Good point. Interestingly enough, Python seems to handle this appropriately:

    >>> -4%2
    0
    >>> -8%2
    0
    >>> -9%2
    1

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!

Prolog is also like this:

    ?- 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.

[1] http://python-history.blogspot.com.au/2010/08/why-pythons-in...