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zGzeNi1p?U@faLx{N{;lm;JN`AqeNekM=?Awnjk4hw3Bc?3JxlY7lY#m50;XB<>EmS z#z3MS!O*=Os31UfX#hjHKuUtx4XMjOOCx>(_Y%=)ARq~NrXaRGpVgeGz3Fdx7( zq_{7{;7Qtp8;a=yCJ4c&P%!}!$}jVp3>sai)?j14|ETJr8>Ka0KZGlc=DU{QO?`UN x%6!q%Y>yYc$>-5g5#ac(%dk$0Z~w{sRux>QHJHrz9RVY_RbtbmNhe?T{{zdHwQT?Z diff --git a/git-obzornik.tex b/git-obzornik.tex index 9e8e003..6777113 100644 --- a/git-obzornik.tex +++ b/git-obzornik.tex @@ -32,11 +32,11 @@ mapi(direktoriju). V glavnem se uporablja za upravljanje z izvorno kodo pri razvoju računalniških programov. Mnogi med nami pa ga uporabljajo tudi pri pisanju besedil v \LaTeX-u. Poleg tega, da Git hrani - zgodovino sprememb, tudi omogoča da več ljudi hkrati sodeluje pri - urejanju istih datotek. Ogledali si bomo, kako Git deluje. Opisali bomo, + zgodovino sprememb, tudi olajša združevanje sprememb, ko več ljudi hkrati + ureja iste datoteke. Ogledali si bomo, kako Git deluje. Opisali bomo, kako Git uporabi \emph{zgoščevalne funkcije}, \emph{Merklejeva drevesa} in \emph{usmerjene aciklične grafe}, da shrani zgodovino različic in - omogoči hkratno urejanje vsebine. Matematični model, ki ga Git uporablja + olajša hkratno urejanje vsebine. Matematični model, ki ga Git uporablja je v resnici zelo preprost in njegovo razumevanje nas lahko reši marsikatere zagate, ki nastane med njegovo uporabo. \end{abstract} @@ -75,47 +75,39 @@ sistem za nadzor različic} (angl. Distributed Version Control System javno spletišče, ki je namenjeno skladiščenju Git repozitorijev. \end{opomba} -V nadaljevanju bomo obravnavali nasledjne teme: - -\begin{itemize} - \item - \emph{Podatkovno skladišče:} Kako Git uporablja - \href{https://sl.wikipedia.org/wiki/Zgo\%C5\%A1\%C4\%8Devalna_funkcija}{zgoščevalno - funkcijo} (angl. hash function)? in - \href{https://en.wikipedia.org/wiki/Merkle_tree}{Merklejeva drevesa} - za hranjenje posnetkov vsebine mape. - \item - \emph{Zgodovina sprememb:} Kako zgodovino predstavimo z +V nadaljevanju si bomo ogledali, kako Git uporablja +\href{https://sl.wikipedia.org/wiki/Zgo\%C5\%A1\%C4\%8Devalna_funkcija}{zgoščevalno funkcijo} +(angl. hash function) in posplošitev +\href{https://en.wikipedia.org/wiki/Merkle_tree}{Merklejevih dreves} +za hranjenje posnetkov vsebine mape. Kako zgodovino sprememb predstavimo z \href{https://en.wikipedia.org/wiki/Directed_acyclic_graph}{usmerjenim acikličnim grafom}, v katerem so vozlišča različice, povezave pa - povežejo različice z njihovimi neposrednimi predhodniki? - \item - \emph{Reference}: Kako preproste reference (kazalci) na vsebino + povežejo različice z njihovimi neposrednimi predhodniki in + kako preproste reference (kazalci) na vsebino omogočajo bliskovito preklaplanje med različicami in preprečijo popolno zmešnjavo, ko več ljudi hkrati spreminja iste datoteke? -\end{itemize} \section{Podatkovno skladišče} Ko ustvarimo nov Git repozitorij, Git ustvari podmapo z imenom -\texttt{.git} z vsemi podatki, ki jih Git potrebuje. Git v mapi -\texttt{.git} hrani različne stvari: +\texttt{.git} z vsemi podatki, ki jih potrebuje. V mapi +\texttt{.git} se hranijo različne stvari: \begin{itemize} \item - vsebino datotek, ki smo jih dodali v repozitorij, + vsebina datotek, ki smo jih dodali v repozitorij, \item - drevesno strukturo korenske mape, ki jo hranimo v repozitoriju, + drevesna struktura korenske mape, ki jo hranimo v repozitoriju, \item - posnetke stanja v različnih trenutkih s podatki o avtoju, datumu in + posnetki stanja v različnih trenutkih s podatki o avtoju, datumu in opisu sprememb, \item - kazalce na posamezne posnetke stanja. + kazalci na posamezne posnetke stanja. \end{itemize} Git repozitorij je vsaka mapa, ki vsebuje podmapo \texttt{.git} z zgoraj -navedenimi podatki. Podrobnosti o tem, kako Git hrani podatke, si lahko -preberete v knjigi Pro Git \cite{chacon_102_nodate}. +navedenimi podatki. Kako Git hrani podatke bomo spoznali v +nadaljevanju, podrobnosti pa si lahko preberete v knjigi Pro Git \cite{chacon_102_nodate}. \section{Zgoščevalna funkcija} @@ -143,9 +135,7 @@ približno enako verjetne. Na ta način zmanjšamo verjetnost trka (glej poglavje \ref{sec_trk}). Verjetnost trka je izjemno majhna, zato Git lahko predpostavi, da je niz \(b\) enolično določen z njegovo zgostitvijo \(H(b)\). - -Git uporablja \(160\) bitno zgoščevalno funkcijo \emph{SHA1}. Funkcija -SHA1 je posebna implementacija zgoščevalne funkcije, ki se je +Git uporablja \(160\) bitno zgoščevalno funkcijo \emph{SHA1}, ki se je uporabljala v kriptografiji\footnote{Leta 2017 so raziskovalci iz CWI Amsterdam in Google Research našli prvi praktični primer dveh različnih pdf datotek, ki imata isto SHA1 @@ -162,7 +152,9 @@ imenom \(h_{3}h_{4}\ldots h_{40}\) v mapi \(h_{1}h_{2}\), kjer je \(h_{1}h_{2}h_{3}\ldots h_{40}\) zapis \(H(b)\) v 16-tiškem sistemu. Datoteka, katere vsebina ima zgostitev \(H(b)\) enako \texttt{8dd6d4bdaeff93016bd49474b54a911131759648} bo shranjena v -\texttt{.git/objects/8d/d6d4bdaeff93016bd49474b54a911131759648}}. +\texttt{.git/objects/8d/d6d4bdaeff93016bd49474b54a911131759648}. Zavoljo preglednosti +bomo v nadaljevanju večrat napačno zatrjevali, da je ime datoteke enako zgostitvi +njene vsebine.