🧪CS-APP Datalab

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! ~ & ^ | + << >>

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//1
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/*
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 * bitXor - x^y using only ~ and &
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 *   Example: bitXor(4, 5) = 1
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 *   Legal ops: ~ &
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 *   Max ops: 14
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 *   Rating: 1
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 */
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int bitXor(int x, int y) {
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  return ~(~x&~y)&~(x&y);
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}

1
/*
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 * tmin - return minimum two's complement integer
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 *   Legal ops: ! ~ & ^ | + << >>
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 *   Max ops: 4
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 *   Rating: 1
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 */
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int tmin(void) {
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  return 1 << 31;
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}

1
/*
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 * isTmax - returns 1 if x is the maximum, two's complement number,
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 *     and 0 otherwise
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 *   Legal ops: ! ~ & ^ | +
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 *   Max ops: 10
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 *   Rating: 1
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 */
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int isTmax(int x) {
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  return !!(~x)&!((~x)^(x+1));
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}

1
/*
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 * allOddBits - return 1 if all odd-numbered bits in word set to 1
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 *   where bits are numbered from 0 (least significant) to 31 (most significant)
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 *   Examples allOddBits(0xFFFFFFFD) = 0, allOddBits(0xAAAAAAAA) = 1
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 *   Legal ops: ! ~ & ^ | + << >>
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 *   Max ops: 12
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 *   Rating: 2
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 */
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int allOddBits(int x) {
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  int mask = 0x55 + (0x55 << 8);
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  mask = mask + (mask << 16);
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  return !(~(mask | x));
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}

1
/*
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 * negate - return -x
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 *   Example: negate(1) = -1.
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 *   Legal ops: ! ~ & ^ | + << >>
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 *   Max ops: 5
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 *   Rating: 2
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 */
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int negate(int x) {
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  return ~x + 1;
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}

1
/*
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 * isAsciiDigit - return 1 if 0x30 <= x <= 0x39 (ASCII codes for characters '0' to '9')
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 *   Example: isAsciiDigit(0x35) = 1.
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 *            isAsciiDigit(0x3a) = 0.
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 *            isAsciiDigit(0x05) = 0.
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 *   Legal ops: ! ~ & ^ | + << >>
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 *   Max ops: 15
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 *   Rating: 3
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 */
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int isAsciiDigit(int x) {
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  int f3 = !((x >> 4) ^ 3);
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  int f0t9 =!! (!(x & 8) + !(x & 6));
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  return f3 & f0t9;
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}

1
/*
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 * conditional - same as x ? y : z
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 *   Example: conditional(2,4,5) = 4
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 *   Legal ops: ! ~ & ^ | + << >>
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 *   Max ops: 16
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 *   Rating: 3
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 */
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int conditional(int x, int y, int z) {
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  int f = !!x;
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  int mask = ~f + 1;
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  return (y & mask) + (z & ~mask);
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}

1
/*
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 * isLessOrEqual - if x <= y  then return 1, else return 0
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 *   Example: isLessOrEqual(4,5) = 1.
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 *   Legal ops: ! ~ & ^ | + << >>
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 *   Max ops: 24
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 *   Rating: 3
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 */
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int isLessOrEqual(int x, int y) {
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  int fx = x >> 31;
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  int fy = y >> 31;
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  int f = fx ^ fy;
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  int z = x + ~y + 1;
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  return !!((f & fx) | ((!f) & ((!z) | z >> 31)));
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}

1
/*
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 * logicalNeg - implement the ! operator, using all of
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 *              the legal operators except !
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 *   Examples: logicalNeg(3) = 0, logicalNeg(0) = 1
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 *   Legal ops: ~ & ^ | + << >>
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 *   Max ops: 12
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 *   Rating: 4
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 */
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int logicalNeg(int x) {
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  return (((~x + 1) | x) >> 31) + 1;
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}

