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<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Dominators.html">SSA form - Dominance frontier</a></li>
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<h1>Source code for Lib.Dominators</h1><div class="highlight"><pre>
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<span></span><span class="sd">"""</span>
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<span class="sd">Utility functions to work with dominators in a :py:class:`CFG <Lib.CFG.CFG>`.</span>
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<span class="sd">Do not hesitate to look at the source of the functions</span>
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<span class="sd">to get a better understanding of the algorithms.</span>
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<span class="sd">"""</span>
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<span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Dict</span><span class="p">,</span> <span class="n">Set</span>
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<span class="kn">from</span> <span class="nn">graphviz</span> <span class="kn">import</span> <span class="n">Digraph</span>
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<span class="kn">from</span> <span class="nn">Lib.CFG</span> <span class="kn">import</span> <span class="n">Block</span><span class="p">,</span> <span class="n">CFG</span>
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<div class="viewcode-block" id="computeDom"><a class="viewcode-back" href="../../api/Lib.Dominators.html#Lib.Dominators.computeDom">[docs]</a><span class="k">def</span> <span class="nf">computeDom</span><span class="p">(</span><span class="n">cfg</span><span class="p">:</span> <span class="n">CFG</span><span class="p">)</span> <span class="o">-></span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]]:</span>
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<span class="w"> </span><span class="sd">"""</span>
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<span class="sd"> `computeDom(cfg)` computes the table associating blocks to their</span>
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<span class="sd"> dominators in `cfg`.</span>
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<span class="sd"> It works by solving the equation system.</span>
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<span class="sd"> This is an helper function called during SSA entry.</span>
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<span class="sd"> """</span>
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<span class="n">all_blocks</span><span class="p">:</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">cfg</span><span class="o">.</span><span class="n">get_blocks</span><span class="p">())</span>
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<span class="n">dominators</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]]</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
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<span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">all_blocks</span><span class="p">:</span>
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<span class="k">if</span> <span class="n">b</span><span class="o">.</span><span class="n">get_in</span><span class="p">():</span> <span class="c1"># If b has some predecessor</span>
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<span class="n">dominators</span><span class="p">[</span><span class="n">b</span><span class="p">]</span> <span class="o">=</span> <span class="n">all_blocks</span>
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<span class="k">else</span><span class="p">:</span> <span class="c1"># If b has no predecessors</span>
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<span class="n">dominators</span><span class="p">[</span><span class="n">b</span><span class="p">]</span> <span class="o">=</span> <span class="p">{</span><span class="n">b</span><span class="p">}</span>
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<span class="n">new_dominators</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]]</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
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<span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
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<span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">all_blocks</span><span class="p">:</span>
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<span class="k">if</span> <span class="n">b</span><span class="o">.</span><span class="n">get_in</span><span class="p">():</span>
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<span class="n">dom_preds</span> <span class="o">=</span> <span class="p">[</span><span class="n">dominators</span><span class="p">[</span><span class="n">b2</span><span class="p">]</span> <span class="k">for</span> <span class="n">b2</span> <span class="ow">in</span> <span class="n">b</span><span class="o">.</span><span class="n">get_in</span><span class="p">()]</span>
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<span class="n">new_dominators</span><span class="p">[</span><span class="n">b</span><span class="p">]</span> <span class="o">=</span> <span class="p">{</span><span class="n">b</span><span class="p">}</span><span class="o">.</span><span class="n">union</span><span class="p">(</span><span class="nb">set</span><span class="o">.</span><span class="n">intersection</span><span class="p">(</span><span class="o">*</span><span class="n">dom_preds</span><span class="p">))</span>
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<span class="k">else</span><span class="p">:</span>
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<span class="n">new_dominators</span><span class="p">[</span><span class="n">b</span><span class="p">]</span> <span class="o">=</span> <span class="p">{</span><span class="n">b</span><span class="p">}</span>
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<span class="k">if</span> <span class="n">dominators</span> <span class="o">==</span> <span class="n">new_dominators</span><span class="p">:</span>
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<span class="k">break</span>
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<span class="k">else</span><span class="p">:</span>
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<span class="n">dominators</span> <span class="o">=</span> <span class="n">new_dominators</span>
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<span class="n">new_dominators</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
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<span class="k">return</span> <span class="n">dominators</span></div>
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<div class="viewcode-block" id="printDT"><a class="viewcode-back" href="../../api/Lib.Dominators.html#Lib.Dominators.printDT">[docs]</a><span class="k">def</span> <span class="nf">printDT</span><span class="p">(</span><span class="n">filename</span><span class="p">:</span> <span class="nb">str</span><span class="p">,</span> <span class="n">graph</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]])</span> <span class="o">-></span> <span class="kc">None</span><span class="p">:</span> <span class="c1"># pragma: no cover</span>
