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numeric_concepts added as in P1813R0
This commit is contained in:
Mateusz Pusz
401
src/include/units/bits/numeric_concepts.h
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401
src/include/units/bits/numeric_concepts.h
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// The MIT License (MIT)
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//
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// Copyright (c) 2018 Mateusz Pusz
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//
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// Permission is hereby granted, free of charge, to any person obtaining a copy
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// of this software and associated documentation files (the "Software"), to deal
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// in the Software without restriction, including without limitation the rights
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// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the Software is
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// furnished to do so, subject to the following conditions:
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//
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// The above copyright notice and this permission notice shall be included in all
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// copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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// SOFTWARE.
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#pragma once
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#include <units/bits/hacks.h>
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// P1813 - A Concept Design for the Numeric Algorithms
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namespace std {
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template<class BOp, class T, class U = T>
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struct left_identity {};
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template<class BOp, class T, class U = T>
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using left_identity_t = decltype(declval<left_identity<BOp, T, U>>()());
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template<class BOp, class T, class U = T>
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struct right_identity {};
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template<class BOp, class T, class U = T>
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using right_identity_t = decltype(declval<right_identity<BOp, T, U>>()());
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namespace detail {
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template<class BOp, class T, class U>
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concept has_two_sided_identity = // exposition only
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requires(BOp bop, const T& t, const U& u) {
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typename left_identity_t<BOp, T, U>;
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typename left_identity_t<BOp, U, T>;
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typename right_identity_t<BOp, T, U>;
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typename right_identity_t<BOp, U, T>;
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requires same_as<left_identity_t<BOp, T, U>, left_identity_t<BOp, U, T>>;
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requires same_as<right_identity_t<BOp, T, U>, right_identity_t<BOp, U, T>>;
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requires same_as<left_identity_t<BOp, T, U>, right_identity_t<BOp, T, U>>;
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};
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}
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template<class BOp, class T, class U = T>
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requires detail::has_two_sided_identity<BOp, T, U>
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struct two_sided_identity {
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constexpr common_type_t<T, U> operator()() const;
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};
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template<class BOp, class T, class U>
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using two_sided_identity_t = decltype(two_sided_identity{}(declval<BOp&>(), declval<T>(), declval<U>()));
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template<class BOp, class T, class U = T>
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struct left_zero {};
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template<class BOp, class T, class U = T>
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using left_zero_t = decltype(declval<left_zero<BOp, T, U>>()());
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template<class BOp, class T, class U = T>
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struct right_zero {};
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template<class BOp, class T, class U = T>
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using right_zero_t = decltype(declval<right_zero<BOp, T, U>>()());
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namespace detail {
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template<class BOp, class T, class U>
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concept has_two_sided_zero = // exposition only
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requires(BOp bop, const T& t, const U& u) {
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typename left_zero_t<BOp, T, U>;
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typename left_zero_t<BOp, U, T>;
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typename right_zero_t<BOp, T, U>;
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typename right_zero_t<BOp, U, T>;
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requires same_as<left_zero_t<BOp, T, U>, left_zero_t<BOp, U, T>>;
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requires same_as<right_zero_t<BOp, T, U>, right_zero_t<BOp, U, T>>;
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requires same_as<left_zero_t<BOp, T, U>, right_zero_t<BOp, T, U>>;
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};
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}
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template<class BOp, class T, class U>
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requires detail::has_two_sided_zero<BOp, T, U>
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struct two_sided_zero {
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constexpr common_type_t<T, U> operator()(BOp bop, T&& t, U&& u) const;
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};
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template<class BOp, class T, class U = T>
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using two_sided_zero_t = decltype(two_sided_zero{}(declval<BOp&>(), declval<T>(), declval<U>()));
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template<class BOp>
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struct inverse_traits {};
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template<class BOp>
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using inverse_operation_t = typename inverse_traits::type;
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template<class BOp, class T, class U>
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concept commutative_operation =
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regular_invocable<BOp, T, U> &&
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regular_invocable<BOp, U, T> &&
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common_with<T, U> &&
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equality_comparable_with<T, U>;
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template<class BOp, class T, class U>
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concept magma =
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std::common_with<T, U> &&
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std::regular_invocable<BOp, T, T> &&
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std::regular_invocable<BOp, U, U> &&
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std::regular_invocable<BOp, T, U> &&
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std::regular_invocable<BOp, U, T> &&
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std::common_with<std::invoke_result_t<BOp&, T, U>, T> &&
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std::common_with<std::invoke_result_t<BOp&, T, U>, U> &&
