Yeah, Python is one of the few languages which actually defines sane behavior for integer division and modulus rather than leaving it up to the hardware. I wish more languages would follow its example!
?- x is -4 mod 2.
X = 0.
?- X is -8 mod 2.
X = 0.
?- X is -9 mod 2.
X = 1.
Using declarative integer arithmetic, we can even express very generally that a number X is a multiple of 2:
?- X #= 2*_.
This is true iff there is any integer (indicated by an anonymous variable _) that, multiplied by 2, yields X. It works for positive and negative integers.
For example:
?- -4 #= 2*_.
true.
?- -9 #= 2*_.
false.
A very nice reference on the general topic of bitwise operations is Donald Knuth's Bitwise Tricks and Techniques in Volume 4 of The Art of Computer Programming.
ISO C doesn't leave it up to the hardware. Integer division is required to truncate toward zero; the remainder harmonizes with that. (If someone designs a new HLL which leaves some arithmetic to the hardware that C doesn't, that is indeed silly.)
The sane language here Common Lisp: it does it in all the ways rather than picking one approach with some hand-waving justification about why it's the good choice.
It has truncate, round, ceiling and floor functions that all return a quotient and remainder.
There are also mod and rem functions that calculate just the remainder from a floor and truncate, respectively.
Guido has written a blog post explaining "Why Python's Integer Division Floors" [1].
Python also uses floor division, and the corresponding "sign-of-modulo matches sign-of-divisor", for floating-point numbers. The blog post claims that this can be problematic in certain cases (compared to C's "sign-of-modulo matches sign-of-dividend"), but does not give any concrete examples.
