src.it.unimi.dsi.fastutil.doubles.DoubleBigArrays Maven / Gradle / Ivy
/* Generic definitions */
/* Assertions (useful to generate conditional code) */
/* Current type and class (and size, if applicable) */
/* Value methods */
/* Interfaces (keys) */
/* Interfaces (values) */
/* Abstract implementations (keys) */
/* Abstract implementations (values) */
/* Static containers (keys) */
/* Static containers (values) */
/* Implementations */
/* Synchronized wrappers */
/* Unmodifiable wrappers */
/* Other wrappers */
/* Methods (keys) */
/* Methods (values) */
/* Methods (keys/values) */
/* Methods that have special names depending on keys (but the special names depend on values) */
/* Equality */
/* Object/Reference-only definitions (keys) */
/* Primitive-type-only definitions (keys) */
/* Object/Reference-only definitions (values) */
/*
* Copyright (C) 2009-2013 Sebastiano Vigna
*
* Licensed 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.
*
*
*
* Copyright (C) 1999 CERN - European Organization for Nuclear Research.
*
* Permission to use, copy, modify, distribute and sell this software and
* its documentation for any purpose is hereby granted without fee,
* provided that the above copyright notice appear in all copies and that
* both that copyright notice and this permission notice appear in
* supporting documentation. CERN makes no representations about the
* suitability of this software for any purpose. It is provided "as is"
* without expressed or implied warranty.
*/
package it.unimi.dsi.fastutil.doubles;
import java.util.Arrays;
import java.util.Random;
import it.unimi.dsi.fastutil.BigArrays;
import it.unimi.dsi.fastutil.Hash;
import static it.unimi.dsi.fastutil.BigArrays.start;
import static it.unimi.dsi.fastutil.BigArrays.segment;
import static it.unimi.dsi.fastutil.BigArrays.displacement;
import static it.unimi.dsi.fastutil.BigArrays.SEGMENT_MASK;
import static it.unimi.dsi.fastutil.BigArrays.SEGMENT_SIZE;
import it.unimi.dsi.fastutil.bytes.ByteBigArrays;
/** A class providing static methods and objects that do useful things with {@linkplain BigArrays big arrays}.
*
* In particular, the ensureCapacity(), grow(),
* trim() and setLength() methods allow to handle
* big arrays much like array lists.
*
*
Note that {@link it.unimi.dsi.fastutil.io.BinIO} and {@link it.unimi.dsi.fastutil.io.TextIO}
* contain several methods that make it possible to load and save big arrays of primitive types as sequences
* of elements in {@link java.io.DataInput} format (i.e., not as objects) or as sequences of lines of text.
*
* @see BigArrays
*/
public class DoubleBigArrays {
private DoubleBigArrays() {}
/** A static, final, empty big array. */
public final static double[][] EMPTY_BIG_ARRAY = {};
/** Returns the element of the given big array of specified index.
*
* @param array a big array.
* @param index a position in the big array.
* @return the element of the big array at the specified position.
*/
public static double get( final double[][] array, final long index ) {
return array[ segment( index ) ][ displacement( index ) ];
}
/** Sets the element of the given big array of specified index.
*
* @param array a big array.
* @param index a position in the big array.
*/
public static void set( final double[][] array, final long index, double value ) {
array[ segment( index ) ][ displacement( index ) ] = value;
}
/** Swaps the element of the given big array of specified indices.
*
* @param array a big array.
* @param first a position in the big array.
* @param second a position in the big array.
*/
public static void swap( final double[][] array, final long first, final long second ) {
final double t = array[ segment( first ) ][ displacement( first ) ];
array[ segment( first ) ][ displacement( first ) ] = array[ segment( second ) ][ displacement( second ) ];
array[ segment( second ) ][ displacement( second ) ] = t;
}
/** Adds the specified increment the element of the given big array of specified index.
*
* @param array a big array.
* @param index a position in the big array.
* @param incr the increment
*/
public static void add( final double[][] array, final long index, double incr ) {
array[ segment( index ) ][ displacement( index ) ] += incr;
}
/** Multiplies by the specified factor the element of the given big array of specified index.
*
* @param array a big array.
* @param index a position in the big array.
* @param factor the factor
*/
public static void mul( final double[][] array, final long index, double factor ) {
array[ segment( index ) ][ displacement( index ) ] *= factor;
}
/** Increments the element of the given big array of specified index.
*
* @param array a big array.
* @param index a position in the big array.
*/
public static void incr( final double[][] array, final long index ) {
array[ segment( index ) ][ displacement( index ) ]++;
}
/** Decrements the element of the given big array of specified index.
*
* @param array a big array.
* @param index a position in the big array.
*/
public static void decr( final double[][] array, final long index ) {
array[ segment( index ) ][ displacement( index ) ]--;
}
/** Returns the length of the given big array.
*
* @param array a big array.
* @return the length of the given big array.
*/
public static long length( final double[][] array ) {
final int length = array.length;
return length == 0 ? 0 : start( length - 1 ) + array[ length - 1 ].length;
}
/** Copies a big array from the specified source big array, beginning at the specified position, to the specified position of the destination big array.
* Handles correctly overlapping regions of the same big array.
*
* @param srcArray the source big array.
* @param srcPos the starting position in the source big array.
* @param destArray the destination big array.
* @param destPos the starting position in the destination data.
* @param length the number of elements to be copied.
