, AMD spun off its chip foundries into an independent company named GlobalFoundries. This breakup of the company was attributed to the increasing costs of each process node. The Emirate of Abu Dhabi purchased the newly created company through its subsidiary Advanced Technology Investment Company (ATIC), purchasing the final stake from AMD in 2009. With the spin-off of its foundries, AMD became a fabless semiconductor manufacturer, designing products to be produced at for-hire foundries. Part of the GlobalFoundries spin-off included an agreement with AMD to produce some number of products at GlobalFoundries. Both prior to the spin-off and after AMD has pursued production with other foundries including TSMC and Samsung. It has been argued that this would reduce risk for AMD by decreasing dependence on any one foundry which has caused issues in the past. In 2018, AMD started shifting the production of their CPUs and GPUs to TSMC, following GlobalFoundries' announcement that they were halting development of their 7 nm process. AMD revised their wafer purchase requirement with GlobalFoundries in 2019, allowing AMD to freely choose foundries for 7 nm nodes and below, while maintaining purchase agreements for 12 nm and above through 2021. Corporate affairs Partnerships AMD uses strategic industry partnerships to further its business interests as well as to rival Intel's dominance and resources: A partnership between AMD and Alpha Processor Inc. developed HyperTransport, a point-to-point interconnect standard which was turned over to an industry standards body for finalization. It is now used in modern motherboards that are compatible with AMD processors. AMD also formed a strategic partnership with IBM, under which AMD gained silicon on insulator (SOI) manufacturing technology, and detailed advice on 90 nm implementation. AMD announced that the partnership would extend to 2011 for 32 nm and 22 nm fabrication-related technologies. To facilitate processor distribution and sales, AMD is loosely partnered with end-user companies, such as HP, Dell, Asus, Acer, and Microsoft. In 1993, AMD established a 50–50 partnership with Fujitsu called FASL, and merged into a new company called FASL LLC in 2003. The joint venture went public under the name Spansion and ticker symbol SPSN in December 2005, with AMD shares dropping 37%. AMD no longer directly participates in the Flash memory devices market now as AMD entered into a non-competition agreement on December 21, 2005, with Fujitsu and Spansion, pursuant to which it agreed not to directly or indirectly engage in a business that manufactures or supplies standalone semiconductor devices (including single-chip, multiple-chip or system devices) containing only Flash memory. On May 18, 2006, Dell announced that it would roll out new servers based on AMD's Opteron chips by year's end, thus ending an exclusive relationship with Intel. In September 2006, Dell began offering AMD Athlon X2 chips in their desktop lineup. In June 2011, HP announced new business and consumer notebooks equipped with the latest versions of AMD APUsaccelerated processing units. AMD will power HP's Intel-based business notebooks as well. In the spring of 2013, AMD announced that it would be powering all three major next-generation consoles. The Xbox One and Sony PlayStation 4 are both powered by a custom-built AMD APU, and the Nintendo Wii U is powered by an AMD GPU. According to AMD, having their processors in all three of these consoles will greatly assist developers with cross-platform development to competing consoles and PCs as well as increased support for their products across the board. AMD has entered into an agreement with Hindustan Semiconductor Manufacturing Corporation (HSMC) for the production of AMD products in India. AMD is a founding member of the HSA Foundation which aims to ease the use of a Heterogeneous System Architecture. A Heterogeneous System Architecture is intended to use both central processing units and graphics processors to complete computational tasks. AMD announced in 2016 that it was creating a joint venture to produce x86 server chips for the Chinese market. On May 7, 2019, it was reported that the U.S. Department of Energy, Oak Ridge National Laboratory, and Cray Inc., are working in collaboration with AMD to develop the Frontier exascale supercomputer. Featuring the AMD Epyc CPUs and Radeon GPUs, the supercomputer is set to produce more than 1.5 exaflops (peak double-precision) in computing performance. It is expected to debut sometime in 2021. On March 5, 2020, it was announced that the U.S. Department of Energy, Lawrence Livermore National Laboratory, and HPE are working in collaboration with AMD to develop the El Capitan exascale supercomputer. Featuring the AMD Epyc CPUs and Radeon GPUs, the supercomputer is set to produce more than 2 exaflops (peak double-precision) in computing performance. It is expected to debut in 2023. In the summer of 2020, it was reported that AMD