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Showing content from https://en.cppreference.com/w/cpp/language/../algorithm/../iterator/ranges/advance.html below:

std::ranges::advance - cppreference.com

1) Increments given iterator i for n times.

2) Increments given iterator i until i == bound.

3) Increments given iterator i for n times, or until i == bound, whichever comes first.

If n is negative, the iterator is decremented. In this case, I must model std::bidirectional_iterator, and S must be the same type as I if bound is provided, otherwise the behavior is undefined.

The function-like entities described on this page are algorithm function objects (informally known as niebloids), that is:

• Explicit template argument lists cannot be specified when calling any of them.
• None of them are visible to argument-dependent lookup.
• When any of them are found by normal unqualified lookup as the name to the left of the function-call operator, argument-dependent lookup is inhibited.

3) The difference between n and the actual distance i traversed.

Linear.

However, if I additionally models std::random_access_iterator, or S models std::sized_sentinel_for<I>, or I and S model std::assignable_from<I&, S>, complexity is constant.

The behavior is undefined if the specified sequence of increments or decrements would require that a non-incrementable iterator (such as the past-the-end iterator) is incremented, or that a non-decrementable iterator (such as the front iterator or the singular iterator) is decremented.

struct advance_fn
{
    template<std::input_or_output_iterator I>
    constexpr void operator()(I& i, std::iter_difference_t<I> n) const
    {
        if constexpr (std::random_access_iterator<I>)
            i += n;
        else
        {
            while (n > 0)
            {
                --n;
                ++i;
            }
 
            if constexpr (std::bidirectional_iterator<I>)
            {
                while (n < 0)
                {
                    ++n;
                    --i;
                }
            }
        }
    }
 
    template<std::input_or_output_iterator I, std::sentinel_for<I> S>
    constexpr void operator()(I& i, S bound) const
    {
        if constexpr (std::assignable_from<I&, S>)
            i = std::move(bound);
        else if constexpr (std::sized_sentinel_for<S, I>)
            (*this)(i, bound - i);
        else
            while (i != bound)
                ++i;
    }
 
    template<std::input_or_output_iterator I, std::sentinel_for<I> S>
    constexpr std::iter_difference_t<I>
    operator()(I& i, std::iter_difference_t<I> n, S bound) const
    {
        if constexpr (std::sized_sentinel_for<S, I>)
        {
            // std::abs is not constexpr until C++23
            auto abs = [](const std::iter_difference_t<I> x) { return x < 0 ? -x : x; };
 
            if (const auto dist = abs(n) - abs(bound - i); dist < 0)
            {
                (*this)(i, bound);
                return -dist;
            }
 
            (*this)(i, n);
            return 0;
        }
        else
        {
            while (n > 0 && i != bound)
            {
                --n;
                ++i;
            }
 
            if constexpr (std::bidirectional_iterator<I>)
            {
                while (n < 0 && i != bound)
                {
                    ++n;
                    --i;
                }
            }
 
            return n;
        }
    }
};
 
inline constexpr auto advance = advance_fn();

#include <iostream>
#include <iterator>
#include <vector>
 
int main()
{
    std::vector<int> v {3, 1, 4};
 
    auto vi = v.begin();
 
    std::ranges::advance(vi, 2);
    std::cout << "1) value: " << *vi << '\n' << std::boolalpha;
 
    std::ranges::advance(vi, v.end());
    std::cout << "2) vi == v.end(): " << (vi == v.end()) << '\n';
 
    std::ranges::advance(vi, -3);
    std::cout << "3) value: " << *vi << '\n';
 
    std::cout << "4) diff: " << std::ranges::advance(vi, 2, v.end())
              << ", value: " << *vi << '\n';
 
    std::cout << "5) diff: " << std::ranges::advance(vi, 4, v.end())
              << ", vi == v.end(): " << (vi == v.end()) << '\n';
}

Output:

1) value: 4
2) vi == v.end(): true
3) value: 3
4) diff: 0, value: 4
5) diff: 3, vi == v.end(): true

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