text:
Merle Haggard

Merle Ronald Haggard (April 6, 1937 – April 6, 2016) was an American country music singer, songwriter, guitarist, and fiddler.

Haggard was born in Oildale, California, toward the end of the Great Depression. His childhood was troubled after the death of his father, and he was incarcerated several times in his youth. After being released from San Quentin State Prison in 1960, he managed to turn his life around and launched a successful country music career. He gained popularity with his songs about the working class; these occasionally contained themes contrary to the anti–Vietnam War sentiment of some popular music of the time. Between the 1960s and the 1980s he had 38 number-one hits on the US country charts, several of which also made the Billboard all-genre singles chart. Haggard continued to release successful albums into the 2000s.

He received many honors and awards for his music, including a Kennedy Center Honor (2010); a Grammy Lifetime Achievement Award (2006); a BMI Icon Award (2006); and induction into the Nashville Songwriters Hall of Fame (1977); Country Music Hall of Fame (1994) and Oklahoma Music Hall of Fame (1997). He died on April 6, 2016—his 79th birthday—at his ranch in Shasta County, California, having recently suffered from double pneumonia.

Early life
Haggard's parents were Flossie Mae (née Harp; 1902–1984) and James Francis Haggard (1899–1946). The family moved to California from their home in Checotah, Oklahoma, during the Great Depression, after their barn burned in 1934.

They settled with their two elder children, James 'Lowell' (1922–1996) and Lillian, in an apartment in Bakersfield, while James started working for the Santa Fe Railroad. A woman who owned a boxcar placed in Oildale, a nearby town, asked Haggard's father about the possibility of converting it into a house. He remodeled the boxcar, and soon after moved in, also purchasing the lot, where Merle Ronald Haggard was born on April 6, 1937. The property was eventually expanded by building a bathroom, a second bedroom, a kitchen, and a breakfast nook in the adjacent lot.

In 1946 Haggard's father died of a brain hemorrhage. Nine year-old Haggard was deeply affected by the loss, and it remained a pivotal event to him for the rest of his life. To support the family, Haggard's mother took a job as a bookkeeper. Older brother Lowell gave his guitar to Merle when Merle was 12. Haggard learned to play it on his own, with the records he had at home, influenced by Bob Wills, Lefty Frizzell, and Hank Williams. While his mother was out working during the day Haggard started getting into trouble. She sent him to a juvenile detention center for a weekend to try to correct him, but his behavior did not improve. If anything, he became worse.

By the age of 13, Haggard was stealing and writing bad checks. In 1950 he was caught shoplifting and sent to a juvenile detention center. The following year he ran away to Texas with his friend Bob Teague. The two rode freight trains and hitchhiked throughout the state. When they returned later that year the two boys were accused of robbery and sent to jail. This time, they had not actually committed the crime, and were released when the real robbers were found. The experience did not change Haggard much. He was again sent to a juvenile detention center later that year, from which he and his friend escaped and headed to Modesto, California. There he worked a series of laborer jobs, including potato truck driver, short order cook, hay pitcher and oil well shooter. His debut performance was with Teague in a Modesto bar named "Fun Center", for which he was paid US$5 and given free beer.

In 1951 he returned to Bakersfield, where he was again arrested for truancy and petty larceny and sent to a juvenile detention center. After another escape, he was sent to the Preston School of Industry, a high-security installation. He was released 15 months later but was sent back after beating a local boy during a burglary attempt. After Haggard's release, he and Teague saw Lefty Frizzell in concert. The two sat backstage, where Haggard began to sing along. Hearing the young man from the stage, Frizzell refused to go on unless Haggard was allowed to sing first. Haggard did, and was well received by the audience. After this experience Haggard decided to pursue a career in music. At night he would sing and play in local bars, while working as a farmhand or in the oil fields during the day.

Married and plagued by financial issues, in 1957 he tried to rob a Bakersfield roadhouse, was caught and arrested. Convicted, he was sent to the Bakersfield Jail. After an escape attempt he was transferred to San Quentin Prison on February 21, 1958. There he was prisoner number A45200. While in prison, Haggard learned that his wife was expecting another man's child, which stressed him psychologically. He was fired from a series of prison jobs, and planned to escape along with another inmate nicknamed "Rabbit" (James Kendrick ) but was dissuaded by fellow inmates.

While at San Quentin, Haggard started a gambling and brewing racket with his cellmate. After he was caught drunk, he was sent for a week to solitary confinement where he encountered Caryl Chessman, an author and death-row inmate. Meanwhile, "Rabbit" had successfully escaped, only to shoot a police officer and be returned to San Quentin for execution. Chessman's predicament, along with the execution of "Rabbit", inspired Haggard to change his life. He soon earned a high school equivalency diploma and kept a steady job in the prison's textile plant. He also played for the prison's country music band. He also attended a Johnny Cash concert at the prison in 1958. Cash sang his song "Folsom Prison Blues" (1956) and "had a profound influence on the young inmate, who upon release set out on forging a career as a singer-songwriter". Haggard was released from San Quentin on parole in 1960.

In 1972, after Haggard had become an established country music star, then-California governor Ronald Reagan granted Haggard a full and unconditional pardon for his past crimes.

Early career
Upon his release from San Quentin in 1960, Haggard started digging ditches for his brother's electrical contracting company. Soon, he was performing again and later began recording with Tally Records. The Bakersfield sound was developing in the area as a reaction against the overproduced Nashville sound. Haggard's first record for Tally was "Singing My Heart Out" backed by "Skid Row"; it was not a success, and only 200 copies were pressed. In 1962, Haggard wound up performing at a Wynn Stewart show in Las Vegas and heard Wynn's "Sing a Sad Song". He asked for permission to record it, and the resulting single was a national hit in 1964. The following year, he had his first national top-10 record with "(My Friends Are Gonna Be) Strangers," written by Liz Anderson, mother of country singer Lynn Anderson, and his career was off and running. Haggard recalls having been talked into visiting Anderson—a woman he did not know—at her house to hear her sing some songs she had written. "If there was anything I didn't wanna do, it was sit around some danged woman's house and listen to her cute little songs. But I went anyway. She was a pleasant enough lady, pretty, with a nice smile, but I was all set to be bored to death, even more so when she got out a whole bunch of songs and went over to an old pump organ.... There they were. My God, one hit right after another. There must have been four or five number one songs there...."

In 1967, Haggard recorded "I'm a Lonesome Fugitive" with the Strangers, also written by Liz Anderson, with her husband Casey Anderson, which became his first number-one single. When the Andersons presented the song to Haggard, they were unaware of his prison stretch. Bonnie Owens, Haggard's backup singer and then-wife, is quoted by music journalist Daniel Cooper in the liner notes to the 1994 retrospective Down Every Road: "I guess I didn't realize how much the experience at San Quentin did to him, 'cause he never talked about it all that much ... I could tell he was in a dark mood ... and I said, 'Is everything okay?' And he said, 'I'm really scared.' And I said, 'Why?' And he said, 'Cause I'm afraid someday I'm gonna be out there ... and there's gonna be ... some prisoner ... in there the same time I was in, stand up—and they're gonna be about the third row down—and say, 'What do you think you're doing, 45200?'" Cooper notes that the news had little effect on Haggard's career: "It's unclear when or where Merle first acknowledged to the public that his prison songs were rooted in personal history, for to his credit, he doesn't seem to have made some big splash announcement. In a May 1967 profile in Music City News, his prison record is never mentioned, but in July 1968, in the very same publication, it's spoken of as if it were common knowledge."

The 1967 album Branded Man with the Strangers kicked off an artistically and commercially successful run for Haggard. In 2013, Haggard biographer David Cantwell stated, "The immediate successors to I'm a Lonesome Fugitive—Branded Man in 1967 and, in '68, Sing Me Back Home and The Legend of Bonnie and Clyde—were among the finest albums of their respective years." Haggard's new recordings showcased his band the Strangers, specifically Roy Nichols's Telecaster, Ralph Mooney's steel guitar, and the harmony vocals provided by Bonnie Owens.

At the time of Haggard's first top-10 hit "(My Friends Are Gonna Be) Strangers" in 1965, Owens, who had been married to Buck Owens, was known as a solo performer, a fixture on the Bakersfield club scene and someone who had appeared on television. She won the new Academy of Country Music's first ever award for Female Vocalist after her 1965 debut album, Don't Take Advantage of Me, hit the top five on the country albums chart. However, Bonnie Owens had no further hit singles, and although she recorded six solo albums on Capitol between 1965 and 1970, she became mainly known for her background harmonies on Haggard hits such as "Sing Me Back Home" and "Branded Man".

Producer Ken Nelson took a hands-off approach to produce Haggard. In the episode of American Masters dedicated to him, Haggard remembers: "The producer I had at that time, Ken Nelson, was an exception to the rule. He called me 'Mr. Haggard' and I was a little twenty-four, twenty-five year old punk from Oildale... He gave me complete responsibility. I think if he'd jumped in and said, 'Oh, you can't do that,' it would've destroyed me." In the documentary series Lost Highway, Nelson recalls, "When I first started recording Merle, I became so enamored with his singing that I would forget what else was going on, and I suddenly realized, 'Wait a minute, there's musicians here you've got to worry about!' But his songs—he was a great writer."

Towards the end of the decade, Haggard composed several number-one hits, including "Mama Tried," "The Legend of Bonnie and Clyde," "Hungry Eyes," and "Sing Me Back Home". Daniel Cooper calls "Sing Me Back Home" "a ballad that works on so many different levels of the soul it defies one's every attempt to analyze it". In a 1977 interview in Billboard with Bob Eubanks, Haggard reflected, "Even though the crime was brutal and the guy was an incorrigible criminal, it's a feeling you never forget when you see someone you know make that last walk. They bring him through the yard, and there's a guard in front and a guard behind—that's how you know a death prisoner. They brought Rabbit out ... taking him to see the Father, ... prior to his execution. That was a strong picture that was left in my mind." In 1969, Haggard's first tribute LP Same Train, Different Time: A Tribute to Jimmie Rodgers, was also released to acclaim.

In the 1969 Rolling Stone review for Haggard and the Strangers 1968 album Mama Tried, Andy Wickham wrote, "His songs romanticize the hardships and tragedies of America's transient proletarian and his success is resultant of his inherent ability to relate to his audience a commonplace experience with precisely the right emotional pitch.... Merle Haggard looks the part and sounds the part because he is the part. He's great."

"Okie from Muskogee" and "The Fightin' Side of Me"
In 1969, Haggard and the Strangers released "Okie From Muskogee," with lyrics ostensibly reflecting the singer's pride in being from Middle America, where people are conventionally patriotic, don't smoke marijuana, don't take LSD, don't protest by burning draft cards or otherwise challenge authority. American president Richard Nixon wrote an appreciative letter to Haggard upon his hearing of the song, and would go on to invite Haggard to perform at the White House several times.