would be powering the next-generation console offerings from Microsoft and Sony. On November 8, 2021, AMD announced a partnership with Meta to make the chips used in the Metaverse. In January 2022, AMD partnered with Samsung to develop a mobile processor to be used in future products. The processor was named Exynos 2022 and works with the AMD RDNA 2 architecture. Litigation with Intel AMD has a long history of litigation with former (and current) partner and x86 creator Intel. In 1986, Intel broke an agreement it had with AMD to allow them to produce Intel's microchips for IBM; AMD filed for arbitration in 1987 and the arbitrator decided in AMD's favor in 1992. Intel disputed this, and the case ended up in the Supreme Court of California. In 1994, that court upheld the arbitrator's decision and awarded damages for breach of contract. In 1990, Intel brought a copyright infringement action alleging illegal use of its 287 microcode. The case ended in 1994 with a jury finding for AMD and its right to use Intel's microcode in its microprocessors through the 486 generation. In 1997, Intel filed suit against AMD and Cyrix Corp. for misuse of the term MMX. AMD and Intel settled, with AMD acknowledging MMX as a trademark owned by Intel, and with Intel granting AMD rights to market the AMD K6 MMX processor. In 2005, following an investigation, the Japan Federal Trade Commission found Intel guilty of a number of violations. On June 27, 2005, AMD won an antitrust suit against Intel in Japan, and on the same day, AMD filed a broad antitrust complaint against Intel in the U.S. Federal District Court in Delaware. The complaint alleges systematic use of secret rebates, special discounts, threats, and other means used by Intel to lock AMD processors out of the global market. Since the start of this action, the court has issued subpoenas to major computer manufacturers including Acer, Dell, Lenovo, HP and Toshiba. In November 2009, Intel agreed to pay AMD $1.25bn and renew a five-year patent cross-licensing agreement as part of a deal to settle all outstanding legal disputes between them. Guinness World Record achievement On August 31, 2011, in Austin, Texas, AMD achieved a Guinness World Record for the "Highest frequency of a computer processor": 8.429 GHz. The company ran an 8-core FX-8150 processor with only one active module (two cores), and cooled with liquid helium. The previous record was 8.308 GHz, with an Intel Celeron 352 (one core). On November 1, 2011, geek.com reported that Andre Yang, an overclocker from Taiwan, used an FX-8150 to set another record: 8.461 GHz. On November 19, 2012, Andre Yang used an FX-8350 to set another record: 8.794 GHz. Acquisitions, mergers and investments Corporate social responsibility In its 2012 report on progress relating to conflict minerals, the Enough Project rated AMD the fifth most progressive of 24 consumer electronics companies. Other initiatives 50x15, digital inclusion, with targeted 50% of world population to be connected through Internet via affordable computers by the year of 2015. The Green Grid, founded by AMD together with other founders, such as IBM, Sun and Microsoft, to seek lower power consumption for grids. See also Bill Gaede List of AMD processors List of AMD accelerated processing units List of AMD graphics processing units List of AMD chipsets List of ATI chipsets 3DNow! Cool'n'Quiet PowerNow! Notes References Rodengen, Jeffrey L. The Spirit of AMD: Advanced Micro Devices. Write Stuff, 1998. Ruiz, Hector. Slingshot: AMD's Fight to Free an Industry from the Ruthless Grip of Intel. Greenleaf Book Group, 2013. External links 1969 establishments in California 1970s initial public offerings American companies established in 1969 Fabless semiconductor companies Companies based in Santa Clara, California Companies formerly listed on the New York Stock Exchange Companies listed on the Nasdaq Companies in the Nasdaq-100 Computer companies of the United States Computer companies established in 1969 Electronics companies established in 1969 Graphics hardware companies HSA Foundation founding members Manufacturing companies based in the San Francisco Bay Area Motherboard companies Semiconductor companies of the United States Superfund sites in California Technology companies based in the San Francisco Bay Area Technology companies established in 1969
Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable as a function of the time lag between them. The analysis of autocorrelation is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal obscured by noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies. It is often used in signal processing for analyzing functions or series of values, such as time domain signals. Different fields of study define autocorrelation differently, and not all of these definitions are equivalent. In some fields, the term is used interchangeably with autocovariance. Unit root processes, trend-stationary processes, autoregressive processes, and moving average processes are specific forms of processes with autocorrelation. Auto-correlation of stochastic processes In statistics, the autocorrelation of a real or complex random process is the Pearson correlation between values of the process at different times, as a function of the two times or of the time lag. Let be a random process, and be any point in time ( may be an integer for a discrete-time process or a real number for a continuous-time process). Then is the value (or realization) produced by a given run of the process at time . Suppose that the process has mean and variance at time , for each . Then the definition of the auto-correlation function between times and is where is the expected value operator and the bar represents complex conjugation. Note that the expectation may not be well defined. Subtracting the mean before multiplication yields the auto-covariance function between times and : Note that this expression is not well defined for all time series or processes, because the mean may not exist, or the variance may be zero (for a constant process) or infinite (for processes with distribution lacking well-behaved moments, such as certain types of power law). Definition for wide-sense stationary stochastic process If is a wide-sense stationary process then the mean and the variance are time-independent, and further the autocovariance function depends only on the lag between and : the autocovariance depends only on the time-distance between the pair of values but not on their position in time. This further implies that the autocovariance and auto-correlation can be expressed as a function of the time-lag, and that this would be an even function of the lag . This gives the more familiar forms for the auto-correlation function and the auto-covariance function: In particular, note that Normalization It is common practice in some disciplines (e.g. statistics and time series analysis) to normalize the autocovariance function to get a time-dependent Pearson correlation coefficient. However, in other disciplines (e.g. engineering) the normalization is usually dropped and the terms "autocorrelation" and "autocovariance" are used interchangeably. The definition of the auto-correlation coefficient of a stochastic process is If the function is well defined, its value must lie in the range , with 1 indicating perfect correlation and −1 indicating perfect anti-correlation. For a wide-sense stationary (WSS) process, the definition is . The normalization is important both because the interpretation of the autocorrelation as a correlation provides a scale-free measure of the strength of statistical dependence, and because the normalization has an effect on the statistical properties of the estimated autocorrelations. Properties Symmetry property The fact that the auto-correlation function is an even function can be stated as respectively for a WSS process: Maximum at zero For a WSS process: Notice that is always real. Cauchy–Schwarz inequality The Cauchy–Schwarz inequality, inequality for stochastic processes: Autocorrelation of white noise The autocorrelation of a continuous-time white noise signal will have a strong peak (represented by a Dirac delta function) at and will be exactly for all other . Wiener–Khinchin theorem The Wiener–Khinchin theorem relates the autocorrelation function to the power spectral density via the Fourier transform: For real-valued functions, the symmetric autocorrelation function has a real symmetric transform, so the Wiener–Khinchin theorem can be re-expressed in terms of real cosines only: Auto-correlation of random vectors The (potentially time-dependent) auto-correlation matrix (also called second moment) of a (potentially time-dependent) random vector is an matrix containing as elements the autocorrelations of all pairs of elements of the random vector . The autocorrelation matrix is used in various digital signal processing algorithms. For a random vector containing random elements whose expected value and variance exist, the auto-correlation matrix is defined by where denotes the transposed matrix of dimensions . Written component-wise: If is a complex random vector, the autocorrelation matrix is instead defined by Here denotes Hermitian transpose. For example, if is a random vector, then is a matrix whose -th entry is . Properties of the autocorrelation matrix The autocorrelation matrix is a Hermitian matrix for complex random vectors and a symmetric matrix for real random vectors. The autocorrelation matrix is a positive semidefinite matrix, i.e. for a real random vector, and respectively in case of a complex random vector. All eigenvalues of the autocorrelation matrix are real and non-negative. The auto-covariance matrix is related to the autocorrelation matrix as follows:Respectively for complex random vectors: Auto-correlation of deterministic signals In signal processing, the above definition is often used without the normalization, that is, without subtracting the mean and