Generating prefix bitmasks

Question

I am looking for a portable way to generate prefix bitmasks which have the first n bits set for 0 <= n <= 32 (or 64 or an arbitrary integer type bit width).

Examples:

prefix_bitmask(0)  = 0b00000000000000000000000000000000u
prefix_bitmask(4)  = 0b00000000000000000000000000001111u
prefix_bitmask(32) = 0b11111111111111111111111111111111u

There are two ways this can already work if we ignore the cases n == 0 or n == 32:

// "constructive": set only the required bits
uint32_t prefix_mask1(int i) { return (uint32_t(1) << i) - 1; }
// "destructive": shift unneeded bits out
uint32_t prefix_mask2(int i) { return ~uint32_t(0) >> (32 - i); } 

prefix_mask1 fails for 32 and prefix_mask2 fails for 0, both because shifts larger than the integer type are undefined behavior (because CPUs are allowed to only use the lowest 5 bits of the shift size).

Is there a "canonical" way to solve this without branching?

Answer 1

((uint32_t) 1 << i/2 << i-i/2) - 1.

The above works where uint32_t may be replaced with any unsigned type, and no other changes are needed. Other options that require knowing the number of bits b in the type and a mask m = 2^b−1 include:

((uint32_t) 1 << (i & m)) - 1 - (i >> b) (from supercat)

and:

((uint32_t) i >> b) ^ 1) << (i & m)) - 1 (derived from a suggestion by Matt Timmermans).

Answer 2

I think it is quite portable

#define PREFIX(type, n) (type)(((sizeof(type) * CHAR_BIT - (n)) == sizeof(type) * CHAR_BIT) ? ((type)0) : (!(sizeof(type) * CHAR_BIT - (n)) ? (~(type)(0)) : ((~(type)(0)) << (sizeof(type) * CHAR_BIT - n))))
#define POSTFIX(type, n) (type)(((sizeof(type) * CHAR_BIT - (n)) == sizeof(type) * CHAR_BIT) ? ((type)0) : (!(sizeof(type) * CHAR_BIT - (n)) ? (~(type)(0)) : ((~(type)(0)) >> (sizeof(type) * CHAR_BIT - n))))

#define TEST_TYPE unsigned long long

void printbin(TEST_TYPE x)
{
    TEST_TYPE mask = (TEST_TYPE)1 << (sizeof(x) * CHAR_BIT - 1);
    while(mask)
    {
        printf("%d", !!(x & mask));
        mask >>= 1;
    }
}


int main()
{
    for(int x = 0; x <= sizeof(TEST_TYPE) * CHAR_BIT; x++)
    {
        printbin(PREFIX(TEST_TYPE, x)); printf("\n");
    }
    printf("\n");
    for(int x = 0; x <= sizeof(TEST_TYPE) * CHAR_BIT; x++)
    {
        printbin(POSTFIX(TEST_TYPE, x)); printf("\n");
    }
}

https://godbolt.org/z/_NadkH

Answer 3

You can cast uint32_t to something with more bits, shift that, and then convert back:

uint32_t prefix_mask(int i) {
  return UINT32_MAX & ((UINT64_C(1) << i) - 1);
}

Answer 4

This can be done using the prefix_mask2 idea with arithmetic shifts to prepare the correct pattern, with three instructions total (assuming shift counts in the CPU are modulo word width):

// minimal instruction dependency (2 cycles), but requires large constant
// that some architectures have trouble generating
uint32_t prefix_mask2a(int i) {
    return ((int32_t) (i + (0x80000000 - 32))) >> ((i ^ 31) & 31);
}

// 3 cycles
uint32_t prefix_mask2b(int i) {
    return (uint32_t) ((int32_t) -i >> 31) >> (-i & 31);
}