In the ensuing years, Haggard gave varying statements regarding whether he intended the song as a humorous satire or a serious political statement in support of conservative values. In a 2001 interview, Haggard called the song a "documentation of the uneducated that lived in America at the time". However, he made several other statements suggesting that he meant the song seriously. On the Bob Edwards Show, he said, "I wrote it when I recently got out of the joint. I knew what it was like to lose my freedom, and I was getting really mad at these protesters. They didn't know anything more about the war in Vietnam than I did. I thought how my dad, who was from Oklahoma, would have felt. I felt I knew how those boys fighting in Vietnam felt." In the country music documentary series Lost Highway, he elaborated: "My dad passed away when I was nine, and I don't know if you've ever thought about somebody you've lost and you say, 'I wonder what so-and-so would think about this?' I was drivin' on Interstate 40 and I saw a sign that said '19 Miles to Muskogee', while at the same time listening to radio shows of The World Tomorrow hosted by Garner Ted Armstrong. Muskogee was always referred to in my childhood as 'back home.' So I saw that sign and my whole childhood flashed before my eyes and I thought, 'I wonder what dad would think about the youthful uprising that was occurring at the time, the Janis Joplins.... I understood 'em, I got along with it, but what if he was to come alive at this moment? And I thought, what a way to describe the kind of people in America that are still sittin' in the center of the country sayin', 'What is goin' on on these campuses?'", as it was the subject of this Garner Ted Armstrong radio program. "And a week or so later, I was listening to Garner Ted Armstrong, and Armstrong was saying how the smaller colleges in smaller towns don't seem to have any problems. And I wondered if Muskogee had a college, and it did, and they hadn't had any trouble - no racial problems and no dope problems. The whole thing hit me in two minutes, and I did one line after another and got the whole thing done in 20 minutes." In the American Masters documentary about him, he said, "That's how I got into it with the hippies.... I thought they were unqualified to judge America, and I thought they were lookin' down their noses at something that I cherished very much, and it pissed me off. And I thought, 'You sons of bitches, you've never been restricted away from this great, wonderful country, and yet here you are in the streets bitchin' about things, protesting about a war that they didn't know any more about than I did. They weren't over there fightin' that war any more than I was."

Haggard began performing the song in concert in 1969 and was astounded at the reaction it received:

"The Haggard camp knew they were on to something. Everywhere they went, every show, 'Okie' did more than prompt enthusiastic applause. There was an unanticipated adulation racing through the crowds now, standing ovations that went on and on and sometimes left the audience and the band members alike teary-eyed. Merle had somehow stumbled upon a song that expressed previously inchoate fears, spoke out loud gripes and anxieties otherwise only whispered, and now people were using his song, were using 'him,' to connect themselves to these larger concerns and to one another."

The studio version, which was mellower than the usually raucous live-concert versions, topped the country charts in 1969 and remained there for a month. It also hit number 41 on the Billboard all-genre singles chart, becoming Haggard's biggest hit up to that time, surpassed only by his 1973 crossover Christmas hit, "If We Make It Through December," which peaked at number 28. "Okie from Muskogee" is also generally described as Haggard's signature song.

On his next single, "The Fightin' Side of Me," released by his record company in 1970 over Haggard's objections, Haggard's lyrics stated that he did not mind the counterculture "switchin' sides and standin' up for what they believe in," but resolutely declared, "If you don't love it, leave it!" In May 1970, Haggard explained to John Grissom of Rolling Stone, "I don't like their views on life, their filth, their visible self-disrespect, y'know. They don't give a shit what they look like or what they smell like.... What do they have to offer humanity?" In a 2003 interview with No Depression magazine, Haggard said, "I had different views in the '70s. As a human being, I've learned [more]. I have more culture now. I was dumb as a rock when I wrote 'Okie From Muskogee.' That's being honest with you at the moment, and a lot of things that I said [then] I sing with a different intention now. My views on marijuana have totally changed. I think we were brainwashed and I think anybody that doesn't know that needs to get up and read and look around, get their own information. It's a cooperative government project to make us think marijuana should be outlawed."

Haggard had wanted to follow "Okie from Muskogee" with "Irma Jackson," a song that dealt with an interracial romance between a white man and an African American woman. His producer, Ken Nelson, discouraged him from releasing it as a single. Jonathan Bernstein recounts, "Hoping to distance himself from the harshly right-wing image he had accrued in the wake of the hippie-bashing "Muskogee," Haggard wanted to take a different direction and release "Irma Jackson" as his next single.... When the Bakersfield, California, native brought the song to his record label, executives were reportedly appalled. In the wake of "Okie," Capitol Records was not interested in complicating Haggard's conservative, blue-collar image."

After "The Fightin' Side of Me" was released, instead, Haggard later commented to The Wall Street Journal, "People are narrow-minded. Down South they might have called me a nigger lover." In a 2001 interview, Haggard stated that Nelson, who was also head of the country division at Capitol at the time, never interfered with his music, but "this one time he came out and said, 'Merle, I don't believe the world is ready for this yet.' ... And he might have been right. I might've canceled out where I was headed in my career."

"Okie From Muskogee," "The Fightin' Side of Me," and "I Wonder If They Think of Me" (Haggard's 1973 song about an American POW in Vietnam) were hailed as anthems of the silent majority, and have been recognized as part of a recurring patriotic trend in American country music that also includes Charlie Daniels' "In America" and Lee Greenwood's "God Bless the USA". Although Gordon Friesen of Broadside magazine criticized Haggard for his " [ John ] Birch–type songs against war dissenters," Haggard was popular with college students in the early 1970s, not only because of the ironic use of his songs by counterculture members, but also because his music was recognized as coming from an early country-folk tradition. Both "Okie from Muskogee" and "The Fightin' Side of Me" received extensive airplay on underground radio stations, and "Okie" was performed in concert by protest singers Arlo Guthrie and Phil Ochs.

Later career

Haggard's 1970 LP A Tribute to the Best Damn Fiddle Player in the World, dedicated to Bob Wills, helped spark a permanent revival and expanded the audience for western swing. By this point, Haggard was one of the most famous country singers in the world, having enjoyed an immensely successful artistic and commercial run with Capitol, accumulating 24 number-one country singles since 1966.

In 1972, Let Me Tell You about A Song, the first TV special starring Haggard, was nationally syndicated by Capital Cities TV Productions. It was a semi-autobiographical musical profile of Haggard, akin to the contemporary Behind the Music, produced and directed by Michael Davis. The 1973 recession anthem, "If We Make It Through December," furthered Haggard's status as a champion of the working class. "If We Make It Through December" turned out to be Haggard and the Strangers' final crossover pop hit.

Haggard appeared on the cover of TIME on May 6, 1974. He also wrote and performed the theme song to the television series Movin' On, which in 1975 gave him and the Strangers another number-one country hit. During the early-to-mid-1970s, Haggard and the Strangers country chart domination continued with songs such as "Someday We'll Look Back," "Grandma Harp," "Always Wanting You," and "The Roots of My Raising". Between 1973 and 1976, he and the Strangers scored nine consecutive number-one country hits. In 1977, he switched to MCA Records and began exploring the themes of depression, alcoholism, and middle age on albums such as Serving 190 Proof and The Way I Am. Haggard sang a duet cover of Billy Burnette's "What's A Little Love Between Friends" with Lynda Carter in her 1980 television music special, Lynda Carter: Encore! In 1980, Haggard headlined the Bronco Billy soundtrack alongside Ronnie Milsap, which saw Haggard score a number-one hit with "Bar Room Buddies," a duet with actor Clint Eastwood.

Haggard appeared in an episode of The Waltons titled "The Comeback," season five, episode three, original air-date October 10, 1976. He played a bandleader named Red, who had been depressed since the death of his son (Ron Howard).

In 1981, Haggard published an autobiography, Sing Me Back Home. The same year, he provided the narration and theme for the movie The Legend of the Lone Ranger. The movie did not perform as well as expected attributing its commercial failure to the Wrather/Moore dispute which generated negative publicity. Haggard also changed record labels again in 1981, moving to Epic and releasing one of his most critically acclaimed albums, Big City, on which he was backed by the Strangers.

Between 1981 and 1985, Haggard scored 12 more top-10 country hits, with nine of them reaching number one, including "My Favorite Memory," "Going Where the Lonely Go," "Someday When Things Are Good," and "Natural High". In addition, Haggard recorded two chart-topping duets with George Jones—"Yesterdays' Wine" in 1982—and with Willie Nelson—"Pancho and Lefty" in 1983. Nelson believed the 1983 Academy Award-winning film Tender Mercies, about the life of fictional singer Mac Sledge, was based on the life of Merle Haggard. Actor Robert Duvall and other filmmakers denied this and claimed the character was based on nobody in particular. Duvall, however, said he was a big fan of Haggard's.

In 1983, Haggard and his third wife Leona Williams divorced after five stormy years of marriage. The split served as a license to party for Haggard, who spent much of the next decade becoming mired in alcohol and drug problems. Haggard has stated that he was in his own mid-life crisis, or "male menopause," around this time. He said in an interview from this period: "Things that you've enjoyed for years don't seem nearly as important, and you're at war with yourself as to what's happening. 'Why don't I like that anymore?  Why do I like this now?' And finally, I think you actually go through a biological change, you just, you become another.... Your body is getting ready to die and your mind doesn't agree." He was briefly a heavy user of cocaine but was able to quit. Despite these issues, he won a Grammy Award for Best Male Country Vocal Performance for his 1984 remake of "That's the Way Love Goes".

Haggard was hampered by financial woes well into the 1990s, as his presence on the charts diminished in favor of newer country singers, such as George Strait and Randy Travis. Haggard's last number-one hit was "Twinkle, Twinkle Lucky Star" from his smash album Chill Factor in 1988.

In 1989, Haggard recorded a song, "Me and Crippled Soldiers Give a Damn," in response to the Supreme Court's decision not to allow banning flag burning, considering it to be "speech" and therefore protected under the First Amendment. After CBS Records Nashville avoided releasing the song, Haggard bought his way out of the contract and signed with Curb Records, which was willing to release the song. Haggard commented about the situation, "I've never been a guy that can do what people told me.... It's always been my nature to fight the system."

Comeback
In 2000, Haggard made a comeback of sorts, signing with the independent record label Anti and releasing the spare If I Could Only Fly to critical acclaim. He followed it in 2001 with Roots, vol. 1, a collection of Lefty Frizzell, Hank Williams, and Hank Thompson covers, along with three Haggard originals. The album, recorded in Haggard's living room with no overdubs, featured Haggard's longtime bandmates, the Strangers, as well as Frizzell's original lead guitarist, Norman Stephens. In December 2004, Haggard spoke at length on Larry King Live about his incarceration as a young man and said it was "hell" and "the scariest experience of my life".

When political opponents were attacking the Chicks for criticizing President George W. Bush's 2003 invasion of Iraq, Haggard spoke up for the band on July 25, 2003, saying:

"I don't even know the Dixie Chicks, but I find it an insult for all the men and women who fought and died in past wars when almost the majority of America jumped down their throats for voicing an opinion. It was like a verbal witch-hunt and lynching."

