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merge.cpp
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merge.cpp
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// The MIT License (MIT)
//
// Copyright (c) 2018 Mateusz Pusz
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
//
//
// This file is taken from: https://github.com/mpusz/units
//
// Full credit to Mateusz Pusz for this fantastic idiom!
//
// Implements the (very clever) downcast template-idiom enabling (where =>
// denotes inheritance):
//
// struct parent => unit<i, j, k> => downcast_base<unit<i, j, k>>
//
// downcast(unit<i, j, k>) -> parent
//
// This is achieved by parent inheriting unit<...> through downcast_child which
// specialises a friend function defined in downcast base. downcast_child has
// full knowledge of parent through the CRTP idiom and can specialise the friend
// function in downcast base to return it. Full inheritance:
//
// parent => make_unit_helper<parent ...> => downcast_child<parent, ...> =>
// unit<...> => downcast_base<unit<...>>
#include <type_traits>
namespace su {
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wnon-template-friend"
template <typename BaseType>
struct downcast_base {
using downcast_base_type = BaseType;
friend auto downcast_guide(downcast_base);
};
#pragma GCC diagnostic pop
template <typename T>
concept Downcastable = requires {
typename T::downcast_base_type;
}
&&std::is_base_of_v<downcast_base<typename T::downcast_base_type>, T>;
template <typename Target, Downcastable T>
struct downcast_child : T {
friend auto downcast_guide(typename downcast_child::downcast_base) {
return Target();
}
};
namespace detail {
template <typename T>
concept has_downcast = requires {
downcast_guide(std::declval<downcast_base<T>>());
};
template <typename T>
constexpr auto downcast_impl() {
if constexpr (has_downcast<T>) {
return decltype(downcast_guide(std::declval<downcast_base<T>>()))();
} else {
return T();
}
}
} // namespace detail
template <Downcastable T>
using downcast = decltype(detail::downcast_impl<T>());
} // namespace su
#include <array>
#include <cstddef> // std::size_t
#include <cstdint> // std::intmax_t
#include <ostream>
#include <string_view>
#include <utility> // index_seq
#if __GNUC__ >= 10
#include <compare>
#endif
// Provides utilities for working with compile time strings and passing string
// literals as template parameters. See fixed_string.test.cpp for examples.
namespace fs {
// The fixed_string class is a literal class, implicitly constructable from
// char* and can therefore used to pass strings to templates. It publicly
// inherits from std::array and therefore inherits all its iterating goodness!
//
// Deduction guides are provided such that the template parameter N should
// almost never have to be explicitly provided, as well as a user defined
// literal allowing for the short syntax "string"_fs.
template <std::size_t N>
struct fixed_string : std::array<char, N> {
//
using std::array<char, N>::data;
using std::array<char, N>::operator[];
fixed_string& operator=(fixed_string&&) = default;
fixed_string& operator=(fixed_string const&) = default;
#if __GNUC__ >= 10
auto operator<=>(const fixed_string&) const = default;
#endif
constexpr fixed_string(char c) : std::array<char, N>{c} {}
constexpr fixed_string(char const* str) {
for (std::size_t i = 0; i < N; ++i) operator[](i) = str[i];
}
constexpr fixed_string() : std::array<char, N>{} {};
constexpr fixed_string(fixed_string const&) = default;
// Construct by concentrating two other fixed_strings
template <std::size_t I, std::size_t J>
constexpr fixed_string(fixed_string<I> const& lhs,
fixed_string<J> const& rhs) {
for (std::size_t i = 0; i < I; ++i) operator[](i) = lhs[i];
for (std::size_t i = 0; i < J; ++i) operator[](i + I) = rhs[i];
}
// Construct by concentrating any number of fixed_strings
template <std::size_t... Is>
constexpr fixed_string(fixed_string<Is> const&... args) requires(
sizeof...(args) > 2) {
*this = (... + args);
}
// Get a view of a sub-string.
