… and abs(float) and abs(long double). And <cmath> should declare abs(int), abs(long), and abs(long long).

As things currently stand, this program is illegal:

#include <cstdlib>

int main() {
  double d = -1.23;
  double dd = std::abs(d);
  return 0;
}

The call is ambiguous because of the various integer overloads, that's because <cstdlib> provides abs(int) but not abs(double).

This lead one commenter on Stackoverflow to state that abs is dangerous, and to recommend using fabs instead.

In general, it makes sense to declare overloaded functions that take user-defined types in the same header as the definition of the user-defined types; it isn't necessary to declare all of the overloads in the same place. But here we're not dealing with any user-defined types; we're dealing with builtin types, which are always defined; all of the overloads should be defined in the same place, to avoid mysterious problems like the one in the code above.

The standard library has six overloads for abs:

int abs(int);  // <cstdlib>
long abs(long); // <cstdlib>
long long abs(long long); // <cstdlib>

float abs(float); // <cmath>
double abs(double); // <cmath>
long double abs(long double); // <cmath>

These should all be declared in both headers.

I have no opinion on <stdlib.h> and <math.h>.