/*
* pvector_get_array_spec -- (internal) translates a global vector index
* into a more concrete position in the array.
*/
static struct array_spec
pvector_get_array_spec(uint64_t idx)
{
struct array_spec s;
/*
* Search for the correct array by looking at the highest bit of the
* element position (offset by the size of initial array), which
* represents its capacity and position in the array of arrays.
*
* Because the vector has large initial embedded array the position bit
* that was calculated must take that into consideration and subtract
* the bit position from which the algorithm starts.
*/
uint64_t pos = idx + PVECTOR_INIT_SIZE;
unsigned hbit = find_highest_bit(pos);
s.idx = (size_t)(hbit - PVECTOR_INIT_SHIFT);
/*
* To find the actual position of the element in the array we simply
* mask the bits of the position that correspond to the size of
* the array. In other words this is: pos - 2^[array index].
*/
s.pos = pos ^ (1ULL << hbit);
return s;
}
int main(int argc, char** argv)
{
if (argc < 2) {
printf("Usage: %s <a-positive-number-N>\n", argv[0]);
printf("Imagine the numbers [0..N-1] written out in sequence one below another forming a matrix.\n");
printf("Each number is written in its binary representation.\n");
printf("Thus, if N is 5, the numbers are written as:-\n");
printf("000\n001\n010\n011\n100\n");
printf("This routine prints the number of 1's in each of the three columns, \n"
"with column number 0 representing the least significant bit.\n");
printf("So, the answer will be for N=5, (1,2,2) indicating that at column number 2, 1 and 0, there\n"
"are 1, 2 and 2 one's respectively\n");
return 1;
}
unsigned int n = atoi(argv[1]);
unsigned int highest_bit = find_highest_bit(n-1);
printf ("Highest bit for N=%u is %u\n", n, highest_bit);
unsigned i = highest_bit;
while (1) {
unsigned Ni = n / two_raised_to(i+1);
unsigned Ri = n % two_raised_to(i+1);
unsigned nr_ones = (Ni * two_raised_to(i)) + (Ri > two_raised_to(i) ? (Ri - two_raised_to(i)) : 0);
printf("Column %u: %u\n", i, nr_ones);
if (i==0) break;
i --;
}
return 0;
}
