bits.c

/* 
 * 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
/* 
 * bitXor - x^y using only ~ and & 
 *   Example: bitXor(4, 5) = 1
 *   Legal ops: ~ &
 *   Max ops: 14
 *   Rating: 1
 */
int bitXor(int x, int y) {
  // using xor's defination and De Morgan's law
  return (~(x & y)) & (~((~x) & (~y)));
}
/* 
 * allOddBits - return 1 if all odd-numbered bits in word set to 1
 *   Examples allOddBits(0xFFFFFFFD) = 0, allOddBits(0xAAAAAAAA) = 1
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 12
 *   Rating: 2
 */
int allOddBits(int x) {
  // build mask: 0xAAAAAAAA
  int mask = (0xAA << 8) + 0xAA;
  mask = (mask << 16) + mask;

  return !((x & mask) ^ mask);
}
/* 
 * getByte - Extract byte n from word x
 *   Bytes numbered from 0 (LSB) to 3 (MSB)
 *   Examples: getByte(0x12345678,1) = 0x56
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 6
 *   Rating: 2
 */
int getByte(int x, int n) {
  // right shift (8 * n) bits 
  // then using mask 0xFF to set other bits to zero
  return (x >> (n << 3)) & 0xFF;
}
/* 
 * reverseBytes - reverse the bytes of x
 *   Example: reverseBytes(0x01020304) = 0x04030201
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 25
 *   Rating: 3
 */
int reverseBytes(int x) {
  // get each byte by right shift
  int mask = 0xFF;
  int byte0 = x & mask;
  int byte1 = (x >> 8) & mask;
  int byte2 = (x >> 16) & mask;
  int byte3 = (x >> 24) & mask;
 
  // assembly each byte reversely
  return byte3 | (byte2 << 8) | (byte1 << 16) | (byte0 << 24);
}
/* 
 * bitMask - Generate a mask consisting of all 1's 
 *   lowbit and highbit
 *   Examples: bitMask(5,3) = 0x38
 *   Assume 0 <= lowbit <= 31, and 0 <= highbit <= 31
 *   If lowbit > highbit, then mask should be all 0's
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 16
 *   Rating: 3
 */
int bitMask(int highbit, int lowbit) {
  /* build two sub-masks based on highbit and lowbit
   * highPart is to right shift -1 to (highbit + 1) bits
   * lowPart is to right shift -1 to lowbit bits
   */
  int negOne = ~0;
  int highPart = (negOne << highbit) << 1;
  int lowPart = negOne << lowbit;
  
  // using xor to get the different part
  // using lowPart as a mask when lowbit > highbit
  return (highPart ^ lowPart) & lowPart;
}
/* 
 * bang - Compute !x without using !
 *   Examples: bang(3) = 0, bang(0) = 1
 *   Legal ops: ~ & ^ | + << >>
 *   Max ops: 12
 *   Rating: 4 
 */
int bang(int x) {
  /*
   * when x = 0, the sign bit of x | (-x) is 0
   * when x != 0, the sign bit of x | (-x) is 1
   * after right shifting 31 bits, it becomes 0 or 0xFFFFFFFF
   * using add 1 instead of ! operation
   */
  int negX = ~x + 1;
  int sign = (x | negX) >> 31;

  return sign + 1;
}
/* 
 * isNegative - return 1 if x < 0, return 0 otherwise 
 *   Example: isNegative(-1) = 1.
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 6
 *   Rating: 2
 */
int isNegative(int x) {
  return (x >> 31) & 1;
}
/* 
 * negate - return -x 
 *   Example: negate(1) = -1.
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 5
 *   Rating: 2
 */
int negate(int x) {
  return ~x + 1;
}
/* 
 * subOK - Determine if can compute x-y without overflow
 *   Example: subOK(0x80000000,0x80000000) = 1,
 *            subOK(0x80000000,0x70000000) = 0, 
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 20
 *   Rating: 3
 */
int subOK(int x, int y) {
  /*
   * overflow of sub happens iff 
   * 1) x and y have different signs
   * 2) res = x - y has different sign with x
   */
  int res = x + (~y + 1);
  int sameSign = x ^ y;
  int resSign = res ^ x;

  return !((sameSign & resSign) >> 31);
}
/* 
 * isLess - if x < y  then return 1, else return 0 
 *   Example: isLess(4,5) = 1.
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 24
 *   Rating: 3
 */
int isLess(int x, int y) {
  /*
   * there are 2 cases can lead to x < y
   * 1) x < 0 and y >= 0
   * 2) x and y have the same sign,
   *    and x - y is negative
   */
  int res = x + (~y + 1);
  int flag1 = x & (~y);
  int flag2 = (~(x ^ y)) & res;

  return (flag1 | flag2) >> 31 & 1;
}
/*
 * multFiveEighths - multiplies by 5/8 rounding toward 0.
 *   Should exactly duplicate effect of C expression (x*5/8),
 *   including overflow behavior.
 *   Examples: multFiveEighths(77) = 48
 *             multFiveEighths(-22) = -13
 *             multFiveEighths(1073741824) = 13421728 (overflow)
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 12
 *   Rating: 3
 */
int multFiveEighths(int x) {
  int multFive = (x << 2) + x;
  
  // if multFive is negative, add 2^3 - 1 = 7 before right shift
  int addNum = 7 & (multFive >> 31);
  int divEight = (multFive + addNum) >> 3;
  
  return divEight;
}
/* 
 * float_abs - Return bit-level equivalent of absolute value of 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_abs(unsigned uf) {
  unsigned mask = 0x7FFFFFFF;		
  unsigned minNaN = 0x7F800001;
  unsigned res = uf & mask;		// set sign bit to 0
  
  // return argument if it is NaN, all NaN >= minimum NaN
  if (res >= minNaN)
  {
    return uf;
  }
  else
  {
    return res;
  }
}
/* 
 * float_f2i - 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 float_f2i(unsigned uf) {
  unsigned sign = uf >> 31;
  unsigned exp = (uf >> 23) & 0xFF;
  unsigned frac =(uf & 0x7FFFFF);
  unsigned bias = 0x7F;
  unsigned res = frac;
  
  // special cases: NaN and Inf
  if (exp == 0xFF) 
  {
    return 0x80000000u;
  } 
  
  // denormalized case and normalized exp less than Bias cases
  if (exp < bias) 
  {
    return 0x0;
  }
  
  // normalized cases
  exp -= bias;
  
  // overflow case
  if (exp >= 31) 
  {
    return 0x80000000u;
  } 
  
  // get integer result after shift corresponding bits
  if (exp > 22) 
  {
    res = frac << (exp - 23);
  } 
  else 
  {
    res = frac >> (23 - exp);
  }

  // add 1 << exp for normalized case
  res += 1 << exp;
  
  // if sign = 1, change its sign
  if (sign) {
    res = -res;
  }
  
  return res;
}