}. Vsebina \(b\) je tako vedno dostopna pod imenom, ki je enako njeni zgostitvi \(H(b)\). Tako dobimo \href{https://en.wikipedia.org/wiki/Content-addressable_storage}{vsebinsko @@ -193,10 +185,10 @@ je seveda zgostitev vsebine \(H(b)\). po sistemu Posix.} \end{figure} -Drevo preprost seznam v tekstovni datoteki, za katerega lahko prav tako izračunamo zgostitev. -Zgostitev datotečnega drevesa natanko določa tako imena datotek, kot +Drevo je preprost seznam v tekstovni datoteki, za katerega lahko prav tako izračunamo zgostitev. +Zgostitev datotečnega drevesa natanko določa tako imena kot tudi vsebino datotek, ki so vsebovane v mapi. Če se katerakoli datoteka -ali ime datoteke v mapi spremeni, se bo spremnila tudi njena zgostitev +ali njeno ime v mapi spremeni, se bo spremnila tudi njena zgostitev in posledično zgostitev za drevo. Poleg posameznih datotek, lahko drevo vsebuje tudi poddrevesa. Tako lahko rekurzivno ustvarimo drevesno podatkovno strukturo, ki zajema mapo z datotekami in podmapami v @@ -207,7 +199,7 @@ podmape. \begin{figure}[h] \centering - \begin{Verbatim}[frame=single] + \begin{Verbatim} ├── bla.txt (vsebina: bla) ├── blabla.txt (vsebina: blabla) └── podmapa @@ -271,10 +263,8 @@ zgostitve za korensko mapo. Zgostitev služi tako kot identifikator vsebine, kot tudi kot kontrolna vsota, ki omogoča detekcijo sprememb. \begin{opomba} - Podatkovna struktura objektov v Gitu je podobna Merklejevim drevesom. - Razlika je v tem, da Gita hrani le eno kopijo datotek z identično - vsebino, zato dobimo usmerjen aciklični graf in ne drevesa. Postopek graditve - datotečnega drevesa v Gitu je soroden veriženju blokov, ki se uporablja v + Podatkovna struktura objektov v Gitu je podobna Merklejevim drevesom\cite{merkle_digital_1988}. + Postopek graditve datotečnega drevesa v Gitu je soroden veriženju blokov, ki se uporablja v kriptovalutah. \end{opomba} @@ -285,11 +275,277 @@ in da lahko do določene vsebine dostopamo le, če poznamo njeno zgostitev. Po d je vsebina za vse praktične primere določena s svojo zgostitvijo. Tako lahko enostavno preverimo verodostojnost vsebine, ki je shranjena v Gitu. +\section{Zgodovinski graf sprememb} + +V prejšnjem poglavju smo videli, kako Git hrani vsebino celotne mape in +kako zgostitev korenske mape določa vsebino vseh shranjenih datotek. +Zgodovinsko drevo sprememb je preprosta razširitev omenjene podatkovne strukture. + +\subsection{Posnetki stanja} + +Osnovna enota v Gitu je \emph{vnos} (angl. \emph{commit}). Vnos je +posnetek stanja zabeleženih datotek v trenutku, ko je bil ustvarjen. +Poleg vsebine datotek vsak vnos vsebuje še metapodatke o avtorju, datumu +vnosa in opisom sprememb. Podobno kot objekt tipa \emph{drevo}, je tudi +vnos objekt v vsebinsko naslovljivi shrambi in ima določeno +\emph{zgostitev vnosa}. Zgostitev vnosa je natanko določena z vsebino +shranjenih datotek in metapodatkov vnosa. + +\begin{figure}[h] + \begin{Verbatim}[frame=single] +tree 65c47feec7465e80492620a48206793e078702e0 +parent 16f2994757f1213935b8edb9ae7fee3a8e9ec98d +author MV 1765235698 +0100 +committer MV 1765235698 +0100 + +Dodaj bla + \end{Verbatim} + \caption{Vnos v Gitu je shranjen v podatkovno shrambo pod imenom, + ki je zgostitev vsebine vnosa: \gitobject{8d}{d6d4bdaeff93016bd49474b54a911131759648}.} +\end{figure} + +Vsak vnos je povezan s točno določenim posnetekom vsebine korenskega +datotečnega drevesa, ki ga identificira zgostitev. Poleg tega so +posamezni vnosi povezani v \emph{usmerjen acikličen graf}, ki +predstavlja zgodovino sprememb. Vsak vnos je \emph{vozlišče} +v grafu in izhaja iz enega ali več starševskih vnosov. Izjema je +prvi vnos. Povezave v grafu povezujejo vnose z njihovimi +starši. + +\begin{figure}[h] + \centering + \includegraphics[width=0.6\linewidth]{slike/commit-history.pdf} + \caption{Vnosi v Gitu kot usmerjen graf. Vsak vnos(razen prvega) ima + povezavo na vnose iz katerih izhaja.