cartesian_product.h

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#pragma once
 
 
 
 
 
//#define DISABLE_CART_PROD_IOTA_SPEC
/* 
Adapted from TartanLlama/ranges: https://github.com/TartanLlama/ranges
Original version License CC0 1.0 Universal (see below)
 
Modified by Gonzalo Brito Gadeschi, NVIDIA corporation
Modifications under MIT license.
 
---
 
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*/
 
#include <algorithm>
#include <concepts>
#include <functional>
#include <iterator>
#include <ranges>
#include <tuple>
#include <type_traits>
#include <utility>
 
namespace tl {
   namespace detail {
      template <class I>
      concept single_pass_iterator = std::input_or_output_iterator<I> && !std::forward_iterator<I>;
 
      template <typename... V>
      constexpr auto common_iterator_category() {
         if constexpr ((std::ranges::random_access_range<V> && ...))
            return std::random_access_iterator_tag{};
         else if constexpr ((std::ranges::bidirectional_range<V> && ...))
            return std::bidirectional_iterator_tag{};
         else if constexpr ((std::ranges::forward_range<V> && ...))
            return std::forward_iterator_tag{};
         else if constexpr ((std::ranges::input_range<V> && ...))
            return std::input_iterator_tag{};
         else
            return std::output_iterator_tag{};
      }
   }
 
   template <class... V>
   using common_iterator_category = decltype(detail::common_iterator_category<V...>());
 
   template <class R>
   concept simple_view = std::ranges::view<R> && std::ranges::range<const R> &&
      std::same_as<std::ranges::iterator_t<R>, std::ranges::iterator_t<const R>> &&
      std::same_as<std::ranges::sentinel_t<R>,
      std::ranges::sentinel_t<const R>>;
 
   struct as_sentinel_t {};
   constexpr inline as_sentinel_t as_sentinel;
 
   template <bool Const, class T>
   using maybe_const = std::conditional_t<Const, const T, T>;
 
   template <std::destructible T>
   class basic_mixin : protected T {
   public:
      constexpr basic_mixin()
         noexcept(std::is_nothrow_default_constructible<T>::value)
         requires std::default_initializable<T> :
         T() {}
      constexpr basic_mixin(const T& t)
         noexcept(std::is_nothrow_copy_constructible<T>::value)
         requires std::copy_constructible<T> :
         T(t) {}
      constexpr basic_mixin(T&& t)
         noexcept(std::is_nothrow_move_constructible<T>::value)
         requires std::move_constructible<T> :
         T(std::move(t)) {}
 
 
      constexpr T& get() & noexcept { return *static_cast<T*>(this); }
      constexpr const T& get() const& noexcept { return *static_cast<T const*>(this); }
      constexpr T&& get() && noexcept { return std::move(*static_cast<T*>(this)); }
      constexpr const T&& get() const&& noexcept { return std::move(*static_cast<T const*>(this)); }
   };
 
   namespace cursor {
      namespace detail {
         template <class C>
         struct tags {
            static constexpr auto single_pass() requires requires { { C::single_pass } -> std::convertible_to<bool>; } {
               return C::single_pass;
            }
            static constexpr auto single_pass() { return false; }
 
            static constexpr auto contiguous() requires requires { { C::contiguous } -> std::convertible_to<bool>; } {
               return C::contiguous;
            }
            static constexpr auto contiguous() { return false; }
         };
      }
      template <class C>
      constexpr bool single_pass = detail::tags<C>::single_pass();
 
      template <class C>
      constexpr bool tagged_contiguous = detail::tags<C>::contiguous();
 
      namespace detail {
         template <class C>
         struct deduced_mixin_t {
            template <class T> static auto deduce(int)-> typename T::mixin;
            template <class T> static auto deduce(...)->tl::basic_mixin<T>;
            using type = decltype(deduce<C>(0));
         };
      }
 
      template <class C>
      using mixin_t = typename detail::deduced_mixin_t<C>::type;
 
      template <class C>
      requires
         requires(const C& c) { c.read(); }
      using reference_t = decltype(std::declval<const C&>().read());
 
      namespace detail {
         template <class C>
         struct deduced_value_t {
            template<class T> static auto deduce(int)-> typename T::value_type;
            template<class T> static auto deduce(...)->std::decay_t<reference_t<T>>;
 
            using type = decltype(deduce<C>(0));
         };
      }
 
      template <class C>
      requires std::same_as<typename detail::deduced_value_t<C>::type, std::decay_t<typename detail::deduced_value_t<C>::type>>
         using value_type_t = typename detail::deduced_value_t<C>::type;
 
      namespace detail {
         template <class C>
         struct deduced_difference_t {
            template <class T> static auto deduce(int)-> typename T::difference_type;
            template <class T>
            static auto deduce(long)->decltype(std::declval<const T&>().distance_to(std::declval<const T&>()));
            template <class T>
            static auto deduce(...)->std::ptrdiff_t;
 
            using type = decltype(deduce<C>(0));
         };
      }
 
      template <class C>
      using difference_type_t = typename detail::deduced_difference_t<C>::type;
 
      template <class C>
      concept cursor = std::semiregular<std::remove_cv_t<C>>
         && std::semiregular<mixin_t<std::remove_cv_t<C>>>
         && requires {typename difference_type_t<C>; };
 
      template <class C>
      concept readable = cursor<C> && requires(const C & c) {
         c.read();
         typename reference_t<C>;
         typename value_type_t<C>;
      };
 
      template <class C>
      concept arrow = readable<C>
         && requires(const C & c) { c.arrow(); };
 
      template <class C, class T>
      concept writable = cursor<C>
         && requires(C & c, T && t) { c.write(std::forward<T>(t)); };
 
      template <class S, class C>
      concept sentinel_for = cursor<C> && std::semiregular<S>
         && requires(const C & c, const S & s) { {c.equal(s)} -> std::same_as<bool>; };
 
      template <class S, class C>
      concept sized_sentinel_for = sentinel_for<S, C> &&
         requires(const C & c, const S & s) {
            {c.distance_to(s)} -> std::same_as<difference_type_t<C>>;
      };
 
      template <class C>
      concept next = cursor<C> && requires(C & c) { c.next(); };
 
      template <class C>
      concept prev = cursor<C> && requires(C & c) { c.prev(); };
 
      template <class C>
      concept advance = cursor<C>
         && requires(C & c, difference_type_t<C> n) { c.advance(n); };
 
      template <class C>
      concept indirect_move = readable<C>
         && requires(const C & c) { c.indirect_move(); };
 
      template <class C, class O>
      concept indirect_swap = readable<C> && readable<O>
         && requires(const C & c, const O & o) {
         c.indirect_swap(o);
         o.indirect_swap(c);
      };
 
      template <class C>
      concept input = readable<C> && next<C>;
      template <class C>
      concept forward = input<C> && sentinel_for<C, C> && !single_pass<C>;
      template <class C>
      concept bidirectional = forward<C> && prev<C>;
      template <class C>
      concept random_access = bidirectional<C> && advance<C> && sized_sentinel_for<C, C>;
      template <class C>
      concept contiguous = random_access<C> && tagged_contiguous<C> && std::is_reference_v<reference_t<C>>;
 
      template <class C>
      constexpr auto cpp20_iterator_category() {
         if constexpr (contiguous<C>)
            return std::contiguous_iterator_tag{};
         else if constexpr (random_access<C>)
            return std::random_access_iterator_tag{};
         else if constexpr (bidirectional<C>)
            return std::bidirectional_iterator_tag{};
         else if constexpr (forward<C>)
            return std::forward_iterator_tag{};
         else
            return std::input_iterator_tag{};
      }
      template <class C>
      using cpp20_iterator_category_t = decltype(cpp20_iterator_category<C>());
 
