Java For-loop changes numeric result when changing type of loop variable

Question

I wrote a program to calculate the PI number with Leibniz formula:

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I wrote a for-loop with type of initialization is "int" , the loop works fine but when i changed the initialization type to "long" the result is changed. This only happens when the loop times over a billion. This makes the "int - loop" calculates PI more accurate than "long - loop". I don't know why this happens. Please help me to understand this issue. Thanks! and here is my code.

public static void main(String[] args) {     double result1 = 0;     double result2 = 0;     double sign = 1;      for (int i = 0; i <= 1607702095; i++) {         result1 += sign/(2 * i + 1);         sign *= -1;     }     sign = 1;      for (long j = 0; j <= 1607702095; j++) {         result2 += sign/(2 * j + 1);         sign *= -1;     }      System.out.println("result1  " + result1 * 4);     System.out.println("result2  " + result2 * 4);     System.out.println("pi       " + Math.PI); } 

And the result is:

result1  3.141592653576877 result2  3.1415926529660116 pi       3.141592653589793 

Answer 1

Actually, your first loop would have int overflow in the calculation of (2 * i + 1) when i is large enough, so I wouldn't rely on the output of it.

The second loop, on the other hand, produces a more correct output, since (2 * j + 1) doesn't overflow, since it performs long multiplication.

This makes the "int - loop" calculates PI more accurate than "long - loop"

That's probably just a coincidence, since the calculations in the int loop overflow.

Answer 2

Because you are getting overflow at the line

result1 += sign/(2 * i + 1); 

Where the value of 2*i cross the max integer value

int range is -2,147,483,648 to 2,147,483,647 but when you do 2*i for greater value it crosses that range.

Better to be stick with long and that gives you correct output.