Changeset 154 for docs/trunk/omega-test-slides/omega-test.tex

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

  r153	r154
  248	248	% 9 blah 4: 2
  249	249	%10 blah 4: 3
  250	(追記) (追記ここまで)
  251	(追記) \begin{frame}<1-5> [fragile] (追記ここまで)
  252	(追記) \frametitle{A Worked Problem} (追記ここまで)
  253	(追記) \begin{tabular}{ll} (追記ここまで)
  254	(追記) Substitution & Equations \\ \hline (追記ここまで)
  255	(追記) (追記ここまで)
  256	(追記) ~ & $\begin{array}{rrrcr} (追記ここまで)
  257	(追記) 5x &- y + & 3z & = & 0 \\ (追記ここまで)
  258	(追記) 18x &- 3y + & 2z & = & 57 \\ (追記ここまで)
  259	(追記) 14x &- 2y + &3z &=& 38 \end{array}$ (追記ここまで)
  260	(追記) (追記ここまで)
  261	(追記) \\ \hline (追記ここまで)
  262	(追記) \only<2->{ (追記ここまで)
  263	(追記) $y = 5x + 3z$ & (追記ここまで)
  264	(追記) $\begin{array}{rrcr} (追記ここまで)
  265	(追記) 3x &- 7z &=& 57 \\ (追記ここまで)
  266	(追記) 4x &- 3z &=& 38 \end{array}$} (追記ここまで)
  267	(追記) (追記ここまで)
  268	(追記) \\ \hline (追記ここまで)
  269	(追記) \only<3->{ (追記ここまで)
  270	(追記) $x = -4\sigma + z - 1$ & (追記ここまで)
  271	(追記) $\begin{array}{rrcr} (追記ここまで)
  272	(追記) -3\sigma &- z &=& 15 \\ (追記ここまで)
  273	(追記) -16\sigma &+ z &=& 42 \end{array}$} (追記ここまで)
  274	(追記) (追記ここまで)
  275	(追記) \\ \hline (追記ここまで)
  276	(追記) \only<4->{ (追記ここまで)
  277	(追記) $z = -3\sigma - 15$ & (追記ここまで)
  278	(追記) $-19\sigma = 57$} (追記ここまで)
  279	(追記) (追記ここまで)
  280	(追記) \\ \hline (追記ここまで)
  281	(追記) \only<5->{ (追記ここまで)
  282	(追記) $\sigma = -3$ & ~ \\} (追記ここまで)
  283	(追記) (追記ここまで)
  284	(追記) \end{tabular} (追記ここまで)
  285	(追記) \end{frame} (追記ここまで)
  250	286
  251	287	\begin{frame}[fragile]
  …	…
  660	696	\frametitle{Flattening Expressions}
  661	697	\begin{itemize}
  662	\item (削除) Addition is left alone, subtraction is turned into addition. (削除ここまで)
  663	\item (削除) Multiplied expressions are multiplied out. (削除ここまで)
  664	\item (削除) Division is problematic if it doesn't cancel out. (削除ここまで)
  665	\item (削除) Modulo is (削除ここまで) special \ldots
  698	\item (追記) \lstinline|3*(7-i)| becomes 21ドル + (-3)i$ (追記ここまで)
  699	\item (追記) Addition is left alone, subtraction is turned into addition (追記ここまで)
  700	\item (追記) Multiplied expressions are multiplied out (追記ここまで)
  701	\item (追記) Division and modulo are (追記ここまで) special \ldots
  666	702	\end{itemize}
  667	703	\end{frame}
  …	…
  676	712	\item They often cancel out anyway:
  677	713	\begin{lstlisting}
  678	PAR i = 0 (削除) for (削除ここまで) 10
  714	PAR i = 0 (追記) FOR (追記ここまで) 10
  679	715	scr[width*y + i] := 255
  680	716	\end{lstlisting}
  …	…
  861	897	% 5x - y + 3z = 0, 18x - 3y + 2z = 57, 14x - 2y + 3z = 38
  862	898
  863	\begin{frame}<(削除) 1- (削除ここまで)5> [fragile]
  864	\frametitle{(削除) A Worked Problem (削除ここまで)}
  899	\begin{frame}<(追記) (追記ここまで)5> [fragile]
  900	\frametitle{(追記) Equality Solutions (追記ここまで)}
  865	901	\begin{tabular}{ll}
  866	902	Substitution & Equations \\ \hline
  …	…
  898	934
  899	935	\begin{frame}<1-4>[fragile]
  900	\frametitle{(削除) A Worked Problem -- Solved (削除ここまで)}
  936	\frametitle{(追記) Equality Solutions (追記ここまで)}
  901	937	\begin{tabular}{l}
  902	938	Substitution/Values \\ \hline
  …	…
  916	952	%variables projected away. So we might need some cleverness to get the original
  917	953	%variables back after all; substitution into the bounds?
  954	(追記) (追記ここまで)
  955	(追記) \begin{frame}[fragile] (追記ここまで)
  956	(追記) \frametitle{Inequality Solutions} (追記ここまで)
  957	(追記) \begin{itemize} (追記ここまで)
  958	(追記) \item Variables eliminated in inequalities are projected away (追記ここまで)
  959	(追記) \begin{itemize} (追記ここまで)
  960	(追記) \item Can't feed back a solution (追記ここまで)
  961	(追記) \end{itemize} (追記ここまで)
  962	(追記) \item Difficult issue (unsolved) (追記ここまで)
  963	(追記) \end{itemize} (追記ここまで)
  964	(追記) \end{frame} (追記ここまで)
  918	965
  919	966	\section{Future Work}
  …	…
  952	999	\frametitle{Future work -- optimising out checks}
  953	1000	\begin{itemize}
  954	\item We c(削除) an (削除ここまで) use the integer analysis to check if array indexes are always within bounds
  1001	\item We c(追記) ould (追記ここまで) use the integer analysis to check if array indexes are always within bounds
  955	1002	\begin{itemize}
  956	1003	\item Hence we can remove run-time checks in places

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