} +\end{figure} +Tudi vnose hrani Git v vsebinsko naslovljivi shrambi pod imenom, ki je enako zgostitvi +vnosa. V shrambi imamo tri vrste objektov: vsebina datotek (blob), datotečna drevesa (tree) +in vnose (commit). Vsi objekti so dostopni, če poznamo njihovo zgostitev in so med seboj +povezani v usmerjen aciklični graf. Zgostitve objektov "na vrhu" natanko določajo vsebino +vseh objektov pod njimi. Na vrhu grafa so vnosi, ki vsebujejo reference na druge vnose in +na posnetke korenske mape. Posnetek korenske mape vsebuje reference na vsebino datotek in +posnetke podmap. +\begin{figure}[h] + \centering + \includegraphics[width=0.6\linewidth]{slike/object-storage.pdf} + \caption{Vsebinsko naslovljiva shramba objektov v Gitu. Naslovi so + zgostitve vsebine. Shramba vsebuje dva vnosa. V prvem vnosu smo dodali + dve datoteki \protect\texttt{bla.txt} in \protect\texttt{blabla.txt}, v + drugem vnosu pa smo spremenili le vsebino datotoeke + \protect\texttt{bla.txt}.} +\end{figure} + +\section{Kazalci: veje in značke} + +Poleg objektov kot so \emph{vnosi}, \emph{posnetki map} in +\emph{posnetki datotek} pozna git še reference. Reference so preproste datoteke, ki vsebujejo +zgostitev za posamezen vnos. Referenc git ne hrani v skladišču objektov, temveč posebej v mapi +\texttt{.git/refs}. + +\begin{figure}[h] + \centering + \includegraphics[width=0.6\linewidth]{slike/branches-tags.pdf} + \caption{Veja \texttt{main} in značka \texttt{v-1.0} sta preprosta kazalca + na posamezen vnos.} +\end{figure} + +Git pozna dve vrste referenc. \emph{Veja} (angl. \emph{branch}) je posebne +vrste referenca, ki se premika, ko dodajamo nove vnose. Vsakič ko ustvarimo nov vnos, se +trenutno aktivna veja premakne na novo ustvarjeni vnos. +Veje uporabljamo za vzdrževanje vzporednih razvojnih linij, ki so med sabo neodvisne. +\emph{Značka} (angl. \emph{tag}) +je referenca, ki je statična. +Za razliko od veje, se oznaka nikoli ne premika samodejno. Zato se uporablja predvsem +za označevanje pomembnih mejnikov v zgodovini na primer verzij posameznih izdaj. + +\begin{figure}[h] + \centering + \includegraphics[width=0.6\linewidth]{slike/branch-move.pdf} + \caption{Ko ustvarimo nov vnos, se aktivna veja \protect\texttt{main} + premakne naprej, značka \protect\texttt{v-1.0} pa ostane tam, kjer je + bila.} +\end{figure} + +\emph{HEAD} je posebna referenca, ki kaže na trenutno aktiven vnos. +Vnos, na katerega kaže \emph{HEAD} bo starševski vnos naslednjeg vnosa, +ki ga bomo dodali. Ko spreminjamo datoteke Git najprej postavi spremenjene datoteke +v \emph{čakalnico} (angl. \emph{staging area}), ki se imenuje tudi +\emph{indeks} (angl. \emph{index}). Šele ko ustvarimo vnos, Git indeks trajno +shrani. + +\begin{figure}[h] + \centering + \includegraphics[width=0.6\linewidth]{slike/head-index.pdf} + \caption{\emph{HEAD} je referenca na trenutno aktiven vnos. + \emph{Index} vsebuje spremembe, ki bodo zabeležene v naslednjem vnosu.} +\end{figure} + +Veje in značke nimajo v Gitu nobenega posebnega pomena, razen tega, da +so reference na vnose. Pomen posamenznih vej je stvar dogovora med +uporabniki. Tako se pogosto uporablja različne veje za različne namene: +\texttt{main} ali \texttt{master} je navadno glavna veja razvoja, veje z +imeni \texttt{stable}, \texttt{production}, \texttt{development} in +podobno označujejo različne stopnje razvoja programske opreme, veje s +predpono \texttt{feature} označujejo razvoj novih funkcionalnosti. +Vse te pomene damo vejam ljudje, ki sodelujemo v nekem Git repozitoriju. +Za Git so vse veje in značke zgolj preprosti kazalci na določen vnos. + +\section{Povzetek} + +Povzemimo sedaj, kaj smo spoznali o podatkovnem modelu Gita. +Git hrani zgodovino sprememb v \emph{vsebinsko naslovljivi shrambi + objektov}, ki hrani tri vrste objektov: + +\begin{itemize} + \item + \texttt{blob}: vsebina datotek, + \item + \texttt{tree}: imena vsebovanih datotek in podmap skupaj z njhovimi zgostitvami, + \item + \texttt{commit}: posnetek stanja projekta v nekem trenutku z metapodatki o avtorju, + času in sporočilom. +\end{itemize} + +Naslovi objektov so \emph{zgostitve} vsebine objekta, zato je zagotovljena +verodostojnost shranjenih podatkov. +Vnosi so povezani v \emph{usmerjen aciklični graf}, ki opiše zgodovino sprememb. +Vsak vnos je določen z \emph{zgostitvijo vnosa} (angl. \emph{commit hash}), ki je 40-mestna +heksadecimalna vrednost, izračunana s SHA1. Zgostitev vnosa je določena na podlagi vsebine +vseh datotek, kot tudi metapodatkov vnosa. + +Izven shrambe objektov hrani Git še reference na posamezne vnose. Poznamo dve vrsti referenc: + +\begin{itemize} + \item + \emph{Veja} (angl. \emph{branch}) je premična referenca, ki kaže + na določen vnos v zgodovini in se samodejno premakne naprej, ko + dodajamo nove vnose. + \item + \emph{Oznaka} (angl. \emph{tag}) je statična referenca, ki trajno + kaže na določen vnos. + \item + \emph{HEAD} je posebna oznaka, ki kaže na trenutno aktiven vnos v + delovni kopiji. +\end{itemize} + +Omenimo še dva pojma, ki jih uporabljamo pri delu z Gitom: + +\begin{itemize} + \item + \emph{Delovna