text: /* 
   * CS:APP Data Lab 
   * 
   * <Please put your name and userid here>
   * 
   * bits.c - Source file with your solutions to the Lab.
   *          This is the file you will hand in to your instructor.
   *
   * WARNING: Do not include the <stdio.h> header; it confuses the dlc
   * compiler. You can still use printf for debugging without including
   * <stdio.h>, although you might get a compiler warning. In general,
   * it's not good practice to ignore compiler warnings, but in this
   * case it's OK.  
   */
  #include <stdio.h>
  #if 0
  /*
   * Instructions to Students:
   *
   * STEP 1: Read the following instructions carefully.
   */
  
  You will provide your solution to the Data Lab by
  editing the collection of functions in this source file.
  
  INTEGER CODING RULES:
   
    Replace the "return" statement in each function with one
    or more lines of C code that implements the function. Your code 
    must conform to the following style:
   
    int Funct(arg1, arg2, ...) {
        /* brief description of how your implementation works */
        int var1 = Expr1;
        ...
        int varM = ExprM;
  
        varJ = ExprJ;
        ...
        varN = ExprN;
        return ExprR;
    }
  
    Each "Expr" is an expression using ONLY the following:
    1. Integer constants 0 through 255 (0xFF), inclusive. You are
        not allowed to use big constants such as 0xffffffff.
    2. Function arguments and local variables (no global variables).
    3. Unary integer operations ! ~
    4. Binary integer operations & ^ | + << >>
      
    Some of the problems restrict the set of allowed operators even further.
    Each "Expr" may consist of multiple operators. You are not restricted to
    one operator per line.
  
    You are expressly forbidden to:
    1. Use any control constructs such as if, do, while, for, switch, etc.
    2. Define or use any macros.
    3. Define any additional functions in this file.
    4. Call any functions.
    5. Use any other operations, such as &&, ||, -, or ?:
    6. Use any form of casting.
    7. Use any data type other than int.  This implies that you
       cannot use arrays, structs, or unions.
  
   
    You may assume that your machine:
    1. Uses 2s complement, 32-bit representations of integers.
    2. Performs right shifts arithmetically.
    3. Has unpredictable behavior when shifting if the shift amount
       is less than 0 or greater than 31.
  
  
  EXAMPLES OF ACCEPTABLE CODING STYLE:
    /*
     * 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;
    }
  
    /*
     * 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;
    }
  
  FLOATING POINT CODING RULES
  
  For the problems that require you to implement floating-point operations,
  the coding rules are less strict.  You are allowed to use looping and
  conditional control.  You are allowed to use both ints and unsigneds.
  You can use arbitrary integer and unsigned constants. You can use any arithmetic,
  logical, or comparison operations on int or unsigned data.
  
  You are expressly forbidden to:
    1. Define or use any macros.
    2. Define any additional functions in this file.
    3. Call any functions.
    4. Use any form of casting.
    5. Use any data type other than int or unsigned.  This means that you
       cannot use arrays, structs, or unions.
    6. Use any floating point data types, operations, or constants.
  
  
  NOTES:
    1. Use the dlc (data lab checker) compiler (described in the handout) to 
       check the legality of your solutions.
    2. Each function has a maximum number of operations (integer, logical,
       or comparison) that you are allowed to use for your implementation
       of the function.  The max operator count is checked by dlc.
       Note that assignment ('=') is not counted; you may use as many of
       these as you want without penalty.
    3. Use the btest test harness to check your functions for correctness.
    4. Use the BDD checker to formally verify your functions
    5. The maximum number of ops for each function is given in the
       header comment for each function. If there are any inconsistencies 
       between the maximum ops in the writeup and in this file, consider
       this file the authoritative source.
  
  /*
   * STEP 2: Modify the following functions according the coding rules.
   * 
   *   IMPORTANT. TO AVOID GRADING SURPRISES:
   *   1. Use the dlc compiler to check that your solutions conform
   *      to the coding rules.
   *   2. Use the BDD checker to formally verify that your solutions produce 
   *      the correct answers.
   */
  