dividing by the variance. When the autocorrelation function is normalized by mean and variance, it is sometimes referred to as the autocorrelation coefficient or autocovariance function. Auto-correlation of continuous-time signal Given a signal , the continuous autocorrelation is most often defined as the continuous cross-correlation integral of with itself, at lag . where represents the complex conjugate of . Note that the parameter in the integral is a dummy variable and is only necessary to calculate the integral. It has no specific meaning. Auto-correlation of discrete-time signal The discrete autocorrelation at lag for a discrete-time signal is The above definitions work for signals that are square integrable, or square summable, that is, of finite energy. Signals that "last forever" are treated instead as random processes, in which case different definitions are needed, based on expected values. For wide-sense-stationary random processes, the autocorrelations are defined as For processes that are not stationary, these will also be functions of , or . For processes that are also ergodic, the expectation can be replaced by the limit of a time average. The autocorrelation of an ergodic process is sometimes defined as or equated to These definitions have the advantage that they give sensible well-defined single-parameter results for periodic functions, even when those functions are not the output of stationary ergodic processes. Alternatively, signals that last forever can be treated by a short-time autocorrelation function analysis, using finite time integrals. (See short-time Fourier transform for a related process.) Definition for periodic signals If is a continuous periodic function of period , the integration from to is replaced by integration over any interval of length : which is equivalent to Properties In the following, we will describe properties of one-dimensional autocorrelations only, since most properties are easily transferred from the one-dimensional case to the multi-dimensional cases. These properties hold for wide-sense stationary processes. A fundamental property of the autocorrelation is symmetry, , which is easy to prove from the definition. In the continuous case, the autocorrelation is an even function when is a real function, and the autocorrelation is a Hermitian function when is a complex function. The continuous autocorrelation function reaches its peak at the origin, where it takes a real value, i.e. for any delay , . This is a consequence of the rearrangement inequality. The same result holds in the discrete case. The autocorrelation of a periodic function is, itself, periodic with the same period. The autocorrelation of the sum of two completely uncorrelated functions (the cross-correlation is zero for all ) is the sum of the autocorrelations of each function separately. Since autocorrelation is a specific type of cross-correlation, it maintains all the properties of cross-correlation. By using the symbol to represent convolution and is a function which manipulates the function and is defined as , the definition for may be written as: Multi-dimensional autocorrelation Multi-dimensional autocorrelation is defined similarly. For example, in three dimensions the autocorrelation of a square-summable discrete signal would be When mean values are subtracted from signals before computing an autocorrelation function, the resulting function is usually called an auto-covariance function. Efficient computation For data expressed as a discrete sequence, it is frequently necessary to compute the autocorrelation with high computational efficiency. A brute force method based on the signal processing definition can be used when the signal size is small. For example, to calculate the autocorrelation of the real signal sequence (i.e. , and for all other values of ) by hand, we first recognize that the definition just given is the same as the "usual" multiplication, but with right shifts, where each vertical addition gives the autocorrelation for particular lag values: Thus the required autocorrelation sequence is , where and the autocorrelation for other lag values being zero. In this calculation we do not perform the carry-over operation during addition as is usual in normal multiplication. Note that we can halve the number of operations required by exploiting the inherent symmetry of the autocorrelation. If the signal happens to be periodic, i.e. then we get a circular autocorrelation (similar to circular convolution) where the left and right tails of the previous autocorrelation sequence will overlap and give which has the same period as the signal sequence The procedure can be regarded as an application of the convolution property of Z-transform of a discrete signal. While the brute force algorithm is order , several efficient algorithms exist which can compute the autocorrelation in order . For example, the Wiener–Khinchin theorem allows computing the autocorrelation from the raw data with two