C++ 中的除法运算符 ( / ) 是否在 num 具有相同符号和 ceil 值的情况下返回 floor 值，当两个数字具有相反的符号时？

Question

In C++, when both numerator and denominator are integers and of same sign, then division operator gives the floor value of the quotient. But when they are of opposite sign, then it gives ceil value. Is my understanding correct or is there more to it?

Answer 1

You have it right. Some 20th-century hardware engineer decided to do it this way, and as far as I know this is how all microprocessors now natively do it. Mathematically, it's often a little inconvenient, which is why Python (for example) corrects in software always to round toward toward floor.

For additional insight, besides p/q for an integer quotient, try p%q for the corresponding remainder.

Your question is tagged C++ but this is really a computer hardware issue and, as such, it may be more helpful to consult the C17 standard, whose sect. 6.5.5(6) reads:

When integers are divided, the result of the / operator is the algebraic quotient with any fractional part discarded. If the quotient a/b is representable, the expression (a/b)*b + a%b shall equal a ....

(I have a shred of a memory from 25 or 30 years ago, reading about a CPU that rounded toward floor. If my memory is not altogether imaginary, then that CPU apparently did not succeed in the marketplace, did it?)