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<title>GNU Compiler Collection (GCC) Internals: Arithmetic</title>
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<a name="Arithmetic"></a>
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<div class="header">
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<p>
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Next: <a href="Comparisons.html#Comparisons" accesskey="n" rel="next">Comparisons</a>, Previous: <a href="Regs-and-Memory.html#Regs-and-Memory" accesskey="p" rel="prev">Regs and Memory</a>, Up: <a href="RTL.html#RTL" accesskey="u" rel="up">RTL</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Option-Index.html#Option-Index" title="Index" rel="index">Index</a>]</p>
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</div>
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<hr>
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<a name="RTL-Expressions-for-Arithmetic"></a>
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<h3 class="section">13.9 RTL Expressions for Arithmetic</h3>
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<a name="index-arithmetic_002c-in-RTL"></a>
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<a name="index-math_002c-in-RTL"></a>
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<a name="index-RTL-expressions-for-arithmetic"></a>
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<p>Unless otherwise specified, all the operands of arithmetic expressions
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must be valid for mode <var>m</var>. An operand is valid for mode <var>m</var>
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if it has mode <var>m</var>, or if it is a <code>const_int</code> or
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<code>const_double</code> and <var>m</var> is a mode of class <code>MODE_INT</code>.
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</p>
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<p>For commutative binary operations, constants should be placed in the
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second operand.
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</p>
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<dl compact="compact">
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<dd><a name="index-plus"></a>
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<a name="index-ss_005fplus"></a>
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<a name="index-us_005fplus"></a>
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<a name="index-RTL-sum"></a>
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<a name="index-RTL-addition"></a>
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<a name="index-RTL-addition-with-signed-saturation"></a>
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<a name="index-RTL-addition-with-unsigned-saturation"></a>
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</dd>
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<dt><code>(plus:<var>m</var> <var>x</var> <var>y</var>)</code></dt>
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<dt><code>(ss_plus:<var>m</var> <var>x</var> <var>y</var>)</code></dt>
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<dt><code>(us_plus:<var>m</var> <var>x</var> <var>y</var>)</code></dt>
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<dd>
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<p>These three expressions all represent the sum of the values
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represented by <var>x</var> and <var>y</var> carried out in machine mode
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<var>m</var>. They differ in their behavior on overflow of integer modes.
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<code>plus</code> wraps round modulo the width of <var>m</var>; <code>ss_plus</code>
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saturates at the maximum signed value representable in <var>m</var>;
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<code>us_plus</code> saturates at the maximum unsigned value.
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</p>
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<a name="index-lo_005fsum"></a>
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</dd>
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<dt><code>(lo_sum:<var>m</var> <var>x</var> <var>y</var>)</code></dt>
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<dd>
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<p>This expression represents the sum of <var>x</var> and the low-order bits
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of <var>y</var>. It is used with <code>high</code> (see <a href="Constants.html#Constants">Constants</a>) to
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represent the typical two-instruction sequence used in RISC machines
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to reference a global memory location.
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</p>
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<p>The number of low order bits is machine-dependent but is
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normally the number of bits in a <code>Pmode</code> item minus the number of
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bits set by <code>high</code>.
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</p>
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<p><var>m</var> should be <code>Pmode</code>.
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</p>
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<a name="index-minus"></a>
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<a name="index-ss_005fminus"></a>
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<a name="index-us_005fminus"></a>
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<a name="index-RTL-difference"></a>
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<a name="index-RTL-subtraction"></a>
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<a name="index-RTL-subtraction-with-signed-saturation"></a>
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<a name="index-RTL-subtraction-with-unsigned-saturation"></a>
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</dd>
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<dt><code>(minus:<var>m</var> <var>x</var> <var>y</var>)</code></dt>
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<dt><code>(ss_minus:<var>m</var> <var>x</var> <var>y</var>)</code></dt>
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<dt><code>(us_minus:<var>m</var> <var>x</var> <var>y</var>)</code></dt>
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<dd>
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<p>These three expressions represent the result of subtracting <var>y</var>
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from <var>x</var>, carried out in mode <var>M</var>. Behavior on overflow is
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the same as for the three variants of <code>plus</code> (see above).
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</p>
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<a name="index-compare"></a>
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<a name="index-RTL-comparison"></a>
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</dd>
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<dt><code>(compare:<var>m</var> <var>x</var> <var>y</var>)</code></dt>
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<dd><p>Represents the result of subtracting <var>y</var> from <var>x</var> for purposes
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of comparison. The result is computed without overflow, as if with
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infinite precision.