      //There were a few changes in requirements on iterators between C++17 and C++20
      //See https://wg21.link/p2259 for discussion
      //- C++17 didn't have contiguous iterators
      //- C++17 input iterators required *it++ to be valid
      //- C++17 forward iterators required the reference type to be exactly value_type&/value_type const& (i.e. not a proxy)
      struct not_a_cpp17_iterator {};
 
      template <class C>
      concept reference_is_value_type_ref =
         (std::same_as<reference_t<C>, value_type_t<C>&> || std::same_as<reference_t<C>, value_type_t<C> const&>);
 
      template <class C>
      concept can_create_postincrement_proxy =
         (std::move_constructible<value_type_t<C>> && std::constructible_from<value_type_t<C>, reference_t<C>>);
 
      template <class C>
      constexpr auto cpp17_iterator_category() {
     if constexpr (random_access<C>
#if !defined(__NVCOMPILER)
               // YOLO: with nvc++ proxy iterators can be random access . . .
               // BUG: Need to update Thrust to C++20 iterator categories
              && reference_is_value_type_ref<C>
#endif
     )
            return std::random_access_iterator_tag{};
         else if constexpr (bidirectional<C> && reference_is_value_type_ref<C>)
            return std::bidirectional_iterator_tag{};
         else if constexpr (forward<C> && reference_is_value_type_ref<C>)
            return std::forward_iterator_tag{};
         else if constexpr (can_create_postincrement_proxy<C>)
            return std::input_iterator_tag{};
         else
            return not_a_cpp17_iterator{};
      }
      template <class C>
      using cpp17_iterator_category_t = decltype(cpp17_iterator_category<C>());
 
      //iterator_concept and iterator_category are tricky; this abstracts them out.
      //Since the rules for iterator categories changed between C++17 and C++20
      //a C++20 iterator may have a weaker category in C++17,
      //or it might not be a valid C++17 iterator at all.
      //iterator_concept will be the C++20 iterator category.
      //iterator_category will be the C++17 iterator category, or it will not exist
      //in the case that the iterator is not a valid C++17 iterator.
      template <cursor C, class category = cpp17_iterator_category_t<C>>
      struct associated_types_category_base {
         using iterator_category = category;
      };
      template <cursor C>
      struct associated_types_category_base<C, not_a_cpp17_iterator> {};
 
      template <cursor C>
      struct associated_types : associated_types_category_base<C> {
         using iterator_concept = cpp20_iterator_category_t<C>;
         using value_type = cursor::value_type_t<C>;
         using difference_type = cursor::difference_type_t<C>;
         using reference = cursor::reference_t<C>;
      };
 
      namespace detail {
         // We assume a cursor is writeable if it's either not readable
         // or it is writeable with the same type it reads to
         template <class C>
         struct is_writable_cursor {
            template <readable T>
            requires requires (C c) {
               c.write(c.read());
            }
            static auto deduce()->std::true_type;
 
            template <readable T>
            static auto deduce()->std::false_type;
 
            template <class T>
            static auto deduce()->std::true_type;
 
            static constexpr bool value = decltype(deduce<C>())::value;
         };
      }
   }
 
   namespace detail {
      template <class T>
      struct post_increment_proxy {
      private:
         T cache_;
 
      public:
         template<typename U>
         constexpr post_increment_proxy(U&& t)
            : cache_(std::forward<U>(t))
         {}
         constexpr T const& operator*() const noexcept
         {
            return cache_;
         }
      };
   }
 
 
   template <cursor::input C>
   class basic_iterator :
      public cursor::mixin_t<C>
   {
   private:
      using mixin = cursor::mixin_t<C>;
 
      constexpr auto& cursor() noexcept { return this->mixin::get(); }
      constexpr auto const& cursor() const noexcept { return this->mixin::get(); }
 
      template <cursor::input>
      friend class basic_iterator;
 
      //TODO these need to change to support output iterators
      using reference_t = decltype(std::declval<C>().read());
      using const_reference_t = reference_t;
 
   public:
      using mixin::get;
 
      using value_type = cursor::value_type_t<C>;
      using difference_type = cursor::difference_type_t<C>;
      using reference = cursor::reference_t<C>;
 
      basic_iterator() = default;
 
      using mixin::mixin;
 
      constexpr explicit basic_iterator(C&& c)
         noexcept(std::is_nothrow_constructible_v<mixin, C&&>) :
         mixin(std::move(c)) {}
 
 
      constexpr explicit basic_iterator(C const& c)
         noexcept(std::is_nothrow_constructible_v<mixin, C const&>) :
         mixin(c) {}
 
      template <std::convertible_to<C> O>
      constexpr basic_iterator(basic_iterator<O>&& that)
         noexcept(std::is_nothrow_constructible<mixin, O&&>::value) :
         mixin(that.cursor()) {}
 
      template <std::convertible_to<C> O>
      constexpr basic_iterator(const basic_iterator<O>& that)
         noexcept(std::is_nothrow_constructible<mixin, const O&>::value) :
         mixin(std::move(that.cursor())) {}
 
      template <std::convertible_to<C> O>
      constexpr basic_iterator& operator=(basic_iterator<O>&& that) &
         noexcept(std::is_nothrow_assignable<C&, O&&>::value) {
         cursor() = std::move(that.cursor());
         return *this;
      }
 
      template <std::convertible_to<C> O>
      constexpr basic_iterator& operator=(const basic_iterator<O>& that) &
         noexcept(std::is_nothrow_assignable<C&, const O&>::value) {
         cursor() = that.cursor();
         return *this;
      }
 
      template <class T>
      requires
         (!std::same_as<std::decay_t<T>, basic_iterator> &&
            !cursor::next<C>&&
            cursor::writable<C, T>)
         constexpr basic_iterator& operator=(T&& t) &
         noexcept(noexcept(std::declval<C&>().write(static_cast<T&&>(t)))) {
         cursor() = std::forward<T>(t);
         return *this;
      }
 
      friend constexpr decltype(auto) iter_move(const basic_iterator& i)
#if !defined(__NVCOMPILER)
    noexcept(noexcept(i.cursor().indirect_move()))
#endif  
         requires cursor::indirect_move<C> {
         return i.cursor().indirect_move();
      }
 
      template <class O>
      requires cursor::indirect_swap<C, O>
         friend constexpr void iter_swap(
            const basic_iterator& x, const basic_iterator<O>& y)
#if !defined(__NVCOMPILER)  
         noexcept(noexcept((void)x.indirect_swap(y)))
#endif
     {
         x.indirect_swap(y);
      }
 
      //Input iterator
      constexpr decltype(auto) operator*() const
         noexcept(noexcept(std::declval<const C&>().read()))
         requires (cursor::readable<C> && !cursor::detail::is_writable_cursor<C>::value) {
         return cursor().read();
      }
 
      //Output iterator
      constexpr decltype(auto) operator*()
         noexcept(noexcept(reference_t{ cursor() }))
         requires (cursor::next<C>&& cursor::detail::is_writable_cursor<C>::value) {
         return reference_t{ cursor() };
      }
 
      //Output iterator
      constexpr decltype(auto) operator*() const
         noexcept(noexcept(
            const_reference_t{ cursor() }))
         requires (cursor::next<C>&& cursor::detail::is_writable_cursor<C>::value) {
         return const_reference_t{ cursor() };
      }
 
      constexpr basic_iterator& operator*() noexcept
         requires (!cursor::next<C>) {
         return *this;
      }
 
      // operator->: "Manual" deduction override,
      constexpr decltype(auto) operator->() const
         noexcept(noexcept(cursor().arrow()))
         requires cursor::arrow<C> {
         return cursor().arrow();
      }
      // operator->: Otherwise, if reference_t is an lvalue reference,
      constexpr decltype(auto) operator->() const
         noexcept(noexcept(*std::declval<const basic_iterator&>()))
         requires (cursor::readable<C> && !cursor::arrow<C>)
         && std::is_lvalue_reference<const_reference_t>::value{
         return std::addressof(**this);
      }
 
         // modifiers
         constexpr basic_iterator& operator++() & noexcept {
         return *this;
      }
      constexpr basic_iterator& operator++() &
    noexcept(noexcept(std::declval<basic_iterator>().cursor().next()))
         requires cursor::next<C> {
         cursor().next();
         return *this;
      }
 
      //C++17 required that *it++ was valid.
      //For input iterators, we can't copy *this, so we need to create a proxy reference.
      constexpr auto operator++(int) &
         noexcept(noexcept(++std::declval<basic_iterator&>()) &&
            std::is_nothrow_move_constructible_v<value_type>&&
            std::is_nothrow_constructible_v<value_type, reference>)
         requires (cursor::single_pass<C>&&
            std::move_constructible<value_type>&&
            std::constructible_from<value_type, reference>) {
         detail::post_increment_proxy<value_type> p(**this);
         ++* this;
         return p;
      }
 
