取模运算在数学定义与机器理解的区别

纪念我c语言第一次课堂作业被坑

取模运算（“MOD”）

数学定义：

谷歌到《Concrete Mathematics》上的一段，原文：

摘自P82：

3.4 ‘MOD’: THE BINARY OPERATION

The quotient of n divided by m is [n/m],when m and n are positive

integers. It’s handy to have a simple notation also for the remainder

of this division, and we call it ‘n mod m’, The basic formula

n = m[n/m]+ n mod m

//NOTE：”m[n/m]” is quotient, “n mod m” is remainder

tells us that we can express n mod m as n-m[n/m] .We can generalize this

to megative integers, and in fact to arbitrary real numbers:

x mod y = x - y[x/y], for y!=0.

在这里的余数（Remainder）其实就是取模（mod)：x mod y=x % y=x-y(x/y),for y!=0.

在概念上数和机器的理解是相同的，然鹅……机器在实现上确是与数学有差异。

1.数学上：[x/y]为x/y的最小下界

举个栗子：

5 mod 2=5 - 2 * [5/2]

=5 - 2 * [2.5]

=5 - 2 * 2

=1

2.机器上：[x/y]=(x/y)其实就是取余

再举个栗子：

5 mod 2 = 5 - 2 * [5/2]

=5 - 2 * (5/2)

=5 - 2 * (2)

=5 - 2 * 2

=

总结：so……以后在用代码实现时要千万记住：mod 是 % 是 取模 取模 取模！

公式：x mod y = x % y = x - y(x/y),for y!=0