1 Motivation
2 Design overview
3 More examples
- 3.1 Change existing code to use parallel range algorithms
- 3.2 Less parallel algorithm calls and better expressiveness
4 Possible implementation of a parallel range algorithm
5 The proposal scope
- 5.1 In-scope
  - 5.1.1 The counterparts of C++17 parallel algorithms in std::ranges namespace
  - 5.1.2 Algorithms in std::ranges namespace only
- 5.2 Out-of-scope
6 Implementation experience
7 Further work
8 Formal wording
9 Revision history
10 Polls
11 Acknowledgments
12 References

Abstract

This paper proposes adding parallel algorithms that work together with the C++ Ranges library.

1 Motivation

Standard parallel algorithms with execution policies which set semantic requirements to user-provided callable objects were a good start for supporting parallelism in the C++ standard.

The C++ Ranges library - ranges, views, etc. - is a powerful facility to produce lazily evaluated pipelines that can be processed by range-based algorithms. Together they provide a productive and expressive API with the room for extra optimizations.

Combining these two powerful features by adding support for execution policies to the range-based algorithms opens an opportunity to fuse several computations into one parallel algorithm call, thus reducing the overhead on parallelism. That is especially valuable for heterogeneous implementations of parallel algorithms, for which the range-based API helps reducing the number of kernels submitted to an accelerator.

Users are already using ranges and range adaptors by passing range iterators to the existing non-range parallel algorithms. [P2408R5] was adopted to enable this. This pattern is often featured when teaching C++ parallel algorithms and appears in many codebases.

iota and cartesian_product are especially common, as many compute workloads want to iterate over indices, not objects, and many work with multidimensional data. transform is also common, as it enables fusion of element-wise operations into a single parallel algorithm call, which can avoid the need for temporary storage and is more performant than two separate calls.

However, passing range iterators to non-range algorithms is unwieldy and verbose. It is surprising to users that they cannot simply pass the ranges to the parallel algorithms as they would for serial algorithms.

Scalar-Vector Multiply
Before	After
`std::span<double> data = …; double C = …; auto indices = std::views::iota(1, data.size()); std::for_each(std::execution::par_unseq, std::ranges::begin(indices), std::ranges::end(indices), [=] (auto i) { data[i] *= C; });`	`std::span<double> data = …; double C = …; std::ranges::for_each(std::execution::par_unseq, std::views::iota(1, data.size()), [=] (auto i) { data[i] *= C; });`

Before

After

std::span<double> data = …;
double C = …;

auto indices = std::views::iota(1, data.size());
std::for_each(std::execution::par_unseq,
  std::ranges::begin(indices),
  std::ranges::end(indices),
  [=] (auto i) { data[i] *= C; });

std::span<double> data = …;
double C = …;

std::ranges::for_each(std::execution::par_unseq,
  std::views::iota(1, data.size()),
  [=] (auto i) { data[i] *= C; });

Matrix Transpose
Before	After
`std::mdspan A{input, N, M}; std::mdspan B{output, M, N}; auto indices = std::views::cartesian_product( std::views::iota(0, A.extent(0)), std::views::iota(0, A.extent(1))); std::for_each(std::execution::par_unseq, std::ranges::begin(indices), std::ranges::end(indices), [=] (auto idx) { auto [i, j] = idx; B[j, i] = A[i, j]; });`	`std::mdspan A{input, N, M}; std::mdspan B{output, M, N}; std::ranges::for_each(std::execution::par_unseq, std::views::cartesian_product( std::views::iota(0, A.extent(0)), std::views::iota(0, A.extent(1))), [=] (auto idx) { auto [i, j] = idx; B[j, i] = A[i, j]; });`

Before

After

std::mdspan A{input,  N, M};
std::mdspan B{output, M, N};

auto indices = std::views::cartesian_product(
  std::views::iota(0, A.extent(0)),
  std::views::iota(0, A.extent(1)));

std::for_each(std::execution::par_unseq,
  std::ranges::begin(indices),
  std::ranges::end(indices),
  [=] (auto idx) {
    auto [i, j] = idx;
    B[j, i] = A[i, j];
  });

std::mdspan A{input,  N, M};
std::mdspan B{output, M, N};

std::ranges::for_each(std::execution::par_unseq,
  std::views::cartesian_product(
    std::views::iota(0, A.extent(0)),
    std::views::iota(0, A.extent(1))),
  [=] (auto idx) {
    auto [i, j] = idx;
    B[j, i] = A[i, j];
  });

Earlier, [P2500R2] proposed to add the range-based C++ parallel algorithms together with its primary goal of extending algorithms with schedulers. We have decided to split those parts to separate papers, which could progress independently.

2 Design overview

This paper proposes execution policy support for C++ range-based algorithms. In the nutshell, the proposal extends C++ range algorithms with overloads taking any standard or implementation defined C++ execution policy as a function parameter. These overloads are further referred to as parallel range algorithms.

The proposal is targeted to C++26.

2.1 Design summary

2.1.1 Differences to serial range algorithms

Comparing to the C++20 serial range algorithms, we propose the following modifications:

The execution policy parameter is added, supporting all standard and implementation-defined execution policies. See Supported execution policies.
for_each and for_each_n return only an iterator but not the function. See Algorithm return types.
Parallel range algorithms take a range, not an iterator, as the output for the overloads with ranges, and additionally take an output sentinel for the “iterator and sentinel” overloads. See Taking range as the output.
Until better parallelism-friendly abstractions are proposed, parallel algorithms require random_access_{iterator,range}. See Requiring random_access_iterator or random_access_range.
All input and output data sequences must be bounded. See Requiring ranges to be bounded.

2.1.2 Differences to C++17 parallel algorithms

In addition to data sequences being passed as either ranges or “iterator and sentinel” pairs, the following differences to the C++17 parallel algorithms are proposed:

for_each returns an iterator, not void.
Algorithms require random_access_{iterator,range}, and not LegacyForwardIterator.
All input and output data sequences must be bounded.

2.1.3 Other design aspects

Except as mentioned above, the parallel range algorithms should return the same type as the corresponding serial range algorithms. See Algorithm return types.
The proposed algorithms extend the overload set of algorithm function objects defined in std::ranges. See Extending the overload sets of algorithm function objects.
The proposed algorithms should require callable object passed to an algorithm to be regular_invocable where possible. See Requirements for callable parameters.
The proposed algorithms should follow the design of C++17 parallel algorithms with regard to constexpr support. See constexpr parallel range algorithms.

2.1.4 An example of the proposed API

The proposed API will look like the following (using transform as an example):

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
         random_access_iterator O, sized_sentinel_for<O> OutS,
         copy_constructible F, class Proj = identity>
  requires indirectly_writable<O, indirect_result_t<F&, projected<I, Proj>>>
  ranges::unary_transform_result<I, O>
    ranges::transform(Ep&& exec, I first, S last, O result, OutS result_last,
                      F op, Proj proj = {});

template<execution-policy Ep, ranges::random-access-sized-range R, ranges::random-access-sized-range OutR,
         copy_constructible F, class Proj = identity>
  requires indirectly_writable<ranges::iterator_t<OutR>, indirect_result_t<F&, projected<ranges::iterator_t<R>, Proj>>>
  ranges::unary_transform_result<ranges::borrowed_iterator_t<R>, ranges::borrowed_iterator_t<OutR>>
    ranges::transform(Ep&& exec, R&& r, OutR&& result, F op, Proj proj = {});

The used exposition-only concepts are described below.

2.2 Coexistence with schedulers

We believe that adding parallel range algorithms does not have the risk of conflict with anticipated scheduler-based algorithms, because an execution policy does not satisfy the requirements for a policy-aware scheduler [P2500R2], a sender [P3300R0], or really anything else from [P2300R10] that can be used to specify such algorithms.

At this point we do not, however, discuss how the appearance of schedulers may or should impact the execution rules for parallel algorithms specified in [algorithms.parallel.exec], and just assume that the same rules apply to the range algorithms with execution policies.

2.3 Supported execution policies

Parallel range algorithms should operate with the same set of execution policies as the existing parallel algorithms, that is, seq, unseq, par, and par_unseq in the std::execution namespace, as well as any implementation-defined execution policies.

The following exposition-only concept simplifies constraining the algorithms with proper execution policy types:

template<class Ep>
concept execution-policy = // exposition only
    is_execution_policy_v<remove_cvref_t<Ep>>;

We do not propose the parallel range algorithms to be customizable for application-defined execution policies. We expect such custom policies to become unnecessary once the standard algorithms are capable of working with schedulers/senders/receivers.

2.4 Algorithm return types

We explored possible algorithm return types and came to conclusion that returning the same type as serial range algorithms is the preferred option to make the changes for enabling parallelism minimal.

auto res = std::ranges::sort(v);

becomes:

auto res = std::ranges::sort(std::execution::par, v);

However, std::ranges::for_each and std::ranges::for_each_n require special consideration because previous design decisions suggest that there should be a difference between serial and parallel versions.

The following table summarizes return value types for the existing variants of these two algorithms:

API	Return type
`std::for_each`	`Function`
Parallel `std::for_each`	`void`
`std::for_each_n`	`Iterator`
Parallel `std::for_each_n`	`Iterator`
`std::ranges::for_each`	`for_each_result<ranges::borrowed_iterator_t<Range>, Function>`
`std::ranges::for_each`, `I` + `S` overload	`for_each_result<Iterator, Function>`
`std::ranges::for_each_n`	`for_each_n_result<Iterator, Function>`

While the serial std::for_each returns the obtained function object with all modifications it might have accumulated, the return type for the parallel std::for_each is void because, as stated in the standard, “parallelization often does not permit efficient state accumulation”. For efficient parallelism an implementation can make multiple copies of the function object, which for that purpose is allowed to be copyable and not just movable like for the serial for_each. That implies that users cannot rely on any state accumulation within that function object, so it does not make sense (and might be even dangerous) to return it.

In std::ranges, the return type of for_each and for_each_n is unified to return both an iterator and the function object.

Based on the analysis above and the feedback from SG9 we think that the most reasonable return type for parallel variants of std::ranges::for_each and std::ranges::for_each_n should be:

API	Return type
Parallel `std::ranges::for_each`	`ranges::borrowed_iterator_t<Range>`
Parallel `std::ranges::for_each`, `I` + `S` overload	`Iterator`
Parallel `std::ranges::for_each_n`	`Iterator`

2.5 Extending the overload sets of algorithm function objects

We believe the proposed functionality should have the same properties and general behavior as serial range algorithms, particularly regarding the name lookup.

With the adoption of [P3136R0], function templates in the std::ranges namespace have been respecified as algorithm function objects. These objects are defined as sets of one or more overloaded function templates, which names designate the objects.

The parallel range algorithms we propose will extend the overload sets for the respective algorithm function objects. The name lookup rules for such objects will apply automatically. It is covered by the wording proposed in [P3136R0]; additional changes are not needed.

From the implementation standpoint, adding parallel versions of the range algorithms to the overload set should not be a problem. Please see Possible implementation of a parallel range algorithm for more information.

2.6 Requiring `random_access_iterator` or `random_access_range`

C++17 parallel algorithms minimally require LegacyForwardIterator for data sequences, but in our opinion, it is not quite suitable for an efficient parallel implementation. Therefore for parallel range algorithms we propose to require random access ranges and iterators.

Using parallel algorithms with forward ranges will in most cases give little to no benefit, and may even reduce performance due to extra overheads. We believe that forward ranges and iterators are bad abstractions for parallel data processing, and allowing those could result in wrong expectations and unsatisfactory user experience with parallel algorithms.

Many parallel programming models that are well known and widely used in the industry, including OpenMP, OpenCL, CUDA, SYCL, oneTBB, define iteration or data spaces for their parallel constructs in ways that allow creating sufficient parallel work quickly and efficiently. A key property for this is the ability to split the work into smaller chunks. These programming models allow to control the amount of work per chunk and sometimes the ways chunks are created and/or scheduled. All these also support iteration spaces up to at least 3 dimensions.

Except for tbb::parallel_for_each in oneTBB which can work with forward iterators, these parallel programming models require random access iterators or some equivalent, such as numeric indexes or pointers. This is natural, as referring to an arbitrary point in the iteration space at constant time is the main and by far simplest way to create parallel work. Forward iterators, on the other hand, are notoriously bad for splitting a sequence that can only be done in linear time. Moreover, if the output of an algorithm should preserve the order of its input, which is typical for the C++ algorithms, it requires additional synchronization or/and additional space with forward iterators and comes almost for granted with random access ones.

These very programming models are often used as backends to implement the C++ standard parallelism. Not surprisingly, most implementations fall back to serial processing if data sequences have no random access. Of the GNU libstdc++, LLVM libc++, and MSVC’s standard library, only the latter attempts to process forward iterator based sequences in parallel, for which it first needs to serially iterate over a whole sequence once or even twice. oneAPI DPC++ library (oneDPL) supports forward iterators only for a very few algorithms, only for par and only in the implementation based on oneTBB.

According to the SG1/SG9 feedback we have got earlier, there seemingly are two main reasons why others do not want to restrict parallel algorithms by only random access ranges:

That would prevent some useful views, such as filter_view, from being used with parallel range algorithms.
That would be inconsistent with the C++17 parallel algorithms.

Given the other aspects of the proposed design, we believe some degree of inconsistency with C++17 parallel algorithms is inevitable and should not become a gating factor for important design decisions.

The question of supporting the standard views that do not provide random access is very important. We think though that it should better be addressed through proper abstractions and new concepts defining iteration spaces, including multidimensional ones, suitable for parallel algorithms. We intend to work on developing these (likely in another paper), however it requires time and effort to make it right, and we think trying to squeeze that into C++26 adds significant risks. For now, random access ranges with known bounds (see Requiring ranges to be bounded) is probably the best approximation that exists in the standard. Starting from that and gradually enabling other types of iteration spaces in a source-compatible manner seems to us better than blanket allowance of any forward_range.

2.7 Taking range as the output

We propose taking a range as the output for the overloads that take ranges for input. Similarly, we propose requiring a sentinel for the output where the input is passed as “iterator and sentinel”.

The benefits of this range-as-the-output approach, comparing to taking a single iterator for the output, are:

It creates a safer API where all data sequences have known bounds. Specifically, the sized_range and sized_sentinel_for concepts will be applied to the output sequences in the same way as to the input sequences.
Not for all algorithms the output size is defined by the input size. An example is copy_if (and similar algorithms with filtering semantics), where the output sequence might be shorter than the input one. Knowing the expected size of the output may open opportunities for more efficient implementations.
Passing a range for the output makes code a bit simpler in the cases typical for parallel execution.

On the joint SG1 and SG9 discussion of [P3179R2] the audience expressed several concerns about the idea and requested to stay with iterators for the output until deeper investigation is made.

To address the concerns, we wrote a separate paper [P3490R0] with the detailed investigation of the topic, suggesting there a compromise solution with adding separate function template overloads for both iterator-as-the-output and range-as-the-output. See [P3490R0] for more details.

Eventually SG9 accepted our original proposal to use ranges for the output, without extra overloads for legacy convenience.

2.8 Requiring ranges to be bounded

One of the requirements we want to put on the parallel range algorithms is to disallow unbounded input and output. The reasons for that are:

For efficient parallel implementation we need to know the iteration space bounds. Otherwise, it’s hard to apply the “divide and conquer” strategy for creating work for multiple execution threads.
While serial range algorithms allow passing an “infinite” range like std::ranges::views::iota(0), it may result in an endless loop. It’s hard to imagine usefulness of that in the case of parallel execution. Requiring data sequences to be bounded potentially prevents errors at run-time.
Using explicitly bounded output ranges follows established practices of secure coding, which recommend or even require to always specify the size of the output in order to prevent out-of-range data modifications.

If several provided ranges or sequences are bounded, an algorithm should stop as soon as the end is reached for the shortest one. There are already precedents in the standard that an algorithm takes two sequences with potentially different input sizes and chooses the smaller size as the number of iterations it is going to make, such as std::ranges::transform and std::ranges::mismatch. For the record, std::transform (including the overload with execution policy) doesn’t support different input sizes, while std::mismatch does.

In the case of two input ranges or sequences, for a few algorithms - namely, mismatch, equal, and transform - it could be sufficient for just one range to be bounded and the other assumed to have at least as many elements as the bounded one. This enables unbounded ranges such as views::repeat in certain useful patterns, for example:

void normalize_parallel(range auto&& v) {
  auto mx = reduce(execution::par, v, ranges::max{});
  transform(execution::par, v, views::repeat(mx), v.begin(), divides);
}

However, SG9 decided to require sized_range for all inputs, with the plan to relax these constraints for transform once there is a way to statically detect infinite ranges like views::repeat (as opposed to finite unsized ranges, such as null terminated strings).

The exposition-only concept random-access-sized-range combines the key requirements to the types of ranges to simplify the signatures of parallel range algorithms:

template<class R>
concept random-access-sized-range = // exposition only
    ranges::random_access_range<R> && ranges::sized_range<R>;

2.9 Requirements for callable parameters

In [P3179R0] we proposed that parallel range algorithms should require function objects for predicates, comparators, etc. to have const-qualified operator(), with the intent to provide compile-time diagnostics for mutable function objects which might be unsafe for parallel execution. We have got contradictory feedback from SG1 and SG9 on that topic: SG1 preferred to keep the behavior consistent with C++17 parallel algorithms, while SG9 supported our design intent.

We did extra investigation and decided that requiring const-qualified operator at compile-time is not strictly necessary because:

The vast majority of the serial range algorithms requires function objects to be regular_invocable (or its derivatives), which already has the semantic requirement of not modifying either the function object or its arguments. While not enforced at compile-time, it seems good enough for our purpose because it demands having the same function object state between invocations (independently of const qualifier), and it is consistent with serial range algorithms.
Remaining algorithms should be considered individually. For example, for_each using a mutable operator() is of less concern if the algorithm does not return the function object (see more detailed analysis below). For generate, a non-mutable callable appears to be of very limited use: in order to produce multiple values while not taking any arguments, a generator should typically maintain and update some state.

The following example works fine for serial code. While it compiles for parallel code, users should not assume that the semantics remains intact. Since the parallel version of for_each requires function object to be copyable, it is not guaranteed that all for_each iterations are processed by the same function object. Practically speaking, users cannot rely on accumulating any state modifications in a parallel for_each call.

struct callable
{
    void operator()(int& x)
    {
        ++x;
        ++i; // a data race if the callable is executed concurrently
    }
    int get_i() const {
        return i;
    }
private:
    int i = 0;
};

callable c;

// serial for_each call
auto fun = std::for_each(v.begin(), v.end(), c);

// parallel for_each call
// The callable object cannot be read because parallel for_each version purposefully returns void
std::for_each(std::execution::par, v.begin(), v.end(), c);

// for_each serial range version call
auto [_, fun] = std::ranges::for_each(v.begin(), v.end(), c);

We allow the same callable to be used in the proposed std::ranges::for_each.

// callable is used from the previous code snippet
callable c;
// The returned iterator is ignored
std::ranges::for_each(std::execution::par, v.begin(), v.end(), c);

Again, even though c accumulates state modifications, one cannot rely on that because an algorithm implementation is allowed to make as many copies of c as it wants. Of course, this can be overcome by using std::reference_wrapper but that might lead to data races.

// callable is used from the previous code snippet
// Wrapping a callable object with std::reference_wrapper compiles, but might result in data races
callable c;
std::ranges::for_each(std::execution::par, v.begin(), v.end(), std::ref(c));

Our conclusion is that it’s user responsibility to provide such a callable that avoids data races, same as for C++17 parallel algorithms.

2.10 `constexpr` parallel range algorithms

[P2902R0] suggests allowing algorithms with execution policies to be used in constant expressions. We do not consider that as a primary design goal for our work, however we will happily align with that proposal in the future once it progresses towards adoption into the working draft.

3 More examples

3.1 Change existing code to use parallel range algorithms

One of the goals is to require a minimal amount of changes when switching from the existing API to parallel range algorithms. However, that simplicity should not create hidden issues negatively impacting the overall user experience. We believe that the proposal provides a good balance in that regard.

As an example, let’s look at using for_each to apply a lambda function to all elements of a std::vector v.

For the serial range-based for_each call:

std::ranges::for_each(v, [](auto& x) { ++x; });

switching to the parallel version will look like:

std::ranges::for_each(std::execution::par, v, [](auto& x) { ++x; });

In this simple case, the only change is an execution policy added as the first function argument. It will also hold for the “iterator and sentinel” overload of std::ranges::for_each.

The C++17 parallel for_each call:

std::for_each(std::execution::par, v.begin(), v.end(), [](auto& x) { ++x; });

can be changed to one of the following:

// Using iterator and sentinel
std::ranges::for_each(std::execution::par, v.begin(), v.end(), [](auto& x) { ++x; });

// Using vector as a range
std::ranges::for_each(std::execution::par, v, [](auto& x) { ++x; });

So, here only changing the namespace is necessary, though users might also change v.begin(), v.end() to just v.

However, for other algorithms more changes might be necessary.

3.2 Less parallel algorithm calls and better expressiveness

Let’s consider the following example:

reverse(policy, begin(data), end(data));
transform(policy, begin(data), end(data), begin(result), [](auto i){ return i * i; });
auto res = find_if(policy, begin(result), end(result), pred);

It has three stages and eventually tries to answer the question if the input sequence contains an element after reversing and transforming it. The interesting considerations are:

Since the example has three parallel stages, it adds extra overhead for parallel computation per algorithm.
The first two stages will complete for all elements before the any_of stage is started, though it is not required for correctness. If reverse and transformation would be done on the fly, a good implementation of any_of might have skipped the remaining work when pred returns true, thus providing more performance.

Let’s make it better:

// With fancy iterators
auto res = find_if(policy,
                  make_transform_iterator(make_reverse_iterator(end(data)),
                                          [](auto i){ return i * i; }),
                  make_transform_iterator(make_reverse_iterator(begin(data)),
                                          [](auto i){ return i * i; }),
                  pred);

Now there is only one parallel algorithm call, and any_of can skip unneeded work. However, this variation also has interesting considerations:

First, it doesn’t compile. We use transform iterator to pass the transformation function, but the two make_transform_iterator expressions use two different lambdas, and the iterator type for any_of cannot be deduced because the types of transform_iterator do not match. One of the options to make it compile is to store a lambda in a variable.
Second, it requires using a non-standard iterator.
Third, the expressiveness of the code is not good: it is hard to read while easy to make a mistake like the one described in the first bullet.

Let’s improve the example further with the proposed API:

// With ranges
auto res = find_if(policy, data | views::reverse | views::transform([](auto i){ return i * i; }),
                  pred);

The example above lacks the drawbacks described for the previous variations:

There is only one algorithm call;
The implementation might skip unnecessary work;
There is no room for the lambda type mistake;
The readability is much better compared to the second variation and not worse than in the first one.

4 Possible implementation of a parallel range algorithm

Here we show a possible implementation of std::ranges::for_each with the new overloads proposed in Modify for_each in [alg.foreach]:

// A possible implementation of std::ranges::for_each
namespace ranges
{
namespace __detail
{
struct __for_each_fn
{
    // ...
    // Existing serial overloads
    // ...

    // The overload for unsequenced and parallel policies. Requires random_access_iterator
    template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
             class Proj = identity, indirectly_unary_invocable<projected<I, Proj>> Fun>
    I operator()(Ep&& exec, I first, S last, Fun f, Proj proj = {}) const
    {
        // properly handle the execution policy;
        // for the reference, a serial implementation is provided
        for (; first != last; ++first)
        {
            std::invoke(f, std::invoke(proj, *first));
        }
        return first;
    }

    template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
             indirectly_unary_invocable<projected<iterator_t<R>, Proj>> Fun>
    ranges::borrowed_iterator_t<R>
    operator()(Ep&& exec, R&& r, Fun f, Proj proj = {}) const
    {
        return (*this)(std::forward<Ep>(exec), std::ranges::begin(r),
                       std::ranges::end(r), f, proj);
    }
}; // struct for_each
} // namespace __detail
inline namespace __for_each_fn_namespace
{
inline constexpr __detail::__for_each_fn for_each;
} // __for_each_fn_namespace
} // namespace ranges

5 The proposal scope

5.1 In-scope

5.1.1 The counterparts of C++17 parallel algorithms in `std::ranges` namespace

`all_of`	`search{_n}`	`remove_copy`	`is_sorted`	`is_heap`
`any_of`	`copy{_n}`	`remove_copy_if`	`is_sorted_until`	`is_heap_until`
`none_of`	`copy_if`	`unique`	`nth_element`	`min_element`
`for_each{_n}`	`move`	`unique_copy`	`is_partitioned`	`max_element`
`find`	`swap_ranges`	`reverse`	`partition`	`minmax_element`
`find_if`	`transform`	`reverse_copy`	`stable_partition`	`lexicographical_compare`
`find_if_not`	`replace`	`rotate`	`partition_copy`	`uninitialized_default_construct{_n}`
`find_end`	`replace_if`	~~`rotate_copy`~~	`merge`	`uninitialized_value_construct{_n}`
`find_first_of`	`replace_copy`	`shift_left`	`inplace_merge`	`uninitialized_copy{_n}`
`adjacent_find`	`replace_copy_if`	`shift_right`	`includes`	`uninitialized_move{_n}`
`count`	`fill{_n}`	`sort`	`set_union`	`uninitialized_fill{_n}`
`count_if`	`generate{_n}`	`stable_sort`	`set_intersection`	`destroy{_n}`
`mismatch`	`remove`	`partial_sort`	`set_difference`
`equal`	`remove_if`	`partial_sort_copy`	`set_symmetric_difference`

5.1.2 Algorithms in `std::ranges` namespace only

The algorithms below are easy to add because they are either expressible via existing parallel algorithms or an analogue with very close semantics exists:

`std::ranges` algorithms to add	`std` algorithms used as the guidance
`contains`	`find`
`contains_subrange`	`search`
`find_last`	`find`
`find_last_if`	`find_if`
`find_last_if_not`	`find_if_not`
`starts_with`	`mismatch`
`ends_with`	`equal`
`min`	`min_element`
`max`	`max_element`
`minmax`	`minmax_element`

5.2 Out-of-scope

5.2.1 Corner cases

Below we list the algorithms where we faced design issue(s). We would like to add them later:

rotate_copy

5.2.2 The counterparts of exiting algorithms without `ExecutionPolicy`

Below we list the algorithms below without ExecutionPolicy in C++17 and where ExecutionPolicy parameter doesn’t seem to add value:

push_heap
pop_heap
sort_heap
next_permutation
prev_permutation
lower_bound
upper_bound
equal_range
binary_search
partition_point

Below we list the algorithms below without ExecutionPolicy in C++17, where ExecutionPolicy parameter might make sense but requires deeper investigation:

iota
make_heap
is_permutation
copy_backward
move_backward
sample (RNG specific)
shuffle (RNG specific)

Below we list std::ranges only algorithms where we don’t add the ExecutionPolicy parameter:

fold_left
fold_left_first
fold_right
fold_right_last
fold_left_with_iter
fold_left_first_with_iter
generate_random (RNG specific, ExecutionPolicy parameter was rejected during [P1068R11] review)

5.2.3 Absence of some serial range-based algorithms

We understand that some useful algorithms do not yet exist in std::ranges, for example, most of generalized numeric operations [numeric.ops]. The goal of this paper is however limited to adding overloads with ExecutionPolicy to the existing algorithms in the std::ranges namespace. Any follow-up paper that adds <numeric> algorithms to std::ranges should also consider adding dedicated overloads with ExecutionPolicy.

6 Implementation experience

The oneAPI DPC++ Library (oneDPL) developer guide covers parallel range algorithms we’ve implemented so far. The oneAPI specification provides formal signatures of these algorithms. The implementation supports execution policies for CPUs (semantically aligned with the C++ standard) and for SYCL devices, and it works with a subset of the standard C++ views.

We use the range-as-the-output approach where applicable: in transform, copy, copy_if, and merge.

We don’t foresee any issues with implementability for the rest of the proposed parallel algorithms because all of them were already implemented in C++17 and new APIs that we propose are expressible via the existing ones.

7 Further work

7.1 Issues to address

Having known bugs and feedback from SG1 and SG9, the plan of work prior to the next committee F2F meeting in Austria, 2025 is the following:

Add testing experience of thread safe access to the views
Add necessary wording modifications to partition_copy and set_ algorithms family (like set_union, etc.)

7.2 LWG questions

C++17 <memory> Parallel Algorithms exist in the <memory> synopsis only. Should it be fixed?
namespace ranges is used (or not used) inconsistently, in our opinion. Need an advice.
For partial_sort_copy range-as-an-output is called R2. For uninitialized_copy and uninitialized_move it’s called OS. For the new wording we call is OutR. We should probably align. The same is true for sentinel-for-output.
ExecutionPolicy function parameter is named exec everywhere, except two places where the name is policy. Should it be fixed?
starts_with, ends_with misses dot at the end of Returns. It should be fixed, right?
find_last doesn’t have T = projected_value… in the synopsis. It must be a bug.
Serial replace_copy_if does not have indent for the second row of function parameters.
unique_copy wording uses N but its never defined.
shift_left doesn’t have extra ‘Returns’ word in Returns section
nth_element in Effects says were sorted. Should it be was?
inplace_merge Remarks is not consistent with the rest, doesn’t have the same link to [algorithm.stable].
How do you want us to refer to execution-policy Ep? Like that? Without Ep? Without execution-policy?
sort might have a potential bug in complexity about projections application.
partial_sort_copy seems to have incomplete wording.

7.3 Thread-safe views examination

We need to understand better whether using some views with parallel algorithms might result in data races. While some investigation was done by other authors in [P3159R0], it’s mostly not about the data races but about ability to parallelize processing of data represented by various views.

We need to invest more time to understand the implications of sharing a state between view and iterator on the possibility of data races. One example is transform_view, where iterators keep pointers to the function object that is stored in the view itself.

Here are questions we want to answer (potentially not a complete list):

Do users have enough control to guarantee absence of data races for such views?
Are races not possible because of implementation strategy chosen by standard libraries?
Do we need to add extra requirements towards thread safety to the standard views?
Should it be allowed for parallel algorithms to copy views?
Should begin()/end()/size() and possibly other operations with ranges be considered like element access functions for the purpose of thread safety definition?

8 Formal wording

8.1 Modify the `__cpp_lib_parallel_algorithm` macro in [version.syn]

- #define __cpp_lib_parallel_algorithm                201603L // also in <algorithm>, <numeric>
+ #define __cpp_lib_parallel_algorithm                20XXXXL // also in <algorithm>, <numeric>, <memory>

8.2 Modify [ranges.syn]

  template<class T>
    concept constant_range = see below;                                             // freestanding
+
+  template<class R>
+    concept random-access-sized-range = see below    // exposition only

8.3 Add an exposition-only concept to [range.refinements]

7 The constant_range concept specifies the requirements of a range type whose elements are not modifiable.

template<class T>
  concept constant_range =
    input_range<T> && constant-iterator<iterator_t<T>>;

X The exposition-only random-access-sized-range concept specifies the requirements of a range type that is sized and allows random access to its elements.

[Note X: This concept constraints some parallel algorithm overloads; see [algorithms] — end note]

  template<class R>
    concept random-access-sized-range =     // exposition only
      random_access_range<R> && sized_range<R>;

8.4 Modify [algorithms.parallel.defns]

2 A parallel algorithm is a function template listed in this ~~document~~Clause with an execution policy ([execpol]) template parameter named ExecutionPolicy or execution-policy Ep.

3 Parallel algorithms access objects indirectly accessible via their arguments by invoking the following functions:

All operations of the categories of the iterators, sentinels, or mdspan types that the algorithm is instantiated with.
Operations on those sequence elements that are required by its specification.
User-provided ~~function~~invocable objects to be applied during the execution of the algorithm, if required by the specification.
Operations on those ~~function~~invocable objects required by the specification.

8.5 Modify [algorithms.parallel.user]

1 Unless otherwise specified, ~~function~~invocable objects passed into parallel algorithms as objects of type Predicate, BinaryPredicate, Compare, UnaryOperation, BinaryOperation, BinaryOperation1, BinaryOperation2, BinaryDivideOp, Proj, and the operators used by the analogous overloads to these parallel algorithms that are formed by an invocation with the specified default predicate or operation (where applicable) shall not directly or indirectly modify objects via their arguments, nor shall they rely on the identity of the provided objects.