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</p>
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<p>Of course, machines can’t really subtract with infinite precision.
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However, they can pretend to do so when only the sign of the result will
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be used, which is the case when the result is stored in the condition
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code. And that is the <em>only</em> way this kind of expression may
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validly be used: as a value to be stored in the condition codes, either
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<code>(cc0)</code> or a register. See <a href="Comparisons.html#Comparisons">Comparisons</a>.
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</p>
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<p>The mode <var>m</var> is not related to the modes of <var>x</var> and <var>y</var>, but
|
instead is the mode of the condition code value. If <code>(cc0)</code> is
|
used, it is <code>VOIDmode</code>. Otherwise it is some mode in class
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<code>MODE_CC</code>, often <code>CCmode</code>. See <a href="Condition-Code.html#Condition-Code">Condition Code</a>. If <var>m</var>
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is <code>VOIDmode</code> or <code>CCmode</code>, the operation returns sufficient
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information (in an unspecified format) so that any comparison operator
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can be applied to the result of the <code>COMPARE</code> operation. For other
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modes in class <code>MODE_CC</code>, the operation only returns a subset of
|
this information.
|
</p>
|
<p>Normally, <var>x</var> and <var>y</var> must have the same mode. Otherwise,
|
<code>compare</code> is valid only if the mode of <var>x</var> is in class
|
<code>MODE_INT</code> and <var>y</var> is a <code>const_int</code> or
|
<code>const_double</code> with mode <code>VOIDmode</code>. The mode of <var>x</var>
|
determines what mode the comparison is to be done in; thus it must not
|
be <code>VOIDmode</code>.
|
</p>
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<p>If one of the operands is a constant, it should be placed in the
|
second operand and the comparison code adjusted as appropriate.
|
</p>
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<p>A <code>compare</code> specifying two <code>VOIDmode</code> constants is not valid
|
since there is no way to know in what mode the comparison is to be
|
performed; the comparison must either be folded during the compilation
|
or the first operand must be loaded into a register while its mode is
|
still known.
|
</p>
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<a name="index-neg"></a>
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<a name="index-ss_005fneg"></a>
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<a name="index-us_005fneg"></a>
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<a name="index-negation"></a>
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<a name="index-negation-with-signed-saturation"></a>
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<a name="index-negation-with-unsigned-saturation"></a>
|
</dd>
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<dt><code>(neg:<var>m</var> <var>x</var>)</code></dt>
|
<dt><code>(ss_neg:<var>m</var> <var>x</var>)</code></dt>
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<dt><code>(us_neg:<var>m</var> <var>x</var>)</code></dt>
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<dd><p>These two expressions represent the negation (subtraction from zero) of
|
the value represented by <var>x</var>, carried out in mode <var>m</var>. They
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differ in the behavior on overflow of integer modes. In the case of
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<code>neg</code>, the negation of the operand may be a number not representable
|
in mode <var>m</var>, in which case it is truncated to <var>m</var>. <code>ss_neg</code>
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and <code>us_neg</code> ensure that an out-of-bounds result saturates to the
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maximum or minimum signed or unsigned value.
|
</p>
|
<a name="index-mult"></a>
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<a name="index-ss_005fmult"></a>
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<a name="index-us_005fmult"></a>
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<a name="index-multiplication"></a>
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<a name="index-product"></a>
|
<a name="index-multiplication-with-signed-saturation"></a>
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<a name="index-multiplication-with-unsigned-saturation"></a>
|
</dd>
|
<dt><code>(mult:<var>m</var> <var>x</var> <var>y</var>)</code></dt>
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<dt><code>(ss_mult:<var>m</var> <var>x</var> <var>y</var>)</code></dt>
|
<dt><code>(us_mult:<var>m</var> <var>x</var> <var>y</var>)</code></dt>
|
<dd><p>Represents the signed product of the values represented by <var>x</var> and
|
<var>y</var> carried out in machine mode <var>m</var>.
|
<code>ss_mult</code> and <code>us_mult</code> ensure that an out-of-bounds result
|
saturates to the maximum or minimum signed or unsigned value.
|
</p>
|
<p>Some machines support a multiplication that generates a product wider
|
than the operands. Write the pattern for this as
|
</p>
|
<div class="smallexample">
|
<pre class="smallexample">(mult:<var>m</var> (sign_extend:<var>m</var> <var>x</var>) (sign_extend:<var>m</var> <var>y</var>))
|
</pre></div>
|
|
<p>where <var>m</var> is wider than the modes of <var>x</var> and <var>y</var>, which need
|
not be the same.
