Sort

Usage

use Sort;

The Sort module is designed to support standard sort routines.

Comparators

Comparators allow sorting data by a mechanism other than the default comparison operations between array elements. To use a comparator, define a record or a class with an appropriate method and then pass an instance of it to the sort function. Examples are shown below.

Comparators need to include at least one of the following methods:

See the section below for discussion of each of these methods.

A comparator can contain both compare and keyPart methods. In that event, the sort algorithm will use whichever is appropriate for the algorithm and expect that they have consistent results.

It is an error for a comparator to contain a key method as well as one of the other methods.

The .key method

The key(a) method accepts 1 argument, which will be an element from the array being sorted.

The default key method would look like this:

proc DefaultComparator.key(a) {
  return a;
}

As an example, if the user wants to sort an array by the absolute values of its elements, the user can define a comparator with a key method as follows:

var Array = [-1, -4, 2, 3];

// Empty record serves as comparator
record Comparator { }

// key method maps an element to the value to be used for comparison
proc Comparator.key(a) { return abs(a); }

var absComparator: Comparator;

sort(Array, comparator=absComparator);

// This will output: -1, 2, 3, -4
writeln(Array);

The return type of key(a) must support the < operator, which is used by the base compare method of all sort routines. If the < operator is not defined for the return type, the user may define it themselves like so:

proc op<(a: returnType, b: returnType): bool {
  ...
}

The .compare method

The compare(a, b) method accepts 2 arguments, which will be 2 elements from the array being sorted. The return value should be a numeric signed type indicating how a and b compare to each other. The conditions between a and b should result in the following return values for compare(a, b):

Return Value Condition
> 0 a > b
0 a == b
< 0 a < b

The default compare method for a signed integral type can look like this:

proc DefaultComparator.compare(a, b) {
  return a - b;
}

The absolute value comparison example from above can alternatively be implemented with a compare method:

var Array = [-1, -4, 2, 3];

// Empty record serves as comparator
record Comparator { }

// compare method defines how 2 elements are compared
proc Comparator.compare(a, b) {
  return abs(a) - abs(b);
}

var absComparator: Comparator;

sort(Array, comparator=absComparator);

// This will output: -1, 2, 3, -4
writeln(Array);

The .keyPart method

A keyPart(a, i) method returns parts of key value at a time. This interface supports radix sorting for variable length data types, such as strings. It accepts two arguments:

  • a is the element being sorted
  • i is the part number of the key requested, starting from 1

A keyPart method should return a tuple consisting of section and a part.

  • The section can be any signed integral type and should have the value -1, 0, or 1. It indicates when the end of the a has been reached and in that event how it should be sorted relative to other array elements.

    Returned section Interpretation
    -1 no more key parts for a, sort it before those with more parts
    0 a key part for a is returned in the second tuple element
    1 no more key parts for a, sort it after those with more parts

  • The part can be any signed or unsigned integral type and can contain any value. The part will be ignored unless the section returned is 0.

Let's consider several example keyPart methods. All of these are simplifications of keyPart methods already available in the DefaultComparator.

This keyPart method supports sorting tuples of 2 integers:

proc keyPart(x:2*int, i:int) {
  if i > 2 then
    return (-1, 0);

  return (0, x(i));
}

Here is a keyPart to support sorting of strings:

proc keyPart(x:string, i:int):(int(8), uint(8)) {
  var len = x.length;
  var section = if i <= len then 0:int(8) else -1:int(8);
  var part =    if i <= len then x.byte(i) else  0:uint(8);
  return (section, part);
}

Reverse Comparator

Sort functions in Chapel do not have a reverse argument. Instead, reverse sorting is handled through the comparator interface.

A module-defined reverseComparator can be passed to a sort function to reverse the default sorting order.

var Array = [-1, -4, 2, 3];

// Using module-defined 'reverseComparator'
sort(Array, comparator=reverseComparator)

// This will output: 3, 2, -1, -4
writeln(Array);

To reverse the sort order of a user-defined comparator, pass the user-defined comparator to the initializer of the module-defined ReverseComparator record, which can be passed to the sort function.

var Array = [-1, -4, 2, 3];

// Empty record serves as comparator
record Comparator { }

// compare method defines how 2 elements are compared
proc Comparator.compare(a, b) {
  return abs(a) - abs(b);
}

var absReverseComparator: ReverseComparator(Comparator);

sort(Array, comparator=absReverseComparator);

// This will output: -4, 3, 2, -1
writeln(Array);
const defaultComparator: DefaultComparator

Instance of DefaultComparator used as default comparator= argument when no comparator is passed to a sort function

const reverseComparator: ReverseComparator(DefaultComparator)

Instance of ReverseComparator. Pass this as the comparator= argument of a sort function to reverse the sort order.

proc sort(Data: [?Dom] ?eltType, comparator: ?rec = defaultComparator)

Sort the elements in an array. It is up to the implementation to choose the sorting algorithm.

Note

This function currently either uses a parallel radix sort or a serial quickSort. The algorithms used will change over time.

