Precision of Floating Point Numbers in C++ (floor(), ceil(), trunc(), round() and setprecision())

The decimal equivalent of 1/3 is 0.33333333333333…. An infinite length number would require infinite memory to store, and we typically have 4 or 8 bytes. Therefore, Floating point numbers store only a certain number of significant digits, and the rest are lost. The precision of a floating-point number defines how many significant digits it can represent without information loss. When outputting floating-point numbers, cout has a default precision of 6 and it truncates anything after that. Below are a few libraries and methods which are used to provide precision to floating-point numbers in C++:

1. floor() Method

Floor rounds off the given value to the closest integer which is less than the given value. It is defined in the <cmath> header file.

CPP

// C++ program to demonstrate working of floor()
// in C/C++
#include <bits/stdc++.h>
using namespace std;

// Driver Code
int main()
{
    double x = 1.411, y = 1.500, z = 1.711;
    cout << floor(x) << endl;
    cout << floor(y) << endl;
    cout << floor(z) << endl;

    double a = -1.411, b = -1.500, c = -1.611;
    cout << floor(a) << endl;
    cout << floor(b) << endl;
    cout << floor(c) << endl;
    return 0;
}

Output

1
1
1
-2
-2
-2

Time Complexity: O(1)

Auxiliary Space: O(1)

2. ceil() Method

Ceil rounds off the given value to the closest integer which is more than the given value. It is defined in the <cmath> header file.

CPP

// C++ program to demonstrate working of ceil()
// in C/C++
#include <bits/stdc++.h>
using namespace std;

// Driver Code
int main()
{
    double x = 1.411, y = 1.500, z = 1.611;
    cout << ceil(x) << endl;
    cout << ceil(y) << endl;
    cout << ceil(z) << endl;

    double a = -1.411, b = -1.500, c = -1.611;
    cout << ceil(a) << endl;
    cout << ceil(b) << endl;
    cout << ceil(c) << endl;
    return 0;
}

Output

2
2
2
-1
-1
-1

Time Complexity: O(1)

Auxiliary Space: O(1)

3. trunc() Method

Trunc rounds remove digits after the decimal point. It is defined in the <cmath> header file.

CPP

// C++ program to demonstrate working of trunc()
// in C/C++
#include <bits/stdc++.h>
using namespace std;

// Driver Code
int main()
{
    double x = 1.411, y = 1.500, z = 1.611;
    cout << trunc(x) << endl;
    cout << trunc(y) << endl;
    cout << trunc(z) << endl;

    double a = -1.411, b = -1.500, c = -1.611;
    cout << trunc(a) << endl;
    cout << trunc(b) << endl;
    cout << trunc(c) << endl;
    return 0;
}

Output

1
1
1
-1
-1
-1

Time Complexity: O(1)

Auxiliary Space: O(1)

4. round()

Rounds gave numbers to the closest integer. It is defined in the header files: <cmath> and <ctgmath>.

CPP

// C++ program to demonstrate working of round()
// in C/C++
#include <bits/stdc++.h>
using namespace std;

// Driver Code
int main()
{
    double x = 1.411, y = 1.500, z = 1.611;

    cout << round(x) << endl;
    cout << round(y) << endl;
    cout << round(z) << endl;

    double a = -1.411, b = -1.500, c = -1.611;
    cout << round(a) << endl;
    cout << round(b) << endl;
    cout << round(c) << endl;
    return 0;
}

Output

1
2
2
-1
-2
-2

Time Complexity: O(1)

Auxiliary Space: O(1)

5. setprecision()

Setprecision when used along with ‘fixed’ provides precision to floating-point numbers correct to decimal numbers mentioned in the brackets of the setprecision. It is defined in header file <iomanip>.

CPP

// C++ program to demonstrate
// working of setprecision()
// in C/C++
#include <bits/stdc++.h>
using namespace std;

// Driver Code
int main()
{
    double pi = 3.14159, npi = -3.14159;
    cout << fixed << setprecision(0) << pi << " " << npi
         << endl;
    cout << fixed << setprecision(1) << pi << " " << npi
         << endl;
    cout << fixed << setprecision(2) << pi << " " << npi
         << endl;
    cout << fixed << setprecision(3) << pi << " " << npi
         << endl;
    cout << fixed << setprecision(4) << pi << " " << npi
         << endl;
    cout << fixed << setprecision(5) << pi << " " << npi
         << endl;
    cout << fixed << setprecision(6) << pi << " " << npi
         << endl;
      return 0;
}

Output

3 -3
3.1 -3.1
3.14 -3.14
3.142 -3.142
3.1416 -3.1416
3.14159 -3.14159
3.141590 -3.141590

Time Complexity: O(1)

Auxiliary Space: O(1)

Note: When the value mentioned in the setprecision() exceeds the number of floating point digits in the original number then 0 is appended to floating point digit to match the precision mentioned by the user.

There exist other methods too to provide precision to floating-point numbers. The above mentioned are a few of the most commonly used methods to provide precision to floating-point numbers during competitive coding.
If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.