From dd8433a7e799b05f6ca9a77b54cefe0a8a93f0a3 Mon Sep 17 00:00:00 2001 From: StephaneDucasse Date: Thu, 25 Apr 2013 18:59:45 +0200 Subject: [PATCH] cleaning more chapters that are in PBE2 --- Float/Float.tex | 397 -- LittleNumbers/LittleNumbers.tex | 650 -- .../figures/16bits-1280shifted8.graffle | 4607 -------------- LittleNumbers/figures/16bits-1280shifted8.pdf | Bin 16531 -> 0 bytes .../figures/16bits-1shifted8.graffle | 4515 -------------- LittleNumbers/figures/16bits-1shifted8.pdf | Bin 14256 -> 0 bytes LittleNumbers/figures/16bits-Empty.graffle | 1129 ---- .../figures/16bits-EmptyAsArray.graffle | 2016 ------ LittleNumbers/figures/16bits-fullOne.graffle | 1136 ---- LittleNumbers/figures/16bits-number.graffle | 3034 --------- LittleNumbers/figures/16bits-number.pdf | Bin 13483 -> 0 bytes LittleNumbers/figures/16bits-number13.graffle | 3757 ------------ LittleNumbers/figures/16bits-number13.pdf | Bin 13915 -> 0 bytes .../16bits-numberMultiplication.graffle | 5412 ---------------- .../figures/16bits-numberMultiplication.pdf | Bin 17066 -> 0 bytes .../16bits-numberMultiplication2.graffle | 5424 ----------------- .../figures/16bits-numberMultiplication2.pdf | Bin 17019 -> 0 bytes LittleNumbers/figures/16bits-powered2.graffle | 2249 ------- LittleNumbers/figures/32bits-empty.graffle | 4149 ------------- LittleNumbers/figures/32bits-powered2.graffle | 4149 ------------- LittleNumbers/figures/8bits-Table.graffle | 4309 ------------- LittleNumbers/figures/8bits-Table.pdf | Bin 12530 -> 0 bytes Magma/Magma.tex | 380 -- 23 files changed, 47313 deletions(-) delete mode 100644 Float/Float.tex delete mode 100644 LittleNumbers/LittleNumbers.tex delete mode 100644 LittleNumbers/figures/16bits-1280shifted8.graffle delete mode 100644 LittleNumbers/figures/16bits-1280shifted8.pdf delete mode 100644 LittleNumbers/figures/16bits-1shifted8.graffle delete mode 100644 LittleNumbers/figures/16bits-1shifted8.pdf delete mode 100644 LittleNumbers/figures/16bits-Empty.graffle delete mode 100644 LittleNumbers/figures/16bits-EmptyAsArray.graffle delete mode 100644 LittleNumbers/figures/16bits-fullOne.graffle delete mode 100644 LittleNumbers/figures/16bits-number.graffle delete mode 100644 LittleNumbers/figures/16bits-number.pdf delete mode 100644 LittleNumbers/figures/16bits-number13.graffle delete mode 100644 LittleNumbers/figures/16bits-number13.pdf delete mode 100644 LittleNumbers/figures/16bits-numberMultiplication.graffle delete mode 100644 LittleNumbers/figures/16bits-numberMultiplication.pdf delete mode 100644 LittleNumbers/figures/16bits-numberMultiplication2.graffle delete mode 100644 LittleNumbers/figures/16bits-numberMultiplication2.pdf delete mode 100644 LittleNumbers/figures/16bits-powered2.graffle delete mode 100644 LittleNumbers/figures/32bits-empty.graffle delete mode 100644 LittleNumbers/figures/32bits-powered2.graffle delete mode 100644 LittleNumbers/figures/8bits-Table.graffle delete mode 100644 LittleNumbers/figures/8bits-Table.pdf delete mode 100644 Magma/Magma.tex diff --git a/Float/Float.tex b/Float/Float.tex deleted file mode 100644 index f1e0c65..0000000 --- a/Float/Float.tex +++ /dev/null @@ -1,397 +0,0 @@ -% $Author: ducasse $ -% $Date: 2009-08-24 10:17:33 +0200 (Mon, 24 Aug 2009) $ -% $Revision: 28563 $ - -% HISTORY: -% 2011-09-11 - Migrated to PharoBox: svn checkout https://XXX@scm.gforge.inria.fr/svn/pharobooks/PharoByExampleTwo-Eng - - -%================================================================= -\ifx\wholebook\relax\else -% -------------------------------------------- -% Lulu: - \documentclass[a4paper,10pt,twoside]{book} - \usepackage[ - papersize={6.13in,9.21in}, - hmargin={.75in,.75in}, - vmargin={.75in,1in}, - ignoreheadfoot - ]{geometry} - \input{../common.tex} - \setboolean{lulu}{true} -% -------------------------------------------- -% A4: -% \documentclass[a4paper,11pt,twoside]{book} -% \input{../common.tex} -% \usepackage{a4wide} -% -------------------------------------------- - \graphicspath{{figures/} {../figures/}} - \begin{document} -\fi -%================================================================= -%\renewmessage{\nnbb}[2]{} % Disable editorial comments -\sloppy -%================================================================= - -\chapter{Fun with Floats} -\chapterauthor{\authornicolas{}} - -Floats are often confusing to programmers, who may expect calculations to be carried out like they learned in school. -In this chapter we explain why that is not so, and introduce you to how they work. -The basic message is that Floats should be used as, and appreciated for what they are: inexact but fast numbers. - - -\section{Never test equality on floats} -The first basic principle is to never compare float equality. -Let's take a simple case: the result of adding two floats may not be equal to the float you would write to represent their sum. For example \ct{0.1 + 0.2} is not equal to \ct{0.3}. - -\begin{code}{} -(0.1 + 0.2) = 0.3 - returns false -\end{code} - -Hey, this is unexpected, you did not learn that in school, did you? This behavior is surprising indeed, but it's normal since floats are inexact numbers. -An important point is that the way floats are printed, also impacts our understanding of what floats are. Some approaches will present a simplified version of the float when printed. In fact, in earlier versions Pharo would also print \ct{0.1 + 0.2} as \ct{0.3}. In newer versions this has changed, it now prints as \ct{0.30000000000000004}. -This modification was guided by the idea that it is better not to lie to the user. -Sooner or later, programmers oblivious to the inexactness of floats will be bitten by it. -Showing, rather than hiding this inexactness when printing hopefully makes it easier to grasp what is really going on. - -\begin{code}{} -(0.2 + 0.1) printString - returns '0.30000000000000004' - -0.3 printString - returns '0.3' -\end{code} - -We can see that we are in presence of two different numbers by looking at their hexadecimal representations: - -\begin{code}{} -(0.1+0.2) hex - returns '3FD3333333333334' -0.3 hex - returns '3FD3333333333333' -\end{code} - - -The method \ct{storeString} also conveys that we are in presence of two different numbers. - -\begin{code}{} -(0.1+0.2) storeString - returns '0.30000000000000004' -0.3 storeString - returns '0.3' -\end{code} - -\paragraph{About \ct{closeTo:}.} One way to know if two floats are probably close enough to look like the same number is to use the message \ct{closeTo:} - -\begin{code}{} -(0.1 + 0.2) closeTo: 0.3 - returns true - -0.3 closeTo: (0.1 + 0.2) - returns true -\end{code} - - -\paragraph{About Scaled Decimals.} There is a solution if you absolutely need exact floating point numbers, use Scaled Decimals. Scaled Decimals are exact numbers so they exhibit the behavior you expected. - -\begin{code}{} -0.1s2 + 0.2s2 = 0.3s2 - returns true -\end{code} - - -\section{Disecting a Float} -To understand what operation is involved in above addition, we must know how Floats are represented internally in the computer: Pharo's Float format is a wide spread standard found on most computers - IEEE 754-1985 double precision on 64 bits -(See \url{http://en.wikipedia.org/wiki/IEEE_754-1985} for more details). -In this format, a Float is represented in base 2 by this formula: \[ sign \cdot mantissa \cdot 2^{exponent} \] -\begin{itemize} -\item The sign is represented on 1 bit. -\item The exponent is represented on 11 bits. -\item The mantissa is a fractional number in base two, with a leading 1 before decimal point, and with 52 binary digits after fraction point. -\end{itemize} - -For example, a serie of 52 bits:\\ -\phantom{\ct{1.}}\ct{0110010000000000000000000000000000000000000000000000}\\ - means the mantissa is:\\ - \ct{1.0110010000000000000000000000000000000000000000000000}\\ - which also represents the following fractions: \[ 1 + \frac{0}{2} + \frac{1}{2^2} + \frac{1}{2^3} + \frac{0}{2^4} + \frac{0}{2^5} + \frac{1}{2^6} + \cdots + \frac{0}{2^{52}} \] -The mantissa value is thus between 1 (included) and 2 (excluded) for normal numbers. - - - -\paragraph{Building a Float.