bit_arithmetic.js

// tags: #bit

// 整数四则位运算

/* 
- 时钟向后拨2（-2）个小时和向前拨10（+10，再 +2 溢出）个小时是一样的（溢出后 -12），补码存在的意义就是让减法变成加法
- 数字以补码存储（~ -2===1）, 正数的补码等于原码, 负数的补码等于原码取反加一（算补码时符号位不参与）, 补码的补码等于原码
- 计算机使用补码计算加法, 计算时符号位也参与计算
*/

function plus(num1, num2) {
  if (num2 === 0) {
    return num1;
  }
  let sum = num1 ^ num2;
  let carry = (num1 & num2) << 1;
  return plus(sum, carry);
}

function minus(num1, num2) {
  let subtractor = plus(~num2, 1); // 带符号位取反加一得到相反数（补码存储）
  return plus(num1, subtractor);
}

function multiply(num1, num2) {
  let num1Abs = num1 < 0 ? plus(~num1, 1) : num1;
  let num2Abs = num2 < 0 ? plus(~num2, 1) : num2;
  let count = 0;
  let result = 0;
  while (count < num2Abs) {
    result = plus(result, num1Abs);
    count = plus(count, 1);
  }
  if ((num1 ^ num2) < 0) {
    result = plus(~result, 1);
  }
  return result;
}

function divide(num1, num2) {
  let num1abs = num1 < 0 ? plus(~num1, 1) : num1;
  let num2abs = num2 < 0 ? plus(~num2, 1) : num2;
  let count = 0;
  let result = num1abs;
  while (result >= num2abs) {
    result = minus(result, num2abs);
    count = plus(count, 1);
  }
  if ((num1 ^ num2) < 0) {
    count = plus(~count, 1);
  }
  return count;
}