*/
public static void copy( final double[][] srcArray, final long srcPos, final double[][] destArray, final long destPos, long length ) {
if ( destPos <= srcPos ) {
int srcSegment = segment( srcPos );
int destSegment = segment( destPos );
int srcDispl = displacement( srcPos );
int destDispl = displacement( destPos );
int l;
while( length > 0 ) {
l = (int)Math.min( length, Math.min( srcArray[ srcSegment ].length - srcDispl, destArray[ destSegment ].length - destDispl ) );
System.arraycopy( srcArray[ srcSegment ], srcDispl, destArray[ destSegment ], destDispl, l );
if ( ( srcDispl += l ) == SEGMENT_SIZE ) {
srcDispl = 0;
srcSegment++;
}
if ( ( destDispl += l ) == SEGMENT_SIZE ) {
destDispl = 0;
destSegment++;
}
length -= l;
}
}
else {
int srcSegment = segment( srcPos + length );
int destSegment = segment( destPos + length );
int srcDispl = displacement( srcPos + length );
int destDispl = displacement( destPos + length );
int l;
while( length > 0 ) {
if ( srcDispl == 0 ) {
srcDispl = SEGMENT_SIZE;
srcSegment--;
}
if ( destDispl == 0 ) {
destDispl = SEGMENT_SIZE;
destSegment--;
}
l = (int)Math.min( length, Math.min( srcDispl, destDispl ) );
System.arraycopy( srcArray[ srcSegment ], srcDispl - l, destArray[ destSegment ], destDispl - l, l );
srcDispl -= l;
destDispl -= l;
length -= l;
}
}
}
/** Copies a big array from the specified source big array, beginning at the specified position, to the specified position of the destination array.
*
* @param srcArray the source big array.
* @param srcPos the starting position in the source big array.
* @param destArray the destination array.
* @param destPos the starting position in the destination data.
* @param length the number of elements to be copied.
*/
public static void copyFromBig( final double[][] srcArray, final long srcPos, final double[] destArray, int destPos, int length ) {
int srcSegment = segment( srcPos );
int srcDispl = displacement( srcPos );
int l;
while( length > 0 ) {
l = Math.min( srcArray[ srcSegment ].length - srcDispl, length );
System.arraycopy( srcArray[ srcSegment ], srcDispl, destArray, destPos, l );
if ( ( srcDispl += l ) == SEGMENT_SIZE ) {
srcDispl = 0;
srcSegment++;
}
destPos += l;
length -= l;
}
}
/** Copies an array from the specified source array, beginning at the specified position, to the specified position of the destination big array.
*
* @param srcArray the source array.
* @param srcPos the starting position in the source array.
* @param destArray the destination big array.
* @param destPos the starting position in the destination data.
* @param length the number of elements to be copied.
*/
public static void copyToBig( final double[] srcArray, int srcPos, final double[][] destArray, final long destPos, long length ) {
int destSegment = segment( destPos );
int destDispl = displacement( destPos );
int l;
while( length > 0 ) {
l = (int)Math.min( destArray[ destSegment ].length - destDispl, length );
System.arraycopy( srcArray, srcPos, destArray[ destSegment ], destDispl, l );
if ( ( destDispl += l ) == SEGMENT_SIZE ) {
destDispl = 0;
destSegment++;
}
srcPos += l;
length -= l;
}
}
/** Creates a new big array.
*
* @param length the length of the new big array.
* @return a new big array of given length.
*/
public static double[][] newBigArray( final long length ) {
if ( length == 0 ) return EMPTY_BIG_ARRAY;
final int baseLength = (int)((length + SEGMENT_MASK) / SEGMENT_SIZE);
double[][] base = new double[ baseLength ][];
final int residual = (int)(length & SEGMENT_MASK);
if ( residual != 0 ) {
for( int i = 0; i < baseLength - 1; i++ ) base[ i ] = new double[ SEGMENT_SIZE ];
base[ baseLength - 1 ] = new double[ residual ];
}
else for( int i = 0; i < baseLength; i++ ) base[ i ] = new double[ SEGMENT_SIZE ];
return base;
}
/** Turns a standard array into a big array.
*
*
Note that the returned big array might contain as a segment the original array.
*
* @param array an array.
* @return a new big array with the same length and content of array.
*/
public static double[][] wrap( final double[] array ) {
if ( array.length == 0 ) return EMPTY_BIG_ARRAY;
if ( array.length <= SEGMENT_SIZE ) return new double[][] { array };
final double[][] bigArray = newBigArray( array.length );
for( int i = 0; i < bigArray.length; i++ ) System.arraycopy( array, (int)start( i ), bigArray[ i ], 0, bigArray[ i ].length );
return bigArray;
}
/** Ensures that a big array can contain the given number of entries.
*
*
If you cannot foresee whether this big array will need again to be
* enlarged, you should probably use grow() instead.
*
*
Warning: the returned array might use part of the segments of the original
* array, which must be considered read-only after calling this method.
*
* @param array a big array.
* @param length the new minimum length for this big array.
* @return array, if it contains length entries or more; otherwise,
* a big array with length entries whose first length(array)
* entries are the same as those of array.
*/
public static double[][] ensureCapacity( final double[][] array, final long length ) {
return ensureCapacity( array, length, length( array ) );
}
/** Ensures that a big array can contain the given number of entries, preserving just a part of the big array.
*
*
Warning: the returned array might use part of the segments of the original
* array, which must be considered read-only after calling this method.
*
* @param array a big array.
* @param length the new minimum length for this big array.
* @param preserve the number of elements of the big array that must be preserved in case a new allocation is necessary.
* @return array, if it can contain length entries or more; otherwise,
* a big array with length entries whose first preserve
* entries are the same as those of array.
