条件码---CF和OF

Question

我读了书CS:APP（第三版）和第 3.6.1 节条件代码。它说：

CF: Carry flag. The most recent operation generated a carry out of the most significant bit. Used to detect overflow for unsigned operations.

OF: Overflow flag. The most recent operation caused a two's-complement overflow--either negative or positive.

但我有以下代码。我编译并执行了它。发生了一些不同的事情。

int main() {
    char x  = 0x66;
    char y =  0x39;
    char x_bit_not = ~x;
    char x_not = !x;
    char x_bit_and_y = x & y;
    char x_and_y = x  && y;
    char  x_bit_or_y = x | y;
    char x_or_y = x || y;


    int x1 = (1<<31)-1;
    int y1 = 1;
    int sum_x1_y1 = x1 + y1;
    int diff_x1_y1 = x1 - y1;
    int diff_y1_x1 = y1 - x1;


    unsigned int x2 = (1<<31)-1;
    unsigned int y2 = 1;
    unsigned int sum_x2_y2 = x2 + y2;
    unsigned int diff_x2_y2   = x2 - y2;
    unsigned int diff_y2_x2   = y2 - x2;
}

算术表达式 int diff_y1_x1 = y1 - x1; 产生 0x80000002，但消息中没有进位。但是经过这条语句，CF等于1.

算术表达式 unsigned int sum_x2_y2 = x2 + y2; 甚至不涉及带符号的变体，但是在这条语句之后，OF 等于 1。这是怎么发生的？

另外，我还有一张图：标题是 CF = Cin XOR Cout 和 OF = Cn XOR Cn-1。这是什么意思？ CS:APP错了吗？或者只是CS:APP不包含所有条件？

Answer 1

我的回答假设是 x86。其他架构的行为可能有所不同。

在 x86 上，CF 和 OF 标志都受到有符号和无符号操作的影响（因为 CPU 不知道有符号）。哪些标志相关取决于具体用例。通常，检查 CF 标志是否有无符号算术，而检查 OF 标志是否有符号算术。另见：about assembly CF(Carry) and OF(Overflow) flag

具体解决您的观察：

CF flag is also set when a borrow from MSB happens. This means, it will be set when subtracting a larger number from a smaller number (like y1 - x1), because that requires a borrow from the MSB. See also :
同样，OF flag is set whenever the MSB of the result is different from the MSB of both operands of an addition。这意味着，当两个数字加起来大于 MAX_INT（如 x2 + y2）时，它会被设置，因为结果会设置 MSB。

条件码---CF和OF

Condition Code---CF and OF

c

x86

assembly

flags