why bigInteger doesn't have bit length for -1?

aligator :

why does BigInteger.bitLength() print 0 for -1 in Java:

System.out.println(BigInteger.valueOf(-1).bitLength());

there is a comment in the source code for BigInteger that says:

bitLength not initialized yet

public int bitLength() {
        int n = bitLengthPlusOne - 1;
        if (n == -1) { // bitLength not initialized yet
            int[] m = mag;
            int len = m.length;
            if (len == 0) {
                n = 0; // offset by one to initialize
            }

Progman :

Check the documentation for the BigInteger.bitLength() method:

Returns the number of bits in the minimal two's-complement representation of this BigInteger, excluding a sign bit. [...]

You need zero "value" bits to represent the value 0. Basically, you "don't need to do anything" and you have the value 0. With the sign bit you can switch between 0 and -1 (as similar to the two's-complement).

When you have the value 1 you need one "value" bit, so BigInteger.bitLength() will return 1 for the BigInteger value 1. Check the following for loop and the output it generates:

for (int i=-16; i<=16; i++) {
    BigInteger x = BigInteger.valueOf(i);
    System.out.println(x+"| bitlength: "+x.bitLength());    
}

The output is:

-16| bitlength: 4
-15| bitlength: 4
-14| bitlength: 4
-13| bitlength: 4
-12| bitlength: 4
-11| bitlength: 4
-10| bitlength: 4
-9| bitlength: 4
-8| bitlength: 3
-7| bitlength: 3
-6| bitlength: 3
-5| bitlength: 3
-4| bitlength: 2
-3| bitlength: 2
-2| bitlength: 1
-1| bitlength: 0
0| bitlength: 0  /* 0b */
1| bitlength: 1  /* 0b1 */
2| bitlength: 2
3| bitlength: 2  /* 0b11 */
4| bitlength: 3
5| bitlength: 3
6| bitlength: 3
7| bitlength: 3  /* 0b111 */
8| bitlength: 4
9| bitlength: 4
10| bitlength: 4
11| bitlength: 4
12| bitlength: 4
13| bitlength: 4
14| bitlength: 4
15| bitlength: 4 /* 0b1111 */
16| bitlength: 5

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