inline constexpr std::string_view view(std::size_t start = 0,
int end = N) const noexcept {
return {data() + start, end - start};
}
inline static constexpr std::size_t size() { return N; }
};
template <std::size_t N>
fixed_string(char const (&)[N])->fixed_string<N - 1>;
fixed_string()->fixed_string<0>;
fixed_string(char)->fixed_string<1>;
template <std::size_t... Is>
fixed_string(fixed_string<Is>...)->fixed_string<(... + Is)>;
// C++20 string literal operator template : "abc"_fs -> fixed_string{"abc"}
template <fixed_string str>
inline constexpr auto operator"" _fs() {
return str;
}
// + operator used for fixed_string concatenation
template <std::size_t I, std::size_t J>
inline constexpr auto operator+(fixed_string<I> const& lhs,
fixed_string<J> const& rhs) {
return fixed_string{lhs, rhs};
}
template <std::size_t N>
std::ostream& operator<<(std::ostream& os, fixed_string<N> const& str) {
return os << str.view();
}
// Standard c-like string comparison.
template <std::size_t I, std::size_t J>
constexpr int compare(fixed_string<I> lhs, fixed_string<J> rhs) {
if constexpr (I < J) {
return -1;
}
if constexpr (I > J) {
return 1;
}
for (std::size_t i = 0; i < I; ++i) {
if (lhs[i] < rhs[i]) {
return -1;
}
if (lhs[i] > rhs[i]) {
return 1;
}
}
return 0;
}
namespace detail {
template <int base>
requires(base > 1) constexpr std::size_t num_digits(std::intmax_t x) {
return x < 0 ? 1 + num_digits<base>(-x)
: x < base ? 1 : 1 + num_digits<base>(x / base);
}
inline constexpr fixed_string digits = {
"0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"};
template <std::intmax_t integer, int base>
requires(base > 1) && (base < digits.size() + 1) constexpr auto ito_fs() {
//
fixed_string<detail::num_digits<base>(integer)> result;
{
std::intmax_t num = integer < 0 ? -integer : integer;
for (auto&& it = result.rbegin(); it != result.rend(); ++it) {
*it = digits[num % base];
num /= base;
}
}
if constexpr (integer < 0) {
result[0] = '-';
}
return result;
}
} // namespace detail
// Convert an integer to a fixed_string at compile time (in arbitrary base).
template <std::intmax_t integer, int base = 10>
inline constexpr fixed_string ito_fs = detail::ito_fs<integer, base>();
namespace detail {
template <auto, typename>
struct expand;
template <auto value>
inline constexpr fixed_string super_impl =
expand<value, std::make_index_sequence<value.size()>>::value;
template <>
inline constexpr fixed_string super_impl<'0'> = "\u2070";
template <>
inline constexpr fixed_string super_impl<'1'> = "\u00b9";
template <>
inline constexpr fixed_string super_impl<'2'> = "\u00b2";
template <>
inline constexpr fixed_string super_impl<'3'> = "\u00b3";
template <>
inline constexpr fixed_string super_impl<'4'> = "\u2074";
template <>
inline constexpr fixed_string super_impl<'5'> = "\u2075";
template <>
inline constexpr fixed_string super_impl<'6'> = "\u2076";
template <>
inline constexpr fixed_string super_impl<'7'> = "\u2077";
template <>
inline constexpr fixed_string super_impl<'8'> = "\u2078";
template <>
inline constexpr fixed_string super_impl<'9'> = "\u2079";
template <>
inline constexpr fixed_string super_impl<'-'> = "\u207b";
template <auto fs, std::size_t... Is>
struct expand<fs, std::index_sequence<Is...>> {
static constexpr fixed_string value = {super_impl<fs[Is]>...};
};
} // namespace detail
// convert a fixed string of numbers 0-9 & '-' into a superscript fixed_string
template <fixed_string value>
inline constexpr fixed_string super = detail::super_impl<value>;
} // namespace fs
#include <cstdint> // std::intmax_t
#include <numeric> // gcd
#include <ratio>
#include <type_traits>
namespace su {
// Convenience struct for inheriting: using type = ...
