DataLab

约 311 个字 9 行代码 预计阅读时间 1 分钟

介绍

This lab requires students to implement simple logical and arithmetic functions, but using a highly restricted subset of C. For example, they must compute the absolute value of a number using only bit-level operations. This lab helps students understand the bit-level representations of C data types and the bit-level behavior of the operations on data.

1. bitXor

x ^ y using only ~ and & 即利用非和与实现异或. e.g. bitXor(4, 5) = 1

涉及到数学的运算：

\[ \begin{align} x \wedge y &= \bar{x}y + x\bar{y} \\ &= (x + y)(\bar{x} + \bar{y}) \\ &= (x + y) \overline{xy} \\ &= x\overline{xy} + y\overline{{xy}} \\ &= \overline{\overline{x\overline{xy} + y\overline{xy}}} \\ &= \overline{\overline{x\overline{xy}} \overline{y\overline{xy}}} \end{align} \]

实现

int bitXor(int x, int y) {
    return ~( ~(x & ~(x & y)) & (~(y & ~(x & y))) );
}

PS: 可利用./dlc -e bits.c查看operators

2. tmin

return minimum two's complement integer（最小二进制补码整数）

即\(-2^{32}\)，利用移位——即1左移31位

实现

int tmin(void) {
    return 1 << 31;
}

3. isTmax

returns 1 if x is the maximum, two's complement number, and 0 otherwise

(若是补码最大即01..1则返回1，否则0)

01..1 加 1取反为01..1，即本身。此时01..1与其异或为0(因为两个数相等)

• 故让x与其x加1取反进行异或，若为0则返回1，否则返回0
• 但有反例：若x为1..1(即-1)加1后变为0
  • 此时两者进行异或为0，但不符合条件，故需要返回0

实现

int isTmax(int x) {
    return !( ~(x + 1) ^ x) & !!( (x + 1) ^ 0x0);//!!可将非0变为1
}

4. allOddBits

5. negate

6. isAsciiDigit

7. conditional

8. isLessOrEqual

9. logicalNeg

10. howManyBits

11. floatScale2

12. floatFloat2Int

13. floatPower2

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