kopija} (angl. \emph{workout copy}) je mapa v kateri + urejamo datoteke, ki jih nato vnesemo v Git. V delovni kopiji imajo na + začetku datoteke isto vsebino kot je vsebina trenutno aktivnega vnosa + (\texttt{HEAD}). Spremembe, ki jih naaredimo na delovni kopiji lahko + zabeležimo v nov vnos. + \item + \emph{Oddaljen repozitorij} (angl. \emph{remote}) je povezava(url) + na drug repozitorij (ponavadi na drugem računalniku), s + katerim lahko izmenjujemo vsebino. +\end{itemize} + + +\section{Git ukazi kot operacije na grafu} + +Gitov podatkovni model omogoča, da je večina operacij v Gitu obrnljivih. +To pomeni, da lahko repozitorij povrnemo v prejšnje stanje. Večina +operacij le dodaja nove vnose in starih ne briše\footnote{Nekatere operacije vnose tudi brišejo (npr. \texttt{git rebase}). +Takim operacijam rečemo, da spreminjajo zgodovino. Uporabniki morajo biti +pri njihovi uporabi posebej pazljivi, da +česa trajno ne zamočijo.}. +Zato so stare različice datotek +vedno na voljo. Git uporabniku daje samozavest, da brez strahu spreminja +vsebino, saj se lahko vedno vrne v času nazaj. Kot bi imel časovni +stroj. + +Opremljeni z razumevanjem podatkovnega modela Gita, lažje razumemo +posamezne operacije, ki jih Git omogoča. Ukazov ne bom +prevajal, ampak jih bom navedel kot jih pozna program \texttt{git}. + +\begin{verbatim} +git checkout referenca +\end{verbatim} +spremeni datoteke v delovni kopiji tako, da se ujemajo z vnosom, na +katerega kaže \texttt{referenca}. Poleg tega prestavi oznako \texttt{HEAD} na +isti vnos. Če je referenca veja, jo nastavi, kot aktivno vejo. Če je +referenca oznaka ali zgostitev vnosa, priedmo v stanje brez aktivne veje +(angl. \emph{deteached HEAD}). + +\begin{verbatim} +git commit -m "Sporočilo za vnos" +\end{verbatim} +ustvari nov vnos, ki kaže na stanje v čakalnici (angl. staging area ali +index). V zgodovinskem grafu ustvari novo vozlišče, ki je povezano s +prejšnjim vnosom. Poleg tega prestavi aktivno vejo in oznako +\texttt{HEAD} na novo ustvarjeni vnos. + +\begin{verbatim} +git add bla.txt +\end{verbatim} +doda vsebino spremenjene datoteke \texttt{bla.txt} v čakalnico. Ukaz ne +spreminja zgodovinskega grafa, pač pa doda novo vsebino in datotečna +drevesa, ki vsebujejo spremembe v shrambo objektov. Vsebina čakalnice bo +zabeležena v naslednjem vnosu. + +\begin{verbatim} +git pull +\end{verbatim} +pobere vsebino(objekte in reference) iz oddaljenega repozitorija in +uskladi lokalno vejo z oddaljeno. Shrambi objektov se preprosto doda +nove objekte, ki so v oddaljeni veji. Če je lokalna veja prednik +oddaljene, se lokalna veja enostavno prestavi, da kaže na isti vnos, kot +oddaljena veja. V nasprotnem primeru, mora uporabnik posredovati in +razrešiti morebitne konflikte. + +\begin{verbatim} +git push +\end{verbatim} +potisne novo vsebino na oddaljeni repozitorij. Push deluje obratno kot +\texttt{pull}. Ukaz je uspešno izveden le, če je oddaljena veja predhodnica +lokalne veje. + +\begin{verbatim} +git fetch +\end{verbatim} +pobere novo vsebino (vnose, veje in oznake) iz oddaljenega repozitorija. +Pri tem ne more priti do konfliktov, ker git preprosto doda nove objekte +v shrambo in obstoječih objektov nikakor ne spreminja. Oddaljenim vejam +in oznakam preprosto doda predpono z imenom oddaljenega repozitorija. + +\begin{verbatim} +git reset referenca +\end{verbatim} +spremeni kam kaže trenutno izbrana veja. Trenutno izbrano vejo prestavi na isti vnos, na +katerega kaže dana \texttt{referenca}. Ukaz ne spremeni zgodovinskega +drevesa, ampak le to, na kateri vnos kaže trenutno izbrana veja. + +\begin{verbatim} +git merge referenca +\end{verbatim} +ustvari nov vnos, ki združi dve ločeni veji v eno (trenutno izbrano in +referenco). Nov vnos ima dva starša: vnos na katerega kaže trenutna veja +in vnos, na katerega kaže \texttt{referenca}. Če pride do konfliktov, jih mora +uporabnik sam razrešiti, preden se ustvari nov vnos. + +\begin{verbatim} +git rebase referenca +\end{verbatim} +prestavi vnose v trenutno izbrani veji tako, da so potomci vnosa, na +katerega kaže \texttt{referenca}. Med ukazi, ki smo jih spoznali, je ta ukaz +edini, ki lahko povzroči izgubo podatkov. Običajno ukazi le dodajajo +nove vnose in prestavljajo reference. Zato je večina ukazov v Gitu +varna, v smislu, da jih lahko kasneje prekličemo in pridemo nazaj na +prejšnje stanje. Ukaz \texttt{rebase} pa spremeni zgodovino in ga ne +moremo preklicati, saj trenutne vnose nadomesti z novimi in stare vnose +pobriše\footnote{Obstaja enostaven način, kako \texttt{rebase} izvedemo tako, da ga lahko + kasneje prekličemo. Na vnos, ki ga želimo prestaviti z \texttt{rebase}, preprosto + postavimo novo vejo ali oznako. To povzroči, da se stari + vnosi ne pobrišejo, ko se izvede ukaz \texttt{rebase}.