C++ 我怎样才能安全地找到 C 中 2 个有符号整数之间的绝对差

发布于06月07日

绝对差值是两个数字之间的差值的绝对值.假设我有2int个变量(x和y)，我想找出绝对差异.一个简单的解决方案是:

unsigned diff = abs(x-y);

然而，如果发生溢出，则这些调用未定义的行为并给出不正确的结果，例如，如果x是INT_MIN,y是INT_MAX.这是returns 1(假设回绕行为)，而不是预期的UINT_MAX.

How to safely and efficiently find `abs((int)num1 - (int)num2)`

/// Safely and efficiently return `abs((int)num1 - (int)num2)`
unsigned int abs_num1_minus_num2_int(int num1, int num2)
{
    unsigned int abs_diff = num1 > num2 ?
        (unsigned int)num1 - (unsigned int)num2 :
        (unsigned int)num2 - (unsigned int)num1;

    return abs_diff;
}

秘诀是对signed个整数值进行num1 > num2个三进制比较，然后将它们重新解释为unsigned个整数值，以便在获得绝对值num1 - num2时允许明确定义的溢出和下溢行为.

以下是我的完整测试代码:

我的eRCaGuy_hello_world份回购中有absolute_value_of_num1_minus_num2.c份:

///usr/bin/env ccache gcc -Wall -Wextra -Werror -O3 -std=gnu17 "$0" -o /tmp/a -lm && /tmp/a "$@"; exit
// For the line just above, see my answer here: https://stackoverflow.com/a/75491834/4561887

#include <limits.h>
#include <stdbool.h> // For `true` (`1`) and `false` (`0`) macros in C
#include <stdint.h>  // For `uint8_t`, `int8_t`, etc.
#include <stdio.h>   // For `printf()`


#define TEST_EQ(func, num1, num2, equals) \
    printf("%s\n", func((num1), (num2)) == (equals) ? "Passed" : "FAILED")

/// Safely and efficiently return `abs((int8_t)num1 - (int8_t)num2)`
uint8_t abs_num1_minus_num2_int8(int8_t num1, int8_t num2)
{
    uint8_t abs_diff = num1 > num2 ?
        (uint8_t)num1 - (uint8_t)num2 :
        (uint8_t)num2 - (uint8_t)num1;

    // debugging
    printf("num1 = %4i (%3u); num2 = %4i (%3u); num1-num2=%3u;  ",
        num1, (uint8_t)num1, num2, (uint8_t)num2, abs_diff);

    return abs_diff;
}

/// Safely and efficiently return `abs((int)num1 - (int)num2)`
unsigned int abs_num1_minus_num2_int(int num1, int num2)
{
    unsigned int abs_diff = num1 > num2 ?
        (unsigned int)num1 - (unsigned int)num2 :
        (unsigned int)num2 - (unsigned int)num1;

    // debugging
    printf("num1 = %11i (%10u); num2 = %11i (%10u); num1-num2=%10u;  ",
        num1, (unsigned int)num1, num2, (unsigned int)num2, abs_diff);

    return abs_diff;
}


int main()
{
    printf("Absolute difference tests.\n");

    // ---------------
    // int8_t types
    // ---------------

    int8_t num1_8;
    int8_t num2_8;

    printf("\n");
    printf("INT8_MIN = %i, INT8_MAX = %i\n", INT8_MIN, INT8_MAX); // -128, 127

    num1_8 = -7;
    num2_8 = -4;
    TEST_EQ(abs_num1_minus_num2_int8, num1_8, num2_8, 3);

    num1_8 = INT8_MIN;
    num2_8 = INT8_MAX;
    TEST_EQ(abs_num1_minus_num2_int8, num1_8, num2_8, UINT8_MAX);

    num1_8 = INT8_MAX;
    num2_8 = INT8_MIN;
    TEST_EQ(abs_num1_minus_num2_int8, num1_8, num2_8, UINT8_MAX);