template <typename T = void>
struct Type {
using type = T;
};
namespace detail {
struct scale_tag {}; // marks class as being of scale type
} // namespace detail
template <std::intmax_t I = 1, std::intmax_t J = 1, std::intmax_t K = 0>
struct ScaleBase : private detail::scale_tag {
using ratio = std::ratio<I, J>;
static constexpr std::intmax_t num = ratio::num;
static constexpr std::intmax_t den = ratio::den;
static constexpr std::intmax_t exp = K;
static_assert(num > 0, "Cannot have zero or negative scaled dimension");
};
template <typename T>
concept Scale = std::is_base_of_v<detail::scale_tag, T>;
// Using a variadic template instead of defaulted results in shorter types
template <std::intmax_t... Is>
struct scale {
static_assert(sizeof...(Is) < 4, "Scale has too many template arguments");
};
template <>
struct scale<> : ScaleBase<> {};
template <std::intmax_t I>
struct scale<I> : ScaleBase<I> {};
template <std::intmax_t I, std::intmax_t J>
struct scale<I, J> : ScaleBase<I, J> {};
template <std::intmax_t I, std::intmax_t J, std::intmax_t K>
struct scale<I, J, K> : ScaleBase<I, J, K> {};
namespace detail {
enum { multiply, done, divide };
template <typename Ratio>
constexpr int standard_direction() {
if constexpr (std::ratio_less_equal_v<Ratio, std::ratio<-10>>) {
return divide;
}
if constexpr (std::ratio_less_equal_v<Ratio, std::ratio<-1>>) {
return done;
}
if constexpr (std::ratio_less_v<Ratio, std::ratio<0>>) {
return multiply;
}
if constexpr (std::ratio_equal_v<Ratio, std::ratio<0>>) {
return done;
}
if constexpr (std::ratio_less_v<Ratio, std::ratio<1>>) {
return multiply;
}
if constexpr (std::ratio_less_v<Ratio, std::ratio<10>>) {
return done;
}
if constexpr (std::ratio_greater_equal_v<Ratio, std::ratio<10>>) {
return divide;
}
}
// forward declaration for standard_form_impl
template <int C, std::intmax_t Exp, typename Ratio>
struct standard_match;
template <std::intmax_t Exp, typename Ratio>
struct standard_form_impl;
template <std::intmax_t Exp, typename Ratio>
struct standard_form_impl
: standard_match<standard_direction<Ratio>(), Exp, Ratio> {};
// end condition
template <std::intmax_t Exp, typename Ratio>
struct standard_match<done, Exp, Ratio> : Type<Ratio> {
static constexpr std::intmax_t exp = Exp;
};
template <std::intmax_t Exp, typename Ratio>
struct standard_match<divide, Exp, Ratio>
: standard_form_impl<Exp + 1, std::ratio_divide<Ratio, std::ratio<10>>> {};
template <std::intmax_t Exp, typename Ratio>
struct standard_match<multiply, Exp, Ratio>
: standard_form_impl<Exp - 1, std::ratio_multiply<Ratio, std::ratio<10>>> {
};
} // namespace detail
// convert a std::ratio to standard form, returns a struct with ::type = the
// standard form ratio and ::exp the base 10 exponent.
template <typename Ratio>
using standard_form = detail::standard_form_impl<0, Ratio>;
namespace detail {
template <std::intmax_t I, std::intmax_t J, std::intmax_t K>
struct scale_make_impl : Type<scale<I, J, K>> {};
template <std::intmax_t I, std::intmax_t J>
struct scale_make_impl<I, J, 0> : Type<scale<I, J>> {};
template <std::intmax_t I>
struct scale_make_impl<I, 1, 0> : Type<scale<I>> {};
template <>
struct scale_make_impl<1, 1, 0> : Type<scale<>> {};
template <std::intmax_t I, std::intmax_t J, std::intmax_t K>
struct scale_make_help {
using standard = standard_form<std::ratio<I, J>>;
using type = scale_make_impl<standard::type::num, standard::type::den,
K + standard::exp>::type;
};
} // namespace detail
// Returns the most minimal possible scale type in standard form
template <std::intmax_t I = 1, std::intmax_t J = 1, std::intmax_t K = 0>
using scale_make = detail::scale_make_help<I, J, K>::type;
namespace detail {
template <Scale A, Scale B>
struct scale_multiply {
using product = std::ratio_multiply<typename A::ratio, typename B::ratio>;
using type = scale_make<product::num, product::den, A::exp + B::exp>;
};
template <Scale A, Scale B>
struct scale_divide {
using product = std::ratio_divide<typename A::ratio, typename B::ratio>;
using type = scale_make<product::num, product::den, A::exp - B::exp>;
};
} // namespace detail
template <Scale A, Scale B>
using scale_multiply_t = detail::scale_multiply<A, B>::type;
template <Scale A, Scale B>
using scale_divide_t = detail::scale_divide<A, B>::type;
namespace detail {
// Stringifys a scale<> into a minimal "(a/b x 10^c)" like form.
