
antim sthaan parr ikai

computer vigyaan aur sankhyaatmak vishleshan mein, antim sthaan yaa nyuntam parishuddhata (yuu. ell. pee.) kii ikai dou lagaatar tairate-bindu sankhyaon key beach kaa antar haye, i.ee.nyuntam mahatvapurna ank (sabse sahee ank) kaa maan darshaata haye kii kyaa yeh 1 haye. iska upayog sankhyaatmak gananaon mein sateekta key maap key roop mein kiya jaataa haye.
paribhasha.
ack paribhasha haih mool sootra mein sateek sootra key saath _ 1, yadi sootra _ 3 haye, tou 
johnn harrison dwara sujhaae gaye ack anya paribhasha, thodi alag haih sootra _ 4 dou nikatatam "faila huaa" floating-point number sootra _ 5 aur sootra _ 1 (i) key beach kii doori haye.ee.sootra _ 7 aur sootra _ 8 vaale, yeh maanate hue kii ghatank seema oopari seema mein naheen haye. yeye paribhaashaaen kewal mooldravya kii hastaaksharit shaktiyon parr bhinn hoti hain.
aaee. ee. ee. ee. 754 vinirdesh-jisake baad sabhi aadhunik floating-point hardware aatey hain-key liye aavashyak haye kii ack praathamik ankganitiya sanchaalan (1985 seey jodd, ghataav, gunan, vibhajan aur vargamool, aur 2008 seey aff. aim. aeye.) kaa parinam sahee dhang seey goal hoe, jiska arth haye kii nikatatam goal karane mein, goal parinam ganitiya roop seey sateek parinam key 0.5 alp key bheetar haye, johnn harrison kii paribhasha kaa upayog karate hue; isake vipareet, iss guna kaa tatparya haye kii goal parinam aur ganitiya roop seey sateek parinam key beach kii doori nyuntam haye (lekin aadhe mamalon key liye, yeh lagaatar dou floating-point sankhyaon dwara santusht haye). pratishthit sankhyaatmak pustakalaya buniyaadi divya karyon kii ganana 0.5 aur lagbhag 1 alp key beach karate hain. kewal kuchh pustakalaya hii unhein 0.05 key bheetar ganana karate hain, yeh samasya table-maker kii duvidha key kaaran jatil haye.
udaaharan.
udaaharan 1.
sootra _ 9 koo ack sakaratmak floating-point sankhya honey dein aur maan lein kii sakriya goal mode goal seey nikatatam haye, summ seey judaa huaa haye, sootra _ 10 koo darshaaya gayaa haye. yadi sootra _ 11 haye, tou sootra _ 12. anyatha, sootra _ 13 yaa sootra _ 14, cumm seey cumm mahatvapurna ank key moolya aur sootra _ 9 key ghatank parr nirbhar kartaa haye. yeh ack samvaadaatmak sanket parr type kiye gaye nimnalikhit haskell code mein pradarshit kiya gayaa haih
> jaba taka (\x-> x = = x + 1) (+ 1) 0:: float
1.6777216e7
> yeh-1
1.6777215e7
> yeh + 1
1.6777216e7
yahaan humm ekal parishuddhata mein 0 seey shuru karate hain aur baar-baar 1 jodate hain jaba taka kii operation moolya koo naheen badalata haye. choonki ack-parishuddhata sankhya key liye mahatva mein 24 bits hotey hain, isaliye pahala purnank joe bilkul pratinidhitva yogya naheen haye vaha 224+1 haye, aur yeh moolya round seey nikatatam mein 224 taka jaataa haye, joe summ seey judaa hotaa haye. iss prakaar parinam 224 key barabar haye.
udaaharan 2.
jaava mein nimnalikhit udaaharan dou dohare maan koshthak sootra _ 16: sootra _ 17 koo dhundhkar ack tairate bindu moolya key roop mein anumaanit kartaa haye.
// 20 dashamlav ankon key saath π
badaa dashamlav π = nayaa badaa dashamlav ("3.14159265358979323846");
// ack dohare tairate bindu parr kaaten
double p0 = π.dohare maan ();
// -> 3.141592653589793 (hexah 0x1.921fb54442d18p1)
// p0, π seey chhota haye, isaliye agali sankhya koo dohare key roop mein darshaaen.
double pee1 = ganit.agala (pee0);
// -> 3.1415926535897936 (hexah 0x1.921fb54442d19p1)
phir sootra _ 18 koo sootra _ 19 key roop mein nirdhaarit kiya jaataa haye.
// alp (π) pee1 aur pee0 key beach kaa antar haye.
bigg decimal alp = nayaa bigg decimal (pee1)।घटाना (nayaa badaa dashamlav (pee0));
// -> 4.44089209850062616169452667236328125e-16
// (yeh thheek 2 * * (-51) haye)
// maanak pustakalaya kaary kaa upayog karate samay samaan parinam
double ulpamaath = ganit.alp (pee0);
// -> 4.440892098500626e-16 (hexah 0x1.0p-51)
udaaharan 3.
ack anya udaaharan, python mein, ack samvaadaatmak sanket parr bhee type kiya gayaa haye, haih
> x = 1
> pee = 0
> jabaki x!= x + 1:
... x = x * 2
... pee = pee + 1
> x
9007199254740992.0
> pee
53
> x + 2 + 1
9007199254740996.0
iss mamle mein, humm cock _ 1 seey shuru karate hain aur ise baar-baar cock _ 2 taka doguna karate hain. udaaharan 1 key samaan, parinam 253 haye kyonki double-parishuddhata floating-point praarup 53-bitt mahatva kaa upayog kartaa haye.
bhasha samarthan.
boost see + + pustakalayon mein kaary pradaan kartaa haye cock _ 3, cock _ 4, cock _ 5 
aur paas key (aur door key) tairate-bindu moolyon koo praapt karane key liye cock _ 6, aur dou doubles key beach tairate-bindu doori kii ganana karane key liye cock _ 7.
see bhasha pustakalaya kissy diye gaye disha mein agali floating-point sankhya kii ganana karane key liye kaary pradaan kartaa haih cock key liye cock 8 aur cock key liye 9, cock key liye cock key liye 11 aur cock key liye 12, cock key liye 14 aur cock key liye 15, cock key liye 17 mein ghoshit kiya gayaa haye. yeh macro cock key liye 18, cock key liye 19, cock key liye 20 bhee pradaan kartaa haye, joe sambandhit prakaar mein 1 aur agali badee pratinidhitva yogya sankhya key beach sakaratmak antar kaa pratinidhitva kartaa haye (i.ee. ack kaa alp).
jaava maanak pustakalaya kaary pradaan kartaa haye aur. unhein jaava 1.5 key saath pesh kiya gayaa thaa.
swift standard library kuchh diye gaye disha mein agale floating-point number taka pahunch pradaan karati haye, udaaharan gunon cock _ 21 aur cock _ 22 key madhyam seey. yeh swift key floating-point prakaron key liye udaaharan guna cock _ 23 aur prakaar guna cock _ 24 (joe cock _ 18 jaise macro key anuroop haye) bhee pradaan kartaa haye.

