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The Apache Cassandra Project develops a highly scalable second-generation distributed database, bringing together Dynamo's fully distributed design and Bigtable's ColumnFamily-based data model.
/*
* Licensed to the Apache Software Foundation (ASF) under one
* or more contributor license agreements. See the NOTICE file
* distributed with this work for additional information
* regarding copyright ownership. The ASF licenses this file
* to you under the Apache License, Version 2.0 (the
* "License"); you may not use this file except in compliance
* with the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.cassandra.utils.obs;
/** A variety of high efficiency bit twiddling routines.
* @lucene.internal
*/
final class BitUtil {
/** Returns the number of bits set in the long */
public static int pop(long x) {
/* Hacker's Delight 32 bit pop function:
* http://www.hackersdelight.org/HDcode/newCode/pop_arrayHS.cc
*
int pop(unsigned x) {
x = x - ((x >> 1) & 0x55555555);
x = (x & 0x33333333) + ((x >> 2) & 0x33333333);
x = (x + (x >> 4)) & 0x0F0F0F0F;
x = x + (x >> 8);
x = x + (x >> 16);
return x & 0x0000003F;
}
***/
// 64 bit java version of the C function from above
x = x - ((x >>> 1) & 0x5555555555555555L);
x = (x & 0x3333333333333333L) + ((x >>>2 ) & 0x3333333333333333L);
x = (x + (x >>> 4)) & 0x0F0F0F0F0F0F0F0FL;
x = x + (x >>> 8);
x = x + (x >>> 16);
x = x + (x >>> 32);
return ((int)x) & 0x7F;
}
/*** Returns the number of set bits in an array of longs. */
public static long pop_array(long A[], int wordOffset, int numWords) {
/*
* Robert Harley and David Seal's bit counting algorithm, as documented
* in the revisions of Hacker's Delight
* http://www.hackersdelight.org/revisions.pdf
* http://www.hackersdelight.org/HDcode/newCode/pop_arrayHS.cc
*
* This function was adapted to Java, and extended to use 64 bit words.
* if only we had access to wider registers like SSE from java...
*
* This function can be transformed to compute the popcount of other functions
* on bitsets via something like this:
* 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], A[i+1])
{
long b=A[i], c=A[i+1];
long u=ones ^ b;
twosA=(ones & b)|( u & c);
ones=u^c;
}
// CSA(twosB, ones, ones, A[i+2], A[i+3])
{
long b=A[i+2], c=A[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], A[i+5])
{
long b=A[i+4], c=A[i+5];
long u=ones^b;
twosA=(ones&b)|(u&c);
ones=u^c;
}
// CSA(twosB, ones, ones, A[i+6], A[i+7])
{
long b=A[i+6], c=A[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);
}
// handle trailing words in a binary-search manner...
// derived from the loop above by setting specific elements to 0.
// the original method in Hackers Delight used a simple for loop:
// for (i = i; i < n; i++) // Add in the last elements
// tot = tot + pop(A[i]);
if (i<=n-4) {
long twosA, twosB, foursA, eights;
{
long b=A[i], c=A[i+1];
long u=ones ^ b;
twosA=(ones & b)|( u & c);
ones=u^c;
}
{
long b=A[i+2], c=A[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], c=A[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>= 1
return i
print ','.join([ str(ntz(i)) for i in range(256) ])
***/
/** keyspaceName 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 a 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 number of trailing zeros in a 32 bit int value. */
public static int ntz(int val) {
// This implementation does a single binary search at the top level only.
// 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 lowByte = val & 0xff;
if (lowByte != 0) return ntzTable[lowByte];
lowByte = (val>>>8) & 0xff;
if (lowByte != 0) return ntzTable[lowByte] + 8;
lowByte = (val>>>16) & 0xff;
if (lowByte != 0) return ntzTable[lowByte] + 16;
// no need to mask off low byte for the last byte.
// no need to check for zero on the last byte either.
return ntzTable[val>>>24] + 24;
}
/** returns 0 based index of first set bit
* (only works for x!=0)
*
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
*
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;
}
}
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