# 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) */
}

// 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)
```

 file: /Techref/method/aa0900.htm, 5KB, , updated: 2006/8/11 07:47, local time: 2018/12/10 22:08, owner: JMN-EFP-786, TOP NEW HELP FIND:  52.91.185.49:LOG IN

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