418 lines
15 KiB
C++
418 lines
15 KiB
C++
// 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/angular/angular.h>
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#include <units/bits/external/hacks.h>
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#include <units/isq/space_and_time.h>
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#include <units/quantity.h>
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#include <units/si/units.h>
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#include <units/unit.h>
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// IWYU pragma: begin_exports
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#include <cmath>
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#include <cstdint>
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// IWYU pragma: end_exports
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#include <limits>
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namespace units {
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/**
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* @brief Computes the value of a quantity raised to the `Num/Den` power
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*
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* Both the quantity value and its quantity specification are the base of the operation.
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*
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* @tparam Num Exponent numerator
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* @tparam Den Exponent denominator
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* @param q Quantity being the base of the operation
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* @return Quantity The result of computation
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*/
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template<std::intmax_t Num, std::intmax_t Den = 1, Quantity Q>
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requires detail::non_zero<Den>
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[[nodiscard]] inline auto pow(const Q& q) noexcept
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requires requires { pow(q.number(), 1.0); } || requires { std::pow(q.number(), 1.0); }
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{
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using rep = TYPENAME Q::rep;
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if constexpr (Num == 0) {
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return rep(1);
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} else if constexpr (ratio{Num, Den} == 1) {
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return q;
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} else {
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using std::pow;
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return quantity<reference<pow<Num, Den>(Q::quantity_spec), pow<Num, Den>(Q::unit)>{}, rep>(
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static_cast<rep>(pow(q.number(), static_cast<double>(Num) / static_cast<double>(Den))));
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}
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}
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/**
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* @brief Computes the square root of a quantity
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*
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* Both the quantity value and its quantity specification are the base of the operation.
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*
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* @param q Quantity being the base of the operation
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* @return Quantity The result of computation
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*/
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template<Quantity Q>
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[[nodiscard]] inline Quantity auto sqrt(const Q& q) noexcept
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requires requires { sqrt(q.number()); } || requires { std::sqrt(q.number()); }
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{
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using rep = TYPENAME Q::rep;
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using std::sqrt;
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return quantity<reference<pow<1, 2>(Q::quantity_spec), pow<1, 2>(Q::unit)>{}, rep>(
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static_cast<rep>(sqrt(q.number())));
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}
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/**
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* @brief Computes the cubic root of a quantity
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*
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* Both the quantity value and its quantity specification are the base of the operation.
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*
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* @param q Quantity being the base of the operation
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* @return Quantity The result of computation
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*/
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template<Quantity Q>
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[[nodiscard]] inline Quantity auto cbrt(const Q& q) noexcept
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requires requires { cbrt(q.number()); } || requires { std::cbrt(q.number()); }
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{
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using rep = TYPENAME Q::rep;
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using std::cbrt;
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return quantity<reference<pow<1, 3>(Q::quantity_spec), pow<1, 3>(Q::unit)>{}, rep>(
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static_cast<rep>(cbrt(q.number())));
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}
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/**
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* @brief Computes Euler's raised to the given power
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*
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* @note Such an operation has sense only for a dimensionless quantity.
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*
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* @param q Quantity being the base of the operation
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* @return Quantity The value of the same quantity type
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*/
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template<quantity_of<dimension_one> Q>
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[[nodiscard]] inline Q exp(const Q& q)
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requires requires { exp(q.number()); } || requires { std::exp(q.number()); }
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{
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using std::exp;
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return quantity_cast<Q::unit>(exp(quantity_cast<one>(q).number()) * dimensionless[one]);
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}
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/**
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* @brief Computes the absolute value of a quantity
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*
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* @param q Quantity being the base of the operation
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* @return Quantity The absolute value of a provided quantity
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*/
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template<Quantity Q>
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[[nodiscard]] inline Q abs(const Q& q) noexcept
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requires requires { abs(q.number()); } || requires { std::abs(q.number()); }
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{
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using std::abs;
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return Q(abs(q.number()));
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}
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/**
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* @brief Returns the epsilon of the quantity
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*
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* The returned value is defined by a <tt>std::numeric_limits<typename Q::rep>::epsilon()</tt>.
