Python Integer Division vs Float to Int Conversion – Key Differences

integer-divisionpythonpython-3.x

I have recently noticed that int() rounds a float towards 0, while integer division rounds a float towards its floor.

for instance:

-7 // 2 == -4
int(-7/2) == -3

I have read the documentation which specifies:

class int(x, base=10)

Return an integer object constructed from a number or string x, or return 0 if no arguments are >given. If x is a number, return x.__int__(). For floating point numbers, this truncates towards zero.

and:

floor division

Mathematical division that rounds down to nearest integer. The floor division operator is //. For example, the expression 11 // 4 evaluates to 2 in contrast to the 2.75 returned by float true division. Note that (-11) // 4 is -3 because that is -2.75 rounded downward. See PEP 238.

But it seems illogical for me that 2 similar operations (float division to integer) should return different results.

Is there any motivation for the differences between the functions?

Best Answer

Consistency.

You'll need to follow some very basic and seemingly irrelevant explanations to understand it.

In school you have learned division with a remainder. And you have done calculations like this:

8 ÷ 4 = 2 R 0
7 ÷ 4 = 1 R 3
6 ÷ 4 = 1 R 2
5 ÷ 4 = 1 R 1
4 ÷ 4 = 1 R 0
3 ÷ 4 = 0 R 3
2 ÷ 4 = 0 R 2
1 ÷ 4 = 0 R 1
0 ÷ 4 = 0 R 0
        ^------ This is the result of x // 4
            ^-- This is the result of x % 4 (modulo)

Later, you have learned divisions for real numbers:

8 ÷ 4 = 2.0
7 ÷ 4 = 1.75
6 ÷ 4 = 1.5
5 ÷ 4 = 1.25
4 ÷ 4 = 1.0
3 ÷ 4 = 0.75
2 ÷ 4 = 0.5
1 ÷ 4 = 0.25
0 ÷ 4 = 0.0
        ^--- Note that the number in front of the . is int(x/4)

Until this point, you might believe that x // 4 and int(x/4) always give the same result. That's your current understanding of the situation.

However, have a look what happens in the integer division: the number behind R cycles from 3, 2, 1 to 0 and then restarts: 3, 2, 1, 0. The number in front of the R decreses every 4th step.

So, how will it go on?

 8 ÷ 4 =  2 R 0
 7 ÷ 4 =  1 R 3
 6 ÷ 4 =  1 R 2
 5 ÷ 4 =  1 R 1
 4 ÷ 4 =  1 R 0
 3 ÷ 4 =  0 R 3
 2 ÷ 4 =  0 R 2
 1 ÷ 4 =  0 R 1
 0 ÷ 4 =  0 R 0
-1 ÷ 4 = -1 R 3
         ^------ We have to decrease now, because we already have 0 four times
              ^-- We have to restart the cycle at 3

At the same time, the real number division gives us:

-1 ÷ 4 = -0.25
          ^----- There is still a 0 in front of the .

That's why -1 // 4 gives -1 but int(-1/4) gives 0.

Is there any motivation for the differences between the functions?

Well, they serve different purposes: // is part of an integer calculation with remainders and int() gives you the part in front of the . of a real number operation.

You decide what you want to calculate, then you decide which operator to use in Python to get the correct result.

Good question. Keep on learning.

Related Question