54 lines
1.5 KiB
Plaintext
54 lines
1.5 KiB
Plaintext
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.NH 2
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Immediate dominators
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.PP
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A basic block B dominates a block C if every path
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in the control flow graph from the procedure entry block
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to C goes through B.
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The immediate dominator of C is the closest dominator
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of C on any path from the entry block.
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See also
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.[~[
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aho compiler design
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.], section 13.1.]
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.PP
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There are a number of algorithms to compute
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the immediate dominator relation.
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.IP 1.
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Purdom and Moore give an algorithm that is
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easy to program and easy to describe (although the
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description they give is unreadable;
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it is given in a very messy Algol60 program full of gotos).
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.[
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predominators
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.]
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.IP 2.
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Aho and Ullman present a bitvector algorithm, which is also
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easy to program and to understand.
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(See
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.[~[
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aho compiler design
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.], section 13.1.]).
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.IP 3
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Lengauer and Tarjan introduce a fast algorithm that is
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hard to understand, yet remarkably easy to implement.
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.[
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lengauer dominators
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.]
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.LP
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The Purdom-Moore algorithm is very slow if the
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number of basic blocks in the flow graph is large.
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The Aho-Ullman algorithm in fact computes the
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dominator relation,
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from which the immediate dominator relation can be computed
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in time quadratic to the number of basic blocks, worst case.
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The storage requirement is also quadratic to the number
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of blocks.
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The running time of the third algorithm is proportional
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to:
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.DS
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(number of edges in the graph) * log(number of blocks).
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.DE
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We have chosen this algorithm because it is fast
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(as shown by experiments done by Lengauer and Tarjan),
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it is easy to program and requires little data space.
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