计算机加减乘除的本质

只应用位运算实现加减乘除是程序员的基本修养，这里应用通俗易懂的python实现加减乘除，其他语言同理。

应对python无限制扩展位数的方法

# 限制变量为32位
def int32(value):
    return -(value & 0x80000000) | (value & 0x7FFFFFFF)
1
2
3

加法,本位+进位

def add(a, b):
    while b:
        carry = a & b
        a = a ^ b
        b = carry << 1
    return a
1
2
3
4
5
6

减法，本位-借位

def subtract(a, b):
    while b:
        borrow = (~a) & b
        a = a ^ b
        b = borrow << 1
    return a

1
2
3
4
5
6
7

乘法

def multiply(a, b):
    result = 0
    neg = a < 0 and b > 0 or a > 0 and b < 0
    a, b = abs(a), abs(b)
    while b:
        if b & 1:
            result = add(result, a)
        a <<= 1
        b >>= 1
    return -result if neg else result
1
2
3
4
5
6
7
8
9
10

除法

def divide(a, b):
    if b == 0:
        raise ValueError("除数不能为零")
    neg = a < 0 and b > 0 or a > 0 and b < 0
    a, b = abs(a), abs(b)
    result = 0
    while a >= b:
        temp, i = b, 1
        while a >= (temp << 1):
            temp <<= 1
            i <<= 1
        a = subtract(a, temp)
        result = add(result, i)
    return -result if neg else result
1
2
3
4
5
6
7
8
9
10
11
12
13
14