8.6 Modify [algorithms.parallel.exec]

1 Parallel algorithms have template parameters named ExecutionPolicy or execution-policy Ep ([execpol]) which describe the manner in which the execution of these algorithms may be parallelized and the manner in which they apply the element access functions.

8.7 Modify [algorithms.parallel.exceptions]

2 During the execution of a parallel algorithm, if the invocation of an element access function exits via an uncaught exception, the behavior is determined by the ~~ExecutionPolicy~~execution policy.

8.8 Modify [algorithms.parallel.overloads]

1 Parallel algorithms are algorithm overloads. Each parallel algorithm overload has an additional template type parameter named ExecutionPolicy or execution-policy Ep, which is the first template parameter. Additionally, each parallel algorithm overload has an additional function parameter of type ExecutionPolicy&& or Ep&&, which is the first function parameter.

[Note 1: Not all algorithms have parallel algorithm overloads. — end note]

2 Unless otherwise specified, the semantics of ~~ExecutionPolicy~~ algorithm overloads with an execution policy are identical to their overloads without.

3 Unless otherwise specified, the complexity requirements of ~~ExecutionPolicy~~ algorithm overloads with an execution policy are relaxed from the complexity requirements of the overloads without as follows: …

4 Parallel algorithms shall not participate in overload resolution unless is_execution_policy_v<remove_cvref_t<ExecutionPolicy>> is true. Parallel algorithms in the std::ranges namespace are constrained with the following exposition-only concept:

template<class Ep>
concept execution-policy = // exposition only
  is_execution_policy_v<remove_cvref_t<Ep>>;

8.9 Modify [algorithm.syn]

namespace ranges {
  template<input_iterator I, sentinel_for<I> S, class Proj = identity,
            indirect_unary_predicate<projected<I, Proj>> Pred>
    constexpr bool all_of(I first, S last, Pred pred, Proj proj = {});
  template<input_range R, class Proj = identity,
            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
    constexpr bool all_of(R&& r, Pred pred, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
+          indirect_unary_predicate<projected<I, Proj>> Pred>
+    bool all_of(Ep&& exec, I first, S last, Pred pred, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+          indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
+    bool all_of(Ep&& exec, R&& r, Pred pred, Proj proj = {});
}

namespace ranges {
  template<input_iterator I, sentinel_for<I> S, class Proj = identity,
            indirect_unary_predicate<projected<I, Proj>> Pred>
    constexpr bool any_of(I first, S last, Pred pred, Proj proj = {});
  template<input_range R, class Proj = identity,
            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
    constexpr bool any_of(R&& r, Pred pred, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
+          indirect_unary_predicate<projected<I, Proj>> Pred>
+    bool any_of(Ep&& exec, I first, S last, Pred pred, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+          indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
+    bool any_of(Ep&& exec, R&& r, Pred pred, Proj proj = {});
}

namespace ranges {
  template<input_iterator I, sentinel_for<I> S, class Proj = identity,
            indirect_unary_predicate<projected<I, Proj>> Pred>
    constexpr bool none_of(I first, S last, Pred pred, Proj proj = {});
  template<input_range R, class Proj = identity,
            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
    constexpr bool none_of(R&& r, Pred pred, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
+          indirect_unary_predicate<projected<I, Proj>> Pred>
+    bool none_of(Ep&& exec, I first, S last, Pred pred, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+          indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
+    bool none_of(Ep&& exec, R&& r, Pred pred, Proj proj = {});
}

namespace ranges {
  template<input_iterator I, sentinel_for<I> S, class Proj = identity,
            class T = projected_value_t<I, Proj>>
    requires indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
    constexpr bool contains(I first, S last, const T& value, Proj proj = {});
  template<input_range R, class Proj = identity,
            class T = projected_value_t<iterator_t<R>, Proj>>
    requires
      indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*>
    constexpr bool contains(R&& r, const T& value, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
+           class T = projected_value_t<I, Proj>>
+    requires indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
+    bool contains(Ep&& exec, I first, S last, const T& value, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+            class T = projected_value_t<iterator_t<R>, Proj>>
+    requires indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*>
+    bool contains(Ep&& exec, R&& r, const T& value, Proj proj = {});

  template<forward_iterator I1, sentinel_for<I1> S1,
            forward_iterator I2, sentinel_for<I2> S2,
            class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
    requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
    constexpr bool contains_subrange(I1 first1, S1 last1, I2 first2, S2 last2,
                                      Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
  template<forward_range R1, forward_range R2,
            class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
    requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
    constexpr bool contains_subrange(R1&& r1, R2&& r2,
                                      Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});

+  template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
+          random_access_iterator I2, sized_sentinel_for<I2> S2,
+          class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
+    requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
+    bool contains_subrange(Ep&& exec, I1 first1, S1 last1, I2 first2, S2 last2,
+                            Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
+  template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
+          class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
+    requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
+    bool contains_subrange(Ep&& exec, R1&& r1, R2&& r2, Pred pred = {},
+                            Proj1 proj1 = {}, Proj2 proj2 = {});
}

namespace ranges {
  template<class I, class F>
    using for_each_result = in_fun_result<I, F>;

  template<input_iterator I, sentinel_for<I> S, class Proj = identity,
            indirectly_unary_invocable<projected<I, Proj>> Fun>
    constexpr for_each_result<I, Fun>
      for_each(I first, S last, Fun f, Proj proj = {});
  template<input_range R, class Proj = identity,
            indirectly_unary_invocable<projected<iterator_t<R>, Proj>> Fun>
    constexpr for_each_result<borrowed_iterator_t<R>, Fun>
      for_each(R&& r, Fun f, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
+          indirectly_unary_invocable<projected<I, Proj>> Fun>
+    I for_each(Ep&& exec, I first, S last, Fun f, Proj proj = {});
+
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+          indirectly_unary_invocable<projected<iterator_t<R>, Proj>> Fun>
+    borrowed_iterator_t<R>
+      for_each(Ep&& exec, R&& r, Fun f, Proj proj = {});
}

namespace ranges {
  template<class I, class F>
    using for_each_n_result = in_fun_result<I, F>;

  template<input_iterator I, class Proj = identity,
            indirectly_unary_invocable<projected<I, Proj>> Fun>
    constexpr for_each_n_result<I, Fun>
      for_each_n(I first, iter_difference_t<I> n, Fun f, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, class Proj = identity,
+          indirectly_unary_invocable<projected<I, Proj>> Fun>
+    I for_each_n(Ep&& exec, I first, iter_difference_t<I> n, Fun f, Proj proj = {});
}

namespace ranges {
  template<input_iterator I, sentinel_for<I> S, class Proj = identity,
            class T = projected_value_t<I, Proj>>
    requires indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
    constexpr I find(I first, S last, const T& value, Proj proj = {});
  template<input_range R, class Proj = identity,
            class T = projected_value_t<iterator_t<R>, Proj>>
    requires indirect_binary_predicate<ranges::equal_to,
                                        projected<iterator_t<R>, Proj>, const T*>
    constexpr borrowed_iterator_t<R>
      find(R&& r, const T& value, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
+            class T = projected_value_t<I, Proj>>
+    requires indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
+    I find(Ep&& exec, I first, S last, const T& value, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R,
+            class Proj = identity, class T = projected_value_t<iterator_t<R>, Proj>>
+    requires indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*>
+    borrowed_iterator_t<R> find(Ep&& exec, R&& r, const T& value, Proj proj = {});

  template<input_iterator I, sentinel_for<I> S, class Proj = identity,
            indirect_unary_predicate<projected<I, Proj>> Pred>
    constexpr I find_if(I first, S last, Pred pred, Proj proj = {});
  template<input_range R, class Proj = identity,
            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
    constexpr borrowed_iterator_t<R>
      find_if(R&& r, Pred pred, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
+            indirect_unary_predicate<projected<I, Proj>> Pred>
+    I find_if(Ep&& exec, I first, S last, Pred pred, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
+    borrowed_iterator_t<R> find_if(Ep&& exec, R&& r, Pred pred, Proj proj = {});

  template<input_iterator I, sentinel_for<I> S, class Proj = identity,
            indirect_unary_predicate<projected<I, Proj>> Pred>
    constexpr I find_if_not(I first, S last, Pred pred, Proj proj = {});
  template<input_range R, class Proj = identity,
            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
    constexpr borrowed_iterator_t<R>
      find_if_not(R&& r, Pred pred, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
+            indirect_unary_predicate<projected<I, Proj>> Pred>
+    I find_if_not(Ep&& exec, I first, S last, Pred pred, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
+    borrowed_iterator_t<R> find_if_not(Ep&& exec, R&& r, Pred pred, Proj proj = {});
}

namespace ranges {
  template<forward_iterator I, sentinel_for<I> S, class T, class Proj = identity>
    requires indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
    constexpr subrange<I> find_last(I first, S last, const T& value, Proj proj = {});
  template<forward_range R, class T, class Proj = identity>
    requires
      indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*>
    constexpr borrowed_subrange_t<R> find_last(R&& r, const T& value, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
+            class T = projected_value_t<I, Proj>>
+    requires indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
+    subrange<I> find_last(Ep&& exec, I first, S last, const T& value, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+            class T = projected_value_t<iterator_t<R>, Proj>>
+    requires indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*>
+    borrowed_subrange_t<R> find_last(Ep&& exec, R&& r, const T& value, Proj proj = {});

  template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
            indirect_unary_predicate<projected<I, Proj>> Pred>
    constexpr subrange<I> find_last_if(I first, S last, Pred pred, Proj proj = {});
  template<forward_range R, class Proj = identity,
            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
    constexpr borrowed_subrange_t<R> find_last_if(R&& r, Pred pred, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
+           indirect_unary_predicate<projected<I, Proj>> Pred>
+    subrange<I> find_last_if(Ep&& exec, I first, S last, Pred pred, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+           indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
+    borrowed_subrange_t<R> find_last_if(Ep&& exec, R&& r, Pred pred, Proj proj = {});

  template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
            indirect_unary_predicate<projected<I, Proj>> Pred>
    constexpr subrange<I> find_last_if_not(I first, S last, Pred pred, Proj proj = {});
  template<forward_range R, class Proj = identity,
            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
    constexpr borrowed_subrange_t<R> find_last_if_not(R&& r, Pred pred, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
+            indirect_unary_predicate<projected<I, Proj>> Pred>
+    subrange<I> find_last_if_not(Ep&& exec, I first, S last, Pred pred, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
+    borrowed_subrange_t<R> find_last_if_not(Ep&& exec, R&& r, Pred pred, Proj proj = {});
}

namespace ranges {
  template<forward_iterator I1, sentinel_for<I1> S1, forward_iterator I2, sentinel_for<I2> S2,
            class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
    requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
    constexpr subrange<I1>
      find_end(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {},
                Proj1 proj1 = {}, Proj2 proj2 = {});
  template<forward_range R1, forward_range R2,
            class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
    requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
    constexpr borrowed_subrange_t<R1>
      find_end(R1&& r1, R2&& r2, Pred pred = {},
                Proj1 proj1 = {}, Proj2 proj2 = {});

+  template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1, random_access_iterator I2,
+           sized_sentinel_for<I2> S2, class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
+    requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
+    subrange<I1> find_end(Ep&& exec, I1 first1, S1 last1, I2 first2, S2 last2,
+                           Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
+  template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
+           class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
+    requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
+    borrowed_subrange_t<R1> find_end(Ep&& exec, R1&& r1, R2&& r2,
+                                      Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
}

namespace ranges {
  template<input_iterator I1, sentinel_for<I1> S1, forward_iterator I2, sentinel_for<I2> S2,
            class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
    requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
    constexpr I1 find_first_of(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {},
                                Proj1 proj1 = {}, Proj2 proj2 = {});
  template<input_range R1, forward_range R2,
            class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
    requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
    constexpr borrowed_iterator_t<R1>
      find_first_of(R1&& r1, R2&& r2, Pred pred = {},
                     Proj1 proj1 = {}, Proj2 proj2 = {});

+  template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
+            random_access_iterator I2, sized_sentinel_for<I2> S2,
+            class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
+    requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
+    I1 find_first_of(Ep&& exec, I1 first1, S1 last1, I2 first2, S2 last2,
+                      Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
+  template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
+           class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
+    requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
+    borrowed_iterator_t<R1> find_first_of(Ep&& exec, R1&& r1, R2&& r2,
+                                           Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
}

namespace ranges {
  template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
            indirect_binary_predicate<projected<I, Proj>,
                                      projected<I, Proj>> Pred = ranges::equal_to>
    constexpr I adjacent_find(I first, S last, Pred pred = {},
                              Proj proj = {});
  template<forward_range R, class Proj = identity,
            indirect_binary_predicate<projected<iterator_t<R>, Proj>,
                                      projected<iterator_t<R>, Proj>> Pred = ranges::equal_to>
    constexpr borrowed_iterator_t<R>
      adjacent_find(R&& r, Pred pred = {}, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
+            indirect_binary_predicate<projected<I, Proj>, projected<I, Proj>> Pred = ranges::equal_to>
+    I adjacent_find(Ep&& exec, I first, S last, Pred pred = {}, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+            indirect_binary_predicate<projected<iterator_t<R>, Proj>, projected<iterator_t<R>, Proj>> Pred
+             = ranges::equal_to>
+    borrowed_iterator_t<R> adjacent_find(Ep&& exec, R&& r, Pred pred = {}, Proj proj = {});
}

namespace ranges {
  template<input_iterator I, sentinel_for<I> S, class Proj = identity,
            class T = projected_value_t<I, Proj>>
    requires indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
    constexpr iter_difference_t<I>
      count(I first, S last, const T& value, Proj proj = {});
  template<input_range R, class Proj = identity,
            class T = projected_value_t<iterator_t<R>, Proj>>
    requires indirect_binary_predicate<ranges::equal_to,
                                        projected<iterator_t<R>, Proj>, const T*>
    constexpr range_difference_t<R>
      count(R&& r, const T& value, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
+            class T = projected_value_t<I, Proj>>
+    requires indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
+    iter_difference_t<I> count(Ep&& exec, I first, S last, const T& value, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+            class T = projected_value_t<iterator_t<R>, Proj>>
+    requires indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*>
+    range_difference_t<R> count(Ep&& exec, R&& r, const T& value, Proj proj = {});

  template<input_iterator I, sentinel_for<I> S, class Proj = identity,
            indirect_unary_predicate<projected<I, Proj>> Pred>
    constexpr iter_difference_t<I>
      count_if(I first, S last, Pred pred, Proj proj = {});
  template<input_range R, class Proj = identity,
            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
    constexpr range_difference_t<R>
      count_if(R&& r, Pred pred, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
+            indirect_unary_predicate<projected<I, Proj>> Pred>
+    iter_difference_t<I> count_if(Ep&& exec, I first, S last, Pred pred, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
+    range_difference_t<R> count_if(Ep&& exec, R&& r, Pred pred, Proj proj = {});
}

namespace ranges {
  template<class I1, class I2>
    using mismatch_result = in_in_result<I1, I2>;

  template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
            class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
    requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
    constexpr mismatch_result<I1, I2>
      mismatch(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {},
                Proj1 proj1 = {}, Proj2 proj2 = {});
  template<input_range R1, input_range R2,
            class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
    requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
    constexpr mismatch_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>>
      mismatch(R1&& r1, R2&& r2, Pred pred = {},
                Proj1 proj1 = {}, Proj2 proj2 = {});

+  template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
+            random_access_iterator I2, sized_sentinel_for<I2> S2,
+            class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
+    requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
+    mismatch_result<I1, I2>
+      mismatch(Ep&& exec, I1 first1, S1 last1, I2 first2, S2 last2,
+                Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
+  template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
+           class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
+    requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
+    mismatch_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>>
+      mismatch(Ep&& exec, R1&& r1, R2&& r2, Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
}

namespace ranges {
  template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
            class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
    requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
    constexpr bool equal(I1 first1, S1 last1, I2 first2, S2 last2,
                          Pred pred = {},
                          Proj1 proj1 = {}, Proj2 proj2 = {});
  template<input_range R1, input_range R2, class Pred = ranges::equal_to,
            class Proj1 = identity, class Proj2 = identity>
    requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
    constexpr bool equal(R1&& r1, R2&& r2, Pred pred = {},
                          Proj1 proj1 = {}, Proj2 proj2 = {});

+  template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
+            random_access_iterator I2, sized_sentinel_for<I2> S2,
+            class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
+    requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
+    bool equal(Ep&& exec, I1 first1, S1 last1, I2 first2, S2 last2,
+                Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
+  template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2, class Pred = ranges::equal_to,
+            class Proj1 = identity, class Proj2 = identity>
+    requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
+    bool equal(Ep&& exec, R1&& r1, R2&& r2,
+                Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
}

namespace ranges {
  template<forward_iterator I1, sentinel_for<I1> S1, forward_iterator I2,
            sentinel_for<I2> S2, class Pred = ranges::equal_to,
            class Proj1 = identity, class Proj2 = identity>
    requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
    constexpr subrange<I1>
      search(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {},
              Proj1 proj1 = {}, Proj2 proj2 = {});
  template<forward_range R1, forward_range R2, class Pred = ranges::equal_to,
            class Proj1 = identity, class Proj2 = identity>
    requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
    constexpr borrowed_subrange_t<R1>
      search(R1&& r1, R2&& r2, Pred pred = {},
              Proj1 proj1 = {}, Proj2 proj2 = {});

+  template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
+            random_access_iterator I2, sized_sentinel_for<I2> S2,
+            class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
+    requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
+      subrange<I1>
+        search(Ep&& exec, I1 first1, S1 last1, I2 first2, S2 last2,
+                Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
+  template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
+           class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
+    requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
+      borrowed_subrange_t<R1>
+        search(Ep&& exec, R1&& r1, R2&& r2,
+                Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
}

namespace ranges {
  template<forward_iterator I, sentinel_for<I> S,
            class Pred = ranges::equal_to, class Proj = identity,
            class T = projected_value_t<I, Proj>>
    requires indirectly_comparable<I, const T*, Pred, Proj>
    constexpr subrange<I>
      search_n(I first, S last, iter_difference_t<I> count,
                const T& value, Pred pred = {}, Proj proj = {});
  template<forward_range R, class Pred = ranges::equal_to,
            class Proj = identity, class T = projected_value_t<I, Proj>>
    requires indirectly_comparable<iterator_t<R>, const T*, Pred, Proj>
    constexpr borrowed_subrange_t<R>
      search_n(R&& r, range_difference_t<R> count,
                const T& value, Pred pred = {}, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            class Pred = ranges::equal_to, class Proj = identity,
+            class T = projected_value_t<I, Proj>>
+    requires indirectly_comparable<I, const T*, Pred, Proj>
+      subrange<I>
+        search_n(Ep&& exec, I first, S last, iter_difference_t<I> count,
+                  const T& value, Pred pred = {}, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Pred = ranges::equal_to,
+            class Proj = identity, class T = projected_value_t<iterator_t<R>, Proj>>
+    requires indirectly_comparable<iterator_t<R>, const T*, Pred, Proj>
+      borrowed_subrange_t<R>
+        search_n(Ep&& exec, R&& r, range_difference_t<R> count,
+                  const T& value, Pred pred = {}, Proj proj = {});
}

namespace ranges {
  // [alg.starts.with], starts with
  template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
            class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
    requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
    constexpr bool starts_with(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {},
                                Proj1 proj1 = {}, Proj2 proj2 = {});
  template<input_range R1, input_range R2, class Pred = ranges::equal_to,
            class Proj1 = identity, class Proj2 = identity>
    requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
    constexpr bool starts_with(R1&& r1, R2&& r2, Pred pred = {},
                                Proj1 proj1 = {}, Proj2 proj2 = {});

+  template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
+            random_access_iterator I2, sized_sentinel_for<I2> S2,
+            class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
+    requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
+    bool starts_with(Ep&& exec, I1 first1, S1 last1, I2 first2, S2 last2,
+                              Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
+  template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
+            class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
+    requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
+    bool starts_with(Ep&& exec, R1&& r1, R2&& r2, Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});

  // [alg.ends.with], ends with
  template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
            class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
    requires (forward_iterator<I1> || sized_sentinel_for<S1, I1>) &&
              (forward_iterator<I2> || sized_sentinel_for<S2, I2>) &&
              indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
    constexpr bool ends_with(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {},
                              Proj1 proj1 = {}, Proj2 proj2 = {});
  template<input_range R1, input_range R2, class Pred = ranges::equal_to,
            class Proj1 = identity, class Proj2 = identity>
    requires (forward_range<R1> || sized_range<R1>) &&
              (forward_range<R2> || sized_range<R2>) &&
              indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
    constexpr bool ends_with(R1&& r1, R2&& r2, Pred pred = {},
                              Proj1 proj1 = {}, Proj2 proj2 = {});

+  template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
+            random_access_iterator I2, sized_sentinel_for<I2> S2,
+            class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
+    requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
+    bool ends_with(Ep&& exec, I1 first1, S1 last1, I2 first2, S2 last2,
+                    Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
+  template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
+            class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
+    requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
+    bool ends_with(Ep&& exec, R1&& r1, R2&& r2,
+                    Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
}

namespace ranges {
  template<class I, class O>
    using copy_result = in_out_result<I, O>;

  template<input_iterator I, sentinel_for<I> S, weakly_incrementable O>
    requires indirectly_copyable<I, O>
    constexpr copy_result<I, O>
      copy(I first, S last, O result);
  template<input_range R, weakly_incrementable O>
    requires indirectly_copyable<iterator_t<R>, O>
    constexpr copy_result<borrowed_iterator_t<R>, O>
      copy(R&& r, O result);

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            random_access_iterator O, sized_sentinel_for<O> OutS>
+    requires indirectly_copyable<I, O>
+    copy_result<I, O> copy(Ep&& exec, I first, S last, O result, OutS result_last);
+  template<execution-policy Ep, random-access-sized-range R, random-access-sized-range OutR>
+    requires indirectly_copyable<iterator_t<R>, iterator_t<OutR>>
+    copy_result<borrowed_iterator_t<R>, borrowed_iterator_t<OutR>>
+      copy(Ep&& exec, R&& r, OutR&& result_r);
}

namespace ranges {
  template<class I, class O>
    using copy_n_result = in_out_result<I, O>;

  template<input_iterator I, weakly_incrementable O>
    requires indirectly_copyable<I, O>
    constexpr copy_n_result<I, O>
      copy_n(I first, iter_difference_t<I> n, O result);

+  template<execution-policy Ep, random_access_iterator I, random_access_iterator O,
+            sized_sentinel_for<O> OutS>
+    requires indirectly_copyable<I, O>
+    copy_n_result<I, O>
+      copy_n(Ep&& exec, I first, iter_difference_t<I> n, O result, OutS result_last);
}

namespace ranges {
  template<class I, class O>
    using copy_if_result = in_out_result<I, O>;

  template<input_iterator I, sentinel_for<I> S, weakly_incrementable O, class Proj = identity,
            indirect_unary_predicate<projected<I, Proj>> Pred>
    requires indirectly_copyable<I, O>
    constexpr copy_if_result<I, O>
      copy_if(I first, S last, O result, Pred pred, Proj proj = {});
  template<input_range R, weakly_incrementable O, class Proj = identity,
            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
    requires indirectly_copyable<iterator_t<R>, O>
    constexpr copy_if_result<borrowed_iterator_t<R>, O>
      copy_if(R&& r, O result, Pred pred, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            random_access_iterator O, sized_sentinel_for<O> OutS,
+            class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
+    requires indirectly_copyable<I, O>
+    copy_if_result<I, O>
+      copy_if(Ep&& exec, I first, S last, O result, OutS result_last,
+               Pred pred, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, random_access_iterator OutR,
+            class Proj = identity, indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
+    requires indirectly_copyable<iterator_t<R>, iterator_t<OutR>>
+    copy_if_result<borrowed_iterator_t<R>, borrowed_iterator_t<OutR>>
+      copy_if(Ep&& exec, R&& r, OutR&& result_r, Pred pred, Proj proj = {});
}

namespace ranges {
  template<class I, class O>
    using move_result = in_out_result<I, O>;

  template<input_iterator I, sentinel_for<I> S, weakly_incrementable O>
    requires indirectly_movable<I, O>
    constexpr move_result<I, O>
      move(I first, S last, O result);
  template<input_range R, weakly_incrementable O>
    requires indirectly_movable<iterator_t<R>, O>
    constexpr move_result<borrowed_iterator_t<R>, O>
      move(R&& r, O result);

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            random_access_iterator O, sized_sentinel_for<O> OutS>
+    requires indirectly_movable<I, O>
+    move_result<I, O> move(Ep&& exec, I first, S last, O result, OutS result_last);
+  template<execution-policy Ep, random-access-sized-range R, random-access-sized-range OutR>
+    requires indirectly_movable<iterator_t<R>, iterator_t<OutR>>
+    move_result<borrowed_iterator_t<R>, borrowed_iterator_t<OutR>>
+      move(Ep&& exec, R&& r, OutR&& result_r);
}

namespace ranges {
  template<class I1, class I2>
    using swap_ranges_result = in_in_result<I1, I2>;

  template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2>
    requires indirectly_swappable<I1, I2>
    constexpr swap_ranges_result<I1, I2>
      swap_ranges(I1 first1, S1 last1, I2 first2, S2 last2);
  template<input_range R1, input_range R2>
    requires indirectly_swappable<iterator_t<R1>, iterator_t<R2>>
    constexpr swap_ranges_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>>
      swap_ranges(R1&& r1, R2&& r2);

+  template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
+            random_access_iterator I2, sized_sentinel_for<I2> S2>
+    requires indirectly_swappable<I1, I2>
+    swap_ranges_result<I1, I2>
+      swap_ranges(Ep&& exec, I1 first1, S1 last1, I2 first2, S2 last2);
+  template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2>
+    requires indirectly_swappable<iterator_t<R1>, iterator_t<R2>>
+    swap_ranges_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>>
+      swap_ranges(Ep&& exec, R1&& r1, R2&& r2);
}

namespace ranges {
  template<class I, class O>
    using unary_transform_result = in_out_result<I, O>;

  template<input_iterator I, sentinel_for<I> S, weakly_incrementable O,
            copy_constructible F, class Proj = identity>
    requires indirectly_writable<O, indirect_result_t<F&, projected<I, Proj>>>
    constexpr unary_transform_result<I, O>
      transform(I first1, S last1, O result, F op, Proj proj = {});
  template<input_range R, weakly_incrementable O, copy_constructible F,
            class Proj = identity>
    requires indirectly_writable<O, indirect_result_t<F&, projected<iterator_t<R>, Proj>>>
    constexpr unary_transform_result<borrowed_iterator_t<R>, O>
      transform(R&& r, O result, F op, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            random_access_iterator O, sized_sentinel_for<O> OutS,
+            copy_constructible F, class Proj = identity>
+    requires indirectly_writable<O, indirect_result_t<F&, projected<I, Proj>>>
+    unary_transform_result<I, O>
+      transform(Ep&& exec, I first, S last, O result, OutS result_last,
+                 F op, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, random-access-sized-range OutR,
+           copy_constructible F, class Proj = identity>
+    requires indirectly_writable<iterator_t<OutR>, indirect_result_t<F&, projected<iterator_t<R>, Proj>>>
+    unary_transform_result<borrowed_iterator_t<R>, borrowed_iterator_t<OutR>>
+      transform(Ep&& exec, R&& r, OutR&& result_r, F op, Proj proj = {});

  template<class I1, class I2, class O>
    using binary_transform_result = in_in_out_result<I1, I2, O>;

  template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
            weakly_incrementable O, copy_constructible F, class Proj1 = identity,
            class Proj2 = identity>
    requires indirectly_writable<O, indirect_result_t<F&, projected<I1, Proj1>,
                                            projected<I2, Proj2>>>
    constexpr binary_transform_result<I1, I2, O>
      transform(I1 first1, S1 last1, I2 first2, S2 last2, O result,
                F binary_op, Proj1 proj1 = {}, Proj2 proj2 = {});
  template<input_range R1, input_range R2, weakly_incrementable O,
            copy_constructible F, class Proj1 = identity, class Proj2 = identity>
    requires indirectly_writable<O, indirect_result_t<F&, projected<iterator_t<R1>, Proj1>,
                                            projected<iterator_t<R2>, Proj2>>>
    constexpr binary_transform_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, O>
      transform(R1&& r1, R2&& r2, O result,
                F binary_op, Proj1 proj1 = {}, Proj2 proj2 = {});

