CSAPP Data Lab

/*
 * 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.

/* 
 * 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);
}

/* 
 * 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) {
  return (x >> (n << 3)) & 0xff;
}

/* 
 * logicalShift - shift x to the right by n, using a logical shift
 *   Can assume that 0 <= n <= 31
 *   Examples: logicalShift(0x87654321,4) = 0x08765432
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 20
 *   Rating: 3 
 */
int logicalShift(int x, int n) {
  int mask;

  mask = ~(((1 << 31) >> n) << 1); // mask 0{n}1{32-n}

  x = (x >> n) & mask;

  return x;
}

/*
 * 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 tmp, mask1, mask2, mask3, mask4, mask5, v;

  tmp = 0x55 | (0x55 << 8);
  mask1 = tmp | (tmp << 16); // 0x55555555

  tmp = 0x33 | (0x33 << 8);
  mask2 = tmp | (tmp << 16); // 0x33333333

  tmp = 0x0F | (0x0F << 8);
  mask3 = tmp | (tmp << 16); // 0x0F0F0F0F

  mask4 = 0xFF | (0xFF << 16); // 0x00FF00FF

  tmp = 0xFF | (0xFF << 8);
  mask5 = tmp | (0 << 16); // 0x0000FFFF

  v = (x & mask1) + ((x >> 1) & mask1);
  v = (v & mask2) + ((v >> 2) & mask2);
  v = (v & mask3) + ((v >> 4) & mask3);
  v = (v & mask4) + ((v >> 8) & mask4);
  v = (v & mask5) + ((v >> 16) & mask5);

  return v;
}

So if I have number 395 in binary 0000000110001011 (0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1)
After the first step I have:      0000000101000110 (0+0 0+0 0+0 0+1 1+0 0+0 1+0 1+1) = 00 00 00 01 01 00 01 10
In the second step I have:        0000000100010011 ( 00+00   00+01   01+00   01+10 ) = 0000 0001 0001 0011
In the fourth step I have:        0000000100000100 (   0000+0001       0001+0011   ) = 00000001 00000100
In the last step I have:          0000000000000101 (       00000001+00000100       )

/* 
 * bang - Compute !x without using !
 *   Examples: bang(3) = 0, bang(0) = 1
 *   Legal ops: ~ & ^ | + << >>
 *   Max ops: 12
 *   Rating: 4 
 */
int bang(int x) {
  return ((x | (~x + 1)) >> 31) + 1;
}

/* 
 * tmin - return minimum two's complement integer 
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 4
 *   Rating: 1
 */
int tmin(void) {
  return 0x80 << 24;
}

/* 
 * 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) {
  // (x << (32 - n)) >> (32 - n) equals x

  int c;

  c = 33 + ~n;

  return !(((x << c) >> c) ^ x); 
}

/* 
 * 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 bias;

  bias = (1 << n) + ~0;
  return (x + ((x >> 31) & 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) {
  int s = x >> 31;

  return !(s | (!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) {
  // x <= y => ! (x > y)
  // x > y => x - y > 0 => x + (~y + 1) > 0

  // return !(((y + (~x + 1)) >> 31) & 1); 
  // breaks down when overflow eg. -x = x when x is 0x80000000

  int sign_x, sign_y, r;

  sign_x = (x >> 31) & 1;
  sign_y = (y >> 31) & 1;

  /* 1) sign_y = sign_x: y >= x if the index of first '1'
   *    in y is larger than in x (reduce to sign(x + ~y) is 1).
   * 2) sign_y != sign_x: y >= x if sign_y = 0 and sign_x = 1
   * */

  r = (!(sign_x ^ sign_y)) & (((x + ~y) >> 31) & 1);
  return r | ((!sign_y) & sign_x);
}

/*
 * 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) {

  int tmp, mask1, mask2, mask3, mask4, mask5, v;

  // most significant bit
  x = x | (x >> 1);
  x = x | (x >> 2);
  x = x | (x >> 4);
  x = x | (x >> 8);
  x = x | (x >> 16);  // eg. 0010 1011 => 0011 1111
  // MSB is x & (~(x >> 1))

  // bitCount  
  tmp = 0x55 | (0x55 << 8);
  mask1 = tmp | (tmp << 16); // 0x55555555

  tmp = 0x33 | (0x33 << 8);
  mask2 = tmp | (tmp << 16); // 0x33333333

  tmp = 0x0F | (0x0F << 8);
  mask3 = tmp | (tmp << 16); // 0x0F0F0F0F

  mask4 = 0xFF | (0xFF << 16); // 0x00FF00FF

  tmp = 0xFF | (0xFF << 8);
  mask5 = tmp | (0 << 16); // 0x0000FFFF

  v = (x & mask1) + ((x >> 1) & mask1);
  v = (v & mask2) + ((v >> 2) & mask2);
  v = (v & mask3) + ((v >> 4) & mask3);
  v = (v & mask4) + ((v >> 8) & mask4);
  v = (v & mask5) + ((v >> 16) & mask5);

  return v + ~0; // x - 1
}

/* 
 * 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) {

  if (((uf << 1) >> 24) == 0xFF && ((uf << 9) != 0))
    return uf;
  return (1 << 31) ^ uf;
}

/* 
 * 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) {
  int sign, exp, frac, bitc, tailb;

  if (x == 0) return 0;
  else if (x == 0x80000000) return 0xCF000000;

  sign = (x >> 31) & 1;
  if (sign) x = -x;

  // count bits to the right of MSB
  bitc = 1;
  while ((x >> bitc) != 0)
    bitc++;
  bitc--;

  exp = bitc + 127;

  x = x << (31 - bitc); // clear all those zeros to the left of MSB
  frac = (x >> 8) & 0x7FFFFF;

  // round to even (nearest) 
  if (bitc > 23) {
    tailb = x & 0xFF; // byte to round

    if ((tailb > 128) || ((tailb == 128) && (frac & 1))) {
      frac += 1;
      if (frac >> 23) {
        exp += 1;
        frac = 0;
      } 
    }
  }

  return (sign << 31) | (exp << 23) | frac;
}

/* 
 * 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) {
  if ((uf & 0x7F800000) == 0) { // denormalized
    uf = ((uf & 0x007FFFFF) << 1) | (0x80000000 & uf);
  } else if ((uf & 0x7F800000) != 0x7F800000) { // normalized
    uf = uf + 0x00800000;
  } // NAN

  return uf;
}