\documentclass[UTF8,punct=kaiming]{ctexart} \usepackage{amsmath} \usepackage[a4paper,left=2cm,right=2cm,top=2.5cm,bottom=2.5cm]{geometry} \usepackage{multicol} \usepackage{makecell} \usepackage{fancyhdr} \usepackage{hyperref} \usepackage[type={CC},modifier={by-sa},version={4.0},lang={chinese-utf8}]{doclicense} \usepackage{amssymb} \usepackage{amsthm} \usepackage[many]{tcolorbox} \usepackage{multirow} \usepackage{listings} \input{insbox} \setlength{\parindent}{0pt} \hypersetup{hidelinks, colorlinks=false, allcolors=black, pdfstartview=Fit, breaklinks=true} \pagestyle{fancy} \fancypagestyle{myfancypagestyle}{ \fancyhf{} \fancyhead[L]{计算机系统基础\uppercase\expandafter{\romannumeral1\relax} 考试用资料} \fancyhead[R]{Made with $\heartsuit$ by \href{https://kagurach.uk/}{kagura} and \href{https://nkid00.name/}{nkid00} \& licensed under \doclicenseNameRef} \fancyfoot[C]{\thepage} \renewcommand{\headrulewidth}{0.4pt} \renewcommand{\footrulewidth}{0pt} } \pagestyle{myfancypagestyle} \tcbuselibrary{listings} \tcbset{colback=white,boxrule=0.3mm,enhanced,size=small} \lstset{basicstyle=\ttfamily,columns=fullflexible} \setlength{\columnsep}{1cm} \setlength{\columnseprule}{0.4pt} \begin{document} \section{数据表示与存储} \subsection{数据的类型及大小} \begin{table}[h] \begin{tabular}{|c|c|c|c|c|} \hline 类型 & 字节数 & 最小值 & 最大值(signed) & 最大值(unsigned) \\ \hline \texttt{char} & 1 & -128 & 127 & 255\\ \hline \texttt{short} & 2 & -32768 & 32767 & 65535\\ \hline \texttt{int} & 4 & -2147483648 & 2147483647 & 4294967295 \\ \hline \texttt{long} & \multirow{2}{*}{8} & \multirow{2}{*}{-9223372036854775808} & \multirow{2}{*}{9223372036854775807} & \multirow{2}{*}{18446744073709551615} \\ \cline{1-1} \texttt{void*} & & & & \\ \hline \texttt{float} & 4 & 1.17549$\times10^{-38}$ & 3.40282$\times10^{38}$& \\ \hline \texttt{double} & 8 & 2.22507$\times10^{-308}$ & 1.79769$\times10^{308}$ & \\ \hline \end{tabular} \end{table} \subsection{计算值域} T: 用 $n$ 位表示数字 \begin{align*} \text{(signed) T} \quad & \text{可表示} \quad -2^{n-1} \sim ~ 2^{n-1}-1 \\ \text{(unsigned) T} \quad & \text{可表示} \quad 0 \sim 2^{n}-1 \end{align*} \subsection{补码} \begin{multicols}{2} \qquad 对应正数补码的“各位取反、末位加1” \begin{align*} +23 & = \texttt{00010111} \\ \text{按位取反} & = \texttt{11101000} \\ & + \hspace{0.3em}\phantom{0000000}\texttt{1} \\ -23_{\text{补码}} & = \texttt{11101001} \end{align*} \columnbreak \qquad 模($2^n$)减去该负数的绝对值 \begin{align*} & \texttt{100000000} \\ - \hspace{0.5em} & \phantom{\texttt{0}}\texttt{00010111} \\[-1em] & \hspace{-1em}\rule{2.5cm}{0.02em} \\[-0.5em] & \phantom{\texttt{0}}\texttt{11101001} \end{align*} \end{multicols} \subsection{GDB查看数据} \texttt{>(gdb) x/4xb} \\[1em] \begin{minipage}{12cm} \begin{multicols}{2} \texttt{b} - byte (8-bit value) \\ \texttt{h} - halfword (16-bit value) \\ \texttt{w} - word (32-bit value) \\ \texttt{g} - giant word (64-bit value) \\ \texttt{o} - octal \\ \texttt{x} - hexadecimal \\ \texttt{d} - decimal \\ \texttt{u} - unsigned decimal \\ \texttt{t} - binary \\ \texttt{f} - floating point \\ \texttt{a} - address \\ \texttt{c} - char \\ \texttt{s} - string \\ \texttt{i} - instruction \end{multicols} \end{minipage} \newpage \subsection{浮点数} \vspace{-1cm} \InsertBoxR{0}{\tcbox[blank]{\begin{tabular}{|c|c|c|c|c|} \hline 二进制位数 & s 符号位 & exp 指数 & frac 尾数 & 总计 \\ \hline \texttt{float} & 1 & 8 & 23 & 32 \\ \hline \texttt{double} & 1 & 11 & 52 & 64 \\ \hline \end{tabular}}} \vspace{1cm} 浮点数表示为 $(-1)^s \cdot M \cdot 2^E$ \InsertBoxR{0}{\tcboxmath{\begin{matrix} \multicolumn{2}{c}{\text{偏置值 Bias}} \\ \texttt{float} & 127 \\ \texttt{double} & 1023 \\ \end{matrix}}\hspace{3cm}} \vspace{-1em} \subsubsection{规格化数 $ \text{exp} \ne 0$ 且 $\text{exp} \ne 11 \dots 1$} $\text{(unsigned)} \ \text{exp} \ = \ E \ + \text{Bias}$ $\text{Bias (偏置值)} = 2^{k-1}-1$ , \(k\) 为 exp 的二进制位数 \begin{multicols}{2} 例1:十进制整数$\rightarrow$二进制浮点数 \begin{align*} \text{float} \ F &= 15213.0 \\ \text{化为二进制数:} \\ 15213_{10} &= 11101101101101_{2} \\ &= 1.1101101101101_{2} \ \times \ 2^{13} \\ \text{计算 frac:} \\ M &= 1.\underbar{1101101101101}_{2} \\ \text{frac} &= \underbar{1101101101101}0000000000_{2}\\ \text{计算 exp:} \\ E &= 13 \qquad \text{来自化为二进制时的指数} \\ \text{Bias} &= 127 \\ \text{exp} &= 140 = 10001100_{2} \end{align*} 结果：\\ \(\begin{matrix} 0 & 10001100 & 11011011011010000000000 \\ \text{s} & \text{exp} & \text{frac} \end{matrix}\) \columnbreak 例2: 二进制浮点数$\rightarrow$十进制数 无符号数，4位阶码(Bias\(=7\))，3个小数位 \\ \quad \(\begin{matrix} 1001 & 111 \\ \text{exp} & \text{frac} \end{matrix}\) \\[0.5em] \(\begin{aligned} \text{计算} \space E &= \text{exp} - \text{Bias} & \\ &= 1001_2 - 7_{10} \\ &= 2_{10} \end{aligned}\) \\[0.5em] 计算 \(M = 1.\underbar{frac} = 1.\underbar{111}\) \\[0.5em] 化为十进制: \(\begin{aligned} 1.111 \times 2^2 & = 111.1_2 \quad \text{小数点右移2位} \\ & = \frac{15}{2} = 7.5 \end{aligned}\) \end{multicols} \InsertBoxR{0}{\tcboxmath{\begin{matrix} \text{非规格化数} \ E = 1 - \text{Bias} \\ \begin{matrix} \texttt{float} & -126 \\ \texttt{double} & -1022 \\ \end{matrix} \end{matrix}} \hspace{2cm}} \vspace{-5mm} \vspace{-0.3em} \subsubsection{非规格化数 $\text{exp} = 0$} frac \(= 00\dots0\) 表示 0 frac \(\ne 00\dots0\) 表示接近 0 的小数 $(-1)^s \cdot M \cdot 2^{E}$ \vspace{-0.3em} \subsubsection{特殊值 $\text{exp} = 11 \dots 1$} \begin{multicols}{2} frac \(= 00\dots0\) 表示 \(\infty\) frac \(\ne 00\dots0\) 表示 NaN \columnbreak \(1.0 / 0.0 = −1.0 / −0.0 = + \infty\) \(1.0 / −0.0 = - \infty\) \(\sqrt{–1.0} = \infty - \infty = \infty \times 0 = \text{NaN}\) \end{multicols} \subsubsection{舍入(到偶数)} \begin{table}[h] \begin{tabular}{|ccc|} \hline 末两位 & 动作 & 例子（保留一位小数） \\ \hline 01 & 舍 & $11.0\underbar{01}_2 \to 11.0_2$ \\ \hline 11 & 入 & $10.0\underbar{11}_2 \to 10.1_2$ \\ \hline 10 & \makecell[c]{强迫结果为偶数(末尾为0)\\010舍 , 110入} &\makecell[c]{$10.0\underbar{10}_2 \to 10.0_2$ \\ $10.1\underbar{10}_2 \to 11.0_2$} \\ \hline \end{tabular} \end{table} \pagebreak \InsertBoxR{0}{\tcboxmath{\begin{matrix} \text{寻址模式} & \text{p. 121} \\ \text{栈帧结构} & \text{p. 164} \\ \text{gdb 操作} & \text{p. 194} \\ \end{matrix}}\hspace{2cm}} \vspace{-1.5em} \section{程序的机器级表示} \subsection{计算数组元素的地址} \begin{multicols}{2} 计算 \texttt{T* D[R][C]} 元素 \texttt{D[i][j]}的地址： \\ \(\texttt{\&D[i][j]} = \texttt{\&D[0][0]} + \texttt{sizeof(T)} \times \left(C \cdot i + j\right)\) \\ 假设 \texttt{sizeof(T) = k}, 将 \texttt{D[i][j]} 复制到 \%eax 中 \\ \texttt{asm: D in \%rdi , i in \%rsi , j in \%rdx } \columnbreak \texttt{1 \ leaq (\%rsi,\%rsi,\$C-1), \%rax \\ 2 \ leaq (\%rdi,\%rax,\$k), \%rax \\ 3 \ movl (\%rax,\%rdx,\$k), \%rax \\ } 结果为 \texttt{D + k $\cdot$ C $\cdot$ i + k $\cdot$ j} \\ 即 \texttt{D + sizeof(T) $\times$ (C $\cdot$ i + j)} \end{multicols} \vspace{-2.5em} \section{链接} \vspace{-1.5em} \subsection{符号表 (.symtab)} \vspace{-1em} \begin{table}[h] \begin{tabular}{l|c|c|c|l} \hline C语言表示 & 类型 & 符号强度 & 节 & 说明\\ \hline \texttt{void swap();} & 全局 & 强 & \texttt{.text} & 非静态函数 \\ \hline \texttt{int *bufp0 = \&buf[0]} & 全局 & 强 & \texttt{.data} & 初始化为其他值的全局变量\\ \hline \texttt{int a = 0;} & 全局 & 强 & \texttt{.bss} & 初始化为 0 的全局变量 \\ \hline \texttt{int *bufp1;} & 全局 & 弱 & \texttt{COMMON} & 未初始化的全局变量 \\ \hline \texttt{extern int buf[];} & 外部 & --- & \texttt{UNDEF} & \makecell[l]{ 未解析的引用符号 \\ 位于实际定义所在位置 } \\ \hline \begin{lstlisting}[language=C,gobble=8] void p() { static int i = 1; } \end{lstlisting} & 局部 & --- & \texttt{.data} & 初始化为其他值的静态局部变量 \\ \hline \begin{lstlisting}[language=C,gobble=8] void p() { static int i; static int j = 0; } \end{lstlisting} & 局部 & --- & \texttt{.bss} & \makecell[l]{未初始化的静态局部变量 \\ 初始化为 0 的静态局部变量} \\ \hline \begin{lstlisting}[language=C,gobble=8] static void q() { int j = 2; } \end{lstlisting} & --- & --- & --- & \makecell[l]{链接不涉及静态函数\\链接不涉及非静态局部变量} \\ \hline \end{tabular} \end{table} \vspace{-2em} \subsection{链接顺序} \vspace{-0.5em} \texttt{\$ gcc -static -o prog2c main2.o ./libvector.a} \\ E 将被合并以组成可执行文件的所有目标文件集合\\ U 当前所有未解析的引用符号的集合\\ D 当前所有定义符号的集合\\ 开始 E、U、D为空，首先扫描 \texttt{main2.o}，将其加入 E，将未找到的符号加入 U, 定义的符号加入 D。 \\ 再扫描 \texttt{./libvector.a}，将匹配到的 U 中的符号转移到 D 并加入到 E， 同时将未找到的符号加入 U。 \\ 最后搜索标准库 \texttt{libc.a}，处理完\texttt{libc.a}时，U一定是空的，D中符号唯一，否则错误。 \vspace{-1em} \subsection{重定位} \vspace{-0.5em} \begin{itemize} \item 重定位 PC 相对引用(\texttt{R\_X86\_64\_PC32}): \\ 重定位值 \( =\texttt{ADDR(r.symbol)} - \underbrace{\left(\texttt{ADDR(.text)} + \texttt{r.offset}\right)}_{\text{重定位值的地址}} + \texttt{r.addend}\) 在asm中表示为 \texttt{4004de: e8 \underbar{05 00 00 00} \quad callq 4004e8 } \item 重定位绝对引用(\texttt{R\_X86\_64\_32}): \\ 重定位值 = \(\texttt{ADDR(r.symbol)} + \texttt{r.addend}\) \\ 在asm中直接以其绝对地址表示\texttt{4004d9: bf \underbar{18 10 60 00} \quad mov \$0x601018 \%edi} \end{itemize} \newpage \end{document}