      //If we can't create a proxy reference, it++ is going to return void
      constexpr void operator++(int) &
         noexcept(noexcept(++std::declval<basic_iterator&>()))
         requires (cursor::single_pass<C> && !(std::move_constructible<value_type>&&
            std::constructible_from<value_type, reference>)) {
         (void)(++(*this));
      }
 
      //If C is a forward cursor then copying it is fine
      constexpr basic_iterator operator++(int) &
         noexcept(std::is_nothrow_copy_constructible_v<C>&&
            std::is_nothrow_move_constructible_v<C> &&
            noexcept(++std::declval<basic_iterator&>()))
         requires (!cursor::single_pass<C>) {
         auto temp = *this;
         ++* this;
         return temp;
      }
 
      constexpr basic_iterator& operator--() &
         noexcept(noexcept(cursor().prev()))
         requires cursor::bidirectional<C> {
         cursor().prev();
         return *this;
      }
 
      //Postfix decrement doesn't have the same issue as postfix increment
      //because bidirectional requires the cursor to be a forward cursor anyway
      //so copying it is fine.
      constexpr basic_iterator operator--(int) &
         noexcept(std::is_nothrow_copy_constructible<basic_iterator>::value&&
            std::is_nothrow_move_constructible<basic_iterator>::value &&
            noexcept(--std::declval<basic_iterator&>()))
         requires cursor::bidirectional<C> {
         auto tmp = *this;
         --* this;
         return tmp;
      }
 
      constexpr basic_iterator& operator+=(difference_type n) &
         noexcept(noexcept(cursor().advance(n)))
         requires cursor::random_access<C> {
         cursor().advance(n);
         return *this;
      }
 
      constexpr basic_iterator& operator-=(difference_type n) &
         noexcept(noexcept(cursor().advance(-n)))
         requires cursor::random_access<C> {
         cursor().advance(-n);
         return *this;
      }
 
      constexpr decltype(auto) operator[](difference_type n) const
         noexcept(noexcept(*(std::declval<basic_iterator&>() + n)))
         requires cursor::random_access<C> {
         return *(*this + n);
      }
 
      // non-template type-symmetric ops to enable implicit conversions
      friend constexpr difference_type operator-(
         const basic_iterator& x, const basic_iterator& y)
         noexcept(noexcept(y.cursor().distance_to(x.cursor())))
         requires cursor::sized_sentinel_for<C, C> {
         return y.cursor().distance_to(x.cursor());
      }
      friend constexpr bool operator==(
         const basic_iterator& x, const basic_iterator& y)
#if !defined(__NVCOMPILER)  
         noexcept(noexcept(x.cursor().equal(y.cursor())))
         requires cursor::sentinel_for<C, C>
#endif
      {
         return x.cursor().equal(y.cursor());
      }
      friend constexpr bool operator!=(
         const basic_iterator& x, const basic_iterator& y)
#if !defined(__NVCOMPILER)      
         noexcept(noexcept(!(x == y)))
         requires cursor::sentinel_for<C, C>
#endif
      { 
         return !(x == y);
      }
      friend constexpr bool operator<(
         const basic_iterator& x, const basic_iterator& y)
#if !defined(__NVCOMPILER)          
         noexcept(noexcept(y - x))
#endif
         requires cursor::sized_sentinel_for<C, C> {
         return 0 < (y - x);
      }
      friend constexpr bool operator>(
         const basic_iterator& x, const basic_iterator& y)
#if !defined(__NVCOMPILER)              
         noexcept(noexcept(y - x))
#endif  
         requires cursor::sized_sentinel_for<C, C> {
         return 0 > (y - x);
      }
      friend constexpr bool operator<=(
         const basic_iterator& x, const basic_iterator& y)
#if !defined(__NVCOMPILER)                  
         noexcept(noexcept(y - x))
#endif  
         requires cursor::sized_sentinel_for<C, C> {
         return 0 <= (y - x);
      }
      friend constexpr bool operator>=(
         const basic_iterator& x, const basic_iterator& y)
#if !defined(__NVCOMPILER)                      
         noexcept(noexcept(y - x))
#endif  
         requires cursor::sized_sentinel_for<C, C> {
         return 0 >= (y - x);
      }
   };
 
   namespace detail {
      template <class C>
      struct is_basic_iterator {
         template <class T>
         static auto deduce(basic_iterator<T> const&)->std::true_type;
         template <class T>
         static auto deduce(...)->std::false_type;
         static constexpr inline bool value = decltype(deduce(std::declval<C>()))::value;
      };
   }
 
   // basic_iterator nonmember functions
   template <class C>
   constexpr basic_iterator<C> operator+(
      const basic_iterator<C>& i, cursor::difference_type_t<C> n)
      noexcept(std::is_nothrow_copy_constructible<basic_iterator<C>>::value&&
         std::is_nothrow_move_constructible<basic_iterator<C>>::value &&
         noexcept(std::declval<basic_iterator<C>&>() += n))
      requires cursor::random_access<C> {
      auto tmp = i;
      tmp += n;
      return tmp;
   }
   template <class C>
   constexpr basic_iterator<C> operator+(
      cursor::difference_type_t<C> n, const basic_iterator<C>& i)
      noexcept(noexcept(i + n))
      requires cursor::random_access<C> {
      return i + n;
   }
 
   template <class C>
   constexpr basic_iterator<C> operator-(
      const basic_iterator<C>& i, cursor::difference_type_t<C> n)
      noexcept(noexcept(i + (-n)))
      requires cursor::random_access<C> {
      return i + (-n);
   }
   template <class C1, class C2>
   requires cursor::sized_sentinel_for<C1, C2>
      constexpr cursor::difference_type_t<C2> operator-(
         const basic_iterator<C1>& lhs, const basic_iterator<C2>& rhs)
      noexcept(noexcept(
         rhs.get().distance_to(lhs.get()))) {
      return rhs.get().distance_to(lhs.get());
   }
   template <class C, class S>
   requires cursor::sized_sentinel_for<S, C>
      constexpr cursor::difference_type_t<C> operator-(
         const S& lhs, const basic_iterator<C>& rhs)
      noexcept(noexcept(rhs.get().distance_to(lhs))) {
      return rhs.get().distance_to(lhs);
   }
   template <class C, class S>
   requires cursor::sized_sentinel_for<S, C>
      constexpr cursor::difference_type_t<C> operator-(
         const basic_iterator<C>& lhs, const S& rhs)
      noexcept(noexcept(-(rhs - lhs))) {
      return -(rhs - lhs);
   }
 
   template <class C1, class C2>
   requires cursor::sentinel_for<C2, C1>
      constexpr bool operator==(
         const basic_iterator<C1>& lhs, const basic_iterator<C2>& rhs)
      noexcept(noexcept(lhs.get().equal(rhs.get()))) {
      return lhs.get().equal(rhs.get());
   }
   template <class C, class S>
   requires cursor::sentinel_for<S, C>
      constexpr bool operator==(
         const basic_iterator<C>& lhs, const S& rhs)
      noexcept(noexcept(lhs.get().equal(rhs))) {
      return lhs.get().equal(rhs);
   }
   template <class C, class S>
   requires cursor::sentinel_for<S, C>
      constexpr bool operator==(
         const S& lhs, const basic_iterator<C>& rhs)
      noexcept(noexcept(rhs == lhs)) {
      return rhs == lhs;
   }
 
   template <class C1, class C2>
   requires cursor::sentinel_for<C2, C1>
      constexpr bool operator!=(
         const basic_iterator<C1>& lhs, const basic_iterator<C2>& rhs)
      noexcept(noexcept(!(lhs == rhs))) {
      return !(lhs == rhs);
   }
   template <class C, class S>
   requires cursor::sentinel_for<S, C>
      constexpr bool operator!=(
         const basic_iterator<C>& lhs, const S& rhs)
      noexcept(noexcept(!lhs.get().equal(rhs))) {
      return !lhs.get().equal(rhs);
   }
   template <class C, class S>
   requires cursor::sentinel_for<S, C>
      constexpr bool operator!=(
         const S& lhs, const basic_iterator<C>& rhs)
      noexcept(noexcept(!rhs.get().equal(lhs))) {
      return !rhs.get().equal(lhs);
   }
 