|
</p>
|
<p>For unsigned widening multiplication, use the same idiom, but with
|
<code>zero_extend</code> instead of <code>sign_extend</code>.
|
</p>
|
<a name="index-fma"></a>
|
</dd>
|
<dt><code>(fma:<var>m</var> <var>x</var> <var>y</var> <var>z</var>)</code></dt>
|
<dd><p>Represents the <code>fma</code>, <code>fmaf</code>, and <code>fmal</code> builtin
|
functions, which compute ‘<samp><var>x</var> * <var>y</var> + <var>z</var></samp>’
|
without doing an intermediate rounding step.
|
</p>
|
<a name="index-div"></a>
|
<a name="index-ss_005fdiv"></a>
|
<a name="index-division"></a>
|
<a name="index-signed-division"></a>
|
<a name="index-signed-division-with-signed-saturation"></a>
|
<a name="index-quotient"></a>
|
</dd>
|
<dt><code>(div:<var>m</var> <var>x</var> <var>y</var>)</code></dt>
|
<dt><code>(ss_div:<var>m</var> <var>x</var> <var>y</var>)</code></dt>
|
<dd><p>Represents the quotient in signed division of <var>x</var> by <var>y</var>,
|
carried out in machine mode <var>m</var>. If <var>m</var> is a floating point
|
mode, it represents the exact quotient; otherwise, the integerized
|
quotient.
|
<code>ss_div</code> ensures that an out-of-bounds result saturates to the maximum
|
or minimum signed value.
|
</p>
|
<p>Some machines have division instructions in which the operands and
|
quotient widths are not all the same; you should represent
|
such instructions using <code>truncate</code> and <code>sign_extend</code> as in,
|
</p>
|
<div class="smallexample">
|
<pre class="smallexample">(truncate:<var>m1</var> (div:<var>m2</var> <var>x</var> (sign_extend:<var>m2</var> <var>y</var>)))
|
</pre></div>
|
|
<a name="index-udiv"></a>
|
<a name="index-unsigned-division"></a>
|
<a name="index-unsigned-division-with-unsigned-saturation"></a>
|
<a name="index-division-1"></a>
|
</dd>
|
<dt><code>(udiv:<var>m</var> <var>x</var> <var>y</var>)</code></dt>
|
<dt><code>(us_div:<var>m</var> <var>x</var> <var>y</var>)</code></dt>
|
<dd><p>Like <code>div</code> but represents unsigned division.
|
<code>us_div</code> ensures that an out-of-bounds result saturates to the maximum
|
or minimum unsigned value.
|
</p>
|
<a name="index-mod"></a>
|
<a name="index-umod"></a>
|
<a name="index-remainder"></a>
|
<a name="index-division-2"></a>
|
</dd>
|
<dt><code>(mod:<var>m</var> <var>x</var> <var>y</var>)</code></dt>
|
<dt><code>(umod:<var>m</var> <var>x</var> <var>y</var>)</code></dt>
|
<dd><p>Like <code>div</code> and <code>udiv</code> but represent the remainder instead of
|
the quotient.
|
</p>
|
<a name="index-smin"></a>
|
<a name="index-smax"></a>
|
<a name="index-signed-minimum"></a>
|
<a name="index-signed-maximum"></a>
|
</dd>
|
<dt><code>(smin:<var>m</var> <var>x</var> <var>y</var>)</code></dt>
|
<dt><code>(smax:<var>m</var> <var>x</var> <var>y</var>)</code></dt>
|
<dd><p>Represents the smaller (for <code>smin</code>) or larger (for <code>smax</code>) of
|
<var>x</var> and <var>y</var>, interpreted as signed values in mode <var>m</var>.
|
When used with floating point, if both operands are zeros, or if either
|
operand is <code>NaN</code>, then it is unspecified which of the two operands
|
is returned as the result.
|
</p>
|
<a name="index-umin"></a>
|
<a name="index-umax"></a>
|
<a name="index-unsigned-minimum-and-maximum"></a>
|
</dd>
|
<dt><code>(umin:<var>m</var> <var>x</var> <var>y</var>)</code></dt>
|
<dt><code>(umax:<var>m</var> <var>x</var> <var>y</var>)</code></dt>
|
<dd><p>Like <code>smin</code> and <code>smax</code>, but the values are interpreted as unsigned
|
integers.
