text:
Multiply–accumulate operation

In computing, especially digital signal processing, the multiply–accumulate (MAC) or multiply-add (MAD) operation is a common step that computes the product of two numbers and adds that product to an accumulator. The hardware unit that performs the operation is known as a multiplier–accumulator (MAC unit); the operation itself is also often called a MAC or a MAD operation. The MAC operation modifies an accumulator a: $$ a \gets a + ( b \times c )$$

When done with floating-point numbers, it might be performed with two roundings (typical in many DSPs), or with a single rounding. When performed with a single rounding, it is called a fused multiply–add (FMA) or fused multiply–accumulate (FMAC).

Modern computers may contain a dedicated MAC, consisting of a multiplier implemented in combinational logic followed by an adder and an accumulator register that stores the result. The output of the register is fed back to one input of the adder, so that on each clock cycle, the output of the multiplier is added to the register. Combinational multipliers require a large amount of logic, but can compute a product much more quickly than the method of shifting and adding typical of earlier computers. Percy Ludgate was the first to conceive a MAC in his Analytical Machine of 1909, and the first to exploit a MAC for division (using multiplication seeded by reciprocal, via the convergent series $(1+x)^{−1}$). The first modern processors to be equipped with MAC units were digital signal processors, but the technique is now also common in general-purpose processors.

In floating-point arithmetic
When done with integers, the operation is typically exact (computed modulo some power of two). However, floating-point numbers have only a certain amount of mathematical precision. That is, digital floating-point arithmetic is generally not associative or distributive. (See .) Therefore, it makes a difference to the result whether the multiply–add is performed with two roundings, or in one operation with a single rounding (a fused multiply–add). IEEE 754-2008 specifies that it must be performed with one rounding, yielding a more accurate result.

Fused multiply–add
A fused multiply–add (FMA or fmadd) is a floating-point multiply–add operation performed in one step (fused operation), with a single rounding. That is, where an unfused multiply–add would compute the product $b × c$, round it to N significant bits, add the result to a, and round back to N significant bits, a fused multiply–add would compute the entire expression $a + (b × c)$ to its full precision before rounding the final result down to N significant bits.

A fast FMA can speed up and improve the accuracy of many computations that involve the accumulation of products:

 * Dot product
 * Matrix multiplication
 * Polynomial evaluation (e.g., with Horner's rule)
 * Newton's method for evaluating functions (from the inverse function)
 * Convolutions and artificial neural networks
 * Multiplication in double-double arithmetic

Fused multiply–add can usually be relied on to give more accurate results. However, William Kahan has pointed out that it can give problems if used unthinkingly. If $x^{2} − y^{2}$ is evaluated as $((x × x) − y × y)$ (following Kahan's suggested notation in which redundant parentheses direct the compiler to round the $(x × x)$ term first) using fused multiply–add, then the result may be negative even when $x = y$ due to the first multiplication discarding low significance bits. This could then lead to an error if, for instance, the square root of the result is then evaluated.

When implemented inside a microprocessor, an FMA can be faster than a multiply operation followed by an add. However, standard industrial implementations based on the original IBM RS/6000 design require a 2N-bit adder to compute the sum properly.

Another benefit of including this instruction is that it allows an efficient software implementation of division (see division algorithm) and square root (see methods of computing square roots) operations, thus eliminating the need for dedicated hardware for those operations.

Dot product instruction
Some machines combine multiple fused multiply add operations into a single step, e.g. performing a four-element dot-product on two 128-bit SIMD registers  with single cycle throughput.

Support
The FMA operation is included in IEEE 754-2008.

The Digital Equipment Corporation (DEC) VAX's  instruction is used for evaluating polynomials with Horner's rule using a succession of multiply and add steps. Instruction descriptions do not specify whether the multiply and add are performed using a single FMA step. This instruction has been a part of the VAX instruction set since its original 11/780 implementation in 1977.

The 1999 standard of the C programming language supports the FMA operation through the  standard math library function and the automatic transformation of a multiplication followed by an addition (contraction of floating-point expressions), which can be explicitly enabled or disabled with standard pragmas (#pragma STDC FP_CONTRACT). The GCC and Clang C compilers do such transformations by default for processor architectures that support FMA instructions. With GCC, which does not support the aforementioned pragma, this can be globally controlled by the  command line option.

The fused multiply–add operation was introduced as "multiply–add fused" in the IBM POWER1 (1990) processor, but has been added to numerous other processors since then:

 * HP PA-8000 (1996) and above
 * Hitachi SuperH SH-4 (1998)
 * SCE-Toshiba Emotion Engine (1999)
 * Intel Itanium (2001)
 * STI Cell (2006)
 * Fujitsu SPARC64 VI (2007) and above
 * (MIPS-compatible) Loongson-2F (2008)
 * Elbrus-8SV (2018)
 * x86 processors with FMA3 and/or FMA4 instruction set
 * AMD Bulldozer (2011, FMA4 only)
 * AMD Piledriver (2012, FMA3 and FMA4)
 * AMD Steamroller (2014)
 * AMD Excavator (2015)
 * AMD Zen (2017, FMA3 only)
 * Intel Haswell (2013, FMA3 only)
 * Intel Skylake (2015, FMA3 only)
 * ARM processors with VFPv4 and/or NEONv2:
 * ARM Cortex-M4F (2010)
 * STM32 Cortex-M33 (VFMA operation)
 * ARM Cortex-A5 (2012)
 * ARM Cortex-A7 (2013)
 * ARM Cortex-A15 (2012)
 * Qualcomm Krait (2012)
 * Apple A6 (2012)
 * All ARMv8 processors
 * Fujitsu A64FX has "Four-operand FMA with Prefix Instruction".
 * IBM z/Architecture (since 1998)
 * GPUs and GPGPU boards:
 * AMD GPUs (2009) and newer
 * TeraScale 2 "Evergreen"-series based
 * Graphics Core Next-based
 * Nvidia GPUs (2010) and newer
 * Fermi-based (2010)
 * Kepler-based (2012)
 * Maxwell-based (2014)
 * Pascal-based (2016)
 * Volta-based (2017)
 * Intel GPUs since Sandy Bridge
 * Intel MIC (2012)
 * ARM Mali T600 Series (2012) and above
 * Vector Processors:
 * NEC SX-Aurora TSUBASA
 * RISC-V instruction set (2010)

title: Multiply–accumulate operation


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Talk:.coop

Swiss retailer Coop
Coop is one of the biggest retailers in Switzerland. I expect a lawsuit. — Preceding unsigned comment added by 46.253.186.62 (talk) 11:16, 21 October 2016 (UTC)

Comments
The formatting suggests that this text is not original. Anyone know from where it originates? — Sverdrup (talk) 01:12, 17 Dec 2003 (UTC)

Operator of the registry
The primary sources themselves seem to conflict:

nic.coop says that the registry is operated by Poptel.

However, the MCD home page says that they operate it (as does this site )

MCD (part of Midcounties Co-operative) seems to be a successor of part of the former Poptel business, so I am going with that as the most recent. --Hroðulf (or Hrothulf) (Talk) 15:56, 3 November 2006 (UTC)

 * A whois lookup of nic.coop on whois.nic.coop lists it as registered by Midcounties Co-operative. So it looks as though they just forgot to update the about page. --Zundark 23:02, 3 November 2006 (UTC)

Sponsored top level domain?
If .coop is a sponsored top-level domain then why is not listed in the article Sponsored top-level domain? Mike R (talk) 19:24, 22 January 2009 (UTC)

 * Good point. Done. --Hroðulf (or Hrothulf) (Talk) 16:33, 24 January 2009 (UTC)

External links modified
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title: Talk:.coop


text:
Hatton Garden

Hatton Garden is a street and commercial zone in the Holborn district of the London Borough of Camden, abutting the narrow precinct of Saffron Hill which then abuts the City of London. It takes its name from Sir Christopher Hatton, a favourite of Queen Elizabeth I, who established a mansion here and gained possession of the garden and orchard of Ely Place, the London seat of the Bishops of Ely. It remained in the Hatton family and was built up as a stylish residential development in the reign of King Charles II. For some decades it often went, outside of the main street, by an alternative name St Alban's Holborn, after the local church built in 1861.

St Etheldreda's Church in Ely Place, all that survives of the old Bishop's Palace, is one of only two remaining buildings in London dating from the reign of Edward I. It is one of the oldest churches in England now in use for Roman Catholic worship, which was re-established there in 1879. The red-brick building now known as Wren House, at the south-east corner of Hatton Garden and St Cross Street, was the Anglican church for the Hatton Garden development. It was taken over by the authorities of a charity school, and the statues of a boy and girl in uniform were then added.

Hatton Garden is London's jewellery quarter and the centre of the diamond trade in the United Kingdom. This specialisation grew up in the early 19th century, spreading out from its more ancient centre in nearby Clerkenwell. Today there are nearly 300 businesses here in the jewellery industry and over 90 shops, representing the largest cluster of jewellery retailers in the UK. The largest of these businesses was De Beers, the international family of companies which dominated the international diamond trade. Their headquarters were in an office and warehouse complex just behind the main Hatton Garden shopping street.

Sir Hiram Maxim had a small factory at 57 Hatton Garden and in 1881, invented and started to produce the Maxim Gun, a prototype machine gun, capable of firing 666 rounds a minute. Hatton Garden has an extensive underground infrastructure of vaults, tunnels, offices and workshops. The area is now home to many media, publishing and creative businesses, including Blinkbox and Grey Advertising. Surrounding streets including Hatton Place and Saffron Hill (the insalubrious setting for Fagin's den in Oliver Twist) were improved during the 20th century and in modern times have been developed with blocks of 'luxury' apartments, including Da Vinci House (occupying the former Punch magazine printworks) and the architecturally distinctive Ziggurat Building.

Hatton Garden development, 1659–1694
The Hatton Garden area between Leather Lane in the west and Saffron Hill in the east, and from Holborn in the south to Hatton Wall in the north, was developed as a new residential district in the Restoration period, between 1659 and 1694. It arose soon after the residential developments in Covent Garden and was contemporary with those of Bloomsbury Square.

It was formerly the site of the medieval palace, gardens and orchard of the Bishops of Ely, forming their City residence. The palace stood in the southeast corner, on the site of Ely Place. During the 1570s Queen Elizabeth's Chancellor and favourite, Sir Christopher Hatton, held a lease of part of the site and developed Hatton House to the northwest of the palace. In 1581, he obtained a more permanent grant from Queen Elizabeth during a vacancy in the see, and after his death, it passed into the possession of Lady Elizabeth Hatton, the widow of Sir Christopher's nephew Sir William Newport (who changed his name to Hatton). At her death in 1646, during the English Civil War, it reverted to Christopher Hatton, 1st Baron Hatton, a close associate of Charles II in his exile in Paris during the Commonwealth period, 1649–1660.