} -Let us construct such a mantissa: -\begin{code}{} -(#(0 2 3 6) detectSum: [:i | (2 raisedTo: i) reciprocal]) asFloat. - returns 1.390625 -\end{code} - -Now let us multiply by $2^3$ to get a non null exponent: -\begin{code}{} -(#(0 2 3 6) detectSum: [:i | (2 raisedTo: i) reciprocal]) asFloat timesTwoPower: 3. - returns 11.125 -\end{code} - -In Pharo, you can retrieve these informations: - \begin{code}{} -11.125 sign. - returns 1 - -11.125 significand. - returns 1.390625 - -11.125 exponent. - returns 3 -\end{code} - -In Pharo, there is no message to handle the normalized mantissa directly. Instead it is possible to handle the mantissa as an Integer after a 52 bits shift to the left. There is one good reason for this: operating on Integer is easier because arithmetic is exact. The result includes the leading 1 and should thus be 53 bits long for a normal number (that's the float precision): - \begin{code}{} -11.125 significandAsInteger printStringBase: 2. - returns '10110010000000000000000000000000000000000000000000000' - -11.125 significandAsInteger highBit. - returns 53 - -Float precision. - returns 53 -\end{code} - -You can also retrieve the exact fraction corresponding to the internal representation of the Float: - \begin{code}{} - 11.125 asTrueFraction. - returns (89/8) - -(#(0 2 3 6) detectSum: [:i | (2 raisedTo: i) reciprocal]) * (2 raisedTo: 3). - returns (89/8) -\end{code} - -Until there we retrieved the exact input we've injected into the Float. Are Float operations exact after all? Hem, no, we only played with fractions having a power of 2 as denominator and a few bits in numerator. If one of these conditions is not met, we won't find any exact Float representation of our numbers. In particular, it is not possible to represent 1/5 with a finite number of binary digits. Consequently, a decimal fraction like 0.1 cannot be represented exactly with above representation. - \begin{code}{} -(1/5) asFloat = (1/5). - returns false - -(1/10) = 0.1 - returns false -\end{code} - -Let us see in detail how we could get the fractional bits of \ct{1/10} \ie \mbox{\ct{2r1/2r101}}. For that, we must lay out the division: - -\[ -\begin{tabular}{r|l} -\multicolumn{1}{r|}{1\phantom{00000000}} & 101 \\ \cline{2-2} -10\phantom{0000000} & 0.00110011 \\ -100\phantom{000000} & \\ -1000\phantom{00000} & \\ --101\phantom{00000} & \\ - 11\phantom{00000} & \\ - 110\phantom{0000} & \\ - -101\phantom{0000} & \\ - 1\phantom{0000} & \\ - 10\phantom{000} & \\ - 100\phantom{00} & \\ - 1000\phantom{0} & \\ - -101\phantom{0} & \\ - 11\phantom{0} & \\ - 110 & \\ - -101 & \\ - 1 & \\ -\end{tabular} - \] - -What we see is that we get a cycle: every 4 Euclidean divisions, we get a quotient \ct{2r0011} and a remainder \ct{1}. That means that we need an infinite series of this bit pattern \ct{0011} to represent 1/5 in base 2. Let us see how Pharo dealt to convert (1/5) to a Float: - - \begin{code}{} -(1/5) asFloat significandAsInteger printStringBase: 2. - returns '11001100110011001100110011001100110011001100110011010' - -(1/5) asFloat exponent. - returns -3 -\end{code} - -That's the bit pattern we expected, except the last bits \ct{001} have been rounded to upper \ct{010}. This is the default rounding mode of Float, round to nearest even. We now know why \ct{0.2} is represented inexactly in machine. It's the same mantissa for \ct{0.1}, and its exponent is \ct{-4}. - -So, when we entered \ct{0.1} + \ct{0.2}, we didn't get exactly (1/10) + (1/5). -Instead of that we got: - - \begin{code}{} -0.1 asTrueFraction + 0.2 asTrueFraction. - returns (10808639105689191/36028797018963968) -\end{code} - -But that's not all the story... Let us inspect the bit pattern of above fraction, and check the span of this bit pattern, that is the position of highest bit set to 1 (leftmost) and position of lowest bit set to 1 (rightmost): - \begin{code}{} -10808639105689191 printStringBase: 2. - returns '100110011001100110011001100110011001100110011001100111' - -10808639105689191 highBit. - returns 54 - -10808639105689191 lowBit. - returns 1 - -36028797018963968 printStringBase: 2. - returns '10000000000000000000000000000000000000000000000000000000' -\end{code} - -The denominator is a power of 2 as we expect, but we need 54 bits of precision to store the numerator... Float only provides 53. There will be another rounding error to fit into Float representation: - -\begin{code}{} -(0.1 asTrueFraction + 0.2 asTrueFraction) asFloat = (0.1 asTrueFraction + 0.2 asTrueFraction). - returns false - -(0.1 asTrueFraction + 0.2 asTrueFraction) asFloat significandAsInteger. - returns '10011001100110011001100110011001100110011001100110100' -\end{code} - -To summarize what happened, including conversions of decimal representation to Float representation:\\ -\begin{tabular}{lll} -(1/10) asFloat & 0.1 & inexact (rounded to upper) \\ -(1/5) asFloat & 0.2 & inexact (rounded to upper) \\ -(0.1 + 0.2) asFloat & $\cdots$ & inexact (rounded to upper) \\ -\end{tabular} - -3 inexact operations occurred, and, bad luck, the 3 rounding operations were all to upper, thus they did cumulate rather than annihilate. -On the other side, interpreting \ct{0.3} is causing a single rounding error (3/10) asFloat. -We now understand why we cannot expect \ct{0.1 + 0.2 = 0.3}. - -As an exercise, you could show why \ct{1.3} * \ct{1.3} $\neq$ \ct{1.69}. - - -\section{With floats, printing is inexact} - -One of the biggest trap we learned with above example is that despite the fact that \ct{0.1} is printed \ct{'0.1'} as if it were exact, it's not. -The name \ct{absPrintExactlyOn:base:} used internally by \ct{printString} is a bit confusing, it does not print exactly, -but it prints the shortest decimal representation that will be rounded -to the same Float when read back (Pharo always converts the decimal representation to the nearest Float). - -Another message exists to print exactly, you need to use \ct{printShowingDecimalPlaces:} instead. -As every finite Float is represented internally as a Fraction with a -denominator being a power of 2, every finite Float has a decimal -representation with a finite number of decimals digits (just multiply -numerator and denominator with adequate power of 5, and you'll get the -digits). Here you go: -\begin{code}{} -0.1 asTrueFraction denominator highBit. - returns 56 -\end{code} -This means that the fraction denominator is $2^{55}$ and that you need 55 decimal digits after the decimal point to really print internal representation of \ct{0.1} exactly. -\begin{code}{} -0.1 printShowingDecimalPlaces: 55. - returns '0.1000000000000000055511151231257827021181583404541015625' -\end{code} -And you can retrieve the digits with: -\begin{code}{} -0.1 asTrueFraction numerator * (5 raisedTo: 55). - returns 1000000000000000055511151231257827021181583404541015625 -\end{code} -You can just check our result with: -\begin{code}{} -1000000000000000055511151231257827021181583404541015625/(10 raisedTo: 55) = 0.1 asTrueFraction - returns true -\end{code} -You see that printing the exact representation of what is implemented in machine would be possible but would be cumbersome. Try printing \ct{1.0e-100} exactly if not convinced. - - - -\section{Float rounding is also inexact} -While float equality is known to be evil, you have to pay attention to other aspects of floats. Let us illustrate that point with the following example. - -\begin{code}{Float truncation can be surprising} -2.8 truncateTo: 0.01 - returns 2.8000000000000003 - -2.8 roundTo: 0.01 - returns 2.8000000000000003 -\end{code} - -It is surprising but not false that \ct{2.8 truncateTo: 0.01} does not return \ct{2.8} but \ct{2.8000000000000003}. This is because \ct{truncateTo:} and \ct{roundTo:} perform several operations on floats: inexact operations on inexact numbers can lead to cumulative rounding errors as you saw above, and that's just what happens again. - -Even if you perform the operations exactly and then round to nearest Float, the result is inexact because of the initial inexact representation of \ct{2.8} and \ct{0.01}. -\begin{code}{} -(2.8 asTrueFraction roundTo: 0.01 asTrueFraction) asFloat - returns 2.8000000000000003 -\end{code} - -Using \ct{0.01s2} rather than \ct{0.01} let this example appear to work: -\begin{code}{} -2.80 truncateTo: 0.01s2 - returns 2.80s2 - -2.80 roundTo: 0.01s2 - returns 2.80s2 -\end{code} - -But it's just a case of luck, the fact that \ct{2.8} is inexact is enough to cause other surprises as illustrated below: -\begin{code}{} -2.8 truncateTo: 0.001s3. - returns 2.799s3 - -2.8 < 2.800s3. - returns true -\end{code} - -Truncating in the Float world is absolutely unsafe. Though, using a