(NaN) An IEEE floating point representation for the result of a numerical operation which cannot return a valid number value. A NaN can result from multiplying an infinity by a zero, or from subtracting one infinity from another. NaN is encoded as a special bit pattern which would otherwise represent a floating-point number. It is used to signal error returns where other mechanisms are not convenient, e.g. a hardware floating-point unit and to allow errors to propagate through a calculation. Similar bit patterns represent positive and negative overflow and underflow and the positive and negative infinities resulting from division by zero.