A.18.5 The Package Containers.Hashed_Maps
Static Semantics
{
AI95-00302-03}
The generic library package Containers.Hashed_Maps has the following
declaration:
generic
type Key_Type
is private;
type Element_Type
is private;
with function Hash (Key : Key_Type)
return Hash_Type;
with function Equivalent_Keys (Left, Right : Key_Type)
return Boolean;
with function "=" (Left, Right : Element_Type)
return Boolean is <>;
package Ada.Containers.Hashed_Maps
is
pragma Preelaborate(Hashed_Maps);
type Map
is tagged private;
pragma Preelaborable_Initialization(Map);
type Cursor
is private;
pragma Preelaborable_Initialization(Cursor);
Empty_Map :
constant Map;
No_Element :
constant Cursor;
function "=" (Left, Right : Map) return Boolean;
function Capacity (Container : Map)
return Count_Type;
procedure Reserve_Capacity (Container :
in out Map;
Capacity :
in Count_Type);
function Length (Container : Map)
return Count_Type;
function Is_Empty (Container : Map)
return Boolean;
procedure Clear (Container :
in out Map);
function Key (Position : Cursor)
return Key_Type;
function Element (Position : Cursor)
return Element_Type;
procedure Replace_Element (Container :
in out Map;
Position :
in Cursor;
New_Item :
in Element_Type);
procedure Query_Element
(Position :
in Cursor;
Process :
not null access procedure (Key :
in Key_Type;
Element :
in Element_Type));
procedure Update_Element
(Container :
in out Map;
Position :
in Cursor;
Process :
not null access procedure
(Key :
in Key_Type;
Element :
in out Element_Type));
procedure Move (Target :
in out Map;
Source :
in out Map);
procedure Insert (Container :
in out Map;
Key :
in Key_Type;
New_Item :
in Element_Type;
Position :
out Cursor;
Inserted :
out Boolean);
procedure Insert (Container :
in out Map;
Key :
in Key_Type;
Position :
out Cursor;
Inserted :
out Boolean);
procedure Insert (Container :
in out Map;
Key :
in Key_Type;
New_Item :
in Element_Type);
procedure Include (Container :
in out Map;
Key :
in Key_Type;
New_Item :
in Element_Type);
procedure Replace (Container :
in out Map;
Key :
in Key_Type;
New_Item :
in Element_Type);
procedure Exclude (Container :
in out Map;
Key :
in Key_Type);
procedure Delete (Container :
in out Map;
Key :
in Key_Type);
procedure Delete (Container :
in out Map;
Position :
in out Cursor);
function First (Container : Map)
return Cursor;
function Next (Position : Cursor)
return Cursor;
procedure Next (Position :
in out Cursor);
function Find (Container : Map;
Key : Key_Type)
return Cursor;
function Element (Container : Map;
Key : Key_Type)
return Element_Type;
function Contains (Container : Map;
Key : Key_Type)
return Boolean;
function Has_Element (Position : Cursor)
return Boolean;
function Equivalent_Keys (Left, Right : Cursor)
return Boolean;
function Equivalent_Keys (Left : Cursor;
Right : Key_Type)
return Boolean;
function Equivalent_Keys (Left : Key_Type;
Right : Cursor)
return Boolean;
procedure Iterate
(Container :
in Map;
Process :
not null access procedure (Position :
in Cursor));
private
... -- not specified by the language
end Ada.Containers.Hashed_Maps;
{
AI95-00302-03}
An object of type Map contains an expandable hash table, which is used
to provide direct access to nodes. The
capacity of an object of
type Map is the maximum number of nodes that can be inserted into the
hash table prior to it being automatically expanded.
{capacity
(of a hashed map)} Implementation Note: The expected implementation
for a Map uses a hash table which is grown when it is too small, with
linked lists hanging off of each bucket. Note that in that implementation
a cursor needs a back pointer to the Map object to implement iteration;
that could either be in the nodes, or in the cursor object. To provide
an average O(1) access time, capacity would typically equal the
number of buckets in such an implementation, so that the average bucket
linked list length would be no more than 1.0.