ScaledDecimal for rounding is unlikely to cause such discrepancy, except when playing with last digits. - - - -\section{Fun with Inexact representations} -To add a nail to the coffin, let's play a bit more with inexact representations. Let us try to see the difference between different numbers: - -\begin{code}{} -{ -((2.8 asTrueFraction roundTo: 0.01 asTrueFraction) - (2.8 predecessor)) abs -> -1. -((2.8 asTrueFraction roundTo: 0.01 asTrueFraction) - (2.8)) abs -> 0. -((2.8 asTrueFraction roundTo: 0.01 asTrueFraction) - (2.8 successor)) abs -> 1. -} detectMin: [:e | e key ] - -returns the pair - 0.0->1 -\end{code} - -The following expression returns \ct{0.0->1}, which means that: - \ct{(2.8 asTrueFraction roundTo: 0.01 asTrueFraction) asFloat = (2.8 successor)} - -But remember that - -\begin{code}{} -(2.8 asTrueFraction roundTo: 0.01 asTrueFraction) ~= (2.8 successor) -\end{code} - -It must be interpreted as the nearest Float to \ct{(2.8 asTrueFraction roundTo: 0.01 asTrueFraction)} is \ct{(2.8 successor)}. - -If you want to know how far it is, then get an idea with: - -\begin{code}{} -((2.8 asTrueFraction roundTo: 0.01 asTrueFraction) - (2.8 successor asTrueFraction)) asFloat - returns -2.0816681711721685e-16 -\end{code} - - - -\section{Conclusion} -Floats are inexact numbers. Pay attention when you manipulate them. -There are much more things to know about floats, and if you are advanced enough, it would be a good idea to check this link from the wikipedia page \href{http://www.validlab.com/goldberg/paper.pdf}{"What Every Computer Scientist Should Know About Floating-Point Arithmetic"}. - - -%========================================================= -\ifx\wholebook\relax\else - \bibliographystyle{jurabib} - \nobibliography{scg} - \end{document} -\fi - -%================================================================= -\ifx\wholebook\relax\else\end{document}\fi -%================================================================= - -%----------------------------------------------------------------- - -%%% Local Variables: -%%% coding: utf-8 -%%% mode: latex -%%% TeX-master: t -%%% TeX-PDF-mode: t -%%% ispell-local-dictionary: "english" -%%% End: \ No newline at end of file diff --git a/LittleNumbers/LittleNumbers.tex b/LittleNumbers/LittleNumbers.tex deleted file mode 100644 index f2ddf80..0000000 --- a/LittleNumbers/LittleNumbers.tex +++ /dev/null @@ -1,650 +0,0 @@ -% $Author: ducasse $ -% $Date: 2009-08-24 10:17:33 +0200 (Mon, 24 Aug 2009) $ -% $Revision: 28563 $ - -% HISTORY: -% 2011-09-08: addressed mariano + nicolas paez comments -% 2011-09-11 - Migrated to PharoBox: svn checkout https://XXX@scm.gforge.inria.fr/svn/pharobooks/PharoByExampleTwo-Eng - - - -%================================================================= -\ifx\wholebook\relax\else -% -------------------------------------------- -% Lulu: - \documentclass[a4paper,10pt,twoside]{book} - \usepackage[ - papersize={6.13in,9.21in}, - hmargin={.75in,.75in}, - vmargin={.75in,1in}, - ignoreheadfoot - ]{geometry} - \input{../common.tex} - \setboolean{lulu}{true} -% -------------------------------------------- -% A4: -% \documentclass[a4paper,11pt,twoside]{book} -% \input{../common.tex} -% \usepackage{a4wide} -% -------------------------------------------- - \graphicspath{{figures/} {../figures/}} - \begin{document} -\fi -%================================================================= -%\renewmessage{\nnbb}[2]{} % Disable editorial comments -\sloppy -%================================================================= - -\chapter{Exploring Little Numbers} - -We manipulate numbers all the time and in this Chapter we propose you a little journey into the way -integers are mapped to their binary representations. We will open the box and take a language implementor perspective and happily explore how small integers are represented. - -We will start with some simple reminders on math that are the basics of our digital world. Then we will have a look at how integers and in particular small integers are encoded. - -\section{Power of 2} - -Let's start with some simple maths. In digital world, information is encoded as powers of 2. Nothing really new. - -\begin{code}{Basics} -2 raisedTo: 0 - returns 1 -2 raisedTo: 2 - returns 4 -2 raisedTo: 8 - returns 256 -\end{code} - -Figure~\ref{power} shows the powers of 2. -\begin{figure}[h] -\begin{center} -\includegraphics[width=0.65\textwidth]{16bits-number} -\caption{Powers of 2 and their numerical equivalence.\label{power}} -\end{center} -\end{figure} - -Using a sequence of bits we can encode numbers. How to encode 13? It cannot be higher than $2^{4}$ because $2^{4}$ = 16. So it should be $8 + 4 + 1$, $2^{3} + 2^{2} + 2^{0}$. So 13 is encoded as 1101. Figure~\ref{16bits-number13} illustrates it. - -\begin{figure}[h] -\begin{center} -\includegraphics[width=0.65\textwidth]{16bits-number13} -\caption{13 = $2^{3} + 2^{2} + 2^{0}$.\label{16bits-number13}} -\end{center} -\end{figure} - -\subsection*{Binary notation} -Smalltalk has a format for representing numbers in different bases. We write \ct{2r1101} where 2 indicates the base or radix, here 2, and the rest the number expressed in this base. Note that we could also write \ct{2r01101} or \ct{2r0001101} since the leading zeroes do not change the number. -\begin{code}{} -2r1101 - returns 13 - -13 printStringBase: 2 - returns '1101' - -Integer readFrom: '1101' base: 2 - returns 13 -\end{code} - -Note that the last two messages \ct{printStringBase:} and \ct{readFrom:base:} do not handle well the internal encoding of negative numbers as we will see later. \ct{-2 printStringBase: 2} returns -10 but this is not the internal number representation known as two's complement. These messages just print/read the number in a given base. - - - -\section{Bit shifting is multiplying by 2 powers} - -Since integers are represented as sequences of bits, if we shift all the bits from a given amount we obtain another integer. Shifting bit is equivalent to perform a multiplication/division by two. Figure~\ref{bitshiftmult} illustrates this point. Smalltalk offers three messages to shift bits: \ct{>> aPositiveInteger}, \ct{<< aPositiveInteger} and \ct{bitShift: anInteger}. \ct{>>} divides the receiver, while \ct{<<} multiply it by a power of two. - -The following examples show how to use them. - - -\begin{code}{Using \ct{>>} and \ct{<<}} -2r000001000 - returns 8 -2r000001000 >> 1 "we divide by two" - returns 4 -(2r000001000 >> 1) printStringBase: 2 - returns '100' -2r000001000 << 1 "we multiply by two" - returns 16 -\end{code} - -The message \ct{bitShift:} is equivalent to \ct{>>} and \ct{<<}, but it uses negative and positive integers to indicate the shift direction. A positive argument offers the same behavior than \ct{<<}, multiplying the receiver by a power of 2. A negative is similar to \ct{>>}. - -\begin{figure}[h] -\begin{center} -\includegraphics[width=0.65\textwidth]{16bits-numberMultiplication} -\caption{Multiplying and dividing by 2.\label{bitshiftmult}} -\end{center} -\end{figure} - -\begin{code}{Using \ct{bitShift:}} -2r000001000 - returns 8 -2r000001000 bitShift: -1 - returns 4 -2r000001000 bitShift: 1 - returns 16 -\end{code} - -Of course we can shift by more than one bit at a time. - -\begin{code}{Using \ct{>>} and \ct{<<}} -2r000001000 - returns 8 -2r000001000 >> 2 "we divide by four" - returns 2 -(2r000001000 >> 2) printStringBase: 2 - returns '10' -2r000001000 << 2 "we multiply by four" - returns 32 -\end{code} - - - - -The previous examples only show bit shifting numbers with one or two bits but there is no constraint at this level. -The complete sequence of bits can be shifted as shown with \ct{2r000001100} below and Figure~\ref{16bits-1280shifted8}. - -\begin{code}{} -(2 raisedTo: 8) + (2 raisedTo: 10) - returns 1280 -2r010100000000 - returns 1280 -2r010100000000 >> 8 - returns 2r0101 - returns 5 -\end{code} - -%\begin{figure}[h] -%\begin{center} -%\includegraphics[width=0.65\textwidth]{16bits-numberMultiplication2} -%\caption{Multiply by 2 or dividing by 2. We can move several bits in one direction.} -%\end{center} -%\end{figure} - -%\begin{figure}[h] -%\begin{center} -%%\includegraphics[width=0.45\textwidth]{16bits-1shifted8} -%\caption{We move 8 times 1 to the left. So from $2^{0}$ we get $2^{8}$. \label{16bits-1shifted8}} -%\end{center} -%\end{figure} - -\begin{figure}[h] -\begin{center} -\includegraphics[width=0.45\textwidth]{16bits-1280shifted8} -\caption{We move 8 times to the right. So from 1280 we get 5.