常见量级的常数

带边框表格

基数 \(b\)	量级 \(p\)	量级 \(\alpha\)	常数	备注	浮动
\(2\)	\(1\)	\(10\)	\(1^1\cdot 4^5\cdot 1^4\)	\(=1024\)	\(0\)
\(10\)	\(2\)	\(3\)	\(114514\) 分钟的小时数	\(\approx 1908.57\)	\(-\)
\(10\)	\(2\)	\(3\)	\(114514^{\circ}\) 的弧度制	\(\approx 1998.65\)	\(-\)
\(10\)	\(1\)	\(3\)	\(114514\%\)	\(=1145.14\)	\(+\)
\(10\)	\(1\)	\(4\)	\(1145\times 14\)	\(=16030\)	\(+\)
\(10\)	\(4\)	\(4\)	\(114514\texttt O\)	\(=39244\)	\(-\)
\(10\)	\(5\)	\(4\)	\(11\times 4514\)	\(=49654\)	\(-\)
\(10\)	\(5\)	\(4\)	\(114\times 514\)	\(=58596\)	\(+\)
\(10\)	\(5\)	\(4\)	\(1!1!4!5!1!4!\)	\(=69120\)	\(++\)
\(10\)	\(1\)	\(5\)	\(114514\)	/	\(+\)
\(10\)	\(1\)	\(5\)	\(1145\text{ shl }14\)	\(=183216\)	\(+\)
\(10\)	\(1\)	\(5\)	\(114514^{\circ}\mathrm C\) 的华氏度	\(\approx206157.2\)	\(+\)
\(10\)	\(2\)	\(5\)	\(114514^{\circ}\) 的百分度制	\(\approx127237.78\)	\(+\)
\(10\)	\(3\)	\(5\)	\(1145141\texttt O\)	\(=313953\)	\(+\)
\(10\)	\(1\)	\(6\)	\(114514\texttt H\)	\(=1131796\)	\(+\)
\(10\)	\(5\)	\(6\)	\(114+51^4\)	\(=6765315\)	\(++\)
\(10\)	\(5\)	\(6\)	\(114514\text{ rad}\) 的角度制	\(\approx 6.56\times10^6\)	\(++\)
\(10\)	\(1\)	\(7\)	\(1145141\texttt H\)	\(=18108737\)	\(+\)
\(10\)	\(1\)	\(9\)	\(114514\) 年中的天数	\(\approx 4.18\times10^7\)	\(+\)
\(10\)	\(1\)	\(9\)	\(114514\) 年中的小时数	\(\approx 10^9\)	\(+\)
\(2\)	\(1\)	\(32\)	\(114514^{1.9}\)	/	\(-\)
\(10\)	\(1\)	\(10\)	\(114514\) 天中的秒数	\(\approx 9.89\times10^9\)	\(+\)
\(10\)	\(1\)	\(10\)	\(\Im((114i)^{5.14})\)	\(\approx 36467308681\)	\(+\)
\(10\)	\(1\)	\(13\)	\(1^{14}5^{14}\)	/	\(+\)
\(10\)	\(1\)	\(16\)	\(11451^4\)	/	\(+\)
\(2\)	\(1\)	\(64\)	\(114514^{3.8}\)	/	\(-\)

按常数大小排序 .

备注：

• 量级 \(L=p\cdot b^{\alpha}\)，其中 \(1\le p<b\) .
• 令常数为 \(C\)，量级为 \(L=p\cdot b^{\alpha}\)，设浮动评价值 \(\delta=C-L\)，则浮动值 \(F\) 的含义为：
  • \(F=++\)：\(\delta>b^{\alpha}\)
  • \(F=+\kern{7.5pt}\)：\(0<\delta<b^{\alpha}\)
  • \(F=0\kern{10.5pt}\)：\(\delta=0\) .
  • \(F=-\kern{7.5pt}\)：\(b^{\alpha}<\delta<0\) .
  • \(F=--\)：\(\delta<0\) .
• 符号注记
  • 数字末尾后缀 \(\tt O\) 表示 \(8\) 进制，后缀 \(\tt H\) 表示 \(16\) 进制 .
  • \(\rm shl\) 为算数左移运算，\(a\text{ shl } b = a\cdot 2^b\) .
  • \(!\) 为阶乘，\(\displaystyle t!=\prod_{i=1}^ti\) .
  • \(\Im(x)\) 为 \(x\) 的虚部 .