Python logical XOR

Question

How do you get the logical xor of two variables in Python?

For example, I have two variables that I expect to be strings. I want to test that only one of them contains a True value (is not None or the empty string):

str1 = raw_input("Enter string one:")str2 = raw_input("Enter string two:")if logical_xor(str1, str2):    print "ok"else:    print "bad"

The ^ operator seems to be bitwise, and not defined on all objects:

>>> 1 ^ 10>>> 2 ^ 13>>> "abc" ^ ""Traceback (most recent call last):  File "<stdin>", line 1, in <module>TypeError: unsupported operand type(s) for ^: 'str' and 'str'

How do you define "xor" for a couple of strings? What do you feel "abc" ^ "" should return that it doesn't? — Jan 11 '09 at 12:39
It should return True, rather than raise an exception, since only one of the strings is True as defined by normal Python's bool type. — Jan 11 '09 at 19:10
I'm amazed that Python doesn't have an infix operator called "xor", which would be the most intuitive, Pythonic implementation. Using "^" is consistent with other languages, but not as blatantly readable as most of Python is. — Nov 11 '12 at 3:50
@MehrdadAfshari The obvious answer to your question is that a xor a is defined as (a and not b) or (not a and b), and so a xor b, when a and b are character strings, or any other types, should yield whatever (a and not b) or (not a and b) yields. — May 14 '13 at 15:57
The issue is that documentation is poor. ^ is "bitwise exclusive or", which literally interpreted means bit by bit, not bool by bool. so x'FFFF00' ^ x'FFFF00' should be x'000000'. Or is this only meant to occur on a char by char basis ? cast as numbers ? We need to iterate the shorter string characters to match the length of the longer string. All this should be built in. — Mar 22 '15 at 2:29

Coady 16.9k31826 · Accepted Answer · 2009-01-11 16:30:46Z

up vote642down voteaccepted

If you're already normalizing the inputs to booleans, then != is xor.

bool(a) != bool(b)

answered Jan 11 '09 at 16:30

Coady

16.9k31826

40

Although this is clever and short, I'm not convinced it's clean. When someone reads this construct in the code, is it immediately obvious to them that this is an xor operation? I felt obliged to add a comment - a sign for me that I'm writing unclear code and try to apologise with a comment. – Erik Mar 19 '12 at 17:25

15

Perhaps "is it clear that it's an XOR?" is the wrong question. We were just trying to see whether the answer to two questions are the same, and thinking we'd use XOR to implement that. For example, if we want to ensure that we are not comparing apples to oranges, is "if xor( isApple(x), isApple(y) )" really clearer than "if isApple(x) != isApple(y)" ? Not to me! – AmigoNico May 21 '12 at 18:27

s/answer/answers/ – AmigoNico May 21 '12 at 18:36

55

There is problem with using "!=" as xor. You would probably expect bool(a) != bool(b) != bool(c) to be the same as bool(a) ^ bool(b) ^ bool(c). So do casts to bool, but I would recommend ^. To know what's going up in the first example look up "operator chaining". – elmo Jul 25 '12 at 11:50

7

@elmo: +1 for pointing out the difference, and +1 for teaching me what operator chaining is! I am in the camp that says that != is not as readable as ^. – mehaase Nov 11 '12 at 3:58

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Zach Hirsch 6,93051927 · Answer 2 · 2009-01-11 12:35:51Z

You can always use the definition of xor to compute it from other logical operations:

(a and not b) or (not a and b)

But this is a little too verbose for me, and isn't particularly clear at first glance. Another way to do it is:

bool(a) ^ bool(b)

The xor operator on two booleans is logical xor (unlike on ints, where it's bitwise). Which makes sense, since bool is just a subclass of int, but is implemented to only have the values 0 and 1. And logical xor is equivalent to bitwise xor when the domain is restricted to 0 and 1.

So the logical_xor function would be implemented like:

def logical_xor(str1, str2):    return bool(str1) ^ bool(str2)

Credit to Nick Coghlan on the Python-3000 mailing list.

i'd give another vote for referencing your sources if i could :) — Jan 11 '09 at 21:01
great post, but of all ways to name your parameters, why 'str1' and 'str2'? — Jul 4 '09 at 16:55
@Token why not. Do you mean because they aren't very Pythonic? — Jan 25 '10 at 6:42
@Zach Hirsch Could you use (not a and b) instead of (b and not a) for readability or would the definition be inconsistent with xor. — Feb 1 '10 at 15:18
You should put the nots first like this (not b and a) or (not a and b) so that it returns the string if there was one, which seems like the pythonic way for the function to operate. — May 7 '11 at 21:06

singingwolfboy 2,02321217 · Answer 3 · 2012-06-14 15:34:09Z

up vote75down vote

Exclusive-or is already built-in to Python, in the operator module:

from operator import xorxor(bool(a), bool(b))

answered Jun 14 '12 at 15:34

singingwolfboy

2,02321217

2

This is what I needed. When reverse engineering malware lots of times strings are mangled until an XOR operation. Using this chr(xor(ord("n"), 0x1A)) = 't' – ril3y Jul 11 '12 at 14:15

