arithmetic by bitwise operators

I have started a new programming library in C which simulates arithmetic using only bitwise operators. This is purely for computer science purposes and to prove that it can be done. The hardest part was getting the division function working correctly. I can prove that these functions work with another program I wrote, but I really want to record a video sometime to show the process of how these work.

For now, here is the source of the 4 arithmetic functions and some global variables used in the division function.

/*
 bitlib.h

 This library simulates the four arithmetic functions: ( addition, subtraction, multiplication, and division )
 Using only bitwise operations: ( AND, OR, XOR, SHL, SHR )
 
 Most of the time I would not need to do this, however, there exist applications where this information may prove useful.
 
 - Programming ARM CPUs which don't have a division instruction.
 - Arbitary Precision Arithmetic involving thousands of digits.

*/

int add(int di,int si)
{
 while(si!=0)
 {
  int ax=di;
  di^=si;
  si&=ax;
  si<<=1;
 }
 return di;
}


int sub(int di,int si)
{
 while(si!=0)
 {
  di^=si;
  si&=di;
  si<<=1;
 }
 return di;
}



int mul(int di,int si)
{
 int ax=0;
 while(si!=0)
 {
  if((si&1)!=0){ax=add(ax,di);}
  di<<=1;
  si>>=1;
 }
 return ax;
}

/*
this division function returns the quotient, but also stores the remainder of division in a global variable
*/

int sign_bit=1<<((sizeof(int)<<3)-1); /*used to extract the most significant bit during division function*/

int mod=0; /*to store the modulus/remainder of the division function*/

int bitdiv(int di,int si)
{
 int ax=0,bx=0,cx=1;
 if(si==0){return 0;} /*division by zero is invalid*/

 while(cx!=0)
 {
  ax<<=1;
  bx<<=1;
  if(di&sign_bit){bx|=1;}
  di<<=1;
  
  if(bx>=si)
  {
   bx=sub(bx,si);
   ax|=1;
  }
 
  cx<<=1;
 }

 mod=bx;
 return ax;
}