   template <class C1, class C2>
   requires cursor::sized_sentinel_for<C1, C2>
      constexpr bool operator<(
         const basic_iterator<C1>& lhs, const basic_iterator<C2>& rhs)
      noexcept(noexcept(lhs - rhs < 0)) {
      return (lhs - rhs) < 0;
   }
 
   template <class C1, class C2>
   requires cursor::sized_sentinel_for<C1, C2>
      constexpr bool operator>(
         const basic_iterator<C1>& lhs, const basic_iterator<C2>& rhs)
      noexcept(noexcept((lhs - rhs) > 0)) {
      return (lhs - rhs) > 0;
   }
 
   template <class C1, class C2>
   requires cursor::sized_sentinel_for<C1, C2>
      constexpr bool operator<=(
         const basic_iterator<C1>& lhs, const basic_iterator<C2>& rhs)
      noexcept(noexcept((lhs - rhs) <= 0)) {
      return (lhs - rhs) <= 0;
   }
 
   template <class C1, class C2>
   requires cursor::sized_sentinel_for<C1, C2>
      constexpr bool operator>=(
         const basic_iterator<C1>& lhs, const basic_iterator<C2>& rhs)
      noexcept(noexcept((lhs - rhs) >= 0)) {
      return (lhs - rhs) >= 0;
   }
 
   template <class V, bool Const>
   class basic_sentinel {
      using Base = std::conditional_t<Const, const V, V>;
 
   public:
      std::ranges::sentinel_t<Base> end_{};
      basic_sentinel() = default;
      constexpr explicit basic_sentinel(std::ranges::sentinel_t<Base> end)
         : end_{ std::move(end) } {}
 
      constexpr basic_sentinel(basic_sentinel<V, !Const> other) requires Const&& std::
         convertible_to<std::ranges::sentinel_t<V>,
         std::ranges::sentinel_t<Base>>
         : end_{ std::move(other.end_) } {}
 
      constexpr auto end() const {
         return end_;
      }
 
      friend class basic_sentinel<V, !Const>;
   };
 
   //tl::compose composes f and g such that compose(f,g)(args...) is f(g(args...)), i.e. g is called first
   template <class F, class G>
   struct compose_fn {
      [[no_unique_address]] F f;
      [[no_unique_address]] G g;
 
      template <class A, class B>
      compose_fn(A&& a, B&& b) : f(std::forward<A>(a)), g(std::forward<B>(b)) {}
 
      template <class A, class B, class ... Args>
      static constexpr auto call(A&& a, B&& b, Args&&... args) {
         if constexpr (std::is_void_v<std::invoke_result_t<G, Args...>>) {
            std::invoke(std::forward<B>(b), std::forward<Args>(args)...);
            return std::invoke(std::forward<A>(a));
         }
         else {
            return std::invoke(std::forward<A>(a), std::invoke(std::forward<B>(b), std::forward<Args>(args)...));
         }
      }
 
      template <class... Args>
      constexpr auto operator()(Args&&... args) & {
         return call(f, g, std::forward<Args>(args)...);
      }
 
      template <class... Args>
      constexpr auto operator()(Args&&... args) const& {
         return call(f, g, std::forward<Args>(args)...);
      }
 
      template <class... Args>
      constexpr auto operator()(Args&&... args)&& {
         return call(std::move(f), std::move(g), std::forward<Args>(args)...);
      }
 
      template <class... Args>
      constexpr auto operator()(Args&&... args) const&& {
         return call(std::move(f), std::move(g), std::forward<Args>(args)...);
      }
   };
 
   template <class F, class G>
   constexpr auto compose(F&& f, G&& g) {
      return compose_fn<std::remove_cvref_t<F>, std::remove_cvref_t<G>>(std::forward<F>(f), std::forward<G>(g));
   }
 
   //tl::pipeable takes some invocable and enables:
   //- Piping a single argument to it such that a | pipeable is the same as pipeable(a)
   //- Piping it to another pipeable object, such that a | b is the same as tl::compose(b, a)
   struct pipeable_base {};
   template <class T>
   concept is_pipeable = std::is_base_of_v<pipeable_base, std::remove_cvref_t<T>>;
 
   template <class F>
   struct pipeable_fn : pipeable_base {
      [[no_unique_address]] F f_;
 
      constexpr pipeable_fn(F f) : f_(std::move(f)) {}
 
      template <class... Args>
      constexpr auto operator()(Args&&... args) const requires std::invocable<F, Args...> {
         return std::invoke(f_, std::forward<Args>(args)...);
      }
   };
 
   template <class F>
   constexpr auto pipeable(F f) {
      return pipeable_fn{ std::move(f) };
   }
 
   template <class V, class Pipe>
   constexpr auto operator|(V&& v, Pipe&& fn)
      requires (!is_pipeable<V> && is_pipeable<Pipe> && std::invocable<Pipe, V>) {
      return std::invoke(std::forward<Pipe>(fn).f_, std::forward<V>(v));
   }
 
   template <class Pipe1, class Pipe2>
   constexpr auto operator|(Pipe1&& p1, Pipe2&& p2)
      requires (is_pipeable<Pipe1>&& is_pipeable<Pipe2>) {
      return pipeable(compose(std::forward<Pipe2>(p2).f_, std::forward<Pipe1>(p1).f_));
   }
 
   //tl::bind_back binds the last N arguments of f to the given ones, returning a new closure
   template <class F, class... Args>
   constexpr auto bind_back(F&& f, Args&&... args) {
      return[f_ = std::forward<F>(f), ...args_ = std::forward<Args>(args)]
      (auto&&... other_args) 
      requires std::invocable<F&, decltype(other_args)..., Args&...> {
         return std::invoke(f_, std::forward<decltype(other_args)>(other_args)..., args_...);
      };
   }
}
 
namespace std {
   template <class C>
   struct iterator_traits<tl::basic_iterator<C>> : tl::cursor::associated_types<C> {};
}
 
namespace tl  {
 
   template <class Tuple>
   constexpr inline std::size_t tuple_size = std::tuple_size_v<std::remove_cvref_t<Tuple>>;
 
   template <std::size_t N>
   using index_constant = std::integral_constant<std::size_t, N>;
 
   namespace meta {
      //Partially-apply the given template with the given arguments
      template <template <class...> class T, class... Args>
      struct partial {
         template <class... MoreArgs>
         struct apply {
            using type = T<Args..., MoreArgs...>;
         };
      };
 
      namespace detail {
         template <class T, template<class...> class Into, std::size_t... Idx>
         constexpr auto repeat_into_impl(std::index_sequence<Idx...>)
            ->Into < typename decltype((Idx, std::type_identity<T>{}))::type... > ;
      }
 
      //Repeat the given type T into the template Into N times
      template <class T, std::size_t N, template <class...> class Into>
      using repeat_into = decltype(tl::meta::detail::repeat_into_impl<T,Into>(std::make_index_sequence<N>{}));
   }
 
   //If the size of Ts is 2, returns pair<Ts...>, otherwise returns tuple<Ts...>
   namespace detail {
      template<class... Ts>
      struct tuple_or_pair_impl : std::type_identity<std::tuple<Ts...>> {};
      template<class Fst, class Snd>
      struct tuple_or_pair_impl<Fst, Snd> : std::type_identity<std::pair<Fst, Snd>> {};
   }
   template<class... Ts>
   using tuple_or_pair = typename detail::tuple_or_pair_impl<Ts...>::type;
 
   template <class Tuple>
   constexpr auto min_tuple(Tuple&& tuple) {
      return std::apply([](auto... sizes) {
         return std::ranges::min({
           std::common_type_t<decltype(sizes)...>(sizes)...
            });
         }, std::forward<Tuple>(tuple));
   }
 
   template <class Tuple>
   constexpr auto max_tuple(Tuple&& tuple) {
      return std::apply([](auto... sizes) {
         return std::ranges::max({
           std::common_type_t<decltype(sizes)...>(sizes)...
            });
         }, std::forward<Tuple>(tuple));
   }
 
