forked from mpusz/mp-units
Fix up for review
- 120 line limit - uppercase template params - doxygen comments for public APIs - `int_base` -> `prime_base`
This commit is contained in:
Chip Hogg
@@ -29,106 +29,165 @@
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namespace units::mag
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{
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template <typename base_, ratio power_ = ratio{1}>
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/**
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* @brief A basis vector in our magnitude representation, raised to some rational power.
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*
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* The set of basis vectors must be linearly independent: that is, no product of basis powers can ever equal 1, unless
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* all exponents are zero. To achieve this, we use arbitrarily many prime numbers as basis vectors, and also various
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* irrational numbers such as pi.
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*
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* @tparam Base A type representing the basis vector. Must have a numeric static `value` member.
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* @tparam Power The rational power to which the base is raised.
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*/
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template<typename Base, ratio Power = ratio{1}>
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struct base_power {
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using base = base_;
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static inline constexpr ratio power = power_;
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using base = Base;
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static inline constexpr ratio power = Power;
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};
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template <typename T>
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/**
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* @brief A type trait and concept to detect whether something is a valid "base power".
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*/
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template<typename T>
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struct is_base_power;
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template <typename T>
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template<typename T>
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inline constexpr bool is_base_power_v = is_base_power<T>::value;
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template <typename T>
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template<typename T>
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concept BasePower = is_base_power_v<T>;
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// A `magnitude` represents a positive real number in a format which optimizes taking products and
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// rational powers.
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template <BasePower... base_powers>
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/**
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* @brief A representation for positive real numbers which optimizes taking products and rational powers.
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*
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* Magnitudes can be treated as values. Each type encodes exactly one value. Users can multiply, divide, and compare
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* for equality using this value API.
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*/
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template<BasePower... BasePowers>
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struct magnitude;
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template <typename T>
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/**
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* @brief A type trait and concept to detect whether something is a valid magnitude.
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*
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* In particular, these traits check for canonicalized forms: the base powers must be sorted by increasing base value,
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* and all exponents must be nonzero.
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*/
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template<typename T>
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struct is_magnitude;
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template <typename T>
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template<typename T>
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inline constexpr bool is_magnitude_v = is_magnitude<T>::value;
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template <typename T>
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template<typename T>
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concept Magnitude = is_magnitude_v<T>;
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template <std::intmax_t N>
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struct int_base : std::integral_constant<std::intmax_t, N> {};
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template <std::intmax_t N, std::intmax_t num = 1, std::intmax_t den = 1>
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using int_base_power = base_power<int_base<N>, ratio{num, den}>;
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template <Magnitude M>
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/**
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* @brief Compute the inverse of a Magnitude.
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*/
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template<Magnitude M>
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struct inverse;
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template <Magnitude M>
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template<Magnitude M>
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using inverse_t = typename inverse<M>::type;
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template <Magnitude... Mags>
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/**
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* @brief Compute the product of 0 or more Magnitudes.
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*/
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template<Magnitude... Mags>
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struct product;
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template <Magnitude... Mags>
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template<Magnitude... Mags>
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using product_t = typename product<Mags...>::type;
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template <Magnitude T, Magnitude U>
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/**
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* @brief Compute the quotient of 2 Magnitudes.
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*/
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template<Magnitude T, Magnitude U>
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using quotient_t = product_t<T, inverse_t<U>>;
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namespace detail
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{
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template <std::intmax_t N>
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// Helpers to perform prime factorization at compile time.
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template<std::intmax_t N>
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struct prime_factorization;
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template <std::intmax_t N>
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template<std::intmax_t N>
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using prime_factorization_t = typename prime_factorization<N>::type;
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// A way to check whether a number is prime at compile time.
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constexpr bool is_prime(std::intmax_t n);
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} // namespace detail
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template <std::intmax_t N, std::intmax_t D = 1>
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/**
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* @brief A template to represent prime number bases.
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*/
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template<std::intmax_t N>
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struct prime_base : std::integral_constant<std::intmax_t, N> {
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static_assert(detail::is_prime(N));
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};
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/**
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* @brief Make a Magnitude that is a rational number.
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*
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* This will be the main way end users create Magnitudes. They should rarely (if ever) create a magnitude<...> by
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* manually adding base powers.
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*/
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template<std::intmax_t N, std::intmax_t D = 1>
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constexpr auto make_ratio() {
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return quotient_t<detail::prime_factorization_t<N>, detail::prime_factorization_t<D>>{};
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}
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template <typename T, std::intmax_t N = 1, std::intmax_t D = 1>
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/**
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* @brief Make a Magnitude from a single base raised to a particular power.
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*
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* This should handle all of the remaining use cases which can't be captured by make_ratio(), i.e., any irrational
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* magnitudes. For example:
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* - `make_base_power<pi>()` to represent pi
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* - `make_base_power<prime_base<2>, 1, 2>()` to represent sqrt(2)
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*/
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template<typename T, std::intmax_t N = 1, std::intmax_t D = 1>
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constexpr auto make_base_power() {
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return magnitude<base_power<T, ratio{N, D}>>{};
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}
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/**
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* @brief A base to represent pi.