|
</p>
|
<a name="index-not"></a>
|
<a name="index-complement_002c-bitwise"></a>
|
<a name="index-bitwise-complement"></a>
|
</dd>
|
<dt><code>(not:<var>m</var> <var>x</var>)</code></dt>
|
<dd><p>Represents the bitwise complement of the value represented by <var>x</var>,
|
carried out in mode <var>m</var>, which must be a fixed-point machine mode.
|
</p>
|
<a name="index-and"></a>
|
<a name="index-logical_002dand_002c-bitwise"></a>
|
<a name="index-bitwise-logical_002dand"></a>
|
</dd>
|
<dt><code>(and:<var>m</var> <var>x</var> <var>y</var>)</code></dt>
|
<dd><p>Represents the bitwise logical-and of the values represented by
|
<var>x</var> and <var>y</var>, carried out in machine mode <var>m</var>, which must be
|
a fixed-point machine mode.
|
</p>
|
<a name="index-ior"></a>
|
<a name="index-inclusive_002dor_002c-bitwise"></a>
|
<a name="index-bitwise-inclusive_002dor"></a>
|
</dd>
|
<dt><code>(ior:<var>m</var> <var>x</var> <var>y</var>)</code></dt>
|
<dd><p>Represents the bitwise inclusive-or of the values represented by <var>x</var>
|
and <var>y</var>, carried out in machine mode <var>m</var>, which must be a
|
fixed-point mode.
|
</p>
|
<a name="index-xor"></a>
|
<a name="index-exclusive_002dor_002c-bitwise"></a>
|
<a name="index-bitwise-exclusive_002dor"></a>
|
</dd>
|
<dt><code>(xor:<var>m</var> <var>x</var> <var>y</var>)</code></dt>
|
<dd><p>Represents the bitwise exclusive-or of the values represented by <var>x</var>
|
and <var>y</var>, carried out in machine mode <var>m</var>, which must be a
|
fixed-point mode.
|
</p>
|
<a name="index-ashift"></a>
|
<a name="index-ss_005fashift"></a>
|
<a name="index-us_005fashift"></a>
|
<a name="index-left-shift"></a>
|
<a name="index-shift"></a>
|
<a name="index-arithmetic-shift"></a>
|
<a name="index-arithmetic-shift-with-signed-saturation"></a>
|
<a name="index-arithmetic-shift-with-unsigned-saturation"></a>
|
</dd>
|
<dt><code>(ashift:<var>m</var> <var>x</var> <var>c</var>)</code></dt>
|
<dt><code>(ss_ashift:<var>m</var> <var>x</var> <var>c</var>)</code></dt>
|
<dt><code>(us_ashift:<var>m</var> <var>x</var> <var>c</var>)</code></dt>
|
<dd><p>These three expressions represent the result of arithmetically shifting <var>x</var>
|
left by <var>c</var> places. They differ in their behavior on overflow of integer
|
modes. An <code>ashift</code> operation is a plain shift with no special behavior
|
in case of a change in the sign bit; <code>ss_ashift</code> and <code>us_ashift</code>
|
saturates to the minimum or maximum representable value if any of the bits
|
shifted out differs from the final sign bit.
|
</p>
|
<p><var>x</var> have mode <var>m</var>, a fixed-point machine mode. <var>c</var>
|
be a fixed-point mode or be a constant with mode <code>VOIDmode</code>; which
|
mode is determined by the mode called for in the machine description
|
entry for the left-shift instruction. For example, on the VAX, the mode
|
of <var>c</var> is <code>QImode</code> regardless of <var>m</var>.
|
</p>
|
<a name="index-lshiftrt"></a>
|
<a name="index-right-shift"></a>
|
<a name="index-ashiftrt"></a>
|
</dd>
|
<dt><code>(lshiftrt:<var>m</var> <var>x</var> <var>c</var>)</code></dt>
|
<dt><code>(ashiftrt:<var>m</var> <var>x</var> <var>c</var>)</code></dt>
|
<dd><p>Like <code>ashift</code> but for right shift. Unlike the case for left shift,
|
these two operations are distinct.
|
</p>
|
<a name="index-rotate-1"></a>
|
<a name="index-rotate"></a>
|
<a name="index-left-rotate"></a>
|
<a name="index-rotatert"></a>
|
<a name="index-right-rotate"></a>
|
</dd>
|
<dt><code>(rotate:<var>m</var> <var>x</var> <var>c</var>)</code></dt>
|
<dt><code>(rotatert:<var>m</var> <var>x</var> <var>c</var>)</code></dt>
|
<dd><p>Similar but represent left and right rotate. If <var>c</var> is a constant,
|
use <code>rotate</code>.
