Add NaN
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3 changed files with 84 additions and 51 deletions
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@ -10,8 +10,9 @@
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\@writefile{toc}{\contentsline {subsection}{\numberline {1.4}GDB查看数据}{1}{subsection.1.4}\protected@file@percent }
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\@writefile{toc}{\contentsline {subsection}{\numberline {1.5}浮点数}{2}{subsection.1.5}\protected@file@percent }
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.1}规格化数 $ \text {exp} \ne 0$ 且 $\text {exp} \ne 11 \dots 1$}{2}{subsubsection.1.5.1}\protected@file@percent }
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.2}非规格化数 $\text {exp} = 0 $}{2}{subsubsection.1.5.2}\protected@file@percent }
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.3}舍入(到偶数)}{2}{subsubsection.1.5.3}\protected@file@percent }
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.2}非规格化数 $\text {exp} = 0$}{2}{subsubsection.1.5.2}\protected@file@percent }
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.3}特殊值 $\text {exp} = 11 \dots 1$}{2}{subsubsection.1.5.3}\protected@file@percent }
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.4}舍入(到偶数)}{2}{subsubsection.1.5.4}\protected@file@percent }
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\@writefile{toc}{\contentsline {section}{\numberline {2}程序的机器级表示}{3}{section.2}\protected@file@percent }
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\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}计算数组元素的地址}{3}{subsection.2.1}\protected@file@percent }
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\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}其他内容}{3}{subsection.2.2}\protected@file@percent }
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复习资料/A.pdf
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复习资料/A.pdf
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复习资料/A.tex
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复习资料/A.tex
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@ -37,7 +37,8 @@
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\lstset{basicstyle=\ttfamily,columns=fullflexible}
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\columnseprule=0.4pt
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\setlength{\columnsep}{1cm}
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\setlength{\columnseprule}{0.4pt}
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\begin{document}
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@ -70,45 +71,45 @@ T: 用 $n$ 位表示数字
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\begin{multicols}{2}
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\qquad 对应正数补码的“各位取反、末位加1”
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\begin{align*}
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+23 & = 00010111 \\
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\text{按位取反} & = 11101000 \\
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& + \hspace{1.8cm} 1 \\
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-23_{\text{补码}} & = 11101001
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+23 & = \texttt{00010111} \\
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\text{按位取反} & = \texttt{11101000} \\
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& + \hspace{0.3em}\phantom{0000000}\texttt{1} \\
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-23_{\text{补码}} & = \texttt{11101001}
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\end{align*}
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\columnbreak
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\qquad 模($2^n$)减去该负数的绝对值
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\begin{align*}
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100000000 & \\
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-00010111 & \\
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\rule{2.5cm}{0.02em} \\
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11101001
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& \texttt{100000000} \\
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- \hspace{0.5em} & \phantom{\texttt{0}}\texttt{00010111} \\[-1em]
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& \hspace{-1em}\rule{2.5cm}{0.02em} \\[-0.5em]
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& \phantom{\texttt{0}}\texttt{11101001}
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\end{align*}
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\end{multicols}
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\subsection{GDB查看数据}
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\texttt{>(gdb) x/4xb} \\[1em]
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\begin{minipage}{12cm}
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\begin{multicols}{2}
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\texttt{>(gdb) x/4xb} \\
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b - byte (8-bit value)\\
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h - halfword (16-bit value) \\
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w - word (32-bit value) \\
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g - giant word (64-bit value)
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\columnbreak
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o - octal \\
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x - hexadecimal \\
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d - decimal \\
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u - unsigned decimal \\
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t - binary \\
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f - floating point \\
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a - address \\
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c - char \\
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s - string \\
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i - instruction
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\texttt{b} - byte (8-bit value) \\
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\texttt{h} - halfword (16-bit value) \\
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\texttt{w} - word (32-bit value) \\
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\texttt{g} - giant word (64-bit value) \\
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\texttt{o} - octal \\
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\texttt{x} - hexadecimal \\
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\texttt{d} - decimal \\
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\texttt{u} - unsigned decimal \\
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\texttt{t} - binary \\
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\texttt{f} - floating point \\
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\texttt{a} - address \\