*/
public static double[][] ensureCapacity( final double[][] array, final long length, final long preserve ) {
final long oldLength = length( array );
if ( length > oldLength ) {
final int valid = array.length - ( array.length == 0 || array.length > 0 && array[ array.length - 1 ].length == SEGMENT_SIZE ? 0 : 1 );
final int baseLength = (int)((length + SEGMENT_MASK) / SEGMENT_SIZE);
final double[][] base = Arrays.copyOf( array, baseLength );
final int residual = (int)(length & SEGMENT_MASK);
if ( residual != 0 ) {
for( int i = valid; i < baseLength - 1; i++ ) base[ i ] = new double[ SEGMENT_SIZE ];
base[ baseLength - 1 ] = new double[ residual ];
}
else for( int i = valid; i < baseLength; i++ ) base[ i ] = new double[ SEGMENT_SIZE ];
if ( preserve - ( valid * (long)SEGMENT_SIZE ) > 0 ) copy( array, valid * (long)SEGMENT_SIZE, base, valid * (long)SEGMENT_SIZE, preserve - ( valid * (long)SEGMENT_SIZE ) );
return base;
}
return array;
}
/** Grows the given big array to the maximum between the given length and
* the current length multiplied by two, provided that the given
* length is larger than the current length.
*
*
If you want complete control on the big array growth, you
* should probably use ensureCapacity() instead.
*
*
Warning: the returned array might use part of the segments of the original
* array, which must be considered read-only after calling this method.
*
* @param array a big array.
* @param length the new minimum length for this big array.
* @return array, if it can contain length
* entries; otherwise, a big array with
* max(length,length(array)/φ) entries whose first
* length(array) entries are the same as those of array.
* */
public static double[][] grow( final double[][] array, final long length ) {
final long oldLength = length( array );
return length > oldLength ? grow( array, length, oldLength ) : array;
}
/** Grows the given big array to the maximum between the given length and
* the current length multiplied by two, provided that the given
* length is larger than the current length, preserving just a part of the big array.
*
*
If you want complete control on the big array growth, you
* should probably use ensureCapacity() instead.
*
*
Warning: the returned array might use part of the segments of the original
* array, which must be considered read-only after calling this method.
*
* @param array a big array.
* @param length the new minimum length for this big array.
* @param preserve the number of elements of the big array that must be preserved in case a new allocation is necessary.
* @return array, if it can contain length
* entries; otherwise, a big array with
* max(length,length(array)/φ) entries whose first
* preserve entries are the same as those of array.
* */
public static double[][] grow( final double[][] array, final long length, final long preserve ) {
final long oldLength = length( array );
return length > oldLength ? ensureCapacity( array, Math.max( 2 * oldLength, length ), preserve ) : array;
}
/** Trims the given big array to the given length.
*
*
Warning: the returned array might use part of the segments of the original
* array, which must be considered read-only after calling this method.
*
* @param array a big array.
* @param length the new maximum length for the big array.
* @return array, if it contains length
* entries or less; otherwise, a big array with
* length entries whose entries are the same as
* the first length entries of array.
*
*/
public static double[][] trim( final double[][] array, final long length ) {
final long oldLength = length( array );
if ( length >= oldLength ) return array;
final int baseLength = (int)((length + SEGMENT_MASK) / SEGMENT_SIZE);
final double[][] base = Arrays.copyOf( array, baseLength );
final int residual = (int)(length & SEGMENT_MASK);
if ( residual != 0 ) base[ baseLength - 1 ] = DoubleArrays.trim( base[ baseLength - 1 ], residual );
return base;
}
/** Sets the length of the given big array.
*
*
Warning: the returned array might use part of the segments of the original
* array, which must be considered read-only after calling this method.
*
* @param array a big array.
* @param length the new length for the big array.
* @return array, if it contains exactly length
* entries; otherwise, if it contains more than
* length entries, a big array with length entries
* whose entries are the same as the first length entries of
* array; otherwise, a big array with length entries
* whose first length(array) entries are the same as those of
* array.
*
*/
public static double[][] setLength( final double[][] array, final long length ) {
final long oldLength = length( array );
if ( length == oldLength ) return array;
if ( length < oldLength ) return trim( array, length );
return ensureCapacity( array, length );
}
/** Returns a copy of a portion of a big array.
*
* @param array a big array.
* @param offset the first element to copy.
* @param length the number of elements to copy.
* @return a new big array containing length elements of array starting at offset.
*/
public static double[][] copy( final double[][] array, final long offset, final long length ) {
ensureOffsetLength( array, offset, length );
final double[][] a =
newBigArray( length );
copy( array, offset, a, 0, length );
return a;
}
/** Returns a copy of a big array.
*
* @param array a big array.
* @return a copy of array.
*/
public static double[][] copy( final double[][] array ) {
final double[][] base = array.clone();
for( int i = base.length; i-- != 0; ) base[ i ] = array[ i ].clone();
return base;
}
/** Fills the given big array with the given value.
*
*
This method uses a backward loop. It is significantly faster than the corresponding
* method in {@link java.util.Arrays}.
*
* @param array a big array.
* @param value the new value for all elements of the big array.
*/
public static void fill( final double[][] array, final double value ) {
for( int i = array.length; i-- != 0; ) DoubleArrays.fill( array[ i ], value );
}
/** Fills a portion of the given big array with the given value.
*
*
If possible (i.e., from is 0) this method uses a
* backward loop. In this case, it is significantly faster than the
* corresponding method in {@link java.util.Arrays}.
*
* @param array a big array.
* @param from the starting index of the portion to fill.
* @param to the end index of the portion to fill.
* @param value the new value for all elements of the specified portion of the big array.