}. + \section{Trki zgostitev in rojstnodnevni paradoks}\label{sec_trk} -Git hrani datoteke pod imeni, ki so enaka zgostitvi vsebine. Če imata -dve datoteki z različno vsebino isto zgostitev, Git shrani le eno -datoteko in pride do izgubil podatkov. Git se zanaša na to, da je +Git hrani datoteke pod imeni, ki so enaka zgostitvi vsebine. Če bi imeli +dve datoteki z različno vsebino isto zgostitev, bi Git shranil le eno +datoteko in bi prišlo do izgube podatkov. Git se zanaša na to, da je verjetnost za to izjemno majhna. Kako bi ocenili to verjetnost? Koliko datotek bi morali shraniti v Git, da bi z znatno verjetnostjo @@ -303,14 +559,16 @@ tako da je vsaka izbira enakomerno porazdeljena. Kolikšna je verjetnost \(p(n,h)\), da bosta vsaj dve števili enaki? Verjetnost \(p(n,h)\) izračunamo elementarno z verjetnostjo nasprotnega dogodka: -\[1 - p(n,h) = \frac{h \cdot (h - 1)\cdots(h - n + 1)}{h^{n}} = - \prod_{k = 1}^{n - 1}\left( 1 - \frac{k}{h} \right).\] +\begin{equation} +1 - p(n,h) = \frac{h \cdot (h - 1)\cdots(h - n + 1)}{h^{n}} = + \prod_{k = 1}^{n - 1}\left( 1 - \frac{k}{h} \right). +\end{equation} Če izraz logaritmiramo, dobimo \begin{eqnarray} - \log(1 - p(n,h)) = \sum_{k = 1}^{n - 1}\log(1 - \frac{k}{h}) < - - \sum_{k = 1}^{n - 1}\frac{k}{h} = \frac{- \left( n(n - 1) \right)}{2h}. - \label{eq_log_ocena} + \log(1 - p(n,h)) = \sum_{k = 1}^{n - 1}\log(1 - \frac{k}{h}) < + - \sum_{k = 1}^{n - 1}\frac{k}{h} = \frac{- \left( n(n - 1) \right)}{2h}. + \label{eq_log_ocena} \end{eqnarray} Res! Logaritem je konveksna funkcija, zato so vrednosti manjše od @@ -327,16 +585,18 @@ Za vrednosti \(1 \ll n \ll h\) je \(1 - e^{- \frac{n^{2}}{2h}}\) tudi dobra aproksimacija za \(p(n,h)\). Da bi odgovorili kako odporna je zgoščevalna funkcija na morebitne -trka, moramo rešiti obratno nalogo: največ koliko števil \(n(p,d)\) +trke, moramo rešiti obratno nalogo: največ koliko števil \(n(p,d)\) lahko izberemo, da bo verjetnost pojava dveh enakih števil manjša od \(p \in \lbrack 0,1\rbrack\)? Natančen odgovor na to vprašanje ni tako preprost \cite{brink_probably_2012}. Lahko pa uporabimo oceno (\ref{eq_ocena}) in čez palec ocenimo vrednost \(n(p,h)\): -\[\begin{array}{r} - - n^{2} \approx \log(1 - p) \Rightarrow \\ - n(p,h) \approx \sqrt{2h\log(\frac{1}{1 - p})} \approx \sqrt{2h}. - \end{array}\] +\begin{equation} +\begin{array}{r} + - n^{2} \approx \log(1 - p) \Rightarrow \\ + n(p,h) \approx \sqrt{2h\log(\frac{1}{1 - p})} \approx \sqrt{2h}. + \end{array} +\end{equation} Funkcija \(\sqrt{\log(\frac{1}{1 - p})}\) zelo počasi narašča, ko se \(p\) približuje \(1\), zato jo lahko zanemarimo. Če je zgoščevalna @@ -347,308 +607,6 @@ različnih verzij datotek v Git. Raziskovalci, ki so razvili napad \emph{SHAttered}, so se posebej potrudili in so potrebovali ``zgolj'' približno \(2^{63}\) primerov, da so prišli do trka. -\section{Zgodovinski graf sprememb} - -V prejšnjem poglavju smo videli, kako Git hrani vsebino celotne mape in -kako je mogoče do vsebine dostopati če poznamo zgostitvijo korenskega -mape. Zgodovinsko drevo sprememb je preprosta razširitev omenjene -podatkovne strukture. - -\section{Posnetki stanja} - -Osnovna enota v Gitu je \emph{vnos} (angl. \emph{commit}). Vnos je -posnetek stanja zabeleženih datotek v trenutku, ko je bil ustvarjen. -Poleg vsebine datotek vsak vnos vsebuje še metapodatke o avtorju, datumu -vnosa in opisom sprememb. Podobno kot objekt tipa \emph{drevo}, je tudi -vnos objekt v vsebinsko naslovljivi shrambi in ima določeno -\emph{zgostitev vnosa}. Zgostitev vnosa je natanko določena z vsebino -shranjenih datotek in metapodatkov vnosa. - -\begin{table} - \begin{Verbatim}[frame=single] -tree 65c47feec7465e80492620a48206793e078702e0 -parent 16f2994757f1213935b8edb9ae7fee3a8e9ec98d -author MV 1765235698 +0100 -committer MV 1765235698 +0100 - -Dodaj bla - \end{Verbatim} - \caption{Vnos v Gitu je shranjen v podatkovno shrambo pod imenom, - ki je zgostitev vsebine vnosa: \gitobject{8d}{d6d4bdaeff93016bd49474b54a911131759648}.} -\end{table} - -Vsak vnos je povezan s točno določenim posnetekom vsebine korenskega -datotečnega drevesa, ki ga identificira zgostitev. Poleg tega so -posamezni vnosi so povezani v \emph{usmerjen acikličen graf}, ki -predstavlja zgodovino sprememb. Vsak vnos je \emph{vozlišče} -v grafu in izhaja iz enega ali več starševskih vnosov. Izjema je -prvi vnos. Povezave v grafu povezujejo vnose z njihovimi -starši. - -\begin{figure} - \centering - \includegraphics[width=0.6\linewidth]{slike/commit-history.pdf} - \caption{Vnosi v Gitu kot usmerjen graf. Vsak vnos(razen prvega) ima - povezavo na vnose iz katerih izhaja.