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]