template <Scale S>
inline constexpr auto anotate() {
using namespace fs; // for string literal operator
constexpr std::intmax_t num = S::num;
constexpr std::intmax_t den = S::den;
constexpr std::intmax_t exp = S::exp;
if constexpr (exp == 0) {
if constexpr (den == 1) {
if constexpr (num == 1) {
return ""_fs;
} else {
return "("_fs + ito_fs<num> + ")"_fs;
}
} else {
return "("_fs + ito_fs<num> + "/"_fs + ito_fs<den> + ")"_fs;
}
} else {
if constexpr (den == 1) {
if constexpr (num == 1) {
return "(10"_fs + super<ito_fs<exp>> + ")"_fs;
} else {
return "("_fs + ito_fs<num> + "\u00D710"_fs +
super<ito_fs<exp>> + ")"_fs;
}
} else {
return "("_fs + ito_fs<num> + "/"_fs + ito_fs<den> + "\u00D710"_fs +
super<ito_fs<exp>> + ")"_fs;
}
}
}
template <std::intmax_t exponent, typename T>
requires(exponent > 0) constexpr T pow10() {
if constexpr (exponent == 0) {
return static_cast<T>(1);
} else if constexpr (exponent == 1) {
return static_cast<T>(10);
} else if constexpr (exponent % 2 == 0) {
return pow10<exponent / 2, T>() * pow10<exponent / 2, T>();
} else {
return pow10<exponent / 2, T>() * pow10<exponent / 2, T>() *
static_cast<T>(10);
}
}
} // namespace detail
template <Scale From, Scale To, typename T>
inline constexpr T scale_convert(T x) {
//
using ratio = std::ratio_divide<typename From::ratio, typename To::ratio>;
constexpr std::intmax_t num = ratio::num;
constexpr std::intmax_t den = ratio::den;
constexpr std::intmax_t exp = From::exp - To::exp;
// Avoid floating point multiplication without -ffast-math
if constexpr (exp == 0) {
if constexpr (num == 1 && den == 1) {
return x;
} else if constexpr (num != 1 && den == 1) {
return x * static_cast<T>(num);
} else if constexpr (num == 1 && den != 1) {
return x / static_cast<T>(den);
} else if constexpr (num != 1 && den != 1) {
return x * static_cast<T>(num) / static_cast<T>(den);
}
} else if constexpr (exp > 0) {
constexpr T pow10 = detail::pow10<exp, T>();
if constexpr (num == 1 && den == 1) {
return x * pow10;
} else if constexpr (num != 1 && den == 1) {
return x * static_cast<T>(num) * pow10;
} else if constexpr (num == 1 && den != 1) {
return x / static_cast<T>(den) * pow10;
} else if constexpr (num != 1 && den != 1) {
return x * static_cast<T>(num) / static_cast<T>(den) * pow10;
}
} else if constexpr (exp < 0) {
constexpr T pow10 = detail::pow10<-exp, T>();
if constexpr (num == 1 && den == 1) {
return x / pow10;
} else if constexpr (num != 1 && den == 1) {
return x * static_cast<T>(num) / pow10;
} else if constexpr (num == 1 && den != 1) {
return x / static_cast<T>(den) / pow10;
} else if constexpr (num != 1 && den != 1) {
return x * static_cast<T>(num) / static_cast<T>(den) / pow10;
}
}
}
} // namespace su
#include <cstddef> // std::size_t
#include <cstdint> // std::intmax_t
#include <ratio>
#include <type_traits>
namespace su {
// Lightweight list type required to separate parameter packs
template <typename... Ts>
struct list {
inline static constexpr std::size_t size() { return sizeof...(Ts); }
};
namespace detail {
template <typename>
struct is_list : std::false_type {};
template <typename... Ts>
struct is_list<list<Ts...>> : std::true_type {};
} // namespace detail
template <typename T>
concept List = detail::is_list<T>::value;
namespace detail {
struct dimension_tag {}; // Marks class as being a dimension type.