+  template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
+            random_access_iterator I2, sized_sentinel_for<I2> S2,
+            random_access_iterator O,  sized_sentinel_for<O> OutS,
+            copy_constructible F, class Proj1 = identity, class Proj2 = identity>
+    requires indirectly_writable<O, indirect_result_t<F&, projected<I1, Proj1>, projected<I2, Proj2>>>
+    binary_transform_result<I1, I2, O>
+      transform(Ep&& exec, I1 first1, S1 last1, I2 first2, S2 last2, O result,
+                 OutS result_last, F binary_op, Proj1 proj1 = {}, Proj2 proj2 = {});
+  template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
+            random-access-sized-range OutR, copy_constructible F, class Proj1 = identity, class Proj2 = identity>
+    requires indirectly_writable<iterator_t<OutR>,
+               indirect_result_t<F&, projected<iterator_t<R1>, Proj1>, projected<iterator_t<R2>, Proj2>>>
+    binary_transform_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, borrowed_iterator_t<OutR>>
+      transform(Ep&& exec, R1&& r1, R2&& r2, OutR&& result_r,
+                 F binary_op, Proj1 proj1 = {}, Proj2 proj2 = {});
}

namespace ranges {
  template<input_iterator I, sentinel_for<I> S, class Proj = identity,
            class T1 = projected_value_t<I, Proj>, class T2 = T1>
    requires indirectly_writable<I, const T2&> &&
              indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T1*>
    constexpr I
      replace(I first, S last, const T1& old_value, const T2& new_value, Proj proj = {});
  template<input_range R, class Proj = identity,
            class T1 = projected_value_t<iterator_t<R>, Proj>, class T2 = T1>
    requires indirectly_writable<iterator_t<R>, const T2&> &&
              indirect_binary_predicate<ranges::equal_to,
                                        projected<iterator_t<R>, Proj>, const T1*>
    constexpr borrowed_iterator_t<R>
      replace(R&& r, const T1& old_value, const T2& new_value, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            class Proj = identity, class T1 = projected_value_t<I, Proj>, class T2 = T1>
+    requires indirectly_writable<I, const T2&> &&
+             indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T1*>
+    I replace(Ep&& exec, I first, S last,
+               const T1& old_value, const T2& new_value, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+            class T1 = projected_value_t<iterator_t<R>, Proj>, class T2 = T1>
+    requires indirectly_writable<iterator_t<R>, const T2&> &&
+              indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T1*>
+    borrowed_iterator_t<R>
+      replace(Ep&& exec, R&& r,
+               const T1& old_value, const T2& new_value, Proj proj = {});

  template<input_iterator I, sentinel_for<I> S, class Proj = identity,
            class T = projected_value_t<I, Proj>,
            indirect_unary_predicate<projected<I, Proj>> Pred>
    requires indirectly_writable<I, const T&>
    constexpr I replace_if(I first, S last, Pred pred, const T& new_value, Proj proj = {});
  template<input_range R, class Proj = identity, class T = projected_value_t<I, Proj>,
            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
    requires indirectly_writable<iterator_t<R>, const T&>
    constexpr borrowed_iterator_t<R>
      replace_if(R&& r, Pred pred, const T& new_value, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
+            class T = projected_value_t<I, Proj>,
+            indirect_unary_predicate<projected<I, Proj>> Pred>
+    requires indirectly_writable<I, const T&>
+    I replace_if(Ep&& exec, I first, S last, Pred pred,
+                  const T& new_value, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+            class T = projected_value_t<iterator_t<R>, Proj>,
+            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
+    requires indirectly_writable<iterator_t<R>, const T&>
+    borrowed_iterator_t<R>
+      replace_if(Ep&& exec, R&& r, Pred pred,
+                  const T& new_value, Proj proj = {});
}

namespace ranges {
  template<class I, class O>
    using replace_copy_result = in_out_result<I, O>;

  template<input_iterator I, sentinel_for<I> S, class O,
            class Proj = identity,
            class T1 = projected_value_t<I, Proj>, class T2 = iter_value_t<O>>
    requires indirectly_copyable<I, O> &&
              indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T1*> &&
              output_iterator<O, const T2&>
    constexpr replace_copy_result<I, O>
      replace_copy(I first, S last, O result, const T1& old_value, const T2& new_value,
                    Proj proj = {});
  template<input_range R, class O, class Proj = identity,
            class T1 = projected_value_t<iterator_t<R>, Proj>, class T2 = iter_value_t<O>>
    requires indirectly_copyable<iterator_t<R>, O> &&
              indirect_binary_predicate<ranges::equal_to,
                                        projected<iterator_t<R>, Proj>, const T1*> &&
              output_iterator<O, const T2&>
    constexpr replace_copy_result<borrowed_iterator_t<R>, O>
      replace_copy(R&& r, O result, const T1& old_value, const T2& new_value,
                    Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            random_access_iterator O, sized_sentinel_for<O> OutS>,
+            class Proj = identity, class T1 = projected_value_t<I, Proj>, class T2 = iter_value_t<O>>
+    requires indirectly_copyable<I, O> &&
+              indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T1*> &&
+              indirectly_writable<O, const T2&>
+    replace_copy_result<I, O>
+      replace_copy(Ep&& exec, I first, S last, O result, OutS result_last,
+                    const T1& old_value, const T2& new_value, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, random-access-sized-range OutR,
+            class Proj = identity, class T1 = projected_value_t<iterator_t<R>, Proj>,
+            class T2 = range_value_t<OutR>>
+    requires indirectly_copyable<iterator_t<R>, iterator_t<OutR>> &&
+              indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T1*> &&
+              indirectly_writable<iterator_t<OutR>, const T2&>
+    replace_copy_result<borrowed_iterator_t<R>, borrowed_iterator_t<OutR>>
+      replace_copy(Ep&& exec, R&& r, OutR&& result_r,
+                    const T1& old_value, const T2& new_value, Proj proj = {});

  template<class I, class O>
    using replace_copy_if_result = in_out_result<I, O>;

  template<input_iterator I, sentinel_for<I> S, class O, class T = iter_value_t<O>
            class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
    requires indirectly_copyable<I, O> && output_iterator<O, const T&>
    constexpr replace_copy_if_result<I, O>
      replace_copy_if(I first, S last, O result, Pred pred, const T& new_value,
                      Proj proj = {});
  template<input_range R, class O, class T = iter_value_t<O>, class Proj = identity,
            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
    requires indirectly_copyable<iterator_t<R>, O> && output_iterator<O, const T&>
    constexpr replace_copy_if_result<borrowed_iterator_t<R>, O>
      replace_copy_if(R&& r, O result, Pred pred, const T& new_value,
                      Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            random_access_iterator O, sized_sentinel_for<O> OutS>, class T = iter_value_t<O>,
+            class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
+    requires indirectly_copyable<I, O> && indirectly_writable<O, const T&>
+    replace_copy_if_result<I, O>
+      replace_copy_if(Ep&& exec, I first, S last, O result, OutS result_last,
+                       Pred pred, const T& new_value, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, random-access-sized-range OutR,
+            class T = range_value_t<OutR>, class Proj = identity,
+            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
+    requires indirectly_copyable<iterator_t<R>, iterator_t<OutR>> &&
+             indirectly_writable<iterator_t<OutR>, const T&>
+    replace_copy_if_result<borrowed_iterator_t<R>, borrowed_iterator_t<OutR>>
+      replace_copy_if(Ep&& exec, R&& r, OutR&& result_r,
+                       Pred pred, const T& new_value, Proj proj = {});
}

namespace ranges {
  template<class O, sentinel_for<O> S, class T = iter_value_t<O>>
    requires output_iterator<O, const T&>
    constexpr O fill(O first, S last, const T& value);
  template<class R, class T = range_value_t<R>>
    requires output_range<R, const T&>
    constexpr borrowed_iterator_t<R> fill(R&& r, const T& value);
  template<class O, class T = iter_value_t<O>>
    requires output_iterator<O, const T&>
    constexpr O fill_n(O first, iter_difference_t<O> n, const T& value);

+ template<execution-policy Ep, random_access_iterator O, sized_sentinel_for<O> S,
+           class T = iter_value_t<O>>
+   requires indirectly_writable<O, const T&>
+   O fill(Ep&& exec, O first, S last, const T& value);
+ template<execution-policy Ep, random-access-sized-range R, class T = range_value_t<R>>
+   requires indirectly_writable<iterator_t<R>, const T&>
+   borrowed_iterator_t<R> fill(Ep&& exec, R&& r, const T& value);
+ template<execution-policy Ep, random_access_iterator O, class T = iter_value_t<O>>
+   requires indirectly_writable<O, const T&>
+   O fill_n(Ep&& exec, O first, iter_difference_t<O> n, const T& value);
}

namespace ranges {
  template<input_or_output_iterator O, sentinel_for<O> S, copy_constructible F>
    requires invocable<F&> && indirectly_writable<O, invoke_result_t<F&>>
    constexpr O generate(O first, S last, F gen);
  template<class R, copy_constructible F>
    requires invocable<F&> && output_range<R, invoke_result_t<F&>>
    constexpr borrowed_iterator_t<R> generate(R&& r, F gen);
  template<input_or_output_iterator O, copy_constructible F>
    requires invocable<F&> && indirectly_writable<O, invoke_result_t<F&>>
    constexpr O generate_n(O first, iter_difference_t<O> n, F gen);
+  template<execution-policy Ep, random_access_iterator O, sized_sentinel_for<O> S,
+            copy_constructible F>
+    requires invocable<F&> && indirectly_writable<O, invoke_result_t<F&>>
+    O generate(Ep&& exec, O first, S last, F gen);
+  template<execution-policy Ep, random-access-sized-range R, copy_constructible F>
+    requires invocable<F&> && indirectly_writable<iterator_t<R>, invoke_result_t<F&>>
+    borrowed_iterator_t<R> generate(Ep&& exec, R&& r, F gen);
+  template<execution-policy Ep, random_access_iterator O, copy_constructible F>
+    requires invocable<F&> && indirectly_writable<O, invoke_result_t<F&>>
+    O generate_n(Ep&& exec, O first, iter_difference_t<O> n, F gen);
}

namespace ranges {
  template<permutable I, sentinel_for<I> S, class Proj = identity,
            class T = projected_value_t<I, Proj>>
    requires indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
    constexpr subrange<I> remove(I first, S last, const T& value, Proj proj = {});
  template<forward_range R, class Proj = identity,
            class T = projected_value_t<iterator_t<R>, Proj>>
    requires permutable<iterator_t<R>> &&
              indirect_binary_predicate<ranges::equal_to,
                                        projected<iterator_t<R>, Proj>, const T*>
    constexpr borrowed_subrange_t<R>
      remove(R&& r, const T& value, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            class Proj = identity, class T = projected_value_t<I, Proj>>
+    requires indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
+    subrange<I> remove(Ep&& exec, I first, S last, const T& value, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+            class T = projected_value_t<iterator_t<R>, Proj>>
+    requires permutable<iterator_t<R>> &&
+             indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*>
+    borrowed_subrange_t<R> remove(Ep&& exec, R&& r, const T& value, Proj proj = {});

  template<permutable I, sentinel_for<I> S, class Proj = identity,
            indirect_unary_predicate<projected<I, Proj>> Pred>
    constexpr subrange<I> remove_if(I first, S last, Pred pred, Proj proj = {});
  template<forward_range R, class Proj = identity,
            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
    requires permutable<iterator_t<R>>
    constexpr borrowed_subrange_t<R>
      remove_if(R&& r, Pred pred, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
+    subrange<I> remove_if(Ep&& exec, I first, S last, Pred pred, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
+    requires permutable<iterator_t<R>>
+    borrowed_subrange_t<R> remove_if(Ep&& exec, R&& r, Pred pred, Proj proj = {});
}

namespace ranges {
  template<class I, class O>
    using remove_copy_result = in_out_result<I, O>;

  template<input_iterator I, sentinel_for<I> S, weakly_incrementable O,
            class Proj = identity, class T = projected_value_t<I, Proj>>
    requires indirectly_copyable<I, O> &&
              indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
    constexpr remove_copy_result<I, O>
      remove_copy(I first, S last, O result, const T& value, Proj proj = {});
  template<input_range R, weakly_incrementable O, class Proj = identity,
            class T = projected_value_t<iterator_t<R>, Proj>>
    requires indirectly_copyable<iterator_t<R>, O> &&
              indirect_binary_predicate<ranges::equal_to,
                                        projected<iterator_t<R>, Proj>, const T*>
    constexpr remove_copy_result<borrowed_iterator_t<R>, O>
      remove_copy(R&& r, O result, const T& value, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            random_access_iterator O, sized_sentinel_for<O> OutS>,
+            class Proj = identity, class T = projected_value_t<I, Proj>>
+    requires indirectly_copyable<I, O> &&
+              indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
+    remove_copy_result<I, O>
+      remove_copy(Ep&& exec, I first, S last, O result,  OutS result_last,
+                   const T& value, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, random-access-sized-range OutR,
+            class Proj = identity, class T = projected_value_t<iterator_t<R>, Proj>>
+    requires indirectly_copyable<iterator_t<R>, iterator_t<OutR>> &&
+              indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*>
+    remove_copy_result<borrowed_iterator_t<R>, borrowed_iterator_t<OutR>>
+      remove_copy(Ep&& exec, R&& r, OutR&& result_r, const T& value, Proj proj = {});

  template<class I, class O>
    using remove_copy_if_result = in_out_result<I, O>;

  template<input_iterator I, sentinel_for<I> S, weakly_incrementable O,
            class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
    requires indirectly_copyable<I, O>
    constexpr remove_copy_if_result<I, O>
      remove_copy_if(I first, S last, O result, Pred pred, Proj proj = {});
  template<input_range R, weakly_incrementable O, class Proj = identity,
            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
    requires indirectly_copyable<iterator_t<R>, O>
    constexpr remove_copy_if_result<borrowed_iterator_t<R>, O>
      remove_copy_if(R&& r, O result, Pred pred, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            random_access_iterator O, sized_sentinel_for<O> OutS>,
+            class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
+    requires indirectly_copyable<I, O>
+    remove_copy_if_result<I, O>
+      remove_copy_if(Ep&& exec, I first, S last, O result, OutS result_last,
+                      Pred pred, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, random-access-sized-range OutR,
+            class Proj = identity,
+            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
+    requires indirectly_copyable<iterator_t<R>, iterator_t<OutR>>
+    remove_copy_if_result<borrowed_iterator_t<R>, borrowed_iterator_t<OutR>>
+      remove_copy_if(Ep&& exec, R&& r, OutR&& result_r, Pred pred, Proj proj = {});
}

namespace ranges {
  template<permutable I, sentinel_for<I> S, class Proj = identity,
            indirect_equivalence_relation<projected<I, Proj>> C = ranges::equal_to>
    constexpr subrange<I> unique(I first, S last, C comp = {}, Proj proj = {});
  template<forward_range R, class Proj = identity,
            indirect_equivalence_relation<projected<iterator_t<R>, Proj>> C = ranges::equal_to>
    requires permutable<iterator_t<R>>
    constexpr borrowed_subrange_t<R>
      unique(R&& r, C comp = {}, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            class Proj = identity,
+            indirect_equivalence_relation<projected<I, Proj>> C = ranges::equal_to>
+    requires permutable<I>
+    subrange<I> unique(Ep&& exec, I first, S last, C comp = {}, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+            indirect_equivalence_relation<projected<iterator_t<R>, Proj>> C = ranges::equal_to>
+    requires permutable<iterator_t<R>>
+    borrowed_subrange_t<R> unique(Ep&& exec, R&& r, C comp = {}, Proj proj = {});
}

namespace ranges {
  template<class I, class O>
    using unique_copy_result = in_out_result<I, O>;

  template<input_iterator I, sentinel_for<I> S, weakly_incrementable O, class Proj = identity,
            indirect_equivalence_relation<projected<I, Proj>> C = ranges::equal_to>
    requires indirectly_copyable<I, O> &&
              (forward_iterator<I> ||
              (input_iterator<O> && same_as<iter_value_t<I>, iter_value_t<O>>) ||
              indirectly_copyable_storable<I, O>)
    constexpr unique_copy_result<I, O>
      unique_copy(I first, S last, O result, C comp = {}, Proj proj = {});
  template<input_range R, weakly_incrementable O, class Proj = identity,
            indirect_equivalence_relation<projected<iterator_t<R>, Proj>> C = ranges::equal_to>
    requires indirectly_copyable<iterator_t<R>, O> &&
              (forward_iterator<iterator_t<R>> ||
              (input_iterator<O> && same_as<range_value_t<R>, iter_value_t<O>>) ||
              indirectly_copyable_storable<iterator_t<R>, O>)
    constexpr unique_copy_result<borrowed_iterator_t<R>, O>
      unique_copy(R&& r, O result, C comp = {}, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            random_access_iterator O, sized_sentinel_for<O> OutS>, class Proj = identity,
+            indirect_equivalence_relation<projected<I, Proj>> C = ranges::equal_to>
+    requires indirectly_copyable<I, O>
+    unique_copy_result<I, O>
+      unique_copy(Ep&& exec, I first, S last, O result, OutS result_last,
+                   C comp = {}, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, random-access-sized-range OutR,
+            class Proj = identity,
+            indirect_equivalence_relation<projected<iterator_t<R>, Proj>> C = ranges::equal_to>
+    requires indirectly_copyable<iterator_t<R>, iterator_t<OutR>>
+    unique_copy_result<borrowed_iterator_t<R>, borrowed_iterator_t<OutR>>
+      unique_copy(Ep&& exec, R&& r, OutR&& result_r,
+                   C comp = {}, Proj proj = {});
}

namespace ranges {
  template<bidirectional_iterator I, sentinel_for<I> S>
    requires permutable<I>
    constexpr I reverse(I first, S last);
  template<bidirectional_range R>
    requires permutable<iterator_t<R>>
    constexpr borrowed_iterator_t<R> reverse(R&& r);

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S>
+    requires permutable<I>
+    I reverse(Ep&& exec, I first, S last);
+  template<execution-policy Ep, random-access-sized-range R>
+    requires permutable<iterator_t<R>>
+    borrowed_iterator_t<R> reverse(Ep&& exec, R&& r);
}

namespace ranges {
  template<class I, class O>
    using reverse_copy_result = in_out_result<I, O>;

  template<bidirectional_iterator I, sentinel_for<I> S, weakly_incrementable O>
    requires indirectly_copyable<I, O>
    constexpr reverse_copy_result<I, O>
      reverse_copy(I first, S last, O result);
  template<bidirectional_range R, weakly_incrementable O>
    requires indirectly_copyable<iterator_t<R>, O>
    constexpr reverse_copy_result<borrowed_iterator_t<R>, O>
      reverse_copy(R&& r, O result);

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            random_access_iterator O, sized_sentinel_for<O> OutS>
+    requires indirectly_copyable<I, O>
+    reverse_copy_result<I, O>
+      reverse_copy(Ep&& exec, I first, S last, O result, OutS result_last);
+  template<execution-policy Ep, random-access-sized-range R, random-access-sized-range OutR>
+    requires indirectly_copyable<iterator_t<R>, iterator_t<OutR>>
+    reverse_copy_result<borrowed_iterator_t<R>, borrowed_iterator_t<OutR>>
+      reverse_copy(Ep&& exec, R&& r, OutR&& result_r);
}

namespace ranges {
  template<permutable I, sentinel_for<I> S>
    constexpr subrange<I> rotate(I first, I middle, S last);
  template<forward_range R>
    requires permutable<iterator_t<R>>
    constexpr borrowed_subrange_t<R> rotate(R&& r, iterator_t<R> middle);

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S>
+    requires permutable<I>
+    subrange<I> rotate(Ep&& exec, I first, I middle, S last);
+  template<execution-policy Ep, random-access-sized-range R>
+    requires permutable<iterator_t<R>>
+    borrowed_subrange_t<R> rotate(Ep&& exec, R&& r, iterator_t<R> middle);
}

namespace ranges {
  template<permutable I, sentinel_for<I> S>
    constexpr subrange<I> shift_left(I first, S last, iter_difference_t<I> n);
  template<forward_range R>
    requires permutable<iterator_t<R>>
    constexpr borrowed_subrange_t<R> shift_left(R&& r, range_difference_t<R> n);

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S>
+    requires permutable<I>
+    subrange<I> shift_left(Ep&& exec, I first, S last, iter_difference_t<I> n);
+  template<execution-policy Ep, random-access-sized-range R>
+    requires permutable<iterator_t<R>>
+    borrowed_subrange_t<R> shift_left(Ep&& exec, R&& r, range_difference_t<R> n);
}

namespace ranges {
  template<permutable I, sentinel_for<I> S>
    constexpr subrange<I> shift_right(I first, S last, iter_difference_t<I> n);
  template<forward_range R>
    requires permutable<iterator_t<R>>
    constexpr borrowed_subrange_t<R> shift_right(R&& r, range_difference_t<R> n);

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S>
+    requires permutable<I>
+    subrange<I> shift_right(Ep&& exec, I first, S last, iter_difference_t<I> n);
+  template<execution-policy Ep, random-access-sized-range R>
+    requires permutable<iterator_t<R>>
+    borrowed_subrange_t<R> shift_right(Ep&& exec, R&& r, range_difference_t<R> n);
}

namespace ranges {
  template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
            class Proj = identity>
    requires sortable<I, Comp, Proj>
    constexpr I
      sort(I first, S last, Comp comp = {}, Proj proj = {});
  template<random_access_range R, class Comp = ranges::less, class Proj = identity>
    requires sortable<iterator_t<R>, Comp, Proj>
    constexpr borrowed_iterator_t<R>
      sort(R&& r, Comp comp = {}, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            class Comp = ranges::less, class Proj = identity>
+    requires sortable<I, Comp, Proj>
+    I sort(Ep&& exec, I first, S last, Comp comp = {}, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Comp = ranges::less,
+            class Proj = identity>
+    requires sortable<iterator_t<R>, Comp, Proj>
+    borrowed_iterator_t<R> sort(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {});
}

namespace ranges {
  template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
            class Proj = identity>
    requires sortable<I, Comp, Proj>
    constexpr I stable_sort(I first, S last, Comp comp = {}, Proj proj = {});
  template<random_access_range R, class Comp = ranges::less, class Proj = identity>
    requires sortable<iterator_t<R>, Comp, Proj>
    constexpr borrowed_iterator_t<R>
      stable_sort(R&& r, Comp comp = {}, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            class Comp = ranges::less, class Proj = identity>
+    requires sortable<I, Comp, Proj>
+    I stable_sort(Ep&& exec, I first, S last, Comp comp = {}, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Comp = ranges::less,
+            class Proj = identity>
+    requires sortable<iterator_t<R>, Comp, Proj>
+    borrowed_iterator_t<R> stable_sort(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {});
}

namespace ranges {
  template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
            class Proj = identity>
    requires sortable<I, Comp, Proj>
    constexpr I
      partial_sort(I first, I middle, S last, Comp comp = {}, Proj proj = {});
  template<random_access_range R, class Comp = ranges::less, class Proj = identity>
    requires sortable<iterator_t<R>, Comp, Proj>
    constexpr borrowed_iterator_t<R>
      partial_sort(R&& r, iterator_t<R> middle, Comp comp = {},
                    Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            class Comp = ranges::less, class Proj = identity>
+    requires sortable<I, Comp, Proj>
+    I partial_sort(Ep&& exec, I first, I middle, S last, Comp comp = {}, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Comp = ranges::less,
+            class Proj = identity>
+    requires sortable<iterator_t<R>, Comp, Proj>
+    borrowed_iterator_t<R> partial_sort(Ep&& exec, R&& r, iterator_t<R> middle,
+                                         Comp comp = {}, Proj proj = {});
}

namespace ranges {
  template<class I, class O>
    using partial_sort_copy_result = in_out_result<I, O>;

  template<input_iterator I1, sentinel_for<I1> S1,
            random_access_iterator I2, sentinel_for<I2> S2,
            class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
    requires indirectly_copyable<I1, I2> && sortable<I2, Comp, Proj2> &&
              indirect_strict_weak_order<Comp, projected<I1, Proj1>, projected<I2, Proj2>>
    constexpr partial_sort_copy_result<I1, I2>
      partial_sort_copy(I1 first, S1 last, I2 result_first, S2 result_last,
                        Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
  template<input_range R1, random_access_range R2, class Comp = ranges::less,
            class Proj1 = identity, class Proj2 = identity>
    requires indirectly_copyable<iterator_t<R1>, iterator_t<R2>> &&
              sortable<iterator_t<R2>, Comp, Proj2> &&
              indirect_strict_weak_order<Comp, projected<iterator_t<R1>, Proj1>,
                                        projected<iterator_t<R2>, Proj2>>
    constexpr partial_sort_copy_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>>
      partial_sort_copy(R1&& r, R2&& result_r, Comp comp = {},
                        Proj1 proj1 = {}, Proj2 proj2 = {});

+  template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
+            random_access_iterator I2, sized_sentinel_for<I2> S2,
+            class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
+    requires indirectly_copyable<I1, I2> && sortable<I2, Comp, Proj2> &&
+              indirect_strict_weak_order<Comp, projected<I1, Proj1>, projected<I2, Proj2>>
+    partial_sort_copy_result<I1, I2>
+      partial_sort_copy(Ep&& exec, I1 first, S1 last, I2 result_first, S2 result_last,
+                         Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
+  template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
+            class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
+    requires indirectly_copyable<iterator_t<R1>, iterator_t<R2>> &&
+              sortable<iterator_t<R2>, Comp, Proj2> &&
+              indirect_strict_weak_order<Comp, projected<iterator_t<R1>, Proj1>,
+                                         projected<iterator_t<R2>, Proj2>>
+    partial_sort_copy_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>>
+      partial_sort_copy(Ep&& exec, R1&& r, R2&& result_r, Comp comp = {},
+                         Proj1 proj1 = {}, Proj2 proj2 = {});
}

namespace ranges {
  template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
            indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
    constexpr bool is_sorted(I first, S last, Comp comp = {}, Proj proj = {});
  template<forward_range R, class Proj = identity,
            indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
    constexpr bool is_sorted(R&& r, Comp comp = {}, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            class Proj = identity, indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
+    bool is_sorted(Ep&& exec, I first, S last, Comp comp = {}, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+            indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
+    bool is_sorted(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {});
}

namespace ranges {
  template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
            indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
    constexpr I is_sorted_until(I first, S last, Comp comp = {}, Proj proj = {});
  template<forward_range R, class Proj = identity,
            indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
    constexpr borrowed_iterator_t<R>
      is_sorted_until(R&& r, Comp comp = {}, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            class Proj = identity,
+            indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
+    I is_sorted_until(Ep&& exec, I first, S last, Comp comp = {}, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+            indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
+    borrowed_iterator_t<R> is_sorted_until(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {});
}

namespace ranges {
  template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
            class Proj = identity>
    requires sortable<I, Comp, Proj>
    constexpr I
      nth_element(I first, I nth, S last, Comp comp = {}, Proj proj = {});
  template<random_access_range R, class Comp = ranges::less, class Proj = identity>
    requires sortable<iterator_t<R>, Comp, Proj>
    constexpr borrowed_iterator_t<R>
      nth_element(R&& r, iterator_t<R> nth, Comp comp = {}, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            class Comp = ranges::less, class Proj = identity>
+    requires sortable<I, Comp, Proj>
+    I nth_element(Ep&& exec, I first, I nth, S last, Comp comp = {}, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Comp = ranges::less,
+            class Proj = identity>
+    requires sortable<iterator_t<R>, Comp, Proj>
+    borrowed_iterator_t<R> nth_element(Ep&& exec, R&& r, iterator_t<R> nth,
+                                        Comp comp = {}, Proj proj = {});
}

namespace ranges {
  template<input_iterator I, sentinel_for<I> S, class Proj = identity,
            indirect_unary_predicate<projected<I, Proj>> Pred>
    constexpr bool is_partitioned(I first, S last, Pred pred, Proj proj = {});
  template<input_range R, class Proj = identity,
            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
    constexpr bool is_partitioned(R&& r, Pred pred, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+           class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
+    bool is_partitioned(Ep&& exec, I first, S last, Pred pred, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+           indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
+    bool is_partitioned(Ep&& exec, R&& r, Pred pred, Proj proj = {});
}

namespace ranges {
  template<permutable I, sentinel_for<I> S, class Proj = identity,
            indirect_unary_predicate<projected<I, Proj>> Pred>
    constexpr subrange<I>
      partition(I first, S last, Pred pred, Proj proj = {});
  template<forward_range R, class Proj = identity,
            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
    requires permutable<iterator_t<R>>
    constexpr borrowed_subrange_t<R>
      partition(R&& r, Pred pred, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
+    subrange<I> partition(Ep&& exec, I first, S last, Pred pred, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
+    requires permutable<iterator_t<R>>
+    borrowed_subrange_t<R> partition(Ep&& exec, R&& r, Pred pred, Proj proj = {});
}

namespace ranges {
  template<bidirectional_iterator I, sentinel_for<I> S, class Proj = identity,
            indirect_unary_predicate<projected<I, Proj>> Pred>
    requires permutable<I>
    constexpr subrange<I> stable_partition(I first, S last, Pred pred, Proj proj = {});
  template<bidirectional_range R, class Proj = identity,
            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
    requires permutable<iterator_t<R>>
    constexpr borrowed_subrange_t<R> stable_partition(R&& r, Pred pred, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
+    requires permutable<I>
+    subrange<I> stable_partition(Ep&& exec, I first, S last, Pred pred, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
+    requires permutable<iterator_t<R>>
+    borrowed_subrange_t<R> stable_partition(Ep&& exec, R&& r, Pred pred, Proj proj = {});
}

namespace ranges {
  template<class I, class O1, class O2>
    using partition_copy_result = in_out_out_result<I, O1, O2>;

  template<input_iterator I, sentinel_for<I> S,
            weakly_incrementable O1, weakly_incrementable O2,
            class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
    requires indirectly_copyable<I, O1> && indirectly_copyable<I, O2>
    constexpr partition_copy_result<I, O1, O2>
      partition_copy(I first, S last, O1 out_true, O2 out_false, Pred pred,
                      Proj proj = {});
  template<input_range R, weakly_incrementable O1, weakly_incrementable O2,
            class Proj = identity,
            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
    requires indirectly_copyable<iterator_t<R>, O1> &&
              indirectly_copyable<iterator_t<R>, O2>
    constexpr partition_copy_result<borrowed_iterator_t<R>, O1, O2>
      partition_copy(R&& r, O1 out_true, O2 out_false, Pred pred, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            random_access_iterator O1, sized_sentinel_for<O1> OutS1,
+            random_access_iterator O2, sized_sentinel_for<O2> OutS2,
+            class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
+    requires indirectly_copyable<I, O1> && indirectly_copyable<I, O2>
+    partition_copy_result<I, O1, O2>
+      partition_copy(Ep&& exec, I first, S last, O1 out_true, OutS1 last_true,
+                      O2 out_false, OutS2 last_false, Pred pred, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, random-access-sized-range OutR1,
+           random-access-sized-range OutR2, class Proj = identity,
+           indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
+    requires indirectly_copyable<iterator_t<R>, iterator_t<OutR1>> &&
+             indirectly_copyable<iterator_t<R>, iterator_t<OutR2>>
+    partition_copy_result<borrowed_iterator_t<R>, borrowed_iterator_t<OutR1>, borrowed_iterator_t<OutR2>>
+      partition_copy(Ep&& exec, R&& r, OutR1&& out_true_r, OutR2&& out_false_r,
+                      Pred pred, Proj proj = {});
}

namespace ranges {
  template<class I1, class I2, class O>
    using merge_result = in_in_out_result<I1, I2, O>;

  template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
            weakly_incrementable O, class Comp = ranges::less, class Proj1 = identity,
            class Proj2 = identity>
    requires mergeable<I1, I2, O, Comp, Proj1, Proj2>
    constexpr merge_result<I1, I2, O>
      merge(I1 first1, S1 last1, I2 first2, S2 last2, O result,
            Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
  template<input_range R1, input_range R2, weakly_incrementable O, class Comp = ranges::less,
            class Proj1 = identity, class Proj2 = identity>
    requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
    constexpr merge_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, O>
      merge(R1&& r1, R2&& r2, O result,
            Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});

+  template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
+            random_access_iterator I2, sized_sentinel_for<I2> S2,
+            random_access_iterator O, sized_sentinel_for<O> OutS, class Comp = ranges::less,
+            class Proj1 = identity, class Proj2 = identity>
+    requires mergeable<I1, I2, O, Comp, Proj1, Proj2>
+    merge_result<I1, I2, O>
+      merge(Ep&& exec, I1 first1, S1 last1,
+             I2 first2, S2 last2, O result, OutS result_last,
+             Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
+  template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
+            random-access-sized-range OutR, class Comp = ranges::less,
+            class Proj1 = identity, class Proj2 = identity>
+    requires mergeable<iterator_t<R1>, iterator_t<R2>, iterator_t<OutR>, Comp, Proj1, Proj2>
+    merge_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, borrowed_iterator_t<OutR>>
+      merge(Ep&& exec, R1&& r1, R2&& r2, OutR&& result_r,
+             Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
}

namespace ranges {
  template<bidirectional_iterator I, sentinel_for<I> S, class Comp = ranges::less,
            class Proj = identity>
    requires sortable<I, Comp, Proj>
    constexpr I inplace_merge(I first, I middle, S last, Comp comp = {}, Proj proj = {});
  template<bidirectional_range R, class Comp = ranges::less, class Proj = identity>
    requires sortable<iterator_t<R>, Comp, Proj>
    constexpr borrowed_iterator_t<R>
      inplace_merge(R&& r, iterator_t<R> middle, Comp comp = {},
                    Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            class Comp = ranges::less, class Proj = identity>
+    requires sortable<I, Comp, Proj>
+    I inplace_merge(Ep&& exec, I first, I middle, S last, Comp comp = {}, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Comp = ranges::less,
+            class Proj = identity>
+    requires sortable<iterator_t<R>, Comp, Proj>
+    borrowed_iterator_t<R> inplace_merge(Ep&& exec, R&& r, iterator_t<R> middle,
+                                          Comp comp = {}, Proj proj = {});
}

namespace ranges {
  template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
            class Proj1 = identity, class Proj2 = identity,
            indirect_strict_weak_order<projected<I1, Proj1>, projected<I2, Proj2>> Comp =
              ranges::less>
    constexpr bool includes(I1 first1, S1 last1, I2 first2, S2 last2, Comp comp = {},
                            Proj1 proj1 = {}, Proj2 proj2 = {});
  template<input_range R1, input_range R2, class Proj1 = identity,
            class Proj2 = identity,
            indirect_strict_weak_order<projected<iterator_t<R1>, Proj1>,
                                      projected<iterator_t<R2>, Proj2>> Comp = ranges::less>
    constexpr bool includes(R1&& r1, R2&& r2, Comp comp = {},
                            Proj1 proj1 = {}, Proj2 proj2 = {});

+  template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
+            random_access_iterator I2, sized_sentinel_for<I2> S2,
+            class Proj1 = identity, class Proj2 = identity,
+            indirect_strict_weak_order<projected<I1, Proj1>, projected<I2, Proj2>> Comp = ranges::less>
+    bool includes(Ep&& exec, I1 first1, S1 last1, I2 first2, S2 last2,
+                   Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
+  template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
+            class Proj1 = identity, class Proj2 = identity,
+            indirect_strict_weak_order<projected<iterator_t<R1>, Proj1>,
+                                       projected<iterator_t<R2>, Proj2>> Comp = ranges::less>
+    bool includes(Ep&& exec, R1&& r1, R2&& r2,
+                   Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
}

namespace ranges {
  template<class I1, class I2, class O>
    using set_union_result = in_in_out_result<I1, I2, O>;

  template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
            weakly_incrementable O, class Comp = ranges::less,
            class Proj1 = identity, class Proj2 = identity>
    requires mergeable<I1, I2, O, Comp, Proj1, Proj2>
    constexpr set_union_result<I1, I2, O>
      set_union(I1 first1, S1 last1, I2 first2, S2 last2, O result, Comp comp = {},
                Proj1 proj1 = {}, Proj2 proj2 = {});
  template<input_range R1, input_range R2, weakly_incrementable O,
            class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
    requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
    constexpr set_union_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, O>
      set_union(R1&& r1, R2&& r2, O result, Comp comp = {},
                Proj1 proj1 = {}, Proj2 proj2 = {});