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std::same_as<std::invoke_result_t<BOp&, T, U>, std::invoke_result_t<BOp&, U, T>>;
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template<class BOp, class T, class U>
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concept semigroup = magma<BOp, T, U>;
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template<class BOp, class T, class U = T>
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concept monoid = semigroup<BOp, T, U> &&
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requires {
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typename two_sided_identity_t<BOp, remove_cvref_t<T>, remove_cvref_t<U>>;
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};
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template<class BOp, class T, class U>
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concept quasigroup = magma<BOp, T, U> &&
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requires {
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typename inverse_operation_t<BOp, T, U>;
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typename inverse_operation_t<inverse_operation_t<BOp, T, U>, T, U>;
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requires same_as<BOp, inverse_operation_t<inverse_operation_t<BOp, T, U>, T, U>>;
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};
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template<class BOp, class T, class U>
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concept loop = quasigroup<BOp, T, U> &&
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requires {
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typename two_sided_identity_t<BOp, remove_cvref_t<T>, remove_cvref_t<U>>;
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};
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template<class BOp, class T, class U>
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concept group = semigroup<BOp, T, U> && quasigroup<BOp, T, U>;
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template<class BOp, class T, class U>
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concept abelian_group = group<BOp, T, U> && commutative_operation<BOp, T, U>;
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template<class BOp1, class BOp2, class T, class U, class V>
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concept weak_magmaring = magma<BOp2, U, V> && magma<BOp1, T, invoke_result_t<BOp2&, U, V>>;
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template<class BOp1, class BOp2, class T, class U, class V>
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concept near_semiring = weak_magmaring<BOp1, BOp2, T, U, V> &&
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monoid<BOp1, T, invoke_result_t<BOp2&, U, V>> && semigroup<BOp2, U, V> &&
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requires {
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typename two_sided_zero_t<BOp2, remove_cvref_t<U>, remove_cvref_t<V>>;
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};
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namespace ranges {
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namespace detail {
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template<class T, class U>
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concept summable_with = // exposition only
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default_initializable<remove_reference_t<T>> &&
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default_initializable<remove_reference_t<U>> &&
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common_reference_with<T, U> &&
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requires(T&& t, U&& u) {
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{ std::forward<T>(t) + std::forward<T>(t) } -> common_with<T>;
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{ std::forward<U>(u) + std::forward<U>(u) } -> common_with<U>;
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{ std::forward<T>(t) + std::forward<U>(u) } -> common_with<T>;
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{ std::forward<U>(u) + std::forward<T>(t) } -> common_with<U>;
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requires same_as<decltype(std::forward<T>(t) + std::forward<U>(u)),
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decltype(std::forward<U>(u) + std::forward<T>(t))>;
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};
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}
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struct plus {
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template<class T, detail::summable_with<T> U>
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constexpr decltype(auto) operator()(T&& t, U&& u) const {
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return std::forward<T>(t) + std::forward<U>(u);
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}
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using is_transparent = std::true_type;
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};
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namespace detail {
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template<class T>
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concept negatable = // exposition only
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summable_with <T, T> &&
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totally_ordered<T> &&
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requires(T&& t) {
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{ -std::forward<T>(t) } -> common_with<T>;
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};
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}
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struct negate {
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template<detail::negatable T>
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constexpr decltype(auto) operator()(T&& t) const {
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return -std::forward<T>(t);
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}
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using is_transparent = std::true_type;
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};
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namespace detail {
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template<class T, class U>
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concept differenceable_with = // exposition only
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summable_with<T, U> &&
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negatable<T> &&
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negatable<U> &&
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totally_ordered_with<T, U> &&
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requires(T&& t, U&& u) {
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{ std::forward<T>(t) - std::forward<T>(t) } -> common_with<T>;
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{ std::forward<U>(u) - std::forward<U>(u) } -> common_with<U>;
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{ std::forward<T>(t) - std::forward<U>(u) } -> common_with<T>;
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{ std::forward<U>(u) - std::forward<T>(t) } -> common_with<U>;
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requires same_as<decltype(std::forward<T>(t) - std::forward<U>(u)),
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decltype(std::forward<U>(u) - std::forward<T>(t))>;
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};
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}
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struct minus {
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template<class T, detail::differenceable_with<T> U>
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constexpr decltype(auto) operator()(T&& t, U&& u) const {
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return std::forward<T>(t) - std::forward<U>(u);
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}
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using is_transparent = std::true_type;
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};
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namespace detail {
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template<class T, class U>
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concept multiplicable_with = // exposition only
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detail::summable_with <T, U> &&
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constructible_from<remove_cvref_t<T>, int> && // specifically T{0} and T{1}
