Improve documentation for packedsets (#16715)

* Improve documentation for packedsets Add more runnableExamples Add deprecated pragma to intsets Replace intsets with packedsets in lib.rst * Apply suggested changes
2025-12-28 17:04:41 +00:00 · 2021-01-16 16:09:53 +01:00
parent 8939de15d7
commit 44ceefa9fe
3 changed files with 154 additions and 151 deletions
--- a/doc/lib.rst
+++ b/doc/lib.rst
@@ -32,15 +32,15 @@ Automatic imports
 * `system <system.html>`_
  Basic procs and operators that every program needs. It also provides IO
  facilities for reading and writing text and binary files. It is imported
-  implicitly by the compiler. Do not import it directly. It relies on compiler 
+  implicitly by the compiler. Do not import it directly. It relies on compiler
  magic to work.

 * `threads <threads.html>`_
-  Basic Nim thread support. **Note**: This is part of the system module. Do not
+  Basic Nim thread support. **Note:** This is part of the system module. Do not
  import it explicitly. Enabled with ``--threads:on``.

 * `channels <channels.html>`_
-  Nim message passing support for threads. **Note**: This is part of the
+  Nim message passing support for threads. **Note:** This is part of the
  system module. Do not import it explicitly. Enabled with ``--threads:on``.


@@ -107,6 +107,7 @@ Collections

 * `intsets <intsets.html>`_
  Efficient implementation of a set of ints as a sparse bit set.
+  **Deprecated:** Use the packedsets module instead.

 * `lists <lists.html>`_
  Nim linked list support. Contains singly and doubly linked lists and
@@ -115,6 +116,9 @@ Collections
 * `options <options.html>`_
  The option type encapsulates an optional value.

+* `packedsets <packedsets.html>`_
+  Efficient implementation of a set of ordinals as a sparse bit set.
+
 * `sets <sets.html>`_
  Nim hash and bit set support.

@@ -154,7 +158,7 @@ String handling

 * `ropes <ropes.html>`_
  This module contains support for a *rope* data type.
-  Ropes can represent very long strings efficiently; 
+  Ropes can represent very long strings efficiently;
  especially concatenation is done in O(1) instead of O(n).

 * `strformat <strformat.html>`_
@@ -231,8 +235,8 @@ Generic Operating System Services

 * `streams <streams.html>`_
  This module provides a stream interface and two implementations thereof:
-  the `FileStream` and the `StringStream` which implement the stream 
-  interface for Nim file objects (`File`) and strings. Other modules 
+  the `FileStream` and the `StringStream` which implement the stream
+  interface for Nim file objects (`File`) and strings. Other modules
  may provide other implementations for this standard stream interface.

 * `terminal <terminal.html>`_
@@ -373,12 +377,12 @@ Docutils
 --------

 * `packages/docutils/highlite <highlite.html>`_
-  Source highlighter for programming or markup languages.  Currently, 
+  Source highlighter for programming or markup languages. Currently,
  only a few languages are supported, other languages may be added.
  The interface supports one language nested in another.

 * `packages/docutils/rst <rst.html>`_
-  This module implements a reStructuredText parser. A large subset 
+  This module implements a reStructuredText parser. A large subset
  is implemented. Some features of the markdown wiki syntax are also supported.

 * `packages/docutils/rstast <rstast.html>`_
@@ -403,8 +407,8 @@ Generators
 ----------

 * `htmlgen <htmlgen.html>`_
-  This module implements a simple XML and HTML code 
-  generator. Each commonly used HTML tag has a corresponding macro 
+  This module implements a simple XML and HTML code
+  generator. Each commonly used HTML tag has a corresponding macro
  that generates a string with its HTML representation.


@@ -489,7 +493,7 @@ Regular expressions
 -------------------

 * `re <re.html>`_
-  This module contains procedures and operators for handling regular 
+  This module contains procedures and operators for handling regular
  expressions. The current implementation uses PCRE.