The bishops disputed the Hattons' title, but, under the Protectorate, Bishop Matthew Wren was a prisoner in the Tower of London, and the palace itself was sequestrated to Parliamentarian uses and was badly damaged. To raise money Lord Hatton granted a long lease of the site in 1654, which became effectively permanent in 1658, though he retained the freehold. In 1659, John Evelyn observed Hatton Street (Hatton Garden road) being laid out from south to north, hard against the west side of the palace, as the beginning of a newly planned town district. Speculative builders took leases to construct tall and spacious adjoining houses to attract wealthy men at court, city officials and country gentlefolk wanting London homes, convenient for Clerkenwell and the Inns of Court. In this way a varied but harmonious townscape, with attractive detail of porches and interior panelling, grew up on a rectangular grid of new streets. Charles Street (at first called Cross Street) was laid west to east as a continuation of Greville Street, and the Bishops' orchard, which (as shown in Richard Newcourt's map of 1658) the Hattons had laid out as a walled knot garden with a central fountain, lay north of that up to Hatton Wall. Hatton Street followed the line of its central path. By 1666, the year of the Great Fire, the development had advanced north to form two principal blocks up to the line of St Cross Street (then called Little Kirby Street). The remaining open land was used as a refuge by Londoners escaping the Fire, which did not consume Hatton Garden.

After Lord Hatton's death in 1670, the northern sector up to Hatton Wall was completed by 1694, in the time of his son Sir Christopher Hatton, 1st Viscount Hatton, whose agent was the noted accountant Stephen Monteage (1623–1687). Work on the Hatton Street church (now Wren House) commenced in 1685–86. Great Kirby Street, parallel to Hatton Street on the east side, enclosed a central block with rear gardens backing, but in the northern sectors, Hatt and Tunn Yard on the east (on the site of Hatton Place) and other small yards on the west provided access to smaller dwellings and coach houses. In the southern sectors King's Head Yard (later Robin Wood Yard, Robin Hood Yard) was similarly enclosed to the west, and to the east Bleeding Heart Yard (Arlidge's Yard, with Union Court ) was developed near the palace by Abraham Arlidge (1645–1717), a carpenter of Kenilworth (Warwickshire) origins who worked extensively on the project and made his fortune by judicious investments. Arlidge's survey of 1694 shows the completed estate in detail: he succeeded Sir John Cass as Master of the Worshipful Company of Carpenters in 1712.

Among early residents were Christopher Merret, Robert Ferguson, John Flamsteed, William Whiston and Captain Thomas Coram.

Later the Hatton Garden estate was inherited by George Finch-Hatton esq (great grandson of the 1st Viscount Hatton). He sold it in 1780s and had received around £100,000 and was to receive even more money as it sold further.

Crime
A "Great Robbery in Hatton Garden" occurred in late December 1678, when twenty men turned up at the house of a wealthy gentleman claiming to have a warrant to search the house for dangerous persons. After letting them in the owner asked to see the search warrant, whereupon he was forced at gunpoint into an inner room and locked in while the intruders rifled the house of its valuables. However, someone managed to escape and raised the alarm, and the thieves made a run for it. They were apprehended two days later while trying to dispose of the stolen property, which was recovered. George Brown, John Butler, Richard Mills, Christopher Bruncker and George Kenian were hanged at Tyburn for the offence on 22 January 1678/9.

In 1685, the notorious informer and confidence trickster Thomas Dangerfield, who was being returned to prison after a public whipping, was killed in Hatton Garden in an altercation with a barrister called Robert  Francis, who struck him in the eye with his cane. Rather to the surprise of the general public, who thought the killing was an accident, Francis was convicted of murder and hanged.

In July 1993, thieves stole £7 million worth of gems belonging to the jewellers Graff Diamonds. This was London's biggest gem heist of modern times.

In April 2015, an underground safe deposit facility in the Hatton Garden area was burgled in the Hatton Garden safe deposit burglary. The total stolen may have had a value of up to £200 million, although court reports referred to £14 million The theft was investigated by the Flying Squad, a branch of the Specialist, Organised & Economic Crime Command within London's Metropolitan Police Service, leading to the arrests and March 2016 convictions of seven perpetrators.

Street name etymologies
This is a list of the etymology of street names in the London district of Hatton Garden. Its area has no formally defined boundaries – those used here are the generally accepted ones of Clerkenwell Road to the north, Farringdon Road to the east, Holborn and Charterhouse Street to the south and Gray's Inn road to the west.

 * Baldwins Gardens – from Richard Baldwin (or Baldwyn), gardener to Queen Elizabeth I and treasurer of the Middle Temple, who owned property in the area in the 16th century
 * Beauchamp Street – from Beauchamp Court, the Warwickshire birthplace of Fulke Greville, 1st Baron Brooke, local property owner
 * Black Bull Yard – unknown; this yard has now largely been covered by shop developments and is not accessible to the public
 * Bleeding Heart Yard – thought to be from the sign of a former pub in this area called the Bleeding Heart
 * Brooke Street, Brooke's Court and Brooke's Market – after Fulke Greville, 1st Baron Brooke, who owned a house near here in the 17th century
 * Charterhouse Street – Anglicisation of "Chartreuse", from Grande Chartreuse, head monastery of the Carthusians in France. A nearby abbey was founded by monks of this order in 1371
 * Clerkenwell Road – from a local well (the clerk's well), which gave its name to the area to this district.
 * Dorrington Street – corruption of ‘Doddington’, from Anne Doddington, wife of Robert Grenville who owned a house near here in the 17th century
 * Ely Court and Ely Place – after the Bishops of Ely, Cambridgeshire who owned much of this area prior to 1659
 * Farringdon Road – from Sir William or Nicholas de Farnedon/Faringdon, local sheriffs or aldermen in the 13th century
 * Gray's Inn Road – from Lord Gray of Wilton, owner of a local inn or townhouse which was later leased to lawyers in the 16th century
 * Greville Street – from Fulke Greville, 1st Baron Brooke, who owned a house near here in the 17th century
 * Hatton Garden, Hatton Place and Hatton Wall – from Sir Christopher Hatton, who was ceded much of this area from the Bishops of Ely by Elizabeth I in 1577–1580
 * Holborn – thought to be from ‘hollow bourne’ i.e. the river Fleet which formerly flowed in a valley near here
 * Kirby Street – from Christopher Hatton's Kirby Hall in Northamptonshire
 * Leather Lane – thought to come not from ‘leather’ but from Leofrun, a personal name in Old English; formerly known as Le Vrunelane (13th century), Loverone Lane (14th century) and Liver Lane
 * Leigh Place – from the Barons Leigh, who bought land in the area from the Baldwin family in 1689
 * Lily Place
 * Onslow Street
 * Portpool Lane – thought to be a corruption of ‘Purta's Pool’, the local area is recorded as the manor of Purtepol in the early 13th century; written "Purple Lane" in Arlidge's Survey
 * Saffron Hill and Saffron Street – these used to be the gardens of the Bishops of Ely, where they grew saffron
 * St Cross Street – originally Cross Street, as it crossed land belonging to the Hatton family; the ‘St’ was added in 1937 to avoid confusion with numerous streets of the same name
 * Verulam Street – from 16th–17th-century lawyer, scientist and philosopher Francis Bacon, later created Baron Verulam, who had chambers at Gray's Inn opposite
 * Viaduct Buildings – after their position directly adjacent to Holborn Viaduct
 * Waterhouse Square – after Alfred Waterhouse, architect of Holborn Bars, also known as the Prudential Assurance Building, which surrounds the square

Hatton Garden in fiction
Michael Flanders and Donald Swann, humorists in the 1960s and 1970s, celebrated Hatton Garden's connection with the jewellery trade in their song of a sewage worker, "Down Below":
 * Hatton Garden is the spot, down below
 * Where we likes to go a lot, down below,
 * Since a bloke from Leather Lane,
 * Dropped a diamond down the drain,
 * We'll be going there again, down below.

In Evelyn Waugh's novel Brideshead Revisited, Rex Mottram takes Julia Marchmain to a dealer in Hatton Garden to buy her engagement ring:

"He bought her a ring, not, as she expected, from a tray in Cartier's, but in a back room in Hatton Garden from a man who brought stones out of a bag in a little safe...then another man in another back room made designs for the setting with a stub of a pencil on a sheet of notepaper, and the result excited the admiration of all her friends."

Hatton Garden features in the children's novel Smith by Leon Garfield, where the main character tries to elude two pursuers through the crumbling streets of 18th-century Holborn.

In Ian Fleming's novel Diamonds Are Forever, James Bond visits the fictional House of Diamonds in Hatton Garden, where he meets the mysterious Rufus B. Saye.

The name of the street appears in a series of books Poldark by Winston Graham. (part 4 - 'Warleggan')

The Avengers, Series 2, Episode 10, "Death on the Rocks," is set in the diamond business in Hatton Garden.

The diamond robbery in the film A Fish Called Wanda takes place in Hatton Garden.

The 1924 mystery novel Inspector French's Greatest Case by Freeman Wills Crofts takes place in and around Hatton Garden.

title: Hatton Garden


text:
List of film awards

This is a list of groups, organizations, and festivals that recognize achievements in cinema, usually by awarding various prizes. The awards sometimes also have popular unofficial names (such as the "Oscar" for Hollywood's Academy Awards), which are mentioned if applicable. Many awards are simply identified by the name of the group presenting the award.

Awards have been divided into four major categories: critics' awards, voted on (usually annually) by a group of critics; festival awards, awards presented to the best film shown in a particular film festival; industry awards, which are selected by professionals working in some branch of the movie industry; and audience awards, which are voted by the general public.

