Rather than a top-down approach starting with you code snippet, I'll take a bottom-up approach to explain some important details about templates and what tools and techniques are involved.
At heart, templates are a tool that let you write C++ code that applies to a range of possible types, not strictly for a fixed type. In a statically-typed language, this is firstly a great tool for reusing code without sacrificing type safety, but in C++ in particular, templates are very powerful because they can be specialized.
Every template declaration begins with the keyword template, and a list of type or non-type (i.e value) parameters. Type parameters use the special keyword typename or class, and are used to let your code work over a range of types. Non-type parameters simply use the name of an existing type, and these let you apply your code to a range of values that are known at compile-time.
A very basic templated function might look like the following:
template<typename T> // declare a template accepting a single type T
void print(T t){ // print accepts a T and returns void
std::cout << t; // we can't know what this means until the point where T is known
}
This lets us reuse code safely for a range of possible types, and we can use it as follows:
int i = 3;
double d = 3.14159;
std::string s = "Hello, world!";
print<int>(i);
print<double>(d);
print<std::string>(s);
The compiler is even smart enough to deduce the template parameter T for each of these, so you can safely get away with the following, functionally identical code:
print(i);
print(d);
print(s);
But suppose you want print to behave differently for one type. Suppose, for example, you have a custom Point2D class that needs special handling. You can do this with a template specialization:
template<> // this begins a (full) template specialization
void print<Point2D>(Point2D p){ // we are specializing the existing template print with T=Point2D
std::cout << '(' << p.x << ',' << p.y << ')';
}
Now, anytime we use print with T=Point2D, the specialization is chosen. This is really useful, for example, if the generic template just doesn't make sense for one specific type.
std::string s = "hello";
Point2D p {0.5, 2.7};
print(s); // > hello
print(p); // > (0.5,2.7)
But what if we want to specialize a template for many types at once, based on a simple condition? This is where things become a little meta. First, let's try to express a condition in a way that lets them be used inside templates. This can be a little tricky because we need compile-time answers.
The condition here will be that T is a floating point number, which is true if T=float or T=double and false otherwise. This is actually fairly simple to achieve with template specialization alone.
// the default implementation of is_floating_point<T> has a static member that is always false
template<typename T>
struct is_floating_point {
static constexpr bool value = false;
};
// the specialization is_floating_point<float> has a static member that is always true
template<>
struct is_floating_point<float> {
static constexpr bool value = true;
};
// the specialization is_floating_point<double> has a static member that is always true
template<>
struct is_floating_point<double> {
static constexpr bool value = true;
}
Now, we can query any type to see if it's a floating point number:
is_floating_point<std::string>::value == false;
is_floating_point<int>::value == false;
is_floating_point<float>::value == true;
is_floating_point<double>::value == true;
But how can we use this compile-time condition inside another template? How can we tell the compiler which template to choose when there are many possible template specializations to choose from?
This is achieved by taking advantage of a C++ rule called SFINAE, which in basic English, says, "when there are many possible template specializations to choose from, and the current one doesn't make sense*, just skip it and try the next one."
- There's a list of errors, when attempting to substitute template arguments into templated code, that cause the template to be ignored without an immediate compiler error. The list is a bit long and complex.
One possible way that a template doesn't make sense is if it tries to use a type that doesn't exist.
template<typename T>
void foo(typename T::nested_type x); // SFINAE error if T does not contain nested_type
This is the exact same trick that std::enable_if uses under the hood. enable_if is a template class accepting a type T and a bool condition, and it contains a nested type type equal to T only when the condition is true. This is also pretty easy to achieve:
template<bool condition, typename T>
struct enable_if {
// no nested type!
};
template<typename T> // partial specialization for condition=true but any T
struct enable_if<true, T> {
typedef T type; // only exists when condition=true
};
Now we have a helper that we can use in place of any type. If the condition we pass is true, then we can safely use the nested type. If the condition we pass is false, then the template is no longer considered.
template<typename T>
typename std::enable_if<std::is_floating_point<T>::value, void>::type // This is the return type!
numberFunction(T t){
std::cout << "T is a floating point";
}
template<typename T>
typename std::enable_if<!std::is_floating_point<T>::value, void>::type
numberFunction(T t){
std::cout << "T is not a floating point";
}
I completely agree that std::enable_if<std::is_floating_point<T>::value, void>::type is a messy way to spell out a type. You can read it as "void if T is floating point, and otherwise stop and try the next overload"
Finally, to take apart your example:
// we are declaring a template
template<
typename T, // that accepts some type T,
size_t M, // a size_t M,
size_t K, // a size_t K,
size_t N, // a size_t N,
// and an unnamed non-type that only makes sense when T is a floating point
typename std::enable_if_t<std::is_floating_point<T>::value, T> = 0
>
void fastor2d(){//...}
Note the = 0 at the end. That's simply a default value for the final template parameter, and it lets you get away with specifying T, M, K, and N but not the fifth parameter. The enable_if used here means that you can provide other templates called fastor2d, with their own sets of conditions.