\label{16bits-1280shifted8}} -\end{center} -\end{figure} - -So far nothing really special. You should have learned that in any basic math lecture, but this is always good -to walk on a hill before climbing a mountain. - - - -\section{Bit Access and Manipulation} -Smalltalk lets you access bit information. The message \ct{bitAt:} returns the value of the bit at a given position. It follows the Smalltalk convention that collections' indexes start with one. - - -\begin{code}{} -2r000001101 bitAt: 1 - returns 1 - -2r000001101 bitAt: 2 - returns 0 - -2r000001101 bitAt: 3 - returns 1 - -2r000001101 bitAt: 4 - returns 1 - -2r000001101 bitAt: 5 - returns 0 -\end{code} - -Here is the implementation of \ct{bitAt:}. - -\begin{code}{} -Integer>>bitAt: anInteger - "Answer 1 if the bit at position anInteger is set to 1, 0 otherwise. - self is considered an infinite sequence of bits, so anInteger can be any strictly positive integer. - Bit at position 1 is the least significant bit. - Negative numbers are in two-complements. - - This is a naive implementation that can be refined in subclass for speed" - - ^(self bitShift: 1 - anInteger) bitAnd: 1 -\end{code} - -We shift to the right from an integer minus one (hence \ct{1 - anInteger}) -and with a \ct{bitAnd:} we know whether there is a one or zero in the location. - -\sd{mmp: show an example, otherwise it is difficult to understand. Use for example 2r000001101 bitAt: 5 -> returns 0. Do the drawing you always do and it will be much clear. }\sd{ok later} - - -Pharo offers the traditional Boolean operations for bit sequence. Hence you can send the messages \ct{bitAnd:}, \ct{bitOr:}, and \ct{bitXor:} to numbers. - -\begin{code}{bitAnd:} -2r000001101 bitAnd: 2r11 - returns 1 -\end{code} - -Again, nothing really special but this was to refresh our memories. Now we will see how numbers are internally encoded in Pharo using two's complement. - -\section{Ten's complement of a number} - -To fully understand 2's complement it is interesting to see how it works with decimal numbers. There is no obvious usage for 10's complement but here the point we want to show is that a complement is the replacement of addition with subtraction (\ie adding the complement of A to B is equivalent to subtracting A from B). - - -The 10's complement of a positive decimal integer $n$ is 10 to the power of $k$ + 1, minus $n$, where $k$ is the number of digits in the decimal representation of $n$. $Complement_{10}(n) = 10^{k+1} - n$. -For example $Complement_{10}(8)= 10^1-8$, $Complement_{10}(1968)=10^{5}-1968=8032$ - - - -It can be calculated in the following way: -\begin{enumerate} -\item replace each digit $d$ of the number by $9-d$ and -\item add one to the resulting number. -\end{enumerate} - -This two steps rule is equivalent to the following one which looks more complex. Computer scientists will probably prefer the first way since it is more regular and adding 1 is cheaper than making more tests. - -\begin{enumerate} -\item All the zeros at the right-hand end of the number remain as zeros. -\item The rightmost non-zero digit $d$ of the number is replaced by $10 - d$. -\item Each other digit $d$ is replaced by $9 - d$. -\end{enumerate} - -\paragraph{Examples.} -The 10's complement of 1968 is $9-1$, $9-9$, $9-6$, $9-8$ + 1 \ie $8031 + 1$ \ie 8032. -Using the rule two we compute $9-1$, $9-9$, $9-6$, $10-8$ \ie 8032. So our 10's complement is 8032. Indeed $1968 + 8032 = 10000 = 10^{5}$. Therefore it correctly follows the definition above: 8032 is the result of $10000 - 1968$. - -The 10's complement of 190680 is then $9-1$, $9-9$, $9-0$, $9-6$, $9-8$, $9-0$ + 1 \ie $809319 + 1$ \ie 809320. Let's verify: $190680 + 809320 = 1000000$. - -So to compute the 10's complement of a number, it is enough to perform \ct{9-d} for each digit and add one to the result. - -\subsection{Subtraction at work} -The key point of complement techniques is to convert subtractions into additions. Let's check that. - -\paragraph{Examples.} -$8 - 3 = 5$. The 10's complement of 3 is $9 - 3 + 1 = 7$. We add 7 to 8 and get 15. -We drop the carry we obtained when from the addition. So we obtain 5. (Note that when using binary representation as we will show later, the carry results in overflow because there will be not enough bits to represent it. Therefore implementors should use tricks to determine if the subtraction is correct - usually the trick is to perform a bitXor on the last two digits). - -Now $98-60$. The 10's complement of 60 is $9-6$, $9-0$ \ie $39 + 1$ \ie 40. - $98-60 = 98 + 40 - 100 = 138 - 100 = 38$. Note that the 100 subtraction is a way to show that we drop the carry. - We could have written $98-60 = 98 + 40 = 138 = 38$ but this is an incorrect use of the $=$ mathematical operator. - - -Now performing $60-80$ works too. 80 10's complement is $9-8$, $9-0$, so 19 + 1, so 20. -$60 - 80 = -20$. Again $60-80$ just requires to compute the complement and perform one addition. - - -\paragraph{Another look at it.} -Imagine that we want to perform the following expression $190680 - 109237$ which is equals to 81443. -The 10's complement takes advantage of the fact that 109237 is also $999999 - 890762$. - -\begin{code}{} -109237 = 999999 - 890762 -109237 = 999999 - 890762 (+ 1 - 1) -109237 = 1000000 - 890762 - 1 -\end{code} - -Now the first subtraction is expressed as: -\begin{code}{} -190680 - 109237 -= 190680 - (1000000 - 890762 - 1) -= 190680 - 1000000 + 890762 + 1 -= 190680 + 890762 + 1 - 1000000 -= 1081443 - 1000000 -= 81443 -\end{code} - - -\section{Two's complement of a number} - -The two's complement is a common method to represent signed integers. The advantages are that addition and subtraction are implemented without having to check the sign of the operands and two's complement has only one representation for zero (avoiding negative zero). Adding numbers of different sign encoded using two's complement does not require any special processing: the sign of the result is determined automatically. - -What the 10's complement shows us that it is achieved by taking the difference of each digit with the largest number available in the base system, 9 in decimal base and adding one. Now in the case of binary, the base is one. -Due to the fact that $1 - 0 = 1$ and $1 - 1 = 0$, computing the \emph{two's complement of number is exactly the same as flipping 1's to 0's and vice versa and adding 1.} - - -Try the following expressions in Pharo and experiment with them. We compute the direct inversion (bitwise NOT) and add one. -Remember a bitwise NOT is turning any 1s into 0s and conversely. - -\begin{code}{} -2 bitString - '0000000000000000000000000000010' -2 bitInvert bitString - '1111111111111111111111111111101' -(2 bitInvert + 1) bitString - '1111111111111111111111111111110' --2 bitString - '1111111111111111111111111111110' -\end{code} - -If you check the length of the printed results, you will notice that they are 31 bits long instead of 32. This is because in Pharo and most Smalltalk implementations, small integers are specially encoded and this encoding requires one bit. - -Note that the two's complement of a negative number is the corresponding positive value as shown by the following expressions: -2 two complement is 2. First we compute the direct inversion (bitwise NOT) and add one. - -\begin{code}{} --2 bitString - '1111111111111111111111111111110' - --2 bitInvert bitString - '0000000000000000000000000000001' - -(-2 bitInvert + 1) bitString - '0000000000000000000000000000010' - -2 bitString - '0000000000000000000000000000010' -\end{code} - -\paragraph{Negative number value.} -To know the value of a positive number it is simple: we just sum all the powers of 2 given by the binary representation as explained at the beginning of this Chapter. Now getting the value of a negative number (in two's complement) is quite simple: we do the same except that we count the \emph{sign bit} as negative, all the other ones as positive. The sign bit is the most significant bit \ie the bit that represents the largest value. For example, on 8 bit representation it will be the one associated with the weight $2^{7}$. - -Let us illustrate that: -$-69$ is represented on 8 a bit encoding as: 1011 1011. So get the value out of the bit representation is simple we sum: $-2^7 + 0*2^6 + 2^5 + 2^4 + 2^3 + 0*2^2 + 2^1 + 2^0$, \ie $-128 + 32 + 16 + 8 + 2 + 1$ and we get $-69$. - - -\paragraph{Subtracting.