java - `bitCount()`的 `bitLength()`和 `BigInteger`有什么区别

Question

bitCount()的描述和 bitLength()相当神秘:

public int bitCount()

Returns the number of bits in the two's complement representation of this BigInteger that differ from its sign bit. This method is useful when implementing bit-vector style sets atop BigIntegers.

Returns: number of bits in the two's complement representation of this BigInteger that differ from its sign bit.

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public int bitLength()

Returns the number of bits in the minimal two's-complement representation of this BigInteger, excluding a sign bit. For positive BigIntegers, this is equivalent to the number of bits in the ordinary binary representation. (Computes (ceil(log2(this < 0 ? -this : this+1))).)

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

这两种方法之间的真正区别是什么？我应该在什么时候使用哪一种？

我偶尔会使用 bitCount 来计算正整数中设置的位数，但我很少使用 bitLength 并且通常当我指的是 bitCount 时 因为描述之间的差异太细微，我无法立即理解。

Google Attractor:Java BigInteger bitCount 与 bitLength

Answer 1

快速演示:

public void test() {
    BigInteger b = BigInteger.valueOf(0x12345L);
    System.out.println("b = " + b.toString(2));
    System.out.println("bitCount(b) = " + b.bitCount());
    System.out.println("bitLength(b) = " + b.bitLength());
}

打印

b = 10010001101000101

bitCount(b) = 7

bitLength(b) = 17

因此，对于正整数:

bitCount() 返回数字中设置的位数。

bitLength() 返回最高设置位的位置 即 数字的二进制表示的长度(即log₂)。