The Explosion of the Ariane 5 '96

[KeligiiJabhad]

4-tii June 1996 ayeey "European Space Agency" hawada sare u dirtay
gantaal (rocket) waday dhowr "satellite". Gantaalkaas waxaa lagu
magacaabay "Ariane 5", qarashka ku baxay sameeyska "Technology"-ga
Ariane wuxuu noqday 7 billion oo doolar. Qiimaha halkaas gantaal iyo
xamuulka uu maalintaas sidayna wuxuu ahaa 500 million doolar.

Waxaa kaloo jirta in gantaalku lahaa sadex "computer" oo hogaaminayey,
maadaama uu kali-socod ahaa ! Laba ka mid ah Kombiyuterada wuxuu xil
ka saarnaa ineey mar walba xisaabiyaan waxyaabo badan oo socdaalka
gantaalka quseeya oo uu ka mid ahaa xaawligiisa (velocity), isla
markaan u gudbiyaan natiijadooda Kombiyutarka sadexaad oo ka weyn
kuwa kale, isaguna cabiro waddada uu haleelayo gantaalku, si uu u
gaaro halkii lala rabay ee uu "satellite"-yada gaarsiin lahaa. Labada
yar-yar mid kamid ahi wuxuu ku jiraa "istaambeey" oo wuxuu hawl galaa
oo keli ah haddii uu kan kale qaribmo. Dhawr iyo soddon sekend markii
uu gantaalkii hawada ku jiray buu is buurtay oo qarxay !
Balada dhacday waa maxay ?


Baladu waxeey ka timid is-afgarsho-waa dhexmaray kombeyutarda
gantaalka. Si aan taas u fahano, bal aan u kuur galno arinkan:
Kaba soo qaad in Aadmigu (dadku) uu 50 Sentimitir (50 cm) ahaan lahaa,
waxeey markaa noqon laheeyd in daaraha (guryaha) iyo maqsinada dadku
ku noolyihiin dhererkoodu yaraan laha, ileen maxaa dad gaa-gaaban
guryo dhaa-dheer loogu dhisaa oo uu qarash "maalaa-yacni" ugu lumaa!
Balse madaama dadku dherer-ahaan isku qasanyahay, ayeey noqotay in
guryaha dhererkoodu noqdo meel dhexe, si aaw gaab iyo aw dheere midna
guri u waayin. Taasi xal wanaagsan maaha. Waxaa taa ka wanaagsanaan
laheeyd hadii aay jiri lahaayeen guryo loo dhisay in markii la rabana
la dheereeyn (waasicin) karo markii la rabana la gaabin karo.


Ka soo qaad waxaa jira hoteel, wuxuu leeyahay 3 qol (maqsin), martida
hoteelkuna waa 2 qof oo dherer caadi ah iyo nin 3 mitir ah! qololkuna
(maqsinaduna) waa 2.5 mitir. Markaa waa inaan Aaw-dheere banaanka
dhignaa. Haddiise dhererka maqsinada la bedeli karo, waxaanu xoogaa
yareeyn laheeyn maqsinada labada nin ee kale, si uu maqsinka sadexaad
u kala baxo oo ninka 3-da mitir ah boos (meel) loogu helo.


Sidoo kale kombiyutarku wuxuu leeyahay maqsino wax keeydiya
(RAM-Memory/CPU-Register). Waxaana halkaa dega oo ku nool "Tiro"
(numbers). Tiraduna isku dherer ma aha. Tirada uu kombiyuterku kala
maamulo (waa markaan tix raacno luqada prograamka ee "C";
C programming language) waxaa ugu yar "integer" ("char" aan iska
iloowno!), waxaa ka weeyn "double", waxaase kasii weeyn "long double".
Kombiyuterka aan anigu shaqsiyan isticmaalo, tiro "integer" ah waxeey
u baahantahay boos (qol!) 4 "byte" ah, tiro "double" ahna waxeey u
baahantahay 8 "byte", "long double" 12 "byte". Sida Guryahaba mitir
lagu cabiro, baa keeydiyaha kombiyuterkana (RAM, Hard Disk,
CPU-Register) "byte" ama "bit" lagu cabiraa (1 byte = 8 bit).


Markaa, hadii aan isku dayno in boos "integer" aan "double" gelino,
waxaa dhacaya qalad, ileen meeshu "double" ma qaadee. Si aanu
qaladkaas u dhicin, waa in aan kombiyuterka u sii sheegnaa inuu
booska "integer" waasiciyo, oo uu ka dhigo meel uu "double" geli karo.
Waa sidii hoteelkii aan kor ku sooo sheegnay , oo maqsinadiisa markii
la rabana la waasicinkaro, markii la rabana la yareeynkaro.Marka aan
"Ariane 5" dib ugu soo noqono; Waxaa dhacday in "program" xisaabinayey
xawaaliga (velocity) gantaalka uu damcay inuu ku keeydiyo natiijadii
xawaaliga (taasoo u baahneeyd boos 8 "byte" ah) boos dhumuciisu yahay
2 "byte" oo keliya. Iyadoon isla marka kombiyuterka loo sheegin inuu
booskaas yar baaxiyo. Qaladkaasi wuxuu keenay in labadii Kombeyuter ee
yaraa aay wareeraan oo aay xisaab qariban u gudbiyaan kombeyuterkii
weeynaa, isla markaana shaqadii ka fariistaan. Mudo kadibna Systeemkii
gantaalku isku dhex yaaco, dabadeedna qarxo.