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<span class="w"> </span><span class="sd">"""Display a graphical rendering of the given domination tree."""</span>
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<span class="n">dot</span> <span class="o">=</span> <span class="n">Digraph</span><span class="p">()</span>
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<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">graph</span><span class="p">:</span>
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<span class="n">dot</span><span class="o">.</span><span class="n">node</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">k</span><span class="o">.</span><span class="n">get_label</span><span class="p">()))</span>
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<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">graph</span><span class="p">:</span>
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||
<span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">graph</span><span class="p">[</span><span class="n">k</span><span class="p">]:</span>
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||
<span class="n">dot</span><span class="o">.</span><span class="n">edge</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">k</span><span class="o">.</span><span class="n">get_label</span><span class="p">()),</span> <span class="nb">str</span><span class="p">(</span><span class="n">v</span><span class="o">.</span><span class="n">get_label</span><span class="p">()))</span>
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||
<span class="n">dot</span><span class="o">.</span><span class="n">render</span><span class="p">(</span><span class="n">filename</span><span class="p">,</span> <span class="n">view</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span></div>
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<div class="viewcode-block" id="computeDT"><a class="viewcode-back" href="../../api/Lib.Dominators.html#Lib.Dominators.computeDT">[docs]</a><span class="k">def</span> <span class="nf">computeDT</span><span class="p">(</span><span class="n">cfg</span><span class="p">:</span> <span class="n">CFG</span><span class="p">,</span> <span class="n">dominators</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]],</span>
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||
<span class="n">dom_graphs</span><span class="p">:</span> <span class="nb">bool</span><span class="p">,</span> <span class="n">basename</span><span class="p">:</span> <span class="nb">str</span><span class="p">)</span> <span class="o">-></span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]]:</span>
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<span class="w"> </span><span class="sd">"""</span>
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||
<span class="sd"> `computeDT(cfg, dominators)` computes the domination tree of `cfg`</span>
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||
<span class="sd"> using the previously computed `dominators`.</span>
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||
<span class="sd"> It returns `DT`, a dictionary which associates a block with its children</span>
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||
<span class="sd"> in the dominator tree.</span>
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||
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||
<span class="sd"> This is an helper function called during SSA entry.</span>
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||
<span class="sd"> """</span>
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||
<span class="c1"># First, compute the immediate dominators</span>
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<span class="n">idominators</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Block</span><span class="p">]</span> <span class="o">=</span> <span class="p">{}</span>
|
||
<span class="k">for</span> <span class="n">b</span><span class="p">,</span> <span class="n">doms</span> <span class="ow">in</span> <span class="n">dominators</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
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<span class="c1"># The immediate dominator of b is the unique vertex n ≠ b</span>
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<span class="c1"># which dominates b and is dominated by all vertices in Dom(b) − b.</span>
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<span class="n">strict_doms</span> <span class="o">=</span> <span class="n">doms</span> <span class="o">-</span> <span class="p">{</span><span class="n">b</span><span class="p">}</span>
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<span class="n">idoms</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
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<span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">strict_doms</span><span class="p">:</span>
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<span class="k">if</span> <span class="n">strict_doms</span><span class="o">.</span><span class="n">issubset</span><span class="p">(</span><span class="n">dominators</span><span class="p">[</span><span class="n">n</span><span class="p">]):</span>
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<span class="n">idoms</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
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<span class="k">if</span> <span class="n">idoms</span><span class="p">:</span>
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<span class="k">assert</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">idoms</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">)</span>
|
||
<span class="n">idominators</span><span class="p">[</span><span class="n">b</span><span class="p">]</span> <span class="o">=</span> <span class="n">idoms</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
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<span class="c1"># Then, simply inverse the relation to obtain the domination tree</span>
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||
<span class="n">DT</span> <span class="o">=</span> <span class="p">{</span><span class="n">b</span><span class="p">:</span> <span class="nb">set</span><span class="p">()</span> <span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">cfg</span><span class="o">.</span><span class="n">get_blocks</span><span class="p">()}</span>
|
||
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">idominator</span> <span class="ow">in</span> <span class="n">idominators</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
|
||
<span class="n">DT</span><span class="p">[</span><span class="n">idominator</span><span class="p">]</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
|
||
<span class="c1"># Print the domination tree if asked</span>
|
||
<span class="k">if</span> <span class="n">dom_graphs</span><span class="p">:</span>
|
||
