# 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 ` `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 ` `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 ` `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 ` `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 ` `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.
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