*/
public static void fill( final double[][] array, final long from, long to, final double value ) {
final long length = length( array );
BigArrays.ensureFromTo( length, from, to );
int fromSegment = segment( from );
int toSegment = segment( to );
int fromDispl = displacement( from );
int toDispl = displacement( to );
if ( fromSegment == toSegment ) {
DoubleArrays.fill( array[ fromSegment ], fromDispl, toDispl, value );
return;
}
if ( toDispl != 0 ) DoubleArrays.fill( array[ toSegment ], 0, toDispl, value );
while( --toSegment > fromSegment ) DoubleArrays.fill( array[ toSegment ], value );
DoubleArrays.fill( array[ fromSegment ], fromDispl, SEGMENT_SIZE, value );
}
/** Returns true if the two big arrays are elementwise equal.
*
*
This method uses a backward loop. It is significantly faster than the corresponding
* method in {@link java.util.Arrays}.
*
* @param a1 a big array.
* @param a2 another big array.
* @return true if the two big arrays are of the same length, and their elements are equal.
*/
public static boolean equals( final double[][] a1, final double a2[][] ) {
if ( length( a1 ) != length( a2 ) ) return false;
int i = a1.length, j;
double[] t, u;
while( i-- != 0 ) {
t = a1[ i ];
u = a2[ i ];
j = t.length;
while( j-- != 0 ) if (! ( (t[ j ]) == (u[ j ]) ) ) return false;
}
return true;
}
/* Returns a string representation of the contents of the specified big array.
*
* The string representation consists of a list of the big array's elements, enclosed in square brackets ("[]"). Adjacent elements are separated by the characters ", " (a comma followed by a space). Returns "null" if a is null.
* @param a the big array whose string representation to return.
* @return the string representation of a.
*/
public static String toString( final double[][] a ) {
if ( a == null ) return "null";
final long last = length( a ) - 1;
if ( last == - 1 ) return "[]";
final StringBuilder b = new StringBuilder();
b.append('[');
for ( long i = 0; ; i++ ) {
b.append( String.valueOf( get( a, i ) ) );
if ( i == last ) return b.append(']').toString();
b.append(", ");
}
}
/** Ensures that a range given by its first (inclusive) and last (exclusive) elements fits a big array.
*
*
This method may be used whenever a big array range check is needed.
*
* @param a a big array.
* @param from a start index (inclusive).
* @param to an end index (inclusive).
* @throws IllegalArgumentException if from is greater than to.
* @throws ArrayIndexOutOfBoundsException if from or to are greater than the big array length or negative.
*/
public static void ensureFromTo( final double[][] a, final long from, final long to ) {
BigArrays.ensureFromTo( length( a ), from, to );
}
/** Ensures that a range given by an offset and a length fits a big array.
*
*
This method may be used whenever a big array range check is needed.
*
* @param a a big array.
* @param offset a start index.
* @param length a length (the number of elements in the range).
* @throws IllegalArgumentException if length is negative.
* @throws ArrayIndexOutOfBoundsException if offset is negative or offset+length is greater than the big array length.
*/
public static void ensureOffsetLength( final double[][] a, final long offset, final long length ) {
BigArrays.ensureOffsetLength( length( a ), offset, length );
}
/** A type-specific content-based hash strategy for big arrays. */
private static final class BigArrayHashStrategy implements Hash.Strategy, java.io.Serializable {
private static final long serialVersionUID = -7046029254386353129L;
public int hashCode( final double[][] o ) {
return java.util.Arrays.deepHashCode( o );
}
public boolean equals( final double[][] a, final double[][] b ) {
return DoubleBigArrays.equals( a, b );
}
}
/** A type-specific content-based hash strategy for big arrays.
*
* This hash strategy may be used in custom hash collections whenever keys are
* big arrays, and they must be considered equal by content. This strategy
* will handle null correctly, and it is serializable.
*/
@SuppressWarnings({"unchecked", "rawtypes"})
public final static Hash.Strategy HASH_STRATEGY = new BigArrayHashStrategy();
private static final int SMALL = 7;
private static final int MEDIUM = 40;
private static void vecSwap( final double[][] x, long a, long b, final long n ) {
for( int i = 0; i < n; i++, a++, b++ ) swap( x, a, b );
}
private static long med3( final double x[][], final long a, final long b, final long c, DoubleComparator comp ) {
int ab = comp.compare( get( x, a ), get( x, b ) );
int ac = comp.compare( get( x, a ), get( x, c ) );
int bc = comp.compare( get( x, b ), get( x, c ) );
return ( ab < 0 ?
( bc < 0 ? b : ac < 0 ? c : a ) :
( bc > 0 ? b : ac > 0 ? c : a ) );
}
private static void selectionSort( final double[][] a, final long from, final long to, final DoubleComparator comp ) {
for( long i = from; i < to - 1; i++ ) {
long m = i;
for( long j = i + 1; j < to; j++ ) if ( comp.compare( DoubleBigArrays.get( a, j ), DoubleBigArrays.get( a, m ) ) < 0 ) m = j;
if ( m != i ) swap( a, i, m );
}
}
/** Sorts the specified range of elements according to the order induced by the specified
* comparator using quicksort.
*
*
The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas
* McIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages
* 1249−1265, 1993.
*
* @param x the big array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
* @param comp the comparator to determine the sorting order.
