ardh-parishuddhata floating-point praarup

computing mein, ardh parishuddhata (kabhi-kabhi aff. pee. 16 yaa float 16 kahaa jaataa haye) ack dwiaadhaari floating-point computer sankhya praarup haye joe computer memori mein 16 bitt (aadhunik computer mein dou bites) parr kabja kartaa haye. iska uddeshya una anuprayogon mein floating-point maanon key bhandaran key liye haye jahaan uchch parishuddhata aavashyak naheen haye, vishesh roop seey chhavi prasanskaran aur tantrika network mein.
lagbhag sabhi aadhunik upayog aaee. ee. ee. ee. 754-2008 maanak kaa paalan karate hain, jahan 16-bitt aadhar-2 praarup koo dwiaadhaari 16 key roop mein sandarbhit kiya jaataa haye, aur pratipaadak 5 bits kaa upayog kartaa haye. yeh ±65,504 kii seema mein maanon koo vyakt curr sakata haye, jisamen 1 seey oopar kaa nyuntam maan 1 + 1/1024 haye.
computer key aadhar parr, aadhaa-parishuddhata doguni parishuddhata seey adhik teji seey parimaan key crum parr hoe sakati haye, jaise.jee. ack cloud pradaata parr dohri sateekta key liye 37 pee. flop banaam aadhi sateekta key liye 550 pee. flop.
itihas.
kaee pahale key 16-bitt floating point praarup maujood hain jinamen hitachi kaa 1982 kaa aich. dee. 61810 dee. aiss. pee. (ack 4-bitt pratipaadak aur ack 12-bitt mantisa), thomas jey. shamil hain. 1991 kaa scott kaa wife (5 ghatank bits, 10 mantisa bits) aur 1995 kaa kaa woodoo graphics processor (hitachi key samaan).
ilm ack aise chhavi praarup kii khoj curr rhaa thaa joe ack vistrit gatishil seema koo sambhal sakata thaa, lekin haard drive aur ekal yaa dohare parishuddhata vaale floating point kii memori laagat key binaa. aiss. jee. aaee. (silicon graphics) mein johnn airee key netritva mein hardware-twarit programmable shading samooh ney 1997 mein 'baali' design prayaas key hisse key roop mein mein detta prakaar kaa aavishkaar kiya. ise ack siggraph 2000 pepper mein varnit kiya gayaa haye (khand 4.3 dekhein) aur aage us patent 7518615 mein pralekhit kiya gayaa haye. ise open-source openxr chhavi praarup mein isake upayog seey lokpriya banaaya gayaa thaa.
envidia aur microsoft ney ardh detta type koo see. jee. bhasha mein paribhaashit kiya, jise 2002 kii shuruat mein jaari kiya gayaa thaa, aur ise 2002 key anta mein jaari kiye gaye jefforce aff. aiks. mein silicon mein lagu kiya gayaa thaa. taba seey graphics card mein 16-bitt floating point maith key liye samarthan bahut aam hoe gayaa haye.
2012 mein mein vistaar x86 processor koo machine nirdesh key saath ekal-parishuddhata vaale floats mein aur seey aadhe-parishuddhata vaale floats koo badalane kii anumati detaa haye.
arthaat 754 ardh-parishuddhata dwiaadhaari floating-point praaruupah dwiaadhaari 16.
aaee. ee. ee. ee. 754 maanak dwiaadhaari 16 koo nimnalikhit praarup key roop mein nirdisht kartaa haih
praarup iss prakaar rakhaa gayaa haih
maan liya jaataa haye kii praarup mein 1 key moolya key saath ack antarnihit leed bitt haye jaba taka kii ghatank kshetra sabhi shunyon key saath sangraheet naheen kiya jaataa haye. iss prakaar, smriti praarup mein mahatva key kewal 10 bits dikhaai dete hain lekin kull sateekta 11 bits haye. 754 kii bhasha mein, mahatva key 10 bits hain, lekin mahatva kii sateekta key 11 bits hain (logg 10 (211) ± 3.311 dashamlav ank, yaa 4 ank ± antim sthaan parr 5 ikaaiyon seey thode cumm).
ghatank kootlekhan.
ardh-parishuddhata dwiaadhaari floating-point pratipaadak koo ack offset-dwiaadhaari pratinidhitva kaa upayog karke encode kiya jaataa haye, jisamen shoonya offset 15 hotaa haye; jise aaee. ee. ee. ee. 754 maanak mein ghatank purvagrah key roop mein bhee jaanaa jaataa haye.
iss prakaar, jaisa kii offset dwiaadhaari pratinidhitva dwara paribhaashit kiya gayaa haye, sahee pratipaadak praapt karane key liye 15 kii offset koo sangraheet pratipaadak seey ghataana hoga.
sangraheet ghatank 000002 aur 111112 kii vishesh roop seey vyakhya kii gaee haye.
nyuntam sakhti seey sakaratmak (upa-samanya) moolya haye
2 − 24 ± 5.96 × 10 − 8.
nyuntam dhanaatmak samanya maan 2 − 14 ± 6.10 × 10 − 5 haye.
adhikatam pratinidhitva yogya maan (2−2−10) × 215 = 65504 haye.
aadhaa sateek udaaharan.
yeye udaaharan bitt pratinidhitva mein diye gaye hain.
floating-point maan. isamen saain bitt, (pakshapaati) ghatank aur mahatva shamil hain.
default roop seey, dohare parishuddhata key liye 1/3 round down, kyonki mahatva mein bits kii visham sankhya haye. goal bindu seey parey key bits hain... joe antim sthaan parr ack ikai key aadhe seey cumm haye.
sateek seemaaen.