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*/
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struct pi {
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static inline constexpr long double value = std::numbers::pi_v<long double>;
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};
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////////////////////////////////////////////////////////////////////////////////////////////////////
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////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
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// Implementation details below.
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////////////////////////////////////////////////////////////////////////////////////////////////////
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////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
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template <BasePower... Bs>
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template<BasePower... Bs>
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struct magnitude {
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template <Magnitude M>
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template<Magnitude M>
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constexpr bool operator==(M) const { return std::is_same_v<magnitude, M>; }
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template <Magnitude M>
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template<Magnitude M>
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constexpr friend auto operator*(magnitude, M) { return product_t<magnitude, M>{}; }
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template <Magnitude M>
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template<Magnitude M>
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constexpr friend auto operator/(magnitude, M) { return quotient_t<magnitude, M>{}; }
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};
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////////////////////////////////////////////////////////////////////////////////////////////////////
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////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
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// BasePower concept implementation.
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template <typename T>
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// Default implementation: most things are not base powers.
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template<typename T>
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struct is_base_power: std::false_type {};
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template <typename B, ratio E>
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// To be a valid base power, one must be a base_power<B, E>, where B has a static value member which is positive.
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template<typename B, ratio E>
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requires requires() { B::value; }
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struct is_base_power<base_power<B, E>>
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: std::bool_constant<(B::value > 0)> {};
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////////////////////////////////////////////////////////////////////////////////////////////////////
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////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
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// Magnitude concept implementation.
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template <typename T>
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// Default implementation: most things are not magnitudes.
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template<typename T>
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struct is_magnitude: std::false_type {};
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// Check whether a tuple of (possibly heterogeneously typed) values are strictly increasing.
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template <typename... Ts>
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template<typename... Ts>
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constexpr bool strictly_increasing(const std::tuple<Ts...> &ts) {
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// Carefully handle different sizes, avoiding unsigned integer underflow.
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constexpr auto num_comparisons = [](auto num_elements) {
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@@ -141,56 +200,53 @@ constexpr bool strictly_increasing(const std::tuple<Ts...> &ts) {
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}(std::make_index_sequence<num_comparisons>());
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}
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template <BasePower... Bs>
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// To be a valid magnitude, one must be a magnitude<...> of BasePowers with nonzero exponents, sorted by increasing base
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// value.
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template<BasePower... Bs>
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struct is_magnitude<magnitude<Bs...>>
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: std::bool_constant<(
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strictly_increasing(std::make_tuple(Bs::base::value...))
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&& ((Bs::power.num != 0) && ...))> {};
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: std::bool_constant<(strictly_increasing(std::make_tuple(Bs::base::value...)) && ((Bs::power.num != 0) && ...))> {};
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////////////////////////////////////////////////////////////////////////////////////////////////////
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////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
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// Inverse implementation.
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// To invert a BasePower, negate all exponents.
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template<BasePower B>
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using base_power_inverse = base_power<typename B::base, -B::power>;
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template <BasePower... Bs>
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struct inverse<magnitude<Bs...>> {
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using type = magnitude<base_power_inverse<Bs>...>;
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};
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template<BasePower... Bs>
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struct inverse<magnitude<Bs...>> { using type = magnitude<base_power_inverse<Bs>...>; };
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////////////////////////////////////////////////////////////////////////////////////////////////////
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////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
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// Product implementation.
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// Convenience utility to prepend a base_power to a magnitude.
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//
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// Assumes that the prepended power has a smaller base than every base power in the magnitude.
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template <BasePower B, Magnitude M>
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template<BasePower B, Magnitude M>
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struct prepend_base;
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template <BasePower B, Magnitude M>
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template<BasePower B, Magnitude M>
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using prepend_base_t = typename prepend_base<B, M>::type;
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template <BasePower B, BasePower... Bs>
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struct prepend_base<B, magnitude<Bs...>> {
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using type = magnitude<B, Bs...>;
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};
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template<BasePower B, BasePower... Bs>
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struct prepend_base<B, magnitude<Bs...>> { using type = magnitude<B, Bs...>; };
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// Nullary case.
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template <>
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template<>
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struct product<> { using type = magnitude<>; };
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// Unary case.
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template <Magnitude M>
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template<Magnitude M>
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struct product<M> { using type = M; };
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// Binary case, where right argument is null magnitude.
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template <Magnitude M>
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template<Magnitude M>
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struct product<M, magnitude<>> { using type = M; };
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// Binary case, where left argument is null magnitude, and right is non-null.
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template <BasePower B, BasePower... Bs>
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template<BasePower B, BasePower... Bs>
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struct product<magnitude<>, magnitude<B, Bs...>> { using type = magnitude<B, Bs...>; };
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// Binary case, with distinct and non-null heads.
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template <BasePower Head1, BasePower... Tail1, BasePower Head2, BasePower... Tail2>
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template<BasePower Head1, BasePower... Tail1, BasePower Head2, BasePower... Tail2>
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struct product<magnitude<Head1, Tail1...>, magnitude<Head2, Tail2...>>
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{
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using type = std::conditional_t<
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@@ -200,7 +256,7 @@ struct product<magnitude<Head1, Tail1...>, magnitude<Head2, Tail2...>>
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};
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// Binary case, same head.