   //Call f on every element of the tuple, returning a new one
   template<class F, class... Tuples>
   constexpr auto tuple_transform(F&& f, Tuples&&... tuples)
   {
      if constexpr (sizeof...(Tuples) > 1) {
         auto call_at_index = []<std::size_t Idx, class Fu, class... Ts>
            (tl::index_constant<Idx>, Fu f, Ts&&... tuples) {
            return f(std::get<Idx>(std::forward<Ts>(tuples))...);
         };
 
         constexpr auto min_size = tl::min_tuple(std::tuple(tl::tuple_size<Tuples>...));
 
         return[&] <std::size_t... Idx>(std::index_sequence<Idx...>) {
            return tuple_or_pair < std::decay_t<decltype(call_at_index(tl::index_constant<Idx>{}, std::move(f), std::forward<Tuples>(tuples)...)) > ... >
               (call_at_index(tl::index_constant<Idx>{}, std::move(f), std::forward<Tuples>(tuples)...)...);
         }(std::make_index_sequence<min_size>{});
      }
      else if constexpr (sizeof...(Tuples) == 1) {
         return std::apply([&]<class... Ts>(Ts&&... elements) {
            return tuple_or_pair<std::invoke_result_t<F&, Ts>...>(
               std::invoke(f, std::forward<Ts>(elements))...
               );
         }, std::forward<Tuples>(tuples)...);
      }
      else {
         return std::tuple{};
      }
   }
 
   //Call f on every element of the tuple
   template<class F, class Tuple>
   constexpr auto tuple_for_each(F&& f, Tuple&& tuple)
   {
      return std::apply([&]<class... Ts>(Ts&&... elements) {
         (std::invoke(f, std::forward<Ts>(elements)), ...);
      }, std::forward<Tuple>(tuple));
   }
 
   template <class Tuple>
   constexpr auto tuple_pop_front(Tuple&& tuple) {
      return std::apply([](auto&& head, auto&&... tail) {
         return std::pair(std::forward<decltype(head)>(head), std::tuple(std::forward<decltype(tail)>(tail)...));
         }, std::forward<Tuple>(tuple));
   }
 
   namespace detail {
      template <class F, class V>
      constexpr auto tuple_fold_impl(F, V v) {
         return v;
      }
      template <class F, class V, class Arg, class... Args>
      constexpr auto tuple_fold_impl(F f, V v, Arg arg, Args&&... args) {
         return tl::detail::tuple_fold_impl(f, 
            std::invoke(f, std::move(v), std::move(arg)), 
            std::forward<Args>(args)...);
      }
   }
 
   template <class F, class T, class Tuple>
   constexpr auto tuple_fold(Tuple tuple, T t, F f) {
      return std::apply([&](auto&&... args) {
         return tl::detail::tuple_fold_impl(std::move(f), std::move(t), std::forward<decltype(args)>(args)...);
         }, std::forward<Tuple>(tuple));
   }
 
   template<class... Tuples>
   constexpr auto tuple_zip(Tuples&&... tuples) {
      auto zip_at_index = []<std::size_t Idx, class... Ts>
         (tl::index_constant<Idx>, Ts&&... tuples) {
         return tuple_or_pair<std::decay_t<decltype(std::get<Idx>(std::forward<Ts>(tuples)))>...>(std::get<Idx>(std::forward<Ts>(tuples))...);
      };
 
      constexpr auto min_size = tl::min_tuple(std::tuple(tl::tuple_size<Tuples>...));
 
      return[&] <std::size_t... Idx>(std::index_sequence<Idx...>) {
         return tuple_or_pair<std::decay_t<decltype(zip_at_index(tl::index_constant<Idx>{}, std::forward<Tuples>(tuples)...))>... >
            (zip_at_index(tl::index_constant<Idx>{}, std::forward<Tuples>(tuples)...)...);
      }(std::make_index_sequence<min_size>{});
   }
 
   template <std::ranges::forward_range... Vs>
   requires (std::ranges::view<Vs> && ...) class cartesian_product_view
      : public std::ranges::view_interface<cartesian_product_view<Vs...>> {
 
      //random access + sized is allowed because we can jump all iterators to the end
      template <class... Ts>
      static constexpr bool am_common = (std::ranges::common_range<Ts> && ...)
         || ((std::ranges::random_access_range<Ts> && ...) && (std::ranges::sized_range<Ts> && ...));
 
      template <class... Ts>
      static constexpr bool am_sized = (std::ranges::sized_range<Ts> && ...);
 
      //requires common because we need to be able to cycle the iterators from begin to end in O(n)
      template <class... Ts>
      static constexpr bool am_bidirectional =
         ((std::ranges::bidirectional_range<Ts> && ...) && (std::ranges::common_range<Ts> && ...));
 
      //requires sized because we need to calculate new positions for iterators using arithmetic modulo the range size
      template <class... Ts>
      static constexpr bool am_random_access =
         ((std::ranges::random_access_range<Ts> && ...) &&
            (std::ranges::sized_range<Ts> && ...));
 
      template <class... Ts>
      static constexpr bool am_distanceable =
         ((std::sized_sentinel_for<std::ranges::iterator_t<Ts>, std::ranges::iterator_t<Ts>>) && ...)
         && am_sized<Ts...>;
 
      std::tuple<Vs...> bases_;
 
      template <bool Const>
      class cursor;
 
      //Wraps the end iterator for the 0th range.
      //This is all that's required because the cursor will only ever set the 0th iterator to end when
      //the cartesian product operation has completed.
      template <bool Const>
      class sentinel {
         using parent = std::conditional_t<Const, const cartesian_product_view, cartesian_product_view>;
         using first_base = decltype(std::get<0>(std::declval<parent>().bases_));
         std::ranges::sentinel_t<first_base> end_;
 
      public:
         sentinel() = default;
         sentinel(std::ranges::sentinel_t<first_base> end) : end_(std::move(end)) {}
 
         //const-converting constructor
         constexpr sentinel(sentinel<!Const> other) requires Const &&
            (std::convertible_to<std::ranges::sentinel_t<first_base>, std::ranges::sentinel_t<const first_base>>)
            : end_(std::move(other.end_)) {
         }
 
         template <bool>
         friend class cursor;
      };
 
      template <bool Const>
      class cursor {
         template<class T>
         using constify = std::conditional_t<Const, const T, T>;
 
     template<class T>
     using intify = std::conditional_t<true, std::int64_t, T>;
     // Instead of storing a pointer to the views, we'll store the sentinels:
     // constify<std::tuple<Vs...>>* bases_;
         std::tuple<std::ranges::iterator_t<constify<Vs>>...> currents_{};
     std::tuple<std::ranges::iterator_t<constify<Vs>>...> begins_{}; 
     std::tuple<std::ranges::sentinel_t<constify<Vs>>...> ends_{};
     std::tuple<intify<Vs>...> counts_{};
     std::int64_t idx_;
 
      public:
         using reference =
            std::tuple<std::ranges::range_reference_t<constify<Vs>>...>;
         using value_type =
            std::tuple<std::ranges::range_value_t<constify<Vs>>...>;
 
         using difference_type = std::ptrdiff_t;
 
         cursor() = default;
         constexpr explicit cursor(constify<std::tuple<Vs...>>* bases)
            : currents_( tl::tuple_transform(std::ranges::begin, *bases) )
        , begins_( currents_ )
        , ends_( tl::tuple_transform(std::ranges::end, *bases) )
        , counts_( tl::tuple_transform(std::ranges::size, *bases) )
        , idx_(0)
         {}
 
         //If the underlying ranges are common, we can get to the end by assigning from end
         constexpr explicit cursor(as_sentinel_t, constify<std::tuple<Vs...>>* bases)
            requires(std::ranges::common_range<Vs> && ...)
            : cursor{ bases }
         {
            std::get<0>(currents_) = std::get<0>(ends_);
         }
 
         //If the underlying ranges are sized and random access, we can get to the end by moving it forward by size
         constexpr explicit cursor(as_sentinel_t, constify<std::tuple<Vs...>>* bases)
            requires(!(std::ranges::common_range<Vs> && ...) && (std::ranges::random_access_range<Vs> && ...) && (std::ranges::sized_range<Vs> && ...))
            : cursor{ bases }
         {
       std::get<0>(currents_) += std::ranges::size(std::ranges::subrange(std::get<0>(begins_), std::get<0>(ends_)));
         }
 