+  template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
+           random_access_iterator I2, sized_sentinel_for<I2> S2,
+           random_access_iterator O, sized_sentinel_for<O> OutS, class Comp = ranges::less,
+           class Proj1 = identity, class Proj2 = identity>
+    requires mergeable<I1, I2, O, Comp, Proj1, Proj2>
+    set_union_result<I1, I2, O>
+      set_union(Ep&& exec, I1 first1, S1 last1,
+                 I2 first2, S2 last2, O result, OutS result_last,
+                 Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
+  template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
+            random-access-sized-range OutR, class Comp = ranges::less,
+            class Proj1 = identity, class Proj2 = identity>
+    requires mergeable<iterator_t<R1>, iterator_t<R2>, iterator_t<OutR>, Comp, Proj1, Proj2>
+    set_union_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, borrowed_iterator_t<OutR>>
+      set_union(Ep&& exec, R1&& r1, R2&& r2, OutR&& result_r,
+                 Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
}

namespace ranges {
  template<class I1, class I2, class O>
    using set_intersection_result = in_in_out_result<I1, I2, O>;

  template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
            weakly_incrementable O, class Comp = ranges::less,
            class Proj1 = identity, class Proj2 = identity>
    requires mergeable<I1, I2, O, Comp, Proj1, Proj2>
    constexpr set_intersection_result<I1, I2, O>
      set_intersection(I1 first1, S1 last1, I2 first2, S2 last2, O result,
                        Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
  template<input_range R1, input_range R2, weakly_incrementable O,
            class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
    requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
    constexpr set_intersection_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, O>
      set_intersection(R1&& r1, R2&& r2, O result,
                        Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});

+  template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
+            random_access_iterator I2, sized_sentinel_for<I2> S2,
+            random_access_iterator O, sized_sentinel_for<O> OutS, class Comp = ranges::less,
+            class Proj1 = identity, class Proj2 = identity>
+    requires mergeable<I1, I2, O, Comp, Proj1, Proj2>
+    set_intersection_result<I1, I2, O>
+      set_intersection(Ep&& exec, I1 first1, S1 last1,
+                        I2 first2, S2 last2, O result, OutS result_last,
+                        Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
+  template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
+            random-access-sized-range OutR, class Comp = ranges::less,
+            class Proj1 = identity, class Proj2 = identity>
+    requires mergeable<iterator_t<R1>, iterator_t<R2>, iterator_t<OutR>, Comp, Proj1, Proj2>
+    rages::set_intersection_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, borrowed_iterator_t<OutR>>
+      set_intersection(Ep&& exec, R1&& r1, R2&& r2, OutR&& result_r,
+                        Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
}

namespace ranges {
  template<class I, class O>
    using set_difference_result = in_out_result<I, O>;

  template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
            weakly_incrementable O, class Comp = ranges::less,
            class Proj1 = identity, class Proj2 = identity>
    requires mergeable<I1, I2, O, Comp, Proj1, Proj2>
    constexpr set_difference_result<I1, O>
      set_difference(I1 first1, S1 last1, I2 first2, S2 last2, O result,
                      Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
  template<input_range R1, input_range R2, weakly_incrementable O,
            class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
    requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
    constexpr set_difference_result<borrowed_iterator_t<R1>, O>
      set_difference(R1&& r1, R2&& r2, O result,
                      Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});

+  template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
+            random_access_iterator I2, sized_sentinel_for<I2> S2,
+            random_access_iterator O, sized_sentinel_for<O> OutS, class Comp = ranges::less,
+            class Proj1 = identity, class Proj2 = identity>
+    requires mergeable<I1, I2, O, Comp, Proj1, Proj2>
+    set_difference_result<I1, O>
+      set_difference(Ep&& exec, I1 first1, S1 last1,
+                      I2 first2, S2 last2, O result, OutS result_last,
+                      Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
+  template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
+            random-access-sized-range OutR, class Comp = ranges::less,
+            class Proj1 = identity, class Proj2 = identity>
+    requires mergeable<iterator_t<R1>, iterator_t<R2>, iterator_t<OutR>, Comp, Proj1, Proj2>
+    set_difference_result<borrowed_iterator_t<R1>, borrowed_iterator_t<OutR>>
+      set_difference(Ep&& exec, R1&& r1, R2&& r2, OutR&& result_r,
+                      Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
}

namespace ranges {
  template<class I1, class I2, class O>
    using set_symmetric_difference_result = in_in_out_result<I1, I2, O>;

  template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
            weakly_incrementable O, class Comp = ranges::less,
            class Proj1 = identity, class Proj2 = identity>
    requires mergeable<I1, I2, O, Comp, Proj1, Proj2>
    constexpr set_symmetric_difference_result<I1, I2, O>
      set_symmetric_difference(I1 first1, S1 last1, I2 first2, S2 last2, O result,
                                Comp comp = {}, Proj1 proj1 = {},
                                Proj2 proj2 = {});
  template<input_range R1, input_range R2, weakly_incrementable O,
            class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
    requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
    constexpr set_symmetric_difference_result<borrowed_iterator_t<R1>,
                                              borrowed_iterator_t<R2>, O>
      set_symmetric_difference(R1&& r1, R2&& r2, O result, Comp comp = {},
                                Proj1 proj1 = {}, Proj2 proj2 = {});

+  template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
+            random_access_iterator I2, sized_sentinel_for<I2> S2,
+            random_access_iterator O, sized_sentinel_for<O> OutS, class Comp = ranges::less,
+            class Proj1 = identity, class Proj2 = identity>
+    requires mergeable<I1, I2, O, Comp, Proj1, Proj2>
+    set_symmetric_difference_result<I1, I2, O>
+      set_symmetric_difference(Ep&& exec, I1 first1, S1 last1,
+                                I2 first2, S2 last2, O result, OutS result_last,
+                                Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
+  template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
+           random-access-sized-range OutR, class Comp = ranges::less,
+           class Proj1 = identity, class Proj2 = identity>
+    requires mergeable<iterator_t<R1>, iterator_t<R2>, iterator_t<OutR>, Comp, Proj1, Proj2>
+    set_symmetric_difference_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, borrowed_iterator_t<OutR>>
+      set_symmetric_difference(Ep&& exec, R1&& r1, R2&& r2, OutR&& result_r,
+                                Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
}

namespace ranges {
  template<random_access_iterator I, sentinel_for<I> S, class Proj = identity,
            indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
    constexpr bool is_heap(I first, S last, Comp comp = {}, Proj proj = {});
  template<random_access_range R, class Proj = identity,
            indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
    constexpr bool is_heap(R&& r, Comp comp = {}, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            class Proj = identity,
+            indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
+    bool is_heap(Ep&& exec, I first, S last, Comp comp = {}, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+            indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
+    bool is_heap(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {});
}

namespace ranges {
  template<random_access_iterator I, sentinel_for<I> S, class Proj = identity,
            indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
    constexpr I is_heap_until(I first, S last, Comp comp = {}, Proj proj = {});
  template<random_access_range R, class Proj = identity,
            indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
    constexpr borrowed_iterator_t<R>
      is_heap_until(R&& r, Comp comp = {}, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            class Proj = identity,
+            indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
+    I is_heap_until(Ep&& exec, I first, S last, Comp comp = {}, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+            indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
+    borrowed_iterator_t<R>
+      is_heap_until(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {});
}

namespace ranges {
  template<class T, class Proj = identity,
            indirect_strict_weak_order<projected<const T*, Proj>> Comp = ranges::less>
    constexpr const T& min(const T& a, const T& b, Comp comp = {}, Proj proj = {});
  template<copyable T, class Proj = identity,
            indirect_strict_weak_order<projected<const T*, Proj>> Comp = ranges::less>
    constexpr T min(initializer_list<T> r, Comp comp = {}, Proj proj = {});
  template<input_range R, class Proj = identity,
            indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
    requires indirectly_copyable_storable<iterator_t<R>, range_value_t<R>*>
    constexpr range_value_t<R>
      min(R&& r, Comp comp = {}, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+            indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
+    requires indirectly_copyable_storable<iterator_t<R>, range_value_t<R>*>
+    range_value_t<R>
+      min(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {});
}

namespace ranges {
  template<class T, class Proj = identity,
            indirect_strict_weak_order<projected<const T*, Proj>> Comp = ranges::less>
    constexpr const T& max(const T& a, const T& b, Comp comp = {}, Proj proj = {});
  template<copyable T, class Proj = identity,
            indirect_strict_weak_order<projected<const T*, Proj>> Comp = ranges::less>
    constexpr T max(initializer_list<T> r, Comp comp = {}, Proj proj = {});
  template<input_range R, class Proj = identity,
            indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
    requires indirectly_copyable_storable<iterator_t<R>, range_value_t<R>*>
    constexpr range_value_t<R>
      max(R&& r, Comp comp = {}, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+            indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
+    requires indirectly_copyable_storable<iterator_t<R>, range_value_t<R>*>
+    range_value_t<R>
+      max(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {});
}

namespace ranges {
  template<class T>
    using minmax_result = min_max_result<T>;

  template<class T, class Proj = identity,
            indirect_strict_weak_order<projected<const T*, Proj>> Comp = ranges::less>
    constexpr minmax_result<const T&>
      minmax(const T& a, const T& b, Comp comp = {}, Proj proj = {});
  template<copyable T, class Proj = identity,
            indirect_strict_weak_order<projected<const T*, Proj>> Comp = ranges::less>
    constexpr minmax_result<T>
      minmax(initializer_list<T> r, Comp comp = {}, Proj proj = {});
  template<input_range R, class Proj = identity,
            indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
    requires indirectly_copyable_storable<iterator_t<R>, range_value_t<R>*>
    constexpr minmax_result<range_value_t<R>>
      minmax(R&& r, Comp comp = {}, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+          indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
+    requires indirectly_copyable_storable<iterator_t<R>, range_value_t<R>*>
+    minmax_result<range_value_t<R>>
+      minmax(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {});
}

namespace ranges {
  template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
            indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
    constexpr I min_element(I first, S last, Comp comp = {}, Proj proj = {});
  template<forward_range R, class Proj = identity,
            indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
    constexpr borrowed_iterator_t<R>
      min_element(R&& r, Comp comp = {}, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            class Proj = identity,
+            indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
+    I min_element(Ep&& exec, I first, S last, Comp comp = {}, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+            indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
+    borrowed_iterator_t<R>
+      min_element(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {});
}

namespace ranges {
  template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
            indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
    constexpr I max_element(I first, S last, Comp comp = {}, Proj proj = {});
  template<forward_range R, class Proj = identity,
            indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
    constexpr borrowed_iterator_t<R>
      max_element(R&& r, Comp comp = {}, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            class Proj = identity,
+            indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
+    I max_element(Ep&& exec, I first, S last, Comp comp = {}, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+            indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
+    borrowed_iterator_t<R>
+      max_element(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {});
}

namespace ranges {
  template<class I>
    using minmax_element_result = min_max_result<I>;

  template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
            indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
    constexpr minmax_element_result<I>
      minmax_element(I first, S last, Comp comp = {}, Proj proj = {});
  template<forward_range R, class Proj = identity,
            indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
    constexpr minmax_element_result<borrowed_iterator_t<R>>
      minmax_element(R&& r, Comp comp = {}, Proj proj = {});

+  template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
+            class Proj = identity,
+            indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
+    minmax_element_result<I>
+      minmax_element(Ep&& exec, I first, S last, Comp comp = {}, Proj proj = {});
+  template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
+            indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
+    minmax_element_result<borrowed_iterator_t<R>>
+      minmax_element(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {});
}

namespace ranges {
  template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
            class Proj1 = identity, class Proj2 = identity,
            indirect_strict_weak_order<projected<I1, Proj1>, projected<I2, Proj2>> Comp =
              ranges::less>
    constexpr bool
      lexicographical_compare(I1 first1, S1 last1, I2 first2, S2 last2,
                              Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
  template<input_range R1, input_range R2, class Proj1 = identity,
            class Proj2 = identity,
            indirect_strict_weak_order<projected<iterator_t<R1>, Proj1>,
                                      projected<iterator_t<R2>, Proj2>> Comp = ranges::less>
    constexpr bool
      lexicographical_compare(R1&& r1, R2&& r2, Comp comp = {},
                              Proj1 proj1 = {}, Proj2 proj2 = {});

+  template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
+            random_access_iterator I2, sized_sentinel_for<I2> S2,
+            class Proj1 = identity, class Proj2 = identity,
+            indirect_strict_weak_order<projected<I1, Proj1>, projected<I2, Proj2>> Comp = ranges::less>
+    bool lexicographical_compare(Ep&& exec, I1 first1, S1 last1, I2 first2, S2 last2,
+                                  Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
+  template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
+            class Proj1 = identity, class Proj2 = identity,
+            indirect_strict_weak_order<projected<iterator_t<R1>, Proj1>,
+                                        projected<iterator_t<R2>, Proj2>> Comp = ranges::less>
+    bool lexicographical_compare(Ep&& exec, R1&& r1, R2&& r2, Comp comp = {},
+                                  Proj1 proj1 = {}, Proj2 proj2 = {});
}

8.10 Modify `all_of` in [alg.all.of]

template<input_iterator I, sentinel_for<I> S, class Proj = identity,
         indirect_unary_predicate<projected<I, Proj>> Pred>
  constexpr bool ranges::all_of(I first, S last, Pred pred, Proj proj = {});
template<input_range R, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  constexpr bool ranges::all_of(R&& r, Pred pred, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
         indirect_unary_predicate<projected<I, Proj>> Pred>
  bool ranges::all_of(Ep&& exec, I first, S last, Pred pred, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  bool ranges::all_of(Ep&& exec, R&& r, Pred pred, Proj proj = {});

1 Let E be:

(1.1) pred(*i) for the overloads in namespace std;
(1.2) invoke(pred, invoke(proj, *i)) for the overloads in namespace ranges.

2 Returns: false if E is false for some iterator i in the range [first, last), and true otherwise.

3 Complexity: At most last - first applications of the predicate and any projection.

8.11 Modify `any_of` in [alg.any.of]

template<input_iterator I, sentinel_for<I> S, class Proj = identity,
         indirect_unary_predicate<projected<I, Proj>> Pred>
  constexpr bool ranges::any_of(I first, S last, Pred pred, Proj proj = {});
template<input_range R, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  constexpr bool ranges::any_of(R&& r, Pred pred, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
         indirect_unary_predicate<projected<I, Proj>> Pred>
  bool ranges::any_of(Ep&& exec, I first, S last, Pred pred, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  bool ranges::any_of(Ep&& exec, R&& r, Pred pred, Proj proj = {});

1 Let E be:

(1.1) pred(*i) for the overloads in namespace std;
(1.2) invoke(pred, invoke(proj, *i)) for the overloads in namespace ranges.

2 Returns: true if E is true for some iterator i in the range [first, last), and false otherwise.

3 Complexity: At most last - first applications of the predicate and any projection.

8.12 Modify `none_of` in [alg.none.of]

template<input_iterator I, sentinel_for<I> S, class Proj = identity,
         indirect_unary_predicate<projected<I, Proj>> Pred>
  constexpr bool ranges::none_of(I first, S last, Pred pred, Proj proj = {});
template<input_range R, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  constexpr bool ranges::none_of(R&& r, Pred pred, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
         indirect_unary_predicate<projected<I, Proj>> Pred>
  bool ranges::none_of(Ep&& exec, I first, S last, Pred pred, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  bool ranges::none_of(Ep&& exec, R&& r, Pred pred, Proj proj = {});

1 Let E be:

(1.1) pred(*i) for the overloads in namespace std;
(1.2) invoke(pred, invoke(proj, *i)) for the overloads in namespace ranges.

2 Returns: false if E is true for some iterator i in the range [first, last), and true otherwise.

3 Complexity: At most last - first applications of the predicate and any projection.

8.13 Modify `contains` in [alg.contains]

template<input_iterator I, sentinel_for<I> S, class Proj = identity,
         class T = projected_value_t<I, Proj>>
  requires indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
  constexpr bool ranges::contains(I first, S last, const T& value, Proj proj = {});
template<input_range R, class Proj = identity, class T = projected_value_t<iterator_t<R>, Proj>>
  requires indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*>
  constexpr bool ranges::contains(R&& r, const T& value, Proj proj = {});

Returns: ranges::find(std::move(first), last, value, proj) != last.

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
         class T = projected_value_t<I, Proj>>
  requires indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
  bool ranges::contains(Ep&& exec, I first, S last, const T& value, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity, class T = projected_value_t<iterator_t<R>, Proj>>
  requires indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*>
  bool ranges::contains(Ep&& exec, R&& r, const T& value, Proj proj = {});

Returns: ranges::find(std::forward<Ep>(exec), std::move(first), last, value, proj) != last.

template<forward_iterator I1, sentinel_for<I1> S1,
         forward_iterator I2, sentinel_for<I2> S2,
         class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
  constexpr bool ranges::contains_subrange(I1 first1, S1 last1, I2 first2, S2 last2,
                                           Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<forward_range R1, forward_range R2,
         class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
  constexpr bool ranges::contains_subrange(R1&& r1, R2&& r2, Pred pred = {},
                                           Proj1 proj1 = {}, Proj2 proj2 = {});

Returns: first2 == last2 || !ranges::search(first1, last1, first2, last2, pred, proj1, proj2).empty().

template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
         random_access_iterator I2, sized_sentinel_for<I2> S2,
         class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
  bool ranges::contains_subrange(Ep&& exec, I1 first1, S1 last1, I2 first2, S2 last2,
                                 Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
         class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
  bool ranges::contains_subrange(Ep&& exec, R1&& r1, R2&& r2, Pred pred = {},
                                 Proj1 proj1 = {}, Proj2 proj2 = {});

Returns: first2 == last2 || !ranges::search(std::forward<Ep>(exec), first1, last1, first2, last2, pred, proj1, proj2).empty().

8.14 Modify `for_each` in [alg.foreach]

template<input_iterator I, sentinel_for<I> S, class Proj = identity,
         indirectly_unary_invocable<projected<I, Proj>> Fun>
  constexpr ranges::for_each_result<I, Fun>
    ranges::for_each(I first, S last, Fun f, Proj proj = {});
template<input_range R, class Proj = identity,
         indirectly_unary_invocable<projected<iterator_t<R>, Proj>> Fun>
  constexpr ranges::for_each_result<borrowed_iterator_t<R>, Fun>
    ranges::for_each(R&& r, Fun f, Proj proj = {});

Effects: Calls invoke(f, invoke(proj, *i)) for every iterator i in the range [first, last), starting from first and proceeding to last - 1.

[Note X: If the result of invoke(proj, *i) is a mutable reference, f can apply non-constant functions. — end note]

Returns: {last, std::move(f)}.

Complexity: Applies f and proj exactly last - first times.

Remarks: If f returns a result, the result is ignored.

[Note X: The overloads in namespace ranges require Fun to model copy_constructible. — end note]

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
         indirectly_unary_invocable<projected<I, Proj>> Fun>
  I ranges::for_each(Ep&& exec, I first, S last, Fun f, Proj proj = {});

template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         indirectly_unary_invocable<projected<iterator_t<R>, Proj>> Fun>
  borrowed_iterator_t<R>
    ranges::for_each(Ep&& exec, R&& r, Fun f, Proj proj = {});

Effects: Calls invoke(f, invoke(proj, *i)) for every iterator i in the range [first, last).

[Note X: If the result of invoke(proj, *i) is a mutable reference, f can apply non-constant functions. — end note]

Returns: last.

Complexity: Applies f and proj exactly last - first times.

Remarks: If f returns a result, the result is ignored. Implementations do not have the freedom granted under [algorithms.parallel.exec] to make arbitrary copies of elements from the input sequence.

[Note X: The overloads in namespace ranges require Fun to model copy_constructible. — end note]

[Note X: Does not return a copy of its Fun parameter, since parallelization often does not permit efficient state accumulation. — end note]

template<input_iterator I, class Proj = identity,
         indirectly_unary_invocable<projected<I, Proj>> Fun>
  constexpr ranges::for_each_n_result<I, Fun>
    ranges::for_each_n(I first, iter_difference_t<I> n, Fun f, Proj proj = {});

Preconditions: n >= 0 is true.

Effects: Calls invoke(f, invoke(proj, *i)) for every iterator i in the range [first, first + n) in order.

[Note X: If the result of invoke(proj, *i) is a mutable reference, f can apply non-constant functions. — end note]

Returns: {first + n, std::move(f)}.

Remarks: If f returns a result, the result is ignored.

[Note X: The overload in namespace ranges requires Fun to model copy_constructible. — end note]

template<execution-policy Ep, random_access_iterator I, class Proj = identity,
         indirectly_unary_invocable<projected<I, Proj>> Fun>
  I ranges::for_each_n(Ep&& exec, I first, iter_difference_t<I> n, Fun f, Proj proj = {});

Preconditions: n >= 0 is true.

Effects: Calls invoke(f, invoke(proj, *i)) for every iterator i in the range [first, first + n).

[Note X: If the result of invoke(proj, *i) is a mutable reference, f can apply non-constant functions. — end note]

Returns: first + n.

[Note X: The overload in namespace ranges requires Fun to model copy_constructible. — end note]

[Note X: Does not return a copy of its Fun parameter, since parallelization often does not permit efficient state accumulation. — end note]

8.15 Modify `find` in [alg.find]

template<input_iterator I, sentinel_for<I> S, class Proj = identity,
         class T = projected_value_t<I, Proj>>
  requires indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
  constexpr I ranges::find(I first, S last, const T& value, Proj proj = {});
template<input_range R, class Proj = identity, class T = projected_value_t<iterator_t<R>, Proj>>
  requires indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*>
  constexpr borrowed_iterator_t<R>
    ranges::find(R&& r, const T& value, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
         class T = projected_value_t<I, Proj>>
  requires indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
  I ranges::find(Ep&& exec, I first, S last, const T& value, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity, class T = projected_value_t<iterator_t<R>, Proj>>
  requires indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*>
  borrowed_iterator_t<R> ranges::find(Ep&& exec, R&& r, const T& value, Proj proj = {});

template<input_iterator I, sentinel_for<I> S, class Proj = identity,
         indirect_unary_predicate<projected<I, Proj>> Pred>
  constexpr I ranges::find_if(I first, S last, Pred pred, Proj proj = {});
template<input_range R, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  constexpr borrowed_iterator_t<R>
    ranges::find_if(R&& r, Pred pred, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
         indirect_unary_predicate<projected<I, Proj>> Pred>
  I ranges::find_if(Ep&& exec, I first, S last, Pred pred, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  borrowed_iterator_t<R> ranges::find_if(Ep&& exec, R&& r, Pred pred, Proj proj = {});

template<input_iterator I, sentinel_for<I> S, class Proj = identity,
         indirect_unary_predicate<projected<I, Proj>> Pred>
  constexpr I ranges::find_if_not(I first, S last, Pred pred, Proj proj = {});
template<input_range R, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  constexpr borrowed_iterator_t<R>
    ranges::find_if_not(R&& r, Pred pred, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
         indirect_unary_predicate<projected<I, Proj>> Pred>
  I ranges::find_if_not(Ep&& exec, I first, S last, Pred pred, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  borrowed_iterator_t<R> ranges::find_if_not(Ep&& exec, R&& r, Pred pred, Proj proj = {});

1 Let E be:

(1.1) *i == value for find;
(1.2) pred(*i) != false for find_if;
(1.3) pred(*i) == false for find_if_not;
(1.4) bool(invoke(proj, *i) == value) for ranges::find;
(1.5) bool(invoke(pred, invoke(proj, *i))) for ranges::find_if;
(1.6) bool(!invoke(pred, invoke(proj, *i))) for ranges::find_if_not.

2 Returns: The first iterator i in the range [first, last) for which E is true. Returns last if no such iterator is found.

3 Complexity: At most last - first applications of the corresponding predicate and any projection.

8.16 Modify `find_last` in [alg.find.last]

template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
         class T = projected_value_t<I, Proj>>
  requires indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
  constexpr subrange<I> ranges::find_last(I first, S last, const T& value, Proj proj = {});
template<forward_range R, class Proj = identity,
         class T = projected_value_t<iterator_t<R>, Proj>>
  requires indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*>
  constexpr borrowed_subrange_t<R> ranges::find_last(R&& r, const T& value, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
         class T = projected_value_t<I, Proj>>
  requires indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
  subrange<I> ranges::find_last(Ep&& exec, I first, S last, const T& value, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity, class T = projected_value_t<iterator_t<R>, Proj>>
  requires indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*>
  borrowed_subrange_t<R> ranges::find_last(Ep&& exec, R&& r, const T& value, Proj proj = {});

template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
         indirect_unary_predicate<projected<I, Proj>> Pred>
  constexpr subrange<I> ranges::find_last_if(I first, S last, Pred pred, Proj proj = {});
template<forward_range R, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  constexpr borrowed_subrange_t<R> ranges::find_last_if(R&& r, Pred pred, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
         indirect_unary_predicate<projected<I, Proj>> Pred>
  subrange<I> ranges::find_last_if(Ep&& exec, I first, S last, Pred pred, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  borrowed_subrange_t<R> ranges::find_last_if(Ep&& exec, R&& r, Pred pred, Proj proj = {});

template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
         indirect_unary_predicate<projected<I, Proj>> Pred>
  constexpr subrange<I> ranges::find_last_if_not(I first, S last, Pred pred, Proj proj = {});
template<forward_range R, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  constexpr borrowed_subrange_t<R> ranges::find_last_if_not(R&& r, Pred pred, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
         indirect_unary_predicate<projected<I, Proj>> Pred>
  subrange<I> ranges::find_last_if_not(Ep&& exec, I first, S last, Pred pred, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  borrowed_subrange_t<R> ranges::find_last_if_not(Ep&& exec, R&& r, Pred pred, Proj proj = {});

1 Let E be:

(1.1) bool(invoke(proj, *i) == value) for ranges::find_last;
(1.2) bool(invoke(pred, invoke(proj, *i))) for ranges::find_last_if;
(1.3) bool(!invoke(pred, invoke(proj, *i))) for ranges::find_last_if_not.

2 Returns: Let i be the last iterator in the range [first, last) for which E is true. Returns {i, last}, or {last, last} if no such iterator is found.

3 Complexity: At most last - first applications of the corresponding predicate and projection.

8.17 Modify `find_end` in [alg.find.end]

template<forward_iterator I1, sentinel_for<I1> S1, forward_iterator I2, sentinel_for<I2> S2,
         class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
  constexpr subrange<I1>
    ranges::find_end(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {},
                     Proj1 proj1 = {}, Proj2 proj2 = {});
template<forward_range R1, forward_range R2,
         class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
  constexpr borrowed_subrange_t<R1>
    ranges::find_end(R1&& r1, R2&& r2, Pred pred = {},
                     Proj1 proj1 = {}, Proj2 proj2 = {});

template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1, random_access_iterator I2,
         sized_sentinel_for<I2> S2, class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
  subrange<I1> ranges::find_end(Ep&& exec, I1 first1, S1 last1, I2 first2, S2 last2,
                                Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
         class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
  borrowed_subrange_t<R1> ranges::find_end(Ep&& exec, R1&& r1, R2&& r2,
                                           Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});

1 Let:

(1.1) pred be equal_to{} for the overloads with no parameter pred;
(1.2) E be:
- (1.2.1) pred(*(i + n), *(first2 + n)) for the overloads in namespace std;
- (1.2.2) invoke(pred, invoke(proj1, *(i + n)), invoke(proj2, *(first2 + n))) for the overloads in namespace ranges;
(1.3) i be last1 if [first2, last2) is empty, or if (last2 - first2) > (last1 - first1) is true, or if there is no iterator in the range [first1, last1 - (last2 - first2)) such that for every non-negative integer n < (last2 - first2), E is true.

Otherwise i is the last such iterator in [first1, last1 - (last2 - first2)).

2 Returns:

(2.1) i for the overloads in namespace std.
(2.2) {i, i + (i == last1 ? 0 : last2 - first2)} for the overloads in namespace ranges.

3 Complexity: At most (last2 - first2) * (last1 - first1 - (last2 - first2) + 1) applications of the corresponding predicate and any projections.

8.18 Modify `find_first_of` in [alg.find.first.of]

template<input_iterator I1, sentinel_for<I1> S1, forward_iterator I2, sentinel_for<I2> S2,
         class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
  constexpr I1 ranges::find_first_of(I1 first1, S1 last1, I2 first2, S2 last2,
                                     Pred pred = {},
                                     Proj1 proj1 = {}, Proj2 proj2 = {});
template<input_range R1, forward_range R2,
         class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
  constexpr borrowed_iterator_t<R1>
    ranges::find_first_of(R1&& r1, R2&& r2, Pred pred = {},
                          Proj1 proj1 = {}, Proj2 proj2 = {});

template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
         random_access_iterator I2, sized_sentinel_for<I2> S2,
         class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
  I1 ranges::find_first_of(Ep&& exec, I1 first1, S1 last1, I2 first2, S2 last2,
                           Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
         class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
  borrowed_iterator_t<R1> ranges::find_first_of(Ep&& exec, R1&& r1, R2&& r2,
                                                Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});

1 Let E be:

(1.1) *i == *j for the overloads with no parameter pred;
(1.2) pred(*i, *j) != false for the overloads with a parameter pred and no parameter proj1;
(1.3) bool(invoke(pred, invoke(proj1, *i), invoke(proj2, *j))) for the overloads with parameters pred and proj1.

2 Effects: Finds an element that matches one of a set of values.

3 Returns: The first iterator i in the range [first1, last1) such that for some iterator j in the range [first2, last2) E holds. Returns last1 if [first2, last2) is empty or if no such iterator is found.

4 Complexity: At most (last1-first1) * (last2-first2) applications of the corresponding predicate and any projections.

8.19 Modify `adjacent_find` in [alg.adjacent.find]

template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
         indirect_binary_predicate<projected<I, Proj>,
                                   projected<I, Proj>> Pred = ranges::equal_to>
  constexpr I ranges::adjacent_find(I first, S last, Pred pred = {}, Proj proj = {});
template<forward_range R, class Proj = identity,
         indirect_binary_predicate<projected<iterator_t<R>, Proj>,
                                   projected<iterator_t<R>, Proj>> Pred = ranges::equal_to>
  constexpr borrowed_iterator_t<R> ranges::adjacent_find(R&& r, Pred pred = {}, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
         indirect_binary_predicate<projected<I, Proj>, projected<I, Proj>> Pred = ranges::equal_to>
  I ranges::adjacent_find(Ep&& exec, I first, S last, Pred pred = {}, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         indirect_binary_predicate<projected<iterator_t<R>, Proj>, projected<iterator_t<R>, Proj>> Pred
           = ranges::equal_to>
  borrowed_iterator_t<R> ranges::adjacent_find(Ep&& exec, R&& r, Pred pred = {}, Proj proj = {});

1 Let E be:

(1.1) *i == *(i + 1) for the overloads with no parameter pred;
(1.2) pred(*i, *(i + 1)) != false for the overloads with a parameter pred and no parameter proj;
(1.3) bool(invoke(pred, invoke(proj, *i), invoke(proj, *(i + 1)))) for the overloads with both parameters pred and proj.

2 Returns: The first iterator i such that both i and i + 1 are in the range [first, last) for which E holds. Returns last if no such iterator is found.

3 Complexity: For the overloads with no ~~ExecutionPolicy~~execution policy, exactly min((i - first) + 1, (last - first) - 1) applications of the corresponding predicate, where i is adjacent_find’s return value. For the overloads with an ~~ExecutionPolicy~~execution policy, O(last - first) applications of the corresponding predicate~~, and no~~. No more than twice as many applications of any projection.