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constructible_from<remove_cvref_t<U>, int> && // specifically U{0} and U{1}
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constructible_from<remove_cvref_t<common_type<T, U>>, int> &&
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common_reference_with<T, U> &&
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requires(T&& t, U&& u) {
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{ std::forward<T>(t) * std::forward<T>(t) } -> common_with<T>;
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{ std::forward<U>(u) * std::forward<U>(u) } -> common_with<U>;
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{ std::forward<T>(t) * std::forward<U>(u) } -> common_with<T>;
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{ std::forward<U>(u) * std::forward<T>(t) } -> common_with<U>;
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requires same_as<decltype(std::forward<T>(t) * std::forward<U>(u)),
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decltype(std::forward<U>(u) * std::forward<T>(t))>;
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};
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}
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struct times {
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template<class T, detail::multiplicable_with <T> U>
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constexpr decltype(auto) operator()(T&& t, U&& u) const
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{ return std::forward<T>(t) * std::forward<U>(u); }
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using is_transparent = std::true_type;
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};
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namespace detail {
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template<class T, class U>
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concept divisible_with = // exposition only
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multiplicable_with <T, U> &&
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subtractible_with <T, U> &&
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requires(T&& t, U&& u) {
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{ std::forward<T>(t) / std::forward<T>(t) } -> common_with<T>;
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{ std::forward<U>(u) / std::forward<U>(u) } -> common_with<U>;
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{ std::forward<T>(t) / std::forward<U>(u) } -> common_with<T>;
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{ std::forward<U>(u) / std::forward<T>(t) } -> common_with<U>;
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requires same_as<decltype(std::forward<T>(t) / std::forward<U>(u)),
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decltype(std::forward<U>(u) / std::forward<T>(t))>;;
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};
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}
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struct divided_by {
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template<class T, detail::divisible_with <T> U>
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constexpr decltype(auto) operator()(T&& t, U&& u) const
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{ return std::forward<T>(t) / std::forward<U>(u); }
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};
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namespace detail {
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template<class T, class Q>
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concept modulo_with = // exposition only
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divisible_with <T, Q> &&
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requires(T&& t, Q&& q) {
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{ std::forward<T>(t) % std::forward<T>(t) } -> common_with<T>;
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{ std::forward<Q>(q) % std::forward<Q>(q) } -> common_with<Q>;
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{ std::forward<T>(t) % std::forward<Q>(q) } -> common_with<T>;
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{ std::forward<Q>(q) % std::forward<T>(t) } -> common_with<Q>;
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requires same_as<decltype(std::forward<T>(t) % std::forward<Q>(q)),
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decltype(std::forward<Q>(q) % std::forward<T>(t))>;
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};
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}
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struct modulus {
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template<class T, detail::modulo_with <T> U>
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constexpr decltype(auto) operator()(T&& t, U&& u) const
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{ return std::forward<T>(t) % std::forward<U>(u); }
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};
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} // namespace ranges
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template<class T, class U>
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requires magma<ranges::plus, T, U>
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struct left_identity<ranges::plus> {
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constexpr common_type_t<T, U> operator()() const { return T{}; }
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};
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template<class T, class U>
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requires magma<ranges::plus, T, U>
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struct right_identity<ranges::plus> {
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constexpr common_type_t<T, U> operator()() const { return U{}; }
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};
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template<>
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struct inverse_traits<ranges::plus> {
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using type = minus;
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constexpr type operator()() const noexcept { return type{}; }
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};
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template<class T, class U>
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struct right_identity<ranges::minus, T, U> : private right_identity<ranges::plus, T, U> {
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using right_identity<ranges::plus, T, U>::operator();
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};
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||||||
|
template<>
|
||||||
|
struct inverse_traits<ranges::minus> {
|
||||||
|
using type = ranges::plus;
|
||||||
|
constexpr type operator()() const noexcept { return type{}; }
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class T, class U>
|
||||||
|
requires magma<times, T, U>
|
||||||
|
struct left_identity<times> {
|
||||||
|
constexpr common_type_t<T, U> operator()() const { return T{1}; }
|
||||||
|
};
|
||||||
|
|
||||||
|
template<class T, class U>
|
||||||
|
requires magma<times, T, U>
|
||||||
|
struct right_identity<times> {
|
||||||
|
constexpr common_type_t<T, U> operator()() const { return U{1}; }
|
||||||
|
};
|
||||||
|
|
||||||
|
template<class T, class U>
|
||||||
|
requires magma<times, T, U>
|
||||||
|
struct left_zero<times> {
|
||||||
|
constexpr common_type_t<T, U> operator()() const { return T{}; }
|
||||||
|
};
|
||||||
|
|
||||||
|
template<class T, class U>
|
||||||
|
requires magma<times, T, U>
|
||||||
|
struct right_zero<times> {
|
||||||
|
constexpr common_type_t<T, U> operator()() const { return U{}; }
|
||||||
|
};
|
||||||
|
|
||||||
|
template<>
|
||||||
|
struct inverse_traits<times> {
|
||||||
|
using type = divided_by;
|
||||||
|
constexpr type operator()() const noexcept { return type{}; }
|
||||||
|
};
|
||||||
|
|
||||||
|
template<class T, class U>
|
||||||
|
requires magma<divided_by, T, U>
|
||||||
|
struct right_identity<divided_by> {
|
||||||
|
constexpr common_type_t<T, U> operator()() const { return U{1}; }
|
||||||
|
};
|
||||||
|
|
||||||
|
template<>
|
||||||
|
struct inverse_traits<divided_by> {
|
||||||
|
using type = times;
|
||||||
|
constexpr type operator()() const noexcept { return type{}; }
|
||||||
|
};
|
||||||
|
|
||||||
|
template<class T, class U>
|
||||||
|
requires magma<modulus, T, U>
|
||||||
|
struct left_zero<modulus> {
|
||||||
|
constexpr common_type_t<T, U> operator()() const { return T{}; }
|
||||||
|
};
|
||||||
|
|
||||||
|
} // namespace std
|
||||||
Reference in New Issue
Block a user