--- a/lib/pure/collections/intsets.nim
+++ b/lib/pure/collections/intsets.nim
@@ -7,9 +7,10 @@
 #    distribution, for details about the copyright.
 #

-## Deprecated by the generic `PackedSet` for ordinal sparse sets.
-## **See also:**
-## * `Ordinal packed sets module <packedsets.html>`_ for more general packed sets
+## Deprecated in favor of the generic `packedsets module <packedsets.html>`_
+## for ordinal sparse sets.
+
+{.deprecated: "Use the 'packedsets' module instead".}

 import std/private/since
 import std/packedsets
--- a/lib/std/packedsets.nim
+++ b/lib/std/packedsets.nim
@@ -7,17 +7,18 @@
 #    distribution, for details about the copyright.
 #

-## The ``packedsets`` module implements an efficient `Ordinal`set implemented as a
+## The `packedsets` module implements an efficient `Ordinal` set implemented as a
 ## `sparse bit set`:idx:.
 ##
 ## Supports any Ordinal type.
 ##
-## **Note**: Currently the assignment operator ``=`` for ``PackedSet[A]``
+## **Note**: Currently the assignment operator `=` for `PackedSet[A]`
 ## performs some rather meaningless shallow copy. Since Nim currently does
-## not allow the assignment operator to be overloaded, use `assign proc
+## not allow the assignment operator to be overloaded, use the `assign proc
 ## <#assign,PackedSet[A],PackedSet[A]>`_ to get a deep copy.
 ##
-## **See also:**
+## See also
+## ========
 ## * `sets module <sets.html>`_ for more general hash sets

 import std/private/since
@@ -45,8 +46,8 @@ type

  TrunkSeq = seq[PTrunk]

-  ## An efficient set of `Ordinal` types implemented as a sparse bit set.
  PackedSet*[A: Ordinal] = object
+    ## An efficient set of `Ordinal` types implemented as a sparse bit set.
    elems: int           # only valid for small numbers
    counter, max: int
    head: PTrunk
@@ -62,7 +63,7 @@ proc nextTry(h, maxHash: Hash, perturb: var Hash): Hash {.inline.} =
  const PERTURB_SHIFT = 5
  var perturb2 = cast[uint](perturb) shr PERTURB_SHIFT
  perturb = cast[Hash](perturb2)
-  result = ((5*h) + 1 + perturb) and maxHash
+  result = ((5 * h) + 1 + perturb) and maxHash

 proc packedSetGet[A](t: PackedSet[A], key: int): PTrunk =
  var h = key and t.max
@@ -77,9 +78,9 @@ proc intSetRawInsert[A](t: PackedSet[A], data: var TrunkSeq, desc: PTrunk) =
  var h = desc.key and t.max
  var perturb = desc.key
  while data[h] != nil:
-    assert(data[h] != desc)
+    assert data[h] != desc
    h = nextTry(h, t.max, perturb)
-  assert(data[h] == nil)
+  assert data[h] == nil
  data[h] = desc

 proc intSetEnlarge[A](t: var PackedSet[A]) =
@@ -103,7 +104,7 @@ proc intSetPut[A](t: var PackedSet[A], key: int): PTrunk =
  h = key and t.max
  perturb = key
  while t.data[h] != nil: h = nextTry(h, t.max, perturb)
-  assert(t.data[h] == nil)
+  assert t.data[h] == nil
  new(result)
  result.next = t.head
  result.key = key
@@ -112,7 +113,7 @@ proc intSetPut[A](t: var PackedSet[A], key: int): PTrunk =

 proc bitincl[A](s: var PackedSet[A], key: int) {.inline.} =
  var ret: PTrunk
-  var t = intSetPut(s, `shr`(key, TrunkShift))
+  var t = intSetPut(s, key shr TrunkShift)
  var u = key and TrunkMask
  t.bits[u shr IntShift] = t.bits[u shr IntShift] or
      (BitScalar(1) shl (u and IntMask))
@@ -121,8 +122,8 @@ proc exclImpl[A](s: var PackedSet[A], key: int) =
  if s.elems <= s.a.len:
    for i in 0..<s.elems:
      if s.a[i] == key:
-        s.a[i] = s.a[s.elems-1]
-        dec s.elems
+        s.a[i] = s.a[s.elems - 1]
+        dec(s.elems)
        return
  else:
    var t = packedSetGet(s, key shr TrunkShift)
@@ -161,13 +162,13 @@ iterator items*[A](s: PackedSet[A]): A {.inline.} =
      r = r.next

