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diff --git a/content/zettel/3a8g4b.md b/content/zettel/3a8g4b.md new file mode 100644 index 0000000..f5186f8 --- /dev/null +++ b/content/zettel/3a8g4b.md @@ -0,0 +1,34 @@ ++++ +title = "Better way of rebuilding the order" +date = "2022-04-29" +author = "Yann Herklotz" +tags = [] +categories = [] +backlinks = ["3a8g4a"] +forwardlinks = [] +zettelid = "3a8g4b" ++++ + +The previous way of rebuilding the order is actually not correct. It's +completely valid to have control-flow graphs where the variables in the +argument list are declared at the same kind of domination point. This +would lead to ambiguities and make it impossible to correctly rebuild +the code using the domination method above, as there is only one order +that is actually correct. + +For μ-functions this is not a problem, because their execution is +dependent on predecessors, which is the same as for φ-functions. In that +case, we only have to look at the previous predecessors and the current +predecessors after having inserted the nodes to convert the η-functions. +If the predecessors are the same, then the registers are switched, and +otherwise they are kept the same, as that means the predecessors have +not changed. + +However, for γ-functions this is a bit more complicated, because one +does not have the correct predecessors available anymore. In that case, +however, it's interesting to note that the only correctness argument +that is really necessary to find the right predecessor is to show that +there exists a path from the dominator to the program counter for which +the chosen predicate simplifies syntactically to the value T. In that +case, on knows that no other predicate will be true, and so this must be +the correct register to pick for that predecessor. |