C中的签名除法 [英] signed division in C

问题描述

我正在阅读安德鲁·科宁(Andrew Koening)在书C Traps and Pitfalls中有关C可移植性的部分.

I was reading the section on C portability in the book C Traps and Pitfalls by Andrew Koening..

以整数除法

q = a/b;
r = a%b;

如果a是一个负数，则提醒 r 显然可以是一个负数或正数，同时满足属性

If a is a negative number, apparently the reminder r can be a negative or positive number, while satisfying the property

q * b + r == a

通常，我期望 r 为负，如果分红 a 为负.这就是我在带有gcc的intel机器中看到的.我很好奇，您是否曾经见过一台在股息为负数时会返回正提醒的机器?

Normally I would expect r to be negative if dividend a is negative. And that is what I see in a intel machine with gcc. I am just curious have you ever seen a machine that would return a positive reminder when the dividend is a negative number ?

推荐答案

C99将其余部分形式化为与股息相同的符号.在C99(C89和K& R)之前，由于两种结果均满足技术要求，因此可以采用任何一种方法.确实有一些不符合C99规范的编译器，尽管我不知道有什么问题.

C99 formalized the remainder as having the same sign as the dividend. Prior to C99 (C89 and K&R), it could have gone either way as both results meet the technical requirements. There are indeed compilers out there non-conforming to the C99 spec in this matter, though I don't know of any off the top of my head.

尤其是，第6.5.5节(乘法运算符)指出:

In particular, section 6.5.5 (Multiplicative operators) states:

¶5/运算符的结果是除以 第一个操作数第二个； ％运算符的结果是 余.在两个操作中，如果第二个操作数的值是 零，则行为未定义.

¶5 The result of the / operator is the quotient from the division of the first operand by the second; the result of the % operator is the remainder. In both operations, if the value of the second operand is zero, the behavior is undefined.

¶6当整数相除时，/运算符的结果是代数商，其中任何 ⁸⁷⁾如果商a/b是可表示的，则表达式 (a/b)*b + a%b应等于a.

¶6 When integers are divided, the result of the / operator is the algebraic quotient with any fractional part discarded.⁸⁷⁾ If the quotient a/b is representable, the expression (a/b)*b + a%b shall equal a.

⁸⁷⁾这通常被称为向零截断".

⁸⁷⁾ This is often called "truncation toward zero".

有了这个新定义，其余的基本上定义为您希望它在数学上说的话.

With this new definition, the remainder is basically defined as what you'd expect it to be mathematically speaking.

编辑

要解决注释中的问题，C99规范还指定(脚注240)，如果余数为零，则在未签名零的系统上，r的符号将与除数x.

To address a question in the comments, the C99 spec also specifies (footnote 240) that if the remainder is zero, on systems where zero is not signed the sign of r will be the same as that of divisor, x.

’‘当y≠0时，不管 通过数学关系r = x − ny的舍入模式，其中n是 最接近x/y确切值的整数；每当n − x/y | = 1/2， 那么n是偶数因此，余数始终是精确的. 如果r = 0，则其 符号应为x..’此定义适用于所有 实施.

‘‘When y ≠ 0, the remainder r = x REM y is defined regardless of the rounding mode by the mathematical relation r = x − ny, where n is the integer nearest the exact value of x/y; whenever | n − x/y | = 1/2, then n is even. Thus, the remainder is always exact. If r = 0, its sign shall be that of x.’’ This definition is applicable for all implementations.

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