 proc initPackedSet*[A]: PackedSet[A] =
-  ## Returns an empty PackedSet[A].
-  ## A must be Ordinal
+  ## Returns an empty `PackedSet[A]`.
+  ## `A` must be `Ordinal`.
  ##
-  ## See also:
-  ## * `toPackedSet[A] proc <#toPackedSet,openArray[A]>`_
+  ## **See also:**
+  ## * `toPackedSet proc <#toPackedSet,openArray[A]>`_
  runnableExamples:
-    var a = initPackedSet[int]()
+    let a = initPackedSet[int]()
    assert len(a) == 0

    type Id = distinct int
@@ -185,21 +186,17 @@ proc initPackedSet*[A]: PackedSet[A] =
 proc contains*[A](s: PackedSet[A], key: A): bool =
  ## Returns true if `key` is in `s`.
  ##
-  ## This allows the usage of `in` operator.
+  ## This allows the usage of the `in` operator.
  runnableExamples:
    type ABCD = enum A, B, C, D

-    var a = initPackedSet[int]()
-    for x in [1, 3, 5]:
-      a.incl(x)
+    let a = [1, 3, 5].toPackedSet
    assert a.contains(3)
    assert 3 in a
-    assert(not a.contains(8))
+    assert not a.contains(8)
    assert 8 notin a

-    var letters = initPackedSet[ABCD]()
-    for x in [A, C]:
-      letters.incl(x)
+    let letters = [A, C].toPackedSet
    assert A in letters
    assert C in letters
    assert B notin letters
@@ -208,7 +205,7 @@ proc contains*[A](s: PackedSet[A], key: A): bool =
    for i in 0..<s.elems:
      if s.a[i] == ord(key): return true
  else:
-    var t = packedSetGet(s, `shr`(ord(key), TrunkShift))
+    var t = packedSetGet(s, ord(key) shr TrunkShift)
    if t != nil:
      var u = ord(key) and TrunkMask
      result = (t.bits[u shr IntShift] and
@@ -221,9 +218,9 @@ proc incl*[A](s: var PackedSet[A], key: A) =
  ##
  ## This doesn't do anything if `key` is already in `s`.
  ##
-  ## See also:
+  ## **See also:**
  ## * `excl proc <#excl,PackedSet[A],A>`_ for excluding an element
-  ## * `incl proc <#incl,PackedSet[A],PackedSet[A]>`_ for including other set
+  ## * `incl proc <#incl,PackedSet[A],PackedSet[A]>`_ for including a set
  ## * `containsOrIncl proc <#containsOrIncl,PackedSet[A],A>`_
  runnableExamples:
    var a = initPackedSet[int]()
@@ -236,10 +233,10 @@ proc incl*[A](s: var PackedSet[A], key: A) =
      if s.a[i] == ord(key): return
    if s.elems < s.a.len:
      s.a[s.elems] = ord(key)
-      inc s.elems
+      inc(s.elems)
      return
    newSeq(s.data, InitIntSetSize)
-    s.max = InitIntSetSize-1
+    s.max = InitIntSetSize - 1
    for i in 0..<s.elems:
      bitincl(s, s.a[i])
    s.elems = s.a.len + 1
@@ -251,35 +248,29 @@ proc incl*[A](s: var PackedSet[A], other: PackedSet[A]) =
  ##
  ## This is the in-place version of `s + other <#+,PackedSet[A],PackedSet[A]>`_.
  ##
-  ## See also:
-  ## * `excl proc <#excl,PackedSet[A],PackedSet[A]>`_ for excluding other set
+  ## **See also:**
+  ## * `excl proc <#excl,PackedSet[A],PackedSet[A]>`_ for excluding a set
  ## * `incl proc <#incl,PackedSet[A],A>`_ for including an element
  ## * `containsOrIncl proc <#containsOrIncl,PackedSet[A],A>`_
  runnableExamples:
-    var
-      a = initPackedSet[int]()
-      b = initPackedSet[int]()
-    a.incl(1)
-    b.incl(5)
-    a.incl(b)
+    var a = [1].toPackedSet
+    a.incl([5].toPackedSet)
    assert len(a) == 2
    assert 5 in a