  #endif
  //1
  /* 
   * 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 2;
  }
  /* 
   * tmin - return minimum two's complement integer 
   *   Legal ops: ! ~ & ^ | + << >>
   *   Max ops: 4
   *   Rating: 1
   */
  int tmin(void)
  {
    /*
    最小的二进制补码数，就是符号位为1，其余位全部为0
    */
    return 0x80000000;
    //return 1 << 31;
  }
  //2
  /*
   * 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)
  {
    /*
    最大的二进制补码：0x7fffffff
    0111...1111, 符号位为0，后面都是1
    这个数字+1后就成为：
    1000...0000, 与直接按位取反(~)结果相同
    而判断两结果是否相同的操作是异或(XOR)
    但是! 要注意0 ^ 1 = 1, 0 ^ 0 = 0
    也就是最后还需要在逻辑上取反一次(!操作符)
    */
    int res = (x + 1) ^ ~x;
    return !res;
  }
  /* 
   * 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) + (0xAA << 16) + (0xAA << 24);
    return !((x & mask) ^ mask);
  }
  /* 
   * negate - return -x 
   *   Example: negate(1) = -1.
   *   Legal ops: ! ~ & ^ | + << >>
   *   Max ops: 5
   *   Rating: 2
   */
  int negate(int x)
  {
    return ~x + 1;
  }
  //3
  /* 
   * 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 r1 = (0x39 + (~x + 1)) >> 31; // if true r1 == 0x0, otherwise, r1 = 0xFFFFFFFF
    int r2 = (x + (~0x30 + 1)) >> 31; // if true r2 == 0x0, otherwise, r2 = 0xFFFFFFFF
  
    return (!r1) & (!r2);
  }
  /* 
   * 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)
  {
    int temp = !!x;
    return (temp & y) | (~temp & 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 sx = (x >> 31) & 0x1;                 // sign bit of x
    int sy = (y >> 31) & 0x1;                 // sign bit of y
    int sdiff = ((y + (~x + 1)) >> 31) & 0x1; // sign bit of y-x
    return (((sx ^ sy) & sx) | !sdiff & !(sx ^ sy));
  }
  //4
  /* 
   * 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)
  {
    int negX = ~x + 1;
    int sign = (negX | x) >> 31;
    return sign + 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;            // signed bit, 0x0 if non-negative, 0xFFFFFFFF if negative
    x = (sign & ~x) | (~sign & x); // If is negative number, flip it.
  
    b16 = !!(x >> 16) << 4; // whether most significant 16 bits have 1. If yes, b16 =16, if not, b16 = 0
    x = x >> b16;           // If yes, right shift 16 bits; if no, do not right shift.
    b8 = !!(x >> 8) << 3;   // whether the rest most significant 8 bits have 1.
    x = x >> b8;
    b4 = !!(x >> 4) << 2;
    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 is the sign bit.
  }
  //float
  /* 
   * 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 s = (uf >> 31) & (0x1);
    unsigned expr = (uf >> 23) & (0xff);
    unsigned frac = uf & 0x7fffff;
  
    //0
    if (expr == 0 && frac == 0)
    {
      return uf;
    }
  
    //INF or NaN
    if (expr == 0xff)
    {
      return uf;
    }
  
    //denormalized非规格化的数
    if (expr == 0)
    {
      //E = expr - bias = expr - 127
      frac = frac << 1;
      return (s << 31) | frac;
    }
  
    //normalized规格化的数
    expr++; //相当于×2
    return (s << 31) | (expr << 23) | frac;
  }
  /* 
   * 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 exp = (uf >> 23) & 0xFF;
    int frac = uf & 0x7FFFFF;
    int sign = uf & (1 << 31); // negative 0x80000000, positive 0x0.
  
    if (exp == 0xFF)
      return 0x80000000u; // if out of range, return 0x80000000
  
    if (exp == 0x0)
      return 0; // if de-norm number, means its range is (-1, 1)
  
    int frac1 = frac | 0x800000; // Add the hidden 1 in front of frac
    int biasedExp = exp - 127;   // E = e - Bias, Bias = 127 = 0x7F, -bias = 0xFFFFFF81
  
    if (biasedExp > 31)
      return 0x80000000;
    else if (biasedExp < 0)
      return 0;
  
    if (biasedExp > 23)
      frac1 <<= (biasedExp - 23);
    else
      frac1 >>= (23 - biasedExp);
  
    if (sign)
      return ~frac1 + 1; // if negative number
    else if (frac1 >> 31)
      return 0x80000000; // if frac1 overflows, return 0x80000000;
    else
      return frac1;
  }
  /* 
   * 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)
  {
    int exp = x + 127;
    if (exp <= 0)
    {
      return 0;
    }
    if (exp >= 255)
    {
      return 0xff << 23;
    }
    return exp << 23;
  }
  