} // namespace detail
// *****************************************************************************
// * User access point for making new dimensions *
// *****************************************************************************
// Dimension base class. Defaults required for variadic instantiation
template <fs::fixed_string Str, std::intmax_t I = 1, std::intmax_t J = 1>
struct dimension : private detail::dimension_tag {
using exp = std::ratio<I, J>;
static constexpr std::intmax_t num = exp::num;
static constexpr std::intmax_t den = exp::den;
static constexpr fs::fixed_string symbol = Str;
};
////////////////////////////////////////////////////////////////////////////////
template <typename T>
concept Dimension = std::is_base_of_v<detail::dimension_tag, T>;
namespace detail {
template <typename, typename>
struct dimension_same : std::false_type {};
template <template <std::intmax_t...> typename Dim, std::intmax_t... Il,
std::intmax_t... Ir>
struct dimension_same<Dim<Il...>, Dim<Ir...>> : std::true_type {};
} // namespace detail
// Test if two types are specialisations of the same dimension type.
template <Dimension A, Dimension B>
inline constexpr bool dimension_same_v = detail::dimension_same<A, B>::value;
namespace detail {
template <typename, typename>
struct dimension_equal : std::false_type {};
template <Dimension A, Dimension B>
struct dimension_equal<A, B> {
static constexpr bool value =
dimension_same_v<A, B> &&
std::ratio_equal_v<typename A::exp, typename B::exp>;
};
template <Dimension... Dl, Dimension... Dr>
requires(sizeof...(Dl) ==
sizeof...(Dr)) struct dimension_equal<list<Dl...>, list<Dr...>> {
static constexpr bool value =
std::conjunction_v<dimension_equal<Dl, Dr>...>;
};
} // namespace detail
// Test if two types are specialisations of the same dimension type and have
// equal exponents.
template <typename A, typename B>
inline constexpr bool dimension_equal_v = detail::dimension_equal<A, B>::value;
namespace detail {
template <typename, std::intmax_t, std::intmax_t>
struct dimension_simplify;
template <template <std::intmax_t...> typename Dim, std::intmax_t I,
std::intmax_t J, std::intmax_t... Is>
struct dimension_simplify<Dim<Is...>, I, J> : Type<Dim<I, J>> {};
template <template <std::intmax_t...> typename Dim, std::intmax_t I,
std::intmax_t... Is>
struct dimension_simplify<Dim<Is...>, I, 1> : Type<Dim<I>> {};
template <template <std::intmax_t...> typename Dim, std::intmax_t... Is>
struct dimension_simplify<Dim<Is...>, 1, 1> : Type<Dim<>> {};
} // namespace detail
// Converts a dimensions into its shortest possible version representation
template <Dimension D>
using dimension_simplify_t =
detail::dimension_simplify<D, D::num, D::den>::type;
namespace detail {
template <typename, typename>
struct dimension_add;
template <template <std::intmax_t...> typename Dim, std::intmax_t... Is,
typename Ratio>
struct dimension_add<Dim<Is...>, Ratio> {
using sum = std::ratio_add<typename Dim<Is...>::exp, Ratio>;
using type = dimension_simplify_t<Dim<sum::num, sum::den>>;
};
} // namespace detail
// Returns new dimension with same type and new exponent equal to the sum of
// std::ratio O and argument dimensions' exponent.
template <Dimension D, typename Ratio>
using dimension_add_t = detail::dimension_add<D, Ratio>::type;
namespace detail {
template <typename, typename>
struct dimension_multiply;
}
// Returns new dimension with same type but and new exponent equal to the
// product of std::ratio O and the argument dimensions' exponent.
template <typename D, typename Ratio>
using dimension_multiply_t = detail::dimension_multiply<D, Ratio>::type;
namespace detail {
template <template <std::intmax_t...> typename Dim, std::intmax_t... Is,
typename Ratio>
struct dimension_multiply<Dim<Is...>, Ratio> {
using product = std::ratio_multiply<typename Dim<Is...>::exp, Ratio>;
using type = dimension_simplify_t<Dim<product::num, product::den>>;
};
template <typename Ratio, Dimension... Dims>
struct dimension_multiply<list<Dims...>, Ratio>
: Type<list<dimension_multiply_t<Dims, Ratio>...>> {};
// Extracts symbol from dimension and returns symbol as a static string
// decorated with exponent in minimal "symbol^x/y" like form.
