C++ Math frexp

This function breaks the floating point number into the binary significand and an integral exponent.

Let the floating point number be x then,

where , 'e' is the exponent and 'significand' is the binary significand

Syntax

Suppose a floating point number be 'x' and pointer be 'exp':

float frexp(float x, int* exp);
double frexp(double x, int* exp);
long double frexp(long double x, int* exp);
double frexp(integral x, int* exp);

Parameter

x : The value which is to be decomposed into the binary significand.

exp : It is a pointer to an int, where the value of exponent is stored.

Return value

It returns the binary significand which is the absolute value lies between 0.5(included) and 1(excluded).

Example 1

Let's see a simple example when the value of x is greater than 1.

#include <iostream>
#include<math.h>
using namespace std;
int main()
{
    double x=2;
    int* e;
    cout<<"Value of x is : "<<x<<'\n';
    double significand = frexp(x,e);
    std::cout <<x<<"="<<significand<<" * "<<"2^"<<*e;
    return 0;
}

Output:

Value of x is : 2
2=0.5 * 2^2

In this example, frexp function calculates the binary significand of a floating point number when the value of x is greater than 1.

Example 2

Let's see a simple example when the value of x is zero

#include <iostream>
#include<math.h>
using namespace std;
int main()
{
    double x=0;
    int* e;
    cout<<"Value of x is : "<<x<<'\n';
    double significand = frexp(x,e);
    std::cout <<x<<"="<<significand<<" * "<<"2^"<<*e;
    return 0;
}

Output:

Value of x is : 0
0=0 * 2^0

In this example, frexp function calculates the binary significand of a floating point number when the value of x is zero.

Example 3

Let's see a simple example when the value of x lies between 0 and 1.

#include <iostream>
#include<math.h>
using namespace std;
int main()
{
    double x=0.4;
    int* e;
    cout<<"Value of x is : "<<x<<'\n';
    double significand = frexp(x,e);
    std::cout <<x<<"="<<significand<<" * "<<"2^"<<*e;
    return 0;
}

Output:

Value of x is : 0.4
0.4=0.8 * 2^-1

In this example, frexp function calculates the binary significand of a floating point number when the value of x lies between 0 and 1.

Example 4

Let's see a simple example when the value of x lies between -1 and 0.

#include <iostream>
#include<math.h>
using namespace std;
int main()
{
    double x= -0.1;
    int* e;
    cout<<"Value of x is : "<<x<<'\n';
    double significand = frexp(x,e);
    std::cout <<x<<"="<<significand<<" * "<<"2^"<<*e;
    return 0;
}

Output:

Value of x is : -0.1
-0.1=-0.8 * 2^-3

In this example, frexp function calculates the binary significand of a floating point number when the value of x lies between -1 and 0.

Example 5

Let's see the simple example when the value of x is less than -1.

#include <iostream>
#include<math.h>
using namespace std;
int main()
{
    double x= -5;
    int* e;
    cout<<"Value of x is : "<<x<<'\n';
    double significand = frexp(x,e);
    std::cout <<x<<"="<<significand<<" * "<<"2^"<<*e;
    return 0;
}

Output:

Value of x is : -5
-5=-0.625 * 2^3

In this example, frexp function calculates the binary significand of a floating point nmber when the value of x is less than -1.