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Sprout/sprout/math/quaternion/arithmetic_operators.hpp
bolero-MURAKAMI 0918194078 add sprout::iterator, and update copyright
2017-07-29 14:20:01 +09:00

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/*=============================================================================
Copyright (c) 2011-2017 Bolero MURAKAMI
https://github.com/bolero-MURAKAMI/Sprout
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
=============================================================================*/
#ifndef SPROUT_MATH_QUATERNION_ARITHMETIC_OPERATORS_HPP
#define SPROUT_MATH_QUATERNION_ARITHMETIC_OPERATORS_HPP
#include <sprout/config.hpp>
#include <sprout/math/quaternion/quaternion.hpp>
namespace sprout {
namespace math {
//
// operator+
//
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator+(T const& lhs, sprout::math::quaternion<T> const& rhs) {
return sprout::math::quaternion<T>(
lhs + rhs.R_component_1(),
rhs.R_component_2(),
rhs.R_component_3(),
rhs.R_component_4()
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator+(sprout::math::quaternion<T> const& lhs, T const& rhs) {
return sprout::math::quaternion<T>(
lhs.R_component_1() + rhs,
lhs.R_component_2(),
lhs.R_component_3(),
lhs.R_component_4()
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator+(sprout::complex<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
return sprout::math::quaternion<T>(
lhs.real() + rhs.R_component_1(),
lhs.imag() + rhs.R_component_2(),
rhs.R_component_3(),
rhs.R_component_4()
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator+(sprout::math::quaternion<T> const& lhs, sprout::complex<T> const& rhs) {
return sprout::math::quaternion<T>(
lhs.R_component_1() + rhs.real(),
lhs.R_component_2() + rhs.imag(),
lhs.R_component_3(),
lhs.R_component_4()
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator+(sprout::math::quaternion<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
return sprout::math::quaternion<T>(
lhs.R_component_1() + rhs.R_component_1(),
lhs.R_component_2() + rhs.R_component_2(),
lhs.R_component_3() + rhs.R_component_3(),
lhs.R_component_4() + rhs.R_component_4()
);
}
//
// operator-
//
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator-(T const& lhs, sprout::math::quaternion<T> const& rhs) {
return sprout::math::quaternion<T>(
lhs - rhs.R_component_1(),
rhs.R_component_2(),
rhs.R_component_3(),
rhs.R_component_4()
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator-(sprout::math::quaternion<T> const& lhs, T const& rhs) {
return sprout::math::quaternion<T>(
lhs.R_component_1() - rhs,
lhs.R_component_2(),
lhs.R_component_3(),
lhs.R_component_4()
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator-(sprout::complex<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
return sprout::math::quaternion<T>(
lhs.real() - rhs.R_component_1(),
lhs.imag() - rhs.R_component_2(),
rhs.R_component_3(),
rhs.R_component_4()
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator-(sprout::math::quaternion<T> const& lhs, sprout::complex<T> const& rhs) {
return sprout::math::quaternion<T>(
lhs.R_component_1() - rhs.real(),
lhs.R_component_2() - rhs.imag(),
lhs.R_component_3(),
lhs.R_component_4()
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator-(sprout::math::quaternion<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
return sprout::math::quaternion<T>(
lhs.R_component_1() - rhs.R_component_1(),
lhs.R_component_2() - rhs.R_component_2(),
lhs.R_component_3() - rhs.R_component_3(),
lhs.R_component_4() - rhs.R_component_4()
);
}
//
// operator*
//
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator*(T const& lhs, sprout::math::quaternion<T> const& rhs) {
return sprout::math::quaternion<T>(
lhs * rhs.R_component_1(),
lhs * rhs.R_component_2(),
lhs * rhs.R_component_3(),
lhs * rhs.R_component_4()
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator*(sprout::math::quaternion<T> const& lhs, T const& rhs) {