20

Be careful, this is also bitwise: xor(1, 2) returns 3. From the docstring: xor(a, b) -- Same as a ^ b. Remember that anything imported from operator is just a functional form of an existing builtin infix operator. – askewchan Sep 15 '13 at 16:59

2

This xor is bitwise and using it has the same effect of the ^ operator. – Diego Queiroz Jan 22 '14 at 13:23

@askewchan: The bool type overloads __xor__ to return booleans. It'll work just fine, but its overkill when bool(a) ^ bool(b) does exactly the same thing. – Martijn Pieters♦ Nov 3 '14 at 12:48

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score 17 · Answer 4 · 2009-02-06 10:49:06Z

As Zach explained, you can use:

xor = bool(a) ^ bool(b)

Personally, I favor a slightly different dialect:

xor = bool(a) + bool(b) == 1

This dialect is inspired from a logical diagramming language I learned in school where "OR" was denoted by a box containing ≥1 (greater than or equal to 1) and "XOR" was denoted by a box containing =1.

This has the advantage of correctly implementing exclusive or on multiple operands.

"1 = a ^ b ^ c..." means the number of true operands is odd. This operator is "parity".
"1 = a + b + c..." means exactly one operand is true. This is "exclusive or", meaning "one to the exclusion of the others".

So, True + True + False + True == 3, and 3 != 1, but True XOR True XOR False XOR True == True. Can you elaborate on "correctly implementing XOR on multiple operands"? — Jan 11 '09 at 22:59
@tzot Your example fails, because according to ddaa's solution, you apply the addition on only two variables at a time. So the right way to write it all out would have to be (((((True + True)==1)+False)==1)+True)==1. The answer given here totally generalizes to multiple operands. — Oct 23 '12 at 21:18
Also, there's a difference between a three-way XOR vs. order-of-operations-grouped set of two XORs. So 3-WAY-XOR(A,B,C) is not the same thing as XOR(XOR(A,B),C). And ddaa's example is the former, while yours assumes the latter. — Oct 23 '12 at 21:20
@EMS: thanks. Your objections clarified (to me) what ddaa meant. — Oct 24 '12 at 21:57

score 14 · Answer 5 · 2009-01-11 13:16:02Z

up vote14down vote

Python logical or: A or B: returns A if bool(A) is True, otherwise returns B
Python logical and: A and B: returns A if bool(A) is False, otherwise returns B

To keep most of that way of thinking, my logical xor definintion would be:

def logical_xor(a, b):    if bool(a) == bool(b):        return False    else:        return a or b

That way it can return a, b, or False:

>>> logical_xor('this', 'that')False>>> logical_xor('', '')False>>> logical_xor('this', '')'this'>>> logical_xor('', 'that')'that'

edited Jan 11 '09 at 13:16

answered Jan 11 '09 at 13:10

nosklo

99.9k28197216

3

This seems bad, or at least weird, to me. None of the other built-in logical operators return one of three possible values. – Zach Hirsch Jan 11 '09 at 19:12

1

@Zach Hirsch: That's why I said "to keep most of that way of thinking" - since there's no good result when both are true or false – nosklo Nov 25 '09 at 22:52

Logical operation must return logical value, so second "return a or b" looks strange, so second return must return True. – Denis Barmenkov Feb 10 '11 at 13:36

5

@Denis Barmenkov: Well, note that python logical operators and and or won't return logical value. 'foo' and 'bar' returns 'bar' ... – nosklo Feb 13 '11 at 2:11

4

At first sight, the 2 previous answers seem like the best, but on second thought, this one is actually the only truly correct one, i.e. it's the only one that provides an example of a xor implementation that is consistent with the built-in and and or. However, of course, in practical situations, bool(a) ^ bool(b) or even a ^ b (if a and b are known to be bool) are more concise of course. – Erik Allik Jan 13 '12 at 13:48

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Markus Jarderot 46.7k890103 · Answer 6 · 2009-01-11 15:29:44Z

How about this?

