/*
 * 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.
 */

#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 an integer by more
     than the word size.

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 implent 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 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 operators (! ~ & ^ | + << >>)
     that you are allowed to use for your implementation of the function.
     The max operator count is checked by dlc. Note that '=' 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
/*
 * bitAnd - x&y using only ~ and |
 *   Example: bitAnd(6, 5) = 4
 *   Legal ops: ~ |
 *   Max ops: 8
 *   Rating: 1
 */
int bitAnd(int x, int y) {
    return ~((~x)|(~y));//運用狄摩根定律
}
/*
 * getByte - Extract//提取 byte n from word x
 *   Bytes numbered from 0 (LSB) to 3 (MSB)//最低有效位為0,依次,最高有效位是3,x中2位為1個位元組
 *   Examples: getByte(0x12345678,1) = 0x56
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 6
 *   Rating: 2
 */
int getByte(int x, int n) {
    int left = n << 3;
    int shift_num = x >> left;//算數右移8*n位
    return shift_num & 0xFF;//保留最後8位
}
/*
 * logicalShift - shift x to the right by n, using a logical shift//邏輯右移
 *   Can assume that 0 <= n <= 31
 *   Examples: logicalShift(0x87654321,4) = 0x08765432
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 20
 *   Rating: 3
 */
int logicalShift(int x, int n) {//n >= 0
    /*if(n == 0){//不能用if
        return x;
    }
    else{
        x = x >> n;
        int temp = ~(1 << 31);//形成0x7FFF
        temp = temp >> (n-1);
        return x & temp;
    }*/
    //另一種解法
    int tmp = ~(1 << 31);
    tmp = ((tmp >> n) << 1) + 1;
    tmp = tmp & (x >> n);
    return tmp;
}
/*
 * bitCount - returns count of number of 1's in word
 *   Examples: bitCount(5) = 2, bitCount(7) = 3
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 40
 *   Rating: 4
 */
int bitCount(int x) {
    int bits = (0x01 << 8) | 0x01;
    bits = (bits << 16) | bits;
    int sum = 0;
    sum += x & bits;
    sum += (x >> 1) & bits;
    sum += (x >> 2) & bits;
    sum += (x >> 3) & bits;
    sum += (x >> 4) & bits;
    sum += (x >> 5) & bits;
    sum += (x >> 6) & bits;
    sum += (x >> 7) & bits;
    //分成4段求解，然後要不斷右移求得各段的sum
    return (sum & 0xFF) + ((sum >> 8) & 0xFF) + ((sum >> 16) & 0xFF) + ((sum >> 24) & 0xFF);
}
/*
 * bang - Compute !x without using !
 *   Examples: bang(3) = 0, bang(0) = 1
 *   Legal ops: ~ & ^ | + << >>
 *   Max ops: 12
 *   Rating: 4
 */
int bang(int x) {
    int temp = ~x + 1;//-x
    x = temp | x;
    return (x >> 31) + 1;//結果為-1+1和0+1
}
/*
 * tmin - return minimum two's complement integer
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 4
 *   Rating: 1
 */
int tmin(void) {
    return 1 << 31;//TMIN為最小的
}
/*
 * fitsBits - return 1 if x can be represented as an
 *  n-bit, two's complement integer.
 *   1 <= n <= 32
 *   Examples: fitsBits(5,3) = 0, fitsBits(-4,3) = 1
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 15
 *   Rating: 2
 */
int fitsBits(int x, int n) {
    int shift = 32 + (~n + 1);
    return !(x ^ ((x << shift) >> shift));//先左移32-n位，再右移32-n位，再異或取反
}
/*
 * divpwr2 - Compute x/(2^n), for 0 <= n <= 30
 *  Round toward zero
 *   Examples: divpwr2(15,1) = 7, divpwr2(-33,4) = -2
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 15
 *   Rating: 2
 */
int divpwr2(int x, int n) {
    int signx = x >> 31;     //全0，或者全1
    int mask = (1 << n) + (~0);//得到2^n - 1