  for item in other.items: incl(s, item)

 proc toPackedSet*[A](x: openArray[A]): PackedSet[A] {.since: (1, 3).} =
-  ## Creates a new PackedSet[A] that contains the elements of `x`.
+  ## Creates a new `PackedSet[A]` that contains the elements of `x`.
  ##
  ## Duplicates are removed.
  ##
-  ## See also:
-  ## * `initPackedSet[A] proc <#initPackedSet>`_
+  ## **See also:**
+  ## * `initPackedSet proc <#initPackedSet>`_
  runnableExamples:
-    var
-      a = toPackedSet([5, 6, 7])
-      b = toPackedSet(@[1, 8, 8, 8])
-    assert len(a) == 3
-    assert len(b) == 2
+    let a = [5, 6, 7, 8, 8].toPackedSet
+    assert len(a) == 4
+    assert $a == "{5, 6, 7, 8}"

  result = initPackedSet[A]()
  for item in x:
@@ -289,11 +280,11 @@ proc containsOrIncl*[A](s: var PackedSet[A], key: A): bool =
  ## Includes `key` in the set `s` and tells if `key` was already in `s`.
  ##
  ## The difference with regards to the `incl proc <#incl,PackedSet[A],A>`_ is
-  ## that this proc returns `true` if `s` already contained `key`. The
-  ## proc will return `false` if `key` was added as a new value to `s` during
+  ## that this proc returns true if `s` already contained `key`. The
+  ## proc will return false if `key` was added as a new value to `s` during
  ## this call.
  ##
-  ## See also:
+  ## **See also:**
  ## * `incl proc <#incl,PackedSet[A],A>`_ for including an element
  ## * `missingOrExcl proc <#missingOrExcl,PackedSet[A],A>`_
  runnableExamples:
@@ -309,7 +300,7 @@ proc containsOrIncl*[A](s: var PackedSet[A], key: A): bool =
    incl(s, key)
    result = false
  else:
-    var t = packedSetGet(s, `shr`(ord(key), TrunkShift))
+    var t = packedSetGet(s, ord(key) shr TrunkShift)
    if t != nil:
      var u = ord(key) and TrunkMask
      result = (t.bits[u shr IntShift] and BitScalar(1) shl (u and IntMask)) != 0
@@ -325,17 +316,17 @@ proc excl*[A](s: var PackedSet[A], key: A) =
  ##
  ## This doesn't do anything if `key` is not found in `s`.
  ##
-  ## See also:
+  ## **See also:**
  ## * `incl proc <#incl,PackedSet[A],A>`_ for including an element
-  ## * `excl proc <#excl,PackedSet[A],PackedSet[A]>`_ for excluding other set
+  ## * `excl proc <#excl,PackedSet[A],PackedSet[A]>`_ for excluding a set
  ## * `missingOrExcl proc <#missingOrExcl,PackedSet[A],A>`_
  runnableExamples:
-    var a = initPackedSet[int]()
-    a.incl(3)
+    var a = [3].toPackedSet
    a.excl(3)
    a.excl(3)
    a.excl(99)
    assert len(a) == 0
+
  exclImpl[A](s, cast[int](key))

 proc excl*[A](s: var PackedSet[A], other: PackedSet[A]) =
@@ -343,18 +334,13 @@ proc excl*[A](s: var PackedSet[A], other: PackedSet[A]) =
  ##
  ## This is the in-place version of `s - other <#-,PackedSet[A],PackedSet[A]>`_.
  ##
-  ## See also:
-  ## * `incl proc <#incl,PackedSet[A],PackedSet[A]>`_ for including other set
+  ## **See also:**
+  ## * `incl proc <#incl,PackedSet[A],PackedSet[A]>`_ for including a set
  ## * `excl proc <#excl,PackedSet[A],A>`_ for excluding an element
  ## * `missingOrExcl proc <#missingOrExcl,PackedSet[A],A>`_
  runnableExamples:
-    var
-      a = initPackedSet[int]()
-      b = initPackedSet[int]()
-    a.incl(1)
-    a.incl(5)
-    b.incl(5)
-    a.excl(b)
+    var a = [1, 5].toPackedSet
+    a.excl([5].toPackedSet)
    assert len(a) == 1
    assert 5 notin a

