Here lists the current overloads of std::abs in C++. I'm wondering why not just define the following template and let go all the ugly C-style overloads?
template <typename T> inline
T abs(const T& v) { return v < 0 ? -v : v; }
See LWG issue 2192. Currently, std::abs(x-y) < 2 fails if x and y are unsigned. This catches a subtle programming error. With the proposed change, it compiles but does entirely the wrong thing. abs(3u-4u) would be much larger than 2, in fact it's UINT_MAX.