abs vs std::abs, what does the reference say?

The official references say… it’s a mess. Pre-C++11 and C11:

• Officially, including <cmath> introduced nothing in ::;
  all of the functions were in std::. Practically, only
  export was less respected, and different compilers did very
  different things. If you included <cmath>, you used std::
  everywhere, or what you got varied from compiler to compiler.

• C didn’t provide any overloads: abs took an int, and was
  declared in <stdlib.h>, fabs took double, and was
  declared in <math.h>.

• If you included <math.h> in C++, it’s not clear what you
  got, but since none of the implementers seemed to care about
  the standard anyway (see the first point above)…

Roughly speaking, either you included <cmath>, and prefixed
all of the uses with std::, or you included <math.h>, and
used fabs if you wanted support for floating point (and the
various suffixes for types other than int or double).

C++11 and C11 added a few new twists:

• <cmath> is now allowed (but not required) to introduce the
  symbols in :: as well. One more thing which can vary
  depending on the implementation. (The goal here was to make
  existing implementations conformant.)

• C has a new header, <tgmath.h>, which uses compiler magic to
  make the functions in <math.h> behave as if they were
  overloaded as in C++. (So it doesn’t apply to abs, but only
  to fabs.) This header had not been added to C++, for the
  obvious reason that C++ doesn’t need any compiler magic for
  this.

All in all, the situation has become slightly worse, and my
recommendations above still hold. Include either <math.h> and
<stdlib.h>, and use abs/fabs and their derivated (e.g.
labs, fabsf, etc.) exclusively, or include <cmath>, and
use std::abs exclusively. Anything else, and you’ll run into
portabiity problems.