    int bias = signx & mask;//如果x是正數，則bias為0，即不用加，直接移位，如果x為負數，加上偏置量之後在移位
    return (x + bias) >> n;
}
/*
 * negate - return -x
 *   Example: negate(1) = -1.
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 5
 *   Rating: 2
 */
int negate(int x) {
    return ~x + 1;
}
/*
 * isPositive - return 1 if x > 0, return 0 otherwise
 *   Example: isPositive(-1) = 0.
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 8
 *   Rating: 3
 */
int isPositive(int x) {
    return !( x >> 31 | (!x));
}
/*
 * 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 singx = (x >> 31) & 1;
    int singy = (y >> 31) & 1;    //比較符號位 1 0 = 1,  0 1 = 0;
    int sing = (singx ^ singy) & singx; //保證singx和singy異號
    int tmp = x + ((~y) + 1); // x - y, 同號情況下,異號情況下會越界 0 0 = , 1 1 =
    tmp = ((tmp>>31)&1) & (!(singx ^ singy));// 保證singx 和 singy 同號
    //int t = (!(x ^ y)); //判斷相等
    return (sing | tmp | ((!(x ^ y)))); //三種情況，複數-正數，同號減不會越界且符號位為1，x==y
}
/*
 * ilog2 - return floor(log base 2 of x), where x > 0
 *   Example: ilog2(16) = 4
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 90
 *   Rating: 4
 */
int ilog2(int x) {//尋找最左邊的1，答案為其後面的位數
    int ans = 0;
    ans += (!!(x >> 16)) << 4;
    ans += (!!(x >> (ans + 8))) << 3;
    ans += (!!(x >> (ans + 4))) << 2;
    ans += (!!(x >> (ans + 2))) << 1;
    ans += (!!(x >> (ans + 1)));//二分的思想
    ans += (!!ans) + (~0) + (!(1 ^ x));//考慮邊界，即x==0和x==1的情況，當x==0或1時，前面的ans為0
    return ans;
}
/*
 * float_neg - Return bit-level equivalent of expression -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 representations of
 *   single-precision floating point values.
 *   When argument is NaN, return argument.
 *   Legal ops: Any integer/unsigned operations incl. ||, &&. also if, while
 *   Max ops: 10
 *   Rating: 2
 */
unsigned float_neg(unsigned uf) {//浮點數取負
    unsigned point = 0x80000000;
    unsigned NaN = 0x7FC00000;
    unsigned inf = 0xFFC00000;//符號位+-兩種情況NaN
    if (uf == NaN || uf == inf)//排除兩種特殊情況
        return uf;
    return uf ^ point;//變符號位即可
}
/*
 * float_i2f - Return bit-level equivalent of expression (float) x
 *   Result is returned as unsigned int, but
 *   it is to be interpreted as the bit-level representation of a
 *   single-precision floating point values.
 *   Legal ops: Any integer/unsigned operations incl. ||, &&. also if, while
 *   Max ops: 30
 *   Rating: 4
 */
unsigned float_i2f(int x) {
    unsigned sign=x>>31&1;
    unsigned i;
    unsigned exponent;
    unsigned fraction;
    unsigned delta;
    unsigned fraction_mask;
    if(x==0)
        return x;
    else if(x==0x80000000)
        exponent=158;
    else{
        if (sign)
            x = -x;

        i = 30;
        while ( !(x >> i) )
            i--;

        exponent = i + 127;
        x = x << (31 - i);
        fraction_mask = 0x7fffff;
        fraction = fraction_mask & (x >> 8);
        x = x & 0xff;
        delta = x > 128 || ((x == 128) && (fraction & 1));
        fraction += delta;
        if(fraction >> 23) {
            fraction &= fraction_mask;
            exponent += 1;
        }
    }
    return (sign<<31)|(exponent<<23)|fraction;
}
/*
 * float_twice - 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 float_twice(unsigned uf) {

    unsigned f = uf;
    if ((f & 0x7F800000) == 0){
        //左移一位
        f = ((f & 0x007FFFFF) << 1) | (0x80000000 & f);
    }
    else if ((f & 0x7F800000) != 0x7F800000){
        f =f + 0x00800000;
    }
    return f;

}