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zYb}!mhGvy+>4g@r@86Z}f}sK5dI^r8sXWEj~16Dp~;836EZU@VXtTwIGK7BxZ_ctRQNi3Qekb zFl5iu^@n%Tp3S<2N;-V4;$FZ$8KLb3Z=W5CkWigkYvObq?sm|OcSDgix$si1PZHjKd+WQQjirHVD8J{11{c>IG zS5Ti&E?sbb*m97wiTrU8ySay7Ei@n;3kvC3zcsdcGj>p3-&3(_vYEAN(NtFI*?kaM z?>l^;w!wv}l@1(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 $\text{exp} \ne 11 \dots 1$} $\text{(unsigned)} \ \text{exp} \ = \ E \ + \text{Bias}$ @@ -161,37 +164,69 @@ $\text{Bias (偏置值)} = 2^{k-1}-1$ , 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] + + \(\begin{aligned} + \text{计算} \space E &= \text{exp} - \text{Bias} & \\ &= 1001_2 - 7_{10} \\ - &= 2_{10} \\ - \text{计算M:} \\ - M = 1.\underbar{frac} &= 1.\underbar{111} \\ - \text{化为十进制:} \\ - 1.111 \times 2^2 &= 111.1_2 \quad \text{小数点右移2位} \\ - &= 7\frac{1}{2} = \frac{15}{2} - \end{align*} + &= 2_{10} + \end{aligned}\) \\[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{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} -\subsubsection{非规格化数 $\text{exp} = 0 $} +\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] @@ -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 } - -\pagebreak - \end{document}