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CSAPP: 位操作实现基本运算

2019-10-25 19:49 2171 查看

目录

@(位操作实现简单函数)

实验要求

给出15个函数,规定了实现每个函数需要的逻辑和算术操作符(规定数量)。
只能使用规定的操作符! ˜ & ˆ | + << >>
不能使用循环或者条件语句
不能使用超过8位的常数(ff)

实现代码

1、pow2plus1

/*
* pow2plus1 - returns 2^x + 1, where 0 <= x <= 31
*/
int pow2plus1(int x) {
/* exploit ability of shifts to compute powers of 2 */
return (1 << x) + 1;
}

2、pow2plus4

/*
* pow2plus4 - returns 2^x + 4, where 0 <= x <= 31
*/
int pow2plus4(int x) {
/* exploit ability of shifts to compute powers of 2 */
int result = (1 << x);
result += 4;
return result;
}

3、bitXor

/*   bitXor - x^y using only ~ and &
*   Example: bitXor(4, 5) = 1
*   Legal ops: ~ &
*   Max ops: 14
*   Rating: 1
*/
int bitXor(int x, int y) {
return (~(x&y))&(~(~x&~y));//列出真值表
}

4、tmin

/*   tmin - return minimum two's complement integer
*   Legal ops: ! ~ & ^ | + << >>
*   Max ops: 4
*   Rating: 1
*/
int tmin(void) {
return 1<<31;//0x80000000
}

5、isTmax

/*   isTmax - returns 1 if x is the maximum, two's complement number,
*     and 0 otherwise
*   Legal ops: ! ~ & ^ | +
*   Max ops: 10
*   Rating: 1
*/
int isTmax(int x) {
return !(x+x+2) & !!(~x);//x+1+x+1溢出并且非全一
//x:        0111 1111 1111 1111 1111 1111 1111 1111
//x+1:  1000 0000 0000 0000 0000 0000 0000 0000
//x+1+x:    1111 1111 1111 1111 1111 1111 1111 1111
//x+1+x+1:0000 0000 0000 0000 0000 0000 0000 0000
}

6、allOddBits

/*   allOddBits - return 1 if all odd-numbered bits in word set to 1
*   where bits are numbered from 0 (least significant) to 31 (most significant)
*   Examples allOddBits(0xFFFFFFFD) = 0, allOddBits(0xAAAAAAAA) = 1
*   Legal ops: ! ~ & ^ | + << >>
*   Max ops: 12
*   Rating: 2
*/
int allOddBits(int x) {
x = (x>>16) & x;
x = (x>>8) & x;
x = (x>>4) & x;
x = (x>>2) & x;
return (x>>1)&1;
// &运算符的“归一性”
//1010 1010 1010 1010 1010 1010 1010 1010
//0000 0000 0000 0000 1010 1010 1010 1010
//0000 0000 0000 0000 0000 0000 1010 1010
//0000 0000 0000 0000 0000 0000 0000 1010
//0000 0000 0000 0000 0000 0000 0000 0010
// 可以反推理解:后四位四次翻转得第一行
// 只要倒数第二位为1成立,反推后所有的奇数位都为1
}

7、negate

/*   negate - return -x
*   Example: negate(1) = -1.
*   Legal ops: ! ~ & ^ | + << >>
*   Max ops: 5
*   Rating: 2
*/
int negate(int x) {
return ~x+1;    //带符号位取反加一即为相反数
}

8、isAsciiDigit

/*   isAsciiDigit - return 1 if 0x30 <= x <= 0x39 (ASCII codes for characters '0' to '9')
*   Example: isAsciiDigit(0x35) = 1.
*            isAsciiDigit(0x3a) = 0.
*            isAsciiDigit(0x05) = 0.
*   Legal ops: ! ~ & ^ | + << >>
*   Max ops: 15
*   Rating: 3
*/
int isAsciiDigit(int x) {
// 0x30 = 0011 0000b   0x39 = 0011 1001b
int a = (x>>4) ^ 0x3;   // 判断5、6位是否全1
int b0 = (x>>3) & 1;    // 判断第4位是否为1
int b1 = (x>>2) ^ 1;    // 判断第3位是否为1
int b2 = (x>>1) ^ 1;    // 判断第2位是否为1
return (!a) & ((!b0) | (b0&b1&b2));
// 如果5、6位全1 且 (4位为0或4位为1,2、3位为0)
}

9、conditional

/*   conditional - same as x ? y : z
*   Example: conditional(2,4,5) = 4
*   Legal ops: ! ~ & ^ | + << >>
*   Max ops: 16
*   Rating: 3
*/
int conditional(int x, int y, int z) {
x = !x; // 将x设置为0或1
x = (x<<31)>>31; // 将x的0或1拓展到32位全0或全1
return (~x&y) | (x&z); // x为真则~x全1返回
1062
y,为假则x全1返回z
}

10、isLessOrEqual

/*   isLessOrEqual - if x <= y  then return 1, else return 0
*   Example: isLessOrEqual(4,5) = 1.
*   Legal ops: ! ~ & ^ | + << >>
*   Max ops: 24
*   Rating: 3
*/
int isLessOrEqual(int x, int y) {
int z,s,sx,sy;
sx = (x>>31)&1; //  取x的符号位
sy = (y>>31)&1; //  取y的符号位
z = x + ~y + 1; //  z = x-y
s =  ((z>>31) & 1) | (!(z^0));
// 取z的符号位,s为真时x<y或者z全0(x==y)
return  ((!(sx^sy))&s) | (sx&(!sy));
// xy同号且z<=0 或 x<=0 y>=0
}

