Incremental addition, subtraction, multiplication and division of integers by bit operations

bitop.c

#include <stdio.h>
#include <stdlib.h>

int plus(int a, int b) {
  int sum = a, carry = b;

  while (carry) {
    int temp = sum;
    sum = temp ^ carry;
    carry = (temp & carry) << 1;
  }

  return sum;
}

int negate(int num) {
  return plus(~num, 1);
}

int abs(int num) {
  return num < 0 ? negate(num) : num;
}

int subtract(int a, int b) {
  return plus(a, negate(b));
}

int multiply(int a, int b) {
  int multiplier = abs(a), multiplicand = abs(b);

  int product = 0;
  while (multiplicand) {
    if (multiplicand & 0x1) {
      product = plus(product, multiplier);
    }
    multiplier = multiplier << 1;
    multiplicand = multiplicand >> 1;
  }

  if ((a ^ b) < 0) {
    product = negate(product);
  }

  return product;
}

int bitlength(int a) {
  int length = 0;
  while (a) {
    length = plus(length, 1);
    a = a >> 1;
  }
  return length;
}

int lengthdiff(int a, int b) {
  return subtract(bitlength(a), bitlength(b));
}

int division(int a, int b) {
  int dividend = abs(a), divisor = abs(b);

  int quotient = 0;
  for (int i = lengthdiff(dividend, divisor); i >= 0; i = subtract(i, 1)) {
    int r = (divisor << i);
    // Left shift divisor until it's smaller than dividend
    if (r <= dividend) {
      quotient |= (1 << i);
      dividend = subtract(dividend, (int) r);
    }
  }

  if ((a ^ b) < 0) {
    quotient = negate(quotient);
  }

  return quotient;
}

int remain(int a, int b) {
  int dividend = abs(a), divisor = abs(b);

  int quotient = 0;
  for (int i = lengthdiff(dividend, divisor); i >= 0; i = subtract(i, 1)) {
    int r = (divisor << i);
    // Left shift divisor until it's smaller than dividend
    if (r <= dividend) {
      dividend = subtract(dividend, (int) r);
    }
  }

  if (a < 0) {
    dividend = negate(dividend);
  }

  return dividend;
}

int main(int argc, char* argv[]) {
  int a = atoi(argv[1]), b = atoi(argv[2]);
  printf("plus: %d, subtract: %d, multiply: %d, division: %d, remainder: %d",
         plus(a, b), subtract(a, b), multiply(a, b), division(a, b), remain(a, b));
  return 0;
}