bitutil.java

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       tot8 += pop(eights);
       i+=4;
     }

     if (i<=n-2) {
       long b=(A[i] | B[i]), c=(A[i+1] | B[i+1]);
       long u=ones ^ b;
       long twosA=(ones & b)|( u & c);
       ones=u^c;

       long foursA=twos&twosA;
       twos=twos^twosA;

       long eights=fours&foursA;
       fours=fours^foursA;

       tot8 += pop(eights);
       i+=2;
     }

     if (i<n) {
       tot += pop((A[i] | B[i]));
     }

     tot += (pop(fours)<<2)
             + (pop(twos)<<1)
             + pop(ones)
             + (tot8<<3);

     return tot;
   }

  /** Returns the popcount or cardinality of A & ~B
   * Neither array is modified.
   */
  public static long pop_andnot(long A[], long B[], int wordOffset, int numWords) {
    // generated from pop_array via sed 's/A\[\([^]]*\)\]/\(A[\1] \& ~B[\1]\)/g'
    int n = wordOffset+numWords;
    long tot=0, tot8=0;
    long ones=0, twos=0, fours=0;

    int i;
    for (i = wordOffset; i <= n - 8; i+=8) {
      /***  C macro from Hacker's Delight
       #define CSA(h,l, a,b,c) \
       {unsigned u = a ^ b; unsigned v = c; \
       h = (a & b) | (u & v); l = u ^ v;}
       ***/

      long twosA,twosB,foursA,foursB,eights;

      // CSA(twosA, ones, ones, (A[i] & ~B[i]), (A[i+1] & ~B[i+1]))
      {
        long b=(A[i] & ~B[i]), c=(A[i+1] & ~B[i+1]);
        long u=ones ^ b;
        twosA=(ones & b)|( u & c);
        ones=u^c;
      }
      // CSA(twosB, ones, ones, (A[i+2] & ~B[i+2]), (A[i+3] & ~B[i+3]))
      {
        long b=(A[i+2] & ~B[i+2]), c=(A[i+3] & ~B[i+3]);
        long u=ones^b;
        twosB =(ones&b)|(u&c);
        ones=u^c;
      }
      //CSA(foursA, twos, twos, twosA, twosB)
      {
        long u=twos^twosA;
        foursA=(twos&twosA)|(u&twosB);
        twos=u^twosB;
      }
      //CSA(twosA, ones, ones, (A[i+4] & ~B[i+4]), (A[i+5] & ~B[i+5]))
      {
        long b=(A[i+4] & ~B[i+4]), c=(A[i+5] & ~B[i+5]);
        long u=ones^b;
        twosA=(ones&b)|(u&c);
        ones=u^c;
      }
      // CSA(twosB, ones, ones, (A[i+6] & ~B[i+6]), (A[i+7] & ~B[i+7]))
      {
        long b=(A[i+6] & ~B[i+6]), c=(A[i+7] & ~B[i+7]);
        long u=ones^b;
        twosB=(ones&b)|(u&c);
        ones=u^c;
      }
      //CSA(foursB, twos, twos, twosA, twosB)
      {
        long u=twos^twosA;
        foursB=(twos&twosA)|(u&twosB);
        twos=u^twosB;
      }

      //CSA(eights, fours, fours, foursA, foursB)
      {
        long u=fours^foursA;
        eights=(fours&foursA)|(u&foursB);
        fours=u^foursB;
      }
      tot8 += pop(eights);
    }


    if (i<=n-4) {
      long twosA, twosB, foursA, eights;
      {
        long b=(A[i] & ~B[i]), c=(A[i+1] & ~B[i+1]);
        long u=ones ^ b;
        twosA=(ones & b)|( u & c);
        ones=u^c;
      }
      {
        long b=(A[i+2] & ~B[i+2]), c=(A[i+3] & ~B[i+3]);
        long u=ones^b;
        twosB =(ones&b)|(u&c);
        ones=u^c;
      }
      {
        long u=twos^twosA;
        foursA=(twos&twosA)|(u&twosB);
        twos=u^twosB;
      }
      eights=fours&foursA;
      fours=fours^foursA;

      tot8 += pop(eights);
      i+=4;
    }

    if (i<=n-2) {
      long b=(A[i] & ~B[i]), c=(A[i+1] & ~B[i+1]);
      long u=ones ^ b;
      long twosA=(ones & b)|( u & c);
      ones=u^c;