International

 * FIPRESCI (Fédération Internationale de la PRESse CInématographique) Awards, given by the international Film Critics at various film festivals
 * African Federation of Film Critics (FACC) : Paulin Soumanou Vieyra Awards at various african film festivals
 * Venice Film Festival is the longest running film festival in Europe and among the most prestigious in the world with its prestigious prize Golden Lion.
 * Cannes Film Festival is one of the most important and selective film festivals with its prestigious prize the Palme d'Or.
 * OFCS (Online Film Critics Society) Awards
 * Hollywood Foreign Press Association
 * Golden Globe Awards

Argentina

 * Asociación de Cronistas Cinematográficos de la Argentina
 * Premios Cóndor de Plata
 * Premios Clarín Espectáculos
 * Konex Awards

Australia

 * ATOM Awards
 * Australian Film Critics Association (AFCA)
 * AWGIE Awards (AWG)
 * Film Critics Circle of Australia (FCCA)
 * Inside Film Awards (IF Awards)
 * South Australian Screen Awards
 * Western Union Short Film Competition

Bangladesh

 * Meril Prothom Alo Awards
 * National Film Awards

Belgium

 * Belgian Film Critics Association (UCC)

Brazil

 * Festival de Gramado
 * Grande Prêmio do Cinema Brasileiro

Canada

 * Toronto Film Critics Association (TFCA)
 * Vancouver Film Critics Circle (VFCC)

Czech Republic

 * Czech Film Critics' Awards
 * Trilobit Awards
 * Bohemia Film Awards(BOFA)

Denmark

 * Bodil Awards from Danish Film Critics Association
 * Lauritzen Award

France

 * Etoiles du Parisien
 * French Syndicate of Cinema Critics
 * Globes de Cristal Award
 * Louis Delluc Prize
 * Paris Film Critics Association Awards

Germany

 * Award of the German Film Critics Association (Preis der deutschen Filmkritik)

Hong Kong

 * Hong Kong Film Critics Society Awards

India

 * Aravindan Puraskaram
 * Asianet Film Awards
 * Bengal Film Journalists' Association Awards
 * Bhojpuri Film Awards
 * CineMAA Awards
 * Cinema Express Awards
 * Edison Tamil Awards
 * Dadasaheb Phalke Award
 * Filmfare Awards
 * Filmfare Awards East
 * Filmfare Awards South
 * Filmfare Marathi Awards
 * Filmfare Short Film Awards
 * IIFA Utsavam
 * International Indian Film Academy Awards
 * John Abraham Award
 * Karnataka State Film Award
 * Kerala Film Critics Association Awards
 * Kerala State Film Awards
 * Maharashtra State Film Awards
 * Nandi Awards
 * National Film Awards (Directorate of Film Festivals)
 * Odisha State Film Awards
 * Padmarajan Award
 * Prag Cine Awards
 * Rajasthan Film Festival
 * RED FM Tulu Film Awards
 * Santosham Film Awards
 * SIIMA Short Film Awards
 * Screen Awards
 * South Indian International Movie Awards
 * Stardust Awards
 * Tamil Nadu State Film Awards
 * Udaya Film Awards
 * Vanitha Film Awards
 * Vijay Awards
 * West Bengal Film Journalists' Association Awards
 * Zee Cine Awards
 * Zee Cine Awards Telugu

Indonesia

 * Citra Awards
 * Maya Awards

Ireland

 * Dublin Film Critics' Circle

Italy

 * Nastro d'Argento
 * Globo d'oro
 * David di Donatello

Japan

 * Japanese Movie Critics Awards

Lebanon

 * The Lebanese Cinema Movie Guide Awards

Mexico

 * Ariel Award
 * Diosas de Plata

Myanmar

 * Myanmar Motion Picture Academy Awards
 * Star Awards

Malaysia

 * Kuala Lumpur Film Critics Council Awards (Anugerah Majlis Pengkritik Filem Kuala Lumpur)
 * Kuala Lumpur Film Critics Council Awards (Anugerah Majlis Pengkritik Filem Kuala Lumpur)
 * Kuala Lumpur Film Critics Council Awards (Anugerah Majlis Pengkritik Filem Kuala Lumpur)

Nigeria

 * Africa Magic Viewers' Choice Awards
 * Africa Movie Academy Awards

Pakistan

 * ARY Film Awards

Philippines

 * Gawad Urian
 * Young Critics Circle Film Desk Awards
 * Gawad PASADO
 * Gawad TANGLAW
 * Gawad Genio Awards
 * The Entertainment Editors' Choice Awards

Portugal

 * Golden Globes (Portugal)

South Africa

 * National Film and TV Awards (NFTA) South Africa

South Korea

 * Korean Association of Film Critics Awards
 * Busan Film Critics Awards

Spain

 * CEC Medals
 * Feroz Awards
 * Fotogramas de Plata
 * Sant Jordi Awards

Turkey

 * SIYAD Awards of Turkish Film Critics Association (SİYAD)
 * Flying Broom International Women's Film Festival (Uçan Süpürge Kadın Filmleri Festivali)
 * International Adana Golden Boll Film Festival (Adana Altın Koza Film Festivali)
 * International Adana Film Festival (Uluslararası Adana Film Festivali)
 * Istanbul Animation Festival (İstanbul Animasyon Festivali)

United Kingdom

 * ODEON National Youth Film Awards
 * National Film Awards UK
 * Evening Standard British Film Awards
 * London Film Critics Circle
 * National Movie Awards
 * Film Critics Association UK
 * Charity Film Awards

United States

 * Alliance of Women Film Journalists
 * American Film Institute (AFI)
 * Atlanta Film Critics Circle (AFCC)
 * Austin Film Critics Association (AFCA)
 * Black Film Critics Circle (BFCC)
 * Boston Online Film Critics Association
 * Boston Society of Film Critics (BSFC)
 * Broadcast Film Critics Association (BFCA)
 * Chicago Film Critics Association (CFCA)
 * Chicago Indie Critics (CIC)
 * Columbus Film Critics Association
 * Critics Association Of Central Florida
 * Critics' Choice Movie Awards
 * Critics' Choice Super Awards
 * Dallas-Fort Worth Film Critics Association (DFWFCA)
 * Denver Film Critics Society
 * Detroit Film Critics Society
 * DiscussingFilm Critic Awards (DFCA)
 * Florida Film Critics Circle (FFCC)
 * Georgia Film Critics Association (GFCA)
 * Golden Raspberry Awards (a.k.a. the Razzies)
 * Gotham Awards
 * Greater Western New York Film Critics Association (GWNYFCA)
 * Hawaii Film Critics Society
 * Hawaii International Film Festival (HIFF)
 * Houston Film Critics Society (HFCS)
 * Indiana Film Journalists Association
 * Iowa Film Critics Association
 * Kansas City Film Critics Circle
 * Las Vegas Film Critics Society
 * LAIFFA Awards (Los Angeles Independent Film Festivals)
 * Latino Entertainment Journalists Association (LEJA)
 * Los Angeles Film Critics Association (LAFCA)
 * Maverick Movie Awards (MMA)
 * Michigan Movie Critics Guild
 * Minnesota Film Critics Alliance (MNFCA)
 * Music City Film Critics Association
 * National Film and TV Awards USA
 * National Society of Film Critics (NSFC)
 * National Board of Review (NBR)
 * Nevada Film Critics Society
 * New Mexico Film Critics
 * New York Film Critics Circle (NYFCC)
 * New York Film Critics Online (NYFCO)
 * New York Film Awards
 * New York Movie Awards
 * Nollywood and African Film Critics Awards (NAFCA)
 * North Carolina Film Critics Association
 * North Dakota Film Society (NDFS)
 * North Texas Film Critics Association (NTFCA)
 * NYU Tisch School of the Arts Wasserman Award
 * Oklahoma Film Critics Circle
 * Online Association of Female Film Critics
 * Online Film Critics Society Awards (OFCS)
 * Online Film & Television Association
 * Philadelphia Film Critics Circle Awards (PFCC)
 * Phoenix Critics Circle (PCC)
 * Phoenix Film Critics Society
 * Political Film Society (PFS)
 * Portland Critics Association
 * Producers Guild of America (PGA)
 * San Diego Film Critics Society (SDFCS)
 * San Francisco Film Critics Circle (SFFCC)
 * Seattle Film Critics Society (SFCS)
 * Southeastern Film Critics Association (SEFCA)
 * St. Louis Gateway Film Critics Association (SLGFCA)
 * Sunset Circle Awards (SCA)
 * Utah Film Critics Association
 * Village Voice Film Poll
 * Washington D.C. Area Film Critics Association (WAFCA)
 * World Film Communities Network (WFCN)
 * Women Film Critics Circle
 * X-Rated Critics Organization (XRCO) Heart-On Awards

Uruguay

 * Uruguayan Film Critics Association Awards 2001

Vietnam

 * HCMC International Film Festival (HIFF)

Significant Festival awards
As of 1998, The Variety Guide to Film Festivals states that "the Triple Crown of international competitive festivals" are Cannes, Venice and Berlin.

Argentina

 * Festival Internacional de Cine de Mar del Plata
 * Ástor
 * BAFICI (Buenos Aires Festival Internacional de Cine Independiente)

Armenia

 * Golden Apricot Yerevan International Film Festival

Australia

 * Flickerfest

Bangladesh

 * Dhaka International Film Festival
 * Rainbow Award (covering all segments)

Belgium

 * Flanders International Film Festival Ghent

Bosnia and Herzegovina

 * Sarajevo Film Festival
 * Heart of Sarajevo
 * Sarajevo Youth Film Festival

Brazil

 * Grande Prêmio do Cinema Brasileiro
 * São Paulo International Film Festival

Burkina Faso

 * Panafrican Film and Television Festival of Ouagadougou (FESPACO)

Canada

 * Atlantic Film Festival
 * Cinéfest Sudbury International Film Festival
 * Hot Docs Canadian International Documentary Festival
 * Inside Out Film and Video Festival
 * Montreal World Film Festival
 * Toronto International Film Festival
 * Vancouver International Film Festival
 * Whistler Film Festival
 * Yorkton Film Festival

China

 * Shanghai International Film Festival
 * Beijing International Film Festival

Croatia

 * Motovun Film Festival
 * Pula Film Festival
 * ZagrebDox

Czech Republic

 * Karlovy Vary International Film Festival
 * Crystal Globe (best picture)
 * Special Jury Prize

Egypt

 * Cairo International Film Festival
 * Golden Pyramid Award (best picture)
 * Luxor African Film Festival
 * Aswan International Women's Film Festival
 * Alexandria International Film Festival
 * El Gouna Film Festival

France

 * Cannes International Film Festival
 * Palme d'Or (best picture)
 * Grand Prize (best picture runner up)
 * Jury Prize
 * Prize Un Certain Regard
 * Caméra d'Or (best first picture)
 * François Chalais Prize
 * Trophée Chopard
 * Vulcan Award

Germany

 * Berlin International Film Festival (Berlinale)
 * Golden Bear (best picture)
 * Silver Bear (jury grand prize, director, actor and actress)
 * Findling Award (Findlingspreis)

Greece

 * International Thessaloniki Film Festival
 * Golden Alexander (best picture)

Hungary

 * Hungarian Film and TV Awards

India

 * International Film Festival of India
 * Golden Peacock for Best Film
 * Golden Peacock for Best Short Film
 * Silver Peacock for Best Film
 * IFFI Best Director Award
 * IFFI Best Actor Award (Male)
 * IFFI Best Actor Award (Female)
 * IFFI ICFT UNESCO Gandhi Medal
 * IFFI Satyajit Ray Lifetime Achievement Award
 * IFFI Indian Film Personality of the Year Award
 * International Film Festival of Kerala
 * Golden Crow Pheasant
 * Mumbai International Film Festival
 * Golden Conch (best fiction and best documentary)

