VHDL中的mod和rem运算符之间的区别？答案

【问题标题】：Difference between mod and rem operators in VHDL?VHDL中的mod和rem运算符之间的区别？
【发布时间】：2014-11-09 00:41:31
【问题描述】：

我在VHDL编程中遇到了这些语句，无法理解mod和rem这两个运算符之间的区别

    9 mod 5
    (-9) mod 5
    9 mod (-5)
    9 rem 5
    (-9) rem 5
    9 rem (-5)

【问题讨论】：

computer-programming-forum.com/42-vhdl/6f9dce015f5ce94f.htm

标签： vhdl

【解决方案1】：

查看不同之处的一种方法是在测试台上运行快速模拟，使用这样的过程的示例：

process is
begin
  report "  9  mod   5  = " & integer'image(9 mod 5);
  report "  9  rem   5  = " & integer'image(9 rem 5);
  report "  9  mod (-5) = " & integer'image(9 mod (-5));
  report "  9  rem (-5) = " & integer'image(9 rem (-5));
  report "(-9) mod   5  = " & integer'image((-9) mod 5);
  report "(-9) rem   5  = " & integer'image((-9) rem 5);
  report "(-9) mod (-5) = " & integer'image((-9) mod (-5));
  report "(-9) rem (-5) = " & integer'image((-9) rem (-5));
  wait;
end process;

显示结果为：

# ** Note:   9  mod   5  =  4
# ** Note:   9  rem   5  =  4
# ** Note:   9  mod (-5) = -1
# ** Note:   9  rem (-5) =  4
# ** Note: (-9) mod   5  =  1
# ** Note: (-9) rem   5  = -4
# ** Note: (-9) mod (-5) = -4
# ** Note: (-9) rem (-5) = -4

Wikipedia - Modulo operation 有详细的描述，包括规则：

mod 有除数符号，因此 n 在 a mod n
rem 有股息的迹象，因此a 在a rem n

mod 运算符给出向下舍入的除法（下除法）的余数，因此为 a = floor_div(a, n) * n + (a mod n)。优点是a mod n 是一个重复的锯齿图，当a 甚至从零开始增加时，这在某些计算中很重要。

rem 运算符给出了正则整数除法 a / n 的余数，它向 0 舍入（截断除法），所以是 a = (a / n) * n + (a rem n)。

【讨论】：

【解决方案2】：

For equal sign:
9/5=-9/-5=1.8 gets 1 
9 mod 5 = 9 rem 5
-9 mod -5 = -9 rem -5
-----------------------------------------
For unequal signs:
9/-5 = -9/5 = -1.8
In "mod" operator : -1.8 gets -2
In "rem" operator : -1.8 gets -1
----------------------------------------
example1: (9,-5)
9 = (-5*-2)-1  then:  (9 mod -5) = -1
9 = (-5*-1)+4  then:  (9 rem -5) = +4
----------------------------------------
example2: (-9,5)
-9 = (5*-2)+1  then:  (-9 mod 5) = +1
-9 = (5*-1)-4  then:  (-9 rem 5) = -4
----------------------------------------
example3: (-9,-5)
-9 = (-5*1)-4  then:  (-9 mod -5) = -4
-9 = (-5*1)-4  then:  (-9 rem -5) = -4
----------------------------------------
example4: (9,5)
9 = (5*1)+4  then:  (9 mod 5) = +4
9 = (5*1)+4  then:  (9 rem 5) = +4

【讨论】：