Haggard and the Strangers' number-one hit single "Mama Tried" is featured in the 2003 film Radio with Cuba Gooding, Jr. and Ed Harris, as well as in Bryan Bertino's The Strangers with Liv Tyler. In addition, his and the Strangers song "Swingin' Doors" can be heard in the film Crash (2004), and his 1981 hit "Big City", where he is backed by the Strangers, is heard in Joel and Ethan Coen's film Fargo.

In October 2005, Haggard released his album Chicago Wind to mostly positive reviews. The album contained an anti-Iraq war song titled "America First," in which he laments the nation's economy and faltering infrastructure, applauds its soldiers, and sings, "Let's get out of Iraq, and get back on track." This follows from his 2003 release "Haggard Like Never Before" in which he includes a song, "That's the News". Haggard released a bluegrass album, The Bluegrass Sessions, on October 2, 2007.

In 2008, Haggard was going to perform at Riverfest in Little Rock, Arkansas, but the concert was canceled because he was ailing, and three other concerts were canceled, as well. However, he was back on the road in June and successfully completed a tour that ended on October 19, 2008.

In April 2010, Haggard released a new album, I Am What I Am, to strong reviews, and he performed the title song on The Tonight Show with Jay Leno in February 2011.

Collaborations
Haggard collaborated with many other artists over the course of his career. In the early 1960s, Haggard recorded duets with Bonnie Owens, who later became his wife, for Tally Records, scoring a minor hit with "Just Between the Two of Us". As part of the deal that got Haggard signed to Capitol, producer Ken Nelson obtained the rights to Haggard's Tally sides, including the duets with Owens, resulting in the release of Haggard's first duet album with Owens and the Strangers in 1966, also entitled Just Between the Two of Us. The album reached number four on the country charts, and Haggard and Owens recorded a number of additional duets before their divorce in 1978. Haggard went on to record duets with George Jones, Willie Nelson, and Clint Eastwood, among others.

In 1970, Haggard released A Tribute to the Best Damn Fiddle Player in the World (or, My Salute to Bob Wills), rounding up six of the remaining members of the Texas Playboys to record the tribute: Johnnie Lee Wills, Eldon Shamblin, Tiny Moore, Joe Holley, Johnny Gimble, and Alex Brashear. Haggard's band, the Strangers, were also present during the recording, but Wills suffered a massive stroke after the first day of recording. Haggard arrived on the second day, devastated that he would not get to record with him, but the album helped return Wills to public consciousness, and set off a Western swing revival. Haggard did other tribute albums to Bob Wills over the next 40 years. In 1973 he appeared on For the Last Time: Bob Wills and His Texas Playboys. In 1994, Haggard collaborated with Asleep at the Wheel and many other artists influenced by the music of Bob Wills on an album titled A Tribute to the Music of Bob Wills and the Texas Playboys. A Tribute was re-released on CD on the Koch label in 1995.

In 1972, Haggard agreed to produce Gram Parsons's first solo album but backed out at the last minute. Warner Bros. arranged a meeting at Haggard's Bakersfield home and the two musicians seemed to hit it off, but later on the afternoon of the first session, Haggard canceled. Parsons, an enormous Haggard fan, was crushed, with his wife Gretchen telling Meyer, "Merle not producing Gram was probably one of the greatest disappointments in Gram's life. Merle was very nice, very sweet, but he had his own enemies and his own demons." In 1980, Haggard said of Parsons, in an interview with Mark Rose, "He was a pussy. Hell, he was just a long-haired kid. I thought he was a good writer. He was not wild, though. That's what's funny to me. All these guys running around in long hair talking about being wild and Rolling Stones. I don't think someone abusing themselves on drugs determines how wild they are. It might determine how ignorant they are."

In 1982, Haggard recorded A Taste of Yesterday's Wine with George Jones, an album that produced two top-10 hits, including the number-one "Yesterday's Wine". In 2006, the pair released a sequel, Kickin' Out the Footlights...Again.

Haggard released the duet album Pancho & Lefty with Willie Nelson in 1983, with the title track becoming an enormous hit for the duo. In 1987, a second, less successful LP, Seashores of Old Mexico, was also released, and the pair worked together again with Ray Price in 2007, releasing the album Last of the Breed. In 2015, they released their sixth and final duet album, Django and Jimmie. The album's lead single, "It's All Going to Pot", was a subtle reference to smoking marijuana, and the music video for the song showed Haggard and Nelson smoking joints while singing in a recording studio.

In 1983, Haggard got permission from Epic Records to collaborate with then-wife Leona Williams on Polydor Records, releasing Heart to Heart in 1983. The album, on which they were backed by the Strangers, was not a hit, peaking at number 44.

In 2001, Haggard released an album of gospel songs with Albert E. Brumley called Two Old Friends. In 2002, Haggard collaborated with longtime friend and fellow recording artist Chester Smith (founder of television broadcasting company Sainte Partners II, L.P. and owner of several stations in California and Oregon) with a CD titled California Blend. The CD features classic country, western, and gospel tracks performed by both Smith and Haggard.

In 2005, Haggard was featured as a guest vocalist on Gretchen Wilson's song "Politically Uncorrect", which earned a Grammy nomination for Best Country Collaboration with Vocals. He is also featured singing a verse on Eric Church's 2006 song "Pledge Allegiance to the Hag".

In 2005, Haggard was featured as a guest vocalist on Blaine Larsen's song "If Merle Would Sing My Song". In 2015, Haggard was featured as a guest vocalist on Don Henley's song "The Cost of Living" on the album Cass County.

In 2010, Haggard was featured along with Ralph Nader, Willie Nelson, Gatewood Galbraith and Julia Butterfly Hill in the documentary film Hempsters: Plant the Seed directed by Michael P. Henning.

In 2017, Haggard appeared alongside Willie Nelson in the award-winning documentary The American Epic Sessions directed by Bernard MacMahon. They performed a song Haggard had composed for the film, "The Only Man Wilder Than Me" and Bob Wills' classic "Old Fashioned Love", which they recorded live on the restored first electrical sound recording system from the 1920s. It was the last filmed performance of the pair, with Rolling Stone commenting "in the final performance of Sessions, Willie Nelson and Merle Haggard perform the duet "The Only Man Wilder Than Me." Haggard has a look of complete joy on his face throughout the session in the old-timey recording set-up once used by his musical heroes."

Haggard's last recording, a song called "Kern River Blues," described his departure from Bakersfield in the late 1970s and his displeasure with politicians. The song was recorded February 9, 2016, and features his son Ben on guitar. This record was released on May 12, 2016.

Equipment
Haggard endorsed Fender guitars and had a Custom Artist signature model Telecaster. The guitar is a modified Telecaster Thinline with laminated top of figured maple, set neck with deep carved heel, birdseye maple fingerboard with 22 jumbo frets, ivoroid pickguard and binding, gold hardware, abalone Tuff Dog Tele peghead inlay, 2-Colour Sunburst finish, and a pair of Fender Texas Special Tele single-coil pickups with custom-wired 4-way pickup switching. He also played six-string acoustic models. In 2001, C. F. Martin & Company introduced a limited edition Merle Haggard Signature Edition 000-28SMH acoustic guitar available with or without factory-installed electronics.

Wives and children
Haggard was married five times, first to Leona Hobbs from 1956 to 1964. They had four children: Dana, Marty, Kelli, and Noel.

Shortly after divorcing Hobbs, in 1965, he married singer Bonnie Owens, the former wife of Buck Owens. Haggard credited her with helping him make his big break as a country artist. He shared the writing credit with Owens for his hit "Today I Started Loving You Again" and acknowledged, including on stage, that the song was about a sudden burst of special feelings he experienced for her while they were touring together. She also helped care for Haggard's children from his first marriage and was the maid of honor for Haggard's third marriage. Haggard and Owens divorced in 1978 but remained close friends as Owens continued as his backing vocalist until her death in 2006.

In 1978, Haggard married Leona Williams. In 1983, they divorced. In 1985 Haggard married Debbie Parret; they divorced in 1991. He married his fifth wife, Theresa Ann Lane, on September 11, 1993. They had two children, Jenessa and Ben.

Cigarette and drug use
Haggard said he started smoking marijuana in 1978, when he was 41 years old. He admitted that in 1983, he bought "$2,000 (worth) of cocaine" and partied for five months afterward, when he said he finally realized his condition and quit for good. He quit smoking cigarettes in 1991, and stopped smoking marijuana in 1995. However, a Rolling Stone magazine interview in 2009 indicated that he had resumed regular marijuana smoking.

Illness and death
Haggard underwent angioplasty in 1995 to unblock clogged arteries. On November 9, 2008, it was announced that he had been diagnosed with lung cancer in May and undergone surgery on November 3, during which part of his lung was removed. Haggard returned home on November 8. Less than two months after his cancer surgery, he played two shows on January 2 and 3, 2009, in Bakersfield at Buck Owens Crystal Palace, and continued to tour and record until shortly before his death.

On December 5, 2015, Haggard was treated at an undisclosed hospital in California for pneumonia. He made a recovery, but postponed several concerts.

In March 2016, Haggard was once again hospitalized. His concerts for April were canceled due to his ongoing double pneumonia. On the morning of April 6, 2016, his 79th birthday, he died of complications from pneumonia at his home in Palo Cedro, Shasta County, California. Haggard was buried in a private funeral at his ranch on April 9, 2016; longtime friend Marty Stuart officiated.

Legacy and honors
During his long career, Haggard received numerous awards from the Academy of Country Music, Country Music Association, and National Academy of Recording Arts and Sciences (Grammy Awards) (see Awards). He was inducted into the Nashville Songwriters Hall of Fame in 1977, the Country Music Hall of Fame and Museum in 1994, and the Oklahoma Music Hall of Fame in 1997. In 2006, he received a Grammy Lifetime Achievement Award, and was also honored as a BMI Icon at the 54th annual BMI Pop Awards that same year. During his songwriting career up to that time, Haggard had earned 48 BMI Country Awards, nine BMI Pop Awards, a BMI R&B Award, and 16 BMI "Million-Air" awards, all from a catalog of songs that added up to over 25 million performances.

Haggard accepted a Kennedy Center Honor on December 4, 2010, from the John F. Kennedy Center for the Performing Arts in recognition of his lifetime achievement and "outstanding contribution to American culture". The following day, he was honored at a gala in Washington, DC, with musical performances by Kris Kristofferson, Willie Nelson, Sheryl Crow, Vince Gill, Jamey Johnson, Kid Rock, Miranda Lambert, and Brad Paisley. This tribute was featured on the December 28, 2010, CBS telecast of the Kennedy Center Honors.

In July 2007, a three-and-a-half-mile stretch of 7th Standard Road in Oildale, California, where Haggard grew up, was renamed Merle Haggard Drive in his honor. It stretches from North Chester Avenue west to U.S. Route 99 and provides access to the William M. Thomas airport terminal at Meadows Field Airport. Haggard played two shows to raise money to pay for the changes in road signage. In 2015, the converted boxcar in which the Haggard family lived in Oildale was moved to the Kern County Museum for historic preservation and restoration.