Indonesia

 * Bali International Film Festival
 * Bandung Film Festival
 * Indonesian Film Festival
 * Jakarta International Film Festival
 * Jogja-NETPAC Asian Film Festival

Iran

 * Fajr International Film Festival
 * Hafez Awards

Italy

 * Venice International Film Festival
 * Golden Lion (best picture)
 * Coppa Volpi (best actor and actress)
 * Rome Film Festival
 * Capri Hollywood International Film Festival
 * Ischia International Film & Music Festival
 * Taormina Film Fest
 * Giffoni Film Festival

Japan

 * Tokyo International Film Festival

Morocco

 * International Film Festival of Marrakech

Malaysia

 * Malaysia Film Festival
 * ASEAN International Film Festival and Awards

Netherlands

 * Cinekid Festival
 * Film by the Sea
 * Netherlands Film Festival
 * Rembrandt Award
 * SCENECS International Debut Film Festival
 * ShortCutz Amsterdam

Nigeria

 * Africa International Film Festival (AFRIFF)

Norway

 * Norwegian International Film Festival
 * Amanda (various categories)
 * Tromsø International Film Festival

Pakistan

 * Kara Film Festival

Poland

 * Gdynia Film Festival
 * Polish Film Academy
 * International Film Festival of the Art of Cinematography CAMERIMAGE

Portugal

 * Fantasporto

Philippines

 * Cinemanila International Film Festival
 * Cinemalaya Philippine Independent Film Festival
 * Cinema One Originals Film Festival
 * Metro Manila Film Festival

Russia

 * Moscow International Film Festival

South Korea

 * Bucheon International Fantastic Film Festival
 * Busan International Film Festival
 * Seoul Independent Film Festival
 * Seoul International Film Festival

Spain

 * Málaga Spanish Film Festival ('Biznaga')
 * San Sebastián International Film Festival ('Shell')
 * Seville European Film Festival ('Giraldillo')
 * Sitges International Fantastic Film Festival of Catalonia
 * Valladolid International Film Festival ('Spike')

Sweden

 * Göteborg Film Festival
 * Stockholm International Film Festival

Switzerland

 * Locarno International Film Festival
 * Neuchâtel International Fantastic Film Festival

Turkey

 * Adana International Film Festival
 * Antalya Film Festival
 * Istanbul Animation Festival
 * Istanbul Film Festival

Ukraine

 * Odesa International Film Festival

United Kingdom

 * BFI London Film Festival
 * Sheffield Doc/Fest
 * UK Film Festival
 * Public Health Film Festival (PHFF)

United States

 * Chicago International Film Festival
 * Sundance Film Festival
 * Hawaii International Film Festival
 * Vilcek New American Filmmakers Award
 * Seattle International Film Festival
 * Golden Space Needle (best picture)
 * Slamdance Film Festival

Vietnam

 * Hanoi International Film Festival
 * Vietnam Film Festival
 * Golden Lotus (for Best Picture)

International

 * IDA (International Documentary Association) Awards
 * Location Managers Guild Awards
 * Taurus World Stunt Awards
 * Webby Awards
 * World Soundtrack Awards

Argentina

 * AACCA (Academia de las Artes y Ciencias Cinematográficas de la Argentina)
 * Premios Sur

Australia

 * AACTA Awards (Australian Academy of Cinema and Television Arts Awards), replaced the AFI Awards (Australian Film Institute Awards)
 * Asia Pacific Screen Awards
 * Australian Production Design Guild
 * Australian Screen Sound Guild
 * AWGIE Awards
 * Casting Guild of Australia (CGA)
 * TV Week Logie Awards

Austria

 * Austrian Film Awards

Bangladesh

 * National Film Awards (Bangladesh)
 * Meril Prothom Alo Awards

Belgium

 * Joseph Plateau Awards
 * Magritte Awards
 * Ensor Awards

Canada

 * Academy of Canadian Cinema and Television
 * Bijou Awards (1981)
 * Canadian Film Awards (1949-1978)
 * Canadian Screen Awards (since 2012)
 * Genie Awards (1980-2012)
 * Alberta Film and Television Awards
 * Canadian Society of Cinematographers
 * Directors Guild of Canada
 * Feminist Porn Awards
 * Leo Awards
 * Prix Iris

Denmark

 * Robert Awards

Estonia

 * Estonian Film and Television Awards

Europe

 * European Film Academy
 * European Film Awards (formerly the Felix)
 * Lux Prize (European Parliament LUX Award)

Finland

 * Jussi Awards

France

 * César Awards
 * Lumières Award
 * Prix Jean Vigo
 * Prix Lumière
 * Prix Romy Schneider
 * Prix Suzanne Bianchetti
 * René Clair Award

Germany

 * Bavarian Film Award (Bayerischer Filmpreis)
 * German Film Award (Deutscher Filmpreis)

Hong Kong

 * Asian Film Awards
 * Golden Bauhinia Awards
 * Hong Kong Film Awards

Ibero-America

 * Platino Awards
 * Fénix Awards

India

 * Filmfare Awards
 * Filmfare Awards South
 * IIFA Awards
 * IIFA Utsavam
 * Maharashtra State Film Awards
 * National Film Awards
 * Nandi Awards (Andhra Pradesh State Film, Music, Television and Arts Awards)
 * Star Screen Awards
 * South Indian International Movie Awards
 * Zee Cine Awards
 * Zee Cine Awards Telugu

Indonesia

 * Citra Awards
 * Indonesian Movie Actors Awards
 * Maya Awards

Ireland

 * IFTA Film & Drama Awards

Israel

 * Israeli Academy of Film and Television
 * Ophir Awards

Italy

 * David di Donatello Awards

Japan

 * Blue Ribbon Awards
 * Hochi Film Award
 * Japan Academy Prize
 * Mainichi Film Awards
 * Nikkan Sports Film Award

Latvia

 * Lielais Kristaps
 * Riga International Film Festival
 * 2Annas

Lithuania

 * Sidabrinė gervė

Mexico

 * Ariel Award

Malaysia

 * Screen Awards (Anugerah Skrin)

Nigeria

 * Africa Movie Academy Awards, popularly known as AMAA and the AMA Awards
 * Nollywood Movies Network
 * Nollywood Movies Awards (NMA)
 * Best of Nollywood Awards (BON)

Pakistan

 * Lux Style Awards
 * Hum Awards
 * ARY Film Awards

Philippines

 * FAMAS Awards
 * Film Academy of the Philippines
 * Luna Awards
 * Star Awards for Movies

Poland

 * Polish Film Awards

Portugal

 * Sophia Awards

Romania

 * Gopo Awards

Russia

 * Nika Award
 * Golden Eagle Award
 * Russian National Movie Awards

South Africa

 * South African Film and Television Awards (SAFTA)

South Korea

 * Blue Dragon Film Awards
 * Buil Film Awards
 * Chunsa Film Art Awards
 * Director's Cut Awards
 * Grand Bell Awards
 * Baeksang Arts Awards
 * Wildflower Film Awards

Spain

 * Actors and Actresses Union Awards
 * Berlanga Awards
 * Carmen Awards
 * Forqué Awards
 * Gaudí Awards
 * Goya Awards
 * Mestre Mateo Awards

Sweden

 * Guldbagge Awards

Taiwan

 * Golden Horse Awards
 * Taipei Film Awards

Thailand

 * Suphannahong National Film Awards

Turkey

 * Yeşilçam Award

United Kingdom

 * British Academy of Film and Television Arts (BAFTA)
 * British Academy Film Awards
 * British Independent Film Awards

United States

 * Academy of Motion Picture Arts and Sciences
 * Academy Awards, popularly known as the Oscars
 * Academy of Science Fiction, Fantasy and Horror Films
 * Saturn Awards
 * American Choreography Awards
 * American Cinema Editors Golden Reels
 * American Society of Cinematographers
 * Art Directors Guild
 * ASCAP (American Society of Composers, Authors, and Publishers) Film and Television Awards
 * AVN (Adult Video News) Awards
 * GayVN Awards
 * BMI Film Music Awards
 * Cinema Audio Society
 * Costume Designers Guild
 * Directors Guild of America Awards
 * Film Your Issue College Film Awards
 * Golden Globe Awards
 * Golden Reel Award for excellence in sound editing in film and television
 * Gotham Awards – Independent Feature Project
 * Hollywood Film Awards
 * Hollywood Makeup and Hairstylist Guild
 * The Hollywood Reporter Key Art Awards
 * Imagen Awards
 * Independent Spirit Awards
 * International Animated Film Society / ASIFA-Hollywood
 * Annie Awards
 * International Online Cinema Awards
 * International Press Academy
 * Satellite Awards
 * JEIFA Awards
 * NAACP
 * Image Awards
 * Producers Guild of America Awards
 * Screen Actors Guild Awards
 * ShoWest/National Association of Theatre Owners Convention
 * Taurus World Stunt Awards
 * Visual Effects Society Awards
 * Writers Guild of America, East & Writers Guild of America, West
 * Writers Guild of America Award - Link
 * Young Artist Awards

Vietnam

 * Kite Awards

International

 * Webby People's Voice Awards

Austria

 * Romy Awards

Bangladesh

 * Meril Prothom Alo Awards

Canada

 * Constellation Awards

Germany

 * Jupiter Award

India

 * Filmfare Awards
 * Filmfare Awards South
 * Vijay Awards
 * South Indian International Movie Awards
 * Santosham Film Awards

Indonesia

 * MTV Indonesia Movie Awards
 * Indonesian Box Office Movie Awards
 * Indonesian Choice Awards
 * Indonesian Movie Actors Awards

Malaysia

 * Popular Star Awards (Anugerah Bintang Popular)
 * MeleTOP Era Awards
 * Blockbuster Awards
 * Shout! Awards

Nigeria

 * Africa Magic Viewers' Choice Awards

Pakistan

 * Lux Style Awards

Poland

 * Polish Academy Audience Award

Spain

 * GoldSpirit Awards - Soundtracks and film music

United Kingdom

 * Empire Awards
 * ITV
 * National Film Awards UK
 * Audience Award for Most Popular Show (now retired)
 * Public Health Film Festival Audience Award
 * SHAFTA Awards

United States

 * MTV Movie & TV Awards
 * Independent Lens Audience Award
 * Kids' Choice Awards Includes both film and other media awards.
 * Teen Choice Awards Includes both film and other media awards.
 * People's Choice Awards Includes both film and other media awards.

Sources and references

 * IMDB search page for data on hundreds of awards and festivals

title: List of film awards


text:
Cessna 170

The Cessna 170 is an American single-engine, four seat, general aviation aircraft produced by the Cessna Aircraft Company between 1948 and 1956.

It is the predecessor of the Cessna 172, the most produced aircraft in history, which replaced the 170 in production in 1956.