    num1_8 = 100;
    num2_8 = 10;
    TEST_EQ(abs_num1_minus_num2_int8, num1_8, num2_8, 90);

    num1_8 = 10;
    num2_8 = 100;
    TEST_EQ(abs_num1_minus_num2_int8, num1_8, num2_8, 90);

    num1_8 = 10;
    num2_8 = 10;
    TEST_EQ(abs_num1_minus_num2_int8, num1_8, num2_8, 0);

    num1_8 = INT8_MAX;
    num2_8 = 1;
    TEST_EQ(abs_num1_minus_num2_int8, num1_8, num2_8, 126);

    num1_8 = 1;
    num2_8 = INT8_MAX;
    TEST_EQ(abs_num1_minus_num2_int8, num1_8, num2_8, 126);

    // ---------------
    // int types
    // ---------------

    int num1;
    int num2;

    printf("\n");
    printf("INT_MIN = %i, INT_MAX = %i\n", INT_MIN, INT_MAX); // -2147483648, 2147483647

    num1 = -7;
    num2 = -4;
    TEST_EQ(abs_num1_minus_num2_int, num1, num2, 3);

    num1 = INT_MIN;
    num2 = INT_MAX;
    TEST_EQ(abs_num1_minus_num2_int, num1, num2, UINT_MAX);

    num1 = INT_MAX;
    num2 = INT_MIN;
    TEST_EQ(abs_num1_minus_num2_int, num1, num2, UINT_MAX);

    num1 = 100;
    num2 = 10;
    TEST_EQ(abs_num1_minus_num2_int, num1, num2, 90);

    num1 = 10;
    num2 = 100;
    TEST_EQ(abs_num1_minus_num2_int, num1, num2, 90);

    num1 = 10;
    num2 = 10;
    TEST_EQ(abs_num1_minus_num2_int, num1, num2, 0);

    num1 = INT_MAX;
    num2 = 1;
    TEST_EQ(abs_num1_minus_num2_int, num1, num2, 2147483646);

    num1 = 1;
    num2 = INT_MAX;
    TEST_EQ(abs_num1_minus_num2_int, num1, num2, 2147483646);


    return 0;
}

示例运行和输出:

eRCaGuy_hello_world/c$ ./absolute_value_of_num1_minus_num2.c
Absolute difference tests.

INT8_MIN = -128, INT8_MAX = 127
num1 =   -7 (249); num2 =   -4 (252); num1-num2=  3;  Passed
num1 = -128 (128); num2 =  127 (127); num1-num2=255;  Passed
num1 =  127 (127); num2 = -128 (128); num1-num2=255;  Passed
num1 =  100 (100); num2 =   10 ( 10); num1-num2= 90;  Passed
num1 =   10 ( 10); num2 =  100 (100); num1-num2= 90;  Passed
num1 =   10 ( 10); num2 =   10 ( 10); num1-num2=  0;  Passed
num1 =  127 (127); num2 =    1 (  1); num1-num2=126;  Passed
num1 =    1 (  1); num2 =  127 (127); num1-num2=126;  Passed

INT_MIN = -2147483648, INT_MAX = 2147483647
num1 =          -7 (4294967289); num2 =          -4 (4294967292); num1-num2=         3;  Passed
num1 = -2147483648 (2147483648); num2 =  2147483647 (2147483647); num1-num2=4294967295;  Passed
num1 =  2147483647 (2147483647); num2 = -2147483648 (2147483648); num1-num2=4294967295;  Passed
num1 =         100 (       100); num2 =          10 (        10); num1-num2=        90;  Passed
num1 =          10 (        10); num2 =         100 (       100); num1-num2=        90;  Passed
num1 =          10 (        10); num2 =          10 (        10); num1-num2=         0;  Passed
num1 =  2147483647 (2147483647); num2 =           1 (         1); num1-num2=2147483646;  Passed
num1 =           1 (         1); num2 =  2147483647 (2147483647); num1-num2=2147483646;  Passed