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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. `(ltu (plus`

`a``b``)`

`b``)`

is converted to`(ltu (plus`

`a``b``)`

`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:`

`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`.