Canonicalization of Instructions#

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.

In addition to algebraic simplifications, following canonicalizations are performed:

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

For these operators, if only one operand is a neg, not, mult, plus, or minus expression, it will be the first operand.
In combinations of neg, mult, plus, and minus, the neg operations (if any) will be moved inside the operations as far as possible. For instance, (neg (mult A B)) is canonicalized as (mult (neg A) B), but (plus (mult (neg B) C) A) is canonicalized as (minus A (mult B C)).
For the compare operator, a constant is always the second operand if the first argument is a condition code register.

For instructions that inherently set a condition code register, the compare operator is always written as the first RTL expression of the parallel instruction pattern. For example,

(define_insn ""
  [(set (reg:CCZ FLAGS_REG)
    (compare:CCZ
      (plus:SI
        (match_operand:SI 1 "register_operand" "%r")
        (match_operand:SI 2 "register_operand" "r"))
      (const_int 0)))
   (set (match_operand:SI 0 "register_operand" "=r")
    (plus:SI (match_dup 1) (match_dup 2)))]
  ""
  "addl %0, %1, %2")

An operand of neg, not, mult, plus, or minus is made the first operand under the same conditions as above.
(ltu (plus ab) b) is converted to (ltu (plus ab) a). Likewise with geu instead of ltu.
(minus x (const_int n)) is converted to (plus x (const_int -n)).
Within address computations (i.e., inside mem), a left shift is converted into the appropriate multiplication by a power of two.
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 not expression, it will be the first one.

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
```
(define_insn ""
  [(set (match_operand:m 0 ...)
        (and:m (not:m (match_operand:m 1 ...))
                     (match_operand:m 2 ...)))]
  "..."
  "...")
```
Similarly, a pattern for a ‘NAND’ instruction should be written
```
(define_insn ""
  [(set (match_operand:m 0 ...)
        (ior:m (not:m (match_operand:m 1 ...))
                     (not:m (match_operand:m 2 ...))))]
  "..."
  "...")
```
In both cases, it is not necessary to include patterns for the many logically equivalent RTL expressions.
The only possible RTL expressions involving both bitwise exclusive-or and bitwise negation are (xor:mxy) and (not:m (xor:mxy)).
The sum of three items, one of which is a constant, will only appear in the form
```
(plus:m (plus:m x y) constant)
```
Equality comparisons of a group of bits (usually a single bit) with zero will be written using zero_extract rather than the equivalent and or sign_extract operations.
(sign_extend:m1 (mult:m2 (sign_extend:m2x) (sign_extend:m2y))) is converted to (mult:m1 (sign_extend:m1x) (sign_extend:m1y)), and likewise for zero_extend.
(sign_extend:m1 (mult:m2 (ashiftrt:m2xs) (sign_extend:m2y))) is converted to (mult:m1 (sign_extend:m1 (ashiftrt:m2xs)) (sign_extend:m1y)), and likewise for patterns using zero_extend and lshiftrt. If the second operand of mult 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.

Further canonicalization rules are defined in the function commutative_operand_precedence in gcc/rtlanal.cc.