Is there any processing logic related to NaN?

Yes. The writer detects NaNs and errors here:

Lines 471 to 474 in e36f225

    
           } else if (isnan([number doubleValue])) { 
        
           	self.error = @"NaN is not a valid number in JSON"; 
        
           	return NO; 
        
           }

For the parser there really is no special handling: there's no way to represent NaN in the JSON grammar, and this parser implements the grammar accurately. Loss of floating-point precision for big numbers is the only issue I am aware of.

	} else if (isnan([number doubleValue])) {
	self.error = @"NaN is not a valid number in JSON";
	return NO;
	}