Add NaN

复习资料/A.aux

@@ -11,7 +11,8 @@
 \@writefile{toc}{\contentsline {subsection}{\numberline {1.5}浮点数}{2}{subsection.1.5}\protected@file@percent }
 \@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 }
 \@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.2}非规格化数 $\text  {exp} = 0$}{2}{subsubsection.1.5.2}\protected@file@percent }
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.3}舍入(到偶数)}{2}{subsubsection.1.5.3}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.3}特殊值 $\text  {exp} = 11 \dots  1$}{2}{subsubsection.1.5.3}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.4}舍入(到偶数)}{2}{subsubsection.1.5.4}\protected@file@percent }
 \@writefile{toc}{\contentsline {section}{\numberline {2}程序的机器级表示}{3}{section.2}\protected@file@percent }
 \@writefile{toc}{\contentsline {subsection}{\numberline {2.1}计算数组元素的地址}{3}{subsection.2.1}\protected@file@percent }
 \@writefile{toc}{\contentsline {subsection}{\numberline {2.2}其他内容}{3}{subsection.2.2}\protected@file@percent }

复习资料/A.tex

@@ -37,7 +37,8 @@
 
 \lstset{basicstyle=\ttfamily,columns=fullflexible}
 
-\columnseprule=0.4pt
+\setlength{\columnsep}{1cm}
+\setlength{\columnseprule}{0.4pt}
 
 \begin{document}
 
@@ -70,45 +71,45 @@ T: 用 $n$ 位表示数字
 \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 
+        +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*}
-        100000000 & \\
-        -00010111 & \\
-        \rule{2.5cm}{0.02em} \\
-        11101001
+        & \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{>(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 
+    \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
 
@@ -127,12 +128,14 @@ i - instruction
 
 浮点数表示为 $(-1)^s \cdot M \cdot 2^E$
 
-\InsertBoxR{1}{\tcboxmath{\begin{matrix}
+\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 $\text{exp} \ne 11 \dots 1$}
 
 $\text{(unsigned)} \ \text{exp} \ = \ E \ + \text{Bias}$
@@ -161,30 +164,42 @@ $\text{Bias (偏置值)} = 2^{k-1}-1$ , k 为 $exp$ 的二进制位数
 \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 \\
+    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]
+
+    \(\begin{aligned}
+        \text{计算} \space E &= \text{exp} - \text{Bias} & \\
           &= 1001_2 - 7_{10} \\
-          &= 2_{10} \\
-        \text{计算M:} \\
-        M = 1.\underbar{frac} &= 1.\underbar{111} \\
-        \text{化为十进制:} \\
+          &= 2_{10}
+    \end{aligned}\) \\[0.5em]
+
+    计算 \(M = 1.\underbar{frac} = 1.\underbar{111}\) \\[0.5em]
+
+    化为十进制:
+
+    \(\begin{aligned}
         1.111 \times 2^2 & = 111.1_2 \quad \text{小数点右移2位} \\
-        &= 7\frac{1}{2} = \frac{15}{2} 
-    \end{align*}
+        & = \frac{15}{2}  = 7.5
+    \end{aligned}\)
 \end{multicols}
 
-\InsertBoxR{1}{\tcboxmath{\begin{matrix}
+\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}}
+\end{matrix}}
+\hspace{2cm}}
+\vspace{-5mm}
+
+\vspace{-0.3em}
 
 \subsubsection{非规格化数 $\text{exp} = 0$}
 
@@ -192,6 +207,26 @@ 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]
@@ -276,7 +311,4 @@ D 当前所有定义符号的集合\\
 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 <sum>}
-
-\pagebreak
-
 \end{document}