整数除法溢出 [英] Integer division overflows

问题描述

我一直在考虑整数（类型为int）的溢出，而在我看来除法可能会溢出。

I have been thinking about integer (type int) overflows, and it occurs to me that division could overflow.

示例：在当前平台上，我有

Example: On my current platform, I have

INT_MIN == -INT_MAX - 1

，因此

INT_MIN < -INT_MAX

，因此

INT_MIN / -1 > -INT_MAX / -1

，因此

INT_MIN / -1 > INT_MAX.

因此，除法（INT_MIN / -1）确实溢出。

Hence, the division ( INT_MIN / -1 ) does overflow.

所以，我有两个问题：

1. 一个人可以写什么（跨平台的）C代码来防止除法溢出（对于（有符号的）int类型）？

1. What (cross-platform) C code could one write in order to prevent division overflows (for type (signed) int)?

什么保证（以C或C ++标准）可能有助于设计代码？

What guarantees (in C or C++ standard) might help to devise the code?

---

例如，如果标准保证我们拥有

---

For example, if the standard guarantees that we have either

INT_MIN == -INT_MAX - 1

或

INT_MIN == -INT_MAX,

然后显示以下代码

#include <limits.h>

/*
      Try to divide integer op1 by op2.
      Return
        0 (success) or
        1 (possibly overflow prevented).
      In case of success, write the quotient to res.
*/

int safe_int_div(int * res, int op1, int op2) {

  /*   assert(res != NULL);   */
  /*   assert(op2 != 0);      */

  if ( op1 == INT_MIN && op2 == -1 )  {
    return 1;
  }
  *res = op1 / op2;
  return 0;
}

推荐答案

什么保证（用C或C ++标准）可能有助于设计代码？

What guarantees (in C or C++ standard) might help to devise the code?

C使用3中的1指定整数形式：符号和大小，二进制补码或二进制补码。鉴于这些形式，只有溢出除以0和 INT_MIN / -1 的补数除法。

C specifies signed integer representation as using 1 of 3 forms: sign and magnitude, two’s complement, or ones’ complement. Given these forms, only division by 0 and two’s complement division of INT_MIN/-1 may overflow.

一个人可以写什么（跨平台的）C代码以防止除法溢出（对于（有符号的）int类型）？

What (cross-platform) C code could one write in order to prevent division overflows (for type (signed) int)?

int safe_int_div(int * res, int op1, int op2) {
  if (op2 == 0) {
    return 1;
  }
  // 2's complement detection
  #if (INT_MIN != -INT_MAX) 
    if (op1 == INT_MIN && op2 == -1)  {
      return 1;
    }
  #endif
  *res = op1 / op2;
  return 0;
}

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