Integer division in Python

Question

I'm confused about the following integer math in python:

-7/3 = -3 since (-3)*3 = -9 < -7. I understand.

7/-3 = -3 I don't get how this is defined. (-3)*(-3) = 9 > 7. In my opinion, it should be -2, because (-3)*(-2) = 6 < 7.

How does this work?

Python generally follows the Principle of Least Astonishment. It just always rounds down for integer division. — Chriszuma
– Chriszuma, Commented Oct 26, 2011 at 14:53
Here is the rationale, straight from the bdfl himself: python-history.blogspot.com/2010/08/… — Gaslight Deceive Subvert
– Gaslight Deceive Subvert, Commented Oct 26, 2011 at 14:56
For people coming here for integer division help: In Python 3, integer division is done using //, e.g. -7 // 3 = -3 but -7 / 3 = -2.33... — poke
– poke, Commented Oct 26, 2011 at 14:57
Btw. mathematically there is no real difference between -7/3 and 7/-3, so having two different results would be a bit more complicated. — poke
– poke, Commented Oct 26, 2011 at 15:00

NPE · Accepted Answer · 2011-10-26 14:52:36Z

14

From the documentation:

For (plain or long) integer division, the result is an integer. The result is always rounded towards minus infinity: 1/2 is 0, (-1)/2 is -1, 1/(-2) is -1, and (-1)/(-2) is 0.

The rounding towards -inf explains the behaviour that you're seeing.

answered Oct 26, 2011 at 14:52

NPE

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robert · Accepted Answer · 2011-10-26 14:53:42Z

4

This is how it works:

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

answered Oct 26, 2011 at 14:53

robert

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amicitas · Accepted Answer · 2011-10-26 15:01:09Z

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Expanding on the answers from aix and robert.

The best way to think of this is in terms of rounding down (towards minus infinity) the floating point result:

-7/3 = floor(-2.33) = -3

7/-3 = floor(-2.33) = -3

answered Oct 26, 2011 at 15:01

amicitas

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BattleDrum · Accepted Answer · 2015-07-15 09:09:09Z

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/ is used for floating point division // is used for integer division(returns a whole number)

And python rounds the result down

answered Jul 15, 2015 at 9:09

BattleDrum

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Rhand · Accepted Answer · 2011-10-26 14:53:59Z

0

Python rounds down. 7/3 = 2 (2+1/3) -7/3 = -3 (-2+1/3)

answered Oct 26, 2011 at 14:53

Rhand

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