@@ -363,6 +349,10 @@ proc excl*[A](s: var PackedSet[A], other: PackedSet[A]) =

 proc len*[A](s: PackedSet[A]): int {.inline.} =
  ## Returns the number of elements in `s`.
+  runnableExamples:
+    let a = [1, 3, 5].toPackedSet
+    assert len(a) == 3
+
  if s.elems < s.a.len:
    result = s.elems
  else:
@@ -372,20 +362,19 @@ proc len*[A](s: PackedSet[A]): int {.inline.} =
      inc(result)

 proc missingOrExcl*[A](s: var PackedSet[A], key: A): bool =
-  ## Excludes `key` in the set `s` and tells if `key` was already missing from `s`.
+  ## Excludes `key` from the set `s` and tells if `key` was already missing from `s`.
  ##
  ## The difference with regards to the `excl proc <#excl,PackedSet[A],A>`_ is
-  ## that this proc returns `true` if `key` was missing from `s`.
-  ## The proc will return `false` if `key` was in `s` and it was removed
+  ## that this proc returns true if `key` was missing from `s`.
+  ## The proc will return false if `key` was in `s` and it was removed
  ## during this call.
  ##
-  ## See also:
+  ## **See also:**
  ## * `excl proc <#excl,PackedSet[A],A>`_ for excluding an element
-  ## * `excl proc <#excl,PackedSet[A],PackedSet[A]>`_ for excluding other set
+  ## * `excl proc <#excl,PackedSet[A],PackedSet[A]>`_ for excluding a set
  ## * `containsOrIncl proc <#containsOrIncl,PackedSet[A],A>`_
  runnableExamples:
-    var a = initPackedSet[int]()
-    a.incl(5)
+    var a = [5].toPackedSet
    assert a.missingOrExcl(5) == false
    assert a.missingOrExcl(5) == true

@@ -394,17 +383,15 @@ proc missingOrExcl*[A](s: var PackedSet[A], key: A): bool =
  result = count == s.len

 proc clear*[A](result: var PackedSet[A]) =
-  ## Clears the PackedSet[A] back to an empty state.
+  ## Clears the `PackedSet[A]` back to an empty state.
  runnableExamples:
-    var a = initPackedSet[int]()
-    a.incl(5)
-    a.incl(7)
+    var a = [5, 7].toPackedSet
    clear(a)
    assert len(a) == 0

  # setLen(result.data, InitIntSetSize)
-  # for i in 0..InitIntSetSize-1: result.data[i] = nil
-  # result.max = InitIntSetSize-1
+  # for i in 0..InitIntSetSize - 1: result.data[i] = nil
+  # result.max = InitIntSetSize - 1
  when defined(nimNoNilSeqs):
    result.data = @[]
  else:
@@ -414,11 +401,21 @@ proc clear*[A](result: var PackedSet[A]) =
  result.head = nil
  result.elems = 0

-proc isNil*[A](x: PackedSet[A]): bool {.inline.} = x.head.isNil and x.elems == 0
+proc isNil*[A](x: PackedSet[A]): bool {.inline.} =
+  ## Returns true if `x` is empty, false otherwise.
+  runnableExamples:
+    var a = initPackedSet[int]()
+    assert a.isNil
+    a.incl(2)
+    assert not a.isNil
+    a.excl(2)
+    assert a.isNil
+
+  x.head.isNil and x.elems == 0

