datalab.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
/* 
 * evenBits - return word with all even-numbered bits set to 1
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 8
 *   Rating: 1
 */
int evenBits(void) {
    int fourth = 85; //0x00000055
    int half = (fourth << 8) | fourth; //0x00005555
    int ans = (half << 16) | half; //0x55555555
    return ans;
}

/* 
 * isEqual - return 1 if x == y, and 0 otherwise 
 *   Examples: isEqual(5,5) = 1, isEqual(4,5) = 0
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 5
 *   Rating: 2
 */
int isEqual(int x, int y) {
    return !(x^y);
}
/* 
 * byteSwap - swaps the nth byte and the mth byte
 *  Examples: byteSwap(0x12345678, 1, 3) = 0x56341278
 *            byteSwap(0xDEADBEEF, 0, 2) = 0xDEEFBEAD
 *  You may assume that 0 <= n <= 3, 0 <= m <= 3
 *  Legal ops: ! ~ & ^ | + << >>
 *  Max ops: 25
 *  Rating: 2
 */
int byteSwap(int x, int n, int m) {
    //bit positions of the bytes
    int npos = n << 3;
    int mpos = m << 3;
    //Use XOR to swap bytes. Might be easier to think of it as
    int diff = ((x>>npos)^(x>>mpos))&0xFF;
    x = x^((diff<<npos)|(diff<<mpos));
    return x;
}
/* 
 * rotateRight - Rotate x to the right by n
 *   Can assume that 0 <= n <= 31
 *   Examples: rotateRight(0x87654321,4) = 0x18765432
 *   Legal ops: ~ & ^ | + << >>
 *   Max ops: 25
 *   Rating: 3 
 */
int rotateRight(int x, int n) {
    int restn = 33+(~n); //32-n
    int nmask = ~((~0) << restn); //First n bits 0, everything else 1
    int big = x << restn; //Get the part that is shifted to the left
    int small = (x >> n) & nmask; //Get the part that's shifted to the right
    return big | small;
}
/* 
 * 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 specx = x | negx; //The sign bit is negative iff x != 0
    int signBit = (specx >> 31) & 1;
    return signBit ^ 1;
}
/* 
 * TMax - return maximum two's complement integer 
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 4
 *   Rating: 1
 */
int tmax(void) {
  return ~(1<<31);
}
/* 
 * sign - return 1 if positive, 0 if zero, and -1 if negative
 *  Examples: sign(130) = 1
 *            sign(-23) = -1
 *  Legal ops: ! ~ & ^ | + << >>
 *  Max ops: 10
 *  Rating: 2
 */
int sign(int x) {
    return (x >> 31) | (!(!x));
}
/* 
 * isGreater - if x > y  then return 1, else return 0 
 *   Example: isGreater(4,5) = 0, isGreater(5,4) = 1
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 24
 *   Rating: 3
 */
int isGreater(int x, int y) {
  int sgnx = x>>31; //< 0 => -1 else 0
  int sgny = y>>31; //< 0 => -1 else 0
  int diffsgn = sgnx ^ sgny; //same => 0 else -1
  int signOfDiff = (y+1+(~x))>>31;
  return !!(((~diffsgn) & signOfDiff) | (diffsgn & sgny));
}
/* 
 * 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) {
  int diff = x+1+(~y);
  return !(((x^y) & (x^diff))>>31);
}
/*
 * satAdd - adds two numbers but when positive overflow occurs, returns
 *          maximum possible value, and when negative overflow occurs,
 *          it returns minimum positive value.
 *   Examples: satAdd(0x40000000,0x40000000) = 0x7fffffff
 *             satAdd(0x80000000,0xffffffff) = 0x80000000
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 30
 *   Rating: 4
 */
int satAdd(int x, int y) {
  int sum = x+y;
  int overflow = ((~(x^y)) & (sum^x))>>31; //-1 if overflow, 0 otherwise
  return ((~overflow) & sum) | (overflow & (((1<<31) + (sum>>31))));
}
/* 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 nx = (x>>31)^x; //Make x positive
  int ans = 0;
  int red;
  int cond;
  int b1, b2;
  //"Binary Search" for max bit position
  red = nx>>16;
  cond = (~(!red))+1; //0 => -1 else 0
  ans = ans+((~cond)&16);
  nx = (cond&nx)^red;
  //Search between 0 and 15
  red = nx>>8;
  cond = (~(!red))+1; //0 => -1 else 0
  ans = ans+((~cond)&8);
  nx = (cond&nx)^red;
  //Search between 0 and 7
  red = nx>>4;
  cond = (~(!red))+1; //0 => -1 else 0
  ans = ans+((~cond)&4);
  nx = (cond&nx)^red;
  //Search between 0 and 3
  red = nx>>2;
  cond = (~(!red))+1; //0 => -1 else 0
  ans = ans+((~cond)&2);
  nx = (cond&nx)^red;
  //Search between 0 and 1
  b2 = nx&2;
  b1 = nx&1;
  return b2 + ((!b2)&b1) + ans + 1;
}
/* 
 * float_half - Return bit-level equivalent of expression 0.5*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_half(unsigned uf) {
  int maxExp = 2139095040; //1 in all the exponent bits
  int lowNormExp = 8388608; //1 in the lowest exponent bit
  int exp = uf&maxExp;
  int fullBase = 8388607;
  int base = uf&fullBase;
  
  if (exp == maxExp) { //NaN or INF
    
  } else if (exp > lowNormExp) {
    exp -= lowNormExp;
  } else {
    base = base|exp;
    exp = 0;
    base = base/2 + ((base%4)==3);
  }

  return (uf&0x80000000u) | exp | base;
}
/* 
 * 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) {
  int lowNormExp = 8388608; //1 in the lowest exponent bit
  int exp = 157 - ((uf>>23)&0xFF);
  int fullBase = 8388607;
  int base = ((uf&fullBase) | lowNormExp)<<7;
  int ans;
  //printf("%d %d\n", base, exp);
  if (exp > 31) return 0;
  else if (exp < 0) return 0x80000000u;
  else ans = base >> exp;
  
  if (uf>>31) return -ans;
  return ans;
}