         //const-converting constructor
         constexpr cursor(cursor<!Const> i) requires Const && (std::convertible_to<
            std::ranges::iterator_t<Vs>,
            std::ranges::iterator_t<constify<Vs>>> && ...)
            : currents_{ std::move(i.currents_) } {}
 
 
         constexpr decltype(auto) read() const {
            return tuple_transform([](auto& i) -> decltype(auto) { return *i; }, currents_);
         }
 
         template <std::size_t N = (sizeof...(Vs) - 1)>
         void update(int idx) {
        if constexpr(N == 0)
          std::get<N>(currents_) = idx + std::get<N>(begins_);
        else
          std::get<N>(currents_) = idx % std::get<N>(counts_) + std::get<N>(begins_);
        if constexpr (N > 0) {
          idx /= std::get<N>(counts_);
          update<N-1>(idx);
        }
     }
    
         //Increment the iterator at std::get<N>(currents_)
         //If that iterator hits its end, recurse to std::get<N-1>
         void next() {
        advance(1);
         }
 
         //Decrement the iterator at std::get<N>(currents_)
         //If that iterator was at its begin, cycle it to end and recurse to std::get<N-1>
         void prev() requires (am_bidirectional<constify<Vs>...>) {
            advance(-1);
         }
 
         void advance(difference_type n) requires (am_random_access<constify<Vs>...>) {
        idx_ += n;
        update(idx_);
         }
 
         constexpr bool equal(const cursor& rhs) const
#if !defined(__NVCOMPILER)     
            requires (std::equality_comparable<std::ranges::iterator_t<constify<Vs>>> && ...)
#endif     
     {
            return currents_ == rhs.currents_;
         }
 
         constexpr bool equal(const sentinel<Const>& s) const {
            return std::get<0>(currents_) == s.end_;
         }
 
         template <std::size_t N = (sizeof...(Vs) - 1)>
         constexpr auto distance_to(cursor const& other) const
            requires (am_distanceable<constify<Vs>...>) {
            if constexpr (N == 0) {
               return std::ranges::distance(std::get<0>(currents_), std::get<0>(other.currents_));
            }
            else {
               auto distance = distance_to<N - 1>(other);
               auto scale = std::ranges::distance(std::get<N>(begins_), std::get<N>(ends_));
               auto diff = std::ranges::distance(std::get<N>(currents_), std::get<N>(other.currents_));
#if !defined(__NVCOMPILER)         
               return difference_type{ distance * scale + diff };
#else
           return static_cast<difference_type>(distance * scale + diff);
#endif
            }
         }
 
         friend class cursor<!Const>;
      };
 
   public:
      cartesian_product_view() = default;
      explicit cartesian_product_view(Vs... bases) : bases_(std::move(bases)...) {}
 
      constexpr auto begin() requires (!(simple_view<Vs> && ...)) {
         return basic_iterator{ cursor<false>(std::addressof(bases_)) };
      }
      constexpr auto begin() const requires (std::ranges::range<const Vs> && ...) {
         return basic_iterator{ cursor<true>(std::addressof(bases_)) };
      }
 
      constexpr auto end() requires (!(simple_view<Vs> && ...) && am_common<Vs...>) {
         return basic_iterator{ cursor<false>(as_sentinel, std::addressof(bases_)) };
      }
 
      constexpr auto end() const requires (am_common<const Vs...>) {
         return basic_iterator{ cursor<true>(as_sentinel, std::addressof(bases_)) };
      }
 
      constexpr auto end() requires(!(simple_view<Vs> && ...) && !am_common<Vs...>) {
         return sentinel<false>(std::ranges::end(std::get<0>(bases_)));
      }
 
      constexpr auto end() const requires ((std::ranges::range<const Vs> && ...) && !am_common<const Vs...>) {
         return sentinel<true>(std::ranges::end(std::get<0>(bases_)));
      }
 
      constexpr auto size() requires (am_sized<Vs...>) {
         //Multiply all the sizes together, returning the common type of all of them
         return std::apply([](auto&&... bases) {
            using size_type = std::common_type_t<std::ranges::range_size_t<decltype(bases)>...>;
            return (static_cast<size_type>(std::ranges::size(bases)) * ...);
            }, bases_);
      }
 
      constexpr auto size() const requires (am_sized<const Vs...>) {
         return std::apply([](auto&&... bases) {
            using size_type = std::common_type_t<std::ranges::range_size_t<decltype(bases)>...>;
            return (static_cast<size_type>(std::ranges::size(bases)) * ...);
            }, bases_);
      }
   };
 
#ifndef DISABLE_CART_PROD_IOTA_SPEC
  template <typename W, typename B>
  requires std::is_integral_v<W> && std::is_integral_v<B>
   class cartesian_product_view<
        std::ranges::iota_view<W, B>, 
        std::ranges::iota_view<W, B>,
        std::ranges::iota_view<W, B>
    >
      : public std::ranges::view_interface<
            cartesian_product_view<
                std::ranges::iota_view<W, B>,
                std::ranges::iota_view<W, B>,
                std::ranges::iota_view<W, B>
            >
        > {
 
    using self = cartesian_product_view<
            std::ranges::iota_view<W, B>,
            std::ranges::iota_view<W, B>,
            std::ranges::iota_view<W, B>
    >;
   public:
     W x_b, y_b, z_b;
     B nx, ny, nz;
   private:
 
      template <bool Const>
      class cursor;
 
      template <bool Const>
      class cursor {
    W x_i, y_i, z_i, x_0, y_0, z_0;
    B nx, ny, nz;
 
      public:
    using reference = std::tuple<W const&, W const&, W const&>;
    using value_type = std::tuple<W, W, W>;
 
         using difference_type = std::ptrdiff_t;
 
         cursor() = default;
         constexpr explicit cursor(
             W x,
             W y,
         W z,
             B nx, 
             B ny,
         B nz) 
        : 
            x_i(x),
            y_i(y),
        z_i(z),
            x_0(x),
            y_0(y),
        z_0(z),
            nx(nx), 
            ny(ny),
        nz(nz)
        {}
 
        constexpr decltype(auto) read() const {
      return std::make_tuple<W const&, W const&, W const&>(x_i, y_i, z_i); 
        }
    constexpr auto linear() const {
      return (z_i - z_0) + nz * (y_i - y_0) + nz * ny * (x_i - x_0);
    }
 
        void advance(difference_type n) {
            auto idx = linear() + n;
            x_i = idx / (nz * ny) + x_0;
            y_i = (idx / nz) % ny + y_0;
        z_i = idx % nz + z_0;
    }
         void next() {
            //advance(1);
             ++z_i;
            if (z_i == (z_0 + nz)) {
                z_i = z_0;
                ++y_i;
        if (y_i == (y_0 + ny)) {
          y_i = y_0;
          ++x_i;
        }
            }
         }
         void prev(){
            advance(-1);
         }
 
         constexpr bool equal(const cursor& rhs) const {
             return x_i == rhs.x_i && y_i == rhs.y_i && z_i == rhs.z_i;
         }
 
         constexpr auto distance_to(cursor const& other) const {
       auto idx = linear();
       auto oidx = other.linear();
           return static_cast<difference_type>(oidx) - static_cast<difference_type>(idx);
         }
 
         friend class cursor<!Const>;
      };
 
   public:
      cartesian_product_view() = default;
      constexpr explicit cartesian_product_view(
          std::ranges::iota_view<W, B> xs,
          std::ranges::iota_view<W, B> ys,
      std::ranges::iota_view<W, B> zs
      ) : x_b(*std::ranges::begin(xs))
        , y_b(*std::ranges::begin(ys))
    , z_b(*std::ranges::begin(zs))
        , nx(std::ranges::size(xs))
        , ny(std::ranges::size(ys))
    , nz(std::ranges::size(zs))   
    {}
 
      constexpr auto begin() {
    return basic_iterator{ cursor<false>(x_b, y_b, z_b, nx, ny, nz) };
      }
      constexpr auto begin() const {
    return basic_iterator{ cursor<true>(x_b, y_b, z_b, nx, ny, nz) };
      }
 