return sprout::math::quaternion<T>(
lhs.R_component_1() * rhs,
lhs.R_component_2() * rhs,
lhs.R_component_3() * rhs,
lhs.R_component_4() * rhs
);
}
namespace detail {
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
mul_qc_impl(T const& a, T const& b, T const& c, T const& d, T const& ar, T const& br) {
return sprout::math::quaternion<T>(
+a * ar - b * br,
+a * br + b * ar,
+c * ar + d * br,
-c * br + d * ar
);
}
} // namespace detail
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator*(sprout::complex<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
return sprout::math::detail::mul_qc_impl(
lhs.R_component_1(), lhs.R_component_2(), lhs.R_component_3(), lhs.R_component_4(),
rhs.real(), rhs.imag()
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator*(sprout::math::quaternion<T> const& lhs, sprout::complex<T> const& rhs) {
return sprout::math::detail::mul_qc_impl(
rhs.R_component_1(), rhs.R_component_2(), rhs.R_component_3(), rhs.R_component_4(),
lhs.real(), lhs.imag()
);
}
namespace detail {
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
mul_qq_impl(T const& a, T const& b, T const& c, T const& d, T const& ar, T const& br, T const& cr, T const& dr) {
return sprout::math::quaternion<T>(
+a * ar - b * br - c * cr - d * dr,
+a * br + b * ar + c * dr - d * cr,
+a * cr - b * dr + c * ar + d * br,
+a * dr + b * cr - c * br + d * ar
);
}
} // namespace detail
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator*(sprout::math::quaternion<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
return sprout::math::detail::mul_qq_impl(
lhs.R_component_1(), lhs.R_component_2(), lhs.R_component_3(), lhs.R_component_4(),
rhs.R_component_1(), rhs.R_component_2(), rhs.R_component_3(), rhs.R_component_4()
);
}
//
// operator/
//
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator/(T const& lhs, sprout::math::quaternion<T> const& rhs) {
return sprout::math::quaternion<T>(
lhs / rhs.R_component_1(),
lhs / rhs.R_component_2(),
lhs / rhs.R_component_3(),
lhs / rhs.R_component_4()
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator/(sprout::math::quaternion<T> const& lhs, T const& rhs) {
return sprout::math::quaternion<T>(
lhs.R_component_1() / rhs,
lhs.R_component_2() / rhs,
lhs.R_component_3() / rhs,
lhs.R_component_4() / rhs
);
}
namespace detail {
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
div_qq_impl_4(sprout::array<T, 4> const& tt) {
return sprout::math::quaternion<T>(
tt[0], tt[1], tt[2], tt[3]
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
div_qq_impl_3(sprout::array<T, 4> const& tr, T const& mixam, sprout::array<T, 4> const& tt) {
return sprout::math::detail::div_qq_impl_3(
sprout::math::detail::mul(tt, mixam / sprout::math::detail::sum(tr))
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
div_qq_impl_2(T const& a, T const& b, T const& c, T const& d, sprout::array<T, 4> const& tr, T const& mixam) {
return sprout::math::detail::div_qq_impl_3(
sprout::math::detail::mul(tr, tr), mixam,
sprout::array<T, 4>{{
+a * tr[0] + b * tr[1] + c * tr[2] + d * tr[3],
-a * tr[1] + b * tr[0] - c * tr[3] + d * tr[2],
-a * tr[2] + b * tr[3] + c * tr[0] - d * tr[1],
-a * tr[3] - b * tr[2] + c * tr[1] + d * tr[0]
}}
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
div_qq_impl_1(T const& a, T const& b, T const& c, T const& d, sprout::array<T, 4> const& tr, T const& mixam) {
return sprout::math::detail::div_qq_impl_2(
a, b, c, d, sprout::math::detail::mul(tr, mixam), mixam
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
div_qq_impl(T const& a, T const& b, T const& c, T const& d, sprout::array<T, 4> const& tr) {
return sprout::math::detail::div_qq_impl_1(
a, b, c, d, tr,
static_cast<T>(1) / sprout::math::detail::abs_max(tr)
);
}
} // namespace detail
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator/(sprout::complex<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