      long foursA=twos&twosA;
      twos=twos^twosA;

      long eights=fours&foursA;
      fours=fours^foursA;

      tot8 += pop(eights);
      i+=2;
    }

    if (i<n) {
      tot += pop((A[i] & ~B[i]));
    }

    tot += (pop(fours)<<2)
            + (pop(twos)<<1)
            + pop(ones)
            + (tot8<<3);

    return tot;
  }

  public static long pop_xor(long A[], long B[], int wordOffset, int numWords) {
    int n = wordOffset+numWords;
    long tot=0, tot8=0;
    long ones=0, twos=0, fours=0;

    int i;
    for (i = wordOffset; i <= n - 8; i+=8) {
      /***  C macro from Hacker's Delight
       #define CSA(h,l, a,b,c) \
       {unsigned u = a ^ b; unsigned v = c; \
       h = (a & b) | (u & v); l = u ^ v;}
       ***/

      long twosA,twosB,foursA,foursB,eights;

      // CSA(twosA, ones, ones, (A[i] ^ B[i]), (A[i+1] ^ B[i+1]))
      {
        long b=(A[i] ^ B[i]), c=(A[i+1] ^ B[i+1]);
        long u=ones ^ b;
        twosA=(ones & b)|( u & c);
        ones=u^c;
      }
      // CSA(twosB, ones, ones, (A[i+2] ^ B[i+2]), (A[i+3] ^ B[i+3]))
      {
        long b=(A[i+2] ^ B[i+2]), c=(A[i+3] ^ B[i+3]);
        long u=ones^b;
        twosB =(ones&b)|(u&c);
        ones=u^c;
      }
      //CSA(foursA, twos, twos, twosA, twosB)
      {
        long u=twos^twosA;
        foursA=(twos&twosA)|(u&twosB);
        twos=u^twosB;
      }
      //CSA(twosA, ones, ones, (A[i+4] ^ B[i+4]), (A[i+5] ^ B[i+5]))
      {
        long b=(A[i+4] ^ B[i+4]), c=(A[i+5] ^ B[i+5]);
        long u=ones^b;
        twosA=(ones&b)|(u&c);
        ones=u^c;
      }
      // CSA(twosB, ones, ones, (A[i+6] ^ B[i+6]), (A[i+7] ^ B[i+7]))
      {
        long b=(A[i+6] ^ B[i+6]), c=(A[i+7] ^ B[i+7]);
        long u=ones^b;
        twosB=(ones&b)|(u&c);
        ones=u^c;
      }
      //CSA(foursB, twos, twos, twosA, twosB)
      {
        long u=twos^twosA;
        foursB=(twos&twosA)|(u&twosB);
        twos=u^twosB;
      }

      //CSA(eights, fours, fours, foursA, foursB)
      {
        long u=fours^foursA;
        eights=(fours&foursA)|(u&foursB);
        fours=u^foursB;
      }
      tot8 += pop(eights);
    }


    if (i<=n-4) {
      long twosA, twosB, foursA, eights;
      {
        long b=(A[i] ^ B[i]), c=(A[i+1] ^ B[i+1]);
        long u=ones ^ b;
        twosA=(ones & b)|( u & c);
        ones=u^c;
      }
      {
        long b=(A[i+2] ^ B[i+2]), c=(A[i+3] ^ B[i+3]);
        long u=ones^b;
        twosB =(ones&b)|(u&c);
        ones=u^c;
      }
      {
        long u=twos^twosA;
        foursA=(twos&twosA)|(u&twosB);
        twos=u^twosB;
      }
      eights=fours&foursA;
      fours=fours^foursA;

      tot8 += pop(eights);
      i+=4;
    }

    if (i<=n-2) {
      long b=(A[i] ^ B[i]), c=(A[i+1] ^ B[i+1]);
      long u=ones ^ b;
      long twosA=(ones & b)|( u & c);
      ones=u^c;

      long foursA=twos&twosA;
      twos=twos^twosA;

      long eights=fours&foursA;
      fours=fours^foursA;

      tot8 += pop(eights);
      i+=2;
    }

    if (i<n) {
      tot += pop((A[i] ^ B[i]));
    }

    tot += (pop(fours)<<2)
            + (pop(twos)<<1)
            + pop(ones)
            + (tot8<<3);

    return tot;
  }

  /* python code to generate ntzTable
  def ntz(val):
    if val==0: return 8
    i=0
    while (val&0x01)==0:
      i = i+1
      val >>= 1
    return i
  print ','.join([ str(ntz(i)) for i in range(256) ])
  ***/
  /** table of number of trailing zeros in a byte */
  public static final byte[] ntzTable = {8,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,5,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,6,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,5,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,7,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,5,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,6,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,5,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0};