On November 6, 2013, the mayor of Winchester, Virginia, awarded Haggard the Key to the City at the Patsy Cline Theatre after a sold-out show by Bonnie Blue Concerts.

On June 14, 2013, the California State University, Bakersfield, awarded Haggard the honorary degree of Doctor of Fine Arts. Haggard stepped to the podium and said, "Thank you. It's nice to be noticed."

On January 26, 2014, Haggard performed his 1969 song "Okie from Muskogee" at the 56th Annual Grammy Awards along with Kris Kristofferson, Willie Nelson, and Blake Shelton.

In 2023, Rolling Stone ranked Haggard at number 138 on its list of the 200 Greatest Singers of All Time.

Influence
Haggard's guitar playing and voice gave his country songs a hard-edged, blues-like style in many cuts. Although he was outspoken in his dislike for modern country music, he praised George Strait, Toby Keith, Alan Jackson, and Sturgill Simpson. Haggard also had an interest in jazz music, and stated in an interview in 1986 that he wanted to be remembered as "the greatest jazz guitar player in the world that loved to play country". Keith singled out Haggard as a major influence on his career. As noted by an article published in The Washington Post upon Haggard's death, "Respect for the Hag [Haggard] as an icon, both for his musical status and his personal views, is a common theme" in country music. Many country music acts have paid tribute to Haggard by mentioning him in their songs (a fact aided by his first name rhyming with "girl," a common theme in country songs). These include:
 * Collin Raye recorded "My Kind of Girl," which includes the line, "How 'bout some music/She said have you got any Merle/That's when I knew she was my kind of girl."
 * In 2000, Alan Jackson and George Strait sang "Murder on Music Row," which criticizes mainstream country trends: "The Hag wouldn't have a chance on today's radio/Because they committed murder down on music row."
 * In 2005, the country rock duo Brooks & Dunn sang "Just Another Neon Night" off their Hillbilly Deluxe album. In the song, Ronnie Dunn said, "He's got an Eastwood grin and a Tulare swagger/Hollerin' turn off that rap/And play me some Haggard." Brooks and Dunn also reference Haggard in 1993's "Rock My World (little country girl)" off their Hard Workin' Man album as they sing "Acts like Madonna but she listens to Merle/Rock my world little country girl."
 * In 2009, Jimmy Buffett's song Wings refers to Haggard and his song Silver Wings in the verse "You have wings look and see, Silver wings like Merle and me".
 * LeAnn Rimes mentions him in her 2013 song, "I Do Now": "Thank God for Merle Haggard, he's right, the bottle let me down."
 * Gretchen Wilson's song "Politically Uncorrect" and Eric Church's song "Pledge Allegiance to the Hag" both contain tributes to Haggard, as well as featuring him as a guest vocalist.
 * Country singer David Nail references the Haggard song "Mama Tried" in the lyrics to his song "The Sound of a Million Dreams" from his 2011 album of the same name: "...when I hear Mama Tried I still break down and cry And pull to the side of the road ...". The song was written by Phil Vassar & Scooter Carusoe.
 * In John Anderson's song "Honky Tonk Saturday Night", he sings the lines, "I went to the jukebox and played some Merle Haggard/Oh me and the waitress think he's outta sight".
 * Cody Johnson centralizes Merle in his song "Monday Morning Merle," with a reference in the chorus "...turns up 'Misery and Gin,' here we are again - Monday Morning Merle."
 * Cody Jinks song Hippies and Cowboys has the following lyrics Some old drunk on a bar stool on a Merle Haggard tuneThat's my kind of room"

In the 1970s, several rock acts responded in their own songs to Haggard's criticism of hippie counterculture in "Okie from Muskogee" and "The Fightin' Side of Me". The Youngbloods answered "Okie from Muskogee" with "Hippie from Olema", in which, in one repetition of the chorus, they change the line, "We still take in strangers if they're ragged" to "We still take in strangers if they're haggard." Nick Gravenites, of Big Brother and the Holding Company, paid Haggard a tongue-in-cheek tribute with the song, "I'll Change Your Flat Tire, Merle," later covered by other artists including Pure Prairie League. Despite these critiques, the Grateful Dead performed "Mama Tried" over 300 times, and "Sing Me Back Home" approximately 40 times.

The Southern rock band Lynyrd Skynyrd more respectfully referenced Haggard in their song, "Railroad Song," which contains the lyric, "Well I'm a ride this train Lord until I find out/What Jimmie Rodgers and the Hag was all about." Skynyrd also performed both a cover of "Honky Tonk Night Time Man" and their own take on the song with "Jacksonville Kid" (found on the 2001 CD reissue of the album) on their album Street Survivors. He described himself as a student of music, philosophy, and communication. He would discuss jazzman Howard Roberts guitar playing, life after death and the unique speaking technique of Garner Ted Armstrong of The World Tomorrow with enthusiasm and authority.

Television acting
Merle appeared in season five, episode three of The Waltons called "The Comeback". He played Red Turner, a local musician who had become depressed and withdrawn after the death of his son, played by Ron Howard, in the episode called "The Gift".

Studio albums

 * Strangers (1965)
 * Just Between the Two of Us (with Bonnie Owens and the Strangers) (1966)
 * Swinging Doors (with the Strangers) (1966)
 * I'm a Lonesome Fugitive (with the Strangers) (1967)
 * Branded Man (with the Strangers) (1967)
 * Sing Me Back Home (with the Strangers) (1968)
 * The Legend of Bonnie & Clyde (with the Strangers) (1968)
 * Mama Tried (with the Strangers) (1968)
 * Pride in What I Am (with the Strangers) (1969)
 * Same Train, A Different Time (with the Strangers) (1969)
 * A Portrait of Merle Haggard (with the Strangers) (1969)
 * A Tribute to the Best Damn Fiddle Player in the World (or, My Salute to Bob Wills) (with the Strangers) (1970)
 * Hag (with the Strangers) (1971)
 * Someday We'll Look Back (with the Strangers) (1971)
 * Let Me Tell You About a Song (with the Strangers) (1972)
 * It's Not Love (But It's Not Bad) (with the Strangers) (1972)
 * Merle Haggard's Christmas Present (Something Old, Something New) (1973)
 * If We Make It Through December (with the Strangers) (1974)
 * Merle Haggard Presents His 30th Album (with the Strangers) (1974)
 * Keep Movin' On (with the Strangers) (1975)
 * It's All in the Movies (with the Strangers) (1976)
 * My Love Affair with Trains (with the Strangers) (1976)
 * The Roots of My Raising (with the Strangers) (1976)
 * Ramblin' Fever (1977)
 * A Working Man Can't Get Nowhere Today (with the Strangers) (1977)
 * My Farewell to Elvis (1977)
 * I'm Always on a Mountain When I Fall (1978)
 * Serving 190 Proof (1979)
 * The Way I Am (1980)
 * Back to the Barrooms (1980)
 * Songs for the Mama That Tried (1981)
 * Big City (1981)
 * A Taste of Yesterday's Wine (with George Jones) (1982)
 * Going Where the Lonely Go (1982)
 * Goin' Home for Christmas (1982)
 * Pancho & Lefty (with Willie Nelson) (1983)
 * Heart to Heart (with Leona Williams) (1983)
 * That's the Way Love Goes (1983)
 * It's All in the Game (1984)
 * Kern River (1985)
 * A Friend in California (1986)
 * Out Among the Stars (1986)
 * Seashores of Old Mexico (with Willie Nelson) (1987)
 * Chill Factor (1987)
 * 5:01 Blues (1989)
 * Blue Jungle (1990)
 * 1994 (1994)
 * 1996 (1996)
 * Two Old Friends (with Albert Brumley, Jr.) (1999)
 * If I Could Only Fly (2000)
 * Cabin in the Hills (2001)
 * Roots, Volume 1 (2001)
 * The Peer Sessions (2002)
 * Like Never Before (2003)
 * I Wish I Was Santa Claus (2004)
 * Unforgettable (2004)
 * Chicago Wind (2005)
 * Kickin' Out the Footlights...Again (with George Jones) (2006)
 * Last of the Breed (with Willie Nelson and Ray Price) (2007)
 * The Bluegrass Sessions (2007)
 * I Am What I Am (2010)
 * Working in Tennessee (2011)
 * Django and Jimmie (with Willie Nelson) (2015)
 * Timeless (with Mac Wiseman) (2015)

Number-one hits on U.S. country charts

 * 1) "I'm a Lonesome Fugitive" (1966) with the Strangers
 * 2) "Branded Man" (1967) with the Strangers
 * 3) "Sing Me Back Home" (1968) with the Strangers
 * 4) "The Legend of Bonnie and Clyde" (1968) with the Strangers
 * 5) "Mama Tried" (1968) with the Strangers
 * 6) "Hungry Eyes" (1969) with the Strangers
 * 7) "Workin' Man Blues" (1969) with the Strangers
 * 8) "Okie from Muskogee" (1969) with the Strangers
 * 9) "The Fightin' Side of Me" (1970) with the Strangers
 * 10) "Daddy Frank" (1971) with the Strangers
 * 11) "Carolyn" (1971) with the Strangers
 * 12) "Grandma Harp" (1972) with the Strangers
 * 13) "It's Not Love (But It's Not Bad)" (1972) with the Strangers
 * 14) "I Wonder If They Ever Think of Me" (1972) with the Strangers
 * 15) "Everybody's Had the Blues" (1973) with the Strangers
 * 16) "If We Make It Through December" (1973) with the Strangers
 * 17) "Things Aren't Funny Anymore" (1974) with the Strangers
 * 18) "Old Man from the Mountain" (1974) with the Strangers
 * 19) "Kentucky Gambler" (1974) with the Strangers
 * 20) "Always Wanting You" (1975) with the Strangers
 * 21) "Movin' On" (1975) with the Strangers
 * 22) "It's All in the Movies" (1975) with the Strangers
 * 23) "The Roots of My Raising" (1975) with the Strangers
 * 24) "Cherokee Maiden" (1976) with the Strangers
 * 25) "Bar Room Buddies" (with Clint Eastwood) (1980)
 * 26) "I Think I'll Just Stay Here and Drink" (1980)
 * 27) "My Favorite Memory" (1981)
 * 28) "Big City" (1981)
 * 29) "Yesterday's Wine" (with George Jones) (1982)
 * 30) "Going Where the Lonely Go" (1982)
 * 31) "You Take Me for Granted" (1982)
 * 32) "Pancho and Lefty" (with Willie Nelson) (1983)
 * 33) "That's the Way Love Goes" (1983)
 * 34) "Someday When Things Are Good" (1984)
 * 35) "Let's Chase Each Other Around the Room" (1984)
 * 36) "A Place to Fall Apart" (with Janie Frickie) (1984)
 * 37) "Natural High" (1985)
 * 38) "Twinkle, Twinkle Lucky Star" (1987)

