[expr] bit-wise "or" operator

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<<pipe>>$b`, as defined above. |
| `$a>=0, $b<0` | `$a<<pipe>>$b == ~(~$a & ~$b)`        De Morgan's Law<<br>>`      == ~(~$a & (-1-$b))`    Extended definition of [~]<<br>>`      == -1-(~$a & (-1-$b))`  Extended definition of [~]<<br>>The expression (-1-$b) is nonnegative, and so the expression (~$a & (-1-$b)) can be evaluated by bitwise operations. |
| `$a<0, $b>=0` | Commute to (`$b <<pipe>> $a`) and solve as above. |
| `$a<0, $b<0` | `$a<<pipe>>$b == ~(~$a & ~$b)`           De Morgan's Law |
|            | `      == -1-((-1-$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. |

----
!!!!!!
%|[Category Syntax]|%
!!!!!!