  /** Returns number of trailing zeros in the 64 bit long value. */
  public static int ntz(long val) {
    // A full binary search to determine the low byte was slower than
    // a linear search for nextSetBit().  This is most likely because
    // the implementation of nextSetBit() shifts bits to the right, increasing
    // the probability that the first non-zero byte is in the rhs.
    //
    // This implementation does a single binary search at the top level only
    // so that all other bit shifting can be done on ints instead of longs to
    // remain friendly to 32 bit architectures.  In addition, the case of a
    // non-zero first byte is checked for first because it is the most common
    // in dense bit arrays.

    int lower = (int)val;
    int lowByte = lower & 0xff;
    if (lowByte != 0) return ntzTable[lowByte];

    if (lower!=0) {
      lowByte = (lower>>>8) & 0xff;
      if (lowByte != 0) return ntzTable[lowByte] + 8;
      lowByte = (lower>>>16) & 0xff;
      if (lowByte != 0) return ntzTable[lowByte] + 16;
      // no need to mask off low byte for the last byte in the 32 bit word
      // no need to check for zero on the last byte either.
      return ntzTable[lower>>>24] + 24;
    } else {
      // grab upper 32 bits
      int upper=(int)(val>>32);
      lowByte = upper & 0xff;
      if (lowByte != 0) return ntzTable[lowByte] + 32;
      lowByte = (upper>>>8) & 0xff;
      if (lowByte != 0) return ntzTable[lowByte] + 40;
      lowByte = (upper>>>16) & 0xff;
      if (lowByte != 0) return ntzTable[lowByte] + 48;
      // no need to mask off low byte for the last byte in the 32 bit word
      // no need to check for zero on the last byte either.
      return ntzTable[upper>>>24] + 56;
    }
  }

  /** returns 0 based index of first set bit
   * (only works for x!=0)
   * <br/> This is an alternate implementation of ntz()
   */
  public static int ntz2(long x) {
   int n = 0;
   int y = (int)x;
   if (y==0) {n+=32; y = (int)(x>>>32); }   // the only 64 bit shift necessary
   if ((y & 0x0000FFFF) == 0) { n+=16; y>>>=16; }
   if ((y & 0x000000FF) == 0) { n+=8; y>>>=8; }
   return (ntzTable[ y & 0xff ]) + n;
  }

  /** returns 0 based index of first set bit
   * <br/> This is an alternate implementation of ntz()
   */
  public static int ntz3(long x) {
   // another implementation taken from Hackers Delight, extended to 64 bits
   // and converted to Java.
   // Many 32 bit ntz algorithms are at http://www.hackersdelight.org/HDcode/ntz.cc
   int n = 1;

   // do the first step as a long, all others as ints.
   int y = (int)x;
   if (y==0) {n+=32; y = (int)(x>>>32); }
   if ((y & 0x0000FFFF) == 0) { n+=16; y>>>=16; }
   if ((y & 0x000000FF) == 0) { n+=8; y>>>=8; }
   if ((y & 0x0000000F) == 0) { n+=4; y>>>=4; }
   if ((y & 0x00000003) == 0) { n+=2; y>>>=2; }
   return n - (y & 1);
  }


  /** returns true if v is a power of two or zero*/
  public static boolean isPowerOfTwo(int v) {
    return ((v & (v-1)) == 0);
  }

  /** returns true if v is a power of two or zero*/
  public static boolean isPowerOfTwo(long v) {
    return ((v & (v-1)) == 0);
  }

  /** returns the next highest power of two, or the current value if it's already a power of two or zero*/
  public static int nextHighestPowerOfTwo(int v) {
    v--;
    v |= v >> 1;
    v |= v >> 2;
    v |= v >> 4;
    v |= v >> 8;
    v |= v >> 16;
    v++;
    return v;
  }

  /** returns the next highest power of two, or the current value if it's already a power of two or zero*/
   public static long nextHighestPowerOfTwo(long v) {
    v--;
    v |= v >> 1;
    v |= v >> 2;
    v |= v >> 4;
    v |= v >> 8;
    v |= v >> 16;
    v |= v >> 32;
    v++;
    return v;
  }

}