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*
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* @tparam Q Quantity type being the base of the operation
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* @return Quantity The epsilon value for quantity's representation type
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*/
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template<Representation Rep, Reference R>
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requires requires { std::numeric_limits<Rep>::epsilon(); }
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[[nodiscard]] constexpr Quantity auto epsilon(R r) noexcept
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{
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return std::numeric_limits<Rep>::epsilon() * r;
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}
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/**
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* @brief Computes the largest quantity with integer representation and unit type To with its number not greater than q
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*
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* @tparam q Quantity being the base of the operation
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* @return Quantity The rounded quantity with unit type To
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*/
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template<Unit auto To, auto R, typename Rep>
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[[nodiscard]] constexpr quantity<reference<R.quantity_spec, To>{}, Rep> floor(const quantity<R, Rep>& q) noexcept
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requires((!treat_as_floating_point<Rep>) || requires { floor(q.number()); } ||
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requires { std::floor(q.number()); }) &&
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(To == R.unit || requires {
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::units::quantity_cast<To>(q);
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quantity<reference<R.quantity_spec, To>{}, Rep>::one();
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})
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{
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const auto handle_signed_results = [&]<typename T>(const T& res) {
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if (res > q) {
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return res - T::one();
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}
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return res;
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};
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if constexpr (treat_as_floating_point<Rep>) {
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using std::floor;
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if constexpr (To == R.unit) {
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return quantity<reference<R.quantity_spec, To>{}, Rep>(floor(q.number()));
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} else {
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return handle_signed_results(
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quantity<reference<R.quantity_spec, To>{}, Rep>(floor(quantity_cast<To>(q).number())));
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}
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} else {
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if constexpr (To == R.unit) {
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return quantity_cast<To>(q);
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} else {
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return handle_signed_results(quantity_cast<To>(q));
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}
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}
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}
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/**
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* @brief Computes the smallest quantity with integer representation and unit type To with its number not less than q
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*
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* @tparam q Quantity being the base of the operation
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* @return Quantity The rounded quantity with unit type To
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*/
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template<Unit auto To, auto R, typename Rep>
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[[nodiscard]] constexpr quantity<reference<R.quantity_spec, To>{}, Rep> ceil(const quantity<R, Rep>& q) noexcept
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requires((!treat_as_floating_point<Rep>) || requires { ceil(q.number()); } || requires { std::ceil(q.number()); }) &&
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(To == R.unit || requires {
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::units::quantity_cast<To>(q);
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quantity<reference<R.quantity_spec, To>{}, Rep>::one();
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})
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{
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const auto handle_signed_results = [&]<typename T>(const T& res) {
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if (res < q) {
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return res + T::one();
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}
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return res;
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};
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if constexpr (treat_as_floating_point<Rep>) {
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using std::ceil;
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if constexpr (To == R.unit) {
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return quantity<reference<R.quantity_spec, To>{}, Rep>(ceil(q.number()));
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} else {
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return handle_signed_results(
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quantity<reference<R.quantity_spec, To>{}, Rep>(ceil(quantity_cast<To>(q).number())));
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}
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} else {
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if constexpr (To == R.unit) {
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return quantity_cast<To>(q);
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} else {
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return handle_signed_results(quantity_cast<To>(q));
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}
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}
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}
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/**
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* @brief Computes the nearest quantity with integer representation and unit type To to q
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*
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* Rounding halfway cases away from zero, regardless of the current rounding mode.
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*
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* @tparam q Quantity being the base of the operation
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* @return Quantity The rounded quantity with unit type To
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*/
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template<Unit auto To, auto R, typename Rep>
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[[nodiscard]] constexpr quantity<reference<R.quantity_spec, To>{}, Rep> round(const quantity<R, Rep>& q) noexcept
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requires((!treat_as_floating_point<Rep>) || requires { round(q.number()); } ||
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requires { std::round(q.number()); }) &&
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(To == R.unit || requires {
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::units::floor<To>(q);
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quantity<reference<R.quantity_spec, To>{}, Rep>::one();
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})
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{
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if constexpr (To == R.unit) {
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if constexpr (treat_as_floating_point<Rep>) {
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using std::round;
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return quantity<reference<R.quantity_spec, To>{}, Rep>(round(q.number()));
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} else {
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return quantity_cast<To>(q);
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}
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} else {
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const auto res_low = units::floor<To>(q);
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const auto res_high = res_low + res_low.one();
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const auto diff0 = q - res_low;
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const auto diff1 = res_high - q;
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if (diff0 == diff1) {
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if (static_cast<int>(res_low.number()) & 1) {
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return res_high;
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}
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return res_low;
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}
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if (diff0 < diff1) {
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return res_low;
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}
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return res_high;
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}
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}
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/**
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* @brief Computes the square root of the sum of the squares of x and y,
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* without undue overflow or underflow at intermediate stages of the computation
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*/
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template<Quantity Q1, Quantity Q2>
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[[nodiscard]] inline quantity_of<common_reference(Q1::reference, Q2::reference)> auto hypot(const Q1& x,
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const Q2& y) noexcept
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requires requires { common_reference(Q1::reference, Q2::reference); } &&
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(
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requires { hypot(x.number(), y.number()); } || requires { std::hypot(x.number(), y.number()); })
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{
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using std::hypot;
