CSAPP 之 DataLab详解，没有比这更详细的了

/* 
 * 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);
}

/* 
 * tmin - return minimum two's complement integer 
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 4
 *   Rating: 1
 */
int tmin(void) {
  return 0x1<<31;
}

/*
 * 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) {
  int i = x+1;//Tmin,1000...
  x=x+i;//-1,1111...
  x=~x;//0,0000...
  i=!i;//exclude x=0xffff...
  x=x+i;//exclude x=0xffff...
  return !x;
}

/* 
 * 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) {
  int mask = 0xAA+(0xAA<<8);
  mask=mask+(mask<<16);
  return !((mask&x)^mask);
}

/* 
 * negate - return -x 
 *   Example: negate(1) = -1.
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 5
 *   Rating: 2
 */
int negate(int x) {
  return ~x+1;
}

/* 
 * 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) {
  int sign = 0x1<<31;
  int upperBound = ~(sign|0x39);
  int lowerBound = ~0x30;
  upperBound = sign&(upperBound+x)>>31;
  lowerBound = sign&(lowerBound+1+x)>>31;
  return !(upperBound|lowerBound);
}

/* 
 * conditional - same as x ? y : z 
 *   Example: conditional(3,4,5) = 4
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 16
 *   Rating: 3
 */
int conditional(int x, int y, int z) {
  x = !!x;
  x = ~x+1;
  return (x&y)|(~x&z);
}

/* 
 * 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 negX=~x+1;//-x
  int addX=negX+y;//y-x
  int checkSign = addX>>31&1; //y-x的符号
  int leftBit = 1<<31;//最大位为1的32位有符号数
  int xLeft = x&leftBit;//x的符号
  int yLeft = y&leftBit;//y的符号
  int bitXor = xLeft ^ yLeft;//x和y符号相同标志位，相同为0不同为1
  bitXor = (bitXor>>31)&1;//符号相同标志位格式化为0或1
  return ((!bitXor)&(!checkSign))|(bitXor&(xLeft>>31));//返回1有两种情况：符号相同标志位为0（相同）位与 y-x 的符号为0（y-x>=0）结果为1；符号相同标志位为1（不同）位与x的符号位为1（x<0）
}

/* 
 * 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) {

  return ((x|(~x+1))>>31)+1;
}

/* 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 b16,b8,b4,b2,b1,b0;
  int sign=x>>31;
  x = (sign&~x)|(~sign&x);//如果x为正则不变，否则按位取反（这样好找最高位为1的，原来是最高位为0的，这样也将符号位去掉了）


// 不断缩小范围
  b16 = !!(x>>16)<<4;//高十六位是否有1
  x = x>>b16;//如果有（至少需要16位），则将原数右移16位
  b8 = !!(x>>8)<<3;//剩余位高8位是否有1
  x = x>>b8;//如果有（至少需要16+8=24位），则右移8位
  b4 = !!(x>>4)<<2;//同理
  x = x>>b4;
  b2 = !!(x>>2)<<1;
  x = x>>b2;
  b1 = !!(x>>1);
  x = x>>b1;
  b0 = x;
  return b16+b8+b4+b2+b1+b0+1;//+1表示加上符号位
}

/* 
 * 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) {
  int exp = (uf&0x7f800000)>>23;
  int sign = uf&(1<<31);
  if(exp==0) return uf<<1|sign;
  if(exp==255) return uf;
  exp++;
  if(exp==255) return 0x7f800000|sign;
  return (exp<<23)|(uf&0x807fffff);
}

/* 
 * 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) {
  int s_    = uf>>31;
  int exp_  = ((uf&0x7f800000)>>23)-127;
  int frac_ = (uf&0x007fffff)|0x00800000;
  if(!(uf&0x7fffffff)) return 0;

  if(exp_ > 31) return 0x80000000;
  if(exp_ < 0) return 0;

  if(exp_ > 23) frac_ <<= (exp_-23);
  else frac_ >>= (23-exp_);

  if(!((frac_>>31)^s_)) return frac_;
  else if(frac_>>31) return 0x80000000;
  else return ~frac_+1;
}

/* 
 * 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: 31 
 *   Rating: 4
 */
unsigned floatPower2(int x) {

  int INF = 0xff<<23;
  int exp = x + 127;
  if(exp <= 0) return 0;
  if(exp >= 255) return INF;
  return exp << 23;
}