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<h1>CombineConversions</h1>
</div>
<div id="content">
<div id="preamble">
<div class="sectionbody">
<div class="paragraph"><p><a href="CombineConversions">CombineConversions</a> is an optimization pass for the <a href="SSA">SSA</a>
<a href="IntermediateLanguage">IntermediateLanguage</a>, invoked from <a href="SSASimplify">SSASimplify</a>.</p></div>
</div>
</div>
<div class="sect1">
<h2 id="_description">Description</h2>
<div class="sectionbody">
<div class="paragraph"><p>This pass looks for and simplifies nested calls to (signed)
extension/truncation.</p></div>
</div>
</div>
<div class="sect1">
<h2 id="_implementation">Implementation</h2>
<div class="sectionbody">
<div class="ulist"><ul>
<li>
<p>
<a href="https://github.com/MLton/mlton/blob/master/mlton/ssa/combine-conversions.fun"><span class="monospaced">combine-conversions.fun</span></a>
</p>
</li>
</ul></div>
</div>
</div>
<div class="sect1">
<h2 id="_details_and_notes">Details and Notes</h2>
<div class="sectionbody">
<div class="paragraph"><p>It processes each block in dfs order (visiting definitions before uses):</p></div>
<div class="ulist"><ul>
<li>
<p>
If the statement is not a <span class="monospaced">PrimApp</span> with <span class="monospaced">Word_extdToWord</span>, skip it.
</p>
</li>
<li>
<p>
After processing a conversion, it tags the <span class="monospaced">Var</span> for subsequent use.
</p>
</li>
<li>
<p>
When inspecting a conversion, check if the <span class="monospaced">Var</span> operand is also the
result of a conversion. If it is, try to combine the two operations.
Repeatedly simplify until hitting either a non-conversion <span class="monospaced">Var</span> or a
case where the conversion cannot be simplified.
</p>
</li>
</ul></div>
<div class="paragraph"><p>The optimization rules are very simple:</p></div>
<div class="listingblock">
<div class="content monospaced">
<pre>x1 = ...
x2 = Word_extdToWord (W1, W2, {signed=s1}) x1
x3 = Word_extdToWord (W2, W3, {signed=s2}) x2</pre>
</div></div>
<div class="ulist"><ul>
<li>
<p>
If <span class="monospaced">W1 = W2</span>, then there is no conversions before <span class="monospaced">x_1</span>.
</p>
<div class="paragraph"><p>This is guaranteed because <span class="monospaced">W2 = W3</span> will always trigger optimization.</p></div>
</li>
<li>
<p>
Case <span class="monospaced">W1 <= W3 <= W2</span>:
</p>
<div class="listingblock">
<div class="content monospaced">
<pre>x3 = Word_extdToWord (W1, W3, {signed=s1}) x1</pre>
</div></div>
</li>
<li>
<p>
Case <span class="monospaced">W1 < W2 < W3 AND ((NOT s1) OR s2)</span>:
</p>
<div class="listingblock">
<div class="content monospaced">
<pre>x3 = Word_extdToWord (W1, W3, {signed=s1}) x1</pre>
</div></div>
</li>
<li>
<p>
Case <span class="monospaced">W1 = W2 < W3</span>:
</p>
<div class="paragraph"><p>unoptimized, because there are no conversions past <span class="monospaced">W1</span> and <span class="monospaced">x2 = x1</span></p></div>
</li>
<li>
<p>
Case <span class="monospaced">W3 <= W2 <= W1 OR W3 <= W1 <= W2</span>:
</p>
<div class="listingblock">
<div class="content monospaced">
<pre>x_3 = Word_extdToWord (W1, W3, {signed=_}) x1</pre>
</div></div>
<div class="paragraph"><p>because <span class="monospaced">W3 <= W1 && W3 <= W2</span>, just clip <span class="monospaced">x1</span></p></div>
</li>
<li>
<p>
Case <span class="monospaced">W2 < W1 <= W3 OR W2 < W3 <= W1</span>:
</p>
<div class="paragraph"><p>unoptimized, because <span class="monospaced">W2 < W1 && W2 < W3</span>, has truncation effect</p></div>
</li>
<li>
<p>
Case <span class="monospaced">W1 < W2 < W3 AND (s1 AND (NOT s2))</span>:
</p>
<div class="paragraph"><p>unoptimized, because each conversion affects the result separately</p></div>
</li>
</ul></div>
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