位运算，用于返回次高的2

Question

I want to create a function that returns the next multiple of 2^p.

Here's an attempt, but not sure if it works...:

#define P 20
#define ALIGN_FORWARD(x, alignment) ((((int)x) + ((alignment)-1)) & (~((alignment)-1)))

int round_up(int x) 
{
  return ALIGN_FORWARD(x, P);
}

Answer 1

This snippet first fills up all bits below the highest set bit. After v |= v >> 1 the first two bits can be copied and so on. Finally the value is incremented by one.

uint32_t v = ...;
v |= v >> 1;
v |= v >> 2;
v |= v >> 4;
v |= v >> 8;
v |= v >> 16;
v += 1;

The unsigned part of uint32_t is important, because otherwise the result would be always 0 , because the sign bit gets extended by the shift operation. If the value is a uint64_t , then you have to add a further shift, if it is a uint16_t , then you have to remove a shift.

For an input of 8 the result would be 16. You need to test if the input is a power of two if you don't like that. Knowing that the binary representation of a power of two is one character shorter when you decrement it (8=0b1000, 7=0b111), you can use this guard:

if ((v & (v - 1)) > 0) {
    …
}

(Reproduced from memory. Original from https://graphics.stanford.edu/~seander/bithacks.html#RoundUpPowerOf2 , which contains many more interesting tricks.)