Sort

Usage

use Sort;

or

import Sort;

This module supports standard algorithms for sorting data. It is designed to be flexible and efficient, allowing the user to define custom comparators to sort any data type, as long as the comparator implements the appropriate sorting interface.

The simplest way to sort an array is to call the sort function on the array. The sort function will use the default comparator to sort the array in ascending order.

var Array = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5];

sort(Array);

// This will output: 1, 1, 2, 3, 3, 4, 5, 5, 5, 6, 9
writeln(Array);

The sort function can also accept a region argument to sort a subset of an array. This is offered as an optimization over using an array slice which may have performance overhead.

var Array = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5];

// Sort only the elements in the range 1..5
// Same as sort(Array[1..5]);
sort(Array, region=1..5);

// This will output: 3, 1, 1, 4, 5, 9, 2, 6, 5, 3, 5
writeln(Array);

The sort function can also be called on a list, be stable or unstable, and accept a custom comparator. See the sort(x: list) function for details.

Comparators

Comparators allow sorting data by a mechanism other than the default comparison operations between array elements.

The sort function can accept a comparator argument, which defines how the data is sorted. If no comparator is passed, the default comparator is used.

Reverse sorting is handled by the reverseComparator. See Reverse Comparator for details.

To use a custom comparator, define a record or a class which implements the appropriate sorting interface.

Comparators need to implement one, and only one, of the following interfaces as well as at least one of their associated methods:

• keyComparator – see The keyComparator interface

• relativeComparator – see The relativeComparator interface

• keyPartComparator – see The keyPartComparator interface

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

Future:

Provide a unified sortComparator interface, which can represent an exclusive or (XOR) of the three interfaces above.

The keyComparator interface

The keyComparator interface is used to sort data by a key value. Records implementing this interface must define a key method.

Today, it is an error for a comparator implementing the keyComparator interface to contain a key method as well as one of the other methods that are part of the relativeComparator or keyPartComparator interfaces. This restriction might be lifted in future releases.

The .key method

The key(elt) 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(elt) {
  return elt;
}

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, implements the keyComparator interface
record absComparator : keyComparator { }

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

var absoluteComparator: absComparator;

sort(Array, comparator=absoluteComparator);

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

The return type of key(elt) 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:

operator <(x: returnType, y: returnType): bool {
  ...
}

The relativeComparator interface

The relativeComparator interface is used to sort data by comparing two elements directly. Records implementing this interface must define a compare method.

The .compare method

The compare(x, y) 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 x and y compare to each other. The conditions between x and y should result in the following return values for compare(x, y):

Return Value	Condition
> 0	x > y
0	x == y
< 0	x < y

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

proc defaultComparator.compare(x, y) {
  return x - y;
}

The absolute value comparison example from above can alternatively be implemented with a relativeComparator as follows:

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

// Empty record serves as comparator
record absComparator : relativeComparator { }

// compare method defines how 2 elements are compared
proc absComparator.compare(x, y) {
  return abs(x) - abs(y);
}

var absoluteComparator: absComparator;

sort(Array, comparator=absoluteComparator);

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

The keyPartComparator interface

The keyPartComparator interface defines how a comparator should sort parts of a key using the keyPart method. This is used for certain sort algorithms. Records implementing this interface must define a keyPart method.

A comparator implementing this interface can optionally also provide a compare method. In that event, the sort algorithm will use whichever is appropriate for the algorithm and expect that they have consistent results.

The .keyPart method

A keyPart(elt, 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:

• elt is the element being sorted

• i is the part number of the key requested, starting from 0

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

• The section must be of type keyPartStatus. It indicates when the end of elt has been reached and in that event how it should be sorted relative to other array elements.

• 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 keyPartStatus.returned.

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(elt: 2*int, i: int) {
  if i > 1 then
    return (keyPartStatus.pre, 0); // second value is not used

  return (keyPartStatus.returned, elt(i));
}

Here is a keyPart to support sorting of strings:

proc keyPart(x: string, i: int): (keyPartStatus, uint(8)) {
  var len = x.numBytes;
  var section = if i < len then keyPartStatus.returned  else keyPartStatus.pre;
  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.

An instance of the type 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 = new 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.

For this example, we will reverse the absolute value comparison from above using the relativeComparator interface, although the same can be done with the keyComparator interface.

