please dont rip this site

Algorithm Alley

From DDJ.com September issue

by Ron Gutman

Listing One

public class BitLinear  {

   public static long reverse (long bits) {
        long rl = 0;
        for (int i = 0; i < 64; i++) {
           rl = (rl << 1) + (bits & 1);
           bits = bits >>> 1;
        }
        return rl;
   }

   public static int count (long bits) {
        int cnt = 0;
        while (bits != 0) {
            cnt += bits & 1;
            bits = bits >>> 1;
        }
        return cnt;
   }

}




Listing Two

public class BitRecursive
{
   // reverse leftmost n bits of V
   static long reversen (long V, int n) {
        if (n <= 1)
            return V;

        int n2 = n/2;

        // reverse rightmost n/2 bits
        long right = reversen( V & ((1L<<n2)-1), n2);

        // reverse lefttmost n/2 bits
        long left =  reversen( V >>> n2, n2);

        // combine in reverse order
        return (right << n2) | left;
   }

   public static long reverse (long bits) {
        return reversen (bits, 64);
   }

}




Listing Three

public class BitLogN {

   public static long reverse (long bits) {
       // >>> fills bits on the left with 0 (no sign extension)
       bits = ((bits&0x00000000ffffffffL) <<  32) |
              ((bits&0xffffffff00000000L) >>> 32);
       bits = ((bits&0x0000ffff0000ffffL) <<  16) |
              ((bits&0xffff0000ffff0000L) >>> 16);
       bits = ((bits&0x00ff00ff00ff00ffL) <<   8) |
              ((bits&0xff00ff00ff00ff00L) >>>  8);
       bits = ((bits&0x0f0f0f0f0f0f0f0fL) <<   4) |
              ((bits&0xf0f0f0f0f0f0f0f0L) >>>  4);
       bits = ((bits&0x3333333333333333L) <<   2) |
              ((bits&0xccccccccccccccccL) >>>  2);
       bits = ((bits&0x5555555555555555L) <<   1) |
              ((bits&0xaaaaaaaaaaaaaaaaL) >>>  1);
       return bits;
   }

   public static int count (long bits) {
       bits = (bits&0x5555555555555555L) +
             ((bits&0xaaaaaaaaaaaaaaaaL) >>>  1);
       bits = (bits&0x3333333333333333L) +
             ((bits&0xccccccccccccccccL) >>>  2);
       bits = (bits&0x0f0f0f0f0f0f0f0fL) +
             ((bits&0xf0f0f0f0f0f0f0f0L) >>>  4);
       bits = (bits&0x00ff00ff00ff00ffL) +
             ((bits&0xff00ff00ff00ff00L) >>>  8);
       bits = (bits&0x0000ffff0000ffffL) +
             ((bits&0xffff0000ffff0000L) >>> 16);
       bits = (bits&0x00000000ffffffffL) +
             ((bits&0xffffffff00000000L) >>> 32);
       return (int) bits;
   }


   public static long mortonKey (int x, int y) {
       /* In C++, the calls to spreadBits could be made in-line    */
       /* to avoid function call overhead.                         */
       /* In C, make the function a macro (admittedly an ugly one) */
       return (spreadBits(x) << 1) | spreadBits(y);
   }


   // For j = 1 to 31, shift bit j j positions to the left
   static long spreadBits (int i) {
       long bits = i;

       // shift bits 16 to 31 16 bits
       bits = (bits & 0x000000000000ffffL) |
             ((bits & 0x00000000ffff0000L) << 16);
       // shift originally odd-numbered bytes 8 bits
       bits = (bits & 0x000000ff000000ffL) |
             ((bits & 0x0000ff000000ff00L) <<  8);
       // shift originally odd-numbered nibbles 4 bits
       bits = (bits & 0x000f000f000f000fL) |
             ((bits & 0x00f000f000f000f0L) <<  4);
       // shift originally odd-numbered bit pairs 2 bits
       bits = (bits & 0x0303030303030303L) |
             ((bits & 0x0c0c0c0c0c0c0c0cL) <<  2);
       // shift originally odd-numbered bit pairs 1 bits
       bits = (bits & 0x1111111111111111L) |
             ((bits & 0x2222222222222222L) <<  1);

       return bits;
   }

}



Listing Four

public class BitTable {

   short[] table = new short[256];

   public BitTable() {
       BitLinear lin = new BitLinear();
       for (int i = 0; i < 256; i++) {
           table[i] = (short) (lin.reverse(i) >>> 56);
      }
   }

   public long reverse (long bits) {
       long rl = 0;
       rl =             table[(int)(bits & 255)]; bits = bits >>> 8;
       rl = (rl << 8) | table[(int)(bits & 255)]; bits = bits >>> 8;
       rl = (rl << 8) | table[(int)(bits & 255)]; bits = bits >>> 8;
       rl = (rl << 8) | table[(int)(bits & 255)]; bits = bits >>> 8;
       rl = (rl << 8) | table[(int)(bits & 255)]; bits = bits >>> 8;
       rl = (rl << 8) | table[(int)(bits & 255)]; bits = bits >>> 8;
       rl = (rl << 8) | table[(int)(bits & 255)]; bits = bits >>> 8;
       rl = (rl << 8) | table[(int)(bits & 255)];
       return rl;
   }

}

Example 1:

  if n equals 1, return V
  set R = right most n/2 bits of V
  set L = left most  n/2 bits of V
  R = reversen(R,n/2)
  L = reversen(L,n/2)
  set RL = n bit value whose left most n/2 bits
     equals R and whose right most n/2 bits equals L
  return RL

Example 2:

  if n equals 1, return V
  set R = right most n/2 bits of V
  set L = left most  n/2 bits of V
  return countn(L,n/2) + countn(R,n/2)

See also:


file: /Techref/method/aa0900.htm, 5KB, , updated: 2006/8/11 07:47, local time: 2024/11/8 13:55, owner: JMN-EFP-786,
TOP NEW HELP FIND: 
3.138.61.232:LOG IN
©2024 PLEASE DON'T RIP! THIS SITE CLOSES OCT 28, 2024 SO LONG AND THANKS FOR ALL THE FISH!

 ©2024 These pages are served without commercial sponsorship. (No popup ads, etc...).Bandwidth abuse increases hosting cost forcing sponsorship or shutdown. This server aggressively defends against automated copying for any reason including offline viewing, duplication, etc... Please respect this requirement and DO NOT RIP THIS SITE. Questions?
Please DO link to this page! Digg it! / MAKE!

<A HREF="http://sxlist.com/Techref/method/aa0900.htm"> Techniques for exploiting the parallelism of bitwise operations [incl bit reversals, counting, and Morton keys] by Ron Gutman</A>

After you find an appropriate page, you are invited to your to this massmind site! (posts will be visible only to you before review) Just type a nice message (short messages are blocked as spam) in the box and press the Post button. (HTML welcomed, but not the <A tag: Instead, use the link box to link to another page. A tutorial is available Members can login to post directly, become page editors, and be credited for their posts.


Link? Put it here: 
if you want a response, please enter your email address: 
Attn spammers: All posts are reviewed before being made visible to anyone other than the poster.
Did you find what you needed?

 

Welcome to sxlist.com!


Site supported by
sales, advertizing,
& kind contributors
just like you!

Please don't rip/copy
(here's why

Copies of the site on CD
are available at minimal cost.
 

Welcome to sxlist.com!

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  .