170
In late 1948, Cessna began sales of the 170, with a metal fuselage and tail and fabric-covered constant-chord wings. These earliest 170s were four-seat versions of the popular 140 with a more powerful 145 hp Continental C145-2 and an extra interconnected fuel tank in one wing for a total of 36 gallons in three tanks. Like the 140, they were constructed of metal with fabric-covered wings supported by a "V" strut.

170A
In 1949, Cessna began marketing the 170A, an all-metal 170 with zero-dihedral wing tapered outboard of the slightly-enlarged plain flaps with 50 degrees maximum deflection, two 21 gallon fuel tanks, and a single strut replacing the "V" strut of the 170. This and subsequent versions of the 170 shared the fin/rudder shape of the larger Cessna 190 and 195 models.

305
In 1950, the United States Air Force, Army and Marines began using the military variant of the 170, the Model 305, designated the L-19 and later O-1 Bird Dog by the military. It was used as a forward air control and reconnaissance aircraft. The Bird Dog was extensively redesigned from the basic 170 and included a revised tandem-seat fuselage and a wing with large modified Fowler flaps that deployed up to 60°.

170B
In 1952, the Cessna 170B was introduced, featuring a new wing tapered outboard of the flaps, incorporating dihedral similar to the military version. The B model was equipped with very effective modified Fowler (slotted, rearward-traveling) wing flaps which deflect up to 40°, adapted from the C-305/Bird Dog, a wing design that lives on in the Cessna light singles of today (constant NACA 2412 section with a chord of 64 in from centerline to 100 in (the outboard end of the flaps), then tapering to 44 in NACA 2412 section chord at 208 inches from centerline, with three-degree washout across the tapered section). The 170B model also included a new tailplane, a revised tailwheel bracket, and other refinements over the 170 and 170A. It was marketed in 1952 for $7245.

In 1955, the previously elliptical rear side windows were changed to a squarer design.

170C
The sole 170C, registered N37892 (c/n 609), was built in November 1954 with a redesigned squared vertical stabilizer. No production followed, and the prototype was converted to 170B standard with a rounded tail in January 1956. However, the 170C was developed into the Cessna 172, with early models sharing the squared tail of the 170C.

Experimental
In 1958, Cessna experimented with a belt driven 145 hp Continental engine. The company completed 1000 hours of test flying. The belt drive reduced vibration, engine noise and propeller noise. A 92 inch propeller with 70 degrees of pitch improved the rate of climb 12 percent. The belts used were developed by Goodyear Tire and Rubber Company and were 3/8-inch wide, 7/16-inch deep, and 41 inches long.

Successor
The 170 is equipped with conventional landing gear, which is more challenging to land than tricycle landing gear. In 1956, Cessna introduced a replacement for the 170 that was essentially a nosewheel-equipped 170B with a square tailfin, designated the 172. 170 production was halted soon after the 172 became available.

Model 309 and 319
Between 1951 and 1955, Cessna used modifications of the 170 and its derivative, the U.S. Army L-19, as test beds for boundary layer control research, under contract to the Office of Naval Research and the Army Transportation Corps, designating them as the models 309 and 319. The project was done in conjunction with the University of Wichita which conducted extensive wind tunnel tests of the concept. The model 309 utilized the German World War II Arado lift-increasing system in which a jet pump inside the wing sucked in stagnant air from the flap area, energized it and blew the higher-speed air over the ailerons. Various chemicals and enhancements were used to power the jet pump. Better results were obtained by departing from the Arado jet pump method and using an engine-driven generator to power electric motors driving axial fans to move the internal air.

This concept was adopted on the Model 319 but substituted an engine-driven hydraulic pump to drive hydraulic-powered axial fans. This model was more successful and resulted in the highest lift capacity, as measured by the maximum lift coefficient, recorded up to that time. The 319 demonstrated the capability of taking off in 190 ft, landing in 160 ft and clearing a 50 ft obstacle in 450 ft. The aircraft had a stall speed of 28 kn. The 309 and 319 were meant to be research aircraft only, and no plans were developed to incorporate boundary layer control technology in then-current Cessna models. Others were also working on the concept, and it was ultimately incorporated into the Lockheed F-104 Starfighter.

Today
Over 5,000 Cessna 170s were built and over 2,000 are still in service today.

Military

 * Dominican Army
 * Air Force of El Salvador
 * Guatemalan Air Force
 * Honduran Air Force
 * Guatemalan Air Force
 * Honduran Air Force
 * Honduran Air Force
 * Honduran Air Force

title: Cessna 170


text:
IEEE 754

The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE). The standard addressed many problems found in the diverse floating-point implementations that made them difficult to use reliably and portably. Many hardware floating-point units use the IEEE 754 standard.

The standard defines:
 * arithmetic formats: sets of binary and decimal floating-point data, which consist of finite numbers (including signed zeros and subnormal numbers), infinities, and special "not a number" values (NaNs)
 * interchange formats: encodings (bit strings) that may be used to exchange floating-point data in an efficient and compact form
 * rounding rules: properties to be satisfied when rounding numbers during arithmetic and conversions
 * operations: arithmetic and other operations (such as trigonometric functions) on arithmetic formats
 * exception handling: indications of exceptional conditions (such as division by zero, overflow, etc.)

IEEE 754-2008, published in August 2008, includes nearly all of the original IEEE 754-1985 standard, plus the IEEE 854-1987 Standard for Radix-Independent Floating-Point Arithmetic. The current version, IEEE 754-2019, was published in July 2019. It is a minor revision of the previous version, incorporating mainly clarifications, defect fixes and new recommended operations.

History
The need for a floating-point standard arose from chaos in the business and scientific computing industry in the 1960s and 1970s. IBM used a hexadecimal floating-point format with. CDC and Cray computers used one's complement representation, which admits a value of +0 and −0. CDC 60-bit computers did not have full 60-bit adders, so integer arithmetic was limited to 48 bits of precision from the floating-point unit. Exception processing from divide-by-zero was different on different computers. Moving data between systems and even repeating the same calculations on different systems was often difficult.

The first IEEE standard for floating-point arithmetic, IEEE 754-1985, was published in 1985. It covered only binary floating-point arithmetic.

A new version, IEEE 754-2008, was published in August 2008, following a seven-year revision process, chaired by Dan Zuras and edited by Mike Cowlishaw. It replaced both IEEE 754-1985 (binary floating-point arithmetic) and IEEE 854-1987 Standard for Radix-Independent Floating-Point Arithmetic. The binary formats in the original standard are included in this new standard along with three new basic formats, one binary and two decimal. To conform to the current standard, an implementation must implement at least one of the basic formats as both an arithmetic format and an interchange format.

The international standard ISO/IEC/IEEE 60559:2011 (with content identical to IEEE 754-2008) has been approved for adoption through ISO/IEC JTC 1/SC 25 under the ISO/IEEE PSDO Agreement and published.

The current version, IEEE 754-2019 published in July 2019, is derived from and replaces IEEE 754-2008, following a revision process started in September 2015, chaired by David G. Hough and edited by Mike Cowlishaw. It incorporates mainly clarifications (e.g. totalOrder) and defect fixes (e.g. minNum), but also includes some new recommended operations (e.g. augmentedAddition).

The international standard ISO/IEC 60559:2020 (with content identical to IEEE 754-2019) has been approved for adoption through ISO/IEC JTC 1/SC 25 and published.

The next projected revision of the standard is in 2028.

Formats
An IEEE 754 format is a "set of representations of numerical values and symbols". A format may also include how the set is encoded.

A floating-point format is specified by
 * a base (also called radix) b, which is either 2 (binary) or 10 (decimal) in IEEE 754;
 * a precision p;
 * an exponent range from emin to emax, with emin = 1 − emax, or equivalently emin = − (emax − 1), for all IEEE 754 formats.

A format comprises
 * Finite numbers, which can be described by three integers: s = a sign (zero or one), c = a significand (or coefficient) having no more than p digits when written in base b (i.e., an integer in the range through 0 to bp − 1), and q = an exponent such that emin ≤ q + p − 1 ≤ emax. The numerical value of such a finite number is (−1)s × c × bq. Moreover, there are two zero values, called signed zeros: the sign bit specifies whether a zero is +0 (positive zero) or −0 (negative zero).
 * Two infinities: +∞ and −∞.
 * Two kinds of NaN (not-a-number): a quiet NaN (qNaN) and a signaling NaN (sNaN).

For example, if b = 10, p = 7, and emax = 96, then emin = −95, the significand satisfies 0 ≤ c ≤ $9,999,999$, and the exponent satisfies −101 ≤ q ≤ 90. Consequently, the smallest non-zero positive number that can be represented is 1×10−101, and the largest is 9999999×1090 (9.999999×1096), so the full range of numbers is −9.999999×1096 through 9.999999×1096. The numbers −b1−emax and b1−emax (here, −1×10−95 and 1×10−95) are the smallest (in magnitude) normal numbers; non-zero numbers between these smallest numbers are called subnormal numbers.

Representation and encoding in memory
Some numbers may have several possible floating-point representations. For instance, if b = 10, and p = 7, then −12.345 can be represented by −12345×10−3, −123450×10−4, and −1234500×10−5. However, for most operations, such as arithmetic operations, the result (value) does not depend on the representation of the inputs.

For the decimal formats, any representation is valid, and the set of these representations is called a cohort. When a result can have several representations, the standard specifies which member of the cohort is chosen.

For the binary formats, the representation is made unique by choosing the smallest representable exponent allowing the value to be represented exactly. Further, the exponent is not represented directly, but a bias is added so that the smallest representable exponent is represented as 1, with 0 used for subnormal numbers. For numbers with an exponent in the normal range (the exponent field being neither all ones nor all zeros), the leading bit of the significand will always be 1. Consequently, a leading 1 can be implied rather than explicitly present in the memory encoding, and under the standard the explicitly represented part of the significand will lie between 0 and 1. This rule is called leading bit convention, implicit bit convention, or hidden bit convention. This rule allows the binary format to have an extra bit of precision. The leading bit convention cannot be used for the subnormal numbers as they have an exponent outside the normal exponent range and scale by the smallest represented exponent as used for the smallest normal numbers.

Due to the possibility of multiple encodings (at least in formats called interchange formats), a NaN may carry other information: a sign bit (which has no meaning, but may be used by some operations) and a payload, which is intended for diagnostic information indicating the source of the NaN (but the payload may have other uses, such as NaN-boxing  ).

Basic and interchange formats
The standard defines five basic formats that are named for their numeric base and the number of bits used in their interchange encoding. There are three binary floating-point basic formats (encoded with 32, 64 or 128 bits) and two decimal floating-point basic formats (encoded with 64 or 128 bits). The binary32 and binary64 formats are the single and double formats of IEEE 754-1985 respectively. A conforming implementation must fully implement at least one of the basic formats.

