How do math.h functions in C accept arguments of multiple types when overloading functions are not supported?

Question

For example, pow() takes double, float or long double arguments in C99. When overloading functions are not supported, how can this be implemented in a simple way?

Answer 1

By using a different name for each function, eg

float powf(float base, float exponent);
double pow(double base, double exponent);
long double powl(long double base, long double exponent);

In addition to this, type-generic math (<tgmath.h>, §7.25 in C11 and §7.22 in C99) defines some macros which do the dirty work without the need of function overloading. You can check this link from this answer to see the internals, but basically it reduces to checks like

sizeof (X) == sizeof (__real__ (X))

or

(__typeof__ (X))1.1 == 1

The example taken from the standard:

EXAMPLE With the declarations

#include <tgmath.h>
int n;
float f;
double d;
long double ld;
float complex fc;
double complex dc;
long double complex ldc;

exp(n) invokes exp(n) (function)
acosh(f) invokes acoshf(f)
sin(f) invokes sin(d) (function)
atan(ld) invokes atanl(ld)
// and so on

Answer 2

With the below, the various types are "actual arguments"

// declaration
double pow(double a,  double b);

/// usage
pow(2.0, 3.0);
pow(2.0f, 3.0f);
pow(2.0L, 3.0L);
pow(2, 3);

In each case, the language itself converts these actual arguments to the formal parameters of the function. In this case, to double.

So one one function pow(), no overloading.

Other similar yet different functions exist that take other parameters

float powf(float a,  float b);