      constexpr auto size() {
         return nx * ny * nz;
      }
 
      constexpr auto size() const {
         return nx * ny * nz;
      }
 
      constexpr auto end() {
         return begin() + size();
      }
 
      constexpr auto end() const {
     return begin() + size();
      }
   };
  
  template <typename W, typename B>
  requires std::is_integral_v<W> && std::is_integral_v<B>
   class cartesian_product_view<
        std::ranges::iota_view<W, B>, 
        std::ranges::iota_view<W, B>
    >
      : public std::ranges::view_interface<
            cartesian_product_view<
                std::ranges::iota_view<W, B>, 
                std::ranges::iota_view<W, B>
            >
        > {
 
    using self = cartesian_product_view<
            std::ranges::iota_view<W, B>, 
            std::ranges::iota_view<W, B>
    >;
   public:
     W x_b, y_b;
     B nx, ny;
   private:
 
      template <bool Const>
      class cursor;
 
      template <bool Const>
      class cursor {
    W x_i, y_i, x_0, y_0;
    B nx, ny;
 
      public:
         using reference = std::tuple<W const&, W const&>;
         using value_type = std::tuple<W, W>;
 
         using difference_type = std::ptrdiff_t;
 
         cursor() = default;
         constexpr explicit cursor(
             W x,
             W y,
             B nx, 
             B ny) 
        : 
            x_i(x),
            y_i(y),
            x_0(x),
            y_0(y),
            nx(nx), 
            ny(ny)
        {}
 
        constexpr decltype(auto) read() const {
            return std::make_tuple<W const&, W const&>(x_i, y_i); 
        }
    constexpr auto linear() const {
      return (y_i - y_0) + ny * (x_i - x_0);
    }
 
        void advance(difference_type n) {
            auto idx = linear() + n;
            x_i = idx / ny + x_0;
            y_i = idx % ny + y_0;
         }
         void next() {
            //advance(1);
             ++y_i;
            if (y_i == (y_0 + ny)) {
                y_i = y_0;
                ++x_i;
            }
         }
         void prev(){
            advance(-1);
         }
 
         constexpr bool equal(const cursor& rhs) const {
             return x_i == rhs.x_i && y_i == rhs.y_i;
         }
 
         constexpr auto distance_to(cursor const& other) const {
       auto idx = linear();
       auto oidx = other.linear();
       return static_cast<difference_type>(oidx) - static_cast<difference_type>(idx);      
         }
 
         friend class cursor<!Const>;
      };
 
   public:
      cartesian_product_view() = default;
      constexpr explicit cartesian_product_view(
          std::ranges::iota_view<W, B> xs,
          std::ranges::iota_view<W, B> ys
      ) : x_b(*std::ranges::begin(xs))
        , y_b(*std::ranges::begin(ys))
        , nx(std::ranges::size(xs))
        , ny(std::ranges::size(ys))
    {}
 
      constexpr auto begin() {
         return basic_iterator{ cursor<false>(x_b, y_b, nx, ny) };
      }
      constexpr auto begin() const {
         return basic_iterator{ cursor<true>(x_b, y_b, nx, ny) };
      }
 
      constexpr auto size() {
         return nx * ny;
      }
 
      constexpr auto size() const {
         return nx * ny;
      }
 
      constexpr auto end() {
         return begin() + size();
      }
 
      constexpr auto end() const {
     return begin() + size();
      }
     
   };
 
  template <typename W, typename B>
  requires std::is_integral_v<W> && std::is_integral_v<B>
   class cartesian_product_view<
        std::ranges::iota_view<W, B>
    >
      : public std::ranges::view_interface<
            cartesian_product_view<
                std::ranges::iota_view<W, B>
            >
        > {
 
     int x_i, x_e;
 
      template <bool Const>
      class cursor;
 
      template <bool Const>
      class cursor {
    long x_i, x_e;
 
      public:
         using reference = std::tuple<int const&>;
         using value_type = std::tuple<int>;
 
         using difference_type = std::ptrdiff_t;
 
         cursor() = default;
         constexpr explicit cursor(
             int x, int x_e) 
        : 
            x_i(x),
            x_e(x_e)
        {}
 
        constexpr decltype(auto) read() const {
            return std::make_tuple<int const&>(x_i); 
        }
        void advance(difference_type n) {
      x_i += n;
         }
         void next() {
            advance(1);
         }
         void prev(){
            advance(-1);
         }
 
         constexpr bool equal(const cursor& rhs) const {
       return x_i == rhs.x_i;
         }
 
         constexpr auto distance_to(cursor const& other) const {
            return static_cast<difference_type>(other.x_i - x_i);
         }
 
         friend class cursor<!Const>;
      };
 
   public:
      cartesian_product_view() = default;
      constexpr explicit cartesian_product_view(
          std::ranges::iota_view<W, B> xs
      ) : x_i(*std::ranges::begin(xs))
        , x_e(*std::ranges::begin(xs) + std::ranges::size(xs))
    {}
 
      constexpr auto begin() {
         return basic_iterator{ cursor<false>(x_i, x_e) };
      }
      constexpr auto begin() const {
         return basic_iterator{ cursor<true>(x_i, x_e) };
      }
 
      constexpr auto size() {
         return x_e - x_i;
      }
 
      constexpr auto size() const {
         return x_e - x_i;
      }
 
      constexpr auto end() {
         return begin() + size();
      }
 
      constexpr auto end() const {
     return begin() + size();
      }
   };
#endif // DISABLE_CART_PROD_IOTA_SPEC
  
   template <class... Rs>
   cartesian_product_view(Rs&&...)->cartesian_product_view<std::views::all_t<Rs>...>;
 
   namespace views {
      namespace detail {
         class cartesian_product_fn {
         public:
            constexpr std::ranges::empty_view<std::tuple<>> operator()() const noexcept {
               return {};
            }
#ifndef DISABLE_CART_PROD_IOTA_SPEC
        template <typename W, typename B>
            constexpr auto operator()(
                std::ranges::iota_view<W, B> xs
            ) const {
               return tl::cartesian_product_view<
                std::ranges::iota_view<W, B>
               >{ std::move(xs) };
            }
 
        template <typename W, typename B>
            constexpr auto operator()(
                std::ranges::iota_view<W, B> xs, 
                std::ranges::iota_view<W, B> ys
            ) const {
               return tl::cartesian_product_view<
                std::ranges::iota_view<W, B>,
                std::ranges::iota_view<W, B>
               >{ std::move(xs), std::move(ys) };
            }
        template <typename W, typename B>
            constexpr auto operator()(
                std::ranges::iota_view<W, B> xs, 
                std::ranges::iota_view<W, B> ys,
                std::ranges::iota_view<W, B> zs     
            ) const {
               return tl::cartesian_product_view<
                std::ranges::iota_view<W, B>,
        std::ranges::iota_view<W, B>,        
                std::ranges::iota_view<W, B>
               >{ std::move(xs), std::move(ys), std::move(zs) };
            }
       
#endif     
            template <std::ranges::viewable_range... V>
            requires ((std::ranges::forward_range<V> && ...) && (sizeof...(V) != 0))
               constexpr auto operator()(V&&... vs) const {
               return tl::cartesian_product_view{ std::views::all(std::forward<V>(vs))... };
            }
         };
      }  // namespace detail
 
      inline constexpr detail::cartesian_product_fn cartesian_product;
   }  // namespace views
 
}  // namespace tl
 
// Strided View
 
namespace tl {
 
template <std::ranges::forward_range V>
   requires std::ranges::view<V> class stride_view
      : public std::ranges::view_interface<stride_view<V>> {
   private:
      //Cannot be common for non-sized bidirectional ranges because calculating the predecessor to end would be O(n).
      template <class T>
      static constexpr bool am_common = std::ranges::common_range<T> &&
         (!std::ranges::bidirectional_range<T> || std::ranges::sized_range<T>);
 
      template <class T> static constexpr bool am_sized = std::ranges::sized_range<T>;
 
      V base_;
      std::ranges::range_difference_t<V> stride_size_;
 
      //The cursor for stride_view may need to keep track of additional state.
      //Consider the case where you have a vector of 0,1,2 and you stride with a size of 2.
      //If you take the end iterator for the stride_view and decrement it, then you should end up at 2, not at 1.
      //As such, there's additional work required to track where to decrement to in the case that the underlying range is bidirectional.
      //This is handled by a bunch of base classes for the cursor.
 
