mp-units/src/include/units/bits/deduced_unit.h

// The MIT License (MIT)
//
// Copyright (c) 2018 Mateusz Pusz
//
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// of this software and associated documentation files (the "Software"), to deal
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// furnished to do so, subject to the following conditions:
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#pragma once

#include <units/derived_dimension.h>

namespace units::detail {

// same_scaled_units
template<typename ExpList, Unit... Us>
inline constexpr bool same_scaled_units = false;

template<typename... Es, Unit... Us>
inline constexpr bool same_scaled_units<exp_list<Es...>, Us...> = (UnitOf<Us, typename Es::dimension> && ...);

// deduced_unit
template<typename Result, int UnitExpNum, int UnitExpDen, typename UnitRatio>
struct ratio_op;

template<typename Result, int UnitExpDen, typename UnitRatio>
struct ratio_op<Result, 0, UnitExpDen, UnitRatio> {
  using ratio = Result;
};

template<typename Result, int UnitExpNum, int UnitExpDen, typename UnitRatio>
struct ratio_op {
  using calc_ratio =
      conditional<(UnitExpNum * UnitExpDen > 0), ratio_multiply<Result, UnitRatio>, ratio_divide<Result, UnitRatio>>;
  static constexpr int value = (UnitExpNum * UnitExpDen > 0) ? (UnitExpNum - UnitExpDen) : (UnitExpNum + UnitExpDen);
  using ratio = ratio_op<calc_ratio, value, UnitExpDen, UnitRatio>::ratio;
};

template<typename ExpList, Unit... Us>
struct derived_ratio;

template<Unit... Us>
struct derived_ratio<exp_list<>, Us...> {
  using ratio = ::units::ratio<1>;
};

template<typename E, typename... ERest, Unit U, Unit... URest>
struct derived_ratio<exp_list<E, ERest...>, U, URest...> {
  using rest_ratio = derived_ratio<exp_list<ERest...>, URest...>::ratio;
  using ratio = ratio_op<rest_ratio, E::num, E::den, typename U::ratio>::ratio;
};

template<DerivedDimension D, Unit... Us>
using deduced_unit =
    scaled_unit<typename D::coherent_unit::reference, typename detail::derived_ratio<typename D::recipe, Us...>::ratio>;

}  // namespace units::detail