The standard also defines interchange formats, which generalize these basic formats. For the binary formats, the leading bit convention is required. The following table summarizes some of the possible interchange formats (including the basic formats).

In the table above, integer values are exact, whereas values in decimal notation (e.g. 1.0) are rounded values. The minimum exponents listed are for normal numbers; the special subnormal number representation allows even smaller (in magnitude) numbers to be represented with some loss of precision. For example, the smallest positive number that can be represented in binary64 is 2−1074; contributions to the −1074 figure include the emin value −1022 and all but one of the 53 significand bits (2−1022 − (53 − 1) = 2−1074).

Decimal digits is the precision of the format expressed in terms of an equivalent number of decimal digits. It is computed as digits × log10 base. E.g. binary128 has approximately the same precision as a 34 digit decimal number.

log10 MAXVAL is a measure of the range of the encoding. Its integer part is the largest exponent shown on the output of a value in scientific notation with one leading digit in the significand before the decimal point (e.g. 1.698·1038 is near the largest value in binary32, 9.999999·1096 is the largest value in decimal32).

The binary32 (single) and binary64 (double) formats are two of the most common formats used today. The figure below shows the absolute precision for both formats over a range of values. This figure can be used to select an appropriate format given the expected value of a number and the required precision.

An example of a layout for 32-bit floating point is and the 64 bit layout is similar.

Extended and extendable precision formats
The standard specifies optional extended and extendable precision formats, which provide greater precision than the basic formats. An extended precision format extends a basic format by using more precision and more exponent range. An extendable precision format allows the user to specify the precision and exponent range. An implementation may use whatever internal representation it chooses for such formats; all that needs to be defined are its parameters (b, p, and emax). These parameters uniquely describe the set of finite numbers (combinations of sign, significand, and exponent for the given radix) that it can represent.

The standard recommends that language standards provide a method of specifying p and emax for each supported base b. The standard recommends that language standards and implementations support an extended format which has a greater precision than the largest basic format supported for each radix b. For an extended format with a precision between two basic formats the exponent range must be as great as that of the next wider basic format. So for instance a 64-bit extended precision binary number must have an 'emax' of at least 16383. The x87 80-bit extended format meets this requirement.

The original IEEE 754-1985 standard also had the concept of extended formats, but without any mandatory relation between emin and emax. For example, the Motorola 68881 80-bit format, where emin = − emax, was a conforming extended format, but it became non-conforming in the 2008 revision.

Interchange formats
Interchange formats are intended for the exchange of floating-point data using a bit string of fixed length for a given format.

Binary
For the exchange of binary floating-point numbers, interchange formats of length 16 bits, 32 bits, 64 bits, and any multiple of 32 bits ≥ 128 are defined. The 16-bit format is intended for the exchange or storage of small numbers (e.g., for graphics).

The encoding scheme for these binary interchange formats is the same as that of IEEE 754-1985: a sign bit, followed by w exponent bits that describe the exponent offset by a bias, and p − 1 bits that describe the significand. The width of the exponent field for a k-bit format is computed as w = round(4 log2(k)) − 13. The existing 64- and 128-bit formats follow this rule, but the 16- and 32-bit formats have more exponent bits (5 and 8 respectively) than this formula would provide (3 and 7 respectively).

As with IEEE 754-1985, the biased-exponent field is filled with all 1 bits to indicate either infinity (trailing significand field = 0) or a NaN (trailing significand field ≠ 0). For NaNs, quiet NaNs and signaling NaNs are distinguished by using the most significant bit of the trailing significand field exclusively, and the payload is carried in the remaining bits.

Decimal
For the exchange of decimal floating-point numbers, interchange formats of any multiple of 32 bits are defined. As with binary interchange, the encoding scheme for the decimal interchange formats encodes the sign, exponent, and significand. Two different bit-level encodings are defined, and interchange is complicated by the fact that some external indicator of the encoding in use may be required.

The two options allow the significand to be encoded as a compressed sequence of decimal digits using densely packed decimal or, alternatively, as a binary integer. The former is more convenient for direct hardware implementation of the standard, while the latter is more suited to software emulation on a binary computer. In either case, the set of numbers (combinations of sign, significand, and exponent) that may be encoded is identical, and special values (±zero with the minimum exponent, ±infinity, quiet NaNs, and signaling NaNs) have identical encodings.

Rounding rules
The standard defines five rounding rules. The first two rules round to a nearest value; the others are called directed roundings:

Roundings to nearest
At the extremes, a value with a magnitude strictly less than $$k=b^{\text{emax}}\left(b-\tfrac{1}{2}b^{1-p}\right)$$ will be rounded to the minimum or maximum finite number (depending on the value's sign). Any numbers with exactly this magnitude are considered ties; this choice of tie may be conceptualized as the midpoint between $$\pm b^{\text{emax}}(b-b^{1-p})$$ and $$\pm b^{\text{emax}+1}$$, which, were the exponent not limited, would be the next representable floating-point numbers larger in magnitude. Numbers with a magnitude strictly larger than $k$ are rounded to the corresponding infinity.
 * Round to nearest, ties to even – rounds to the nearest value; if the number falls midway, it is rounded to the nearest value with an even least significant digit.
 * Round to nearest, ties away from zero (or ties to away) – rounds to the nearest value; if the number falls midway, it is rounded to the nearest value above (for positive numbers) or below (for negative numbers).

"Round to nearest, ties to even" is the default for binary floating point and the recommended default for decimal. "Round to nearest, ties to away" is only required for decimal implementations.

Directed roundings

 * Round toward 0 – directed rounding towards zero (also known as truncation).
 * Round toward +∞ – directed rounding towards positive infinity (also known as rounding up or ceiling).
 * Round toward −∞ – directed rounding towards negative infinity (also known as rounding down or floor).

Unless specified otherwise, the floating-point result of an operation is determined by applying the rounding function on the infinitely precise (mathematical) result. Such an operation is said to be correctly rounded. This requirement is called correct rounding.

Required operations
Required operations for a supported arithmetic format (including the basic formats) include:

 * Conversions to and from integer
 * Previous and next consecutive values
 * Arithmetic operations (add, subtract, multiply, divide, square root, fused multiply–add, remainder, minimum, maximum)
 * Conversions (between formats, to and from strings, etc.)
 * Scaling and (for decimal) quantizing
 * Copying and manipulating the sign (abs, negate, etc.)
 * Comparisons and total ordering
 * Classification of numbers (subnormal, finite, etc.) and testing for NaNs
 * Testing and setting status flags

Comparison predicates
The standard provides comparison predicates to compare one floating-point datum to another in the supported arithmetic format. Any comparison with a NaN is treated as unordered. −0 and +0 compare as equal.

Total-ordering predicate
The standard provides a predicate totalOrder, which defines a total ordering on canonical members of the supported arithmetic format. The predicate agrees with the comparison predicates (see section ) when one floating-point number is less than the other. The main differences are:
 * NaN is sortable.
 * NaN is treated as if it had a larger absolute value than Infinity (or any other floating-point numbers). (−NaN < −Infinity; +Infinity < +NaN.)
 * qNaN and sNaN are treated as if qNaN had a larger absolute value than sNaN. (−qNaN < −sNaN; +sNaN < +qNaN.)
 * NaN is then sorted according to the payload. In IEEE 754-2008, a NaN with a lesser payload is treated as having a lesser absolute value. In IEEE 754-2019, any implementation-defined ordering is acceptable.
 * Negative zero is treated as smaller than positive zero.
 * If both sides of the comparison refer to the same floating-point datum, the one with the lesser exponent is treated as having a lesser absolute value.

The totalOrder predicate does not impose a total ordering on all encodings in a format. In particular, it does not distinguish among different encodings of the same floating-point representation, as when one or both encodings are non-canonical. IEEE 754-2019 incorporates clarifications of totalOrder.

For the binary interchange formats whose encoding follows the IEEE 754-2008 recommendation on placement of the NaN signaling bit, the comparison is identical to one that type puns the floating-point numbers to a sign–magnitude integer (assuming a payload ordering consistent with this comparison), an old trick for FP comparison without an FPU.

Exception handling
The standard defines five exceptions, each of which returns a default value and has a corresponding status flag that is raised when the exception occurs. No other exception handling is required, but additional non-default alternatives are recommended (see ).

The five possible exceptions are
 * Invalid operation: mathematically undefined, e.g., the square root of a negative number. By default, returns qNaN.
 * Division by zero: an operation on finite operands gives an exact infinite result, e.g., 1/0 or log(0). By default, returns ±infinity.
 * Overflow: a finite result is too large to be represented accurately (i.e., its exponent with an unbounded exponent range would be larger than emax). By default, returns ±infinity for the round-to-nearest modes (and follows the rounding rules for the directed rounding modes).
 * Underflow: a result is very small (outside the normal range). By default, returns a number less than or equal to the minimum positive normal number in magnitude (following the rounding rules); a subnormal number always implies an underflow exception, but by default, if it is exact, no flag is raised.
 * Inexact: the exact (i.e., unrounded) result is not representable exactly. By default, returns the correctly rounded result.

These are the same five exceptions as were defined in IEEE 754-1985, but the division by zero exception has been extended to operations other than the division.

Some decimal floating-point implementations define additional exceptions, which are not part of IEEE 754:
 * Clamped: a result's exponent is too large for the destination format. By default, trailing zeros will be added to the coefficient to reduce the exponent to the largest usable value. If this is not possible (because this would cause the number of digits needed to be more than the destination format) then an overflow exception occurs.
 * Rounded: a result's coefficient requires more digits than the destination format provides. An inexact exception is signaled if any non-zero digits are discarded.

Additionally, operations like quantize when either operand is infinite, or when the result does not fit the destination format, will also signal invalid operation exception.

Signed zero
In the IEEE 754 standard, zero is signed, meaning that there exist both a "positive zero" (+0) and a "negative zero" (−0). In most run-time environments, positive zero is usually printed as " " and the negative zero as " ". The two values behave as equal in numerical comparisons, but some operations return different results for +0 and −0. For instance, 1/(−0) returns negative infinity, while 1/(+0) returns positive infinity (so that the identity $1/(1/±∞) = ±∞$ is maintained). Other common functions with a discontinuity at x=0 which might treat +0 and −0 differently include log(x), signum(x), and the principal square root of $y + xi$ for any negative number y. As with any approximation scheme, operations involving "negative zero" can occasionally cause confusion. For example, in IEEE 754, $x = y$ does not always imply $1/x = 1/y$, as 0 = −0 but 1/0 ≠ 1/(−0).

Subnormal numbers
Subnormal values fill the underflow gap with values where the absolute distance between them is the same as for adjacent values just outside the underflow gap. This is an improvement over the older practice to just have zero in the underflow gap, and where underflowing results were replaced by zero (flush to zero).