8.20 Modify `count` in [alg.count]

template<input_iterator I, sentinel_for<I> S, class Proj = identity,
         class T = projected_value_t<I, Proj>>
  requires indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
  constexpr iter_difference_t<I>
    ranges::count(I first, S last, const T& value, Proj proj = {});
template<input_range R, class Proj = identity, class T = projected_value_t<iterator_t<R>, Proj>>
  requires indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*>
  constexpr range_difference_t<R>
    ranges::count(R&& r, const T& value, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
         class T = projected_value_t<I, Proj>>
  requires indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
  iter_difference_t<I> ranges::count(Ep&& exec, I first, S last, const T& value, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity, class T = projected_value_t<iterator_t<R>, Proj>>
  requires indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*>
  range_difference_t<R> ranges::count(Ep&& exec, R&& r, const T& value, Proj proj = {});

template<input_iterator I, sentinel_for<I> S, class Proj = identity,
         indirect_unary_predicate<projected<I, Proj>> Pred>
  constexpr iter_difference_t<I>
    ranges::count_if(I first, S last, Pred pred, Proj proj = {});
template<input_range R, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  constexpr range_difference_t<R>
    ranges::count_if(R&& r, Pred pred, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
         indirect_unary_predicate<projected<I, Proj>> Pred>
  iter_difference_t<I> ranges::count_if(Ep&& exec, I first, S last, Pred pred, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  range_difference_t<R> ranges::count_if(Ep&& exec, R&& r, Pred pred, Proj proj = {});

1 Let E be:

(1.1) *i == value for the overloads with no parameter pred or proj;
(1.2) pred(*i) != false for the overloads with a parameter pred but no parameter proj;
(1.3) invoke(proj, *i) == value for the overloads with a parameter proj but no parameter pred;
(1.4) bool(invoke(pred, invoke(proj, *i))) for the overloads with both parameters proj and pred.

2 Effects: Returns the number of iterators i in the range [first, last) for which E holds.

3 Complexity: Exactly last - first applications of the corresponding predicate and any projection.

8.21 Modify `mismatch` in [alg.mismatch]

template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
         class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
  constexpr ranges::mismatch_result<I1, I2>
    ranges::mismatch(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {},
                     Proj1 proj1 = {}, Proj2 proj2 = {});
template<input_range R1, input_range R2,
         class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
  constexpr ranges::mismatch_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>>
    ranges::mismatch(R1&& r1, R2&& r2, Pred pred = {},
                     Proj1 proj1 = {}, Proj2 proj2 = {});

template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
         random_access_iterator I2, sized_sentinel_for<I2> S2,
         class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
  ranges::mismatch_result<I1, I2>
    ranges::mismatch(Ep&& exec, I1 first1, S1 last1, I2 first2, S2 last2,
                     Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
         class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
  ranges::mismatch_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>>
    ranges::mismatch(Ep&& exec, R1&& r1, R2&& r2, Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});

1 Let last2 be first2 + (last1 - first1) for the overloads with no parameter last2 or r2.

2 Let E be:

(2.1) !(*(first1 + n) == *(first2 + n)) for the overloads with no parameter pred;
(2.2) pred(*(first1 + n), *(first2 + n)) == false for the overloads with a parameter pred and no parameter proj1;
(2.3) !invoke(pred, invoke(proj1, *(first1 + n)), invoke(proj2, *(first2 + n))) for the overloads with both parameters pred and proj1.

3 Let N be min(last1 - first1, last2 - first2).

4 Returns: { first1 + n, first2 + n }, where n is the smallest integer in [0, N) such that E holds, or N if no such integer exists.

5 Complexity: At most N applications of the corresponding predicate and any projections.

8.22 Modify `equal` in [alg.equal]

template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
         class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
  constexpr bool ranges::equal(I1 first1, S1 last1, I2 first2, S2 last2,
                               Pred pred = {},
                               Proj1 proj1 = {}, Proj2 proj2 = {});
template<input_range R1, input_range R2, class Pred = ranges::equal_to,
         class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
  constexpr bool ranges::equal(R1&& r1, R2&& r2, Pred pred = {},
                               Proj1 proj1 = {}, Proj2 proj2 = {});

template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
         random_access_iterator I2, sized_sentinel_for<I2> S2,
         class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
  bool ranges::equal(Ep&& exec, I1 first1, S1 last1, I2 first2, S2 last2,
                     Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2, class Pred = ranges::equal_to,
         class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
  bool ranges::equal(Ep&& exec, R1&& r1, R2&& r2,
                     Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});

1 Let:

(1.1) last2 be first2 + (last1 - first1) for the overloads with no parameter last2 or r2;
(1.2) pred be equal_to{} for the overloads with no parameter pred;
(1.3) E be:
- (1.3.1) pred(*i, *(first2 + (i - first1))) for the overloads with no parameter proj1;
- (1.3.2) invoke(pred, invoke(proj1, *i), invoke(proj2, *(first2 + (i - first1)))) for the overloads with parameter proj1.

2 Returns: If last1 - first1 != last2 - first2, return false. Otherwise return true if E holds for every iterator i in the range [first1, last1). Otherwise, returns false.

3 Complexity: If

(3.1) the types of first1, last1, first2, and last2 meet the Cpp17RandomAccessIterator requirements ([random.access.iterators]) and last1 - first1 != last2 - first2 for the overloads in namespace std;
(3.2) the types of first1, last1, first2, and last2 pairwise model sized_sentinel_for ([iterator.concept.sizedsentinel]) and last1 - first1 != last2 - first2 for the first overload in namespace ranges,
(3.3) R1 and R2 each model sized_range and ranges::distance(r1) != ranges::distance(r2) for the second overload in namespace ranges,

then no applications of the corresponding predicate and each projection; otherwise,

(3.4) For the overloads with no ~~ExecutionPolicy~~execution policy, at most min(last1 - first1, last2 - first2) applications of the corresponding predicate and any projections.
(3.5) For the overloads with an ~~ExecutionPolicy~~execution policy, O(min(last1 - first1, last2 - first2)) applications of the corresponding predicate.

8.23 Modify `search` in [alg.search]

template<forward_iterator I1, sentinel_for<I1> S1, forward_iterator I2,
         sentinel_for<I2> S2, class Pred = ranges::equal_to,
         class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
  constexpr subrange<I1>
    ranges::search(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {},
                   Proj1 proj1 = {}, Proj2 proj2 = {});
template<forward_range R1, forward_range R2, class Pred = ranges::equal_to,
         class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
  constexpr borrowed_subrange_t<R1>
    ranges::search(R1&& r1, R2&& r2, Pred pred = {},
                   Proj1 proj1 = {}, Proj2 proj2 = {});

template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
         random_access_iterator I2, sized_sentinel_for<I2> S2,
         class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
    subrange<I1>
      ranges::search(Ep&& exec, I1 first1, S1 last1, I2 first2, S2 last2,
                     Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
         class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
    borrowed_subrange_t<R1>
      ranges::search(Ep&& exec, R1&& r1, R2&& r2,
                     Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});

3 Returns:

(3.1) {i, i + (last2 - first2)}, where i is the first iterator in the range [first1, last1 - (last2 - first2)) such that for every non-negative integer n less than last2 - first2 the condition bool(invoke(pred, invoke(proj1, *(i + n)), invoke(proj2, *(first2 + n)))) is true.
(3.2) Returns {last1, last1} if no such iterator exists.

4 Complexity: At most (last1 - first1) * (last2 - first2) applications of the corresponding predicate and projections.

template<forward_iterator I, sentinel_for<I> S,
         class Pred = ranges::equal_to, class Proj = identity,
         class T = projected_value_t<I, Proj>>
  requires indirectly_comparable<I, const T*, Pred, Proj>
  constexpr subrange<I>
    ranges::search_n(I first, S last, iter_difference_t<I> count,
                     const T& value, Pred pred = {}, Proj proj = {});
template<forward_range R, class Pred = ranges::equal_to,
         class Proj = identity, class T = projected_value_t<iterator_t<R>, Proj>>
  requires indirectly_comparable<iterator_t<R>, const T*, Pred, Proj>
  constexpr borrowed_subrange_t<R>
    ranges::search_n(R&& r, range_difference_t<R> count,
                     const T& value, Pred pred = {}, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
         class Pred = ranges::equal_to, class Proj = identity,
         class T = projected_value_t<I, Proj>>
  requires indirectly_comparable<I, const T*, Pred, Proj>
    subrange<I>
      ranges::search_n(Ep&& exec, I first, S last, iter_difference_t<I> count,
                       const T& value, Pred pred = {}, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Pred = ranges::equal_to,
         class Proj = identity, class T = projected_value_t<iterator_t<R>, Proj>>
  requires indirectly_comparable<iterator_t<R>, const T*, Pred, Proj>
    borrowed_subrange_t<R>
      ranges::search_n(Ep&& exec, R&& r, range_difference_t<R> count,
                       const T& value, Pred pred = {}, Proj proj = {});

9 Returns: {i, i + count} where i is the first iterator in the range [first, last - count) such that for every non-negative integer n less than count, the following condition holds: invoke(pred, invoke(proj, *(i + n)), value). Returns {last, last} if no such iterator is found.

10 Complexity: At most last - first applications of the corresponding predicate and projection.

8.24 Modify `starts_with` in [alg.starts.with]

template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
         class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
  constexpr bool ranges::starts_with(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {},
                                     Proj1 proj1 = {}, Proj2 proj2 = {});
template<input_range R1, input_range R2, class Pred = ranges::equal_to, class Proj1 = identity,
         class Proj2 = identity>
  requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
  constexpr bool ranges::starts_with(R1&& r1, R2&& r2, Pred pred = {},
                                     Proj1 proj1 = {}, Proj2 proj2 = {});

Returns: ranges::mismatch(std::move(first1), last1, std::move(first2), last2, pred, proj1, proj2).in2 == last2

template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
         random_access_iterator I2, sized_sentinel_for<I2> S2,
         class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
  bool ranges::starts_with(Ep&& exec, I1 first1, S1 last1, I2 first2, S2 last2,
                           Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2, class Pred = ranges::equal_to,
         class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
  bool ranges::starts_with(Ep&& exec, R1&& r1, R2&& r2, Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});

Returns: ranges::mismatch(std::forward<Ep>(exec), std::move(first1), last1, std::move(first2), last2, pred, proj1, proj2).in2 == last2

8.25 Modify `ends_with` in [alg.ends.with]

template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
         class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
  requires (forward_iterator<I1> || sized_sentinel_for<S1, I1>) &&
           (forward_iterator<I2> || sized_sentinel_for<S2, I2>) &&
           indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
  constexpr bool ranges::ends_with(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {},
                                   Proj1 proj1 = {}, Proj2 proj2 = {});

Let N1 be last1 - first1 and N2 be last2 - first2.

Returns: false if N1 < N2, otherwise ranges::equal(std::move(first1) + (N1 - N2), last1, std::move(first2), last2, pred, proj1, proj2)

template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
         random_access_iterator I2, sized_sentinel_for<I2> S2,
         class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
  bool ranges::ends_with(Ep&& exec, I1 first1, S1 last1, I2 first2, S2 last2,
                         Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});

Let N1 be last1 - first1 and N2 be last2 - first2.

Returns: false if N1 < N2, otherwise ranges::equal(std::forward<Ep>(exec), std::move(first1) + (N1 - N2), last1, std::move(first2), last2, pred, proj1, proj2)

template<input_range R1, input_range R2, class Pred = ranges::equal_to, class Proj1 = identity,
         class Proj2 = identity>
  requires (forward_range<R1> || sized_range<R1>) &&
           (forward_range<R2> || sized_range<R2>) &&
           indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
  constexpr bool ranges::ends_with(R1&& r1, R2&& r2, Pred pred = {},
                                   Proj1 proj1 = {}, Proj2 proj2 = {});

Let N1 be ranges::distance(r1) and N2 be ranges::distance(r2).

Returns: false if N1 < N2, otherwise ranges::equal(views::drop(ranges::ref_view(r1), N1 - static_cast<decltype(N1)>(N2)), r2, pred, proj1, proj2)

template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
         class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
  bool ranges::ends_with(Ep&& exec, R1&& r1, R2&& r2,
                         Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});

Let N1 be ranges::distance(r1) and N2 be ranges::distance(r2).

Returns: false if N1 < N2, otherwise ranges::equal(std::forward<Ep>, views::drop(ranges::ref_view(r1), N1 - static_cast<decltype(N1)>(N2)), r2, pred, proj1, proj2)

8.26 Modify `copy` in [alg.copy]

template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2>
  ForwardIterator2 copy(ExecutionPolicy&& policy,
                        ForwardIterator1 first, ForwardIterator1 last,
                        ForwardIterator2 result);

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
         random_access_iterator O, sized_sentinel_for<O> OutS>
  requires indirectly_copyable<I, O>
  ranges::copy_result<I, O> ranges::copy(Ep&& exec, I first, S last, O result, OutS result_last);
template<execution-policy Ep, random-access-sized-range R, random-access-sized-range OutR>
  requires indirectly_copyable<iterator_t<R>, iterator_t<OutR>>
  ranges::copy_result<borrowed_iterator_t<R>, borrowed_iterator_t<OutR>>
    ranges::copy(Ep&& exec, R&& r, OutR&& result_r);

x Let result_last be result + (last - first) for the overloads with no parameter result_last or result_r.

x Let N be min(last - first, result_last - result).

6 Preconditions: The ranges [first, lastfirst + N) and [result, result + (last - first)N) do not overlap.

7 Effects: Copies elements in the range [first, lastfirst + N) into the range [result, result + (last - first)N). For each non-negative integer n < (last - first)N, performs *(result + n) = *(first + n).

8 Returns:~~result + (last - first).~~

(x.1) result + N for the overloads in namespace std.
(x.2) {first + N, result + N} for the overloads in namespace ranges.

9 Complexity: Exactly (last - first)N assignments.

template<input_iterator I, weakly_incrementable O>
  requires indirectly_copyable<I, O>
  constexpr ranges::copy_n_result<I, O>
    ranges::copy_n(I first, iter_difference_t<I> n, O result);

template<execution-policy Ep, random_access_iterator I, random_access_iterator O,
         sized_sentinel_for<O> OutS>
  requires indirectly_copyable<I, O>
  ranges::copy_n_result<I, O>
    ranges::copy_n(Ep&& exec, I first, iter_difference_t<I> n, O result, OutS result_last);

x Let result_last be result + (last - first) for the overloads with no parameter result_last.

10 Let N be max(0, nmin(n, result_last - result)).

11 Mandates: The type Size is convertible to an integral type ([conv.integral], [class.conv]).

12 Effects: For each non-negative integer i < N, performs *(result + i) = *(first + i).

13 Returns:

(13.1) result + N for the overloads in namespace std.
(13.2) {first + N, result + N} for the overloads in namespace ranges.

14 Complexity: Exactly N assignments.

template<input_iterator I, sentinel_for<I> S, weakly_incrementable O, class Proj = identity,
         indirect_unary_predicate<projected<I, Proj>> Pred>
  requires indirectly_copyable<I, O>
  constexpr ranges::copy_if_result<I, O>
    ranges::copy_if(I first, S last, O result, Pred pred, Proj proj = {});
template<input_range R, weakly_incrementable O, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  requires indirectly_copyable<iterator_t<R>, O>
  constexpr ranges::copy_if_result<borrowed_iterator_t<R>, O>
    ranges::copy_if(R&& r, O result, Pred pred, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
         random_access_iterator O, sized_sentinel_for<O> OutS,
         class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
  requires indirectly_copyable<I, O>
  ranges::copy_if_result<I, O>
    ranges::copy_if(Ep&& exec, I first, S last, O result, OutS result_last,
                    Pred pred, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, random_access_iterator OutR,
         class Proj = identity, indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  requires indirectly_copyable<iterator_t<R>, iterator_t<OutR>>
  ranges::copy_if_result<borrowed_iterator_t<R>, borrowed_iterator_t<OutR>>
    ranges::copy_if(Ep&& exec, R&& r, OutR&& result_r, Pred pred, Proj proj = {});

15 Let E be:

(15.1) bool(pred(*i)) for the overloads in namespace std;
(15.2) bool(invoke(pred, invoke(proj, *i))) for the overloads in namespace ranges,

and N be the number of iterators i in the range [first, last) for which the condition E holds.

x Let:

(x.1) result_last be result + (last - first) for the overloads with no parameter result_last or result_r;
(x.2) E be:
- (x.2.1) bool(pred(*i)) for the overloads in namespace std;
- (x.2.2) bool(invoke(pred, invoke(proj, *i))) for the overloads in namespace ranges,
(x.3) M be the number of iterators i in the range [first, last) for which the condition E holds;
(x.4) N be min(M, result_last - result).

16 Preconditions: The ranges [first, last) and [result, result + (last - first)N) do not overlap.

[Note 1: For the overload with an ExecutionPolicy, there might be a performance cost if iterator_traits<ForwardIterator1>::value_type is not Cpp17MoveConstructible (Table 31). For the overloads with an execution-policy, there might be a performance cost if iter_value_t<I> is not move_constructible. — end note]

17 Effects: Copies ~~all of the~~N elements referred to by the iterator i in the range [first, last) for which E is true into the range [result, result + N).

18 Returns:

(18.1) result + N for the overloads in namespace std.
(18.2) {lastj, result + N} for the overloads in namespace ranges, where the iterator j points to a position in the range [first, last) past the last copied element if result + N == result_last, and j == last otherwise.

19 Complexity: ~~Exactly~~At most last - first applications of the corresponding predicate and any projection.

20 Remarks: Stable ([algorithm.stable]).

8.27 Modify `move` in [alg.move]

template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2>
  ForwardIterator2 move(ExecutionPolicy&& policy,
                        ForwardIterator1 first, ForwardIterator1 last,
                        ForwardIterator2 result);

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
         random_access_iterator O, sized_sentinel_for<O> OutS>
  requires indirectly_movable<I, O>
  ranges::move_result<I, O> ranges::move(Ep&& exec, I first, S last, O result, OutS result_last);
template<execution-policy Ep, random-access-sized-range R, random-access-sized-range OutR>
  requires indirectly_movable<iterator_t<R>, iterator_t<OutR>>
  ranges::move_result<borrowed_iterator_t<R>, borrowed_iterator_t<OutR>>
    ranges::move(Ep&& exec, R&& r, OutR&& result_r);

x Let E be:

(x.1) std::move(*(first + n)) for the overload in namespace std;
(x.2) ranges::iter_move(first + n) for the overloads in namespace ranges.

x Let result_last be result + (last - first) for the overloads with no parameter result_last or result_r.

6 Let N be min(last - first, result_last - result).

7 Preconditions: The ranges [first, lastfirst + N) and [result, result + N) do not overlap.

8 Effects: Moves elements in the range [first, lastfirst + N) into the range [result, result + N). For each non-negative integer n < N, performs *(result + n) = std::move(*(first + _n_))E.

9 Returns:~~result + N.~~

(x.1) result + N for the overload in namespace std.
(x.2) {first + N, result + N} for the overloads in namespace ranges.

10 Complexity: Exactly N assignments.

8.28 Modify `swap_ranges` in [alg.swap]

template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2>
  requires indirectly_swappable<I1, I2>
  constexpr ranges::swap_ranges_result<I1, I2>
    ranges::swap_ranges(I1 first1, S1 last1, I2 first2, S2 last2);
template<input_range R1, input_range R2>
  requires indirectly_swappable<iterator_t<R1>, iterator_t<R2>>
  constexpr ranges::swap_ranges_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>>
    ranges::swap_ranges(R1&& r1, R2&& r2);

template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
         random_access_iterator I2, sized_sentinel_for<I2> S2>
  requires indirectly_swappable<I1, I2>
  ranges::swap_ranges_result<I1, I2>
    ranges::swap_ranges(Ep&& exec, I1 first1, S1 last1, I2 first2, S2 last2);
template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2>
  requires indirectly_swappable<iterator_t<R1>, iterator_t<R2>>
  ranges::swap_ranges_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>>
    ranges::swap_ranges(Ep&& exec, R1&& r1, R2&& r2);

1 Let:

(1.1) last2 be first2 + (last1 - first1) for the overloads with no parameter named last2;
(1.2) M be min(last1 - first1, last2 - first2).

2 Preconditions: The two ranges [first1, last1) and [first2, last2) do not overlap. For the overloads in namespace std, *(first1 + n) is swappable with ([swappable.requirements]) *(first2 + n).

3 Effects: For each non-negative integer n < M performs:

(3.1) swap(*(first1 + n), *(first2 + n)) for the overloads in namespace std;
(3.2) ranges::iter_swap(first1 + n, first2 + n) for the overloads in namespace ranges.

4 Returns:

(4.1) last2 for the overloads in namespace std.
(4.2) {first1 + M, first2 + M} for the overloads in namespace ranges.

5 Complexity: Exactly M swaps.

8.29 Modify `transform` in [alg.transform]

template<input_iterator I, sentinel_for<I> S, weakly_incrementable O,
         copy_constructible F, class Proj = identity>
  requires indirectly_writable<O, indirect_result_t<F&, projected<I, Proj>>>
  constexpr ranges::unary_transform_result<I, O>
    ranges::transform(I first1, S last1, O result, F op, Proj proj = {});
template<input_range R, weakly_incrementable O, copy_constructible F,
         class Proj = identity>
  requires indirectly_writable<O, indirect_result_t<F&, projected<iterator_t<R>, Proj>>>
  constexpr ranges::unary_transform_result<borrowed_iterator_t<R>, O>
    ranges::transform(R&& r, O result, F op, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
         random_access_iterator O, sized_sentinel_for<O> OutS,
         copy_constructible F, class Proj = identity>
  requires indirectly_writable<O, indirect_result_t<F&, projected<I, Proj>>>
  ranges::unary_transform_result<I, O>
    ranges::transform(Ep&& exec, I first, S last, O result, OutS result_last,
                      F op, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, random-access-sized-range OutR,
         copy_constructible F, class Proj = identity>
  requires indirectly_writable<iterator_t<OutR>, indirect_result_t<F&, projected<iterator_t<R>, Proj>>>
  ranges::unary_transform_result<borrowed_iterator_t<R>, borrowed_iterator_t<OutR>>
    ranges::transform(Ep&& exec, R&& r, OutR&& result_r, F op, Proj proj = {});

template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
         weakly_incrementable O, copy_constructible F, class Proj1 = identity,
         class Proj2 = identity>
  requires indirectly_writable<O, indirect_result_t<F&, projected<I1, Proj1>,
                                         projected<I2, Proj2>>>
  constexpr ranges::binary_transform_result<I1, I2, O>
    ranges::transform(I1 first1, S1 last1, I2 first2, S2 last2, O result,
                      F binary_op, Proj1 proj1 = {}, Proj2 proj2 = {});
template<input_range R1, input_range R2, weakly_incrementable O,
         copy_constructible F, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_writable<O, indirect_result_t<F&, projected<iterator_t<R1>, Proj1>,
                                         projected<iterator_t<R2>, Proj2>>>
  constexpr ranges::binary_transform_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, O>
    ranges::transform(R1&& r1, R2&& r2, O result,
                      F binary_op, Proj1 proj1 = {}, Proj2 proj2 = {});

template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
         random_access_iterator I2, sized_sentinel_for<I2> S2,
         random_access_iterator O,  sized_sentinel_for<O> OutS,
         copy_constructible F, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_writable<O, indirect_result_t<F&, projected<I1, Proj1>, projected<I2, Proj2>>>
  ranges::binary_transform_result<I1, I2, O>
    ranges::transform(Ep&& exec, I1 first1, S1 last1, I2 first2, S2 last2, O result,
                      OutS result_last, F binary_op, Proj1 proj1 = {}, Proj2 proj2 = {});
template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2, random-access-sized-range OutR,
         copy_constructible F, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_writable<iterator_t<OutR>,
             indirect_result_t<F&, projected<iterator_t<R1>, Proj1>, projected<iterator_t<R2>, Proj2>>>
  ranges::binary_transform_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, borrowed_iterator_t<OutR>>
    ranges::transform(Ep&& exec, R1&& r1, R2&& r2, OutR&& result_r,
                      F binary_op, Proj1 proj1 = {}, Proj2 proj2 = {});

1 Let:

(1.1) last2 be first2 + (last1 - first1) for the overloads with parameter first2 but no parameter last2;
(1.2) NM be last1 - first1 for unary transforms, or min(last1 - first1, last2 - first2) for binary transforms;

(1.x) result_last be result + M for the overloads with no parameter result_last or result_r;
(1.x) N be min(M, result_last - result);

(1.3) E be
- (1.3.1) op(*(first1 + (i - result))) for unary transforms defined in namespace std;
- (1.3.2) binary_op(*(first1 + (i - result)), *(first2 + (i - result))) for binary transforms defined in namespace std;
- (1.3.3) invoke(op, invoke(proj, *(first1 + (i - result)))) for unary transforms defined in namespace ranges;
- (1.3.4) invoke(binary_op, invoke(proj1, *(first1 + (i - result))), invoke(proj2, *(first2 + (i - result)))) for binary transforms defined in namespace ranges.

2 Preconditions: op and binary_op do not invalidate iterators or subranges, nor modify elements in the ranges

(2.1) [first1, first1 + N],
(2.2) [first2, first2 + N], and
(2.3) [result, result + N].

3 Effects: Assigns through every iterator i in the range [result, result + N) a new corresponding value equal to E.

4 Returns:

(4.1) result + N for the overloads defined in namespace std.
(4.2) {first1 + N, result + N} for unary transforms defined in namespace ranges.
(4.3) {first1 + N, first2 + N, result + N} for binary transforms defined in namespace ranges.

5 Complexity: Exactly N applications of op or binary_op, and any projections. ~~This requirement also applies to the overload with an ExecutionPolicy.~~

6 Remarks: result may be equal to first1 or first2.

8.30 Modify `replace` in [alg.replace]

template<input_iterator I, sentinel_for<I> S, class Proj = identity,
         class T1 = projected_value_t<I, Proj>, class T2 = T1>
  requires indirectly_writable<I, const T2&> &&
           indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T1*>
  constexpr I
    ranges::replace(I first, S last, const T1& old_value, const T2& new_value, Proj proj = {});
template<input_range R, class Proj = identity,
         class T1 = projected_value_t<iterator_t<R>, Proj>, class T2 = T1>
  requires indirectly_writable<iterator_t<R>, const T2&> &&
           indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T1*>
  constexpr borrowed_iterator_t<R>
    ranges::replace(R&& r, const T1& old_value, const T2& new_value, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
         class T1 = projected_value_t<I, Proj>, class T2 = T1>
  requires indirectly_writable<I, const T2&> &&
           indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T1*>
  I ranges::replace(Ep&& exec, I first, S last,
                    const T1& old_value, const T2& new_value, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         class T1 = projected_value_t<iterator_t<R>, Proj>, class T2 = T1>
  requires indirectly_writable<iterator_t<R>, const T2&> &&
           indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T1*>
  borrowed_iterator_t<R>
    ranges::replace(Ep&& exec, R&& r,
                    const T1& old_value, const T2& new_value, Proj proj = {});

template<input_iterator I, sentinel_for<I> S, class Proj = identity,
         class T = projected_value_t<I, Proj>,
         indirect_unary_predicate<projected<I, Proj>> Pred>
  requires indirectly_writable<I, const T&>
  constexpr I ranges::replace_if(I first, S last, Pred pred, const T& new_value, Proj proj = {});
template<input_range R, class Proj = identity, class T = projected_value_t<iterator_t<R>, Proj>,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  requires indirectly_writable<iterator_t<R>, const T&>
  constexpr borrowed_iterator_t<R>
    ranges::replace_if(R&& r, Pred pred, const T& new_value, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
         class T = projected_value_t<I, Proj>,
         indirect_unary_predicate<projected<I, Proj>> Pred>
  requires indirectly_writable<I, const T&>
  I ranges::replace_if(Ep&& exec, I first, S last, Pred pred,
                       const T& new_value, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         class T = projected_value_t<iterator_t<R>, Proj>,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  requires indirectly_writable<iterator_t<R>, const T&>
  borrowed_iterator_t<R>
    ranges::replace_if(Ep&& exec, R&& r, Pred pred,
                       const T& new_value, Proj proj = {});

1 Let E be

(1.1) bool(*i == old_value) for replace;
(1.2) bool(pred(*i)) for replace_if;
(1.3) bool(invoke(proj, *i) == old_value) for ranges::replace;
(1.4) bool(invoke(pred, invoke(proj, *i))) for ranges::replace_if.

2 Mandates: new_value is writable ([iterator.requirements.general]) to first.

3 Effects: Substitutes elements referred by the iterator i in the range [first, last) with new_value, when E is true.

4 Returns: last for the overloads in namespace ranges.

5 Complexity: Exactly last - first applications of the corresponding predicate and any projection.

template<input_iterator I, sentinel_for<I> S, class O,
         class Proj = identity, class T1 = projected_value_t<I, Proj>, class T2 = iter_value_t<O>>
  requires indirectly_copyable<I, O> &&
           indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T1*> &&
           output_iterator<O, const T2&>
  constexpr ranges::replace_copy_result<I, O>
    ranges::replace_copy(I first, S last, O result, const T1& old_value, const T2& new_value,
                         Proj proj = {});
template<input_range R, class O, class Proj = identity,
         class T1 = projected_value_t<iterator_t<R>, Proj>, class T2 = iter_value_t<O>>
  requires indirectly_copyable<iterator_t<R>, O> &&
           indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T1*>
           && output_iterator<O, const T2&>
  constexpr ranges::replace_copy_result<borrowed_iterator_t<R>, O>
    ranges::replace_copy(R&& r, O result, const T1& old_value, const T2& new_value,
                         Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
         random_access_iterator O, sized_sentinel_for<O> OutS>,
         class Proj = identity, class T1 = projected_value_t<I, Proj>, class T2 = iter_value_t<O>>
  requires indirectly_copyable<I, O> &&
           indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T1*> &&
           indirectly_writable<O, const T2&>
  ranges::replace_copy_result<I, O>
    ranges::replace_copy(Ep&& exec, I first, S last, O result, OutS result_last,
                         const T1& old_value, const T2& new_value, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, random-access-sized-range OutR,
         class Proj = identity, class T1 = projected_value_t<iterator_t<R>, Proj>,
         class T2 = range_value_t<OutR>>
  requires indirectly_copyable<iterator_t<R>, iterator_t<OutR>> &&
           indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T1*> &&
           indirectly_writable<iterator_t<OutR>, const T2&>
  ranges::replace_copy_result<borrowed_iterator_t<R>, borrowed_iterator_t<OutR>>
    ranges::replace_copy(Ep&& exec, R&& r, OutR&& result_r,
                         const T1& old_value, const T2& new_value, Proj proj = {});

template<input_iterator I, sentinel_for<I> S,class O, class T = iter_value_t<O>,
         class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
  requires indirectly_copyable<I, O> && output_iterator<O, const T&>
  constexpr ranges::replace_copy_if_result<I, O>
    ranges::replace_copy_if(I first, S last, O result, Pred pred, const T& new_value,
                            Proj proj = {});
template<input_range R, class O, class T = iter_value_t<O>, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  requires indirectly_copyable<iterator_t<R>, O> && output_iterator<O, const T&>
  constexpr ranges::replace_copy_if_result<borrowed_iterator_t<R>, O>
    ranges::replace_copy_if(R&& r, O result, Pred pred, const T& new_value,
                            Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
         random_access_iterator O, sized_sentinel_for<O> OutS>, class T = iter_value_t<O>,
         class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
  requires indirectly_copyable<I, O> && indirectly_writable<O, const T&>
  ranges::replace_copy_if_result<I, O>
    ranges::replace_copy_if(Ep&& exec, I first, S last, O result, OutS result_last,
                            Pred pred, const T& new_value, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, random-access-sized-range OutR,
         class T = range_value_t<OutR>, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  requires indirectly_copyable<iterator_t<R>, iterator_t<OutR>> &&
           indirectly_writable<iterator_t<OutR>, const T&>
  ranges::replace_copy_if_result<borrowed_iterator_t<R>, borrowed_iterator_t<OutR>>
    ranges::replace_copy_if(Ep&& exec, R&& r, OutR&& result_r,
                            Pred pred, const T& new_value, Proj proj = {});

6 Let E be

(6.1) bool(*(first + (i - result)) == old_value) for replace_copy;
(6.2) bool(pred(*(first + (i - result)))) for replace_copy_if;
(6.3) bool(invoke(proj, *(first + (i - result))) == old_value) for ranges::replace_copy;
(6.4) bool(invoke(pred, invoke(proj, *(first + (i - result))))) for ranges::replace_copy_if.

x Let

(x.1) result_last be result + (last - first) for the overloads with no parameter result_last or result_r;
(x.2) N be min(last - first, result_last - result).

