How to Define and Use Negative Infinity in C++

1. Use Negative Product of numeric_limits::infinity() in C++
2. Use the INFINITY Definition From the cmath Library

This article discusses the problem of representing negative infinity in C++ and lists some possible solutions.

C++ uses the IEEE-754 standard to represent the floating-point numbers. There are three floating-point data types: float, double, and long double.

All of these variable types allow the storage of numerical values that cannot be stored in the int data type.

Infinity is written as inf in C++ and results in dividing a positive numeric value by a null value or by calculating a numerical value greater than what can be stored in 64 bits.

The unsigned or positive floating infinity value is defined in various C++ libraries such as cmath and limits, but there is no standard for negative infinity in C++.

Since there is no standard way to represent negative infinity in C++, here are several reliable methods to represent and use negative infinity in C++.

Use Negative Product of numeric_limits::infinity() in C++

Use the limits library in C++.

#include <iostream>
#include <limits>

using namespace std;

int main() {
  float f = numeric_limits<float>::infinity();

  float negInf = f * -1;

  cout << "The value of f is = " << f << endl;
  cout << "The value of negInf is = " << negInf << endl;
  cout << "The value of f + negInf is = " << f + negInf << endl;

  return 0;
}

In the code snippet above, the infinity method from the limits library returns the value of positive infinity.

The syntax is as follows.

numeric_limits<T>::infinity()

In the definition above, the T in between the angled brackets stands for template class and, in actual implementation, is replaced by the data type with which you want to use the numeric_limits methods. In the code snippet above, the float data type is used, but double can also be used similarly.

However, the infinity() method is valid only for non-integral data types as integral data types like int and bool are inherently finite.

The output for the code above is as follows.

The value of f is = inf
The value of negInf is = -inf
The value of f + negInf is = nan

As seen in the example above, using the infinity() method, the value of positive infinity is assigned to the float type variable f. Then a very simple and intuitive approach, namely multiplying f by -1, is used, and the result is stored in the variable named negInf, which results in the value of negative infinity being stored in negInf.

As seen in the output above, this valid method assigns a negative infinity value to a variable. To further test this method, f and negInf are added together, resulting in nan being returned, which stands for Not-a-Number and indicates an incalculable value.

This result is consistent with the IEEE-754 rules for infinity values and hence computationally safe.

Use the INFINITY Definition From the cmath Library

The cmath library is another C++ library with many useful methods and functions to deal with common mathematical operations and transformations.

The library also includes its definition of the infinity value, which is named INFINITY and can be used in much the same way as numeric_limits<T>::infinity() and can directly be assigned to both float and double data types.

Using the same method as in the previous example, multiplying the value of unsigned or positive infinity by a negative value returns us to the negative infinity value.

#include <cmath>
#include <iostream>

using namespace std;

int main() {
  long double f = INFINITY;
  long double negInf = f * -1;

  cout << "The value of f is = " << f << endl;
  cout << "The value of negInf is = " << negInf << endl;

  cout << "The value of f + negInf is = " << f + negInf << endl;
  return 0;
}

The output for the code above is as follows.

The value of f is = inf
The value of negInf is = -inf
The value of f + negInf is = nan

As can be seen, both methods produce the same output, and both can be safely used to implement negative infinity in C++.