*/
public static void quickSort( final double[][] x, final long from, final long to, final DoubleComparator comp ) {
final long len = to - from;
// Selection sort on smallest arrays
if ( len < SMALL ) {
selectionSort( x, from, to, comp );
return;
}
// Choose a partition element, v
long m = from + len / 2; // Small arrays, middle element
if ( len > SMALL ) {
long l = from;
long n = to - 1;
if ( len > MEDIUM ) { // Big arrays, pseudomedian of 9
long s = len / 8;
l = med3( x, l, l + s, l + 2 * s, comp );
m = med3( x, m - s, m, m + s, comp );
n = med3( x, n - 2 * s, n - s, n, comp );
}
m = med3( x, l, m, n, comp ); // Mid-size, med of 3
}
final double v = get( x, m );
// Establish Invariant: v* (v)* v*
long a = from, b = a, c = to - 1, d = c;
while(true) {
int comparison;
while ( b <= c && ( comparison = comp.compare( get( x, b ), v ) ) <= 0 ) {
if ( comparison == 0 ) swap( x, a++, b );
b++;
}
while (c >= b && ( comparison = comp.compare( get( x, c ), v ) ) >=0 ) {
if ( comparison == 0 ) swap( x, c, d-- );
c--;
}
if ( b > c ) break;
swap( x, b++, c-- );
}
// Swap partition elements back to middle
long s, n = to;
s = Math.min( a - from, b - a );
vecSwap( x, from, b - s, s );
s = Math.min( d - c, n - d- 1 );
vecSwap( x, b, n - s, s );
// Recursively sort non-partition-elements
if ( ( s = b - a ) > 1 ) quickSort( x, from, from + s, comp );
if ( ( s = d - c ) > 1 ) quickSort( x, n - s, n, comp );
}
@SuppressWarnings("unchecked")
private static long med3( final double x[][], final long a, final long b, final long c ) {
int ab = ( Double.compare((get( x, a )),(get( x, b ))) );
int ac = ( Double.compare((get( x, a )),(get( x, c ))) );
int bc = ( Double.compare((get( x, b )),(get( x, c ))) );
return ( ab < 0 ?
( bc < 0 ? b : ac < 0 ? c : a ) :
( bc > 0 ? b : ac > 0 ? c : a ) );
}
@SuppressWarnings("unchecked")
private static void selectionSort( final double[][] a, final long from, final long to ) {
for( long i = from; i < to - 1; i++ ) {
long m = i;
for( long j = i + 1; j < to; j++ ) if ( ( Double.compare((DoubleBigArrays.get( a, j )),(DoubleBigArrays.get( a, m ))) < 0 ) ) m = j;
if ( m != i ) swap( a, i, m );
}
}
/** Sorts the specified big array according to the order induced by the specified
* comparator using quicksort.
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas
* McIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages
* 1249−1265, 1993.
*
* @param x the big array to be sorted.
* @param comp the comparator to determine the sorting order.
*
*/
public static void quickSort( final double[][] x, final DoubleComparator comp ) {
quickSort( x, 0, DoubleBigArrays.length( x ), comp );
}
/** Sorts the specified range of elements according to the natural ascending order using quicksort.
*
*
The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas
* McIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages
* 1249−1265, 1993.
*
* @param x the big array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
*/
@SuppressWarnings("unchecked")
public static void quickSort( final double[][] x, final long from, final long to ) {
final long len = to - from;
// Selection sort on smallest arrays
if ( len < SMALL ) {
selectionSort( x, from, to );
return;
}
// Choose a partition element, v
long m = from + len / 2; // Small arrays, middle element
if ( len > SMALL ) {
long l = from;
long n = to - 1;
if ( len > MEDIUM ) { // Big arrays, pseudomedian of 9
long s = len / 8;
l = med3( x, l, l + s, l + 2 * s );
m = med3( x, m - s, m, m + s );
n = med3( x, n - 2 * s, n - s, n );
}
m = med3( x, l, m, n ); // Mid-size, med of 3
}
final double v = get( x, m );
// Establish Invariant: v* (v)* v*
long a = from, b = a, c = to - 1, d = c;
while(true) {
int comparison;
while ( b <= c && ( comparison = ( Double.compare((get( x, b )),(v)) ) ) <= 0 ) {
if ( comparison == 0 ) swap( x, a++, b );
b++;
}
while (c >= b && ( comparison = ( Double.compare((get( x, c )),(v)) ) ) >=0 ) {
if ( comparison == 0 ) swap( x, c, d-- );
c--;
}
if ( b > c ) break;
swap( x, b++, c-- );
}
// Swap partition elements back to middle
long s, n = to;
s = Math.min( a - from, b - a );
vecSwap( x, from, b - s, s );
s = Math.min( d - c, n - d- 1 );
vecSwap( x, b, n - s, s );
// Recursively sort non-partition-elements
if ( ( s = b - a ) > 1 ) quickSort( x, from, from + s );
if ( ( s = d - c ) > 1 ) quickSort( x, n - s, n );
}
/** Sorts the specified big array according to the natural ascending order using quicksort.
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas
* McIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages
* 1249−1265, 1993.
*
* @param x the big array to be sorted.
*/
@SuppressWarnings("unchecked")
public static void quickSort( final double[][] x ) {
quickSort( x, 0, DoubleBigArrays.length( x ) );
}
/**
* Searches a range of the specified big array for the specified value using
* the binary search algorithm. The range must be sorted prior to making this call.
* If it is not sorted, the results are undefined. If the range contains multiple elements with
* the specified value, there is no guarantee which one will be found.
*
* @param a the big array to be searched.
* @param from the index of the first element (inclusive) to be searched.
* @param to the index of the last element (exclusive) to be searched.
* @param key the value to be searched for.
* @return index of the search key, if it is contained in the big array;
* otherwise, (-(insertion point) - 1). The insertion
* point is defined as the the point at which the value would
* be inserted into the big array: the index of the first
* element greater than the key, or the length of the big array, if all
* elements in the big array are less than the specified key. Note
* that this guarantees that the return value will be >= 0 if
* and only if the key is found.
