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|Theories and practice of polymorphism|
In computer science, dynamic dispatch is the process of selecting which implementation of a polymorphic operation (method or function) to call at runtime. Dynamic dispatch contrasts with static dispatch in which the implementation of a polymorphic operation is selected at compile-time. The purpose of dynamic dispatch is to support cases where the appropriate implementation of a polymorphic operation can't be determined at compile time because it depends on the runtime type of one or more actual parameters to the operation.
Dynamic dispatch is different from dynamic or late binding. In the context of selecting an operation, binding refers to the process of associating a name with an operation. Dispatching refers to choosing an implementation for the operation after you have decided which operation a name refers to. With dynamic dispatch, the name may be bound to a polymorphic operation at compile time, but the implementation not be chosen until runtime (this is how dynamic dispatch works in C++). However, late binding does imply dynamic dispatching since you cannot choose which implementation of a polymorphic operation to select until you have selected the operation that the name refers to.
Dynamic dispatch is often used in object-oriented languages when different classes contain different implementations of the same method due to common inheritance. For example, suppose you have classes A, B, and C, where B and C both inherit the method foo() from A. Now suppose x is variable of class A. At run time, x may actually have a value of type B or C and in general you can't know what it is at compile time.
With static dispatch, a method call x.foo() will always refer to the the implemention of foo() for class A because static binding only looks at the declared type of the object. With dynamic dispatch the language will determine the type of the value of x at run-time and call the version of foo() that is associated with whatever type the value has, whether A, B, or C.
Single and multiple dispatch 
If the decision of which version of a method to call is based entirely on the class of the object x, then this is known as single dispatch because an implementation is chosen based on a single type — the type of the instance. Single dispatch is supported by many object-oriented languages, including statically typed languages such as C++ and Java, and dynamically typed languages such as Smalltalk and Objective-C.
In a small number of languages such as Common Lisp and Dylan, methods or functions can also be dynamically dispatched based on the run-time type of arguments. Expressed in pseudocode, the code manager.handle(y) could call different implementations depending on the type of object y. This is known as multiple dispatch.
Multiple dispatch is more commonly associated with static dispatch. For example in C some operations such as "+" are polymorphic on the types of both arguments. In the case of "+", if both arguments are integers then an integer operation is used. If either of them is a floating-point number then a floating-point operation is used.
Dynamic dispatch mechanisms 
A language may be implemented with different dynamic dispatch mechanisms. The choices of the dynamic dispatch mechanism offered by a language to a large extent alter the programming paradigms that are available or are most natural to use within a given language.
Normally, in a typed language, the dispatch mechanism will be performed based on the type of the arguments (most commonly based on the type of the receiver of a message). This might be dubbed 'per type dynamic dispatch'. Languages with weak or no typing systems often carry a dispatch table as part of the object data for each object. This allows instance behaviour as each instance may map a given message to a separate method.
Some languages offer a hybrid approach.
Dynamic dispatch will always incur an overhead so some languages offer static dispatch for particular methods.
C++ Implementation 
C++ uses early binding and offers both dynamic and static dispatch. The default form of dispatch is static. To get dynamic dispatch you must declare a method as virtual.
C++ implements dynamic dispatch with a data structure called a virtual table that defines the message to method mapping for a given class. Instances of that type will then store a pointer to this table as part of their instance data. This is complicated when multiple inheritance is used. Since C++ does not support late binding, the virtual table in a C++ object cannot be modified at run-time, which limits the potential set of dispatch targets to a finite set chosen at compile-time.
Type overloading does not produce dynamic dispatch in C++ as the language considers the types of the message parameters part of the formal message name. This means that the message name the programmer sees is not the formal name used for binding.
There is a separate mechanism that allows a class template to be created with a single constructor and to have default methods attached to it. These default methods will then be available to every instance of that type.
Smalltalk Implementation 
Smalltalk uses a type based message dispatcher. Each instance has a single type whose definition contains the methods. When an instance receives a message, the dispatcher looks up the corresponding method in the message-to-method map for the type and then invokes the method.
A naive implementation of Smalltalk's mechanism would seem to have a significantly higher overhead than that of C++ and this overhead would be incurred for each and every message that an object receives.
In real Smalltalk implementations, a technique known as inline caching is often used that makes method dispatch very fast. Inline caching basically stores the previous destination method address and object class of this call site (or multiple pairs for multi-way caching). The cache method is initialized with the most common target method (or just the cache miss handler), based on the method selector. When the method call site is reached during execution, it just calls the address in the cache (in a dynamic code generator, this call is a direct call as the direct address is back patched by cache miss logic). Prologue code in the called method then compares the cached class with the actual object class, and if they don't match, execution branches to a cache miss handler to find the correct method in the class. A fast implementation may have multiple cache entries and it often only takes a couple of instructions to get execution to the correct method on an initial cache miss. The common case will be a cached class match, and execution will just continue in the method.
Out-of-line caching can also be used in the method invocation logic, using the object class and method selector. In one design, the class and method selector are hashed, and used as an index into a method dispatch cache table.