7 Mandates: The results of the expressions *first and new_value are writable ([iterator.requirements.general]) to result.

8 Preconditions: The ranges [first, lastfirst + N) and [result, result + (last - first)N) do not overlap.

9 Effects: Assigns through every iterator i in the range [result, result + (last - first)N) a new corresponding value

(9.1) new_value if E is true or
(9.2) *(first + (i - result)) otherwise.

10 Returns:

(10.1) result + (last - first)N for the overloads in namespace std.
(10.2) {lastfirst + N, `result + (last - first)N`} for the overloads in namespace ranges.

11 Complexity: Exactly ~~last - first~~N applications of the corresponding predicate and any projection.

8.31 Modify `fill` in [alg.fill]

template<class O, sentinel_for<O> S, class T = iter_value_t<O>>
  requires output_iterator<O, const T&>
  constexpr O ranges::fill(O first, S last, const T& value);
template<class R, class T = range_value_t<R>>
  requires output_range<R, const T&>
  constexpr borrowed_iterator_t<R> ranges::fill(R&& r, const T& value);
template<class O, class T = iter_value_t<O>>
  requires output_iterator<O, const T&>
  constexpr O ranges::fill_n(O first, iter_difference_t<O> n, const T& value);

template<execution-policy Ep, random_access_iterator O, sized_sentinel_for<O> S,
         class T = iter_value_t<O>>
  requires indirectly_writable<O, const T&>
  O ranges::fill(Ep&& exec, O first, S last, const T& value);
template<execution-policy Ep, random-access-sized-range R, class T = range_value_t<R>>
  requires indirectly_writable<iterator_t<R>, const T&>
  borrowed_iterator_t<R> ranges::fill(Ep&& exec, R&& r, const T& value);
template<execution-policy Ep, random_access_iterator O, class T = iter_value_t<O>>
  requires indirectly_writable<O, const T&>
  O ranges::fill_n(Ep&& exec, O first, iter_difference_t<O> n, const T& value);

1 Let N be max(0, n) for the fill_n algorithms, and last - first for the fill algorithms.

2 Mandates: The expression value is writable ([iterator.requirements.general]) to the output iterator. The type Size is convertible to an integral type ([conv.integral], [class.conv]).

3 Effects: Assigns value through all the iterators in the range [first, first + N).

4 Returns: first + N.

5 Complexity: Exactly N assignments.

8.32 Modify `generate` in [alg.generate]

template<input_or_output_iterator O, sentinel_for<O> S, copy_constructible F>
  requires invocable<F&> && indirectly_writable<O, invoke_result_t<F&>>
  constexpr O ranges::generate(O first, S last, F gen);
template<class R, copy_constructible F>
  requires invocable<F&> && output_range<R, invoke_result_t<F&>>
  constexpr borrowed_iterator_t<R> ranges::generate(R&& r, F gen);
template<input_or_output_iterator O, copy_constructible F>
  requires invocable<F&> && indirectly_writable<O, invoke_result_t<F&>>
  constexpr O ranges::generate_n(O first, iter_difference_t<O> n, F gen);

template<execution-policy Ep, random_access_iterator O, sized_sentinel_for<O> S, copy_constructible F>
  requires invocable<F&> && indirectly_writable<O, invoke_result_t<F&>>
  O ranges::generate(Ep&& exec, O first, S last, F gen);
template<execution-policy Ep, random-access-sized-range R, copy_constructible F>
  requires invocable<F&> && indirectly_writable<iterator_t<R>, invoke_result_t<F&>>
  borrowed_iterator_t<R> ranges::generate(Ep&& exec, R&& r, F gen);
template<execution-policy Ep, random_access_iterator O, copy_constructible F>
  requires invocable<F&> && indirectly_writable<O, invoke_result_t<F&>>
  O ranges::generate_n(Ep&& exec, O first, iter_difference_t<O> n, F gen);

1 Let N be max(0, n) for the generate_n algorithms, and last - first for the generate algorithms.

2 Mandates: Size is convertible to an integral type ([conv.integral], [class.conv]).

3 Effects: Assigns the result of successive evaluations of gen() through each iterator in the range [first, first + N).

4 Returns: first + N.

5 Complexity: Exactly N evaluations of gen() and assignments.

8.33 Modify `remove` in [alg.remove]

template<permutable I, sentinel_for<I> S, class Proj = identity,
         class T = projected_value_t<I, Proj>>
  requires indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
  constexpr subrange<I> ranges::remove(I first, S last, const T& value, Proj proj = {});
template<forward_range R, class Proj = identity,
         class T = projected_value_t<iterator_t<R>, Proj>>
  requires permutable<iterator_t<R>> &&
           indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*>
  constexpr borrowed_subrange_t<R>
    ranges::remove(R&& r, const T& value, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
         class T = projected_value_t<I, Proj>>
  requires indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
  subrange<I> ranges::remove(Ep&& exec, I first, S last, const T& value, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         class T = projected_value_t<iterator_t<R>, Proj>>
  requires permutable<iterator_t<R>> &&
           indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*>
  borrowed_subrange_t<R> ranges::remove(Ep&& exec, R&& r, const T& value, Proj proj = {});

template<permutable I, sentinel_for<I> S, class Proj = identity,
         indirect_unary_predicate<projected<I, Proj>> Pred>
  constexpr subrange<I> ranges::remove_if(I first, S last, Pred pred, Proj proj = {});
template<forward_range R, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  requires permutable<iterator_t<R>>
  constexpr borrowed_subrange_t<R>
    ranges::remove_if(R&& r, Pred pred, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
         indirect_unary_predicate<projected<I, Proj>> Pred>
  subrange<I> ranges::remove_if(Ep&& exec, I first, S last, Pred pred, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  requires permutable<iterator_t<R>>
  borrowed_subrange_t<R> ranges::remove_if(Ep&& exec, R&& r, Pred pred, Proj proj = {});

1 Let E be

(1.1) bool(*i == value) for remove;
(1.2) bool(pred(*i)) for remove_if;
(1.3) bool(invoke(proj, *i) == value) for ranges::remove;
(1.4) bool(invoke(pred, invoke(proj, *i))) for ranges::remove_if.

2 Preconditions: For the algorithms in namespace std, the type of *first meets the Cpp17MoveAssignable requirements (Table 33).

3 Effects: Eliminates all the elements referred to by iterator i in the range [first, last) for which E holds.

4 Returns: Let j be the end of the resulting range. Returns:

(4.1) j for the overloads in namespace std.
(4.2) {j, last} for the overloads in namespace ranges.

5 Complexity: Exactly last - first applications of the corresponding predicate and any projection.

6 Remarks: Stable ([algorithm.stable]).

7 [Note 1: Each element in the range [ret, last), where ret is the returned value, has a valid but unspecified state, because the algorithms can eliminate elements by moving from elements that were originally in that range. — end note]

template<input_iterator I, sentinel_for<I> S, weakly_incrementable O,
         class Proj = identity, class T = projected_value_t<I, Proj>>
  requires indirectly_copyable<I, O> &&
           indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
  constexpr ranges::remove_copy_result<I, O>
    ranges::remove_copy(I first, S last, O result, const T& value, Proj proj = {});
template<input_range R, weakly_incrementable O, class Proj = identity,
         class T = projected_value_t<iterator_t<R>, Proj>>
  requires indirectly_copyable<iterator_t<R>, O> &&
           indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*>
  constexpr ranges::remove_copy_result<borrowed_iterator_t<R>, O>
    ranges::remove_copy(R&& r, O result, const T& value, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
         random_access_iterator O, sized_sentinel_for<O> OutS>,
         class Proj = identity, class T = projected_value_t<I, Proj>>
  requires indirectly_copyable<I, O> &&
           indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
  ranges::remove_copy_result<I, O>
    ranges::remove_copy(Ep&& exec, I first, S last, O result,  OutS result_last,
                        const T& value, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, random-access-sized-range OutR, class Proj = identity,
         class T = projected_value_t<iterator_t<R>, Proj>>
  requires indirectly_copyable<iterator_t<R>, iterator_t<OutR>> &&
           indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*>
  ranges::remove_copy_result<borrowed_iterator_t<R>, borrowed_iterator_t<OutR>>
    ranges::remove_copy(Ep&& exec, R&& r, OutR&& result_r, const T& value, Proj proj = {});

template<input_iterator I, sentinel_for<I> S, weakly_incrementable O,
         class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
  requires indirectly_copyable<I, O>
  constexpr ranges::remove_copy_if_result<I, O>
    ranges::remove_copy_if(I first, S last, O result, Pred pred, Proj proj = {});
template<input_range R, weakly_incrementable O, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  requires indirectly_copyable<iterator_t<R>, O>
  constexpr ranges::remove_copy_if_result<borrowed_iterator_t<R>, O>
    ranges::remove_copy_if(R&& r, O result, Pred pred, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
         random_access_iterator O, sized_sentinel_for<O> OutS>,
         class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
  requires indirectly_copyable<I, O>
  ranges::remove_copy_if_result<I, O>
    ranges::remove_copy_if(Ep&& exec, I first, S last, O result, OutS result_last,
                           Pred pred, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, random-access-sized-range OutR, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  requires indirectly_copyable<iterator_t<R>, iterator_t<OutR>>
  ranges::remove_copy_if_result<borrowed_iterator_t<R>, borrowed_iterator_t<OutR>>
    ranges::remove_copy_if(Ep&& exec, R&& r, OutR&& result_r, Pred pred, Proj proj = {});

8 Let E be

(8.1) bool(*i == value) for remove_copy;
(8.2) bool(pred(*i)) for remove_copy_if;
(8.3) bool(invoke(proj, *i) == value) for ranges::remove_copy;
(8.4) bool(invoke(pred, invoke(proj, *i))) for ranges::remove_copy_if.

9 Let N be the number of elements in [first, last) for which E is false.

x Let

(x.1) result_last be result + (last - first) for the overloads with no parameter result_last or result_r;
(x.2) M be the number of elements in [first, last) for which E is false;
(x.3) N be min(M, result_last - result).

10 Mandates: *first is writable ([iterator.requirements.general]) to result.

11 Preconditions: The ranges [first, last) and [result, result + (last - first)N) do not overlap.

[Note 2: For the overloads with an ExecutionPolicy, there might be a performance cost if iterator_traits<ForwardIterator1>::value_type does not meet the Cpp17MoveConstructible (Table 31) requirements. For the overloads with an execution-policy, there might be a performance cost if iter_value_t<I> is not move_constructible. — end note]

12 Effects: Copies ~~all the~~N elements referred to by the iterator i in the range [first, last) for which E is false into the range [result, result + N).

13 Returns:

(13.1) result + N, for the algorithms in namespace std.
(13.2) {lastj, result + N}, for the algorithms in namespace ranges, where the iterator j points to a position in the range [first, last) past the last copied element if result + N == result_last, and j == last otherwise.

14 Complexity: ~~Exactly~~At most last - first applications of the corresponding predicate and any projection.

15 Remarks: Stable ([algorithm.stable]).

8.34 Modify `unique` in [alg.unique]

template<permutable I, sentinel_for<I> S, class Proj = identity,
         indirect_equivalence_relation<projected<I, Proj>> C = ranges::equal_to>
  constexpr subrange<I> ranges::unique(I first, S last, C comp = {}, Proj proj = {});
template<forward_range R, class Proj = identity,
         indirect_equivalence_relation<projected<iterator_t<R>, Proj>> C = ranges::equal_to>
  requires permutable<iterator_t<R>>
  constexpr borrowed_subrange_t<R>
    ranges::unique(R&& r, C comp = {}, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
         class Proj = identity,
         indirect_equivalence_relation<projected<I, Proj>> C = ranges::equal_to>
  requires permutable<I>
  subrange<I> ranges::unique(Ep&& exec, I first, S last, C comp = {}, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         indirect_equivalence_relation<projected<iterator_t<R>, Proj>> C = ranges::equal_to>
  requires permutable<iterator_t<R>>
  borrowed_subrange_t<R> ranges::unique(Ep&& exec, R&& r, C comp = {}, Proj proj = {});

1 Let pred be equal_to{} for the overloads with no parameter pred, and let E be

(1.1) bool(pred(*(i - 1), *i)) for the overloads in namespace std;
(1.2) bool(invoke(comp, invoke(proj, *(i - 1)), invoke(proj, *i))) for the overloads in namespace ranges.

2 Preconditions: For the overloads in namespace std, pred is an equivalence relation and the type of *first meets the Cpp17MoveAssignable requirements (Table 33).

3 Effects: For a nonempty range, eliminates all but the first element from every consecutive group of equivalent elements referred to by the iterator i in the range [first + 1, last) for which E is true.

4 Returns: Let j be the end of the resulting range. Returns:

(4.1) j for the overloads in namespace std.
(4.2) {j, last} for the overloads in namespace ranges.

5 Complexity: For nonempty ranges, exactly (last - first) - 1 applications of the corresponding predicate and no more than twice as many applications of any projection.

template<input_iterator I, sentinel_for<I> S, weakly_incrementable O, class Proj = identity,
         indirect_equivalence_relation<projected<I, Proj>> C = ranges::equal_to>
  requires indirectly_copyable<I, O> &&
           (forward_iterator<I> ||
            (input_iterator<O> && same_as<iter_value_t<I>, iter_value_t<O>>) ||
            indirectly_copyable_storable<I, O>)
  constexpr ranges::unique_copy_result<I, O>
    ranges::unique_copy(I first, S last, O result, C comp = {}, Proj proj = {});
template<input_range R, weakly_incrementable O, class Proj = identity,
         indirect_equivalence_relation<projected<iterator_t<R>, Proj>> C = ranges::equal_to>
  requires indirectly_copyable<iterator_t<R>, O> &&
           (forward_iterator<iterator_t<R>> ||
            (input_iterator<O> && same_as<range_value_t<R>, iter_value_t<O>>) ||
            indirectly_copyable_storable<iterator_t<R>, O>)
  constexpr ranges::unique_copy_result<borrowed_iterator_t<R>, O>
    ranges::unique_copy(R&& r, O result, C comp = {}, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
         random_access_iterator O, sized_sentinel_for<O> OutS>, class Proj = identity,
         indirect_equivalence_relation<projected<I, Proj>> C = ranges::equal_to>
  requires indirectly_copyable<I, O>
  ranges::unique_copy_result<I, O>
    ranges::unique_copy(Ep&& exec, I first, S last, O result, OutS result_last,
                        C comp = {}, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, random-access-sized-range OutR,
         class Proj = identity,
         indirect_equivalence_relation<projected<iterator_t<R>, Proj>> C = ranges::equal_to>
  requires indirectly_copyable<iterator_t<R>, iterator_t<OutR>>
  ranges::unique_copy_result<borrowed_iterator_t<R>, borrowed_iterator_t<OutR>>
    ranges::unique_copy(Ep&& exec, R&& r, OutR&& result_r,
                        C comp = {}, Proj proj = {});

6 Let pred be equal_to{} for the overloads in namespace std with no parameter pred, and let E be

(6.1) bool(pred(*i, *(i - 1))) for the overloads in namespace std;
(6.2) bool(invoke(comp, invoke(proj, *i), invoke(proj, *(i - 1)))) for the overloads in namespace ranges.

Let

(x.1) result_last be result + (last - first) for the overloads with no parameter result_last or result_r;
(x.2) M be the number of elements in the range [first + 1, last) for which E is false.
(x.3) N be min(M + 1, result_last - result).

7 Mandates: *first is writable ([iterator.requirements.general]) to result.

8 Preconditions:

(8.1) The ranges [first, last) and [result, result + (last - first)N) do not overlap.
(8.2) For the overloads in namespace std:
- (8.2.1) The comparison function is an equivalence relation.
- (8.2.2) For the overloads with no ExecutionPolicy, let T be the value type of InputIterator. If InputIterator models forward_iterator ([iterator.concept.forward]), then there are no additional requirements for T. Otherwise, if OutputIterator meets the Cpp17ForwardIterator requirements and its value type is the same as T, then T meets the Cpp17CopyAssignable (Table 34) requirements. Otherwise, T meets both the Cpp17CopyConstructible (Table 32) and Cpp17CopyAssignable requirements.
  
  [Note 1: For the overloads with an ExecutionPolicy, there might be a performance cost if the value type of ForwardIterator1 does not meet both the Cpp17CopyConstructible and Cpp17CopyAssignable requirements. — end note]

[Note 1: For the overloads with an ExecutionPolicy, there might be a performance cost if the value type of ForwardIterator1 does not meet both the Cpp17CopyConstructible and Cpp17CopyAssignable requirements. For the overloads with an execution-policy, there might be a performance cost if iter_value_t<I> does not meet both the copy_constructible and copy_assignable. — end note]

9 Effects: Copies only the first element from ~~every~~N consecutive groups of equal elements referred to by the iterator i in the range [first, last) for which E holds into a range [result, result + N).

10 Returns:

(10.1) result + N for the overloads in namespace std.
(10.2) {lastj, result + N} for the overloads in namespace ranges, where the iterator j points to a position in the range [first, last) past the last copied element if result + N == result_last, and j == last otherwise.

11 Complexity: ~~Exactly~~At most last - first - 1 applications of the corresponding predicate and no more than twice as many applications of any projection.

8.35 Modify `reverse` in [alg.reverse]

template<bidirectional_iterator I, sentinel_for<I> S>
  requires permutable<I>
  constexpr I ranges::reverse(I first, S last);
template<bidirectional_range R>
  requires permutable<iterator_t<R>>
  constexpr borrowed_iterator_t<R> ranges::reverse(R&& r);

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S>
  requires permutable<I>
  I ranges::reverse(Ep&& exec, I first, S last);
template<execution-policy Ep, random-access-sized-range R>
  requires permutable<iterator_t<R>>
  borrowed_iterator_t<R> ranges::reverse(Ep&& exec, R&& r);

1 Preconditions: For the overloads in namespace std, BidirectionalIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]).

2 Effects: For each non-negative integer i < (last - first) / 2, applies std::iter_swap, or ranges::iter_swap for the overloads in namespace ranges, to all pairs of iterators first + i, (last - i) - 1.

3 Returns: last for the overloads in namespace ranges.

4 Complexity: Exactly (last - first)/2 swaps.

template<bidirectional_iterator I, sentinel_for<I> S, weakly_incrementable O>
  requires indirectly_copyable<I, O>
  constexpr ranges::reverse_copy_result<I, O>
    ranges::reverse_copy(I first, S last, O result);
template<bidirectional_range R, weakly_incrementable O>
  requires indirectly_copyable<iterator_t<R>, O>
  constexpr ranges::reverse_copy_result<borrowed_iterator_t<R>, O>
    ranges::reverse_copy(R&& r, O result);

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
         random_access_iterator O, sized_sentinel_for<O> OutS>
  requires indirectly_copyable<I, O>
  ranges::reverse_copy_result<I, O>
    ranges::reverse_copy(Ep&& exec, I first, S last, O result, OutS result_last);
template<execution-policy Ep, random-access-sized-range R, random-access-sized-range OutR>
  requires indirectly_copyable<iterator_t<R>, iterator_t<OutR>>
  ranges::reverse_copy_result<borrowed_iterator_t<R>, borrowed_iterator_t<OutR>>
    ranges::reverse_copy(Ep&& exec, R&& r, OutR&& result_r);

x Let result_last be result + (last - first) for the overloads with no parameter result_last or result_r.

5 Let N be ~~last - first~~min(last - first, result_last - result).

x Let NEW_FIRST be first + (last - first) - N.

6 Preconditions: The ranges [firstNEW_FIRST, last) and [result, result + N) do not overlap.

7 Effects: Copies the range [firstNEW_FIRST, last) to the range [result, result + N) such that for every non-negative integer i < N the following assignment takes place: *(result + N - 1 - i) = *(firstNEW_FIRST + i).

8 Returns:

(8.1) result + N for the overloads in namespace std.
(8.2) {lastNEW_FIRST, result + N} for the overloads in namespace ranges.

9 Complexity: Exactly N assignments.

8.36 Modify `rotate` in [alg.rotate]

template<permutable I, sentinel_for<I> S>
  constexpr subrange<I> ranges::rotate(I first, I middle, S last);

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S>
  requires permutable<I>
  subrange<I> ranges::rotate(Ep&& exec, I first, I middle, S last);

1 Preconditions: [first, middle) and [middle, last) are valid ranges. For the overloads in namespace std, ForwardIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]), and the type of *first meets the Cpp17MoveConstructible (Table 31) and Cpp17MoveAssignable (Table 33) requirements.

2 Effects: For each non-negative integer i < (last - first), places the element from the position first + i into position first + (i + (last - middle)) % (last - first).

[Note 1: This is a left rotate. — end note]

3 Returns:

(3.1) first + (last - middle) for the overloads in namespace std.
(3.2) {first + (last - middle), last} for the overload in namespace ranges.

4 Complexity: At most last - first swaps.

template<forward_range R>
  requires permutable<iterator_t<R>>
  constexpr borrowed_subrange_t<R> ranges::rotate(R&& r, iterator_t<R> middle);

Effects: Equivalent to: return ranges::rotate(ranges::begin(r), middle, ranges::end(r));

template<execution-policy Ep, random-access-sized-range R>
  requires permutable<iterator_t<R>>
  borrowed_subrange_t<R> ranges::rotate(Ep&& exec, R&& r, iterator_t<R> middle);

Effects: Equivalent to: return ranges::rotate(std::forward<Ep>(exec), ranges::begin(r), middle, ranges::end(r));

8.37 Modify `shift` in [alg.shift]

template<permutable I, sentinel_for<I> S>
  constexpr subrange<I> ranges::shift_left(I first, S last, iter_difference_t<I> n);
template<forward_range R>
  requires permutable<iterator_t<R>>
  constexpr borrowed_subrange_t<R> ranges::shift_left(R&& r, range_difference_t<R> n)

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S>
  requires permutable<I>
  subrange<I> ranges::shift_left(Ep&& exec, I first, S last, iter_difference_t<I> n);
template<execution-policy Ep, random-access-sized-range R>
  requires permutable<iterator_t<R>>
  borrowed_subrange_t<R> ranges::shift_left(Ep&& exec, R&& r, range_difference_t<R> n);

1 Preconditions: n >= 0 is true. For the overloads in namespace std, the type of *first meets the Cpp17MoveAssignable requirements.

2 Effects: If n == 0 or n >= last - first, does nothing. Otherwise, moves the element from position first + n + i into position first + i for each non-negative integer i < (last - first) - n. For the overloads without an ~~ExecutionPolicy template parameter~~execution policy, does so in order starting from i = 0 and proceeding to i = (last - first) - n - 1.

3 Returns: Let NEW_LAST be first + (last - first - n) if n < last - first, otherwise first.

(3.1) NEW_LAST for the overloads in namespace std.
(3.2) {first, NEW_LAST} for the overloads in namespace ranges.

4 Complexity: At most (last - first) - n assignments.

template<permutable I, sentinel_for<I> S>
  constexpr subrange<I> ranges::shift_right(I first, S last, iter_difference_t<I> n);
template<forward_range R>
  requires permutable<iterator_t<R>>
  constexpr borrowed_subrange_t<R> ranges::shift_right(R&& r, range_difference_t<R> n);

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S>
  requires permutable<I>
  subrange<I> ranges::shift_right(Ep&& exec, I first, S last, iter_difference_t<I> n);
template<execution-policy Ep, random-access-sized-range R>
  requires permutable<iterator_t<R>>
  borrowed_subrange_t<R> ranges::shift_right(Ep&& exec, R&& r, range_difference_t<R> n);

5 Preconditions: n >= 0 is true. For the overloads in namespace std, the type of *first meets the Cpp17MoveAssignable requirements, and ForwardIterator meets the Cpp17BidirectionalIterator requirements ([bidirectional.iterators]) or the Cpp17ValueSwappable requirements.

6 Effects: If n == 0 or n >= last - first, does nothing. Otherwise, moves the element from position first + i into position first + n + i for each non-negative integer i < (last - first) - n. Does so in order starting from i = (last - first) - n - 1 and proceeding to i = 0 if

(6.1) for the overload in namespace std without an ExecutionPolicy template parameter, ForwardIterator meets the Cpp17BidirectionalIterator requirements,
(6.2) for the overloads in namespace ranges without an execution-policy, I models bidirectional_iterator.

7 Returns: Let NEW_FIRST be first + n if n < last - first, otherwise last.

(7.1) NEW_FIRST for the overloads in namespace std.
(7.2) {NEW_FIRST, last} for the overloads in namespace ranges.

8 Complexity: At most (last - first) - n assignments or swaps.

8.38 Modify `sort` in [sort]

template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
         class Proj = identity>
  requires sortable<I, Comp, Proj>
  constexpr I
    ranges::sort(I first, S last, Comp comp = {}, Proj proj = {});
template<random_access_range R, class Comp = ranges::less, class Proj = identity>
  requires sortable<iterator_t<R>, Comp, Proj>
  constexpr borrowed_iterator_t<R>
    ranges::sort(R&& r, Comp comp = {}, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Comp = ranges::less,
         class Proj = identity>
  requires sortable<I, Comp, Proj>
  I ranges::sort(Ep&& exec, I first, S last, Comp comp = {}, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Comp = ranges::less, class Proj = identity>
  requires sortable<iterator_t<R>, Comp, Proj>
  borrowed_iterator_t<R> ranges::sort(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {});

1 Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.

2 Preconditions: For the overloads in namespace std, RandomAccessIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]) and the type of *first meets the Cpp17MoveConstructible (Table 31) and Cpp17MoveAssignable (Table 33) requirements.

3 Effects: Sorts the elements in the range [first, last) with respect to comp and proj.

4 Returns: last for the overloads in namespace ranges.

5 Complexity: Let N be last - first. O(NlogN) comparisons and projections.

8.39 Modify `stable_sort` in [stable.sort]

template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
         class Proj = identity>
  requires sortable<I, Comp, Proj>
  constexpr I ranges::stable_sort(I first, S last, Comp comp = {}, Proj proj = {});
template<random_access_range R, class Comp = ranges::less, class Proj = identity>
  requires sortable<iterator_t<R>, Comp, Proj>
  constexpr borrowed_iterator_t<R>
    ranges::stable_sort(R&& r, Comp comp = {}, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Comp = ranges::less,
         class Proj = identity>
  requires sortable<I, Comp, Proj>
  I ranges::stable_sort(Ep&& exec, I first, S last, Comp comp = {}, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Comp = ranges::less, class Proj = identity>
  requires sortable<iterator_t<R>, Comp, Proj>
  borrowed_iterator_t<R> ranges::stable_sort(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {});

1 Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.

3 Effects: Sorts the elements in the range [first, last) with respect to comp and proj.

4 Returns: last for the overloads in namespace ranges.

5 Complexity: Let N be last - first. If enough extra memory is available, Nlog(N) comparisons. Otherwise, at most Nlog²(N) comparisons. In either case, twice as many projections as the number of comparisons.

6 Remarks: Stable ([algorithm.stable]).

8.40 Modify `partial_sort` in [partial.sort]

template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
         class Proj = identity>
  requires sortable<I, Comp, Proj>
  constexpr I
    ranges::partial_sort(I first, I middle, S last, Comp comp = {}, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Comp = ranges::less,
         class Proj = identity>
  requires sortable<I, Comp, Proj>
  I ranges::partial_sort(Ep&& exec, I first, I middle, S last, Comp comp = {}, Proj proj = {});

1 Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.

2 Preconditions: [first, middle) and [middle, last) are valid ranges. For the overloads in namespace std, RandomAccessIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]) and the type of *first meets the Cpp17MoveConstructible (Table 31) and Cpp17MoveAssignable (Table 33) requirements.

3 Effects: Places the first middle - first elements from the range [first, last) as sorted with respect to comp and proj into the range [first, middle). The rest of the elements in the range [middle, last) are placed in an unspecified order.

4 Returns: last for the overload in namespace ranges.

5 Complexity: Approximately (last - first) * log(middle - first) comparisons, and twice as many projections.

template<random_access_range R, class Comp = ranges::less, class Proj = identity>
  requires sortable<iterator_t<R>, Comp, Proj>
  constexpr borrowed_iterator_t<R>
    ranges::partial_sort(R&& r, iterator_t<R> middle, Comp comp = {}, Proj proj = {});

Effects: Equivalent to: return ranges::partial_sort(ranges::begin(r), middle, ranges::end(r), comp, proj);

template<execution-policy Ep, random-access-sized-range R, class Comp = ranges::less, class Proj = identity>
  requires sortable<iterator_t<R>, Comp, Proj>
  borrowed_iterator_t<R> ranges::partial_sort(Ep&& exec, R&& r, iterator_t<R> middle,
                                              Comp comp = {}, Proj proj = {});

Effects: Equivalent to: return ranges::partial_sort(std::forward<Ep>(exec), ranges::begin(r), middle, ranges::end(r), comp, proj);

8.41 Modify `partial_sort_copy` in [partial.sort.copy]

template<input_iterator I1, sentinel_for<I1> S1, random_access_iterator I2, sentinel_for<I2> S2,
         class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_copyable<I1, I2> && sortable<I2, Comp, Proj2> &&
           indirect_strict_weak_order<Comp, projected<I1, Proj1>, projected<I2, Proj2>>
  constexpr ranges::partial_sort_copy_result<I1, I2>
    ranges::partial_sort_copy(I1 first, S1 last, I2 result_first, S2 result_last,
                              Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<input_range R1, random_access_range R2, class Comp = ranges::less,
         class Proj1 = identity, class Proj2 = identity>
  requires indirectly_copyable<iterator_t<R1>, iterator_t<R2>> &&
           sortable<iterator_t<R2>, Comp, Proj2> &&
           indirect_strict_weak_order<Comp, projected<iterator_t<R1>, Proj1>,
                                      projected<iterator_t<R2>, Proj2>>
  constexpr ranges::partial_sort_copy_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>>
    ranges::partial_sort_copy(R1&& r, R2&& result_r, Comp comp = {},
                              Proj1 proj1 = {}, Proj2 proj2 = {});

template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
         random_access_iterator I2, sized_sentinel_for<I2> S2,
         class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
  requires indirectly_copyable<I1, I2> && sortable<I2, Comp, Proj2> &&
           indirect_strict_weak_order<Comp, projected<I1, Proj1>, projected<I2, Proj2>>
  ranges::partial_sort_copy_result<I1, I2>
    ranges::partial_sort_copy(Ep&& exec, I1 first, S1 last, I2 result_first, S2 result_last,
                              Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2, class Comp = ranges::less,
         class Proj1 = identity, class Proj2 = identity>
  requires indirectly_copyable<iterator_t<R1>, iterator_t<R2>> &&
           sortable<iterator_t<R2>, Comp, Proj2> &&
           indirect_strict_weak_order<Comp, projected<iterator_t<R1>, Proj1>,
                                      projected<iterator_t<R2>, Proj2>>
  ranges::partial_sort_copy_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>>
    ranges::partial_sort_copy(Ep&& exec, R1&& r, R2&& result_r, Comp comp = {},
                              Proj1 proj1 = {}, Proj2 proj2 = {});

1 Let N be min(last - first, result_last - result_first). Let comp be less{}, and proj1 and proj2 be identity{} for the overloads with no parameters by those names.

2 Mandates: For the overloads in namespace std, the expression *first is writable ([iterator.requirements.general]) to result_first.

3 Preconditions: For the overloads in namespace std, RandomAccessIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]), the type of *result_first meets the Cpp17MoveConstructible (Table 31) and Cpp17MoveAssignable (Table 33) requirements.