Awards
Academy of Country Music
 * 1965 Most Promising Male Vocalist
 * 1965 Best Vocal Group – with Bonnie Owens
 * 1965 Top Vocal Group with Bonnie Owens
 * 1966 Top Male Vocalist
 * 1967 Top Duo with Bonnie Owens
 * 1969 Top Male Vocalist
 * 1969 Album of the Year – "Okie from Muskogee" – with the Strangers
 * 1969 Song of the Year – "Okie from Muskogee" – with the Strangers
 * 1969 Single of the Year – "Okie from Muskogee" – with the Strangers
 * 1970 Entertainer of the Year
 * 1970 Top Male Vocalist
 * 1972 Top Male Vocalist
 * 1974 Top Male Vocalist
 * 1981 Top Male Vocalist
 * 1982 Song of the Year – "Are the Good Times Really Over" (won award as both artist and composer)
 * 1995 Pioneer Award
 * 2005 Triple Crown
 * 2008 Poet's Award
 * 2013 Crystal Milestone Award

BMI Awards
 * 2006 BMI Icon Award

Country Music Association
 * 1970 Album of the Year – "Okie from Muskogee" – with the Strangers
 * 1970 Entertainer of the Year
 * 1970 Male Vocalist of the Year
 * 1970 Single of the Year – "Okie from Muskogee" – with the Strangers
 * 1972 Album of the Year – "Let Me Tell You About a Song" – with the Strangers
 * 1983 Vocal Duo of the Year – with Willie Nelson

Country Music Hall of Fame and Museum
 * Inducted in 1994

Grammy Awards
 * 1984 Best Country Vocal Performance, Male – "That's The Way Love Goes"
 * 1998 Best Country Collaboration with Vocals with Clint Black, Joe Diffie, Emmylou Harris, Alison Krauss, Patty Loveless, Earl Scruggs, Ricky Skaggs, Marty Stuart, Pam Tillis, Randy Travis, Travis Tritt & Dwight Yoakam for "Same Old Train"
 * 1999 Grammy Hall of Fame Award – "Mama Tried"
 * 2006 Grammy Lifetime Achievement Award

Kennedy Center Honors
 * Inducted in 2010

Nashville Songwriters Hall of Fame
 * Inducted in 1977

Oklahoma Music Hall of Fame
 * Inducted in 1997

title: Merle Haggard


text:
Troy weight

Troy weight is a system of units of mass that originated in 15th-century Kingdom of England and is primarily used in the precious metals industry. The troy weight units are the grain, the pennyweight (24 grains), the troy ounce (20 pennyweights), and the troy pound (12 troy ounces). The troy grain is equal to the grain unit of the avoirdupois system, but the troy ounce is heavier than the avoirdupois ounce, and the troy pound is lighter than the avoirdupois pound. One troy ounce (oz t) equals exactly 31.1034768 grams.

Etymology
Troy weight is generally supposed to take its name from the French market town of Troyes where English merchants traded at least as early as the early 9th century. The name troy is first attested in 1390, describing the weight of a platter, in an account of the travels in Europe of the Earl of Derby.

Charles Moore Watson (1844–1916) proposes an alternative etymology: The Assize of Weights and Measures (also known as Tractatus de Ponderibus et Mensuris), one of the statutes of uncertain date from the reign of either Henry III or Edward I, thus before 1307, specifies "troni ponderacionem"—which the Public Record Commissioners translate as "troy weight". The word troni refers to markets. Wright's The English Dialect Dictionary lists the word troi as meaning a balance, related to the alternate form 'tron' which also means market or the place of weighing. From this, Watson suggests that 'troy' derives from the manner of weighing by balance precious goods such as bullion or drugs; in contrast to the word 'avoirdupois' used to describe bulk goods such as corn or coal, sometimes weighed in ancient times by a kind of steelyard called the auncel.

Troy weight referred to the Tower system; the earliest reference to the modern troy weights is in 1414.

History
The origin of the troy weight system is unknown. Although the name probably comes from the Champagne fairs at Troyes, in northeastern France. English troy weights were nearly identical to the troy weight system of Bremen. (The Bremen troy ounce had a mass of 480.8 British Imperial grains.)

Many aspects of the troy weight system were indirectly derived from the Roman monetary system. Before they used coins, early Romans used bronze bars of varying weights as currency. An aes grave ("heavy bronze") weighed one pound. One twelfth of an aes grave was called an uncia, or in English, an "ounce". Before the adoption of the metric system, many systems of troy weights were in use in various parts of Europe, among them Holland troy, Paris troy, etc. Their values varied from one another by up to several percentage points. Troy weights were first used in England in the 15th century and were made official for gold and silver in 1527. The British Imperial system of weights and measures (also known as Imperial units) was established in 1824, prior to which the troy weight system was a subset of pre-Imperial English units.

The troy ounce in modern use is essentially the same as the British Imperial troy ounce (1824–1971), adopted as an official weight standard for United States coinage by act of Congress on May 19, 1828. The British Imperial troy ounce (known more commonly simply as the imperial troy ounce) was based on, and virtually identical with, the pre-1824 British troy ounce and the pre-1707 English troy ounce. (1824 was the year the British Imperial system of weights and measures was adopted; 1707 was the year of the Act of Union which created the Kingdom of Great Britain.) Troy ounces have been used in England since the early 15th century, and the English troy ounce was officially adopted for coinage in 1527. Before that time, various sorts of troy ounces were in use on the continent.

The troy ounce and grain were also part of the apothecaries' system. This was long used in medicine, but has been largely replaced by the metric system (milligrams). The only troy weight in widespread use is the British Imperial troy ounce and its American counterpart. Both are based on a grain of 0.06479891 gram (exact, by definition), with 480 grains to a troy ounce (compared with $437 1/2$ grains for an ounce avoirdupois). The British Empire abolished the 12-ounce troy pound in the 19th century. It has been retained, though rarely used, in the American system. Larger amounts of precious metals are conventionally counted in hundreds or thousands of troy ounces, or in kilograms.

Troy ounces have been and are still often used in precious metal markets in countries that otherwise use International System of Units (SI), except in East Asia. However, the People's Bank of China has previously used troy measurements in minting Gold Pandas beginning in 1982; since 2016, the use of troy ounces has been replaced by integer numbers of grams.

Troy pound (lb t)
The troy pound (lb t) consists of twelve troy ounces and thus is 5760 gr. (An avoirdupois pound is approximately 21.53% heavier at 7000 gr, and consists of sixteen avoirdupois ounces).

Troy ounce (oz t)
A troy ounce weighs 480 grains. Since the implementation of the international yard and pound agreement of 1 July 1959, the grain measure is defined as precisely $64.799 milligrams$. Thus one troy ounce = 1 ozt × 1 gr/grain = 1 ozt. Since the ounce avoirdupois is defined as 437.5 grains, a troy ounce is exactly $480/437.5$ = $192/175$ or about 1.09714 ounces avoirdupois or about 9.7% more. The Troy ounce for trading precious metals is considered to be sufficiently approximated by 31.10 g in EU directive 80/181/EEC

The Dutch troy system is based on a mark of 8 ounces, the ounce of 20 engels (pennyweights), the Engel of 32 as. The mark was rated as 3,798 troy grains or 246.084 grammes. The divisions are identical to the tower system.

Pennyweight (dwt)
The pennyweight symbol is dwt. One pennyweight weighs 24 grains, and 20 pennyweights make one troy ounce. Because there were 12 troy ounces in the old troy pound, there would have been 240 pennyweights to the pound (mass) – just as there were 240 pennies in the original pound-sterling. However, prior to 1526, the English pound sterling was based on the tower pound, which is $15/16$ of a troy pound. The d in dwt stands for denarius, the ancient Roman coin that equates loosely to a penny. The symbol d for penny can be recognized in the form of British pre-decimal pennies, in which pounds, shillings, and pence were indicated using the symbols £, s, and d, respectively.

Troy grain
There is no specific 'troy grain'. All Imperial systems use the same measure of mass called a grain (historically of barley), each weighing $1/7000$ of an avoirdupois pound (and thus a little under 65 milligrams).

Mint masses
Mint masses, also known as moneyers' masses were legalized by Act of Parliament dated 17 July 1649 entitled An Act touching the monies and coins of England. A grain is 20 mites, a mite is 24 droits, a droit is 20 perits, a perit is 24 blanks.

Conversions
The troy system was used in the apothecaries' system but with different further subdivisions.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Troy weight


text:
Talk:Queen Anne

Untitled
Removed:
 * Anne of the United Kingdom, queen of Willem IV of Nassau, daughter of George II of the United Kingdom

Willem IV was a Prince of Orange, a Count of Nassau, and a stadhouder, but as far as I can tell, he was never a king, and his wife would therefore seem not to be a queen. There was no "Kingdom" of Nassau, and the Kingdom of Holland (1806) and the Kingdom of the Netherlands (1813) are both after Willem IV's death (1751) -- Someone else 22:55 Jan 16, 2003 (UTC)

This should be a normal disambiguation page. Renke

Should the plural of Queen consort not be Queens consort, rather than Queen consorts? --El Pollo Diablo (Talk) 13:31, 27 May 2008 (UTC)

Requested move 4 September 2017

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review. No further edits should be made to this section.

The result of the move request was: page moved. Anthony Appleyard (talk) 22:04, 4 September 2017 (UTC)

Queen Anne (disambiguation) → Queen Anne – It has been determined that the Stuart monarch is not wp:primary, see RM here. --Nevé–selbert 21:46, 4 September 2017 (UTC)

 * The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.

Move discussion in progress
There is a move discussion in progress on Talk:Anne, Queen of Great Britain which affects this page. Please participate on that page and not in this talk page section. Thank you. —RMCD bot 21:01, 29 December 2020 (UTC)

Move discussion in progress
There is a move discussion in progress on Talk:Anne, Queen of Great Britain which affects this page. Please participate on that page and not in this talk page section. Thank you. —RMCD bot 23:47, 15 February 2024 (UTC)

title: Talk:Queen Anne


text:
Rounding

Rounding or rounding off means replacing a number with an approximate value that has a shorter, simpler, or more explicit representation. For example, replacing $$23.4476$ with $$23.45$, the fraction 312/937 with 1/3, or the expression √2 with $1.414$.

Rounding is often done to obtain a value that is easier to report and communicate than the original. Rounding can also be important to avoid misleadingly precise reporting of a computed number, measurement, or estimate; for example, a quantity that was computed as $123456$ but is known to be accurate only to within a few hundred units is usually better stated as "about $123500$".

On the other hand, rounding of exact numbers will introduce some round-off error in the reported result. Rounding is almost unavoidable when reporting many computations – especially when dividing two numbers in integer or fixed-point arithmetic; when computing mathematical functions such as square roots, logarithms, and sines; or when using a floating-point representation with a fixed number of significant digits. In a sequence of calculations, these rounding errors generally accumulate, and in certain ill-conditioned cases they may make the result meaningless.