      //Case when underlying range is not bidirectional, i.e. we don't care about calculating offsets
      template <bool Const, class Base = std::conditional_t<Const, const V, V>, bool = std::ranges::bidirectional_range<Base>, bool = std::ranges::sized_range<Base>>
      struct cursor_base {
         cursor_base() = default;
         constexpr explicit cursor_base(std::ranges::range_difference_t<Base> offs) {}
 
         //These are both no-ops
         void set_offset(std::ranges::range_difference_t<Base> off) {}
         std::ranges::range_difference_t<Base> get_offset() {
            return 0;
         }
      };
 
      //Case when underlying range is bidirectional but not sized. We need to keep track of the offset if we hit the end iterator.
      template <bool Const, class Base>
      struct cursor_base<Const, Base, true, false> {
         using difference_type = std::ranges::range_difference_t<Base>;
         difference_type offset_{};
 
         cursor_base() = default;
         constexpr explicit cursor_base(difference_type offset)
            : offset_{ offset } {}
 
         void set_offset(difference_type off) {
            offset_ = off;
         }
 
         difference_type get_offset() {
            return offset_;
         }
      };
 
      //Case where underlying is bidirectional and sized. We can calculate offsets from the end on construction.
      template <bool Const, class Base>
      struct cursor_base<Const, Base, true, true> {
         using difference_type = std::ranges::range_difference_t<Base>;
         difference_type offset_{};
 
         cursor_base() = default;
         constexpr explicit cursor_base(difference_type offset)
            : offset_{ offset } {}
 
         //No-op because we're precomputing the offset
         void set_offset(std::ranges::range_difference_t<Base>) {}
 
         std::ranges::range_difference_t<Base> get_offset() {
            return offset_;
         }
      };
 
      template <bool Const>
      struct cursor : cursor_base<Const> {
         template <class T>
         using constify = std::conditional_t<Const, const T, T>;
         using Base = constify<V>;
 
         using difference_type = std::ranges::range_difference_t<Base>;
 
         std::ranges::iterator_t<Base> current_{};
         std::ranges::sentinel_t<Base> end_{};
         std::ranges::range_difference_t<Base> stride_size_{};
 
         cursor() = default;
 
         //Pre-calculate the offset for sized ranges
         constexpr cursor(std::ranges::iterator_t<Base> begin, Base* base, std::ranges::range_difference_t<Base> stride_size)
            requires(std::ranges::sized_range<Base>)
            : cursor_base<Const>(stride_size - (std::ranges::size(*base) % stride_size)),
            current_(std::move(begin)), end_(std::ranges::end(*base)), stride_size_(stride_size) {}
 
         constexpr cursor(std::ranges::iterator_t<Base> begin, Base* base, std::ranges::range_difference_t<Base> stride_size)
            requires(!std::ranges::sized_range<Base>)
            : cursor_base<Const>(), current_(std::move(begin)), end_(std::ranges::end(*base)), stride_size_(stride_size) {}
 
         //const-converting constructor
         constexpr cursor(cursor<!Const> i) requires Const&& std::convertible_to<
            std::ranges::iterator_t<V>,
            std::ranges::iterator_t<const V>>
            : cursor_base<Const>(i.get_offset()) {}
 
         constexpr decltype(auto) read() const {
            return *current_;
         }
 
         constexpr void next() {
            auto delta = std::ranges::advance(current_, stride_size_, end_);
            //This will track the amount we actually moved by last advance, 
            //which will be less than the stride size if range_size % stride_size != 0
            this->set_offset(delta);
         }
 
         constexpr void prev() requires std::ranges::bidirectional_range<Base> {
            auto delta = -stride_size_;
            //If we're at the end we may need to offset the amount to move back by
            if (current_ == end_) {
               delta += this->get_offset();
            }
            std::advance(current_, delta);
         }
 
         constexpr void advance(difference_type x)
            requires std::ranges::random_access_range<Base> {
            if (x == 0) return;
 
            x *= stride_size_;
 
            if (x > 0) {
               auto delta = std::ranges::advance(current_, x, end_); // TODO: submit PR with this bugfix
               this->set_offset(delta);
            }
            else if (x < 0) {
               if (current_ == end_) {
                  x += this->get_offset();
               }
               std::advance(this->current_, x);  // TODO: submit PR with this bugfix
            }
         }
 
     // TODO: submit PR with distance_to
     constexpr auto distance_to(cursor const& other) const
       // am_distanceable<V>:
       requires (std::sized_sentinel_for<std::ranges::iterator_t<V>, std::ranges::iterator_t<V>>)
         && std::ranges::sized_range<V>  
     {
       auto delta = std::ranges::distance(this->current_, other.current_);
       if (delta < 0)
         delta -= stride_size_ - 1;
       else
         delta += stride_size_ -1;
       return delta / stride_size_;
     }
 
         constexpr bool equal(cursor const& rhs) const {
            return current_ == rhs.current_;
         }
         constexpr bool equal(basic_sentinel<V, Const> const& rhs) const {
            return current_ == rhs.end_;
         }
 
         friend struct cursor<!Const>;
      };
 
   public:
      stride_view() = default;
      stride_view(V v, std::ranges::range_difference_t<V> n) : base_(std::move(v)), stride_size_(n) {}
 
      constexpr auto begin() requires (!simple_view<V>) {
         return basic_iterator{ cursor<false>{ std::ranges::begin(base_), std::addressof(base_), stride_size_ } };
      }
 
      constexpr auto begin() const requires (std::ranges::range<const V>) {
         return basic_iterator{ cursor<true>{ std::ranges::begin(base_), std::addressof(base_), stride_size_ } };
      }
 
      constexpr auto end() requires (!simple_view<V>&& am_common<V>) {
         return basic_iterator{ cursor<false>(std::ranges::end(base_), std::addressof(base_), stride_size_) };
      }
 
      constexpr auto end() const requires (std::ranges::range<const V>&& am_common<const V>) {
         return basic_iterator{ cursor<true>(std::ranges::end(base_), std::addressof(base_), stride_size_) };
      }
 
      constexpr auto end() requires (!simple_view<V> && !am_common<V>) {
         return basic_sentinel<V, false>(std::ranges::end(base_));
      }
 
      constexpr auto end() const requires (std::ranges::range<const V> && !am_common<const V>) {
         return basic_sentinel<V, true>(std::ranges::end(base_));
      }
 
      constexpr auto size() requires (am_sized<V>) {
         return (std::ranges::size(base_) + stride_size_ - 1) / stride_size_;
      }
 
      constexpr auto size() const requires (am_sized<const V>) {
         return (std::ranges::size(base_) + stride_size_ - 1) / stride_size_;
      }
 
      auto& base() {
         return base_;
      }
 
      auto const& base() const {
         return base_;
      }
   };
 
   template <class R, class N>
   stride_view(R&&, N n)->stride_view<std::views::all_t<R>>;
 
   namespace views {
      namespace detail {
         struct stride_fn_base {
            template <std::ranges::viewable_range R>
            constexpr auto operator()(R&& r, std::ranges::range_difference_t<R> n) const
               requires std::ranges::forward_range<R> {
               return stride_view(std::forward<R>(r), n);
            }
         };
 
         struct stride_fn : stride_fn_base {
            using stride_fn_base::operator();
 
            template <std::integral N>
            constexpr auto operator()(N n) const {
               return pipeable(bind_back(stride_fn_base{}, n));
            }
         };
      }
 
      constexpr inline detail::stride_fn stride;
   }
}
 
namespace std::ranges {
   template <class R>
   inline constexpr bool enable_borrowed_range<tl::stride_view<R>> = enable_borrowed_range<R>;
}
 
// std::ranges::views re-export:
 
namespace std {
  namespace ranges {
    using tl::cartesian_product_view;
    namespace views {
      inline constexpr tl::views::detail::cartesian_product_fn cartesian_product;
      inline constexpr tl::views::detail::stride_fn stride;
    } // namespace views
  } // namespace ranges
} // namespace std