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using type = quantity<common_reference(Q1::reference, Q2::reference), decltype(hypot(x.number(), y.number()))>;
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return type{hypot(type{x}.number(), type{y}.number())};
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}
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/**
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* @brief Computes the square root of the sum of the squares of x, y, and z,
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* without undue overflow or underflow at intermediate stages of the computation
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*/
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template<Quantity Q1, Quantity Q2, Quantity Q3>
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[[nodiscard]] inline quantity_of<common_reference(Q1::reference, Q2::reference, Q3::reference)> auto hypot(
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const Q1& x, const Q2& y, const Q3& z) noexcept
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requires requires { common_reference(Q1::reference, Q2::reference, Q3::reference); } &&
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(
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requires { hypot(x.number(), y.number(), z.number()); } ||
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requires { std::hypot(x.number(), y.number(), z.number()); })
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{
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using std::hypot;
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using type = quantity<common_reference(Q1::reference, Q2::reference, Q3::reference),
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decltype(hypot(x.number(), y.number(), z.number()))>;
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return type{hypot(type{x}.number(), type{y}.number(), type{z}.number())};
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}
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namespace isq {
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template<weak_quantity_of<angular_measure> Q>
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requires treat_as_floating_point<typename Q::rep>
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[[nodiscard]] inline quantity_of<dimensionless[one]> auto sin(const Q& q) noexcept
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requires requires { sin(q.number()); } || requires { std::sin(q.number()); }
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{
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using std::sin;
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return quantity{sin(q[si::radian].number())};
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}
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template<weak_quantity_of<angular_measure> Q>
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requires treat_as_floating_point<typename Q::rep>
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[[nodiscard]] inline quantity_of<dimensionless[one]> auto cos(const Q& q) noexcept
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requires requires { cos(q.number()); } || requires { std::cos(q.number()); }
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{
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using std::cos;
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return quantity{cos(q[si::radian].number())};
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}
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template<weak_quantity_of<angular_measure> Q>
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requires treat_as_floating_point<typename Q::rep>
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[[nodiscard]] inline quantity_of<dimensionless[one]> auto tan(const Q& q) noexcept
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requires requires { tan(q.number()); } || requires { std::tan(q.number()); }
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{
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using std::tan;
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return quantity{tan(q[si::radian].number())};
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}
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template<quantity_of<dimension_one> Q>
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requires treat_as_floating_point<typename Q::rep>
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[[nodiscard]] inline quantity_of<angular_measure[si::radian]> auto asin(const Q& q) noexcept
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requires requires { asin(q.number()); } || requires { std::asin(q.number()); }
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{
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using std::asin;
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return asin(quantity_cast<one>(q).number()) * angular_measure[si::radian];
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}
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template<quantity_of<dimension_one> Q>
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requires treat_as_floating_point<typename Q::rep>
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[[nodiscard]] inline quantity_of<angular_measure[si::radian]> auto acos(const Q& q) noexcept
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requires requires { acos(q.number()); } || requires { std::acos(q.number()); }
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{
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using std::acos;
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return acos(quantity_cast<one>(q).number()) * angular_measure[si::radian];
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}
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template<quantity_of<dimension_one> Q>
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requires treat_as_floating_point<typename Q::rep>
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[[nodiscard]] inline quantity_of<angular_measure[si::radian]> auto atan(const Q& q) noexcept
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requires requires { atan(q.number()); } || requires { std::atan(q.number()); }
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{
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using std::atan;
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return atan(quantity_cast<one>(q).number()) * angular_measure[si::radian];
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}
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} // namespace isq
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namespace angular {
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// TODO cannot use `weak_quantity_of<angle>` as it is not interconvertible with `isq_angle::angular_measure`
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template<quantity_of<dim_angle> Q>
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requires treat_as_floating_point<typename Q::rep>
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[[nodiscard]] inline quantity_of<dimensionless[one]> auto sin(const Q& q) noexcept
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requires requires { sin(q.number()); } || requires { std::sin(q.number()); }
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{
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using std::sin;
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return quantity{sin(q[radian].number())};
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}
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template<quantity_of<dim_angle> Q>
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requires treat_as_floating_point<typename Q::rep>
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[[nodiscard]] inline quantity_of<dimensionless[one]> auto cos(const Q& q) noexcept
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requires requires { cos(q.number()); } || requires { std::cos(q.number()); }
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{
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using std::cos;
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return quantity{cos(q[radian].number())};
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}
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template<quantity_of<dim_angle> Q>
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requires treat_as_floating_point<typename Q::rep>
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[[nodiscard]] inline quantity_of<dimensionless[one]> auto tan(const Q& q) noexcept
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requires requires { tan(q.number()); } || requires { std::tan(q.number()); }
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{
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using std::tan;
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return quantity{tan(q[radian].number())};
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}
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template<quantity_of<dimension_one> Q>
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requires treat_as_floating_point<typename Q::rep>
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[[nodiscard]] inline quantity_of<angle[radian]> auto asin(const Q& q) noexcept
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requires requires { asin(q.number()); } || requires { std::asin(q.number()); }
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{
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using std::asin;
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return asin(quantity_cast<one>(q).number()) * angle[radian];
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}
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template<quantity_of<dimension_one> Q>
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requires treat_as_floating_point<typename Q::rep>
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[[nodiscard]] inline quantity_of<angle[radian]> auto acos(const Q& q) noexcept
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requires requires { acos(q.number()); } || requires { std::acos(q.number()); }
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{
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using std::acos;
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return acos(quantity_cast<one>(q).number()) * angle[radian];
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}
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template<quantity_of<dimension_one> Q>
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requires treat_as_floating_point<typename Q::rep>
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[[nodiscard]] inline quantity_of<angle[radian]> auto atan(const Q& q) noexcept
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requires requires { atan(q.number()); } || requires { std::atan(q.number()); }
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{
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using std::atan;
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return atan(quantity_cast<one>(q).number()) * angle[radian];
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}
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} // namespace angular
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} // namespace units
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