Fesetround() and Fegetround() in C++ and their application

Introduction:

Floating-point numbers are used to represent real numbers that can have fractional values. However, there are limitations to the accuracy of floating-point numbers, which can result in errors when performing arithmetic operations. To mitigate this, C++ provides two functions called fesetround() and fegetround() that help in rounding floating-point numbers.

What is fesetround() in C++?

fesetround() is a C++ standard library function that sets the rounding direction for floating-point operations. It takes one argument, which can be one of the following predefined constants:

• FE_DOWNWARD: Round to the nearest number towards negative infinity.
• FE_TOWARDZERO: Round to the nearest number toward zero.
• FE_TONEAREST: Round to the nearest number.
• FE_UPWARD: Round to the nearest number towards positive infinity.

The default rounding mode for floating-point operations in C++ is FE_TONEAREST. However, in some cases, it may be necessary to use a different rounding mode. For example, in financial applications, it may be necessary to round toward zero or toward negative infinity, depending on the specific requirements of the calculation.

To use fesetround(), you must first include the header file. The syntax for fesetround() is as follows:

#include <cfenv>
int fesetround(int round_mode);

Here, round_mode is the rounding mode you wish to set. It should be one of the predefined constants mentioned above.

The return value of fesetround() is zero if the rounding mode was set successfully and a non-zero value otherwise. If an invalid rounding mode is specified, fesetround() returns a non-zero value and leaves the rounding mode unchanged.

It is important to note that fesetround() affects all floating-point operations after it is called. If you need to change the rounding mode for a specific operation, you can use the std::fesetround() function, which takes a local environment as an argument.

Here is an example program that demonstrates how to use fesetround() in C++ to set the rounding mode for floating-point operations:

#include <iostream>
#include <cmath>


#include <cfenv>


int main() {
    double x = 1.5;
    double y = -1.5;


    // Set rounding mode to "round towards zero."
    std::fesetround(FE_TOWARDZERO);


    // Round x and y to the nearest integer
    double rounded_x = std::round(x);
    double rounded_y = std::round(y);


    // Print the results
    std::cout << "x rounded to the nearest integer: " << rounded_x << std::endl;
    std::cout << "y rounded to the nearest integer: " << rounded_y << std::endl;


    return 0;
}

Explanation:

• This C++ program demonstrates how to round a floating-point number to the nearest integer using the std::round function and how to set the rounding mode using the std::fesetround function from the header.
• The program starts by declaring two double variables, x, and y, and initializing them to 1.5 and -1.5, respectively.
• Next, the rounding mode is set to "round towards zero" using the std::fesetround function with the FE_TOWARDZERO argument.
• This means that the result of rounding a number that is exactly halfway between two integers will be rounded toward zero (i.e., towards the nearest integer with a smaller absolute value).
• Then, the program calls the std::round function to round x and y to the nearest integer. The std::round function takes a double argument and returns the nearest integer as a double value.
• Finally, the program prints the rounded values of x and y using std::cout.

Program output:

What is fegetround() in C++?

fegetround() is a C++ standard library function that returns the current rounding mode for floating-point operations. It takes no arguments and returns one of the following predefined constants:

• FE_DOWNWARD: Round to the nearest number towards negative infinity.
• FE_TOWARDZERO: Round to the nearest number toward zero.
• FE_TONEAREST: Round to the nearest number.
• FE_UPWARD: Round to the nearest number towards positive infinity.

The default rounding mode for floating-point operations in C++ is FE_TONEAREST. However, in some cases, it may be necessary to determine the current rounding mode. For example, if your application requires precise rounding, you may want to verify that the correct rounding mode is being used.

To use fegetround(), you must first include the <cfenv> header file. The syntax for fegetround() is as follows:

#include <cfenv>
int fegetround();

The return value of fegetround() is the current rounding mode, as one of the predefined constants mentioned above.

It is important to note that fegetround() returns the rounding mode for the current environment. If you need to determine the rounding mode for a specific operation, you can use the std::fegetround() function, which takes a local environment as an argument.

Here is an example program that demonstrates the use of fegetround() in C++ to retrieve the current rounding mode for floating-point operations:

#include <iostream>
#include <cfenv>


int main() {
    // Get the current rounding mode
    int current_rounding_mode = std::fegetround();


    // Print the current rounding mode
    if (current_rounding_mode == FE_DOWNWARD) {
        std::cout << "The current rounding mode is FE_DOWNWARD" << std::endl;
    } else if (current_rounding_mode == FE_TOWARDZERO) {
        std::cout << "The current rounding mode is FE_TOWARDZERO" << std::endl;
    } else if (current_rounding_mode == FE_TONEAREST) {
        std::cout << "The current rounding mode is FE_TONEAREST" << std::endl;
    } else if (current_rounding_mode == FE_UPWARD) {
        std::cout << "The current rounding mode is FE_UPWARD" << std::endl;
    } else {
        std::cout << "Unknown rounding mode" << std::endl;
    }


    return 0;
}

Explanation:

• The main function of the program starts by declaring an integer variable called "current_rounding_mode". The value of this variable will later be set to the current rounding mode.
• Next, the program uses the "fegetround" function from the "cfenv" library to get the current rounding mode. This function returns an integer value that represents the current rounding mode.
• The program then checks the value of the "current_rounding_mode" variable to determine which rounding mode is currently being used.
• If the value is FE_DOWNWARD, the program prints "The current rounding mode is FE_DOWNWARD" to the console.
• If the value is FE_TOWARDZERO, the program prints "The current rounding mode is FE_TOWARDZERO" to the console.
• If the value is FE_TONEAREST, the program prints "The current rounding mode is FE_TONEAREST" to the console.
• If the value is FE_UPWARD, the program prints "The current rounding mode is FE_UPWARD" to the console.
• If the value is none of these values, the program prints "Unknown rounding mode" to the console.

Program Output:

Application of fesetround() and fegetround():

The main application of fesetround() and fegetround() is to control the rounding behavior of floating-point operations in C++. This is particularly useful in cases where precise rounding is required, such as in financial applications. The following are some examples of their usage:

Financial Applications:

In financial applications, rounding errors can have a significant impact on calculations. For example, when calculating interest rates, even a small rounding error can lead to a significant difference in the final result. In such cases, it is necessary to use precise rounding methods. fesetround() and fegetround() can be used to ensure that the correct rounding method is used.

Graphics Applications:

In graphics applications, floating-point numbers are used to represent positions and orientations of objects. In such cases, rounding errors can result in visual artifacts, such as flickering or jagged edges. By using fesetround() and fegetround(), the rounding behavior can be controlled to reduce these artifacts.

Scientific Applications:

In scientific applications, floating-point numbers are used to represent physical quantities. In some cases, rounding errors can lead to incorrect results, which can have serious consequences. For example, in simulations of physical systems, rounding errors can cause the simulation to diverge from reality. By using fesetround() and fegetround(), the rounding behavior can be controlled to ensure that the simulation is as accurate as possible.

Conclusion:

In conclusion, fesetround() and fegetround() are C++ functions that are used to set and retrieve the rounding mode for floating-point arithmetic operations. They are part of the <cfenv> header and provide a way to ensure that arithmetic operations are performed consistently across different platforms and compilers.

The applications of fesetround() and fegetround() are numerous and include financial calculations, numerical simulations, optimization algorithms, and cryptography. In these applications, the choice of rounding mode can affect the accuracy, stability, and security of the calculations, making it important to use a consistent rounding mode throughout the computation.

Overall, fesetround() and fegetround() provide a flexible and efficient way to control the rounding mode in floating-point arithmetic, which is important in many applications where numerical accuracy and consistency are critical.