programer310 - 1 month ago 15

Java Question

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

[

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

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.