essay7.txt

Java Essay Serials 1 - Java Basics - 7, what is the exact result of Math.round(11.5)? Math.round(-11.5)? and Math.round(-11.5001)?
The result will be 12, -11, -12.
Java supplies 3 similar methods: ceil(),floor() and round().
To better understand round(), we should have a look at the methods ceil() and floor().
the methods signatures are the following:
public static double floor(double a)
public static double ceil(double a)
public static long round(double a)

According to the JDK document, the method floor() returns the largest (closest to positive infinity) double value that is less than or equal to the argument and is equal to a mathematical integer. 
with this definition, to apply the floor() method to 11.5,-11.5 and -11.5001,the results will be :11.0,-12.0 and -12.0.
But there are special cases:if the argument is NaN or an infinity or positive zero or negative zero, then the result is the same as the argument.

And the method ceil() returns the smallest (closest to negative infinity) double value that is greater than or equal to theargument and is equal to a mathematical integer. So with this definition, to apply the ceil() method to 11.5,-11.5 and -11.5001,the results will be :12.0,-11.0 and -11.0.
Special cases: If the argument is NaN or an infinity orpositive zero or negative zero, then the result is the same asthe argument. 
If the argument value is less than zero but greater than -1.0, then the result is negative zero.

Note that the value of Math.ceil(x) is exactly the value of -Math.floor(-x).

Now let's have a look at method round(), it will return the closest int to the argument. But this is not very clear, some still confused with it.
for example, for the case Math.round(-11.5), why the closest number is -11 not -12 instead? 
the JDK document has a further explanation :with ties rounding to positive infinity.
with this explanation, we will choose -11 as the closest number.
the result is equal to the value of the expression:        
  (int)math.floor(a  +  0.5)  

Special cases for round(): 
If the argument is NaN, the result is 0. 
If the argument is negative infinity or any value less than or equal to the value of Long.MIN_VALUE, the result isequal to the value of Long.MIN_VALUE. 
If the argument is positive infinity or any value greater than or equal to the value of Long.MAX_VALUE, the result isequal to the value of Long.MAX_VALUE.