In C bits, multiply by 3 and divide by 16

Question

A buddy of mine had these puzzles and this is one that is eluding me. Here is the problem, you are given a number and you want to return that number times 3 and divided by 1

Answer 1

This seems to work (as long as no overflow occurs):

((num<<2)+~num+1)>>4

Try this JavaScript code, run in console:

for (var num = -128; num <= 128; ++num) {
  var a = Math.floor(num * 3 / 16);
  var b = ((num<<2)+~num+1)>>4;
  console.log(
    "Input:", num,
    "Regular math:", a,
    "Bit math:", b,
    "Equal: ", a===b
  );
}