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template <typename Base, ratio Pow1, ratio Pow2, BasePower... Tail1, BasePower... Tail2>
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template<typename Base, ratio Pow1, ratio Pow2, BasePower... Tail1, BasePower... Tail2>
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struct product<magnitude<base_power<Base, Pow1>, Tail1...>,
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magnitude<base_power<Base, Pow2>, Tail2...>>
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{
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@@ -212,16 +268,13 @@ struct product<magnitude<base_power<Base, Pow1>, Tail1...>,
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};
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// N-ary case (N > 2).
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template <Magnitude T, Magnitude U, Magnitude... Tail>
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struct product<T, U, Tail...>
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{
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using type = product_t<product_t<T, U>, Tail...>;
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};
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template<Magnitude T, Magnitude U, Magnitude... Tail>
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struct product<T, U, Tail...> { using type = product_t<product_t<T, U>, Tail...>; };
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namespace detail
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{
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////////////////////////////////////////////////////////////////////////////////////////////////////
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////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
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// Prime factorization implementation.
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// Find the smallest prime factor of `n`.
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@@ -251,19 +304,16 @@ constexpr std::intmax_t multiplicity(std::intmax_t factor, std::intmax_t n)
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// Undefined unless base > 1, pow >= 0, and (base ^ pow) evenly divides n.
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constexpr std::intmax_t remove_power(std::intmax_t base, std::intmax_t pow, std::intmax_t n)
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{
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while (pow-- > 0)
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{
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n /= base;
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}
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while (pow-- > 0) { n /= base; }
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return n;
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}
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// Specialization for the prime factorization of 1 (base case).
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template <>
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template<>
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struct prime_factorization<1> { using type = magnitude<>; };
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// Specialization for the prime factorization of larger numbers (recursive case).
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template <std::intmax_t N>
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template<std::intmax_t N>
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struct prime_factorization {
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static_assert(N > 1, "Can only factor positive integers.");
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@@ -272,8 +322,10 @@ struct prime_factorization {
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static inline constexpr std::intmax_t remainder = remove_power(first_base, first_power, N);
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using type = product_t<
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magnitude<int_base_power<first_base, first_power>>, prime_factorization_t<remainder>>;
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magnitude<base_power<prime_base<first_base>, ratio{first_power}>>, prime_factorization_t<remainder>>;
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};
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constexpr bool is_prime(std::intmax_t n) { return (n > 1) && (find_first_factor(n) == n); }
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} // namespace detail
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} // namespace units::mag
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@@ -28,6 +28,9 @@
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namespace units::mag
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{
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template<std::intmax_t N, std::intmax_t Num = 1, std::intmax_t Den = 1>
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using int_base_power = base_power<prime_base<N>, ratio{Num, Den}>;
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TEST_CASE("Magnitude is invertible")
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{
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CHECK(std::is_same_v<inverse_t<magnitude<>>, magnitude<>>);
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@@ -138,12 +141,6 @@ TEST_CASE("is_base_power detects well formed base powers")
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CHECK(is_base_power_v<base_power<pi, ratio{-2, 3}>>);
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}
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SECTION ("base_power disqualified by negative or zero base")
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{
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CHECK(!is_base_power_v<int_base_power<0>>);
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CHECK(!is_base_power_v<int_base_power<-1>>);
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}
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SECTION ("base_power disqualified by base without value")
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{
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CHECK(!is_base_power_v<base_power<int>>);
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@@ -238,8 +235,8 @@ TEST_CASE("make_magnitude handles arbitrary bases")
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{
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SECTION("Equivalent to std::integral_constant for integer bases")
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{
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CHECK(make_base_power<int_base<2>>() == make_ratio<2>());
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CHECK(make_base_power<int_base<7>>() == make_ratio<7>());
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CHECK(make_base_power<prime_base<2>>() == make_ratio<2>());
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CHECK(make_base_power<prime_base<7>>() == make_ratio<7>());
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}
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SECTION("Handles non-integer bases")
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@@ -348,6 +345,35 @@ TEST_CASE("Prime factorization")
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}
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}
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TEST_CASE("is_prime detects primes")
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{
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SECTION("Non-positive numbers are not prime")
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{
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CHECK(!is_prime(-1328));
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CHECK(!is_prime(-1));
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CHECK(!is_prime(0));
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}
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SECTION("1 is not prime")
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{
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CHECK(!is_prime(1));
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}
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SECTION("Discriminates between primes and non-primes")
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{
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CHECK(is_prime(2));
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CHECK(is_prime(3));
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CHECK(!is_prime(4));
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CHECK(is_prime(5));
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CHECK(!is_prime(6));
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CHECK(is_prime(7));
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CHECK(!is_prime(8));
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CHECK(!is_prime(9));
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CHECK(is_prime(7919));
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}
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}
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} // namespace detail
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} // namespace units::mag
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