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

// Empty record serves as comparator
record absComparator : relativeComparator{ }

// compare method defines how 2 elements are compared
proc absComparator.compare(x, y) {
  return abs(x) - abs(y); // ascending order
}

var absReverseComparator: reverseComparator(absComparator); // reverse order

sort(Array, comparator=absReverseComparator);

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

proc sort(ref x: [], comparator: ? = new defaultComparator(), param stable: bool = false)

Sort the elements in the 1D rectangular array x. After the call, x will store elements in sorted order.

The choice of sorting algorithm used is made by the implementation.

Note

When reordering elements, the sort implementation might use assignment, memory moves, or the swap operator. Additionally, the sort might copy-initialize some elements, for example, to create a pivot in quicksort.

Note

This function currently either uses a parallel radix sort or a parallel improved quick sort. For stable sort, it uses Timsort. 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

• real

• tuples of real

• imag

• tuples of imag

• string

• c_string

Arguments:

• x : array – The array to be sorted

• comparator – Comparator record that defines how the data is sorted.

• stable – Defaults to false. If it is false, the implementation can sort in a way that reorders equal keys. If it is true, it will use a stable algorithm in order to preserve the order of equal keys.

proc sort(ref x: list(?), comparator: ? = new defaultComparator(), param stable: bool = false)

Sort the elements in the list x. After the call, x will store elements in sorted order.

See sort declared above for details.

Warning

Sorting the elements of a list may invalidate existing references to the elements contained in the list.

Arguments:

• x : list – The list to be sorted

• comparator – Comparator record that defines how the data is sorted.

• stable – Defaults to false. If it is false, the implementation can sort in a way that reorders equal keys. If it is true, it will use a stable algorithm in order to preserve the order of equal keys.

proc sort(ref x: [], comparator, region: range(?), param stable: bool = false)

Sort the elements in the range ‘region’ within in the 1D rectangular array x. After the call, x[region] will store elements in sorted order. This function accepts a ‘region’ range as an optimized alternative to using an array view.

See the sort declared just above for details.

Note

Due to uncertainty about the usefulness of this routine, it is unstable. Please comment on https://github.com/chapel-lang/chapel/issues/25648 if you find this routine important in your work.

proc sort(ref Data: [?Dom] ?eltType, comparator: ?rec = new defaultComparator(), param stable: bool = false, param inPlaceAlgorithm: bool = false)

Warning

The ‘sort’ function with ‘Data’ and ‘inPlaceAlgorithm’ arguments has been deprecated, please use the ‘sort’ function with an ‘x’ argument instead

Sort the elements in the 1D rectangular array Data. After the call, Data will store elements in sorted order.

The choice of sorting algorithm used is made by the implementation.

Note

When reordering elements, the sort implementation might use assignment, memory moves, or the swap operator. Additionally, the sort might copy-initialize some elements, for example, to create a pivot in quicksort.

Note

This function currently either uses a parallel radix sort or a parallel improved quick sort. For stable sort, use sort with stable=true. 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

• real

• tuples of real

• imag

• tuples of imag

• string

• c_string

Arguments:

• Data : [] eltType – The array to be sorted

• comparator – Comparator record that defines how the data is sorted.

• stable – Defaults to false. If it is false, the implementation can sort in a way that reorders equal keys. If it is true, it will use a stable algorithm in order to preserve the order of equal keys.

• inPlaceAlgorithm – Defaults to false. If it is false, the implementation can make a copy of Data for scratch storage during the sort. If it is true, it will use an in-place algorithm in order to use less memory.

proc isSorted(x: [], comparator: ? = new defaultComparator()) : bool

Check if array x is in sorted order

Arguments:

• x : array – The array to verify

• comparator – Comparator record that defines how the data is sorted.

Returns:

true if array is sorted

Return type:

bool

proc isSorted(x: list(?), comparator: ? = new defaultComparator()) : bool

Check if list x is in sorted order

Arguments:

• x : list – The list to verify

• comparator – Comparator record that defines how the data is sorted.

