Since C++14 a generator for compile-time integer sequences is available in the standard library. How does this work? How to create your own implementation if this is not available in your distribution? How to modify the sequence? Here, we want to look at these questions and want to show and analyze some different implementations found in the web.

A compile-time integer sequence is a variadic class template with integer non-type template parameters, e.g.

template <int... Is>
struct Seq { using type = Seq; };

Sometimes it is necessary to have a specific sequence of increasing values, that can be used in parameter pack expansions. As an example we want to store all values of an std::array in a C-Array, using the template function std::get<I>(array). Here, an integer sequence is used as a function parameter that can be deduces and unpacked automatically, to have all the indices at hand and to be used in a pack expansion:

template <class T, int N, int... Is>
void foo(std::array<T, N> const& source, Seq<Is...>) {
  T target[] = {std::get<Is>(source)...};
  // ...

// function call:
foo(array, Seq<0,1,2,3,4,5,6,(...)>());

The question is, how to generate the template Seq<0,1,2,3,(...),N-1> automatically, for any given upper index N-1.

Linear complexity

Version A/B

The simplest (direct) approach has linear complexity in the template recursion depth and recursively pushes back an integer number to the sequence. If we have the template class Seq as above, then a push-back class that adds an integer to the end of a sequence could look like:

// primary template
template <int I, class S>
struct PushBack;

// specialization for Seq<I0,I1,(...)>
template <int I, int... Is>
struct PushBack<I, Seq<Is...>> {
  using type = Seq<Is..., I>;

or simply

template <int I, int... Is>
struct PushBack<I, Seq<Is...>> : Seq<Is..., I> {};

for the specialization, since Seq itself provides a type type-attribute.

An integer sequence can now be generated, by adding the upper index recursively to an already generated smaller sequence. Therefore, we have to write a break condition for the smallest sequence, e.g. a sequence with length 0. We write a template class MakeSeq<N> with a type attribute, that represents the Seq<0,1,...,N-1> sequence with N integers:

template <int N>
struct MakeSeq 
  using type = typename PushBack<N-1, typename MakeSeq<N-2>::type>::type;

template <> struct MakeSeq<1> { using type = Seq<0>; };
template <> struct MakeSeq<0> { using type = Seq<>; };

or a bit shorter:

template <int N>
struct MakeSeq : PushBack<N-1, typename MakeSeq<N-2>::type>::type {};

template <> struct MakeSeq<1> : Seq<0> {};
template <> struct MakeSeq<0> : Seq<> {};

That’s it. A small test could be to compare the length of the sequence to N:

template <int... Is>
constexpr unsigned size(Seq<Is...>) {
  return sizeof...(Is);

int main() {
  static_assert( size(typename MakeSeq<LENGTH>::type()) == LENGTH, "" );

Version C

On Stackoverflow another variant of the sequential implementation to create an integer sequence is published. There, the break condition is realized using a std::conditional statement and the PushBack helper class is included in the MakeSeq class directly. This may reduce the number of templates to be instantiated by the compiler and may be preferable in this context:

// helper meta-class that represents the template type.
template <class T> struct id  { using type = T; };

template <int N, int... Is>
struct MakeSeq
   using type = typename std::conditional< N == 0, // if
                  id< Seq<Is...> >,                // then
                  MakeSeq< N-1, N-1, Is...          // else

Version D

Motivated by the implementation in the standard library a variant of the integer sequence generation is provided that works directly on the variadic integer sequences, i.e. the Seq template, and adds a type attribute next that represents a sequence with one more integer appended:

template <int... Is>
struct Seq
  using next = Seq<Is..., sizeof...(Is)>;

The generator template MakeSeq now simply adds an alias that calls the next type:

template <int N>
struct MakeSeq
  using type = typename MakeSeq<N-1>::type::next;

template <> struct MakeSeq<0> { using type = Seq<>; };

Time measurement

A measurement of the time to instantiate (generate) the integer-sequence shows, that there is a difference between compilers and also between the way of implementing the classes, i.e. using an own type attribute (Version A), deriving from the Seq class (Version B), or using the Stackoverflow one-class implementation (Version C). For LENGTH=900 we get the average timings in seconds

Version A B C D
clang-3.6 0.690 0.692 0.572 0.311
clang-3.7 0.636 0.624 0.516 0.280
g++-4.8.5 0.865 1.273 0.877 0.727
g++-5.3.0 1.727 2.530 1.719 1.428

for the call COMPILER -std=c++11 -DLENGTH=900 -ftemplate-depth=1000 The clang compilers have problems with larger LENGTH parameters and stop with a Segmentation fault. This is not the case for g++. There the template instantiation depth could be increased a lot further.

