The C programming frexp function is defined in the math.h header file and is used to decompose a given double value into a normalized fraction and an exponent. The function returns the normalized fraction and also stores the exponent in an integer pointed to by the exponent argument.

The frexp function takes two arguments: a double value x, which is the value to be decomposed, and a pointer to an int value exponent, which will be set to the calculated exponent. The function returns a double value, which represents the normalized fraction.

Here's an example usage of the frexp function to decompose a given input:

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

int main() {
    double x = 123.456;
    int exponent;
    double fraction = frexp(x, &exponent);
    
    printf("The value %f can be decomposed into %f * 2^%d\n", x, fraction, exponent);
    
    return 0;
}

In this example, the frexp function is used to decompose the value 123.456 into a normalized fraction and an exponent. The normalized fraction is stored in the fraction variable, and the calculated exponent is stored in the exponent variable by passing a pointer to it as the second argument to frexp. The decomposed values are then printed to the console using the printf function.

Note that the frexp function is commonly used in conjunction with the ldexp function to recombine the fraction and exponent into the original value. The ldexp function takes a normalized fraction and an exponent, and returns the corresponding double value.