Haddii aan Arinka sii faaqidno, bal aan qorno program kombiyuter,
kaasoo noo xisaabinaya tiro si xaawli ah (very fast) u tarmeeysa.
Programku wuxuu kombiyuterka u sheegayaa inuu tiradaas boos
"long double" ah (12 Byte) ku keeydiyo kuna magacaabo booskaas "y":


Formula: long double y = x * x
x (bilaw = initial) = 3


natiijo : y = 3 * 3 = 9
y = 9 * 9 = 81
y = 81 * 81 = 6561
y = 6561 * 6561 = 4.30467e+07
y = 1.85302e+15
y = 3.43368e+30
y = 1.17902e+61
y = 1.39008e+122
y = 1.93233e+244
y = 3.73392e+488


Waxeeynu markaa aragnaa in kombiyuterku hawshii si wanaagsan inoogu
fuliyey. Haddiise aanu u sheegno kombiyuterka inuu "y" inoogu keeydiyo
boos "integer" qaadaya (4 Bytes), waxuu ina siinayaa xisaab qaldan :


y = 3 * 3 = 9
y = 9 * 9 = 81
y = 81 * 81 = 6561
y = 6561 * 6561 = 43046721
y = = -501334399
y = = 2038349057
y = = -1970898431
y = = 120648705
y = = 1995565057
y = = -1876701183


Waxeeynu aragnaa in marka la dhaafo "round"-ka 3-aad tirada
kombiyuterku ina siinayo qalad tahay. Mar alle markii aay natiijada
"y" ka badato tiri booskeedu ka weeynyahay "integer", waxaa wareer ku
dhacayaa kombiyuterka. Xusuuso Ariane 5 !


Program-keenu (natiijada quman) oo ku qoran "C" (C programming
language) waa kan :


#include <stdio.h>


int main ()
{
long double x = 3;


int i;
for (i = 0; i < 10; i++)
{
x = x * x;
printf ("%d\n", x);
}
return 0;



}


Haddii aan sadarka afaraad ku bedelno " integer x = 3 " waxaa dhacaya
qaladkii aanu kor ku soo sheegnay. Haddii aad meesha (program-ka) ka
weeyso "y", ha yaabin oo "y" maqnaashaheedu wax macnaa oo saa u weeyn
ma sameeyneeyso ! Xalka xisaabta waxaan ku helnay inagoo
isticmaaleeyna waxa loo yaqaano "iteration" oo aad ugu dhaw
"recursion"

Ugu dambeeyn, tusaale kale :


Aan xisaabino "formula"-da hoos ku qoran inagoo ka bilaabeeyna x = 0.5
ilaa x = 110, kuna keeydineeyno boos "long double" (12 Bytes) ah.
Natiijada inoo soo baxda, waxeeynu barbar dhigeeynaa natiijada
dhabta ah (exact arithmetic !). Programka xalka keenaya wuxuu
adeegsanayaa "iteration".


Formula : X i+1 = 3.75 * Xi * (1 - Xi) ; X0 = 0.5


Natiijo :


X exact arithmetic "C" long double (waxaa xisaabiyey
program isticmaalaya boos "long double")
---------------------------------------------------------------------
. . .
. . .
. . .


X =60 0.7990863343... 0.79908633 70...
X =70 0.4521952998... 0.4521952 586...
X =80 0.8561779966... 0.85617 59906...
X =90 0.7399137486... 0.7 400517104...
X =100 0.8882939922... 0. 9017659679...
X =110 0.7156795292... 0. 2201217854...


Waxaan aragnaa in marka la gaaro x=60 uu dhalanayo is-qilaaf natiijada
dhabta ah iyo tan programku soo saaray (oo aan kala siibnay si
qilaafku u muuqdo), oo marba marka ka sii dambeeysa qilaafku kasii
darayo. Waxaa kaloo inoo muuqda, in xitaa "long double" waxba inoo
qaban karin mar haddii xisaabtu faraha ka baxdo !


Prograamkiina waa kan :


#include <stdio.h>


int main ()
{
long double x = 0.5;


int i;
for (i = 1; i <= 110; i++)
{
x = 3.75 * x * (1 - x);
if (i > 59 && i % 10 == 0)
{
printf ("%.10Lf\n", x);
}
}


return 0;



}


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By Lama