quotRem和divMod之间的区别何时有用？ [英] When is the difference between quotRem and divMod useful?

问题描述

从haskell报告：

如果y，quot，rem，div和mod类
方法满足这些定律是
非零：

 （x`quot` y）* y +（x`rem` y） == x 
（x`div` y）* y +（x`mod` y）== x 
  

quot 是整数除法将
截断为零，而 div $的结果b $ b被截断为负无穷。

例如：

 前奏> （-12）``5 
 -2 
前奏> （-12）`div` 5 
 -3 
  

什么是一些例子

解决方案

许多语言都有一个mod或％运算符，它给出了剩余的截断后向0分割;例如C，C ++和Java以及C＃可能会说：

$ p $ （ - 11）/ 5 = -2
（-11）％5 = -1
5 *（（ - 11）/ 5）+（-11）％5 = 5 *（ - 2）+（-1）= - 11。


Haskell的 quot 和 rem 是为了模仿这种行为。我可以想象，在某些人为的情况下，与某些C程序的输出兼容可能是可取的。

Haskell的 div 和 mod ，随后是Python的/和％，遵循数学家（至少是数理论家）的惯例总是截断向下划分（而不是0 - 朝向负无穷），以便余数总是非负的。因此，在Python中，

 （ -  11）/ 5 = -3 
（-11）％5 = 4 
 5 *（（ -  11）/ 5）+（ -  11）％5 = 5 *（ -  3）+ 4 = -11。 
  

Haskell的 div 和 mod 遵循此行为。

From the haskell report:

The quot, rem, div, and mod class methods satisfy these laws if y is non-zero:

(x `quot` y)*y + (x `rem` y) == x
(x `div`  y)*y + (x `mod` y) == x

quot is integer division truncated toward zero, while the result of div is truncated toward negative infinity.

For example:

Prelude> (-12) `quot` 5
-2
Prelude> (-12) `div` 5
-3

What are some examples of where the difference between how the result is truncated matters?

解决方案

Many languages have a "mod" or "%" operator that gives the remainder after division with truncation towards 0; for example C, C++, and Java, and probably C#, would say:

(-11)/5 = -2
(-11)%5 = -1
5*((-11)/5) + (-11)%5 = 5*(-2) + (-1) = -11.

Haskell's quot and rem are intended to imitate this behaviour. I can imagine compatibility with the output of some C program might be desirable in some contrived situation.

Haskell's div and mod, and subsequently Python's / and %, follow the convention of mathematicians (at least number-theorists) in always truncating down division (not towards 0 -- towards negative infinity) so that the remainder is always nonnegative. Thus in Python,

(-11)/5 = -3
(-11)%5 = 4
5*((-11)/5) + (-11)%5 = 5*(-3) + 4 = -11.

Haskell's div and mod follow this behaviour.

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