} -To subtract a number to another one, we will add the second number's two complement to the first one. - -When we want to compute $110110 - 101$, we will compute the 2's completement and add it. -So we will add 110110 and 111011, and get 110001. This is correct: $54 - 5 = 49$. - - -\begin{code}{} -110110 - 101 - 110110 -+ 111011 ----------- - 110001 -\end{code} - -Let us test in Pharo -\begin{code}{} -(2r110110 - 2r101) bitString - returns '0000000000000000000000000110001' -(2r110110 bitString) - returns '0000000000000000000000000110110' -2r101 bitString - returns '0000000000000000000000000000101' - -(2r101 bitInvert + 1) bitString - returns '1111111111111111111111111111011' -2r101 negated bitString - returns '1111111111111111111111111111011' -\end{code} - -Posing the addition using only 8 bits we see the following: - -\begin{code}{} -carry 1111111 - 00110110 -+ 11111011 - ---------------------------------- - 00110001 -\end{code} - -Note that the overflowing carry is dropped. - -\paragraph{Representing negative numbers.} -What is nice with the 2's complement is that we can use it to represent a negative number. Indeed, we can negate a number by computing its two complement. The two's complement of a positive number represents the negative form of that number. - -Let's look at 2. 2 is encoded on 8 bits as 000000010 and -2 as 11111110 as shown in Figure~\ref{negativePositive}. -000000010 flipped is: 11111101 and we add one: so we get 11111110. - - - -The difference between -2 (11111110) and 126 (01111110) is given by the most significant bit which conveys the sign of the integer. - -\begin{figure}[h] -\begin{center} -\includegraphics[width=0.35\textwidth]{8bits-Table} -\caption{Overview of two's complement on 8 bits.\label{negativePositive}} -\end{center} -\end{figure} - - - -There is one exception. One a given number of bits, let's say 8 bits as in Figure~\ref{negativePositive}, -we obtained the negative of a number but computing its two's complement (flipping all the bits and adding 1), except for the most negative number. On a 8 bits representation, the most negative number is -128 (1000 0000), inverting it is (0111 1111), and adding one results in itself (1000 0000). We cannot encode 128 on 8 bits signed convention. Here the carry is "eaten" by the sign bit. - - -\paragraph{In Pharo.} -Let's try with Pharo to check a bit our understanding. -If your Smalltalk does not offer the \ct{bitString} method. You can define it as follow: -\begin{code}{} -SmallInteger>>bitString - "Returns the bit representation of the receiver." - ^ String streamContents: [:s | - 30 to: 1 by: -1 do: [:i | s nextPut: ((self bitAt: i) + 48) asCharacter ] . - s contents ] -\end{code} - -In Pharo, you can experiment to confirm the fact that the two's complement is the negative version of a number. - -\begin{code}{} -2 bitString - returns '0000000000000000000000000000010' - -'0000000000000000000000000000010' - collect: [:each | $0 = each ifTrue: [$1] ifFalse: [$0]] - returns '1111111111111111111111111111101' - --2 bitString - returns '1111111111111111111111111111110' -\end{code} - - -Creating a two complement version of a number equals negating the number bits and adding one. -\begin{code}{Calculating two complement of 3} -3 bitString - returns '0000000000000000000000000000011' -3 bitInvert bitString - returns '1111111111111111111111111111100' -(3 bitInvert + 1) bitString - returns '1111111111111111111111111111101' --3 bitString - returns '1111111111111111111111111111101' -\end{code} - - -Now the case where the result is a negative number is also well handled. For example, if we want to compute $-15 + 5$, we should get 10 and this is what we get. - -\begin{code}{} --15 bitString - returns '1111111111111111111111111110001' - -5 bitString - returns '0000000000000000000000000000101' - --10 bitString - returns '1111111111111111111111111110110' -\end{code} - - -\paragraph{Maximum value encoding.} -As we will show in a subsequent section, Pharo's small integers are encoded on 31 bits (because their internal representation requires one bit) and the smallest (small integer) negative integer is \ct{SmallInteger maxVal negated - 1}. Here we see the exception of the most negative integer. - - -\begin{code}{} -"we negate the maximum number encoded on a small integer" -SmallInteger maxVal negated - returns -1073741823 -"we still obtain a small integer" -SmallInteger maxVal negated class - returns SmallInteger -"adding one to the maximum number encoded on a small integer gets a large positive integer" -(SmallInteger maxVal + 1) class - returns LargePositiveInteger -"But the smallest negative is one less than the negated largest positive small integer" -(SmallInteger maxVal negated - 1) - returns -1073741824 -(SmallInteger maxVal negated - 1) class - returns SmallInteger -\end{code} - - -\paragraph{Understanding some methods.} -Now you should be able to understand the implementation of \ct{SmallInteger>>bitInvert} method. - -\begin{code}{} -SmallInteger>>bitInvert - "Answer an Integer whose bits are the logical negation of the receiver's bits. - Numbers are interpreted as having 2's-complement representation." - - ^ -1 - self. -\end{code} - -\begin{code}{} -2 bitString - returns '0000000000000000000000000000010' -2 bitInvert. - returns '1111111111111111111111111111101' - --1 bitString - returns '1111111111111111111111111111111' -2 negated (two complement) - returns '1111111111111111111111111111110' -\end{code} - - -\section{SmallIntegers in Pharo} - -Smalltalk small integers use a two's complement arithmetic on 31 bits. A N-bit two's-complement numeral system can represent every integer in the range $-1 * 2^{N-1}\ to\ 2^{N-1}-1$. So for 31 bits Smalltalk systems small integers values are the range -1073741824 to 1073741823. Remember in Smalltalk integers are special objects and this marking requires one bit, therefore on 32 bits we have 31 bits for small signed integers. Of course since we also have automatic coercion this is not really a concern for the end programmer. Here we take a language implementation perspective. - Let's check that a bit (this is the occasion to say it). - -If you want to know the number of bits used to represent a -SmallInteger, just evaluate: - -\begin{code}{} -SmallInteger maxVal highBit + 1 - returns 31 -\end{code} - -\ct{SmallInteger maxVal highBit} tells the highest bit which can be used to -represent a positive SmallInteger, and + 1 accounts for the sign bit -of the SmallInteger (0 for positive, 1 for negative). - - -Let us explore a bit. - -\begin{code}{} -2 raisedTo: 29 - returns 536870912 - -536870912 class - returns SmallInteger - -2 raisedTo: 30 - returns 1073741824 - -1073741824 class - returns LargePositiveInteger - -(1073741824 - 1) class - returns SmallInteger - --1073741824 class - returns SmallInteger - -2 class maxVal - returns 1073741823 - --1 * (2 raisedTo: (31-1)) - returns -1073741824 - -(2 raisedTo: 30) - 1 - returns 1073741823 - -(2 raisedTo: 30) - 1 = SmallInteger maxVal - returns true -\end{code} - -\section{Hexadecimal} -We cannot finish this Chapter without talking about hexadecimal. In Smalltalk, the same syntax than for binary is used for hexadecimal. \ct{16rF} indicates that \ct{F} is encoded in 16 base. - -We can get the hexadecimal equivalent of a number using the message \ct{hex}. -Using the message \ct{printStringHex} we get the number printed in hexadecimal without the radix notation. - -\begin{code} -15 hex - returns '16rF' - -15 printStringHex - returns 'F' - -16rF printIt - returns 15 -\end{code} - -The following snippet lists some equivalence between a number and its hexadecimal equivalent. -\begin{code} -(1 to: 15) collect: [:each | each -> each hex] - -{(1->'16r1'). (2->'16r2'). (3->'16r3'). (4->'16r4'). (5->'16r5'). (6->'16r6'). (7->'16r7'). (8->'16r8'). (9->'16r9'). (10->'16rA'). (11->'16rB'). (12->'16rC'). (13->'16rD'). (14->'16rE'). (15->'16rF')} -\end{code} - -When doing bit manipulation it is often shorter to use an hexadecimal notation over a binary one. Even if for bitAnd: the binary notation may be more readable -\begin{code}{} -16rF printStringBase: 2 - returns '1111' -2r00101001101 bitAnd: 2r1111 - returns 2r1101 -2r00101001101 bitAnd: 16rF - returns 2r1101 -\end{code} - - -\subsection*{Information subpart extraction} -Often numbers are used to encode in a compact manner multiple information: we could imagine to use 1 bit for gender, 6 bits for age.... The resulting number would be meaningless but information extracted from it is meaningful. -Now we are armed to select subpart of number to get such information. - -\begin{code}{} -2r1100010100000000 - returns 50432 -\end{code} - -Imagine that only 4 bits interest us starting at the 8th bit. -To get the encoded value, we shift out the 8 first ones and clear all the others after the next 4: so we bit shift and bit and as follows: - -\begin{code}{} -(2r1100010100000000 >> 8) - returns 2r11000101 - returns 197 - -(2r1100010100000000 >> 8) bitAnd: 16rF - returns 2r0101 - returns 5 - -2r11000101 bitAnd: 2r1111 - returns 2r0101 - returns 5 -\end{code} - -\section{Conclusion} - -Smalltalk uses two's complement encoding for its internal number representation and supports bit manipulation of their internal representation. 