 proc assign*[A](dest: var PackedSet[A], src: PackedSet[A]) =
  ## Copies `src` to `dest`.
-  ## `dest` does not need to be initialized by `initPackedSet[A] proc <#initPackedSet>`_.
+  ## `dest` does not need to be initialized by the `initPackedSet proc <#initPackedSet>`_.
  runnableExamples:
    var
      a = initPackedSet[int]()
@@ -449,7 +446,7 @@ proc assign*[A](dest: var PackedSet[A], src: PackedSet[A]) =
      var h = it.key and dest.max
      var perturb = it.key
      while dest.data[h] != nil: h = nextTry(h, dest.max, perturb)
-      assert(dest.data[h] == nil)
+      assert dest.data[h] == nil
      var n: PTrunk
      new(n)
      n.next = dest.head
@@ -464,13 +461,12 @@ proc union*[A](s1, s2: PackedSet[A]): PackedSet[A] =
  ##
  ## The same as `s1 + s2 <#+,PackedSet[A],PackedSet[A]>`_.
  runnableExamples:
-    var
-      a = initPackedSet[int]()
-      b = initPackedSet[int]()
-    a.incl(1); a.incl(2); a.incl(3)
-    b.incl(3); b.incl(4); b.incl(5)
-    assert union(a, b).len == 5
-    ## {1, 2, 3, 4, 5}
+    let
+      a = [1, 2, 3].toPackedSet
+      b = [3, 4, 5].toPackedSet
+      c = union(a, b)
+    assert c.len == 5
+    assert c == [1, 2, 3, 4, 5].toPackedSet

  result.assign(s1)
  incl(result, s2)
@@ -480,13 +476,12 @@ proc intersection*[A](s1, s2: PackedSet[A]): PackedSet[A] =
  ##
  ## The same as `s1 * s2 <#*,PackedSet[A],PackedSet[A]>`_.
  runnableExamples:
-    var
-      a = initPackedSet[int]()
-      b = initPackedSet[int]()
-    a.incl(1); a.incl(2); a.incl(3)
-    b.incl(3); b.incl(4); b.incl(5)
-    assert intersection(a, b).len == 1
-    ## {3}
+    let
+      a = [1, 2, 3].toPackedSet
+      b = [3, 4, 5].toPackedSet
+      c = intersection(a, b)
+    assert c.len == 1
+    assert c == [3].toPackedSet

  result = initPackedSet[A]()
  for item in s1.items:
@@ -498,13 +493,12 @@ proc difference*[A](s1, s2: PackedSet[A]): PackedSet[A] =
  ##
  ## The same as `s1 - s2 <#-,PackedSet[A],PackedSet[A]>`_.
  runnableExamples:
-    var
-      a = initPackedSet[int]()
-      b = initPackedSet[int]()
-    a.incl(1); a.incl(2); a.incl(3)
-    b.incl(3); b.incl(4); b.incl(5)
-    assert difference(a, b).len == 2
-    ## {1, 2}
+    let
+      a = [1, 2, 3].toPackedSet
+      b = [3, 4, 5].toPackedSet
+      c = difference(a, b)
+    assert c.len == 2
+    assert c == [1, 2].toPackedSet

  result = initPackedSet[A]()
  for item in s1.items:
@@ -514,17 +508,17 @@ proc difference*[A](s1, s2: PackedSet[A]): PackedSet[A] =
 proc symmetricDifference*[A](s1, s2: PackedSet[A]): PackedSet[A] =
  ## Returns the symmetric difference of the sets `s1` and `s2`.
  runnableExamples:
-    var
-      a = initPackedSet[int]()
-      b = initPackedSet[int]()
-    a.incl(1); a.incl(2); a.incl(3)
-    b.incl(3); b.incl(4); b.incl(5)
-    assert symmetricDifference(a, b).len == 4
-    ## {1, 2, 4, 5}
+    let
+      a = [1, 2, 3].toPackedSet
+      b = [3, 4, 5].toPackedSet
+      c = symmetricDifference(a, b)
+    assert c.len == 4
+    assert c == [1, 2, 4, 5].toPackedSet

  result.assign(s1)
  for item in s2.items:
-    if containsOrIncl(result, item): excl(result, item)
+    if containsOrIncl(result, item):
+      excl(result, item)

