On Tuesday 12 April 2005 20:45, Darren Duncan wrote: > At 8:27 PM -0400 4/12/05, John Macdonald wrote: > >The mathematical definition of xor for two arguments is "true if > >exactly one argument is true, false otherwise". > > Yes. > > >When that gets > >generalized to multiple arguments it means "true if an odd number > >of the arguments are true, false otherwise". > > Is this the official mathematics position?
It's simply chaining a series of 2-arg xor's together. As it happens, the result of such chaining comes out as "odd number true" and has the nice properties of being commutative [a xor b === b xor a] and associative [((a xor b) xor c) === (a xor (b xor c))]. > If not, I would generalize it like this: true If >= 1 arg is true > and >= 1 arg is false, otherwise false. > > Is that better or worse? The "mathematical" definition can generalize down to one or zero elements as well as up to n. > > So, you cannot short > >circuit the evaluation because any value, if it happens to be true, > >changes the result of the expression. > > If my assertion is used, then all you can short circuit once you find > a true value and a false value. Well, it's a function that can be short circuited, but it's not xor and would have different uses.
