expr bit-wise "or" operator, dual of &
Arguments must be integers, result is an integer.
Bit n of the result is 0 if bit n of each argument is 0. Otherwise, bit n of the result is 1.
For negative arguments, observe that ~$n==(-1-n) (See the ~ operator for further discussion.) The following cases then exist:
| Case | Result |
|---|---|
| $a>=0,$b>=0 | $a|$b, as defined above. |
| $a>=0,$b<0 | $a|$b == ~(~$a & ~$b) De Morgan's Law $a|$b == ~(~$a & (-1-$b)) Extended definition of ~ $a|$b == -1-(~$a & (-1-$b)) Extended definition of ~ The expression (-1-$b) is nonnegative, and so the expression (~$a & (-1-$b)) can be evaluated by bitwise operations. |
| $a<0,$b>=0 | Commute to ($b | $a) and solve as above. |
| $a<0,$b<0 | $a|$b == ~(~$a & ~$b) De Morgan's Law $a|$b == -1-((-1-$a) & (-1-$b)) Extended definition of ~ Since (-1-$a) and (-1-$b) are both nonnegative, the & in the expression above can be evaluated wuth bitwise operations. |
For logical/short-cut "or" use the || operator.
AMG: Like &, | has lower precedence than the comparison operators. See & for discussion, examples, and references.