• Move computations from run-time to compile-time
  • Code generation
  • Enable self-adapting code (portability, efficiency)
  • Facilitate domain-specific programming
  • Express complex software patterns and concepts in a more straightforward way


  • Numeric results ::value
  • Type result ::type
template <typename T> struct SizeOfT {
enum { value = sizeof(T) };
template <typename T> struct TPtr {
typedef T* type;

Template args can be types or numbers

template <size_t N> struct IsEven {
enum { value = (N %2 ) ? 0 : 1 };


  • remove_cv

NOT tools of metaprogramming

  • No variables
  • Which means no for loops: use recursion


  • Purely numeric computations almost always quicker with constexpr
  • constexpr also has recursion depth limits but higher than templates and faster
  • Use precomputed static values when it's simpler (pi)
gcc template recusion depth 10000

if then else

  • No loops but std::conditional
template <size_t N> struct IsPower2 {
enum { value = (N & (N - 1)) == 0 };

static_assert(IsPower2<N>::value, "N must be 2^n");
  • remove_ptr returns the type if it's not a pointer
std::integral_constant // wrap constant with its type

std::bool_constant // template alias

true_type and false_type are called nullary metafunctions because they have no params.



Substitution failure is not an error: this is where compiler errors go to hide.

Argument non-evaluation

  • Operands of sizeof, decltype, declval, alignof, typeid and noexcept are never evaluated
  • Not even at compile time


constexpr silently decays to not-compile time unless you use it in a context that needs to be known at compile time: within square brackets.



A template is a C++ entity that defines one of the following:

  • a family of classes (class template), which may be nested classes
  • a family of functions (function template), which may be member functions
  • an alias to a family of types (alias template) (since C++11)
  • a family of variables (variable template) (since C++14)
  • a concept (constraints and concepts) (since C++20)


  • Technically a class with zero+ template params and zero+ return types and values
  • Convention is that a metafunction should return on thing (like a regular function)

Example traits


  • Class template
  • One template argument (mostly)
  • Cpp17DefaultConstructible
  • Cpp17CopyConstructible
  • Publiclly and unambiguously derived from a specialisation of std::integral_constant


  • As above
  • But two arguments


  • Class template
  • one template arg
  • Define a publicy accessible nested type name "type"
  • No default/copy constructible req
  • No inheritance req
  • remove_const

Undefined behaviour

  • Do not specialise standard type traits
  • be careful when using incomplete types

Type metafunctions

  • Workhorse (expectially with advent of constexpr)
  • Returns a type
  • std::type_identity (C++20)
  • value metatfunctions use variable templates ending with "_v"

Explicit spectialisation

template <> // explicit speciailisation

Printing the type

std::cout << typeid(Type1).name() << 'n';

Compiler support

Now most compilers implement traits with intrinsics.

Primary type categories (traits)

All inherit from either true_type or false_type, and all should yield the same result in light of cv qualifiers.

For any given type T, exactle one of th eprimary type categories shall yield true_type.

  • is_void
  • is_null_pointer
  • is_integral
  • is_floating_point
  • is_array
  • etc

Equals combinatorial explosion!


Metafunction abstractions

  • Treat metafunction programming like regular programming
  • blah_t is involing blah

Function overload resolution

  • decltype: compiler, don't call this function but what type would it return?
  • declval: gives a reference to something as if you had created one
  • tag despatch

Comparisons with auto in C++20

  • Auto uses the same rules as template type params
  • auto will never deduce a reference#
  • constness will be deduced
  • decltype(auto) will deduce a reference (should only see in very special cases)
  • Generally prefer auto (according to Jason Turner)
  • Value types are always copies

These generate the same code:

template <typename T>
T func(T t) {
return t;

auto func2(auto t) {
return t;

See Jason Turner.

Other C++ standards

  • International standard on Mathematical Special Functions in C++
  • C++ template metaprogramming uses template instatiation to drive compile-time evalulation
  • Template metapgrammamers exploit this machinary to improve a) source code flexibility b) runtime performance
  • at compile time can't rely on mutabilty, virtual functions (runtime dispatch), other RTTI, no variables etc: not hard but a difference in mindset... no runtime!
  • Call syntax is a "request for the published value"
template<int N>
struct abs{
static_assert (N != INT_MIN); // 2s comp
static constexpr int value = (N < 0) ? -N : N; // initialise value not assign, takes place of return

// call
abs<n>value // instantiation yields a complile-time constant

Compile time recursion: metafunction that calls itself

template <unsigned M, unsigned N>
struct gcd {
static int const value = gcd<N, M%N>::value; // per Euclid

Suppply base case with a specialisation

template <unsigned M>
struct gcd<M, 0>{
static_assert (M!=0);
static int const value = M;

What's the relationship between constexpr functions and templates?

  • Familiar syntax
  • metafunction is a struct -- can make things public with a struct (not a constexpr function)
  • Structs offer public member function decclarations
  • Can write a template that takes a type as an argument: e.g., size of can take a type

See also Walter E. Brown.

Identity metafunction

template <class T>
struct type_is {using type = T};
  • std::conditional -- compile time IF
  • one case you can have a type for true or nothing otherwise: enable_if

enable_if::type -- always an error? No! Welcome to SFINAE


void is one of the 15 types that C++ describes

is_void<T>::value // since TR1
bool(is_void<T>{}) // instantiate/cast C++11
is_void<T>{}() // variable templates C++14
is_void_v<T> // value returning metafunctions C++17
using true_type = bool_constant<true>;
using false_type = bool_constant<false>;


  • Solid math foundation: solid, well-baked idea
  • integral_constant: inherit from provides more options
  • bool_constant

First parameter packs

template <class T, class... P0toN>
struct is_one_of; // declaration not implementation
// base cases
struct is_one_of<T> : false_type{};
struct is_one_of<T, T, P1toN...> : true_type{};
struct is_one_of<T, P0, P1toN>
: is_one_of<T, P1toN...>{};

Not evaluated

sizeof, typeid, decltype and noexcept are never evaluated, not even at compile time.

  • No code is generated
  • Don't need a definition
  • decltype( foo(declval<T>{}) )



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