random(?)

[Christos Ricudis]

Hello Linux-greek-users!

  On 17 Feb 99, Linux-greek-users wrote to Christos Ricudis with subject "Re:
random(?)":


 L> Argisa ligo na apantisw alla koitaxa merika pragmata sto metaxy.
 L> H rand() dinei statistika tyxaious arithmous kai oxi tyxaious me tin
 L> ennoia pou xrhsimopoioume synithos. 

Dooooing.

Eyxaristoume poy paiksate, alla dystyxws xasate. 

Oi Linear Congruential Generators poy xrhsimopoioyntai synh8ws gia th
dhmiourgia pseudorandom sequences xrhsimopoiwntas th sxesh 

Zx+1 = Zx*a+c mod n

parousiazoyn mia seira apo problhmata. Kat'arxas, profanws h akoloy8ia
epanalambanetai me periodo n. Se polla library implementations ths rand() to n
einai arketa mikro, kai to ANSI protypo ka8orizei aplws oti prepei na einai
toylaxiston 32768. Profanws otan xrhsimopoieis enan random number generator gia
na kaneis p.x. oloklhrwsh me monte-carlo 8a protimoses 640.000 random deviates,
kai oxi 20 seires apo ta idia 32768 random deviates :>. 

Epishs, oi LGC's pasxoyn apo arketa megala sequential correlations. An
xrhsimopoihseis mia K-ada synexomenwn klhsewn ths rand() ws shmeia ston K-
diastato xwro, 8a deis oti anti ta shmeia na "gemizoyn" omoiomorfa ayto to
xwro, sygkentrwnontai se ena ari8mo (K-1)-diastatwn epipedwn, to plh8os twn
opoiwn einai to poly n^(1/K) (kai synh8ws einai mikrotero, logw kakhs epiloghs
twn a, c kai n). Skepsoy aplws thn periptwsh n=32768 kai K=3, otan prospa8eis
na gemiseis me shmeia ena kybo. 8a deis oti ta shmeia sygkentrwnontai se molis
32 2-diastata epipeda...

8eleis ki alla? Ta least significant bits twn random deviates poy paragontai
apo ena LGC einai poly ligotero omoiomorfa katanemhmena apo ta most significant
bits. Kai mia poy o synh8ismenos tropos na pairneis random deviates < j einai
na pairneis to ((MAXRAND*rand()) mod j), poy pairnei aplws ta least significant
bits, katalhgeis se akoma xeirotera apotelesmata. 

Poio einai to ma8hma? Na xrhsimopoieite PANTOTE dikous sas random number
generators, parmenoys kyriws apo th bibliografia (deite ton trito tomo toy
Knuth, to "Numerical Recipes in C" (Press, Vetterling, Teukolsky, Flannery) kai
opoiodhpote biblio asxoleitai me simulation - egw exw to "Simulation Modelling
and Analysis" (Law,Kelton). 

Pisteyw pantws oti ta deviates ths /dev/random prepei na exoyn arketa kales
idiothtes, alla gnwrizw oti den exoyn tyxei sobarhs meleths apo kanenan, gi
ayto kai ta fobamai...


--
Christos Ricudis
Prof:    So the American government went to IBM to come up with a data
         encryption standard and they came up with ...
Student: EBCDIC!
--
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