Changeset 144 for docs/trunk/omega-test-slides/omega-test.tex

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• docs/trunk/omega-test-slides/omega-test.tex

  r143	r144
  684	684	\begin{itemize}
  685	685	\item $x \operatorname{REM} y = x - \operatorname{sign}(x)|y| \lfloor \frac{|x|}{|y|} \rfloor$
  686	(追記) \only<1>{ (追記ここまで)
  687	(追記) \item $y = 0$ implies division by zero (追記ここまで)
  688	(追記) \item $y = \pm 1$ will almost certainly be unsafe ($\forall x: x \operatorname{REM} \pm 1 = 0$) (追記ここまで)
  689	(追記) } (追記ここまで)
  690	(追記) \only<2>{ (追記ここまで)
  686	691	\item Consider all three possibilities:
  687	\begin{itemize}
  688	\item $x = 0, x \operatorname{REM} y = 0$
  689	\item $m = -\lfloor \frac{|x|}{|y|} \rfloor: x \geq 1, x \operatorname{REM} y = x + m|y|, |y| - 1 \geq x + m|y| \geq 0, m \leq 0$
  690	\item $m = \lfloor \frac{|x|}{|y|} \rfloor: x \leq -1, x \operatorname{REM} y = x + m|y|, 1 - |y| \leq x + m|y| \leq 0, m \geq 0$
  691	\end{itemize}
  692	}
  693	\end{itemize}
  694	\only<2>
  695	{
  696	\begin{tabular}{lll}
  697	& $x = 0,ドル & $x \operatorname{REM} y = 0$ \\
  698	\hline
  699	$m = -\lfloor \frac{|x|}{|y|} \rfloor$:& $x \geq 1,ドル& $x \operatorname{REM} y = x + m|y|,ドル \\
  700	& $m \leq 0,ドル& $|y| - 1 \geq x + m|y| \geq 0$ \\
  701	\hline
  702	$m = \lfloor \frac{|x|}{|y|} \rfloor$:& $x \leq -1,ドル& $x \operatorname{REM} y = x + m|y|,ドル \\
  703	& $m \geq 0,ドル & 1ドル - |y| \leq x + m|y| \leq 0$ \\
  704	\end{tabular}
  692	705	\note{Technically, the first case is subsumed by the latter two.
  693	706	But I expect that it will prove useful for efficiency reasons;
  …	…
  695	708	deal with. The first problem should therefore be easy and quick.
  696	709	}
  697	\item $y = 0$ implies division by zero
  698	\item $y = \pm 1$ will almost certainly be unsafe ($\forall x: x \operatorname{REM} \pm 1 = 0$)
  699	\end{itemize}
  700
  710	}
  701	711	\end{frame}
  702	712

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