template <Dimension D>
inline constexpr auto anotate() {
using namespace fs; // for string literal operator
constexpr std::intmax_t num = D::num;
constexpr std::intmax_t den = D::den;
if constexpr (num == 1 && den == 1) {
return D::symbol;
} else if constexpr (num != 1 && den == 1) {
return D::symbol + super<ito_fs<num>>;
} else if constexpr (den != 1) {
return D::symbol + "^{"_fs + ito_fs<num> + "/"_fs + ito_fs<den> +
"}"_fs;
}
}
template <typename>
struct ordered_impl;
template <>
struct ordered_impl<list<>> : std::true_type {};
template <Dimension D>
struct ordered_impl<list<D>> : std::true_type {};
template <Dimension First, Dimension Second, Dimension... Tail>
struct ordered_impl<list<First, Second, Tail...>> {
static constexpr bool value =
fs::compare(First::symbol, Second::symbol) < 0 &&
ordered_impl<list<Second, Tail...>>::value;
};
} // namespace detail
// Checks if a list<...> of dimensions satisfies strict ordering,
// e.g. d_n < d_n+1 == true for all n < N.
template <List L>
inline constexpr bool ordered_v = detail::ordered_impl<L>::value;
/////////////////////////// list<> meta ////////////////////////
namespace detail {
template <typename, typename>
struct concat;
template <typename Head, typename... Tail>
struct concat<Head, list<Tail...>> : Type<list<Head, Tail...>> {};
template <typename... Head, typename Tail>
struct concat<list<Head...>, Tail> : Type<list<Head..., Tail>> {};
template <typename... Head, typename... Tail>
struct concat<list<Head...>, list<Tail...>> : Type<list<Head..., Tail...>> {};
} // namespace detail
// Concatenates two lists or list and non list;
template <typename A, typename B>
requires List<A> || List<B> using concat_t = detail::concat<A, B>::type;
namespace detail {
// Recursively concatenates A/B into L choosing 'smallest' each time to maintain
// order, dimensions comparing equal are summed
template <int, List L, List A, List B>
struct match;
template <List, List, List>
struct merge;
// Nothing left to merge end case
template <List L>
struct merge<L, list<>, list<>> : Type<L> {};
// End cases for different length lists
template <List L, Dimension... Dims>
struct merge<L, list<Dims...>, list<>> : concat<L, list<Dims...>> {};
// End cases for different length lists
template <List L, Dimension... Dims>
struct merge<L, list<>, list<Dims...>> : concat<L, list<Dims...>> {};
// General case performs string comparison and despatches to match<...>
template <List L, Dimension A, Dimension... As, Dimension B, Dimension... Bs>
struct merge<L, list<A, As...>, list<B, Bs...>>
: match<compare(A::symbol, B::symbol), L, list<A, As...>, list<B, Bs...>> {
};
// Concatenate head of A into L
template <List L, Dimension A, Dimension... As, List B>
struct match<-1, L, list<A, As...>, B> : merge<concat_t<L, A>, list<As...>, B> {
};
// Concatenate head of B into L
template <List L, List A, Dimension B, Dimension... Bs>
struct match<1, L, A, list<B, Bs...>> : merge<concat_t<L, B>, A, list<Bs...>> {
};
// Equal comparison case means we sum the dimension exponents
template <List L, Dimension A, Dimension... As, Dimension B, Dimension... Bs>
struct match<0, L, list<A, As...>, list<B, Bs...>> {
static_assert(dimension_same_v<A, B>, "Dimensions cannot have == symbols.");
using dim_sum = dimension_add_t<A, typename B::exp>;
using type = std::conditional_t<
std::ratio_equal_v<typename dim_sum::exp, std::ratio<0>>,
typename merge<L, list<As...>, list<Bs...>>::type,
typename merge<concat_t<L, dim_sum>, list<As...>, list<Bs...>>::type>;
};
} // namespace detail
// Merge two sorted lists of dimensions into a new sorted list summing any
// dimensions of the same type.
template <List A, List B>
requires ordered_v<A>&& ordered_v<B> using merge_sum_sorted_t =
detail::merge<list<>, A, B>::type;
namespace detail {
// Bottom-up, compile time merge sorting!
