Python: the result of (8%3) is 2 but (-8%3) is 1. shouldn't it be -2? and why?

Question

Here is the proof:

-8 == -2 * 3 - 2

that means -8%3 should be equal to -2. but python returns 1 and it's driving me crazy

Both ways work (with the matching convention for integer division), but it's more practical from a programming standpoint if the result of a % b is always in [0 .. b). — hobbs, Jan 21 '14 at 19:17
-8/3 is also -3, so your example starts with a faulty premise. Just because your equation is true doesn't mean that's how division is defined. — chepner, Jan 21 '14 at 19:19
My [answer](http://stackoverflow.com/a/15594441/1126841) to a related question may be illuminating. — chepner, Jan 21 '14 at 19:20
Seems like every programming language has their opinion : http://en.wikipedia.org/wiki/Modulo_operation — Zzyrk, Jan 21 '14 at 19:26

score 10 · Answer 1 · answered Jan 21 '14 at 19:17

10

In python, the sign matches the denominator.

>>> -8 % 3
1
>>> -8 % -3
-2

For an explanation of why it was implemented this way, read the blog post by Guido.

answered Jan 21 '14 at 19:17

wim

1

From the docs "The modulo operator always yields a result with the same sign as its second operand (or zero); the absolute value of the result is strictly smaller than the absolute value of the second operand". This agrees with that as well. – SethMMorton Jan 21 '14 at 19:18

mhlester · Answer 2 · 2014-01-21T20:02:25.703

5

integer math is funny:

>>> -8//3  # (-8/3 in python2 does the same thing)
-3
>>> 8//3   # (8/3 in python2 does the same thing)
2
>>>

Rounding is done down, not towards zero.

edited Jan 21 '14 at 20:02

answered Jan 21 '14 at 19:16

mhlester

"Rounding is done *towards zero*, not just down." - but the interpreter snippet shows the exact opposite. – user2357112 Jan 21 '14 at 19:19
Python division is floored, towards negative infinity, not truncated, towards 0. – Ryan Haining Jan 21 '14 at 19:19
Sorry guys, my example was correct, my wording was reversed – mhlester Jan 21 '14 at 19:23
Did you know you can use `//` on any Python since 2.2? The only thing that changed is the way `/` works on integers. – Mark Ransom Jan 21 '14 at 19:46
@MarkRansom I did not. Apparently you can even do it on explicit floats, and get a floored float back (`4.0 // 3.0 -> 1.0`) – mhlester Jan 21 '14 at 19:54
it's more necessary in Python3 where dividing 2 ints gives you a float. As a result, even in 2, if your intention is integer division, you should be using `//` – Ryan Haining Jan 21 '14 at 20:16

score 1 · Answer 3 · answered Jan 21 '14 at 19:21

1

 3%3 = 0
 2%3 = 2
 1%3 = 1
 0%3 = 0
-1%3 = 2
-2%3 = 1
-3%3 = 0

...

-7%3 = 2
-8%3 = 1

Be careful: (-8)%3 != -(8%3)

answered Jan 21 '14 at 19:21

WebF0x

score 1 · Answer 4 · answered Jan 21 '14 at 19:23

1

Let's look at (one common interpretation of) integer division:

Given a, b, d, r in N and b > 0 and 0 <= r < b, then:

a // b = d and a % b = r

iff

a = d * b + r.

Hence: From -8 = -3 * 3 + 1 and -8 // 3 = -3 follows -8 % 3 = 1

>>> -8 == -3 * 3 + 1
True
>>> -8 // 3 
-3
>>> -8 % 3
1
>>> (-8 // 3) * 3 + (-8 % 3) == -8
True

answered Jan 21 '14 at 19:23

Hyperboreus

thanks I rememberd in highschool they thought us: -2|1 – Java Guy Jan 21 '14 at 19:30

score 0 · Answer 5 · answered Jan 21 '14 at 19:21

0

-8 = -3*3 + 1

In math the rest is ALWAYS positive so that in a = m*k + r k is integer and r is integer but with 0 <= r < |m|

answered Jan 21 '14 at 19:21

Alvaro Fuentes

5 Answers5