"1" in a binary integer

Here, we mainly use the technique of bit arithmetic to find out the number of 1 in the binary representation of an integer or the position of some special 1.

Number of 1

In order to find the number of 1 in binary representation, there is an algorithm with a time complexity of O (n) (the number of n 1). The main point is that if the integer x is not 0, the expression (refers to the C language expression) x& (x-1) The result of the operation is the binary representation of x the rightmost 1 of the value of the elimination, if X is 0, the value of the expression is 0. Thus, if X is not 0, we can repeatedly eliminate the rightmost 1 of x by the expression x = x& (x-1) until X is 0, eliminating the number of 1.

C Language code (input is 32-bit unsigned integer)

1 int Number_of_ones (uint32_t x) {2     int 0 ; 3      while (x) {4         1); 5         result++; 6     }7     return  result; 8 }

Right-most 1 position

The rightmost 1 position is calculated from the expression x ^ (x & (X-1)), e.g., x:0x12345678, x ^ (x & (X-1)): 0x00000008

1 uint32_t Right_most_one (uint32_t x) {2     return 1 )); 3 }

Left-most 1 position

The position of the leftmost 1 is relatively complex, the following is a more straightforward algorithm.

 1  uint32_t Left_most_one (uint32_t x) {   2  uint32_t test = x & (X-1  ); 3   (test) { 4  x = test;  5  test = x & (X-1  ); 6   7  return   X;  8 } 

A more interesting algorithm is found in the Java arraydeque allocateelements source code, which is used to calculate an integer power of 2 greater than one number. We can find the position of the leftmost 1 by shifting the bitwise right one to the power of 2.

Here is the source code PS: Think about the principle of the algorithm:)

1 uint32_t Left_most_one2 (uint32_t x) {2uint32_t tmp =x;3TMP |= (TMP >>1);4TMP |= (TMP >>2);5TMP |= (TMP >>4);6TMP |= (TMP >>8);7TMP |= (TMP >> -);8tmp++;9     returnTmp? (TMP >>1) : (0x80000000);Ten}

Reference

Http://grepcode.com/file/repository.grepcode.com/java/root/jdk/openjdk/6-b14/java/util/ArrayDeque.java

"1" in a binary integer