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-%================================================================= -\ifx\wholebook\relax\else -% -------------------------------------------- -% Lulu: - \documentclass[a4paper,10pt,twoside]{book} - \usepackage[ - papersize={6.13in,9.21in}, - hmargin={.75in,.75in}, - vmargin={.75in,1in}, - ignoreheadfoot - ]{geometry} - \input{../common.tex} - \setboolean{lulu}{true} -% -------------------------------------------- -% A4: -% \documentclass[a4paper,11pt,twoside]{book} -% \input{../common.tex} -% \usepackage{a4wide} -% -------------------------------------------- - \graphicspath{{figures/} {../figures/}} - \begin{document} -\fi -%================================================================= -%\renewcommand{\nnbb}[2]{} % Disable editorial comments -\sloppy -%================================================================= -\chapter{Installing }\chalabel{basic} - -\sd{Harvested from \url{http://wiki.squeak.org/squeak/2665} with permission from Chris Muller. (To be rewritten with his help.)} - -Magma is a fully supported, multi-user object database for Squeak 3.7, 3.8, 3.9, 3.10, and Croquet distributions. - -Magma provides transparent access to a large-scale shared persistent object model, -supports multiple users concurrently via optimistic locking, utilizes a simple transaction protocol, including nested transactions, supports collaborative program development via live class evolution, peer-to-peer model sharing and Monticello integration, supports for large, indexed collections with robust querying, runs with pretty good performance and provides performance tuning mechanisms, -learning basic usage takes just a few minutes, is fault tolerant, includes a small suite of tools, is written 100\% in intelligible, well-factored Smalltalk. -Magma includes rigorous SUnit tests that utilize multiple images to simulate testing in a multi-user environment. - -Magma is stable and usable within its limits, and is still under active development. - -\section{Vocabulary point} - -\subsection{What is meant by transparent access?} - -Most object programs that interface to a database do so using an explicit interface, meaning at any point in the program where you "need some data," you write code to make a call to the database (perhaps through some kind of persistence framework). - -By contrast, when you connect your Squeak image to a Magma repository, you think of your local image as "expanded" to include the objects in the repository. Magma client programs can and should be written as if they are operating in one large image on a computer with lots of memory. You don't ever need to "read some data" because you are already "in" the data. Your program is free to explore the persistent object model and, through transactions, make changes. Magma uses weak collections for its caching, so your program only consumes as much memory as the objects it references. - -This level of transparency allows existing objects which have never been designed to reside in a database to reside in Magma. For example, no Morph knows anything about Magma, but Morphs may be stored, shared and collaborated via Magma. - -Object databases allow you to design complex domain relationships without reservation or compromise. Domain code remains pure, and completely independent of storage. - -A number of commit-strategies allow Magma to be suitable for a variety of programs and users. - -\subsection{About optimistic locking} - -Locking of objects is done in multi-user systems to preserve integrity of changes; so that one persons changes do not accidently overwrite another. - -\paragraph{Optimistic locking.} - -With optimistic locking, you write your program under the assumption that any commit has a chance to fail on account of at least one the objects being committed was changed by someone else since you began the transaction. - -Optimistic locking offers reduced contention and higher performance than pessimistic locking. It also avoids deadlocks. - -\paragraph{Pessimistic locking.} -In pessimistic locking, your program must explicitly obtain a lock on one or more objects before making any changes. This prevents any other session from making changes to those objects, so you can be more assured that committing the transaction will succeed. - -Once changes are complete, the objects are unlocked so that others may make changes to them. - -Pessimistic locking increases contention because objects are tied up for longer periods. Locking objects also imposes more work on the database server. When there is a conflict, sessions have to "get in line" to wait for an object to become unlocked. These sessions may, themselves, already have other objects locked up while they're waiting. If any of these objects needed by a session are farther ahead in line then you will have a "deadlock," which can be difficult to manage. ok - - - - -\section{Getting started with Magma} - -\subsection{Getting Started} - -To use Magma, first download and install the code. Then you may decide in what mode would your magma be running and follow these steps: - -\paragraph{If Running in Server/Client Mode} - -\begin{itemize} - \item create a repository - \item start the server - \item open a session -\end{itemize} - -\paragraph{If Running in Single-user Mode} -\begin{itemize} -\item create a repository -\item open a session, in a different way(see: Single-user mode below) -\end{itemize} - -\subsection{Creating a repository} - -To create a repository, you must provide two things: -\begin{itemize} -\item a path to the directory magma may use to keep and maintain its files -\item the root object of the repository -\end{itemize} - -Magma maintains a single directory on the filesystem for each repository. When creating or opening Magma repositories, you specify the fully-qualified directory in which it may create its various files. - -You should also provide the root object of the repository. This is the root of your domain object in the domain is referenced. - -The code, thus: - -\begin{code}{} - MagmaRepositoryController - create: 'c:\myMagmaFolder' - root: Dictionary new -\end{code} - -\paragraph{Starting the server.