Changeset 126 for docs/trunk

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

  r125	r126
  66	66	can we determine if this is safe:
  67	67	\begin{lstlisting}
  68	(追記) [10]INT a: (追記ここまで)
  68	69	PAR
  69	a[p(削除) (削除ここまで)] := 7
  70	a[p(追記) + (3 * r) (追記ここまで)] := 7
  70	71	a[p + q] := 8
  71	72	a[p - q + r] := 9
  …	…
  73	74	\end{frame}
  74	75
  75	%TODO remember to point out that each pair is a different problem
  76
  77	%TODO point out no solution = safe, solution = unsafe
  76	\begin{frame}[fragile]
  77	\frametitle{Parallel Usage}
  78	\begin{lstlisting}
  79	[10]INT a:
  80	PAR
  81	a[p + (3 * r)] := 7
  82	a[p + q] := 8
  83	a[p - q + r] := 9
  84	\end{lstlisting}
  85	Phrase as mathematical problems. Is there a solution to any of:
  86
  87	%TODO tidy up the formatting here
  88
  89	$p + 3r = p + q,ドル 0ドル \leq p + 3r \leq 9,ドル 0ドル \leq p + q \leq 9$
  90
  91	$p + 3r = p - q + r,ドル 0ドル \leq p + 3r \leq 9,ドル 0ドル \leq p - q + r \leq 9$
  92
  93	$p + q = p - q + r,ドル 0ドル \leq p + q \leq 9,ドル 0ドル \leq p - q + r \leq 9$
  94
  95	\note{We are checking if any of array indexes can be equal to each other.
  96	Note that we must check each possible pairing.
  97	No solution to any of the equations means the indexes are disjoint, and
  98	hence the access is safe. If there is a solution to any of them, the
  99	access is unsafe}
  100
  101	\end{frame}
  78	102
  79	103	%TODO mention occam STOPping on integer overflow and array out of bounds being very useful
  …	…
  420	444	\end{frame}
  421	445
  422	(削除) %TODO probably best shown in two dimensions (削除ここまで)
  423	(削除) (削除ここまで)
  424	(削除) (削除ここまで)
  425	(削除) %TODO show tightening inequalities during normalisation. Maybe show two normalising to an equality? (削除ここまで)
  426	(削除) (削除ここまで)
  427	(削除) %TODO show a triangle of inequalities, then demonstrate projecting this onto one dimension: (削除ここまで)
  428	446
  429	447	% 2y <= 17 - 5x, 2y <= 3x + 1, 2y >= 5

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