java algorithm-fast power

The operation of exponentiation is generally a multiplication of b times, for example, 2^4 = 2 *2 *2 * 2. For decimals, we can accumulate and multiply in this way. For larger times, there is a simpler method.

For example:
5 ^ 11 = 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5

The binary number of 11 is 1011, which is 2 to the power of zero, 1, 2 to the power of 1, 2, and 2 to the power of 3, 8.

Exactly 5 ^ 11 = 5 ^ 1 * 5 ^ 2 * 5 ^ 8

It used to be multiplied by 11 times, but now it only needs to be multiplied by 4 times.
This is the process of fast power deduction.

Source code:

public class Qmi {
    
    

	public static int qmi(int a,int b) {
    
    
		int res = 1;
		while(b!=0) {
    
                循环右移直到数为0
			if((b&1)==1) {
    
           对次数进行位运算判断最后一位是否为1
				res = res*a;     累乘
			}
			a=a*a;               a ^ 1, a ^ 2, a ^ 4, a ^ 8 .....
			b=b>>1;              循环右移
		}
		return res;
	}