} - -Magma utilizes TCP/IP for its network communications. To enable multi-user access to a Magma repository, you may start the Magma server in its own image and inspect the following: - -\begin{code}{} -MagmaServerConsole new - open: 'c:\myMagmaFolder' ; - processOn: 51001 -\end{code} - -Be sure to inspect this so you will have access to console commands, such as \ct{shutdown}. - -\subsection{Open a MagmaSession} - -Once the server is running, a \clsind{MagmaSession} can be connected from the same or another image to gain access and change objects in the repository. Connecting a session requires the following information: - -\begin{itemize} - \item a name to identify your session. When someone tries to overlay changes you've made to objects, they will be notified that those objects were changed by your session, identified by the name you provide. - \item the IP address of the machine hosting the Magma repository, and the port it is listening on. -\end{itemize} - -\begin{code}{} - | mySession | - mySession := MagmaSession - hostAddress: #(192 168 1 13) asByteArray - port: 51001. - mySession connectAs: 'chris' -\end{code} -If you run this from a Workspace, be sure to inspect the result so you will be able to properly disconnect from the server. - -Once connected, changes to the persistent model are committed through transactions. - -\begin{code}{} -mySession commit: - [ mySession root - at: 'persons' - put: (OrderedCollection with: (Person name: 'Paula')) ] -\end{code} - -While your session is connected, it is recommended you keep up-to-date every 30 seconds or so changes made by other users will be reflected in the objects you visit. If you know there are very few users then this less important, but your session may eventually get booted if you wait too long. You can do this simply by aborting, even if you don't have a transaction: - -\begin{code}{} - mySession abort -\end{code} -This will allow you to see changes to the persistent model that were made by others. - -You can access the root of the repository later and navigate from there. - -\begin{code}{} - mySession root at: 'persons' -\end{code} - -To minimize concurrency it is recommended that transactions begin just before you make changes, and commit immediately after. - -Once you're done using the session, you should disconnect it: -\begin{code}{} - mySession disconnect -\end{code} - -\paragraph{Single-user mode} - -If you know will be operating in a single-user environment, starting a second image to run the server may not always be convenient. Thankfully, Magma supports a "direct-connect" single-user mode, where a single Magma session connects directly to the repository in one image. - -To run in single-user mode, you do not need to use MagmaServerConsole. - -Instead, you must specify the name of the object file when opening a MagmaSession instead of the IP and port. - -\begin{code}{} - myMagmaSession := MagmaSession openLocal: 'c:\myMagmaFolder\myRepository.magma'. - myMagmaSession connectAs: 'chris' -\end{code} - -Additionally, when you're ready to disconnect your last session, you also should close the repository: - -\begin{code}{} - myMagmaSession disconnect; closeRepository -\end{code} - -The repository can then be opened again in single or multi-user mode. - - -\subsection{Objects are persisted by reachability} - -With object databases, there is no notion of, "inserting objects into the database". Instead, you merely attach new objects to persistent ones and commit. All directly or indirectly referenced objects from any persistent object are automatically detected and saved into the database. - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\section{Designing for an ODBMS} -Now we discuss some programming guidelines and best practices. -Here are some advices - -\begin{itemize} - \item Web programming caution! - Do not share objects between MagmaSession instances. Two or more separate MagmaSessions should never reference the same identical object intance, including proxies. Each session must always keep its own separate view of the persistent model, they should never be linked across sessions. The persistent objects are still identical within the repository, just not in the image across session views. - -\item Try to keep transactions short. - -Short transactions are essential for good server health and avoiding getting kicked off. That's right. Magma server will disconnect any sessions that accumulate too many "challengers". The default maximumNumberOfChallengers is 1000. That means if 1000 commits by other users are performed and you haven't refreshed, you're outta there. - -\item Custom indexes. - -Custom index types must inherit from MaIndexDefinition because all index definitions are part of the protocol between clients and server. This also means that the server must be started after the custom index was created and must be present in the servers image. - -Since the server requires no other domain classes (though it won't hurt to have them), you may wish to define your custom index types in a separate package. - -\end{itemize} - -There are a number of design considerations when writing a Magma program such as the commit strategies, - -%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subsection{Magma Commit Strategies} -One important and interesting question is how to avoid to maintain a MagmaSession in our domain objects. How can we perform the necessary commits, while still keeping it decoupled from Magma? There are at least three approaches that can be used. - - - -\paragraph{1) Program-controlled transactions:} You signal commit notifications in your domain. A controller catches these notifications and applies them to its session. When no controller is listening, the notifications are ignored, allowing testing of the domain with or without the database. While you do not have to reference a MagmaSession, it is not completely transparent because you do have to signal the notifications: - -\begin{code}{} - name: aString - MagmaSessionRequest signalCommit: [ name := aString ] -\end{code} - -This approach gives the program control over when commits are performed. It also allows the user to be free of any concern about remembering to "save"; everything that requires a transaction will be committed without them thinking about it. - -One disadvantage is reduced concurrency-detection. The message \ct{signalCommit:} does the refresh, update and commit without the user ever seeing whether the changed value was already changed. For this reason, this sort of commmit strategy is useful for low-concurrency models, \ie where different analysts work on their "own" domain objects. - - -\paragraph{2) User-controlled transactions, with auto-begin:} With this approach, the user is always in a transaction. The program provides a "Save" or "Commit" button which the user occasionally presses as they modify the domain model. The program could also provide its own "Cancel" function (which would send \ct{abort}, followed by \ct{begin} to the MagmaSession) to provide a rudimentary undo function. To use auto-begin, your program does an initial \ct{begin} when connecting the session, then every commit should instead use \ct{commitAndBegin} instead of \ct{commit}. - -Since Magma needs transactions to be short, this approach is most suitable for programs with very frequent domain changes; such as programs that support "data entry" activities. Performance is increased because the \ct{begin} step occurs right after the commit automatically with only one trip to the server. - -This approach also allows complete transparency; \ie, the domain can be written with no awareness of any database. No commits or signals are needed in the code. - -Concurrency detection is also much better; consider our name: setter example from above. This time, the code is, simply: - -\begin{code}{} - name: aString - name := aString -\end{code} - -This time, if this object has changed the user will get a commit-error when they commit and the object will update to the current value. - -Users decide when to "save", therefore the program should be written so the user has control only when the domain is in a consistent state worthy of being committed. For example, in a banking application, when a user initiates a transfer, don't let them commit between the withdraw and the deposit, only after both. - -This approach is less favorable for programs that do not update the domain model frequently. Because users are always in a transaction, their MagmaSessions will not receive auto-abort signals. It is therefore up to the users to keep their views refreshed by either committing or aborting. If they do not, and there are lots of changes happening to the domain by other users, Magma will eventually terminate the an inactive users session, bloated with pending changes, and the user will have to log in again. - - -\paragraph{3) User-controlled transactions, user-controlled begin:} In this approach, the program provides the user with both a "begin" as well as "commit" button somewhere, so they are in complete control of transactions. This is just like the previous option except, since the user is not always in a transaction, auto-abort signals will be received. This is in exchange for the additioonal clicking the user must do to explicitly \ct{begin} their transactions. - - -\paragraph{About refreshPersistentObjectsEvenWhenChangedOnlyByMe} - -Within each of these strategies, another option further enhances their flexibility: -\begin{code}{} - mySession