|
</p>
|
<a name="index-abs"></a>
|
<a name="index-ss_005fabs"></a>
|
<a name="index-absolute-value"></a>
|
</dd>
|
<dt><code>(abs:<var>m</var> <var>x</var>)</code></dt>
|
<dt><code>(ss_abs:<var>m</var> <var>x</var>)</code></dt>
|
<dd><p>Represents the absolute value of <var>x</var>, computed in mode <var>m</var>.
|
<code>ss_abs</code> ensures that an out-of-bounds result saturates to the
|
maximum signed value.
|
</p>
|
|
<a name="index-sqrt"></a>
|
<a name="index-square-root"></a>
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</dd>
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<dt><code>(sqrt:<var>m</var> <var>x</var>)</code></dt>
|
<dd><p>Represents the square root of <var>x</var>, computed in mode <var>m</var>.
|
Most often <var>m</var> will be a floating point mode.
|
</p>
|
<a name="index-ffs"></a>
|
</dd>
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<dt><code>(ffs:<var>m</var> <var>x</var>)</code></dt>
|
<dd><p>Represents one plus the index of the least significant 1-bit in
|
<var>x</var>, represented as an integer of mode <var>m</var>. (The value is
|
zero if <var>x</var> is zero.) The mode of <var>x</var> must be <var>m</var>
|
or <code>VOIDmode</code>.
|
</p>
|
<a name="index-clrsb"></a>
|
</dd>
|
<dt><code>(clrsb:<var>m</var> <var>x</var>)</code></dt>
|
<dd><p>Represents the number of redundant leading sign bits in <var>x</var>,
|
represented as an integer of mode <var>m</var>, starting at the most
|
significant bit position. This is one less than the number of leading
|
sign bits (either 0 or 1), with no special cases. The mode of <var>x</var>
|
must be <var>m</var> or <code>VOIDmode</code>.
|
</p>
|
<a name="index-clz"></a>
|
</dd>
|
<dt><code>(clz:<var>m</var> <var>x</var>)</code></dt>
|
<dd><p>Represents the number of leading 0-bits in <var>x</var>, represented as an
|
integer of mode <var>m</var>, starting at the most significant bit position.
|
If <var>x</var> is zero, the value is determined by
|
<code>CLZ_DEFINED_VALUE_AT_ZERO</code> (see <a href="Misc.html#Misc">Misc</a>). Note that this is one of
|
the few expressions that is not invariant under widening. The mode of
|
<var>x</var> must be <var>m</var> or <code>VOIDmode</code>.
|
</p>
|
<a name="index-ctz"></a>
|
</dd>
|
<dt><code>(ctz:<var>m</var> <var>x</var>)</code></dt>
|
<dd><p>Represents the number of trailing 0-bits in <var>x</var>, represented as an
|
integer of mode <var>m</var>, starting at the least significant bit position.
|
If <var>x</var> is zero, the value is determined by
|
<code>CTZ_DEFINED_VALUE_AT_ZERO</code> (see <a href="Misc.html#Misc">Misc</a>). Except for this case,
|
<code>ctz(x)</code> is equivalent to <code>ffs(<var>x</var>) - 1</code>. The mode of
|
<var>x</var> must be <var>m</var> or <code>VOIDmode</code>.
|
</p>
|
<a name="index-popcount"></a>
|
</dd>
|
<dt><code>(popcount:<var>m</var> <var>x</var>)</code></dt>
|
<dd><p>Represents the number of 1-bits in <var>x</var>, represented as an integer of
|
mode <var>m</var>. The mode of <var>x</var> must be <var>m</var> or <code>VOIDmode</code>.
|
</p>
|
<a name="index-parity"></a>
|
</dd>
|
<dt><code>(parity:<var>m</var> <var>x</var>)</code></dt>
|
<dd><p>Represents the number of 1-bits modulo 2 in <var>x</var>, represented as an
|
integer of mode <var>m</var>. The mode of <var>x</var> must be <var>m</var> or
|
<code>VOIDmode</code>.
|
</p>
|
<a name="index-bswap"></a>
|
</dd>
|
<dt><code>(bswap:<var>m</var> <var>x</var>)</code></dt>
|
<dd><p>Represents the value <var>x</var> with the order of bytes reversed, carried out
|
in mode <var>m</var>, which must be a fixed-point machine mode.
|
The mode of <var>x</var> must be <var>m</var> or <code>VOIDmode</code>.
|
</p></dd>
|
</dl>
|
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<hr>
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<div class="header">
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<p>
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