public class BigArrays extends Object
A big array is an arrayofarrays representation of an array. The length of a big array
is bounded by Long.MAX_VALUE
rather than Integer.MAX_VALUE
. The type of a big array
is that of an arrayofarrays, so a big array of integers is of type int[][]
.
If a
is a big array, a[0]
, a[1]
, … are called
the segments of the big array. All segments, except possibly for the last one, are of length
SEGMENT_SIZE
. Given an index i
into a big array, there is an associated
segment and an associated displacement
into that segment. Access to single members happens by means of accessors defined in the typespecific
versions (see, e.g., IntBigArrays.get(int[][], long)
and IntBigArrays.set(int[][], long, int)
),
but you can also use the methods segment(long)
/displacement(long)
to access entries manually.
You can scan a big array using the following idiomatic form:
for( int s = 0; s < a.length; s++ ) { final int[] t = a[ s ]; final int l = t.length; for( int d = 0; d < l; d++ ) { do something with t[ d ] } }or using the (simpler and usually faster) reversed version:
for( int s = a.length; s != 0; ) { final int[] t = a[ s ]; for( int d = t.length; d != 0; ) { do something with t[ d ] } }
Inside the inner loop, the original index in a
can be retrieved using index(segment, displacement)
.
Do not use an additional variable to keep track of the value of the original index, as
computing it on the fly is significantly faster. For instance, to inizialise the ith element of a big array of
long integers to the value i you should use
for( int s = a.length; s != 0; ) { final long[] t = a[ s ]; for( int d = t.length; d != 0; ) t[ d ] = index( s, d ); }
Note that caching is essential in making these loops essentially as fast as those scanning standard arrays (as iterations of the outer loop happen very rarely). Using loops of this kind is extremely faster than using a standard loop and accessors.
In some situations, you might want to iterate over a part of a big array having an offset and a length. In this case, the idiomatic loops are as follows:
for( int s = segment( offset ); s < segment( offset + length + SEGMENT_MASK ); s++ ) { final int[] t = a[ s ]; final int l = (int)Math.min( t.length, offset + length  start( s ) ); for( int d = (int)Math.max( 0, offset  start( s ) ); d < l; d++ ) { do something with t[ d ] } }or, in a reversed form,
for( int s = segment( offset + length + SEGMENT_MASK ); s != segment( offset ); ) { final int[] t = a[ s ]; final int b = (int)Math.max( 0, offset  start( s ) ); for( int d = (int)Math.min( t.length, offset + length  start( s ) ); d != b ; ) { do something with t[ d ] } }
A literal big array can be easily created by using the suitable typespecific wrap()
method
(e.g., IntBigArrays.wrap(int[])
) around a literal standard array. Alternatively, for very small
arrays you can just declare a literal arrayofarray (e.g., new int[][] { { 1, 2 } }
). Be warned,
however, that this can lead to creating illegal big arrays if for some reason (e.g., stress testing) SEGMENT_SIZE
is set to a value smaller than the inner array length.
If you find the kind of “bare hands” approach to big arrays not enough objectoriented, please use
big lists based on big arrays (.e.g, IntBigArrayBigList
). Big arrays follow the Java tradition of
considering arrays as a “legal alien”—something inbetween an object and a primitive type. This
approach lacks the consistency of a full objectoriented approach, but provides some significant performance gains.
In addition to commodity methods, this class contains BigSwapper
based implementations
of quicksort and of
a stable, inplace mergesort. These
generic sorting methods can be used to sort any kind of list, but they find their natural
usage, for instance, in sorting big arrays in parallel.
Arrays
Modifier and Type  Field and Description 

static int 
SEGMENT_MASK
The mask used to compute the displacement associated to an index.

static int 
SEGMENT_SHIFT
The shift used to compute the segment associated with an index (equivalently, the logarithm of the segment size).

static int 
SEGMENT_SIZE
The current size of a segment (2^{27}) is the largest size that makes
the physical memory allocation for a single segment strictly smaller
than 2^{31} bytes.

Modifier and Type  Method and Description 

static int 
displacement(long index)
Computes the displacement associated with a given index.

static void 
ensureFromTo(long bigArrayLength,
long from,
long to)
Ensures that a range given by its first (inclusive) and last (exclusive) elements fits a big array of given length.

static void 
ensureOffsetLength(long bigArrayLength,
long offset,
long length)
Ensures that a range given by an offset and a length fits a big array of given length.

static long 
index(int segment,
int displacement)
Computes the index associated with given segment and displacement.

static void 
main(String[] arg) 
static void 
mergeSort(long from,
long to,
LongComparator comp,
BigSwapper swapper)
Sorts the specified range of elements using the specified big swapper and according to the order induced by the specified
comparator using mergesort.

static void 
quickSort(long from,
long to,
LongComparator comp,
BigSwapper swapper)
Sorts the specified range of elements using the specified big swapper and according to the order induced by the specified
comparator using quicksort.

static int 
segment(long index)
Computes the segment associated with a given index.

static long 
start(int segment)
Computes the starting index of a given segment.

public static final int SEGMENT_SHIFT
public static final int SEGMENT_SIZE
public static final int SEGMENT_MASK
public static int segment(long index)
index
 an index into a big array.public static int displacement(long index)
index
 an index into a big array.public static long start(int segment)
segment
 the segment of a big array.public static long index(int segment, int displacement)
segment
 the segment of a big array.displacement
 the displacement into the segment.segment(index(segment, displacement)) == segment
and
displacement(index(segment, displacement)) == displacement
.public static void ensureFromTo(long bigArrayLength, long from, long to)
This method may be used whenever a big array range check is needed.
bigArrayLength
 a bigarray length.from
 a start index (inclusive).to
 an end index (inclusive).IllegalArgumentException
 if from
is greater than to
.ArrayIndexOutOfBoundsException
 if from
or to
are greater than bigArrayLength
or negative.public static void ensureOffsetLength(long bigArrayLength, long offset, long length)
This method may be used whenever a big array range check is needed.
bigArrayLength
 a bigarray length.offset
 a start index for the fragmentlength
 a length (the number of elements in the fragment).IllegalArgumentException
 if length
is negative.ArrayIndexOutOfBoundsException
 if offset
is negative or offset
+length
is greater than bigArrayLength
.public static void mergeSort(long from, long to, LongComparator comp, BigSwapper swapper)
This sort is guaranteed to be stable: equal elements will not be reordered as a result of the sort. The sorting algorithm is an inplace mergesort that is significantly slower than a standard mergesort, as its running time is O(n (log n)^{2}), but it does not allocate additional memory; as a result, it can be used as a generic sorting algorithm.
from
 the index of the first element (inclusive) to be sorted.to
 the index of the last element (exclusive) to be sorted.comp
 the comparator to determine the order of the generic data (arguments are positions).swapper
 an object that knows how to swap the elements at any two positions.public static void quickSort(long from, long to, LongComparator comp, BigSwapper swapper)
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.
from
 the index of the first element (inclusive) to be sorted.to
 the index of the last element (exclusive) to be sorted.comp
 the comparator to determine the order of the generic data.swapper
 an object that knows how to swap the elements at any two positions.public static void main(String[] arg)