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### 14.9 RTL Expressions for Arithmetic

Unless otherwise specified, all the operands of arithmetic expressions must be valid for mode m. An operand is valid for mode m if it has mode m, or if it is a `const_int` or `const_double` and m is a mode of class `MODE_INT`.

For commutative binary operations, constants should be placed in the second operand.

`(plus:m x y)`
`(ss_plus:m x y)`
`(us_plus:m x y)`

These three expressions all represent the sum of the values represented by x and y carried out in machine mode m. They differ in their behavior on overflow of integer modes. `plus` wraps round modulo the width of m; `ss_plus` saturates at the maximum signed value representable in m; `us_plus` saturates at the maximum unsigned value.

`(lo_sum:m x y)`

This expression represents the sum of x and the low-order bits of y. It is used with `high` (see Constants) to represent the typical two-instruction sequence used in RISC machines to reference large immediate values and/or link-time constants such as global memory addresses. In the latter case, m is `Pmode` and y is usually a constant expression involving `symbol_ref`.

The number of low order bits is machine-dependent but is normally the number of bits in mode m minus the number of bits set by `high`.

`(minus:m x y)`
`(ss_minus:m x y)`
`(us_minus:m x y)`

These three expressions represent the result of subtracting y from x, carried out in mode M. Behavior on overflow is the same as for the three variants of `plus` (see above).

`(compare:m x y)`

Represents the result of subtracting y from x for purposes of comparison. The result is computed without overflow, as if with infinite precision.

Of course, machines cannot 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 only way this kind of expression may validly be used: as a value to be stored in the condition codes, in a register. See Comparisons.

The mode m is not related to the modes of x and y, but instead is the mode of the condition code value. It is some mode in class `MODE_CC`, often `CCmode`. See Condition Code. If m is `CCmode`, the operation returns sufficient information (in an unspecified format) so that any comparison operator can be applied to the result of the `COMPARE` operation. For other modes in class `MODE_CC`, the operation only returns a subset of this information.

Normally, x and y must have the same mode. Otherwise, `compare` is valid only if the mode of x is in class `MODE_INT` and y is a `const_int` or `const_double` with mode `VOIDmode`. The mode of x determines what mode the comparison is to be done in; thus it must not be `VOIDmode`.

If one of the operands is a constant, it should be placed in the second operand and the comparison code adjusted as appropriate.

A `compare` specifying two `VOIDmode` 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.

`(neg:m x)`
`(ss_neg:m x)`
`(us_neg:m x)`

These two expressions represent the negation (subtraction from zero) of the value represented by x, carried out in mode m. They differ in the behavior on overflow of integer modes. In the case of `neg`, the negation of the operand may be a number not representable in mode m, in which case it is truncated to m. `ss_neg` and `us_neg` ensure that an out-of-bounds result saturates to the maximum or minimum signed or unsigned value.

`(mult:m x y)`
`(ss_mult:m x y)`
`(us_mult:m x y)`

Represents the signed product of the values represented by x and y carried out in machine mode m. `ss_mult` and `us_mult` ensure that an out-of-bounds result saturates to the maximum or minimum signed or unsigned value.

Some machines support a multiplication that generates a product wider than the operands. Write the pattern for this as

```(mult:m (sign_extend:m x) (sign_extend:m y))
```

where m is wider than the modes of x and y, which need not be the same.

For unsigned widening multiplication, use the same idiom, but with `zero_extend` instead of `sign_extend`.

`(fma:m x y z)`

Represents the `fma`, `fmaf`, and `fmal` builtin functions, which compute ‘x * y + z’ without doing an intermediate rounding step.

`(div:m x y)`
`(ss_div:m x y)`

Represents the quotient in signed division of x by y, carried out in machine mode m. If m is a floating point mode, it represents the exact quotient; otherwise, the integerized quotient. `ss_div` ensures that an out-of-bounds result saturates to the maximum or minimum signed value.