} -\end{figure} - -Git hrani zgodovino sprememb v \emph{vsebinsko naslovljivi shrambi - objektov}, ki hrani tri vrste objektov: - -\begin{itemize} - \item - \texttt{blob}: vsebina datotek, - \item - \texttt{tree}: vsebina mape, - \item - \texttt{commit}: posnetek vsebine v določenem trenutku. -\end{itemize} - -Objekti so poevazni v \emph{usmerjen aciklični graf}. Podgraf na vnosih -določa zgodovino sprememb. Naslovi objektov so \emph{zgostitve} vsebine -objekta, zato je zagotovljena verodostojnost shranjenih podatkov. - -\begin{figure} - \centering - \includegraphics[width=0.6\linewidth]{slike/object-storage.pdf} - \caption{Vsebinsko naslovljiva shramba objektov v Gitu. Naslovi so - zgostitve vsebine. Shramba vsebuje dva vnosa. V prvem vnosu smo dodali - dve datoteki \protect\texttt{bla.txt} in \protect\texttt{blabla.txt}, v - drugem vnosu pa smo spremenili le vsebino datotoeke - \protect\texttt{bla.txt}.} -\end{figure} - -\section{Kazalci: veje in značke} - -Poleg objektov kot so \emph{vnosi}, \emph{posnetki map} in -\emph{posnetki datotek} pozna git še reference. Reference so kazalci z -določenim imenom na posamezen vnos. - -\begin{figure} - \centering - \includegraphics[width=0.6\linewidth]{slike/branches-tags.pdf} - \caption{Veja (angl. branch) ali značka(angl. tag) je preprost kazalec - na posamezen vnos(angl. commit).} -\end{figure} - -Referenc git ne hrani v skladišču objektov, temveč posebej v mapi -\texttt{.git/refs}. Reference vezane na posamezen repozitorij in se -lahko razlikujejo med različnimi kloni določenega repozitorija. - -\textbf{Veja} (angl. \textbf{branch}) je posebne vrste referenca, ki se -premika, ko dodajamo nove vnose. Vsakič ko ustvarimo nov vnos, se -trenutno aktivna veja premakne na novo ustvarjeni vnos. - -\textbf{Značka} (angl. \textbf{tag}) je referenca, ki je statična in se -ne premika več, ko jo enkrat ustvarimo. - -\begin{figure} - \centering - \includegraphics[width=0.6\linewidth]{slike/branch-move.pdf} - \caption{Ko ustvarimo nov vnos, se aktivna veja \protect\texttt{main} - premakne naprej, značka \protect\texttt{v-1.0} pa ostane tam, kjer je - bila.} -\end{figure} - -Veje in značke nimajo v Gitu nobenega posebnega pomena, razen tega, da -so reference na vnose. Pomen posamenznih vej je stvar dogovora med -uporabniki. Tako se pogosto uporablja različne veje za različne namene: -\texttt{main} ali \texttt{master} je navadno glavna veja razvoja, veje z -imeni \texttt{stable}, \texttt{production}, \texttt{development} in -podobno označujejo različne stopnje razvoja programske opreme, veje s -predpono \texttt{feature-*} označujejo razvoj novih funkcionalnosti. -Vse te pomene damo vejam ljudje, ki sodelujemo v nekem Git repozitoriju. -Za Git so vse veje in značke zgolj preprosti kazalci na določen vnos. - -\textbf{HEAD} je posebna referenca, ki kaže na trenutno aktiven vnos. -Vnos, na katerega kaže \emph{HEAD} bo starševski vnos naslednjeg vnosa, -ki ga bomo dodali. - -\begin{figure} - \centering - \includegraphics[width=0.6\linewidth]{slike/head-index.pdf} - \caption{\textbf{HEAD} je referenca na trenutno aktiven vnos. - \emph{Index} vsebuje spremembe, ki bodo zabeležene v naslednjem vnosu.} -\end{figure} - -\section{Povzetek} - -Povzemimo sedaj, kaj smo spoznali o podatkovnem modelu Gita. V vsebinsko -naslovljivi shrambi hrani Git posnetke stanja celotne mape, ki ga vodimo -v repozitoriju skupaj z metapodatki o spremembah. Najpomembnejša pojma -sta: - -\begin{itemize} - \item - \textbf{Vnos} (angl. \textbf{commit}) je posnetek trenutnega stanja - projekta, shranjen kot vozlišče v zgodovinskem grafu, ki vsebuje - posnetek stanja datotek ter metapodatke (avtor, čas, sporočilo). - \item - \textbf{zgostitev vnosa} (angl. \textbf{commit hash}) je 40-mestna - heksadecimalna vrednost, izračunana s SHA1, ki enolično identificira - vnos na podlagi vsebine posnetka in metapodatkov. -\end{itemize} - -Izven shrambe objektov hrani Git še reference na posamezne vnose. -Poznamo dve vrsti referenc: - -\begin{itemize} - \item - \textbf{Veja} (angl. \textbf{branch}) je premična reference, ki kaže - na določen vnos v zgodovini in se samodejno premakne naprej, ko - dodajamo nove vnose. Veje omogočajo vzporedne razvojne linije ki so - med sabo neodvisne. - \item - \textbf{Oznaka} (angl. \textbf{tag}) je statična referenca, ki trajno - kaže na določen vnos. Za razliko od veje se oznaka, nikoli ne premika - samodejno, zato se uporablja predvsem za označevanje pomembnih točk v - zgodovini, kot so izdaje ali stabilne verzije. - \item - \textbf{HEAD} je posebna oznaka, ki kaže na trenutno aktiven vnos v - delovni kopiji. -\end{itemize} - -Omenimo še dva pojma, ki jih uporabljamo pri delu z Gitom: - -\begin{itemize} - \item - \textbf{Delovna kopija} (angl. \textbf{workout copy}) je mapa v