refreshPersistentObjectsEvenWhenChangedOnlyByMe: true -\end{code} - -Setting this option to true does reduce performance slightly, but is used to be "more-connected" to the repository. It causes your changes to be lost if they were changed by someone else. - -The default value is false which, when using commit-strategy (3), allows users to make changes to an object, "test" them, and, only after that, \ct{begin} and immediately \ct{commit} a transaction. The \ct{begin} is non-destructive to their own changes which were not changed by another user. In this way it is a sort of "merge" with the users local model. - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subsection{About read strategies} - -Magma provides programs with transparent access to an arbitrarily large, persistent object model. Memory consumption is minimized by way of the well-known "Proxy" design pattern. Parts of the object-model that are not being used by your program are "truncated" in your local image with a lightweight proxy object. Should the program happen to send a message to the proxy, the object it represents is materialized from the repository automatically. The proxy then "becomes" the real object. - -There is a cost to this materialization process, so doing too many of them may cause performance issues. When a proxy is materialized, it is usually assumed that you will send a message to it that will require access to at least one of its instance variables. For this reason, it is generally desirable to bring back the proxy and several of the objects it references. - -But bringing back more objects creates more work for the server, network and your client. For ideal performance, you want each materialization to bring back just the objects that will be needed, but not too many that won't be. - -Magma's default ReadStrategy will read one level deep by default, which means the proxy object and the objects each of its instance variables refers to. As a programmer, you can change this default 0, 1, 2 or 3 (or maybe even 4, but I wouldn't go beyond that) by supplying a ReadStrategy. - -minimumDepth, plus delta-depth - -The minimumDepth is how far it reads for any objects, all objects, every time, all the time. Therefore, you want to keep it very small, probably 0 or 1. Then, you can use a ReadStrategy to specify how much deeper to read, below the minimumDepth, by class and instance-variable. So what this means exactly is, whenever the server is reading a graph and encounters a buffer for the specified class, it will be sure to also grab n-levels deeper, regardless of how deep it already is, for whatever variable name specified. - -\paragraph{Example.} -Let's say you are about to display a list of Employees and their department names in a list. The Employee class defines a 'name' attribute, which is a String, and a 'department' object, an instance of class Department. Departments also have a name. If the list was to include each employee name and their department name, the default ReadStrategy would retrieve each Employee with its Department as a proxy. So the list would populate slowly because each Department would be materialized one at a time. To improve this performance, you could specify the ReadStrategy to read one additional level on the 'department' object. - -\begin{code}{} - | employeeListReadStrategy | - employeeListReadStrategy := - (MaReadStrategy minimumDepth: 1) - forVariableNamed: 'department' - onAny: Employee - readToDepth: 1 - mySession readStrategy: employeeListReadStrategy. "returns instantly, no server call" - "now enumerate the collection" - myEmployees do: [ :each | ".. display name and department name in your list.." ] -\end{code} - - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subsection{Optimizing Magma's Performance} - -Efficiency was always a goal when building Magma. The work-load is heavy for the client but relatively light for the server, especially with short transactions allowing, theoretically, for consistent performance more client sessions connect. - -If profiling your program reveals a lot of time spent in Magma, considering the following performance-sensitive guidelines may help. - - -\paragraph{Use ReadStrategies.} Read strategies can be used to optimize how many objects are accessed within a single call to the server. - -\paragraph{Keep your commits medium-small.} Commits should be put in your program as close to the mutations to the persistent model as possible. Commits are serialized on the server, so large commits that take several seconds will most likely cause requests to queue in the server. - -At the same time, you don't want commits to be so microscopic that you end up smothering the network with requests. For example, if building an OrderedCollection of 100 medium-sized objects, you should do those in one commit instead of 100 commits. However, if the objects are very large and completely non-persistent, you may want to do 100 commits. - -\paragraph{Keep your cachedObjectCount as low as possible.} - -With a connected Magma session, evaluate: \ct{mySession cachedObjectCount} -This number reprensents how many entries Magma has in its IdentityDictionaries. Magma tries to avoid the performance issues related to Squeak's IdentityDictionaries, but it can still slow down if you allow tens of thousands of objects to be cached in memory. - -If you're not sure why your \ct{cachedObjectCount} is growing, you can use \ct{cachedObjectCountByClass} to see which ones are the most proliferate (they are sorted by most-occurrences at the top). If you see "UndefinedObject" near the top of the list, you need to send \ct{finalizeOids} to your session. This is because Squeak can be lazy about finalizing the entries in its \ct{WeakDictionary}'s. - -As you traverse parts of the model, you should \ct{stubOut:} objects you no longer need. For example, after iterating a collection of large objects, \ct{stubOut:} the collection object if you no longer need them. \ct{MagmaSession>>stubOut:} chops off large branches of objects so the memory they consume can be reclaimed by the garbage collector. - -But avoid too many calls to \ct{stubOut:}. For example, after you've enumerated the collection of large objects, \ct{stubOut:} the Collection object itself, not each object in the collection. This is due to unfortunate irony that \ct{stubOut:} requires use of one of Squeak's most inefficienct methods; \ct{Dictionary>>>removeKey:}. While fast in other Smalltalks, this method is VERY slow in Squeak but required for \ct{stubOut:}. - -Finally, after you've stubbed out a large object, you may find it necessary to call "mySession finalizeOids". Unfortunately, Squeak's WeakIdentityKeyDictionary does not always remove finalized entries in a timely fashion, resulting in, once again, these very important Dictionaries slowing everything down. - mySession finalizeOids - -\paragraph{Other optimizations.} - -Don't use MagmaSession>>refreshPersistentObjectsEvenWhenChangedOnlyByMe. -Use \ct{commitAndBegin} for bulk-load programs. Experiment and optimize your key and record sizes of your MagmaCollections. Avoid too many duplicate keys (\eg, don't index the word "the"). - - -\paragraph{Know thy indexes.} -MagmaCollections have good read performance, but adding and removing objects is very slow. In theory, starting with an empty MagmaCollection, the rate-of-insertion will deteriorate a little bit before settling on a relatively fixed rate, IF you have a good key-dispersal. - -If you put in a lot of duplicate keys, it will gradually get more costly to keep adding more of that key because a linear search for the "end" of that chain of keys is performed to find the point of insertion. So, for example, when you build a simple keyword index, consider eliminating prepositions such as "the" and "at". - -Removing from MagmaCollections is even more expensive than insertions. Avoid using this operation for performance-intensive operations. - - - - - - - - - - - -%================================================================= -\ifx\wholebook\relax\else\end{document}\fi -%================================================================= - -%----------------------------------------------------------------- - -%%% Local Variables: -%%% coding: utf-8 -%%% mode: latex -%%% TeX-master: t -%%% TeX-PDF-mode: t -%%% ispell-local-dictionary: "english" -%%% End: \ No newline at end of file