Multiple Relational Operators in a Single Statement

Dec 25, 2012 at 9:53am
Griffiduck (4)
While studying C, I came across a peculiar problem that also persists in Python. The problem is mainly about using several relational operators within an expression without any logical operators.

Such usage was bugged and the expressions kept returning arbitrary results.Although bugged, I still wonder how the runtime handles such situations.

An example expression is such as:
if(a < b < c)

Expression-result couplings are such as following. The results are the values displayed when the expression is put into printf() or cout:

You may assume all of the expressions to be in cout as: cout << (a < b < c);

1
2
3
4
5
6
7
8
 
           //Output
1 < 2 < 3  //1
2 < 2 < 3  //1
3 < 2 < 3  //1
-3 < 2 < 3 //1
4 < 3 < 2  //1
3 < 2 < -3 //0
1 < 2 < 0  //0


I'd appreciate help if anyone knows how such statements are handled.
Dec 25, 2012 at 10:17am
lesshardtofind (5)
You need to write your statements as follows

 
 
if(a < b && b < c)


This should get the results you expect.

My compiler displays

 
 
7:20: error: comparisons like ‘X<=Y<=Z’ do not have their mathematical meaning


Maybe turn up the warnings?
Dec 25, 2012 at 11:26am
vlad from moscow (6539)
Let consider expression

1 < 2 < 3;

used in a Python code.

It is calculated from left to right and the return type of a relational operator is bool.

So the expression can be rewritten as

( 1 < 2 ) < 3;

As 1 is less than 2 then the result of ( 1 < 2 ) is boolean value true. Then the next subexpression is calculated:

( true ) < 3;

Boolean value true is promoted to int and we get

( 1 ) < 3;

As 1 is less than 3 the result of the whole expression is true.

Let consider another expression

3 < 2 < -3;

Rewrite it

( 3 < 2 ) < -3;

Again after calculation of the first subexpression we get

( false ) < -3;

because 3 is not less than 2

false is promoted to int value 0 and we get

( 0 ) < - 3;

As 0 is greater than -3 then the result is false.

To correectly process these relational expressions you should write them as


1 < 2 && 2 < 3;

3 < 2 && 2 < -3;
Last edited on Dec 25, 2012 at 11:53am
Dec 25, 2012 at 12:28pm
Chervil (7320)
The answers are all very helpful.

I just wanted to add, that the confusion is probably because the programming language looks a bit like some mathematics as the same symbols are used. But it has a different meaning.
For example, the = sign. In mathematics, we could write
x = x/2 + 3
That's an equation, we can solve it and get the result, x = 6.

But in C OR Python, the = sign means assignment of a value,
x = x/2 +3 ;
after execution, the value of x will depend on its previous value, and will change every time it is executed

OK, so I got off topic here. But my point is, don't mix up the meaning of symbols in mathematics with their meaning when programming.



Dec 25, 2012 at 1:36pm
Griffiduck (4)
The answers indeed were helpful. I had just missed the point of operation orders. Thanks.
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