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<a name="Insn-Canonicalizations"></a>
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<hr>
<a name="Canonicalization-of-Instructions"></a>
<h3 class="section">16.14 Canonicalization of Instructions</h3>
<a name="index-canonicalization-of-instructions"></a>
<a name="index-insn-canonicalization"></a>

<p>There are often cases where multiple RTL expressions could represent an
operation performed by a single machine instruction.  This situation is
most commonly encountered with logical, branch, and multiply-accumulate
instructions.  In such cases, the compiler attempts to convert these
multiple RTL expressions into a single canonical form to reduce the
number of insn patterns required.
</p>
<p>In addition to algebraic simplifications, following canonicalizations
are performed:
</p>
<ul>
<li> For commutative and comparison operators, a constant is always made the
second operand.  If a machine only supports a constant as the second
operand, only patterns that match a constant in the second operand need
be supplied.

</li><li> For associative operators, a sequence of operators will always chain
to the left; for instance, only the left operand of an integer <code>plus</code>
can itself be a <code>plus</code>.  <code>and</code>, <code>ior</code>, <code>xor</code>,
<code>plus</code>, <code>mult</code>, <code>smin</code>, <code>smax</code>, <code>umin</code>, and
<code>umax</code> are associative when applied to integers, and sometimes to
floating-point.

</li><li> <a name="index-neg_002c-canonicalization-of"></a>
<a name="index-not_002c-canonicalization-of"></a>
<a name="index-mult_002c-canonicalization-of"></a>
<a name="index-plus_002c-canonicalization-of"></a>
<a name="index-minus_002c-canonicalization-of"></a>
For these operators, if only one operand is a <code>neg</code>, <code>not</code>,
<code>mult</code>, <code>plus</code>, or <code>minus</code> expression, it will be the
first operand.

</li><li> In combinations of <code>neg</code>, <code>mult</code>, <code>plus</code>, and
<code>minus</code>, the <code>neg</code> operations (if any) will be moved inside
the operations as far as possible.  For instance,
<code>(neg (mult A B))</code> is canonicalized as <code>(mult (neg A) B)</code>, but
<code>(plus (mult (neg B) C) A)</code> is canonicalized as
<code>(minus A (mult B C))</code>.

</li><li> <a name="index-compare_002c-canonicalization-of"></a>
For the <code>compare</code> operator, a constant is always the second operand
if the first argument is a condition code register or <code>(cc0)</code>.

</li><li> An operand of <code>neg</code>, <code>not</code>, <code>mult</code>, <code>plus</code>, or
<code>minus</code> is made the first operand under the same conditions as
above.

</li><li> <code>(ltu (plus <var>a</var> <var>b</var>) <var>b</var>)</code> is converted to
<code>(ltu (plus <var>a</var> <var>b</var>) <var>a</var>)</code>. Likewise with <code>geu</code> instead
of <code>ltu</code>.

</li><li> <code>(minus <var>x</var> (const_int <var>n</var>))</code> is converted to
<code>(plus <var>x</var> (const_int <var>-n</var>))</code>.

</li><li> Within address computations (i.e., inside <code>mem</code>), a left shift is
converted into the appropriate multiplication by a power of two.

</li><li> <a name="index-ior_002c-canonicalization-of"></a>
<a name="index-and_002c-canonicalization-of"></a>
<a name="index-De-Morgan_0027s-law"></a>
De Morgan&rsquo;s Law is used to move bitwise negation inside a bitwise
logical-and or logical-or operation.  If this results in only one
operand being a <code>not</code> expression, it will be the first one.

<p>A machine that has an instruction that performs a bitwise logical-and of one
operand with the bitwise negation of the other should specify the pattern
for that instruction as
</p>
<div class="smallexample">
<pre class="smallexample">(define_insn &quot;&quot;
  [(set (match_operand:<var>m</var> 0 &hellip;)
        (and:<var>m</var> (not:<var>m</var> (match_operand:<var>m</var> 1 &hellip;))
                     (match_operand:<var>m</var> 2 &hellip;)))]
  &quot;&hellip;&quot;
  &quot;&hellip;&quot;)
</pre></div>

<p>Similarly, a pattern for a &ldquo;NAND&rdquo; instruction should be written
</p>
<div class="smallexample">
<pre class="smallexample">(define_insn &quot;&quot;
  [(set (match_operand:<var>m</var> 0 &hellip;)
        (ior:<var>m</var> (not:<var>m</var> (match_operand:<var>m</var> 1 &hellip;))
                     (not:<var>m</var> (match_operand:<var>m</var> 2 &hellip;))))]
  &quot;&hellip;&quot;
  &quot;&hellip;&quot;)
</pre></div>

<p>In both cases, it is not necessary to include patterns for the many
logically equivalent RTL expressions.
</p>
</li><li> <a name="index-xor_002c-canonicalization-of"></a>
The only possible RTL expressions involving both bitwise exclusive-or
and bitwise negation are <code>(xor:<var>m</var> <var>x</var> <var>y</var>)</code>
and <code>(not:<var>m</var> (xor:<var>m</var> <var>x</var> <var>y</var>))</code>.

</li><li> The sum of three items, one of which is a constant, will only appear in
the form

<div class="smallexample">
<pre class="smallexample">(plus:<var>m</var> (plus:<var>m</var> <var>x</var> <var>y</var>) <var>constant</var>)
</pre></div>

</li><li> <a name="index-zero_005fextract_002c-canonicalization-of"></a>
<a name="index-sign_005fextract_002c-canonicalization-of"></a>
Equality comparisons of a group of bits (usually a single bit) with zero
will be written using <code>zero_extract</code> rather than the equivalent
<code>and</code> or <code>sign_extract</code> operations.

</li><li> <a name="index-mult_002c-canonicalization-of-1"></a>
<code>(sign_extend:<var>m1</var> (mult:<var>m2</var> (sign_extend:<var>m2</var> <var>x</var>)
(sign_extend:<var>m2</var> <var>y</var>)))</code> is converted to <code>(mult:<var>m1</var>
(sign_extend:<var>m1</var> <var>x</var>) (sign_extend:<var>m1</var> <var>y</var>))</code>, and likewise
for <code>zero_extend</code>.

</li><li> <code>(sign_extend:<var>m1</var> (mult:<var>m2</var> (ashiftrt:<var>m2</var>
<var>x</var> <var>s</var>) (sign_extend:<var>m2</var> <var>y</var>)))</code> is converted
to <code>(mult:<var>m1</var> (sign_extend:<var>m1</var> (ashiftrt:<var>m2</var>
<var>x</var> <var>s</var>)) (sign_extend:<var>m1</var> <var>y</var>))</code>, and likewise for
patterns using <code>zero_extend</code> and <code>lshiftrt</code>.  If the second
operand of <code>mult</code> is also a shift, then that is extended also.
This transformation is only applied when it can be proven that the
original operation had sufficient precision to prevent overflow.

</li></ul>

<p>Further canonicalization rules are defined in the function
<code>commutative_operand_precedence</code> in <samp>gcc/rtlanal.c</samp>.
</p>
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