There is no defined relationship between elements
in a hashed map. Typically, iteration will return elements in the order
that they are hashed in.
{
AI95-00302-03}
{equivalent key (of a hashed map)}
Two keys
K1 and
K2 are defined to be
equivalent if Equivalent_Keys (
K1,
K2) returns True.
{
AI95-00302-03}
The actual function for the generic formal function Hash is expected
to return the same value each time it is called with a particular key
value. For any two equivalent key values, the actual for Hash is expected
to return the same value. If the actual for Hash behaves in some other
manner, the behavior of this package is unspecified. Which subprograms
of this package call Hash, and how many times they call it, is unspecified.
{unspecified
[partial]} Implementation Note: The implementation
is not required to protect against Hash raising an exception, or returning
random numbers, or any other “bad” behavior. It's not practical
to do so, and a broken Hash function makes the container unusable.
The implementation can call Hash whenever it
is needed; we don't want to specify how often that happens. The result
must remain the same (this is logically a pure function), or the behavior
is unspecified.
{
AI95-00302-03}
The actual function for the generic formal function Equivalent_Keys on
Key_Type values is expected to return the same value each time it is
called with a particular pair of key values. It should define an equivalence
relationship, that is, be reflexive, symmetric, and transitive. If the
actual for Equivalent_Keys behaves in some other manner, the behavior
of this package is unspecified. Which subprograms of this package call
Equivalent_Keys, and how many times they call it, is unspecified.
{unspecified
[partial]} Implementation Note: As with Hash, the
implementation is not required to protect against Equivalent_Keys raising
an exception or returning random results. Similarly, the implementation
can call this operation whenever it is needed. The result must remain
the same (this is a logically pure function), or the behavior is unspecified.
{
AI95-00302-03}
If the value of a key stored in a node of a map is changed other than
by an operation in this package such that at least one of Hash or Equivalent_Keys
give different results, the behavior of this package is unspecified.
{unspecified
[partial]} Implementation Note: The implementation
is not required to protect against changes to key values other than via
the operations declared in the Hashed_Maps package.
To see how this
could happen, imagine an instance of Hashed_Maps where the key type is
an access-to-variable type and Hash returns a value derived from the
components of the designated object. Then, any operation that has a key
value could modify those components and change the hash value:
Key (Map).Some_Component := New_Value;
This is really a design error on the part of
the user of the map; it shouldn't be possible to modify keys stored in
a map. But we can't prevent this error anymore than we can prevent someone
passing as Hash a random number generator.
{
AI95-00302-03}
{first node (of a hashed map)}
{last node (of a
hashed map)} {successor
node (of a hashed map)} Which nodes are
the first node and the last node of a map, and which node is the successor
of a given node, are unspecified, other than the general semantics described
in
A.18.4.
{unspecified
[partial]} Implementation Note: Typically the first
node will be the first node in the first bucket, the last node will be
the last node in the last bucket, and the successor will be obtained
by following the collision list, and going to the next bucket at the
end of each bucket.
function Capacity (Container : Map) return Count_Type;
procedure Reserve_Capacity (Container : in out Map;
Capacity : in Count_Type);
{
AI95-00302-03}
Reserve_Capacity allocates a new hash table such that the length of the
resulting map can become at least the value Capacity without requiring
an additional call to Reserve_Capacity, and is large enough to hold the
current length of Container. Reserve_Capacity then rehashes the nodes
in Container onto the new hash table. It replaces the old hash table
with the new hash table, and then deallocates the old hash table. Any
exception raised during allocation is propagated and Container is not
modified.
Reserve_Capacity
tampers with the cursors of Container.
Implementation Note: This routine is
used to preallocate the internal hash table to the specified capacity
such that future Inserts do not require expansion of the hash table.
Therefore, the implementation should allocate the needed memory to make
that true at this point, even though the visible semantics could be preserved
by waiting until enough elements are inserted.
While Reserve_Capacity can be used to reduce
the capacity of a map, we do not specify whether an implementation actually
supports reduction of the capacity. Since the actual capacity can be
anything greater than or equal to Count, an implementation never has
to reduce the capacity.