* @see java.util.Arrays
*/
@SuppressWarnings({"unchecked","rawtypes"})
public static long binarySearch( final double[][] a, long from, long to, final double key ) {
double midVal;
to--;
while (from <= to) {
final long mid = (from + to) >>> 1;
midVal = get( a, mid );
if (midVal < key) from = mid + 1;
else if (midVal > key) to = mid - 1;
else return mid;
}
return -( from + 1 );
}
/**
* Searches a big array for the specified value using
* the binary search algorithm. The range must be sorted prior to making this call.
* If it is not sorted, the results are undefined. If the range contains multiple elements with
* the specified value, there is no guarantee which one will be found.
*
* @param a the big array to be searched.
* @param key the value to be searched for.
* @return index of the search key, if it is contained in the big array;
* otherwise, (-(insertion point) - 1). The insertion
* point is defined as the the point at which the value would
* be inserted into the big array: the index of the first
* element greater than the key, or the length of the big array, if all
* elements in the big array are less than the specified key. Note
* that this guarantees that the return value will be >= 0 if
* and only if the key is found.
* @see java.util.Arrays
*/
public static long binarySearch( final double[][] a, final double key ) {
return binarySearch( a, 0, DoubleBigArrays.length( a ), key );
}
/**
* Searches a range of the specified big array for the specified value using
* the binary search algorithm and a specified comparator. The range must be sorted following the comparator prior to making this call.
* If it is not sorted, the results are undefined. If the range contains multiple elements with
* the specified value, there is no guarantee which one will be found.
*
* @param a the big array to be searched.
* @param from the index of the first element (inclusive) to be searched.
* @param to the index of the last element (exclusive) to be searched.
* @param key the value to be searched for.
* @param c a comparator.
* @return index of the search key, if it is contained in the big array;
* otherwise, (-(insertion point) - 1). The insertion
* point is defined as the the point at which the value would
* be inserted into the big array: the index of the first
* element greater than the key, or the length of the big array, if all
* elements in the big array are less than the specified key. Note
* that this guarantees that the return value will be >= 0 if
* and only if the key is found.
* @see java.util.Arrays
*/
public static long binarySearch( final double[][] a, long from, long to, final double key, final DoubleComparator c ) {
double midVal;
to--;
while (from <= to) {
final long mid = (from + to) >>> 1;
midVal = get( a, mid );
final int cmp = c.compare( midVal, key );
if ( cmp < 0 ) from = mid + 1;
else if (cmp > 0) to = mid - 1;
else return mid; // key found
}
return -( from + 1 );
}
/**
* Searches a big array for the specified value using
* the binary search algorithm and a specified comparator. The range must be sorted following the comparator prior to making this call.
* If it is not sorted, the results are undefined. If the range contains multiple elements with
* the specified value, there is no guarantee which one will be found.
*
* @param a the big array to be searched.
* @param key the value to be searched for.
* @param c a comparator.
* @return index of the search key, if it is contained in the big array;
* otherwise, (-(insertion point) - 1). The insertion
* point is defined as the the point at which the value would
* be inserted into the big array: the index of the first
* element greater than the key, or the length of the big array, if all
* elements in the big array are less than the specified key. Note
* that this guarantees that the return value will be >= 0 if
* and only if the key is found.
* @see java.util.Arrays
*/
public static long binarySearch( final double[][] a, final double key, final DoubleComparator c ) {
return binarySearch( a, 0, DoubleBigArrays.length( a ), key, c );
}
/** The size of a digit used during radix sort (must be a power of 2). */
private static final int DIGIT_BITS = 8;
/** The mask to extract a digit of {@link #DIGIT_BITS} bits. */
private static final int DIGIT_MASK = ( 1 << DIGIT_BITS ) - 1;
/** The number of digits per element. */
private static final int DIGITS_PER_ELEMENT = Double.SIZE / DIGIT_BITS;
/** This method fixes negative numbers so that the combination exponent/significand is lexicographically sorted. */
private static final long fixDouble( final double d ) {
final long l = Double.doubleToRawLongBits( d );
return l >= 0 ? l : l ^ 0x7FFFFFFFFFFFFFFFL;
}
/** Sorts the specified big array using radix sort.
*
*
The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
* McIlroy, “Engineering radix sort”, Computing Systems, 6(1), pages 5−27 (1993),
* and further improved using the digit-oracle idea described by
* Juha Kärkkäinen and Tommi Rantala in “Engineering radix sort for strings”,
* String Processing and Information Retrieval, 15th International Symposium, volume 5280 of
* Lecture Notes in Computer Science, pages 3−14, Springer (2008).
*
*
This implementation is significantly faster than quicksort
* already at small sizes (say, more than 10000 elements), but it can only
* sort in ascending order.
* It will allocate a support array of bytes with the same number of elements as the array to be sorted.
*
* @param a the big array to be sorted.
*/
public static void radixSort( final double[][] a ) {
radixSort( a, 0, DoubleBigArrays.length( a ) );
}
/** Sorts the specified big array using radix sort.
*
*
The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
* McIlroy, “Engineering radix sort”, Computing Systems, 6(1), pages 5−27 (1993),
* and further improved using the digit-oracle idea described by
* Juha Kärkkäinen and Tommi Rantala in “Engineering radix sort for strings”,
* String Processing and Information Retrieval, 15th International Symposium, volume 5280 of
* Lecture Notes in Computer Science, pages 3−14, Springer (2008).
*
*
This implementation is significantly faster than quicksort
* already at small sizes (say, more than 10000 elements), but it can only
* sort in ascending order.
* It will allocate a support array of bytes with the same number of elements as the array to be sorted.
