为什么这会归还无限？ （JAVA）

Question

Im trying to find the result of 1/1 + 1/4 + 1/9 + 1/16 + 1/25 ...

These is the lines I wrote that give the result Infinity :

public class BaselProblem {
    public static void main(String[] args) {
        int testLimit = 100000;
        double sum = 0;
        for (int i = 1; i<testLimit; i++) 
        {
            sum = sum + 1.0/(i*i);
        }
        System.out.println(sum);
    }
}

Changing 1.0/(i*i) to 1/(1.0*i*i) gives the correct result 1.6449240667982423 . Why is it that only the 2nd form work but not the 1st?

Also, because (i*i) > 1 , then 1.0/(i*i) should be < 1 , so how can it leads to in Infinity ?

Answer 1

Because your testLimit as well as your i are defined as int . Since you put the expression i*i in parentheses, it will be calculated first, and will try to find the multiple of two integers - which will reach overflow pretty quickly and reset to zero.

Specifically, when i reaches 2¹⁶, i*i will be 2³². This means 1 followed by 32 zeros in binary, of which, only the 32 zeros are kept, which means zero. (Thanks @templatetypedef).

Therefore, you'll have a number divided by zero, which is infinity.

Change your loop declaration so that i is double . Or multiply by a double (1.0) on the left hand of i*i . This will cause the expression to be changed into double before multiplying by the second i .

Answer 2

Java integer have a maximum value of 2,147,483,647. You're eventually surpassing that maximum with the integer that results from i*i.

If you do 1.0*i*i, you're converting the result to a double which can hold a maximum value of 1.79769313486231570E+308.

Your maximum value for i*i will be 10,000,000 which a double can hold, but an integer can't.