PROGRAM STRUCTURE TREES - Software Systems Lab

1 introduction
Nowadays modern static analysis tools as well as optimizing compilers
apply powerful optimization techniques and analysis on programs.
To achieve the best results possible analysis and transformations are
developed that are powerful, but often only applicable if the program
to analyse fulfilles certain properties. In general a complete program
does not fulfill the restrictions imposed by the intended analysis.
However it is possible to extract and analyse just the regions of a
program, that satisfy the required restrictions. A way to find these
regions is to find all possible regions and to remove the ones, that do
not satisfy the restrictions.
Therefore it is interesting to understand the different algorithms
available to detect the regions in a program and to investigate the
(dis)advantages each of them has.
2 basic components
2.1 Control flow graph
In compilers the code of a function as seen in Figure 1 can be described
using a control flow graph (CFG) G. G = (V, E) consists of a set of
vertices V, called basic blocks, and a set of edges E connecting these
basic blocks. Every basic block contains a list of statements.
The execution of a function is defined as a walk over the CFG, where
every time a basic block is passed its statements are executed in linear
order. The walk starts always at a specific basic block, the entry basic
block, and ends if it arrives at a basic block, that is terminated with a
”return” statement.
To represent non linear control flow, branch statements may terminate
a basic block. These branch statements pass, based on the result of a
condition, the control to another basic block. The control flow is always
following the edges of the CFG.
2.2 (Simple) Region
A connected subgraph of the CFG, that has only two connections to
the remaining CFG, an incoming and an outcoming edge, is called a
(single entry single exit) region. Such a region can be analyzed and
transformed like a separate function. This can be modeled as seen in 2
by replacing the orange region with a call to a function, that contains
the orange CFG region. Moving or replacing the entire region is as
simple as moving two edges in the CFG or if extracted as a function,
changing a function call.
A region is called trivial region, if it contains exactly one basic block.
A region A is called canonical region, if it there is no set of regions
that can be combined to construct A.
2.3 Refined Region
The definition of a region can be extended to a so called refined region.
A refined region is a connected subgraph of a CFG, that can be transformed
to a region by inserting two empty bbs, that join multiple entry
or exit edges.
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