return sprout::math::detail::div_qq_impl(
lhs.real(), lhs.imag(), static_cast<T>(0), static_cast<T>(0),
sprout::array<T, 4>{{rhs.R_component_1(), rhs.R_component_2(), rhs.R_component_3(), rhs.R_component_4()}}
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator/(sprout::math::quaternion<T> const& lhs, sprout::complex<T> const& rhs) {
return sprout::math::detail::div_qq_impl(
lhs.R_component_1(), lhs.R_component_2(), lhs.R_component_3(), lhs.R_component_4(),
sprout::array<T, 4>{{rhs.real(), rhs.imag(), static_cast<T>(0), static_cast<T>(0)}}
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator/(sprout::math::quaternion<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
return sprout::math::detail::div_qq_impl(
lhs.R_component_1(), lhs.R_component_2(), lhs.R_component_3(), lhs.R_component_4(),
sprout::array<T, 4>{{rhs.R_component_1(), rhs.R_component_2(), rhs.R_component_3(), rhs.R_component_4()}}
);
}
//
// operator+
// operator-
//
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator+(sprout::math::quaternion<T> const& q) {
return q;
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator-(sprout::math::quaternion<T> const& q) {
return sprout::math::quaternion<T>(-q.R_component_1(), -q.R_component_2(), -q.R_component_3(), -q.R_component_4());
}
//
// operator==
// operator!=
//
template<typename T>
inline SPROUT_CONSTEXPR bool
operator==(T const& lhs, sprout::math::quaternion<T> const& rhs) {
return rhs.R_component_1() == lhs
&& rhs.R_component_2() == static_cast<T>(0)
&& rhs.R_component_3() == static_cast<T>(0)
&& rhs.R_component_4() == static_cast<T>(0)
;
}
template<typename T>
inline SPROUT_CONSTEXPR bool
operator==(sprout::math::quaternion<T> const& lhs, T const& rhs) {
return lhs.R_component_1() == rhs
&& lhs.R_component_2() == static_cast<T>(0)
&& lhs.R_component_3() == static_cast<T>(0)
&& lhs.R_component_4() == static_cast<T>(0)
;
}
template<typename T>
inline SPROUT_CONSTEXPR bool
operator==(sprout::complex<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
return rhs.R_component_1() == lhs.real()
&& rhs.R_component_2() == lhs.imag()
&& rhs.R_component_3() == static_cast<T>(0)
&& rhs.R_component_4() == static_cast<T>(0)
;
}
template<typename T>
inline SPROUT_CONSTEXPR bool
operator==(sprout::math::quaternion<T> const& lhs, sprout::complex<T> const& rhs) {
return lhs.R_component_1() == rhs.real()
&& lhs.R_component_2() == rhs.imag()
&& lhs.R_component_3() == static_cast<T>(0)
&& lhs.R_component_4() == static_cast<T>(0)
;
}
template<typename T>
inline SPROUT_CONSTEXPR bool
operator==(sprout::math::quaternion<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
return rhs.R_component_1() == lhs.R_component_1()
&& rhs.R_component_2() == lhs.R_component_2()
&& rhs.R_component_3() == lhs.R_component_3()
&& rhs.R_component_4() == lhs.R_component_4()
;
}
#define SPROUT_QUATERNION_NOT_EQUAL_GENERATOR \
{ \
return !(lhs == rhs); \
}
template<typename T>
inline SPROUT_CONSTEXPR bool
operator!=(T const& lhs, sprout::math::quaternion<T> const& rhs)
SPROUT_QUATERNION_NOT_EQUAL_GENERATOR
template<typename T>
inline SPROUT_CONSTEXPR bool
operator!=(sprout::math::quaternion<T> const& lhs, T const& rhs)
SPROUT_QUATERNION_NOT_EQUAL_GENERATOR
template<typename T>
inline SPROUT_CONSTEXPR bool
operator!=(sprout::complex<T> const& lhs, sprout::math::quaternion<T> const& rhs)
SPROUT_QUATERNION_NOT_EQUAL_GENERATOR
template<typename T>
inline SPROUT_CONSTEXPR bool
operator!=(sprout::math::quaternion<T> const& lhs, sprout::complex<T> const& rhs)
SPROUT_QUATERNION_NOT_EQUAL_GENERATOR
template<typename T>
inline SPROUT_CONSTEXPR bool
operator!=(sprout::math::quaternion<T> const& lhs, sprout::math::quaternion<T> const& rhs)
SPROUT_QUATERNION_NOT_EQUAL_GENERATOR
#undef SPROUT_QUATERNION_NOT_EQUAL_GENERATOR
} // namespace math
} // namespace sprout
#endif // #ifndef SPROUT_MATH_QUATERNION_ARITHMETIC_OPERATORS_HPP
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