Reserve_Capacity tampers with the cursors, as
rehashing probably will change the order that elements are stored in
the map.
procedure Clear (Container : in out Map);
{
AI95-00302-03}
In addition to the semantics described in
A.18.4,
Clear does not affect the capacity of Container.
Implementation
Note: In:
procedure Move (Target : in out Map;
Source : in out Map);
The intended implementation is that the internal
hash table of Target is first deallocated; then the internal hash table
is removed from Source and moved to Target.
procedure Insert (Container : in out Map;
Key : in Key_Type;
New_Item : in Element_Type;
Position : out Cursor;
Inserted : out Boolean);
{
AI95-00302-03}
In addition to the semantics described in
A.18.4,
if Length (Container) equals Capacity (Container), then Insert first
calls Reserve_Capacity to increase the capacity of Container to some
larger value.
Implementation Note: Insert should only
compare keys that hash to the same bucket in the hash table.
We specify when Reserve_Capacity is called to
bound the overhead of capacity expansion operations (which are potentially
expensive). Moreover, expansion can be predicted by comparing Capacity(Map)
to Length(Map). Since we don't specify by how much the hash table is
expanded, this only can be used to predict the next expansion, not later
ones.
Implementation
Note: In:
procedure Exclude (Container : in out Map;
Key : in Key_Type);
Exclude should only compare keys that hash to
the same bucket in the hash table.
Implementation
Note: In:
procedure Delete (Container : in out Map;
Key : in Key_Type);
Delete should only compare keys that hash to
the same bucket in the hash table. The node containing the element may
be deallocated now, or it may be saved and reused later.
Implementation
Note: In:
function First (Container : Map) return Cursor;
In a typical implementation, this will be the
first node in the lowest numbered hash bucket that contains a node.
Implementation
Note: In:
function Next (Position : Cursor) return Cursor;
In a typical implementation, this will return
the next node in a bucket; if Position is the last node in a bucket,
this will return the first node in the next non-empty bucket.
A typical implementation will need to a keep
a pointer at the map container in the cursor in order to implement this
function.
Implementation
Note: In:
function Find (Container : Map;
Key : Key_Type) return Cursor;
Find should only compare keys that hash to the
same bucket in the hash table.
function Equivalent_Keys (Left, Right : Cursor)
return Boolean;
{
AI95-00302-03}
Equivalent to Equivalent_Keys (Key (Left), Key (Right)).
function Equivalent_Keys (Left : Cursor;
Right : Key_Type) return Boolean;
{
AI95-00302-03}
Equivalent to Equivalent_Keys (Key (Left), Right).
function Equivalent_Keys (Left : Key_Type;
Right : Cursor) return Boolean;
{
AI95-00302-03}
Equivalent to Equivalent_Keys (Left, Key (Right)).
Implementation Advice
{
AI95-00302-03}
If
N is the length of a map, the average time complexity of the
subprograms Element, Insert, Include, Replace, Delete, Exclude and Find
that take a key parameter should be
O(log
N). The average
time complexity of the subprograms that take a cursor parameter should
be
O(1). The average time complexity of Reserve_Capacity should
be
O(
N).
Implementation Advice: The average time
complexity of Element, Insert, Include, Replace, Delete, Exclude and
Find operations that take a key parameter for Containers.Hashed_Maps
should be O(log N). The average time complexity of the
subprograms of Containers.Hashed_Maps that take a cursor parameter should
be O(1).
Reason: We do not mean to overly constrain
implementation strategies here. However, it is important for portability
that the performance of large containers has roughly the same factors
on different implementations. If a program is moved to an implementation
for which Find is O(N), that program could be unusable
when the maps are large. We allow O(log N) access because
the proportionality constant and caching effects are likely to be larger
than the log factor, and we don't want to discourage innovative implementations.
Extensions to Ada 95
{
AI95-00302-03}
{
extensions to Ada 95}
The generic package
Containers.Hashed_Maps is new.
Sponsored by Ada-Europe