Some machines have division instructions in which the operands and quotient widths are not all the same; you should represent such instructions using `truncate` and `sign_extend` as in,

```(truncate:m1 (div:m2 x (sign_extend:m2 y)))
```
`(udiv:m x y)`
`(us_div:m x y)`

Like `div` but represents unsigned division. `us_div` ensures that an out-of-bounds result saturates to the maximum or minimum unsigned value.

`(mod:m x y)`
`(umod:m x y)`

Like `div` and `udiv` but represent the remainder instead of the quotient.

`(smin:m x y)`
`(smax:m x y)`

Represents the smaller (for `smin`) or larger (for `smax`) of x and y, interpreted as signed values in mode m. When used with floating point, if both operands are zeros, or if either operand is `NaN`, then it is unspecified which of the two operands is returned as the result.

`(umin:m x y)`
`(umax:m x y)`

Like `smin` and `smax`, but the values are interpreted as unsigned integers.

`(not:m x)`

Represents the bitwise complement of the value represented by x, carried out in mode m, which must be a fixed-point machine mode.

`(and:m x y)`

Represents the bitwise logical-and of the values represented by x and y, carried out in machine mode m, which must be a fixed-point machine mode.

`(ior:m x y)`

Represents the bitwise inclusive-or of the values represented by x and y, carried out in machine mode m, which must be a fixed-point mode.

`(xor:m x y)`

Represents the bitwise exclusive-or of the values represented by x and y, carried out in machine mode m, which must be a fixed-point mode.

`(ashift:m x c)`
`(ss_ashift:m x c)`
`(us_ashift:m x c)`

These three expressions represent the result of arithmetically shifting x left by c places. They differ in their behavior on overflow of integer modes. An `ashift` operation is a plain shift with no special behavior in case of a change in the sign bit; `ss_ashift` and `us_ashift` saturates to the minimum or maximum representable value if any of the bits shifted out differs from the final sign bit.

x have mode m, a fixed-point machine mode. c be a fixed-point mode or be a constant with mode `VOIDmode`; 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 c is `QImode` regardless of m.

`(lshiftrt:m x c)`
`(ashiftrt:m x c)`

Like `ashift` but for right shift. Unlike the case for left shift, these two operations are distinct.

`(rotate:m x c)`
`(rotatert:m x c)`

Similar but represent left and right rotate. If c is a constant, use `rotate`.

`(abs:m x)`
`(ss_abs:m x)`

Represents the absolute value of x, computed in mode m. `ss_abs` ensures that an out-of-bounds result saturates to the maximum signed value.

`(sqrt:m x)`

Represents the square root of x, computed in mode m. Most often m will be a floating point mode.

`(ffs:m x)`

Represents one plus the index of the least significant 1-bit in x, represented as an integer of mode m. (The value is zero if x is zero.) The mode of x must be m or `VOIDmode`.

`(clrsb:m x)`

Represents the number of redundant leading sign bits in x, represented as an integer of mode m, 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 x must be m or `VOIDmode`.

`(clz:m x)`

Represents the number of leading 0-bits in x, represented as an integer of mode m, starting at the most significant bit position. If x is zero, the value is determined by `CLZ_DEFINED_VALUE_AT_ZERO` (see Misc). Note that this is one of the few expressions that is not invariant under widening. The mode of x must be m or `VOIDmode`.

`(ctz:m x)`

Represents the number of trailing 0-bits in x, represented as an integer of mode m, starting at the least significant bit position. If x is zero, the value is determined by `CTZ_DEFINED_VALUE_AT_ZERO` (see Misc). Except for this case, `ctz(x)` is equivalent to `ffs(x) - 1`. The mode of x must be m or `VOIDmode`.

`(popcount:m x)`

Represents the number of 1-bits in x, represented as an integer of mode m. The mode of x must be m or `VOIDmode`.

`(parity:m x)`

Represents the number of 1-bits modulo 2 in x, represented as an integer of mode m. The mode of x must be m or `VOIDmode`.

`(bswap:m x)`

Represents the value x with the order of bytes reversed, carried out in mode m, which must be a fixed-point machine mode. The mode of x must be m or `VOIDmode`.

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