4 For iterators a1 and b1 in [first, last), and iterators x2 and y2 in [result_first, result_last), after evaluating the assignment *y2 = *b1, let E be the value of

bool(invoke(comp, invoke(proj1, *a1), invoke(proj2, *y2))).

Then, after evaluating the assignment *x2 = *a1, E is equal to

bool(invoke(comp, invoke(proj2, *x2), invoke(proj2, *y2))).

[Note 1: Writing a value from the input range into the output range does not affect how it is ordered by comp and proj1 or proj2. — end note]

5 Effects: Places the first N elements as sorted with respect to comp and proj2 into the range [result_first, result_first + N).

6 Returns:

(6.1) result_first + N for the overloads in namespace std.
(6.2) {last, result_first + N} for the overloads in namespace ranges.

7 Complexity: Approximately (last - first) * logN comparisons, and twice as many projections.

8.42 Modify `is_sorted` in [is.sorted]

template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
         indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
  constexpr bool ranges::is_sorted(I first, S last, Comp comp = {}, Proj proj = {});
template<forward_range R, class Proj = identity,
         indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
  constexpr bool ranges::is_sorted(R&& r, Comp comp = {}, Proj proj = {});

Effects: Equivalent to: return ranges::is_sorted_until(first, last, comp, proj) == last;

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S, class Proj = identity,
         indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
  bool ranges::is_sorted(Ep&& exec, I first, S last, Comp comp = {}, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
  bool ranges::is_sorted(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {});

Effects: Equivalent to: return ranges::is_sorted_until(std::forward<Ep>(exec), first, last, comp, proj) == last;

template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
         indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
  constexpr I ranges::is_sorted_until(I first, S last, Comp comp = {}, Proj proj = {});
template<forward_range R, class Proj = identity,
         indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
  constexpr borrowed_iterator_t<R>
    ranges::is_sorted_until(R&& r, Comp comp = {}, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
         class Proj = identity,
         indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
  I ranges::is_sorted_until(Ep&& exec, I first, S last, Comp comp = {}, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
  borrowed_iterator_t<R> ranges::is_sorted_until(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {});

6 Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.

7 Returns: The last iterator i in [first, last] for which the range [first, i) is sorted with respect to comp and proj.

8 Complexity: Linear.

8.43 Modify `nth_element` in [alg.nth.element]

template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
         class Proj = identity>
  requires sortable<I, Comp, Proj>
  constexpr I
    ranges::nth_element(I first, I nth, S last, Comp comp = {}, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
         class Comp = ranges::less, class Proj = identity>
  requires sortable<I, Comp, Proj>
  I ranges::nth_element(Ep&& exec, I first, I nth, S last, Comp comp = {}, Proj proj = {});

1 Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.

2 Preconditions: [first, nth) and [nth, last) are valid ranges. For the overloads in namespace std, RandomAccessIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]), and the type of *first meets the Cpp17MoveConstructible (Table 31) and Cpp17MoveAssignable (Table 33) requirements.

3 Effects: After nth_element the element in the position pointed to by nth is the element that would be in that position if the whole range were sorted with respect to comp and proj, unless nth == last. Also for every iterator i in the range [first, nth) and every iterator j in the range [nth, last) it holds that: bool(invoke(comp, invoke(proj, *j), invoke(proj, *i))) is false.

4 Returns: last for the overload in namespace ranges.

5 Complexity: For the overloads with no ~~ExecutionPolicy~~execution policy, linear on average. For the overloads with an ~~ExecutionPolicy~~execution policy, O(N) applications of the predicate, and O(NlogN) swaps, where N = last - first.

template<random_access_range R, class Comp = ranges::less, class Proj = identity>
  requires sortable<iterator_t<R>, Comp, Proj>
  constexpr borrowed_iterator_t<R>
    ranges::nth_element(R&& r, iterator_t<R> nth, Comp comp = {}, Proj proj = {});

Effects: Equivalent to: return ranges::nth_element(ranges::begin(r), nth, ranges::end(r), comp, proj);

template<execution-policy Ep, random-access-sized-range R, class Comp = ranges::less,
         class Proj = identity>
  requires sortable<iterator_t<R>, Comp, Proj>
  borrowed_iterator_t<R> ranges::nth_element(Ep&& exec, R&& r, iterator_t<R> nth,
                                             Comp comp = {}, Proj proj = {});

Effects: Equivalent to: return ranges::nth_element(std::forward<Ep>(exec), ranges::begin(r), nth, ranges::end(r), comp, proj);

8.44 Modify `partitions` in [alg.partitions]

template<input_iterator I, sentinel_for<I> S, class Proj = identity,
         indirect_unary_predicate<projected<I, Proj>> Pred>
  constexpr bool ranges::is_partitioned(I first, S last, Pred pred, Proj proj = {});
template<input_range R, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  constexpr bool ranges::is_partitioned(R&& r, Pred pred, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
         class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
  bool ranges::is_partitioned(Ep&& exec, I first, S last, Pred pred, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  bool ranges::is_partitioned(Ep&& exec, R&& r, Pred pred, Proj proj = {});

1 Let proj be identity{} for the overloads with no parameter named proj.

2 Returns: true if and only if the elements e of [first, last) are partitioned with respect to the expression bool(invoke(pred, invoke(proj, e))).

3 Complexity: Linear. At most last - first applications of pred and proj.

template<permutable I, sentinel_for<I> S, class Proj = identity,
         indirect_unary_predicate<projected<I, Proj>> Pred>
  constexpr subrange<I>
    ranges::partition(I first, S last, Pred pred, Proj proj = {});
template<forward_range R, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  requires permutable<iterator_t<R>>
  constexpr borrowed_subrange_t<R>
    ranges::partition(R&& r, Pred pred, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
          class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
  subrange<I> ranges::partition(Ep&& exec, I first, S last, Pred pred, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  requires permutable<iterator_t<R>>
  borrowed_subrange_t<R> ranges::partition(Ep&& exec, R&& r, Pred pred, Proj proj = {});

4 Let proj be identity{} for the overloads with no parameter named proj and let E(x) be bool(invoke(pred, invoke(proj, x))).

5 Preconditions: For the overloads in namespace std, ForwardIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]).

6 Effects: Places all the elements e in [first, last) that satisfy E(e) before all the elements that do not.

7 Returns: Let i be an iterator such that E(*j) is true for every iterator j in [first, i) and false for every iterator j in [i, last). Returns:

(7.1) i for the overloads in namespace std.
(7.2) {i, last} for the overloads in namespace ranges.

8 Complexity: Let N = last - first:

(8.1) For the overload with no ~~ExecutionPolicy~~execution policy, exactly N applications of the predicate and projection. At most N / 2 swaps if the type of first meets the Cpp17BidirectionalIterator requirements for the overloads in namespace std or models bidirectional_iterator for the overloads in namespace ranges, and at most N swaps otherwise.
(8.2) For the overload with an ~~ExecutionPolicy~~execution policy, O(NlogN) swaps and O(N) applications of the predicate.

template<bidirectional_iterator I, sentinel_for<I> S, class Proj = identity,
         indirect_unary_predicate<projected<I, Proj>> Pred>
  requires permutable<I>
  constexpr subrange<I> ranges::stable_partition(I first, S last, Pred pred, Proj proj = {});
template<bidirectional_range R, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  requires permutable<iterator_t<R>>
  constexpr borrowed_subrange_t<R> ranges::stable_partition(R&& r, Pred pred, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
         class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
  requires permutable<I>
  subrange<I> ranges::stable_partition(Ep&& exec, I first, S last, Pred pred, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  requires permutable<iterator_t<R>>
  borrowed_subrange_t<R> ranges::stable_partition(Ep&& exec, R&& r, Pred pred, Proj proj = {});

9 Let proj be identity{} for the overloads with no parameter named proj and let E(x) be bool(invoke(pred, invoke(proj, x))).

10 Preconditions: For the overloads in namespace std, BidirectionalIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]) and the type of *first meets the Cpp17MoveConstructible (Table 31) and Cpp17MoveAssignable (Table 33) requirements.

11 Effects: Places all the elements e in [first, last) that satisfy E(e) before all the elements that do not. The relative order of the elements in both groups is preserved.

12 Returns: Let i be an iterator such that for every iterator j in [first, i), E(*j) is true, and for every iterator j in the range [i, last), E(*j) is false. Returns:

(12.1) i for the overloads in namespace std.
(12.2) {i, last} for the overloads in namespace ranges.

13 Complexity: Let N = last - first:

(13.1) For the overloads with no ~~ExecutionPolicy~~execution policy, at most Nlog₂N swaps, but only O(N) swaps if there is enough extra memory. Exactly N applications of the predicate and projection.
(13.2) For the overloads with an ~~ExecutionPolicy~~execution policy, O(NlogN) swaps and O(N) applications of the predicate.

template<input_iterator I, sentinel_for<I> S, weakly_incrementable O1, weakly_incrementable O2,
         class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
  requires indirectly_copyable<I, O1> && indirectly_copyable<I, O2>
  constexpr ranges::partition_copy_result<I, O1, O2>
    ranges::partition_copy(I first, S last, O1 out_true, O2 out_false, Pred pred,
                           Proj proj = {});
template<input_range R, weakly_incrementable O1, weakly_incrementable O2,
         class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  requires indirectly_copyable<iterator_t<R>, O1> &&
           indirectly_copyable<iterator_t<R>, O2>
  constexpr ranges::partition_copy_result<borrowed_iterator_t<R>, O1, O2>
    ranges::partition_copy(R&& r, O1 out_true, O2 out_false, Pred pred, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
         random_access_iterator O1, sized_sentinel_for<O1> OutS1,
         random_access_iterator O2, sized_sentinel_for<O2> OutS2,
         class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
  requires indirectly_copyable<I, O1> && indirectly_copyable<I, O2>
  ranges::partition_copy_result<I, O1, O2>
    ranges::partition_copy(Ep&& exec, I first, S last, O1 out_true, OutS1 last_true,
                           O2 out_false, OutS2 last_false, Pred pred, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, random-access-sized-range OutR1,
         random-access-sized-range OutR2, class Proj = identity,
         indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
  requires indirectly_copyable<iterator_t<R>, iterator_t<OutR1>> &&
           indirectly_copyable<iterator_t<R>, iterator_t<OutR2>>
  ranges::partition_copy_result<borrowed_iterator_t<R>, borrowed_iterator_t<OutR1>, borrowed_iterator_t<OutR2>>
    ranges::partition_copy(Ep&& exec, R&& r, OutR1&& out_true_r, OutR2&& out_false_r,
                           Pred pred, Proj proj = {});

14 Let proj be identity{} for the overloads with no parameter named proj and let E(x) be bool(invoke(pred, invoke(proj, x))).

15 Mandates: For the overloads in namespace std, the expression *first is writable ([iterator.requirements.general]) to out_true and out_false.

16 Preconditions: The input range and output ranges do not overlap.

[Note 1: For the overload with an ExecutionPolicy, there might be a performance cost if first’s value type does not meet the Cpp17CopyConstructible requirements. For the overloads with an execution-policy, there might be a performance cost if first’s value type does not meet the copy_constructible requirements. — end note.]

17 Effects: For each iterator i in [first, last), copies *i to the output range beginning with out_true if E(*i) is true, or to the output range beginning with out_false otherwise.

18 Returns: Let o1 be the end of the output range beginning at out_true, and o2 the end of the output range beginning at out_false. Returns

(18.1) {o1, o2} for the overloads in namespace std.
(18.2) {last, o1, o2} for the overloads in namespace ranges.

19 Complexity: Exactly last - first applications of pred and proj.

8.45 Modify `merge` in [alg.merge]

template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
         weakly_incrementable O, class Comp = ranges::less, class Proj1 = identity,
         class Proj2 = identity>
  requires mergeable<I1, I2, O, Comp, Proj1, Proj2>
  constexpr ranges::merge_result<I1, I2, O>
    ranges::merge(I1 first1, S1 last1, I2 first2, S2 last2, O result,
                  Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<input_range R1, input_range R2, weakly_incrementable O, class Comp = ranges::less,
         class Proj1 = identity, class Proj2 = identity>
  requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
  constexpr ranges::merge_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, O>
    ranges::merge(R1&& r1, R2&& r2, O result,
                  Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});

template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
         random_access_iterator I2, sized_sentinel_for<I2> S2,
         random_access_iterator O, sized_sentinel_for<O> OutS, class Comp = ranges::less,
         class Proj1 = identity, class Proj2 = identity>
  requires mergeable<I1, I2, O, Comp, Proj1, Proj2>
  ranges::merge_result<I1, I2, O>
    ranges::merge(Ep&& exec, I1 first1, S1 last1,
                  I2 first2, S2 last2, O result, OutS result_last,
                  Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
         random-access-sized-range OutR, class Comp = ranges::less,
         class Proj1 = identity, class Proj2 = identity>
  requires mergeable<iterator_t<R1>, iterator_t<R2>, iterator_t<OutR>, Comp, Proj1, Proj2>
  ranges::merge_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, borrowed_iterator_t<OutR>>
    ranges::merge(Ep&& exec, R1&& r1, R2&& r2, OutR&& result_r,
                  Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});

1 Let N be (last1 - first1) + (last2 - first2). Let comp be less{}, proj1 be identity{}, and proj2 be identity{}, for the overloads with no parameters by those names.

x Let

(x.1) M be (last1 - first1) + (last2 - first2);
(x.2) comp be less{}, proj1 be identity{}, and proj2 be identity{}, for the overloads with no parameters by those names;
(x.3) result_last be result + M for the overloads with no parameter result_last or result_r;
(x.4) N be min(M, result_last - result);
(x.5) E be bool(invoke(comp, invoke(proj2, e2), invoke(proj1, e1)));
(x.6) K be the rightmost position of an element e2 in [first2, last2) such that the number of elements e1 in [first1, last1) for which E holds is less than or equal to N - K.

2 Preconditions: The ranges [first1, last1) and [first2, last2) are sorted with respect to comp and proj1 or proj2, respectively. The resulting range does not overlap with either of the original ranges.

3 Effects: ~~Copies all the elements of the two ranges [first1, last1) and [first2, last2) into the range [result, result_last), where result_last is result + N~~Copies first1 + N - K elements of the range [first1, last1) and first2 + K elements of the range [first2, last2) into the range [result, result_lastresult + N)~~, where result_last is result + N~~. If an element a precedes b in an input range, a is copied into the output range before b. If e1 is an element of [first1, last1) and e2 of [first2, last2), e2 is copied into the output range before e1 if and only if ~~bool(invoke(comp, invoke(proj2, e2), invoke(proj1, e1)))~~E is true.

4 Returns:

(4.1) result_last for the overloads in namespace std.
(4.2) ~~{last1, last2, result_last}~~{first1 + N - K, first2 + K, result + N} for the overloads in namespace ranges.

5 Complexity:

(5.1) For the overloads with no ~~ExecutionPolicy~~execution policy, at most N − 1 comparisons and applications of each projection.
(5.2) For the overloads with an ~~ExecutionPolicy~~execution policy, O(N) comparisons and applications of each projection.

6 Remarks: Stable ([algorithm.stable]).

template<bidirectional_iterator I, sentinel_for<I> S, class Comp = ranges::less,
         class Proj = identity>
  requires sortable<I, Comp, Proj>
  constexpr I ranges::inplace_merge(I first, I middle, S last, Comp comp = {}, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
         class Comp = ranges::less, class Proj = identity>
  requires sortable<I, Comp, Proj>
  I ranges::inplace_merge(Ep&& exec, I first, I middle, S last, Comp comp = {}, Proj proj = {});

7 Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.

8 Preconditions: [first, middle) and [middle, last) are valid ranges sorted with respect to comp and proj. For the overloads in namespace std, BidirectionalIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]) and the type of *first meets the Cpp17MoveConstructible (Table 31) and Cpp17MoveAssignable (Table 33) requirements.

9 Effects: Merges two sorted consecutive ranges [first, middle) and [middle, last), putting the result of the merge into the range [first, last). The resulting range is sorted with respect to comp and proj.

10 Returns: last for the overload in namespace ranges.

11 Complexity: Let N = last - first:

(11.1) For the overloads with no ~~ExecutionPolicy~~execution policy, and if enough additional memory is available, exactly N − 1 comparisons.
(11.2) Otherwise, O(NlogN) comparisons.

In either case, twice as many projections as comparisons.

12 Remarks: Stable.

template<bidirectional_range R, class Comp = ranges::less, class Proj = identity>
  requires sortable<iterator_t<R>, Comp, Proj>
  constexpr borrowed_iterator_t<R>
    ranges::inplace_merge(R&& r, iterator_t<R> middle, Comp comp = {}, Proj proj = {});

Effects: Equivalent to: return ranges::inplace_merge(ranges::begin(r), middle, ranges::end(r), comp, proj);

template<execution-policy Ep, random-access-sized-range R, class Comp = ranges::less,
         class Proj = identity>
  requires sortable<iterator_t<R>, Comp, Proj>
  borrowed_iterator_t<R> ranges::inplace_merge(Ep&& exec, R&& r, iterator_t<R> middle,
                                               Comp comp = {}, Proj proj = {});

Effects: Equivalent to: return ranges::inplace_merge(std::forward<Ep>(exec), ranges::begin(r), middle, ranges::end(r), comp, proj);

8.46 Modify `includes` in [includes]

template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
         class Proj1 = identity, class Proj2 = identity,
         indirect_strict_weak_order<projected<I1, Proj1>,
                                    projected<I2, Proj2>> Comp = ranges::less>
  constexpr bool ranges::includes(I1 first1, S1 last1, I2 first2, S2 last2, Comp comp = {},
                                  Proj1 proj1 = {}, Proj2 proj2 = {});
template<input_range R1, input_range R2, class Proj1 = identity,
         class Proj2 = identity,
         indirect_strict_weak_order<projected<iterator_t<R1>, Proj1>,
                                    projected<iterator_t<R2>, Proj2>> Comp = ranges::less>
  constexpr bool ranges::includes(R1&& r1, R2&& r2, Comp comp = {},
                                  Proj1 proj1 = {}, Proj2 proj2 = {});

template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
         random_access_iterator I2, sized_sentinel_for<I2> S2,
         class Proj1 = identity, class Proj2 = identity,
         indirect_strict_weak_order<projected<I1, Proj1>, projected<I2, Proj2>> Comp = ranges::less>
  bool ranges::includes(Ep&& exec, I1 first1, S1 last1, I2 first2, S2 last2,
                        Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
         class Proj1 = identity, class Proj2 = identity,
         indirect_strict_weak_order<projected<iterator_t<R1>, Proj1>,
                                    projected<iterator_t<R2>, Proj2>> Comp = ranges::less>
  bool ranges::includes(Ep&& exec, R1&& r1, R2&& r2,
                        Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});

1 Let comp be less{}, proj1 be identity{}, and proj2 be identity{}, for the overloads with no parameters by those names.

2 Preconditions: The ranges [first1, last1) and [first2, last2) are sorted with respect to comp and proj1 or proj2, respectively.

3 Returns: true if and only if [first2, last2) is a subsequence of [first1, last1).

[Note 1: A sequence S is a subsequence of another sequence T if S can be obtained from T by removing some, all, or none of T’s elements and keeping the remaining elements in the same order. — end note]

4 Complexity: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons and applications of each projection.

8.47 Modify `set_union` in [set.union]

template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
         weakly_incrementable O, class Comp = ranges::less,
         class Proj1 = identity, class Proj2 = identity>
  requires mergeable<I1, I2, O, Comp, Proj1, Proj2>
  constexpr ranges::set_union_result<I1, I2, O>
    ranges::set_union(I1 first1, S1 last1, I2 first2, S2 last2, O result, Comp comp = {},
                      Proj1 proj1 = {}, Proj2 proj2 = {});
template<input_range R1, input_range R2, weakly_incrementable O,
         class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
  requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
  constexpr ranges::set_union_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, O>
    ranges::set_union(R1&& r1, R2&& r2, O result, Comp comp = {},
                      Proj1 proj1 = {}, Proj2 proj2 = {});

template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
         random_access_iterator I2, sized_sentinel_for<I2> S2,
         random_access_iterator O, sized_sentinel_for<O> OutS, class Comp = ranges::less,
         class Proj1 = identity, class Proj2 = identity>
  requires mergeable<I1, I2, O, Comp, Proj1, Proj2>
  ranges::set_union_result<I1, I2, O>
    ranges::set_union(Ep&& exec, I1 first1, S1 last1,
                      I2 first2, S2 last2, O result, OutS result_last,
                      Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
         random-access-sized-range OutR, class Comp = ranges::less,
         class Proj1 = identity, class Proj2 = identity>
  requires mergeable<iterator_t<R1>, iterator_t<R2>, iterator_t<OutR>, Comp, Proj1, Proj2>
  ranges::set_union_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, borrowed_iterator_t<OutR>>
    ranges::set_union(Ep&& exec, R1&& r1, R2&& r2, OutR&& result_r,
                      Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});

1 Let comp be less{}, and proj1 and proj2 be identity{} for the overloads with no parameters by those names.

3 Effects: Constructs a sorted union of the elements from the two ranges; that is, the set of elements that are present in one or both of the ranges.

4 Returns: Let result_last be the end of the constructed range. Returns

(4.1) result_last for the overloads in namespace std.
(4.2) {last1, last2, result_last} for the overloads in namespace ranges.

5 Complexity: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons and applications of each projection.

6 Remarks: Stable ([algorithm.stable]). If [first1, last1) contains m elements that are equivalent to each other and [first2, last2) contains n elements that are equivalent to them, then all m elements from the first range are copied to the output range, in order, and then the final max(n − m, 0) elements from the second range are copied to the output range, in order.

8.48 Modify `set_intersection` in [set.intersection]

template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
         weakly_incrementable O, class Comp = ranges::less,
         class Proj1 = identity, class Proj2 = identity>
  requires mergeable<I1, I2, O, Comp, Proj1, Proj2>
  constexpr ranges::set_intersection_result<I1, I2, O>
    ranges::set_intersection(I1 first1, S1 last1, I2 first2, S2 last2, O result,
                             Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<input_range R1, input_range R2, weakly_incrementable O,
         class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
  requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
  constexpr ranges::set_intersection_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, O>
    ranges::set_intersection(R1&& r1, R2&& r2, O result,
                             Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});

template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
         random_access_iterator I2, sized_sentinel_for<I2> S2,
         random_access_iterator O, sized_sentinel_for<O> OutS, class Comp = ranges::less,
         class Proj1 = identity, class Proj2 = identity>
  requires mergeable<I1, I2, O, Comp, Proj1, Proj2>
  ranges::set_intersection_result<I1, I2, O>
    ranges::set_intersection(Ep&& exec, I1 first1, S1 last1,
                             I2 first2, S2 last2, O result, OutS result_last,
                             Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
         random-access-sized-range OutR, class Comp = ranges::less,
         class Proj1 = identity, class Proj2 = identity>
  requires mergeable<iterator_t<R1>, iterator_t<R2>, iterator_t<OutR>, Comp, Proj1, Proj2>
  ranges::set_intersection_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, borrowed_iterator_t<OutR>>
    ranges::set_intersection(Ep&& exec, R1&& r1, R2&& r2, OutR&& result_r,
                             Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});

1 Let comp be less{}, and proj1 and proj2 be identity{} for the overloads with no parameters by those names.

3 Effects: Constructs a sorted intersection of the elements from the two ranges; that is, the set of elements that are present in both of the ranges.

4 Returns: Let result_last be the end of the constructed range. Returns

(4.1) result_last for the overloads in namespace std.
(4.2) {last1, last2, result_last} for the overloads in namespace ranges.

5 Complexity: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons and applications of each projection.

8.49 Modify `set_difference` in [set.difference]

template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
         weakly_incrementable O, class Comp = ranges::less,
         class Proj1 = identity, class Proj2 = identity>
  requires mergeable<I1, I2, O, Comp, Proj1, Proj2>
  constexpr ranges::set_difference_result<I1, O>
    ranges::set_difference(I1 first1, S1 last1, I2 first2, S2 last2, O result,
                           Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<input_range R1, input_range R2, weakly_incrementable O,
         class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
  requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
  constexpr ranges::set_difference_result<borrowed_iterator_t<R1>, O>
    ranges::set_difference(R1&& r1, R2&& r2, O result,
                           Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});

template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
         random_access_iterator I2, sized_sentinel_for<I2> S2,
         random_access_iterator O, sized_sentinel_for<O> OutS, class Comp = ranges::less,
         class Proj1 = identity, class Proj2 = identity>
  requires mergeable<I1, I2, O, Comp, Proj1, Proj2>
  ranges::set_difference_result<I1, O>
    ranges::set_difference(Ep&& exec, I1 first1, S1 last1,
                           I2 first2, S2 last2, O result, OutS result_last,
                           Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
         random-access-sized-range OutR, class Comp = ranges::less,
         class Proj1 = identity, class Proj2 = identity>
  requires mergeable<iterator_t<R1>, iterator_t<R2>, iterator_t<OutR>, Comp, Proj1, Proj2>
  ranges::set_difference_result<borrowed_iterator_t<R1>, borrowed_iterator_t<OutR>>
    ranges::set_difference(Ep&& exec, R1&& r1, R2&& r2, OutR&& result_r,
                           Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});

1 Let comp be less{}, and proj1 and proj2 be identity{} for the overloads with no parameters by those names.

3 Effects: Copies the elements of the range [first1, last1) which are not present in the range [first2, last2) to the range beginning at result. The elements in the constructed range are sorted.

4 Returns: Let result_last be the end of the constructed range. Returns

(4.1) result_last for the overloads in namespace std.
(4.2) {last1, result_last} for the overloads in namespace ranges.

5 Complexity: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons and applications of each projection.

6 Remarks: If [first1, last1) contains m elements that are equivalent to each other and [first2, last2) contains n elements that are equivalent to them, the last max(m − n, 0) elements from [first1, last1) are copied to the output range, in order.

8.50 Modify `set_symmetric_difference` in [set.symmetric.difference]

template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
         weakly_incrementable O, class Comp = ranges::less,
         class Proj1 = identity, class Proj2 = identity>
  requires mergeable<I1, I2, O, Comp, Proj1, Proj2>
  constexpr ranges::set_symmetric_difference_result<I1, I2, O>
    ranges::set_symmetric_difference(I1 first1, S1 last1, I2 first2, S2 last2, O result,
                                     Comp comp = {}, Proj1 proj1 = {},
                                     Proj2 proj2 = {});
template<input_range R1, input_range R2, weakly_incrementable O,
         class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
  requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
  constexpr ranges::set_symmetric_difference_result<borrowed_iterator_t<R1>,
                                                    borrowed_iterator_t<R2>, O>
    ranges::set_symmetric_difference(R1&& r1, R2&& r2, O result, Comp comp = {},
                                     Proj1 proj1 = {}, Proj2 proj2 = {});

template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
         random_access_iterator I2, sized_sentinel_for<I2> S2,
         random_access_iterator O, sized_sentinel_for<O> OutS, class Comp = ranges::less,
         class Proj1 = identity, class Proj2 = identity>
  requires mergeable<I1, I2, O, Comp, Proj1, Proj2>
  ranges::set_symmetric_difference_result<I1, I2, O>
    ranges::set_symmetric_difference(Ep&& exec, I1 first1, S1 last1,
                                     I2 first2, S2 last2, O result, OutS result_last,
                                     Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
         random-access-sized-range OutR, class Comp = ranges::less,
         class Proj1 = identity, class Proj2 = identity>
  requires mergeable<iterator_t<R1>, iterator_t<R2>, iterator_t<OutR>, Comp, Proj1, Proj2>
  ranges::set_symmetric_difference_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, borrowed_iterator_t<OutR>>
    ranges::set_symmetric_difference(Ep&& exec, R1&& r1, R2&& r2, OutR&& result_r,
                                    Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});

1 Let comp be less{}, and proj1 and proj2 be identity{} for the overloads with no parameters by those names.

3 Effects: Copies the elements of the range [first1, last1) that are not present in the range [first2, last2), and the elements of the range [first2, last2) that are not present in the range [first1, last1) to the range beginning at result. The elements in the constructed range are sorted.

4 Returns: Let result_last be the end of the constructed range. Returns

[4.1] result_last for the overloads in namespace std.
[4.2] {last1, last2, result_last} for the overloads in namespace ranges.

5 Complexity: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons and applications of each projection.

6 Remarks: Stable ([algorithm.stable]). If [first1, last1) contains m elements that are equivalent to each other and [first2, last2) contains n elements that are equivalent to them, then |m − n| of those elements shall be copied to the output range: the last m − n of these elements from [first1, last1) if m > n, and the last n − m of these elements from [first2, last2) if m < n. In either case, the elements are copied in order.

8.51 Modify `is_heap` in [is.heap]

template<random_access_iterator I, sentinel_for<I> S, class Proj = identity,
         indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
  constexpr bool ranges::is_heap(I first, S last, Comp comp = {}, Proj proj = {});
template<random_access_range R, class Proj = identity,
         indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
  constexpr bool ranges::is_heap(R&& r, Comp comp = {}, Proj proj = {});

Effects: Equivalent to: return ranges::is_heap_until(first, last, comp, proj) == last;

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
         class Proj = identity,
         indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
  bool ranges::is_heap(Ep&& exec, I first, S last, Comp comp = {}, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
  bool ranges::is_heap(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {});

Effects: Equivalent to: return ranges::is_heap_until(std::forward<Ep>(exec), first, last, comp, proj) == last;

template<random_access_iterator I, sentinel_for<I> S, class Proj = identity,
         indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
  constexpr I ranges::is_heap_until(I first, S last, Comp comp = {}, Proj proj = {});
template<random_access_range R, class Proj = identity,
         indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
  constexpr borrowed_iterator_t<R>
    ranges::is_heap_until(R&& r, Comp comp = {}, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
         class Proj = identity,
         indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
  I ranges::is_heap_until(Ep&& exec, I first, S last, Comp comp = {}, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
  borrowed_iterator_t<R>
    ranges::is_heap_until(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {});

6 Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.

7 Returns: The last iterator i in [first, last] for which the range [first, i) is a heap with respect to comp and proj.

8 Complexity: Linear.

8.52 Modify `min`, `max`, `minmax` in [alg.min.max]

template<input_range R, class Proj = identity,
         indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
  requires indirectly_copyable_storable<iterator_t<R>, range_value_t<R>*>
  constexpr range_value_t<R>
    ranges::min(R&& r, Comp comp = {}, Proj proj = {});

template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
  requires indirectly_copyable_storable<iterator_t<R>, range_value_t<R>*>
  range_value_t<R>
    ranges::min(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {});

5 Preconditions: ranges::distance(r) > 0. For the overloads in namespace std, T meets the Cpp17CopyConstructible requirements. For the first form, T meets the Cpp17LessThanComparable requirements (Table 29).

6 Returns: The smallest value in the input range. Returns a copy of the leftmost element when several elements are equivalent to the smallest.

7 Complexity: Exactly ranges::distance(r) - 1 comparisons and twice as many applications of the projection, if any.

8 Remarks: An invocation may explicitly specify an argument for the template parameter T of the overloads in namespace std.

template<input_range R, class Proj = identity,
         indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
  requires indirectly_copyable_storable<iterator_t<R>, range_value_t<R>*>
  constexpr range_value_t<R>
    ranges::max(R&& r, Comp comp = {}, Proj proj = {});

template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
  requires indirectly_copyable_storable<iterator_t<R>, range_value_t<R>*>
  range_value_t<R>
    ranges::max(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {});

13 Preconditions: ranges::distance(r) > 0. For the overloads in namespace std, T meets the Cpp17CopyConstructible requirements. For the first form, T meets the Cpp17LessThanComparable requirements (Table 29).

14 Returns: The largest value in the input range. Returns a copy of the leftmost element when several elements are equivalent to the largest.

15 Complexity: Exactly ranges::distance(r) - 1 comparisons and twice as many applications of the projection, if any.

16 Remarks: An invocation may explicitly specify an argument for the template parameter T of the overloads in namespace std.

template<input_range R, class Proj = identity,
         indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
  requires indirectly_copyable_storable<iterator_t<R>, range_value_t<R>*>
  constexpr ranges::minmax_result<range_value_t<R>>
    ranges::minmax(R&& r, Comp comp = {}, Proj proj = {});

template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
  requires indirectly_copyable_storable<iterator_t<R>, range_value_t<R>*>
  ranges::minmax_result<range_value_t<R>>
    ranges::minmax(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {});

21 Preconditions: ranges::distance(r) > 0. For the overloads in namespace std, T meets the Cpp17CopyConstructible requirements. For the first form, type T meets the Cpp17LessThanComparable requirements (Table 29).

