c++ - Why are some functions in <cmath> not in the std namespace?

Question

I am developing a project which works with multiple arithmetic types. So I made a header, where the minimal requirements for a user defined arithmetic type are defined:

user_defined_arithmetic.h :

typedef double ArithmeticF;   // The user chooses what type he 
                              // wants to use to represent a real number

namespace arithmetic          // and defines the functions related to that type
{

const ArithmeticF sin(const ArithmeticF& x);
const ArithmeticF cos(const ArithmeticF& x);
const ArithmeticF tan(const ArithmeticF& x);
...
}

What is troubling me is that when I use code like this:

#include "user_defined_arithmetic.h"

void some_function()
{
    using namespace arithmetic;
    ArithmeticF lala(3);
    sin(lala);
}

I get a compiler error:

error: call of overloaded 'sin(ArithmeticF&)' is ambiguous
candidates are:
double sin(double)
const ArithmeticF arithmetic::sin(const ArithmeticF&)

I have never used the <math.h> header, only the <cmath>. I have never used the using namespace std in a header file.

I am using gcc 4.6.*. I checked what is the header containing the ambiguous declaration and it turns out to be:

mathcalls.h :

Prototype declarations for math functions; helper file for <math.h>.
...

I know, that <cmath> includes <math.h>, but it should shield the declarations by the std namespace. I dig into the <cmath> header and find:

cmath.h :

...

#include <math.h>

...

// Get rid of those macros defined in <math.h> in lieu of real functions.
#undef abs
#undef div
#undef acos
...

namespace std _GLIBCXX_VISIBILITY(default)
{
...

So the namespace std begins after the #include <math.h>. Is there something wrong here, or did I misunderstand something?

Answer 1

Implementations of the C++ standard library are permitted to declare C library functions in the global namespace as well as in std. Some would call this a mistake, since (as you've found) the namespace pollution can cause conflicts with your own names. However, that's the way it is, so we must live with it. You'll just have to qualify your name as arithmetic::sin.

In the words of the standard (C++11 17.6.1.2/4):

In the C++ standard library, however, the declarations (except for names which are defined as macros in C) are within namespace scope (3.3.6) of the namespace std. It is unspecified whether these names are first declared within the global namespace scope and are then injected into namespace std by explicit using-declarations (7.3.3).