If you know the size of type, you could do something like: uint i = 17; uint j = i << 1 | i >> 31; … which would perform a circular shift of a 32 bit value. As a generalization to circular shift left n bits, on a b bit variable: /*some unsigned numeric … Read more
An integer is represented as a sequence of bits in memory. For interaction with humans, the computer has to display it as decimal digits, but all the calculations are carried out as binary. 123 in decimal is stored as 1111011 in memory. The & operator is a bitwise “And”. The result is the bits that … Read more
A ^ 0 == A A ^ A == 0 A ^ B == B ^ A (A ^ B) ^ C == A ^ (B ^ C) (3) and (4) together mean that the order in which numbers are xored doesn’t matter. Which means that, for example, A^B^X^C^B^A^C is equal to A^A ^ B^B … Read more
I’m going to be more explicit here because I think bitwise masks are a great tool that should be in any devs belt. I’m going to try to expand on the answers above. First, an example of using an integer to maintain state flags (common usage): // These are my masks private static final int … Read more
Here is an example for your amusement unsigned int myAdd(unsigned int a, unsigned int b) { unsigned int carry = a & b; unsigned int result = a ^ b; while(carry != 0) { unsigned int shiftedcarry = carry << 1; carry = result & shiftedcarry; result ^= shiftedcarry; } return result; } The loop … Read more
First remember that machine words are of fixed size. Say 4, and that your input is: +—+—+—+—+ | a | b | c | d | +—+—+—+—+ Then pushing everything one position to the left gives: +—+—+—+—+ | b | c | d | X | +—+—+—+—+ Question what to put as X? with a … Read more
Two’s complement is a clever way of storing integers so that common math problems are very simple to implement. To understand, you have to think of the numbers in binary. It basically says, for zero, use all 0’s. for positive integers, start counting up, with a maximum of 2(number of bits – 1)-1. for negative … Read more
Setting a bit Use the bitwise OR operator (|) to set a bit. number |= 1UL << n; That will set the nth bit of number. n should be zero, if you want to set the 1st bit and so on upto n-1, if you want to set the nth bit. Use 1ULL if number … Read more
If you can limit yourself to gcc, there are a set of builtin functions which return the number of leading zero bits and can be used to do what you want with a little work: int __builtin_clz (unsigned int x) int __builtin_clzl (unsigned long) int __builtin_clzll (unsigned long long)
I believe the key to performance here is to focus on the larger problem rather than on micro-optimizing the extraction of bit positions out of a random integer. Judging by your sample code and previous SO question you are enumerating all words with K bits set in order, and extracting the bit indices out of … Read more