NaN Boxing Scheme in JavaScript

JavaScript's NaN (Not a Number) has some peculiar behavior, particularly when it comes to comparisons. NaN !== NaN is a well-known quirk. This challenge asks you to implement a "boxing" scheme that allows you to reliably compare NaN values and also efficiently check if a value is NaN without relying on the standard Number.isNaN() function (which can be problematic due to type coercion). This is useful in scenarios where you need to ensure strict NaN equality checks, especially when dealing with data from external sources or complex calculations.

Problem Description

You are tasked with creating a JavaScript object, NaNBox, that encapsulates NaN values and provides methods for comparing and identifying them. The NaNBox should behave as follows:

1. Construction: The NaNBox constructor should accept a single argument, which can be any value. If the argument is NaN, the NaNBox should store a special internal flag indicating that it represents NaN. Otherwise, it should store the original value.

2. isNaN() Method: This method should return true if the NaNBox represents NaN, and false otherwise.

3. equals(other) Method: This method should compare the NaNBox with another NaNBox object. It should return true if both NaNBox objects represent NaN, and false otherwise. It should not perform type coercion. If other is not a NaNBox instance, it should return false.

4. valueOf() Method: This method should return the underlying value stored within the NaNBox. If the NaNBox represents NaN, it should return NaN. Otherwise, it should return the original value.

5. toString() Method: This method should return a string representation of the NaNBox. If the NaNBox represents NaN, it should return the string "NaN". Otherwise, it should return the string representation of the original value.

Examples

Example 1:

Input: new NaNBox(NaN), new NaNBox(NaN)
Output: true
Explanation: Both NaNBox instances represent NaN, so equals() returns true.

Example 2:

Input: new NaNBox(NaN), new NaNBox(5)
Output: false
Explanation: One NaNBox represents NaN, the other represents 5. equals() returns false.

Example 3:

Input: new NaNBox(5), new NaNBox(5)
Output: true
Explanation: Both NaNBox instances represent 5, so equals() returns true.

Example 4:

Input: new NaNBox(NaN).isNaN()
Output: true
Explanation: The NaNBox represents NaN, so isNaN() returns true.

Example 5:

Input: new NaNBox(5).isNaN()
Output: false
Explanation: The NaNBox represents 5, so isNaN() returns false.

Example 6:

Input: new NaNBox(NaN).valueOf()
Output: NaN
Explanation: The valueOf() method returns NaN when the NaNBox represents NaN.

Constraints

• The NaNBox constructor should accept any JavaScript value as input.
• The equals() method should only compare with other NaNBox instances.
• The isNaN() method should be efficient and avoid unnecessary computations.
• The valueOf() and toString() methods should behave as described above.
• The solution should be well-structured and readable.

Notes

• Consider using a private flag within the NaNBox to track whether the instance represents NaN.
• The equals() method should not rely on type coercion. Direct comparison is key.
• Think about how the valueOf() and toString() methods can be implemented to provide consistent behavior.
• This problem tests your understanding of JavaScript's NaN behavior and your ability to create custom objects with specific methods. Focus on correctness and clarity.