fast Fourier transforms (FFT): where IFFT denotes the inverse fast Fourier transform. The asterisk denotes complex conjugate. Alternatively, a multiple correlation can be performed by using brute force calculation for low values, and then progressively binning the data with a logarithmic density to compute higher values, resulting in the same efficiency, but with lower memory requirements. Estimation For a discrete process with known mean and variance for which we observe observations , an estimate of the autocorrelation coefficient may be obtained as for any positive integer . When the true mean and variance are known, this estimate is unbiased. If the true mean and variance of the process are not known there are several possibilities: If and are replaced by the standard formulae for sample mean and sample variance, then this is a biased estimate. A periodogram-based estimate replaces in the above formula with . This estimate is always biased; however, it usually has a smaller mean squared error. Other possibilities derive from treating the two portions of data and separately and calculating separate sample means and/or sample variances for use in defining the estimate. The advantage of estimates of the last type is that the set of estimated autocorrelations, as a function of , then form a function which is a valid autocorrelation in the sense that it is possible to define a theoretical process having exactly that autocorrelation. Other estimates can suffer from the problem that, if they are used to calculate the variance of a linear combination of the 's, the variance calculated may turn out to be negative. Regression analysis In regression analysis using time series data, autocorrelation in a variable of interest is typically modeled either with an autoregressive model (AR), a moving average model (MA), their combination as an autoregressive-moving-average model (ARMA), or an extension of the latter called an autoregressive integrated moving average model (ARIMA). With multiple interrelated data series, vector autoregression (VAR) or its extensions are used. In ordinary least squares (OLS), the adequacy of a model specification can be checked in part by establishing whether there is autocorrelation of the regression residuals. Problematic autocorrelation of the errors, which themselves are unobserved, can generally be detected because it produces autocorrelation in the observable residuals. (Errors are also known as "error terms" in econometrics.) Autocorrelation of the errors violates the ordinary least squares assumption that the error terms are uncorrelated, meaning that the Gauss Markov theorem does not apply, and that OLS estimators are no longer the Best Linear Unbiased Estimators (BLUE). While it does not bias the OLS coefficient estimates, the standard errors tend to be underestimated (and the t-scores overestimated) when the autocorrelations of the errors at low lags are positive. The traditional test for the presence of first-order autocorrelation is the Durbin–Watson statistic or, if the explanatory variables include a lagged dependent variable, Durbin's h statistic. The Durbin-Watson can be linearly mapped however to the Pearson correlation between values and their lags. A more flexible test, covering autocorrelation of higher orders and applicable whether or not the regressors include lags of the dependent variable, is the Breusch–Godfrey test. This involves an auxiliary regression, wherein the residuals obtained from estimating the model of interest are regressed on (a) the original regressors and (b) k lags of the residuals, where 'k' is the order of the test. The simplest version of the test statistic from this auxiliary regression is TR2, where T is the sample size and R2 is the coefficient of determination. Under the null hypothesis of no autocorrelation, this statistic is asymptotically distributed as with k degrees of freedom. Responses to nonzero autocorrelation include generalized least squares and the Newey–West HAC estimator (Heteroskedasticity and Autocorrelation Consistent). In the estimation of a moving average model (MA), the autocorrelation function is used to determine the appropriate number of lagged error terms to be included. This is based on the fact that for an MA process of order q, we have , for , and , for . Applications Autocorrelation analysis is used heavily in fluorescence correlation spectroscopy to provide quantitative insight into molecular-level diffusion and chemical reactions. Another application of autocorrelation is the measurement of optical spectra and the measurement of very-short-duration light pulses produced by lasers, both using optical autocorrelators. Autocorrelation is used to analyze dynamic light scattering data, which notably enables determination of the particle size distributions of nanometer-sized particles or micelles suspended in a fluid. A laser shining into the mixture produces a speckle pattern that results from the motion of the