c# NaN comparison differences between Equals() and ==

Question

Check this out :

    var a = Double.NaN;

    Console.WriteLine(a == a);
    Console.ReadKey();

Prints \"False\"

    var a          


        

Answer 1

Equals is made for things like hashtables. And thus it contract requires that a.Equals(a).

MSDN states:

The following statements must be true for all implementations of the Equals method. In the list, x, y, and z represent object references that are not null.

x.Equals(x) returns true, except in cases that involve floating-point types. See IEC 60559:1989, Binary Floating-point Arithmetic for Microprocessor Systems.

x.Equals(y) returns the same value as y.Equals(x).

x.Equals(y) returns true if both x and y are NaN.

If (x.Equals(y) && y.Equals(z)) returns true, then x.Equals(z) returns true.

Successive calls to x.Equals(y) return the same value as long as the objects referenced by x and y are not modified.

x.Equals(null) returns false.

See GetHashCode for additional required behaviors pertaining to the Equals method.

What I find strange is that it states "x.Equals(x) returns true, except in cases that involve floating-point types. See IEC 60559:1989, Binary Floating-point Arithmetic for Microprocessor Systems." but at the same time requires that NaN equals NaN. So why did they put that exception in? Because of different NaNs?

In a similar way when using an IComparer the floating-point standard must be violated too. Since IComparer requires a consistent total ordering.