为什么 % 运算符有时输出正数有时输出负数? [英] Why does the % operator sometimes output positive and sometimes negative?

问题描述

当我发现一些奇怪的东西时，我正在统一编写脚本，完成脚本后，我在一个 Visual Studio 控制台项目中测试了我的实现.

I was working on a script in unity when i realized something odd and after I finished the script I tested my realization in a visual studio console project.

class Program
{
    static void Main(string[] args)
    {
        Console.WriteLine(-3.5 % 1);
        Console.WriteLine(3.5 % (-1));
    }
}

输出是:

-0.5

0.5

模数运算符不应该在两种情况下都给我 -0.5 吗?

Shouldn't the modulus operator give me -0.5 in both cases?

推荐答案

模数运算符不应该在两种情况下都给我 -0.5 吗?

Shouldn't the modulus operator give me -0.5 in both cases?

为什么要这样做?从数学上讲，这两种情况的 0.5 和 -0.5 都是正确的.

Why should it? Mathematically, both 0.5 and -0.5 are correct for the both cases.

-3.5 = -3 * 1 + (-0.5)
-3.5 = -4 * 1 + 0.5
3.5 = -3 * (-1) + 0.5
3.5 = -4 * (-1) + (-0.5)

以编程方式，它由 C# 语言规范定义.

Programmatically, it's defined by the C# language specification.

7.8.3 余数运算符

7.8.3 Remainder operator

浮点余数:

float operator %(float x, float y);
double operator %(double x, double y); 

下表列出了所有可能组合的结果非零有限值、零、无穷大和 NaN.在表中，xy 是正的有限值.z 是 x % y 的结果，并且是计算为 x – n * y，其中 n 是最大的可能整数，即小于或等于 x/y.这种计算余数的方法是类似于用于整数操作数的，但不同于 IEEE754 定义(其中 n 是最接近 x/y 的整数).

The following table lists the results of all possible combinations of nonzero finite values, zeros, infinities, and NaN’s. In the table, x and y are positive finite values. z is the result of x % y and is computed as x – n * y, where n is the largest possible integer that is less than or equal to x / y. This method of computing the remainder is analogous to that used for integer operands, but differs from the IEEE 754 definition (in which n is the integer closest to x / y).

该表表示余数的符号与第一个操作数 x 的符号相同.

The table says that the sign of the remainder is the same as the sign of the first operand x.

在-3.5 % 1的情况下:

x = 3.5
y = 1
n = 3
z = 3.5 - 3 * 1 = 0.5

根据表格，结果是-z，即-0.5.

According to the table, the result is -z, that is -0.5.

在3.5 % -1、x、y、n、z的情况下 同上.根据表格，结果是+z，即0.5.

In the case of 3.5 % -1, x, y, n, z are the same as above. According to the table, the result is +z, that is 0.5.

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