Floor division with negative number

Question

The expression 6 // 4 yields 1 , where floor division produces the whole number after dividing a number.

But with a negative number, why does -6 // 4 return -2 ?

Answer 1

The // operator explicitly floors the result. Quoting the Binary arithmetic operations documentation :

the result is that of mathematical division with the 'floor' function applied to the result.

Flooring is not the same thing as rounding to 0; flooring always moves to the lower integer value . See the math.floor() function :

Return the floor of x , the largest integer less than or equal to x .

For -6 // 4 , first the result of -6 / 4 is calculated, so -1.5 . Flooring then moves to the lower integer value, so -2 .

If you want to round towards zero instead, you'll have to do so explicitly; you could do this with the int() function on true division:

>>> int(-6 / 4)
-1

int() removes the decimal portion, so always rounds towards zero instead.

Answer 2

Floor division will also round down to the next lowest number, not the next lowest absolute value.

6 // 4 = 1.5 , which rounds down to 1, and up to 2.

-6 // 4 = -1.5 , which rounds down to -2, and up to -1.

Answer 3

// in Python is a "floor division" operator. That means that the result of such division is the floor of the result of regular division (performed with / operator).

The floor of the given number is the biggest integer smaller than the this number. For example

7 / 2 = 3.5 so 7 // 2 = floor of 3.5 = 3.

For negative numbers it is less intuitive: -7 / 2 = -3.5, so -7 // 2 = floor of -3.5 = -4 . Similarly -1 // 10 = floor of -0.1 = -1.

// is defined to do the same thing as math.floor() : return the largest integer value less than or equal to the floating-point result. Zero is not less than or equal to -0.1.

Answer 4

A useful way to understand why floor division // yields the results it does for negative values is see this as complimenting the modulo, or remainder, % operator.

5/3  is equivalent to 1 remainder 2 

ie

5//3 = 1
5%3 = 2

But

-5/3 = -2
-5%3 = 1

Or

-2 + 1/3rd which is -1.6667 (ish)

It can seem strange, but it ensures results such as -2,-2,-2,-1,-1,-1,0,0,0,1,1,1,2,2,2,3,3,3 etc. when generating sequences.