Modern floating-point hardware usually handles subnormal values (as well as normal values), and does not require software emulation for subnormals.

Infinities
The infinities of the extended real number line can be represented in IEEE floating-point datatypes, just like ordinary floating-point values like 1, 1.5, etc. They are not error values in any way, though they are often (depends on the rounding) used as replacement values when there is an overflow. Upon a divide-by-zero exception, a positive or negative infinity is returned as an exact result. An infinity can also be introduced as a numeral (like C's "INFINITY" macro, or "$∞$" if the programming language allows that syntax).

IEEE 754 requires infinities to be handled in a reasonable way, such as
 * $(+∞) + (+7) = (+∞)$ NaN – there is no meaningful thing to do
 * $(+∞) × (−2) = (−∞)$ NaN – there is no meaningful thing to do
 * $(+∞) × 0 =$ NaN – there is no meaningful thing to do

NaNs
IEEE 754 specifies a special value called "Not a Number" (NaN) to be returned as the result of certain "invalid" operations, such as 0/0, $∞×0$, or sqrt(−1). In general, NaNs will be propagated, i.e. most operations involving a NaN will result in a NaN, although functions that would give some defined result for any given floating-point value will do so for NaNs as well, e.g. NaN ^ 0 = 1. There are two kinds of NaNs: the default quiet NaNs and, optionally, signaling NaNs. A signaling NaN in any arithmetic operation (including numerical comparisons) will cause an "invalid operation" exception to be signaled.

The representation of NaNs specified by the standard has some unspecified bits that could be used to encode the type or source of error; but there is no standard for that encoding. In theory, signaling NaNs could be used by a runtime system to flag uninitialized variables, or extend the floating-point numbers with other special values without slowing down the computations with ordinary values, although such extensions are not common.

Design rationale

It is a common misconception that the more esoteric features of the IEEE 754 standard discussed here, such as extended formats, NaN, infinities, subnormals etc., are only of interest to numerical analysts, or for advanced numerical applications. In fact the opposite is true: these features are designed to give safe robust defaults for numerically unsophisticated programmers, in addition to supporting sophisticated numerical libraries by experts. The key designer of IEEE 754, William Kahan notes that it is incorrect to "... [deem] features of IEEE Standard 754 for Binary Floating-Point Arithmetic that ...[are] not appreciated to be features usable by none but numerical experts. The facts are quite the opposite. In 1977 those features were designed into the Intel 8087 to serve the widest possible market... Error-analysis tells us how to design floating-point arithmetic, like IEEE Standard 754, moderately tolerant of well-meaning ignorance among programmers".
 * The special values such as infinity and NaN ensure that the floating-point arithmetic is algebraically complete: every floating-point operation produces a well-defined result and will not—by default—throw a machine interrupt or trap. Moreover, the choices of special values returned in exceptional cases were designed to give the correct answer in many cases. For instance, under IEEE 754 arithmetic, continued fractions such as R(z) := 7 − 3/[z − 2 − 1/(z − 7 + 10/[z − 2 − 2/(z − 3)])] will give the correct answer on all inputs, as the potential divide by zero, e.g. for z = 3, is correctly handled by giving +infinity, and so such exceptions can be safely ignored. As noted by Kahan, the unhandled trap consecutive to a floating-point to 16-bit integer conversion overflow that caused the loss of an Ariane 5 rocket would not have happened under the default IEEE 754 floating-point policy.
 * Subnormal numbers ensure that for finite floating-point numbers x and y, x − y = 0 if and only if x = y, as expected, but which did not hold under earlier floating-point representations.
 * On the design rationale of the x87 80-bit format, Kahan notes: "This Extended format is designed to be used, with negligible loss of speed, for all but the simplest arithmetic with float and double operands. For example, it should be used for scratch variables in loops that implement recurrences like polynomial evaluation, scalar products, partial and continued fractions. It often averts premature Over/Underflow or severe local cancellation that can spoil simple algorithms". Computing intermediate results in an extended format with high precision and extended exponent has precedents in the historical practice of scientific calculation and in the design of scientific calculators e.g. Hewlett-Packard's financial calculators performed arithmetic and financial functions to three more significant decimals than they stored or displayed. The implementation of extended precision enabled standard elementary function libraries to be readily developed that normally gave double precision results within one unit in the last place (ULP) at high speed.
 * Correct rounding of values to the nearest representable value avoids systematic biases in calculations and slows the growth of errors. Rounding ties to even removes the statistical bias that can occur in adding similar figures.
 * Directed rounding was intended as an aid with checking error bounds, for instance in interval arithmetic. It is also used in the implementation of some functions.
 * The mathematical basis of the operations, in particular correct rounding, allows one to prove mathematical properties and design floating-point algorithms such as 2Sum, Fast2Sum and Kahan summation algorithm, e.g. to improve accuracy or implement multiple-precision arithmetic subroutines relatively easily.

A property of the single- and double-precision formats is that their encoding allows one to easily sort them without using floating-point hardware, as if the bits represented sign-magnitude integers, although it is unclear whether this was a design consideration (it seems noteworthy that the earlier IBM hexadecimal floating-point representation also had this property for normalized numbers). With the prevalent two's-complement representation, interpreting the bits as signed integers sorts the positives correctly, but with the negatives reversed; as one possible correction for that, with an xor to flip the sign bit for positive values and all bits for negative values, all the values become sortable as unsigned integers (with −0 < +0).

Alternate exception handling
The standard recommends optional exception handling in various forms, including presubstitution of user-defined default values, and traps (exceptions that change the flow of control in some way) and other exception handling models that interrupt the flow, such as try/catch. The traps and other exception mechanisms remain optional, as they were in IEEE 754-1985.

Recommended operations
Clause 9 in the standard recommends additional mathematical operations that language standards should define. None are required in order to conform to the standard.

The following are recommended arithmetic operations, which must round correctly:
 * $e^x$, $$2^x$$, $$10^x$$
 * $e^x - 1$, $$2^x - 1$$, $$10^x - 1$$
 * $\ln x$, $\log_{2} x$, $\log_{10} x$
 * $\ln (1 + x)$, $$\log_{2} (1 + x)$$, $$\log_{10} (1 + x)$$
 * $\sqrt{x^2 + y^2}$
 * $1\big/\sqrt{x\vphantom{t}}$
 * $$(1 + x)^n$$ for $$x \ge -1$$ (named compound and used to compute an exponential growth, whose rate cannot be less than −1)
 * $x^{\frac{1}{n}}$
 * $x^n$, $x^y$
 * $\sin x$, $\cos x$, $\tan x$
 * $\arcsin x$, $\arccos x$, $\arctan x$, $\operatorname{atan2}(y, x)$
 * $$\operatorname{sinPi} x = \sin \pi x$$, $$\operatorname{cosPi} x = \cos \pi x$$, $$\operatorname{tanPi} x = \tan \pi x$$ (see also: Multiples of π)
 * $$\operatorname{asinPi} x = \tfrac1\pi \arcsin x$$, $$\operatorname{acosPi} x = \tfrac1\pi \arccos x$$, $$\operatorname{atanPi} x = \tfrac1\pi \arctan x$$, $$\operatorname{atan2Pi} (y, x) = \tfrac1\pi \operatorname{atan2}(y, x)$$ (see also: Multiples of π)
 * $\sinh x$, $\cosh x$, $\tanh x$
 * $\operatorname{arsinh} x$, $\operatorname{arcosh} x$, $\operatorname{artanh} x$

The $$\operatorname{asinPi}$$, $$\operatorname{acosPi}$$ and $$\operatorname{tanPi}$$ functions were not part of the IEEE 754-2008 standard because they were deemed less necessary. $$\operatorname{asinPi}$$ and $$\operatorname{acosPi}$$ were mentioned, but this was regarded as an error. All three were added in the 2019 revision.

The recommended operations also include setting and accessing dynamic mode rounding direction, and implementation-defined vector reduction operations such as sum, scaled product, and dot product, whose accuracy is unspecified by the standard.

, augmented arithmetic operations for the binary formats are also recommended. These operations, specified for addition, subtraction and multiplication, produce a pair of values consisting of a result correctly rounded to nearest in the format and the error term, which is representable exactly in the format. At the time of publication of the standard, no hardware implementations are known, but very similar operations were already implemented in software using well-known algorithms. The history and motivation for their standardization are explained in a background document.

As of 2019, the formerly required minNum, maxNum, minNumMag, and maxNumMag in IEEE 754-2008 are now deprecated due to their non-associativity. Instead, two sets of new minimum and maximum operations are recommended. The first set contains minimum, minimumNumber, maximum and maximumNumber. The second set contains minimumMagnitude, minimumMagnitudeNumber, maximumMagnitude and maximumMagnitudeNumber. The history and motivation for this change are explained in a background document.

Expression evaluation
The standard recommends how language standards should specify the semantics of sequences of operations, and points out the subtleties of literal meanings and optimizations that change the value of a result. By contrast, the previous 1985 version of the standard left aspects of the language interface unspecified, which led to inconsistent behavior between compilers, or different optimization levels in an optimizing compiler.

Programming languages should allow a user to specify a minimum precision for intermediate calculations of expressions for each radix. This is referred to as preferredWidth in the standard, and it should be possible to set this on a per-block basis. Intermediate calculations within expressions should be calculated, and any temporaries saved, using the maximum of the width of the operands and the preferred width if set. Thus, for instance, a compiler targeting x87 floating-point hardware should have a means of specifying that intermediate calculations must use the double-extended format. The stored value of a variable must always be used when evaluating subsequent expressions, rather than any precursor from before rounding and assigning to the variable.

Reproducibility
The IEEE 754-1985 version of the standard allowed many variations in implementations (such as the encoding of some values and the detection of certain exceptions). IEEE 754-2008 has reduced these allowances, but a few variations still remain (especially for binary formats). The reproducibility clause recommends that language standards should provide a means to write reproducible programs (i.e., programs that will produce the same result in all implementations of a language) and describes what needs to be done to achieve reproducible results.

Character representation
The standard requires operations to convert between basic formats and external character sequence formats. Conversions to and from a decimal character format are required for all formats. Conversion to an external character sequence must be such that conversion back using round to nearest, ties to even will recover the original number. There is no requirement to preserve the payload of a quiet NaN or signaling NaN, and conversion from the external character sequence may turn a signaling NaN into a quiet NaN.

The original binary value will be preserved by converting to decimal and back again using:
 * 5 decimal digits for binary16,
 * 9 decimal digits for binary32,
 * 17 decimal digits for binary64,
 * 36 decimal digits for binary128.

For other binary formats, the required number of decimal digits is

 * $$1 + \lceil p\log_{10}(2)\rceil,$$

where p is the number of significant bits in the binary format, e.g. 237 bits for binary256.