Returns:

true if list is sorted

Return type:

bool

proc isSorted(Data: [?Dom] ?eltType, comparator: ?rec = new defaultComparator()) : bool

Warning

‘isSorted’ with the argument name ‘Data’ is deprecated, please use the version with the argument name ‘x’ instead

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: ? = new defaultComparator())

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

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

interface keyComparator

Warning

keyComparator is not yet stable

The keyComparator interface defines how a comparator should sort elements by returning a key for each element in the array.

proc Self.key(elt)

Given an array element, returns a key element to sort by.

Arguments:

elt – the array element being compared

Returns:

a key element to sort by

Return type:

a type that support ‘<’

enum keyPartStatus { pre = -1, returned = 0, post = 1 }

Indicates when the end of an element has been reached and in that event how it should be sorted relative to other array elements.

enum constant pre = -1

No more key parts for element, sort it before those with more parts

enum constant returned = 0

A key part for element is being returned

enum constant post = 1

No more key parts for element, sort it after those with more parts

interface keyPartComparator

Warning

keyPartComparator is not yet stable

The keyPartComparator interface defines how a comparator should sort parts of a key, by defining keyPart. This is used for certain sort algorithms. If keyPart is not appropriate, the sort implementation may use compare instead.

proc Self.keyPart(elt, i: int) : (keyPartStatus, integral)

A keyPart(elt, 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:

• elt is the element being sorted

• i is the part number of the key requested, starting from 0

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

• The section must be of type keyPartStatus. It indicates when the end of elt has been reached and in that event how it should be sorted relative to other array elements.

• 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 keyPartStatus.returned.

Arguments:

• elt – the element being sorted

• i – the part number requested

Returns:

(section, part) where section is a keyPartStatus and part is an integral type.

proc Self.compare(x, y: x.type)

Defines a comparison between two elements of the same type. This method is not required to be implemented by comparators that implement the keyPartComparator interface.

Arguments:

• x – the first element to compare

• y – the second element to compare

Returns:

-1 if x should be sorted before y, 1 if x should be sorted after y, and 0 if x and y are equal

Return type:

a signed integral

interface relativeComparator

Warning

relativeComparator is not yet stable

The relativeComparator interface defines a comparison between two elements

proc Self.compare(x, y: x.type)

Defines a comparison between two elements of the same type.

Arguments:

• x – the first element to compare

• y – the second element to compare

Returns:

-1 if x should be sorted before y, 1 if x should be sorted after y, and 0 if x and y are equal

Return type:

a signed integral

type DefaultComparator = defaultComparator

Warning

The DefaultComparator record has been renamed to defaultComparator, please use that name instead

Default comparator used in sort functions.

record defaultComparator : keyPartComparator

Default comparator used in sort functions.

proc compare(a, b)

Warning

compare with ‘a’ and ‘b’ arguments is deprecated, please use compare with ‘x’ and ‘y’ arguments instead

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 compare(x, y: x.type)

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

Returns:

1 if y < x

Returns:

0 if x == y

Returns:

-1 if x < y

proc keyPart(elt: integral, i: int) : (keyPartStatus, elt.type)  where useKeyPartStatus

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

Arguments:

• elt – the int or uint of any size to sort

• i – the part number requested

Returns:

(keyPartStatus.returned, x) if i==0, or (keyPartStatus.pre, x) otherwise

proc keyPart(x: integral, i: int) : (int(8), x.type)  where !useKeyPartStatus

Warning

Using keyPart without ‘keyPartStatus’ is deprecated, compile with ‘-suseKeyPartStatus’ and update your types if necessary

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(elt: real(?), i: int) : (keyPartStatus, uint(numBits(elt.type)))  where useKeyPartStatus

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

Arguments:

• elt – the real of any width to sort

• i – the part number requested

Returns:

(keyPartStatus.returned, u) if i==0, or (keyPartStatus.pre, u) otherwise, where u is a uint storing the bits of the real but with some transformations applied to produce the correct sort order.

proc keyPart(x: chpl_anyreal, i: int) : (int(8), uint(numBits(x.type)))  where !useKeyPartStatus

Warning

Using keyPart without ‘keyPartStatus’ is deprecated, compile with ‘-suseKeyPartStatus’ and update your types if necessary

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

Arguments:

• x – the real of any width to sort

• i – the part number requested

Returns:

(0, u) if i==0, or (-1, u) otherwise, where u is a uint storing the bits of the real but with some transformations applied to produce the correct sort order.