(not b and a) or (not a and b)

will give a if b is false
will give b if a is false
will give False otherwise

Or with the Python 2.5+ ternary expression:

(False if a else b) if b else a

S.Lott 246k49350623 · Answer 7 · 2009-01-11 13:39:48Z

up vote3down vote

Exclusive Or is defined as follows

def xor( a, b ):    return (a or b) and not (a and b)

answered Jan 11 '09 at 13:39

S.Lott

246k49350623

2

that would return True for xor('this', '') and to follow python's way, it should return 'this'. – nosklo Jan 11 '09 at 13:45

@nosklo: Take it up with the BDFL, please, not me. Since Python returns True, then that must be Python's way. – S.Lott Jan 11 '09 at 14:15

2

I mean for consistency with the other python logical operators - Python doesn't return True when I do ('this' or ''), it returns 'this'. But in your function xor('this', '') returns True. It should return 'this' as the "or" python builtin does. – nosklo Jan 11 '09 at 15:09

7

Python and and or do short-circuit. Any xor implementation can't short-circuit, so there is already a discrepancy; therefore, there is no reason that xor should operate like and+or do. – tzot Jan 11 '09 at 23:12

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score 3 · Answer 8 · 2010-04-20 14:18:51Z

As I don't see the simple variant of xor using variable arguments and only operation on Truth values True or False, I'll just throw it here for anyone to use. It's as noted by others, pretty (not to say very) straightforward.

def xor(*vars):    sum = bool(False)    for v in vars:        sum = sum ^ bool(v)    return sum

And usage is straightforward as well:

if xor(False, False, True, False):    print "Hello World!"

As this is the generalized n-ary logical XOR, it's truth value will be True whenever the number of True operands is odd (and not only when exactly one is True, this is just one case in which n-ary XOR is True).

Thus if you are in search of a n-ary predicate that is only True when exactly one of it's operands is, you might want to use:

def isOne(*vars):    sum = bool(False)    for v in vars:        if sum and v:            return False        else:            sum = sum or v    return sum

For improving this answer: (bool(False) is False) == True. You can just use False on those lines. — Apr 25 '15 at 6:01

score 2 · Answer 9 · 2009-07-04 13:58:03Z

Some of the implementations suggested here will cause repeated evaluation of the operands in some cases, which may lead to unintended side effects and therefore must be avoided.

That said, a xor implementation that returns either True or False is fairly simple; one that returns one of the operands, if possible, is much trickier, because no consensus exists as to which operand should be the chosen one, especially when there are more than two operands. For instance, should xor(None, -1, [], True) return None, [] or False? I bet each answer appears to some people as the most intuitive one.

For either the True- or the False-result, there are as many as five possible choices: return first operand (if it matches end result in value, else boolean), return first match (if at least one exists, else boolean), return last operand (if ... else ...), return last match (if ... else ...), or always return boolean. Altogether, that's 5 ** 2 = 25 flavors of xor.

def xor(*operands, falsechoice = -2, truechoice = -2):  """A single-evaluation, multi-operand, full-choice xor implementation  falsechoice, truechoice: 0 = always bool, +/-1 = first/last operand, +/-2 = first/last match"""  if not operands:    raise TypeError('at least one operand expected')  choices = [falsechoice, truechoice]  matches = {}  result = False  first = True  value = choice = None  # avoid using index or slice since operands may be an infinite iterator  for operand in operands:    # evaluate each operand once only so as to avoid unintended side effects    value = bool(operand)    # the actual xor operation    result ^= value    # choice for the current operand, which may or may not match end result    choice = choices[value]    # if choice is last match;    # or last operand and the current operand, in case it is last, matches result;    # or first operand and the current operand is indeed first;    # or first match and there hasn't been a match so far    if choice < -1 or (choice == -1 and value == result) or (choice == 1 and first) or (choice > 1 and value not in matches):      # store the current operand      matches[value] = operand    # next operand will no longer be first    first = False  # if choice for result is last operand, but they mismatch  if (choices[result] == -1) and (result != value):    return result  else:    # return the stored matching operand, if existing, else result as bool    return matches.get(result, result)testcases = [  (-1, None, True, {None: None}, [], 'a'),  (None, -1, {None: None}, 'a', []),  (None, -1, True, {None: None}, 'a', []),  (-1, None, {None: None}, [], 'a')]choices = {-2: 'last match', -1: 'last operand', 0: 'always bool', 1: 'first operand', 2: 'first match'}for c in testcases:  print(c)  for f in sorted(choices.keys()):    for t in sorted(choices.keys()):      x = xor(*c, falsechoice = f, truechoice = t)      print('f: %d (%s)\tt: %d (%s)\tx: %s' % (f, choices[f], t, choices[t], x))  print()

Denis Barmenkov 1,6701818 · Answer 10 · 2011-02-10 13:34:36Z

It's easy when you know what XOR does:

def logical_xor(a, b):    return (a and not b) or (not a and b)test_data = [  [False, False],  [False, True],  [True, False],  [True, True],]for a, b in test_data:    print '%r xor %s = %r' % (a, b, logical_xor(a, b))

score 2 · Answer 11

Sometimes I find myself working with 1 and 0 instead of boolean True and False values. In this case xor can be defined as

z = (x + y) % 2

which has the following truth table:

     x   |0|1|  -+-+-+  0|0|1|y -+-+-+  1|1|0|

Python logical XOR

14 Answers