mod(取模)and rem(取余)

VHDL has mod and rem. They return the same value if both arguments are positive.

but, they produce different results for negative inputs:

5 mod 3 = 2

(-5) mod 3 = 1

5 mod (-3) = -1

(-5) mod (-3) = -2

for mod， the result has the same sign with the first argument.

whereas

5 rem 3 = 2

(-5) rem 3 = -2

5 rem (-3) = 2

(-5) rem (-3) = -2

for rem，the result has the same sign with the second argument.

A rem B = A - ( A / B ) * B --余数运算符 利用操作数A决定结果的正负号

取余运算（a REM b）的符号与a相同，其绝对值小于b的绝对值。

A mod B = A - B * N --取模运算符 利用操作数B决定结果的正负号

取模运算（a MOD b）的符号与b相同，其绝对值小于b的绝对值。