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\texttt{c} - char \\
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\texttt{s} - string \\
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\texttt{i} - instruction
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\end{multicols}
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\end{minipage}
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\newpage
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@ -127,12 +128,14 @@ i - instruction
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浮点数表示为 $(-1)^s \cdot M \cdot 2^E$
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\InsertBoxR{1}{\tcboxmath{\begin{matrix}
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\InsertBoxR{0}{\tcboxmath{\begin{matrix}
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\multicolumn{2}{c}{\text{偏置值 Bias}} \\
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\texttt{float} & 127 \\
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\texttt{double} & 1023 \\
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\end{matrix}}\hspace{3cm}}
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\vspace{-1em}
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\subsubsection{规格化数 $ \text{exp} \ne 0$ 且 $\text{exp} \ne 11 \dots 1$}
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$\text{(unsigned)} \ \text{exp} \ = \ E \ + \text{Bias}$
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@ -161,37 +164,69 @@ $\text{Bias (偏置值)} = 2^{k-1}-1$ , k 为 $exp$ 的二进制位数
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\end{matrix}\)
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\columnbreak
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例2:二进制浮点数$\rightarrow$十进制数\\
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无符号数，4位阶码(Bias=7)，3个小数位
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\begin{align*}
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1001 \quad 111 \\
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exp \quad frac \\
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\text{计算E:} \\
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E &= exp - Bias \\
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例2: 二进制浮点数$\rightarrow$十进制数
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无符号数，4位阶码(Bias\(=7\))，3个小数位 \\
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\quad \(\begin{matrix}
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1001 & 111 \\
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\text{exp} & \text{frac}
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\end{matrix}\) \\[0.5em]
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\(\begin{aligned}
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\text{计算} \space E &= \text{exp} - \text{Bias} & \\
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&= 1001_2 - 7_{10} \\
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&= 2_{10} \\
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\text{计算M:} \\
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M = 1.\underbar{frac} &= 1.\underbar{111} \\
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\text{化为十进制:} \\
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1.111 \times 2^2 &= 111.1_2 \quad \text{小数点右移2位} \\
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&= 7\frac{1}{2} = \frac{15}{2}
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\end{align*}
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&= 2_{10}
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\end{aligned}\) \\[0.5em]
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计算 \(M = 1.\underbar{frac} = 1.\underbar{111}\) \\[0.5em]
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化为十进制:
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\(\begin{aligned}
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1.111 \times 2^2 & = 111.1_2 \quad \text{小数点右移2位} \\
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& = \frac{15}{2} = 7.5
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\end{aligned}\)
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\end{multicols}
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\InsertBoxR{1}{\tcboxmath{\begin{matrix}
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\InsertBoxR{0}{\tcboxmath{\begin{matrix}
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\text{非规格化数} \ E = 1 - \text{Bias} \\
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\begin{matrix}
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\texttt{float} & -126 \\
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\texttt{double} & -1022 \\
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\end{matrix}
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\end{matrix}}\hspace{2cm}}
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\end{matrix}}
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\hspace{2cm}}
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\vspace{-5mm}
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\subsubsection{非规格化数 $\text{exp} = 0 $}
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\vspace{-0.3em}
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\subsubsection{非规格化数 $\text{exp} = 0$}
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frac \(= 00\dots0\) 表示 0
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frac \(\ne 00\dots0\) 表示接近 0 的小数 $(-1)^s \cdot M \cdot 2^{E}$
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\vspace{-0.3em}
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\subsubsection{特殊值 $\text{exp} = 11 \dots 1$}
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\begin{multicols}{2}
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frac \(= 00\dots0\) 表示 \(\infty\)
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frac \(\ne 00\dots0\) 表示 NaN
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\columnbreak
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\(1.0 / 0.0 = −1.0 / −0.0 = + \infty\)
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\(1.0 / −0.0 = - \infty\)
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\(\sqrt{–1.0} = \infty - \infty = \infty \times 0 = \text{NaN}\)
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\end{multicols}
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\subsubsection{舍入(到偶数)}
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\begin{table}[h]
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@ -276,7 +311,4 @@ D 当前所有定义符号的集合\\
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PC相对地址下重定位值计算公式：\\
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\texttt{ADDR(r.symble)-((ADDR(.text)+r.offset)-r.addend)}\\
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在asm中表示为 \texttt{4004de: e8 \underbar{05 00 00 00} \quad callq 4004e8 <sum>}
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\pagebreak
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\end{document}
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