Question

In looking at this question I was trying to figure out this function

_shl: function (a, b){
  for (++b; --b; a = ((a %= 0x7fffffff + 1) & 0x40000000) == 0x40000000 ? a * 2 : (a - 0x40000000) * 2 + 0x7fffffff + 1);
  return a;
}

I figured out the javascript syntax and also found an uncompressed version of the function used in a md5 javascript implementation

function shl1(a) {
  a=a%(0x7fffffff+1);
  if (a&0x40000000==0x40000000)
  {
    a-=0x40000000;  
    a*=2;
    a+=(0x7fffffff+1);
  } else
    a*=2;
  return a;
}

function shl(a,b) {
  a=integer(a);
  b=integer(b);
  for (var i=0;i<b;i++) a=shl1(a);
  return a;
}

My question is what is significant about 0x40000000 and 0x7fffffff. I somewhat understand the idea of a bitwise shift, but I am lost about the importance of these two numbers.

Answer 1

The 0x7fffffff is, in binary, a 0 followed by 31 1s. Adding one to it gives 0x80000000, a 1 followed by 31 0s. I don’t know why the direct constant isn’t there. %ing by 0x80000000 will cut off the 32nd and all higher bits.

The 0x40000000 is, in binary, a 0, a 1, and then 30 0s. &ing with 0x40000000 and checking for equality to 0x40000000 checks whether that 31st bit (counting from the right this time) is set.

As far as I can tell, the section (a - 0x40000000) * 2 + 0x7fffffff + 1) should be the same as a. Not sure why the extended code is required.