Logarithmic complexity

How to improve the implementation further? In a linear implementation where indices are appended to the sequence one by one, the compiler can not reuse already instantiated parts of the template and must go down the full depth.

A recursive implementation with logarithmic instantiation depth can be formulated by splitting the sequence into two parts [0,N/2] and [N/2+1,N], creating sequences for both parts recursively, and finally concatenating the partial sequences.

Version E

The first implementation creates a linear sequence [start, start+1, start+2, …, end] by splitting in the middle of the interval [start, end]. Therefore, we introduce a template with two parameters and a corresponding alias template as shortcut:

template <int Start, int End>
struct MakeSeqImpl;

template <int Start, int End>
using MakeSeqImpl_t = typename MakeSeqImpl<Start, End>::type;

and the MakeSeq class can be recapitulated from MakeSeqImpl by template specialization:

template <int N> 
using MakeSeq_t = typename MakeSeqImpl<0, N-1>::type;

here implemented as alias template.

Similar to the PushBack template of above, a Concat template is used that pushes all the indices from the second sequence at the end of the indices of the first sequence:

template <class S1, class S2> struct Concat;
template <class S1, class S2> using  Concat_t = typename Concat<S1,S2>::type;

template <int... I1s, int... I2s>
struct Concat<Seq<I1s...>, Seq<I2s...>> {
  using type = Seq<I1s..., I2s...>;

The implementation of MakeSeqImpl now calls Concat of two subsequences:

template <int Start, int End>
struct MakeSeqImpl<Start, End> {
  using type = Concat_t<MakeSeqImpl_t<Start, (Start+End)/2>, 
                        MakeSeqImpl_t<(Start+End)/2+1, End> >;

// break condition:
template <int I>
struct MakeSeqImpl<I,I> {
  using type = Seq<I>;

Version F

A slightly more involved implementation introduces a shift in the concatenation and creates recursively two sequences that do overlap, where the second one is shifted by the length of the first one. This variant is show on Stackoverflow/Answer-1 by user Xeo.

The Concat template is modified slightly:

template <int... I1, int... I2>
struct Concat<Seq<I1...>, Seq<I2...>> {
  using type = Seq<I1..., (sizeof...(I1) + I2)...>;

and the MakeSeq class can now be implemented directly, without the help of the class MakeSeqImpl, by

template <int N> struct MakeSeq;
template <int N> using  MakeSeq_t = typename MakeSeq<N>::type;

template <int N> 
struct MakeSeq
  using type = Concat_t<MakeSeq_t<N/2>, MakeSeq_t<N - N/2>>;

// break conditions
template <> struct MakeSeq<1> { using type = Seq<0>; };
template <> struct MakeSeq<0> { using type = Seq<>; };

where the parameter N is now, as before, the length of the sequence. We need both break conditions, since each of those can not be implemented without the other one.

The advantage of this variant is that both ranges may be the same and thus, the compiler may reuse the instantiation of one.

Version G

On Stackoverflow/Answer-2 the user Khurshid posted an answer that uses this idea even more strictly, by creating twice the same sequence and concatenating those, using Concat as above. Only in the case that N is not divisible by two, a final index is added to the sequence.

template <int N>
struct MakeSeq {
  using type = typename IncSeq_if< (N % 2 != 0), 
    typename Concat<N/2, typename MakeSeq<N/2>::type>::type >::type;

// break condition
template <> struct MakeSeq<0> { using type = Seq<>; };

where IncSeq_if implements the push-back of the final index, in the case that the first template argument is true:

template <bool /* = false */, class S>
struct IncSeq_if { using type = S; }; // do not increase

template <int... Is>
struct IncSeq_if<true, Seq<Is...>> // Seq<0,1,...,Size-1>
  using type = Seq<Is..., sizeof...(Is)>;

and Concat is slightly modified to reuse the same sequence twice:

template <int Size, class S>
struct Concat;

template <int Size, int... Is>
struct Concat<Size, Seq<Is... >>
    using type = Seq<Is..., (Size + Is)... >;

Time measurement

In a same way as above we measure the time to compile the various variants of the logarithmic integer sequence implementation, using the compilers clang and g++:

Version E F G
clang-3.6 0.115 0.062 0.060
clang-3.7 0.104 0.057 0.055
g++-4.8.5 0.131 0.059 0.034
g++-5.3.0 0.169 0.049 0.047

We see that the compilation times are about a factor > 5 lower than for the linear implementation and that the most specialized variant F outperforms all the other implementations. Thus, it makes sense to optimize the way of instantiating templates when large instantiation depth are necessary and if we want to reduce compilation times.

Download source files

You can download all the source-files, by following the links in the table below:

Version Link
A source
B source
C source
D source
E source
F source
G source