ISO/IEC JTC1 SC22 WG21 N3658 = 2013-04-18

Jonathan Wakely, cxx@kayari.org
Revision History

Introduction

Rationale and examples of use

Piecewise construction of `std::pair`

.

Convert array to tuple

N3466 `more_perfect_forwarding_async`

example

Solution

Type of integers in the sequence

Non-consecutive integer sequences

Members of integer sequences

Efficiency considerations

Impact on standard

20.x Compile-time integer sequences [intseq]

20.x.1 In general [intseq.general]

20.x.2 Class template `integer_sequence`

[intseq.intseq]

20.x.3 Alias template `make_integer_sequence`

[intseq.make]

References

N3658 Revision 1 (post-Bristol mailing)

- Rename all
`xxx_seq`

templates to`xxx_sequence.`

- Rename
`to_index_sequence`

to`index_sequence_for`

. - Add efficiency considerations.
- Remove
`int`

and`unsigned`

alias templates. - Remove
`next`

and`append`

, change`size`

to function. - Rename
`type`

typedef to`value_type`

. - Fix typos.

N3493 Initial paper (Spring 2013 mid-term mailing)

In a function template such as

```
template<class... T>
void f(T... t);
```

performing some operation using every member of the parameter pack is
as simple as `expr(`

,
because *t*...)

can be used directly in a pack expansion.
When the parameter pack appears as part of another type such as
*t*`std::tuple`

, the function parameter is not a
parameter pack so can't be expanded directly.
For example, in the function template

```
template<class... T>
void foo(std::tuple<T...> t);
```

performing an operation on every element of the tuple requires additional
code because `t`

is not a parameter pack and
`expr(t...)`

is not valid.
(By comparison, in Python unpacking tuples to pass to variadic functions
is built in to the language and is as convenient as `func(*t)`

[Python].)

For unpacking a tuple in C++ the brute force alternative to
`expr(t...)`

is to instantiate a class template with a
static member function, such as

`DoExpr<0>::apply(t);`

which calls

`DoExpr<1>::apply(t, std::get<0>(t));`

which calls

`DoExpr<2>::apply(t, t0, std::get<1>(t));`

and so on for each element until
```
DoExpr<sizeof...(T)>
```

is instantiated and can call `expr(t0, t1, ..., tN)`

.
This requires the user to write a recursive class template (and a
specialization to terminate the recursion) with a variadic member function
template and to use perfect forwarding (not shown here) to avoid
O(N^{2}) copies.
To make a generic, reusable solution that can apply an arbitrary
function object to each element requires template partial
specialization and is probably beyond the abilities of many users of
`std::tuple`

, so the alternative is to write non-generic code
and then rewrite it slightly differently when a different operation on
tuples is needed. This is a fairly complicated task and the end result is
not even a very natural way to write the desired operation.
The call to

`DoExpr<0>::apply(t);`

is far less expressive than something like `expr(t...)`

.

A simpler and more natural solution is to introduce a new parameter pack,

, consisting of integers [0,N] and then use it in
a pack expansion such as *I*`expr(std::get<I>(t)...)`

.
This requires no recursion and no class template specializations.
This proposal is to standardize a mechanism for creating a parameter
pack containing an integer sequence.

The proposal is to add a type like

`template<int...> struct index_sequence { };`

so that an instantiation like `index_sequence<0, 1, 2, 3>`

can be passed to a function template that deduces a parameter
pack containing the integer sequence 0, 1, 2, 3.

In order to pass an `index_sequence`

to a function it must be
possible to construct the desired specialization either from the length of
sequence desired or from a parameter pack from which the length can be
deduced. This proposal offers both options, so that given the type
`tuple<T...>`

the sequence `[0, sizeof...(T))`

needed to expand the tuple can be created by using the alias
`make_index_sequence<sizeof...(T)>`

(or equivalently
`make_index_sequence<tuple_size<tuple<T...>>::value>`

)
or by using the alias `index_sequence_for<T...>`

.

With such a type in your toolbox it is easy to write the generic, reusable solution described above for expanding tuple elements as arguments to a function object:

```
template<typename F, typename Tuple, size_t... I>
auto
apply_(F&& f, Tuple&& args, index_sequence<I...>)
-> decltype(std::forward<F>(f)(std::get<I>(std::forward<Tuple>(args))...))
{
return std::forward<F>(f)(std::get<I>(std::forward<Tuple>(args))...);
}
template<typename F, typename Tuple,
typename Indices = make_index_sequence<std::tuple_size<Tuple>::value>>
auto
apply(F&& f, Tuple&& args)
-> decltype(apply_(std::forward<F>(f), std::forward<Tuple>(args), Indices()))
{
return apply_(std::forward<F>(f), std::forward<Tuple>(args), Indices());
}
```

This solution still uses recursion and template specialization, but
only in the implementation of `make_index_sequence`

, where users don't
need to write or understand it.
Standardizing the components makes it trivial for users to expand
tuple-like types in any situation, including the examples below.
A type like `index_sequence`

is a good candidate for standardization,
as similar types are already used in at least two major standard library
implementations and have been reinvented often.
Similar types feature in several answers to questions on sites such as
Stack Overflow
[Schaub]
[Wakely]
[Kühl],
where the number of questions about unpacking tuples
and the number of times types like `index_sequence`

are used in answers
demonstrates the demand for a solution to the problem.