kateri - urejamo datoteke, ki jih nato vnesemo v Git. V delovni kopiji imajo na - začetku datoteke isto vsebino kot je vsebina trenutno aktivnega vnosa - (\texttt{HEAD}). Spremembe, ki jih naaredimo na delovni kopiji lahko - zabeležimo v nov vnos. - \item - \textbf{Oddaljen repozitorij} (angl. \textbf{remote}) je povezava(url) - na isti repozitorij na drugem računalniku(ponavadi strežniku), s - katerim lahko izmenjujemo vsebino. -\end{itemize} - -Gitov podatkovni model omogoča, da je večina operacij v Gitu obrnljivih. -To pomeni, da lahko repozitorij povrnemo v prejšnje stanje. Običajne -operacije le dodajajo nove vnose in starih ne brišejo. Prav tako se v -zgodovinsko drevo le dodaja nove povezave in starih se ne briše. Zato -daje delo z Gitom uporabniku samozavest, da brez strahu spreminja -vsebino, saj se lahko vedno vrne v času nazaj, kot da bi imel časovni -stroj. - -Nekatere operacije pa tudi brišejo vnose (npr. \texttt{git\ rebase}). -Takim operacijam rečemo, da spreminjajo zgodovino. Uporabniki morajo -biti pri uporabi operacij, ki spreminjajo zgodovino posebej pazljivi, da -česa trajno ne zamočijo. - -\section{Git ukazi kot operacije na grafu} - -Ko smo opremljeni z razumevanjem podatkovnega modela Gita, razložimo kaj -pomenijo posamezne operacije, ki jih Git omogoča. Ukazov ne bom -prevajal, ampak jih bom navedel kot jih pozna program \texttt{git}. - -Ukaz - -\begin{verbatim} -git checkout referenca -\end{verbatim} - -spremeni datoteke v delovni kopiji tako, da se ujemajo z vnosom, na -katerega kaže \texttt{referenca}. Poleg tega prestavi oznako \texttt{HEAD} na -isti vnos. Če je referenca veja, jo nastavi, kot aktivno vejo. Če je -referenca oznaka ali zgostitev vnosa, priedmo v stanje brez aktivne veje -(angl. \emph{deteached HEAD}). - -Ukaz - -\begin{verbatim} -git commit -m "Sporočilo za vnos" -\end{verbatim} - -ustvari nov vnos, ki kaže na stanje v čakalnici (angl. staging area ali -index). V zgodovinskem grafu ustvari novo vozlišče, ki je povezano s -prejšnjim vnosom. Poleg tega prestavi aktivno vejo in oznako -\texttt{HEAD} na novo ustvarjeni vnos. - -Ukaz - -\begin{verbatim} -git add bla.txt -\end{verbatim} - -doda vsebino spremenjene datoteke \texttt{bla.txt} v čakalnico. Ukaz ne -spreminja zgodovinskega grafa, pač pa doda novo vsebino in datotečna -drevesa, ki vsebujejo spremembe v shrambo objektov. Vsebina čakalnice bo -zabeležena v naslednjem vnosu. - -Ukaz - -\begin{verbatim} -git pull -\end{verbatim} - -pobere vsebino(objekte in reference) iz oddaljenega repozitorija in -uskladi lokalno vejo z oddaljeno. Shrambi objektov se preprosto doda -nove objekte, ki so v oddaljeni veji. Če je lokalna veja prednik -oddaljene, se lokalna veja enostavno prestavi, da kaže na isti vnos, kot -oddaljena veja. V nasprotnem primeru, mora uporabnik posredovati in -razrešiti morebitne konflikte. - -Ukaz - -\begin{verbatim} -git push -\end{verbatim} - -potisne novo vsebino na oddaljeni repozitorij. Push deluje obratno kot -\texttt{pull}. Ukaz je uspešno izveden le, če je oddaljena veja prednica -lokalne veje in ni konflikotov. - -Ukaz - -\begin{verbatim} -git fetch -\end{verbatim} - -pobere novo vsebino (vnose, veje in oznake) iz oddaljenega repozitorija. -Pri tem ne more priti do konfliktov, ker git preprosto doda nove objekte -v shrambo in obstoječih objektov nikakor ne spreminja. Oddaljenim vejam -in oznakam preprosto doda predpono z imenom oddaljenega repozitorija. - -Ukaz - -\begin{verbatim} -git reset referenca -\end{verbatim} - -spremeni kam kaže trenutno izbrana veja. Trenutno izbrano vejo prestavi na isti vnos, na -katerega kaže dana \texttt{referenca}. Ukaz ne spremeni zgodovinskega -drevesa, ampak le to, na kateri vnos kaže trenutno izbrana veja. - -Ukaz - -\begin{verbatim} -git merge referenca -\end{verbatim} - -ustvari nov vnos, ki združi dve ločeni veji v eno (trenutno izbrano in -referenco). Nov vnos ima dva starša: vnos na katerega kaže trenutna veja -in vnos, na katerega kaže referenca. Če pride do konfliktov, jih mora -uporabnik sam razrešiti, preden se ustvari nov vnos. - -Ukaz - -\begin{verbatim} -git rebase referenca -\end{verbatim} - -prestavi vnose v trenutno izbrani veji tako, da so potomci vnosa, na -katerega kaže referenca. Med ukazi, ki smo jih spoznali, je ta ukaz -edini, ki lahko povzroči izgubo podatkov. Običajno ukazi le dodajajo -nove vnose in prestavljajo reference. Zato je večina ukazov v Gitu -varna, v smislu, da jih lahko kasneje prekličemo in pridemo nazaj na -prejšnje stanje. Ukaz \texttt{rebase} pa spremeni zgodovino in ga ne -moremo preklicati, saj trenutne vnose nadomesti z novimi in stare vnose -pobriše\footnote{Obstaja enostaven način, kako \texttt{rebase} izvedemo tako, da ga lahko - kasneje prekličemo. Na vnos, ki ga želimo prestaviti z \texttt{rebase}, preprosto - postavimo novo vejo ali oznako. To povzroči, da se stari - vnosi ne pobrišejo, ko se izvede ukaz \texttt{rebase}.