<span class="n">s</span> <span class="o">=</span> <span class="s2">"</span><span class="si">{}</span><span class="s2">.</span><span class="si">{}</span><span class="s2">.ssa.DT.dot"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">basename</span><span class="p">,</span> <span class="n">cfg</span><span class="o">.</span><span class="n">fdata</span><span class="o">.</span><span class="n">get_name</span><span class="p">())</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s2">"SSA - domination tree graph:"</span><span class="p">,</span> <span class="n">s</span><span class="p">)</span>
|
||
<span class="n">printDT</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">DT</span><span class="p">)</span>
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<span class="k">return</span> <span class="n">DT</span></div>
|
||
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||
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||
<span class="k">def</span> <span class="nf">_computeDF_at_block</span><span class="p">(</span>
|
||
<span class="n">cfg</span><span class="p">:</span> <span class="n">CFG</span><span class="p">,</span>
|
||
<span class="n">dominators</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]],</span>
|
||
<span class="n">DT</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]],</span>
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<span class="n">b</span><span class="p">:</span> <span class="n">Block</span><span class="p">,</span>
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<span class="n">DF</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]])</span> <span class="o">-></span> <span class="kc">None</span><span class="p">:</span>
|
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<span class="w"> </span><span class="sd">"""</span>
|
||
<span class="sd"> `_computeDF_at_block(...)` computes the dominance frontier at the given block,</span>
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||
<span class="sd"> by updating `DF`.</span>
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||
|
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<span class="sd"> This is an helper function called during SSA entry.</span>
|
||
<span class="sd"> """</span>
|
||
<span class="n">S</span><span class="p">:</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]</span> <span class="o">=</span> <span class="p">{</span><span class="n">succ</span> <span class="k">for</span> <span class="n">succ</span> <span class="ow">in</span> <span class="n">cfg</span><span class="o">.</span><span class="n">out_blocks</span><span class="p">(</span><span class="n">b</span><span class="p">)</span> <span class="k">if</span> <span class="n">succ</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">DT</span><span class="p">[</span><span class="n">b</span><span class="p">]}</span>
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||
<span class="k">for</span> <span class="n">b_succ</span> <span class="ow">in</span> <span class="n">DT</span><span class="p">[</span><span class="n">b</span><span class="p">]:</span>
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||
<span class="n">_computeDF_at_block</span><span class="p">(</span><span class="n">cfg</span><span class="p">,</span> <span class="n">dominators</span><span class="p">,</span> <span class="n">DT</span><span class="p">,</span> <span class="n">b_succ</span><span class="p">,</span> <span class="n">DF</span><span class="p">)</span>
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||
<span class="k">for</span> <span class="n">b_frontier</span> <span class="ow">in</span> <span class="n">DF</span><span class="p">[</span><span class="n">b_succ</span><span class="p">]:</span>
|
||
<span class="k">if</span> <span class="n">b</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">(</span><span class="n">dominators</span><span class="p">[</span><span class="n">b_frontier</span><span class="p">]</span> <span class="o">-</span> <span class="p">{</span><span class="n">b_frontier</span><span class="p">}):</span>
|
||
<span class="n">S</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">b_frontier</span><span class="p">)</span>
|
||
<span class="n">DF</span><span class="p">[</span><span class="n">b</span><span class="p">]</span> <span class="o">=</span> <span class="n">S</span>
|
||
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<div class="viewcode-block" id="computeDF"><a class="viewcode-back" href="../../api/Lib.Dominators.html#Lib.Dominators.computeDF">[docs]</a><span class="k">def</span> <span class="nf">computeDF</span><span class="p">(</span><span class="n">cfg</span><span class="p">:</span> <span class="n">CFG</span><span class="p">,</span> <span class="n">dominators</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]],</span>
|
||
<span class="n">DT</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]],</span> <span class="n">dom_graphs</span><span class="p">:</span> <span class="nb">bool</span><span class="p">,</span> <span class="n">basename</span><span class="p">:</span> <span class="nb">str</span>
|
||
<span class="p">)</span> <span class="o">-></span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]]:</span>
|
||
<span class="w"> </span><span class="sd">"""</span>
|
||
<span class="sd"> `computeDF(...)` computes the dominance frontier of a CFG.</span>
|
||
<span class="sd"> It returns `DF` which associates a block to its frontier.</span>
|
||
|
||
<span class="sd"> This is an helper function called during SSA entry.</span>
|
||
<span class="sd"> """</span>
|
||
<span class="n">DF</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]]</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
|
||
<span class="k">for</span> <span class="n">b_entry</span> <span class="ow">in</span> <span class="n">cfg</span><span class="o">.</span><span class="n">get_entries</span><span class="p">():</span>
|
||
<span class="n">_computeDF_at_block</span><span class="p">(</span><span class="n">cfg</span><span class="p">,</span> <span class="n">dominators</span><span class="p">,</span> <span class="n">DT</span><span class="p">,</span> <span class="n">b_entry</span><span class="p">,</span> <span class="n">DF</span><span class="p">)</span>
|
||
<span class="c1"># Print the domination frontier on the CFG if asked</span>
|
||
<span class="k">if</span> <span class="n">dom_graphs</span><span class="p">:</span>
|
||
<span class="n">s</span> <span class="o">=</span> <span class="s2">"</span><span class="si">{}</span><span class="s2">.</span><span class="si">{}</span><span class="s2">.ssa.DF.dot"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">basename</span><span class="p">,</span> <span class="n">cfg</span><span class="o">.</span><span class="n">fdata</span><span class="o">.</span><span class="n">get_name</span><span class="p">())</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s2">"SSA - dominance frontier graph:"</span><span class="p">,</span> <span class="n">s</span><span class="p">)</span>
|
||
<span class="n">cfg</span><span class="o">.</span><span class="n">print_dot</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">DF</span><span class="p">,</span> <span class="kc">True</span><span class="p">)</span>
|
||
<span class="k">return</span> <span class="n">DF</span></div>
|
||
</pre></div>
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||
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