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<h3 class="section">16.14 Canonicalization of Instructions</h3>
<p><a name="index-canonicalization-of-instructions-3679"></a><a name="index-insn-canonicalization-3680"></a>
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>In addition to algebraic simplifications, following canonicalizations
are performed:
<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>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><a name="index-g_t_0040code_007bneg_007d_002c-canonicalization-of-3681"></a><a name="index-g_t_0040code_007bnot_007d_002c-canonicalization-of-3682"></a><a name="index-g_t_0040code_007bmult_007d_002c-canonicalization-of-3683"></a><a name="index-g_t_0040code_007bplus_007d_002c-canonicalization-of-3684"></a><a name="index-g_t_0040code_007bminus_007d_002c-canonicalization-of-3685"></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>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>.
<p><a name="index-g_t_0040code_007bcompare_007d_002c-canonicalization-of-3686"></a><li>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>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><code>(ltu (plus </code><var>a</var> <var>b</var><code>) </code><var>b</var><code>)</code> is converted to
<code>(ltu (plus </code><var>a</var> <var>b</var><code>) </code><var>a</var><code>)</code>. Likewise with <code>geu</code> instead
of <code>ltu</code>.
<li><code>(minus </code><var>x</var><code> (const_int </code><var>n</var><code>))</code> is converted to
<code>(plus </code><var>x</var><code> (const_int </code><var>-n</var><code>))</code>.
<li>Within address computations (i.e., inside <code>mem</code>), a left shift is
converted into the appropriate multiplication by a power of two.
<p><a name="index-g_t_0040code_007bior_007d_002c-canonicalization-of-3687"></a><a name="index-g_t_0040code_007band_007d_002c-canonicalization-of-3688"></a><a name="index-De-Morgan_0027s-law-3689"></a><li>De Morgan'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
<pre class="smallexample"> (define_insn ""
[(set (match_operand:<var>m</var> 0 ...)
(and:<var>m</var> (not:<var>m</var> (match_operand:<var>m</var> 1 ...))
(match_operand:<var>m</var> 2 ...)))]
"..."
"...")
</pre>
<p class="noindent">Similarly, a pattern for a “NAND” instruction should be written
<pre class="smallexample"> (define_insn ""
[(set (match_operand:<var>m</var> 0 ...)
(ior:<var>m</var> (not:<var>m</var> (match_operand:<var>m</var> 1 ...))
(not:<var>m</var> (match_operand:<var>m</var> 2 ...))))]
"..."
"...")
</pre>
<p>In both cases, it is not necessary to include patterns for the many
logically equivalent RTL expressions.
<p><a name="index-g_t_0040code_007bxor_007d_002c-canonicalization-of-3690"></a><li>The only possible RTL expressions involving both bitwise exclusive-or
and bitwise negation are <code>(xor:</code><var>m</var> <var>x</var> <var>y</var><code>)</code>
and <code>(not:</code><var>m</var><code> (xor:</code><var>m</var> <var>x</var> <var>y</var><code>))</code>.
<li>The sum of three items, one of which is a constant, will only appear in
the form
<pre class="smallexample"> (plus:<var>m</var> (plus:<var>m</var> <var>x</var> <var>y</var>) <var>constant</var>)
</pre>
<p><a name="index-g_t_0040code_007bzero_005fextract_007d_002c-canonicalization-of-3691"></a><a name="index-g_t_0040code_007bsign_005fextract_007d_002c-canonicalization-of-3692"></a><li>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.
<p><a name="index-g_t_0040code_007bmult_007d_002c-canonicalization-of-3693"></a><li><code>(sign_extend:</code><var>m1</var><code> (mult:</code><var>m2</var><code> (sign_extend:</code><var>m2</var> <var>x</var><code>)
(sign_extend:</code><var>m2</var> <var>y</var><code>)))</code> is converted to <code>(mult:</code><var>m1</var><code>
(sign_extend:</code><var>m1</var> <var>x</var><code>) (sign_extend:</code><var>m1</var> <var>y</var><code>))</code>, and likewise
for <code>zero_extend</code>.
<li><code>(sign_extend:</code><var>m1</var><code> (mult:</code><var>m2</var><code> (ashiftrt:</code><var>m2</var>
<var>x</var> <var>s</var><code>) (sign_extend:</code><var>m2</var> <var>y</var><code>)))</code> is converted
to <code>(mult:</code><var>m1</var><code> (sign_extend:</code><var>m1</var><code> (ashiftrt:</code><var>m2</var>
<var>x</var> <var>s</var><code>)) (sign_extend:</code><var>m1</var> <var>y</var><code>))</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.
</ul>
<p>Further canonicalization rules are defined in the function
<code>commutative_operand_precedence</code> in <samp><span class="file">gcc/rtlanal.c</span></samp>.
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