*
* @param a the big array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
*/
public static void radixSort( final double[][] a, final long from, final long to ) {
final int maxLevel = DIGITS_PER_ELEMENT - 1;
final int stackSize = ( ( 1 << DIGIT_BITS ) - 1 ) * ( DIGITS_PER_ELEMENT - 1 ) + 1;
final long[] offsetStack = new long[ stackSize ];
int offsetPos = 0;
final long[] lengthStack = new long[ stackSize ];
int lengthPos = 0;
final int[] levelStack = new int[ stackSize ];
int levelPos = 0;
offsetStack[ offsetPos++ ] = from;
lengthStack[ lengthPos++ ] = to - from;
levelStack[ levelPos++ ] = 0;
final long[] count = new long[ 1 << DIGIT_BITS ];
final long[] pos = new long[ 1 << DIGIT_BITS ];
final byte[][] digit = ByteBigArrays.newBigArray( to - from );
while( offsetPos > 0 ) {
final long first = offsetStack[ --offsetPos ];
final long length = lengthStack[ --lengthPos ];
final int level = levelStack[ --levelPos ];
final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
if ( length < MEDIUM ) {
selectionSort( a, first, first + length );
continue;
}
final int shift = ( DIGITS_PER_ELEMENT - 1 - level % DIGITS_PER_ELEMENT ) * DIGIT_BITS; // This is the shift that extract the right byte from a key
// Count keys.
for( long i = length; i-- != 0; ) ByteBigArrays.set( digit, i, (byte)( ( ( fixDouble(DoubleBigArrays.get( a, first + i )) >>> shift ) & DIGIT_MASK ) ^ signMask ));
for( long i = length; i-- != 0; ) count[ ByteBigArrays.get( digit, i ) & 0xFF ]++;
// Compute cumulative distribution and push non-singleton keys on stack.
int lastUsed = -1;
long p = 0;
for( int i = 0; i < 1 << DIGIT_BITS; i++ ) {
if ( count[ i ] != 0 ) {
lastUsed = i;
if ( level < maxLevel && count[ i ] > 1 ){
//System.err.println( " Pushing " + new StackEntry( first + pos[ i - 1 ], first + pos[ i ], level + 1 ) );
offsetStack[ offsetPos++ ] = p + first;
lengthStack[ lengthPos++ ] = count[ i ];
levelStack[ levelPos++ ] = level + 1;
}
}
pos[ i ] = ( p += count[ i ] );
}
// When all slots are OK, the last slot is necessarily OK.
final long end = length - count[ lastUsed ];
count[ lastUsed ] = 0;
// i moves through the start of each block
int c = -1;
for( long i = 0, d; i < end; i += count[ c ], count[ c ] = 0 ) {
double t = DoubleBigArrays.get( a, i +first );
c = ByteBigArrays.get( digit, i ) & 0xFF;
while( ( d = --pos[ c ] ) > i ) {
final double z = t;
final int zz = c;
t = DoubleBigArrays.get( a, d + first );
c = ByteBigArrays.get( digit, d ) & 0xFF;
DoubleBigArrays.set( a, d + first, z );
ByteBigArrays.set( digit, d, (byte)zz );
}
DoubleBigArrays.set( a, i + first, t );
}
}
}
private static void selectionSort( final double[][] a, final double[][] b, final long from, final long to ) {
for( long i = from; i < to - 1; i++ ) {
long m = i;
for( long j = i + 1; j < to; j++ )
if ( ( Double.compare((DoubleBigArrays.get( a, j )),(DoubleBigArrays.get( a, m ))) < 0 ) || ( Double.compare((DoubleBigArrays.get( a, j )),(DoubleBigArrays.get( a, m ))) == 0 ) && ( Double.compare((DoubleBigArrays.get( b, j )),(DoubleBigArrays.get( b, m ))) < 0 ) ) m = j;
if ( m != i ) {
double t = DoubleBigArrays.get( a, i );
DoubleBigArrays.set( a, i, DoubleBigArrays.get( a, m ) );
DoubleBigArrays.set( a, m, t );
t = DoubleBigArrays.get( b, i );
DoubleBigArrays.set( b, i, DoubleBigArrays.get( b, m ) );
DoubleBigArrays.set( b, m, t );
}
}
}
/** Sorts the specified pair of big arrays lexicographically using radix sort.
*
The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
* McIlroy, “Engineering radix sort”, Computing Systems, 6(1), pages 5−27 (1993),
* and further improved using the digit-oracle idea described by
* Juha Kärkkäinen and Tommi Rantala in “Engineering radix sort for strings”,
* String Processing and Information Retrieval, 15th International Symposium, volume 5280 of
* Lecture Notes in Computer Science, pages 3−14, Springer (2008).
*
*
This method implements a lexicographical sorting of the arguments. Pairs of elements
* in the same position in the two provided arrays will be considered a single key, and permuted
* accordingly. In the end, either a[ i ] < a[ i + 1 ] or a[ i ] == a[ i + 1 ] and b[ i ] <= b[ i + 1 ].
*
*
This implementation is significantly faster than quicksort
* already at small sizes (say, more than 10000 elements), but it can only
* sort in ascending order. It will allocate a support array of bytes with the same number of elements as the arrays to be sorted.
*
* @param a the first big array to be sorted.
* @param b the second big array to be sorted.
*/
public static void radixSort( final double[][] a, final double[][] b ) {
radixSort( a, b, 0, DoubleBigArrays.length( a ) );
}
/** Sorts the specified pair of big arrays lexicographically using radix sort.