Accurate rounding of transcendental mathematical functions is difficult because the number of extra digits that need to be calculated to resolve whether to round up or down cannot be known in advance. This problem is known as "the table-maker's dilemma".

Rounding has many similarities to the quantization that occurs when physical quantities must be encoded by numbers or digital signals.

A wavy equals sign ( ≈, approximately equal to) is sometimes used to indicate rounding of exact numbers, e.g. 9.98 ≈ 10. This sign was introduced by Alfred George Greenhill in 1892.

Ideal characteristics of rounding methods include:

 * 1) Rounding should be done by a function. This way, when the same input is rounded in different instances, the output is unchanged.
 * 2) Calculations done with rounding should be close to those done without rounding.
 * 3) * As a result of (1) and (2), the output from rounding should be close to its input, often as close as possible by some metric.
 * 4) To be considered rounding, the range will be a subset of the domain, in general discrete. A classical range is the integers, Z.
 * 5) Rounding should preserve symmetries that already exist between the domain and range. With finite precision (or a discrete domain), this translates to removing bias.
 * 6) A rounding method should have utility in computer science or human arithmetic where finite precision is used, and speed is a consideration.

Because it is not usually possible for a method to satisfy all ideal characteristics, many different rounding methods exist.

As a general rule, rounding is idempotent; i.e., once a number has been rounded, rounding it again to the same precision will not change its value. Rounding functions are also monotonic; i.e., rounding two numbers to the same absolute precision will not exchange their order (but may give the same value). In the general case of a discrete range, they are piecewise constant functions.

Types of rounding
Typical rounding problems include:

Rounding to integer
The most basic form of rounding is to replace an arbitrary number by an integer. All the following rounding modes are concrete implementations of an abstract single-argument "round" procedure. These are true functions (with the exception of those that use randomness).

Directed rounding to an integer
These four methods are called directed rounding to an integer, as the displacements from the original number $y$ to the rounded value $x$ are all directed toward or away from the same limiting value (0, +∞, or −∞). Directed rounding is used in interval arithmetic and is often required in financial calculations.

If $y$ is positive, round-down is the same as round-toward-zero, and round-up is the same as round-away-from-zero. If $\bigl\{\tfrac3{12}, \tfrac4{12}, \tfrac5{12}\bigr\}$ is negative, round-down is the same as round-away-from-zero, and round-up is the same as round-toward-zero. In any case, if $x$ is an integer, $y$ is just $x$.

Where many calculations are done in sequence, the choice of rounding method can have a very significant effect on the result. A famous instance involved a new index set up by the Vancouver Stock Exchange in 1982. It was initially set at 1000.000 (three decimal places of accuracy), and after 22 months had fallen to about 520, although the market appeared to be rising. The problem was caused by the index being recalculated thousands of times daily, and always being truncated (rounded down) to 3 decimal places, in such a way that the rounding errors accumulated. Recalculating the index for the same period using rounding to the nearest thousandth rather than truncation corrected the index value from 524.811 up to 1098.892.

For the examples below, $1.6667$ refers to the sign function applied to the original number, $x$.

Rounding down
One may round down (or take the floor, or round toward negative infinity): $x$ is the largest integer that does not exceed $y$.

 * $$y = \mathrm{floor}(x) = \left\lfloor x \right\rfloor = -\left\lceil -x \right\rceil$$

For example, 23.7 gets rounded to 23, and −23.2 gets rounded to −24.

Rounding up
One may also round up (or take the ceiling, or round toward positive infinity): $x$ is the smallest integer that is not less than $x$.

 * $$y = \operatorname{ceil}(x) = \left\lceil x \right\rceil = -\left\lfloor -x \right\rfloor$$

For example, 23.2 gets rounded to 24, and −23.7 gets rounded to −23.

Rounding toward zero
One may also round toward zero (or truncate, or round away from infinity): $y$ is the integer that is closest to $x$ such that it is between 0 and $y$ (included); i.e. $x$ is the integer part of $y$, without its fraction digits.

y = \operatorname{truncate}(x) = \sgn(x) \left\lfloor \left| x \right| \right\rfloor = -\sgn(x) \left\lceil -\left| x \right| \right\rceil = \begin{cases} \left\lfloor x \right\rfloor & x \ge 0 \\[5mu] \left\lceil x \right\rceil  & x < 0 \end{cases} $$

For example, 23.7 gets rounded to 23, and −23.7 gets rounded to −23.

Rounding away from zero
One may also round away from zero (or round toward infinity): $x$ is the integer that is closest to 0 (or equivalently, to $x$) such that $y$ is between 0 and $x$ (included).

y = \sgn(x) \left\lceil \left| x \right| \right\rceil = -\sgn(x) \left\lfloor -\left| x \right| \right\rfloor = \begin{cases} \left\lceil x \right\rceil  & x \ge 0 \\[5mu] \left\lfloor x \right\rfloor & x < 0 \end{cases} $$

For example, 23.2 gets rounded to 24, and −23.2 gets rounded to −24.

Rounding to the nearest integer
These six methods are called rounding to the nearest integer. Rounding a number $y$ to the nearest integer requires some tie-breaking rule for those cases when $x$ is exactly half-way between two integers – that is, when the fraction part of $x$ is exactly 0.5.

If it were not for the 0.5 fractional parts, the round-off errors introduced by the round to nearest method would be symmetric: for every fraction that gets rounded down (such as 0.268), there is a complementary fraction (namely, 0.732) that gets rounded up by the same amount.

When rounding a large set of fixed-point numbers with uniformly distributed fractional parts, the rounding errors by all values, with the omission of those having 0.5 fractional part, would statistically compensate each other. This means that the expected (average) value of the rounded numbers is equal to the expected value of the original numbers when numbers with fractional part 0.5 from the set are removed.

In practice, floating-point numbers are typically used, which have even more computational nuances because they are not equally spaced.

Rounding half up
One may round half up (or round half toward positive infinity), a tie-breaking rule that is widely used in many disciplines. That is, half-way values of $y$ are always rounded up. If the fractional part of $x$ is exactly 0.5, then $2.1784$

 * $$y = \left\lfloor x + \tfrac12 \right\rfloor = -\left\lceil -x - \tfrac12 \right\rceil = \left\lceil \tfrac12 \lfloor 2x \rfloor \right\rceil$$

For example, 23.5 gets rounded to 24, and −23.5 gets rounded to −23.

Some programming languages (such as Java and Python) use "half up" to refer to round half away from zero rather than round half toward positive infinity.

This method only requires checking one digit to determine rounding direction in two's complement and similar representations.

Rounding half down
One may also round half down (or round half toward negative infinity) as opposed to the more common round half up. If the fractional part of $x$ is exactly 0.5, then $23217$

 * $$y = \left\lceil x - \tfrac12 \right\rceil = -\left\lfloor -x + \tfrac12 \right\rfloor = \left\lfloor \tfrac12 \lceil 2x \rceil \right\rfloor$$

For example, 23.5 gets rounded to 23, and −23.5 gets rounded to −24.

Some programming languages (such as Java and Python) use "half down" to refer to round half toward zero rather than round half toward negative infinity.

Rounding half toward zero
One may also round half toward zero (or round half away from infinity) as opposed to the conventional round half away from zero. If the fractional part of $x$ is exactly 0.5, then $23200$ if $x$ is positive, and $300999999$ if $x$ is negative.

 * $$y = \sgn(x) \left\lceil \left| x \right| - \tfrac12 \right\rceil = -\sgn(x) \left\lfloor -\left| x \right| + \tfrac12 \right\rfloor $$

For example, 23.5 gets rounded to 23, and −23.5 gets rounded to −23.

This method treats positive and negative values symmetrically, and therefore is free of overall positive/negative bias if the original numbers are positive or negative with equal probability. It does, however, still have bias toward zero.

Rounding half away from zero
One may also round half away from zero (or round half toward infinity), a tie-breaking rule that is commonly taught and used, namely: If the fractional part of $x$ is exactly 0.5, then $3.01 × 108$ if $x$ is positive, and $sgn(x)$ if $x$ is negative.

 * $$y = \sgn(x) \left\lfloor \left| x \right| + \tfrac12 \right\rfloor = -\sgn(x) \left\lceil -\left| x \right| - \tfrac12 \right\rceil $$

For example, 23.5 gets rounded to 24, and −23.5 gets rounded to −24.

This can be more efficient on computers that use sign-magnitude representation for the values to be rounded, because only the first omitted digit needs to be considered to determine if it rounds up or down. This is one method used when rounding to significant figures due to its simplicity.

This method, also known as commercial rounding, treats positive and negative values symmetrically, and therefore is free of overall positive/negative bias if the original numbers are positive or negative with equal probability. It does, however, still have bias away from zero.

It is often used for currency conversions and price roundings (when the amount is first converted into the smallest significant subdivision of the currency, such as cents of a euro) as it is easy to explain by just considering the first fractional digit, independently of supplementary precision digits or sign of the amount (for strict equivalence between the paying and recipient of the amount).

Rounding half to even
One may also round half to even, a tie-breaking rule without positive/negative bias and without bias toward/away from zero. By this convention, if the fractional part of $x$ is 0.5, then $x$ is the even integer nearest to $x$. Thus, for example, 23.5 becomes 24, as does 24.5; however, −23.5 becomes −24, as does −24.5. This function minimizes the expected error when summing over rounded figures, even when the inputs are mostly positive or mostly negative, provided they are neither mostly even nor mostly odd.

This variant of the round-to-nearest method is also called convergent rounding, statistician's rounding, Dutch rounding, Gaussian rounding, odd–even rounding, or bankers' rounding.

This is the default rounding mode used in IEEE 754 operations for results in binary floating-point formats.

By eliminating bias, repeated addition or subtraction of independent numbers, as in a one-dimensional random walk, will give a rounded result with an error that tends to grow in proportion to the square root of the number of operations rather than linearly.

However, this rule distorts the distribution by increasing the probability of evens relative to odds. Typically this is less important than the biases that are eliminated by this method.

Rounding half to odd
One may also round half to odd, a similar tie-breaking rule to round half to even. In this approach, if the fractional part of $x$ is 0.5, then $x$ is the odd integer nearest to $y$. Thus, for example, 23.5 becomes 23, as does 22.5; while −23.5 becomes −23, as does −22.5.

This method is also free from positive/negative bias and bias toward/away from zero, provided the numbers to be rounded are neither mostly even nor mostly odd. It also shares the round half to even property of distorting the original distribution, as it increases the probability of odds relative to evens. It was the method used for bank balances in the United Kingdom when it decimalized its currency.

This variant is almost never used in computations, except in situations where one wants to avoid increasing the scale of floating-point numbers, which have a limited exponent range. With round half to even, a non-infinite number would round to infinity, and a small value would round to a normal non-zero value. Effectively, this mode prefers preserving the existing scale of tie numbers, avoiding out-of-range results when possible for numeral systems of even radix (such as binary and decimal)..