 proc `+`*[A](s1, s2: PackedSet[A]): PackedSet[A] {.inline.} =
  ## Alias for `union(s1, s2) <#union,PackedSet[A],PackedSet[A]>`_.
@@ -541,14 +535,12 @@ proc `-`*[A](s1, s2: PackedSet[A]): PackedSet[A] {.inline.} =
 proc disjoint*[A](s1, s2: PackedSet[A]): bool =
  ## Returns true if the sets `s1` and `s2` have no items in common.
  runnableExamples:
-    var
-      a = initPackedSet[int]()
-      b = initPackedSet[int]()
-    a.incl(1); a.incl(2)
-    b.incl(2); b.incl(3)
+    let
+      a = [1, 2].toPackedSet
+      b = [2, 3].toPackedSet
+      c = [3, 4].toPackedSet
    assert disjoint(a, b) == false
-    b.excl(2)
-    assert disjoint(a, b) == true
+    assert disjoint(a, c) == true

  for item in s1.items:
    if contains(s2, item):
@@ -557,24 +549,24 @@ proc disjoint*[A](s1, s2: PackedSet[A]): bool =

 proc card*[A](s: PackedSet[A]): int {.inline.} =
  ## Alias for `len() <#len,PackedSet[A]>`_.
+  ##
+  ## Card stands for the [cardinality](http://en.wikipedia.org/wiki/Cardinality)
+  ## of a set.
  result = s.len()

 proc `<=`*[A](s1, s2: PackedSet[A]): bool =
-  ## Returns true if `s1` is subset of `s2`.
+  ## Returns true if `s1` is a subset of `s2`.
  ##
-  ## A subset `s1` has all of its elements in `s2`, and `s2` doesn't necessarily
+  ## A subset `s1` has all of its elements in `s2`, but `s2` doesn't necessarily
  ## have more elements than `s1`. That is, `s1` can be equal to `s2`.
  runnableExamples:
-    var
-      a = initPackedSet[int]()
-      b = initPackedSet[int]()
-    a.incl(1)
-    b.incl(1); b.incl(2)
+    let
+      a = [1].toPackedSet
+      b = [1, 2].toPackedSet
+      c = [1, 3].toPackedSet
    assert a <= b
-    a.incl(2)
-    assert a <= b
-    a.incl(3)
-    assert(not (a <= b))
+    assert b <= b
+    assert not (c <= b)

  for item in s1.items:
    if not s2.contains(item):
@@ -582,27 +574,33 @@ proc `<=`*[A](s1, s2: PackedSet[A]): bool =
  return true

 proc `<`*[A](s1, s2: PackedSet[A]): bool =
-  ## Returns true if `s1` is proper subset of `s2`.
+  ## Returns true if `s1` is a proper subset of `s2`.
  ##
  ## A strict or proper subset `s1` has all of its elements in `s2`, but `s2` has
  ## more elements than `s1`.
  runnableExamples:
-    var
-      a = initPackedSet[int]()
-      b = initPackedSet[int]()
-    a.incl(1)
-    b.incl(1); b.incl(2)
+    let
+      a = [1].toPackedSet
+      b = [1, 2].toPackedSet
+      c = [1, 3].toPackedSet
    assert a < b
-    a.incl(2)
-    assert(not (a < b))
+    assert not (b < b)
+    assert not (c < b)
+
  return s1 <= s2 and not (s2 <= s1)

 proc `==`*[A](s1, s2: PackedSet[A]): bool =
  ## Returns true if both `s1` and `s2` have the same elements and set size.
+  runnableExamples:
+    assert [1, 2].toPackedSet == [2, 1].toPackedSet
+    assert [1, 2].toPackedSet == [2, 1, 2].toPackedSet
+
  return s1 <= s2 and s2 <= s1

 proc `$`*[A](s: PackedSet[A]): string =
-  ## The `$` operator for int sets.
-  ##
-  ## Converts the set `s` to a string, mostly for logging and printing purposes.
+  ## Converts `s` to a string.
+  runnableExamples:
+    let a = [1, 2, 3].toPackedSet
+    assert $a == "{1, 2, 3}"
+
  dollarImpl()