How does floor division work in python?

Question

Can someone explain the logic behind this?

http://python-history.blogspot.com/2010/08/why-pythons-integer-division-floors.html might help you. — Akshat Harit, Jul 15 '15 at 20:18
similar to [Integer division & modulo operation with negative operands in Python](http://stackoverflow.com/questions/14348219/integer-division-modulo-operation-with-negative-operands-in-python) — vaultah, Jul 15 '15 at 20:18

Kevin · Answer 1 · 2015-07-15T20:31:09.910

4

This is always true, ignoring floating point issues:

b*(a // b) + a % b == a

This is also always true:

((b > 0) == (a % b > 0)) or (a % b == 0)

Finally,

abs(a % b) < abs(b)

To provide this behavior, integer division rounds towards negative infinity, rather than towards zero.

edited Jul 15 '15 at 20:31

answered Jul 15 '15 at 20:17

Kevin

Plus one although the undisclosed mention of floating point issues is a distraction. – Bathsheba Jul 16 '15 at 08:24
@Bathsheba: You can do integer division with floats, but you get floats back, which aren't precise. – Kevin Jul 16 '15 at 12:02

score 3 · Answer 2 · answered Jul 15 '15 at 20:17

3

Floor division works in Python the way it's mathematically defined.

x // y == math.floor(x/y)

In other words x // y is the largest integer less than or equal to x / y

answered Jul 15 '15 at 20:17

Adam Smith

Or: `fdiv = lambda a, b: (a - a % b) / b` – Malik Brahimi Jul 15 '15 at 20:22
@AdamSmith It certainly doesn't work that way. Compare `1 // 0.1` to `math.floor(1 / 0.1)`. – Selcuk Aug 20 '19 at 23:45
@Selcuk that appears to be just floating point inaccuracies. `1 / 0.1` is very nearly 10, so flooring it becomes 9. `math.floor(1 / 0.1)` lets the `__truediv__` operator handle the floating point weirdness which it correctly accounts for, then floors afterwards. – Adam Smith Aug 21 '19 at 06:15
@Selcuk note that `1 // Decimal('0.1') == Decimal('10')`. Similarly for a decimal whose binary floating-point is precise like `0.5`: `5 // 0.5 == 10` – Adam Smith Aug 21 '19 at 06:17

score 3 · Accepted Answer · answered Jul 15 '15 at 20:17

3

The way it should:

5 / 2 = 2.5        (2)
5 / 7 = 0.714285   (0)
5 / -6 = −0.8333   (-1 is the integer below -0.833333)
5 / -2 = −2.5      (-3)
5 / -3 = −1.6666   (-2)

It's a basic floor. It divides it, and then makes it the integer below.

answered Jul 15 '15 at 20:17

Tim

3 Answers3