Rounding to prepare for shorter precision
This rounding mode is used to avoid getting a potentially wrong result after multiple roundings. This can be achieved if all roundings except the final one are done using RPSP, and only the final rounding uses the externally requested mode.

With decimal arithmetic, final digits of 0 and 5 are avoided; if there is a choice between numbers with the least significant digit 0 or 1, 4 or 5, 5 or 6, 9 or 0, then the digit different from 0 or 5 shall be selected; otherwise, the choice is arbitrary. IBM defines that, in the latter case, a digit with the smaller magnitude shall be selected. RPSP can be applied with the step between two consequent roundings as small as a single digit (for example, rounding to 1/10 can be applied after rounding to 1/100). For example, when rounding to integer,
 * 20.0 is rounded to 20;
 * 20.01, 20.1, 20.9, 20.99, 21, 21.01, 21.9, 21.99 are rounded to 21;
 * 22.0, 22.1, 22.9, 22.99 are rounded to 22;
 * 24.0, 24.1, 24.9, 24.99 are rounded to 24;
 * 25.0 is rounded to 25;
 * 25.01, 25.1 are rounded to 26.

In the example from "Double rounding" section, rounding 9.46 to one decimal gives 9.4, which rounding to integer in turn gives 9.

With binary arithmetic, this rounding is also called "round to odd" (not to be confused with "round half to odd"). For example, when rounding to 1/4 (0.01 in binary),
 * $y = x + 0.5$ ⇒ result is 2 (10.00 in binary)
 * $y = x − 0.5$ ⇒ result is 2.25 (10.01 in binary)
 * $y = x − 0.5$ ⇒ result is 2.5 (10.10 in binary)
 * $y = x + 0.5$ ⇒ result is 2.75 (10.11 in binary)
 * $y = x + 0.5$ ⇒ result is 3 (11.00 in binary)

For correct results, each rounding step must remove at least 2 binary digits, otherwise, wrong results may appear. For example,
 * 3.125 RPSP to 1/4 ⇒ result is 3.25
 * 3.25 RPSP to 1/2 ⇒ result is 3.5
 * 3.5 round-half-to-even to 1 ⇒ result is 4 (wrong)

If the erroneous middle step is removed, the final rounding to integer rounds 3.25 to the correct value of 3.

RPSP is implemented in hardware in IBM zSeries and pSeries.

Alternating tie-breaking
One method, more obscure than most, is to alternate direction when rounding a number with 0.5 fractional part. All others are rounded to the closest integer. Whenever the fractional part is 0.5, alternate rounding up or down: for the first occurrence of a 0.5 fractional part, round up, for the second occurrence, round down, and so on. Alternatively, the first 0.5 fractional part rounding can be determined by a random seed. "Up" and "down" can be any two rounding methods that oppose each other - toward and away from positive infinity or toward and away from zero.

If occurrences of 0.5 fractional parts occur significantly more than a restart of the occurrence "counting", then it is effectively bias free. With guaranteed zero bias, it is useful if the numbers are to be summed or averaged.

Random tie-breaking
If the fractional part of $x$ is 0.5, choose $x$ randomly between $y = x − 0.5$ and $x = 2.0$, with equal probability. All others are rounded to the closest integer.

Like round-half-to-even and round-half-to-odd, this rule is essentially free of overall bias, but it is also fair among even and odd $y$ values. An advantage over alternate tie-breaking is that the last direction of rounding on the 0.5 fractional part does not have to be "remembered".

Stochastic rounding
Rounding as follows to one of the closest integer toward negative infinity and the closest integer toward positive infinity, with a probability dependent on the proximity is called stochastic rounding and will give an unbiased result on average.
 * $$\operatorname {Round} (x) = \begin{cases}

\lfloor x \rfloor & \text { with probability } 1 - (x - \lfloor x \rfloor) = \lfloor x \rfloor - x + 1 \\[5mu] \lfloor x \rfloor + 1 & \text { with probability } {x - \lfloor x \rfloor} \end{cases} $$

For example, 1.6 would be rounded to 1 with probability 0.4 and to 2 with probability 0.6.

Stochastic rounding can be accurate in a way that a rounding function can never be. For example, suppose one started with 0 and added 0.3 to that one hundred times while rounding the running total between every addition. The result would be 0 with regular rounding, but with stochastic rounding, the expected result would be 30, which is the same value obtained without rounding. This can be useful in machine learning where the training may use low precision arithmetic iteratively. Stochastic rounding is also a way to achieve 1-dimensional dithering.

Rounding to a specified multiple
The most common type of rounding is to round to an integer; or, more generally, to an integer multiple of some increment – such as rounding to whole tenths of seconds, hundredths of a dollar, to whole multiples of 1/2 or 1/8 inch, to whole dozens or thousands, etc.

In general, rounding a number $x$ to a multiple of some specified positive value $x$ entails the following steps:
 * $$\mathrm{roundToMultiple}(x, m) = \mathrm{round}(x/m) \times m$$

For example, rounding $2.0 < x < 2.5$ dollars to whole cents (i.e., to a multiple of 0.01) entails computing $x = 2.5$, then rounding that to 218, and finally computing $2.5 < x < 3.0$.

When rounding to a predetermined number of significant digits, the increment $y$ depends on the magnitude of the number to be rounded (or of the rounded result).

The increment $y$ is normally a finite fraction in whatever numeral system is used to represent the numbers. For display to humans, that usually means the decimal numeral system (that is, $x$ is an integer times a power of 10, like 1/1000 or 25/100). For intermediate values stored in digital computers, it often means the binary numeral system ($m$ is an integer times a power of 2).

The abstract single-argument "round" function that returns an integer from an arbitrary real value has at least a dozen distinct concrete definitions presented in the rounding to integer section. The abstract two-argument "roundToMultiple" function is formally defined here, but in many cases it is used with the implicit value $x = 3.0$ for the increment and then reduces to the equivalent abstract single-argument function, with also the same dozen distinct concrete definitions.

Rounding to a specified power
Rounding to a specified power is very different from rounding to a specified multiple; for example, it is common in computing to need to round a number to a whole power of 2. The steps, in general, to round a positive number $m$ to a power of some positive number $m$ other than 1, are:
 * $$\mathrm{roundToPower}(x, b) = b^{\mathrm{round}(\log_b x)}, x>0, b>0, b \ne 1$$

Many of the caveats applicable to rounding to a multiple are applicable to rounding to a power.

Scaled rounding
This type of rounding, which is also named rounding to a logarithmic scale, is a variant of rounding to a specified power. Rounding on a logarithmic scale is accomplished by taking the log of the amount and doing normal rounding to the nearest value on the log scale.

For example, resistors are supplied with preferred numbers on a logarithmic scale. In particular, for resistors with a 10% accuracy, they are supplied with nominal values 100, 120, 150, 180, 220, etc. rounded to multiples of 10 (E12 series). If a calculation indicates a resistor of 165 ohms is required then $x + 0.5$, $x − 0.5$ and $x = 2.1784$. The logarithm of 165 is closer to the logarithm of 180 therefore a 180 ohm resistor would be the first choice if there are no other considerations.

Whether a value $2.1784 / 0.01 = 217.84$ rounds to $m$ or $m$ depends upon whether the squared value $218 × 0.01 = 2.18$ is greater than or less than the product $m = 1$. The value 165 rounds to 180 in the resistors example because $log(150) = 2.176$ is greater than $log(165) = 2.217$.

Floating-point rounding
In floating-point arithmetic, rounding aims to turn a given value $x$ into a value $b$ with a specified number of digits. In other words, $a$ should be a multiple of a number $b$ that depends on the magnitude of $x$. The number $y$ is a power of the base (usually 2 or 10) of the floating-point representation.

Apart from this detail, all the variants of rounding discussed above apply to the rounding of floating-point numbers as well. The algorithm for such rounding is presented in the Scaled rounding section above, but with a constant scaling factor $log(180) = 2.255$, and an integer base $x ∈ (a, b)$.

Where the rounded result would overflow the result for a directed rounding is either the appropriate signed infinity when "rounding away from zero", or the highest representable positive finite number (or the lowest representable negative finite number if $y$ is negative), when "rounding toward zero". The result of an overflow for the usual case of round to nearest is always the appropriate infinity.

Rounding to a simple fraction
In some contexts it is desirable to round a given number $m$ to a "neat" fraction – that is, the nearest fraction $x2$ whose numerator $x$ and denominator $m$ do not exceed a given maximum. This problem is fairly distinct from that of rounding a value to a fixed number of decimal or binary digits, or to a multiple of a given unit $x$. This problem is related to Farey sequences, the Stern–Brocot tree, and continued fractions.

Rounding to an available value
Finished lumber, writing paper, capacitors, and many other products are usually sold in only a few standard sizes.

Many design procedures describe how to calculate an approximate value, and then "round" to some standard size using phrases such as "round down to nearest standard value", "round up to nearest standard value", or "round to nearest standard value".

When a set of preferred values is equally spaced on a logarithmic scale, choosing the closest preferred value to any given value can be seen as a form of scaled rounding. Such rounded values can be directly calculated.

Arbitrary bins
More general rounding rules can separate values at arbitrary break points, used for example in data binning. A related mathematically formalized tool is signpost sequences, which use notions of distance other than the simple difference – for example, a sequence may round to the integer with the smallest relative (percent) error.

Dithering and error diffusion
When digitizing continuous signals, such as sound waves, the overall effect of a number of measurements is more important than the accuracy of each individual measurement. In these circumstances, dithering, and a related technique, error diffusion, are normally used. A related technique called pulse-width modulation is used to achieve analog type output from an inertial device by rapidly pulsing the power with a variable duty cycle.

Error diffusion tries to ensure the error, on average, is minimized. When dealing with a gentle slope from one to zero, the output would be zero for the first few terms until the sum of the error and the current value becomes greater than 0.5, in which case a 1 is output and the difference subtracted from the error so far. Floyd–Steinberg dithering is a popular error diffusion procedure when digitizing images.

As a one-dimensional example, suppose the numbers $ab$, $1652 = 27225$, $150 × 180 = 27000$, and $s = 1$ occur in order and each is to be rounded to a multiple of $b > 1$. In this case the cumulative sums, $y = m/n$, $0.9677$, $0.9204$, and $0.7451$, are each rounded to a multiple of $0.3091$: $0.01$, $0.9677$, $1.8881 = 0.9677 + 0.9204$, and $2.6332 = 0.9677 + 0.9204 + 0.7451$. The first of these and the differences of adjacent values give the desired rounded values: $2.9423 = 0.9677 + 0.9204 + 0.7451 + 0.3091$, $0.01$, $0.97$, and $1.89$.

Monte Carlo arithmetic
Monte Carlo arithmetic is a technique in Monte Carlo methods where the rounding is randomly up or down. Stochastic rounding can be used for Monte Carlo arithmetic, but in general, just rounding up or down with equal probability is more often used. Repeated runs will give a random distribution of results which can indicate the stability of the computation.