}. - \section{Zaključek} Spoznali smo, kako deluje Git in s katerimi matematičnimi pojmi lahko opišemo njegov podatkovni model. @@ -661,8 +619,7 @@ Pri pisanju tega članka sem sevada uporabljal Git. V \href{https://git.fri.uni-lj.si/martin.vuk/git-intro}{javno dostopnem repozitoriju} \cite{vuk_git-intro_nodate} si lahko ogledate celotno zgodovino nastajanja tega članka. - -Pri pripravi dokumenta sem uporabil Gemini 3, a sem vse odgovore njegove odgovore skrbno preveril +Pri pripravi dokumenta sem uporabil Gemini 3, a sem vse odgovore skrbno preveril in uredil po svoje. \bibliographystyle{plainurl} diff --git a/reference.bib b/reference.bib index b9d7735..e5ac59a 100644 --- a/reference.bib +++ b/reference.bib @@ -1,15 +1,10 @@ -@inproceedings{stevens_first_2017, - address = {Cham}, - title = {The {First} {Collision} for {Full} {SHA}-1}, - isbn = {978-3-319-63688-7}, - abstract = {SHA-1 is a widely used 1995 NIST cryptographic hash function standard that was officially deprecated by NIST in 2011 due to fundamental security weaknesses demonstrated in various analyses and theoretical attacks.}, - booktitle = {Advances in {Cryptology} – {CRYPTO} 2017}, - publisher = {Springer International Publishing}, - author = {Stevens, Marc and Bursztein, Elie and Karpman, Pierre and Albertini, Ange and Markov, Yarik}, - editor = {Katz, Jonathan and Shacham, Hovav}, - year = {2017}, - pages = {570--596}, +@incollection{chacon_102_nodate, + title = {10.2 {Git} {Internals} - {Git} {Objects}}, + url = {https://git-scm.com/book/en/v2/Git-Internals-Git-Objects}, + urldate = {2026-01-03}, + booktitle = {Pro {Git}}, + author = {Chacon, Scott and Straub, Ben}, } @misc{vuk_git-intro_nodate, @@ -22,12 +17,11 @@ file = {Snapshot:/home/martinv/Zotero/storage/3V3R4YCH/git-intro.html:text/html}, } -@incollection{chacon_102_nodate, - title = {10.2 {Git} {Internals} - {Git} {Objects}}, - url = {https://git-scm.com/book/en/v2/Git-Internals-Git-Objects}, - urldate = {2026-01-03}, - booktitle = {Pro {Git}}, - author = {Chacon, Scott and Straub, Ben}, +@misc{noauthor_git_nodate, + title = {Git - hash-function-transition {Documentation}}, + url = {https://git-scm.com/docs/hash-function-transition}, + urldate = {2026-01-09}, + file = {Git - hash-function-transition Documentation:C\:\\Users\\marti\\Zotero\\storage\\A9YDF4KZ\\hash-function-transition.html:text/html}, } @article{brink_probably_2012, @@ -44,3 +38,33 @@ year = {2012}, pages = {223--238}, } + +@inproceedings{stevens_first_2017, + address = {Cham}, + title = {The {First} {Collision} for {Full} {SHA}-1}, + isbn = {978-3-319-63688-7}, + abstract = {SHA-1 is a widely used 1995 NIST cryptographic hash function standard that was officially deprecated by NIST in 2011 due to fundamental security weaknesses demonstrated in various analyses and theoretical attacks.}, + booktitle = {Advances in {Cryptology} – {CRYPTO} 2017}, + publisher = {Springer International Publishing}, + author = {Stevens, Marc and Bursztein, Elie and Karpman, Pierre and Albertini, Ange and Markov, Yarik}, + editor = {Katz, Jonathan and Shacham, Hovav}, + year = {2017}, + pages = {570--596}, +} + +@inproceedings{merkle_digital_1988, + address = {Berlin, Heidelberg}, + title = {A {Digital} {Signature} {Based} on a {Conventional} {Encryption} {Function}}, + isbn = {978-3-540-48184-3}, + doi = {10.1007/3-540-48184-2_32}, + abstract = {A new digital signature based only on a conventional encryption function (such as DES) is described which is as secure as the underlying encryption function -- the security does not depend on the difficulty of factoring and the high computational costs of modular arithmetic are avoided. The signature system can sign an unlimited number of messages, and the signature size increases logarithmically as a function of the number of messages signed. Signature size in a ‘typical’ system might range from a few hundred bytes to a few kilobytes, and generation of a signature might require a few hundred to a few thousand computations of the underlying conventional encryption function.}, + language = {en}, + booktitle = {Advances in {Cryptology} — {CRYPTO} ’87}, + publisher = {Springer}, + author = {Merkle, Ralph C.}, + editor = {Pomerance, Carl}, + year = {1988}, + keywords = {Count Field, Encryption Function, Infinite Tree, Modular Arithmetic, Signature Size}, + pages = {369--378}, + file = {Full Text PDF:C\:\\Users\\marti\\Zotero\\storage\\9CPCST7H\\Merkle - 1988 - A Digital Signature Based on a Conventional Encryption Function.pdf:application/pdf}, +}