`std::pair`

.
Piecewise construction of `std::pair`

requires two
`tuple`

s of arguments to be expanded to form constructor
arguments for the pair members. One implementation technique is to
delegate to a private constructor for `pair`

that takes
two types like `index_sequence`

, for example

```
template<class... Args1, class... Args2>
pair(piecewise_construct_t, tuple<Args1...> args1, tuple<Args2...> args2)
: pair(args1, args2, index_sequence_for<Args1...>{}, index_sequence_for<Args2...>{})
{ }
private:
template<class... A1, class... A2, size_t... I1, size_t... I2>
pair(tuple<A1...>& a1, tuple<A2...>& a2, index_sequence<I1...>, index_sequence<I2...>)
: first(std::get<I1>(std::move(a1))...),
second(std::get<I2>(std::move(a2))...)
{ }
```

A note in [tuple.creation] says that implementations might support using
`std::tuple_cat`

with other tuple-like type such as
`std::array`

, but it's not required.
Users who need to implement it themselves can do so using a recursive
template, using `tuple_cat`

to build up a `tuple`

element by element, but this creates lots of temporaries and instantiations.
An implementation is shown here for comparison with the
`index_sequence`

solution:

```
template<typename T, std::size_t N, std::size_t I = 0>
struct a2t_
{
static_assert( I < N, "index within array bound" );
template<typename... Elts>
static auto
cat(std::tuple<Elts...>&& t, const std::array<T, N>& a)
-> decltype(a2t_<T, N, I+1>::cat(std::tuple_cat(t, std::make_tuple(a[I])), a))
{
return a2t_<T, N, I+1>::cat(std::tuple_cat(t, std::make_tuple(a[I])), a);
}
};
template<typename T, std::size_t N>
struct a2t_<T, N, N>
{
template<typename... Elts>
static std::tuple<Elts...>
cat(std::tuple<Elts...>&& t, const std::array<T, N>& a)
{
return t;
}
};
template<typename T, std::size_t N>
auto
a2t(const std::array<T, N>& a)
-> decltype(a2t_<T, N>::cat(std::tuple<>(), a))
{
return a2t_<T, N>::cat(std::tuple<>(), a);
}
```

Using `index_sequence`

the implementation is almost trivial:

```
template<typename Array, size_t... I>
auto
a2t_(const Array& a, index_sequence<I...>)
-> decltype(std::make_tuple(a[I]...))
{
return std::make_tuple(a[I]...);
}
template<typename T, std::size_t N, typename Indices = make_index_sequence<N>>
auto
a2t(const std::array<T, N>& a)
-> decltype(a2t_(a, Indices()))
{
return a2t_(a, Indices());
}
```

`more_perfect_forwarding_async`

example
The `more_perfect_forwarding_async`

example in
N3466
refers to a "complicated template metafunction" [DRayX]
which can be replaced with the comparatively simple `apply()`

function template defined above.

While I hope there will be broad agreement that some form of integer sequence template should be standardized there are some parts of the solution which might be harder to agree on. The changes to the working paper proposed below are my preferred solution but the specific details are less important than getting some kind of template that makes it easy to solve the problems described above.

It's not obvious to me what type of integer should be used in the
parameter pack of the class template. The natural type for indexing into
tuples and arrays is `std::size_t`

, but that type has a far
larger range of values than needed. I consider it unlikely that any
compiler will support parameter packs that can accept `SIZE_MAX`
arguments for the foreseeable future.
Another question is whether the integer type should be signed or unsigned.
Indices are naturally unsigned, but there could be other interesting uses
for integer sequences other than unpacking tuples and arrays which would
be more difficult if the values cannot be negative.
Conversely there might be valid use cases where the wrapping behaviour of
unsigned integers is preferable to worrying about overflow.

