The C programming atan function is defined in the math.h header file and is used to calculate the arctangent of a given value x, in radians. The arctangent function, denoted atan(x), returns the angle (in radians) whose tangent is x.

The atan function takes a single argument of type double, which represents the value whose arctangent is to be calculated. The function returns a double value, which represents the calculated arctangent in radians.

Here's an example usage of the atan function to calculate the arctangent of a given input:

#include <stdio.h>
#include <math.h>

int main() {
    double x = 0.5;
    double arctangent = atan(x);
    
    printf("The arctangent of %f is %f radians\n", x, arctangent);
    
    return 0;
}

In this example, the atan function is used to calculate the arctangent of 0.5, which is stored in the x variable. The calculated arctangent in radians is then stored in the arctangent variable, and printed to the console using the printf function.

Note that the atan function returns a value between -π/2 and π/2 radians, inclusive. Also note that the input x can be any real number, and the result will be within the range of -π/2 to π/2 radians, inclusive.