Creating a mask with N least significant bits set

Question

I would like to create a macro or function¹ mask(n) which given a number n returns an unsigned integer with its n least sig

Answer 1

#include 

uint64_t mask_n_bits(const unsigned n){
  uint64_t ret = n < 64;
  ret <<= n&63; //the &63 is typically optimized away
  ret -= 1;
  return ret;
}

Results:

mask_n_bits:
    xor     eax, eax
    cmp     edi, 63
    setbe   al
    shlx    rax, rax, rdi
    dec     rax
    ret

Returns expected results and if passed a constant value it will be optimized to a constant mask in clang and gcc as well as icc at -O2 (but not -Os) .

Explanation:

The &63 gets optimized away, but ensures the shift is <=64.

For values less than 64 it just sets the first n bits using (1<. 1< sets the nth bit (equivalent pow(2,n)) and subtracting 1 from a power of 2 sets all bits less than that.

By using the conditional to set the initial 1 to be shifted, no branch is created, yet it gives you a 0 for all values >=64 because left shifting a 0 will always yield 0. Therefore when we subtract 1, we get all bits set for values of 64 and larger (because of 2s complement representation for -1).

Caveats:

• 1s complement systems must die - requires special casing if you have one
• some compilers may not optimize the &63 away