Why the following bitwise operation will generate a Numeric Overflow?

问题

I have the following rather straight forward bit-wise operation

final int mask = ((1 << 31) - 1);

However, I'm really can't figure out why, Android Studio (IntelliJ) IDE will give me Numeric Overflow warning

---

I did a quick run in desktop

public static void main(String[] args) {
    final int mask = ((1 << 31) - 1);
    System.out.println(mask);               // 2147483647
    System.out.println(Integer.MAX_VALUE);  // 2147483647
}

It seems fine to me. However, I was puzzling, why IDE gives me such warning?

回答1:

It seems that it was an issue in IntelliJ 2018.1. Here is explanation,

IDEA-182699 Numeric overflow: add an option to ignore if left bitwise shift result makes number negative - Its question

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The compiler gets 1 as int. What about?

final int mask = (int)((1L << 31) - 1);

Mathematically,

  1000 0000 0000 0000 0000 0000 0000 0000    (1 << 31)
  1111 1111 1111 1111 1111 1111 1111 1111    (-1)
-----------------------------------------
1 0111 1111 1111 1111 1111 1111 1111 1111    +
^

  0111 1111 1111 1111 1111 1111 1111 1111    (truncate)

回答2:

You shifted into the sign bit: 1<<31 = 2³¹ and Integer.MAX_VALUE = 2³¹ - 1. Hence there is (sign) overflow, you actually got Integer.MIN_VALUE. Further subtracting 1 can be called an overflow (carry) too, and probably triggered the error.

来源：https://stackoverflow.com/questions/51651590/why-the-following-bitwise-operation-will-generate-a-numeric-overflow