It currently uses parallel radix sort if the following conditions are met:

  • the array being sorted is over a non-strided domain
  • comparator includes a keyPart method for eltType or includes a key returning a value for which the default comparator includes a keyPart method

Note that the default comparator includes keyPart methods for:

  • int
  • tuples of int
  • uint
  • tuples of uint
  • string
Arguments:
  • Data : [] eltType -- The array to be sorted
  • comparator -- Comparator record that defines how the data is sorted.
proc isSorted(Data: [?Dom] ?eltType, comparator: ?rec = defaultComparator): bool

Check if array Data is in sorted order

Arguments:
  • Data : [] eltType -- The array to verify
  • comparator -- Comparator record that defines how the data is sorted.
Returns:

true if array is sorted
Return type:

bool
iter sorted(x, comparator: ?rec = defaultComparator)

Yield the elements of argument x in sorted order, using sort algorithm.

Arguments:
  • x : iterable -- An iterable value to be sorted and yielded element by element
  • comparator -- Comparator record that defines how the data is sorted.
Yields:

The elements of x in sorted order
Yield type:

x's element type
proc bubbleSort(Data: [?Dom] ?eltType, comparator: ?rec = defaultComparator)

Sort the 1D array Data in-place using a sequential bubble sort algorithm.

Arguments:
  • Data : [] eltType -- The array to be sorted
  • comparator -- Comparator record that defines how the data is sorted.
proc heapSort(Data: [?Dom] ?eltType, comparator: ?rec = defaultComparator)

Sort the 1D array Data in-place using a sequential heap sort algorithm.

Arguments:
  • Data : [] eltType -- The array to be sorted
  • comparator -- Comparator record that defines how the data is sorted.
proc insertionSort(Data: [?Dom] ?eltType, comparator: ?rec = defaultComparator)

Sort the 1D array Data in-place using a sequential insertion sort algorithm.

Arguments:
  • Data : [] eltType -- The array to be sorted
  • comparator -- Comparator record that defines how the data is sorted.
proc binaryInsertionSort(Data: [?Dom] ?eltType, comparator: ?rec = defaultComparator)

Sort the 1D array Data in-place using a sequential, stable binary insertion sort algorithm. Should be used when there is a high cost of comparison.

Arguments:
  • Data : [] eltType -- The array to be sorted
  • comparator -- Comparator record that defines how the data is sorted.
proc mergeSort(Data: [?Dom] ?eltType, minlen = 16, comparator: ?rec = defaultComparator)

Sort the 1D array Data using a parallel merge sort algorithm.

Arguments:
  • Data : [] eltType -- The array to be sorted
  • minlen : integral -- When the array size is less than minlen use insertionSort algorithm
  • comparator -- Comparator record that defines how the data is sorted.
proc quickSort(Data: [?Dom] ?eltType, minlen = 16, comparator: ?rec = defaultComparator)

Sort the 1D array Data in-place using a sequential quick sort algorithm.

Arguments:
  • Data : [] eltType -- The array to be sorted
  • minlen : integral -- When the array size is less than minlen use insertionSort algorithm
  • comparator -- Comparator record that defines how the data is sorted.
proc selectionSort(Data: [?Dom] ?eltType, comparator: ?rec = defaultComparator)

Sort the 1D array Data in-place using a sequential selection sort algorithm.

Arguments:
  • Data : [] eltType -- The array to be sorted
  • comparator -- Comparator record that defines how the data is sorted.
record DefaultComparator

Default comparator used in sort functions.

proc compare(a, b)

Default compare method used in sort functions. Uses the < operator to compute the ordering between a and b. See also The .compare method.

Returns:1 if b < a
Returns:0 if a == b
Returns:-1 if a < b
proc keyPart(x: integral, i: int): (int(8), x.type )

Default keyPart method for integral values. See also The .keyPart method.

Arguments:
  • x -- the int or uint of any size to sort
  • i -- the part number requested
Returns:

(0, x) if i==0, or (-1, x) otherwise
proc keyPart(x: _tuple, i: int)

Default keyPart method for tuples of integral values. See also The .keyPart method.

Arguments:
  • x -- tuple of the int or uint (of any bit width) to sort
  • i -- the part number requested
Returns:

(0, x(i)) if i <= x.size, or (-1, 0) otherwise
proc keyPart(x: string, i: int): (int(8), uint(8))

Default keyPart method for sorting strings. See also The .keyPart method.

Note

Currently assumes that the string is local.

Arguments:
  • x -- the string to sort
  • i -- the part number requested
Returns:

(0, byte i of string) or (-1, 0) if i > x.size
record ReverseComparator

Reverse comparator built from another comparator.

var comparator

Generic comparator defined in initializer.

proc init()

Initializer - builds a comparator with a compare method that reverses the sort order of the default comparator.

proc init(comparator)

Initializer - builds a comparator with a compare method that reverses the sort order of the argument-provided comparator.

Arguments:comparator -- Comparator record that defines how the data is sorted.
proc keyPart(a, i)

Reverses comparator.keyPart. See also The .keyPart method.

proc compare(a, b)

Reverses comparator.compare. See also The .compare method.