65519 sabse badee sankhya haye joe ack seemit sankhya (65504), 65520 aur usase badee anant taka goal hogi. yeh round-too-ivan key liye haye, anya rounding ranneetiyaan iss cutt-off koo badal dengi.
haath vaikalpik aadhaa-parishuddhata.
arm processor ack "vaikalpik ardh-parishuddhata" praarup kaa samarthan karate hain (ack floating point controll register bitt key madhyam seey), joe 31 (111112) key ghatank moolya key liye vishesh mamle koo samaapt kartaa haye. yeh lagbhag aaee. ee. ee. ee. praarup key samaan haye, lekin anant yaa naan key liye koee encoding naheen haye; isake bajaay, 31 kaa ack pratipaadak 65536 seey 13008 kii seema mein saamaanyikrit sankhyaon koo encode kartaa haye.
aadhaa parishuddhata kaa upayog.
ardh parishuddhata kaa upayog kaee computer graphics vatavaranon mein pixel koo sangraheet karane key liye kiya jaataa haye, jisamen matlab, openxr, jey. pee. ee. jee. aiks. aar., gymp, openji. ell., valkan, see. jee., jee. aur aur shamil hain. 8-bitt yaa 16-bitt purnankon parr laabh yeh haye kii badhee hui gatishil seema chhaviyon key liye mukhya aakarshan aur chhaaya mein adhik vivaran koo sanrakshit karane kii anumati detee haye, aur teevrata key raikhik pratinidhitva seey ganana karna aasaan hoe jaataa haye. 32-bitt ekal-parishuddhata floating point parr laabh yeh haye kii isake liye aadhe bhandaran aur bandwidth (parishuddhata aur seema kii keemat parr) kii aavashyakta hoti haye.
jaali matra nirdhaaran key liye aadhaa parishuddhata upayogi hoe sakati haye. jaal detta koo aamtaur parr sheershon key liye 32-bitt ekal parishuddhata floats kaa upayog karke sangraheet kiya jaataa haye, halanki kuchh sthitiyon mein sateekta koo kewal 16-bitt aadhe parishuddhata taka cumm karna sweekarya haye, kuchh parishuddhata kii keemat parr kewal aadhe bhandaran kii aavashyakta hoti haye. jaal parimanikaran aavashyaktaon key aadhar parr 8-bitt yaa 16-bitt nishchit sateekta key saath bhee kiya jaa sakata haye.
machine learning yaa tantrika network key liye hardware aur software aadhe parishuddhata kaa upayog karate hainh aise anuprayog aamtaur parr badee matra mein ganana karate hain, lekin uchch star kii sateekta kii aavashyakta naheen hoti haye. hardware key kaaran aamtaur parr 16-bitt ardh-parishuddhata floats kaa samarthan naheen kartaa haye, tantrika network aksar bee. aff. float 16 praarup kaa upayog karate hain, joe kii ekal parishuddhata float praarup haye jise 16 bits mein kaataa jaataa haye.
yadi hardware mein ardh-parishuddhata ganit kii ganana karane key nirdesh hain, tou yeh aksar ekal yaa dohri parishuddhata seey tej hotaa haye. yadi pranaliyon mein simdi nirdesh hain joe ack nirdesh key bheetar kaee floating-point nambaron koo sambhal sakate hain, tou ack saath doguni sankhya parr kaam karke aadhi sateekta doguni teji seey hoe sakati haye.
hardware samarthan.
bhuja vastukala key kaee sanskaranon mein aadhi sateekta key liye samarthan haye.
x86 nirdesh sett mein aadhi sateekta key liye samarthan intell neelam rapids processor mein lagu kiye gaye avx-512 _ fp16 nirdesh sett vistaar mein nirdisht kiya gayaa haye.
risk-vee parr, cocksey _ 1 aur cocksey _ 2 extension 16-bitt ardh parishuddhata floats key liye hardware samarthan pradaan karate hain. cocksey _ 2 vistaar cocksey _ 1 kaa ack nyuntam vikalp haye.
power isa parr, vee. aiss. aiks. aur abhee taka anumodit naheen aiss. vee. pee. 64 vistaar 16-bitt ardh parishuddhata floats key liye hardware samarthan pradaan kartaa haye joe pavrisa v3.1b aur baad mein hotaa haye.

