To begin with, let's have a simple scenario to highlight this problem. This scenario may materialize in the following simple class:

public class Function {

  private final int x;

  public Function(int x) {

    this.x = x;
  }

  public int xMinusY(int y) {

    return x - y;
  }

  public static int oneMinusY(int y) {

    return 1 - y;
  }
}

Notice that the preceding snippet of code doesn't assume any range restrictions over x and y. Now, let's impose the following ranges (this is very common with mathematical functions):

• x must be between 0 (inclusive) and 11 (exclusive), so x belongs to [0, 11].
• In the xMinusY() method, y must be between 0 (inclusive) and x (exclusive), so y belongs to [0, x].
• In the oneMinusY() method, y must be between 0 (inclusive) and 16 (exclusive), so y belongs to [0, 16).

These ranges can be imposed in code via the if statements, as follows:

public class Function {

  private static final int X_UPPER_BOUND = 11;
  private static final int Y_UPPER_BOUND = 16;
  private final int x;

  public Function(int x) {

    if (x < 0 || x >= X_UPPER_BOUND) {
      throw new IndexOutOfBoundsException("..."); 
    }

    this.x = x;
  }

  public int xMinusY(int y) {

    if (y < 0 || y >= x) {
      throw new IndexOutOfBoundsException("...");
    }

    return x - y;
  }

  public static int oneMinusY(int y) {

    if (y < 0 || y >= Y_UPPER_BOUND) {
      throw new IndexOutOfBoundsException("...");
    }

    return 1 - y;
  }
}

Consider replacing IndexOutOfBoundsException with a more meaningful exception (for example, extend IndexOutOfBoundsException and create a custom exception of type, RangeOutOfBoundsException).

Starting with JDK 9, the code can be rewritten to use the Objects.checkIndex() method. This method verifies whether the given index is in the range [0, length] and returns the given index in this range or throws IndexOutOfBoundsException:

public class Function {

  private static final int X_UPPER_BOUND = 11;
  private static final int Y_UPPER_BOUND = 16;
  private final int x;

  public Function(int x) {

    this.x = Objects.checkIndex(x, X_UPPER_BOUND);
  }

  public int xMinusY(int y) {

    Objects.checkIndex(y, x);

    return x - y;
  }

  public static int oneMinusY(int y) {

    Objects.checkIndex(y, Y_UPPER_BOUND);

    return 1 - y;
  }
}

For example, calling oneMinusY(), as shown in the next code snippet, will result in IndexOutOfBoundsException since y can take values between [0, 16):

int result = Function.oneMinusY(20);

Now, let's go further and check the subrange in a range from 0 to the given length.