Integer division: is a//b == int(a/b) true for all integers a,b?

Question

I know that integer division will always return the same answer as truncation of a floating point result if the numbers are both positive. Is it true if one or both of them are negative?

I was just curious to know if there was an integer division expression that would return the same results in Python 2 and Python 3 (and yes, I know about from __future__ import division).

P.S. Let's ignore floating point overflow for the moment.

Answer 1

It is not true in Python 3, and you can test it for yourself:

>>> int(-1/3) == -1//3
False

Integer division and modulo of a and b giving q (quotient) and r (remainder) respectively will always return numbers that satisfy b*q + r == a and (a*b)>0 == q>0 (i.e. a*b and q have the same sign) and abs(r) < abs(q). The expression int(q) simply always rounds towards 0 if q is a floating point number.

It will always be true for Python 2 unless you do from __future__ import division, but that's because a/b == a//b if a and b are integers in Python 2.