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+\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} + +\lstset{basicstyle=\ttfamily,columns=fullflexible} + +\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] + \caption{数据的类型及大小} + \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 & = 00010111 \\ + \text{按位取反} & = 11101000 \\ + & + \hspace{1.8cm} 1 \\ + -23_{\text{补码}} & = 11101001 + \end{align*} + + \columnbreak + + \qquad 模($2^n$)减去该负数的绝对值 + \begin{align*} + 100000000 & \\ + -00010111 & \\ + \rule{2.5cm}{0.02em} \\ + 11101001 + \end{align*} + +\end{multicols} + +\subsection{GDB查看数据} +\begin{multicols}{2} +\texttt{>(gdb) x/4xb} \\ +b - byte (8-bit value)\\ +h - halfword (16-bit value) \\ +w - word (32-bit value) \\ +g - giant word (64-bit value) + +\columnbreak + +o - octal \\ +x - hexadecimal \\ +d - decimal \\ +u - unsigned decimal \\ +t - binary \\ +f - floating point \\ +a - address \\ +c - char \\ +s - string \\ +i - instruction +\end{multicols} + +\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{1}{\tcboxmath{\begin{matrix} + \multicolumn{2}{c}{\text{偏置值 Bias}} \\ + \texttt{float} & 127 \\ + \texttt{double} & 1023 \\ +\end{matrix}}\hspace{3cm}} + +\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 + \begin{align*} + 1001 \quad 111 \\ + exp \quad frac \\ + \text{计算E:} \\ + E &= exp - Bias \\ + &= 1001_2 - 7_{10} \\ + &= 2_{10} \\ + \text{计算M:} \\ + M = 1.\underbar{frac} &= 1.\underbar{111} \\ + \text{化为十进制:} \\ + 1.111 \times 2^2 &= 111.1_2 \quad \text{小数点右移2位} \\ + &= 7\frac{1}{2} = \frac{15}{2} + \end{align*} +\end{multicols} + +\InsertBoxR{1}{\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}} + +\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 $(-1)^s \cdot M \cdot 2^{E}$ + +\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 +\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{-1cm} + +\subsection{其他内容} +\vspace{-2mm} +\begin{table}[h] + \begin{tabular}{c|c|c|c} \hline + 内容 & 操作数计算方式& 栈&gdb常用操作\\ \hline + 页码 & P121&P164&P194 \\ + + \hline +\end{tabular} +\end{table} + +\vspace{-5mm} + +\section{链接} +\subsection{符号表 (.symtab)} + +\begin{table}[h] + \begin{tabular}{l|c|c|c|c} + \hline + C语言表示 & 类型 & 符号强度 & 节 & 说明\\ \hline + \texttt{void swap();} & 全局 & 强 & \texttt{.text} & 函数在.text \\ \hline + \texttt{extern int buf[];} & 外部 & --- & 实际定义所在位置 & 默认\texttt{UND}（未解析的引用符号） \\ \hline + \texttt{int *bufp0 = \&buf[0]} & 全局 & 强 & \texttt{.data} & 初始化的全局变量\\ \hline + \texttt{int *bufp1;} & 全局 & 弱 & \texttt{COMMON} & 未初始化的全局变量 \\ \hline + \begin{lstlisting}[language=C,gobble=8] + void p() { + static int i = 1; } + \end{lstlisting} + & 局部 & \makecell[c]{强\ ，不同\\函数可重} & \texttt{.data} 或 \texttt{.bss} & \makecell[l]{未初始化或初始化为0在 \ \texttt{.bss}\\初始化为其他在 \ \texttt{.data}} \\ \hline + \begin{lstlisting}[language=C,gobble=8] + void q() { + int j = 2; } + \end{lstlisting} + & 都不是 & --- & 节里没有，在栈里 & 链接器不看局部\underbar{变量} \\ \hline + \end{tabular} +\end{table} + +\subsection{链接顺序} +\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。 + +\subsection{重定位} +PC相对地址下重定位值计算公式：\\ +\texttt{ADDR(r.symble)-((ADDR(.text)+r.offset)-r.addend)}\\ +在asm中表示为 \texttt{4004de: e8 \underbar{05 00 00 00} \quad callq 4004e8 } + +\pagebreak + +\end{document} diff --git a/复习资料/missfont.log b/复习资料/missfont.log new file mode 100644 index 0000000..da81738 --- /dev/null +++ b/复习资料/missfont.log @@ -0,0 +1,15 @@ +mktextfm font +mktextfm font +mktextfm font +mktextfm font/BI +mktextfm font +mktextfm font/B +mktextfm font +mktextfm font/I +mktextfm font +mktextfm font +mktextfm font +mktextfm +mktextfm +mktextfm +mktextfm