The proposed solution is to define a generic `integer_sequence`

class template which can be instantiated as
`integer_sequence<int>`

or
`integer_sequence<unsigned char>`

or any other integer type.
By using alias templates to denote specializations for common types it is
just as convenient to use the generic template as it would be if it wasn't
parameterized by the integer type, for instance the examples above work
equally well whether `index_sequence<I...>`

is a specialization
of a class template or an alias for ```
integer_sequence<size_t,
I...>
```

.

There is no reason to restrict the values in an integer sequence to
consecutive integers starting from zero.
It is very simple to transform
`index_sequence<I...>`

to `index_sequence<I+n...>`

or `index_sequence<I*n...>`

.
Such sequences would be useful to access only the even elements of an array,
for example, but such transformations are not necessary for the main
purpose of unpacking tuples. If the standard provides the
`integer_sequence`

type and simple metafunctions for generating
basic sequences users can more easily create custom sequences.

For most uses

`template<int...> struct index_sequence { };`

is sufficient, but it's simple to define `type`

and
`size`

members describing the type and to provide
`append`

and `next`

members for extending
sequences, as shown in the proposed changes below.

These members are not essential to the proposal and the suggestion
might be due to my own bias as the `next`

member is used
by my implementation of the proposed changes below
[integer_seq]
i.e. in the unspecified details of how `make_integer_sequence`

works.

For a sequence of N integers the reference implementation recursively
instantiates N templates, limiting the length of sequences to (at most)
the instantiation depth of the compiler.
It is quite easy to reduce the number of instantiations to
log_{2}(N) by starting at both ends of the sequence and working
inwards to meet the middle.

A compiler intrinisic could be used to instantiate an arbitrary-length
`integer_sequence`

with no recursion.

There have been suggestions of a core feature that would define
`...3`

as the parameter pack `{0, 1, 2, 3}`

,
which would provide an alternative way to solve the problems solved
by this proposal.
This language feature will not be in C++14 if accepted at all, so
should not prevent solving the problem now.

This is a pure addition to the library.
It is expected that implementations would be able to replace existing
equivalent code with uses of `integer_sequence`

if desired.

Add to the synopsis in [utility] paragraph 2, after the declaration of
`tuple`

:

`// 20.x Compile-time integer sequences template<class T, T...> struct integer_sequence; template<size_t... I> using index_sequence = integer_sequence<size_t, I...>; template<class T, T N> using make_integer_sequence = integer_sequence<T, see below>; template<size_t N> using make_index_sequence = make_integer_sequence<size_t, N>; template<class... T> using index_sequence_for = make_index_sequence<sizeof...(T)>;`

Add a new subclause after [pairs]:

## 20.x Compile-time integer sequences [intseq]

## 20.x.1 In general [intseq.general]

The library provides a class template that can represent an integer sequence. When used as an argument to a function template the parameter pack defining the sequence can be deduced and used in a pack expansion.

[

Example:`template<class F, class Tuple, std::size_t... I> auto apply_impl(F&& f, Tuple&& t, index_sequence<I...>) -> decltype(std::forward<F>(f)(std::get<I>(std::forward<Tuple>(t))...) { return std::forward<F>(f)(std::get<I>(std::forward<Tuple>(t))...); } template<class F, class Tuple, class Indices = make_index_sequence<std::tuple_size<Tuple>::value>> auto apply(F&& f, Tuple&& t) -> decltype(apply_impl(std::forward<F>(f), std::forward<Tuple>(t), Indices())) { return apply_impl(std::forward<F>(f), std::forward<Tuple>(t), Indices()); }`

— end example]## 20.x.2 Class template

`integer_sequence`

[intseq.intseq]`namespace std { template<class T, T... I> struct integer_sequence { typedef T value_type; static constexpr size_t size() noexcept { return sizeof...(I); } }; } // namespace std`

Tshall be an integer type.## 20.x.3 Alias template

`make_integer_sequence`

[intseq.make]`template<class T, T N> using make_integer_sequence = integer_sequence<T, see below>;`

If

`N`

is negative the program is ill-formed. The alias template`make_integer_sequence`

denotes a specialization of`integer_sequence`

with`N`

template non-type arguments. The type`make_integer_sequence<T, N>`

denotes the type`integer_sequence<T, 0, 1, ..., N-1>`

. [Note:`make_integer_sequence<int, 0>`

denotes the type`integer_sequence<int>`

— end note]

- [Python]
- Python, The Python Tutorial, 10 January 2013, Unpacking Argument Lists, http://docs.python.org/dev/tutorial/controlflow.html#unpacking-argument-lists
- [Schaub]
- Johannes Schaub, "unpacking" a tuple to call a matching function pointer, 22 October 2011, http://stackoverflow.com/a/7858971
- [Wakely]
- Jonathan Wakely, Variadic templates: iterate over type/template argument, 27 December 2012, http://stackoverflow.com/a/11196263
- [Kühl]
- Dietmar Kühl, How to guarantee order of argument evaluation when calling a function object?, 27 December 2012, http://stackoverflow.com/a/14059084
- [DRayX]
- DRayX, How do I expand a tuple into variadic template function's arguments?, 29 September 2012, http://stackoverflow.com/a/12650100
- [integer_seq]
- Jonathan Wakely, integer_seq, 10 January 2013, <integer_seq.h>, https://gitorious.org/redistd/integer_seq/blobs/master/integer_seq.h