*
*
The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
* McIlroy, “Engineering radix sort”, Computing Systems, 6(1), pages 5−27 (1993),
* and further improved using the digit-oracle idea described by
* Juha Kärkkäinen and Tommi Rantala in “Engineering radix sort for strings”,
* String Processing and Information Retrieval, 15th International Symposium, volume 5280 of
* Lecture Notes in Computer Science, pages 3−14, Springer (2008).
*
*
This method implements a lexicographical sorting of the arguments. Pairs of elements
* in the same position in the two provided arrays will be considered a single key, and permuted
* accordingly. In the end, either a[ i ] < a[ i + 1 ] or a[ i ] == a[ i + 1 ] and b[ i ] <= b[ i + 1 ].
*
*
This implementation is significantly faster than quicksort
* already at small sizes (say, more than 10000 elements), but it can only
* sort in ascending order. It will allocate a support array of bytes with the same number of elements as the arrays to be sorted.
*
* @param a the first big array to be sorted.
* @param b the second big array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
*/
public static void radixSort( final double[][] a, final double[][] b, final long from, final long to ) {
final int layers = 2;
if ( DoubleBigArrays.length( a ) != DoubleBigArrays.length( b ) ) throw new IllegalArgumentException( "Array size mismatch." );
final int maxLevel = DIGITS_PER_ELEMENT * layers - 1;
final int stackSize = ( ( 1 << DIGIT_BITS ) - 1 ) * ( layers * DIGITS_PER_ELEMENT - 1 ) + 1;
final long[] offsetStack = new long[ stackSize ];
int offsetPos = 0;
final long[] lengthStack = new long[ stackSize ];
int lengthPos = 0;
final int[] levelStack = new int[ stackSize ];
int levelPos = 0;
offsetStack[ offsetPos++ ] = from;
lengthStack[ lengthPos++ ] = to - from;
levelStack[ levelPos++ ] = 0;
final long[] count = new long[ 1 << DIGIT_BITS ];
final long[] pos = new long[ 1 << DIGIT_BITS ];
final byte[][] digit = ByteBigArrays.newBigArray( to - from );
while( offsetPos > 0 ) {
final long first = offsetStack[ --offsetPos ];
final long length = lengthStack[ --lengthPos ];
final int level = levelStack[ --levelPos ];
final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
if ( length < MEDIUM ) {
selectionSort( a, b, first, first + length );
continue;
}
final double[][] k = level < DIGITS_PER_ELEMENT ? a : b; // This is the key array
final int shift = ( DIGITS_PER_ELEMENT - 1 - level % DIGITS_PER_ELEMENT ) * DIGIT_BITS; // This is the shift that extract the right byte from a key
// Count keys.
for( long i = length; i-- != 0; ) ByteBigArrays.set( digit, i, (byte)( ( ( fixDouble(DoubleBigArrays.get( k, first + i )) >>> shift ) & DIGIT_MASK ) ^ signMask ) );
for( long i = length; i-- != 0; ) count[ ByteBigArrays.get( digit, i ) & 0xFF ]++;
// Compute cumulative distribution and push non-singleton keys on stack.
int lastUsed = -1;
long p = 0;
for( int i = 0; i < 1 << DIGIT_BITS; i++ ) {
if ( count[ i ] != 0 ) {
lastUsed = i;
if ( level < maxLevel && count[ i ] > 1 ){
offsetStack[ offsetPos++ ] = p + first;
lengthStack[ lengthPos++ ] = count[ i ];
levelStack[ levelPos++ ] = level + 1;
}
}
pos[ i ] = ( p += count[ i ] );
}
// When all slots are OK, the last slot is necessarily OK.
final long end = length - count[ lastUsed ];
count[ lastUsed ] = 0;
// i moves through the start of each block
int c = -1;
for( long i = 0, d; i < end; i += count[ c ], count[ c ] = 0 ) {
double t = DoubleBigArrays.get( a, i + first );
double u = DoubleBigArrays.get( b, i + first );
c = ByteBigArrays.get( digit, i ) & 0xFF;
while( ( d = --pos[ c ] ) > i ) {
double z = t;
final int zz = c;
t = DoubleBigArrays.get( a, d + first );
DoubleBigArrays.set( a, d + first, z );
z = u;
u = DoubleBigArrays.get( b, d + first );
DoubleBigArrays.set( b, d + first, z );
c = ByteBigArrays.get( digit, d ) & 0xFF;
ByteBigArrays.set( digit, d, (byte)zz );
}
DoubleBigArrays.set( a, i + first, t );
DoubleBigArrays.set( b, i + first, u );
}
}
}
/** Shuffles the specified big array fragment using the specified pseudorandom number generator.
*
* @param a the big array to be shuffled.
* @param from the index of the first element (inclusive) to be shuffled.
* @param to the index of the last element (exclusive) to be shuffled.
* @param random a pseudorandom number generator (please use a XorShift* generator).
* @return a.
*/
public static double[][] shuffle( final double[][] a, final long from, final long to, final Random random ) {
for( long i = to - from; i-- != 0; ) {
final long p = ( random.nextLong() & 0x7FFFFFFFFFFFFFFFL ) % ( i + 1 );
final double t = get( a, from + i );
set( a, from + i, get( a, from + p ) );
set( a, from + p, t );
}
return a;
}
/** Shuffles the specified big array using the specified pseudorandom number generator.
*
* @param a the big array to be shuffled.
* @param random a pseudorandom number generator (please use a XorShift* generator).
* @return a.
*/
public static double[][] shuffle( final double[][] a, final Random random ) {
for( long i = length( a ); i-- != 0; ) {
final long p = ( random.nextLong() & 0x7FFFFFFFFFFFFFFFL ) % ( i + 1 );
final double t = get( a, i );
set( a, i, get( a, p ) );
set( a, p, t );
}
return a;
}
}