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/* howManyBits - return the minimum number of bits required to represent x in
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 *             two's complement
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 *  Examples: howManyBits(12) = 5
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 *            howManyBits(298) = 10
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 *            howManyBits(-5) = 4
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 *            howManyBits(0)  = 1
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 *            howManyBits(-1) = 1
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 *            howManyBits(0x80000000) = 32
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 *  Legal ops: ! ~ & ^ | + << >>
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 *  Max ops: 90
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 *  Rating: 4
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 */
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int howManyBits(int x) {
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  int f = !!(x >> 31);
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  f = ~f + 1;
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  x = (x & ~f) + (~x & f);
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  int b16 = (!!(x >> 16)) << 4;
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  x = x >> b16;
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  int b8 = (!!(x >> 8)) << 3;
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  x = x >> b8;
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  int b4 = (!!(x >> 4)) << 2;
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  x = x >> b4;
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  int b2 = (!!(x >> 2)) << 1;
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  x = x >> b2;
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  int b1 = !!(x >> 1);
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  x = x >> b1;
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  return b16 + b8 + b4 + b2 + b1 + x + 1;
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}

1
/*
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 * floatScale2 - Return bit-level equivalent of expression 2*f for
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 *   floating point argument f.
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 *   Both the argument and result are passed as unsigned int's, but
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 *   they are to be interpreted as the bit-level representation of
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 *   single-precision floating point values.
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 *   When argument is NaN, return argument
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 *   Legal ops: Any integer/unsigned operations incl. ||, &&. also if, while
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 *   Max ops: 30
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 *   Rating: 4
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 */
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unsigned floatScale2(unsigned uf) {
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  unsigned s = uf & 0x80000000;
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  unsigned exp = uf & 0x7f800000;
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  unsigned f = uf & 0x007fffff;
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  if(!exp){
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    return s | (uf << 1);
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  }
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  if(!(exp ^ 0x7f800000)){
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    return uf;
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  }
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  exp = exp + 0x00800000;
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  if(exp == 0x7f800000){
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    return 0x7f800000 | s;
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  }
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  return s | (exp & 0x7f800000) | f;
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}

1
/*
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 * floatFloat2Int - Return bit-level equivalent of expression (int) f
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 *   for floating point argument f.
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 *   Argument is passed as unsigned int, but
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 *   it is to be interpreted as the bit-level representation of a
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 *   single-precision floating point value.
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 *   Anything out of range (including NaN and infinity) should return
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 *   0x80000000u.
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 *   Legal ops: Any integer/unsigned operations incl. ||, &&. also if, while
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 *   Max ops: 30
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 *   Rating: 4
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 */
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int floatFloat2Int(unsigned uf) {
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  unsigned s = uf & 0x80000000,
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           e = uf & 0x7f800000,
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           f = uf & 0x007fffff;
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  int exp = (e >> 23) - 0x7f;
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  unsigned res = f | 0x00800000;
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  if(exp < 0) return 0;
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  if(exp >= 31) return 0x80000000;
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  if(exp < 23)exp = 23 - exp;
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  else exp = exp - 23;
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  res = res >> exp;
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  if(s)return -res;
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  else return res;
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}

1
/*
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 * floatPower2 - Return bit-level equivalent of the expression 2.0^x
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 *   (2.0 raised to the power x) for any 32-bit integer x.
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 *
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 *   The unsigned value that is returned should have the identical bit
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 *   representation as the single-precision floating-point number 2.0^x.
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 *   If the result is too small to be represented as a denorm, return
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 *   0. If too large, return +INF.
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 *
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 *   Legal ops: Any integer/unsigned operations incl. ||, &&. Also if, while
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 *   Max ops: 30
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 *   Rating: 4
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 */
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unsigned floatPower2(int x) {
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  int exp = 0x7f + x;
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  if(exp < 0x00)return 0;
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  if(exp >= 0xff)return 0x7f800000;
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  if(exp == 0x00)return 1;
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  return exp << 23;
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}