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| <a name="Arithmetic"></a> |
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| <hr> |
| <a name="RTL-Expressions-for-Arithmetic"></a> |
| <h3 class="section">13.9 RTL Expressions for Arithmetic</h3> |
| <a name="index-arithmetic_002c-in-RTL"></a> |
| <a name="index-math_002c-in-RTL"></a> |
| <a name="index-RTL-expressions-for-arithmetic"></a> |
| |
| <p>Unless otherwise specified, all the operands of arithmetic expressions |
| must be valid for mode <var>m</var>. An operand is valid for mode <var>m</var> |
| if it has mode <var>m</var>, or if it is a <code>const_int</code> or |
| <code>const_double</code> and <var>m</var> is a mode of class <code>MODE_INT</code>. |
| </p> |
| <p>For commutative binary operations, constants should be placed in the |
| second operand. |
| </p> |
| <dl compact="compact"> |
| <dd><a name="index-plus"></a> |
| <a name="index-ss_005fplus"></a> |
| <a name="index-us_005fplus"></a> |
| <a name="index-RTL-sum"></a> |
| <a name="index-RTL-addition"></a> |
| <a name="index-RTL-addition-with-signed-saturation"></a> |
| <a name="index-RTL-addition-with-unsigned-saturation"></a> |
| </dd> |
| <dt><code>(plus:<var>m</var> <var>x</var> <var>y</var>)</code></dt> |
| <dt><code>(ss_plus:<var>m</var> <var>x</var> <var>y</var>)</code></dt> |
| <dt><code>(us_plus:<var>m</var> <var>x</var> <var>y</var>)</code></dt> |
| <dd> |
| <p>These three expressions all represent the sum of the values |
| represented by <var>x</var> and <var>y</var> carried out in machine mode |
| <var>m</var>. They differ in their behavior on overflow of integer modes. |
| <code>plus</code> wraps round modulo the width of <var>m</var>; <code>ss_plus</code> |
| saturates at the maximum signed value representable in <var>m</var>; |
| <code>us_plus</code> saturates at the maximum unsigned value. |
| </p> |
| |
| <a name="index-lo_005fsum"></a> |
| </dd> |
| <dt><code>(lo_sum:<var>m</var> <var>x</var> <var>y</var>)</code></dt> |
| <dd> |
| <p>This expression represents the sum of <var>x</var> and the low-order bits |
| of <var>y</var>. It is used with <code>high</code> (see <a href="Constants.html#Constants">Constants</a>) to |
| represent the typical two-instruction sequence used in RISC machines |
| to reference a global memory location. |
| </p> |
| <p>The number of low order bits is machine-dependent but is |
| normally the number of bits in a <code>Pmode</code> item minus the number of |
| bits set by <code>high</code>. |
| </p> |
| <p><var>m</var> should be <code>Pmode</code>. |
| </p> |
| <a name="index-minus"></a> |
| <a name="index-ss_005fminus"></a> |
| <a name="index-us_005fminus"></a> |
| <a name="index-RTL-difference"></a> |
| <a name="index-RTL-subtraction"></a> |
| <a name="index-RTL-subtraction-with-signed-saturation"></a> |
| <a name="index-RTL-subtraction-with-unsigned-saturation"></a> |
| </dd> |
| <dt><code>(minus:<var>m</var> <var>x</var> <var>y</var>)</code></dt> |
| <dt><code>(ss_minus:<var>m</var> <var>x</var> <var>y</var>)</code></dt> |
| <dt><code>(us_minus:<var>m</var> <var>x</var> <var>y</var>)</code></dt> |
| <dd> |
| <p>These three expressions represent the result of subtracting <var>y</var> |
| from <var>x</var>, carried out in mode <var>M</var>. Behavior on overflow is |
| the same as for the three variants of <code>plus</code> (see above). |
| </p> |
| <a name="index-compare"></a> |
| <a name="index-RTL-comparison"></a> |
| </dd> |
| <dt><code>(compare:<var>m</var> <var>x</var> <var>y</var>)</code></dt> |
| <dd><p>Represents the result of subtracting <var>y</var> from <var>x</var> for purposes |
| of comparison. The result is computed without overflow, as if with |
| infinite precision. |
| </p> |
| <p>Of course, machines can’t really subtract with infinite precision. |
| However, they can pretend to do so when only the sign of the result will |
| be used, which is the case when the result is stored in the condition |
| code. And that is the <em>only</em> way this kind of expression may |
| validly be used: as a value to be stored in the condition codes, either |
| <code>(cc0)</code> or a register. See <a href="Comparisons.html#Comparisons">Comparisons</a>. |
| </p> |
| <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 |
| <code>MODE_CC</code>, often <code>CCmode</code>. See <a href="Condition-Code.html#Condition-Code">Condition Code</a>. If <var>m</var> |
| is <code>VOIDmode</code> or <code>CCmode</code>, the operation returns sufficient |
| information (in an unspecified format) so that any comparison operator |
| can be applied to the result of the <code>COMPARE</code> operation. For other |
| 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> |
| <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> |
| <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> |
| <a name="index-neg"></a> |
| <a name="index-ss_005fneg"></a> |
| <a name="index-us_005fneg"></a> |
| <a name="index-negation"></a> |
| <a name="index-negation-with-signed-saturation"></a> |
| <a name="index-negation-with-unsigned-saturation"></a> |
| </dd> |
| <dt><code>(neg:<var>m</var> <var>x</var>)</code></dt> |
| <dt><code>(ss_neg:<var>m</var> <var>x</var>)</code></dt> |
| <dt><code>(us_neg:<var>m</var> <var>x</var>)</code></dt> |
| <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 |
| differ in the behavior on overflow of integer modes. In the case of |
| <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> |
| and <code>us_neg</code> ensure that an out-of-bounds result saturates to the |
| maximum or minimum signed or unsigned value. |
| </p> |
| <a name="index-mult"></a> |
| <a name="index-ss_005fmult"></a> |
| <a name="index-us_005fmult"></a> |
| <a name="index-multiplication"></a> |
| <a name="index-product"></a> |
| <a name="index-multiplication-with-signed-saturation"></a> |
| <a name="index-multiplication-with-unsigned-saturation"></a> |
| </dd> |
| <dt><code>(mult:<var>m</var> <var>x</var> <var>y</var>)</code></dt> |
| <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 that do a combined multiply of <var>x</var> and <var>y</var> and then |
| adding to<var>z</var> 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> |
| </dd> |
| <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> |
| <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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