particles. Autocorrelation of the signal can be analyzed in terms of the diffusion of the particles. From this, knowing the viscosity of the fluid, the sizes of the particles can be calculated. Utilized in the GPS system to correct for the propagation delay, or time shift, between the point of time at the transmission of the carrier signal at the satellites, and the point of time at the receiver on the ground. This is done by the receiver generating a replica signal of the 1,023-bit C/A (Coarse/Acquisition) code, and generating lines of code chips [-1,1] in packets of ten at a time, or 10,230 chips (1,023 × 10), shifting slightly as it goes along in order to accommodate for the doppler shift in the incoming satellite signal, until the receiver replica signal and the satellite signal codes match up. The small-angle X-ray scattering intensity of a nanostructured system is the Fourier transform of the spatial autocorrelation function of the electron density. In surface science and scanning probe microscopy, autocorrelation is used to establish a link between surface morphology and functional characteristics. In optics, normalized autocorrelations and cross-correlations give the degree of coherence of an electromagnetic field. In signal processing, autocorrelation can give information about repeating events like musical beats (for example, to determine tempo) or pulsar frequencies, though it cannot tell the position in time of the beat. It can also be used to estimate the pitch of a musical tone. In music recording, autocorrelation is used as a pitch detection algorithm prior to vocal processing, as a distortion effect or to eliminate undesired mistakes and inaccuracies. Autocorrelation in space rather than time, via the Patterson function, is used by X-ray diffractionists to help recover the "Fourier phase information" on atom positions not available through diffraction alone. In statistics, spatial autocorrelation between sample locations also helps one estimate mean value uncertainties when sampling a heterogeneous population. The SEQUEST algorithm for analyzing mass spectra makes use of autocorrelation in conjunction with cross-correlation to score the similarity of an observed spectrum to an idealized spectrum representing a peptide. In astrophysics, autocorrelation is used to study and characterize the spatial distribution of galaxies in the universe and in multi-wavelength observations of low mass X-ray binaries. In panel data, spatial autocorrelation refers to correlation of a variable with itself through space. In analysis of Markov chain Monte Carlo data, autocorrelation must be taken into account for correct error determination. In geosciences (specifically in geophysics) it can be used to compute an autocorrelation seismic attribute, out of a 3D seismic survey of the underground. In medical ultrasound imaging, autocorrelation is used to visualize blood flow. In intertemporal portfolio choice, the presence or absence of autocorrelation in an asset's rate of return can affect the optimal portion of the portfolio to hold in that asset. Autocorrelation has been used to accurately measure power system frequency in numerical relays. Serial dependence Serial dependence is closely linked to the notion of autocorrelation, but represents a distinct concept (see Correlation and dependence). In particular, it is possible to have serial dependence but no (linear) correlation. In some fields however, the two terms are used as synonyms. A time series of a random variable has serial dependence if the value at some time in the series is statistically dependent on the value at another time . A series is serially independent if there is no dependence between any pair. If a time series is stationary, then statistical dependence between the pair would imply that there is statistical dependence between all pairs of values at the same lag . See also Autocorrelation matrix Autocorrelation of a formal word Autocorrelation technique Autocorrelator Cochrane–Orcutt estimation (transformation for autocorrelated error terms) Correlation function Correlogram Cross-correlation CUSUM Fluorescence correlation spectroscopy Optical autocorrelation Partial autocorrelation function Phylogenetic autocorrelation (Galton's problem} Pitch detection algorithm Prais–Winsten transformation Scaled correlation Triple correlation Unbiased estimation of standard deviation References Further reading Mojtaba Soltanalian, and Petre Stoica. "Computational design of sequences with good correlation properties." IEEE Transactions on Signal Processing, 60.5 (2012): 2180–2193. Solomon W. Golomb, and Guang Gong. Signal design for good correlation: for wireless communication, cryptography, and radar. Cambridge University Press, 2005. Klapetek, Petr (2018). Quantitative Data Processing in Scanning Probe Microscopy: SPM Applications for Nanometrology (Second ed.). Elsevier. pp. 108–112 . Signal processing Time domain analysis
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