22 Returns: Let X be the return type. Returns X{x, y}, where x is a copy of the leftmost element with the smallest value and y a copy of the rightmost element with the largest value in the input range.

23 Complexity: At most (3/2)ranges::distance(r) applications of the corresponding predicate and twice as many applications of the projection, if any.

24 Remarks: An invocation may explicitly specify an argument for the template parameter T of the overloads in namespace std.

template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
         indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
  constexpr I ranges::min_element(I first, S last, Comp comp = {}, Proj proj = {});
template<forward_range R, class Proj = identity,
         indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
  constexpr borrowed_iterator_t<R>
    ranges::min_element(R&& r, Comp comp = {}, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
         class Proj = identity,
         indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
  I ranges::min_element(Ep&& exec, I first, S last, Comp comp = {}, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
  borrowed_iterator_t<R>
    ranges::min_element(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {});

25 Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.

26 Returns: The first iterator i in the range [first, last) such that for every iterator j in the range [first, last),

bool(invoke(comp, invoke(proj, *j), invoke(proj, *i)))

is false. Returns last if first == last.

27 Complexity: Exactly max(last - first - 1, 0) comparisons and twice as many projections.

template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
         indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
  constexpr I ranges::max_element(I first, S last, Comp comp = {}, Proj proj = {});
template<forward_range R, class Proj = identity,
         indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
  constexpr borrowed_iterator_t<R>
    ranges::max_element(R&& r, Comp comp = {}, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
         class Proj = identity,
         indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
  I ranges::max_element(Ep&& exec, I first, S last, Comp comp = {}, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
  borrowed_iterator_t<R>
    ranges::max_element(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {});

28 Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.

29 Returns: The first iterator i in the range [first, last) such that for every iterator j in the range [first, last),

bool(invoke(comp, invoke(proj, *i), invoke(proj, *j)))

is false. Returns last if first == last.

30 Complexity: Exactly max(last - first - 1, 0) comparisons and twice as many projections.

template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
         indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
  constexpr ranges::minmax_element_result<I>
    ranges::minmax_element(I first, S last, Comp comp = {}, Proj proj = {});
template<forward_range R, class Proj = identity,
         indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
  constexpr ranges::minmax_element_result<borrowed_iterator_t<R>>
    ranges::minmax_element(R&& r, Comp comp = {}, Proj proj = {});

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
         class Proj = identity,
         indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
  ranges::minmax_element_result<I>
    ranges::minmax_element(Ep&& exec, I first, S last, Comp comp = {}, Proj proj = {});
template<execution-policy Ep, random-access-sized-range R, class Proj = identity,
         indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
  ranges::minmax_element_result<borrowed_iterator_t<R>>
    ranges::minmax_element(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {});

31 Returns: {first, first} if [first, last) is empty, otherwise {m, M}, where m is the first iterator in [first, last) such that no iterator in the range refers to a smaller element, and where M is the last iterator²⁰⁹ in [first, last) such that no iterator in the range refers to a larger element.

32 Complexity: Let N be last - first. At most max(⌊\(\frac{3}{2}\)(N − 1)⌋, 0) comparisons and twice as many applications of the projection, if any.

8.53 Modify `lexicographical_compare` in [alg.lex.comparison]

template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
         class Proj1 = identity, class Proj2 = identity,
         indirect_strict_weak_order<projected<I1, Proj1>,
                                    projected<I2, Proj2>> Comp = ranges::less>
  constexpr bool
    ranges::lexicographical_compare(I1 first1, S1 last1, I2 first2, S2 last2,
                                    Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<input_range R1, input_range R2, class Proj1 = identity,
         class Proj2 = identity,
         indirect_strict_weak_order<projected<iterator_t<R1>, Proj1>,
                                    projected<iterator_t<R2>, Proj2>> Comp = ranges::less>
  constexpr bool
    ranges::lexicographical_compare(R1&& r1, R2&& r2, Comp comp = {},
                                    Proj1 proj1 = {}, Proj2 proj2 = {});

template<execution-policy Ep, random_access_iterator I1, sized_sentinel_for<I1> S1,
         random_access_iterator I2, sized_sentinel_for<I2> S2,
         class Proj1 = identity, class Proj2 = identity,
         indirect_strict_weak_order<projected<I1, Proj1>, projected<I2, Proj2>> Comp = ranges::less>
  bool ranges::lexicographical_compare(Ep&& exec, I1 first1, S1 last1, I2 first2, S2 last2,
                                       Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<execution-policy Ep, random-access-sized-range R1, random-access-sized-range R2,
         class Proj1 = identity, class Proj2 = identity,
         indirect_strict_weak_order<projected<iterator_t<R1>, Proj1>,
                                    projected<iterator_t<R2>, Proj2>> Comp = ranges::less>
  bool ranges::lexicographical_compare(Ep&& exec, R1&& r1, R2&& r2, Comp comp = {},
                                       Proj1 proj1 = {}, Proj2 proj2 = {});

1 Returns: true if and only if the sequence of elements defined by the range [first1, last1) is lexicographically less than the sequence of elements defined by the range [first2, last2).

2 Complexity: At most 2 min(last1 - first1, last2 - first2) applications of the corresponding comparison and each projection, if any.

3 Remarks: If two sequences have the same number of elements and their corresponding elements (if any) are equivalent, then neither sequence is lexicographically less than the other. If one sequence is a proper prefix of the other, then the shorter sequence is lexicographically less than the longer sequence. Otherwise, the lexicographical comparison of the sequences yields the same result as the comparison of the first corresponding pair of elements that are not equivalent.

[ Example: ranges::lexicographical_compare(I1, S1, I2, S2, Comp, Proj1, Proj2) can be implemented as:

for ( ; first1 != last1 && first2 != last2 ; ++first1, (void) ++first2) {
  if (invoke(comp, invoke(proj1, *first1), invoke(proj2, *first2))) return true;
  if (invoke(comp, invoke(proj2, *first2), invoke(proj1, *first1))) return false;
}
return first1 == last1 && first2 != last2;

— end example ]

5 [Note 1: An empty sequence is lexicographically less than any non-empty sequence, but not less than any empty sequence. — end note]

8.54 Modify [memory.syn]

// [specialized.algorithms], specialized algorithms
// [special.mem.concepts], special memory concepts
template<class I>
  concept nothrow-input-iterator = see below;       // exposition only
template<class I>
  concept nothrow-forward-iterator = see below;     // exposition only

template<class I>
  concept nothrow-bidirectional-iterator = see below;  // exposition only
template<class I>
  concept nothrow-random-access-iterator = see below;  // exposition only

template<class S, class I>
  concept nothrow-sentinel-for = see below;         // exposition only

template<class S, class I>
  concept nothrow-sized-sentinel-for = see below;   // exposition only

template<class R>
  concept nothrow-input-range = see below;          // exposition only
template<class R>
  concept nothrow-forward-range = see below;        // exposition only

template<class I>
  concept nothrow-bidirectional-range = see below;     // exposition only
template<class I>
  concept nothrow-random-access-range = see below;     // exposition only
template<class I>
  concept nothrow-random-access-sized-range = see below;     // exposition only

template<nothrow-forward-iterator I, nothrow-sentinel-for<I> S>
  requires default_initializable<iter_value_t<I>>
    I uninitialized_default_construct(I first, S last);                         // freestanding
template<nothrow-forward-range R>
  requires default_initializable<range_value_t<R>>
    borrowed_iterator_t<R> uninitialized_default_construct(R&& r);              // freestanding

template<nothrow-forward-iterator I>
  requires default_initializable<iter_value_t<I>>
    I uninitialized_default_construct_n(I first, iter_difference_t<I> n);       // freestanding

template<execution-policy Ep, nothrow-random-access-iterator I, nothrow-sized-sentinel-for<I> S>
  requires default_initializable<iter_value_t<I>>
  I uninitialized_default_construct(Ep&& exec, I first, S last); // see [algorithms.parallel.overloads]

template<execution-policy Ep, nothrow-random-access-sized-range R>
  requires default_initializable<range_value_t<R>>
  borrowed_iterator_t<R> uninitialized_default_construct(Ep&& exec, R&& r); // see [algorithms.parallel.overloads]

template<execution-policy Ep, nothrow-random-access-iterator I>
  requires default_initializable<iter_value_t<I>>
  I uninitialized_default_construct_n(Ep&& exec, I first, iter_difference_t<I> n); // see [algorithms.parallel.overloads]

template<nothrow-forward-iterator I, nothrow-sentinel-for<I> S>
  requires default_initializable<iter_value_t<I>>
    I uninitialized_value_construct(I first, S last);                           // freestanding
template<nothrow-forward-range R>
  requires default_initializable<range_value_t<R>>
    borrowed_iterator_t<R> uninitialized_value_construct(R&& r);                // freestanding

template<nothrow-forward-iterator I>
  requires default_initializable<iter_value_t<I>>
    I uninitialized_value_construct_n(I first, iter_difference_t<I> n);         // freestanding

template<execution-policy Ep, nothrow-random-access-iterator I, nothrow-sized-sentinel-for<I> S>
  requires default_initializable<iter_value_t<I>>
  I uninitialized_value_construct(Ep&& exec, I first, S last); // see [algorithms.parallel.overloads]

template<execution-policy Ep, nothrow-random-access-sized-range R>
  requires default_initializable<range_value_t<R>>
  borrowed_iterator_t<R> uninitialized_value_construct(Ep&& exec, R&& r); // see [algorithms.parallel.overloads]

template<execution-policy Ep, nothrow-random-access-iterator I>
  requires default_initializable<iter_value_t<I>>
  I uninitialized_value_construct_n(Ep&& exec, I first, iter_difference_t<I> n); // see [algorithms.parallel.overloads]

template<input_iterator I, sentinel_for<I> S1,
          nothrow-forward-iterator O, nothrow-sentinel-for<O> S2>
  requires constructible_from<iter_value_t<O>, iter_reference_t<I>>
    uninitialized_copy_result<I, O>
      uninitialized_copy(I ifirst, S1 ilast, O ofirst, S2 olast);               // freestanding
template<input_range IR, nothrow-forward-range OR>
  requires constructible_from<range_value_t<OR>, range_reference_t<IR>>
    uninitialized_copy_result<borrowed_iterator_t<IR>, borrowed_iterator_t<OR>>
      uninitialized_copy(IR&& in_range, OR&& out_range);                        // freestanding

template<class I, class O>
  using uninitialized_copy_n_result = in_out_result<I, O>;                      // freestanding
template<input_iterator I, nothrow-forward-iterator O, nothrow-sentinel-for<O> S>
  requires constructible_from<iter_value_t<O>, iter_reference_t<I>>
    uninitialized_copy_n_result<I, O>
      uninitialized_copy_n(I ifirst, iter_difference_t<I> n,                    // freestanding
                           O ofirst, S olast);

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S1,
         nothrow-random-access-iterator O, nothrow-sized-sentinel-for<O> S2>
  requires constructible_from<iter_value_t<O>, iter_reference_t<I>>
    uninitialized_copy_result<I, O>
      uninitialized_copy(Ep&& exec, I ifirst, S1 ilast, O ofirst, S2 olast); // see [algorithms.parallel.overloads]
template<execution-policy Ep, random-access-sized-range IR, nothrow-random-access-sized-range OR>
  requires constructible_from<range_value_t<OR>, range_reference_t<IR>>
    uninitialized_copy_result<borrowed_iterator_t<IR>, borrowed_iterator_t<OR>>
      uninitialized_copy(Ep&& exec, IR&& in_range, OR&& out_range); // see [algorithms.parallel.overloads]

template<execution-policy Ep, random_access_iterator I, nothrow-random-access-iterator O,
         nothrow-sized-sentinel-for<O> S>
  requires constructible_from<iter_value_t<O>, iter_reference_t<I>>
    uninitialized_copy_n_result<I, O>
      uninitialized_copy_n(Ep&& exec, I ifirst, iter_difference_t<I> n, // see [algorithms.parallel.overloads]
                           O ofirst, S olast);

template<input_iterator I, sentinel_for<I> S1,
          nothrow-forward-iterator O, nothrow-sentinel-for<O> S2>
  requires constructible_from<iter_value_t<O>, iter_rvalue_reference_t<I>>
    uninitialized_move_result<I, O>
      uninitialized_move(I ifirst, S1 ilast, O ofirst, S2 olast);              // freestanding
template<input_range IR, nothrow-forward-range OR>
  requires constructible_from<range_value_t<OR>, range_rvalue_reference_t<IR>>
    uninitialized_move_result<borrowed_iterator_t<IR>, borrowed_iterator_t<OR>>
      uninitialized_move(IR&& in_range, OR&& out_range);                       // freestanding

template<input_iterator I,
          nothrow-forward-iterator O, nothrow-sentinel-for<O> S>
  requires constructible_from<iter_value_t<O>, iter_rvalue_reference_t<I>>
    uninitialized_move_n_result<I, O>
      uninitialized_move_n(I ifirst, iter_difference_t<I> n,                // freestanding
                           O ofirst, S olast);

template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S1,
         nothrow-random-access-iterator O, nothrow-sized-sentinel-for<O> S2>
  requires constructible_from<iter_value_t<O>, iter_rvalue_reference_t<I>>
    uninitialized_move_result<I, O>
      uninitialized_move(Ep&& exec, I ifirst, S1 ilast, O ofirst, S2 olast); // see [algorithms.parallel.overloads]

template<execution-policy Ep, random-access-sized-range IR, nothrow-random-access-sized-range OR>
  requires constructible_from<range_value_t<OR>, range_rvalue_reference_t<IR>>
    uninitialized_move_result<borrowed_iterator_t<IR>, borrowed_iterator_t<OR>>
      uninitialized_move(Ep&& exec, IR&& in_range, OR&& out_range);        // see [algorithms.parallel.overloads]

template<execution-policy Ep, random_access_iterator I,
    nothrow-random-access-iterator O, nothrow-sized-sentinel-for<O> S>
  requires constructible_from<iter_value_t<O>, iter_rvalue_reference_t<I>>
    uninitialized_move_n_result<I, O>
      uninitialized_move_n(Ep&& exec, I ifirst, iter_difference_t<I> n, // see [algorithms.parallel.overloads]
                           O ofirst, S olast);

template<nothrow-forward-iterator I, nothrow-sentinel-for<I> S, class T>
  requires constructible_from<iter_value_t<I>, const T&>
    I uninitialized_fill(I first, S last, const T& x);                          // freestanding
template<nothrow-forward-range R, class T>
  requires constructible_from<range_value_t<R>, const T&>
    borrowed_iterator_t<R> uninitialized_fill(R&& r, const T& x);               // freestanding

template<nothrow-forward-iterator I, class T>
  requires constructible_from<iter_value_t<I>, const T&>
    I uninitialized_fill_n(I first, iter_difference_t<I> n, const T& x);        // freestanding

template<execution-policy Ep, nothrow-random-access-iterator I, nothrow-sized-sentinel-for<I> S, class T>
  requires constructible_from<iter_value_t<I>, const T&>
    I uninitialized_fill(Ep&& exec, I first, S last, const T& x);                // see [algorithms.parallel.overloads]
template<execution-policy Ep, nothrow-random-access-sized-range R, class T>
  requires constructible_from<range_value_t<R>, const T&>
    borrowed_iterator_t<R> uninitialized_fill(Ep&& exec, R&& r, const T& x);     // see [algorithms.parallel.overloads]

template<execution-policy Ep, nothrow-random-access-iterator I, class T>
  requires constructible_from<iter_value_t<I>, const T&>
    I uninitialized_fill_n(Ep&& exec, I first, iter_difference_t<I> n, const T& x); // see [algorithms.parallel.overloads]

template<nothrow-input-iterator I, nothrow-sentinel-for<I> S>
  requires destructible<iter_value_t<I>>
    constexpr I destroy(I first, S last) noexcept;                              // freestanding
template<nothrow-input-range R>
  requires destructible<range_value_t<R>>
    constexpr borrowed_iterator_t<R> destroy(R&& r) noexcept;                   // freestanding

template<nothrow-input-iterator I>
  requires destructible<iter_value_t<I>>
    constexpr I destroy_n(I first, iter_difference_t<I> n) noexcept;            // freestanding

template<execution-policy Ep, nothrow-random-access-iterator I, nothrow-sized-sentinel-for<I> S>
  requires destructible<iter_value_t<I>>
    I destroy(Ep&& exec, I first, S last) noexcept;                           // see [algorithms.parallel.overloads]

template<execution-policy Ep, nothrow-random-access-sized-range R>
  requires destructible<range_value_t<R>>
    borrowed_iterator_t<R> destroy(Ep&& exec, R&& r) noexcept;                // see [algorithms.parallel.overloads]

template<execution-policy Ep, nothrow-random-access-iterator I>
  requires destructible<iter_value_t<I>>
    I destroy_n(Ep&& exec, I first, iter_difference_t<I> n) noexcept;         // see [algorithms.parallel.overloads]

8.55 Add exposition only concepts to [special.mem.concepts]

template<class S, class I>
concept nothrow-sentinel-for = sentinel_for<S, I>; // exposition only

Types S and I model nothrow-sentinel-for only if no exceptions are thrown from copy construction, move construction, copy assignment, move assignment, or comparisons between valid values of type I and S.

[Note X: This concept allows some sentinel_for ([iterator.concept.sentinel]) operations to throw exceptions. — end note]

template<class S, class I>
concept nothrow-sized-sentinel-for = // exposition only
  nothrow-sentinel-for<S, I> &&
  sized_sentinel_for<S, I>;

Types S and I model nothrow-sized-sentinel-for only if no exceptions are thrown from the - operator for valid values of type I and S.

[Note X: This concept allows some sized_sentinel_for ([iterator.concept.sizedsentinel]) operations to throw exceptions. — end note]

template<class I>
concept nothrow-forward-iterator = // exposition only
  nothrow-input-iterator<I> &&
  forward_iterator<I> &&
  nothrow-sentinel-for<I, I>;

[Note X: This concept allows some forward_iterator ([iterator.concept.forward]) operations to throw exceptions. — end note]

template<class R>
concept nothrow-forward-range = // exposition only
  nothrow-input-range<R> &&
  nothrow-forward-iterator<iterator_t<R>>;

template<class I>
concept nothrow-bidirectional-iterator = // exposition only
  nothrow-forward-iterator<I> &&
  bidirectional_iterator<I>;

A type I models nothrow-bidirectional-iterator only if no exceptions are thrown from decrementing valid iterators.

[Note X: This concept allows some bidirectional_iterator ([iterator.concept.bidir]) operations to throw exceptions. — end note]

template<class R>
concept nothrow-bidirectional-range = // exposition only
  nothrow-forward-range<R> &&
  nothrow-bidirectional-iterator<iterator_t<R>>;

template<class I>
concept nothrow-random-access-iterator = // exposition only
  nothrow-bidirectional-iterator<I> &&
  random_access_iterator<I> &&
  nothrow-sized-sentinel-for<I, I>;

A type I models nothrow-random-access-iterator only if no exceptions are thrown from advancement with +=, +, -=, and -, comparisons, or applying the [] subscript operator to valid iterators.

[Note X: This concept allows some random_access_iterator ([iterator.concept.random.access]) operations to throw exceptions. — end note]

template<class R>
concept nothrow-random-access-range = // exposition only
  nothrow-bidirectional-range<R> &&
  nothrow-random-access-iterator<iterator_t<R>>;

template<class R>
concept nothrow-random-access-sized-range = // exposition only
  nothrow-random-access-range<R> && sized_range<R>;

9 Revision history

9.1 R4 => R5

Add the necessary wording to [algorithm.syn]
Add the contextual algorithms description to the wording, even if no changes are made
Add random-access-sized-range as an exposition-only concept for wording simplification
Suggest to bump the existing feature testing macro as was voted in LEWG
Shorten the ExecutionPolicy parameter, italicize execution-policy concept in wording
Support result_last or similar for the algorithms where range-as-the-output is a novelty (copy, transform, etc.), unless stated otherwise in Issues to address or in Out-of-scope
Modify fill and generate algorithms family to use indirectly_writable instead of output_iterator and output_range for design consistency
Add sentinel-for-output for copy_n algorithm family
Add short descriptions of the new exposition-only concepts to the design overview
Remove rotate_copy from scope due to design issues

9.2 R3 => R4

Revert back to range-as-the-output design aspect, change the formal wording accordingly
Revert back to requiring all ranges to be sized (&& instead of ||)
Clarify which execution policies are supported
Clarify that new APIs extend algorithm function objects in std::ranges
Add the feature test macro
Add implementation experience and thoughts on implementability
Fix known bugs in the signatures
Address other feedback from SG1 and SG9:
- Decide on constraining the execution policy template parameter
- List all the algorithms that are being given execution policy overloads
- List range algorithms that are being excluded

9.3 R2 => R3

Use iterator as an output
Add wording

9.4 R1 => R2

Summarize proposed differences from the serial range algorithms and from the non-range parallel algorithms
Allow all but one input sequences to be unbounded
List existing algorithms that take ranges for output
Update arguments and mitigation for using ranges for output
Add more arguments in support of random access ranges
Fix the signatures of for_each to match the proposed design

9.5 R0 => R1

Address the feedback from SG1 and SG9 review
Add more information about iterator constraints
Propose range as an output for the algorithms
Require ranges to be bounded

10 Polls

10.1 SG9, Wroclaw, 2024

Poll 1: Change mismatch and equal to require sized_range for both inputs (“&& instead of ||”).

SF	F	N	A	SA
4	3	1	0	0

Poll 2: Change transform to require sized_range for both inputs (“&& instead of ||”), with the plan to relax these constraints once we have a way to statically detect infinite ranges.

SF	F	N	A	SA
3	3	0	1	1

Poll 3: We want to remove the “legacy” overload that includes only an iterator as output for convenience, because we know it’s unsafe.

SF	F	N	A	SA
4	4	0	0	0

Poll 4 Forward [P3179R3] with the changes in [P3490R0] (as updated above) to LEWG for inclusion in C++26 with these changes polled above.

SF	F	N	A	SA
4	5	0	0	0

10.2 SG1, Wroclaw, 2024

Forward [P3179R3] to LEWG with the following notes:

The intention is that algorithms call begin/end only once, in serial code (we do not think any new words are needed)
The intention is that mismatch, transform and equal assume the unsized range is at least as large as the sized one (UB / precondition) or require && sized

SF	F	N	A	SA
4	8	0	0	0

10.3 Joint SG1 + SG9, St. Louis, 2024

Poll: Continue work on [P3179R2] for IS’26 with these notes: 1. RandomAccess for inputs and outputs 2. Iterators for outputs 3. We believe the overloads are worth it

SF	F	N	A	SA
7	4	2	1	0

10.4 SG9, Tokyo, 2024

Poll 1: for_each shouldn’t return the callable

SF	F	N	A	SA
2	4	2	0	0

Poll 2: Parallel std::ranges algos should return the same type as serial std::ranges algos

Unanimous consent.

Poll 3: Parallel ranges algos should require forward_range, not random_access_range

SF	F	N	A	SA
3	2	3	1	1

Poll 4: Range-based parallel algos should require const operator()

SF	F	N	A	SA
0	7	2	0	0

11 Acknowledgments

Thanks to Jonathan Muller for the wording review and providing useful feedback.

12 References

[P1068R11] Ilya Burylov, Pavel Dyakov, Ruslan Arutyunyan, Andrey Nikolaev, Alina Elizarova. 2024-04-02. Vector API for random number generation.

https://wg21.link/p1068r11

[P2300R10] Eric Niebler, Michał Dominiak, Georgy Evtushenko, Lewis Baker, Lucian Radu Teodorescu, Lee Howes, Kirk Shoop, Michael Garland, Bryce Adelstein Lelbach. 2024-06-28. `std::execution`.

https://wg21.link/p2300r10

[P2408R5] David Olsen. 2022-04-22. Ranges iterators as inputs to non-Ranges algorithms.

https://wg21.link/p2408r5

[P2500R2] Ruslan Arutyunyan, Alexey Kukanov. 2023-10-15. C++ parallel algorithms and P2300.

https://wg21.link/p2500r2

[P2902R0] Oliver Rosten. 2023-06-17. constexpr “Parallel” Algorithms.

https://wg21.link/p2902r0

[P3136R0] Tim Song. 2024-02-15. Retiring niebloids.

https://wg21.link/p3136r0

[P3159R0] Bryce Adelstein Lelbach. 2024-03-18. C++ Range Adaptors and Parallel Algorithms.

https://wg21.link/p3159r0

[P3179R0] Ruslan Arutyunyan, Alexey Kukanov. 2024-03-15. C++ parallel range algorithms.

https://wg21.link/p3179r0

[P3179R2] Ruslan Arutyunyan, Alexey Kukanov, Bryce Adelstein Lelbach. 2024-06-25. C++ parallel range algorithms.

https://wg21.link/p3179r2

[P3179R3] Ruslan Arutyunyan, Alexey Kukanov, Bryce Adelstein Lelbach. 2024-10-16. C++ parallel range algorithms.

https://wg21.link/p3179r3

[P3300R0] Bryce Adelstein Lelbach. 2024-02-15. C++ Asynchronous Parallel Algorithms.

https://wg21.link/p3300r0

[P3490R0] Alexey Kukanov, Ruslan Arutyunyan. 2024-11-14. Justification for ranges as the output of parallel range algorithms.

https://wg21.link/p3490r0

Document #:	P3179R5 [Latest] [Status]
Date:	2025-01-13
Project:	Programming Language C++
Audience:	LEWG
Reply-to:	Ruslan Arutyunyan <ruslan.arutyunyan@intel.com> Alexey Kukanov <alexey.kukanov@intel.com> Bryce Adelstein Lelbach (he/him/his) <brycelelbach@gmail.com>

Contents

Abstract

1 Motivation

2 Design overview

2.1 Design summary

2.1.1 Differences to serial range algorithms

2.1.2 Differences to C++17 parallel algorithms

2.1.3 Other design aspects

2.1.4 An example of the proposed API

2.2 Coexistence with schedulers

2.3 Supported execution policies

2.4 Algorithm return types

2.5 Extending the overload sets of algorithm function objects

2.6 Requiring random_access_iterator or random_access_range

2.7 Taking range as the output

2.8 Requiring ranges to be bounded

2.9 Requirements for callable parameters

2.10 constexpr parallel range algorithms

3 More examples

3.1 Change existing code to use parallel range algorithms

3.2 Less parallel algorithm calls and better expressiveness

4 Possible implementation of a parallel range algorithm

5 The proposal scope

5.1 In-scope

5.1.1 The counterparts of C++17 parallel algorithms in std::ranges namespace

5.1.2 Algorithms in std::ranges namespace only

5.2 Out-of-scope

5.2.1 Corner cases

5.2.2 The counterparts of exiting algorithms without ExecutionPolicy

5.2.3 Absence of some serial range-based algorithms

6 Implementation experience

7 Further work

7.1 Issues to address

7.2 LWG questions

7.3 Thread-safe views examination

8 Formal wording

8.1 Modify the __cpp_lib_parallel_algorithm macro in [version.syn]

8.2 Modify [ranges.syn]

8.3 Add an exposition-only concept to [range.refinements]

8.4 Modify [algorithms.parallel.defns]

8.5 Modify [algorithms.parallel.user]

8.6 Modify [algorithms.parallel.exec]

8.7 Modify [algorithms.parallel.exceptions]

8.8 Modify [algorithms.parallel.overloads]

8.9 Modify [algorithm.syn]

8.10 Modify all_of in [alg.all.of]

8.11 Modify any_of in [alg.any.of]

8.12 Modify none_of in [alg.none.of]

8.13 Modify contains in [alg.contains]

8.14 Modify for_each in [alg.foreach]

8.15 Modify find in [alg.find]

8.16 Modify find_last in [alg.find.last]

8.17 Modify find_end in [alg.find.end]

8.18 Modify find_first_of in [alg.find.first.of]

8.19 Modify adjacent_find in [alg.adjacent.find]

8.20 Modify count in [alg.count]

8.21 Modify mismatch in [alg.mismatch]

8.22 Modify equal in [alg.equal]

8.23 Modify search in [alg.search]

8.24 Modify starts_with in [alg.starts.with]

8.25 Modify ends_with in [alg.ends.with]

8.26 Modify copy in [alg.copy]

8.27 Modify move in [alg.move]

8.28 Modify swap_ranges in [alg.swap]

8.29 Modify transform in [alg.transform]

8.30 Modify replace in [alg.replace]

8.31 Modify fill in [alg.fill]

8.32 Modify generate in [alg.generate]

8.33 Modify remove in [alg.remove]

8.34 Modify unique in [alg.unique]

8.35 Modify reverse in [alg.reverse]

8.36 Modify rotate in [alg.rotate]

8.37 Modify shift in [alg.shift]

8.38 Modify sort in [sort]

8.39 Modify stable_sort in [stable.sort]

8.40 Modify partial_sort in [partial.sort]

8.41 Modify partial_sort_copy in [partial.sort.copy]

8.42 Modify is_sorted in [is.sorted]

8.43 Modify nth_element in [alg.nth.element]

8.44 Modify partitions in [alg.partitions]

2.6 Requiring `random_access_iterator` or `random_access_range`

2.10 `constexpr` parallel range algorithms

5.1.1 The counterparts of C++17 parallel algorithms in `std::ranges` namespace

5.1.2 Algorithms in `std::ranges` namespace only

5.2.2 The counterparts of exiting algorithms without `ExecutionPolicy`

8.1 Modify the `__cpp_lib_parallel_algorithm` macro in [version.syn]

8.10 Modify `all_of` in [alg.all.of]

8.11 Modify `any_of` in [alg.any.of]

8.12 Modify `none_of` in [alg.none.of]

8.13 Modify `contains` in [alg.contains]

8.14 Modify `for_each` in [alg.foreach]

8.15 Modify `find` in [alg.find]

8.16 Modify `find_last` in [alg.find.last]

8.17 Modify `find_end` in [alg.find.end]

8.18 Modify `find_first_of` in [alg.find.first.of]

8.19 Modify `adjacent_find` in [alg.adjacent.find]

8.20 Modify `count` in [alg.count]

8.21 Modify `mismatch` in [alg.mismatch]

8.22 Modify `equal` in [alg.equal]

8.23 Modify `search` in [alg.search]

8.24 Modify `starts_with` in [alg.starts.with]

8.25 Modify `ends_with` in [alg.ends.with]

8.26 Modify `copy` in [alg.copy]

8.27 Modify `move` in [alg.move]

8.28 Modify `swap_ranges` in [alg.swap]

8.29 Modify `transform` in [alg.transform]

8.30 Modify `replace` in [alg.replace]

8.31 Modify `fill` in [alg.fill]

8.32 Modify `generate` in [alg.generate]

8.33 Modify `remove` in [alg.remove]

8.34 Modify `unique` in [alg.unique]

8.35 Modify `reverse` in [alg.reverse]

8.36 Modify `rotate` in [alg.rotate]

8.37 Modify `shift` in [alg.shift]

8.38 Modify `sort` in [sort]

8.39 Modify `stable_sort` in [stable.sort]

8.40 Modify `partial_sort` in [partial.sort]

8.41 Modify `partial_sort_copy` in [partial.sort.copy]

8.42 Modify `is_sorted` in [is.sorted]

8.43 Modify `nth_element` in [alg.nth.element]

8.44 Modify `partitions` in [alg.partitions]

8.45 Modify `merge` in [alg.merge]

8.46 Modify `includes` in [includes]

8.47 Modify `set_union` in [set.union]

8.48 Modify `set_intersection` in [set.intersection]

8.49 Modify `set_difference` in [set.difference]

8.50 Modify `set_symmetric_difference` in [set.symmetric.difference]

8.51 Modify `is_heap` in [is.heap]

8.52 Modify `min`, `max`, `minmax` in [alg.min.max]

8.53 Modify `lexicographical_compare` in [alg.lex.comparison]