11、logicalNeg

/*   logicalNeg - implement the ! operator, using all of
*              the legal operators except !
*   Examples: logicalNeg(3) = 0, logicalNeg(0) = 1
*   Legal ops: ~ & ^ | + << >>
*   Max ops: 12
*   Rating: 4
*/
int logicalNeg(int x) {
// |运算符的“分裂性”
x |= x>>16; // 若高16位有1,则传递给低16位的对应位
x |= x>>8;  // 若低16位的高8位有1,则传递给低8位的对应位
x |= x>>4;  // 若低8位的高4位有1,则传递给低4位的对应位
x |= x>>2;  // 若低4位的高2位有1,则传递给低2位的对应位
x |= x>>1;  // 若低2位的高1位有1,则传递给最低1位
x ^= 1;     // 只要x包含1,则必定会导致此时的x为1,x^=1即取反
return x&1;
}

12、howManyBits

/*  howManyBits - return the minimum number of bits required to represent x in
*             two's complement
*  Examples: howManyBits(12) = 5
*            howManyBits(298) = 10
*            howManyBits(-5) = 4
*            howManyBits(0)  = 1
*            howManyBits(-1) = 1
*            howManyBits(0x80000000) = 32
*  Legal ops: ! ~ & ^ | + << >>
*  Max ops: 90
*  Rating: 4
*/
int howManyBits(int x) {
int s,c1,c2,c3,c4,c5,c6;
int cnt = 0;    //  计数
s = (x>>31)&1;  //  符号位
x = ((s<<31)>>31) ^ x; // 取反x
s = !!(x>>16);  // 判断高16位是否有1,有则s为1
c1 = s<<4;      // 若高16位有1,则低16位可以计数16
x >>= c1;       // 右移将已经计数的位移除,c1若为0,则用折半的长度判断
s = !!(x>>8);   // 用8位的长度去判断,有效位的个数计入c2
c2 = s<<3;
x >>= c2;
s = !!(x>>4);   // 用4位的长度去判断,有效位的个数计入c3
c3 = s<<2;
x >>= c3;
s = !!(x>>2);   // 用2位的长度去判断,有效位的个数计入c4
c4 = s<<1;
x >>= c4;
s = !!(x>>1);   // 用1位的长度去判断,有效位的个数计入c5
c5 = s;
x >>= c5;
c6 = !!x;       // 判断最低位是否为1
cnt = c1+c2+c3+c4+c5+c6+1;  // 将每次获得的低位有效位相加,再加1位符号位
return cnt;
}

13、floatScale2

/*   floatScale2 - Return bit-level equivalent of expression 2*f for
*   floating point argument f.
*   Both the argument and result are passed as unsigned int's, but
*   they are to be interpreted as the bit-level representation of
*   single-precision floating point values.
*   When argument is NaN, return argument
*   Legal ops: Any integer/unsigned operations incl. ||, &&. also if, while
*   Max ops: 30
*   Rating: 4
*/
unsigned floatScale2(unsigned uf) {
unsigned f = uf;
if ((f & 0x7F800000) == 0)// 如果阶码为0
f = ((f & 0x007FFFFF) << 1) | (0x80000000 & f);
// 尾数不为0则尾数左移1位,尾数第1位为1则阶码加1,尾数为0则uf为0返回0
else if ((f & 0x7F800000) != 0x7F800000)// 如果阶码不为0,且非全1
f = f + 0x00800000;// 阶码加1
return f;
}

14、floatFloat2Int

/*   floatFloat2Int - Return bit-level equivalent of expression (int) f
*   for floating point argument f.
*   Argument is passed as unsigned int, but
*   it is to be interpreted as the bit-level representation of a
*   single-precision floating point value.
*   Anything out of range (including NaN and infinity) should return
*   0x80000000u.
*   Legal ops: Any integer/unsigned operations incl. ||, &&. also if, while
*   Max ops: 30
*   Rating: 4
*/
int floatFloat2Int(unsigned uf) {
unsigned INF = 1<<31;   // INF = MaxInt+1
int e = (uf>>23) & 0xff;// 阶码
int s = (uf>>31) & 1;   // 符号位
if (uf == 0) return 0;
uf <<= 8;       // 左移保留至阶码最后1位
uf |= 1<<31;    // 阶码最后一位设为1
uf >>= 8;       // 高八位全0
e -= 127;       // 阶数
if ((uf & 0x7f80000) == 0x7f80000 || e >= 32)
return INF; // 超过int范围返回INF
if (e < 0) // 小数返回0
return 0;
if (e <= 22) // 位数小于等于22位,尾数位右移
uf >>= 23-e;
else
uf <<= e-23; // 尾数大于22位,尾数为左移
if (s)
uf = ~uf + 1;// 若原uf为负数,则对此处的正数uf取反加1得其相反数
return uf;
}

15、floatPower2

/*   floatPower2 - Return bit-level equivalent of the expression 2.0^x
*   (2.0 raised to the power x) for any 32-bit integer x.
*
*   The unsigned value that is returned should have the identical bit
*   representation as the single-precision floating-point number 2.0^x.
*   If the result is too small to be represented as a denorm, return
*   0. If too large, return +INF.
*
*   Legal ops: Any integer/unsigned operations incl. ||, &&. Also if, while
*   Max ops: 30
*   Rating: 4
*/
unsigned floatPower2(int x) {
unsigned INF = 0xff << 23; // 阶码全1
int e = 127 + x;    // 得到阶码
if (x < 0) // 阶数小于0直接返回0
return 0;
if (e >= 255) // 阶码>=255直接返回INF
return INF;
return e << 23;
// 直接将阶码左移23位,尾数全0,规格化时尾数隐藏有1个1作为底数
}
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