template <List...>
struct sort_impl;
// Empty list (sorting nothing) end case
template <>
struct sort_impl<list<>> : Type<list<>> {};
// End condition = working list contains single (sorted) list
template <List Single>
struct sort_impl<list<Single>> : Type<Single> {};
// Re-curse condition = no more sub-list, expand working list and rerun
template <List... Ls>
struct sort_impl<list<Ls...>> : sort_impl<list<>, Ls...> {};
// Concatenate leftover (odd) sub-list into working list
template <List Working, List Odd>
struct sort_impl<Working, Odd> : sort_impl<concat_t<Working, list<Odd>>> {};
// General case - merge sub-lists and concatenate into working list
template <List Working, List First, List Second, List... Tail>
struct sort_impl<Working, First, Second, Tail...>
: sort_impl<concat_t<Working, list<merge_sum_sorted_t<First, Second>>>,
Tail...> {};
} // namespace detail
// Compile time bottom-up merge sort a parameter pack of dimensions into a list
template <Dimension... Dims>
using sort_t = detail::sort_impl<list<>, list<Dims>...>::type;
} // namespace su
#include <type_traits>
namespace su {
namespace detail {
// Join annotated scale and dimensions with correct spaces.
template <typename Scale>
inline constexpr auto join(Scale scale) {
// for string literal operator
using namespace fs;
if constexpr (Scale::size() == 0) {
return "dimensionless"_fs;
} else {
return scale + " dimensionless"_fs;
}
}
template <typename Scale, typename Head, typename... Tail>
inline constexpr auto join(Scale scale, Head head, Tail... tail) {
// for string literal operator
using namespace fs;
if constexpr (Scale::size() == 0) {
return fixed_string{head, ("\u22C5"_fs + tail)...};
} else {
return fixed_string{scale, " "_fs, head, ("\u22C5"_fs + tail)...};
}
}
struct unit_tag {}; // marks unit for concept
} // namespace detail
// Base class representing a general unit.
template <Scale S, Dimension... Dims>
struct nameless : downcast_base<nameless<S, Dims...>>, detail::unit_tag {
public:
using scale_factor = S;
using dimensions = list<Dims...>;
static_assert((... && (Dims::num != 0)),
"Unit dimension exponents cannot be zero.");
static_assert(ordered_v<dimensions>,
"Unit dimensions must satisfy strict ordering.");
// Symbol contains scale info and dimension symbols / exponents.
static constexpr fs::fixed_string m_base_symbol =
detail::join(detail::anotate<S>(), detail::anotate<Dims>()...);
static constexpr fs::fixed_string m_symbol = m_base_symbol;
};
template <typename T>
concept Unit = std::is_base_of_v<detail::unit_tag, T>;
// Units which have scale<1, 1, 0> are coherent and therefore we can exclude
// the scale from the template parameter list to shorten the quantity
// definition.
template <Dimension... Dims>
struct coherent : nameless<scale<>, Dims...> {};
namespace detail {
// Case for unique downcast
template <Unit U, Unit D>
struct downcast_unit_impl : Type<D> {};
// Case for no downcast but unit is coherent
template <Unit U, Dimension... Dims>
struct downcast_unit_impl<U, nameless<scale<>, Dims...>>
: Type<coherent<Dims...>> {};
// General case for no downcast
template <Unit U>
requires(!std::is_same_v<typename U::scale_factor,
scale<>>) struct downcast_unit_impl<U, U> : Type<U> {};
} // namespace detail
// Downcast a unit to either an user defined unit an 'coherent' unit or an
// non-coherent 'nameless' unit
template <Unit U>
using downcast_unit = detail::downcast_unit_impl<U, downcast<U>>::type;
namespace detail {
// inheritance injection to change symbol when using named_unit<...> helper
template <auto Name, Unit U>
struct named_unit : U {
static constexpr fs::fixed_string m_symbol = Name;
};
template <bool, Scale, List>
struct unit_make_impl;
// sorted case
template <Scale S, Dimension... Dims>
struct unit_make_impl<true, S, list<Dims...>> : Type<nameless<S, Dims...>> {};
// unsorted case
template <Scale S, Dimension... Dims>
struct unit_make_impl<false, S, list<Dims...>>
: unit_make_impl<true, S, sort_t<Dims...>> {};
} // namespace detail
// Makes a unit type from a dimension list<...> by simplifying and sorting it
// and simplifying the scale.
template <Scale S, List L>
using unit_make_t =
detail::unit_make_impl<ordered_v<L>, scale_make<S::num, S::den, S::exp>,
L>::type;
// *****************************************************************************
// * User access points for making new units *
// *****************************************************************************
template <typename Target, Scale S, Dimension... Dims>
struct unit : downcast_child<Target, unit_make_t<S, list<Dims...>>> {};
template <typename Target, fs::fixed_string Sym, Scale S, Dimension... Dims>