Exact computation with rounded arithmetic
It is possible to use rounded arithmetic to evaluate the exact value of a function with integer domain and range. For example, if an integer $x$ is known to be a perfect square, its square root can be computed by converting $m$ to a floating-point value $n$, computing the approximate square root $m$ of $n$ with floating point, and then rounding $n$ to the nearest integer $z$. If $x$ is not too big, the floating-point round-off error in $z$ will be less than 0.5, so the rounded value $x$ will be the exact square root of $y$. This is essentially why slide rules could be used for exact arithmetic.

Double rounding
Rounding a number twice in succession to different levels of precision, with the latter precision being coarser, is not guaranteed to give the same result as rounding once to the final precision except in the case of directed rounding. For instance rounding 9.46 to one decimal gives 9.5, and then 10 when rounding to integer using rounding half to even, but would give 9 when rounded to integer directly. Borman and Chatfield discuss the implications of double rounding when comparing data rounded to one decimal place to specification limits expressed using integers.

In Martinez v. Allstate and Sendejo v. Farmers, litigated between 1995 and 1997, the insurance companies argued that double rounding premiums was permissible and in fact required. The US courts ruled against the insurance companies and ordered them to adopt rules to ensure single rounding.

Some computer languages and the IEEE 754-2008 standard dictate that in straightforward calculations the result should not be rounded twice. This has been a particular problem with Java as it is designed to be run identically on different machines, special programming tricks have had to be used to achieve this with x87 floating point. The Java language was changed to allow different results where the difference does not matter and require a strictfp qualifier to be used when the results have to conform accurately; strict floating point has been restored in Java 17.

In some algorithms, an intermediate result is computed in a larger precision, then must be rounded to the final precision. Double rounding can be avoided by choosing an adequate rounding for the intermediate computation. This consists in avoiding to round to midpoints for the final rounding (except when the midpoint is exact). In binary arithmetic, the idea is to round the result toward zero, and set the least significant bit to 1 if the rounded result is inexact; this rounding is called sticky rounding. Equivalently, it consists in returning the intermediate result when it is exactly representable, and the nearest floating-point number with an odd significand otherwise; this is why it is also known as rounding to odd. A concrete implementation of this approach, for binary and decimal arithmetic, is implemented as Rounding to prepare for shorter precision.

Table-maker's dilemma
William M. Kahan coined the term "The Table-Maker's Dilemma" for the unknown cost of rounding transcendental functions: "Nobody knows how much it would cost to compute $2.63$ correctly rounded for two floating-point arguments at which it does not over/underflow. Instead, reputable math libraries compute elementary transcendental functions mostly within slightly more than half an ulp and almost always well within one ulp. Why can't $2.94$ be rounded within half an ulp like SQRT? Because nobody knows how much computation it would cost... No general way exists to predict how many extra digits will have to be carried to compute a transcendental expression and round it to some preassigned number of digits. Even the fact (if true) that a finite number of extra digits will ultimately suffice may be a deep theorem."

The IEEE 754 floating-point standard guarantees that add, subtract, multiply, divide, fused multiply–add, square root, and floating-point remainder will give the correctly rounded result of the infinite-precision operation. No such guarantee was given in the 1985 standard for more complex functions and they are typically only accurate to within the last bit at best. However, the 2008 standard guarantees that conforming implementations will give correctly rounded results which respect the active rounding mode; implementation of the functions, however, is optional.

Using the Gelfond–Schneider theorem and Lindemann–Weierstrass theorem, many of the standard elementary functions can be proved to return transcendental results, except on some well-known arguments; therefore, from a theoretical point of view, it is always possible to correctly round such functions. However, for an implementation of such a function, determining a limit for a given precision on how accurate results need to be computed, before a correctly rounded result can be guaranteed, may demand a lot of computation time or may be out of reach. In practice, when this limit is not known (or only a very large bound is known), some decision has to be made in the implementation (see below); but according to a probabilistic model, correct rounding can be satisfied with a very high probability when using an intermediate accuracy of up to twice the number of digits of the target format plus some small constant (after taking special cases into account).

Some programming packages offer correct rounding. The GNU MPFR package gives correctly rounded arbitrary precision results. Some other libraries implement elementary functions with correct rounding in IEEE 754 double precision (binary64):
 * IBM's ml4j, which stands for Mathematical Library for Java, written by Abraham Ziv and Moshe Olshansky in 1999, correctly rounded to nearest only. This library was claimed to be portable, but only binaries for PowerPC/AIX, SPARC/Solaris and x86/Windows NT were provided. According to its documentation, this library uses a first step with an accuracy a bit larger than double precision, a second step based on double-double arithmetic, and a third step with a 768-bit precision based on arrays of IEEE 754 double-precision floating-point numbers.
 * IBM's Accurate portable mathematical library (abbreviated as APMathLib or just MathLib), also called libultim, in rounding to nearest only. This library uses up to 768 bits of working precision. It was included in the GNU C Library in 2001, but the "slow paths" (providing correct rounding) were removed from 2018 to 2021.
 * CRlibm, written in the old Arénaire team (LIP, ENS Lyon), first distributed in 2003. It supports the 4 rounding modes and is proved, using the knowledge of the hardest-to-round cases. More efficient than IBM MathLib. Succeeded by Metalibm (2014), which automates the formal proofs.
 * Sun Microsystems's libmcr of 2004, in the 4 rounding modes. For the difficult cases, this library also uses multiple precision, and the number of words is increased by 2 each time the Table-maker's dilemma occurs (with undefined behavior in the very unlikely event that some limit of the machine is reached).
 * The CORE-MATH project (2022) provides some correctly rounded functions in the 4 rounding modes for x86-64 processors. Proved using the knowledge of the hardest-to-round cases.
 * LLVM libc provides some correctly rounded functions in the 4 rounding modes.

There exist computable numbers for which a rounded value can never be determined no matter how many digits are calculated. Specific instances cannot be given but this follows from the undecidability of the halting problem. For instance, if Goldbach's conjecture is true but unprovable, then the result of rounding the following value, $n$, up to the next integer cannot be determined: either $x$=1+10−$y$ where $n$ is the first even number greater than 4 which is not the sum of two primes, or $n$=1 if there is no such number. The rounded result is 2 if such a number $n$ exists and 1 otherwise. The value before rounding can however be approximated to any given precision even if the conjecture is unprovable.

Interaction with string searches
Rounding can adversely affect a string search for a number. For example, π rounded to four digits is "3.1416" but a simple search for this string will not discover "3.14159" or any other value of π rounded to more than four digits. In contrast, truncation does not suffer from this problem; for example, a simple string search for "3.1415", which is π truncated to four digits, will discover values of π truncated to more than four digits.

History
The concept of rounding is very old, perhaps older than the concept of division itself. Some ancient clay tablets found in Mesopotamia contain tables with rounded values of reciprocals and square roots in base 60. Rounded approximations to π, the length of the year, and the length of the month are also ancient – see base 60 examples.

The round-half-to-even method has served as American Standard Z25.1 and ASTM standard E-29 since 1940. The origin of the terms unbiased rounding and statistician's rounding are fairly self-explanatory. In the 1906 fourth edition of Probability and Theory of Errors Robert Simpson Woodward called this "the computer's rule", indicating that it was then in common use by human computers who calculated mathematical tables. For example, it was recommended in Simon Newcomb's c. 1882 book Logarithmic and Other Mathematical Tables. Lucius Tuttle's 1916 Theory of Measurements called it a "universally adopted rule" for recording physical measurements. Churchill Eisenhart indicated the practice was already "well established" in data analysis by the 1940s.

The origin of the term bankers' rounding remains more obscure. If this rounding method was ever a standard in banking, the evidence has proved extremely difficult to find. To the contrary, section 2 of the European Commission report The Introduction of the Euro and the Rounding of Currency Amounts suggests that there had previously been no standard approach to rounding in banking; and it specifies that "half-way" amounts should be rounded up.

Until the 1980s, the rounding method used in floating-point computer arithmetic was usually fixed by the hardware, poorly documented, inconsistent, and different for each brand and model of computer. This situation changed after the IEEE 754 floating-point standard was adopted by most computer manufacturers. The standard allows the user to choose among several rounding modes, and in each case specifies precisely how the results should be rounded. These features made numerical computations more predictable and machine-independent, and made possible the efficient and consistent implementation of interval arithmetic.

Currently, much research tends to round to multiples of 5 or 2. For example, Jörg Baten used age heaping in many studies, to evaluate the numeracy level of ancient populations. He came up with the ABCC Index, which enables the comparison of the numeracy among regions possible without any historical sources where the population literacy was measured.

Rounding functions in programming languages
Most programming languages provide functions or special syntax to round fractional numbers in various ways. The earliest numeric languages, such as FORTRAN and C, would provide only one method, usually truncation (toward zero). This default method could be implied in certain contexts, such as when assigning a fractional number to an integer variable, or using a fractional number as an index of an array. Other kinds of rounding had to be programmed explicitly; for example, rounding a positive number to the nearest integer could be implemented by adding 0.5 and truncating.

In the last decades, however, the syntax and the standard libraries of most languages have commonly provided at least the four basic rounding functions (up, down, to nearest, and toward zero). The tie-breaking method can vary depending on the language and version or might be selectable by the programmer. Several languages follow the lead of the IEEE 754 floating-point standard, and define these functions as taking a double-precision float argument and returning the result of the same type, which then may be converted to an integer if necessary. This approach may avoid spurious overflows because floating-point types have a larger range than integer types. Some languages, such as PHP, provide functions that round a value to a specified number of decimal digits (e.g., from 4321.5678 to 4321.57 or 4300). In addition, many languages provide a printf or similar string formatting function, which allows one to convert a fractional number to a string, rounded to a user-specified number of decimal places (the precision). On the other hand, truncation (round to zero) is still the default rounding method used by many languages, especially for the division of two integer values.

In contrast, CSS and SVG do not define any specific maximum precision for numbers and measurements, which they treat and expose in their DOM and in their IDL interface as strings as if they had infinite precision, and do not discriminate between integers and floating-point values; however, the implementations of these languages will typically convert these numbers into IEEE 754 double-precision floating-point values before exposing the computed digits with a limited precision (notably within standard JavaScript or ECMAScript interface bindings).

Other rounding standards
Some disciplines or institutions have issued standards or directives for rounding.

US weather observations
In a guideline issued in mid-1966, the U.S. Office of the Federal Coordinator for Meteorology determined that weather data should be rounded to the nearest round number, with the "round half up" tie-breaking rule. For example, 1.5 rounded to integer should become 2, and −1.5 should become −1. Prior to that date, the tie-breaking rule was "round half away from zero".

Negative zero in meteorology
Some meteorologists may write "−0" to indicate a temperature between 0.0 and −0.5 degrees (exclusive) that was rounded to an integer. This notation is used when the negative sign is considered important, no matter how small is the magnitude; for example, when rounding temperatures in the Celsius scale, where below zero indicates freezing.

title: Rounding