proc keyPart(elt: imag(?), i: int) : (keyPartStatus, uint(numBits(elt.type)))  where useKeyPartStatus

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

This method works by calling keyPart with the corresponding real value.

proc keyPart(x: chpl_anyimag, i: int) : (int(8), uint(numBits(x.type)))  where !useKeyPartStatus

Warning

Using keyPart without ‘keyPartStatus’ is deprecated, compile with ‘-suseKeyPartStatus’ and update your types if necessary

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

This method works by calling keyPart with the corresponding real value.

proc keyPart(elt: _tuple, i: int)  where useKeyPartStatus && isHomogeneousTuple(elt) && (isInt(elt(0)) || isUint(elt(0)) || isReal(elt(0)) || isImag(elt(0)))

Default keyPart method for tuples of int, uint, real, or imag values. See also The .keyPart method.

Arguments:

• elt – homogeneous tuple of the numeric type (of any bit width) to sort

• i – the part number requested

Returns:

For int and uint, returns (keyPartStatus.pre, elt(i)) if i < elt.size, or (keyPartStatus.returned, 0) otherwise. For real and imag, uses keyPart to find the uint to provide the sorting order.

proc keyPart(x: _tuple, i: int)  where !useKeyPartStatus && isHomogeneousTuple(x) && (isInt(x(0)) || isUint(x(0)) || isReal(x(0)) || isImag(x(0)))

Warning

Using keyPart without ‘keyPartStatus’ is deprecated, compile with ‘-suseKeyPartStatus’ and update your types if necessary

Default keyPart method for tuples of int, uint, real, or imag values. See also The .keyPart method.

Arguments:

• x – homogeneous tuple of the numeric type (of any bit width) to sort

• i – the part number requested

Returns:

For int and uint, returns (0, x(i)) if i < x.size, or (-1, 0) otherwise. For real and imag, uses keyPart to find the uint to provide the sorting order.

proc keyPart(elt: string, i: int) : (keyPartStatus, uint(8))  where useKeyPartStatus

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

Note

Currently assumes that the string is local.

Arguments:

• elt – the string to sort

• i – the part number requested

Returns:

(keyPartStatus.returned, byte i of string) or (keyPartStatus.pre, 0) if i > elt.size

proc keyPart(x: string, i: int) : (int(8), uint(8))  where !useKeyPartStatus

Warning

Using keyPart without ‘keyPartStatus’ is deprecated, compile with ‘-suseKeyPartStatus’ and update your types if necessary

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

proc keyPart(elt: c_ptrConst(c_char), i: int) : (keyPartStatus, uint(8))  where useKeyPartStatus

Default keyPart method for sorting c_ptrConst(c_char). See also The .keyPart method.

Arguments:

• elt – the c_ptrConst(c_char) to sort

• i – the part number requested

Returns:

(keyPartStatus.returned, byte i of string) or (keyPartStatus.pre, 0) if byte i is 0

proc keyPart(x: c_ptrConst(c_char), i: int) : (int(8), uint(8))  where !useKeyPartStatus

Warning

Using keyPart without ‘keyPartStatus’ is deprecated, compile with ‘-suseKeyPartStatus’ and update your types if necessary

Default keyPart method for sorting c_ptrConst(c_char). See also The .keyPart method. :arg x: the c_ptrConst(c_char) to sort :arg i: the part number requested :returns: (0, byte i of string) or (-1, 0) if byte i is 0

type ReverseComparator = reverseComparator

Warning

The ReverseComparator record has been renamed to reverseComparator, please use that name instead

Reverse comparator built from another comparator.

record reverseComparator : keyPartComparator

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(elt, i)  where useKeyPartStatus && (hasKeyPart(elt) || hasKeyPartFromKey(elt))

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

proc keyPart(a, i)  where !useKeyPartStatus && (hasKeyPart(a) || hasKeyPartFromKey(a))

Warning

Using keyPart without ‘keyPartStatus’ is deprecated, compile with ‘-suseKeyPartStatus’ and update your types if necessary

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

proc compare(a, b)  where hasCompare(a, b) || hasCompareFromKey(a)

Warning

compare with ‘a’ and ‘b’ arguments is deprecated, please use compare with ‘x’ and ‘y’ arguments instead

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

proc compare(x, y: x.type)  where hasCompare(x, y) || hasCompareFromKey(x)

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