Insn Canonicalizations - GNU Compiler Collection (GCC) Internals

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14.14 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 A) B) C) is canonicalized as (minus A (mult B C)).
For the compare operator, a constant is always the second operand on machines where cc0 is used (see Jump Patterns). On other machines, there are rare cases where the compiler might want to construct a compare with a constant as the first operand. However, these cases are not common enough for it to be worthwhile to provide a pattern matching a constant as the first operand unless the machine actually has such an instruction.
An operand of neg, not, mult, plus, or minus is made the first operand under the same conditions as above.
(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:m x y) and (not:m (xor:m x y)).
The sum of three items, one of which is a constant, will only appear in the form
```
          (plus:m (plus:m x y) constant)
     
```
On machines that do not use cc0, (compare x (const_int 0)) will be converted to x.
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.

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