When using a decimal floating-point format, the decimal representation will be preserved using:
 * 7 decimal digits for decimal32,
 * 16 decimal digits for decimal64,
 * 34 decimal digits for decimal128.

Algorithms, with code, for correctly rounded conversion from binary to decimal and decimal to binary are discussed by Gay, and for testing – by Paxson and Kahan.

Hexadecimal literals
The standard recommends providing conversions to and from external hexadecimal-significand character sequences, based on C99's hexadecimal floating point literals. Such a literal consists of an optional sign ( or  ), the indicator "0x", a hexadecimal number with or without a period, an exponent indicator "p", and a decimal exponent with optional sign. The syntax is not case-sensitive. The decimal exponent scales by powers of 2, so for example  is 1/256.

Secondary references

 * Decimal floating-point arithmetic, FAQs, bibliography, and links
 * Comparing binary floats
 * IEEE 754 Reference Material
 * IEEE 854-1987 – History and minutes
 * Supplementary readings for IEEE 754. Includes historical perspectives.

title: IEEE 754


text:
Chaldean

Chaldean (also Chaldaean or Chaldee) may refer to:

Language

 * an old name for the Aramaic language, particularly Biblical Aramaic
 * Chaldean Neo-Aramaic, a modern Aramaic language
 * Chaldean script, a variant of the Syriac alphabet

People

 * Ancient Chaldeans, ancient Semitic people in southern Mesopotamia
 * Modern Chaldeans, modern self-identification of Chaldean Catholics

Places

 * Chaldea, an ancient region whose inhabitants were known as Chaldeans
 * Neo-Babylonian Empire, also called the Chaldean Empire
 * Chaldean Town, a neighborhood of Detroit, Michigan, U.S.

Religion

 * Chaldean Catholics, adherents of the Chaldean Catholic Church
 * Chaldean Catholic Church, Eastern Rite Catholic Church in full communion with the Catholic Church
 * Chaldean Rite, the East Syriac Rite of the Chaldean Catholics
 * Chaldean Oracles, texts widely used by Neoplatonist philosophers from 3rd to 6th centuries AD; referred to by some of the Christian Church Fathers
 * Chaldean Syrian Church, title used for the Assyrian Church of the East in India

Other

 * Chaldean (horse) (foaled 2020), Thoroughbred racehorse

title: Chaldean


text:
Blackheath, New South Wales

Blackheath (postcode: 2785) is a town located near the highest point of the Blue Mountains, between Katoomba and Mount Victoria in New South Wales, Australia. The town's altitude is about 1065 m and it is located about 120 km west north-west of Sydney, 11 km north-west of Katoomba, and about 30 km south-east of Lithgow.

Blackheath has a vibrant artistic community and hosts two monthly markets – the Blackheath Growers Market and The Blackheath Community Market, as well as annual Christmas markets, antique markets and bimonthly craft markets. The town has many community activities, such as the Blackheath Philosophy Forum, which was founded in 2002 to arrange public discussion forums on philosophy and related topics.

As Blackheath has grown, more and more shops have appeared. Various shops from the late 1800s still stand in Blackheath.

History
The surrounding areas of Blackheath were thought to be a summer corroboree meeting place for peoples of the Darug, Gundungurra and Wiradjuri nations.

Following European settlement of Australia, the site was originally named Hounslow. After crossing the Blue Mountains in 1815 and returning from Bathurst, Governor Lachlan Macquarie renamed the settlement as "Black-Heath", in reference to the colour and texture of the native shrubbery in the area. Macquarie recorded in his journal: "'This place having a black wild appearance I have this day named it Black-Heath.'"

The first building in Blackheath, the "Scotch Thistle Inn", was erected by Andrew Gardner in 1831 and Charles Darwin visited the inn in 1836. The extent of the original grant of land to Gardner can be seen today as the area bound by the Great Western Highway, Govetts Leap Road and (the misspelt) Gardiners Crescent.

Blackheath developed into a town after the Main Western railway line was built in 1869; the current station location was completed in 1883. A large dam built to supply water for railway steam engines became the public baths well before steam operations ceased upon electrification. The baths opened for public swimming in 1931 and since then have been redeveloped to include swimming pools, children's play facilities and surrounding park lands. Blackheath's original post office opened in 1910 and has now been converted into a gift shop and cafe.

Blackheath's sporting claim to fame is that Don Bradman hit a century off three overs for the Blackheath team in November 1931 at Blackheath Oval in a social match against Lithgow. He went on to make 256.

Heritage listings
Blackheath has a number of heritage listed sites, including:
 * Blue Mountains National Park: Blue Mountains walking tracks
 * Main Western railway: Blackheath railway station

People
At the, Blackheath had a population of 4,479 people. Of these:
 * Age distribution: The residents' median age was 53 years, which is fifteen years older than the national median age of 38. Children aged under 15 years made up 13.6% of the population (national average is 18.2%) and people aged 65 years and over made up 29.9% of the population (national average is 17.2%).
 *  Ethnic diversity: 73.0% of people were born in Australia. The next most common country of birth was England at 6.9%. 87.8% of people only spoke English at home.
 * Finances: The median household weekly income was $1,322, compared to the national median of $1,746. This difference is also reflected in real estate, with the median mortgage payment being $1,842 per month, compared to the national median of $1,721.
 * Housing: Of occupied private dwellings in Blackheath, 96.2% were separate houses. The average household size was 2.0 people.
 * Religion: The most common responses for religion were No Religion 51.9%, Anglican 11.5% and Catholic 12.7%.

Govetts Leap
From Blackheath town centre, a short drive to the east-north-east takes visitors to Govetts Leap, a lookout with views of the Grose Valley and nearby waterfalls. The fall is named after William Romaine Govett, an assistant to the Surveyor General at the time, who first came upon the falls in June 1831. The name 'leap' is an old Scottish word meaning waterfall or cascade.

Evans Lookout
Evans Lookout provides an alternate vantage point for views, also into Grose Valley.

Other lookouts, walking tracks and attractions
Pulpit Rock, Perrys Lookdown, and Anvil Rock are other lookouts to the north-northeast of the town centre, off Hat Hill Road. There are several walking tracks starting from the lookouts, including short walks to enjoy different views, longer half and whole day walks, and walks involving camping overnight or several days' walk. Canyoners and rockclimbers also base themselves at Blackheath for activities in the surrounding national park. The Blue Gum Forest may be accessed from Perrys Lookdown.

The area is known today for its colourful blooms in Spring and golden Autumn foliage as the weather begins to cool. In September, daffodils bloom, and on the first weekend of November, Blackheath hosts an annual Rhododendron Festival.

The Campbell Rhododendron Gardens are located north-north-east of the town centre, in Bachante Street. The 18.5 ha gardens comprise rhododendrons/azaleas planted underneath a native Australian bush canopy tended by the volunteers of The Blue Mountains Rhododendron Society of NSW.

The ornamental cherry trees that line the streets are usually in full bloom in the first week of October.

Mount Boyce lookout is located northwest of Blackheath, towards Lithgow. The Megalong Valley can be accessed from Blackheath, about 18 km away to the west, via Mount Victoria.

Blackheath has a number of cafés and restaurants, a large antique centre, and other shops. It is a common destination for people from Sydney for a weekend excursion or a Sunday drive. Due to the climate, Blackheath is a popular destination for Christmas in July.

Transport
Blackheath was connected to the Main Western railway line in 1869, and the town is now served by the Blackheath railway station located on the Blue Mountains Line.

The Great Western Highway is the main road access route, through the town's main business district. To the northwest of Blackheath, at Mount Victoria, the Darling Causeway connects the Great Western Highway to the Bells Line of Road at Bell. Several proposals have been investigated for upgrading the Great Western Highway west of Blackheath as a tunnel. As of 2024, the tunnel project has been indefinitely shelved.

On the day of the 2016 Census, the most common methods of travel to work for employed people were: Car, as driver 56.6%, Worked at home 12.7% and Train 5.4%.

Blue Mountains Transit operates two bus routes through the suburb of Blackheath:

 * 698: Katoomba to Blackheath
 * 698V: Katoomba to Mount Victoria

Wildlife
A large amount of wildlife inhabit in and around Blackheath. Mammals such as the Eastern Grey Kangaroo and Echidna live in the forests around Blackheath.

Rare bird species also occur, such as the Lesser Sooty Owl and Regent Honeyeater.

Geography and climate
The area around Blackheath has views over the Grose Valley from Evans Lookout and Govetts Leap in the east, and the vista of the Megalong Valley from Hargraves Lookout in the west, past the small hamlet of Shipley. As the highest town in the Blue Mountains, Blackheath receives snow in winter (two settled falls per season is the average with another five to ten days of light snow showers) and even in summer the temperatures are generally mild in comparison to other locations at the same latitude. Average maximum temperature in winter is around 9 to 10 C although some days struggle to get above 5 to 6 C. Frosts are fairly common but not as common or strong as frosts on the Oberon Plateau or in places further west, like Bathurst and Orange. Local topography tends to keep minimum temperatures in the -3 to 5 C range as the coldest air during radiative cooling (clear, calm nights) drains into the valleys.

In summer, average maximum temperatures are around 23 C but temperatures occasionally peak at 30 C on some days during mid-summer and can also drop to the mid teens, or lower, during southerly changes or when onshore troughs persist on the east coast. Minimum temperatures in summer are typically around 10 to 15 C but minimums in single figures also occur, more commonly in December. In December 2011, a minimum of 2.4 C was recorded.

Blackheath's location on a high ridge makes it vulnerable to strong and sometimes destructive winds, especially in the winter months when cold fronts surge up from the Southern Ocean, producing land gales. On 5 July 2011 a strong cold front passed over the area that produced winds that officially gusted up to 139 km/h, causing many trees to be uprooted and extensive damage to some property. The Venturi effect, where airflow is constricted by vertical cliffs and deep valleys, would probably have produced winds notably stronger than this in vulnerable locations in town and nearby. Land gales are more likely to occur from around April to November but vary in their intensity from year to year. Spring and summer storms can also produce fresh to strong winds, typically in the range of 70 to 90 km/h.

Blackheath can also be prone to fogs and thunderstorms, although this varies notably from year to year. Some days in summer are quite humid, allowing for moisture to build during the day, sometimes creating severe storms that can last for hours. The most common cause for quite frequent spring/summer thunderstorms in and around Blackheath is related to the early, mid morning heating of the lower atmosphere, due to the town's elevation.

Blackheath is surrounded by the Blue Mountains National Park which is prone to bushfires. In November 2006 severe bushfires threatened Blackheath from the north.

Blackheath experiences a subtropical highland climate with monthly average temperatures not falling below -3 C and not exceeding 25 C. Blackheath's average annual precipitation is just over 1000 mm.

title: Blackheath, New South Wales